LMFDB - Embedded newform 669.2.i.b.4.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [720] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$20$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	669.4
Dual form			669.2.i.b.502.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923374 - 0.326249i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-0.809890 + 0.653940i) q^{4} +(-0.542942 - 0.881794i) q^{5} +(0.0415633 - 0.978433i) q^{6} +(-0.395566 + 3.08903i) q^{7} +(-1.56141 + 2.53589i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-0.789024 - 0.637092i) q^{10} +(-0.114373 + 2.69244i) q^{11} +(0.304811 + 0.995313i) q^{12} +(0.786933 + 1.95836i) q^{13} +(0.642538 + 2.98139i) q^{14} +(-1.02065 + 0.175007i) q^{15} +(-0.175824 + 0.815827i) q^{16} +(-0.173781 + 4.09095i) q^{17} +(-0.892380 - 0.403381i) q^{18} +(2.86357 - 0.745617i) q^{19} +(1.01636 + 0.359104i) q^{20} +(2.71879 + 1.51881i) q^{21} +(0.772796 + 2.52344i) q^{22} +(1.80851 + 2.93720i) q^{23} +(1.77084 + 2.39434i) q^{24} +(1.76824 - 3.50710i) q^{25} +(1.36555 + 1.55156i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(-1.69968 - 2.76045i) q^{28} +(-0.941045 + 4.36647i) q^{29} +(-0.885343 + 0.494582i) q^{30} +(-4.74931 + 0.404226i) q^{31} +(-0.652717 - 5.09716i) q^{32} +(2.45564 + 1.11002i) q^{33} +(1.17420 + 3.83417i) q^{34} +(2.93866 - 1.32836i) q^{35} +(1.03719 + 0.0882780i) q^{36} +(-0.332228 - 7.82089i) q^{37} +(2.40089 - 1.62272i) q^{38} +2.11055 q^{39} +3.08389 q^{40} +(-5.28595 + 3.57268i) q^{41} +(3.00597 + 0.515425i) q^{42} +(1.89066 + 3.74989i) q^{43} +(-1.66806 - 2.25537i) q^{44} +(-0.218167 + 1.01230i) q^{45} +(2.62819 + 2.12211i) q^{46} +(6.47331 + 1.68552i) q^{47} +(0.691440 + 0.467332i) q^{48} +(-2.61151 - 0.679984i) q^{49} +(0.488563 - 3.81526i) q^{50} +(3.73115 + 1.68659i) q^{51} +(-1.91798 - 1.07145i) q^{52} +(-4.47330 + 5.08265i) q^{53} +(-0.707023 + 0.677626i) q^{54} +(2.43628 - 1.36099i) q^{55} +(-7.21580 - 5.82635i) q^{56} +(0.375853 - 2.93509i) q^{57} +(0.555618 + 4.33890i) q^{58} +(0.822438 - 2.68554i) q^{59} +(0.712167 - 0.809179i) q^{60} +(-1.68521 - 4.19381i) q^{61} +(-4.25351 + 1.92271i) q^{62} +(2.42300 - 1.95644i) q^{63} +(-3.01709 - 5.98404i) q^{64} +(1.29961 - 1.75719i) q^{65} +(2.62962 + 0.223814i) q^{66} +(-4.54819 + 3.67241i) q^{67} +(-2.53449 - 3.42686i) q^{68} +(3.39971 - 0.582939i) q^{69} +(2.28011 - 2.18531i) q^{70} +(-0.486560 + 1.58879i) q^{71} +(2.88195 - 0.750401i) q^{72} +(6.89434 + 3.85141i) q^{73} +(-2.85833 - 7.11323i) q^{74} +(-2.59490 - 2.94838i) q^{75} +(-1.83159 + 2.47647i) q^{76} +(-8.27179 - 1.41834i) q^{77} +(1.94883 - 0.688565i) q^{78} +(4.53403 - 3.06447i) q^{79} +(0.814854 - 0.287906i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-3.71533 + 5.02345i) q^{82} +(-3.36588 + 6.67582i) q^{83} +(-3.19513 + 0.547860i) q^{84} +(3.70173 - 2.06791i) q^{85} +(2.96918 + 2.84573i) q^{86} +(3.70072 + 2.50125i) q^{87} +(-6.64914 - 4.49404i) q^{88} +(3.32810 - 5.40519i) q^{89} +(0.128812 + 1.00591i) q^{90} +(-6.36071 + 1.65620i) q^{91} +(-3.38544 - 1.19615i) q^{92} +(-1.39573 + 4.55755i) q^{93} +(6.52719 - 0.555546i) q^{94} +(-2.21224 - 2.12026i) q^{95} +(-4.97297 - 1.29486i) q^{96} +(-0.409311 + 0.664763i) q^{97} +(-2.63324 + 0.224122i) q^{98} +(1.94558 - 1.86468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) $ 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

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 $

$2$	0.923374	−	0.326249i	0.652924	−	0.230693i	0.0139284	−	0.999903i	$-0.495566\pi$
$2$	0.923374	−	0.326249i	0.652924	−	0.230693i	0.638996	+	0.769210i	$0.279350\pi$
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$4$	−0.809890	+	0.653940i	−0.404945	+	0.326970i
$5$	−0.542942	−	0.881794i	−0.242811	−	0.394350i	0.706981	−	0.707233i	$-0.250057\pi$
$5$	−0.542942	−	0.881794i	−0.242811	−	0.394350i	−0.949792	+	0.312882i	$0.898705\pi$
$6$	0.0415633	−	0.978433i	0.0169682	−	0.399444i
$7$	−0.395566	+	3.08903i	−0.149510	+	1.16754i	0.727166	+	0.686462i	$0.240837\pi$
$7$	−0.395566	+	3.08903i	−0.149510	+	1.16754i	−0.876676	+	0.481082i	$0.840244\pi$
$8$	−1.56141	+	2.53589i	−0.552041	+	0.896572i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	−0.789024	−	0.637092i	−0.249511	−	0.201466i
$11$	−0.114373	+	2.69244i	−0.0344849	+	0.811801i	0.895689	+	0.444681i	$0.146683\pi$
$11$	−0.114373	+	2.69244i	−0.0344849	+	0.811801i	−0.930174	+	0.367120i	$0.880344\pi$
$12$	0.304811	+	0.995313i	0.0879914	+	0.287322i
$13$	0.786933	+	1.95836i	0.218256	+	0.543151i	0.996385	−	0.0849537i	$-0.0270742\pi$
$13$	0.786933	+	1.95836i	0.218256	+	0.543151i	−0.778129	+	0.628105i	$0.783831\pi$
$14$	0.642538	+	2.98139i	0.171725	+	0.796809i
$15$	−1.02065	+	0.175007i	−0.263530	+	0.0451867i
$16$	−0.175824	+	0.815827i	−0.0439560	+	0.203957i
$17$	−0.173781	+	4.09095i	−0.0421482	+	0.992200i	0.846153	+	0.532940i	$0.178913\pi$
$17$	−0.173781	+	4.09095i	−0.0421482	+	0.992200i	−0.888301	+	0.459261i	$0.848114\pi$
$18$	−0.892380	−	0.403381i	−0.210336	−	0.0950779i
$19$	2.86357	−	0.745617i	0.656949	−	0.171056i	0.0914557	−	0.995809i	$-0.470848\pi$
$19$	2.86357	−	0.745617i	0.656949	−	0.171056i	0.565493	+	0.824753i	$0.308686\pi$
$20$	1.01636	+	0.359104i	0.227266	+	0.0802982i
$21$	2.71879	+	1.51881i	0.593288	+	0.331431i
$22$	0.772796	+	2.52344i	0.164761	+	0.538000i
$23$	1.80851	+	2.93720i	0.377099	+	0.612448i	0.983112	−	0.183007i	$-0.0585831\pi$
$23$	1.80851	+	2.93720i	0.377099	+	0.612448i	−0.606012	+	0.795455i	$0.707232\pi$
$24$	1.77084	+	2.39434i	0.361472	+	0.488742i
$25$	1.76824	−	3.50710i	0.353649	−	0.701420i
$26$	1.36555	+	1.55156i	0.267806	+	0.304286i
$27$	−0.911228	+	0.411901i	−0.175366	+	0.0792704i
$28$	−1.69968	−	2.76045i	−0.321209	−	0.521676i
$29$	−0.941045	+	4.36647i	−0.174748	+	0.810832i	0.802150	+	0.597123i	$0.203690\pi$
$29$	−0.941045	+	4.36647i	−0.174748	+	0.810832i	−0.976897	+	0.213709i	$0.931446\pi$
$30$	−0.885343	+	0.494582i	−0.161641	+	0.0902980i
$31$	−4.74931	+	0.404226i	−0.853002	+	0.0726011i	−0.503145	−	0.864202i	$-0.667824\pi$
$31$	−4.74931	+	0.404226i	−0.853002	+	0.0726011i	−0.349857	+	0.936803i	$0.613770\pi$
$32$	−0.652717	−	5.09716i	−0.115385	−	0.901060i
$33$	2.45564	+	1.11002i	0.427472	+	0.193230i
$34$	1.17420	+	3.83417i	0.201374	+	0.657555i
$35$	2.93866	−	1.32836i	0.496724	−	0.224533i
$36$	1.03719	+	0.0882780i	0.172865	+	0.0147130i
$37$	−0.332228	−	7.82089i	−0.0546179	−	1.28575i	−0.792105	−	0.610385i	$-0.791015\pi$
$37$	−0.332228	−	7.82089i	−0.0546179	−	1.28575i	0.737487	−	0.675362i	$-0.236012\pi$
$38$	2.40089	−	1.62272i	0.389476	−	0.263240i
$39$	2.11055			0.337959
$40$	3.08389			0.487605
$41$	−5.28595	+	3.57268i	−0.825526	+	0.557958i	−0.898296	−	0.439390i	$-0.855195\pi$
$41$	−5.28595	+	3.57268i	−0.825526	+	0.557958i	0.0727699	+	0.997349i	$0.476816\pi$
$42$	3.00597	+	0.515425i	0.463831	+	0.0795318i
$43$	1.89066	+	3.74989i	0.288322	+	0.571853i	0.990070	−	0.140572i	$-0.0448941\pi$
$43$	1.89066	+	3.74989i	0.288322	+	0.571853i	−0.701748	+	0.712425i	$0.747597\pi$
$44$	−1.66806	−	2.25537i	−0.251470	−	0.340010i
$45$	−0.218167	+	1.01230i	−0.0325225	+	0.150905i
$46$	2.62819	+	2.12211i	0.387505	+	0.312888i
$47$	6.47331	+	1.68552i	0.944229	+	0.245858i	0.692072	−	0.721828i	$-0.256698\pi$
$47$	6.47331	+	1.68552i	0.944229	+	0.245858i	0.252157	+	0.967686i	$0.418860\pi$
$48$	0.691440	+	0.467332i	0.0998007	+	0.0674535i
$49$	−2.61151	−	0.679984i	−0.373073	−	0.0971406i
$50$	0.488563	−	3.81526i	0.0690932	−	0.539559i
$51$	3.73115	+	1.68659i	0.522465	+	0.236169i
$52$	−1.91798	−	1.07145i	−0.265976	−	0.148583i
$53$	−4.47330	+	5.08265i	−0.614455	+	0.698156i	−0.971797	−	0.235817i	$-0.924223\pi$
$53$	−4.47330	+	5.08265i	−0.614455	+	0.698156i	0.357343	+	0.933973i	$0.383683\pi$
$54$	−0.707023	+	0.677626i	−0.0962136	+	0.0922133i
$55$	2.43628	−	1.36099i	0.328507	−	0.183515i
$56$	−7.21580	−	5.82635i	−0.964252	−	0.778579i
$57$	0.375853	−	2.93509i	0.0497829	−	0.388762i
$58$	0.555618	+	4.33890i	0.0729562	+	0.569725i
$59$	0.822438	−	2.68554i	0.107072	−	0.349628i	−0.886514	−	0.462701i	$-0.846880\pi$
$59$	0.822438	−	2.68554i	0.107072	−	0.349628i	0.993587	+	0.113073i	$0.0360695\pi$
$60$	0.712167	−	0.809179i	0.0919403	−	0.104465i
$61$	−1.68521	−	4.19381i	−0.215769	−	0.536962i	0.780314	−	0.625388i	$-0.215059\pi$
$61$	−1.68521	−	4.19381i	−0.215769	−	0.536962i	−0.996083	+	0.0884264i	$0.971816\pi$
$62$	−4.25351	+	1.92271i	−0.540197	+	0.244184i
$63$	2.42300	−	1.95644i	0.305270	−	0.246488i
$64$	−3.01709	−	5.98404i	−0.377136	−	0.748005i
$65$	1.29961	−	1.75719i	0.161197	−	0.217952i
$66$	2.62962	+	0.223814i	0.323684	+	0.0275495i
$67$	−4.54819	+	3.67241i	−0.555650	+	0.448656i	−0.864628	−	0.502413i	$-0.832446\pi$
$67$	−4.54819	+	3.67241i	−0.555650	+	0.448656i	0.308977	+	0.951069i	$0.400013\pi$
$68$	−2.53449	−	3.42686i	−0.307352	−	0.415568i
$69$	3.39971	−	0.582939i	0.409277	−	0.0701776i
$70$	2.28011	−	2.18531i	0.272525	−	0.261194i
$71$	−0.486560	+	1.58879i	−0.0577441	+	0.188554i	−0.980380	−	0.197119i	$-0.936842\pi$
$71$	−0.486560	+	1.58879i	−0.0577441	+	0.188554i	0.922636	+	0.385673i	$0.126031\pi$
$72$	2.88195	−	0.750401i	0.339641	−	0.0884356i
$73$	6.89434	+	3.85141i	0.806921	+	0.450773i	0.835950	−	0.548805i	$-0.184917\pi$
$73$	6.89434	+	3.85141i	0.806921	+	0.450773i	−0.0290291	+	0.999579i	$0.509242\pi$
$74$	−2.85833	−	7.11323i	−0.332274	−	0.826896i
$75$	−2.59490	−	2.94838i	−0.299633	−	0.340450i
$76$	−1.83159	+	2.47647i	−0.210098	+	0.284071i
$77$	−8.27179	−	1.41834i	−0.942658	−	0.161635i
$78$	1.94883	−	0.688565i	0.220662	−	0.0779647i
$79$	4.53403	−	3.06447i	0.510119	−	0.344780i	−0.277720	−	0.960662i	$-0.589579\pi$
$79$	4.53403	−	3.06447i	0.510119	−	0.344780i	0.787838	+	0.615882i	$0.211200\pi$
$80$	0.814854	−	0.287906i	0.0911035	−	0.0321889i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	−3.71533	+	5.02345i	−0.410289	+	0.554748i
$83$	−3.36588	+	6.67582i	−0.369453	+	0.732766i	−0.999024	−	0.0441768i	$-0.985934\pi$
$83$	−3.36588	+	6.67582i	−0.369453	+	0.732766i	0.629571	+	0.776943i	$0.283231\pi$
$84$	−3.19513	+	0.547860i	−0.348617	+	0.0597764i
$85$	3.70173	−	2.06791i	0.401509	−	0.224296i
$86$	2.96918	+	2.84573i	0.320175	+	0.306863i
$87$	3.70072	+	2.50125i	0.396759	+	0.268162i
$88$	−6.64914	−	4.49404i	−0.708801	−	0.479066i
$89$	3.32810	−	5.40519i	0.352778	−	0.572949i	−0.625505	−	0.780220i	$-0.715107\pi$
$89$	3.32810	−	5.40519i	0.352778	−	0.572949i	0.978283	+	0.207272i	$0.0664584\pi$
$90$	0.128812	+	1.00591i	0.0135779	+	0.106032i
$91$	−6.36071	+	1.65620i	−0.666784	+	0.173617i
$92$	−3.38544	−	1.19615i	−0.352957	−	0.124708i
$93$	−1.39573	+	4.55755i	−0.144731	+	0.472596i
$94$	6.52719	−	0.555546i	0.673228	−	0.0573002i
$95$	−2.21224	−	2.12026i	−0.226971	−	0.217534i
$96$	−4.97297	−	1.29486i	−0.507552	−	0.132156i
$97$	−0.409311	+	0.664763i	−0.0415592	+	0.0674965i	−0.871640	−	0.490147i	$-0.836943\pi$
$97$	−0.409311	+	0.664763i	−0.0415592	+	0.0674965i	0.830080	+	0.557644i	$0.188294\pi$
$98$	−2.63324	+	0.224122i	−0.265998	+	0.0226398i
$99$	1.94558	−	1.86468i	0.195538	−	0.187408i
$100$	0.861353	+	3.99669i	0.0861353	+	0.399669i
$101$	−3.96932	−	4.51002i	−0.394962	−	0.448764i	0.518872	−	0.854852i	$-0.326352\pi$
$101$	−3.96932	−	4.51002i	−0.394962	−	0.448764i	−0.913834	+	0.406088i	$0.866893\pi$
$102$	3.99549	+	0.340067i	0.395613	+	0.0336716i
$103$	0.0744472	−	0.185269i	0.00733550	−	0.0182551i	−0.924176	−	0.381966i	$-0.875247\pi$
$103$	0.0744472	−	0.185269i	0.00733550	−	0.0182551i	0.931512	+	0.363711i	$0.118490\pi$
$104$	−6.19490	−	1.06222i	−0.607460	−	0.104160i
$105$	−0.136870	−	3.22204i	−0.0133572	−	0.314439i
$106$	−2.47232	+	6.15260i	−0.240133	+	0.597593i
$107$	0.0871504	+	0.172852i	0.00842514	+	0.0167103i	0.897099	−	0.441829i	$-0.145670\pi$
$107$	0.0871504	+	0.172852i	0.00842514	+	0.0167103i	−0.888674	+	0.458539i	$0.848373\pi$
$108$	0.468636	−	0.929483i	0.0450945	−	0.0894396i
$109$	−1.36443	−	6.33100i	−0.130689	−	0.606399i	−0.994691	−	0.102910i	$-0.967185\pi$
$109$	−1.36443	−	6.33100i	−0.130689	−	0.606399i	0.864002	−	0.503489i	$-0.167951\pi$
$110$	1.80558	−	2.05153i	0.172155	−	0.195606i
$111$	−7.38080	−	2.60780i	−0.700554	−	0.247522i
$112$	−2.45056	−	0.865840i	−0.231557	−	0.0818142i
$113$	7.94291	−	9.02489i	0.747206	−	0.848991i	−0.245520	−	0.969392i	$-0.578959\pi$
$113$	7.94291	−	9.02489i	0.747206	−	0.848991i	0.992725	+	0.120401i	$0.0384180\pi$
$114$	−0.610516	−	2.83281i	−0.0571801	−	0.265317i
$115$	1.60809	−	3.18946i	0.149955	−	0.297419i
$116$	−2.09326	−	4.15174i	−0.194355	−	0.385480i
$117$	0.786933	−	1.95836i	0.0727520	−	0.181050i
$118$	−0.116737	−	2.74808i	−0.0107465	−	0.252981i
$119$	−12.5683	−	2.15505i	−1.15214	−	0.197554i
$120$	1.14985	−	2.86150i	0.104966	−	0.261218i
$121$	3.72422	+	0.316978i	0.338566	+	0.0288162i
$122$	−2.92431	−	3.32266i	−0.264754	−	0.300819i
$123$	1.34415	+	6.23687i	0.121198	+	0.562360i
$124$	3.58208	−	3.43314i	0.321680	−	0.308305i
$125$	−9.21166	+	0.784027i	−0.823916	+	0.0701255i
$126$	1.59905	−	2.59703i	0.142455	−	0.231361i
$127$	3.06499	+	0.798062i	0.271974	+	0.0708165i	0.385465	−	0.922723i	$-0.374041\pi$
$127$	3.06499	+	0.798062i	0.271974	+	0.0708165i	−0.113491	+	0.993539i	$0.536203\pi$
$128$	2.68177	+	2.57026i	0.237037	+	0.227181i
$129$	4.18443	−	0.356147i	0.368418	−	0.0313570i
$130$	0.626746	−	2.04654i	0.0549692	−	0.179493i
$131$	−4.05609	−	1.43311i	−0.354382	−	0.125211i	0.150013	−	0.988684i	$-0.452068\pi$
$131$	−4.05609	−	1.43311i	−0.354382	−	0.125211i	−0.504395	+	0.863473i	$0.668285\pi$
$132$	−2.71468	+	0.706849i	−0.236283	+	0.0615233i
$133$	1.17050	+	9.14061i	0.101495	+	0.792591i
$134$	−3.00157	+	4.87485i	−0.259296	+	0.421123i
$135$	0.857957	+	0.579878i	0.0738412	+	0.0499079i
$136$	−10.1028	−	6.82833i	−0.866311	−	0.585524i
$137$	5.04181	+	4.83219i	0.430751	+	0.412841i	0.875807	−	0.482661i	$-0.160330\pi$
$137$	5.04181	+	4.83219i	0.430751	+	0.412841i	−0.445056	+	0.895503i	$0.646816\pi$
$138$	2.94902	−	1.64742i	0.251037	−	0.140238i
$139$	18.1304	−	3.10876i	1.53780	−	0.263682i	0.663167	−	0.748472i	$-0.269212\pi$
$139$	18.1304	−	3.10876i	1.53780	−	0.263682i	0.874631	+	0.484790i	$0.161104\pi$
$140$	−1.51132	+	2.99753i	−0.127730	+	0.253338i
$141$	3.97759	−	5.37806i	0.334974	−	0.452914i
$142$	0.0690624	+	1.62578i	0.00579559	+	0.136433i
$143$	−5.36277	+	1.89479i	−0.448457	+	0.158450i
$144$	0.691440	−	0.467332i	0.0576200	−	0.0389443i
$145$	4.36126	−	1.54093i	0.362183	−	0.127967i
$146$	7.62257	+	1.30702i	0.630848	+	0.108170i
$147$	−1.60467	+	2.16965i	−0.132351	+	0.178950i
$148$	5.38346	+	6.11680i	0.442518	+	0.502798i
$149$	−1.09289	−	2.71977i	−0.0895334	−	0.222812i	0.876410	−	0.481566i	$-0.159932\pi$
$149$	−1.09289	−	2.71977i	−0.0895334	−	0.222812i	−0.965944	+	0.258753i	$0.916688\pi$
$150$	−3.35797	−	1.87587i	−0.274177	−	0.153165i
$151$	16.2778	−	4.23842i	1.32467	−	0.344918i	0.478622	−	0.878021i	$-0.341136\pi$
$151$	16.2778	−	4.23842i	1.32467	−	0.344918i	0.846050	+	0.533103i	$0.178974\pi$
$152$	−2.58041	+	8.42592i	−0.209299	+	0.683432i
$153$	2.95615	−	2.83324i	0.238990	−	0.229054i
$154$	−8.10069	+	1.38900i	−0.652772	+	0.111929i
$155$	2.93505	+	3.96845i	0.235749	+	0.318753i
$156$	−1.70931	+	1.38017i	−0.136855	+	0.110502i
$157$	−11.4467	−	0.974257i	−0.913545	−	0.0777542i	−0.381403	−	0.924409i	$-0.624559\pi$
$157$	−11.4467	−	0.974257i	−0.913545	−	0.0777542i	−0.532143	+	0.846655i	$0.678613\pi$
$158$	3.18683	−	4.30888i	0.253531	−	0.342796i
$159$	3.04824	+	6.04582i	0.241741	+	0.479465i
$160$	−4.14026	+	3.34303i	−0.327316	+	0.264290i
$161$	−9.78848	+	4.42467i	−0.771441	+	0.348713i
$162$	0.365144	+	0.908696i	0.0286884	+	0.0713939i
$163$	11.8294	−	13.4408i	0.926550	−	1.05276i	−0.0719172	−	0.997411i	$-0.522912\pi$
$163$	11.8294	−	13.4408i	0.926550	−	1.05276i	0.998467	−	0.0553542i	$-0.0176288\pi$
$164$	1.94472	−	6.35017i	0.151857	−	0.495865i
$165$	−0.354462	−	2.76805i	−0.0275948	−	0.215492i
$166$	−0.929986	+	7.26239i	−0.0721809	+	0.563671i
$167$	−11.3152	−	9.13636i	−0.875594	−	0.706993i	0.0815298	−	0.996671i	$-0.474019\pi$
$167$	−11.3152	−	9.13636i	−0.875594	−	0.706993i	−0.957124	+	0.289678i	$0.906452\pi$
$168$	−8.09666	+	4.52307i	−0.624671	+	0.348962i
$169$	6.16953	−	5.91301i	0.474579	−	0.454847i
$170$	2.74343	−	3.11714i	0.210411	−	0.239074i
$171$	−2.58330	−	1.44312i	−0.197550	−	0.110358i
$172$	−3.98343	−	1.80062i	−0.303734	−	0.137296i
$173$	−1.56127	+	12.1922i	−0.118701	+	0.926956i	0.817607	+	0.575777i	$0.195300\pi$
$173$	−1.56127	+	12.1922i	−0.118701	+	0.926956i	−0.936308	+	0.351179i	$0.885781\pi$
$174$	4.23318	+	1.10223i	0.320917	+	0.0835602i
$175$	10.1341	+	6.84945i	0.766065	+	0.517770i
$176$	−2.17646	−	0.566705i	−0.164057	−	0.0427170i
$177$	−2.18523	−	1.76445i	−0.164252	−	0.132624i
$178$	1.30965	−	6.07680i	0.0981625	−	0.455475i
$179$	9.52384	+	12.8771i	0.711845	+	0.962478i	0.999988	+	0.00489100i	$0.00155686\pi$
$179$	9.52384	+	12.8771i	0.711845	+	0.962478i	−0.288143	+	0.957587i	$0.593038\pi$
$180$	−0.485292	−	0.962519i	−0.0361715	−	0.0717420i
$181$	−10.5601	−	1.81071i	−0.784928	−	0.134589i	−0.237439	−	0.971402i	$-0.576308\pi$
$181$	−10.5601	−	1.81071i	−0.784928	−	0.134589i	−0.547489	+	0.836813i	$0.684416\pi$
$182$	−5.33299	+	3.60447i	−0.395307	+	0.267181i
$183$	−4.51973			−0.334108
$184$	−10.2722			−0.757279
$185$	−6.71604	+	4.53925i	−0.493773	+	0.333732i
$186$	0.198111	+	4.66368i	0.0145262	+	0.341958i
$187$	−10.9948	−	0.935791i	−0.804016	−	0.0684318i
$188$	−6.34490	+	2.86807i	−0.462749	+	0.209176i
$189$	−0.911925	−	2.97775i	−0.0663328	−	0.216599i
$190$	−2.73445	−	1.23605i	−0.198378	−	0.0896726i
$191$	−1.30911	−	10.2231i	−0.0947241	−	0.739714i	−0.967727	−	0.252000i	$-0.918912\pi$
$191$	−1.30911	−	10.2231i	−0.0947241	−	0.739714i	0.873003	−	0.487715i	$-0.162169\pi$
$192$	−6.67747	+	0.568336i	−0.481905	+	0.0410161i
$193$	−2.70344	+	1.51023i	−0.194598	+	0.108709i	−0.581955	−	0.813221i	$-0.697712\pi$
$193$	−2.70344	+	1.51023i	−0.194598	+	0.108709i	0.387358	+	0.921930i	$0.373388\pi$
$194$	−0.161069	+	0.747363i	−0.0115641	+	0.0536575i
$195$	−1.14591	−	1.86107i	−0.0820602	−	0.133274i
$196$	2.55970	−	1.15706i	0.182836	−	0.0826470i
$197$	5.97870	+	6.79312i	0.425965	+	0.483990i	0.923579	−	0.383409i	$-0.125250\pi$
$197$	5.97870	+	6.79312i	0.425965	+	0.483990i	−0.497614	+	0.867398i	$0.665790\pi$
$198$	1.18814	−	2.35654i	0.0844377	−	0.167472i
$199$	9.28187	+	12.5499i	0.657975	+	0.889640i	0.998723	−	0.0505141i	$-0.0160860\pi$
$199$	9.28187	+	12.5499i	0.657975	+	0.889640i	−0.340749	+	0.940154i	$0.610681\pi$
$200$	6.13267	+	9.96009i	0.433645	+	0.704285i
$201$	1.71177	+	5.58950i	0.120739	+	0.394253i
$202$	−5.13656	−	2.86945i	−0.361407	−	0.201894i
$203$	−13.1159	−	4.63414i	−0.920556	−	0.325253i
$204$	−4.12474	+	1.07400i	−0.288790	+	0.0751950i
$205$	6.02033	+	2.72136i	0.420478	+	0.190068i
$206$	0.00829883	−	0.195361i	0.000578207	−	0.0136114i
$207$	0.726701	−	3.37190i	0.0505092	−	0.234364i
$208$	−1.73604	+	0.297675i	−0.120373	+	0.0206400i
$209$	1.68001	+	7.79528i	0.116209	+	0.539211i
$210$	−1.17757	−	2.93049i	−0.0812600	−	0.202223i
$211$	−2.80117	−	9.14680i	−0.192841	−	0.629691i	−0.999264	−	0.0383529i	$-0.987789\pi$
$211$	−2.80117	−	9.14680i	−0.192841	−	0.629691i	0.806423	−	0.591339i	$-0.201400\pi$
$212$	0.299126	−	7.04166i	0.0205440	−	0.483623i
$213$	1.29280	+	1.04386i	0.0885812	+	0.0715243i
$214$	0.136865	+	0.131175i	0.00935592	+	0.00896693i
$215$	2.28012	−	3.70315i	0.155503	−	0.252553i
$216$	0.378264	−	2.95392i	0.0257376	−	0.200989i
$217$	0.629999	−	14.8307i	0.0427671	−	1.00677i
$218$	−3.32536	−	5.40073i	−0.225222	−	0.365784i
$219$	6.14428	−	4.96116i	0.415192	−	0.335244i
$220$	−1.08311	+	2.69543i	−0.0730234	+	0.181726i
$221$	−8.14829	+	2.87898i	−0.548114	+	0.193661i
$222$	−7.66603			−0.514510
$223$	14.7572	−	2.28594i	0.988214	−	0.153078i
$223$	14.7572	−	2.28594i	0.988214	−	0.153078i
$224$	16.0035			1.06928
$225$	−3.70329	+	1.30846i	−0.246886	+	0.0872305i
$226$	4.38991	−	10.9247i	0.292013	−	0.726702i
$227$	19.7318	−	15.9323i	1.30965	−	1.05747i	0.315556	−	0.948907i	$-0.397809\pi$
$227$	19.7318	−	15.9323i	1.30965	−	1.05747i	0.994090	−	0.108559i	$-0.0346236\pi$
$228$	1.61497	+	2.62288i	0.106954	+	0.173705i
$229$	−0.901288	+	21.2170i	−0.0595588	+	1.40206i	0.682088	+	0.731270i	$0.261072\pi$
$229$	−0.901288	+	21.2170i	−0.0595588	+	1.40206i	−0.741647	+	0.670790i	$0.765955\pi$
$230$	0.444313	−	3.46970i	0.0292971	−	0.228786i
$231$	−4.40025	+	7.14646i	−0.289515	+	0.470203i
$232$	−9.60351	−	9.20422i	−0.630502	−	0.604287i
$233$	−12.0706	−	9.74630i	−0.790769	−	0.638501i	0.145669	−	0.989333i	$-0.453466\pi$
$233$	−12.0706	−	9.74630i	−0.790769	−	0.638501i	−0.936438	+	0.350832i	$0.885899\pi$
$234$	0.0877216	−	2.06503i	0.00573454	−	0.134996i
$235$	−2.02835	−	6.62327i	−0.132315	−	0.432054i
$236$	1.09010	+	2.71282i	0.0709595	+	0.176589i
$237$	−1.15295	−	5.34969i	−0.0748919	−	0.347500i
$238$	−12.3083	+	2.11048i	−0.797832	+	0.136802i
$239$	−0.217647	+	1.00989i	−0.0140784	+	0.0653242i	−0.984049	−	0.177900i	$-0.943070\pi$
$239$	−0.217647	+	1.00989i	−0.0140784	+	0.0653242i	0.969970	+	0.243224i	$0.0782049\pi$
$240$	0.0366786	−	0.863442i	0.00236759	−	0.0557349i
$241$	6.15002	+	2.77999i	0.396158	+	0.179075i	0.600131	−	0.799902i	$-0.295115\pi$
$241$	6.15002	+	2.77999i	0.396158	+	0.179075i	−0.203973	+	0.978977i	$0.565385\pi$
$242$	3.54226	−	0.922334i	0.227705	−	0.0592899i
$243$	0.942877	+	0.333140i	0.0604856	+	0.0213709i
$244$	4.10733	+	2.29449i	0.262945	+	0.146890i
$245$	0.818293	+	2.67201i	0.0522788	+	0.170708i
$246$	3.27592	+	5.32044i	0.208865	+	0.339219i
$247$	3.71363	+	5.02115i	0.236292	+	0.319488i
$248$	6.39054	−	12.6749i	0.405800	−	0.804856i
$249$	4.93943	+	5.61228i	0.313024	+	0.355664i
$250$	−8.25002	+	3.72924i	−0.521777	+	0.235858i
$251$	−7.04454	−	11.4411i	−0.444647	−	0.722153i	0.548861	−	0.835914i	$-0.315062\pi$
$251$	−7.04454	−	11.4411i	−0.444647	−	0.722153i	−0.993508	+	0.113760i	$0.963710\pi$
$252$	−0.682971	+	3.16900i	−0.0430231	+	0.199628i
$253$	−8.11508	+	4.53335i	−0.510191	+	0.285010i
$254$	3.09050	−	0.263041i	0.193915	−	0.0165046i
$255$	−0.538577	−	4.20582i	−0.0337270	−	0.263379i
$256$	15.5282	+	7.01919i	0.970513	+	0.438700i
$257$	4.86978	+	15.9015i	0.303769	+	0.991909i	0.969371	+	0.245602i	$0.0789856\pi$
$257$	4.86978	+	15.9015i	0.303769	+	0.991909i	−0.665602	+	0.746307i	$0.731825\pi$
$258$	3.74760	−	1.69402i	0.233316	−	0.105465i
$259$	24.2904	+	2.06742i	1.50933	+	0.128463i
$260$	0.0965557	+	2.27300i	0.00598813	+	0.140965i
$261$	3.70072	−	2.50125i	0.229069	−	0.154824i
$262$	−4.21284			−0.260270
$263$	14.0583			0.866869			0.433435	−	0.901185i	$-0.357301\pi$
$263$	14.0583			0.866869			0.433435	+	0.901185i	$0.357301\pi$
$264$	−6.64914	+	4.49404i	−0.409226	+	0.276589i
$265$	6.91060	+	1.18494i	0.424515	+	0.0727903i
$266$	4.06292	+	8.05833i	0.249114	+	0.494088i
$267$	−3.77451	−	5.10347i	−0.230996	−	0.312327i
$268$	1.28200	−	5.94849i	0.0783105	−	0.363362i
$269$	−15.0631	−	12.1626i	−0.918413	−	0.741567i	0.0479228	−	0.998851i	$-0.484740\pi$
$269$	−15.0631	−	12.1626i	−0.918413	−	0.741567i	−0.966336	+	0.257284i	$0.917172\pi$
$270$	0.981400	+	0.255537i	0.0597261	+	0.0155515i
$271$	−15.2138	−	10.2827i	−0.924173	−	0.624632i	0.00270404	−	0.999996i	$-0.499139\pi$
$271$	−15.2138	−	10.2827i	−0.924173	−	0.624632i	−0.926877	+	0.375364i	$0.877518\pi$
$272$	−3.30695	−	0.861063i	−0.200513	−	0.0522096i
$273$	−0.834863	+	6.51956i	−0.0505282	+	0.394582i
$274$	6.23198	+	2.81703i	0.376487	+	0.170183i
$275$	9.24042	+	5.16201i	0.557218	+	0.311281i
$276$	−2.37218	+	2.69532i	−0.142789	+	0.162239i
$277$	15.4404	−	14.7984i	0.927725	−	0.889152i	−0.0663562	−	0.997796i	$-0.521137\pi$
$277$	15.4404	−	14.7984i	0.927725	−	0.889152i	0.994081	+	0.108644i	$0.0346509\pi$
$278$	15.7269	−	8.78556i	0.943236	−	0.526923i
$279$	3.70849	+	2.99440i	0.222022	+	0.179270i
$280$	−1.21988	+	9.52622i	−0.0729018	+	0.569301i
$281$	2.74646	+	21.4475i	0.163840	+	1.27945i	0.839955	+	0.542656i	$0.182581\pi$
$281$	2.74646	+	21.4475i	0.163840	+	1.27945i	−0.676115	+	0.736796i	$0.736338\pi$
$282$	1.91822	−	6.26365i	0.114228	−	0.372995i
$283$	18.0187	−	20.4733i	1.07110	−	1.21701i	0.0959715	−	0.995384i	$-0.469404\pi$
$283$	18.0187	−	20.4733i	1.07110	−	1.21701i	0.975132	−	0.221626i	$-0.0711363\pi$
$284$	−0.644911	−	1.60492i	−0.0382684	−	0.0952346i
$285$	−2.79221	+	1.26216i	−0.165396	+	0.0747638i
$286$	−4.33367	+	3.49919i	−0.256255	+	0.206912i
$287$	−8.94517	−	17.7417i	−0.528017	−	1.04726i
$288$	−3.05569	+	4.13157i	−0.180058	+	0.243455i
$289$	0.233114	+	0.0198409i	0.0137126	+	0.00116711i
$290$	3.52435	−	2.84571i	0.206957	−	0.167106i
$291$	0.464212	+	0.627657i	0.0272126	+	0.0367939i
$292$	−8.10224	+	1.38927i	−0.474148	+	0.0813008i
$293$	3.16603	−	3.03440i	0.184962	−	0.177271i	−0.593758	−	0.804644i	$-0.702356\pi$
$293$	3.16603	−	3.03440i	0.184962	−	0.177271i	0.778719	+	0.627373i	$0.215870\pi$
$294$	−0.773862	+	2.52692i	−0.0451325	+	0.147373i
$295$	−2.81463	+	0.732874i	−0.163874	+	0.0426695i
$296$	20.3517	+	11.3691i	1.18292	+	0.660817i
$297$	−1.00480	−	2.50054i	−0.0583044	−	0.145096i
$298$	−1.89647	−	2.15481i	−0.109860	−	0.124825i
$299$	−4.32892	+	5.85308i	−0.250348	+	0.338492i
$300$	4.02965	+	0.690952i	0.232652	+	0.0398922i
$301$	−12.3314	+	4.35697i	−0.710771	+	0.251131i
$302$	13.6478	−	9.22428i	0.785341	−	0.530798i
$303$	−5.66479	+	2.00150i	−0.325433	+	0.114983i
$304$	0.104809	+	2.46728i	0.00601119	+	0.141508i
$305$	−2.78310	+	3.76300i	−0.159360	+	0.215469i
$306$	1.80529	−	3.58058i	0.103202	−	0.204688i
$307$	−5.23745	+	0.898052i	−0.298917	+	0.0512545i	−0.316505	−	0.948591i	$-0.602509\pi$
$307$	−5.23745	+	0.898052i	−0.298917	+	0.0512545i	0.0175878	+	0.999845i	$0.494401\pi$
$308$	7.62674	−	4.26056i	0.434574	−	0.242768i
$309$	−0.144151	−	0.138157i	−0.00820046	−	0.00785950i
$310$	4.00485	+	2.70680i	0.227460	+	0.153736i
$311$	0.366551	+	0.247745i	0.0207852	+	0.0140483i	0.570323	−	0.821420i	$-0.306818\pi$
$311$	0.366551	+	0.247745i	0.0207852	+	0.0140483i	−0.549538	+	0.835469i	$0.685196\pi$
$312$	−3.29543	+	5.35213i	−0.186567	+	0.303004i
$313$	1.67762	+	13.1007i	0.0948245	+	0.740498i	0.967620	+	0.252412i	$0.0812237\pi$
$313$	1.67762	+	13.1007i	0.0948245	+	0.740498i	−0.872795	+	0.488086i	$0.837695\pi$
$314$	−10.8874	+	2.83487i	−0.614413	+	0.159981i
$315$	−3.04073	−	1.07436i	−0.171325	−	0.0605331i
$316$	−1.66809	+	5.44687i	−0.0938371	+	0.306410i
$317$	25.8967	−	2.20413i	1.45450	−	0.123796i	0.669280	−	0.743011i	$-0.266603\pi$
$317$	25.8967	−	2.20413i	1.45450	−	0.123796i	0.785222	+	0.619214i	$0.212549\pi$
$318$	4.78711	+	4.58807i	0.268448	+	0.257286i
$319$	−11.6488	−	3.03312i	−0.652208	−	0.169822i
$320$	−3.63859	+	5.90944i	−0.203403	+	0.330348i
$321$	0.192882	−	0.0164167i	0.0107657	−	0.000916292i
$322$	−7.59489	+	7.27911i	−0.423247	+	0.405649i
$323$	2.55264	+	11.8443i	0.142033	+	0.659035i
$324$	−0.687724	−	0.781406i	−0.0382069	−	0.0434114i
$325$	8.25965	+	0.703000i	0.458163	+	0.0389954i
$326$	6.53791	−	16.2702i	0.362101	−	0.901124i
$327$	−6.38320	−	1.09451i	−0.352992	−	0.0605265i
$328$	−0.806387	−	18.9830i	−0.0445253	−	1.04816i
$329$	−7.76724	+	19.3295i	−0.428222	+	1.06567i
$330$	−1.23037	−	2.44030i	−0.0677298	−	0.134334i
$331$	−16.0323	+	31.7982i	−0.881215	+	1.74779i	−0.257227	+	0.966351i	$0.582809\pi$
$331$	−16.0323	+	31.7982i	−0.881215	+	1.74779i	−0.623987	+	0.781434i	$0.714488\pi$
$332$	−1.63960	−	7.60776i	−0.0899846	−	0.417530i
$333$	−5.17173	+	5.87622i	−0.283409	+	0.322015i
$334$	−13.4289	−	4.74472i	−0.734795	−	0.259620i
$335$	5.70772	+	2.01666i	0.311846	+	0.110182i
$336$	−1.71711	+	1.95102i	−0.0936761	+	0.106437i
$337$	2.67469	+	12.4106i	0.145700	+	0.676049i	0.990103	+	0.140341i	$0.0448200\pi$
$337$	2.67469	+	12.4106i	0.145700	+	0.676049i	−0.844404	+	0.535708i	$0.820045\pi$
$338$	3.76767	−	7.47272i	0.204934	−	0.406463i
$339$	−5.41254	−	10.7351i	−0.293969	−	0.583052i
$340$	−1.64570	+	4.09549i	−0.0892507	+	0.222109i
$341$	−0.545159	−	12.8335i	−0.0295220	−	0.694971i
$342$	−2.85616	−	0.489738i	−0.154444	−	0.0264820i
$343$	−4.99468	+	12.4297i	−0.269687	+	0.671142i
$344$	−12.4614	−	1.06062i	−0.671874	−	0.0571849i
$345$	−2.35988	−	2.68134i	−0.127052	−	0.144359i
$346$	2.53605	+	11.7673i	0.136339	+	0.632616i
$347$	−11.6508	+	11.1664i	−0.625449	+	0.599445i	−0.936380	−	0.350988i	$-0.885846\pi$
$347$	−11.6508	+	11.1664i	−0.625449	+	0.599445i	0.310931	+	0.950433i	$0.399359\pi$
$348$	−4.63284	+	0.394313i	−0.248346	+	0.0211374i
$349$	−3.76063	+	6.10765i	−0.201302	+	0.326935i	−0.936342	−	0.351088i	$-0.885812\pi$
$349$	−3.76063	+	6.10765i	−0.201302	+	0.326935i	0.735040	+	0.678023i	$0.237163\pi$
$350$	11.5922	+	3.01837i	0.619628	+	0.161339i
$351$	−1.52373	−	1.46037i	−0.0813305	−	0.0779490i
$352$	13.7985	−	1.17442i	0.735460	−	0.0625969i
$353$	−9.31577	+	30.4192i	−0.495828	+	1.61905i	0.260932	+	0.965357i	$0.415970\pi$
$353$	−9.31577	+	30.4192i	−0.495828	+	1.61905i	−0.756760	+	0.653692i	$0.773219\pi$
$354$	−2.59344	−	0.916321i	−0.137840	−	0.0487019i
$355$	1.66516	−	0.433573i	0.0883773	−	0.0230117i
$356$	0.839271	+	6.55399i	0.0444813	+	0.347361i
$357$	−6.68583	+	10.8585i	−0.353852	+	0.574692i
$358$	12.9952	+	8.78323i	0.686818	+	0.464208i
$359$	13.3061	+	8.99338i	0.702271	+	0.474652i	0.858332	−	0.513095i	$-0.171501\pi$
$359$	13.3061	+	8.99338i	0.702271	+	0.474652i	−0.156061	+	0.987747i	$0.549880\pi$
$360$	−2.22643	−	2.13386i	−0.117343	−	0.112464i
$361$	−8.94316	+	4.99595i	−0.470693	+	0.262945i
$362$	−10.3417	+	1.77326i	−0.543547	+	0.0932005i
$363$	1.68272	−	3.33748i	0.0883199	−	0.175172i
$364$	4.06842	−	5.50087i	0.213243	−	0.288324i
$365$	−0.347078	−	8.17048i	−0.0181669	−	0.427662i
$366$	−4.17340	+	1.47456i	−0.218147	+	0.0770763i
$367$	−6.04153	+	4.08336i	−0.315365	+	0.213150i	−0.707422	−	0.706791i	$-0.750142\pi$
$367$	−6.04153	+	4.08336i	−0.315365	+	0.213150i	0.392057	+	0.919941i	$0.371764\pi$
$368$	−2.71423	+	0.958997i	−0.141489	+	0.0499912i
$369$	6.28830	+	1.07824i	0.327356	+	0.0561308i
$370$	−4.72049	+	6.38253i	−0.245407	+	0.331812i
$371$	−13.9310	−	15.8287i	−0.723261	−	0.821784i
$372$	−1.84998	−	4.60384i	−0.0959168	−	0.238698i
$373$	30.1546	+	16.8454i	1.56135	+	0.872220i	0.998972	+	0.0453366i	$0.0144360\pi$
$373$	30.1546	+	16.8454i	1.56135	+	0.872220i	0.562374	+	0.826883i	$0.309888\pi$
$374$	−10.4576	+	2.72294i	−0.540748	+	0.140800i
$375$	−2.70714	+	8.83972i	−0.139796	+	0.456481i
$376$	−14.3818	+	13.7838i	−0.741683	+	0.710846i
$377$	−9.29164	+	1.59321i	−0.478544	+	0.0820546i
$378$	−1.81353	−	2.45206i	−0.0932782	−	0.126120i
$379$	7.93703	−	6.40871i	0.407698	−	0.329193i	−0.402425	−	0.915453i	$-0.631833\pi$
$379$	7.93703	−	6.40871i	0.407698	−	0.329193i	0.810123	+	0.586260i	$0.199400\pi$
$380$	3.17819	+	0.270504i	0.163038	+	0.0138765i
$381$	1.88332	−	2.54641i	0.0964852	−	0.130457i
$382$	−4.54406	−	9.01261i	−0.232494	−	0.461125i
$383$	8.63221	−	6.97003i	0.441085	−	0.356152i	−0.381910	−	0.924199i	$-0.624734\pi$
$383$	8.63221	−	6.97003i	0.441085	−	0.356152i	0.822996	+	0.568048i	$0.192301\pi$
$384$	3.38483	−	1.53004i	0.172732	−	0.0780796i
$385$	3.24042	+	8.06409i	0.165147	+	0.410984i
$386$	−2.00357	+	2.27650i	−0.101979	+	0.115871i
$387$	1.22973	−	4.01548i	0.0625105	−	0.204118i
$388$	−0.103219	−	0.806050i	−0.00524014	−	0.0409210i
$389$	−2.96702	+	23.1699i	−0.150434	+	1.17476i	0.724065	+	0.689732i	$0.242272\pi$
$389$	−2.96702	+	23.1699i	−0.150434	+	1.17476i	−0.874499	+	0.485028i	$0.838809\pi$
$390$	−1.66528	−	1.34462i	−0.0843245	−	0.0680873i
$391$	−12.3302	+	6.88807i	−0.623566	+	0.348345i
$392$	5.80200	−	5.56076i	0.293045	−	0.280861i
$393$	−2.84210	+	3.22926i	−0.143365	+	0.162895i
$394$	7.73682	+	4.32205i	0.389776	+	0.217742i
$395$	−5.16395	−	2.33425i	−0.259827	−	0.117449i
$396$	−0.356310	+	2.78248i	−0.0179053	+	0.139825i
$397$	−36.0588	−	9.38898i	−1.80974	−	0.471219i	−0.815533	−	0.578711i	$-0.803556\pi$
$397$	−36.0588	−	9.38898i	−1.80974	−	0.471219i	−0.994206	+	0.107492i	$0.965718\pi$
$398$	12.6650	+	8.56007i	0.634841	+	0.429078i
$399$	8.91790	+	2.32204i	0.446453	+	0.116247i
$400$	2.55029	+	2.05921i	0.127514	+	0.102961i
$401$	4.05853	−	18.8317i	0.202674	−	0.940409i	−0.755706	−	0.654911i	$-0.772706\pi$
$401$	4.05853	−	18.8317i	0.202674	−	0.940409i	0.958379	−	0.285497i	$-0.0921588\pi$
$402$	3.40417	+	4.60274i	0.169784	+	0.229564i
$403$	−4.52901	−	8.98276i	−0.225606	−	0.447463i
$404$	6.16399	+	1.05692i	0.306670	+	0.0525839i
$405$	0.857957	−	0.579878i	0.0426322	−	0.0288143i
$406$	−13.6228			−0.676087
$407$	21.0953			1.04565
$408$	−10.1028	+	6.82833i	−0.500165	+	0.338053i
$409$	−0.445322	−	10.4832i	−0.0220198	−	0.518362i	−0.975906	−	0.218193i	$-0.929984\pi$
$409$	−0.445322	−	10.4832i	−0.0220198	−	0.518362i	0.953886	−	0.300169i	$-0.0970432\pi$
$410$	6.44686	+	0.548709i	0.318388	+	0.0270988i
$411$	6.36360	−	2.87653i	0.313893	−	0.141889i
$412$	0.0608608	+	0.198731i	0.00299840	+	0.00979079i
$413$	7.97040	+	3.60285i	0.392198	+	0.177285i
$414$	−0.429063	−	3.35062i	−0.0210873	−	0.164674i
$415$	7.71418	−	0.656573i	0.378674	−	0.0322299i
$416$	9.46843	−	5.28938i	0.464228	−	0.259333i
$417$	3.87544	−	17.9821i	0.189781	−	0.880587i
$418$	4.09448	+	6.64986i	0.200268	+	0.325255i
$419$	27.7396	−	12.5391i	1.35517	−	0.612575i	0.402175	−	0.915563i	$-0.368254\pi$
$419$	27.7396	−	12.5391i	1.35517	−	0.612575i	0.952994	+	0.302988i	$0.0979841\pi$
$420$	2.21787	+	2.51999i	0.108221	+	0.122963i
$421$	−9.39629	+	18.6364i	−0.457947	+	0.908284i	0.539838	+	0.841769i	$0.318485\pi$
$421$	−9.39629	+	18.6364i	−0.457947	+	0.908284i	−0.997785	+	0.0665151i	$0.978812\pi$
$422$	−5.57067	−	7.53204i	−0.271176	−	0.366654i
$423$	−3.50717	−	5.69601i	−0.170524	−	0.276949i
$424$	−5.90440	−	19.2799i	−0.286743	−	0.936314i
$425$	14.0401	+	7.84326i	0.681044	+	0.380454i
$426$	1.53430	+	0.542102i	0.0743369	+	0.0262649i
$427$	13.6214	−	3.54674i	0.659186	−	0.171639i
$428$	−0.183617	−	0.0830003i	−0.00887548	−	0.00401197i
$429$	−0.241391	+	5.68254i	−0.0116545	+	0.274355i
$430$	0.897255	−	4.16328i	0.0432695	−	0.200771i
$431$	32.5604	−	5.58304i	1.56838	−	0.268926i	0.681813	−	0.731527i	$-0.261192\pi$
$431$	32.5604	−	5.58304i	1.56838	−	0.268926i	0.886567	+	0.462601i	$0.153084\pi$
$432$	−0.175824	−	0.815827i	−0.00845934	−	0.0392515i
$433$	−8.73309	−	21.7331i	−0.419685	−	1.04443i	−0.976831	−	0.214012i	$-0.931347\pi$
$433$	−8.73309	−	21.7331i	−0.419685	−	1.04443i	0.557146	−	0.830415i	$-0.311896\pi$
$434$	−4.25677	−	13.8998i	−0.204331	−	0.667212i
$435$	0.196311	−	4.62131i	0.00941238	−	0.221575i
$436$	5.24513	+	4.23515i	0.251196	+	0.202827i
$437$	7.36881	+	7.06244i	0.352498	+	0.337842i
$438$	4.05490	−	6.58557i	0.193750	−	0.314671i
$439$	−2.63862	+	20.6054i	−0.125934	+	0.983440i	0.798472	+	0.602032i	$0.205642\pi$
$439$	−2.63862	+	20.6054i	−0.125934	+	0.983440i	−0.924407	+	0.381408i	$0.875439\pi$
$440$	−0.352715	+	8.30318i	−0.0168150	+	0.395839i
$441$	1.41489	+	2.29792i	0.0673756	+	0.109425i
$442$	−6.58466	+	5.31674i	−0.313201	+	0.252892i
$443$	0.246594	−	0.613672i	0.0117160	−	0.0291564i	−0.921916	−	0.387389i	$-0.873377\pi$
$443$	0.246594	−	0.613672i	0.0117160	−	0.0291564i	0.933633	+	0.358232i	$0.116620\pi$
$444$	7.68298	−	2.71457i	0.364618	−	0.128828i
$445$	−6.57323			−0.311601
$446$	12.8806	−	6.92529i	0.609915	−	0.327922i
$447$	−2.93114			−0.138638
$448$	19.6783	−	6.95280i	0.929714	−	0.328489i
$449$	−14.4074	+	35.8542i	−0.679928	+	1.69206i	0.0410970	+	0.999155i	$0.486915\pi$
$449$	−14.4074	+	35.8542i	−0.679928	+	1.69206i	−0.721025	+	0.692910i	$0.756329\pi$
$450$	−2.99264	+	2.41639i	−0.141075	+	0.113910i
$451$	−9.01465	−	14.6407i	−0.424483	−	0.689404i
$452$	−0.531136	+	12.5034i	−0.0249825	+	0.588108i
$453$	2.13652	−	16.6844i	0.100382	−	0.783900i
$454$	13.0219	−	21.1490i	0.611150	−	0.992571i
$455$	4.91393	+	4.70962i	0.230369	+	0.220790i
$456$	6.85619	+	5.53599i	0.321071	+	0.259246i
$457$	0.556934	−	13.1107i	0.0260523	−	0.613291i	−0.937851	−	0.347038i	$-0.887187\pi$
$457$	0.556934	−	13.1107i	0.0260523	−	0.613291i	0.963903	−	0.266253i	$-0.0857856\pi$
$458$	6.08981	+	19.8853i	0.284558	+	0.929179i
$459$	−1.52671	−	3.79937i	−0.0712608	−	0.177339i
$460$	0.783339	+	3.63471i	0.0365234	+	0.169469i
$461$	−32.1051	+	5.50497i	−1.49528	+	0.256392i	−0.857764	−	0.514044i	$-0.828147\pi$
$461$	−32.1051	+	5.50497i	−1.49528	+	0.256392i	−0.637518	+	0.770435i	$0.720039\pi$
$462$	−1.73155	+	8.03444i	−0.0805592	+	0.373796i
$463$	0.0735122	−	1.73053i	0.00341640	−	0.0804247i	−0.996581	−	0.0826192i	$-0.973671\pi$
$463$	0.0735122	−	1.73053i	0.00341640	−	0.0804247i	0.999998	+	0.00219446i	$0.000698517\pi$
$464$	−3.39682	−	1.53546i	−0.157694	−	0.0712820i
$465$	4.77663	−	1.24374i	0.221511	−	0.0576769i
$466$	−14.3254	−	5.06148i	−0.663610	−	0.234468i
$467$	10.7675	+	6.01508i	0.498260	+	0.278345i	0.716546	−	0.697540i	$-0.245722\pi$
$467$	10.7675	+	6.01508i	0.498260	+	0.278345i	−0.218285	+	0.975885i	$0.570046\pi$
$468$	0.643320	+	2.10066i	0.0297375	+	0.0971031i
$469$	−9.54508	−	15.5022i	−0.440751	−	0.715825i
$470$	−4.03376	−	5.45401i	−0.186064	−	0.251575i
$471$	−5.17197	+	10.2580i	−0.238312	+	0.472664i
$472$	5.52608	+	6.27884i	0.254358	+	0.289007i
$473$	−10.3126	+	4.66159i	−0.474174	+	0.214340i
$474$	−2.80993	−	4.56362i	−0.129064	−	0.209614i
$475$	2.44854	−	11.3613i	0.112347	−	0.521291i
$476$	11.5882	−	6.47357i	0.531146	−	0.296716i
$477$	6.74641	−	0.574204i	0.308897	−	0.0262910i
$478$	0.128505	+	1.00351i	0.00587766	+	0.0458995i
$479$	7.37654	+	3.33440i	0.337043	+	0.152353i	0.573317	−	0.819333i	$-0.305656\pi$
$479$	7.37654	+	3.33440i	0.337043	+	0.152353i	−0.236275	+	0.971686i	$0.575927\pi$
$480$	1.55824	+	5.08817i	0.0711234	+	0.232242i
$481$	15.0547	−	6.80514i	0.686434	−	0.310288i
$482$	6.58574	+	0.560529i	0.299972	+	0.0255314i
$483$	0.455907	+	10.7324i	0.0207445	+	0.488341i
$484$	−3.22349	+	2.17870i	−0.146522	+	0.0990319i
$485$	0.808417			0.0367083
$486$	0.979315			0.0444226
$487$	−15.6223	+	10.5589i	−0.707916	+	0.478468i	−0.860257	−	0.509860i	$-0.829697\pi$
$487$	−15.6223	+	10.5589i	−0.707916	+	0.478468i	0.152341	+	0.988328i	$0.451319\pi$
$488$	13.2663	+	2.27474i	0.600539	+	0.102973i
$489$	−8.06091	−	15.9879i	−0.364527	−	0.722996i
$490$	1.62733	+	2.20030i	0.0735153	+	0.0993992i
$491$	−4.25144	+	19.7268i	−0.191865	+	0.890256i	0.774398	+	0.632699i	$0.218053\pi$
$491$	−4.25144	+	19.7268i	−0.191865	+	0.890256i	−0.966263	+	0.257557i	$0.917082\pi$
$492$	−5.16715	−	4.17218i	−0.232953	−	0.188097i
$493$	−17.6994	−	4.60858i	−0.797143	−	0.207560i
$494$	5.06721	+	3.42484i	0.227985	+	0.154091i
$495$	−2.70060	−	0.703182i	−0.121383	−	0.0316057i
$496$	0.505265	−	3.94569i	0.0226871	−	0.177167i
$497$	−4.71534	−	2.13147i	−0.211512	−	0.0956094i
$498$	6.39195	+	3.57075i	0.286430	+	0.160009i
$499$	25.4385	−	28.9037i	1.13878	−	1.29391i	0.188657	−	0.982043i	$-0.439586\pi$
$499$	25.4385	−	28.9037i	1.13878	−	1.29391i	0.950126	−	0.311866i	$-0.100954\pi$
$500$	6.94772	−	6.65885i	0.310711	−	0.297793i
$501$	−12.6965	+	7.09267i	−0.567236	+	0.316877i
$502$	−10.2374	−	8.26611i	−0.456917	−	0.368934i
$503$	3.87771	−	30.2816i	0.172899	−	1.35019i	−0.640265	−	0.768154i	$-0.721175\pi$
$503$	3.87771	−	30.2816i	0.172899	−	1.35019i	0.813163	−	0.582035i	$-0.197744\pi$
$504$	1.17801	+	9.19926i	0.0524728	+	0.409768i
$505$	−1.82180	+	5.94880i	−0.0810691	+	0.264718i
$506$	−6.01425	+	6.83352i	−0.267366	+	0.303787i
$507$	−3.18627	−	7.92934i	−0.141507	−	0.352154i
$508$	−3.00419	+	1.35798i	−0.133289	+	0.0602506i
$509$	−14.2521	+	11.5078i	−0.631713	+	0.510072i	−0.889979	−	0.456001i	$-0.849281\pi$
$509$	−14.2521	+	11.5078i	−0.631713	+	0.510072i	0.258266	+	0.966074i	$0.416849\pi$
$510$	−1.86945	−	3.70784i	−0.0827808	−	0.164186i
$511$	−14.6243	+	19.7733i	−0.646940	+	0.874721i
$512$	9.22596	+	0.785245i	0.407734	+	0.0347032i
$513$	−2.30225	+	1.85894i	−0.101647	+	0.0820741i
$514$	9.68448	+	13.0943i	0.427164	+	0.577564i
$515$	−0.203790	+	0.0349432i	−0.00898004	+	0.00153978i
$516$	−3.15603	+	3.02481i	−0.138936	+	0.133160i
$517$	−5.27853	+	17.2362i	−0.232150	+	0.758048i
$518$	23.1036	−	6.01572i	1.01512	−	0.264315i
$519$	10.7309	+	5.99463i	0.471033	+	0.263135i
$520$	2.42681	+	6.03936i	0.106423	+	0.264843i
$521$	−6.42487	−	7.30007i	−0.281479	−	0.319822i	0.592703	−	0.805421i	$-0.298061\pi$
$521$	−6.42487	−	7.30007i	−0.281479	−	0.319822i	−0.874181	+	0.485599i	$0.838601\pi$
$522$	2.60112	−	3.51695i	0.113848	−	0.153933i
$523$	1.62594	+	0.278795i	0.0710973	+	0.0121909i	0.204440	−	0.978879i	$-0.434463\pi$
$523$	1.62594	+	0.278795i	0.0710973	+	0.0121909i	−0.133342	+	0.991070i	$0.542571\pi$
$524$	4.22215	−	1.49178i	0.184446	−	0.0651688i
$525$	10.1341	−	6.84945i	0.442288	−	0.298934i
$526$	12.9810	−	4.58649i	0.566000	−	0.199981i
$527$	−0.828326	−	19.4994i	−0.0360824	−	0.849408i
$528$	−1.33734	+	1.80821i	−0.0582005	+	0.0786922i
$529$	4.99824	−	9.91341i	0.217315	−	0.431018i
$530$	6.76765	−	1.16043i	0.293968	−	0.0504059i
$531$	−2.45200	+	1.36977i	−0.106408	+	0.0594428i
$532$	−6.92539	−	6.63745i	−0.300254	−	0.287770i
$533$	−11.1563	−	7.54032i	−0.483232	−	0.326608i
$534$	−5.15029	−	3.48099i	−0.222875	−	0.150637i
$535$	0.105103	−	0.170698i	0.00454399	−	0.00737990i
$536$	−2.21123	−	17.2678i	−0.0955107	−	0.745857i
$537$	15.4995	−	4.03576i	0.668854	−	0.174156i
$538$	−17.8769	−	6.31631i	−0.770728	−	0.272316i
$539$	2.12950	−	6.95356i	0.0917242	−	0.299511i
$540$	−1.07406	+	0.0914156i	−0.0462200	+	0.00393390i
$541$	−26.2754	−	25.1829i	−1.12967	−	1.08270i	−0.995787	−	0.0916990i	$-0.970770\pi$
$541$	−26.2754	−	25.1829i	−1.12967	−	1.08270i	−0.133879	−	0.990998i	$-0.542743\pi$
$542$	−17.4028	−	4.53133i	−0.747513	−	0.194637i
$543$	−5.61755	+	9.12349i	−0.241072	+	0.391526i
$544$	20.9657	−	1.78444i	0.898895	−	0.0765072i
$545$	−4.84183	+	4.64052i	−0.207401	+	0.198778i
$546$	1.35611	+	6.29237i	0.0580361	+	0.269289i
$547$	20.6938	+	23.5128i	0.884804	+	1.00533i	0.999928	+	0.0119817i	$0.00381398\pi$
$547$	20.6938	+	23.5128i	0.884804	+	1.00533i	−0.115124	+	0.993351i	$0.536727\pi$
$548$	−7.24327	−	0.616493i	−0.309417	−	0.0263353i
$549$	−1.68521	+	4.19381i	−0.0719230	+	0.178987i
$550$	10.2165	+	1.75179i	0.435632	+	0.0746966i
$551$	0.560957	+	13.2054i	0.0238976	+	0.562567i
$552$	−3.83007	+	9.53149i	−0.163018	+	0.405687i
$553$	7.67274	+	15.2180i	0.326278	+	0.647134i
$554$	9.42931	−	18.7019i	0.400613	−	0.794568i
$555$	1.70780	+	7.92423i	0.0724922	+	0.336365i
$556$	−12.6506	+	14.3739i	−0.536507	+	0.609590i
$557$	−1.09148	−	0.385646i	−0.0462477	−	0.0163403i	0.309916	−	0.950764i	$-0.399699\pi$
$557$	−1.09148	−	0.385646i	−0.0462477	−	0.0163403i	−0.356163	+	0.934424i	$0.615915\pi$
$558$	4.40125	+	1.55506i	0.186320	+	0.0658309i
$559$	−5.85582	+	6.65350i	−0.247675	+	0.281413i
$560$	0.567023	+	2.63100i	0.0239611	+	0.111180i
$561$	−4.96777	+	9.85299i	−0.209740	+	0.415994i
$562$	9.53324	+	18.9081i	0.402136	+	0.797588i
$563$	11.7807	−	29.3175i	0.496498	−	1.23558i	−0.444074	−	0.895990i	$-0.646467\pi$
$563$	11.7807	−	29.3175i	0.496498	−	1.23558i	0.940572	−	0.339594i	$-0.110290\pi$
$564$	0.295519	+	6.95674i	0.0124436	+	0.292932i
$565$	−12.2706	−	2.10401i	−0.516230	−	0.0885165i
$566$	9.95867	−	24.7831i	0.418594	−	1.04171i
$567$	−3.10304	−	0.264107i	−0.130315	−	0.0110915i
$568$	−3.26926	−	3.71461i	−0.137175	−	0.155861i
$569$	4.05210	+	18.8018i	0.169873	+	0.788214i	0.979528	+	0.201308i	$0.0645191\pi$
$569$	4.05210	+	18.8018i	0.169873	+	0.788214i	−0.809655	+	0.586906i	$0.800346\pi$
$570$	−2.16648	+	2.07640i	−0.0907437	+	0.0869708i
$571$	−44.2554	+	3.76669i	−1.85203	+	0.157631i	−0.957323	−	0.289020i	$-0.906671\pi$
$571$	−44.2554	+	3.76669i	−1.85203	+	0.157631i	−0.894708	+	0.446651i	$0.852617\pi$
$572$	3.10417	−	5.04150i	0.129792	−	0.210796i
$573$	−9.97397	−	2.59702i	−0.416669	−	0.108492i
$574$	−14.0479	−	13.4639i	−0.586350	−	0.561971i
$575$	13.4989	−	1.14893i	0.562945	−	0.0479137i
$576$	−1.96238	+	6.40786i	−0.0817660	+	0.266994i
$577$	−29.8938	−	10.5621i	−1.24449	−	0.439708i	−0.371955	−	0.928251i	$-0.621312\pi$
$577$	−29.8938	−	10.5621i	−1.24449	−	0.439708i	−0.872540	+	0.488543i	$0.837528\pi$
$578$	0.221724	−	0.0577325i	0.00922251	−	0.00240136i
$579$	0.393332	+	3.07159i	0.0163463	+	0.127651i
$580$	−2.52446	+	4.09999i	−0.104823	+	0.170243i
$581$	−19.2904	−	13.0380i	−0.800300	−	0.540908i
$582$	0.633414	+	0.428113i	0.0262559	+	0.0177459i
$583$	−13.1731	−	12.6254i	−0.545574	−	0.522891i
$584$	−20.5316	+	11.4696i	−0.849604	+	0.474617i
$585$	−2.15413	+	0.369362i	−0.0890623	+	0.0152713i
$586$	1.93347	−	3.83480i	0.0798707	−	0.158414i
$587$	7.41180	−	10.0214i	0.305918	−	0.413628i	−0.623983	−	0.781438i	$-0.714487\pi$
$587$	7.41180	−	10.0214i	0.305918	−	0.413628i	0.929901	+	0.367809i	$0.119892\pi$
$588$	−0.119220	−	2.80654i	−0.00491656	−	0.115740i
$589$	−13.2986	+	4.69870i	−0.547960	+	0.193606i
$590$	−2.35986	+	1.59499i	−0.0971540	+	0.0656646i
$591$	8.53246	−	3.01471i	0.350978	−	0.124009i
$592$	6.43891	+	1.10406i	0.264638	+	0.0453767i
$593$	21.4030	−	28.9387i	0.878915	−	1.18837i	−0.102165	−	0.994767i	$-0.532577\pi$
$593$	21.4030	−	28.9387i	0.878915	−	1.18837i	0.981080	−	0.193604i	$-0.0620177\pi$
$594$	−1.74360	−	1.98112i	−0.0715409	−	0.0812863i
$595$	4.92356	+	12.2527i	0.201846	+	0.502313i
$596$	2.66369	+	1.48803i	0.109109	+	0.0609520i
$597$	15.1057	−	3.93323i	0.618237	−	0.160976i
$598$	−2.08765	+	6.81689i	−0.0853703	+	0.278763i
$599$	−33.0329	+	31.6595i	−1.34969	+	1.29357i	−0.428985	+	0.903312i	$0.641129\pi$
$599$	−33.0329	+	31.6595i	−1.34969	+	1.29357i	−0.920704	+	0.390261i	$0.872385\pi$
$600$	11.5285	−	1.97675i	0.470647	−	0.0807006i
$601$	−7.16965	−	9.69401i	−0.292456	−	0.395427i	0.633080	−	0.774087i	$-0.281791\pi$
$601$	−7.16965	−	9.69401i	−0.292456	−	0.395427i	−0.925536	+	0.378660i	$0.876385\pi$
$602$	−9.96506	+	8.04622i	−0.406146	+	0.327940i
$603$	5.82468	+	0.495753i	0.237199	+	0.0201886i
$604$	−10.4116	+	14.0774i	−0.423641	+	0.572801i
$605$	−1.74253	−	3.45610i	−0.0708438	−	0.140510i
$606$	−4.57773	+	3.69626i	−0.185958	+	0.150150i
$607$	−6.19099	+	2.79850i	−0.251284	+	0.113588i	−0.533609	−	0.845731i	$-0.679165\pi$
$607$	−6.19099	+	2.79850i	−0.251284	+	0.113588i	0.282325	+	0.959319i	$0.408894\pi$
$608$	−5.66963	−	14.1094i	−0.229934	−	0.572213i
$609$	−9.19032	+	10.4422i	−0.372411	+	0.423141i
$610$	−1.34217	+	4.38265i	−0.0543429	+	0.177448i
$611$	1.79321	+	14.0035i	0.0725456	+	0.566519i
$612$	−0.541385	+	4.22775i	−0.0218842	+	0.170897i
$613$	−30.9000	−	24.9500i	−1.24804	−	1.00772i	−0.999233	−	0.0391685i	$-0.987529\pi$
$613$	−30.9000	−	24.9500i	−1.24804	−	1.00772i	−0.248807	−	0.968553i	$-0.580038\pi$
$614$	−4.54314	+	2.53795i	−0.183346	+	0.102423i
$615$	4.76984	−	4.57152i	0.192339	−	0.184342i
$616$	16.5124	−	18.7617i	0.665303	−	0.755931i
$617$	−27.0036	−	15.0851i	−1.08713	−	0.607305i	−0.161932	−	0.986802i	$-0.551773\pi$
$617$	−27.0036	−	15.0851i	−1.08713	−	0.607305i	−0.925193	+	0.379497i	$0.876097\pi$
$618$	−0.178179	−	0.0805420i	−0.00716741	−	0.00323987i
$619$	4.04512	−	31.5889i	0.162587	−	1.26967i	−0.680844	−	0.732428i	$-0.738387\pi$
$619$	4.04512	−	31.5889i	0.162587	−	1.26967i	0.843431	−	0.537237i	$-0.180532\pi$
$620$	−4.97219	−	1.29466i	−0.199688	−	0.0519947i
$621$	−2.85780	−	1.93153i	−0.114679	−	0.0775098i
$622$	0.419290	+	0.109175i	0.0168120	+	0.00437750i
$623$	15.3803	+	12.4187i	0.616199	+	0.497546i
$624$	−0.371086	+	1.72185i	−0.0148553	+	0.0689290i
$625$	−5.98481	−	8.09200i	−0.239393	−	0.323680i
$626$	5.82317	+	11.5496i	0.232741	+	0.461614i
$627$	7.85956	+	1.34766i	0.313880	+	0.0538202i
$628$	9.90766	−	6.69641i	0.395359	−	0.267216i
$629$	32.0526			1.27802
$630$	−3.15824			−0.125827
$631$	12.7760	−	8.63505i	0.508603	−	0.343756i	−0.278643	−	0.960395i	$-0.589885\pi$
$631$	12.7760	−	8.63505i	0.508603	−	0.343756i	0.787246	+	0.616639i	$0.211506\pi$
$632$	0.691680	+	16.2827i	0.0275136	+	0.647691i
$633$	−9.53165	−	0.811263i	−0.378849	−	0.0322448i
$634$	23.1932	−	10.4840i	0.921121	−	0.416373i
$635$	−0.960388	−	3.13599i	−0.0381118	−	0.124448i
$636$	−6.42234	−	2.90308i	−0.254663	−	0.115115i
$637$	−0.723431	−	5.64937i	−0.0286634	−	0.223836i
$638$	−11.7458	+	0.999712i	−0.465019	+	0.0395790i
$639$	1.45062	−	0.810364i	0.0573855	−	0.0320575i
$640$	0.810400	−	3.76027i	0.0320339	−	0.148638i
$641$	5.39254	+	8.75804i	0.212993	+	0.345922i	0.940275	−	0.340417i	$-0.110568\pi$
$641$	5.39254	+	8.75804i	0.212993	+	0.345922i	−0.727282	+	0.686339i	$0.759217\pi$
$642$	0.172747	−	0.0780865i	0.00681777	−	0.00308183i
$643$	2.90995	+	3.30635i	0.114757	+	0.130390i	0.805215	−	0.592984i	$-0.202050\pi$
$643$	2.90995	+	3.30635i	0.114757	+	0.130390i	−0.690457	+	0.723373i	$0.742591\pi$
$644$	5.03412	−	9.98458i	0.198372	−	0.393448i
$645$	−2.58595	−	3.49644i	−0.101822	−	0.137672i
$646$	6.22123	+	10.1039i	0.244771	+	0.397534i
$647$	−13.9514	−	45.5560i	−0.548484	−	1.79099i	−0.609420	−	0.792848i	$-0.708598\pi$
$647$	−13.9514	−	45.5560i	−0.548484	−	1.79099i	0.0609358	−	0.998142i	$-0.480592\pi$
$648$	−2.59987	−	1.45238i	−0.102133	−	0.0570547i
$649$	7.13660	+	2.52152i	0.280136	+	0.0989783i
$650$	7.85611	−	2.04557i	0.308142	−	0.0802339i
$651$	−13.5263	−	6.11428i	−0.530138	−	0.239638i
$652$	−0.791022	+	18.6213i	−0.0309788	+	0.729266i
$653$	2.09391	−	9.71578i	0.0819410	−	0.380208i	−0.917922	−	0.396761i	$-0.870134\pi$
$653$	2.09391	−	9.71578i	0.0819410	−	0.380208i	0.999863	+	0.0165532i	$0.00526930\pi$
$654$	−6.25116	+	1.07187i	−0.244440	+	0.0419134i
$655$	0.938517	+	4.35473i	0.0366709	+	0.170153i
$656$	−1.98529	−	4.94058i	−0.0775125	−	0.192897i
$657$	−2.31247	−	7.55101i	−0.0902180	−	0.294593i
$658$	−0.865836	+	20.3824i	−0.0337538	+	0.794590i
$659$	−12.6955	−	10.2509i	−0.494547	−	0.399319i	0.348374	−	0.937355i	$-0.386734\pi$
$659$	−12.6955	−	10.2509i	−0.494547	−	0.399319i	−0.842921	+	0.538037i	$0.819166\pi$
$660$	2.09721	+	2.01001i	0.0816339	+	0.0782397i
$661$	16.0704	−	26.0999i	0.625065	−	1.01517i	−0.371178	−	0.928562i	$-0.621046\pi$
$661$	16.0704	−	26.0999i	0.625065	−	1.01517i	0.996242	−	0.0866079i	$-0.0276027\pi$
$662$	−4.42970	+	34.5921i	−0.172165	+	1.34446i
$663$	−0.366774	+	8.63416i	−0.0142443	+	0.335323i
$664$	−11.6736	−	18.9592i	−0.453024	−	0.735759i
$665$	7.42462	−	5.99496i	0.287915	−	0.232475i
$666$	−2.85833	+	7.11323i	−0.110758	+	0.275632i
$667$	−14.5271	+	5.13274i	−0.562490	+	0.198740i
$668$	15.1387			0.585733
$669$	3.38121	−	14.5454i	0.130725	−	0.562356i
$670$	5.92829			0.229030
$671$	11.4843	−	4.05767i	0.443347	−	0.156645i
$672$	5.96700	−	14.8495i	0.230182	−	0.572830i
$673$	28.1455	−	22.7259i	1.08493	−	0.876019i	0.0921219	−	0.995748i	$-0.470635\pi$
$673$	28.1455	−	22.7259i	1.08493	−	0.876019i	0.992807	+	0.119729i	$0.0382026\pi$
$674$	6.51869	+	10.5870i	0.251091	+	0.407797i
$675$	−0.166694	+	3.92411i	−0.00641607	+	0.151039i
$676$	−1.12988	+	8.82339i	−0.0434569	+	0.339361i
$677$	−6.21133	+	10.0878i	−0.238721	+	0.387707i	−0.948530	−	0.316686i	$-0.897430\pi$
$677$	−6.21133	+	10.0878i	−0.238721	+	0.387707i	0.709809	+	0.704394i	$0.248781\pi$
$678$	−8.50012	−	8.14671i	−0.326445	−	0.312872i
$679$	−1.89156	−	1.52733i	−0.0725916	−	0.0586136i
$680$	−0.535922	+	12.6160i	−0.0205517	+	0.483802i
$681$	−7.42630	−	24.2494i	−0.284576	−	0.929239i
$682$	−4.69029	−	11.6722i	−0.179601	−	0.446953i
$683$	−5.23609	−	24.2956i	−0.200354	−	0.929644i	−0.960151	−	0.279483i	$-0.909837\pi$
$683$	−5.23609	−	24.2956i	−0.200354	−	0.929644i	0.759797	−	0.650160i	$-0.225298\pi$
$684$	3.03590	−	0.520557i	0.116080	−	0.0199040i
$685$	1.52358	−	7.06944i	0.0582130	−	0.270109i
$686$	−0.556770	+	13.1068i	−0.0212576	+	0.500420i
$687$	19.3510	+	8.74720i	0.738286	+	0.333727i
$688$	−3.39169	+	0.883127i	−0.129307	+	0.0336689i
$689$	−13.4738	−	4.76061i	−0.513312	−	0.181365i
$690$	−3.05384	−	1.70597i	−0.116258	−	0.0649454i
$691$	1.51335	+	4.94161i	0.0575706	+	0.187988i	0.980321	−	0.197411i	$-0.0632532\pi$
$691$	1.51335	+	4.94161i	0.0575706	+	0.187988i	−0.922750	+	0.385398i	$0.874064\pi$
$692$	−6.70851	−	10.8953i	−0.255019	−	0.414178i
$693$	4.99046	+	6.74755i	0.189572	+	0.256318i
$694$	−7.11505	+	14.1119i	−0.270084	+	0.535679i
$695$	−12.5850	−	14.2994i	−0.477377	−	0.542406i
$696$	−12.1212	+	5.47914i	−0.459454	+	0.207686i
$697$	−13.6970	−	22.2454i	−0.518812	−	0.842604i
$698$	−1.47986	+	6.86655i	−0.0560133	+	0.259903i
$699$	−13.5441	+	7.56617i	−0.512284	+	0.286179i
$700$	−12.6866	+	1.07979i	−0.479509	+	0.0408123i
$701$	−4.19977	−	32.7966i	−0.158623	−	1.23871i	−0.854080	−	0.520142i	$-0.825879\pi$
$701$	−4.19977	−	32.7966i	−0.158623	−	1.23871i	0.695457	−	0.718568i	$-0.255202\pi$
$702$	−1.88341	−	0.851357i	−0.0710849	−	0.0321324i
$703$	−6.78275	−	22.1480i	−0.255816	−	0.835327i
$704$	16.4567	−	7.43892i	0.620237	−	0.280365i
$705$	−6.90194	−	0.587442i	−0.259942	−	0.0221243i
$706$	1.32228	+	31.1276i	0.0497647	+	1.17150i
$707$	15.5017	−	10.4773i	0.583002	−	0.394041i
$708$	2.92365			0.109877
$709$	−26.6657			−1.00145			−0.500726	−	0.865606i	$-0.666934\pi$
$709$	−26.6657			−1.00145			−0.500726	+	0.865606i	$0.666934\pi$
$710$	1.39611	−	0.943606i	0.0523951	−	0.0354129i
$711$	−5.39380	−	0.924860i	−0.202283	−	0.0346850i
$712$	8.51042	+	16.8794i	0.318941	+	0.632582i
$713$	−9.77645	−	13.2186i	−0.366131	−	0.495042i
$714$	−2.63096	+	12.2077i	−0.0984611	+	0.456861i
$715$	4.58248	+	3.70010i	0.171375	+	0.138376i
$716$	−16.1341	−	4.20099i	−0.602960	−	0.156999i
$717$	0.855912	+	0.578495i	0.0319646	+	0.0216043i
$718$	15.2206	+	3.96314i	0.568029	+	0.147903i
$719$	−5.96788	+	46.6040i	−0.222564	+	1.73804i	0.366917	+	0.930254i	$0.380413\pi$
$719$	−5.96788	+	46.6040i	−0.222564	+	1.73804i	−0.589481	+	0.807782i	$0.700668\pi$
$720$	−0.787502	−	0.355974i	−0.0293485	−	0.0132664i
$721$	0.542853	+	0.303256i	0.0202169	+	0.0112938i
$722$	−6.62796	+	7.53083i	−0.246667	+	0.280268i
$723$	4.87259	−	4.67000i	0.181214	−	0.173679i
$724$	9.73663	−	5.43921i	0.361859	−	0.202147i
$725$	13.6496	+	11.0213i	0.506935	+	0.409321i
$726$	0.464933	−	3.63073i	0.0172553	−	0.134749i
$727$	3.53845	+	27.6323i	0.131234	+	1.02482i	0.914911	+	0.403656i	$0.132261\pi$
$727$	3.53845	+	27.6323i	0.131234	+	1.02482i	−0.783677	+	0.621169i	$0.786658\pi$
$728$	5.73173	−	18.7161i	0.212432	−	0.693664i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	−2.98609	−	7.43118i	−0.110520	−	0.275040i
$731$	−15.6692	+	7.08291i	−0.579545	+	0.261971i
$732$	3.66048	−	2.95563i	0.135295	−	0.109243i
$733$	−2.92320	−	5.79783i	−0.107971	−	0.214148i	0.832497	−	0.554029i	$-0.186910\pi$
$733$	−2.92320	−	5.79783i	−0.107971	−	0.214148i	−0.940468	+	0.339881i	$0.889613\pi$
$734$	−4.24640	+	5.74151i	−0.156737	+	0.211923i
$735$	2.78443	+	0.236990i	0.102705	+	0.00874151i
$736$	13.7909	−	11.1354i	0.508341	−	0.410457i
$737$	−9.36755	−	12.6658i	−0.345058	−	0.466549i
$738$	6.15823	−	1.05593i	0.226687	−	0.0388695i
$739$	28.4518	−	27.2689i	1.04662	−	1.00310i	0.0466260	−	0.998912i	$-0.485153\pi$
$739$	28.4518	−	27.2689i	1.04662	−	1.00310i	0.999991	−	0.00418894i	$-0.00133338\pi$
$740$	2.47085	−	8.06818i	0.0908304	−	0.296592i
$741$	6.04372	−	1.57366i	0.222022	−	0.0578100i
$742$	−18.0276	−	10.0708i	−0.661814	−	0.369712i
$743$	−6.64082	−	16.5263i	−0.243628	−	0.606292i	0.755158	−	0.655542i	$-0.227560\pi$
$743$	−6.64082	−	16.5263i	−0.243628	−	0.606292i	−0.998786	+	0.0492508i	$0.984317\pi$
$744$	−9.37813	−	10.6556i	−0.343819	−	0.390654i
$745$	−1.80490	+	2.44039i	−0.0661265	+	0.0894089i
$746$	33.3398	+	5.71668i	1.22066	+	0.209302i
$747$	7.04927	−	2.49067i	0.257919	−	0.0911287i
$748$	9.51649	−	6.43202i	0.347957	−	0.235178i
$749$	−0.568420	+	0.200836i	−0.0207696	+	0.00733838i
$750$	0.384251	+	9.04558i	0.0140309	+	0.330298i
$751$	−10.3860	+	14.0427i	−0.378989	+	0.512427i	−0.951575	−	0.307418i	$-0.900535\pi$
$751$	−10.3860	+	14.0427i	−0.378989	+	0.512427i	0.572586	+	0.819845i	$0.305940\pi$
$752$	−2.51326	+	4.98475i	−0.0916490	+	0.181775i
$753$	−13.2426	+	2.27068i	−0.482589	+	0.0827481i
$754$	−8.05988	+	4.50252i	−0.293524	+	0.163972i
$755$	−12.5754	−	12.0525i	−0.457664	−	0.438635i
$756$	2.68583	+	1.81530i	0.0976826	+	0.0660219i
$757$	−26.8641	−	18.1570i	−0.976392	−	0.659926i	−0.0357621	−	0.999360i	$-0.511386\pi$
$757$	−26.8641	−	18.1570i	−0.976392	−	0.659926i	−0.940630	+	0.339435i	$0.889764\pi$
$758$	5.23802	−	8.50708i	0.190253	−	0.308991i
$759$	1.18069	+	9.22018i	0.0428564	+	0.334671i
$760$	8.83094	−	2.29940i	0.320332	−	0.0834079i
$761$	6.83568	+	2.41520i	0.247793	+	0.0875509i	0.454148	−	0.890926i	$-0.349944\pi$
$761$	6.83568	+	2.41520i	0.247793	+	0.0875509i	−0.206355	+	0.978477i	$0.566160\pi$
$762$	0.908241	−	2.96572i	0.0329021	−	0.107437i
$763$	20.0964	−	1.71045i	0.727537	−	0.0619225i
$764$	7.74550	+	7.42346i	0.280223	+	0.268572i
$765$	−4.10335	−	1.06843i	−0.148357	−	0.0386291i
$766$	5.69680	−	9.25219i	0.205834	−	0.334295i
$767$	5.90646	−	0.502714i	0.213270	−	0.0181519i
$768$	12.3028	−	11.7913i	0.443940	−	0.425482i
$769$	8.00857	+	37.1599i	0.288796	+	1.34002i	0.856227	+	0.516599i	$0.172802\pi$
$769$	8.00857	+	37.1599i	0.288796	+	1.34002i	−0.567431	+	0.823421i	$0.692063\pi$
$770$	5.62302	+	6.38899i	0.202640	+	0.230243i
$771$	16.5706	+	1.41036i	0.596774	+	0.0507930i
$772$	1.20189	−	2.99101i	0.0432568	−	0.107649i
$773$	−33.3776	−	5.72316i	−1.20051	−	0.205848i	−0.466209	−	0.884674i	$-0.654381\pi$
$773$	−33.3776	−	5.72316i	−1.20051	−	0.205848i	−0.734299	+	0.678827i	$0.762489\pi$
$774$	−0.174548	−	4.10899i	−0.00627398	−	0.147694i
$775$	−6.98028	+	17.3711i	−0.250739	+	0.623988i
$776$	−1.04666	−	2.07593i	−0.0375730	−	0.0745217i
$777$	10.9752	−	21.7679i	0.393732	−	0.780921i
$778$	4.81948	+	22.3625i	0.172787	+	0.801733i
$779$	−12.4729	+	14.1719i	−0.446886	+	0.507762i
$780$	2.14509	+	0.757908i	0.0768065	+	0.0271375i
$781$	−4.22206	−	1.49175i	−0.151077	−	0.0533790i
$782$	−9.13818	+	10.3830i	−0.326781	+	0.371295i
$783$	−0.941045	−	4.36647i	−0.0336302	−	0.156045i
$784$	1.01392	−	2.01098i	0.0362113	−	0.0718208i
$785$	5.35580	+	10.6226i	0.191157	+	0.379137i
$786$	−1.57078	+	3.90905i	−0.0560280	+	0.139431i
$787$	−0.370319	−	8.71759i	−0.0132004	−	0.310749i	−0.993544	−	0.113449i	$-0.963810\pi$
$787$	−0.370319	−	8.71759i	−0.0132004	−	0.310749i	0.980343	−	0.197299i	$-0.0632170\pi$
$788$	−9.28438	−	1.59197i	−0.330742	−	0.0567115i
$789$	5.24171	−	13.0445i	0.186610	−	0.464397i
$790$	−5.52981	−	0.470656i	−0.196742	−	0.0167452i
$791$	24.7362	+	28.1058i	0.879519	+	0.999328i
$792$	1.69079	+	7.84530i	0.0600796	+	0.278771i
$793$	6.88683	−	6.60049i	0.244559	−	0.234390i
$794$	−36.3589	+	3.09460i	−1.29033	+	0.109823i
$795$	3.67615	−	5.97045i	0.130380	−	0.211750i
$796$	−15.7242	−	4.09426i	−0.557329	−	0.145117i
$797$	−10.0515	−	9.63357i	−0.356042	−	0.341238i	0.492552	−	0.870283i	$-0.336064\pi$
$797$	−10.0515	−	9.63357i	−0.356042	−	0.341238i	−0.848594	+	0.529044i	$0.822550\pi$
$798$	8.99212	−	0.765342i	0.318318	−	0.0270928i
$799$	−8.02031	+	26.1891i	−0.283738	+	0.926502i
$800$	−19.0304	−	6.72388i	−0.672828	−	0.237725i
$801$	−6.14280	+	1.59946i	−0.217045	+	0.0565142i
$802$	−2.39626	−	18.7128i	−0.0846150	−	0.660771i
$803$	−11.1582	+	18.1221i	−0.393765	+	0.639514i
$804$	−5.04154	−	3.40749i	−0.177801	−	0.120173i
$805$	9.21623	+	6.22909i	0.324830	+	0.219546i
$806$	−7.11259	−	6.81686i	−0.250530	−	0.240114i
$807$	−16.9019	+	9.44197i	−0.594976	+	0.332373i
$808$	17.6346	−	3.02376i	0.620384	−	0.106376i
$809$	−9.66813	+	19.1756i	−0.339913	+	0.674178i	−0.996811	−	0.0798022i	$-0.974571\pi$
$809$	−9.66813	+	19.1756i	−0.339913	+	0.674178i	0.656897	+	0.753980i	$0.271868\pi$
$810$	0.603031	−	0.815352i	0.0211883	−	0.0286485i
$811$	−2.29821	−	54.1017i	−0.0807011	−	1.89977i	−0.350059	−	0.936728i	$-0.613838\pi$
$811$	−2.29821	−	54.1017i	−0.0807011	−	1.89977i	0.269358	−	0.963040i	$-0.413189\pi$
$812$	13.6529	−	4.82387i	0.479122	−	0.169285i
$813$	−15.2138	+	10.2827i	−0.533572	+	0.360632i
$814$	19.4788	−	6.88231i	0.682733	−	0.241225i
$815$	−18.2747	−	3.13351i	−0.640135	−	0.109762i
$816$	−2.03199	+	2.74743i	−0.0711338	+	0.0961793i
$817$	8.21002	+	9.32839i	0.287232	+	0.326359i
$818$	−3.83134	−	9.53466i	−0.133960	−	0.333372i
$819$	5.73815	+	3.20552i	0.200507	+	0.112010i
$820$	−6.65541	+	1.73293i	−0.232417	+	0.0605167i
$821$	−3.60733	+	11.7792i	−0.125897	+	0.411096i	−0.996760	−	0.0804288i	$-0.974371\pi$
$821$	−3.60733	+	11.7792i	−0.125897	+	0.411096i	0.870864	+	0.491525i	$0.163560\pi$
$822$	4.93752	−	4.73223i	0.172216	−	0.165056i
$823$	−22.6174	+	3.87815i	−0.788395	+	0.135184i	−0.549093	−	0.835761i	$-0.685027\pi$
$823$	−22.6174	+	3.87815i	−0.788395	+	0.135184i	−0.239302	+	0.970945i	$0.576919\pi$
$824$	0.353579	+	0.478070i	0.0123175	+	0.0166544i
$825$	8.23512	−	6.64940i	0.286710	−	0.231502i
$826$	8.53509	+	0.726443i	0.296974	+	0.0252762i
$827$	−15.8853	+	21.4784i	−0.552386	+	0.746876i	−0.988201	−	0.153161i	$-0.951055\pi$
$827$	−15.8853	+	21.4784i	−0.552386	+	0.746876i	0.435815	+	0.900036i	$0.356460\pi$
$828$	1.61648	+	3.20609i	0.0561764	+	0.111419i
$829$	4.45389	−	3.59626i	0.154690	−	0.124903i	−0.547763	−	0.836633i	$-0.684520\pi$
$829$	4.45389	−	3.59626i	0.154690	−	0.124903i	0.702453	+	0.711730i	$0.252088\pi$
$830$	6.90887	−	3.12301i	0.239810	−	0.108401i
$831$	−7.97425	−	19.8447i	−0.276624	−	0.688404i
$832$	9.34465	−	10.6176i	0.323967	−	0.368098i
$833$	3.23561	−	10.5654i	0.112107	−	0.366069i
$834$	−2.28816	−	17.8686i	−0.0792324	−	0.618737i
$835$	−1.91291	+	14.9382i	−0.0661989	+	0.516957i
$836$	−6.45827	−	5.21469i	−0.223364	−	0.180354i
$837$	4.16121	−	2.32459i	0.143832	−	0.0803496i
$838$	21.5232	−	20.6283i	0.743506	−	0.712593i
$839$	15.3395	−	17.4291i	0.529579	−	0.601718i	−0.422955	−	0.906151i	$-0.639007\pi$
$839$	15.3395	−	17.4291i	0.529579	−	0.601718i	0.952534	+	0.304432i	$0.0984667\pi$
$840$	8.38444	+	4.68383i	0.289291	+	0.161607i
$841$	8.24517	+	3.72705i	0.284316	+	0.128519i
$842$	−2.59618	+	20.2739i	−0.0894702	+	0.698686i
$843$	20.9250	+	5.44843i	0.720694	+	0.187654i
$844$	8.25010	+	5.57609i	0.283980	+	0.191937i
$845$	−8.56376	−	2.22983i	−0.294602	−	0.0767084i
$846$	−5.09675	−	4.11534i	−0.175230	−	0.141488i
$847$	−2.45233	+	11.3788i	−0.0842630	+	0.390982i
$848$	−3.36005	−	4.54309i	−0.115385	−	0.156010i
$849$	−12.2785	−	24.3530i	−0.421398	−	0.835792i
$850$	15.5231	+	2.66170i	0.532438	+	0.0912957i
$851$	22.3707	−	15.1200i	0.766858	−	0.518305i
$852$	−1.72965			−0.0592568
$853$	22.8580			0.782642			0.391321	−	0.920254i	$-0.372018\pi$
$853$	22.8580			0.782642			0.391321	+	0.920254i	$0.372018\pi$
$854$	11.4205	−	7.71894i	0.390803	−	0.264137i
$855$	0.130049	+	3.06146i	0.00444760	+	0.104700i
$856$	−0.574412	−	0.0488897i	−0.0196330	−	0.00167101i
$857$	14.2794	−	6.45471i	0.487776	−	0.220489i	−0.152986	−	0.988228i	$-0.548889\pi$
$857$	14.2794	−	6.45471i	0.487776	−	0.220489i	0.640762	+	0.767740i	$0.278619\pi$
$858$	1.63103	+	5.32586i	0.0556823	+	0.181822i
$859$	−1.95525	−	0.883830i	−0.0667124	−	0.0301559i	0.378269	−	0.925696i	$-0.376519\pi$
$859$	−1.95525	−	0.883830i	−0.0667124	−	0.0301559i	−0.444981	+	0.895540i	$0.646790\pi$
$860$	0.574993	+	4.49020i	0.0196071	+	0.153115i
$861$	−19.7976	+	1.68502i	−0.674700	+	0.0574254i
$862$	28.2440	−	15.7780i	0.961994	−	0.537402i
$863$	−1.56160	+	7.24587i	−0.0531576	+	0.246652i	−0.996324	−	0.0856698i	$-0.972697\pi$
$863$	−1.56160	+	7.24587i	−0.0531576	+	0.246652i	0.943166	+	0.332322i	$0.107832\pi$
$864$	2.69430	+	4.37583i	0.0916620	+	0.148869i
$865$	11.5987	−	5.24294i	0.394367	−	0.178265i
$866$	−15.1543	−	17.2186i	−0.514965	−	0.585113i
$867$	0.105328	−	0.208906i	0.00357713	−	0.00709481i
$868$	9.18814	+	12.4232i	0.311866	+	0.421670i
$869$	7.73233	+	12.5581i	0.262301	+	0.426005i
$870$	−1.32643	−	4.33125i	−0.0449702	−	0.146843i
$871$	−10.7710	−	6.01705i	−0.364962	−	0.203880i
$872$	18.1851	+	6.42522i	0.615826	+	0.217585i
$873$	0.755480	−	0.196712i	0.0255691	−	0.00665768i
$874$	9.10829	+	4.11720i	0.308092	+	0.139267i
$875$	1.22193	−	28.7652i	0.0413088	−	0.972442i
$876$	−1.73189	+	8.03598i	−0.0585150	+	0.271511i
$877$	26.0179	−	4.46121i	0.878561	−	0.150644i	0.287993	−	0.957632i	$-0.407012\pi$
$877$	26.0179	−	4.46121i	0.878561	−	0.150644i	0.590568	+	0.806988i	$0.298904\pi$
$878$	4.28604	+	19.8873i	0.144647	+	0.671164i
$879$	−1.63511	−	4.06912i	−0.0551508	−	0.137248i
$880$	0.681973	+	2.22687i	0.0229893	+	0.0750679i
$881$	−1.27328	+	29.9740i	−0.0428980	+	1.00985i	0.840670	+	0.541548i	$0.182162\pi$
$881$	−1.27328	+	29.9740i	−0.0428980	+	1.00985i	−0.883568	+	0.468303i	$0.844865\pi$
$882$	2.05617	+	1.66024i	0.0692347	+	0.0559031i
$883$	33.5536	+	32.1585i	1.12917	+	1.08222i	0.995837	+	0.0911476i	$0.0290535\pi$
$883$	33.5536	+	32.1585i	1.12917	+	1.08222i	0.133330	+	0.991072i	$0.457433\pi$
$884$	4.71654	−	7.66015i	0.158634	−	0.257639i
$885$	−0.369429	+	2.88492i	−0.0124182	+	0.0969757i
$886$	0.0274885	−	0.647100i	0.000923493	−	0.0217398i
$887$	22.4541	+	36.4678i	0.753935	+	1.22447i	0.968805	+	0.247825i	$0.0797158\pi$
$887$	22.4541	+	36.4678i	0.753935	+	1.22447i	−0.214870	+	0.976643i	$0.568933\pi$
$888$	18.1375	−	14.6450i	0.608656	−	0.491455i
$889$	−3.67764	+	9.15217i	−0.123344	+	0.306954i
$890$	−6.06955	+	2.14451i	−0.203452	+	0.0718841i
$891$	−2.69487			−0.0902815
$892$	−10.4568	+	11.5017i	−0.350120	+	0.385105i
$893$	19.7936			0.662366
$894$	−2.70654	+	0.956281i	−0.0905202	+	0.0319828i
$895$	6.18404	−	15.3896i	0.206710	−	0.514417i
$896$	−9.00044	+	7.26735i	−0.300684	+	0.242785i
$897$	3.81695	+	6.19911i	0.127444	+	0.206982i
$898$	−1.60603	+	37.8073i	−0.0535940	+	1.26164i
$899$	2.70428	−	21.1181i	0.0901927	−	0.704328i
$900$	2.14361	−	3.48144i	0.0714536	−	0.116048i
$901$	−20.0155	−	19.1833i	−0.666813	−	0.639088i
$902$	−13.1004	−	10.5778i	−0.436196	−	0.352204i
$903$	−0.555067	+	13.0667i	−0.0184715	+	0.434833i
$904$	10.4840	+	34.2339i	0.348693	+	1.13860i
$905$	4.13686	+	10.2950i	0.137514	+	0.342216i
$906$	−3.47045	−	16.1029i	−0.115298	−	0.534985i
$907$	20.5855	−	3.52974i	0.683531	−	0.117203i	0.183250	−	0.983066i	$-0.441338\pi$
$907$	20.5855	−	3.52974i	0.683531	−	0.117203i	0.500281	+	0.865863i	$0.333230\pi$
$908$	−5.56180	+	25.8068i	−0.184575	+	0.856430i
$909$	−0.254986	+	6.00256i	−0.00845734	+	0.199092i
$910$	6.07391	+	2.74558i	0.201348	+	0.0910150i
$911$	−29.0801	+	7.57186i	−0.963466	+	0.250867i	−0.700272	−	0.713876i	$-0.746938\pi$
$911$	−29.0801	+	7.57186i	−0.963466	+	0.250867i	−0.263194	+	0.964743i	$0.584776\pi$
$912$	2.32844	+	0.822690i	0.0771023	+	0.0272420i
$913$	−17.5893	−	9.82596i	−0.582120	−	0.325192i
$914$	−3.76308	−	12.2877i	−0.124472	−	0.406443i
$915$	2.45395	+	3.98547i	0.0811252	+	0.131756i
$916$	−13.1447	−	17.7728i	−0.434314	−	0.587231i
$917$	6.03136	−	11.9625i	0.199173	−	0.395037i
$918$	−2.64927	−	3.01015i	−0.0874388	−	0.0993498i
$919$	13.8632	−	6.26655i	0.457304	−	0.206714i	−0.170071	−	0.985432i	$-0.554400\pi$
$919$	13.8632	−	6.26655i	0.457304	−	0.206714i	0.627375	+	0.778717i	$0.284129\pi$
$920$	5.57723	+	9.05799i	0.183876	+	0.298633i
$921$	−1.11953	+	5.19462i	−0.0368897	+	0.171169i
$922$	−27.8490	+	15.5574i	−0.917158	+	0.512355i
$923$	−3.49430	+	0.297409i	−0.115016	+	0.00978933i
$924$	−1.10964	−	8.66535i	−0.0365045	−	0.285069i
$925$	−28.0161	−	12.6641i	−0.921165	−	0.416393i
$926$	−0.496705	−	1.62191i	−0.0163228	−	0.0532994i
$927$	−0.181942	+	0.0822431i	−0.00597577	+	0.00270122i
$928$	22.8708	+	1.94659i	0.750772	+	0.0639001i
$929$	0.215799	+	5.08008i	0.00708014	+	0.166672i	0.999157	+	0.0410427i	$0.0130680\pi$
$929$	0.215799	+	5.08008i	0.00708014	+	0.166672i	−0.992077	+	0.125629i	$0.959905\pi$
$930$	4.00485	−	2.70680i	0.131324	−	0.0887596i
$931$	−7.98526			−0.261706
$932$	16.1493			0.528989
$933$	0.366551	−	0.247745i	0.0120003	−	0.00811081i
$934$	11.9048	+	2.04129i	0.389538	+	0.0667931i
$935$	5.14434	+	10.2032i	0.168238	+	0.333680i
$936$	3.73745	+	5.05337i	0.122163	+	0.165175i
$937$	−9.37825	+	43.5152i	−0.306374	+	1.42158i	0.517925	+	0.855426i	$0.326705\pi$
$937$	−9.37825	+	43.5152i	−0.306374	+	1.42158i	−0.824299	+	0.566154i	$0.808431\pi$
$938$	−13.8713	−	11.2003i	−0.452912	−	0.365701i
$939$	12.7815	+	3.32806i	0.417110	+	0.108607i
$940$	5.97396	+	4.03769i	0.194849	+	0.131695i
$941$	−15.1124	−	3.93496i	−0.492650	−	0.128276i	−0.00264652	−	0.999996i	$-0.500842\pi$
$941$	−15.1124	−	3.93496i	−0.492650	−	0.128276i	−0.490004	+	0.871720i	$0.663005\pi$
$942$	−1.42901	+	11.1593i	−0.0465596	+	0.363590i
$943$	−20.0533	−	9.06468i	−0.653026	−	0.295187i
$944$	2.04633	+	1.14315i	0.0666025	+	0.0372064i
$945$	−2.13064	+	2.42088i	−0.0693097	+	0.0787511i
$946$	−8.00156	+	7.66887i	−0.260153	+	0.249336i
$947$	−16.3592	+	9.13881i	−0.531604	+	0.296972i	−0.730343	−	0.683081i	$-0.760640\pi$
$947$	−16.3592	+	9.13881i	−0.531604	+	0.296972i	0.198739	+	0.980052i	$0.436315\pi$
$948$	4.43213	+	3.57870i	0.143949	+	0.116231i
$949$	−2.11705	+	16.5324i	−0.0687225	+	0.536664i
$950$	−1.44568	−	11.2895i	−0.0469042	−	0.366281i
$951$	7.61055	−	24.8511i	0.246789	−	0.805851i
$952$	25.0893	−	28.5069i	0.813147	−	0.923915i
$953$	11.6621	+	29.0223i	0.377773	+	0.940123i	0.988899	+	0.148590i	$0.0474735\pi$
$953$	11.6621	+	29.0223i	0.377773	+	0.940123i	−0.611126	+	0.791533i	$0.709283\pi$
$954$	6.04213	−	2.73121i	0.195621	−	0.0884263i
$955$	−8.30386	+	6.70490i	−0.268707	+	0.216965i
$956$	−0.484135	−	0.960225i	−0.0156581	−	0.0310559i
$957$	−7.15773	+	9.67789i	−0.231377	+	0.312842i
$958$	7.89915	+	0.672317i	0.255210	+	0.0217216i
$959$	−16.9211	+	13.6629i	−0.546412	+	0.441197i
$960$	4.12663	+	5.57958i	0.133187	+	0.180080i
$961$	−8.16153	+	1.39943i	−0.263275	+	0.0451430i
$962$	11.6809	−	11.1953i	0.376608	−	0.360950i
$963$	0.0566846	−	0.185095i	0.00182664	−	0.00596459i
$964$	−6.79878	+	1.77027i	−0.218974	+	0.0570164i
$965$	2.79952	+	1.56391i	0.0901198	+	0.0503440i
$966$	3.92240	+	9.76128i	0.126201	+	0.314064i
$967$	20.1917	+	22.9422i	0.649321	+	0.737772i	0.978443	−	0.206515i	$-0.0662124\pi$
$967$	20.1917	+	22.9422i	0.649321	+	0.737772i	−0.329123	+	0.944287i	$0.606753\pi$
$968$	−6.61885	+	8.94928i	−0.212738	+	0.287641i
$969$	11.9420	+	2.04766i	0.383631	+	0.0657802i
$970$	0.746471	−	0.263745i	0.0239678	−	0.00846835i
$971$	−0.0681547	+	0.0460645i	−0.00218719	+	0.00147828i	−0.561068	−	0.827770i	$-0.689609\pi$
$971$	−0.0681547	+	0.0460645i	−0.00218719	+	0.00147828i	0.558881	+	0.829248i	$0.311231\pi$
$972$	−0.981480	+	0.346779i	−0.0314810	+	0.0111229i
$973$	2.43131	+	57.2350i	0.0779443	+	1.83487i
$974$	−10.9805	+	14.8466i	−0.351837	+	0.475714i
$975$	3.73197	−	7.40192i	0.119519	−	0.237051i
$976$	3.71772	−	0.637468i	0.119001	−	0.0204048i
$977$	−16.4842	+	9.20864i	−0.527377	+	0.294610i	−0.728605	−	0.684934i	$-0.759831\pi$
$977$	−16.4842	+	9.20864i	−0.527377	+	0.294610i	0.201228	+	0.979544i	$0.435507\pi$
$978$	−12.6593	−	12.1329i	−0.404798	−	0.387968i
$979$	14.1725	+	9.57893i	0.452955	+	0.306144i
$980$	−2.41006	−	1.62892i	−0.0769865	−	0.0520338i
$981$	−3.39560	+	5.51481i	−0.108413	+	0.176074i
$982$	2.51016	+	19.6022i	0.0801024	+	0.625531i
$983$	18.2374	−	4.74864i	0.581682	−	0.151458i	0.0505118	−	0.998723i	$-0.483915\pi$
$983$	18.2374	−	4.74864i	0.581682	−	0.151458i	0.531170	+	0.847265i	$0.321753\pi$
$984$	−17.9148	−	6.32969i	−0.571102	−	0.201783i
$985$	2.74405	−	8.96025i	0.0874326	−	0.285497i
$986$	−17.8468	+	1.51898i	−0.568356	+	0.0483743i
$987$	15.0396	+	14.4143i	0.478715	+	0.458811i
$988$	−6.29116	−	1.63809i	−0.200148	−	0.0521146i
$989$	−7.59492	+	12.3349i	−0.241505	+	0.392228i
$990$	−2.72308	+	0.231768i	−0.0865452	+	0.00736608i
$991$	−19.7193	+	18.8995i	−0.626406	+	0.600361i	−0.936638	−	0.350300i	$-0.886080\pi$
$991$	−19.7193	+	18.8995i	−0.626406	+	0.600361i	0.310232	+	0.950661i	$0.399593\pi$
$992$	5.16036	+	23.9442i	0.163842	+	0.760228i
$993$	23.5274	+	26.7323i	0.746620	+	0.848325i
$994$	−5.04941	−	0.429769i	−0.160158	−	0.0136314i
$995$	6.02693	−	14.9986i	0.191066	−	0.475487i
$996$	−7.67049	−	1.31524i	−0.243049	−	0.0416749i
$997$	0.696476	+	16.3956i	0.0220576	+	0.519254i	0.975805	+	0.218644i	$0.0701632\pi$
$997$	0.696476	+	16.3956i	0.0220576	+	0.519254i	−0.953747	+	0.300610i	$0.902810\pi$
$998$	14.0594	−	34.9883i	0.445044	−	1.10753i
$999$	3.52417	+	6.98978i	0.111500	+	0.221147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.b.4.14	✓	720
223.56	even	37	inner	669.2.i.b.502.14	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.b.4.14	✓	720	1.1	even	1	trivial
669.2.i.b.502.14	yes	720	223.56	even	37	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:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923374 - 0.326249i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-0.809890 + 0.653940i) q^{4} +(-0.542942 - 0.881794i) q^{5} +(0.0415633 - 0.978433i) q^{6} +(-0.395566 + 3.08903i) q^{7} +(-1.56141 + 2.53589i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-0.789024 - 0.637092i) q^{10} +(-0.114373 + 2.69244i) q^{11} +(0.304811 + 0.995313i) q^{12} +(0.786933 + 1.95836i) q^{13} +(0.642538 + 2.98139i) q^{14} +(-1.02065 + 0.175007i) q^{15} +(-0.175824 + 0.815827i) q^{16} +(-0.173781 + 4.09095i) q^{17} +(-0.892380 - 0.403381i) q^{18} +(2.86357 - 0.745617i) q^{19} +(1.01636 + 0.359104i) q^{20} +(2.71879 + 1.51881i) q^{21} +(0.772796 + 2.52344i) q^{22} +(1.80851 + 2.93720i) q^{23} +(1.77084 + 2.39434i) q^{24} +(1.76824 - 3.50710i) q^{25} +(1.36555 + 1.55156i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(-1.69968 - 2.76045i) q^{28} +(-0.941045 + 4.36647i) q^{29} +(-0.885343 + 0.494582i) q^{30} +(-4.74931 + 0.404226i) q^{31} +(-0.652717 - 5.09716i) q^{32} +(2.45564 + 1.11002i) q^{33} +(1.17420 + 3.83417i) q^{34} +(2.93866 - 1.32836i) q^{35} +(1.03719 + 0.0882780i) q^{36} +(-0.332228 - 7.82089i) q^{37} +(2.40089 - 1.62272i) q^{38} +2.11055 q^{39} +3.08389 q^{40} +(-5.28595 + 3.57268i) q^{41} +(3.00597 + 0.515425i) q^{42} +(1.89066 + 3.74989i) q^{43} +(-1.66806 - 2.25537i) q^{44} +(-0.218167 + 1.01230i) q^{45} +(2.62819 + 2.12211i) q^{46} +(6.47331 + 1.68552i) q^{47} +(0.691440 + 0.467332i) q^{48} +(-2.61151 - 0.679984i) q^{49} +(0.488563 - 3.81526i) q^{50} +(3.73115 + 1.68659i) q^{51} +(-1.91798 - 1.07145i) q^{52} +(-4.47330 + 5.08265i) q^{53} +(-0.707023 + 0.677626i) q^{54} +(2.43628 - 1.36099i) q^{55} +(-7.21580 - 5.82635i) q^{56} +(0.375853 - 2.93509i) q^{57} +(0.555618 + 4.33890i) q^{58} +(0.822438 - 2.68554i) q^{59} +(0.712167 - 0.809179i) q^{60} +(-1.68521 - 4.19381i) q^{61} +(-4.25351 + 1.92271i) q^{62} +(2.42300 - 1.95644i) q^{63} +(-3.01709 - 5.98404i) q^{64} +(1.29961 - 1.75719i) q^{65} +(2.62962 + 0.223814i) q^{66} +(-4.54819 + 3.67241i) q^{67} +(-2.53449 - 3.42686i) q^{68} +(3.39971 - 0.582939i) q^{69} +(2.28011 - 2.18531i) q^{70} +(-0.486560 + 1.58879i) q^{71} +(2.88195 - 0.750401i) q^{72} +(6.89434 + 3.85141i) q^{73} +(-2.85833 - 7.11323i) q^{74} +(-2.59490 - 2.94838i) q^{75} +(-1.83159 + 2.47647i) q^{76} +(-8.27179 - 1.41834i) q^{77} +(1.94883 - 0.688565i) q^{78} +(4.53403 - 3.06447i) q^{79} +(0.814854 - 0.287906i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-3.71533 + 5.02345i) q^{82} +(-3.36588 + 6.67582i) q^{83} +(-3.19513 + 0.547860i) q^{84} +(3.70173 - 2.06791i) q^{85} +(2.96918 + 2.84573i) q^{86} +(3.70072 + 2.50125i) q^{87} +(-6.64914 - 4.49404i) q^{88} +(3.32810 - 5.40519i) q^{89} +(0.128812 + 1.00591i) q^{90} +(-6.36071 + 1.65620i) q^{91} +(-3.38544 - 1.19615i) q^{92} +(-1.39573 + 4.55755i) q^{93} +(6.52719 - 0.555546i) q^{94} +(-2.21224 - 2.12026i) q^{95} +(-4.97297 - 1.29486i) q^{96} +(-0.409311 + 0.664763i) q^{97} +(-2.63324 + 0.224122i) q^{98} +(1.94558 - 1.86468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) \) 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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