LMFDB - Embedded newform 630.2.ce.c.53.4

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			53.4
Character	$\chi$	$=$	630.53
Dual form			630.2.ce.c.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.22449 + 0.227291i) q^{5} +(1.18959 + 2.36324i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.22449 + 0.227291i) q^{5} +(1.18959 + 2.36324i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.795286 + 2.08986i) q^{10} +(-1.10233 - 0.636431i) q^{11} +(2.15117 + 2.15117i) q^{13} +(-2.59060 + 0.537402i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-5.80038 + 1.55421i) q^{17} +(6.20956 - 3.58509i) q^{19} +(-1.81282 - 1.30908i) q^{20} +(0.900050 - 0.900050i) q^{22} +(4.14634 + 1.11101i) q^{23} +(4.89668 + 1.01121i) q^{25} +(-2.63464 + 1.52111i) q^{26} +(0.151406 - 2.64142i) q^{28} -1.25304 q^{29} +(-2.35619 + 4.08105i) q^{31} +(-0.965926 + 0.258819i) q^{32} -6.00499i q^{34} +(2.10908 + 5.52737i) q^{35} +(-1.99953 - 0.535773i) q^{37} +(1.85578 + 6.92586i) q^{38} +(1.73367 - 1.41223i) q^{40} -0.655854i q^{41} +(7.20489 + 7.20489i) q^{43} +(0.636431 + 1.10233i) q^{44} +(-2.14630 + 3.71751i) q^{46} +(-2.80555 + 10.4704i) q^{47} +(-4.16977 + 5.62255i) q^{49} +(-2.24411 + 4.46811i) q^{50} +(-0.787384 - 2.93856i) q^{52} +(-3.55426 - 13.2647i) q^{53} +(-2.30747 - 1.66628i) q^{55} +(2.51222 + 0.829895i) q^{56} +(0.324311 - 1.21035i) q^{58} +(-0.688544 + 1.19259i) q^{59} +(-2.57772 - 4.46475i) q^{61} +(-3.33216 - 3.33216i) q^{62} -1.00000i q^{64} +(4.29631 + 5.27420i) q^{65} +(1.12287 + 4.19060i) q^{67} +(5.80038 + 1.55421i) q^{68} +(-5.88490 + 0.606624i) q^{70} +0.159361i q^{71} +(9.90347 - 2.65363i) q^{73} +(1.03503 - 1.79273i) q^{74} -7.17018 q^{76} +(0.192719 - 3.36216i) q^{77} +(-9.23605 + 5.33244i) q^{79} +(0.915403 + 2.04011i) q^{80} +(0.633506 + 0.169748i) q^{82} +(6.09168 - 6.09168i) q^{83} +(-13.2561 + 2.13894i) q^{85} +(-8.82415 + 5.09463i) q^{86} +(-1.22949 + 0.329441i) q^{88} +(-3.79369 - 6.57086i) q^{89} +(-2.52472 + 7.64274i) q^{91} +(-3.03533 - 3.03533i) q^{92} +(-9.38755 - 5.41990i) q^{94} +(14.6279 - 6.56361i) q^{95} +(10.9935 - 10.9935i) q^{97} +(-4.35175 - 5.48291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.22449	+	0.227291i	0.994820	+	0.101648i
$5$	2.22449	+	0.227291i	0.994820	+	0.101648i
$6$		0			0
$7$	1.18959	+	2.36324i	0.449622	+	0.893219i
$7$	1.18959	+	2.36324i	0.449622	+	0.893219i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.795286	+	2.08986i	−0.251491	+	0.660872i
$11$	−1.10233	−	0.636431i	−0.332365	−	0.191891i	0.324525	−	0.945877i	$-0.394795\pi$
$11$	−1.10233	−	0.636431i	−0.332365	−	0.191891i	−0.656891	+	0.753986i	$0.728129\pi$
$12$		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
$17$	−5.80038	+	1.55421i	−1.40680	+	0.376950i	−0.880781	−	0.473524i	$-0.842982\pi$
$17$	−5.80038	+	1.55421i	−1.40680	+	0.376950i	−0.526017	+	0.850474i	$0.676315\pi$
$18$		0			0
$19$	6.20956	−	3.58509i	1.42457	−	0.822476i	0.427885	−	0.903833i	$-0.359259\pi$
$19$	6.20956	−	3.58509i	1.42457	−	0.822476i	0.996685	+	0.0813571i	$0.0259254\pi$
$20$	−1.81282	−	1.30908i	−0.405358	−	0.292720i
$21$		0			0
$22$	0.900050	−	0.900050i	0.191891	−	0.191891i
$23$	4.14634	+	1.11101i	0.864571	+	0.231661i	0.663739	−	0.747964i	$-0.268969\pi$
$23$	4.14634	+	1.11101i	0.864571	+	0.231661i	0.200833	+	0.979626i	$0.435635\pi$
$24$		0			0
$25$	4.89668	+	1.01121i	0.979336	+	0.202242i
$26$	−2.63464	+	1.52111i	−0.516695	+	0.298314i
$27$		0			0
$28$	0.151406	−	2.64142i	0.0286130	−	0.499181i
$29$	−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	−0.996249	−	0.0865329i	$-0.972421\pi$
$31$	−2.35619	+	4.08105i	−0.423185	+	0.732978i	0.573064	+	0.819510i	$0.305755\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$		−	6.00499i		−	1.02985i
$35$	2.10908	+	5.52737i	0.356499	+	0.934296i
$36$		0			0
$37$	−1.99953	−	0.535773i	−0.328721	−	0.0880805i	0.0906841	−	0.995880i	$-0.471095\pi$
$37$	−1.99953	−	0.535773i	−0.328721	−	0.0880805i	−0.419405	+	0.907799i	$0.637761\pi$
$38$	1.85578	+	6.92586i	0.301047	+	1.12352i
$39$		0			0
$40$	1.73367	−	1.41223i	0.274117	−	0.223293i
$41$		−	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
$47$	−2.80555	+	10.4704i	−0.409231	+	1.52727i	0.386885	+	0.922128i	$0.373551\pi$
$47$	−2.80555	+	10.4704i	−0.409231	+	1.52727i	−0.796116	+	0.605144i	$0.793116\pi$
$48$		0			0
$49$	−4.16977	+	5.62255i	−0.595681	+	0.803221i
$50$	−2.24411	+	4.46811i	−0.317365	+	0.631886i
$51$		0			0
$52$	−0.787384	−	2.93856i	−0.109191	−	0.407505i
$53$	−3.55426	−	13.2647i	−0.488215	−	1.82204i	−0.565124	−	0.825006i	$-0.691172\pi$
$53$	−3.55426	−	13.2647i	−0.488215	−	1.82204i	0.0769086	−	0.997038i	$-0.475495\pi$
$54$		0			0
$55$	−2.30747	−	1.66628i	−0.311139	−	0.224682i
$56$	2.51222	+	0.829895i	0.335710	+	0.110899i
$57$		0			0
$58$	0.324311	−	1.21035i	0.0425842	−	0.158926i
$59$	−0.688544	+	1.19259i	−0.0896409	+	0.155263i	−0.907359	−	0.420356i	$-0.861905\pi$
$59$	−0.688544	+	1.19259i	−0.0896409	+	0.155263i	0.817718	+	0.575618i	$0.195239\pi$
$60$		0			0
$61$	−2.57772	−	4.46475i	−0.330044	−	0.571652i	0.652476	−	0.757809i	$-0.273730\pi$
$61$	−2.57772	−	4.46475i	−0.330044	−	0.571652i	−0.982520	+	0.186157i	$0.940397\pi$
$62$	−3.33216	−	3.33216i	−0.423185	−	0.423185i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	4.29631	+	5.27420i	0.532892	+	0.654184i
$66$		0			0
$67$	1.12287	+	4.19060i	0.137180	+	0.511964i	0.999979	+	0.00641674i	$0.00204253\pi$
$67$	1.12287	+	4.19060i	0.137180	+	0.511964i	−0.862799	+	0.505547i	$0.831291\pi$
$68$	5.80038	+	1.55421i	0.703399	+	0.188475i
$69$		0			0
$70$	−5.88490	+	0.606624i	−0.703380	+	0.0725054i
$71$			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
$73$	9.90347	−	2.65363i	1.15911	−	0.310584i	0.372502	−	0.928031i	$-0.378500\pi$
$73$	9.90347	−	2.65363i	1.15911	−	0.310584i	0.786612	+	0.617448i	$0.211833\pi$
$74$	1.03503	−	1.79273i	0.120320	−	0.208401i
$75$		0			0
$76$	−7.17018			−0.822476
$77$	0.192719	−	3.36216i	0.0219623	−	0.383154i
$78$		0			0
$79$	−9.23605	+	5.33244i	−1.03914	+	0.599946i	−0.919589	−	0.392882i	$-0.871478\pi$
$79$	−9.23605	+	5.33244i	−1.03914	+	0.599946i	−0.119548	+	0.992828i	$0.538145\pi$
$80$	0.915403	+	2.04011i	0.102345	+	0.228091i
$81$		0			0
$82$	0.633506	+	0.169748i	0.0699591	+	0.0187455i
$83$	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
$88$	−1.22949	+	0.329441i	−0.131064	+	0.0351185i
$89$	−3.79369	−	6.57086i	−0.402130	−	0.696510i	0.591852	−	0.806046i	$-0.298397\pi$
$89$	−3.79369	−	6.57086i	−0.402130	−	0.696510i	−0.993983	+	0.109536i	$0.965063\pi$
$90$		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
$95$	14.6279	−	6.56361i	1.50079	−	0.673412i
$96$		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	$-0.0395488\pi$
$98$	−4.35175	−	5.48291i	−0.439593	−	0.553857i
$99$		0			0
$100$	−3.73504	−	3.32407i	−0.373504	−	0.332407i
$101$	−3.07715	−	1.77660i	−0.306188	−	0.176778i	0.339031	−	0.940775i	$-0.389901\pi$
$101$	−3.07715	−	1.77660i	−0.306188	−	0.176778i	−0.645220	+	0.763997i	$0.723234\pi$
$102$		0			0
$103$	1.52719	−	5.69956i	0.150479	−	0.561595i	−0.848971	−	0.528439i	$-0.822778\pi$
$103$	1.52719	−	5.69956i	0.150479	−	0.561595i	0.999450	−	0.0331558i	$-0.0105558\pi$
$104$	3.04222			0.298314
$105$		0			0
$106$	13.7326			1.33383
$107$	1.53230	−	5.71860i	0.148133	−	0.552838i	−0.851463	−	0.524414i	$-0.824284\pi$
$107$	1.53230	−	5.71860i	0.148133	−	0.552838i	0.999596	−	0.0284243i	$-0.00904895\pi$
$108$		0			0
$109$	−15.9866	−	9.22986i	−1.53124	−	0.884061i	−0.999305	−	0.0372741i	$-0.988133\pi$
$109$	−15.9866	−	9.22986i	−1.53124	−	0.884061i	−0.531933	−	0.846787i	$-0.678534\pi$
$110$	2.20672	−	1.79758i	0.210403	−	0.171392i
$111$		0			0
$112$	−1.45183	+	2.21183i	−0.137185	+	0.208998i
$113$	−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
$115$	8.97095	+	3.41385i	0.836545	+	0.318343i
$116$	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
$122$	4.97978	−	1.33433i	0.450848	−	0.120804i
$123$		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	$0.148370\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	−6.20645	+	2.78486i	−0.544342	+	0.244248i
$131$	16.7853	−	9.69100i	1.46654	−	0.846706i	0.467239	−	0.884131i	$-0.345249\pi$
$131$	16.7853	−	9.69100i	1.46654	−	0.846706i	0.999299	+	0.0374245i	$0.0119154\pi$
$132$		0			0
$133$	15.8592	+	10.4099i	1.37517	+	0.902651i
$134$	−4.33843			−0.374783
$135$		0			0
$136$	−3.00250	+	5.20048i	−0.257462	+	0.445937i
$137$	6.13584	−	1.64409i	0.524220	−	0.140464i	0.0130023	−	0.999915i	$-0.495861\pi$
$137$	6.13584	−	1.64409i	0.524220	−	0.140464i	0.511218	+	0.859451i	$0.329194\pi$
$138$		0			0
$139$		−	7.61018i		−	0.645487i	−0.946486	−	0.322744i	$-0.895395\pi$
$139$		−	7.61018i		−	0.645487i	0.946486	−	0.322744i	$-0.104605\pi$
$140$	0.937170	−	5.84138i	0.0792053	−	0.493687i
$141$		0			0
$142$	−0.153931	−	0.0412458i	−0.0129176	−	0.00346127i
$143$	−1.00223	−	3.74038i	−0.0838108	−	0.312786i
$144$		0			0
$145$	−2.78738	−	0.284805i	−0.231479	−	0.0236518i
$146$			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	0.995327	−	0.0965628i	$-0.0307848\pi$
$149$	5.05397	+	8.75374i	0.414038	+	0.717134i	−0.581289	+	0.813697i	$0.697452\pi$
$150$		0			0
$151$	0.957672	−	1.65874i	0.0779342	−	0.134986i	−0.824424	−	0.565972i	$-0.808501\pi$
$151$	0.957672	−	1.65874i	0.0779342	−	0.134986i	0.902359	+	0.430986i	$0.141834\pi$
$152$	1.85578	−	6.92586i	0.150524	−	0.561762i
$153$		0			0
$154$	3.19772	+	1.05634i	0.257679	+	0.0851225i
$155$	−6.16890	+	8.54269i	−0.495498	+	0.686165i
$156$		0			0
$157$	−4.02672	−	15.0279i	−0.321368	−	1.19936i	−0.917913	−	0.396781i	$-0.870127\pi$
$157$	−4.02672	−	15.0279i	−0.321368	−	1.19936i	0.596546	−	0.802579i	$-0.296539\pi$
$158$	−2.76027	−	10.3015i	−0.219596	−	0.819542i
$159$		0			0
$160$	−2.20752	+	0.356193i	−0.174519	+	0.0281595i
$161$	2.30686	+	11.1204i	0.181806	+	0.876412i
$162$		0			0
$163$	−3.02616	+	11.2938i	−0.237027	+	0.884599i	0.740197	+	0.672390i	$0.234732\pi$
$163$	−3.02616	+	11.2938i	−0.237027	+	0.884599i	−0.977224	+	0.212208i	$0.931934\pi$
$164$	−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
$170$	1.36488	−	13.3580i	0.104682	−	1.02451i
$171$		0			0
$172$	−2.63717	−	9.84207i	−0.201083	−	0.750450i
$173$	4.80092	+	1.28640i	0.365007	+	0.0978034i	0.436661	−	0.899626i	$-0.356161\pi$
$173$	4.80092	+	1.28640i	0.365007	+	0.0978034i	−0.0716536	+	0.997430i	$0.522828\pi$
$174$		0			0
$175$	3.43529	+	12.7749i	0.259684	+	0.965694i
$176$		−	1.27286i		−	0.0959456i
$177$		0			0
$178$	7.32885	−	1.96376i	0.549320	−	0.147190i
$179$	10.2521	−	17.7572i	0.766281	−	1.32724i	−0.173286	−	0.984872i	$-0.555438\pi$
$179$	10.2521	−	17.7572i	0.766281	−	1.32724i	0.939567	−	0.342366i	$-0.111228\pi$
$180$		0			0
$181$	−6.09745			−0.453220			−0.226610	−	0.973986i	$-0.572764\pi$
$181$	−6.09745			−0.453220			−0.226610	+	0.973986i	$0.572764\pi$
$182$	−6.72887	−	4.41678i	−0.498777	−	0.327394i
$183$		0			0
$184$	3.71751	−	2.14630i	0.274058	−	0.158228i
$185$	−4.32615	−	1.64630i	−0.318065	−	0.121038i
$186$		0			0
$187$	7.38308	+	1.97829i	0.539905	+	0.144667i
$188$	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	$-0.525347\pi$
$191$	10.2818	−	5.93620i	0.743965	−	0.429528i	0.823509	+	0.567303i	$0.192013\pi$
$192$		0			0
$193$	−14.8683	+	3.98395i	−1.07024	+	0.286771i	−0.750593	−	0.660765i	$-0.770232\pi$
$193$	−14.8683	+	3.98395i	−1.07024	+	0.286771i	−0.319650	+	0.947536i	$0.603565\pi$
$194$	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	$-0.449839\pi$
$199$	−8.74465	−	5.04873i	−0.619892	−	0.357895i	−0.776827	+	0.629714i	$0.783172\pi$
$200$	4.17751	−	2.74744i	0.295394	−	0.194273i
$201$		0			0
$202$	2.51249	−	2.51249i	0.176778	−	0.176778i
$203$	−1.49060	−	2.96124i	−0.104620	−	0.207838i
$204$		0			0
$205$	0.149070	−	1.45894i	0.0104115	−	0.101897i
$206$	5.11009	+	2.95031i	0.356037	+	0.205558i
$207$		0			0
$208$	−0.787384	+	2.93856i	−0.0545953	+	0.203752i
$209$	−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	$0.913362\pi$
$212$	−3.55426	+	13.2647i	−0.244108	+	0.911022i
$213$		0			0
$214$	5.12716	+	2.96017i	0.350486	+	0.202353i
$215$	14.3896	+	17.6648i	0.981361	+	1.20473i
$216$		0			0
$217$	−12.4474	−	0.713482i	−0.844983	−	0.0484343i
$218$	13.0530	−	13.0530i	0.884061	−	0.884061i
$219$		0			0
$220$	1.16518	+	2.59678i	0.0785566	+	0.175075i
$221$	−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
$227$	10.8596	−	2.90981i	0.720775	−	0.193131i	0.120258	−	0.992743i	$-0.461628\pi$
$227$	10.8596	−	2.90981i	0.720775	−	0.193131i	0.600518	+	0.799611i	$0.294961\pi$
$228$		0			0
$229$	9.38944	−	5.42100i	0.620472	−	0.358230i	−0.156581	−	0.987665i	$-0.550047\pi$
$229$	9.38944	−	5.42100i	0.620472	−	0.358230i	0.777053	+	0.629436i	$0.216714\pi$
$230$	−5.61938	+	7.78170i	−0.370531	+	0.513110i
$231$		0			0
$232$	−0.886035	+	0.886035i	−0.0581711	+	0.0581711i
$233$	−16.4685	−	4.41272i	−1.07889	−	0.289087i	−0.324747	−	0.945801i	$-0.605279\pi$
$233$	−16.4685	−	4.41272i	−1.07889	−	0.289087i	−0.754140	+	0.656714i	$0.771946\pi$
$234$		0			0
$235$	−8.62074	+	22.6537i	−0.562355	+	1.47776i
$236$	1.19259	−	0.688544i	0.0776313	−	0.0448204i
$237$		0			0
$238$	14.1912	−	7.14346i	0.919880	−	0.463042i
$239$	−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	−0.497870	−	0.867251i	$-0.665884\pi$
$241$	7.79510	−	13.5015i	0.502127	−	0.869709i	0.999997	−	0.00245737i	$-0.000782207\pi$
$242$	9.06021	−	2.42768i	0.582412	−	0.156057i
$243$		0			0
$244$			5.15545i			0.330044i
$245$	−10.5535	+	11.5595i	−0.674241	+	0.738511i
$246$		0			0
$247$	21.0700	+	5.64568i	1.34065	+	0.359226i
$248$	1.21966	+	4.55182i	0.0774482	+	0.289041i
$249$		0			0
$250$	−6.00755	+	9.42918i	−0.379951	+	0.596353i
$251$			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
$257$	−3.70172	+	13.8150i	−0.230907	+	0.861756i	0.749044	+	0.662520i	$0.230513\pi$
$257$	−3.70172	+	13.8150i	−0.230907	+	0.861756i	−0.979951	+	0.199237i	$0.936154\pi$
$258$		0			0
$259$	−1.11246	−	5.36271i	−0.0691248	−	0.333223i
$260$	−1.08362	−	6.71575i	−0.0672031	−	0.416493i
$261$		0			0
$262$	5.01643	+	18.7216i	0.309916	+	1.15662i
$263$	1.41762	+	5.29064i	0.0874144	+	0.326235i	0.995760	−	0.0919845i	$-0.0293210\pi$
$263$	1.41762	+	5.29064i	0.0874144	+	0.326235i	−0.908346	+	0.418219i	$0.862654\pi$
$264$		0			0
$265$	−4.89146	−	30.3150i	−0.300480	−	1.86223i
$266$	−14.1598	+	12.6246i	−0.868195	+	0.774061i
$267$		0			0
$268$	1.12287	−	4.19060i	0.0685901	−	0.255982i
$269$	−11.0192	+	19.0857i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$269$	−11.0192	+	19.0857i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$270$		0			0
$271$	−3.14477	−	5.44691i	−0.191031	−	0.330876i	0.754561	−	0.656230i	$-0.227850\pi$
$271$	−3.14477	−	5.44691i	−0.191031	−	0.330876i	−0.945592	+	0.325354i	$0.894517\pi$
$272$	−4.24617	−	4.24617i	−0.257462	−	0.257462i
$273$		0			0
$274$			6.35229i			0.383756i
$275$	−4.75420	−	4.23109i	−0.286689	−	0.255144i
$276$		0			0
$277$	−5.68345	−	21.2109i	−0.341485	−	1.27444i	−0.896665	−	0.442710i	$-0.854017\pi$
$277$	−5.68345	−	21.2109i	−0.341485	−	1.27444i	0.555180	−	0.831730i	$-0.312649\pi$
$278$	7.35087	+	1.96966i	0.440876	+	0.118132i
$279$		0			0
$280$	5.39978	+	2.41710i	0.322699	+	0.144449i
$281$			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
$283$	16.7878	−	4.49829i	0.997933	−	0.267395i	0.277354	−	0.960768i	$-0.410543\pi$
$283$	16.7878	−	4.49829i	0.997933	−	0.267395i	0.720579	+	0.693372i	$0.243876\pi$
$284$	0.0796807	−	0.138011i	0.00472818	−	0.00818945i
$285$		0			0
$286$	3.87233			0.228975
$287$	1.54994	−	0.780195i	0.0914899	−	0.0460535i
$288$		0			0
$289$	16.5064	−	9.52996i	0.970964	−	0.560586i
$290$	0.996527	−	2.61869i	0.0585181	−	0.153775i
$291$		0			0
$292$	−9.90347	−	2.65363i	−0.579557	−	0.155292i
$293$	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
$298$	−9.76353	+	2.61613i	−0.565586	+	0.151548i
$299$	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
$305$	−4.71931	−	10.5177i	−0.270227	−	0.602240i
$306$		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	$0.348651\pi$
$308$	−1.84798	+	2.81536i	−0.105298	+	0.160420i
$309$		0			0
$310$	−6.65497	−	8.16971i	−0.377977	−	0.464009i
$311$	1.13329	+	0.654305i	0.0642630	+	0.0371022i	0.531787	−	0.846878i	$-0.321521\pi$
$311$	1.13329	+	0.654305i	0.0642630	+	0.0371022i	−0.467524	+	0.883980i	$0.654854\pi$
$312$		0			0
$313$	6.01619	−	22.4527i	0.340055	−	1.26910i	−0.558229	−	0.829687i	$-0.688519\pi$
$313$	6.01619	−	22.4527i	0.340055	−	1.26910i	0.898284	−	0.439416i	$-0.144815\pi$
$314$	15.5581			0.877993
$315$		0			0
$316$	10.6649			0.599946
$317$	−6.28546	+	23.4577i	−0.353027	+	1.31751i	0.529923	+	0.848046i	$0.322221\pi$
$317$	−6.28546	+	23.4577i	−0.353027	+	1.31751i	−0.882949	+	0.469468i	$0.844446\pi$
$318$		0			0
$319$	1.38127	+	0.797476i	0.0773362	+	0.0446501i
$320$	0.227291	−	2.22449i	0.0127060	−	0.124353i
$321$		0			0
$322$	−11.3386	−	0.649925i	−0.631873	−	0.0362189i
$323$	−30.4458	+	30.4458i	−1.69405	+	1.69405i
$324$		0			0
$325$	8.35831	+	12.7089i	0.463636	+	0.704963i
$326$	−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	0.945512	−	0.325586i	$-0.105562\pi$
$331$	3.47113	+	6.01217i	0.190790	+	0.330458i	−0.754722	+	0.656045i	$0.772228\pi$
$332$	−8.32139	+	2.22971i	−0.456695	+	0.122371i
$333$		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	$0.350763\pi$
$338$	3.61730	+	0.969254i	0.196755	+	0.0527204i
$339$		0			0
$340$	12.5496	+	4.77568i	0.680598	+	0.258998i
$341$	5.19461	−	2.99911i	0.281304	−	0.162411i
$342$		0			0
$343$	−18.2477	−	3.16563i	−0.985283	−	0.170928i
$344$	10.1893			0.549368
$345$		0			0
$346$	−2.48514	+	4.30439i	−0.133602	+	0.231405i
$347$	−16.4333	+	4.40330i	−0.882188	+	0.236381i	−0.671351	−	0.741140i	$-0.734286\pi$
$347$	−16.4333	+	4.40330i	−0.882188	+	0.236381i	−0.210837	+	0.977521i	$0.567619\pi$
$348$		0			0
$349$			36.2149i			1.93854i	0.246004	+	0.969269i	$0.420883\pi$
$349$			36.2149i			1.93854i	−0.246004	+	0.969269i	$0.579117\pi$
$350$	−13.2288	+	0.0118417i	−0.707106	+	0.000632963i
$351$		0			0
$352$	1.22949	+	0.329441i	0.0655321	+	0.0175593i
$353$	2.71380	+	10.1280i	0.144441	+	0.539061i	0.999780	+	0.0209920i	$0.00668245\pi$
$353$	2.71380	+	10.1280i	0.144441	+	0.539061i	−0.855339	+	0.518069i	$0.826651\pi$
$354$		0			0
$355$	−0.0362214	+	0.354497i	−0.00192243	+	0.0188148i
$356$			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	0.941981	+	0.335667i	$0.108962\pi$
$359$	14.4319	+	24.9968i	0.761686	+	1.31928i	−0.180294	+	0.983613i	$0.557705\pi$
$360$		0			0
$361$	16.2057	−	28.0692i	0.852934	−	1.47732i
$362$	1.57814	−	5.88969i	0.0829451	−	0.309555i
$363$		0			0
$364$	6.00784	−	5.35644i	0.314896	−	0.280754i
$365$	22.6333	−	3.65199i	1.18468	−	0.191154i
$366$		0			0
$367$	0.535122	+	1.99710i	0.0279331	+	0.104248i	0.978485	−	0.206318i	$-0.0661481\pi$
$367$	0.535122	+	1.99710i	0.0279331	+	0.104248i	−0.950552	+	0.310566i	$0.899481\pi$
$368$	1.11101	+	4.14634i	0.0579153	+	0.216143i
$369$		0			0
$370$	2.70989	−	3.75265i	0.140880	−	0.195091i
$371$	27.1195	−	24.1790i	1.40797	−	1.25531i
$372$		0			0
$373$	−9.27766	+	34.6247i	−0.480379	+	1.79280i	0.119644	+	0.992817i	$0.461825\pi$
$373$	−9.27766	+	34.6247i	−0.480379	+	1.79280i	−0.600023	+	0.799982i	$0.704842\pi$
$374$	−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	$-0.0350614\pi$
$380$	−15.9500	−	1.62972i	−0.818216	−	0.0836028i
$381$		0			0
$382$	3.07280	+	11.4679i	0.157218	+	0.586746i
$383$	−5.06354	−	1.35677i	−0.258735	−	0.0693278i	0.127120	−	0.991887i	$-0.459427\pi$
$383$	−5.06354	−	1.35677i	−0.258735	−	0.0693278i	−0.385855	+	0.922560i	$0.626093\pi$
$384$		0			0
$385$	1.19289	−	7.43527i	0.0607952	−	0.378937i
$386$		−	15.3928i		−	0.783472i
$387$		0			0
$388$	−15.0174	+	4.02389i	−0.762391	+	0.204282i
$389$	−14.0642	+	24.3599i	−0.713082	+	1.23509i	0.250613	+	0.968087i	$0.419368\pi$
$389$	−14.0642	+	24.3599i	−0.713082	+	1.23509i	−0.963695	+	0.267007i	$0.913965\pi$
$390$		0			0
$391$	−25.7771			−1.30360
$392$	1.02727	+	6.92421i	0.0518850	+	0.349726i
$393$		0			0
$394$	5.68280	−	3.28097i	0.286295	−	0.165293i
$395$	−21.7575	+	9.76266i	−1.09474	+	0.491213i
$396$		0			0
$397$	−3.25806	−	0.872995i	−0.163518	−	0.0438144i	0.176131	−	0.984367i	$-0.443642\pi$
$397$	−3.25806	−	0.872995i	−0.163518	−	0.0438144i	−0.339649	+	0.940552i	$0.610308\pi$
$398$	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	$-0.450994\pi$
$401$	21.7433	−	12.5535i	1.08581	−	0.626891i	0.932457	+	0.361281i	$0.117660\pi$
$402$		0			0
$403$	−13.8476	+	3.71046i	−0.689799	+	0.184831i
$404$	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	$-0.252478\pi$
$409$	8.80234	+	5.08203i	0.435248	+	0.251290i	−0.266332	+	0.963881i	$0.585812\pi$
$410$	1.37064	+	0.521591i	0.0676913	+	0.0257596i
$411$		0			0
$412$	−4.17237	+	4.17237i	−0.205558	+	0.205558i
$413$	−3.63746	−	0.208499i	−0.178988	−	0.0102596i
$414$		0			0
$415$	14.9354	−	12.1663i	0.733152	−	0.597219i
$416$	−2.63464	−	1.52111i	−0.129174	−	0.0745785i
$417$		0			0
$418$	2.36215	−	8.81567i	0.115537	−	0.431189i
$419$	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	$0.263928\pi$
$422$	7.24233	−	27.0287i	0.352551	−	1.31574i
$423$		0			0
$424$	−11.8928	−	6.86630i	−0.577565	−	0.333457i
$425$	−29.9742	+	1.74504i	−1.45396	+	0.0846468i
$426$		0			0
$427$	7.48483	−	11.4030i	0.362216	−	0.551829i
$428$	−4.18631	+	4.18631i	−0.202353	+	0.202353i
$429$		0			0
$430$	−20.7872	+	9.32728i	−1.00245	+	0.449801i
$431$	−2.85680	−	1.64937i	−0.137607	−	0.0794475i	0.429616	−	0.903012i	$-0.358649\pi$
$431$	−2.85680	−	1.64937i	−0.137607	−	0.0794475i	−0.567223	+	0.823564i	$0.691982\pi$
$432$		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
$437$	29.7300	−	7.96613i	1.42218	−	0.381072i
$438$		0			0
$439$	10.1671	−	5.86996i	0.485248	−	0.280158i	−0.237353	−	0.971423i	$-0.576280\pi$
$439$	10.1671	−	5.86996i	0.485248	−	0.280158i	0.722601	+	0.691266i	$0.242947\pi$
$440$	−2.80986	+	0.453385i	−0.133955	+	0.0216143i
$441$		0			0
$442$	12.9178	−	12.9178i	0.614436	−	0.614436i
$443$	−13.2896	−	3.56095i	−0.631410	−	0.169186i	−0.0711005	−	0.997469i	$-0.522651\pi$
$443$	−13.2896	−	3.56095i	−0.631410	−	0.169186i	−0.560309	+	0.828283i	$0.689318\pi$
$444$		0			0
$445$	−6.94551	−	15.4791i	−0.329249	−	0.733778i
$446$	−9.03072	+	5.21389i	−0.427617	+	0.246885i
$447$		0			0
$448$	2.36324	−	1.18959i	0.111652	−	0.0562027i
$449$	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
$452$	12.0067	−	3.21719i	0.564748	−	0.151324i
$453$		0			0
$454$			11.2427i			0.527644i
$455$	−7.35334	+	16.4273i	−0.344730	+	0.770124i
$456$		0			0
$457$	10.6667	+	2.85813i	0.498967	+	0.133698i	0.499520	−	0.866302i	$-0.333510\pi$
$457$	10.6667	+	2.85813i	0.498967	+	0.133698i	−0.000553622		1.00000i	$0.500176\pi$
$458$	2.80611	+	10.4726i	0.131121	+	0.489351i
$459$		0			0
$460$	−6.06215	−	7.44195i	−0.282649	−	0.346983i
$461$		−	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
$467$	−2.05567	+	7.67187i	−0.0951251	+	0.355012i	−0.997038	−	0.0769053i	$-0.975496\pi$
$467$	−2.05567	+	7.67187i	−0.0951251	+	0.355012i	0.901913	+	0.431917i	$0.142163\pi$
$468$		0			0
$469$	−8.56763	+	7.63869i	−0.395616	+	0.352722i
$470$	−19.6506	−	14.1902i	−0.906413	−	0.654545i
$471$		0			0
$472$	0.356417	+	1.33017i	0.0164054	+	0.0612258i
$473$	−3.35676	−	12.5276i	−0.154344	−	0.576020i
$474$		0			0
$475$	34.0315	−	11.2759i	1.56147	−	0.517372i
$476$	3.22710	+	15.5565i	0.147914	+	0.713032i
$477$		0			0
$478$	6.60308	−	24.6430i	0.302018	−	1.12715i
$479$	20.3520	−	35.2507i	0.929906	−	1.61064i	0.146431	−	0.989221i	$-0.453221\pi$
$479$	20.3520	−	35.2507i	0.929906	−	1.61064i	0.783475	−	0.621424i	$-0.213445\pi$
$480$		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
$485$	26.9535	−	21.9561i	1.22390	−	0.996976i
$486$		0			0
$487$	10.6050	+	39.5785i	0.480560	+	1.79347i	0.599272	+	0.800546i	$0.295457\pi$
$487$	10.6050	+	39.5785i	0.480560	+	1.79347i	−0.118712	+	0.992929i	$0.537876\pi$
$488$	−4.97978	−	1.33433i	−0.225424	−	0.0604022i
$489$		0			0
$490$	−8.43419	−	13.1858i	−0.381018	−	0.595672i
$491$		−	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
$493$	7.26812	−	1.94749i	0.327340	−	0.0877104i
$494$	−10.9066	+	18.8908i	−0.490712	+	0.849939i
$495$		0			0
$496$	−4.71239			−0.211592
$497$	−0.376609	+	0.189574i	−0.0168932	+	0.00850357i
$498$		0			0
$499$	−0.480426	+	0.277374i	−0.0215068	+	0.0124170i	−0.510715	−	0.859750i	$-0.670619\pi$
$499$	−0.480426	+	0.277374i	−0.0215068	+	0.0124170i	0.489208	+	0.872167i	$0.337286\pi$
$500$	−7.55302	−	8.24330i	−0.337781	−	0.368651i
$501$		0			0
$502$	−10.4705	−	2.80556i	−0.467321	−	0.125218i
$503$	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
$508$	−6.83354	+	1.83104i	−0.303189	+	0.0812393i
$509$	−14.5500	−	25.2013i	−0.644916	−	1.11703i	−0.984321	−	0.176386i	$-0.943559\pi$
$509$	−14.5500	−	25.2013i	−0.644916	−	1.11703i	0.339405	−	0.940640i	$-0.389774\pi$
$510$		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
$515$	4.69268	−	12.3315i	0.206784	−	0.543390i
$516$		0			0
$517$	9.75636	−	9.75636i	0.429084	−	0.429084i
$518$	5.46791	+	0.313420i	0.240246	+	0.0137709i
$519$		0			0
$520$	6.76737	+	0.691469i	0.296769	+	0.0303229i
$521$	−16.9185	−	9.76787i	−0.741211	−	0.427938i	0.0812985	−	0.996690i	$-0.474093\pi$
$521$	−16.9185	−	9.76787i	−0.741211	−	0.427938i	−0.822509	+	0.568752i	$0.807427\pi$
$522$		0			0
$523$	−1.49335	+	5.57326i	−0.0652996	+	0.243702i	−0.990859	−	0.134901i	$-0.956928\pi$
$523$	−1.49335	+	5.57326i	−0.0652996	+	0.243702i	0.925559	+	0.378602i	$0.123595\pi$
$524$	−19.3820			−0.846706
$525$		0			0
$526$	−5.47727			−0.238821
$527$	7.32402	−	27.3336i	0.319039	−	1.19067i
$528$		0			0
$529$	−3.96080	−	2.28677i	−0.172209	−	0.0994247i
$530$	30.5480	+	3.12130i	1.32692	+	0.135581i
$531$		0			0
$532$	−8.52955	−	16.9448i	−0.369803	−	0.734651i
$533$	1.41086	−	1.41086i	0.0611109	−	0.0611109i
$534$		0			0
$535$	4.70836	−	12.3727i	0.203560	−	0.534918i
$536$	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	0.599696	−	0.800228i	$-0.295288\pi$
$541$	−9.14490	−	15.8394i	−0.393170	−	0.680991i	−0.992866	+	0.119238i	$0.961955\pi$
$542$	6.07524	−	1.62785i	0.260954	−	0.0699224i
$543$		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	$0.307379\pi$
$548$	−6.13584	−	1.64409i	−0.262110	−	0.0702322i
$549$		0			0
$550$	5.31740	−	3.49711i	0.226734	−	0.149117i
$551$	−7.78084	+	4.49227i	−0.331475	+	0.191377i
$552$		0			0
$553$	−23.5889	−	15.4836i	−1.00310	−	0.658429i
$554$	21.9591			0.932955
$555$		0			0
$556$	−3.80509	+	6.59061i	−0.161372	+	0.279504i
$557$	11.1495	−	2.98750i	0.472420	−	0.126584i	−0.0147511	−	0.999891i	$-0.504696\pi$
$557$	11.1495	−	2.98750i	0.472420	−	0.126584i	0.487171	+	0.873307i	$0.338029\pi$
$558$		0			0
$559$			30.9979i			1.31107i
$560$	−3.73230	+	4.59020i	−0.157719	+	0.193971i
$561$		0			0
$562$	−11.9584	−	3.20425i	−0.504436	−	0.135163i
$563$	5.23840	+	19.5500i	0.220772	+	0.823932i	0.984054	+	0.177867i	$0.0569198\pi$
$563$	5.23840	+	19.5500i	0.220772	+	0.823932i	−0.763282	+	0.646065i	$0.776413\pi$
$564$		0			0
$565$	−21.5500	+	17.5544i	−0.906613	+	0.738519i
$566$			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	−0.981404	−	0.191956i	$-0.938517\pi$
$569$	−15.6705	−	27.1421i	−0.656941	−	1.13785i	0.324463	−	0.945898i	$-0.394816\pi$
$570$		0			0
$571$	11.5290	−	19.9688i	0.482473	−	0.835669i	−0.517324	−	0.855790i	$-0.673072\pi$
$571$	11.5290	−	19.9688i	0.482473	−	0.835669i	0.999798	+	0.0201210i	$0.00640514\pi$
$572$	−1.00223	+	3.74038i	−0.0419054	+	0.156393i
$573$		0			0
$574$	0.352457	+	1.69905i	0.0147113	+	0.0709172i
$575$	19.1798	+	9.63307i	0.799854	+	0.401727i
$576$		0			0
$577$	4.03678	+	15.0655i	0.168053	+	0.627183i	0.997631	+	0.0687922i	$0.0219145\pi$
$577$	4.03678	+	15.0655i	0.168053	+	0.627183i	−0.829578	+	0.558391i	$0.811419\pi$
$578$	4.93307	+	18.4105i	0.205189	+	0.765775i
$579$		0			0
$580$	2.27154	+	1.64034i	0.0943204	+	0.0681113i
$581$	21.6426	+	7.14949i	0.897888	+	0.296611i
$582$		0			0
$583$	−4.52409	+	16.8841i	−0.187369	+	0.699269i
$584$	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
$590$	−1.94477	−	2.38742i	−0.0800648	−	0.0982883i
$591$		0			0
$592$	−0.535773	−	1.99953i	−0.0220201	−	0.0821803i
$593$	−24.5541	−	6.57925i	−1.00832	−	0.270177i	−0.283390	−	0.959005i	$-0.591459\pi$
$593$	−24.5541	−	6.57925i	−1.00832	−	0.270177i	−0.724925	+	0.688827i	$0.758126\pi$
$594$		0			0
$595$	−20.8241	−	28.7829i	−0.853705	−	1.17998i
$596$		−	10.1079i		−	0.414038i
$597$		0			0
$598$	−12.6141	+	3.37993i	−0.515828	+	0.138216i
$599$	6.77896	−	11.7415i	0.276981	−	0.479745i	−0.693652	−	0.720310i	$-0.743999\pi$
$599$	6.77896	−	11.7415i	0.276981	−	0.479745i	0.970633	+	0.240565i	$0.0773328\pi$
$600$		0			0
$601$	−22.8479			−0.931983			−0.465992	−	0.884789i	$-0.654302\pi$
$601$	−22.8479			−0.931983			−0.465992	+	0.884789i	$0.654302\pi$
$602$	−22.5369	−	14.7931i	−0.918536	−	0.602920i
$603$		0			0
$604$	−1.65874	+	0.957672i	−0.0674930	+	0.0389671i
$605$	−8.58632	−	19.1358i	−0.349083	−	0.777982i
$606$		0			0
$607$	−43.9900	−	11.7871i	−1.78550	−	0.478423i	−0.793929	−	0.608010i	$-0.791968\pi$
$607$	−43.9900	−	11.7871i	−1.78550	−	0.478423i	−0.991568	+	0.129588i	$0.958635\pi$
$608$	−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
$613$	−16.8749	+	4.52161i	−0.681570	+	0.182626i	−0.582961	−	0.812500i	$-0.698106\pi$
$613$	−16.8749	+	4.52161i	−0.681570	+	0.182626i	−0.0986088	+	0.995126i	$0.531439\pi$
$614$	−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	$-0.482879\pi$
$619$	−19.5089	−	11.2635i	−0.784130	−	0.452718i	−0.837892	+	0.545836i	$0.816212\pi$
$620$	9.61377	−	4.31373i	0.386098	−	0.173244i
$621$		0			0
$622$	−0.925327	+	0.925327i	−0.0371022	+	0.0371022i
$623$	11.0156	−	16.7820i	0.441330	−	0.672356i
$624$		0			0
$625$	22.9549	+	9.90315i	0.918196	+	0.396126i
$626$	20.1306	+	11.6224i	0.804579	+	0.464524i
$627$		0			0
$628$	−4.02672	+	15.0279i	−0.160684	+	0.599680i
$629$	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	$0.280018\pi$
$632$	−2.76027	+	10.3015i	−0.109798	+	0.409771i
$633$		0			0
$634$	−21.0316	−	12.1426i	−0.835270	−	0.482244i
$635$	12.2650	−	9.99096i	0.486722	−	0.396479i
$636$		0			0
$637$	−21.0650	+	3.12518i	−0.834624	+	0.123824i
$638$	−1.12780	+	1.12780i	−0.0446501	+	0.0446501i
$639$		0			0
$640$	2.08986	+	0.795286i	0.0826090	+	0.0314364i
$641$	12.6297	+	7.29176i	0.498843	+	0.288007i	0.728236	−	0.685327i	$-0.240341\pi$
$641$	12.6297	+	7.29176i	0.498843	+	0.288007i	−0.229392	+	0.973334i	$0.573674\pi$
$642$		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
$647$	6.05702	−	1.62297i	0.238126	−	0.0638057i	−0.137782	−	0.990463i	$-0.543997\pi$
$647$	6.05702	−	1.62297i	0.238126	−	0.0638057i	0.375908	+	0.926657i	$0.377331\pi$
$648$		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
$653$	14.9295	+	4.00035i	0.584237	+	0.156546i	0.538818	−	0.842422i	$-0.318871\pi$
$653$	14.9295	+	4.00035i	0.584237	+	0.156546i	0.0454190	+	0.998968i	$0.485538\pi$
$654$		0			0
$655$	39.5413	−	17.7423i	1.54501	−	0.693251i
$656$	0.567986	−	0.327927i	0.0221761	−	0.0128034i
$657$		0			0
$658$	1.64121	−	28.6324i	0.0639809	−	1.11621i
$659$	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	−0.569045	−	0.822307i	$-0.692687\pi$
$661$	10.9940	−	19.0421i	0.427616	−	0.740653i	0.996661	+	0.0816540i	$0.0260202\pi$
$662$	−6.70570	+	1.79679i	−0.260624	+	0.0698341i
$663$		0			0
$664$		−	8.61493i		−	0.334324i
$665$	32.9125	+	26.7613i	1.27629	+	1.03776i
$666$		0			0
$667$	−5.19554	−	1.39214i	−0.201172	−	0.0539039i
$668$	3.24055	+	12.0939i	0.125381	+	0.467927i
$669$		0			0
$670$	−9.65078	−	0.986086i	−0.372842	−	0.0380958i
$671$			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
$677$	−2.87769	+	10.7397i	−0.110599	+	0.412760i	−0.998920	−	0.0464625i	$-0.985205\pi$
$677$	−2.87769	+	10.7397i	−0.110599	+	0.412760i	0.888321	+	0.459222i	$0.151872\pi$
$678$		0			0
$679$	39.0579	+	12.9025i	1.49890	+	0.495152i
$680$	−7.86103	+	10.8859i	−0.301457	+	0.417457i
$681$		0			0
$682$	1.55245	+	5.79384i	0.0594465	+	0.221857i
$683$	8.87917	+	33.1375i	0.339752	+	1.26797i	0.898625	+	0.438718i	$0.144567\pi$
$683$	8.87917	+	33.1375i	0.339752	+	1.26797i	−0.558873	+	0.829253i	$0.688766\pi$
$684$		0			0
$685$	14.0228	−	2.26264i	0.535783	−	0.0864511i
$686$	7.78062	−	16.8066i	0.297066	−	0.641679i
$687$		0			0
$688$	−2.63717	+	9.84207i	−0.100541	+	0.375225i
$689$	20.8888	−	36.1805i	0.795800	−	1.37837i
$690$		0			0
$691$	−3.62966	−	6.28676i	−0.138079	−	0.239160i	0.788690	−	0.614790i	$-0.210759\pi$
$691$	−3.62966	−	6.28676i	−0.138079	−	0.239160i	−0.926769	+	0.375631i	$0.877426\pi$
$692$	−3.51452	−	3.51452i	−0.133602	−	0.133602i
$693$		0			0
$694$		−	17.0130i		−	0.645806i
$695$	1.72973	−	16.9287i	0.0656123	−	0.642144i
$696$		0			0
$697$	1.01933	+	3.80420i	0.0386100	+	0.144094i
$698$	−34.9809	−	9.37310i	−1.32405	−	0.354777i
$699$		0			0
$700$	3.41241	−	12.7811i	0.128977	−	0.483079i
$701$			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
$703$	−14.3370	+	3.84159i	−0.540730	+	0.144888i
$704$	−0.636431	+	1.10233i	−0.0239864	+	0.0415457i
$705$		0			0
$706$	−10.4853			−0.394620
$707$	0.537973	−	9.38546i	0.0202326	−	0.352976i
$708$		0			0
$709$	−28.6346	+	16.5322i	−1.07540	+	0.620880i	−0.929651	−	0.368442i	$-0.879891\pi$
$709$	−28.6346	+	16.5322i	−1.07540	+	0.620880i	−0.145745	+	0.989322i	$0.546558\pi$
$710$	−0.333043	−	0.126738i	−0.0124989	−	0.00475639i
$711$		0			0
$712$	−7.32885	−	1.96376i	−0.274660	−	0.0735950i
$713$	−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
$718$	−27.8803	+	7.47050i	−1.04048	+	0.278797i
$719$	−0.519410	−	0.899644i	−0.0193707	−	0.0335511i	0.856178	−	0.516682i	$-0.172833\pi$
$719$	−0.519410	−	0.899644i	−0.0193707	−	0.0335511i	−0.875548	+	0.483131i	$0.839500\pi$
$720$		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
$725$	−6.13575	−	1.26709i	−0.227876	−	0.0470586i
$726$		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	$0.971574\pi$
$728$	3.61898	+	7.18948i	0.134128	+	0.266460i
$729$		0			0
$730$	−2.33038	+	22.8073i	−0.0862511	+	0.844135i
$731$	−52.9890	−	30.5932i	−1.95987	−	1.13153i
$732$		0			0
$733$	2.01726	−	7.52853i	0.0745094	−	0.278073i	−0.918612	−	0.395160i	$-0.870689\pi$
$733$	2.01726	−	7.52853i	0.0745094	−	0.278073i	0.993122	+	0.117087i	$0.0373558\pi$
$734$	−2.06755			−0.0763148
$735$		0			0
$736$	−4.29261			−0.158228
$737$	1.42926	−	5.33406i	0.0526474	−	0.196483i
$738$		0			0
$739$	6.75740	+	3.90139i	0.248575	+	0.143515i	0.619112	−	0.785303i	$-0.287493\pi$
$739$	6.75740	+	3.90139i	0.248575	+	0.143515i	−0.370537	+	0.928818i	$0.620826\pi$
$740$	2.92341	+	3.58881i	0.107467	+	0.131927i
$741$		0			0
$742$	16.3361	+	32.4534i	0.599718	+	1.19140i
$743$	−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
$745$	9.25285	+	20.6213i	0.338998	+	0.755506i
$746$	−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	0.883563	−	0.468313i	$-0.155138\pi$
$751$	0.992322	+	1.71875i	0.0362103	+	0.0627182i	−0.847352	+	0.531031i	$0.821805\pi$
$752$	−10.4704	+	2.80555i	−0.381818	+	0.102308i
$753$		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	$0.476398\pi$
$758$	4.13422	+	1.10776i	0.150162	+	0.0402357i
$759$		0			0
$760$	5.70234	−	14.9847i	0.206846	−	0.543552i
$761$	37.3770	−	21.5796i	1.35492	−	0.782261i	0.365982	−	0.930622i	$-0.380733\pi$
$761$	37.3770	−	21.5796i	1.35492	−	0.782261i	0.988933	+	0.148361i	$0.0473998\pi$
$762$		0			0
$763$	2.79491	−	48.7598i	0.101182	−	1.76522i
$764$	−11.8724			−0.429528
$765$		0			0
$766$	2.62108	−	4.53985i	0.0947035	−	0.164031i
$767$	−4.04665	+	1.08430i	−0.146116	+	0.0391517i
$768$		0			0
$769$			21.4012i			0.771748i	0.922551	+	0.385874i	$0.126100\pi$
$769$			21.4012i			0.771748i	−0.922551	+	0.385874i	$0.873900\pi$
$770$	6.87318	+	3.07663i	0.247692	+	0.110874i
$771$		0			0
$772$	14.8683	+	3.98395i	0.535121	+	0.143385i
$773$	1.77969	+	6.64191i	0.0640111	+	0.238893i	0.990518	−	0.137386i	$-0.0438701\pi$
$773$	1.77969	+	6.64191i	0.0640111	+	0.238893i	−0.926506	+	0.376279i	$0.877203\pi$
$774$		0			0
$775$	−15.6643	+	17.6010i	−0.562679	+	0.632245i
$776$		−	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
$782$	6.67159	−	24.8987i	0.238576	−	0.890377i
$783$		0			0
$784$	−6.95415	−	0.799850i	−0.248363	−	0.0285661i
$785$	−5.54168	−	34.3447i	−0.197791	−	1.22581i
$786$		0			0
$787$	−8.40128	−	31.3540i	−0.299473	−	1.11765i	−0.937599	−	0.347718i	$-0.886957\pi$
$787$	−8.40128	−	31.3540i	−0.299473	−	1.11765i	0.638126	−	0.769932i	$-0.279710\pi$
$788$	1.69835	+	6.33834i	0.0605013	+	0.225794i
$789$		0			0
$790$	−3.79876	−	23.5429i	−0.135154	−	0.837618i
$791$	−31.2276	−	10.3158i	−1.11033	−	0.366788i
$792$		0			0
$793$	4.05932	−	15.1496i	0.144151	−	0.537977i
$794$	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
$800$	−4.99155	+	0.290598i	−0.176478	+	0.0102742i
$801$		0			0
$802$	6.49816	+	24.2515i	0.229458	+	0.856349i
$803$	−12.6058	−	3.37770i	−0.444848	−	0.119197i
$804$		0			0
$805$	2.60400	+	25.2615i	0.0917788	+	0.890352i
$806$		−	14.3361i		−	0.504968i
$807$		0			0
$808$	−3.43212	+	0.919634i	−0.120742	+	0.0323526i
$809$	−27.6293	+	47.8553i	−0.971393	+	1.68250i	−0.280036	+	0.959989i	$0.590346\pi$
$809$	−27.6293	+	47.8553i	−0.971393	+	1.68250i	−0.691357	+	0.722513i	$0.742987\pi$
$810$		0			0
$811$	−13.2246			−0.464380			−0.232190	−	0.972671i	$-0.574589\pi$
$811$	−13.2246			−0.464380			−0.232190	+	0.972671i	$0.574589\pi$
$812$	−0.189718	+	3.30981i	−0.00665779	+	0.116151i
$813$		0			0
$814$	−2.28190	+	1.31746i	−0.0799806	+	0.0461768i
$815$	−9.29864	+	24.4351i	−0.325717	+	0.855923i
$816$		0			0
$817$	70.5694	+	18.9090i	2.46891	+	0.661542i
$818$	−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	$-0.759437\pi$
$821$	−14.2602	+	8.23311i	−0.497683	+	0.287337i	0.230073	+	0.973173i	$0.426103\pi$
$822$		0			0
$823$	33.9396	−	9.09410i	1.18306	−	0.317000i	0.386921	−	0.922113i	$-0.373539\pi$
$823$	33.9396	−	9.09410i	1.18306	−	0.317000i	0.796140	+	0.605112i	$0.206872\pi$
$824$	−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	$-0.118050\pi$
$829$	31.2154	+	18.0222i	1.08416	+	0.625938i	0.152141	+	0.988359i	$0.451383\pi$
$830$	7.88614	+	17.5754i	0.273732	+	0.610050i
$831$		0			0
$832$	2.15117	−	2.15117i	0.0745785	−	0.0745785i
$833$	15.4476	−	39.0936i	0.535228	−	1.35451i
$834$		0			0
$835$	−17.6819	−	21.7065i	−0.611907	−	0.751183i
$836$	7.90391	+	4.56333i	0.273363	+	0.157826i
$837$		0			0
$838$	−5.52458	+	20.6180i	−0.190843	+	0.712237i
$839$	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
$842$	−7.17451	+	26.7756i	−0.247250	+	0.922749i
$843$		0			0
$844$	24.2333	+	13.9911i	0.834144	+	0.481593i
$845$	0.851184	−	8.33050i	0.0292816	−	0.286578i
$846$		0			0
$847$	13.6179	−	20.7466i	0.467916	−	0.712861i
$848$	9.71042	−	9.71042i	0.333457	−	0.333457i
$849$		0			0
$850$	6.07232	−	29.4045i	0.208279	−	1.00857i
$851$	−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
$857$	8.06522	−	2.16107i	0.275503	−	0.0738207i	−0.118422	−	0.992963i	$-0.537784\pi$
$857$	8.06522	−	2.16107i	0.275503	−	0.0738207i	0.393925	+	0.919143i	$0.371117\pi$
$858$		0			0
$859$	−42.1088	+	24.3115i	−1.43674	+	0.829499i	−0.997621	−	0.0689321i	$-0.978041\pi$
$859$	−42.1088	+	24.3115i	−1.43674	+	0.829499i	−0.439114	+	0.898431i	$0.644707\pi$
$860$	−3.62934	−	22.4929i	−0.123760	−	0.767003i
$861$		0			0
$862$	2.33257	−	2.33257i	0.0794475	−	0.0794475i
$863$	13.9055	+	3.72597i	0.473349	+	0.126834i	0.487604	−	0.873065i	$-0.337871\pi$
$863$	13.9055	+	3.72597i	0.473349	+	0.126834i	−0.0142549	+	0.999898i	$0.504538\pi$
$864$		0			0
$865$	10.3872	+	3.95279i	0.353175	+	0.134399i
$866$	−1.63205	+	0.942266i	−0.0554594	+	0.0320195i
$867$		0			0
$868$	10.4230	+	6.84158i	0.353780	+	0.232218i
$869$	13.5749			0.460498
$870$		0			0
$871$	−6.59923	+	11.4302i	−0.223606	+	0.387297i
$872$	−17.8307	+	4.77773i	−0.603825	+	0.161794i
$873$		0			0
$874$			30.7788i			1.04111i
$875$	4.73813	+	29.1985i	0.160178	+	0.987088i
$876$		0			0
$877$	37.2132	+	9.97124i	1.25660	+	0.336705i	0.824882	−	0.565304i	$-0.191241\pi$
$877$	37.2132	+	9.97124i	1.25660	+	0.336705i	0.431717	+	0.902009i	$0.357908\pi$
$878$	3.03851	+	11.3399i	0.102545	+	0.382703i
$879$		0			0
$880$	0.289310	−	2.83147i	0.00975265	−	0.0954487i
$881$			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
$887$	−10.9098	+	40.7161i	−0.366317	+	1.36711i	0.499311	+	0.866423i	$0.333587\pi$
$887$	−10.9098	+	40.7161i	−0.366317	+	1.36711i	−0.865627	+	0.500689i	$0.833080\pi$
$888$		0			0
$889$	17.7730	+	5.87118i	0.596087	+	0.196913i
$890$	16.7493	−	2.70257i	0.561437	−	0.0905904i
$891$		0			0
$892$	−2.69891	−	10.0725i	−0.0903661	−	0.337251i
$893$	20.1163	+	75.0750i	0.673166	+	2.51229i
$894$		0			0
$895$	26.8418	−	37.1705i	0.897222	−	1.24247i
$896$	0.537402	+	2.59060i	0.0179533	+	0.0865458i
$897$		0			0
$898$	−2.97997	+	11.1214i	−0.0994429	+	0.371126i
$899$	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
$905$	−13.5637	−	1.38590i	−0.450873	−	0.0460688i
$906$		0			0
$907$	14.0020	+	52.2562i	0.464929	+	1.73514i	0.657124	+	0.753783i	$0.271773\pi$
$907$	14.0020	+	52.2562i	0.464929	+	1.73514i	−0.192195	+	0.981357i	$0.561560\pi$
$908$	−10.8596	−	2.90981i	−0.360388	−	0.0965656i
$909$		0			0
$910$	−13.9644	−	11.3545i	−0.462915	−	0.376397i
$911$		−	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
$913$	−10.5920	+	2.83811i	−0.350543	+	0.0939278i
$914$	−5.52149	+	9.56350i	−0.182635	+	0.316332i
$915$		0			0
$916$	−10.8420			−0.358230
$917$	42.8697	+	28.1393i	1.41568	+	0.929243i
$918$		0			0
$919$	−24.5646	+	14.1824i	−0.810310	+	0.467833i	−0.847064	−	0.531492i	$-0.821632\pi$
$919$	−24.5646	+	14.1824i	−0.810310	+	0.467833i	0.0367535	+	0.999324i	$0.488298\pi$
$920$	8.75738	−	3.92947i	0.288722	−	0.129551i
$921$		0			0
$922$	0.979957	+	0.262579i	0.0322732	+	0.00864757i
$923$	−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
$928$	1.21035	−	0.324311i	0.0397316	−	0.0106460i
$929$	−23.6445	−	40.9535i	−0.775752	−	1.34364i	−0.934371	−	0.356301i	$-0.884038\pi$
$929$	−23.6445	−	40.9535i	−0.775752	−	1.34364i	0.158619	−	0.987340i	$-0.449296\pi$
$930$		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
$935$	15.9739	+	6.07879i	0.522403	+	0.198798i
$936$		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	$-0.157618\pi$
$938$	−5.16094	−	10.2527i	−0.168511	−	0.334764i
$939$		0			0
$940$	18.7926	−	15.3083i	0.612948	−	0.499302i
$941$	−22.6321	−	13.0667i	−0.737786	−	0.425961i	0.0834777	−	0.996510i	$-0.473397\pi$
$941$	−22.6321	−	13.0667i	−0.737786	−	0.425961i	−0.821264	+	0.570549i	$0.806731\pi$
$942$		0			0
$943$	0.728659	−	2.71939i	0.0237284	−	0.0885556i
$944$	−1.37709			−0.0448204
$945$		0			0
$946$	12.9695			0.421676
$947$	−7.73689	+	28.8745i	−0.251415	+	0.938294i	0.718635	+	0.695388i	$0.244767\pi$
$947$	−7.73689	+	28.8745i	−0.251415	+	0.938294i	−0.970050	+	0.242906i	$0.921899\pi$
$948$		0			0
$949$	27.0125	+	15.5957i	0.876863	+	0.506257i
$950$	2.08364	+	35.7903i	0.0676022	+	1.16119i
$951$		0			0
$952$	−15.8617	−	0.909190i	−0.514080	−	0.0294670i
$953$	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
$955$	24.2210	−	10.8680i	0.783772	−	0.351681i
$956$	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
$962$	6.08301	−	1.62994i	0.196124	−	0.0525513i
$963$		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	$0.457240\pi$
$968$	−9.06021	−	2.42768i	−0.291206	−	0.0780285i
$969$		0			0
$970$	14.2319	+	31.7178i	0.456958	+	1.01840i
$971$	−3.66101	+	2.11368i	−0.117487	+	0.0678313i	−0.557592	−	0.830115i	$-0.688275\pi$
$971$	−3.66101	+	2.11368i	−0.117487	+	0.0678313i	0.440105	+	0.897946i	$0.354941\pi$
$972$		0			0
$973$	17.9847	−	9.05297i	0.576562	−	0.290225i
$974$	−40.9747			−1.31291
$975$		0			0
$976$	2.57772	−	4.46475i	0.0825109	−	0.142913i
$977$	−31.5835	+	8.46277i	−1.01045	+	0.270748i	−0.725816	−	0.687889i	$-0.758537\pi$
$977$	−31.5835	+	8.46277i	−1.01045	+	0.270748i	−0.284630	+	0.958637i	$0.591871\pi$
$978$		0			0
$979$			9.65769i			0.308661i
$980$	14.9194	−	4.73407i	0.476583	−	0.151224i
$981$		0			0
$982$	25.9832	+	6.96217i	0.829156	+	0.222172i
$983$	−2.76365	−	10.3141i	−0.0881467	−	0.328968i	0.907745	−	0.419523i	$-0.137803\pi$
$983$	−2.76365	−	10.3141i	−0.0881467	−	0.328968i	−0.995891	+	0.0905549i	$0.971136\pi$
$984$		0			0
$985$	−9.26696	−	11.3762i	−0.295270	−	0.362476i
$986$			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	−0.0297806	−	0.999556i	$-0.509481\pi$
$991$	26.7818	−	46.3874i	0.850751	−	1.47354i	0.880532	−	0.473987i	$-0.157186\pi$
$992$	1.21966	−	4.55182i	0.0387241	−	0.144520i
$993$		0			0
$994$	−0.0856412	−	0.412841i	−0.00271637	−	0.0130945i
$995$	−18.3048	−	13.2184i	−0.580302	−	0.419052i
$996$		0			0
$997$	1.67474	+	6.25021i	0.0530395	+	0.197946i	0.987362	−	0.158484i	$-0.0506605\pi$
$997$	1.67474	+	6.25021i	0.0530395	+	0.197946i	−0.934322	+	0.356430i	$0.883994\pi$
$998$	−0.143580	−	0.535846i	−0.00454493	−	0.0169619i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.c.53.4	✓	32	1.1	even	1	trivial
630.2.ce.c.53.5	yes	32	3.2	odd	2	inner
630.2.ce.c.107.4	yes	32	105.2	even	12	inner
630.2.ce.c.107.5	yes	32	35.2	odd	12	inner
630.2.ce.c.233.3	yes	32	21.2	odd	6	inner
630.2.ce.c.233.6	yes	32	7.2	even	3	inner
630.2.ce.c.557.3	yes	32	5.2	odd	4	inner
630.2.ce.c.557.6	yes	32	15.2	even	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.22449 + 0.227291i) q^{5} +(1.18959 + 2.36324i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.22449 + 0.227291i) q^{5} +(1.18959 + 2.36324i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.795286 + 2.08986i) q^{10} +(-1.10233 - 0.636431i) q^{11} +(2.15117 + 2.15117i) q^{13} +(-2.59060 + 0.537402i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-5.80038 + 1.55421i) q^{17} +(6.20956 - 3.58509i) q^{19} +(-1.81282 - 1.30908i) q^{20} +(0.900050 - 0.900050i) q^{22} +(4.14634 + 1.11101i) q^{23} +(4.89668 + 1.01121i) q^{25} +(-2.63464 + 1.52111i) q^{26} +(0.151406 - 2.64142i) q^{28} -1.25304 q^{29} +(-2.35619 + 4.08105i) q^{31} +(-0.965926 + 0.258819i) q^{32} -6.00499i q^{34} +(2.10908 + 5.52737i) q^{35} +(-1.99953 - 0.535773i) q^{37} +(1.85578 + 6.92586i) q^{38} +(1.73367 - 1.41223i) q^{40} -0.655854i q^{41} +(7.20489 + 7.20489i) q^{43} +(0.636431 + 1.10233i) q^{44} +(-2.14630 + 3.71751i) q^{46} +(-2.80555 + 10.4704i) q^{47} +(-4.16977 + 5.62255i) q^{49} +(-2.24411 + 4.46811i) q^{50} +(-0.787384 - 2.93856i) q^{52} +(-3.55426 - 13.2647i) q^{53} +(-2.30747 - 1.66628i) q^{55} +(2.51222 + 0.829895i) q^{56} +(0.324311 - 1.21035i) q^{58} +(-0.688544 + 1.19259i) q^{59} +(-2.57772 - 4.46475i) q^{61} +(-3.33216 - 3.33216i) q^{62} -1.00000i q^{64} +(4.29631 + 5.27420i) q^{65} +(1.12287 + 4.19060i) q^{67} +(5.80038 + 1.55421i) q^{68} +(-5.88490 + 0.606624i) q^{70} +0.159361i q^{71} +(9.90347 - 2.65363i) q^{73} +(1.03503 - 1.79273i) q^{74} -7.17018 q^{76} +(0.192719 - 3.36216i) q^{77} +(-9.23605 + 5.33244i) q^{79} +(0.915403 + 2.04011i) q^{80} +(0.633506 + 0.169748i) q^{82} +(6.09168 - 6.09168i) q^{83} +(-13.2561 + 2.13894i) q^{85} +(-8.82415 + 5.09463i) q^{86} +(-1.22949 + 0.329441i) q^{88} +(-3.79369 - 6.57086i) q^{89} +(-2.52472 + 7.64274i) q^{91} +(-3.03533 - 3.03533i) q^{92} +(-9.38755 - 5.41990i) q^{94} +(14.6279 - 6.56361i) q^{95} +(10.9935 - 10.9935i) q^{97} +(-4.35175 - 5.48291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{7}+O(q^{10}) \) 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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