LMFDB - Embedded newform 930.2.br.a.761.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.16
Character	$\chi$	$=$	930.761
Dual form			930.2.br.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.587767 - 1.62927i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0555271 - 1.73116i) q^{6} +(-0.309626 + 2.94590i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.30906 + 1.91527i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587767 - 1.62927i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0555271 - 1.73116i) q^{6} +(-0.309626 + 2.94590i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.30906 + 1.91527i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(-0.630734 + 0.280821i) q^{11} +(0.482149 - 1.66359i) q^{12} +(-0.960045 + 4.51666i) q^{13} +(-1.20480 + 2.70604i) q^{14} +(-0.305615 + 1.70488i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.12963 + 0.948174i) q^{17} +(-2.78790 + 1.10799i) q^{18} +(-0.844454 + 0.179494i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(4.98166 - 1.22704i) q^{21} +(-0.686642 + 0.0721689i) q^{22} +(-0.00251392 + 0.00182647i) q^{23} +(0.972628 - 1.43318i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.30878 + 3.99892i) q^{26} +(4.47768 + 2.63635i) q^{27} +(-1.98205 + 2.20129i) q^{28} +(-2.51022 + 7.72566i) q^{29} +(-0.817492 + 1.52699i) q^{30} +(-5.16920 + 2.06867i) q^{31} +1.00000i q^{32} +(0.828258 + 0.862580i) q^{33} +(1.73240 + 1.55986i) q^{34} +(1.74109 - 2.39641i) q^{35} +(-2.99383 + 0.192253i) q^{36} +(0.876733 - 0.506182i) q^{37} +(-0.858591 - 0.0902415i) q^{38} +(7.92315 - 1.09057i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(2.95825 - 2.66362i) q^{41} +(5.11702 + 0.372436i) q^{42} +(-0.490022 - 2.30537i) q^{43} +(-0.675336 - 0.143547i) q^{44} +(2.95734 - 0.504140i) q^{45} +(-0.00295529 + 0.000960231i) q^{46} +(10.3956 - 3.37775i) q^{47} +(1.36790 - 1.06247i) q^{48} +(-1.73542 - 0.368874i) q^{49} +(0.207912 + 0.978148i) q^{50} +(0.293105 - 4.02706i) q^{51} +(-3.43152 + 3.08975i) q^{52} +(-0.465783 - 4.43163i) q^{53} +(3.44385 + 3.89100i) q^{54} +(0.686642 + 0.0721689i) q^{55} +(-2.56528 + 1.48106i) q^{56} +(0.788788 + 1.27035i) q^{57} +(-4.77472 + 6.57184i) q^{58} +(6.90993 + 6.22172i) q^{59} +(-1.24935 + 1.19964i) q^{60} +4.47690i q^{61} +(-5.55545 + 0.370056i) q^{62} +(-4.92724 - 7.39527i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(3.08975 - 3.43152i) q^{65} +(0.521168 + 1.07631i) q^{66} +(-6.17417 + 10.6940i) q^{67} +(1.16559 + 2.01886i) q^{68} +(0.00445341 + 0.00302232i) q^{69} +(2.39641 - 1.74109i) q^{70} +(-1.89851 + 0.199542i) q^{71} +(-2.90671 - 0.742302i) q^{72} +(-0.242796 - 0.545329i) q^{73} +(0.990242 - 0.210482i) q^{74} +(1.11711 - 1.32366i) q^{75} +(-0.788682 - 0.351144i) q^{76} +(-0.631977 - 1.94503i) q^{77} +(7.87236 + 1.41119i) q^{78} +(-3.21842 + 7.22868i) q^{79} +(0.207912 - 0.978148i) q^{80} +(1.66351 - 8.84493i) q^{81} +(3.63656 - 1.61910i) q^{82} +(-6.89351 - 7.65602i) q^{83} +(4.75148 + 1.93545i) q^{84} +(-1.37023 - 1.88596i) q^{85} +(0.246360 - 2.34396i) q^{86} +(14.0626 - 0.451060i) q^{87} +(-0.597925 - 0.345212i) q^{88} +(-2.82405 - 2.05179i) q^{89} +(2.96838 + 0.434401i) q^{90} +(-13.0084 - 4.22667i) q^{91} -0.00310737 q^{92} +(6.40872 + 7.20613i) q^{93} +10.9306 q^{94} +(0.821066 + 0.266781i) q^{95} +(1.62927 - 0.587767i) q^{96} +(-8.31828 - 6.04358i) q^{97} +(-1.53649 - 0.887094i) q^{98} +(0.918554 - 1.85645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.587767	−	1.62927i	−0.339348	−	0.940661i
$3$	−0.587767	−	1.62927i	−0.339348	−	0.940661i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.0555271	−	1.73116i	−0.0226689	−	0.706743i
$7$	−0.309626	+	2.94590i	−0.117028	+	1.11345i	0.765582	+	0.643338i	$0.222451\pi$
$7$	−0.309626	+	2.94590i	−0.117028	+	1.11345i	−0.882610	+	0.470107i	$0.844215\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−2.30906	+	1.91527i	−0.769686	+	0.638422i
$10$	−0.669131	−	0.743145i	−0.211598	−	0.235003i
$11$	−0.630734	+	0.280821i	−0.190173	+	0.0846706i	−0.499614	−	0.866248i	$-0.666525\pi$
$11$	−0.630734	+	0.280821i	−0.190173	+	0.0846706i	0.309441	+	0.950919i	$0.399858\pi$
$12$	0.482149	−	1.66359i	0.139184	−	0.480237i
$13$	−0.960045	+	4.51666i	−0.266269	+	1.25269i	0.618172	+	0.786043i	$0.287873\pi$
$13$	−0.960045	+	4.51666i	−0.266269	+	1.25269i	−0.884441	+	0.466652i	$0.845460\pi$
$14$	−1.20480	+	2.70604i	−0.321998	+	0.723219i
$15$	−0.305615	+	1.70488i	−0.0789094	+	0.440197i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.12963	+	0.948174i	0.516512	+	0.229966i	0.648402	−	0.761298i	$-0.275438\pi$
$17$	2.12963	+	0.948174i	0.516512	+	0.229966i	−0.131890	+	0.991264i	$0.542104\pi$
$18$	−2.78790	+	1.10799i	−0.657113	+	0.261155i
$19$	−0.844454	+	0.179494i	−0.193731	+	0.0411788i	−0.303755	−	0.952750i	$-0.598241\pi$
$19$	−0.844454	+	0.179494i	−0.193731	+	0.0411788i	0.110024	+	0.993929i	$0.464907\pi$
$20$	−0.406737	−	0.913545i	−0.0909491	−	0.204275i
$21$	4.98166	−	1.22704i	1.08709	−	0.267762i
$22$	−0.686642	+	0.0721689i	−0.146392	+	0.0153865i
$23$	−0.00251392	+	0.00182647i	−0.000524188	+	0.000380845i	−0.588047	−	0.808827i	$-0.700103\pi$
$23$	−0.00251392	+	0.00182647i	−0.000524188	+	0.000380845i	0.587523	+	0.809207i	$0.300103\pi$
$24$	0.972628	−	1.43318i	0.198537	−	0.292546i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.30878	+	3.99892i	−0.452789	+	0.784254i
$27$	4.47768	+	2.63635i	0.861730	+	0.507367i
$28$	−1.98205	+	2.20129i	−0.374572	+	0.416004i
$29$	−2.51022	+	7.72566i	−0.466136	+	1.43462i	0.391412	+	0.920216i	$0.371987\pi$
$29$	−2.51022	+	7.72566i	−0.466136	+	1.43462i	−0.857548	+	0.514404i	$0.828013\pi$
$30$	−0.817492	+	1.52699i	−0.149253	+	0.278789i
$31$	−5.16920	+	2.06867i	−0.928415	+	0.371545i
$31$	−5.16920	+	2.06867i	−0.928415	+	0.371545i
$32$			1.00000i			0.176777i
$33$	0.828258	+	0.862580i	0.144181	+	0.150156i
$34$	1.73240	+	1.55986i	0.297104	+	0.267514i
$35$	1.74109	−	2.39641i	0.294299	−	0.405067i
$36$	−2.99383	+	0.192253i	−0.498972	+	0.0320421i
$37$	0.876733	−	0.506182i	0.144134	−	0.0832159i	−0.426199	−	0.904630i	$-0.640148\pi$
$37$	0.876733	−	0.506182i	0.144134	−	0.0832159i	0.570333	+	0.821414i	$0.306814\pi$
$38$	−0.858591	−	0.0902415i	−0.139282	−	0.0146391i
$39$	7.92315	−	1.09057i	1.26872	−	0.174631i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	2.95825	−	2.66362i	0.462000	−	0.415987i	−0.404983	−	0.914324i	$-0.632723\pi$
$41$	2.95825	−	2.66362i	0.462000	−	0.415987i	0.866983	+	0.498337i	$0.166056\pi$
$42$	5.11702	+	0.372436i	0.789573	+	0.0574681i
$43$	−0.490022	−	2.30537i	−0.0747276	−	0.351566i	0.924859	−	0.380310i	$-0.124183\pi$
$43$	−0.490022	−	2.30537i	−0.0747276	−	0.351566i	−0.999587	+	0.0287439i	$0.990849\pi$
$44$	−0.675336	−	0.143547i	−0.101811	−	0.0216406i
$45$	2.95734	−	0.504140i	0.440854	−	0.0751528i
$46$	−0.00295529		0.000960231i	−0.000435733		0.000141578i
$47$	10.3956	−	3.37775i	1.51636	−	0.492695i	0.571620	−	0.820518i	$-0.306315\pi$
$47$	10.3956	−	3.37775i	1.51636	−	0.492695i	0.944739	+	0.327823i	$0.106315\pi$
$48$	1.36790	−	1.06247i	0.197439	−	0.153355i
$49$	−1.73542	−	0.368874i	−0.247917	−	0.0526963i
$50$	0.207912	+	0.978148i	0.0294032	+	0.138331i
$51$	0.293105	−	4.02706i	0.0410429	−	0.563901i
$52$	−3.43152	+	3.08975i	−0.475866	+	0.428471i
$53$	−0.465783	−	4.43163i	−0.0639802	−	0.608731i	−0.978793	−	0.204853i	$-0.934328\pi$
$53$	−0.465783	−	4.43163i	−0.0639802	−	0.608731i	0.914813	−	0.403879i	$-0.132338\pi$
$54$	3.44385	+	3.89100i	0.468649	+	0.529498i
$55$	0.686642	+	0.0721689i	0.0925867	+	0.00973126i
$56$	−2.56528	+	1.48106i	−0.342799	+	0.197915i
$57$	0.788788	+	1.27035i	0.104478	+	0.168261i
$58$	−4.77472	+	6.57184i	−0.626952	+	0.862925i
$59$	6.90993	+	6.22172i	0.899596	+	0.810000i	0.982443	−	0.186563i	$-0.0597347\pi$
$59$	6.90993	+	6.22172i	0.899596	+	0.810000i	−0.0828474	+	0.996562i	$0.526401\pi$
$60$	−1.24935	+	1.19964i	−0.161290	+	0.154872i
$61$			4.47690i			0.573208i	0.958049	+	0.286604i	$0.0925265\pi$
$61$			4.47690i			0.573208i	−0.958049	+	0.286604i	$0.907474\pi$
$62$	−5.55545	+	0.370056i	−0.705543	+	0.0469972i
$63$	−4.92724	−	7.39527i	−0.620773	−	0.931717i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	3.08975	−	3.43152i	0.383236	−	0.425627i
$66$	0.521168	+	1.07631i	0.0641514	+	0.132484i
$67$	−6.17417	+	10.6940i	−0.754295	+	1.30648i	0.191430	+	0.981506i	$0.438688\pi$
$67$	−6.17417	+	10.6940i	−0.754295	+	1.30648i	−0.945724	+	0.324970i	$0.894646\pi$
$68$	1.16559	+	2.01886i	0.141348	+	0.244822i
$69$	0.00445341	+	0.00302232i	0.000536128	+	0.000363844i
$70$	2.39641	−	1.74109i	0.286426	−	0.208100i
$71$	−1.89851	+	0.199542i	−0.225312	+	0.0236812i	−0.216512	−	0.976280i	$-0.569468\pi$
$71$	−1.89851	+	0.199542i	−0.225312	+	0.0236812i	−0.00880025	+	0.999961i	$0.502801\pi$
$72$	−2.90671	−	0.742302i	−0.342560	−	0.0874812i
$73$	−0.242796	−	0.545329i	−0.0284171	−	0.0638259i	0.898779	−	0.438401i	$-0.144455\pi$
$73$	−0.242796	−	0.545329i	−0.0284171	−	0.0638259i	−0.927196	+	0.374575i	$0.877788\pi$
$74$	0.990242	−	0.210482i	0.115113	−	0.0244681i
$75$	1.11711	−	1.32366i	0.128992	−	0.152843i
$76$	−0.788682	−	0.351144i	−0.0904680	−	0.0402790i
$77$	−0.631977	−	1.94503i	−0.0720205	−	0.221656i
$78$	7.87236	+	1.41119i	0.891370	+	0.159786i
$79$	−3.21842	+	7.22868i	−0.362100	+	0.813290i	0.637000	+	0.770864i	$0.280175\pi$
$79$	−3.21842	+	7.22868i	−0.362100	+	0.813290i	−0.999100	+	0.0424258i	$0.986491\pi$
$80$	0.207912	−	0.978148i	0.0232452	−	0.109360i
$81$	1.66351	−	8.84493i	0.184834	−	0.982770i
$82$	3.63656	−	1.61910i	0.401591	−	0.178800i
$83$	−6.89351	−	7.65602i	−0.756661	−	0.840357i	0.234625	−	0.972086i	$-0.424614\pi$
$83$	−6.89351	−	7.65602i	−0.756661	−	0.840357i	−0.991286	+	0.131729i	$0.957947\pi$
$84$	4.75148	+	1.93545i	0.518429	+	0.211175i
$85$	−1.37023	−	1.88596i	−0.148622	−	0.204561i
$86$	0.246360	−	2.34396i	0.0265657	−	0.252756i
$87$	14.0626	−	0.451060i	1.50767	−	0.0483587i
$88$	−0.597925	−	0.345212i	−0.0637390	−	0.0367997i
$89$	−2.82405	−	2.05179i	−0.299349	−	0.217490i	0.427964	−	0.903796i	$-0.359231\pi$
$89$	−2.82405	−	2.05179i	−0.299349	−	0.217490i	−0.727313	+	0.686306i	$0.759231\pi$
$90$	2.96838	+	0.434401i	0.312895	+	0.0457899i
$91$	−13.0084	−	4.22667i	−1.36365	−	0.443075i
$92$	−0.00310737			−0.000323966
$93$	6.40872	+	7.20613i	0.664553	+	0.747241i
$94$	10.9306			1.12741
$95$	0.821066	+	0.266781i	0.0842396	+	0.0273711i
$96$	1.62927	−	0.587767i	0.166287	−	0.0599888i
$97$	−8.31828	−	6.04358i	−0.844593	−	0.613633i	0.0790567	−	0.996870i	$-0.474809\pi$
$97$	−8.31828	−	6.04358i	−0.844593	−	0.613633i	−0.923650	+	0.383237i	$0.874809\pi$
$98$	−1.53649	−	0.887094i	−0.155209	−	0.0896100i
$99$	0.918554	−	1.85645i	0.0923182	−	0.186581i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	5.13792	+	7.07173i	0.511242	+	0.703664i	0.984128	−	0.177460i	$-0.0567879\pi$
$101$	5.13792	+	7.07173i	0.511242	+	0.703664i	−0.472886	+	0.881123i	$0.656788\pi$
$102$	1.52319	−	3.73939i	0.150818	−	0.370255i
$103$	−7.52831	−	8.36103i	−0.741786	−	0.823837i	0.247643	−	0.968851i	$-0.420344\pi$
$103$	−7.52831	−	8.36103i	−0.741786	−	0.823837i	−0.989430	+	0.145014i	$0.953677\pi$
$104$	−4.21835	+	1.87813i	−0.413643	+	0.184166i
$105$	−4.92776	−	1.42818i	−0.480900	−	0.139377i
$106$	0.926463	−	4.35867i	0.0899861	−	0.423351i
$107$	4.70138	−	10.5595i	0.454500	−	1.02082i	−0.530408	−	0.847743i	$-0.677961\pi$
$107$	4.70138	−	10.5595i	0.454500	−	1.02082i	0.984908	−	0.173081i	$-0.0553721\pi$
$108$	2.07291	+	4.76477i	0.199466	+	0.458490i
$109$	6.20347	+	19.0923i	0.594185	+	1.82871i	0.558742	+	0.829341i	$0.311284\pi$
$109$	6.20347	+	19.0923i	0.594185	+	1.82871i	0.0354424	+	0.999372i	$0.488716\pi$
$110$	0.630734	+	0.280821i	0.0601381	+	0.0267752i
$111$	−1.34002	−	1.13092i	−0.127189	−	0.107342i
$112$	−2.89740	+	0.615861i	−0.273778	+	0.0581933i
$113$	−3.13828	−	7.04868i	−0.295224	−	0.663084i	0.703649	−	0.710548i	$-0.251553\pi$
$113$	−3.13828	−	7.04868i	−0.295224	−	0.663084i	−0.998873	+	0.0474636i	$0.984886\pi$
$114$	0.357624	+	1.45192i	0.0334945	+	0.135985i
$115$	0.00309035		0.000324809i	0.000288177		3.02886e-5i
$116$	−6.57184	+	4.77472i	−0.610180	+	0.443322i
$117$	−6.43380	−	12.2680i	−0.594805	−	1.13417i
$118$	4.64911	+	8.05250i	0.427985	+	0.741292i
$119$	−3.45262	+	5.98011i	−0.316501	+	0.548195i
$120$	−1.55891	+	0.754853i	−0.142308	+	0.0689083i
$121$	−7.04147	+	7.82035i	−0.640134	+	0.710941i
$122$	−1.38344	+	4.25779i	−0.125251	+	0.385482i
$123$	−6.07852	−	3.25420i	−0.548082	−	0.293422i
$124$	−5.39790	−	1.36479i	−0.484746	−	0.122561i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.40082	−	8.55592i	−0.213882	−	0.762222i
$127$	−15.3221	−	13.7961i	−1.35962	−	1.22421i	−0.950115	−	0.311901i	$-0.899034\pi$
$127$	−15.3221	−	13.7961i	−1.35962	−	1.22421i	−0.409506	−	0.912307i	$-0.634299\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−3.46806	+	2.15340i	−0.305346	+	0.189596i
$130$	3.99892	−	2.30878i	0.350729	−	0.202493i
$131$	14.4710	+	1.52096i	1.26434	+	0.132887i	0.712861	−	0.701305i	$-0.247399\pi$
$131$	14.4710	+	1.52096i	1.26434	+	0.132887i	0.551474	+	0.834192i	$0.314066\pi$
$132$	0.163063	+	1.18468i	0.0141928	+	0.103113i
$133$	−0.267307	−	2.54325i	−0.0231784	−	0.220528i
$134$	−9.17660	+	8.26265i	−0.792738	+	0.713784i
$135$	−2.55961	−	4.52199i	−0.220296	−	0.389191i
$136$	0.484678	+	2.28023i	0.0415608	+	0.195528i
$137$	−4.99555	−	1.06184i	−0.426799	−	0.0907189i	−0.0104959	−	0.999945i	$-0.503341\pi$
$137$	−4.99555	−	1.06184i	−0.426799	−	0.0907189i	−0.416303	+	0.909226i	$0.636674\pi$
$138$	0.00330150	+	0.00425058i	0.000281042	+	0.000361833i
$139$	−4.38568	+	1.42499i	−0.371989	+	0.120866i	−0.489044	−	0.872259i	$-0.662654\pi$
$139$	−4.38568	+	1.42499i	−0.371989	+	0.120866i	0.117056	+	0.993125i	$0.462654\pi$
$140$	2.81715	−	0.915347i	0.238093	−	0.0773610i
$141$	−11.6135	−	14.9520i	−0.978032	−	1.25919i
$142$	−1.86725	−	0.396897i	−0.156696	−	0.0333068i
$143$	−0.662838	−	3.11841i	−0.0554293	−	0.260774i
$144$	−2.53507	−	1.60420i	−0.211255	−	0.133683i
$145$	6.03675	−	5.43551i	0.501325	−	0.451395i
$146$	−0.0623969	−	0.593667i	−0.00516400	−	0.0491322i
$147$	0.419025	+	3.04428i	0.0345606	+	0.251088i
$148$	1.00682	+	0.105821i	0.0827600	+	0.00869843i
$149$	−7.51618	+	4.33947i	−0.615749	+	0.355503i	−0.775212	−	0.631701i	$-0.782357\pi$
$149$	−7.51618	+	4.33947i	−0.615749	+	0.355503i	0.159463	+	0.987204i	$0.449024\pi$
$150$	1.47147	−	0.913668i	0.120145	−	0.0746007i
$151$	13.8048	−	19.0007i	1.12342	−	1.54625i	0.323414	−	0.946258i	$-0.395169\pi$
$151$	13.8048	−	19.0007i	1.12342	−	1.54625i	0.800004	−	0.599994i	$-0.204831\pi$
$152$	−0.641572	−	0.577674i	−0.0520383	−	0.0468555i
$153$	−6.73346	+	1.88943i	−0.544368	+	0.152751i
$154$		−	2.04512i		−	0.164801i
$155$	5.51099	+	0.793074i	0.442654	+	0.0637012i
$156$	7.05098	+	3.77482i	0.564530	+	0.302228i
$157$	−1.03270	+	3.17833i	−0.0824185	+	0.253658i	−0.983771	−	0.179428i	$-0.942575\pi$
$157$	−1.03270	+	3.17833i	−0.0824185	+	0.253658i	0.901353	+	0.433086i	$0.142575\pi$
$158$	−5.29468	+	5.88034i	−0.421222	+	0.467815i
$159$	−6.94656	+	3.36366i	−0.550898	+	0.266755i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.00460221	−	0.00797127i	−0.000362705	−	0.000628224i
$162$	4.31532	−	7.89797i	0.339044	−	0.620524i
$163$	16.4947	−	11.9841i	1.29197	−	0.938668i	0.292122	−	0.956381i	$-0.405639\pi$
$163$	16.4947	−	11.9841i	1.29197	−	0.938668i	0.999843	+	0.0177130i	$0.00563852\pi$
$164$	3.95891	−	0.416098i	0.309139	−	0.0324918i
$165$	−0.286003	−	1.16114i	−0.0222653	−	0.0903950i
$166$	−4.19028	−	9.41152i	−0.325229	−	0.730476i
$167$	10.1156	−	2.15014i	0.782771	−	0.166383i	0.200843	−	0.979623i	$-0.435632\pi$
$167$	10.1156	−	2.15014i	0.782771	−	0.166383i	0.581928	+	0.813240i	$0.302299\pi$
$168$	3.92084	+	3.30901i	0.302499	+	0.255296i
$169$	−7.60240	−	3.38481i	−0.584800	−	0.260370i
$170$	−0.720373	−	2.21708i	−0.0552501	−	0.170042i
$171$	1.60612	−	2.03182i	0.122823	−	0.155377i
$172$	0.958627	−	2.15311i	0.0730946	−	0.164173i
$173$	−4.25903	+	20.0372i	−0.323808	+	1.52340i	0.451763	+	0.892138i	$0.350795\pi$
$173$	−4.25903	+	20.0372i	−0.323808	+	1.52340i	−0.775571	+	0.631260i	$0.782538\pi$
$174$	13.5138	+	3.91661i	1.02447	+	0.296917i
$175$	−2.70604	+	1.20480i	−0.204557	+	0.0910747i
$176$	−0.461984	−	0.513085i	−0.0348233	−	0.0386752i
$177$	6.07546	−	14.9151i	0.456659	−	1.12109i
$178$	−2.05179	−	2.82405i	−0.153788	−	0.211672i
$179$	1.40972	−	13.4126i	0.105367	−	1.00250i	−0.806282	−	0.591532i	$-0.798523\pi$
$179$	1.40972	−	13.4126i	0.105367	−	1.00250i	0.911649	−	0.410970i	$-0.134810\pi$
$180$	2.68886	+	1.33042i	0.200416	+	0.0991637i
$181$	8.31904	+	4.80300i	0.618349	+	0.357004i	0.776226	−	0.630455i	$-0.217132\pi$
$181$	8.31904	+	4.80300i	0.618349	+	0.357004i	−0.157877	+	0.987459i	$0.550465\pi$
$182$	−11.0656	−	8.03961i	−0.820234	−	0.595935i
$183$	7.29409	−	2.63138i	0.539195	−	0.194517i
$184$	−0.00295529		0.000960231i	−0.000217867		7.07892e-5i
$185$	−1.01236			−0.0744305
$186$	3.86824	+	8.83384i	0.283633	+	0.647729i
$187$	−1.60950			−0.117698
$188$	10.3956	+	3.37775i	0.758180	+	0.246348i
$189$	−9.15284	+	12.3745i	−0.665771	+	0.900113i
$190$	0.698441	+	0.507447i	0.0506702	+	0.0368141i
$191$	2.67383	+	1.54374i	0.193472	+	0.111701i	0.593607	−	0.804755i	$-0.297703\pi$
$191$	2.67383	+	1.54374i	0.193472	+	0.111701i	−0.400135	+	0.916456i	$0.631037\pi$
$192$	1.73116	−	0.0555271i	0.124936	−	0.00400732i
$193$	−0.234825	+	2.23421i	−0.0169030	+	0.160822i	−0.999717	−	0.0237754i	$-0.992431\pi$
$193$	−0.234825	+	2.23421i	−0.0169030	+	0.160822i	0.982814	+	0.184597i	$0.0590980\pi$
$194$	−6.04358	−	8.31828i	−0.433904	−	0.597218i
$195$	−7.40693	−	3.01711i	−0.530421	−	0.216060i
$196$	−1.18716	−	1.31848i	−0.0847974	−	0.0941770i
$197$	−16.3397	+	7.27491i	−1.16416	+	0.518316i	−0.895561	−	0.444938i	$-0.853226\pi$
$197$	−16.3397	+	7.27491i	−1.16416	+	0.518316i	−0.268594	+	0.963253i	$0.586559\pi$
$198$	1.44727	−	1.48174i	0.102853	−	0.105303i
$199$	0.602835	−	2.83612i	0.0427339	−	0.201047i	−0.951602	−	0.307334i	$-0.900563\pi$
$199$	0.602835	−	2.83612i	0.0427339	−	0.201047i	0.994335	+	0.106287i	$0.0338963\pi$
$200$	−0.406737	+	0.913545i	−0.0287606	+	0.0645974i
$201$	21.0524	+	3.77383i	1.48492	+	0.266186i
$202$	2.70116	+	8.31332i	0.190053	+	0.584923i
$203$	−21.9818	−	9.78692i	−1.54282	−	0.686907i
$204$	2.60417	−	3.08568i	0.182329	−	0.216041i
$205$	−3.89372	+	0.827637i	−0.271950	+	0.0578047i
$206$	−4.57615	−	10.2782i	−0.318835	−	0.716115i
$207$	0.00230661	−	0.00903224i	0.000160320	−	0.000627784i
$208$	−4.59227	+	0.482667i	−0.318416	+	0.0334669i
$209$	0.482220	−	0.350353i	0.0333559	−	0.0242344i
$210$	−4.24525	−	2.88105i	−0.292950	−	0.198811i
$211$	3.15415	+	5.46315i	0.217141	+	0.376099i	0.953933	−	0.300021i	$-0.0969936\pi$
$211$	3.15415	+	5.46315i	0.217141	+	0.376099i	−0.736792	+	0.676120i	$0.763660\pi$
$212$	2.22802	−	3.85905i	0.153021	−	0.265040i
$213$	1.44099	+	2.97591i	0.0987351	+	0.203906i
$214$	7.73434	−	8.58985i	0.528708	−	0.587190i
$215$	−0.728314	+	2.24152i	−0.0496706	+	0.152870i
$216$	0.499059	+	5.17213i	0.0339567	+	0.351919i
$217$	−4.49358	−	15.8684i	−0.305044	−	1.07722i
$218$			20.0749i			1.35964i
$219$	−0.745782	+	0.716108i	−0.0503953	+	0.0483901i
$220$	0.513085	+	0.461984i	0.0345922	+	0.0311469i
$221$	−6.32712	+	8.70853i	−0.425608	+	0.585799i
$222$	−0.924965	−	1.48966i	−0.0620796	−	0.0999794i
$223$	21.4152	−	12.3641i	1.43407	−	0.827960i	0.436641	−	0.899636i	$-0.356168\pi$
$223$	21.4152	−	12.3641i	1.43407	−	0.827960i	0.997428	+	0.0716761i	$0.0228348\pi$
$224$	−2.94590	−	0.309626i	−0.196831	−	0.0206878i
$225$	−2.81320	−	1.04207i	−0.187547	−	0.0694713i
$226$	−0.806515	−	7.67348i	−0.0536486	−	0.510432i
$227$	9.71196	−	8.74469i	0.644606	−	0.580406i	−0.280622	−	0.959818i	$-0.590541\pi$
$227$	9.71196	−	8.74469i	0.644606	−	0.580406i	0.925227	+	0.379413i	$0.123874\pi$
$228$	−0.108547	+	1.49137i	−0.00718873	+	0.0987683i
$229$	3.52908	+	16.6030i	0.233208	+	1.09716i	0.926440	+	0.376443i	$0.122853\pi$
$229$	3.52908	+	16.6030i	0.233208	+	1.09716i	−0.693232	+	0.720715i	$0.743814\pi$
$230$	0.00303947		0.000646059i	0.000200417		4.25999e-5i
$231$	−2.79752	+	2.17289i	−0.184063	+	0.142965i
$232$	−7.72566	+	2.51022i	−0.507215	+	0.164804i
$233$	12.8828	−	4.18586i	0.843977	−	0.274225i	0.145056	−	0.989423i	$-0.453664\pi$
$233$	12.8828	−	4.18586i	0.843977	−	0.274225i	0.698921	+	0.715199i	$0.253664\pi$
$234$	−2.32790	−	13.6557i	−0.152179	−	0.892700i
$235$	−10.6918	−	2.27260i	−0.697454	−	0.148248i
$236$	1.93321	+	9.09503i	0.125841	+	0.592036i
$237$	13.6692	+	0.994894i	0.887908	+	0.0646253i
$238$	−5.13159	+	4.62050i	−0.332631	+	0.299503i
$239$	−0.978883	−	9.31345i	−0.0633187	−	0.602437i	−0.979468	−	0.201600i	$-0.935386\pi$
$239$	−0.978883	−	9.31345i	−0.0633187	−	0.602437i	0.916149	−	0.400837i	$-0.131281\pi$
$240$	−1.71587	+	0.236178i	−0.110759	+	0.0152453i
$241$	−0.486597	−	0.0511435i	−0.0313445	−	0.00329444i	0.0888432	−	0.996046i	$-0.471683\pi$
$241$	−0.486597	−	0.0511435i	−0.0313445	−	0.00329444i	−0.120188	+	0.992751i	$0.538350\pi$
$242$	−9.11346	+	5.26166i	−0.585835	+	0.338232i
$243$	−15.3886	+	2.48846i	−0.987176	+	0.159635i
$244$	−2.63146	+	3.62189i	−0.168462	+	0.231868i
$245$	1.31848	+	1.18716i	0.0842345	+	0.0758451i
$246$	−4.77541	−	4.97330i	−0.304469	−	0.317086i
$247$		−	3.98643i		−	0.253651i
$248$	−4.71197	−	2.96603i	−0.299210	−	0.188343i
$249$	−8.42196	+	15.7314i	−0.533720	+	0.996935i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	6.51060	−	7.23076i	0.410946	−	0.456401i	−0.501767	−	0.865003i	$-0.667317\pi$
$251$	6.51060	−	7.23076i	0.410946	−	0.456401i	0.912713	+	0.408601i	$0.133983\pi$
$252$	0.360613	−	8.87906i	0.0227165	−	0.559328i
$253$	0.00107270	−	0.00185797i	6.74402e−5	−	0.000116810i
$254$	−10.3090	−	17.8557i	−0.646844	−	1.12037i
$255$	−2.26737	+	3.34098i	−0.141988	+	0.209221i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	7.06007	−	0.742044i	0.440395	−	0.0462874i	0.118263	−	0.992982i	$-0.462267\pi$
$257$	7.06007	−	0.742044i	0.440395	−	0.0462874i	0.322132	+	0.946695i	$0.395601\pi$
$258$	−3.96376	+	0.976317i	−0.246773	+	0.0607828i
$259$	1.21970	+	2.73950i	0.0757886	+	0.170224i
$260$	4.51666	−	0.960045i	0.280111	−	0.0595395i
$261$	−9.00046	−	22.6468i	−0.557115	−	1.40180i
$262$	13.2927	+	5.91830i	0.821227	+	0.365634i
$263$	2.54768	+	7.84095i	0.157097	+	0.483494i	0.998367	−	0.0571205i	$-0.0181919\pi$
$263$	2.54768	+	7.84095i	0.157097	+	0.483494i	−0.841271	+	0.540614i	$0.818192\pi$
$264$	−0.211004	+	1.17709i	−0.0129864	+	0.0724447i
$265$	−1.81244	+	4.07080i	−0.111337	+	0.250067i
$266$	0.531685	−	2.50138i	0.0325997	−	0.153369i
$267$	−1.68305	+	5.80713i	−0.103001	+	0.355390i
$268$	−11.2808	+	5.02252i	−0.689082	+	0.306799i
$269$	7.41593	+	8.23622i	0.452157	+	0.502171i	0.925521	−	0.378695i	$-0.123627\pi$
$269$	7.41593	+	8.23622i	0.452157	+	0.502171i	−0.473364	+	0.880867i	$0.656961\pi$
$270$	−1.03696	−	5.09163i	−0.0631074	−	0.309867i
$271$	4.95813	+	6.82429i	0.301185	+	0.414546i	0.932607	−	0.360894i	$-0.117528\pi$
$271$	4.95813	+	6.82429i	0.301185	+	0.414546i	−0.631422	+	0.775440i	$0.717528\pi$
$272$	−0.243674	+	2.31840i	−0.0147749	+	0.140574i
$273$	0.759489	+	23.6785i	0.0459663	+	1.43309i
$274$	−4.42292	−	2.55358i	−0.267199	−	0.154267i
$275$	−0.558565	−	0.405821i	−0.0336827	−	0.0244719i
$276$	0.00182641	+	0.00506276i	0.000109937	+	0.000304742i
$277$	−13.0266	−	4.23261i	−0.782694	−	0.254313i	−0.109704	−	0.993964i	$-0.534990\pi$
$277$	−13.0266	−	4.23261i	−0.782694	−	0.254313i	−0.672990	+	0.739652i	$0.734990\pi$
$278$	−4.61138			−0.276572
$279$	7.97392	−	14.6771i	0.477386	−	0.878694i
$280$	2.96213			0.177021
$281$	5.29506	+	1.72047i	0.315877	+	0.102635i	0.462664	−	0.886533i	$-0.346893\pi$
$281$	5.29506	+	1.72047i	0.315877	+	0.102635i	−0.146788	+	0.989168i	$0.546893\pi$
$282$	−6.42466	−	17.8090i	−0.382583	−	1.06051i
$283$	22.1074	+	16.0620i	1.31415	+	0.954785i	0.999985	+	0.00541616i	$0.00172403\pi$
$283$	22.1074	+	16.0620i	1.31415	+	0.954785i	0.314164	+	0.949369i	$0.398276\pi$
$284$	−1.65322	−	0.954484i	−0.0981003	−	0.0566382i
$285$	−0.0479377	−	1.49455i	−0.00283958	−	0.0885292i
$286$	0.333244	−	3.17061i	0.0197052	−	0.187482i
$287$	6.93079	+	9.53942i	0.409112	+	0.563094i
$288$	−1.91527	−	2.30906i	−0.112858	−	0.136063i
$289$	−7.73891	−	8.59493i	−0.455230	−	0.505584i
$290$	7.42095	−	3.30402i	0.435773	−	0.194019i
$291$	−4.95743	+	17.1050i	−0.290610	+	1.00271i
$292$	0.124110	−	0.583892i	0.00726300	−	0.0341697i
$293$	−4.72697	+	10.6170i	−0.276153	+	0.620249i	−0.997371	−	0.0724583i	$-0.976916\pi$
$293$	−4.72697	+	10.6170i	−0.276153	+	0.620249i	0.721219	+	0.692707i	$0.243582\pi$
$294$	−0.542218	+	3.02477i	−0.0316228	+	0.176408i
$295$	−2.87331	−	8.84313i	−0.167290	−	0.514867i
$296$	0.924841	+	0.411766i	0.0537553	+	0.0239334i
$297$	−3.56457	−	0.405412i	−0.206837	−	0.0235244i
$298$	−8.48928	+	1.80445i	−0.491771	+	0.104529i
$299$	−0.00583605	−	0.0131080i	−0.000337508	−	0.000758055i
$300$	1.68179	−	0.414242i	0.0970979	−	0.0239163i
$301$	6.94311	−	0.729751i	0.400194	−	0.0420621i
$302$	19.0007	−	13.8048i	1.09337	−	0.794376i
$303$	8.50188	−	12.5276i	0.488420	−	0.719692i
$304$	−0.431660	−	0.747657i	−0.0247574	−	0.0428811i
$305$	2.23845	−	3.87711i	0.128173	−	0.222003i
$306$	−6.98776	−	0.283800i	−0.399464	−	0.0162238i
$307$	−0.332892	+	0.369714i	−0.0189992	+	0.0211007i	−0.752570	−	0.658513i	$-0.771186\pi$
$307$	−0.332892	+	0.369714i	−0.0189992	+	0.0211007i	0.733570	+	0.679614i	$0.237852\pi$
$308$	0.631977	−	1.94503i	0.0360103	−	0.110828i
$309$	−9.19751	+	17.1800i	−0.523228	+	0.977337i
$310$	4.99619	+	2.45725i	0.283765	+	0.139562i
$311$		−	27.1482i		−	1.53943i	−0.638386	−	0.769717i	$-0.720397\pi$
$311$		−	27.1482i		−	1.53943i	0.638386	−	0.769717i	$-0.279603\pi$
$312$	5.53940	+	5.76894i	0.313607	+	0.326602i
$313$	18.4004	+	16.5678i	1.04005	+	0.936468i	0.998036	−	0.0626488i	$-0.0199548\pi$
$313$	18.4004	+	16.5678i	1.04005	+	0.936468i	0.0420175	+	0.999117i	$0.486621\pi$
$314$	−1.96431	+	2.70365i	−0.110853	+	0.152576i
$315$	0.569477	+	8.86811i	0.0320864	+	0.499661i
$316$	−6.85266	+	3.95639i	−0.385492	+	0.222564i
$317$	24.6269	+	2.58839i	1.38319	+	0.145379i	0.766709	−	0.641994i	$-0.221893\pi$
$317$	24.6269	+	2.58839i	1.38319	+	0.145379i	0.616477	+	0.787373i	$0.288559\pi$
$318$	−7.64600	+	1.05242i	−0.428766	+	0.0590168i
$319$	−0.586246	−	5.57776i	−0.0328235	−	0.312294i
$320$	0.743145	−	0.669131i	0.0415431	−	0.0374055i
$321$	−19.9676	−	1.45332i	−1.11448	−	0.0811162i
$322$	−0.00191371	−	0.00900329i	−0.000106647	−	0.000501734i
$323$	−1.96857	−	0.418433i	−0.109534	−	0.0232822i
$324$	6.54472	−	6.17791i	0.363596	−	0.343217i
$325$	−4.39156	+	1.42690i	−0.243600	+	0.0791504i
$326$	19.3907	−	6.30042i	1.07395	−	0.348948i
$327$	27.4604	−	21.3290i	1.51856	−	1.17950i
$328$	3.89372	+	0.827637i	0.214995	+	0.0456986i
$329$	6.73174	+	31.6703i	0.371133	+	1.74604i
$330$	0.0868088	−	1.19269i	0.00477867	−	0.0656557i
$331$	−13.3948	+	12.0607i	−0.736245	+	0.662918i	−0.949389	−	0.314103i	$-0.898296\pi$
$331$	−13.3948	+	12.0607i	−0.736245	+	0.662918i	0.213144	+	0.977021i	$0.431630\pi$
$332$	−1.07687	−	10.2458i	−0.0591010	−	0.562309i
$333$	−1.05495	+	2.84798i	−0.0578112	+	0.156069i
$334$	10.2850	+	1.08099i	0.562768	+	0.0591493i
$335$	10.6940	−	6.17417i	0.584274	−	0.337331i
$336$	2.70640	+	4.35867i	0.147646	+	0.237785i
$337$	14.2575	−	19.6238i	0.776657	−	1.06898i	−0.218986	−	0.975728i	$-0.570275\pi$
$337$	14.2575	−	19.6238i	0.776657	−	1.06898i	0.995643	−	0.0932487i	$-0.0297252\pi$
$338$	−6.18435	−	5.56842i	−0.336384	−	0.302882i
$339$	−9.63965	+	9.25609i	−0.523554	+	0.502722i
$340$		−	2.33117i		−	0.126426i
$341$	2.67946	−	2.75640i	0.145101	−	0.149267i
$342$	2.15537	−	1.43606i	0.116549	−	0.0776531i
$343$	−4.78343	+	14.7219i	−0.258281	+	0.794907i
$344$	1.57706	−	1.75150i	0.0850292	−	0.0944345i
$345$	−0.00234561	−	0.00484411i	−0.000126283	−	0.000260798i
$346$	−10.2424	+	17.7404i	−0.550635	+	0.953728i
$347$	−4.77021	−	8.26224i	−0.256078	−	0.443540i	0.709110	−	0.705098i	$-0.249097\pi$
$347$	−4.77021	−	8.26224i	−0.256078	−	0.443540i	−0.965188	+	0.261558i	$0.915764\pi$
$348$	11.6420	+	7.90090i	0.624079	+	0.423533i
$349$	8.43526	−	6.12857i	0.451529	−	0.328055i	−0.338670	−	0.940905i	$-0.609977\pi$
$349$	8.43526	−	6.12857i	0.451529	−	0.328055i	0.790199	+	0.612850i	$0.209977\pi$
$350$	−2.94590	+	0.309626i	−0.157465	+	0.0165502i
$351$	−16.2063	+	17.6931i	−0.865027	+	0.944389i
$352$	−0.280821	−	0.630734i	−0.0149678	−	0.0336182i
$353$	29.9071	−	6.35694i	1.59179	−	0.338346i	0.675033	−	0.737787i	$-0.264129\pi$
$353$	29.9071	−	6.35694i	1.59179	−	0.338346i	0.916759	+	0.399442i	$0.130796\pi$
$354$	10.3871	−	12.3077i	0.552069	−	0.654145i
$355$	1.74393	+	0.776448i	0.0925582	+	0.0412096i
$356$	−1.07869	−	3.31987i	−0.0571705	−	0.175953i
$357$	11.7726	+	2.11034i	0.623070	+	0.111691i
$358$	5.48543	−	12.3205i	0.289914	−	0.651157i
$359$	1.58337	−	7.44917i	0.0835671	−	0.393152i	−0.916408	−	0.400246i	$-0.868925\pi$
$359$	1.58337	−	7.44917i	0.0835671	−	0.393152i	0.999975	+	0.00709367i	$0.00225801\pi$
$360$	2.14614	+	2.09621i	0.113111	+	0.110480i
$361$	−16.6765	+	7.42485i	−0.877709	+	0.390781i
$362$	6.42767	+	7.13865i	0.337831	+	0.375199i
$363$	16.8802	+	6.87593i	0.885982	+	0.360893i
$364$	−8.03961	−	11.0656i	−0.421390	−	0.579993i
$365$	−0.0623969	+	0.593667i	−0.00326600	+	0.0310739i
$366$	7.75023	−	0.248589i	0.405111	−	0.0129940i
$367$	5.41712	+	3.12757i	0.282771	+	0.163258i	0.634677	−	0.772777i	$-0.281133\pi$
$367$	5.41712	+	3.12757i	0.282771	+	0.163258i	−0.351906	+	0.936035i	$0.614466\pi$
$368$	−0.00251392	−	0.00182647i	−0.000131047	−	9.52112e-5i
$369$	−1.72923	+	11.8163i	−0.0900200	+	0.615131i
$370$	−0.962816	−	0.312838i	−0.0500544	−	0.0162637i
$371$	13.1994			0.685276
$372$	0.949105	+	9.59683i	0.0492088	+	0.497573i
$373$	33.0274			1.71009			0.855047	−	0.518551i	$-0.173528\pi$
$373$	33.0274			1.71009			0.855047	+	0.518551i	$0.173528\pi$
$374$	−1.53072	−	0.497362i	−0.0791518	−	0.0257180i
$375$	−1.62927	+	0.587767i	−0.0841353	+	0.0303522i
$376$	8.84306	+	6.42486i	0.456046	+	0.331337i
$377$	−32.4842	−	18.7548i	−1.67302	−	0.965921i
$378$	−12.5288	+	8.94048i	−0.644412	+	0.459848i
$379$	−1.17734	+	11.2016i	−0.0604758	+	0.575389i	0.921763	+	0.387754i	$0.126749\pi$
$379$	−1.17734	+	11.2016i	−0.0604758	+	0.575389i	−0.982239	+	0.187635i	$0.939918\pi$
$380$	0.507447	+	0.698441i	0.0260315	+	0.0358292i
$381$	−13.4718	+	33.0729i	−0.690181	+	1.69437i
$382$	2.06592	+	2.29444i	0.105702	+	0.117394i
$383$	−16.3350	+	7.27281i	−0.834679	+	0.371623i	−0.779153	−	0.626834i	$-0.784350\pi$
$383$	−16.3350	+	7.27281i	−0.834679	+	0.371623i	−0.0555264	+	0.998457i	$0.517684\pi$
$384$	1.66359	+	0.482149i	0.0848947	+	0.0246045i
$385$	−0.425205	+	2.00043i	−0.0216704	+	0.101951i
$386$	−0.913739	+	2.05229i	−0.0465081	+	0.104459i
$387$	5.54689	+	4.38472i	0.281964	+	0.222888i
$388$	−3.17730	−	9.77872i	−0.161303	−	0.496439i
$389$	−15.7275	−	7.00233i	−0.797415	−	0.355032i	−0.0327529	−	0.999463i	$-0.510427\pi$
$389$	−15.7275	−	7.00233i	−0.797415	−	0.355032i	−0.764662	+	0.644431i	$0.777094\pi$
$390$	−6.11207	−	5.15831i	−0.309497	−	0.261201i
$391$	−0.00708553	+	0.00150608i	−0.000358331	+	7.61656e-5i
$392$	−0.721627	−	1.62080i	−0.0364477	−	0.0818628i
$393$	−6.02751	−	24.4711i	−0.304048	−	1.23441i
$394$	−17.7881	+	1.86960i	−0.896149	+	0.0941891i
$395$	6.40157	−	4.65101i	0.322098	−	0.234018i
$396$	1.83432	−	0.961991i	0.0921782	−	0.0483418i
$397$	13.1922	+	22.8495i	0.662097	+	1.14678i	0.980064	+	0.198683i	$0.0636665\pi$
$397$	13.1922	+	22.8495i	0.662097	+	1.14678i	−0.317967	+	0.948102i	$0.603000\pi$
$398$	1.44974	−	2.51102i	0.0726688	−	0.125866i
$399$	−3.98654	+	1.93036i	−0.199577	+	0.0966387i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	1.48810	−	4.57991i	0.0743123	−	0.228710i	−0.907000	−	0.421130i	$-0.861634\pi$
$401$	1.48810	−	4.57991i	0.0743123	−	0.228710i	0.981313	+	0.192420i	$0.0616337\pi$
$402$	18.8558	+	10.0947i	0.940443	+	0.503476i
$403$	−4.38083	−	25.3335i	−0.218225	−	1.26195i
$404$			8.74114i			0.434888i
$405$	−5.86310	+	6.82818i	−0.291340	+	0.339295i
$406$	−17.8816	−	16.1007i	−0.887449	−	0.799063i
$407$	−0.410839	+	0.565471i	−0.0203645	+	0.0280294i
$408$	3.43024	−	2.12992i	0.169822	−	0.105447i
$409$	3.75856	−	2.17001i	0.185849	−	0.107300i	−0.404189	−	0.914676i	$-0.632446\pi$
$409$	3.75856	−	2.17001i	0.185849	−	0.107300i	0.590038	+	0.807376i	$0.299113\pi$
$410$	−3.95891	−	0.416098i	−0.195516	−	0.0205496i
$411$	1.20620	+	8.76323i	0.0594974	+	0.432258i
$412$	−1.17604	−	11.1892i	−0.0579392	−	0.551255i
$413$	−20.4681	+	18.4295i	−1.00717	+	0.906858i
$414$	0.00498483	−	0.00787739i	0.000244991	−	0.000387153i
$415$	2.14195	+	10.0771i	0.105144	+	0.494664i
$416$	−4.51666	−	0.960045i	−0.221447	−	0.0470701i
$417$	4.89946	+	6.30791i	0.239928	+	0.308899i
$418$	0.566884	−	0.184192i	0.0277272	−	0.00900911i
$419$	−15.7408	+	5.11451i	−0.768991	+	0.249860i	−0.667133	−	0.744939i	$-0.732479\pi$
$419$	−15.7408	+	5.11451i	−0.768991	+	0.249860i	−0.101858	+	0.994799i	$0.532479\pi$
$420$	−3.14718	−	4.05189i	−0.153567	−	0.197712i
$421$	−10.3319	−	2.19612i	−0.503548	−	0.107032i	−0.0508676	−	0.998705i	$-0.516199\pi$
$421$	−10.3319	−	2.19612i	−0.503548	−	0.107032i	−0.452680	+	0.891673i	$0.649532\pi$
$422$	1.31157	+	6.17045i	0.0638462	+	0.300373i
$423$	−17.5349	+	27.7098i	−0.852574	+	1.34730i
$424$	3.31148	−	2.98167i	0.160820	−	0.144803i
$425$	0.243674	+	2.31840i	0.0118199	+	0.112459i
$426$	0.450857	+	3.27555i	0.0218441	+	0.158701i
$427$	−13.1885	−	1.38617i	−0.638236	−	0.0670813i
$428$	10.0102	−	5.77939i	0.483861	−	0.279358i
$429$	−4.69114	+	2.91284i	−0.226490	+	0.140633i
$430$	−1.38534	+	1.90675i	−0.0668068	+	0.0919517i
$431$	5.86646	+	5.28219i	0.282578	+	0.254434i	0.798215	−	0.602373i	$-0.205778\pi$
$431$	5.86646	+	5.28219i	0.282578	+	0.254434i	−0.515637	+	0.856807i	$0.672445\pi$
$432$	−1.12364	+	5.07321i	−0.0540613	+	0.244085i
$433$		−	3.18600i		−	0.153109i	−0.997065	−	0.0765546i	$-0.975608\pi$
$433$		−	3.18600i		−	0.153109i	0.997065	−	0.0765546i	$-0.0243920\pi$
$434$	0.629967	−	16.4804i	0.0302394	−	0.791084i
$435$	−12.4041	−	6.64069i	−0.594733	−	0.318397i
$436$	−6.20347	+	19.0923i	−0.297092	+	0.914356i
$437$	0.00179505	−	0.00199360i	8.58688e−5	−	9.53669e-5i
$438$	−0.930570	+	0.450600i	−0.0444644	+	0.0215305i
$439$	−1.49420	+	2.58803i	−0.0713142	+	0.123520i	−0.899478	−	0.436967i	$-0.856053\pi$
$439$	−1.49420	+	2.58803i	−0.0713142	+	0.123520i	0.828163	+	0.560487i	$0.189386\pi$
$440$	0.345212	+	0.597925i	0.0164573	+	0.0285049i
$441$	4.71367	−	2.47203i	0.224461	−	0.117716i
$442$	−8.70853	+	6.32712i	−0.414223	+	0.300950i
$443$	−9.46017	+	0.994304i	−0.449466	+	0.0472408i	−0.326558	−	0.945177i	$-0.605889\pi$
$443$	−9.46017	+	0.994304i	−0.449466	+	0.0472408i	−0.122908	+	0.992418i	$0.539222\pi$
$444$	−0.419364	−	1.70258i	−0.0199021	−	0.0808009i
$445$	1.41980	+	3.18893i	0.0673051	+	0.151170i
$446$	24.1878	−	5.14127i	1.14532	−	0.243446i
$447$	11.4879	+	9.69531i	0.543361	+	0.458572i
$448$	−2.70604	−	1.20480i	−0.127848	−	0.0569217i
$449$	−2.05547	−	6.32608i	−0.0970035	−	0.298546i	0.890767	−	0.454460i	$-0.150168\pi$
$449$	−2.05547	−	6.32608i	−0.0970035	−	0.298546i	−0.987771	+	0.155914i	$0.950168\pi$
$450$	−2.35349	−	1.86039i	−0.110945	−	0.0876998i
$451$	−1.11787	+	2.51077i	−0.0526383	+	0.118227i
$452$	1.60419	−	7.54714i	0.0754549	−	0.354987i
$453$	−39.0713	−	11.3238i	−1.83573	−	0.532038i
$454$	11.9389	−	5.31553i	0.560320	−	0.249470i
$455$	9.15223	+	10.1646i	0.429063	+	0.476523i
$456$	−0.564093	+	1.38483i	−0.0264161	+	0.0648508i
$457$	−5.97055	−	8.21775i	−0.279290	−	0.384410i	0.646208	−	0.763161i	$-0.276354\pi$
$457$	−5.97055	−	8.21775i	−0.279290	−	0.384410i	−0.925499	+	0.378751i	$0.876354\pi$
$458$	−1.77426	+	16.8809i	−0.0829056	+	0.788794i
$459$	7.03610	+	9.86009i	0.328417	+	0.460230i
$460$	0.00269106	+	0.00155369i	0.000125471	+	7.24410e-5i
$461$	8.03554	+	5.83816i	0.374253	+	0.271910i	0.758972	−	0.651123i	$-0.225702\pi$
$461$	8.03554	+	5.83816i	0.374253	+	0.271910i	−0.384720	+	0.923034i	$0.625702\pi$
$462$	−3.33206	+	1.20206i	−0.155022	+	0.0559247i
$463$	22.4908	+	7.30772i	1.04524	+	0.339618i	0.780798	−	0.624784i	$-0.214813\pi$
$463$	22.4908	+	7.30772i	1.04524	+	0.339618i	0.264440	+	0.964402i	$0.414813\pi$
$464$	−8.12324			−0.377112
$465$	−1.94705	−	9.44505i	−0.0902922	−	0.438004i
$466$	13.5457			0.627494
$467$	−25.4368	−	8.26490i	−1.17707	−	0.382454i	−0.345794	−	0.938310i	$-0.612391\pi$
$467$	−25.4368	−	8.26490i	−1.17707	−	0.382454i	−0.831278	+	0.555856i	$0.812391\pi$
$468$	2.00587	−	13.7067i	0.0927216	−	0.633592i
$469$	−29.5917	−	21.4996i	−1.36642	−	0.992760i
$470$	−9.46619	−	5.46531i	−0.436643	−	0.252096i
$471$	5.78535	−	0.185566i	0.266575	−	0.00855041i
$472$	−0.971929	+	9.24728i	−0.0447366	+	0.425641i
$473$	0.956469	+	1.31647i	0.0439785	+	0.0605312i
$474$	12.6927	+	5.17021i	0.582996	+	0.237475i
$475$	−0.577674	−	0.641572i	−0.0265055	−	0.0294373i
$476$	−6.30824	+	2.80861i	−0.289138	+	0.128732i
$477$	9.56328	+	9.34080i	0.437872	+	0.427686i
$478$	1.94704	−	9.16011i	0.0890556	−	0.418974i
$479$	−2.54632	+	5.71914i	−0.116344	+	0.261314i	−0.962326	−	0.271898i	$-0.912349\pi$
$479$	−2.54632	+	5.71914i	−0.116344	+	0.261314i	0.845982	+	0.533212i	$0.179015\pi$
$480$	−1.70488	−	0.305615i	−0.0778166	−	0.0139493i
$481$	1.44455	+	4.44586i	0.0658657	+	0.202714i
$482$	−0.446977	−	0.199007i	−0.0203593	−	0.00906453i
$483$	−0.0102823	+	0.0121835i	−0.000467863	+	0.000554369i
$484$	−10.2934	+	2.18792i	−0.467880	+	0.0994509i
$485$	4.18205	+	9.39304i	0.189897	+	0.426516i
$486$	−15.4044	−	2.38866i	−0.698756	−	0.108352i
$487$	−26.6615	+	2.80224i	−1.20815	+	0.126982i	−0.687111	−	0.726552i	$-0.741122\pi$
$487$	−26.6615	+	2.80224i	−1.20815	+	0.126982i	−0.521038	+	0.853534i	$0.674455\pi$
$488$	−3.62189	+	2.63146i	−0.163955	+	0.119120i
$489$	−29.2204	−	19.8305i	−1.32139	−	0.896767i
$490$	0.887094	+	1.53649i	0.0400748	+	0.0694116i
$491$	−3.45616	+	5.98624i	−0.155974	+	0.270155i	−0.933413	−	0.358803i	$-0.883185\pi$
$491$	−3.45616	+	5.98624i	−0.155974	+	0.270155i	0.777439	+	0.628958i	$0.216518\pi$
$492$	−3.00485	−	6.20557i	−0.135469	−	0.279769i
$493$	−12.6711	+	14.0727i	−0.570679	+	0.633803i
$494$	1.23188	−	3.79132i	0.0554247	−	0.170580i
$495$	−1.72372	+	1.14846i	−0.0774754	+	0.0516194i
$496$	−3.56480	−	4.27694i	−0.160064	−	0.192040i
$497$		−	5.65461i		−	0.253644i
$498$	−12.8710	+	12.3589i	−0.576764	+	0.553815i
$499$	2.04425	+	1.84065i	0.0915132	+	0.0823989i	0.713618	−	0.700535i	$-0.247055\pi$
$499$	2.04425	+	1.84065i	0.0915132	+	0.0823989i	−0.622104	+	0.782934i	$0.713722\pi$
$500$	0.587785	−	0.809017i	0.0262866	−	0.0361803i
$501$	−9.44881	−	15.2173i	−0.422142	−	0.679860i
$502$	8.42638	−	4.86497i	0.376088	−	0.217134i
$503$	33.3446	+	3.50466i	1.48676	+	0.156265i	0.812818	−	0.582518i	$-0.197932\pi$
$503$	33.3446	+	3.50466i	1.48676	+	0.156265i	0.673944	+	0.738783i	$0.264599\pi$
$504$	3.08674	−	8.33305i	0.137494	−	0.371184i
$505$	−0.913698	−	8.69326i	−0.0406590	−	0.386845i
$506$	0.00159435	−	0.00143556i	7.08773e−5	−	6.38182e-5i
$507$	−1.04633	+	14.3759i	−0.0464691	+	0.638455i
$508$	−4.28672	−	20.1674i	−0.190192	−	0.894785i
$509$	−10.0502	−	2.13623i	−0.445465	−	0.0946865i	−0.0202829	−	0.999794i	$-0.506457\pi$
$509$	−10.0502	−	2.13623i	−0.445465	−	0.0946865i	−0.425182	+	0.905108i	$0.639790\pi$
$510$	−3.18881	+	2.47681i	−0.141203	+	0.109675i
$511$	1.68166	−	0.546405i	0.0743923	−	0.0241715i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−4.25441	−	1.42256i	−0.187837	−	0.0628077i
$514$	6.94383	+	1.47596i	0.306279	+	0.0651017i
$515$	2.33919	+	11.0050i	0.103077	+	0.484939i
$516$	−4.07146	−	0.296336i	−0.179236	−	0.0130455i
$517$	−5.60834	+	5.04977i	−0.246654	+	0.222089i
$518$	0.313455	+	2.98232i	0.0137724	+	0.131036i
$519$	35.1493	−	4.83807i	1.54289	−	0.212368i
$520$	4.59227	+	0.482667i	0.201384	+	0.0211663i
$521$	25.6621	−	14.8160i	1.12428	−	0.649102i	0.181788	−	0.983338i	$-0.441812\pi$
$521$	25.6621	−	14.8160i	1.12428	−	0.649102i	0.942489	+	0.334236i	$0.108478\pi$
$522$	−1.56172	−	24.3196i	−0.0683544	−	1.06444i
$523$	22.6437	−	31.1664i	0.990141	−	1.36281i	0.0589586	−	0.998260i	$-0.481222\pi$
$523$	22.6437	−	31.1664i	0.990141	−	1.36281i	0.931183	−	0.364552i	$-0.118778\pi$
$524$	10.8133	+	9.73631i	0.472380	+	0.425333i
$525$	3.55348	+	3.70073i	0.155086	+	0.161513i
$526$			8.24446i			0.359476i
$527$	−12.9700	−	0.495780i	−0.564980	−	0.0215965i
$528$	−0.564416	+	1.05427i	−0.0245631	+	0.0458813i
$529$	−7.10739	+	21.8743i	−0.309017	+	0.951056i
$530$	−2.98167	+	3.31148i	−0.129516	+	0.143842i
$531$	−27.8717	−	1.13198i	−1.20953	−	0.0491236i
$532$	1.27863	−	2.21465i	0.0554357	−	0.0960174i
$533$	9.19059	+	15.9186i	0.398089	+	0.689510i
$534$	−3.39517	+	5.00282i	−0.146923	+	0.216493i
$535$	−9.35126	+	6.79408i	−0.404290	+	0.293734i
$536$	−12.2807	+	1.29075i	−0.530445	+	0.0557520i
$537$	−22.6813	+	5.58665i	−0.978770	+	0.241082i
$538$	4.50783	+	10.1248i	0.194347	+	0.436509i
$539$	1.19817	−	0.254680i	0.0516090	−	0.0109698i
$540$	0.587193	−	5.16287i	0.0252688	−	0.222174i
$541$	37.4082	+	16.6552i	1.60830	+	0.716063i	0.997150	−	0.0754481i	$-0.0240387\pi$
$541$	37.4082	+	16.6552i	1.60830	+	0.716063i	0.611155	+	0.791511i	$0.290705\pi$
$542$	2.60665	+	8.02243i	0.111965	+	0.344593i
$543$	2.93574	−	16.3770i	0.125984	−	0.702806i
$544$	−0.948174	+	2.12963i	−0.0406526	+	0.0913073i
$545$	4.17380	−	19.6362i	0.178786	−	0.841121i
$546$	−6.59473	+	22.7542i	−0.282228	+	0.973792i
$547$	22.6089	−	10.0661i	0.966687	−	0.430397i	0.138200	−	0.990404i	$-0.455868\pi$
$547$	22.6089	−	10.0661i	0.966687	−	0.430397i	0.828488	+	0.560007i	$0.189202\pi$
$548$	−3.41735	−	3.79535i	−0.145982	−	0.162130i
$549$	−8.57446	−	10.3374i	−0.365949	−	0.441191i
$550$	−0.405821	−	0.558565i	−0.0173043	−	0.0238173i
$551$	0.733054	−	6.97454i	0.0312291	−	0.297125i
$552$	0.000172543		0.00537936i	7.34394e−6		0.000228961i
$553$	−20.2985	−	11.7193i	−0.863178	−	0.498356i
$554$	−11.0811	−	8.05090i	−0.470791	−	0.342050i
$555$	0.595035	+	1.64942i	0.0252578	+	0.0700139i
$556$	−4.38568	−	1.42499i	−0.185994	−	0.0604332i
$557$	−36.3511			−1.54024			−0.770122	−	0.637896i	$-0.779805\pi$
$557$	−36.3511			−1.54024			−0.770122	+	0.637896i	$0.779805\pi$
$558$	12.1191	−	11.4947i	0.513043	−	0.486608i
$559$	10.8830			0.460302
$560$	2.81715	+	0.915347i	0.119046	+	0.0386805i
$561$	0.946011	+	2.62231i	0.0399406	+	0.110714i
$562$	4.50424	+	3.27252i	0.190000	+	0.138043i
$563$	9.44660	+	5.45400i	0.398127	+	0.229859i	0.685675	−	0.727907i	$-0.259507\pi$
$563$	9.44660	+	5.45400i	0.398127	+	0.229859i	−0.287549	+	0.957766i	$0.592840\pi$
$564$	−0.606946	−	18.9227i	−0.0255570	−	0.796788i
$565$	−0.806515	+	7.67348i	−0.0339303	+	0.322826i
$566$	16.0620	+	22.1074i	0.675135	+	0.929244i
$567$	25.5412	+	7.63914i	1.07263	+	0.320814i
$568$	−1.27735	−	1.41864i	−0.0535964	−	0.0595248i
$569$	−14.7488	+	6.56659i	−0.618302	+	0.275286i	−0.691890	−	0.722003i	$-0.743222\pi$
$569$	−14.7488	+	6.56659i	−0.618302	+	0.275286i	0.0735883	+	0.997289i	$0.476555\pi$
$570$	0.416249	−	1.43621i	0.0174347	−	0.0601563i
$571$	−1.38761	+	6.52820i	−0.0580697	+	0.273197i	−0.997598	−	0.0692761i	$-0.977931\pi$
$571$	−1.38761	+	6.52820i	−0.0580697	+	0.273197i	0.939528	+	0.342473i	$0.111264\pi$
$572$	1.29671	−	2.91245i	0.0542180	−	0.121776i
$573$	0.943577	−	5.26376i	0.0394185	−	0.219897i
$574$	3.64373	+	11.2143i	0.152087	+	0.468074i
$575$	−0.00283873	−	0.00126388i	−0.000118383	−	5.27075e-5i
$576$	−1.10799	−	2.78790i	−0.0461662	−	0.116162i
$577$	−27.2027	+	5.78211i	−1.13246	+	0.240712i	−0.735765	−	0.677237i	$-0.763177\pi$
$577$	−27.2027	+	5.78211i	−1.13246	+	0.240712i	−0.396697	+	0.917949i	$0.629844\pi$
$578$	−4.70416	−	10.5657i	−0.195667	−	0.439476i
$579$	3.77815	−	0.930601i	0.157015	−	0.0386744i
$580$	8.07874	−	0.849110i	0.335452	−	0.0352574i
$581$	24.6883	−	17.9371i	1.02424	−	0.744156i
$582$	−10.0005	+	14.7359i	−0.414535	+	0.610821i
$583$	1.53828	+	2.66438i	0.0637090	+	0.110347i
$584$	0.298468	−	0.516963i	0.0123507	−	0.0213921i
$585$	−0.562148	+	13.8413i	−0.0232419	+	0.572266i
$586$	−7.77644	+	8.63661i	−0.321242	+	0.356775i
$587$	−9.19053	+	28.2855i	−0.379334	+	1.16747i	0.561174	+	0.827698i	$0.310350\pi$
$587$	−9.19053	+	28.2855i	−0.379334	+	1.16747i	−0.940508	+	0.339771i	$0.889650\pi$
$588$	−1.45038	+	2.70917i	−0.0598129	+	0.111724i
$589$	3.99384	−	2.67474i	0.164563	−	0.110211i
$590$		−	9.29822i		−	0.382802i
$591$	21.4568	+	22.3459i	0.882613	+	0.919187i
$592$	0.752333	+	0.677404i	0.0309207	+	0.0278411i
$593$	−2.59570	+	3.57267i	−0.106592	+	0.146712i	−0.858981	−	0.512008i	$-0.828902\pi$
$593$	−2.59570	+	3.57267i	−0.106592	+	0.146712i	0.752388	+	0.658720i	$0.228902\pi$
$594$	−3.26483	−	1.48708i	−0.133957	−	0.0610157i
$595$	5.98011	−	3.45262i	0.245160	−	0.141543i
$596$	−8.63139	−	0.907196i	−0.353556	−	0.0371602i
$597$	−4.97514	+	0.684794i	−0.203619	+	0.0280268i
$598$	−0.00149982	−	0.0142699i	−6.13324e−5	−	0.000583539i
$599$	−9.38033	+	8.44609i	−0.383270	+	0.345098i	−0.838135	−	0.545462i	$-0.816354\pi$
$599$	−9.38033	+	8.44609i	−0.383270	+	0.345098i	0.454865	+	0.890560i	$0.349687\pi$
$600$	1.72748	+	0.125733i	0.0705241	+	0.00513301i
$601$	2.95849	+	13.9186i	0.120679	+	0.567752i	0.996388	+	0.0849126i	$0.0270611\pi$
$601$	2.95849	+	13.9186i	0.120679	+	0.567752i	−0.875709	+	0.482839i	$0.839606\pi$
$602$	6.82880	+	1.45151i	0.278321	+	0.0591590i
$603$	−6.22529	−	36.5182i	−0.253514	−	1.48714i
$604$	22.3366	−	7.25761i	0.908864	−	0.295308i
$605$	10.0083	−	3.25188i	0.406894	−	0.132208i
$606$	11.9570	−	9.28723i	0.485720	−	0.377268i
$607$	43.7761	+	9.30490i	1.77682	+	0.377674i	0.975402	−	0.220434i	$-0.0707474\pi$
$607$	43.7761	+	9.30490i	1.77682	+	0.377674i	0.801415	+	0.598108i	$0.204081\pi$
$608$	−0.179494	−	0.844454i	−0.00727946	−	0.0342471i
$609$	−3.02539	+	41.5668i	−0.122595	+	1.68437i
$610$	3.32699	−	2.99563i	0.134706	−	0.121290i
$611$	5.27584	+	50.1963i	0.213438	+	2.03073i
$612$	−6.55806	−	2.42925i	−0.265094	−	0.0981965i
$613$	16.3736	+	1.72094i	0.661324	+	0.0695080i	0.429244	−	0.903189i	$-0.358780\pi$
$613$	16.3736	+	1.72094i	0.661324	+	0.0695080i	0.232080	+	0.972697i	$0.425447\pi$
$614$	−0.430847	+	0.248750i	−0.0173876	+	0.0100387i
$615$	3.63705	+	5.85748i	0.146660	+	0.236196i
$616$	1.20209	−	1.65454i	0.0484337	−	0.0666633i
$617$	−15.6373	−	14.0799i	−0.629536	−	0.566836i	0.291376	−	0.956609i	$-0.405887\pi$
$617$	−15.6373	−	14.0799i	−0.629536	−	0.566836i	−0.920911	+	0.389772i	$0.872554\pi$
$618$	−14.0563	+	13.4970i	−0.565426	+	0.542928i
$619$			20.4583i			0.822290i	0.911570	+	0.411145i	$0.134871\pi$
$619$			20.4583i			0.822290i	−0.911570	+	0.411145i	$0.865129\pi$
$620$	3.99233	+	3.88089i	0.160336	+	0.155860i
$621$	−0.0160717	+	0.00155076i	−0.000644937	+	6.22300e-5i
$622$	8.38926	−	25.8195i	0.336379	−	1.03527i
$623$	6.91878	−	7.68408i	0.277195	−	0.307856i
$624$	3.48558	+	7.19836i	0.139535	+	0.288165i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	12.3801	+	21.4430i	0.494808	+	0.857033i
$627$	−0.854254	−	0.579742i	−0.0341156	−	0.0231526i
$628$	−2.70365	+	1.96431i	−0.107887	+	0.0783846i
$629$	2.34707	−	0.246687i	0.0935838	−	0.00983606i
$630$	−2.19879	+	8.61005i	−0.0876020	+	0.343033i
$631$	−9.56508	−	21.4835i	−0.380780	−	0.855246i	−0.997672	−	0.0681979i	$-0.978275\pi$
$631$	−9.56508	−	21.4835i	−0.380780	−	0.855246i	0.616892	−	0.787048i	$-0.288392\pi$
$632$	−7.73986	+	1.64516i	−0.307875	+	0.0654409i
$633$	7.04706	−	8.35004i	0.280095	−	0.331884i
$634$	22.6217	+	10.0718i	0.898424	+	0.400004i
$635$	6.37131	+	19.6089i	0.252838	+	0.778154i
$636$	−7.59700	−	1.36183i	−0.301240	−	0.0540002i
$637$	3.33216	−	7.48415i	0.132025	−	0.296533i
$638$	1.16607	−	5.48592i	0.0461651	−	0.217190i
$639$	4.00160	−	4.09691i	0.158301	−	0.162071i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	32.5879	+	36.1925i	1.28715	+	1.42952i	0.847000	+	0.531593i	$0.178407\pi$
$641$	32.5879	+	36.1925i	1.28715	+	1.42952i	0.440146	+	0.897926i	$0.354927\pi$
$642$	−18.5412	−	7.55251i	−0.731763	−	0.298074i
$643$	23.5502	+	32.4141i	0.928730	+	1.27829i	0.960353	+	0.278787i	$0.0899325\pi$
$643$	23.5502	+	32.4141i	0.928730	+	1.27829i	−0.0316227	+	0.999500i	$0.510068\pi$
$644$	0.000962125	−	0.00915400i	3.79130e−5	−	0.000360718i
$645$	4.08013	−	0.130870i	0.160655	−	0.00515302i
$646$	−1.74292	−	1.00627i	−0.0685742	−	0.0395914i
$647$	−3.05629	−	2.22053i	−0.120155	−	0.0872979i	0.526085	−	0.850432i	$-0.323659\pi$
$647$	−3.05629	−	2.22053i	−0.120155	−	0.0872979i	−0.646240	+	0.763134i	$0.723659\pi$
$648$	8.13348	−	3.85311i	0.319513	−	0.151365i
$649$	−6.10551	−	1.98380i	−0.239662	−	0.0778710i
$650$	−4.61756			−0.181116
$651$	−23.2128	+	16.6482i	−0.909783	+	0.652495i
$652$	20.3886			0.798479
$653$	−18.9136	−	6.14541i	−0.740148	−	0.240489i	−0.0854113	−	0.996346i	$-0.527220\pi$
$653$	−18.9136	−	6.14541i	−0.740148	−	0.240489i	−0.654737	+	0.755857i	$0.727220\pi$
$654$	32.7074	−	11.7993i	1.27896	−	0.461391i
$655$	−11.7718	−	8.55268i	−0.459960	−	0.334181i
$656$	3.44740	+	1.99036i	0.134598	+	0.0777104i
$657$	1.60508	+	0.794177i	0.0626202	+	0.0309838i
$658$	−3.38441	+	32.2005i	−0.131938	+	1.25531i
$659$	1.24535	+	1.71408i	0.0485121	+	0.0667712i	0.832584	−	0.553899i	$-0.186861\pi$
$659$	1.24535	+	1.71408i	0.0485121	+	0.0667712i	−0.784072	+	0.620670i	$0.786861\pi$
$660$	0.451123	−	1.10749i	0.0175599	−	0.0431092i
$661$	13.0432	+	14.4859i	0.507320	+	0.563436i	0.941337	−	0.337469i	$-0.109571\pi$
$661$	13.0432	+	14.4859i	0.507320	+	0.563436i	−0.434016	+	0.900905i	$0.642904\pi$
$662$	−16.4662	+	7.33122i	−0.639977	+	0.284936i
$663$	17.9075	+	5.19001i	0.695468	+	0.201563i
$664$	2.14195	−	10.0771i	0.0831236	−	0.391066i
$665$	−1.04013	+	2.33618i	−0.0403346	+	0.0905930i
$666$	−1.88340	+	2.38259i	−0.0729801	+	0.0923236i
$667$	−0.00780019	−	0.0240065i	−0.000302025	−	0.000929536i
$668$	9.44754	+	4.20631i	0.365536	+	0.162747i
$669$	−32.7316	−	27.6240i	−1.26548	−	1.06801i
$670$	12.0785	−	2.56736i	0.466633	−	0.0991859i
$671$	−1.25721	−	2.82373i	−0.0485339	−	0.109009i
$672$	1.22704	+	4.98166i	0.0473340	+	0.192172i
$673$	−27.4194	+	2.88190i	−1.05694	+	0.111089i	−0.617020	−	0.786948i	$-0.711660\pi$
$673$	−27.4194	+	2.88190i	−1.05694	+	0.111089i	−0.439921	+	0.898037i	$0.644993\pi$
$674$	19.6238	−	14.2575i	0.755881	−	0.549179i
$675$	−0.0443095	+	5.19596i	−0.00170547	+	0.199993i
$676$	−4.16093	−	7.20695i	−0.160036	−	0.277190i
$677$	17.4259	−	30.1825i	0.669731	−	1.16001i	−0.308248	−	0.951306i	$-0.599743\pi$
$677$	17.4259	−	30.1825i	0.669731	−	1.16001i	0.977979	−	0.208702i	$-0.0669239\pi$
$678$	−12.0281	+	5.82425i	−0.461938	+	0.223679i
$679$	20.3793	−	22.6336i	0.782087	−	0.868596i
$680$	0.720373	−	2.21708i	0.0276250	−	0.0850211i
$681$	−19.9559	−	10.6836i	−0.764710	−	0.409396i
$682$	3.40009	−	1.79349i	0.130196	−	0.0686764i
$683$		−	49.0063i		−	1.87517i	−0.347752	−	0.937587i	$-0.613055\pi$
$683$		−	49.0063i		−	1.87517i	0.347752	−	0.937587i	$-0.386945\pi$
$684$	2.49365	−	0.699725i	0.0953470	−	0.0267546i
$685$	3.79535	+	3.41735i	0.145013	+	0.130570i
$686$	−9.09863	+	12.5232i	−0.347387	+	0.478138i
$687$	24.9765	−	15.5085i	0.952914	−	0.591687i
$688$	2.04111	−	1.17844i	0.0778167	−	0.0449275i
$689$	20.4633	+	2.15078i	0.779591	+	0.0819383i
$690$	−0.000733895	−	0.00533186i	−2.79389e−5	−	0.000202980i
$691$	−0.439855	−	4.18494i	−0.0167329	−	0.159203i	0.982965	−	0.183794i	$-0.0588381\pi$
$691$	−0.439855	−	4.18494i	−0.0167329	−	0.159203i	−0.999698	+	0.0245918i	$0.992171\pi$
$692$	−15.2232	+	13.7070i	−0.578699	+	0.521063i
$693$	5.18452	+	3.28078i	0.196944	+	0.124626i
$694$	−1.98356	−	9.33193i	−0.0752950	−	0.354235i
$695$	4.51061	+	0.958759i	0.171097	+	0.0363678i
$696$	8.63073	+	11.1118i	0.327147	+	0.421191i
$697$	8.82555	−	2.86760i	0.334292	−	0.108618i
$698$	9.91624	−	3.22198i	0.375335	−	0.121954i
$699$	−14.3920	−	18.5292i	−0.544354	−	0.700839i
$700$	−2.89740	−	0.615861i	−0.109511	−	0.0232773i
$701$	−10.4177	−	49.0112i	−0.393470	−	1.85113i	−0.513126	−	0.858313i	$-0.671513\pi$
$701$	−10.4177	−	49.0112i	−0.393470	−	1.85113i	0.119657	−	0.992815i	$-0.461821\pi$
$702$	−20.8806	+	11.8191i	−0.788086	+	0.446085i
$703$	−0.649505	+	0.584817i	−0.0244965	+	0.0220568i
$704$	−0.0721689	−	0.686642i	−0.00271997	−	0.0258788i
$705$	2.58158	+	18.7556i	0.0972278	+	0.706375i
$706$	30.4077	+	3.19598i	1.14441	+	0.120282i
$707$	−22.4234	+	12.9462i	−0.843320	+	0.486891i
$708$	13.6820	−	8.49549i	0.514201	−	0.319280i
$709$	28.2250	−	38.8484i	1.06001	−	1.45898i	0.180218	−	0.983627i	$-0.442320\pi$
$709$	28.2250	−	38.8484i	1.06001	−	1.45898i	0.879794	−	0.475355i	$-0.157680\pi$
$710$	1.41864	+	1.27735i	0.0532406	+	0.0479381i
$711$	−6.41334	−	22.8556i	−0.240519	−	0.857151i
$712$		−	3.49072i		−	0.130820i
$713$	0.00921657	−	0.0146418i	0.000345163	−	0.000548341i
$714$	10.5442	+	5.64497i	0.394608	+	0.211258i
$715$	−0.985169	+	3.03204i	−0.0368432	+	0.113392i
$716$	9.02419	−	10.0224i	0.337250	−	0.374554i
$717$	−14.5988	+	7.06901i	−0.545202	+	0.263997i
$718$	3.80780	−	6.59530i	0.142106	−	0.246134i
$719$	13.5965	+	23.5498i	0.507063	+	0.878259i	0.999967	+	0.00817528i	$0.00260230\pi$
$719$	13.5965	+	23.5498i	0.507063	+	0.878259i	−0.492903	+	0.870084i	$0.664064\pi$
$720$	1.39333	+	2.65681i	0.0519265	+	0.0990133i
$721$	26.9617	−	19.5888i	1.00411	−	0.729526i
$722$	−18.1547	+	1.90813i	−0.675647	+	0.0710134i
$723$	0.202680	+	0.822860i	0.00753773	+	0.0306025i
$724$	3.90711	+	8.77552i	0.145207	+	0.326140i
$725$	−7.94573	+	1.68892i	−0.295097	+	0.0627248i
$726$	13.9293	+	11.7557i	0.516964	+	0.436294i
$727$	22.2633	+	9.91225i	0.825699	+	0.367625i	0.775682	−	0.631124i	$-0.217406\pi$
$727$	22.2633	+	9.91225i	0.825699	+	0.367625i	0.0500166	+	0.998748i	$0.484073\pi$
$728$	−4.22667	−	13.0084i	−0.156651	−	0.482122i
$729$	13.0993	+	23.6095i	0.485158	+	0.874427i
$730$	−0.242796	+	0.545329i	−0.00898629	+	0.0201835i
$731$	1.14233	−	5.37422i	0.0422505	−	0.198773i
$732$	7.44773	+	2.15853i	0.275276	+	0.0797816i
$733$	7.60340	−	3.38525i	0.280838	−	0.125037i	−0.261484	−	0.965208i	$-0.584212\pi$
$733$	7.60340	−	3.38525i	0.280838	−	0.125037i	0.542322	+	0.840171i	$0.317545\pi$
$734$	4.18551	+	4.64848i	0.154490	+	0.171579i
$735$	1.15925	−	2.84594i	0.0427597	−	0.104974i
$736$	−0.00182647	−	0.00251392i	−6.73245e−5	−	9.26642e-5i
$737$	0.891166	−	8.47888i	0.0328265	−	0.312324i
$738$	−5.29602	+	10.7036i	−0.194949	+	0.394005i
$739$	−1.97748	−	1.14170i	−0.0727426	−	0.0419980i	0.463188	−	0.886260i	$-0.346706\pi$
$739$	−1.97748	−	1.14170i	−0.0727426	−	0.0419980i	−0.535930	+	0.844262i	$0.680039\pi$
$740$	−0.819020	−	0.595053i	−0.0301078	−	0.0218746i
$741$	−6.49499	+	2.34310i	−0.238599	+	0.0860758i
$742$	12.5533	+	4.07882i	0.460847	+	0.149738i
$743$	4.02889			0.147805			0.0739027	−	0.997265i	$-0.476455\pi$
$743$	4.02889			0.147805			0.0739027	+	0.997265i	$0.476455\pi$
$744$	−2.06293	+	9.42042i	−0.0756308	+	0.345369i
$745$	8.67894			0.317972
$746$	31.4109	+	10.2060i	1.15004	+	0.373669i
$747$	30.5808	+	4.47529i	1.11889	+	0.163742i
$748$	−1.30211	−	0.946039i	−0.0476099	−	0.0345906i
$749$	29.6515	+	17.1193i	1.08344	+	0.625525i
$750$	−1.73116	+	0.0555271i	−0.0632130	+	0.00202756i
$751$	2.49700	−	23.7573i	0.0911167	−	0.866918i	−0.849532	−	0.527537i	$-0.823116\pi$
$751$	2.49700	−	23.7573i	0.0911167	−	0.866918i	0.940649	−	0.339381i	$-0.110218\pi$
$752$	6.42486	+	8.84306i	0.234290	+	0.322473i
$753$	−15.6076	−	6.35755i	−0.568773	−	0.231682i
$754$	−25.0988	−	27.8750i	−0.914044	−	1.01515i
$755$	−21.4556	+	9.55266i	−0.780850	+	0.347657i
$756$	−14.6784	+	4.63128i	−0.533847	+	0.168438i
$757$	−1.46112	+	6.87405i	−0.0531055	+	0.249842i	−0.996691	−	0.0812884i	$-0.974097\pi$
$757$	−1.46112	+	6.87405i	−0.0531055	+	0.249842i	0.943585	+	0.331130i	$0.107430\pi$
$758$	−4.58121	+	10.2896i	−0.166397	+	0.373734i
$759$	−0.00365765		0.000655667i	−0.000132764		2.37992e-5i
$760$	0.266781	+	0.821066i	0.00967715	+	0.0297832i
$761$	−39.7347	−	17.6911i	−1.44038	−	0.641300i	−0.469955	−	0.882690i	$-0.655730\pi$
$761$	−39.7347	−	17.6911i	−1.44038	−	0.641300i	−0.970428	+	0.241390i	$0.922397\pi$
$762$	−23.0325	+	27.2912i	−0.834380	+	0.988654i
$763$	−58.1648	+	12.3633i	−2.10571	+	0.447582i
$764$	1.25579	+	2.82055i	0.0454328	+	0.102044i
$765$	6.77606	+	1.73044i	0.244989	+	0.0625640i
$766$	−17.7829	+	1.86906i	−0.642523	+	0.0675319i
$767$	−34.7352	+	25.2366i	−1.25422	+	0.911242i
$768$	1.43318	+	0.972628i	0.0517153	+	0.0350967i
$769$	11.0942	+	19.2157i	0.400066	+	0.692934i	0.993733	−	0.111776i	$-0.0356539\pi$
$769$	11.0942	+	19.2157i	0.400066	+	0.692934i	−0.593668	+	0.804710i	$0.702321\pi$
$770$	−1.02256	+	1.77113i	−0.0368505	+	0.0638270i
$771$	−5.35867	−	11.0666i	−0.192988	−	0.398555i
$772$	−1.50321	+	1.66948i	−0.0541017	+	0.0600861i
$773$	7.45336	−	22.9391i	0.268079	−	0.825061i	−0.722889	−	0.690964i	$-0.757186\pi$
$773$	7.45336	−	22.9391i	0.268079	−	0.825061i	0.990968	−	0.134098i	$-0.0428136\pi$
$774$	3.92045	+	5.88420i	0.140918	+	0.211503i
$775$	−4.37612	−	3.44232i	−0.157195	−	0.123652i
$776$		−	10.2820i		−	0.369101i
$777$	3.74648	−	3.59741i	0.134404	−	0.129056i
$778$	−12.7939	−	11.5197i	−0.458683	−	0.413000i
$779$	−2.02000	+	2.78029i	−0.0723740	+	0.0996143i
$780$	−4.21892	−	6.79458i	−0.151061	−	0.243285i
$781$	1.14142	−	0.658999i	0.0408432	−	0.0235808i
$782$	−0.00720415		0.000757186i	−0.000257620		2.70769e-5i
$783$	−31.6076	+	27.9752i	−1.12956	+	0.999753i
$784$	−0.185453	−	1.76447i	−0.00662332	−	0.0630167i
$785$	2.48351	−	2.23616i	0.0886402	−	0.0798120i
$786$	1.82950	−	25.1360i	0.0652560	−	0.896573i
$787$	0.393874	+	1.85303i	0.0140401	+	0.0660535i	0.984610	−	0.174766i	$-0.0559170\pi$
$787$	0.393874	+	1.85303i	0.0140401	+	0.0660535i	−0.970570	+	0.240820i	$0.922584\pi$
$788$	−17.4952	−	3.71872i	−0.623240	−	0.132474i
$789$	11.2776	−	8.75952i	0.401493	−	0.311847i
$790$	7.52550	−	2.44518i	0.267745	−	0.0869957i
$791$	21.7364	−	7.06258i	0.772857	−	0.251117i
$792$	2.04182	−	0.348071i	0.0725528	−	0.0123681i
$793$	−20.2206	−	4.29802i	−0.718055	−	0.152627i
$794$	5.48562	+	25.8078i	0.194677	+	0.915885i
$795$	7.69773	+	0.560270i	0.273010	+	0.0198707i
$796$	2.15473	−	1.94013i	0.0763724	−	0.0687661i
$797$	3.20838	+	30.5257i	0.113647	+	1.08127i	0.891560	+	0.452903i	$0.149612\pi$
$797$	3.20838	+	30.5257i	0.113647	+	1.08127i	−0.777913	+	0.628372i	$0.783722\pi$
$798$	−4.38794	+	0.603970i	−0.155331	+	0.0213803i
$799$	25.3416	+	2.66351i	0.896521	+	0.0942282i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	10.4506	−	0.671100i	0.369255	−	0.0237122i
$802$	2.83054	−	3.89590i	0.0999498	−	0.137569i
$803$	0.306279	+	0.275775i	0.0108084	+	0.00973189i
$804$	14.8135	+	15.4274i	0.522433	+	0.544081i
$805$			0.00920443i			0.000324413i
$806$	3.66207	−	25.4473i	0.128991	−	0.896344i
$807$	9.06021	−	16.9236i	0.318935	−	0.595737i
$808$	−2.70116	+	8.31332i	−0.0950265	+	0.292462i
$809$	−23.1023	+	25.6577i	−0.812234	+	0.902078i	−0.996734	−	0.0807548i	$-0.974267\pi$
$809$	−23.1023	+	25.6577i	−0.812234	+	0.902078i	0.184500	+	0.982833i	$0.440934\pi$
$810$	−7.68616	+	4.68219i	−0.270064	+	0.164515i
$811$	20.1394	−	34.8825i	0.707190	−	1.22489i	−0.258706	−	0.965956i	$-0.583296\pi$
$811$	20.1394	−	34.8825i	0.707190	−	1.22489i	0.965895	−	0.258932i	$-0.0833707\pi$
$812$	−12.0310	−	20.8384i	−0.422207	−	0.731283i
$813$	8.20439	−	12.0892i	0.287741	−	0.423988i
$814$	−0.565471	+	0.410839i	−0.0198197	+	0.0143999i
$815$	−20.2769	+	2.13119i	−0.710269	+	0.0746522i
$816$	3.92054	−	0.965671i	0.137246	−	0.0338052i
$817$	0.827602	+	1.85882i	0.0289541	+	0.0650320i
$818$	4.24518	−	0.902340i	0.148429	−	0.0315496i
$819$	38.1323	−	15.1548i	1.33245	−	0.529553i
$820$	−3.63656	−	1.61910i	−0.126994	−	0.0565415i
$821$	8.65665	+	26.6424i	0.302119	+	0.929827i	0.980737	+	0.195335i	$0.0625795\pi$
$821$	8.65665	+	26.6424i	0.302119	+	0.929827i	−0.678617	+	0.734492i	$0.737420\pi$
$822$	−1.56082	+	8.70706i	−0.0544399	+	0.303694i
$823$	3.34087	−	7.50371i	0.116455	−	0.261563i	−0.845908	−	0.533329i	$-0.820941\pi$
$823$	3.34087	−	7.50371i	0.116455	−	0.261563i	0.962363	+	0.271766i	$0.0876076\pi$
$824$	2.33919	−	11.0050i	0.0814895	−	0.383378i
$825$	−0.332887	+	1.14858i	−0.0115896	+	0.0399885i
$826$	−25.1613	+	11.2025i	−0.875474	+	0.389786i
$827$	−33.3862	−	37.0792i	−1.16095	−	1.28937i	−0.950134	−	0.311843i	$-0.899054\pi$
$827$	−33.3862	−	37.0792i	−1.16095	−	1.28937i	−0.210819	−	0.977525i	$-0.567613\pi$
$828$	0.00717511	−	0.00595145i	0.000249352	−	0.000206827i
$829$	−9.07918	−	12.4964i	−0.315333	−	0.434019i	0.621702	−	0.783254i	$-0.286441\pi$
$829$	−9.07918	−	12.4964i	−0.315333	−	0.434019i	−0.937035	+	0.349235i	$0.886441\pi$
$830$	−1.07687	+	10.2458i	−0.0373788	+	0.355635i
$831$	0.760555	+	23.7117i	0.0263834	+	0.822550i
$832$	−3.99892	−	2.30878i	−0.138638	−	0.0800426i
$833$	−3.34605	−	2.43104i	−0.115934	−	0.0842307i
$834$	2.71042	+	7.51319i	0.0938541	+	0.260161i
$835$	−9.83546	−	3.19574i	−0.340370	−	0.110593i
$836$	0.596057			0.0206151
$837$	−28.5998	−	4.36497i	−0.988553	−	0.150876i
$838$	−16.5509			−0.571742
$839$	−44.4385	−	14.4389i	−1.53419	−	0.498488i	−0.584422	−	0.811450i	$-0.698679\pi$
$839$	−44.4385	−	14.4389i	−1.53419	−	0.498488i	−0.949765	+	0.312963i	$0.898679\pi$
$840$	−1.74104	−	4.82611i	−0.0600716	−	0.166517i
$841$	−29.9232	−	21.7405i	−1.03183	−	0.749671i
$842$	−9.14761	−	5.28138i	−0.315248	−	0.182008i
$843$	−0.309150	−	9.63832i	−0.0106477	−	0.331962i
$844$	−0.659397	+	6.27375i	−0.0226974	+	0.215951i
$845$	4.89147	+	6.73253i	0.168272	+	0.231606i
$846$	−25.2394	+	20.9351i	−0.867750	+	0.719762i
$847$	−20.8577	−	23.1648i	−0.716680	−	0.795954i
$848$	4.07080	−	1.81244i	0.139792	−	0.0622393i
$849$	13.1753	−	45.4597i	0.452176	−	1.56017i
$850$	−0.484678	+	2.28023i	−0.0166243	+	0.0782113i
$851$	−0.00127951	+	0.00287383i	−4.38610e−5	+	9.85135e-5i
$852$	−0.583409	+	3.25455i	−0.0199873	+	0.111499i
$853$	−15.0702	−	46.3812i	−0.515993	−	1.58806i	−0.781468	−	0.623945i	$-0.785529\pi$
$853$	−15.0702	−	46.3812i	−0.515993	−	1.58806i	0.265475	−	0.964118i	$-0.414471\pi$
$854$	−12.1147	−	5.39379i	−0.414555	−	0.184572i
$855$	−2.40685	+	0.956549i	−0.0823124	+	0.0327133i
$856$	11.3062	−	2.40321i	0.386438	−	0.0821399i
$857$	12.3373	+	27.7100i	0.421433	+	0.946554i	0.992109	+	0.125379i	$0.0400146\pi$
$857$	12.3373	+	27.7100i	0.421433	+	0.946554i	−0.570676	+	0.821175i	$0.693319\pi$
$858$	−5.36166	+	1.32063i	−0.183044	+	0.0450857i
$859$	−43.8183	+	4.60549i	−1.49506	+	0.157137i	−0.816473	−	0.577383i	$-0.804074\pi$
$859$	−43.8183	+	4.60549i	−1.49506	+	0.157137i	−0.678587	+	0.734520i	$0.737407\pi$
$860$	−1.90675	+	1.38534i	−0.0650197	+	0.0472396i
$861$	11.4686	−	16.8991i	0.390850	−	0.575920i
$862$	3.94705	+	6.83650i	0.134437	+	0.232852i
$863$	8.77373	−	15.1965i	0.298661	−	0.517297i	−0.677169	−	0.735828i	$-0.736793\pi$
$863$	8.77373	−	15.1965i	0.298661	−	0.517297i	0.975830	+	0.218531i	$0.0701266\pi$
$864$	−2.63635	+	4.47768i	−0.0896906	+	0.152334i
$865$	13.7070	−	15.2232i	0.466053	−	0.517604i
$866$	0.984527	−	3.03006i	0.0334556	−	0.102966i
$867$	−9.45481	+	17.6606i	−0.321102	+	0.599786i
$868$	5.69185	−	15.4791i	0.193194	−	0.525395i
$869$		−	5.46317i		−	0.185325i
$870$	−9.74495	−	10.1488i	−0.330385	−	0.344075i
$871$	−42.3735	−	38.1533i	−1.43577	−	1.29277i
$872$	−11.7997	+	16.2409i	−0.399588	+	0.549986i
$873$	30.7825	−	1.97673i	1.04183	−	0.0669023i
$874$	0.00232325	−	0.00134133i	7.85851e−5	−	4.53711e-5i
$875$	2.94590	+	0.309626i	0.0995896	+	0.0104673i
$876$	−1.02427	+	0.140984i	−0.0346068	+	0.00476340i
$877$	−0.904835	−	8.60893i	−0.0305541	−	0.290703i	−0.999120	−	0.0419454i	$-0.986644\pi$
$877$	−0.904835	−	8.60893i	−0.0305541	−	0.290703i	0.968566	−	0.248757i	$-0.0800222\pi$
$878$	−2.22081	+	1.99963i	−0.0749488	+	0.0674842i
$879$	20.0763	+	1.46123i	0.677156	+	0.0492860i
$880$	0.143547	+	0.675336i	0.00483897	+	0.0227656i
$881$	−40.4909	−	8.60661i	−1.36417	−	0.289964i	−0.533065	−	0.846074i	$-0.678960\pi$
$881$	−40.4909	−	8.60661i	−1.36417	−	0.289964i	−0.831109	+	0.556110i	$0.812293\pi$
$882$	5.24687	−	0.894440i	0.176671	−	0.0301173i
$883$	27.1717	−	8.82862i	0.914401	−	0.297107i	0.186233	−	0.982506i	$-0.440372\pi$
$883$	27.1717	−	8.82862i	0.914401	−	0.297107i	0.728168	+	0.685399i	$0.240372\pi$
$884$	−10.2375	+	3.32636i	−0.344324	+	0.111878i
$885$	−12.7190	+	9.87911i	−0.427546	+	0.332083i
$886$	−9.30442	−	1.97771i	−0.312588	−	0.0664426i
$887$	7.94422	+	37.3746i	0.266741	+	1.25492i	0.883749	+	0.467961i	$0.155011\pi$
$887$	7.94422	+	37.3746i	0.266741	+	1.25492i	−0.617008	+	0.786957i	$0.711655\pi$
$888$	0.127287	−	1.74884i	0.00427148	−	0.0586873i
$889$	45.3861	−	40.8659i	1.52220	−	1.37060i
$890$	0.364879	+	3.47160i	0.0122308	+	0.116368i
$891$	1.43461	+	6.04594i	0.0480612	+	0.202547i
$892$	24.5927	+	2.58480i	0.823424	+	0.0865454i
$893$	−8.17236	+	4.71831i	−0.273477	+	0.157892i
$894$	7.92967	+	12.7708i	0.265208	+	0.427118i
$895$	−7.92713	+	10.9108i	−0.264975	+	0.364706i
$896$	−2.20129	−	1.98205i	−0.0735399	−	0.0662156i
$897$	−0.0179262	+	0.0172130i	−0.000598540	+	0.000574724i
$898$		−	6.65163i		−	0.221968i
$899$	−3.00606	−	45.1283i	−0.100258	−	1.50511i
$900$	−1.66341	−	2.49661i	−0.0554471	−	0.0832203i
$901$	3.21001	−	9.87939i	0.106941	−	0.329130i
$902$	−1.83902	+	2.04244i	−0.0612328	+	0.0680059i
$903$	−5.26990	−	10.8833i	−0.175371	−	0.362174i
$904$	3.85787	−	6.68203i	0.128311	−	0.222241i
$905$	−4.80300	−	8.31904i	−0.159657	−	0.276534i
$906$	−33.6597	−	22.8433i	−1.11827	−	0.758916i
$907$	−24.0503	+	17.4736i	−0.798578	+	0.580201i	−0.910497	−	0.413516i	$-0.864301\pi$
$907$	−24.0503	+	17.4736i	−0.798578	+	0.580201i	0.111918	+	0.993717i	$0.464301\pi$
$908$	12.9971	−	1.36605i	0.431325	−	0.0453341i
$909$	−25.4080	−	6.48857i	−0.842730	−	0.215212i
$910$	5.56326	+	12.4953i	0.184420	+	0.414215i
$911$	−44.9170	+	9.54739i	−1.48817	+	0.316319i	−0.879037	−	0.476753i	$-0.841814\pi$
$911$	−44.9170	+	9.54739i	−1.48817	+	0.316319i	−0.609128	+	0.793072i	$0.708480\pi$
$912$	−0.964422	+	1.14274i	−0.0319352	+	0.0378399i
$913$	6.49794	+	2.89307i	0.215050	+	0.0957466i
$914$	−3.13890	−	9.66055i	−0.103826	−	0.319542i
$915$	−7.63256	−	1.36821i	−0.252325	−	0.0452315i
$916$	−6.90392	+	15.5064i	−0.228112	+	0.512347i
$917$	−8.96119	+	42.1591i	−0.295925	+	1.39222i
$918$	3.64479	+	11.5518i	0.120296	+	0.381266i
$919$	13.4287	−	5.97886i	0.442973	−	0.197224i	−0.173115	−	0.984902i	$-0.555383\pi$
$919$	13.4287	−	5.97886i	0.442973	−	0.197224i	0.616088	+	0.787677i	$0.288717\pi$
$920$	0.00207924	+	0.00230923i	6.85504e−5	+	7.61330e-5i
$921$	0.798028	+	0.325066i	0.0262959	+	0.0107113i
$922$	5.83816	+	8.03554i	0.192270	+	0.264637i
$923$	0.921395	−	8.76649i	0.0303281	−	0.288553i
$924$	−3.54043	+	0.113560i	−0.116472	+	0.00373584i
$925$	0.876733	+	0.506182i	0.0288268	+	0.0166432i
$926$	19.1318	+	13.9001i	0.628712	+	0.456786i
$927$	33.3969	+	4.88740i	1.09690	+	0.160523i
$928$	−7.72566	−	2.51022i	−0.253607	−	0.0824020i
$929$	55.2244			1.81185			0.905926	−	0.423436i	$-0.139176\pi$
$929$	55.2244			1.81185			0.905926	+	0.423436i	$0.139176\pi$
$930$	1.06693	−	9.58445i	0.0349860	−	0.314286i
$931$	1.53169			0.0501992
$932$	12.8828	+	4.18586i	0.421989	+	0.137112i
$933$	−44.2318	+	15.9568i	−1.44808	+	0.522403i
$934$	−21.6378	−	15.7208i	−0.708010	−	0.514400i
$935$	1.39387	+	0.804749i	0.0455843	+	0.0263181i
$936$	6.14330	−	12.4160i	0.200800	−	0.405829i
$937$	5.04903	−	48.0383i	0.164944	−	1.56934i	−0.528564	−	0.848893i	$-0.677269\pi$
$937$	5.04903	−	48.0383i	0.164944	−	1.56934i	0.693508	−	0.720449i	$-0.256064\pi$
$938$	−21.4996	−	29.5917i	−0.701987	−	0.966202i
$939$	16.1783	−	39.7173i	0.527959	−	1.29613i
$940$	−7.31401	−	8.12303i	−0.238557	−	0.264944i
$941$	39.2320	−	17.4672i	1.27893	−	0.569415i	0.348987	−	0.937127i	$-0.386526\pi$
$941$	39.2320	−	17.4672i	1.27893	−	0.569415i	0.929939	+	0.367713i	$0.119859\pi$
$942$	5.55954	+	1.61129i	0.181139	+	0.0524986i
$943$	−0.00257178	+	0.0120993i	−8.37485e−5	+	0.000394006i
$944$	−3.78193	+	8.49435i	−0.123091	+	0.276467i
$945$	14.1139	−	6.14022i	0.459124	−	0.199741i
$946$	0.502846	+	1.54760i	0.0163489	+	0.0503168i
$947$	−15.0053	−	6.68081i	−0.487608	−	0.217097i	0.148180	−	0.988960i	$-0.452658\pi$
$947$	−15.0053	−	6.68081i	−0.487608	−	0.217097i	−0.635789	+	0.771863i	$0.719325\pi$
$948$	10.4738	+	8.83942i	0.340173	+	0.287091i
$949$	2.69616	−	0.573086i	0.0875210	−	0.0186032i
$950$	−0.351144	−	0.788682i	−0.0113926	−	0.0255882i
$951$	−10.2577	−	41.6454i	−0.332629	−	1.35044i
$952$	−6.86740	+	0.721793i	−0.222574	+	0.0233935i
$953$	37.6932	−	27.3857i	1.22100	−	0.887110i	0.224819	−	0.974401i	$-0.427821\pi$
$953$	37.6932	−	27.3857i	1.22100	−	0.887110i	0.996183	+	0.0872911i	$0.0278210\pi$
$954$	6.20875	+	11.8388i	0.201016	+	0.383297i
$955$	−1.54374	−	2.67383i	−0.0499541	−	0.0865231i
$956$	4.68238	−	8.11011i	0.151439	−	0.262300i
$957$	−8.74311	+	4.23358i	−0.282625	+	0.136852i
$958$	−4.18901	+	4.65236i	−0.135341	+	0.150311i
$959$	4.67482	−	14.3876i	0.150958	−	0.464600i
$960$	−1.52699	−	0.817492i	−0.0492835	−	0.0263845i
$961$	22.4412	−	21.3868i	0.723909	−	0.689895i
$962$			4.67465i			0.150717i
$963$	9.36845	+	33.3869i	0.301894	+	1.07588i
$964$	−0.363604	−	0.327391i	−0.0117109	−	0.0105445i
$965$	1.32047	−	1.81747i	0.0425073	−	0.0585063i
$966$	−0.0135440	+	0.00840979i	−0.000435771	+	0.000270581i
$967$	26.2780	−	15.1716i	0.845043	−	0.487886i	−0.0139321	−	0.999903i	$-0.504435\pi$
$967$	26.2780	−	15.1716i	0.845043	−	0.487886i	0.858975	+	0.512017i	$0.171102\pi$
$968$	−10.4657	−	1.09999i	−0.336379	−	0.0353549i
$969$	0.475321	+	3.45328i	0.0152695	+	0.110935i
$970$	1.07476	+	10.2256i	0.0345084	+	0.328325i
$971$	−17.8852	+	16.1039i	−0.573962	+	0.516798i	−0.904205	−	0.427098i	$-0.859536\pi$
$971$	−17.8852	+	16.1039i	−0.573962	+	0.516798i	0.330243	+	0.943896i	$0.392869\pi$
$972$	−13.9123	−	7.03196i	−0.446237	−	0.225550i
$973$	−2.83997	−	13.3610i	−0.0910451	−	0.428334i
$974$	−26.2226	−	5.57378i	−0.840225	−	0.178595i
$975$	4.90603	+	6.31636i	0.157119	+	0.202285i
$976$	−4.25779	+	1.38344i	−0.136288	+	0.0442828i
$977$	−17.4212	+	5.66050i	−0.557355	+	0.181096i	−0.574131	−	0.818764i	$-0.694660\pi$
$977$	−17.4212	+	5.66050i	−0.557355	+	0.181096i	0.0167759	+	0.999859i	$0.494660\pi$
$978$	−21.6623	−	27.8896i	−0.692685	−	0.891810i
$979$	2.35741	+	0.501083i	0.0753431	+	0.0160147i
$980$	0.368874	+	1.73542i	0.0117833	+	0.0554359i
$981$	−50.8911	−	32.2040i	−1.62483	−	1.02819i
$982$	−5.13685	+	4.62524i	−0.163924	+	0.147597i
$983$	1.01667	+	9.67298i	0.0324268	+	0.308520i	0.998699	+	0.0509967i	$0.0162398\pi$
$983$	1.01667	+	9.67298i	0.0324268	+	0.308520i	−0.966272	+	0.257523i	$0.917094\pi$
$984$	−0.940159	−	6.83040i	−0.0299712	−	0.217745i
$985$	17.7881	+	1.86960i	0.566774	+	0.0595704i
$986$	−16.3997	+	9.46835i	−0.522272	+	0.301534i
$987$	47.6429	−	29.5826i	1.51649	−	0.941625i
$988$	2.34317	−	3.22509i	0.0745460	−	0.102604i
$989$	0.00544256	+	0.00490050i	0.000173063	+	0.000155827i
$990$	−1.99425	+	0.559592i	−0.0633813	+	0.0177850i
$991$		−	23.4738i		−	0.745671i	−0.927898	−	0.372835i	$-0.878386\pi$
$991$		−	23.4738i		−	0.745671i	0.927898	−	0.372835i	$-0.121614\pi$
$992$	−2.06867	−	5.16920i	−0.0656805	−	0.164122i
$993$	27.5233	+	14.7349i	0.873424	+	0.467597i
$994$	1.74737	−	5.37785i	0.0554232	−	0.170575i
$995$	−1.94013	+	2.15473i	−0.0615062	+	0.0683096i
$996$	−16.0602	+	7.77664i	−0.508886	+	0.246412i
$997$	−10.1165	+	17.5224i	−0.320394	+	0.554939i	−0.980569	−	0.196173i	$-0.937149\pi$
$997$	−10.1165	+	17.5224i	−0.320394	+	0.554939i	0.660175	+	0.751112i	$0.270482\pi$
$998$	1.37541	+	2.38227i	0.0435377	+	0.0754095i
$999$	5.26021	+	0.0448574i	0.166426	+	0.00141923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.761.16	yes	176
3.2	odd	2	inner	930.2.br.a.761.2	yes	176
31.11	odd	30	inner	930.2.br.a.11.2	✓	176
93.11	even	30	inner	930.2.br.a.11.16	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.2	✓	176	31.11	odd	30	inner
930.2.br.a.11.16	yes	176	93.11	even	30	inner
930.2.br.a.761.2	yes	176	3.2	odd	2	inner
930.2.br.a.761.16	yes	176	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587767 - 1.62927i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0555271 - 1.73116i) q^{6} +(-0.309626 + 2.94590i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.30906 + 1.91527i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587767 - 1.62927i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0555271 - 1.73116i) q^{6} +(-0.309626 + 2.94590i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.30906 + 1.91527i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(-0.630734 + 0.280821i) q^{11} +(0.482149 - 1.66359i) q^{12} +(-0.960045 + 4.51666i) q^{13} +(-1.20480 + 2.70604i) q^{14} +(-0.305615 + 1.70488i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.12963 + 0.948174i) q^{17} +(-2.78790 + 1.10799i) q^{18} +(-0.844454 + 0.179494i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(4.98166 - 1.22704i) q^{21} +(-0.686642 + 0.0721689i) q^{22} +(-0.00251392 + 0.00182647i) q^{23} +(0.972628 - 1.43318i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.30878 + 3.99892i) q^{26} +(4.47768 + 2.63635i) q^{27} +(-1.98205 + 2.20129i) q^{28} +(-2.51022 + 7.72566i) q^{29} +(-0.817492 + 1.52699i) q^{30} +(-5.16920 + 2.06867i) q^{31} +1.00000i q^{32} +(0.828258 + 0.862580i) q^{33} +(1.73240 + 1.55986i) q^{34} +(1.74109 - 2.39641i) q^{35} +(-2.99383 + 0.192253i) q^{36} +(0.876733 - 0.506182i) q^{37} +(-0.858591 - 0.0902415i) q^{38} +(7.92315 - 1.09057i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(2.95825 - 2.66362i) q^{41} +(5.11702 + 0.372436i) q^{42} +(-0.490022 - 2.30537i) q^{43} +(-0.675336 - 0.143547i) q^{44} +(2.95734 - 0.504140i) q^{45} +(-0.00295529 + 0.000960231i) q^{46} +(10.3956 - 3.37775i) q^{47} +(1.36790 - 1.06247i) q^{48} +(-1.73542 - 0.368874i) q^{49} +(0.207912 + 0.978148i) q^{50} +(0.293105 - 4.02706i) q^{51} +(-3.43152 + 3.08975i) q^{52} +(-0.465783 - 4.43163i) q^{53} +(3.44385 + 3.89100i) q^{54} +(0.686642 + 0.0721689i) q^{55} +(-2.56528 + 1.48106i) q^{56} +(0.788788 + 1.27035i) q^{57} +(-4.77472 + 6.57184i) q^{58} +(6.90993 + 6.22172i) q^{59} +(-1.24935 + 1.19964i) q^{60} +4.47690i q^{61} +(-5.55545 + 0.370056i) q^{62} +(-4.92724 - 7.39527i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(3.08975 - 3.43152i) q^{65} +(0.521168 + 1.07631i) q^{66} +(-6.17417 + 10.6940i) q^{67} +(1.16559 + 2.01886i) q^{68} +(0.00445341 + 0.00302232i) q^{69} +(2.39641 - 1.74109i) q^{70} +(-1.89851 + 0.199542i) q^{71} +(-2.90671 - 0.742302i) q^{72} +(-0.242796 - 0.545329i) q^{73} +(0.990242 - 0.210482i) q^{74} +(1.11711 - 1.32366i) q^{75} +(-0.788682 - 0.351144i) q^{76} +(-0.631977 - 1.94503i) q^{77} +(7.87236 + 1.41119i) q^{78} +(-3.21842 + 7.22868i) q^{79} +(0.207912 - 0.978148i) q^{80} +(1.66351 - 8.84493i) q^{81} +(3.63656 - 1.61910i) q^{82} +(-6.89351 - 7.65602i) q^{83} +(4.75148 + 1.93545i) q^{84} +(-1.37023 - 1.88596i) q^{85} +(0.246360 - 2.34396i) q^{86} +(14.0626 - 0.451060i) q^{87} +(-0.597925 - 0.345212i) q^{88} +(-2.82405 - 2.05179i) q^{89} +(2.96838 + 0.434401i) q^{90} +(-13.0084 - 4.22667i) q^{91} -0.00310737 q^{92} +(6.40872 + 7.20613i) q^{93} +10.9306 q^{94} +(0.821066 + 0.266781i) q^{95} +(1.62927 - 0.587767i) q^{96} +(-8.31828 - 6.04358i) q^{97} +(-1.53649 - 0.887094i) q^{98} +(0.918554 - 1.85645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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