LMFDB - Embedded newform 810.2.s.a.413.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			413.6
Character	$\chi$	$=$	810.413
Dual form			810.2.s.a.557.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 + 0.573576i) q^{2} +(0.342020 - 0.939693i) q^{4} +(0.463117 + 2.18758i) q^{5} +(-1.78738 + 3.83305i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.819152 + 0.573576i) q^{2} +(0.342020 - 0.939693i) q^{4} +(0.463117 + 2.18758i) q^{5} +(-1.78738 + 3.83305i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-1.63411 - 1.52633i) q^{10} +(-3.34414 + 3.98539i) q^{11} +(-0.215597 + 0.307904i) q^{13} +(-0.734411 - 4.16505i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(1.58114 - 5.90088i) q^{17} +(-2.93211 - 1.69286i) q^{19} +(2.21405 + 0.313010i) q^{20} +(0.453432 - 5.18276i) q^{22} +(1.01274 - 0.472247i) q^{23} +(-4.57105 + 2.02621i) q^{25} -0.375881i q^{26} +(2.99057 + 2.99057i) q^{28} +(1.75816 - 9.97103i) q^{29} +(-3.35678 - 1.22177i) q^{31} +(0.996195 + 0.0871557i) q^{32} +(2.08941 + 5.74062i) q^{34} +(-9.21289 - 2.13490i) q^{35} +(5.63980 + 1.51118i) q^{37} +(3.37283 - 0.295084i) q^{38} +(-1.99318 + 1.01353i) q^{40} +(-4.77146 + 0.841337i) q^{41} +(0.570435 + 6.52010i) q^{43} +(2.60128 + 4.50554i) q^{44} +(-0.558716 + 0.967725i) q^{46} +(6.65173 + 3.10175i) q^{47} +(-6.99804 - 8.33994i) q^{49} +(2.58219 - 4.28162i) q^{50} +(0.215597 + 0.307904i) q^{52} +(-6.39299 + 6.39299i) q^{53} +(-10.2671 - 5.46988i) q^{55} +(-4.16505 - 0.734411i) q^{56} +(4.27895 + 9.17623i) q^{58} +(-2.30891 + 1.93741i) q^{59} +(-7.18421 + 2.61484i) q^{61} +(3.45049 - 0.924557i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(-0.773412 - 0.329040i) q^{65} +(0.199873 + 0.139953i) q^{67} +(-5.00423 - 3.50400i) q^{68} +(8.77128 - 3.53549i) q^{70} +(-0.0530319 + 0.0306180i) q^{71} +(6.38669 - 1.71131i) q^{73} +(-5.48663 + 1.99697i) q^{74} +(-2.59360 + 2.17629i) q^{76} +(-9.29895 - 19.9417i) q^{77} +(-5.15835 - 0.909556i) q^{79} +(1.05138 - 1.97347i) q^{80} +(3.42598 - 3.42598i) q^{82} +(2.73944 + 3.91233i) q^{83} +(13.6409 + 0.726069i) q^{85} +(-4.20705 - 5.01377i) q^{86} +(-4.71511 - 2.19869i) q^{88} +(-4.63875 + 8.03454i) q^{89} +(-0.794859 - 1.37674i) q^{91} +(-0.0973907 - 1.11318i) q^{92} +(-7.22787 + 1.27447i) q^{94} +(2.34535 - 7.19823i) q^{95} +(-15.6011 + 1.36492i) q^{97} +(10.5161 + 2.81777i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−0.819152	+	0.573576i	−0.579228	+	0.405580i
$2$	−0.819152	+	0.573576i	−0.579228	+	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	−	0.939693i	0.171010	−	0.469846i
$5$	0.463117	+	2.18758i	0.207112	+	0.978317i
$5$	0.463117	+	2.18758i	0.207112	+	0.978317i
$6$		0			0
$7$	−1.78738	+	3.83305i	−0.675567	+	1.44876i	0.206890	+	0.978364i	$0.433666\pi$
$7$	−1.78738	+	3.83305i	−0.675567	+	1.44876i	−0.882457	+	0.470393i	$0.844112\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$		0			0
$10$	−1.63411	−	1.52633i	−0.516751	−	0.482668i
$11$	−3.34414	+	3.98539i	−1.00830	+	1.20164i	−0.0289216	+	0.999582i	$0.509207\pi$
$11$	−3.34414	+	3.98539i	−1.00830	+	1.20164i	−0.979374	+	0.202058i	$0.935237\pi$
$12$		0			0
$13$	−0.215597	+	0.307904i	−0.0597958	+	0.0853972i	−0.847936	−	0.530098i	$-0.822155\pi$
$13$	−0.215597	+	0.307904i	−0.0597958	+	0.0853972i	0.788141	+	0.615495i	$0.211044\pi$
$14$	−0.734411	−	4.16505i	−0.196280	−	1.11316i
$15$		0			0
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	1.58114	−	5.90088i	0.383482	−	1.43117i	−0.457065	−	0.889433i	$-0.651099\pi$
$17$	1.58114	−	5.90088i	0.383482	−	1.43117i	0.840546	−	0.541739i	$-0.182234\pi$
$18$		0			0
$19$	−2.93211	−	1.69286i	−0.672672	−	0.388368i	0.124416	−	0.992230i	$-0.460294\pi$
$19$	−2.93211	−	1.69286i	−0.672672	−	0.388368i	−0.797088	+	0.603863i	$0.793628\pi$
$20$	2.21405	+	0.313010i	0.495077	+	0.0699912i
$21$		0			0
$22$	0.453432	−	5.18276i	0.0966721	−	1.10497i
$23$	1.01274	−	0.472247i	0.211170	−	0.0984704i	−0.314155	−	0.949372i	$-0.601721\pi$
$23$	1.01274	−	0.472247i	0.211170	−	0.0984704i	0.525326	+	0.850901i	$0.323943\pi$
$24$		0			0
$25$	−4.57105	+	2.02621i	−0.914209	+	0.405243i
$26$		−	0.375881i		−	0.0737164i
$27$		0			0
$28$	2.99057	+	2.99057i	0.565165	+	0.565165i
$29$	1.75816	−	9.97103i	0.326483	−	1.85157i	−0.172563	−	0.984999i	$-0.555205\pi$
$29$	1.75816	−	9.97103i	0.326483	−	1.85157i	0.499045	−	0.866576i	$-0.333684\pi$
$30$		0			0
$31$	−3.35678	−	1.22177i	−0.602896	−	0.219436i	0.0224959	−	0.999747i	$-0.492839\pi$
$31$	−3.35678	−	1.22177i	−0.602896	−	0.219436i	−0.625392	+	0.780311i	$0.715061\pi$
$32$	0.996195	+	0.0871557i	0.176104	+	0.0154071i
$33$		0			0
$34$	2.08941	+	5.74062i	0.358331	+	0.984508i
$35$	−9.21289	−	2.13490i	−1.55726	−	0.360863i
$36$		0			0
$37$	5.63980	+	1.51118i	0.927178	+	0.248436i	0.690651	−	0.723188i	$-0.257324\pi$
$37$	5.63980	+	1.51118i	0.927178	+	0.248436i	0.236527	+	0.971625i	$0.423991\pi$
$38$	3.37283	−	0.295084i	0.547145	−	0.0478690i
$39$		0			0
$40$	−1.99318	+	1.01353i	−0.315149	+	0.160252i
$41$	−4.77146	+	0.841337i	−0.745177	+	0.131395i	−0.533329	−	0.845908i	$-0.679059\pi$
$41$	−4.77146	+	0.841337i	−0.745177	+	0.131395i	−0.211848	+	0.977303i	$0.567948\pi$
$42$		0			0
$43$	0.570435	+	6.52010i	0.0869905	+	0.994306i	0.906770	+	0.421626i	$0.138541\pi$
$43$	0.570435	+	6.52010i	0.0869905	+	0.994306i	−0.819779	+	0.572680i	$0.805904\pi$
$44$	2.60128	+	4.50554i	0.392157	+	0.679236i
$45$		0			0
$46$	−0.558716	+	0.967725i	−0.0823782	+	0.142683i
$47$	6.65173	+	3.10175i	0.970254	+	0.452437i	0.842102	−	0.539318i	$-0.181318\pi$
$47$	6.65173	+	3.10175i	0.970254	+	0.452437i	0.128152	+	0.991755i	$0.459096\pi$
$48$		0			0
$49$	−6.99804	−	8.33994i	−0.999721	−	1.19142i
$50$	2.58219	−	4.28162i	0.365177	−	0.605513i
$51$		0			0
$52$	0.215597	+	0.307904i	0.0298979	+	0.0426986i
$53$	−6.39299	+	6.39299i	−0.878144	+	0.878144i	−0.993343	−	0.115198i	$-0.963250\pi$
$53$	−6.39299	+	6.39299i	−0.878144	+	0.878144i	0.115198	+	0.993343i	$0.463250\pi$
$54$		0			0
$55$	−10.2671	−	5.46988i	−1.38441	−	0.737558i
$56$	−4.16505	−	0.734411i	−0.556579	−	0.0981398i
$57$		0			0
$58$	4.27895	+	9.17623i	0.561853	+	1.20490i
$59$	−2.30891	+	1.93741i	−0.300595	+	0.252229i	−0.780592	−	0.625041i	$-0.785082\pi$
$59$	−2.30891	+	1.93741i	−0.300595	+	0.252229i	0.479997	+	0.877270i	$0.340638\pi$
$60$		0			0
$61$	−7.18421	+	2.61484i	−0.919844	+	0.334796i	−0.758176	−	0.652049i	$-0.773909\pi$
$61$	−7.18421	+	2.61484i	−0.919844	+	0.334796i	−0.161668	+	0.986845i	$0.551687\pi$
$62$	3.45049	−	0.924557i	0.438213	−	0.117419i
$63$		0			0
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	−0.773412	−	0.329040i	−0.0959300	−	0.0408124i
$66$		0			0
$67$	0.199873	+	0.139953i	0.0244184	+	0.0170979i	0.585722	−	0.810512i	$-0.300811\pi$
$67$	0.199873	+	0.139953i	0.0244184	+	0.0170979i	−0.561304	+	0.827610i	$0.689700\pi$
$68$	−5.00423	−	3.50400i	−0.606852	−	0.424922i
$69$		0			0
$70$	8.77128	−	3.53549i	1.04837	−	0.422572i
$71$	−0.0530319	+	0.0306180i	−0.00629373	+	0.00363369i	−0.503144	−	0.864203i	$-0.667823\pi$
$71$	−0.0530319	+	0.0306180i	−0.00629373	+	0.00363369i	0.496850	+	0.867837i	$0.334490\pi$
$72$		0			0
$73$	6.38669	−	1.71131i	0.747506	−	0.200294i	0.135094	−	0.990833i	$-0.456866\pi$
$73$	6.38669	−	1.71131i	0.747506	−	0.200294i	0.612412	+	0.790539i	$0.290200\pi$
$74$	−5.48663	+	1.99697i	−0.637808	+	0.232143i
$75$		0			0
$76$	−2.59360	+	2.17629i	−0.297507	+	0.249638i
$77$	−9.29895	−	19.9417i	−1.05971	−	2.27256i
$78$		0			0
$79$	−5.15835	−	0.909556i	−0.580360	−	0.102333i	−0.124241	−	0.992252i	$-0.539650\pi$
$79$	−5.15835	−	0.909556i	−0.580360	−	0.102333i	−0.456119	+	0.889919i	$0.650761\pi$
$80$	1.05138	−	1.97347i	0.117548	−	0.220641i
$81$		0			0
$82$	3.42598	−	3.42598i	0.378336	−	0.378336i
$83$	2.73944	+	3.91233i	0.300693	+	0.429434i	0.940857	−	0.338804i	$-0.110022\pi$
$83$	2.73944	+	3.91233i	0.300693	+	0.429434i	−0.640164	+	0.768238i	$0.721134\pi$
$84$		0			0
$85$	13.6409	+	0.726069i	1.47956	+	0.0787533i
$86$	−4.20705	−	5.01377i	−0.453658	−	0.540648i
$87$		0			0
$88$	−4.71511	−	2.19869i	−0.502633	−	0.234382i
$89$	−4.63875	+	8.03454i	−0.491706	+	0.851660i	−0.999954	−	0.00955058i	$-0.996960\pi$
$89$	−4.63875	+	8.03454i	−0.491706	+	0.851660i	0.508248	+	0.861211i	$0.330293\pi$
$90$		0			0
$91$	−0.794859	−	1.37674i	−0.0833238	−	0.144321i
$92$	−0.0973907	−	1.11318i	−0.0101537	−	0.116057i
$93$		0			0
$94$	−7.22787	+	1.27447i	−0.745497	+	0.131451i
$95$	2.34535	−	7.19823i	0.240628	−	0.738523i
$96$		0			0
$97$	−15.6011	+	1.36492i	−1.58405	+	0.138587i	−0.844890	−	0.534940i	$-0.820334\pi$
$97$	−15.6011	+	1.36492i	−1.58405	+	0.138587i	−0.739163	+	0.673527i	$0.764779\pi$
$98$	10.5161	+	2.81777i	1.06228	+	0.284638i
$99$		0			0
$100$	0.340629	+	4.98838i	0.0340629	+	0.498838i
$101$	3.00976	+	8.26924i	0.299482	+	0.822820i	0.994587	+	0.103912i	$0.0331359\pi$
$101$	3.00976	+	8.26924i	0.299482	+	0.822820i	−0.695104	+	0.718909i	$0.744642\pi$
$102$		0			0
$103$	−0.00174607		0.000152761i	−0.000172045		1.50520e-5i	0.0870697	−	0.996202i	$-0.472250\pi$
$103$	−0.00174607		0.000152761i	−0.000172045		1.50520e-5i	−0.0872418	+	0.996187i	$0.527805\pi$
$104$	−0.353213	−	0.128559i	−0.0346354	−	0.0126062i
$105$		0			0
$106$	1.56996	−	8.90369i	0.152488	−	0.864803i
$107$	7.92458	+	7.92458i	0.766098	+	0.766098i	0.977417	−	0.211319i	$-0.0677759\pi$
$107$	7.92458	+	7.92458i	0.766098	+	0.766098i	−0.211319	+	0.977417i	$0.567776\pi$
$108$		0			0
$109$		−	2.21477i		−	0.212137i	−0.994359	−	0.106068i	$-0.966174\pi$
$109$		−	2.21477i		−	0.212137i	0.994359	−	0.106068i	$-0.0338262\pi$
$110$	11.5477	−	1.40830i	1.10103	−	0.134276i
$111$		0			0
$112$	3.83305	−	1.78738i	0.362189	−	0.168892i
$113$	0.109693	−	1.25379i	0.0103190	−	0.117947i	−0.989288	−	0.145976i	$-0.953368\pi$
$113$	0.109693	−	1.25379i	0.0103190	−	0.117947i	0.999607	+	0.0280294i	$0.00892322\pi$
$114$		0			0
$115$	1.50210	+	1.99674i	0.140071	+	0.186197i
$116$	−8.76838	−	5.06243i	−0.814124	−	0.470034i
$117$		0			0
$118$	0.780099	−	2.91137i	0.0718139	−	0.268013i
$119$	19.7923	+	16.6077i	1.81435	+	1.52242i
$120$		0			0
$121$	−2.78993	−	15.8225i	−0.253630	−	1.43841i
$122$	4.38515	−	6.26265i	0.397013	−	0.566993i
$123$		0			0
$124$	−2.29618	+	2.73648i	−0.206203	+	0.245743i
$125$	−6.54944	−	9.06117i	−0.585800	−	0.810456i
$126$		0			0
$127$	−1.93774	−	7.23174i	−0.171947	−	0.641713i	−0.997052	−	0.0767340i	$-0.975551\pi$
$127$	−1.93774	−	7.23174i	−0.171947	−	0.641713i	0.825105	−	0.564979i	$-0.191116\pi$
$128$	0.422618	−	0.906308i	0.0373545	−	0.0801070i
$129$		0			0
$130$	0.822272	−	0.174077i	0.0721180	−	0.0152676i
$131$	−4.22294	+	11.6024i	−0.368960	+	1.01371i	0.606797	+	0.794856i	$0.292454\pi$
$131$	−4.22294	+	11.6024i	−0.368960	+	1.01371i	−0.975758	+	0.218853i	$0.929768\pi$
$132$		0			0
$133$	11.7296	−	8.21316i	1.01709	−	0.712171i
$134$	−0.244000			−0.0210784
$135$		0			0
$136$	6.10904			0.523846
$137$	−10.4036	+	7.28471i	−0.888843	+	0.622374i	−0.926243	−	0.376926i	$-0.876981\pi$
$137$	−10.4036	+	7.28471i	−0.888843	+	0.622374i	0.0374006	+	0.999300i	$0.488092\pi$
$138$		0			0
$139$	1.49351	−	4.10338i	0.126678	−	0.348045i	−0.860099	−	0.510126i	$-0.829599\pi$
$139$	1.49351	−	4.10338i	0.126678	−	0.348045i	0.986777	+	0.162082i	$0.0518209\pi$
$140$	−5.15714	+	7.92711i	−0.435858	+	0.669963i
$141$		0			0
$142$	0.0258794	−	0.0554986i	0.00217175	−	0.00465734i
$143$	−0.506132	−	1.88891i	−0.0423249	−	0.157959i
$144$		0			0
$145$	22.6267	−	0.771628i	1.87905	−	0.0640802i
$146$	−4.25011	+	5.06508i	−0.351741	+	0.419189i
$147$		0			0
$148$	3.34897	−	4.78283i	0.275284	−	0.393146i
$149$	−0.130359	−	0.739301i	−0.0106794	−	0.0605659i	0.979002	−	0.203849i	$-0.0653452\pi$
$149$	−0.130359	−	0.739301i	−0.0106794	−	0.0605659i	−0.989682	+	0.143283i	$0.954234\pi$
$150$		0			0
$151$	1.91410	+	1.60612i	0.155767	+	0.130704i	0.717340	−	0.696723i	$-0.245359\pi$
$151$	1.91410	+	1.60612i	0.155767	+	0.130704i	−0.561573	+	0.827427i	$0.689804\pi$
$152$	0.876286	−	3.27034i	0.0710762	−	0.265260i
$153$		0			0
$154$	19.0553	+	11.0016i	1.53552	+	0.886534i
$155$	1.11814	−	7.90907i	0.0898111	−	0.635272i
$156$		0			0
$157$	−0.594827	+	6.79890i	−0.0474723	+	0.542611i	0.934803	+	0.355167i	$0.115576\pi$
$157$	−0.594827	+	6.79890i	−0.0474723	+	0.542611i	−0.982275	+	0.187444i	$0.939980\pi$
$158$	4.74717	−	2.21364i	0.377665	−	0.176108i
$159$		0			0
$160$	0.270694	+	2.21962i	0.0214003	+	0.175477i
$161$			4.72596i			0.372458i
$162$		0			0
$163$	−0.670477	−	0.670477i	−0.0525158	−	0.0525158i	0.680361	−	0.732877i	$-0.261823\pi$
$163$	−0.670477	−	0.670477i	−0.0525158	−	0.0525158i	−0.732877	+	0.680361i	$0.761823\pi$
$164$	−0.841337	+	4.77146i	−0.0656974	+	0.372588i
$165$		0			0
$166$	−4.48804	−	1.63351i	−0.348340	−	0.126785i
$167$	4.99662	+	0.437147i	0.386650	+	0.0338275i	0.278824	−	0.960342i	$-0.410055\pi$
$167$	4.99662	+	0.437147i	0.386650	+	0.0338275i	0.107826	+	0.994170i	$0.465611\pi$
$168$		0			0
$169$	4.39794	+	12.0832i	0.338303	+	0.929480i
$170$	−11.5904	+	7.22934i	−0.888946	+	0.554465i
$171$		0			0
$172$	6.32199	+	1.69397i	0.482047	+	0.129164i
$173$	−5.65464	+	0.494717i	−0.429915	+	0.0376127i	−0.300060	−	0.953920i	$-0.597007\pi$
$173$	−5.65464	+	0.494717i	−0.429915	+	0.0376127i	−0.129855	+	0.991533i	$0.541451\pi$
$174$		0			0
$175$	0.403616	−	21.1427i	0.0305105	−	1.59824i
$176$	5.12351	−	0.903414i	0.386199	−	0.0680974i
$177$		0			0
$178$	−0.808587	−	9.24219i	−0.0606061	−	0.692731i
$179$	7.12420	+	12.3395i	0.532488	+	0.922296i	0.999280	+	0.0379289i	$0.0120760\pi$
$179$	7.12420	+	12.3395i	0.532488	+	0.922296i	−0.466793	+	0.884367i	$0.654591\pi$
$180$		0			0
$181$	−6.55430	+	11.3524i	−0.487177	+	0.843816i	−0.999891	−	0.0147438i	$-0.995307\pi$
$181$	−6.55430	+	11.3524i	−0.487177	+	0.843816i	0.512714	+	0.858559i	$0.328640\pi$
$182$	1.44077	+	0.671843i	0.106797	+	0.0498004i
$183$		0			0
$184$	0.718272	+	0.856003i	0.0529517	+	0.0631054i
$185$	−0.693945	+	13.0374i	−0.0510199	+	0.958528i
$186$		0			0
$187$	18.2297	+	26.0348i	1.33309	+	1.90385i
$188$	5.18972	−	5.18972i	0.378499	−	0.378499i
$189$		0			0
$190$	2.20753	+	7.24168i	0.160151	+	0.525367i
$191$	−1.41468	−	0.249446i	−0.102363	−	0.0180493i	0.122232	−	0.992502i	$-0.460995\pi$
$191$	−1.41468	−	0.249446i	−0.102363	−	0.0180493i	−0.224595	+	0.974452i	$0.572106\pi$
$192$		0			0
$193$	8.30860	+	17.8178i	0.598066	+	1.28256i	0.939467	+	0.342639i	$0.111321\pi$
$193$	8.30860	+	17.8178i	0.598066	+	1.28256i	−0.341401	+	0.939918i	$0.610902\pi$
$194$	11.9968	−	10.0665i	0.861320	−	0.722733i
$195$		0			0
$196$	−10.2305	+	3.72358i	−0.730747	+	0.265970i
$197$	−19.0913	+	5.11551i	−1.36020	+	0.364465i	−0.863890	−	0.503680i	$-0.831979\pi$
$197$	−19.0913	+	5.11551i	−1.36020	+	0.364465i	−0.496311	+	0.868145i	$0.665312\pi$
$198$		0			0
$199$	−6.74271	+	3.89290i	−0.477978	+	0.275961i	−0.719573	−	0.694416i	$-0.755663\pi$
$199$	−6.74271	+	3.89290i	−0.477978	+	0.275961i	0.241596	+	0.970377i	$0.422329\pi$
$200$	−3.14025	−	3.89087i	−0.222049	−	0.275126i
$201$		0			0
$202$	−7.20849	−	5.04744i	−0.507188	−	0.355137i
$203$	35.0770	+	24.5612i	2.46192	+	1.72386i
$204$		0			0
$205$	−4.05024	−	10.0483i	−0.282881	−	0.701806i
$206$	0.00151792		0.000876370i	0.000105758		6.10596e-5i
$207$		0			0
$208$	0.363074	−	0.0972853i	0.0251746	−	0.00674552i
$209$	16.5521	−	6.02446i	1.14493	−	0.416721i
$210$		0			0
$211$	0.399400	−	0.335137i	0.0274959	−	0.0230718i	−0.628936	−	0.777457i	$-0.716509\pi$
$211$	0.399400	−	0.335137i	0.0274959	−	0.0230718i	0.656432	+	0.754385i	$0.272065\pi$
$212$	3.82091	+	8.19397i	0.262421	+	0.562764i
$213$		0			0
$214$	−11.0368	−	1.94608i	−0.754459	−	0.133032i
$215$	−13.9991	+	4.26745i	−0.954730	+	0.291037i
$216$		0			0
$217$	10.6830	−	10.6830i	0.725207	−	0.725207i
$218$	1.27034	+	1.81424i	0.0860384	+	0.122876i
$219$		0			0
$220$	−8.65156	+	7.77710i	−0.583288	+	0.524332i
$221$	1.47602	+	1.75905i	0.0992876	+	0.118326i
$222$		0			0
$223$	7.85795	+	3.66422i	0.526208	+	0.245375i	0.667522	−	0.744590i	$-0.267355\pi$
$223$	7.85795	+	3.66422i	0.526208	+	0.245375i	−0.141314	+	0.989965i	$0.545133\pi$
$224$	−2.11465	+	3.66269i	−0.141291	+	0.244723i
$225$		0			0
$226$	0.629291	+	1.08996i	0.0418598	+	0.0725033i
$227$	−0.540947	−	6.18305i	−0.0359039	−	0.410383i	−0.992785	−	0.119905i	$-0.961741\pi$
$227$	−0.540947	−	6.18305i	−0.0359039	−	0.410383i	0.956882	−	0.290479i	$-0.0938145\pi$
$228$		0			0
$229$	23.6091	−	4.16292i	1.56013	−	0.275093i	0.674073	−	0.738665i	$-0.264543\pi$
$229$	23.6091	−	4.16292i	1.56013	−	0.275093i	0.886060	+	0.463571i	$0.153432\pi$
$230$	−2.37573	−	0.774069i	−0.156651	−	0.0510406i
$231$		0			0
$232$	10.0863	−	0.882439i	0.662200	−	0.0579350i
$233$	11.2846	+	3.02370i	0.739278	+	0.198089i	0.608757	−	0.793357i	$-0.291668\pi$
$233$	11.2846	+	3.02370i	0.739278	+	0.198089i	0.130521	+	0.991446i	$0.458335\pi$
$234$		0			0
$235$	−3.70481	+	15.9877i	−0.241675	+	1.04292i
$236$	1.03087	+	2.83230i	0.0671041	+	0.184367i
$237$		0			0
$238$	−25.7387	−	2.25184i	−1.66839	−	0.145965i
$239$	−17.3288	−	6.30716i	−1.12091	−	0.407976i	−0.285923	−	0.958253i	$-0.592300\pi$
$239$	−17.3288	−	6.30716i	−1.12091	−	0.407976i	−0.834983	+	0.550276i	$0.814522\pi$
$240$		0			0
$241$	0.864030	−	4.90016i	0.0556571	−	0.315647i	−0.944251	−	0.329227i	$-0.893212\pi$
$241$	0.864030	−	4.90016i	0.0556571	−	0.315647i	0.999908	+	0.0135803i	$0.00432289\pi$
$242$	11.3608	+	11.3608i	0.730298	+	0.730298i
$243$		0			0
$244$			7.64528i			0.489439i
$245$	15.0034	−	19.1712i	0.958533	−	1.22480i
$246$		0			0
$247$	1.15339	−	0.537835i	0.0733885	−	0.0342216i
$248$	0.311339	−	3.55862i	0.0197700	−	0.225973i
$249$		0			0
$250$	10.5623	+	3.66587i	0.668016	+	0.231850i
$251$	−11.3319	−	6.54248i	−0.715264	−	0.412958i	0.0977433	−	0.995212i	$-0.468838\pi$
$251$	−11.3319	−	6.54248i	−0.715264	−	0.412958i	−0.813007	+	0.582254i	$0.802171\pi$
$252$		0			0
$253$	−1.50465	+	5.61541i	−0.0945962	+	0.353038i
$254$	5.73526	+	4.81246i	0.359862	+	0.301960i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−1.16005	+	1.65673i	−0.0723622	+	0.103344i	−0.853702	−	0.520762i	$-0.825648\pi$
$257$	−1.16005	+	1.65673i	−0.0723622	+	0.103344i	0.781340	+	0.624106i	$0.214537\pi$
$258$		0			0
$259$	−15.8729	+	18.9166i	−0.986295	+	1.17542i
$260$	−0.573719	+	0.614231i	−0.0355806	+	0.0380930i
$261$		0			0
$262$	−3.19565	−	11.9263i	−0.197428	−	0.736812i
$263$	4.72696	−	10.1370i	0.291477	−	0.625074i	−0.704976	−	0.709232i	$-0.749042\pi$
$263$	4.72696	−	10.1370i	0.291477	−	0.625074i	0.996452	+	0.0841574i	$0.0268198\pi$
$264$		0			0
$265$	−16.9459	−	11.0245i	−1.04098	−	0.677229i
$266$	−4.89746	+	13.4556i	−0.300282	+	0.825019i
$267$		0			0
$268$	0.199873	−	0.139953i	0.0122092	−	0.00854896i
$269$	9.40361			0.573348			0.286674	−	0.958028i	$-0.407450\pi$
$269$	9.40361			0.573348			0.286674	+	0.958028i	$0.407450\pi$
$270$		0			0
$271$	−1.37745			−0.0836741			−0.0418370	−	0.999124i	$-0.513321\pi$
$271$	−1.37745			−0.0836741			−0.0418370	+	0.999124i	$0.513321\pi$
$272$	−5.00423	+	3.50400i	−0.303426	+	0.212461i
$273$		0			0
$274$	4.34383	−	11.9346i	0.262420	−	0.720993i
$275$	7.21095	−	24.9933i	0.434837	−	1.50715i
$276$		0			0
$277$	12.2207	−	26.2073i	0.734269	−	1.57465i	−0.0817715	−	0.996651i	$-0.526058\pi$
$277$	12.2207	−	26.2073i	0.734269	−	1.57465i	0.816041	−	0.577994i	$-0.196164\pi$
$278$	1.13019	+	4.21794i	0.0677845	+	0.252975i
$279$		0			0
$280$	−0.322321	−	9.45152i	−0.0192624	−	0.564836i
$281$	20.9375	−	24.9523i	1.24903	−	1.48853i	0.443151	−	0.896447i	$-0.353860\pi$
$281$	20.9375	−	24.9523i	1.24903	−	1.48853i	0.805875	−	0.592085i	$-0.201695\pi$
$282$		0			0
$283$	−15.0389	+	21.4778i	−0.893970	+	1.27672i	0.0663434	+	0.997797i	$0.478867\pi$
$283$	−15.0389	+	21.4778i	−0.893970	+	1.27672i	−0.960313	+	0.278924i	$0.910022\pi$
$284$	0.0106335	+	0.0603057i	0.000630983	+	0.00357848i
$285$		0			0
$286$	1.49803	+	1.25700i	0.0885805	+	0.0743279i
$287$	5.30353	−	19.7930i	0.313057	−	1.16835i
$288$		0			0
$289$	−17.5979	−	10.1602i	−1.03517	−	0.597657i
$290$	−18.0921	+	13.6102i	−1.06241	+	0.799220i
$291$		0			0
$292$	0.576273	−	6.58683i	0.0337238	−	0.385465i
$293$	21.1017	−	9.83988i	1.23277	−	0.574852i	0.306561	−	0.951851i	$-0.400822\pi$
$293$	21.1017	−	9.83988i	1.23277	−	0.574852i	0.926214	+	0.376999i	$0.123044\pi$
$294$		0			0
$295$	−5.30754	−	4.15369i	−0.309017	−	0.241837i
$296$			5.83875i			0.339371i
$297$		0			0
$298$	0.530829	+	0.530829i	0.0307501	+	0.0307501i
$299$	−0.0729361	+	0.413641i	−0.00421800	+	0.0239215i
$300$		0			0
$301$	−26.0115	−	9.46740i	−1.49928	−	0.545692i
$302$	−2.48917	−	0.217774i	−0.143235	−	0.0125315i
$303$		0			0
$304$	1.15798	+	3.18153i	0.0664148	+	0.182473i
$305$	−9.04731	−	14.5051i	−0.518047	−	0.830559i
$306$		0			0
$307$	−14.1397	−	3.78873i	−0.806997	−	0.216234i	−0.168343	−	0.985728i	$-0.553842\pi$
$307$	−14.1397	−	3.78873i	−0.806997	−	0.216234i	−0.638654	+	0.769494i	$0.720508\pi$
$308$	−21.9195	+	1.91770i	−1.24898	+	0.109271i
$309$		0			0
$310$	3.62053	+	7.12007i	0.205632	+	0.404393i
$311$	−13.9613	+	2.46175i	−0.791672	+	0.139593i	−0.554840	−	0.831957i	$-0.687220\pi$
$311$	−13.9613	+	2.46175i	−0.791672	+	0.139593i	−0.236833	+	0.971550i	$0.576109\pi$
$312$		0			0
$313$	0.580982	+	6.64066i	0.0328391	+	0.375352i	0.994776	+	0.102081i	$0.0325501\pi$
$313$	0.580982	+	6.64066i	0.0328391	+	0.375352i	−0.961937	+	0.273271i	$0.911894\pi$
$314$	−3.41244	−	5.91051i	−0.192575	−	0.333550i
$315$		0			0
$316$	−2.61896	+	4.53618i	−0.147328	+	0.255180i
$317$	−5.98543	−	2.79105i	−0.336175	−	0.156761i	0.247199	−	0.968965i	$-0.420490\pi$
$317$	−5.98543	−	2.79105i	−0.336175	−	0.156761i	−0.583374	+	0.812204i	$0.698268\pi$
$318$		0			0
$319$	33.8589	+	40.3515i	1.89573	+	2.25925i
$320$	−1.49486	−	1.66294i	−0.0835654	−	0.0929614i
$321$		0			0
$322$	−2.71070	−	3.87128i	−0.151061	−	0.215738i
$323$	−14.6254	+	14.6254i	−0.813779	+	0.813779i
$324$		0			0
$325$	0.361623	−	1.84429i	0.0200592	−	0.102303i
$326$	0.933793	+	0.164653i	0.0517180	+	0.00911928i
$327$		0			0
$328$	−2.04761	−	4.39112i	−0.113061	−	0.242459i
$329$	−23.7783	+	19.9524i	−1.31094	+	1.10001i
$330$		0			0
$331$	8.71424	−	3.17172i	0.478978	−	0.174334i	−0.0912370	−	0.995829i	$-0.529082\pi$
$331$	8.71424	−	3.17172i	0.478978	−	0.174334i	0.570215	+	0.821495i	$0.306860\pi$
$332$	4.61333	−	1.23614i	0.253190	−	0.0678419i
$333$		0			0
$334$	−4.34373	+	2.50785i	−0.237678	+	0.137224i
$335$	−0.213593	+	0.502053i	−0.0116698	+	0.0274301i
$336$		0			0
$337$	28.8075	+	20.1713i	1.56925	+	1.09880i	0.949397	+	0.314078i	$0.101695\pi$
$337$	28.8075	+	20.1713i	1.56925	+	1.09880i	0.619849	+	0.784721i	$0.287194\pi$
$338$	−10.5332	−	7.37545i	−0.572933	−	0.401172i
$339$		0			0
$340$	5.34775	−	12.5699i	0.290022	−	0.681700i
$341$	16.0948	−	9.29232i	0.871581	−	0.503207i
$342$		0			0
$343$	15.8792	−	4.25483i	0.857399	−	0.229739i
$344$	−6.15030	+	2.23852i	−0.331602	+	0.120693i
$345$		0			0
$346$	4.34826	−	3.64862i	0.233764	−	0.196151i
$347$	7.84524	+	16.8242i	0.421155	+	0.903169i	0.996367	+	0.0851649i	$0.0271417\pi$
$347$	7.84524	+	16.8242i	0.421155	+	0.903169i	−0.575212	+	0.818004i	$0.695081\pi$
$348$		0			0
$349$	−9.68283	−	1.70734i	−0.518310	−	0.0913920i	−0.0916271	−	0.995793i	$-0.529207\pi$
$349$	−9.68283	−	1.70734i	−0.518310	−	0.0913920i	−0.426683	+	0.904401i	$0.640318\pi$
$350$	11.7963	+	17.5506i	0.630540	+	0.938117i
$351$		0			0
$352$	−3.67876	+	3.67876i	−0.196079	+	0.196079i
$353$	−1.87815	−	2.68228i	−0.0999639	−	0.142763i	0.766054	−	0.642776i	$-0.222217\pi$
$353$	−1.87815	−	2.68228i	−0.0999639	−	0.142763i	−0.866018	+	0.500013i	$0.833329\pi$
$354$		0			0
$355$	−0.0915394	−	0.101832i	−0.00485841	−	0.00540468i
$356$	5.96346	+	7.10697i	0.316063	+	0.376669i
$357$		0			0
$358$	−12.9134	−	6.02163i	−0.682496	−	0.318253i
$359$	8.24511	−	14.2809i	0.435160	−	0.753719i	−0.562149	−	0.827036i	$-0.690025\pi$
$359$	8.24511	−	14.2809i	0.435160	−	0.753719i	0.997309	+	0.0733169i	$0.0233584\pi$
$360$		0			0
$361$	−3.76848	−	6.52720i	−0.198341	−	0.343537i
$362$	−1.14249	−	13.0587i	−0.0600479	−	0.686351i
$363$		0			0
$364$	−1.56557	+	0.276051i	−0.0820579	+	0.0144690i
$365$	6.70142	+	13.1789i	0.350768	+	0.689815i
$366$		0			0
$367$	−32.6051	+	2.85258i	−1.70197	+	0.148903i	−0.896297	−	0.443455i	$-0.853753\pi$
$367$	−32.6051	+	2.85258i	−1.70197	+	0.148903i	−0.805675	+	0.592358i	$0.798197\pi$
$368$	−1.07936	−	0.289213i	−0.0562654	−	0.0150763i
$369$		0			0
$370$	−6.90949	−	11.0776i	−0.359207	−	0.575899i
$371$	−13.0779	−	35.9314i	−0.678973	−	1.86546i
$372$		0			0
$373$	−6.17963	−	0.540647i	−0.319969	−	0.0279937i	−0.0739600	−	0.997261i	$-0.523564\pi$
$373$	−6.17963	−	0.540647i	−0.319969	−	0.0279937i	−0.246009	+	0.969268i	$0.579119\pi$
$374$	−29.8659	−	10.8703i	−1.54433	−	0.562089i
$375$		0			0
$376$	−1.27447	+	7.22787i	−0.0657257	+	0.372749i
$377$	2.69107	+	2.69107i	0.138597	+	0.138597i
$378$		0			0
$379$		−	6.82213i		−	0.350429i	−0.984530	−	0.175215i	$-0.943938\pi$
$379$		−	6.82213i		−	0.350429i	0.984530	−	0.175215i	$-0.0560620\pi$
$380$	−5.96196	−	4.66585i	−0.305842	−	0.239353i
$381$		0			0
$382$	1.30191	−	0.607093i	0.0666117	−	0.0310616i
$383$	−0.301009	+	3.44055i	−0.0153808	+	0.175804i	0.984619	+	0.174718i	$0.0559013\pi$
$383$	−0.301009	+	3.44055i	−0.0153808	+	0.175804i	−0.999999	+	0.00108604i	$0.999654\pi$
$384$		0			0
$385$	39.3175	−	29.5776i	2.00381	−	1.50741i
$386$	−17.0259	−	9.82991i	−0.866596	−	0.500329i
$387$		0			0
$388$	−4.05329	+	15.1271i	−0.205775	+	0.767961i
$389$	−9.14718	−	7.67539i	−0.463780	−	0.389158i	0.380739	−	0.924682i	$-0.375669\pi$
$389$	−9.14718	−	7.67539i	−0.463780	−	0.389158i	−0.844520	+	0.535525i	$0.820114\pi$
$390$		0			0
$391$	−1.18540	−	6.72273i	−0.0599482	−	0.339983i
$392$	6.24454	−	8.91813i	0.315397	−	0.450433i
$393$		0			0
$394$	12.7046	−	15.1407i	0.640047	−	0.762778i
$395$	−0.399189	−	11.7056i	−0.0200854	−	0.588970i
$396$		0			0
$397$	0.674193	+	2.51612i	0.0338368	+	0.126280i	0.980778	−	0.195125i	$-0.0625113\pi$
$397$	0.674193	+	2.51612i	0.0338368	+	0.126280i	−0.946942	+	0.321406i	$0.895845\pi$
$398$	3.29042	−	7.05634i	0.164934	−	0.353702i
$399$		0			0
$400$	4.80405	+	1.38604i	0.240202	+	0.0693020i
$401$	−2.31034	+	6.34761i	−0.115373	+	0.316984i	−0.983917	−	0.178628i	$-0.942834\pi$
$401$	−2.31034	+	6.34761i	−0.115373	+	0.316984i	0.868544	+	0.495612i	$0.165056\pi$
$402$		0			0
$403$	1.09990	−	0.770158i	0.0547899	−	0.0383643i
$404$	8.79994			0.437814
$405$		0			0
$406$	−42.8211			−2.12518
$407$	−24.8829	+	17.4232i	−1.23340	+	0.863636i
$408$		0			0
$409$	1.32960	−	3.65304i	0.0657444	−	0.180631i	−0.902470	−	0.430752i	$-0.858248\pi$
$409$	1.32960	−	3.65304i	0.0657444	−	0.180631i	0.968215	+	0.250121i	$0.0804704\pi$
$410$	9.08125	+	5.90799i	0.448491	+	0.291775i
$411$		0			0
$412$	−0.000740740		0.00158852i	−3.64936e−5		7.82609e-5i
$413$	−3.29928	−	12.3131i	−0.162347	−	0.605886i
$414$		0			0
$415$	−7.28987	+	7.80463i	−0.357846	+	0.383114i
$416$	−0.241612	+	0.287942i	−0.0118460	+	0.0141175i
$417$		0			0
$418$	−10.1032	+	14.4288i	−0.494162	+	0.705737i
$419$	−2.47543	−	14.0389i	−0.120933	−	0.685844i	−0.983641	−	0.180141i	$-0.942344\pi$
$419$	−2.47543	−	14.0389i	−0.120933	−	0.685844i	0.862708	−	0.505703i	$-0.168767\pi$
$420$		0			0
$421$	21.8367	+	18.3232i	1.06426	+	0.893018i	0.994520	−	0.104547i	$-0.0333392\pi$
$421$	21.8367	+	18.3232i	1.06426	+	0.893018i	0.0697379	+	0.997565i	$0.477784\pi$
$422$	−0.134943	+	0.503615i	−0.00656893	+	0.0245156i
$423$		0			0
$424$	−7.82978	−	4.52052i	−0.380248	−	0.219536i
$425$	4.72900	+	30.1769i	0.229390	+	1.46379i
$426$		0			0
$427$	2.81811	−	32.2112i	0.136378	−	1.55881i
$428$	10.1570	−	4.73630i	0.490959	−	0.228938i
$429$		0			0
$430$	9.01968	−	11.5252i	0.434968	−	0.555796i
$431$			38.9178i			1.87461i	0.348515	+	0.937303i	$0.386686\pi$
$431$			38.9178i			1.87461i	−0.348515	+	0.937303i	$0.613314\pi$
$432$		0			0
$433$	8.50667	+	8.50667i	0.408804	+	0.408804i	0.881321	−	0.472517i	$-0.156655\pi$
$433$	8.50667	+	8.50667i	0.408804	+	0.408804i	−0.472517	+	0.881321i	$0.656655\pi$
$434$	−2.62347	+	14.8785i	−0.125931	+	0.714189i
$435$		0			0
$436$	−2.08121	−	0.757497i	−0.0996717	−	0.0362775i
$437$	−3.76891	−	0.329737i	−0.180291	−	0.0157734i
$438$		0			0
$439$	−12.9045	−	35.4547i	−0.615896	−	1.69216i	−0.716813	−	0.697266i	$-0.754400\pi$
$439$	−12.9045	−	35.4547i	−0.615896	−	1.69216i	0.100917	−	0.994895i	$-0.467822\pi$
$440$	2.62618	−	11.3330i	0.125198	−	0.540278i
$441$		0			0
$442$	−2.21803	−	0.594319i	−0.105501	−	0.0282689i
$443$	−37.0206	+	3.23888i	−1.75890	+	0.153884i	−0.920391	−	0.390999i	$-0.872129\pi$
$443$	−37.0206	+	3.23888i	−1.75890	+	0.153884i	−0.838512	+	0.544883i	$0.816574\pi$
$444$		0			0
$445$	−19.7245	−	6.42671i	−0.935032	−	0.304655i
$446$	−8.53857	+	1.50558i	−0.404313	+	0.0712913i
$447$		0			0
$448$	−0.368608	−	4.21321i	−0.0174151	−	0.199056i
$449$	−19.5467	−	33.8559i	−0.922466	−	1.59776i	−0.795587	−	0.605839i	$-0.792838\pi$
$449$	−19.5467	−	33.8559i	−0.922466	−	1.59776i	−0.126878	−	0.991918i	$-0.540496\pi$
$450$		0			0
$451$	12.6034	−	21.8297i	0.593469	−	1.02792i
$452$	−1.14066	−	0.531900i	−0.0536523	−	0.0250185i
$453$		0			0
$454$	3.98957	+	4.75458i	0.187240	+	0.223144i
$455$	2.64361	−	2.37641i	0.123934	−	0.111408i
$456$		0			0
$457$	5.09288	+	7.27339i	0.238235	+	0.340235i	0.920410	−	0.390954i	$-0.127855\pi$
$457$	5.09288	+	7.27339i	0.238235	+	0.340235i	−0.682175	+	0.731189i	$0.738966\pi$
$458$	−16.9517	+	16.9517i	−0.792100	+	0.792100i
$459$		0			0
$460$	2.39007	−	0.728583i	0.111438	−	0.0339704i
$461$	33.1532	+	5.84580i	1.54410	+	0.272266i	0.879851	−	0.475249i	$-0.157642\pi$
$461$	33.1532	+	5.84580i	1.54410	+	0.272266i	0.664245	+	0.747515i	$0.268753\pi$
$462$		0			0
$463$	4.18344	+	8.97141i	0.194421	+	0.416937i	0.979216	−	0.202818i	$-0.0650099\pi$
$463$	4.18344	+	8.97141i	0.194421	+	0.416937i	−0.784796	+	0.619755i	$0.787232\pi$
$464$	−7.75609	+	6.50813i	−0.360067	+	0.302132i
$465$		0			0
$466$	−10.9781	+	3.99571i	−0.508551	+	0.185098i
$467$	7.67657	−	2.05693i	0.355229	−	0.0951834i	−0.0767911	−	0.997047i	$-0.524467\pi$
$467$	7.67657	−	2.05693i	0.355229	−	0.0951834i	0.432021	+	0.901864i	$0.357801\pi$
$468$		0			0
$469$	−0.893695	+	0.515975i	−0.0412670	+	0.0238255i
$470$	−6.13535	−	15.2213i	−0.283003	−	0.702108i
$471$		0			0
$472$	−2.46898	−	1.72880i	−0.113644	−	0.0795745i
$473$	−27.8927	−	19.5307i	−1.28251	−	0.898023i
$474$		0			0
$475$	16.8329	+	1.79703i	0.772346	+	0.0824535i
$476$	22.3755	−	12.9185i	1.02558	−	0.592118i
$477$		0			0
$478$	17.8125	−	4.77286i	0.814727	−	0.218305i
$479$	−14.8140	+	5.39184i	−0.676867	+	0.246359i	−0.657502	−	0.753453i	$-0.728387\pi$
$479$	−14.8140	+	5.39184i	−0.676867	+	0.246359i	−0.0193652	+	0.999812i	$0.506165\pi$
$480$		0			0
$481$	−1.68122	+	1.41071i	−0.0766571	+	0.0643229i
$482$	2.10284	+	4.50956i	0.0957819	+	0.205405i
$483$		0			0
$484$	−15.8225	−	2.78993i	−0.719203	−	0.126815i
$485$	−10.2110	−	33.4966i	−0.463659	−	1.52100i
$486$		0			0
$487$	−6.08544	+	6.08544i	−0.275758	+	0.275758i	−0.831413	−	0.555655i	$-0.812467\pi$
$487$	−6.08544	+	6.08544i	−0.275758	+	0.275758i	0.555655	+	0.831413i	$0.312467\pi$
$488$	−4.38515	−	6.26265i	−0.198506	−	0.283497i
$489$		0			0
$490$	−1.29394	+	24.3097i	−0.0584543	+	1.09820i
$491$	19.9695	+	23.7987i	0.901209	+	1.07402i	0.996906	+	0.0786084i	$0.0250477\pi$
$491$	19.9695	+	23.7987i	0.901209	+	1.07402i	−0.0956967	+	0.995411i	$0.530508\pi$
$492$		0			0
$493$	−56.0579	−	26.1402i	−2.52472	−	1.17730i
$494$	−0.636313	+	1.10213i	−0.0286291	+	0.0495870i
$495$		0			0
$496$	1.78611	+	3.09363i	0.0801986	+	0.138908i
$497$	−0.0225721	−	0.258000i	−0.00101250	−	0.0115729i
$498$		0			0
$499$	−12.8962	+	2.27395i	−0.577313	+	0.101796i	−0.454678	−	0.890656i	$-0.650246\pi$
$499$	−12.8962	+	2.27395i	−0.577313	+	0.101796i	−0.122635	+	0.992452i	$0.539134\pi$
$500$	−10.7548	+	3.05536i	−0.480967	+	0.136640i
$501$		0			0
$502$	13.0352	−	1.14043i	0.581788	−	0.0508999i
$503$	6.77201	+	1.81455i	0.301949	+	0.0809070i	0.406613	−	0.913601i	$-0.366710\pi$
$503$	6.77201	+	1.81455i	0.301949	+	0.0809070i	−0.104664	+	0.994508i	$0.533377\pi$
$504$		0			0
$505$	−16.6958	+	10.4137i	−0.742953	+	0.463405i
$506$	−1.98833	−	5.46291i	−0.0883923	−	0.242856i
$507$		0			0
$508$	−7.45836	−	0.652522i	−0.330911	−	0.0289510i
$509$	15.4656	+	5.62900i	0.685499	+	0.249501i	0.661207	−	0.750204i	$-0.270045\pi$
$509$	15.4656	+	5.62900i	0.685499	+	0.249501i	0.0242921	+	0.999705i	$0.492267\pi$
$510$		0			0
$511$	−4.85592	+	27.5393i	−0.214813	+	1.21827i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	2.02249i		−	0.0892083i
$515$	−0.000474457	−	0.00389042i	−2.09071e−5	−	0.000171432i
$516$		0			0
$517$	−34.6060	+	16.1370i	−1.52197	+	0.709706i
$518$	2.15221	−	24.5999i	0.0945628	−	1.08086i
$519$		0			0
$520$	0.117655	−	0.832221i	0.00515950	−	0.0364953i
$521$	−0.953086	−	0.550265i	−0.0417555	−	0.0241075i	0.478977	−	0.877827i	$-0.341008\pi$
$521$	−0.953086	−	0.550265i	−0.0417555	−	0.0241075i	−0.520732	+	0.853720i	$0.674341\pi$
$522$		0			0
$523$	−0.834549	+	3.11458i	−0.0364923	+	0.136191i	−0.981769	−	0.190080i	$-0.939125\pi$
$523$	−0.834549	+	3.11458i	−0.0364923	+	0.136191i	0.945276	+	0.326271i	$0.105792\pi$
$524$	9.45840	+	7.93654i	0.413192	+	0.346709i
$525$		0			0
$526$	1.94224	+	11.0150i	0.0846859	+	0.480278i
$527$	−12.5170	+	17.8762i	−0.545251	+	0.778699i
$528$		0			0
$529$	−13.9815	+	16.6625i	−0.607891	+	0.724456i
$530$	20.2047	−	0.689030i	0.877634	−	0.0299295i
$531$		0			0
$532$	−3.70608	−	13.8313i	−0.160679	−	0.599662i
$533$	0.769660	−	1.65054i	0.0333377	−	0.0714929i
$534$		0			0
$535$	−13.6657	+	21.0057i	−0.590819	+	0.908155i
$536$	−0.0834528	+	0.229285i	−0.00360461	+	0.00990359i
$537$		0			0
$538$	−7.70299	+	5.39369i	−0.332099	+	0.232538i
$539$	56.6403			2.43967
$540$		0			0
$541$	45.1758			1.94226			0.971129	−	0.238553i	$-0.0766732\pi$
$541$	45.1758			1.94226			0.971129	+	0.238553i	$0.0766732\pi$
$542$	1.12834	−	0.790072i	0.0484664	−	0.0339365i
$543$		0			0
$544$	2.08941	−	5.74062i	0.0895829	−	0.246127i
$545$	4.84500	−	1.02570i	0.207537	−	0.0439361i
$546$		0			0
$547$	−18.1023	+	38.8206i	−0.774000	+	1.65985i	−0.0228315	+	0.999739i	$0.507268\pi$
$547$	−18.1023	+	38.8206i	−0.774000	+	1.65985i	−0.751169	+	0.660110i	$0.770510\pi$
$548$	3.28713	+	12.2677i	0.140419	+	0.524052i
$549$		0			0
$550$	8.42872	+	24.6094i	0.359402	+	1.04935i
$551$	−22.0346	+	26.2599i	−0.938707	+	1.11871i
$552$		0			0
$553$	12.7063	−	18.1465i	0.540327	−	0.771668i
$554$	5.02131	+	28.4773i	0.213335	+	1.20988i
$555$		0			0
$556$	−3.34511	−	2.80688i	−0.141864	−	0.119038i
$557$	5.41667	−	20.2153i	0.229512	−	0.856549i	−0.751035	−	0.660262i	$-0.770445\pi$
$557$	5.41667	−	20.2153i	0.229512	−	0.856549i	0.980547	−	0.196286i	$-0.0628882\pi$
$558$		0			0
$559$	−2.13055	−	1.23007i	−0.0901127	−	0.0520266i
$560$	5.68520	+	7.55736i	0.240243	+	0.319357i
$561$		0			0
$562$	−2.83892	+	32.4490i	−0.119753	+	1.36878i
$563$	33.8407	−	15.7802i	1.42621	−	0.665055i	0.452279	−	0.891877i	$-0.350611\pi$
$563$	33.8407	−	15.7802i	1.42621	−	0.665055i	0.973936	+	0.226822i	$0.0728335\pi$
$564$		0			0
$565$	2.79358	−	0.340691i	0.117527	−	0.0143330i
$566$		−	26.2195i		−	1.10209i
$567$		0			0
$568$	−0.0433004	−	0.0433004i	−0.00181684	−	0.00181684i
$569$	−4.38237	+	24.8537i	−0.183719	+	1.04192i	0.743872	+	0.668322i	$0.232987\pi$
$569$	−4.38237	+	24.8537i	−0.183719	+	1.04192i	−0.927591	+	0.373598i	$0.878124\pi$
$570$		0			0
$571$	32.0935	+	11.6811i	1.34307	+	0.488837i	0.910778	−	0.412897i	$-0.135483\pi$
$571$	32.0935	+	11.6811i	1.34307	+	0.488837i	0.432292	+	0.901734i	$0.357705\pi$
$572$	−1.94810	−	0.170437i	−0.0814542	−	0.00712632i
$573$		0			0
$574$	7.00843	+	19.2555i	0.292526	+	0.803709i
$575$	−3.67240	+	4.21069i	−0.153149	+	0.175598i
$576$		0			0
$577$	−22.6289	−	6.06339i	−0.942052	−	0.252422i	−0.245066	−	0.969506i	$-0.578810\pi$
$577$	−22.6289	−	6.06339i	−0.942052	−	0.252422i	−0.696986	+	0.717084i	$0.745476\pi$
$578$	20.2430	−	1.77103i	0.841998	−	0.0736653i
$579$		0			0
$580$	7.01370	−	21.5261i	0.291228	−	0.893821i
$581$	−19.8926	+	3.50760i	−0.825284	+	0.145520i
$582$		0			0
$583$	−4.09950	−	46.8575i	−0.169784	−	1.94064i
$584$	3.30600	+	5.72615i	0.136803	+	0.236950i
$585$		0			0
$586$	−11.6416	+	20.1638i	−0.480909	+	0.832959i
$587$	−19.1692	−	8.93875i	−0.791198	−	0.368942i	−0.0153665	−	0.999882i	$-0.504891\pi$
$587$	−19.1692	−	8.93875i	−0.791198	−	0.368942i	−0.775831	+	0.630940i	$0.782669\pi$
$588$		0			0
$589$	7.77418	+	9.26491i	0.320330	+	0.381754i
$590$	6.73014	+	0.358227i	0.277075	+	0.0147480i
$591$		0			0
$592$	−3.34897	−	4.78283i	−0.137642	−	0.196573i
$593$	1.68491	−	1.68491i	0.0691910	−	0.0691910i	−0.671664	−	0.740855i	$-0.734420\pi$
$593$	1.68491	−	1.68491i	0.0691910	−	0.0691910i	0.740855	+	0.671664i	$0.234420\pi$
$594$		0			0
$595$	−27.1646	+	50.9886i	−1.11364	+	2.09033i
$596$	−0.739301	−	0.130359i	−0.0302829	−	0.00533970i
$597$		0			0
$598$	−0.177509	−	0.380669i	−0.00725888	−	0.0155667i
$599$	−11.6914	+	9.81029i	−0.477700	+	0.400838i	−0.849594	−	0.527438i	$-0.823153\pi$
$599$	−11.6914	+	9.81029i	−0.477700	+	0.400838i	0.371894	+	0.928275i	$0.378708\pi$
$600$		0			0
$601$	43.3179	−	15.7664i	1.76697	−	0.643126i	0.766974	−	0.641678i	$-0.221761\pi$
$601$	43.3179	−	15.7664i	1.76697	−	0.643126i	0.999999	−	0.00144762i	$-0.000460792\pi$
$602$	26.7376	−	7.16433i	1.08974	−	0.291996i
$603$		0			0
$604$	2.16392	−	1.24934i	0.0880485	−	0.0508348i
$605$	33.3209	−	13.4309i	1.35469	−	0.546042i
$606$		0			0
$607$	23.6505	+	16.5602i	0.959942	+	0.672159i	0.944773	−	0.327726i	$-0.106282\pi$
$607$	23.6505	+	16.5602i	0.959942	+	0.672159i	0.0151695	+	0.999885i	$0.495171\pi$
$608$	−2.77341	−	1.94196i	−0.112477	−	0.0787570i
$609$		0			0
$610$	15.7309	+	6.69255i	0.636926	+	0.270973i
$611$	−2.38913	+	1.37937i	−0.0966539	+	0.0558032i
$612$		0			0
$613$	−26.4834	+	7.09621i	−1.06966	+	0.286613i	−0.750351	−	0.661039i	$-0.770116\pi$
$613$	−26.4834	+	7.09621i	−1.06966	+	0.286613i	−0.319304	+	0.947652i	$0.603449\pi$
$614$	13.7557	−	5.00667i	0.555135	−	0.202053i
$615$		0			0
$616$	16.8554	−	14.1434i	0.679124	−	0.569853i
$617$	0.481909	+	1.03346i	0.0194009	+	0.0416054i	0.915769	−	0.401704i	$-0.131582\pi$
$617$	0.481909	+	1.03346i	0.0194009	+	0.0416054i	−0.896369	+	0.443310i	$0.853804\pi$
$618$		0			0
$619$	36.3650	+	6.41213i	1.46163	+	0.257725i	0.847213	−	0.531254i	$-0.178279\pi$
$619$	36.3650	+	6.41213i	1.46163	+	0.257725i	0.614420	+	0.788979i	$0.289390\pi$
$620$	−7.04967	−	3.75577i	−0.283121	−	0.150835i
$621$		0			0
$622$	10.0244	−	10.0244i	0.401943	−	0.401943i
$623$	−22.5056	−	32.1414i	−0.901669	−	1.28772i
$624$		0			0
$625$	16.7889	−	18.5238i	0.671556	−	0.740953i
$626$	−4.28484	−	5.10647i	−0.171257	−	0.204096i
$627$		0			0
$628$	6.18543	+	2.88432i	0.246826	+	0.115097i
$629$	17.8346	−	30.8904i	0.711111	−	1.23168i
$630$		0			0
$631$	−23.0047	−	39.8453i	−0.915802	−	1.58622i	−0.805723	−	0.592292i	$-0.798223\pi$
$631$	−23.0047	−	39.8453i	−0.915802	−	1.58622i	−0.110078	−	0.993923i	$-0.535110\pi$
$632$	−0.456515	−	5.21799i	−0.0181592	−	0.207561i
$633$		0			0
$634$	6.50386	−	1.14681i	0.258301	−	0.0455455i
$635$	14.9226	−	7.58811i	0.592187	−	0.301125i
$636$		0			0
$637$	4.07666	−	0.356661i	0.161523	−	0.0141314i
$638$	−50.8802	−	13.6333i	−2.01437	−	0.539748i
$639$		0			0
$640$	2.17835	+	0.504786i	0.0861067	+	0.0199534i
$641$	2.49833	+	6.86411i	0.0986782	+	0.271116i	0.979203	−	0.202885i	$-0.0650317\pi$
$641$	2.49833	+	6.86411i	0.0986782	+	0.271116i	−0.880524	+	0.474001i	$0.842809\pi$
$642$		0			0
$643$	39.1523	+	3.42538i	1.54402	+	0.135084i	0.827092	−	0.562066i	$-0.189993\pi$
$643$	39.1523	+	3.42538i	1.54402	+	0.135084i	0.716925	+	0.697150i	$0.245549\pi$
$644$	4.44095	+	1.61637i	0.174998	+	0.0636941i
$645$		0			0
$646$	3.59164	−	20.3692i	0.141311	−	0.801415i
$647$	24.0132	+	24.0132i	0.944058	+	0.944058i	0.998516	−	0.0544579i	$-0.0173431\pi$
$647$	24.0132	+	24.0132i	0.944058	+	0.944058i	−0.0544579	+	0.998516i	$0.517343\pi$
$648$		0			0
$649$		−	15.6809i		−	0.615528i
$650$	0.761616	+	1.71817i	0.0298730	+	0.0673922i
$651$		0			0
$652$	−0.859359	+	0.400726i	−0.0336551	+	0.0156936i
$653$	0.161787	−	1.84923i	0.00633120	−	0.0723659i	−0.992372	−	0.123281i	$-0.960658\pi$
$653$	0.161787	−	1.84923i	0.00633120	−	0.0723659i	0.998703	+	0.0509153i	$0.0162138\pi$
$654$		0			0
$655$	−27.3370	−	3.86475i	−1.06815	−	0.151008i
$656$	4.19595	+	2.42253i	0.163824	+	0.0945840i
$657$		0			0
$658$	8.03385	−	29.9828i	0.313192	−	1.16885i
$659$	−7.92888	−	6.65312i	−0.308865	−	0.259169i	0.475158	−	0.879901i	$-0.342391\pi$
$659$	−7.92888	−	6.65312i	−0.308865	−	0.259169i	−0.784023	+	0.620732i	$0.786835\pi$
$660$		0			0
$661$	4.12789	+	23.4104i	0.160556	+	0.910561i	0.953529	+	0.301303i	$0.0974215\pi$
$661$	4.12789	+	23.4104i	0.160556	+	0.910561i	−0.792972	+	0.609258i	$0.791467\pi$
$662$	−5.31906	+	7.59641i	−0.206731	+	0.295243i
$663$		0			0
$664$	−3.07000	+	3.65868i	−0.119139	+	0.141985i
$665$	23.3991	+	21.8558i	0.907380	+	0.847533i
$666$		0			0
$667$	−2.92824	−	10.9283i	−0.113382	−	0.423147i
$668$	2.11973	−	4.54577i	0.0820147	−	0.175881i
$669$		0			0
$670$	−0.113000	−	0.533770i	−0.00436559	−	0.0206213i
$671$	13.6038	−	37.3762i	0.525170	−	1.44289i
$672$		0			0
$673$	5.79958	−	4.06091i	0.223558	−	0.156537i	−0.456432	−	0.889758i	$-0.650873\pi$
$673$	5.79958	−	4.06091i	0.223558	−	0.156537i	0.679990	+	0.733221i	$0.261984\pi$
$674$	−35.1675			−1.35460
$675$		0			0
$676$	12.8587			0.494566
$677$	−19.3267	+	13.5327i	−0.742787	+	0.520105i	−0.882630	−	0.470068i	$-0.844229\pi$
$677$	−19.3267	+	13.5327i	−0.742787	+	0.520105i	0.139843	+	0.990174i	$0.455340\pi$
$678$		0			0
$679$	22.6533	−	62.2395i	0.869355	−	2.38853i
$680$	2.82920	+	13.3640i	0.108495	+	0.512487i
$681$		0			0
$682$	−7.85421	+	16.8434i	−0.300753	+	0.644967i
$683$	12.1872	+	45.4832i	0.466330	+	1.74037i	0.652442	+	0.757839i	$0.273745\pi$
$683$	12.1872	+	45.4832i	0.466330	+	1.74037i	−0.186112	+	0.982529i	$0.559589\pi$
$684$		0			0
$685$	−20.7540	−	19.3852i	−0.792970	−	0.740669i
$686$	−10.5670	+	12.5933i	−0.403452	+	0.480815i
$687$		0			0
$688$	3.75406	−	5.36136i	0.143122	−	0.204400i
$689$	−0.590119	−	3.34673i	−0.0224818	−	0.127500i
$690$		0			0
$691$	12.4777	+	10.4701i	0.474675	+	0.398300i	0.848497	−	0.529201i	$-0.177508\pi$
$691$	12.4777	+	10.4701i	0.474675	+	0.398300i	−0.373821	+	0.927501i	$0.621953\pi$
$692$	−1.46912	+	5.48283i	−0.0558476	+	0.208426i
$693$		0			0
$694$	−16.0764	−	9.28171i	−0.610252	−	0.352329i
$695$	9.66817	+	1.36683i	0.366734	+	0.0518468i
$696$		0			0
$697$	−2.57970	+	29.4861i	−0.0977129	+	1.11686i
$698$	8.91100	−	4.15527i	0.337286	−	0.157279i
$699$		0			0
$700$	−19.7296	−	7.61050i	−0.745708	−	0.287650i
$701$			20.7744i			0.784637i	0.919829	+	0.392319i	$0.128327\pi$
$701$			20.7744i			0.784637i	−0.919829	+	0.392319i	$0.871673\pi$
$702$		0			0
$703$	−13.9783	−	13.9783i	−0.527202	−	0.527202i
$704$	0.903414	−	5.12351i	0.0340487	−	0.193100i
$705$		0			0
$706$	3.07698	+	1.11993i	0.115804	+	0.0421491i
$707$	−37.0760	−	3.24373i	−1.39439	−	0.121993i
$708$		0			0
$709$	13.3009	+	36.5440i	0.499527	+	1.37244i	0.891733	+	0.452561i	$0.149490\pi$
$709$	13.3009	+	36.5440i	0.499527	+	1.37244i	−0.392207	+	0.919877i	$0.628288\pi$
$710$	0.133393	+	0.0309111i	0.00500616	+	0.00116007i
$711$		0			0
$712$	−8.96137	−	2.40119i	−0.335842	−	0.0899885i
$713$	−3.97652	+	0.347900i	−0.148922	+	0.0130290i
$714$		0			0
$715$	3.89775	−	1.98199i	0.145768	−	0.0741223i
$716$	14.0319	−	2.47421i	0.524398	−	0.0924655i
$717$		0			0
$718$	1.43722	+	16.4275i	0.0536365	+	0.613067i
$719$	−6.20709	−	10.7510i	−0.231485	−	0.400945i	0.726760	−	0.686891i	$-0.241025\pi$
$719$	−6.20709	−	10.7510i	−0.231485	−	0.400945i	−0.958245	+	0.285947i	$0.907692\pi$
$720$		0			0
$721$	0.00370644	−	0.00641974i	0.000138035	−	0.000239083i
$722$	6.83081	+	3.18526i	0.254216	+	0.118543i
$723$		0			0
$724$	8.42604	+	10.0418i	0.313151	+	0.373199i
$725$	12.1668	+	49.1405i	0.451864	+	1.82503i
$726$		0			0
$727$	−7.81380	−	11.1593i	−0.289798	−	0.413874i	0.647684	−	0.761909i	$-0.275738\pi$
$727$	−7.81380	−	11.1593i	−0.289798	−	0.413874i	−0.937481	+	0.348035i	$0.886849\pi$
$728$	1.12410	−	1.12410i	0.0416619	−	0.0416619i
$729$		0			0
$730$	−13.0486	−	6.95174i	−0.482950	−	0.257295i
$731$	39.3763	+	6.94310i	1.45638	+	0.256800i
$732$		0			0
$733$	7.31307	+	15.6829i	0.270115	+	0.579263i	0.993840	−	0.110826i	$-0.0353495\pi$
$733$	7.31307	+	15.6829i	0.270115	+	0.579263i	−0.723725	+	0.690088i	$0.757572\pi$
$734$	25.0724	−	21.0382i	0.925437	−	0.776534i
$735$		0			0
$736$	1.05004	−	0.382184i	0.0387051	−	0.0140875i
$737$	−1.22617	+	0.328551i	−0.0451665	+	0.0121023i
$738$		0			0
$739$	−28.8265	+	16.6430i	−1.06040	+	0.612223i	−0.925543	−	0.378642i	$-0.876391\pi$
$739$	−28.8265	+	16.6430i	−1.06040	+	0.612223i	−0.134858	+	0.990865i	$0.543058\pi$
$740$	12.0138	+	5.11115i	0.441636	+	0.187889i
$741$		0			0
$742$	31.3222	+	21.9320i	1.14987	+	0.805151i
$743$	14.7359	+	10.3182i	0.540607	+	0.378537i	0.811753	−	0.584001i	$-0.198514\pi$
$743$	14.7359	+	10.3182i	0.540607	+	0.378537i	−0.271146	+	0.962538i	$0.587402\pi$
$744$		0			0
$745$	1.55691	−	0.627553i	0.0570408	−	0.0229918i
$746$	5.37216	−	3.10162i	0.196689	−	0.113558i
$747$		0			0
$748$	30.6996	−	8.22594i	1.12249	−	0.300770i
$749$	−44.5396	+	16.2111i	−1.62744	+	0.592340i
$750$		0			0
$751$	15.4184	−	12.9376i	0.562627	−	0.472100i	−0.316563	−	0.948571i	$-0.602529\pi$
$751$	15.4184	−	12.9376i	0.562627	−	0.472100i	0.879190	+	0.476471i	$0.158084\pi$
$752$	−3.10175	−	6.65173i	−0.113109	−	0.242563i
$753$		0			0
$754$	−3.74793	−	0.660860i	−0.136491	−	0.0240671i
$755$	−2.62707	+	4.93106i	−0.0956087	+	0.179460i
$756$		0			0
$757$	−18.5041	+	18.5041i	−0.672541	+	0.672541i	−0.958301	−	0.285760i	$-0.907754\pi$
$757$	−18.5041	+	18.5041i	−0.672541	+	0.672541i	0.285760	+	0.958301i	$0.407754\pi$
$758$	3.91301	+	5.58836i	0.142127	+	0.202979i
$759$		0			0
$760$	7.55998	+	0.402397i	0.274229	+	0.0145965i
$761$	−13.7056	−	16.3338i	−0.496829	−	0.592098i	0.458111	−	0.888895i	$-0.348526\pi$
$761$	−13.7056	−	16.3338i	−0.496829	−	0.592098i	−0.954941	+	0.296797i	$0.904082\pi$
$762$		0			0
$763$	8.48934	+	3.95864i	0.307335	+	0.143313i
$764$	−0.718252	+	1.24405i	−0.0259854	+	0.0450081i
$765$		0			0
$766$	−1.72684	−	2.99098i	−0.0623934	−	0.108069i
$767$	−0.0987416	−	1.12862i	−0.00356535	−	0.0407522i
$768$		0			0
$769$	−13.6805	+	2.41225i	−0.493332	+	0.0869878i	−0.414779	−	0.909922i	$-0.636141\pi$
$769$	−13.6805	+	2.41225i	−0.493332	+	0.0869878i	−0.0785532	+	0.996910i	$0.525030\pi$
$770$	−15.2421	+	46.7801i	−0.549286	+	1.68584i
$771$		0			0
$772$	19.5850	−	1.71347i	0.704880	−	0.0616690i
$773$	26.7372	+	7.16421i	0.961671	+	0.257679i	0.705307	−	0.708902i	$-0.250809\pi$
$773$	26.7372	+	7.16421i	0.961671	+	0.257679i	0.256363	+	0.966580i	$0.417476\pi$
$774$		0			0
$775$	17.8196	−	1.21680i	0.640098	−	0.0437088i
$776$	−5.35628	−	14.7163i	−0.192279	−	0.528283i
$777$		0			0
$778$	11.8954	+	1.04071i	0.426469	+	0.0373112i
$779$	15.4147	+	5.61050i	0.552289	+	0.201017i
$780$		0			0
$781$	0.0553214	−	0.313743i	0.00197956	−	0.0112266i
$782$	4.82702	+	4.82702i	0.172614	+	0.172614i
$783$		0			0
$784$			10.8870i			0.388822i
$785$	−15.1486	+	1.84745i	−0.540678	+	0.0659384i
$786$		0			0
$787$	3.50081	−	1.63245i	0.124790	−	0.0581906i	−0.359220	−	0.933253i	$-0.616957\pi$
$787$	3.50081	−	1.63245i	0.124790	−	0.0581906i	0.484011	+	0.875062i	$0.339180\pi$
$788$	−1.72262	+	19.6896i	−0.0613657	+	0.701413i
$789$		0			0
$790$	7.04103	+	9.35966i	0.250508	+	0.333002i
$791$	4.60979	+	2.66146i	0.163905	+	0.0946308i
$792$		0			0
$793$	0.743773	−	2.77580i	0.0264122	−	0.0985715i
$794$	−1.99545	−	1.67438i	−0.0708160	−	0.0594217i
$795$		0			0
$796$	1.35199	+	7.66752i	0.0479201	+	0.271768i
$797$	−7.23990	+	10.3397i	−0.256451	+	0.366249i	−0.926646	−	0.375935i	$-0.877321\pi$
$797$	−7.23990	+	10.3397i	−0.256451	+	0.366249i	0.670195	+	0.742185i	$0.266210\pi$
$798$		0			0
$799$	28.8203	−	34.3467i	1.01959	−	1.21510i
$800$	−4.73025	+	1.62011i	−0.167239	+	0.0572796i
$801$		0			0
$802$	−1.74832	−	6.52481i	−0.0617353	−	0.230399i
$803$	−14.5377	+	31.1763i	−0.513026	+	1.10019i
$804$		0			0
$805$	−10.3384	+	2.18867i	−0.364382	+	0.0771406i
$806$	−0.459240	+	1.26175i	−0.0161761	+	0.0444433i
$807$		0			0
$808$	−7.20849	+	5.04744i	−0.253594	+	0.177568i
$809$	−9.03399			−0.317618			−0.158809	−	0.987309i	$-0.550765\pi$
$809$	−9.03399			−0.317618			−0.158809	+	0.987309i	$0.550765\pi$
$810$		0			0
$811$	−18.4143			−0.646613			−0.323307	−	0.946294i	$-0.604795\pi$
$811$	−18.4143			−0.646613			−0.323307	+	0.946294i	$0.604795\pi$
$812$	35.0770	−	24.5612i	1.23096	−	0.861928i
$813$		0			0
$814$	10.3893	−	28.5445i	0.364146	−	1.00048i
$815$	1.15622	−	1.77723i	0.0405005	−	0.0622538i
$816$		0			0
$817$	9.36501	−	20.0833i	0.327640	−	0.702627i
$818$	1.00616	+	3.75502i	0.0351794	+	0.131291i
$819$		0			0
$820$	−10.8276	+	0.369249i	−0.378116	+	0.0128947i
$821$	2.83979	−	3.38433i	0.0991094	−	0.118114i	−0.714210	−	0.699932i	$-0.753214\pi$
$821$	2.83979	−	3.38433i	0.0991094	−	0.118114i	0.813319	+	0.581818i	$0.197658\pi$
$822$		0			0
$823$	−23.3920	+	33.4072i	−0.815394	+	1.16450i	0.168492	+	0.985703i	$0.446110\pi$
$823$	−23.3920	+	33.4072i	−0.815394	+	1.16450i	−0.983885	+	0.178800i	$0.942779\pi$
$824$	−0.000304360	−	0.00172611i	−1.06029e−5	−	6.01320e-5i
$825$		0			0
$826$	9.76509	+	8.19389i	0.339771	+	0.285102i
$827$	0.320175	−	1.19491i	0.0111336	−	0.0415511i	−0.960136	−	0.279535i	$-0.909820\pi$
$827$	0.320175	−	1.19491i	0.0111336	−	0.0415511i	0.971269	+	0.237984i	$0.0764865\pi$
$828$		0			0
$829$	16.1883	+	9.34633i	0.562243	+	0.324611i	0.754045	−	0.656822i	$-0.228100\pi$
$829$	16.1883	+	9.34633i	0.562243	+	0.324611i	−0.191802	+	0.981434i	$0.561433\pi$
$830$	1.49496	−	10.5745i	0.0518908	−	0.367045i
$831$		0			0
$832$	0.0327602	−	0.374451i	0.00113576	−	0.0129818i
$833$	−60.2778	+	28.1080i	−2.08850	+	0.973885i
$834$		0			0
$835$	1.35772	+	11.1330i	0.0469859	+	0.385272i
$836$		−	17.6143i		−	0.609205i
$837$		0			0
$838$	10.0801	+	10.0801i	0.348212	+	0.348212i
$839$	−0.681446	+	3.86467i	−0.0235261	+	0.133423i	−0.994309	−	0.106538i	$-0.966024\pi$
$839$	−0.681446	+	3.86467i	−0.0235261	+	0.133423i	0.970783	+	0.239961i	$0.0771346\pi$
$840$		0			0
$841$	−69.0793	−	25.1428i	−2.38204	−	0.866993i
$842$	−28.3974	−	2.48445i	−0.978638	−	0.0856197i
$843$		0			0
$844$	−0.178323	−	0.489937i	−0.00613811	−	0.0168643i
$845$	−24.3963	+	15.2168i	−0.839259	+	0.523474i
$846$		0			0
$847$	65.6350	+	17.5869i	2.25525	+	0.604292i
$848$	9.00664	−	0.787979i	0.309289	−	0.0270593i
$849$		0			0
$850$	−21.1825	−	22.0070i	−0.726555	−	0.754835i
$851$	6.42529	−	1.13295i	0.220256	−	0.0388371i
$852$		0			0
$853$	−4.22873	−	48.3346i	−0.144789	−	1.65494i	−0.627096	−	0.778942i	$-0.715757\pi$
$853$	−4.22873	−	48.3346i	−0.144789	−	1.65494i	0.482307	−	0.876002i	$-0.339799\pi$
$854$	16.1671	+	28.0023i	0.553227	+	0.958217i
$855$		0			0
$856$	−5.60352	+	9.70559i	−0.191524	+	0.331730i
$857$	47.8835	+	22.3284i	1.63567	+	0.762725i	0.999958	−	0.00920138i	$-0.00292893\pi$
$857$	47.8835	+	22.3284i	1.63567	+	0.762725i	0.635712	+	0.771927i	$0.280707\pi$
$858$		0			0
$859$	−15.5714	−	18.5573i	−0.531291	−	0.633168i	0.431921	−	0.901912i	$-0.357836\pi$
$859$	−15.5714	−	18.5573i	−0.531291	−	0.633168i	−0.963212	+	0.268744i	$0.913392\pi$
$860$	−0.777885	+	14.6144i	−0.0265257	+	0.498347i
$861$		0			0
$862$	−22.3224	−	31.8796i	−0.760302	−	1.08582i
$863$	−13.3492	+	13.3492i	−0.454411	+	0.454411i	−0.896816	−	0.442405i	$-0.854126\pi$
$863$	−13.3492	+	13.3492i	−0.454411	+	0.454411i	0.442405	+	0.896816i	$0.354126\pi$
$864$		0			0
$865$	−3.70100	−	12.1409i	−0.125838	−	0.412803i
$866$	−11.8475	−	2.08903i	−0.402594	−	0.0709881i
$867$		0			0
$868$	−6.38491	−	13.6925i	−0.216718	−	0.464753i
$869$	20.8752	−	17.5163i	0.708141	−	0.594201i
$870$		0			0
$871$	−0.0861839	+	0.0313684i	−0.00292023	+	0.00106288i
$872$	2.13931	−	0.573225i	0.0724460	−	0.0194119i
$873$		0			0
$874$	3.27644	−	1.89165i	0.110827	−	0.0639861i
$875$	46.4383	−	8.90859i	1.56990	−	0.301165i
$876$		0			0
$877$	3.54626	+	2.48312i	0.119749	+	0.0838489i	0.631917	−	0.775036i	$-0.282269\pi$
$877$	3.54626	+	2.48312i	0.119749	+	0.0838489i	−0.512168	+	0.858885i	$0.671157\pi$
$878$	30.9067	+	21.6411i	1.04305	+	0.730352i
$879$		0			0
$880$	4.34908	+	10.7897i	0.146607	+	0.363722i
$881$	15.2989	−	8.83285i	0.515434	−	0.297586i	−0.219630	−	0.975583i	$-0.570485\pi$
$881$	15.2989	−	8.83285i	0.515434	−	0.297586i	0.735065	+	0.677997i	$0.237152\pi$
$882$		0			0
$883$	52.4360	−	14.0502i	1.76461	−	0.472826i	0.776967	−	0.629542i	$-0.216757\pi$
$883$	52.4360	−	14.0502i	1.76461	−	0.472826i	0.987644	+	0.156716i	$0.0500906\pi$
$884$	2.15779	−	0.785372i	0.0725744	−	0.0264149i
$885$		0			0
$886$	28.4678	−	23.8873i	0.956393	−	0.802509i
$887$	−11.3090	−	24.2523i	−0.379721	−	0.814313i	−0.999562	−	0.0295865i	$-0.990581\pi$
$887$	−11.3090	−	24.2523i	−0.379721	−	0.814313i	0.619842	−	0.784727i	$-0.287197\pi$
$888$		0			0
$889$	31.1831	+	5.49843i	1.04585	+	0.184411i
$890$	19.8436	−	6.04907i	0.665159	−	0.202765i
$891$		0			0
$892$	6.13082	−	6.13082i	0.205275	−	0.205275i
$893$	−14.2528	−	20.3551i	−0.476951	−	0.681157i
$894$		0			0
$895$	−23.6943	+	21.2994i	−0.792013	+	0.711961i
$896$	2.71855	+	3.23984i	0.0908202	+	0.108235i
$897$		0			0
$898$	35.4306	+	16.5216i	1.18234	+	0.551332i
$899$	−18.0841	+	31.3225i	−0.603138	+	1.04467i
$900$		0			0
$901$	27.6160	+	47.8324i	0.920024	+	1.59353i
$902$	2.19691	+	25.1108i	0.0731491	+	0.836098i
$903$		0			0
$904$	1.23946	−	0.218550i	0.0412239	−	0.00726888i
$905$	−27.8697	−	9.08060i	−0.926420	−	0.301849i
$906$		0			0
$907$	3.91052	−	0.342126i	0.129847	−	0.0113601i	−0.0220472	−	0.999757i	$-0.507018\pi$
$907$	3.91052	−	0.342126i	0.129847	−	0.0113601i	0.151894	+	0.988397i	$0.451463\pi$
$908$	−5.99518	−	1.60640i	−0.198957	−	0.0533104i
$909$		0			0
$910$	−0.802467	+	3.46295i	−0.0266015	+	0.114796i
$911$	−10.6171	−	29.1702i	−0.351760	−	0.966452i	−0.981805	−	0.189893i	$-0.939186\pi$
$911$	−10.6171	−	29.1702i	−0.351760	−	0.966452i	0.630045	−	0.776559i	$-0.283036\pi$
$912$		0			0
$913$	−24.7532	−	2.16563i	−0.819212	−	0.0716718i
$914$	−8.34368	−	3.03685i	−0.275985	−	0.100450i
$915$		0			0
$916$	4.16292	−	23.6091i	0.137547	−	0.780066i
$917$	−36.9248	−	36.9248i	−1.21936	−	1.21936i
$918$		0			0
$919$		−	36.3601i		−	1.19941i	−0.800222	−	0.599705i	$-0.795285\pi$
$919$		−	36.3601i		−	1.19941i	0.800222	−	0.599705i	$-0.204715\pi$
$920$	−1.53993	+	1.96771i	−0.0507701	+	0.0648734i
$921$		0			0
$922$	−30.5105	+	14.2273i	−1.00481	+	0.468550i
$923$	0.00200610	−	0.0229299i	6.60317e−5	−	0.000754746i
$924$		0			0
$925$	−28.8418	+	4.51977i	−0.948311	+	0.148609i
$926$	−8.57266	−	4.94943i	−0.281715	−	0.162648i
$927$		0			0
$928$	2.62050	−	9.77986i	0.0860223	−	0.321040i
$929$	−23.1288	−	19.4073i	−0.758830	−	0.636734i	0.178992	−	0.983850i	$-0.442716\pi$
$929$	−23.1288	−	19.4073i	−0.758830	−	0.636734i	−0.937822	+	0.347117i	$0.887161\pi$
$930$		0			0
$931$	6.40073	+	36.3003i	0.209775	+	1.18969i
$932$	6.70090	−	9.56988i	0.219495	−	0.313472i
$933$		0			0
$934$	−5.10847	+	6.08804i	−0.167154	+	0.199207i
$935$	−48.5107	+	51.9362i	−1.58647	+	1.69850i
$936$		0			0
$937$	1.58532	+	5.91649i	0.0517901	+	0.193283i	0.986974	−	0.160879i	$-0.0514328\pi$
$937$	1.58532	+	5.91649i	0.0517901	+	0.193283i	−0.935184	+	0.354162i	$0.884766\pi$
$938$	0.436121	−	0.935264i	0.0142398	−	0.0305375i
$939$		0			0
$940$	13.7564	+	8.94949i	0.448684	+	0.291900i
$941$	−10.4752	+	28.7803i	−0.341481	+	0.938212i	0.643484	+	0.765460i	$0.277488\pi$
$941$	−10.4752	+	28.7803i	−0.341481	+	0.938212i	−0.984965	+	0.172753i	$0.944734\pi$
$942$		0			0
$943$	−4.43492	+	3.10536i	−0.144421	+	0.101125i
$944$	3.01407			0.0980996
$945$		0			0
$946$	34.0508			1.10709
$947$	−6.30587	+	4.41542i	−0.204913	+	0.143482i	−0.671529	−	0.740978i	$-0.734362\pi$
$947$	−6.30587	+	4.41542i	−0.204913	+	0.143482i	0.466616	+	0.884460i	$0.345473\pi$
$948$		0			0
$949$	−0.850031	+	2.33544i	−0.0275932	+	0.0758116i
$950$	−14.8194	+	8.18291i	−0.480806	+	0.265489i
$951$		0			0
$952$	−10.9192	+	23.4163i	−0.353893	+	0.758925i
$953$	−6.78716	−	25.3300i	−0.219858	−	0.820520i	−0.984400	−	0.175946i	$-0.943701\pi$
$953$	−6.78716	−	25.3300i	−0.219858	−	0.820520i	0.764542	−	0.644574i	$-0.222965\pi$
$954$		0			0
$955$	−0.109478	−	3.21025i	−0.00354262	−	0.103881i
$956$	−11.8536	+	14.1265i	−0.383372	+	0.456885i
$957$		0			0
$958$	9.04225	−	12.9137i	0.292142	−	0.417222i
$959$	−9.32739	−	52.8982i	−0.301197	−	1.70817i
$960$		0			0
$961$	−13.9721	−	11.7240i	−0.450713	−	0.378193i
$962$	0.568024	−	2.11990i	0.0183138	−	0.0683482i
$963$		0			0
$964$	−4.30913	−	2.48788i	−0.138788	−	0.0801291i
$965$	−35.1302	+	26.4275i	−1.13088	+	0.850731i
$966$		0			0
$967$	4.09918	−	46.8539i	0.131821	−	1.50672i	−0.585898	−	0.810385i	$-0.699258\pi$
$967$	4.09918	−	46.8539i	0.131821	−	1.50672i	0.717718	−	0.696333i	$-0.245187\pi$
$968$	14.5613	−	6.79002i	0.468016	−	0.218240i
$969$		0			0
$970$	27.5773	+	21.5820i	0.885452	+	0.692957i
$971$		−	52.7240i		−	1.69199i	−0.533188	−	0.845997i	$-0.679006\pi$
$971$		−	52.7240i		−	1.69199i	0.533188	−	0.845997i	$-0.320994\pi$
$972$		0			0
$973$	13.0590	+	13.0590i	0.418653	+	0.418653i
$974$	1.49444	−	8.47537i	0.0478848	−	0.271568i
$975$		0			0
$976$	7.18421	+	2.61484i	0.229961	+	0.0836990i
$977$	42.1182	+	3.68487i	1.34748	+	0.117889i	0.737941	−	0.674866i	$-0.235798\pi$
$977$	42.1182	+	3.68487i	1.34748	+	0.117889i	0.609541	+	0.792755i	$0.291354\pi$
$978$		0			0
$979$	−16.5082	−	45.3558i	−0.527603	−	1.44958i
$980$	−12.8835	−	20.6555i	−0.411550	−	0.659817i
$981$		0			0
$982$	−30.0084	−	8.04072i	−0.957606	−	0.256590i
$983$	−26.4689	+	2.31573i	−0.844226	+	0.0738602i	−0.501058	−	0.865414i	$-0.667056\pi$
$983$	−26.4689	+	2.31573i	−0.844226	+	0.0738602i	−0.343168	+	0.939274i	$0.611500\pi$
$984$		0			0
$985$	−20.0321	−	39.3948i	−0.638277	−	1.25522i
$986$	60.9134	−	10.7407i	1.93988	−	0.342053i
$987$		0			0
$988$	−0.110917	−	1.26778i	−0.00352873	−	0.0403335i
$989$	3.65680	+	6.33377i	0.116280	+	0.201402i
$990$		0			0
$991$	−1.05011	+	1.81884i	−0.0333578	+	0.0577774i	−0.882222	−	0.470833i	$-0.843953\pi$
$991$	−1.05011	+	1.81884i	−0.0333578	+	0.0577774i	0.848865	+	0.528610i	$0.177287\pi$
$992$	−3.23753	−	1.50968i	−0.102792	−	0.0479325i
$993$		0			0
$994$	0.166473	+	0.198395i	0.00528020	+	0.00629269i
$995$	−11.6387	−	12.9474i	−0.368972	−	0.410459i
$996$		0			0
$997$	−28.4801	−	40.6738i	−0.901975	−	1.28815i	−0.957125	−	0.289675i	$-0.906453\pi$
$997$	−28.4801	−	40.6738i	−0.901975	−	1.28815i	0.0551503	−	0.998478i	$-0.482436\pi$
$998$	9.25966	−	9.25966i	0.293109	−	0.293109i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.413.6		216
3.2	odd	2		270.2.r.a.83.18	✓	216
5.2	odd	4	inner	810.2.s.a.737.8		216
15.2	even	4		270.2.r.a.137.13	yes	216
27.13	even	9		270.2.r.a.203.13	yes	216
27.14	odd	18	inner	810.2.s.a.233.8		216
135.67	odd	36		270.2.r.a.257.18	yes	216
135.122	even	36	inner	810.2.s.a.557.6		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.18	✓	216	3.2	odd	2
270.2.r.a.137.13	yes	216	15.2	even	4
270.2.r.a.203.13	yes	216	27.13	even	9
270.2.r.a.257.18	yes	216	135.67	odd	36
810.2.s.a.233.8		216	27.14	odd	18	inner
810.2.s.a.413.6		216	1.1	even	1	trivial
810.2.s.a.557.6		216	135.122	even	36	inner
810.2.s.a.737.8		216	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 + 0.573576i) q^{2} +(0.342020 - 0.939693i) q^{4} +(0.463117 + 2.18758i) q^{5} +(-1.78738 + 3.83305i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.819152 + 0.573576i) q^{2} +(0.342020 - 0.939693i) q^{4} +(0.463117 + 2.18758i) q^{5} +(-1.78738 + 3.83305i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-1.63411 - 1.52633i) q^{10} +(-3.34414 + 3.98539i) q^{11} +(-0.215597 + 0.307904i) q^{13} +(-0.734411 - 4.16505i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(1.58114 - 5.90088i) q^{17} +(-2.93211 - 1.69286i) q^{19} +(2.21405 + 0.313010i) q^{20} +(0.453432 - 5.18276i) q^{22} +(1.01274 - 0.472247i) q^{23} +(-4.57105 + 2.02621i) q^{25} -0.375881i q^{26} +(2.99057 + 2.99057i) q^{28} +(1.75816 - 9.97103i) q^{29} +(-3.35678 - 1.22177i) q^{31} +(0.996195 + 0.0871557i) q^{32} +(2.08941 + 5.74062i) q^{34} +(-9.21289 - 2.13490i) q^{35} +(5.63980 + 1.51118i) q^{37} +(3.37283 - 0.295084i) q^{38} +(-1.99318 + 1.01353i) q^{40} +(-4.77146 + 0.841337i) q^{41} +(0.570435 + 6.52010i) q^{43} +(2.60128 + 4.50554i) q^{44} +(-0.558716 + 0.967725i) q^{46} +(6.65173 + 3.10175i) q^{47} +(-6.99804 - 8.33994i) q^{49} +(2.58219 - 4.28162i) q^{50} +(0.215597 + 0.307904i) q^{52} +(-6.39299 + 6.39299i) q^{53} +(-10.2671 - 5.46988i) q^{55} +(-4.16505 - 0.734411i) q^{56} +(4.27895 + 9.17623i) q^{58} +(-2.30891 + 1.93741i) q^{59} +(-7.18421 + 2.61484i) q^{61} +(3.45049 - 0.924557i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(-0.773412 - 0.329040i) q^{65} +(0.199873 + 0.139953i) q^{67} +(-5.00423 - 3.50400i) q^{68} +(8.77128 - 3.53549i) q^{70} +(-0.0530319 + 0.0306180i) q^{71} +(6.38669 - 1.71131i) q^{73} +(-5.48663 + 1.99697i) q^{74} +(-2.59360 + 2.17629i) q^{76} +(-9.29895 - 19.9417i) q^{77} +(-5.15835 - 0.909556i) q^{79} +(1.05138 - 1.97347i) q^{80} +(3.42598 - 3.42598i) q^{82} +(2.73944 + 3.91233i) q^{83} +(13.6409 + 0.726069i) q^{85} +(-4.20705 - 5.01377i) q^{86} +(-4.71511 - 2.19869i) q^{88} +(-4.63875 + 8.03454i) q^{89} +(-0.794859 - 1.37674i) q^{91} +(-0.0973907 - 1.11318i) q^{92} +(-7.22787 + 1.27447i) q^{94} +(2.34535 - 7.19823i) q^{95} +(-15.6011 + 1.36492i) q^{97} +(10.5161 + 2.81777i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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