LMFDB - Embedded newform 630.2.ce.c.233.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("630.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.6
Character	$\chi$	$=$	630.233
Dual form			630.2.ce.c.557.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.915403 - 2.04011i) q^{5} +(-2.36324 - 1.18959i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.915403 - 2.04011i) q^{5} +(-2.36324 - 1.18959i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.41223 - 1.73367i) q^{10} +(1.10233 - 0.636431i) q^{11} +(2.15117 + 2.15117i) q^{13} +(-2.59060 - 0.537402i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.55421 - 5.80038i) q^{17} +(-6.20956 - 3.58509i) q^{19} +(-1.81282 - 1.30908i) q^{20} +(0.900050 - 0.900050i) q^{22} +(-1.11101 - 4.14634i) q^{23} +(-3.32407 + 3.73504i) q^{25} +(2.63464 + 1.52111i) q^{26} +(-2.64142 + 0.151406i) q^{28} -1.25304 q^{29} +(-2.35619 - 4.08105i) q^{31} +(0.258819 - 0.965926i) q^{32} -6.00499i q^{34} +(-0.263570 + 5.91021i) q^{35} +(0.535773 + 1.99953i) q^{37} +(-6.92586 - 1.85578i) q^{38} +(-2.08986 - 0.795286i) q^{40} -0.655854i q^{41} +(7.20489 + 7.20489i) q^{43} +(0.636431 - 1.10233i) q^{44} +(-2.14630 - 3.71751i) q^{46} +(10.4704 - 2.80555i) q^{47} +(4.16977 + 5.62255i) q^{49} +(-2.24411 + 4.46811i) q^{50} +(2.93856 + 0.787384i) q^{52} +(13.2647 + 3.55426i) q^{53} +(-2.30747 - 1.66628i) q^{55} +(-2.51222 + 0.829895i) q^{56} +(-1.21035 + 0.324311i) q^{58} +(-0.688544 - 1.19259i) q^{59} +(-2.57772 + 4.46475i) q^{61} +(-3.33216 - 3.33216i) q^{62} -1.00000i q^{64} +(2.41943 - 6.35781i) q^{65} +(-4.19060 - 1.12287i) q^{67} +(-1.55421 - 5.80038i) q^{68} +(1.27508 + 5.77704i) q^{70} +0.159361i q^{71} +(-2.65363 + 9.90347i) q^{73} +(1.03503 + 1.79273i) q^{74} -7.17018 q^{76} +(-3.36216 + 0.192719i) q^{77} +(9.23605 + 5.33244i) q^{79} +(-2.22449 - 0.227291i) q^{80} +(-0.169748 - 0.633506i) q^{82} +(6.09168 - 6.09168i) q^{83} +(-13.2561 + 2.13894i) q^{85} +(8.82415 + 5.09463i) q^{86} +(0.329441 - 1.22949i) q^{88} +(-3.79369 + 6.57086i) q^{89} +(-2.52472 - 7.64274i) q^{91} +(-3.03533 - 3.03533i) q^{92} +(9.38755 - 5.41990i) q^{94} +(-1.62972 + 15.9500i) q^{95} +(10.9935 - 10.9935i) q^{97} +(5.48291 + 4.35175i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{7}+O(q^{10}) $ 32 * q - 12 * q^7	$ 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) $ 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.915403	−	2.04011i	−0.409381	−	0.912364i
$5$	−0.915403	−	2.04011i	−0.409381	−	0.912364i
$6$		0			0
$7$	−2.36324	−	1.18959i	−0.893219	−	0.449622i
$7$	−2.36324	−	1.18959i	−0.893219	−	0.449622i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−1.41223	−	1.73367i	−0.446586	−	0.548234i
$11$	1.10233	−	0.636431i	0.332365	−	0.191891i	−0.324525	−	0.945877i	$-0.605205\pi$
$11$	1.10233	−	0.636431i	0.332365	−	0.191891i	0.656891	+	0.753986i	$0.271871\pi$
$12$		0			0
$13$	2.15117	+	2.15117i	0.596628	+	0.596628i	0.939414	−	0.342786i	$-0.111370\pi$
$13$	2.15117	+	2.15117i	0.596628	+	0.596628i	−0.342786	+	0.939414i	$0.611370\pi$
$14$	−2.59060	−	0.537402i	−0.692366	−	0.143627i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.55421	−	5.80038i	0.376950	−	1.40680i	−0.473524	−	0.880781i	$-0.657018\pi$
$17$	1.55421	−	5.80038i	0.376950	−	1.40680i	0.850474	−	0.526017i	$-0.176315\pi$
$18$		0			0
$19$	−6.20956	−	3.58509i	−1.42457	−	0.822476i	−0.427885	−	0.903833i	$-0.640741\pi$
$19$	−6.20956	−	3.58509i	−1.42457	−	0.822476i	−0.996685	+	0.0813571i	$0.974075\pi$
$20$	−1.81282	−	1.30908i	−0.405358	−	0.292720i
$21$		0			0
$22$	0.900050	−	0.900050i	0.191891	−	0.191891i
$23$	−1.11101	−	4.14634i	−0.231661	−	0.864571i	−0.979626	−	0.200833i	$-0.935635\pi$
$23$	−1.11101	−	4.14634i	−0.231661	−	0.864571i	0.747964	−	0.663739i	$-0.231031\pi$
$24$		0			0
$25$	−3.32407	+	3.73504i	−0.664815	+	0.747008i
$26$	2.63464	+	1.52111i	0.516695	+	0.298314i
$27$		0			0
$28$	−2.64142	+	0.151406i	−0.499181	+	0.0286130i
$29$	−1.25304			−0.232684			−0.116342	−	0.993209i	$-0.537117\pi$
$29$	−1.25304			−0.232684			−0.116342	+	0.993209i	$0.537117\pi$
$30$		0			0
$31$	−2.35619	−	4.08105i	−0.423185	−	0.732978i	0.573064	−	0.819510i	$-0.305755\pi$
$31$	−2.35619	−	4.08105i	−0.423185	−	0.732978i	−0.996249	+	0.0865329i	$0.972421\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$		−	6.00499i		−	1.02985i
$35$	−0.263570	+	5.91021i	−0.0445515	+	0.999007i
$36$		0			0
$37$	0.535773	+	1.99953i	0.0880805	+	0.328721i	0.995880	−	0.0906841i	$-0.0289054\pi$
$37$	0.535773	+	1.99953i	0.0880805	+	0.328721i	−0.907799	+	0.419405i	$0.862239\pi$
$38$	−6.92586	−	1.85578i	−1.12352	−	0.301047i
$39$		0			0
$40$	−2.08986	−	0.795286i	−0.330436	−	0.125746i
$41$		−	0.655854i		−	0.102427i	−0.998688	−	0.0512136i	$-0.983691\pi$
$41$		−	0.655854i		−	0.102427i	0.998688	−	0.0512136i	$-0.0163089\pi$
$42$		0			0
$43$	7.20489	+	7.20489i	1.09874	+	1.09874i	0.994559	+	0.104177i	$0.0332208\pi$
$43$	7.20489	+	7.20489i	1.09874	+	1.09874i	0.104177	+	0.994559i	$0.466779\pi$
$44$	0.636431	−	1.10233i	0.0959456	−	0.166183i
$45$		0			0
$46$	−2.14630	−	3.71751i	−0.316455	−	0.548116i
$47$	10.4704	−	2.80555i	1.52727	−	0.409231i	0.605144	−	0.796116i	$-0.293116\pi$
$47$	10.4704	−	2.80555i	1.52727	−	0.409231i	0.922128	+	0.386885i	$0.126449\pi$
$48$		0			0
$49$	4.16977	+	5.62255i	0.595681	+	0.803221i
$50$	−2.24411	+	4.46811i	−0.317365	+	0.631886i
$51$		0			0
$52$	2.93856	+	0.787384i	0.407505	+	0.109191i
$53$	13.2647	+	3.55426i	1.82204	+	0.488215i	0.997038	−	0.0769086i	$-0.0245050\pi$
$53$	13.2647	+	3.55426i	1.82204	+	0.488215i	0.825006	+	0.565124i	$0.191172\pi$
$54$		0			0
$55$	−2.30747	−	1.66628i	−0.311139	−	0.224682i
$56$	−2.51222	+	0.829895i	−0.335710	+	0.110899i
$57$		0			0
$58$	−1.21035	+	0.324311i	−0.158926	+	0.0425842i
$59$	−0.688544	−	1.19259i	−0.0896409	−	0.155263i	0.817718	−	0.575618i	$-0.195239\pi$
$59$	−0.688544	−	1.19259i	−0.0896409	−	0.155263i	−0.907359	+	0.420356i	$0.861905\pi$
$60$		0			0
$61$	−2.57772	+	4.46475i	−0.330044	+	0.571652i	−0.982520	−	0.186157i	$-0.940397\pi$
$61$	−2.57772	+	4.46475i	−0.330044	+	0.571652i	0.652476	+	0.757809i	$0.273730\pi$
$62$	−3.33216	−	3.33216i	−0.423185	−	0.423185i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.41943	−	6.35781i	0.300094	−	0.788590i
$66$		0			0
$67$	−4.19060	−	1.12287i	−0.511964	−	0.137180i	−0.00641674	−	0.999979i	$-0.502043\pi$
$67$	−4.19060	−	1.12287i	−0.511964	−	0.137180i	−0.505547	+	0.862799i	$0.668709\pi$
$68$	−1.55421	−	5.80038i	−0.188475	−	0.703399i
$69$		0			0
$70$	1.27508	+	5.77704i	0.152402	+	0.690488i
$71$			0.159361i			0.0189127i	0.999955	+	0.00945636i	$0.00301010\pi$
$71$			0.159361i			0.0189127i	−0.999955	+	0.00945636i	$0.996990\pi$
$72$		0			0
$73$	−2.65363	+	9.90347i	−0.310584	+	1.15911i	0.617448	+	0.786612i	$0.288167\pi$
$73$	−2.65363	+	9.90347i	−0.310584	+	1.15911i	−0.928031	+	0.372502i	$0.878500\pi$
$74$	1.03503	+	1.79273i	0.120320	+	0.208401i
$75$		0			0
$76$	−7.17018			−0.822476
$77$	−3.36216	+	0.192719i	−0.383154	+	0.0219623i
$78$		0			0
$79$	9.23605	+	5.33244i	1.03914	+	0.599946i	0.919589	−	0.392882i	$-0.128522\pi$
$79$	9.23605	+	5.33244i	1.03914	+	0.599946i	0.119548	+	0.992828i	$0.461855\pi$
$80$	−2.22449	−	0.227291i	−0.248705	−	0.0254119i
$81$		0			0
$82$	−0.169748	−	0.633506i	−0.0187455	−	0.0699591i
$83$	6.09168	−	6.09168i	0.668648	−	0.668648i	−0.288755	−	0.957403i	$-0.593241\pi$
$83$	6.09168	−	6.09168i	0.668648	−	0.668648i	0.957403	+	0.288755i	$0.0932412\pi$
$84$		0			0
$85$	−13.2561	+	2.13894i	−1.43783	+	0.232000i
$86$	8.82415	+	5.09463i	0.951533	+	0.549368i
$87$		0			0
$88$	0.329441	−	1.22949i	0.0351185	−	0.131064i
$89$	−3.79369	+	6.57086i	−0.402130	+	0.696510i	−0.993983	−	0.109536i	$-0.965063\pi$
$89$	−3.79369	+	6.57086i	−0.402130	+	0.696510i	0.591852	+	0.806046i	$0.298397\pi$
$90$		0			0
$91$	−2.52472	−	7.64274i	−0.264663	−	0.801176i
$92$	−3.03533	−	3.03533i	−0.316455	−	0.316455i
$93$		0			0
$94$	9.38755	−	5.41990i	0.968251	−	0.559020i
$95$	−1.62972	+	15.9500i	−0.167206	+	1.63643i
$96$		0			0
$97$	10.9935	−	10.9935i	1.11622	−	1.11622i	0.123927	−	0.992291i	$-0.460451\pi$
$97$	10.9935	−	10.9935i	1.11622	−	1.11622i	0.992291	−	0.123927i	$-0.0395488\pi$
$98$	5.48291	+	4.35175i	0.553857	+	0.439593i
$99$		0			0
$100$	−1.01121	+	4.89668i	−0.101121	+	0.489668i
$101$	3.07715	−	1.77660i	0.306188	−	0.176778i	−0.339031	−	0.940775i	$-0.610099\pi$
$101$	3.07715	−	1.77660i	0.306188	−	0.176778i	0.645220	+	0.763997i	$0.276766\pi$
$102$		0			0
$103$	−5.69956	+	1.52719i	−0.561595	+	0.150479i	−0.528439	−	0.848971i	$-0.677222\pi$
$103$	−5.69956	+	1.52719i	−0.561595	+	0.150479i	−0.0331558	+	0.999450i	$0.510556\pi$
$104$	3.04222			0.298314
$105$		0			0
$106$	13.7326			1.33383
$107$	−5.71860	+	1.53230i	−0.552838	+	0.148133i	−0.524414	−	0.851463i	$-0.675716\pi$
$107$	−5.71860	+	1.53230i	−0.552838	+	0.148133i	−0.0284243	+	0.999596i	$0.509049\pi$
$108$		0			0
$109$	15.9866	−	9.22986i	1.53124	−	0.884061i	0.531933	−	0.846787i	$-0.321466\pi$
$109$	15.9866	−	9.22986i	1.53124	−	0.884061i	0.999305	−	0.0372741i	$-0.0118675\pi$
$110$	−2.66011	−	1.01229i	−0.253631	−	0.0965180i
$111$		0			0
$112$	−2.21183	+	1.45183i	−0.208998	+	0.137185i
$113$	−8.78952	+	8.78952i	−0.826849	+	0.826849i	−0.987080	−	0.160231i	$-0.948776\pi$
$113$	−8.78952	+	8.78952i	−0.826849	+	0.826849i	0.160231	+	0.987080i	$0.448776\pi$
$114$		0			0
$115$	−7.44195	+	6.06215i	−0.693966	+	0.565298i
$116$	−1.08517	+	0.626522i	−0.100755	+	0.0581711i
$117$		0			0
$118$	−0.973749	−	0.973749i	−0.0896409	−	0.0896409i
$119$	−10.5730	+	11.8588i	−0.969226	+	1.08709i
$120$		0			0
$121$	−4.68991	+	8.12316i	−0.426355	+	0.738469i
$122$	−1.33433	+	4.97978i	−0.120804	+	0.450848i
$123$		0			0
$124$	−4.08105	−	2.35619i	−0.366489	−	0.211592i
$125$	10.6628	+	3.36240i	0.953706	+	0.300742i
$126$		0			0
$127$	5.00250	−	5.00250i	0.443900	−	0.443900i	−0.449421	−	0.893320i	$-0.648370\pi$
$127$	5.00250	−	5.00250i	0.443900	−	0.443900i	0.893320	+	0.449421i	$0.148370\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	0.691469	−	6.76737i	0.0606458	−	0.593538i
$131$	−16.7853	−	9.69100i	−1.46654	−	0.846706i	−0.467239	−	0.884131i	$-0.654751\pi$
$131$	−16.7853	−	9.69100i	−1.46654	−	0.846706i	−0.999299	+	0.0374245i	$0.988085\pi$
$132$		0			0
$133$	10.4099	+	15.8592i	0.902651	+	1.37517i
$134$	−4.33843			−0.374783
$135$		0			0
$136$	−3.00250	−	5.20048i	−0.257462	−	0.445937i
$137$	−1.64409	+	6.13584i	−0.140464	+	0.524220i	0.859451	+	0.511218i	$0.170806\pi$
$137$	−1.64409	+	6.13584i	−0.140464	+	0.524220i	−0.999915	+	0.0130023i	$0.995861\pi$
$138$		0			0
$139$		−	7.61018i		−	0.645487i	−0.946486	−	0.322744i	$-0.895395\pi$
$139$		−	7.61018i		−	0.645487i	0.946486	−	0.322744i	$-0.104605\pi$
$140$	2.72684	+	5.25017i	0.230460	+	0.443721i
$141$		0			0
$142$	0.0412458	+	0.153931i	0.00346127	+	0.0129176i
$143$	3.74038	+	1.00223i	0.312786	+	0.0838108i
$144$		0			0
$145$	1.14704	+	2.55634i	0.0952565	+	0.212293i
$146$			10.2528i			0.848530i
$147$		0			0
$148$	1.46376	+	1.46376i	0.120320	+	0.120320i
$149$	5.05397	−	8.75374i	0.414038	−	0.717134i	−0.581289	−	0.813697i	$-0.697452\pi$
$149$	5.05397	−	8.75374i	0.414038	−	0.717134i	0.995327	+	0.0965628i	$0.0307848\pi$
$150$		0			0
$151$	0.957672	+	1.65874i	0.0779342	+	0.134986i	0.902359	−	0.430986i	$-0.141834\pi$
$151$	0.957672	+	1.65874i	0.0779342	+	0.134986i	−0.824424	+	0.565972i	$0.808501\pi$
$152$	−6.92586	+	1.85578i	−0.561762	+	0.150524i
$153$		0			0
$154$	−3.19772	+	1.05634i	−0.257679	+	0.0851225i
$155$	−6.16890	+	8.54269i	−0.495498	+	0.686165i
$156$		0			0
$157$	15.0279	+	4.02672i	1.19936	+	0.321368i	0.802579	−	0.596546i	$-0.203461\pi$
$157$	15.0279	+	4.02672i	1.19936	+	0.321368i	0.396781	+	0.917913i	$0.370127\pi$
$158$	10.3015	+	2.76027i	0.819542	+	0.219596i
$159$		0			0
$160$	−2.20752	+	0.356193i	−0.174519	+	0.0281595i
$161$	−2.30686	+	11.1204i	−0.181806	+	0.876412i
$162$		0			0
$163$	11.2938	−	3.02616i	0.884599	−	0.237027i	0.212208	−	0.977224i	$-0.431934\pi$
$163$	11.2938	−	3.02616i	0.884599	−	0.237027i	0.672390	+	0.740197i	$0.265268\pi$
$164$	−0.327927	−	0.567986i	−0.0256068	−	0.0443523i
$165$		0			0
$166$	4.30747	−	7.46075i	0.334324	−	0.579067i
$167$	−8.85336	−	8.85336i	−0.685093	−	0.685093i	0.276050	−	0.961143i	$-0.410974\pi$
$167$	−8.85336	−	8.85336i	−0.685093	−	0.685093i	−0.961143	+	0.276050i	$0.910974\pi$
$168$		0			0
$169$		−	3.74491i		−	0.288070i
$170$	−12.2508	+	5.49699i	−0.939595	+	0.421600i
$171$		0			0
$172$	9.84207	+	2.63717i	0.750450	+	0.201083i
$173$	−1.28640	−	4.80092i	−0.0978034	−	0.365007i	0.899626	−	0.436661i	$-0.143839\pi$
$173$	−1.28640	−	4.80092i	−0.0978034	−	0.365007i	−0.997430	+	0.0716536i	$0.977172\pi$
$174$		0			0
$175$	12.2987	−	4.87251i	0.929696	−	0.368327i
$176$		−	1.27286i		−	0.0959456i
$177$		0			0
$178$	−1.96376	+	7.32885i	−0.147190	+	0.549320i
$179$	10.2521	+	17.7572i	0.766281	+	1.32724i	0.939567	+	0.342366i	$0.111228\pi$
$179$	10.2521	+	17.7572i	0.766281	+	1.32724i	−0.173286	+	0.984872i	$0.555438\pi$
$180$		0			0
$181$	−6.09745			−0.453220			−0.226610	−	0.973986i	$-0.572764\pi$
$181$	−6.09745			−0.453220			−0.226610	+	0.973986i	$0.572764\pi$
$182$	−4.41678	−	6.72887i	−0.327394	−	0.498777i
$183$		0			0
$184$	−3.71751	−	2.14630i	−0.274058	−	0.158228i
$185$	3.58881	−	2.92341i	0.263855	−	0.214934i
$186$		0			0
$187$	−1.97829	−	7.38308i	−0.144667	−	0.539905i
$188$	7.66490	−	7.66490i	0.559020	−	0.559020i
$189$		0			0
$190$	2.55397	+	15.8283i	0.185284	+	1.14830i
$191$	−10.2818	−	5.93620i	−0.743965	−	0.429528i	0.0795444	−	0.996831i	$-0.474653\pi$
$191$	−10.2818	−	5.93620i	−0.743965	−	0.429528i	−0.823509	+	0.567303i	$0.807987\pi$
$192$		0			0
$193$	3.98395	−	14.8683i	0.286771	−	1.07024i	−0.660765	−	0.750593i	$-0.729768\pi$
$193$	3.98395	−	14.8683i	0.286771	−	1.07024i	0.947536	−	0.319650i	$-0.103565\pi$
$194$	7.77356	−	13.4642i	0.558109	−	0.966673i
$195$		0			0
$196$	6.42240	+	2.78439i	0.458743	+	0.198885i
$197$	−4.63999	−	4.63999i	−0.330585	−	0.330585i	0.522223	−	0.852809i	$-0.325103\pi$
$197$	−4.63999	−	4.63999i	−0.330585	−	0.330585i	−0.852809	+	0.522223i	$0.825103\pi$
$198$		0			0
$199$	8.74465	−	5.04873i	0.619892	−	0.357895i	−0.156935	−	0.987609i	$-0.550161\pi$
$199$	8.74465	−	5.04873i	0.619892	−	0.357895i	0.776827	+	0.629714i	$0.216828\pi$
$200$	0.290598	+	4.99155i	0.0205484	+	0.352956i
$201$		0			0
$202$	2.51249	−	2.51249i	0.176778	−	0.176778i
$203$	2.96124	+	1.49060i	0.207838	+	0.104620i
$204$		0			0
$205$	−1.33801	+	0.600371i	−0.0934509	+	0.0419317i
$206$	−5.11009	+	2.95031i	−0.356037	+	0.205558i
$207$		0			0
$208$	2.93856	−	0.787384i	0.203752	−	0.0545953i
$209$	−9.12665			−0.631304
$210$		0			0
$211$	−27.9822			−1.92637			−0.963187	−	0.268832i	$-0.913362\pi$
$211$	−27.9822			−1.92637			−0.963187	+	0.268832i	$0.913362\pi$
$212$	13.2647	−	3.55426i	0.911022	−	0.244108i
$213$		0			0
$214$	−5.12716	+	2.96017i	−0.350486	+	0.202353i
$215$	8.10337	−	21.2941i	0.552645	−	1.45225i
$216$		0			0
$217$	0.713482	+	12.4474i	0.0484343	+	0.844983i
$218$	13.0530	−	13.0530i	0.884061	−	0.884061i
$219$		0			0
$220$	−2.83147	−	0.289310i	−0.190897	−	0.0195053i
$221$	15.8210	−	9.13425i	1.06423	−	0.614436i
$222$		0			0
$223$	7.37355	+	7.37355i	0.493769	+	0.493769i	0.909492	−	0.415722i	$-0.136471\pi$
$223$	7.37355	+	7.37355i	0.493769	+	0.493769i	−0.415722	+	0.909492i	$0.636471\pi$
$224$	−1.76070	+	1.97482i	−0.117642	+	0.131948i
$225$		0			0
$226$	−6.21513	+	10.7649i	−0.413424	+	0.716072i
$227$	−2.90981	+	10.8596i	−0.193131	+	0.720775i	0.799611	+	0.600518i	$0.205039\pi$
$227$	−2.90981	+	10.8596i	−0.193131	+	0.720775i	−0.992743	+	0.120258i	$0.961628\pi$
$228$		0			0
$229$	−9.38944	−	5.42100i	−0.620472	−	0.358230i	0.156581	−	0.987665i	$-0.449953\pi$
$229$	−9.38944	−	5.42100i	−0.620472	−	0.358230i	−0.777053	+	0.629436i	$0.783286\pi$
$230$	−5.61938	+	7.78170i	−0.370531	+	0.513110i
$231$		0			0
$232$	−0.886035	+	0.886035i	−0.0581711	+	0.0581711i
$233$	4.41272	+	16.4685i	0.289087	+	1.07889i	0.945801	+	0.324747i	$0.105279\pi$
$233$	4.41272	+	16.4685i	0.289087	+	1.07889i	−0.656714	+	0.754140i	$0.728054\pi$
$234$		0			0
$235$	−15.3083	−	18.7926i	−0.998603	−	1.22590i
$236$	−1.19259	−	0.688544i	−0.0776313	−	0.0448204i
$237$		0			0
$238$	−7.14346	+	14.1912i	−0.463042	+	0.919880i
$239$	−25.5123			−1.65026			−0.825128	−	0.564946i	$-0.808897\pi$
$239$	−25.5123			−1.65026			−0.825128	+	0.564946i	$0.808897\pi$
$240$		0			0
$241$	7.79510	+	13.5015i	0.502127	+	0.869709i	0.999997	+	0.00245737i	$0.000782207\pi$
$241$	7.79510	+	13.5015i	0.502127	+	0.869709i	−0.497870	+	0.867251i	$0.665884\pi$
$242$	−2.42768	+	9.06021i	−0.156057	+	0.582412i
$243$		0			0
$244$			5.15545i			0.330044i
$245$	7.65358	−	13.6537i	0.488969	−	0.872301i
$246$		0			0
$247$	−5.64568	−	21.0700i	−0.359226	−	1.34065i
$248$	−4.55182	−	1.21966i	−0.289041	−	0.0774482i
$249$		0			0
$250$	11.1697	+	0.488103i	0.706433	+	0.0308703i
$251$			10.8399i			0.684206i	0.939662	+	0.342103i	$0.111139\pi$
$251$			10.8399i			0.684206i	−0.939662	+	0.342103i	$0.888861\pi$
$252$		0			0
$253$	−3.86356	−	3.86356i	−0.242900	−	0.242900i
$254$	3.53730	−	6.12678i	0.221950	−	0.384428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.8150	−	3.70172i	0.861756	−	0.230907i	0.199237	−	0.979951i	$-0.436154\pi$
$257$	13.8150	−	3.70172i	0.861756	−	0.230907i	0.662520	+	0.749044i	$0.269487\pi$
$258$		0			0
$259$	1.11246	−	5.36271i	0.0691248	−	0.333223i
$260$	−1.08362	−	6.71575i	−0.0672031	−	0.416493i
$261$		0			0
$262$	−18.7216	−	5.01643i	−1.15662	−	0.309916i
$263$	−5.29064	−	1.41762i	−0.326235	−	0.0874144i	0.0919845	−	0.995760i	$-0.470679\pi$
$263$	−5.29064	−	1.41762i	−0.326235	−	0.0874144i	−0.418219	+	0.908346i	$0.637346\pi$
$264$		0			0
$265$	−4.89146	−	30.3150i	−0.300480	−	1.86223i
$266$	14.1598	+	12.6246i	0.868195	+	0.774061i
$267$		0			0
$268$	−4.19060	+	1.12287i	−0.255982	+	0.0685901i
$269$	−11.0192	−	19.0857i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$269$	−11.0192	−	19.0857i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$270$		0			0
$271$	−3.14477	+	5.44691i	−0.191031	+	0.330876i	−0.945592	−	0.325354i	$-0.894517\pi$
$271$	−3.14477	+	5.44691i	−0.191031	+	0.330876i	0.754561	+	0.656230i	$0.227850\pi$
$272$	−4.24617	−	4.24617i	−0.257462	−	0.257462i
$273$		0			0
$274$			6.35229i			0.383756i
$275$	−1.28713	+	6.23280i	−0.0776171	+	0.375852i
$276$		0			0
$277$	21.2109	+	5.68345i	1.27444	+	0.341485i	0.831730	−	0.555180i	$-0.187351\pi$
$277$	21.2109	+	5.68345i	1.27444	+	0.341485i	0.442710	+	0.896665i	$0.354017\pi$
$278$	−1.96966	−	7.35087i	−0.118132	−	0.440876i
$279$		0			0
$280$	3.99277	+	4.36552i	0.238614	+	0.260890i
$281$			12.3803i			0.738545i	0.929321	+	0.369273i	$0.120393\pi$
$281$			12.3803i			0.738545i	−0.929321	+	0.369273i	$0.879607\pi$
$282$		0			0
$283$	−4.49829	+	16.7878i	−0.267395	+	0.997933i	0.693372	+	0.720579i	$0.256124\pi$
$283$	−4.49829	+	16.7878i	−0.267395	+	0.997933i	−0.960768	+	0.277354i	$0.910543\pi$
$284$	0.0796807	+	0.138011i	0.00472818	+	0.00818945i
$285$		0			0
$286$	3.87233			0.228975
$287$	−0.780195	+	1.54994i	−0.0460535	+	0.0914899i
$288$		0			0
$289$	−16.5064	−	9.52996i	−0.970964	−	0.560586i
$290$	1.76959	+	2.17236i	0.103914	+	0.127565i
$291$		0			0
$292$	2.65363	+	9.90347i	0.155292	+	0.579557i
$293$	19.7746	−	19.7746i	1.15525	−	1.15525i	0.169760	−	0.985485i	$-0.445701\pi$
$293$	19.7746	−	19.7746i	1.15525	−	1.15525i	0.985485	−	0.169760i	$-0.0542992\pi$
$294$		0			0
$295$	−1.80272	+	2.49641i	−0.104959	+	0.145347i
$296$	1.79273	+	1.03503i	0.104200	+	0.0601601i
$297$		0			0
$298$	2.61613	−	9.76353i	0.151548	−	0.565586i
$299$	6.52952	−	11.3095i	0.377612	−	0.654043i
$300$		0			0
$301$	−8.45602	−	25.5977i	−0.487397	−	1.47543i
$302$	1.35435	+	1.35435i	0.0779342	+	0.0779342i
$303$		0			0
$304$	−6.20956	+	3.58509i	−0.356143	+	0.205619i
$305$	11.4682	+	1.17179i	0.656668	+	0.0670963i
$306$		0			0
$307$	−7.55718	+	7.55718i	−0.431311	+	0.431311i	−0.889074	−	0.457763i	$-0.848651\pi$
$307$	−7.55718	+	7.55718i	−0.431311	+	0.431311i	0.457763	+	0.889074i	$0.348651\pi$
$308$	−2.81536	+	1.84798i	−0.160420	+	0.105298i
$309$		0			0
$310$	−3.74769	+	9.84823i	−0.212855	+	0.559342i
$311$	−1.13329	+	0.654305i	−0.0642630	+	0.0371022i	−0.531787	−	0.846878i	$-0.678479\pi$
$311$	−1.13329	+	0.654305i	−0.0642630	+	0.0371022i	0.467524	+	0.883980i	$0.345146\pi$
$312$		0			0
$313$	−22.4527	+	6.01619i	−1.26910	+	0.340055i	−0.829687	−	0.558229i	$-0.811481\pi$
$313$	−22.4527	+	6.01619i	−1.26910	+	0.340055i	−0.439416	+	0.898284i	$0.644815\pi$
$314$	15.5581			0.877993
$315$		0			0
$316$	10.6649			0.599946
$317$	23.4577	−	6.28546i	1.31751	−	0.353027i	0.469468	−	0.882949i	$-0.344446\pi$
$317$	23.4577	−	6.28546i	1.31751	−	0.353027i	0.848046	+	0.529923i	$0.177779\pi$
$318$		0			0
$319$	−1.38127	+	0.797476i	−0.0773362	+	0.0446501i
$320$	−2.04011	+	0.915403i	−0.114045	+	0.0511726i
$321$		0			0
$322$	0.649925	+	11.3386i	0.0362189	+	0.631873i
$323$	−30.4458	+	30.4458i	−1.69405	+	1.69405i
$324$		0			0
$325$	−15.1854	+	0.884063i	−0.842333	+	0.0490390i
$326$	10.1257	−	5.84610i	0.560813	−	0.323786i
$327$		0			0
$328$	−0.463759	−	0.463759i	−0.0256068	−	0.0256068i
$329$	−28.0816	−	5.82533i	−1.54819	−	0.321161i
$330$		0			0
$331$	3.47113	−	6.01217i	0.190790	−	0.330458i	−0.754722	−	0.656045i	$-0.772228\pi$
$331$	3.47113	−	6.01217i	0.190790	−	0.330458i	0.945512	+	0.325586i	$0.105562\pi$
$332$	2.22971	−	8.32139i	0.122371	−	0.456695i
$333$		0			0
$334$	−10.8431	−	6.26027i	−0.593308	−	0.342547i
$335$	1.54532	+	9.57715i	0.0844298	+	0.523256i
$336$		0			0
$337$	−8.08169	+	8.08169i	−0.440237	+	0.440237i	−0.892092	−	0.451854i	$-0.850763\pi$
$337$	−8.08169	+	8.08169i	−0.440237	+	0.440237i	0.451854	+	0.892092i	$0.350763\pi$
$338$	−0.969254	−	3.61730i	−0.0527204	−	0.196755i
$339$		0			0
$340$	−10.4107	+	8.48043i	−0.564598	+	0.459916i
$341$	−5.19461	−	2.99911i	−0.281304	−	0.162411i
$342$		0			0
$343$	−3.16563	−	18.2477i	−0.170928	−	0.985283i
$344$	10.1893			0.549368
$345$		0			0
$346$	−2.48514	−	4.30439i	−0.133602	−	0.231405i
$347$	4.40330	−	16.4333i	0.236381	−	0.882188i	−0.741140	−	0.671351i	$-0.765714\pi$
$347$	4.40330	−	16.4333i	0.236381	−	0.882188i	0.977521	−	0.210837i	$-0.0676189\pi$
$348$		0			0
$349$			36.2149i			1.93854i	0.246004	+	0.969269i	$0.420883\pi$
$349$			36.2149i			1.93854i	−0.246004	+	0.969269i	$0.579117\pi$
$350$	10.6186	−	7.88963i	0.567586	−	0.421718i
$351$		0			0
$352$	−0.329441	−	1.22949i	−0.0175593	−	0.0655321i
$353$	−10.1280	−	2.71380i	−0.539061	−	0.144441i	−0.0209920	−	0.999780i	$-0.506682\pi$
$353$	−10.1280	−	2.71380i	−0.539061	−	0.144441i	−0.518069	+	0.855339i	$0.673349\pi$
$354$		0			0
$355$	0.325114	−	0.145880i	0.0172553	−	0.00774251i
$356$			7.58738i			0.402130i
$357$		0			0
$358$	14.4987	+	14.4987i	0.766281	+	0.766281i
$359$	14.4319	−	24.9968i	0.761686	−	1.31928i	−0.180294	−	0.983613i	$-0.557705\pi$
$359$	14.4319	−	24.9968i	0.761686	−	1.31928i	0.941981	−	0.335667i	$-0.108962\pi$
$360$		0			0
$361$	16.2057	+	28.0692i	0.852934	+	1.47732i
$362$	−5.88969	+	1.57814i	−0.309555	+	0.0829451i
$363$		0			0
$364$	−6.00784	−	5.35644i	−0.314896	−	0.280754i
$365$	22.6333	−	3.65199i	1.18468	−	0.191154i
$366$		0			0
$367$	−1.99710	−	0.535122i	−0.104248	−	0.0279331i	0.206318	−	0.978485i	$-0.433852\pi$
$367$	−1.99710	−	0.535122i	−0.104248	−	0.0279331i	−0.310566	+	0.950552i	$0.600519\pi$
$368$	−4.14634	−	1.11101i	−0.216143	−	0.0579153i
$369$		0			0
$370$	2.70989	−	3.75265i	0.140880	−	0.195091i
$371$	−27.1195	−	24.1790i	−1.40797	−	1.25531i
$372$		0			0
$373$	34.6247	−	9.27766i	1.79280	−	0.480379i	0.799982	−	0.600023i	$-0.204842\pi$
$373$	34.6247	−	9.27766i	1.79280	−	0.480379i	0.992817	+	0.119644i	$0.0381754\pi$
$374$	−3.82177	−	6.61949i	−0.197619	−	0.342286i
$375$		0			0
$376$	5.41990	−	9.38755i	0.279510	−	0.484126i
$377$	−2.69551	−	2.69551i	−0.138826	−	0.138826i
$378$		0			0
$379$		−	4.28006i		−	0.219852i	−0.993940	−	0.109926i	$-0.964939\pi$
$379$		−	4.28006i		−	0.219852i	0.993940	−	0.109926i	$-0.0350614\pi$
$380$	6.56361	+	14.6279i	0.336706	+	0.750397i
$381$		0			0
$382$	−11.4679	−	3.07280i	−0.586746	−	0.157218i
$383$	1.35677	+	5.06354i	0.0693278	+	0.258735i	0.991887	−	0.127120i	$-0.0405733\pi$
$383$	1.35677	+	5.06354i	0.0693278	+	0.258735i	−0.922560	+	0.385855i	$0.873907\pi$
$384$		0			0
$385$	3.47090	+	6.68275i	0.176893	+	0.340584i
$386$		−	15.3928i		−	0.783472i
$387$		0			0
$388$	4.02389	−	15.0174i	0.204282	−	0.762391i
$389$	−14.0642	−	24.3599i	−0.713082	−	1.23509i	−0.963695	−	0.267007i	$-0.913965\pi$
$389$	−14.0642	−	24.3599i	−0.713082	−	1.23509i	0.250613	−	0.968087i	$-0.419368\pi$
$390$		0			0
$391$	−25.7771			−1.30360
$392$	6.92421	+	1.02727i	0.349726	+	0.0518850i
$393$		0			0
$394$	−5.68280	−	3.28097i	−0.286295	−	0.165293i
$395$	2.42403	−	23.7239i	0.121966	−	1.19368i
$396$		0			0
$397$	0.872995	+	3.25806i	0.0438144	+	0.163518i	0.984367	−	0.176131i	$-0.0563584\pi$
$397$	0.872995	+	3.25806i	0.0438144	+	0.163518i	−0.940552	+	0.339649i	$0.889692\pi$
$398$	7.13998	−	7.13998i	0.357895	−	0.357895i
$399$		0			0
$400$	1.57260	+	4.74625i	0.0786302	+	0.237313i
$401$	−21.7433	−	12.5535i	−1.08581	−	0.626891i	−0.153350	−	0.988172i	$-0.549006\pi$
$401$	−21.7433	−	12.5535i	−1.08581	−	0.626891i	−0.932457	+	0.361281i	$0.882340\pi$
$402$		0			0
$403$	3.71046	−	13.8476i	0.184831	−	0.689799i
$404$	1.77660	−	3.07715i	0.0883889	−	0.153094i
$405$		0			0
$406$	3.24613	+	0.673388i	0.161103	+	0.0334197i
$407$	1.86316	+	1.86316i	0.0923536	+	0.0923536i
$408$		0			0
$409$	−8.80234	+	5.08203i	−0.435248	+	0.251290i	−0.701580	−	0.712591i	$-0.747522\pi$
$409$	−8.80234	+	5.08203i	−0.435248	+	0.251290i	0.266332	+	0.963881i	$0.414188\pi$
$410$	−1.13703	+	0.926217i	−0.0561541	+	0.0457426i
$411$		0			0
$412$	−4.17237	+	4.17237i	−0.205558	+	0.205558i
$413$	0.208499	+	3.63746i	0.0102596	+	0.178988i
$414$		0			0
$415$	−18.0040	−	6.85133i	−0.883782	−	0.336319i
$416$	2.63464	−	1.52111i	0.129174	−	0.0745785i
$417$		0			0
$418$	−8.81567	+	2.36215i	−0.431189	+	0.115537i
$419$	21.3453			1.04279			0.521394	−	0.853316i	$-0.325412\pi$
$419$	21.3453			1.04279			0.521394	+	0.853316i	$0.325412\pi$
$420$		0			0
$421$	27.7202			1.35100			0.675499	−	0.737360i	$-0.263928\pi$
$421$	27.7202			1.35100			0.675499	+	0.737360i	$0.263928\pi$
$422$	−27.0287	+	7.24233i	−1.31574	+	0.352551i
$423$		0			0
$424$	11.8928	−	6.86630i	0.577565	−	0.333457i
$425$	16.4984	+	25.0859i	0.800288	+	1.21685i
$426$		0			0
$427$	11.4030	−	7.48483i	0.551829	−	0.362216i
$428$	−4.18631	+	4.18631i	−0.202353	+	0.202353i
$429$		0			0
$430$	2.31593	−	22.6659i	0.111684	−	1.09304i
$431$	2.85680	−	1.64937i	0.137607	−	0.0794475i	−0.429616	−	0.903012i	$-0.641351\pi$
$431$	2.85680	−	1.64937i	0.137607	−	0.0794475i	0.567223	+	0.823564i	$0.308018\pi$
$432$		0			0
$433$	1.33257	+	1.33257i	0.0640390	+	0.0640390i	0.738401	−	0.674362i	$-0.235581\pi$
$433$	1.33257	+	1.33257i	0.0640390	+	0.0640390i	−0.674362	+	0.738401i	$0.735581\pi$
$434$	3.91079	+	11.8386i	0.187724	+	0.568270i
$435$		0			0
$436$	9.22986	−	15.9866i	0.442030	−	0.765619i
$437$	−7.96613	+	29.7300i	−0.381072	+	1.42218i
$438$		0			0
$439$	−10.1671	−	5.86996i	−0.485248	−	0.280158i	0.237353	−	0.971423i	$-0.423720\pi$
$439$	−10.1671	−	5.86996i	−0.485248	−	0.280158i	−0.722601	+	0.691266i	$0.757053\pi$
$440$	−2.80986	+	0.453385i	−0.133955	+	0.0216143i
$441$		0			0
$442$	12.9178	−	12.9178i	0.614436	−	0.614436i
$443$	3.56095	+	13.2896i	0.169186	+	0.631410i	0.997469	+	0.0711005i	$0.0226511\pi$
$443$	3.56095	+	13.2896i	0.169186	+	0.631410i	−0.828283	+	0.560309i	$0.810682\pi$
$444$		0			0
$445$	16.8780	+	1.72454i	0.800095	+	0.0817512i
$446$	9.03072	+	5.21389i	0.427617	+	0.246885i
$447$		0			0
$448$	−1.18959	+	2.36324i	−0.0562027	+	0.111652i
$449$	11.5137			0.543366			0.271683	−	0.962387i	$-0.412420\pi$
$449$	11.5137			0.543366			0.271683	+	0.962387i	$0.412420\pi$
$450$		0			0
$451$	−0.417406	−	0.722969i	−0.0196549	−	0.0340433i
$452$	−3.21719	+	12.0067i	−0.151324	+	0.564748i
$453$		0			0
$454$			11.2427i			0.527644i
$455$	−13.2809	+	12.1469i	−0.622616	+	0.569455i
$456$		0			0
$457$	−2.85813	−	10.6667i	−0.133698	−	0.498967i	0.866302	−	0.499520i	$-0.166490\pi$
$457$	−2.85813	−	10.6667i	−0.133698	−	0.498967i	−1.00000		0.000553622i	$0.999824\pi$
$458$	−10.4726	−	2.80611i	−0.489351	−	0.131121i
$459$		0			0
$460$	−3.41385	+	8.97095i	−0.159171	+	0.418273i
$461$		−	1.01453i		−	0.0472512i	−0.999721	−	0.0236256i	$-0.992479\pi$
$461$		−	1.01453i		−	0.0472512i	0.999721	−	0.0236256i	$-0.00752096\pi$
$462$		0			0
$463$	−12.8011	−	12.8011i	−0.594916	−	0.594916i	0.344039	−	0.938955i	$-0.388205\pi$
$463$	−12.8011	−	12.8011i	−0.594916	−	0.594916i	−0.938955	+	0.344039i	$0.888205\pi$
$464$	−0.626522	+	1.08517i	−0.0290855	+	0.0503776i
$465$		0			0
$466$	8.52472	+	14.7653i	0.394900	+	0.683987i
$467$	7.67187	−	2.05567i	0.355012	−	0.0951251i	−0.0769053	−	0.997038i	$-0.524504\pi$
$467$	7.67187	−	2.05567i	0.355012	−	0.0951251i	0.431917	+	0.901913i	$0.357837\pi$
$468$		0			0
$469$	8.56763	+	7.63869i	0.395616	+	0.352722i
$470$	−19.6506	−	14.1902i	−0.906413	−	0.654545i
$471$		0			0
$472$	−1.33017	−	0.356417i	−0.0612258	−	0.0164054i
$473$	12.5276	+	3.35676i	0.576020	+	0.154344i
$474$		0			0
$475$	34.0315	−	11.2759i	1.56147	−	0.517372i
$476$	−3.22710	+	15.5565i	−0.147914	+	0.713032i
$477$		0			0
$478$	−24.6430	+	6.60308i	−1.12715	+	0.302018i
$479$	20.3520	+	35.2507i	0.929906	+	1.61064i	0.783475	+	0.621424i	$0.213445\pi$
$479$	20.3520	+	35.2507i	0.929906	+	1.61064i	0.146431	+	0.989221i	$0.453221\pi$
$480$		0			0
$481$	−3.14880	+	5.45388i	−0.143573	+	0.248676i
$482$	11.0239	+	11.0239i	0.502127	+	0.502127i
$483$		0			0
$484$			9.37982i			0.426355i
$485$	−32.4913	−	12.3644i	−1.47536	−	0.561439i
$486$		0			0
$487$	−39.5785	−	10.6050i	−1.79347	−	0.480560i	−0.800546	−	0.599272i	$-0.795457\pi$
$487$	−39.5785	−	10.6050i	−1.79347	−	0.480560i	−0.992929	+	0.118712i	$0.962124\pi$
$488$	1.33433	+	4.97978i	0.0604022	+	0.225424i
$489$		0			0
$490$	3.85896	−	15.1693i	0.174330	−	0.685280i
$491$		−	26.8998i		−	1.21397i	−0.794714	−	0.606985i	$-0.792379\pi$
$491$		−	26.8998i		−	1.21397i	0.794714	−	0.606985i	$-0.207621\pi$
$492$		0			0
$493$	−1.94749	+	7.26812i	−0.0877104	+	0.327340i
$494$	−10.9066	−	18.8908i	−0.490712	−	0.849939i
$495$		0			0
$496$	−4.71239			−0.211592
$497$	0.189574	−	0.376609i	0.00850357	−	0.0168932i
$498$		0			0
$499$	0.480426	+	0.277374i	0.0215068	+	0.0124170i	0.510715	−	0.859750i	$-0.329381\pi$
$499$	0.480426	+	0.277374i	0.0215068	+	0.0124170i	−0.489208	+	0.872167i	$0.662714\pi$
$500$	10.9154	−	2.41945i	0.488152	−	0.108201i
$501$		0			0
$502$	2.80556	+	10.4705i	0.125218	+	0.467321i
$503$	6.68061	−	6.68061i	0.297874	−	0.297874i	−0.542307	−	0.840181i	$-0.682449\pi$
$503$	6.68061	−	6.68061i	0.297874	−	0.297874i	0.840181	+	0.542307i	$0.182449\pi$
$504$		0			0
$505$	−6.44128	−	4.65142i	−0.286633	−	0.206986i
$506$	−4.73187	−	2.73195i	−0.210357	−	0.121450i
$507$		0			0
$508$	1.83104	−	6.83354i	0.0812393	−	0.303189i
$509$	−14.5500	+	25.2013i	−0.644916	+	1.11703i	0.339405	+	0.940640i	$0.389774\pi$
$509$	−14.5500	+	25.2013i	−0.644916	+	1.11703i	−0.984321	+	0.176386i	$0.943559\pi$
$510$		0			0
$511$	18.0522	−	20.2475i	0.798582	−	0.895697i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	12.3862	−	7.15117i	0.546332	−	0.315425i
$515$	8.33304	+	10.2297i	0.367197	+	0.450775i
$516$		0			0
$517$	9.75636	−	9.75636i	0.429084	−	0.429084i
$518$	−0.313420	−	5.46791i	−0.0137709	−	0.240246i
$519$		0			0
$520$	−2.78486	−	6.20645i	−0.122124	−	0.272171i
$521$	16.9185	−	9.76787i	0.741211	−	0.427938i	−0.0812985	−	0.996690i	$-0.525907\pi$
$521$	16.9185	−	9.76787i	0.741211	−	0.427938i	0.822509	+	0.568752i	$0.192573\pi$
$522$		0			0
$523$	5.57326	−	1.49335i	0.243702	−	0.0652996i	−0.134901	−	0.990859i	$-0.543072\pi$
$523$	5.57326	−	1.49335i	0.243702	−	0.0652996i	0.378602	+	0.925559i	$0.376405\pi$
$524$	−19.3820			−0.846706
$525$		0			0
$526$	−5.47727			−0.238821
$527$	−27.3336	+	7.32402i	−1.19067	+	0.319039i
$528$		0			0
$529$	3.96080	−	2.28677i	0.172209	−	0.0994247i
$530$	−12.5709	−	28.0160i	−0.546044	−	1.21694i
$531$		0			0
$532$	16.9448	+	8.52955i	0.734651	+	0.369803i
$533$	1.41086	−	1.41086i	0.0611109	−	0.0611109i
$534$		0			0
$535$	8.36088	+	10.2639i	0.361472	+	0.443747i
$536$	−3.75719	+	2.16922i	−0.162286	+	0.0936958i
$537$		0			0
$538$	−15.5834	−	15.5834i	−0.671850	−	0.671850i
$539$	8.17483	+	3.54414i	0.352115	+	0.152657i
$540$		0			0
$541$	−9.14490	+	15.8394i	−0.393170	+	0.680991i	−0.992866	−	0.119238i	$-0.961955\pi$
$541$	−9.14490	+	15.8394i	−0.393170	+	0.680991i	0.599696	+	0.800228i	$0.295288\pi$
$542$	−1.62785	+	6.07524i	−0.0699224	+	0.260954i
$543$		0			0
$544$	−5.20048	−	3.00250i	−0.222969	−	0.128731i
$545$	−33.4641	−	24.1653i	−1.43344	−	1.03513i
$546$		0			0
$547$	−5.93008	+	5.93008i	−0.253552	+	0.253552i	−0.822425	−	0.568873i	$-0.807379\pi$
$547$	−5.93008	+	5.93008i	−0.253552	+	0.253552i	0.568873	+	0.822425i	$0.307379\pi$
$548$	1.64409	+	6.13584i	0.0702322	+	0.262110i
$549$		0			0
$550$	0.369891	+	6.35356i	0.0157722	+	0.270917i
$551$	7.78084	+	4.49227i	0.331475	+	0.191377i
$552$		0			0
$553$	−15.4836	−	23.5889i	−0.658429	−	1.00310i
$554$	21.9591			0.932955
$555$		0			0
$556$	−3.80509	−	6.59061i	−0.161372	−	0.279504i
$557$	−2.98750	+	11.1495i	−0.126584	+	0.472420i	−0.999891	−	0.0147511i	$-0.995304\pi$
$557$	−2.98750	+	11.1495i	−0.126584	+	0.472420i	0.873307	+	0.487171i	$0.161971\pi$
$558$		0			0
$559$			30.9979i			1.31107i
$560$	4.98660	+	3.18336i	0.210722	+	0.134522i
$561$		0			0
$562$	3.20425	+	11.9584i	0.135163	+	0.504436i
$563$	−19.5500	−	5.23840i	−0.823932	−	0.220772i	−0.177867	−	0.984054i	$-0.556920\pi$
$563$	−19.5500	−	5.23840i	−0.823932	−	0.220772i	−0.646065	+	0.763282i	$0.723587\pi$
$564$		0			0
$565$	25.9775	+	9.88561i	1.09288	+	0.415891i
$566$			17.3800i			0.730538i
$567$		0			0
$568$	0.112686	+	0.112686i	0.00472818	+	0.00472818i
$569$	−15.6705	+	27.1421i	−0.656941	+	1.13785i	0.324463	+	0.945898i	$0.394816\pi$
$569$	−15.6705	+	27.1421i	−0.656941	+	1.13785i	−0.981404	+	0.191956i	$0.938517\pi$
$570$		0			0
$571$	11.5290	+	19.9688i	0.482473	+	0.835669i	0.999798	−	0.0201210i	$-0.00640514\pi$
$571$	11.5290	+	19.9688i	0.482473	+	0.835669i	−0.517324	+	0.855790i	$0.673072\pi$
$572$	3.74038	−	1.00223i	0.156393	−	0.0419054i
$573$		0			0
$574$	−0.352457	+	1.69905i	−0.0147113	+	0.0709172i
$575$	19.1798	+	9.63307i	0.799854	+	0.401727i
$576$		0			0
$577$	−15.0655	−	4.03678i	−0.627183	−	0.168053i	−0.0687922	−	0.997631i	$-0.521915\pi$
$577$	−15.0655	−	4.03678i	−0.627183	−	0.168053i	−0.558391	+	0.829578i	$0.688581\pi$
$578$	−18.4105	−	4.93307i	−0.765775	−	0.205189i
$579$		0			0
$580$	2.27154	+	1.64034i	0.0943204	+	0.0681113i
$581$	−21.6426	+	7.14949i	−0.897888	+	0.296611i
$582$		0			0
$583$	16.8841	−	4.52409i	0.699269	−	0.187369i
$584$	5.12641	+	8.87921i	0.212133	+	0.367424i
$585$		0			0
$586$	13.9828	−	24.2189i	0.577623	−	1.00047i
$587$	11.2057	+	11.2057i	0.462508	+	0.462508i	0.899477	−	0.436969i	$-0.143948\pi$
$587$	11.2057	+	11.2057i	0.462508	+	0.462508i	−0.436969	+	0.899477i	$0.643948\pi$
$588$		0			0
$589$			33.7887i			1.39224i
$590$	−1.09518	+	2.87792i	−0.0450878	+	0.118482i
$591$		0			0
$592$	1.99953	+	0.535773i	0.0821803	+	0.0220201i
$593$	6.57925	+	24.5541i	0.270177	+	1.00832i	0.959005	+	0.283390i	$0.0914592\pi$
$593$	6.57925	+	24.5541i	0.270177	+	1.00832i	−0.688827	+	0.724925i	$0.741874\pi$
$594$		0			0
$595$	33.8718	+	10.7145i	1.38861	+	0.439251i
$596$		−	10.1079i		−	0.414038i
$597$		0			0
$598$	3.37993	−	12.6141i	0.138216	−	0.515828i
$599$	6.77896	+	11.7415i	0.276981	+	0.479745i	0.970633	−	0.240565i	$-0.0773328\pi$
$599$	6.77896	+	11.7415i	0.276981	+	0.479745i	−0.693652	+	0.720310i	$0.743999\pi$
$600$		0			0
$601$	−22.8479			−0.931983			−0.465992	−	0.884789i	$-0.654302\pi$
$601$	−22.8479			−0.931983			−0.465992	+	0.884789i	$0.654302\pi$
$602$	−14.7931	−	22.5369i	−0.602920	−	0.918536i
$603$		0			0
$604$	1.65874	+	0.957672i	0.0674930	+	0.0389671i
$605$	20.8653	+	2.13195i	0.848294	+	0.0866761i
$606$		0			0
$607$	11.7871	+	43.9900i	0.478423	+	1.78550i	0.608010	+	0.793929i	$0.291968\pi$
$607$	11.7871	+	43.9900i	0.478423	+	1.78550i	−0.129588	+	0.991568i	$0.541365\pi$
$608$	−5.07008	+	5.07008i	−0.205619	+	0.205619i
$609$		0			0
$610$	11.3807	−	1.83633i	0.460792	−	0.0743510i
$611$	28.5590	+	16.4885i	1.15537	+	0.667054i
$612$		0			0
$613$	4.52161	−	16.8749i	0.182626	−	0.681570i	−0.812500	−	0.582961i	$-0.801894\pi$
$613$	4.52161	−	16.8749i	0.182626	−	0.681570i	0.995126	−	0.0986088i	$-0.0314392\pi$
$614$	−5.34373	+	9.25562i	−0.215656	+	0.373526i
$615$		0			0
$616$	−2.24113	+	2.51368i	−0.0902978	+	0.101279i
$617$	22.6199	+	22.6199i	0.910643	+	0.910643i	0.996323	−	0.0856796i	$-0.0273061\pi$
$617$	22.6199	+	22.6199i	0.910643	+	0.910643i	−0.0856796	+	0.996323i	$0.527306\pi$
$618$		0			0
$619$	19.5089	−	11.2635i	0.784130	−	0.452718i	−0.0537621	−	0.998554i	$-0.517121\pi$
$619$	19.5089	−	11.2635i	0.784130	−	0.452718i	0.837892	+	0.545836i	$0.183788\pi$
$620$	−1.07108	+	10.4826i	−0.0430157	+	0.420993i
$621$		0			0
$622$	−0.925327	+	0.925327i	−0.0371022	+	0.0371022i
$623$	16.7820	−	11.0156i	0.672356	−	0.441330i
$624$		0			0
$625$	−2.90107	−	24.8311i	−0.116043	−	0.993244i
$626$	−20.1306	+	11.6224i	−0.804579	+	0.464524i
$627$		0			0
$628$	15.0279	−	4.02672i	0.599680	−	0.160684i
$629$	12.4307			0.495646
$630$		0			0
$631$	32.0217			1.27476			0.637381	−	0.770549i	$-0.280018\pi$
$631$	32.0217			1.27476			0.637381	+	0.770549i	$0.280018\pi$
$632$	10.3015	−	2.76027i	0.409771	−	0.109798i
$633$		0			0
$634$	21.0316	−	12.1426i	0.835270	−	0.482244i
$635$	−14.7849	−	5.62633i	−0.586722	−	0.223274i
$636$		0			0
$637$	−3.12518	+	21.0650i	−0.123824	+	0.834624i
$638$	−1.12780	+	1.12780i	−0.0446501	+	0.0446501i
$639$		0			0
$640$	−1.73367	+	1.41223i	−0.0685293	+	0.0558233i
$641$	−12.6297	+	7.29176i	−0.498843	+	0.288007i	−0.728236	−	0.685327i	$-0.759659\pi$
$641$	−12.6297	+	7.29176i	−0.498843	+	0.288007i	0.229392	+	0.973334i	$0.426326\pi$
$642$		0			0
$643$	28.0979	+	28.0979i	1.10807	+	1.10807i	0.993404	+	0.114671i	$0.0365814\pi$
$643$	28.0979	+	28.0979i	1.10807	+	1.10807i	0.114671	+	0.993404i	$0.463419\pi$
$644$	3.56241	+	10.7840i	0.140379	+	0.424949i
$645$		0			0
$646$	−21.5284	+	37.2883i	−0.847025	+	1.46709i
$647$	−1.62297	+	6.05702i	−0.0638057	+	0.238126i	−0.990463	−	0.137782i	$-0.956003\pi$
$647$	−1.62297	+	6.05702i	−0.0638057	+	0.238126i	0.926657	+	0.375908i	$0.122669\pi$
$648$		0			0
$649$	−1.51801	−	0.876423i	−0.0595870	−	0.0344026i
$650$	−14.4391	+	4.78420i	−0.566350	+	0.187652i
$651$		0			0
$652$	8.26763	−	8.26763i	0.323786	−	0.323786i
$653$	−4.00035	−	14.9295i	−0.156546	−	0.584237i	−0.998968	−	0.0454190i	$-0.985538\pi$
$653$	−4.00035	−	14.9295i	−0.156546	−	0.584237i	0.842422	−	0.538818i	$-0.181129\pi$
$654$		0			0
$655$	−4.40535	+	43.1150i	−0.172131	+	1.68464i
$656$	−0.567986	−	0.327927i	−0.0221761	−	0.0128034i
$657$		0			0
$658$	−28.6324	+	1.64121i	−1.11621	+	0.0639809i
$659$	33.1206			1.29019			0.645097	−	0.764101i	$-0.276817\pi$
$659$	33.1206			1.29019			0.645097	+	0.764101i	$0.276817\pi$
$660$		0			0
$661$	10.9940	+	19.0421i	0.427616	+	0.740653i	0.996661	−	0.0816540i	$-0.0260202\pi$
$661$	10.9940	+	19.0421i	0.427616	+	0.740653i	−0.569045	+	0.822307i	$0.692687\pi$
$662$	1.79679	−	6.70570i	0.0698341	−	0.260624i
$663$		0			0
$664$		−	8.61493i		−	0.334324i
$665$	22.8253	−	35.7548i	0.885126	−	1.38651i
$666$		0			0
$667$	1.39214	+	5.19554i	0.0539039	+	0.201172i
$668$	−12.0939	−	3.24055i	−0.467927	−	0.125381i
$669$		0			0
$670$	3.97141	+	8.85086i	0.153429	+	0.341939i
$671$			6.56218i			0.253330i
$672$		0			0
$673$	−29.8413	−	29.8413i	−1.15030	−	1.15030i	−0.986493	−	0.163806i	$-0.947623\pi$
$673$	−29.8413	−	29.8413i	−1.15030	−	1.15030i	−0.163806	−	0.986493i	$-0.552377\pi$
$674$	−5.71461	+	9.89800i	−0.220119	+	0.381257i
$675$		0			0
$676$	−1.87245	−	3.24319i	−0.0720175	−	0.124738i
$677$	10.7397	−	2.87769i	0.412760	−	0.110599i	−0.0464625	−	0.998920i	$-0.514795\pi$
$677$	10.7397	−	2.87769i	0.412760	−	0.110599i	0.459222	+	0.888321i	$0.348128\pi$
$678$		0			0
$679$	−39.0579	+	12.9025i	−1.49890	+	0.495152i
$680$	−7.86103	+	10.8859i	−0.301457	+	0.417457i
$681$		0			0
$682$	−5.79384	−	1.55245i	−0.221857	−	0.0594465i
$683$	−33.1375	−	8.87917i	−1.26797	−	0.339752i	−0.438718	−	0.898625i	$-0.644567\pi$
$683$	−33.1375	−	8.87917i	−1.26797	−	0.339752i	−0.829253	+	0.558873i	$0.811234\pi$
$684$		0			0
$685$	14.0228	−	2.26264i	0.535783	−	0.0864511i
$686$	−7.78062	−	16.8066i	−0.297066	−	0.641679i
$687$		0			0
$688$	9.84207	−	2.63717i	0.375225	−	0.100541i
$689$	20.8888	+	36.1805i	0.795800	+	1.37837i
$690$		0			0
$691$	−3.62966	+	6.28676i	−0.138079	+	0.239160i	−0.926769	−	0.375631i	$-0.877426\pi$
$691$	−3.62966	+	6.28676i	−0.138079	+	0.239160i	0.788690	+	0.614790i	$0.210759\pi$
$692$	−3.51452	−	3.51452i	−0.133602	−	0.133602i
$693$		0			0
$694$		−	17.0130i		−	0.645806i
$695$	−15.5256	+	6.96639i	−0.588919	+	0.264250i
$696$		0			0
$697$	−3.80420	−	1.01933i	−0.144094	−	0.0386100i
$698$	9.37310	+	34.9809i	0.354777	+	1.32405i
$699$		0			0
$700$	8.21475	−	10.3691i	0.310489	−	0.391914i
$701$			26.7254i			1.00940i	0.863294	+	0.504702i	$0.168398\pi$
$701$			26.7254i			1.00940i	−0.863294	+	0.504702i	$0.831602\pi$
$702$		0			0
$703$	3.84159	−	14.3370i	0.144888	−	0.540730i
$704$	−0.636431	−	1.10233i	−0.0239864	−	0.0415457i
$705$		0			0
$706$	−10.4853			−0.394620
$707$	−9.38546	+	0.537973i	−0.352976	+	0.0202326i
$708$		0			0
$709$	28.6346	+	16.5322i	1.07540	+	0.620880i	0.929651	−	0.368442i	$-0.120109\pi$
$709$	28.6346	+	16.5322i	1.07540	+	0.620880i	0.145745	+	0.989322i	$0.453442\pi$
$710$	0.276280	−	0.225055i	0.0103686	−	0.00844616i
$711$		0			0
$712$	1.96376	+	7.32885i	0.0735950	+	0.274660i
$713$	−14.3037	+	14.3037i	−0.535676	+	0.535676i
$714$		0			0
$715$	−1.37930	−	8.54822i	−0.0515827	−	0.319685i
$716$	17.7572	+	10.2521i	0.663619	+	0.383140i
$717$		0			0
$718$	7.47050	−	27.8803i	0.278797	−	1.04048i
$719$	−0.519410	+	0.899644i	−0.0193707	+	0.0335511i	−0.875548	−	0.483131i	$-0.839500\pi$
$719$	−0.519410	+	0.899644i	−0.0193707	+	0.0335511i	0.856178	+	0.516682i	$0.172833\pi$
$720$		0			0
$721$	15.2861	+	3.17101i	0.569286	+	0.118094i
$722$	22.9184	+	22.9184i	0.852934	+	0.852934i
$723$		0			0
$724$	−5.28055	+	3.04873i	−0.196250	+	0.113305i
$725$	4.16521	−	4.68017i	0.154692	−	0.173817i
$726$		0			0
$727$	−29.2601	+	29.2601i	−1.08520	+	1.08520i	−0.0891830	+	0.996015i	$0.528426\pi$
$727$	−29.2601	+	29.2601i	−1.08520	+	1.08520i	−0.996015	+	0.0891830i	$0.971574\pi$
$728$	−7.18948	−	3.61898i	−0.266460	−	0.134128i
$729$		0			0
$730$	20.9169	−	9.38547i	0.774168	−	0.347372i
$731$	52.9890	−	30.5932i	1.95987	−	1.13153i
$732$		0			0
$733$	−7.52853	+	2.01726i	−0.278073	+	0.0745094i	−0.395160	−	0.918612i	$-0.629311\pi$
$733$	−7.52853	+	2.01726i	−0.278073	+	0.0745094i	0.117087	+	0.993122i	$0.462644\pi$
$734$	−2.06755			−0.0763148
$735$		0			0
$736$	−4.29261			−0.158228
$737$	−5.33406	+	1.42926i	−0.196483	+	0.0526474i
$738$		0			0
$739$	−6.75740	+	3.90139i	−0.248575	+	0.143515i	−0.619112	−	0.785303i	$-0.712507\pi$
$739$	−6.75740	+	3.90139i	−0.248575	+	0.143515i	0.370537	+	0.928818i	$0.379174\pi$
$740$	1.64630	−	4.32615i	0.0605190	−	0.159033i
$741$		0			0
$742$	−32.4534	−	16.3361i	−1.19140	−	0.599718i
$743$	−22.5054	+	22.5054i	−0.825641	+	0.825641i	−0.986910	−	0.161269i	$-0.948441\pi$
$743$	−22.5054	+	22.5054i	−0.825641	+	0.825641i	0.161269	+	0.986910i	$0.448441\pi$
$744$		0			0
$745$	−22.4850	−	2.29745i	−0.823786	−	0.0841719i
$746$	31.0437	−	17.9231i	1.13659	−	0.656210i
$747$		0			0
$748$	−5.40479	−	5.40479i	−0.197619	−	0.197619i
$749$	15.3372	+	3.18160i	0.560409	+	0.116253i
$750$		0			0
$751$	0.992322	−	1.71875i	0.0362103	−	0.0627182i	−0.847352	−	0.531031i	$-0.821805\pi$
$751$	0.992322	−	1.71875i	0.0362103	−	0.0627182i	0.883563	+	0.468313i	$0.155138\pi$
$752$	2.80555	−	10.4704i	0.102308	−	0.381818i
$753$		0			0
$754$	−3.30132	−	1.90602i	−0.120227	−	0.0694130i
$755$	2.50734	−	3.47217i	0.0912516	−	0.126365i
$756$		0			0
$757$	−25.3998	+	25.3998i	−0.923171	+	0.923171i	−0.997252	−	0.0740808i	$-0.976398\pi$
$757$	−25.3998	+	25.3998i	−0.923171	+	0.923171i	0.0740808	+	0.997252i	$0.476398\pi$
$758$	−1.10776	−	4.13422i	−0.0402357	−	0.150162i
$759$		0			0
$760$	10.1259	+	12.4307i	0.367307	+	0.450909i
$761$	−37.3770	−	21.5796i	−1.35492	−	0.782261i	−0.365982	−	0.930622i	$-0.619267\pi$
$761$	−37.3770	−	21.5796i	−1.35492	−	0.782261i	−0.988933	+	0.148361i	$0.952600\pi$
$762$		0			0
$763$	−48.7598	+	2.79491i	−1.76522	+	0.101182i
$764$	−11.8724			−0.429528
$765$		0			0
$766$	2.62108	+	4.53985i	0.0947035	+	0.164031i
$767$	1.08430	−	4.04665i	0.0391517	−	0.146116i
$768$		0			0
$769$			21.4012i			0.771748i	0.922551	+	0.385874i	$0.126100\pi$
$769$			21.4012i			0.771748i	−0.922551	+	0.385874i	$0.873900\pi$
$770$	5.08225	+	5.55671i	0.183152	+	0.200250i
$771$		0			0
$772$	−3.98395	−	14.8683i	−0.143385	−	0.535121i
$773$	−6.64191	−	1.77969i	−0.238893	−	0.0640111i	0.137386	−	0.990518i	$-0.456130\pi$
$773$	−6.64191	−	1.77969i	−0.238893	−	0.0640111i	−0.376279	+	0.926506i	$0.622797\pi$
$774$		0			0
$775$	23.0750	+	4.76522i	0.828880	+	0.171172i
$776$		−	15.5471i		−	0.558109i
$777$		0			0
$778$	−19.8897	−	19.8897i	−0.713082	−	0.713082i
$779$	−2.35130	+	4.07256i	−0.0842439	+	0.145915i
$780$		0			0
$781$	0.101423	+	0.175669i	0.00362919	+	0.00628594i
$782$	−24.8987	+	6.67159i	−0.890377	+	0.238576i
$783$		0			0
$784$	6.95415	−	0.799850i	0.248363	−	0.0285661i
$785$	−5.54168	−	34.3447i	−0.197791	−	1.22581i
$786$		0			0
$787$	31.3540	+	8.40128i	1.11765	+	0.299473i	0.769932	−	0.638126i	$-0.220290\pi$
$787$	31.3540	+	8.40128i	1.11765	+	0.299473i	0.347718	+	0.937599i	$0.386957\pi$
$788$	−6.33834	−	1.69835i	−0.225794	−	0.0605013i
$789$		0			0
$790$	−3.79876	−	23.5429i	−0.135154	−	0.837618i
$791$	31.2276	−	10.3158i	1.11033	−	0.366788i
$792$		0			0
$793$	−15.1496	+	4.05932i	−0.537977	+	0.144151i
$794$	1.68650	+	2.92110i	0.0598516	+	0.103666i
$795$		0			0
$796$	5.04873	−	8.74465i	0.178947	−	0.309946i
$797$	−3.51487	−	3.51487i	−0.124503	−	0.124503i	0.642110	−	0.766613i	$-0.278059\pi$
$797$	−3.51487	−	3.51487i	−0.124503	−	0.124503i	−0.766613	+	0.642110i	$0.778059\pi$
$798$		0			0
$799$		−	65.0929i		−	2.30282i
$800$	2.74744	+	4.17751i	0.0971366	+	0.147697i
$801$		0			0
$802$	−24.2515	−	6.49816i	−0.856349	−	0.229458i
$803$	3.37770	+	12.6058i	0.119197	+	0.444848i
$804$		0			0
$805$	24.7985	−	5.47343i	0.874034	−	0.192913i
$806$		−	14.3361i		−	0.504968i
$807$		0			0
$808$	0.919634	−	3.43212i	0.0323526	−	0.120742i
$809$	−27.6293	−	47.8553i	−0.971393	−	1.68250i	−0.691357	−	0.722513i	$-0.742987\pi$
$809$	−27.6293	−	47.8553i	−0.971393	−	1.68250i	−0.280036	−	0.959989i	$-0.590346\pi$
$810$		0			0
$811$	−13.2246			−0.464380			−0.232190	−	0.972671i	$-0.574589\pi$
$811$	−13.2246			−0.464380			−0.232190	+	0.972671i	$0.574589\pi$
$812$	3.30981	−	0.189718i	0.116151	−	0.00665779i
$813$		0			0
$814$	2.28190	+	1.31746i	0.0799806	+	0.0461768i
$815$	−16.5121	−	20.2704i	−0.578393	−	0.710041i
$816$		0			0
$817$	−18.9090	−	70.5694i	−0.661542	−	2.46891i
$818$	−7.18708	+	7.18708i	−0.251290	+	0.251290i
$819$		0			0
$820$	−0.858567	+	1.18894i	−0.0299825	+	0.0415197i
$821$	14.2602	+	8.23311i	0.497683	+	0.287337i	0.727756	−	0.685836i	$-0.240563\pi$
$821$	14.2602	+	8.23311i	0.497683	+	0.287337i	−0.230073	+	0.973173i	$0.573897\pi$
$822$		0			0
$823$	−9.09410	+	33.9396i	−0.317000	+	1.18306i	0.605112	+	0.796140i	$0.293128\pi$
$823$	−9.09410	+	33.9396i	−0.317000	+	1.18306i	−0.922113	+	0.386921i	$0.873539\pi$
$824$	−2.95031	+	5.11009i	−0.102779	+	0.178018i
$825$		0			0
$826$	1.14284	+	3.45956i	0.0397645	+	0.120373i
$827$	−27.5730	−	27.5730i	−0.958808	−	0.958808i	0.0403769	−	0.999185i	$-0.487144\pi$
$827$	−27.5730	−	27.5730i	−0.958808	−	0.958808i	−0.999185	+	0.0403769i	$0.987144\pi$
$828$		0			0
$829$	−31.2154	+	18.0222i	−1.08416	+	0.625938i	−0.932014	−	0.362421i	$-0.881950\pi$
$829$	−31.2154	+	18.0222i	−1.08416	+	0.625938i	−0.152141	+	0.988359i	$0.548617\pi$
$830$	−19.1638	−	1.95810i	−0.665185	−	0.0679665i
$831$		0			0
$832$	2.15117	−	2.15117i	0.0745785	−	0.0745785i
$833$	39.0936	−	15.4476i	1.35451	−	0.535228i
$834$		0			0
$835$	−9.95740	+	26.1662i	−0.344590	+	0.905518i
$836$	−7.90391	+	4.56333i	−0.273363	+	0.157826i
$837$		0			0
$838$	20.6180	−	5.52458i	0.712237	−	0.190843i
$839$	16.9254			0.584331			0.292165	−	0.956368i	$-0.405624\pi$
$839$	16.9254			0.584331			0.292165	+	0.956368i	$0.405624\pi$
$840$		0			0
$841$	−27.4299			−0.945858
$842$	26.7756	−	7.17451i	0.922749	−	0.247250i
$843$		0			0
$844$	−24.2333	+	13.9911i	−0.834144	+	0.481593i
$845$	−7.64001	+	3.42810i	−0.262824	+	0.117930i
$846$		0			0
$847$	20.7466	−	13.6179i	0.712861	−	0.467916i
$848$	9.71042	−	9.71042i	0.333457	−	0.333457i
$849$		0			0
$850$	22.4289	+	19.9610i	0.769305	+	0.684658i
$851$	7.69549	−	4.44299i	0.263798	−	0.152304i
$852$		0			0
$853$	−1.10865	−	1.10865i	−0.0379596	−	0.0379596i	0.687872	−	0.725832i	$-0.258545\pi$
$853$	−1.10865	−	1.10865i	−0.0379596	−	0.0379596i	−0.725832	+	0.687872i	$0.758545\pi$
$854$	9.07721	−	10.1811i	0.310616	−	0.348390i
$855$		0			0
$856$	−2.96017	+	5.12716i	−0.101176	+	0.175243i
$857$	−2.16107	+	8.06522i	−0.0738207	+	0.275503i	−0.992963	−	0.118422i	$-0.962216\pi$
$857$	−2.16107	+	8.06522i	−0.0738207	+	0.275503i	0.919143	+	0.393925i	$0.128883\pi$
$858$		0			0
$859$	42.1088	+	24.3115i	1.43674	+	0.829499i	0.997621	−	0.0689321i	$-0.0219592\pi$
$859$	42.1088	+	24.3115i	1.43674	+	0.829499i	0.439114	+	0.898431i	$0.355293\pi$
$860$	−3.62934	−	22.4929i	−0.123760	−	0.767003i
$861$		0			0
$862$	2.33257	−	2.33257i	0.0794475	−	0.0794475i
$863$	−3.72597	−	13.9055i	−0.126834	−	0.473349i	0.873065	−	0.487604i	$-0.162129\pi$
$863$	−3.72597	−	13.9055i	−0.126834	−	0.473349i	−0.999898	+	0.0142549i	$0.995462\pi$
$864$		0			0
$865$	−8.61682	+	7.01918i	−0.292981	+	0.238659i
$866$	1.63205	+	0.942266i	0.0554594	+	0.0320195i
$867$		0			0
$868$	6.84158	+	10.4230i	0.232218	+	0.353780i
$869$	13.5749			0.460498
$870$		0			0
$871$	−6.59923	−	11.4302i	−0.223606	−	0.387297i
$872$	4.77773	−	17.8307i	0.161794	−	0.603825i
$873$		0			0
$874$			30.7788i			1.04111i
$875$	−21.1987	−	20.6304i	−0.716648	−	0.697435i
$876$		0			0
$877$	−9.97124	−	37.2132i	−0.336705	−	1.25660i	−0.902009	−	0.431717i	$-0.857908\pi$
$877$	−9.97124	−	37.2132i	−0.336705	−	1.25660i	0.565304	−	0.824882i	$-0.308759\pi$
$878$	−11.3399	−	3.03851i	−0.382703	−	0.102545i
$879$		0			0
$880$	−2.59678	+	1.16518i	−0.0875373	+	0.0392783i
$881$			46.3316i			1.56095i	0.625187	+	0.780475i	$0.285023\pi$
$881$			46.3316i			1.56095i	−0.625187	+	0.780475i	$0.714977\pi$
$882$		0			0
$883$	4.38151	+	4.38151i	0.147450	+	0.147450i	0.776978	−	0.629528i	$-0.216752\pi$
$883$	4.38151	+	4.38151i	0.147450	+	0.147450i	−0.629528	+	0.776978i	$0.716752\pi$
$884$	9.13425	−	15.8210i	0.307218	−	0.532117i
$885$		0			0
$886$	6.87922	+	11.9152i	0.231112	+	0.400298i
$887$	40.7161	−	10.9098i	1.36711	−	0.366317i	0.500689	−	0.865627i	$-0.333080\pi$
$887$	40.7161	−	10.9098i	1.36711	−	0.366317i	0.866423	+	0.499311i	$0.166413\pi$
$888$		0			0
$889$	−17.7730	+	5.87118i	−0.596087	+	0.196913i
$890$	16.7493	−	2.70257i	0.561437	−	0.0905904i
$891$		0			0
$892$	10.0725	+	2.69891i	0.337251	+	0.0903661i
$893$	−75.0750	−	20.1163i	−2.51229	−	0.673166i
$894$		0			0
$895$	26.8418	−	37.1705i	0.897222	−	1.24247i
$896$	−0.537402	+	2.59060i	−0.0179533	+	0.0865458i
$897$		0			0
$898$	11.1214	−	2.97997i	0.371126	−	0.0994429i
$899$	2.95241	+	5.11373i	0.0984684	+	0.170552i
$900$		0			0
$901$	41.2321	−	71.4161i	1.37364	−	2.37922i
$902$	−0.590301	−	0.590301i	−0.0196549	−	0.0196549i
$903$		0			0
$904$			12.4303i			0.413424i
$905$	5.58163	+	12.4395i	0.185540	+	0.413502i
$906$		0			0
$907$	−52.2562	−	14.0020i	−1.73514	−	0.464929i	−0.753783	−	0.657124i	$-0.771773\pi$
$907$	−52.2562	−	14.0020i	−1.73514	−	0.464929i	−0.981357	+	0.192195i	$0.938440\pi$
$908$	2.90981	+	10.8596i	0.0965656	+	0.360388i
$909$		0			0
$910$	−9.68448	+	15.1703i	−0.321037	+	0.502892i
$911$		−	35.0545i		−	1.16141i	−0.814115	−	0.580704i	$-0.802777\pi$
$911$		−	35.0545i		−	1.16141i	0.814115	−	0.580704i	$-0.197223\pi$
$912$		0			0
$913$	2.83811	−	10.5920i	0.0939278	−	0.350543i
$914$	−5.52149	−	9.56350i	−0.182635	−	0.316332i
$915$		0			0
$916$	−10.8420			−0.358230
$917$	28.1393	+	42.8697i	0.929243	+	1.41568i
$918$		0			0
$919$	24.5646	+	14.1824i	0.810310	+	0.467833i	0.847064	−	0.531492i	$-0.178368\pi$
$919$	24.5646	+	14.1824i	0.810310	+	0.467833i	−0.0367535	+	0.999324i	$0.511702\pi$
$920$	−0.975671	+	9.54884i	−0.0321669	+	0.314816i
$921$		0			0
$922$	−0.262579	−	0.979957i	−0.00864757	−	0.0322732i
$923$	−0.342814	+	0.342814i	−0.0112839	+	0.0112839i
$924$		0			0
$925$	−9.24928	−	4.64546i	−0.304115	−	0.152742i
$926$	−15.6780	−	9.05172i	−0.515212	−	0.297458i
$927$		0			0
$928$	−0.324311	+	1.21035i	−0.0106460	+	0.0397316i
$929$	−23.6445	+	40.9535i	−0.775752	+	1.34364i	0.158619	+	0.987340i	$0.449296\pi$
$929$	−23.6445	+	40.9535i	−0.775752	+	1.34364i	−0.934371	+	0.356301i	$0.884038\pi$
$930$		0			0
$931$	−5.73507	−	49.8625i	−0.187959	−	1.63418i
$932$	12.0558	+	12.0558i	0.394900	+	0.394900i
$933$		0			0
$934$	6.87841	−	3.97125i	0.225069	−	0.129943i
$935$	−13.2513	+	10.7944i	−0.433365	+	0.353015i
$936$		0			0
$937$	41.4793	−	41.4793i	1.35507	−	1.35507i	0.475182	−	0.879888i	$-0.342382\pi$
$937$	41.4793	−	41.4793i	1.35507	−	1.35507i	0.879888	−	0.475182i	$-0.157618\pi$
$938$	10.2527	+	5.16094i	0.334764	+	0.168511i
$939$		0			0
$940$	−22.6537	−	8.62074i	−0.738882	−	0.281178i
$941$	22.6321	−	13.0667i	0.737786	−	0.425961i	−0.0834777	−	0.996510i	$-0.526603\pi$
$941$	22.6321	−	13.0667i	0.737786	−	0.425961i	0.821264	+	0.570549i	$0.193269\pi$
$942$		0			0
$943$	−2.71939	+	0.728659i	−0.0885556	+	0.0237284i
$944$	−1.37709			−0.0448204
$945$		0			0
$946$	12.9695			0.421676
$947$	28.8745	−	7.73689i	0.938294	−	0.251415i	0.242906	−	0.970050i	$-0.421899\pi$
$947$	28.8745	−	7.73689i	0.938294	−	0.251415i	0.695388	+	0.718635i	$0.255233\pi$
$948$		0			0
$949$	−27.0125	+	15.5957i	−0.876863	+	0.506257i
$950$	29.9535	−	19.6996i	0.971819	−	0.639141i
$951$		0			0
$952$	0.909190	+	15.8617i	0.0294670	+	0.514080i
$953$	10.7391	−	10.7391i	0.347873	−	0.347873i	−0.511444	−	0.859317i	$-0.670889\pi$
$953$	10.7391	−	10.7391i	0.347873	−	0.347873i	0.859317	+	0.511444i	$0.170889\pi$
$954$		0			0
$955$	−2.69849	+	26.4100i	−0.0873211	+	0.854607i
$956$	−22.0943	+	12.7562i	−0.714582	+	0.412564i
$957$		0			0
$958$	28.7821	+	28.7821i	0.929906	+	0.929906i
$959$	11.1845	−	12.5446i	0.361166	−	0.405088i
$960$		0			0
$961$	4.39671	−	7.61532i	0.141829	−	0.245656i
$962$	−1.62994	+	6.08301i	−0.0525513	+	0.196124i
$963$		0			0
$964$	13.5015	+	7.79510i	0.434854	+	0.251063i
$965$	−33.9798	+	5.48280i	−1.09385	+	0.176498i
$966$		0			0
$967$	−26.6517	+	26.6517i	−0.857060	+	0.857060i	−0.990991	−	0.133931i	$-0.957240\pi$
$967$	−26.6517	+	26.6517i	−0.857060	+	0.857060i	0.133931	+	0.990991i	$0.457240\pi$
$968$	2.42768	+	9.06021i	0.0780285	+	0.291206i
$969$		0			0
$970$	−34.5844	−	3.53372i	−1.11044	−	0.113461i
$971$	3.66101	+	2.11368i	0.117487	+	0.0678313i	0.557592	−	0.830115i	$-0.311725\pi$
$971$	3.66101	+	2.11368i	0.117487	+	0.0678313i	−0.440105	+	0.897946i	$0.645059\pi$
$972$		0			0
$973$	−9.05297	+	17.9847i	−0.290225	+	0.576562i
$974$	−40.9747			−1.31291
$975$		0			0
$976$	2.57772	+	4.46475i	0.0825109	+	0.142913i
$977$	8.46277	−	31.5835i	0.270748	−	1.01045i	−0.687889	−	0.725816i	$-0.741463\pi$
$977$	8.46277	−	31.5835i	0.270748	−	1.01045i	0.958637	−	0.284630i	$-0.0918707\pi$
$978$		0			0
$979$			9.65769i			0.308661i
$980$	−0.198639	−	15.6512i	−0.00634530	−	0.499960i
$981$		0			0
$982$	−6.96217	−	25.9832i	−0.222172	−	0.829156i
$983$	10.3141	+	2.76365i	0.328968	+	0.0881467i	0.419523	−	0.907745i	$-0.362197\pi$
$983$	10.3141	+	2.76365i	0.328968	+	0.0881467i	−0.0905549	+	0.995891i	$0.528864\pi$
$984$		0			0
$985$	−5.21861	+	13.7135i	−0.166279	+	0.436949i
$986$			7.52451i			0.239629i
$987$		0			0
$988$	−15.4243	−	15.4243i	−0.490712	−	0.490712i
$989$	21.8692	−	37.8786i	0.695401	−	1.20447i
$990$		0			0
$991$	26.7818	+	46.3874i	0.850751	+	1.47354i	0.880532	+	0.473987i	$0.157186\pi$
$991$	26.7818	+	46.3874i	0.850751	+	1.47354i	−0.0297806	+	0.999556i	$0.509481\pi$
$992$	−4.55182	+	1.21966i	−0.144520	+	0.0387241i
$993$		0			0
$994$	0.0856412	−	0.412841i	0.00271637	−	0.0130945i
$995$	−18.3048	−	13.2184i	−0.580302	−	0.419052i
$996$		0			0
$997$	−6.25021	−	1.67474i	−0.197946	−	0.0530395i	0.158484	−	0.987362i	$-0.449339\pi$
$997$	−6.25021	−	1.67474i	−0.197946	−	0.0530395i	−0.356430	+	0.934322i	$0.616006\pi$
$998$	0.535846	+	0.143580i	0.0169619	+	0.00454493i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.c.233.6	yes	32
3.2	odd	2	inner	630.2.ce.c.233.3	yes	32
5.2	odd	4	inner	630.2.ce.c.107.5	yes	32
7.4	even	3	inner	630.2.ce.c.53.4	✓	32
15.2	even	4	inner	630.2.ce.c.107.4	yes	32
21.11	odd	6	inner	630.2.ce.c.53.5	yes	32
35.32	odd	12	inner	630.2.ce.c.557.3	yes	32
105.32	even	12	inner	630.2.ce.c.557.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.c.53.4	✓	32	7.4	even	3	inner
630.2.ce.c.53.5	yes	32	21.11	odd	6	inner
630.2.ce.c.107.4	yes	32	15.2	even	4	inner
630.2.ce.c.107.5	yes	32	5.2	odd	4	inner
630.2.ce.c.233.3	yes	32	3.2	odd	2	inner
630.2.ce.c.233.6	yes	32	1.1	even	1	trivial
630.2.ce.c.557.3	yes	32	35.32	odd	12	inner
630.2.ce.c.557.6	yes	32	105.32	even	12	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.915403 - 2.04011i) q^{5} +(-2.36324 - 1.18959i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.915403 - 2.04011i) q^{5} +(-2.36324 - 1.18959i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.41223 - 1.73367i) q^{10} +(1.10233 - 0.636431i) q^{11} +(2.15117 + 2.15117i) q^{13} +(-2.59060 - 0.537402i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.55421 - 5.80038i) q^{17} +(-6.20956 - 3.58509i) q^{19} +(-1.81282 - 1.30908i) q^{20} +(0.900050 - 0.900050i) q^{22} +(-1.11101 - 4.14634i) q^{23} +(-3.32407 + 3.73504i) q^{25} +(2.63464 + 1.52111i) q^{26} +(-2.64142 + 0.151406i) q^{28} -1.25304 q^{29} +(-2.35619 - 4.08105i) q^{31} +(0.258819 - 0.965926i) q^{32} -6.00499i q^{34} +(-0.263570 + 5.91021i) q^{35} +(0.535773 + 1.99953i) q^{37} +(-6.92586 - 1.85578i) q^{38} +(-2.08986 - 0.795286i) q^{40} -0.655854i q^{41} +(7.20489 + 7.20489i) q^{43} +(0.636431 - 1.10233i) q^{44} +(-2.14630 - 3.71751i) q^{46} +(10.4704 - 2.80555i) q^{47} +(4.16977 + 5.62255i) q^{49} +(-2.24411 + 4.46811i) q^{50} +(2.93856 + 0.787384i) q^{52} +(13.2647 + 3.55426i) q^{53} +(-2.30747 - 1.66628i) q^{55} +(-2.51222 + 0.829895i) q^{56} +(-1.21035 + 0.324311i) q^{58} +(-0.688544 - 1.19259i) q^{59} +(-2.57772 + 4.46475i) q^{61} +(-3.33216 - 3.33216i) q^{62} -1.00000i q^{64} +(2.41943 - 6.35781i) q^{65} +(-4.19060 - 1.12287i) q^{67} +(-1.55421 - 5.80038i) q^{68} +(1.27508 + 5.77704i) q^{70} +0.159361i q^{71} +(-2.65363 + 9.90347i) q^{73} +(1.03503 + 1.79273i) q^{74} -7.17018 q^{76} +(-3.36216 + 0.192719i) q^{77} +(9.23605 + 5.33244i) q^{79} +(-2.22449 - 0.227291i) q^{80} +(-0.169748 - 0.633506i) q^{82} +(6.09168 - 6.09168i) q^{83} +(-13.2561 + 2.13894i) q^{85} +(8.82415 + 5.09463i) q^{86} +(0.329441 - 1.22949i) q^{88} +(-3.79369 + 6.57086i) q^{89} +(-2.52472 - 7.64274i) q^{91} +(-3.03533 - 3.03533i) q^{92} +(9.38755 - 5.41990i) q^{94} +(-1.62972 + 15.9500i) q^{95} +(10.9935 - 10.9935i) q^{97} +(5.48291 + 4.35175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{7}+O(q^{10}) \) 32 * q - 12 * q^7	\( 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) \) 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

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