LMFDB - Embedded newform 185.2.p.a.88.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.p (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			88.7
Character	$\chi$	$=$	185.88
Dual form			185.2.p.a.82.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.412077 + 0.713738i) q^{2} +(1.77336 + 0.475172i) q^{3} +(0.660386 + 1.14382i) q^{4} +(1.99238 + 1.01510i) q^{5} +(-1.06991 + 1.06991i) q^{6} +(-1.19739 - 0.320840i) q^{7} -2.73682 q^{8} +(0.320958 + 0.185305i) q^{9} +(-1.54553 + 1.00374i) q^{10} -4.12374i q^{11} +(0.627593 + 2.34221i) q^{12} +(-2.46040 - 4.26154i) q^{13} +(0.722412 - 0.722412i) q^{14} +(3.05086 + 2.74687i) q^{15} +(-0.192990 + 0.334268i) q^{16} +(1.73008 + 0.998860i) q^{17} +(-0.264518 + 0.152720i) q^{18} +(-0.608896 + 2.27243i) q^{19} +(0.154643 + 2.94928i) q^{20} +(-1.97096 - 1.13793i) q^{21} +(2.94327 + 1.69930i) q^{22} -0.794336 q^{23} +(-4.85339 - 1.30046i) q^{24} +(2.93914 + 4.04493i) q^{25} +4.05550 q^{26} +(-3.41346 - 3.41346i) q^{27} +(-0.423756 - 1.58148i) q^{28} +(1.67939 - 1.67939i) q^{29} +(-3.21773 + 1.04560i) q^{30} +(6.42495 + 6.42495i) q^{31} +(-2.89588 - 5.01581i) q^{32} +(1.95948 - 7.31290i) q^{33} +(-1.42585 + 0.823214i) q^{34} +(-2.05997 - 1.85471i) q^{35} +0.489491i q^{36} +(-0.962921 + 6.00606i) q^{37} +(-1.37101 - 1.37101i) q^{38} +(-2.33823 - 8.72639i) q^{39} +(-5.45279 - 2.77815i) q^{40} +(9.74356 - 5.62545i) q^{41} +(1.62437 - 0.937830i) q^{42} -11.4197 q^{43} +(4.71682 - 2.72326i) q^{44} +(0.451365 + 0.695002i) q^{45} +(0.327327 - 0.566948i) q^{46} +(-2.19390 + 2.19390i) q^{47} +(-0.501076 + 0.501076i) q^{48} +(-4.73137 - 2.73166i) q^{49} +(-4.09817 + 0.430952i) q^{50} +(2.59343 + 2.59343i) q^{51} +(3.24963 - 5.62853i) q^{52} +(3.50202 - 0.938365i) q^{53} +(3.84292 - 1.02971i) q^{54} +(4.18601 - 8.21605i) q^{55} +(3.27705 + 0.878082i) q^{56} +(-2.15959 + 3.74052i) q^{57} +(0.506608 + 1.89069i) q^{58} +(1.41608 - 0.379437i) q^{59} +(-1.12718 + 5.30364i) q^{60} +(-1.72489 + 6.43736i) q^{61} +(-7.23330 + 1.93816i) q^{62} +(-0.324858 - 0.324858i) q^{63} +4.00134 q^{64} +(-0.576154 - 10.9882i) q^{65} +(4.41203 + 4.41203i) q^{66} +(1.52915 - 5.70687i) q^{67} +2.63853i q^{68} +(-1.40865 - 0.377446i) q^{69} +(2.17264 - 0.705996i) q^{70} +(-3.30595 - 5.72607i) q^{71} +(-0.878404 - 0.507147i) q^{72} +(-5.14518 + 5.14518i) q^{73} +(-3.88996 - 3.16223i) q^{74} +(3.29013 + 8.56973i) q^{75} +(-3.00136 + 0.804213i) q^{76} +(-1.32306 + 4.93773i) q^{77} +(7.19188 + 1.92706i) q^{78} +(-2.30362 + 8.59723i) q^{79} +(-0.723825 + 0.470084i) q^{80} +(-4.98724 - 8.63815i) q^{81} +9.27246i q^{82} +(-1.15830 + 0.310366i) q^{83} -3.00590i q^{84} +(2.43302 + 3.74631i) q^{85} +(4.70581 - 8.15069i) q^{86} +(3.77618 - 2.18018i) q^{87} +11.2860i q^{88} +(1.87621 + 7.00209i) q^{89} +(-0.682046 + 0.0357624i) q^{90} +(1.57879 + 5.89213i) q^{91} +(-0.524568 - 0.908579i) q^{92} +(8.34083 + 14.4467i) q^{93} +(-0.661816 - 2.46993i) q^{94} +(-3.51990 + 3.90945i) q^{95} +(-2.75208 - 10.2709i) q^{96} +11.7662i q^{97} +(3.89938 - 2.25131i) q^{98} +(0.764149 - 1.32355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.412077	+	0.713738i	−0.291382	+	0.504689i	−0.974137	−	0.225959i	$-0.927448\pi$
$2$	−0.412077	+	0.713738i	−0.291382	+	0.504689i	0.682755	+	0.730648i	$0.260782\pi$
$3$	1.77336	+	0.475172i	1.02385	+	0.274340i	0.731407	−	0.681942i	$-0.238864\pi$
$3$	1.77336	+	0.475172i	1.02385	+	0.274340i	0.292446	+	0.956282i	$0.405531\pi$
$4$	0.660386	+	1.14382i	0.330193	+	0.571911i
$5$	1.99238	+	1.01510i	0.891018	+	0.453967i
$5$	1.99238	+	1.01510i	0.891018	+	0.453967i
$6$	−1.06991	+	1.06991i	−0.436789	+	0.436789i
$7$	−1.19739	−	0.320840i	−0.452571	−	0.121266i	0.0253311	−	0.999679i	$-0.491936\pi$
$7$	−1.19739	−	0.320840i	−0.452571	−	0.121266i	−0.477902	+	0.878413i	$0.658603\pi$
$8$	−2.73682			−0.967614
$9$	0.320958	+	0.185305i	0.106986	+	0.0617683i
$10$	−1.54553	+	1.00374i	−0.488739	+	0.317409i
$11$		−	4.12374i		−	1.24335i	−0.783273	−	0.621677i	$-0.786452\pi$
$11$		−	4.12374i		−	1.24335i	0.783273	−	0.621677i	$-0.213548\pi$
$12$	0.627593	+	2.34221i	0.181171	+	0.676138i
$13$	−2.46040	−	4.26154i	−0.682393	−	1.18194i	−0.974248	−	0.225477i	$-0.927606\pi$
$13$	−2.46040	−	4.26154i	−0.682393	−	1.18194i	0.291855	−	0.956463i	$-0.405727\pi$
$14$	0.722412	−	0.722412i	0.193073	−	0.193073i
$15$	3.05086	+	2.74687i	0.787730	+	0.709238i
$16$	−0.192990	+	0.334268i	−0.0482475	+	0.0835671i
$17$	1.73008	+	0.998860i	0.419605	+	0.242259i	0.694908	−	0.719098i	$-0.255445\pi$
$17$	1.73008	+	0.998860i	0.419605	+	0.242259i	−0.275303	+	0.961357i	$0.588778\pi$
$18$	−0.264518	+	0.152720i	−0.0623475	+	0.0359964i
$19$	−0.608896	+	2.27243i	−0.139690	+	0.521331i	0.860244	+	0.509882i	$0.170311\pi$
$19$	−0.608896	+	2.27243i	−0.139690	+	0.521331i	−0.999934	+	0.0114491i	$0.996356\pi$
$20$	0.154643	+	2.94928i	0.0345792	+	0.659480i
$21$	−1.97096	−	1.13793i	−0.430098	−	0.248317i
$22$	2.94327	+	1.69930i	0.627507	+	0.362291i
$23$	−0.794336			−0.165631			−0.0828153	−	0.996565i	$-0.526391\pi$
$23$	−0.794336			−0.165631			−0.0828153	+	0.996565i	$0.526391\pi$
$24$	−4.85339	−	1.30046i	−0.990694	−	0.265456i
$25$	2.93914	+	4.04493i	0.587828	+	0.808986i
$26$	4.05550			0.795349
$27$	−3.41346	−	3.41346i	−0.656920	−	0.656920i
$28$	−0.423756	−	1.58148i	−0.0800824	−	0.298871i
$29$	1.67939	−	1.67939i	0.311856	−	0.311856i	−0.533772	−	0.845628i	$-0.679226\pi$
$29$	1.67939	−	1.67939i	0.311856	−	0.311856i	0.845628	+	0.533772i	$0.179226\pi$
$30$	−3.21773	+	1.04560i	−0.587475	+	0.190899i
$31$	6.42495	+	6.42495i	1.15396	+	1.15396i	0.985752	+	0.168203i	$0.0537965\pi$
$31$	6.42495	+	6.42495i	1.15396	+	1.15396i	0.168203	+	0.985752i	$0.446203\pi$
$32$	−2.89588	−	5.01581i	−0.511924	−	0.886678i
$33$	1.95948	−	7.31290i	0.341102	−	1.27301i
$34$	−1.42585	+	0.823214i	−0.244531	+	0.141180i
$35$	−2.05997	−	1.85471i	−0.348198	−	0.313503i
$36$			0.489491i			0.0815818i
$37$	−0.962921	+	6.00606i	−0.158303	+	0.987391i
$37$	−0.962921	+	6.00606i	−0.158303	+	0.987391i
$38$	−1.37101	−	1.37101i	−0.222407	−	0.222407i
$39$	−2.33823	−	8.72639i	−0.374416	−	1.39734i
$40$	−5.45279	−	2.77815i	−0.862162	−	0.439265i
$41$	9.74356	−	5.62545i	1.52169	−	0.878547i	0.522016	−	0.852936i	$-0.325180\pi$
$41$	9.74356	−	5.62545i	1.52169	−	0.878547i	0.999672	−	0.0256114i	$-0.00815325\pi$
$42$	1.62437	−	0.937830i	0.250646	−	0.144710i
$43$	−11.4197			−1.74149			−0.870747	−	0.491732i	$-0.836364\pi$
$43$	−11.4197			−1.74149			−0.870747	+	0.491732i	$0.836364\pi$
$44$	4.71682	−	2.72326i	0.711088	−	0.410547i
$45$	0.451365	+	0.695002i	0.0672856	+	0.103605i
$46$	0.327327	−	0.566948i	0.0482618	−	0.0835919i
$47$	−2.19390	+	2.19390i	−0.320014	+	0.320014i	−0.848772	−	0.528758i	$-0.822658\pi$
$47$	−2.19390	+	2.19390i	−0.320014	+	0.320014i	0.528758	+	0.848772i	$0.322658\pi$
$48$	−0.501076	+	0.501076i	−0.0723241	+	0.0723241i
$49$	−4.73137	−	2.73166i	−0.675910	−	0.390237i
$50$	−4.09817	+	0.430952i	−0.579569	+	0.0609458i
$51$	2.59343	+	2.59343i	0.363152	+	0.363152i
$52$	3.24963	−	5.62853i	0.450643	−	0.780536i
$53$	3.50202	−	0.938365i	0.481040	−	0.128894i	−0.0101468	−	0.999949i	$-0.503230\pi$
$53$	3.50202	−	0.938365i	0.481040	−	0.128894i	0.491187	+	0.871054i	$0.336563\pi$
$54$	3.84292	−	1.02971i	0.522955	−	0.140125i
$55$	4.18601	−	8.21605i	0.564442	−	1.10785i
$56$	3.27705	+	0.878082i	0.437914	+	0.117339i
$57$	−2.15959	+	3.74052i	−0.286045	+	0.495444i
$58$	0.506608	+	1.89069i	0.0665209	+	0.248259i
$59$	1.41608	−	0.379437i	0.184358	−	0.0493985i	−0.165459	−	0.986217i	$-0.552911\pi$
$59$	1.41608	−	0.379437i	0.184358	−	0.0493985i	0.349817	+	0.936818i	$0.386244\pi$
$60$	−1.12718	+	5.30364i	−0.145518	+	0.684696i
$61$	−1.72489	+	6.43736i	−0.220849	+	0.824220i	0.763176	+	0.646190i	$0.223639\pi$
$61$	−1.72489	+	6.43736i	−0.220849	+	0.824220i	−0.984025	+	0.178029i	$0.943028\pi$
$62$	−7.23330	+	1.93816i	−0.918631	+	0.246146i
$63$	−0.324858	−	0.324858i	−0.0409283	−	0.0409283i
$64$	4.00134			0.500167
$65$	−0.576154	−	10.9882i	−0.0714631	−	1.36291i
$66$	4.41203	+	4.41203i	0.543083	+	0.543083i
$67$	1.52915	−	5.70687i	0.186816	−	0.697205i	−0.807419	−	0.589978i	$-0.799136\pi$
$67$	1.52915	−	5.70687i	0.186816	−	0.697205i	0.994235	−	0.107227i	$-0.0341971\pi$
$68$			2.63853i			0.319969i
$69$	−1.40865	−	0.377446i	−0.169581	−	0.0454392i
$70$	2.17264	−	0.705996i	0.259680	−	0.0843827i
$71$	−3.30595	−	5.72607i	−0.392344	−	0.679559i	0.600414	−	0.799689i	$-0.295002\pi$
$71$	−3.30595	−	5.72607i	−0.392344	−	0.679559i	−0.992758	+	0.120130i	$0.961669\pi$
$72$	−0.878404	−	0.507147i	−0.103521	−	0.0597679i
$73$	−5.14518	+	5.14518i	−0.602197	+	0.602197i	−0.940895	−	0.338698i	$-0.890014\pi$
$73$	−5.14518	+	5.14518i	−0.602197	+	0.602197i	0.338698	+	0.940895i	$0.390014\pi$
$74$	−3.88996	−	3.16223i	−0.452198	−	0.367602i
$75$	3.29013	+	8.56973i	0.379911	+	0.989547i
$76$	−3.00136	+	0.804213i	−0.344280	+	0.0922495i
$77$	−1.32306	+	4.93773i	−0.150777	+	0.562706i
$78$	7.19188	+	1.92706i	0.814320	+	0.218196i
$79$	−2.30362	+	8.59723i	−0.259178	+	0.967264i	0.706541	+	0.707672i	$0.250255\pi$
$79$	−2.30362	+	8.59723i	−0.259178	+	0.967264i	−0.965718	+	0.259592i	$0.916412\pi$
$80$	−0.723825	+	0.470084i	−0.0809261	+	0.0525570i
$81$	−4.98724	−	8.63815i	−0.554138	−	0.959795i
$82$			9.27246i			1.02397i
$83$	−1.15830	+	0.310366i	−0.127140	+	0.0340671i	−0.321828	−	0.946798i	$-0.604297\pi$
$83$	−1.15830	+	0.310366i	−0.127140	+	0.0340671i	0.194688	+	0.980865i	$0.437631\pi$
$84$		−	3.00590i		−	0.327970i
$85$	2.43302	+	3.74631i	0.263898	+	0.406344i
$86$	4.70581	−	8.15069i	0.507440	−	0.878912i
$87$	3.77618	−	2.18018i	0.404849	−	0.233740i
$88$			11.2860i			1.20309i
$89$	1.87621	+	7.00209i	0.198877	+	0.742220i	0.991229	+	0.132156i	$0.0421899\pi$
$89$	1.87621	+	7.00209i	0.198877	+	0.742220i	−0.792352	+	0.610065i	$0.791143\pi$
$90$	−0.682046	+	0.0357624i	−0.0718940	+	0.00376969i
$91$	1.57879	+	5.89213i	0.165502	+	0.617663i
$92$	−0.524568	−	0.908579i	−0.0546900	−	0.0947259i
$93$	8.34083	+	14.4467i	0.864904	+	1.49806i
$94$	−0.661816	−	2.46993i	−0.0682611	−	0.254754i
$95$	−3.51990	+	3.90945i	−0.361134	+	0.401101i
$96$	−2.75208	−	10.2709i	−0.280883	−	1.04827i
$97$			11.7662i			1.19468i	0.801990	+	0.597338i	$0.203775\pi$
$97$			11.7662i			1.19468i	−0.801990	+	0.597338i	$0.796225\pi$
$98$	3.89938	−	2.25131i	0.393896	−	0.227416i
$99$	0.764149	−	1.32355i	0.0767999	−	0.133021i
$100$	−2.68571	+	6.03306i	−0.268571	+	0.603306i
$101$			3.14602i			0.313041i	0.987675	+	0.156521i	$0.0500277\pi$
$101$			3.14602i			0.313041i	−0.987675	+	0.156521i	$0.949972\pi$
$102$	−2.91972	+	0.782335i	−0.289095	+	0.0774628i
$103$		−	7.98036i		−	0.786328i	−0.919468	−	0.393164i	$-0.871380\pi$
$103$		−	7.98036i		−	0.786328i	0.919468	−	0.393164i	$-0.128620\pi$
$104$	6.73369	+	11.6631i	0.660293	+	1.14366i
$105$	−2.77177	−	4.26791i	−0.270497	−	0.416505i
$106$	−0.773356	+	2.88620i	−0.0751150	+	0.280333i
$107$	−2.08941	−	0.559856i	−0.201991	−	0.0541233i	0.156405	−	0.987693i	$-0.450010\pi$
$107$	−2.08941	−	0.559856i	−0.201991	−	0.0541233i	−0.358396	+	0.933570i	$0.616676\pi$
$108$	1.65019	−	6.15858i	0.158789	−	0.592610i
$109$	10.4305	−	2.79484i	0.999059	−	0.267697i	0.278008	−	0.960579i	$-0.410326\pi$
$109$	10.4305	−	2.79484i	0.999059	−	0.267697i	0.721051	+	0.692882i	$0.243659\pi$
$110$	4.13914	+	6.37336i	0.394652	+	0.607676i
$111$	−4.56152	+	10.1934i	−0.432960	+	0.967513i
$112$	0.338331	−	0.338331i	0.0319692	−	0.0319692i
$113$	−1.86976	−	1.07951i	−0.175892	−	0.101552i	0.409469	−	0.912324i	$-0.365714\pi$
$113$	−1.86976	−	1.07951i	−0.175892	−	0.101552i	−0.585361	+	0.810773i	$0.699047\pi$
$114$	−1.77983	−	3.08276i	−0.166697	−	0.288727i
$115$	−1.58262	−	0.806332i	−0.147580	−	0.0751908i
$116$	3.02998	+	0.811879i	0.281326	+	0.0753811i
$117$		−	1.82370i		−	0.168601i
$118$	−0.312715	+	1.16707i	−0.0287877	+	0.107437i
$119$	−1.75110	−	1.75110i	−0.160523	−	0.160523i
$120$	−8.34968	−	7.51769i	−0.762218	−	0.686268i
$121$	−6.00524			−0.545931
$122$	−3.88380	−	3.88380i	−0.351623	−	0.351623i
$123$	19.9519	−	5.34610i	1.79901	−	0.482042i
$124$	−3.10605	+	11.5919i	−0.278932	+	1.04099i
$125$	1.74986	+	11.0426i	0.156512	+	0.987676i
$126$	0.365730	−	0.0979971i	0.0325818	−	0.00873027i
$127$	−0.979445	−	3.65534i	−0.0869117	−	0.324359i	0.908758	−	0.417324i	$-0.137032\pi$
$127$	−0.979445	−	3.65534i	−0.0869117	−	0.324359i	−0.995669	+	0.0929655i	$0.970365\pi$
$128$	4.14290	−	7.17571i	0.366184	−	0.634249i
$129$	−20.2514	−	5.42633i	−1.78303	−	0.477762i
$130$	8.08009	+	4.11674i	0.708671	+	0.361062i
$131$	−9.54260	+	2.55693i	−0.833741	+	0.223400i	−0.650345	−	0.759639i	$-0.725376\pi$
$131$	−9.54260	+	2.55693i	−0.833741	+	0.223400i	−0.183396	+	0.983039i	$0.558709\pi$
$132$	9.65866	−	2.58803i	0.840679	−	0.225259i
$133$	1.45817	−	2.52563i	0.126440	−	0.219000i
$134$	3.44308	+	3.44308i	0.297437	+	0.297437i
$135$	−3.33589	−	10.2659i	−0.287108	−	0.883548i
$136$	−4.73491	−	2.73370i	−0.406016	−	0.234413i
$137$	14.9643	−	14.9643i	1.27849	−	1.27849i	0.336976	−	0.941513i	$-0.390596\pi$
$137$	14.9643	−	14.9643i	1.27849	−	1.27849i	0.941513	−	0.336976i	$-0.109404\pi$
$138$	0.849868	−	0.849868i	0.0723456	−	0.0723456i
$139$	11.0779	−	19.1876i	0.939619	−	1.62747i	0.173436	−	0.984845i	$-0.444513\pi$
$139$	11.0779	−	19.1876i	0.939619	−	1.62747i	0.766183	−	0.642623i	$-0.222154\pi$
$140$	0.761079	−	3.58106i	0.0643230	−	0.302655i
$141$	−4.93307	+	2.84811i	−0.415440	+	0.239854i
$142$	5.44922			0.457288
$143$	−17.5735	+	10.1461i	−1.46957	+	0.848457i
$144$	−0.123883	+	0.0715239i	−0.0103236	+	0.00596033i
$145$	5.05074	−	1.64123i	0.419441	−	0.136297i
$146$	−1.55210	−	5.79251i	−0.128453	−	0.479392i
$147$	−7.09244	−	7.09244i	−0.584975	−	0.584975i
$148$	−7.50576	+	2.86491i	−0.616970	+	0.235494i
$149$		−	15.3831i		−	1.26024i	−0.776499	−	0.630118i	$-0.783006\pi$
$149$		−	15.3831i		−	1.26024i	0.776499	−	0.630118i	$-0.216994\pi$
$150$	−7.47233	−	1.18310i	−0.610113	−	0.0965996i
$151$	−14.2305	+	8.21599i	−1.15806	+	0.668608i	−0.950839	−	0.309686i	$-0.899776\pi$
$151$	−14.2305	+	8.21599i	−1.15806	+	0.668608i	−0.207224	+	0.978294i	$0.566443\pi$
$152$	1.66644	−	6.21925i	0.135166	−	0.504447i
$153$	0.370187	+	0.641183i	0.0299279	+	0.0518366i
$154$	−2.97904	−	2.97904i	−0.240058	−	0.240058i
$155$	6.27895	+	19.3229i	0.504338	+	1.55205i
$156$	8.43730	−	8.43730i	0.675524	−	0.675524i
$157$	2.19684	+	8.19871i	0.175327	+	0.654328i	0.996496	+	0.0836433i	$0.0266556\pi$
$157$	2.19684	+	8.19871i	0.175327	+	0.654328i	−0.821169	+	0.570685i	$0.806678\pi$
$158$	−5.18690	−	5.18690i	−0.412647	−	0.412647i
$159$	6.65625			0.527875
$160$	−0.678129	−	12.9330i	−0.0536108	−	1.02244i
$161$	0.951131	+	0.254855i	0.0749596	+	0.0200854i
$162$	8.22050			0.645863
$163$	−0.821119	−	0.474073i	−0.0643150	−	0.0371323i	0.467498	−	0.883994i	$-0.345156\pi$
$163$	−0.821119	−	0.474073i	−0.0643150	−	0.0371323i	−0.531813	+	0.846862i	$0.678489\pi$
$164$	12.8690	+	7.42993i	1.00490	+	0.580180i
$165$	11.3274	−	12.5810i	0.881834	−	0.979428i
$166$	0.255789	−	0.954618i	0.0198531	−	0.0740928i
$167$	1.60343	−	0.925739i	0.124077	−	0.0716358i	−0.436677	−	0.899618i	$-0.643845\pi$
$167$	1.60343	−	0.925739i	0.124077	−	0.0716358i	0.560754	+	0.827983i	$0.310511\pi$
$168$	5.39416	+	3.11432i	0.416168	+	0.240275i
$169$	−5.60717	+	9.71191i	−0.431321	+	0.747070i
$170$	−3.67647	+	0.192772i	−0.281973	+	0.0147850i
$171$	−0.616522	+	0.616522i	−0.0471467	+	0.0471467i
$172$	−7.54143	−	13.0621i	−0.575029	−	0.995979i
$173$	−0.520009	−	1.94070i	−0.0395356	−	0.147549i	0.943337	−	0.331837i	$-0.107669\pi$
$173$	−0.520009	−	1.94070i	−0.0395356	−	0.147549i	−0.982872	+	0.184289i	$0.941002\pi$
$174$			3.59360i			0.272430i
$175$	−2.22152	−	5.78635i	−0.167931	−	0.437407i
$176$	1.37844	+	0.795840i	0.103903	+	0.0599887i
$177$	2.69152			0.202307
$178$	−5.77080	−	1.54628i	−0.432540	−	0.115899i
$179$	−16.5221	+	16.5221i	−1.23492	+	1.23492i	−0.272865	+	0.962052i	$0.587971\pi$
$179$	−16.5221	+	16.5221i	−1.23492	+	1.23492i	−0.962052	+	0.272865i	$0.912029\pi$
$180$	−0.496883	+	0.975251i	−0.0370355	+	0.0726909i
$181$	−0.609064	−	1.05493i	−0.0452713	−	0.0784123i	0.842502	−	0.538693i	$-0.181082\pi$
$181$	−0.609064	−	1.05493i	−0.0452713	−	0.0784123i	−0.887773	+	0.460281i	$0.847749\pi$
$182$	−4.85602	−	1.30117i	−0.359952	−	0.0964488i
$183$	−6.11770	+	10.5962i	−0.452234	+	0.783292i
$184$	2.17396			0.160266
$185$	−8.01527	+	10.9889i	−0.589294	+	0.807919i
$186$	−13.7482			−1.00807
$187$	4.11904	−	7.13438i	0.301214	−	0.521718i
$188$	−3.95826	−	1.06061i	−0.288686	−	0.0773531i
$189$	2.99207	+	5.18241i	0.217641	+	0.376965i
$190$	−1.33985	−	4.12328i	−0.0972032	−	0.299134i
$191$	−5.47122	+	5.47122i	−0.395883	+	0.395883i	−0.876778	−	0.480895i	$-0.840312\pi$
$191$	−5.47122	+	5.47122i	−0.395883	+	0.395883i	0.480895	+	0.876778i	$0.340312\pi$
$192$	7.09583	+	1.90132i	0.512097	+	0.137216i
$193$	20.4352			1.47096			0.735480	−	0.677546i	$-0.236957\pi$
$193$	20.4352			1.47096			0.735480	+	0.677546i	$0.236957\pi$
$194$	−8.39797	−	4.84857i	−0.602939	−	0.348107i
$195$	4.19953	−	19.7598i	0.300735	−	1.41503i
$196$		−	7.21579i		−	0.515414i
$197$	7.18146	+	26.8016i	0.511658	+	1.90953i	0.402232	+	0.915538i	$0.368235\pi$
$197$	7.18146	+	26.8016i	0.511658	+	1.90953i	0.109426	+	0.993995i	$0.465099\pi$
$198$	0.629776	+	1.09080i	0.0447562	+	0.0775201i
$199$	−12.8241	+	12.8241i	−0.909074	+	0.909074i	−0.996198	−	0.0871235i	$-0.972233\pi$
$199$	−12.8241	+	12.8241i	−0.909074	+	0.909074i	0.0871235	+	0.996198i	$0.472233\pi$
$200$	−8.04391	−	11.0703i	−0.568790	−	0.782786i
$201$	5.42349	−	9.39375i	0.382543	−	0.662584i
$202$	−2.24544	−	1.29640i	−0.157988	−	0.0912146i
$203$	−2.54971	+	1.47207i	−0.178954	+	0.103319i
$204$	−1.25375	+	4.67908i	−0.0877804	+	0.327601i
$205$	25.1232	−	1.31731i	1.75468	−	0.0920052i
$206$	5.69588	+	3.28852i	0.396851	+	0.229122i
$207$	−0.254948	−	0.147194i	−0.0177201	−	0.0102307i
$208$	1.89933			0.131695
$209$	9.37092	+	2.51093i	0.648200	+	0.173685i
$210$	4.18835	−	0.219612i	0.289024	−	0.0151547i
$211$	−18.6491			−1.28386			−0.641928	−	0.766765i	$-0.721865\pi$
$211$	−18.6491			−1.28386			−0.641928	+	0.766765i	$0.721865\pi$
$212$	3.38601	+	3.38601i	0.232552	+	0.232552i
$213$	−3.14179	−	11.7253i	−0.215272	−	0.803404i
$214$	1.26059	−	1.26059i	0.0861720	−	0.0861720i
$215$	−22.7524	−	11.5922i	−1.55170	−	0.790581i
$216$	9.34203	+	9.34203i	0.635645	+	0.635645i
$217$	−5.63180	−	9.75456i	−0.382311	−	0.662182i
$218$	−2.30338	+	8.59632i	−0.156004	+	0.582216i
$219$	−11.5691	+	6.67943i	−0.781768	+	0.451354i
$220$	12.1621	−	0.637707i	0.819967	−	0.0429942i
$221$		−	9.83039i		−	0.661264i
$222$	−5.39571	−	7.45618i	−0.362136	−	0.500426i
$223$	7.82604	+	7.82604i	0.524071	+	0.524071i	0.918798	−	0.394728i	$-0.129161\pi$
$223$	7.82604	+	7.82604i	0.524071	+	0.524071i	−0.394728	+	0.918798i	$0.629161\pi$
$224$	1.85823	+	6.93499i	0.124158	+	0.463364i
$225$	0.193793	+	1.84289i	0.0129195	+	0.122859i
$226$	1.54097	−	0.889680i	0.102504	−	0.0591806i
$227$	7.29033	−	4.20907i	0.483876	−	0.279366i	−0.238154	−	0.971227i	$-0.576542\pi$
$227$	7.29033	−	4.20907i	0.483876	−	0.279366i	0.722030	+	0.691861i	$0.243209\pi$
$228$	−5.70465			−0.377800
$229$	17.6546	−	10.1929i	1.16665	−	0.673566i	0.213762	−	0.976886i	$-0.431428\pi$
$229$	17.6546	−	10.1929i	1.16665	−	0.673566i	0.952889	+	0.303319i	$0.0980949\pi$
$230$	1.22767	−	0.797304i	0.0809501	−	0.0525726i
$231$	−4.69254	+	8.12771i	−0.308746	+	0.534764i
$232$	−4.59621	+	4.59621i	−0.301756	+	0.301756i
$233$	6.42167	−	6.42167i	0.420698	−	0.420698i	−0.464746	−	0.885444i	$-0.653854\pi$
$233$	6.42167	−	6.42167i	0.420698	−	0.420698i	0.885444	+	0.464746i	$0.153854\pi$
$234$	1.30164	+	0.751504i	0.0850911	+	0.0491274i
$235$	−6.59812	+	2.14405i	−0.430414	+	0.139862i
$236$	1.36917	+	1.36917i	0.0891252	+	0.0891252i
$237$	−8.17032	+	14.1514i	−0.530719	+	0.919233i
$238$	1.97142	−	0.528239i	0.127788	−	0.0342407i
$239$	5.80797	−	1.55624i	0.375686	−	0.100665i	−0.0660347	−	0.997817i	$-0.521035\pi$
$239$	5.80797	−	1.55624i	0.375686	−	0.100665i	0.441721	+	0.897152i	$0.354368\pi$
$240$	−1.50698	+	0.489690i	−0.0972749	+	0.0316093i
$241$	−0.252833	−	0.0677464i	−0.0162864	−	0.00436393i	0.250667	−	0.968073i	$-0.419350\pi$
$241$	−0.252833	−	0.0677464i	−0.0162864	−	0.00436393i	−0.266953	+	0.963710i	$0.586017\pi$
$242$	2.47462	−	4.28616i	0.159074	−	0.275525i
$243$	−0.991354	−	3.69978i	−0.0635954	−	0.237341i
$244$	−8.50228	+	2.27818i	−0.544303	+	0.145846i
$245$	−6.65377	−	10.2453i	−0.425094	−	0.654549i
$246$	−4.40601	+	16.4435i	−0.280917	+	1.04840i
$247$	11.1822	−	2.99626i	0.711506	−	0.190647i
$248$	−17.5840	−	17.5840i	−1.11658	−	1.11658i
$249$	−2.20157			−0.139519
$250$	−8.60256	−	3.30144i	−0.544074	−	0.208801i
$251$	−17.9819	−	17.9819i	−1.13500	−	1.13500i	−0.989333	−	0.145672i	$-0.953466\pi$
$251$	−17.9819	−	17.9819i	−1.13500	−	1.13500i	−0.145672	−	0.989333i	$-0.546534\pi$
$252$	0.157048	−	0.586112i	0.00989310	−	0.0369216i
$253$			3.27564i			0.205938i
$254$	3.01256	+	0.807212i	0.189025	+	0.0506490i
$255$	2.53449	+	7.79967i	0.158716	+	0.488434i
$256$	7.41572	+	12.8444i	0.463482	+	0.802775i
$257$	−12.2117	−	7.05043i	−0.761745	−	0.439794i	0.0681767	−	0.997673i	$-0.478282\pi$
$257$	−12.2117	−	7.05043i	−0.761745	−	0.439794i	−0.829922	+	0.557879i	$0.811615\pi$
$258$	12.2181	−	12.2181i	0.760665	−	0.760665i
$259$	3.07998	−	6.88266i	0.191380	−	0.427667i
$260$	12.1880	−	7.91544i	0.755869	−	0.490895i
$261$	0.850214	−	0.227814i	0.0526269	−	0.0141013i
$262$	2.10730	−	7.86457i	0.130190	−	0.485875i
$263$	11.3707	+	3.04678i	0.701149	+	0.187872i	0.591745	−	0.806125i	$-0.298439\pi$
$263$	11.3707	+	3.04678i	0.701149	+	0.187872i	0.109404	+	0.993997i	$0.465106\pi$
$264$	−5.36277	+	20.0141i	−0.330055	+	1.23178i
$265$	7.92989	+	1.68533i	0.487129	+	0.103529i
$266$	1.20176	+	2.08151i	0.0736845	+	0.127625i
$267$			13.3088i			0.814484i
$268$	7.53747	−	2.01966i	0.460424	−	0.123370i
$269$			23.2856i			1.41975i	0.704328	+	0.709875i	$0.251248\pi$
$269$			23.2856i			1.41975i	−0.704328	+	0.709875i	$0.748752\pi$
$270$	8.70180	+	1.84939i	0.529575	+	0.112550i
$271$	3.22003	−	5.57726i	0.195603	−	0.338794i	−0.751495	−	0.659739i	$-0.770667\pi$
$271$	3.22003	−	5.57726i	0.195603	−	0.338794i	0.947098	+	0.320944i	$0.104000\pi$
$272$	−0.667774	+	0.385540i	−0.0404898	+	0.0233768i
$273$			11.1991i			0.677800i
$274$	4.51416	+	16.8471i	0.272710	+	1.01777i
$275$	16.6802	−	12.1202i	1.00586	−	0.730878i
$276$	−0.498520	−	1.86050i	−0.0300074	−	0.111989i
$277$	9.18139	+	15.9026i	0.551656	+	0.955497i	0.998155	+	0.0607125i	$0.0193373\pi$
$277$	9.18139	+	15.9026i	0.551656	+	0.955497i	−0.446499	+	0.894784i	$0.647329\pi$
$278$	9.12992	+	15.8135i	0.547576	+	0.948430i
$279$	0.871562	+	3.25271i	0.0521790	+	0.194735i
$280$	5.63777	+	5.07601i	0.336921	+	0.303349i
$281$	5.16431	+	19.2735i	0.308077	+	1.14976i	0.930264	+	0.366890i	$0.119577\pi$
$281$	5.16431	+	19.2735i	0.308077	+	1.14976i	−0.622188	+	0.782868i	$0.713756\pi$
$282$		−	4.69456i		−	0.279557i
$283$	9.62911	−	5.55937i	0.572391	−	0.330470i	−0.185713	−	0.982604i	$-0.559459\pi$
$283$	9.62911	−	5.55937i	0.572391	−	0.330470i	0.758104	+	0.652134i	$0.226126\pi$
$284$	4.36640	−	7.56283i	0.259098	−	0.448771i
$285$	−8.09972	+	5.26032i	−0.479786	+	0.311595i
$286$		−	16.7238i		−	0.988901i
$287$	−13.4717	+	3.60973i	−0.795210	+	0.213076i
$288$		−	2.14648i		−	0.126483i
$289$	−6.50456	−	11.2662i	−0.382621	−	0.662719i
$290$	−0.909884	+	4.28122i	−0.0534302	+	0.251402i
$291$	−5.59096	+	20.8657i	−0.327748	+	1.22317i
$292$	−9.28297	−	2.48736i	−0.543244	−	0.145562i
$293$	−7.53277	+	28.1127i	−0.440069	+	1.64236i	0.288568	+	0.957459i	$0.406821\pi$
$293$	−7.53277	+	28.1127i	−0.440069	+	1.64236i	−0.728637	+	0.684900i	$0.759846\pi$
$294$	7.98477	−	2.13951i	0.465681	−	0.124779i
$295$	3.20653	+	0.681482i	0.186692	+	0.0396774i
$296$	2.63535	−	16.4375i	0.153176	−	0.955413i
$297$	−14.0762	+	14.0762i	−0.816784	+	0.816784i
$298$	10.9795	+	6.33904i	0.636027	+	0.367211i
$299$	1.95439	+	3.38510i	0.113025	+	0.195765i
$300$	−7.62949	+	9.42265i	−0.440489	+	0.544017i
$301$	13.6739	+	3.66390i	0.788149	+	0.211184i
$302$		−	13.5425i		−	0.779282i
$303$	−1.49490	+	5.57905i	−0.0858798	+	0.320508i
$304$	−0.642091	−	0.642091i	−0.0368264	−	0.0368264i
$305$	−9.97120	+	11.0747i	−0.570949	+	0.634137i
$306$	−0.610182			−0.0348818
$307$	−17.5892	−	17.5892i	−1.00387	−	1.00387i	−0.999992	−	0.00387509i	$-0.998767\pi$
$307$	−17.5892	−	17.5892i	−1.00387	−	1.00387i	−0.00387509	−	0.999992i	$-0.501233\pi$
$308$	−6.52161	+	1.74746i	−0.371603	+	0.0995708i
$309$	3.79204	−	14.1521i	0.215722	−	0.805084i
$310$	−16.3789	−	3.48099i	−0.930259	−	0.197707i
$311$	21.0337	−	5.63596i	1.19271	−	0.319586i	0.392754	−	0.919644i	$-0.371522\pi$
$311$	21.0337	−	5.63596i	1.19271	−	0.319586i	0.799957	+	0.600058i	$0.204856\pi$
$312$	6.39932	+	23.8826i	0.362290	+	1.35209i
$313$	14.4447	−	25.0189i	0.816460	−	1.41415i	−0.0918148	−	0.995776i	$-0.529267\pi$
$313$	14.4447	−	25.0189i	0.816460	−	1.41415i	0.908275	−	0.418374i	$-0.137400\pi$
$314$	−6.75699	−	1.81053i	−0.381319	−	0.102174i
$315$	−0.317476	−	0.977004i	−0.0178878	−	0.0550480i
$316$	−11.3550	+	3.04256i	−0.638767	+	0.171157i
$317$	1.06308	−	0.284851i	0.0597084	−	0.0159988i	−0.228841	−	0.973464i	$-0.573494\pi$
$317$	1.06308	−	0.284851i	0.0597084	−	0.0159988i	0.288550	+	0.957465i	$0.406827\pi$
$318$	−2.74289	+	4.75082i	−0.153813	+	0.266413i
$319$	−6.92539	−	6.92539i	−0.387747	−	0.387747i
$320$	7.97217	+	4.06176i	0.445658	+	0.227059i
$321$	−3.43926	−	1.98566i	−0.191961	−	0.110829i
$322$	−0.573838	+	0.573838i	−0.0319787	+	0.0319787i
$323$	−3.32328	+	3.32328i	−0.184912	+	0.184912i
$324$	6.58700	−	11.4090i	0.365945	−	0.633835i
$325$	10.0062	−	22.4774i	0.555043	−	1.24682i
$326$	0.676728	−	0.390709i	0.0374805	−	0.0216394i
$327$	19.8251			1.09633
$328$	−26.6664	+	15.3959i	−1.47241	+	0.850094i
$329$	3.33085	−	1.92307i	0.183636	−	0.106022i
$330$	4.31177	+	13.2691i	0.237355	+	0.730439i
$331$	0.504686	+	1.88351i	0.0277400	+	0.103527i	0.978408	−	0.206684i	$-0.0662670\pi$
$331$	0.504686	+	1.88351i	0.0277400	+	0.103527i	−0.950668	+	0.310211i	$0.899600\pi$
$332$	−1.11993	−	1.11993i	−0.0614641	−	0.0614641i
$333$	−1.42201	+	1.74926i	−0.0779257	+	0.0958587i
$334$			1.52590i			0.0834936i
$335$	8.83970	−	9.81800i	0.482964	−	0.536415i
$336$	0.760749	−	0.439219i	0.0415023	−	0.0239613i
$337$	−0.218091	+	0.813925i	−0.0118802	+	0.0443373i	−0.971611	−	0.236582i	$-0.923973\pi$
$337$	−0.218091	+	0.813925i	−0.0118802	+	0.0443373i	0.959731	+	0.280920i	$0.0906394\pi$
$338$	−4.62117	−	8.00410i	−0.251359	−	0.435366i
$339$	−2.80282	−	2.80282i	−0.152228	−	0.152228i
$340$	−2.67838	+	5.25695i	−0.145255	+	0.285098i
$341$	26.4948	−	26.4948i	1.43478	−	1.43478i
$342$	−0.185981	−	0.694090i	−0.0100567	−	0.0375321i
$343$	10.9247	+	10.9247i	0.589880	+	0.589880i
$344$	31.2538			1.68509
$345$	−2.42341	−	2.18194i	−0.130472	−	0.117471i
$346$	1.59944	+	0.428568i	0.0859862	+	0.0230399i
$347$	−25.8472			−1.38755			−0.693776	−	0.720191i	$-0.744054\pi$
$347$	−25.8472			−1.38755			−0.693776	+	0.720191i	$0.744054\pi$
$348$	4.98747	+	2.87952i	0.267356	+	0.154358i
$349$	−15.4393	−	8.91390i	−0.826448	−	0.477150i	0.0261867	−	0.999657i	$-0.491664\pi$
$349$	−15.4393	−	8.91390i	−0.826448	−	0.477150i	−0.852635	+	0.522507i	$0.824997\pi$
$350$	5.04538	+	0.798838i	0.269687	+	0.0426997i
$351$	−6.14811	+	22.9451i	−0.328162	+	1.22472i
$352$	−20.6839	+	11.9418i	−1.10245	+	0.636503i
$353$	6.09669	+	3.51992i	0.324494	+	0.187347i	0.653394	−	0.757018i	$-0.273345\pi$
$353$	6.09669	+	3.51992i	0.324494	+	0.187347i	−0.328900	+	0.944365i	$0.606678\pi$
$354$	−1.10911	+	1.92104i	−0.0589487	+	0.102102i
$355$	−0.774155	−	14.7644i	−0.0410879	−	0.783611i
$356$	−6.77013	+	6.77013i	−0.358816	+	0.358816i
$357$	−2.27327	−	3.93742i	−0.120314	−	0.208390i
$358$	−4.98406	−	18.6008i	−0.263416	−	0.983082i
$359$		−	18.3910i		−	0.970639i	−0.874337	−	0.485320i	$-0.838703\pi$
$359$		−	18.3910i		−	0.970639i	0.874337	−	0.485320i	$-0.161297\pi$
$360$	−1.23531	−	1.90210i	−0.0651064	−	0.100249i
$361$	11.6613	+	6.73265i	0.613752	+	0.354350i
$362$	1.00392			0.0527650
$363$	−10.6495	−	2.85352i	−0.558952	−	0.149771i
$364$	−5.69693	+	5.69693i	−0.298600	+	0.298600i
$365$	−15.4740	+	5.02826i	−0.809947	+	0.263191i
$366$	−5.04192	−	8.73287i	−0.263546	−	0.456474i
$367$	15.8316	+	4.24206i	0.826402	+	0.221434i	0.647143	−	0.762368i	$-0.275964\pi$
$367$	15.8316	+	4.24206i	0.826402	+	0.221434i	0.179258	+	0.983802i	$0.442630\pi$
$368$	0.153299	−	0.265521i	0.00799125	−	0.0138413i
$369$	4.16969			0.217065
$370$	−4.54028	−	10.2491i	−0.236038	−	0.532823i
$371$	−4.49435			−0.233335
$372$	−11.0163	+	19.0808i	−0.571170	+	0.989295i
$373$	5.18993	+	1.39064i	0.268724	+	0.0720045i	0.390665	−	0.920533i	$-0.372245\pi$
$373$	5.18993	+	1.39064i	0.268724	+	0.0720045i	−0.121941	+	0.992537i	$0.538912\pi$
$374$	3.39472	+	5.87983i	0.175537	+	0.304039i
$375$	−2.14397	+	20.4140i	−0.110714	+	1.05417i
$376$	6.00433	−	6.00433i	0.309650	−	0.309650i
$377$	−11.2888	−	3.02483i	−0.581403	−	0.155786i
$378$	−4.93184			−0.253667
$379$	−17.5612	−	10.1389i	−0.902057	−	0.520803i	−0.0241899	−	0.999707i	$-0.507701\pi$
$379$	−17.5612	−	10.1389i	−0.902057	−	0.520803i	−0.877867	+	0.478905i	$0.841034\pi$
$380$	−6.79620	−	1.44439i	−0.348638	−	0.0740957i
$381$		−	6.94765i		−	0.355939i
$382$	−1.65045	−	6.15958i	−0.0844445	−	0.315151i
$383$	3.46096	+	5.99456i	0.176847	+	0.306308i	0.940799	−	0.338965i	$-0.110077\pi$
$383$	3.46096	+	5.99456i	0.176847	+	0.306308i	−0.763952	+	0.645273i	$0.776744\pi$
$384$	10.7566	−	10.7566i	0.548919	−	0.548919i
$385$	−7.64833	+	8.49478i	−0.389795	+	0.432934i
$386$	−8.42088	+	14.5854i	−0.428612	+	0.742377i
$387$	−3.66525	−	2.11613i	−0.186315	−	0.107569i
$388$	−13.4584	+	7.77022i	−0.683248	+	0.394473i
$389$	9.03222	−	33.7087i	0.457952	−	1.70910i	−0.221311	−	0.975203i	$-0.571033\pi$
$389$	9.03222	−	33.7087i	0.457952	−	1.70910i	0.679262	−	0.733896i	$-0.262300\pi$
$390$	12.3728	+	11.1399i	0.626520	+	0.564092i
$391$	−1.37426	−	0.793431i	−0.0694994	−	0.0401255i
$392$	12.9489	+	7.47607i	0.654020	+	0.377599i
$393$	−18.1375			−0.914916
$394$	−22.0886	−	5.91862i	−1.11281	−	0.298176i
$395$	−13.3167	+	14.7905i	−0.670038	+	0.744192i
$396$	2.01853			0.101435
$397$	−8.75997	−	8.75997i	−0.439650	−	0.439650i	0.452244	−	0.891894i	$-0.350624\pi$
$397$	−8.75997	−	8.75997i	−0.439650	−	0.439650i	−0.891894	+	0.452244i	$0.850624\pi$
$398$	−3.86852	−	14.4375i	−0.193911	−	0.723687i
$399$	3.78598	−	3.78598i	0.189536	−	0.189536i
$400$	−1.91932	+	0.201830i	−0.0959658	+	0.0100915i
$401$	−22.1660	−	22.1660i	−1.10692	−	1.10692i	−0.993553	−	0.113365i	$-0.963837\pi$
$401$	−22.1660	−	22.1660i	−1.10692	−	1.10692i	−0.113365	−	0.993553i	$-0.536163\pi$
$402$	4.46978	+	7.74189i	0.222933	+	0.386130i
$403$	11.5722	−	43.1882i	0.576455	−	2.15136i
$404$	−3.59849	+	2.07759i	−0.179032	+	0.103364i
$405$	−1.16786	−	22.2730i	−0.0580316	−	1.10675i
$406$		−	2.42643i		−	0.120422i
$407$	24.7674	+	3.97084i	1.22768	+	0.196827i
$408$	−7.09775	−	7.09775i	−0.351391	−	0.351391i
$409$	−7.06463	−	26.3656i	−0.349324	−	1.30369i	−0.887479	−	0.460848i	$-0.847545\pi$
$409$	−7.06463	−	26.3656i	−0.349324	−	1.30369i	0.538156	−	0.842845i	$-0.319121\pi$
$410$	−9.41249	+	18.4742i	−0.464850	+	0.912378i
$411$	33.6478	−	19.4266i	1.65973	−	0.958243i
$412$	9.12810	−	5.27011i	0.449709	−	0.259640i
$413$	−1.81734			−0.0894254
$414$	0.210116	−	0.121311i	0.0103267	−	0.00596210i
$415$	−2.62283	−	0.557428i	−0.128750	−	0.0273630i
$416$	−14.2501	+	24.6818i	−0.698667	+	1.21013i
$417$	28.7626	−	28.7626i	1.40851	−	1.40851i
$418$	−5.65368	+	5.65368i	−0.276531	+	0.276531i
$419$	30.6436	+	17.6921i	1.49704	+	0.864315i	0.999994	−	0.00341085i	$-0.00108571\pi$
$419$	30.6436	+	17.6921i	1.49704	+	0.864315i	0.497043	+	0.867726i	$0.334419\pi$
$420$	3.05129	−	5.98888i	0.148888	−	0.292227i
$421$	6.45054	+	6.45054i	0.314380	+	0.314380i	0.846604	−	0.532224i	$-0.178643\pi$
$421$	6.45054	+	6.45054i	0.314380	+	0.314380i	−0.532224	+	0.846604i	$0.678643\pi$
$422$	7.68485	−	13.3105i	0.374093	−	0.647947i
$423$	−1.11069	+	0.297609i	−0.0540037	+	0.0144702i
$424$	−9.58443	+	2.56814i	−0.465461	+	0.124720i
$425$	1.04461	+	9.93382i	0.0506712	+	0.481861i
$426$	9.66345	+	2.58931i	0.468195	+	0.125453i
$427$	4.13072	−	7.15462i	0.199900	−	0.346236i
$428$	−0.739442	−	2.75963i	−0.0357423	−	0.133392i
$429$	−35.9854	+	9.64225i	−1.73739	+	0.465532i
$430$	17.6495	−	11.4624i	0.851136	−	0.552766i
$431$	−6.64876	+	24.8135i	−0.320259	+	1.19522i	0.598733	+	0.800949i	$0.295671\pi$
$431$	−6.64876	+	24.8135i	−0.320259	+	1.19522i	−0.918992	+	0.394276i	$0.870996\pi$
$432$	1.79977	−	0.482247i	0.0865916	−	0.0232021i
$433$	−17.0203	−	17.0203i	−0.817941	−	0.817941i	0.167868	−	0.985809i	$-0.446312\pi$
$433$	−17.0203	−	17.0203i	−0.817941	−	0.817941i	−0.985809	+	0.167868i	$0.946312\pi$
$434$	9.28293			0.445595
$435$	9.73668	−	0.510533i	0.466838	−	0.0244782i
$436$	10.0849	+	10.0849i	0.482981	+	0.482981i
$437$	0.483668	−	1.80507i	0.0231370	−	0.0863484i
$438$		−	11.0098i		−	0.526066i
$439$	14.3903	+	3.85588i	0.686814	+	0.184031i	0.585317	−	0.810805i	$-0.300970\pi$
$439$	14.3903	+	3.85588i	0.686814	+	0.184031i	0.101497	+	0.994836i	$0.467637\pi$
$440$	−11.4564	+	22.4859i	−0.546162	+	1.07197i
$441$	−1.01238	−	1.75349i	−0.0482086	−	0.0834997i
$442$	7.01632	+	4.05088i	0.333732	+	0.192681i
$443$	19.1200	−	19.1200i	0.908420	−	0.908420i	−0.0877248	−	0.996145i	$-0.527960\pi$
$443$	19.1200	−	19.1200i	0.908420	−	0.908420i	0.996145	+	0.0877248i	$0.0279596\pi$
$444$	−14.6718	+	1.51400i	−0.696292	+	0.0718512i
$445$	−3.36973	+	15.8554i	−0.159740	+	0.751616i
$446$	−8.81067	+	2.36081i	−0.417197	+	0.111788i
$447$	7.30964	−	27.2799i	0.345734	−	1.29030i
$448$	−4.79116	−	1.28379i	−0.226361	−	0.0606533i
$449$	−1.83666	+	6.85450i	−0.0866772	+	0.323484i	−0.995627	−	0.0934229i	$-0.970219\pi$
$449$	−1.83666	+	6.85450i	−0.0866772	+	0.323484i	0.908949	+	0.416907i	$0.136886\pi$
$450$	−1.39520	−	0.621094i	−0.0657702	−	0.0292786i
$451$	−23.1979	−	40.1799i	−1.09235	−	1.89200i
$452$		−	2.85157i		−	0.134126i
$453$	−29.1399	+	7.80801i	−1.36911	+	0.366852i
$454$			6.93784i			0.325609i
$455$	−2.83556	+	13.3420i	−0.132933	+	0.625481i
$456$	5.91042	−	10.2371i	0.276781	−	0.479398i
$457$	11.3465	−	6.55090i	0.530767	−	0.306438i	−0.210562	−	0.977581i	$-0.567529\pi$
$457$	11.3465	−	6.55090i	0.530767	−	0.306438i	0.741329	+	0.671142i	$0.234196\pi$
$458$			16.8010i			0.785061i
$459$	−2.49597	−	9.31510i	−0.116502	−	0.434792i
$460$	−0.122838	−	2.34272i	−0.00572737	−	0.109230i
$461$	−5.66561	−	21.1444i	−0.263874	−	0.984791i	−0.962936	−	0.269730i	$-0.913066\pi$
$461$	−5.66561	−	21.1444i	−0.263874	−	0.984791i	0.699062	−	0.715061i	$-0.253601\pi$
$462$	−3.86737	−	6.69848i	−0.179926	−	0.311641i
$463$	13.5846	+	23.5293i	0.631331	+	1.09350i	0.987280	+	0.158992i	$0.0508245\pi$
$463$	13.5846	+	23.5293i	0.631331	+	1.09350i	−0.355949	+	0.934506i	$0.615842\pi$
$464$	0.237262	+	0.885474i	0.0110146	+	0.0411071i
$465$	1.95318	+	37.2501i	0.0905764	+	1.72743i
$466$	1.93717	+	7.22961i	0.0897376	+	0.334905i
$467$		−	11.4311i		−	0.528967i	−0.964390	−	0.264483i	$-0.914799\pi$
$467$		−	11.4311i		−	0.528967i	0.964390	−	0.264483i	$-0.0852015\pi$
$468$	2.08599	−	1.20435i	0.0964248	−	0.0556709i
$469$	−3.66198	+	6.34274i	−0.169095	+	0.292880i
$470$	1.18864	−	5.59284i	0.0548280	−	0.257979i
$471$			15.5832i			0.718035i
$472$	−3.87556	+	1.03845i	−0.178387	+	0.0477987i
$473$			47.0920i			2.16529i
$474$	−6.73360	−	11.6629i	−0.309284	−	0.535696i
$475$	−10.9815	+	4.21605i	−0.503864	+	0.193445i
$476$	0.846546	−	3.15935i	0.0388014	−	0.144809i
$477$	1.29788	+	0.347767i	0.0594261	+	0.0159232i
$478$	−1.28258	+	4.78666i	−0.0586639	+	0.218937i
$479$	9.48503	−	2.54151i	0.433382	−	0.116124i	−0.0355313	−	0.999369i	$-0.511312\pi$
$479$	9.48503	−	2.54151i	0.433382	−	0.116124i	0.468913	+	0.883244i	$0.344646\pi$
$480$	4.94282	−	23.2571i	0.225608	−	1.06154i
$481$	27.9643	−	10.6738i	1.27506	−	0.486684i
$482$	0.152540	−	0.152540i	0.00694799	−	0.00694799i
$483$	1.56560	+	0.903900i	0.0712373	+	0.0411289i
$484$	−3.96577	−	6.86892i	−0.180262	−	0.312224i
$485$	−11.9439	+	23.4427i	−0.542343	+	1.06448i
$486$	3.04919	+	0.817028i	0.138314	+	0.0370611i
$487$			28.7566i			1.30308i	0.758613	+	0.651542i	$0.225878\pi$
$487$			28.7566i			1.30308i	−0.758613	+	0.651542i	$0.774122\pi$
$488$	4.72071	−	17.6179i	0.213696	−	0.797526i
$489$	−1.23088	−	1.23088i	−0.0556622	−	0.0556622i
$490$	10.0543	−	0.527189i	0.454209	−	0.0238160i
$491$	31.5099			1.42202			0.711010	−	0.703182i	$-0.248238\pi$
$491$	31.5099			1.42202			0.711010	+	0.703182i	$0.248238\pi$
$492$	19.2910	+	19.2910i	0.869704	+	0.869704i
$493$	4.58296	−	1.22800i	0.206406	−	0.0553063i
$494$	−2.46938	+	9.21584i	−0.111103	+	0.414640i
$495$	2.86601	−	1.86131i	0.128817	−	0.0836598i
$496$	−3.38761	+	0.907707i	−0.152108	+	0.0407572i
$497$	2.12136	+	7.91702i	0.0951560	+	0.355127i
$498$	0.907215	−	1.57134i	0.0406533	−	0.0704136i
$499$	28.6886	+	7.68709i	1.28428	+	0.344121i	0.835485	−	0.549514i	$-0.185187\pi$
$499$	28.6886	+	7.68709i	1.28428	+	0.344121i	0.448794	+	0.893635i	$0.351854\pi$
$500$	−11.4751	+	9.29387i	−0.513183	+	0.415634i
$501$	3.28334	−	0.879770i	0.146689	−	0.0393052i
$502$	20.2442	−	5.42443i	0.903544	−	0.242104i
$503$	8.69325	−	15.0571i	0.387613	−	0.671365i	−0.604515	−	0.796594i	$-0.706633\pi$
$503$	8.69325	−	15.0571i	0.387613	−	0.671365i	0.992128	+	0.125229i	$0.0399665\pi$
$504$	0.889080	+	0.889080i	0.0396028	+	0.0396028i
$505$	−3.19353	+	6.26807i	−0.142110	+	0.278925i
$506$	−2.33795	−	1.34981i	−0.103934	−	0.0600065i
$507$	−14.5584	+	14.5584i	−0.646561	+	0.646561i
$508$	3.53424	−	3.53424i	0.156807	−	0.156807i
$509$	−4.46764	+	7.73818i	−0.198025	+	0.342989i	−0.947888	−	0.318604i	$-0.896786\pi$
$509$	−4.46764	+	7.73818i	−0.198025	+	0.342989i	0.749863	+	0.661593i	$0.230119\pi$
$510$	−6.61133	−	1.40510i	−0.292754	−	0.0622189i
$511$	7.81156	−	4.51001i	0.345563	−	0.199511i
$512$	4.34822			0.192166
$513$	9.83528	−	5.67840i	0.434238	−	0.250708i
$514$	10.0643	−	5.81064i	0.443918	−	0.256296i
$515$	8.10087	−	15.8999i	0.356967	−	0.700633i
$516$	−7.16695	−	26.7474i	−0.315507	−	1.17749i
$517$	9.04709	+	9.04709i	0.397891	+	0.397891i
$518$	3.64323	+	5.03448i	0.160074	+	0.221202i
$519$		−	3.68867i		−	0.161914i
$520$	1.57683	+	30.0727i	0.0691487	+	1.31877i
$521$	5.50222	−	3.17671i	0.241057	−	0.139174i	−0.374606	−	0.927184i	$-0.622222\pi$
$521$	5.50222	−	3.17671i	0.241057	−	0.139174i	0.615662	+	0.788010i	$0.288889\pi$
$522$	−0.187754	+	0.700707i	−0.00821776	+	0.0306691i
$523$	−1.56065	−	2.70312i	−0.0682423	−	0.118199i	0.829885	−	0.557934i	$-0.188406\pi$
$523$	−1.56065	−	2.70312i	−0.0682423	−	0.118199i	−0.898128	+	0.439735i	$0.855072\pi$
$524$	−9.22647	−	9.22647i	−0.403060	−	0.403060i
$525$	−1.19006	−	11.3169i	−0.0519383	−	0.493911i
$526$	−6.86021	+	6.86021i	−0.299119	+	0.299119i
$527$	4.69803	+	17.5333i	0.204649	+	0.763762i
$528$	2.06631	+	2.06631i	0.0899245	+	0.0899245i
$529$	−22.3690			−0.972567
$530$	−4.47061	+	4.96538i	−0.194191	+	0.215682i
$531$	0.524813	+	0.140623i	0.0227749	+	0.00610253i
$532$	3.85183			0.166998
$533$	−47.9462	−	27.6817i	−2.07678	−	1.19903i
$534$	−9.49898	−	5.48424i	−0.411061	−	0.237326i
$535$	−3.59459	−	3.23641i	−0.155407	−	0.139922i
$536$	−4.18502	+	15.6187i	−0.180765	+	0.674625i
$537$	−37.1505	+	21.4488i	−1.60316	+	0.925585i
$538$	−16.6198	−	9.59546i	−0.716531	−	0.413690i
$539$	−11.2647	+	19.5110i	−0.485203	+	0.840396i
$540$	9.53938	−	10.5951i	0.410510	−	0.455941i
$541$	−2.14088	+	2.14088i	−0.0920435	+	0.0920435i	−0.751629	−	0.659586i	$-0.770732\pi$
$541$	−2.14088	+	2.14088i	−0.0920435	+	0.0920435i	0.659586	+	0.751629i	$0.270732\pi$
$542$	2.65380	+	4.59651i	0.113990	+	0.197437i
$543$	−0.578819	−	2.16018i	−0.0248395	−	0.0927023i
$544$		−	11.5703i		−	0.496073i
$545$	23.6185	+	5.01962i	1.01171	+	0.215017i
$546$	−7.99321	−	4.61488i	−0.342078	−	0.197499i
$547$	−45.1561			−1.93074			−0.965368	−	0.260891i	$-0.915984\pi$
$547$	−45.1561			−1.93074			−0.965368	+	0.260891i	$0.915984\pi$
$548$	26.9988	+	7.23429i	1.15333	+	0.309034i
$549$	−1.74649	+	1.74649i	−0.0745384	+	0.0745384i
$550$	1.77713	+	16.8998i	0.0757773	+	0.720609i
$551$	2.79373	+	4.83888i	0.119017	+	0.206143i
$552$	3.85522	+	1.03300i	0.164089	+	0.0439676i
$553$	5.51667	−	9.55515i	0.234593	−	0.406326i
$554$	−15.1337			−0.642971
$555$	−19.4356	+	15.6787i	−0.824995	+	0.665522i
$556$	29.2629			1.24102
$557$	−0.578894	+	1.00267i	−0.0245285	+	0.0424847i	−0.878029	−	0.478607i	$-0.841142\pi$
$557$	−0.578894	+	1.00267i	−0.0245285	+	0.0424847i	0.853501	+	0.521092i	$0.174475\pi$
$558$	−2.68073	−	0.718300i	−0.113485	−	0.0304081i
$559$	28.0972	+	48.6657i	1.18838	+	2.05834i
$560$	1.01752	−	0.330643i	0.0429982	−	0.0139722i
$561$	10.6946	−	10.6946i	0.451527	−	0.451527i
$562$	−15.8843	−	4.25618i	−0.670038	−	0.179536i
$563$	9.05216			0.381503			0.190751	−	0.981638i	$-0.438908\pi$
$563$	9.05216			0.381503			0.190751	+	0.981638i	$0.438908\pi$
$564$	−6.51546	−	3.76170i	−0.274350	−	0.158396i
$565$	−2.62946	−	4.04879i	−0.110622	−	0.170334i
$566$			9.16354i			0.385172i
$567$	3.20021	+	11.9433i	0.134396	+	0.501573i
$568$	9.04780	+	15.6712i	0.379637	+	0.657551i
$569$	0.221126	−	0.221126i	0.00927008	−	0.00927008i	−0.702457	−	0.711727i	$-0.747913\pi$
$569$	0.221126	−	0.221126i	0.00927008	−	0.00927008i	0.711727	+	0.702457i	$0.247913\pi$
$570$	−0.416784	−	7.94874i	−0.0174572	−	0.332936i
$571$	−14.6005	+	25.2888i	−0.611012	+	1.05830i	0.380058	+	0.924963i	$0.375904\pi$
$571$	−14.6005	+	25.2888i	−0.611012	+	1.05830i	−0.991070	+	0.133342i	$0.957429\pi$
$572$	−23.2106	−	13.4006i	−0.970483	−	0.560309i
$573$	−12.3022	+	7.10270i	−0.513933	+	0.296719i
$574$	2.97497	−	11.1028i	0.124173	−	0.463420i
$575$	−2.33466	−	3.21304i	−0.0973622	−	0.133993i
$576$	1.28426	+	0.741467i	0.0535108	+	0.0308945i
$577$	12.7689	+	7.37214i	0.531577	+	0.306906i	0.741658	−	0.670778i	$-0.234040\pi$
$577$	12.7689	+	7.37214i	0.531577	+	0.306906i	−0.210081	+	0.977684i	$0.567373\pi$
$578$	10.7215			0.445956
$579$	36.2391	+	9.71024i	1.50605	+	0.403544i
$580$	5.21272	+	4.69330i	0.216446	+	0.194879i
$581$	1.48652			0.0616711
$582$	−12.5888	−	12.5888i	−0.521821	−	0.521821i
$583$	−3.86957	−	14.4414i	−0.160261	−	0.598103i
$584$	14.0814	−	14.0814i	0.582694	−	0.582694i
$585$	1.85124	−	3.63350i	0.0765394	−	0.150227i
$586$	−16.9610	−	16.9610i	−0.700652	−	0.700652i
$587$	−17.1107	−	29.6366i	−0.706233	−	1.22323i	−0.966245	−	0.257627i	$-0.917060\pi$
$587$	−17.1107	−	29.6366i	−0.706233	−	1.22323i	0.260011	−	0.965606i	$-0.416274\pi$
$588$	3.42874	−	12.7962i	0.141399	−	0.527708i
$589$	−18.5124	+	10.6881i	−0.762790	+	0.440397i
$590$	−1.80774	+	2.00780i	−0.0744233	+	0.0826599i
$591$			50.9414i			2.09545i
$592$	−1.82180	−	1.48098i	−0.0748756	−	0.0608680i
$593$	2.15764	+	2.15764i	0.0886036	+	0.0886036i	0.750019	−	0.661416i	$-0.230044\pi$
$593$	2.15764	+	2.15764i	0.0886036	+	0.0886036i	−0.661416	+	0.750019i	$0.730044\pi$
$594$	−4.24624	−	15.8472i	−0.174225	−	0.650218i
$595$	−1.71131	−	5.26640i	−0.0701569	−	0.215901i
$596$	17.5956	−	10.1588i	0.720743	−	0.416121i
$597$	−28.8354	+	16.6481i	−1.18015	+	0.681362i
$598$	−3.22143			−0.131734
$599$	6.31443	−	3.64564i	0.258000	−	0.148957i	−0.365422	−	0.930842i	$-0.619075\pi$
$599$	6.31443	−	3.64564i	0.258000	−	0.148957i	0.623422	+	0.781885i	$0.285742\pi$
$600$	−9.00450	−	23.4539i	−0.367607	−	0.957500i
$601$	−6.91912	+	11.9843i	−0.282237	+	0.488849i	−0.971935	−	0.235248i	$-0.924410\pi$
$601$	−6.91912	+	11.9843i	−0.282237	+	0.488849i	0.689699	+	0.724097i	$0.257743\pi$
$602$	−8.24975	+	8.24975i	−0.336235	+	0.336235i
$603$	1.54830	−	1.54830i	0.0630518	−	0.0630518i
$604$	−18.7953	−	10.8514i	−0.764768	−	0.441539i
$605$	−11.9647	−	6.09592i	−0.486434	−	0.247835i
$606$	−3.36596	−	3.36596i	−0.136733	−	0.136733i
$607$	−4.71740	+	8.17078i	−0.191473	+	0.331642i	−0.945739	−	0.324928i	$-0.894660\pi$
$607$	−4.71740	+	8.17078i	−0.191473	+	0.331642i	0.754265	+	0.656570i	$0.227993\pi$
$608$	13.1614	−	3.52658i	0.533764	−	0.143022i
$609$	−5.22105	+	1.39898i	−0.211568	+	0.0566893i
$610$	−3.79555	−	11.6805i	−0.153677	−	0.472928i
$611$	14.7473	+	3.95153i	0.596612	+	0.159862i
$612$	−0.488933	+	0.846856i	−0.0197639	+	0.0342321i
$613$	6.95785	+	25.9670i	0.281025	+	1.04880i	0.951696	+	0.307043i	$0.0993397\pi$
$613$	6.95785	+	25.9670i	0.281025	+	1.04880i	−0.670671	+	0.741755i	$0.733994\pi$
$614$	19.8022	−	5.30597i	0.799150	−	0.214132i
$615$	45.1786	+	9.60178i	1.82178	+	0.387181i
$616$	3.62098	−	13.5137i	0.145894	−	0.544482i
$617$	27.7937	−	7.44729i	1.11893	−	0.299817i	0.348481	−	0.937316i	$-0.386698\pi$
$617$	27.7937	−	7.44729i	1.11893	−	0.299817i	0.770451	+	0.637499i	$0.220031\pi$
$618$	8.53826	+	8.53826i	0.343459	+	0.343459i
$619$	33.9719			1.36544			0.682722	−	0.730678i	$-0.260796\pi$
$619$	33.9719			1.36544			0.682722	+	0.730678i	$0.260796\pi$
$620$	−17.9554	+	19.9426i	−0.721108	+	0.800913i
$621$	2.71143	+	2.71143i	0.108806	+	0.108806i
$622$	−4.64489	+	17.3350i	−0.186243	+	0.695069i
$623$		−	8.98620i		−	0.360025i
$624$	3.36821	+	0.902509i	0.134836	+	0.0361293i
$625$	−7.72293	+	23.7772i	−0.308917	+	0.951089i
$626$	11.9046	+	20.6194i	0.475804	+	0.824116i
$627$	15.4249	+	8.90559i	0.616012	+	0.355655i
$628$	−7.92710	+	7.92710i	−0.316326	+	0.316326i
$629$	−7.66514	+	9.42912i	−0.305629	+	0.375964i
$630$	0.828149	+	0.176006i	0.0329943	+	0.00701224i
$631$	24.1532	−	6.47184i	0.961525	−	0.257640i	0.256279	−	0.966603i	$-0.417503\pi$
$631$	24.1532	−	6.47184i	0.961525	−	0.257640i	0.705246	+	0.708963i	$0.250837\pi$
$632$	6.30461	−	23.5291i	0.250784	−	0.935938i
$633$	−33.0716	−	8.86151i	−1.31448	−	0.352213i
$634$	−0.234761	+	0.876139i	−0.00932355	+	0.0347959i
$635$	1.75911	−	8.27705i	0.0698083	−	0.328465i
$636$	4.39569	+	7.61356i	0.174301	+	0.301897i
$637$			26.8839i			1.06518i
$638$	7.79670	−	2.08912i	0.308674	−	0.0827090i
$639$		−	2.45043i		−	0.0969377i
$640$	15.5383	−	10.0913i	0.614205	−	0.398892i
$641$	−0.440835	+	0.763549i	−0.0174119	+	0.0301584i	−0.874600	−	0.484845i	$-0.838876\pi$
$641$	−0.440835	+	0.763549i	−0.0174119	+	0.0301584i	0.857188	+	0.515003i	$0.172209\pi$
$642$	2.83448	−	1.63649i	0.111868	−	0.0645870i
$643$		−	27.9848i		−	1.10361i	−0.833972	−	0.551807i	$-0.813938\pi$
$643$		−	27.9848i		−	1.10361i	0.833972	−	0.551807i	$-0.186062\pi$
$644$	0.336605	+	1.25623i	0.0132641	+	0.0495022i
$645$	−34.8401	−	31.3685i	−1.37183	−	1.23513i
$646$	−1.00250	−	3.74139i	−0.0394430	−	0.147203i
$647$	−11.6327	−	20.1484i	−0.457327	−	0.792114i	0.541491	−	0.840706i	$-0.317860\pi$
$647$	−11.6327	−	20.1484i	−0.457327	−	0.792114i	−0.998819	+	0.0485920i	$0.984527\pi$
$648$	13.6492	+	23.6411i	0.536191	+	0.928710i
$649$	−1.56470	−	5.83955i	−0.0614199	−	0.229222i
$650$	11.9197	+	16.4042i	0.467528	+	0.643426i
$651$	−5.35214	−	19.9745i	−0.209767	−	0.782861i
$652$		−	1.25228i		−	0.0490433i
$653$	−34.5194	+	19.9298i	−1.35085	+	0.779914i	−0.988369	−	0.152077i	$-0.951404\pi$
$653$	−34.5194	+	19.9298i	−1.35085	+	0.779914i	−0.362482	+	0.931991i	$0.618070\pi$
$654$	−8.16945	+	14.1499i	−0.319451	+	0.553305i
$655$	−21.6080	−	4.59233i	−0.844295	−	0.179437i
$656$			4.34262i			0.169551i
$657$	−2.60481	+	0.697957i	−0.101623	+	0.0272299i
$658$			3.16981i			0.123572i
$659$	5.64501	+	9.77745i	0.219898	+	0.380875i	0.954777	−	0.297324i	$-0.0960941\pi$
$659$	5.64501	+	9.77745i	0.219898	+	0.380875i	−0.734878	+	0.678199i	$0.762761\pi$
$660$	21.8708	+	4.64819i	0.851320	+	0.180930i
$661$	1.49956	−	5.59642i	0.0583259	−	0.217675i	−0.930612	−	0.366008i	$-0.880724\pi$
$661$	1.49956	−	5.59642i	0.0583259	−	0.217675i	0.988937	+	0.148333i	$0.0473908\pi$
$662$	−1.55230	−	0.415939i	−0.0603320	−	0.0161659i
$663$	4.67112	−	17.4329i	0.181411	−	0.677037i
$664$	3.17007	−	0.849418i	0.123023	−	0.0329638i
$665$	5.46900	−	3.55181i	0.212079	−	0.137733i
$666$	−0.662534	−	1.73577i	−0.0256727	−	0.0672597i
$667$	−1.33400	+	1.33400i	−0.0516528	+	0.0516528i
$668$	2.11776	+	1.22269i	0.0819386	+	0.0473073i
$669$	10.1597	+	17.5971i	0.392797	+	0.680345i
$670$	3.36484	+	10.3550i	0.129995	+	0.400048i
$671$	26.5460	+	7.11298i	1.02480	+	0.274594i
$672$			13.1812i			0.508478i
$673$	−9.14711	+	34.1375i	−0.352595	+	1.31590i	0.530888	+	0.847442i	$0.321858\pi$
$673$	−9.14711	+	34.1375i	−0.352595	+	1.31590i	−0.883484	+	0.468462i	$0.844808\pi$
$674$	−0.491059	−	0.491059i	−0.0189149	−	0.0189149i
$675$	3.77458	−	23.8398i	0.145283	−	0.917595i
$676$	−14.8116			−0.569676
$677$	−26.8736	−	26.8736i	−1.03284	−	1.03284i	−0.999442	−	0.0333951i	$-0.989368\pi$
$677$	−26.8736	−	26.8736i	−1.03284	−	1.03284i	−0.0333951	−	0.999442i	$-0.510632\pi$
$678$	3.15545	−	0.845501i	0.121184	−	0.0324713i
$679$	3.77506	−	14.0887i	0.144874	−	0.540675i
$680$	−6.65875	−	10.2530i	−0.255351	−	0.393184i
$681$	14.9284	−	4.00006i	0.572059	−	0.153283i
$682$	7.99246	+	29.8283i	0.306047	+	1.14218i
$683$	−5.53913	+	9.59406i	−0.211949	+	0.367107i	−0.952324	−	0.305087i	$-0.901314\pi$
$683$	−5.53913	+	9.59406i	−0.211949	+	0.367107i	0.740375	+	0.672194i	$0.234648\pi$
$684$	−1.11233	−	0.298049i	−0.0425312	−	0.0113962i
$685$	45.0049	−	14.6243i	1.71955	−	0.558765i
$686$	−12.2992	+	3.29556i	−0.469586	+	0.125825i
$687$	36.1515	−	9.68676i	1.37927	−	0.369573i
$688$	2.20389	−	3.81725i	0.0840226	−	0.145531i
$689$	−12.6153	−	12.6153i	−0.480604	−	0.480604i
$690$	2.55596	−	0.830556i	0.0973038	−	0.0316187i
$691$	3.68751	+	2.12898i	0.140279	+	0.0809904i	0.568497	−	0.822685i	$-0.307525\pi$
$691$	3.68751	+	2.12898i	0.140279	+	0.0809904i	−0.428218	+	0.903676i	$0.640858\pi$
$692$	1.87641	−	1.87641i	0.0713304	−	0.0713304i
$693$	−1.33963	+	1.33963i	−0.0508884	+	0.0508884i
$694$	10.6510	−	18.4481i	0.404308	−	0.700281i
$695$	41.5488	−	26.9836i	1.57603	−	1.02355i
$696$	−10.3347	+	5.96676i	−0.391737	+	0.226170i
$697$	22.4761			0.851344
$698$	12.7244	−	7.34642i	0.481625	−	0.278066i
$699$	14.4394	−	8.33657i	0.546147	−	0.315318i
$700$	5.15150	−	6.36225i	0.194708	−	0.240470i
$701$	−9.60225	−	35.8361i	−0.362672	−	1.35351i	−0.870549	−	0.492081i	$-0.836236\pi$
$701$	−9.60225	−	35.8361i	−0.362672	−	1.35351i	0.507878	−	0.861429i	$-0.330430\pi$
$702$	−13.8433	−	13.8433i	−0.522481	−	0.522481i
$703$	−13.0620	−	5.84524i	−0.492644	−	0.220457i
$704$		−	16.5005i		−	0.621885i
$705$	−12.7197	+	0.666944i	−0.479050	+	0.0251186i
$706$	−5.02460	+	2.90096i	−0.189103	+	0.109179i
$707$	1.00937	−	3.76702i	0.0379612	−	0.141673i
$708$	1.77744	+	3.07862i	0.0668004	+	0.115702i
$709$	−25.2496	−	25.2496i	−0.948269	−	0.948269i	0.0504569	−	0.998726i	$-0.483932\pi$
$709$	−25.2496	−	25.2496i	−0.948269	−	0.948269i	−0.998726	+	0.0504569i	$0.983932\pi$
$710$	10.8569	+	5.53151i	0.407452	+	0.207594i
$711$	−2.33247	+	2.33247i	−0.0874746	+	0.0874746i
$712$	−5.13484	−	19.1635i	−0.192436	−	0.718183i
$713$	−5.10357	−	5.10357i	−0.191130	−	0.191130i
$714$	3.74704			0.140230
$715$	−45.3123	+	2.37591i	−1.69459	+	0.0888540i
$716$	−29.8092	−	7.98736i	−1.11402	−	0.298502i
$717$	11.0391			0.412264
$718$	13.1263	+	7.57849i	0.489871	+	0.282827i
$719$	−37.1866	−	21.4697i	−1.38683	−	0.800685i	−0.393871	−	0.919166i	$-0.628864\pi$
$719$	−37.1866	−	21.4697i	−1.38683	−	0.800685i	−0.992956	+	0.118480i	$0.962198\pi$
$720$	−0.319426	+	0.0167488i	−0.0119043	+	0.000624191i
$721$	−2.56042	+	9.55560i	−0.0953549	+	0.355869i
$722$	−9.61069	+	5.54874i	−0.357673	+	0.206503i
$723$	−0.416174	−	0.240278i	−0.0154777	−	0.00893604i
$724$	0.804434	−	1.39332i	0.0298965	−	0.0517823i
$725$	11.7290	+	1.85706i	0.435604	+	0.0689696i
$726$	6.42506	−	6.42506i	0.238456	−	0.238456i
$727$	−3.45179	−	5.97867i	−0.128020	−	0.221737i	0.794890	−	0.606754i	$-0.207529\pi$
$727$	−3.45179	−	5.97867i	−0.128020	−	0.221737i	−0.922909	+	0.385017i	$0.874195\pi$
$728$	−4.32087	−	16.1257i	−0.160142	−	0.597659i
$729$			22.8913i			0.847826i
$730$	2.78762	−	13.1164i	0.103174	−	0.485460i
$731$	−19.7570	−	11.4067i	−0.730739	−	0.421893i
$732$	−16.1602			−0.597297
$733$	−7.12522	−	1.90920i	−0.263176	−	0.0705178i	0.124818	−	0.992180i	$-0.460165\pi$
$733$	−7.12522	−	1.90920i	−0.263176	−	0.0705178i	−0.387994	+	0.921662i	$0.626832\pi$
$734$	−9.55154	+	9.55154i	−0.352554	+	0.352554i
$735$	−6.93127	−	21.3304i	−0.255664	−	0.786783i
$736$	2.30030	+	3.98424i	0.0847902	+	0.146861i
$737$	−23.5337	−	6.30582i	−0.866873	−	0.232278i
$738$	−1.71823	+	2.97607i	−0.0632490	+	0.109550i
$739$	14.9613			0.550359			0.275179	−	0.961393i	$-0.411263\pi$
$739$	14.9613			0.550359			0.275179	+	0.961393i	$0.411263\pi$
$740$	−17.8625	−	1.91113i	−0.656638	−	0.0702547i
$741$	21.2538			0.780780
$742$	1.85202	−	3.20779i	0.0679897	−	0.117762i
$743$	−16.4018	−	4.39484i	−0.601723	−	0.161231i	−0.0549175	−	0.998491i	$-0.517490\pi$
$743$	−16.4018	−	4.39484i	−0.601723	−	0.161231i	−0.546805	+	0.837260i	$0.684156\pi$
$744$	−22.8274	−	39.5382i	−0.836893	−	1.44954i
$745$	15.6155	−	30.6490i	0.572106	−	1.12289i
$746$	−3.13120	+	3.13120i	−0.114641	+	0.114641i
$747$	−0.429278	−	0.115025i	−0.0157065	−	0.00420853i
$748$	10.8806			0.397835
$749$	2.32222	+	1.34073i	0.0848519	+	0.0489893i
$750$	−13.6867	−	9.94235i	−0.499769	−	0.363043i
$751$			25.3188i			0.923895i	0.886907	+	0.461947i	$0.152849\pi$
$751$			25.3188i			0.923895i	−0.886907	+	0.461947i	$0.847151\pi$
$752$	−0.309951	−	1.15675i	−0.0113028	−	0.0421825i
$753$	−23.3439	−	40.4329i	−0.850700	−	1.47346i
$754$	6.81078	−	6.81078i	0.248034	−	0.248034i
$755$	−36.6926	+	1.92394i	−1.33538	+	0.0700194i
$756$	−3.95184	+	6.84478i	−0.143727	+	0.248942i
$757$	14.7900	+	8.53899i	0.537551	+	0.310355i	0.744086	−	0.668084i	$-0.232885\pi$
$757$	14.7900	+	8.53899i	0.537551	+	0.310355i	−0.206535	+	0.978439i	$0.566219\pi$
$758$	14.4731	−	8.35605i	0.525687	−	0.303505i
$759$	−1.55649	+	5.80890i	−0.0564970	+	0.210850i
$760$	9.63335	−	10.6995i	0.349438	−	0.388111i
$761$	−44.0238	−	25.4171i	−1.59586	−	0.921370i	−0.992273	−	0.124073i	$-0.960404\pi$
$761$	−44.0238	−	25.4171i	−1.59586	−	0.921370i	−0.603587	−	0.797297i	$-0.706262\pi$
$762$	4.95880	+	2.86296i	0.179638	+	0.103714i
$763$	−13.3861			−0.484608
$764$	−9.87121	−	2.64498i	−0.357128	−	0.0956921i
$765$	0.0866869	+	1.65326i	0.00313417	+	0.0597736i
$766$	−5.70472			−0.206120
$767$	−5.10112	−	5.10112i	−0.184191	−	0.184191i
$768$	7.04748	+	26.3015i	0.254304	+	0.949075i
$769$	−34.2637	+	34.2637i	−1.23558	+	1.23558i	−0.273790	+	0.961790i	$0.588277\pi$
$769$	−34.2637	+	34.2637i	−1.23558	+	1.23558i	−0.961790	+	0.273790i	$0.911723\pi$
$770$	−2.91134	−	8.95940i	−0.104918	−	0.322874i
$771$	−18.3056	−	18.3056i	−0.659262	−	0.659262i
$772$	13.4951	+	23.3743i	0.485701	+	0.841258i
$773$	1.84298	−	6.87810i	0.0662874	−	0.247388i	−0.924829	−	0.380382i	$-0.875792\pi$
$773$	1.84298	−	6.87810i	0.0662874	−	0.247388i	0.991117	+	0.132994i	$0.0424592\pi$
$774$	3.02073	−	1.74402i	0.108578	−	0.0626874i
$775$	−7.10467	+	44.8723i	−0.255207	+	1.61186i
$776$		−	32.2020i		−	1.15598i
$777$	8.73236	−	10.7419i	0.313272	−	0.385365i
$778$	20.3372	+	20.3372i	0.729124	+	0.729124i
$779$	6.85062	+	25.5669i	0.245449	+	0.916028i
$780$	25.3750	−	8.24557i	0.908570	−	0.295239i
$781$	−23.6128	+	13.6329i	−0.844933	+	0.487822i
$782$	1.13260	−	0.653908i	0.0405018	−	0.0233837i
$783$	−11.4651			−0.409728
$784$	1.82621	−	1.05436i	0.0652219	−	0.0376559i
$785$	−3.94559	+	18.5649i	−0.140824	+	0.662611i
$786$	7.47404	−	12.9454i	0.266590	−	0.461748i
$787$	−19.6130	+	19.6130i	−0.699129	+	0.699129i	−0.964223	−	0.265094i	$-0.914597\pi$
$787$	−19.6130	+	19.6130i	−0.699129	+	0.699129i	0.265094	+	0.964223i	$0.414597\pi$
$788$	−25.9137	+	25.9137i	−0.923137	+	0.923137i
$789$	18.7167	+	10.8061i	0.666332	+	0.384707i
$790$	−5.06903	−	15.5995i	−0.180348	−	0.555005i
$791$	1.89249	+	1.89249i	0.0672891	+	0.0672891i
$792$	−2.09134	+	3.62231i	−0.0743126	+	0.128713i
$793$	31.6770	−	8.48783i	1.12488	−	0.301412i
$794$	9.86210	−	2.64254i	0.349993	−	0.0937803i
$795$	13.2618	+	6.75677i	0.470346	+	0.239638i
$796$	−23.1373	−	6.19961i	−0.820079	−	0.219739i
$797$	24.8552	−	43.0504i	0.880415	−	1.52492i	0.0295340	−	0.999564i	$-0.490598\pi$
$797$	24.8552	−	43.0504i	0.880415	−	1.52492i	0.850881	−	0.525359i	$-0.176069\pi$
$798$	1.14208	+	4.26231i	0.0404293	+	0.150884i
$799$	−5.98703	+	1.60422i	−0.211806	+	0.0567532i
$800$	11.7772	−	26.4558i	0.416387	−	0.935353i
$801$	−0.695340	+	2.59504i	−0.0245686	+	0.0916914i
$802$	24.9548	−	6.68662i	0.881185	−	0.236113i
$803$	21.2174	+	21.2174i	0.748745	+	0.748745i
$804$	14.3264			0.505252
$805$	1.63631	+	1.47326i	0.0576723	+	0.0519256i
$806$	26.0564	+	26.0564i	0.917797	+	0.917797i
$807$	−11.0647	+	41.2939i	−0.389495	+	1.45361i
$808$		−	8.61011i		−	0.302903i
$809$	15.7995	+	4.23346i	0.555480	+	0.148841i	0.525629	−	0.850714i	$-0.323830\pi$
$809$	15.7995	+	4.23346i	0.555480	+	0.148841i	0.0298512	+	0.999554i	$0.490497\pi$
$810$	16.3783	+	8.34464i	0.575476	+	0.293201i
$811$	−7.45897	−	12.9193i	−0.261920	−	0.453659i	0.704832	−	0.709374i	$-0.251022\pi$
$811$	−7.45897	−	12.9193i	−0.261920	−	0.453659i	−0.966752	+	0.255716i	$0.917689\pi$
$812$	−3.36758	−	1.94427i	−0.118179	−	0.0682306i
$813$	8.36044	−	8.36044i	0.293214	−	0.293214i
$814$	−13.0402	+	16.0412i	−0.457060	+	0.562243i
$815$	−1.15475	−	1.77805i	−0.0404490	−	0.0622825i
$816$	−1.36740	+	0.366395i	−0.0478687	+	0.0128264i
$817$	6.95343	−	25.9506i	0.243270	−	0.907895i
$818$	21.7293	+	5.82234i	0.759746	+	0.203573i
$819$	−0.585115	+	2.18368i	−0.0204456	+	0.0763040i
$820$	18.0978	+	27.8666i	0.632003	+	0.973143i
$821$	5.80160	+	10.0487i	0.202477	+	0.350701i	0.949326	−	0.314293i	$-0.101767\pi$
$821$	5.80160	+	10.0487i	0.202477	+	0.350701i	−0.746849	+	0.664994i	$0.768434\pi$
$822$			32.0210i			1.11686i
$823$	22.8515	−	6.12304i	0.796553	−	0.213436i	0.162483	−	0.986711i	$-0.448050\pi$
$823$	22.8515	−	6.12304i	0.796553	−	0.213436i	0.634070	+	0.773276i	$0.281383\pi$
$824$			21.8408i			0.760862i
$825$	35.3394	−	13.5676i	1.23036	−	0.472364i
$826$	0.748883	−	1.29710i	0.0260570	−	0.0451320i
$827$	5.59136	−	3.22817i	0.194431	−	0.112255i	−0.399624	−	0.916679i	$-0.630859\pi$
$827$	5.59136	−	3.22817i	0.194431	−	0.112255i	0.594055	+	0.804424i	$0.297526\pi$
$828$		−	0.388820i		−	0.0135124i
$829$	2.90505	+	10.8418i	0.100897	+	0.376551i	0.997847	−	0.0655791i	$-0.0208895\pi$
$829$	2.90505	+	10.8418i	0.100897	+	0.376551i	−0.896951	+	0.442131i	$0.854223\pi$
$830$	1.47866	−	1.64231i	0.0513252	−	0.0570054i
$831$	8.72547	+	32.5639i	0.302683	+	1.12963i
$832$	−9.84490	−	17.0519i	−0.341310	−	0.591167i
$833$	−5.45709	−	9.45196i	−0.189077	−	0.327491i
$834$	8.67656	+	32.3814i	0.300445	+	1.12127i
$835$	4.13435	−	0.216781i	0.143075	−	0.00750201i
$836$	3.31636	+	12.3768i	0.114699	+	0.428062i
$837$		−	43.8626i		−	1.51611i
$838$	−25.2550	+	14.5810i	−0.872420	+	0.503692i
$839$	−19.3905	+	33.5854i	−0.669435	+	1.15950i	0.308628	+	0.951183i	$0.400130\pi$
$839$	−19.3905	+	33.5854i	−0.669435	+	1.15950i	−0.978062	+	0.208312i	$0.933203\pi$
$840$	7.58585	+	11.6805i	0.261737	+	0.403016i
$841$			23.3593i			0.805492i
$842$	−7.26211	+	1.94588i	−0.250269	+	0.0670593i
$843$			36.6328i			1.26170i
$844$	−12.3156	−	21.3312i	−0.423920	−	0.734251i
$845$	−21.0302	+	13.6579i	−0.723460	+	0.469847i
$846$	0.245275	−	0.915380i	0.00843274	−	0.0314714i
$847$	7.19061	+	1.92672i	0.247072	+	0.0662028i
$848$	−0.362190	+	1.35171i	−0.0124376	+	0.0464179i
$849$	19.7176	−	5.28331i	0.676705	−	0.181323i
$850$	−7.52061	−	3.34792i	−0.257955	−	0.114833i
$851$	0.764883	−	4.77083i	0.0262199	−	0.163542i
$852$	11.3369	−	11.3369i	0.388395	−	0.388395i
$853$	33.5407	+	19.3647i	1.14841	+	0.663035i	0.948499	−	0.316779i	$-0.102601\pi$
$853$	33.5407	+	19.3647i	1.14841	+	0.663035i	0.199911	+	0.979814i	$0.435935\pi$
$854$	3.40435	+	5.89651i	0.116494	+	0.201774i
$855$	−1.85418	+	0.602513i	−0.0634116	+	0.0206055i
$856$	5.71835	+	1.53223i	0.195449	+	0.0523705i
$857$			32.5958i			1.11345i	0.830696	+	0.556726i	$0.187943\pi$
$857$			32.5958i			1.11345i	−0.830696	+	0.556726i	$0.812057\pi$
$858$	7.94669	−	29.6574i	0.271295	−	1.01249i
$859$	−25.5200	−	25.5200i	−0.870731	−	0.870731i	0.121821	−	0.992552i	$-0.461127\pi$
$859$	−25.5200	−	25.5200i	−0.870731	−	0.870731i	−0.992552	+	0.121821i	$0.961127\pi$
$860$	−1.76598	−	33.6800i	−0.0602194	−	1.14848i
$861$	−25.6055			−0.872633
$862$	−14.9705	−	14.9705i	−0.509898	−	0.509898i
$863$	−7.88799	+	2.11358i	−0.268510	+	0.0719471i	−0.390562	−	0.920577i	$-0.627719\pi$
$863$	−7.88799	+	2.11358i	−0.268510	+	0.0719471i	0.122052	+	0.992524i	$0.461053\pi$
$864$	−7.23629	+	27.0062i	−0.246183	+	0.918769i
$865$	0.933954	−	4.39447i	0.0317554	−	0.149417i
$866$	19.1617	−	5.13435i	0.651139	−	0.174472i
$867$	−6.18156	−	23.0699i	−0.209937	−	0.783495i
$868$	7.43831	−	12.8835i	0.252473	−	0.437296i
$869$	35.4527	+	9.49953i	1.20265	+	0.322250i
$870$	−3.64787	+	7.15981i	−0.123674	+	0.242740i
$871$	−28.0824	+	7.52466i	−0.951536	+	0.254963i
$872$	−28.5464	+	7.64898i	−0.966703	+	0.259027i
$873$	−2.18033	+	3.77645i	−0.0737931	+	0.127813i
$874$	1.08904	+	1.08904i	0.0368374	+	0.0368374i
$875$	1.44763	−	13.7837i	0.0489387	−	0.465973i
$876$	−15.2802	−	8.82200i	−0.516269	−	0.298068i
$877$	9.48217	−	9.48217i	0.320190	−	0.320190i	−0.528650	−	0.848840i	$-0.677302\pi$
$877$	9.48217	−	9.48217i	0.320190	−	0.320190i	0.848840	+	0.528650i	$0.177302\pi$
$878$	−8.68201	+	8.68201i	−0.293004	+	0.293004i
$879$	−26.7167	+	46.2747i	−0.901131	+	1.56081i
$880$	1.93851	+	2.98487i	0.0653470	+	0.100620i
$881$	−18.1684	+	10.4895i	−0.612110	+	0.353402i	−0.773791	−	0.633441i	$-0.781642\pi$
$881$	−18.1684	+	10.4895i	−0.612110	+	0.353402i	0.161681	+	0.986843i	$0.448308\pi$
$882$	1.66871			0.0561885
$883$	21.2792	−	12.2856i	0.716103	−	0.413442i	−0.0972140	−	0.995264i	$-0.530993\pi$
$883$	21.2792	−	12.2856i	0.716103	−	0.413442i	0.813316	+	0.581822i	$0.197660\pi$
$884$	11.2442	−	6.49185i	0.378184	−	0.218345i
$885$	5.36253	+	2.73217i	0.180260	+	0.0918409i
$886$	5.76777	+	21.5256i	0.193772	+	0.723167i
$887$	7.43917	+	7.43917i	0.249783	+	0.249783i	0.820881	−	0.571099i	$-0.193483\pi$
$887$	7.43917	+	7.43917i	0.249783	+	0.249783i	−0.571099	+	0.820881i	$0.693483\pi$
$888$	12.4841	−	27.8975i	0.418938	−	0.936179i
$889$			4.69111i			0.157335i
$890$	−9.92798	−	8.93872i	−0.332787	−	0.299627i
$891$	−35.6215	+	20.5661i	−1.19336	+	0.688990i
$892$	−3.78339	+	14.1198i	−0.126677	+	0.472766i
$893$	−3.64964	−	6.32136i	−0.122130	−	0.211536i
$894$	16.4586	+	16.4586i	0.550457	+	0.550457i
$895$	−49.6898	+	16.1466i	−1.66095	+	0.539722i
$896$	−7.26292	+	7.26292i	−0.242637	+	0.242637i
$897$	1.85734	+	6.93168i	0.0620148	+	0.231442i
$898$	−4.13547	−	4.13547i	−0.138002	−	0.138002i
$899$	21.5801			0.719735
$900$	−1.97996	+	1.43868i	−0.0659986	+	0.0479560i
$901$	6.99606	+	1.87459i	0.233073	+	0.0624516i
$902$	38.2372			1.27316
$903$	22.5078	+	12.9949i	0.749012	+	0.432442i
$904$	5.11721	+	2.95442i	0.170196	+	0.0982627i
$905$	−0.142625	−	2.72008i	−0.00474101	−	0.0904185i
$906$	6.43500	−	24.0157i	0.213788	−	0.797870i
$907$	30.9017	−	17.8411i	1.02607	−	0.592404i	0.110216	−	0.993908i	$-0.464846\pi$
$907$	30.9017	−	17.8411i	1.02607	−	0.592404i	0.915857	+	0.401504i	$0.131512\pi$
$908$	9.62885	+	5.55922i	0.319545	+	0.184489i
$909$	−0.582974	+	1.00974i	−0.0193360	+	0.0334910i
$910$	−8.35420	−	7.52176i	−0.276939	−	0.249344i
$911$	−14.7906	+	14.7906i	−0.490033	+	0.490033i	−0.908317	−	0.418283i	$-0.862632\pi$
$911$	−14.7906	+	14.7906i	−0.490033	+	0.490033i	0.418283	+	0.908317i	$0.362632\pi$
$912$	−0.833558	−	1.44376i	−0.0276019	−	0.0478078i
$913$	1.27987	+	4.77654i	0.0423575	+	0.158080i
$914$			10.7979i			0.357163i
$915$	−22.9450	+	14.9015i	−0.758537	+	0.492628i
$916$	23.3177	+	13.4625i	0.770440	+	0.444814i
$917$	12.2466			0.404418
$918$	7.67707	+	2.05707i	0.253381	+	0.0678933i
$919$	−11.5779	+	11.5779i	−0.381920	+	0.381920i	−0.871794	−	0.489873i	$-0.837043\pi$
$919$	−11.5779	+	11.5779i	−0.381920	+	0.381920i	0.489873	+	0.871794i	$0.337043\pi$
$920$	4.33135	+	2.20679i	0.142800	+	0.0727557i
$921$	−22.8342	−	39.5499i	−0.752411	−	1.30321i
$922$	17.4262	+	4.66933i	0.573901	+	0.153776i
$923$	−16.2679	+	28.1769i	−0.535466	+	0.927454i
$924$	−12.3955			−0.407783
$925$	−27.1243	+	13.7577i	−0.891840	+	0.452350i
$926$	−22.3916			−0.735835
$927$	1.47880	−	2.56136i	0.0485701	−	0.0841259i
$928$	−13.2868	−	3.56020i	−0.436162	−	0.116869i
$929$	−7.03355	−	12.1825i	−0.230763	−	0.399694i	0.727270	−	0.686352i	$-0.240789\pi$
$929$	−7.03355	−	12.1825i	−0.230763	−	0.399694i	−0.958033	+	0.286658i	$0.907456\pi$
$930$	−27.3917	−	13.9559i	−0.898209	−	0.457631i
$931$	9.08842	−	9.08842i	0.297861	−	0.297861i
$932$	11.5860	+	3.10447i	0.379513	+	0.101690i
$933$	39.9784			1.30884
$934$	8.15879	+	4.71048i	0.266964	+	0.154132i
$935$	15.4488	−	10.0331i	0.505230	−	0.328119i
$936$			4.99115i			0.163141i
$937$	−6.57057	−	24.5217i	−0.214651	−	0.801090i	−0.986289	−	0.165027i	$-0.947229\pi$
$937$	−6.57057	−	24.5217i	−0.214651	−	0.801090i	0.771638	−	0.636062i	$-0.219438\pi$
$938$	−3.01803	−	5.22739i	−0.0985423	−	0.170680i
$939$	37.5039	−	37.5039i	1.22389	−	1.22389i
$940$	−6.80972	−	6.13117i	−0.222108	−	0.199977i
$941$	29.3296	−	50.8003i	0.956116	−	1.65604i	0.224324	−	0.974515i	$-0.427983\pi$
$941$	29.3296	−	50.8003i	0.956116	−	1.65604i	0.731793	−	0.681527i	$-0.238684\pi$
$942$	−11.1223	−	6.42146i	−0.362384	−	0.209223i
$943$	−7.73966	+	4.46850i	−0.252038	+	0.145514i
$944$	−0.146455	+	0.546578i	−0.00476671	+	0.0177896i
$945$	0.700654	+	13.3626i	0.0227923	+	0.434684i
$946$	−33.6114	−	19.4055i	−1.09280	−	0.630928i
$947$	35.2526	+	20.3531i	1.14555	+	0.661386i	0.947800	−	0.318865i	$-0.103302\pi$
$947$	35.2526	+	20.3531i	1.14555	+	0.661386i	0.197754	+	0.980252i	$0.436635\pi$
$948$	−21.5822			−0.700959
$949$	34.5856	+	9.26719i	1.12270	+	0.300826i
$950$	1.51605	−	9.57521i	0.0491872	−	0.310661i
$951$	2.02058			0.0655217
$952$	4.79246	+	4.79246i	0.155325	+	0.155325i
$953$	1.80402	+	6.73269i	0.0584379	+	0.218093i	0.988970	−	0.148118i	$-0.0473215\pi$
$953$	1.80402	+	6.73269i	0.0584379	+	0.218093i	−0.930532	+	0.366211i	$0.880655\pi$
$954$	−0.783042	+	0.783042i	−0.0253519	+	0.0253519i
$955$	−16.4546	+	5.34689i	−0.532458	+	0.173021i
$956$	5.61556	+	5.61556i	0.181620	+	0.181620i
$957$	−8.99049	−	15.5720i	−0.290621	−	0.503371i
$958$	−2.09459	+	7.81712i	−0.0676731	+	0.252560i
$959$	−22.7193	+	13.1170i	−0.733644	+	0.423570i
$960$	12.2075	+	10.9911i	0.393996	+	0.354737i
$961$			51.5600i			1.66323i
$962$	−3.90513	+	24.3576i	−0.125906	+	0.785320i
$963$	−0.566868	−	0.566868i	−0.0182671	−	0.0182671i
$964$	−0.0894775	−	0.333935i	−0.00288188	−	0.0107553i
$965$	40.7147	+	20.7438i	1.31065	+	0.667768i
$966$	−1.29030	+	0.744953i	−0.0415146	+	0.0239685i
$967$	0.886281	−	0.511694i	0.0285009	−	0.0164550i	−0.485682	−	0.874136i	$-0.661429\pi$
$967$	0.886281	−	0.511694i	0.0285009	−	0.0164550i	0.514183	+	0.857681i	$0.328095\pi$
$968$	16.4353			0.528250
$969$	−7.47251	+	4.31425i	−0.240052	+	0.138594i
$970$	−11.8101	−	18.1850i	−0.379201	−	0.583884i
$971$	7.81561	−	13.5370i	0.250815	−	0.434424i	−0.712936	−	0.701230i	$-0.752635\pi$
$971$	7.81561	−	13.5370i	0.250815	−	0.434424i	0.963750	+	0.266805i	$0.0859681\pi$
$972$	3.57722	−	3.57722i	0.114739	−	0.114739i
$973$	−19.4208	+	19.4208i	−0.622601	+	0.622601i
$974$	−20.5246	−	11.8499i	−0.657652	−	0.379695i
$975$	28.4253	−	35.1060i	0.910337	−	1.12429i
$976$	−1.81892	−	1.81892i	−0.0582222	−	0.0582222i
$977$	−10.6345	+	18.4196i	−0.340229	+	0.589295i	−0.984475	−	0.175524i	$-0.943838\pi$
$977$	−10.6345	+	18.4196i	−0.340229	+	0.589295i	0.644246	+	0.764819i	$0.277171\pi$
$978$	1.38574	−	0.371308i	0.0443111	−	0.0118731i
$979$	28.8748	−	7.73698i	0.922843	−	0.247275i
$980$	7.32476	−	14.3766i	0.233981	−	0.459243i
$981$	3.86564	+	1.03579i	0.123420	+	0.0330704i
$982$	−12.9845	+	22.4898i	−0.414351	+	0.717677i
$983$	−12.3694	−	46.1634i	−0.394524	−	1.47238i	−0.822590	−	0.568635i	$-0.807472\pi$
$983$	−12.3694	−	46.1634i	−0.394524	−	1.47238i	0.428066	−	0.903748i	$-0.359195\pi$
$984$	−54.6049	+	14.6313i	−1.74074	+	0.466430i
$985$	−12.8981	+	60.6888i	−0.410969	+	1.93370i
$986$	−1.01206	+	3.77706i	−0.0322306	+	0.120286i
$987$	6.82060	−	1.82757i	0.217102	−	0.0581723i
$988$	10.8118	+	10.8118i	0.343968	+	0.343968i
$989$	9.07111			0.288445
$990$	0.147475	+	2.81258i	0.00468706	+	0.0893897i
$991$	−35.6021	−	35.6021i	−1.13094	−	1.13094i	−0.990021	−	0.140916i	$-0.954995\pi$
$991$	−35.6021	−	35.6021i	−1.13094	−	1.13094i	−0.140916	−	0.990021i	$-0.545005\pi$
$992$	13.6204	−	50.8322i	0.432450	−	1.61392i
$993$			3.57997i			0.113607i
$994$	−6.52484	−	1.74833i	−0.206955	−	0.0554535i
$995$	−38.5681	+	12.5327i	−1.22269	+	0.397312i
$996$	−1.45388	−	2.51820i	−0.0460681	−	0.0797923i
$997$	−25.4796	−	14.7106i	−0.806947	−	0.465891i	0.0389477	−	0.999241i	$-0.487599\pi$
$997$	−25.4796	−	14.7106i	−0.806947	−	0.465891i	−0.845894	+	0.533350i	$0.820933\pi$
$998$	−17.3085	+	17.3085i	−0.547890	+	0.547890i
$999$	23.7883	−	17.2145i	0.752629	−	0.544644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.88.7	yes	68
5.2	odd	4		185.2.u.a.162.7	yes	68
5.3	odd	4		925.2.y.b.532.11		68
5.4	even	2		925.2.t.b.643.11		68
37.8	odd	12		185.2.u.a.8.7	yes	68
185.8	even	12		925.2.t.b.82.11		68
185.82	even	12	inner	185.2.p.a.82.7	✓	68
185.119	odd	12		925.2.y.b.193.11		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.7	✓	68	185.82	even	12	inner
185.2.p.a.88.7	yes	68	1.1	even	1	trivial
185.2.u.a.8.7	yes	68	37.8	odd	12
185.2.u.a.162.7	yes	68	5.2	odd	4
925.2.t.b.82.11		68	185.8	even	12
925.2.t.b.643.11		68	5.4	even	2
925.2.y.b.193.11		68	185.119	odd	12
925.2.y.b.532.11		68	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.412077 + 0.713738i) q^{2} +(1.77336 + 0.475172i) q^{3} +(0.660386 + 1.14382i) q^{4} +(1.99238 + 1.01510i) q^{5} +(-1.06991 + 1.06991i) q^{6} +(-1.19739 - 0.320840i) q^{7} -2.73682 q^{8} +(0.320958 + 0.185305i) q^{9} +(-1.54553 + 1.00374i) q^{10} -4.12374i q^{11} +(0.627593 + 2.34221i) q^{12} +(-2.46040 - 4.26154i) q^{13} +(0.722412 - 0.722412i) q^{14} +(3.05086 + 2.74687i) q^{15} +(-0.192990 + 0.334268i) q^{16} +(1.73008 + 0.998860i) q^{17} +(-0.264518 + 0.152720i) q^{18} +(-0.608896 + 2.27243i) q^{19} +(0.154643 + 2.94928i) q^{20} +(-1.97096 - 1.13793i) q^{21} +(2.94327 + 1.69930i) q^{22} -0.794336 q^{23} +(-4.85339 - 1.30046i) q^{24} +(2.93914 + 4.04493i) q^{25} +4.05550 q^{26} +(-3.41346 - 3.41346i) q^{27} +(-0.423756 - 1.58148i) q^{28} +(1.67939 - 1.67939i) q^{29} +(-3.21773 + 1.04560i) q^{30} +(6.42495 + 6.42495i) q^{31} +(-2.89588 - 5.01581i) q^{32} +(1.95948 - 7.31290i) q^{33} +(-1.42585 + 0.823214i) q^{34} +(-2.05997 - 1.85471i) q^{35} +0.489491i q^{36} +(-0.962921 + 6.00606i) q^{37} +(-1.37101 - 1.37101i) q^{38} +(-2.33823 - 8.72639i) q^{39} +(-5.45279 - 2.77815i) q^{40} +(9.74356 - 5.62545i) q^{41} +(1.62437 - 0.937830i) q^{42} -11.4197 q^{43} +(4.71682 - 2.72326i) q^{44} +(0.451365 + 0.695002i) q^{45} +(0.327327 - 0.566948i) q^{46} +(-2.19390 + 2.19390i) q^{47} +(-0.501076 + 0.501076i) q^{48} +(-4.73137 - 2.73166i) q^{49} +(-4.09817 + 0.430952i) q^{50} +(2.59343 + 2.59343i) q^{51} +(3.24963 - 5.62853i) q^{52} +(3.50202 - 0.938365i) q^{53} +(3.84292 - 1.02971i) q^{54} +(4.18601 - 8.21605i) q^{55} +(3.27705 + 0.878082i) q^{56} +(-2.15959 + 3.74052i) q^{57} +(0.506608 + 1.89069i) q^{58} +(1.41608 - 0.379437i) q^{59} +(-1.12718 + 5.30364i) q^{60} +(-1.72489 + 6.43736i) q^{61} +(-7.23330 + 1.93816i) q^{62} +(-0.324858 - 0.324858i) q^{63} +4.00134 q^{64} +(-0.576154 - 10.9882i) q^{65} +(4.41203 + 4.41203i) q^{66} +(1.52915 - 5.70687i) q^{67} +2.63853i q^{68} +(-1.40865 - 0.377446i) q^{69} +(2.17264 - 0.705996i) q^{70} +(-3.30595 - 5.72607i) q^{71} +(-0.878404 - 0.507147i) q^{72} +(-5.14518 + 5.14518i) q^{73} +(-3.88996 - 3.16223i) q^{74} +(3.29013 + 8.56973i) q^{75} +(-3.00136 + 0.804213i) q^{76} +(-1.32306 + 4.93773i) q^{77} +(7.19188 + 1.92706i) q^{78} +(-2.30362 + 8.59723i) q^{79} +(-0.723825 + 0.470084i) q^{80} +(-4.98724 - 8.63815i) q^{81} +9.27246i q^{82} +(-1.15830 + 0.310366i) q^{83} -3.00590i q^{84} +(2.43302 + 3.74631i) q^{85} +(4.70581 - 8.15069i) q^{86} +(3.77618 - 2.18018i) q^{87} +11.2860i q^{88} +(1.87621 + 7.00209i) q^{89} +(-0.682046 + 0.0357624i) q^{90} +(1.57879 + 5.89213i) q^{91} +(-0.524568 - 0.908579i) q^{92} +(8.34083 + 14.4467i) q^{93} +(-0.661816 - 2.46993i) q^{94} +(-3.51990 + 3.90945i) q^{95} +(-2.75208 - 10.2709i) q^{96} +11.7662i q^{97} +(3.89938 - 2.25131i) q^{98} +(0.764149 - 1.32355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

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