LMFDB - Embedded newform 29.9.f.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(2,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	29.2
Dual form			29.9.f.a.15.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.2835 + 1.60937i) q^{2} +(128.283 + 80.6053i) q^{3} +(-48.1524 - 10.9905i) q^{4} +(-467.828 + 373.081i) q^{5} +(1702.60 + 1357.78i) q^{6} +(469.147 + 2055.47i) q^{7} +(-4143.33 - 1449.81i) q^{8} +(7112.49 + 14769.2i) q^{9} +O(q^{10})$	\(q+(14.2835 + 1.60937i) q^{2} +(128.283 + 80.6053i) q^{3} +(-48.1524 - 10.9905i) q^{4} +(-467.828 + 373.081i) q^{5} +(1702.60 + 1357.78i) q^{6} +(469.147 + 2055.47i) q^{7} +(-4143.33 - 1449.81i) q^{8} +(7112.49 + 14769.2i) q^{9} +(-7282.66 + 4576.00i) q^{10} +(3281.42 - 1148.22i) q^{11} +(-5291.23 - 5291.23i) q^{12} +(15354.5 - 31883.9i) q^{13} +(3393.07 + 30114.3i) q^{14} +(-90086.4 + 10150.3i) q^{15} +(-45456.1 - 21890.5i) q^{16} +(58865.3 - 58865.3i) q^{17} +(77822.3 + 222403. i) q^{18} +(104673. + 166586. i) q^{19} +(26627.4 - 12823.1i) q^{20} +(-105498. + 301496. i) q^{21} +(48718.1 - 11119.6i) q^{22} +(105113. - 131807. i) q^{23} +(-414654. - 519959. i) q^{24} +(-7248.12 + 31756.1i) q^{25} +(270629. - 430703. i) q^{26} +(-166775. + 1.48017e6i) q^{27} -104132. i q^{28} +(462133. - 535424. i) q^{29} -1.30309e6 q^{30} +(114780. + 12932.5i) q^{31} +(337464. + 212043. i) q^{32} +(513501. + 117203. i) q^{33} +(935540. - 746069. i) q^{34} +(-986334. - 786575. i) q^{35} +(-180163. - 789344. i) q^{36} +(-2.78593e6 - 974840. i) q^{37} +(1.22700e6 + 2.54789e6i) q^{38} +(4.53972e6 - 2.85249e6i) q^{39} +(2.47926e6 - 867531. i) q^{40} +(1.13415e6 + 1.13415e6i) q^{41} +(-1.99210e6 + 4.13664e6i) q^{42} +(-456696. - 4.05329e6i) q^{43} +(-170628. + 19225.1i) q^{44} +(-8.83754e6 - 4.25593e6i) q^{45} +(1.71350e6 - 1.71350e6i) q^{46} +(-314564. - 898972. i) q^{47} +(-4.06674e6 - 6.47218e6i) q^{48} +(1.18906e6 - 572623. i) q^{49} +(-154636. + 441924. i) q^{50} +(1.22962e7 - 2.80654e6i) q^{51} +(-1.08977e6 + 1.36653e6i) q^{52} +(-709359. - 889508. i) q^{53} +(-4.76427e6 + 2.08736e7i) q^{54} +(-1.10676e6 + 1.76140e6i) q^{55} +(1.03621e6 - 9.19664e6i) q^{56} +2.98072e7i q^{57} +(7.46259e6 - 6.90400e6i) q^{58} -1.88666e7 q^{59} +(4.44944e6 + 501331. i) q^{60} +(1.83853e7 + 1.15522e7i) q^{61} +(1.61864e6 + 369445. i) q^{62} +(-2.70209e7 + 2.15484e7i) q^{63} +(1.45769e7 + 1.16247e7i) q^{64} +(4.71200e6 + 2.06446e7i) q^{65} +(7.14599e6 + 2.50049e6i) q^{66} +(-5.31041e6 - 1.10272e7i) q^{67} +(-3.48147e6 + 2.18755e6i) q^{68} +(2.41085e7 - 8.43591e6i) q^{69} +(-1.28224e7 - 1.28224e7i) q^{70} +(1.42714e7 - 2.96348e7i) q^{71} +(-8.05674e6 - 7.15055e7i) q^{72} +(-4.13546e7 + 4.65955e6i) q^{73} +(-3.82241e7 - 1.84077e7i) q^{74} +(-3.48951e6 + 3.48951e6i) q^{75} +(-3.20939e6 - 9.17191e6i) q^{76} +(3.89959e6 + 6.20616e6i) q^{77} +(6.94339e7 - 3.34376e7i) q^{78} +(1.64623e7 - 4.70466e7i) q^{79} +(2.94326e7 - 6.71780e6i) q^{80} +(-7.36461e7 + 9.23493e7i) q^{81} +(1.43743e7 + 1.80249e7i) q^{82} +(-1.46101e7 + 6.40111e7i) q^{83} +(8.39357e6 - 1.33583e7i) q^{84} +(-5.57735e6 + 4.95004e7i) q^{85} -5.86302e7i q^{86} +(1.02442e8 - 3.14352e7i) q^{87} -1.52607e7 q^{88} +(2.17945e7 + 2.45566e6i) q^{89} +(-1.19382e8 - 7.50126e7i) q^{90} +(7.27397e7 + 1.66024e7i) q^{91} +(-6.51005e6 + 5.19159e6i) q^{92} +(1.36818e7 + 1.09109e7i) q^{93} +(-3.04631e6 - 1.33467e7i) q^{94} +(-1.11119e8 - 3.88821e7i) q^{95} +(2.61990e7 + 5.44028e7i) q^{96} +(6.50103e6 - 4.08487e6i) q^{97} +(1.79056e7 - 6.26543e6i) q^{98} +(4.02974e7 + 4.02974e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) $ 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{28}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	14.2835	+	1.60937i	0.892721	+	0.100585i	0.546394	−	0.837528i	$-0.316000\pi$
$2$	14.2835	+	1.60937i	0.892721	+	0.100585i	0.346327	+	0.938114i	$0.387429\pi$
$3$	128.283	+	80.6053i	1.58374	+	0.995127i	0.980252	+	0.197751i	$0.0633636\pi$
$3$	128.283	+	80.6053i	1.58374	+	0.995127i	0.603483	+	0.797376i	$0.293779\pi$
$4$	−48.1524	−	10.9905i	−0.188095	−	0.0429316i
$5$	−467.828	+	373.081i	−0.748525	+	0.596929i	−0.921673	−	0.387967i	$-0.873177\pi$
$5$	−467.828	+	373.081i	−0.748525	+	0.596929i	0.173148	+	0.984896i	$0.444606\pi$
$6$	1702.60	+	1357.78i	1.31374	+	1.04767i
$7$	469.147	+	2055.47i	0.195396	+	0.856088i	0.973634	+	0.228117i	$0.0732569\pi$
$7$	469.147	+	2055.47i	0.195396	+	0.856088i	−0.778237	+	0.627970i	$0.783886\pi$
$8$	−4143.33	−	1449.81i	−1.01155	−	0.353958i
$9$	7112.49	+	14769.2i	1.08406	+	2.25107i
$10$	−7282.66	+	4576.00i	−0.728266	+	0.457600i
$11$	3281.42	−	1148.22i	0.224125	−	0.0784248i	−0.215880	−	0.976420i	$-0.569262\pi$
$11$	3281.42	−	1148.22i	0.224125	−	0.0784248i	0.440006	+	0.897995i	$0.354976\pi$
$12$	−5291.23	−	5291.23i	−0.255171	−	0.255171i
$13$	15354.5	−	31883.9i	0.537602	−	1.11634i	−0.438440	−	0.898761i	$-0.644469\pi$
$13$	15354.5	−	31883.9i	0.537602	−	1.11634i	0.976042	−	0.217582i	$-0.0698170\pi$
$14$	3393.07	+	30114.3i	0.0883244	+	0.783901i
$15$	−90086.4	+	10150.3i	−1.77949	+	0.200500i
$16$	−45456.1	−	21890.5i	−0.693606	−	0.334023i
$17$	58865.3	−	58865.3i	0.704797	−	0.704797i	−0.260639	−	0.965436i	$-0.583933\pi$
$17$	58865.3	−	58865.3i	0.704797	−	0.704797i	0.965436	+	0.260639i	$0.0839334\pi$
$18$	77822.3	+	222403.i	0.741334	+	2.11861i
$19$	104673.	+	166586.i	0.803192	+	1.27827i	0.956976	+	0.290168i	$0.0937112\pi$
$19$	104673.	+	166586.i	0.803192	+	1.27827i	−0.153784	+	0.988105i	$0.549146\pi$
$20$	26627.4	−	12823.1i	0.166421	−	0.0801442i
$21$	−105498.	+	301496.i	−0.542459	+	1.55026i
$22$	48718.1	−	11119.6i	0.207970	−	0.0474677i
$23$	105113.	−	131807.i	0.375615	−	0.471007i	−0.557711	−	0.830035i	$-0.688320\pi$
$23$	105113.	−	131807.i	0.375615	−	0.471007i	0.933327	+	0.359028i	$0.116892\pi$
$24$	−414654.	−	519959.i	−1.24980	−	1.56720i
$25$	−7248.12	+	31756.1i	−0.0185552	+	0.0812956i
$26$	270629.	−	430703.i	0.592216	−	0.942507i
$27$	−166775.	+	1.48017e6i	−0.313817	+	2.78520i
$28$		−	104132.i		−	0.169415i
$29$	462133.	−	535424.i	0.653394	−	0.757018i
$29$	462133.	−	535424.i	0.653394	−	0.757018i
$30$	−1.30309e6			−1.60875
$31$	114780.	+	12932.5i	0.124285	+	0.0140035i	0.173888	−	0.984765i	$-0.444367\pi$
$31$	114780.	+	12932.5i	0.124285	+	0.0140035i	−0.0496030	+	0.998769i	$0.515796\pi$
$32$	337464.	+	212043.i	0.321831	+	0.202220i
$33$	513501.	+	117203.i	0.432998	+	0.0988289i
$34$	935540.	−	746069.i	0.700079	−	0.558294i
$35$	−986334.	−	786575.i	−0.657282	−	0.524165i
$36$	−180163.	−	789344.i	−0.107264	−	0.469955i
$37$	−2.78593e6	−	974840.i	−1.48650	−	0.520147i	−0.539665	−	0.841880i	$-0.681449\pi$
$37$	−2.78593e6	−	974840.i	−1.48650	−	0.520147i	−0.946831	+	0.321733i	$0.895735\pi$
$38$	1.22700e6	+	2.54789e6i	0.588450	+	1.22193i
$39$	4.53972e6	−	2.85249e6i	1.96232	−	1.23301i
$40$	2.47926e6	−	867531.i	0.968461	−	0.338879i
$41$	1.13415e6	+	1.13415e6i	0.401359	+	0.401359i	0.878712	−	0.477353i	$-0.158404\pi$
$41$	1.13415e6	+	1.13415e6i	0.401359	+	0.401359i	−0.477353	+	0.878712i	$0.658404\pi$
$42$	−1.99210e6	+	4.13664e6i	−0.640198	+	1.32939i
$43$	−456696.	−	4.05329e6i	−0.133584	−	1.18559i	−0.864325	−	0.502933i	$-0.832254\pi$
$43$	−456696.	−	4.05329e6i	−0.133584	−	1.18559i	0.730742	−	0.682654i	$-0.239174\pi$
$44$	−170628.	+	19225.1i	−0.0455239	+	0.00512931i
$45$	−8.83754e6	−	4.25593e6i	−2.15517	−	1.03787i
$46$	1.71350e6	−	1.71350e6i	0.382696	−	0.382696i
$47$	−314564.	−	898972.i	−0.0644640	−	0.184228i	0.907146	−	0.420816i	$-0.138256\pi$
$47$	−314564.	−	898972.i	−0.0644640	−	0.184228i	−0.971610	+	0.236589i	$0.923971\pi$
$48$	−4.06674e6	−	6.47218e6i	−0.766093	−	1.21923i
$49$	1.18906e6	−	572623.i	0.206263	−	0.0993309i
$50$	−154636.	+	441924.i	−0.0247417	+	0.0707078i
$51$	1.22962e7	−	2.80654e6i	1.81757	−	0.414849i
$52$	−1.08977e6	+	1.36653e6i	−0.149047	+	0.186899i
$53$	−709359.	−	889508.i	−0.0899006	−	0.112732i	0.734847	−	0.678233i	$-0.237254\pi$
$53$	−709359.	−	889508.i	−0.0899006	−	0.112732i	−0.824747	+	0.565501i	$0.808683\pi$
$54$	−4.76427e6	+	2.08736e7i	−0.560301	+	2.45484i
$55$	−1.10676e6	+	1.76140e6i	−0.120949	+	0.192490i
$56$	1.03621e6	−	9.19664e6i	0.105365	−	0.935141i
$57$			2.98072e7i			2.82372i
$58$	7.46259e6	−	6.90400e6i	0.659444	−	0.610083i
$59$	−1.88666e7			−1.55699			−0.778496	−	0.627649i	$-0.784017\pi$
$59$	−1.88666e7			−1.55699			−0.778496	+	0.627649i	$0.784017\pi$
$60$	4.44944e6	+	501331.i	0.343321	+	0.0386830i
$61$	1.83853e7	+	1.15522e7i	1.32786	+	0.834348i	0.994116	−	0.108317i	$-0.0345463\pi$
$61$	1.83853e7	+	1.15522e7i	1.32786	+	0.834348i	0.333740	+	0.942665i	$0.391689\pi$
$62$	1.61864e6	+	369445.i	0.109543	+	0.0250025i
$63$	−2.70209e7	+	2.15484e7i	−1.71529	+	1.36790i
$64$	1.45769e7	+	1.16247e7i	0.868853	+	0.692887i
$65$	4.71200e6	+	2.06446e7i	0.263968	+	1.15652i
$66$	7.14599e6	+	2.50049e6i	0.376605	+	0.131780i
$67$	−5.31041e6	−	1.10272e7i	−0.263529	−	0.547224i	0.726653	−	0.687004i	$-0.241075\pi$
$67$	−5.31041e6	−	1.10272e7i	−0.263529	−	0.547224i	−0.990183	+	0.139780i	$0.955360\pi$
$68$	−3.48147e6	+	2.18755e6i	−0.162827	+	0.102311i
$69$	2.41085e7	−	8.43591e6i	1.06359	−	0.372165i
$70$	−1.28224e7	−	1.28224e7i	−0.534046	−	0.534046i
$71$	1.42714e7	−	2.96348e7i	0.561607	−	1.16619i	−0.406034	−	0.913858i	$-0.633089\pi$
$71$	1.42714e7	−	2.96348e7i	0.561607	−	1.16619i	0.967641	−	0.252331i	$-0.0811971\pi$
$72$	−8.05674e6	−	7.15055e7i	−0.299798	−	2.66078i
$73$	−4.13546e7	+	4.65955e6i	−1.45624	+	0.164079i	−0.804314	−	0.594204i	$-0.797467\pi$
$73$	−4.13546e7	+	4.65955e6i	−1.45624	+	0.164079i	−0.651925	+	0.758283i	$0.726038\pi$
$74$	−3.82241e7	−	1.84077e7i	−1.27471	−	0.613866i
$75$	−3.48951e6	+	3.48951e6i	−0.110286	+	0.110286i
$76$	−3.20939e6	−	9.17191e6i	−0.0961985	−	0.274920i
$77$	3.89959e6	+	6.20616e6i	0.110932	+	0.176547i
$78$	6.94339e7	−	3.34376e7i	1.87583	−	0.903351i
$79$	1.64623e7	−	4.70466e7i	0.422652	−	1.20787i	−0.514056	−	0.857757i	$-0.671857\pi$
$79$	1.64623e7	−	4.70466e7i	0.422652	−	1.20787i	0.936707	−	0.350113i	$-0.113857\pi$
$80$	2.94326e7	−	6.71780e6i	0.718569	−	0.164009i
$81$	−7.36461e7	+	9.23493e7i	−1.71084	+	2.14533i
$82$	1.43743e7	+	1.80249e7i	0.317931	+	0.398673i
$83$	−1.46101e7	+	6.40111e7i	−0.307852	+	1.34879i	0.550119	+	0.835086i	$0.314582\pi$
$83$	−1.46101e7	+	6.40111e7i	−0.307852	+	1.34879i	−0.857970	+	0.513699i	$0.828275\pi$
$84$	8.39357e6	−	1.33583e7i	0.168589	−	0.268308i
$85$	−5.57735e6	+	4.95004e7i	−0.106845	+	0.948271i
$86$		−	5.86302e7i		−	1.07183i
$87$	1.02442e8	−	3.14352e7i	1.78813	−	0.548705i
$88$	−1.52607e7			−0.254474
$89$	2.17945e7	+	2.45566e6i	0.347366	+	0.0391388i	0.283924	−	0.958847i	$-0.408364\pi$
$89$	2.17945e7	+	2.45566e6i	0.347366	+	0.0391388i	0.0634422	+	0.997986i	$0.479792\pi$
$90$	−1.19382e8	−	7.50126e7i	−1.81957	−	1.14331i
$91$	7.27397e7	+	1.66024e7i	1.06073	+	0.242105i
$92$	−6.51005e6	+	5.19159e6i	−0.0908726	+	0.0724685i
$93$	1.36818e7	+	1.09109e7i	0.182899	+	0.145857i
$94$	−3.04631e6	−	1.33467e7i	−0.0390177	−	0.170948i
$95$	−1.11119e8	−	3.88821e7i	−1.36425	−	0.477371i
$96$	2.61990e7	+	5.44028e7i	0.308461	+	0.640525i
$97$	6.50103e6	−	4.08487e6i	0.0734336	−	0.0461414i	−0.494815	−	0.868998i	$-0.664764\pi$
$97$	6.50103e6	−	4.08487e6i	0.0734336	−	0.0461414i	0.568248	+	0.822857i	$0.307621\pi$
$98$	1.79056e7	−	6.26543e6i	0.194126	−	0.0679277i
$99$	4.02974e7	+	4.02974e7i	0.419504	+	0.419504i
$100$	698029.	−	1.44947e6i	0.00698029	−	0.0144947i
$101$	1.24626e7	+	1.10608e8i	0.119763	+	1.06292i	0.899531	+	0.436856i	$0.143908\pi$
$101$	1.24626e7	+	1.10608e8i	0.119763	+	1.06292i	−0.779768	+	0.626068i	$0.784663\pi$
$102$	1.80151e8	−	2.02981e7i	1.66431	−	0.187523i
$103$	−2.74358e7	−	1.32124e7i	−0.243763	−	0.117390i	0.308014	−	0.951382i	$-0.400336\pi$
$103$	−2.74358e7	−	1.32124e7i	−0.243763	−	0.117390i	−0.551777	+	0.833992i	$0.686050\pi$
$104$	−1.09844e8	+	1.09844e8i	−0.938952	+	0.938952i
$105$	−6.31274e7	−	1.80408e8i	−0.519350	−	1.48422i
$106$	−8.70060e6	−	1.38469e7i	−0.0689169	−	0.109681i
$107$	2.88494e7	−	1.38932e7i	0.220091	−	0.105990i	−0.320590	−	0.947218i	$-0.603881\pi$
$107$	2.88494e7	−	1.38932e7i	0.220091	−	0.105990i	0.540681	+	0.841228i	$0.318167\pi$
$108$	2.42984e7	−	6.94408e7i	0.178600	−	0.510411i
$109$	−1.41888e8	+	3.23850e7i	−1.00517	+	0.229424i	−0.693260	−	0.720688i	$-0.743826\pi$
$109$	−1.41888e8	+	3.23850e7i	−1.00517	+	0.229424i	−0.311911	+	0.950111i	$0.600969\pi$
$110$	−1.86432e7	+	2.33779e7i	−0.127336	+	0.159674i
$111$	−2.78809e8	−	3.49616e8i	−1.83660	−	2.30303i
$112$	2.36696e7	−	1.03703e8i	0.150425	−	0.659054i
$113$	−2.52167e7	+	4.01321e7i	−0.154659	+	0.246138i	−0.915062	−	0.403313i	$-0.867858\pi$
$113$	−2.52167e7	+	4.01321e7i	−0.154659	+	0.246138i	0.760403	+	0.649451i	$0.225001\pi$
$114$	−4.79708e7	+	4.25752e8i	−0.284025	+	2.52080i
$115$			1.00879e8i			0.576776i
$116$	−2.81374e7	+	2.07029e7i	−0.155400	+	0.114340i
$117$	5.80109e8			3.09575
$118$	−2.69482e8	−	3.03633e7i	−1.38996	−	0.156611i
$119$	1.48612e8	+	9.33792e7i	0.741082	+	0.465653i
$120$	3.87973e8	+	8.85524e7i	1.87101	+	0.427047i
$121$	−1.58143e8	+	1.26115e8i	−0.737750	+	0.588336i
$122$	2.44015e8	+	1.94596e8i	1.10148	+	0.878402i
$123$	5.40730e7	+	2.36909e8i	0.236243	+	1.03505i
$124$	−5.38478e6	−	1.88422e6i	−0.0227762	−	0.00796973i
$125$	−1.09873e8	−	2.28153e8i	−0.450039	−	0.934515i
$126$	−4.20633e8	+	2.64301e8i	−1.66886	+	1.04862i
$127$	−2.09567e8	+	7.33308e7i	−0.805580	+	0.281885i	−0.701487	−	0.712683i	$-0.747480\pi$
$127$	−2.09567e8	+	7.33308e7i	−0.805580	+	0.281885i	−0.104094	+	0.994567i	$0.533194\pi$
$128$	1.17356e8	+	1.17356e8i	0.437185	+	0.437185i
$129$	2.68130e8	−	5.56778e8i	0.968249	−	2.01059i
$130$	3.40792e7	+	3.02461e8i	0.119321	+	1.05900i
$131$	2.20725e8	−	2.48697e7i	0.749490	−	0.0844473i	0.271047	−	0.962566i	$-0.412630\pi$
$131$	2.20725e8	−	2.48697e7i	0.749490	−	0.0844473i	0.478443	+	0.878119i	$0.341201\pi$
$132$	−2.34382e7	−	1.12872e7i	−0.0772020	−	0.0371785i
$133$	−2.93304e8	+	2.93304e8i	−0.937372	+	0.937372i
$134$	−5.81046e7	−	1.66053e8i	−0.180215	−	0.515025i
$135$	−4.74200e8	−	7.54685e8i	−1.42767	−	2.27212i
$136$	−3.29242e8	+	1.58555e8i	−0.962409	+	0.463472i
$137$	−2.34370e7	+	6.69791e7i	−0.0665303	+	0.190133i	−0.972349	−	0.233533i	$-0.924971\pi$
$137$	−2.34370e7	+	6.69791e7i	−0.0665303	+	0.190133i	0.905819	+	0.423666i	$0.139257\pi$
$138$	3.57930e8	−	8.16952e7i	0.986920	−	0.225258i
$139$	8.00984e7	−	1.00440e8i	0.214568	−	0.269060i	−0.662886	−	0.748720i	$-0.730669\pi$
$139$	8.00984e7	−	1.00440e8i	0.214568	−	0.269060i	0.877454	+	0.479660i	$0.159240\pi$
$140$	3.88496e7	+	4.87158e7i	0.101129	+	0.126811i
$141$	3.21088e7	−	1.40678e8i	0.0812358	−	0.355917i
$142$	2.51539e8	−	4.00322e8i	0.618660	−	0.984591i
$143$	1.37748e7	−	1.22255e8i	0.0329413	−	0.292362i
$144$		−	8.27049e8i		−	1.92345i
$145$	−1.64427e7	+	4.22900e8i	−0.0371964	+	0.956677i
$146$	−5.98189e8			−1.31652
$147$	1.98693e8	+	2.23873e7i	0.425512	+	0.0479437i
$148$	1.23435e8	+	7.75596e7i	0.257272	+	0.161655i
$149$	2.96555e8	+	6.76866e7i	0.601672	+	0.137328i	0.512498	−	0.858688i	$-0.328720\pi$
$149$	2.96555e8	+	6.76866e7i	0.601672	+	0.137328i	0.0891737	+	0.996016i	$0.471577\pi$
$150$	−5.54585e7	+	4.42267e7i	−0.109548	+	0.0873613i
$151$	−3.62936e8	−	2.89432e8i	−0.698107	−	0.556722i	0.208848	−	0.977948i	$-0.433028\pi$
$151$	−3.62936e8	−	2.89432e8i	−0.698107	−	0.556722i	−0.906956	+	0.421226i	$0.861600\pi$
$152$	−1.92175e8	−	8.41975e8i	−0.360017	−	1.57734i
$153$	1.28808e9	+	4.50717e8i	2.35058	+	0.822504i
$154$	4.57119e7	+	9.49218e7i	0.0812730	+	0.168765i
$155$	−5.85220e7	+	3.67718e7i	−0.101389	+	0.0637071i
$156$	−2.49949e8	+	8.74608e7i	−0.422039	+	0.147678i
$157$	4.65485e8	+	4.65485e8i	0.766138	+	0.766138i	0.977424	−	0.211286i	$-0.0677652\pi$
$157$	4.65485e8	+	4.65485e8i	0.766138	+	0.766138i	−0.211286	+	0.977424i	$0.567765\pi$
$158$	3.10855e8	−	6.45498e8i	0.498804	−	1.03578i
$159$	−1.92993e7	−	1.71286e8i	−0.0301963	−	0.268000i
$160$	−2.36984e8	+	2.67017e7i	−0.361609	+	0.0407436i
$161$	3.20238e8	+	1.54219e8i	0.476617	+	0.229527i
$162$	−1.20055e9	+	1.20055e9i	−1.74309	+	1.74309i
$163$	−3.95264e8	−	1.12960e9i	−0.559933	−	1.60020i	−0.780724	−	0.624876i	$-0.785149\pi$
$163$	−3.95264e8	−	1.12960e9i	−0.559933	−	1.60020i	0.220790	−	0.975321i	$-0.429136\pi$
$164$	−4.21471e7	−	6.70767e7i	−0.0582629	−	0.0927248i
$165$	−2.83957e8	+	1.36746e8i	−0.383104	+	0.184493i
$166$	−3.11701e8	+	8.90791e8i	−0.410494	+	1.17312i
$167$	1.35676e9	−	3.09671e8i	1.74436	−	0.398139i	0.772748	−	0.634713i	$-0.218882\pi$
$167$	1.35676e9	−	3.09671e8i	1.74436	−	0.398139i	0.971613	+	0.236574i	$0.0760246\pi$
$168$	8.74226e8	−	1.09624e9i	1.09745	−	1.37616i
$169$	−2.72221e8	−	3.41355e8i	−0.333715	−	0.418465i
$170$	−1.59329e8	+	6.98064e8i	−0.190765	+	0.835794i
$171$	−1.71586e9	+	2.73078e9i	−2.00677	+	3.19376i
$172$	−2.25566e7	+	2.00195e8i	−0.0257726	+	0.228739i
$173$		−	7.43654e8i		−	0.830208i	−0.909774	−	0.415104i	$-0.863745\pi$
$173$		−	7.43654e8i		−	0.830208i	0.909774	−	0.415104i	$-0.136255\pi$
$174$	1.51382e9	−	2.84139e8i	1.65149	−	0.309980i
$175$	−6.86740e7			−0.0732217
$176$	−1.74296e8	−	1.96384e7i	−0.181650	−	0.0204671i
$177$	−2.42026e9	−	1.52075e9i	−2.46586	−	1.54940i
$178$	3.07351e8	+	7.01509e7i	0.306164	+	0.0698800i
$179$	1.60794e8	−	1.28229e8i	0.156624	−	0.124904i	−0.542042	−	0.840351i	$-0.682349\pi$
$179$	1.60794e8	−	1.28229e8i	0.156624	−	0.124904i	0.698666	+	0.715448i	$0.253777\pi$
$180$	3.78774e8	+	3.02062e8i	0.360820	+	0.287744i
$181$	−4.91802e7	−	2.15473e8i	−0.0458222	−	0.200760i	0.946835	−	0.321718i	$-0.104260\pi$
$181$	−4.91802e7	−	2.15473e8i	−0.0458222	−	0.200760i	−0.992658	+	0.120958i	$0.961403\pi$
$182$	1.01226e9	+	3.54205e8i	0.922585	+	0.322827i
$183$	1.42734e9	+	2.96390e9i	1.27269	+	2.64277i
$184$	−6.26611e8	+	3.93726e8i	−0.546672	+	0.343497i
$185$	1.66703e9	−	5.83319e8i	1.42317	−	0.497989i
$186$	1.77864e8	+	1.77864e8i	0.148606	+	0.148606i
$187$	1.25572e8	−	2.60752e8i	0.102689	−	0.213236i
$188$	5.26688e6	+	4.67449e7i	0.00421621	+	0.0374199i
$189$	−3.12068e9	+	3.51616e8i	−2.44569	+	0.275563i
$190$	−1.52459e9	−	7.34205e8i	−1.16987	−	0.563382i
$191$	6.63169e8	−	6.63169e8i	0.498300	−	0.498300i	−0.412609	−	0.910908i	$-0.635382\pi$
$191$	6.63169e8	−	6.63169e8i	0.498300	−	0.498300i	0.910908	+	0.412609i	$0.135382\pi$
$192$	9.32953e8	+	2.66623e9i	0.686523	+	1.96197i
$193$	−1.30206e9	−	2.07221e9i	−0.938428	−	1.49350i	−0.868347	−	0.495958i	$-0.834817\pi$
$193$	−1.30206e9	−	2.07221e9i	−0.938428	−	1.49350i	−0.0700813	−	0.997541i	$-0.522326\pi$
$194$	9.94316e7	−	4.78837e7i	0.0701969	−	0.0338050i
$195$	−1.05960e9	+	3.02816e9i	−0.732829	+	2.09430i
$196$	−6.35497e7	+	1.45048e7i	−0.0430615	+	0.00982851i
$197$	1.27057e9	−	1.59325e9i	0.843596	−	1.05784i	−0.153967	−	0.988076i	$-0.549205\pi$
$197$	1.27057e9	−	1.59325e9i	0.843596	−	1.05784i	0.997564	−	0.0697604i	$-0.0222235\pi$
$198$	5.10735e8	+	6.40442e8i	0.332304	+	0.416696i
$199$	−7.52161e7	+	3.29543e8i	−0.0479621	+	0.210136i	−0.993231	−	0.116157i	$-0.962942\pi$
$199$	−7.52161e7	+	3.29543e8i	−0.0479621	+	0.210136i	0.945269	+	0.326293i	$0.105800\pi$
$200$	7.60717e7	−	1.21067e8i	0.0475448	−	0.0756671i
$201$	2.07616e8	−	1.84264e9i	0.127197	−	1.12890i
$202$			1.59993e9i			0.960941i
$203$	1.31735e9	+	6.98707e8i	0.775744	+	0.411444i
$204$	−6.22940e8			−0.359687
$205$	−9.53713e8	−	1.07458e8i	−0.540010	−	0.0608446i
$206$	−3.70616e8	−	2.32874e8i	−0.205805	−	0.129316i
$207$	2.69430e9	+	6.14957e8i	1.46746	+	0.334937i
$208$	−1.39591e9	+	1.11320e9i	−0.745768	+	0.594730i
$209$	5.34752e8	+	4.26450e8i	0.280264	+	0.223503i
$210$	−6.11339e8	−	2.67845e9i	−0.314344	−	1.37723i
$211$	1.06297e9	+	3.71950e8i	0.536281	+	0.187653i	0.584812	−	0.811169i	$-0.301168\pi$
$211$	1.06297e9	+	3.71950e8i	0.536281	+	0.187653i	−0.0485312	+	0.998822i	$0.515454\pi$
$212$	2.43812e7	+	5.06281e7i	0.0120701	+	0.0250639i
$213$	4.21949e9	−	2.65128e9i	2.04994	−	1.28806i
$214$	4.34431e8	−	1.52014e8i	0.207141	−	0.0724817i
$215$	1.72586e9	+	1.72586e9i	0.807702	+	0.807702i
$216$	2.83697e9	−	5.89103e9i	1.30329	−	2.70630i
$217$	2.72660e7	+	2.41993e8i	0.0122965	+	0.109135i
$218$	−2.07878e9	+	2.34222e8i	−0.920413	+	0.103706i
$219$	−5.68066e9	−	2.73566e9i	−2.46958	−	1.18929i
$220$	7.26520e7	−	7.26520e7i	0.0310139	−	0.0310139i
$221$	−9.73009e8	−	2.78070e9i	−0.407894	−	1.16569i
$222$	−3.41972e9	−	5.44245e9i	−1.40792	−	2.24069i
$223$	−3.11770e9	+	1.50140e9i	−1.26071	+	0.607125i	−0.940362	−	0.340176i	$-0.889513\pi$
$223$	−3.11770e9	+	1.50140e9i	−1.26071	+	0.607125i	−0.320346	+	0.947301i	$0.603799\pi$
$224$	−2.77527e8	+	7.93126e8i	−0.110233	+	0.315029i
$225$	−5.20565e8	+	1.18816e8i	−0.203116	+	0.0463600i
$226$	−4.24770e8	+	5.32645e8i	−0.162825	+	0.204176i
$227$	−5.57710e8	−	6.99347e8i	−0.210042	−	0.263384i	0.665640	−	0.746273i	$-0.268159\pi$
$227$	−5.57710e8	−	6.99347e8i	−0.210042	−	0.263384i	−0.875681	+	0.482889i	$0.839587\pi$
$228$	3.27596e8	−	1.43529e9i	0.121227	−	0.531129i
$229$	−5.74269e8	+	9.13944e8i	−0.208821	+	0.332336i	−0.934669	−	0.355518i	$-0.884304\pi$
$229$	−5.74269e8	+	9.13944e8i	−0.208821	+	0.332336i	0.725849	+	0.687854i	$0.241447\pi$
$230$	−1.62351e8	+	1.44090e9i	−0.0580153	+	0.514900i
$231$			1.11047e9i			0.389995i
$232$	−2.69103e9	+	1.54843e9i	−0.928896	+	0.534490i
$233$	−1.59224e9			−0.540237			−0.270119	−	0.962827i	$-0.587063\pi$
$233$	−1.59224e9			−0.540237			−0.270119	+	0.962827i	$0.587063\pi$
$234$	8.28600e9	+	9.33608e8i	2.76364	+	0.311387i
$235$	4.82551e8	+	3.03207e8i	0.158224	+	0.0994185i
$236$	9.08475e8	+	2.07353e8i	0.292863	+	0.0668441i
$237$	5.90404e9	−	4.70831e9i	1.87135	−	1.49235i
$238$	1.97242e9	+	1.57296e9i	0.614742	+	0.490240i
$239$	4.34614e8	+	1.90417e9i	0.133202	+	0.583598i	0.996837	+	0.0794786i	$0.0253255\pi$
$239$	4.34614e8	+	1.90417e9i	0.133202	+	0.583598i	−0.863634	+	0.504119i	$0.831817\pi$
$240$	4.31718e9	+	1.51065e9i	1.30123	+	0.455321i
$241$	1.58563e9	+	3.29259e9i	0.470039	+	0.976046i	0.992369	+	0.123302i	$0.0393485\pi$
$241$	1.58563e9	+	3.29259e9i	0.470039	+	0.976046i	−0.522330	+	0.852743i	$0.674937\pi$
$242$	−2.46181e9	+	1.54686e9i	−0.717782	+	0.451013i
$243$	−7.66694e9	+	2.68278e9i	−2.19886	+	0.769413i
$244$	−7.58332e8	−	7.58332e8i	−0.213944	−	0.213944i
$245$	−3.42643e8	+	7.11506e8i	−0.0950993	+	0.197476i
$246$	3.91079e8	+	3.47092e9i	0.106788	+	0.947773i
$247$	6.91859e9	−	7.79538e8i	1.85879	−	0.209435i
$248$	−4.56819e8	−	2.19993e8i	−0.120764	−	0.0581569i
$249$	−7.03385e9	+	7.03385e9i	−1.82977	+	1.82977i
$250$	−1.20219e9	−	3.43566e9i	−0.307760	−	0.879528i
$251$	1.69549e9	+	2.69835e9i	0.427168	+	0.679835i	0.989083	−	0.147361i	$-0.0470778\pi$
$251$	1.69549e9	+	2.69835e9i	0.427168	+	0.679835i	−0.561914	+	0.827195i	$0.689935\pi$
$252$	1.53795e9	−	7.40637e8i	0.381364	−	0.183655i
$253$	1.93575e8	−	5.53206e8i	0.0472463	−	0.135022i
$254$	−3.11138e9	+	7.10152e8i	−0.747512	+	0.170615i
$255$	−4.70547e9	+	5.90047e9i	−1.11286	+	1.39549i
$256$	−1.48854e9	−	1.86657e9i	−0.346578	−	0.434595i
$257$	1.83763e8	−	8.05120e8i	0.0421237	−	0.184556i	−0.949489	−	0.313800i	$-0.898398\pi$
$257$	1.83763e8	−	8.05120e8i	0.0421237	−	0.184556i	0.991613	+	0.129244i	$0.0412550\pi$
$258$	4.72591e9	−	7.52124e9i	1.06661	−	1.69750i
$259$	6.96739e8	−	6.18373e9i	0.154836	−	1.37421i
$260$		−	1.04588e9i		−	0.228869i
$261$	1.11947e10	+	3.01716e9i	2.41241	+	0.650184i
$262$	3.19275e9			0.677579
$263$	−7.62164e9	−	8.58753e8i	−1.59304	−	0.179492i	−0.729572	−	0.683904i	$-0.760281\pi$
$263$	−7.62164e9	−	8.58753e8i	−1.59304	−	0.179492i	−0.863463	+	0.504412i	$0.831709\pi$
$264$	−1.95768e9	−	1.23009e9i	−0.403019	−	0.253234i
$265$	6.63716e8	+	1.51489e8i	0.134586	+	0.0307183i
$266$	−4.66146e9	+	3.71739e9i	−0.931098	+	0.742526i
$267$	2.59792e9	+	2.07177e9i	0.511188	+	0.407659i
$268$	1.34515e8	+	5.89349e8i	0.0260754	+	0.114244i
$269$	−5.08748e9	−	1.78019e9i	−0.971614	−	0.339983i	−0.202634	−	0.979255i	$-0.564950\pi$
$269$	−5.08748e9	−	1.78019e9i	−0.971614	−	0.339983i	−0.768981	+	0.639272i	$0.779236\pi$
$270$	−5.55868e9	−	1.15427e10i	−1.04596	−	2.17197i
$271$	−2.82728e9	+	1.77650e9i	−0.524194	+	0.329373i	−0.767999	−	0.640452i	$-0.778747\pi$
$271$	−2.82728e9	+	1.77650e9i	−0.524194	+	0.329373i	0.243805	+	0.969824i	$0.421604\pi$
$272$	−3.96438e9	+	1.38720e9i	−0.724269	+	0.253433i
$273$	7.99300e9	+	7.99300e9i	1.43899	+	1.43899i
$274$	−4.42557e8	+	9.18979e8i	−0.0785176	+	0.163043i
$275$	1.26788e7	+	1.12527e8i	0.00221691	+	0.0196756i
$276$	−1.25360e9	+	1.41246e8i	−0.216033	+	0.0243411i
$277$	2.10204e9	+	1.01229e9i	0.357044	+	0.171943i	0.603803	−	0.797134i	$-0.293651\pi$
$277$	2.10204e9	+	1.01229e9i	0.357044	+	0.171943i	−0.246759	+	0.969077i	$0.579366\pi$
$278$	1.30573e9	−	1.30573e9i	0.218613	−	0.218613i
$279$	6.25364e8	+	1.78719e9i	0.103209	+	0.294954i
$280$	2.94632e9	+	4.68904e9i	0.479344	+	0.762872i
$281$	1.02431e10	−	4.93280e9i	1.64288	−	0.791167i	0.643200	−	0.765698i	$-0.277606\pi$
$281$	1.02431e10	−	4.93280e9i	1.64288	−	0.791167i	0.999676	−	0.0254692i	$-0.00810798\pi$
$282$	6.85029e8	−	1.95770e9i	0.108321	−	0.309564i
$283$	−8.57869e9	+	1.95803e9i	−1.33744	+	0.305263i	−0.830645	−	0.556802i	$-0.812028\pi$
$283$	−8.57869e9	+	1.95803e9i	−1.33744	+	0.305263i	−0.506798	+	0.862065i	$0.669171\pi$
$284$	−1.01290e9	+	1.27014e9i	−0.155702	+	0.195244i
$285$	−1.11205e10	−	1.39447e10i	−1.68556	−	2.11363i
$286$	3.93505e8	−	1.72406e9i	0.0588147	−	0.257684i
$287$	−1.79912e9	+	2.86328e9i	−0.265175	+	0.422023i
$288$	−7.31500e8	+	6.49224e9i	−0.106327	+	0.943680i
$289$			4.55036e7i			0.00652311i
$290$	−9.15460e8	+	6.01403e9i	−0.129434	+	0.850303i
$291$	1.16323e9			0.162216
$292$	2.04254e9	+	2.30139e8i	0.280956	+	0.0316562i
$293$	3.57318e8	+	2.24518e8i	0.0484824	+	0.0304635i	0.556055	−	0.831145i	$-0.312314\pi$
$293$	3.57318e8	+	2.24518e8i	0.0484824	+	0.0304635i	−0.507573	+	0.861609i	$0.669457\pi$
$294$	2.80200e9	+	6.39538e8i	0.375041	+	0.0856007i
$295$	8.82634e9	−	7.03877e9i	1.16545	−	0.929414i
$296$	1.01297e10	+	8.07816e9i	1.31956	+	1.05231i
$297$	1.15230e9	+	5.04855e9i	0.148095	+	0.648845i
$298$	4.12691e9	+	1.44407e9i	0.523311	+	0.183115i
$299$	−2.58857e9	−	5.37522e9i	−0.323873	−	0.672530i
$300$	2.06380e8	−	1.29677e8i	0.0254790	−	0.0160095i
$301$	8.11714e9	−	2.84031e9i	0.988865	−	0.346019i
$302$	−4.71820e9	−	4.71820e9i	−0.567217	−	0.567217i
$303$	−7.31689e9	+	1.51937e10i	−0.868072	+	1.80257i
$304$	−1.11137e9	−	9.86369e9i	−0.130126	−	1.15490i
$305$	−1.29111e10	+	1.45473e9i	−1.49198	+	0.168106i
$306$	1.76729e10	+	8.51081e9i	2.01568	+	0.970701i
$307$	−5.10598e9	+	5.10598e9i	−0.574812	+	0.574812i	−0.933469	−	0.358657i	$-0.883235\pi$
$307$	−5.10598e9	+	5.10598e9i	−0.574812	+	0.574812i	0.358657	+	0.933469i	$0.383235\pi$
$308$	−1.19566e8	−	3.41700e8i	−0.0132863	−	0.0379702i
$309$	−2.45454e9	−	3.90638e9i	−0.269238	−	0.428490i
$310$	−8.95080e8	+	4.31048e8i	−0.0969203	+	0.0466744i
$311$	4.59408e9	−	1.31291e10i	0.491085	−	1.40344i	−0.385729	−	0.922612i	$-0.626050\pi$
$311$	4.59408e9	−	1.31291e10i	0.491085	−	1.40344i	0.876814	−	0.480829i	$-0.159664\pi$
$312$	−2.29451e10	+	5.23707e9i	−2.42143	+	0.552675i
$313$	4.23995e9	−	5.31673e9i	0.441757	−	0.553946i	−0.510248	−	0.860027i	$-0.670447\pi$
$313$	4.23995e9	−	5.31673e9i	0.441757	−	0.553946i	0.952005	+	0.306081i	$0.0990180\pi$
$314$	5.89963e9	+	7.39790e9i	0.606885	+	0.761010i
$315$	4.60183e9	−	2.01619e10i	0.467399	−	2.04781i
$316$	−1.30977e9	+	2.08448e9i	−0.131355	+	0.209050i
$317$	−9.84383e8	+	8.73664e9i	−0.0974826	+	0.865182i	0.845870	+	0.533390i	$0.179082\pi$
$317$	−9.84383e8	+	8.73664e9i	−0.0974826	+	0.865182i	−0.943352	+	0.331793i	$0.892347\pi$
$318$		−	2.47763e9i		−	0.242286i
$319$	9.01670e8	−	2.28758e9i	0.0870732	−	0.220909i
$320$	−1.11565e10			−1.06396
$321$	4.82074e9	+	5.43167e8i	0.454039	+	0.0511580i
$322$	4.32594e9	+	2.71817e9i	0.402399	+	0.252844i
$323$	1.59677e10	+	3.64453e9i	1.46701	+	0.334835i
$324$	4.56120e9	−	3.63744e9i	0.413904	−	0.330077i
$325$	9.01216e8	+	7.18695e8i	0.0807784	+	0.0644186i
$326$	−3.82782e9	−	1.67708e10i	−0.338907	−	1.48485i
$327$	−2.08122e10	−	7.28249e9i	−1.82023	−	0.636926i
$328$	−3.05484e9	−	6.34343e9i	−0.263932	−	0.548061i
$329$	1.70023e9	−	1.06832e9i	0.145119	−	0.0911842i
$330$	−4.27598e9	+	1.49623e9i	−0.360562	+	0.126166i
$331$	−9.27437e9	−	9.27437e9i	−0.772632	−	0.772632i	0.205934	−	0.978566i	$-0.433977\pi$
$331$	−9.27437e9	−	9.27437e9i	−0.772632	−	0.772632i	−0.978566	+	0.205934i	$0.933977\pi$
$332$	1.40703e9	−	2.92172e9i	0.115811	−	0.240484i
$333$	−5.41727e9	−	4.80796e10i	−0.440559	−	3.91007i
$334$	1.98777e10	−	2.23967e9i	1.59727	−	0.179970i
$335$	6.59838e9	+	3.17761e9i	0.523912	+	0.252303i
$336$	1.13954e10	−	1.13954e10i	0.894075	−	0.894075i
$337$	1.75663e9	+	5.02016e9i	0.136195	+	0.389223i	0.991700	−	0.128571i	$-0.0410391\pi$
$337$	1.75663e9	+	5.02016e9i	0.136195	+	0.389223i	−0.855505	+	0.517794i	$0.826753\pi$
$338$	−3.33892e9	−	5.31386e9i	−0.255823	−	0.407139i
$339$	−6.46972e9	+	3.11565e9i	−0.489877	+	0.235912i
$340$	8.12596e8	−	2.32227e9i	0.0608077	−	0.173779i
$341$	3.91489e8	−	8.93548e7i	0.0289536	−	0.00660846i
$342$	−2.89034e10	+	3.62437e10i	−2.11273	+	2.64928i
$343$	9.31280e9	+	1.16779e10i	0.672827	+	0.843699i
$344$	−3.98427e9	+	1.74562e10i	−0.284521	+	1.24657i
$345$	−8.13134e9	+	1.29410e10i	−0.573965	+	0.913461i
$346$	1.19681e9	−	1.06220e10i	0.0835068	−	0.741143i
$347$			1.04536e10i			0.721023i	0.932755	+	0.360511i	$0.117398\pi$
$347$			1.04536e10i			0.721023i	−0.932755	+	0.360511i	$0.882602\pi$
$348$	−5.27830e9	+	3.87798e8i	−0.359896	+	0.0264417i
$349$	7.80384e9			0.526026			0.263013	−	0.964792i	$-0.415284\pi$
$349$	7.80384e9			0.526026			0.263013	+	0.964792i	$0.415284\pi$
$350$	−9.80907e8	−	1.10522e8i	−0.0653665	−	0.00736504i
$351$	4.46328e10	+	2.80446e10i	2.94053	+	1.84766i
$352$	1.35083e9	+	3.08319e8i	0.0879895	+	0.0200830i
$353$	2.28766e9	−	1.82435e9i	0.147331	−	0.117492i	−0.547051	−	0.837100i	$-0.684250\pi$
$353$	2.28766e9	−	1.82435e9i	0.147331	−	0.117492i	0.694381	+	0.719607i	$0.255678\pi$
$354$	−3.21224e10	−	2.56168e10i	−2.04548	−	1.63122i
$355$	4.37962e9	+	1.91884e10i	0.275755	+	1.20816i
$356$	−1.02247e9	−	3.57778e8i	−0.0636577	−	0.0222748i
$357$	1.15375e10	+	2.39578e10i	0.710295	+	1.47494i
$358$	2.50308e9	−	1.57279e9i	0.152385	−	0.0957499i
$359$	−4.75722e9	+	1.66462e9i	−0.286401	+	0.100216i	−0.469657	−	0.882849i	$-0.655622\pi$
$359$	−4.75722e9	+	1.66462e9i	−0.286401	+	0.100216i	0.183255	+	0.983065i	$0.441337\pi$
$360$	3.04465e10	+	3.04465e10i	1.81271	+	1.81271i
$361$	−9.42553e9	+	1.95723e10i	−0.554980	+	1.15243i
$362$	−3.55693e8	−	3.15686e9i	−0.0207129	−	0.183832i
$363$	−3.04525e10	+	3.43118e9i	−1.75387	+	0.197614i
$364$	−3.32013e9	−	1.59889e9i	−0.189125	−	0.0910778i
$365$	1.76085e10	−	1.76085e10i	0.992088	−	0.992088i
$366$	1.56174e10	+	4.46321e10i	0.870334	+	2.48727i
$367$	−1.27755e10	−	2.03321e10i	−0.704228	−	1.12077i	−0.986865	−	0.161546i	$-0.948352\pi$
$367$	−1.27755e10	−	2.03321e10i	−0.704228	−	1.12077i	0.282637	−	0.959227i	$-0.408791\pi$
$368$	−7.66334e9	+	3.69047e9i	−0.417856	+	0.201229i
$369$	−8.68387e9	+	2.48171e10i	−0.468390	+	1.33858i
$370$	2.47499e10	−	5.64899e9i	1.32058	−	0.301415i
$371$	1.49556e9	−	1.87537e9i	0.0789420	−	0.0989901i
$372$	−5.38895e8	−	6.75753e8i	−0.0281406	−	0.0352871i
$373$	1.30738e9	−	5.72800e9i	0.0675408	−	0.295916i	−0.929865	−	0.367901i	$-0.880076\pi$
$373$	1.30738e9	−	5.72800e9i	0.0675408	−	0.295916i	0.997406	+	0.0719856i	$0.0229336\pi$
$374$	2.21325e9	−	3.52237e9i	0.113121	−	0.180031i
$375$	4.29559e9	−	3.81244e10i	0.217219	−	1.92787i
$376$			4.18079e9i			0.209174i
$377$	−9.97558e9	−	2.29557e10i	−0.493825	−	1.13639i
$378$	−4.51402e10			−2.21104
$379$	−1.62924e10	−	1.83572e9i	−0.789640	−	0.0889710i	−0.292072	−	0.956396i	$-0.594345\pi$
$379$	−1.62924e10	−	1.83572e9i	−0.789640	−	0.0889710i	−0.497567	+	0.867425i	$0.665773\pi$
$380$	4.92331e9	+	3.09352e9i	0.236114	+	0.148360i
$381$	−3.27947e10	−	7.48517e9i	−1.55634	−	0.355224i
$382$	1.05397e10	−	8.40511e9i	0.494964	−	0.394721i
$383$	7.76030e9	+	6.18863e9i	0.360648	+	0.287607i	0.787003	−	0.616949i	$-0.211631\pi$
$383$	7.76030e9	+	6.18863e9i	0.360648	+	0.287607i	−0.426356	+	0.904556i	$0.640203\pi$
$384$	5.59521e9	+	2.45142e10i	0.257331	+	1.12744i
$385$	−4.13974e9	−	1.44856e9i	−0.188421	−	0.0659314i
$386$	−1.52630e10	−	3.16940e10i	−0.687529	−	1.42767i
$387$	5.66157e10	−	3.55740e10i	2.52402	−	1.58595i
$388$	−3.57935e8	+	1.25247e8i	−0.0157935	+	0.00552637i
$389$	4.17754e9	+	4.17754e9i	0.182441	+	0.182441i	0.792419	−	0.609978i	$-0.208822\pi$
$389$	4.17754e9	+	4.17754e9i	0.182441	+	0.182441i	−0.609978	+	0.792419i	$0.708822\pi$
$390$	−2.00082e10	+	4.15475e10i	−0.864868	+	1.79592i
$391$	−1.57138e9	−	1.39464e10i	−0.0672316	−	0.596697i
$392$	−5.75687e9	+	6.48644e8i	−0.243805	+	0.0274702i
$393$	3.03198e10	+	1.46012e10i	1.27103	+	0.612096i
$394$	2.07124e10	−	2.07124e10i	0.859499	−	0.859499i
$395$	9.85064e9	+	2.81515e10i	0.404647	+	1.15641i
$396$	−1.49753e9	−	2.38330e9i	−0.0608968	−	0.0969167i
$397$	1.32508e10	−	6.38126e9i	0.533435	−	0.256889i	−0.147719	−	0.989029i	$-0.547193\pi$
$397$	1.32508e10	−	6.38126e9i	0.533435	−	0.256889i	0.681153	+	0.732141i	$0.261479\pi$
$398$	−1.60471e9	+	4.58599e9i	−0.0639534	+	0.182768i
$399$	−6.12677e10	+	1.39840e10i	−2.41735	+	0.551745i
$400$	1.02463e9	−	1.28484e9i	0.0400246	−	0.0501892i
$401$	2.06975e10	+	2.59539e10i	0.800463	+	1.00375i	0.999717	+	0.0238005i	$0.00757665\pi$
$401$	2.06975e10	+	2.59539e10i	0.800463	+	1.00375i	−0.199254	+	0.979948i	$0.563852\pi$
$402$	5.93097e9	−	2.59853e10i	0.227102	−	0.995000i
$403$	2.17472e9	−	3.46104e9i	0.0824485	−	0.131216i
$404$	6.15536e8	−	5.46303e9i	0.0231062	−	0.205073i
$405$		−	7.06796e10i		−	2.62708i
$406$	1.76920e10	+	1.21001e10i	0.651138	+	0.445333i
$407$	−1.02611e10			−0.373954
$408$	−5.50163e10	−	6.19885e9i	−1.98541	−	0.223702i
$409$	7.84126e9	+	4.92699e9i	0.280216	+	0.176071i	0.664806	−	0.747016i	$-0.268514\pi$
$409$	7.84126e9	+	4.92699e9i	0.280216	+	0.176071i	−0.384590	+	0.923087i	$0.625657\pi$
$410$	−1.34494e10	−	3.06975e9i	−0.475958	−	0.108634i
$411$	−8.40542e9	+	6.70310e9i	−0.294573	+	0.234914i
$412$	1.17589e9	+	9.37740e8i	0.0408110	+	0.0325457i
$413$	−8.85122e9	−	3.87797e10i	−0.304231	−	1.33292i
$414$	3.74944e10	+	1.31199e10i	1.27634	+	0.446610i
$415$	−1.70463e10	−	3.53969e10i	−0.574694	−	1.19337i
$416$	1.19423e10	−	7.50386e9i	0.398764	−	0.250560i
$417$	1.83712e10	−	6.42838e9i	0.607567	−	0.212597i
$418$	6.95183e9	+	6.95183e9i	0.227716	+	0.227716i
$419$	1.57585e9	−	3.27229e9i	0.0511281	−	0.106168i	−0.873840	−	0.486214i	$-0.838377\pi$
$419$	1.57585e9	−	3.27229e9i	0.0511281	−	0.106168i	0.924968	+	0.380046i	$0.124092\pi$
$420$	1.05697e9	+	9.38087e9i	0.0339676	+	0.301471i
$421$	−3.27783e10	+	3.69322e9i	−1.04342	+	0.117565i	−0.617001	−	0.786963i	$-0.711652\pi$
$421$	−3.27783e10	+	3.69322e9i	−1.04342	+	0.117565i	−0.426416	+	0.904527i	$0.640224\pi$
$422$	1.45844e10	+	7.02347e9i	0.459874	+	0.221463i
$423$	1.10398e10	−	1.10398e10i	0.344826	−	0.344826i
$424$	1.64948e9	+	4.71396e9i	0.0510370	+	0.145855i
$425$	1.44267e9	+	2.29600e9i	0.0442192	+	0.0703745i
$426$	6.45361e10	−	3.10789e10i	1.95959	−	0.943687i
$427$	−1.51198e10	+	4.32100e10i	−0.454816	+	1.29979i
$428$	−1.54186e9	+	3.51920e8i	−0.0459484	+	0.0104874i
$429$	1.16214e10	−	1.45728e10i	0.343108	−	0.430243i
$430$	2.18738e10	+	2.74289e10i	0.639809	+	0.802295i
$431$	1.29876e9	−	5.69025e9i	0.0376375	−	0.164901i	−0.952616	−	0.304174i	$-0.901620\pi$
$431$	1.29876e9	−	5.69025e9i	0.0376375	−	0.164901i	0.990254	+	0.139273i	$0.0444767\pi$
$432$	3.99826e10	−	6.36320e10i	1.14799	−	1.82701i
$433$	−3.60052e9	+	3.19555e10i	−0.102427	+	0.909063i	0.832452	+	0.554097i	$0.186936\pi$
$433$	−3.60052e9	+	3.19555e10i	−0.102427	+	0.909063i	−0.934879	+	0.354966i	$0.884492\pi$
$434$			3.50039e9i			0.0986637i
$435$	−3.61972e10	+	5.29253e10i	−1.01092	+	1.47811i
$436$	7.18818e9			0.198918
$437$	3.29596e10	+	3.71366e9i	0.903766	+	0.101830i
$438$	−7.67372e10	−	4.82172e10i	−2.08502	−	1.31010i
$439$	−1.36733e10	−	3.12084e9i	−0.368141	−	0.0840259i	0.0344481	−	0.999406i	$-0.489033\pi$
$439$	−1.36733e10	−	3.12084e9i	−0.368141	−	0.0840259i	−0.402590	+	0.915381i	$0.631890\pi$
$440$	7.13938e9	−	5.69347e9i	0.190480	−	0.151903i
$441$	1.69144e10	+	1.34888e10i	0.447201	+	0.356631i
$442$	−9.42283e9	−	4.12841e10i	−0.246884	−	1.08167i
$443$	−4.59318e10	−	1.60722e10i	−1.19261	−	0.417313i	−0.340285	−	0.940322i	$-0.610523\pi$
$443$	−4.59318e10	−	1.60722e10i	−1.19261	−	0.417313i	−0.852327	+	0.523010i	$0.824809\pi$
$444$	9.58290e9	+	1.98991e10i	0.246584	+	0.512037i
$445$	−1.11123e10	+	6.98230e9i	−0.283376	+	0.178057i
$446$	−4.69480e10	+	1.64278e10i	−1.18653	+	0.415184i
$447$	3.25869e10	+	3.25869e10i	0.816230	+	0.816230i
$448$	−1.70555e10	+	3.54161e10i	−0.423401	+	0.879202i
$449$	6.04880e9	+	5.36846e10i	0.148828	+	1.32088i	0.816897	+	0.576784i	$0.195693\pi$
$449$	6.04880e9	+	5.36846e10i	0.148828	+	1.32088i	−0.668069	+	0.744100i	$0.732879\pi$
$450$	−7.62673e9	+	8.59326e8i	−0.185989	+	0.0209560i
$451$	5.02385e9	+	2.41936e9i	0.121431	+	0.0584782i
$452$	1.65532e9	−	1.65532e9i	0.0396577	−	0.0396577i
$453$	−2.32286e10	−	6.63836e10i	−0.551608	−	1.57641i
$454$	−6.84057e9	−	1.08867e10i	−0.161016	−	0.256255i
$455$	−4.02237e10	+	1.93707e10i	−0.938505	+	0.451960i
$456$	4.32149e10	−	1.23501e11i	0.999480	−	2.85635i
$457$	−5.48417e10	+	1.25173e10i	−1.25732	+	0.286975i	−0.798739	−	0.601677i	$-0.794499\pi$
$457$	−5.48417e10	+	1.25173e10i	−1.25732	+	0.286975i	−0.458581	+	0.888652i	$0.651642\pi$
$458$	−9.67346e9	+	1.21301e10i	−0.219847	+	0.275679i
$459$	7.73134e10	+	9.69479e10i	1.74182	+	2.18418i
$460$	1.10870e9	−	4.85755e9i	0.0247619	−	0.108489i
$461$	7.31071e8	−	1.16349e9i	0.0161866	−	0.0257608i	−0.838533	−	0.544851i	$-0.816586\pi$
$461$	7.31071e8	−	1.16349e9i	0.0161866	−	0.0257608i	0.854720	+	0.519090i	$0.173729\pi$
$462$	−1.78715e9	+	1.58614e10i	−0.0392278	+	0.348156i
$463$		−	1.16149e9i		−	0.0252750i	−0.999920	−	0.0126375i	$-0.995977\pi$
$463$		−	1.16149e9i		−	0.0252750i	0.999920	−	0.0126375i	$-0.00402274\pi$
$464$	−3.27275e10	+	1.42220e10i	−0.706059	+	0.306823i
$465$	−1.04713e10			−0.223970
$466$	−2.27428e10	−	2.56250e9i	−0.482281	−	0.0543400i
$467$	4.11328e10	+	2.58454e10i	0.864810	+	0.543396i	0.889831	−	0.456291i	$-0.150822\pi$
$467$	4.11328e10	+	2.58454e10i	0.864810	+	0.543396i	−0.0250209	+	0.999687i	$0.507965\pi$
$468$	−2.79337e10	−	6.37567e9i	−0.582297	−	0.132905i
$469$	2.01746e10	−	1.60887e10i	0.416979	−	0.332529i
$470$	6.40455e9	+	5.10746e9i	0.131249	+	0.104668i
$471$	2.21931e10	+	9.72341e10i	0.450955	+	1.97576i
$472$	7.81706e10	+	2.73531e10i	1.57498	+	0.551110i
$473$	−6.15267e9	−	1.27761e10i	−0.122919	−	0.255244i
$474$	9.19079e10	−	5.77495e10i	1.82070	−	1.14402i
$475$	−6.04879e9	+	2.11656e9i	−0.118821	+	0.0415774i
$476$	−6.12976e9	−	6.12976e9i	−0.119403	−	0.119403i
$477$	8.09204e9	−	1.68033e10i	0.156309	−	0.324580i
$478$	3.14331e9	+	2.78977e10i	0.0602110	+	0.534388i
$479$	2.30151e10	−	2.59318e9i	0.437191	−	0.0492596i	0.109374	−	0.994001i	$-0.465115\pi$
$479$	2.30151e10	−	2.59318e9i	0.437191	−	0.0492596i	0.327818	+	0.944741i	$0.393687\pi$
$480$	−3.25533e10	−	1.56768e10i	−0.613239	−	0.295320i
$481$	−7.38581e10	+	7.38581e10i	−1.37981	+	1.37981i
$482$	1.73494e10	+	4.95817e10i	0.321437	+	0.918615i
$483$	2.86501e10	+	4.55964e10i	0.526427	+	0.837804i
$484$	9.00105e9	−	4.33467e9i	0.164026	−	0.0789905i
$485$	−1.51738e9	+	4.33642e9i	−0.0274238	+	0.0783726i
$486$	−1.13829e11	+	2.59806e10i	−2.04036	+	0.465698i
$487$	−3.02225e10	+	3.78978e10i	−0.537297	+	0.673749i	−0.974181	−	0.225769i	$-0.927511\pi$
$487$	−3.02225e10	+	3.78978e10i	−0.537297	+	0.673749i	0.436884	+	0.899518i	$0.356082\pi$
$488$	−5.94277e10	−	7.45199e10i	−1.04787	−	1.31399i
$489$	4.03462e10	−	1.76768e11i	0.705613	−	3.09149i
$490$	−6.03922e9	+	9.61137e9i	−0.104760	+	0.166725i
$491$	−1.07271e10	+	9.52057e10i	−0.184568	+	1.63809i	0.470417	+	0.882444i	$0.344104\pi$
$491$	−1.07271e10	+	9.52057e10i	−0.184568	+	1.63809i	−0.654985	+	0.755642i	$0.727325\pi$
$492$		−	1.20020e10i		−	0.204831i
$493$	−4.31428e9	−	5.87216e10i	−0.0730333	−	0.994054i
$494$	1.00076e11			1.68044
$495$	−3.38864e10	−	3.81808e9i	−0.564423	−	0.0635952i
$496$	−4.93433e9	−	3.10045e9i	−0.0815271	−	0.0512269i
$497$	6.76087e10	+	1.54312e10i	1.10810	+	0.252916i
$498$	−1.11788e11	+	8.91482e10i	−1.81752	+	1.44942i
$499$	−4.71394e9	−	3.75924e9i	−0.0760295	−	0.0606315i	0.584738	−	0.811222i	$-0.301197\pi$
$499$	−4.71394e9	−	3.75924e9i	−0.0760295	−	0.0606315i	−0.660767	+	0.750591i	$0.729769\pi$
$500$	2.78313e9	+	1.21937e10i	0.0445300	+	0.195099i
$501$	1.99009e11	+	6.96364e10i	3.15881	+	1.10531i
$502$	1.98749e10	+	4.12706e10i	0.312961	+	0.649869i
$503$	5.77993e9	−	3.63177e9i	0.0902922	−	0.0567344i	−0.486129	−	0.873887i	$-0.661592\pi$
$503$	5.77993e9	−	3.63177e9i	0.0902922	−	0.0567344i	0.576421	+	0.817153i	$0.304449\pi$
$504$	1.43197e11	−	5.01069e10i	2.21929	−	0.776561i
$505$	−4.70962e10	−	4.70962e10i	−0.724136	−	0.724136i
$506$	3.65525e9	−	7.59020e9i	0.0557590	−	0.115785i
$507$	−7.40626e9	−	6.57324e10i	−0.112090	−	0.994827i
$508$	1.08971e10	−	1.22781e9i	0.163628	−	0.0184364i
$509$	−7.42500e10	−	3.57569e10i	−1.10618	−	0.532707i	−0.210583	−	0.977576i	$-0.567536\pi$
$509$	−7.42500e10	−	3.57569e10i	−1.10618	−	0.532707i	−0.895596	+	0.444869i	$0.853250\pi$
$510$	−7.67067e10	+	7.67067e10i	−1.13384	+	1.13384i
$511$	−2.89789e10	−	8.28171e10i	−0.425010	−	1.21461i
$512$	−4.08623e10	−	6.50319e10i	−0.594624	−	0.946339i
$513$	−2.64032e11	+	1.27151e11i	−3.81230	+	1.83591i
$514$	3.92052e9	−	1.12042e10i	0.0561683	−	0.160520i
$515$	1.77645e10	−	4.05463e9i	0.252537	−	0.0576398i
$516$	−1.90304e10	+	2.38633e10i	−0.268441	+	0.336614i
$517$	−2.06443e9	−	2.58871e9i	−0.0288960	−	0.0362345i
$518$	1.99038e10	−	8.72042e10i	0.276450	−	1.21121i
$519$	5.99425e10	−	9.53979e10i	0.826162	−	1.31483i
$520$	1.04075e10	−	9.23689e10i	0.142342	−	1.26332i
$521$		−	1.88280e10i		−	0.255537i	−0.991804	−	0.127768i	$-0.959219\pi$
$521$		−	1.88280e10i		−	0.255537i	0.991804	−	0.127768i	$-0.0407814\pi$
$522$	1.55044e11	+	6.11121e10i	2.08821	+	0.823086i
$523$	8.25182e10			1.10292			0.551459	−	0.834202i	$-0.314071\pi$
$523$	8.25182e10			1.10292			0.551459	+	0.834202i	$0.314071\pi$
$524$	−1.09018e10	−	1.22833e9i	−0.144601	−	0.0162926i
$525$	−8.80967e9	−	5.53548e9i	−0.115964	−	0.0728649i
$526$	−1.07482e11	−	2.45320e10i	−1.40408	−	0.320472i
$527$	7.51781e9	−	5.99526e9i	0.0974651	−	0.0777258i
$528$	−2.07761e10	−	1.65684e10i	−0.267319	−	0.213179i
$529$	1.11014e10	+	4.86384e10i	0.141760	+	0.621093i
$530$	9.23640e9	+	3.23196e9i	0.117058	+	0.0409602i
$531$	−1.34189e11	−	2.78646e11i	−1.68787	−	3.50489i
$532$	1.73469e10	−	1.08998e10i	0.216558	−	0.136073i
$533$	5.35751e10	−	1.87467e10i	0.663826	−	0.232283i
$534$	3.37732e10	+	3.37732e10i	0.415344	+	0.415344i
$535$	−8.31331e9	+	1.72628e10i	−0.101475	+	0.210715i
$536$	6.01541e9	+	5.33883e10i	0.0728796	+	0.646825i
$537$	3.09631e10	−	3.48870e9i	0.372346	−	0.0419533i
$538$	−6.98022e10	−	3.36150e10i	−0.833183	−	0.401240i
$539$	3.24432e9	−	3.24432e9i	0.0384387	−	0.0384387i
$540$	1.45395e10	+	4.15516e10i	0.170992	+	0.488667i
$541$	−1.28553e10	−	2.04590e10i	−0.150069	−	0.238834i	0.763226	−	0.646131i	$-0.223614\pi$
$541$	−1.28553e10	−	2.04590e10i	−0.150069	−	0.238834i	−0.913296	+	0.407297i	$0.866471\pi$
$542$	−4.32426e10	+	2.08245e10i	−0.501089	+	0.241312i
$543$	1.10593e10	−	3.16056e10i	0.127212	−	0.363550i
$544$	3.23469e10	−	7.38297e9i	0.369349	−	0.0843016i
$545$	5.42970e10	−	6.80863e10i	0.615446	−	0.771745i
$546$	1.01305e11	+	1.27032e11i	1.13988	+	1.42936i
$547$	−2.41784e10	+	1.05932e11i	−0.270071	+	1.18326i	0.639858	+	0.768493i	$0.278993\pi$
$547$	−2.41784e10	+	1.05932e11i	−0.270071	+	1.18326i	−0.909929	+	0.414765i	$0.863864\pi$
$548$	1.86468e9	−	2.96762e9i	0.0206767	−	0.0329069i
$549$	−3.98526e10	+	3.53702e11i	−0.438700	+	3.89357i
$550$			1.62769e9i			0.0177878i
$551$	1.37567e11	+	2.09405e10i	1.49248	+	0.227186i
$552$	−1.12120e11			−1.20761
$553$	1.04426e11	+	1.17660e10i	1.11663	+	0.125814i
$554$	2.83954e10	+	1.78420e10i	0.301445	+	0.189411i
$555$	2.60870e11	+	5.95418e10i	2.74949	+	0.627552i
$556$	−4.96082e9	+	3.95612e9i	−0.0519104	+	0.0413972i
$557$	−5.70082e10	−	4.54625e10i	−0.592266	−	0.472316i	0.280902	−	0.959737i	$-0.409366\pi$
$557$	−5.70082e10	−	4.54625e10i	−0.592266	−	0.472316i	−0.873167	+	0.487420i	$0.837938\pi$
$558$	6.05617e9	+	2.65338e10i	0.0624685	+	0.273692i
$559$	−1.36247e11	−	4.76748e10i	−1.39534	−	0.488249i
$560$	2.76164e10	+	5.73461e10i	0.280812	+	0.583111i
$561$	3.71266e10	−	2.33282e10i	0.374830	−	0.235521i
$562$	1.54246e11	−	5.39729e10i	1.54621	−	0.541042i
$563$	−1.08358e11	−	1.08358e11i	−1.07852	−	1.07852i	−0.996642	−	0.0818790i	$-0.973908\pi$
$563$	−1.08358e11	−	1.08358e11i	−1.07852	−	1.07852i	−0.0818790	−	0.996642i	$-0.526092\pi$
$564$	−3.09223e9	+	6.42109e9i	−0.0305602	+	0.0634589i
$565$	−3.17544e9	−	2.81828e10i	−0.0311609	−	0.276560i
$566$	−1.25685e11	+	1.41613e10i	−1.22467	+	0.137987i
$567$	−2.24372e11	−	1.08052e11i	−2.17088	−	1.04544i
$568$	−1.02096e11	+	1.02096e11i	−0.980878	+	0.980878i
$569$	−3.45783e10	−	9.88192e10i	−0.329879	−	0.942741i	−0.982696	−	0.185225i	$-0.940699\pi$
$569$	−3.45783e10	−	9.88192e10i	−0.329879	−	0.942741i	0.652817	−	0.757516i	$-0.273587\pi$
$570$	−1.36398e11	−	2.17076e11i	−1.29214	−	2.05642i
$571$	1.64324e11	−	7.91342e10i	1.54581	−	0.744423i	0.549940	−	0.835204i	$-0.314651\pi$
$571$	1.64324e11	−	7.91342e10i	1.54581	−	0.744423i	0.995871	+	0.0907807i	$0.0289362\pi$
$572$	−2.00693e9	+	5.73546e9i	−0.0187477	+	0.0535777i
$573$	1.38528e11	−	3.16181e10i	1.28505	−	0.293303i
$574$	−3.03058e10	+	3.80023e10i	−0.279176	+	0.350076i
$575$	3.42381e9	+	4.29332e9i	0.0313212	+	0.0392755i
$576$	−6.80099e10	+	2.97971e11i	−0.617849	+	2.70697i
$577$	2.02750e10	−	3.22675e10i	0.182919	−	0.291113i	−0.742660	−	0.669669i	$-0.766436\pi$
$577$	2.02750e10	−	3.22675e10i	0.182919	−	0.291113i	0.925579	+	0.378555i	$0.123579\pi$
$578$	−7.32320e7	+	6.49952e8i	−0.000656130	+	0.00582331i
$579$		−	3.70781e11i		−	3.29916i
$580$	5.43962e9	−	2.01829e10i	0.0480681	−	0.178350i
$581$	−1.38427e11			−1.21483
$582$	1.66150e10	+	1.87206e9i	0.144813	+	0.0163166i
$583$	−3.34905e9	−	2.10435e9i	−0.0289900	−	0.0182156i
$584$	1.78101e11	+	4.06504e10i	1.53114	+	0.349473i
$585$	−2.71391e11	+	2.16427e11i	−2.31725	+	1.84794i
$586$	4.74243e9	+	3.78196e9i	0.0402171	+	0.0320720i
$587$	−2.38823e10	−	1.04635e11i	−0.201152	−	0.881303i	−0.970237	−	0.242157i	$-0.922145\pi$
$587$	−2.38823e10	−	1.04635e11i	−0.201152	−	0.881303i	0.769085	−	0.639146i	$-0.220712\pi$
$588$	−9.32148e9	−	3.26173e9i	−0.0779786	−	0.0272859i
$589$	9.85991e9	+	2.04743e10i	0.0819241	+	0.170117i
$590$	1.37399e11	−	8.63337e10i	1.13390	−	0.712479i
$591$	2.91416e11	−	1.01971e11i	2.38871	−	0.835847i
$592$	1.05298e11	+	1.05298e11i	0.857301	+	0.857301i
$593$	−8.16991e10	+	1.69650e11i	−0.660691	+	1.37194i	0.253770	+	0.967265i	$0.418329\pi$
$593$	−8.16991e10	+	1.69650e11i	−0.660691	+	1.37194i	−0.914461	+	0.404674i	$0.867385\pi$
$594$	8.33391e9	+	7.39655e10i	0.0669427	+	0.594133i
$595$	−1.04363e11	+	1.17589e10i	−0.832680	+	0.0938206i
$596$	−1.35359e10	−	6.51855e9i	−0.107276	−	0.0516614i
$597$	−3.62118e10	+	3.62118e10i	−0.285071	+	0.285071i
$598$	−2.83232e10	−	8.09431e10i	−0.221482	−	0.632958i
$599$	3.67097e10	+	5.84232e10i	0.285150	+	0.453814i	0.958329	−	0.285665i	$-0.0922146\pi$
$599$	3.67097e10	+	5.84232e10i	0.285150	+	0.453814i	−0.673179	+	0.739479i	$0.735072\pi$
$600$	1.95173e10	−	9.39905e9i	0.150597	−	0.0725236i
$601$	−2.32162e10	+	6.63482e10i	−0.177948	+	0.508547i	−0.997963	−	0.0637955i	$-0.979679\pi$
$601$	−2.32162e10	+	6.63482e10i	−0.177948	+	0.508547i	0.820015	+	0.572342i	$0.193965\pi$
$602$	1.20512e11	−	2.75062e10i	0.917584	−	0.209433i
$603$	1.25093e11	−	1.56861e11i	0.946156	−	1.18644i
$604$	1.42953e10	+	1.79257e10i	0.107410	+	0.134688i
$605$	2.69328e10	−	1.18000e11i	0.201030	−	0.880768i
$606$	−1.28963e11	+	2.05244e11i	−0.956258	+	1.52188i
$607$	−1.13792e10	+	1.00993e11i	−0.0838215	+	0.743937i	0.879557	+	0.475793i	$0.157839\pi$
$607$	−1.13792e10	+	1.00993e11i	−0.0838215	+	0.743937i	−0.963379	+	0.268144i	$0.913590\pi$
$608$			7.84119e10i			0.573809i
$609$	1.12674e11	+	1.95818e11i	0.819134	+	1.42358i
$610$	−1.86757e11			−1.34883
$611$	−3.34926e10	−	3.77371e9i	−0.240317	−	0.0270772i
$612$	−5.70704e10	−	3.58597e10i	−0.406822	−	0.255623i
$613$	−1.44570e11	−	3.29971e10i	−1.02385	−	0.233687i	−0.322549	−	0.946553i	$-0.604540\pi$
$613$	−1.44570e11	−	3.29971e10i	−1.02385	−	0.233687i	−0.701300	+	0.712866i	$0.747397\pi$
$614$	−8.11488e10	+	6.47140e10i	−0.570964	+	0.455329i
$615$	−1.13683e11	−	9.06592e10i	−0.794685	−	0.633740i
$616$	−7.15950e9	−	3.13678e10i	−0.0497233	−	0.217852i
$617$	2.60837e11	+	9.12709e10i	1.79982	+	0.629784i	0.999545	+	0.0301480i	$0.00959786\pi$
$617$	2.60837e11	+	9.12709e10i	1.79982	+	0.629784i	0.800273	+	0.599636i	$0.204688\pi$
$618$	−2.87727e10	−	5.97472e10i	−0.197255	−	0.409604i
$619$	−2.21779e11	+	1.39353e11i	−1.51063	+	0.949190i	−0.514860	+	0.857274i	$0.672156\pi$
$619$	−2.21779e11	+	1.39353e11i	−1.51063	+	0.949190i	−0.995767	+	0.0919155i	$0.970701\pi$
$620$	3.22212e9	−	1.12747e9i	0.0218059	−	0.00763022i
$621$	1.77566e11	+	1.77566e11i	1.19397	+	1.19397i
$622$	8.67493e10	−	1.80137e11i	0.579568	−	1.20348i
$623$	5.17732e9	+	4.59500e10i	0.0343679	+	0.305024i
$624$	−2.68801e11	+	3.02866e10i	−1.77293	+	0.199761i
$625$	1.25057e11	+	6.02244e10i	0.819576	+	0.394687i
$626$	6.91180e10	−	6.91180e10i	0.450084	−	0.450084i
$627$	3.42252e10	+	9.78100e10i	0.221450	+	0.632868i
$628$	−1.72983e10	−	2.75301e10i	−0.111216	−	0.176999i
$629$	−2.21379e11	+	1.06611e11i	−1.41428	+	0.681079i
$630$	9.81782e10	−	2.80577e11i	0.623237	−	1.78111i
$631$	−9.09676e10	+	2.07628e10i	−0.573811	+	0.130969i	−0.499573	−	0.866272i	$-0.666510\pi$
$631$	−9.09676e10	+	2.07628e10i	−0.573811	+	0.130969i	−0.0742384	+	0.997241i	$0.523653\pi$
$632$	−1.36418e11	+	1.71062e11i	−0.855071	+	1.07222i
$633$	1.06380e11	+	1.33396e11i	0.662588	+	0.830859i
$634$	−2.81209e10	+	1.23206e11i	−0.174049	+	0.762561i
$635$	7.06832e10	−	1.12492e11i	0.434732	−	0.691872i
$636$	−9.53209e8	+	8.45996e9i	−0.00582585	+	0.0517059i
$637$		−	4.67043e10i		−	0.283660i
$638$	1.65606e10	−	3.12236e10i	0.0999523	−	0.188452i
$639$	5.39189e11			3.23398
$640$	−9.86856e10	−	1.11192e10i	−0.588212	−	0.0662756i
$641$	8.32136e10	+	5.22866e10i	0.492904	+	0.309712i	0.755449	−	0.655208i	$-0.227419\pi$
$641$	8.32136e10	+	5.22866e10i	0.492904	+	0.309712i	−0.262545	+	0.964920i	$0.584562\pi$
$642$	6.79830e10	+	1.55167e10i	0.400185	+	0.0913395i
$643$	−1.64258e11	+	1.30992e11i	−0.960911	+	0.766301i	−0.972325	−	0.233634i	$-0.924938\pi$
$643$	−1.64258e11	+	1.30992e11i	−0.960911	+	0.766301i	0.0114136	+	0.999935i	$0.496367\pi$
$644$	−1.37253e10	−	1.09456e10i	−0.0797956	−	0.0636348i
$645$	8.22842e10	+	3.60511e11i	0.475420	+	2.08295i
$646$	2.22210e11	+	7.77546e10i	1.27595	+	0.446474i
$647$	8.66072e10	+	1.79842e11i	0.494239	+	1.02630i	0.987675	+	0.156516i	$0.0500263\pi$
$647$	8.66072e10	+	1.79842e11i	0.494239	+	1.02630i	−0.493436	+	0.869782i	$0.664259\pi$
$648$	4.39029e11	−	2.75860e11i	2.48997	−	1.56455i
$649$	−6.19093e10	+	2.16630e10i	−0.348961	+	0.122107i
$650$	1.17159e10	+	1.17159e10i	0.0656330	+	0.0656330i
$651$	−1.60081e10	+	3.32412e10i	−0.0891285	+	0.185077i
$652$	6.61808e9	+	5.87370e10i	0.0366219	+	0.325029i
$653$	−1.05869e11	+	1.19286e10i	−0.582261	+	0.0656050i	−0.398182	−	0.917306i	$-0.630359\pi$
$653$	−1.05869e11	+	1.19286e10i	−0.582261	+	0.0656050i	−0.184079	+	0.982912i	$0.558930\pi$
$654$	−2.85551e11	−	1.37514e11i	−1.56089	−	0.751686i
$655$	−9.39829e10	+	9.39829e10i	−0.510603	+	0.510603i
$656$	−2.67268e10	−	7.63809e10i	−0.144322	−	0.412448i
$657$	−3.62952e11	−	5.77636e11i	−1.94800	−	3.10022i
$658$	2.60046e10	−	1.25232e10i	0.138722	−	0.0668052i
$659$	3.22051e10	−	9.20368e10i	0.170759	−	0.488000i	−0.826421	−	0.563053i	$-0.809627\pi$
$659$	3.22051e10	−	9.20368e10i	0.170759	−	0.488000i	0.997180	+	0.0750526i	$0.0239125\pi$
$660$	1.51761e10	−	3.46385e9i	0.0799806	−	0.0182550i
$661$	−7.45735e10	+	9.35122e10i	−0.390642	+	0.489849i	−0.937798	−	0.347181i	$-0.887139\pi$
$661$	−7.45735e10	+	9.35122e10i	−0.390642	+	0.489849i	0.547156	+	0.837030i	$0.315710\pi$
$662$	−1.17545e11	−	1.47397e11i	−0.612029	−	0.767460i
$663$	9.93190e10	−	4.35145e11i	0.514018	−	2.25206i
$664$	1.53339e11	−	2.44037e11i	0.788822	−	1.25540i
$665$	2.77899e10	−	2.46642e11i	0.142102	−	1.26119i
$666$		−	6.95465e11i		−	3.53491i
$667$	−2.19966e10	−	1.17192e11i	−0.111135	−	0.592101i
$668$	−6.87346e10			−0.345199
$669$	−5.20967e11	−	5.86989e10i	−2.60079	−	0.293039i
$670$	8.91342e10	+	5.60067e10i	0.442329	+	0.277934i
$671$	7.35943e10	+	1.67974e10i	0.363040	+	0.0828615i
$672$	−9.95319e10	+	7.93741e10i	−0.488074	+	0.389226i
$673$	3.84111e10	+	3.06318e10i	0.187239	+	0.149318i	0.712623	−	0.701547i	$-0.247507\pi$
$673$	3.84111e10	+	3.06318e10i	0.187239	+	0.149318i	−0.525384	+	0.850865i	$0.676078\pi$
$674$	1.70116e10	+	7.45327e10i	0.0824339	+	0.361166i
$675$	−4.57956e10	−	1.60246e10i	−0.220601	−	0.0771918i
$676$	9.35647e9	+	1.94289e10i	0.0448049	+	0.0930383i
$677$	6.81476e10	−	4.28200e10i	0.324411	−	0.203841i	−0.359973	−	0.932963i	$-0.617214\pi$
$677$	6.81476e10	−	4.28200e10i	0.324411	−	0.203841i	0.684384	+	0.729122i	$0.260071\pi$
$678$	−9.74246e10	+	3.40904e10i	−0.461052	+	0.161329i
$679$	1.14462e10	+	1.14462e10i	0.0538497	+	0.0538497i
$680$	9.48750e10	−	1.97010e11i	0.443727	−	0.921409i
$681$	−1.51735e10	−	1.34668e11i	−0.0705499	−	0.626148i
$682$	5.73565e9	−	6.46253e8i	0.0265122	−	0.00298720i
$683$	2.31254e11	+	1.11366e11i	1.06269	+	0.511764i	0.881744	−	0.471729i	$-0.156370\pi$
$683$	2.31254e11	+	1.11366e11i	1.06269	+	0.511764i	0.180946	+	0.983493i	$0.442084\pi$
$684$	1.12635e11	−	1.12635e11i	0.514577	−	0.514577i
$685$	−1.40241e10	−	4.00786e10i	−0.0636961	−	0.182033i
$686$	1.14226e11	+	1.81789e11i	0.515783	+	0.820864i
$687$	−1.47337e11	+	7.09539e10i	−0.661433	+	0.318529i
$688$	−6.79690e10	+	1.94244e11i	−0.303359	+	0.866950i
$689$	−3.92528e10	+	8.95919e9i	−0.174178	+	0.0397550i
$690$	−1.36971e11	+	1.71756e11i	−0.604271	+	0.757732i
$691$	5.37257e10	+	6.73698e10i	0.235651	+	0.295497i	0.885570	−	0.464507i	$-0.153768\pi$
$691$	5.37257e10	+	6.73698e10i	0.235651	+	0.295497i	−0.649918	+	0.760004i	$0.725197\pi$
$692$	−8.17312e9	+	3.58088e10i	−0.0356421	+	0.156158i
$693$	−6.39245e10	+	1.01735e11i	−0.277162	+	0.441102i
$694$	−1.68237e10	+	1.49315e11i	−0.0725244	+	0.643672i
$695$			7.68720e10i			0.329480i
$696$	−4.70024e11	−	1.82750e10i	−2.00301	−	0.0778788i
$697$	1.33524e11			0.565753
$698$	1.11466e11	+	1.25593e10i	0.469594	+	0.0529105i
$699$	−2.04257e11	−	1.28343e11i	−0.855593	−	0.537605i
$700$	3.30682e9	+	7.54760e8i	0.0137727	+	0.00314352i
$701$	2.40629e11	−	1.91895e11i	0.996497	−	0.794680i	0.0177688	−	0.999842i	$-0.494344\pi$
$701$	2.40629e11	−	1.91895e11i	0.996497	−	0.794680i	0.978728	+	0.205163i	$0.0657723\pi$
$702$	5.92379e11	+	4.72407e11i	2.43922	+	1.94521i
$703$	−1.29217e11	−	5.66136e11i	−0.529051	−	2.31792i
$704$	6.11808e10	+	2.14081e10i	0.249072	+	0.0871539i
$705$	3.74628e10	+	7.77922e10i	0.151650	+	0.314905i
$706$	3.56120e10	−	2.23765e10i	0.143343	−	0.0900685i
$707$	−2.21505e11	+	7.75079e10i	−0.886555	+	0.310219i
$708$	9.98276e10	+	9.98276e10i	0.397299	+	0.397299i
$709$	6.24907e10	−	1.29763e11i	0.247304	−	0.513531i	−0.739955	−	0.672657i	$-0.765153\pi$
$709$	6.24907e10	−	1.29763e11i	0.247304	−	0.513531i	0.987258	+	0.159125i	$0.0508674\pi$
$710$	3.16753e10	+	2.81126e11i	0.124649	+	1.10629i
$711$	8.11931e11	−	9.14827e10i	3.17717	−	0.357981i
$712$	−8.67417e10	−	4.17726e10i	−0.337526	−	0.162544i
$713$	1.37694e10	−	1.37694e10i	0.0532790	−	0.0532790i
$714$	1.26239e11	+	3.60771e11i	0.485737	+	1.38816i
$715$	3.91666e10	+	6.23332e10i	0.149862	+	0.238504i
$716$	−9.15194e9	+	4.40734e9i	−0.0348226	+	0.0167697i
$717$	−9.77325e10	+	2.79304e11i	−0.369796	+	1.05682i
$718$	−7.06288e10	+	1.61206e10i	−0.265757	+	0.0606572i
$719$	−1.02062e11	+	1.27982e11i	−0.381900	+	0.478887i	−0.935213	−	0.354086i	$-0.884792\pi$
$719$	−1.02062e11	+	1.27982e11i	−0.381900	+	0.478887i	0.553313	+	0.832973i	$0.313363\pi$
$720$	3.08556e11	+	3.86917e11i	1.14816	+	1.43975i
$721$	1.42862e10	−	6.25919e10i	0.0528658	−	0.231620i
$722$	−1.66129e11	+	2.64393e11i	−0.611359	+	0.972973i
$723$	−6.19918e10	+	5.50193e11i	−0.226872	+	2.01355i
$724$			1.09160e10i			0.0397293i
$725$	1.36534e10	+	1.85564e10i	0.0494183	+	0.0671647i
$726$	−4.40492e11			−1.58559
$727$	−1.47000e11	−	1.65630e10i	−0.526236	−	0.0592926i	−0.155150	−	0.987891i	$-0.549586\pi$
$727$	−1.47000e11	−	1.65630e10i	−0.526236	−	0.0592926i	−0.371086	+	0.928598i	$0.621015\pi$
$728$	−2.77314e11	−	1.74248e11i	−0.987293	−	0.620358i
$729$	−4.44231e11	−	1.01393e11i	−1.57289	−	0.359002i
$730$	2.79850e11	−	2.23173e11i	0.985447	−	0.785868i
$731$	−2.65482e11	−	2.11715e11i	−0.929748	−	0.741449i
$732$	−3.61552e10	−	1.58406e11i	−0.125929	−	0.551732i
$733$	4.92566e11	+	1.72356e11i	1.70627	+	0.597051i	0.994441	−	0.105298i	$-0.0335798\pi$
$733$	4.92566e11	+	1.72356e11i	1.70627	+	0.597051i	0.711833	+	0.702349i	$0.247866\pi$
$734$	−1.49757e11	−	3.10974e11i	−0.515945	−	1.07137i
$735$	−1.01306e11	+	6.36549e10i	−0.347126	+	0.218113i
$736$	6.34205e10	−	2.21918e10i	0.216132	−	0.0756277i
$737$	−3.00873e10	−	3.00873e10i	−0.101979	−	0.101979i
$738$	−1.63976e11	+	3.40500e11i	−0.552783	+	1.14787i
$739$	1.67954e9	+	1.49063e10i	0.00563135	+	0.0499796i	0.996214	−	0.0869393i	$-0.0277086\pi$
$739$	1.67954e9	+	1.49063e10i	0.00563135	+	0.0499796i	−0.990582	+	0.136919i	$0.956280\pi$
$740$	−8.66826e10	+	9.76678e9i	−0.289071	+	0.0325705i
$741$	9.50369e11	+	4.57674e11i	3.15224	+	1.51804i
$742$	2.43800e10	−	2.43800e10i	0.0804301	−	0.0804301i
$743$	−4.58665e10	−	1.31079e11i	−0.150501	−	0.430108i	0.843807	−	0.536646i	$-0.180309\pi$
$743$	−4.58665e10	−	1.31079e11i	−0.150501	−	0.430108i	−0.994309	+	0.106538i	$0.966023\pi$
$744$	−4.08694e10	−	6.50432e10i	−0.133385	−	0.212281i
$745$	−1.63989e11	+	7.89730e10i	−0.532341	+	0.256362i
$746$	2.78925e10	−	7.97121e10i	0.0900599	−	0.257376i
$747$	−1.04931e12	+	2.39498e11i	−3.36993	+	0.769165i
$748$	−8.91237e9	+	1.11758e10i	−0.0284699	+	0.0357002i
$749$	4.20915e10	+	5.27811e10i	0.133742	+	0.167707i
$750$	1.22712e11	−	5.37637e11i	0.387831	−	1.69920i
$751$	2.05962e11	−	3.27787e11i	0.647482	−	1.03046i	−0.348181	−	0.937427i	$-0.613201\pi$
$751$	2.05962e11	−	3.27787e11i	0.647482	−	1.03046i	0.995663	−	0.0930342i	$-0.0296566\pi$
$752$	−5.38010e9	+	4.77498e10i	−0.0168236	+	0.149314i
$753$			4.82816e11i			1.50176i
$754$	−1.05542e11	−	3.43943e11i	−0.326544	−	1.06415i
$755$	2.77773e11			0.854874
$756$	1.54133e11	+	1.73666e10i	0.471854	+	0.0531652i
$757$	2.14878e11	+	1.35017e11i	0.654347	+	0.411153i	0.817883	−	0.575384i	$-0.195147\pi$
$757$	2.14878e11	+	1.35017e11i	0.654347	+	0.411153i	−0.163537	+	0.986537i	$0.552290\pi$
$758$	−2.29759e11	−	5.24410e10i	−0.695978	−	0.158852i
$759$	6.94237e10	−	5.53635e10i	0.209190	−	0.166823i
$760$	4.04029e11	+	3.22203e11i	1.21104	+	0.965773i
$761$	−1.04971e11	−	4.59909e11i	−0.312991	−	1.37130i	−0.849580	−	0.527459i	$-0.823145\pi$
$761$	−1.04971e11	−	4.59909e11i	−0.312991	−	1.37130i	0.536589	−	0.843843i	$-0.319712\pi$
$762$	−4.56377e11	−	1.59693e11i	−1.35364	−	0.473660i
$763$	−1.33133e11	−	2.76453e11i	−0.392814	−	0.815686i
$764$	−3.92217e10	+	2.46446e10i	−0.115121	+	0.0723351i
$765$	−7.70752e11	+	2.69698e11i	−2.25045	+	0.787465i
$766$	1.00885e11	+	1.00885e11i	0.293029	+	0.293029i
$767$	−2.89687e11	+	6.01541e11i	−0.837043	+	1.73814i
$768$	−4.04983e10	−	3.59433e11i	−0.116411	−	1.03317i
$769$	−4.35431e9	+	4.90613e8i	−0.0124513	+	0.00140292i	−0.118188	−	0.992991i	$-0.537709\pi$
$769$	−4.35431e9	+	4.90613e8i	−0.0124513	+	0.00140292i	0.105737	+	0.994394i	$0.466280\pi$
$770$	−5.67988e10	−	2.73529e10i	−0.161576	−	0.0778108i
$771$	8.84705e10	−	8.84705e10i	0.250369	−	0.250369i
$772$	3.99226e10	+	1.14092e11i	0.112396	+	0.321209i
$773$	7.41783e10	+	1.18054e11i	0.207759	+	0.330646i	0.934307	−	0.356469i	$-0.116020\pi$
$773$	7.41783e10	+	1.18054e11i	0.207759	+	0.330646i	−0.726548	+	0.687115i	$0.758877\pi$
$774$	8.65924e11	−	4.17007e11i	2.41277	−	1.16193i
$775$	−1.24262e9	+	3.55121e9i	−0.00344455	+	0.00984396i
$776$	−3.28582e10	+	7.49966e9i	−0.0906142	+	0.0206821i
$777$	5.87821e11	−	7.37104e11i	1.61273	−	2.02230i
$778$	5.29469e10	+	6.63933e10i	0.144518	+	0.181220i
$779$	−7.02183e10	+	3.07647e11i	−0.190678	+	0.835415i
$780$	8.43031e10	−	1.34168e11i	0.227754	−	0.362468i
$781$	1.28031e10	−	1.13631e11i	0.0344122	−	0.305416i
$782$		−	2.01732e11i		−	0.539446i
$783$	7.15446e11	+	7.73331e11i	1.90340	+	2.05740i
$784$	−6.65853e10			−0.176244
$785$	−3.91430e11	−	4.41036e10i	−1.03080	−	0.116144i
$786$	4.09575e11	+	2.57353e11i	1.07311	+	0.674277i
$787$	2.39263e11	+	5.46103e10i	0.623702	+	0.142356i	0.522681	−	0.852528i	$-0.324932\pi$
$787$	2.39263e11	+	5.46103e10i	0.623702	+	0.142356i	0.101021	+	0.994884i	$0.467789\pi$
$788$	−7.86917e10	+	6.27546e10i	−0.204091	+	0.162757i
$789$	−9.08503e11	−	7.24507e11i	−2.34433	−	1.86954i
$790$	9.53958e10	+	4.17956e11i	0.244918	+	1.07306i
$791$	−9.43205e10	−	3.30042e10i	−0.240935	−	0.0843069i
$792$	−1.08542e11	−	2.25389e11i	−0.275864	−	0.572838i
$793$	6.50626e11	−	4.08816e11i	1.64528	−	1.03380i
$794$	1.99538e11	−	6.98215e10i	0.502047	−	0.175674i
$795$	7.29324e10	+	7.29324e10i	0.182579	+	0.182579i
$796$	7.24368e9	−	1.50416e10i	0.0180429	−	0.0374665i
$797$	−1.48209e10	−	1.31539e11i	−0.0367318	−	0.326003i	−0.998618	−	0.0525538i	$-0.983264\pi$
$797$	−1.48209e10	−	1.31539e11i	−0.0367318	−	0.326003i	0.961886	−	0.273450i	$-0.0881647\pi$
$798$	−8.97625e11	+	1.01138e11i	−2.21352	+	0.249404i
$799$	−7.14352e10	−	3.44014e10i	−0.175277	−	0.0844089i
$800$	−9.17963e9	+	9.17963e9i	−0.0224112	+	0.0224112i
$801$	1.18745e11	+	3.39355e11i	0.288461	+	0.824373i
$802$	2.53864e11	+	4.04023e11i	0.613627	+	0.976582i
$803$	−1.30352e11	+	6.27741e10i	−0.313512	+	0.150980i
$804$	−3.02487e10	+	8.64458e10i	−0.0723906	+	0.206881i
$805$	−2.07352e11	+	4.73268e10i	−0.493771	+	0.112700i
$806$	3.66327e10	−	4.59360e10i	0.0868019	−	0.108846i
$807$	−5.09143e11	−	6.38445e11i	−1.20045	−	1.50532i
$808$	1.08725e11	−	4.76355e11i	0.255084	−	1.11760i
$809$	−1.16818e11	+	1.85914e11i	−0.272719	+	0.434029i	−0.954801	−	0.297246i	$-0.903932\pi$
$809$	−1.16818e11	+	1.85914e11i	−0.272719	+	0.434029i	0.682082	+	0.731276i	$0.261075\pi$
$810$	1.13749e11	−	1.00955e12i	0.264246	−	2.34525i
$811$			7.26425e11i			1.67922i	0.543190	+	0.839610i	$0.317216\pi$
$811$			7.26425e11i			1.67922i	−0.543190	+	0.839610i	$0.682784\pi$
$812$	−5.57547e10	−	4.81228e10i	−0.128250	−	0.110695i
$813$	−5.05886e11			−1.15795
$814$	−1.46565e11	−	1.65139e10i	−0.333836	−	0.0376143i
$815$	6.06347e11	+	3.80993e11i	1.37433	+	0.863548i
$816$	−6.20377e11	−	1.41597e11i	−1.39925	−	0.319369i
$817$	6.27416e11	−	5.00348e11i	1.40821	−	1.12301i
$818$	1.04071e11	+	8.29942e10i	0.232444	+	0.185368i
$819$	2.72156e11	+	1.19239e12i	0.604899	+	2.65023i
$820$	4.47426e10	+	1.56561e10i	0.0989613	+	0.0346281i
$821$	8.31049e10	+	1.72569e11i	0.182917	+	0.379831i	0.972184	−	0.234219i	$-0.0752534\pi$
$821$	8.31049e10	+	1.72569e11i	0.182917	+	0.379831i	−0.789267	+	0.614050i	$0.789539\pi$
$822$	−1.30847e11	+	8.22165e10i	−0.286600	+	0.180083i
$823$	3.48699e11	−	1.22015e11i	0.760067	−	0.265959i	0.0777080	−	0.996976i	$-0.475240\pi$
$823$	3.48699e11	−	1.22015e11i	0.760067	−	0.265959i	0.682359	+	0.731017i	$0.260954\pi$
$824$	9.45199e10	+	9.45199e10i	0.205029	+	0.205029i
$825$	−7.44383e9	+	1.54573e10i	−0.0160687	+	0.0333670i
$826$	−6.40158e10	−	5.68156e11i	−0.137520	−	1.22053i
$827$	−3.72402e11	+	4.19596e10i	−0.796140	+	0.0897034i	−0.500658	−	0.865645i	$-0.666909\pi$
$827$	−3.72402e11	+	4.19596e10i	−0.796140	+	0.0897034i	−0.295482	+	0.955348i	$0.595480\pi$
$828$	−1.22979e11	−	5.92233e10i	−0.261642	−	0.126000i
$829$	2.71858e11	−	2.71858e11i	0.575605	−	0.575605i	−0.358084	−	0.933689i	$-0.616570\pi$
$829$	2.71858e11	−	2.71858e11i	0.575605	−	0.575605i	0.933689	+	0.358084i	$0.116570\pi$
$830$	−1.86514e11	−	5.33027e11i	−0.393006	−	1.12315i
$831$	1.88059e11	+	2.99294e11i	0.394358	+	0.627616i
$832$	5.94462e11	−	2.86278e11i	1.24060	−	0.597440i
$833$	3.62870e10	−	1.03702e11i	0.0753652	−	0.215381i
$834$	2.72752e11	−	6.22538e10i	0.563772	−	0.128677i
$835$	−5.19197e11	+	6.51053e11i	−1.06804	+	1.33928i
$836$	−2.10627e10	−	2.64118e10i	−0.0431210	−	0.0540721i
$837$	−3.82847e10	+	1.67736e11i	−0.0780052	+	0.341763i
$838$	2.77750e10	−	4.42037e10i	0.0563221	−	0.0896361i
$839$	9.26092e10	−	8.21929e11i	0.186899	−	1.65877i	−0.453893	−	0.891056i	$-0.649965\pi$
$839$	9.26092e10	−	8.21929e11i	0.186899	−	1.65877i	0.640791	−	0.767715i	$-0.278606\pi$
$840$			8.39010e11i			1.68520i
$841$	−7.31118e10	−	4.94875e11i	−0.146151	−	0.989262i
$842$	−4.74133e11			−0.943304
$843$	1.71162e12	+	1.92853e11i	3.38919	+	0.381870i
$844$	−4.70968e10	−	2.95929e10i	−0.0928157	−	0.0583200i
$845$	2.54706e11	+	5.81349e10i	0.499588	+	0.114028i
$846$	1.75454e11	−	1.39920e11i	0.342517	−	0.273148i
$847$	−3.33418e11	−	2.65892e11i	−0.647821	−	0.516620i
$848$	1.27729e10	+	5.59618e10i	0.0247006	+	0.108220i
$849$	−1.25832e12	−	4.40307e11i	−2.42193	−	0.847470i
$850$	1.69113e10	+	3.51167e10i	0.0323968	+	0.0672726i
$851$	−4.21327e11	+	2.64737e11i	−0.803344	+	0.504774i
$852$	−2.32318e11	+	8.12914e10i	−0.440883	+	0.154272i
$853$	−6.77094e11	−	6.77094e11i	−1.27895	−	1.27895i	−0.941257	−	0.337691i	$-0.890354\pi$
$853$	−6.77094e11	−	6.77094e11i	−1.27895	−	1.27895i	−0.337691	−	0.941257i	$-0.609646\pi$
$854$	−2.85506e11	+	5.92859e11i	−0.536764	+	1.11460i
$855$	−2.16072e11	−	1.91769e12i	−0.404327	−	3.58851i
$856$	−1.39675e11	+	1.57376e10i	−0.260150	+	0.0293119i
$857$	7.58033e11	+	3.65049e11i	1.40529	+	0.676750i	0.974226	−	0.225573i	$-0.0724255\pi$
$857$	7.58033e11	+	3.65049e11i	1.40529	+	0.676750i	0.431060	+	0.902323i	$0.358140\pi$
$858$	1.89448e11	−	1.89448e11i	0.349575	−	0.349575i
$859$	−6.72169e10	−	1.92095e11i	−0.123454	−	0.352812i	0.865525	−	0.500865i	$-0.166985\pi$
$859$	−6.72169e10	−	1.92095e11i	−0.123454	−	0.352812i	−0.988979	+	0.148054i	$0.952699\pi$
$860$	−6.41363e10	−	1.02072e11i	−0.117249	−	0.186601i
$861$	−4.61591e11	+	2.22290e11i	−0.839932	+	0.404490i
$862$	2.77086e10	−	7.91867e10i	0.0501864	−	0.143424i
$863$	9.76669e10	−	2.22918e10i	0.176078	−	0.0401886i	−0.133573	−	0.991039i	$-0.542645\pi$
$863$	9.76669e10	−	2.22918e10i	0.176078	−	0.0401886i	0.309651	+	0.950850i	$0.399788\pi$
$864$	−3.70140e11	+	4.64141e11i	−0.664218	+	0.832903i
$865$	2.77443e11	+	3.47902e11i	0.495575	+	0.621431i
$866$	−1.02856e11	+	4.50643e11i	−0.182877	+	0.801236i
$867$	−3.66783e9	+	5.83732e9i	−0.00649132	+	0.0103309i
$868$	1.34669e9	−	1.19522e10i	0.00237240	−	0.0210557i
$869$		−	1.73282e11i		−	0.303861i
$870$	−6.02200e11	+	6.97705e11i	−1.05115	+	1.21785i
$871$	−4.33127e11			−0.752563
$872$	6.34841e11	+	7.15294e10i	1.09799	+	0.123714i
$873$	1.06569e11	+	6.69616e10i	0.183473	+	0.115284i
$874$	4.64803e11	+	1.06088e11i	0.796568	+	0.181811i
$875$	4.17415e11	−	3.32877e11i	0.712091	−	0.567873i
$876$	2.43471e11	+	1.94162e11i	0.413458	+	0.329722i
$877$	9.91589e10	+	4.34444e11i	0.167623	+	0.734404i	0.986943	+	0.161068i	$0.0514939\pi$
$877$	9.91589e10	+	4.34444e11i	0.167623	+	0.734404i	−0.819320	+	0.573336i	$0.805649\pi$
$878$	−1.90280e11	−	6.65819e10i	−0.320196	−	0.112041i
$879$	2.77403e10	+	5.76034e10i	0.0464682	+	0.0964923i
$880$	8.88672e10	−	5.58389e10i	0.148187	−	0.0931122i
$881$	1.33068e11	−	4.65624e10i	0.220886	−	0.0772915i	−0.217567	−	0.976045i	$-0.569812\pi$
$881$	1.33068e11	−	4.65624e10i	0.220886	−	0.0772915i	0.438454	+	0.898754i	$0.355526\pi$
$882$	2.19889e11	+	2.19889e11i	0.363353	+	0.363353i
$883$	−3.07249e11	+	6.38009e11i	−0.505414	+	1.04950i	0.479673	+	0.877447i	$0.340755\pi$
$883$	−3.07249e11	+	6.38009e11i	−0.505414	+	1.04950i	−0.985087	+	0.172056i	$0.944959\pi$
$884$	1.62915e10	+	1.44591e11i	0.0266780	+	0.236773i
$885$	1.69963e12	−	1.91502e11i	2.77064	−	0.312177i
$886$	−6.30203e11	−	3.03490e11i	−1.02269	−	0.492503i
$887$	−3.21637e11	+	3.21637e11i	−0.519602	+	0.519602i	−0.917451	−	0.397849i	$-0.869757\pi$
$887$	−3.21637e11	+	3.21637e11i	−0.519602	+	0.519602i	0.397849	+	0.917451i	$0.369757\pi$
$888$	6.48320e11	+	1.85279e12i	1.04265	+	2.97972i
$889$	−2.49047e11	−	3.96356e11i	−0.398726	−	0.634568i
$890$	−1.69959e11	+	8.18481e10i	−0.270885	+	0.130451i
$891$	−1.35627e11	+	3.87599e11i	−0.215196	+	0.614995i
$892$	1.66626e11	−	3.80313e10i	0.263198	−	0.0600733i
$893$	1.16830e11	−	1.46500e11i	0.183716	−	0.230373i
$894$	4.13011e11	+	5.17900e11i	0.646565	+	0.810766i
$895$	−2.73843e10	+	1.19979e11i	−0.0426786	+	0.186987i
$896$	−1.86164e11	+	2.96278e11i	−0.288844	+	0.459693i
$897$	1.01203e11	−	8.98199e11i	0.156323	−	1.38740i
$898$			7.76541e11i			1.19415i
$899$	5.99679e10	−	5.54792e10i	0.0918078	−	0.0849359i
$900$	2.63723e10			0.0401956
$901$	−9.41178e10	−	1.06045e10i	−0.142815	−	0.0160913i
$902$	6.78647e10	+	4.26422e10i	0.102522	+	0.0644190i
$903$	1.27023e12	+	2.89922e11i	1.91043	+	0.436044i
$904$	1.62665e11	−	1.29721e11i	0.243568	−	0.194239i
$905$	1.03397e11	+	8.24560e10i	0.154139	+	0.122922i
$906$	−2.24951e11	−	9.85575e11i	−0.333868	−	1.46277i
$907$	−4.31156e10	−	1.50868e10i	−0.0637097	−	0.0222930i	0.298236	−	0.954492i	$-0.403602\pi$
$907$	−4.31156e10	−	1.50868e10i	−0.0637097	−	0.0222930i	−0.361946	+	0.932199i	$0.617887\pi$
$908$	1.91690e10	+	3.98047e10i	0.0282004	+	0.0585587i
$909$	−1.54496e12	+	9.70763e11i	−2.26288	+	1.42186i
$910$	−6.05711e11	+	2.11947e11i	−0.883283	+	0.309074i
$911$	−5.39079e11	−	5.39079e11i	−0.782670	−	0.782670i	0.197611	−	0.980281i	$-0.436682\pi$
$911$	−5.39079e11	−	5.39079e11i	−0.782670	−	0.782670i	−0.980281	+	0.197611i	$0.936682\pi$
$912$	6.52496e11	−	1.35492e12i	0.943188	−	1.95855i
$913$	2.55568e10	+	2.26823e11i	0.0367810	+	0.326440i
$914$	−8.03478e11	+	9.05302e10i	−1.15130	+	0.129721i
$915$	−1.77352e12	−	8.54084e11i	−2.53019	−	1.21847i
$916$	3.76971e10	−	3.76971e10i	0.0535459	−	0.0535459i
$917$	1.54671e11	+	4.42025e11i	0.218742	+	0.625129i
$918$	9.48283e11	+	1.50918e12i	1.33526	+	2.12506i
$919$	4.36900e11	−	2.10400e11i	0.612520	−	0.294974i	−0.101787	−	0.994806i	$-0.532456\pi$
$919$	4.36900e11	−	2.10400e11i	0.612520	−	0.294974i	0.714307	+	0.699832i	$0.246742\pi$
$920$	1.46255e11	−	4.17973e11i	0.204155	−	0.583440i
$921$	−1.06658e12	+	2.43439e11i	−1.48236	+	0.338339i
$922$	1.23148e10	−	1.54422e10i	0.0170413	−	0.0213691i
$923$	−7.25743e11	−	9.10053e11i	−0.999945	−	1.25389i
$924$	1.22046e10	−	5.34718e10i	0.0167431	−	0.0733563i
$925$	5.11499e10	−	8.14045e10i	0.0698679	−	0.111194i
$926$	1.86926e9	−	1.65901e10i	0.00254229	−	0.0225635i
$927$		−	4.99178e11i		−	0.675985i
$928$	2.69486e11	−	8.26945e10i	0.363367	−	0.111502i
$929$	4.75999e11			0.639063			0.319531	−	0.947576i	$-0.396475\pi$
$929$	4.75999e11			0.639063			0.319531	+	0.947576i	$0.396475\pi$
$930$	−1.49568e11	−	1.68522e10i	−0.199943	−	0.0225282i
$931$	2.19853e11	+	1.38143e11i	0.292641	+	0.183878i
$932$	7.66702e10	+	1.74995e10i	0.101616	+	0.0231932i
$933$	1.64762e12	−	1.31393e12i	2.17435	−	1.73399i
$934$	5.45926e11	+	4.35362e11i	0.717376	+	0.572088i
$935$	3.85356e10	+	1.68835e11i	0.0504215	+	0.220911i
$936$	−2.40358e12	−	8.41049e11i	−3.13152	−	1.09577i
$937$	−1.37201e11	−	2.84900e11i	−0.177991	−	0.369602i	0.792817	−	0.609459i	$-0.208613\pi$
$937$	−1.37201e11	−	2.84900e11i	−0.177991	−	0.369602i	−0.970808	+	0.239858i	$0.922899\pi$
$938$	3.14057e11	−	1.97335e11i	0.405693	−	0.254914i
$939$	9.72468e11	−	3.40281e11i	1.25087	−	0.437699i
$940$	−1.99036e10	−	1.99036e10i	−0.0254930	−	0.0254930i
$941$	−5.80018e11	+	1.20442e12i	−0.739747	+	1.53610i	0.101130	+	0.994873i	$0.467754\pi$
$941$	−5.80018e11	+	1.20442e12i	−0.739747	+	1.53610i	−0.840877	+	0.541226i	$0.817960\pi$
$942$	1.60510e11	+	1.42456e12i	0.203844	+	1.80917i
$943$	2.68701e11	−	3.02754e10i	0.339800	−	0.0382862i
$944$	8.57605e11	+	4.13001e11i	1.07994	+	0.520071i
$945$	1.32876e12	−	1.32876e12i	1.66617	−	1.66617i
$946$	−6.73203e10	−	1.92390e11i	−0.0840585	−	0.240225i
$947$	−2.63678e11	−	4.19641e11i	−0.327849	−	0.521768i	0.641607	−	0.767033i	$-0.278268\pi$
$947$	−2.63678e11	−	4.19641e11i	−0.327849	−	0.521768i	−0.969456	+	0.245265i	$0.921125\pi$
$948$	−3.36040e11	+	1.61828e11i	−0.416062	+	0.200365i
$949$	−4.86414e11	+	1.39009e12i	−0.599710	+	1.71387i
$950$	−8.98044e10	+	2.04973e10i	−0.110256	+	0.0251653i
$951$	−8.30499e11	+	1.04141e12i	−1.01535	+	1.27321i
$952$	−4.80366e11	−	6.02360e11i	−0.584823	−	0.733345i
$953$	1.60835e11	−	7.04664e11i	0.194989	−	0.854301i	−0.778877	−	0.627176i	$-0.784211\pi$
$953$	1.60835e11	−	7.04664e11i	0.194989	−	0.854301i	0.973866	−	0.227124i	$-0.0729323\pi$
$954$	1.42626e11	−	2.26987e11i	0.172188	−	0.274036i
$955$	−6.28337e10	+	5.57664e11i	−0.0755403	+	0.670439i
$956$		−	9.64669e10i		−	0.115491i
$957$	3.00060e11	−	2.20777e11i	0.357734	−	0.263213i
$958$	3.32911e11			0.395244
$959$	−1.48669e11	−	1.67509e10i	−0.175770	−	0.0198045i
$960$	−1.43118e12	−	8.99269e11i	−1.68504	−	1.05878i
$961$	−8.18500e11	−	1.86817e11i	−0.959677	−	0.219040i
$962$	−1.17382e12	+	9.36090e11i	−1.37057	+	1.09299i
$963$	4.10383e11	+	3.27269e11i	0.477182	+	0.380540i
$964$	−4.01648e10	−	1.75973e11i	−0.0465090	−	0.203769i
$965$	1.38224e12	+	4.83667e11i	1.59395	+	0.557747i
$966$	3.35844e11	+	6.97386e11i	0.385681	+	0.800875i
$967$	−6.63950e11	+	4.17187e11i	−0.759328	+	0.477117i	−0.855214	−	0.518275i	$-0.826574\pi$
$967$	−6.63950e11	+	4.17187e11i	−0.759328	+	0.477117i	0.0958862	+	0.995392i	$0.469432\pi$
$968$	8.38082e11	−	2.93258e11i	0.954520	−	0.334001i
$969$	1.75461e12	+	1.75461e12i	1.99015	+	1.99015i
$970$	−2.86524e10	+	5.94974e10i	−0.0323649	+	0.0672064i
$971$	−5.12037e10	−	4.54446e11i	−0.0576003	−	0.511217i	−0.989075	−	0.147411i	$-0.952906\pi$
$971$	−5.12037e10	−	4.54446e11i	−0.0576003	−	0.511217i	0.931475	−	0.363805i	$-0.118523\pi$
$972$	3.98667e11	−	4.49190e10i	0.446627	−	0.0503228i
$973$	2.44030e11	+	1.17518e11i	0.272264	+	0.131116i
$974$	−4.92675e11	+	4.92675e11i	−0.547425	+	0.547425i
$975$	5.76796e10	+	1.64839e11i	0.0638269	+	0.182407i
$976$	−5.82840e11	−	9.27584e11i	−0.642318	−	1.02224i
$977$	1.22595e12	−	5.90387e11i	1.34554	−	0.647976i	0.384173	−	0.923261i	$-0.374487\pi$
$977$	1.22595e12	−	5.90387e11i	1.34554	−	0.647976i	0.961363	+	0.275285i	$0.0887722\pi$
$978$	8.60770e11	−	2.45994e12i	0.940875	−	2.68887i
$979$	7.43367e10	−	1.69669e10i	0.0809231	−	0.0184702i
$980$	2.43189e10	−	3.04949e10i	0.0263657	−	0.0330615i
$981$	−1.48748e12	−	1.86524e12i	−1.60611	−	2.01400i
$982$	−3.06442e11	+	1.34261e12i	−0.329535	+	1.44379i
$983$	−2.47721e11	+	3.94245e11i	−0.265307	+	0.422233i	−0.952636	−	0.304113i	$-0.901640\pi$
$983$	−2.47721e11	+	3.94245e11i	−0.265307	+	0.422233i	0.687329	+	0.726346i	$0.258783\pi$
$984$	1.19432e11	−	1.05999e12i	0.127391	−	1.13063i
$985$			1.21939e12i			1.29538i
$986$	3.28813e10	−	8.45694e11i	0.0347890	−	0.894758i
$987$	3.04222e11			0.320570
$988$	−3.41714e11	−	3.85020e10i	−0.358621	−	0.0404069i
$989$	−5.82256e11	−	3.65856e11i	−0.608596	−	0.382406i
$990$	−4.77873e11	−	1.09071e11i	−0.497475	−	0.113545i
$991$	−1.05817e12	+	8.43863e11i	−1.09714	+	0.874938i	−0.992821	−	0.119606i	$-0.961837\pi$
$991$	−1.05817e12	+	8.43863e11i	−1.09714	+	0.874938i	−0.104316	+	0.994544i	$0.533265\pi$
$992$	3.59917e10	+	2.87025e10i	0.0371669	+	0.0296396i
$993$	−4.42177e11	−	1.93730e12i	−0.454778	−	1.99251i
$994$	9.40857e11	+	3.29220e11i	0.963780	+	0.337241i
$995$	−8.77579e10	−	1.82231e11i	−0.0895353	−	0.185922i
$996$	4.16003e11	−	2.61392e11i	0.422726	−	0.265616i
$997$	−1.28769e12	+	4.50582e11i	−1.30326	+	0.456030i	−0.890572	−	0.454842i	$-0.849696\pi$
$997$	−1.28769e12	+	4.50582e11i	−1.30326	+	0.456030i	−0.412688	+	0.910873i	$0.635410\pi$
$998$	−6.12817e10	−	6.12817e10i	−0.0617744	−	0.0617744i
$999$	1.90755e12	−	3.96107e12i	1.91520	−	3.97695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.2.13	✓	228
29.15	odd	28	inner	29.9.f.a.15.13	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.13	✓	228	1.1	even	1	trivial
29.9.f.a.15.13	yes	228	29.15	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(14.2835 + 1.60937i) q^{2} +(128.283 + 80.6053i) q^{3} +(-48.1524 - 10.9905i) q^{4} +(-467.828 + 373.081i) q^{5} +(1702.60 + 1357.78i) q^{6} +(469.147 + 2055.47i) q^{7} +(-4143.33 - 1449.81i) q^{8} +(7112.49 + 14769.2i) q^{9} +O(q^{10})\)	\(q+(14.2835 + 1.60937i) q^{2} +(128.283 + 80.6053i) q^{3} +(-48.1524 - 10.9905i) q^{4} +(-467.828 + 373.081i) q^{5} +(1702.60 + 1357.78i) q^{6} +(469.147 + 2055.47i) q^{7} +(-4143.33 - 1449.81i) q^{8} +(7112.49 + 14769.2i) q^{9} +(-7282.66 + 4576.00i) q^{10} +(3281.42 - 1148.22i) q^{11} +(-5291.23 - 5291.23i) q^{12} +(15354.5 - 31883.9i) q^{13} +(3393.07 + 30114.3i) q^{14} +(-90086.4 + 10150.3i) q^{15} +(-45456.1 - 21890.5i) q^{16} +(58865.3 - 58865.3i) q^{17} +(77822.3 + 222403. i) q^{18} +(104673. + 166586. i) q^{19} +(26627.4 - 12823.1i) q^{20} +(-105498. + 301496. i) q^{21} +(48718.1 - 11119.6i) q^{22} +(105113. - 131807. i) q^{23} +(-414654. - 519959. i) q^{24} +(-7248.12 + 31756.1i) q^{25} +(270629. - 430703. i) q^{26} +(-166775. + 1.48017e6i) q^{27} -104132. i q^{28} +(462133. - 535424. i) q^{29} -1.30309e6 q^{30} +(114780. + 12932.5i) q^{31} +(337464. + 212043. i) q^{32} +(513501. + 117203. i) q^{33} +(935540. - 746069. i) q^{34} +(-986334. - 786575. i) q^{35} +(-180163. - 789344. i) q^{36} +(-2.78593e6 - 974840. i) q^{37} +(1.22700e6 + 2.54789e6i) q^{38} +(4.53972e6 - 2.85249e6i) q^{39} +(2.47926e6 - 867531. i) q^{40} +(1.13415e6 + 1.13415e6i) q^{41} +(-1.99210e6 + 4.13664e6i) q^{42} +(-456696. - 4.05329e6i) q^{43} +(-170628. + 19225.1i) q^{44} +(-8.83754e6 - 4.25593e6i) q^{45} +(1.71350e6 - 1.71350e6i) q^{46} +(-314564. - 898972. i) q^{47} +(-4.06674e6 - 6.47218e6i) q^{48} +(1.18906e6 - 572623. i) q^{49} +(-154636. + 441924. i) q^{50} +(1.22962e7 - 2.80654e6i) q^{51} +(-1.08977e6 + 1.36653e6i) q^{52} +(-709359. - 889508. i) q^{53} +(-4.76427e6 + 2.08736e7i) q^{54} +(-1.10676e6 + 1.76140e6i) q^{55} +(1.03621e6 - 9.19664e6i) q^{56} +2.98072e7i q^{57} +(7.46259e6 - 6.90400e6i) q^{58} -1.88666e7 q^{59} +(4.44944e6 + 501331. i) q^{60} +(1.83853e7 + 1.15522e7i) q^{61} +(1.61864e6 + 369445. i) q^{62} +(-2.70209e7 + 2.15484e7i) q^{63} +(1.45769e7 + 1.16247e7i) q^{64} +(4.71200e6 + 2.06446e7i) q^{65} +(7.14599e6 + 2.50049e6i) q^{66} +(-5.31041e6 - 1.10272e7i) q^{67} +(-3.48147e6 + 2.18755e6i) q^{68} +(2.41085e7 - 8.43591e6i) q^{69} +(-1.28224e7 - 1.28224e7i) q^{70} +(1.42714e7 - 2.96348e7i) q^{71} +(-8.05674e6 - 7.15055e7i) q^{72} +(-4.13546e7 + 4.65955e6i) q^{73} +(-3.82241e7 - 1.84077e7i) q^{74} +(-3.48951e6 + 3.48951e6i) q^{75} +(-3.20939e6 - 9.17191e6i) q^{76} +(3.89959e6 + 6.20616e6i) q^{77} +(6.94339e7 - 3.34376e7i) q^{78} +(1.64623e7 - 4.70466e7i) q^{79} +(2.94326e7 - 6.71780e6i) q^{80} +(-7.36461e7 + 9.23493e7i) q^{81} +(1.43743e7 + 1.80249e7i) q^{82} +(-1.46101e7 + 6.40111e7i) q^{83} +(8.39357e6 - 1.33583e7i) q^{84} +(-5.57735e6 + 4.95004e7i) q^{85} -5.86302e7i q^{86} +(1.02442e8 - 3.14352e7i) q^{87} -1.52607e7 q^{88} +(2.17945e7 + 2.45566e6i) q^{89} +(-1.19382e8 - 7.50126e7i) q^{90} +(7.27397e7 + 1.66024e7i) q^{91} +(-6.51005e6 + 5.19159e6i) q^{92} +(1.36818e7 + 1.09109e7i) q^{93} +(-3.04631e6 - 1.33467e7i) q^{94} +(-1.11119e8 - 3.88821e7i) q^{95} +(2.61990e7 + 5.44028e7i) q^{96} +(6.50103e6 - 4.08487e6i) q^{97} +(1.79056e7 - 6.26543e6i) q^{98} +(4.02974e7 + 4.02974e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

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