LMFDB - Embedded newform 930.2.br.a.11.2

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			11.2
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.68179 + 0.414242i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.47147 - 0.913668i) q^{6} +(-0.309626 - 2.94590i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.65681 - 1.39333i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.68179 + 0.414242i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.47147 - 0.913668i) q^{6} +(-0.309626 - 2.94590i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.65681 - 1.39333i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(0.630734 + 0.280821i) q^{11} +(-1.11711 + 1.32366i) q^{12} +(-0.960045 - 4.51666i) q^{13} +(1.20480 + 2.70604i) q^{14} +(-1.24935 + 1.19964i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.12963 + 0.948174i) q^{17} +(-2.09621 + 2.14614i) q^{18} +(-0.844454 - 0.179494i) q^{19} +(0.406737 - 0.913545i) q^{20} +(1.74104 + 4.82611i) q^{21} +(-0.686642 - 0.0721689i) q^{22} +(0.00251392 + 0.00182647i) q^{23} +(0.653400 - 1.60408i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.30878 + 3.99892i) q^{26} +(-3.89100 + 3.44385i) 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} +(-1.17709 - 0.211004i) q^{33} +(1.73240 - 1.55986i) q^{34} +(-1.74109 - 2.39641i) q^{35} +(1.33042 - 2.68886i) q^{36} +(0.876733 + 0.506182i) q^{37} +(0.858591 - 0.0902415i) q^{38} +(3.48558 + 7.19836i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-2.95825 - 2.66362i) q^{41} +(-3.14718 - 4.05189i) q^{42} +(-0.490022 + 2.30537i) q^{43} +(0.675336 - 0.143547i) q^{44} +(1.60420 - 2.53507i) q^{45} +(-0.00295529 - 0.000960231i) q^{46} +(-10.3956 - 3.37775i) q^{47} +(-0.125733 + 1.72748i) q^{48} +(-1.73542 + 0.368874i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(3.18881 - 2.47681i) q^{51} +(-3.43152 - 3.08975i) q^{52} +(0.465783 - 4.43163i) q^{53} +(2.63635 - 4.47768i) q^{54} +(0.686642 - 0.0721689i) q^{55} +(2.56528 + 1.48106i) q^{56} +(1.49455 - 0.0479377i) q^{57} +(-4.77472 - 6.57184i) q^{58} +(-6.90993 + 6.22172i) q^{59} +(-0.305615 + 1.70488i) 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} +(1.18468 - 0.163063i) q^{66} +(-6.17417 - 10.6940i) q^{67} +(-1.16559 + 2.01886i) q^{68} +(-0.00498447 - 0.00203036i) q^{69} +(2.39641 + 1.74109i) q^{70} +(1.89851 + 0.199542i) q^{71} +(-0.434401 + 2.96838i) q^{72} +(-0.242796 + 0.545329i) q^{73} +(-0.990242 - 0.210482i) q^{74} +(-0.482149 + 1.66359i) q^{75} +(-0.788682 + 0.351144i) q^{76} +(0.631977 - 1.94503i) q^{77} +(-5.53940 - 5.76894i) q^{78} +(-3.21842 - 7.22868i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(5.11724 - 7.40364i) q^{81} +(3.63656 + 1.61910i) q^{82} +(6.89351 - 7.65602i) q^{83} +(4.24525 + 2.88105i) q^{84} +(-1.37023 + 1.88596i) q^{85} +(-0.246360 - 2.34396i) q^{86} +(-7.42195 - 11.9531i) q^{87} +(-0.597925 + 0.345212i) q^{88} +(2.82405 - 2.05179i) q^{89} +(-0.742302 + 2.90671i) q^{90} +(-13.0084 + 4.22667i) q^{91} +0.00310737 q^{92} +(9.55041 + 1.33777i) q^{93} +10.9306 q^{94} +(-0.821066 + 0.266781i) q^{95} +(-0.414242 - 1.68179i) q^{96} +(-8.31828 + 6.04358i) q^{97} +(1.53649 - 0.887094i) q^{98} +(2.06701 - 0.132736i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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
$3$	−1.68179	+	0.414242i	−0.970979	+	0.239163i
$3$	−1.68179	+	0.414242i	−0.970979	+	0.239163i
$4$	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
$6$	1.47147	−	0.913668i	0.600723	−	0.373003i
$7$	−0.309626	−	2.94590i	−0.117028	−	1.11345i	−0.882610	−	0.470107i	$-0.844215\pi$
$7$	−0.309626	−	2.94590i	−0.117028	−	1.11345i	0.765582	−	0.643338i	$-0.222451\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	2.65681	−	1.39333i	0.885602	−	0.464444i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	0.630734	+	0.280821i	0.190173	+	0.0846706i	0.499614	−	0.866248i	$-0.333475\pi$
$11$	0.630734	+	0.280821i	0.190173	+	0.0846706i	−0.309441	+	0.950919i	$0.600142\pi$
$12$	−1.11711	+	1.32366i	−0.322481	+	0.382107i
$13$	−0.960045	−	4.51666i	−0.266269	−	1.25269i	−0.884441	−	0.466652i	$-0.845460\pi$
$13$	−0.960045	−	4.51666i	−0.266269	−	1.25269i	0.618172	−	0.786043i	$-0.287873\pi$
$14$	1.20480	+	2.70604i	0.321998	+	0.723219i
$15$	−1.24935	+	1.19964i	−0.322580	+	0.309745i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.12963	+	0.948174i	−0.516512	+	0.229966i	−0.648402	−	0.761298i	$-0.724562\pi$
$17$	−2.12963	+	0.948174i	−0.516512	+	0.229966i	0.131890	+	0.991264i	$0.457896\pi$
$18$	−2.09621	+	2.14614i	−0.494081	+	0.505849i
$19$	−0.844454	−	0.179494i	−0.193731	−	0.0411788i	0.110024	−	0.993929i	$-0.464907\pi$
$19$	−0.844454	−	0.179494i	−0.193731	−	0.0411788i	−0.303755	+	0.952750i	$0.598241\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	1.74104	+	4.82611i	0.379926	+	1.05314i
$22$	−0.686642	−	0.0721689i	−0.146392	−	0.0153865i
$23$	0.00251392	+	0.00182647i	0.000524188	+	0.000380845i	0.588047	−	0.808827i	$-0.299897\pi$
$23$	0.00251392	+	0.00182647i	0.000524188	+	0.000380845i	−0.587523	+	0.809207i	$0.699897\pi$
$24$	0.653400	−	1.60408i	0.133375	−	0.327431i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.30878	+	3.99892i	0.452789	+	0.784254i
$27$	−3.89100	+	3.44385i	−0.748824	+	0.662769i
$28$	−1.98205	−	2.20129i	−0.374572	−	0.416004i
$29$	2.51022	+	7.72566i	0.466136	+	1.43462i	0.857548	+	0.514404i	$0.171987\pi$
$29$	2.51022	+	7.72566i	0.466136	+	1.43462i	−0.391412	+	0.920216i	$0.628013\pi$
$30$	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
$33$	−1.17709	−	0.211004i	−0.204904	−	0.0367310i
$34$	1.73240	−	1.55986i	0.297104	−	0.267514i
$35$	−1.74109	−	2.39641i	−0.294299	−	0.405067i
$36$	1.33042	−	2.68886i	0.221737	−	0.448144i
$37$	0.876733	+	0.506182i	0.144134	+	0.0832159i	0.570333	−	0.821414i	$-0.306814\pi$
$37$	0.876733	+	0.506182i	0.144134	+	0.0832159i	−0.426199	+	0.904630i	$0.640148\pi$
$38$	0.858591	−	0.0902415i	0.139282	−	0.0146391i
$39$	3.48558	+	7.19836i	0.558139	+	1.15266i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−2.95825	−	2.66362i	−0.462000	−	0.415987i	0.404983	−	0.914324i	$-0.367277\pi$
$41$	−2.95825	−	2.66362i	−0.462000	−	0.415987i	−0.866983	+	0.498337i	$0.833944\pi$
$42$	−3.14718	−	4.05189i	−0.485620	−	0.625221i
$43$	−0.490022	+	2.30537i	−0.0747276	+	0.351566i	−0.999587	−	0.0287439i	$-0.990849\pi$
$43$	−0.490022	+	2.30537i	−0.0747276	+	0.351566i	0.924859	+	0.380310i	$0.124183\pi$
$44$	0.675336	−	0.143547i	0.101811	−	0.0216406i
$45$	1.60420	−	2.53507i	0.239139	−	0.377905i
$46$	−0.00295529		0.000960231i	−0.000435733		0.000141578i
$47$	−10.3956	−	3.37775i	−1.51636	−	0.492695i	−0.571620	−	0.820518i	$-0.693685\pi$
$47$	−10.3956	−	3.37775i	−1.51636	−	0.492695i	−0.944739	+	0.327823i	$0.893685\pi$
$48$	−0.125733	+	1.72748i	−0.0181479	+	0.249340i
$49$	−1.73542	+	0.368874i	−0.247917	+	0.0526963i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	3.18881	−	2.47681i	0.446523	−	0.346823i
$52$	−3.43152	−	3.08975i	−0.475866	−	0.428471i
$53$	0.465783	−	4.43163i	0.0639802	−	0.608731i	−0.914813	−	0.403879i	$-0.867662\pi$
$53$	0.465783	−	4.43163i	0.0639802	−	0.608731i	0.978793	−	0.204853i	$-0.0656715\pi$
$54$	2.63635	−	4.47768i	0.358762	−	0.609335i
$55$	0.686642	−	0.0721689i	0.0925867	−	0.00973126i
$56$	2.56528	+	1.48106i	0.342799	+	0.197915i
$57$	1.49455	−	0.0479377i	0.197957	−	0.00634950i
$58$	−4.77472	−	6.57184i	−0.626952	−	0.862925i
$59$	−6.90993	+	6.22172i	−0.899596	+	0.810000i	−0.982443	−	0.186563i	$-0.940265\pi$
$59$	−6.90993	+	6.22172i	−0.899596	+	0.810000i	0.0828474	+	0.996562i	$0.473599\pi$
$60$	−0.305615	+	1.70488i	−0.0394547	+	0.220098i
$61$		−	4.47690i		−	0.573208i	−0.958049	−	0.286604i	$-0.907474\pi$
$61$		−	4.47690i		−	0.573208i	0.958049	−	0.286604i	$-0.0925265\pi$
$62$	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
$66$	1.18468	−	0.163063i	0.145824	−	0.0200717i
$67$	−6.17417	−	10.6940i	−0.754295	−	1.30648i	−0.945724	−	0.324970i	$-0.894646\pi$
$67$	−6.17417	−	10.6940i	−0.754295	−	1.30648i	0.191430	−	0.981506i	$-0.438688\pi$
$68$	−1.16559	+	2.01886i	−0.141348	+	0.244822i
$69$	−0.00498447	−	0.00203036i	−0.000600060	−	0.000244426i
$70$	2.39641	+	1.74109i	0.286426	+	0.208100i
$71$	1.89851	+	0.199542i	0.225312	+	0.0236812i	0.216512	−	0.976280i	$-0.430532\pi$
$71$	1.89851	+	0.199542i	0.225312	+	0.0236812i	0.00880025	+	0.999961i	$0.497199\pi$
$72$	−0.434401	+	2.96838i	−0.0511947	+	0.349827i
$73$	−0.242796	+	0.545329i	−0.0284171	+	0.0638259i	−0.927196	−	0.374575i	$-0.877788\pi$
$73$	−0.242796	+	0.545329i	−0.0284171	+	0.0638259i	0.898779	+	0.438401i	$0.144455\pi$
$74$	−0.990242	−	0.210482i	−0.115113	−	0.0244681i
$75$	−0.482149	+	1.66359i	−0.0556737	+	0.192095i
$76$	−0.788682	+	0.351144i	−0.0904680	+	0.0402790i
$77$	0.631977	−	1.94503i	0.0720205	−	0.221656i
$78$	−5.53940	−	5.76894i	−0.627213	−	0.653204i
$79$	−3.21842	−	7.22868i	−0.362100	−	0.813290i	−0.999100	−	0.0424258i	$-0.986491\pi$
$79$	−3.21842	−	7.22868i	−0.362100	−	0.813290i	0.637000	−	0.770864i	$-0.280175\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	5.11724	−	7.40364i	0.568583	−	0.822626i
$82$	3.63656	+	1.61910i	0.401591	+	0.178800i
$83$	6.89351	−	7.65602i	0.756661	−	0.840357i	−0.234625	−	0.972086i	$-0.575386\pi$
$83$	6.89351	−	7.65602i	0.756661	−	0.840357i	0.991286	+	0.131729i	$0.0420527\pi$
$84$	4.24525	+	2.88105i	0.463195	+	0.314348i
$85$	−1.37023	+	1.88596i	−0.148622	+	0.204561i
$86$	−0.246360	−	2.34396i	−0.0265657	−	0.252756i
$87$	−7.42195	−	11.9531i	−0.795716	−	1.28150i
$88$	−0.597925	+	0.345212i	−0.0637390	+	0.0367997i
$89$	2.82405	−	2.05179i	0.299349	−	0.217490i	−0.427964	−	0.903796i	$-0.640769\pi$
$89$	2.82405	−	2.05179i	0.299349	−	0.217490i	0.727313	+	0.686306i	$0.240769\pi$
$90$	−0.742302	+	2.90671i	−0.0782455	+	0.306395i
$91$	−13.0084	+	4.22667i	−1.36365	+	0.443075i
$92$	0.00310737			0.000323966
$93$	9.55041	+	1.33777i	0.990332	+	0.138720i
$94$	10.9306			1.12741
$95$	−0.821066	+	0.266781i	−0.0842396	+	0.0273711i
$96$	−0.414242	−	1.68179i	−0.0422784	−	0.171647i
$97$	−8.31828	+	6.04358i	−0.844593	+	0.613633i	−0.923650	−	0.383237i	$-0.874809\pi$
$97$	−8.31828	+	6.04358i	−0.844593	+	0.613633i	0.0790567	+	0.996870i	$0.474809\pi$
$98$	1.53649	−	0.887094i	0.155209	−	0.0896100i
$99$	2.06701	−	0.132736i	0.207743	−	0.0133405i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−5.13792	+	7.07173i	−0.511242	+	0.703664i	−0.984128	−	0.177460i	$-0.943212\pi$
$101$	−5.13792	+	7.07173i	−0.511242	+	0.703664i	0.472886	+	0.881123i	$0.343212\pi$
$102$	−2.26737	+	3.34098i	−0.224503	+	0.330807i
$103$	−7.52831	+	8.36103i	−0.741786	+	0.823837i	−0.989430	−	0.145014i	$-0.953677\pi$
$103$	−7.52831	+	8.36103i	−0.741786	+	0.823837i	0.247643	+	0.968851i	$0.420344\pi$
$104$	4.21835	+	1.87813i	0.413643	+	0.184166i
$105$	3.92084	+	3.30901i	0.382635	+	0.322927i
$106$	0.926463	+	4.35867i	0.0899861	+	0.423351i
$107$	−4.70138	−	10.5595i	−0.454500	−	1.02082i	−0.984908	−	0.173081i	$-0.944628\pi$
$107$	−4.70138	−	10.5595i	−0.454500	−	1.02082i	0.530408	−	0.847743i	$-0.322039\pi$
$108$	−1.12364	+	5.07321i	−0.108123	+	0.488170i
$109$	6.20347	−	19.0923i	0.594185	−	1.82871i	0.0354424	−	0.999372i	$-0.488716\pi$
$109$	6.20347	−	19.0923i	0.594185	−	1.82871i	0.558742	−	0.829341i	$-0.311284\pi$
$110$	−0.630734	+	0.280821i	−0.0601381	+	0.0267752i
$111$	−1.68416	−	0.488110i	−0.159853	−	0.0463294i
$112$	−2.89740	−	0.615861i	−0.273778	−	0.0581933i
$113$	3.13828	−	7.04868i	0.295224	−	0.663084i	−0.703649	−	0.710548i	$-0.748447\pi$
$113$	3.13828	−	7.04868i	0.295224	−	0.663084i	0.998873	+	0.0474636i	$0.0151138\pi$
$114$	−1.40658	+	0.507431i	−0.131739	+	0.0475253i
$115$	0.00309035		0.000324809i	0.000288177		3.02886e-5i
$116$	6.57184	+	4.77472i	0.610180	+	0.443322i
$117$	−8.84386	−	10.6622i	−0.817615	−	0.985723i
$118$	4.64911	−	8.05250i	0.427985	−	0.741292i
$119$	3.45262	+	5.98011i	0.316501	+	0.548195i
$120$	−0.236178	−	1.71587i	−0.0215600	−	0.156637i
$121$	−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
$126$	6.97134	+	5.51072i	0.621057	+	0.490934i
$127$	−15.3221	+	13.7961i	−1.35962	+	1.22421i	−0.409506	+	0.912307i	$0.634299\pi$
$127$	−15.3221	+	13.7961i	−1.35962	+	1.22421i	−0.950115	+	0.311901i	$0.899034\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−0.130870	−	4.08013i	−0.0115225	−	0.359235i
$130$	3.99892	+	2.30878i	0.350729	+	0.202493i
$131$	−14.4710	+	1.52096i	−1.26434	+	0.132887i	−0.712861	−	0.701305i	$-0.752601\pi$
$131$	−14.4710	+	1.52096i	−1.26434	+	0.132887i	−0.551474	+	0.834192i	$0.685934\pi$
$132$	−1.07631	+	0.521168i	−0.0936806	+	0.0453619i
$133$	−0.267307	+	2.54325i	−0.0231784	+	0.220528i
$134$	9.17660	+	8.26265i	0.792738	+	0.713784i
$135$	−1.64778	+	4.92796i	−0.141818	+	0.424131i
$136$	0.484678	−	2.28023i	0.0415608	−	0.195528i
$137$	4.99555	−	1.06184i	0.426799	−	0.0907189i	0.0104959	−	0.999945i	$-0.496659\pi$
$137$	4.99555	−	1.06184i	0.426799	−	0.0907189i	0.416303	+	0.909226i	$0.363326\pi$
$138$	0.00536793		0.000390698i	0.000456948		3.32584e-5i
$139$	−4.38568	−	1.42499i	−0.371989	−	0.120866i	0.117056	−	0.993125i	$-0.462654\pi$
$139$	−4.38568	−	1.42499i	−0.371989	−	0.120866i	−0.489044	+	0.872259i	$0.662654\pi$
$140$	−2.81715	−	0.915347i	−0.238093	−	0.0773610i
$141$	18.8824	+	1.37434i	1.59019	+	0.115740i
$142$	−1.86725	+	0.396897i	−0.156696	+	0.0333068i
$143$	0.662838	−	3.11841i	0.0554293	−	0.260774i
$144$	−0.504140	−	2.95734i	−0.0420117	−	0.246445i
$145$	6.03675	+	5.43551i	0.501325	+	0.451395i
$146$	0.0623969	−	0.593667i	0.00516400	−	0.0491322i
$147$	2.76580	−	1.33925i	0.228119	−	0.110460i
$148$	1.00682	−	0.105821i	0.0827600	−	0.00869843i
$149$	7.51618	+	4.33947i	0.615749	+	0.355503i	0.775212	−	0.631701i	$-0.217643\pi$
$149$	7.51618	+	4.33947i	0.615749	+	0.355503i	−0.159463	+	0.987204i	$0.550976\pi$
$150$	−0.0555271	−	1.73116i	−0.00453377	−	0.141349i
$151$	13.8048	+	19.0007i	1.12342	+	1.54625i	0.800004	+	0.599994i	$0.204831\pi$
$151$	13.8048	+	19.0007i	1.12342	+	1.54625i	0.323414	+	0.946258i	$0.395169\pi$
$152$	0.641572	−	0.577674i	0.0520383	−	0.0468555i
$153$	−4.33690	+	5.48641i	−0.350618	+	0.443550i
$154$			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	0.901353	−	0.433086i	$-0.142575\pi$
$157$	−1.03270	−	3.17833i	−0.0824185	−	0.253658i	−0.983771	+	0.179428i	$0.942575\pi$
$158$	5.29468	+	5.88034i	0.421222	+	0.467815i
$159$	1.05242	+	7.64600i	0.0834624	+	0.606367i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.00460221	−	0.00797127i	0.000362705	−	0.000628224i
$162$	−2.57894	+	8.62259i	−0.202621	+	0.677455i
$163$	16.4947	+	11.9841i	1.29197	+	0.938668i	0.999843	−	0.0177130i	$-0.00563852\pi$
$163$	16.4947	+	11.9841i	1.29197	+	0.938668i	0.292122	+	0.956381i	$0.405639\pi$
$164$	−3.95891	−	0.416098i	−0.309139	−	0.0324918i
$165$	−1.12489	+	0.405809i	−0.0875725	+	0.0315922i
$166$	−4.19028	+	9.41152i	−0.325229	+	0.730476i
$167$	−10.1156	−	2.15014i	−0.782771	−	0.166383i	−0.200843	−	0.979623i	$-0.564368\pi$
$167$	−10.1156	−	2.15014i	−0.782771	−	0.166383i	−0.581928	+	0.813240i	$0.697701\pi$
$168$	−4.92776	−	1.42818i	−0.380185	−	0.110187i
$169$	−7.60240	+	3.38481i	−0.584800	+	0.260370i
$170$	0.720373	−	2.21708i	0.0552501	−	0.170042i
$171$	−2.49365	+	0.699725i	−0.190694	+	0.0535093i
$172$	0.958627	+	2.15311i	0.0730946	+	0.164173i
$173$	4.25903	+	20.0372i	0.323808	+	1.52340i	0.775571	+	0.631260i	$0.217462\pi$
$173$	4.25903	+	20.0372i	0.323808	+	1.52340i	−0.451763	+	0.892138i	$0.649205\pi$
$174$	10.7524	+	9.07454i	0.815137	+	0.687939i
$175$	−2.70604	−	1.20480i	−0.204557	−	0.0910747i
$176$	0.461984	−	0.513085i	0.0348233	−	0.0386752i
$177$	9.04371	−	13.3260i	0.679767	−	1.00164i
$178$	−2.05179	+	2.82405i	−0.153788	+	0.211672i
$179$	−1.40972	−	13.4126i	−0.105367	−	1.00250i	−0.911649	−	0.410970i	$-0.865190\pi$
$179$	−1.40972	−	13.4126i	−0.105367	−	1.00250i	0.806282	−	0.591532i	$-0.201477\pi$
$180$	−0.192253	−	2.99383i	−0.0143297	−	0.223147i
$181$	8.31904	−	4.80300i	0.618349	−	0.357004i	−0.157877	−	0.987459i	$-0.550465\pi$
$181$	8.31904	−	4.80300i	0.618349	−	0.357004i	0.776226	+	0.630455i	$0.217132\pi$
$182$	11.0656	−	8.03961i	0.820234	−	0.595935i
$183$	1.85452	+	7.52919i	0.137090	+	0.556574i
$184$	−0.00295529		0.000960231i	−0.000217867		7.07892e-5i
$185$	1.01236			0.0744305
$186$	−9.49637	+	1.67895i	−0.696308	+	0.123106i
$187$	−1.60950			−0.117698
$188$	−10.3956	+	3.37775i	−0.758180	+	0.246348i
$189$	11.3500	+	10.3962i	0.825590	+	0.756212i
$190$	0.698441	−	0.507447i	0.0506702	−	0.0368141i
$191$	−2.67383	+	1.54374i	−0.193472	+	0.111701i	−0.593607	−	0.804755i	$-0.702297\pi$
$191$	−2.67383	+	1.54374i	−0.193472	+	0.111701i	0.400135	+	0.916456i	$0.368963\pi$
$192$	0.913668	+	1.47147i	0.0659383	+	0.106194i
$193$	−0.234825	−	2.23421i	−0.0169030	−	0.160822i	0.982814	−	0.184597i	$-0.0590980\pi$
$193$	−0.234825	−	2.23421i	−0.0169030	−	0.160822i	−0.999717	+	0.0237754i	$0.992431\pi$
$194$	6.04358	−	8.31828i	0.433904	−	0.597218i
$195$	6.61778	+	4.49117i	0.473909	+	0.321619i
$196$	−1.18716	+	1.31848i	−0.0847974	+	0.0941770i
$197$	16.3397	+	7.27491i	1.16416	+	0.518316i	0.895561	−	0.444938i	$-0.146774\pi$
$197$	16.3397	+	7.27491i	1.16416	+	0.518316i	0.268594	+	0.963253i	$0.413441\pi$
$198$	−1.92483	+	0.764982i	−0.136792	+	0.0543649i
$199$	0.602835	+	2.83612i	0.0427339	+	0.201047i	0.994335	−	0.106287i	$-0.0338963\pi$
$199$	0.602835	+	2.83612i	0.0427339	+	0.201047i	−0.951602	+	0.307334i	$0.900563\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	14.8135	+	15.4274i	1.04487	+	1.08816i
$202$	2.70116	−	8.31332i	0.190053	−	0.584923i
$203$	21.9818	−	9.78692i	1.54282	−	0.686907i
$204$	1.12397	−	3.87812i	0.0786938	−	0.271523i
$205$	−3.89372	−	0.827637i	−0.271950	−	0.0578047i
$206$	4.57615	−	10.2782i	0.318835	−	0.716115i
$207$	0.00922387	+	0.00134985i	0.000641103	+	9.38209e-5i
$208$	−4.59227	−	0.482667i	−0.318416	−	0.0334669i
$209$	−0.482220	−	0.350353i	−0.0333559	−	0.0242344i
$210$	−4.75148	−	1.93545i	−0.327883	−	0.133559i
$211$	3.15415	−	5.46315i	0.217141	−	0.376099i	−0.736792	−	0.676120i	$-0.763660\pi$
$211$	3.15415	−	5.46315i	0.217141	−	0.376099i	0.953933	+	0.300021i	$0.0969936\pi$
$212$	−2.22802	−	3.85905i	−0.153021	−	0.265040i
$213$	−3.27555	+	0.450857i	−0.224437	+	0.0308922i
$214$	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
$219$	0.182433	−	1.01770i	0.0123277	−	0.0687700i
$220$	0.513085	−	0.461984i	0.0345922	−	0.0311469i
$221$	6.32712	+	8.70853i	0.425608	+	0.585799i
$222$	1.75257	−	0.0562137i	0.117624	−	0.00377282i
$223$	21.4152	+	12.3641i	1.43407	+	0.827960i	0.997428	−	0.0716761i	$-0.0228348\pi$
$223$	21.4152	+	12.3641i	1.43407	+	0.827960i	0.436641	+	0.899636i	$0.356168\pi$
$224$	2.94590	−	0.309626i	0.196831	−	0.0206878i
$225$	0.121741	−	2.99753i	0.00811608	−	0.199835i
$226$	−0.806515	+	7.67348i	−0.0536486	+	0.510432i
$227$	−9.71196	−	8.74469i	−0.644606	−	0.580406i	0.280622	−	0.959818i	$-0.409459\pi$
$227$	−9.71196	−	8.74469i	−0.644606	−	0.580406i	−0.925227	+	0.379413i	$0.876126\pi$
$228$	1.18094	−	0.917254i	0.0782094	−	0.0607466i
$229$	3.52908	−	16.6030i	0.233208	−	1.09716i	−0.693232	−	0.720715i	$-0.743814\pi$
$229$	3.52908	−	16.6030i	0.233208	−	1.09716i	0.926440	−	0.376443i	$-0.122853\pi$
$230$	−0.00303947		0.000646059i	−0.000200417		4.25999e-5i
$231$	−0.257139	+	3.53291i	−0.0169185	+	0.232448i
$232$	−7.72566	−	2.51022i	−0.507215	−	0.164804i
$233$	−12.8828	−	4.18586i	−0.843977	−	0.274225i	−0.145056	−	0.989423i	$-0.546336\pi$
$233$	−12.8828	−	4.18586i	−0.843977	−	0.274225i	−0.698921	+	0.715199i	$0.746336\pi$
$234$	11.7058	+	7.40747i	0.765233	+	0.484241i
$235$	−10.6918	+	2.27260i	−0.697454	+	0.148248i
$236$	−1.93321	+	9.09503i	−0.125841	+	0.592036i
$237$	8.40711	+	10.8239i	0.546100	+	0.703087i
$238$	−5.13159	−	4.62050i	−0.332631	−	0.299503i
$239$	0.978883	−	9.31345i	0.0633187	−	0.602437i	−0.916149	−	0.400837i	$-0.868719\pi$
$239$	0.978883	−	9.31345i	0.0633187	−	0.602437i	0.979468	−	0.201600i	$-0.0646140\pi$
$240$	0.754853	+	1.55891i	0.0487255	+	0.100627i
$241$	−0.486597	+	0.0511435i	−0.0313445	+	0.00329444i	−0.120188	−	0.992751i	$-0.538350\pi$
$241$	−0.486597	+	0.0511435i	−0.0313445	+	0.00329444i	0.0888432	+	0.996046i	$0.471683\pi$
$242$	9.11346	+	5.26166i	0.585835	+	0.338232i
$243$	−5.53921	+	14.5711i	−0.355340	+	0.934737i
$244$	−2.63146	−	3.62189i	−0.168462	−	0.231868i
$245$	−1.31848	+	1.18716i	−0.0842345	+	0.0758451i
$246$	−6.78662	−	1.21656i	−0.432699	−	0.0775653i
$247$			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	$-0.332683\pi$
$251$	−6.51060	−	7.23076i	−0.410946	−	0.456401i	−0.912713	+	0.408601i	$0.866017\pi$
$252$	−8.33305	−	3.08674i	−0.524933	−	0.194447i
$253$	0.00107270	+	0.00185797i	6.74402e−5	+	0.000116810i
$254$	10.3090	−	17.8557i	0.646844	−	1.12037i
$255$	1.52319	−	3.73939i	0.0953858	−	0.234170i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−7.06007	−	0.742044i	−0.440395	−	0.0462874i	−0.118263	−	0.992982i	$-0.537733\pi$
$257$	−7.06007	−	0.742044i	−0.440395	−	0.0462874i	−0.322132	+	0.946695i	$0.604399\pi$
$258$	1.38529	+	3.83999i	0.0862446	+	0.239067i
$259$	1.21970	−	2.73950i	0.0757886	−	0.170224i
$260$	−4.51666	−	0.960045i	−0.280111	−	0.0595395i
$261$	17.4336	+	17.0280i	1.07911	+	1.05401i
$262$	13.2927	−	5.91830i	0.821227	−	0.365634i
$263$	−2.54768	+	7.84095i	−0.157097	+	0.483494i	−0.998367	−	0.0571205i	$-0.981808\pi$
$263$	−2.54768	+	7.84095i	−0.157097	+	0.483494i	0.841271	+	0.540614i	$0.181808\pi$
$264$	0.862580	−	0.828258i	0.0530881	−	0.0509758i
$265$	−1.81244	−	4.07080i	−0.111337	−	0.250067i
$266$	−0.531685	−	2.50138i	−0.0325997	−	0.153369i
$267$	−3.89951	+	4.62052i	−0.238646	+	0.282771i
$268$	−11.2808	−	5.02252i	−0.689082	−	0.306799i
$269$	−7.41593	+	8.23622i	−0.452157	+	0.502171i	−0.925521	−	0.378695i	$-0.876373\pi$
$269$	−7.41593	+	8.23622i	−0.452157	+	0.502171i	0.473364	+	0.880867i	$0.343039\pi$
$270$	0.0443095	−	5.19596i	0.00269659	−	0.316216i
$271$	4.95813	−	6.82429i	0.301185	−	0.414546i	−0.631422	−	0.775440i	$-0.717528\pi$
$271$	4.95813	−	6.82429i	0.301185	−	0.414546i	0.932607	+	0.360894i	$0.117528\pi$
$272$	0.243674	+	2.31840i	0.0147749	+	0.140574i
$273$	20.1264	−	12.4970i	1.21811	−	0.756351i
$274$	−4.42292	+	2.55358i	−0.267199	+	0.154267i
$275$	0.558565	−	0.405821i	0.0336827	−	0.0244719i
$276$	−0.00522593	+	0.00128720i	−0.000314564	+	7.74806e-5i
$277$	−13.0266	+	4.23261i	−0.782694	+	0.254313i	−0.672990	−	0.739652i	$-0.734990\pi$
$277$	−13.0266	+	4.23261i	−0.782694	+	0.254313i	−0.109704	+	0.993964i	$0.534990\pi$
$278$	4.61138			0.276572
$279$	−16.6159	+	1.70635i	−0.994768	+	0.102156i
$280$	2.96213			0.177021
$281$	−5.29506	+	1.72047i	−0.315877	+	0.102635i	−0.462664	−	0.886533i	$-0.653107\pi$
$281$	−5.29506	+	1.72047i	−0.315877	+	0.102635i	0.146788	+	0.989168i	$0.453107\pi$
$282$	−18.3830	+	4.52792i	−1.09469	+	0.269634i
$283$	22.1074	−	16.0620i	1.31415	−	0.954785i	0.314164	−	0.949369i	$-0.398276\pi$
$283$	22.1074	−	16.0620i	1.31415	−	0.954785i	0.999985	−	0.00541616i	$-0.00172403\pi$
$284$	1.65322	−	0.954484i	0.0981003	−	0.0566382i
$285$	1.27035	−	0.788788i	0.0752488	−	0.0467238i
$286$	0.333244	+	3.17061i	0.0197052	+	0.187482i
$287$	−6.93079	+	9.53942i	−0.409112	+	0.563094i
$288$	1.39333	+	2.65681i	0.0821030	+	0.156554i
$289$	−7.73891	+	8.59493i	−0.455230	+	0.505584i
$290$	−7.42095	−	3.30402i	−0.435773	−	0.194019i
$291$	11.4861	−	13.6098i	0.673324	−	0.797820i
$292$	0.124110	+	0.583892i	0.00726300	+	0.0341697i
$293$	4.72697	+	10.6170i	0.276153	+	0.620249i	0.997371	−	0.0724583i	$-0.0230844\pi$
$293$	4.72697	+	10.6170i	0.276153	+	0.620249i	−0.721219	+	0.692707i	$0.756418\pi$
$294$	−2.21658	+	2.12838i	−0.129273	+	0.124130i
$295$	−2.87331	+	8.84313i	−0.167290	+	0.514867i
$296$	−0.924841	+	0.411766i	−0.0537553	+	0.0239334i
$297$	−3.42129	+	1.07948i	−0.198523	+	0.0626377i
$298$	−8.48928	−	1.80445i	−0.491771	−	0.104529i
$299$	0.00583605	−	0.0131080i	0.000337508	−	0.000758055i
$300$	0.587767	+	1.62927i	0.0339348	+	0.0940661i
$301$	6.94311	+	0.729751i	0.400194	+	0.0420621i
$302$	−19.0007	−	13.8048i	−1.09337	−	0.794376i
$303$	5.71146	−	14.0215i	0.328115	−	0.805513i
$304$	−0.431660	+	0.747657i	−0.0247574	+	0.0428811i
$305$	−2.23845	−	3.87711i	−0.128173	−	0.222003i
$306$	2.42925	−	6.55806i	0.138871	−	0.374899i
$307$	−0.332892	−	0.369714i	−0.0189992	−	0.0211007i	0.733570	−	0.679614i	$-0.237852\pi$
$307$	−0.332892	−	0.369714i	−0.0189992	−	0.0211007i	−0.752570	+	0.658513i	$0.771186\pi$
$308$	−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	$-0.279603\pi$
$312$	−7.87236	−	1.41119i	−0.445685	−	0.0798932i
$313$	18.4004	−	16.5678i	1.04005	−	0.936468i	0.0420175	−	0.999117i	$-0.486621\pi$
$313$	18.4004	−	16.5678i	1.04005	−	0.936468i	0.998036	+	0.0626488i	$0.0199548\pi$
$314$	1.96431	+	2.70365i	0.110853	+	0.152576i
$315$	−7.96475	−	3.94087i	−0.448763	−	0.222043i
$316$	−6.85266	−	3.95639i	−0.385492	−	0.222564i
$317$	−24.6269	+	2.58839i	−1.38319	+	0.145379i	−0.766709	−	0.641994i	$-0.778107\pi$
$317$	−24.6269	+	2.58839i	−1.38319	+	0.145379i	−0.616477	+	0.787373i	$0.711441\pi$
$318$	−3.36366	−	6.94656i	−0.188624	−	0.389544i
$319$	−0.586246	+	5.57776i	−0.0328235	+	0.312294i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	12.2809	+	15.8113i	0.685453	+	0.882499i
$322$	−0.00191371	+	0.00900329i	−0.000106647	+	0.000501734i
$323$	1.96857	−	0.418433i	0.109534	−	0.0232822i
$324$	−0.211810	−	8.99751i	−0.0117672	−	0.499862i
$325$	−4.39156	−	1.42690i	−0.243600	−	0.0791504i
$326$	−19.3907	−	6.30042i	−1.07395	−	0.348948i
$327$	−2.52406	+	34.6789i	−0.139581	+	1.91775i
$328$	3.89372	−	0.827637i	0.214995	−	0.0456986i
$329$	−6.73174	+	31.6703i	−0.371133	+	1.74604i
$330$	0.944431	−	0.733557i	0.0519892	−	0.0403810i
$331$	−13.3948	−	12.0607i	−0.736245	−	0.662918i	0.213144	−	0.977021i	$-0.431630\pi$
$331$	−13.3948	−	12.0607i	−0.736245	−	0.662918i	−0.949389	+	0.314103i	$0.898296\pi$
$332$	1.07687	−	10.2458i	0.0591010	−	0.562309i
$333$	3.03459	+	0.123247i	0.166295	+	0.00675387i
$334$	10.2850	−	1.08099i	0.562768	−	0.0591493i
$335$	−10.6940	−	6.17417i	−0.584274	−	0.337331i
$336$	5.12791	−	0.164478i	0.279751	−	0.00897303i
$337$	14.2575	+	19.6238i	0.776657	+	1.06898i	0.995643	+	0.0932487i	$0.0297252\pi$
$337$	14.2575	+	19.6238i	0.776657	+	1.06898i	−0.218986	+	0.975728i	$0.570275\pi$
$338$	6.18435	−	5.56842i	0.336384	−	0.302882i
$339$	−2.35805	+	13.1544i	−0.128071	+	0.714448i
$340$			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
$345$	−0.00533186		0.000733895i	−0.000287057		3.95116e-5i
$346$	−10.2424	−	17.7404i	−0.550635	−	0.953728i
$347$	4.77021	−	8.26224i	0.256078	−	0.443540i	−0.709110	−	0.705098i	$-0.750903\pi$
$347$	4.77021	−	8.26224i	0.256078	−	0.443540i	0.965188	+	0.261558i	$0.0842362\pi$
$348$	−13.0303	−	5.30773i	−0.698499	−	0.284524i
$349$	8.43526	+	6.12857i	0.451529	+	0.328055i	0.790199	−	0.612850i	$-0.209977\pi$
$349$	8.43526	+	6.12857i	0.451529	+	0.328055i	−0.338670	+	0.940905i	$0.609977\pi$
$350$	2.94590	+	0.309626i	0.157465	+	0.0165502i
$351$	19.2902	+	14.2681i	1.02964	+	0.761573i
$352$	−0.280821	+	0.630734i	−0.0149678	+	0.0336182i
$353$	−29.9071	−	6.35694i	−1.59179	−	0.338346i	−0.675033	−	0.737787i	$-0.735871\pi$
$353$	−29.9071	−	6.35694i	−1.59179	−	0.338346i	−0.916759	+	0.399442i	$0.869204\pi$
$354$	−4.48312	+	15.4684i	−0.238275	+	0.822138i
$355$	1.74393	−	0.776448i	0.0925582	−	0.0412096i
$356$	1.07869	−	3.31987i	0.0571705	−	0.175953i
$357$	−8.28377	−	8.62704i	−0.438424	−	0.456591i
$358$	5.48543	+	12.3205i	0.289914	+	0.651157i
$359$	−1.58337	−	7.44917i	−0.0835671	−	0.393152i	0.916408	−	0.400246i	$-0.131075\pi$
$359$	−1.58337	−	7.44917i	−0.0835671	−	0.393152i	−0.999975	+	0.00709367i	$0.997742\pi$
$360$	1.10799	+	2.78790i	0.0583961	+	0.146935i
$361$	−16.6765	−	7.42485i	−0.877709	−	0.390781i
$362$	−6.42767	+	7.13865i	−0.337831	+	0.375199i
$363$	15.0818	+	10.2353i	0.791587	+	0.537213i
$364$	−8.03961	+	11.0656i	−0.421390	+	0.579993i
$365$	0.0623969	+	0.593667i	0.00326600	+	0.0310739i
$366$	−4.09040	−	6.58760i	−0.213809	−	0.344340i
$367$	5.41712	−	3.12757i	0.282771	−	0.163258i	−0.351906	−	0.936035i	$-0.614466\pi$
$367$	5.41712	−	3.12757i	0.282771	−	0.163258i	0.634677	+	0.772777i	$0.281133\pi$
$368$	0.00251392	−	0.00182647i	0.000131047	−	9.52112e-5i
$369$	−11.5708	−	2.95489i	−0.602351	−	0.153826i
$370$	−0.962816	+	0.312838i	−0.0500544	+	0.0162637i
$371$	−13.1994			−0.685276
$372$	8.51277	−	4.53132i	0.441366	−	0.234938i
$373$	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
$375$	0.414242	+	1.68179i	0.0213914	+	0.0868470i
$376$	8.84306	−	6.42486i	0.456046	−	0.331337i
$377$	32.4842	−	18.7548i	1.67302	−	0.965921i
$378$	−14.0071	−	6.38003i	−0.720447	−	0.328153i
$379$	−1.17734	−	11.2016i	−0.0604758	−	0.575389i	−0.982239	−	0.187635i	$-0.939918\pi$
$379$	−1.17734	−	11.2016i	−0.0604758	−	0.575389i	0.921763	−	0.387754i	$-0.126749\pi$
$380$	−0.507447	+	0.698441i	−0.0260315	+	0.0358292i
$381$	20.0536	−	29.5492i	1.02738	−	1.51385i
$382$	2.06592	−	2.29444i	0.105702	−	0.117394i
$383$	16.3350	+	7.27281i	0.834679	+	0.371623i	0.779153	−	0.626834i	$-0.215650\pi$
$383$	16.3350	+	7.27281i	0.834679	+	0.371623i	0.0555264	+	0.998457i	$0.482316\pi$
$384$	−1.32366	−	1.11711i	−0.0675476	−	0.0570072i
$385$	−0.425205	−	2.00043i	−0.0216704	−	0.101951i
$386$	0.913739	+	2.05229i	0.0465081	+	0.104459i
$387$	1.91026	+	6.80769i	0.0971038	+	0.346054i
$388$	−3.17730	+	9.77872i	−0.161303	+	0.496439i
$389$	15.7275	−	7.00233i	0.797415	−	0.355032i	0.0327529	−	0.999463i	$-0.489573\pi$
$389$	15.7275	−	7.00233i	0.797415	−	0.355032i	0.764662	+	0.644431i	$0.222906\pi$
$390$	−7.68173	−	2.22635i	−0.388979	−	0.112736i
$391$	−0.00708553	−	0.00150608i	−0.000358331	−	7.61656e-5i
$392$	0.721627	−	1.62080i	0.0364477	−	0.0818628i
$393$	23.7070	−	8.55242i	1.19586	−	0.431413i
$394$	−17.7881	−	1.86960i	−0.896149	−	0.0941891i
$395$	−6.40157	−	4.65101i	−0.322098	−	0.234018i
$396$	1.59423	−	1.32235i	0.0801130	−	0.0664504i
$397$	13.1922	−	22.8495i	0.662097	−	1.14678i	−0.317967	−	0.948102i	$-0.603000\pi$
$397$	13.1922	−	22.8495i	0.662097	−	1.14678i	0.980064	−	0.198683i	$-0.0636665\pi$
$398$	−1.44974	−	2.51102i	−0.0726688	−	0.125866i
$399$	−0.603970	−	4.38794i	−0.0302363	−	0.219672i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−1.48810	−	4.57991i	−0.0743123	−	0.228710i	0.907000	−	0.421130i	$-0.138366\pi$
$401$	−1.48810	−	4.57991i	−0.0743123	−	0.228710i	−0.981313	+	0.192420i	$0.938366\pi$
$402$	−18.8558	−	10.0947i	−0.940443	−	0.503476i
$403$	−4.38083	+	25.3335i	−0.218225	+	1.26195i
$404$			8.74114i			0.434888i
$405$	0.729846	−	8.97036i	0.0362663	−	0.445741i
$406$	−17.8816	+	16.1007i	−0.887449	+	0.799063i
$407$	0.410839	+	0.565471i	0.0203645	+	0.0280294i
$408$	0.129443	+	4.03564i	0.00640840	+	0.199794i
$409$	3.75856	+	2.17001i	0.185849	+	0.107300i	0.590038	−	0.807376i	$-0.299113\pi$
$409$	3.75856	+	2.17001i	0.185849	+	0.107300i	−0.404189	+	0.914676i	$0.632446\pi$
$410$	3.95891	−	0.416098i	0.195516	−	0.0205496i
$411$	−7.96159	+	3.85515i	−0.392716	+	0.190161i
$412$	−1.17604	+	11.1892i	−0.0579392	+	0.551255i
$413$	20.4681	+	18.4295i	1.00717	+	0.906858i
$414$	−0.00918955	+	0.00156655i	−0.000451642	+	7.69918e-5i
$415$	2.14195	−	10.0771i	0.105144	−	0.494664i
$416$	4.51666	−	0.960045i	0.221447	−	0.0470701i
$417$	7.96607	+	0.579801i	0.390100	+	0.0283930i
$418$	0.566884	+	0.184192i	0.0277272	+	0.00900911i
$419$	15.7408	+	5.11451i	0.768991	+	0.249860i	0.667133	−	0.744939i	$-0.267521\pi$
$419$	15.7408	+	5.11451i	0.768991	+	0.249860i	0.101858	+	0.994799i	$0.467521\pi$
$420$	5.11702	+	0.372436i	0.249685	+	0.0181730i
$421$	−10.3319	+	2.19612i	−0.503548	+	0.107032i	−0.452680	−	0.891673i	$-0.649532\pi$
$421$	−10.3319	+	2.19612i	−0.503548	+	0.107032i	−0.0508676	+	0.998705i	$0.516199\pi$
$422$	−1.31157	+	6.17045i	−0.0638462	+	0.300373i
$423$	−32.3255	+	5.51057i	−1.57172	+	0.267933i
$424$	3.31148	+	2.98167i	0.160820	+	0.144803i
$425$	−0.243674	+	2.31840i	−0.0118199	+	0.112459i
$426$	2.97591	−	1.44099i	0.144183	−	0.0698162i
$427$	−13.1885	+	1.38617i	−0.638236	+	0.0670813i
$428$	−10.0102	−	5.77939i	−0.483861	−	0.279358i
$429$	0.177025	+	5.51907i	0.00854683	+	0.266463i
$430$	−1.38534	−	1.90675i	−0.0668068	−	0.0919517i
$431$	−5.86646	+	5.28219i	−0.282578	+	0.254434i	−0.798215	−	0.602373i	$-0.794222\pi$
$431$	−5.86646	+	5.28219i	−0.282578	+	0.254434i	0.515637	+	0.856807i	$0.327555\pi$
$432$	2.07291	+	4.76477i	0.0997329	+	0.229245i
$433$			3.18600i			0.153109i	0.997065	+	0.0765546i	$0.0243920\pi$
$433$			3.18600i			0.153109i	−0.997065	+	0.0765546i	$0.975608\pi$
$434$	−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
$438$	0.140984	+	1.02427i	0.00673646	+	0.0489414i
$439$	−1.49420	−	2.58803i	−0.0713142	−	0.123520i	0.828163	−	0.560487i	$-0.189386\pi$
$439$	−1.49420	−	2.58803i	−0.0713142	−	0.123520i	−0.899478	+	0.436967i	$0.856053\pi$
$440$	−0.345212	+	0.597925i	−0.0164573	+	0.0285049i
$441$	−4.09670	+	3.39804i	−0.195081	+	0.161812i
$442$	−8.70853	−	6.32712i	−0.414223	−	0.300950i
$443$	9.46017	+	0.994304i	0.449466	+	0.0472408i	0.326558	−	0.945177i	$-0.394111\pi$
$443$	9.46017	+	0.994304i	0.449466	+	0.0472408i	0.122908	+	0.992418i	$0.460778\pi$
$444$	−1.64942	+	0.595035i	−0.0782779	+	0.0282391i
$445$	1.41980	−	3.18893i	0.0673051	−	0.151170i
$446$	−24.1878	−	5.14127i	−1.14532	−	0.243446i
$447$	−14.4382	−	4.18454i	−0.682903	−	0.197922i
$448$	−2.70604	+	1.20480i	−0.127848	+	0.0569217i
$449$	2.05547	−	6.32608i	0.0970035	−	0.298546i	−0.890767	−	0.454460i	$-0.849832\pi$
$449$	2.05547	−	6.32608i	0.0970035	−	0.298546i	0.987771	+	0.155914i	$0.0498323\pi$
$450$	0.810505	+	2.88844i	0.0382075	+	0.136162i
$451$	−1.11787	−	2.51077i	−0.0526383	−	0.118227i
$452$	−1.60419	−	7.54714i	−0.0754549	−	0.354987i
$453$	−31.0876	−	26.2365i	−1.46062	−	1.23270i
$454$	11.9389	+	5.31553i	0.560320	+	0.249470i
$455$	−9.15223	+	10.1646i	−0.429063	+	0.476523i
$456$	−0.839689	+	1.23729i	−0.0393221	+	0.0579414i
$457$	−5.97055	+	8.21775i	−0.279290	+	0.384410i	−0.925499	−	0.378751i	$-0.876354\pi$
$457$	−5.97055	+	8.21775i	−0.279290	+	0.384410i	0.646208	+	0.763161i	$0.276354\pi$
$458$	1.77426	+	16.8809i	0.0829056	+	0.788794i
$459$	5.02104	−	11.0235i	0.234362	−	0.514532i
$460$	0.00269106	−	0.00155369i	0.000125471	−	7.24410e-5i
$461$	−8.03554	+	5.83816i	−0.374253	+	0.271910i	−0.758972	−	0.651123i	$-0.774298\pi$
$461$	−8.03554	+	5.83816i	−0.374253	+	0.271910i	0.384720	+	0.923034i	$0.374298\pi$
$462$	−0.847176	−	3.43946i	−0.0394142	−	0.160018i
$463$	22.4908	−	7.30772i	1.04524	−	0.339618i	0.264440	−	0.964402i	$-0.414813\pi$
$463$	22.4908	−	7.30772i	1.04524	−	0.339618i	0.780798	+	0.624784i	$0.214813\pi$
$464$	8.12324			0.377112
$465$	8.93978	−	3.61667i	0.414573	−	0.167719i
$466$	13.5457			0.627494
$467$	25.4368	−	8.26490i	1.17707	−	0.382454i	0.345794	−	0.938310i	$-0.387609\pi$
$467$	25.4368	−	8.26490i	1.17707	−	0.382454i	0.831278	+	0.555856i	$0.187609\pi$
$468$	−13.4219	−	3.42763i	−0.620429	−	0.158442i
$469$	−29.5917	+	21.4996i	−1.36642	+	0.992760i
$470$	9.46619	−	5.46531i	0.436643	−	0.252096i
$471$	3.05338	+	4.91748i	0.140692	+	0.226585i
$472$	−0.971929	−	9.24728i	−0.0447366	−	0.425641i
$473$	−0.956469	+	1.31647i	−0.0439785	+	0.0605312i
$474$	−11.3404	−	7.69619i	−0.520882	−	0.353498i
$475$	−0.577674	+	0.641572i	−0.0265055	+	0.0294373i
$476$	6.30824	+	2.80861i	0.289138	+	0.128732i
$477$	−4.93724	−	12.4230i	−0.226061	−	0.568809i
$478$	1.94704	+	9.16011i	0.0890556	+	0.418974i
$479$	2.54632	+	5.71914i	0.116344	+	0.261314i	0.962326	−	0.271898i	$-0.0876514\pi$
$479$	2.54632	+	5.71914i	0.116344	+	0.261314i	−0.845982	+	0.533212i	$0.820985\pi$
$480$	−1.19964	−	1.24935i	−0.0547557	−	0.0570247i
$481$	1.44455	−	4.44586i	0.0658657	−	0.202714i
$482$	0.446977	−	0.199007i	0.0203593	−	0.00906453i
$483$	−0.00443790	+	0.0153124i	−0.000201932	+	0.000696738i
$484$	−10.2934	−	2.18792i	−0.467880	−	0.0994509i
$485$	−4.18205	+	9.39304i	−0.189897	+	0.426516i
$486$	0.765382	−	15.5697i	0.0347184	−	0.706254i
$487$	−26.6615	−	2.80224i	−1.20815	−	0.126982i	−0.521038	−	0.853534i	$-0.674455\pi$
$487$	−26.6615	−	2.80224i	−1.20815	−	0.126982i	−0.687111	+	0.726552i	$0.741122\pi$
$488$	3.62189	+	2.63146i	0.163955	+	0.119120i
$489$	−32.7049	−	13.3219i	−1.47897	−	0.602437i
$490$	0.887094	−	1.53649i	0.0400748	−	0.0694116i
$491$	3.45616	+	5.98624i	0.155974	+	0.270155i	0.933413	−	0.358803i	$-0.116815\pi$
$491$	3.45616	+	5.98624i	0.155974	+	0.270155i	−0.777439	+	0.628958i	$0.783482\pi$
$492$	6.83040	−	0.940159i	0.307938	−	0.0423856i
$493$	−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
$498$	3.14850	−	17.5640i	0.141088	−	0.787060i
$499$	2.04425	−	1.84065i	0.0915132	−	0.0823989i	−0.622104	−	0.782934i	$-0.713722\pi$
$499$	2.04425	−	1.84065i	0.0915132	−	0.0823989i	0.713618	+	0.700535i	$0.247055\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	17.9030	−	0.574240i	0.799847	−	0.0256552i
$502$	8.42638	+	4.86497i	0.376088	+	0.217134i
$503$	−33.3446	+	3.50466i	−1.48676	+	0.156265i	−0.812818	−	0.582518i	$-0.802068\pi$
$503$	−33.3446	+	3.50466i	−1.48676	+	0.156265i	−0.673944	+	0.738783i	$0.735401\pi$
$504$	8.87906	+	0.360613i	0.395505	+	0.0160630i
$505$	−0.913698	+	8.69326i	−0.0406590	+	0.386845i
$506$	−0.00159435	−	0.00143556i	−7.08773e−5	−	6.38182e-5i
$507$	11.3835	−	8.84176i	0.505558	−	0.392676i
$508$	−4.28672	+	20.1674i	−0.190192	+	0.894785i
$509$	10.0502	−	2.13623i	0.445465	−	0.0946865i	0.0202829	−	0.999794i	$-0.493543\pi$
$509$	10.0502	−	2.13623i	0.445465	−	0.0946865i	0.425182	+	0.905108i	$0.360210\pi$
$510$	−0.293105	+	4.02706i	−0.0129789	+	0.178321i
$511$	1.68166	+	0.546405i	0.0743923	+	0.0241715i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	3.90393	−	2.20976i	0.172363	−	0.0975633i
$514$	6.94383	−	1.47596i	0.306279	−	0.0651017i
$515$	−2.33919	+	11.0050i	−0.103077	+	0.484939i
$516$	−2.50412	−	3.22397i	−0.110238	−	0.141927i
$517$	−5.60834	−	5.04977i	−0.246654	−	0.222089i
$518$	−0.313455	+	2.98232i	−0.0137724	+	0.131036i
$519$	−15.4630	−	31.9340i	−0.678752	−	1.40175i
$520$	4.59227	−	0.482667i	0.201384	−	0.0211663i
$521$	−25.6621	−	14.8160i	−1.12428	−	0.649102i	−0.181788	−	0.983338i	$-0.558188\pi$
$521$	−25.6621	−	14.8160i	−1.12428	−	0.649102i	−0.942489	+	0.334236i	$0.891522\pi$
$522$	−21.8423	−	10.8073i	−0.956011	−	0.473024i
$523$	22.6437	+	31.1664i	0.990141	+	1.36281i	0.931183	+	0.364552i	$0.118778\pi$
$523$	22.6437	+	31.1664i	0.990141	+	1.36281i	0.0589586	+	0.998260i	$0.481222\pi$
$524$	−10.8133	+	9.73631i	−0.472380	+	0.425333i
$525$	5.05005	+	0.905269i	0.220402	+	0.0395092i
$526$		−	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
$531$	−9.68940	+	26.1577i	−0.420484	+	1.13515i
$532$	1.27863	+	2.21465i	0.0554357	+	0.0960174i
$533$	−9.19059	+	15.9186i	−0.398089	+	0.689510i
$534$	2.28084	−	5.59939i	0.0987014	−	0.242309i
$535$	−9.35126	−	6.79408i	−0.404290	−	0.293734i
$536$	12.2807	+	1.29075i	0.530445	+	0.0557520i
$537$	7.92689	+	21.9731i	0.342071	+	0.948209i
$538$	4.50783	−	10.1248i	0.194347	−	0.436509i
$539$	−1.19817	−	0.254680i	−0.0516090	−	0.0109698i
$540$	1.56350	+	4.95535i	0.0672823	+	0.213244i
$541$	37.4082	−	16.6552i	1.60830	−	0.716063i	0.611155	−	0.791511i	$-0.290705\pi$
$541$	37.4082	−	16.6552i	1.60830	−	0.716063i	0.997150	+	0.0754481i	$0.0240387\pi$
$542$	−2.60665	+	8.02243i	−0.111965	+	0.344593i
$543$	−12.0012	+	11.5237i	−0.515022	+	0.494530i
$544$	−0.948174	−	2.12963i	−0.0406526	−	0.0913073i
$545$	−4.17380	−	19.6362i	−0.178786	−	0.841121i
$546$	−15.2796	+	18.1047i	−0.653905	+	0.774810i
$547$	22.6089	+	10.0661i	0.966687	+	0.430397i	0.828488	−	0.560007i	$-0.189202\pi$
$547$	22.6089	+	10.0661i	0.966687	+	0.430397i	0.138200	+	0.990404i	$0.455868\pi$
$548$	3.41735	−	3.79535i	0.145982	−	0.162130i
$549$	−6.23781	−	11.8943i	−0.266223	−	0.507635i
$550$	−0.405821	+	0.558565i	−0.0173043	+	0.0238173i
$551$	−0.733054	−	6.97454i	−0.0312291	−	0.297125i
$552$	0.00457239	−	0.00283911i	0.000194614	−	0.000120840i
$553$	−20.2985	+	11.7193i	−0.863178	+	0.498356i
$554$	11.0811	−	8.05090i	0.470791	−	0.342050i
$555$	−1.70258	+	0.419364i	−0.0722705	+	0.0178010i
$556$	−4.38568	+	1.42499i	−0.185994	+	0.0604332i
$557$	36.3511			1.54024			0.770122	−	0.637896i	$-0.220195\pi$
$557$	36.3511			1.54024			0.770122	+	0.637896i	$0.220195\pi$
$558$	15.2754	−	6.75743i	0.646658	−	0.286065i
$559$	10.8830			0.460302
$560$	−2.81715	+	0.915347i	−0.119046	+	0.0386805i
$561$	2.70683	−	0.666722i	0.114283	−	0.0281490i
$562$	4.50424	−	3.27252i	0.190000	−	0.138043i
$563$	−9.44660	+	5.45400i	−0.398127	+	0.229859i	−0.685675	−	0.727907i	$-0.740493\pi$
$563$	−9.44660	+	5.45400i	−0.398127	+	0.229859i	0.287549	+	0.957766i	$0.407160\pi$
$564$	16.0840	−	9.98696i	0.677260	−	0.420527i
$565$	−0.806515	−	7.67348i	−0.0339303	−	0.322826i
$566$	−16.0620	+	22.1074i	−0.675135	+	0.929244i
$567$	−23.3948	−	12.7825i	−0.982489	−	0.536815i
$568$	−1.27735	+	1.41864i	−0.0535964	+	0.0595248i
$569$	14.7488	+	6.56659i	0.618302	+	0.275286i	0.691890	−	0.722003i	$-0.256778\pi$
$569$	14.7488	+	6.56659i	0.618302	+	0.275286i	−0.0735883	+	0.997289i	$0.523445\pi$
$570$	−0.964422	+	1.14274i	−0.0403952	+	0.0478641i
$571$	−1.38761	−	6.52820i	−0.0580697	−	0.273197i	0.939528	−	0.342473i	$-0.111264\pi$
$571$	−1.38761	−	6.52820i	−0.0580697	−	0.273197i	−0.997598	+	0.0692761i	$0.977931\pi$
$572$	−1.29671	−	2.91245i	−0.0542180	−	0.121776i
$573$	3.85733	−	3.70385i	0.161142	−	0.154730i
$574$	3.64373	−	11.2143i	0.152087	−	0.468074i
$575$	0.00283873	−	0.00126388i	0.000118383	−	5.27075e-5i
$576$	−2.14614	−	2.09621i	−0.0894224	−	0.0873421i
$577$	−27.2027	−	5.78211i	−1.13246	−	0.240712i	−0.396697	−	0.917949i	$-0.629844\pi$
$577$	−27.2027	−	5.78211i	−1.13246	−	0.240712i	−0.735765	+	0.677237i	$0.763177\pi$
$578$	4.70416	−	10.5657i	0.195667	−	0.439476i
$579$	1.32043	+	3.66018i	0.0548751	+	0.152112i
$580$	8.07874	+	0.849110i	0.335452	+	0.0352574i
$581$	−24.6883	−	17.9371i	−1.02424	−	0.744156i
$582$	−6.71823	+	16.4931i	−0.278480	+	0.683660i
$583$	1.53828	−	2.66438i	0.0637090	−	0.110347i
$584$	−0.298468	−	0.516963i	−0.0123507	−	0.0213921i
$585$	−12.9901	−	4.81182i	−0.537075	−	0.198944i
$586$	−7.77644	−	8.63661i	−0.321242	−	0.356775i
$587$	9.19053	+	28.2855i	0.379334	+	1.16747i	0.940508	+	0.339771i	$0.110350\pi$
$587$	9.19053	+	28.2855i	0.379334	+	1.16747i	−0.561174	+	0.827698i	$0.689650\pi$
$588$	1.45038	−	2.70917i	0.0598129	−	0.111724i
$589$	3.99384	+	2.67474i	0.164563	+	0.110211i
$590$		−	9.29822i		−	0.382802i
$591$	−30.4935	−	5.46624i	−1.25433	−	0.224851i
$592$	0.752333	−	0.677404i	0.0309207	−	0.0278411i
$593$	2.59570	+	3.57267i	0.106592	+	0.146712i	0.858981	−	0.512008i	$-0.171098\pi$
$593$	2.59570	+	3.57267i	0.106592	+	0.146712i	−0.752388	+	0.658720i	$0.771098\pi$
$594$	2.92026	−	2.08388i	0.119820	−	0.0855027i
$595$	5.98011	+	3.45262i	0.245160	+	0.141543i
$596$	8.63139	−	0.907196i	0.353556	−	0.0371602i
$597$	−2.18868	−	4.52002i	−0.0895767	−	0.184992i
$598$	−0.00149982	+	0.0142699i	−6.13324e−5	+	0.000583539i
$599$	9.38033	+	8.44609i	0.383270	+	0.345098i	0.838135	−	0.545462i	$-0.183646\pi$
$599$	9.38033	+	8.44609i	0.383270	+	0.345098i	−0.454865	+	0.890560i	$0.650313\pi$
$600$	−1.06247	−	1.36790i	−0.0433753	−	0.0558443i
$601$	2.95849	−	13.9186i	0.120679	−	0.567752i	−0.875709	−	0.482839i	$-0.839606\pi$
$601$	2.95849	−	13.9186i	0.120679	−	0.567752i	0.996388	−	0.0849126i	$-0.0270611\pi$
$602$	−6.82880	+	1.45151i	−0.278321	+	0.0591590i
$603$	−31.3038	−	19.8091i	−1.27479	−	0.806691i
$604$	22.3366	+	7.25761i	0.908864	+	0.295308i
$605$	−10.0083	−	3.25188i	−0.406894	−	0.132208i
$606$	−1.09905	+	15.1002i	−0.0446457	+	0.613402i
$607$	43.7761	−	9.30490i	1.77682	−	0.377674i	0.801415	−	0.598108i	$-0.204081\pi$
$607$	43.7761	−	9.30490i	1.77682	−	0.377674i	0.975402	+	0.220434i	$0.0707474\pi$
$608$	0.179494	−	0.844454i	0.00727946	−	0.0342471i
$609$	−32.9145	+	25.5653i	−1.33376	+	1.03596i
$610$	3.32699	+	2.99563i	0.134706	+	0.121290i
$611$	−5.27584	+	50.1963i	−0.213438	+	2.03073i
$612$	−0.283800	+	6.98776i	−0.0114719	+	0.282464i
$613$	16.3736	−	1.72094i	0.661324	−	0.0695080i	0.232080	−	0.972697i	$-0.425447\pi$
$613$	16.3736	−	1.72094i	0.661324	−	0.0695080i	0.429244	+	0.903189i	$0.358780\pi$
$614$	0.430847	+	0.248750i	0.0173876	+	0.0100387i
$615$	6.89125	−	0.221038i	0.277882	−	0.00891309i
$616$	1.20209	+	1.65454i	0.0484337	+	0.0666633i
$617$	15.6373	−	14.0799i	0.629536	−	0.566836i	−0.291376	−	0.956609i	$-0.594113\pi$
$617$	15.6373	−	14.0799i	0.629536	−	0.566836i	0.920911	+	0.389772i	$0.127446\pi$
$618$	−3.43844	+	19.1813i	−0.138314	+	0.771587i
$619$		−	20.4583i		−	0.822290i	−0.911570	−	0.411145i	$-0.865129\pi$
$619$		−	20.4583i		−	0.822290i	0.911570	−	0.411145i	$-0.134871\pi$
$620$	−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
$624$	7.92315	−	1.09057i	0.317180	−	0.0436577i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.3801	+	21.4430i	−0.494808	+	0.857033i
$627$	0.956122	+	0.389463i	0.0381838	+	0.0155537i
$628$	−2.70365	−	1.96431i	−0.107887	−	0.0783846i
$629$	−2.34707	−	0.246687i	−0.0935838	−	0.00983606i
$630$	8.79272	+	1.28675i	0.350310	+	0.0512654i
$631$	−9.56508	+	21.4835i	−0.380780	+	0.855246i	0.616892	+	0.787048i	$0.288392\pi$
$631$	−9.56508	+	21.4835i	−0.380780	+	0.855246i	−0.997672	+	0.0681979i	$0.978275\pi$
$632$	7.73986	+	1.64516i	0.307875	+	0.0654409i
$633$	−3.04154	+	10.4944i	−0.120890	+	0.417116i
$634$	22.6217	−	10.0718i	0.898424	−	0.400004i
$635$	−6.37131	+	19.6089i	−0.252838	+	0.778154i
$636$	5.34563	+	5.56715i	0.211968	+	0.220752i
$637$	3.33216	+	7.48415i	0.132025	+	0.296533i
$638$	−1.16607	−	5.48592i	−0.0461651	−	0.217190i
$639$	5.32201	−	2.11512i	0.210535	−	0.0836727i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	−32.5879	+	36.1925i	−1.28715	+	1.42952i	−0.440146	+	0.897926i	$0.645073\pi$
$641$	−32.5879	+	36.1925i	−1.28715	+	1.42952i	−0.847000	+	0.531593i	$0.821593\pi$
$642$	−16.5658	−	11.2424i	−0.653799	−	0.443702i
$643$	23.5502	−	32.4141i	0.928730	−	1.27829i	−0.0316227	−	0.999500i	$-0.510068\pi$
$643$	23.5502	−	32.4141i	0.928730	−	1.27829i	0.960353	−	0.278787i	$-0.0899325\pi$
$644$	−0.000962125	−	0.00915400i	−3.79130e−5	−	0.000360718i
$645$	−2.15340	−	3.46806i	−0.0847901	−	0.136555i
$646$	−1.74292	+	1.00627i	−0.0685742	+	0.0395914i
$647$	3.05629	−	2.22053i	0.120155	−	0.0872979i	−0.526085	−	0.850432i	$-0.676341\pi$
$647$	3.05629	−	2.22053i	0.120155	−	0.0872979i	0.646240	+	0.763134i	$0.276341\pi$
$648$	2.98183	+	8.49169i	0.117137	+	0.333585i
$649$	−6.10551	+	1.98380i	−0.239662	+	0.0778710i
$650$	4.61756			0.181116
$651$	0.983865	−	28.5488i	0.0385607	−	1.11891i
$652$	20.3886			0.798479
$653$	18.9136	−	6.14541i	0.740148	−	0.240489i	0.0854113	−	0.996346i	$-0.472780\pi$
$653$	18.9136	−	6.14541i	0.740148	−	0.240489i	0.654737	+	0.755857i	$0.272780\pi$
$654$	−8.31585	−	33.7616i	−0.325176	−	1.32018i
$655$	−11.7718	+	8.55268i	−0.459960	+	0.334181i
$656$	−3.44740	+	1.99036i	−0.134598	+	0.0777104i
$657$	0.114763	+	1.78713i	0.00447732	+	0.0697226i
$658$	−3.38441	−	32.2005i	−0.131938	−	1.25531i
$659$	−1.24535	+	1.71408i	−0.0485121	+	0.0667712i	−0.832584	−	0.553899i	$-0.813139\pi$
$659$	−1.24535	+	1.71408i	−0.0485121	+	0.0667712i	0.784072	+	0.620670i	$0.213139\pi$
$660$	−0.671526	+	0.989499i	−0.0261391	+	0.0385162i
$661$	13.0432	−	14.4859i	0.507320	−	0.563436i	−0.434016	−	0.900905i	$-0.642904\pi$
$661$	13.0432	−	14.4859i	0.507320	−	0.563436i	0.941337	+	0.337469i	$0.109571\pi$
$662$	16.4662	+	7.33122i	0.639977	+	0.284936i
$663$	−14.2483	−	12.0249i	−0.553358	−	0.467009i
$664$	2.14195	+	10.0771i	0.0831236	+	0.391066i
$665$	1.04013	+	2.33618i	0.0403346	+	0.0905930i
$666$	−2.92415	+	0.820526i	−0.113309	+	0.0317947i
$667$	−0.00780019	+	0.0240065i	−0.000302025	+	0.000929536i
$668$	−9.44754	+	4.20631i	−0.365536	+	0.162747i
$669$	−41.1375	−	11.9226i	−1.59047	−	0.460956i
$670$	12.0785	+	2.56736i	0.466633	+	0.0991859i
$671$	1.25721	−	2.82373i	0.0485339	−	0.109009i
$672$	−4.82611	+	1.74104i	−0.186171	+	0.0671621i
$673$	−27.4194	−	2.88190i	−1.05694	−	0.111089i	−0.439921	−	0.898037i	$-0.644993\pi$
$673$	−27.4194	−	2.88190i	−1.05694	−	0.111089i	−0.617020	+	0.786948i	$0.711660\pi$
$674$	−19.6238	−	14.2575i	−0.755881	−	0.549179i
$675$	1.03696	+	5.09163i	0.0399126	+	0.195977i
$676$	−4.16093	+	7.20695i	−0.160036	+	0.277190i
$677$	−17.4259	−	30.1825i	−0.669731	−	1.16001i	−0.977979	−	0.208702i	$-0.933076\pi$
$677$	−17.4259	−	30.1825i	−0.669731	−	1.16001i	0.308248	−	0.951306i	$-0.400257\pi$
$678$	−1.82229	−	13.2392i	−0.0699847	−	0.508450i
$679$	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	$-0.386945\pi$
$684$	−1.60612	+	2.03182i	−0.0614114	+	0.0776885i
$685$	3.79535	−	3.41735i	0.145013	−	0.130570i
$686$	9.09863	+	12.5232i	0.347387	+	0.478138i
$687$	0.942513	+	29.3846i	0.0359591	+	1.12109i
$688$	2.04111	+	1.17844i	0.0778167	+	0.0449275i
$689$	−20.4633	+	2.15078i	−0.779591	+	0.0819383i
$690$	0.00484411	−	0.00234561i	0.000184412	−	8.92958e-5i
$691$	−0.439855	+	4.18494i	−0.0167329	+	0.159203i	−0.999698	−	0.0245918i	$-0.992171\pi$
$691$	−0.439855	+	4.18494i	−0.0167329	+	0.159203i	0.982965	+	0.183794i	$0.0588381\pi$
$692$	15.2232	+	13.7070i	0.578699	+	0.521063i
$693$	−1.03103	−	6.04812i	−0.0391655	−	0.229749i
$694$	−1.98356	+	9.33193i	−0.0752950	+	0.354235i
$695$	−4.51061	+	0.958759i	−0.171097	+	0.0363678i
$696$	14.0328	+	1.02136i	0.531910	+	0.0387144i
$697$	8.82555	+	2.86760i	0.334292	+	0.108618i
$698$	−9.91624	−	3.22198i	−0.375335	−	0.121954i
$699$	23.4000	+	1.70314i	0.885069	+	0.0644187i
$700$	−2.89740	+	0.615861i	−0.109511	+	0.0232773i
$701$	10.4177	−	49.0112i	0.393470	−	1.85113i	−0.119657	−	0.992815i	$-0.538179\pi$
$701$	10.4177	−	49.0112i	0.393470	−	1.85113i	0.513126	−	0.858313i	$-0.328487\pi$
$702$	−22.7552	−	7.60873i	−0.858838	−	0.287173i
$703$	−0.649505	−	0.584817i	−0.0244965	−	0.0220568i
$704$	0.0721689	−	0.686642i	0.00271997	−	0.0258788i
$705$	17.0398	−	8.25101i	0.641758	−	0.310751i
$706$	30.4077	−	3.19598i	1.14441	−	0.120282i
$707$	22.4234	+	12.9462i	0.843320	+	0.486891i
$708$	−0.516303	−	16.0967i	−0.0194039	−	0.604952i
$709$	28.2250	+	38.8484i	1.06001	+	1.45898i	0.879794	+	0.475355i	$0.157680\pi$
$709$	28.2250	+	38.8484i	1.06001	+	1.45898i	0.180218	+	0.983627i	$0.442320\pi$
$710$	−1.41864	+	1.27735i	−0.0532406	+	0.0479381i
$711$	−18.6227	−	14.7209i	−0.698405	−	0.552076i
$712$			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
$717$	2.21175	+	16.0687i	0.0825994	+	0.600097i
$718$	3.80780	+	6.59530i	0.142106	+	0.246134i
$719$	−13.5965	+	23.5498i	−0.507063	+	0.878259i	0.492903	+	0.870084i	$0.335936\pi$
$719$	−13.5965	+	23.5498i	−0.507063	+	0.878259i	−0.999967	+	0.00817528i	$0.997398\pi$
$720$	−1.91527	−	2.30906i	−0.0713778	−	0.0860535i
$721$	26.9617	+	19.5888i	1.00411	+	0.729526i
$722$	18.1547	+	1.90813i	0.675647	+	0.0710134i
$723$	0.797167	−	0.287582i	0.0296470	−	0.0106953i
$724$	3.90711	−	8.77552i	0.145207	−	0.326140i
$725$	7.94573	+	1.68892i	0.295097	+	0.0627248i
$726$	−17.5065	−	5.07380i	−0.649727	−	0.188306i
$727$	22.2633	−	9.91225i	0.825699	−	0.367625i	0.0500166	−	0.998748i	$-0.484073\pi$
$727$	22.2633	−	9.91225i	0.825699	−	0.367625i	0.775682	+	0.631124i	$0.217406\pi$
$728$	4.22667	−	13.0084i	0.156651	−	0.482122i
$729$	3.27980	−	26.8001i	0.121474	−	0.992595i
$730$	−0.242796	−	0.545329i	−0.00898629	−	0.0201835i
$731$	−1.14233	−	5.37422i	−0.0422505	−	0.198773i
$732$	5.92588	+	5.00118i	0.219027	+	0.184849i
$733$	7.60340	+	3.38525i	0.280838	+	0.125037i	0.542322	−	0.840171i	$-0.317545\pi$
$733$	7.60340	+	3.38525i	0.280838	+	0.125037i	−0.261484	+	0.965208i	$0.584212\pi$
$734$	−4.18551	+	4.64848i	−0.154490	+	0.171579i
$735$	1.72562	−	2.54272i	0.0636506	−	0.0937898i
$736$	−0.00182647	+	0.00251392i	−6.73245e−5	+	9.26642e-5i
$737$	−0.891166	−	8.47888i	−0.0328265	−	0.312324i
$738$	11.9176	−	0.765303i	0.438693	−	0.0281712i
$739$	−1.97748	+	1.14170i	−0.0727426	+	0.0419980i	−0.535930	−	0.844262i	$-0.680039\pi$
$739$	−1.97748	+	1.14170i	−0.0727426	+	0.0419980i	0.463188	+	0.886260i	$0.346706\pi$
$740$	0.819020	−	0.595053i	0.0301078	−	0.0218746i
$741$	−1.65135	−	6.70433i	−0.0606638	−	0.246290i
$742$	12.5533	−	4.07882i	0.460847	−	0.149738i
$743$	−4.02889			−0.147805			−0.0739027	−	0.997265i	$-0.523545\pi$
$743$	−4.02889			−0.147805			−0.0739027	+	0.997265i	$0.523545\pi$
$744$	−6.69587	+	6.94013i	−0.245482	+	0.254437i
$745$	8.67894			0.317972
$746$	−31.4109	+	10.2060i	−1.15004	+	0.373669i
$747$	7.64734	−	29.9455i	0.279802	−	1.09565i
$748$	−1.30211	+	0.946039i	−0.0476099	+	0.0345906i
$749$	−29.6515	+	17.1193i	−1.08344	+	0.625525i
$750$	−0.913668	−	1.47147i	−0.0333624	−	0.0537303i
$751$	2.49700	+	23.7573i	0.0911167	+	0.866918i	0.940649	+	0.339381i	$0.110218\pi$
$751$	2.49700	+	23.7573i	0.0911167	+	0.866918i	−0.849532	+	0.527537i	$0.823116\pi$
$752$	−6.42486	+	8.84306i	−0.234290	+	0.322473i
$753$	13.9447	+	9.46362i	0.508174	+	0.344873i
$754$	−25.0988	+	27.8750i	−0.914044	+	1.01515i
$755$	21.4556	+	9.55266i	0.780850	+	0.347657i
$756$	15.2931	+	1.73934i	0.556203	+	0.0632591i
$757$	−1.46112	−	6.87405i	−0.0531055	−	0.249842i	0.943585	−	0.331130i	$-0.107430\pi$
$757$	−1.46112	−	6.87405i	−0.0531055	−	0.249842i	−0.996691	+	0.0812884i	$0.974097\pi$
$758$	4.58121	+	10.2896i	0.166397	+	0.373734i
$759$	−0.00257371	−	0.00268036i	−9.34196e−5	−	9.72908e-5i
$760$	0.266781	−	0.821066i	0.00967715	−	0.0297832i
$761$	39.7347	−	17.6911i	1.44038	−	0.641300i	0.469955	−	0.882690i	$-0.344270\pi$
$761$	39.7347	−	17.6911i	1.44038	−	0.641300i	0.970428	+	0.241390i	$0.0776033\pi$
$762$	−9.94093	+	34.2999i	−0.360122	+	1.24255i
$763$	−58.1648	−	12.3633i	−2.10571	−	0.447582i
$764$	−1.25579	+	2.82055i	−0.0454328	+	0.102044i
$765$	−1.01267	+	6.91982i	−0.0366130	+	0.250187i
$766$	−17.7829	−	1.86906i	−0.642523	−	0.0675319i
$767$	34.7352	+	25.2366i	1.25422	+	0.911242i
$768$	1.60408	+	0.653400i	0.0578822	+	0.0235775i
$769$	11.0942	−	19.2157i	0.400066	−	0.692934i	−0.593668	−	0.804710i	$-0.702321\pi$
$769$	11.0942	−	19.2157i	0.400066	−	0.692934i	0.993733	+	0.111776i	$0.0356539\pi$
$770$	1.02256	+	1.77113i	0.0368505	+	0.0638270i
$771$	12.1809	−	1.67662i	0.438685	−	0.0603821i
$772$	−1.50321	−	1.66948i	−0.0541017	−	0.0600861i
$773$	−7.45336	−	22.9391i	−0.268079	−	0.825061i	−0.990968	−	0.134098i	$-0.957186\pi$
$773$	−7.45336	−	22.9391i	−0.268079	−	0.825061i	0.722889	−	0.690964i	$-0.242814\pi$
$774$	−3.92045	−	5.88420i	−0.140918	−	0.211503i
$775$	−4.37612	+	3.44232i	−0.157195	+	0.123652i
$776$		−	10.2820i		−	0.369101i
$777$	−0.916463	+	5.11250i	−0.0328779	+	0.183410i
$778$	−12.7939	+	11.5197i	−0.458683	+	0.413000i
$779$	2.02000	+	2.78029i	0.0723740	+	0.0996143i
$780$	7.99374	−	0.256400i	0.286222	−	0.00918059i
$781$	1.14142	+	0.658999i	0.0408432	+	0.0235808i
$782$	0.00720415		0.000757186i	0.000257620		2.70769e-5i
$783$	−36.3733	−	21.4158i	−1.29988	−	0.765337i
$784$	−0.185453	+	1.76447i	−0.00662332	+	0.0630167i
$785$	−2.48351	−	2.23616i	−0.0886402	−	0.0798120i
$786$	−19.9039	+	15.4597i	−0.709948	+	0.551430i
$787$	0.393874	−	1.85303i	0.0140401	−	0.0660535i	−0.970570	−	0.240820i	$-0.922584\pi$
$787$	0.393874	−	1.85303i	0.0140401	−	0.0660535i	0.984610	+	0.174766i	$0.0559170\pi$
$788$	17.4952	−	3.71872i	0.623240	−	0.132474i
$789$	1.03660	−	14.2422i	0.0369039	−	0.507034i
$790$	7.52550	+	2.44518i	0.267745	+	0.0869957i
$791$	−21.7364	−	7.06258i	−0.772857	−	0.251117i
$792$	−1.10757	+	1.75027i	−0.0393560	+	0.0621931i
$793$	−20.2206	+	4.29802i	−0.718055	+	0.152627i
$794$	−5.48562	+	25.8078i	−0.194677	+	0.915885i
$795$	4.73442	+	6.09542i	0.167913	+	0.216182i
$796$	2.15473	+	1.94013i	0.0763724	+	0.0687661i
$797$	−3.20838	+	30.5257i	−0.113647	+	1.08127i	0.777913	+	0.628372i	$0.216278\pi$
$797$	−3.20838	+	30.5257i	−0.113647	+	1.08127i	−0.891560	+	0.452903i	$0.850388\pi$
$798$	1.93036	+	3.98654i	0.0683339	+	0.141122i
$799$	25.3416	−	2.66351i	0.896521	−	0.0942282i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	4.64413	−	9.38606i	0.164092	−	0.331640i
$802$	2.83054	+	3.89590i	0.0999498	+	0.137569i
$803$	−0.306279	+	0.275775i	−0.0108084	+	0.00973189i
$804$	21.0524	+	3.77383i	0.742460	+	0.133093i
$805$		−	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	$-0.0257331\pi$
$809$	23.1023	+	25.6577i	0.812234	+	0.902078i	−0.184500	+	0.982833i	$0.559066\pi$
$810$	2.07787	+	8.75685i	0.0730089	+	0.307684i
$811$	20.1394	+	34.8825i	0.707190	+	1.22489i	0.965895	+	0.258932i	$0.0833707\pi$
$811$	20.1394	+	34.8825i	0.707190	+	1.22489i	−0.258706	+	0.965956i	$0.583296\pi$
$812$	12.0310	−	20.8384i	0.422207	−	0.731283i
$813$	−5.51161	+	13.5309i	−0.193301	+	0.474548i
$814$	−0.565471	−	0.410839i	−0.0198197	−	0.0143999i
$815$	20.2769	+	2.13119i	0.710269	+	0.0746522i
$816$	−1.37019	−	3.79812i	−0.0479662	−	0.132961i
$817$	0.827602	−	1.85882i	0.0289541	−	0.0650320i
$818$	−4.24518	−	0.902340i	−0.148429	−	0.0315496i
$819$	−28.6715	+	29.3544i	−1.00186	+	1.02573i
$820$	−3.63656	+	1.61910i	−0.126994	+	0.0565415i
$821$	−8.65665	+	26.6424i	−0.302119	+	0.929827i	0.678617	+	0.734492i	$0.262580\pi$
$821$	−8.65665	+	26.6424i	−0.302119	+	0.929827i	−0.980737	+	0.195335i	$0.937420\pi$
$822$	6.38061	−	6.12673i	0.222549	−	0.213694i
$823$	3.34087	+	7.50371i	0.116455	+	0.261563i	0.962363	−	0.271766i	$-0.0876076\pi$
$823$	3.34087	+	7.50371i	0.116455	+	0.261563i	−0.845908	+	0.533329i	$0.820941\pi$
$824$	−2.33919	−	11.0050i	−0.0814895	−	0.383378i
$825$	−0.771278	+	0.913885i	−0.0268524	+	0.0318174i
$826$	−25.1613	−	11.2025i	−0.875474	−	0.389786i
$827$	33.3862	−	37.0792i	1.16095	−	1.28937i	0.210819	−	0.977525i	$-0.432387\pi$
$827$	33.3862	−	37.0792i	1.16095	−	1.28937i	0.950134	−	0.311843i	$-0.100946\pi$
$828$	0.00825569	−	0.00432961i	0.000286905	−	0.000150464i
$829$	−9.07918	+	12.4964i	−0.315333	+	0.434019i	−0.937035	−	0.349235i	$-0.886441\pi$
$829$	−9.07918	+	12.4964i	−0.315333	+	0.434019i	0.621702	+	0.783254i	$0.286441\pi$
$830$	1.07687	+	10.2458i	0.0373788	+	0.355635i
$831$	20.1547	−	12.5145i	0.699158	−	0.434124i
$832$	−3.99892	+	2.30878i	−0.138638	+	0.0800426i
$833$	3.34605	−	2.43104i	0.115934	−	0.0842307i
$834$	−7.75535	+	1.91023i	−0.268546	+	0.0661458i
$835$	−9.83546	+	3.19574i	−0.340370	+	0.110593i
$836$	−0.596057			−0.0206151
$837$	27.2376	−	9.75272i	0.941468	−	0.337103i
$838$	−16.5509			−0.571742
$839$	44.4385	−	14.4389i	1.53419	−	0.498488i	0.584422	−	0.811450i	$-0.301321\pi$
$839$	44.4385	−	14.4389i	1.53419	−	0.498488i	0.949765	+	0.312963i	$0.101321\pi$
$840$	−4.98166	+	1.22704i	−0.171884	+	0.0423368i
$841$	−29.9232	+	21.7405i	−1.03183	+	0.749671i
$842$	9.14761	−	5.28138i	0.315248	−	0.182008i
$843$	8.19246	−	5.08689i	0.282163	−	0.175202i
$844$	−0.659397	−	6.27375i	−0.0226974	−	0.215951i
$845$	−4.89147	+	6.73253i	−0.168272	+	0.231606i
$846$	29.0405	−	15.2300i	0.998435	−	0.523618i
$847$	−20.8577	+	23.1648i	−0.716680	+	0.795954i
$848$	−4.07080	−	1.81244i	−0.139792	−	0.0622393i
$849$	−30.5264	+	36.1706i	−1.04766	+	1.24137i
$850$	−0.484678	−	2.28023i	−0.0166243	−	0.0782113i
$851$	0.00127951	+	0.00287383i	4.38610e−5	+	9.85135e-5i
$852$	−2.38497	+	2.29007i	−0.0817076	+	0.0784565i
$853$	−15.0702	+	46.3812i	−0.515993	+	1.58806i	0.265475	+	0.964118i	$0.414471\pi$
$853$	−15.0702	+	46.3812i	−0.515993	+	1.58806i	−0.781468	+	0.623945i	$0.785529\pi$
$854$	12.1147	−	5.39379i	0.414555	−	0.184572i
$855$	−1.80970	+	1.85280i	−0.0618904	+	0.0633645i
$856$	11.3062	+	2.40321i	0.386438	+	0.0821399i
$857$	−12.3373	+	27.7100i	−0.421433	+	0.946554i	0.570676	+	0.821175i	$0.306681\pi$
$857$	−12.3373	+	27.7100i	−0.421433	+	0.946554i	−0.992109	+	0.125379i	$0.959985\pi$
$858$	−1.87385	−	5.19424i	−0.0639720	−	0.177328i
$859$	−43.8183	−	4.60549i	−1.49506	−	0.157137i	−0.678587	−	0.734520i	$-0.737407\pi$
$859$	−43.8183	−	4.60549i	−1.49506	−	0.157137i	−0.816473	+	0.577383i	$0.804074\pi$
$860$	1.90675	+	1.38534i	0.0650197	+	0.0472396i
$861$	7.70448	−	18.9143i	0.262568	−	0.644597i
$862$	3.94705	−	6.83650i	0.134437	−	0.232852i
$863$	−8.77373	−	15.1965i	−0.298661	−	0.517297i	0.677169	−	0.735828i	$-0.263207\pi$
$863$	−8.77373	−	15.1965i	−0.298661	−	0.517297i	−0.975830	+	0.218531i	$0.929873\pi$
$864$	−3.44385	−	3.89100i	−0.117162	−	0.132375i
$865$	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
$870$	13.8491	+	2.48258i	0.469529	+	0.0841675i
$871$	−42.3735	+	38.1533i	−1.43577	+	1.29277i
$872$	11.7997	+	16.2409i	0.399588	+	0.549986i
$873$	−13.6793	+	27.6468i	−0.462975	+	0.935701i
$874$	0.00232325	+	0.00134133i	7.85851e−5	+	4.53711e-5i
$875$	−2.94590	+	0.309626i	−0.0995896	+	0.0104673i
$876$	−0.450600	−	0.930570i	−0.0152244	−	0.0314411i
$877$	−0.904835	+	8.60893i	−0.0305541	+	0.290703i	0.968566	+	0.248757i	$0.0800222\pi$
$877$	−0.904835	+	8.60893i	−0.0305541	+	0.290703i	−0.999120	+	0.0419454i	$0.986644\pi$
$878$	2.22081	+	1.99963i	0.0749488	+	0.0674842i
$879$	−12.3477	−	15.8973i	−0.416479	−	0.536204i
$880$	0.143547	−	0.675336i	0.00483897	−	0.0227656i
$881$	40.4909	−	8.60661i	1.36417	−	0.289964i	0.533065	−	0.846074i	$-0.321040\pi$
$881$	40.4909	−	8.60661i	1.36417	−	0.289964i	0.831109	+	0.556110i	$0.187707\pi$
$882$	2.84614	−	4.49768i	0.0958346	−	0.151445i
$883$	27.1717	+	8.82862i	0.914401	+	0.297107i	0.728168	−	0.685399i	$-0.240372\pi$
$883$	27.1717	+	8.82862i	0.914401	+	0.297107i	0.186233	+	0.982506i	$0.440372\pi$
$884$	10.2375	+	3.32636i	0.344324	+	0.111878i
$885$	1.16909	−	16.0625i	0.0392985	−	0.539935i
$886$	−9.30442	+	1.97771i	−0.312588	+	0.0664426i
$887$	−7.94422	+	37.3746i	−0.266741	+	1.25492i	0.617008	+	0.786957i	$0.288345\pi$
$887$	−7.94422	+	37.3746i	−0.266741	+	1.25492i	−0.883749	+	0.467961i	$0.844989\pi$
$888$	1.38481	−	1.07561i	0.0464713	−	0.0360951i
$889$	45.3861	+	40.8659i	1.52220	+	1.37060i
$890$	−0.364879	+	3.47160i	−0.0122308	+	0.116368i
$891$	5.30671	−	3.23269i	0.177782	−	0.108299i
$892$	24.5927	−	2.58480i	0.823424	−	0.0865454i
$893$	8.17236	+	4.71831i	0.273477	+	0.157892i
$894$	15.0246	−	0.481916i	0.502499	−	0.0161177i
$895$	−7.92713	−	10.9108i	−0.264975	−	0.364706i
$896$	2.20129	−	1.98205i	0.0735399	−	0.0662156i
$897$	−0.00438511	+	0.0244624i	−0.000146414	+	0.000816775i
$898$			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
$903$	−11.9791	+	1.64885i	−0.398640	+	0.0548702i
$904$	3.85787	+	6.68203i	0.128311	+	0.222241i
$905$	4.80300	−	8.31904i	0.159657	−	0.276534i
$906$	37.6736	+	15.3458i	1.25162	+	0.509831i
$907$	−24.0503	−	17.4736i	−0.798578	−	0.580201i	0.111918	−	0.993717i	$-0.464301\pi$
$907$	−24.0503	−	17.4736i	−0.798578	−	0.580201i	−0.910497	+	0.413516i	$0.864301\pi$
$908$	−12.9971	−	1.36605i	−0.431325	−	0.0453341i
$909$	−3.79717	+	25.9471i	−0.125944	+	0.860610i
$910$	5.56326	−	12.4953i	0.184420	−	0.414215i
$911$	44.9170	+	9.54739i	1.48817	+	0.316319i	0.879037	−	0.476753i	$-0.158186\pi$
$911$	44.9170	+	9.54739i	1.48817	+	0.316319i	0.609128	+	0.793072i	$0.291520\pi$
$912$	0.416249	−	1.43621i	0.0137834	−	0.0475577i
$913$	6.49794	−	2.89307i	0.215050	−	0.0957466i
$914$	3.13890	−	9.66055i	0.103826	−	0.319542i
$915$	5.37066	+	5.59321i	0.177548	+	0.184906i
$916$	−6.90392	−	15.5064i	−0.228112	−	0.512347i
$917$	8.96119	+	42.1591i	0.295925	+	1.39222i
$918$	−1.36885	+	12.0355i	−0.0451788	+	0.397232i
$919$	13.4287	+	5.97886i	0.442973	+	0.197224i	0.616088	−	0.787677i	$-0.288717\pi$
$919$	13.4287	+	5.97886i	0.442973	+	0.197224i	−0.173115	+	0.984902i	$0.555383\pi$
$920$	−0.00207924	+	0.00230923i	−6.85504e−5	+	7.61330e-5i
$921$	0.713004	+	0.483882i	0.0234943	+	0.0159445i
$922$	5.83816	−	8.03554i	0.192270	−	0.264637i
$923$	−0.921395	−	8.76649i	−0.0303281	−	0.288553i
$924$	1.86856	+	3.00933i	0.0614712	+	0.0989996i
$925$	0.876733	−	0.506182i	0.0288268	−	0.0166432i
$926$	−19.1318	+	13.9001i	−0.628712	+	0.456786i
$927$	−8.35155	+	32.7031i	−0.274301	+	1.07411i
$928$	−7.72566	+	2.51022i	−0.253607	+	0.0824020i
$929$	−55.2244			−1.81185			−0.905926	−	0.423436i	$-0.860824\pi$
$929$	−55.2244			−1.81185			−0.905926	+	0.423436i	$0.860824\pi$
$930$	−7.38463	+	6.20220i	−0.242151	+	0.203378i
$931$	1.53169			0.0501992
$932$	−12.8828	+	4.18586i	−0.421989	+	0.137112i
$933$	11.2459	+	45.6575i	0.368175	+	1.49476i
$934$	−21.6378	+	15.7208i	−0.708010	+	0.514400i
$935$	−1.39387	+	0.804749i	−0.0455843	+	0.0263181i
$936$	13.8242	−	0.887739i	0.451858	−	0.0290166i
$937$	5.04903	+	48.0383i	0.164944	+	1.56934i	0.693508	+	0.720449i	$0.256064\pi$
$937$	5.04903	+	48.0383i	0.164944	+	1.56934i	−0.528564	+	0.848893i	$0.677269\pi$
$938$	21.4996	−	29.5917i	0.701987	−	0.966202i
$939$	−24.0825	+	35.4857i	−0.785902	+	1.15803i
$940$	−7.31401	+	8.12303i	−0.238557	+	0.264944i
$941$	−39.2320	−	17.4672i	−1.27893	−	0.569415i	−0.348987	−	0.937127i	$-0.613474\pi$
$941$	−39.2320	−	17.4672i	−1.27893	−	0.569415i	−0.929939	+	0.367713i	$0.880141\pi$
$942$	−4.42352	−	3.73325i	−0.144126	−	0.121636i
$943$	−0.00257178	−	0.0120993i	−8.37485e−5	−	0.000394006i
$944$	3.78193	+	8.49435i	0.123091	+	0.276467i
$945$	15.0275	+	3.32837i	0.488844	+	0.108272i
$946$	0.502846	−	1.54760i	0.0163489	−	0.0503168i
$947$	15.0053	−	6.68081i	0.487608	−	0.217097i	−0.148180	−	0.988960i	$-0.547342\pi$
$947$	15.0053	−	6.68081i	0.487608	−	0.217097i	0.635789	+	0.771863i	$0.280675\pi$
$948$	13.1636	+	3.81513i	0.427534	+	0.123910i
$949$	2.69616	+	0.573086i	0.0875210	+	0.0186032i
$950$	0.351144	−	0.788682i	0.0113926	−	0.0255882i
$951$	40.3450	−	14.5546i	1.30828	−	0.471966i
$952$	−6.86740	−	0.721793i	−0.222574	−	0.0233935i
$953$	−37.6932	−	27.3857i	−1.22100	−	0.887110i	−0.224819	−	0.974401i	$-0.572179\pi$
$953$	−37.6932	−	27.3857i	−1.22100	−	0.887110i	−0.996183	+	0.0872911i	$0.972179\pi$
$954$	8.53451	+	10.2893i	0.276315	+	0.333127i
$955$	−1.54374	+	2.67383i	−0.0499541	+	0.0865231i
$956$	−4.68238	−	8.11011i	−0.151439	−	0.262300i
$957$	−1.32460	−	9.62344i	−0.0428183	−	0.311082i
$958$	−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
$963$	−27.2035	−	21.5039i	−0.876622	−	0.692953i
$964$	−0.363604	+	0.327391i	−0.0117109	+	0.0105445i
$965$	−1.32047	−	1.81747i	−0.0425073	−	0.0585063i
$966$	−0.000511095	−	0.0159343i	−1.64442e−5	−	0.000512679i
$967$	26.2780	+	15.1716i	0.845043	+	0.487886i	0.858975	−	0.512017i	$-0.171102\pi$
$967$	26.2780	+	15.1716i	0.845043	+	0.487886i	−0.0139321	+	0.999903i	$0.504435\pi$
$968$	10.4657	−	1.09999i	0.336379	−	0.0353549i
$969$	−3.13738	+	1.51918i	−0.100787	+	0.0488031i
$970$	1.07476	−	10.2256i	0.0345084	−	0.328325i
$971$	17.8852	+	16.1039i	0.573962	+	0.516798i	0.904205	−	0.427098i	$-0.140464\pi$
$971$	17.8852	+	16.1039i	0.573962	+	0.516798i	−0.330243	+	0.943896i	$0.607131\pi$
$972$	4.08337	+	15.0441i	0.130974	+	0.482541i
$973$	−2.83997	+	13.3610i	−0.0910451	+	0.428334i
$974$	26.2226	−	5.57378i	0.840225	−	0.178595i
$975$	7.97675	+	0.580578i	0.255460	+	0.0185934i
$976$	−4.25779	−	1.38344i	−0.136288	−	0.0442828i
$977$	17.4212	+	5.66050i	0.557355	+	0.181096i	0.574131	−	0.818764i	$-0.305340\pi$
$977$	17.4212	+	5.66050i	0.557355	+	0.181096i	−0.0167759	+	0.999859i	$0.505340\pi$
$978$	35.2209	+	2.56351i	1.12624	+	0.0819720i
$979$	2.35741	−	0.501083i	0.0753431	−	0.0160147i
$980$	−0.368874	+	1.73542i	−0.0117833	+	0.0554359i
$981$	−10.1205	−	59.3681i	−0.323124	−	1.89548i
$982$	−5.13685	−	4.62524i	−0.163924	−	0.147597i
$983$	−1.01667	+	9.67298i	−0.0324268	+	0.308520i	0.966272	+	0.257523i	$0.0829065\pi$
$983$	−1.01667	+	9.67298i	−0.0324268	+	0.308520i	−0.998699	+	0.0509967i	$0.983760\pi$
$984$	−6.20557	+	3.00485i	−0.197826	+	0.0957912i
$985$	17.7881	−	1.86960i	0.566774	−	0.0595704i
$986$	16.3997	+	9.46835i	0.522272	+	0.301534i
$987$	−1.79785	−	56.0513i	−0.0572262	−	1.78413i
$988$	2.34317	+	3.22509i	0.0745460	+	0.102604i
$989$	−0.00544256	+	0.00490050i	−0.000173063	+	0.000155827i
$990$	−1.28446	+	1.62491i	−0.0408228	+	0.0516430i
$991$			23.4738i			0.745671i	0.927898	+	0.372835i	$0.121614\pi$
$991$			23.4738i			0.745671i	−0.927898	+	0.372835i	$0.878386\pi$
$992$	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
$996$	2.43316	+	17.6773i	0.0770975	+	0.560125i
$997$	−10.1165	−	17.5224i	−0.320394	−	0.554939i	0.660175	−	0.751112i	$-0.270482\pi$
$997$	−10.1165	−	17.5224i	−0.320394	−	0.554939i	−0.980569	+	0.196173i	$0.937149\pi$
$998$	−1.37541	+	2.38227i	−0.0435377	+	0.0754095i
$999$	−5.15459	+	1.04978i	−0.163084	+	0.0332136i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.2	✓	176	1.1	even	1	trivial
930.2.br.a.11.16	yes	176	3.2	odd	2	inner
930.2.br.a.761.2	yes	176	93.17	even	30	inner
930.2.br.a.761.16	yes	176	31.17	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.68179 + 0.414242i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.47147 - 0.913668i) q^{6} +(-0.309626 - 2.94590i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.65681 - 1.39333i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.68179 + 0.414242i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.47147 - 0.913668i) q^{6} +(-0.309626 - 2.94590i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.65681 - 1.39333i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(0.630734 + 0.280821i) q^{11} +(-1.11711 + 1.32366i) q^{12} +(-0.960045 - 4.51666i) q^{13} +(1.20480 + 2.70604i) q^{14} +(-1.24935 + 1.19964i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.12963 + 0.948174i) q^{17} +(-2.09621 + 2.14614i) q^{18} +(-0.844454 - 0.179494i) q^{19} +(0.406737 - 0.913545i) q^{20} +(1.74104 + 4.82611i) q^{21} +(-0.686642 - 0.0721689i) q^{22} +(0.00251392 + 0.00182647i) q^{23} +(0.653400 - 1.60408i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.30878 + 3.99892i) q^{26} +(-3.89100 + 3.44385i) 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} +(-1.17709 - 0.211004i) q^{33} +(1.73240 - 1.55986i) q^{34} +(-1.74109 - 2.39641i) q^{35} +(1.33042 - 2.68886i) q^{36} +(0.876733 + 0.506182i) q^{37} +(0.858591 - 0.0902415i) q^{38} +(3.48558 + 7.19836i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-2.95825 - 2.66362i) q^{41} +(-3.14718 - 4.05189i) q^{42} +(-0.490022 + 2.30537i) q^{43} +(0.675336 - 0.143547i) q^{44} +(1.60420 - 2.53507i) q^{45} +(-0.00295529 - 0.000960231i) q^{46} +(-10.3956 - 3.37775i) q^{47} +(-0.125733 + 1.72748i) q^{48} +(-1.73542 + 0.368874i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(3.18881 - 2.47681i) q^{51} +(-3.43152 - 3.08975i) q^{52} +(0.465783 - 4.43163i) q^{53} +(2.63635 - 4.47768i) q^{54} +(0.686642 - 0.0721689i) q^{55} +(2.56528 + 1.48106i) q^{56} +(1.49455 - 0.0479377i) q^{57} +(-4.77472 - 6.57184i) q^{58} +(-6.90993 + 6.22172i) q^{59} +(-0.305615 + 1.70488i) 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} +(1.18468 - 0.163063i) q^{66} +(-6.17417 - 10.6940i) q^{67} +(-1.16559 + 2.01886i) q^{68} +(-0.00498447 - 0.00203036i) q^{69} +(2.39641 + 1.74109i) q^{70} +(1.89851 + 0.199542i) q^{71} +(-0.434401 + 2.96838i) q^{72} +(-0.242796 + 0.545329i) q^{73} +(-0.990242 - 0.210482i) q^{74} +(-0.482149 + 1.66359i) q^{75} +(-0.788682 + 0.351144i) q^{76} +(0.631977 - 1.94503i) q^{77} +(-5.53940 - 5.76894i) q^{78} +(-3.21842 - 7.22868i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(5.11724 - 7.40364i) q^{81} +(3.63656 + 1.61910i) q^{82} +(6.89351 - 7.65602i) q^{83} +(4.24525 + 2.88105i) q^{84} +(-1.37023 + 1.88596i) q^{85} +(-0.246360 - 2.34396i) q^{86} +(-7.42195 - 11.9531i) q^{87} +(-0.597925 + 0.345212i) q^{88} +(2.82405 - 2.05179i) q^{89} +(-0.742302 + 2.90671i) q^{90} +(-13.0084 + 4.22667i) q^{91} +0.00310737 q^{92} +(9.55041 + 1.33777i) q^{93} +10.9306 q^{94} +(-0.821066 + 0.266781i) q^{95} +(-0.414242 - 1.68179i) q^{96} +(-8.31828 + 6.04358i) q^{97} +(1.53649 - 0.887094i) q^{98} +(2.06701 - 0.132736i) 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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