LMFDB - Embedded newform 484.2.g.f.403.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,2,Mod(215,484)] 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("484.215"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.g (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-5,0,-1,4,10,0,-5,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			403.3
Root			$1.40874 + 0.124276i$ of defining polynomial
Character	$\chi$	$=$	484.403
Dual form			484.2.g.f.239.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.317132 + 1.37820i) q^{2} +(2.58584 + 0.840191i) q^{3} +(-1.79885 - 0.874140i) q^{4} +(1.88723 - 1.37116i) q^{5} +(-1.97800 + 3.29735i) q^{6} +(-0.399009 - 1.22802i) q^{7} +(1.77521 - 2.20196i) q^{8} +(3.55361 + 2.58185i) q^{9} +(1.29122 + 3.03582i) q^{10} +(-3.91711 - 3.77177i) q^{12} +(-0.172519 + 0.237451i) q^{13} +(1.81900 - 0.160468i) q^{14} +(6.03212 - 1.95995i) q^{15} +(2.47176 + 3.14490i) q^{16} +(1.74459 + 2.40122i) q^{17} +(-4.68526 + 4.07879i) q^{18} +(-0.529677 + 1.63018i) q^{19} +(-4.59344 + 0.816802i) q^{20} -3.51072i q^{21} +0.525735i q^{23} +(6.44048 - 4.20240i) q^{24} +(0.136498 - 0.420099i) q^{25} +(-0.272544 - 0.313068i) q^{26} +(2.22541 + 3.06301i) q^{27} +(-0.355706 + 2.55783i) q^{28} +(7.83802 - 2.54673i) q^{29} +(0.788227 + 8.93502i) q^{30} +(-2.61308 + 3.59660i) q^{31} +(-5.11817 + 2.40922i) q^{32} +(-3.86263 + 1.64289i) q^{34} +(-2.43684 - 1.77046i) q^{35} +(-4.13553 - 7.75072i) q^{36} +(-1.61424 - 4.96811i) q^{37} +(-2.07873 - 1.24698i) q^{38} +(-0.645610 + 0.469063i) q^{39} +(0.331012 - 6.58970i) q^{40} +(-5.32043 - 1.72871i) q^{41} +(4.83846 + 1.11336i) q^{42} -3.49429 q^{43} +10.2466 q^{45} +(-0.724567 - 0.166727i) q^{46} +(-7.28477 - 2.36696i) q^{47} +(3.74925 + 10.2090i) q^{48} +(4.31428 - 3.13451i) q^{49} +(0.535691 + 0.321349i) q^{50} +(2.49375 + 7.67498i) q^{51} +(0.517902 - 0.276335i) q^{52} +(-1.26920 - 0.922128i) q^{53} +(-4.92719 + 2.09567i) q^{54} +(-3.41238 - 1.30140i) q^{56} +(-2.73932 + 3.77036i) q^{57} +(1.02421 + 11.6100i) q^{58} +(-13.3851 + 4.34909i) q^{59} +(-12.5642 - 1.74725i) q^{60} +(-5.55273 - 7.64268i) q^{61} +(-4.12814 - 4.74194i) q^{62} +(1.75265 - 5.39410i) q^{63} +(-1.69724 - 7.81789i) q^{64} +0.684676i q^{65} +10.4249i q^{67} +(-1.03926 - 5.84447i) q^{68} +(-0.441718 + 1.35947i) q^{69} +(3.21285 - 2.79697i) q^{70} +(-2.11308 - 2.90841i) q^{71} +(11.9935 - 3.24157i) q^{72} +(-4.07207 + 1.32310i) q^{73} +(7.35896 - 0.649191i) q^{74} +(0.705927 - 0.971625i) q^{75} +(2.37782 - 2.46944i) q^{76} +(-0.441718 - 1.03853i) q^{78} +(7.96895 + 5.78978i) q^{79} +(8.97693 + 2.54600i) q^{80} +(-0.891031 - 2.74231i) q^{81} +(4.06978 - 6.78437i) q^{82} +(-3.04177 + 2.20997i) q^{83} +(-3.06886 + 6.31528i) q^{84} +(6.58490 + 2.13956i) q^{85} +(1.10815 - 4.81582i) q^{86} +22.4076 q^{87} +0.598152 q^{89} +(-3.24952 + 14.1218i) q^{90} +(0.360433 + 0.117112i) q^{91} +(0.459567 - 0.945722i) q^{92} +(-9.77886 + 7.10476i) q^{93} +(5.57237 - 9.28920i) q^{94} +(1.23560 + 3.80280i) q^{95} +(-15.2590 + 1.92962i) q^{96} +(6.73607 + 4.89404i) q^{97} +(2.95178 + 6.93999i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{4} + 4 q^{5} + 10 q^{6} - 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} - 10 q^{17} - 15 q^{18} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} - 30 q^{28} + 40 q^{29} + 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 5 * q^2 - q^4 + 4 * q^5 + 10 * q^6 - 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 - 10 * q^17 - 15 * q^18 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 - 30 * q^28 + 40 * q^29 + 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 - 50 * q^41 + 24 * q^42 + 40 * q^45 - 40 * q^46 - q^48 + 16 * q^49 + 25 * q^50 - 20 * q^52 - 12 * q^53 - 12 * q^56 - 50 * q^57 - 48 * q^60 + 20 * q^61 - 30 * q^62 - 37 * q^64 + 35 * q^68 + 4 * q^69 + 22 * q^70 - 10 * q^72 - 30 * q^73 + 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 - 10 * q^84 + 60 * q^85 + 46 * q^86 - 36 * q^89 - 40 * q^90 - 54 * q^92 + 2 * q^93 + 60 * q^94 - 55 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.317132	+	1.37820i	−0.224246	+	0.974533i
$2$	−0.317132	+	1.37820i	−0.224246	+	0.974533i
$3$	2.58584	+	0.840191i	1.49294	+	0.485085i	0.937949	−	0.346774i	$-0.112723\pi$
$3$	2.58584	+	0.840191i	1.49294	+	0.485085i	0.554988	+	0.831858i	$0.312723\pi$
$4$	−1.79885	−	0.874140i	−0.899427	−	0.437070i
$5$	1.88723	−	1.37116i	0.843997	−	0.613199i	−0.0794877	−	0.996836i	$-0.525328\pi$
$5$	1.88723	−	1.37116i	0.843997	−	0.613199i	0.923484	+	0.383636i	$0.125328\pi$
$6$	−1.97800	+	3.29735i	−0.807516	+	1.34614i
$7$	−0.399009	−	1.22802i	−0.150811	−	0.464149i	0.846901	−	0.531750i	$-0.178466\pi$
$7$	−0.399009	−	1.22802i	−0.150811	−	0.464149i	−0.997712	+	0.0676009i	$0.978466\pi$
$8$	1.77521	−	2.20196i	0.627632	−	0.778510i
$9$	3.55361	+	2.58185i	1.18454	+	0.860616i
$10$	1.29122	+	3.03582i	0.408320	+	0.960010i
$11$		0			0
$11$		0			0
$12$	−3.91711	−	3.77177i	−1.13077	−	1.08882i
$13$	−0.172519	+	0.237451i	−0.0478480	+	0.0658572i	−0.832271	−	0.554370i	$-0.812959\pi$
$13$	−0.172519	+	0.237451i	−0.0478480	+	0.0658572i	0.784423	+	0.620227i	$0.212959\pi$
$14$	1.81900	−	0.160468i	0.486148	−	0.0428868i
$15$	6.03212	−	1.95995i	1.55749	−	0.506058i
$16$	2.47176	+	3.14490i	0.617939	+	0.786226i
$17$	1.74459	+	2.40122i	0.423126	+	0.582382i	0.966358	−	0.257200i	$-0.0827999\pi$
$17$	1.74459	+	2.40122i	0.423126	+	0.582382i	−0.543233	+	0.839582i	$0.682800\pi$
$18$	−4.68526	+	4.07879i	−1.10433	+	0.961379i
$19$	−0.529677	+	1.63018i	−0.121516	+	0.373989i	−0.993250	−	0.115991i	$-0.962996\pi$
$19$	−0.529677	+	1.63018i	−0.121516	+	0.373989i	0.871734	+	0.489979i	$0.162996\pi$
$20$	−4.59344	+	0.816802i	−1.02712	+	0.182643i
$21$		−	3.51072i		−	0.766102i
$22$		0			0
$23$			0.525735i			0.109623i	0.998497	+	0.0548117i	$0.0174559\pi$
$23$			0.525735i			0.109623i	−0.998497	+	0.0548117i	$0.982544\pi$
$24$	6.44048	−	4.20240i	1.31466	−	0.857811i
$25$	0.136498	−	0.420099i	0.0272997	−	0.0840198i
$26$	−0.272544	−	0.313068i	−0.0534502	−	0.0613977i
$27$	2.22541	+	3.06301i	0.428280	+	0.589477i
$28$	−0.355706	+	2.55783i	−0.0672221	+	0.483384i
$29$	7.83802	−	2.54673i	1.45548	−	0.472915i	0.528796	−	0.848749i	$-0.322644\pi$
$29$	7.83802	−	2.54673i	1.45548	−	0.472915i	0.926687	+	0.375834i	$0.122644\pi$
$30$	0.788227	+	8.93502i	0.143910	+	1.63130i
$31$	−2.61308	+	3.59660i	−0.469324	+	0.645969i	−0.976410	−	0.215927i	$-0.930723\pi$
$31$	−2.61308	+	3.59660i	−0.469324	+	0.645969i	0.507086	+	0.861896i	$0.330723\pi$
$32$	−5.11817	+	2.40922i	−0.904773	+	0.425894i
$33$		0			0
$34$	−3.86263	+	1.64289i	−0.662435	+	0.281753i
$35$	−2.43684	−	1.77046i	−0.411900	−	0.299263i
$36$	−4.13553	−	7.75072i	−0.689255	−	1.29179i
$37$	−1.61424	−	4.96811i	−0.265379	−	0.816752i	−0.991606	−	0.129297i	$-0.958728\pi$
$37$	−1.61424	−	4.96811i	−0.265379	−	0.816752i	0.726227	−	0.687455i	$-0.241272\pi$
$38$	−2.07873	−	1.24698i	−0.337215	−	0.202287i
$39$	−0.645610	+	0.469063i	−0.103380	+	0.0751103i
$40$	0.331012	−	6.58970i	0.0523376	−	1.04192i
$41$	−5.32043	−	1.72871i	−0.830911	−	0.269979i	−0.137482	−	0.990504i	$-0.543901\pi$
$41$	−5.32043	−	1.72871i	−0.830911	−	0.269979i	−0.693429	+	0.720525i	$0.743901\pi$
$42$	4.83846	+	1.11336i	0.746591	+	0.171795i
$43$	−3.49429			−0.532874			−0.266437	−	0.963852i	$-0.585846\pi$
$43$	−3.49429			−0.532874			−0.266437	+	0.963852i	$0.585846\pi$
$44$		0			0
$45$	10.2466			1.52747
$46$	−0.724567	−	0.166727i	−0.106832	−	0.0245826i
$47$	−7.28477	−	2.36696i	−1.06259	−	0.345257i	−0.274994	−	0.961446i	$-0.588676\pi$
$47$	−7.28477	−	2.36696i	−1.06259	−	0.345257i	−0.787598	+	0.616189i	$0.788676\pi$
$48$	3.74925	+	10.2090i	0.541158	+	1.47354i
$49$	4.31428	−	3.13451i	0.616326	−	0.447787i
$50$	0.535691	+	0.321349i	0.0757582	+	0.0454455i
$51$	2.49375	+	7.67498i	0.349195	+	1.07471i
$52$	0.517902	−	0.276335i	0.0718200	−	0.0383208i
$53$	−1.26920	−	0.922128i	−0.174338	−	0.126664i	0.497194	−	0.867639i	$-0.334364\pi$
$53$	−1.26920	−	0.922128i	−0.174338	−	0.126664i	−0.671532	+	0.740975i	$0.734364\pi$
$54$	−4.92719	+	2.09567i	−0.670505	+	0.285185i
$55$		0			0
$56$	−3.41238	−	1.30140i	−0.455999	−	0.173907i
$57$	−2.73932	+	3.77036i	−0.362832	+	0.499396i
$58$	1.02421	+	11.6100i	0.134485	+	1.52447i
$59$	−13.3851	+	4.34909i	−1.74260	+	0.566204i	−0.995172	−	0.0981434i	$-0.968710\pi$
$59$	−13.3851	+	4.34909i	−1.74260	+	0.566204i	−0.747424	+	0.664347i	$0.768710\pi$
$60$	−12.5642	−	1.74725i	−1.62203	−	0.225569i
$61$	−5.55273	−	7.64268i	−0.710954	−	0.978545i	−0.999776	−	0.0211619i	$-0.993263\pi$
$61$	−5.55273	−	7.64268i	−0.710954	−	0.978545i	0.288822	−	0.957383i	$-0.406737\pi$
$62$	−4.12814	−	4.74194i	−0.524274	−	0.602227i
$63$	1.75265	−	5.39410i	0.220813	−	0.679592i
$64$	−1.69724	−	7.81789i	−0.212156	−	0.977236i
$65$			0.684676i			0.0849236i
$66$		0			0
$67$			10.4249i			1.27361i	0.771026	+	0.636803i	$0.219744\pi$
$67$			10.4249i			1.27361i	−0.771026	+	0.636803i	$0.780256\pi$
$68$	−1.03926	−	5.84447i	−0.126029	−	0.708746i
$69$	−0.441718	+	1.35947i	−0.0531766	+	0.163661i
$70$	3.21285	−	2.79697i	0.384009	−	0.334302i
$71$	−2.11308	−	2.90841i	−0.250777	−	0.345164i	0.665007	−	0.746838i	$-0.268429\pi$
$71$	−2.11308	−	2.90841i	−0.250777	−	0.345164i	−0.915783	+	0.401673i	$0.868429\pi$
$72$	11.9935	−	3.24157i	1.41345	−	0.382023i
$73$	−4.07207	+	1.32310i	−0.476600	+	0.154857i	−0.537459	−	0.843290i	$-0.680616\pi$
$73$	−4.07207	+	1.32310i	−0.476600	+	0.154857i	0.0608594	+	0.998146i	$0.480616\pi$
$74$	7.35896	−	0.649191i	0.855462	−	0.0754669i
$75$	0.705927	−	0.971625i	0.0815134	−	0.112194i
$76$	2.37782	−	2.46944i	0.272754	−	0.283265i
$77$		0			0
$78$	−0.441718	−	1.03853i	−0.0500147	−	0.117591i
$79$	7.96895	+	5.78978i	0.896577	+	0.651401i	0.937585	−	0.347757i	$-0.113057\pi$
$79$	7.96895	+	5.78978i	0.896577	+	0.651401i	−0.0410074	+	0.999159i	$0.513057\pi$
$80$	8.97693	+	2.54600i	1.00365	+	0.284652i
$81$	−0.891031	−	2.74231i	−0.0990034	−	0.304701i
$82$	4.06978	−	6.78437i	0.449432	−	0.749208i
$83$	−3.04177	+	2.20997i	−0.333877	+	0.242576i	−0.742074	−	0.670318i	$-0.766158\pi$
$83$	−3.04177	+	2.20997i	−0.333877	+	0.242576i	0.408197	+	0.912894i	$0.366158\pi$
$84$	−3.06886	+	6.31528i	−0.334840	+	0.689053i
$85$	6.58490	+	2.13956i	0.714233	+	0.232068i
$86$	1.10815	−	4.81582i	0.119495	−	0.519303i
$87$	22.4076			2.40235
$88$		0			0
$89$	0.598152			0.0634039			0.0317020	−	0.999497i	$-0.489907\pi$
$89$	0.598152			0.0634039			0.0317020	+	0.999497i	$0.489907\pi$
$90$	−3.24952	+	14.1218i	−0.342530	+	1.48857i
$91$	0.360433	+	0.117112i	0.0377836	+	0.0122766i
$92$	0.459567	−	0.945722i	0.0479131	−	0.0985983i
$93$	−9.77886	+	7.10476i	−1.01402	+	0.736729i
$94$	5.57237	−	9.28920i	0.574746	−	0.958108i
$95$	1.23560	+	3.80280i	0.126770	+	0.390159i
$96$	−15.2590	+	1.92962i	−1.55736	+	0.196941i
$97$	6.73607	+	4.89404i	0.683944	+	0.496914i	0.874664	−	0.484730i	$-0.161082\pi$
$97$	6.73607	+	4.89404i	0.683944	+	0.496914i	−0.190720	+	0.981645i	$0.561082\pi$
$98$	2.95178	+	6.93999i	0.298175	+	0.701045i
$99$		0			0
$100$	−0.612766	+	0.636378i	−0.0612766	+	0.0636378i
$101$	−4.51580	+	6.21547i	−0.449339	+	0.618462i	−0.972255	−	0.233922i	$-0.924844\pi$
$101$	−4.51580	+	6.21547i	−0.449339	+	0.618462i	0.522916	+	0.852384i	$0.324844\pi$
$102$	−11.3685	+	1.00290i	−1.12565	+	0.0993020i
$103$	0.392207	−	0.127436i	0.0386454	−	0.0125566i	−0.289631	−	0.957139i	$-0.593532\pi$
$103$	0.392207	−	0.127436i	0.0386454	−	0.0125566i	0.328276	+	0.944582i	$0.393532\pi$
$104$	0.216601	+	0.801405i	0.0212395	+	0.0785843i
$105$	−4.81374	−	6.62555i	−0.469773	−	0.646587i
$106$	1.67338	−	1.45677i	0.162533	−	0.141494i
$107$	1.59944	−	4.92256i	0.154623	−	0.475882i	−0.843499	−	0.537131i	$-0.819508\pi$
$107$	1.59944	−	4.92256i	0.154623	−	0.475882i	0.998123	+	0.0612485i	$0.0195082\pi$
$108$	−1.32568	−	7.45524i	−0.127564	−	0.717381i
$109$		−	12.5948i		−	1.20636i	−0.797604	−	0.603181i	$-0.793899\pi$
$109$		−	12.5948i		−	1.20636i	0.797604	−	0.603181i	$-0.206101\pi$
$110$		0			0
$111$		−	14.2030i		−	1.34809i
$112$	2.87576	−	4.29022i	0.271734	−	0.405388i
$113$	−0.822214	+	2.53051i	−0.0773474	+	0.238051i	−0.982253	−	0.187562i	$-0.939941\pi$
$113$	−0.822214	+	2.53051i	−0.0773474	+	0.238051i	0.904905	+	0.425613i	$0.139941\pi$
$114$	−4.32757	−	4.97103i	−0.405314	−	0.465579i
$115$	0.720865	+	0.992186i	0.0672210	+	0.0925218i
$116$	−16.3256	−	2.27034i	−1.51580	−	0.210795i
$117$	−1.22613	+	0.398393i	−0.113355	+	0.0368314i
$118$	−1.74906	−	19.8266i	−0.161014	−	1.82519i
$119$	2.25265	−	3.10051i	0.206500	−	0.284223i
$120$	6.39255	−	16.7618i	0.583558	−	1.53014i
$121$		0			0
$122$	12.2941	−	5.22902i	1.11305	−	0.473413i
$123$	−12.3053	−	8.94035i	−1.10954	−	0.806125i
$124$	7.84450	−	4.18556i	0.704457	−	0.375875i
$125$	3.28588	+	10.1129i	0.293898	+	0.904525i
$126$	6.87831	+	4.12613i	0.612768	+	0.367585i
$127$	16.1527	−	11.7356i	1.43332	−	1.04137i	0.443937	−	0.896058i	$-0.353581\pi$
$127$	16.1527	−	11.7356i	1.43332	−	1.04137i	0.989386	−	0.145312i	$-0.0464187\pi$
$128$	11.3128	+	0.140163i	0.999923	+	0.0123888i
$129$	−9.03569	−	2.93587i	−0.795548	−	0.258489i
$130$	−0.943619	−	0.217133i	−0.0827608	−	0.0190438i
$131$	−20.5136			−1.79228			−0.896139	−	0.443773i	$-0.853640\pi$
$131$	−20.5136			−1.79228			−0.896139	+	0.443773i	$0.853640\pi$
$132$		0			0
$133$	2.21324			0.191913
$134$	−14.3676	−	3.30607i	−1.24117	−	0.285601i
$135$	8.39974	+	2.72924i	0.722934	+	0.234896i
$136$	8.38441	+	0.421163i	0.718958	+	0.0361145i
$137$	5.06882	−	3.68271i	0.433058	−	0.314635i	−0.349812	−	0.936820i	$-0.613755\pi$
$137$	5.06882	−	3.68271i	0.433058	−	0.314635i	0.782871	+	0.622185i	$0.213755\pi$
$138$	−1.73353	−	1.03991i	−0.147568	−	0.0885226i
$139$	−4.16564	−	12.8205i	−0.353325	−	1.08742i	−0.956974	−	0.290173i	$-0.906287\pi$
$139$	−4.16564	−	12.8205i	−0.353325	−	1.08742i	0.603649	−	0.797250i	$-0.293713\pi$
$140$	2.83588	+	5.31494i	0.239675	+	0.449195i
$141$	−16.8486	−	12.2412i	−1.41890	−	1.03089i
$142$	4.67848	−	1.98989i	0.392609	−	0.166988i
$143$		0			0
$144$	0.663995	+	17.5575i	0.0553329	+	1.46312i
$145$	11.3002	−	15.5534i	0.938431	−	1.29164i
$146$	−0.532104	−	6.03171i	−0.0440372	−	0.499188i
$147$	13.7896	−	4.48053i	1.13735	−	0.369548i
$148$	−1.43905	+	10.3480i	−0.118289	+	0.850599i
$149$	10.2569	+	14.1174i	0.840279	+	1.15654i	0.985922	+	0.167207i	$0.0534750\pi$
$149$	10.2569	+	14.1174i	0.840279	+	1.15654i	−0.145643	+	0.989337i	$0.546525\pi$
$150$	1.11522	+	1.28104i	0.0910572	+	0.104596i
$151$	−3.03594	+	9.34365i	−0.247061	+	0.760375i	0.748230	+	0.663440i	$0.230904\pi$
$151$	−3.03594	+	9.34365i	−0.247061	+	0.760375i	−0.995291	+	0.0969356i	$0.969096\pi$
$152$	2.64930	+	4.06024i	0.214886	+	0.329329i
$153$			13.0373i			1.05400i
$154$		0			0
$155$			10.3706i			0.832985i
$156$	1.57139	−	0.279423i	0.125812	−	0.0223717i
$157$	4.76013	−	14.6502i	0.379900	−	1.16921i	−0.560213	−	0.828349i	$-0.689281\pi$
$157$	4.76013	−	14.6502i	0.379900	−	1.16921i	0.940113	−	0.340864i	$-0.110719\pi$
$158$	−10.5067	+	9.14666i	−0.835866	+	0.727669i
$159$	−2.50719	−	3.45085i	−0.198833	−	0.273670i
$160$	−6.35577	+	11.5646i	−0.502468	+	0.914259i
$161$	0.645616	−	0.209773i	0.0508816	−	0.0165324i
$162$	4.06202	−	0.358342i	0.319142	−	0.0281540i
$163$	6.32884	−	8.71090i	0.495713	−	0.682290i	−0.485716	−	0.874117i	$-0.661441\pi$
$163$	6.32884	−	8.71090i	0.495713	−	0.682290i	0.981429	+	0.191827i	$0.0614411\pi$
$164$	8.05954	+	7.76050i	0.629344	+	0.605994i
$165$		0			0
$166$	−2.08114	−	4.89301i	−0.161528	−	0.379771i
$167$	−5.19553	−	3.77477i	−0.402042	−	0.292101i	0.368330	−	0.929695i	$-0.379930\pi$
$167$	−5.19553	−	3.77477i	−0.402042	−	0.292101i	−0.770372	+	0.637594i	$0.779930\pi$
$168$	−7.73046	−	6.23227i	−0.596418	−	0.480830i
$169$	3.99060	+	12.2818i	0.306969	+	0.944754i
$170$	−5.03702	+	8.39677i	−0.386322	+	0.644003i
$171$	−6.09114	+	4.42547i	−0.465801	+	0.338424i
$172$	6.28572	+	3.05450i	0.479282	+	0.232904i
$173$	3.44076	+	1.11797i	0.261596	+	0.0849977i	0.436879	−	0.899520i	$-0.356084\pi$
$173$	3.44076	+	1.11797i	0.261596	+	0.0849977i	−0.175283	+	0.984518i	$0.556084\pi$
$174$	−7.10617	+	30.8821i	−0.538717	+	2.34117i
$175$	−0.570356			−0.0431148
$176$		0			0
$177$	−38.2659			−2.87624
$178$	−0.189693	+	0.824371i	−0.0142181	+	0.0617892i
$179$	4.76264	+	1.54748i	0.355976	+	0.115664i	0.481545	−	0.876421i	$-0.340076\pi$
$179$	4.76264	+	1.54748i	0.355976	+	0.115664i	−0.125569	+	0.992085i	$0.540076\pi$
$180$	−18.4322	−	8.95697i	−1.37385	−	0.667613i
$181$	−7.92994	+	5.76144i	−0.589428	+	0.428244i	−0.842111	−	0.539305i	$-0.818687\pi$
$181$	−7.92994	+	5.76144i	−0.589428	+	0.428244i	0.252683	+	0.967549i	$0.418687\pi$
$182$	−0.275708	+	0.459607i	−0.0204368	+	0.0340684i
$183$	−7.93718	−	24.4281i	−0.586733	−	1.80578i
$184$	1.15765	+	0.933292i	0.0853429	+	0.0688032i
$185$	−9.85849	−	7.16261i	−0.724811	−	0.526606i
$186$	−6.69057	−	15.7303i	−0.490576	−	1.15340i
$187$		0			0
$188$	11.0352	+	10.6257i	0.804823	+	0.774961i
$189$	2.87350	−	3.95503i	0.209016	−	0.287686i
$190$	−5.63286	+	0.496918i	−0.408650	+	0.0360502i
$191$	11.1175	−	3.61231i	0.804437	−	0.261378i	0.122197	−	0.992506i	$-0.461006\pi$
$191$	11.1175	−	3.61231i	0.804437	−	0.261378i	0.682240	+	0.731128i	$0.261006\pi$
$192$	2.17971	−	21.6418i	0.157307	−	1.56186i
$193$	−0.678643	−	0.934071i	−0.0488498	−	0.0672359i	0.783893	−	0.620896i	$-0.213231\pi$
$193$	−0.678643	−	0.934071i	−0.0488498	−	0.0672359i	−0.832743	+	0.553660i	$0.813231\pi$
$194$	−8.88117	+	7.73157i	−0.637631	+	0.555095i
$195$	−0.575259	+	1.77046i	−0.0411951	+	0.126786i
$196$	−10.5008	+	1.86724i	−0.750055	+	0.133374i
$197$			15.6248i			1.11322i	0.830774	+	0.556610i	$0.187898\pi$
$197$			15.6248i			1.11322i	−0.830774	+	0.556610i	$0.812102\pi$
$198$		0			0
$199$		−	10.9684i		−	0.777526i	−0.921338	−	0.388763i	$-0.872902\pi$
$199$		−	10.9684i		−	0.777526i	0.921338	−	0.388763i	$-0.127098\pi$
$200$	−0.682727	−	1.04633i	−0.0482761	−	0.0739866i
$201$	−8.75892	+	26.9572i	−0.617807	+	1.90141i
$202$	−7.13404	−	8.19479i	−0.501949	−	0.576583i
$203$	−6.25488	−	8.60910i	−0.439007	−	0.604241i
$204$	2.22311	−	15.9861i	0.155649	−	1.11925i
$205$	−12.4112	+	4.03265i	−0.866838	+	0.281653i
$206$	0.0512504	+	0.580953i	0.00357078	+	0.0404769i
$207$	−1.35737	+	1.86826i	−0.0943436	+	0.129853i
$208$	−1.17319	+	0.0443680i	−0.0813458	+	0.00307637i
$209$		0			0
$210$	10.6579	−	4.53311i	0.735465	−	0.312815i
$211$	15.6170	+	11.3464i	1.07512	+	0.781120i	0.976826	−	0.214037i	$-0.0686613\pi$
$211$	15.6170	+	11.3464i	1.07512	+	0.781120i	0.0982944	+	0.995157i	$0.468661\pi$
$212$	1.47704	+	2.76823i	0.101443	+	0.190123i
$213$	−3.02048	−	9.29607i	−0.206960	−	0.636956i
$214$	6.27703	+	3.76544i	0.429089	+	0.257400i
$215$	−6.59454	+	4.79122i	−0.449744	+	0.326758i
$216$	10.6952	+	0.537238i	0.727716	+	0.0365544i
$217$	5.45936	+	1.77385i	0.370605	+	0.120417i
$218$	17.3581	+	3.99421i	1.17564	+	0.270522i
$219$	−11.6414			−0.786652
$220$		0			0
$221$	−0.871148			−0.0585998
$222$	19.5746	+	4.50423i	1.31376	+	0.302304i
$223$	−10.3085	−	3.34944i	−0.690310	−	0.224295i	−0.0572062	−	0.998362i	$-0.518219\pi$
$223$	−10.3085	−	3.34944i	−0.690310	−	0.224295i	−0.633103	+	0.774067i	$0.718219\pi$
$224$	5.00078	+	5.32393i	0.334128	+	0.355720i
$225$	1.56969	−	1.14045i	0.104646	−	0.0760299i
$226$	−3.22680	−	1.93568i	−0.214643	−	0.128759i
$227$	7.41543	+	22.8224i	0.492180	+	1.51477i	0.821306	+	0.570487i	$0.193246\pi$
$227$	7.41543	+	22.8224i	0.492180	+	1.51477i	−0.329127	+	0.944286i	$0.606754\pi$
$228$	8.22347	−	4.38777i	0.544612	−	0.290587i
$229$	19.8867	+	14.4485i	1.31415	+	0.954784i	0.999985	+	0.00541531i	$0.00172376\pi$
$229$	19.8867	+	14.4485i	1.31415	+	0.954784i	0.314163	+	0.949369i	$0.398276\pi$
$230$	−1.59604	+	0.678840i	−0.105240	+	0.0447614i
$231$		0			0
$232$	8.30636	−	21.7800i	0.545339	−	1.42992i
$233$	−8.40808	+	11.5727i	−0.550831	+	0.758154i	−0.990125	−	0.140189i	$-0.955229\pi$
$233$	−8.40808	+	11.5727i	−0.550831	+	0.758154i	0.439293	+	0.898344i	$0.355229\pi$
$234$	−0.160220	−	1.81619i	−0.0104739	−	0.118728i
$235$	−16.9935	+	5.52153i	−1.10854	+	0.360185i
$236$	27.8796	+	3.87710i	1.81481	+	0.252378i
$237$	15.7419	+	21.6669i	1.02255	+	1.40742i
$238$	3.55873	+	4.08787i	0.230678	+	0.264977i
$239$	−6.10738	+	18.7966i	−0.395053	+	1.21585i	0.533867	+	0.845569i	$0.320738\pi$
$239$	−6.10738	+	18.7966i	−0.395053	+	1.21585i	−0.928920	+	0.370280i	$0.879262\pi$
$240$	21.0738	+	14.1259i	1.36031	+	0.911823i
$241$			6.53055i			0.420669i	0.977629	+	0.210335i	$0.0674554\pi$
$241$			6.53055i			0.420669i	−0.977629	+	0.210335i	$0.932545\pi$
$242$		0			0
$243$		−	19.1981i		−	1.23156i
$244$	3.30778	+	18.6019i	0.211759	+	1.19087i
$245$	3.84416	−	11.8311i	0.245594	−	0.755862i
$246$	16.2240	−	14.1239i	1.03440	−	0.900508i
$247$	−0.295709	−	0.407009i	−0.0188155	−	0.0258973i
$248$	3.28079	+	12.1386i	0.208330	+	0.770804i
$249$	−9.72233	+	3.15898i	−0.616128	+	0.200192i
$250$	−14.9796	+	1.32147i	−0.947394	+	0.0835770i
$251$	2.80407	−	3.85947i	0.176991	−	0.243608i	−0.711300	−	0.702889i	$-0.751893\pi$
$251$	2.80407	−	3.85947i	0.176991	−	0.243608i	0.888291	+	0.459281i	$0.151893\pi$
$252$	−7.86796	+	8.17114i	−0.495635	+	0.514733i
$253$		0			0
$254$	11.0515	+	25.9834i	0.693432	+	1.63034i
$255$	15.2299	+	11.0652i	0.953732	+	0.692927i
$256$	−3.78083	+	15.5469i	−0.236302	+	0.971680i
$257$	−0.938463	−	2.88829i	−0.0585397	−	0.180167i	0.917511	−	0.397711i	$-0.130195\pi$
$257$	−0.938463	−	2.88829i	−0.0585397	−	0.180167i	−0.976050	+	0.217544i	$0.930195\pi$
$258$	6.91171	−	11.5219i	0.430305	−	0.717322i
$259$	−5.45686	+	3.96464i	−0.339073	+	0.246351i
$260$	0.598503	−	1.23163i	0.0371176	−	0.0763826i
$261$	34.4285	+	11.1865i	2.13107	+	0.692427i
$262$	6.50550	−	28.2717i	0.401911	−	1.74663i
$263$	−14.1671			−0.873580			−0.436790	−	0.899564i	$-0.643885\pi$
$263$	−14.1671			−0.873580			−0.436790	+	0.899564i	$0.643885\pi$
$264$		0			0
$265$	−3.65966			−0.224811
$266$	−0.701890	+	3.05029i	−0.0430357	+	0.187025i
$267$	1.54673	+	0.502562i	0.0946581	+	0.0307563i
$268$	9.11284	−	18.7529i	0.556655	−	1.14552i
$269$	−0.810435	+	0.588816i	−0.0494131	+	0.0359007i	−0.612218	−	0.790689i	$-0.709722\pi$
$269$	−0.810435	+	0.588816i	−0.0494131	+	0.0359007i	0.562805	+	0.826590i	$0.309722\pi$
$270$	−6.42525	+	10.7110i	−0.391029	+	0.651848i
$271$	5.49774	+	16.9203i	0.333964	+	1.02784i	0.967230	+	0.253902i	$0.0817140\pi$
$271$	5.49774	+	16.9203i	0.333964	+	1.02784i	−0.633266	+	0.773934i	$0.718286\pi$
$272$	−3.23941	+	11.4218i	−0.196418	+	0.692549i
$273$	0.833625	+	0.605664i	0.0504533	+	0.0366565i
$274$	3.46802	+	8.15373i	0.209511	+	0.492585i
$275$		0			0
$276$	1.98295	−	2.05936i	0.119360	−	0.123959i
$277$	11.3952	−	15.6842i	0.684672	−	0.942370i	−0.315306	−	0.948990i	$-0.602107\pi$
$277$	11.3952	−	15.6842i	0.684672	−	0.942370i	0.999978	+	0.00661973i	$0.00210714\pi$
$278$	18.9903	−	1.67528i	1.13896	−	0.100477i
$279$	−18.5718	+	6.03433i	−1.11186	+	0.361266i
$280$	−8.22439	+	2.22286i	−0.491501	+	0.132841i
$281$	−8.63830	−	11.8896i	−0.515318	−	0.709274i	0.469487	−	0.882940i	$-0.344439\pi$
$281$	−8.63830	−	11.8896i	−0.515318	−	0.709274i	−0.984805	+	0.173665i	$0.944439\pi$
$282$	22.2140	−	19.3386i	1.32282	−	1.15159i
$283$	0.771579	−	2.37467i	0.0458656	−	0.141160i	−0.925501	−	0.378745i	$-0.876356\pi$
$283$	0.771579	−	2.37467i	0.0458656	−	0.141160i	0.971367	+	0.237585i	$0.0763558\pi$
$284$	1.25877	+	7.07893i	0.0746943	+	0.420057i
$285$			10.8716i			0.643977i
$286$		0			0
$287$			7.22339i			0.426383i
$288$	−24.4082	−	4.65291i	−1.43827	−	0.274175i
$289$	2.53101	−	7.78965i	0.148883	−	0.458215i
$290$	17.8520	+	20.5064i	1.04831	+	1.20418i
$291$	13.3065	+	18.3148i	0.780040	+	1.07363i
$292$	8.48164	+	1.17950i	0.496350	+	0.0690253i
$293$	−7.15088	+	2.32346i	−0.417759	+	0.135738i	−0.510351	−	0.859966i	$-0.670485\pi$
$293$	−7.15088	+	2.32346i	−0.417759	+	0.135738i	0.0925923	+	0.995704i	$0.470485\pi$
$294$	1.80191	+	20.4258i	0.105090	+	1.19126i
$295$	−19.2976	+	26.5609i	−1.12355	+	1.54643i
$296$	−13.8052	−	5.26497i	−0.802410	−	0.306020i
$297$		0			0
$298$	−22.7094	+	9.65896i	−1.31552	+	0.559529i
$299$	−0.124837	−	0.0906991i	−0.00721949	−	0.00524527i
$300$	−2.11920	+	1.13073i	−0.122352	+	0.0652829i
$301$	1.39425	+	4.29107i	0.0803635	+	0.247333i
$302$	−11.9146	−	7.14729i	−0.685608	−	0.411280i
$303$	−16.8993	+	12.2781i	−0.970841	+	0.705358i
$304$	−6.43599	+	2.36362i	−0.369129	+	0.135563i
$305$	−20.9586	−	6.80986i	−1.20009	−	0.389932i
$306$	−17.9679	−	4.13454i	−1.02716	−	0.236356i
$307$	25.7991			1.47243			0.736216	−	0.676747i	$-0.236611\pi$
$307$	25.7991			1.47243			0.736216	+	0.676747i	$0.236611\pi$
$308$		0			0
$309$	1.12126			0.0637861
$310$	−14.2927	−	3.28884i	−0.811771	−	0.186794i
$311$	−2.81928	−	0.916039i	−0.159867	−	0.0519438i	0.227990	−	0.973663i	$-0.426785\pi$
$311$	−2.81928	−	0.916039i	−0.159867	−	0.0519438i	−0.387857	+	0.921720i	$0.626785\pi$
$312$	−0.113237	+	2.25429i	−0.00641078	+	0.127624i
$313$	−0.488641	+	0.355018i	−0.0276196	+	0.0200668i	−0.601509	−	0.798866i	$-0.705434\pi$
$313$	−0.488641	+	0.355018i	−0.0276196	+	0.0200668i	0.573890	+	0.818933i	$0.305434\pi$
$314$	18.6813	+	11.2064i	1.05424	+	0.632416i
$315$	−4.08849	−	12.5831i	−0.230360	−	0.708976i
$316$	−9.27390	−	17.3810i	−0.521698	−	0.977755i
$317$	−18.5633	−	13.4870i	−1.04262	−	0.757506i	−0.0718223	−	0.997417i	$-0.522881\pi$
$317$	−18.5633	−	13.4870i	−1.04262	−	0.757506i	−0.970795	+	0.239912i	$0.922881\pi$
$318$	5.55106	−	2.36102i	0.311288	−	0.132400i
$319$		0			0
$320$	−13.9226	−	12.4270i	−0.778299	−	0.694690i
$321$	8.27179	−	11.3851i	0.461686	−	0.635456i
$322$	0.0843636	+	0.956311i	0.00470140	+	0.0532932i
$323$	−4.83849	+	1.57212i	−0.269221	+	0.0874752i
$324$	−0.794330	+	5.71191i	−0.0441294	+	0.317328i
$325$	0.0762046	+	0.104887i	0.00422707	+	0.00581806i
$326$	9.99826	+	11.4849i	0.553752	+	0.636089i
$327$	10.5820	−	32.5682i	0.585188	−	1.80102i
$328$	−13.2514	+	8.64653i	−0.731688	+	0.477425i
$329$			9.89031i			0.545270i
$330$		0			0
$331$		−	4.43442i		−	0.243738i	−0.992546	−	0.121869i	$-0.961111\pi$
$331$		−	4.43442i		−	0.243738i	0.992546	−	0.121869i	$-0.0388887\pi$
$332$	7.40352	−	1.31649i	0.406321	−	0.0722517i
$333$	7.09054	−	21.8224i	0.388559	−	1.19586i
$334$	6.85005	−	5.96336i	0.374818	−	0.326301i
$335$	14.2942	+	19.6743i	0.780975	+	1.07492i
$336$	11.0409	−	8.67765i	0.602329	−	0.473404i
$337$	−16.8925	+	5.48871i	−0.920193	+	0.298989i	−0.730546	−	0.682863i	$-0.760734\pi$
$337$	−16.8925	+	5.48871i	−0.920193	+	0.298989i	−0.189647	+	0.981852i	$0.560734\pi$
$338$	−18.1923	+	1.60488i	−0.989530	+	0.0872941i
$339$	−4.25223	+	5.85269i	−0.230949	+	0.317875i
$340$	−9.97500	−	9.60490i	−0.540971	−	0.520899i
$341$		0			0
$342$	−4.16748	−	9.79825i	−0.225351	−	0.529829i
$343$	−12.8830	−	9.36007i	−0.695618	−	0.505396i
$344$	−6.20311	+	7.69428i	−0.334449	+	0.414848i
$345$	1.03042	+	3.17130i	0.0554758	+	0.170737i
$346$	−2.63196	+	4.38750i	−0.141495	+	0.235873i
$347$	−3.13936	+	2.28088i	−0.168530	+	0.122444i	−0.668853	−	0.743395i	$-0.733214\pi$
$347$	−3.13936	+	2.28088i	−0.168530	+	0.122444i	0.500323	+	0.865839i	$0.333214\pi$
$348$	−40.3080	−	19.5874i	−2.16074	−	1.04999i
$349$	18.7530	+	6.09320i	1.00382	+	0.326162i	0.764392	−	0.644752i	$-0.223039\pi$
$349$	18.7530	+	6.09320i	1.00382	+	0.326162i	0.239431	+	0.970913i	$0.423039\pi$
$350$	0.180878	−	0.786063i	0.00966833	−	0.0420168i
$351$	−1.11124			−0.0593137
$352$		0			0
$353$	−1.59623			−0.0849587			−0.0424794	−	0.999097i	$-0.513526\pi$
$353$	−1.59623			−0.0849587			−0.0424794	+	0.999097i	$0.513526\pi$
$354$	12.1353	−	52.7380i	0.644986	−	2.80299i
$355$	−7.97575	−	2.59148i	−0.423309	−	0.137541i
$356$	−1.07599	−	0.522868i	−0.0570272	−	0.0277120i
$357$	8.43002	−	6.12477i	0.446164	−	0.324157i
$358$	−3.64311	+	6.07310i	−0.192544	+	0.320973i
$359$	−4.76587	−	14.6679i	−0.251533	−	0.774140i	−0.994493	−	0.104803i	$-0.966579\pi$
$359$	−4.76587	−	14.6679i	−0.251533	−	0.774140i	0.742960	−	0.669336i	$-0.233421\pi$
$360$	18.1899	−	22.5626i	0.958692	−	1.18915i
$361$	12.9944	+	9.44098i	0.683916	+	0.496894i
$362$	−5.42556	−	12.7562i	−0.285161	−	0.670449i
$363$		0			0
$364$	−0.545994	−	0.525735i	−0.0286178	−	0.0275560i
$365$	−5.87078	+	8.08044i	−0.307291	+	0.422949i
$366$	36.1839	−	3.19206i	1.89136	−	0.166852i
$367$	10.0355	−	3.26074i	0.523850	−	0.170209i	−0.0351418	−	0.999382i	$-0.511188\pi$
$367$	10.0355	−	3.26074i	0.523850	−	0.170209i	0.558992	+	0.829173i	$0.311188\pi$
$368$	−1.65339	+	1.29949i	−0.0861888	+	0.0677406i
$369$	−14.4434	−	19.8797i	−0.751896	−	1.03490i
$370$	12.9979	−	11.3155i	0.675731	−	0.588262i
$371$	−0.625972	+	1.92654i	−0.0324989	+	0.100021i
$372$	23.8013	−	4.23233i	1.23404	−	0.219436i
$373$		−	37.4953i		−	1.94143i	−0.240225	−	0.970717i	$-0.577221\pi$
$373$		−	37.4953i		−	1.94143i	0.240225	−	0.970717i	$-0.422779\pi$
$374$		0			0
$375$			28.9111i			1.49296i
$376$	−18.1440	+	11.8389i	−0.935703	+	0.610544i
$377$	−0.747480	+	2.30051i	−0.0384972	+	0.118482i
$378$	4.53953	+	5.21451i	0.233488	+	0.268205i
$379$	−12.5368	−	17.2555i	−0.643974	−	0.886354i	0.354846	−	0.934925i	$-0.384533\pi$
$379$	−12.5368	−	17.2555i	−0.643974	−	0.886354i	−0.998820	+	0.0485707i	$0.984533\pi$
$380$	1.10151	−	7.92077i	0.0565061	−	0.406327i
$381$	51.6286	−	16.7751i	2.64501	−	0.859417i
$382$	1.45275	+	16.4677i	0.0743290	+	0.842563i
$383$	16.9465	−	23.3249i	0.865928	−	1.19185i	−0.114195	−	0.993458i	$-0.536429\pi$
$383$	16.9465	−	23.3249i	0.865928	−	1.19185i	0.980123	−	0.198389i	$-0.0635710\pi$
$384$	29.1355	+	9.86739i	1.48681	+	0.503543i
$385$		0			0
$386$	1.50255	−	0.639079i	0.0764780	−	0.0325283i
$387$	−12.4173	−	9.02173i	−0.631209	−	0.458600i
$388$	−7.83913	−	14.6919i	−0.397972	−	0.745870i
$389$	−10.7783	−	33.1721i	−0.546480	−	1.68189i	−0.717446	−	0.696615i	$-0.754689\pi$
$389$	−10.7783	−	33.1721i	−0.546480	−	1.68189i	0.170966	−	0.985277i	$-0.445311\pi$
$390$	−2.25762	−	1.35429i	−0.114319	−	0.0685772i
$391$	−1.26241	+	0.917193i	−0.0638427	+	0.0463845i
$392$	0.756705	−	15.0643i	0.0382194	−	0.760862i
$393$	−53.0448	−	17.2353i	−2.67576	−	0.869406i
$394$	−21.5340	−	4.95512i	−1.08487	−	0.249635i
$395$	22.9780			1.15615
$396$		0			0
$397$	16.9102			0.848698			0.424349	−	0.905499i	$-0.360503\pi$
$397$	16.9102			0.848698			0.424349	+	0.905499i	$0.360503\pi$
$398$	15.1166	+	3.47842i	0.757725	+	0.174357i
$399$	5.72310	+	1.85955i	0.286513	+	0.0930939i
$400$	1.65856	−	0.609108i	0.0829281	−	0.0304554i
$401$	−12.8310	+	9.32226i	−0.640749	+	0.465532i	−0.860108	−	0.510113i	$-0.829604\pi$
$401$	−12.8310	+	9.32226i	−0.640749	+	0.465532i	0.219358	+	0.975644i	$0.429604\pi$
$402$	−34.3746	−	20.6205i	−1.71445	−	1.02846i
$403$	−0.403213	−	1.24096i	−0.0200855	−	0.0618167i
$404$	13.5565	−	7.23328i	0.674459	−	0.359869i
$405$	−5.44172	−	3.95364i	−0.270401	−	0.196458i
$406$	13.8487	−	5.89024i	0.687298	−	0.292328i
$407$		0			0
$408$	21.3269	+	8.13357i	1.05584	+	0.402672i
$409$	−16.2664	+	22.3887i	−0.804320	+	1.10705i	0.187855	+	0.982197i	$0.439846\pi$
$409$	−16.2664	+	22.3887i	−0.804320	+	1.10705i	−0.992175	+	0.124855i	$0.960154\pi$
$410$	−1.62179	−	18.3840i	−0.0800947	−	0.907921i
$411$	16.2013	−	5.26414i	0.799153	−	0.259661i
$412$	−0.816921	−	0.113606i	−0.0402468	−	0.00559695i
$413$	10.6816	+	14.7019i	0.525606	+	0.723435i
$414$	−2.14436	−	2.46321i	−0.105390	−	0.121060i
$415$	−2.71031	+	8.34147i	−0.133044	+	0.409467i
$416$	0.310907	−	1.63095i	0.0152435	−	0.0799640i
$417$		−	36.6518i		−	1.79485i
$418$		0			0
$419$		−	22.9710i		−	1.12221i	−0.827746	−	0.561103i	$-0.810377\pi$
$419$		−	22.9710i		−	1.12221i	0.827746	−	0.561103i	$-0.189623\pi$
$420$	2.86756	+	16.1263i	0.139923	+	0.786882i
$421$	−9.30438	+	28.6359i	−0.453468	+	1.39563i	0.419457	+	0.907775i	$0.362220\pi$
$421$	−9.30438	+	28.6359i	−0.453468	+	1.39563i	−0.872925	+	0.487855i	$0.837780\pi$
$422$	−20.5903	+	17.9250i	−1.00232	+	0.872576i
$423$	−19.7761	−	27.2194i	−0.961545	−	1.32345i
$424$	−4.28359	+	1.15775i	−0.208029	+	0.0562255i
$425$	1.24689	−	0.405138i	0.0604828	−	0.0196521i
$426$	13.7697	−	1.21473i	0.667145	−	0.0588540i
$427$	−7.16980	+	9.86839i	−0.346971	+	0.477565i
$428$	−7.18017	+	7.45684i	−0.347066	+	0.360440i
$429$		0			0
$430$	−4.51190	−	10.6080i	−0.217583	−	0.511565i
$431$	−8.23029	−	5.97965i	−0.396439	−	0.288030i	0.371650	−	0.928373i	$-0.378792\pi$
$431$	−8.23029	−	5.97965i	−0.396439	−	0.288030i	−0.768089	+	0.640343i	$0.778792\pi$
$432$	−4.13221	+	14.5697i	−0.198811	+	0.700986i
$433$	8.50878	+	26.1873i	0.408906	+	1.25848i	0.917589	+	0.397530i	$0.130132\pi$
$433$	8.50878	+	26.1873i	0.408906	+	1.25848i	−0.508683	+	0.860954i	$0.669868\pi$
$434$	−4.17606	+	6.96153i	−0.200457	+	0.334164i
$435$	42.2884	−	30.7243i	2.02757	−	1.47312i
$436$	−11.0096	+	22.6562i	−0.527265	+	1.08504i
$437$	−0.857043	−	0.278470i	−0.0409979	−	0.0133210i
$438$	3.69186	−	16.0441i	0.176404	−	0.766618i
$439$	−11.5438			−0.550957			−0.275479	−	0.961307i	$-0.588836\pi$
$439$	−11.5438			−0.550957			−0.275479	+	0.961307i	$0.588836\pi$
$440$		0			0
$441$	23.4241			1.11543
$442$	0.276269	−	1.20061i	0.0131408	−	0.0571074i
$443$	16.1592	+	5.25043i	0.767745	+	0.249455i	0.666599	−	0.745416i	$-0.267749\pi$
$443$	16.1592	+	5.25043i	0.767745	+	0.249455i	0.101146	+	0.994872i	$0.467749\pi$
$444$	−12.4154	+	25.5492i	−0.589210	+	1.21251i
$445$	1.12885	−	0.820159i	0.0535127	−	0.0388793i
$446$	7.88535	−	13.1450i	0.373382	−	0.622432i
$447$	14.6614	+	45.1232i	0.693461	+	2.13425i
$448$	−8.92334	+	5.20367i	−0.421588	+	0.245850i
$449$	−4.94849	−	3.59529i	−0.233534	−	0.169672i	0.464864	−	0.885382i	$-0.346103\pi$
$449$	−4.94849	−	3.59529i	−0.233534	−	0.169672i	−0.698398	+	0.715710i	$0.746103\pi$
$450$	1.07396	+	2.52502i	0.0506271	+	0.119031i
$451$		0			0
$452$	3.69107	−	3.83330i	0.173613	−	0.180303i
$453$	−15.7009	+	21.6104i	−0.737693	+	1.01535i
$454$	−33.8054	+	2.98223i	−1.58656	+	0.139963i
$455$	0.840799	−	0.273192i	0.0394172	−	0.0128074i
$456$	3.43929	+	12.7251i	0.161059	+	0.595905i
$457$	−3.83457	−	5.27783i	−0.179373	−	0.246886i	0.709857	−	0.704346i	$-0.248760\pi$
$457$	−3.83457	−	5.27783i	−0.179373	−	0.246886i	−0.889231	+	0.457459i	$0.848760\pi$
$458$	−26.2196	+	22.8257i	−1.22516	+	1.06657i
$459$	−3.47255	+	10.6874i	−0.162085	+	0.498846i
$460$	−0.429422	−	2.41493i	−0.0200219	−	0.112597i
$461$			19.0882i			0.889026i	0.895773	+	0.444513i	$0.146623\pi$
$461$			19.0882i			0.889026i	−0.895773	+	0.444513i	$0.853377\pi$
$462$		0			0
$463$			13.0359i			0.605829i	0.953018	+	0.302915i	$0.0979597\pi$
$463$			13.0359i			0.605829i	−0.953018	+	0.302915i	$0.902040\pi$
$464$	27.3829	+	18.3549i	1.27122	+	0.852106i
$465$	−8.71326	+	26.8167i	−0.404068	+	1.24359i
$466$	−13.2830	−	15.2581i	−0.615324	−	0.706816i
$467$	8.92128	+	12.2791i	0.412827	+	0.568208i	0.963905	−	0.266246i	$-0.0857832\pi$
$467$	8.92128	+	12.2791i	0.412827	+	0.568208i	−0.551078	+	0.834454i	$0.685783\pi$
$468$	2.55388	+	0.355156i	0.118053	+	0.0164171i
$469$	12.8020	−	4.15964i	0.591144	−	0.192074i
$470$	−2.22057	−	25.1715i	−0.102427	−	1.16107i
$471$	24.6179	−	33.8837i	1.13433	−	1.56128i
$472$	−14.1849	+	37.1941i	−0.652914	+	1.71200i
$473$		0			0
$474$	−34.8535	+	14.8242i	−1.60088	+	0.680899i
$475$	0.612536	+	0.445034i	0.0281051	+	0.0204195i
$476$	−6.76248	+	3.60823i	−0.309958	+	0.165383i
$477$	−2.12945	−	6.55376i	−0.0975006	−	0.300076i
$478$	−23.9685	−	14.3782i	−1.09630	−	0.657642i
$479$	21.1996	−	15.4024i	0.968633	−	0.703753i	0.0134937	−	0.999909i	$-0.495705\pi$
$479$	21.1996	−	15.4024i	0.968633	−	0.703753i	0.955140	+	0.296156i	$0.0957047\pi$
$480$	−26.1515	+	24.5641i	−1.19365	+	1.12119i
$481$	1.45817	+	0.473788i	0.0664869	+	0.0216029i
$482$	−9.00038	−	2.07104i	−0.409956	−	0.0943335i
$483$	1.84571			0.0839827
$484$		0			0
$485$	19.4230			0.881954
$486$	26.4588	+	6.08833i	1.20019	+	0.276172i
$487$	25.9179	+	8.42123i	1.17445	+	0.381602i	0.830303	−	0.557313i	$-0.188168\pi$
$487$	25.9179	+	8.42123i	1.17445	+	0.381602i	0.344149	+	0.938915i	$0.388168\pi$
$488$	−26.6861	−	1.34049i	−1.20802	−	0.0606811i
$489$	23.6842	−	17.2076i	1.07104	−	0.778153i
$490$	15.0865	+	9.05003i	0.681538	+	0.408839i
$491$	−6.61682	−	20.3645i	−0.298613	−	0.919035i	−0.981984	−	0.188964i	$-0.939487\pi$
$491$	−6.61682	−	20.3645i	−0.298613	−	0.919035i	0.683371	−	0.730071i	$-0.260513\pi$
$492$	14.3204	+	26.8390i	0.645613	+	1.21000i
$493$	19.7894	+	14.3778i	0.891269	+	0.647545i
$494$	0.654717	−	0.278470i	0.0294571	−	0.0125290i
$495$		0			0
$496$	−17.7699	+	0.672029i	−0.797891	+	0.0301750i
$497$	−2.72845	+	3.75539i	−0.122388	+	0.168452i
$498$	−1.27043	−	14.4011i	−0.0569294	−	0.645329i
$499$	29.3376	−	9.53238i	1.31333	−	0.426728i	0.433133	−	0.901330i	$-0.357408\pi$
$499$	29.3376	−	9.53238i	1.31333	−	0.426728i	0.880200	+	0.474602i	$0.157408\pi$
$500$	2.92927	−	21.0640i	0.131001	−	0.942008i
$501$	−10.2633	−	14.1262i	−0.458530	−	0.631112i
$502$	4.42985	+	5.08852i	0.197714	+	0.227112i
$503$	9.80786	−	30.1855i	0.437311	−	1.34590i	−0.453389	−	0.891313i	$-0.649785\pi$
$503$	9.80786	−	30.1855i	0.437311	−	1.34590i	0.890700	−	0.454592i	$-0.150215\pi$
$504$	−8.76626	−	13.4349i	−0.390480	−	0.598439i
$505$			17.9219i			0.797515i
$506$		0			0
$507$			35.1117i			1.55936i
$508$	−39.3150	+	6.99097i	−1.74432	+	0.310174i
$509$	2.06712	−	6.36194i	0.0916235	−	0.281988i	−0.894736	−	0.446596i	$-0.852636\pi$
$509$	2.06712	−	6.36194i	0.0916235	−	0.281988i	0.986359	+	0.164608i	$0.0526360\pi$
$510$	−20.0798	+	17.4807i	−0.889150	+	0.774057i
$511$	3.24959	+	4.47267i	0.143753	+	0.197859i
$512$	−20.2276	−	10.1411i	−0.893944	−	0.448179i
$513$	−6.17201	+	2.00541i	−0.272501	+	0.0885409i
$514$	4.27825	−	0.377417i	0.188706	−	0.0166472i
$515$	0.565453	−	0.778279i	0.0249168	−	0.0342951i
$516$	13.6875	+	13.1797i	0.602560	+	0.580202i
$517$		0			0
$518$	−3.73351	−	8.77795i	−0.164041	−	0.385681i
$519$	7.95795	+	5.78179i	0.349315	+	0.253792i
$520$	1.50763	+	1.21545i	0.0661139	+	0.0533008i
$521$	3.82221	+	11.7636i	0.167454	+	0.515371i	0.999209	−	0.0397725i	$-0.0126633\pi$
$521$	3.82221	+	11.7636i	0.167454	+	0.515371i	−0.831755	+	0.555144i	$0.812663\pi$
$522$	−26.3356	+	43.9017i	−1.15268	+	1.92152i
$523$	5.04862	−	3.66804i	0.220761	−	0.160392i	−0.471908	−	0.881648i	$-0.656435\pi$
$523$	5.04862	−	3.66804i	0.220761	−	0.160392i	0.692669	+	0.721256i	$0.256435\pi$
$524$	36.9009	+	17.9317i	1.61202	+	0.783351i
$525$	−1.47485	−	0.479208i	−0.0643677	−	0.0209143i
$526$	4.49283	−	19.5250i	0.195897	−	0.851332i
$527$	−13.1950			−0.574784
$528$		0			0
$529$	22.7236			0.987983
$530$	1.16059	−	5.04373i	0.0504130	−	0.219086i
$531$	−58.7942	−	19.1034i	−2.55145	−	0.829017i
$532$	−3.98131	−	1.93469i	−0.172611	−	0.0838793i
$533$	1.32836	−	0.965108i	0.0575376	−	0.0418035i
$534$	−1.18314	+	1.97231i	−0.0511997	+	0.0853504i
$535$	−3.73109	−	11.4831i	−0.161309	−	0.496458i
$536$	22.9552	+	18.5064i	0.991515	+	0.799356i
$537$	11.0153	+	8.00306i	0.475344	+	0.345357i
$538$	−0.554489	−	1.30367i	−0.0239057	−	0.0562053i
$539$		0			0
$540$	−12.7242	−	12.2521i	−0.547561	−	0.527245i
$541$	15.2241	−	20.9541i	0.654534	−	0.900889i	−0.344751	−	0.938694i	$-0.612037\pi$
$541$	15.2241	−	20.9541i	0.654534	−	0.900889i	0.999285	+	0.0378054i	$0.0120367\pi$
$542$	−25.0630	+	2.21100i	−1.07655	+	0.0949708i
$543$	−25.3463	+	8.23551i	−1.08771	+	0.353419i
$544$	−14.7142	−	8.08677i	−0.630866	−	0.346717i
$545$	−17.2694	−	23.7693i	−0.739741	−	1.01817i
$546$	−1.09909	+	0.956825i	−0.0470369	+	0.0409483i
$547$	−5.15788	+	15.8743i	−0.220535	+	0.678737i	0.778179	+	0.628042i	$0.216143\pi$
$547$	−5.15788	+	15.8743i	−0.220535	+	0.678737i	−0.998714	+	0.0506945i	$0.983857\pi$
$548$	−12.3373	+	2.19380i	−0.527022	+	0.0937147i
$549$		−	41.4954i		−	1.77098i
$550$		0			0
$551$			14.1263i			0.601801i
$552$	2.20935	+	3.38599i	0.0940362	+	0.144117i
$553$	3.93031	−	12.0962i	0.167134	−	0.514384i
$554$	18.0021	+	20.6788i	0.764836	+	0.878558i
$555$	−19.4745	−	26.8044i	−0.826648	−	1.13778i
$556$	−3.71356	+	26.7036i	−0.157490	+	1.13249i
$557$	17.6599	−	5.73806i	0.748276	−	0.243130i	0.0900368	−	0.995938i	$-0.471302\pi$
$557$	17.6599	−	5.73806i	0.748276	−	0.243130i	0.658239	+	0.752809i	$0.271302\pi$
$558$	−2.42680	−	27.5092i	−0.102735	−	1.16456i
$559$	0.602830	−	0.829724i	0.0254970	−	0.0350936i
$560$	−0.455325	−	12.0398i	−0.0192410	−	0.508773i
$561$		0			0
$562$	19.1257	−	8.13471i	0.806769	−	0.343142i
$563$	18.3480	+	13.3306i	0.773277	+	0.561819i	0.902954	−	0.429738i	$-0.141394\pi$
$563$	18.3480	+	13.3306i	0.773277	+	0.561819i	−0.129677	+	0.991556i	$0.541394\pi$
$564$	19.6076	+	36.7481i	0.825628	+	1.54738i
$565$	1.91802	+	5.90305i	0.0806916	+	0.248343i
$566$	3.02808	+	1.81647i	0.127280	+	0.0763520i
$567$	−3.01209	+	2.18841i	−0.126496	+	0.0919048i
$568$	−10.1554	−	0.510121i	−0.426109	−	0.0214042i
$569$	−0.141422	−	0.0459508i	−0.00592872	−	0.00192636i	0.306051	−	0.952015i	$-0.400992\pi$
$569$	−0.141422	−	0.0459508i	−0.00592872	−	0.00192636i	−0.311980	+	0.950089i	$0.600992\pi$
$570$	−14.9832	−	3.44772i	−0.627576	−	0.144409i
$571$	22.0331			0.922057			0.461028	−	0.887385i	$-0.347481\pi$
$571$	22.0331			0.922057			0.461028	+	0.887385i	$0.347481\pi$
$572$		0			0
$573$	31.7832			1.32776
$574$	−9.95525	−	2.29077i	−0.415524	−	0.0956147i
$575$	0.220861	+	0.0717621i	0.00921054	+	0.00299268i
$576$	14.1532	−	32.1637i	0.589719	−	1.34016i
$577$	−3.18631	+	2.31499i	−0.132648	+	0.0963743i	−0.652131	−	0.758107i	$-0.726125\pi$
$577$	−3.18631	+	2.31499i	−0.132648	+	0.0963743i	0.519483	+	0.854481i	$0.326125\pi$
$578$	9.93301	+	5.95858i	0.413159	+	0.247844i
$579$	−0.970064	−	2.98555i	−0.0403145	−	0.124075i
$580$	−33.9233	+	18.1003i	−1.40859	+	0.751576i
$581$	3.92759	+	2.85356i	0.162944	+	0.118386i
$582$	−29.4613	+	12.5307i	−1.22121	+	0.519416i
$583$		0			0
$584$	−4.31539	+	11.3153i	−0.178572	+	0.468231i
$585$	−1.76773	+	2.43307i	−0.0730866	+	0.100595i
$586$	−0.934417	−	10.5922i	−0.0386004	−	0.437559i
$587$	18.0331	−	5.85930i	0.744305	−	0.241839i	0.0877761	−	0.996140i	$-0.472024\pi$
$587$	18.0331	−	5.85930i	0.744305	−	0.241839i	0.656529	+	0.754301i	$0.272024\pi$
$588$	−28.7222	−	3.99427i	−1.18448	−	0.164721i
$589$	−4.47901	−	6.16483i	−0.184555	−	0.254018i
$590$	−30.4862	−	35.0192i	−1.25510	−	1.44172i
$591$	−13.1278	+	40.4032i	−0.540006	+	1.66197i
$592$	11.6342	−	17.3566i	0.478164	−	0.713351i
$593$		−	31.9983i		−	1.31401i	−0.753885	−	0.657007i	$-0.771822\pi$
$593$		−	31.9983i		−	1.31401i	0.753885	−	0.657007i	$-0.228178\pi$
$594$		0			0
$595$		−	8.94012i		−	0.366509i
$596$	−6.11008	−	34.3612i	−0.250279	−	1.40749i
$597$	9.21552	−	28.3624i	0.377166	−	1.16080i
$598$	0.164591	−	0.143286i	0.00673062	−	0.00585940i
$599$	5.08850	+	7.00371i	0.207910	+	0.286164i	0.900219	−	0.435438i	$-0.143406\pi$
$599$	5.08850	+	7.00371i	0.207910	+	0.286164i	−0.692309	+	0.721602i	$0.743406\pi$
$600$	−0.886308	−	3.27926i	−0.0361834	−	0.133875i
$601$	20.9520	−	6.80772i	0.854650	−	0.277693i	0.151258	−	0.988494i	$-0.451668\pi$
$601$	20.9520	−	6.80772i	0.854650	−	0.277693i	0.703392	+	0.710802i	$0.251668\pi$
$602$	−6.35611	+	0.560721i	−0.259056	+	0.0228533i
$603$	−26.9155	+	37.0461i	−1.09609	+	1.50863i
$604$	13.6289	−	14.1540i	0.554551	−	0.575919i
$605$		0			0
$606$	−11.5623	−	27.1844i	−0.469687	−	1.10429i
$607$	−34.5592	−	25.1088i	−1.40272	−	1.01913i	−0.994332	−	0.106323i	$-0.966092\pi$
$607$	−34.5592	−	25.1088i	−1.40272	−	1.01913i	−0.408385	−	0.912810i	$-0.633908\pi$
$608$	−1.21648	−	9.61964i	−0.0493348	−	0.390128i
$609$	−8.94084	−	27.5171i	−0.362301	−	1.11505i
$610$	16.0320	−	26.7255i	0.649116	−	1.08208i
$611$	1.81880	−	1.32143i	0.0735806	−	0.0534594i
$612$	11.3964	−	23.4522i	0.460673	−	0.947998i
$613$	9.29962	+	3.02163i	0.375608	+	0.122042i	0.490736	−	0.871308i	$-0.336728\pi$
$613$	9.29962	+	3.02163i	0.375608	+	0.122042i	−0.115128	+	0.993351i	$0.536728\pi$
$614$	−8.18171	+	35.5562i	−0.330187	+	1.43493i
$615$	−35.4817			−1.43076
$616$		0			0
$617$	−22.4213			−0.902649			−0.451324	−	0.892360i	$-0.649048\pi$
$617$	−22.4213			−0.902649			−0.451324	+	0.892360i	$0.649048\pi$
$618$	−0.355586	+	1.54531i	−0.0143038	+	0.0621616i
$619$	18.3360	+	5.95771i	0.736984	+	0.239461i	0.653371	−	0.757038i	$-0.273354\pi$
$619$	18.3360	+	5.95771i	0.736984	+	0.239461i	0.0836131	+	0.996498i	$0.473354\pi$
$620$	9.06534	−	18.6552i	0.364073	−	0.749209i
$621$	−1.61033	+	1.16998i	−0.0646205	+	0.0469495i
$622$	2.15657	−	3.59502i	0.0864704	−	0.144147i
$623$	−0.238668	−	0.734544i	−0.00956203	−	0.0294289i
$624$	−3.07095	−	0.870971i	−0.122936	−	0.0348668i
$625$	21.8544	+	15.8781i	0.874174	+	0.635125i
$626$	−0.334322	−	0.786031i	−0.0133622	−	0.0314161i
$627$		0			0
$628$	−21.3691	+	22.1925i	−0.852720	+	0.885579i
$629$	9.11336	−	12.5435i	0.363373	−	0.500141i
$630$	18.6385	−	1.64425i	0.742577	−	0.0655085i
$631$	−36.4092	+	11.8301i	−1.44943	+	0.470947i	−0.924822	−	0.380400i	$-0.875786\pi$
$631$	−36.4092	+	11.8301i	−1.44943	+	0.470947i	−0.524604	+	0.851347i	$0.675786\pi$
$632$	26.8954	−	7.26921i	1.06984	−	0.289154i
$633$	30.8500	+	42.4614i	1.22618	+	1.68769i
$634$	24.4748	−	21.3067i	0.972017	−	0.846197i
$635$	14.3926	−	44.2958i	0.571152	−	1.75783i
$636$	1.49354	+	8.39921i	0.0592227	+	0.333050i
$637$			1.56519i			0.0620153i
$638$		0			0
$639$		−	15.7910i		−	0.624682i
$640$	21.5422	−	15.2471i	0.851529	−	0.602696i
$641$	−9.77625	+	30.0882i	−0.386139	+	1.18841i	0.549512	+	0.835486i	$0.314814\pi$
$641$	−9.77625	+	30.0882i	−0.386139	+	1.18841i	−0.935651	+	0.352927i	$0.885186\pi$
$642$	13.0677	+	15.0107i	0.515742	+	0.592427i
$643$	8.75854	+	12.0551i	0.345403	+	0.475407i	0.946010	−	0.324138i	$-0.105074\pi$
$643$	8.75854	+	12.0551i	0.345403	+	0.475407i	−0.600607	+	0.799545i	$0.705074\pi$
$644$	−1.34474	−	0.187007i	−0.0529902	−	0.00736911i
$645$	−21.0780	+	6.84865i	−0.829945	+	0.269665i
$646$	−0.632254	−	7.16697i	−0.0248757	−	0.281981i
$647$	−24.1610	+	33.2547i	−0.949866	+	1.30738i	0.00172043	+	0.999999i	$0.499452\pi$
$647$	−24.1610	+	33.2547i	−0.949866	+	1.30738i	−0.951587	+	0.307380i	$0.900548\pi$
$648$	−7.62022	−	2.90617i	−0.299351	−	0.114165i
$649$		0			0
$650$	−0.168721	+	0.0717621i	−0.00661780	+	0.00281474i
$651$	12.6267	+	9.17381i	0.494878	+	0.359550i
$652$	−18.9992	+	10.1373i	−0.744066	+	0.397009i
$653$	1.41618	+	4.35856i	0.0554194	+	0.170564i	0.974935	−	0.222490i	$-0.0714186\pi$
$653$	1.41618	+	4.35856i	0.0554194	+	0.170564i	−0.919515	+	0.393054i	$0.871419\pi$
$654$	41.5294	+	24.9125i	1.62393	+	0.974157i
$655$	−38.7139	+	28.1273i	−1.51268	+	1.09902i
$656$	−7.71417	−	21.0052i	−0.301188	−	0.820115i
$657$	−17.8866	−	5.81170i	−0.697822	−	0.226736i
$658$	−13.6308	−	3.13653i	−0.531384	−	0.122275i
$659$	38.0732			1.48312			0.741560	−	0.670886i	$-0.234086\pi$
$659$	38.0732			1.48312			0.741560	+	0.670886i	$0.234086\pi$
$660$		0			0
$661$	−9.34038			−0.363299			−0.181649	−	0.983363i	$-0.558144\pi$
$661$	−9.34038			−0.363299			−0.181649	+	0.983363i	$0.558144\pi$
$662$	6.11150	+	1.40630i	0.237530	+	0.0546572i
$663$	−2.25265	−	0.731931i	−0.0874858	−	0.0284258i
$664$	−0.533512	+	10.6210i	−0.0207043	+	0.412175i
$665$	4.17691	−	3.03470i	0.161974	−	0.117681i
$666$	27.8270	+	16.6927i	1.07827	+	0.646831i
$667$	1.33890	+	4.12072i	0.0518426	+	0.159555i
$668$	6.04632	+	11.3319i	0.233939	+	0.438444i
$669$	−23.8420	−	17.3223i	−0.921787	−	0.669717i
$670$	−31.6481	+	13.4609i	−1.22267	+	0.520039i
$671$		0			0
$672$	8.45810	+	17.9685i	0.326278	+	0.693148i
$673$	8.33504	−	11.4722i	0.321292	−	0.442221i	−0.617569	−	0.786517i	$-0.711882\pi$
$673$	8.33504	−	11.4722i	0.321292	−	0.442221i	0.938861	+	0.344296i	$0.111882\pi$
$674$	−2.20737	−	25.0218i	−0.0850247	−	0.963805i
$675$	1.59053	−	0.516796i	0.0612197	−	0.0198915i
$676$	3.55751	−	25.5815i	0.136827	−	0.983905i
$677$	−2.77000	−	3.81258i	−0.106460	−	0.146529i	0.752463	−	0.658635i	$-0.228866\pi$
$677$	−2.77000	−	3.81258i	−0.106460	−	0.146529i	−0.858923	+	0.512105i	$0.828866\pi$
$678$	−6.71765	−	7.71649i	−0.257990	−	0.296350i
$679$	3.32225	−	10.2248i	0.127496	−	0.392393i
$680$	16.4008	−	10.7015i	0.628943	−	0.410384i
$681$			65.2454i			2.50021i
$682$		0			0
$683$		−	18.0462i		−	0.690519i	−0.938507	−	0.345260i	$-0.887791\pi$
$683$		−	18.0462i		−	0.690519i	0.938507	−	0.345260i	$-0.112209\pi$
$684$	14.8256	−	2.63627i	0.566869	−	0.100800i
$685$	4.51647	−	13.9003i	0.172566	−	0.531102i
$686$	16.9856	−	14.7870i	0.648515	−	0.564569i
$687$	39.2843	+	54.0702i	1.49879	+	2.06291i
$688$	−8.63704	−	10.9892i	−0.329284	−	0.418960i
$689$	0.437921	−	0.142289i	0.0166835	−	0.00542079i
$690$	−4.69745	+	0.414399i	−0.178829	+	0.0157759i
$691$	−0.790392	+	1.08788i	−0.0300679	+	0.0413849i	−0.823786	−	0.566900i	$-0.808142\pi$
$691$	−0.790392	+	1.08788i	−0.0300679	+	0.0413849i	0.793718	+	0.608285i	$0.208142\pi$
$692$	−5.21216	−	5.01877i	−0.198137	−	0.190785i
$693$		0			0
$694$	−2.14791	−	5.05000i	−0.0815336	−	0.191695i
$695$	−25.4405	−	18.4836i	−0.965012	−	0.701122i
$696$	39.7783	−	49.3406i	1.50779	−	1.87025i
$697$	−5.13095	−	15.7914i	−0.194349	−	0.598143i
$698$	−14.3448	+	23.9129i	−0.542959	+	0.905117i
$699$	−31.4653	+	22.8609i	−1.19013	+	0.864677i
$700$	1.02599	+	0.498571i	0.0387787	+	0.0188442i
$701$	15.8467	+	5.14892i	0.598523	+	0.194472i	0.592582	−	0.805510i	$-0.298109\pi$
$701$	15.8467	+	5.14892i	0.598523	+	0.194472i	0.00594136	+	0.999982i	$0.498109\pi$
$702$	0.352410	−	1.53151i	0.0133009	−	0.0578031i
$703$	8.95393			0.337704
$704$		0			0
$705$	−48.5817			−1.82969
$706$	0.506215	−	2.19992i	0.0190517	−	0.0827950i
$707$	9.43459	+	3.06548i	0.354824	+	0.115289i
$708$	68.8348	+	33.4498i	2.58697	+	1.25712i
$709$	−19.4666	+	14.1433i	−0.731083	+	0.531163i	−0.889906	−	0.456144i	$-0.849230\pi$
$709$	−19.4666	+	14.1433i	−0.731083	+	0.531163i	0.158823	+	0.987307i	$0.449230\pi$
$710$	6.10094	−	10.1703i	0.228964	−	0.381685i
$711$	13.3702	+	41.1492i	0.501422	+	1.54322i
$712$	1.06185	−	1.31710i	0.0397944	−	0.0493606i
$713$	−1.89086	−	1.37379i	−0.0708133	−	0.0514489i
$714$	5.76771	+	13.5606i	0.215851	+	0.507493i
$715$		0			0
$716$	−7.21459	−	6.94690i	−0.269622	−	0.259618i
$717$	−31.5854	+	43.4736i	−1.17958	+	1.62355i
$718$	21.7266	−	1.91667i	0.810830	−	0.0715295i
$719$	10.7749	−	3.50096i	0.401834	−	0.130564i	−0.101126	−	0.994874i	$-0.532244\pi$
$719$	10.7749	−	3.50096i	0.401834	−	0.130564i	0.502960	+	0.864310i	$0.332244\pi$
$720$	25.3271	+	32.2246i	0.943886	+	1.20094i
$721$	−0.312989	−	0.430792i	−0.0116563	−	0.0160435i
$722$	−17.1325	+	14.9148i	−0.637605	+	0.555072i
$723$	−5.48691	+	16.8870i	−0.204060	+	0.628033i
$724$	19.3011	−	3.43211i	0.717320	−	0.127553i
$725$		−	3.64037i		−	0.135200i
$726$		0			0
$727$			0.700673i			0.0259865i	0.999916	+	0.0129933i	$0.00413600\pi$
$727$			0.700673i			0.0259865i	−0.999916	+	0.0129933i	$0.995864\pi$
$728$	0.897719	−	0.585760i	0.0332717	−	0.0217097i
$729$	13.4570	−	41.4163i	0.498407	−	1.53394i
$730$	−9.27462	−	10.6537i	−0.343269	−	0.394310i
$731$	−6.09611	−	8.39057i	−0.225473	−	0.310337i
$732$	−7.07578	+	50.8808i	−0.261528	+	1.88061i
$733$	−28.5106	+	9.26367i	−1.05306	+	0.342162i	−0.783870	−	0.620924i	$-0.786757\pi$
$733$	−28.5106	+	9.26367i	−1.05306	+	0.342162i	−0.269194	+	0.963086i	$0.586757\pi$
$734$	1.31136	+	14.8650i	0.0484031	+	0.548678i
$735$	19.8808	−	27.3636i	0.733314	−	1.00932i
$736$	−1.26661	−	2.69080i	−0.0466879	−	0.0991843i
$737$		0			0
$738$	31.9786	−	13.6014i	1.17715	−	0.500676i
$739$	35.2943	+	25.6428i	1.29832	+	0.943286i	0.999938	−	0.0111594i	$-0.00355221\pi$
$739$	35.2943	+	25.6428i	1.29832	+	0.943286i	0.298385	+	0.954446i	$0.403552\pi$
$740$	11.4729	+	21.5022i	0.421751	+	0.790437i
$741$	−0.422692	−	1.30091i	−0.0155280	−	0.0477902i
$742$	−2.45664	−	1.47368i	−0.0901862	−	0.0541006i
$743$	−27.6735	+	20.1060i	−1.01524	+	0.737616i	−0.965302	−	0.261136i	$-0.915903\pi$
$743$	−27.6735	+	20.1060i	−1.01524	+	0.737616i	−0.0499398	+	0.998752i	$0.515903\pi$
$744$	−1.71517	+	34.1451i	−0.0628810	+	1.25182i
$745$	38.7144	+	12.5791i	1.41839	+	0.460861i
$746$	51.6760	+	11.8910i	1.89199	+	0.435359i
$747$	−16.5151			−0.604255
$748$		0			0
$749$	−6.68321			−0.244199
$750$	−39.8452	−	9.16864i	−1.45494	−	0.334791i
$751$	−1.37755	−	0.447593i	−0.0502675	−	0.0163329i	0.283775	−	0.958891i	$-0.408413\pi$
$751$	−1.37755	−	0.447593i	−0.0502675	−	0.0163329i	−0.334043	+	0.942558i	$0.608413\pi$
$752$	−10.5623	−	28.7604i	−0.385167	−	1.04879i
$753$	10.4936	−	7.62403i	0.382407	−	0.277835i
$754$	−2.93350	−	1.75974i	−0.106832	−	0.0640859i
$755$	7.08208	+	21.7964i	0.257743	+	0.793252i
$756$	−8.62625	+	4.60268i	−0.313734	+	0.167398i
$757$	−24.6383	−	17.9008i	−0.895495	−	0.650615i	0.0418101	−	0.999126i	$-0.486688\pi$
$757$	−24.6383	−	17.9008i	−0.895495	−	0.650615i	−0.937305	+	0.348511i	$0.886688\pi$
$758$	27.7573	−	11.8060i	1.00819	−	0.428812i
$759$		0			0
$760$	10.5671	+	4.03002i	0.383308	+	0.146184i
$761$	14.1354	−	19.4557i	0.512408	−	0.705269i	−0.471915	−	0.881644i	$-0.656437\pi$
$761$	14.1354	−	19.4557i	0.512408	−	0.705269i	0.984323	+	0.176375i	$0.0564371\pi$
$762$	6.74639	+	76.4743i	0.244396	+	2.77037i
$763$	−15.4667	+	5.02544i	−0.559933	+	0.181933i
$764$	−23.1565	−	3.22028i	−0.837773	−	0.116505i
$765$	17.8761	+	24.6044i	0.646313	+	0.889573i
$766$	26.7720	+	30.7528i	0.967313	+	1.11114i
$767$	1.27649	−	3.92862i	0.0460912	−	0.141854i
$768$	−22.8390	+	37.0251i	−0.824131	+	1.33603i
$769$			14.6461i			0.528151i	0.964502	+	0.264076i	$0.0850669\pi$
$769$			14.6461i			0.528151i	−0.964502	+	0.264076i	$0.914933\pi$
$770$		0			0
$771$		−	8.25715i		−	0.297374i
$772$	0.404270	+	2.27349i	0.0145500	+	0.0818246i
$773$	−8.20185	+	25.2427i	−0.295000	+	0.907917i	0.688221	+	0.725501i	$0.258392\pi$
$773$	−8.20185	+	25.2427i	−0.295000	+	0.907917i	−0.983221	+	0.182416i	$0.941608\pi$
$774$	16.3717	−	14.2525i	0.588467	−	0.512294i
$775$	1.15425	+	1.58868i	0.0414618	+	0.0570672i
$776$	22.7344	−	6.14459i	0.816118	−	0.220578i
$777$	−17.4416	+	5.66713i	−0.625715	+	0.203307i
$778$	49.1358	−	4.33465i	1.76160	−	0.155405i
$779$	5.63622	−	7.75759i	0.201939	−	0.277945i
$780$	2.58244	−	2.68195i	0.0924662	−	0.0960293i
$781$		0			0
$782$	−0.863723	−	2.03072i	−0.0308867	−	0.0726184i
$783$	25.2435	+	18.3404i	0.902128	+	0.655434i
$784$	20.5216	+	5.82026i	0.732914	+	0.207866i
$785$	−11.1042	−	34.1752i	−0.396326	−	1.21977i
$786$	40.5759	−	67.6404i	1.44729	−	2.41265i
$787$	−16.5940	+	12.0562i	−0.591512	+	0.429758i	−0.842856	−	0.538139i	$-0.819127\pi$
$787$	−16.5940	+	12.0562i	−0.591512	+	0.429758i	0.251344	+	0.967898i	$0.419127\pi$
$788$	13.6583	−	28.1067i	0.486555	−	1.00126i
$789$	−36.6338	−	11.9031i	−1.30420	−	0.423760i
$790$	−7.28705	+	31.6682i	−0.259261	+	1.12670i
$791$	3.43560			0.122156
$792$		0			0
$793$	2.77271			0.0984620
$794$	−5.36276	+	23.3056i	−0.190317	+	0.827083i
$795$	−9.46329	−	3.07481i	−0.335628	−	0.109052i
$796$	−9.58788	+	19.7305i	−0.339834	+	0.699328i
$797$	26.5766	−	19.3091i	0.941393	−	0.683962i	−0.00736271	−	0.999973i	$-0.502344\pi$
$797$	26.5766	−	19.3091i	0.941393	−	0.683962i	0.948756	+	0.316011i	$0.102344\pi$
$798$	−4.37780	+	7.29784i	−0.154973	+	0.258341i
$799$	−7.02533	−	21.6217i	−0.248538	−	0.764922i
$800$	0.313489	+	2.47899i	0.0110835	+	0.0876456i
$801$	2.12560	+	1.54434i	0.0751042	+	0.0545664i
$802$	−8.77880	−	20.6400i	−0.309990	−	0.728825i
$803$		0			0
$804$	39.3204	−	40.8356i	1.38672	−	1.44016i
$805$	0.930796	−	1.28113i	0.0328062	−	0.0451539i
$806$	1.83816	−	0.162158i	0.0647465	−	0.00571178i
$807$	−2.59037	+	0.841664i	−0.0911855	+	0.0296280i
$808$	5.66970	+	20.9774i	0.199459	+	0.737982i
$809$	10.9876	+	15.1232i	0.386304	+	0.531702i	0.957241	−	0.289292i	$-0.0934198\pi$
$809$	10.9876	+	15.1232i	0.386304	+	0.531702i	−0.570937	+	0.820994i	$0.693420\pi$
$810$	7.17464	−	6.24594i	0.252091	−	0.219460i
$811$	8.46018	−	26.0378i	0.297077	−	0.914309i	−0.685439	−	0.728130i	$-0.740390\pi$
$811$	8.46018	−	26.0378i	0.297077	−	0.914309i	0.982516	−	0.186179i	$-0.0596104\pi$
$812$	3.72606	+	20.9542i	0.130759	+	0.735347i
$813$			48.3724i			1.69650i
$814$		0			0
$815$		−	25.1173i		−	0.879821i
$816$	−17.9731	+	26.8133i	−0.629185	+	0.938653i
$817$	1.85085	−	5.69632i	0.0647529	−	0.199289i
$818$	−25.6975	−	29.5184i	−0.898492	−	1.03209i
$819$	0.978472	+	1.34675i	0.0341906	+	0.0470593i
$820$	25.8511	+	3.59500i	0.902759	+	0.125543i
$821$	−8.19415	+	2.66244i	−0.285978	+	0.0929199i	−0.448493	−	0.893786i	$-0.648039\pi$
$821$	−8.19415	+	2.66244i	−0.285978	+	0.0929199i	0.162515	+	0.986706i	$0.448039\pi$
$822$	2.11705	+	23.9981i	0.0738408	+	0.837029i
$823$	−2.24958	+	3.09628i	−0.0784154	+	0.107930i	−0.846423	−	0.532511i	$-0.821248\pi$
$823$	−2.24958	+	3.09628i	−0.0784154	+	0.107930i	0.768007	+	0.640441i	$0.221248\pi$
$824$	0.415643	−	1.08985i	0.0144796	−	0.0379667i
$825$		0			0
$826$	−23.6496	+	10.0589i	−0.822876	+	0.349993i
$827$	22.1298	+	16.0783i	0.769530	+	0.559096i	0.901818	−	0.432115i	$-0.142233\pi$
$827$	22.1298	+	16.0783i	0.769530	+	0.559096i	−0.132289	+	0.991211i	$0.542233\pi$
$828$	4.07483	−	2.17419i	0.141610	−	0.0755584i
$829$	5.44082	+	16.7451i	0.188968	+	0.581582i	0.999994	−	0.00342699i	$-0.00109085\pi$
$829$	5.44082	+	16.7451i	0.188968	+	0.581582i	−0.811027	+	0.585009i	$0.801091\pi$
$830$	−10.6367	−	6.38069i	−0.369204	−	0.221477i
$831$	42.6439	−	30.9826i	1.47930	−	1.07478i
$832$	2.14917	+	0.945717i	0.0745092	+	0.0327869i
$833$	15.0533	+	4.89112i	0.521567	+	0.169467i
$834$	50.5134	+	11.6235i	1.74914	+	0.402487i
$835$	−14.9810			−0.518438
$836$		0			0
$837$	−16.8316			−0.581786
$838$	31.6585	+	7.28483i	1.09363	+	0.251650i
$839$	0.241041	+	0.0783188i	0.00832164	+	0.00270387i	0.313175	−	0.949695i	$-0.398607\pi$
$839$	0.241041	+	0.0783188i	0.00832164	+	0.00270387i	−0.304853	+	0.952399i	$0.598607\pi$
$840$	−23.1346	−	1.16209i	−0.798220	−	0.0400959i
$841$	31.4872	−	22.8768i	1.08577	−	0.788855i
$842$	−36.5152	−	21.9046i	−1.25840	−	0.754883i
$843$	−12.3478	−	38.0025i	−0.425279	−	1.30887i
$844$	−18.1744	−	34.0620i	−0.625588	−	1.17246i
$845$	24.3715	+	17.7069i	0.838404	+	0.609136i
$846$	43.7853	−	18.6232i	1.50537	−	0.640278i
$847$		0			0
$848$	−0.237151	−	6.27079i	−0.00814381	−	0.215340i
$849$	3.99036	−	5.49226i	0.136949	−	0.188494i
$850$	0.162932	+	1.84694i	0.00558854	+	0.0633494i
$851$	2.61191	−	0.848661i	0.0895352	−	0.0290917i
$852$	−2.69267	+	19.3626i	−0.0922494	+	0.663352i
$853$	−21.8156	−	30.0267i	−0.746954	−	1.02809i	−0.998188	−	0.0601672i	$-0.980837\pi$
$853$	−21.8156	−	30.0267i	−0.746954	−	1.02809i	0.251235	−	0.967926i	$-0.419163\pi$
$854$	−11.3268	−	13.0110i	−0.387595	−	0.445227i
$855$	−5.42739	+	16.7038i	−0.185613	+	0.571258i
$856$	−7.99994	−	12.2605i	−0.273432	−	0.419055i
$857$		−	20.9360i		−	0.715161i	−0.933882	−	0.357580i	$-0.883602\pi$
$857$		−	20.9360i		−	0.715161i	0.933882	−	0.357580i	$-0.116398\pi$
$858$		0			0
$859$		−	20.6926i		−	0.706022i	−0.935619	−	0.353011i	$-0.885158\pi$
$859$		−	20.6926i		−	0.706022i	0.935619	−	0.353011i	$-0.114842\pi$
$860$	16.0508	−	2.85415i	0.547328	−	0.0973255i
$861$	−6.06902	+	18.6785i	−0.206832	+	0.636563i
$862$	10.8512	−	9.44662i	0.369594	−	0.321753i
$863$	−22.2064	−	30.5645i	−0.755914	−	1.04043i	−0.997543	−	0.0700579i	$-0.977682\pi$
$863$	−22.2064	−	30.5645i	−0.755914	−	1.04043i	0.241629	−	0.970369i	$-0.422318\pi$
$864$	−18.7695	−	10.3155i	−0.638551	−	0.350941i
$865$	8.02642	−	2.60794i	0.272907	−	0.0886727i
$866$	−38.7897	+	3.42194i	−1.31813	+	0.116282i
$867$	13.0896	−	18.0163i	0.444546	−	0.611865i
$868$	−8.27000	−	7.96315i	−0.280702	−	0.270287i
$869$		0			0
$870$	28.9332	+	68.0254i	0.980926	+	2.30628i
$871$	−2.47541	−	1.79849i	−0.0838761	−	0.0609396i
$872$	−27.7332	−	22.3584i	−0.939166	−	0.757152i
$873$	11.3017	+	34.7830i	0.382504	+	1.17723i
$874$	0.655582	−	1.09286i	0.0221754	−	0.0369666i
$875$	11.1078	−	8.07028i	0.375512	−	0.272825i
$876$	20.9412	+	10.1762i	0.707537	+	0.343822i
$877$	−11.0189	−	3.58026i	−0.372083	−	0.120897i	0.117006	−	0.993131i	$-0.462670\pi$
$877$	−11.0189	−	3.58026i	−0.372083	−	0.120897i	−0.489088	+	0.872234i	$0.662670\pi$
$878$	3.66092	−	15.9097i	0.123550	−	0.536926i
$879$	−20.4432			−0.689532
$880$		0			0
$881$	−24.6157			−0.829325			−0.414662	−	0.909975i	$-0.636100\pi$
$881$	−24.6157			−0.829325			−0.414662	+	0.909975i	$0.636100\pi$
$882$	−7.42853	+	32.2830i	−0.250132	+	1.08703i
$883$	37.2302	+	12.0968i	1.25290	+	0.407091i	0.858958	−	0.512046i	$-0.171112\pi$
$883$	37.2302	+	12.0968i	1.25290	+	0.407091i	0.393939	+	0.919137i	$0.371112\pi$
$884$	1.56707	+	0.761506i	0.0527062	+	0.0256122i
$885$	−72.2167	+	52.4685i	−2.42754	+	1.76371i
$886$	−12.3607	+	20.6054i	−0.415266	+	0.692253i
$887$	−14.7026	−	45.2499i	−0.493665	−	1.51934i	−0.819027	−	0.573755i	$-0.805486\pi$
$887$	−14.7026	−	45.2499i	−0.493665	−	1.51934i	0.325363	−	0.945589i	$-0.394514\pi$
$888$	−31.2745	−	25.2134i	−1.04950	−	0.846105i
$889$	−20.8567	−	15.1533i	−0.699513	−	0.508226i
$890$	0.772346	+	1.81588i	0.0258891	+	0.0608684i
$891$		0			0
$892$	15.6157	+	15.0363i	0.522851	+	0.503451i
$893$	7.71715	−	10.6217i	0.258245	−	0.355443i
$894$	−66.8383	+	5.89632i	−2.23541	+	0.197202i
$895$	11.1100	−	3.60987i	0.371368	−	0.120665i
$896$	−4.34180	−	13.9484i	−0.145049	−	0.465982i
$897$	−0.246603	−	0.339420i	−0.00823384	−	0.0113329i
$898$	6.52434	−	5.67981i	0.217720	−	0.189538i
$899$	−11.3218	+	34.8450i	−0.377605	+	1.16215i
$900$	−3.82056	+	0.679370i	−0.127352	+	0.0226457i
$901$		−	4.65637i		−	0.155126i
$902$		0			0
$903$			12.2675i			0.408236i
$904$	4.11248	+	6.30268i	0.136779	+	0.209624i
$905$	−7.06582	+	21.7464i	−0.234876	+	0.722873i
$906$	−24.8042	−	28.4923i	−0.824064	−	0.946593i
$907$	−2.12114	−	2.91950i	−0.0704313	−	0.0969403i	0.772348	−	0.635200i	$-0.219082\pi$
$907$	−2.12114	−	2.91950i	−0.0704313	−	0.0969403i	−0.842779	+	0.538259i	$0.819082\pi$
$908$	6.61066	−	47.5362i	0.219382	−	1.57755i
$909$	−32.0948	+	10.4282i	−1.06452	+	0.345883i
$910$	0.109868	+	1.24542i	0.00364210	+	0.0412854i
$911$	−18.4726	+	25.4254i	−0.612026	+	0.842381i	−0.996742	−	0.0806536i	$-0.974299\pi$
$911$	−18.4726	+	25.4254i	−0.612026	+	0.842381i	0.384716	+	0.923035i	$0.374299\pi$
$912$	−18.6283	+	0.704495i	−0.616846	+	0.0233282i
$913$		0			0
$914$	8.48995	−	3.61102i	0.280823	−	0.119442i
$915$	−48.4741	−	35.2185i	−1.60250	−	1.16429i
$916$	−23.1432	−	43.3745i	−0.764673	−	1.43313i
$917$	8.18510	+	25.1911i	0.270296	+	0.831885i
$918$	−13.6281	−	8.17518i	−0.449795	−	0.269821i
$919$	21.1750	−	15.3845i	0.698498	−	0.507488i	−0.180945	−	0.983493i	$-0.557916\pi$
$919$	21.1750	−	15.3845i	0.698498	−	0.507488i	0.879443	+	0.476005i	$0.157916\pi$
$920$	3.46444	+	0.174025i	0.114219	+	0.00573742i
$921$	66.7123	+	21.6762i	2.19825	+	0.714254i
$922$	−26.3073	−	6.05347i	−0.866384	−	0.199361i
$923$	1.05515			0.0347307
$924$		0			0
$925$	−2.30744			−0.0758681
$926$	−17.9660	−	4.13410i	−0.590400	−	0.135855i
$927$	1.72277	+	0.559762i	0.0565833	+	0.0183850i
$928$	−33.9807	+	31.9181i	−1.11547	+	1.04776i
$929$	−22.8207	+	16.5802i	−0.748721	+	0.543978i	−0.895430	−	0.445202i	$-0.853132\pi$
$929$	−22.8207	+	16.5802i	−0.748721	+	0.543978i	0.146709	+	0.989180i	$0.453132\pi$
$930$	−34.1954	−	20.5130i	−1.12131	−	0.672648i
$931$	2.82464	+	8.69334i	0.0925737	+	0.284913i
$932$	25.2411	−	13.4678i	0.826800	−	0.441153i
$933$	−6.52056	−	4.73747i	−0.213474	−	0.155098i
$934$	−19.7522	+	8.40119i	−0.646312	+	0.274895i
$935$		0			0
$936$	−1.29939	+	3.40711i	−0.0424719	+	0.111365i
$937$	12.6263	−	17.3786i	0.412484	−	0.567735i	−0.551338	−	0.834282i	$-0.685883\pi$
$937$	12.6263	−	17.3786i	0.412484	−	0.567735i	0.963822	+	0.266547i	$0.0858826\pi$
$938$	1.67286	+	18.9629i	0.0546209	+	0.619161i
$939$	−1.56183	+	0.507470i	−0.0509684	+	0.0165606i
$940$	35.3955	+	4.92230i	1.15447	+	0.160548i
$941$	16.8196	+	23.1501i	0.548302	+	0.754673i	0.989781	−	0.142599i	$-0.0455458\pi$
$941$	16.8196	+	23.1501i	0.548302	+	0.754673i	−0.441478	+	0.897272i	$0.645546\pi$
$942$	38.8912	+	44.6739i	1.26714	+	1.45556i
$943$	0.908845	−	2.79714i	0.0295961	−	0.0910873i
$944$	−46.7623	−	31.3451i	−1.52198	−	1.02019i
$945$		−	11.4041i		−	0.370974i
$946$		0			0
$947$		−	0.894236i		−	0.0290588i	−0.999894	−	0.0145294i	$-0.995375\pi$
$947$		−	0.894236i		−	0.0290588i	0.999894	−	0.0145294i	$-0.00462501\pi$
$948$	−9.37753	−	52.7363i	−0.304568	−	1.71279i
$949$	0.388337	−	1.19518i	0.0126060	−	0.0387971i
$950$	−0.807599	+	0.703062i	−0.0262020	+	0.0228103i
$951$	−36.6700	−	50.4720i	−1.18911	−	1.63667i
$952$	−2.82826	−	10.4643i	−0.0916644	−	0.339150i
$953$	8.21027	−	2.66768i	0.265957	−	0.0864146i	−0.173003	−	0.984921i	$-0.555347\pi$
$953$	8.21027	−	2.66768i	0.265957	−	0.0864146i	0.438960	+	0.898507i	$0.355347\pi$
$954$	9.70769	−	0.856390i	0.314298	−	0.0277266i
$955$	16.0284	−	22.0612i	0.518666	−	0.713882i
$956$	27.4171	−	28.4736i	0.886733	−	0.920902i
$957$		0			0
$958$	14.5045	+	34.1018i	0.468618	+	1.10178i
$959$	−6.54496	−	4.75519i	−0.211348	−	0.153553i
$960$	−25.5607	−	43.8319i	−0.824968	−	1.41467i
$961$	3.47219	+	10.6863i	0.112006	+	0.344719i
$962$	−1.11541	+	1.85939i	−0.0359621	+	0.0599492i
$963$	18.3931	−	13.3634i	0.592709	−	0.430628i
$964$	5.70861	−	11.7475i	0.183862	−	0.378362i
$965$	−2.56151	−	0.832286i	−0.0824581	−	0.0267922i
$966$	−0.585333	+	2.54375i	−0.0188328	+	0.0818439i
$967$	−23.2776			−0.748557			−0.374278	−	0.927316i	$-0.622110\pi$
$967$	−23.2776			−0.748557			−0.374278	+	0.927316i	$0.622110\pi$
$968$		0			0
$969$	−13.8325			−0.444363
$970$	−6.15966	+	26.7688i	−0.197775	+	0.859493i
$971$	−30.6871	−	9.97085i	−0.984796	−	0.319980i	−0.228022	−	0.973656i	$-0.573226\pi$
$971$	−30.6871	−	9.97085i	−0.984796	−	0.319980i	−0.756774	+	0.653676i	$0.773226\pi$
$972$	−16.7818	+	34.5346i	−0.538278	+	1.10770i
$973$	−14.0818	+	10.2310i	−0.451441	+	0.327991i
$974$	−19.8255	+	33.0493i	−0.635250	+	1.05897i
$975$	0.108928	+	0.335247i	0.00348850	+	0.0107365i
$976$	10.3105	−	36.3537i	0.330031	−	1.16365i
$977$	−7.50527	−	5.45290i	−0.240115	−	0.174454i	0.461220	−	0.887286i	$-0.347412\pi$
$977$	−7.50527	−	5.45290i	−0.240115	−	0.174454i	−0.701334	+	0.712832i	$0.747412\pi$
$978$	16.2044	+	38.0986i	0.518160	+	1.21826i
$979$		0			0
$980$	−17.2571	+	17.9221i	−0.551259	+	0.572501i
$981$	32.5178	−	44.7570i	1.03821	−	1.42898i
$982$	30.1646	−	2.66106i	0.962593	−	0.0849177i
$983$	22.1486	−	7.19653i	0.706432	−	0.229534i	0.0663013	−	0.997800i	$-0.478880\pi$
$983$	22.1486	−	7.19653i	0.706432	−	0.229534i	0.640131	+	0.768266i	$0.278880\pi$
$984$	−41.5309	+	11.2248i	−1.32396	+	0.357835i
$985$	21.4240	+	29.4876i	0.682625	+	0.939553i
$986$	−26.0913	+	22.7140i	−0.830918	+	0.723362i
$987$	−8.30975	+	25.5748i	−0.264502	+	0.814054i
$988$	0.176155	+	0.990641i	0.00560424	+	0.0315165i
$989$		−	1.83707i		−	0.0584155i
$990$		0			0
$991$			42.4003i			1.34689i	0.739237	+	0.673446i	$0.235186\pi$
$991$			42.4003i			1.34689i	−0.739237	+	0.673446i	$0.764814\pi$
$992$	4.70921	−	24.7035i	0.149517	−	0.784337i
$993$	3.72576	−	11.4667i	0.118233	−	0.363885i
$994$	−4.31039	−	4.95130i	−0.136717	−	0.157046i
$995$	−15.0393	−	20.6999i	−0.476779	−	0.656229i
$996$	20.2504	+	2.81614i	0.641660	+	0.0892329i
$997$	4.22586	−	1.37307i	0.133834	−	0.0434855i	−0.241334	−	0.970442i	$-0.577585\pi$
$997$	4.22586	−	1.37307i	0.133834	−	0.0434855i	0.375168	+	0.926957i	$0.377585\pi$
$998$	3.83360	+	43.4561i	0.121350	+	1.37558i
$999$	11.6251	−	16.0005i	0.367800	−	0.506234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.g.f.403.3		16
4.3	odd	2	inner	484.2.g.f.403.2		16
11.2	odd	10		44.2.g.a.39.2	yes	16
11.3	even	5		484.2.g.j.239.3		16
11.4	even	5		44.2.g.a.35.1	✓	16
11.5	even	5		484.2.c.d.483.7		16
11.6	odd	10		484.2.c.d.483.10		16
11.7	odd	10		484.2.g.i.475.4		16
11.8	odd	10	inner	484.2.g.f.239.2		16
11.9	even	5		484.2.g.i.215.3		16
11.10	odd	2		484.2.g.j.403.2		16
33.2	even	10		396.2.r.a.127.3		16
33.26	odd	10		396.2.r.a.343.4		16
44.3	odd	10		484.2.g.j.239.2		16
44.7	even	10		484.2.g.i.475.3		16
44.15	odd	10		44.2.g.a.35.2	yes	16
44.19	even	10	inner	484.2.g.f.239.3		16
44.27	odd	10		484.2.c.d.483.9		16
44.31	odd	10		484.2.g.i.215.4		16
44.35	even	10		44.2.g.a.39.1	yes	16
44.39	even	10		484.2.c.d.483.8		16
44.43	even	2		484.2.g.j.403.3		16
88.13	odd	10		704.2.u.c.127.1		16
88.35	even	10		704.2.u.c.127.4		16
88.37	even	10		704.2.u.c.255.4		16
88.59	odd	10		704.2.u.c.255.1		16
132.35	odd	10		396.2.r.a.127.4		16
132.59	even	10		396.2.r.a.343.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.35.1	✓	16	11.4	even	5
44.2.g.a.35.2	yes	16	44.15	odd	10
44.2.g.a.39.1	yes	16	44.35	even	10
44.2.g.a.39.2	yes	16	11.2	odd	10
396.2.r.a.127.3		16	33.2	even	10
396.2.r.a.127.4		16	132.35	odd	10
396.2.r.a.343.3		16	132.59	even	10
396.2.r.a.343.4		16	33.26	odd	10
484.2.c.d.483.7		16	11.5	even	5
484.2.c.d.483.8		16	44.39	even	10
484.2.c.d.483.9		16	44.27	odd	10
484.2.c.d.483.10		16	11.6	odd	10
484.2.g.f.239.2		16	11.8	odd	10	inner
484.2.g.f.239.3		16	44.19	even	10	inner
484.2.g.f.403.2		16	4.3	odd	2	inner
484.2.g.f.403.3		16	1.1	even	1	trivial
484.2.g.i.215.3		16	11.9	even	5
484.2.g.i.215.4		16	44.31	odd	10
484.2.g.i.475.3		16	44.7	even	10
484.2.g.i.475.4		16	11.7	odd	10
484.2.g.j.239.2		16	44.3	odd	10
484.2.g.j.239.3		16	11.3	even	5
484.2.g.j.403.2		16	11.10	odd	2
484.2.g.j.403.3		16	44.43	even	2
704.2.u.c.127.1		16	88.13	odd	10
704.2.u.c.127.4		16	88.35	even	10
704.2.u.c.255.1		16	88.59	odd	10
704.2.u.c.255.4		16	88.37	even	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.317132 + 1.37820i) q^{2} +(2.58584 + 0.840191i) q^{3} +(-1.79885 - 0.874140i) q^{4} +(1.88723 - 1.37116i) q^{5} +(-1.97800 + 3.29735i) q^{6} +(-0.399009 - 1.22802i) q^{7} +(1.77521 - 2.20196i) q^{8} +(3.55361 + 2.58185i) q^{9} +(1.29122 + 3.03582i) q^{10} +(-3.91711 - 3.77177i) q^{12} +(-0.172519 + 0.237451i) q^{13} +(1.81900 - 0.160468i) q^{14} +(6.03212 - 1.95995i) q^{15} +(2.47176 + 3.14490i) q^{16} +(1.74459 + 2.40122i) q^{17} +(-4.68526 + 4.07879i) q^{18} +(-0.529677 + 1.63018i) q^{19} +(-4.59344 + 0.816802i) q^{20} -3.51072i q^{21} +0.525735i q^{23} +(6.44048 - 4.20240i) q^{24} +(0.136498 - 0.420099i) q^{25} +(-0.272544 - 0.313068i) q^{26} +(2.22541 + 3.06301i) q^{27} +(-0.355706 + 2.55783i) q^{28} +(7.83802 - 2.54673i) q^{29} +(0.788227 + 8.93502i) q^{30} +(-2.61308 + 3.59660i) q^{31} +(-5.11817 + 2.40922i) q^{32} +(-3.86263 + 1.64289i) q^{34} +(-2.43684 - 1.77046i) q^{35} +(-4.13553 - 7.75072i) q^{36} +(-1.61424 - 4.96811i) q^{37} +(-2.07873 - 1.24698i) q^{38} +(-0.645610 + 0.469063i) q^{39} +(0.331012 - 6.58970i) q^{40} +(-5.32043 - 1.72871i) q^{41} +(4.83846 + 1.11336i) q^{42} -3.49429 q^{43} +10.2466 q^{45} +(-0.724567 - 0.166727i) q^{46} +(-7.28477 - 2.36696i) q^{47} +(3.74925 + 10.2090i) q^{48} +(4.31428 - 3.13451i) q^{49} +(0.535691 + 0.321349i) q^{50} +(2.49375 + 7.67498i) q^{51} +(0.517902 - 0.276335i) q^{52} +(-1.26920 - 0.922128i) q^{53} +(-4.92719 + 2.09567i) q^{54} +(-3.41238 - 1.30140i) q^{56} +(-2.73932 + 3.77036i) q^{57} +(1.02421 + 11.6100i) q^{58} +(-13.3851 + 4.34909i) q^{59} +(-12.5642 - 1.74725i) q^{60} +(-5.55273 - 7.64268i) q^{61} +(-4.12814 - 4.74194i) q^{62} +(1.75265 - 5.39410i) q^{63} +(-1.69724 - 7.81789i) q^{64} +0.684676i q^{65} +10.4249i q^{67} +(-1.03926 - 5.84447i) q^{68} +(-0.441718 + 1.35947i) q^{69} +(3.21285 - 2.79697i) q^{70} +(-2.11308 - 2.90841i) q^{71} +(11.9935 - 3.24157i) q^{72} +(-4.07207 + 1.32310i) q^{73} +(7.35896 - 0.649191i) q^{74} +(0.705927 - 0.971625i) q^{75} +(2.37782 - 2.46944i) q^{76} +(-0.441718 - 1.03853i) q^{78} +(7.96895 + 5.78978i) q^{79} +(8.97693 + 2.54600i) q^{80} +(-0.891031 - 2.74231i) q^{81} +(4.06978 - 6.78437i) q^{82} +(-3.04177 + 2.20997i) q^{83} +(-3.06886 + 6.31528i) q^{84} +(6.58490 + 2.13956i) q^{85} +(1.10815 - 4.81582i) q^{86} +22.4076 q^{87} +0.598152 q^{89} +(-3.24952 + 14.1218i) q^{90} +(0.360433 + 0.117112i) q^{91} +(0.459567 - 0.945722i) q^{92} +(-9.77886 + 7.10476i) q^{93} +(5.57237 - 9.28920i) q^{94} +(1.23560 + 3.80280i) q^{95} +(-15.2590 + 1.92962i) q^{96} +(6.73607 + 4.89404i) q^{97} +(2.95178 + 6.93999i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{4} + 4 q^{5} + 10 q^{6} - 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} - 10 q^{17} - 15 q^{18} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} - 30 q^{28} + 40 q^{29} + 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 5 * q^2 - q^4 + 4 * q^5 + 10 * q^6 - 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 - 10 * q^17 - 15 * q^18 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 - 30 * q^28 + 40 * q^29 + 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 - 50 * q^41 + 24 * q^42 + 40 * q^45 - 40 * q^46 - q^48 + 16 * q^49 + 25 * q^50 - 20 * q^52 - 12 * q^53 - 12 * q^56 - 50 * q^57 - 48 * q^60 + 20 * q^61 - 30 * q^62 - 37 * q^64 + 35 * q^68 + 4 * q^69 + 22 * q^70 - 10 * q^72 - 30 * q^73 + 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 - 10 * q^84 + 60 * q^85 + 46 * q^86 - 36 * q^89 - 40 * q^90 - 54 * q^92 + 2 * q^93 + 60 * q^94 - 55 * q^96 + 72 * q^97

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