LMFDB - Embedded newform 558.2.bb.b.103.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(7,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 28])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.bb (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	558.103
Dual form			558.2.bb.b.493.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.650370 + 1.60531i) q^{3} +(-0.978148 - 0.207912i) q^{4} -2.97220 q^{5} +(-1.52853 - 0.814608i) q^{6} +(0.365303 + 1.12429i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.15404 - 2.08809i) q^{9} +(0.310680 - 2.95592i) q^{10} +(-0.868708 - 0.184650i) q^{11} +(0.969921 - 1.43501i) q^{12} +(0.198101 - 0.143929i) q^{13} +(-1.15631 + 0.245782i) q^{14} +(1.93303 - 4.77130i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-2.26710 - 2.51787i) q^{17} +(2.30181 - 1.92397i) q^{18} +(1.75275 - 0.780374i) q^{19} +(2.90725 + 0.617956i) q^{20} +(-2.04241 - 0.144778i) q^{21} +(0.274443 - 0.844648i) q^{22} +(0.282393 + 0.313629i) q^{23} +(1.32576 + 1.11461i) q^{24} +3.83399 q^{25} +(0.122433 + 0.212061i) q^{26} +(4.75295 - 2.09987i) q^{27} +(-0.123568 - 1.17567i) q^{28} +(0.403223 - 3.83641i) q^{29} +(4.54311 + 2.42118i) q^{30} +(2.91420 - 4.74420i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.861401 - 1.27445i) q^{33} +(2.74105 - 1.99149i) q^{34} +(-1.08575 - 3.34161i) q^{35} +(1.67283 + 2.49031i) q^{36} +(-2.89098 + 5.00732i) q^{37} +(0.592887 + 1.82472i) q^{38} +(0.102212 + 0.411621i) q^{39} +(-0.918461 + 2.82673i) q^{40} +(-4.33837 - 3.15201i) q^{41} +(0.357475 - 2.01609i) q^{42} +(-0.293152 - 0.212988i) q^{43} +(0.811334 + 0.361229i) q^{44} +(6.40224 + 6.20623i) q^{45} +(-0.341429 + 0.248063i) q^{46} +(-2.11667 - 0.942400i) q^{47} +(-1.24708 + 1.20199i) q^{48} +(4.53255 - 3.29309i) q^{49} +(-0.400761 + 3.81298i) q^{50} +(5.51641 - 2.00185i) q^{51} +(-0.223697 + 0.0995963i) q^{52} +(-5.35015 + 1.13721i) q^{53} +(1.59154 + 4.94641i) q^{54} +(2.58198 + 0.548816i) q^{55} +1.18214 q^{56} +(0.112807 + 3.32124i) q^{57} +(3.77325 + 0.802029i) q^{58} +(-5.91128 - 2.63187i) q^{59} +(-2.88280 + 4.26514i) q^{60} +(-1.12426 - 1.94728i) q^{61} +(4.41360 + 3.39414i) q^{62} +(1.56073 - 3.18454i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.588798 + 0.427786i) q^{65} +(1.17743 + 0.989899i) q^{66} -8.26352 q^{67} +(1.69406 + 2.93420i) q^{68} +(-0.687131 + 0.249353i) q^{69} +(3.43679 - 0.730513i) q^{70} +(-1.99592 + 0.424245i) q^{71} +(-2.65153 + 1.40336i) q^{72} +(-9.35224 + 10.3867i) q^{73} +(-4.67770 - 3.39855i) q^{74} +(-2.49351 + 6.15474i) q^{75} +(-1.87670 + 0.398904i) q^{76} +(-0.109742 - 1.04413i) q^{77} +(-0.420050 + 0.0586255i) q^{78} +(3.64946 - 11.2319i) q^{79} +(-2.71524 - 1.20890i) q^{80} +(0.279756 + 8.99565i) q^{81} +(3.58823 - 3.98513i) q^{82} +(-2.84558 + 1.26693i) q^{83} +(1.96768 + 0.566255i) q^{84} +(6.73827 + 7.48361i) q^{85} +(0.242464 - 0.269283i) q^{86} +(5.89639 + 3.14239i) q^{87} +(-0.444058 + 0.769130i) q^{88} +(-4.02154 - 12.3770i) q^{89} +(-6.84145 + 5.71844i) q^{90} +(0.234184 + 0.170145i) q^{91} +(-0.211015 - 0.365488i) q^{92} +(5.72060 + 7.76368i) q^{93} +(1.15849 - 2.00656i) q^{94} +(-5.20952 + 2.31943i) q^{95} +(-1.06505 - 1.36589i) q^{96} +(10.8108 - 12.0066i) q^{97} +(2.80127 + 4.85194i) q^{98} +(1.48566 + 2.21168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 2 q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 32 q^{8} - 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 20 q^{13} - q^{14} - 22 q^{15} + 16 q^{16} + 4 q^{17} - 2 q^{18} - 4 q^{19} + q^{20}+ \cdots + 15 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 32 * q^8 - 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 - 20 * q^13 - q^14 - 22 * q^15 + 16 * q^16 + 4 * q^17 - 2 * q^18 - 4 * q^19 + q^20 + 19 * q^21 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 122 * q^25 - 20 * q^26 - 37 * q^27 + 9 * q^28 - 12 * q^29 - 14 * q^30 + 25 * q^31 - 64 * q^32 + 22 * q^33 - 8 * q^34 + 6 * q^36 - 66 * q^37 - 12 * q^38 + 11 * q^39 - 2 * q^40 + 20 * q^41 + 10 * q^42 - 31 * q^43 + 2 * q^44 + 64 * q^45 + 13 * q^46 + 11 * q^47 - 3 * q^48 - 46 * q^49 + 19 * q^50 + 17 * q^51 + 10 * q^52 + 27 * q^53 - 13 * q^54 - 19 * q^55 + 2 * q^56 + 20 * q^57 + 3 * q^58 - 9 * q^59 + 11 * q^60 - 57 * q^61 + 14 * q^62 - 38 * q^63 - 32 * q^64 - 66 * q^65 - 20 * q^66 - 16 * q^67 - 16 * q^68 - 8 * q^69 - 7 * q^71 + q^72 - 7 * q^73 - 28 * q^74 + 74 * q^75 + 6 * q^76 + 46 * q^77 - 24 * q^78 - 48 * q^79 - 9 * q^80 - 64 * q^81 + 50 * q^82 - 99 * q^83 + q^84 + 27 * q^85 + 33 * q^86 + 81 * q^87 - 8 * q^88 - 52 * q^89 - 45 * q^90 + 11 * q^91 + q^92 + 30 * q^93 + 6 * q^94 + 19 * q^95 - 4 * q^96 + 35 * q^97 - 77 * q^98 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.650370	+	1.60531i	−0.375491	+	0.926826i
$3$	−0.650370	+	1.60531i	−0.375491	+	0.926826i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−2.97220			−1.32921			−0.664605	−	0.747195i	$-0.731400\pi$
$5$	−2.97220			−1.32921			−0.664605	+	0.747195i	$0.731400\pi$
$6$	−1.52853	−	0.814608i	−0.624021	−	0.332562i
$7$	0.365303	+	1.12429i	0.138071	+	0.424940i	0.996055	−	0.0887368i	$-0.0282830\pi$
$7$	0.365303	+	1.12429i	0.138071	+	0.424940i	−0.857984	+	0.513677i	$0.828283\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−2.15404	−	2.08809i	−0.718013	−	0.696030i
$10$	0.310680	−	2.95592i	0.0982456	−	0.934744i
$11$	−0.868708	−	0.184650i	−0.261925	−	0.0556739i	0.0750771	−	0.997178i	$-0.476080\pi$
$11$	−0.868708	−	0.184650i	−0.261925	−	0.0556739i	−0.337002	+	0.941504i	$0.609413\pi$
$12$	0.969921	−	1.43501i	0.279992	−	0.414252i
$13$	0.198101	−	0.143929i	0.0549434	−	0.0399188i	−0.559975	−	0.828510i	$-0.689189\pi$
$13$	0.198101	−	0.143929i	0.0549434	−	0.0399188i	0.614918	+	0.788591i	$0.289189\pi$
$14$	−1.15631	+	0.245782i	−0.309037	+	0.0656879i
$15$	1.93303	−	4.77130i	0.499107	−	1.23195i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−2.26710	−	2.51787i	−0.549852	−	0.610672i	0.402595	−	0.915378i	$-0.368108\pi$
$17$	−2.26710	−	2.51787i	−0.549852	−	0.610672i	−0.952446	+	0.304706i	$0.901442\pi$
$18$	2.30181	−	1.92397i	0.542542	−	0.453485i
$19$	1.75275	−	0.780374i	0.402108	−	0.179030i	−0.195710	−	0.980662i	$-0.562701\pi$
$19$	1.75275	−	0.780374i	0.402108	−	0.179030i	0.597818	+	0.801632i	$0.296034\pi$
$20$	2.90725	+	0.617956i	0.650081	+	0.138179i
$21$	−2.04241	−	0.144778i	−0.445690	−	0.0315932i
$22$	0.274443	−	0.844648i	0.0585114	−	0.180080i
$23$	0.282393	+	0.313629i	0.0588829	+	0.0653961i	0.771867	−	0.635785i	$-0.219323\pi$
$23$	0.282393	+	0.313629i	0.0588829	+	0.0653961i	−0.712984	+	0.701181i	$0.752657\pi$
$24$	1.32576	+	1.11461i	0.270621	+	0.227518i
$25$	3.83399			0.766797
$26$	0.122433	+	0.212061i	0.0240112	+	0.0415886i
$27$	4.75295	−	2.09987i	0.914706	−	0.404119i
$28$	−0.123568	−	1.17567i	−0.0233521	−	0.222180i
$29$	0.403223	−	3.83641i	0.0748767	−	0.712404i	−0.891106	−	0.453796i	$-0.850069\pi$
$29$	0.403223	−	3.83641i	0.0748767	−	0.712404i	0.965982	−	0.258608i	$-0.0832639\pi$
$30$	4.54311	+	2.42118i	0.829455	+	0.442045i
$31$	2.91420	−	4.74420i	0.523405	−	0.852084i
$31$	2.91420	−	4.74420i	0.523405	−	0.852084i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.861401	−	1.27445i	0.149951	−	0.221854i
$34$	2.74105	−	1.99149i	0.470086	−	0.341538i
$35$	−1.08575	−	3.34161i	−0.183526	−	0.564834i
$36$	1.67283	+	2.49031i	0.278805	+	0.415052i
$37$	−2.89098	+	5.00732i	−0.475274	+	0.823198i	−0.999599	−	0.0283198i	$-0.990984\pi$
$37$	−2.89098	+	5.00732i	−0.475274	+	0.823198i	0.524325	+	0.851518i	$0.324318\pi$
$38$	0.592887	+	1.82472i	0.0961790	+	0.296008i
$39$	0.102212	+	0.411621i	0.0163669	+	0.0659122i
$40$	−0.918461	+	2.82673i	−0.145221	+	0.446946i
$41$	−4.33837	−	3.15201i	−0.677539	−	0.492261i	0.195001	−	0.980803i	$-0.437529\pi$
$41$	−4.33837	−	3.15201i	−0.677539	−	0.492261i	−0.872540	+	0.488542i	$0.837529\pi$
$42$	0.357475	−	2.01609i	0.0551596	−	0.311089i
$43$	−0.293152	−	0.212988i	−0.0447053	−	0.0324803i	0.565208	−	0.824948i	$-0.308796\pi$
$43$	−0.293152	−	0.212988i	−0.0447053	−	0.0324803i	−0.609914	+	0.792468i	$0.708796\pi$
$44$	0.811334	+	0.361229i	0.122313	+	0.0544573i
$45$	6.40224	+	6.20623i	0.954389	+	0.925170i
$46$	−0.341429	+	0.248063i	−0.0503409	+	0.0365748i
$47$	−2.11667	−	0.942400i	−0.308747	−	0.137463i	0.246514	−	0.969139i	$-0.420715\pi$
$47$	−2.11667	−	0.942400i	−0.308747	−	0.137463i	−0.555261	+	0.831676i	$0.687382\pi$
$48$	−1.24708	+	1.20199i	−0.180001	+	0.173493i
$49$	4.53255	−	3.29309i	0.647507	−	0.470441i
$50$	−0.400761	+	3.81298i	−0.0566761	+	0.539237i
$51$	5.51641	−	2.00185i	0.772451	−	0.280315i
$52$	−0.223697	+	0.0995963i	−0.0310212	+	0.0138115i
$53$	−5.35015	+	1.13721i	−0.734900	+	0.156208i	−0.560134	−	0.828402i	$-0.689250\pi$
$53$	−5.35015	+	1.13721i	−0.734900	+	0.156208i	−0.174766	+	0.984610i	$0.555917\pi$
$54$	1.59154	+	4.94641i	0.216582	+	0.673121i
$55$	2.58198	+	0.548816i	0.348154	+	0.0740023i
$56$	1.18214			0.157971
$57$	0.112807	+	3.32124i	0.0149416	+	0.439908i
$58$	3.77325	+	0.802029i	0.495452	+	0.105312i
$59$	−5.91128	−	2.63187i	−0.769583	−	0.342640i	−0.0158956	−	0.999874i	$-0.505060\pi$
$59$	−5.91128	−	2.63187i	−0.769583	−	0.342640i	−0.753687	+	0.657233i	$0.771727\pi$
$60$	−2.88280	+	4.26514i	−0.372168	+	0.550627i
$61$	−1.12426	−	1.94728i	−0.143947	−	0.249324i	0.785032	−	0.619455i	$-0.212646\pi$
$61$	−1.12426	−	1.94728i	−0.143947	−	0.249324i	−0.928980	+	0.370131i	$0.879313\pi$
$62$	4.41360	+	3.39414i	0.560527	+	0.431056i
$63$	1.56073	−	3.18454i	0.196634	−	0.401214i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.588798	+	0.427786i	−0.0730313	+	0.0530604i
$66$	1.17743	+	0.989899i	0.144932	+	0.121848i
$67$	−8.26352			−1.00955			−0.504775	−	0.863251i	$-0.668424\pi$
$67$	−8.26352			−1.00955			−0.504775	+	0.863251i	$0.668424\pi$
$68$	1.69406	+	2.93420i	0.205435	+	0.355824i
$69$	−0.687131	+	0.249353i	−0.0827209	+	0.0300186i
$70$	3.43679	−	0.730513i	0.410775	−	0.0873130i
$71$	−1.99592	+	0.424245i	−0.236872	+	0.0503487i	−0.324818	−	0.945777i	$-0.605303\pi$
$71$	−1.99592	+	0.424245i	−0.236872	+	0.0503487i	0.0879461	+	0.996125i	$0.471970\pi$
$72$	−2.65153	+	1.40336i	−0.312485	+	0.165387i
$73$	−9.35224	+	10.3867i	−1.09460	+	1.21567i	−0.119749	+	0.992804i	$0.538209\pi$
$73$	−9.35224	+	10.3867i	−1.09460	+	1.21567i	−0.974848	+	0.222869i	$0.928458\pi$
$74$	−4.67770	−	3.39855i	−0.543772	−	0.395073i
$75$	−2.49351	+	6.15474i	−0.287926	+	0.710688i
$76$	−1.87670	+	0.398904i	−0.215272	+	0.0457574i
$77$	−0.109742	−	1.04413i	−0.0125063	−	0.118990i
$78$	−0.420050	+	0.0586255i	−0.0475613	+	0.00663803i
$79$	3.64946	−	11.2319i	0.410596	−	1.26368i	−0.505536	−	0.862806i	$-0.668705\pi$
$79$	3.64946	−	11.2319i	0.410596	−	1.26368i	0.916131	−	0.400878i	$-0.131295\pi$
$80$	−2.71524	−	1.20890i	−0.303573	−	0.135160i
$81$	0.279756	+	8.99565i	0.0310840	+	0.999517i
$82$	3.58823	−	3.98513i	0.396253	−	0.440084i
$83$	−2.84558	+	1.26693i	−0.312343	+	0.139064i	−0.556921	−	0.830566i	$-0.688017\pi$
$83$	−2.84558	+	1.26693i	−0.312343	+	0.139064i	0.244578	+	0.969630i	$0.421351\pi$
$84$	1.96768	+	0.566255i	0.214691	+	0.0617835i
$85$	6.73827	+	7.48361i	0.730868	+	0.811711i
$86$	0.242464	−	0.269283i	0.0261455	−	0.0290375i
$87$	5.89639	+	3.14239i	0.632159	+	0.336899i
$88$	−0.444058	+	0.769130i	−0.0473367	+	0.0819896i
$89$	−4.02154	−	12.3770i	−0.426283	−	1.31196i	−0.901761	−	0.432236i	$-0.857725\pi$
$89$	−4.02154	−	12.3770i	−0.426283	−	1.31196i	0.475478	−	0.879728i	$-0.342275\pi$
$90$	−6.84145	+	5.71844i	−0.721152	+	0.602776i
$91$	0.234184	+	0.170145i	0.0245492	+	0.0178360i
$92$	−0.211015	−	0.365488i	−0.0219998	−	0.0381048i
$93$	5.72060	+	7.76368i	0.593199	+	0.805056i
$94$	1.15849	−	2.00656i	0.119489	−	0.206961i
$95$	−5.20952	+	2.31943i	−0.534486	+	0.237968i
$96$	−1.06505	−	1.36589i	−0.108702	−	0.139406i
$97$	10.8108	−	12.0066i	1.09767	−	1.21909i	0.123723	−	0.992317i	$-0.460517\pi$
$97$	10.8108	−	12.0066i	1.09767	−	1.21909i	0.973948	−	0.226770i	$-0.0728167\pi$
$98$	2.80127	+	4.85194i	0.282971	+	0.490120i
$99$	1.48566	+	2.21168i	0.149315	+	0.222282i
$100$	−3.75021	−	0.797131i	−0.375021	−	0.0797131i
$101$	−3.77059	+	0.801464i	−0.375188	+	0.0797486i	−0.391646	−	0.920116i	$-0.628094\pi$
$101$	−3.77059	+	0.801464i	−0.375188	+	0.0797486i	0.0164583	+	0.999865i	$0.494761\pi$
$102$	1.41426	+	5.69544i	0.140033	+	0.563932i
$103$	−6.57543	−	4.77733i	−0.647897	−	0.470724i	0.214657	−	0.976689i	$-0.431137\pi$
$103$	−6.57543	−	4.77733i	−0.647897	−	0.470724i	−0.862554	+	0.505965i	$0.831137\pi$
$104$	−0.0756680	−	0.232882i	−0.00741986	−	0.0228360i
$105$	6.07045	+	0.430310i	0.592415	+	0.0419939i
$106$	−0.571737	−	5.43972i	−0.0555320	−	0.528352i
$107$	−4.89596	−	5.43751i	−0.473310	−	0.525664i	0.458459	−	0.888716i	$-0.348402\pi$
$107$	−4.89596	−	5.43751i	−0.473310	−	0.525664i	−0.931769	+	0.363051i	$0.881735\pi$
$108$	−5.08568	+	1.06578i	−0.489369	+	0.102555i
$109$	−13.5312	+	9.83097i	−1.29605	+	0.941636i	−0.999909	−	0.0135073i	$-0.995700\pi$
$109$	−13.5312	+	9.83097i	−1.29605	+	0.941636i	−0.296143	+	0.955144i	$0.595700\pi$
$110$	−0.815699	+	2.51046i	−0.0777739	+	0.239363i
$111$	−6.15809	−	7.89753i	−0.584500	−	0.749600i
$112$	−0.123568	+	1.17567i	−0.0116761	+	0.111090i
$113$	−0.225129	−	0.692875i	−0.0211783	−	0.0651802i	0.939909	−	0.341426i	$-0.110910\pi$
$113$	−0.225129	−	0.692875i	−0.0211783	−	0.0651802i	−0.961087	+	0.276245i	$0.910910\pi$
$114$	−3.31483	−	0.234975i	−0.310463	−	0.0220074i
$115$	−0.839328	−	0.932168i	−0.0782678	−	0.0869252i
$116$	−1.19205	+	3.66874i	−0.110679	+	0.340634i
$117$	−0.727255	−	0.103625i	−0.0672347	−	0.00958013i
$118$	3.23535	−	5.60379i	0.297838	−	0.515871i
$119$	2.00262	−	3.46865i	0.183580	−	0.317970i
$120$	−3.94044	−	3.31284i	−0.359711	−	0.302419i
$121$	−9.32844	−	4.15329i	−0.848040	−	0.377572i
$122$	2.05413	−	0.914559i	0.185973	−	0.0828003i
$123$	7.88150	−	4.91445i	0.710651	−	0.443121i
$124$	−3.83689	+	4.03463i	−0.344563	+	0.362321i
$125$	3.46563			0.309975
$126$	3.00395	+	1.88506i	0.267613	+	0.167934i
$127$	−0.711699	−	6.77137i	−0.0631531	−	0.600862i	−0.979635	−	0.200786i	$-0.935650\pi$
$127$	−0.711699	−	6.77137i	−0.0631531	−	0.600862i	0.916482	−	0.400076i	$-0.131016\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	0.532569	−	0.332079i	0.0468900	−	0.0292380i
$130$	−0.363897	−	0.630288i	−0.0319159	−	0.0552799i
$131$	−14.3579	+	15.9460i	−1.25445	+	1.39321i	−0.368371	+	0.929679i	$0.620084\pi$
$131$	−14.3579	+	15.9460i	−1.25445	+	1.39321i	−0.886081	+	0.463531i	$0.846582\pi$
$132$	−1.10755	+	1.06751i	−0.0964000	+	0.0929148i
$133$	1.51765	+	1.68552i	0.131597	+	0.146153i
$134$	0.863773	−	8.21825i	0.0746186	−	0.709949i
$135$	−14.1267	+	6.24123i	−1.21584	+	0.537159i
$136$	−3.09520	+	1.37807i	−0.265412	+	0.118169i
$137$	1.39002	+	13.2252i	0.118758	+	1.12991i	0.877854	+	0.478927i	$0.158974\pi$
$137$	1.39002	+	13.2252i	0.118758	+	1.12991i	−0.759097	+	0.650978i	$0.774359\pi$
$138$	−0.176162	−	0.709431i	−0.0149959	−	0.0603908i
$139$	−1.76018	−	16.7470i	−0.149297	−	1.42046i	−0.770812	−	0.637062i	$-0.780149\pi$
$139$	−1.76018	−	16.7470i	−0.149297	−	1.42046i	0.621515	−	0.783402i	$-0.286517\pi$
$140$	0.367268	+	3.49432i	0.0310398	+	0.295324i
$141$	2.88946	−	2.78499i	0.243336	−	0.234539i
$142$	−0.213291	−	2.02933i	−0.0178990	−	0.170298i
$143$	−0.198669	+	0.0884530i	−0.0166135	+	0.00739681i
$144$	−1.11851	−	2.78369i	−0.0932090	−	0.231974i
$145$	−1.19846	+	11.4026i	−0.0995268	+	0.946934i
$146$	−9.35224	−	10.3867i	−0.773997	−	0.859611i
$147$	2.33859	+	9.41787i	0.192884	+	0.776772i
$148$	3.86888	−	4.29683i	0.318020	−	0.353197i
$149$	7.00844	+	12.1390i	0.574154	+	0.994464i	0.996133	+	0.0878583i	$0.0280023\pi$
$149$	7.00844	+	12.1390i	0.574154	+	0.994464i	−0.421979	+	0.906606i	$0.638664\pi$
$150$	−5.86038	−	3.12320i	−0.478498	−	0.255008i
$151$	2.20643	−	2.45048i	0.179556	−	0.199418i	−0.646647	−	0.762789i	$-0.723829\pi$
$151$	2.20643	−	2.45048i	0.179556	−	0.199418i	0.826204	+	0.563372i	$0.190496\pi$
$152$	−0.200551	−	1.90811i	−0.0162668	−	0.154768i
$153$	−0.374120	+	10.1575i	−0.0302458	+	0.821184i
$154$	1.04988			0.0846018
$155$	−8.66159	+	14.1007i	−0.695715	+	1.13260i
$156$	−0.0143971	−	0.423877i	−0.00115269	−	0.0339373i
$157$	17.0562	−	7.59389i	1.36123	−	0.606059i	0.409307	−	0.912397i	$-0.365770\pi$
$157$	17.0562	−	7.59389i	1.36123	−	0.606059i	0.951923	+	0.306338i	$0.0991037\pi$
$158$	10.7889	+	4.80351i	0.858316	+	0.382147i
$159$	1.65401	−	9.32826i	0.131171	−	0.739779i
$160$	1.48610	−	2.57400i	0.117487	−	0.203493i
$161$	−0.249450	+	0.432060i	−0.0196594	+	0.0340511i
$162$	−8.97561	−	0.662078i	−0.705191	−	0.0520177i
$163$	−3.87783	+	11.9347i	−0.303735	+	0.934801i	0.676411	+	0.736524i	$0.263534\pi$
$163$	−3.87783	+	11.9347i	−0.303735	+	0.934801i	−0.980146	+	0.198276i	$0.936466\pi$
$164$	3.58823	+	3.98513i	0.280193	+	0.311186i
$165$	−2.56026	+	3.78794i	−0.199316	+	0.294890i
$166$	−0.962549	−	2.96242i	−0.0747083	−	0.229928i
$167$	0.142889	−	1.35950i	0.0110571	−	0.105201i	−0.987601	−	0.156983i	$-0.949823\pi$
$167$	0.142889	−	1.35950i	0.0110571	−	0.105201i	0.998658	+	0.0517817i	$0.0164900\pi$
$168$	−0.768831	+	1.89771i	−0.0593166	+	0.146411i
$169$	−3.99869	+	12.3067i	−0.307592	+	0.946670i
$170$	−8.14695	+	5.91911i	−0.624843	+	0.453975i
$171$	−5.40498	−	1.97894i	−0.413329	−	0.151334i
$172$	0.242464	+	0.269283i	0.0184877	+	0.0205326i
$173$	1.07593	+	10.2368i	0.0818016	+	0.778290i	0.956127	+	0.292951i	$0.0946373\pi$
$173$	1.07593	+	10.2368i	0.0818016	+	0.778290i	−0.874326	+	0.485339i	$0.838696\pi$
$174$	−3.74151	+	5.53562i	−0.283643	+	0.419654i
$175$	1.40057	+	4.31050i	0.105873	+	0.325843i
$176$	−0.718500	−	0.522021i	−0.0541590	−	0.0393488i
$177$	8.06948	−	7.77774i	0.606540	−	0.584611i
$178$	12.7296	−	2.70576i	0.954124	−	0.202805i
$179$	7.16260	+	1.52246i	0.535358	+	0.113794i	0.467654	−	0.883912i	$-0.345099\pi$
$179$	7.16260	+	1.52246i	0.535358	+	0.113794i	0.0677040	+	0.997705i	$0.478433\pi$
$180$	−4.97198	−	7.40171i	−0.370590	−	0.551691i
$181$	6.91829	+	11.9828i	0.514233	+	0.890677i	0.999864	+	0.0165132i	$0.00525654\pi$
$181$	6.91829	+	11.9828i	0.514233	+	0.890677i	−0.485631	+	0.874164i	$0.661410\pi$
$182$	−0.193692	+	0.215117i	−0.0143574	+	0.0159455i
$183$	3.85718	−	0.538338i	0.285131	−	0.0397951i
$184$	0.385543	−	0.171655i	0.0284226	−	0.0126546i
$185$	8.59257	−	14.8828i	0.631738	−	1.09420i
$186$	−8.31911	+	4.87774i	−0.609987	+	0.357653i
$187$	1.50452	+	2.60591i	0.110022	+	0.190563i
$188$	1.87447	+	1.36189i	0.136710	+	0.0993257i
$189$	4.09712	+	4.57659i	0.298021	+	0.332898i
$190$	−1.76218	−	5.42343i	−0.127842	−	0.393457i
$191$	−6.55031	+	11.3455i	−0.473964	+	0.820929i	−0.999556	−	0.0298078i	$-0.990510\pi$
$191$	−6.55031	+	11.3455i	−0.473964	+	0.820929i	0.525592	+	0.850737i	$0.323844\pi$
$192$	1.46974	−	0.916445i	0.106069	−	0.0661387i
$193$	−3.29411	+	3.65848i	−0.237115	+	0.263343i	−0.849944	−	0.526872i	$-0.823365\pi$
$193$	−3.29411	+	3.65848i	−0.237115	+	0.263343i	0.612829	+	0.790215i	$0.290031\pi$
$194$	10.8108	+	12.0066i	0.776171	+	0.862025i
$195$	−0.303793	−	1.22342i	−0.0217551	−	0.0876111i
$196$	−5.11817	+	2.27876i	−0.365584	+	0.162768i
$197$	−0.833794	+	0.926022i	−0.0594054	+	0.0659763i	−0.772115	−	0.635483i	$-0.780801\pi$
$197$	−0.833794	+	0.926022i	−0.0594054	+	0.0659763i	0.712710	+	0.701459i	$0.247468\pi$
$198$	−2.35486	+	1.24634i	−0.167353	+	0.0885737i
$199$	−11.8728	−	5.28609i	−0.841638	−	0.374721i	−0.0598056	−	0.998210i	$-0.519048\pi$
$199$	−11.8728	−	5.28609i	−0.841638	−	0.374721i	−0.781832	+	0.623489i	$0.785715\pi$
$200$	1.18477	−	3.64634i	0.0837757	−	0.257835i
$201$	5.37434	−	13.2655i	0.379077	−	0.935676i
$202$	−0.402939	−	3.83371i	−0.0283507	−	0.269739i
$203$	4.46052	−	0.948114i	0.313067	−	0.0665445i
$204$	−5.81207	+	0.811177i	−0.406926	+	0.0567938i
$205$	12.8945	+	9.36841i	0.900592	+	0.654318i
$206$	5.43848	−	6.04004i	0.378917	−	0.420830i
$207$	0.0466009	−	1.26523i	0.00323899	−	0.0879396i
$208$	0.239516	−	0.0509107i	0.0166074	−	0.00353002i
$209$	−1.66672	+	0.354273i	−0.115290	+	0.0245056i
$210$	−1.06249	+	5.99222i	−0.0733186	+	0.413502i
$211$	−6.19638	−	10.7325i	−0.426577	−	0.738852i	0.569990	−	0.821652i	$-0.306947\pi$
$211$	−6.19638	−	10.7325i	−0.426577	−	0.738852i	−0.996566	+	0.0827995i	$0.973614\pi$
$212$	5.46968			0.375659
$213$	0.617040	−	3.47998i	0.0422789	−	0.238444i
$214$	5.91949	−	4.30076i	0.404648	−	0.293994i
$215$	0.871308	+	0.633042i	0.0594227	+	0.0431731i
$216$	−0.528348	−	5.16922i	−0.0359495	−	0.351721i
$217$	6.39840	+	1.54332i	0.434352	+	0.104768i
$218$	−8.36273	−	14.4847i	−0.566395	−	0.981025i
$219$	−10.5915	−	21.7685i	−0.715706	−	1.47098i
$220$	−2.41145	−	1.07365i	−0.162580	−	0.0723852i
$221$	−0.811509	−	0.172492i	−0.0545880	−	0.0116030i
$222$	8.49796	−	5.29884i	0.570346	−	0.355635i
$223$	1.65879			0.111081			0.0555404	−	0.998456i	$-0.482312\pi$
$223$	1.65879			0.111081			0.0555404	+	0.998456i	$0.482312\pi$
$224$	−1.15631	−	0.245782i	−0.0772593	−	0.0164220i
$225$	−8.25855	−	8.00571i	−0.550570	−	0.533714i
$226$	0.712612	−	0.151470i	0.0474022	−	0.0100757i
$227$	17.7257	−	7.89200i	1.17650	−	0.523810i	0.277057	−	0.960854i	$-0.410641\pi$
$227$	17.7257	−	7.89200i	1.17650	−	0.523810i	0.899440	+	0.437043i	$0.143974\pi$
$228$	0.580182	−	3.27211i	0.0384235	−	0.216701i
$229$	−0.821420	+	7.81529i	−0.0542810	+	0.516449i	0.933273	+	0.359168i	$0.116939\pi$
$229$	−0.821420	+	7.81529i	−0.0542810	+	0.516449i	−0.987554	+	0.157281i	$0.949727\pi$
$230$	1.01480	−	0.737292i	0.0669136	−	0.0486156i
$231$	1.74752	+	0.502900i	0.114979	+	0.0330884i
$232$	−3.52404	−	1.56901i	−0.231365	−	0.103010i
$233$	5.37393	−	3.90439i	0.352058	−	0.255785i	−0.397674	−	0.917527i	$-0.630182\pi$
$233$	5.37393	−	3.90439i	0.352058	−	0.255785i	0.749732	+	0.661742i	$0.230182\pi$
$234$	0.179076	−	0.712439i	0.0117066	−	0.0465736i
$235$	6.29116	+	2.80100i	0.410390	+	0.182717i
$236$	5.23491	+	3.80338i	0.340763	+	0.247579i
$237$	15.6571	+	13.1634i	1.01704	+	0.855053i
$238$	3.24032	+	2.35423i	0.210038	+	0.152602i
$239$	7.20771	−	22.1830i	0.466228	−	1.43490i	−0.391204	−	0.920304i	$-0.627941\pi$
$239$	7.20771	−	22.1830i	0.466228	−	1.43490i	0.857432	−	0.514598i	$-0.172059\pi$
$240$	3.70658	−	3.57257i	0.239258	−	0.230608i
$241$	0.734130	+	2.25942i	0.0472894	+	0.145542i	0.971913	−	0.235340i	$-0.0756204\pi$
$241$	0.734130	+	2.25942i	0.0472894	+	0.145542i	−0.924624	+	0.380882i	$0.875620\pi$
$242$	5.10563	−	8.84320i	0.328202	−	0.568463i
$243$	−14.6227	−	5.40141i	−0.938050	−	0.346500i
$244$	0.694834	+	2.13848i	0.0444822	+	0.136902i
$245$	−13.4716	+	9.78772i	−0.860672	+	0.625315i
$246$	4.06369	+	8.35202i	0.259091	+	0.532505i
$247$	0.234903	−	0.406865i	0.0149466	−	0.0258882i
$248$	−3.61147	−	4.23761i	−0.229328	−	0.269088i
$249$	−0.183141	−	5.39201i	−0.0116061	−	0.341705i
$250$	−0.362257	+	3.44664i	−0.0229111	+	0.217985i
$251$	−1.14024	−	10.8487i	−0.0719713	−	0.684761i	−0.969714	−	0.244242i	$-0.921461\pi$
$251$	−1.14024	−	10.8487i	−0.0719713	−	0.684761i	0.897743	−	0.440519i	$-0.145206\pi$
$252$	−2.18873	+	2.79045i	−0.137877	+	0.175782i
$253$	−0.187405	−	0.324596i	−0.0117821	−	0.0204071i
$254$	6.80867			0.427214
$255$	−16.3959	+	5.94990i	−1.02675	+	0.372597i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	5.63317	−	17.3371i	0.351388	−	1.08146i	−0.606687	−	0.794941i	$-0.707502\pi$
$257$	5.63317	−	17.3371i	0.351388	−	1.08146i	0.958075	−	0.286519i	$-0.0924982\pi$
$258$	0.274592	+	0.564363i	0.0170953	+	0.0351357i
$259$	−6.68574	−	1.42110i	−0.415432	−	0.0883027i
$260$	0.664873	−	0.296020i	0.0412337	−	0.0183584i
$261$	−8.87934	+	7.42181i	−0.549617	+	0.459399i
$262$	−14.3579	−	15.9460i	−0.887031	−	0.985148i
$263$	26.7398	+	11.9053i	1.64885	+	0.734113i	0.999649	−	0.0265073i	$-0.00843851\pi$
$263$	26.7398	+	11.9053i	1.64885	+	0.734113i	0.649197	+	0.760621i	$0.275105\pi$
$264$	−0.945891	−	1.21307i	−0.0582155	−	0.0746593i
$265$	15.9017	−	3.38002i	0.976836	−	0.207633i
$266$	−1.83492	+	1.33315i	−0.112506	+	0.0817406i
$267$	22.4845	+	1.59383i	1.37603	+	0.0975410i
$268$	8.08294	+	1.71808i	0.493744	+	0.104949i
$269$	0.0885680	−	0.842668i	0.00540009	−	0.0513784i	−0.991490	−	0.130183i	$-0.958444\pi$
$269$	0.0885680	−	0.842668i	0.00540009	−	0.0513784i	0.996890	+	0.0788044i	$0.0251103\pi$
$270$	−4.73039	−	14.7017i	−0.287882	−	0.894719i
$271$	−0.543253	+	1.67196i	−0.0330003	+	0.101564i	−0.966200	−	0.257794i	$-0.917004\pi$
$271$	−0.543253	+	1.67196i	−0.0330003	+	0.101564i	0.933200	+	0.359358i	$0.117004\pi$
$272$	−1.04699	−	3.22230i	−0.0634830	−	0.195380i
$273$	−0.425442	+	0.265281i	−0.0257489	+	0.0160556i
$274$	−13.2981			−0.803365
$275$	−3.33061	−	0.707944i	−0.200844	−	0.0426906i
$276$	0.723959	−	0.101041i	0.0435772	−	0.00608197i
$277$	−3.07565	+	29.2629i	−0.184798	+	1.75823i	0.372603	+	0.927991i	$0.378465\pi$
$277$	−3.07565	+	29.2629i	−0.184798	+	1.75823i	−0.557400	+	0.830244i	$0.688201\pi$
$278$	16.8393			1.00995
$279$	−16.1836	+	4.13408i	−0.968888	+	0.247501i
$280$	−3.51357			−0.209976
$281$	1.26807	−	12.0649i	0.0756465	−	0.719729i	−0.889307	−	0.457310i	$-0.848813\pi$
$281$	1.26807	−	12.0649i	0.0756465	−	0.719729i	0.964954	−	0.262419i	$-0.0845203\pi$
$282$	2.46771	+	3.16474i	0.146950	+	0.188458i
$283$	−3.59931	−	0.765057i	−0.213957	−	0.0454779i	0.0996861	−	0.995019i	$-0.468216\pi$
$283$	−3.59931	−	0.765057i	−0.213957	−	0.0454779i	−0.313643	+	0.949541i	$0.601549\pi$
$284$	2.04051			0.121082
$285$	−0.335284	−	9.87139i	−0.0198605	−	0.584730i
$286$	−0.0672019	−	0.206826i	−0.00397373	−	0.0122299i
$287$	1.95894	−	6.02900i	0.115633	−	0.355881i
$288$	2.88536	−	0.821406i	0.170021	−	0.0484018i
$289$	0.577062	−	5.49038i	0.0339448	−	0.322963i
$290$	−11.2149	−	2.38379i	−0.658559	−	0.139981i
$291$	12.2433	+	25.1634i	0.717716	+	1.47511i
$292$	11.3074	−	8.21530i	0.661715	−	0.480764i
$293$	15.0257	−	3.19380i	0.877809	−	0.186584i	0.253099	−	0.967441i	$-0.418550\pi$
$293$	15.0257	−	3.19380i	0.877809	−	0.186584i	0.624711	+	0.780856i	$0.285217\pi$
$294$	−9.61072	+	1.34135i	−0.560509	+	0.0782289i
$295$	17.5695	+	7.82245i	1.02294	+	0.455441i
$296$	3.86888	+	4.29683i	0.224874	+	0.249748i
$297$	−4.51667	+	0.946539i	−0.262084	+	0.0549238i
$298$	−12.8051	+	5.70118i	−0.741777	+	0.330261i
$299$	0.101083	+	0.0214858i	0.00584576	+	0.00124256i
$300$	3.71866	−	5.50181i	0.214697	−	0.317647i
$301$	0.132370	−	0.407392i	0.00762966	−	0.0234817i
$302$	2.20643	+	2.45048i	0.126966	+	0.141009i
$303$	1.16568	−	6.57421i	0.0669667	−	0.377679i
$304$	1.91862			0.110041
$305$	3.34154	+	5.78772i	0.191336	+	0.331404i
$306$	−10.0627	−	1.43382i	−0.575248	−	0.0819659i
$307$	−2.34543	−	22.3152i	−0.133861	−	1.27360i	−0.830842	−	0.556509i	$-0.812141\pi$
$307$	−2.34543	−	22.3152i	−0.133861	−	1.27360i	0.696981	−	0.717090i	$-0.254526\pi$
$308$	−0.109742	+	1.04413i	−0.00625315	+	0.0594948i
$309$	11.9456	−	7.44857i	0.679559	−	0.423734i
$310$	−13.1181	−	10.0881i	−0.745058	−	0.572964i
$311$	4.21944	−	7.30829i	0.239263	−	0.414415i	−0.721240	−	0.692685i	$-0.756428\pi$
$311$	4.21944	−	7.30829i	0.239263	−	0.414415i	0.960503	+	0.278270i	$0.0897610\pi$
$312$	0.423060	+	0.0299890i	0.0239511	+	0.00169779i
$313$	−8.74457	+	6.35330i	−0.494272	+	0.359110i	−0.806825	−	0.590791i	$-0.798816\pi$
$313$	−8.74457	+	6.35330i	−0.494272	+	0.359110i	0.312553	+	0.949900i	$0.398816\pi$
$314$	5.76944	+	17.7565i	0.325588	+	1.00206i
$315$	−4.63882	+	9.46509i	−0.261368	+	0.533298i
$316$	−5.90494	+	10.2277i	−0.332179	+	0.575351i
$317$	5.35708	+	16.4874i	0.300884	+	0.926025i	0.981181	+	0.193089i	$0.0618506\pi$
$317$	5.35708	+	16.4874i	0.300884	+	0.926025i	−0.680297	+	0.732936i	$0.738149\pi$
$318$	9.10427	+	2.62001i	0.510542	+	0.146923i
$319$	−1.05868	+	3.25827i	−0.0592745	+	0.182428i
$320$	2.40456	+	1.74702i	0.134419	+	0.0976612i
$321$	11.9131	−	4.32313i	0.664923	−	0.241294i
$322$	−0.403618	−	0.293246i	−0.0224928	−	0.0163419i
$323$	−5.93853	−	2.64400i	−0.330429	−	0.147116i
$324$	1.59666	−	8.85724i	0.0887032	−	0.492069i
$325$	0.759518	−	0.551822i	0.0421305	−	0.0306096i
$326$	−11.4640	−	5.10411i	−0.634933	−	0.282690i
$327$	−6.98149	−	28.1155i	−0.386077	−	1.55479i
$328$	−4.33837	+	3.15201i	−0.239546	+	0.174041i
$329$	0.286304	−	2.72400i	0.0157844	−	0.150179i
$330$	−3.49957	−	2.94218i	−0.192645	−	0.161962i
$331$	−26.4695	+	11.7850i	−1.45490	+	0.647762i	−0.973489	−	0.228735i	$-0.926541\pi$
$331$	−26.4695	+	11.7850i	−1.45490	+	0.647762i	−0.481408	+	0.876497i	$0.659874\pi$
$332$	3.04681	−	0.647619i	0.167215	−	0.0355427i
$333$	16.6830	−	4.74933i	0.914224	−	0.260262i
$334$	1.33711	+	0.284212i	0.0731636	+	0.0155514i
$335$	24.5608			1.34190
$336$	−1.80695	−	0.962984i	−0.0985770	−	0.0525351i
$337$	−24.5353	−	5.21514i	−1.33652	−	0.284087i	−0.516436	−	0.856326i	$-0.672742\pi$
$337$	−24.5353	−	5.21514i	−1.33652	−	0.284087i	−0.820087	+	0.572239i	$0.806075\pi$
$338$	−11.8213	−	5.26319i	−0.642995	−	0.286280i
$339$	1.25870	+	0.0892238i	0.0683630	+	0.00484597i
$340$	−5.03509	−	8.72104i	−0.273066	−	0.472965i
$341$	−3.40760	+	3.58322i	−0.184532	+	0.194042i
$342$	2.53308	−	5.16851i	0.136973	−	0.279481i
$343$	12.0527	+	8.75683i	0.650787	+	0.472824i
$344$	−0.293152	+	0.212988i	−0.0158057	+	0.0114835i
$345$	2.04229	−	0.741127i	0.109953	−	0.0399009i
$346$	−10.2932			−0.553366
$347$	8.76298	+	15.1779i	0.470422	+	0.814794i	0.999428	−	0.0338239i	$-0.0107685\pi$
$347$	8.76298	+	15.1779i	0.470422	+	0.814794i	−0.529006	+	0.848618i	$0.677435\pi$
$348$	−5.11420	−	4.29965i	−0.274150	−	0.230485i
$349$	8.34624	−	1.77405i	0.446764	−	0.0949626i	0.0209645	−	0.999780i	$-0.493326\pi$
$349$	8.34624	−	1.77405i	0.446764	−	0.0949626i	0.425799	+	0.904818i	$0.359993\pi$
$350$	−4.43328	+	0.942323i	−0.236969	+	0.0503693i
$351$	0.639335	−	1.10007i	0.0341252	−	0.0587176i
$352$	0.594265	−	0.659998i	0.0316744	−	0.0351780i
$353$	−27.9609	−	20.3148i	−1.48821	−	1.08125i	−0.974794	−	0.223108i	$-0.928380\pi$
$353$	−27.9609	−	20.3148i	−1.48821	−	1.08125i	−0.513417	−	0.858140i	$-0.671620\pi$
$354$	6.89164	+	8.83827i	0.366287	+	0.469749i
$355$	5.93227	−	1.26094i	0.314852	−	0.0669239i
$356$	1.36033	+	12.9427i	0.0720975	+	0.685961i
$357$	4.26581	+	5.47074i	0.225770	+	0.289542i
$358$	−2.26281	+	6.96423i	−0.119593	+	0.368071i
$359$	5.82627	+	2.59402i	0.307499	+	0.136907i	0.554684	−	0.832061i	$-0.312839\pi$
$359$	5.82627	+	2.59402i	0.307499	+	0.136907i	−0.247186	+	0.968968i	$0.579506\pi$
$360$	7.88087	−	4.17106i	0.415358	−	0.219834i
$361$	−10.2503	+	11.3842i	−0.539491	+	0.599166i
$362$	−12.6403	+	5.62785i	−0.664362	+	0.295793i
$363$	12.7343	−	12.2739i	0.668375	−	0.644211i
$364$	−0.193692	−	0.215117i	−0.0101522	−	0.0112752i
$365$	27.7968	−	30.8714i	1.45495	−	1.61588i
$366$	0.132204	+	3.89232i	0.00691040	+	0.203455i
$367$	−0.121209	+	0.209941i	−0.00632708	+	0.0109588i	−0.869172	−	0.494511i	$-0.835347\pi$
$367$	−0.121209	+	0.209941i	−0.00632708	+	0.0109588i	0.862845	+	0.505469i	$0.168681\pi$
$368$	0.130414	+	0.401374i	0.00679831	+	0.0209230i
$369$	2.76333	+	15.8485i	0.143853	+	0.825038i
$370$	13.9031	+	10.1012i	0.722786	+	0.525135i
$371$	−3.23297	−	5.59968i	−0.167848	−	0.290721i
$372$	−3.98144	−	8.78340i	−0.206428	−	0.455398i
$373$	−1.85992	+	3.22148i	−0.0963032	+	0.166802i	−0.910152	−	0.414275i	$-0.864035\pi$
$373$	−1.85992	+	3.22148i	−0.0963032	+	0.166802i	0.813849	+	0.581077i	$0.197369\pi$
$374$	−2.74890	+	1.22389i	−0.142142	+	0.0632858i
$375$	−2.25394	+	5.56340i	−0.116393	+	0.287293i
$376$	−1.55036	+	1.72185i	−0.0799538	+	0.0887977i
$377$	−0.472293	−	0.818035i	−0.0243243	−	0.0421309i
$378$	−4.97979	+	3.59629i	−0.256133	+	0.184973i
$379$	21.5887	+	4.58882i	1.10894	+	0.235712i	0.725749	−	0.687959i	$-0.241493\pi$
$379$	21.5887	+	4.58882i	1.10894	+	0.235712i	0.383187	+	0.923671i	$0.374827\pi$
$380$	5.57792	−	1.18562i	0.286141	−	0.0608212i
$381$	11.3330	+	3.26140i	0.580608	+	0.167086i
$382$	−10.5986	−	7.70035i	−0.542272	−	0.393984i
$383$	−5.04157	−	15.5163i	−0.257612	−	0.792848i	−0.993304	−	0.115532i	$-0.963143\pi$
$383$	−5.04157	−	15.5163i	−0.257612	−	0.792848i	0.735692	−	0.677316i	$-0.236857\pi$
$384$	0.757795	+	1.55748i	0.0386711	+	0.0794799i
$385$	0.326177	+	3.10336i	0.0166235	+	0.158162i
$386$	−3.29411	−	3.65848i	−0.167666	−	0.186212i
$387$	0.186724	+	1.07091i	0.00949170	+	0.0544375i
$388$	−13.0709	+	9.49655i	−0.663573	+	0.482114i
$389$	8.91400	−	27.4345i	0.451958	−	1.39098i	−0.422712	−	0.906264i	$-0.638922\pi$
$389$	8.91400	−	27.4345i	0.451958	−	1.39098i	0.874670	−	0.484719i	$-0.161078\pi$
$390$	1.24847	−	0.174247i	0.0632190	−	0.00882333i
$391$	0.149464	−	1.42205i	0.00755871	−	0.0719164i
$392$	−1.73128	−	5.32833i	−0.0874428	−	0.269121i
$393$	−16.2604	−	33.4196i	−0.820227	−	1.68580i
$394$	−0.833794	−	0.926022i	−0.0420059	−	0.0466523i
$395$	−10.8469	+	33.3834i	−0.545768	+	1.67970i
$396$	−0.993364	−	2.47224i	−0.0499184	−	0.124235i
$397$	4.44883	−	7.70560i	0.223281	−	0.386733i	−0.732522	−	0.680744i	$-0.761657\pi$
$397$	4.44883	−	7.70560i	0.223281	−	0.386733i	0.955802	+	0.294011i	$0.0949901\pi$
$398$	6.49818	−	11.2552i	0.325724	−	0.564171i
$399$	−3.69281	+	1.34008i	−0.184872	+	0.0670881i
$400$	3.50252	+	1.55942i	0.175126	+	0.0779712i
$401$	−5.55135	+	2.47162i	−0.277221	+	0.123427i	−0.540638	−	0.841255i	$-0.681817\pi$
$401$	−5.55135	+	2.47162i	−0.277221	+	0.123427i	0.263417	+	0.964682i	$0.415151\pi$
$402$	12.6311	+	6.73153i	0.629980	+	0.335738i
$403$	−0.105522	−	1.35927i	−0.00525642	−	0.0677101i
$404$	3.85483			0.191785
$405$	−0.831493	−	26.7369i	−0.0413172	−	1.32857i
$406$	0.476668	+	4.53519i	0.0236566	+	0.225078i
$407$	3.43601	−	3.81608i	0.170317	−	0.189156i
$408$	−0.199207	−	5.86502i	−0.00986221	−	0.290362i
$409$	−12.8522	−	22.2606i	−0.635499	−	1.10072i	−0.986409	−	0.164307i	$-0.947461\pi$
$409$	−12.8522	−	22.2606i	−0.635499	−	1.10072i	0.350910	−	0.936409i	$-0.385872\pi$
$410$	−10.6649	+	11.8446i	−0.526703	+	0.584963i
$411$	−22.1346	−	6.36986i	−1.09182	−	0.314202i
$412$	5.43848	+	6.04004i	0.267935	+	0.297572i
$413$	0.799569	−	7.60740i	0.0393442	−	0.374335i
$414$	1.25343	+	0.178598i	0.0616026	+	0.00877762i
$415$	8.45763	−	3.76558i	0.415169	−	0.184845i
$416$	0.0255956	+	0.243525i	0.00125493	+	0.0119398i
$417$	28.0289	+	8.06612i	1.37258	+	0.395000i
$418$	−0.178112	−	1.69462i	−0.00871175	−	0.0828867i
$419$	2.46619	+	23.4643i	0.120481	+	1.14630i	0.872996	+	0.487728i	$0.162174\pi$
$419$	2.46619	+	23.4643i	0.120481	+	1.14630i	−0.752514	+	0.658576i	$0.771159\pi$
$420$	−5.84833	−	1.68302i	−0.285369	−	0.0821232i
$421$	1.85415	+	17.6410i	0.0903656	+	0.859772i	0.941995	+	0.335627i	$0.108948\pi$
$421$	1.85415	+	17.6410i	0.0903656	+	0.859772i	−0.851629	+	0.524145i	$0.824385\pi$
$422$	11.3214	−	5.04059i	0.551115	−	0.245372i
$423$	2.59156	+	6.44975i	0.126006	+	0.313598i
$424$	−0.571737	+	5.43972i	−0.0277660	+	0.264176i
$425$	−8.69202	−	9.65347i	−0.421625	−	0.468262i
$426$	3.39642	+	0.977417i	0.164557	+	0.0473560i
$427$	1.77861	−	1.97534i	0.0860728	−	0.0955935i
$428$	3.65845	+	6.33662i	0.176838	+	0.306292i
$429$	−0.0127863	−	0.376452i	−0.000617328	−	0.0181753i
$430$	−0.720651	+	0.800364i	−0.0347529	+	0.0385970i
$431$	2.28301	+	21.7214i	0.109969	+	1.04628i	0.900795	+	0.434244i	$0.142984\pi$
$431$	2.28301	+	21.7214i	0.109969	+	1.04628i	−0.790826	+	0.612041i	$0.790349\pi$
$432$	5.19613	+	0.0148774i	0.249999	+	0.000715787i
$433$	−25.9974			−1.24935			−0.624677	−	0.780883i	$-0.714769\pi$
$433$	−25.9974			−1.24935			−0.624677	+	0.780883i	$0.714769\pi$
$434$	−2.20368	+	6.20203i	−0.105780	+	0.297707i
$435$	−17.5253	−	9.33981i	−0.840272	−	0.447810i
$436$	15.2795	−	6.80285i	0.731753	−	0.325798i
$437$	0.739711	+	0.329341i	0.0353852	+	0.0157545i
$438$	22.7563	−	8.25804i	1.08734	−	0.394584i
$439$	−12.0024	+	20.7887i	−0.572841	+	0.992190i	0.423431	+	0.905928i	$0.360826\pi$
$439$	−12.0024	+	20.7887i	−0.572841	+	0.992190i	−0.996272	+	0.0862621i	$0.972508\pi$
$440$	1.31983	−	2.28601i	0.0629204	−	0.108981i
$441$	−16.6395	−	2.37093i	−0.792359	−	0.112902i
$442$	0.256373	−	0.789034i	0.0121944	−	0.0375305i
$443$	8.69220	+	9.65367i	0.412979	+	0.458660i	0.913364	−	0.407143i	$-0.133475\pi$
$443$	8.69220	+	9.65367i	0.412979	+	0.458660i	−0.500385	+	0.865803i	$0.666808\pi$
$444$	4.38154	+	9.00529i	0.207939	+	0.427372i
$445$	11.9528	+	36.7871i	0.566619	+	1.74387i
$446$	−0.173391	+	1.64970i	−0.00821030	+	0.0781157i
$447$	−24.0449	+	3.35589i	−1.13728	+	0.158728i
$448$	0.365303	−	1.12429i	0.0172589	−	0.0531175i
$449$	−5.24604	+	3.81147i	−0.247576	+	0.179874i	−0.704652	−	0.709553i	$-0.748897\pi$
$449$	−5.24604	+	3.81147i	−0.247576	+	0.179874i	0.457076	+	0.889428i	$0.348897\pi$
$450$	8.82511	−	7.37649i	0.416020	−	0.347731i
$451$	3.18676	+	3.53925i	0.150059	+	0.166657i
$452$	0.0761523	+	0.724541i	0.00358190	+	0.0340795i
$453$	2.49879	+	5.13572i	0.117403	+	0.241297i
$454$	5.99592	+	18.4536i	0.281403	+	0.866068i
$455$	−0.696044	−	0.505705i	−0.0326310	−	0.0237078i
$456$	3.19354	+	0.919033i	0.149551	+	0.0430377i
$457$	24.4376	−	5.19438i	1.14314	−	0.242983i	0.402850	−	0.915266i	$-0.368020\pi$
$457$	24.4376	−	5.19438i	1.14314	−	0.242983i	0.740294	+	0.672283i	$0.234686\pi$
$458$	−7.68662	−	1.63384i	−0.359172	−	0.0763444i
$459$	−16.0626	−	7.20670i	−0.749737	−	0.336380i
$460$	0.627178	+	1.08630i	0.0292423	+	0.0506492i
$461$	−8.32924	+	9.25055i	−0.387931	+	0.430841i	−0.905203	−	0.424980i	$-0.860281\pi$
$461$	−8.32924	+	9.25055i	−0.387931	+	0.430841i	0.517271	+	0.855821i	$0.326948\pi$
$462$	−0.682811	+	1.68538i	−0.0317672	+	0.0784111i
$463$	−26.5771	+	11.8329i	−1.23514	+	0.549920i	−0.917290	−	0.398221i	$-0.869628\pi$
$463$	−26.5771	+	11.8329i	−1.23514	+	0.549920i	−0.317851	+	0.948141i	$0.602961\pi$
$464$	1.92877	−	3.34073i	0.0895410	−	0.155090i
$465$	−17.0028	−	23.0752i	−0.788486	−	1.07009i
$466$	3.32127	+	5.75261i	0.153855	+	0.266485i
$467$	−23.3507	−	16.9653i	−1.08054	−	0.785060i	−0.102765	−	0.994706i	$-0.532769\pi$
$467$	−23.3507	−	16.9653i	−1.08054	−	0.785060i	−0.977777	+	0.209645i	$0.932769\pi$
$468$	0.689818	+	0.252565i	0.0318868	+	0.0116748i
$469$	−3.01868	−	9.29056i	−0.139390	−	0.428998i
$470$	−3.44326	+	5.96391i	−0.158826	+	0.275095i
$471$	1.09773	+	32.3193i	0.0505808	+	1.48919i
$472$	−4.32974	+	4.80867i	−0.199293	+	0.221337i
$473$	0.215336	+	0.239154i	0.00990114	+	0.0109963i
$474$	−14.7279	+	14.1954i	−0.676474	+	0.652017i
$475$	6.72002	−	2.99194i	0.308335	−	0.137280i
$476$	−2.68004	+	2.97648i	−0.122839	+	0.136427i
$477$	13.8990	+	8.72201i	0.636393	+	0.399354i
$478$	21.3081	+	9.48698i	0.974610	+	0.433925i
$479$	11.6661	−	35.9045i	0.533036	−	1.64052i	−0.214818	−	0.976654i	$-0.568916\pi$
$479$	11.6661	−	35.9045i	0.533036	−	1.64052i	0.747854	−	0.663863i	$-0.231084\pi$
$480$	3.16556	+	4.05971i	0.144487	+	0.185299i
$481$	0.147992	+	1.40805i	0.00674787	+	0.0642017i
$482$	−2.32378	+	0.493934i	−0.105845	+	0.0224981i
$483$	−0.531355	−	0.681443i	−0.0241775	−	0.0310067i
$484$	8.26108	+	6.00202i	0.375503	+	0.272819i
$485$	−32.1319	+	35.6861i	−1.45903	+	1.62042i
$486$	6.90031	−	13.9780i	0.313004	−	0.634057i
$487$	19.1443	−	4.06924i	0.867510	−	0.184395i	0.247403	−	0.968913i	$-0.420423\pi$
$487$	19.1443	−	4.06924i	0.867510	−	0.184395i	0.620106	+	0.784518i	$0.287089\pi$
$488$	−2.19939	+	0.467495i	−0.0995619	+	0.0211625i
$489$	−16.6369	−	13.9871i	−0.752348	−	0.632519i
$490$	−8.32593	−	14.4209i	−0.376127	−	0.651472i
$491$	−12.3039			−0.555266			−0.277633	−	0.960687i	$-0.589550\pi$
$491$	−12.3039			−0.555266			−0.277633	+	0.960687i	$0.589550\pi$
$492$	−8.73104	+	3.16840i	−0.393626	+	0.142843i
$493$	−10.5737	+	7.68226i	−0.476217	+	0.345992i
$494$	0.380082	+	0.276146i	0.0171007	+	0.0124244i
$495$	−4.41570	−	6.57357i	−0.198471	−	0.295460i
$496$	4.59189	−	3.14873i	0.206182	−	0.141382i
$497$	−1.20609	−	2.08900i	−0.0541004	−	0.0937046i
$498$	5.38161	+	0.381481i	0.241156	+	0.0170946i
$499$	−19.8205	−	8.82463i	−0.887285	−	0.395045i	−0.0880873	−	0.996113i	$-0.528075\pi$
$499$	−19.8205	−	8.82463i	−0.887285	−	0.395045i	−0.799198	+	0.601068i	$0.794742\pi$
$500$	−3.38989	−	0.720544i	−0.151601	−	0.0322237i
$501$	2.08948	+	1.11356i	0.0933512	+	0.0497500i
$502$	10.9084			0.486866
$503$	38.1260	+	8.10393i	1.69995	+	0.361337i	0.952867	−	0.303389i	$-0.0981180\pi$
$503$	38.1260	+	8.10393i	1.69995	+	0.361337i	0.747088	+	0.664725i	$0.231451\pi$
$504$	−2.54638	−	2.46842i	−0.113425	−	0.109952i
$505$	11.2070	−	2.38211i	0.498703	−	0.106003i
$506$	0.342407	−	0.152449i	0.0152218	−	0.00677719i
$507$	−17.1554	−	14.4231i	−0.761900	−	0.640550i
$508$	−0.711699	+	6.77137i	−0.0315766	+	0.300431i
$509$	−24.0810	+	17.4959i	−1.06737	+	0.775491i	−0.975438	−	0.220274i	$-0.929305\pi$
$509$	−24.0810	+	17.4959i	−1.06737	+	0.775491i	−0.0919343	+	0.995765i	$0.529305\pi$
$510$	−4.20347	−	16.9280i	−0.186133	−	0.749584i
$511$	−15.0940	−	6.72030i	−0.667721	−	0.297289i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	6.69205	−	7.38962i	0.295461	−	0.326260i
$514$	16.6533	+	7.41454i	0.734547	+	0.327041i
$515$	19.5435	+	14.1992i	0.861190	+	0.625691i
$516$	−0.589974	+	0.214095i	−0.0259722	+	0.00942503i
$517$	1.66475	+	1.20951i	0.0732156	+	0.0531943i
$518$	2.11216	−	6.50057i	0.0928031	−	0.285619i
$519$	−17.1330	−	4.93051i	−0.752056	−	0.216425i
$520$	0.224901	+	0.692173i	0.00986255	+	0.0303538i
$521$	−14.1843	+	24.5679i	−0.621426	+	1.07634i	0.367795	+	0.929907i	$0.380113\pi$
$521$	−14.1843	+	24.5679i	−0.621426	+	1.07634i	−0.989220	+	0.146434i	$0.953220\pi$
$522$	−6.45301	−	9.60649i	−0.282441	−	0.420465i
$523$	−0.272576	−	0.838901i	−0.0119189	−	0.0366826i	0.944920	−	0.327301i	$-0.106139\pi$
$523$	−0.272576	−	0.838901i	−0.0119189	−	0.0366826i	−0.956839	+	0.290618i	$0.906139\pi$
$524$	17.3595	−	12.6124i	0.758352	−	0.550975i
$525$	−7.83057	−	0.555077i	−0.341754	−	0.0242256i
$526$	−14.6352	+	25.3489i	−0.638124	+	1.10526i
$527$	−18.5520	+	3.41800i	−0.808139	+	0.148891i
$528$	1.30530	−	0.813909i	0.0568057	−	0.0354208i
$529$	2.38554	−	22.6969i	0.103719	−	0.986820i
$530$	1.69932	+	16.1679i	0.0738137	+	0.702290i
$531$	7.23753	+	18.0124i	0.314082	+	0.781673i
$532$	−1.13404	−	1.96422i	−0.0491670	−	0.0851598i
$533$	−1.31310			−0.0568768
$534$	−3.93537	+	22.1947i	−0.170300	+	0.960458i
$535$	14.5518	+	16.1614i	0.629128	+	0.698718i
$536$	−2.55357	+	7.85907i	−0.110297	+	0.339460i
$537$	−7.10236	+	10.5080i	−0.306489	+	0.453455i
$538$	0.828794	+	0.176166i	0.0357318	+	0.00759504i
$539$	−4.54553	+	2.02380i	−0.195790	+	0.0871712i
$540$	15.1157	−	3.16773i	0.650474	−	0.136317i
$541$	−0.496770	−	0.551719i	−0.0213578	−	0.0237203i	0.732371	−	0.680906i	$-0.238414\pi$
$541$	−0.496770	−	0.551719i	−0.0213578	−	0.0237203i	−0.753729	+	0.657185i	$0.771747\pi$
$542$	−1.60602	−	0.715045i	−0.0689843	−	0.0307138i
$543$	−23.7356	+	3.31273i	−1.01859	+	0.142163i
$544$	3.31408	−	0.704430i	0.142090	−	0.0302022i
$545$	40.2174	−	29.2196i	1.72272	−	1.25163i
$546$	−0.219357	−	0.450841i	−0.00938763	−	0.0192942i
$547$	−4.59260	−	0.976187i	−0.196365	−	0.0417387i	0.108679	−	0.994077i	$-0.465338\pi$
$547$	−4.59260	−	0.976187i	−0.196365	−	0.0417387i	−0.305044	+	0.952338i	$0.598671\pi$
$548$	1.39002	−	13.2252i	0.0593789	−	0.564953i
$549$	−1.64440	+	6.54209i	−0.0701811	+	0.279210i
$550$	1.05221	−	3.23837i	0.0448664	−	0.138085i
$551$	−2.28709	−	7.03894i	−0.0974333	−	0.299869i
$552$	0.0248135	+	0.730555i	0.00105613	+	0.0310945i
$553$	13.9610			0.593682
$554$	−28.7811	−	6.11760i	−1.22279	−	0.259912i
$555$	18.3031	+	23.4730i	0.776923	+	0.996375i
$556$	−1.76018	+	16.7470i	−0.0746484	+	0.710232i
$557$	−40.5527			−1.71827			−0.859137	−	0.511746i	$-0.828999\pi$
$557$	−40.5527			−1.71827			−0.859137	+	0.511746i	$0.828999\pi$
$558$	−2.41978	−	16.5271i	−0.102438	−	0.699647i
$559$	−0.0887290			−0.00375284
$560$	0.367268	−	3.49432i	0.0155199	−	0.147662i
$561$	−5.16179	+	0.720419i	−0.217931	+	0.0304161i
$562$	11.8662	+	2.52224i	0.500546	+	0.106394i
$563$	−32.6905			−1.37774			−0.688870	−	0.724885i	$-0.741893\pi$
$563$	−32.6905			−1.37774			−0.688870	+	0.724885i	$0.741893\pi$
$564$	−3.40535	+	2.12338i	−0.143391	+	0.0894105i
$565$	0.669128	+	2.05936i	0.0281504	+	0.0866381i
$566$	1.13710	−	3.49962i	0.0477957	−	0.147100i
$567$	−10.0115	+	3.60066i	−0.420443	+	0.151214i
$568$	−0.213291	+	2.02933i	−0.00894950	+	0.0851488i
$569$	7.60110	+	1.61566i	0.318655	+	0.0677322i	0.364462	−	0.931218i	$-0.381253\pi$
$569$	7.60110	+	1.61566i	0.318655	+	0.0677322i	−0.0458076	+	0.998950i	$0.514586\pi$
$570$	9.85236	+	0.698393i	0.412670	+	0.0292525i
$571$	−23.7018	+	17.2203i	−0.991888	+	0.720649i	−0.960334	−	0.278853i	$-0.910046\pi$
$571$	−23.7018	+	17.2203i	−0.991888	+	0.720649i	−0.0315546	+	0.999502i	$0.510046\pi$
$572$	0.212718	−	0.0452146i	0.00889418	−	0.00189052i
$573$	−13.9529	−	17.8940i	−0.582889	−	0.747533i
$574$	5.79121	+	2.57841i	0.241720	+	0.107621i
$575$	1.08269	+	1.20245i	0.0451513	+	0.0501456i
$576$	0.515304	+	2.95541i	0.0214710	+	0.123142i
$577$	−31.5708	+	14.0562i	−1.31431	+	0.585168i	−0.939695	−	0.342014i	$-0.888891\pi$
$577$	−31.5708	+	14.0562i	−1.31431	+	0.585168i	−0.374613	+	0.927181i	$0.622224\pi$
$578$	5.39998	+	1.14780i	0.224610	+	0.0477423i
$579$	−3.73060	−	7.66743i	−0.155038	−	0.318647i
$580$	3.54301	−	10.9043i	0.147115	−	0.452774i
$581$	−2.46389	−	2.73643i	−0.102219	−	0.113526i
$582$	−26.3054	+	9.54595i	−1.09039	+	0.395692i
$583$	4.85771			0.201186
$584$	6.98835	+	12.1042i	0.289180	+	0.500875i
$585$	2.16155	+	0.307994i	0.0893690	+	0.0127340i
$586$	1.60570	+	15.2772i	0.0663308	+	0.631095i
$587$	2.71077	−	25.7912i	0.111885	−	1.06452i	−0.784161	−	0.620557i	$-0.786906\pi$
$587$	2.71077	−	25.7912i	0.111885	−	1.06452i	0.896046	−	0.443960i	$-0.146427\pi$
$588$	−0.329405	−	9.69828i	−0.0135844	−	0.399950i
$589$	1.40561	−	10.5896i	0.0579170	−	0.436335i
$590$	−9.61611	+	16.6556i	−0.395889	+	0.685700i
$591$	−0.944278	−	1.94075i	−0.0388424	−	0.0798320i
$592$	−4.67770	+	3.39855i	−0.192252	+	0.139679i
$593$	6.51695	+	20.0571i	0.267619	+	0.823647i	0.991078	+	0.133280i	$0.0425509\pi$
$593$	6.51695	+	20.0571i	0.267619	+	0.823647i	−0.723459	+	0.690367i	$0.757449\pi$
$594$	−0.469234	−	4.59086i	−0.0192529	−	0.188365i
$595$	−5.95221	+	10.3095i	−0.244017	+	0.422649i
$596$	−4.33146	−	13.3309i	−0.177423	−	0.546053i
$597$	16.2075	−	15.6215i	0.663329	−	0.639347i
$598$	−0.0319341	+	0.0982831i	−0.00130588	+	0.00401909i
$599$	8.40764	+	6.10851i	0.343527	+	0.249587i	0.746148	−	0.665780i	$-0.231901\pi$
$599$	8.40764	+	6.10851i	0.343527	+	0.249587i	−0.402622	+	0.915367i	$0.631901\pi$
$600$	5.08296	+	4.27339i	0.207511	+	0.174460i
$601$	−1.76799	−	1.28452i	−0.0721176	−	0.0523965i	0.551142	−	0.834411i	$-0.314192\pi$
$601$	−1.76799	−	1.28452i	−0.0721176	−	0.0523965i	−0.623260	+	0.782015i	$0.714192\pi$
$602$	0.391324	+	0.174229i	0.0159492	+	0.00710103i
$603$	17.7999	+	17.2550i	0.724869	+	0.702677i
$604$	−2.66769	+	1.93819i	−0.108547	+	0.0788640i
$605$	27.7260	+	12.3444i	1.12722	+	0.501872i
$606$	6.41635	+	1.84649i	0.260646	+	0.0750085i
$607$	32.4742	−	23.5939i	1.31809	−	0.957648i	0.318135	−	0.948045i	$-0.396943\pi$
$607$	32.4742	−	23.5939i	1.31809	−	0.957648i	0.999954	−	0.00960213i	$-0.00305650\pi$
$608$	−0.200551	+	1.90811i	−0.00813340	+	0.0773842i
$609$	−1.37898	+	7.77715i	−0.0558789	+	0.315146i
$610$	−6.10530	+	2.71826i	−0.247196	+	0.110059i
$611$	−0.554953	+	0.117959i	−0.0224510	+	0.00477211i
$612$	2.47780	−	9.85773i	0.100159	−	0.398475i
$613$	−42.5742	−	9.04942i	−1.71955	−	0.365503i	−0.760634	−	0.649180i	$-0.775112\pi$
$613$	−42.5742	−	9.04942i	−1.71955	−	0.365503i	−0.958920	+	0.283678i	$0.908445\pi$
$614$	22.4382			0.905531
$615$	−23.4254	+	14.6067i	−0.944603	+	0.589001i
$616$	−1.02694	−	0.218282i	−0.0413765	−	0.00879485i
$617$	23.4647	+	10.4472i	0.944654	+	0.420587i	0.820481	−	0.571673i	$-0.193706\pi$
$617$	23.4647	+	10.4472i	0.944654	+	0.420587i	0.124173	+	0.992261i	$0.460372\pi$
$618$	6.15912	+	12.6587i	0.247756	+	0.509208i
$619$	−14.6293	−	25.3387i	−0.588002	−	1.01845i	−0.994494	−	0.104795i	$-0.966582\pi$
$619$	−14.6293	−	25.3387i	−0.588002	−	1.01845i	0.406492	−	0.913654i	$-0.366752\pi$
$620$	11.4040	−	11.9917i	0.457996	−	0.481600i
$621$	2.00078	+	0.897677i	0.0802884	+	0.0360225i
$622$	6.82720	+	4.96025i	0.273746	+	0.198888i
$623$	12.4462	−	9.04273i	0.498648	−	0.362289i
$624$	−0.0740466	+	0.417608i	−0.00296424	+	0.0167177i
$625$	−29.4705			−1.17882
$626$	−5.40444	−	9.36077i	−0.216005	−	0.374132i
$627$	0.515269	−	2.90601i	0.0205779	−	0.116055i
$628$	−18.2623	+	3.88177i	−0.728745	+	0.154900i
$629$	19.1619	−	4.07299i	0.764035	−	0.162401i
$630$	−8.92835	−	5.60278i	−0.355714	−	0.223220i
$631$	4.85243	−	5.38917i	0.193172	−	0.214539i	−0.638776	−	0.769393i	$-0.720559\pi$
$631$	4.85243	−	5.38917i	0.193172	−	0.214539i	0.831948	+	0.554853i	$0.187226\pi$
$632$	−9.55440	−	6.94168i	−0.380054	−	0.276125i
$633$	21.2588	−	2.96705i	0.844963	−	0.117930i
$634$	−16.9571	+	3.60433i	−0.673451	+	0.143146i
$635$	2.11531	+	20.1259i	0.0839437	+	0.798671i
$636$	−3.55732	+	8.78053i	−0.141057	+	0.348171i
$637$	0.423933	−	1.30473i	0.0167968	−	0.0516953i
$638$	−3.12976	−	1.39346i	−0.123908	−	0.0551675i
$639$	5.18514	+	3.25382i	0.205121	+	0.128719i
$640$	−1.98879	+	2.20878i	−0.0786139	+	0.0873096i
$641$	−36.4134	+	16.2123i	−1.43824	+	0.640348i	−0.969968	−	0.243234i	$-0.921792\pi$
$641$	−36.4134	+	16.2123i	−1.43824	+	0.640348i	−0.468277	+	0.883582i	$0.655125\pi$
$642$	3.05419	+	12.2997i	0.120539	+	0.485431i
$643$	16.3979	+	18.2118i	0.646672	+	0.718202i	0.973959	−	0.226723i	$-0.0728012\pi$
$643$	16.3979	+	18.2118i	0.646672	+	0.718202i	−0.327287	+	0.944925i	$0.606135\pi$
$644$	0.333829	−	0.370755i	0.0131547	−	0.0146098i
$645$	−1.58290	+	0.987007i	−0.0623267	+	0.0388634i
$646$	3.25026	−	5.62962i	0.127880	−	0.221495i
$647$	6.07762	+	18.7050i	0.238936	+	0.735369i	0.996575	+	0.0826951i	$0.0263528\pi$
$647$	6.07762	+	18.7050i	0.238936	+	0.735369i	−0.757639	+	0.652674i	$0.773647\pi$
$648$	8.64182	+	2.51374i	0.339483	+	0.0987492i
$649$	4.64920	+	3.37784i	0.182497	+	0.132592i
$650$	0.469408	+	0.813039i	0.0184117	+	0.0318900i
$651$	−6.63884	+	9.26769i	−0.260197	+	0.363229i
$652$	6.27446	−	10.8677i	0.245727	−	0.425611i
$653$	−31.7405	+	14.1318i	−1.24210	+	0.553020i	−0.919341	−	0.393461i	$-0.871278\pi$
$653$	−31.7405	+	14.1318i	−1.24210	+	0.553020i	−0.322761	+	0.946480i	$0.604611\pi$
$654$	28.6912	−	4.00437i	1.12192	−	0.156583i
$655$	42.6744	−	47.3948i	1.66743	−	1.85187i
$656$	−2.68126	−	4.64408i	−0.104686	−	0.181321i
$657$	41.8335	−	2.84505i	1.63208	−	0.110996i
$658$	2.67915	+	0.569471i	0.104444	+	0.0222003i
$659$	35.3054	−	7.50439i	1.37530	−	0.292329i	0.539789	−	0.841800i	$-0.318504\pi$
$659$	35.3054	−	7.50439i	1.37530	−	0.292329i	0.835513	+	0.549471i	$0.185171\pi$
$660$	3.29187	−	3.17285i	0.128136	−	0.123503i
$661$	−16.6964	−	12.1306i	−0.649414	−	0.471827i	0.213657	−	0.976909i	$-0.431462\pi$
$661$	−16.6964	−	12.1306i	−0.649414	−	0.471827i	−0.863072	+	0.505082i	$0.831462\pi$
$662$	−8.95361	−	27.5564i	−0.347992	−	1.07101i
$663$	0.804684	−	1.19054i	0.0312513	−	0.0462368i
$664$	0.325593	+	3.09781i	0.0126355	+	0.120218i
$665$	−4.51075	−	5.00970i	−0.174920	−	0.194268i
$666$	2.97947	+	17.0881i	0.115452	+	0.662149i
$667$	1.31708	−	0.956913i	0.0509974	−	0.0370518i
$668$	−0.422422	+	1.30008i	−0.0163440	+	0.0503016i
$669$	−1.07883	+	2.66287i	−0.0417099	+	0.102953i
$670$	−2.56731	+	24.4263i	−0.0991837	+	0.943670i
$671$	0.617092	+	1.89922i	0.0238226	+	0.0733184i
$672$	1.14659	−	1.69639i	0.0442305	−	0.0654396i
$673$	12.3121	+	13.6739i	0.474595	+	0.527091i	0.932141	−	0.362095i	$-0.117938\pi$
$673$	12.3121	+	13.6739i	0.474595	+	0.527091i	−0.457546	+	0.889186i	$0.651272\pi$
$674$	7.75121	−	23.8558i	0.298565	−	0.918890i
$675$	18.2228	−	8.05086i	0.701394	−	0.309878i
$676$	6.47002	−	11.2064i	0.248847	−	0.431016i
$677$	1.60018	−	2.77159i	0.0614998	−	0.106521i	−0.833636	−	0.552314i	$-0.813745\pi$
$677$	1.60018	−	2.77159i	0.0614998	−	0.106521i	0.895136	+	0.445793i	$0.147078\pi$
$678$	−0.220305	+	1.24247i	−0.00846074	+	0.0477169i
$679$	17.4481	+	7.76839i	0.669596	+	0.298123i
$680$	9.19957	−	4.09591i	0.352788	−	0.157071i
$681$	1.14082	+	33.5880i	0.0437165	+	1.28709i
$682$	−3.20740	−	3.76348i	−0.122818	−	0.144111i
$683$	39.5988			1.51521			0.757603	−	0.652715i	$-0.226370\pi$
$683$	39.5988			1.51521			0.757603	+	0.652715i	$0.226370\pi$
$684$	4.87542	+	3.05946i	0.186416	+	0.116981i
$685$	−4.13144	−	39.3080i	−0.157854	−	1.50188i
$686$	−9.96872	+	11.0714i	−0.380607	+	0.422707i
$687$	−12.0117	−	6.40146i	−0.458276	−	0.244231i
$688$	−0.181178	−	0.313810i	−0.00690735	−	0.0119639i
$689$	−0.896196	+	0.995326i	−0.0341423	+	0.0379189i
$690$	0.523590	+	2.10857i	0.0199327	+	0.0802720i
$691$	−22.2208	−	24.6787i	−0.845318	−	0.938821i	0.153464	−	0.988154i	$-0.450957\pi$
$691$	−22.2208	−	24.6787i	−0.845318	−	0.938821i	−0.998782	+	0.0493335i	$0.984290\pi$
$692$	1.07593	−	10.2368i	0.0409008	−	0.389145i
$693$	−1.94385	+	2.47825i	−0.0738406	+	0.0941407i
$694$	−16.0108	+	7.12845i	−0.607760	+	0.270592i
$695$	5.23162	+	49.7756i	0.198447	+	1.88809i
$696$	4.81067	−	4.63675i	0.182348	−	0.175755i
$697$	1.89916	+	18.0693i	0.0719360	+	0.684425i
$698$	0.891910	+	8.48595i	0.0337593	+	0.321198i
$699$	2.77271	+	11.1661i	0.104874	+	0.422342i
$700$	−0.473757	−	4.50750i	−0.0179063	−	0.170367i
$701$	−4.69905	+	2.09215i	−0.177481	+	0.0790195i	−0.493554	−	0.869715i	$-0.664302\pi$
$701$	−4.69905	+	2.09215i	−0.177481	+	0.0790195i	0.316073	+	0.948735i	$0.397636\pi$
$702$	1.02722	+	0.750822i	0.0387699	+	0.0283379i
$703$	−1.15957	+	11.0326i	−0.0437342	+	0.416103i
$704$	0.594265	+	0.659998i	0.0223972	+	0.0248746i
$705$	−8.58806	+	8.27757i	−0.323445	+	0.311751i
$706$	23.1262	−	25.6843i	0.870367	−	0.966641i
$707$	−2.27848	−	3.94644i	−0.0856911	−	0.148421i
$708$	−9.51023	+	5.93004i	−0.357416	+	0.222864i
$709$	4.53422	−	5.03576i	0.170286	−	0.189122i	−0.651961	−	0.758252i	$-0.726053\pi$
$709$	4.53422	−	5.03576i	0.170286	−	0.189122i	0.822247	+	0.569131i	$0.192720\pi$
$710$	0.633944	+	6.03158i	0.0237915	+	0.226361i
$711$	−31.3142	+	16.5735i	−1.17438	+	0.621554i
$712$	−13.0140			−0.487720
$713$	2.31087	−	0.425751i	0.0865426	−	0.0159445i
$714$	−5.88667	+	3.67059i	−0.220303	+	0.137368i
$715$	0.590484	−	0.262900i	0.0220828	−	0.00983191i
$716$	−6.68955	−	2.97838i	−0.250000	−	0.111307i
$717$	30.9230	+	25.9978i	1.15484	+	0.970905i
$718$	−3.18882	+	5.52320i	−0.119006	+	0.206124i
$719$	1.14295	−	1.97964i	0.0426247	−	0.0738281i	−0.843926	−	0.536460i	$-0.819761\pi$
$719$	1.14295	−	1.97964i	0.0426247	−	0.0738281i	0.886551	+	0.462632i	$0.153095\pi$
$720$	3.32443	+	8.27369i	0.123894	+	0.308342i
$721$	2.96906	−	9.13784i	0.110574	−	0.340311i
$722$	−10.2503	−	11.3842i	−0.381478	−	0.423674i
$723$	−4.10452	−	0.290953i	−0.152649	−	0.0108207i
$724$	−4.27574	−	13.1594i	−0.158907	−	0.489064i
$725$	1.54595	−	14.7088i	0.0574153	−	0.546270i
$726$	10.8755	+	13.9475i	0.403629	+	0.517639i
$727$	9.09217	−	27.9828i	0.337210	−	1.03783i	−0.628413	−	0.777880i	$-0.716295\pi$
$727$	9.09217	−	27.9828i	0.337210	−	1.03783i	0.965623	−	0.259946i	$-0.0837048\pi$
$728$	0.234184	−	0.170145i	0.00867945	−	0.00630599i
$729$	18.1811	−	19.9611i	0.673375	−	0.739301i
$730$	27.7968	+	30.8714i	1.02880	+	1.14260i
$731$	0.128330	+	1.22098i	0.00474647	+	0.0451596i
$732$	−3.88482	−	0.275379i	−0.143587	−	0.0101783i
$733$	12.3465	+	37.9987i	0.456030	+	1.40351i	0.869922	+	0.493189i	$0.164169\pi$
$733$	12.3465	+	37.9987i	0.456030	+	1.40351i	−0.413893	+	0.910326i	$0.635831\pi$
$734$	−0.196121	−	0.142490i	−0.00723895	−	0.00525941i
$735$	−6.95077	−	27.9918i	−0.256383	−	1.03249i
$736$	−0.412807	+	0.0877448i	−0.0152163	+	0.00323432i
$737$	7.17858	+	1.52585i	0.264426	+	0.0562056i
$738$	−16.0505	+	1.09158i	−0.590826	+	0.0401815i
$739$	−0.283091	−	0.490327i	−0.0104137	−	0.0180370i	0.860772	−	0.508991i	$-0.169981\pi$
$739$	−0.283091	−	0.490327i	−0.0104137	−	0.0180370i	−0.871185	+	0.490954i	$0.836648\pi$
$740$	−11.4991	+	12.7710i	−0.422716	+	0.469473i
$741$	0.500370	+	0.641705i	0.0183815	+	0.0235736i
$742$	5.90694	−	2.62994i	0.216851	−	0.0965481i
$743$	20.3771	−	35.2941i	0.747562	−	1.29482i	−0.201426	−	0.979504i	$-0.564558\pi$
$743$	20.3771	−	35.2941i	0.747562	−	1.29482i	0.948988	−	0.315312i	$-0.102109\pi$
$744$	9.15146	−	3.04151i	0.335509	−	0.111507i
$745$	−20.8305	−	36.0795i	−0.763171	−	1.32185i
$746$	−3.00942	−	2.18647i	−0.110183	−	0.0800524i
$747$	8.77495	+	3.21280i	0.321059	+	0.117550i
$748$	−0.929846	−	2.86177i	−0.0339985	−	0.104637i
$749$	4.32481	−	7.49079i	0.158025	−	0.273708i
$750$	−5.29733	−	2.82313i	−0.193431	−	0.103086i
$751$	33.0837	−	36.7432i	1.20724	−	1.34078i	0.282931	−	0.959140i	$-0.408693\pi$
$751$	33.0837	−	36.7432i	1.20724	−	1.34078i	0.924312	−	0.381639i	$-0.124640\pi$
$752$	−1.55036	−	1.72185i	−0.0565359	−	0.0627894i
$753$	18.1570	+	5.22520i	0.661679	+	0.190417i
$754$	0.862921	−	0.384197i	0.0314257	−	0.0139916i
$755$	−6.55794	+	7.28333i	−0.238668	+	0.265068i
$756$	−3.05606	−	5.32842i	−0.111148	−	0.193793i
$757$	−39.8010	−	17.7205i	−1.44659	−	0.644064i	−0.474840	−	0.880072i	$-0.657494\pi$
$757$	−39.8010	−	17.7205i	−1.44659	−	0.644064i	−0.971751	+	0.236008i	$0.924161\pi$
$758$	−6.82031	+	20.9908i	−0.247725	+	0.762418i
$759$	0.642959	−	0.0897363i	0.0233379	−	0.00325722i
$760$	0.596077	+	5.67130i	0.0216220	+	0.205719i
$761$	5.78280	−	1.22917i	0.209626	−	0.0445575i	−0.101901	−	0.994795i	$-0.532493\pi$
$761$	5.78280	−	1.22917i	0.209626	−	0.0445575i	0.311528	+	0.950237i	$0.399159\pi$
$762$	−4.42815	+	10.9300i	−0.160415	+	0.395953i
$763$	−15.9958	−	11.6216i	−0.579087	−	0.420731i
$764$	8.76602	−	9.73565i	0.317143	−	0.352224i
$765$	1.11196	−	30.1901i	0.0402030	−	1.09153i
$766$	15.9583	−	3.39205i	0.576598	−	0.122560i
$767$	−1.54984	+	0.329428i	−0.0559613	+	0.0118949i
$768$	−1.62816	+	0.590843i	−0.0587512	+	0.0213202i
$769$	−16.9462	−	29.3516i	−0.611094	−	1.05845i	−0.991056	−	0.133444i	$-0.957396\pi$
$769$	−16.9462	−	29.3516i	−0.611094	−	1.05845i	0.379963	−	0.925002i	$-0.375937\pi$
$770$	−3.12046			−0.112453
$771$	24.1678	+	20.3185i	0.870382	+	0.731754i
$772$	3.98276	−	2.89365i	0.143343	−	0.104145i
$773$	−0.303766	−	0.220699i	−0.0109257	−	0.00793798i	0.582309	−	0.812968i	$-0.302149\pi$
$773$	−0.303766	−	0.220699i	−0.0109257	−	0.00793798i	−0.593235	+	0.805030i	$0.702149\pi$
$774$	−1.08456	+	0.0737600i	−0.0389838	+	0.00265125i
$775$	11.1730	−	18.1892i	0.401346	−	0.653376i
$776$	−8.07825	−	13.9919i	−0.289992	−	0.502281i
$777$	6.62951	−	9.80845i	0.237832	−	0.351876i
$778$	26.3524	+	11.7329i	0.944780	+	0.420643i
$779$	−10.0638	−	2.13913i	−0.360574	−	0.0766423i
$780$	0.0427911	+	1.25985i	0.00153217	+	0.0451098i
$781$	1.81221			0.0648458
$782$	1.39864	+	0.297290i	0.0500153	+	0.0106311i
$783$	−6.13945	−	19.0810i	−0.219406	−	0.681900i
$784$	5.48011	−	1.16483i	0.195718	−	0.0416012i
$785$	−50.6944	+	22.5706i	−1.80936	+	0.805579i
$786$	34.9362	−	12.6780i	1.24613	−	0.452209i
$787$	1.54867	−	14.7346i	0.0552040	−	0.525231i	−0.931620	−	0.363434i	$-0.881604\pi$
$787$	1.54867	−	14.7346i	0.0552040	−	0.525231i	0.986824	−	0.161797i	$-0.0517291\pi$
$788$	1.00810	−	0.732431i	0.0359122	−	0.0260918i
$789$	−36.5025	+	35.1828i	−1.29952	+	1.25254i
$790$	−32.0667	−	14.2770i	−1.14088	−	0.507953i
$791$	0.696749	−	0.506218i	0.0247736	−	0.0179990i
$792$	2.56253	−	0.729503i	0.0910556	−	0.0259218i
$793$	−0.502989	−	0.223945i	−0.0178617	−	0.00795253i
$794$	7.19836	+	5.22992i	0.255460	+	0.185603i
$795$	−4.91604	+	27.7255i	−0.174354	+	0.983321i
$796$	10.5143	+	7.63907i	0.372669	+	0.270760i
$797$	6.71570	−	20.6688i	0.237882	−	0.732127i	−0.758844	−	0.651273i	$-0.774235\pi$
$797$	6.71570	−	20.6688i	0.237882	−	0.732127i	0.996726	−	0.0808538i	$-0.0257647\pi$
$798$	−0.946738	−	3.81266i	−0.0335142	−	0.134967i
$799$	2.42585	+	7.46599i	0.0858203	+	0.264128i
$800$	−1.91699	+	3.32033i	−0.0677760	+	0.117391i
$801$	−17.1818	+	35.0579i	−0.607090	+	1.23871i
$802$	−1.87781	−	5.77930i	−0.0663077	−	0.204074i
$803$	10.0423	−	7.29614i	0.354384	−	0.257475i
$804$	−8.01495	+	11.8582i	−0.282666	+	0.418208i
$805$	0.741415	−	1.28417i	0.0261314	−	0.0452610i
$806$	1.36285	+	0.0371387i	0.0480045	+	0.00130816i
$807$	1.29514	+	0.690225i	0.0455911	+	0.0242971i
$808$	−0.402939	+	3.83371i	−0.0141754	+	0.134869i
$809$	−3.74930	−	35.6722i	−0.131818	−	1.25417i	−0.837816	−	0.545953i	$-0.816168\pi$
$809$	−3.74930	−	35.6722i	−0.131818	−	1.25417i	0.705997	−	0.708214i	$-0.250499\pi$
$810$	26.6773	+	1.96783i	0.937346	+	0.0691425i
$811$	10.2001	+	17.6671i	0.358174	+	0.620376i	0.987656	−	0.156639i	$-0.0500661\pi$
$811$	10.2001	+	17.6671i	0.358174	+	0.620376i	−0.629482	+	0.777015i	$0.716733\pi$
$812$	−4.56018			−0.160031
$813$	−2.33070	−	1.95948i	−0.0817412	−	0.0687221i
$814$	3.43601	+	3.81608i	0.120432	+	0.133754i
$815$	11.5257	−	35.4725i	0.403728	−	1.24255i
$816$	5.85371	+	0.414946i	0.204921	+	0.0145260i
$817$	−0.680032	−	0.144545i	−0.0237913	−	0.00505700i
$818$	23.4821	−	10.4549i	0.821032	−	0.365547i
$819$	−0.149164	−	0.855497i	−0.00521221	−	0.0298935i
$820$	−10.6649	−	11.8446i	−0.372436	−	0.413632i
$821$	28.3630	+	12.6280i	0.989876	+	0.440721i	0.836809	−	0.547494i	$-0.184418\pi$
$821$	28.3630	+	12.6280i	0.989876	+	0.440721i	0.153067	+	0.988216i	$0.451085\pi$
$822$	8.64865	−	21.3475i	0.301656	−	0.744579i
$823$	8.39719	−	1.78488i	0.292708	−	0.0622169i	−0.0592175	−	0.998245i	$-0.518861\pi$
$823$	8.39719	−	1.78488i	0.292708	−	0.0622169i	0.351925	+	0.936028i	$0.385527\pi$
$824$	−6.57543	+	4.77733i	−0.229066	+	0.166426i
$825$	3.30260	−	4.88624i	0.114982	−	0.170117i
$826$	7.48214	+	1.59038i	0.260337	+	0.0553364i
$827$	3.79080	−	36.0671i	0.131819	−	1.25417i	−0.705994	−	0.708218i	$-0.749500\pi$
$827$	3.79080	−	36.0671i	0.131819	−	1.25417i	0.837813	−	0.545957i	$-0.183834\pi$
$828$	−0.308639	+	1.22789i	−0.0107259	+	0.0426722i
$829$	13.7969	−	42.4624i	0.479185	−	1.47478i	−0.361045	−	0.932548i	$-0.617580\pi$
$829$	13.7969	−	42.4624i	0.479185	−	1.47478i	0.840230	−	0.542230i	$-0.182420\pi$
$830$	2.86089	+	8.80491i	0.0993029	+	0.305623i
$831$	−44.9756	−	23.9691i	−1.56019	−	0.831477i
$832$	−0.244867			−0.00848923
$833$	−18.5673	−	3.94660i	−0.643318	−	0.136741i
$834$	−10.9518	+	27.0322i	−0.379228	+	0.936050i
$835$	−0.424695	+	4.04070i	−0.0146972	+	0.139834i
$836$	1.70396			0.0589326
$837$	3.88886	−	28.6684i	0.134419	−	0.990925i
$838$	−23.5935			−0.815024
$839$	−4.46670	+	42.4978i	−0.154207	+	1.46719i	0.594399	+	0.804171i	$0.297390\pi$
$839$	−4.46670	+	42.4978i	−0.154207	+	1.46719i	−0.748606	+	0.663015i	$0.769276\pi$
$840$	2.28512	−	5.64037i	0.0788442	−	0.194611i
$841$	13.8108	+	2.93558i	0.476234	+	0.101227i
$842$	−17.7382			−0.611299
$843$	18.5431	+	9.88226i	0.638659	+	0.340363i
$844$	3.82958	+	11.7862i	0.131819	+	0.405698i
$845$	11.8849	−	36.5780i	0.408854	−	1.25832i
$846$	−6.68531	+	1.90318i	−0.229846	+	0.0654327i
$847$	1.26178	−	12.0050i	0.0433553	−	0.412498i
$848$	−5.35015	−	1.13721i	−0.183725	−	0.0390520i
$849$	3.56904	−	5.28044i	0.122489	−	0.181224i
$850$	10.5091	−	7.63534i	0.360461	−	0.261890i
$851$	−2.38683	+	0.507337i	−0.0818195	+	0.0173913i
$852$	−1.32709	+	3.27565i	−0.0454652	+	0.112222i
$853$	2.49793	+	1.11215i	0.0855275	+	0.0380793i	0.449055	−	0.893504i	$-0.351761\pi$
$853$	2.49793	+	1.11215i	0.0855275	+	0.0380793i	−0.363527	+	0.931584i	$0.618428\pi$
$854$	1.77861	+	1.97534i	0.0608627	+	0.0675948i
$855$	16.0647	+	5.88182i	0.549401	+	0.201154i
$856$	−6.68431	+	2.97605i	−0.228465	+	0.101719i
$857$	−24.9521	−	5.30374i	−0.852348	−	0.181172i	−0.239034	−	0.971011i	$-0.576831\pi$
$857$	−24.9521	−	5.30374i	−0.852348	−	0.181172i	−0.613314	+	0.789839i	$0.710164\pi$
$858$	0.375726	+	0.0266337i	0.0128271	+	0.000909260i
$859$	12.2661	−	37.7513i	0.418515	−	1.28806i	−0.490554	−	0.871411i	$-0.663206\pi$
$859$	12.2661	−	37.7513i	0.418515	−	1.28806i	0.909069	−	0.416646i	$-0.136794\pi$
$860$	−0.720651	−	0.800364i	−0.0245740	−	0.0272922i
$861$	8.40438	+	7.06579i	0.286421	+	0.240802i
$862$	−21.8411			−0.743910
$863$	13.8748	+	24.0319i	0.472304	+	0.818054i	0.999498	−	0.0316911i	$-0.0100893\pi$
$863$	13.8748	+	24.0319i	0.472304	+	0.818054i	−0.527194	+	0.849745i	$0.676756\pi$
$864$	−0.557939	+	5.16611i	−0.0189815	+	0.175755i
$865$	−3.19789	−	30.4259i	−0.108731	−	1.03451i
$866$	2.71747	−	25.8550i	0.0923432	−	0.878587i
$867$	8.43845	+	4.49714i	0.286585	+	0.152731i
$868$	−5.93771	−	2.83990i	−0.201539	−	0.0963925i
$869$	−5.24427	+	9.08334i	−0.177900	+	0.308131i
$870$	11.1205	−	16.4530i	0.377021	−	0.557808i
$871$	−1.63701	+	1.18936i	−0.0554681	+	0.0402999i
$872$	5.16845	+	15.9068i	0.175026	+	0.538674i
$873$	−48.3578	+	3.28876i	−1.63666	+	0.111308i
$874$	−0.404857	+	0.701234i	−0.0136945	+	0.0237196i
$875$	1.26600	+	3.89635i	0.0427987	+	0.131721i
$876$	5.83411	+	23.4949i	0.197116	+	0.793818i
$877$	−7.61098	+	23.4242i	−0.257005	+	0.790979i	0.736423	+	0.676521i	$0.236513\pi$
$877$	−7.61098	+	23.4242i	−0.257005	+	0.790979i	−0.993428	+	0.114458i	$0.963487\pi$
$878$	−19.4202	−	14.1096i	−0.655401	−	0.476177i
$879$	−4.64520	+	26.1980i	−0.156679	+	0.883637i
$880$	2.13553	+	1.55155i	0.0719887	+	0.0523028i
$881$	−20.0664	−	8.93412i	−0.676053	−	0.300998i	0.0398423	−	0.999206i	$-0.487314\pi$
$881$	−20.0664	−	8.93412i	−0.676053	−	0.300998i	−0.715895	+	0.698208i	$0.753981\pi$
$882$	4.09725	−	16.3006i	0.137962	−	0.548868i
$883$	2.90537	−	2.11087i	0.0977734	−	0.0710365i	−0.537824	−	0.843057i	$-0.680754\pi$
$883$	2.90537	−	2.11087i	0.0977734	−	0.0710365i	0.635598	+	0.772020i	$0.280754\pi$
$884$	0.757913	+	0.337445i	0.0254914	+	0.0113495i
$885$	−23.9841	+	23.1170i	−0.806218	+	0.777070i
$886$	−10.5094	+	7.63550i	−0.353069	+	0.256520i
$887$	−5.22069	+	49.6716i	−0.175294	+	1.66781i	0.454273	+	0.890862i	$0.349899\pi$
$887$	−5.22069	+	49.6716i	−0.175294	+	1.66781i	−0.629567	+	0.776946i	$0.716768\pi$
$888$	−9.41395	+	3.41623i	−0.315911	+	0.114641i
$889$	7.35297	−	3.27375i	0.246611	−	0.109798i
$890$	−37.8349	+	8.04207i	−1.26823	+	0.269571i
$891$	1.41802	−	7.86625i	0.0475053	−	0.263529i
$892$	−1.62254	−	0.344882i	−0.0543267	−	0.0115475i
$893$	−4.44541			−0.148760
$894$	−0.824132	−	24.2640i	−0.0275631	−	0.811508i
$895$	−21.2887	−	4.52505i	−0.711603	−	0.151256i
$896$	1.07994	+	0.480821i	0.0360783	+	0.0160631i
$897$	−0.100233	+	0.148295i	−0.00334667	+	0.00495144i
$898$	−3.24223	−	5.61571i	−0.108195	−	0.187399i
$899$	−17.0256	−	13.0930i	−0.567837	−	0.436677i
$900$	6.41360	+	9.54782i	0.213787	+	0.318261i
$901$	14.9927	+	10.8928i	0.499478	+	0.362892i
$902$	−3.85297	+	2.79935i	−0.128290	+	0.0932081i
$903$	0.567901	+	0.477450i	0.0188986	+	0.0158885i
$904$	−0.728532			−0.0242306
$905$	−20.5626	−	35.6154i	−0.683523	−	1.18390i
$906$	−5.36878	+	1.94827i	−0.178366	+	0.0647271i
$907$	26.4746	−	5.62735i	0.879075	−	0.186853i	0.253799	−	0.967257i	$-0.418320\pi$
$907$	26.4746	−	5.62735i	0.879075	−	0.186853i	0.625276	+	0.780404i	$0.284986\pi$
$908$	−18.9792	+	4.03415i	−0.629847	+	0.133878i
$909$	9.79552	+	6.14695i	0.324897	+	0.203881i
$910$	0.575691	−	0.639370i	0.0190840	−	0.0211949i
$911$	−46.0052	−	33.4248i	−1.52422	−	1.10741i	−0.959345	−	0.282237i	$-0.908924\pi$
$911$	−46.0052	−	33.4248i	−1.52422	−	1.10741i	−0.564877	−	0.825175i	$-0.691076\pi$
$912$	−1.24781	+	3.07998i	−0.0413193	+	0.101988i
$913$	2.70591	−	0.575160i	0.0895527	−	0.0190350i
$914$	2.61150	+	24.8467i	0.0863806	+	0.821857i
$915$	−11.4643	+	1.60005i	−0.378999	+	0.0528960i
$916$	2.42836	−	7.47372i	0.0802353	−	0.246939i
$917$	−23.1728	−	10.3172i	−0.765235	−	0.340704i
$918$	8.84622	−	15.2213i	0.291969	−	0.502377i
$919$	20.2058	−	22.4408i	0.666526	−	0.740252i	−0.311152	−	0.950360i	$-0.600715\pi$
$919$	20.2058	−	22.4408i	0.666526	−	0.740252i	0.977678	+	0.210108i	$0.0673815\pi$
$920$	−1.14591	+	0.510193i	−0.0377796	+	0.0168206i
$921$	37.3483	+	10.7480i	1.23067	+	0.354160i
$922$	−8.32924	−	9.25055i	−0.274309	−	0.304651i
$923$	−0.334333	+	0.371314i	−0.0110047	+	0.0122220i
$924$	−1.60478	−	0.855241i	−0.0527933	−	0.0281354i
$925$	−11.0840	+	19.1980i	−0.364439	+	0.631226i
$926$	−8.98999	−	27.6683i	−0.295429	−	0.909238i
$927$	4.18823	+	24.0207i	0.137559	+	0.788942i
$928$	3.12082	+	2.26741i	0.102446	+	0.0744313i
$929$	25.3559	+	43.9177i	0.831901	+	1.44089i	0.896529	+	0.442985i	$0.146080\pi$
$929$	25.3559	+	43.9177i	0.831901	+	1.44089i	−0.0646286	+	0.997909i	$0.520586\pi$
$930$	24.7261	−	14.4976i	0.810800	−	0.475396i
$931$	5.37457	−	9.30904i	0.176145	−	0.305091i
$932$	−6.06827	+	2.70177i	−0.198773	+	0.0884993i
$933$	8.98786	+	11.5266i	0.294249	+	0.377364i
$934$	19.3132	−	21.4494i	0.631946	−	0.701847i
$935$	−4.47174	−	7.74529i	−0.146242	−	0.253298i
$936$	−0.323287	+	0.659639i	−0.0105670	+	0.0215610i
$937$	48.8333	+	10.3798i	1.59531	+	0.339094i	0.917994	−	0.396595i	$-0.129808\pi$
$937$	48.8333	+	10.3798i	1.59531	+	0.339094i	0.677319	+	0.735689i	$0.263142\pi$
$938$	9.55520	−	2.03102i	0.311988	−	0.0663152i
$939$	−4.51181	−	18.1697i	−0.147237	−	0.592947i
$940$	−5.57132	−	4.04780i	−0.181716	−	0.132025i
$941$	1.21860	+	3.75045i	0.0397251	+	0.122261i	0.968952	−	0.247247i	$-0.0795260\pi$
$941$	1.21860	+	3.75045i	0.0397251	+	0.122261i	−0.929227	+	0.369509i	$0.879526\pi$
$942$	−32.2570	−	2.28656i	−1.05099	−	0.0745003i
$943$	−0.236563	−	2.25074i	−0.00770354	−	0.0732942i
$944$	−4.32974	−	4.80867i	−0.140921	−	0.156509i
$945$	−12.1775	−	13.6026i	−0.396133	−	0.442491i
$946$	−0.260353	+	0.189158i	−0.00846481	+	0.00615004i
$947$	9.26431	−	28.5126i	0.301050	−	0.926536i	−0.680072	−	0.733145i	$-0.738052\pi$
$947$	9.26431	−	28.5126i	0.301050	−	0.926536i	0.981122	−	0.193391i	$-0.0619485\pi$
$948$	−12.5782	−	16.1310i	−0.408520	−	0.523911i
$949$	−0.357742	+	3.40368i	−0.0116128	+	0.110488i
$950$	2.27312	+	6.99595i	0.0737498	+	0.226978i
$951$	−29.9515	−	2.12314i	−0.971243	−	0.0688475i
$952$	−2.68004	−	2.97648i	−0.0868604	−	0.0964683i
$953$	11.5399	−	35.5162i	0.373814	−	1.15048i	−0.570461	−	0.821325i	$-0.693235\pi$
$953$	11.5399	−	35.5162i	0.373814	−	1.15048i	0.944275	−	0.329157i	$-0.106765\pi$
$954$	−10.1271	+	12.9112i	−0.327876	+	0.418015i
$955$	19.4688	−	33.7210i	0.629997	−	1.09119i
$956$	−11.6623	+	20.1997i	−0.377186	+	0.653306i
$957$	−4.54200	−	3.81858i	−0.146822	−	0.123437i
$958$	34.4883	+	15.3552i	1.11427	+	0.496104i
$959$	−14.3611	+	6.39399i	−0.463745	+	0.206473i
$960$	−4.36836	+	2.72386i	−0.140988	+	0.0879122i
$961$	−14.0149	−	27.6511i	−0.452093	−	0.891971i
$962$	−1.41581			−0.0456475
$963$	−0.807940	+	21.9358i	−0.0260355	+	0.706872i
$964$	−0.248328	−	2.36268i	−0.00799809	−	0.0760968i
$965$	9.79075	−	10.8737i	0.315176	−	0.350038i
$966$	0.733251	−	0.457214i	0.0235920	−	0.0147106i
$967$	6.08526	+	10.5400i	0.195689	+	0.338943i	0.947126	−	0.320861i	$-0.103972\pi$
$967$	6.08526	+	10.5400i	0.195689	+	0.338943i	−0.751437	+	0.659805i	$0.770639\pi$
$968$	−6.83266	+	7.58844i	−0.219610	+	0.243902i
$969$	8.10669	−	7.81360i	0.260424	−	0.251009i
$970$	−32.1319	−	35.6861i	−1.03169	−	1.14581i
$971$	−1.56540	+	14.8938i	−0.0502361	+	0.477964i	0.940263	+	0.340448i	$0.110579\pi$
$971$	−1.56540	+	14.8938i	−0.0502361	+	0.477964i	−0.990499	+	0.137516i	$0.956088\pi$
$972$	13.1802	+	8.32361i	0.422755	+	0.266980i
$973$	18.1854	−	8.09668i	0.582999	−	0.259568i
$974$	2.04583	+	19.4647i	0.0655525	+	0.623691i
$975$	0.391878	+	1.57815i	0.0125501	+	0.0505413i
$976$	−0.235035	−	2.23621i	−0.00752330	−	0.0715794i
$977$	4.96962	+	47.2828i	0.158992	+	1.51271i	0.725252	+	0.688484i	$0.241723\pi$
$977$	4.96962	+	47.2828i	0.158992	+	1.51271i	−0.566260	+	0.824227i	$0.691610\pi$
$978$	15.6495	−	15.0837i	0.500417	−	0.482325i
$979$	1.20813	+	11.4946i	0.0386121	+	0.367369i
$980$	15.2122	−	6.77293i	0.485937	−	0.216353i
$981$	49.6746	+	7.07803i	1.58599	+	0.225984i
$982$	1.28611	−	12.2365i	0.0410413	−	0.390482i
$983$	−1.45682	−	1.61797i	−0.0464655	−	0.0516051i	0.719464	−	0.694530i	$-0.244388\pi$
$983$	−1.45682	−	1.61797i	−0.0464655	−	0.0516051i	−0.765929	+	0.642925i	$0.777721\pi$
$984$	−2.23841	−	9.01440i	−0.0713578	−	0.287368i
$985$	2.47820	−	2.75233i	0.0789622	−	0.0876964i
$986$	−6.53492	−	11.3188i	−0.208114	−	0.360465i
$987$	4.18666	+	2.23121i	0.133263	+	0.0710203i
$988$	−0.314362	+	0.349135i	−0.0100012	+	0.0111075i
$989$	−0.0159850	−	0.152087i	−0.000508294	−	0.00483609i
$990$	6.99912	−	3.70438i	0.222447	−	0.117733i
$991$	10.7587			0.341762			0.170881	−	0.985292i	$-0.445339\pi$
$991$	10.7587			0.341762			0.170881	+	0.985292i	$0.445339\pi$
$992$	2.65150	+	4.89587i	0.0841852	+	0.155444i
$993$	−1.70357	−	50.1564i	−0.0540613	−	1.59166i
$994$	2.20363	−	0.981120i	0.0698949	−	0.0311192i
$995$	35.2883	+	15.7113i	1.11871	+	0.498083i
$996$	−0.941923	+	5.31226i	−0.0298460	+	0.168325i
$997$	10.4072	−	18.0258i	0.329600	−	0.570883i	−0.652833	−	0.757502i	$-0.726420\pi$
$997$	10.4072	−	18.0258i	0.329600	−	0.570883i	0.982432	+	0.186619i	$0.0597529\pi$
$998$	10.8481	−	18.7894i	0.343390	−	0.594770i
$999$	−3.22598	+	29.8702i	−0.102066	+	0.945052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.bb.b.103.7	yes	128
9.7	even	3		558.2.y.b.475.12	yes	128
31.28	even	15		558.2.y.b.121.12	✓	128
279.214	even	15	inner	558.2.bb.b.493.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.y.b.121.12	✓	128	31.28	even	15
558.2.y.b.475.12	yes	128	9.7	even	3
558.2.bb.b.103.7	yes	128	1.1	even	1	trivial
558.2.bb.b.493.7	yes	128	279.214	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.bb (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.650370 + 1.60531i) q^{3} +(-0.978148 - 0.207912i) q^{4} -2.97220 q^{5} +(-1.52853 - 0.814608i) q^{6} +(0.365303 + 1.12429i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.15404 - 2.08809i) q^{9} +(0.310680 - 2.95592i) q^{10} +(-0.868708 - 0.184650i) q^{11} +(0.969921 - 1.43501i) q^{12} +(0.198101 - 0.143929i) q^{13} +(-1.15631 + 0.245782i) q^{14} +(1.93303 - 4.77130i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-2.26710 - 2.51787i) q^{17} +(2.30181 - 1.92397i) q^{18} +(1.75275 - 0.780374i) q^{19} +(2.90725 + 0.617956i) q^{20} +(-2.04241 - 0.144778i) q^{21} +(0.274443 - 0.844648i) q^{22} +(0.282393 + 0.313629i) q^{23} +(1.32576 + 1.11461i) q^{24} +3.83399 q^{25} +(0.122433 + 0.212061i) q^{26} +(4.75295 - 2.09987i) q^{27} +(-0.123568 - 1.17567i) q^{28} +(0.403223 - 3.83641i) q^{29} +(4.54311 + 2.42118i) q^{30} +(2.91420 - 4.74420i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.861401 - 1.27445i) q^{33} +(2.74105 - 1.99149i) q^{34} +(-1.08575 - 3.34161i) q^{35} +(1.67283 + 2.49031i) q^{36} +(-2.89098 + 5.00732i) q^{37} +(0.592887 + 1.82472i) q^{38} +(0.102212 + 0.411621i) q^{39} +(-0.918461 + 2.82673i) q^{40} +(-4.33837 - 3.15201i) q^{41} +(0.357475 - 2.01609i) q^{42} +(-0.293152 - 0.212988i) q^{43} +(0.811334 + 0.361229i) q^{44} +(6.40224 + 6.20623i) q^{45} +(-0.341429 + 0.248063i) q^{46} +(-2.11667 - 0.942400i) q^{47} +(-1.24708 + 1.20199i) q^{48} +(4.53255 - 3.29309i) q^{49} +(-0.400761 + 3.81298i) q^{50} +(5.51641 - 2.00185i) q^{51} +(-0.223697 + 0.0995963i) q^{52} +(-5.35015 + 1.13721i) q^{53} +(1.59154 + 4.94641i) q^{54} +(2.58198 + 0.548816i) q^{55} +1.18214 q^{56} +(0.112807 + 3.32124i) q^{57} +(3.77325 + 0.802029i) q^{58} +(-5.91128 - 2.63187i) q^{59} +(-2.88280 + 4.26514i) q^{60} +(-1.12426 - 1.94728i) q^{61} +(4.41360 + 3.39414i) q^{62} +(1.56073 - 3.18454i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.588798 + 0.427786i) q^{65} +(1.17743 + 0.989899i) q^{66} -8.26352 q^{67} +(1.69406 + 2.93420i) q^{68} +(-0.687131 + 0.249353i) q^{69} +(3.43679 - 0.730513i) q^{70} +(-1.99592 + 0.424245i) q^{71} +(-2.65153 + 1.40336i) q^{72} +(-9.35224 + 10.3867i) q^{73} +(-4.67770 - 3.39855i) q^{74} +(-2.49351 + 6.15474i) q^{75} +(-1.87670 + 0.398904i) q^{76} +(-0.109742 - 1.04413i) q^{77} +(-0.420050 + 0.0586255i) q^{78} +(3.64946 - 11.2319i) q^{79} +(-2.71524 - 1.20890i) q^{80} +(0.279756 + 8.99565i) q^{81} +(3.58823 - 3.98513i) q^{82} +(-2.84558 + 1.26693i) q^{83} +(1.96768 + 0.566255i) q^{84} +(6.73827 + 7.48361i) q^{85} +(0.242464 - 0.269283i) q^{86} +(5.89639 + 3.14239i) q^{87} +(-0.444058 + 0.769130i) q^{88} +(-4.02154 - 12.3770i) q^{89} +(-6.84145 + 5.71844i) q^{90} +(0.234184 + 0.170145i) q^{91} +(-0.211015 - 0.365488i) q^{92} +(5.72060 + 7.76368i) q^{93} +(1.15849 - 2.00656i) q^{94} +(-5.20952 + 2.31943i) q^{95} +(-1.06505 - 1.36589i) q^{96} +(10.8108 - 12.0066i) q^{97} +(2.80127 + 4.85194i) q^{98} +(1.48566 + 2.21168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 2 q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 32 q^{8} - 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 20 q^{13} - q^{14} - 22 q^{15} + 16 q^{16} + 4 q^{17} - 2 q^{18} - 4 q^{19} + q^{20}+ \cdots + 15 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 32 * q^8 - 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 - 20 * q^13 - q^14 - 22 * q^15 + 16 * q^16 + 4 * q^17 - 2 * q^18 - 4 * q^19 + q^20 + 19 * q^21 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 122 * q^25 - 20 * q^26 - 37 * q^27 + 9 * q^28 - 12 * q^29 - 14 * q^30 + 25 * q^31 - 64 * q^32 + 22 * q^33 - 8 * q^34 + 6 * q^36 - 66 * q^37 - 12 * q^38 + 11 * q^39 - 2 * q^40 + 20 * q^41 + 10 * q^42 - 31 * q^43 + 2 * q^44 + 64 * q^45 + 13 * q^46 + 11 * q^47 - 3 * q^48 - 46 * q^49 + 19 * q^50 + 17 * q^51 + 10 * q^52 + 27 * q^53 - 13 * q^54 - 19 * q^55 + 2 * q^56 + 20 * q^57 + 3 * q^58 - 9 * q^59 + 11 * q^60 - 57 * q^61 + 14 * q^62 - 38 * q^63 - 32 * q^64 - 66 * q^65 - 20 * q^66 - 16 * q^67 - 16 * q^68 - 8 * q^69 - 7 * q^71 + q^72 - 7 * q^73 - 28 * q^74 + 74 * q^75 + 6 * q^76 + 46 * q^77 - 24 * q^78 - 48 * q^79 - 9 * q^80 - 64 * q^81 + 50 * q^82 - 99 * q^83 + q^84 + 27 * q^85 + 33 * q^86 + 81 * q^87 - 8 * q^88 - 52 * q^89 - 45 * q^90 + 11 * q^91 + q^92 + 30 * q^93 + 6 * q^94 + 19 * q^95 - 4 * q^96 + 35 * q^97 - 77 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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