LMFDB - Embedded newform 29.9.c.a.12.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.15
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.6258 + 13.6258i) q^{2} +(70.4012 + 70.4012i) q^{3} +115.327i q^{4} +729.288i q^{5} +1918.55i q^{6} -3525.11 q^{7} +(1916.79 - 1916.79i) q^{8} +3351.66i q^{9} +O(q^{10})$	\(q+(13.6258 + 13.6258i) q^{2} +(70.4012 + 70.4012i) q^{3} +115.327i q^{4} +729.288i q^{5} +1918.55i q^{6} -3525.11 q^{7} +(1916.79 - 1916.79i) q^{8} +3351.66i q^{9} +(-9937.16 + 9937.16i) q^{10} +(17337.9 + 17337.9i) q^{11} +(-8119.14 + 8119.14i) q^{12} -16494.4i q^{13} +(-48032.6 - 48032.6i) q^{14} +(-51342.8 + 51342.8i) q^{15} +81759.4 q^{16} +(-68442.0 - 68442.0i) q^{17} +(-45669.2 + 45669.2i) q^{18} +(137533. + 137533. i) q^{19} -84106.4 q^{20} +(-248172. - 248172. i) q^{21} +472486. i q^{22} -357099. q^{23} +269889. q^{24} -141236. q^{25} +(224750. - 224750. i) q^{26} +(225941. - 225941. i) q^{27} -406540. i q^{28} +(469340. + 529119. i) q^{29} -1.39918e6 q^{30} +(448252. + 448252. i) q^{31} +(623342. + 623342. i) q^{32} +2.44121e6i q^{33} -1.86516e6i q^{34} -2.57082e6i q^{35} -386536. q^{36} +(2.04945e6 - 2.04945e6i) q^{37} +3.74801e6i q^{38} +(1.16123e6 - 1.16123e6i) q^{39} +(1.39789e6 + 1.39789e6i) q^{40} +(1.04687e6 - 1.04687e6i) q^{41} -6.76311e6i q^{42} +(939515. + 939515. i) q^{43} +(-1.99952e6 + 1.99952e6i) q^{44} -2.44433e6 q^{45} +(-4.86577e6 - 4.86577e6i) q^{46} +(2.42167e6 - 2.42167e6i) q^{47} +(5.75596e6 + 5.75596e6i) q^{48} +6.66162e6 q^{49} +(-1.92446e6 - 1.92446e6i) q^{50} -9.63680e6i q^{51} +1.90225e6 q^{52} -9.91331e6 q^{53} +6.15728e6 q^{54} +(-1.26443e7 + 1.26443e7i) q^{55} +(-6.75690e6 + 6.75690e6i) q^{56} +1.93650e7i q^{57} +(-814535. + 1.36048e7i) q^{58} +382704. q^{59} +(-5.92120e6 - 5.92120e6i) q^{60} +(-1.67264e6 - 1.67264e6i) q^{61} +1.22156e7i q^{62} -1.18150e7i q^{63} -3.94330e6i q^{64} +1.20292e7 q^{65} +(-3.32636e7 + 3.32636e7i) q^{66} +1.74200e7i q^{67} +(7.89319e6 - 7.89319e6i) q^{68} +(-2.51402e7 - 2.51402e7i) q^{69} +(3.50296e7 - 3.50296e7i) q^{70} -3.31202e7i q^{71} +(6.42444e6 + 6.42444e6i) q^{72} +(2.13687e6 - 2.13687e6i) q^{73} +5.58508e7 q^{74} +(-9.94320e6 - 9.94320e6i) q^{75} +(-1.58612e7 + 1.58612e7i) q^{76} +(-6.11179e7 - 6.11179e7i) q^{77} +3.16454e7 q^{78} +(-1.68475e7 - 1.68475e7i) q^{79} +5.96262e7i q^{80} +5.38033e7 q^{81} +2.85290e7 q^{82} -5.94394e7 q^{83} +(2.86209e7 - 2.86209e7i) q^{84} +(4.99139e7 - 4.99139e7i) q^{85} +2.56034e7i q^{86} +(-4.20850e6 + 7.02927e7i) q^{87} +6.64661e7 q^{88} +(-3.70551e7 - 3.70551e7i) q^{89} +(-3.33060e7 - 3.33060e7i) q^{90} +5.81447e7i q^{91} -4.11831e7i q^{92} +6.31149e7i q^{93} +6.59947e7 q^{94} +(-1.00301e8 + 1.00301e8i) q^{95} +8.77680e7i q^{96} +(3.89686e7 - 3.89686e7i) q^{97} +(9.07702e7 + 9.07702e7i) q^{98} +(-5.81107e7 + 5.81107e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	13.6258	+	13.6258i	0.851615	+	0.851615i	0.990332	−	0.138717i	$-0.0442979\pi$
$2$	13.6258	+	13.6258i	0.851615	+	0.851615i	−0.138717	+	0.990332i	$0.544298\pi$
$3$	70.4012	+	70.4012i	0.869151	+	0.869151i	0.992378	−	0.123228i	$-0.0393245\pi$
$3$	70.4012	+	70.4012i	0.869151	+	0.869151i	−0.123228	+	0.992378i	$0.539325\pi$
$4$			115.327i			0.450495i
$5$			729.288i			1.16686i	0.812163	+	0.583431i	$0.198290\pi$
$5$			729.288i			1.16686i	−0.812163	+	0.583431i	$0.801710\pi$
$6$			1918.55i			1.48036i
$7$	−3525.11			−1.46819			−0.734093	−	0.679049i	$-0.762392\pi$
$7$	−3525.11			−1.46819			−0.734093	+	0.679049i	$0.762392\pi$
$8$	1916.79	−	1916.79i	0.467966	−	0.467966i
$9$			3351.66i			0.510846i
$10$	−9937.16	+	9937.16i	−0.993716	+	0.993716i
$11$	17337.9	+	17337.9i	1.18420	+	1.18420i	0.978646	+	0.205553i	$0.0658993\pi$
$11$	17337.9	+	17337.9i	1.18420	+	1.18420i	0.205553	+	0.978646i	$0.434101\pi$
$12$	−8119.14	+	8119.14i	−0.391548	+	0.391548i
$13$		−	16494.4i		−	0.577516i	−0.957402	−	0.288758i	$-0.906758\pi$
$13$		−	16494.4i		−	0.577516i	0.957402	−	0.288758i	$-0.0932423\pi$
$14$	−48032.6	−	48032.6i	−1.25033	−	1.25033i
$15$	−51342.8	+	51342.8i	−1.01418	+	1.01418i
$16$	81759.4			1.24755
$17$	−68442.0	−	68442.0i	−0.819459	−	0.819459i	0.166571	−	0.986029i	$-0.446731\pi$
$17$	−68442.0	−	68442.0i	−0.819459	−	0.819459i	−0.986029	+	0.166571i	$0.946731\pi$
$18$	−45669.2	+	45669.2i	−0.435044	+	0.435044i
$19$	137533.	+	137533.i	1.05534	+	1.05534i	0.998376	+	0.0569645i	$0.0181422\pi$
$19$	137533.	+	137533.i	1.05534	+	1.05534i	0.0569645	+	0.998376i	$0.481858\pi$
$20$	−84106.4			−0.525665
$21$	−248172.	−	248172.i	−1.27607	−	1.27607i
$22$			472486.i			2.01696i
$23$	−357099.			−1.27608			−0.638039	−	0.770004i	$-0.720254\pi$
$23$	−357099.			−1.27608			−0.638039	+	0.770004i	$0.720254\pi$
$24$	269889.			0.813467
$25$	−141236.			−0.361565
$26$	224750.	−	224750.i	0.491821	−	0.491821i
$27$	225941.	−	225941.i	0.425148	−	0.425148i
$28$		−	406540.i		−	0.661410i
$29$	469340.	+	529119.i	0.663583	+	0.748102i
$29$	469340.	+	529119.i	0.663583	+	0.748102i
$30$	−1.39918e6			−1.72738
$31$	448252.	+	448252.i	0.485372	+	0.485372i	0.906842	−	0.421470i	$-0.138486\pi$
$31$	448252.	+	448252.i	0.485372	+	0.485372i	−0.421470	+	0.906842i	$0.638486\pi$
$32$	623342.	+	623342.i	0.594465	+	0.594465i
$33$			2.44121e6i			2.05850i
$34$		−	1.86516e6i		−	1.39573i
$35$		−	2.57082e6i		−	1.71317i
$36$	−386536.			−0.230134
$37$	2.04945e6	−	2.04945e6i	1.09353	−	1.09353i	0.0983781	−	0.995149i	$-0.468635\pi$
$37$	2.04945e6	−	2.04945e6i	1.09353	−	1.09353i	0.995149	−	0.0983781i	$-0.0313654\pi$
$38$			3.74801e6i			1.79749i
$39$	1.16123e6	−	1.16123e6i	0.501948	−	0.501948i
$40$	1.39789e6	+	1.39789e6i	0.546052	+	0.546052i
$41$	1.04687e6	−	1.04687e6i	0.370474	−	0.370474i	−0.497176	−	0.867650i	$-0.665630\pi$
$41$	1.04687e6	−	1.04687e6i	0.370474	−	0.370474i	0.867650	+	0.497176i	$0.165630\pi$
$42$		−	6.76311e6i		−	2.17345i
$43$	939515.	+	939515.i	0.274808	+	0.274808i	0.831032	−	0.556224i	$-0.187750\pi$
$43$	939515.	+	939515.i	0.274808	+	0.274808i	−0.556224	+	0.831032i	$0.687750\pi$
$44$	−1.99952e6	+	1.99952e6i	−0.533476	+	0.533476i
$45$	−2.44433e6			−0.596087
$46$	−4.86577e6	−	4.86577e6i	−1.08673	−	1.08673i
$47$	2.42167e6	−	2.42167e6i	0.496277	−	0.496277i	−0.414000	−	0.910277i	$-0.635869\pi$
$47$	2.42167e6	−	2.42167e6i	0.496277	−	0.496277i	0.910277	+	0.414000i	$0.135869\pi$
$48$	5.75596e6	+	5.75596e6i	1.08431	+	1.08431i
$49$	6.66162e6			1.15557
$50$	−1.92446e6	−	1.92446e6i	−0.307914	−	0.307914i
$51$		−	9.63680e6i		−	1.42447i
$52$	1.90225e6			0.260168
$53$	−9.91331e6			−1.25636			−0.628182	−	0.778067i	$-0.716200\pi$
$53$	−9.91331e6			−1.25636			−0.628182	+	0.778067i	$0.716200\pi$
$54$	6.15728e6			0.724125
$55$	−1.26443e7	+	1.26443e7i	−1.38180	+	1.38180i
$56$	−6.75690e6	+	6.75690e6i	−0.687061	+	0.687061i
$57$			1.93650e7i			1.83450i
$58$	−814535.	+	1.36048e7i	−0.0719777	+	1.20221i
$59$	382704.			0.0315831			0.0157916	−	0.999875i	$-0.494973\pi$
$59$	382704.			0.0315831			0.0157916	+	0.999875i	$0.494973\pi$
$60$	−5.92120e6	−	5.92120e6i	−0.456882	−	0.456882i
$61$	−1.67264e6	−	1.67264e6i	−0.120804	−	0.120804i	0.644120	−	0.764924i	$-0.277224\pi$
$61$	−1.67264e6	−	1.67264e6i	−0.120804	−	0.120804i	−0.764924	+	0.644120i	$0.777224\pi$
$62$			1.22156e7i			0.826701i
$63$		−	1.18150e7i		−	0.750017i
$64$		−	3.94330e6i		−	0.235039i
$65$	1.20292e7			0.673881
$66$	−3.32636e7	+	3.32636e7i	−1.75304	+	1.75304i
$67$			1.74200e7i			0.864466i	0.901762	+	0.432233i	$0.142274\pi$
$67$			1.74200e7i			0.864466i	−0.901762	+	0.432233i	$0.857726\pi$
$68$	7.89319e6	−	7.89319e6i	0.369162	−	0.369162i
$69$	−2.51402e7	−	2.51402e7i	−1.10910	−	1.10910i
$70$	3.50296e7	−	3.50296e7i	1.45896	−	1.45896i
$71$		−	3.31202e7i		−	1.30334i	−0.758501	−	0.651672i	$-0.774068\pi$
$71$		−	3.31202e7i		−	1.30334i	0.758501	−	0.651672i	$-0.225932\pi$
$72$	6.42444e6	+	6.42444e6i	0.239059	+	0.239059i
$73$	2.13687e6	−	2.13687e6i	0.0752464	−	0.0752464i	−0.668482	−	0.743728i	$-0.733056\pi$
$73$	2.13687e6	−	2.13687e6i	0.0752464	−	0.0752464i	0.743728	+	0.668482i	$0.233056\pi$
$74$	5.58508e7			1.86253
$75$	−9.94320e6	−	9.94320e6i	−0.314254	−	0.314254i
$76$	−1.58612e7	+	1.58612e7i	−0.475426	+	0.475426i
$77$	−6.11179e7	−	6.11179e7i	−1.73862	−	1.73862i
$78$	3.16454e7			0.854933
$79$	−1.68475e7	−	1.68475e7i	−0.432540	−	0.432540i	0.456951	−	0.889492i	$-0.348941\pi$
$79$	−1.68475e7	−	1.68475e7i	−0.432540	−	0.432540i	−0.889492	+	0.456951i	$0.848941\pi$
$80$			5.96262e7i			1.45572i
$81$	5.38033e7			1.24988
$82$	2.85290e7			0.631003
$83$	−5.94394e7			−1.25245			−0.626227	−	0.779641i	$-0.715402\pi$
$83$	−5.94394e7			−1.25245			−0.626227	+	0.779641i	$0.715402\pi$
$84$	2.86209e7	−	2.86209e7i	0.574865	−	0.574865i
$85$	4.99139e7	−	4.99139e7i	0.956194	−	0.956194i
$86$			2.56034e7i			0.468062i
$87$	−4.20850e6	+	7.02927e7i	−0.0734598	+	1.22697i
$88$	6.64661e7			1.10833
$89$	−3.70551e7	−	3.70551e7i	−0.590593	−	0.590593i	0.347199	−	0.937792i	$-0.387133\pi$
$89$	−3.70551e7	−	3.70551e7i	−0.590593	−	0.590593i	−0.937792	+	0.347199i	$0.887133\pi$
$90$	−3.33060e7	−	3.33060e7i	−0.507636	−	0.507636i
$91$			5.81447e7i			0.847900i
$92$		−	4.11831e7i		−	0.574867i
$93$			6.31149e7i			0.843724i
$94$	6.59947e7			0.845274
$95$	−1.00301e8	+	1.00301e8i	−1.23144	+	1.23144i
$96$			8.77680e7i			1.03336i
$97$	3.89686e7	−	3.89686e7i	0.440177	−	0.440177i	−0.451894	−	0.892071i	$-0.649252\pi$
$97$	3.89686e7	−	3.89686e7i	0.440177	−	0.440177i	0.892071	+	0.451894i	$0.149252\pi$
$98$	9.07702e7	+	9.07702e7i	0.984099	+	0.984099i
$99$	−5.81107e7	+	5.81107e7i	−0.604944	+	0.604944i
$100$		−	1.62883e7i		−	0.162883i
$101$	−9.61281e7	−	9.61281e7i	−0.923772	−	0.923772i	0.0735212	−	0.997294i	$-0.476576\pi$
$101$	−9.61281e7	−	9.61281e7i	−0.923772	−	0.923772i	−0.997294	+	0.0735212i	$0.976576\pi$
$102$	1.31309e8	−	1.31309e8i	1.21310	−	1.21310i
$103$	−1.10984e8			−0.986074			−0.493037	−	0.870008i	$-0.664113\pi$
$103$	−1.10984e8			−0.986074			−0.493037	+	0.870008i	$0.664113\pi$
$104$	−3.16164e7	−	3.16164e7i	−0.270258	−	0.270258i
$105$	1.80989e8	−	1.80989e8i	1.48900	−	1.48900i
$106$	−1.35077e8	−	1.35077e8i	−1.06994	−	1.06994i
$107$	1.43988e8			1.09848			0.549238	−	0.835666i	$-0.314918\pi$
$107$	1.43988e8			1.09848			0.549238	+	0.835666i	$0.314918\pi$
$108$	2.60571e7	+	2.60571e7i	0.191527	+	0.191527i
$109$		−	7.79809e7i		−	0.552436i	−0.961095	−	0.276218i	$-0.910919\pi$
$109$		−	7.79809e7i		−	0.552436i	0.961095	−	0.276218i	$-0.0890812\pi$
$110$	−3.44578e8			−2.35352
$111$	2.88567e8			1.90088
$112$	−2.88211e8			−1.83163
$113$	−7.91779e7	+	7.91779e7i	−0.485613	+	0.485613i	−0.906919	−	0.421306i	$-0.861572\pi$
$113$	−7.91779e7	+	7.91779e7i	−0.485613	+	0.485613i	0.421306	+	0.906919i	$0.361572\pi$
$114$	−2.63864e8	+	2.63864e8i	−1.56229	+	1.56229i
$115$		−	2.60428e8i		−	1.48901i
$116$	−6.10215e7	+	5.41274e7i	−0.337016	+	0.298941i
$117$	5.52838e7			0.295022
$118$	5.21466e6	+	5.21466e6i	0.0268966	+	0.0268966i
$119$	2.41266e8	+	2.41266e8i	1.20312	+	1.20312i
$120$			1.96827e8i			0.949203i
$121$			3.86844e8i			1.80466i
$122$		−	4.55821e7i		−	0.205757i
$123$	1.47402e8			0.643996
$124$	−5.16954e7	+	5.16954e7i	−0.218658	+	0.218658i
$125$			1.81876e8i			0.744965i
$126$	1.60989e8	−	1.60989e8i	0.638726	−	0.638726i
$127$	−1.28111e8	−	1.28111e8i	−0.492461	−	0.492461i	0.416620	−	0.909081i	$-0.363215\pi$
$127$	−1.28111e8	−	1.28111e8i	−0.492461	−	0.492461i	−0.909081	+	0.416620i	$0.863215\pi$
$128$	2.13306e8	−	2.13306e8i	0.794628	−	0.794628i
$129$			1.32286e8i			0.477700i
$130$	1.63908e8	+	1.63908e8i	0.573887	+	0.573887i
$131$	−5.28340e7	+	5.28340e7i	−0.179402	+	0.179402i	−0.791095	−	0.611693i	$-0.790489\pi$
$131$	−5.28340e7	+	5.28340e7i	−0.179402	+	0.179402i	0.611693	+	0.791095i	$0.290489\pi$
$132$	−2.81537e8			−0.927342
$133$	−4.84820e8	−	4.84820e8i	−1.54944	−	1.54944i
$134$	−2.37361e8	+	2.37361e8i	−0.736192	+	0.736192i
$135$	1.64776e8	+	1.64776e8i	0.496089	+	0.496089i
$136$	−2.62378e8			−0.766958
$137$	−1.40080e8	−	1.40080e8i	−0.397643	−	0.397643i	0.479758	−	0.877401i	$-0.340725\pi$
$137$	−1.40080e8	−	1.40080e8i	−0.397643	−	0.397643i	−0.877401	+	0.479758i	$0.840725\pi$
$138$		−	6.85113e8i		−	1.88906i
$139$	1.93969e8			0.519604			0.259802	−	0.965662i	$-0.416343\pi$
$139$	1.93969e8			0.519604			0.259802	+	0.965662i	$0.416343\pi$
$140$	2.96485e8			0.771774
$141$	3.40978e8			0.862679
$142$	4.51290e8	−	4.51290e8i	1.10995	−	1.10995i
$143$	2.85978e8	−	2.85978e8i	0.683894	−	0.683894i
$144$			2.74030e8i			0.637306i
$145$	−3.85880e8	+	3.42284e8i	−0.872932	+	0.774309i
$146$	5.82332e7			0.128162
$147$	4.68986e8	+	4.68986e8i	1.00436	+	1.00436i
$148$	2.36356e8	+	2.36356e8i	0.492629	+	0.492629i
$149$		−	1.28739e8i		−	0.261195i	−0.991435	−	0.130598i	$-0.958310\pi$
$149$		−	1.28739e8i		−	0.261195i	0.991435	−	0.130598i	$-0.0416896\pi$
$150$		−	2.70969e8i		−	0.535247i
$151$			5.49491e8i			1.05695i	0.848950	+	0.528473i	$0.177235\pi$
$151$			5.49491e8i			1.05695i	−0.848950	+	0.528473i	$0.822765\pi$
$152$	5.27244e8			0.987728
$153$	2.29395e8	−	2.29395e8i	0.418617	−	0.418617i
$154$		−	1.66557e9i		−	2.96128i
$155$	−3.26905e8	+	3.26905e8i	−0.566362	+	0.566362i
$156$	1.33921e8	+	1.33921e8i	0.226125	+	0.226125i
$157$	−2.75221e8	+	2.75221e8i	−0.452985	+	0.452985i	−0.896344	−	0.443359i	$-0.853787\pi$
$157$	−2.75221e8	+	2.75221e8i	−0.452985	+	0.452985i	0.443359	+	0.896344i	$0.353787\pi$
$158$		−	4.59122e8i		−	0.736715i
$159$	−6.97909e8	−	6.97909e8i	−1.09197	−	1.09197i
$160$	−4.54596e8	+	4.54596e8i	−0.693658	+	0.693658i
$161$	1.25881e9			1.87352
$162$	7.33115e8	+	7.33115e8i	1.06442	+	1.06442i
$163$	−2.51043e8	+	2.51043e8i	−0.355630	+	0.355630i	−0.862199	−	0.506569i	$-0.830913\pi$
$163$	−2.51043e8	+	2.51043e8i	−0.355630	+	0.355630i	0.506569	+	0.862199i	$0.330913\pi$
$164$	1.20732e8	+	1.20732e8i	0.166897	+	0.166897i
$165$	−1.78035e9			−2.40198
$166$	−8.09911e8	−	8.09911e8i	−1.06661	−	1.06661i
$167$		−	1.08510e9i		−	1.39510i	−0.716538	−	0.697548i	$-0.754274\pi$
$167$		−	1.08510e9i		−	1.39510i	0.716538	−	0.697548i	$-0.245726\pi$
$168$	−9.51388e8			−1.19432
$169$	5.43665e8			0.666476
$170$	1.36024e9			1.62862
$171$	−4.60964e8	+	4.60964e8i	−0.539117	+	0.539117i
$172$	−1.08351e8	+	1.08351e8i	−0.123800	+	0.123800i
$173$			6.30173e8i			0.703518i	0.936091	+	0.351759i	$0.114416\pi$
$173$			6.30173e8i			0.703518i	−0.936091	+	0.351759i	$0.885584\pi$
$174$	−1.01514e9	+	9.00452e8i	−1.10746	+	0.982344i
$175$	4.97874e8			0.530844
$176$	1.41753e9	+	1.41753e9i	1.47735	+	1.47735i
$177$	2.69428e7	+	2.69428e7i	0.0274505	+	0.0274505i
$178$		−	1.00981e9i		−	1.00592i
$179$			3.59196e8i			0.349880i	0.984579	+	0.174940i	$0.0559731\pi$
$179$			3.59196e8i			0.349880i	−0.984579	+	0.174940i	$0.944027\pi$
$180$		−	2.81896e8i		−	0.268534i
$181$	−2.00120e8			−0.186456			−0.0932278	−	0.995645i	$-0.529718\pi$
$181$	−2.00120e8			−0.186456			−0.0932278	+	0.995645i	$0.529718\pi$
$182$	−7.92270e8	+	7.92270e8i	−0.722084	+	0.722084i
$183$		−	2.35511e8i		−	0.209994i
$184$	−6.84484e8	+	6.84484e8i	−0.597162	+	0.597162i
$185$	1.49464e9	+	1.49464e9i	1.27599	+	1.27599i
$186$	−8.59994e8	+	8.59994e8i	−0.718528	+	0.718528i
$187$		−	2.37328e9i		−	1.94080i
$188$	2.79284e8	+	2.79284e8i	0.223570	+	0.223570i
$189$	−7.96468e8	+	7.96468e8i	−0.624197	+	0.624197i
$190$	−2.73338e9			−2.09742
$191$	5.09797e7	+	5.09797e7i	0.0383057	+	0.0383057i	0.726000	−	0.687694i	$-0.241377\pi$
$191$	5.09797e7	+	5.09797e7i	0.0383057	+	0.0383057i	−0.687694	+	0.726000i	$0.741377\pi$
$192$	2.77613e8	−	2.77613e8i	0.204285	−	0.204285i
$193$	−5.56576e8	−	5.56576e8i	−0.401139	−	0.401139i	0.477495	−	0.878634i	$-0.341545\pi$
$193$	−5.56576e8	−	5.56576e8i	−0.401139	−	0.401139i	−0.878634	+	0.477495i	$0.841545\pi$
$194$	1.06196e9			0.749722
$195$	8.46870e8	+	8.46870e8i	0.585704	+	0.585704i
$196$			7.68263e8i			0.520578i
$197$	−3.03997e6			−0.00201839			−0.00100919	−	0.999999i	$-0.500321\pi$
$197$	−3.03997e6			−0.00201839			−0.00100919	+	0.999999i	$0.500321\pi$
$198$	−1.58361e9			−1.03036
$199$	1.49781e9			0.955089			0.477544	−	0.878608i	$-0.341527\pi$
$199$	1.49781e9			0.955089			0.477544	+	0.878608i	$0.341527\pi$
$200$	−2.70720e8	+	2.70720e8i	−0.169200	+	0.169200i
$201$	−1.22639e9	+	1.22639e9i	−0.751351	+	0.751351i
$202$		−	2.61965e9i		−	1.57340i
$203$	−1.65448e9	−	1.86520e9i	−0.974263	−	1.09835i
$204$	1.11138e9			0.641715
$205$	7.63471e8	+	7.63471e8i	0.432292	+	0.432292i
$206$	−1.51224e9	−	1.51224e9i	−0.839755	−	0.839755i
$207$		−	1.19688e9i		−	0.651880i
$208$		−	1.34857e9i		−	0.720479i
$209$			4.76906e9i			2.49947i
$210$	4.93225e9			2.53611
$211$	1.61137e9	−	1.61137e9i	0.812953	−	0.812953i	−0.172123	−	0.985076i	$-0.555063\pi$
$211$	1.61137e9	−	1.61137e9i	0.812953	−	0.812953i	0.985076	+	0.172123i	$0.0550626\pi$
$212$		−	1.14327e9i		−	0.565985i
$213$	2.33170e9	−	2.33170e9i	1.13280	−	1.13280i
$214$	1.96195e9	+	1.96195e9i	0.935479	+	0.935479i
$215$	−6.85177e8	+	6.85177e8i	−0.320663	+	0.320663i
$216$		−	8.66164e8i		−	0.397910i
$217$	−1.58014e9	−	1.58014e9i	−0.712617	−	0.712617i
$218$	1.06255e9	−	1.06255e9i	0.470463	−	0.470463i
$219$	3.00876e8			0.130801
$220$	−1.45823e9	−	1.45823e9i	−0.622492	−	0.622492i
$221$	−1.12891e9	+	1.12891e9i	−0.473250	+	0.473250i
$222$	3.93197e9	+	3.93197e9i	1.61882	+	1.61882i
$223$	−7.09439e8			−0.286877			−0.143438	−	0.989659i	$-0.545816\pi$
$223$	−7.09439e8			−0.286877			−0.143438	+	0.989659i	$0.545816\pi$
$224$	−2.19735e9	−	2.19735e9i	−0.872785	−	0.872785i
$225$		−	4.73376e8i		−	0.184704i
$226$	−2.15773e9			−0.827110
$227$	−2.84198e9			−1.07033			−0.535164	−	0.844748i	$-0.679750\pi$
$227$	−2.84198e9			−1.07033			−0.535164	+	0.844748i	$0.679750\pi$
$228$	−2.23330e9			−0.826434
$229$	−1.14002e8	+	1.14002e8i	−0.0414545	+	0.0414545i	−0.727530	−	0.686076i	$-0.759332\pi$
$229$	−1.14002e8	+	1.14002e8i	−0.0414545	+	0.0414545i	0.686076	+	0.727530i	$0.259332\pi$
$230$	3.54855e9	−	3.54855e9i	1.26806	−	1.26806i
$231$		−	8.60555e9i		−	3.02225i
$232$	1.91384e9	+	1.14583e8i	0.660621	+	0.0395521i
$233$	2.49716e9			0.847272			0.423636	−	0.905833i	$-0.360754\pi$
$233$	2.49716e9			0.847272			0.423636	+	0.905833i	$0.360754\pi$
$234$	7.53287e8	+	7.53287e8i	0.251245	+	0.251245i
$235$	1.76610e9	+	1.76610e9i	0.579086	+	0.579086i
$236$			4.41360e7i			0.0142280i
$237$		−	2.37217e9i		−	0.751886i
$238$			6.57490e9i			2.04918i
$239$	4.64315e9			1.42305			0.711527	−	0.702659i	$-0.248004\pi$
$239$	4.64315e9			1.42305			0.711527	+	0.702659i	$0.248004\pi$
$240$	−4.19775e9	+	4.19775e9i	−1.26524	+	1.26524i
$241$			5.88296e9i			1.74393i	0.489572	+	0.871963i	$0.337153\pi$
$241$			5.88296e9i			1.74393i	−0.489572	+	0.871963i	$0.662847\pi$
$242$	−5.27107e9	+	5.27107e9i	−1.53687	+	1.53687i
$243$	2.30542e9	+	2.30542e9i	0.661188	+	0.661188i
$244$	1.92900e8	−	1.92900e8i	0.0544217	−	0.0544217i
$245$			4.85824e9i			1.34839i
$246$	2.00848e9	+	2.00848e9i	0.548437	+	0.548437i
$247$	2.26853e9	−	2.26853e9i	0.609476	−	0.609476i
$248$	1.71841e9			0.454276
$249$	−4.18460e9	−	4.18460e9i	−1.08857	−	1.08857i
$250$	−2.47822e9	+	2.47822e9i	−0.634423	+	0.634423i
$251$	−4.56637e9	−	4.56637e9i	−1.15047	−	1.15047i	−0.986458	−	0.164014i	$-0.947556\pi$
$251$	−4.56637e9	−	4.56637e9i	−1.15047	−	1.15047i	−0.164014	−	0.986458i	$-0.552444\pi$
$252$	1.36258e9			0.337879
$253$	−6.19133e9	−	6.19133e9i	−1.51113	−	1.51113i
$254$		−	3.49124e9i		−	0.838775i
$255$	7.02800e9			1.66215
$256$	4.80347e9			1.11839
$257$	−6.56545e9			−1.50498			−0.752492	−	0.658602i	$-0.771148\pi$
$257$	−6.56545e9			−1.50498			−0.752492	+	0.658602i	$0.771148\pi$
$258$	−1.80251e9	+	1.80251e9i	−0.406816	+	0.406816i
$259$	−7.22453e9	+	7.22453e9i	−1.60550	+	1.60550i
$260$			1.38729e9i			0.303580i
$261$	−1.77343e9	+	1.57307e9i	−0.382165	+	0.338989i
$262$	−1.43981e9			−0.305563
$263$	6.00994e9	+	6.00994e9i	1.25617	+	1.25617i	0.952908	+	0.303258i	$0.0980745\pi$
$263$	6.00994e9	+	6.00994e9i	1.25617	+	1.25617i	0.303258	+	0.952908i	$0.401925\pi$
$264$	4.67929e9	+	4.67929e9i	0.963307	+	0.963307i
$265$		−	7.22966e9i		−	1.46600i
$266$		−	1.32121e10i		−	2.63904i
$267$		−	5.21745e9i		−	1.02663i
$268$	−2.00899e9			−0.389438
$269$	−3.04771e9	+	3.04771e9i	−0.582056	+	0.582056i	−0.935468	−	0.353412i	$-0.885021\pi$
$269$	−3.04771e9	+	3.04771e9i	−0.582056	+	0.582056i	0.353412	+	0.935468i	$0.385021\pi$
$270$			4.49043e9i			0.844953i
$271$	6.35669e9	−	6.35669e9i	1.17857	−	1.17857i	0.198455	−	0.980110i	$-0.436408\pi$
$271$	6.35669e9	−	6.35669e9i	1.17857	−	1.17857i	0.980110	−	0.198455i	$-0.0635924\pi$
$272$	−5.59578e9	−	5.59578e9i	−1.02231	−	1.02231i
$273$	−4.09346e9	+	4.09346e9i	−0.736953	+	0.736953i
$274$		−	3.81741e9i		−	0.677278i
$275$	−2.44873e9	−	2.44873e9i	−0.428165	−	0.428165i
$276$	2.89934e9	−	2.89934e9i	0.499646	−	0.499646i
$277$	5.36164e9			0.910707			0.455354	−	0.890311i	$-0.349513\pi$
$277$	5.36164e9			0.910707			0.455354	+	0.890311i	$0.349513\pi$
$278$	2.64299e9	+	2.64299e9i	0.442503	+	0.442503i
$279$	−1.50239e9	+	1.50239e9i	−0.247951	+	0.247951i
$280$	−4.92773e9	−	4.92773e9i	−0.801705	−	0.801705i
$281$	2.16148e9			0.346678			0.173339	−	0.984862i	$-0.444544\pi$
$281$	2.16148e9			0.346678			0.173339	+	0.984862i	$0.444544\pi$
$282$	4.64610e9	+	4.64610e9i	0.734670	+	0.734670i
$283$			7.67546e9i			1.19663i	0.801262	+	0.598313i	$0.204162\pi$
$283$			7.67546e9i			1.19663i	−0.801262	+	0.598313i	$0.795838\pi$
$284$	3.81964e9			0.587150
$285$	−1.41227e10			−2.14061
$286$	7.79338e9			1.16483
$287$	−3.69034e9	+	3.69034e9i	−0.543925	+	0.543925i
$288$	−2.08923e9	+	2.08923e9i	−0.303680	+	0.303680i
$289$			2.39286e9i			0.343025i
$290$	−9.92184e9	−	5.94031e8i	−1.40281	−	0.0839880i
$291$	5.48687e9			0.765160
$292$	2.46438e8	+	2.46438e8i	0.0338981	+	0.0338981i
$293$	2.57101e9	+	2.57101e9i	0.348845	+	0.348845i	0.859679	−	0.510834i	$-0.170663\pi$
$293$	2.57101e9	+	2.57101e9i	0.348845	+	0.348845i	−0.510834	+	0.859679i	$0.670663\pi$
$294$			1.27807e10i			1.71066i
$295$			2.79101e8i			0.0368531i
$296$		−	7.85672e9i		−	1.02347i
$297$	7.83467e9			1.00692
$298$	1.75418e9	−	1.75418e9i	0.222438	−	0.222438i
$299$			5.89014e9i			0.736955i
$300$	1.14672e9	−	1.14672e9i	0.141570	−	0.141570i
$301$	−3.31190e9	−	3.31190e9i	−0.403470	−	0.403470i
$302$	−7.48728e9	+	7.48728e9i	−0.900111	+	0.900111i
$303$		−	1.35351e10i		−	1.60580i
$304$	1.12446e10	+	1.12446e10i	1.31659	+	1.31659i
$305$	1.21983e9	−	1.21983e9i	0.140962	−	0.140962i
$306$	6.25138e9			0.713001
$307$	6.19041e9	+	6.19041e9i	0.696893	+	0.696893i	0.963739	−	0.266847i	$-0.0859817\pi$
$307$	6.19041e9	+	6.19041e9i	0.696893	+	0.696893i	−0.266847	+	0.963739i	$0.585982\pi$
$308$	7.04853e9	−	7.04853e9i	0.783242	−	0.783242i
$309$	−7.81337e9	−	7.81337e9i	−0.857047	−	0.857047i
$310$	−8.90870e9			−0.964645
$311$	1.13786e9	+	1.13786e9i	0.121632	+	0.121632i	0.765303	−	0.643671i	$-0.222589\pi$
$311$	1.13786e9	+	1.13786e9i	0.121632	+	0.121632i	−0.643671	+	0.765303i	$0.722589\pi$
$312$		−	4.45166e9i		−	0.469790i
$313$	−7.66761e9			−0.798882			−0.399441	−	0.916759i	$-0.630796\pi$
$313$	−7.66761e9			−0.798882			−0.399441	+	0.916759i	$0.630796\pi$
$314$	−7.50024e9			−0.771537
$315$	8.61653e9			0.875166
$316$	1.94297e9	−	1.94297e9i	0.194857	−	0.194857i
$317$	7.03787e9	−	7.03787e9i	0.696954	−	0.696954i	−0.266798	−	0.963752i	$-0.585966\pi$
$317$	7.03787e9	−	7.03787e9i	0.696954	−	0.696954i	0.963752	+	0.266798i	$0.0859658\pi$
$318$		−	1.90192e10i		−	1.85987i
$319$	−1.03644e9	+	1.73111e10i	−0.100087	+	1.67172i
$320$	2.87581e9			0.274258
$321$	1.01369e10	+	1.01369e10i	0.954742	+	0.954742i
$322$	1.71524e10	+	1.71524e10i	1.59552	+	1.59552i
$323$		−	1.88261e10i		−	1.72962i
$324$			6.20496e9i			0.563066i
$325$			2.32961e9i			0.208809i
$326$	−6.84135e9			−0.605719
$327$	5.48995e9	−	5.48995e9i	0.480150	−	0.480150i
$328$		−	4.01327e9i		−	0.346739i
$329$	−8.53668e9	+	8.53668e9i	−0.728627	+	0.728627i
$330$	−2.42587e10	−	2.42587e10i	−2.04556	−	2.04556i
$331$	1.38768e10	−	1.38768e10i	1.15605	−	1.15605i	0.170734	−	0.985317i	$-0.445386\pi$
$331$	1.38768e10	−	1.38768e10i	1.15605	−	1.15605i	0.985317	−	0.170734i	$-0.0546137\pi$
$332$		−	6.85495e9i		−	0.564224i
$333$	6.86905e9	+	6.86905e9i	0.558624	+	0.558624i
$334$	1.47854e10	−	1.47854e10i	1.18808	−	1.18808i
$335$	−1.27042e10			−1.00871
$336$	−2.02904e10	−	2.02904e10i	−1.59197	−	1.59197i
$337$	1.21883e10	−	1.21883e10i	0.944982	−	0.944982i	−0.0535813	−	0.998563i	$-0.517064\pi$
$337$	1.21883e10	−	1.21883e10i	0.944982	−	0.944982i	0.998563	+	0.0535813i	$0.0170636\pi$
$338$	7.40788e9	+	7.40788e9i	0.567580	+	0.567580i
$339$	−1.11484e10			−0.844142
$340$	5.75641e9	+	5.75641e9i	0.430761	+	0.430761i
$341$			1.55434e10i			1.14956i
$342$	−1.25621e10			−0.918240
$343$	−3.16139e9			−0.228403
$344$	3.60171e9			0.257202
$345$	1.83345e10	−	1.83345e10i	1.29417	−	1.29417i
$346$	−8.58663e9	+	8.58663e9i	−0.599126	+	0.599126i
$347$			2.02951e10i			1.39982i	0.714230	+	0.699911i	$0.246777\pi$
$347$			2.02951e10i			1.39982i	−0.714230	+	0.699911i	$0.753223\pi$
$348$	−8.10663e9	−	4.85352e8i	−0.552743	−	0.0330933i
$349$	−1.91346e10			−1.28979			−0.644894	−	0.764272i	$-0.723098\pi$
$349$	−1.91346e10			−1.28979			−0.644894	+	0.764272i	$0.723098\pi$
$350$	6.78394e9	+	6.78394e9i	0.452075	+	0.452075i
$351$	−3.72677e9	−	3.72677e9i	−0.245530	−	0.245530i
$352$			2.16148e10i			1.40793i
$353$		−	4.34782e9i		−	0.280010i	−0.990151	−	0.140005i	$-0.955288\pi$
$353$		−	4.34782e9i		−	0.280010i	0.990151	−	0.140005i	$-0.0447118\pi$
$354$			7.34237e8i			0.0467545i
$355$	2.41542e10			1.52082
$356$	4.27345e9	−	4.27345e9i	0.266059	−	0.266059i
$357$			3.39708e10i			2.09138i
$358$	−4.89434e9	+	4.89434e9i	−0.297963	+	0.297963i
$359$	−5.10242e9	−	5.10242e9i	−0.307184	−	0.307184i	0.536632	−	0.843816i	$-0.319696\pi$
$359$	−5.10242e9	−	5.10242e9i	−0.307184	−	0.307184i	−0.843816	+	0.536632i	$0.819696\pi$
$360$	−4.68526e9	+	4.68526e9i	−0.278949	+	0.278949i
$361$			2.08471e10i			1.22749i
$362$	−2.72680e9	−	2.72680e9i	−0.158788	−	0.158788i
$363$	−2.72343e10	+	2.72343e10i	−1.56852	+	1.56852i
$364$	−6.70564e9			−0.381975
$365$	1.55839e9	+	1.55839e9i	0.0878021	+	0.0878021i
$366$	3.20904e9	−	3.20904e9i	0.178834	−	0.178834i
$367$	−1.24919e10	−	1.24919e10i	−0.688594	−	0.688594i	0.273327	−	0.961921i	$-0.411876\pi$
$367$	−1.24919e10	−	1.24919e10i	−0.688594	−	0.688594i	−0.961921	+	0.273327i	$0.911876\pi$
$368$	−2.91962e10			−1.59197
$369$	3.50876e9	+	3.50876e9i	0.189255	+	0.189255i
$370$			4.07313e10i			2.17331i
$371$	3.49455e10			1.84457
$372$	−7.27884e9			−0.380093
$373$	−2.85813e10			−1.47654			−0.738272	−	0.674503i	$-0.764358\pi$
$373$	−2.85813e10			−1.47654			−0.738272	+	0.674503i	$0.764358\pi$
$374$	3.23379e10	−	3.23379e10i	1.65282	−	1.65282i
$375$	−1.28043e10	+	1.28043e10i	−0.647487	+	0.647487i
$376$		−	9.28368e9i		−	0.464482i
$377$	8.72751e9	−	7.74149e9i	0.432041	−	0.383230i
$378$	−2.17051e10			−1.06315
$379$	−6.56796e9	−	6.56796e9i	−0.318327	−	0.318327i	0.529797	−	0.848124i	$-0.322268\pi$
$379$	−6.56796e9	−	6.56796e9i	−0.318327	−	0.318327i	−0.848124	+	0.529797i	$0.822268\pi$
$380$	−1.15674e10	−	1.15674e10i	−0.554756	−	0.554756i
$381$		−	1.80384e10i		−	0.856046i
$382$			1.38928e9i			0.0652434i
$383$			3.01489e10i			1.40113i	0.713591	+	0.700563i	$0.247068\pi$
$383$			3.01489e10i			1.40113i	−0.713591	+	0.700563i	$0.752932\pi$
$384$	3.00340e10			1.38130
$385$	4.45726e10	−	4.45726e10i	2.02873	−	2.02873i
$386$		−	1.51676e10i		−	0.683232i
$387$	−3.14894e9	+	3.14894e9i	−0.140385	+	0.140385i
$388$	4.49412e9	+	4.49412e9i	0.198298	+	0.198298i
$389$	−1.53639e10	+	1.53639e10i	−0.670969	+	0.670969i	−0.957939	−	0.286971i	$-0.907352\pi$
$389$	−1.53639e10	+	1.53639e10i	−0.670969	+	0.670969i	0.286971	+	0.957939i	$0.407352\pi$
$390$			2.30786e10i			0.997588i
$391$	2.44406e10	+	2.44406e10i	1.04569	+	1.04569i
$392$	1.27689e10	−	1.27689e10i	0.540767	−	0.540767i
$393$	−7.43915e9			−0.311855
$394$	−4.14222e7	−	4.14222e7i	−0.00171889	−	0.00171889i
$395$	1.22867e10	−	1.22867e10i	0.504715	−	0.504715i
$396$	−6.70171e9	−	6.70171e9i	−0.272524	−	0.272524i
$397$	−3.59745e10			−1.44821			−0.724107	−	0.689687i	$-0.757748\pi$
$397$	−3.59745e10			−1.44821			−0.724107	+	0.689687i	$0.757748\pi$
$398$	2.04089e10	+	2.04089e10i	0.813368	+	0.813368i
$399$		−	6.82638e10i		−	2.69339i
$400$	−1.15474e10			−0.451070
$401$	−4.34014e10			−1.67852			−0.839260	−	0.543731i	$-0.817011\pi$
$401$	−4.34014e10			−1.67852			−0.839260	+	0.543731i	$0.817011\pi$
$402$	−3.34211e10			−1.27972
$403$	7.39365e9	−	7.39365e9i	0.280310	−	0.280310i
$404$	1.10861e10	−	1.10861e10i	0.416155	−	0.416155i
$405$			3.92381e10i			1.45844i
$406$	2.87133e9	−	4.79586e10i	0.105677	−	1.76507i
$407$	7.10660e10			2.58991
$408$	−1.84717e10	−	1.84717e10i	−0.666602	−	0.666602i
$409$	2.36800e10	+	2.36800e10i	0.846229	+	0.846229i	0.989660	−	0.143432i	$-0.0458137\pi$
$409$	2.36800e10	+	2.36800e10i	0.846229	+	0.846229i	−0.143432	+	0.989660i	$0.545814\pi$
$410$			2.08059e10i			0.736292i
$411$		−	1.97236e10i		−	0.691224i
$412$		−	1.27994e10i		−	0.444222i
$413$	−1.34907e9			−0.0463699
$414$	1.63084e10	−	1.63084e10i	0.555151	−	0.555151i
$415$		−	4.33484e10i		−	1.46144i
$416$	1.02817e10	−	1.02817e10i	0.343313	−	0.343313i
$417$	1.36556e10	+	1.36556e10i	0.451615	+	0.451615i
$418$	−6.49824e10	+	6.49824e10i	−2.12858	+	2.12858i
$419$		−	5.20091e10i		−	1.68742i	−0.536800	−	0.843710i	$-0.680367\pi$
$419$		−	5.20091e10i		−	1.68742i	0.536800	−	0.843710i	$-0.319633\pi$
$420$	2.08729e10	+	2.08729e10i	0.670788	+	0.670788i
$421$	−5.49583e9	+	5.49583e9i	−0.174946	+	0.174946i	−0.789149	−	0.614202i	$-0.789478\pi$
$421$	−5.49583e9	+	5.49583e9i	−0.174946	+	0.174946i	0.614202	+	0.789149i	$0.289478\pi$
$422$	4.39125e10			1.38464
$423$	8.11664e9	+	8.11664e9i	0.253521	+	0.253521i
$424$	−1.90017e10	+	1.90017e10i	−0.587936	+	0.587936i
$425$	9.66649e9	+	9.66649e9i	0.296287	+	0.296287i
$426$	6.35427e10			1.92942
$427$	5.89623e9	+	5.89623e9i	0.177363	+	0.177363i
$428$			1.66056e10i			0.494858i
$429$	4.02664e10			1.18881
$430$	−1.86722e10			−0.546163
$431$	−9.63948e8			−0.0279347			−0.0139674	−	0.999902i	$-0.504446\pi$
$431$	−9.63948e8			−0.0279347			−0.0139674	+	0.999902i	$0.504446\pi$
$432$	1.84728e10	−	1.84728e10i	0.530393	−	0.530393i
$433$	−3.82678e9	+	3.82678e9i	−0.108863	+	0.108863i	−0.759440	−	0.650577i	$-0.774527\pi$
$433$	−3.82678e9	+	3.82678e9i	−0.108863	+	0.108863i	0.650577	+	0.759440i	$0.274527\pi$
$434$		−	4.30614e10i		−	1.21375i
$435$	−5.12636e10	−	3.06921e9i	−1.43170	−	0.0857174i
$436$	8.99328e9			0.248870
$437$	−4.91129e10	−	4.91129e10i	−1.34670	−	1.34670i
$438$	4.09969e9	+	4.09969e9i	0.111392	+	0.111392i
$439$			2.48032e10i			0.667804i	0.942608	+	0.333902i	$0.108365\pi$
$439$			2.48032e10i			0.667804i	−0.942608	+	0.333902i	$0.891635\pi$
$440$			4.84729e10i			1.29327i
$441$			2.23275e10i			0.590318i
$442$	−3.07647e10			−0.806054
$443$	−2.06562e10	+	2.06562e10i	−0.536334	+	0.536334i	−0.922450	−	0.386116i	$-0.873816\pi$
$443$	−2.06562e10	+	2.06562e10i	−0.536334	+	0.536334i	0.386116	+	0.922450i	$0.373816\pi$
$444$			3.32795e10i			0.856337i
$445$	2.70239e10	−	2.70239e10i	0.689140	−	0.689140i
$446$	−9.66670e9	−	9.66670e9i	−0.244309	−	0.244309i
$447$	9.06339e9	−	9.06339e9i	0.227018	−	0.227018i
$448$			1.39006e10i			0.345081i
$449$	−1.90292e10	−	1.90292e10i	−0.468203	−	0.468203i	0.433129	−	0.901332i	$-0.357409\pi$
$449$	−1.90292e10	−	1.90292e10i	−0.468203	−	0.468203i	−0.901332	+	0.433129i	$0.857409\pi$
$450$	6.45015e9	−	6.45015e9i	0.157297	−	0.157297i
$451$	3.63010e10			0.877431
$452$	−9.13133e9	−	9.13133e9i	−0.218766	−	0.218766i
$453$	−3.86849e10	+	3.86849e10i	−0.918646	+	0.918646i
$454$	−3.87243e10	−	3.87243e10i	−0.911507	−	0.911507i
$455$	−4.24043e10			−0.989382
$456$	3.71186e10	+	3.71186e10i	0.858485	+	0.858485i
$457$			1.34813e10i			0.309077i	0.987987	+	0.154539i	$0.0493891\pi$
$457$			1.34813e10i			0.309077i	−0.987987	+	0.154539i	$0.950611\pi$
$458$	−3.10675e9			−0.0706065
$459$	−3.09277e10			−0.696783
$460$	3.00343e10			0.670790
$461$	−5.18998e10	+	5.18998e10i	−1.14911	+	1.14911i	−0.162383	+	0.986728i	$0.551918\pi$
$461$	−5.18998e10	+	5.18998e10i	−1.14911	+	1.14911i	−0.986728	+	0.162383i	$0.948082\pi$
$462$	1.17258e11	−	1.17258e11i	2.57379	−	2.57379i
$463$			2.41499e10i			0.525523i	0.964861	+	0.262761i	$0.0846332\pi$
$463$			2.41499e10i			0.525523i	−0.964861	+	0.262761i	$0.915367\pi$
$464$	3.83729e10	+	4.32604e10i	0.827853	+	0.933295i
$465$	−4.60290e10			−0.984508
$466$	3.40259e10	+	3.40259e10i	0.721549	+	0.721549i
$467$	−5.85814e10	−	5.85814e10i	−1.23166	−	1.23166i	−0.963324	−	0.268341i	$-0.913525\pi$
$467$	−5.85814e10	−	5.85814e10i	−1.23166	−	1.23166i	−0.268341	−	0.963324i	$-0.586475\pi$
$468$			6.37570e9i			0.132906i
$469$		−	6.14073e10i		−	1.26920i
$470$			4.81291e10i			0.986317i
$471$	−3.87518e10			−0.787424
$472$	7.33563e8	−	7.33563e8i	0.0147798	−	0.0147798i
$473$			3.25784e10i			0.650856i
$474$	3.23228e10	−	3.23228e10i	0.640317	−	0.640317i
$475$	−1.94246e10	−	1.94246e10i	−0.381574	−	0.381574i
$476$	−2.78244e10	+	2.78244e10i	−0.541998	+	0.541998i
$477$		−	3.32261e10i		−	0.641809i
$478$	6.32668e10	+	6.32668e10i	1.21189	+	1.21189i
$479$	8.21492e9	−	8.21492e9i	0.156049	−	0.156049i	−0.624764	−	0.780813i	$-0.714805\pi$
$479$	8.21492e9	−	8.21492e9i	0.156049	−	0.156049i	0.780813	+	0.624764i	$0.214805\pi$
$480$	−6.40082e10			−1.20579
$481$	−3.38044e10	−	3.38044e10i	−0.631529	−	0.631529i
$482$	−8.01603e10	+	8.01603e10i	−1.48515	+	1.48515i
$483$	8.86221e10	+	8.86221e10i	1.62837	+	1.62837i
$484$	−4.46134e10			−0.812988
$485$	2.84193e10	+	2.84193e10i	0.513625	+	0.513625i
$486$			6.28265e10i			1.12615i
$487$	−2.78936e10			−0.495894			−0.247947	−	0.968774i	$-0.579756\pi$
$487$	−2.78936e10			−0.495894			−0.247947	+	0.968774i	$0.579756\pi$
$488$	−6.41218e9			−0.113065
$489$	−3.53475e10			−0.618192
$490$	−6.61976e10	+	6.61976e10i	−1.14831	+	1.14831i
$491$	5.50524e10	−	5.50524e10i	0.947219	−	0.947219i	−0.0514561	−	0.998675i	$-0.516386\pi$
$491$	5.50524e10	−	5.50524e10i	0.947219	−	0.947219i	0.998675	+	0.0514561i	$0.0163862\pi$
$492$			1.69994e10i			0.290117i
$493$	4.09138e9	−	6.83365e10i	0.0692599	−	1.15682i
$494$	6.18212e10			1.03808
$495$	−4.23794e10	−	4.23794e10i	−0.705885	−	0.705885i
$496$	3.66488e10	+	3.66488e10i	0.605526	+	0.605526i
$497$			1.16752e11i			1.91355i
$498$		−	1.14037e11i		−	1.85409i
$499$		−	3.77890e10i		−	0.609485i	−0.952435	−	0.304743i	$-0.901430\pi$
$499$		−	3.77890e10i		−	0.609485i	0.952435	−	0.304743i	$-0.0985704\pi$
$500$	−2.09752e10			−0.335603
$501$	7.63924e10	−	7.63924e10i	1.21255	−	1.21255i
$502$		−	1.24441e11i		−	1.95952i
$503$	−6.72286e10	+	6.72286e10i	−1.05022	+	1.05022i	−0.0515547	+	0.998670i	$0.516418\pi$
$503$	−6.72286e10	+	6.72286e10i	−1.05022	+	1.05022i	−0.998670	+	0.0515547i	$0.983582\pi$
$504$	−2.26469e10	−	2.26469e10i	−0.350983	−	0.350983i
$505$	7.01051e10	−	7.01051e10i	1.07791	−	1.07791i
$506$		−	1.68724e11i		−	2.57380i
$507$	3.82746e10	+	3.82746e10i	0.579268	+	0.579268i
$508$	1.47746e10	−	1.47746e10i	0.221851	−	0.221851i
$509$	−5.03164e10			−0.749615			−0.374808	−	0.927103i	$-0.622291\pi$
$509$	−5.03164e10			−0.749615			−0.374808	+	0.927103i	$0.622291\pi$
$510$	9.57624e10	+	9.57624e10i	1.41551	+	1.41551i
$511$	−7.53269e9	+	7.53269e9i	−0.110476	+	0.110476i
$512$	1.08448e10	+	1.08448e10i	0.157813	+	0.157813i
$513$	6.21488e10			0.897353
$514$	−8.94597e10	−	8.94597e10i	−1.28167	−	1.28167i
$515$		−	8.09390e10i		−	1.15061i
$516$	−1.52561e10			−0.215201
$517$	8.39733e10			1.17538
$518$	−1.96880e11			−2.73454
$519$	−4.43649e10	+	4.43649e10i	−0.611463	+	0.611463i
$520$	2.30574e10	−	2.30574e10i	0.315353	−	0.315353i
$521$			3.61449e10i			0.490564i	0.969452	+	0.245282i	$0.0788806\pi$
$521$			3.61449e10i			0.490564i	−0.969452	+	0.245282i	$0.921119\pi$
$522$	−4.55988e10	−	2.73005e9i	−0.614146	−	0.0367696i
$523$	5.99782e10			0.801653			0.400827	−	0.916154i	$-0.368723\pi$
$523$	5.99782e10			0.801653			0.400827	+	0.916154i	$0.368723\pi$
$524$	−6.09317e9	−	6.09317e9i	−0.0808199	−	0.0808199i
$525$	3.50509e10	+	3.50509e10i	0.461383	+	0.461383i
$526$			1.63781e11i			2.13954i
$527$		−	6.13585e10i		−	0.795485i
$528$			1.99592e11i			2.56807i
$529$	4.92088e10			0.628376
$530$	9.85101e10	−	9.85101e10i	1.24847	−	1.24847i
$531$			1.28269e9i			0.0161341i
$532$	5.59127e10	−	5.59127e10i	0.698013	−	0.698013i
$533$	−1.72676e10	−	1.72676e10i	−0.213955	−	0.213955i
$534$	7.10921e10	−	7.10921e10i	0.874292	−	0.874292i
$535$			1.05009e11i			1.28177i
$536$	3.33904e10	+	3.33904e10i	0.404541	+	0.404541i
$537$	−2.52878e10	+	2.52878e10i	−0.304098	+	0.304098i
$538$	−8.30552e10			−0.991375
$539$	1.15498e11	+	1.15498e11i	1.36842	+	1.36842i
$540$	−1.90031e10	+	1.90031e10i	−0.223486	+	0.223486i
$541$	−5.81699e10	−	5.81699e10i	−0.679061	−	0.679061i	0.280726	−	0.959788i	$-0.409425\pi$
$541$	−5.81699e10	−	5.81699e10i	−0.679061	−	0.679061i	−0.959788	+	0.280726i	$0.909425\pi$
$542$	1.73230e11			2.00737
$543$	−1.40887e10	−	1.40887e10i	−0.162058	−	0.162058i
$544$		−	8.53255e10i		−	0.974279i
$545$	5.68705e10			0.644616
$546$	−1.11554e11			−1.25520
$547$	−5.59398e10			−0.624844			−0.312422	−	0.949943i	$-0.601140\pi$
$547$	−5.59398e10			−0.624844			−0.312422	+	0.949943i	$0.601140\pi$
$548$	1.61550e10	−	1.61550e10i	0.179136	−	0.179136i
$549$	5.60611e9	−	5.60611e9i	0.0617124	−	0.0617124i
$550$		−	6.67321e10i		−	0.729262i
$551$	−8.22155e9	+	1.37321e11i	−0.0891964	+	1.48981i
$552$	−9.63770e10			−1.03805
$553$	5.93893e10	+	5.93893e10i	0.635049	+	0.635049i
$554$	7.30569e10	+	7.30569e10i	0.775572	+	0.775572i
$555$			2.10448e11i			2.21806i
$556$			2.23698e10i			0.234079i
$557$		−	1.30362e11i		−	1.35435i	−0.735823	−	0.677174i	$-0.763205\pi$
$557$		−	1.30362e11i		−	1.35435i	0.735823	−	0.677174i	$-0.236795\pi$
$558$	−4.09426e10			−0.422317
$559$	1.54968e10	−	1.54968e10i	0.158706	−	0.158706i
$560$		−	2.10189e11i		−	2.13726i
$561$	1.67081e11	−	1.67081e11i	1.68685	−	1.68685i
$562$	2.94520e10	+	2.94520e10i	0.295236	+	0.295236i
$563$	3.62232e10	−	3.62232e10i	0.360540	−	0.360540i	−0.503472	−	0.864012i	$-0.667944\pi$
$563$	3.62232e10	−	3.62232e10i	0.360540	−	0.360540i	0.864012	+	0.503472i	$0.167944\pi$
$564$			3.93238e10i			0.388633i
$565$	−5.77435e10	−	5.77435e10i	−0.566643	−	0.566643i
$566$	−1.04585e11	+	1.04585e11i	−1.01906	+	1.01906i
$567$	−1.89663e11			−1.83506
$568$	−6.34844e10	−	6.34844e10i	−0.609921	−	0.609921i
$569$	1.93542e10	−	1.93542e10i	0.184640	−	0.184640i	−0.608734	−	0.793374i	$-0.708322\pi$
$569$	1.93542e10	−	1.93542e10i	0.184640	−	0.184640i	0.793374	+	0.608734i	$0.208322\pi$
$570$	−1.92433e11	−	1.92433e11i	−1.82297	−	1.82297i
$571$	7.53044e10			0.708395			0.354198	−	0.935171i	$-0.384754\pi$
$571$	7.53044e10			0.708395			0.354198	+	0.935171i	$0.384754\pi$
$572$	3.29809e10	+	3.29809e10i	0.308091	+	0.308091i
$573$			7.17806e9i			0.0665869i
$574$	−1.00568e11			−0.926429
$575$	5.04353e10			0.461385
$576$	1.32166e10			0.120069
$577$	1.66110e10	−	1.66110e10i	0.149862	−	0.149862i	−0.628194	−	0.778057i	$-0.716206\pi$
$577$	1.66110e10	−	1.66110e10i	0.149862	−	0.149862i	0.778057	+	0.628194i	$0.216206\pi$
$578$	−3.26047e10	+	3.26047e10i	−0.292125	+	0.292125i
$579$		−	7.83672e10i		−	0.697301i
$580$	−3.94745e10	−	4.45023e10i	−0.348823	−	0.393251i
$581$	2.09530e11			1.83883
$582$	7.47632e10	+	7.47632e10i	0.651622	+	0.651622i
$583$	−1.71876e11	−	1.71876e11i	−1.48778	−	1.48778i
$584$		−	8.19185e9i		−	0.0704256i
$585$			4.03178e10i			0.344249i
$586$			7.00642e10i			0.594163i
$587$	6.21812e10			0.523729			0.261865	−	0.965105i	$-0.415663\pi$
$587$	6.21812e10			0.523729			0.261865	+	0.965105i	$0.415663\pi$
$588$	−5.40867e10	+	5.40867e10i	−0.452461	+	0.452461i
$589$			1.23299e11i			1.02447i
$590$	−3.80299e9	+	3.80299e9i	−0.0313846	+	0.0313846i
$591$	−2.14018e8	−	2.14018e8i	−0.00175428	−	0.00175428i
$592$	1.67561e11	−	1.67561e11i	1.36423	−	1.36423i
$593$			1.07847e11i			0.872150i	0.899910	+	0.436075i	$0.143632\pi$
$593$			1.07847e11i			0.872150i	−0.899910	+	0.436075i	$0.856368\pi$
$594$	1.06754e11	+	1.06754e11i	0.857508	+	0.857508i
$595$	−1.75952e11	+	1.75952e11i	−1.40387	+	1.40387i
$596$	1.48471e10			0.117667
$597$	1.05447e11	+	1.05447e11i	0.830116	+	0.830116i
$598$	−8.02581e10	+	8.02581e10i	−0.627602	+	0.627602i
$599$	−7.11735e10	−	7.11735e10i	−0.552855	−	0.552855i	0.374409	−	0.927264i	$-0.377846\pi$
$599$	−7.11735e10	−	7.11735e10i	−0.552855	−	0.552855i	−0.927264	+	0.374409i	$0.877846\pi$
$600$	−3.81181e10			−0.294121
$601$	8.01677e10	+	8.01677e10i	0.614472	+	0.614472i	0.944108	−	0.329636i	$-0.106926\pi$
$601$	8.01677e10	+	8.01677e10i	0.614472	+	0.614472i	−0.329636	+	0.944108i	$0.606926\pi$
$602$		−	9.02547e10i		−	0.687201i
$603$	−5.83858e10			−0.441609
$604$	−6.33710e10			−0.476149
$605$	−2.82121e11			−2.10578
$606$	1.84427e11	−	1.84427e11i	1.36752	−	1.36752i
$607$	1.49411e11	−	1.49411e11i	1.10060	−	1.10060i	0.106260	−	0.994338i	$-0.466112\pi$
$607$	1.49411e11	−	1.49411e11i	1.10060	−	1.10060i	0.994338	−	0.106260i	$-0.0338877\pi$
$608$			1.71460e11i			1.25473i
$609$	1.48354e10	−	2.47790e11i	0.107853	−	1.80142i
$610$	3.32425e10			0.240090
$611$	−3.99441e10	−	3.99441e10i	−0.286608	−	0.286608i
$612$	2.64553e10	+	2.64553e10i	0.188585	+	0.188585i
$613$			1.37759e11i			0.975614i	0.872952	+	0.487807i	$0.162203\pi$
$613$			1.37759e11i			0.975614i	−0.872952	+	0.487807i	$0.837797\pi$
$614$			1.68699e11i			1.18697i
$615$			1.07499e11i			0.751454i
$616$	−2.34300e11			−1.62724
$617$	−9.21066e10	+	9.21066e10i	−0.635550	+	0.635550i	−0.949455	−	0.313904i	$-0.898363\pi$
$617$	−9.21066e10	+	9.21066e10i	−0.635550	+	0.635550i	0.313904	+	0.949455i	$0.398363\pi$
$618$		−	2.12928e11i		−	1.45975i
$619$	6.13829e10	−	6.13829e10i	0.418105	−	0.418105i	−0.466445	−	0.884550i	$-0.654466\pi$
$619$	6.13829e10	−	6.13829e10i	0.418105	−	0.418105i	0.884550	+	0.466445i	$0.154466\pi$
$620$	−3.77009e10	−	3.77009e10i	−0.255143	−	0.255143i
$621$	−8.06834e10	+	8.06834e10i	−0.542523	+	0.542523i
$622$			3.10086e10i			0.207167i
$623$	1.30623e11	+	1.30623e11i	0.867100	+	0.867100i
$624$	9.49413e10	−	9.49413e10i	0.626205	−	0.626205i
$625$	−1.87811e11			−1.23084
$626$	−1.04478e11	−	1.04478e11i	−0.680340	−	0.680340i
$627$	−3.35747e11	+	3.35747e11i	−2.17241	+	2.17241i
$628$	−3.17404e10	−	3.17404e10i	−0.204067	−	0.204067i
$629$	−2.80536e11			−1.79220
$630$	1.17407e11	+	1.17407e11i	0.745304	+	0.745304i
$631$			1.43522e11i			0.905318i	0.891684	+	0.452659i	$0.149525\pi$
$631$			1.43522e11i			0.905318i	−0.891684	+	0.452659i	$0.850475\pi$
$632$	−6.45862e10			−0.404829
$633$	2.26885e11			1.41316
$634$	1.91794e11			1.18707
$635$	9.34300e10	−	9.34300e10i	0.574634	−	0.574634i
$636$	8.04876e10	−	8.04876e10i	0.491927	−	0.491927i
$637$		−	1.09880e11i		−	0.667359i
$638$	−2.50001e11	+	2.21756e11i	−1.50889	+	1.33842i
$639$	1.11008e11			0.665809
$640$	1.55562e11	+	1.55562e11i	0.927220	+	0.927220i
$641$	4.53246e10	+	4.53246e10i	0.268474	+	0.268474i	0.828485	−	0.560011i	$-0.189203\pi$
$641$	4.53246e10	+	4.53246e10i	0.268474	+	0.268474i	−0.560011	+	0.828485i	$0.689203\pi$
$642$			2.76248e11i			1.62614i
$643$			1.24748e11i			0.729774i	0.931052	+	0.364887i	$0.118892\pi$
$643$			1.24748e11i			0.729774i	−0.931052	+	0.364887i	$0.881108\pi$
$644$			1.45175e11i			0.844012i
$645$	−9.64746e10			−0.557409
$646$	2.56521e11	−	2.56521e11i	1.47297	−	1.47297i
$647$		−	4.33922e10i		−	0.247625i	−0.992306	−	0.123813i	$-0.960488\pi$
$647$		−	4.33922e10i		−	0.247625i	0.992306	−	0.123813i	$-0.0395122\pi$
$648$	1.03130e11	−	1.03130e11i	0.584903	−	0.584903i
$649$	6.63527e9	+	6.63527e9i	0.0374007	+	0.0374007i
$650$	−3.17429e10	+	3.17429e10i	−0.177825	+	0.177825i
$651$		−	2.22487e11i		−	1.23874i
$652$	−2.89520e10	−	2.89520e10i	−0.160209	−	0.160209i
$653$	2.09457e11	−	2.09457e11i	1.15197	−	1.15197i	0.165813	−	0.986157i	$-0.446975\pi$
$653$	2.09457e11	−	2.09457e11i	1.15197	−	1.15197i	0.986157	−	0.165813i	$-0.0530249\pi$
$654$	1.49610e11			0.817806
$655$	−3.85312e10	−	3.85312e10i	−0.209338	−	0.209338i
$656$	8.55916e10	−	8.55916e10i	0.462185	−	0.462185i
$657$	7.16205e9	+	7.16205e9i	0.0384394	+	0.0384394i
$658$	−2.32639e11			−1.24102
$659$	7.78761e10	+	7.78761e10i	0.412917	+	0.412917i	0.882753	−	0.469837i	$-0.155687\pi$
$659$	7.78761e10	+	7.78761e10i	0.412917	+	0.412917i	−0.469837	+	0.882753i	$0.655687\pi$
$660$		−	2.05322e11i		−	1.08208i
$661$	1.44172e11			0.755220			0.377610	−	0.925965i	$-0.376746\pi$
$661$	1.44172e11			0.755220			0.377610	+	0.925965i	$0.376746\pi$
$662$	3.78166e11			1.96902
$663$	−1.58954e11			−0.822652
$664$	−1.13933e11	+	1.13933e11i	−0.586106	+	0.586106i
$665$	3.53573e11	−	3.53573e11i	1.80798	−	1.80798i
$666$			1.87193e11i			0.951465i
$667$	−1.67601e11	−	1.88948e11i	−0.846784	−	0.954637i
$668$	1.25141e11			0.628484
$669$	−4.99454e10	−	4.99454e10i	−0.249339	−	0.249339i
$670$	−1.73105e11	−	1.73105e11i	−0.859033	−	0.859033i
$671$		−	5.79998e10i		−	0.286112i
$672$		−	3.09392e11i		−	1.51716i
$673$		−	2.69528e11i		−	1.31384i	−0.753959	−	0.656922i	$-0.771858\pi$
$673$		−	2.69528e11i		−	1.31384i	0.753959	−	0.656922i	$-0.228142\pi$
$674$	3.32152e11			1.60952
$675$	−3.19111e10	+	3.19111e10i	−0.153719	+	0.153719i
$676$			6.26991e10i			0.300244i
$677$	1.05743e11	−	1.05743e11i	0.503380	−	0.503380i	−0.409107	−	0.912487i	$-0.634160\pi$
$677$	1.05743e11	−	1.05743e11i	0.503380	−	0.503380i	0.912487	+	0.409107i	$0.134160\pi$
$678$	−1.51907e11	−	1.51907e11i	−0.718884	−	0.718884i
$679$	−1.37369e11	+	1.37369e11i	−0.646262	+	0.646262i
$680$		−	1.91349e11i		−	0.894934i
$681$	−2.00079e11	−	2.00079e11i	−0.930276	−	0.930276i
$682$	−2.11792e11	+	2.11792e11i	−0.978978	+	0.978978i
$683$	−3.94974e11			−1.81504			−0.907518	−	0.420013i	$-0.862025\pi$
$683$	−3.94974e11			−1.81504			−0.907518	+	0.420013i	$0.862025\pi$
$684$	−5.31615e10	−	5.31615e10i	−0.242870	−	0.242870i
$685$	1.02159e11	−	1.02159e11i	0.463994	−	0.463994i
$686$	−4.30766e10	−	4.30766e10i	−0.194512	−	0.194512i
$687$	−1.60518e10			−0.0720604
$688$	7.68142e10	+	7.68142e10i	0.342837	+	0.342837i
$689$			1.63514e11i			0.725569i
$690$	4.99645e11			2.20427
$691$	−8.59175e10			−0.376851			−0.188425	−	0.982088i	$-0.560338\pi$
$691$	−8.59175e10			−0.376851			−0.188425	+	0.982088i	$0.560338\pi$
$692$	−7.26758e10			−0.316932
$693$	2.04847e11	−	2.04847e11i	0.888170	−	0.888170i
$694$	−2.76537e11	+	2.76537e11i	−1.19211	+	1.19211i
$695$			1.41459e11i			0.606306i
$696$	1.26670e11	+	1.42803e11i	0.539803	+	0.608556i
$697$	−1.43300e11			−0.607177
$698$	−2.60725e11	−	2.60725e11i	−1.09840	−	1.09840i
$699$	1.75803e11	+	1.75803e11i	0.736407	+	0.736407i
$700$			5.74181e10i			0.239143i
$701$			1.56701e11i			0.648934i	0.945897	+	0.324467i	$0.105185\pi$
$701$			1.56701e11i			0.648934i	−0.945897	+	0.324467i	$0.894815\pi$
$702$		−	1.01561e11i		−	0.418194i
$703$	5.63733e11			2.30809
$704$	6.83685e10	−	6.83685e10i	0.278333	−	0.278333i
$705$			2.48671e11i			1.00663i
$706$	5.92427e10	−	5.92427e10i	0.238460	−	0.238460i
$707$	3.38863e11	+	3.38863e11i	1.35627	+	1.35627i
$708$	−3.10723e9	+	3.10723e9i	−0.0123663	+	0.0123663i
$709$		−	3.56548e11i		−	1.41102i	−0.708700	−	0.705510i	$-0.750718\pi$
$709$		−	3.56548e11i		−	1.41102i	0.708700	−	0.705510i	$-0.249282\pi$
$710$	3.29120e11	+	3.29120e11i	1.29515	+	1.29515i
$711$	5.64671e10	−	5.64671e10i	0.220962	−	0.220962i
$712$	−1.42054e11			−0.552755
$713$	−1.60070e11	−	1.60070e11i	−0.619373	−	0.619373i
$714$	−4.62881e11	+	4.62881e11i	−1.78105	+	1.78105i
$715$	2.08560e11	+	2.08560e11i	0.798009	+	0.798009i
$716$	−4.14249e10			−0.157619
$717$	3.26883e11	+	3.26883e11i	1.23685	+	1.23685i
$718$		−	1.39049e11i		−	0.523205i
$719$	−3.19327e11			−1.19487			−0.597434	−	0.801918i	$-0.703813\pi$
$719$	−3.19327e11			−1.19487			−0.597434	+	0.801918i	$0.703813\pi$
$720$	−1.99847e11			−0.743648
$721$	3.91229e11			1.44774
$722$	−2.84059e11	+	2.84059e11i	−1.04535	+	1.04535i
$723$	−4.14168e11	+	4.14168e11i	−1.51573	+	1.51573i
$724$		−	2.30792e10i		−	0.0839973i
$725$	−6.62878e10	−	7.47307e10i	−0.239928	−	0.270487i
$726$	−7.42180e11			−2.67154
$727$	−1.88754e11	−	1.88754e11i	−0.675707	−	0.675707i	0.283319	−	0.959026i	$-0.408564\pi$
$727$	−1.88754e11	−	1.88754e11i	−0.675707	−	0.675707i	−0.959026	+	0.283319i	$0.908564\pi$
$728$	1.11451e11	+	1.11451e11i	0.396789	+	0.396789i
$729$		−	2.83949e10i		−	0.100538i
$730$			4.24688e10i			0.149547i
$731$		−	1.28605e11i		−	0.450388i
$732$	2.71607e10			0.0946013
$733$	−6.62075e10	+	6.62075e10i	−0.229346	+	0.229346i	−0.812419	−	0.583073i	$-0.801850\pi$
$733$	−6.62075e10	+	6.62075e10i	−0.229346	+	0.229346i	0.583073	+	0.812419i	$0.301850\pi$
$734$		−	3.40424e11i		−	1.17283i
$735$	−3.42026e11	+	3.42026e11i	−1.17195	+	1.17195i
$736$	−2.22595e11	−	2.22595e11i	−0.758584	−	0.758584i
$737$	−3.02025e11	+	3.02025e11i	−1.02370	+	1.02370i
$738$			9.56196e10i			0.322345i
$739$	2.48648e11	+	2.48648e11i	0.833695	+	0.833695i	0.988020	−	0.154326i	$-0.0493204\pi$
$739$	2.48648e11	+	2.48648e11i	0.833695	+	0.833695i	−0.154326	+	0.988020i	$0.549320\pi$
$740$	−1.72372e11	+	1.72372e11i	−0.574829	+	0.574829i
$741$	3.19414e11			1.05945
$742$	4.76162e11	+	4.76162e11i	1.57087	+	1.57087i
$743$	3.70165e11	−	3.70165e11i	1.21462	−	1.21462i	0.245129	−	0.969491i	$-0.421170\pi$
$743$	3.70165e11	−	3.70165e11i	1.21462	−	1.21462i	0.969491	−	0.245129i	$-0.0788302\pi$
$744$	1.20978e11	+	1.20978e11i	0.394834	+	0.394834i
$745$	9.38879e10			0.304779
$746$	−3.89444e11	−	3.89444e11i	−1.25745	−	1.25745i
$747$		−	1.99221e11i		−	0.639811i
$748$	2.73702e11			0.874323
$749$	−5.07573e11			−1.61277
$750$	−3.48939e11			−1.10282
$751$	2.64707e11	−	2.64707e11i	0.832158	−	0.832158i	−0.155653	−	0.987812i	$-0.549748\pi$
$751$	2.64707e11	−	2.64707e11i	0.832158	−	0.832158i	0.987812	+	0.155653i	$0.0497483\pi$
$752$	1.97995e11	−	1.97995e11i	0.619130	−	0.619130i
$753$		−	6.42956e11i		−	1.99987i
$754$	2.24404e11	+	1.34353e10i	0.694297	+	0.0415683i
$755$	−4.00737e11			−1.23331
$756$	−9.18541e10	−	9.18541e10i	−0.281197	−	0.281197i
$757$	1.55380e11	+	1.55380e11i	0.473165	+	0.473165i	0.902937	−	0.429773i	$-0.141406\pi$
$757$	1.55380e11	+	1.55380e11i	0.473165	+	0.473165i	−0.429773	+	0.902937i	$0.641406\pi$
$758$		−	1.78988e11i		−	0.542184i
$759$		−	8.71755e11i		−	2.62680i
$760$			3.84513e11i			1.15254i
$761$	−1.10447e11			−0.329317			−0.164659	−	0.986351i	$-0.552652\pi$
$761$	−1.10447e11			−0.329317			−0.164659	+	0.986351i	$0.552652\pi$
$762$	2.45788e11	−	2.45788e11i	0.729022	−	0.729022i
$763$			2.74891e11i			0.811079i
$764$	−5.87932e9	+	5.87932e9i	−0.0172565	+	0.0172565i
$765$	1.67295e11	+	1.67295e11i	0.488468	+	0.488468i
$766$	−4.10804e11	+	4.10804e11i	−1.19322	+	1.19322i
$767$		−	6.31248e9i		−	0.0182397i
$768$	3.38170e11	+	3.38170e11i	0.972053	+	0.972053i
$769$	−4.60808e11	+	4.60808e11i	−1.31770	+	1.31770i	−0.402099	+	0.915596i	$0.631719\pi$
$769$	−4.60808e11	+	4.60808e11i	−1.31770	+	1.31770i	−0.915596	+	0.402099i	$0.868281\pi$
$770$	1.21468e12			3.45540
$771$	−4.62215e11	−	4.62215e11i	−1.30806	−	1.30806i
$772$	6.41881e10	−	6.41881e10i	0.180711	−	0.180711i
$773$	−2.10836e10	−	2.10836e10i	−0.0590508	−	0.0590508i	0.676965	−	0.736016i	$-0.263295\pi$
$773$	−2.10836e10	−	2.10836e10i	−0.0590508	−	0.0590508i	−0.736016	+	0.676965i	$0.763295\pi$
$774$	−8.58138e10			−0.239108
$775$	−6.33094e10	−	6.33094e10i	−0.175494	−	0.175494i
$776$		−	1.49389e11i		−	0.411976i
$777$	−1.01723e12			−2.79084
$778$	−4.18691e11			−1.14281
$779$	2.87959e11			0.781953
$780$	−9.76667e10	+	9.76667e10i	−0.263857	+	0.263857i
$781$	5.74233e11	−	5.74233e11i	1.54342	−	1.54342i
$782$			6.66046e11i			1.78106i
$783$	2.25593e11	+	1.35065e10i	0.600176	+	0.0359332i
$784$	5.44650e11			1.44163
$785$	−2.00716e11	−	2.00716e11i	−0.528570	−	0.528570i
$786$	−1.01365e11	−	1.01365e11i	−0.265581	−	0.265581i
$787$			9.56738e10i			0.249399i	0.992195	+	0.124699i	$0.0397966\pi$
$787$			9.56738e10i			0.249399i	−0.992195	+	0.124699i	$0.960203\pi$
$788$		−	3.50590e8i		−	0.000909274i
$789$			8.46214e11i			2.18360i
$790$	3.34832e11			0.859645
$791$	2.79111e11	−	2.79111e11i	0.712970	−	0.712970i
$792$			2.22772e11i			0.566187i
$793$	−2.75892e10	+	2.75892e10i	−0.0697663	+	0.0697663i
$794$	−4.90183e11	−	4.90183e11i	−1.23332	−	1.23332i
$795$	5.08977e11	−	5.08977e11i	1.27418	−	1.27418i
$796$			1.72737e11i			0.430263i
$797$	−1.31959e11	−	1.31959e11i	−0.327043	−	0.327043i	0.524418	−	0.851461i	$-0.324283\pi$
$797$	−1.31959e11	−	1.31959e11i	−0.327043	−	0.327043i	−0.851461	+	0.524418i	$0.824283\pi$
$798$	9.30151e11	−	9.30151e11i	2.29373	−	2.29373i
$799$	−3.31488e11			−0.813357
$800$	−8.80384e10	−	8.80384e10i	−0.214937	−	0.214937i
$801$	1.24196e11	−	1.24196e11i	0.301702	−	0.301702i
$802$	−5.91380e11	−	5.91380e11i	−1.42945	−	1.42945i
$803$	7.40974e10			0.178213
$804$	−1.41435e11	−	1.41435e11i	−0.338480	−	0.338480i
$805$			9.18039e11i			2.18614i
$806$	2.01489e11			0.477433
$807$	−4.29125e11			−1.01179
$808$	−3.68515e11			−0.864589
$809$	−3.26432e11	+	3.26432e11i	−0.762076	+	0.762076i	−0.976697	−	0.214621i	$-0.931148\pi$
$809$	−3.26432e11	+	3.26432e11i	−0.762076	+	0.762076i	0.214621	+	0.976697i	$0.431148\pi$
$810$	−5.34652e11	+	5.34652e11i	−1.24203	+	1.24203i
$811$			1.53505e11i			0.354845i	0.984135	+	0.177422i	$0.0567759\pi$
$811$			1.53505e11i			0.354845i	−0.984135	+	0.177422i	$0.943224\pi$
$812$	2.15108e11	−	1.90805e11i	0.494803	−	0.438901i
$813$	8.95037e11			2.04870
$814$	9.68334e11	+	9.68334e11i	2.20560	+	2.20560i
$815$	−1.83083e11	−	1.83083e11i	−0.414971	−	0.414971i
$816$		−	7.87899e11i		−	1.77709i
$817$			2.58429e11i			0.580033i
$818$			6.45318e11i			1.44132i
$819$	−1.94882e11			−0.433147
$820$	−8.80487e10	+	8.80487e10i	−0.194745	+	0.194745i
$821$			2.96972e11i			0.653646i	0.945086	+	0.326823i	$0.105978\pi$
$821$			2.96972e11i			0.653646i	−0.945086	+	0.326823i	$0.894022\pi$
$822$	2.68750e11	−	2.68750e11i	0.588656	−	0.588656i
$823$	−1.67199e11	−	1.67199e11i	−0.364447	−	0.364447i	0.501000	−	0.865447i	$-0.332966\pi$
$823$	−1.67199e11	−	1.67199e11i	−0.364447	−	0.364447i	−0.865447	+	0.501000i	$0.832966\pi$
$824$	−2.12732e11	+	2.12732e11i	−0.461450	+	0.461450i
$825$		−	3.44788e11i		−	0.744279i
$826$	−1.83823e10	−	1.83823e10i	−0.0394893	−	0.0394893i
$827$	5.93909e11	−	5.93909e11i	1.26969	−	1.26969i	0.323442	−	0.946248i	$-0.395160\pi$
$827$	5.93909e11	−	5.93909e11i	1.26969	−	1.26969i	0.946248	−	0.323442i	$-0.104840\pi$
$828$	1.38032e11			0.293669
$829$	1.06971e10	+	1.06971e10i	0.0226489	+	0.0226489i	0.718341	−	0.695692i	$-0.244902\pi$
$829$	1.06971e10	+	1.06971e10i	0.0226489	+	0.0226489i	−0.695692	+	0.718341i	$0.744902\pi$
$830$	5.90658e11	−	5.90658e11i	1.24458	−	1.24458i
$831$	3.77466e11	+	3.77466e11i	0.791542	+	0.791542i
$832$	−6.50425e10			−0.135739
$833$	−4.55935e11	−	4.55935e11i	−0.946940	−	0.946940i
$834$			3.72139e11i			0.769203i
$835$	7.91351e11			1.62788
$836$	−5.50000e11			−1.12600
$837$	2.02557e11			0.412711
$838$	7.08667e11	−	7.08667e11i	1.43703	−	1.43703i
$839$	−4.46730e11	+	4.46730e11i	−0.901565	+	0.901565i	−0.995572	−	0.0940062i	$-0.970033\pi$
$839$	−4.46730e11	+	4.46730e11i	−0.901565	+	0.901565i	0.0940062	+	0.995572i	$0.470033\pi$
$840$		−	6.93836e11i		−	1.39361i
$841$	−5.96866e10	+	4.96673e11i	−0.119314	+	0.992857i
$842$	−1.49771e11			−0.297974
$843$	1.52171e11	+	1.52171e11i	0.301316	+	0.301316i
$844$	1.85834e11	+	1.85834e11i	0.366231	+	0.366231i
$845$			3.96488e11i			0.777684i
$846$			2.21192e11i			0.431805i
$847$		−	1.36367e12i		−	2.64957i
$848$	−8.10506e11			−1.56737
$849$	−5.40362e11	+	5.40362e11i	−1.04005	+	1.04005i
$850$			2.63428e11i			0.504645i
$851$	−7.31855e11	+	7.31855e11i	−1.39543	+	1.39543i
$852$	2.68907e11	+	2.68907e11i	0.510322	+	0.510322i
$853$	9.56423e10	−	9.56423e10i	0.180657	−	0.180657i	−0.610985	−	0.791642i	$-0.709227\pi$
$853$	9.56423e10	−	9.56423e10i	0.180657	−	0.180657i	0.791642	+	0.610985i	$0.209227\pi$
$854$			1.60682e11i			0.302090i
$855$	−3.36176e11	−	3.36176e11i	−0.629075	−	0.629075i
$856$	2.75995e11	−	2.75995e11i	0.514050	−	0.514050i
$857$	5.21445e11			0.966685			0.483343	−	0.875431i	$-0.339423\pi$
$857$	5.21445e11			0.966685			0.483343	+	0.875431i	$0.339423\pi$
$858$	5.48663e11	+	5.48663e11i	1.01241	+	1.01241i
$859$	1.42875e11	−	1.42875e11i	0.262412	−	0.262412i	−0.563621	−	0.826033i	$-0.690592\pi$
$859$	1.42875e11	−	1.42875e11i	0.262412	−	0.262412i	0.826033	+	0.563621i	$0.190592\pi$
$860$	−7.90193e10	−	7.90193e10i	−0.144457	−	0.144457i
$861$	−5.19609e11			−0.945506
$862$	−1.31346e10	−	1.31346e10i	−0.0237896	−	0.0237896i
$863$			3.32078e11i			0.598683i	0.954146	+	0.299342i	$0.0967670\pi$
$863$			3.32078e11i			0.598683i	−0.954146	+	0.299342i	$0.903233\pi$
$864$	2.81677e11			0.505471
$865$	−4.59578e11			−0.820908
$866$	−1.04286e11			−0.185419
$867$	−1.68460e11	+	1.68460e11i	−0.298140	+	0.298140i
$868$	1.82232e11	−	1.82232e11i	0.321030	−	0.321030i
$869$		−	5.84199e11i		−	1.02443i
$870$	−6.56689e11	−	7.40330e11i	−1.14626	−	1.29226i
$871$	2.87332e11			0.499243
$872$	−1.49473e11	−	1.49473e11i	−0.258522	−	0.258522i
$873$	1.30609e11	+	1.30609e11i	0.224863	+	0.224863i
$874$		−	1.33841e12i		−	2.29373i
$875$		−	6.41135e11i		−	1.09375i
$876$			3.46990e10i			0.0589252i
$877$	1.79193e11			0.302916			0.151458	−	0.988464i	$-0.451603\pi$
$877$	1.79193e11			0.302916			0.151458	+	0.988464i	$0.451603\pi$
$878$	−3.37964e11	+	3.37964e11i	−0.568711	+	0.568711i
$879$			3.62004e11i			0.606398i
$880$	−1.03379e12	+	1.03379e12i	−1.72386	+	1.72386i
$881$	−1.20255e11	−	1.20255e11i	−0.199618	−	0.199618i	0.600218	−	0.799836i	$-0.295080\pi$
$881$	−1.20255e11	−	1.20255e11i	−0.199618	−	0.199618i	−0.799836	+	0.600218i	$0.795080\pi$
$882$	−3.04231e11	+	3.04231e11i	−0.502723	+	0.502723i
$883$			5.00867e11i			0.823909i	0.911204	+	0.411955i	$0.135154\pi$
$883$			5.00867e11i			0.823909i	−0.911204	+	0.411955i	$0.864846\pi$
$884$	−1.30194e11	−	1.30194e11i	−0.213197	−	0.213197i
$885$	−1.96491e10	+	1.96491e10i	−0.0320309	+	0.0320309i
$886$	−5.62916e11			−0.913500
$887$	−4.55151e11	−	4.55151e11i	−0.735295	−	0.735295i	0.236369	−	0.971663i	$-0.424043\pi$
$887$	−4.55151e11	−	4.55151e11i	−0.735295	−	0.735295i	−0.971663	+	0.236369i	$0.924043\pi$
$888$	5.53122e11	−	5.53122e11i	0.889548	−	0.889548i
$889$	4.51606e11	+	4.51606e11i	0.723025	+	0.723025i
$890$	7.36445e11			1.17376
$891$	9.32835e11	+	9.32835e11i	1.48011	+	1.48011i
$892$		−	8.18173e10i		−	0.129237i
$893$	6.66120e11			1.04748
$894$	2.46992e11			0.386664
$895$	−2.61957e11			−0.408261
$896$	−7.51929e11	+	7.51929e11i	−1.16666	+	1.16666i
$897$	−4.14673e11	+	4.14673e11i	−0.640525	+	0.640525i
$898$		−	5.18576e11i		−	0.797457i
$899$	−2.67959e10	+	4.47561e11i	−0.0410232	+	0.685193i
$900$	5.45929e10			0.0832083
$901$	6.78487e11	+	6.78487e11i	1.02954	+	1.02954i
$902$	4.94632e11	+	4.94632e11i	0.747233	+	0.747233i
$903$		−	4.66323e11i		−	0.701352i
$904$			3.03535e11i			0.454501i
$905$		−	1.45945e11i		−	0.217568i
$906$	−1.05423e12			−1.56466
$907$	7.33069e11	−	7.33069e11i	1.08322	−	1.08322i	0.0870101	−	0.996207i	$-0.472269\pi$
$907$	7.33069e11	−	7.33069e11i	1.08322	−	1.08322i	0.996207	−	0.0870101i	$-0.0277312\pi$
$908$		−	3.27756e11i		−	0.482178i
$909$	3.22189e11	−	3.22189e11i	0.471906	−	0.471906i
$910$	−5.77793e11	−	5.77793e11i	−0.842572	−	0.842572i
$911$	−6.20597e11	+	6.20597e11i	−0.901023	+	0.901023i	−0.995525	−	0.0945015i	$-0.969874\pi$
$911$	−6.20597e11	+	6.20597e11i	−0.901023	+	0.901023i	0.0945015	+	0.995525i	$0.469874\pi$
$912$			1.58327e12i			2.28863i
$913$	−1.03055e12	−	1.03055e12i	−1.48315	−	1.48315i
$914$	−1.83694e11	+	1.83694e11i	−0.263215	+	0.263215i
$915$	1.71755e11			0.245034
$916$	−1.31475e10	−	1.31475e10i	−0.0186750	−	0.0186750i
$917$	1.86246e11	−	1.86246e11i	0.263396	−	0.263396i
$918$	−4.21416e11	−	4.21416e11i	−0.593390	−	0.593390i
$919$	2.18939e11			0.306946			0.153473	−	0.988153i	$-0.450954\pi$
$919$	2.18939e11			0.306946			0.153473	+	0.988153i	$0.450954\pi$
$920$	−4.99186e11	−	4.99186e11i	−0.696805	−	0.696805i
$921$			8.71625e11i			1.21141i
$922$	−1.41436e12			−1.95720
$923$	−5.46298e11			−0.752702
$924$	9.92450e11			1.36151
$925$	−2.89456e11	+	2.89456e11i	−0.395381	+	0.395381i
$926$	−3.29063e11	+	3.29063e11i	−0.447543	+	0.447543i
$927$		−	3.71979e11i		−	0.503732i
$928$	−3.72626e10	+	6.22381e11i	−0.0502436	+	0.839198i
$929$	6.94523e11			0.932446			0.466223	−	0.884667i	$-0.345614\pi$
$929$	6.94523e11			0.932446			0.466223	+	0.884667i	$0.345614\pi$
$930$	−6.27183e11	−	6.27183e11i	−0.838422	−	0.838422i
$931$	9.16193e11	+	9.16193e11i	1.21952	+	1.21952i
$932$			2.87989e11i			0.381692i
$933$			1.60213e11i			0.211433i
$934$		−	1.59644e12i		−	2.09781i
$935$	1.73080e12			2.26465
$936$	1.05967e11	−	1.05967e11i	0.138060	−	0.138060i
$937$		−	6.02711e11i		−	0.781899i	−0.920412	−	0.390950i	$-0.872147\pi$
$937$		−	6.02711e11i		−	0.781899i	0.920412	−	0.390950i	$-0.127853\pi$
$938$	8.36726e11	−	8.36726e11i	1.08087	−	1.08087i
$939$	−5.39809e11	−	5.39809e11i	−0.694349	−	0.694349i
$940$	−2.03678e11	+	2.03678e11i	−0.260876	+	0.260876i
$941$		−	1.05680e11i		−	0.134782i	−0.997727	−	0.0673911i	$-0.978532\pi$
$941$		−	1.05680e11i		−	0.134782i	0.997727	−	0.0673911i	$-0.0214675\pi$
$942$	−5.28026e11	−	5.28026e11i	−0.670582	−	0.670582i
$943$	−3.73837e11	+	3.73837e11i	−0.472754	+	0.472754i
$944$	3.12896e10			0.0394015
$945$	−5.80855e11	−	5.80855e11i	−0.728351	−	0.728351i
$946$	−4.43907e11	+	4.43907e11i	−0.554278	+	0.554278i
$947$	9.85544e11	+	9.85544e11i	1.22540	+	1.22540i	0.965687	+	0.259708i	$0.0836263\pi$
$947$	9.85544e11	+	9.85544e11i	1.22540	+	1.22540i	0.259708	+	0.965687i	$0.416374\pi$
$948$	2.73574e11			0.338721
$949$	−3.52464e10	−	3.52464e10i	−0.0434560	−	0.0434560i
$950$		−	5.29354e11i		−	0.649908i
$951$	9.90949e11			1.21152
$952$	9.24912e11			1.12604
$953$	−1.48429e11			−0.179948			−0.0899742	−	0.995944i	$-0.528678\pi$
$953$	−1.48429e11			−0.179948			−0.0899742	+	0.995944i	$0.528678\pi$
$954$	4.52733e11	−	4.52733e11i	0.546574	−	0.546574i
$955$	−3.71789e10	+	3.71789e10i	−0.0446974	+	0.0446974i
$956$			5.35479e11i			0.641079i
$957$	−1.29169e12	+	1.14576e12i	−1.53997	+	1.36598i
$958$	2.23870e11			0.265787
$959$	4.93797e11	+	4.93797e11i	0.583814	+	0.583814i
$960$	2.02460e11	+	2.02460e11i	0.238372	+	0.238372i
$961$		−	4.51032e11i		−	0.528827i
$962$		−	9.21227e11i		−	1.07564i
$963$			4.82599e11i			0.561153i
$964$	−6.78463e11			−0.785630
$965$	4.05904e11	−	4.05904e11i	0.468074	−	0.468074i
$966$			2.41510e12i			2.77349i
$967$	−9.97360e11	+	9.97360e11i	−1.14063	+	1.14063i	−0.152299	+	0.988335i	$0.548668\pi$
$967$	−9.97360e11	+	9.97360e11i	−1.14063	+	1.14063i	−0.988335	+	0.152299i	$0.951332\pi$
$968$	7.41499e11	+	7.41499e11i	0.844518	+	0.844518i
$969$	1.32538e12	−	1.32538e12i	1.50330	−	1.50330i
$970$			7.74474e11i			0.874822i
$971$	−1.52627e11	−	1.52627e11i	−0.171693	−	0.171693i	0.616030	−	0.787723i	$-0.288740\pi$
$971$	−1.52627e11	−	1.52627e11i	−0.171693	−	0.171693i	−0.787723	+	0.616030i	$0.788740\pi$
$972$	−2.65877e11	+	2.65877e11i	−0.297862	+	0.297862i
$973$	−6.83762e11			−0.762876
$974$	−3.80074e11	−	3.80074e11i	−0.422311	−	0.422311i
$975$	−1.64007e11	+	1.64007e11i	−0.181487	+	0.181487i
$976$	−1.36754e11	−	1.36754e11i	−0.150709	−	0.150709i
$977$	8.51052e9			0.00934067			0.00467034	−	0.999989i	$-0.498513\pi$
$977$	8.51052e9			0.00934067			0.00467034	+	0.999989i	$0.498513\pi$
$978$	−4.81639e11	−	4.81639e11i	−0.526461	−	0.526461i
$979$		−	1.28491e12i		−	1.39876i
$980$	−5.60285e11			−0.607442
$981$	2.61366e11			0.282210
$982$	1.50027e12			1.61333
$983$	1.04913e12	−	1.04913e12i	1.12361	−	1.12361i	0.132419	−	0.991194i	$-0.457726\pi$
$983$	1.04913e12	−	1.04913e12i	1.12361	−	1.12361i	0.991194	−	0.132419i	$-0.0422745\pi$
$984$	2.82539e11	−	2.82539e11i	0.301369	−	0.301369i
$985$		−	2.21702e9i		−	0.00235518i
$986$	9.86890e11	−	8.75393e11i	1.04415	−	0.926180i
$987$	−1.20198e12			−1.26657
$988$	2.61622e11	+	2.61622e11i	0.274566	+	0.274566i
$989$	−3.35500e11	−	3.35500e11i	−0.350677	−	0.350677i
$990$		−	1.15491e12i		−	1.20228i
$991$			9.53879e10i			0.0989005i	0.998777	+	0.0494503i	$0.0157469\pi$
$991$			9.53879e10i			0.0989005i	−0.998777	+	0.0494503i	$0.984253\pi$
$992$			5.58828e11i			0.577074i
$993$	1.95389e12			2.00956
$994$	−1.59085e12	+	1.59085e12i	−1.62961	+	1.62961i
$995$			1.09233e12i			1.11446i
$996$	4.82597e11	−	4.82597e11i	0.490396	−	0.490396i
$997$	1.58727e9	+	1.58727e9i	0.00160646	+	0.00160646i	0.707910	−	0.706303i	$-0.249638\pi$
$997$	1.58727e9	+	1.58727e9i	0.00160646	+	0.00160646i	−0.706303	+	0.707910i	$0.749638\pi$
$998$	5.14907e11	−	5.14907e11i	0.519046	−	0.519046i
$999$		−	9.26109e11i		−	0.929822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.15	✓	38
29.17	odd	4	inner	29.9.c.a.17.15	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.15	✓	38	1.1	even	1	trivial
29.9.c.a.17.15	yes	38	29.17	odd	4	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.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(13.6258 + 13.6258i) q^{2} +(70.4012 + 70.4012i) q^{3} +115.327i q^{4} +729.288i q^{5} +1918.55i q^{6} -3525.11 q^{7} +(1916.79 - 1916.79i) q^{8} +3351.66i q^{9} +O(q^{10})\)	\(q+(13.6258 + 13.6258i) q^{2} +(70.4012 + 70.4012i) q^{3} +115.327i q^{4} +729.288i q^{5} +1918.55i q^{6} -3525.11 q^{7} +(1916.79 - 1916.79i) q^{8} +3351.66i q^{9} +(-9937.16 + 9937.16i) q^{10} +(17337.9 + 17337.9i) q^{11} +(-8119.14 + 8119.14i) q^{12} -16494.4i q^{13} +(-48032.6 - 48032.6i) q^{14} +(-51342.8 + 51342.8i) q^{15} +81759.4 q^{16} +(-68442.0 - 68442.0i) q^{17} +(-45669.2 + 45669.2i) q^{18} +(137533. + 137533. i) q^{19} -84106.4 q^{20} +(-248172. - 248172. i) q^{21} +472486. i q^{22} -357099. q^{23} +269889. q^{24} -141236. q^{25} +(224750. - 224750. i) q^{26} +(225941. - 225941. i) q^{27} -406540. i q^{28} +(469340. + 529119. i) q^{29} -1.39918e6 q^{30} +(448252. + 448252. i) q^{31} +(623342. + 623342. i) q^{32} +2.44121e6i q^{33} -1.86516e6i q^{34} -2.57082e6i q^{35} -386536. q^{36} +(2.04945e6 - 2.04945e6i) q^{37} +3.74801e6i q^{38} +(1.16123e6 - 1.16123e6i) q^{39} +(1.39789e6 + 1.39789e6i) q^{40} +(1.04687e6 - 1.04687e6i) q^{41} -6.76311e6i q^{42} +(939515. + 939515. i) q^{43} +(-1.99952e6 + 1.99952e6i) q^{44} -2.44433e6 q^{45} +(-4.86577e6 - 4.86577e6i) q^{46} +(2.42167e6 - 2.42167e6i) q^{47} +(5.75596e6 + 5.75596e6i) q^{48} +6.66162e6 q^{49} +(-1.92446e6 - 1.92446e6i) q^{50} -9.63680e6i q^{51} +1.90225e6 q^{52} -9.91331e6 q^{53} +6.15728e6 q^{54} +(-1.26443e7 + 1.26443e7i) q^{55} +(-6.75690e6 + 6.75690e6i) q^{56} +1.93650e7i q^{57} +(-814535. + 1.36048e7i) q^{58} +382704. q^{59} +(-5.92120e6 - 5.92120e6i) q^{60} +(-1.67264e6 - 1.67264e6i) q^{61} +1.22156e7i q^{62} -1.18150e7i q^{63} -3.94330e6i q^{64} +1.20292e7 q^{65} +(-3.32636e7 + 3.32636e7i) q^{66} +1.74200e7i q^{67} +(7.89319e6 - 7.89319e6i) q^{68} +(-2.51402e7 - 2.51402e7i) q^{69} +(3.50296e7 - 3.50296e7i) q^{70} -3.31202e7i q^{71} +(6.42444e6 + 6.42444e6i) q^{72} +(2.13687e6 - 2.13687e6i) q^{73} +5.58508e7 q^{74} +(-9.94320e6 - 9.94320e6i) q^{75} +(-1.58612e7 + 1.58612e7i) q^{76} +(-6.11179e7 - 6.11179e7i) q^{77} +3.16454e7 q^{78} +(-1.68475e7 - 1.68475e7i) q^{79} +5.96262e7i q^{80} +5.38033e7 q^{81} +2.85290e7 q^{82} -5.94394e7 q^{83} +(2.86209e7 - 2.86209e7i) q^{84} +(4.99139e7 - 4.99139e7i) q^{85} +2.56034e7i q^{86} +(-4.20850e6 + 7.02927e7i) q^{87} +6.64661e7 q^{88} +(-3.70551e7 - 3.70551e7i) q^{89} +(-3.33060e7 - 3.33060e7i) q^{90} +5.81447e7i q^{91} -4.11831e7i q^{92} +6.31149e7i q^{93} +6.59947e7 q^{94} +(-1.00301e8 + 1.00301e8i) q^{95} +8.77680e7i q^{96} +(3.89686e7 - 3.89686e7i) q^{97} +(9.07702e7 + 9.07702e7i) q^{98} +(-5.81107e7 + 5.81107e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

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