LMFDB - Embedded newform 92.10.b.c.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,10,Mod(91,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("92.91");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	92.b (of order $2$, degree $1$, 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:	$47.3832969271$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	92.91
Dual form			92.10.b.c.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.5102 - 2.30032i) q^{2} +230.553i q^{3} +(501.417 + 103.561i) q^{4} -660.081i q^{5} +(530.348 - 5189.80i) q^{6} -9465.28 q^{7} +(-11048.8 - 3484.61i) q^{8} -33471.9 q^{9} +O(q^{10})$	\(q+(-22.5102 - 2.30032i) q^{2} +230.553i q^{3} +(501.417 + 103.561i) q^{4} -660.081i q^{5} +(530.348 - 5189.80i) q^{6} -9465.28 q^{7} +(-11048.8 - 3484.61i) q^{8} -33471.9 q^{9} +(-1518.40 + 14858.6i) q^{10} -36155.5 q^{11} +(-23876.4 + 115603. i) q^{12} -11071.2 q^{13} +(213065. + 21773.2i) q^{14} +152184. q^{15} +(240694. + 103855. i) q^{16} -218051. i q^{17} +(753458. + 76996.1i) q^{18} -546966. q^{19} +(68359.0 - 330976. i) q^{20} -2.18225e6i q^{21} +(813868. + 83169.5i) q^{22} +(-1.10972e6 + 754773. i) q^{23} +(803388. - 2.54733e6i) q^{24} +1.51742e6 q^{25} +(249215. + 25467.3i) q^{26} -3.17907e6i q^{27} +(-4.74605e6 - 980238. i) q^{28} +1.85257e6 q^{29} +(-3.42569e6 - 350072. i) q^{30} +1.02018e6i q^{31} +(-5.17917e6 - 2.89147e6i) q^{32} -8.33578e6i q^{33} +(-501588. + 4.90837e6i) q^{34} +6.24785e6i q^{35} +(-1.67834e7 - 3.46639e6i) q^{36} +2.76059e6i q^{37} +(1.23123e7 + 1.25820e6i) q^{38} -2.55250e6i q^{39} +(-2.30013e6 + 7.29308e6i) q^{40} +1.14512e7 q^{41} +(-5.01989e6 + 4.91229e7i) q^{42} -2.60053e7 q^{43} +(-1.81290e7 - 3.74432e6i) q^{44} +2.20941e7i q^{45} +(2.67161e7 - 1.44374e7i) q^{46} -3.36551e7i q^{47} +(-2.39441e7 + 5.54928e7i) q^{48} +4.92378e7 q^{49} +(-3.41574e7 - 3.49055e6i) q^{50} +5.02724e7 q^{51} +(-5.55128e6 - 1.14655e6i) q^{52} -9.84380e7i q^{53} +(-7.31289e6 + 7.15614e7i) q^{54} +2.38656e7i q^{55} +(1.04580e8 + 3.29828e7i) q^{56} -1.26105e8i q^{57} +(-4.17016e7 - 4.26150e6i) q^{58} +1.42305e8i q^{59} +(7.63076e7 + 1.57604e7i) q^{60} +5.39933e7i q^{61} +(2.34675e6 - 2.29645e7i) q^{62} +3.16820e8 q^{63} +(1.09933e8 + 7.70013e7i) q^{64} +7.30789e6i q^{65} +(-1.91750e7 + 1.87640e8i) q^{66} +1.51893e8 q^{67} +(2.25817e7 - 1.09335e8i) q^{68} +(-1.74015e8 - 2.55849e8i) q^{69} +(1.43721e7 - 1.40640e8i) q^{70} +3.36094e7i q^{71} +(3.69823e8 + 1.16636e8i) q^{72} +1.77811e8 q^{73} +(6.35025e6 - 6.21414e7i) q^{74} +3.49846e8i q^{75} +(-2.74258e8 - 5.66446e7i) q^{76} +3.42222e8 q^{77} +(-5.87158e6 + 5.74573e7i) q^{78} -1.20388e7 q^{79} +(6.85527e7 - 1.58878e8i) q^{80} +7.41181e7 q^{81} +(-2.57769e8 - 2.63415e7i) q^{82} +4.10407e8 q^{83} +(2.25997e8 - 1.09422e9i) q^{84} -1.43931e8 q^{85} +(5.85384e8 + 5.98206e7i) q^{86} +4.27115e8i q^{87} +(3.99474e8 + 1.25988e8i) q^{88} +1.07083e9i q^{89} +(5.08237e7 - 4.97343e8i) q^{90} +1.04792e8 q^{91} +(-6.34596e8 + 2.63532e8i) q^{92} -2.35207e8 q^{93} +(-7.74176e7 + 7.57583e8i) q^{94} +3.61042e8i q^{95} +(6.66638e8 - 1.19407e9i) q^{96} +8.61478e8i q^{97} +(-1.10835e9 - 1.13263e8i) q^{98} +1.21019e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 32 q^{2} - 856 q^{4} + 12080 q^{6} - 44920 q^{8} - 551128 q^{9}+O(q^{10}) $ 100 * q + 32 * q^2 - 856 * q^4 + 12080 * q^6 - 44920 * q^8 - 551128 * q^9	$ 100 q + 32 q^{2} - 856 q^{4} + 12080 q^{6} - 44920 q^{8} - 551128 q^{9} - 266288 q^{12} - 4 q^{13} + 251152 q^{16} - 3213936 q^{18} - 1616600 q^{24} - 50000004 q^{25} - 9377960 q^{26} + 2611028 q^{29} - 1326128 q^{32} - 46192944 q^{36} - 3633996 q^{41} + 117081608 q^{46} + 403873120 q^{48} + 817907260 q^{49} - 253720248 q^{50} - 181337560 q^{52} - 432447896 q^{54} + 29270048 q^{58} + 897716584 q^{62} - 379488256 q^{64} + 8977204 q^{69} - 810209096 q^{70} + 390187056 q^{72} - 4 q^{73} - 413720696 q^{77} + 769707392 q^{78} + 2942959780 q^{81} + 3918346912 q^{82} - 911342216 q^{85} - 1806222144 q^{92} + 8161391316 q^{93} - 2542324232 q^{94} - 1019589584 q^{96} - 911301448 q^{98}+O(q^{100}) $ 100 * q + 32 * q^2 - 856 * q^4 + 12080 * q^6 - 44920 * q^8 - 551128 * q^9 - 266288 * q^12 - 4 * q^13 + 251152 * q^16 - 3213936 * q^18 - 1616600 * q^24 - 50000004 * q^25 - 9377960 * q^26 + 2611028 * q^29 - 1326128 * q^32 - 46192944 * q^36 - 3633996 * q^41 + 117081608 * q^46 + 403873120 * q^48 + 817907260 * q^49 - 253720248 * q^50 - 181337560 * q^52 - 432447896 * q^54 + 29270048 * q^58 + 897716584 * q^62 - 379488256 * q^64 + 8977204 * q^69 - 810209096 * q^70 + 390187056 * q^72 - 4 * q^73 - 413720696 * q^77 + 769707392 * q^78 + 2942959780 * q^81 + 3918346912 * q^82 - 911342216 * q^85 - 1806222144 * q^92 + 8161391316 * q^93 - 2542324232 * q^94 - 1019589584 * q^96 - 911301448 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−22.5102	−	2.30032i	−0.994819	−	0.101661i
$2$	−22.5102	−	2.30032i	−0.994819	−	0.101661i
$3$			230.553i			1.64333i	0.569968	+	0.821667i	$0.306956\pi$
$3$			230.553i			1.64333i	−0.569968	+	0.821667i	$0.693044\pi$
$4$	501.417	+	103.561i	0.979330	+	0.202268i
$5$		−	660.081i		−	0.472316i	−0.971715	−	0.236158i	$-0.924112\pi$
$5$		−	660.081i		−	0.472316i	0.971715	−	0.236158i	$-0.0758882\pi$
$6$	530.348	−	5189.80i	0.167063	−	1.63482i
$7$	−9465.28			−1.49002			−0.745010	−	0.667053i	$-0.767555\pi$
$7$	−9465.28			−1.49002			−0.745010	+	0.667053i	$0.767555\pi$
$8$	−11048.8	−	3484.61i	−0.953694	−	0.300780i
$9$	−33471.9			−1.70055
$10$	−1518.40	+	14858.6i	−0.0480161	+	0.469869i
$11$	−36155.5			−0.744574			−0.372287	−	0.928118i	$-0.621426\pi$
$11$	−36155.5			−0.744574			−0.372287	+	0.928118i	$0.621426\pi$
$12$	−23876.4	+	115603.i	−0.332395	+	1.60937i
$13$	−11071.2			−0.107510			−0.0537551	−	0.998554i	$-0.517119\pi$
$13$	−11071.2			−0.107510			−0.0537551	+	0.998554i	$0.517119\pi$
$14$	213065.	+	21773.2i	1.48230	+	0.151477i
$15$	152184.			0.776172
$16$	240694.	+	103855.i	0.918175	+	0.396175i
$17$		−	218051.i		−	0.633196i	−0.948560	−	0.316598i	$-0.897459\pi$
$17$		−	218051.i		−	0.633196i	0.948560	−	0.316598i	$-0.102541\pi$
$18$	753458.	+	76996.1i	1.69174	+	0.172879i
$19$	−546966.			−0.962873			−0.481436	−	0.876481i	$-0.659885\pi$
$19$	−546966.			−0.962873			−0.481436	+	0.876481i	$0.659885\pi$
$20$	68359.0	−	330976.i	0.0955346	−	0.462553i
$21$		−	2.18225e6i		−	2.44860i
$22$	813868.	+	83169.5i	0.740716	+	0.0756941i
$23$	−1.10972e6	+	754773.i	−0.826869	+	0.562394i
$23$	−1.10972e6	+	754773.i	−0.826869	+	0.562394i
$24$	803388.	−	2.54733e6i	0.494282	−	1.56724i
$25$	1.51742e6			0.776918
$26$	249215.	+	25467.3i	0.106953	+	0.0109296i
$27$		−	3.17907e6i		−	1.15123i
$28$	−4.74605e6	−	980238.i	−1.45922	−	0.301384i
$29$	1.85257e6			0.486388			0.243194	−	0.969978i	$-0.421805\pi$
$29$	1.85257e6			0.486388			0.243194	+	0.969978i	$0.421805\pi$
$30$	−3.42569e6	−	350072.i	−0.772151	−	0.0789064i
$31$			1.02018e6i			0.198404i	0.995067	+	0.0992020i	$0.0316290\pi$
$31$			1.02018e6i			0.198404i	−0.995067	+	0.0992020i	$0.968371\pi$
$32$	−5.17917e6	−	2.89147e6i	−0.873142	−	0.487465i
$33$		−	8.33578e6i		−	1.22358i
$34$	−501588.	+	4.90837e6i	−0.0643713	+	0.629916i
$35$			6.24785e6i			0.703760i
$36$	−1.67834e7	−	3.46639e6i	−1.66540	−	0.343967i
$37$			2.76059e6i			0.242155i	0.992643	+	0.121078i	$0.0386350\pi$
$37$			2.76059e6i			0.242155i	−0.992643	+	0.121078i	$0.961365\pi$
$38$	1.23123e7	+	1.25820e6i	0.957884	+	0.0978866i
$39$		−	2.55250e6i		−	0.176675i
$40$	−2.30013e6	+	7.29308e6i	−0.142063	+	0.450444i
$41$	1.14512e7			0.632883			0.316441	−	0.948612i	$-0.397512\pi$
$41$	1.14512e7			0.632883			0.316441	+	0.948612i	$0.397512\pi$
$42$	−5.01989e6	+	4.91229e7i	−0.248927	+	2.43591i
$43$	−2.60053e7			−1.15999			−0.579994	−	0.814621i	$-0.696945\pi$
$43$	−2.60053e7			−1.15999			−0.579994	+	0.814621i	$0.696945\pi$
$44$	−1.81290e7	−	3.74432e6i	−0.729184	−	0.150604i
$45$			2.20941e7i			0.803195i
$46$	2.67161e7	−	1.44374e7i	0.879759	−	0.475420i
$47$		−	3.36551e7i		−	1.00603i	−0.864278	−	0.503014i	$-0.832224\pi$
$47$		−	3.36551e7i		−	1.00603i	0.864278	−	0.503014i	$-0.167776\pi$
$48$	−2.39441e7	+	5.54928e7i	−0.651048	+	1.50887i
$49$	4.92378e7			1.22016
$50$	−3.41574e7	−	3.49055e6i	−0.772893	−	0.0789822i
$51$	5.02724e7			1.04055
$52$	−5.55128e6	−	1.14655e6i	−0.105288	−	0.0217459i
$53$		−	9.84380e7i		−	1.71365i	−0.515609	−	0.856824i	$-0.672434\pi$
$53$		−	9.84380e7i		−	1.71365i	0.515609	−	0.856824i	$-0.327566\pi$
$54$	−7.31289e6	+	7.15614e7i	−0.117035	+	1.14527i
$55$			2.38656e7i			0.351674i
$56$	1.04580e8	+	3.29828e7i	1.42102	+	0.448168i
$57$		−	1.26105e8i		−	1.58232i
$58$	−4.17016e7	−	4.26150e6i	−0.483868	−	0.0494466i
$59$			1.42305e8i			1.52893i	0.644666	+	0.764464i	$0.276996\pi$
$59$			1.42305e8i			1.52893i	−0.644666	+	0.764464i	$0.723004\pi$
$60$	7.63076e7	+	1.57604e7i	0.760129	+	0.156995i
$61$			5.39933e7i			0.499293i	0.968337	+	0.249647i	$0.0803144\pi$
$61$			5.39933e7i			0.499293i	−0.968337	+	0.249647i	$0.919686\pi$
$62$	2.34675e6	−	2.29645e7i	0.0201699	−	0.197376i
$63$	3.16820e8			2.53385
$64$	1.09933e8	+	7.70013e7i	0.819063	+	0.573704i
$65$			7.30789e6i			0.0507787i
$66$	−1.91750e7	+	1.87640e8i	−0.124391	+	1.21724i
$67$	1.51893e8			0.920874			0.460437	−	0.887692i	$-0.347693\pi$
$67$	1.51893e8			0.920874			0.460437	+	0.887692i	$0.347693\pi$
$68$	2.25817e7	−	1.09335e8i	0.128076	−	0.620108i
$69$	−1.74015e8	−	2.55849e8i	−0.924202	−	1.35882i
$70$	1.43721e7	−	1.40640e8i	0.0715449	−	0.700114i
$71$			3.36094e7i			0.156963i	0.996916	+	0.0784817i	$0.0250072\pi$
$71$			3.36094e7i			0.156963i	−0.996916	+	0.0784817i	$0.974993\pi$
$72$	3.69823e8	+	1.16636e8i	1.62180	+	0.511491i
$73$	1.77811e8			0.732833			0.366417	−	0.930451i	$-0.380585\pi$
$73$	1.77811e8			0.732833			0.366417	+	0.930451i	$0.380585\pi$
$74$	6.35025e6	−	6.21414e7i	0.0246177	−	0.240901i
$75$			3.49846e8i			1.27674i
$76$	−2.74258e8	−	5.66446e7i	−0.942970	−	0.194759i
$77$	3.42222e8			1.10943
$78$	−5.87158e6	+	5.74573e7i	−0.0179609	+	0.175760i
$79$	−1.20388e7			−0.0347744			−0.0173872	−	0.999849i	$-0.505535\pi$
$79$	−1.20388e7			−0.0347744			−0.0173872	+	0.999849i	$0.505535\pi$
$80$	6.85527e7	−	1.58878e8i	0.187120	−	0.433668i
$81$	7.41181e7			0.191312
$82$	−2.57769e8	−	2.63415e7i	−0.629604	−	0.0643395i
$83$	4.10407e8			0.949211			0.474606	−	0.880199i	$-0.342591\pi$
$83$	4.10407e8			0.949211			0.474606	+	0.880199i	$0.342591\pi$
$84$	2.25997e8	−	1.09422e9i	0.495275	−	2.39799i
$85$	−1.43931e8			−0.299068
$86$	5.85384e8	+	5.98206e7i	1.15398	+	0.117926i
$87$			4.27115e8i			0.799297i
$88$	3.99474e8	+	1.25988e8i	0.710095	+	0.223953i
$89$			1.07083e9i			1.80910i	0.426363	+	0.904552i	$0.359795\pi$
$89$			1.07083e9i			1.80910i	−0.426363	+	0.904552i	$0.640205\pi$
$90$	5.08237e7	−	4.97343e8i	0.0816535	−	0.799033i
$91$	1.04792e8			0.160192
$92$	−6.34596e8	+	2.63532e8i	−0.923533	+	0.383520i
$93$	−2.35207e8			−0.326044
$94$	−7.74176e7	+	7.57583e8i	−0.102274	+	1.00082i
$95$			3.61042e8i			0.454780i
$96$	6.66638e8	−	1.19407e9i	0.801068	−	1.43486i
$97$			8.61478e8i			0.988033i	0.869453	+	0.494016i	$0.164472\pi$
$97$			8.61478e8i			0.988033i	−0.869453	+	0.494016i	$0.835528\pi$
$98$	−1.10835e9	−	1.13263e8i	−1.21384	−	0.124043i
$99$	1.21019e9			1.26618
$100$	7.60859e8	+	1.57146e8i	0.760859	+	0.157146i
$101$	−1.03411e9			−0.988823			−0.494411	−	0.869228i	$-0.664616\pi$
$101$	−1.03411e9			−0.988823			−0.494411	+	0.869228i	$0.664616\pi$
$102$	−1.13164e9	−	1.15643e8i	−1.03516	−	0.105784i
$103$	−6.56560e8			−0.574787			−0.287393	−	0.957813i	$-0.592789\pi$
$103$	−6.56560e8			−0.574787			−0.287393	+	0.957813i	$0.592789\pi$
$104$	1.22323e8	+	3.85788e7i	0.102532	+	0.0323369i
$105$	−1.44046e9			−1.15651
$106$	−2.26439e8	+	2.21586e9i	−0.174211	+	1.70477i
$107$	2.18553e9			1.61187			0.805934	−	0.592006i	$-0.201664\pi$
$107$	2.18553e9			1.61187			0.805934	+	0.592006i	$0.201664\pi$
$108$	3.29229e8	−	1.59404e9i	0.232858	−	1.12744i
$109$			2.02961e9i			1.37719i	0.725146	+	0.688596i	$0.241772\pi$
$109$			2.02961e9i			1.37719i	−0.725146	+	0.688596i	$0.758228\pi$
$110$	5.48986e7	−	5.37219e8i	0.0357515	−	0.349852i
$111$	−6.36463e8			−0.397942
$112$	−2.27824e9	−	9.83016e8i	−1.36810	−	0.590309i
$113$		−	4.08933e8i		−	0.235939i	−0.993017	−	0.117969i	$-0.962362\pi$
$113$		−	4.08933e8i		−	0.235939i	0.993017	−	0.117969i	$-0.0376385\pi$
$114$	−2.90082e8	+	2.83864e9i	−0.160860	+	1.57412i
$115$	4.98211e8	+	7.32503e8i	0.265628	+	0.390543i
$116$	9.28908e8	+	1.91854e8i	0.476334	+	0.0983809i
$117$	3.70573e8			0.182826
$118$	3.27348e8	−	3.20332e9i	0.155432	−	1.52101i
$119$			2.06391e9i			0.943475i
$120$	−1.68144e9	−	5.30302e8i	−0.740231	−	0.233457i
$121$	−1.05072e9			−0.445610
$122$	1.24202e8	−	1.21540e9i	0.0507586	−	0.496706i
$123$			2.64011e9i			1.04004i
$124$	−1.05652e8	+	5.11537e8i	−0.0401309	+	0.194303i
$125$		−	2.29084e9i		−	0.839266i
$126$	−7.13168e9	−	7.28790e8i	−2.52072	−	0.257593i
$127$		−	5.32324e9i		−	1.81576i	−0.419227	−	0.907881i	$-0.637699\pi$
$127$		−	5.32324e9i		−	1.81576i	0.419227	−	0.907881i	$-0.362301\pi$
$128$	−2.29748e9	−	1.98619e9i	−0.756496	−	0.653999i
$129$		−	5.99561e9i		−	1.90625i
$130$	1.68105e7	−	1.64502e8i	0.00516221	−	0.0505156i
$131$		−	4.18956e9i		−	1.24293i	−0.783441	−	0.621466i	$-0.786537\pi$
$131$		−	4.18956e9i		−	1.24293i	0.783441	−	0.621466i	$-0.213463\pi$
$132$	8.63266e8	−	4.17970e9i	0.247492	−	1.19829i
$133$	5.17718e9			1.43470
$134$	−3.41913e9	−	3.49403e8i	−0.916103	−	0.0936170i
$135$	−2.09844e9			−0.543745
$136$	−7.59823e8	+	2.40920e9i	−0.190453	+	0.603875i
$137$		−	4.90611e9i		−	1.18986i	−0.803779	−	0.594928i	$-0.797181\pi$
$137$		−	4.90611e9i		−	1.18986i	0.803779	−	0.594928i	$-0.202819\pi$
$138$	3.32858e9	+	6.15950e9i	0.781274	+	1.44574i
$139$			7.75727e8i			0.176255i	0.996109	+	0.0881277i	$0.0280883\pi$
$139$			7.75727e8i			0.176255i	−0.996109	+	0.0881277i	$0.971912\pi$
$140$	−6.47037e8	+	3.13278e9i	−0.142348	+	0.689213i
$141$	7.75930e9			1.65324
$142$	7.73126e7	−	7.56555e8i	0.0159571	−	0.156150i
$143$	4.00285e8			0.0800492
$144$	−8.05648e9	−	3.47622e9i	−1.56140	−	0.673714i
$145$		−	1.22284e9i		−	0.229728i
$146$	−4.00255e9	−	4.09022e8i	−0.729036	−	0.0745005i
$147$			1.13519e10i			2.00513i
$148$	−2.85891e8	+	1.38421e9i	−0.0489804	+	0.237150i
$149$			1.14630e10i			1.90528i	0.304094	+	0.952642i	$0.401646\pi$
$149$			1.14630e10i			1.90528i	−0.304094	+	0.952642i	$0.598354\pi$
$150$	8.04759e8	−	7.87509e9i	0.129794	−	1.27012i
$151$		−	3.03012e9i		−	0.474312i	−0.971472	−	0.237156i	$-0.923785\pi$
$151$		−	3.03012e9i		−	0.474312i	0.971472	−	0.237156i	$-0.0762152\pi$
$152$	6.04330e9	+	1.90596e9i	0.918286	+	0.289613i
$153$			7.29858e9i			1.07678i
$154$	−7.70349e9	−	7.87222e8i	−1.10368	−	0.112786i
$155$	6.73404e8			0.0937093
$156$	2.64341e8	−	1.27987e9i	0.0357358	−	0.173023i
$157$		−	1.35428e10i		−	1.77893i	−0.457005	−	0.889464i	$-0.651078\pi$
$157$		−	1.35428e10i		−	1.77893i	0.457005	−	0.889464i	$-0.348922\pi$
$158$	2.70995e8	+	2.76931e7i	0.0345943	+	0.00353520i
$159$	2.26952e10			2.81610
$160$	−1.90860e9	+	3.41867e9i	−0.230237	+	0.412399i
$161$	1.05038e10	−	7.14413e9i	1.23205	−	0.837979i
$162$	−1.66841e9	−	1.70496e8i	−0.190321	−	0.0194489i
$163$			1.20246e10i			1.33422i	0.744961	+	0.667108i	$0.232468\pi$
$163$			1.20246e10i			1.33422i	−0.744961	+	0.667108i	$0.767532\pi$
$164$	5.74182e9	+	1.18590e9i	0.619801	+	0.128012i
$165$	−5.50229e9			−0.577918
$166$	−9.23833e9	−	9.44068e8i	−0.944294	−	0.0964977i
$167$			2.29959e9i			0.228785i	0.993436	+	0.114392i	$0.0364921\pi$
$167$			2.29959e9i			0.228785i	−0.993436	+	0.114392i	$0.963508\pi$
$168$	−7.60429e9	+	2.41112e10i	−0.736490	+	2.33521i
$169$	−1.04819e10			−0.988442
$170$	3.23992e9	+	3.31089e8i	0.297519	+	0.0304036i
$171$	1.83080e10			1.63741
$172$	−1.30395e10	−	2.69315e9i	−1.13601	−	0.234629i
$173$	1.15952e10			0.984173			0.492087	−	0.870546i	$-0.336234\pi$
$173$	1.15952e10			0.984173			0.492087	+	0.870546i	$0.336234\pi$
$174$	9.82503e8	−	9.61444e9i	0.0812573	−	0.795156i
$175$	−1.43628e10			−1.15762
$176$	−8.70242e9	−	3.75493e9i	−0.683649	−	0.294982i
$177$	−3.28090e10			−2.51254
$178$	2.46325e9	−	2.41045e10i	0.183915	−	1.79973i
$179$			3.09341e9i			0.225216i	0.993640	+	0.112608i	$0.0359204\pi$
$179$			3.09341e9i			0.225216i	−0.993640	+	0.112608i	$0.964080\pi$
$180$	−2.28810e9	+	1.10784e10i	−0.162461	+	0.786593i
$181$		−	5.26826e9i		−	0.364849i	−0.983220	−	0.182425i	$-0.941605\pi$
$181$		−	5.26826e9i		−	0.364849i	0.983220	−	0.182425i	$-0.0583946\pi$
$182$	−2.35888e9	−	2.41055e8i	−0.159362	−	0.0162853i
$183$	−1.24483e10			−0.820505
$184$	1.48911e10	−	4.47238e9i	0.957737	−	0.287646i
$185$	1.82221e9			0.114374
$186$	5.29455e9	+	5.41052e8i	0.324355	+	0.0331460i
$187$			7.88376e9i			0.471461i
$188$	3.48537e9	−	1.68752e10i	0.203488	−	0.985234i
$189$			3.00907e10i			1.71536i
$190$	8.30513e8	−	8.12712e9i	0.0462334	−	0.452424i
$191$	1.33560e10			0.726151			0.363075	−	0.931760i	$-0.381727\pi$
$191$	1.33560e10			0.726151			0.363075	+	0.931760i	$0.381727\pi$
$192$	−1.77529e10	+	2.53454e10i	−0.942788	+	1.34599i
$193$	−2.17157e10			−1.12659			−0.563295	−	0.826256i	$-0.690466\pi$
$193$	−2.17157e10			−1.12659			−0.563295	+	0.826256i	$0.690466\pi$
$194$	1.98168e9	−	1.93920e10i	0.100444	−	0.982914i
$195$	−1.68486e9			−0.0834464
$196$	2.46887e10	+	5.09914e9i	1.19494	+	0.246800i
$197$	2.57390e10			1.21757			0.608784	−	0.793336i	$-0.291658\pi$
$197$	2.57390e10			1.21757			0.608784	+	0.793336i	$0.291658\pi$
$198$	−2.72417e10	−	2.78384e9i	−1.25962	−	0.128721i
$199$	−3.57229e9			−0.161476			−0.0807380	−	0.996735i	$-0.525728\pi$
$199$	−3.57229e9			−0.161476			−0.0807380	+	0.996735i	$0.525728\pi$
$200$	−1.67656e10	−	5.28761e9i	−0.740942	−	0.233681i
$201$			3.50194e10i			1.51330i
$202$	2.32779e10	+	2.37878e9i	0.983700	+	0.100525i
$203$	−1.75350e10			−0.724727
$204$	2.52075e10	+	5.20629e9i	1.01904	+	0.210471i
$205$		−	7.55872e9i		−	0.298921i
$206$	1.47793e10	+	1.51030e9i	0.571809	+	0.0584334i
$207$	3.71443e10	−	2.52636e10i	1.40613	−	0.956378i
$208$	−2.66477e9	−	1.14980e9i	−0.0987131	−	0.0425928i
$209$	1.97758e10			0.716930
$210$	3.24251e10	+	3.31353e9i	1.15052	+	0.117572i
$211$		−	5.48943e10i		−	1.90659i	−0.302047	−	0.953293i	$-0.597670\pi$
$211$		−	5.48943e10i		−	1.90659i	0.302047	−	0.953293i	$-0.402330\pi$
$212$	1.01944e10	−	4.93585e10i	0.346617	−	1.67823i
$213$	−7.74877e9			−0.257943
$214$	−4.91966e10	−	5.02742e9i	−1.60352	−	0.163864i
$215$			1.71656e10i			0.547881i
$216$	−1.10778e10	+	3.51248e10i	−0.346268	+	1.09792i
$217$		−	9.65632e9i		−	0.295626i
$218$	4.66877e9	−	4.56870e10i	0.140007	−	1.37006i
$219$			4.09949e10i			1.20429i
$220$	−2.47156e9	+	1.19666e10i	−0.0711326	+	0.344405i
$221$			2.41409e9i			0.0680750i
$222$	1.43269e10	+	1.46407e9i	0.395880	+	0.0404552i
$223$			3.58600e8i			0.00971044i	0.999988	+	0.00485522i	$0.00154547\pi$
$223$			3.58600e8i			0.00971044i	−0.999988	+	0.00485522i	$0.998455\pi$
$224$	4.90223e10	+	2.73685e10i	1.30100	+	0.726333i
$225$	−5.07908e10			−1.32118
$226$	−9.40679e8	+	9.20517e9i	−0.0239858	+	0.234717i
$227$	6.02987e10			1.50727			0.753636	−	0.657292i	$-0.228298\pi$
$227$	6.02987e10			1.50727			0.753636	+	0.657292i	$0.228298\pi$
$228$	1.30596e10	−	6.32311e10i	0.320054	−	1.54962i
$229$		−	2.11403e10i		−	0.507986i	−0.967206	−	0.253993i	$-0.918256\pi$
$229$		−	2.11403e10i		−	0.507986i	0.967206	−	0.253993i	$-0.0817440\pi$
$230$	−9.52983e9	−	1.76348e10i	−0.224548	−	0.415524i
$231$			7.89005e10i			1.82316i
$232$	−2.04686e10	−	6.45547e9i	−0.463865	−	0.146296i
$233$	7.99621e10			1.77739			0.888695	−	0.458499i	$-0.151613\pi$
$233$	7.99621e10			1.77739			0.888695	+	0.458499i	$0.151613\pi$
$234$	−8.34168e9	−	8.52439e8i	−0.181879	−	0.0185863i
$235$	−2.22151e10			−0.475163
$236$	−1.47373e10	+	7.13543e10i	−0.309254	+	1.49733i
$237$		−	2.77558e9i		−	0.0571460i
$238$	4.74767e9	−	4.64591e10i	0.0959145	−	0.938587i
$239$			4.96898e10i			0.985092i	0.870287	+	0.492546i	$0.163934\pi$
$239$			4.96898e10i			0.985092i	−0.870287	+	0.492546i	$0.836066\pi$
$240$	3.66298e10	+	1.58051e10i	0.712662	+	0.307500i
$241$		−	4.85546e10i		−	0.927158i	−0.886056	−	0.463579i	$-0.846565\pi$
$241$		−	4.85546e10i		−	0.927158i	0.886056	−	0.463579i	$-0.153435\pi$
$242$	2.36520e10	+	2.41701e9i	0.443301	+	0.0453011i
$243$		−	4.54854e10i		−	0.836843i
$244$	−5.59162e9	+	2.70732e10i	−0.100991	+	0.488973i
$245$		−	3.25010e10i		−	0.576300i
$246$	6.07311e9	−	5.94294e10i	0.105731	−	1.03465i
$247$	6.05556e9			0.103519
$248$	3.55494e9	−	1.12718e10i	0.0596760	−	0.189217i
$249$			9.46206e10i			1.55987i
$250$	−5.26968e9	+	5.15672e10i	−0.0853206	+	0.834918i
$251$	−3.32748e9			−0.0529156			−0.0264578	−	0.999650i	$-0.508423\pi$
$251$	−3.32748e9			−0.0529156			−0.0264578	+	0.999650i	$0.508423\pi$
$252$	1.58859e11	+	3.28104e10i	2.48147	+	0.512518i
$253$	4.01224e10	−	2.72892e10i	0.615665	−	0.418744i
$254$	−1.22452e10	+	1.19827e11i	−0.184592	+	1.80636i
$255$		−	3.31839e10i		−	0.491469i
$256$	4.71478e10	+	4.99945e10i	0.686090	+	0.727516i
$257$	−6.25932e10			−0.895010			−0.447505	−	0.894281i	$-0.647687\pi$
$257$	−6.25932e10			−0.895010			−0.447505	+	0.894281i	$0.647687\pi$
$258$	−1.37918e10	+	1.34962e11i	−0.193791	+	1.89637i
$259$		−	2.61297e10i		−	0.360816i
$260$	−7.56815e8	+	3.66430e9i	−0.0102709	+	0.0497291i
$261$	−6.20088e10			−0.827125
$262$	−9.63734e9	+	9.43078e10i	−0.126358	+	1.23649i
$263$	4.91557e10			0.633539			0.316769	−	0.948503i	$-0.397402\pi$
$263$	4.91557e10			0.633539			0.316769	+	0.948503i	$0.397402\pi$
$264$	−2.90469e10	+	9.21001e10i	−0.368030	+	1.16692i
$265$	−6.49771e10			−0.809383
$266$	−1.16539e11	−	1.19092e10i	−1.42727	−	0.145853i
$267$	−2.46882e11			−2.97296
$268$	7.61616e10	+	1.57302e10i	0.901840	+	0.186264i
$269$	6.95880e10			0.810306			0.405153	−	0.914249i	$-0.367218\pi$
$269$	6.95880e10			0.810306			0.405153	+	0.914249i	$0.367218\pi$
$270$	4.72363e10	+	4.82710e9i	0.540928	+	0.0552776i
$271$		−	1.46004e11i		−	1.64438i	−0.569211	−	0.822192i	$-0.692751\pi$
$271$		−	1.46004e11i		−	1.64438i	0.569211	−	0.822192i	$-0.307249\pi$
$272$	2.26457e10	−	5.24836e10i	0.250857	−	0.581385i
$273$			2.41601e10i			0.263249i
$274$	−1.12856e10	+	1.10437e11i	−0.120962	+	1.18369i
$275$	−5.48631e10			−0.578473
$276$	−6.07582e10	−	1.46308e11i	−0.630252	−	1.51767i
$277$	9.91775e10			1.01217			0.506086	−	0.862483i	$-0.331092\pi$
$277$	9.91775e10			1.01217			0.506086	+	0.862483i	$0.331092\pi$
$278$	1.78442e9	−	1.74618e10i	0.0179183	−	0.175342i
$279$		−	3.41474e10i		−	0.337395i
$280$	2.17713e10	−	6.90310e10i	0.211677	−	0.671171i
$281$		−	1.29082e11i		−	1.23506i	−0.786547	−	0.617531i	$-0.788133\pi$
$281$		−	1.29082e11i		−	1.23506i	0.786547	−	0.617531i	$-0.211867\pi$
$282$	−1.74663e11	−	1.78489e10i	−1.64468	−	0.168070i
$283$	−5.44613e10			−0.504719			−0.252359	−	0.967634i	$-0.581206\pi$
$283$	−5.44613e10			−0.504719			−0.252359	+	0.967634i	$0.581206\pi$
$284$	−3.48064e9	+	1.68523e10i	−0.0317488	+	0.153719i
$285$	−8.32394e10			−0.747355
$286$	−9.01049e9	−	9.20785e8i	−0.0796345	−	0.00813788i
$287$	−1.08389e11			−0.943008
$288$	1.73356e11	+	9.67828e10i	1.48482	+	0.828957i
$289$	7.10416e10			0.599063
$290$	−2.81294e9	+	2.75264e10i	−0.0233544	+	0.228538i
$291$	−1.98617e11			−1.62367
$292$	8.91573e10	+	1.84143e10i	0.717686	+	0.148229i
$293$		−	2.41301e11i		−	1.91274i	−0.292161	−	0.956369i	$-0.594374\pi$
$293$		−	2.41301e11i		−	1.91274i	0.292161	−	0.956369i	$-0.405626\pi$
$294$	2.61132e10	−	2.55534e11i	0.203843	−	1.99474i
$295$	9.39330e10			0.722137
$296$	9.61957e9	−	3.05011e10i	0.0728355	−	0.230942i
$297$			1.14941e11i			0.857177i
$298$	2.63686e10	−	2.58034e11i	0.193693	−	1.89541i
$299$	1.22859e10	−	8.35623e9i	0.0888968	−	0.0604631i
$300$	−3.62305e10	+	1.75419e11i	−0.258243	+	1.25035i
$301$	2.46147e11			1.72841
$302$	−6.97026e9	+	6.82086e10i	−0.0482190	+	0.471854i
$303$		−	2.38416e11i		−	1.62497i
$304$	−1.31651e11	−	5.68051e10i	−0.884086	−	0.381466i
$305$	3.56400e10			0.235824
$306$	1.67891e10	−	1.64292e11i	0.109466	−	1.07120i
$307$		−	1.12106e11i		−	0.720285i	−0.932897	−	0.360142i	$-0.882728\pi$
$307$		−	1.12106e11i		−	0.720285i	0.932897	−	0.360142i	$-0.117272\pi$
$308$	1.71596e11	+	3.54410e10i	1.08650	+	0.224403i
$309$		−	1.51372e11i		−	0.944566i
$310$	−1.51584e10	−	1.54905e9i	−0.0932238	−	0.00952658i
$311$			7.36911e9i			0.0446677i	0.999751	+	0.0223338i	$0.00710967\pi$
$311$			7.36911e9i			0.0446677i	−0.999751	+	0.0223338i	$0.992890\pi$
$312$	−8.89447e9	+	2.82020e10i	−0.0531403	+	0.168494i
$313$			8.56189e10i			0.504220i	0.967699	+	0.252110i	$0.0811245\pi$
$313$			8.56189e10i			0.504220i	−0.967699	+	0.252110i	$0.918875\pi$
$314$	−3.11527e10	+	3.04850e11i	−0.180848	+	1.76971i
$315$		−	2.09127e11i		−	1.19678i
$316$	−6.03644e9	−	1.24675e9i	−0.0340556	−	0.00703377i
$317$	−2.70059e11			−1.50208			−0.751038	−	0.660259i	$-0.770446\pi$
$317$	−2.70059e11			−1.50208			−0.751038	+	0.660259i	$0.770446\pi$
$318$	−5.10874e11	−	5.22064e10i	−2.80151	−	0.286287i
$319$	−6.69805e10			−0.362151
$320$	5.08271e10	−	7.25645e10i	0.270969	−	0.386856i
$321$			5.03881e11i			2.64884i
$322$	−2.52876e11	+	1.36654e11i	−1.31086	+	0.708386i
$323$			1.19267e11i			0.609687i
$324$	3.71641e10	+	7.67578e9i	0.187357	+	0.0386963i
$325$	−1.67996e10			−0.0835265
$326$	2.76604e10	−	2.70676e11i	0.135638	−	1.32730i
$327$	−4.67934e11			−2.26318
$328$	−1.26522e11	−	3.99029e10i	−0.603576	−	0.190359i
$329$			3.18555e11i			1.49900i
$330$	1.23858e11	+	1.26571e10i	0.574924	+	0.0587517i
$331$			2.64163e11i			1.20961i	0.796374	+	0.604805i	$0.206749\pi$
$331$			2.64163e11i			1.20961i	−0.796374	+	0.604805i	$0.793251\pi$
$332$	2.05785e11	+	4.25023e10i	0.929591	+	0.191996i
$333$		−	9.24020e10i		−	0.411796i
$334$	5.28981e9	−	5.17642e10i	0.0232584	−	0.227599i
$335$		−	1.00262e11i		−	0.434943i
$336$	2.26638e11	−	5.25255e11i	0.970075	−	2.24824i
$337$			1.85032e11i			0.781472i	0.920503	+	0.390736i	$0.127779\pi$
$337$			1.85032e11i			0.781472i	−0.920503	+	0.390736i	$0.872221\pi$
$338$	2.35950e11	+	2.41118e10i	0.983321	+	0.100486i
$339$	9.42810e10			0.387726
$340$	−7.21697e10	−	1.49058e10i	−0.292887	−	0.0604921i
$341$		−	3.68853e10i		−	0.147726i
$342$	−4.12116e11	−	4.21142e10i	−1.62893	−	0.166461i
$343$	−8.40917e10			−0.328042
$344$	2.87326e11	+	9.06183e10i	1.10627	+	0.348902i
$345$	−1.68881e11	+	1.14864e11i	−0.641793	+	0.436515i
$346$	−2.61011e11	−	2.66728e10i	−0.979074	−	0.100052i
$347$		−	2.53864e11i		−	0.939981i	−0.882672	−	0.469990i	$-0.844257\pi$
$347$		−	2.53864e11i		−	0.939981i	0.882672	−	0.469990i	$-0.155743\pi$
$348$	−4.42327e10	+	2.14163e11i	−0.161673	+	0.782776i
$349$	−4.75057e11			−1.71408			−0.857040	−	0.515251i	$-0.827699\pi$
$349$	−4.75057e11			−1.71408			−0.857040	+	0.515251i	$0.827699\pi$
$350$	3.23309e11	+	3.30390e10i	1.15163	+	0.117685i
$351$			3.51961e10i			0.123769i
$352$	1.87256e11	+	1.04543e11i	0.650119	+	0.362954i
$353$	−2.13470e10			−0.0731731			−0.0365865	−	0.999330i	$-0.511648\pi$
$353$	−2.13470e10			−0.0731731			−0.0365865	+	0.999330i	$0.511648\pi$
$354$	7.38536e11	+	7.54713e10i	2.49952	+	0.255427i
$355$	2.21850e10			0.0741363
$356$	−1.10896e11	+	5.36930e11i	−0.365925	+	1.77171i
$357$	−4.75842e11			−1.55044
$358$	7.11584e9	−	6.96332e10i	0.0228956	−	0.224049i
$359$	3.48706e11			1.10799			0.553994	−	0.832521i	$-0.313103\pi$
$359$	3.48706e11			1.10799			0.553994	+	0.832521i	$0.313103\pi$
$360$	7.69895e10	−	2.44113e11i	0.241585	−	0.766002i
$361$	−2.35161e10			−0.0728758
$362$	−1.21187e10	+	1.18590e11i	−0.0370909	+	0.362959i
$363$		−	2.42248e11i		−	0.732285i
$364$	5.25444e10	+	1.08524e10i	0.156881	+	0.0324018i
$365$		−	1.17370e11i		−	0.346129i
$366$	2.80214e11	+	2.86352e10i	0.816254	+	0.0834133i
$367$	−6.18653e11			−1.78012			−0.890061	−	0.455842i	$-0.849338\pi$
$367$	−6.18653e11			−1.78012			−0.890061	+	0.455842i	$0.849338\pi$
$368$	−3.45489e11	+	6.64197e10i	−0.982017	+	0.188791i
$369$	−3.83293e11			−1.07625
$370$	−4.10183e10	−	4.19168e9i	−0.113781	−	0.0116273i
$371$			9.31743e11i			2.55337i
$372$	−1.17937e11	−	2.43583e10i	−0.319305	−	0.0659484i
$373$		−	1.12014e11i		−	0.299628i	−0.988714	−	0.149814i	$-0.952133\pi$
$373$		−	1.12014e11i		−	0.299628i	0.988714	−	0.149814i	$-0.0478675\pi$
$374$	1.81352e10	−	1.77465e11i	0.0479292	−	0.469019i
$375$	5.28161e11			1.37919
$376$	−1.17275e11	+	3.71847e11i	−0.302594	+	0.959443i
$377$	−2.05101e10			−0.0522916
$378$	6.92185e10	−	6.77348e11i	0.174385	−	1.70647i
$379$	2.93368e11			0.730358			0.365179	−	0.930937i	$-0.381008\pi$
$379$	2.93368e11			0.730358			0.365179	+	0.930937i	$0.381008\pi$
$380$	−3.73900e10	+	1.81033e11i	−0.0919877	+	0.445380i
$381$	1.22729e12			2.98390
$382$	−3.00646e11	−	3.07232e10i	−0.722388	−	0.0738211i
$383$	3.11232e11			0.739077			0.369538	−	0.929215i	$-0.379516\pi$
$383$	3.11232e11			0.739077			0.369538	+	0.929215i	$0.379516\pi$
$384$	4.57924e11	−	5.29691e11i	1.07474	−	1.24318i
$385$		−	2.25894e11i		−	0.524001i
$386$	4.88824e11	+	4.99531e10i	1.12075	+	0.114530i
$387$	8.70445e11			1.97261
$388$	−8.92159e10	+	4.31960e11i	−0.199848	+	0.967610i
$389$		−	2.95902e11i		−	0.655201i	−0.944816	−	0.327600i	$-0.893760\pi$
$389$		−	2.95902e11i		−	0.655201i	0.944816	−	0.327600i	$-0.106240\pi$
$390$	3.79265e10	+	3.87572e9i	0.0830140	+	0.00848324i
$391$	1.64579e11	+	2.41975e11i	0.356106	+	0.523570i
$392$	−5.44017e11	−	1.71575e11i	−1.16366	−	0.367000i
$393$	9.65917e11			2.04255
$394$	−5.79389e11	−	5.92080e10i	−1.21126	−	0.123779i
$395$			7.94656e9i			0.0164245i
$396$	6.06811e11	+	1.25329e11i	1.24001	+	0.256109i
$397$	9.08356e11			1.83527			0.917633	−	0.397429i	$-0.130097\pi$
$397$	9.08356e11			1.83527			0.917633	+	0.397429i	$0.130097\pi$
$398$	8.04130e10	+	8.21743e9i	0.160640	+	0.0164158i
$399$			1.19362e12i			2.35769i
$400$	3.65233e11	+	1.57591e11i	0.713347	+	0.307796i
$401$			4.78119e11i			0.923392i	0.887038	+	0.461696i	$0.152759\pi$
$401$			4.78119e11i			0.923392i	−0.887038	+	0.461696i	$0.847241\pi$
$402$	8.05559e10	−	7.88293e11i	0.153844	−	1.50546i
$403$		−	1.12946e10i		−	0.0213304i
$404$	−5.18518e11	−	1.07093e11i	−0.968384	−	0.200008i
$405$		−	4.89239e10i		−	0.0903595i
$406$	3.94717e11	+	4.03363e10i	0.720972	+	0.0736764i
$407$		−	9.98106e10i		−	0.180303i
$408$	−5.55448e11	−	1.75180e11i	−0.992368	−	0.312978i
$409$	−1.93870e11			−0.342574			−0.171287	−	0.985221i	$-0.554793\pi$
$409$	−1.93870e11			−0.342574			−0.171287	+	0.985221i	$0.554793\pi$
$410$	−1.73875e10	+	1.70148e11i	−0.0303885	+	0.297372i
$411$	1.13112e12			1.95533
$412$	−3.29210e11	−	6.79943e10i	−0.562906	−	0.116261i
$413$		−	1.34696e12i		−	2.27813i
$414$	−8.94239e11	+	4.83245e11i	−1.49607	+	0.808474i
$415$		−	2.70902e11i		−	0.448327i
$416$	5.73396e10	+	3.20120e10i	0.0938716	+	0.0524074i
$417$	−1.78846e11			−0.289646
$418$	−4.45158e11	−	4.54909e10i	−0.713216	−	0.0728838i
$419$	4.21305e11			0.667781			0.333890	−	0.942612i	$-0.391638\pi$
$419$	4.21305e11			0.667781			0.333890	+	0.942612i	$0.391638\pi$
$420$	−7.22273e11	−	1.49176e11i	−1.13261	−	0.233926i
$421$		−	6.36523e11i		−	0.987517i	−0.869599	−	0.493758i	$-0.835623\pi$
$421$		−	6.36523e11i		−	0.987517i	0.869599	−	0.493758i	$-0.164377\pi$
$422$	−1.26275e11	+	1.23568e12i	−0.193825	+	1.89671i
$423$			1.12650e12i			1.71080i
$424$	−3.43018e11	+	1.08762e12i	−0.515431	+	1.63429i
$425$		−	3.30875e11i		−	0.491941i
$426$	1.74426e11	+	1.78247e10i	0.256607	+	0.0262228i
$427$		−	5.11061e11i		−	0.743957i
$428$	1.09586e12	+	2.26336e11i	1.57855	+	0.326030i
$429$			9.22871e10i			0.131548i
$430$	3.94865e10	−	3.86401e11i	0.0556981	−	0.545042i
$431$	7.36723e11			1.02839			0.514193	−	0.857674i	$-0.328091\pi$
$431$	7.36723e11			1.02839			0.514193	+	0.857674i	$0.328091\pi$
$432$	3.30162e11	−	7.65182e11i	0.456089	−	1.05703i
$433$		−	4.56378e10i		−	0.0623920i	−0.999513	−	0.0311960i	$-0.990068\pi$
$433$		−	4.56378e10i		−	0.0623920i	0.999513	−	0.0311960i	$-0.00993161\pi$
$434$	−2.22127e10	+	2.17365e11i	−0.0300536	+	0.294094i
$435$	2.81931e11			0.377521
$436$	−2.10190e11	+	1.01768e12i	−0.278562	+	1.34872i
$437$	6.06977e11	−	4.12835e11i	0.796170	−	0.541514i
$438$	9.43015e10	−	9.22802e11i	0.122429	−	1.19805i
$439$		−	8.95862e11i		−	1.15120i	−0.817731	−	0.575600i	$-0.804769\pi$
$439$		−	8.95862e11i		−	1.15120i	0.817731	−	0.575600i	$-0.195231\pi$
$440$	8.31623e10	−	2.63685e11i	0.105777	−	0.335389i
$441$	−1.64808e12			−2.07494
$442$	5.55318e9	−	5.43415e10i	0.00692057	−	0.0677223i
$443$		−	2.48942e11i		−	0.307101i	−0.988141	−	0.153550i	$-0.950929\pi$
$443$		−	2.48942e11i		−	0.307101i	0.988141	−	0.153550i	$-0.0490708\pi$
$444$	−3.19133e11	−	6.59130e10i	−0.389717	−	0.0804911i
$445$	7.06832e11			0.854468
$446$	8.24897e8	−	8.07216e9i	0.000987172	−	0.00966013i
$447$	−2.64283e12			−3.13102
$448$	−1.04054e12	−	7.28838e11i	−1.22042	−	0.854831i
$449$	−1.11054e12			−1.28951			−0.644755	−	0.764389i	$-0.723041\pi$
$449$	−1.11054e12			−1.28951			−0.644755	+	0.764389i	$0.723041\pi$
$450$	1.14331e12	+	1.16835e11i	1.31434	+	0.134313i
$451$	−4.14024e11			−0.471228
$452$	4.23497e10	−	2.05046e11i	0.0477230	−	0.231062i
$453$	6.98605e11			0.779453
$454$	−1.35733e12	−	1.38707e11i	−1.49946	−	0.153231i
$455$		−	6.91712e10i		−	0.0756613i
$456$	−4.39426e11	+	1.39330e12i	−0.475931	+	1.50905i
$457$			5.28900e11i			0.567219i	0.958940	+	0.283610i	$0.0915320\pi$
$457$			5.28900e11i			0.567219i	−0.958940	+	0.283610i	$0.908468\pi$
$458$	−4.86296e10	+	4.75872e11i	−0.0516423	+	0.505354i
$459$	−6.93199e11			−0.728955
$460$	1.73953e11	+	4.18885e11i	0.181143	+	0.436199i
$461$	2.50505e11			0.258322			0.129161	−	0.991624i	$-0.458772\pi$
$461$	2.50505e11			0.258322			0.129161	+	0.991624i	$0.458772\pi$
$462$	1.81497e11	−	1.77606e12i	0.185345	−	1.81372i
$463$		−	2.50290e11i		−	0.253122i	−0.991959	−	0.126561i	$-0.959606\pi$
$463$		−	2.50290e11i		−	0.253122i	0.991959	−	0.126561i	$-0.0403939\pi$
$464$	4.45901e11	+	1.92398e11i	0.446589	+	0.192695i
$465$			1.55256e11i			0.153996i
$466$	−1.79996e12	−	1.83939e11i	−1.76818	−	0.180691i
$467$	−1.25280e12			−1.21887			−0.609434	−	0.792837i	$-0.708603\pi$
$467$	−1.25280e12			−1.21887			−0.609434	+	0.792837i	$0.708603\pi$
$468$	1.85812e11	+	3.83771e10i	0.179047	+	0.0369799i
$469$	−1.43771e12			−1.37212
$470$	5.00066e11	+	5.11019e10i	0.472701	+	0.0483055i
$471$	3.12233e12			2.92337
$472$	4.95878e11	−	1.57230e12i	0.459871	−	1.45813i
$473$	9.40236e11			0.863697
$474$	−6.38473e9	+	6.24788e10i	−0.00580951	+	0.0568499i
$475$	−8.29976e11			−0.748073
$476$	−2.13742e11	+	1.03488e12i	−0.190835	+	0.923973i
$477$			3.29490e12i			2.91414i
$478$	1.14303e11	−	1.11853e12i	0.100145	−	0.979988i
$479$	1.49782e12			1.30002			0.650008	−	0.759927i	$-0.274765\pi$
$479$	1.49782e12			1.30002			0.650008	+	0.759927i	$0.274765\pi$
$480$	−7.88186e11	−	4.40035e11i	−0.677709	−	0.378357i
$481$		−	3.05630e10i		−	0.0260341i
$482$	−1.11691e11	+	1.09297e12i	−0.0942558	+	0.922355i
$483$	1.64710e12	+	2.42168e12i	1.37708	+	2.02467i
$484$	−5.26851e11	−	1.08815e11i	−0.436399	−	0.0901328i
$485$	5.68645e11			0.466663
$486$	−1.04631e11	+	1.02388e12i	−0.0850742	+	0.832507i
$487$		−	1.94413e11i		−	0.156619i	−0.996929	−	0.0783094i	$-0.975048\pi$
$487$		−	1.94413e11i		−	0.156619i	0.996929	−	0.0783094i	$-0.0249522\pi$
$488$	1.88146e11	−	5.96559e11i	0.150177	−	0.476173i
$489$	−2.77231e12			−2.19256
$490$	−7.47628e10	+	7.31603e11i	−0.0585872	+	0.573315i
$491$			5.33049e11i			0.413905i	0.978351	+	0.206953i	$0.0663546\pi$
$491$			5.33049e11i			0.413905i	−0.978351	+	0.206953i	$0.933645\pi$
$492$	−2.73414e11	+	1.32380e12i	−0.210367	+	1.01854i
$493$		−	4.03954e11i		−	0.307979i
$494$	−1.36312e11	−	1.39298e10i	−0.102982	−	0.0105238i
$495$		−	7.98826e11i		−	0.598038i
$496$	−1.05951e11	+	2.45552e11i	−0.0786028	+	0.182170i
$497$		−	3.18123e11i		−	0.233879i
$498$	2.17658e11	−	2.12993e12i	0.158578	−	1.55179i
$499$			2.16822e12i			1.56549i	0.622341	+	0.782746i	$0.286182\pi$
$499$			2.16822e12i			1.56549i	−0.622341	+	0.782746i	$0.713818\pi$
$500$	2.37243e11	−	1.14867e12i	0.169757	−	0.821919i
$501$	−5.30179e11			−0.375969
$502$	7.49022e10	+	7.65428e9i	0.0526415	+	0.00537945i
$503$	4.67481e11			0.325618			0.162809	−	0.986658i	$-0.447945\pi$
$503$	4.67481e11			0.325618			0.162809	+	0.986658i	$0.447945\pi$
$504$	−3.50047e12	−	1.10400e12i	−2.41651	−	0.762131i
$505$			6.82593e11i			0.467037i
$506$	−9.65937e11	+	5.21991e11i	−0.655045	+	0.353986i
$507$		−	2.41664e12i		−	1.62434i
$508$	5.51282e11	−	2.66916e12i	0.367272	−	1.77823i
$509$	1.78854e12			1.18105			0.590524	−	0.807020i	$-0.298921\pi$
$509$	1.78854e12			1.18105			0.590524	+	0.807020i	$0.298921\pi$
$510$	−7.63337e10	+	7.46975e11i	−0.0499632	+	0.488923i
$511$	−1.68303e12			−1.09194
$512$	−9.46302e11	−	1.23384e12i	−0.608576	−	0.793496i
$513$			1.73884e12i			1.10849i
$514$	1.40898e12	+	1.43985e11i	0.890373	+	0.0909875i
$515$			4.33383e11i			0.271481i
$516$	6.20914e11	−	3.00630e12i	0.385574	−	1.86685i
$517$			1.21682e12i			0.749063i
$518$	−6.01069e10	+	5.88185e11i	−0.0366809	+	0.358947i
$519$			2.67332e12i			1.61733i
$520$	2.54651e10	−	8.07431e10i	0.0152732	−	0.0484273i
$521$			2.02033e12i			1.20130i	0.799511	+	0.600651i	$0.205092\pi$
$521$			2.02033e12i			1.20130i	−0.799511	+	0.600651i	$0.794908\pi$
$522$	1.39583e12	+	1.42640e11i	0.822839	+	0.0840863i
$523$	−2.76287e12			−1.61474			−0.807370	−	0.590045i	$-0.799110\pi$
$523$	−2.76287e12			−1.61474			−0.807370	+	0.590045i	$0.799110\pi$
$524$	4.33877e11	−	2.10072e12i	0.251406	−	1.21724i
$525$		−	3.31139e12i		−	1.90236i
$526$	−1.10650e12	−	1.13074e11i	−0.630257	−	0.0644062i
$527$	2.22452e11			0.125629
$528$	8.65712e11	−	2.00637e12i	0.484754	−	1.12346i
$529$	6.61789e11	−	1.67517e12i	0.367425	−	0.930053i
$530$	1.46265e12	+	1.49468e11i	0.805189	+	0.0822826i
$531$		−	4.76322e12i		−	2.60001i
$532$	2.59593e12	+	5.36157e11i	1.40504	+	0.290195i
$533$	−1.26778e11			−0.0680413
$534$	5.55737e12	+	5.67910e11i	2.95756	+	0.302234i
$535$		−	1.44263e12i		−	0.761310i
$536$	−1.67823e12	−	5.29287e11i	−0.878232	−	0.276981i
$537$	−7.13196e11			−0.370105
$538$	−1.56644e12	−	1.60075e11i	−0.806108	−	0.0823765i
$539$	−1.78022e12			−0.908499
$540$	−1.05219e12	−	2.17318e11i	−0.532506	−	0.109982i
$541$	1.53750e12			0.771661			0.385831	−	0.922570i	$-0.373915\pi$
$541$	1.53750e12			0.771661			0.385831	+	0.922570i	$0.373915\pi$
$542$	−3.35857e11	+	3.28658e12i	−0.167170	+	1.63586i
$543$	1.21462e12			0.599569
$544$	−6.30488e11	+	1.12932e12i	−0.308661	+	0.552870i
$545$	1.33971e12			0.650469
$546$	5.55761e10	−	5.43849e11i	0.0267622	−	0.261885i
$547$		−	2.63421e12i		−	1.25808i	−0.777375	−	0.629038i	$-0.783449\pi$
$547$		−	2.63421e12i		−	1.25808i	0.777375	−	0.629038i	$-0.216551\pi$
$548$	5.08084e11	−	2.46001e12i	0.240670	−	1.16526i
$549$		−	1.80726e12i		−	0.849071i
$550$	1.23498e12	+	1.26203e11i	0.575476	+	0.0588081i
$551$	−1.01329e12			−0.468329
$552$	1.03112e12	+	3.43319e12i	0.472698	+	1.57388i
$553$	1.13950e11			0.0518146
$554$	−2.23250e12	−	2.28140e11i	−1.00693	−	0.102898i
$555$			4.20117e11i			0.187954i
$556$	−8.03354e10	+	3.88963e11i	−0.0356509	+	0.172612i
$557$			7.25002e11i			0.319147i	0.987186	+	0.159574i	$0.0510119\pi$
$557$			7.25002e11i			0.319147i	−0.987186	+	0.159574i	$0.948988\pi$
$558$	−7.85502e10	+	7.68665e11i	−0.0342999	+	0.335647i
$559$	2.87910e11			0.124711
$560$	−6.48870e11	+	1.50382e12i	−0.278812	+	0.646175i
$561$	−1.81763e12			−0.774768
$562$	−2.96931e11	+	2.90567e12i	−0.125558	+	1.22866i
$563$	1.47624e12			0.619255			0.309628	−	0.950858i	$-0.399796\pi$
$563$	1.47624e12			0.619255			0.309628	+	0.950858i	$0.399796\pi$
$564$	3.89064e12	+	8.03564e11i	1.61907	+	0.334399i
$565$	−2.69929e11			−0.111438
$566$	1.22593e12	+	1.25279e11i	0.502104	+	0.0513102i
$567$	−7.01548e11			−0.285058
$568$	1.17116e11	−	3.71343e11i	0.0472115	−	0.149695i
$569$		−	2.82090e12i		−	1.12819i	−0.825709	−	0.564096i	$-0.809225\pi$
$569$		−	2.82090e12i		−	1.12819i	0.825709	−	0.564096i	$-0.190775\pi$
$570$	1.87373e12	+	1.91478e11i	0.743483	+	0.0759768i
$571$	−2.84946e12			−1.12176			−0.560880	−	0.827897i	$-0.689537\pi$
$571$	−2.84946e12			−1.12176			−0.560880	+	0.827897i	$0.689537\pi$
$572$	2.00710e11	+	4.14541e10i	0.0783946	+	0.0161914i
$573$			3.07927e12i			1.19331i
$574$	2.43985e12	+	2.49329e11i	0.938123	+	0.0958671i
$575$	−1.68390e12	+	1.14531e12i	−0.642409	+	0.436934i
$576$	−3.67965e12	−	2.57738e12i	−1.39285	−	0.975611i
$577$	−2.55700e12			−0.960372			−0.480186	−	0.877167i	$-0.659431\pi$
$577$	−2.55700e12			−0.960372			−0.480186	+	0.877167i	$0.659431\pi$
$578$	−1.59916e12	−	1.63419e11i	−0.595959	−	0.0609013i
$579$		−	5.00663e12i		−	1.85136i
$580$	1.26639e11	−	6.13154e11i	0.0464668	−	0.224980i
$581$	−3.88461e12			−1.41434
$582$	4.47090e12	+	4.56883e11i	1.61526	+	0.165064i
$583$			3.55908e12i			1.27594i
$584$	−1.96459e12	−	6.19601e11i	−0.698898	−	0.220422i
$585$		−	2.44609e11i		−	0.0863516i
$586$	−5.55071e11	+	5.43174e12i	−0.194451	+	1.90283i
$587$		−	1.42354e12i		−	0.494878i	−0.968904	−	0.247439i	$-0.920411\pi$
$587$		−	1.42354e12i		−	0.494878i	0.968904	−	0.247439i	$-0.0795889\pi$
$588$	−1.17562e12	+	5.69206e12i	−0.405574	+	1.96368i
$589$		−	5.58005e11i		−	0.191038i
$590$	−2.11445e12	−	2.16076e11i	−0.718395	−	0.0734131i
$591$			5.93421e12i			2.00087i
$592$	−2.86701e11	+	6.64457e11i	−0.0959359	+	0.222341i
$593$	3.62278e12			1.20309			0.601543	−	0.798841i	$-0.294553\pi$
$593$	3.62278e12			1.20309			0.601543	+	0.798841i	$0.294553\pi$
$594$	2.64401e11	−	2.58734e12i	0.0871414	−	0.852736i
$595$	1.36235e12			0.445618
$596$	−1.18712e12	+	5.74774e12i	−0.385379	+	1.86590i
$597$		−	8.23604e11i		−	0.265359i
$598$	−2.95780e11	+	1.59839e11i	−0.0945830	+	0.0511125i
$599$		−	1.07952e12i		−	0.342619i	−0.985217	−	0.171309i	$-0.945200\pi$
$599$		−	1.07952e12i		−	0.342619i	0.985217	−	0.171309i	$-0.0547997\pi$
$600$	1.21908e12	−	3.86536e12i	0.384017	−	1.21761i
$601$	−1.72439e11			−0.0539137			−0.0269569	−	0.999637i	$-0.508582\pi$
$601$	−1.72439e11			−0.0539137			−0.0269569	+	0.999637i	$0.508582\pi$
$602$	−5.54082e12	−	5.66219e11i	−1.71945	−	0.175711i
$603$	−5.08413e12			−1.56599
$604$	3.13804e11	−	1.51935e12i	0.0959383	−	0.464508i
$605$			6.93563e11i			0.210468i
$606$	−5.48435e11	+	5.36680e12i	−0.165196	+	1.61655i
$607$		−	1.63886e12i		−	0.489996i	−0.969524	−	0.244998i	$-0.921213\pi$
$607$		−	1.63886e12i		−	0.489996i	0.969524	−	0.244998i	$-0.0787873\pi$
$608$	2.83283e12	+	1.58153e12i	0.840725	+	0.469367i
$609$		−	4.04276e12i		−	1.19097i
$610$	−8.02262e11	−	8.19835e10i	−0.234602	−	0.0239741i
$611$			3.72602e11i			0.108158i
$612$	−7.55851e11	+	3.65963e12i	−0.217799	+	1.05452i
$613$		−	4.45896e12i		−	1.27545i	−0.770266	−	0.637723i	$-0.779877\pi$
$613$		−	4.45896e12i		−	1.27545i	0.770266	−	0.637723i	$-0.220123\pi$
$614$	−2.57879e11	+	2.52352e12i	−0.0732248	+	0.716553i
$615$	1.74269e12			0.491226
$616$	−3.78113e12	−	1.19251e12i	−1.05806	−	0.333695i
$617$			6.58424e12i			1.82904i	0.404545	+	0.914518i	$0.367430\pi$
$617$			6.58424e12i			1.82904i	−0.404545	+	0.914518i	$0.632570\pi$
$618$	−3.48205e11	+	3.40741e12i	−0.0960255	+	0.939673i
$619$	5.23334e12			1.43275			0.716376	−	0.697714i	$-0.245800\pi$
$619$	5.23334e12			1.43275			0.716376	+	0.697714i	$0.245800\pi$
$620$	3.37656e11	+	6.97387e10i	0.0917724	+	0.0189544i
$621$	2.39947e12	+	3.52786e12i	0.647446	+	0.951918i
$622$	1.69513e10	−	1.65880e11i	0.00454096	−	0.0444362i
$623$		−	1.01357e13i		−	2.69560i
$624$	2.65090e11	−	6.14372e11i	0.0699943	−	0.162219i
$625$	1.45157e12			0.380519
$626$	1.96951e11	−	1.92730e12i	0.0512595	−	0.501608i
$627$			4.55939e12i			1.17816i
$628$	1.40251e12	−	6.79057e12i	0.359821	−	1.74216i
$629$	6.01950e11			0.153332
$630$	−4.81060e11	+	4.70749e12i	−0.121665	+	1.19058i
$631$	4.84670e11			0.121707			0.0608533	−	0.998147i	$-0.480618\pi$
$631$	4.84670e11			0.121707			0.0608533	+	0.998147i	$0.480618\pi$
$632$	1.33013e11	+	4.19504e10i	0.0331641	+	0.0104595i
$633$	1.26561e13			3.13316
$634$	6.07908e12	+	6.21223e11i	1.49429	+	0.152702i
$635$	−3.51377e12			−0.857613
$636$	1.13798e13	+	2.35035e12i	2.75789	+	0.569607i
$637$	−5.45122e11			−0.131179
$638$	1.50774e12	+	1.54077e11i	0.360275	+	0.0368167i
$639$		−	1.12497e12i		−	0.266924i
$640$	−1.31105e12	+	1.51652e12i	−0.308894	+	0.357305i
$641$		−	5.23550e12i		−	1.22489i	−0.790513	−	0.612445i	$-0.790186\pi$
$641$		−	5.23550e12i		−	1.22489i	0.790513	−	0.612445i	$-0.209814\pi$
$642$	1.15909e12	−	1.13425e13i	0.269283	−	2.63511i
$643$	−2.53647e12			−0.585169			−0.292584	−	0.956240i	$-0.594515\pi$
$643$	−2.53647e12			−0.585169			−0.292584	+	0.956240i	$0.594515\pi$
$644$	6.00663e12	−	2.49440e12i	1.37608	−	0.571453i
$645$	−3.95759e12			−0.900351
$646$	2.74352e11	−	2.68471e12i	0.0619814	−	0.606529i
$647$			7.14041e12i			1.60197i	0.598685	+	0.800984i	$0.295690\pi$
$647$			7.14041e12i			1.60197i	−0.598685	+	0.800984i	$0.704310\pi$
$648$	−8.18913e11	−	2.58273e11i	−0.182453	−	0.0575428i
$649$		−	5.14513e12i		−	1.13840i
$650$	3.78163e11	+	3.86446e10i	0.0830938	+	0.00849139i
$651$	2.22630e12			0.485812
$652$	−1.24528e12	+	6.02933e12i	−0.269870	+	1.30664i
$653$	3.36164e12			0.723506			0.361753	−	0.932274i	$-0.382178\pi$
$653$	3.36164e12			0.723506			0.361753	+	0.932274i	$0.382178\pi$
$654$	1.05333e13	+	1.07640e12i	2.25146	+	0.230077i
$655$	−2.76545e12			−0.587056
$656$	2.75623e12	+	1.18926e12i	0.581097	+	0.250733i
$657$	−5.95166e12			−1.24622
$658$	7.32779e11	−	7.17073e12i	0.152390	−	1.49124i
$659$	−6.39951e12			−1.32179			−0.660895	−	0.750479i	$-0.729823\pi$
$659$	−6.39951e12			−1.32179			−0.660895	+	0.750479i	$0.729823\pi$
$660$	−2.75894e12	−	5.69826e11i	−0.565972	−	0.116895i
$661$			1.50415e12i			0.306467i	0.988190	+	0.153233i	$0.0489687\pi$
$661$			1.50415e12i			0.306467i	−0.988190	+	0.153233i	$0.951031\pi$
$662$	6.07659e11	−	5.94635e12i	0.122970	−	1.20334i
$663$	−5.56576e11			−0.111870
$664$	−4.53449e12	−	1.43011e12i	−0.905257	−	0.285504i
$665$		−	3.41736e12i		−	0.677631i
$666$	−2.12555e11	+	2.07999e12i	−0.0418636	+	0.409663i
$667$	−2.05582e12	+	1.39827e12i	−0.402179	+	0.273542i
$668$	−2.38149e11	+	1.15305e12i	−0.0462759	+	0.224056i
$669$	−8.26765e10			−0.0159575
$670$	−2.30634e11	+	2.25691e12i	−0.0442168	+	0.432690i
$671$		−	1.95216e12i		−	0.371761i
$672$	−6.30991e12	+	1.13022e13i	−1.19361	+	2.13798i
$673$	−1.34419e12			−0.252576			−0.126288	−	0.991994i	$-0.540306\pi$
$673$	−1.34419e12			−0.252576			−0.126288	+	0.991994i	$0.540306\pi$
$674$	4.25635e11	−	4.16511e12i	0.0794451	−	0.777423i
$675$		−	4.82397e12i		−	0.894413i
$676$	−5.25582e12	−	1.08552e12i	−0.968011	−	0.199931i
$677$			5.60534e9i			0.00102554i	1.00000		0.000512771i	$0.000163220\pi$
$677$			5.60534e9i			0.00102554i	−1.00000		0.000512771i	$0.999837\pi$
$678$	−2.12228e12	−	2.16877e11i	−0.385718	−	0.0394166i
$679$		−	8.15412e12i		−	1.47219i
$680$	1.59027e12	+	5.01545e11i	0.285220	+	0.0899539i
$681$			1.39021e13i			2.47695i
$682$	−8.48481e10	+	8.30295e11i	−0.0150180	+	0.146961i
$683$		−	1.75024e12i		−	0.307754i	−0.988090	−	0.153877i	$-0.950824\pi$
$683$		−	1.75024e12i		−	0.307754i	0.988090	−	0.153877i	$-0.0491760\pi$
$684$	9.17992e12	+	1.89600e12i	1.60356	+	0.331196i
$685$	−3.23843e12			−0.561988
$686$	1.89292e12	+	1.93438e11i	0.326342	+	0.0333491i
$687$	4.87397e12			0.834791
$688$	−6.25932e12	−	2.70078e12i	−1.06507	−	0.459559i
$689$			1.08983e12i			0.184234i
$690$	4.06577e12	−	2.19714e12i	0.682844	−	0.369008i
$691$			2.09093e11i			0.0348890i	0.999848	+	0.0174445i	$0.00555304\pi$
$691$			2.09093e11i			0.0348890i	−0.999848	+	0.0174445i	$0.994447\pi$
$692$	5.81404e12	+	1.20082e12i	0.963830	+	0.199067i
$693$	−1.14548e13			−1.88664
$694$	−5.83970e11	+	5.71453e12i	−0.0955593	+	0.935111i
$695$	5.12043e11			0.0832482
$696$	1.48833e12	−	4.71909e12i	0.240413	−	0.762285i
$697$		−	2.49695e12i		−	0.400739i
$698$	1.06936e13	+	1.09278e12i	1.70520	+	0.174255i
$699$			1.84355e13i			2.92084i
$700$	−7.20174e12	−	1.48743e12i	−1.13370	−	0.234151i
$701$			1.30487e12i			0.204097i	0.994779	+	0.102048i	$0.0325396\pi$
$701$			1.30487e12i			0.204097i	−0.994779	+	0.102048i	$0.967460\pi$
$702$	8.09624e10	−	7.92270e11i	0.0125825	−	0.123128i
$703$		−	1.50995e12i		−	0.233165i
$704$	−3.97468e12	−	2.78402e12i	−0.609853	−	0.427165i
$705$		−	5.12177e12i		−	0.780852i
$706$	4.80526e11	+	4.91051e10i	0.0727940	+	0.00743884i
$707$	9.78809e12			1.47337
$708$	−1.64510e13	−	3.39774e12i	−2.46061	−	0.508207i
$709$			1.09495e13i			1.62737i	0.581309	+	0.813683i	$0.302541\pi$
$709$			1.09495e13i			1.62737i	−0.581309	+	0.813683i	$0.697459\pi$
$710$	−4.99388e11	−	5.10326e10i	−0.0737522	−	0.00753677i
$711$	4.02960e11			0.0591355
$712$	3.73141e12	−	1.18313e13i	0.544143	−	1.72533i
$713$	−7.70006e11	−	1.13211e12i	−0.111581	−	0.164054i
$714$	1.07113e13	+	1.09459e12i	1.54241	+	0.157620i
$715$		−	2.64221e11i		−	0.0378085i
$716$	−3.20358e11	+	1.55109e12i	−0.0455540	+	0.220561i
$717$	−1.14561e13			−1.61883
$718$	−7.84944e12	−	8.02137e11i	−1.10225	−	0.112639i
$719$		−	4.69130e12i		−	0.654657i	−0.944911	−	0.327328i	$-0.893852\pi$
$719$		−	4.69130e12i		−	0.654657i	0.944911	−	0.327328i	$-0.106148\pi$
$720$	−2.29459e12	+	5.31793e12i	−0.318206	+	0.737473i
$721$	6.21452e12			0.856444
$722$	5.29352e11	+	5.40947e10i	0.0724982	+	0.00740862i
$723$	1.11944e13			1.52363
$724$	5.45589e11	−	2.64160e12i	0.0737975	−	0.357308i
$725$	2.81112e12			0.377883
$726$	−5.57249e11	+	5.45305e12i	−0.0744448	+	0.728492i
$727$	4.15265e12			0.551342			0.275671	−	0.961252i	$-0.411100\pi$
$727$	4.15265e12			0.551342			0.275671	+	0.961252i	$0.411100\pi$
$728$	−1.15782e12	−	3.65159e11i	−0.152774	−	0.0481826i
$729$	1.19457e13			1.56652
$730$	−2.69988e11	+	2.64201e12i	−0.0351878	+	0.344335i
$731$			5.67048e12i			0.734500i
$732$	−6.24181e12	−	1.28917e12i	−0.803546	−	0.165962i
$733$			7.51302e11i			0.0961272i	0.998844	+	0.0480636i	$0.0153050\pi$
$733$			7.51302e11i			0.0961272i	−0.998844	+	0.0480636i	$0.984695\pi$
$734$	1.39260e13	+	1.42310e12i	1.77090	+	0.180969i
$735$	7.49321e12			0.947054
$736$	7.92981e12	−	7.00383e11i	0.996122	−	0.0879804i
$737$	−5.49176e12			−0.685659
$738$	8.62799e12	+	8.81697e11i	1.07067	+	0.109412i
$739$			1.13181e13i			1.39596i	0.716118	+	0.697979i	$0.245917\pi$
$739$			1.13181e13i			1.39596i	−0.716118	+	0.697979i	$0.754083\pi$
$740$	9.13688e11	+	1.88711e11i	0.112010	+	0.0231342i
$741$			1.39613e12i			0.170116i
$742$	2.14331e12	−	2.09737e13i	0.259578	−	2.54014i
$743$	−8.27216e12			−0.995794			−0.497897	−	0.867236i	$-0.665894\pi$
$743$	−8.27216e12			−0.995794			−0.497897	+	0.867236i	$0.665894\pi$
$744$	2.59874e12	+	8.19603e11i	0.310946	+	0.0980676i
$745$	7.56651e12			0.899896
$746$	−2.57668e11	+	2.52145e12i	−0.0304604	+	0.298076i
$747$	−1.37371e13			−1.61418
$748$	−8.16454e11	+	3.95305e12i	−0.0953618	+	0.461716i
$749$	−2.06866e13			−2.40171
$750$	−1.18890e13	−	1.21494e12i	−1.37205	−	0.140210i
$751$	5.14925e11			0.0590696			0.0295348	−	0.999564i	$-0.490597\pi$
$751$	5.14925e11			0.0590696			0.0295348	+	0.999564i	$0.490597\pi$
$752$	3.49525e12	−	8.10058e12i	0.398564	−	0.923711i
$753$		−	7.67162e11i		−	0.0869580i
$754$	4.61686e11	+	4.71799e10i	0.0520207	+	0.00531601i
$755$	−2.00013e12			−0.224025
$756$	−3.11624e12	+	1.50880e13i	−0.346963	+	1.67990i
$757$			7.02355e12i			0.777365i	0.921372	+	0.388683i	$0.127070\pi$
$757$			7.02355e12i			0.777365i	−0.921372	+	0.388683i	$0.872930\pi$
$758$	−6.60376e12	−	6.74841e11i	−0.726574	−	0.0742489i
$759$	6.29162e12	+	9.25036e12i	0.688136	+	1.01174i
$760$	1.25809e12	−	3.98907e12i	0.136789	−	0.433721i
$761$	4.74214e12			0.512559			0.256279	−	0.966603i	$-0.417503\pi$
$761$	4.74214e12			0.512559			0.256279	+	0.966603i	$0.417503\pi$
$762$	−2.76265e13	−	2.82317e12i	−2.96845	−	0.303347i
$763$		−	1.92109e13i		−	2.05204i
$764$	6.69693e12	+	1.38317e12i	0.711141	+	0.146877i
$765$	4.81765e12			0.508580
$766$	−7.00589e12	−	7.15934e11i	−0.735248	−	0.0751353i
$767$		−	1.57549e12i		−	0.164375i
$768$	−1.15264e13	+	1.08701e13i	−1.19555	+	1.12748i
$769$			9.40460e12i			0.969777i	0.874576	+	0.484888i	$0.161140\pi$
$769$			9.40460e12i			0.969777i	−0.874576	+	0.484888i	$0.838860\pi$
$770$	−5.19630e11	+	5.08493e12i	−0.0532704	+	0.521286i
$771$		−	1.44311e13i		−	1.47080i
$772$	−1.08886e13	−	2.24891e12i	−1.10330	−	0.227874i
$773$		−	5.08511e12i		−	0.512263i	−0.966642	−	0.256131i	$-0.917552\pi$
$773$		−	5.08511e12i		−	0.512263i	0.966642	−	0.256131i	$-0.0824480\pi$
$774$	−1.95939e13	−	2.00231e12i	−1.96239	−	0.200538i
$775$			1.54804e12i			0.154144i
$776$	3.00191e12	−	9.51827e12i	0.297181	−	0.942280i
$777$	6.02430e12			0.592941
$778$	−6.80670e11	+	6.66080e12i	−0.0666083	+	0.651806i
$779$	−6.26341e12			−0.609386
$780$	−8.44816e11	−	1.74486e11i	−0.0817215	−	0.0168786i
$781$		−	1.21517e12i		−	0.116871i
$782$	−3.14808e12	−	5.82549e12i	−0.301034	−	0.557060i
$783$		−	5.88943e12i		−	0.559945i
$784$	1.18513e13	+	5.11359e12i	1.12032	+	0.483397i
$785$	−8.93932e12			−0.840216
$786$	−2.17430e13	−	2.22192e12i	−2.03197	−	0.207648i
$787$	−6.81557e12			−0.633310			−0.316655	−	0.948541i	$-0.602560\pi$
$787$	−6.81557e12			−0.633310			−0.316655	+	0.948541i	$0.602560\pi$
$788$	1.29060e13	+	2.66557e12i	1.19240	+	0.246276i
$789$			1.13330e13i			1.04112i
$790$	1.82797e10	−	1.78879e11i	0.00166973	−	0.0163394i
$791$			3.87067e12i			0.351554i
$792$	−1.33711e13	−	4.21705e12i	−1.20755	−	0.380843i
$793$		−	5.97770e11i		−	0.0536791i
$794$	−2.04473e13	−	2.08951e12i	−1.82576	−	0.186575i
$795$		−	1.49807e13i		−	1.33009i
$796$	−1.79121e12	−	3.69952e11i	−0.158138	−	0.0326615i
$797$			6.11365e12i			0.536708i	0.963320	+	0.268354i	$0.0864797\pi$
$797$			6.11365e12i			0.536708i	−0.963320	+	0.268354i	$0.913520\pi$
$798$	2.74571e12	−	2.68685e13i	0.239685	−	2.34548i
$799$	−7.33853e12			−0.637014
$800$	−7.85896e12	−	4.38757e12i	−0.678360	−	0.378720i
$801$		−	3.58425e13i		−	3.07647i
$802$	1.09983e12	−	1.07625e13i	0.0938729	−	0.918608i
$803$	−6.42884e12			−0.545648
$804$	−3.62666e12	+	1.75593e13i	−0.306094	+	1.48202i
$805$	−4.71571e12	−	6.93334e12i	−0.395790	−	0.581917i
$806$	−2.59813e10	+	2.54245e11i	−0.00216847	+	0.0212199i
$807$			1.60437e13i			1.33160i
$808$	1.14256e13	+	3.60345e12i	0.943034	+	0.297418i
$809$	−4.01189e11			−0.0329292			−0.0164646	−	0.999864i	$-0.505241\pi$
$809$	−4.01189e11			−0.0329292			−0.0164646	+	0.999864i	$0.505241\pi$
$810$	−1.12541e11	+	1.10129e12i	−0.00918603	+	0.0898914i
$811$			4.97597e12i			0.403910i	0.979395	+	0.201955i	$0.0647294\pi$
$811$			4.97597e12i			0.403910i	−0.979395	+	0.201955i	$0.935271\pi$
$812$	−8.79237e12	−	1.81595e12i	−0.709747	−	0.146589i
$813$	3.36617e13			2.70227
$814$	−2.29597e11	+	2.24675e12i	−0.0183297	+	0.179368i
$815$	7.93720e12			0.630171
$816$	1.21003e13	+	5.22104e12i	0.955409	+	0.412241i
$817$	1.42240e13			1.11692
$818$	4.36404e12	+	4.45963e11i	0.340799	+	0.0348264i
$819$	−3.50758e12			−0.272414
$820$	7.82792e11	−	3.79007e12i	0.0604622	−	0.292742i
$821$	6.88725e12			0.529056			0.264528	−	0.964378i	$-0.414784\pi$
$821$	6.88725e12			0.529056			0.264528	+	0.964378i	$0.414784\pi$
$822$	−2.54617e13	−	2.60194e12i	−1.94520	−	0.198781i
$823$			1.89747e13i			1.44170i	0.693090	+	0.720851i	$0.256249\pi$
$823$			1.89747e13i			1.44170i	−0.693090	+	0.720851i	$0.743751\pi$
$824$	7.25417e12	+	2.28785e12i	0.548170	+	0.172884i
$825$		−	1.26489e13i		−	0.950624i
$826$	−3.09844e12	+	3.03203e13i	−0.231597	+	2.26633i
$827$	−5.17205e11			−0.0384492			−0.0192246	−	0.999815i	$-0.506120\pi$
$827$	−5.17205e11			−0.0384492			−0.0192246	+	0.999815i	$0.506120\pi$
$828$	2.12411e13	−	8.82090e12i	1.57051	−	0.652194i
$829$	7.44048e12			0.547149			0.273575	−	0.961851i	$-0.411794\pi$
$829$	7.44048e12			0.547149			0.273575	+	0.961851i	$0.411794\pi$
$830$	−6.23162e11	+	6.09805e12i	−0.0455774	+	0.446005i
$831$			2.28657e13i			1.66334i
$832$	−1.21709e12	−	8.52496e11i	−0.0880575	−	0.0616790i
$833$		−	1.07364e13i		−	0.772600i
$834$	4.02587e12	+	4.11405e11i	0.288146	+	0.0294457i
$835$	1.51792e12			0.108059
$836$	9.91595e12	+	2.04802e12i	0.702111	+	0.145012i
$837$	3.24323e12			0.228409
$838$	−9.48366e12	−	9.69139e11i	−0.664321	−	0.0678872i
$839$	9.06725e12			0.631752			0.315876	−	0.948800i	$-0.397702\pi$
$839$	9.06725e12			0.631752			0.315876	+	0.948800i	$0.397702\pi$
$840$	1.59153e13	+	5.01945e12i	1.10296	+	0.347856i
$841$	−1.10751e13			−0.763427
$842$	−1.46421e12	+	1.43282e13i	−0.100392	+	0.982400i
$843$	2.97604e13			2.02962
$844$	5.68494e12	−	2.75250e13i	0.385642	−	1.86718i
$845$			6.91892e12i			0.466856i
$846$	2.59131e12	−	2.53577e13i	0.173921	−	1.70194i
$847$	9.94540e12			0.663967
$848$	1.02233e13	−	2.36934e13i	0.678905	−	1.57343i
$849$		−	1.25562e13i		−	0.829421i
$850$	−7.61119e11	+	7.44805e12i	−0.0500112	+	0.489393i
$851$	−2.08362e12	−	3.06347e12i	−0.136187	−	0.200231i
$852$	−3.88536e12	−	8.02474e11i	−0.252612	−	0.0521738i
$853$	−1.21254e13			−0.784198			−0.392099	−	0.919923i	$-0.628251\pi$
$853$	−1.21254e13			−0.784198			−0.392099	+	0.919923i	$0.628251\pi$
$854$	−1.17561e12	+	1.15041e13i	−0.0756313	+	0.740102i
$855$		−	1.20847e13i		−	0.773374i
$856$	−2.41474e13	−	7.61571e12i	−1.53723	−	0.484818i
$857$	−7.99814e12			−0.506495			−0.253248	−	0.967401i	$-0.581499\pi$
$857$	−7.99814e12			−0.506495			−0.253248	+	0.967401i	$0.581499\pi$
$858$	2.12290e11	−	2.07740e12i	0.0133733	−	0.130866i
$859$		−	2.70624e13i		−	1.69589i	−0.530084	−	0.847945i	$-0.677840\pi$
$859$		−	2.70624e13i		−	1.69589i	0.530084	−	0.847945i	$-0.322160\pi$
$860$	−1.77770e12	+	8.60713e12i	−0.110819	+	0.536556i
$861$		−	2.49894e13i		−	1.54968i
$862$	−1.65838e13	−	1.69470e12i	−1.02306	−	0.104547i
$863$			1.07998e13i			0.662774i	0.943495	+	0.331387i	$0.107517\pi$
$863$			1.07998e13i			0.662774i	−0.943495	+	0.331387i	$0.892483\pi$
$864$	−9.19217e12	+	1.64649e13i	−0.561185	+	1.00519i
$865$		−	7.65379e12i		−	0.464840i
$866$	−1.04982e11	+	1.02732e12i	−0.00634283	+	0.0620688i
$867$			1.63789e13i			0.984460i
$868$	1.00002e12	−	4.84184e12i	0.0597958	−	0.289515i
$869$	4.35268e11			0.0258921
$870$	−6.34631e12	−	6.48532e11i	−0.375565	−	0.0383791i
$871$	−1.68163e12			−0.0990033
$872$	7.07241e12	−	2.24247e13i	0.414232	−	1.31342i
$873$		−	2.88353e13i		−	1.68020i
$874$	−1.46128e13	+	7.89675e12i	−0.847096	+	0.457769i
$875$			2.16834e13i			1.25052i
$876$	−4.24549e12	+	2.05555e13i	−0.243590	+	1.17940i
$877$	−2.45190e13			−1.39960			−0.699802	−	0.714337i	$-0.746728\pi$
$877$	−2.45190e13			−1.39960			−0.699802	+	0.714337i	$0.746728\pi$
$878$	−2.06077e12	+	2.01660e13i	−0.117032	+	1.14524i
$879$	5.56328e13			3.14327
$880$	−2.47856e12	+	5.74431e12i	−0.139324	+	0.322898i
$881$		−	1.63670e12i		−	0.0915329i	−0.998952	−	0.0457664i	$-0.985427\pi$
$881$		−	1.63670e12i		−	0.0915329i	0.998952	−	0.0457664i	$-0.0145730\pi$
$882$	3.70986e13	+	3.79112e12i	2.06419	+	0.210940i
$883$			8.78202e11i			0.0486151i	0.999705	+	0.0243076i	$0.00773810\pi$
$883$			8.78202e11i			0.0486151i	−0.999705	+	0.0243076i	$0.992262\pi$
$884$	−2.50006e11	+	1.21046e12i	−0.0137694	+	0.0666679i
$885$			2.16566e13i			1.18671i
$886$	−5.72647e11	+	5.60373e12i	−0.0312202	+	0.305510i
$887$		−	2.96390e13i		−	1.60771i	−0.594828	−	0.803853i	$-0.702780\pi$
$887$		−	2.96390e13i		−	1.60771i	0.594828	−	0.803853i	$-0.297220\pi$
$888$	7.03213e12	+	2.21783e12i	0.379515	+	0.119693i
$889$			5.03859e13i			2.70552i
$890$	−1.59109e13	−	1.62594e12i	−0.850041	−	0.0868660i
$891$	−2.67978e12			−0.142446
$892$	−3.71372e10	+	1.79808e11i	−0.00196412	+	0.00950972i
$893$			1.84082e13i			0.968678i
$894$	5.94906e13	+	6.07937e12i	3.11480	+	0.318302i
$895$	2.04190e12			0.106373
$896$	2.17463e13	+	1.87999e13i	1.12719	+	0.974471i
$897$	1.92656e12	+	2.83255e12i	0.0993610	+	0.146087i
$898$	2.49984e13	+	2.55460e12i	1.28283	+	0.131093i
$899$			1.88996e12i			0.0965013i
$900$	−2.54674e13	−	5.25997e12i	−1.29388	−	0.267234i
$901$	−2.14645e13			−1.08508
$902$	9.31976e12	+	9.52390e11i	0.468787	+	0.0479055i
$903$			5.67501e13i			2.84035i
$904$	−1.42497e12	+	4.51821e12i	−0.0709657	+	0.225013i
$905$	−3.47748e12			−0.172324
$906$	−1.57257e13	−	1.60702e12i	−0.775414	−	0.0792399i
$907$	−2.48792e12			−0.122069			−0.0610343	−	0.998136i	$-0.519440\pi$
$907$	−2.48792e12			−0.122069			−0.0610343	+	0.998136i	$0.519440\pi$
$908$	3.02348e13	+	6.24462e12i	1.47612	+	0.304873i
$909$	3.46134e13			1.68154
$910$	−1.59116e11	+	1.55706e12i	−0.00769180	+	0.0752693i
$911$	−4.93192e12			−0.237238			−0.118619	−	0.992940i	$-0.537847\pi$
$911$	−4.93192e12			−0.237238			−0.118619	+	0.992940i	$0.537847\pi$
$912$	1.30966e13	−	3.03527e13i	0.626877	−	1.45285i
$913$	−1.48385e13			−0.706758
$914$	1.21664e12	−	1.19056e13i	0.0576640	−	0.564281i
$915$			8.21691e12i			0.387537i
$916$	2.18932e12	−	1.06001e13i	0.102750	−	0.497486i
$917$			3.96553e13i			1.85199i
$918$	1.56040e13	+	1.59458e12i	0.725179	+	0.0741063i
$919$	3.55757e13			1.64526			0.822628	−	0.568580i	$-0.192507\pi$
$919$	3.55757e13			1.64526			0.822628	+	0.568580i	$0.192507\pi$
$920$	−2.95213e12	−	9.82933e12i	−0.135860	−	0.452354i
$921$	2.58463e13			1.18367
$922$	−5.63891e12	−	5.76242e11i	−0.256984	−	0.0262613i
$923$		−	3.72097e11i		−	0.0168752i
$924$	−8.17105e12	+	3.95620e13i	−0.368769	+	1.78548i
$925$			4.18897e12i			0.188135i
$926$	−5.75749e11	+	5.63408e12i	−0.0257326	+	0.251810i
$927$	2.19763e13			0.977451
$928$	−9.59475e12	−	5.35663e12i	−0.424686	−	0.237097i
$929$	−2.94665e13			−1.29795			−0.648975	−	0.760810i	$-0.724802\pi$
$929$	−2.94665e13			−1.29795			−0.648975	+	0.760810i	$0.724802\pi$
$930$	3.57138e11	−	3.49483e12i	0.0156554	−	0.153198i
$931$	−2.69314e13			−1.17486
$932$	4.00944e13	+	8.28099e12i	1.74065	+	0.359510i
$933$	−1.69897e12			−0.0734039
$934$	2.82008e13	+	2.88185e12i	1.21255	+	0.123911i
$935$	5.20392e12			0.222679
$936$	−4.09438e12	−	1.29130e12i	−0.174360	−	0.0549904i
$937$			2.88232e13i			1.22156i	0.791801	+	0.610779i	$0.209144\pi$
$937$			2.88232e13i			1.22156i	−0.791801	+	0.610779i	$0.790856\pi$
$938$	3.23630e13	+	3.30719e12i	1.36501	+	0.139491i
$939$	−1.97397e13			−0.828602
$940$	−1.11390e13	−	2.30063e12i	−0.465342	−	0.0961105i
$941$			2.31363e13i			0.961925i	0.876741	+	0.480962i	$0.159713\pi$
$941$			2.31363e13i			0.961925i	−0.876741	+	0.480962i	$0.840287\pi$
$942$	−7.02842e13	−	7.18236e12i	−2.90823	−	0.297193i
$943$	−1.27076e13	+	8.64305e12i	−0.523311	+	0.355930i
$944$	−1.47791e13	+	3.42520e13i	−0.605723	+	1.40382i
$945$	1.98623e13			0.810191
$946$	−2.11649e13	−	2.16285e12i	−0.859223	−	0.0878043i
$947$		−	4.42528e13i		−	1.78799i	−0.448074	−	0.893996i	$-0.647890\pi$
$947$		−	4.42528e13i		−	1.78799i	0.448074	−	0.893996i	$-0.352110\pi$
$948$	2.87443e11	−	1.39172e12i	0.0115588	−	0.0559648i
$949$	−1.96858e12			−0.0787870
$950$	1.86829e13	+	1.90921e12i	0.744198	+	0.0760498i
$951$		−	6.22630e13i		−	2.46841i
$952$	7.19194e12	−	2.28037e13i	0.283779	−	0.899786i
$953$			1.01271e13i			0.397709i	0.980029	+	0.198854i	$0.0637221\pi$
$953$			1.01271e13i			0.397709i	−0.980029	+	0.198854i	$0.936278\pi$
$954$	7.57935e12	−	7.41689e13i	0.296254	−	2.89904i
$955$		−	8.81605e12i		−	0.342972i
$956$	−5.14595e12	+	2.49153e13i	−0.199253	+	0.964730i
$957$		−	1.54426e13i		−	0.595136i
$958$	−3.37161e13	−	3.44546e12i	−1.29328	−	0.132161i
$959$			4.64376e13i			1.77291i
$960$	1.67300e13	+	1.17184e13i	0.635734	+	0.445293i
$961$	2.53988e13			0.960636
$962$	−7.03048e10	+	6.87979e11i	−0.00264666	+	0.0258993i
$963$	−7.31537e13			−2.74106
$964$	5.02839e12	−	2.43461e13i	0.187535	−	0.907994i
$965$			1.43341e13i			0.532106i
$966$	−3.15060e13	−	5.83013e13i	−1.16411	−	2.15418i
$967$			5.65605e12i			0.208015i	0.994577	+	0.104007i	$0.0331665\pi$
$967$			5.65605e12i			0.208015i	−0.994577	+	0.104007i	$0.966833\pi$
$968$	1.16092e13	+	3.66136e12i	0.424975	+	0.134031i
$969$	−2.74973e13			−1.00192
$970$	−1.28003e13	−	1.30807e12i	−0.464246	−	0.0474414i
$971$	2.71056e13			0.978527			0.489264	−	0.872136i	$-0.337266\pi$
$971$	2.71056e13			0.978527			0.489264	+	0.872136i	$0.337266\pi$
$972$	4.71054e12	−	2.28072e13i	0.169267	−	0.819545i
$973$		−	7.34247e12i		−	0.262624i
$974$	−4.47212e11	+	4.37626e12i	−0.0159220	+	0.155807i
$975$		−	3.87321e12i		−	0.137262i
$976$	−5.60747e12	+	1.29959e13i	−0.197808	+	0.458438i
$977$		−	3.01841e13i		−	1.05987i	−0.848039	−	0.529934i	$-0.822217\pi$
$977$		−	3.01841e13i		−	1.05987i	0.848039	−	0.529934i	$-0.177783\pi$
$978$	6.24052e13	+	6.37721e12i	2.18120	+	0.222898i
$979$		−	3.87163e13i		−	1.34701i
$980$	3.36585e12	−	1.62965e13i	0.116567	−	0.564388i
$981$		−	6.79349e13i		−	2.34198i
$982$	1.22619e12	−	1.19990e13i	0.0420780	−	0.411761i
$983$	−1.70177e13			−0.581315			−0.290657	−	0.956827i	$-0.593874\pi$
$983$	−1.70177e13			−0.581315			−0.290657	+	0.956827i	$0.593874\pi$
$984$	9.19976e12	−	2.91700e13i	0.312823	−	0.991878i
$985$		−	1.69898e13i		−	0.575077i
$986$	−9.29225e11	+	9.09308e12i	−0.0313094	+	0.306383i
$987$	−7.34439e13			−2.46336
$988$	3.03636e12	+	6.27123e11i	0.101379	+	0.0209385i
$989$	2.88585e13	−	1.96281e13i	0.959159	−	0.652371i
$990$	−1.83756e12	+	1.79817e13i	−0.0607971	+	0.594939i
$991$		−	1.25807e13i		−	0.414355i	−0.978303	−	0.207177i	$-0.933572\pi$
$991$		−	1.25807e13i		−	0.414355i	0.978303	−	0.207177i	$-0.0664278\pi$
$992$	2.94983e12	−	5.28370e12i	0.0967151	−	0.173235i
$993$	−6.09036e13			−1.98779
$994$	−7.31785e11	+	7.16100e12i	−0.0237763	+	0.232667i
$995$			2.35800e12i			0.0762677i
$996$	−9.79905e12	+	4.74444e13i	−0.315513	+	1.52763i
$997$	−4.12766e13			−1.32305			−0.661524	−	0.749924i	$-0.730090\pi$
$997$	−4.12766e13			−1.32305			−0.661524	+	0.749924i	$0.730090\pi$
$998$	4.98761e12	−	4.88070e13i	0.159149	−	1.55738i
$999$	8.77610e12			0.278777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.10.b.c.91.5	✓	100
4.3	odd	2	inner	92.10.b.c.91.7	yes	100
23.22	odd	2	inner	92.10.b.c.91.6	yes	100
92.91	even	2	inner	92.10.b.c.91.8	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.10.b.c.91.5	✓	100	1.1	even	1	trivial
92.10.b.c.91.6	yes	100	23.22	odd	2	inner
92.10.b.c.91.7	yes	100	4.3	odd	2	inner
92.10.b.c.91.8	yes	100	92.91	even	2	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	92.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.5102 - 2.30032i) q^{2} +230.553i q^{3} +(501.417 + 103.561i) q^{4} -660.081i q^{5} +(530.348 - 5189.80i) q^{6} -9465.28 q^{7} +(-11048.8 - 3484.61i) q^{8} -33471.9 q^{9} +O(q^{10})\)	\(q+(-22.5102 - 2.30032i) q^{2} +230.553i q^{3} +(501.417 + 103.561i) q^{4} -660.081i q^{5} +(530.348 - 5189.80i) q^{6} -9465.28 q^{7} +(-11048.8 - 3484.61i) q^{8} -33471.9 q^{9} +(-1518.40 + 14858.6i) q^{10} -36155.5 q^{11} +(-23876.4 + 115603. i) q^{12} -11071.2 q^{13} +(213065. + 21773.2i) q^{14} +152184. q^{15} +(240694. + 103855. i) q^{16} -218051. i q^{17} +(753458. + 76996.1i) q^{18} -546966. q^{19} +(68359.0 - 330976. i) q^{20} -2.18225e6i q^{21} +(813868. + 83169.5i) q^{22} +(-1.10972e6 + 754773. i) q^{23} +(803388. - 2.54733e6i) q^{24} +1.51742e6 q^{25} +(249215. + 25467.3i) q^{26} -3.17907e6i q^{27} +(-4.74605e6 - 980238. i) q^{28} +1.85257e6 q^{29} +(-3.42569e6 - 350072. i) q^{30} +1.02018e6i q^{31} +(-5.17917e6 - 2.89147e6i) q^{32} -8.33578e6i q^{33} +(-501588. + 4.90837e6i) q^{34} +6.24785e6i q^{35} +(-1.67834e7 - 3.46639e6i) q^{36} +2.76059e6i q^{37} +(1.23123e7 + 1.25820e6i) q^{38} -2.55250e6i q^{39} +(-2.30013e6 + 7.29308e6i) q^{40} +1.14512e7 q^{41} +(-5.01989e6 + 4.91229e7i) q^{42} -2.60053e7 q^{43} +(-1.81290e7 - 3.74432e6i) q^{44} +2.20941e7i q^{45} +(2.67161e7 - 1.44374e7i) q^{46} -3.36551e7i q^{47} +(-2.39441e7 + 5.54928e7i) q^{48} +4.92378e7 q^{49} +(-3.41574e7 - 3.49055e6i) q^{50} +5.02724e7 q^{51} +(-5.55128e6 - 1.14655e6i) q^{52} -9.84380e7i q^{53} +(-7.31289e6 + 7.15614e7i) q^{54} +2.38656e7i q^{55} +(1.04580e8 + 3.29828e7i) q^{56} -1.26105e8i q^{57} +(-4.17016e7 - 4.26150e6i) q^{58} +1.42305e8i q^{59} +(7.63076e7 + 1.57604e7i) q^{60} +5.39933e7i q^{61} +(2.34675e6 - 2.29645e7i) q^{62} +3.16820e8 q^{63} +(1.09933e8 + 7.70013e7i) q^{64} +7.30789e6i q^{65} +(-1.91750e7 + 1.87640e8i) q^{66} +1.51893e8 q^{67} +(2.25817e7 - 1.09335e8i) q^{68} +(-1.74015e8 - 2.55849e8i) q^{69} +(1.43721e7 - 1.40640e8i) q^{70} +3.36094e7i q^{71} +(3.69823e8 + 1.16636e8i) q^{72} +1.77811e8 q^{73} +(6.35025e6 - 6.21414e7i) q^{74} +3.49846e8i q^{75} +(-2.74258e8 - 5.66446e7i) q^{76} +3.42222e8 q^{77} +(-5.87158e6 + 5.74573e7i) q^{78} -1.20388e7 q^{79} +(6.85527e7 - 1.58878e8i) q^{80} +7.41181e7 q^{81} +(-2.57769e8 - 2.63415e7i) q^{82} +4.10407e8 q^{83} +(2.25997e8 - 1.09422e9i) q^{84} -1.43931e8 q^{85} +(5.85384e8 + 5.98206e7i) q^{86} +4.27115e8i q^{87} +(3.99474e8 + 1.25988e8i) q^{88} +1.07083e9i q^{89} +(5.08237e7 - 4.97343e8i) q^{90} +1.04792e8 q^{91} +(-6.34596e8 + 2.63532e8i) q^{92} -2.35207e8 q^{93} +(-7.74176e7 + 7.57583e8i) q^{94} +3.61042e8i q^{95} +(6.66638e8 - 1.19407e9i) q^{96} +8.61478e8i q^{97} +(-1.10835e9 - 1.13263e8i) q^{98} +1.21019e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 32 q^{2} - 856 q^{4} + 12080 q^{6} - 44920 q^{8} - 551128 q^{9}+O(q^{10}) \) 100 * q + 32 * q^2 - 856 * q^4 + 12080 * q^6 - 44920 * q^8 - 551128 * q^9	\( 100 q + 32 q^{2} - 856 q^{4} + 12080 q^{6} - 44920 q^{8} - 551128 q^{9} - 266288 q^{12} - 4 q^{13} + 251152 q^{16} - 3213936 q^{18} - 1616600 q^{24} - 50000004 q^{25} - 9377960 q^{26} + 2611028 q^{29} - 1326128 q^{32} - 46192944 q^{36} - 3633996 q^{41} + 117081608 q^{46} + 403873120 q^{48} + 817907260 q^{49} - 253720248 q^{50} - 181337560 q^{52} - 432447896 q^{54} + 29270048 q^{58} + 897716584 q^{62} - 379488256 q^{64} + 8977204 q^{69} - 810209096 q^{70} + 390187056 q^{72} - 4 q^{73} - 413720696 q^{77} + 769707392 q^{78} + 2942959780 q^{81} + 3918346912 q^{82} - 911342216 q^{85} - 1806222144 q^{92} + 8161391316 q^{93} - 2542324232 q^{94} - 1019589584 q^{96} - 911301448 q^{98}+O(q^{100}) \) 100 * q + 32 * q^2 - 856 * q^4 + 12080 * q^6 - 44920 * q^8 - 551128 * q^9 - 266288 * q^12 - 4 * q^13 + 251152 * q^16 - 3213936 * q^18 - 1616600 * q^24 - 50000004 * q^25 - 9377960 * q^26 + 2611028 * q^29 - 1326128 * q^32 - 46192944 * q^36 - 3633996 * q^41 + 117081608 * q^46 + 403873120 * q^48 + 817907260 * q^49 - 253720248 * q^50 - 181337560 * q^52 - 432447896 * q^54 + 29270048 * q^58 + 897716584 * q^62 - 379488256 * q^64 + 8977204 * q^69 - 810209096 * q^70 + 390187056 * q^72 - 4 * q^73 - 413720696 * q^77 + 769707392 * q^78 + 2942959780 * q^81 + 3918346912 * q^82 - 911342216 * q^85 - 1806222144 * q^92 + 8161391316 * q^93 - 2542324232 * q^94 - 1019589584 * q^96 - 911301448 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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