LMFDB - Embedded newform 51.2.i.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,2,Mod(5,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5]))

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

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

chi := DirichletCharacter("51.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			14.2
Character	$\chi$	$=$	51.14
Dual form			51.2.i.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.503008 - 1.21437i) q^{2} +(0.802099 + 1.53513i) q^{3} +(0.192538 - 0.192538i) q^{4} +(-0.0781694 - 0.116989i) q^{5} +(1.46076 - 1.74623i) q^{6} +(-1.47102 - 0.982905i) q^{7} +(-2.75940 - 1.14298i) q^{8} +(-1.71327 + 2.46266i) q^{9} +(-0.102748 + 0.153773i) q^{10} +(0.710485 + 3.57185i) q^{11} +(0.450006 + 0.141137i) q^{12} +(-0.0825311 - 0.0825311i) q^{13} +(-0.453674 + 2.28077i) q^{14} +(0.116894 - 0.213837i) q^{15} +3.38128i q^{16} +(-1.03609 - 3.99080i) q^{17} +(3.85237 + 0.841809i) q^{18} +(-6.20278 + 2.56928i) q^{19} +(-0.0375753 - 0.00747420i) q^{20} +(0.328986 - 3.04660i) q^{21} +(3.98016 - 2.65946i) q^{22} +(6.15884 - 1.22507i) q^{23} +(-0.458684 - 5.15283i) q^{24} +(1.90584 - 4.60111i) q^{25} +(-0.0587094 + 0.141737i) q^{26} +(-5.15473 - 0.654807i) q^{27} +(-0.472474 + 0.0939809i) q^{28} +(3.27292 - 2.18690i) q^{29} +(-0.318476 - 0.0343905i) q^{30} +(8.78185 + 1.74682i) q^{31} +(-1.41268 + 0.585150i) q^{32} +(-4.91339 + 3.95567i) q^{33} +(-4.32515 + 3.26560i) q^{34} +0.248926i q^{35} +(0.144285 + 0.804026i) q^{36} +(0.0726522 - 0.365247i) q^{37} +(6.24010 + 6.24010i) q^{38} +(0.0604982 - 0.192895i) q^{39} +(0.0819847 + 0.412165i) q^{40} +(-2.44315 + 3.65643i) q^{41} +(-3.86518 + 1.13296i) q^{42} +(1.94823 + 0.806985i) q^{43} +(0.824512 + 0.550921i) q^{44} +(0.422029 + 0.00792913i) q^{45} +(-4.58563 - 6.86288i) q^{46} +(-2.11141 + 2.11141i) q^{47} +(-5.19072 + 2.71212i) q^{48} +(-1.48098 - 3.57541i) q^{49} -6.54610 q^{50} +(5.29537 - 4.79156i) q^{51} -0.0317807 q^{52} +(-2.45113 - 5.91755i) q^{53} +(1.79769 + 6.58912i) q^{54} +(0.362328 - 0.362328i) q^{55} +(2.93569 + 4.39357i) q^{56} +(-8.91943 - 7.46129i) q^{57} +(-4.30201 - 2.87451i) q^{58} +(8.83540 + 3.65974i) q^{59} +(-0.0186653 - 0.0636782i) q^{60} +(-2.20784 + 3.30427i) q^{61} +(-2.29606 - 11.5431i) q^{62} +(4.94082 - 1.93864i) q^{63} +(6.20303 + 6.20303i) q^{64} +(-0.00320381 + 0.0161066i) q^{65} +(7.27511 + 3.97693i) q^{66} +5.81844i q^{67} +(-0.967868 - 0.568894i) q^{68} +(6.82064 + 8.47201i) q^{69} +(0.302288 - 0.125212i) q^{70} +(-12.7462 - 2.53537i) q^{71} +(7.54238 - 4.83722i) q^{72} +(-3.71467 + 2.48206i) q^{73} +(-0.480089 + 0.0954957i) q^{74} +(8.59199 - 0.764823i) q^{75} +(-0.699588 + 1.68895i) q^{76} +(2.46565 - 5.95260i) q^{77} +(-0.264676 + 0.0235604i) q^{78} +(2.39893 - 0.477177i) q^{79} +(0.395572 - 0.264312i) q^{80} +(-3.12939 - 8.43842i) q^{81} +(5.66918 + 1.12767i) q^{82} +(-5.11813 + 2.12000i) q^{83} +(-0.523244 - 0.649928i) q^{84} +(-0.385889 + 0.433170i) q^{85} -2.77180i q^{86} +(5.98239 + 3.27027i) q^{87} +(2.12204 - 10.6682i) q^{88} +(-2.89760 - 2.89760i) q^{89} +(-0.202655 - 0.516488i) q^{90} +(0.0402848 + 0.202525i) q^{91} +(0.949937 - 1.42168i) q^{92} +(4.36231 + 14.8824i) q^{93} +(3.62608 + 1.50197i) q^{94} +(0.785444 + 0.524817i) q^{95} +(-2.03139 - 1.69930i) q^{96} +(-2.54849 - 3.81409i) q^{97} +(-3.59692 + 3.59692i) q^{98} +(-10.0135 - 4.36987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−0.503008	−	1.21437i	−0.355681	−	0.858689i	−0.995897	−	0.0904942i	$-0.971155\pi$
$2$	−0.503008	−	1.21437i	−0.355681	−	0.858689i	0.640216	−	0.768195i	$-0.278845\pi$
$3$	0.802099	+	1.53513i	0.463092	+	0.886310i
$3$	0.802099	+	1.53513i	0.463092	+	0.886310i
$4$	0.192538	−	0.192538i	0.0962690	−	0.0962690i
$5$	−0.0781694	−	0.116989i	−0.0349584	−	0.0523190i	0.813579	−	0.581455i	$-0.197516\pi$
$5$	−0.0781694	−	0.116989i	−0.0349584	−	0.0523190i	−0.848537	+	0.529136i	$0.822516\pi$
$6$	1.46076	−	1.74623i	0.596352	−	0.712895i
$7$	−1.47102	−	0.982905i	−0.555994	−	0.371503i	0.245601	−	0.969371i	$-0.421015\pi$
$7$	−1.47102	−	0.982905i	−0.555994	−	0.371503i	−0.801595	+	0.597868i	$0.796015\pi$
$8$	−2.75940	−	1.14298i	−0.975595	−	0.404105i
$9$	−1.71327	+	2.46266i	−0.571091	+	0.820887i
$10$	−0.102748	+	0.153773i	−0.0324917	+	0.0486272i
$11$	0.710485	+	3.57185i	0.214219	+	1.07695i	0.926855	+	0.375419i	$0.122501\pi$
$11$	0.710485	+	3.57185i	0.214219	+	1.07695i	−0.712636	+	0.701534i	$0.752499\pi$
$12$	0.450006	+	0.141137i	0.129906	+	0.0407427i
$13$	−0.0825311	−	0.0825311i	−0.0228900	−	0.0228900i	0.695569	−	0.718459i	$-0.255152\pi$
$13$	−0.0825311	−	0.0825311i	−0.0228900	−	0.0228900i	−0.718459	+	0.695569i	$0.755152\pi$
$14$	−0.453674	+	2.28077i	−0.121249	+	0.609562i
$15$	0.116894	−	0.213837i	0.0301819	−	0.0552125i
$16$			3.38128i			0.845320i
$17$	−1.03609	−	3.99080i	−0.251289	−	0.967912i
$17$	−1.03609	−	3.99080i	−0.251289	−	0.967912i
$18$	3.85237	+	0.841809i	0.908012	+	0.198416i
$19$	−6.20278	+	2.56928i	−1.42302	+	0.589432i	−0.955616	−	0.294614i	$-0.904809\pi$
$19$	−6.20278	+	2.56928i	−1.42302	+	0.589432i	−0.467399	+	0.884046i	$0.654809\pi$
$20$	−0.0375753	−	0.00747420i	−0.00840210	−	0.00167128i
$21$	0.328986	−	3.04660i	0.0717906	−	0.664823i
$22$	3.98016	−	2.65946i	0.848574	−	0.566999i
$23$	6.15884	−	1.22507i	1.28421	−	0.255444i	0.494633	−	0.869102i	$-0.335302\pi$
$23$	6.15884	−	1.22507i	1.28421	−	0.255444i	0.789573	+	0.613657i	$0.210302\pi$
$24$	−0.458684	−	5.15283i	−0.0936284	−	1.05182i
$25$	1.90584	−	4.60111i	0.381168	−	0.920222i
$26$	−0.0587094	+	0.141737i	−0.0115139	+	0.0277969i
$27$	−5.15473	−	0.654807i	−0.992028	−	0.126018i
$28$	−0.472474	+	0.0939809i	−0.0892891	+	0.0177607i
$29$	3.27292	−	2.18690i	0.607766	−	0.406097i	−0.213253	−	0.976997i	$-0.568406\pi$
$29$	3.27292	−	2.18690i	0.607766	−	0.406097i	0.821019	+	0.570900i	$0.193406\pi$
$30$	−0.318476	−	0.0343905i	−0.0581455	−	0.00627881i
$31$	8.78185	+	1.74682i	1.57727	+	0.313738i	0.904618	−	0.426224i	$-0.140156\pi$
$31$	8.78185	+	1.74682i	1.57727	+	0.313738i	0.672649	+	0.739962i	$0.265156\pi$
$32$	−1.41268	+	0.585150i	−0.249728	+	0.103441i
$33$	−4.91339	+	3.95567i	−0.855311	+	0.688593i
$34$	−4.32515	+	3.26560i	−0.741757	+	0.560046i
$35$			0.248926i			0.0420762i
$36$	0.144285	+	0.804026i	0.0240475	+	0.134004i
$37$	0.0726522	−	0.365247i	0.0119439	−	0.0600462i	−0.974354	−	0.225022i	$-0.927755\pi$
$37$	0.0726522	−	0.365247i	0.0119439	−	0.0600462i	0.986298	+	0.164976i	$0.0527546\pi$
$38$	6.24010	+	6.24010i	1.01228	+	1.01228i
$39$	0.0604982	−	0.192895i	0.00968747	−	0.0308878i
$40$	0.0819847	+	0.412165i	0.0129629	+	0.0651690i
$41$	−2.44315	+	3.65643i	−0.381556	+	0.571039i	−0.971688	−	0.236268i	$-0.924076\pi$
$41$	−2.44315	+	3.65643i	−0.381556	+	0.571039i	0.590132	+	0.807307i	$0.299076\pi$
$42$	−3.86518	+	1.13296i	−0.596410	+	0.174819i
$43$	1.94823	+	0.806985i	0.297103	+	0.123064i	0.526256	−	0.850326i	$-0.323596\pi$
$43$	1.94823	+	0.806985i	0.297103	+	0.123064i	−0.229153	+	0.973390i	$0.573596\pi$
$44$	0.824512	+	0.550921i	0.124300	+	0.0830545i
$45$	0.422029	+	0.00792913i	0.0629124	+	0.00118201i
$46$	−4.58563	−	6.86288i	−0.676114	−	1.01188i
$47$	−2.11141	+	2.11141i	−0.307980	+	0.307980i	−0.844126	−	0.536145i	$-0.819880\pi$
$47$	−2.11141	+	2.11141i	−0.307980	+	0.307980i	0.536145	+	0.844126i	$0.319880\pi$
$48$	−5.19072	+	2.71212i	−0.749215	+	0.391461i
$49$	−1.48098	−	3.57541i	−0.211569	−	0.510773i
$50$	−6.54610			−0.925758
$51$	5.29537	−	4.79156i	0.741500	−	0.670952i
$52$	−0.0317807			−0.00440720
$53$	−2.45113	−	5.91755i	−0.336688	−	0.812837i	−0.998029	−	0.0627519i	$-0.980012\pi$
$53$	−2.45113	−	5.91755i	−0.336688	−	0.812837i	0.661341	−	0.750085i	$-0.269988\pi$
$54$	1.79769	+	6.58912i	0.244635	+	0.896665i
$55$	0.362328	−	0.362328i	0.0488563	−	0.0488563i
$56$	2.93569	+	4.39357i	0.392298	+	0.587116i
$57$	−8.91943	−	7.46129i	−1.18141	−	0.988272i
$58$	−4.30201	−	2.87451i	−0.564881	−	0.377442i
$59$	8.83540	+	3.65974i	1.15027	+	0.476458i	0.874624	−	0.484801i	$-0.161108\pi$
$59$	8.83540	+	3.65974i	1.15027	+	0.476458i	0.275647	+	0.961259i	$0.411108\pi$
$60$	−0.0186653	−	0.0636782i	−0.00240967	−	0.00822083i
$61$	−2.20784	+	3.30427i	−0.282685	+	0.423068i	−0.945454	−	0.325756i	$-0.894381\pi$
$61$	−2.20784	+	3.30427i	−0.282685	+	0.423068i	0.662769	+	0.748824i	$0.269381\pi$
$62$	−2.29606	−	11.5431i	−0.291600	−	1.46597i
$63$	4.94082	−	1.93864i	0.622485	−	0.244246i
$64$	6.20303	+	6.20303i	0.775378	+	0.775378i
$65$	−0.00320381	+	0.0161066i	−0.000397383	+	0.00199778i
$66$	7.27511	+	3.97693i	0.895505	+	0.489527i
$67$			5.81844i			0.710836i	0.934707	+	0.355418i	$0.115661\pi$
$67$			5.81844i			0.710836i	−0.934707	+	0.355418i	$0.884339\pi$
$68$	−0.967868	−	0.568894i	−0.117371	−	0.0689886i
$69$	6.82064	+	8.47201i	0.821109	+	1.01991i
$70$	0.302288	−	0.125212i	0.0361303	−	0.0149657i
$71$	−12.7462	−	2.53537i	−1.51269	−	0.300893i	−0.632143	−	0.774851i	$-0.717825\pi$
$71$	−12.7462	−	2.53537i	−1.51269	−	0.300893i	−0.880547	+	0.473959i	$0.842825\pi$
$72$	7.54238	−	4.83722i	0.888878	−	0.570072i
$73$	−3.71467	+	2.48206i	−0.434769	+	0.290504i	−0.753631	−	0.657298i	$-0.771699\pi$
$73$	−3.71467	+	2.48206i	−0.434769	+	0.290504i	0.318862	+	0.947801i	$0.396699\pi$
$74$	−0.480089	+	0.0954957i	−0.0558093	+	0.0111012i
$75$	8.59199	−	0.764823i	0.992118	−	0.0883142i
$76$	−0.699588	+	1.68895i	−0.0802482	+	0.193736i
$77$	2.46565	−	5.95260i	0.280987	−	0.678362i
$78$	−0.264676	+	0.0235604i	−0.0299687	+	0.00266769i
$79$	2.39893	−	0.477177i	0.269901	−	0.0536866i	−0.0582845	−	0.998300i	$-0.518563\pi$
$79$	2.39893	−	0.477177i	0.269901	−	0.0536866i	0.328185	+	0.944613i	$0.393563\pi$
$80$	0.395572	−	0.264312i	0.0442262	−	0.0295510i
$81$	−3.12939	−	8.43842i	−0.347710	−	0.937602i
$82$	5.66918	+	1.12767i	0.626057	+	0.124530i
$83$	−5.11813	+	2.12000i	−0.561788	+	0.232700i	−0.645461	−	0.763793i	$-0.723335\pi$
$83$	−5.11813	+	2.12000i	−0.561788	+	0.232700i	0.0836731	+	0.996493i	$0.473335\pi$
$84$	−0.523244	−	0.649928i	−0.0570906	−	0.0709130i
$85$	−0.385889	+	0.433170i	−0.0418555	+	0.0469838i
$86$		−	2.77180i		−	0.298890i
$87$	5.98239	+	3.27027i	0.641379	+	0.350609i
$88$	2.12204	−	10.6682i	0.226210	−	1.13724i
$89$	−2.89760	−	2.89760i	−0.307145	−	0.307145i	0.536656	−	0.843801i	$-0.319687\pi$
$89$	−2.89760	−	2.89760i	−0.307145	−	0.307145i	−0.843801	+	0.536656i	$0.819687\pi$
$90$	−0.202655	−	0.516488i	−0.0213617	−	0.0544426i
$91$	0.0402848	+	0.202525i	0.00422299	+	0.0212304i
$92$	0.949937	−	1.42168i	0.0990378	−	0.148221i
$93$	4.36231	+	14.8824i	0.452351	+	1.54324i
$94$	3.62608	+	1.50197i	0.374002	+	0.154917i
$95$	0.785444	+	0.524817i	0.0805849	+	0.0538451i
$96$	−2.03139	−	1.69930i	−0.207328	−	0.173434i
$97$	−2.54849	−	3.81409i	−0.258760	−	0.387262i	0.679229	−	0.733926i	$-0.262314\pi$
$97$	−2.54849	−	3.81409i	−0.258760	−	0.387262i	−0.937989	+	0.346664i	$0.887314\pi$
$98$	−3.59692	+	3.59692i	−0.363344	+	0.363344i
$99$	−10.0135	−	4.36987i	−1.00639	−	0.439189i
$100$	−0.518941	−	1.25283i	−0.0518941	−	0.125283i
$101$	5.06729			0.504214			0.252107	−	0.967699i	$-0.418877\pi$
$101$	5.06729			0.504214			0.252107	+	0.967699i	$0.418877\pi$
$102$	−8.48234	−	4.02034i	−0.839877	−	0.398073i
$103$	−15.9760			−1.57416			−0.787080	−	0.616851i	$-0.788408\pi$
$103$	−15.9760			−1.57416			−0.787080	+	0.616851i	$0.788408\pi$
$104$	0.133405	+	0.322068i	0.0130814	+	0.0315813i
$105$	−0.382135	+	0.199663i	−0.0372925	+	0.0194851i
$106$	−5.95315	+	5.95315i	−0.578221	+	0.578221i
$107$	0.756986	+	1.13291i	0.0731806	+	0.109522i	0.866255	−	0.499603i	$-0.166521\pi$
$107$	0.756986	+	1.13291i	0.0731806	+	0.109522i	−0.793074	+	0.609125i	$0.791521\pi$
$108$	−1.11856	+	0.866406i	−0.107633	+	0.0833699i
$109$	9.54382	+	6.37698i	0.914132	+	0.610804i	0.921165	−	0.389171i	$-0.127239\pi$
$109$	9.54382	+	6.37698i	0.914132	+	0.610804i	−0.00703284	+	0.999975i	$0.502239\pi$
$110$	−0.622254	−	0.257746i	−0.0593296	−	0.0245751i
$111$	0.618977	−	0.181434i	0.0587507	−	0.0172209i
$112$	3.32347	−	4.97393i	0.314039	−	0.469992i
$113$	2.64375	+	13.2910i	0.248703	+	1.25031i	0.880076	+	0.474834i	$0.157492\pi$
$113$	2.64375	+	13.2910i	0.248703	+	1.25031i	−0.631373	+	0.775479i	$0.717508\pi$
$114$	−4.57421	+	14.5846i	−0.428414	+	1.36597i
$115$	−0.624752	−	0.624752i	−0.0582584	−	0.0582584i
$116$	0.209101	−	1.05122i	0.0194146	−	0.0976035i
$117$	0.344645	−	0.0618477i	0.0318624	−	0.00571782i
$118$		−	12.5703i		−	1.15719i
$119$	−2.39847	+	6.88893i	−0.219867	+	0.631507i
$120$	−0.566968	+	0.456454i	−0.0517569	+	0.0416684i
$121$	−2.09064	+	0.865970i	−0.190058	+	0.0787246i
$122$	5.12316	+	1.01906i	0.463829	+	0.0922614i
$123$	−7.57276	−	0.817741i	−0.682813	−	0.0737332i
$124$	2.02717	−	1.35451i	0.182045	−	0.121639i
$125$	−1.37724	+	0.273951i	−0.123184	+	0.0245029i
$126$	−4.83950	−	5.02483i	−0.431137	−	0.447647i
$127$	3.78439	−	9.13631i	0.335810	−	0.810717i	−0.662299	−	0.749240i	$-0.730419\pi$
$127$	3.78439	−	9.13631i	0.335810	−	0.810717i	0.998109	−	0.0614768i	$-0.0195810\pi$
$128$	3.24229	−	7.82759i	0.286581	−	0.691867i
$129$	0.323847	+	3.63808i	0.0285131	+	0.320315i
$130$	0.0211709	−	0.00421116i	0.00185681	−	0.000369343i
$131$	−10.8334	+	7.23868i	−0.946523	+	0.632446i	−0.930056	−	0.367418i	$-0.880242\pi$
$131$	−10.8334	+	7.23868i	−0.946523	+	0.632446i	−0.0164667	+	0.999864i	$0.505242\pi$
$132$	−0.184398	+	1.70763i	−0.0160497	+	0.148630i
$133$	11.6498	+	2.31728i	1.01016	+	0.200934i
$134$	7.06574	−	2.92672i	0.610387	−	0.252830i
$135$	0.326337	+	0.654231i	0.0280866	+	0.0563073i
$136$	−1.70242	+	12.1965i	−0.145982	+	1.04584i
$137$			3.20492i			0.273815i	0.990584	+	0.136907i	$0.0437163\pi$
$137$			3.20492i			0.273815i	−0.990584	+	0.136907i	$0.956284\pi$
$138$	6.85731	−	12.5443i	0.583733	−	1.06784i
$139$	0.993879	−	4.99657i	0.0842997	−	0.423803i	−0.915471	−	0.402384i	$-0.868182\pi$
$139$	0.993879	−	4.99657i	0.0842997	−	0.423803i	0.999771	−	0.0214191i	$-0.00681842\pi$
$140$	0.0479277	+	0.0479277i	0.00405063	+	0.00405063i
$141$	−4.93485	−	1.54773i	−0.415589	−	0.130343i
$142$	3.33255	+	16.7539i	0.279661	+	1.40595i
$143$	0.236152	−	0.353426i	0.0197480	−	0.0295550i
$144$	−8.32694	−	5.79306i	−0.693912	−	0.482755i
$145$	−0.511685	−	0.211947i	−0.0424931	−	0.0176012i
$146$	4.88265	+	3.26248i	0.404091	+	0.270005i
$147$	4.30084	−	5.14134i	0.354727	−	0.424051i
$148$	−0.0563356	−	0.0843122i	−0.00463076	−	0.00693042i
$149$	15.7137	−	15.7137i	1.28731	−	1.28731i	0.350902	−	0.936412i	$-0.385875\pi$
$149$	15.7137	−	15.7137i	1.28731	−	1.28731i	0.936412	−	0.350902i	$-0.114125\pi$
$150$	−5.25062	−	10.0491i	−0.428711	−	0.820509i
$151$	−1.57857	−	3.81101i	−0.128462	−	0.310135i	0.846542	−	0.532322i	$-0.178681\pi$
$151$	−1.57857	−	3.81101i	−0.128462	−	0.310135i	−0.975004	+	0.222187i	$0.928681\pi$
$152$	20.0526			1.62648
$153$	11.6031	+	4.28580i	0.938055	+	0.346486i
$154$	−8.46890			−0.682443
$155$	−0.482114	−	1.16393i	−0.0387243	−	0.0934887i
$156$	−0.0254913	−	0.0487877i	−0.00204094	−	0.00390614i
$157$	−9.87094	+	9.87094i	−0.787787	+	0.787787i	−0.981131	−	0.193344i	$-0.938067\pi$
$157$	−9.87094	+	9.87094i	−0.787787	+	0.787787i	0.193344	+	0.981131i	$0.438067\pi$
$158$	−1.78615	−	2.67316i	−0.142098	−	0.212665i
$159$	7.11818	−	8.50927i	0.564508	−	0.674829i
$160$	0.178884	+	0.119526i	0.0141420	+	0.00944940i
$161$	−10.2639	−	4.25145i	−0.808909	−	0.335061i
$162$	−8.67325	+	8.04483i	−0.681435	+	0.632061i
$163$	6.19697	−	9.27442i	0.485384	−	0.726429i	−0.505250	−	0.862973i	$-0.668600\pi$
$163$	6.19697	−	9.27442i	0.485384	−	0.726429i	0.990634	+	0.136544i	$0.0435996\pi$
$164$	0.233603	+	1.17440i	0.0182413	+	0.0917053i
$165$	0.846845	+	0.265599i	0.0659268	+	0.0206769i
$166$	5.14893	+	5.14893i	0.399634	+	0.399634i
$167$	0.409682	−	2.05961i	0.0317021	−	0.159377i	−0.961692	−	0.274134i	$-0.911609\pi$
$167$	0.409682	−	2.05961i	0.0317021	−	0.159377i	0.993394	+	0.114757i	$0.0366088\pi$
$168$	−4.39001	+	8.03076i	−0.338697	+	0.619587i
$169$		−	12.9864i		−	0.998952i
$170$	0.720133	+	0.250723i	0.0552317	+	0.0192296i
$171$	4.29981	−	19.6772i	0.328815	−	1.50475i
$172$	0.530484	−	0.219734i	0.0404490	−	0.0167545i
$173$	12.0778	+	2.40243i	0.918260	+	0.182653i	0.631524	−	0.775356i	$-0.282430\pi$
$173$	12.0778	+	2.40243i	0.918260	+	0.182653i	0.286736	+	0.958010i	$0.407430\pi$
$174$	0.962121	−	8.90980i	0.0729382	−	0.675450i
$175$	−7.32598	+	4.89506i	−0.553792	+	0.370032i
$176$	−12.0774	+	2.40235i	−0.910369	+	0.181084i
$177$	1.46867	+	16.4990i	0.110392	+	1.24014i
$178$	−2.06124	+	4.97628i	−0.154497	+	0.372988i
$179$	−7.07462	+	17.0796i	−0.528782	+	1.27659i	0.403540	+	0.914962i	$0.367780\pi$
$179$	−7.07462	+	17.0796i	−0.528782	+	1.27659i	−0.932322	+	0.361630i	$0.882220\pi$
$180$	0.0827833	−	0.0797299i	0.00617030	−	0.00594272i
$181$	−2.08780	+	0.415290i	−0.155185	+	0.0308683i	−0.272071	−	0.962277i	$-0.587709\pi$
$181$	−2.08780	+	0.415290i	−0.155185	+	0.0308683i	0.116886	+	0.993145i	$0.462709\pi$
$182$	0.225677	−	0.150792i	0.0167283	−	0.0111775i
$183$	−6.84340	−	0.738981i	−0.505879	−	0.0546271i
$184$	−18.3949	−	3.65898i	−1.35609	−	0.269743i
$185$	−0.0484090	+	0.0200517i	−0.00355910	+	0.00147423i
$186$	15.8785	−	12.7834i	1.16427	−	0.937328i
$187$	13.5184	−	6.53616i	0.988565	−	0.477972i
$188$			0.813051i			0.0592979i
$189$	6.93910	+	6.02984i	0.504745	+	0.438606i
$190$	0.242237	−	1.21781i	0.0175737	−	0.0883490i
$191$	−12.2604	−	12.2604i	−0.887130	−	0.887130i	0.107116	−	0.994247i	$-0.465838\pi$
$191$	−12.2604	−	12.2604i	−0.887130	−	0.887130i	−0.994247	+	0.107116i	$0.965838\pi$
$192$	−4.54703	+	14.4979i	−0.328154	+	1.04630i
$193$	3.16756	+	15.9244i	0.228006	+	1.14626i	0.909904	+	0.414818i	$0.136155\pi$
$193$	3.16756	+	15.9244i	0.228006	+	1.14626i	−0.681898	+	0.731447i	$0.738845\pi$
$194$	−3.34980	+	5.01333i	−0.240501	+	0.359936i
$195$	−0.0272956	+	0.00800084i	−0.00195468	+	0.000572952i
$196$	−0.973548	−	0.403257i	−0.0695391	−	0.0288040i
$197$	6.52782	+	4.36175i	0.465088	+	0.310762i	0.765944	−	0.642908i	$-0.222272\pi$
$197$	6.52782	+	4.36175i	0.465088	+	0.310762i	−0.300855	+	0.953670i	$0.597272\pi$
$198$	−0.269763	+	14.3582i	−0.0191712	+	1.02039i
$199$	7.11102	+	10.6424i	0.504087	+	0.754419i	0.993026	−	0.117899i	$-0.0376159\pi$
$199$	7.11102	+	10.6424i	0.504087	+	0.754419i	−0.488939	+	0.872318i	$0.662616\pi$
$200$	−10.5180	+	10.5180i	−0.743732	+	0.743732i
$201$	−8.93209	+	4.66697i	−0.630021	+	0.329183i
$202$	−2.54889	−	6.15356i	−0.179339	−	0.432963i
$203$	−6.96405			−0.488780
$204$	0.0970031	−	1.94212i	0.00679158	−	0.135975i
$205$	0.618741			0.0432147
$206$	8.03605	+	19.4007i	0.559898	+	1.35171i
$207$	−7.53484	+	17.2660i	−0.523708	+	1.20007i
$208$	0.279061	−	0.279061i	0.0193494	−	0.0193494i
$209$	−13.5840	−	20.3300i	−0.939628	−	1.40625i
$210$	0.434682	+	0.363620i	0.0299959	+	0.0250922i
$211$	−4.25722	−	2.84458i	−0.293079	−	0.195829i	0.400334	−	0.916369i	$-0.368894\pi$
$211$	−4.25722	−	2.84458i	−0.293079	−	0.195829i	−0.693413	+	0.720540i	$0.743894\pi$
$212$	−1.61129	−	0.667417i	−0.110664	−	0.0458384i
$213$	−6.33155	−	21.6007i	−0.433831	−	1.48005i
$214$	0.995000	−	1.48912i	0.0680168	−	0.101794i
$215$	−0.0578841	−	0.291003i	−0.00394766	−	0.0198462i
$216$	13.4755	+	7.69863i	0.916893	+	0.523825i
$217$	−11.2013	−	11.2013i	−0.760395	−	0.760395i
$218$	2.94339	−	14.7974i	0.199351	−	1.00221i
$219$	−6.78984	−	3.71166i	−0.458815	−	0.250810i
$220$		−	0.139524i		−	0.00940669i
$221$	−0.243856	+	0.414875i	−0.0164035	+	0.0279075i
$222$	−0.531678	−	0.660405i	−0.0356839	−	0.0443235i
$223$	0.174491	−	0.0722764i	0.0116848	−	0.00483999i	−0.376833	−	0.926281i	$-0.622987\pi$
$223$	0.174491	−	0.0722764i	0.0116848	−	0.00483999i	0.388518	+	0.921441i	$0.372987\pi$
$224$	2.65322	+	0.527759i	0.177276	+	0.0352624i
$225$	8.06574	+	12.5764i	0.537716	+	0.838426i
$226$	14.8104	−	9.89597i	0.985171	−	0.658270i
$227$	−2.08928	+	0.415583i	−0.138670	+	0.0275832i	−0.263937	−	0.964540i	$-0.585021\pi$
$227$	−2.08928	+	0.415583i	−0.138670	+	0.0275832i	0.125267	+	0.992123i	$0.460021\pi$
$228$	−3.15391	+	0.280748i	−0.208873	+	0.0185930i
$229$	6.61427	−	15.9683i	0.437084	−	1.05521i	−0.539868	−	0.841750i	$-0.681526\pi$
$229$	6.61427	−	15.9683i	0.437084	−	1.05521i	0.976951	−	0.213463i	$-0.0684743\pi$
$230$	−0.444424	+	1.07293i	−0.0293045	+	0.0707472i
$231$	11.1157	−	0.989476i	0.731362	−	0.0651028i
$232$	−11.5309	+	2.29363i	−0.757039	+	0.150584i
$233$	8.14185	−	5.44021i	0.533390	−	0.356400i	−0.259521	−	0.965738i	$-0.583565\pi$
$233$	8.14185	−	5.44021i	0.533390	−	0.356400i	0.792911	+	0.609337i	$0.208565\pi$
$234$	−0.248465	−	0.387416i	−0.0162427	−	0.0253262i
$235$	0.412058	+	0.0819634i	0.0268797	+	0.00534670i
$236$	2.40579	−	0.996510i	0.156603	−	0.0648673i
$237$	2.65671	+	3.29993i	0.172572	+	0.214354i
$238$	9.57216	−	0.552563i	0.620471	−	0.0358173i
$239$		−	22.4367i		−	1.45131i	−0.688059	−	0.725654i	$-0.741537\pi$
$239$		−	22.4367i		−	1.45131i	0.688059	−	0.725654i	$-0.258463\pi$
$240$	0.723043	+	0.395251i	0.0466722	+	0.0255133i
$241$	0.0791082	−	0.397704i	0.00509581	−	0.0256184i	−0.978154	−	0.207883i	$-0.933343\pi$
$241$	0.0791082	−	0.397704i	0.00509581	−	0.0256184i	0.983250	+	0.182265i	$0.0583427\pi$
$242$	2.10322	+	2.10322i	0.135200	+	0.135200i
$243$	10.4440	−	11.5725i	0.669985	−	0.742375i
$244$	0.211104	+	1.06129i	0.0135145	+	0.0679421i
$245$	−0.302515	+	0.452746i	−0.0193270	+	0.0289249i
$246$	2.81612	+	9.60746i	0.179549	+	0.612549i
$247$	0.723968	+	0.299877i	0.0460650	+	0.0190807i
$248$	−22.2360	−	14.8577i	−1.41199	−	0.943462i
$249$	−7.35974	−	6.15657i	−0.466404	−	0.390157i
$250$	1.02544	+	1.53468i	0.0648547	+	0.0970619i
$251$	0.749951	−	0.749951i	0.0473365	−	0.0473365i	−0.683042	−	0.730379i	$-0.739344\pi$
$251$	0.749951	−	0.749951i	0.0473365	−	0.0473365i	0.730379	+	0.683042i	$0.239344\pi$
$252$	0.578034	−	1.32456i	0.0364127	−	0.0834392i
$253$	8.75152	+	21.1280i	0.550203	+	1.32831i
$254$	−12.9984			−0.815594
$255$	−0.974494	−	0.244946i	−0.0610252	−	0.0153391i
$256$	6.40833			0.400521
$257$	7.70425	+	18.5997i	0.480578	+	1.16022i	0.959335	+	0.282270i	$0.0910874\pi$
$257$	7.70425	+	18.5997i	0.480578	+	1.16022i	−0.478757	+	0.877947i	$0.658913\pi$
$258$	4.25508	−	2.22326i	0.264910	−	0.138414i
$259$	−0.465876	+	0.465876i	−0.0289481	+	0.0289481i
$260$	0.00248428	+	0.00371799i	0.000154069	+	0.000230580i
$261$	−0.221828	+	11.8068i	−0.0137308	+	0.730826i
$262$	14.2397	+	9.51469i	0.879734	+	0.587820i
$263$	−5.10116	−	2.11297i	−0.314551	−	0.130291i	0.219822	−	0.975540i	$-0.429452\pi$
$263$	−5.10116	−	2.11297i	−0.314551	−	0.130291i	−0.534373	+	0.845249i	$0.679452\pi$
$264$	18.0792	−	5.29936i	1.11270	−	0.326153i
$265$	−0.500683	+	0.749325i	−0.0307567	+	0.0460307i
$266$	−3.04589	−	15.3127i	−0.186756	−	0.938884i
$267$	2.12404	−	6.77237i	0.129989	−	0.414462i
$268$	1.12027	+	1.12027i	0.0684314	+	0.0684314i
$269$	−1.78305	+	8.96401i	−0.108715	+	0.546545i	0.887588	+	0.460637i	$0.152379\pi$
$269$	−1.78305	+	8.96401i	−0.108715	+	0.546545i	−0.996303	+	0.0859079i	$0.972621\pi$
$270$	0.630328	−	0.725377i	0.0383605	−	0.0441451i
$271$		−	2.64822i		−	0.160868i	−0.996760	−	0.0804339i	$-0.974369\pi$
$271$		−	2.64822i		−	0.160868i	0.996760	−	0.0804339i	$-0.0256306\pi$
$272$	13.4940	−	3.50331i	0.818195	−	0.212419i
$273$	−0.278591	+	0.224288i	−0.0168611	+	0.0135745i
$274$	3.89196	−	1.61210i	0.235122	−	0.0973906i
$275$	17.7885	+	3.53836i	1.07269	+	0.213371i
$276$	2.94442	+	0.317951i	0.177233	+	0.0191384i
$277$	−17.2028	+	11.4945i	−1.03362	+	0.690640i	−0.952023	−	0.306026i	$-0.901001\pi$
$277$	−17.2028	+	11.4945i	−1.03362	+	0.690640i	−0.0815922	+	0.996666i	$0.526001\pi$
$278$	−6.56761	+	1.30638i	−0.393899	+	0.0783514i
$279$	−19.3475	+	18.6339i	−1.15831	+	1.11558i
$280$	0.284517	−	0.686886i	0.0170032	−	0.0410493i
$281$	−3.93729	+	9.50546i	−0.234879	+	0.567048i	−0.996739	−	0.0806938i	$-0.974286\pi$
$281$	−3.93729	+	9.50546i	−0.234879	+	0.567048i	0.761860	+	0.647742i	$0.224286\pi$
$282$	0.602748	+	6.77125i	0.0358931	+	0.403222i
$283$	12.5960	−	2.50549i	0.748753	−	0.148936i	0.194058	−	0.980990i	$-0.437835\pi$
$283$	12.5960	−	2.50549i	0.748753	−	0.148936i	0.554695	+	0.832054i	$0.312835\pi$
$284$	−2.94227	+	1.96596i	−0.174592	+	0.116659i
$285$	−0.175660	+	1.62672i	−0.0104052	+	0.0963584i
$286$	−0.547976	−	0.108999i	−0.0324025	−	0.00644525i
$287$	7.18785	−	2.97730i	0.424285	−	0.175745i
$288$	0.979277	−	4.48146i	0.0577044	−	0.264073i
$289$	−14.8530	+	8.26967i	−0.873708	+	0.486451i
$290$			0.727985i			0.0427488i
$291$	3.81099	−	6.97155i	0.223404	−	0.408680i
$292$	−0.237324	+	1.19311i	−0.0138883	+	0.0698213i
$293$	0.797696	+	0.797696i	0.0466019	+	0.0466019i	0.730024	−	0.683422i	$-0.239509\pi$
$293$	0.797696	+	0.797696i	0.0466019	+	0.0466019i	−0.683422	+	0.730024i	$0.739509\pi$
$294$	−8.40685	−	2.63667i	−0.490297	−	0.153774i
$295$	−0.262509	−	1.31972i	−0.0152839	−	0.0768372i
$296$	−0.617947	+	0.924822i	−0.0359174	+	0.0537542i
$297$	−1.32348	−	18.8771i	−0.0767964	−	1.09536i
$298$	−26.9863	−	11.1781i	−1.56327	−	0.647530i
$299$	−0.609402	−	0.407189i	−0.0352426	−	0.0235484i
$300$	1.50703	−	1.80154i	0.0870082	−	0.104012i
$301$	−2.07270	−	3.10202i	−0.119469	−	0.178797i
$302$	−3.83394	+	3.83394i	−0.220618	+	0.220618i
$303$	4.06447	+	7.77896i	0.233497	+	0.446890i
$304$	−8.68744	−	20.9733i	−0.498259	−	1.20290i
$305$	0.559148			0.0320167
$306$	−0.631910	−	16.2462i	−0.0361239	−	0.928736i
$307$	−19.5814			−1.11757			−0.558785	−	0.829312i	$-0.688732\pi$
$307$	−19.5814			−1.11757			−0.558785	+	0.829312i	$0.688732\pi$
$308$	−0.671371	−	1.62083i	−0.0382549	−	0.0923555i
$309$	−12.8143	−	24.5253i	−0.728981	−	1.39519i
$310$	−1.17093	+	1.17093i	−0.0665042	+	0.0665042i
$311$	16.3199	+	24.4244i	0.925415	+	1.38498i	0.922923	+	0.384985i	$0.125793\pi$
$311$	16.3199	+	24.4244i	0.925415	+	1.38498i	0.00249223	+	0.999997i	$0.499207\pi$
$312$	−0.387413	+	0.463125i	−0.0219330	+	0.0262193i
$313$	−14.8171	−	9.90044i	−0.837509	−	0.559606i	0.0612125	−	0.998125i	$-0.480503\pi$
$313$	−14.8171	−	9.90044i	−0.837509	−	0.559606i	−0.898722	+	0.438519i	$0.855503\pi$
$314$	16.9521	+	7.02180i	0.956664	+	0.396263i
$315$	−0.613020	−	0.426478i	−0.0345398	−	0.0240293i
$316$	0.370010	−	0.553759i	0.0208147	−	0.0311514i
$317$	−2.75488	−	13.8497i	−0.154729	−	0.777877i	−0.977735	−	0.209844i	$-0.932704\pi$
$317$	−2.75488	−	13.8497i	−0.154729	−	0.777877i	0.823006	−	0.568033i	$-0.192296\pi$
$318$	−13.9139	−	4.36387i	−0.780253	−	0.244713i
$319$	10.1366	+	10.1366i	0.567542	+	0.567542i
$320$	0.240798	−	1.21057i	0.0134610	−	0.0676730i
$321$	−1.13199	+	2.07078i	−0.0631815	+	0.115580i
$322$			14.6027i			0.813775i
$323$	16.6801	+	22.0921i	0.928107	+	1.22924i
$324$	−2.22724	−	1.02219i	−0.123736	−	0.0567883i
$325$	−0.537026	+	0.222443i	−0.0297888	+	0.0123389i
$326$	−14.3797	−	2.86030i	−0.796418	−	0.158417i
$327$	−2.13442	+	19.7660i	−0.118034	+	1.09306i
$328$	10.9209	−	7.29708i	0.603003	−	0.402914i
$329$	5.18123	−	1.03061i	0.285651	−	0.0568194i
$330$	−0.103435	−	1.16198i	−0.00569389	−	0.0639649i
$331$	−2.76796	+	6.68245i	−0.152141	+	0.367301i	−0.981513	−	0.191396i	$-0.938698\pi$
$331$	−2.76796	+	6.68245i	−0.152141	+	0.367301i	0.829372	+	0.558697i	$0.188698\pi$
$332$	−0.577254	+	1.39362i	−0.0316810	+	0.0764846i
$333$	0.775006	+	0.804686i	0.0424701	+	0.0440965i
$334$	−2.70720	+	0.538496i	−0.148131	+	0.0294652i
$335$	0.680692	−	0.454824i	0.0371902	−	0.0248497i
$336$	10.3014	+	1.11239i	0.561988	+	0.0606860i
$337$	13.1112	+	2.60797i	0.714210	+	0.142065i	0.538804	−	0.842431i	$-0.318876\pi$
$337$	13.1112	+	2.60797i	0.714210	+	0.142065i	0.175406	+	0.984496i	$0.443876\pi$
$338$	−15.7703	+	6.53226i	−0.857789	+	0.355308i
$339$	−18.2829	+	14.7192i	−0.992993	+	0.799438i
$340$	0.00910339	+	0.157700i	0.000493701	+	0.00855247i
$341$			32.6085i			1.76585i
$342$	−26.0582	+	4.67625i	−1.40907	+	0.252862i
$343$	−3.75178	+	18.8615i	−0.202577	+	1.01842i
$344$	−4.45359	−	4.45359i	−0.240121	−	0.240121i
$345$	0.457965	−	1.46019i	0.0246560	−	0.0786140i
$346$	−3.15781	−	15.8754i	−0.169765	−	0.853466i
$347$	18.5966	−	27.8318i	0.998320	−	1.49409i	0.134106	−	0.990967i	$-0.457184\pi$
$347$	18.5966	−	27.8318i	0.998320	−	1.49409i	0.864214	−	0.503124i	$-0.167816\pi$
$348$	1.78149	−	0.522186i	0.0954977	−	0.0279921i
$349$	25.7122	+	10.6503i	1.37634	+	0.570099i	0.943500	−	0.331372i	$-0.107511\pi$
$349$	25.7122	+	10.6503i	1.37634	+	0.570099i	0.432840	+	0.901471i	$0.357511\pi$
$350$	9.62945	+	6.43419i	0.514715	+	0.343922i
$351$	0.371384	+	0.479468i	0.0198230	+	0.0255921i
$352$	−3.09375	−	4.63013i	−0.164898	−	0.246787i
$353$	5.10785	−	5.10785i	0.271864	−	0.271864i	−0.557986	−	0.829850i	$-0.688426\pi$
$353$	5.10785	−	5.10785i	0.271864	−	0.271864i	0.829850	+	0.557986i	$0.188426\pi$
$354$	19.2971	−	10.0826i	1.02563	−	0.535886i
$355$	0.699750	+	1.68935i	0.0371389	+	0.0896611i
$356$	−1.11580			−0.0591371
$357$	−12.4992	+	1.84364i	−0.661530	+	0.0975756i
$358$	24.2996			1.28427
$359$	−10.5450	−	25.4579i	−0.556544	−	1.34362i	−0.912486	−	0.409108i	$-0.865840\pi$
$359$	−10.5450	−	25.4579i	−0.556544	−	1.34362i	0.355942	−	0.934508i	$-0.384160\pi$
$360$	−1.15548	−	0.504251i	−0.0608993	−	0.0265763i
$361$	18.4383	−	18.4383i	0.970437	−	0.970437i
$362$	1.55450	+	2.32647i	0.0817026	+	0.122277i
$363$	−3.00628	−	2.51481i	−0.157789	−	0.131994i
$364$	0.0467501	+	0.0312374i	0.00245037	+	0.00163729i
$365$	0.580747	+	0.240553i	0.0303977	+	0.0125911i
$366$	2.54489	+	8.68213i	0.133024	+	0.453822i
$367$	−6.24111	+	9.34048i	−0.325783	+	0.487569i	−0.957820	−	0.287370i	$-0.907219\pi$
$367$	−6.24111	+	9.34048i	−0.325783	+	0.487569i	0.632037	+	0.774939i	$0.282219\pi$
$368$	4.14230	+	20.8247i	0.215932	+	1.08556i
$369$	−4.81876	−	12.2811i	−0.250855	−	0.639329i
$370$	0.0487002	+	0.0487002i	0.00253180	+	0.00253180i
$371$	−2.21072	+	11.1141i	−0.114775	+	0.577013i
$372$	3.70534	+	2.02552i	0.192113	+	0.105018i
$373$		−	5.50325i		−	0.284948i	−0.989799	−	0.142474i	$-0.954494\pi$
$373$		−	5.50325i		−	0.284948i	0.989799	−	0.142474i	$-0.0455057\pi$
$374$	−14.7372	−	13.1286i	−0.762042	−	0.678864i
$375$	−1.52524	−	1.89452i	−0.0787630	−	0.0978326i
$376$	8.23951	−	3.41292i	0.424920	−	0.176008i
$377$	−0.450605	−	0.0896309i	−0.0232073	−	0.00461623i
$378$	3.83203	−	11.4597i	0.197098	−	0.589423i
$379$	−4.37931	+	2.92616i	−0.224950	+	0.150307i	−0.662939	−	0.748674i	$-0.730691\pi$
$379$	−4.37931	+	2.92616i	−0.224950	+	0.150307i	0.437989	+	0.898981i	$0.355691\pi$
$380$	0.252275	−	0.0501806i	0.0129414	−	0.00257421i
$381$	17.0609	−	1.51869i	0.874057	−	0.0778049i
$382$	−8.72156	+	21.0557i	−0.446234	+	1.07730i
$383$	8.09691	−	19.5477i	0.413733	−	0.998840i	−0.570394	−	0.821372i	$-0.693209\pi$
$383$	8.09691	−	19.5477i	0.413733	−	0.998840i	0.984127	−	0.177468i	$-0.0567907\pi$
$384$	14.6170	−	1.30115i	0.745922	−	0.0663989i
$385$	−0.889126	+	0.176858i	−0.0453140	+	0.00901352i
$386$	17.7448	−	11.8567i	0.903188	−	0.603491i
$387$	−5.32519	+	3.41525i	−0.270694	+	0.173607i
$388$	−1.22504	−	0.243675i	−0.0621919	−	0.0123707i
$389$	11.5459	−	4.78245i	0.585398	−	0.242480i	−0.0702713	−	0.997528i	$-0.522387\pi$
$389$	11.5459	−	4.78245i	0.585398	−	0.242480i	0.655669	+	0.755048i	$0.272387\pi$
$390$	0.0234459	+	0.0291224i	0.00118723	+	0.00147467i
$391$	−11.2701	−	23.3094i	−0.569954	−	1.17881i
$392$			11.5587i			0.583804i
$393$	−19.8018	−	10.8247i	−0.998871	−	0.546032i
$394$	2.01323	−	10.1212i	0.101425	−	0.509898i
$395$	−0.243347	−	0.243347i	−0.0122441	−	0.0122441i
$396$	−2.76934	+	1.08661i	−0.139165	+	0.0546044i
$397$	−7.58893	−	38.1521i	−0.380877	−	1.91480i	−0.403334	−	0.915053i	$-0.632149\pi$
$397$	−7.58893	−	38.1521i	−0.380877	−	1.91480i	0.0224569	−	0.999748i	$-0.492851\pi$
$398$	9.34689	−	13.9886i	0.468517	−	0.701186i
$399$	5.78693	+	19.7427i	0.289709	+	0.988369i
$400$	15.5576	+	6.44418i	0.777881	+	0.322209i
$401$	−22.6390	−	15.1269i	−1.13054	−	0.755401i	−0.157837	−	0.987465i	$-0.550452\pi$
$401$	−22.6390	−	15.1269i	−1.13054	−	0.755401i	−0.972701	+	0.232064i	$0.925452\pi$
$402$	10.1603	+	8.49933i	0.506752	+	0.423908i
$403$	−0.580609	−	0.868943i	−0.0289222	−	0.0432851i
$404$	0.975645	−	0.975645i	0.0485401	−	0.0485401i
$405$	−0.742578	+	1.02573i	−0.0368990	+	0.0509689i
$406$	3.50297	+	8.45693i	0.173850	+	0.419710i
$407$	1.35623			0.0672256
$408$	−20.0887	+	7.16932i	−0.994539	+	0.354934i
$409$	28.2231			1.39554			0.697770	−	0.716322i	$-0.254176\pi$
$409$	28.2231			1.39554			0.697770	+	0.716322i	$0.254176\pi$
$410$	−0.311232	−	0.751380i	−0.0153706	−	0.0371080i
$411$	−4.91998	+	2.57066i	−0.242685	+	0.126801i
$412$	−3.07598	+	3.07598i	−0.151543	+	0.151543i
$413$	−9.39988	−	14.0679i	−0.462538	−	0.692237i
$414$	24.7574	+	0.465145i	1.21676	+	0.0228606i
$415$	0.648098	+	0.433045i	0.0318139	+	0.0212573i
$416$	0.164883	+	0.0682967i	0.00808405	+	0.00334852i
$417$	8.46759	−	2.48201i	0.414660	−	0.121544i
$418$	−17.8552	+	26.7222i	−0.873326	+	1.30703i
$419$	1.82223	+	9.16095i	0.0890216	+	0.447542i	0.999428	+	0.0338260i	$0.0107692\pi$
$419$	1.82223	+	9.16095i	0.0890216	+	0.447542i	−0.910406	+	0.413716i	$0.864231\pi$
$420$	−0.0351327	+	0.112018i	−0.00171430	+	0.00546593i
$421$	−9.40617	−	9.40617i	−0.458429	−	0.458429i	0.439711	−	0.898139i	$-0.355081\pi$
$421$	−9.40617	−	9.40617i	−0.458429	−	0.458429i	−0.898139	+	0.439711i	$0.855081\pi$
$422$	−1.31296	+	6.60069i	−0.0639138	+	0.321316i
$423$	−1.58226	−	8.81709i	−0.0769320	−	0.428702i
$424$			19.1305i			0.929057i
$425$	−20.3367	−	2.83867i	−0.986477	−	0.137696i
$426$	−23.0464	+	18.5542i	−1.11660	+	0.898952i
$427$	6.49556	−	2.69055i	0.314342	−	0.130205i
$428$	0.363877	+	0.0723795i	0.0175886	+	0.00349860i
$429$	0.731973	+	0.0790418i	0.0353400	+	0.00381617i
$430$	−0.324269	+	0.216670i	−0.0156376	+	0.0104487i
$431$	14.3298	−	2.85038i	0.690243	−	0.137298i	0.162508	−	0.986707i	$-0.448042\pi$
$431$	14.3298	−	2.85038i	0.690243	−	0.137298i	0.527734	+	0.849409i	$0.323042\pi$
$432$	2.21409	−	17.4296i	0.106525	−	0.838581i
$433$	−6.82738	+	16.4827i	−0.328103	+	0.792110i	0.670631	+	0.741792i	$0.266024\pi$
$433$	−6.82738	+	16.4827i	−0.328103	+	0.792110i	−0.998733	+	0.0503185i	$0.983976\pi$
$434$	−7.96819	+	19.2369i	−0.382485	+	0.923401i
$435$	−0.0850552	−	0.955507i	−0.00407809	−	0.0458131i
$436$	3.06536	−	0.609738i	0.146804	−	0.0292011i
$437$	−35.0544	+	23.4226i	−1.67688	+	1.12045i
$438$	−1.09198	+	10.1124i	−0.0521768	+	0.483187i
$439$	−25.8533	−	5.14255i	−1.23391	−	0.245440i	−0.465299	−	0.885154i	$-0.654053\pi$
$439$	−25.8533	−	5.14255i	−1.23391	−	0.245440i	−0.768614	+	0.639713i	$0.779053\pi$
$440$	−1.41394	+	0.585674i	−0.0674070	+	0.0279209i
$441$	11.3424	+	2.47850i	0.540112	+	0.118024i
$442$	0.626473	+	0.0874454i	0.0297983	+	0.00415935i
$443$			9.67036i			0.459453i	0.973255	+	0.229726i	$0.0737831\pi$
$443$			9.67036i			0.459453i	−0.973255	+	0.229726i	$0.926217\pi$
$444$	0.0842438	−	0.154109i	0.00399803	−	0.00731371i
$445$	−0.112483	+	0.565491i	−0.00533221	+	0.0268068i
$446$	−0.175541	−	0.175541i	−0.00831208	−	0.00831208i
$447$	36.7265	+	11.5187i	1.73710	+	0.544814i
$448$	−3.02780	−	15.2218i	−0.143050	−	0.719161i
$449$	−0.587080	+	0.878627i	−0.0277060	+	0.0414650i	−0.845064	−	0.534665i	$-0.820438\pi$
$449$	−0.587080	+	0.878627i	−0.0277060	+	0.0414650i	0.817358	+	0.576130i	$0.195438\pi$
$450$	11.2153	−	16.1208i	0.528692	−	0.759942i
$451$	−14.7960	−	6.12872i	−0.696718	−	0.288590i
$452$	3.06805	+	2.05000i	0.144309	+	0.0964240i
$453$	4.58424	−	5.48012i	0.215386	−	0.257479i
$454$	1.55560	+	2.32811i	0.0730077	+	0.109264i
$455$	0.0205441	−	0.0205441i	0.000963124	−	0.000963124i
$456$	16.0842	+	30.7834i	0.753210	+	1.44157i
$457$	8.19942	+	19.7952i	0.383553	+	0.925978i	0.991273	+	0.131827i	$0.0420843\pi$
$457$	8.19942	+	19.7952i	0.383553	+	0.925978i	−0.607720	+	0.794151i	$0.707916\pi$
$458$	−22.7184			−1.06156
$459$	2.72756	+	21.2500i	0.127312	+	0.991863i
$460$	−0.240577			−0.0112169
$461$	−9.42954	−	22.7649i	−0.439177	−	1.06027i	−0.976233	−	0.216721i	$-0.930464\pi$
$461$	−9.42954	−	22.7649i	−0.439177	−	1.06027i	0.537056	−	0.843547i	$-0.319536\pi$
$462$	−6.79290	−	13.0009i	−0.316034	−	0.604856i
$463$	13.6466	−	13.6466i	0.634213	−	0.634213i	−0.314909	−	0.949122i	$-0.601974\pi$
$463$	13.6466	−	13.6466i	0.634213	−	0.634213i	0.949122	+	0.314909i	$0.101974\pi$
$464$	7.39451	+	11.0667i	0.343281	+	0.513757i
$465$	1.40008	−	1.67369i	0.0649271	−	0.0776156i
$466$	−10.7018	−	7.15074i	−0.495753	−	0.331252i
$467$	−11.4980	−	4.76264i	−0.532066	−	0.220389i	0.100442	−	0.994943i	$-0.467974\pi$
$467$	−11.4980	−	4.76264i	−0.532066	−	0.220389i	−0.632508	+	0.774554i	$0.717974\pi$
$468$	0.0544491	−	0.0782652i	0.00251691	−	0.00361781i
$469$	5.71897	−	8.55905i	0.264078	−	0.395220i
$470$	−0.107735	−	0.541619i	−0.00496943	−	0.0249830i
$471$	−23.0707	−	7.23574i	−1.06304	−	0.333405i
$472$	−20.1974	−	20.1974i	−0.929660	−	0.929660i
$473$	−1.49824	+	7.53215i	−0.0688890	+	0.346329i
$474$	2.67099	−	4.88612i	0.122683	−	0.224427i
$475$			33.4363i			1.53416i
$476$	0.864585	+	1.78818i	0.0396282	+	0.0819610i
$477$	18.7724	+	4.10208i	0.859527	+	0.187821i
$478$	−27.2464	+	11.2858i	−1.24622	+	0.516202i
$479$	−22.2629	−	4.42837i	−1.01722	−	0.202337i	−0.341801	−	0.939772i	$-0.611037\pi$
$479$	−22.2629	−	4.42837i	−1.01722	−	0.202337i	−0.675418	+	0.737435i	$0.736037\pi$
$480$	−0.0400064	+	0.370483i	−0.00182604	+	0.0169102i
$481$	−0.0361403	+	0.0241482i	−0.00164786	+	0.00110106i
$482$	−0.522751	+	0.103982i	−0.0238107	+	0.00473624i
$483$	−1.70613	−	19.1665i	−0.0776314	−	0.872108i
$484$	−0.235795	+	0.569259i	−0.0107179	+	0.0258754i
$485$	−0.246991	+	0.596290i	−0.0112153	+	0.0270761i
$486$	−19.3067	−	6.86185i	−0.875770	−	0.311260i
$487$	22.5436	−	4.48421i	1.02155	−	0.203199i	0.344228	−	0.938886i	$-0.388141\pi$
$487$	22.5436	−	4.48421i	1.02155	−	0.203199i	0.677322	+	0.735687i	$0.263141\pi$
$488$	9.86902	−	6.59427i	0.446750	−	0.298509i
$489$	19.2081	+	2.07417i	0.868619	+	0.0937974i
$490$	0.701969	+	0.139630i	0.0317117	+	0.00630785i
$491$	18.8224	−	7.79649i	0.849443	−	0.351851i	0.0848732	−	0.996392i	$-0.472951\pi$
$491$	18.8224	−	7.79649i	0.849443	−	0.351851i	0.764570	+	0.644541i	$0.222951\pi$
$492$	−1.61549	+	1.30060i	−0.0728319	+	0.0586355i
$493$	−12.1185	−	10.7958i	−0.545791	−	0.486217i
$494$		−	1.03001i		−	0.0463421i
$495$	0.271524	+	1.51306i	0.0122041	+	0.0680069i
$496$	−5.90648	+	29.6939i	−0.265209	+	1.33329i
$497$	16.2578	+	16.2578i	0.729264	+	0.729264i
$498$	−3.77434	+	12.0342i	−0.169132	+	0.539267i
$499$	−0.210533	−	1.05842i	−0.00942477	−	0.0473815i	0.975787	−	0.218724i	$-0.0701895\pi$
$499$	−0.210533	−	1.05842i	−0.00942477	−	0.0473815i	−0.985211	+	0.171343i	$0.945189\pi$
$500$	−0.212426	+	0.317918i	−0.00949997	+	0.0142177i
$501$	3.49038	−	1.02309i	0.155939	−	0.0457085i
$502$	−1.28795	−	0.533486i	−0.0574840	−	0.0238106i
$503$	7.80319	+	5.21393i	0.347927	+	0.232478i	0.717238	−	0.696829i	$-0.245406\pi$
$503$	7.80319	+	5.21393i	0.347927	+	0.232478i	−0.369311	+	0.929306i	$0.620406\pi$
$504$	−15.8495	−	0.297783i	−0.705994	−	0.0132643i
$505$	−0.396107	−	0.592815i	−0.0176265	−	0.0263799i
$506$	21.2552	−	21.2552i	0.944907	−	0.944907i
$507$	19.9358	−	10.4164i	0.885381	−	0.462607i
$508$	−1.03045	−	2.48772i	−0.0457188	−	0.110375i
$509$	−7.99190			−0.354235			−0.177117	−	0.984190i	$-0.556677\pi$
$509$	−7.99190			−0.354235			−0.177117	+	0.984190i	$0.556677\pi$
$510$	0.192724	+	1.30661i	0.00853397	+	0.0578575i
$511$	7.90399			0.349652
$512$	−9.70803	−	23.4372i	−0.429038	−	1.03579i
$513$	33.6560	−	9.18230i	1.48595	−	0.405408i
$514$	18.7116	−	18.7116i	0.825334	−	0.825334i
$515$	1.24883	+	1.86901i	0.0550301	+	0.0823584i
$516$	0.762822	+	0.638116i	0.0335814	+	0.0280915i
$517$	−9.04174	−	6.04150i	−0.397655	−	0.265705i
$518$	0.800085	+	0.331406i	0.0351537	+	0.0145611i
$519$	5.99957	+	20.4681i	0.263352	+	0.898449i
$520$	0.0272501	−	0.0407827i	0.00119500	−	0.00178844i
$521$	−0.307543	−	1.54613i	−0.0134737	−	0.0677370i	0.973463	−	0.228842i	$-0.0734941\pi$
$521$	−0.307543	−	1.54613i	−0.0134737	−	0.0677370i	−0.986937	+	0.161105i	$0.948494\pi$
$522$	14.4495	−	5.66956i	0.632435	−	0.248150i
$523$	24.2095	+	24.2095i	1.05861	+	1.05861i	0.998172	+	0.0604341i	$0.0192485\pi$
$523$	24.2095	+	24.2095i	1.05861	+	1.05861i	0.0604341	+	0.998172i	$0.480751\pi$
$524$	−0.692129	+	3.47957i	−0.0302358	+	0.152006i
$525$	−13.3907	−	7.32004i	−0.584420	−	0.319473i
$526$			7.25753i			0.316443i
$527$	−2.12758	−	36.8565i	−0.0926789	−	1.60549i
$528$	−13.3752	−	16.6135i	−0.582081	−	0.723011i
$529$	15.1812	−	6.28827i	0.660054	−	0.273403i
$530$	1.16181	+	0.231097i	0.0504656	+	0.0100382i
$531$	−24.1502	+	15.4884i	−1.04803	+	0.672141i
$532$	2.68919	−	1.79686i	0.116591	−	0.0779037i
$533$	0.503405	−	0.100134i	0.0218049	−	0.00433727i
$534$	−9.29257	+	0.827186i	−0.402129	+	0.0357958i
$535$	0.0733645	−	0.177118i	0.00317183	−	0.00765746i
$536$	6.65037	−	16.0554i	0.287252	−	0.693488i
$537$	−31.8941	+	2.83908i	−1.37633	+	0.122515i
$538$	11.7825	−	2.34369i	0.507980	−	0.101043i
$539$	11.7186	−	7.83012i	0.504756	−	0.337267i
$540$	0.188797	+	0.0631321i	0.00812451	+	0.00271677i
$541$	−2.97344	−	0.591454i	−0.127838	−	0.0254286i	0.130756	−	0.991415i	$-0.458259\pi$
$541$	−2.97344	−	0.591454i	−0.127838	−	0.0254286i	−0.258595	+	0.965986i	$0.583259\pi$
$542$	−3.21592	+	1.33208i	−0.138135	+	0.0572176i
$543$	−2.31215	−	2.87196i	−0.0992239	−	0.123247i
$544$	3.79888	+	5.03145i	0.162876	+	0.215722i
$545$		−	1.61500i		−	0.0691792i
$546$	0.412502	+	0.225494i	0.0176535	+	0.00965024i
$547$	0.339058	−	1.70456i	0.0144971	−	0.0728817i	−0.972860	−	0.231396i	$-0.925671\pi$
$547$	0.339058	−	1.70456i	0.0144971	−	0.0728817i	0.987357	+	0.158515i	$0.0506705\pi$
$548$	0.617069	+	0.617069i	0.0263599	+	0.0263599i
$549$	−4.35465	−	11.0983i	−0.185852	−	0.473663i
$550$	−4.65090	−	23.3817i	−0.198315	−	0.996998i
$551$	−14.6825	+	21.9739i	−0.625495	+	0.936119i
$552$	−9.13753	−	31.1735i	−0.388919	−	1.32683i
$553$	−3.99789	−	1.65598i	−0.170008	−	0.0704195i
$554$	22.6118	+	15.1087i	0.960681	+	0.641907i
$555$	−0.0696108	−	0.0582308i	−0.00295481	−	0.00247176i
$556$	−0.770669	−	1.15339i	−0.0326837	−	0.0489146i
$557$	−29.9311	+	29.9311i	−1.26822	+	1.26822i	−0.321217	+	0.947006i	$0.604092\pi$
$557$	−29.9311	+	29.9311i	−1.26822	+	1.26822i	−0.947006	+	0.321217i	$0.895908\pi$
$558$	32.3604	+	14.1220i	1.36993	+	0.597833i
$559$	−0.0941886	−	0.227391i	−0.00398375	−	0.00961763i
$560$	−0.841688			−0.0355678
$561$	20.8770	+	15.5099i	0.881428	+	0.654830i
$562$	13.5236			0.570460
$563$	10.8784	+	26.2627i	0.458468	+	1.10684i	0.969018	+	0.246991i	$0.0794420\pi$
$563$	10.8784	+	26.2627i	0.458468	+	1.10684i	−0.510550	+	0.859848i	$0.670558\pi$
$564$	−1.24814	+	0.652148i	−0.0525563	+	0.0274604i
$565$	1.34824	−	1.34824i	0.0567208	−	0.0567208i
$566$	−9.37847	−	14.0359i	−0.394207	−	0.589972i
$567$	−3.69077	+	15.4890i	−0.154998	+	0.650476i
$568$	32.2739	+	21.5647i	1.35418	+	0.904835i
$569$	19.2820	+	7.98685i	0.808342	+	0.334826i	0.748292	−	0.663369i	$-0.230874\pi$
$569$	19.2820	+	7.98685i	0.808342	+	0.334826i	0.0600499	+	0.998195i	$0.480874\pi$
$570$	2.06379	−	0.604936i	0.0864428	−	0.0253380i
$571$	−3.48855	+	5.22099i	−0.145991	+	0.218492i	−0.897257	−	0.441508i	$-0.854444\pi$
$571$	−3.48855	+	5.22099i	−0.145991	+	0.218492i	0.751266	+	0.660000i	$0.229444\pi$
$572$	−0.0225797	−	0.113516i	−0.000944106	−	0.00474634i
$573$	8.98729	−	28.6554i	0.375449	−	1.19710i
$574$	−7.23109	−	7.23109i	−0.301820	−	0.301820i
$575$	6.10109	−	30.6723i	0.254433	−	1.27912i
$576$	−25.9034	+	4.64846i	−1.07931	+	0.193686i
$577$		−	36.1978i		−	1.50693i	−0.657485	−	0.753467i	$-0.728380\pi$
$577$		−	36.1978i		−	1.50693i	0.657485	−	0.753467i	$-0.271620\pi$
$578$	17.5136	+	13.8774i	0.728471	+	0.577222i
$579$	−21.9054	+	17.6356i	−0.910358	+	0.732911i
$580$	−0.139326	+	0.0577109i	−0.00578522	+	0.00239632i
$581$	9.61264	+	1.91207i	0.398799	+	0.0793261i
$582$	−10.3830	−	1.12120i	−0.430389	−	0.0464754i
$583$	19.3951	−	12.9594i	0.803262	−	0.536723i
$584$	13.0872	−	2.60321i	0.541553	−	0.107722i
$585$	−0.0341761	−	0.0354849i	−0.00141301	−	0.00146712i
$586$	0.567450	−	1.36995i	0.0234412	−	0.0565919i
$587$	−2.98442	+	7.20502i	−0.123180	+	0.297383i	−0.973426	−	0.229003i	$-0.926453\pi$
$587$	−2.98442	+	7.20502i	−0.123180	+	0.297383i	0.850246	+	0.526386i	$0.176453\pi$
$588$	−0.161829	−	1.81798i	−0.00667371	−	0.0749722i
$589$	−58.9600	+	11.7279i	−2.42940	+	0.483238i
$590$	−1.47059	+	0.982614i	−0.0605431	+	0.0404536i
$591$	−1.45991	+	13.5196i	−0.0600528	+	0.556124i
$592$	1.23500	+	0.245657i	0.0507583	+	0.0100964i
$593$	−28.0114	+	11.6027i	−1.15029	+	0.476465i	−0.874630	−	0.484790i	$-0.838896\pi$
$593$	−28.0114	+	11.6027i	−1.15029	+	0.476465i	−0.275659	+	0.961256i	$0.588896\pi$
$594$	−22.2581	+	11.1026i	−0.913261	+	0.455543i
$595$	0.993414	−	0.257910i	0.0407260	−	0.0105733i
$596$		−	6.05095i		−	0.247857i
$597$	−10.6338	+	19.4526i	−0.435211	+	0.796143i
$598$	−0.187944	+	0.944859i	−0.00768561	+	0.0386381i
$599$	17.7610	+	17.7610i	0.725695	+	0.725695i	0.969759	−	0.244064i	$-0.0784808\pi$
$599$	17.7610	+	17.7610i	0.725695	+	0.725695i	−0.244064	+	0.969759i	$0.578481\pi$
$600$	−24.5829	−	7.71003i	−1.00359	−	0.314761i
$601$	5.94298	+	29.8774i	0.242419	+	1.21872i	0.889726	+	0.456494i	$0.150895\pi$
$601$	5.94298	+	29.8774i	0.242419	+	1.21872i	−0.647307	+	0.762229i	$0.724105\pi$
$602$	−2.72441	+	4.07737i	−0.111039	+	0.166181i
$603$	−14.3288	−	9.96858i	−0.583516	−	0.405952i
$604$	−1.03770	−	0.429829i	−0.0422233	−	0.0174895i
$605$	0.264733	+	0.176889i	0.0107629	+	0.00719155i
$606$	7.40207	−	8.84865i	0.300689	−	0.359452i
$607$	12.1073	+	18.1199i	0.491421	+	0.735464i	0.991442	−	0.130550i	$-0.0416742\pi$
$607$	12.1073	+	18.1199i	0.491421	+	0.735464i	−0.500020	+	0.866014i	$0.666674\pi$
$608$	7.25911	−	7.25911i	0.294396	−	0.294396i
$609$	−5.58586	−	10.6907i	−0.226350	−	0.433211i
$610$	−0.281256	−	0.679012i	−0.0113877	−	0.0274924i
$611$	0.348513			0.0140993
$612$	3.05922	−	1.40886i	0.123661	−	0.0569497i
$613$	17.5623			0.709337			0.354668	−	0.934992i	$-0.384594\pi$
$613$	17.5623			0.709337			0.354668	+	0.934992i	$0.384594\pi$
$614$	9.84962	+	23.7791i	0.397498	+	0.959646i
$615$	0.496292	+	0.949850i	0.0200124	+	0.0383017i
$616$	−13.6074	+	13.6074i	−0.548258	+	0.548258i
$617$	13.1285	+	19.6482i	0.528534	+	0.791007i	0.995648	−	0.0931902i	$-0.0297065\pi$
$617$	13.1285	+	19.6482i	0.528534	+	0.791007i	−0.467115	+	0.884197i	$0.654706\pi$
$618$	−23.3370	+	27.8977i	−0.938753	+	1.12221i
$619$	−33.2074	−	22.1885i	−1.33472	−	0.891831i	−0.335973	−	0.941872i	$-0.609065\pi$
$619$	−33.2074	−	22.1885i	−1.33472	−	0.891831i	−0.998747	+	0.0500404i	$0.984065\pi$
$620$	−0.316925	−	0.131275i	−0.0127280	−	0.00527211i
$621$	−32.5493	+	2.28205i	−1.30616	+	0.0915754i
$622$	21.4512	−	32.1040i	0.860116	−	1.28725i
$623$	1.41437	+	7.11050i	0.0566654	+	0.284876i
$624$	0.652230	+	0.204561i	0.0261101	+	0.00818901i
$625$	−17.4680	−	17.4680i	−0.698719	−	0.698719i
$626$	−4.56969	+	22.9734i	−0.182642	+	0.918201i
$627$	20.3135	−	37.1600i	0.811242	−	1.48403i
$628$			3.80106i			0.151679i
$629$	−1.53290	+	0.0884885i	−0.0611209	+	0.00352827i
$630$	−0.209548	+	0.958955i	−0.00834859	+	0.0382057i
$631$	−24.7481	+	10.2510i	−0.985205	+	0.408085i	−0.816351	−	0.577556i	$-0.804007\pi$
$631$	−24.7481	+	10.2510i	−0.985205	+	0.408085i	−0.168854	+	0.985641i	$0.554007\pi$
$632$	−7.16501	−	1.42521i	−0.285009	−	0.0566917i
$633$	0.952104	−	8.81704i	0.0378428	−	0.350446i
$634$	−15.4329	+	10.3120i	−0.612920	+	0.409540i
$635$	−1.36467	+	0.271450i	−0.0541552	+	0.0107721i
$636$	−0.267838	−	3.00888i	−0.0106205	−	0.119310i
$637$	−0.172855	+	0.417310i	−0.00684878	+	0.0165344i
$638$	7.21080	−	17.4084i	0.285478	−	0.689206i
$639$	28.0814	−	27.0457i	1.11088	−	1.06991i
$640$	−1.16919	+	0.232566i	−0.0462162	+	0.00919297i
$641$	35.4034	−	23.6558i	1.39835	−	0.934349i	0.398500	−	0.917168i	$-0.369531\pi$
$641$	35.4034	−	23.6558i	1.39835	−	0.934349i	0.999852	−	0.0171805i	$-0.00546901\pi$
$642$	3.08409	+	0.333034i	0.121719	+	0.0131438i
$643$	−25.2906	−	5.03062i	−0.997365	−	0.198388i	−0.330692	−	0.943739i	$-0.607282\pi$
$643$	−25.2906	−	5.03062i	−0.997365	−	0.198388i	−0.666673	+	0.745351i	$0.732282\pi$
$644$	−2.79475	+	1.15763i	−0.110129	+	0.0456168i
$645$	0.400300	−	0.322273i	0.0157618	−	0.0126895i
$646$	18.4377	−	31.3683i	0.725422	−	1.23417i
$647$		−	38.1903i		−	1.50142i	−0.660634	−	0.750709i	$-0.729712\pi$
$647$		−	38.1903i		−	1.50142i	0.660634	−	0.750709i	$-0.270288\pi$
$648$	−1.00972	+	26.8618i	−0.0396656	+	1.05523i
$649$	−6.79463	+	34.1589i	−0.266712	+	1.34085i
$650$	0.540257	+	0.540257i	0.0211906	+	0.0211906i
$651$	8.21096	−	26.1801i	0.321813	−	1.02608i
$652$	−0.592526	−	2.97883i	−0.0232051	−	0.116660i
$653$	−19.0588	+	28.5236i	−0.745830	+	1.11621i	0.243412	+	0.969923i	$0.421733\pi$
$653$	−19.0588	+	28.5236i	−0.745830	+	1.11621i	−0.989242	+	0.146290i	$0.953267\pi$
$654$	25.0769	−	7.35049i	0.980584	−	0.287427i
$655$	1.69369	+	0.701548i	0.0661778	+	0.0274118i
$656$	−12.3634	−	8.26097i	−0.482710	−	0.322537i
$657$	0.251769	−	13.4004i	0.00982243	−	0.522800i
$658$	−3.85774	−	5.77352i	−0.150391	−	0.225075i
$659$	−24.7106	+	24.7106i	−0.962589	+	0.962589i	−0.999325	−	0.0367361i	$-0.988304\pi$
$659$	−24.7106	+	24.7106i	−0.962589	+	0.962589i	0.0367361	+	0.999325i	$0.488304\pi$
$660$	0.214188	−	0.111912i	0.00833724	−	0.00435616i
$661$	4.65040	+	11.2271i	0.180880	+	0.436682i	0.988148	−	0.153502i	$-0.0490552\pi$
$661$	4.65040	+	11.2271i	0.180880	+	0.436682i	−0.807269	+	0.590184i	$0.799055\pi$
$662$	9.50727			0.369510
$663$	−0.832486	−	0.0415803i	−0.0323311	−	0.00161484i
$664$	16.5461			0.642113
$665$	−0.639559	−	1.54403i	−0.0248011	−	0.0598750i
$666$	0.587351	−	1.34591i	0.0227594	−	0.0521528i
$667$	17.4783	−	17.4783i	0.676762	−	0.676762i
$668$	−0.317674	−	0.475432i	−0.0122912	−	0.0183950i
$669$	0.250913	+	0.209894i	0.00970085	+	0.00811496i
$670$	−0.894718	−	0.597832i	−0.0345660	−	0.0230962i
$671$	−13.3710	−	5.53844i	−0.516181	−	0.213809i
$672$	1.31797	+	4.49637i	0.0508417	+	0.173451i
$673$	−22.5244	+	33.7102i	−0.868252	+	1.29943i	0.0847298	+	0.996404i	$0.472997\pi$
$673$	−22.5244	+	33.7102i	−0.868252	+	1.29943i	−0.952982	+	0.303027i	$0.902003\pi$
$674$	−3.42798	−	17.2336i	−0.132041	−	0.663814i
$675$	−12.8369	+	22.4695i	−0.494094	+	0.864852i
$676$	−2.50037	−	2.50037i	−0.0961681	−	0.0961681i
$677$	−1.33713	+	6.72222i	−0.0513902	+	0.258356i	−0.997936	−	0.0642128i	$-0.979546\pi$
$677$	−1.33713	+	6.72222i	−0.0513902	+	0.258356i	0.946546	+	0.322569i	$0.104546\pi$
$678$	27.0710	+	14.7984i	1.03966	+	0.568327i
$679$			8.11552i			0.311445i
$680$	1.55993	−	0.754225i	0.0598204	−	0.0289232i
$681$	−2.31378	−	2.87398i	−0.0886644	−	0.110131i
$682$	39.5988	−	16.4024i	1.51632	−	0.628079i
$683$	−9.68496	−	1.92646i	−0.370585	−	0.0737139i	0.00628472	−	0.999980i	$-0.497999\pi$
$683$	−9.68496	−	1.92646i	−0.370585	−	0.0737139i	−0.376870	+	0.926266i	$0.622999\pi$
$684$	−2.96073	−	4.61649i	−0.113206	−	0.176516i
$685$	0.374940	−	0.250527i	0.0143257	−	0.00957213i
$686$	24.7920	−	4.93143i	0.946562	−	0.188283i
$687$	29.8187	−	2.65434i	1.13766	−	0.101269i
$688$	−2.72864	+	6.58752i	−0.104028	+	0.251147i
$689$	−0.286087	+	0.690676i	−0.0108991	+	0.0263127i
$690$	−2.00357	+	0.178349i	−0.0762746	+	0.00678965i
$691$	13.6051	−	2.70622i	0.517563	−	0.102950i	0.0706044	−	0.997504i	$-0.477507\pi$
$691$	13.6051	−	2.70622i	0.517563	−	0.102950i	0.446958	+	0.894555i	$0.352507\pi$
$692$	2.78800	−	1.86288i	0.105984	−	0.0708161i
$693$	10.4349	+	16.2705i	0.396389	+	0.618065i
$694$	−43.1524	−	8.58354i	−1.63804	−	0.325827i
$695$	−0.662233	+	0.274306i	−0.0251199	+	0.0104050i
$696$	−12.7699	−	15.8617i	−0.484044	−	0.601237i
$697$	17.1234	+	5.96174i	0.648596	+	0.225817i
$698$		−	36.5813i		−	1.38462i
$699$	14.8820	+	8.13525i	0.562890	+	0.307703i
$700$	−0.468044	+	2.35301i	−0.0176904	+	0.0889356i
$701$	−7.15325	−	7.15325i	−0.270175	−	0.270175i	0.558996	−	0.829170i	$-0.311187\pi$
$701$	−7.15325	−	7.15325i	−0.270175	−	0.270175i	−0.829170	+	0.558996i	$0.811187\pi$
$702$	0.395442	−	0.692173i	0.0149250	−	0.0261244i
$703$	0.487775	+	2.45221i	0.0183968	+	0.0924869i
$704$	−17.7491	+	26.5634i	−0.668945	+	1.00115i
$705$	0.204687	+	0.698307i	0.00770894	+	0.0262998i
$706$	−8.77211	−	3.63353i	−0.330143	−	0.136750i
$707$	−7.45408	−	4.98066i	−0.280340	−	0.187317i
$708$	3.45946	+	2.89391i	0.130014	+	0.108760i
$709$	25.0275	+	37.4563i	0.939929	+	1.40670i	0.913404	+	0.407054i	$0.133444\pi$
$709$	25.0275	+	37.4563i	0.939929	+	1.40670i	0.0265247	+	0.999648i	$0.491556\pi$
$710$	1.69951	−	1.69951i	0.0637814	−	0.0637814i
$711$	−2.93490	+	6.72528i	−0.110067	+	0.252218i
$712$	4.68374	+	11.3075i	0.175531	+	0.423768i
$713$	56.2259			2.10568
$714$	8.52608	+	14.2513i	0.319081	+	0.533343i
$715$	−0.0598067			−0.00223664
$716$	1.92635	+	4.65061i	0.0719909	+	0.173801i
$717$	34.4433	−	17.9965i	1.28631	−	0.672090i
$718$	−25.6111	+	25.6111i	−0.955796	+	0.955796i
$719$	−15.9794	−	23.9148i	−0.595929	−	0.891871i	0.403807	−	0.914844i	$-0.367687\pi$
$719$	−15.9794	−	23.9148i	−0.595929	−	0.891871i	−0.999736	+	0.0229732i	$0.992687\pi$
$720$	−0.0268106	+	1.42700i	−0.000999172	+	0.0531811i
$721$	23.5010	+	15.7029i	0.875222	+	0.584805i
$722$	−31.6655	−	13.1163i	−1.17847	−	0.488138i
$723$	0.673981	−	0.197556i	0.0250656	−	0.00734719i
$724$	−0.322022	+	0.481940i	−0.0119679	+	0.0179112i
$725$	−3.82448	−	19.2269i	−0.142038	−	0.714071i
$726$	−1.54173	+	4.91571i	−0.0572190	+	0.182439i
$727$	−1.86673	−	1.86673i	−0.0692331	−	0.0692331i	0.671642	−	0.740876i	$-0.265589\pi$
$727$	−1.86673	−	1.86673i	−0.0692331	−	0.0692331i	−0.740876	+	0.671642i	$0.765589\pi$
$728$	0.120321	−	0.604893i	0.00445938	−	0.0224188i
$729$	26.1425	+	6.75071i	0.968239	+	0.250026i
$730$		−	0.826242i		−	0.0305806i
$731$	1.20197	−	8.61113i	0.0444565	−	0.318494i
$732$	−1.45990	+	1.17533i	−0.0539593	+	0.0434415i
$733$	28.9600	−	11.9956i	1.06966	−	0.443068i	0.222790	−	0.974866i	$-0.428484\pi$
$733$	28.9600	−	11.9956i	1.06966	−	0.443068i	0.846871	+	0.531798i	$0.178484\pi$
$734$	14.4821	+	2.88067i	0.534545	+	0.106328i
$735$	−0.937673	−	0.101254i	−0.0345866	−	0.00373482i
$736$	−7.98360	+	5.33447i	−0.294279	+	0.196631i
$737$	−20.7826	+	4.13391i	−0.765537	+	0.152275i
$738$	−12.4899	+	12.0293i	−0.459761	+	0.442803i
$739$	1.82751	−	4.41201i	0.0672262	−	0.162298i	−0.886696	−	0.462354i	$-0.847005\pi$
$739$	1.82751	−	4.41201i	0.0672262	−	0.162298i	0.953922	+	0.300055i	$0.0970051\pi$
$740$	−0.00545986	+	0.0131813i	−0.000200708	+	0.000484553i
$741$	0.120342	+	1.35192i	0.00442088	+	0.0496640i
$742$	14.6086	−	2.90583i	0.536298	−	0.106676i
$743$	−17.5085	+	11.6988i	−0.642325	+	0.429188i	−0.833615	−	0.552346i	$-0.813733\pi$
$743$	−17.5085	+	11.6988i	−0.642325	+	0.429188i	0.191290	+	0.981534i	$0.438733\pi$
$744$	4.97297	−	46.0526i	0.182318	−	1.68837i
$745$	−3.06665	−	0.609995i	−0.112353	−	0.0223485i
$746$	−6.68298	+	2.76818i	−0.244681	+	0.101350i
$747$	3.54792	−	16.2364i	0.129812	−	0.594058i
$748$	1.34435	−	3.86127i	0.0491543	−	0.141182i
$749$		−	2.41058i		−	0.0880806i
$750$	−1.53344	+	2.80516i	−0.0559933	+	0.102430i
$751$	4.52121	−	22.7296i	0.164981	−	0.829416i	−0.806305	−	0.591500i	$-0.798536\pi$
$751$	4.52121	−	22.7296i	0.164981	−	0.829416i	0.971286	−	0.237916i	$-0.0764642\pi$
$752$	−7.13925	−	7.13925i	−0.260342	−	0.260342i
$753$	1.75281	+	0.549740i	0.0638759	+	0.0200336i
$754$	0.117813	+	0.592286i	0.00429050	+	0.0215698i
$755$	−0.322449	+	0.482579i	−0.0117351	+	0.0175629i
$756$	2.49701	−	0.175067i	0.0908155	−	0.00636711i
$757$	−23.7983	−	9.85760i	−0.864965	−	0.358280i	−0.0943180	−	0.995542i	$-0.530067\pi$
$757$	−23.7983	−	9.85760i	−0.864965	−	0.358280i	−0.770647	+	0.637262i	$0.780067\pi$
$758$	5.75627	+	3.84622i	0.209077	+	0.139701i
$759$	−25.4148	+	30.3815i	−0.922498	+	1.10278i
$760$	−1.56750	−	2.34593i	−0.0568591	−	0.0850957i
$761$	15.9336	−	15.9336i	0.577594	−	0.577594i	−0.356646	−	0.934240i	$-0.616080\pi$
$761$	15.9336	−	15.9336i	0.577594	−	0.577594i	0.934240	+	0.356646i	$0.116080\pi$
$762$	−10.4260	−	19.9543i	−0.377695	−	0.722870i
$763$	−7.77120	−	18.7613i	−0.281336	−	0.679206i
$764$	−4.72118			−0.170806
$765$	−0.405617	−	1.69245i	−0.0146651	−	0.0611907i
$766$	−27.8109			−1.00485
$767$	−0.427153	−	1.03124i	−0.0154236	−	0.0372359i
$768$	5.14012	+	9.83764i	0.185478	+	0.354985i
$769$	10.2112	−	10.2112i	0.368226	−	0.368226i	−0.498604	−	0.866830i	$-0.666154\pi$
$769$	10.2112	−	10.2112i	0.368226	−	0.368226i	0.866830	+	0.498604i	$0.166154\pi$
$770$	0.662009	+	0.990766i	0.0238571	+	0.0357047i
$771$	−22.3735	+	26.7459i	−0.805761	+	0.963229i
$772$	3.67593	+	2.45618i	0.132300	+	0.0883998i
$773$	−2.24744	−	0.930920i	−0.0808348	−	0.0334829i	0.341900	−	0.939736i	$-0.388930\pi$
$773$	−2.24744	−	0.930920i	−0.0808348	−	0.0334829i	−0.422734	+	0.906254i	$0.638930\pi$
$774$	6.82599	+	4.74884i	0.245355	+	0.170694i
$775$	24.7741	−	37.0771i	0.889912	−	1.33185i
$776$	2.67288	+	13.4375i	0.0959507	+	0.482377i
$777$	−1.08886	−	0.341503i	−0.0390626	−	0.0122514i
$778$	−11.6153	−	11.6153i	−0.416429	−	0.416429i
$779$	5.75994	−	28.9572i	0.206371	−	1.03750i
$780$	−0.00371497	+	0.00679590i	−0.000133017	+	0.000243332i
$781$		−	47.3287i		−	1.69355i
$782$	−22.6373	+	25.4109i	−0.809508	+	0.908693i
$783$	−18.3030	+	9.12973i	−0.654097	+	0.326270i
$784$	12.0895	−	5.00762i	0.431766	−	0.178844i
$785$	1.92639	+	0.383184i	0.0687559	+	0.0136764i
$786$	−3.18464	+	29.4916i	−0.113592	+	1.05193i
$787$	−26.3671	+	17.6179i	−0.939884	+	0.628010i	−0.928264	−	0.371922i	$-0.878699\pi$
$787$	−26.3671	+	17.6179i	−0.939884	+	0.628010i	−0.0116199	+	0.999932i	$0.503699\pi$
$788$	2.09666	−	0.417051i	0.0746903	−	0.0148568i
$789$	−0.847945	−	9.52578i	−0.0301876	−	0.339127i
$790$	−0.173108	+	0.417919i	−0.00615889	+	0.0148689i
$791$	9.17479	−	22.1499i	0.326218	−	0.787560i
$792$	22.6366	+	23.5035i	0.804356	+	0.835159i
$793$	0.454920	−	0.0904893i	0.0161547	−	0.00321337i
$794$	−42.5135	+	28.4066i	−1.50875	+	1.00811i
$795$	−1.55191	−	0.167583i	−0.0550407	−	0.00594354i
$796$	3.41820	+	0.679923i	0.121155	+	0.0240992i
$797$	−41.8726	+	17.3442i	−1.48320	+	0.614363i	−0.969825	−	0.243800i	$-0.921606\pi$
$797$	−41.8726	+	17.3442i	−1.48320	+	0.614363i	−0.513377	+	0.858163i	$0.671606\pi$
$798$	21.0640	−	16.9582i	0.745658	−	0.600314i
$799$	10.6138	+	6.23860i	0.375490	+	0.220706i
$800$			7.61508i			0.269234i
$801$	12.1002	−	2.17142i	0.427539	−	0.0767235i
$802$	−6.98204	+	35.1011i	−0.246544	+	1.23946i
$803$	−11.5048	−	11.5048i	−0.405995	−	0.405995i
$804$	−0.821198	+	2.61833i	−0.0289614	+	0.0923415i
$805$	0.304951	+	1.53309i	0.0107481	+	0.0540345i
$806$	−0.763166	+	1.14216i	−0.0268814	+	0.0402308i
$807$	−15.1911	+	4.45280i	−0.534753	+	0.156746i
$808$	−13.9827	−	5.79181i	−0.491908	−	0.203755i
$809$	20.9122	+	13.9731i	0.735233	+	0.491267i	0.865936	−	0.500155i	$-0.166724\pi$
$809$	20.9122	+	13.9731i	0.735233	+	0.491267i	−0.130703	+	0.991422i	$0.541724\pi$
$810$	1.61914	+	0.385814i	0.0568907	+	0.0135561i
$811$	12.9298	+	19.3507i	0.454025	+	0.679496i	0.985902	−	0.167325i	$-0.0535130\pi$
$811$	12.9298	+	19.3507i	0.454025	+	0.679496i	−0.531877	+	0.846822i	$0.678513\pi$
$812$	−1.34084	+	1.34084i	−0.0470544	+	0.0470544i
$813$	4.06537	−	2.12413i	0.142579	−	0.0744966i
$814$	−0.682192	−	1.64696i	−0.0239108	−	0.0577259i
$815$	−1.56942			−0.0549743
$816$	16.2016	+	17.9051i	0.567169	+	0.626805i
$817$	−14.1578			−0.495320
$818$	−14.1964	−	34.2732i	−0.496367	−	1.19834i
$819$	−0.567770	−	0.247773i	−0.0198395	−	0.00865790i
$820$	0.119131	−	0.119131i	0.00416024	−	0.00416024i
$821$	24.0120	+	35.9365i	0.838025	+	1.25419i	0.964990	+	0.262286i	$0.0844765\pi$
$821$	24.0120	+	35.9365i	0.838025	+	1.25419i	−0.126965	+	0.991907i	$0.540524\pi$
$822$	5.59653	+	4.68161i	0.195201	+	0.163290i
$823$	−14.0236	−	9.37028i	−0.488833	−	0.326627i	0.286608	−	0.958048i	$-0.407472\pi$
$823$	−14.0236	−	9.37028i	−0.488833	−	0.326627i	−0.775441	+	0.631420i	$0.782472\pi$
$824$	44.0841	+	18.2602i	1.53574	+	0.636125i
$825$	8.83631	+	30.1459i	0.307641	+	1.04955i
$826$	−12.3554	+	18.4912i	−0.429900	+	0.643391i
$827$	4.32515	+	21.7440i	0.150400	+	0.756114i	0.980193	+	0.198042i	$0.0634584\pi$
$827$	4.32515	+	21.7440i	0.150400	+	0.756114i	−0.829793	+	0.558071i	$0.811542\pi$
$828$	1.87362	+	4.77510i	0.0651127	+	0.165946i
$829$	19.3451	+	19.3451i	0.671883	+	0.671883i	0.958150	−	0.286267i	$-0.0924145\pi$
$829$	19.3451	+	19.3451i	0.671883	+	0.671883i	−0.286267	+	0.958150i	$0.592415\pi$
$830$	0.199878	−	1.00486i	0.00693787	−	0.0348790i
$831$	−31.4440	−	17.1888i	−1.09078	−	0.596274i
$832$		−	1.02389i		−	0.0354968i
$833$	−12.7343	+	9.61477i	−0.441218	+	0.333132i
$834$	−7.27334	−	9.03431i	−0.251855	−	0.312833i
$835$	−0.272976	+	0.113070i	−0.00944672	+	0.00391296i
$836$	−6.52973	−	1.29884i	−0.225836	−	0.0449215i
$837$	−44.1242	−	14.7548i	−1.52516	−	0.510000i
$838$	10.2082	−	6.82089i	0.352636	−	0.235624i
$839$	−24.3543	+	4.84436i	−0.840802	+	0.167246i	−0.596661	−	0.802494i	$-0.703506\pi$
$839$	−24.3543	+	4.84436i	−0.840802	+	0.167246i	−0.244142	+	0.969740i	$0.578506\pi$
$840$	1.28267	−	0.114178i	0.0442564	−	0.00393952i
$841$	−5.16832	+	12.4774i	−0.178218	+	0.430256i
$842$	−6.69119	+	16.1539i	−0.230593	+	0.556702i
$843$	−17.7502	+	1.58005i	−0.611351	+	0.0544199i
$844$	−1.36737	+	0.271986i	−0.0470667	+	0.00936215i
$845$	−1.51926	+	1.01514i	−0.0522641	+	0.0349218i
$846$	−9.91131	+	6.35651i	−0.340758	+	0.218541i
$847$	3.92654	+	0.781037i	0.134917	+	0.0268367i
$848$	20.0089	−	8.28795i	0.687107	−	0.284609i
$849$	13.9495	+	17.3269i	0.478745	+	0.594656i
$850$	6.78235	+	26.1242i	0.232633	+	0.896052i
$851$		−	2.33850i		−	0.0801628i
$852$	−5.37801	−	2.93989i	−0.184248	−	0.100719i
$853$	5.82018	−	29.2600i	0.199279	−	1.00184i	−0.743578	−	0.668649i	$-0.766873\pi$
$853$	5.82018	−	29.2600i	0.199279	−	1.00184i	0.942858	−	0.333196i	$-0.108127\pi$
$854$	−6.53464	−	6.53464i	−0.223611	−	0.223611i
$855$	−2.63813	+	1.03513i	−0.0902220	+	0.0354006i
$856$	−0.793933	−	3.99137i	−0.0271361	−	0.136422i
$857$	18.9054	−	28.2940i	0.645798	−	0.966505i	−0.353717	−	0.935353i	$-0.615082\pi$
$857$	18.9054	−	28.2940i	0.645798	−	0.966505i	0.999515	−	0.0311521i	$-0.00991763\pi$
$858$	−0.272203	−	0.928644i	−0.00929284	−	0.0317034i
$859$	18.2111	+	7.54327i	0.621354	+	0.257373i	0.671074	−	0.741390i	$-0.265833\pi$
$859$	18.2111	+	7.54327i	0.621354	+	0.257373i	−0.0497206	+	0.998763i	$0.515833\pi$
$860$	−0.0671740	−	0.0448842i	−0.00229061	−	0.00153054i
$861$	10.3359	+	8.64622i	0.352247	+	0.294662i
$862$	−10.6694	−	15.9679i	−0.363402	−	0.543869i
$863$	4.36492	−	4.36492i	0.148584	−	0.148584i	−0.628901	−	0.777485i	$-0.716495\pi$
$863$	4.36492	−	4.36492i	0.148584	−	0.148584i	0.777485	+	0.628901i	$0.216495\pi$
$864$	7.66513	−	2.09126i	0.260773	−	0.0711460i
$865$	−0.663059	−	1.60077i	−0.0225447	−	0.0544277i
$866$	23.4504			0.796876
$867$	−24.6087	−	16.1683i	−0.835754	−	0.549104i
$868$	−4.31336			−0.146405
$869$	3.40880	+	8.22958i	0.115636	+	0.279169i
$870$	−1.11755	+	0.583916i	−0.0378887	+	0.0197966i
$871$	0.480203	−	0.480203i	0.0162710	−	0.0162710i
$872$	−19.0465	−	28.5050i	−0.644994	−	0.965302i
$873$	13.7591	+	0.258507i	0.465674	+	0.00874913i
$874$	46.0763	+	30.7872i	1.55855	+	1.04139i
$875$	2.29522	+	0.950712i	0.0775927	+	0.0321399i
$876$	−2.02194	+	0.592666i	−0.0683149	+	0.0200243i
$877$	5.29644	−	7.92668i	0.178848	−	0.267665i	−0.731204	−	0.682159i	$-0.761041\pi$
$877$	5.29644	−	7.92668i	0.178848	−	0.267665i	0.910052	+	0.414494i	$0.136041\pi$
$878$	6.75949	+	33.9822i	0.228122	+	1.14685i
$879$	−0.584739	+	1.86440i	−0.0197228	+	0.0628847i
$880$	1.22513	+	1.22513i	0.0412992	+	0.0412992i
$881$	8.39169	−	42.1879i	0.282723	−	1.42135i	−0.534570	−	0.845124i	$-0.679527\pi$
$881$	8.39169	−	42.1879i	0.282723	−	1.42135i	0.817294	−	0.576222i	$-0.195473\pi$
$882$	−2.69548	−	15.0205i	−0.0907617	−	0.505767i
$883$		−	41.3162i		−	1.39040i	−0.718816	−	0.695200i	$-0.755316\pi$
$883$		−	41.3162i		−	1.39040i	0.718816	−	0.695200i	$-0.244684\pi$
$884$	0.0329277	+	0.126831i	0.00110748	+	0.00426578i
$885$	1.81539	−	1.46153i	0.0610237	−	0.0491289i
$886$	11.7434	−	4.86427i	0.394527	−	0.163418i
$887$	−14.5578	−	2.89572i	−0.488801	−	0.0972287i	−0.0554646	−	0.998461i	$-0.517664\pi$
$887$	−14.5578	−	2.89572i	−0.488801	−	0.0972287i	−0.433337	+	0.901232i	$0.642664\pi$
$888$	−1.91538	−	0.206831i	−0.0642760	−	0.00694081i
$889$	−14.5470	+	9.72002i	−0.487892	+	0.325999i
$890$	0.743294	−	0.147850i	0.0249153	−	0.00495596i
$891$	27.9174	−	17.1731i	0.935267	−	0.575319i
$892$	0.0196801	−	0.0475120i	0.000658939	−	0.00159082i
$893$	7.67180	−	18.5214i	0.256727	−	0.619794i
$894$	−4.48582	−	50.3935i	−0.150028	−	1.68541i
$895$	2.55114	−	0.507454i	0.0852754	−	0.0169623i
$896$	−12.4632	+	8.32768i	−0.416368	+	0.278208i
$897$	0.136289	−	1.26212i	0.00455057	−	0.0421410i
$898$	1.36228	+	0.270975i	0.0454600	+	0.00904256i
$899$	32.5624	−	13.4878i	1.08602	−	0.449843i
$900$	3.97439	+	0.868473i	0.132480	+	0.0289491i
$901$	−21.0762	+	15.9131i	−0.702149	+	0.530142i
$902$			21.0507i			0.700910i
$903$	3.09950	−	5.67001i	0.103145	−	0.188686i
$904$	7.89621	−	39.6970i	0.262624	−	1.32030i
$905$	0.211787	+	0.211787i	0.00704002	+	0.00704002i
$906$	−8.96080	−	2.81041i	−0.297703	−	0.0933696i
$907$	3.33756	+	16.7791i	0.110822	+	0.557140i	0.995804	+	0.0915140i	$0.0291706\pi$
$907$	3.33756	+	16.7791i	0.110822	+	0.557140i	−0.884982	+	0.465626i	$0.845829\pi$
$908$	−0.322250	+	0.482281i	−0.0106942	+	0.0160050i
$909$	−8.68165	+	12.4790i	−0.287952	+	0.413902i
$910$	−0.0352820	−	0.0146143i	−0.00116959	−	0.000484459i
$911$	45.9977	+	30.7347i	1.52397	+	1.01829i	0.984319	+	0.176398i	$0.0564446\pi$
$911$	45.9977	+	30.7347i	1.52397	+	1.01829i	0.539653	+	0.841887i	$0.318555\pi$
$912$	25.2287	−	30.1591i	0.835406	−	0.998667i
$913$	−11.2087	−	16.7750i	−0.370953	−	0.555171i
$914$	19.9143	−	19.9143i	0.658705	−	0.658705i
$915$	0.448492	+	0.858366i	0.0148267	+	0.0283767i
$916$	−1.80100	−	4.34800i	−0.0595067	−	0.143662i
$917$	23.0511			0.761216
$918$	24.4333	−	14.0012i	0.806419	−	0.462107i
$919$	−57.0283			−1.88119			−0.940595	−	0.339530i	$-0.889732\pi$
$919$	−57.0283			−1.88119			−0.940595	+	0.339530i	$0.889732\pi$
$920$	1.00986	+	2.43802i	0.0332941	+	0.0803791i
$921$	−15.7062	−	30.0601i	−0.517538	−	0.990514i
$922$	−22.9019	+	22.9019i	−0.754233	+	0.754233i
$923$	0.842708	+	1.26120i	0.0277381	+	0.0415130i
$924$	1.94969	−	2.33071i	0.0641401	−	0.0766748i
$925$	−1.54208	−	1.03038i	−0.0507032	−	0.0338788i
$926$	−23.4364	−	9.70769i	−0.770169	−	0.319014i
$927$	27.3712	−	39.3434i	0.898989	−	1.29221i
$928$	−3.34392	+	5.00453i	−0.109770	+	0.164282i
$929$	−6.98713	−	35.1267i	−0.229240	−	1.15247i	−0.908278	−	0.418366i	$-0.862603\pi$
$929$	−6.98713	−	35.1267i	−0.229240	−	1.15247i	0.679038	−	0.734103i	$-0.262397\pi$
$930$	−2.73673	−	0.858331i	−0.0897410	−	0.0281458i
$931$	18.3724	+	18.3724i	0.602132	+	0.602132i
$932$	0.520168	−	2.61506i	0.0170387	−	0.0856592i
$933$	−24.4046	+	44.6440i	−0.798971	+	1.46158i
$934$			16.3585i			0.535267i
$935$	−1.82138	−	1.07058i	−0.0595656	−	0.0350116i
$936$	−1.02170	−	0.223259i	−0.0333954	−	0.00729746i
$937$	−18.6808	+	7.73785i	−0.610276	+	0.252785i	−0.666347	−	0.745642i	$-0.732143\pi$
$937$	−18.6808	+	7.73785i	−0.610276	+	0.252785i	0.0560704	+	0.998427i	$0.482143\pi$
$938$	−13.2705	−	2.63967i	−0.433298	−	0.0861884i
$939$	3.31375	−	30.6873i	0.108140	−	1.00144i
$940$	0.0951179	−	0.0635557i	0.00310240	−	0.00207296i
$941$	7.61499	−	1.51472i	0.248242	−	0.0493783i	−0.0694010	−	0.997589i	$-0.522109\pi$
$941$	7.61499	−	1.51472i	0.248242	−	0.0493783i	0.317643	+	0.948211i	$0.397109\pi$
$942$	2.81788	+	31.6560i	0.0918116	+	1.03141i
$943$	−10.5676	+	25.5124i	−0.344128	+	0.830798i
$944$	−12.3746	+	29.8749i	−0.402759	+	0.972347i
$945$	0.162998	−	1.28315i	0.00530234	−	0.0417407i
$946$	9.90043	−	1.96932i	0.321891	−	0.0640281i
$947$	−2.99573	+	2.00168i	−0.0973480	+	0.0650459i	−0.603291	−	0.797521i	$-0.706144\pi$
$947$	−2.99573	+	2.00168i	−0.0973480	+	0.0650459i	0.505943	+	0.862567i	$0.331144\pi$
$948$	1.14688	+	0.123845i	0.0372489	+	0.00402231i
$949$	0.511424	+	0.101728i	0.0166015	+	0.00330225i
$950$	40.6040	−	16.8187i	1.31737	−	0.545672i
$951$	19.0515	−	15.3379i	0.617786	−	0.497367i
$952$	14.4922	−	16.2679i	0.469696	−	0.527246i
$953$			22.5397i			0.730132i	0.930982	+	0.365066i	$0.118954\pi$
$953$			22.5397i			0.730132i	−0.930982	+	0.365066i	$0.881046\pi$
$954$	−4.46121	−	24.8600i	−0.144437	−	0.804871i
$955$	−0.475940	+	2.39271i	−0.0154011	+	0.0774264i
$956$	−4.31991	−	4.31991i	−0.139716	−	0.139716i
$957$	−7.43050	+	23.6917i	−0.240194	+	0.765843i
$958$	5.82076	+	29.2629i	0.188060	+	0.945442i
$959$	3.15013	−	4.71450i	0.101723	−	0.152239i
$960$	2.05153	−	0.601342i	0.0662129	−	0.0194082i
$961$	45.4292	+	18.8174i	1.46546	+	0.607013i
$962$	0.0475037	+	0.0317410i	0.00153158	+	0.00102337i
$963$	−4.08689	−	0.0767851i	−0.131698	−	0.00247436i
$964$	−0.0613417	−	0.0918044i	−0.00197568	−	0.00295682i
$965$	1.61537	−	1.61537i	0.0520007	−	0.0520007i
$966$	−22.4171	+	11.7128i	−0.721257	+	0.376853i
$967$	8.59605	+	20.7527i	0.276430	+	0.667362i	0.999732	−	0.0231709i	$-0.00737619\pi$
$967$	8.59605	+	20.7527i	0.276430	+	0.667362i	−0.723301	+	0.690533i	$0.757376\pi$
$968$	6.75869			0.217233
$969$	−20.5352	+	43.3263i	−0.659686	+	1.39184i
$970$	0.848355			0.0272390
$971$	13.1165	+	31.6660i	0.420928	+	1.01621i	0.982075	+	0.188493i	$0.0603603\pi$
$971$	13.1165	+	31.6660i	0.420928	+	1.01621i	−0.561147	+	0.827716i	$0.689640\pi$
$972$	−0.217270	−	4.23901i	−0.00696893	−	0.135966i
$973$	−6.37317	+	6.37317i	−0.204314	+	0.204314i
$974$	−16.7851	−	25.1207i	−0.537830	−	0.804920i
$975$	−0.772229	−	0.645985i	−0.0247311	−	0.0206881i
$976$	−11.1726	−	7.46532i	−0.357628	−	0.238959i
$977$	26.0166	+	10.7764i	0.832345	+	0.344769i	0.757831	−	0.652451i	$-0.226259\pi$
$977$	26.0166	+	10.7764i	0.832345	+	0.344769i	0.0745143	+	0.997220i	$0.476259\pi$
$978$	−7.14301	−	24.3690i	−0.228408	−	0.779235i
$979$	8.29109	−	12.4085i	0.264985	−	0.396577i
$980$	0.0289251	+	0.145416i	0.000923980	+	0.00464516i
$981$	−32.0555	+	12.5777i	−1.02345	+	0.401574i
$982$	−18.9356	−	18.9356i	−0.604261	−	0.604261i
$983$	−8.14020	+	40.9235i	−0.259632	+	1.30526i	0.602314	+	0.798259i	$0.294245\pi$
$983$	−8.14020	+	40.9235i	−0.259632	+	1.30526i	−0.861946	+	0.506999i	$0.830755\pi$
$984$	19.9616	+	10.9120i	0.636353	+	0.347862i
$985$		−	1.10464i		−	0.0351967i
$986$	−7.01434	+	20.1467i	−0.223382	+	0.641602i
$987$	5.73799	+	7.12723i	0.182642	+	0.226862i
$988$	0.197129	−	0.0816535i	0.00627151	−	0.00259774i
$989$	12.9875	+	2.58337i	0.412977	+	0.0821463i
$990$	1.70083	−	1.09081i	0.0540560	−	0.0346682i
$991$	8.43842	−	5.63837i	0.268055	−	0.179109i	−0.414277	−	0.910151i	$-0.635966\pi$
$991$	8.43842	−	5.63837i	0.268055	−	0.179109i	0.682333	+	0.731042i	$0.260966\pi$
$992$	−13.4281	+	2.67101i	−0.426341	+	0.0848046i
$993$	−12.4786	+	1.11080i	−0.395998	+	0.0352500i
$994$	11.5652	−	27.9208i	0.366826	−	0.885595i
$995$	0.689176	−	1.66382i	0.0218483	−	0.0527466i
$996$	−2.60240	+	0.231655i	−0.0824603	+	0.00734027i
$997$	−39.1586	+	7.78912i	−1.24016	+	0.246684i	−0.771234	−	0.636552i	$-0.780360\pi$
$997$	−39.1586	+	7.78912i	−1.24016	+	0.246684i	−0.468930	+	0.883235i	$0.655360\pi$
$998$	−1.17942	+	0.788061i	−0.0373338	+	0.0249456i
$999$	−0.613668	+	1.83518i	−0.0194156	+	0.0580624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.i.a.14.2	yes	32
3.2	odd	2	inner	51.2.i.a.14.3	yes	32
4.3	odd	2		816.2.cj.c.65.1		32
12.11	even	2		816.2.cj.c.65.4		32
17.2	even	8		867.2.i.b.158.3		32
17.3	odd	16		867.2.i.i.653.2		32
17.4	even	4		867.2.i.d.224.3		32
17.5	odd	16		867.2.i.f.503.3		32
17.6	odd	16		867.2.i.h.827.3		32
17.7	odd	16		867.2.i.d.329.2		32
17.8	even	8		867.2.i.g.131.2		32
17.9	even	8		867.2.i.f.131.2		32
17.10	odd	16		867.2.i.c.329.2		32
17.11	odd	16	inner	51.2.i.a.11.3	yes	32
17.12	odd	16		867.2.i.g.503.3		32
17.13	even	4		867.2.i.c.224.3		32
17.14	odd	16		867.2.i.b.653.2		32
17.15	even	8		867.2.i.i.158.3		32
17.16	even	2		867.2.i.h.65.2		32
51.2	odd	8		867.2.i.b.158.2		32
51.5	even	16		867.2.i.f.503.2		32
51.8	odd	8		867.2.i.g.131.3		32
51.11	even	16	inner	51.2.i.a.11.2	✓	32
51.14	even	16		867.2.i.b.653.3		32
51.20	even	16		867.2.i.i.653.3		32
51.23	even	16		867.2.i.h.827.2		32
51.26	odd	8		867.2.i.f.131.3		32
51.29	even	16		867.2.i.g.503.2		32
51.32	odd	8		867.2.i.i.158.2		32
51.38	odd	4		867.2.i.d.224.2		32
51.41	even	16		867.2.i.d.329.3		32
51.44	even	16		867.2.i.c.329.3		32
51.47	odd	4		867.2.i.c.224.2		32
51.50	odd	2		867.2.i.h.65.3		32
68.11	even	16		816.2.cj.c.113.4		32
204.11	odd	16		816.2.cj.c.113.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.11.2	✓	32	51.11	even	16	inner
51.2.i.a.11.3	yes	32	17.11	odd	16	inner
51.2.i.a.14.2	yes	32	1.1	even	1	trivial
51.2.i.a.14.3	yes	32	3.2	odd	2	inner
816.2.cj.c.65.1		32	4.3	odd	2
816.2.cj.c.65.4		32	12.11	even	2
816.2.cj.c.113.1		32	204.11	odd	16
816.2.cj.c.113.4		32	68.11	even	16
867.2.i.b.158.2		32	51.2	odd	8
867.2.i.b.158.3		32	17.2	even	8
867.2.i.b.653.2		32	17.14	odd	16
867.2.i.b.653.3		32	51.14	even	16
867.2.i.c.224.2		32	51.47	odd	4
867.2.i.c.224.3		32	17.13	even	4
867.2.i.c.329.2		32	17.10	odd	16
867.2.i.c.329.3		32	51.44	even	16
867.2.i.d.224.2		32	51.38	odd	4
867.2.i.d.224.3		32	17.4	even	4
867.2.i.d.329.2		32	17.7	odd	16
867.2.i.d.329.3		32	51.41	even	16
867.2.i.f.131.2		32	17.9	even	8
867.2.i.f.131.3		32	51.26	odd	8
867.2.i.f.503.2		32	51.5	even	16
867.2.i.f.503.3		32	17.5	odd	16
867.2.i.g.131.2		32	17.8	even	8
867.2.i.g.131.3		32	51.8	odd	8
867.2.i.g.503.2		32	51.29	even	16
867.2.i.g.503.3		32	17.12	odd	16
867.2.i.h.65.2		32	17.16	even	2
867.2.i.h.65.3		32	51.50	odd	2
867.2.i.h.827.2		32	51.23	even	16
867.2.i.h.827.3		32	17.6	odd	16
867.2.i.i.158.2		32	51.32	odd	8
867.2.i.i.158.3		32	17.15	even	8
867.2.i.i.653.2		32	17.3	odd	16
867.2.i.i.653.3		32	51.20	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.503008 - 1.21437i) q^{2} +(0.802099 + 1.53513i) q^{3} +(0.192538 - 0.192538i) q^{4} +(-0.0781694 - 0.116989i) q^{5} +(1.46076 - 1.74623i) q^{6} +(-1.47102 - 0.982905i) q^{7} +(-2.75940 - 1.14298i) q^{8} +(-1.71327 + 2.46266i) q^{9} +(-0.102748 + 0.153773i) q^{10} +(0.710485 + 3.57185i) q^{11} +(0.450006 + 0.141137i) q^{12} +(-0.0825311 - 0.0825311i) q^{13} +(-0.453674 + 2.28077i) q^{14} +(0.116894 - 0.213837i) q^{15} +3.38128i q^{16} +(-1.03609 - 3.99080i) q^{17} +(3.85237 + 0.841809i) q^{18} +(-6.20278 + 2.56928i) q^{19} +(-0.0375753 - 0.00747420i) q^{20} +(0.328986 - 3.04660i) q^{21} +(3.98016 - 2.65946i) q^{22} +(6.15884 - 1.22507i) q^{23} +(-0.458684 - 5.15283i) q^{24} +(1.90584 - 4.60111i) q^{25} +(-0.0587094 + 0.141737i) q^{26} +(-5.15473 - 0.654807i) q^{27} +(-0.472474 + 0.0939809i) q^{28} +(3.27292 - 2.18690i) q^{29} +(-0.318476 - 0.0343905i) q^{30} +(8.78185 + 1.74682i) q^{31} +(-1.41268 + 0.585150i) q^{32} +(-4.91339 + 3.95567i) q^{33} +(-4.32515 + 3.26560i) q^{34} +0.248926i q^{35} +(0.144285 + 0.804026i) q^{36} +(0.0726522 - 0.365247i) q^{37} +(6.24010 + 6.24010i) q^{38} +(0.0604982 - 0.192895i) q^{39} +(0.0819847 + 0.412165i) q^{40} +(-2.44315 + 3.65643i) q^{41} +(-3.86518 + 1.13296i) q^{42} +(1.94823 + 0.806985i) q^{43} +(0.824512 + 0.550921i) q^{44} +(0.422029 + 0.00792913i) q^{45} +(-4.58563 - 6.86288i) q^{46} +(-2.11141 + 2.11141i) q^{47} +(-5.19072 + 2.71212i) q^{48} +(-1.48098 - 3.57541i) q^{49} -6.54610 q^{50} +(5.29537 - 4.79156i) q^{51} -0.0317807 q^{52} +(-2.45113 - 5.91755i) q^{53} +(1.79769 + 6.58912i) q^{54} +(0.362328 - 0.362328i) q^{55} +(2.93569 + 4.39357i) q^{56} +(-8.91943 - 7.46129i) q^{57} +(-4.30201 - 2.87451i) q^{58} +(8.83540 + 3.65974i) q^{59} +(-0.0186653 - 0.0636782i) q^{60} +(-2.20784 + 3.30427i) q^{61} +(-2.29606 - 11.5431i) q^{62} +(4.94082 - 1.93864i) q^{63} +(6.20303 + 6.20303i) q^{64} +(-0.00320381 + 0.0161066i) q^{65} +(7.27511 + 3.97693i) q^{66} +5.81844i q^{67} +(-0.967868 - 0.568894i) q^{68} +(6.82064 + 8.47201i) q^{69} +(0.302288 - 0.125212i) q^{70} +(-12.7462 - 2.53537i) q^{71} +(7.54238 - 4.83722i) q^{72} +(-3.71467 + 2.48206i) q^{73} +(-0.480089 + 0.0954957i) q^{74} +(8.59199 - 0.764823i) q^{75} +(-0.699588 + 1.68895i) q^{76} +(2.46565 - 5.95260i) q^{77} +(-0.264676 + 0.0235604i) q^{78} +(2.39893 - 0.477177i) q^{79} +(0.395572 - 0.264312i) q^{80} +(-3.12939 - 8.43842i) q^{81} +(5.66918 + 1.12767i) q^{82} +(-5.11813 + 2.12000i) q^{83} +(-0.523244 - 0.649928i) q^{84} +(-0.385889 + 0.433170i) q^{85} -2.77180i q^{86} +(5.98239 + 3.27027i) q^{87} +(2.12204 - 10.6682i) q^{88} +(-2.89760 - 2.89760i) q^{89} +(-0.202655 - 0.516488i) q^{90} +(0.0402848 + 0.202525i) q^{91} +(0.949937 - 1.42168i) q^{92} +(4.36231 + 14.8824i) q^{93} +(3.62608 + 1.50197i) q^{94} +(0.785444 + 0.524817i) q^{95} +(-2.03139 - 1.69930i) q^{96} +(-2.54849 - 3.81409i) q^{97} +(-3.59692 + 3.59692i) q^{98} +(-10.0135 - 4.36987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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