LMFDB - Embedded newform 429.2.n.c.157.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.7
Character	$\chi$	$=$	429.157
Dual form			429.2.n.c.235.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10438 - 1.52892i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.47277 - 4.53273i) q^{4} +(-1.86590 - 1.35565i) q^{5} +(-2.10438 - 1.52892i) q^{6} +(-0.646959 + 1.99114i) q^{7} +(-2.22331 - 6.84263i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(2.10438 - 1.52892i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.47277 - 4.53273i) q^{4} +(-1.86590 - 1.35565i) q^{5} +(-2.10438 - 1.52892i) q^{6} +(-0.646959 + 1.99114i) q^{7} +(-2.22331 - 6.84263i) q^{8} +(-0.809017 + 0.587785i) q^{9} -5.99924 q^{10} +(2.96377 - 1.48865i) q^{11} -4.76599 q^{12} +(-0.809017 + 0.587785i) q^{13} +(1.68284 + 5.17925i) q^{14} +(-0.712710 + 2.19349i) q^{15} +(-7.42897 - 5.39746i) q^{16} +(4.25254 + 3.08965i) q^{17} +(-0.803800 + 2.47384i) q^{18} +(-0.875538 - 2.69463i) q^{19} +(-8.89286 + 6.46104i) q^{20} +2.09360 q^{21} +(3.96085 - 7.66405i) q^{22} +0.893590 q^{23} +(-5.82069 + 4.22898i) q^{24} +(0.0986921 + 0.303743i) q^{25} +(-0.803800 + 2.47384i) q^{26} +(0.809017 + 0.587785i) q^{27} +(8.07246 + 5.86498i) q^{28} +(1.08828 - 3.34939i) q^{29} +(1.85387 + 5.70561i) q^{30} +(3.81609 - 2.77255i) q^{31} -9.49608 q^{32} +(-2.33165 - 2.35869i) q^{33} +13.6728 q^{34} +(3.90645 - 2.83820i) q^{35} +(1.47277 + 4.53273i) q^{36} +(-1.10886 + 3.41273i) q^{37} +(-5.96233 - 4.33189i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-5.12778 + 15.7817i) q^{40} +(0.761977 + 2.34512i) q^{41} +(4.40573 - 3.20095i) q^{42} -6.82825 q^{43} +(-2.38271 - 15.6264i) q^{44} +2.30638 q^{45} +(1.88045 - 1.36623i) q^{46} +(2.77765 + 8.54872i) q^{47} +(-2.83761 + 8.73327i) q^{48} +(2.11705 + 1.53813i) q^{49} +(0.672084 + 0.488298i) q^{50} +(1.62432 - 4.99916i) q^{51} +(1.47277 + 4.53273i) q^{52} +(9.06525 - 6.58629i) q^{53} +2.60115 q^{54} +(-7.54819 - 1.24016i) q^{55} +15.0630 q^{56} +(-2.29219 + 1.66537i) q^{57} +(-2.83079 - 8.71227i) q^{58} +(-4.50961 + 13.8792i) q^{59} +(8.89286 + 6.46104i) q^{60} +(-9.72309 - 7.06423i) q^{61} +(3.79149 - 11.6690i) q^{62} +(-0.646959 - 1.99114i) q^{63} +(-5.12539 + 3.72382i) q^{64} +2.30638 q^{65} +(-8.51291 - 1.39867i) q^{66} +10.5775 q^{67} +(20.2676 - 14.7252i) q^{68} +(-0.276135 - 0.849855i) q^{69} +(3.88126 - 11.9453i) q^{70} +(-5.69458 - 4.13735i) q^{71} +(5.82069 + 4.22898i) q^{72} +(-2.47462 + 7.61611i) q^{73} +(2.88432 + 8.87703i) q^{74} +(0.258379 - 0.187724i) q^{75} -13.5035 q^{76} +(1.04668 + 6.86436i) q^{77} +2.60115 q^{78} +(-1.29119 + 0.938104i) q^{79} +(6.54460 + 20.1422i) q^{80} +(0.309017 - 0.951057i) q^{81} +(5.18899 + 3.77002i) q^{82} +(-4.29768 - 3.12245i) q^{83} +(3.08340 - 9.48974i) q^{84} +(-3.74630 - 11.5299i) q^{85} +(-14.3692 + 10.4398i) q^{86} -3.52176 q^{87} +(-16.7757 - 16.9702i) q^{88} +17.5579 q^{89} +(4.85349 - 3.52626i) q^{90} +(-0.646959 - 1.99114i) q^{91} +(1.31606 - 4.05040i) q^{92} +(-3.81609 - 2.77255i) q^{93} +(18.9155 + 13.7429i) q^{94} +(-2.01932 + 6.21483i) q^{95} +(2.93445 + 9.03131i) q^{96} +(-13.8097 + 10.0333i) q^{97} +6.80675 q^{98} +(-1.52273 + 2.94640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	2.10438	−	1.52892i	1.48802	−	1.08111i	0.513158	−	0.858294i	$-0.328475\pi$
$2$	2.10438	−	1.52892i	1.48802	−	1.08111i	0.974861	−	0.222815i	$-0.0715245\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.47277	−	4.53273i	0.736386	−	2.26636i
$5$	−1.86590	−	1.35565i	−0.834455	−	0.606267i	0.0863612	−	0.996264i	$-0.472476\pi$
$5$	−1.86590	−	1.35565i	−0.834455	−	0.606267i	−0.920816	+	0.389997i	$0.872476\pi$
$6$	−2.10438	−	1.52892i	−0.859108	−	0.624179i
$7$	−0.646959	+	1.99114i	−0.244528	+	0.752579i	0.751186	+	0.660090i	$0.229482\pi$
$7$	−0.646959	+	1.99114i	−0.244528	+	0.752579i	−0.995714	+	0.0924882i	$0.970518\pi$
$8$	−2.22331	−	6.84263i	−0.786058	−	2.41924i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−5.99924			−1.89713
$11$	2.96377	−	1.48865i	0.893609	−	0.448846i
$11$	2.96377	−	1.48865i	0.893609	−	0.448846i
$12$	−4.76599			−1.37582
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	1.68284	+	5.17925i	0.449758	+	1.38421i
$15$	−0.712710	+	2.19349i	−0.184021	+	0.566358i
$16$	−7.42897	−	5.39746i	−1.85724	−	1.34936i
$17$	4.25254	+	3.08965i	1.03139	+	0.749350i	0.968587	−	0.248676i	$-0.0799954\pi$
$17$	4.25254	+	3.08965i	1.03139	+	0.749350i	0.0628049	+	0.998026i	$0.479995\pi$
$18$	−0.803800	+	2.47384i	−0.189458	+	0.583090i
$19$	−0.875538	−	2.69463i	−0.200862	−	0.618190i	−0.999858	−	0.0168538i	$-0.994635\pi$
$19$	−0.875538	−	2.69463i	−0.200862	−	0.618190i	0.798996	−	0.601337i	$-0.205365\pi$
$20$	−8.89286	+	6.46104i	−1.98850	+	1.44473i
$21$	2.09360			0.456862
$22$	3.96085	−	7.66405i	0.844455	−	1.63398i
$23$	0.893590			0.186326			0.0931632	−	0.995651i	$-0.470302\pi$
$23$	0.893590			0.186326			0.0931632	+	0.995651i	$0.470302\pi$
$24$	−5.82069	+	4.22898i	−1.18814	+	0.863237i
$25$	0.0986921	+	0.303743i	0.0197384	+	0.0607486i
$26$	−0.803800	+	2.47384i	−0.157638	+	0.485161i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	8.07246	+	5.86498i	1.52555	+	1.10838i
$29$	1.08828	−	3.34939i	0.202089	−	0.621966i	−0.797731	−	0.603013i	$-0.793967\pi$
$29$	1.08828	−	3.34939i	0.202089	−	0.621966i	0.999820	−	0.0189531i	$-0.00603331\pi$
$30$	1.85387	+	5.70561i	0.338468	+	1.04170i
$31$	3.81609	−	2.77255i	0.685391	−	0.497965i	−0.189751	−	0.981832i	$-0.560768\pi$
$31$	3.81609	−	2.77255i	0.685391	−	0.497965i	0.875142	+	0.483867i	$0.160768\pi$
$32$	−9.49608			−1.67869
$33$	−2.33165	−	2.35869i	−0.405888	−	0.410595i
$34$	13.6728			2.34486
$35$	3.90645	−	2.83820i	0.660311	−	0.479744i
$36$	1.47277	+	4.53273i	0.245462	+	0.755455i
$37$	−1.10886	+	3.41273i	−0.182296	+	0.561050i	−0.999891	−	0.0147438i	$-0.995307\pi$
$37$	−1.10886	+	3.41273i	−0.182296	+	0.561050i	0.817595	+	0.575793i	$0.195307\pi$
$38$	−5.96233	−	4.33189i	−0.967218	−	0.702725i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	−5.12778	+	15.7817i	−0.810774	+	2.49530i
$41$	0.761977	+	2.34512i	0.119001	+	0.366247i	0.992760	−	0.120111i	$-0.0383251\pi$
$41$	0.761977	+	2.34512i	0.119001	+	0.366247i	−0.873760	+	0.486358i	$0.838325\pi$
$42$	4.40573	−	3.20095i	0.679819	−	0.493917i
$43$	−6.82825			−1.04130			−0.520649	−	0.853771i	$-0.674310\pi$
$43$	−6.82825			−1.04130			−0.520649	+	0.853771i	$0.674310\pi$
$44$	−2.38271	−	15.6264i	−0.359208	−	2.35577i
$45$	2.30638			0.343814
$46$	1.88045	−	1.36623i	0.277257	−	0.201439i
$47$	2.77765	+	8.54872i	0.405161	+	1.24696i	0.920760	+	0.390128i	$0.127569\pi$
$47$	2.77765	+	8.54872i	0.405161	+	1.24696i	−0.515599	+	0.856830i	$0.672431\pi$
$48$	−2.83761	+	8.73327i	−0.409574	+	1.26054i
$49$	2.11705	+	1.53813i	0.302436	+	0.219733i
$50$	0.672084	+	0.488298i	0.0950470	+	0.0690557i
$51$	1.62432	−	4.99916i	0.227451	−	0.700022i
$52$	1.47277	+	4.53273i	0.204237	+	0.628576i
$53$	9.06525	−	6.58629i	1.24521	−	0.904697i	0.247274	−	0.968946i	$-0.420465\pi$
$53$	9.06525	−	6.58629i	1.24521	−	0.904697i	0.997934	+	0.0642491i	$0.0204652\pi$
$54$	2.60115			0.353972
$55$	−7.54819	−	1.24016i	−1.01780	−	0.167224i
$56$	15.0630			2.01288
$57$	−2.29219	+	1.66537i	−0.303608	+	0.220584i
$58$	−2.83079	−	8.71227i	−0.371701	−	1.14398i
$59$	−4.50961	+	13.8792i	−0.587102	+	1.80691i	0.00355994	+	0.999994i	$0.498867\pi$
$59$	−4.50961	+	13.8792i	−0.587102	+	1.80691i	−0.590662	+	0.806919i	$0.701133\pi$
$60$	8.89286	+	6.46104i	1.14806	+	0.834117i
$61$	−9.72309	−	7.06423i	−1.24491	−	0.904483i	−0.246998	−	0.969016i	$-0.579444\pi$
$61$	−9.72309	−	7.06423i	−1.24491	−	0.904483i	−0.997916	+	0.0645334i	$0.979444\pi$
$62$	3.79149	−	11.6690i	0.481519	−	1.48196i
$63$	−0.646959	−	1.99114i	−0.0815092	−	0.250860i
$64$	−5.12539	+	3.72382i	−0.640674	+	0.465477i
$65$	2.30638			0.286071
$66$	−8.51291	−	1.39867i	−1.04787	−	0.172164i
$67$	10.5775			1.29224			0.646122	−	0.763234i	$-0.276390\pi$
$67$	10.5775			1.29224			0.646122	+	0.763234i	$0.276390\pi$
$68$	20.2676	−	14.7252i	2.45780	−	1.78570i
$69$	−0.276135	−	0.849855i	−0.0332427	−	0.102311i
$70$	3.88126	−	11.9453i	0.463900	−	1.42774i
$71$	−5.69458	−	4.13735i	−0.675822	−	0.491013i	0.196147	−	0.980574i	$-0.437157\pi$
$71$	−5.69458	−	4.13735i	−0.675822	−	0.491013i	−0.871969	+	0.489561i	$0.837157\pi$
$72$	5.82069	+	4.22898i	0.685975	+	0.498390i
$73$	−2.47462	+	7.61611i	−0.289633	+	0.891398i	0.695339	+	0.718682i	$0.255254\pi$
$73$	−2.47462	+	7.61611i	−0.289633	+	0.891398i	−0.984972	+	0.172716i	$0.944746\pi$
$74$	2.88432	+	8.87703i	0.335296	+	1.03193i
$75$	0.258379	−	0.187724i	0.0298351	−	0.0216764i
$76$	−13.5035			−1.54896
$77$	1.04668	+	6.86436i	0.119280	+	0.782266i
$78$	2.60115			0.294523
$79$	−1.29119	+	0.938104i	−0.145270	+	0.105545i	−0.658047	−	0.752977i	$-0.728617\pi$
$79$	−1.29119	+	0.938104i	−0.145270	+	0.105545i	0.512776	+	0.858522i	$0.328617\pi$
$80$	6.54460	+	20.1422i	0.731709	+	2.25197i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	5.18899	+	3.77002i	0.573028	+	0.416329i
$83$	−4.29768	−	3.12245i	−0.471731	−	0.342733i	0.326384	−	0.945237i	$-0.394170\pi$
$83$	−4.29768	−	3.12245i	−0.471731	−	0.342733i	−0.798116	+	0.602504i	$0.794170\pi$
$84$	3.08340	−	9.48974i	0.336427	−	1.03542i
$85$	−3.74630	−	11.5299i	−0.406344	−	1.25060i
$86$	−14.3692	+	10.4398i	−1.54947	+	1.12576i
$87$	−3.52176			−0.377572
$88$	−16.7757	−	16.9702i	−1.78829	−	1.80903i
$89$	17.5579			1.86113			0.930564	−	0.366128i	$-0.119317\pi$
$89$	17.5579			1.86113			0.930564	+	0.366128i	$0.119317\pi$
$90$	4.85349	−	3.52626i	0.511602	−	0.371701i
$91$	−0.646959	−	1.99114i	−0.0678198	−	0.208728i
$92$	1.31606	−	4.05040i	0.137208	−	0.422284i
$93$	−3.81609	−	2.77255i	−0.395710	−	0.287500i
$94$	18.9155	+	13.7429i	1.95099	+	1.41747i
$95$	−2.01932	+	6.21483i	−0.207178	+	0.637628i
$96$	2.93445	+	9.03131i	0.299496	+	0.921754i
$97$	−13.8097	+	10.0333i	−1.40216	+	1.01873i	−0.407760	+	0.913089i	$0.633690\pi$
$97$	−13.8097	+	10.0333i	−1.40216	+	1.01873i	−0.994404	+	0.105643i	$0.966310\pi$
$98$	6.80675			0.687586
$99$	−1.52273	+	2.94640i	−0.153040	+	0.296125i
$100$	1.52214			0.152214
$101$	−9.28302	+	6.74451i	−0.923695	+	0.671104i	−0.944441	−	0.328681i	$-0.893396\pi$
$101$	−9.28302	+	6.74451i	−0.923695	+	0.671104i	0.0207460	+	0.999785i	$0.493396\pi$
$102$	−4.22512	−	13.0036i	−0.418349	−	1.28755i
$103$	−3.18492	+	9.80217i	−0.313819	+	0.965837i	0.662418	+	0.749134i	$0.269530\pi$
$103$	−3.18492	+	9.80217i	−0.313819	+	0.965837i	−0.976238	+	0.216703i	$0.930470\pi$
$104$	5.82069	+	4.22898i	0.570766	+	0.414686i
$105$	−3.90645	−	2.83820i	−0.381231	−	0.276980i
$106$	9.00680	−	27.7201i	0.874817	−	2.69241i
$107$	1.99653	+	6.14467i	0.193011	+	0.594028i	0.999994	+	0.00345291i	$0.00109910\pi$
$107$	1.99653	+	6.14467i	0.193011	+	0.594028i	−0.806983	+	0.590575i	$0.798901\pi$
$108$	3.85577	−	2.80138i	0.371022	−	0.269563i
$109$	−2.47162			−0.236738			−0.118369	−	0.992970i	$-0.537767\pi$
$109$	−2.47162			−0.236738			−0.118369	+	0.992970i	$0.537767\pi$
$110$	−17.7803	+	8.93079i	−1.69529	+	0.851518i
$111$	3.58836			0.340592
$112$	15.5533	−	11.3001i	1.46965	−	1.06776i
$113$	3.94846	+	12.1521i	0.371440	+	1.14318i	0.945849	+	0.324607i	$0.105232\pi$
$113$	3.94846	+	12.1521i	0.371440	+	1.14318i	−0.574409	+	0.818569i	$0.694768\pi$
$114$	−2.27741	+	7.00914i	−0.213299	+	0.656466i
$115$	−1.66735	−	1.21140i	−0.155481	−	0.112964i
$116$	−13.5791	−	9.86578i	−1.26079	−	0.916015i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	11.7302	+	36.1018i	1.07985	+	3.32344i
$119$	−8.90313	+	6.46850i	−0.816148	+	0.592967i
$120$	16.5939			1.51480
$121$	6.56782	−	8.82405i	0.597074	−	0.802186i
$122$	−31.2617			−2.83030
$123$	1.99488	−	1.44937i	0.179872	−	0.130685i
$124$	−6.94700	−	21.3807i	−0.623859	−	1.92004i
$125$	−3.33593	+	10.2669i	−0.298374	+	0.918302i
$126$	−4.40573	−	3.20095i	−0.392494	−	0.285163i
$127$	8.89541	+	6.46289i	0.789340	+	0.573489i	0.907768	−	0.419474i	$-0.137785\pi$
$127$	8.89541	+	6.46289i	0.789340	+	0.573489i	−0.118427	+	0.992963i	$0.537785\pi$
$128$	0.776556	−	2.38999i	0.0686385	−	0.211248i
$129$	2.11005	+	6.49405i	0.185779	+	0.571769i
$130$	4.85349	−	3.52626i	0.425679	−	0.309274i
$131$	19.5496			1.70806			0.854028	−	0.520227i	$-0.174153\pi$
$131$	19.5496			1.70806			0.854028	+	0.520227i	$0.174153\pi$
$132$	−14.1253	+	7.09492i	−1.22945	+	0.617533i
$133$	5.93181			0.514353
$134$	22.2590	−	16.1721i	1.92288	−	1.39706i
$135$	−0.712710	−	2.19349i	−0.0613403	−	0.188786i
$136$	11.6866	−	35.9678i	1.00212	−	3.08421i
$137$	−8.90378	−	6.46897i	−0.760701	−	0.552682i	0.138424	−	0.990373i	$-0.455796\pi$
$137$	−8.90378	−	6.46897i	−0.760701	−	0.552682i	−0.899125	+	0.437691i	$0.855796\pi$
$138$	−1.88045	−	1.36623i	−0.160075	−	0.116301i
$139$	1.17320	−	3.61073i	0.0995094	−	0.306259i	−0.888893	−	0.458114i	$-0.848525\pi$
$139$	1.17320	−	3.61073i	0.0995094	−	0.306259i	0.988403	+	0.151856i	$0.0485250\pi$
$140$	−7.11149	−	21.8869i	−0.601031	−	1.84978i
$141$	7.27197	−	5.28340i	0.612410	−	0.444942i
$142$	−18.3092			−1.53647
$143$	−1.52273	+	2.94640i	−0.127337	+	0.246391i
$144$	9.18271			0.765226
$145$	−6.57124	+	4.77429i	−0.545712	+	0.396483i
$146$	6.43688	+	19.8107i	0.532720	+	1.63954i
$147$	0.808642	−	2.48875i	0.0666957	−	0.205268i
$148$	13.8359	+	10.0524i	1.13730	+	0.826299i
$149$	−18.1474	−	13.1848i	−1.48669	−	1.08014i	−0.975323	−	0.220783i	$-0.929139\pi$
$149$	−18.1474	−	13.1848i	−1.48669	−	1.08014i	−0.511369	−	0.859362i	$-0.670861\pi$
$150$	0.256713	−	0.790082i	0.0209605	−	0.0645099i
$151$	−0.562595	−	1.73149i	−0.0457833	−	0.140906i	0.925552	−	0.378621i	$-0.123602\pi$
$151$	−0.562595	−	1.73149i	−0.0457833	−	0.140906i	−0.971335	+	0.237715i	$0.923602\pi$
$152$	−16.4918	+	11.9820i	−1.33766	+	0.971867i
$153$	−5.25642			−0.424957
$154$	12.6977	+	12.8449i	1.02321	+	1.03507i
$155$	−10.8791			−0.873828
$156$	3.85577	−	2.80138i	0.308709	−	0.224290i
$157$	−6.41421	−	19.7409i	−0.511909	−	1.57549i	−0.788836	−	0.614604i	$-0.789316\pi$
$157$	−6.41421	−	19.7409i	−0.511909	−	1.57549i	0.276927	−	0.960891i	$-0.410684\pi$
$158$	−1.28286	+	3.94825i	−0.102059	+	0.314106i
$159$	−9.06525	−	6.58629i	−0.718921	−	0.522327i
$160$	17.7187	+	12.8734i	1.40079	+	1.01773i
$161$	−0.578117	+	1.77926i	−0.0455620	+	0.140225i
$162$	−0.803800	−	2.47384i	−0.0631525	−	0.194363i
$163$	11.2436	−	8.16895i	0.880667	−	0.639842i	−0.0527611	−	0.998607i	$-0.516802\pi$
$163$	11.2436	−	8.16895i	0.880667	−	0.639842i	0.933428	+	0.358765i	$0.116802\pi$
$164$	11.7520			0.917679
$165$	1.15305	+	7.56198i	0.0897649	+	0.588700i
$166$	−13.8179			−1.07248
$167$	−1.99743	+	1.45122i	−0.154565	+	0.112298i	−0.662380	−	0.749168i	$-0.730454\pi$
$167$	−1.99743	+	1.45122i	−0.154565	+	0.112298i	0.507814	+	0.861466i	$0.330454\pi$
$168$	−4.65472	−	14.3258i	−0.359120	−	1.10526i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−25.5120	−	18.5355i	−1.95668	−	1.42161i
$171$	2.29219	+	1.66537i	0.175288	+	0.127354i
$172$	−10.0565	+	30.9506i	−0.766798	+	2.35996i
$173$	−4.11378	−	12.6609i	−0.312765	−	0.962592i	−0.976665	−	0.214770i	$-0.931100\pi$
$173$	−4.11378	−	12.6609i	−0.312765	−	0.962592i	0.663899	−	0.747822i	$-0.268900\pi$
$174$	−7.41110	+	5.38448i	−0.561834	+	0.408196i
$175$	−0.668644			−0.0505447
$176$	−30.0527	−	4.93764i	−2.26531	−	0.372189i
$177$	14.5934			1.09691
$178$	36.9483	−	26.8445i	2.76939	−	2.01208i
$179$	5.26079	+	16.1911i	0.393210	+	1.21018i	0.930347	+	0.366681i	$0.119506\pi$
$179$	5.26079	+	16.1911i	0.393210	+	1.21018i	−0.537137	+	0.843495i	$0.680494\pi$
$180$	3.39677	−	10.4542i	0.253180	−	0.779209i
$181$	−8.52352	−	6.19270i	−0.633548	−	0.460300i	0.224080	−	0.974571i	$-0.428062\pi$
$181$	−8.52352	−	6.19270i	−0.633548	−	0.460300i	−0.857628	+	0.514271i	$0.828062\pi$
$182$	−4.40573	−	3.20095i	−0.326575	−	0.237270i
$183$	−3.71389	+	11.4302i	−0.274539	+	0.844943i
$184$	−1.98673	−	6.11451i	−0.146463	−	0.450768i
$185$	6.69551	−	4.86457i	0.492264	−	0.357651i
$186$	−12.2695			−0.899644
$187$	17.2029	+	2.82644i	1.25800	+	0.206690i
$188$	42.8399			3.12442
$189$	−1.69376	+	1.23059i	−0.123203	+	0.0895122i
$190$	5.25256	+	16.1657i	0.381061	+	1.17278i
$191$	−3.90194	+	12.0089i	−0.282335	+	0.868937i	0.704850	+	0.709356i	$0.251014\pi$
$191$	−3.90194	+	12.0089i	−0.282335	+	0.868937i	−0.987185	+	0.159581i	$0.948986\pi$
$192$	5.12539	+	3.72382i	0.369893	+	0.268743i
$193$	−13.8369	−	10.0531i	−0.996002	−	0.723638i	−0.0347748	−	0.999395i	$-0.511071\pi$
$193$	−13.8369	−	10.0531i	−0.996002	−	0.723638i	−0.961227	+	0.275757i	$0.911071\pi$
$194$	−13.7207	+	42.2279i	−0.985087	+	3.03178i
$195$	−0.712710	−	2.19349i	−0.0510382	−	0.157079i
$196$	10.0899	−	7.33071i	0.720704	−	0.523622i
$197$	−8.68367			−0.618686			−0.309343	−	0.950951i	$-0.600109\pi$
$197$	−8.68367			−0.618686			−0.309343	+	0.950951i	$0.600109\pi$
$198$	1.30042	+	8.52847i	0.0924169	+	0.606092i
$199$	−8.43484			−0.597930			−0.298965	−	0.954264i	$-0.596641\pi$
$199$	−8.43484			−0.597930			−0.298965	+	0.954264i	$0.596641\pi$
$200$	1.85898	−	1.35063i	0.131450	−	0.0955038i
$201$	−3.26862	−	10.0598i	−0.230551	−	0.709562i
$202$	−9.22316	+	28.3860i	−0.648939	+	1.99723i
$203$	5.96502	+	4.33384i	0.418662	+	0.304176i
$204$	−20.2676	−	14.7252i	−1.41901	−	1.03097i
$205$	1.75741	−	5.40874i	0.122743	−	0.377763i
$206$	8.28446	+	25.4969i	0.577206	+	1.77646i
$207$	−0.722930	+	0.525239i	−0.0502471	+	0.0365067i
$208$	9.18271			0.636706
$209$	−6.60626	−	6.68288i	−0.456965	−	0.462264i
$210$	−12.5600			−0.866724
$211$	−4.34761	+	3.15872i	−0.299302	+	0.217455i	−0.727292	−	0.686328i	$-0.759222\pi$
$211$	−4.34761	+	3.15872i	−0.299302	+	0.217455i	0.427991	+	0.903783i	$0.359222\pi$
$212$	−16.5028	−	50.7904i	−1.13342	−	3.48830i
$213$	−2.17513	+	6.69438i	−0.149038	+	0.458691i
$214$	13.5962	+	9.87818i	0.929414	+	0.675259i
$215$	12.7408	+	9.25675i	0.868917	+	0.631305i
$216$	2.22331	−	6.84263i	0.151277	−	0.465582i
$217$	3.05167	+	9.39209i	0.207161	+	0.637577i
$218$	−5.20122	+	3.77891i	−0.352271	+	0.255940i
$219$	8.00805			0.541134
$220$	−16.7381	+	32.3874i	−1.12848	+	2.18356i
$221$	−5.25642			−0.353585
$222$	7.55126	−	5.48631i	0.506807	−	0.368217i
$223$	2.26696	+	6.97697i	0.151807	+	0.467212i	0.997823	−	0.0659437i	$-0.0210058\pi$
$223$	2.26696	+	6.97697i	0.151807	+	0.467212i	−0.846017	+	0.533156i	$0.821006\pi$
$224$	6.14358	−	18.9080i	0.410485	−	1.26334i
$225$	−0.258379	−	0.187724i	−0.0172253	−	0.0125149i
$226$	26.8887	+	19.5358i	1.78861	+	1.29950i
$227$	−6.25706	+	19.2572i	−0.415295	+	1.27815i	0.496691	+	0.867927i	$0.334548\pi$
$227$	−6.25706	+	19.2572i	−0.415295	+	1.27815i	−0.911986	+	0.410220i	$0.865452\pi$
$228$	4.17281	+	12.8426i	0.276351	+	0.850521i
$229$	−22.6204	+	16.4347i	−1.49480	+	1.08603i	−0.522399	+	0.852701i	$0.674963\pi$
$229$	−22.6204	+	16.4347i	−1.49480	+	1.08603i	−0.972397	+	0.233331i	$0.925037\pi$
$230$	−5.36086			−0.353485
$231$	6.20495	−	3.11665i	0.408256	−	0.205061i
$232$	−25.3382			−1.66354
$233$	10.6462	−	7.73490i	0.697454	−	0.506730i	−0.181648	−	0.983364i	$-0.558143\pi$
$233$	10.6462	−	7.73490i	0.697454	−	0.506730i	0.879102	+	0.476634i	$0.158143\pi$
$234$	−0.803800	−	2.47384i	−0.0525461	−	0.161720i
$235$	6.40630	−	19.7166i	0.417901	−	1.28617i
$236$	56.2688	+	40.8817i	3.66279	+	2.66117i
$237$	1.29119	+	0.938104i	0.0838718	+	0.0609364i
$238$	−8.84572	+	27.2243i	−0.573383	+	1.76469i
$239$	4.73460	+	14.5716i	0.306256	+	0.942558i	0.979206	+	0.202870i	$0.0650270\pi$
$239$	4.73460	+	14.5716i	0.306256	+	0.942558i	−0.672950	+	0.739688i	$0.734973\pi$
$240$	17.1340	−	12.4486i	1.10599	−	0.803552i
$241$	−23.4187			−1.50853			−0.754265	−	0.656570i	$-0.772007\pi$
$241$	−23.4187			−1.50853			−0.754265	+	0.656570i	$0.772007\pi$
$242$	0.329903	−	28.6108i	0.0212070	−	1.83917i
$243$	−1.00000			−0.0641500
$244$	−46.3402	+	33.6681i	−2.96662	+	2.15538i
$245$	−1.86503	−	5.73998i	−0.119153	−	0.366714i
$246$	1.98202	−	6.10002i	0.126369	−	0.388923i
$247$	2.29219	+	1.66537i	0.145848	+	0.105965i
$248$	−27.4559	−	19.9479i	−1.74345	−	1.26669i
$249$	−1.64157	+	5.05222i	−0.104030	+	0.320172i
$250$	8.67725	+	26.7058i	0.548798	+	1.68903i
$251$	16.5911	−	12.0542i	1.04722	−	0.760852i	0.0755409	−	0.997143i	$-0.475932\pi$
$251$	16.5911	−	12.0542i	1.04722	−	0.760852i	0.971682	+	0.236290i	$0.0759317\pi$
$252$	−9.97810			−0.628561
$253$	2.64839	−	1.33025i	0.166503	−	0.0836319i
$254$	28.6005			1.79456
$255$	−9.80795	+	7.12589i	−0.614198	+	0.446241i
$256$	−5.93539	−	18.2673i	−0.370962	−	1.14170i
$257$	7.91765	−	24.3680i	0.493890	−	1.52004i	−0.324791	−	0.945786i	$-0.605294\pi$
$257$	7.91765	−	24.3680i	0.493890	−	1.52004i	0.818680	−	0.574250i	$-0.194706\pi$
$258$	14.3692	+	10.4398i	0.894588	+	0.649956i
$259$	−6.07782	−	4.41580i	−0.377658	−	0.274384i
$260$	3.39677	−	10.4542i	0.210659	−	0.648341i
$261$	1.08828	+	3.34939i	0.0673630	+	0.207322i
$262$	41.1397	−	29.8898i	2.54162	−	1.84660i
$263$	−2.24928			−0.138697			−0.0693483	−	0.997593i	$-0.522092\pi$
$263$	−2.24928			−0.138697			−0.0693483	+	0.997593i	$0.522092\pi$
$264$	−10.9557	+	21.1987i	−0.674275	+	1.30469i
$265$	−25.8436			−1.58756
$266$	12.4828	−	9.06926i	0.765367	−	0.556072i
$267$	−5.42568	−	16.6985i	−0.332046	−	1.02193i
$268$	15.5782	−	47.9448i	0.951591	−	2.92870i
$269$	−11.7452	−	8.53338i	−0.716117	−	0.520289i	0.169025	−	0.985612i	$-0.445938\pi$
$269$	−11.7452	−	8.53338i	−0.716117	−	0.520289i	−0.885141	+	0.465323i	$0.845938\pi$
$270$	−4.85349	−	3.52626i	−0.295374	−	0.214602i
$271$	2.01796	−	6.21063i	0.122582	−	0.377269i	−0.870871	−	0.491512i	$-0.836444\pi$
$271$	2.01796	−	6.21063i	0.122582	−	0.377269i	0.993453	+	0.114243i	$0.0364443\pi$
$272$	−14.9157	−	45.9058i	−0.904397	−	2.78345i
$273$	−1.69376	+	1.23059i	−0.102511	+	0.0744787i
$274$	−28.6274			−1.72945
$275$	0.744669	+	0.753305i	0.0449052	+	0.0454260i
$276$	−4.25885			−0.256352
$277$	−7.22471	+	5.24906i	−0.434090	+	0.315385i	−0.783282	−	0.621666i	$-0.786456\pi$
$277$	−7.22471	+	5.24906i	−0.434090	+	0.315385i	0.349192	+	0.937051i	$0.386456\pi$
$278$	−3.05167	−	9.39207i	−0.183027	−	0.563299i
$279$	−1.45762	+	4.48609i	−0.0872653	+	0.268575i
$280$	−28.1060	−	20.4202i	−1.67966	−	1.22034i
$281$	7.14202	+	5.18898i	0.426057	+	0.309549i	0.780070	−	0.625692i	$-0.215183\pi$
$281$	7.14202	+	5.18898i	0.426057	+	0.309549i	−0.354013	+	0.935240i	$0.615183\pi$
$282$	7.22508	−	22.2365i	0.430247	−	1.32416i
$283$	−4.15368	−	12.7837i	−0.246911	−	0.759912i	−0.995316	−	0.0966713i	$-0.969180\pi$
$283$	−4.15368	−	12.7837i	−0.246911	−	0.759912i	0.748406	−	0.663241i	$-0.230820\pi$
$284$	−27.1403	+	19.7186i	−1.61048	+	1.17008i
$285$	6.53466			0.387080
$286$	1.30042	+	8.52847i	0.0768955	+	0.504299i
$287$	−5.16243			−0.304728
$288$	7.68249	−	5.58166i	0.452695	−	0.328902i
$289$	3.28485	+	10.1097i	0.193226	+	0.594690i
$290$	−6.52887	+	20.0938i	−0.383388	+	1.17995i
$291$	13.8097	+	10.0333i	0.809540	+	0.588165i
$292$	30.8772	+	22.4336i	1.80695	+	1.31283i
$293$	1.54267	−	4.74787i	0.0901240	−	0.277373i	−0.895828	−	0.444400i	$-0.853417\pi$
$293$	1.54267	−	4.74787i	0.0901240	−	0.277373i	0.985952	+	0.167027i	$0.0534168\pi$
$294$	−2.10340	−	6.47360i	−0.122673	−	0.377548i
$295$	27.2298	−	19.7836i	1.58538	−	1.15185i
$296$	25.8174			1.50061
$297$	3.27275	+	0.537711i	0.189904	+	0.0312012i
$298$	−58.3475			−3.37998
$299$	−0.722930	+	0.525239i	−0.0418081	+	0.0303754i
$300$	−0.470366	−	1.44764i	−0.0271566	−	0.0835794i
$301$	4.41760	−	13.5960i	0.254626	−	0.783659i
$302$	−3.83122	−	2.78354i	−0.220462	−	0.160175i
$303$	9.28302	+	6.74451i	0.533296	+	0.387462i
$304$	−8.03981	+	24.7440i	−0.461115	+	1.41917i
$305$	8.56563	+	26.3623i	0.490466	+	1.50950i
$306$	−11.0615	+	8.03665i	−0.632344	+	0.459425i
$307$	−7.37880			−0.421130			−0.210565	−	0.977580i	$-0.567530\pi$
$307$	−7.37880			−0.421130			−0.210565	+	0.977580i	$0.567530\pi$
$308$	32.6558	+	5.36534i	1.86074	+	0.305718i
$309$	10.3066			0.586323
$310$	−22.8936	+	16.6332i	−1.30027	+	0.944703i
$311$	−4.52813	−	13.9361i	−0.256767	−	0.790246i	−0.993476	−	0.114037i	$-0.963622\pi$
$311$	−4.52813	−	13.9361i	−0.256767	−	0.790246i	0.736710	−	0.676209i	$-0.236378\pi$
$312$	2.22331	−	6.84263i	0.125870	−	0.387388i
$313$	−2.34815	−	1.70603i	−0.132725	−	0.0964306i	0.519442	−	0.854506i	$-0.326140\pi$
$313$	−2.34815	−	1.70603i	−0.132725	−	0.0964306i	−0.652167	+	0.758075i	$0.726140\pi$
$314$	−43.6801	−	31.7355i	−2.46501	−	1.79094i
$315$	−1.49213	+	4.59231i	−0.0840721	+	0.258747i
$316$	2.35054	+	7.23423i	0.132228	+	0.406957i
$317$	10.3004	−	7.48366i	0.578527	−	0.420324i	−0.259666	−	0.965699i	$-0.583612\pi$
$317$	10.3004	−	7.48366i	0.578527	−	0.420324i	0.838193	+	0.545374i	$0.183612\pi$
$318$	−29.1466			−1.63446
$319$	−1.76067	−	11.5469i	−0.0985786	−	0.646501i
$320$	14.6117			0.816817
$321$	5.22697	−	3.79762i	0.291741	−	0.211962i
$322$	1.50377	+	4.62813i	0.0838018	+	0.257915i
$323$	4.60220	−	14.1641i	0.256073	−	0.788113i
$324$	−3.85577	−	2.80138i	−0.214209	−	0.155632i
$325$	−0.258379	−	0.187724i	−0.0143323	−	0.0104130i
$326$	11.1711	−	34.3811i	0.618710	−	1.90419i
$327$	0.763772	+	2.35065i	0.0422367	+	0.129991i
$328$	14.3527	−	10.4279i	0.792496	−	0.575782i
$329$	−18.8187			−1.03751
$330$	13.9881	+	14.1503i	0.770020	+	0.778950i
$331$	−17.9172			−0.984818			−0.492409	−	0.870364i	$-0.663884\pi$
$331$	−17.9172			−0.984818			−0.492409	+	0.870364i	$0.663884\pi$
$332$	−20.4827	+	14.8816i	−1.12413	+	0.816731i
$333$	−1.10886	−	3.41273i	−0.0607654	−	0.187017i
$334$	−1.98455	+	6.10781i	−0.108590	+	0.334204i
$335$	−19.7365	−	14.3394i	−1.07832	−	0.783445i
$336$	−15.5533	−	11.3001i	−0.848503	−	0.616473i
$337$	−3.04699	+	9.37767i	−0.165980	+	0.510834i	−0.999107	−	0.0422474i	$-0.986548\pi$
$337$	−3.04699	+	9.37767i	−0.165980	+	0.510834i	0.833127	+	0.553082i	$0.186548\pi$
$338$	−0.803800	−	2.47384i	−0.0437210	−	0.134559i
$339$	10.3372	−	7.51043i	0.561440	−	0.407910i
$340$	−57.7796			−3.13354
$341$	7.18263	−	13.8980i	0.388961	−	0.752621i
$342$	7.36985			0.398516
$343$	−16.2886	+	11.8344i	−0.879502	+	0.638995i
$344$	15.1813	+	46.7232i	0.818520	+	2.51915i
$345$	−0.636871	+	1.96009i	−0.0342880	+	0.105527i
$346$	−28.0145	−	20.3537i	−1.50607	−	1.09422i
$347$	12.5556	+	9.12219i	0.674021	+	0.489705i	0.871369	−	0.490629i	$-0.163233\pi$
$347$	12.5556	+	9.12219i	0.674021	+	0.489705i	−0.197348	+	0.980334i	$0.563233\pi$
$348$	−5.18675	+	15.9632i	−0.278039	+	0.855716i
$349$	0.253141	+	0.779089i	0.0135504	+	0.0417037i	0.957603	−	0.288091i	$-0.0930205\pi$
$349$	0.253141	+	0.779089i	0.0135504	+	0.0417037i	−0.944053	+	0.329795i	$0.893021\pi$
$350$	−1.40708	+	1.02230i	−0.0752115	+	0.0546443i
$351$	−1.00000			−0.0533761
$352$	−28.1442	+	14.1364i	−1.50009	+	0.753472i
$353$	29.6412			1.57764			0.788821	−	0.614623i	$-0.210692\pi$
$353$	29.6412			1.57764			0.788821	+	0.614623i	$0.210692\pi$
$354$	30.7100	−	22.3121i	1.63222	−	1.18588i
$355$	5.01668	+	15.4398i	0.266258	+	0.819457i
$356$	25.8587	−	79.5850i	1.37051	−	4.21800i
$357$	8.90313	+	6.46850i	0.471204	+	0.342349i
$358$	35.8255	+	26.0287i	1.89344	+	1.37566i
$359$	8.41588	−	25.9014i	0.444173	−	1.36702i	−0.439215	−	0.898382i	$-0.644743\pi$
$359$	8.41588	−	25.9014i	0.444173	−	1.36702i	0.883388	−	0.468642i	$-0.155257\pi$
$360$	−5.12778	−	15.7817i	−0.270258	−	0.831768i
$361$	8.87686	−	6.44942i	0.467203	−	0.339443i
$362$	−27.4048			−1.44037
$363$	−10.4217	−	3.51958i	−0.546999	−	0.184730i
$364$	−9.97810			−0.522995
$365$	14.9422	−	10.8562i	0.782111	−	0.568237i
$366$	9.66039	+	29.7316i	0.504957	+	1.55410i
$367$	−1.62687	+	5.00698i	−0.0849217	+	0.261362i	−0.984496	−	0.175405i	$-0.943877\pi$
$367$	−1.62687	+	5.00698i	−0.0849217	+	0.261362i	0.899575	+	0.436767i	$0.143877\pi$
$368$	−6.63845	−	4.82312i	−0.346053	−	0.251422i
$369$	−1.99488	−	1.44937i	−0.103849	−	0.0754510i
$370$	6.65234	−	20.4738i	0.345839	−	1.06438i
$371$	7.24935	+	22.3112i	0.376368	+	1.15834i
$372$	−18.1875	+	13.2140i	−0.942977	+	0.685113i
$373$	38.1938			1.97760			0.988800	−	0.149245i	$-0.0476842\pi$
$373$	38.1938			1.97760			0.988800	+	0.149245i	$0.0476842\pi$
$374$	40.5229	−	20.3540i	2.09539	−	1.05248i
$375$	10.7953			0.557466
$376$	52.3202	−	38.0128i	2.69821	−	1.96036i
$377$	1.08828	+	3.34939i	0.0560494	+	0.172502i
$378$	−1.68284	+	5.17925i	−0.0865559	+	0.266392i
$379$	13.8206	+	10.0413i	0.709918	+	0.515786i	0.883147	−	0.469096i	$-0.155420\pi$
$379$	13.8206	+	10.0413i	0.709918	+	0.515786i	−0.173229	+	0.984882i	$0.555420\pi$
$380$	25.1961	+	18.3061i	1.29254	+	0.939082i
$381$	3.39774	−	10.4572i	0.174072	−	0.535738i
$382$	10.1495	+	31.2371i	0.519296	+	1.59823i
$383$	12.3526	−	8.97469i	0.631189	−	0.458585i	−0.225623	−	0.974215i	$-0.572442\pi$
$383$	12.3526	−	8.97469i	0.631189	−	0.458585i	0.856812	+	0.515629i	$0.172442\pi$
$384$	−2.51299			−0.128240
$385$	7.35270	−	14.2271i	0.374729	−	0.725082i
$386$	−44.4884			−2.26440
$387$	5.52417	−	4.01354i	0.280809	−	0.204020i
$388$	25.1399	+	77.3725i	1.27628	+	3.92800i
$389$	3.82050	−	11.7583i	0.193707	−	0.596169i	−0.806282	−	0.591531i	$-0.798524\pi$
$389$	3.82050	−	11.7583i	0.193707	−	0.596169i	0.999989	−	0.00463794i	$-0.00147631\pi$
$390$	−4.85349	−	3.52626i	−0.245766	−	0.178559i
$391$	3.80003	+	2.76088i	0.192176	+	0.139624i
$392$	5.81800	−	17.9059i	0.293853	−	0.904387i
$393$	−6.04116	−	18.5928i	−0.304736	−	0.937881i
$394$	−18.2737	+	13.2766i	−0.920616	+	0.668867i
$395$	3.68097			0.185210
$396$	11.1126	+	11.2415i	0.558430	+	0.564907i
$397$	24.7837			1.24386			0.621930	−	0.783073i	$-0.286349\pi$
$397$	24.7837			1.24386			0.621930	+	0.783073i	$0.286349\pi$
$398$	−17.7501	+	12.8962i	−0.889731	+	0.646427i
$399$	−1.83303	−	5.64149i	−0.0917663	−	0.282428i
$400$	0.906261	−	2.78918i	0.0453130	−	0.139459i
$401$	−10.2916	−	7.47726i	−0.513936	−	0.373396i	0.300379	−	0.953820i	$-0.402887\pi$
$401$	−10.2916	−	7.47726i	−0.513936	−	0.373396i	−0.814315	+	0.580424i	$0.802887\pi$
$402$	−22.2590	−	16.1721i	−1.11018	−	0.806591i
$403$	−1.45762	+	4.48609i	−0.0726091	+	0.223468i
$404$	16.8993	+	52.0105i	0.840769	+	2.58762i
$405$	−1.86590	+	1.35565i	−0.0927172	+	0.0673630i
$406$	19.1787			0.951824
$407$	1.79397	+	11.7653i	0.0889236	+	0.583182i
$408$	−37.8188			−1.87231
$409$	−4.12152	+	2.99446i	−0.203796	+	0.148066i	−0.685002	−	0.728541i	$-0.740199\pi$
$409$	−4.12152	+	2.99446i	−0.203796	+	0.148066i	0.481206	+	0.876607i	$0.340199\pi$
$410$	−4.57128	−	14.0690i	−0.225759	−	0.694816i
$411$	−3.40094	+	10.4670i	−0.167756	+	0.516300i
$412$	39.7399	+	28.8728i	1.95785	+	1.42246i
$413$	−24.7178	−	17.9585i	−1.21628	−	0.883680i
$414$	−0.718268	+	2.21060i	−0.0353010	+	0.108645i
$415$	3.78607	+	11.6523i	0.185851	+	0.571990i
$416$	7.68249	−	5.58166i	0.376665	−	0.273663i
$417$	−3.79655			−0.185918
$418$	−24.1196	−	3.96285i	−1.17973	−	0.193829i
$419$	9.93320			0.485269			0.242634	−	0.970118i	$-0.421988\pi$
$419$	9.93320			0.485269			0.242634	+	0.970118i	$0.421988\pi$
$420$	−18.6181	+	13.5269i	−0.908472	+	0.660043i
$421$	6.88334	+	21.1847i	0.335473	+	1.03248i	0.966488	+	0.256710i	$0.0826386\pi$
$421$	6.88334	+	21.1847i	0.335473	+	1.03248i	−0.631015	+	0.775771i	$0.717361\pi$
$422$	−4.31957	+	13.2943i	−0.210273	+	0.647155i
$423$	−7.27197	−	5.28340i	−0.353575	−	0.256888i
$424$	−65.2224	−	47.3868i	−3.16748	−	2.30131i
$425$	−0.518768	+	1.59660i	−0.0251639	+	0.0774466i
$426$	5.65786	+	17.4131i	0.274124	+	0.843667i
$427$	20.3563	−	14.7897i	0.985110	−	0.715724i
$428$	30.7926			1.48842
$429$	3.27275	+	0.537711i	0.158010	+	0.0259609i
$430$	40.9643			1.97547
$431$	−28.4567	+	20.6750i	−1.37071	+	0.995880i	−0.373030	+	0.927819i	$0.621681\pi$
$431$	−28.4567	+	20.6750i	−1.37071	+	0.995880i	−0.997681	+	0.0680602i	$0.978319\pi$
$432$	−2.83761	−	8.73327i	−0.136525	−	0.420180i
$433$	4.65375	−	14.3228i	0.223645	−	0.688308i	−0.774782	−	0.632229i	$-0.782140\pi$
$433$	4.65375	−	14.3228i	0.223645	−	0.688308i	0.998426	−	0.0560788i	$-0.0178598\pi$
$434$	20.7816	+	15.0987i	0.997550	+	0.724762i
$435$	6.57124	+	4.77429i	0.315067	+	0.228909i
$436$	−3.64013	+	11.2032i	−0.174331	+	0.536535i
$437$	−0.782373	−	2.40790i	−0.0374260	−	0.115185i
$438$	16.8520	−	12.2437i	0.805218	−	0.585025i
$439$	19.9657			0.952909			0.476455	−	0.879199i	$-0.341922\pi$
$439$	19.9657			0.952909			0.476455	+	0.879199i	$0.341922\pi$
$440$	8.29594	+	54.4067i	0.395493	+	2.59374i
$441$	−2.61682			−0.124611
$442$	−11.0615	+	8.03665i	−0.526142	+	0.382264i
$443$	−1.17623	−	3.62007i	−0.0558845	−	0.171995i	0.919218	−	0.393749i	$-0.128822\pi$
$443$	−1.17623	−	3.62007i	−0.0558845	−	0.171995i	−0.975103	+	0.221754i	$0.928822\pi$
$444$	5.28484	−	16.2651i	0.250807	−	0.771905i
$445$	−32.7612	−	23.8024i	−1.55303	−	1.12834i
$446$	15.4377	+	11.2162i	0.730999	+	0.531102i
$447$	−6.93168	+	21.3335i	−0.327857	+	1.00904i
$448$	−4.09870	−	12.6145i	−0.193646	−	0.595980i
$449$	−17.2224	+	12.5128i	−0.812775	+	0.590515i	−0.914634	−	0.404283i	$-0.867521\pi$
$449$	−17.2224	+	12.5128i	−0.812775	+	0.590515i	0.101859	+	0.994799i	$0.467521\pi$
$450$	−0.830741			−0.0391615
$451$	5.74940	+	5.81608i	0.270729	+	0.273868i
$452$	60.8975			2.86438
$453$	−1.47289	+	1.07012i	−0.0692025	+	0.0502785i
$454$	16.2756	+	50.0910i	0.763850	+	2.35089i
$455$	−1.49213	+	4.59231i	−0.0699522	+	0.215291i
$456$	16.4918	+	11.9820i	0.772298	+	0.561107i
$457$	5.76458	+	4.18821i	0.269656	+	0.195916i	0.714393	−	0.699745i	$-0.246703\pi$
$457$	5.76458	+	4.18821i	0.269656	+	0.195916i	−0.444737	+	0.895661i	$0.646703\pi$
$458$	−22.4745	+	69.1694i	−1.05016	+	3.23207i
$459$	1.62432	+	4.99916i	0.0758170	+	0.233341i
$460$	−7.94657	+	5.77352i	−0.370511	+	0.269192i
$461$	−4.46750			−0.208072			−0.104036	−	0.994574i	$-0.533176\pi$
$461$	−4.46750			−0.208072			−0.104036	+	0.994574i	$0.533176\pi$
$462$	8.29245	−	16.0455i	0.385799	−	0.746503i
$463$	−3.21024			−0.149192			−0.0745962	−	0.997214i	$-0.523767\pi$
$463$	−3.21024			−0.149192			−0.0745962	+	0.997214i	$0.523767\pi$
$464$	−26.1630	+	19.0085i	−1.21459	+	0.882449i
$465$	3.36182	+	10.3466i	0.155900	+	0.479812i
$466$	10.5775	−	32.5543i	0.489994	−	1.50805i
$467$	4.75046	+	3.45141i	0.219825	+	0.159712i	0.692248	−	0.721660i	$-0.256620\pi$
$467$	4.75046	+	3.45141i	0.219825	+	0.159712i	−0.472423	+	0.881372i	$0.656620\pi$
$468$	−3.85577	−	2.80138i	−0.178233	−	0.129494i
$469$	−6.84319	+	21.0612i	−0.315989	+	0.972515i
$470$	−16.6638	−	51.2858i	−0.768642	−	2.36564i
$471$	−16.7926	+	12.2005i	−0.773763	+	0.562171i
$472$	104.996			4.83285
$473$	−20.2373	+	10.1649i	−0.930513	+	0.467383i
$474$	4.15143			0.190682
$475$	0.732066	−	0.531877i	0.0335895	−	0.0244042i
$476$	16.2077	+	49.8821i	0.742878	+	2.28634i
$477$	−3.46262	+	10.6568i	−0.158542	+	0.487943i
$478$	32.2422	+	23.4253i	1.47472	+	1.07145i
$479$	−6.50424	−	4.72561i	−0.297186	−	0.215919i	0.429192	−	0.903213i	$-0.358798\pi$
$479$	−6.50424	−	4.72561i	−0.297186	−	0.215919i	−0.726379	+	0.687294i	$0.758798\pi$
$480$	6.76795	−	20.8296i	0.308913	−	0.950737i
$481$	−1.10886	−	3.41273i	−0.0505598	−	0.155607i
$482$	−49.2817	+	35.8053i	−2.24472	+	1.63089i
$483$	1.87082			0.0851255
$484$	−30.3241	−	42.7659i	−1.37837	−	1.94391i
$485$	39.3693			1.78767
$486$	−2.10438	+	1.52892i	−0.0954565	+	0.0693532i
$487$	1.04532	+	3.21715i	0.0473678	+	0.145783i	0.971943	−	0.235217i	$-0.0755799\pi$
$487$	1.04532	+	3.21715i	0.0473678	+	0.145783i	−0.924575	+	0.381000i	$0.875580\pi$
$488$	−26.7206	+	82.2375i	−1.20958	+	3.72272i
$489$	−11.2436	−	8.16895i	−0.508453	−	0.369413i
$490$	−12.7007	−	9.22760i	−0.573759	−	0.416861i
$491$	5.40804	−	16.6442i	0.244061	−	0.751144i	−0.751728	−	0.659473i	$-0.770779\pi$
$491$	5.40804	−	16.6442i	0.244061	−	0.751144i	0.995789	−	0.0916705i	$-0.0292207\pi$
$492$	−3.63158	−	11.1768i	−0.163724	−	0.503891i
$493$	14.9764	−	10.8810i	0.674503	−	0.490055i
$494$	7.36985			0.331585
$495$	6.83556	−	3.43340i	0.307236	−	0.154320i
$496$	−43.3144			−1.94487
$497$	11.9222	−	8.66198i	0.534783	−	0.388543i
$498$	4.26997	+	13.1416i	0.191342	+	0.588889i
$499$	−4.15413	+	12.7851i	−0.185964	+	0.572339i	−0.999964	−	0.00852655i	$-0.997286\pi$
$499$	−4.15413	+	12.7851i	−0.185964	+	0.572339i	0.813999	+	0.580866i	$0.197286\pi$
$500$	41.6241	+	30.2417i	1.86149	+	1.35245i
$501$	1.99743	+	1.45122i	0.0892384	+	0.0648355i
$502$	16.4842	−	50.7330i	0.735724	−	2.26433i
$503$	1.58454	+	4.87670i	0.0706510	+	0.217441i	0.980147	−	0.198271i	$-0.0635325\pi$
$503$	1.58454	+	4.87670i	0.0706510	+	0.217441i	−0.909496	+	0.415712i	$0.863532\pi$
$504$	−12.1862	+	8.85381i	−0.542818	+	0.394380i
$505$	26.4644			1.17765
$506$	3.53937	−	6.84852i	0.157344	−	0.304454i
$507$	−1.00000			−0.0444116
$508$	42.3955	−	30.8021i	1.88100	−	1.36662i
$509$	−1.41758	−	4.36287i	−0.0628332	−	0.193381i	0.914712	−	0.404106i	$-0.132417\pi$
$509$	−1.41758	−	4.36287i	−0.0628332	−	0.193381i	−0.977545	+	0.210725i	$0.932417\pi$
$510$	−9.74471	+	29.9911i	−0.431503	+	1.32803i
$511$	−13.5637	−	9.85463i	−0.600024	−	0.435943i
$512$	−36.3534	−	26.4123i	−1.60661	−	1.16727i
$513$	0.875538	−	2.69463i	0.0386560	−	0.118971i
$514$	−20.5950	−	63.3849i	−0.908407	−	2.79579i
$515$	19.2311	−	13.9722i	0.847423	−	0.615689i
$516$	32.5434			1.43264
$517$	20.9584	+	21.2014i	0.921748	+	0.932438i
$518$	−19.5414			−0.858601
$519$	−10.7700	+	7.82488i	−0.472752	+	0.343474i
$520$	−5.12778	−	15.7817i	−0.224868	−	0.692073i
$521$	3.39977	−	10.4634i	0.148946	−	0.458410i	−0.848551	−	0.529114i	$-0.822524\pi$
$521$	3.39977	−	10.4634i	0.148946	−	0.458410i	0.997497	+	0.0707037i	$0.0225245\pi$
$522$	7.41110	+	5.38448i	0.324375	+	0.235672i
$523$	−1.16163	−	0.843972i	−0.0507944	−	0.0369043i	0.562098	−	0.827070i	$-0.309994\pi$
$523$	−1.16163	−	0.843972i	−0.0507944	−	0.0369043i	−0.612893	+	0.790166i	$0.709994\pi$
$524$	28.7921	−	88.6130i	1.25779	−	3.87108i
$525$	0.206622	+	0.635918i	0.00901773	+	0.0277537i
$526$	−4.73334	+	3.43897i	−0.206383	+	0.149946i
$527$	24.7943			1.08006
$528$	4.59081	+	30.1076i	0.199789	+	1.31027i
$529$	−22.2015			−0.965282
$530$	−54.3846	+	39.5127i	−2.36232	+	1.71632i
$531$	−4.50961	−	13.8792i	−0.195701	−	0.602304i
$532$	8.73621	−	26.8873i	0.378763	−	1.16571i
$533$	−1.99488	−	1.44937i	−0.0864079	−	0.0627790i
$534$	−36.9483	−	26.8445i	−1.59891	−	1.16168i
$535$	4.60474	−	14.1719i	0.199080	−	0.612706i
$536$	−23.5170	−	72.3777i	−1.01578	−	3.12624i
$537$	13.7729	−	10.0066i	0.594346	−	0.431818i
$538$	−37.7631			−1.62808
$539$	8.56419	+	1.40709i	0.368886	+	0.0606078i
$540$	−10.9922			−0.473028
$541$	−22.4903	+	16.3401i	−0.966933	+	0.702518i	−0.954750	−	0.297408i	$-0.903878\pi$
$541$	−22.4903	+	16.3401i	−0.966933	+	0.702518i	−0.0121821	+	0.999926i	$0.503878\pi$
$542$	−5.24901	−	16.1548i	−0.225464	−	0.693908i
$543$	−3.25569	+	10.0200i	−0.139715	+	0.429999i
$544$	−40.3824	−	29.3395i	−1.73138	−	1.25792i
$545$	4.61179	+	3.35066i	0.197547	+	0.143527i
$546$	−1.68284	+	5.17925i	−0.0720189	+	0.221651i
$547$	3.14813	+	9.68894i	0.134604	+	0.414269i	0.995528	−	0.0944643i	$-0.0301138\pi$
$547$	3.14813	+	9.68894i	0.134604	+	0.414269i	−0.860924	+	0.508734i	$0.830114\pi$
$548$	−42.4353	+	30.8311i	−1.81275	+	1.31704i
$549$	12.0184			0.512933
$550$	2.71881	+	0.446699i	0.115930	+	0.0190473i
$551$	−9.97820			−0.425086
$552$	−5.20131	+	3.77898i	−0.221383	+	0.160844i
$553$	−1.03255	−	3.17785i	−0.0439083	−	0.135136i
$554$	−7.17812	+	22.0920i	−0.304969	+	0.938598i
$555$	−6.69551	−	4.86457i	−0.284209	−	0.206490i
$556$	−14.6386	−	10.6356i	−0.620816	−	0.451049i
$557$	8.66364	−	26.6639i	0.367090	−	1.12979i	−0.581572	−	0.813495i	$-0.697562\pi$
$557$	8.66364	−	26.6639i	0.367090	−	1.12979i	0.948662	−	0.316292i	$-0.102438\pi$
$558$	3.79149	+	11.6690i	0.160506	+	0.493988i
$559$	5.52417	−	4.01354i	0.233647	−	0.169755i
$560$	−44.3400			−1.87371
$561$	−2.62790	−	17.2344i	−0.110950	−	0.727636i
$562$	22.9630			0.968637
$563$	−10.3327	+	7.50713i	−0.435471	+	0.316388i	−0.783833	−	0.620972i	$-0.786738\pi$
$563$	−10.3327	+	7.50713i	−0.435471	+	0.316388i	0.348362	+	0.937360i	$0.386738\pi$
$564$	−13.2382	−	40.7431i	−0.557431	−	1.71559i
$565$	9.10665	−	28.0274i	0.383120	−	1.17912i
$566$	−28.2862	−	20.5511i	−1.18896	−	0.863827i
$567$	1.69376	+	1.23059i	0.0711313	+	0.0516799i
$568$	−15.6496	+	48.1645i	−0.656642	+	2.02094i
$569$	−6.87060	−	21.1455i	−0.288030	−	0.886467i	−0.985474	−	0.169827i	$-0.945679\pi$
$569$	−6.87060	−	21.1455i	−0.288030	−	0.886467i	0.697443	−	0.716640i	$-0.254321\pi$
$570$	13.7514	−	9.99097i	0.575982	−	0.418476i
$571$	−1.77737			−0.0743807			−0.0371904	−	0.999308i	$-0.511841\pi$
$571$	−1.77737			−0.0743807			−0.0371904	+	0.999308i	$0.511841\pi$
$572$	11.1126	+	11.2415i	0.464642	+	0.470031i
$573$	12.6269			0.527498
$574$	−10.8637	+	7.89293i	−0.453442	+	0.329445i
$575$	0.0881903	+	0.271422i	0.00367779	+	0.0113191i
$576$	1.95773	−	6.02526i	0.0815719	−	0.251053i
$577$	10.6460	+	7.73477i	0.443199	+	0.322003i	0.786905	−	0.617075i	$-0.211682\pi$
$577$	10.6460	+	7.73477i	0.443199	+	0.322003i	−0.343706	+	0.939077i	$0.611682\pi$
$578$	22.3695	+	16.2524i	0.930449	+	0.676011i
$579$	−5.28523	+	16.2663i	−0.219647	+	0.676003i
$580$	11.9626	+	36.8171i	0.496720	+	1.52875i
$581$	8.99764	−	6.53717i	0.373285	−	0.271207i
$582$	44.4010			1.84048
$583$	17.0626	−	33.0152i	0.706659	−	1.36735i
$584$	57.6161			2.38417
$585$	−1.86590	+	1.35565i	−0.0771454	+	0.0560494i
$586$	−4.01273	−	12.3499i	−0.165764	−	0.510171i
$587$	7.64966	−	23.5432i	0.315735	−	0.971734i	−0.659715	−	0.751516i	$-0.729323\pi$
$587$	7.64966	−	23.5432i	0.315735	−	0.971734i	0.975451	−	0.220218i	$-0.0706769\pi$
$588$	−10.0899	−	7.33071i	−0.416099	−	0.302314i
$589$	−10.8121	−	7.85548i	−0.445507	−	0.323679i
$590$	27.0542	−	83.2644i	1.11381	−	3.42794i
$591$	2.68340	+	8.25866i	0.110380	+	0.339716i
$592$	26.6578	−	19.3680i	1.09563	−	0.796021i
$593$	−4.16574			−0.171066			−0.0855332	−	0.996335i	$-0.527259\pi$
$593$	−4.16574			−0.171066			−0.0855332	+	0.996335i	$0.527259\pi$
$594$	7.70921	−	3.87222i	0.316313	−	0.158879i
$595$	25.3814			1.04054
$596$	−86.4903	+	62.8389i	−3.54278	+	2.57398i
$597$	2.60651	+	8.02201i	0.106677	+	0.328319i
$598$	−0.718268	+	2.21060i	−0.0293722	+	0.0903983i
$599$	5.36242	+	3.89603i	0.219103	+	0.159187i	0.691923	−	0.721972i	$-0.256764\pi$
$599$	5.36242	+	3.89603i	0.219103	+	0.159187i	−0.472820	+	0.881159i	$0.656764\pi$
$600$	−1.85898	−	1.35063i	−0.0758925	−	0.0551392i
$601$	10.0501	−	30.9309i	0.409950	−	1.26170i	−0.506740	−	0.862099i	$-0.669150\pi$
$601$	10.0501	−	30.9309i	0.409950	−	1.26170i	0.916690	−	0.399599i	$-0.130850\pi$
$602$	−11.4908	−	35.3652i	−0.468332	−	1.44138i
$603$	−8.55735	+	6.21728i	−0.348482	+	0.253187i
$604$	−8.67694			−0.353060
$605$	−24.2172	+	7.56109i	−0.984570	+	0.307402i
$606$	29.8468			1.21244
$607$	−30.3459	+	22.0476i	−1.23170	+	0.894885i	−0.997017	−	0.0771856i	$-0.975407\pi$
$607$	−30.3459	+	22.0476i	−1.23170	+	0.894885i	−0.234687	+	0.972071i	$0.575407\pi$
$608$	8.31418	+	25.5884i	0.337185	+	1.03775i
$609$	2.27843	−	7.01230i	0.0923268	−	0.284153i
$610$	58.3311	+	42.3800i	2.36176	+	1.71592i
$611$	−7.27197	−	5.28340i	−0.294192	−	0.213743i
$612$	−7.74152	+	23.8259i	−0.312932	+	0.963107i
$613$	8.90085	+	27.3940i	0.359502	+	1.10643i	0.953353	+	0.301858i	$0.0976069\pi$
$613$	8.90085	+	27.3940i	0.359502	+	1.10643i	−0.593851	+	0.804575i	$0.702393\pi$
$614$	−15.5278	+	11.2816i	−0.626650	+	0.455288i
$615$	−5.68708			−0.229325
$616$	44.6432	−	22.4236i	1.79873	−	0.903473i
$617$	−9.71370			−0.391059			−0.195529	−	0.980698i	$-0.562643\pi$
$617$	−9.71370			−0.391059			−0.195529	+	0.980698i	$0.562643\pi$
$618$	21.6890	−	15.7580i	0.872460	−	0.633879i
$619$	12.9361	+	39.8134i	0.519948	+	1.60023i	0.774096	+	0.633069i	$0.218205\pi$
$619$	12.9361	+	39.8134i	0.519948	+	1.60023i	−0.254148	+	0.967165i	$0.581795\pi$
$620$	−16.0224	+	49.3119i	−0.643475	+	1.98041i
$621$	0.722930	+	0.525239i	0.0290102	+	0.0210771i
$622$	−30.8361	−	22.4038i	−1.23642	−	0.898309i
$623$	−11.3592	+	34.9601i	−0.455097	+	1.40065i
$624$	−2.83761	−	8.73327i	−0.113595	−	0.349611i
$625$	21.4348	−	15.5733i	0.857392	−	0.622932i
$626$	−7.54978			−0.301750
$627$	−4.31435	+	8.34805i	−0.172298	+	0.333389i
$628$	−98.9268			−3.94761
$629$	−15.2596	+	11.0868i	−0.608441	+	0.442058i
$630$	3.88126	+	11.9453i	0.154633	+	0.475912i
$631$	−6.47345	+	19.9232i	−0.257704	+	0.793132i	0.735581	+	0.677437i	$0.236909\pi$
$631$	−6.47345	+	19.9232i	−0.257704	+	0.793132i	−0.993285	+	0.115695i	$0.963091\pi$
$632$	9.28981	+	6.74944i	0.369529	+	0.268478i
$633$	4.34761	+	3.15872i	0.172802	+	0.125548i
$634$	10.2340	−	31.4969i	0.406442	−	1.25090i
$635$	−7.83648	−	24.1182i	−0.310981	−	0.957102i
$636$	−43.2049	+	31.3902i	−1.71319	+	1.24470i
$637$	−2.61682			−0.103682
$638$	−21.3594	−	21.6071i	−0.845625	−	0.855432i
$639$	7.03888			0.278454
$640$	−4.68898	+	3.40674i	−0.185348	+	0.134663i
$641$	−12.8726	−	39.6178i	−0.508437	−	1.56481i	−0.794914	−	0.606722i	$-0.792484\pi$
$641$	−12.8726	−	39.6178i	−0.508437	−	1.56481i	0.286476	−	0.958087i	$-0.407516\pi$
$642$	5.19327	−	15.9832i	0.204962	−	0.630808i
$643$	2.94437	+	2.13921i	0.116115	+	0.0843623i	0.644327	−	0.764750i	$-0.277138\pi$
$643$	2.94437	+	2.13921i	0.116115	+	0.0843623i	−0.528212	+	0.849112i	$0.677138\pi$
$644$	7.21347	+	5.24089i	0.284251	+	0.206520i
$645$	4.86656	−	14.9777i	0.191621	−	0.589748i
$646$	−11.9710	−	36.8430i	−0.470994	−	1.44957i
$647$	10.0035	−	7.26796i	0.393278	−	0.285733i	−0.373520	−	0.927622i	$-0.621849\pi$
$647$	10.0035	−	7.26796i	0.393278	−	0.285733i	0.766797	+	0.641889i	$0.221849\pi$
$648$	−7.19477			−0.282637
$649$	7.29584	+	47.8478i	0.286387	+	1.87819i
$650$	−0.830741			−0.0325844
$651$	7.98939	−	5.80463i	0.313129	−	0.227501i
$652$	−20.4684	−	62.9952i	−0.801604	−	2.46708i
$653$	3.96601	−	12.2061i	0.155202	−	0.477662i	−0.842979	−	0.537946i	$-0.819201\pi$
$653$	3.96601	−	12.2061i	0.155202	−	0.477662i	0.998181	+	0.0602836i	$0.0192005\pi$
$654$	5.20122	+	3.77891i	0.203384	+	0.147767i
$655$	−36.4776	−	26.5025i	−1.42530	−	1.03554i
$656$	6.99701	−	21.5346i	0.273187	−	0.840784i
$657$	−2.47462	−	7.61611i	−0.0965443	−	0.297133i
$658$	−39.6016	+	28.7722i	−1.54383	+	1.12166i
$659$	−17.8310			−0.694597			−0.347298	−	0.937755i	$-0.612901\pi$
$659$	−17.8310			−0.694597			−0.347298	+	0.937755i	$0.612901\pi$
$660$	35.9746	+	5.91061i	1.40031	+	0.230070i
$661$	−13.5013			−0.525139			−0.262569	−	0.964913i	$-0.584570\pi$
$661$	−13.5013			−0.525139			−0.262569	+	0.964913i	$0.584570\pi$
$662$	−37.7045	+	27.3939i	−1.46543	+	1.06470i
$663$	1.62432	+	4.99916i	0.0630835	+	0.194151i
$664$	−11.8107	+	36.3496i	−0.458344	+	1.41064i
$665$	−11.0682	−	8.04149i	−0.429205	−	0.311835i
$666$	−7.55126	−	5.48631i	−0.292605	−	0.212590i
$667$	0.972479	−	2.99298i	0.0376545	−	0.115889i
$668$	3.63621	+	11.1911i	0.140689	+	0.432997i
$669$	5.93497	−	4.31200i	0.229459	−	0.166712i
$670$	−63.4568			−2.45155
$671$	−39.3332	−	6.46242i	−1.51844	−	0.249479i
$672$	−19.8810			−0.766927
$673$	−21.2751	+	15.4573i	−0.820095	+	0.595834i	−0.916740	−	0.399485i	$-0.869189\pi$
$673$	−21.2751	+	15.4573i	−0.820095	+	0.595834i	0.0966444	+	0.995319i	$0.469189\pi$
$674$	7.92568	+	24.3927i	0.305286	+	0.939574i
$675$	−0.0986921	+	0.303743i	−0.00379866	+	0.0116911i
$676$	−3.85577	−	2.80138i	−0.148299	−	0.107745i
$677$	26.0199	+	18.9046i	1.00003	+	0.726562i	0.962094	−	0.272718i	$-0.0879226\pi$
$677$	26.0199	+	18.9046i	1.00003	+	0.726562i	0.0379330	+	0.999280i	$0.487923\pi$
$678$	10.2706	−	31.6095i	0.394438	−	1.21396i
$679$	−11.0434	−	33.9882i	−0.423808	−	1.30435i
$680$	−70.5660	+	51.2692i	−2.70608	+	1.96608i
$681$	20.2483			0.775915
$682$	−6.13402	−	40.2284i	−0.234884	−	1.54042i
$683$	32.3740			1.23876			0.619379	−	0.785092i	$-0.287384\pi$
$683$	32.3740			1.23876			0.619379	+	0.785092i	$0.287384\pi$
$684$	10.9246	−	7.93716i	0.417711	−	0.303485i
$685$	7.84385	+	24.1409i	0.299698	+	0.922376i
$686$	−16.1836	+	49.8079i	−0.617892	+	1.90167i
$687$	22.6204	+	16.4347i	0.863021	+	0.627021i
$688$	50.7268	+	36.8552i	1.93394	+	1.40509i
$689$	−3.46262	+	10.6568i	−0.131915	+	0.405993i
$690$	1.65660	+	5.09848i	0.0630656	+	0.194096i
$691$	−25.3561	+	18.4223i	−0.964592	+	0.700817i	−0.954213	−	0.299129i	$-0.903304\pi$
$691$	−25.3561	+	18.4223i	−0.964592	+	0.700817i	−0.0103795	+	0.999946i	$0.503304\pi$
$692$	−63.4472			−2.41190
$693$	−4.88155	−	4.93816i	−0.185435	−	0.187585i
$694$	40.3688			1.53238
$695$	−7.08398	+	5.14681i	−0.268711	+	0.195230i
$696$	7.82994	+	24.0981i	0.296793	+	0.913436i
$697$	−4.00527	+	12.3270i	−0.151711	+	0.466917i
$698$	1.72387	+	1.25246i	0.0652494	+	0.0474065i
$699$	−10.6462	−	7.73490i	−0.402675	−	0.292561i
$700$	−0.984760	+	3.03078i	−0.0372204	+	0.114553i
$701$	8.31945	+	25.6046i	0.314221	+	0.967074i	0.976074	+	0.217440i	$0.0697705\pi$
$701$	8.31945	+	25.6046i	0.314221	+	0.967074i	−0.661853	+	0.749634i	$0.730229\pi$
$702$	−2.10438	+	1.52892i	−0.0794246	+	0.0577053i
$703$	10.1669			0.383452
$704$	−9.64699	+	18.6665i	−0.363585	+	0.703519i
$705$	−20.7312			−0.780783
$706$	62.3762	−	45.3190i	2.34756	−	1.70560i
$707$	−7.42350	−	22.8472i	−0.279189	−	0.859257i
$708$	21.4928	−	66.1480i	0.807748	−	2.48599i
$709$	−22.9672	−	16.6867i	−0.862553	−	0.626681i	0.0660254	−	0.997818i	$-0.478968\pi$
$709$	−22.9672	−	16.6867i	−0.862553	−	0.626681i	−0.928578	+	0.371137i	$0.878968\pi$
$710$	34.1631	+	24.8210i	1.28212	+	0.931514i
$711$	0.493190	−	1.51788i	0.0184961	−	0.0569251i
$712$	−39.0365	−	120.142i	−1.46295	−	4.50251i
$713$	3.41002	−	2.47753i	0.127706	−	0.0927841i
$714$	28.6253			1.07128
$715$	6.83556	−	3.43340i	0.255635	−	0.128402i
$716$	81.1376			3.03225
$717$	12.3953	−	9.00574i	0.462913	−	0.336326i
$718$	−21.8910	−	67.3735i	−0.816964	−	2.51436i
$719$	−13.9278	+	42.8652i	−0.519418	+	1.59860i	0.255680	+	0.966762i	$0.417701\pi$
$719$	−13.9278	+	42.8652i	−0.519418	+	1.59860i	−0.775097	+	0.631842i	$0.782299\pi$
$720$	−17.1340	−	12.4486i	−0.638546	−	0.463931i
$721$	−17.4569	−	12.6832i	−0.650131	−	0.472348i
$722$	8.81962	−	27.1440i	0.328232	−	1.01020i
$723$	7.23677	+	22.2725i	0.269138	+	0.828323i
$724$	−40.6230	+	29.5144i	−1.50974	+	1.09689i
$725$	1.12476			0.0417725
$726$	−27.3124	+	8.52746i	−1.01366	+	0.316484i
$727$	7.15786			0.265470			0.132735	−	0.991152i	$-0.457624\pi$
$727$	7.15786			0.265470			0.132735	+	0.991152i	$0.457624\pi$
$728$	−12.1862	+	8.85381i	−0.451652	+	0.328144i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	14.8459	−	45.6909i	0.549470	−	1.69109i
$731$	−29.0374	−	21.0969i	−1.07399	−	0.780297i
$732$	46.3402	+	33.6681i	1.71278	+	1.24441i
$733$	−5.59234	+	17.2114i	−0.206558	+	0.635719i	0.793088	+	0.609107i	$0.208472\pi$
$733$	−5.59234	+	17.2114i	−0.206558	+	0.635719i	−0.999646	+	0.0266122i	$0.991528\pi$
$734$	4.23172	+	13.0239i	0.156196	+	0.480721i
$735$	−4.88272	+	3.54751i	−0.180102	+	0.130852i
$736$	−8.48561			−0.312784
$737$	31.3491	−	15.7462i	1.15476	−	0.580019i
$738$	−6.41394			−0.236101
$739$	8.36246	−	6.07568i	0.307618	−	0.223498i	−0.423256	−	0.906010i	$-0.639113\pi$
$739$	8.36246	−	6.07568i	0.307618	−	0.223498i	0.730874	+	0.682513i	$0.239113\pi$
$740$	−12.1888	−	37.5134i	−0.448070	−	1.37902i
$741$	0.875538	−	2.69463i	0.0321637	−	0.0989897i
$742$	49.3674	+	35.8675i	1.81233	+	1.31674i
$743$	−20.5387	−	14.9222i	−0.753492	−	0.547444i	0.143415	−	0.989663i	$-0.454191\pi$
$743$	−20.5387	−	14.9222i	−0.753492	−	0.547444i	−0.896907	+	0.442219i	$0.854191\pi$
$744$	−10.4872	+	32.2764i	−0.384480	+	1.18331i
$745$	15.9871	+	49.2032i	0.585721	+	1.80266i
$746$	80.3742	−	58.3952i	2.94271	−	2.13800i
$747$	5.31222			0.194364
$748$	38.1475	−	73.8136i	1.39481	−	2.69889i
$749$	−13.5266			−0.494249
$750$	22.7173	−	16.5051i	0.829520	−	0.602682i
$751$	−6.43704	−	19.8112i	−0.234891	−	0.722920i	−0.997136	−	0.0756310i	$-0.975903\pi$
$751$	−6.43704	−	19.8112i	−0.234891	−	0.722920i	0.762245	−	0.647289i	$-0.224097\pi$
$752$	25.5063	−	78.5003i	0.930119	−	2.86261i
$753$	−16.5911	−	12.0542i	−0.604615	−	0.439278i
$754$	7.41110	+	5.38448i	0.269896	+	0.196091i
$755$	−1.29756	+	3.99346i	−0.0472229	+	0.145337i
$756$	3.08340	+	9.48974i	0.112142	+	0.345139i
$757$	−6.38783	+	4.64103i	−0.232169	+	0.168681i	−0.697788	−	0.716305i	$-0.745832\pi$
$757$	−6.38783	+	4.64103i	−0.232169	+	0.168681i	0.465618	+	0.884986i	$0.345832\pi$
$758$	44.4361			1.61399
$759$	−2.08354	−	2.10770i	−0.0756277	−	0.0765047i
$760$	47.0154			1.70543
$761$	25.3222	−	18.3976i	0.917928	−	0.666914i	−0.0250792	−	0.999685i	$-0.507984\pi$
$761$	25.3222	−	18.3976i	0.917928	−	0.666914i	0.943007	+	0.332772i	$0.107984\pi$
$762$	−8.83805	−	27.2007i	−0.320169	−	0.985378i
$763$	1.59904	−	4.92133i	0.0578890	−	0.178164i
$764$	48.6866	+	35.3729i	1.76142	+	1.27975i
$765$	9.80795	+	7.12589i	0.354607	+	0.257637i
$766$	12.2730	−	37.7723i	0.443440	−	1.36477i
$767$	−4.50961	−	13.8792i	−0.162833	−	0.501148i
$768$	−15.5391	+	11.2898i	−0.560718	+	0.407385i
$769$	−17.8853			−0.644959			−0.322479	−	0.946576i	$-0.604516\pi$
$769$	−17.8853			−0.644959			−0.322479	+	0.946576i	$0.604516\pi$
$770$	−6.27927	−	41.1809i	−0.226289	−	1.48406i
$771$	−25.6221			−0.922756
$772$	−65.9466	+	47.9130i	−2.37347	+	1.72443i
$773$	2.58763	+	7.96390i	0.0930705	+	0.286442i	0.986746	−	0.162272i	$-0.0518823\pi$
$773$	2.58763	+	7.96390i	0.0930705	+	0.286442i	−0.893676	+	0.448714i	$0.851882\pi$
$774$	5.48855	−	16.8920i	0.197282	−	0.607171i
$775$	1.21876	+	0.885483i	0.0437792	+	0.0318075i
$776$	99.3577	+	72.1876i	3.56674	+	2.59138i
$777$	−2.32152	+	7.14491i	−0.0832841	+	0.256322i
$778$	−9.93770	−	30.5851i	−0.356284	−	1.09653i
$779$	5.65210	−	4.10649i	0.202507	−	0.147130i
$780$	−10.9922			−0.393583
$781$	−23.0365	−	3.78488i	−0.824310	−	0.135434i
$782$	12.2178			0.436909
$783$	2.84916	−	2.07004i	0.101821	−	0.0739771i
$784$	−7.42553	−	22.8534i	−0.265197	−	0.816193i
$785$	−14.7936	+	45.5299i	−0.528005	+	1.62503i
$786$	−41.1397	−	29.8898i	−1.46741	−	1.06613i
$787$	29.3080	+	21.2935i	1.04472	+	0.759031i	0.971201	−	0.238263i	$-0.0765780\pi$
$787$	29.3080	+	21.2935i	1.04472	+	0.759031i	0.0735160	+	0.997294i	$0.476578\pi$
$788$	−12.7891	+	39.3607i	−0.455592	+	1.40217i
$789$	0.695066	+	2.13919i	0.0247450	+	0.0761573i
$790$	7.74615	−	5.62791i	0.275596	−	0.200232i
$791$	−26.7510			−0.951157
$792$	23.5467	+	3.86871i	0.836694	+	0.137469i
$793$	12.0184			0.426786
$794$	52.1543	−	37.8923i	1.85089	−	1.34475i
$795$	7.98610	+	24.5787i	0.283238	+	0.871716i
$796$	−12.4226	+	38.2328i	−0.440308	+	1.35513i
$797$	27.3241	+	19.8521i	0.967869	+	0.703198i	0.954965	−	0.296718i	$-0.0958923\pi$
$797$	27.3241	+	19.8521i	0.967869	+	0.703198i	0.0129043	+	0.999917i	$0.495892\pi$
$798$	−12.4828	−	9.06926i	−0.441885	−	0.321048i
$799$	−14.6005	+	44.9357i	−0.516528	+	1.58971i
$800$	−0.937188	−	2.88437i	−0.0331346	−	0.101978i
$801$	−14.2046	+	10.3202i	−0.501895	+	0.364648i
$802$	−33.0894			−1.16843
$803$	4.00355	+	26.2562i	0.141282	+	0.926562i
$804$	−50.4121			−1.77790
$805$	3.49077	−	2.53619i	0.123033	−	0.0893890i
$806$	3.79149	+	11.6690i	0.133549	+	0.411023i
$807$	−4.48626	+	13.8073i	−0.157924	+	0.486040i
$808$	66.7892	+	48.5252i	2.34964	+	1.70711i
$809$	10.5363	+	7.65506i	0.370436	+	0.269138i	0.757392	−	0.652961i	$-0.226473\pi$
$809$	10.5363	+	7.65506i	0.370436	+	0.269138i	−0.386956	+	0.922098i	$0.626473\pi$
$810$	−1.85387	+	5.70561i	−0.0651382	+	0.200475i
$811$	−14.7727	−	45.4658i	−0.518741	−	1.59652i	−0.776370	−	0.630278i	$-0.782941\pi$
$811$	−14.7727	−	45.4658i	−0.518741	−	1.59652i	0.257628	−	0.966244i	$-0.417059\pi$
$812$	28.4292	−	20.6550i	0.997670	−	0.724850i
$813$	−6.53025			−0.229026
$814$	21.7633	+	22.0157i	0.762803	+	0.771650i
$815$	−32.0537			−1.12279
$816$	−39.0498	+	28.3713i	−1.36702	+	0.993196i
$817$	5.97839	+	18.3996i	0.209158	+	0.643721i
$818$	−4.09494	+	12.6029i	−0.143176	+	0.440651i
$819$	1.69376	+	1.23059i	0.0591848	+	0.0430003i
$820$	−21.9281	−	15.9317i	−0.765762	−	0.556359i
$821$	−13.8247	+	42.5480i	−0.482485	+	1.48493i	0.353107	+	0.935583i	$0.385125\pi$
$821$	−13.8247	+	42.5480i	−0.482485	+	1.48493i	−0.835591	+	0.549352i	$0.814875\pi$
$822$	8.84636	+	27.2263i	0.308552	+	0.949627i
$823$	−42.0658	+	30.5626i	−1.46632	+	1.06534i	−0.484661	+	0.874702i	$0.661057\pi$
$823$	−42.0658	+	30.5626i	−1.46632	+	1.06534i	−0.981660	+	0.190642i	$0.938943\pi$
$824$	74.1537			2.58327
$825$	0.486320	−	0.941006i	0.0169315	−	0.0327616i
$826$	−79.4726			−2.76520
$827$	−31.5409	+	22.9158i	−1.09679	+	0.796861i	−0.980532	−	0.196359i	$-0.937088\pi$
$827$	−31.5409	+	22.9158i	−1.09679	+	0.796861i	−0.116253	+	0.993220i	$0.537088\pi$
$828$	1.31606	+	4.05040i	0.0457361	+	0.140761i
$829$	16.2221	−	49.9265i	0.563416	−	1.73402i	−0.109194	−	0.994020i	$-0.534827\pi$
$829$	16.2221	−	49.9265i	0.563416	−	1.73402i	0.672610	−	0.739997i	$-0.265173\pi$
$830$	25.7828	+	18.7323i	0.894934	+	0.650207i
$831$	7.22471	+	5.24906i	0.250622	+	0.182088i
$832$	1.95773	−	6.02526i	0.0678719	−	0.208888i
$833$	4.25057	+	13.0819i	0.147273	+	0.453261i
$834$	−7.98937	+	5.80462i	−0.276649	+	0.200998i
$835$	5.69434			0.197061
$836$	−40.0212	+	20.1020i	−1.38416	+	0.695244i
$837$	4.71695			0.163042
$838$	20.9032	−	15.1871i	0.722089	−	0.524628i
$839$	0.0558127	+	0.171774i	0.00192687	+	0.00593029i	0.952015	−	0.306050i	$-0.0990076\pi$
$839$	0.0558127	+	0.171774i	0.00192687	+	0.00593029i	−0.950088	+	0.311981i	$0.899008\pi$
$840$	−10.7355	+	33.0406i	−0.370412	+	1.14001i
$841$	13.4274	+	9.75561i	0.463015	+	0.336400i
$842$	46.8749	+	34.0566i	1.61541	+	1.17367i
$843$	2.72801	−	8.39594i	0.0939576	−	0.289172i
$844$	7.91459	+	24.3586i	0.272431	+	0.838458i
$845$	−1.86590	+	1.35565i	−0.0641888	+	0.0466359i
$846$	−23.3809			−0.803850
$847$	13.3208	+	18.7862i	0.457707	+	0.645502i
$848$	−102.895			−3.53342
$849$	−10.8745	+	7.90076i	−0.373211	+	0.271154i
$850$	1.34939	+	4.15301i	0.0462838	+	0.142447i
$851$	−0.990870	+	3.04958i	−0.0339666	+	0.104538i
$852$	27.1403	+	19.7186i	0.929812	+	0.675548i
$853$	−39.7334	−	28.8680i	−1.36044	−	0.988421i	−0.998417	−	0.0562538i	$-0.982084\pi$
$853$	−39.7334	−	28.8680i	−1.36044	−	0.988421i	−0.362028	−	0.932167i	$-0.617916\pi$
$854$	20.2250	−	62.2462i	0.692086	−	2.13002i
$855$	−2.01932	−	6.21483i	−0.0690593	−	0.212543i
$856$	37.6069	−	27.3230i	1.28538	−	0.933881i
$857$	−30.7804			−1.05144			−0.525719	−	0.850659i	$-0.676204\pi$
$857$	−30.7804			−1.05144			−0.525719	+	0.850659i	$0.676204\pi$
$858$	7.70921	−	3.87222i	0.263188	−	0.132195i
$859$	−0.500033			−0.0170609			−0.00853046	−	0.999964i	$-0.502715\pi$
$859$	−0.500033			−0.0170609			−0.00853046	+	0.999964i	$0.502715\pi$
$860$	60.7227	−	44.1176i	2.07063	−	1.50440i
$861$	1.59528	+	4.90976i	0.0543669	+	0.167324i
$862$	−28.2732	+	87.0160i	−0.962989	+	2.96378i
$863$	−14.9838	−	10.8864i	−0.510054	−	0.370576i	0.302790	−	0.953057i	$-0.402082\pi$
$863$	−14.9838	−	10.8864i	−0.510054	−	0.370576i	−0.812844	+	0.582481i	$0.802082\pi$
$864$	−7.68249	−	5.58166i	−0.261364	−	0.189892i
$865$	−9.48794	+	29.2009i	−0.322600	+	0.992859i
$866$	−12.1051	−	37.2557i	−0.411348	−	1.26600i
$867$	8.59985	−	6.24816i	0.292066	−	0.212199i
$868$	47.0662			1.59753
$869$	−2.43027	+	4.70246i	−0.0824413	+	0.159520i
$870$	21.1279			0.716301
$871$	−8.55735	+	6.21728i	−0.289955	+	0.210665i
$872$	5.49517	+	16.9124i	0.186090	+	0.572726i
$873$	5.27484	−	16.2343i	0.178526	−	0.549448i
$874$	−5.32788	−	3.87093i	−0.180218	−	0.130936i
$875$	−18.2846	−	13.2846i	−0.618134	−	0.449100i
$876$	11.7940	−	36.2983i	0.398484	−	1.22641i
$877$	2.34376	+	7.21336i	0.0791433	+	0.243578i	0.982798	−	0.184684i	$-0.0591261\pi$
$877$	2.34376	+	7.21336i	0.0791433	+	0.243578i	−0.903655	+	0.428262i	$0.859126\pi$
$878$	42.0153	−	30.5259i	1.41795	−	1.03020i
$879$	−4.99220			−0.168383
$880$	49.3815	+	49.9542i	1.66465	+	1.68395i
$881$	−39.2273			−1.32160			−0.660801	−	0.750561i	$-0.729783\pi$
$881$	−39.2273			−1.32160			−0.660801	+	0.750561i	$0.729783\pi$
$882$	−5.50678	+	4.00091i	−0.185423	+	0.134718i
$883$	−15.3110	−	47.1223i	−0.515255	−	1.58579i	−0.782818	−	0.622251i	$-0.786218\pi$
$883$	−15.3110	−	47.1223i	−0.515255	−	1.58579i	0.267562	−	0.963541i	$-0.413782\pi$
$884$	−7.74152	+	23.8259i	−0.260375	+	0.801353i
$885$	−27.2298	−	19.7836i	−0.915321	−	0.665019i
$886$	−8.01004	−	5.81963i	−0.269102	−	0.195514i
$887$	−8.04427	+	24.7577i	−0.270100	+	0.831282i	0.720374	+	0.693585i	$0.243970\pi$
$887$	−8.04427	+	24.7577i	−0.270100	+	0.831282i	−0.990474	+	0.137697i	$0.956030\pi$
$888$	−7.97802	−	24.5538i	−0.267725	−	0.823972i
$889$	−18.6235	+	13.5307i	−0.624611	+	0.453807i
$890$	−105.334			−3.53079
$891$	−0.499941	−	3.27873i	−0.0167486	−	0.109842i
$892$	34.9634			1.17066
$893$	20.6037	−	14.9695i	0.689476	−	0.500934i
$894$	18.0304	+	55.4918i	0.603026	+	1.85592i
$895$	12.1334	−	37.3427i	0.405574	−	1.24823i
$896$	4.25640	+	3.09246i	0.142196	+	0.103312i
$897$	0.722930	+	0.525239i	0.0241379	+	0.0175372i
$898$	−17.1113	+	52.6633i	−0.571013	+	1.75740i
$899$	−5.13338	−	15.7989i	−0.171208	−	0.526923i
$900$	−1.23143	+	0.894689i	−0.0410478	+	0.0298230i
$901$	58.8996			1.96223
$902$	20.9912	+	3.44885i	0.698931	+	0.114834i
$903$	−14.2957			−0.475729
$904$	74.3739	−	54.0358i	2.47364	−	1.79720i
$905$	7.50886	+	23.1099i	0.249603	+	0.768199i
$906$	−1.46339	+	4.50386i	−0.0486180	+	0.149631i
$907$	6.78533	+	4.92983i	0.225303	+	0.163692i	0.694711	−	0.719289i	$-0.255532\pi$
$907$	6.78533	+	4.92983i	0.225303	+	0.163692i	−0.469407	+	0.882982i	$0.655532\pi$
$908$	78.0726	+	56.7231i	2.59093	+	1.88242i
$909$	3.54580	−	10.9128i	0.117607	−	0.361956i
$910$	3.88126	+	11.9453i	0.128663	+	0.395983i
$911$	20.7278	−	15.0597i	0.686744	−	0.498949i	−0.188844	−	0.982007i	$-0.560474\pi$
$911$	20.7278	−	15.0597i	0.686744	−	0.498949i	0.875588	+	0.483058i	$0.160474\pi$
$912$	26.0174			0.861521
$913$	−17.3856	−	2.85644i	−0.575378	−	0.0945344i
$914$	18.5343			0.613060
$915$	22.4251	−	16.2928i	0.741351	−	0.538623i
$916$	41.1792	+	126.737i	1.36060	+	4.18749i
$917$	−12.6478	+	38.9259i	−0.417667	+	1.28545i
$918$	11.0615	+	8.03665i	0.365084	+	0.265249i
$919$	−7.52622	−	5.46812i	−0.248267	−	0.180376i	0.456691	−	0.889625i	$-0.349034\pi$
$919$	−7.52622	−	5.46812i	−0.248267	−	0.180376i	−0.704958	+	0.709249i	$0.749034\pi$
$920$	−4.58214	+	14.1024i	−0.151069	+	0.464941i
$921$	2.28017	+	7.01765i	0.0751343	+	0.231240i
$922$	−9.40131	+	6.83045i	−0.309616	+	0.224949i
$923$	7.03888			0.231688
$924$	−4.98846	−	32.7155i	−0.164108	−	1.07626i
$925$	−1.14603			−0.0376812
$926$	−6.75555	+	4.90819i	−0.222001	+	0.161293i
$927$	−3.18492	−	9.80217i	−0.104606	−	0.321946i
$928$	−10.3344	+	31.8061i	−0.339244	+	1.04409i
$929$	11.9571	+	8.68736i	0.392301	+	0.285023i	0.766398	−	0.642366i	$-0.222047\pi$
$929$	11.9571	+	8.68736i	0.392301	+	0.285023i	−0.374097	+	0.927390i	$0.622047\pi$
$930$	22.8936	+	16.6332i	0.750712	+	0.545424i
$931$	2.29113	−	7.05137i	0.0750887	−	0.231099i
$932$	−19.3808	−	59.6479i	−0.634839	−	1.95383i
$933$	−11.8548	+	8.61301i	−0.388108	+	0.281977i
$934$	15.2737			0.499771
$935$	−28.2673	−	28.5951i	−0.924438	−	0.935159i
$936$	−7.19477			−0.235168
$937$	−20.2901	+	14.7416i	−0.662849	+	0.481588i	−0.867624	−	0.497221i	$-0.834354\pi$
$937$	−20.2901	+	14.7416i	−0.662849	+	0.481588i	0.204775	+	0.978809i	$0.434354\pi$
$938$	17.8002	+	54.7833i	0.581197	+	1.78874i
$939$	−0.896914	+	2.76042i	−0.0292697	+	0.0900828i
$940$	−79.9348	−	58.0760i	−2.60719	−	1.89423i
$941$	−30.8971	−	22.4481i	−1.00722	−	0.731787i	−0.0435942	−	0.999049i	$-0.513881\pi$
$941$	−30.8971	−	22.4481i	−1.00722	−	0.731787i	−0.963624	+	0.267263i	$0.913881\pi$
$942$	−16.6843	+	51.3491i	−0.543605	+	1.67304i
$943$	0.680895	+	2.09558i	0.0221730	+	0.0682415i
$944$	108.414	−	78.7674i	3.52857	−	2.56366i
$945$	4.82864			0.157076
$946$	−27.0456	+	52.3320i	−0.879330	+	1.70146i
$947$	−3.33261			−0.108295			−0.0541477	−	0.998533i	$-0.517244\pi$
$947$	−3.33261			−0.108295			−0.0541477	+	0.998533i	$0.517244\pi$
$948$	6.15380	−	4.47100i	0.199866	−	0.145211i
$949$	−2.47462	−	7.61611i	−0.0803297	−	0.247229i
$950$	0.727346	−	2.23854i	0.0235982	−	0.0726279i
$951$	−10.3004	−	7.48366i	−0.334013	−	0.242674i
$952$	64.0560	+	46.5394i	2.07607	+	1.50835i
$953$	6.69614	−	20.6086i	0.216909	−	0.667579i	−0.782103	−	0.623149i	$-0.785853\pi$
$953$	6.69614	−	20.6086i	0.216909	−	0.667579i	0.999013	−	0.0444295i	$-0.0141470\pi$
$954$	9.00680	+	27.7201i	0.291606	+	0.897470i
$955$	23.5606	−	17.1178i	0.762403	−	0.553918i
$956$	73.0221			2.36170
$957$	−10.4377	+	5.24268i	−0.337402	+	0.169472i
$958$	−20.9124			−0.675651
$959$	18.6410	−	13.5435i	0.601949	−	0.437341i
$960$	−4.51525	−	13.8965i	−0.145729	−	0.448508i
$961$	−2.70402	+	8.32210i	−0.0872263	+	0.268455i
$962$	−7.55126	−	5.48631i	−0.243462	−	0.176886i
$963$	−5.22697	−	3.79762i	−0.168437	−	0.122377i
$964$	−34.4904	+	106.151i	−1.11086	+	3.41888i
$965$	12.1897	+	37.5161i	0.392401	+	1.20769i
$966$	3.93692	−	2.86034i	0.126668	−	0.0920299i
$967$	22.1932			0.713686			0.356843	−	0.934164i	$-0.383853\pi$
$967$	22.1932			0.713686			0.356843	+	0.934164i	$0.383853\pi$
$968$	−74.9820	−	25.3226i	−2.41001	−	0.813899i
$969$	−14.8930			−0.478433
$970$	82.8478	−	60.1924i	2.66008	−	1.93266i
$971$	−3.49395	−	10.7533i	−0.112126	−	0.345089i	0.879211	−	0.476433i	$-0.158071\pi$
$971$	−3.49395	−	10.7533i	−0.112126	−	0.345089i	−0.991337	+	0.131345i	$0.958071\pi$
$972$	−1.47277	+	4.53273i	−0.0472392	+	0.145387i
$973$	6.43045	+	4.67200i	0.206151	+	0.149777i
$974$	7.11850	+	5.17189i	0.228091	+	0.165718i
$975$	−0.0986921	+	0.303743i	−0.00316068	+	0.00972756i
$976$	34.1035	+	104.960i	1.09163	+	3.35969i
$977$	−45.9605	+	33.3922i	−1.47041	+	1.06831i	−0.489910	+	0.871773i	$0.662970\pi$
$977$	−45.9605	+	33.3922i	−1.47041	+	1.06831i	−0.980496	+	0.196540i	$0.937030\pi$
$978$	−36.1504			−1.15596
$979$	52.0374	−	26.1376i	1.66312	−	0.835361i
$980$	−28.7646			−0.918850
$981$	1.99958	−	1.45278i	0.0638417	−	0.0463837i
$982$	−14.0671	−	43.2942i	−0.448900	−	1.38157i
$983$	17.8728	−	55.0070i	0.570055	−	1.75445i	−0.0823759	−	0.996601i	$-0.526251\pi$
$983$	17.8728	−	55.0070i	0.570055	−	1.75445i	0.652431	−	0.757848i	$-0.273749\pi$
$984$	−14.3527	−	10.4279i	−0.457548	−	0.332428i
$985$	16.2028	+	11.7721i	0.516265	+	0.375089i
$986$	14.8798	−	45.7954i	0.473870	−	1.45842i
$987$	5.81529	+	17.8976i	0.185103	+	0.569688i
$988$	10.9246	−	7.93716i	0.347557	−	0.252515i
$989$	−6.10166			−0.194021
$990$	9.13521	−	17.6762i	0.290336	−	0.561786i
$991$	32.3196			1.02667			0.513334	−	0.858189i	$-0.328410\pi$
$991$	32.3196			1.02667			0.513334	+	0.858189i	$0.328410\pi$
$992$	−36.2379	+	26.3284i	−1.15056	+	0.835927i
$993$	5.53672	+	17.0403i	0.175702	+	0.540756i
$994$	11.8453	−	36.4561i	0.375710	−	1.15632i
$995$	15.7386	+	11.4347i	0.498946	+	0.362505i
$996$	20.4827	+	14.8816i	0.649019	+	0.471540i
$997$	1.87253	−	5.76307i	0.0593038	−	0.182518i	−0.917016	−	0.398850i	$-0.869409\pi$
$997$	1.87253	−	5.76307i	0.0593038	−	0.182518i	0.976320	+	0.216332i	$0.0694093\pi$
$998$	10.8055	+	33.2560i	0.342043	+	1.05270i
$999$	−2.90304	+	2.10918i	−0.0918482	+	0.0667316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.157.7	✓	28
11.2	odd	10		4719.2.a.bo.1.14		14
11.4	even	5	inner	429.2.n.c.235.7	yes	28
11.9	even	5		4719.2.a.bp.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.157.7	✓	28	1.1	even	1	trivial
429.2.n.c.235.7	yes	28	11.4	even	5	inner
4719.2.a.bo.1.14		14	11.2	odd	10
4719.2.a.bp.1.1		14	11.9	even	5

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10438 - 1.52892i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.47277 - 4.53273i) q^{4} +(-1.86590 - 1.35565i) q^{5} +(-2.10438 - 1.52892i) q^{6} +(-0.646959 + 1.99114i) q^{7} +(-2.22331 - 6.84263i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.10438 - 1.52892i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.47277 - 4.53273i) q^{4} +(-1.86590 - 1.35565i) q^{5} +(-2.10438 - 1.52892i) q^{6} +(-0.646959 + 1.99114i) q^{7} +(-2.22331 - 6.84263i) q^{8} +(-0.809017 + 0.587785i) q^{9} -5.99924 q^{10} +(2.96377 - 1.48865i) q^{11} -4.76599 q^{12} +(-0.809017 + 0.587785i) q^{13} +(1.68284 + 5.17925i) q^{14} +(-0.712710 + 2.19349i) q^{15} +(-7.42897 - 5.39746i) q^{16} +(4.25254 + 3.08965i) q^{17} +(-0.803800 + 2.47384i) q^{18} +(-0.875538 - 2.69463i) q^{19} +(-8.89286 + 6.46104i) q^{20} +2.09360 q^{21} +(3.96085 - 7.66405i) q^{22} +0.893590 q^{23} +(-5.82069 + 4.22898i) q^{24} +(0.0986921 + 0.303743i) q^{25} +(-0.803800 + 2.47384i) q^{26} +(0.809017 + 0.587785i) q^{27} +(8.07246 + 5.86498i) q^{28} +(1.08828 - 3.34939i) q^{29} +(1.85387 + 5.70561i) q^{30} +(3.81609 - 2.77255i) q^{31} -9.49608 q^{32} +(-2.33165 - 2.35869i) q^{33} +13.6728 q^{34} +(3.90645 - 2.83820i) q^{35} +(1.47277 + 4.53273i) q^{36} +(-1.10886 + 3.41273i) q^{37} +(-5.96233 - 4.33189i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-5.12778 + 15.7817i) q^{40} +(0.761977 + 2.34512i) q^{41} +(4.40573 - 3.20095i) q^{42} -6.82825 q^{43} +(-2.38271 - 15.6264i) q^{44} +2.30638 q^{45} +(1.88045 - 1.36623i) q^{46} +(2.77765 + 8.54872i) q^{47} +(-2.83761 + 8.73327i) q^{48} +(2.11705 + 1.53813i) q^{49} +(0.672084 + 0.488298i) q^{50} +(1.62432 - 4.99916i) q^{51} +(1.47277 + 4.53273i) q^{52} +(9.06525 - 6.58629i) q^{53} +2.60115 q^{54} +(-7.54819 - 1.24016i) q^{55} +15.0630 q^{56} +(-2.29219 + 1.66537i) q^{57} +(-2.83079 - 8.71227i) q^{58} +(-4.50961 + 13.8792i) q^{59} +(8.89286 + 6.46104i) q^{60} +(-9.72309 - 7.06423i) q^{61} +(3.79149 - 11.6690i) q^{62} +(-0.646959 - 1.99114i) q^{63} +(-5.12539 + 3.72382i) q^{64} +2.30638 q^{65} +(-8.51291 - 1.39867i) q^{66} +10.5775 q^{67} +(20.2676 - 14.7252i) q^{68} +(-0.276135 - 0.849855i) q^{69} +(3.88126 - 11.9453i) q^{70} +(-5.69458 - 4.13735i) q^{71} +(5.82069 + 4.22898i) q^{72} +(-2.47462 + 7.61611i) q^{73} +(2.88432 + 8.87703i) q^{74} +(0.258379 - 0.187724i) q^{75} -13.5035 q^{76} +(1.04668 + 6.86436i) q^{77} +2.60115 q^{78} +(-1.29119 + 0.938104i) q^{79} +(6.54460 + 20.1422i) q^{80} +(0.309017 - 0.951057i) q^{81} +(5.18899 + 3.77002i) q^{82} +(-4.29768 - 3.12245i) q^{83} +(3.08340 - 9.48974i) q^{84} +(-3.74630 - 11.5299i) q^{85} +(-14.3692 + 10.4398i) q^{86} -3.52176 q^{87} +(-16.7757 - 16.9702i) q^{88} +17.5579 q^{89} +(4.85349 - 3.52626i) q^{90} +(-0.646959 - 1.99114i) q^{91} +(1.31606 - 4.05040i) q^{92} +(-3.81609 - 2.77255i) q^{93} +(18.9155 + 13.7429i) q^{94} +(-2.01932 + 6.21483i) q^{95} +(2.93445 + 9.03131i) q^{96} +(-13.8097 + 10.0333i) q^{97} +6.80675 q^{98} +(-1.52273 + 2.94640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

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