LMFDB - Embedded newform 54.9.f.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	54.5
Dual form			54.9.f.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.27231 - 8.66680i) q^{2} +(-71.9819 + 37.1430i) q^{3} +(-22.2270 + 126.055i) q^{4} +(242.781 + 667.036i) q^{5} +(845.386 + 353.737i) q^{6} +(702.244 + 3982.62i) q^{7} +(1254.14 - 724.077i) q^{8} +(3801.79 - 5347.25i) q^{9} +O(q^{10})$	\(q+(-7.27231 - 8.66680i) q^{2} +(-71.9819 + 37.1430i) q^{3} +(-22.2270 + 126.055i) q^{4} +(242.781 + 667.036i) q^{5} +(845.386 + 353.737i) q^{6} +(702.244 + 3982.62i) q^{7} +(1254.14 - 724.077i) q^{8} +(3801.79 - 5347.25i) q^{9} +(4015.49 - 6955.03i) q^{10} +(-675.075 + 1854.75i) q^{11} +(-3082.14 - 9899.28i) q^{12} +(5274.86 + 4426.14i) q^{13} +(29409.7 - 35049.1i) q^{14} +(-42251.6 - 38996.9i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(85996.5 + 49650.1i) q^{17} +(-73991.4 + 5937.54i) q^{18} +(79817.2 + 138247. i) q^{19} +(-89479.7 + 15777.7i) q^{20} +(-198476. - 260593. i) q^{21} +(20984.1 - 7637.60i) q^{22} +(-383459. - 67614.1i) q^{23} +(-63380.9 + 98703.0i) q^{24} +(-86757.9 + 72798.6i) q^{25} -77904.4i q^{26} +(-75046.7 + 526116. i) q^{27} -517640. q^{28} +(584464. + 696538. i) q^{29} +(-30711.5 + 649784. i) q^{30} +(70920.0 - 402207. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-20298.0 - 158583. i) q^{33} +(-195086. - 1.10639e6i) q^{34} +(-2.48606e6 + 1.43533e6i) q^{35} +(589548. + 598089. i) q^{36} +(-1.78613e6 + 3.09367e6i) q^{37} +(617708. - 1.69714e6i) q^{38} +(-544095. - 122677. i) q^{39} +(787467. + 660763. i) q^{40} +(1.55285e6 - 1.85062e6i) q^{41} +(-815135. + 3.61526e6i) q^{42} +(-5.76395e6 - 2.09791e6i) q^{43} +(-218797. - 126322. i) q^{44} +(4.48981e6 + 1.23772e6i) q^{45} +(2.20263e6 + 3.81507e6i) q^{46} +(3.95927e6 - 698125. i) q^{47} +(1.31636e6 - 168489. i) q^{48} +(-9.95099e6 + 3.62187e6i) q^{49} +(1.26186e6 + 222500. i) q^{50} +(-8.03435e6 - 379737. i) q^{51} +(-675183. + 566545. i) q^{52} -9.23813e6i q^{53} +(5.10550e6 - 3.17566e6i) q^{54} -1.40108e6 q^{55} +(3.76444e6 + 4.48628e6i) q^{56} +(-1.08803e7 - 6.98666e6i) q^{57} +(1.78635e6 - 1.01309e7i) q^{58} +(2.34478e6 + 6.44224e6i) q^{59} +(5.85489e6 - 4.45926e6i) q^{60} +(-4.42096e6 - 2.50725e7i) q^{61} +(-4.00160e6 + 2.31033e6i) q^{62} +(2.39659e7 + 1.13860e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-1.67175e6 + 4.59311e6i) q^{65} +(-1.22679e6 + 1.32918e6i) q^{66} +(-3.41561e6 - 2.86604e6i) q^{67} +(-8.17010e6 + 9.73675e6i) q^{68} +(3.01135e7 - 9.37583e6i) q^{69} +(3.05191e7 + 1.11080e7i) q^{70} +(1.78601e7 + 1.03116e7i) q^{71} +(896145. - 9.45899e6i) q^{72} +(-4.93456e6 - 8.54690e6i) q^{73} +(3.98015e7 - 7.01808e6i) q^{74} +(3.54104e6 - 8.46263e6i) q^{75} +(-1.92009e7 + 6.98857e6i) q^{76} +(-7.86085e6 - 1.38608e6i) q^{77} +(2.89361e6 + 5.60771e6i) q^{78} +(-2.85868e6 + 2.39872e6i) q^{79} -1.16301e7i q^{80} +(-1.41395e7 - 4.06583e7i) q^{81} -2.73318e7 q^{82} +(2.82890e6 + 3.37135e6i) q^{83} +(3.72607e7 - 1.92267e7i) q^{84} +(-1.22401e7 + 6.94168e7i) q^{85} +(2.37351e7 + 6.52116e7i) q^{86} +(-6.79424e7 - 2.84293e7i) q^{87} +(496347. + 2.81492e6i) q^{88} +(5.18273e7 - 2.99225e7i) q^{89} +(-2.19243e7 - 4.79134e7i) q^{90} +(-1.39234e7 + 2.41160e7i) q^{91} +(1.70463e7 - 4.68342e7i) q^{92} +(9.83425e6 + 3.15858e7i) q^{93} +(-3.48435e7 - 2.92372e7i) q^{94} +(-7.28379e7 + 8.68048e7i) q^{95} +(-1.10333e7 - 1.01834e7i) q^{96} +(-2.82465e7 - 1.02809e7i) q^{97} +(1.03757e8 + 5.99040e7i) q^{98} +(7.35134e6 + 1.06612e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−7.27231	−	8.66680i	−0.454519	−	0.541675i
$2$	−7.27231	−	8.66680i	−0.454519	−	0.541675i
$3$	−71.9819	+	37.1430i	−0.888665	+	0.458556i
$3$	−71.9819	+	37.1430i	−0.888665	+	0.458556i
$4$	−22.2270	+	126.055i	−0.0868241	+	0.492404i
$5$	242.781	+	667.036i	0.388450	+	1.06726i	0.967699	+	0.252107i	$0.0811235\pi$
$5$	242.781	+	667.036i	0.388450	+	1.06726i	−0.579249	+	0.815150i	$0.696654\pi$
$6$	845.386	+	353.737i	0.652304	+	0.272945i
$7$	702.244	+	3982.62i	0.292480	+	1.65873i	0.677273	+	0.735732i	$0.263162\pi$
$7$	702.244	+	3982.62i	0.292480	+	1.65873i	−0.384793	+	0.923003i	$0.625727\pi$
$8$	1254.14	−	724.077i	0.306186	−	0.176777i
$9$	3801.79	−	5347.25i	0.579453	−	0.815006i
$10$	4015.49	−	6955.03i	0.401549	−	0.695503i
$11$	−675.075	+	1854.75i	−0.0461085	+	0.126682i	−0.960610	−	0.277901i	$-0.910361\pi$
$11$	−675.075	+	1854.75i	−0.0461085	+	0.126682i	0.914501	+	0.404583i	$0.132583\pi$
$12$	−3082.14	−	9899.28i	−0.148637	−	0.477396i
$13$	5274.86	+	4426.14i	0.184688	+	0.154971i	0.730444	−	0.682973i	$-0.239313\pi$
$13$	5274.86	+	4426.14i	0.184688	+	0.154971i	−0.545756	+	0.837944i	$0.683758\pi$
$14$	29409.7	−	35049.1i	0.765558	−	0.912356i
$15$	−42251.6	−	38996.9i	−0.834599	−	0.770309i
$16$	−15395.9	−	5603.66i	−0.234923	−	0.0855050i
$17$	85996.5	+	49650.1i	1.02964	+	0.594462i	0.916881	−	0.399160i	$-0.130698\pi$
$17$	85996.5	+	49650.1i	1.02964	+	0.594462i	0.112758	+	0.993623i	$0.464032\pi$
$18$	−73991.4	+	5937.54i	−0.704841	+	0.0565609i
$19$	79817.2	+	138247.i	0.612466	+	1.06082i	0.990823	+	0.135163i	$0.0431558\pi$
$19$	79817.2	+	138247.i	0.612466	+	1.06082i	−0.378357	+	0.925660i	$0.623511\pi$
$20$	−89479.7	+	15777.7i	−0.559248	+	0.0986106i
$21$	−198476.	−	260593.i	−1.02054	−	1.33994i
$22$	20984.1	−	7637.60i	0.0895778	−	0.0326037i
$23$	−383459.	−	67614.1i	−1.37027	−	0.241616i	−0.560401	−	0.828221i	$-0.689353\pi$
$23$	−383459.	−	67614.1i	−1.37027	−	0.241616i	−0.809873	+	0.586605i	$0.800464\pi$
$24$	−63380.9	+	98703.0i	−0.191035	+	0.297499i
$25$	−86757.9	+	72798.6i	−0.222100	+	0.186364i
$26$		−	77904.4i		−	0.170478i
$27$	−75046.7	+	526116.i	−0.141214	+	0.989979i
$28$	−517640.			−0.842162
$29$	584464.	+	696538.i	0.826354	+	0.984810i	1.00000		2.05117e-6i	$6.52909e-7\pi$
$29$	584464.	+	696538.i	0.826354	+	0.984810i	−0.173646	+	0.984808i	$0.555555\pi$
$30$	−30711.5	+	649784.i	−0.0379155	+	0.802202i
$31$	70920.0	−	402207.i	0.0767931	−	0.435515i	−0.922035	−	0.387107i	$-0.873474\pi$
$31$	70920.0	−	402207.i	0.0767931	−	0.435515i	0.998828	−	0.0484076i	$-0.0154146\pi$
$32$	63398.2	+	174185.i	0.0604612	+	0.166116i
$33$	−20298.0	−	158583.i	−0.0171158	−	0.133721i
$34$	−195086.	−	1.10639e6i	−0.145985	−	0.827925i
$35$	−2.48606e6	+	1.43533e6i	−1.65668	+	0.956486i
$36$	589548.	+	598089.i	0.351002	+	0.356087i
$37$	−1.78613e6	+	3.09367e6i	−0.953030	+	1.65070i	−0.214216	+	0.976786i	$0.568720\pi$
$37$	−1.78613e6	+	3.09367e6i	−0.953030	+	1.65070i	−0.738814	+	0.673910i	$0.764614\pi$
$38$	617708.	−	1.69714e6i	0.296244	−	0.813923i
$39$	−544095.	−	122677.i	−0.235189	−	0.0530280i
$40$	787467.	+	660763.i	0.307604	+	0.258111i
$41$	1.55285e6	−	1.85062e6i	0.549535	−	0.654910i	−0.417762	−	0.908556i	$-0.637186\pi$
$41$	1.55285e6	−	1.85062e6i	0.549535	−	0.654910i	0.967297	+	0.253646i	$0.0816300\pi$
$42$	−815135.	+	3.61526e6i	−0.261958	+	1.16183i
$43$	−5.76395e6	−	2.09791e6i	−1.68596	−	0.613638i	−0.691849	−	0.722042i	$-0.743204\pi$
$43$	−5.76395e6	−	2.09791e6i	−1.68596	−	0.613638i	−0.994107	+	0.108405i	$0.965426\pi$
$44$	−218797.	−	126322.i	−0.0583755	−	0.0337031i
$45$	4.48981e6	+	1.23772e6i	1.09491	+	0.301836i
$46$	2.20263e6	+	3.81507e6i	0.491939	+	0.852063i
$47$	3.95927e6	−	698125.i	0.811378	−	0.143068i	0.247459	−	0.968898i	$-0.420404\pi$
$47$	3.95927e6	−	698125.i	0.811378	−	0.143068i	0.563918	+	0.825830i	$0.309293\pi$
$48$	1.31636e6	−	168489.i	0.247977	−	0.0317401i
$49$	−9.95099e6	+	3.62187e6i	−1.72616	+	0.628272i
$50$	1.26186e6	+	222500.i	0.201898	+	0.0356000i
$51$	−8.03435e6	−	379737.i	−1.18760	−	0.0561310i
$52$	−675183.	+	566545.i	−0.0923438	+	0.0774857i
$53$		−	9.23813e6i		−	1.17079i	−0.810747	−	0.585397i	$-0.800939\pi$
$53$		−	9.23813e6i		−	1.17079i	0.810747	−	0.585397i	$-0.199061\pi$
$54$	5.10550e6	−	3.17566e6i	0.600432	−	0.373473i
$55$	−1.40108e6			−0.153113
$56$	3.76444e6	+	4.48628e6i	0.382779	+	0.456178i
$57$	−1.08803e7	−	6.98666e6i	−1.03072	−	0.661866i
$58$	1.78635e6	−	1.01309e7i	0.157853	−	0.895231i
$59$	2.34478e6	+	6.44224e6i	0.193506	+	0.531654i	0.998062	−	0.0622227i	$-0.0198189\pi$
$59$	2.34478e6	+	6.44224e6i	0.193506	+	0.531654i	−0.804556	+	0.593877i	$0.797597\pi$
$60$	5.85489e6	−	4.45926e6i	0.451766	−	0.344079i
$61$	−4.42096e6	−	2.50725e7i	−0.319299	−	1.81083i	−0.547033	−	0.837111i	$-0.684243\pi$
$61$	−4.42096e6	−	2.50725e7i	−0.319299	−	1.81083i	0.227734	−	0.973723i	$-0.426868\pi$
$62$	−4.00160e6	+	2.31033e6i	−0.270812	+	0.156353i
$63$	2.39659e7	+	1.13860e7i	1.52136	+	0.722786i
$64$	1.04858e6	−	1.81619e6i	0.0625000	−	0.108253i
$65$	−1.67175e6	+	4.59311e6i	−0.0936524	+	0.257308i
$66$	−1.22679e6	+	1.32918e6i	−0.0646541	+	0.0700502i
$67$	−3.41561e6	−	2.86604e6i	−0.169500	−	0.142227i	0.554092	−	0.832456i	$-0.313066\pi$
$67$	−3.41561e6	−	2.86604e6i	−0.169500	−	0.142227i	−0.723592	+	0.690228i	$0.757510\pi$
$68$	−8.17010e6	+	9.73675e6i	−0.382113	+	0.455385i
$69$	3.01135e7	−	9.37583e6i	1.32851	−	0.413631i
$70$	3.05191e7	+	1.11080e7i	1.27110	+	0.462642i
$71$	1.78601e7	+	1.03116e7i	0.702832	+	0.405780i	0.808401	−	0.588632i	$-0.200333\pi$
$71$	1.78601e7	+	1.03116e7i	0.702832	+	0.405780i	−0.105569	+	0.994412i	$0.533666\pi$
$72$	896145.	−	9.45899e6i	0.0333464	−	0.351977i
$73$	−4.93456e6	−	8.54690e6i	−0.173763	−	0.300966i	0.765970	−	0.642877i	$-0.222259\pi$
$73$	−4.93456e6	−	8.54690e6i	−0.173763	−	0.300966i	−0.939732	+	0.341911i	$0.888926\pi$
$74$	3.98015e7	−	7.01808e6i	1.32731	−	0.234041i
$75$	3.54104e6	−	8.46263e6i	0.111914	−	0.267461i
$76$	−1.92009e7	+	6.98857e6i	−0.575530	+	0.209476i
$77$	−7.86085e6	−	1.38608e6i	−0.223618	−	0.0394299i
$78$	2.89361e6	+	5.60771e6i	0.0781738	+	0.151498i
$79$	−2.85868e6	+	2.39872e6i	−0.0733934	+	0.0615844i	−0.678746	−	0.734373i	$-0.737476\pi$
$79$	−2.85868e6	+	2.39872e6i	−0.0733934	+	0.0615844i	0.605353	+	0.795957i	$0.293032\pi$
$80$		−	1.16301e7i		−	0.283938i
$81$	−1.41395e7	−	4.06583e7i	−0.328469	−	0.944515i
$82$	−2.73318e7			−0.604523
$83$	2.82890e6	+	3.37135e6i	0.0596080	+	0.0710381i	0.795025	−	0.606577i	$-0.207458\pi$
$83$	2.82890e6	+	3.37135e6i	0.0596080	+	0.0710381i	−0.735417	+	0.677615i	$0.763013\pi$
$84$	3.72607e7	−	1.92267e7i	0.748400	−	0.386178i
$85$	−1.22401e7	+	6.94168e7i	−0.234481	+	1.32981i
$86$	2.37351e7	+	6.52116e7i	0.433907	+	1.19215i
$87$	−6.79424e7	−	2.84293e7i	−1.18594	−	0.496237i
$88$	496347.	+	2.81492e6i	0.00827666	+	0.0469392i
$89$	5.18273e7	−	2.99225e7i	0.826035	−	0.476911i	−0.0264584	−	0.999650i	$-0.508423\pi$
$89$	5.18273e7	−	2.99225e7i	0.826035	−	0.476911i	0.852493	+	0.522739i	$0.175090\pi$
$90$	−2.19243e7	−	4.79134e7i	−0.334160	−	0.730276i
$91$	−1.39234e7	+	2.41160e7i	−0.203039	+	0.351674i
$92$	1.70463e7	−	4.68342e7i	0.237946	−	0.653750i
$93$	9.83425e6	+	3.15858e7i	0.131465	+	0.422241i
$94$	−3.48435e7	−	2.92372e7i	−0.446283	−	0.374476i
$95$	−7.28379e7	+	8.68048e7i	−0.894258	+	1.06574i
$96$	−1.10333e7	−	1.01834e7i	−0.129903	−	0.119896i
$97$	−2.82465e7	−	1.02809e7i	−0.319064	−	0.116130i	0.177523	−	0.984117i	$-0.443192\pi$
$97$	−2.82465e7	−	1.02809e7i	−0.319064	−	0.116130i	−0.496587	+	0.867987i	$0.665414\pi$
$98$	1.03757e8	+	5.99040e7i	1.12489	+	0.649458i
$99$	7.35134e6	+	1.06612e7i	0.0765290	+	0.110985i
$100$	−7.24829e6	−	1.25544e7i	−0.0724829	−	0.125544i
$101$	−6.71968e7	+	1.18486e7i	−0.645748	+	0.113863i	−0.486925	−	0.873444i	$-0.661881\pi$
$101$	−6.71968e7	+	1.18486e7i	−0.645748	+	0.113863i	−0.158824	+	0.987307i	$0.550770\pi$
$102$	5.51372e7	+	7.23937e7i	0.509382	+	0.668806i
$103$	−1.52788e8	+	5.56104e7i	−1.35750	+	0.494091i	−0.915282	−	0.402814i	$-0.868032\pi$
$103$	−1.52788e8	+	5.56104e7i	−1.35750	+	0.494091i	−0.442222	+	0.896905i	$0.645810\pi$
$104$	9.82028e6	+	1.73158e6i	0.0839441	+	0.0148016i
$105$	1.25639e8	−	1.95657e8i	1.03363	−	1.60968i
$106$	−8.00651e7	+	6.71826e7i	−0.634190	+	0.532149i
$107$			9.46785e7i			0.722297i	0.932508	+	0.361149i	$0.117615\pi$
$107$			9.46785e7i			0.722297i	−0.932508	+	0.361149i	$0.882385\pi$
$108$	−6.46516e7	−	2.11540e7i	−0.475209	−	0.155488i
$109$	−1.08729e7			−0.0770264			−0.0385132	−	0.999258i	$-0.512262\pi$
$109$	−1.08729e7			−0.0770264			−0.0385132	+	0.999258i	$0.512262\pi$
$110$	1.01891e7	+	1.21429e7i	0.0695930	+	0.0829377i
$111$	1.36608e7	−	2.89031e8i	0.0899880	−	1.90393i
$112$	1.15056e7	−	6.52513e7i	0.0731199	−	0.414684i
$113$	−2.94142e7	−	8.08148e7i	−0.180403	−	0.495652i	0.816223	−	0.577737i	$-0.196064\pi$
$113$	−2.94142e7	−	8.08148e7i	−0.180403	−	0.495652i	−0.996625	+	0.0820853i	$0.973842\pi$
$114$	1.85731e7	+	1.45107e8i	0.109968	+	0.859149i
$115$	−4.79955e7	−	2.72196e8i	−0.274416	−	1.55629i
$116$	−1.00793e8	+	5.81930e7i	−0.556672	+	0.321395i
$117$	4.37216e7	−	1.13788e7i	0.233320	−	0.0607230i
$118$	3.87817e7	−	6.71718e7i	0.200031	−	0.346465i
$119$	−1.37347e8	+	3.77358e8i	−0.684907	+	1.88177i
$120$	−8.12261e7	−	1.83141e7i	−0.391715	−	0.0883202i
$121$	1.61224e8	+	1.35283e8i	0.752122	+	0.631105i
$122$	−1.85148e8	+	2.20651e8i	−0.835757	+	0.996016i
$123$	−4.30397e7	+	1.90889e8i	−0.188040	+	0.833988i
$124$	4.91241e7	+	1.78797e7i	0.207782	+	0.0756264i
$125$	1.70512e8	+	9.84450e7i	0.698416	+	0.403231i
$126$	−7.56070e7	−	2.90510e8i	−0.299971	−	1.15260i
$127$	−1.38425e6	−	2.39758e6i	−0.00532106	−	0.00921635i	0.863353	−	0.504601i	$-0.168360\pi$
$127$	−1.38425e6	−	2.39758e6i	−0.00532106	−	0.00921635i	−0.868674	+	0.495385i	$0.835027\pi$
$128$	−2.33661e7	+	4.12008e6i	−0.0870455	+	0.0153485i
$129$	4.92822e8	−	6.30793e7i	1.77964	−	0.227787i
$130$	5.19651e7	−	1.89137e7i	0.181944	−	0.0662222i
$131$	1.11185e8	+	1.96049e7i	0.377538	+	0.0665702i	0.359197	−	0.933262i	$-0.383050\pi$
$131$	1.11185e8	+	1.96049e7i	0.377538	+	0.0665702i	0.0183409	+	0.999832i	$0.494162\pi$
$132$	2.04414e7	+	966147.i	0.0673310	+	0.00318235i
$133$	−4.94536e8	+	4.14965e8i	−1.58049	+	1.32619i
$134$			5.04451e7i			0.156459i
$135$	−3.69158e8	+	7.76721e7i	−1.11142	+	0.233846i
$136$	1.43802e8			0.420348
$137$	2.70102e8	+	3.21895e8i	0.766736	+	0.913760i	0.998254	−	0.0590707i	$-0.0188137\pi$
$137$	2.70102e8	+	3.21895e8i	0.766736	+	0.913760i	−0.231518	+	0.972831i	$0.574369\pi$
$138$	−3.00253e8	−	1.92804e8i	−0.827888	−	0.531617i
$139$	1.30957e7	−	7.42693e7i	0.0350808	−	0.198953i	−0.962230	−	0.272236i	$-0.912237\pi$
$139$	1.30957e7	−	7.42693e7i	0.0350808	−	0.198953i	0.997311	+	0.0732835i	$0.0233478\pi$
$140$	−1.25673e8	−	3.45284e8i	−0.327138	−	0.898803i
$141$	−2.59065e8	+	1.97312e8i	−0.655439	+	0.499202i
$142$	−4.05163e7	−	2.29779e8i	−0.0996498	−	0.565142i
$143$	−1.17703e7	+	6.79560e6i	−0.0281478	+	0.0162511i
$144$	−8.84962e7	+	6.10220e7i	−0.205814	+	0.141918i
$145$	−3.22719e8	+	5.58965e8i	−0.730049	+	1.26448i
$146$	−3.81887e7	+	1.04923e8i	−0.0840472	+	0.230918i
$147$	5.81764e8	−	6.30319e8i	1.24588	−	1.34987i
$148$	−3.50274e8	−	2.93914e8i	−0.730063	−	0.612596i
$149$	4.67586e8	−	5.57248e8i	0.948674	−	1.13059i	−0.0426432	−	0.999090i	$-0.513578\pi$
$149$	4.67586e8	−	5.57248e8i	0.948674	−	1.13059i	0.991317	−	0.131495i	$-0.0419777\pi$
$150$	−9.90955e7	+	3.08534e7i	−0.195744	+	0.0609450i
$151$	−5.95781e6	−	2.16847e6i	−0.0114599	−	0.00417105i	0.336284	−	0.941761i	$-0.390830\pi$
$151$	−5.95781e6	−	2.16847e6i	−0.0114599	−	0.00417105i	−0.347744	+	0.937590i	$0.613052\pi$
$152$	2.00204e8	+	1.15588e8i	0.375058	+	0.216540i
$153$	5.92432e8	−	2.71086e8i	1.08112	−	0.494699i
$154$	4.51537e7	+	7.82084e7i	0.0802805	+	0.139050i
$155$	2.85505e8	−	5.03422e7i	0.494637	−	0.0872178i
$156$	2.75577e7	−	6.58594e7i	0.0465312	−	0.111204i
$157$	2.34275e8	−	8.52691e7i	0.385591	−	0.140344i	−0.141948	−	0.989874i	$-0.545337\pi$
$157$	2.34275e8	−	8.52691e7i	0.385591	−	0.140344i	0.527540	+	0.849530i	$0.323115\pi$
$158$	4.15784e7	+	7.33139e6i	0.0667174	+	0.0117641i
$159$	3.43132e8	+	6.64978e8i	0.536875	+	1.04044i
$160$	−1.00796e8	+	8.45777e7i	−0.153802	+	0.129055i
$161$		−	1.57465e9i		−	2.34359i
$162$	−2.49550e8	+	4.18224e8i	−0.362325	+	0.607224i
$163$	7.93998e8			1.12478			0.562392	−	0.826871i	$-0.309881\pi$
$163$	7.93998e8			1.12478			0.562392	+	0.826871i	$0.309881\pi$
$164$	1.98765e8	+	2.36879e8i	0.274767	+	0.327455i
$165$	1.00853e8	−	5.20405e7i	0.136067	−	0.0702110i
$166$	8.64619e6	−	4.90350e7i	0.0113866	−	0.0645764i
$167$	1.66507e8	+	4.57473e8i	0.214075	+	0.588166i	0.999527	−	0.0307566i	$-0.00979168\pi$
$167$	1.66507e8	+	4.57473e8i	0.214075	+	0.588166i	−0.785452	+	0.618923i	$0.787569\pi$
$168$	−4.37606e8	−	1.83108e8i	−0.549346	−	0.229864i
$169$	−1.33417e8	−	7.56643e8i	−0.163555	−	0.927565i
$170$	6.90636e8	−	3.98739e8i	0.826901	−	0.477411i
$171$	1.04269e9	+	9.87848e7i	1.21947	+	0.115533i
$172$	3.92567e8	−	6.79947e8i	0.448539	−	0.776893i
$173$	3.42628e8	−	9.41363e8i	0.382506	−	1.05093i	−0.587791	−	0.809013i	$-0.700002\pi$
$173$	3.42628e8	−	9.41363e8i	0.382506	−	1.05093i	0.970297	−	0.241915i	$-0.0777755\pi$
$174$	2.47707e8	+	7.95590e8i	0.270235	+	0.867945i
$175$	−3.50854e8	−	2.94402e8i	−0.374089	−	0.313898i
$176$	2.07868e7	−	2.47728e7i	0.0216639	−	0.0258181i
$177$	−4.08067e8	−	3.76633e8i	−0.415755	−	0.383729i
$178$	−6.36236e8	−	2.31571e8i	−0.633780	−	0.230677i
$179$	−1.59488e8	−	9.20804e7i	−0.155352	−	0.0896923i	0.420309	−	0.907381i	$-0.361922\pi$
$179$	−1.59488e8	−	9.20804e7i	−0.155352	−	0.0896923i	−0.575661	+	0.817689i	$0.695255\pi$
$180$	−2.55816e8	+	5.38454e8i	−0.243690	+	0.512931i
$181$	6.15746e8	+	1.06650e9i	0.573703	+	0.993683i	0.996181	+	0.0873096i	$0.0278269\pi$
$181$	6.15746e8	+	1.06650e9i	0.573703	+	0.993683i	−0.422478	+	0.906373i	$0.638840\pi$
$182$	3.10264e8	−	5.47079e7i	0.282778	−	0.0498614i
$183$	1.24950e9	+	1.64056e9i	1.11412	+	1.46281i
$184$	−5.29869e8	+	1.92856e8i	−0.462271	+	0.168253i
$185$	−2.49723e9	−	4.40329e8i	−2.13192	−	0.375915i
$186$	2.02231e8	−	3.14934e8i	0.168964	−	0.263128i
$187$	−1.50143e8	+	1.25985e8i	−0.122783	+	0.103027i
$188$			5.14604e8i			0.411947i
$189$	−2.14802e9	+	7.05786e7i	−1.68342	+	0.0553128i
$190$	1.28202e9			0.983740
$191$	−1.29373e9	−	1.54181e9i	−0.972097	−	1.15850i	−0.987340	−	0.158617i	$-0.949297\pi$
$191$	−1.29373e9	−	1.54181e9i	−0.972097	−	1.15850i	0.0152429	−	0.999884i	$-0.495148\pi$
$192$	−8.01979e6	+	1.69680e8i	−0.00590144	+	0.124861i
$193$	−1.28709e7	+	7.29942e7i	−0.00927637	+	0.0526089i	−0.989095	−	0.147282i	$-0.952948\pi$
$193$	−1.28709e7	+	7.29942e7i	−0.00927637	+	0.0526089i	0.979818	+	0.199891i	$0.0640587\pi$
$194$	1.16315e8	+	3.19573e8i	0.0821163	+	0.225613i
$195$	−5.02659e7	−	3.92714e8i	−0.0347644	−	0.271605i
$196$	−2.35375e8	−	1.33488e9i	−0.159491	−	0.904519i
$197$	−8.60301e8	+	4.96695e8i	−0.571196	+	0.329780i	−0.757627	−	0.652688i	$-0.773641\pi$
$197$	−8.60301e8	+	4.96695e8i	−0.571196	+	0.329780i	0.186431	+	0.982468i	$0.440308\pi$
$198$	3.89371e7	−	1.41244e8i	0.0253339	−	0.0918987i
$199$	−4.67190e8	+	8.09197e8i	−0.297907	+	0.515991i	−0.975657	−	0.219302i	$-0.929622\pi$
$199$	−4.67190e8	+	8.09197e8i	−0.297907	+	0.515991i	0.677750	+	0.735293i	$0.262955\pi$
$200$	−5.60947e7	+	1.54119e8i	−0.0350592	+	0.0963244i
$201$	3.52315e8	+	7.94366e7i	0.215848	+	0.0486672i
$202$	5.91366e8	+	4.96215e8i	0.355182	+	0.298033i
$203$	−2.36361e9	+	2.81684e9i	−1.39185	+	1.65874i
$204$	2.26447e8	−	1.00433e9i	0.130751	−	0.579905i
$205$	1.61143e9	+	5.86514e8i	0.912424	+	0.332095i
$206$	1.59309e9	+	9.19770e8i	0.884649	+	0.510752i
$207$	−1.81938e9	+	1.79340e9i	−0.990928	+	0.976776i
$208$	−5.64088e7	−	9.77030e7i	−0.0301366	−	0.0521981i
$209$	−3.10298e8	+	5.47138e7i	−0.162627	+	0.0286756i
$210$	−2.60941e9	+	3.33994e8i	−1.34173	+	0.171736i
$211$	2.78983e6	−	1.01542e6i	0.00140750	−	0.000512288i	−0.341316	−	0.939949i	$-0.610873\pi$
$211$	2.78983e6	−	1.01542e6i	0.00140750	−	0.000512288i	0.342724	+	0.939436i	$0.388651\pi$
$212$	1.16452e9	+	2.05336e8i	0.576504	+	0.101653i
$213$	−1.66861e9	−	7.88656e7i	−0.810656	−	0.0383150i
$214$	8.20560e8	−	6.88531e8i	0.391251	−	0.328298i
$215$		−	4.35409e9i		−	2.03772i
$216$	2.86829e8	+	7.14161e8i	0.131768	+	0.328081i
$217$	1.65164e9			0.744864
$218$	7.90712e7	+	9.42334e7i	0.0350100	+	0.0417233i
$219$	6.72657e8	+	4.31938e8i	0.292427	+	0.187778i
$220$	3.11418e7	−	1.76614e8i	0.0132939	−	0.0753936i
$221$	2.33862e8	+	6.42530e8i	0.0980370	+	0.269354i
$222$	−2.60432e9	+	1.98353e9i	−1.07222	+	0.816631i
$223$	6.34114e8	+	3.59624e9i	0.256418	+	1.45422i	0.792407	+	0.609993i	$0.208828\pi$
$223$	6.34114e8	+	3.59624e9i	0.256418	+	1.45422i	−0.535989	+	0.844225i	$0.680061\pi$
$224$	−6.49192e8	+	3.74811e8i	−0.257858	+	0.148875i
$225$	5.94370e7	+	7.40682e8i	0.0231914	+	0.289002i
$226$	−4.86497e8	+	8.42637e8i	−0.186486	+	0.323003i
$227$	6.28627e8	−	1.72714e9i	0.236750	−	0.650464i	−0.763241	−	0.646114i	$-0.776393\pi$
$227$	6.28627e8	−	1.72714e9i	0.236750	−	0.650464i	0.999991	−	0.00435027i	$-0.00138474\pi$
$228$	1.12254e9	−	1.21623e9i	0.415397	−	0.450067i
$229$	−2.61461e9	−	2.19392e9i	−0.950746	−	0.797771i	0.0286767	−	0.999589i	$-0.490871\pi$
$229$	−2.61461e9	−	2.19392e9i	−0.950746	−	0.797771i	−0.979423	+	0.201818i	$0.935315\pi$
$230$	−2.01003e9	+	2.39546e9i	−0.718277	+	0.856009i
$231$	6.17322e8	−	1.92203e8i	0.216802	−	0.0675014i
$232$	1.23735e9	+	4.50357e8i	0.427110	+	0.155455i
$233$	3.58659e9	+	2.07072e9i	1.21691	+	0.702583i	0.964256	−	0.264974i	$-0.0853633\pi$
$233$	3.58659e9	+	2.07072e9i	1.21691	+	0.702583i	0.252654	+	0.967557i	$0.418697\pi$
$234$	−4.16575e8	−	2.96176e8i	−0.138941	−	0.0987840i
$235$	1.42691e9	+	2.47148e9i	0.467870	+	0.810374i
$236$	−8.64197e8	+	1.52381e8i	−0.278590	+	0.0491228i
$237$	1.16677e8	−	2.78844e8i	0.0369823	−	0.0883829i
$238$	4.26932e9	−	1.55390e9i	1.33061	−	0.484302i
$239$	−6.02082e9	−	1.06163e9i	−1.84529	−	0.325374i	−0.861927	−	0.507032i	$-0.830743\pi$
$239$	−6.02082e9	−	1.06163e9i	−1.84529	−	0.325374i	−0.983362	+	0.181658i	$0.941854\pi$
$240$	4.31977e8	+	8.37156e8i	0.130201	+	0.252326i
$241$	1.47882e9	−	1.24088e9i	0.438377	−	0.367842i	−0.396725	−	0.917938i	$-0.629853\pi$
$241$	1.47882e9	−	1.24088e9i	0.438377	−	0.367842i	0.835101	+	0.550096i	$0.185409\pi$
$242$		−	2.38112e9i		−	0.694256i
$243$	2.52796e9	+	2.40147e9i	0.725012	+	0.688736i
$244$	3.25879e9			0.919385
$245$	−4.83183e9	−	5.75835e9i	−1.34106	−	1.59821i
$246$	1.96739e9	−	1.01519e9i	0.537218	−	0.277208i
$247$	−1.90877e8	+	1.08252e9i	−0.0512822	+	0.290836i
$248$	−2.02286e8	−	5.55775e8i	−0.0534759	−	0.146924i
$249$	−3.28851e8	−	1.37602e8i	−0.0855465	−	0.0357955i
$250$	−3.86811e8	−	2.19371e9i	−0.0990236	−	0.561591i
$251$	−5.97597e8	+	3.45023e8i	−0.150561	+	0.0869267i	−0.573388	−	0.819284i	$-0.694371\pi$
$251$	−5.97597e8	+	3.45023e8i	−0.150561	+	0.0869267i	0.422827	+	0.906211i	$0.361038\pi$
$252$	−1.96796e9	+	2.76795e9i	−0.487993	+	0.686367i
$253$	3.84271e8	−	6.65577e8i	0.0937898	−	0.162449i
$254$	−1.07127e7	+	2.94330e7i	−0.00257374	+	0.00707130i
$255$	−1.69729e9	−	5.45139e9i	−0.401416	−	1.28928i
$256$	2.05633e8	+	1.72547e8i	0.0478778	+	0.0401742i
$257$	3.98306e9	−	4.74683e9i	0.913029	−	1.08811i	−0.0827723	−	0.996568i	$-0.526377\pi$
$257$	3.98306e9	−	4.74683e9i	0.913029	−	1.08811i	0.995802	−	0.0915375i	$-0.0291781\pi$
$258$	−4.13065e9	−	3.81246e9i	−0.932267	−	0.860452i
$259$	−1.35752e10	−	4.94098e9i	−3.01681	−	1.09803i
$260$	−5.41828e8	−	3.12824e8i	−0.118568	−	0.0684553i
$261$	5.94657e9	−	4.77191e8i	1.28146	−	0.102832i
$262$	−6.38660e8	−	1.10619e9i	−0.135539	−	0.234761i
$263$	−6.66556e6	+	1.17532e6i	−0.00139320	+	0.000245659i	−0.174345	−	0.984685i	$-0.555781\pi$
$263$	−6.66556e6	+	1.17532e6i	−0.00139320	+	0.000245659i	0.172952	+	0.984930i	$0.444670\pi$
$264$	−1.40283e8	−	1.84188e8i	−0.0288795	−	0.0379180i
$265$	6.16217e9	−	2.24284e9i	1.24954	−	0.454795i
$266$	7.19285e9	+	1.26829e9i	1.43673	+	0.253334i
$267$	−2.61921e9	+	4.07890e9i	−0.515378	+	0.802598i
$268$	4.37198e8	−	3.66853e8i	0.0847499	−	0.0711136i
$269$			7.72710e9i			1.47573i	0.674948	+	0.737866i	$0.264166\pi$
$269$			7.72710e9i			1.47573i	−0.674948	+	0.737866i	$0.735834\pi$
$270$	3.35780e9	+	2.63456e9i	0.631829	+	0.495739i
$271$	2.76351e9			0.512370			0.256185	−	0.966628i	$-0.417534\pi$
$271$	2.76351e9			0.512370			0.256185	+	0.966628i	$0.417534\pi$
$272$	−1.04577e9	−	1.24630e9i	−0.191057	−	0.227692i
$273$	1.06490e8	−	2.25307e9i	0.0191716	−	0.405625i
$274$	8.25535e8	−	4.68184e9i	0.146465	−	0.830643i
$275$	−7.64553e7	−	2.10059e8i	−0.0133683	−	0.0367291i
$276$	5.12543e8	+	4.00436e9i	0.0883271	+	0.690077i
$277$	1.98050e9	+	1.12320e10i	0.336400	+	1.90782i	0.412949	+	0.910754i	$0.364499\pi$
$277$	1.98050e9	+	1.12320e10i	0.336400	+	1.90782i	−0.0765485	+	0.997066i	$0.524390\pi$
$278$	−7.38914e8	+	4.26612e8i	−0.123713	+	0.0714256i
$279$	−1.88108e9	−	1.90833e9i	−0.310449	−	0.314947i
$280$	−2.07858e9	+	3.60020e9i	−0.338169	+	0.585726i
$281$	5.48141e8	−	1.50601e9i	0.0879159	−	0.241547i	−0.887941	−	0.459957i	$-0.847865\pi$
$281$	5.48141e8	−	1.50601e9i	0.0879159	−	0.241547i	0.975857	+	0.218410i	$0.0700871\pi$
$282$	3.59406e9	+	8.10354e8i	0.568315	+	0.128138i
$283$	8.98926e9	+	7.54289e9i	1.40145	+	1.17596i	0.960450	+	0.278452i	$0.0898214\pi$
$283$	8.98926e9	+	7.54289e9i	1.40145	+	1.17596i	0.441002	+	0.897506i	$0.354623\pi$
$284$	−1.69680e9	+	2.02217e9i	−0.260831	+	0.310846i
$285$	2.01882e9	−	8.95380e9i	0.305997	−	1.35715i
$286$	1.44494e8	+	5.25913e7i	0.0215965	+	0.00786050i
$287$	8.46080e9	+	4.88484e9i	1.24705	+	0.719985i
$288$	1.17244e9	+	3.23209e8i	0.170420	+	0.0469800i
$289$	1.44238e9	+	2.49828e9i	0.206771	+	0.358138i
$290$	7.19135e9	−	1.26803e9i	1.01676	−	0.179282i
$291$	2.41510e9	−	3.09124e8i	0.336794	−	0.0431082i
$292$	1.18706e9	−	4.32056e8i	0.163284	−	0.0594304i
$293$	−3.96303e9	−	6.98788e8i	−0.537720	−	0.0948146i	−0.101809	−	0.994804i	$-0.532463\pi$
$293$	−3.96303e9	−	6.98788e8i	−0.537720	−	0.0948146i	−0.435912	+	0.899989i	$0.643574\pi$
$294$	−9.69362e9	−	4.58162e8i	−1.29747	−	0.0613238i
$295$	−3.72794e9	+	3.12811e9i	−0.492244	+	0.413042i
$296$			5.17319e9i			0.673894i
$297$	−9.25152e8	−	4.94361e8i	−0.118902	−	0.0635357i
$298$	−8.22999e9			−1.04360
$299$	−1.72342e9	−	2.05390e9i	−0.215629	−	0.256977i
$300$	9.88054e8	+	6.34466e8i	0.121982	+	0.0783292i
$301$	4.30747e9	−	2.44289e10i	0.524754	−	2.97603i
$302$	2.45334e7	+	6.74050e7i	0.00294937	+	0.00810334i
$303$	4.39686e9	−	3.34878e9i	0.521642	−	0.397298i
$304$	−4.54168e8	−	2.57572e9i	−0.0531768	−	0.301581i
$305$	1.56509e10	−	9.03608e9i	1.80859	−	1.04419i
$306$	−6.65780e9	−	3.16307e9i	−0.759355	−	0.360764i
$307$	−5.37386e9	+	9.30780e9i	−0.604969	+	1.04784i	0.387088	+	0.922043i	$0.373481\pi$
$307$	−5.37386e9	+	9.30780e9i	−0.604969	+	1.04784i	−0.992056	+	0.125793i	$0.959852\pi$
$308$	3.49446e8	−	9.60094e8i	0.0388308	−	0.106687i
$309$	8.93245e9	−	9.67796e9i	0.979799	−	1.06157i
$310$	−2.51259e9	−	2.10831e9i	−0.272066	−	0.228290i
$311$	−5.50012e9	+	6.55478e9i	−0.587936	+	0.700675i	−0.975208	−	0.221290i	$-0.928973\pi$
$311$	−5.50012e9	+	6.55478e9i	−0.587936	+	0.700675i	0.387272	+	0.921966i	$0.373418\pi$
$312$	−7.71198e8	+	2.40113e8i	−0.0813856	+	0.0253394i
$313$	−1.01977e10	−	3.71165e9i	−1.06249	−	0.386714i	−0.249125	−	0.968471i	$-0.580143\pi$
$313$	−1.01977e10	−	3.71165e9i	−1.06249	−	0.386714i	−0.813362	+	0.581758i	$0.802365\pi$
$314$	−2.44273e9	−	1.41031e9i	−0.251280	−	0.145076i
$315$	−1.77642e9	+	1.87504e10i	−0.180427	+	1.90445i
$316$	−2.38831e8	−	4.13668e8i	−0.0239521	−	0.0414862i
$317$	−8.13198e9	+	1.43389e9i	−0.805303	+	0.141997i	−0.561122	−	0.827733i	$-0.689630\pi$
$317$	−8.13198e9	+	1.43389e9i	−0.805303	+	0.141997i	−0.244181	+	0.969730i	$0.578519\pi$
$318$	3.26787e9	−	7.80979e9i	0.319563	−	0.763714i
$319$	−1.68646e9	+	6.13822e8i	−0.162860	+	0.0592761i
$320$	1.46604e9	+	2.58502e8i	0.139812	+	0.0246526i
$321$	−3.51665e9	−	6.81514e9i	−0.331214	−	0.641881i
$322$	−1.36472e10	+	1.14514e10i	−1.26946	+	1.06521i
$323$			1.58517e10i			1.45635i
$324$	5.43947e9	−	8.78653e8i	0.493602	−	0.0797329i
$325$	−7.79853e8			−0.0699003
$326$	−5.77420e9	−	6.88143e9i	−0.511236	−	0.609268i
$327$	7.82653e8	−	4.03853e8i	0.0684507	−	0.0353209i
$328$	6.07503e8	−	3.44532e9i	0.0524871	−	0.297669i
$329$	5.56074e9	+	1.52780e10i	0.474623	+	1.30402i
$330$	−1.18446e9	−	4.95615e8i	−0.0998765	−	0.0417916i
$331$	1.65181e9	+	9.36789e9i	0.137610	+	0.780423i	0.973007	+	0.230776i	$0.0741265\pi$
$331$	1.65181e9	+	9.36789e9i	0.137610	+	0.780423i	−0.835397	+	0.549647i	$0.814762\pi$
$332$	−4.87854e8	+	2.81663e8i	−0.0401548	+	0.0231834i
$333$	9.75215e9	+	2.13124e10i	0.793091	+	1.73323i
$334$	2.75394e9	−	4.76997e9i	0.221294	−	0.383292i
$335$	1.08250e9	−	2.97415e9i	0.0859508	−	0.236148i
$336$	1.59544e9	+	5.12426e9i	0.125177	+	0.402045i
$337$	−1.57499e10	−	1.32157e10i	−1.22112	−	1.02464i	−0.998766	−	0.0496732i	$-0.984182\pi$
$337$	−1.57499e10	−	1.32157e10i	−1.22112	−	1.02464i	−0.222352	−	0.974966i	$-0.571374\pi$
$338$	−5.58743e9	+	6.65884e9i	−0.428100	+	0.510190i
$339$	5.11899e9	+	4.72467e9i	0.387602	+	0.357744i
$340$	−8.47831e9	−	3.08585e9i	−0.634444	−	0.230919i
$341$	6.98119e8	+	4.03059e8i	0.0516312	+	0.0298093i
$342$	−6.72664e9	−	9.75521e9i	−0.491693	−	0.713070i
$343$	−9.75595e9	−	1.68978e10i	−0.704844	−	1.22083i
$344$	−8.74784e9	+	1.54248e9i	−0.624693	+	0.110150i
$345$	1.35650e10	+	1.78105e10i	0.957511	+	1.25719i
$346$	−1.06503e10	+	3.87640e9i	−0.743118	+	0.270473i
$347$	1.04431e8	+	1.84140e7i	0.00720297	+	0.00127008i	0.177249	−	0.984166i	$-0.443280\pi$
$347$	1.04431e8	+	1.84140e7i	0.00720297	+	0.00127008i	−0.170046	+	0.985436i	$0.554391\pi$
$348$	5.09382e9	−	7.93261e9i	0.347318	−	0.540877i
$349$	−1.04354e10	+	8.75633e9i	−0.703407	+	0.590229i	−0.922741	−	0.385421i	$-0.874056\pi$
$349$	−1.04354e10	+	8.75633e9i	−0.703407	+	0.590229i	0.219334	+	0.975650i	$0.429612\pi$
$350$			5.18177e9i			0.345307i
$351$	−2.72452e9	+	2.44302e9i	−0.179499	+	0.160953i
$352$	−3.65869e8			−0.0238317
$353$	−1.20150e10	−	1.43190e10i	−0.773795	−	0.922174i	0.224840	−	0.974396i	$-0.427814\pi$
$353$	−1.20150e10	−	1.43190e10i	−0.773795	−	0.922174i	−0.998635	+	0.0522222i	$0.983370\pi$
$354$	−2.96612e8	+	6.27562e9i	−0.0188876	+	0.399617i
$355$	−2.54207e9	+	1.44168e10i	−0.160057	+	0.907728i
$356$	2.61993e9	+	7.19819e9i	0.163113	+	0.448150i
$357$	−4.12972e9	−	3.22644e10i	−0.254242	−	1.98633i
$358$	3.61803e8	+	2.05189e9i	0.0220262	+	0.124917i
$359$	1.74027e10	−	1.00474e10i	1.04770	−	0.604892i	0.125698	−	0.992069i	$-0.459883\pi$
$359$	1.74027e10	−	1.00474e10i	1.04770	−	0.604892i	0.922006	+	0.387176i	$0.126550\pi$
$360$	6.52705e9	−	1.69870e9i	0.388604	−	0.101136i
$361$	−4.24980e9	+	7.36087e9i	−0.250230	+	0.433411i
$362$	4.76528e9	−	1.30925e10i	0.277494	−	0.762409i
$363$	−1.66300e10	−	3.74958e9i	−0.957782	−	0.215951i
$364$	−2.73048e9	−	2.29114e9i	−0.155537	−	0.130511i
$365$	4.50307e9	−	5.36655e9i	0.253710	−	0.302360i
$366$	5.13166e9	−	2.27598e10i	0.285979	−	1.26837i
$367$	−1.40639e8	−	5.11886e7i	−0.00775252	−	0.00282169i	0.338141	−	0.941095i	$-0.390202\pi$
$367$	−1.40639e8	−	5.11886e7i	−0.00775252	−	0.00282169i	−0.345893	+	0.938274i	$0.612424\pi$
$368$	5.52482e9	+	3.18975e9i	0.301250	+	0.173927i
$369$	−3.99211e9	−	1.53392e10i	−0.215326	−	0.827363i
$370$	1.43444e10	+	2.48452e10i	0.765376	+	1.32567i
$371$	3.67920e10	−	6.48742e9i	1.94204	−	0.342434i
$372$	−4.20015e9	+	5.37603e8i	−0.219327	+	0.0280730i
$373$	1.13441e10	−	4.12890e9i	0.586048	−	0.213304i	−0.0319421	−	0.999490i	$-0.510169\pi$
$373$	1.13441e10	−	4.12890e9i	0.586048	−	0.213304i	0.617991	+	0.786186i	$0.287947\pi$
$374$	2.18377e9	+	3.85058e8i	0.111614	+	0.0196806i
$375$	−1.59303e10	−	7.52934e8i	−0.805562	−	0.0380743i
$376$	4.45997e9	−	3.74236e9i	0.223142	−	0.187238i
$377$			6.26106e9i			0.309943i
$378$	1.62328e10	+	1.81032e10i	0.795107	+	0.886723i
$379$	8.29503e9			0.402033			0.201016	−	0.979588i	$-0.435576\pi$
$379$	8.29503e9			0.402033			0.201016	+	0.979588i	$0.435576\pi$
$380$	−9.32325e9	−	1.11110e10i	−0.447129	−	0.532868i
$381$	1.88694e8	+	1.21168e8i	0.00895486	+	0.00575025i
$382$	−3.95413e9	+	2.24250e10i	−0.185694	+	1.05312i
$383$	1.21645e10	+	3.34216e10i	0.565325	+	1.55322i	0.811720	+	0.584047i	$0.198532\pi$
$383$	1.21645e10	+	3.34216e10i	0.565325	+	1.55322i	−0.246395	+	0.969169i	$0.579246\pi$
$384$	1.52890e9	−	1.16446e9i	0.0703162	−	0.0535549i
$385$	−9.83901e8	−	5.57998e9i	−0.0447825	−	0.253974i
$386$	7.26228e8	−	4.19288e8i	0.0327132	−	0.0188870i
$387$	−3.31313e10	+	2.28455e10i	−1.47705	+	1.01849i
$388$	1.92380e9	−	3.33212e9i	0.0848853	−	0.147026i
$389$	−1.18173e10	+	3.24677e10i	−0.516082	+	1.41792i	0.358720	+	0.933445i	$0.383213\pi$
$389$	−1.18173e10	+	3.24677e10i	−0.516082	+	1.41792i	−0.874803	+	0.484479i	$0.839009\pi$
$390$	−3.03803e9	+	3.29159e9i	−0.131321	+	0.142281i
$391$	−2.96191e10	−	2.48533e10i	−1.26726	−	1.06335i
$392$	−9.85742e9	+	1.17476e10i	−0.417464	+	0.497514i
$393$	−8.73150e9	+	2.71855e9i	−0.366031	+	0.113964i
$394$	1.05611e10	+	3.84394e9i	0.438254	+	0.159511i
$395$	−2.29406e9	−	1.32448e9i	−0.0942360	−	0.0544072i
$396$	−1.50730e9	+	6.89711e8i	−0.0612940	+	0.0280470i
$397$	2.31647e10	+	4.01225e10i	0.932535	+	1.61520i	0.778971	+	0.627060i	$0.215742\pi$
$397$	2.31647e10	+	4.01225e10i	0.932535	+	1.61520i	0.153564	+	0.988139i	$0.450925\pi$
$398$	1.04107e10	−	1.83569e9i	0.414904	−	0.0731588i
$399$	2.01846e10	−	4.82386e10i	0.796395	−	1.90328i
$400$	1.74366e9	−	6.34639e8i	0.0681116	−	0.0247906i
$401$	1.22543e10	+	2.16077e9i	0.473927	+	0.0835661i	0.405510	−	0.914091i	$-0.367094\pi$
$401$	1.22543e10	+	2.16077e9i	0.473927	+	0.0835661i	0.0684171	+	0.997657i	$0.478205\pi$
$402$	−1.87369e9	−	3.63114e9i	−0.0717451	−	0.139040i
$403$	2.15432e9	−	1.80769e9i	0.0816751	−	0.0685335i
$404$		−	8.73388e9i		−	0.327855i
$405$	2.36877e10	−	1.93026e10i	0.880446	−	0.717458i
$406$	4.16019e10			1.53112
$407$	−4.53222e9	−	5.40129e9i	−0.165171	−	0.196843i
$408$	−1.03511e10	+	5.34124e9i	−0.373549	+	0.192753i
$409$	9.14542e9	−	5.18662e10i	0.326821	−	1.85350i	−0.169733	−	0.985490i	$-0.554291\pi$
$409$	9.14542e9	−	5.18662e10i	0.326821	−	1.85350i	0.496554	−	0.868006i	$-0.334598\pi$
$410$	−6.63564e9	−	1.82313e10i	−0.234827	−	0.645181i
$411$	−3.13986e10	−	1.31382e10i	−1.10038	−	0.460436i
$412$	−3.61397e9	−	2.04958e10i	−0.125428	−	0.711339i
$413$	−2.40104e10	+	1.38624e10i	−0.825276	+	0.476474i
$414$	2.87741e10	+	2.72606e9i	0.979491	+	0.0927971i
$415$	−1.56201e9	+	2.70547e9i	−0.0526612	+	0.0912118i
$416$	−4.36550e8	+	1.19941e9i	−0.0145767	+	0.0400493i
$417$	1.81594e9	+	5.83246e9i	0.0600560	+	0.192889i
$418$	2.73078e9	+	2.29139e9i	0.0894501	+	0.0750575i
$419$	−3.58659e10	+	4.27433e10i	−1.16366	+	1.38679i	−0.256216	+	0.966620i	$0.582476\pi$
$419$	−3.58659e10	+	4.27433e10i	−1.16366	+	1.38679i	−0.907443	+	0.420175i	$0.861969\pi$
$420$	2.18711e10	+	2.01863e10i	0.702868	+	0.648724i
$421$	2.15748e10	+	7.85258e9i	0.686781	+	0.249968i	0.661756	−	0.749719i	$-0.269811\pi$
$421$	2.15748e10	+	7.85258e9i	0.686781	+	0.249968i	0.0250247	+	0.999687i	$0.492034\pi$
$422$	−2.90889e7	−	1.67945e7i	−0.000917229	−	0.000529562i
$423$	1.13192e10	−	2.38253e10i	0.353554	−	0.744179i
$424$	−6.68912e9	−	1.15859e10i	−0.206969	−	0.358481i
$425$	−1.10753e10	+	1.95288e9i	−0.339470	+	0.0598577i
$426$	1.14511e10	+	1.50351e10i	0.347705	+	0.456527i
$427$	9.67498e10	−	3.52141e10i	2.91031	−	1.05926i
$428$	−1.19347e10	−	2.10441e9i	−0.355662	−	0.0627128i
$429$	5.94841e8	−	9.26346e8i	0.0175619	−	0.0273492i
$430$	−3.77361e10	+	3.16643e10i	−1.10378	+	0.926182i
$431$		−	2.03309e10i		−	0.589181i	−0.955624	−	0.294590i	$-0.904817\pi$
$431$		−	2.03309e10i		−	0.589181i	0.955624	−	0.294590i	$-0.0951832\pi$
$432$	4.10359e9	−	7.67950e9i	0.117823	−	0.220495i
$433$	−4.65175e10			−1.32332			−0.661660	−	0.749804i	$-0.730148\pi$
$433$	−4.65175e10			−1.32332			−0.661660	+	0.749804i	$0.730148\pi$
$434$	−1.20113e10	−	1.43145e10i	−0.338555	−	0.403475i
$435$	2.46824e9	−	5.22221e10i	0.0689334	−	1.45847i
$436$	2.41672e8	−	1.37059e9i	0.00668775	−	0.0379281i
$437$	−2.12591e10	−	5.84090e10i	−0.582935	−	1.60160i
$438$	−1.14825e9	−	8.97097e9i	−0.0311989	−	0.243749i
$439$	−9.64451e9	−	5.46967e10i	−0.259670	−	1.47266i	−0.783794	−	0.621020i	$-0.786718\pi$
$439$	−9.64451e9	−	5.46967e10i	−0.259670	−	1.47266i	0.524124	−	0.851642i	$-0.324393\pi$
$440$	−1.75715e9	+	1.01449e9i	−0.0468812	+	0.0270669i
$441$	−1.84645e10	+	6.69801e10i	−0.488185	+	1.77089i
$442$	3.86796e9	−	6.69951e9i	0.101343	−	0.175531i
$443$	1.68761e9	−	4.63668e9i	0.0438186	−	0.120390i	−0.915853	−	0.401513i	$-0.868484\pi$
$443$	1.68761e9	−	4.63668e9i	0.0438186	−	0.120390i	0.959672	+	0.281122i	$0.0907067\pi$
$444$	3.61302e10	+	8.14629e9i	0.929691	+	0.209618i
$445$	3.25421e10	+	2.73060e10i	0.829860	+	0.696335i
$446$	2.65564e10	−	3.16487e10i	0.671167	−	0.799865i
$447$	−1.29599e10	+	5.74793e10i	−0.324617	+	1.43973i
$448$	7.96954e9	+	2.90068e9i	0.197843	+	0.0720091i
$449$	2.41517e9	+	1.39440e9i	0.0594242	+	0.0343086i	0.529418	−	0.848361i	$-0.322410\pi$
$449$	2.41517e9	+	1.39440e9i	0.0594242	+	0.0343086i	−0.469994	+	0.882670i	$0.655744\pi$
$450$	5.98710e9	−	5.90160e9i	0.146005	−	0.143919i
$451$	2.38415e9	+	4.12947e9i	0.0576272	+	0.0998132i
$452$	1.08409e10	−	1.91155e9i	0.259724	−	0.0457964i
$453$	5.09398e8	−	6.52009e7i	0.0120966	−	0.00154832i
$454$	−1.95403e10	+	7.11210e9i	−0.459948	+	0.167407i
$455$	−1.94666e10	−	3.43248e9i	−0.454197	−	0.0800872i
$456$	−1.87043e10	−	8.84046e8i	−0.432596	−	0.0204463i
$457$	1.24495e10	−	1.04464e10i	0.285422	−	0.239498i	−0.488824	−	0.872383i	$-0.662574\pi$
$457$	1.24495e10	−	1.04464e10i	0.285422	−	0.239498i	0.774246	+	0.632885i	$0.218129\pi$
$458$			3.86151e10i			0.877598i
$459$	−3.25754e10	+	4.15180e10i	−0.733904	+	0.935375i
$460$	3.53786e10			0.790150
$461$	2.51076e10	+	2.99221e10i	0.555906	+	0.662503i	0.968675	−	0.248333i	$-0.0798826\pi$
$461$	2.51076e10	+	2.99221e10i	0.555906	+	0.662503i	−0.412768	+	0.910836i	$0.635438\pi$
$462$	−6.15515e9	−	3.95245e9i	−0.135105	−	0.0867558i
$463$	−5.99186e9	+	3.39815e10i	−0.130388	+	0.739468i	0.847573	+	0.530679i	$0.178063\pi$
$463$	−5.99186e9	+	3.39815e10i	−0.130388	+	0.739468i	−0.977961	+	0.208788i	$0.933048\pi$
$464$	−5.09521e9	−	1.39990e10i	−0.109923	−	0.302012i
$465$	−1.86813e10	+	1.42282e10i	−0.399572	+	0.304326i
$466$	−8.13629e9	−	4.61432e10i	−0.172537	−	0.978507i
$467$	6.86368e10	−	3.96275e10i	1.44308	−	0.833161i	0.445024	−	0.895519i	$-0.353195\pi$
$467$	6.86368e10	−	3.96275e10i	1.44308	−	0.833161i	0.998054	+	0.0623571i	$0.0198618\pi$
$468$	4.62561e8	+	5.76426e9i	0.00964240	+	0.120160i
$469$	9.01575e9	−	1.56157e10i	0.186342	−	0.322754i
$470$	1.10429e10	−	3.03401e10i	0.226304	−	0.621764i
$471$	−1.36964e10	+	1.48395e10i	−0.278306	+	0.301534i
$472$	7.60537e9	+	6.38166e9i	0.153233	+	0.128578i
$473$	7.78219e9	−	9.27446e9i	0.155474	−	0.185287i
$474$	−3.26520e9	+	1.01662e9i	−0.0646840	+	0.0201394i
$475$	−1.69890e10	−	6.18349e9i	−0.333729	−	0.121467i
$476$	−4.45152e10	−	2.57009e10i	−0.867123	−	0.500633i
$477$	−4.93986e10	−	3.51214e10i	−0.954205	−	0.678420i
$478$	3.45843e10	+	5.99018e10i	0.662473	+	1.14744i
$479$	1.87072e10	−	3.29859e9i	0.355359	−	0.0626594i	0.00688102	−	0.999976i	$-0.497810\pi$
$479$	1.87072e10	−	3.29859e9i	0.355359	−	0.0626594i	0.348478	+	0.937317i	$0.386699\pi$
$480$	4.11400e9	−	9.83192e9i	0.0774995	−	0.185214i
$481$	−2.31146e10	+	8.41303e9i	−0.431823	+	0.157171i
$482$	−2.15089e10	−	3.79260e9i	−0.398501	−	0.0702665i
$483$	5.84874e10	+	1.13347e11i	1.07467	+	2.08267i
$484$	−2.06367e10	+	1.73162e10i	−0.376061	+	0.315553i
$485$		−	2.13375e10i		−	0.385634i
$486$	2.42898e9	−	3.93736e10i	0.0435391	−	0.705765i
$487$	−3.15914e10			−0.561634			−0.280817	−	0.959761i	$-0.590605\pi$
$487$	−3.15914e10			−0.561634			−0.280817	+	0.959761i	$0.590605\pi$
$488$	−2.36989e10	−	2.82433e10i	−0.417878	−	0.498008i
$489$	−5.71535e10	+	2.94915e10i	−0.999557	+	0.515777i
$490$	−1.47679e10	+	8.37530e10i	−0.256174	+	1.45283i
$491$	−2.70031e10	−	7.41904e10i	−0.464609	−	1.27650i	−0.921984	−	0.387229i	$-0.873432\pi$
$491$	−2.70031e10	−	7.41904e10i	−0.464609	−	1.27650i	0.457375	−	0.889274i	$-0.348790\pi$
$492$	−2.31059e10	−	9.66827e9i	−0.394333	−	0.165002i
$493$	1.56787e10	+	8.89185e10i	0.265414	+	1.50524i
$494$	1.07701e10	−	6.21812e9i	0.180847	−	0.104412i
$495$	−5.32662e9	+	7.49194e9i	−0.0887219	+	0.124788i
$496$	−3.34571e9	+	5.79494e9i	−0.0552792	+	0.0957464i
$497$	−2.85249e10	+	7.83715e10i	−0.467518	+	1.28449i
$498$	1.19894e9	+	3.85078e9i	0.0194930	+	0.0626082i
$499$	−1.88053e10	−	1.57796e10i	−0.303305	−	0.254503i	0.478414	−	0.878135i	$-0.341212\pi$
$499$	−1.88053e10	−	1.57796e10i	−0.303305	−	0.254503i	−0.781718	+	0.623632i	$0.785656\pi$
$500$	−1.61995e10	+	1.93058e10i	−0.259192	+	0.308893i
$501$	−2.89774e10	−	2.67452e10i	−0.459948	−	0.424517i
$502$	7.33616e9	+	2.67014e9i	0.115519	+	0.0420455i
$503$	2.60618e10	+	1.50468e10i	0.407129	+	0.235056i	0.689555	−	0.724233i	$-0.257806\pi$
$503$	2.60618e10	+	1.50468e10i	0.407129	+	0.235056i	−0.282426	+	0.959289i	$0.591139\pi$
$504$	3.83009e10	−	3.07351e9i	0.593590	−	0.0476334i
$505$	−2.42176e10	−	4.19461e10i	−0.372362	−	0.644950i
$506$	−8.56297e9	+	1.50988e9i	−0.130624	+	0.0230325i
$507$	3.77076e10	+	4.95091e10i	0.570686	+	0.749296i
$508$	3.32996e8	−	1.21201e8i	0.00500016	−	0.00181991i
$509$	−6.41370e10	−	1.13091e10i	−0.955515	−	0.168483i	−0.325912	−	0.945400i	$-0.605671\pi$
$509$	−6.41370e10	−	1.13091e10i	−0.955515	−	0.168483i	−0.629603	+	0.776917i	$0.716783\pi$
$510$	−3.49029e10	+	5.43543e10i	−0.515918	+	0.803439i
$511$	3.05738e10	−	2.56545e10i	0.448401	−	0.376253i
$512$		−	3.03700e9i		−	0.0441942i
$513$	−7.87242e10	+	3.16181e10i	−1.13668	+	0.456526i
$514$	−7.01059e10			−1.00439
$515$	−7.41882e10	−	8.84141e10i	−1.05464	−	1.25688i
$516$	−3.00246e9	+	6.35250e10i	−0.0423524	+	0.896078i
$517$	−1.37795e9	+	7.81475e9i	−0.0192873	+	0.109384i
$518$	5.59008e10	+	1.53586e11i	0.776424	+	2.13321i
$519$	1.03021e10	+	8.04874e10i	0.141989	+	1.10932i
$520$	1.22915e9	+	6.97087e9i	0.0168110	+	0.0953397i
$521$	2.91089e10	−	1.68060e10i	0.395071	−	0.228094i	−0.289284	−	0.957243i	$-0.593417\pi$
$521$	2.91089e10	−	1.68060e10i	0.395071	−	0.228094i	0.684355	+	0.729149i	$0.260084\pi$
$522$	−4.73811e10	−	4.80675e10i	−0.638150	−	0.647395i
$523$	6.01584e10	−	1.04197e11i	0.804061	−	1.39268i	−0.112861	−	0.993611i	$-0.536002\pi$
$523$	6.01584e10	−	1.04197e11i	0.804061	−	1.39268i	0.916923	−	0.399064i	$-0.130665\pi$
$524$	−4.94261e9	+	1.35797e10i	−0.0655588	+	0.180121i
$525$	3.61901e10	+	8.15980e9i	0.476380	+	0.107409i
$526$	5.86603e7	+	4.92219e7i	0.000766305	+	0.000643006i
$527$	2.60685e10	−	3.10672e10i	0.337966	−	0.402773i
$528$	−5.76139e8	+	2.55528e9i	−0.00741295	+	0.0328777i
$529$	6.88808e10	+	2.50706e10i	0.879580	+	0.320141i
$530$	−6.42515e10	−	3.70956e10i	−0.814291	−	0.470131i
$531$	4.33627e10	+	1.19539e10i	0.545429	+	0.150360i
$532$	−4.13166e10	−	7.15624e10i	−0.515796	−	0.893384i
$533$	1.63822e10	−	2.88862e9i	0.202985	−	0.0357916i
$534$	5.43988e10	−	6.96282e9i	0.668997	−	0.0856289i
$535$	−6.31539e10	+	2.29861e10i	−0.770877	+	0.280576i
$536$	−6.35888e9	−	1.12124e9i	−0.0770409	−	0.0135844i
$537$	1.49004e10	+	7.04256e8i	0.179185	+	0.00846902i
$538$	6.69692e10	−	5.61939e10i	0.799367	−	0.670749i
$539$		−	2.09017e10i		−	0.247643i
$540$	−1.58573e9	−	4.82607e10i	−0.0186489	−	0.567569i
$541$	1.37460e11			1.60468			0.802340	−	0.596868i	$-0.203588\pi$
$541$	1.37460e11			1.60468			0.802340	+	0.596868i	$0.203588\pi$
$542$	−2.00971e10	−	2.39508e10i	−0.232882	−	0.277538i
$543$	−8.39357e10	−	5.38982e10i	−0.965489	−	0.619977i
$544$	−3.19628e9	+	1.81270e10i	−0.0364964	+	0.206981i
$545$	−2.63974e9	−	7.25262e9i	−0.0299209	−	0.0822070i
$546$	−2.03014e10	+	1.54621e10i	−0.228431	+	0.173980i
$547$	2.71788e9	+	1.54139e10i	0.0303586	+	0.172172i	0.996217	−	0.0868974i	$-0.0276952\pi$
$547$	2.71788e9	+	1.54139e10i	0.0303586	+	0.172172i	−0.965859	+	0.259069i	$0.916584\pi$
$548$	−4.65802e10	+	2.68931e10i	−0.516510	+	0.298207i
$549$	−1.50877e11	−	7.16804e10i	−1.66086	−	0.789062i
$550$	−1.26453e9	+	2.19024e9i	−0.0138191	+	0.0239354i
$551$	−4.96442e10	+	1.36396e11i	−0.538595	+	1.47978i
$552$	3.09777e10	−	3.35631e10i	0.333651	−	0.361498i
$553$	−1.15607e10	−	9.70055e9i	−0.123618	−	0.103728i
$554$	8.29426e10	−	9.88471e10i	0.880518	−	1.04936i
$555$	1.96110e11	−	6.10589e10i	2.06694	−	0.643543i
$556$	9.07097e9	+	3.30156e9i	0.0949193	+	0.0345478i
$557$	8.78769e10	+	5.07358e10i	0.912965	+	0.527101i	0.881384	−	0.472401i	$-0.156612\pi$
$557$	8.78769e10	+	5.07358e10i	0.912965	+	0.527101i	0.0315811	+	0.999501i	$0.489946\pi$
$558$	−2.85935e9	+	3.01810e10i	−0.0294938	+	0.311312i
$559$	−2.11184e10	−	3.65782e10i	−0.216279	−	0.374606i
$560$	4.63183e10	−	8.16716e9i	0.470978	−	0.0830461i
$561$	6.12810e9	−	1.46454e10i	0.0618692	−	0.147859i
$562$	−1.70385e10	+	6.20151e9i	−0.170799	+	0.0621659i
$563$	3.88073e9	+	6.84278e8i	0.0386260	+	0.00681081i	0.192928	−	0.981213i	$-0.438202\pi$
$563$	3.88073e9	+	6.84278e8i	0.0386260	+	0.00681081i	−0.154302	+	0.988024i	$0.549313\pi$
$564$	−1.91140e10	−	3.70422e10i	−0.188901	−	0.366083i
$565$	4.67651e10	−	3.92406e10i	0.458911	−	0.385072i
$566$		−	1.32762e11i		−	1.29363i
$567$	1.51997e11	−	8.48644e10i	1.47063	−	0.821095i
$568$	2.98655e10			0.286930
$569$	6.55995e10	+	7.81784e10i	0.625823	+	0.745826i	0.982060	−	0.188569i	$-0.0603850\pi$
$569$	6.55995e10	+	7.81784e10i	0.625823	+	0.745826i	−0.356237	+	0.934396i	$0.615941\pi$
$570$	−9.22823e10	+	4.76181e10i	−0.874216	+	0.451100i
$571$	−1.88156e10	+	1.06708e11i	−0.177000	+	1.00382i	0.758811	+	0.651311i	$0.225781\pi$
$571$	−1.88156e10	+	1.06708e11i	−0.177000	+	1.00382i	−0.935810	+	0.352504i	$0.885330\pi$
$572$	−5.95003e8	−	1.63476e9i	−0.00555821	−	0.0152711i
$573$	1.50392e11	+	6.29291e10i	1.39511	+	0.583758i
$574$	−1.91936e10	−	1.08852e11i	−0.176811	−	1.00274i
$575$	3.81903e10	−	2.20492e10i	0.349367	−	0.201707i
$576$	−5.72515e9	−	1.25118e10i	−0.0520112	−	0.113665i
$577$	−1.53465e10	+	2.65809e10i	−0.138454	+	0.239810i	−0.926912	−	0.375279i	$-0.877547\pi$
$577$	−1.53465e10	+	2.65809e10i	−0.138454	+	0.239810i	0.788457	+	0.615089i	$0.210880\pi$
$578$	1.11627e10	−	3.06691e10i	0.100013	−	0.274783i
$579$	−1.78476e9	−	5.73233e9i	−0.0158805	−	0.0510055i
$580$	−6.32875e10	−	5.31045e10i	−0.559250	−	0.469266i
$581$	−1.14402e10	+	1.36339e10i	−0.100399	+	0.119651i
$582$	−2.02425e10	−	1.86832e10i	−0.176430	−	0.162839i
$583$	1.71345e10	+	6.23643e9i	0.148319	+	0.0539836i
$584$	−1.23772e10	−	7.14600e9i	−0.106408	−	0.0614344i
$585$	1.82048e10	+	2.64013e10i	0.155440	+	0.225425i
$586$	2.27641e10	+	3.94286e10i	0.193046	+	0.334365i
$587$	1.44651e11	−	2.55058e10i	1.21834	−	0.214826i	0.472729	−	0.881208i	$-0.343269\pi$
$587$	1.44651e11	−	2.55058e10i	1.21834	−	0.214826i	0.745611	+	0.666381i	$0.232158\pi$
$588$	6.65243e10	+	8.73446e10i	0.556507	+	0.730679i
$589$	6.12648e10	−	2.22986e10i	0.509038	−	0.185275i
$590$	5.42214e10	+	9.56070e9i	0.447469	+	0.0789009i
$591$	4.34773e10	−	6.77072e10i	0.356380	−	0.554990i
$592$	4.48350e10	−	3.76210e10i	0.365032	−	0.306298i
$593$		−	6.91940e10i		−	0.559563i	−0.960064	−	0.279782i	$-0.909738\pi$
$593$		−	6.91940e10i		−	0.559563i	0.960064	−	0.279782i	$-0.0902621\pi$
$594$	2.44347e9	+	1.16133e10i	0.0196273	+	0.0932842i
$595$	−2.85057e11			−2.27438
$596$	5.98511e10	+	7.13277e10i	0.474337	+	0.565293i
$597$	3.57320e9	−	7.56004e10i	0.0281293	−	0.595151i
$598$	−5.26744e9	+	2.98732e10i	−0.0411903	+	0.233602i
$599$	−7.20305e10	−	1.97902e11i	−0.559511	−	1.53724i	−0.820350	−	0.571862i	$-0.806221\pi$
$599$	−7.20305e10	−	1.97902e11i	−0.559511	−	1.53724i	0.260838	−	0.965382i	$-0.416001\pi$
$600$	−1.68664e9	−	1.31773e10i	−0.0130142	−	0.101677i
$601$	2.08879e10	+	1.18461e11i	0.160102	+	0.907982i	0.953972	+	0.299895i	$0.0969517\pi$
$601$	2.08879e10	+	1.18461e11i	0.160102	+	0.907982i	−0.793870	+	0.608087i	$0.791937\pi$
$602$	−2.43045e11	+	1.40322e11i	−1.85055	+	1.06842i
$603$	−2.83108e10	+	7.36806e9i	−0.214133	+	0.0557294i
$604$	4.05771e8	−	7.02816e8i	0.00304883	−	0.00528073i
$605$	−5.10965e10	+	1.40386e11i	−0.381390	+	1.04786i
$606$	−6.09986e10	−	1.37534e10i	−0.452303	−	0.101981i
$607$	−9.53115e10	−	7.99759e10i	−0.702087	−	0.589121i	0.220280	−	0.975437i	$-0.429303\pi$
$607$	−9.53115e10	−	7.99759e10i	−0.702087	−	0.589121i	−0.922366	+	0.386316i	$0.873747\pi$
$608$	−1.90204e10	+	2.26676e10i	−0.139189	+	0.165879i
$609$	6.55111e10	−	2.90553e11i	0.476262	−	2.11230i
$610$	−1.92132e11	−	6.99305e10i	−1.38765	−	0.505065i
$611$	2.39746e10	+	1.38417e10i	0.172023	+	0.0993174i
$612$	2.10039e10	+	8.07047e10i	0.149725	+	0.575298i
$613$	5.49077e10	+	9.51030e10i	0.388859	+	0.673523i	0.992296	−	0.123887i	$-0.0395361\pi$
$613$	5.49077e10	+	9.51030e10i	0.388859	+	0.673523i	−0.603438	+	0.797410i	$0.706203\pi$
$614$	1.19749e11	−	2.11150e10i	0.842557	−	0.148566i
$615$	−1.37779e11	+	1.76352e10i	−0.963124	+	0.123276i
$616$	−1.08622e10	+	3.95353e9i	−0.0754390	+	0.0274576i
$617$	1.09270e11	+	1.92672e10i	0.753979	+	0.132947i	0.537411	−	0.843321i	$-0.319403\pi$
$617$	1.09270e11	+	1.92672e10i	0.753979	+	0.132947i	0.216568	+	0.976268i	$0.430514\pi$
$618$	−1.48837e11	−	7.03465e9i	−1.02037	−	0.0482268i
$619$	8.50284e10	−	7.13473e10i	0.579164	−	0.485976i	−0.305509	−	0.952189i	$-0.598827\pi$
$619$	8.50284e10	−	7.13473e10i	0.579164	−	0.485976i	0.884672	+	0.466213i	$0.154382\pi$
$620$			3.71084e10i			0.251134i
$621$	6.43502e10	−	1.96669e11i	0.432697	−	1.32242i
$622$	9.68076e10			0.646767
$623$	1.55565e11	+	1.85396e11i	1.03267	+	1.23069i
$624$	7.68940e9	+	4.93765e9i	0.0507171	+	0.0325673i
$625$	−3.19515e10	+	1.81206e11i	−0.209397	+	1.18755i
$626$	4.19925e10	+	1.15373e11i	0.273448	+	0.751292i
$627$	2.03036e10	−	1.54638e10i	0.131372	−	0.100057i
$628$	5.54141e9	+	3.14269e10i	0.0356272	+	0.202052i
$629$	−3.07202e11	+	1.77363e11i	−1.96255	+	1.13308i
$630$	1.75425e11	−	1.20963e11i	1.11360	−	0.767874i
$631$	−7.66099e10	+	1.32692e11i	−0.483245	+	0.837006i	−0.999815	−	0.0192397i	$-0.993875\pi$
$631$	−7.66099e10	+	1.32692e11i	−0.483245	+	0.837006i	0.516569	+	0.856245i	$0.327209\pi$
$632$	−1.84832e9	+	5.07823e9i	−0.0115854	+	0.0318305i
$633$	−1.63102e8	+	1.76714e8i	−0.00101588	+	0.00110067i
$634$	7.15655e10	+	6.00506e10i	0.442942	+	0.371673i
$635$	1.26321e9	−	1.50543e9i	0.00776925	−	0.00925903i
$636$	−9.14509e10	+	2.84732e10i	−0.558933	+	0.174024i
$637$	−6.85210e10	−	2.49396e10i	−0.416165	−	0.151472i
$638$	1.75844e10	+	1.01523e10i	0.106131	+	0.0612750i
$639$	1.23039e11	−	5.63004e10i	0.737971	−	0.337682i
$640$	−8.42109e9	−	1.45858e10i	−0.0501936	−	0.0869379i
$641$	−1.24077e11	+	2.18781e10i	−0.734950	+	0.129592i	−0.528581	−	0.848883i	$-0.677276\pi$
$641$	−1.24077e11	+	2.18781e10i	−0.734950	+	0.129592i	−0.206369	+	0.978474i	$0.566165\pi$
$642$	−3.34913e10	+	8.00399e10i	−0.197148	+	0.471158i
$643$	3.23763e10	−	1.17840e10i	0.189402	−	0.0689366i	−0.245578	−	0.969377i	$-0.578978\pi$
$643$	3.23763e10	−	1.17840e10i	0.189402	−	0.0689366i	0.434980	+	0.900440i	$0.356756\pi$
$644$	1.98494e11	+	3.49998e10i	1.15399	+	0.203480i
$645$	1.61724e11	+	3.13416e11i	0.934407	+	1.81085i
$646$	1.37384e11	−	1.15279e11i	0.788870	−	0.661941i
$647$		−	8.19366e10i		−	0.467585i	−0.972286	−	0.233793i	$-0.924886\pi$
$647$		−	8.19366e10i		−	0.467585i	0.972286	−	0.233793i	$-0.0751137\pi$
$648$	−4.71726e10	−	4.07530e10i	−0.267541	−	0.231132i
$649$	−1.35317e10			−0.0762734
$650$	5.67133e9	+	6.75883e9i	0.0317711	+	0.0378633i
$651$	−1.18888e11	+	6.13470e10i	−0.661935	+	0.341562i
$652$	−1.76482e10	+	1.00088e11i	−0.0976584	+	0.553848i
$653$	2.54459e10	+	6.99121e10i	0.139948	+	0.384503i	0.989790	−	0.142534i	$-0.0455251\pi$
$653$	2.54459e10	+	6.99121e10i	0.139948	+	0.384503i	−0.849842	+	0.527037i	$0.823303\pi$
$654$	−9.19181e9	−	3.84615e9i	−0.0502447	−	0.0210240i
$655$	1.39164e10	+	7.89241e10i	0.0756072	+	0.428790i
$656$	−3.42779e10	+	1.97903e10i	−0.185097	+	0.106866i
$657$	−6.44626e10	−	6.10719e9i	−0.345976	−	0.0327778i
$658$	9.19720e10	−	1.59300e11i	0.490628	−	0.849792i
$659$	2.56927e8	−	7.05901e8i	0.00136229	−	0.00374285i	−0.939010	−	0.343891i	$-0.888255\pi$
$659$	2.56927e8	−	7.05901e8i	0.00136229	−	0.00374285i	0.940372	+	0.340148i	$0.110477\pi$
$660$	4.31833e9	+	1.38697e10i	0.0227583	+	0.0730957i
$661$	−1.83035e11	−	1.53585e11i	−0.958802	−	0.804530i	0.0219558	−	0.999759i	$-0.493011\pi$
$661$	−1.83035e11	−	1.53585e11i	−0.958802	−	0.804530i	−0.980758	+	0.195229i	$0.937455\pi$
$662$	6.91772e10	−	8.24422e10i	0.360189	−	0.429257i
$663$	−4.06993e10	−	3.75642e10i	−0.210636	−	0.194410i
$664$	5.98894e9	+	2.17980e9i	0.0308090	+	0.0112136i
$665$	−3.96861e11	−	2.29128e11i	−2.02933	−	1.17163i
$666$	1.13790e11	−	2.39510e11i	0.578370	−	1.21738i
$667$	−1.77022e11	−	3.06612e11i	−0.894385	−	1.54912i
$668$	−6.13679e10	+	1.08208e10i	−0.308202	+	0.0543443i
$669$	−1.79220e11	−	2.35311e11i	−0.894710	−	1.17473i
$670$	−3.36487e10	+	1.22471e10i	−0.166982	+	0.0607764i
$671$	4.94878e10	+	8.72604e9i	0.244123	+	0.0430454i
$672$	3.28085e10	−	5.10926e10i	0.160882	−	0.250542i
$673$	−2.08496e11	+	1.74949e11i	−1.01634	+	0.852808i	−0.989163	−	0.146822i	$-0.953095\pi$
$673$	−2.08496e11	+	1.74949e11i	−1.01634	+	0.852808i	−0.0271745	+	0.999631i	$0.508651\pi$
$674$			2.32610e11i			1.12717i
$675$	−3.17896e10	−	5.11080e10i	−0.153133	−	0.246192i
$676$	9.83444e10			0.470937
$677$	1.33683e11	+	1.59318e11i	0.636389	+	0.758419i	0.983795	−	0.179296i	$-0.0573819\pi$
$677$	1.33683e11	+	1.59318e11i	0.636389	+	0.758419i	−0.347406	+	0.937715i	$0.612937\pi$
$678$	3.72086e9	−	7.87246e10i	0.0176086	−	0.372556i
$679$	2.11090e10	−	1.19715e11i	0.0993089	−	0.563209i
$680$	3.49124e10	+	9.59211e10i	0.163284	+	0.448620i
$681$	1.89014e10	+	1.47672e11i	0.0878831	+	0.686608i
$682$	−1.58370e9	−	8.98163e9i	−0.00732043	−	0.0415162i
$683$	−1.05924e11	+	6.11550e10i	−0.486754	+	0.281028i	−0.723227	−	0.690610i	$-0.757342\pi$
$683$	−1.05924e11	+	6.11550e10i	−0.486754	+	0.281028i	0.236473	+	0.971638i	$0.424009\pi$
$684$	−3.56283e10	+	1.29241e11i	−0.162768	+	0.590442i
$685$	−1.49140e11	+	2.58318e11i	−0.677379	+	1.17325i
$686$	−7.55016e10	+	2.07439e11i	−0.340926	+	0.936685i
$687$	2.69693e11	+	6.08078e10i	1.21072	+	0.272981i
$688$	7.69854e10	+	6.45984e10i	0.343601	+	0.288315i
$689$	4.08892e10	−	4.87299e10i	0.181440	−	0.216231i
$690$	5.57112e10	−	2.47089e11i	0.245780	−	1.09008i
$691$	3.16234e11	+	1.15100e11i	1.38706	+	0.504849i	0.924312	−	0.381639i	$-0.124640\pi$
$691$	3.16234e11	+	1.15100e11i	1.38706	+	0.504849i	0.462751	+	0.886488i	$0.346862\pi$
$692$	1.11048e11	+	6.41138e10i	0.484270	+	0.279593i
$693$	−3.72970e10	+	3.67644e10i	−0.161712	+	0.159402i
$694$	−5.99864e8	−	1.03900e9i	−0.00258592	−	0.00447895i
$695$	5.27197e10	−	9.29590e9i	0.225961	−	0.0398430i
$696$	−1.05794e11	+	1.35412e10i	−0.450843	+	0.0577061i
$697$	2.25423e11	−	8.20474e10i	0.955142	−	0.347643i
$698$	1.51779e11	+	2.67627e10i	0.639424	+	0.112748i
$699$	−3.35083e11	−	1.58374e10i	−1.40360	−	0.0663400i
$700$	4.49094e10	−	3.76834e10i	0.187044	−	0.156949i
$701$		−	1.43165e11i		−	0.592877i	−0.955052	−	0.296438i	$-0.904201\pi$
$701$		−	1.43165e11i		−	0.592877i	0.955052	−	0.296438i	$-0.0957990\pi$
$702$	4.09867e10	+	5.84647e9i	0.168770	+	0.0240739i
$703$	−5.70256e11			−2.33479
$704$	2.66071e9	+	3.17091e9i	0.0108320	+	0.0129090i
$705$	−1.94510e11	−	1.24902e11i	−0.787382	−	0.505607i
$706$	−3.67225e10	+	2.08264e11i	−0.147813	+	0.838292i
$707$	−9.43771e10	−	2.59299e11i	−0.377737	−	1.03782i
$708$	5.65466e10	−	4.30676e10i	0.225047	−	0.171403i
$709$	6.31309e10	+	3.58033e11i	0.249837	+	1.41690i	0.808985	+	0.587829i	$0.200017\pi$
$709$	6.31309e10	+	3.58033e11i	0.249837	+	1.41690i	−0.559148	+	0.829068i	$0.688872\pi$
$710$	1.43434e11	−	8.28119e10i	0.564443	−	0.325881i
$711$	1.95845e9	+	2.44055e10i	0.00766363	+	0.0955013i
$712$	4.33324e10	−	7.50539e10i	0.168614	−	0.292047i
$713$	−5.43898e10	+	1.49435e11i	−0.210455	+	0.578221i
$714$	−2.49597e11	+	2.70428e11i	−0.960387	+	1.04054i
$715$	−7.39052e9	−	6.20138e9i	−0.0282781	−	0.0237282i
$716$	1.51522e10	−	1.80577e10i	0.0576531	−	0.0687083i
$717$	4.72823e11	−	1.47213e11i	1.78905	−	0.557020i
$718$	−2.13637e11	−	7.77575e10i	−0.803857	−	0.292580i
$719$	4.30933e11	+	2.48799e11i	1.61248	+	0.930966i	0.988793	+	0.149291i	$0.0476991\pi$
$719$	4.30933e11	+	2.48799e11i	1.61248	+	0.930966i	0.623686	+	0.781675i	$0.285634\pi$
$720$	−6.21891e10	−	4.42152e10i	−0.231411	−	0.164529i
$721$	−3.28770e11	−	5.69446e11i	−1.21661	−	2.10723i
$722$	9.47010e10	−	1.66983e10i	0.348503	−	0.0614504i
$723$	−6.03583e10	+	1.44249e11i	−0.220894	+	0.527908i
$724$	−1.48125e11	+	5.39129e10i	−0.539104	+	0.196218i
$725$	−1.01414e11	−	1.78820e10i	−0.367067	−	0.0647238i
$726$	8.84419e10	+	1.71397e11i	0.318355	+	0.616961i
$727$	3.80302e10	−	3.19111e10i	0.136142	−	0.114236i	−0.572174	−	0.820132i	$-0.693900\pi$
$727$	3.80302e10	−	3.19111e10i	0.136142	−	0.114236i	0.708316	+	0.705896i	$0.249455\pi$
$728$			4.03264e10i			0.143570i
$729$	−2.71166e11	−	7.89665e10i	−0.960117	−	0.279597i
$730$	−7.92586e10			−0.279097
$731$	−3.91518e11	−	4.66593e11i	−1.37114	−	1.63406i
$732$	−2.34574e11	+	1.21041e11i	−0.817025	+	0.421589i
$733$	−9.00309e10	+	5.10591e11i	−0.311872	+	1.76871i	0.277379	+	0.960761i	$0.410534\pi$
$733$	−9.00309e10	+	5.10591e11i	−0.311872	+	1.76871i	−0.589250	+	0.807951i	$0.700577\pi$
$734$	5.79133e8	+	1.59115e9i	0.00199523	+	0.00548186i
$735$	5.61687e11	+	2.35028e11i	1.92462	+	0.805324i
$736$	−1.25332e10	−	7.10794e10i	−0.0427121	−	0.242233i
$737$	7.62158e9	−	4.40032e9i	0.0258330	−	0.0149147i
$738$	−1.03910e11	+	1.46150e11i	−0.350292	+	0.492690i
$739$	3.44230e10	−	5.96224e10i	0.115417	−	0.199909i	−0.802529	−	0.596613i	$-0.796513\pi$
$739$	3.44230e10	−	5.96224e10i	0.115417	−	0.199909i	0.917946	+	0.396704i	$0.129846\pi$
$740$	1.11012e11	−	3.05002e11i	0.370204	−	1.01713i
$741$	−2.64683e10	−	8.50115e10i	−0.0877917	−	0.281971i
$742$	−3.23788e11	−	2.71690e11i	−1.06818	−	0.896311i
$743$	3.59436e11	−	4.28359e11i	1.17941	−	1.40557i	0.284886	−	0.958561i	$-0.408044\pi$
$743$	3.59436e11	−	4.28359e11i	1.17941	−	1.40557i	0.894529	−	0.447011i	$-0.147511\pi$
$744$	3.52041e10	+	3.24923e10i	0.114895	+	0.106045i
$745$	4.85225e11	+	1.76608e11i	1.57514	+	0.573303i
$746$	−1.18282e11	−	6.82901e10i	−0.381912	−	0.220497i
$747$	2.87823e10	−	2.30968e9i	0.0924365	−	0.00741769i
$748$	−1.25438e10	−	2.17266e10i	−0.0400704	−	0.0694040i
$749$	−3.77069e11	+	6.64874e10i	−1.19810	+	0.211257i
$750$	1.09325e11	+	1.43540e11i	0.345520	+	0.453659i
$751$	1.86899e11	−	6.80257e10i	0.587553	−	0.213852i	−0.0310996	−	0.999516i	$-0.509901\pi$
$751$	1.86899e11	−	6.80257e10i	0.587553	−	0.213852i	0.618653	+	0.785664i	$0.287679\pi$
$752$	−6.48686e10	−	1.14381e10i	−0.202844	−	0.0357670i
$753$	3.02010e10	−	4.70320e10i	0.0939380	−	0.146290i
$754$	5.42634e10	−	4.55324e10i	0.167889	−	0.140875i
$755$		−	4.50054e9i		−	0.0138509i
$756$

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.27231 - 8.66680i) q^{2} +(-71.9819 + 37.1430i) q^{3} +(-22.2270 + 126.055i) q^{4} +(242.781 + 667.036i) q^{5} +(845.386 + 353.737i) q^{6} +(702.244 + 3982.62i) q^{7} +(1254.14 - 724.077i) q^{8} +(3801.79 - 5347.25i) q^{9} +O(q^{10})\)	\(q+(-7.27231 - 8.66680i) q^{2} +(-71.9819 + 37.1430i) q^{3} +(-22.2270 + 126.055i) q^{4} +(242.781 + 667.036i) q^{5} +(845.386 + 353.737i) q^{6} +(702.244 + 3982.62i) q^{7} +(1254.14 - 724.077i) q^{8} +(3801.79 - 5347.25i) q^{9} +(4015.49 - 6955.03i) q^{10} +(-675.075 + 1854.75i) q^{11} +(-3082.14 - 9899.28i) q^{12} +(5274.86 + 4426.14i) q^{13} +(29409.7 - 35049.1i) q^{14} +(-42251.6 - 38996.9i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(85996.5 + 49650.1i) q^{17} +(-73991.4 + 5937.54i) q^{18} +(79817.2 + 138247. i) q^{19} +(-89479.7 + 15777.7i) q^{20} +(-198476. - 260593. i) q^{21} +(20984.1 - 7637.60i) q^{22} +(-383459. - 67614.1i) q^{23} +(-63380.9 + 98703.0i) q^{24} +(-86757.9 + 72798.6i) q^{25} -77904.4i q^{26} +(-75046.7 + 526116. i) q^{27} -517640. q^{28} +(584464. + 696538. i) q^{29} +(-30711.5 + 649784. i) q^{30} +(70920.0 - 402207. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-20298.0 - 158583. i) q^{33} +(-195086. - 1.10639e6i) q^{34} +(-2.48606e6 + 1.43533e6i) q^{35} +(589548. + 598089. i) q^{36} +(-1.78613e6 + 3.09367e6i) q^{37} +(617708. - 1.69714e6i) q^{38} +(-544095. - 122677. i) q^{39} +(787467. + 660763. i) q^{40} +(1.55285e6 - 1.85062e6i) q^{41} +(-815135. + 3.61526e6i) q^{42} +(-5.76395e6 - 2.09791e6i) q^{43} +(-218797. - 126322. i) q^{44} +(4.48981e6 + 1.23772e6i) q^{45} +(2.20263e6 + 3.81507e6i) q^{46} +(3.95927e6 - 698125. i) q^{47} +(1.31636e6 - 168489. i) q^{48} +(-9.95099e6 + 3.62187e6i) q^{49} +(1.26186e6 + 222500. i) q^{50} +(-8.03435e6 - 379737. i) q^{51} +(-675183. + 566545. i) q^{52} -9.23813e6i q^{53} +(5.10550e6 - 3.17566e6i) q^{54} -1.40108e6 q^{55} +(3.76444e6 + 4.48628e6i) q^{56} +(-1.08803e7 - 6.98666e6i) q^{57} +(1.78635e6 - 1.01309e7i) q^{58} +(2.34478e6 + 6.44224e6i) q^{59} +(5.85489e6 - 4.45926e6i) q^{60} +(-4.42096e6 - 2.50725e7i) q^{61} +(-4.00160e6 + 2.31033e6i) q^{62} +(2.39659e7 + 1.13860e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-1.67175e6 + 4.59311e6i) q^{65} +(-1.22679e6 + 1.32918e6i) q^{66} +(-3.41561e6 - 2.86604e6i) q^{67} +(-8.17010e6 + 9.73675e6i) q^{68} +(3.01135e7 - 9.37583e6i) q^{69} +(3.05191e7 + 1.11080e7i) q^{70} +(1.78601e7 + 1.03116e7i) q^{71} +(896145. - 9.45899e6i) q^{72} +(-4.93456e6 - 8.54690e6i) q^{73} +(3.98015e7 - 7.01808e6i) q^{74} +(3.54104e6 - 8.46263e6i) q^{75} +(-1.92009e7 + 6.98857e6i) q^{76} +(-7.86085e6 - 1.38608e6i) q^{77} +(2.89361e6 + 5.60771e6i) q^{78} +(-2.85868e6 + 2.39872e6i) q^{79} -1.16301e7i q^{80} +(-1.41395e7 - 4.06583e7i) q^{81} -2.73318e7 q^{82} +(2.82890e6 + 3.37135e6i) q^{83} +(3.72607e7 - 1.92267e7i) q^{84} +(-1.22401e7 + 6.94168e7i) q^{85} +(2.37351e7 + 6.52116e7i) q^{86} +(-6.79424e7 - 2.84293e7i) q^{87} +(496347. + 2.81492e6i) q^{88} +(5.18273e7 - 2.99225e7i) q^{89} +(-2.19243e7 - 4.79134e7i) q^{90} +(-1.39234e7 + 2.41160e7i) q^{91} +(1.70463e7 - 4.68342e7i) q^{92} +(9.83425e6 + 3.15858e7i) q^{93} +(-3.48435e7 - 2.92372e7i) q^{94} +(-7.28379e7 + 8.68048e7i) q^{95} +(-1.10333e7 - 1.01834e7i) q^{96} +(-2.82465e7 - 1.02809e7i) q^{97} +(1.03757e8 + 5.99040e7i) q^{98} +(7.35134e6 + 1.06612e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

L-functions

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