LMFDB - Embedded newform 361.2.k.a.4.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(4,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(342)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.k (of order $171$, degree $108$, 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$3348$
Relative dimension:	$31$ over $\Q(\zeta_{171})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{171}]$

Embedding invariants

Embedding label			4.13
Character	$\chi$	$=$	361.4
Dual form			361.2.k.a.271.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.720055 - 0.0132303i) q^{2} +(-1.41262 + 0.941535i) q^{3} +(-1.48035 - 0.0544180i) q^{4} +(1.90263 + 3.93762i) q^{5} +(1.02962 - 0.659268i) q^{6} +(-4.52008 + 1.83590i) q^{7} +(2.50338 + 0.138115i) q^{8} +(-0.0454172 + 0.108939i) q^{9} +(-1.31790 - 2.86047i) q^{10} +(0.977593 - 3.12554i) q^{11} +(2.14240 - 1.31693i) q^{12} +(2.07594 - 0.505453i) q^{13} +(3.27900 - 1.26215i) q^{14} +(-6.39509 - 3.77095i) q^{15} +(1.15395 + 0.0849541i) q^{16} +(-2.01084 - 3.20490i) q^{17} +(0.0341442 - 0.0778409i) q^{18} +(-3.10935 + 3.05482i) q^{19} +(-2.60227 - 5.93257i) q^{20} +(4.65658 - 6.84924i) q^{21} +(-0.745272 + 2.23763i) q^{22} +(0.770458 - 0.381048i) q^{23} +(-3.66635 + 2.16191i) q^{24} +(-8.77766 + 11.0663i) q^{25} +(-1.50148 + 0.336489i) q^{26} +(-1.01478 - 5.19510i) q^{27} +(6.79119 - 2.47179i) q^{28} +(4.39265 + 1.41834i) q^{29} +(4.55492 + 2.79990i) q^{30} +(0.633831 - 0.552003i) q^{31} +(-5.82301 - 0.536408i) q^{32} +(1.56184 + 5.33562i) q^{33} +(1.40551 + 2.33431i) q^{34} +(-15.8291 - 14.3053i) q^{35} +(0.0731613 - 0.158795i) q^{36} +(-6.08282 - 6.60770i) q^{37} +(2.27932 - 2.15850i) q^{38} +(-2.45660 + 2.66858i) q^{39} +(4.21915 + 10.1201i) q^{40} +(2.23615 + 6.32391i) q^{41} +(-3.44361 + 4.87022i) q^{42} +(-3.49734 - 4.94621i) q^{43} +(-1.61726 + 4.57368i) q^{44} +(-0.515370 + 0.0284338i) q^{45} +(-0.559814 + 0.264182i) q^{46} +(0.630913 + 0.326593i) q^{47} +(-1.71008 + 0.966479i) q^{48} +(12.0431 - 11.7157i) q^{49} +(6.46681 - 7.85222i) q^{50} +(5.85807 + 2.63402i) q^{51} +(-3.10061 + 0.635277i) q^{52} +(0.110211 + 2.39787i) q^{53} +(0.661964 + 3.75418i) q^{54} +(14.1672 - 2.09734i) q^{55} +(-11.5690 + 3.97165i) q^{56} +(1.51609 - 7.24286i) q^{57} +(-3.14419 - 1.07940i) q^{58} +(1.68971 + 0.313972i) q^{59} +(9.26173 + 5.93032i) q^{60} +(-0.699872 + 5.83284i) q^{61} +(-0.463696 + 0.389087i) q^{62} +(0.00528934 - 0.575792i) q^{63} +(1.88569 + 0.208708i) q^{64} +(5.94002 + 7.21256i) q^{65} +(-1.05402 - 3.86261i) q^{66} +(-2.05342 + 8.78383i) q^{67} +(2.80233 + 4.85378i) q^{68} +(-0.729591 + 1.26369i) q^{69} +(11.2086 + 10.5100i) q^{70} +(1.30323 + 10.8614i) q^{71} +(-0.128742 + 0.266441i) q^{72} +(1.92353 - 3.63373i) q^{73} +(4.29254 + 4.83839i) q^{74} +(1.98015 - 23.8969i) q^{75} +(4.76915 - 4.35299i) q^{76} +(1.31937 + 15.9224i) q^{77} +(1.80419 - 1.88902i) q^{78} +(-2.13155 + 0.196355i) q^{79} +(1.86102 + 4.70546i) q^{80} +(6.07564 + 6.13171i) q^{81} +(-1.52648 - 4.58315i) q^{82} +(-6.95081 - 1.96550i) q^{83} +(-7.26606 + 9.88583i) q^{84} +(8.79379 - 14.0156i) q^{85} +(2.45284 + 3.60782i) q^{86} +(-7.54055 + 2.13226i) q^{87} +(2.87897 - 7.68938i) q^{88} +(-5.93665 - 11.2149i) q^{89} +(0.371471 - 0.0136554i) q^{90} +(-8.45545 + 6.09590i) q^{91} +(-1.16128 + 0.522156i) q^{92} +(-0.375628 + 1.37654i) q^{93} +(-0.449972 - 0.243512i) q^{94} +(-17.9447 - 6.43125i) q^{95} +(8.73073 - 4.72483i) q^{96} +(1.63780 + 7.00595i) q^{97} +(-8.82672 + 8.27664i) q^{98} +(0.296092 + 0.248451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) $ 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{171}\right)$

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 $

$2$	−0.720055	−	0.0132303i	−0.509156	−	0.00935521i	−0.236813	−	0.971555i	$-0.576103\pi$
$2$	−0.720055	−	0.0132303i	−0.509156	−	0.00935521i	−0.272343	+	0.962200i	$0.587799\pi$
$3$	−1.41262	+	0.941535i	−0.815574	+	0.543596i	−0.891237	−	0.453538i	$-0.850162\pi$
$3$	−1.41262	+	0.941535i	−0.815574	+	0.543596i	0.0756628	+	0.997133i	$0.475893\pi$
$4$	−1.48035	−	0.0544180i	−0.740173	−	0.0272090i
$5$	1.90263	+	3.93762i	0.850880	+	1.76096i	0.613792	+	0.789468i	$0.289643\pi$
$5$	1.90263	+	3.93762i	0.850880	+	1.76096i	0.237088	+	0.971488i	$0.423807\pi$
$6$	1.02962	−	0.659268i	0.420340	−	0.269145i
$7$	−4.52008	+	1.83590i	−1.70843	+	0.693904i	−0.999930	−	0.0118069i	$-0.996242\pi$
$7$	−4.52008	+	1.83590i	−1.70843	+	0.693904i	−0.708500	+	0.705711i	$0.750628\pi$
$8$	2.50338	+	0.138115i	0.885077	+	0.0488311i
$9$	−0.0454172	+	0.108939i	−0.0151391	+	0.0363128i
$10$	−1.31790	−	2.86047i	−0.416757	−	0.904561i
$11$	0.977593	−	3.12554i	0.294755	−	0.942385i	−0.682602	−	0.730790i	$-0.739152\pi$
$11$	0.977593	−	3.12554i	0.294755	−	0.942385i	0.977357	−	0.211595i	$-0.0678658\pi$
$12$	2.14240	−	1.31693i	0.618457	−	0.380164i
$13$	2.07594	−	0.505453i	0.575762	−	0.140187i	0.0619330	−	0.998080i	$-0.480273\pi$
$13$	2.07594	−	0.505453i	0.575762	−	0.140187i	0.513829	+	0.857893i	$0.328227\pi$
$14$	3.27900	−	1.26215i	0.876349	−	0.337323i
$15$	−6.39509	−	3.77095i	−1.65120	−	0.973655i
$16$	1.15395	+	0.0849541i	0.288488	+	0.0212385i
$17$	−2.01084	−	3.20490i	−0.487700	−	0.777302i	0.508801	−	0.860884i	$-0.330089\pi$
$17$	−2.01084	−	3.20490i	−0.487700	−	0.777302i	−0.996501	+	0.0835821i	$0.973364\pi$
$18$	0.0341442	−	0.0778409i	0.00804786	−	0.0183473i
$19$	−3.10935	+	3.05482i	−0.713334	+	0.700824i
$19$	−3.10935	+	3.05482i	−0.713334	+	0.700824i
$20$	−2.60227	−	5.93257i	−0.581885	−	1.32656i
$21$	4.65658	−	6.84924i	1.01615	−	1.49463i
$22$	−0.745272	+	2.23763i	−0.158893	+	0.477064i
$23$	0.770458	−	0.381048i	0.160652	−	0.0794541i	−0.361209	−	0.932485i	$-0.617636\pi$
$23$	0.770458	−	0.381048i	0.160652	−	0.0794541i	0.521860	+	0.853031i	$0.325238\pi$
$24$	−3.66635	+	2.16191i	−0.748391	+	0.441299i
$25$	−8.77766	+	11.0663i	−1.75553	+	2.21326i
$26$	−1.50148	+	0.336489i	−0.294464	+	0.0659909i
$27$	−1.01478	−	5.19510i	−0.195294	−	0.999797i
$28$	6.79119	−	2.47179i	1.28341	−	0.467124i
$29$	4.39265	+	1.41834i	0.815695	+	0.263380i	0.685466	−	0.728104i	$-0.259598\pi$
$29$	4.39265	+	1.41834i	0.815695	+	0.263380i	0.130229	+	0.991484i	$0.458429\pi$
$30$	4.55492	+	2.79990i	0.831612	+	0.511190i
$31$	0.633831	−	0.552003i	0.113839	−	0.0991428i	−0.597959	−	0.801527i	$-0.704021\pi$
$31$	0.633831	−	0.552003i	0.113839	−	0.0991428i	0.711798	+	0.702384i	$0.247881\pi$
$32$	−5.82301	−	0.536408i	−1.02937	−	0.0948245i
$33$	1.56184	+	5.33562i	0.271882	+	0.928813i
$34$	1.40551	+	2.33431i	0.241044	+	0.400331i
$35$	−15.8291	−	14.3053i	−2.67560	−	2.41804i
$36$	0.0731613	−	0.158795i	0.0121936	−	0.0264659i
$37$	−6.08282	−	6.60770i	−1.00001	−	1.08630i	−0.996269	−	0.0863064i	$-0.972494\pi$
$37$	−6.08282	−	6.60770i	−1.00001	−	1.08630i	−0.00374045	−	0.999993i	$-0.501191\pi$
$38$	2.27932	−	2.15850i	0.369755	−	0.350155i
$39$	−2.45660	+	2.66858i	−0.393371	+	0.427315i
$40$	4.21915	+	10.1201i	0.667105	+	1.60013i
$41$	2.23615	+	6.32391i	0.349227	+	0.987629i	0.977738	+	0.209828i	$0.0672904\pi$
$41$	2.23615	+	6.32391i	0.349227	+	0.987629i	−0.628511	+	0.777801i	$0.716335\pi$
$42$	−3.44361	+	4.87022i	−0.531360	+	0.751491i
$43$	−3.49734	−	4.94621i	−0.533339	−	0.754290i	0.457518	−	0.889200i	$-0.348738\pi$
$43$	−3.49734	−	4.94621i	−0.533339	−	0.754290i	−0.990858	+	0.134910i	$0.956926\pi$
$44$	−1.61726	+	4.57368i	−0.243811	+	0.689508i
$45$	−0.515370	+	0.0284338i	−0.0768268	+	0.00423865i
$46$	−0.559814	+	0.264182i	−0.0825400	+	0.0389516i
$47$	0.630913	+	0.326593i	0.0920282	+	0.0476385i	0.505107	−	0.863057i	$-0.331453\pi$
$47$	0.630913	+	0.326593i	0.0920282	+	0.0476385i	−0.413079	+	0.910695i	$0.635547\pi$
$48$	−1.71008	+	0.966479i	−0.246829	+	0.139499i
$49$	12.0431	−	11.7157i	1.72045	−	1.67368i
$50$	6.46681	−	7.85222i	0.914545	−	1.11047i
$51$	5.85807	+	2.63402i	0.820294	+	0.368836i
$52$	−3.10061	+	0.635277i	−0.429977	+	0.0880971i
$53$	0.110211	+	2.39787i	0.0151386	+	0.329373i	0.992846	+	0.119401i	$0.0380974\pi$
$53$	0.110211	+	2.39787i	0.0151386	+	0.329373i	−0.977707	+	0.209972i	$0.932663\pi$
$54$	0.661964	+	3.75418i	0.0900818	+	0.510880i
$55$	14.1672	−	2.09734i	1.91030	−	0.282806i
$56$	−11.5690	+	3.97165i	−1.54598	+	0.530735i
$57$	1.51609	−	7.24286i	0.200812	−	0.959340i
$58$	−3.14419	−	1.07940i	−0.412852	−	0.141732i
$59$	1.68971	+	0.313972i	0.219981	+	0.0408757i	0.291531	−	0.956561i	$-0.405835\pi$
$59$	1.68971	+	0.313972i	0.219981	+	0.0408757i	−0.0715496	+	0.997437i	$0.522794\pi$
$60$	9.26173	+	5.93032i	1.19568	+	0.765601i
$61$	−0.699872	+	5.83284i	−0.0896094	+	0.746818i	0.875180	+	0.483797i	$0.160743\pi$
$61$	−0.699872	+	5.83284i	−0.0896094	+	0.746818i	−0.964790	+	0.263022i	$0.915281\pi$
$62$	−0.463696	+	0.389087i	−0.0588895	+	0.0494141i
$63$	0.00528934	−	0.575792i	0.000666395	−	0.0725430i
$64$	1.88569	+	0.208708i	0.235711	+	0.0260885i
$65$	5.94002	+	7.21256i	0.736768	+	0.894608i
$66$	−1.05402	−	3.86261i	−0.129741	−	0.475454i
$67$	−2.05342	+	8.78383i	−0.250865	+	1.07312i	0.687148	+	0.726517i	$0.258862\pi$
$67$	−2.05342	+	8.78383i	−0.250865	+	1.07312i	−0.938014	+	0.346599i	$0.887337\pi$
$68$	2.80233	+	4.85378i	0.339833	+	0.588608i
$69$	−0.729591	+	1.26369i	−0.0878324	+	0.152130i
$70$	11.2086	+	10.5100i	1.33968	+	1.25619i
$71$	1.30323	+	10.8614i	0.154665	+	1.28901i	0.832597	+	0.553880i	$0.186853\pi$
$71$	1.30323	+	10.8614i	0.154665	+	1.28901i	−0.677931	+	0.735125i	$0.737123\pi$
$72$	−0.128742	+	0.266441i	−0.0151724	+	0.0314004i
$73$	1.92353	−	3.63373i	0.225132	−	0.425295i	−0.745279	−	0.666753i	$-0.767684\pi$
$73$	1.92353	−	3.63373i	0.225132	−	0.425295i	0.970411	+	0.241457i	$0.0776253\pi$
$74$	4.29254	+	4.83839i	0.498998	+	0.562451i
$75$	1.98015	−	23.8969i	0.228649	−	2.75938i
$76$	4.76915	−	4.35299i	0.547059	−	0.499322i
$77$	1.31937	+	15.9224i	0.150356	+	1.81453i
$78$	1.80419	−	1.88902i	0.204285	−	0.213890i
$79$	−2.13155	+	0.196355i	−0.239818	+	0.0220917i	−0.210972	−	0.977492i	$-0.567663\pi$
$79$	−2.13155	+	0.196355i	−0.239818	+	0.0220917i	−0.0288462	+	0.999584i	$0.509183\pi$
$80$	1.86102	+	4.70546i	0.208069	+	0.526086i
$81$	6.07564	+	6.13171i	0.675071	+	0.681301i
$82$	−1.52648	−	4.58315i	−0.168572	−	0.506124i
$83$	−6.95081	−	1.96550i	−0.762950	−	0.215742i	−0.131667	−	0.991294i	$-0.542033\pi$
$83$	−6.95081	−	1.96550i	−0.762950	−	0.215742i	−0.631283	+	0.775552i	$0.717472\pi$
$84$	−7.26606	+	9.88583i	−0.792792	+	1.07863i
$85$	8.79379	−	14.0156i	0.953820	−	1.52021i
$86$	2.45284	+	3.60782i	0.264496	+	0.389041i
$87$	−7.54055	+	2.13226i	−0.808432	+	0.228603i
$88$	2.87897	−	7.68938i	0.306899	−	0.819691i
$89$	−5.93665	−	11.2149i	−0.629284	−	1.18877i	−0.968723	−	0.248146i	$-0.920179\pi$
$89$	−5.93665	−	11.2149i	−0.629284	−	1.18877i	0.339439	−	0.940628i	$-0.389763\pi$
$90$	0.371471	−	0.0136554i	0.0391565	−	0.00143940i
$91$	−8.45545	+	6.09590i	−0.886372	+	0.639024i
$92$	−1.16128	+	0.522156i	−0.121072	+	0.0544386i
$93$	−0.375628	+	1.37654i	−0.0389508	+	0.142741i
$94$	−0.449972	−	0.243512i	−0.0464110	−	0.0251164i
$95$	−17.9447	−	6.43125i	−1.84108	−	0.659832i
$96$	8.73073	−	4.72483i	0.891076	−	0.482226i
$97$	1.63780	+	7.00595i	0.166293	+	0.711346i	0.989612	+	0.143766i	$0.0459214\pi$
$97$	1.63780	+	7.00595i	0.166293	+	0.711346i	−0.823318	+	0.567580i	$0.807880\pi$
$98$	−8.82672	+	8.27664i	−0.891633	+	0.836067i
$99$	0.296092	+	0.248451i	0.0297584	+	0.0249702i
$100$	13.5962	−	15.9043i	1.35962	−	1.59043i
$101$	−0.506255	−	0.662911i	−0.0503743	−	0.0659621i	0.768877	−	0.639396i	$-0.220816\pi$
$101$	−0.506255	−	0.662911i	−0.0503743	−	0.0659621i	−0.819252	+	0.573434i	$0.805611\pi$
$102$	−4.18329	−	1.97414i	−0.414207	−	0.195469i
$103$	−6.74181	−	2.73829i	−0.664290	−	0.269811i	0.0191514	−	0.999817i	$-0.493904\pi$
$103$	−6.74181	−	2.73829i	−0.664290	−	0.269811i	−0.683442	+	0.730005i	$0.739518\pi$
$104$	5.26667	−	0.978621i	0.516439	−	0.0959617i
$105$	35.8294	+	5.30428i	3.49659	+	0.517644i
$106$	−0.0476335	−	1.72806i	−0.00462658	−	0.167844i
$107$	−1.38305	+	7.08047i	−0.133705	+	0.684495i	0.852992	+	0.521924i	$0.174786\pi$
$107$	−1.38305	+	7.08047i	−0.133705	+	0.684495i	−0.986697	+	0.162571i	$0.948021\pi$
$108$	1.21952	+	7.74576i	0.117348	+	0.745336i
$109$	0.249487	−	5.42811i	0.0238965	−	0.519918i	−0.952579	−	0.304291i	$-0.901581\pi$
$109$	0.249487	−	5.42811i	0.0238965	−	0.519918i	0.976476	−	0.215627i	$-0.0691797\pi$
$110$	−10.2289	+	1.32277i	−0.975286	+	0.126121i
$111$	14.8141	+	3.60696i	1.40609	+	0.342357i
$112$	−5.37192	+	1.73454i	−0.507599	+	0.163899i
$113$	−13.5347	+	10.5345i	−1.27324	+	0.991000i	−0.273662	+	0.961826i	$0.588235\pi$
$113$	−13.5347	+	10.5345i	−1.27324	+	0.991000i	−0.999574	+	0.0291736i	$0.990712\pi$
$114$	−1.18750	+	5.19520i	−0.111219	+	0.486575i
$115$	2.96632	+	2.30878i	0.276610	+	0.215294i
$116$	−6.42546	−	2.33868i	−0.596589	−	0.217141i
$117$	−0.0392200	+	0.249106i	−0.00362589	+	0.0230298i
$118$	−1.21253	−	0.248432i	−0.111622	−	0.0228701i
$119$	14.9730	+	10.7947i	1.37258	+	0.989549i
$120$	−15.4885	−	10.3234i	−1.41390	−	0.942390i
$121$	0.226255	+	0.156882i	0.0205686	+	0.0142620i
$122$	0.581116	−	4.19071i	0.0526118	−	0.379409i
$123$	−9.11300	−	6.82784i	−0.821691	−	0.615646i
$124$	−0.968327	+	0.782664i	−0.0869583	+	0.0702853i
$125$	−38.9387	−	8.72637i	−3.48279	−	0.780511i
$126$	−0.0114265	+	0.414532i	−0.00101795	+	0.0369295i
$127$	−0.343293	+	1.94691i	−0.0304623	+	0.172760i	−0.996243	−	0.0865987i	$-0.972400\pi$
$127$	−0.343293	+	1.94691i	−0.0304623	+	0.172760i	0.965781	+	0.259359i	$0.0835113\pi$
$128$	10.2437	+	1.32469i	0.905425	+	0.117087i
$129$	9.59743	+	3.69423i	0.845007	+	0.325259i
$130$	−4.18171	−	5.27203i	−0.366761	−	0.462388i
$131$	−10.7659	−	8.70167i	−0.940619	−	0.760268i	0.0303340	−	0.999540i	$-0.490343\pi$
$131$	−10.7659	−	8.70167i	−0.940619	−	0.760268i	−0.970953	+	0.239271i	$0.923091\pi$
$132$	−2.02171	−	7.98356i	−0.175967	−	0.694880i
$133$	8.44617	−	19.5165i	0.732376	−	1.69229i
$134$	1.59479	−	6.29768i	0.137769	−	0.544036i
$135$	18.5256	−	13.8801i	1.59443	−	1.19461i
$136$	−4.59125	−	8.30080i	−0.393696	−	0.711788i
$137$	−14.0876	+	4.26459i	−1.20358	+	0.364348i	−0.827089	−	0.562071i	$-0.810005\pi$
$137$	−14.0876	+	4.26459i	−1.20358	+	0.364348i	−0.376493	+	0.926419i	$0.622870\pi$
$138$	0.542065	−	0.900273i	0.0461436	−	0.0766363i
$139$	6.49958	+	1.70960i	0.551287	+	0.145006i	0.519472	−	0.854487i	$-0.326129\pi$
$139$	6.49958	+	1.70960i	0.551287	+	0.145006i	0.0318150	+	0.999494i	$0.489871\pi$
$140$	22.6541	+	22.0382i	1.91462	+	1.86257i
$141$	−1.19874	+	0.132676i	−0.100952	+	0.0111734i
$142$	−0.794702	−	7.83801i	−0.0666899	−	0.657752i
$143$	0.449609	−	6.98255i	0.0375982	−	0.583910i
$144$	−0.0616640	+	0.121851i	−0.00513867	+	0.0101543i
$145$	2.77268	+	19.9952i	0.230259	+	1.66051i
$146$	−1.43312	+	2.59103i	−0.118606	+	0.214436i
$147$	−5.98154	+	27.8889i	−0.493349	+	2.30024i
$148$	8.64509	+	10.1127i	0.710622	+	0.831259i
$149$	0.0159741	+	1.73892i	0.00130865	+	0.142458i	0.998072	+	0.0620666i	$0.0197691\pi$
$149$	0.0159741	+	1.73892i	0.00130865	+	0.142458i	−0.996763	+	0.0803915i	$0.974383\pi$
$150$	−1.74198	+	17.1809i	−0.142232	+	1.40281i
$151$	9.19126	+	1.53375i	0.747974	+	0.124815i	0.526292	−	0.850304i	$-0.323582\pi$
$151$	9.19126	+	1.53375i	0.747974	+	0.124815i	0.221682	+	0.975119i	$0.428845\pi$
$152$	−8.20579	+	7.21792i	−0.665578	+	0.585451i
$153$	0.440464	−	0.0735004i	0.0356094	−	0.00594215i
$154$	−0.739362	−	11.4825i	−0.0595795	−	0.925286i
$155$	3.37952	+	1.44553i	0.271450	+	0.116107i
$156$	3.78184	−	3.81674i	0.302789	−	0.305584i
$157$	−6.96272	−	3.44358i	−0.555686	−	0.274828i	0.143641	−	0.989630i	$-0.454119\pi$
$157$	−6.96272	−	3.44358i	−0.555686	−	0.274828i	−0.699327	+	0.714802i	$0.746517\pi$
$158$	1.53743	−	0.113186i	0.122311	−	0.00900458i
$159$	−2.41336	−	3.28350i	−0.191392	−	0.260398i
$160$	−8.96684	−	23.9494i	−0.708891	−	1.89336i
$161$	−2.78297	+	3.13685i	−0.219328	+	0.247219i
$162$	−4.29367	−	4.49555i	−0.337343	−	0.353204i
$163$	10.4170	+	9.07217i	0.815923	+	0.710588i	0.960310	−	0.278934i	$-0.0899809\pi$
$163$	10.4170	+	9.07217i	0.815923	+	0.710588i	−0.144388	+	0.989521i	$0.546121\pi$
$164$	−2.96613	−	9.48326i	−0.231616	−	0.740518i
$165$	−18.0380	+	16.3016i	−1.40426	+	1.26908i
$166$	4.97896	+	1.50723i	0.386442	+	0.116984i
$167$	−3.03798	−	14.1645i	−0.235086	−	1.09609i	−0.927278	−	0.374373i	$-0.877858\pi$
$167$	−3.03798	−	14.1645i	−0.235086	−	1.09609i	0.692193	−	0.721713i	$-0.256645\pi$
$168$	12.6031	−	16.5031i	0.972354	−	1.27324i
$169$	−7.49086	+	3.87766i	−0.576220	+	0.298281i
$170$	−6.51745	+	9.97569i	−0.499865	+	0.765101i
$171$	−0.191570	−	0.477469i	−0.0146497	−	0.0365130i
$172$	4.90811	+	7.51242i	0.374240	+	0.572817i
$173$	16.0735	+	9.08420i	1.22204	+	0.690659i	0.961501	−	0.274803i	$-0.0886126\pi$
$173$	16.0735	+	9.08420i	1.22204	+	0.690659i	0.260544	+	0.965462i	$0.416098\pi$
$174$	5.45782	−	1.43558i	0.413756	−	0.108831i
$175$	19.3591	−	66.1355i	1.46341	−	4.99937i
$176$	1.39362	−	3.52367i	0.105048	−	0.265607i
$177$	−2.68253	+	1.14740i	−0.201631	+	0.0862438i
$178$	4.12634	+	8.15387i	0.309282	+	0.611159i
$179$	−10.7404	+	7.44725i	−0.802777	+	0.556633i	−0.898602	−	0.438765i	$-0.855416\pi$
$179$	−10.7404	+	7.44725i	−0.802777	+	0.556633i	0.0958247	+	0.995398i	$0.469451\pi$
$180$	0.764473	−	0.0140464i	0.0569805	−	0.00104696i
$181$	−13.2367	+	0.243211i	−0.983880	+	0.0180778i	−0.507933	−	0.861396i	$-0.669590\pi$
$181$	−13.2367	+	0.243211i	−0.983880	+	0.0180778i	−0.475947	+	0.879474i	$0.657894\pi$
$182$	6.16904	−	4.27752i	0.457280	−	0.317071i
$183$	−4.50317	−	8.89852i	−0.332884	−	0.657797i
$184$	1.98138	−	0.847495i	0.146069	−	0.0624782i
$185$	14.4453	−	36.5238i	1.06204	−	2.68528i
$186$	0.288685	−	0.986217i	0.0211674	−	0.0723130i
$187$	−11.9828	+	3.15187i	−0.876270	+	0.230488i
$188$	−0.916197	−	0.517804i	−0.0668206	−	0.0377648i
$189$	14.1245	+	21.6192i	1.02741	+	1.57257i
$190$	12.8361	+	4.86826i	0.931225	+	0.353181i
$191$	−2.88088	+	4.40952i	−0.208453	+	0.319062i	−0.926053	−	0.377395i	$-0.876820\pi$
$191$	−2.88088	+	4.40952i	−0.208453	+	0.319062i	0.717599	+	0.696456i	$0.245241\pi$
$192$	−2.86026	+	1.48062i	−0.206421	+	0.106854i
$193$	−14.1463	+	18.5237i	−1.01827	+	1.33336i	−0.0765134	+	0.997069i	$0.524379\pi$
$193$	−14.1463	+	18.5237i	−1.01827	+	1.33336i	−0.941756	+	0.336296i	$0.890826\pi$
$194$	−1.08662	−	5.06634i	−0.0780144	−	0.363742i
$195$	−15.1818	−	4.59585i	−1.08719	−	0.329115i
$196$	−18.4655	+	16.6880i	−1.31897	+	1.19200i
$197$	−3.25639	−	10.4113i	−0.232008	−	0.741772i	−0.995397	−	0.0958330i	$-0.969449\pi$
$197$	−3.25639	−	10.4113i	−0.232008	−	0.741772i	0.763389	−	0.645939i	$-0.223534\pi$
$198$	−0.209915	−	0.182816i	−0.0149180	−	0.0129921i
$199$	−4.55595	−	4.77016i	−0.322963	−	0.338148i	0.541634	−	0.840615i	$-0.317806\pi$
$199$	−4.55595	−	4.77016i	−0.322963	−	0.338148i	−0.864596	+	0.502467i	$0.832426\pi$
$200$	−23.5022	+	26.4908i	−1.66186	+	1.87318i
$201$	−5.36959	−	14.3415i	−0.378742	−	1.01157i
$202$	0.355761	+	0.484031i	0.0250313	+	0.0340563i
$203$	−22.4591	+	1.65344i	−1.57632	+	0.116049i
$204$	−8.52863	−	4.21804i	−0.597124	−	0.295322i
$205$	−20.6466	+	20.8371i	−1.44202	+	1.45533i
$206$	4.81825	+	2.06091i	0.335703	+	0.143591i
$207$	0.00651880	+	0.101239i	0.000453088	+	0.00703657i
$208$	2.43847	−	0.406909i	0.169078	−	0.0282141i
$209$	6.50829	+	12.7048i	0.450188	+	0.878807i
$210$	−25.7290	−	4.29340i	−1.77547	−	0.296273i
$211$	−1.42958	+	14.0997i	−0.0984163	+	0.970664i	0.819283	+	0.573389i	$0.194372\pi$
$211$	−1.42958	+	14.0997i	−0.0984163	+	0.970664i	−0.917700	+	0.397275i	$0.869956\pi$
$212$	−0.0326631	−	3.55567i	−0.00224331	−	0.244204i
$213$	−12.0673	−	14.1159i	−0.826839	−	0.967204i
$214$	1.08955	−	5.08003i	0.0744803	−	0.347264i
$215$	12.8222	−	23.1820i	0.874464	−	1.58100i
$216$	−1.82285	−	13.1454i	−0.124029	−	0.894434i
$217$	−1.85154	+	3.65875i	−0.125691	+	0.248372i
$218$	−0.251460	+	3.90524i	−0.0170310	+	0.264496i
$219$	0.704070	+	6.94413i	0.0475767	+	0.469241i
$220$	−21.0864	+	2.33385i	−1.42165	+	0.157348i
$221$	−5.79431	−	5.63679i	−0.389767	−	0.379171i
$222$	−10.6192	−	2.79320i	−0.712716	−	0.187467i
$223$	−2.08703	+	3.46618i	−0.139758	+	0.232113i	−0.918675	−	0.395014i	$-0.870740\pi$
$223$	−2.08703	+	3.46618i	−0.139758	+	0.232113i	0.778917	+	0.627126i	$0.215769\pi$
$224$	27.3053	−	8.26585i	1.82441	−	0.552285i
$225$	−0.806889	−	1.45883i	−0.0537926	−	0.0972550i
$226$	9.88510	−	7.40633i	0.657547	−	0.492662i
$227$	−0.699004	+	2.76030i	−0.0463945	+	0.183208i	−0.988260	−	0.152783i	$-0.951176\pi$
$227$	−0.699004	+	2.76030i	−0.0463945	+	0.183208i	0.941865	+	0.335991i	$0.109071\pi$
$228$	−2.63848	+	10.6394i	−0.174738	+	0.704613i
$229$	−3.30492	−	13.0508i	−0.218395	−	0.862424i	−0.977410	−	0.211351i	$-0.932214\pi$
$229$	−3.30492	−	13.0508i	−0.218395	−	0.862424i	0.759015	−	0.651073i	$-0.225681\pi$
$230$	−2.10537	−	1.70169i	−0.138824	−	0.112206i
$231$	−16.8553	−	21.2501i	−1.10900	−	1.39815i
$232$	10.8006	+	4.15734i	0.709092	+	0.272943i
$233$	10.9014	+	1.40974i	0.714177	+	0.0923551i	0.476736	−	0.879047i	$-0.341820\pi$
$233$	10.9014	+	1.40974i	0.714177	+	0.0923551i	0.237441	+	0.971402i	$0.423691\pi$
$234$	0.0315363	−	0.178851i	0.00206159	−	0.0116919i
$235$	−0.0856075	+	3.10568i	−0.00558442	+	0.202592i
$236$	−2.48427	−	0.556737i	−0.161712	−	0.0362405i
$237$	2.82618	−	2.28430i	0.183580	−	0.148381i
$238$	−10.6386	−	7.97088i	−0.689597	−	0.516676i
$239$	−0.885723	+	6.38737i	−0.0572926	+	0.413165i	0.940094	+	0.340915i	$0.110737\pi$
$239$	−0.885723	+	6.38737i	−0.0572926	+	0.413165i	−0.997387	+	0.0722492i	$0.976982\pi$
$240$	−7.05927	−	4.89479i	−0.455674	−	0.315957i
$241$	−8.94237	−	5.96026i	−0.576028	−	0.383934i	0.232319	−	0.972640i	$-0.425369\pi$
$241$	−8.94237	−	5.96026i	−0.576028	−	0.383934i	−0.808347	+	0.588706i	$0.799638\pi$
$242$	−0.160841	−	0.115957i	−0.0103392	−	0.00745400i
$243$	1.20090	+	0.246050i	0.0770379	+	0.0157841i
$244$	1.35346	−	8.59653i	0.0866466	−	0.550337i
$245$	69.0457	+	25.1306i	4.41117	+	1.60553i
$246$	6.47153	+	5.03699i	0.412610	+	0.321147i
$247$	−4.91075	+	7.91325i	−0.312464	+	0.503508i
$248$	1.66296	−	1.29433i	0.105598	−	0.0821901i
$249$	11.6694	−	3.76793i	0.739519	−	0.238783i
$250$	27.9226	+	6.79864i	1.76598	+	0.429984i
$251$	−7.54162	+	0.975259i	−0.476023	+	0.0615578i	−0.362512	−	0.931979i	$-0.618081\pi$
$251$	−7.54162	+	0.975259i	−0.476023	+	0.0615578i	−0.113511	+	0.993537i	$0.536210\pi$
$252$	−0.0391635	+	0.852084i	−0.00246707	+	0.0536762i
$253$	−0.437787	−	2.78061i	−0.0275234	−	0.174815i
$254$	0.272948	−	1.39734i	0.0171263	−	0.0876770i
$255$	0.773975	+	28.0784i	0.0484682	+	1.75834i
$256$	−11.1120	−	1.64505i	−0.694501	−	0.102816i
$257$	13.3984	−	2.48962i	0.835770	−	0.155298i	0.252521	−	0.967591i	$-0.418740\pi$
$257$	13.3984	−	2.48962i	0.835770	−	0.155298i	0.583249	+	0.812293i	$0.301781\pi$
$258$	−6.86181	−	2.78702i	−0.427197	−	0.173513i
$259$	39.6259	+	18.6999i	2.46223	+	1.16196i
$260$	−8.40078	−	11.0003i	−0.520994	−	0.682211i
$261$	−0.354014	+	0.414112i	−0.0219129	+	0.0256329i
$262$	7.63690	+	6.40812i	0.471809	+	0.395895i
$263$	−9.72037	+	9.11460i	−0.599384	+	0.562031i	−0.923312	−	0.384051i	$-0.874529\pi$
$263$	−9.72037	+	9.11460i	−0.599384	+	0.562031i	0.323928	+	0.946082i	$0.394996\pi$
$264$	3.17295	+	13.5728i	0.195281	+	0.835348i
$265$	−9.23220	+	4.99621i	−0.567129	+	0.306915i
$266$	−6.33992	+	13.9412i	−0.388725	+	0.854790i
$267$	18.9454	+	10.2527i	1.15944	+	0.627458i
$268$	3.51777	−	12.8914i	0.214882	−	0.787465i
$269$	11.1202	−	5.00005i	0.678008	−	0.304858i	−0.0417055	−	0.999130i	$-0.513279\pi$
$269$	11.1202	−	5.00005i	0.678008	−	0.304858i	0.719713	+	0.694271i	$0.244273\pi$
$270$	−13.5231	+	9.74936i	−0.822987	+	0.593327i
$271$	21.4229	−	0.787514i	1.30135	−	0.0478381i	0.622794	−	0.782386i	$-0.285998\pi$
$271$	21.4229	−	0.787514i	1.30135	−	0.0478381i	0.678557	+	0.734548i	$0.262606\pi$
$272$	−2.04814	−	3.86913i	−0.124187	−	0.234600i
$273$	6.20480	−	16.5723i	0.375531	−	1.00300i
$274$	10.2002	−	2.88435i	0.616219	−	0.174250i
$275$	26.0072	+	38.2533i	1.56829	+	2.30676i
$276$	1.14881	−	1.83099i	0.0691505	−	0.110213i
$277$	−0.707477	+	0.962557i	−0.0425082	+	0.0578344i	−0.826500	−	0.562937i	$-0.809672\pi$
$277$	−0.707477	+	0.962557i	−0.0425082	+	0.0578344i	0.783992	+	0.620771i	$0.213180\pi$
$278$	−4.65744	−	1.31700i	−0.279335	−	0.0789883i
$279$	0.0313476	+	0.0941190i	0.00187673	+	0.00563476i
$280$	−37.6504	−	37.9978i	−2.25004	−	2.27081i
$281$	7.90796	+	19.9947i	0.471749	+	1.19278i	0.949354	+	0.314208i	$0.101739\pi$
$281$	7.90796	+	19.9947i	0.471749	+	1.19278i	−0.477605	+	0.878575i	$0.658495\pi$
$282$	0.864913	−	0.0796746i	0.0515048	−	0.00474455i
$283$	19.1108	−	20.0093i	1.13602	−	1.18943i	0.156584	−	0.987665i	$-0.449952\pi$
$283$	19.1108	−	20.0093i	1.13602	−	1.18943i	0.979434	−	0.201766i	$-0.0646679\pi$
$284$	−1.33818	−	16.1495i	−0.0794066	−	0.958295i
$285$	31.4041	−	7.81065i	1.86022	−	0.462663i
$286$	−0.416124	+	5.02187i	−0.0246059	+	0.296950i
$287$	−21.7176	−	24.4792i	−1.28195	−	1.44496i
$288$	0.322900	−	0.609988i	0.0190271	−	0.0359439i
$289$	1.16821	−	2.41770i	0.0687184	−	0.142218i
$290$	−1.73194	−	14.4343i	−0.101703	−	0.847611i
$291$	−8.90993	−	8.35467i	−0.522309	−	0.489759i
$292$	−3.04523	+	5.27450i	−0.178209	+	0.308667i
$293$	5.86033	+	10.1504i	0.342364	+	0.592992i	0.984871	−	0.173288i	$-0.0554390\pi$
$293$	5.86033	+	10.1504i	0.342364	+	0.592992i	−0.642507	+	0.766280i	$0.722106\pi$
$294$	4.67601	−	20.0024i	0.272711	−	1.16656i
$295$	1.97858	+	7.25080i	0.115198	+	0.422158i
$296$	−14.3150	−	17.3817i	−0.832040	−	1.01029i
$297$	−17.2295	−	1.90696i	−0.999758	−	0.110653i
$298$	0.0115042	−	1.25233i	0.000666419	−	0.0725456i
$299$	1.40682	−	1.18046i	0.0813586	−	0.0682679i
$300$	−4.23173	+	35.2679i	−0.244319	+	2.03620i
$301$	24.8890	+	15.9365i	1.43458	+	0.918566i
$302$	−6.59792	−	1.22599i	−0.379668	−	0.0705477i
$303$	1.33930	+	0.459782i	0.0769407	+	0.0264138i
$304$	−3.84756	+	3.26097i	−0.220673	+	0.187029i
$305$	−24.2991	+	8.34188i	−1.39136	+	0.477655i
$306$	−0.318131	+	0.0470969i	−0.0181863	+	0.00269235i
$307$	3.80946	+	21.6045i	0.217417	+	1.23303i	0.876662	+	0.481106i	$0.159765\pi$
$307$	3.80946	+	21.6045i	0.217417	+	1.23303i	−0.659245	+	0.751928i	$0.729124\pi$
$308$	−1.08666	−	23.6425i	−0.0619181	−	1.34716i
$309$	12.1018	−	2.47951i	0.688446	−	0.141054i
$310$	−2.41432	−	1.08557i	−0.137124	−	0.0616562i
$311$	7.09003	−	8.60894i	0.402039	−	0.488168i	−0.531291	−	0.847189i	$-0.678293\pi$
$311$	7.09003	−	8.60894i	0.402039	−	0.488168i	0.933329	+	0.359021i	$0.116889\pi$
$312$	−6.51837	+	6.34117i	−0.369030	+	0.358998i
$313$	−5.27776	+	2.98282i	−0.298317	+	0.168599i	−0.633907	−	0.773409i	$-0.718550\pi$
$313$	−5.27776	+	2.98282i	−0.298317	+	0.168599i	0.335590	+	0.942008i	$0.391064\pi$
$314$	4.96798	+	2.57169i	0.280360	+	0.145129i
$315$	2.27731	−	1.07469i	0.128312	−	0.0605519i
$316$	3.16611	−	0.174679i	0.178108	−	0.00982648i
$317$	5.03572	−	14.2412i	0.282834	−	0.799866i	−0.712348	−	0.701826i	$-0.752368\pi$
$317$	5.03572	−	14.2412i	0.282834	−	0.799866i	0.995182	−	0.0980401i	$-0.0312574\pi$
$318$	1.69431	+	2.39623i	0.0950124	+	0.134374i
$319$	8.72731	−	12.3428i	0.488635	−	0.691066i
$320$	2.76595	+	7.82221i	0.154621	+	0.437275i
$321$	−4.71279	−	11.3042i	−0.263042	−	0.630938i
$322$	2.04539	−	2.22189i	0.113985	−	0.123821i
$323$	16.0428	+	3.82240i	0.892646	+	0.212684i
$324$	−8.66037	−	9.40767i	−0.481132	−	0.522648i
$325$	−12.6284	+	27.4097i	−0.700497	+	1.52041i
$326$	−7.38079	−	6.67029i	−0.408784	−	0.369433i
$327$	4.75833	+	7.90273i	0.263136	+	0.437022i
$328$	4.72449	+	16.1400i	0.260866	+	0.891181i
$329$	−3.45137	−	0.317936i	−0.190280	−	0.0175284i
$330$	13.2041	−	11.4994i	0.726860	−	0.633023i
$331$	24.1428	+	14.8405i	1.32701	+	0.815708i	0.991967	−	0.126496i	$-0.0403732\pi$
$331$	24.1428	+	14.8405i	1.32701	+	0.815708i	0.335039	+	0.942204i	$0.391250\pi$
$332$	10.1826	+	3.28787i	0.558845	+	0.180445i
$333$	0.996098	−	0.362550i	0.0545858	−	0.0198676i
$334$	2.00011	+	10.2394i	0.109441	+	0.560278i
$335$	−38.4943	+	8.62676i	−2.10317	+	0.471330i
$336$	5.95534	−	7.50810i	0.324890	−	0.409600i
$337$	16.7411	−	9.87161i	0.911945	−	0.537741i	0.0250368	−	0.999687i	$-0.492030\pi$
$337$	16.7411	−	9.87161i	0.911945	−	0.537741i	0.886908	+	0.461945i	$0.152848\pi$
$338$	5.44513	−	2.69302i	0.296176	−	0.146481i
$339$	9.20074	−	27.6245i	0.499716	−	1.50036i
$340$	−13.7806	+	20.2695i	−0.747355	+	1.09927i
$341$	−1.10568	−	2.52070i	−0.0598759	−	0.136503i
$342$	0.131624	+	0.346339i	0.00711740	+	0.0187279i
$343$	−19.2088	+	43.7916i	−1.03718	+	2.36452i
$344$	−8.07201	−	12.8653i	−0.435214	−	0.693649i
$345$	−6.36406	−	0.468523i	−0.342629	−	0.0252244i
$346$	−11.4536	−	6.75378i	−0.615750	−	0.363086i
$347$	9.47588	−	3.64744i	0.508692	−	0.195805i	−0.0912811	−	0.995825i	$-0.529096\pi$
$347$	9.47588	−	3.64744i	0.508692	−	0.195805i	0.599973	+	0.800020i	$0.295178\pi$
$348$	11.2787	−	2.74615i	0.604599	−	0.147209i
$349$	−0.441826	+	0.271589i	−0.0236504	+	0.0145378i	−0.535448	−	0.844568i	$-0.679857\pi$
$349$	−0.441826	+	0.271589i	−0.0236504	+	0.0145378i	0.511797	+	0.859106i	$0.328980\pi$
$350$	−14.8146	+	47.3651i	−0.791876	+	2.53177i
$351$	−4.73249	−	10.2718i	−0.252602	−	0.548267i
$352$	−7.36910	+	17.6757i	−0.392774	+	0.942116i
$353$	−30.4545	−	1.68022i	−1.62093	−	0.0894291i	−0.778288	−	0.627907i	$-0.783912\pi$
$353$	−30.4545	−	1.68022i	−1.62093	−	0.0894291i	−0.842639	+	0.538478i	$0.818999\pi$
$354$	1.94675	−	0.790700i	0.103468	−	0.0420252i
$355$	−40.2883	+	25.7967i	−2.13828	+	1.36915i
$356$	8.17801	+	16.9250i	0.433433	+	0.897021i
$357$	−31.3147	−	1.15114i	−1.65735	−	0.0609248i
$358$	7.83223	−	5.22033i	0.413946	−	0.275903i
$359$	2.64683	+	0.0486328i	0.139695	+	0.00256674i	0.0881732	−	0.996105i	$-0.471897\pi$
$359$	2.64683	+	0.0486328i	0.139695	+	0.00256674i	0.0515213	+	0.998672i	$0.483593\pi$
$360$	−1.29409			−0.0682047
$361$	0.336118	−	18.9970i	0.0176904	−	0.999844i
$362$	9.53441			0.501117
$363$	−0.467321	−	0.00858654i	−0.0245280	−	0.000450677i
$364$	12.8487	−	8.56391i	0.673455	−	0.448871i
$365$	17.9680	+	0.660509i	0.940487	+	0.0345726i
$366$	3.12480	+	6.46700i	0.163336	+	0.338036i
$367$	7.13358	−	4.56766i	0.372370	−	0.238430i	−0.339707	−	0.940531i	$-0.610328\pi$
$367$	7.13358	−	4.56766i	0.372370	−	0.238430i	0.712077	+	0.702102i	$0.247755\pi$
$368$	0.921443	−	0.374258i	0.0480336	−	0.0195095i
$369$	−0.790477	−	0.0436118i	−0.0411506	−	0.00227034i
$370$	−10.8846	+	26.1080i	−0.565864	+	1.35729i
$371$	−4.90040	−	10.6362i	−0.254416	−	0.552205i
$372$	0.630968	−	2.01732i	0.0327142	−	0.104593i
$373$	17.8150	−	10.9508i	0.922424	−	0.567012i	0.0209193	−	0.999781i	$-0.493341\pi$
$373$	17.8150	−	10.9508i	0.922424	−	0.567012i	0.901505	+	0.432769i	$0.142464\pi$
$374$	8.66999	−	2.11098i	0.448315	−	0.109156i
$375$	63.2217	−	24.3352i	3.26475	−	1.25666i
$376$	1.53431	+	0.904725i	0.0791258	+	0.0466576i
$377$	9.83578	+	0.724111i	0.506568	+	0.0372936i
$378$	−9.88443	−	15.7539i	−0.508400	−	0.810294i
$379$	−4.64977	+	10.6004i	−0.238842	+	0.544506i	−0.993789	−	0.111280i	$-0.964505\pi$
$379$	−4.64977	+	10.6004i	−0.238842	+	0.544506i	0.754947	+	0.655786i	$0.227663\pi$
$380$	26.2143	+	10.4970i	1.34477	+	0.538484i
$381$	−1.34814	−	3.07346i	−0.0690675	−	0.157458i
$382$	2.13273	−	3.13698i	0.109120	−	0.160502i
$383$	−7.30852	+	21.9433i	−0.373448	+	1.12125i	0.578681	+	0.815554i	$0.303568\pi$
$383$	−7.30852	+	21.9433i	−0.373448	+	1.12125i	−0.952129	+	0.305696i	$0.901111\pi$
$384$	−15.7177	+	7.77355i	−0.802089	+	0.396692i
$385$	−60.1862	+	35.4896i	−3.06737	+	1.80872i
$386$	10.4312	−	13.1509i	0.530932	−	0.669364i
$387$	0.697672	−	0.156352i	0.0354647	−	0.00794782i
$388$	−2.04326	−	10.4603i	−0.103731	−	0.531044i
$389$	−19.3079	+	7.02749i	−0.978948	+	0.356308i	−0.781431	−	0.623992i	$-0.785510\pi$
$389$	−19.3079	+	7.02749i	−0.978948	+	0.356308i	−0.197517	+	0.980300i	$0.563288\pi$
$390$	10.8710	+	3.51012i	0.550473	+	0.177742i
$391$	−2.77049	−	1.70301i	−0.140110	−	0.0861251i
$392$	31.7666	−	27.6656i	1.60446	−	1.39732i
$393$	23.4010	+	2.15567i	1.18042	+	0.108739i
$394$	2.20704	+	7.53977i	0.111189	+	0.379848i
$395$	−4.82871	−	8.01963i	−0.242959	−	0.403511i
$396$	−0.424798	−	0.383906i	−0.0213469	−	0.0192920i
$397$	−9.67201	+	20.9929i	−0.485424	+	1.05360i	0.497138	+	0.867671i	$0.334384\pi$
$397$	−9.67201	+	20.9929i	−0.485424	+	1.05360i	−0.982563	+	0.185932i	$0.940470\pi$
$398$	3.21743	+	3.49506i	0.161275	+	0.175191i
$399$	6.44428	+	35.5217i	0.322617	+	1.77831i
$400$	−11.0691	+	12.0243i	−0.553457	+	0.601214i
$401$	−2.70526	−	6.48890i	−0.135094	−	0.324040i	0.841120	−	0.540849i	$-0.181897\pi$
$401$	−2.70526	−	6.48890i	−0.135094	−	0.324040i	−0.976214	+	0.216809i	$0.930435\pi$
$402$	3.67666	+	10.3977i	0.183375	+	0.518593i
$403$	1.03678	−	1.46630i	0.0516457	−	0.0730414i
$404$	0.713359	+	1.00889i	0.0354909	+	0.0501940i
$405$	−12.5846	+	35.5899i	−0.625336	+	1.76848i
$406$	16.1936	−	0.893428i	0.803677	−	0.0443401i
$407$	−26.5991	+	12.5524i	−1.31847	+	0.622201i
$408$	14.3012	+	7.40302i	0.708013	+	0.366504i
$409$	18.2587	−	10.3192i	0.902835	−	0.510252i	0.0307063	−	0.999528i	$-0.490224\pi$
$409$	18.2587	−	10.3192i	0.902835	−	0.510252i	0.872129	+	0.489276i	$0.162739\pi$
$410$	15.1424	−	14.7307i	0.747828	−	0.727498i
$411$	15.8851	−	19.2882i	0.783552	−	0.951415i
$412$	9.83119	+	4.42049i	0.484348	+	0.217782i
$413$	−8.21404	+	1.68296i	−0.404187	+	0.0828128i
$414$	−0.00335448	−	0.0729837i	−0.000164864	−	0.00358695i
$415$	−5.48540	−	31.1092i	−0.269268	−	1.52709i
$416$	−12.3593	+	1.82971i	−0.605967	+	0.0897089i
$417$	−10.7911	+	3.70458i	−0.528441	+	0.181414i
$418$	−4.51824	−	9.23424i	−0.220994	−	0.451661i
$419$	−11.7739	−	4.04198i	−0.575192	−	0.197464i	0.0217287	−	0.999764i	$-0.493083\pi$
$419$	−11.7739	−	4.04198i	−0.575192	−	0.197464i	−0.596921	+	0.802300i	$0.703609\pi$
$420$	−52.7512	−	9.80193i	−2.57400	−	0.478285i
$421$	29.2055	+	18.7004i	1.42339	+	0.911402i	0.999985	+	0.00546219i	$0.00173868\pi$
$421$	29.2055	+	18.7004i	1.42339	+	0.911402i	0.423406	+	0.905940i	$0.360834\pi$
$422$	1.21592	−	10.1337i	0.0591900	−	0.493299i
$423$	−0.0642329	+	0.0538978i	−0.00312311	+	0.00262060i
$424$	−0.0552825	+	6.01799i	−0.00268475	+	0.292259i
$425$	53.1169	+	5.87897i	2.57655	+	0.285172i
$426$	8.50238	+	10.3239i	0.411941	+	0.500193i
$427$	−7.54502	−	27.6498i	−0.365129	−	1.33807i
$428$	2.43270	−	10.4063i	0.117589	−	0.503006i
$429$	5.93920	+	10.2870i	0.286747	+	0.496660i
$430$	−9.53936	+	16.5227i	−0.460029	+	0.796794i
$431$	−6.88729	−	6.45808i	−0.331749	−	0.311075i	0.500218	−	0.865899i	$-0.333253\pi$
$431$	−6.88729	−	6.45808i	−0.331749	−	0.311075i	−0.831967	+	0.554825i	$0.812785\pi$
$432$	−0.729660	−	6.08110i	−0.0351058	−	0.292577i
$433$	11.6155	−	24.0391i	0.558207	−	1.15525i	−0.411598	−	0.911365i	$-0.635029\pi$
$433$	11.6155	−	24.0391i	0.558207	−	1.15525i	0.969805	−	0.243882i	$-0.0784210\pi$
$434$	1.38162	−	2.61000i	0.0663199	−	0.125284i
$435$	−22.7429	−	25.6349i	−1.09044	−	1.22910i
$436$	−0.664713	+	8.02190i	−0.0318340	+	0.384179i
$437$	−1.23159	+	3.53842i	−0.0589149	+	0.169266i
$438$	−0.415097	−	5.00947i	−0.0198341	−	0.239362i
$439$	8.68773	−	9.09621i	0.414643	−	0.434138i	−0.482489	−	0.875902i	$-0.660267\pi$
$439$	8.68773	−	9.09621i	0.414643	−	0.434138i	0.897131	+	0.441764i	$0.145647\pi$
$440$	35.7554	−	3.29374i	1.70457	−	0.157023i
$441$	0.729330	+	1.84406i	0.0347300	+	0.0878122i
$442$	4.09764	+	4.13546i	0.194905	+	0.196704i
$443$	−12.6420	−	37.9567i	−0.600639	−	1.80337i	−0.595455	−	0.803388i	$-0.703028\pi$
$443$	−12.6420	−	37.9567i	−0.600639	−	1.80337i	−0.00518369	−	0.999987i	$-0.501650\pi$
$444$	−21.7337	−	6.14569i	−1.03143	−	0.291662i
$445$	32.8647	−	44.7140i	1.55793	−	2.11965i
$446$	1.54863	−	2.46823i	0.0733299	−	0.116874i
$447$	−1.65982	−	2.44139i	−0.0785069	−	0.115474i
$448$	−8.90663	+	2.51856i	−0.420799	+	0.118991i
$449$	−1.24835	+	3.33420i	−0.0589134	+	0.157351i	−0.962657	−	0.270723i	$-0.912737\pi$
$449$	−1.24835	+	3.33420i	−0.0589134	+	0.157351i	0.903744	+	0.428073i	$0.140808\pi$
$450$	0.561704	+	1.06111i	0.0264790	+	0.0500212i
$451$	21.9517	−	0.806950i	1.03366	−	0.0379978i
$452$	20.6093	−	14.8581i	0.969379	−	0.698867i
$453$	−14.4278	+	6.48730i	−0.677877	+	0.304800i
$454$	0.539841	−	1.97832i	0.0253360	−	0.0928473i
$455$	−40.0909	−	21.6961i	−1.87949	−	1.01713i
$456$	4.79570	−	17.9222i	0.224579	−	0.839284i
$457$	−20.0816	+	10.8676i	−0.939376	+	0.508365i	−0.872077	−	0.489368i	$-0.837227\pi$
$457$	−20.0816	+	10.8676i	−0.939376	+	0.508365i	−0.0672986	+	0.997733i	$0.521438\pi$
$458$	2.20706	+	9.44105i	0.103129	+	0.441151i
$459$	−14.6092	+	13.6988i	−0.681899	+	0.639404i
$460$	−4.26553	−	3.57921i	−0.198882	−	0.166881i
$461$	−0.808837	+	0.946146i	−0.0376713	+	0.0440664i	−0.778624	−	0.627491i	$-0.784082\pi$
$461$	−0.808837	+	0.946146i	−0.0376713	+	0.0440664i	0.740953	+	0.671557i	$0.234374\pi$
$462$	11.8556	+	15.5242i	0.551573	+	0.722252i
$463$	5.19997	+	2.45392i	0.241663	+	0.114044i	0.543781	−	0.839227i	$-0.316992\pi$
$463$	5.19997	+	2.45392i	0.241663	+	0.114044i	−0.302118	+	0.953270i	$0.597694\pi$
$464$	4.94842	+	2.00987i	0.229724	+	0.0933060i
$465$	−6.13498	+	1.13997i	−0.284503	+	0.0528647i
$466$	−7.83098	−	1.15932i	−0.362763	−	0.0537044i
$467$	0.561610	+	20.3742i	0.0259882	+	0.942805i	0.894482	+	0.447104i	$0.147545\pi$
$467$	0.561610	+	20.3742i	0.0259882	+	0.942805i	−0.868494	+	0.495700i	$0.834911\pi$
$468$	0.0716149	−	0.366629i	0.00331040	−	0.0169474i
$469$	−6.84459	−	43.4735i	−0.316054	−	2.00742i
$470$	0.102731	−	2.23513i	0.00473863	−	0.103099i
$471$	13.0779	−	1.69119i	0.602598	−	0.0779261i
$472$	4.18661	+	1.01936i	0.192705	+	0.0469200i
$473$	−18.8785	+	6.09569i	−0.868037	+	0.280280i
$474$	−2.06523	+	1.60743i	−0.0948592	+	0.0738319i
$475$	−6.51275	−	61.2232i	−0.298826	−	2.80911i
$476$	−21.5778	−	16.7947i	−0.989018	−	0.769784i
$477$	−0.266226	−	0.0968982i	−0.0121896	−	0.00443666i
$478$	0.722276	−	4.58754i	0.0330361	−	0.209829i
$479$	−1.89036	−	0.387312i	−0.0863728	−	0.0176967i	0.157336	−	0.987545i	$-0.449709\pi$
$479$	−1.89036	−	0.387312i	−0.0863728	−	0.0176967i	−0.243709	+	0.969848i	$0.578364\pi$
$480$	35.2159	+	25.3887i	1.60738	+	1.15883i
$481$	−15.9674	−	10.6426i	−0.728053	−	0.485261i
$482$	6.36014	+	4.41002i	0.289697	+	0.200871i
$483$	0.977806	−	7.05143i	0.0444917	−	0.320851i
$484$	−0.326399	−	0.244552i	−0.0148363	−	0.0111160i
$485$	−24.4706	+	19.7787i	−1.11115	+	0.898106i
$486$	−0.861460	−	0.193058i	−0.0390766	−	0.00875728i
$487$	0.265313	−	9.62506i	0.0120225	−	0.436153i	−0.969531	−	0.244967i	$-0.921223\pi$
$487$	0.265313	−	9.62506i	0.0120225	−	0.436153i	0.981554	−	0.191186i	$-0.0612333\pi$
$488$	−2.55765	+	14.5051i	−0.115779	+	0.656616i
$489$	−23.2570	−	3.00752i	−1.05172	−	0.136005i
$490$	−49.3842	−	19.0089i	−2.23095	−	0.858734i
$491$	0.668919	+	0.843329i	0.0301879	+	0.0380589i	0.798328	−	0.602223i	$-0.205718\pi$
$491$	0.668919	+	0.843329i	0.0301879	+	0.0380589i	−0.768140	+	0.640282i	$0.778818\pi$
$492$	13.1188	+	10.6035i	0.591442	+	0.478042i
$493$	−4.28727	−	16.9301i	−0.193089	−	0.762492i
$494$	3.64071	−	5.63301i	0.163803	−	0.253441i
$495$	−0.414951	+	1.63861i	−0.0186507	+	0.0736498i
$496$	0.778305	−	0.583139i	0.0349469	−	0.0261837i
$497$	−25.8311	−	46.7016i	−1.15868	−	2.09485i
$498$	−8.45247	+	2.55873i	−0.378764	+	0.114659i
$499$	−9.32572	+	15.4884i	−0.417477	+	0.693354i	−0.992153	−	0.125026i	$-0.960099\pi$
$499$	−9.32572	+	15.4884i	−0.417477	+	0.693354i	0.574677	+	0.818380i	$0.305128\pi$
$500$	57.1679	+	15.0370i	2.55663	+	0.672476i
$501$	17.6279	+	17.1487i	0.787557	+	0.766148i
$502$	5.44329	−	0.602463i	0.242946	−	0.0268892i
$503$	2.29541	+	22.6393i	0.102347	+	1.00944i	0.908544	+	0.417789i	$0.137195\pi$
$503$	2.29541	+	22.6393i	0.102347	+	1.00944i	−0.806197	+	0.591647i	$0.798478\pi$
$504$	0.0927668	−	1.44069i	0.00413216	−	0.0641736i
$505$	1.64708	−	3.25471i	0.0732939	−	0.144833i
$506$	0.278442	+	2.00798i	0.0123783	+	0.0892657i
$507$	6.93076	−	12.5305i	0.307806	−	0.556501i
$508$	0.614139	−	2.86342i	0.0272480	−	0.127044i
$509$	2.69330	+	3.15051i	0.119378	+	0.139644i	0.816583	−	0.577228i	$-0.195866\pi$
$509$	2.69330	+	3.15051i	0.119378	+	0.139644i	−0.697205	+	0.716872i	$0.745573\pi$
$510$	−0.185821	−	20.2282i	−0.00822827	−	0.895721i
$511$	−2.02337	+	19.9561i	−0.0895085	+	0.882808i
$512$	−12.3968	−	2.06866i	−0.547865	−	0.0914226i
$513$	19.0254	+	13.0534i	0.839992	+	0.576322i
$514$	−9.68054	+	1.61540i	−0.426990	+	0.0712521i
$515$	−2.04482	−	31.7566i	−0.0901055	−	1.39936i
$516$	−14.0065	−	5.99101i	−0.616601	−	0.263739i
$517$	1.63756	−	1.65267i	0.0720197	−	0.0726843i
$518$	−28.2854	−	13.9892i	−1.24279	−	0.614651i
$519$	−31.2588	+	2.30127i	−1.37211	+	0.101015i
$520$	13.8739	+	18.8762i	0.608412	+	0.827775i
$521$	−3.02958	−	8.09166i	−0.132728	−	0.354502i	0.853220	−	0.521551i	$-0.174646\pi$
$521$	−3.02958	−	8.09166i	−0.132728	−	0.354502i	−0.985949	+	0.167049i	$0.946576\pi$
$522$	0.260388	−	0.293500i	0.0113969	−	0.0128461i
$523$	22.2269	+	23.2719i	0.971914	+	1.01761i	0.999838	+	0.0180007i	$0.00573012\pi$
$523$	22.2269	+	23.2719i	0.971914	+	1.01761i	−0.0279244	+	0.999610i	$0.508890\pi$
$524$	15.4637	+	13.4673i	0.675534	+	0.588323i
$525$	34.9218	+	111.651i	1.52411	+	4.87286i
$526$	7.11979	−	6.43442i	0.310438	−	0.280554i
$527$	−3.04365	−	0.921372i	−0.132583	−	0.0401356i
$528$	1.34901	+	6.28974i	0.0587080	+	0.273726i
$529$	−13.5112	+	17.6921i	−0.587442	+	0.769220i
$530$	6.71379	−	3.47541i	0.291628	−	0.150962i
$531$	−0.110945	+	0.169815i	−0.00481462	+	0.00736933i
$532$	−13.5653	+	28.4315i	−0.588130	+	1.23266i
$533$	7.83854	+	11.9978i	0.339525	+	0.519681i
$534$	−13.5061	−	7.63320i	−0.584466	−	0.330321i
$535$	−30.5116	+	8.02554i	−1.31913	+	0.346975i
$536$	−6.35366	+	21.7056i	−0.274437	+	0.937540i
$537$	8.16025	−	20.6326i	0.352141	−	0.890362i
$538$	−8.07328	+	3.45319i	−0.348064	+	0.148878i
$539$	−24.8447	−	49.0945i	−1.07014	−	2.11465i
$540$	−28.1796	+	19.5393i	−1.21266	+	0.840836i
$541$	37.4421	−	0.687960i	1.60976	−	0.0295777i	0.793983	−	0.607940i	$-0.208004\pi$
$541$	37.4421	−	0.687960i	1.60976	−	0.0295777i	0.815780	+	0.578362i	$0.196308\pi$
$542$	−15.4361	+	0.283623i	−0.663038	+	0.0121826i
$543$	18.4695	−	12.8064i	0.792600	−	0.549577i
$544$	9.99001	+	19.7408i	0.428318	+	0.846380i
$545$	21.8485	−	9.34527i	0.935886	−	0.400307i
$546$	−4.68705	+	11.8509i	−0.200587	+	0.507170i
$547$	−3.66334	+	12.5148i	−0.156633	+	0.535095i	−0.999997	−	0.00224644i	$-0.999285\pi$
$547$	−3.66334	+	12.5148i	−0.156633	+	0.535095i	0.843365	+	0.537342i	$0.180571\pi$
$548$	21.0865	−	5.54644i	0.900772	−	0.236932i
$549$	−0.603635	−	0.341154i	−0.0257625	−	0.0145601i
$550$	−18.2205	−	27.8885i	−0.776924	−	1.18917i
$551$	−17.9911	+	9.00865i	−0.766446	+	0.383781i
$552$	−2.00098	+	3.06272i	−0.0851672	+	0.130358i
$553$	9.27428	−	4.80085i	0.394383	−	0.204153i
$554$	0.522157	−	0.683734i	0.0221843	−	0.0290491i
$555$	13.9828	+	65.1948i	0.593538	+	2.76737i
$556$	−9.52859	−	2.88449i	−0.404102	−	0.122330i
$557$	−2.00570	+	1.81263i	−0.0849844	+	0.0768035i	−0.711886	−	0.702295i	$-0.752159\pi$
$557$	−2.00570	+	1.81263i	−0.0849844	+	0.0768035i	0.626902	+	0.779098i	$0.284323\pi$
$558$	−0.0213268	−	0.0681856i	−0.000902836	−	0.00288653i
$559$	−9.76034	−	8.50029i	−0.412818	−	0.359524i
$560$	−17.0507	−	17.8524i	−0.720524	−	0.754402i
$561$	13.9595	−	15.7346i	0.589372	−	0.664317i
$562$	−5.42963	−	14.5019i	−0.229035	−	0.611726i
$563$	3.88390	+	5.28424i	0.163687	+	0.222704i	0.879877	−	0.475201i	$-0.157625\pi$
$563$	3.88390	+	5.28424i	0.163687	+	0.222704i	−0.716190	+	0.697905i	$0.754116\pi$
$564$	1.78177	−	0.131174i	0.0750259	−	0.00552342i
$565$	−67.2322	−	33.2513i	−2.82848	−	1.39889i
$566$	−14.0255	+	14.1550i	−0.589537	+	0.594978i
$567$	−38.7196	−	16.5616i	−1.62607	−	0.695520i
$568$	1.76237	+	27.3701i	0.0739473	+	1.14842i
$569$	36.3114	−	6.05930i	1.52225	−	0.254019i	0.656437	−	0.754381i	$-0.272063\pi$
$569$	36.3114	−	6.05930i	1.52225	−	0.254019i	0.865817	+	0.500361i	$0.166800\pi$
$570$	−22.7161	+	5.20861i	−0.951471	+	0.218165i
$571$	11.8921	+	1.98444i	0.497668	+	0.0830461i	0.408105	−	0.912935i	$-0.366190\pi$
$571$	11.8921	+	1.98444i	0.497668	+	0.0830461i	0.0895631	+	0.995981i	$0.471453\pi$
$572$	−1.04555	+	10.3121i	−0.0437168	+	0.431172i
$573$	−0.0821376	−	8.94142i	−0.00343135	−	0.373533i
$574$	15.3140	+	17.9137i	0.639194	+	0.747705i
$575$	−2.54603	+	11.8708i	−0.106177	+	0.495048i
$576$	−0.108379	+	0.195945i	−0.00451579	+	0.00816438i
$577$	−0.868649	−	6.26424i	−0.0361623	−	0.260784i	0.963821	−	0.266550i	$-0.0858838\pi$
$577$	−0.868649	−	6.26424i	−0.0361623	−	0.260784i	−0.999983	+	0.00576639i	$0.998164\pi$
$578$	−0.873165	+	1.72542i	−0.0363189	+	0.0717680i
$579$	2.54252	−	39.4861i	0.105664	−	1.64098i
$580$	−3.01644	−	29.7506i	−0.125251	−	1.23533i
$581$	35.0267	−	3.87675i	1.45315	−	0.160835i
$582$	6.30511	+	6.13370i	0.261355	+	0.254250i
$583$	7.60237	+	1.99967i	0.314858	+	0.0828179i
$584$	5.31720	−	8.83092i	0.220027	−	0.365426i
$585$	−1.05550	+	0.319522i	−0.0436397	+	0.0132106i
$586$	−4.08547	−	7.38638i	−0.168769	−	0.305128i
$587$	−30.6131	+	22.9367i	−1.26354	+	0.946697i	−0.999840	−	0.0179077i	$-0.994299\pi$
$587$	−30.6131	+	22.9367i	−1.26354	+	0.946697i	−0.263700	+	0.964605i	$0.584943\pi$
$588$	10.3724	−	40.9597i	0.427750	−	1.68915i
$589$	−0.284528	+	3.65261i	−0.0117238	+	0.150503i
$590$	−1.32876	−	5.24715i	−0.0547042	−	0.216022i
$591$	14.4026	+	11.6411i	0.592444	+	0.478851i
$592$	−6.45793	−	8.14173i	−0.265419	−	0.334623i
$593$	−2.43801	−	0.938436i	−0.100117	−	0.0385369i	0.308650	−	0.951176i	$-0.400123\pi$
$593$	−2.43801	−	0.938436i	−0.100117	−	0.0385369i	−0.408767	+	0.912639i	$0.634041\pi$
$594$	12.3810	+	1.60107i	0.507997	+	0.0656927i
$595$	−14.0173	+	79.4963i	−0.574655	+	3.25903i
$596$	0.0709815	−	2.57508i	0.00290751	−	0.105479i
$597$	10.9271	+	2.44882i	0.447216	+	0.100223i
$598$	−1.02861	+	0.831386i	−0.0420629	+	0.0339979i
$599$	−6.38337	−	4.78269i	−0.260817	−	0.195415i	0.461189	−	0.887302i	$-0.347423\pi$
$599$	−6.38337	−	4.78269i	−0.260817	−	0.195415i	−0.722006	+	0.691887i	$0.756780\pi$
$600$	8.25760	−	59.5495i	0.337115	−	2.43110i
$601$	3.65272	+	2.53274i	0.148998	+	0.103313i	0.641961	−	0.766738i	$-0.278121\pi$
$601$	3.65272	+	2.53274i	0.148998	+	0.103313i	−0.492963	+	0.870050i	$0.664086\pi$
$602$	−17.7106	−	11.8045i	−0.721831	−	0.481114i
$603$	−0.863637	−	0.622633i	−0.0351700	−	0.0253556i
$604$	−13.5228	−	2.77065i	−0.550234	−	0.112736i
$605$	−0.187262	+	1.18939i	−0.00761327	+	0.0483557i
$606$	−0.958286	−	0.348788i	−0.0389277	−	0.0141685i
$607$	−27.0715	−	21.0706i	−1.09880	−	0.855228i	−0.108487	−	0.994098i	$-0.534600\pi$
$607$	−27.0715	−	21.0706i	−1.09880	−	0.855228i	−0.990311	+	0.138870i	$0.955653\pi$
$608$	19.7444	−	16.1204i	0.800742	−	0.653768i
$609$	30.1693	−	23.4817i	1.22252	−	0.951526i
$610$	17.6070	−	5.68513i	0.712888	−	0.230184i
$611$	1.47482	+	0.359091i	0.0596646	+	0.0145273i
$612$	−0.656038	+	0.0848368i	−0.0265188	+	0.00342933i
$613$	−0.422101	+	9.18368i	−0.0170485	+	0.370925i	0.973054	+	0.230578i	$0.0740617\pi$
$613$	−0.422101	+	9.18368i	−0.0170485	+	0.370925i	−0.990102	+	0.140347i	$0.955178\pi$
$614$	−2.45719	−	15.6068i	−0.0991640	−	0.629841i
$615$	9.54681	−	48.8743i	0.384964	−	1.97080i
$616$	1.10375	+	40.0421i	0.0444715	+	1.61334i
$617$	−7.63214	−	1.12988i	−0.307258	−	0.0454873i	−0.00895949	−	0.999960i	$-0.502852\pi$
$617$	−7.63214	−	1.12988i	−0.307258	−	0.0454873i	−0.298299	+	0.954473i	$0.596419\pi$
$618$	−8.74675	+	1.62527i	−0.351846	+	0.0653780i
$619$	36.7247	+	14.9163i	1.47609	+	0.599536i	0.965526	−	0.260305i	$-0.0838231\pi$
$619$	36.7247	+	14.9163i	1.47609	+	0.599536i	0.510563	+	0.859841i	$0.329437\pi$
$620$	−4.92420	−	2.32378i	−0.197760	−	0.0933254i
$621$	−2.76143	−	3.61592i	−0.110812	−	0.145102i
$622$	−5.21911	+	6.10511i	−0.209267	+	0.244793i
$623$	47.4235	+	39.7931i	1.89998	+	1.59428i
$624$	−3.06151	+	2.87072i	−0.122558	+	0.114921i
$625$	−23.6482	−	101.159i	−0.945928	−	4.04636i
$626$	3.83975	−	2.07797i	0.153467	−	0.0830522i
$627$	−21.1557	−	11.8192i	−0.844877	−	0.472012i
$628$	10.1198	+	5.47658i	0.403826	+	0.218540i
$629$	−8.94545	+	32.7818i	−0.356678	+	1.30710i
$630$	−1.65401	+	0.743707i	−0.0658973	+	0.0296300i
$631$	−36.5051	+	26.3181i	−1.45324	+	1.04771i	−0.466664	+	0.884435i	$0.654544\pi$
$631$	−36.5051	+	26.3181i	−1.45324	+	1.04771i	−0.986581	+	0.163273i	$0.947795\pi$
$632$	−5.36319	+	0.197153i	−0.213336	+	0.00784231i
$633$	−11.2559	−	21.2635i	−0.447383	−	0.845148i
$634$	−3.81441	+	10.1878i	−0.151490	+	0.404611i
$635$	−8.31934	+	2.35249i	−0.330143	+	0.0933556i
$636$	3.39393	+	4.99204i	0.134578	+	0.197947i
$637$	19.0790	−	30.4084i	0.755939	−	1.20482i
$638$	−6.44744	+	8.77206i	−0.255257	+	0.347289i
$639$	−1.24241	−	0.351320i	−0.0491489	−	0.0138980i
$640$	14.2739	+	42.8562i	0.564224	+	1.69404i
$641$	26.6351	+	26.8809i	1.05202	+	1.06173i	0.998001	+	0.0631927i	$0.0201283\pi$
$641$	26.6351	+	26.8809i	1.05202	+	1.06173i	0.0540226	+	0.998540i	$0.482796\pi$
$642$	3.24391	+	8.20198i	0.128027	+	0.323706i
$643$	−46.4678	+	4.28055i	−1.83251	+	0.168809i	−0.952178	−	0.305545i	$-0.901161\pi$
$643$	−46.4678	+	4.28055i	−1.83251	+	0.168809i	−0.880334	+	0.474354i	$0.842682\pi$
$644$	4.29045	−	4.49218i	0.169068	−	0.177017i
$645$	3.71387	+	44.8198i	0.146234	+	1.76478i
$646$	−11.5011	−	2.96459i	−0.452506	−	0.116640i
$647$	−0.526319	+	6.35173i	−0.0206917	+	0.249712i	0.978386	+	0.206785i	$0.0663000\pi$
$647$	−0.526319	+	6.35173i	−0.0206917	+	0.249712i	−0.999078	+	0.0429274i	$0.986332\pi$
$648$	14.3627	+	16.1891i	0.564221	+	0.635968i
$649$	2.63318	−	4.97431i	0.103361	−	0.195259i
$650$	9.45578	−	19.5694i	0.370886	−	0.767574i
$651$	−0.829322	−	6.91170i	−0.0325037	−	0.270891i
$652$	−14.9271	−	13.9968i	−0.584589	−	0.548158i
$653$	−8.72025	+	15.1039i	−0.341250	+	0.591062i	−0.984665	−	0.174455i	$-0.944184\pi$
$653$	−8.72025	+	15.1039i	−0.341250	+	0.591062i	0.643415	+	0.765517i	$0.277517\pi$
$654$	−3.32170	−	5.75336i	−0.129889	−	0.224974i
$655$	13.7804	−	58.9479i	0.538445	−	2.30329i
$656$	2.04316	+	7.48746i	0.0797721	+	0.292336i
$657$	0.308491	+	0.374580i	0.0120354	+	0.0146138i
$658$	2.48097	+	0.274594i	0.0967184	+	0.0107048i
$659$	−0.164180	+	17.8725i	−0.00639555	+	0.696212i	0.934212	+	0.356717i	$0.116104\pi$
$659$	−0.164180	+	17.8725i	−0.00639555	+	0.696212i	−0.940608	+	0.339495i	$0.889744\pi$
$660$	27.5896	−	23.1505i	1.07393	−	0.901130i
$661$	−1.78871	+	14.9074i	−0.0695727	+	0.579829i	0.914822	+	0.403857i	$0.132331\pi$
$661$	−1.78871	+	14.9074i	−0.0695727	+	0.579829i	−0.984395	+	0.175973i	$0.943693\pi$
$662$	−17.1878	−	11.0054i	−0.668022	−	0.427737i
$663$	13.4924	+	2.50707i	0.524000	+	0.0973666i
$664$	−17.1290	−	5.88040i	−0.664735	−	0.228204i
$665$	92.9184	−	3.87481i	3.60322	−	0.150258i
$666$	−0.722042	+	0.247877i	−0.0279786	+	0.00960505i
$667$	3.92481	−	0.581039i	0.151969	−	0.0224979i
$668$	3.72645	+	21.1337i	0.144181	+	0.817689i
$669$	−0.315364	−	6.86140i	−0.0121927	−	0.265277i
$670$	27.8321	−	5.70246i	1.07525	−	0.220305i
$671$	17.5466	+	7.88962i	0.677378	+	0.304575i
$672$	−30.7893	+	37.3854i	−1.18772	+	1.44217i
$673$	19.8240	−	19.2851i	0.764159	−	0.743386i	−0.207893	−	0.978152i	$-0.566660\pi$
$673$	19.8240	−	19.2851i	0.764159	−	0.743386i	0.972052	+	0.234766i	$0.0754324\pi$
$674$	−12.1851	+	6.88662i	−0.469353	+	0.265263i
$675$	66.3979	+	34.3710i	2.55566	+	1.32294i
$676$	11.3001	−	5.33263i	0.434618	−	0.205101i
$677$	−37.5964	+	2.07425i	−1.44495	+	0.0797199i	−0.760498	−	0.649341i	$-0.775045\pi$
$677$	−37.5964	+	2.07425i	−1.44495	+	0.0797199i	−0.684449	+	0.729061i	$0.739957\pi$
$678$	−6.99052	+	19.7695i	−0.268469	+	0.759242i
$679$	−20.2652	−	28.6606i	−0.777707	−	1.09989i
$680$	23.9499	−	33.8719i	0.918438	−	1.29893i
$681$	−1.61150	−	4.55738i	−0.0617528	−	0.174639i
$682$	0.762801	+	1.82967i	0.0292092	+	0.0700616i
$683$	21.8087	−	23.6906i	0.834488	−	0.906495i	−0.162287	−	0.986744i	$-0.551887\pi$
$683$	21.8087	−	23.6906i	0.834488	−	0.906495i	0.996775	+	0.0802483i	$0.0255713\pi$
$684$	0.257607	+	0.717245i	0.00984984	+	0.0274245i
$685$	−43.5957	−	47.3575i	−1.66571	−	1.80944i
$686$	14.4108	−	31.2782i	0.550205	−	1.19421i
$687$	16.9564	+	15.3241i	0.646928	+	0.584652i
$688$	−3.61556	−	6.00481i	−0.137842	−	0.228931i
$689$	1.44080	+	4.92212i	0.0548901	+	0.187518i
$690$	4.57628	+	0.421560i	0.174216	+	0.0160485i
$691$	−16.2149	+	14.1216i	−0.616846	+	0.537211i	−0.907734	−	0.419546i	$-0.862189\pi$
$691$	−16.2149	+	14.1216i	−0.616846	+	0.537211i	0.290889	+	0.956757i	$0.406049\pi$
$692$	−23.3000	−	14.3224i	−0.885732	−	0.544458i
$693$	−1.79449	−	0.579422i	−0.0681670	−	0.0220104i
$694$	−6.87141	+	2.50099i	−0.260835	+	0.0949363i
$695$	5.63452	+	28.8456i	0.213729	+	1.09418i
$696$	−19.1713	+	4.29640i	−0.726688	+	0.162855i
$697$	15.7710	−	19.8830i	0.597368	−	0.753122i
$698$	0.321732	−	0.189714i	0.0121777	−	0.00718077i
$699$	−16.7269	+	8.27267i	−0.632668	+	0.312901i
$700$	−32.2572	+	96.8499i	−1.21921	+	3.66058i
$701$	18.9334	−	27.8487i	0.715106	−	1.05183i	−0.280652	−	0.959810i	$-0.590551\pi$
$701$	18.9334	−	27.8487i	0.715106	−	1.05183i	0.995757	−	0.0920205i	$-0.0293325\pi$
$702$	3.27176	+	7.45886i	0.123485	+	0.281517i
$703$	39.0990	+	1.96373i	1.47465	+	0.0740635i
$704$	2.49576	−	5.68976i	0.0940625	−	0.214441i
$705$	−2.80318	−	4.46774i	−0.105574	−	0.168265i
$706$	21.9067	+	1.61277i	0.824468	+	0.0606974i
$707$	3.50535	+	2.06698i	0.131832	+	0.0777368i
$708$	4.03350	−	1.55257i	0.151588	−	0.0583491i
$709$	−49.2420	+	11.9895i	−1.84932	+	0.450276i	−0.997314	−	0.0732507i	$-0.976663\pi$
$709$	−49.2420	+	11.9895i	−1.84932	+	0.450276i	−0.852009	+	0.523527i	$0.824616\pi$
$710$	29.3511	−	18.0420i	1.10153	−	0.677106i
$711$	0.0754183	−	0.241126i	0.00282841	−	0.00904292i
$712$	−13.3127	−	28.8950i	−0.498916	−	1.08289i
$713$	0.278000	−	0.666815i	0.0104112	−	0.0249724i
$714$	22.5331	+	1.24319i	0.843281	+	0.0465251i
$715$	28.3501	−	11.5148i	1.06023	−	0.430629i
$716$	16.3048	−	10.4400i	0.609339	−	0.390162i
$717$	−4.76275	−	9.85684i	−0.177868	−	0.368110i
$718$	−1.90522	−	0.0700366i	−0.0711023	−	0.00261374i
$719$	13.3099	−	8.87128i	0.496374	−	0.330843i	−0.281184	−	0.959654i	$-0.590727\pi$
$719$	13.3099	−	8.87128i	0.496374	−	0.330843i	0.777558	+	0.628811i	$0.216458\pi$
$720$	−0.597128	−	0.0109716i	−0.0222536	−	0.000408887i
$721$	35.5007			1.32212
$722$	−0.493359	+	13.6745i	−0.0183609	+	0.508911i
$723$	18.2439			0.678499
$724$	19.6082	+	0.360280i	0.728733	+	0.0133897i
$725$	−54.2530	+	36.1607i	−2.01491	+	1.34297i
$726$	0.336384	+	0.0123656i	0.0124844	+	0.000458929i
$727$	10.0526	+	20.8046i	0.372832	+	0.771601i	0.999973	−	0.00730428i	$-0.00232504\pi$
$727$	10.0526	+	20.8046i	0.372832	+	0.771601i	−0.627142	+	0.778905i	$0.715775\pi$
$728$	−22.0091	+	14.0925i	−0.815712	+	0.522303i
$729$	−25.9205	+	10.5280i	−0.960020	+	0.389926i
$730$	−12.9292	−	0.713324i	−0.478531	−	0.0264013i
$731$	−8.81952	+	21.1547i	−0.326202	+	0.782434i
$732$	6.18202	+	13.4179i	0.228494	+	0.495941i
$733$	4.66862	−	14.9264i	0.172439	−	0.551319i	−0.827509	−	0.561452i	$-0.810243\pi$
$733$	4.66862	−	14.9264i	0.172439	−	0.551319i	0.999949	+	0.0101326i	$0.00322538\pi$
$734$	−5.19700	+	3.19459i	−0.191825	+	0.117914i
$735$	−121.196	+	29.5091i	−4.47039	+	1.08846i
$736$	−4.69078	+	1.80557i	−0.172905	+	0.0665541i
$737$	25.4468	+	15.0051i	0.937345	+	0.552718i
$738$	0.568610	+	0.0418611i	0.0209308	+	0.00154093i
$739$	20.9373	+	33.3701i	0.770190	+	1.22754i	0.968893	+	0.247479i	$0.0796020\pi$
$739$	20.9373	+	33.3701i	0.770190	+	1.22754i	−0.198703	+	0.980060i	$0.563673\pi$
$740$	−23.3715	+	53.2818i	−0.859155	+	1.95868i
$741$	−0.513606	−	15.8020i	−0.0188678	−	0.580502i
$742$	3.38784	+	7.72350i	0.124372	+	0.283539i
$743$	−21.3414	+	31.3904i	−0.782938	+	1.15160i	0.202116	+	0.979361i	$0.435218\pi$
$743$	−21.3414	+	31.3904i	−0.782938	+	1.15160i	−0.985055	+	0.172242i	$0.944899\pi$
$744$	−1.13046	+	3.39413i	−0.0414447	+	0.124435i
$745$	−6.81682	+	3.37142i	−0.249749	+	0.123519i
$746$	−12.9726	+	7.64950i	−0.474962	+	0.280068i
$747$	0.529805	−	0.667943i	0.0193845	−	0.0244388i
$748$	17.9102	−	4.01378i	0.654863	−	0.146758i
$749$	−6.74750	−	34.5434i	−0.246548	−	1.26219i
$750$	−45.8451	+	16.6862i	−1.67402	+	0.609295i
$751$	−50.3667	−	16.2629i	−1.83791	−	0.593442i	−0.998773	−	0.0495181i	$-0.984231\pi$
$751$	−50.3667	−	16.2629i	−1.83791	−	0.593442i	−0.839135	−	0.543924i	$-0.816938\pi$
$752$	0.700299	+	0.430472i	0.0255373	+	0.0156977i
$753$	9.73517	−	8.47837i	0.354769	−	0.308969i
$754$	−7.07272	−	0.651530i	−0.257573	−	0.0237273i
$755$	11.4482	+	39.1098i	0.416643	+	1.42335i
$756$	−19.7327	−	32.7726i	−0.717673	−	1.19193i
$757$	7.96428	+	7.19761i	0.289467	+	0.261602i	0.802346	−	0.596859i	$-0.203585\pi$
$757$	7.96428	+	7.19761i	0.289467	+	0.261602i	−0.512879	+	0.858461i	$0.671421\pi$
$758$	3.48834	−	7.57136i	0.126702	−	0.275004i
$759$	3.23646	+	3.51574i	0.117476	+	0.127613i
$760$	−44.0340	−	18.5783i	−1.59728	−	0.673904i
$761$	14.5242	−	15.7775i	0.526502	−	0.571934i	−0.414622	−	0.909994i	$-0.636086\pi$
$761$	14.5242	−	15.7775i	0.526502	−	0.571934i	0.941125	+	0.338060i	$0.109771\pi$
$762$	0.930075	+	2.23090i	0.0336931	+	0.0808168i
$763$	8.83775	+	24.9935i	0.319948	+	0.904826i
$764$	4.50466	−	6.37084i	0.162973	−	0.230489i
$765$	1.12745	+	1.59453i	0.0407632	+	0.0576505i
$766$	5.55285	−	15.7037i	0.200633	−	0.567398i
$767$	3.66643	−	0.202283i	0.132387	−	0.00730400i
$768$	17.2459	−	8.13853i	0.622307	−	0.293674i
$769$	13.6748	+	7.07877i	0.493125	+	0.255267i	0.688199	−	0.725522i	$-0.258401\pi$
$769$	13.6748	+	7.07877i	0.493125	+	0.255267i	−0.195075	+	0.980788i	$0.562495\pi$
$770$	43.8069	−	24.7582i	1.57869	−	0.892224i
$771$	−16.5828	+	16.1320i	−0.597213	+	0.580978i
$772$	21.9494	−	26.6516i	0.789975	−	0.959214i
$773$	9.66112	+	4.34401i	0.347486	+	0.156243i	0.576324	−	0.817221i	$-0.304487\pi$
$773$	9.66112	+	4.34401i	0.347486	+	0.156243i	−0.228838	+	0.973465i	$0.573492\pi$
$774$	−0.504431	+	0.103352i	−0.0181314	+	0.00371490i
$775$	0.545085	+	11.8595i	0.0195800	+	0.426004i
$776$	3.13240	+	17.7647i	0.112447	+	0.637717i
$777$	−73.5828	+	10.8934i	−2.63977	+	0.390798i
$778$	13.9957	−	4.80473i	0.501770	−	0.172258i
$779$	−26.2714	−	12.8322i	−0.941270	−	0.459762i
$780$	22.2243	+	7.62960i	0.795757	+	0.273184i
$781$	35.2216	+	6.54467i	1.26033	+	0.234187i
$782$	1.97237	+	1.26292i	0.0705319	+	0.0451619i
$783$	2.91086	−	24.2596i	0.104026	−	0.866966i
$784$	14.8925	−	12.4963i	0.531875	−	0.446296i
$785$	0.312040	−	33.9684i	0.0111372	−	1.21238i
$786$	−16.8215	−	1.86180i	−0.600002	−	0.0664082i
$787$	16.2225	+	19.6979i	0.578270	+	0.702154i	0.976594	−	0.215091i	$-0.0690047\pi$
$787$	16.2225	+	19.6979i	0.578270	+	0.702154i	−0.398324	+	0.917245i	$0.630408\pi$
$788$	4.25403	+	15.5895i	0.151543	+	0.555352i
$789$	5.14943	−	22.0275i	0.183325	−	0.784200i
$790$	3.37084	+	5.83846i	0.119929	+	0.207723i
$791$	41.8377	−	72.4650i	1.48758	−	2.57656i
$792$	0.706915	+	0.662860i	0.0251191	+	0.0235537i
$793$	1.49534	+	12.4624i	0.0531010	+	0.442552i
$794$	7.24212	−	14.9881i	0.257013	−	0.531907i
$795$	8.33743	−	15.7502i	0.295698	−	0.558601i
$796$	6.48480	+	7.30941i	0.229848	+	0.259075i
$797$	−1.83179	+	22.1064i	−0.0648854	+	0.783050i	0.884012	+	0.467465i	$0.154832\pi$
$797$	−1.83179	+	22.1064i	−0.0648854	+	0.783050i	−0.948897	+	0.315585i	$0.897799\pi$
$798$	−4.17027	−	25.6628i	−0.147626	−	0.908454i
$799$	−0.221967	−	2.67874i	−0.00785262	−	0.0947671i
$800$	57.0485	−	59.7308i	2.01697	−	2.11180i
$801$	1.49136	−	0.137382i	0.0526945	−	0.00485415i
$802$	1.86209	+	4.70816i	0.0657527	+	0.166251i
$803$	−9.47692	−	9.56438i	−0.334433	−	0.337519i
$804$	7.16842	+	21.5227i	0.252811	+	0.759045i
$805$	−17.6467	−	4.99000i	−0.621963	−	0.175874i
$806$	−0.765939	+	1.04210i	−0.0269791	+	0.0367063i
$807$	−11.0008	+	17.5332i	−0.387246	+	0.617197i
$808$	−1.17579	−	1.72944i	−0.0413641	−	0.0608414i
$809$	7.25134	−	2.05048i	0.254944	−	0.0720912i	−0.142234	−	0.989833i	$-0.545428\pi$
$809$	7.25134	−	2.05048i	0.254944	−	0.0720912i	0.397177	+	0.917742i	$0.369990\pi$
$810$	9.53250	−	25.4602i	0.334938	−	0.894580i
$811$	7.14875	+	13.5046i	0.251027	+	0.474212i	0.976923	−	0.213592i	$-0.0685163\pi$
$811$	7.14875	+	13.5046i	0.251027	+	0.474212i	−0.725896	+	0.687804i	$0.758575\pi$
$812$	33.3372	−	1.22548i	1.16991	−	0.0430061i
$813$	−29.5209	+	21.2829i	−1.03534	+	0.746424i
$814$	19.3189	−	8.68653i	0.677128	−	0.304463i
$815$	−15.9031	+	58.2791i	−0.557061	+	2.04143i
$816$	6.53616	+	3.53720i	0.228812	+	0.123827i
$817$	25.9843	+	4.69575i	0.909074	+	0.164284i
$818$	−13.2838	+	7.18884i	−0.464457	+	0.251352i
$819$	−0.280056	−	1.19798i	−0.00978594	−	0.0418609i
$820$	31.6980	−	29.7226i	1.10694	−	1.03796i
$821$	−0.698568	−	0.586168i	−0.0243802	−	0.0204574i	0.630516	−	0.776176i	$-0.282843\pi$
$821$	−0.698568	−	0.586168i	−0.0243802	−	0.0204574i	−0.654896	+	0.755719i	$0.727288\pi$
$822$	−11.6933	+	13.6784i	−0.407851	+	0.477088i
$823$	−9.80345	−	12.8370i	−0.341727	−	0.447471i	0.591743	−	0.806126i	$-0.298440\pi$
$823$	−9.80345	−	12.8370i	−0.341727	−	0.447471i	−0.933470	+	0.358656i	$0.883235\pi$
$824$	−16.4991	−	7.78611i	−0.574773	−	0.271242i
$825$	−72.7549	−	29.5505i	−2.53300	−	1.02882i
$826$	5.93683	−	1.10315i	0.206569	−	0.0383834i
$827$	−27.0069	−	3.99817i	−0.939121	−	0.139030i	−0.340664	−	0.940185i	$-0.610652\pi$
$827$	−27.0069	−	3.99817i	−0.939121	−	0.139030i	−0.598457	+	0.801155i	$0.704219\pi$
$828$	−0.00414087	−	0.150223i	−0.000143905	−	0.00522061i
$829$	−5.05418	+	25.8746i	−0.175539	+	0.898662i	0.784783	+	0.619770i	$0.212774\pi$
$829$	−5.05418	+	25.8746i	−0.175539	+	0.898662i	−0.960322	+	0.278892i	$0.910033\pi$
$830$	3.53821	+	22.4729i	0.122813	+	0.780047i
$831$	0.0931116	−	2.02584i	0.00323001	−	0.0702755i
$832$	4.02007	−	0.519862i	0.139371	−	0.0180230i
$833$	−61.7646	−	15.0385i	−2.14002	−	0.521055i
$834$	7.81917	−	2.52473i	0.270756	−	0.0874243i
$835$	49.9944	−	38.9122i	1.73013	−	1.34661i
$836$	−8.94314	−	19.1616i	−0.309305	−	0.662718i
$837$	−3.51091	−	2.73265i	−0.121355	−	0.0944542i
$838$	8.42437	+	3.06622i	0.291015	+	0.105921i
$839$	1.02846	−	6.53225i	0.0355063	−	0.225518i	−0.963622	−	0.267270i	$-0.913879\pi$
$839$	1.02846	−	6.53225i	0.0355063	−	0.225518i	0.999128	+	0.0417514i	$0.0132937\pi$
$840$	88.9619	+	18.2272i	3.06948	+	0.628898i
$841$	−6.24028	−	4.49889i	−0.215182	−	0.155134i
$842$	−20.7822	−	13.8517i	−0.716202	−	0.477362i
$843$	−29.9966	−	20.7992i	−1.03314	−	0.716362i
$844$	2.88355	−	20.7947i	0.0992559	−	0.715782i
$845$	−29.5210	−	22.1184i	−1.01555	−	0.760896i
$846$	0.0469643	−	0.0379596i	0.00161467	−	0.00130508i
$847$	−1.31071	−	0.293737i	−0.0450365	−	0.0100929i
$848$	−0.0765306	+	2.77639i	−0.00262807	+	0.0953416i
$849$	−8.15670	+	46.2590i	−0.279937	+	1.58760i
$850$	−38.1693	−	4.93593i	−1.30920	−	0.169301i
$851$	−7.20441	−	2.77311i	−0.246964	−	0.0950610i
$852$	17.0956	+	21.5531i	0.585687	+	0.738396i
$853$	−10.8636	−	8.78070i	−0.371964	−	0.300645i	0.424386	−	0.905482i	$-0.360490\pi$
$853$	−10.8636	−	8.78070i	−0.371964	−	0.300645i	−0.796350	+	0.604836i	$0.793239\pi$
$854$	5.06702	+	20.0092i	0.173390	+	0.684701i
$855$	1.51561	−	1.66277i	0.0518326	−	0.0568657i
$856$	−4.44023	+	17.5341i	−0.151764	+	0.599302i
$857$	−29.8907	+	22.3954i	−1.02105	+	0.765012i	−0.972285	−	0.233798i	$-0.924885\pi$
$857$	−29.8907	+	22.3954i	−1.02105	+	0.765012i	−0.0487626	+	0.998810i	$0.515528\pi$
$858$	−4.14045	−	7.48578i	−0.141353	−	0.255560i
$859$	6.05413	−	1.83271i	0.206564	−	0.0625311i	−0.184761	−	0.982783i	$-0.559151\pi$
$859$	6.05413	−	1.83271i	0.206564	−	0.0625311i	0.391325	+	0.920252i	$0.372017\pi$
$860$	−20.2427	+	33.6196i	−0.690272	+	1.14642i
$861$	53.7267	+	14.1319i	1.83100	+	0.481613i
$862$	4.87379	+	4.74130i	0.166002	+	0.161489i
$863$	50.9102	−	5.63474i	1.73300	−	0.191809i	0.812611	−	0.582807i	$-0.198045\pi$
$863$	50.9102	−	5.63474i	1.73300	−	0.191809i	0.920392	+	0.390998i	$0.127870\pi$
$864$	3.12237	+	30.7954i	0.106225	+	1.04768i
$865$	−5.18826	+	80.5751i	−0.176406	+	2.73964i
$866$	−8.68187	+	17.1558i	−0.295022	+	0.582979i
$867$	0.626112	+	4.51519i	0.0212639	+	0.153344i
$868$	2.94003	−	5.31545i	0.0997910	−	0.180418i
$869$	−1.47007	+	6.85419i	−0.0498687	+	0.232513i
$870$	16.0370	+	18.7594i	0.543704	+	0.636004i
$871$	0.177042	+	19.2726i	0.00599884	+	0.653027i
$872$	1.37426	−	13.5541i	0.0465384	−	0.459001i
$873$	−0.837602	−	0.139771i	−0.0283485	−	0.00473053i
$874$	0.933626	−	2.53157i	0.0315804	−	0.0856315i
$875$	192.027	−	32.0436i	6.49170	−	1.08327i
$876$	−0.664382	−	10.3180i	−0.0224474	−	0.348614i
$877$	7.95741	+	3.40363i	0.268703	+	0.114932i	0.523396	−	0.852089i	$-0.324665\pi$
$877$	7.95741	+	3.40363i	0.268703	+	0.114932i	−0.254694	+	0.967022i	$0.581975\pi$
$878$	−6.37599	+	6.43483i	−0.215179	+	0.217165i
$879$	−17.8354	−	8.82090i	−0.601572	−	0.297521i
$880$	16.5264	−	1.21668i	0.557105	−	0.0410142i
$881$	12.7151	+	17.2995i	0.428382	+	0.582835i	0.965412	−	0.260728i	$-0.0839626\pi$
$881$	12.7151	+	17.2995i	0.428382	+	0.582835i	−0.537030	+	0.843563i	$0.680454\pi$
$882$	−0.500760	−	1.33747i	−0.0168615	−	0.0450350i
$883$	4.35255	−	4.90603i	0.146475	−	0.165101i	−0.670236	−	0.742148i	$-0.733807\pi$
$883$	4.35255	−	4.90603i	0.146475	−	0.165101i	0.816711	+	0.577047i	$0.195795\pi$
$884$	8.27083	+	8.65971i	0.278178	+	0.291258i
$885$	−9.62186	−	8.37969i	−0.323435	−	0.281680i
$886$	8.60075	+	27.4981i	0.288948	+	0.923818i
$887$	29.2889	−	26.4694i	0.983424	−	0.888756i	−0.0103748	−	0.999946i	$-0.503302\pi$
$887$	29.2889	−	26.4694i	0.983424	−	0.888756i	0.993799	+	0.111190i	$0.0354662\pi$
$888$	36.5870	+	11.0756i	1.22778	+	0.371673i
$889$	−2.02262	−	9.43044i	−0.0678364	−	0.316287i
$890$	−24.2559	+	31.7617i	−0.813061	+	1.06466i
$891$	25.1044	−	12.9953i	0.841029	−	0.435360i
$892$	3.27815	−	5.01758i	0.109760	−	0.168001i
$893$	−2.95942	+	0.911835i	−0.0990331	+	0.0305134i
$894$	1.16286	+	1.77990i	0.0388920	+	0.0595286i
$895$	−49.7594	−	28.1224i	−1.66327	−	0.940027i
$896$	−48.7344	+	12.8187i	−1.62810	+	0.428244i
$897$	−0.875850	+	2.99211i	−0.0292438	+	0.0999037i
$898$	0.942995	−	2.38429i	0.0314681	−	0.0795648i
$899$	3.56713	−	1.52577i	0.118970	−	0.0508873i
$900$	1.11509	+	2.20348i	0.0371696	+	0.0734492i
$901$	7.46331	−	5.17494i	0.248639	−	0.172402i
$902$	−15.8171	+	0.290622i	−0.526651	+	0.00967666i
$903$	−50.1634	+	0.921700i	−1.66933	+	0.0306723i
$904$	−35.3374	+	24.5024i	−1.17530	+	0.814938i
$905$	−26.1423	−	51.6585i	−0.868998	−	1.71719i
$906$	10.4746	−	4.48033i	0.347997	−	0.148849i
$907$	−1.96829	+	4.97669i	−0.0653562	+	0.165248i	−0.958912	−	0.283704i	$-0.908437\pi$
$907$	−1.96829	+	4.97669i	−0.0653562	+	0.165248i	0.893556	+	0.448952i	$0.148203\pi$
$908$	1.18498	−	4.04816i	0.0393248	−	0.134343i
$909$	0.0952093	−	0.0250431i	0.00315789	−	0.000830628i
$910$	28.5806	+	16.1528i	0.947438	+	0.535460i
$911$	1.34252	+	2.05488i	0.0444796	+	0.0680812i	0.858714	−	0.512455i	$-0.171264\pi$
$911$	1.34252	+	2.05488i	0.0444796	+	0.0680812i	−0.814234	+	0.580536i	$0.802843\pi$
$912$	2.36481	−	8.22911i	0.0783067	−	0.272493i
$913$	−12.9383	+	19.8036i	−0.428196	+	0.655402i
$914$	14.6036	−	7.55959i	0.483045	−	0.250049i
$915$	26.4711	−	34.6623i	0.875107	−	1.14590i
$916$	4.18223	+	19.4996i	0.138185	+	0.644285i
$917$	64.6380	+	19.5672i	2.13453	+	0.646166i
$918$	10.7007	−	9.67059i	0.353175	−	0.319177i
$919$	−6.54980	−	20.9409i	−0.216058	−	0.690775i	−0.997746	−	0.0671057i	$-0.978624\pi$
$919$	−6.54980	−	20.9409i	−0.216058	−	0.690775i	0.781688	−	0.623670i	$-0.214359\pi$
$920$	7.10693	+	6.18943i	0.234309	+	0.204059i
$921$	−25.7227	−	26.9321i	−0.847592	−	0.887444i
$922$	0.594925	−	0.670576i	0.0195928	−	0.0220843i
$923$	8.19534	+	21.8888i	0.269753	+	0.720478i
$924$	23.7953	+	32.3747i	0.782808	+	1.06505i
$925$	126.516	−	9.31410i	4.15981	−	0.306246i
$926$	−3.71180	−	1.83576i	−0.121977	−	0.0603267i
$927$	0.604499	−	0.610077i	0.0198543	−	0.0200376i
$928$	−24.8177	−	10.6153i	−0.814679	−	0.348464i
$929$	0.759048	+	11.7882i	0.0249036	+	0.386759i	0.991469	+	0.130340i	$0.0416070\pi$
$929$	0.759048	+	11.7882i	0.0249036	+	0.386759i	−0.966566	+	0.256419i	$0.917457\pi$
$930$	4.43261	−	0.739671i	0.145351	−	0.0242548i
$931$	−1.65681	+	73.2180i	−0.0542997	+	2.39962i
$932$	−16.0612	−	2.68014i	−0.526101	−	0.0877908i
$933$	−1.90986	+	18.8366i	−0.0625260	+	0.616684i
$934$	−0.134835	−	14.6780i	−0.00441193	−	0.480278i
$935$	−35.2097	−	41.1869i	−1.15148	−	1.34696i
$936$	−0.132588	+	0.618189i	−0.00433376	+	0.0202061i
$937$	20.6989	−	37.4228i	0.676203	−	1.22255i	−0.288063	−	0.957611i	$-0.593011\pi$
$937$	20.6989	−	37.4228i	0.676203	−	1.22255i	0.964266	−	0.264937i	$-0.0853513\pi$
$938$	4.35332	+	31.3939i	0.142141	+	1.02505i
$939$	4.64703	−	9.18278i	0.151650	−	0.299669i
$940$	0.295734	−	4.59282i	0.00964576	−	0.149801i
$941$	−4.73503	−	46.7008i	−0.154357	−	1.52240i	−0.717801	−	0.696248i	$-0.754851\pi$
$941$	−4.73503	−	46.7008i	−0.154357	−	1.52240i	0.563444	−	0.826154i	$-0.309476\pi$
$942$	−9.43919	+	1.04473i	−0.307545	+	0.0340391i
$943$	4.13257	+	4.02023i	0.134575	+	0.130917i
$944$	1.92317	+	0.505856i	0.0625939	+	0.0164642i
$945$	−58.2545	+	96.7504i	−1.89502	+	3.14729i
$946$	13.6742	−	4.13947i	0.444588	−	0.134586i
$947$	22.5974	+	40.8553i	0.734318	+	1.32762i	0.937330	+	0.348444i	$0.113290\pi$
$947$	22.5974	+	40.8553i	0.734318	+	1.32762i	−0.203011	+	0.979176i	$0.565073\pi$
$948$	−4.30804	+	3.22776i	−0.139919	+	0.104833i
$949$	2.15645	−	8.51565i	0.0700015	−	0.276430i
$950$	3.87954	+	44.1703i	0.125869	+	1.43307i
$951$	6.29507	+	24.8587i	0.204132	+	0.806098i
$952$	35.9922	+	29.0912i	1.16651	+	0.942852i
$953$	26.5773	+	33.5069i	0.860923	+	1.08540i	0.995525	+	0.0944953i	$0.0301237\pi$
$953$	26.5773	+	33.5069i	0.860923	+	1.08540i	−0.134602	+	0.990900i	$0.542976\pi$
$954$	0.190415	+	0.0732943i	0.00616492	+	0.00237299i
$955$	−22.8443	−	2.95415i	−0.739223	−	0.0955940i
$956$	1.65876	−	9.40732i	0.0536482	−	0.304254i
$957$	−0.707113	+	25.6528i	−0.0228577	+	0.829236i
$958$	1.35604	+	0.303896i	0.0438117	+	0.00981843i
$959$	55.8476	−	45.1396i	1.80341	−	1.45763i
$960$	−11.2721	−	8.44554i	−0.363806	−	0.272579i
$961$	−4.16093	+	30.0064i	−0.134223	+	0.967949i
$962$	11.3566	+	7.87451i	0.366153	+	0.253885i
$963$	−0.708521	−	0.472243i	−0.0228318	−	0.0152178i
$964$	12.9134	+	9.30987i	0.415914	+	0.299851i
$965$	−99.8542	−	20.4589i	−3.21442	−	0.658595i
$966$	−0.797367	+	5.06448i	−0.0256549	+	0.162947i
$967$	48.5107	+	17.6564i	1.56000	+	0.567793i	0.970736	−	0.240149i	$-0.0771962\pi$
$967$	48.5107	+	17.6564i	1.56000	+	0.567793i	0.589262	+	0.807942i	$0.299418\pi$
$968$	0.544734	+	0.423983i	0.0175084	+	0.0136273i
$969$	−26.2612	+	9.70529i	−0.843633	+	0.311779i
$970$	17.8819	−	13.9180i	0.574152	−	0.446881i
$971$	11.1739	−	3.60795i	0.358589	−	0.115785i	−0.122472	−	0.992472i	$-0.539082\pi$
$971$	11.1739	−	3.60795i	0.358589	−	0.115785i	0.481060	+	0.876687i	$0.340252\pi$
$972$	−1.76436	−	0.429589i	−0.0565919	−	0.0137791i
$973$	−32.5173	+	4.20503i	−1.04246	+	0.134807i
$974$	−0.318382	+	6.92706i	−0.0102016	+	0.221957i
$975$	−7.96809	−	50.6094i	−0.255183	−	1.62080i
$976$	−1.30314	+	6.67136i	−0.0417126	+	0.213545i
$977$	0.501196	+	18.1825i	0.0160347	+	0.581708i	0.964388	+	0.264492i	$0.0852043\pi$
$977$	0.501196	+	18.1825i	0.0160347	+	0.581708i	−0.948353	+	0.317216i	$0.897252\pi$
$978$	16.7065	+	2.47328i	0.534216	+	0.0790867i
$979$	−40.8562	+	7.59165i	−1.30577	+	0.242630i
$980$	−100.844	−	40.9592i	−3.22134	−	1.30840i
$981$	0.579999	+	0.273708i	0.0185179	+	0.00873882i
$982$	−0.470501	−	0.616093i	−0.0150143	−	0.0196603i
$983$	16.1159	−	18.8518i	0.514018	−	0.601278i	−0.441117	−	0.897450i	$-0.645418\pi$
$983$	16.1159	−	18.8518i	0.514018	−	0.601278i	0.955135	+	0.296172i	$0.0957100\pi$
$984$	−21.8702	−	18.3513i	−0.697198	−	0.585018i
$985$	34.7999	−	32.6312i	1.10882	−	1.03972i
$986$	2.86309	+	12.2473i	0.0911792	+	0.390034i
$987$	5.17481	−	2.80047i	0.164716	−	0.0891399i
$988$	7.70023	−	11.4471i	0.244977	−	0.364181i
$989$	−4.57930	−	2.47819i	−0.145613	−	0.0788019i
$990$	0.320467	−	1.17440i	0.0101851	−	0.0373248i
$991$	−1.10158	+	0.495313i	−0.0349928	+	0.0157341i	−0.427512	−	0.904010i	$-0.640610\pi$
$991$	−1.10158	+	0.495313i	−0.0349928	+	0.0157341i	0.392519	+	0.919744i	$0.371604\pi$
$992$	−3.98690	+	2.87433i	−0.126584	+	0.0912601i
$993$	−48.0773	+	1.76734i	−1.52569	+	0.0560848i
$994$	17.9819	+	33.9695i	0.570352	+	1.07745i
$995$	10.1148	−	27.0154i	0.320661	−	0.856446i
$996$	−17.4798	+	4.94282i	−0.553869	+	0.156619i
$997$	−11.9532	−	17.5816i	−0.378561	−	0.556815i	0.589424	−	0.807824i	$-0.299355\pi$
$997$	−11.9532	−	17.5816i	−0.378561	−	0.556815i	−0.967985	+	0.251009i	$0.919238\pi$
$998$	6.91995	−	11.0291i	0.219047	−	0.349120i
$999$	−28.1549	+	38.3062i	−0.890783	+	1.21195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.k.a.4.13	✓	3348
361.271	even	171	inner	361.2.k.a.271.13	yes	3348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.k.a.4.13	✓	3348	1.1	even	1	trivial
361.2.k.a.271.13	yes	3348	361.271	even	171	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.k (of order \(171\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.720055 - 0.0132303i) q^{2} +(-1.41262 + 0.941535i) q^{3} +(-1.48035 - 0.0544180i) q^{4} +(1.90263 + 3.93762i) q^{5} +(1.02962 - 0.659268i) q^{6} +(-4.52008 + 1.83590i) q^{7} +(2.50338 + 0.138115i) q^{8} +(-0.0454172 + 0.108939i) q^{9} +(-1.31790 - 2.86047i) q^{10} +(0.977593 - 3.12554i) q^{11} +(2.14240 - 1.31693i) q^{12} +(2.07594 - 0.505453i) q^{13} +(3.27900 - 1.26215i) q^{14} +(-6.39509 - 3.77095i) q^{15} +(1.15395 + 0.0849541i) q^{16} +(-2.01084 - 3.20490i) q^{17} +(0.0341442 - 0.0778409i) q^{18} +(-3.10935 + 3.05482i) q^{19} +(-2.60227 - 5.93257i) q^{20} +(4.65658 - 6.84924i) q^{21} +(-0.745272 + 2.23763i) q^{22} +(0.770458 - 0.381048i) q^{23} +(-3.66635 + 2.16191i) q^{24} +(-8.77766 + 11.0663i) q^{25} +(-1.50148 + 0.336489i) q^{26} +(-1.01478 - 5.19510i) q^{27} +(6.79119 - 2.47179i) q^{28} +(4.39265 + 1.41834i) q^{29} +(4.55492 + 2.79990i) q^{30} +(0.633831 - 0.552003i) q^{31} +(-5.82301 - 0.536408i) q^{32} +(1.56184 + 5.33562i) q^{33} +(1.40551 + 2.33431i) q^{34} +(-15.8291 - 14.3053i) q^{35} +(0.0731613 - 0.158795i) q^{36} +(-6.08282 - 6.60770i) q^{37} +(2.27932 - 2.15850i) q^{38} +(-2.45660 + 2.66858i) q^{39} +(4.21915 + 10.1201i) q^{40} +(2.23615 + 6.32391i) q^{41} +(-3.44361 + 4.87022i) q^{42} +(-3.49734 - 4.94621i) q^{43} +(-1.61726 + 4.57368i) q^{44} +(-0.515370 + 0.0284338i) q^{45} +(-0.559814 + 0.264182i) q^{46} +(0.630913 + 0.326593i) q^{47} +(-1.71008 + 0.966479i) q^{48} +(12.0431 - 11.7157i) q^{49} +(6.46681 - 7.85222i) q^{50} +(5.85807 + 2.63402i) q^{51} +(-3.10061 + 0.635277i) q^{52} +(0.110211 + 2.39787i) q^{53} +(0.661964 + 3.75418i) q^{54} +(14.1672 - 2.09734i) q^{55} +(-11.5690 + 3.97165i) q^{56} +(1.51609 - 7.24286i) q^{57} +(-3.14419 - 1.07940i) q^{58} +(1.68971 + 0.313972i) q^{59} +(9.26173 + 5.93032i) q^{60} +(-0.699872 + 5.83284i) q^{61} +(-0.463696 + 0.389087i) q^{62} +(0.00528934 - 0.575792i) q^{63} +(1.88569 + 0.208708i) q^{64} +(5.94002 + 7.21256i) q^{65} +(-1.05402 - 3.86261i) q^{66} +(-2.05342 + 8.78383i) q^{67} +(2.80233 + 4.85378i) q^{68} +(-0.729591 + 1.26369i) q^{69} +(11.2086 + 10.5100i) q^{70} +(1.30323 + 10.8614i) q^{71} +(-0.128742 + 0.266441i) q^{72} +(1.92353 - 3.63373i) q^{73} +(4.29254 + 4.83839i) q^{74} +(1.98015 - 23.8969i) q^{75} +(4.76915 - 4.35299i) q^{76} +(1.31937 + 15.9224i) q^{77} +(1.80419 - 1.88902i) q^{78} +(-2.13155 + 0.196355i) q^{79} +(1.86102 + 4.70546i) q^{80} +(6.07564 + 6.13171i) q^{81} +(-1.52648 - 4.58315i) q^{82} +(-6.95081 - 1.96550i) q^{83} +(-7.26606 + 9.88583i) q^{84} +(8.79379 - 14.0156i) q^{85} +(2.45284 + 3.60782i) q^{86} +(-7.54055 + 2.13226i) q^{87} +(2.87897 - 7.68938i) q^{88} +(-5.93665 - 11.2149i) q^{89} +(0.371471 - 0.0136554i) q^{90} +(-8.45545 + 6.09590i) q^{91} +(-1.16128 + 0.522156i) q^{92} +(-0.375628 + 1.37654i) q^{93} +(-0.449972 - 0.243512i) q^{94} +(-17.9447 - 6.43125i) q^{95} +(8.73073 - 4.72483i) q^{96} +(1.63780 + 7.00595i) q^{97} +(-8.82672 + 8.27664i) q^{98} +(0.296092 + 0.248451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) \) 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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