LMFDB - Embedded newform 950.2.q.a.407.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	950.407
Dual form			950.2.q.a.943.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.22474 - 2.12132i) q^{6} +(3.22474 + 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.22474 - 2.12132i) q^{6} +(3.22474 + 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +3.44949 q^{11} +(1.73205 - 1.73205i) q^{12} +(1.26795 - 4.73205i) q^{13} +(-2.28024 + 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.73205 - 0.732051i) q^{17} +(2.12132 + 2.12132i) q^{18} +(1.25529 - 4.17423i) q^{19} +(-9.67423 - 5.58542i) q^{21} +(0.892794 + 3.33195i) q^{22} +(5.01910 + 1.34486i) q^{23} +(2.12132 + 1.22474i) q^{24} +4.89898 q^{26} +(-4.40508 - 1.18034i) q^{28} +(-0.389270 - 0.674235i) q^{29} +7.70674i q^{31} +(0.965926 + 0.258819i) q^{32} +(-8.16158 + 2.18689i) q^{33} +(1.41421 + 2.44949i) q^{34} +(-1.50000 + 2.59808i) q^{36} +(0.389270 - 0.389270i) q^{37} +(4.35690 + 0.132150i) q^{38} +12.0000i q^{39} +(-1.50000 - 0.866025i) q^{41} +(2.89123 - 10.7902i) q^{42} +(0.933552 + 3.48406i) q^{43} +(-2.98735 + 1.72474i) q^{44} +5.19615i q^{46} +(1.79315 - 6.69213i) q^{47} +(-0.633975 + 2.36603i) q^{48} +13.7980i q^{49} +(-6.00000 + 3.46410i) q^{51} +(1.26795 + 4.73205i) q^{52} +(-2.67838 + 9.99585i) q^{53} -4.56048i q^{56} +(-0.323701 + 10.6722i) q^{57} +(0.550510 - 0.550510i) q^{58} +(1.73205 - 3.00000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-7.44414 + 1.99465i) q^{62} +(13.2153 + 3.54102i) q^{63} +1.00000i q^{64} +(-4.22474 - 7.31747i) q^{66} +(-9.22508 - 2.47185i) q^{67} +(-2.00000 + 2.00000i) q^{68} -12.7279 q^{69} +(-3.00000 - 1.73205i) q^{71} +(-2.89778 - 0.776457i) q^{72} +(0.567526 + 2.11804i) q^{73} +(0.476756 + 0.275255i) q^{74} +(1.00000 + 4.24264i) q^{76} +(11.1237 + 11.1237i) q^{77} +(-11.5911 + 3.10583i) q^{78} +(5.97469 - 10.3485i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(0.448288 - 1.67303i) q^{82} +(2.34847 - 2.34847i) q^{83} +11.1708 q^{84} +(-3.12372 + 1.80348i) q^{86} +(1.34847 + 1.34847i) q^{87} +(-2.43916 - 2.43916i) q^{88} +(-1.64456 - 2.84847i) q^{89} +(19.3485 - 11.1708i) q^{91} +(-5.01910 + 1.34486i) q^{92} +(-4.88588 - 18.2343i) q^{93} +6.92820 q^{94} -2.44949 q^{96} +(2.47185 + 9.22508i) q^{97} +(-13.3278 + 3.57117i) q^{98} +(8.96204 - 5.17423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 16 q^{7}+O(q^{10}) $ 8 * q - 12 * q^3 + 16 * q^7	$ 8 q - 12 q^{3} + 16 q^{7} + 8 q^{11} + 24 q^{13} + 4 q^{16} + 8 q^{17} - 48 q^{21} + 12 q^{22} - 8 q^{28} - 12 q^{33} - 12 q^{36} + 12 q^{38} - 12 q^{41} - 12 q^{42} - 20 q^{43} - 12 q^{48} - 48 q^{51} + 24 q^{52} - 36 q^{53} + 12 q^{57} + 24 q^{58} + 32 q^{61} - 12 q^{62} + 24 q^{63} - 24 q^{66} + 12 q^{67} - 16 q^{68} - 24 q^{71} - 16 q^{73} + 8 q^{76} + 40 q^{77} - 36 q^{81} - 40 q^{83} + 24 q^{86} - 48 q^{87} + 96 q^{91} + 24 q^{93} - 12 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 12 * q^3 + 16 * q^7 + 8 * q^11 + 24 * q^13 + 4 * q^16 + 8 * q^17 - 48 * q^21 + 12 * q^22 - 8 * q^28 - 12 * q^33 - 12 * q^36 + 12 * q^38 - 12 * q^41 - 12 * q^42 - 20 * q^43 - 12 * q^48 - 48 * q^51 + 24 * q^52 - 36 * q^53 + 12 * q^57 + 24 * q^58 + 32 * q^61 - 12 * q^62 + 24 * q^63 - 24 * q^66 + 12 * q^67 - 16 * q^68 - 24 * q^71 - 16 * q^73 + 8 * q^76 + 40 * q^77 - 36 * q^81 - 40 * q^83 + 24 * q^86 - 48 * q^87 + 96 * q^91 + 24 * q^93 - 12 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−2.36603	+	0.633975i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−2.36603	+	0.633975i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.22474	−	2.12132i	−0.500000	−	0.866025i
$7$	3.22474	+	3.22474i	1.21884	+	1.21884i	0.968039	+	0.250800i	$0.0806937\pi$
$7$	3.22474	+	3.22474i	1.21884	+	1.21884i	0.250800	+	0.968039i	$0.419306\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.59808	−	1.50000i	0.866025	−	0.500000i
$10$		0			0
$11$	3.44949			1.04006			0.520030	−	0.854148i	$-0.325921\pi$
$11$	3.44949			1.04006			0.520030	+	0.854148i	$0.325921\pi$
$12$	1.73205	−	1.73205i	0.500000	−	0.500000i
$13$	1.26795	−	4.73205i	0.351666	−	1.31243i	−0.532963	−	0.846139i	$-0.678921\pi$
$13$	1.26795	−	4.73205i	0.351666	−	1.31243i	0.884629	−	0.466296i	$-0.154412\pi$
$14$	−2.28024	+	3.94949i	−0.609419	+	1.05555i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.73205	−	0.732051i	0.662620	−	0.177548i	0.0881917	−	0.996104i	$-0.471891\pi$
$17$	2.73205	−	0.732051i	0.662620	−	0.177548i	0.574428	+	0.818555i	$0.305225\pi$
$18$	2.12132	+	2.12132i	0.500000	+	0.500000i
$19$	1.25529	−	4.17423i	0.287984	−	0.957635i
$19$	1.25529	−	4.17423i	0.287984	−	0.957635i
$20$		0			0
$21$	−9.67423	−	5.58542i	−2.11109	−	1.21884i
$22$	0.892794	+	3.33195i	0.190344	+	0.710374i
$23$	5.01910	+	1.34486i	1.04655	+	0.280423i	0.740827	−	0.671696i	$-0.234434\pi$
$23$	5.01910	+	1.34486i	1.04655	+	0.280423i	0.305727	+	0.952119i	$0.401100\pi$
$24$	2.12132	+	1.22474i	0.433013	+	0.250000i
$25$		0			0
$26$	4.89898			0.960769
$27$		0			0
$28$	−4.40508	−	1.18034i	−0.832483	−	0.223063i
$29$	−0.389270	−	0.674235i	−0.0722855	−	0.125202i	0.827617	−	0.561293i	$-0.189696\pi$
$29$	−0.389270	−	0.674235i	−0.0722855	−	0.125202i	−0.899903	+	0.436091i	$0.856363\pi$
$30$		0			0
$31$			7.70674i			1.38417i	0.721815	+	0.692086i	$0.243308\pi$
$31$			7.70674i			1.38417i	−0.721815	+	0.692086i	$0.756692\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−8.16158	+	2.18689i	−1.42075	+	0.380688i
$34$	1.41421	+	2.44949i	0.242536	+	0.420084i
$35$		0			0
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	0.389270	−	0.389270i	0.0639955	−	0.0639955i	−0.674385	−	0.738380i	$-0.735591\pi$
$37$	0.389270	−	0.389270i	0.0639955	−	0.0639955i	0.738380	+	0.674385i	$0.235591\pi$
$38$	4.35690	+	0.132150i	0.706782	+	0.0214376i
$39$			12.0000i			1.92154i
$40$		0			0
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	0.378275	−	0.925693i	$-0.376517\pi$
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	−0.612536	+	0.790443i	$0.709851\pi$
$42$	2.89123	−	10.7902i	0.446126	−	1.66497i
$43$	0.933552	+	3.48406i	0.142365	+	0.531314i	0.999859	+	0.0168193i	$0.00535399\pi$
$43$	0.933552	+	3.48406i	0.142365	+	0.531314i	−0.857493	+	0.514495i	$0.827979\pi$
$44$	−2.98735	+	1.72474i	−0.450359	+	0.260015i
$45$		0			0
$46$			5.19615i			0.766131i
$47$	1.79315	−	6.69213i	0.261558	−	0.976148i	−0.702766	−	0.711421i	$-0.748052\pi$
$47$	1.79315	−	6.69213i	0.261558	−	0.976148i	0.964324	−	0.264726i	$-0.0852816\pi$
$48$	−0.633975	+	2.36603i	−0.0915064	+	0.341506i
$49$			13.7980i			1.97114i
$50$		0			0
$51$	−6.00000	+	3.46410i	−0.840168	+	0.485071i
$52$	1.26795	+	4.73205i	0.175833	+	0.656217i
$53$	−2.67838	+	9.99585i	−0.367904	+	1.37304i	0.495537	+	0.868587i	$0.334971\pi$
$53$	−2.67838	+	9.99585i	−0.367904	+	1.37304i	−0.863441	+	0.504449i	$0.831695\pi$
$54$		0			0
$55$		0			0
$56$		−	4.56048i		−	0.609419i
$57$	−0.323701	+	10.6722i	−0.0428752	+	1.41356i
$58$	0.550510	−	0.550510i	0.0722855	−	0.0722855i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	−7.44414	+	1.99465i	−0.945407	+	0.253321i
$63$	13.2153	+	3.54102i	1.66497	+	0.446126i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−4.22474	−	7.31747i	−0.520030	−	0.900719i
$67$	−9.22508	−	2.47185i	−1.12702	−	0.301985i	−0.353301	−	0.935510i	$-0.614941\pi$
$67$	−9.22508	−	2.47185i	−1.12702	−	0.301985i	−0.773722	+	0.633525i	$0.781608\pi$
$68$	−2.00000	+	2.00000i	−0.242536	+	0.242536i
$69$	−12.7279			−1.53226
$70$		0			0
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	0.311305	−	0.950310i	$-0.399234\pi$
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	−0.667340	+	0.744753i	$0.732567\pi$
$72$	−2.89778	−	0.776457i	−0.341506	−	0.0915064i
$73$	0.567526	+	2.11804i	0.0664239	+	0.247897i	0.991152	−	0.132731i	$-0.0423745\pi$
$73$	0.567526	+	2.11804i	0.0664239	+	0.247897i	−0.924728	+	0.380628i	$0.875708\pi$
$74$	0.476756	+	0.275255i	0.0554217	+	0.0319978i
$75$		0			0
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$	11.1237	+	11.1237i	1.26767	+	1.26767i
$78$	−11.5911	+	3.10583i	−1.31243	+	0.351666i
$79$	5.97469	−	10.3485i	0.672205	−	1.16429i	−0.305072	−	0.952329i	$-0.598681\pi$
$79$	5.97469	−	10.3485i	0.672205	−	1.16429i	0.977277	−	0.211964i	$-0.0679861\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	0.448288	−	1.67303i	0.0495051	−	0.184756i
$83$	2.34847	−	2.34847i	0.257778	−	0.257778i	−0.566372	−	0.824150i	$-0.691653\pi$
$83$	2.34847	−	2.34847i	0.257778	−	0.257778i	0.824150	+	0.566372i	$0.191653\pi$
$84$	11.1708			1.21884
$85$		0			0
$86$	−3.12372	+	1.80348i	−0.336840	+	0.194475i
$87$	1.34847	+	1.34847i	0.144571	+	0.144571i
$88$	−2.43916	−	2.43916i	−0.260015	−	0.260015i
$89$	−1.64456	−	2.84847i	−0.174323	−	0.301937i	0.765603	−	0.643313i	$-0.222441\pi$
$89$	−1.64456	−	2.84847i	−0.174323	−	0.301937i	−0.939927	+	0.341376i	$0.889107\pi$
$90$		0			0
$91$	19.3485	−	11.1708i	2.02827	−	1.17102i
$92$	−5.01910	+	1.34486i	−0.523277	+	0.140212i
$93$	−4.88588	−	18.2343i	−0.506642	−	1.89081i
$94$	6.92820			0.714590
$95$		0			0
$96$	−2.44949			−0.250000
$97$	2.47185	+	9.22508i	0.250979	+	0.936665i	0.970284	+	0.241971i	$0.0777938\pi$
$97$	2.47185	+	9.22508i	0.250979	+	0.936665i	−0.719305	+	0.694695i	$0.755540\pi$
$98$	−13.3278	+	3.57117i	−1.34631	+	0.360743i
$99$	8.96204	−	5.17423i	0.900719	−	0.520030i
$100$		0			0
$101$	−8.34847	−	14.4600i	−0.830704	−	1.43882i	−0.897481	−	0.441053i	$-0.854605\pi$
$101$	−8.34847	−	14.4600i	−0.830704	−	1.43882i	0.0667772	−	0.997768i	$-0.478728\pi$
$102$	−4.89898	−	4.89898i	−0.485071	−	0.485071i
$103$	5.58542	+	5.58542i	0.550348	+	0.550348i	0.926541	−	0.376193i	$-0.122767\pi$
$103$	5.58542	+	5.58542i	0.550348	+	0.550348i	−0.376193	+	0.926541i	$0.622767\pi$
$104$	−4.24264	+	2.44949i	−0.416025	+	0.240192i
$105$		0			0
$106$	−10.3485			−1.00513
$107$	−8.66025	+	8.66025i	−0.837218	+	0.837218i	−0.988492	−	0.151274i	$-0.951663\pi$
$107$	−8.66025	+	8.66025i	−0.837218	+	0.837218i	0.151274	+	0.988492i	$0.451663\pi$
$108$		0			0
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$		0			0
$111$	−0.674235	+	1.16781i	−0.0639955	+	0.110843i
$112$	4.40508	−	1.18034i	0.416241	−	0.111532i
$113$	−4.41761	−	4.41761i	−0.415574	−	0.415574i	0.468101	−	0.883675i	$-0.344938\pi$
$113$	−4.41761	−	4.41761i	−0.415574	−	0.415574i	−0.883675	+	0.468101i	$0.844938\pi$
$114$	−10.3923	+	2.44949i	−0.973329	+	0.229416i
$115$		0			0
$116$	0.674235	+	0.389270i	0.0626011	+	0.0361428i
$117$	−3.80385	−	14.1962i	−0.351666	−	1.31243i
$118$	3.34607	+	0.896575i	0.308030	+	0.0825365i
$119$	11.1708	+	6.44949i	1.02403	+	0.591224i
$120$		0			0
$121$	0.898979			0.0817254
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	4.09808	+	1.09808i	0.369511	+	0.0990102i
$124$	−3.85337	−	6.67423i	−0.346043	−	0.599364i
$125$		0			0
$126$			13.6814i			1.21884i
$127$	−3.96128	−	1.06142i	−0.351507	−	0.0941860i	0.0787452	−	0.996895i	$-0.474909\pi$
$127$	−3.96128	−	1.06142i	−0.351507	−	0.0941860i	−0.430252	+	0.902709i	$0.641575\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−4.41761	−	7.65153i	−0.388949	−	0.673680i
$130$		0			0
$131$	8.62372	−	14.9367i	0.753458	−	1.30503i	−0.192679	−	0.981262i	$-0.561718\pi$
$131$	8.62372	−	14.9367i	0.753458	−	1.30503i	0.946137	−	0.323766i	$-0.104949\pi$
$132$	5.97469	−	5.97469i	0.520030	−	0.520030i
$133$	17.5088	−	9.41284i	1.51821	−	0.816196i
$134$		−	9.55051i		−	0.825038i
$135$		0			0
$136$	−2.44949	−	1.41421i	−0.210042	−	0.121268i
$137$	−0.732051	+	2.73205i	−0.0625433	+	0.233415i	−0.990121	−	0.140215i	$-0.955220\pi$
$137$	−0.732051	+	2.73205i	−0.0625433	+	0.233415i	0.927578	+	0.373630i	$0.121887\pi$
$138$	−3.29423	−	12.2942i	−0.280423	−	1.04655i
$139$	−6.14966	+	3.55051i	−0.521608	+	0.301150i	−0.737592	−	0.675246i	$-0.764037\pi$
$139$	−6.14966	+	3.55051i	−0.521608	+	0.301150i	0.215984	+	0.976397i	$0.430704\pi$
$140$		0			0
$141$			16.9706i			1.42918i
$142$	0.896575	−	3.34607i	0.0752389	−	0.280796i
$143$	4.37378	−	16.3232i	0.365754	−	1.36501i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	−1.89898	+	1.09638i	−0.157161	+	0.0907367i
$147$	−8.74756	−	32.6463i	−0.721486	−	2.69262i
$148$	−0.142483	+	0.531752i	−0.0117120	+	0.0437098i
$149$	−1.34278	−	0.775255i	−0.110005	−	0.0635114i	0.443988	−	0.896033i	$-0.353563\pi$
$149$	−1.34278	−	0.775255i	−0.110005	−	0.0635114i	−0.553993	+	0.832521i	$0.686897\pi$
$150$		0			0
$151$			8.48528i			0.690522i	0.938507	+	0.345261i	$0.112210\pi$
$151$			8.48528i			0.690522i	−0.938507	+	0.345261i	$0.887790\pi$
$152$	−3.83926	+	2.06400i	−0.311405	+	0.167413i
$153$	6.00000	−	6.00000i	0.485071	−	0.485071i
$154$	−7.86566	+	13.6237i	−0.633833	+	1.09783i
$155$		0			0
$156$	−6.00000	−	10.3923i	−0.480384	−	0.832050i
$157$	3.65307	−	0.978838i	0.291547	−	0.0781198i	−0.110081	−	0.993923i	$-0.535111\pi$
$157$	3.65307	−	0.978838i	0.291547	−	0.0781198i	0.401628	+	0.915803i	$0.368444\pi$
$158$	11.5422	+	3.09273i	0.918250	+	0.246044i
$159$		−	25.3485i		−	2.01026i
$160$		0			0
$161$	11.8485	+	20.5222i	0.933790	+	1.61737i
$162$	−8.69333	−	2.32937i	−0.683013	−	0.183013i
$163$	−5.34847	+	5.34847i	−0.418924	+	0.418924i	−0.884833	−	0.465908i	$-0.845728\pi$
$163$	−5.34847	+	5.34847i	−0.418924	+	0.418924i	0.465908	+	0.884833i	$0.345728\pi$
$164$	1.73205			0.135250
$165$		0			0
$166$	2.87628	+	1.66062i	0.223242	+	0.128889i
$167$	22.8895	+	6.13322i	1.77124	+	0.474603i	0.988942	−	0.148300i	$-0.0473802\pi$
$167$	22.8895	+	6.13322i	1.77124	+	0.474603i	0.782299	+	0.622903i	$0.214047\pi$
$168$	2.89123	+	10.7902i	0.223063	+	0.832483i
$169$	−9.52628	−	5.50000i	−0.732791	−	0.423077i
$170$		0			0
$171$	−3.00000	−	12.7279i	−0.229416	−	0.973329i
$172$	−2.55051	−	2.55051i	−0.194475	−	0.194475i
$173$	−5.26380	+	1.41043i	−0.400200	+	0.107233i	−0.453304	−	0.891356i	$-0.649755\pi$
$173$	−5.26380	+	1.41043i	−0.400200	+	0.107233i	0.0531048	+	0.998589i	$0.483088\pi$
$174$	−0.953512	+	1.65153i	−0.0722855	+	0.125202i
$175$		0			0
$176$	1.72474	−	2.98735i	0.130008	−	0.225180i
$177$	−2.19615	+	8.19615i	−0.165073	+	0.616061i
$178$	2.32577	−	2.32577i	0.174323	−	0.174323i
$179$	5.97469			0.446569			0.223285	−	0.974753i	$-0.428322\pi$
$179$	5.97469			0.446569			0.223285	+	0.974753i	$0.428322\pi$
$180$		0			0
$181$	11.3258	−	6.53893i	0.841838	−	0.486035i	−0.0160509	−	0.999871i	$-0.505109\pi$
$181$	11.3258	−	6.53893i	0.841838	−	0.486035i	0.857888	+	0.513836i	$0.171776\pi$
$182$	15.7980	+	15.7980i	1.17102	+	1.17102i
$183$	−13.8564	−	13.8564i	−1.02430	−	1.02430i
$184$	−2.59808	−	4.50000i	−0.191533	−	0.331744i
$185$		0			0
$186$	16.3485	−	9.43879i	1.19873	−	0.692086i
$187$	9.42418	−	2.52520i	0.689164	−	0.184661i
$188$	1.79315	+	6.69213i	0.130779	+	0.488074i
$189$		0			0
$190$		0			0
$191$	8.24745			0.596764			0.298382	−	0.954446i	$-0.403553\pi$
$191$	8.24745			0.596764			0.298382	+	0.954446i	$0.403553\pi$
$192$	−0.633975	−	2.36603i	−0.0457532	−	0.170753i
$193$	1.30252	−	0.349010i	0.0937575	−	0.0251223i	−0.211635	−	0.977349i	$-0.567879\pi$
$193$	1.30252	−	0.349010i	0.0937575	−	0.0251223i	0.305393	+	0.952226i	$0.401212\pi$
$194$	−8.27098	+	4.77526i	−0.593822	+	0.342843i
$195$		0			0
$196$	−6.89898	−	11.9494i	−0.492784	−	0.853527i
$197$	−12.6742	−	12.6742i	−0.903002	−	0.903002i	0.0926929	−	0.995695i	$-0.470453\pi$
$197$	−12.6742	−	12.6742i	−0.903002	−	0.903002i	−0.995695	+	0.0926929i	$0.970453\pi$
$198$	7.31747	+	7.31747i	0.520030	+	0.520030i
$199$	−8.48528	+	4.89898i	−0.601506	+	0.347279i	−0.769634	−	0.638486i	$-0.779561\pi$
$199$	−8.48528	+	4.89898i	−0.601506	+	0.347279i	0.168128	+	0.985765i	$0.446228\pi$
$200$		0			0
$201$	23.3939			1.65008
$202$	11.8065	−	11.8065i	0.830704	−	0.830704i
$203$	0.918940	−	3.42953i	0.0644969	−	0.240706i
$204$	3.46410	−	6.00000i	0.242536	−	0.420084i
$205$		0			0
$206$	−3.94949	+	6.84072i	−0.275174	+	0.476615i
$207$	15.0573	−	4.03459i	1.04655	−	0.280423i
$208$	−3.46410	−	3.46410i	−0.240192	−	0.240192i
$209$	4.33013	−	14.3990i	0.299521	−	0.995998i
$210$		0			0
$211$	23.1742	+	13.3797i	1.59538	+	0.921093i	0.992361	+	0.123366i	$0.0393690\pi$
$211$	23.1742	+	13.3797i	1.59538	+	0.921093i	0.603019	+	0.797727i	$0.293964\pi$
$212$	−2.67838	−	9.99585i	−0.183952	−	0.686518i
$213$	8.19615	+	2.19615i	0.561591	+	0.150478i
$214$	−10.6066	−	6.12372i	−0.725052	−	0.418609i
$215$		0			0
$216$		0			0
$217$	−24.8523	+	24.8523i	−1.68708	+	1.68708i
$218$		0			0
$219$	−2.68556	−	4.65153i	−0.181473	−	0.314321i
$220$		0			0
$221$		−	13.8564i		−	0.932083i
$222$	−1.30252	−	0.349010i	−0.0874195	−	0.0234240i
$223$	−17.0939	+	4.58030i	−1.14469	+	0.306720i	−0.780837	−	0.624735i	$-0.785207\pi$
$223$	−17.0939	+	4.58030i	−1.14469	+	0.306720i	−0.363857	+	0.931455i	$0.618540\pi$
$224$	2.28024	+	3.94949i	0.152355	+	0.263886i
$225$		0			0
$226$	3.12372	−	5.41045i	0.207787	−	0.359898i
$227$	14.4600	−	14.4600i	0.959742	−	0.959742i	−0.0394783	−	0.999220i	$-0.512570\pi$
$227$	14.4600	−	14.4600i	0.959742	−	0.959742i	0.999220	+	0.0394783i	$0.0125696\pi$
$228$	−5.05575	−	9.40422i	−0.334825	−	0.622810i
$229$			20.4495i			1.35134i	0.737204	+	0.675670i	$0.236146\pi$
$229$			20.4495i			1.35134i	−0.737204	+	0.675670i	$0.763854\pi$
$230$		0			0
$231$	−33.3712	−	19.2669i	−2.19566	−	1.26767i
$232$	−0.201501	+	0.752011i	−0.0132292	+	0.0493719i
$233$	−0.896575	−	3.34607i	−0.0587366	−	0.219208i	0.930319	−	0.366751i	$-0.119530\pi$
$233$	−0.896575	−	3.34607i	−0.0587366	−	0.219208i	−0.989056	+	0.147543i	$0.952863\pi$
$234$	12.7279	−	7.34847i	0.832050	−	0.480384i
$235$		0			0
$236$			3.46410i			0.225494i
$237$	−7.57561	+	28.2725i	−0.492088	+	1.83650i
$238$	−3.33850	+	12.4595i	−0.216403	+	0.807627i
$239$		−	5.79796i		−	0.375039i	−0.982261	−	0.187519i	$-0.939955\pi$
$239$		−	5.79796i		−	0.375039i	0.982261	−	0.187519i	$-0.0600447\pi$
$240$		0			0
$241$	−5.69694	+	3.28913i	−0.366972	+	0.211871i	−0.672135	−	0.740429i	$-0.734622\pi$
$241$	−5.69694	+	3.28913i	−0.366972	+	0.211871i	0.305163	+	0.952300i	$0.401289\pi$
$242$	0.232673	+	0.868348i	0.0149568	+	0.0558195i
$243$	5.70577	−	21.2942i	0.366025	−	1.36603i
$244$	−6.92820	−	4.00000i	−0.443533	−	0.256074i
$245$		0			0
$246$			4.24264i			0.270501i
$247$	−18.1610	−	11.2328i	−1.15556	−	0.714728i
$248$	5.44949	−	5.44949i	0.346043	−	0.346043i
$249$	−4.06767	+	7.04541i	−0.257778	+	0.446485i
$250$		0			0
$251$	−4.44949	−	7.70674i	−0.280849	−	0.486445i	0.690745	−	0.723099i	$-0.257283\pi$
$251$	−4.44949	−	7.70674i	−0.280849	−	0.486445i	−0.971594	+	0.236653i	$0.923949\pi$
$252$	−13.2153	+	3.54102i	−0.832483	+	0.223063i
$253$	17.3133	+	4.63909i	1.08848	+	0.291657i
$254$		−	4.10102i		−	0.257321i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.9571	−	3.73980i	−0.870622	−	0.233283i	−0.204265	−	0.978916i	$-0.565481\pi$
$257$	−13.9571	−	3.73980i	−0.870622	−	0.233283i	−0.666357	+	0.745633i	$0.732147\pi$
$258$	6.24745	−	6.24745i	0.388949	−	0.388949i
$259$	2.51059			0.156000
$260$		0			0
$261$	−2.02270	−	1.16781i	−0.125202	−	0.0722855i
$262$	16.6598	+	4.46397i	1.02924	+	0.275785i
$263$	7.45637	+	27.8275i	0.459779	+	1.71592i	0.673644	+	0.739056i	$0.264728\pi$
$263$	7.45637	+	27.8275i	0.459779	+	1.71592i	−0.213864	+	0.976863i	$0.568605\pi$
$264$	7.31747	+	4.22474i	0.450359	+	0.260015i
$265$		0			0
$266$	13.6237	+	14.4760i	0.835324	+	0.887582i
$267$	5.69694	+	5.69694i	0.348647	+	0.348647i
$268$	9.22508	−	2.47185i	0.563512	−	0.150993i
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	−0.740883	−	0.671634i	$-0.765593\pi$
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	0.952093	+	0.305807i	$0.0989263\pi$
$270$		0			0
$271$	−16.3485	+	28.3164i	−0.993099	+	1.72010i	−0.394981	+	0.918689i	$0.629249\pi$
$271$	−16.3485	+	28.3164i	−0.993099	+	1.72010i	−0.598118	+	0.801408i	$0.704084\pi$
$272$	0.732051	−	2.73205i	0.0443871	−	0.165655i
$273$	−38.6969	+	38.6969i	−2.34205	+	2.34205i
$274$	−2.82843			−0.170872
$275$		0			0
$276$	11.0227	−	6.36396i	0.663489	−	0.383065i
$277$	5.79796	+	5.79796i	0.348366	+	0.348366i	0.859500	−	0.511135i	$-0.170775\pi$
$277$	5.79796	+	5.79796i	0.348366	+	0.348366i	−0.511135	+	0.859500i	$0.670775\pi$
$278$	−5.02118	−	5.02118i	−0.301150	−	0.301150i
$279$	11.5601	+	20.0227i	0.692086	+	1.19873i
$280$		0			0
$281$	−10.5000	+	6.06218i	−0.626377	+	0.361639i	−0.779348	−	0.626592i	$-0.784449\pi$
$281$	−10.5000	+	6.06218i	−0.626377	+	0.361639i	0.152970	+	0.988231i	$0.451116\pi$
$282$	−16.3923	+	4.39230i	−0.976148	+	0.261558i
$283$	1.62863	+	6.07812i	0.0968118	+	0.361306i	0.997288	−	0.0735989i	$-0.0234485\pi$
$283$	1.62863	+	6.07812i	0.0968118	+	0.361306i	−0.900476	+	0.434905i	$0.856782\pi$
$284$	3.46410			0.205557
$285$		0			0
$286$	16.8990			0.999258
$287$	−2.04441	−	7.62983i	−0.120677	−	0.450375i
$288$	2.89778	−	0.776457i	0.170753	−	0.0457532i
$289$	−7.79423	+	4.50000i	−0.458484	+	0.264706i
$290$		0			0
$291$	−11.6969	−	20.2597i	−0.685687	−	1.18764i
$292$	−1.55051	−	1.55051i	−0.0907367	−	0.0907367i
$293$	−1.94635	−	1.94635i	−0.113707	−	0.113707i	0.647964	−	0.761671i	$-0.275621\pi$
$293$	−1.94635	−	1.94635i	−0.113707	−	0.113707i	−0.761671	+	0.647964i	$0.775621\pi$
$294$	29.2699	−	16.8990i	1.70705	−	0.985568i
$295$		0			0
$296$	−0.550510			−0.0319978
$297$		0			0
$298$	0.401302	−	1.49768i	0.0232468	−	0.0867582i
$299$	12.7279	−	22.0454i	0.736075	−	1.27492i
$300$		0			0
$301$	−8.22474	+	14.2457i	−0.474066	+	0.821107i
$302$	−8.19615	+	2.19615i	−0.471636	+	0.126374i
$303$	28.9199	+	28.9199i	1.66141	+	1.66141i
$304$	−2.98735	−	3.17423i	−0.171336	−	0.182055i
$305$		0			0
$306$	7.34847	+	4.24264i	0.420084	+	0.242536i
$307$	0.349010	+	1.30252i	0.0199190	+	0.0743388i	0.975170	−	0.221458i	$-0.0710816\pi$
$307$	0.349010	+	1.30252i	0.0199190	+	0.0743388i	−0.955251	+	0.295797i	$0.904415\pi$
$308$	−15.1953	−	4.07157i	−0.865832	−	0.231999i
$309$	−16.7563	−	9.67423i	−0.953231	−	0.550348i
$310$		0			0
$311$	6.20204			0.351685			0.175843	−	0.984418i	$-0.443735\pi$
$311$	6.20204			0.351685			0.175843	+	0.984418i	$0.443735\pi$
$312$	8.48528	−	8.48528i	0.480384	−	0.480384i
$313$	−31.4806	−	8.43520i	−1.77939	−	0.476786i	−0.788917	−	0.614499i	$-0.789358\pi$
$313$	−31.4806	−	8.43520i	−1.77939	−	0.476786i	−0.990472	+	0.137713i	$0.956025\pi$
$314$	1.89097	+	3.27526i	0.106714	+	0.184833i
$315$		0			0
$316$			11.9494i			0.672205i
$317$	−8.93235	−	2.39342i	−0.501691	−	0.134428i	−0.000906171	−	1.00000i	$-0.500288\pi$
$317$	−8.93235	−	2.39342i	−0.501691	−	0.134428i	−0.500785	+	0.865572i	$0.666955\pi$
$318$	24.4847	−	6.56067i	1.37304	−	0.367904i
$319$	−1.34278	−	2.32577i	−0.0751813	−	0.130218i
$320$		0			0
$321$	15.0000	−	25.9808i	0.837218	−	1.45010i
$322$	−16.7563	+	16.7563i	−0.933790	+	0.933790i
$323$	0.373778	−	12.3232i	0.0207975	−	0.685679i
$324$		−	9.00000i		−	0.500000i
$325$		0			0
$326$	−6.55051	−	3.78194i	−0.362799	−	0.209462i
$327$		0			0
$328$	0.448288	+	1.67303i	0.0247525	+	0.0923778i
$329$	27.3629	−	15.7980i	1.50856	−	0.870970i
$330$		0			0
$331$		−	21.3882i		−	1.17560i	−0.809006	−	0.587800i	$-0.799994\pi$
$331$		−	21.3882i		−	1.17560i	0.809006	−	0.587800i	$-0.200006\pi$
$332$	−0.859599	+	3.20807i	−0.0471766	+	0.176066i
$333$	0.427448	−	1.59526i	0.0234240	−	0.0874195i
$334$			23.6969i			1.29664i
$335$		0			0
$336$	−9.67423	+	5.58542i	−0.527773	+	0.304710i
$337$	−4.65874	−	17.3867i	−0.253778	−	0.947112i	−0.968766	−	0.247976i	$-0.920235\pi$
$337$	−4.65874	−	17.3867i	−0.253778	−	0.947112i	0.714988	−	0.699136i	$-0.246432\pi$
$338$	2.84701	−	10.6252i	0.154857	−	0.577934i
$339$	13.2528	+	7.65153i	0.719795	+	0.415574i
$340$		0			0
$341$			26.5843i			1.43962i
$342$	11.5178	−	6.19201i	0.622810	−	0.334825i
$343$	−21.9217	+	21.9217i	−1.18366	+	1.18366i
$344$	1.80348	−	3.12372i	0.0972373	−	0.168420i
$345$		0			0
$346$	−2.72474	−	4.71940i	−0.146483	−	0.253716i
$347$	29.1626	−	7.81408i	1.56553	−	0.419482i	0.631119	−	0.775686i	$-0.282596\pi$
$347$	29.1626	−	7.81408i	1.56553	−	0.419482i	0.934408	+	0.356204i	$0.115929\pi$
$348$	−1.84204	−	0.493574i	−0.0987439	−	0.0264583i
$349$			28.8990i			1.54693i	0.633841	+	0.773463i	$0.281477\pi$
$349$			28.8990i			1.54693i	−0.633841	+	0.773463i	$0.718523\pi$
$350$		0			0
$351$		0			0
$352$	3.33195	+	0.892794i	0.177594	+	0.0475861i
$353$	16.3485	−	16.3485i	0.870141	−	0.870141i	−0.122346	−	0.992487i	$-0.539042\pi$
$353$	16.3485	−	16.3485i	0.870141	−	0.870141i	0.992487	+	0.122346i	$0.0390418\pi$
$354$	−8.48528			−0.450988
$355$		0			0
$356$	2.84847	+	1.64456i	0.150969	+	0.0871617i
$357$	−30.5193	−	8.17763i	−1.61525	−	0.432806i
$358$	1.54636	+	5.77111i	0.0817279	+	0.305013i
$359$	−3.63907	−	2.10102i	−0.192063	−	0.110888i	0.400885	−	0.916128i	$-0.368703\pi$
$359$	−3.63907	−	2.10102i	−0.192063	−	0.110888i	−0.592948	+	0.805241i	$0.702036\pi$
$360$		0			0
$361$	−15.8485	−	10.4798i	−0.834130	−	0.551568i
$362$	9.24745	+	9.24745i	0.486035	+	0.486035i
$363$	−2.12701	+	0.569930i	−0.111639	+	0.0299136i
$364$	−11.1708	+	19.3485i	−0.585511	+	1.01414i
$365$		0			0
$366$	9.79796	−	16.9706i	0.512148	−	0.887066i
$367$	6.84355	−	25.5405i	0.357231	−	1.33320i	−0.520423	−	0.853908i	$-0.674226\pi$
$367$	6.84355	−	25.5405i	0.357231	−	1.33320i	0.877654	−	0.479295i	$-0.159107\pi$
$368$	3.67423	−	3.67423i	0.191533	−	0.191533i
$369$	−5.19615			−0.270501
$370$		0			0
$371$	−40.8712	+	23.5970i	−2.12193	+	1.22509i
$372$	13.3485	+	13.3485i	0.692086	+	0.692086i
$373$	−12.6886	−	12.6886i	−0.656991	−	0.656991i	0.297676	−	0.954667i	$-0.403788\pi$
$373$	−12.6886	−	12.6886i	−0.656991	−	0.656991i	−0.954667	+	0.297676i	$0.903788\pi$
$374$	4.87832	+	8.44949i	0.252252	+	0.436913i
$375$		0			0
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$	−3.68409	+	0.987148i	−0.189740	+	0.0508407i
$378$		0			0
$379$	−21.9917			−1.12964			−0.564820	−	0.825214i	$-0.691054\pi$
$379$	−21.9917			−1.12964			−0.564820	+	0.825214i	$0.691054\pi$
$380$		0			0
$381$	10.0454			0.514642
$382$	2.13460	+	7.96642i	0.109215	+	0.407598i
$383$	−9.46410	+	2.53590i	−0.483593	+	0.129578i	−0.492375	−	0.870383i	$-0.663871\pi$
$383$	−9.46410	+	2.53590i	−0.483593	+	0.129578i	0.00878215	+	0.999961i	$0.497205\pi$
$384$	2.12132	−	1.22474i	0.108253	−	0.0625000i
$385$		0			0
$386$	0.674235	+	1.16781i	0.0343176	+	0.0594399i
$387$	7.65153	+	7.65153i	0.388949	+	0.388949i
$388$	−6.75323	−	6.75323i	−0.342843	−	0.342843i
$389$	−5.97469	+	3.44949i	−0.302929	+	0.174896i	−0.643758	−	0.765229i	$-0.722626\pi$
$389$	−5.97469	+	3.44949i	−0.302929	+	0.174896i	0.340829	+	0.940125i	$0.389292\pi$
$390$		0			0
$391$	14.6969			0.743256
$392$	9.75663	−	9.75663i	0.492784	−	0.492784i
$393$	−10.9344	+	40.8079i	−0.551570	+	2.05849i
$394$	8.96204	−	15.5227i	0.451501	−	0.782023i
$395$		0			0
$396$	−5.17423	+	8.96204i	−0.260015	+	0.450359i
$397$	11.2352	−	3.01047i	0.563879	−	0.151091i	0.0343912	−	0.999408i	$-0.489051\pi$
$397$	11.2352	−	3.01047i	0.563879	−	0.151091i	0.529488	+	0.848318i	$0.322384\pi$
$398$	−6.92820	−	6.92820i	−0.347279	−	0.347279i
$399$	−35.4589	+	33.3712i	−1.77516	+	1.67065i
$400$		0			0
$401$	−15.0000	−	8.66025i	−0.749064	−	0.432472i	0.0762914	−	0.997086i	$-0.475692\pi$
$401$	−15.0000	−	8.66025i	−0.749064	−	0.432472i	−0.825356	+	0.564613i	$0.809025\pi$
$402$	6.05478	+	22.5967i	0.301985	+	1.12702i
$403$	36.4687	+	9.77176i	1.81664	+	0.486766i
$404$	14.4600	+	8.34847i	0.719411	+	0.415352i
$405$		0			0
$406$	3.55051			0.176209
$407$	1.34278	−	1.34278i	0.0665592	−	0.0665592i
$408$	6.69213	+	1.79315i	0.331310	+	0.0887742i
$409$	7.79423	+	13.5000i	0.385400	+	0.667532i	0.991825	−	0.127609i	$-0.0407302\pi$
$409$	7.79423	+	13.5000i	0.385400	+	0.667532i	−0.606425	+	0.795141i	$0.707397\pi$
$410$		0			0
$411$		−	6.92820i		−	0.341743i
$412$	−7.62983	−	2.04441i	−0.375895	−	0.100721i
$413$	15.2597	−	4.08881i	0.750879	−	0.201197i
$414$	7.79423	+	13.5000i	0.383065	+	0.663489i
$415$		0			0
$416$	2.44949	−	4.24264i	0.120096	−	0.208013i
$417$	12.2993	−	12.2993i	0.602301	−	0.602301i
$418$	15.0291	+	0.455851i	0.735096	+	0.0222964i
$419$			6.34847i			0.310143i	0.987903	+	0.155072i	$0.0495608\pi$
$419$			6.34847i			0.310143i	−0.987903	+	0.155072i	$0.950439\pi$
$420$		0			0
$421$	15.6742	+	9.04952i	0.763915	+	0.441047i	0.830700	−	0.556721i	$-0.187941\pi$
$421$	15.6742	+	9.04952i	0.763915	+	0.441047i	−0.0667843	+	0.997767i	$0.521274\pi$
$422$	−6.92582	+	25.8475i	−0.337143	+	1.25824i
$423$	−5.37945	−	20.0764i	−0.261558	−	0.976148i
$424$	8.96204	−	5.17423i	0.435235	−	0.251283i
$425$		0			0
$426$			8.48528i			0.411113i
$427$	−9.44271	+	35.2407i	−0.456965	+	1.70542i
$428$	3.16987	−	11.8301i	0.153222	−	0.571831i
$429$			41.3939i			1.99852i
$430$		0			0
$431$	−2.02270	+	1.16781i	−0.0974302	+	0.0562514i	−0.547923	−	0.836528i	$-0.684581\pi$
$431$	−2.02270	+	1.16781i	−0.0974302	+	0.0562514i	0.450493	+	0.892780i	$0.351248\pi$
$432$		0			0
$433$	−1.20390	+	4.49303i	−0.0578560	+	0.215921i	−0.988802	−	0.149237i	$-0.952318\pi$
$433$	−1.20390	+	4.49303i	−0.0578560	+	0.215921i	0.930946	+	0.365158i	$0.118985\pi$
$434$	−30.4377	−	17.5732i	−1.46106	−	0.843541i
$435$		0			0
$436$		0			0
$437$	11.9142	−	19.2627i	0.569935	−	0.921460i
$438$	3.79796	−	3.79796i	0.181473	−	0.181473i
$439$	15.8028	−	27.3712i	0.754224	−	1.30635i	−0.191535	−	0.981486i	$-0.561346\pi$
$439$	15.8028	−	27.3712i	0.754224	−	1.30635i	0.945759	−	0.324869i	$-0.105320\pi$
$440$		0			0
$441$	20.6969	+	35.8481i	0.985568	+	1.70705i
$442$	13.3843	−	3.58630i	0.636624	−	0.170583i
$443$	−29.7766	−	7.97861i	−1.41473	−	0.379075i	−0.531117	−	0.847298i	$-0.678228\pi$
$443$	−29.7766	−	7.97861i	−1.41473	−	0.379075i	−0.883610	+	0.468223i	$0.844894\pi$
$444$		−	1.34847i		−	0.0639955i
$445$		0			0
$446$	−8.84847	−	15.3260i	−0.418987	−	0.725707i
$447$	3.66855	+	0.982984i	0.173516	+	0.0464936i
$448$	−3.22474	+	3.22474i	−0.152355	+	0.152355i
$449$	−8.66025			−0.408703			−0.204351	−	0.978898i	$-0.565508\pi$
$449$	−8.66025			−0.408703			−0.204351	+	0.978898i	$0.565508\pi$
$450$		0			0
$451$	−5.17423	−	2.98735i	−0.243645	−	0.140669i
$452$	6.03457	+	1.61696i	0.283842	+	0.0760553i
$453$	−5.37945	−	20.0764i	−0.252749	−	0.943271i
$454$	17.7098	+	10.2247i	0.831161	+	0.479871i
$455$		0			0
$456$	7.77526	−	7.31747i	0.364110	−	0.342672i
$457$	−5.24745	−	5.24745i	−0.245465	−	0.245465i	0.573641	−	0.819107i	$-0.305530\pi$
$457$	−5.24745	−	5.24745i	−0.245465	−	0.245465i	−0.819107	+	0.573641i	$0.805530\pi$
$458$	−19.7527	+	5.29272i	−0.922983	+	0.247312i
$459$		0			0
$460$		0			0
$461$	17.8990	−	31.0019i	0.833639	−	1.44390i	−0.0614955	−	0.998107i	$-0.519587\pi$
$461$	17.8990	−	31.0019i	0.833639	−	1.44390i	0.895134	−	0.445797i	$-0.147080\pi$
$462$	9.97326	−	37.2207i	0.463998	−	1.73166i
$463$	8.77526	−	8.77526i	0.407821	−	0.407821i	−0.473157	−	0.880978i	$-0.656886\pi$
$463$	8.77526	−	8.77526i	0.407821	−	0.407821i	0.880978	+	0.473157i	$0.156886\pi$
$464$	−0.778539			−0.0361428
$465$		0			0
$466$	3.00000	−	1.73205i	0.138972	−	0.0802357i
$467$	−18.5505	−	18.5505i	−0.858415	−	0.858415i	0.132736	−	0.991151i	$-0.457624\pi$
$467$	−18.5505	−	18.5505i	−0.858415	−	0.858415i	−0.991151	+	0.132736i	$0.957624\pi$
$468$	10.3923	+	10.3923i	0.480384	+	0.480384i
$469$	−21.7774	−	37.7196i	−1.00559	−	1.74173i
$470$		0			0
$471$	−8.02270	+	4.63191i	−0.369667	+	0.213427i
$472$	−3.34607	+	0.896575i	−0.154015	+	0.0412682i
$473$	3.22028	+	12.0182i	0.148068	+	0.552599i
$474$	−29.2699			−1.34441
$475$		0			0
$476$	−12.8990			−0.591224
$477$	8.03514	+	29.9876i	0.367904	+	1.37304i
$478$	5.60040	−	1.50062i	0.256156	−	0.0686369i
$479$	−27.1879	+	15.6969i	−1.24225	+	0.717211i	−0.969551	−	0.244889i	$-0.921248\pi$
$479$	−27.1879	+	15.6969i	−1.24225	+	0.717211i	−0.272695	+	0.962100i	$0.587915\pi$
$480$		0			0
$481$	−1.34847	−	2.33562i	−0.0614849	−	0.106495i
$482$	−4.65153	−	4.65153i	−0.211871	−	0.211871i
$483$	−41.0443	−	41.0443i	−1.86758	−	1.86758i
$484$	−0.778539	+	0.449490i	−0.0353881	+	0.0204314i
$485$		0			0
$486$	22.0454			1.00000
$487$	−30.2627	+	30.2627i	−1.37134	+	1.37134i	−0.512867	+	0.858468i	$0.671417\pi$
$487$	−30.2627	+	30.2627i	−1.37134	+	1.37134i	−0.858468	+	0.512867i	$0.828583\pi$
$488$	2.07055	−	7.72741i	0.0937295	−	0.349803i
$489$	9.26382	−	16.0454i	0.418924	−	0.725598i
$490$		0			0
$491$	−2.82577	+	4.89437i	−0.127525	+	0.220880i	−0.922717	−	0.385478i	$-0.874037\pi$
$491$	−2.82577	+	4.89437i	−0.127525	+	0.220880i	0.795192	+	0.606358i	$0.207370\pi$
$492$	−4.09808	+	1.09808i	−0.184756	+	0.0495051i
$493$	−1.55708	−	1.55708i	−0.0701273	−	0.0701273i
$494$	6.14966	−	20.4495i	0.276686	−	0.920066i
$495$		0			0
$496$	6.67423	+	3.85337i	0.299682	+	0.173021i
$497$	−4.08881	−	15.2597i	−0.183408	−	0.684489i
$498$	−7.85813	−	2.10558i	−0.352131	−	0.0943533i
$499$	2.81237	+	1.62372i	0.125899	+	0.0726879i	0.561627	−	0.827391i	$-0.310176\pi$
$499$	2.81237	+	1.62372i	0.125899	+	0.0726879i	−0.435728	+	0.900078i	$0.643509\pi$
$500$		0			0
$501$	−58.0454			−2.59328
$502$	6.29253	−	6.29253i	0.280849	−	0.280849i
$503$	34.1816	+	9.15895i	1.52408	+	0.408377i	0.921084	−	0.389364i	$-0.127305\pi$
$503$	34.1816	+	9.15895i	1.52408	+	0.408377i	0.603000	+	0.797741i	$0.293972\pi$
$504$	−6.84072	−	11.8485i	−0.304710	−	0.527773i
$505$		0			0
$506$			17.9241i			0.796822i
$507$	26.0263	+	6.97372i	1.15587	+	0.309714i
$508$	3.96128	−	1.06142i	0.175753	−	0.0470930i
$509$	−6.53893	−	11.3258i	−0.289833	−	0.502006i	0.683937	−	0.729541i	$-0.260266\pi$
$509$	−6.53893	−	11.3258i	−0.289833	−	0.502006i	−0.973770	+	0.227536i	$0.926933\pi$
$510$		0			0
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	14.4495i		−	0.637340i
$515$		0			0
$516$	7.65153	+	4.41761i	0.336840	+	0.194475i
$517$	6.18546	−	23.0844i	0.272036	−	1.01525i
$518$	0.649788	+	2.42504i	0.0285501	+	0.106550i
$519$	11.5601	−	6.67423i	0.507433	−	0.292966i
$520$		0			0
$521$		−	15.0635i		−	0.659946i	−0.943990	−	0.329973i	$-0.892960\pi$
$521$		−	15.0635i		−	0.659946i	0.943990	−	0.329973i	$-0.107040\pi$
$522$	0.604502	−	2.25603i	0.0264583	−	0.0987439i
$523$	9.09656	−	33.9488i	0.397765	−	1.48448i	−0.419254	−	0.907869i	$-0.637708\pi$
$523$	9.09656	−	33.9488i	0.397765	−	1.48448i	0.817019	−	0.576610i	$-0.195625\pi$
$524$			17.2474i			0.753458i
$525$		0			0
$526$	−24.9495	+	14.4046i	−1.08785	+	0.628070i
$527$	5.64173	+	21.0552i	0.245757	+	0.917179i
$528$	−2.18689	+	8.16158i	−0.0951721	+	0.355187i
$529$	3.46410	+	2.00000i	0.150613	+	0.0869565i
$530$		0			0
$531$		−	10.3923i		−	0.450988i
$532$	−10.4567	+	16.9062i	−0.453355	+	0.732976i
$533$	−6.00000	+	6.00000i	−0.259889	+	0.259889i
$534$	−4.02834	+	6.97730i	−0.174323	+	0.301937i
$535$		0			0
$536$	4.77526	+	8.27098i	0.206260	+	0.357252i
$537$	−14.1363	+	3.78780i	−0.610025	+	0.163456i
$538$	6.69213	+	1.79315i	0.288518	+	0.0773082i
$539$			47.5959i			2.05010i
$540$		0			0
$541$	4.77526	+	8.27098i	0.205304	+	0.355597i	0.950230	−	0.311550i	$-0.100848\pi$
$541$	4.77526	+	8.27098i	0.205304	+	0.355597i	−0.744925	+	0.667148i	$0.767515\pi$
$542$	−31.5828	−	8.46259i	−1.35660	−	0.363499i
$543$	−22.6515	+	22.6515i	−0.972070	+	0.972070i
$544$	2.82843			0.121268
$545$		0			0
$546$	−47.3939	−	27.3629i	−2.02827	−	1.17102i
$547$	17.3867	+	4.65874i	0.743400	+	0.199193i	0.610589	−	0.791948i	$-0.290933\pi$
$547$	17.3867	+	4.65874i	0.743400	+	0.199193i	0.132811	+	0.991141i	$0.457600\pi$
$548$	−0.732051	−	2.73205i	−0.0312717	−	0.116707i
$549$	20.7846	+	12.0000i	0.887066	+	0.512148i
$550$		0			0
$551$	−3.30306	+	0.778539i	−0.140715	+	0.0331669i
$552$	9.00000	+	9.00000i	0.383065	+	0.383065i
$553$	52.6380	−	14.1043i	2.23840	−	0.599777i
$554$	−4.09978	+	7.10102i	−0.174183	+	0.301693i
$555$		0			0
$556$	3.55051	−	6.14966i	0.150575	−	0.260804i
$557$	−4.54852	+	16.9753i	−0.192727	+	0.719267i	0.800117	+	0.599844i	$0.204771\pi$
$557$	−4.54852	+	16.9753i	−0.192727	+	0.719267i	−0.992844	+	0.119422i	$0.961896\pi$
$558$	−16.3485	+	16.3485i	−0.692086	+	0.692086i
$559$	17.6705			0.747381
$560$		0			0
$561$	−20.6969	+	11.9494i	−0.873825	+	0.504503i
$562$	−8.57321	−	8.57321i	−0.361639	−	0.361639i
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	0.967623	−	0.252399i	$-0.0812196\pi$
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	−0.252399	+	0.967623i	$0.581220\pi$
$564$	−8.48528	−	14.6969i	−0.357295	−	0.618853i
$565$		0			0
$566$	−5.44949	+	3.14626i	−0.229059	+	0.132247i
$567$	−39.6458	+	10.6230i	−1.66497	+	0.446126i
$568$	0.896575	+	3.34607i	0.0376195	+	0.140398i
$569$	18.7026			0.784054			0.392027	−	0.919954i	$-0.371774\pi$
$569$	18.7026			0.784054			0.392027	+	0.919954i	$0.371774\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	4.37378	+	16.3232i	0.182877	+	0.682506i
$573$	−19.5137	+	5.22867i	−0.815195	+	0.218431i
$574$	6.84072	−	3.94949i	0.285526	−	0.164849i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	19.2474	+	19.2474i	0.801282	+	0.801282i	0.983296	−	0.182014i	$-0.0582617\pi$
$577$	19.2474	+	19.2474i	0.801282	+	0.801282i	−0.182014	+	0.983296i	$0.558262\pi$
$578$	−6.36396	−	6.36396i	−0.264706	−	0.264706i
$579$	−2.86054	+	1.65153i	−0.118880	+	0.0686353i
$580$		0			0
$581$	15.1464			0.628380
$582$	16.5420	−	16.5420i	0.685687	−	0.685687i
$583$	−9.23905	+	34.4806i	−0.382642	+	1.42804i
$584$	1.09638	−	1.89898i	0.0453684	−	0.0785803i
$585$		0			0
$586$	1.37628	−	2.38378i	0.0568534	−	0.0984730i
$587$	13.3843	−	3.58630i	0.552428	−	0.148023i	0.0282024	−	0.999602i	$-0.491022\pi$
$587$	13.3843	−	3.58630i	0.552428	−	0.148023i	0.524225	+	0.851580i	$0.324355\pi$
$588$	23.8988	+	23.8988i	0.985568	+	0.985568i
$589$	32.1698	+	9.67423i	1.32553	+	0.398620i
$590$		0			0
$591$	38.0227	+	21.9524i	1.56405	+	0.903002i
$592$	−0.142483	−	0.531752i	−0.00585600	−	0.0218549i
$593$	−39.6147	−	10.6147i	−1.62678	−	0.435895i	−0.673798	−	0.738915i	$-0.735338\pi$
$593$	−39.6147	−	10.6147i	−1.62678	−	0.435895i	−0.952984	+	0.303020i	$0.902005\pi$
$594$		0			0
$595$		0			0
$596$	1.55051			0.0635114
$597$	16.9706	−	16.9706i	0.694559	−	0.694559i
$598$	24.5885	+	6.58846i	1.00550	+	0.269422i
$599$	−6.14966	−	10.6515i	−0.251268	−	0.435210i	0.712607	−	0.701564i	$-0.247514\pi$
$599$	−6.14966	−	10.6515i	−0.251268	−	0.435210i	−0.963875	+	0.266354i	$0.914181\pi$
$600$		0			0
$601$			17.1455i			0.699381i	0.936865	+	0.349690i	$0.113713\pi$
$601$			17.1455i			0.699381i	−0.936865	+	0.349690i	$0.886287\pi$
$602$	−15.8890	−	4.25744i	−0.647587	−	0.173520i
$603$	−27.6753	+	7.41556i	−1.12702	+	0.301985i
$604$	−4.24264	−	7.34847i	−0.172631	−	0.299005i
$605$		0			0
$606$	−20.4495	+	35.4196i	−0.830704	+	1.43882i
$607$	−5.58542	+	5.58542i	−0.226705	+	0.226705i	−0.811315	−	0.584610i	$-0.801248\pi$
$607$	−5.58542	+	5.58542i	−0.226705	+	0.226705i	0.584610	+	0.811315i	$0.301248\pi$
$608$	2.29289	−	3.70711i	0.0929891	−	0.150343i
$609$			8.69694i			0.352418i
$610$		0			0
$611$	−29.3939	−	16.9706i	−1.18915	−	0.686555i
$612$	−2.19615	+	8.19615i	−0.0887742	+	0.331310i
$613$	−10.8412	−	40.4598i	−0.437871	−	1.63416i	−0.734102	−	0.679039i	$-0.762397\pi$
$613$	−10.8412	−	40.4598i	−0.437871	−	1.63416i	0.296231	−	0.955116i	$-0.404270\pi$
$614$	−1.16781	+	0.674235i	−0.0471289	+	0.0272099i
$615$		0			0
$616$		−	15.7313i		−	0.633833i
$617$	7.70315	−	28.7486i	0.310117	−	1.15737i	−0.618333	−	0.785916i	$-0.712192\pi$
$617$	7.70315	−	28.7486i	0.310117	−	1.15737i	0.928450	−	0.371457i	$-0.121142\pi$
$618$	5.00775	−	18.6892i	0.201441	−	0.751789i
$619$			25.0454i			1.00666i	0.864094	+	0.503330i	$0.167892\pi$
$619$			25.0454i			1.00666i	−0.864094	+	0.503330i	$0.832108\pi$
$620$		0			0
$621$		0			0
$622$	1.60521	+	5.99071i	0.0643629	+	0.240206i
$623$	3.88229	−	14.4889i	0.155540	−	0.580485i
$624$	10.3923	+	6.00000i	0.416025	+	0.240192i
$625$		0			0
$626$		−	32.5911i		−	1.30260i
$627$	−1.11660	+	36.8135i	−0.0445928	+	1.47019i
$628$	−2.67423	+	2.67423i	−0.106714	+	0.106714i
$629$	0.778539	−	1.34847i	0.0310424	−	0.0537670i
$630$		0			0
$631$	−1.00000	−	1.73205i	−0.0398094	−	0.0689519i	0.845434	−	0.534080i	$-0.179342\pi$
$631$	−1.00000	−	1.73205i	−0.0398094	−	0.0689519i	−0.885244	+	0.465128i	$0.846008\pi$
$632$	−11.5422	+	3.09273i	−0.459125	+	0.123022i
$633$	−63.3132	−	16.9647i	−2.51647	−	0.674287i
$634$		−	9.24745i		−	0.367263i
$635$		0			0
$636$	12.6742	+	21.9524i	0.502566	+	0.870470i
$637$	65.2926	+	17.4951i	2.58699	+	0.693182i
$638$	1.89898	−	1.89898i	0.0751813	−	0.0751813i
$639$	−10.3923			−0.411113
$640$		0			0
$641$	−7.65153	−	4.41761i	−0.302217	−	0.174485i	0.341221	−	0.939983i	$-0.389159\pi$
$641$	−7.65153	−	4.41761i	−0.302217	−	0.174485i	−0.643439	+	0.765498i	$0.722493\pi$
$642$	28.9778	+	7.76457i	1.14366	+	0.306443i
$643$	6.44055	+	24.0365i	0.253991	+	0.947906i	0.968649	+	0.248432i	$0.0799154\pi$
$643$	6.44055	+	24.0365i	0.253991	+	0.947906i	−0.714659	+	0.699473i	$0.753418\pi$
$644$	−20.5222	−	11.8485i	−0.808686	−	0.466895i
$645$		0			0
$646$	12.0000	−	2.82843i	0.472134	−	0.111283i
$647$	17.6742	+	17.6742i	0.694846	+	0.694846i	0.963294	−	0.268448i	$-0.0865108\pi$
$647$	17.6742	+	17.6742i	0.694846	+	0.694846i	−0.268448	+	0.963294i	$0.586511\pi$
$648$	8.69333	−	2.32937i	0.341506	−	0.0915064i
$649$	5.97469	−	10.3485i	0.234527	−	0.406213i
$650$		0			0
$651$	43.0454	−	74.5568i	1.68708	−	2.92211i
$652$	1.95768	−	7.30614i	0.0766685	−	0.286131i
$653$	−12.0227	+	12.0227i	−0.470485	+	0.470485i	−0.902071	−	0.431587i	$-0.857954\pi$
$653$	−12.0227	+	12.0227i	−0.470485	+	0.470485i	0.431587	+	0.902071i	$0.357954\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	+	0.866025i	−0.0585652	+	0.0338126i
$657$	4.65153	+	4.65153i	0.181473	+	0.181473i
$658$	22.3417	+	22.3417i	0.870970	+	0.870970i
$659$	14.1582	+	24.5227i	0.551525	+	0.955269i	0.998165	+	0.0605552i	$0.0192871\pi$
$659$	14.1582	+	24.5227i	0.551525	+	0.955269i	−0.446640	+	0.894714i	$0.647380\pi$
$660$		0			0
$661$	33.0681	−	19.0919i	1.28620	−	0.742588i	0.308226	−	0.951313i	$-0.400265\pi$
$661$	33.0681	−	19.0919i	1.28620	−	0.742588i	0.977974	+	0.208725i	$0.0669313\pi$
$662$	20.6594	−	5.53567i	0.802950	−	0.215150i
$663$	8.78461	+	32.7846i	0.341166	+	1.27325i
$664$	−3.32124			−0.128889
$665$		0			0
$666$	1.65153			0.0639955
$667$	−1.04703	−	3.90756i	−0.0405411	−	0.151301i
$668$	−22.8895	+	6.13322i	−0.885621	+	0.237301i
$669$	37.5409	−	21.6742i	1.45141	−	0.837974i
$670$		0			0
$671$	13.7980	+	23.8988i	0.532664	+	0.922602i
$672$	−7.89898	−	7.89898i	−0.304710	−	0.304710i
$673$	30.8270	+	30.8270i	1.18829	+	1.18829i	0.977539	+	0.210753i	$0.0675916\pi$
$673$	30.8270	+	30.8270i	1.18829	+	1.18829i	0.210753	+	0.977539i	$0.432408\pi$
$674$	15.5885	−	9.00000i	0.600445	−	0.346667i
$675$		0			0
$676$	11.0000			0.423077
$677$	−21.9524	+	21.9524i	−0.843700	+	0.843700i	−0.989338	−	0.145638i	$-0.953477\pi$
$677$	−21.9524	+	21.9524i	−0.843700	+	0.843700i	0.145638	+	0.989338i	$0.453477\pi$
$678$	−3.96072	+	14.7816i	−0.152111	+	0.567685i
$679$	−21.7774	+	37.7196i	−0.835742	+	1.44755i
$680$		0			0
$681$	−25.0454	+	43.3799i	−0.959742	+	1.66232i
$682$	−25.6785	+	6.88053i	−0.983280	+	0.263469i
$683$	8.83523	+	8.83523i	0.338071	+	0.338071i	0.855641	−	0.517570i	$-0.173163\pi$
$683$	8.83523	+	8.83523i	0.338071	+	0.338071i	−0.517570	+	0.855641i	$0.673163\pi$
$684$	8.96204	+	9.52270i	0.342672	+	0.364110i
$685$		0			0
$686$	−26.8485	−	15.5010i	−1.02508	−	0.591830i
$687$	−12.9645	−	48.3840i	−0.494625	−	1.84597i
$688$	3.48406	+	0.933552i	0.132829	+	0.0355913i
$689$	43.9048	+	25.3485i	1.67264	+	0.965700i
$690$		0			0
$691$	11.4495			0.435559			0.217780	−	0.975998i	$-0.430119\pi$
$691$	11.4495			0.435559			0.217780	+	0.975998i	$0.430119\pi$
$692$	3.85337	−	3.85337i	0.146483	−	0.146483i
$693$	45.5859	+	12.2147i	1.73166	+	0.463998i
$694$	15.0956	+	26.1464i	0.573023	+	0.992505i
$695$		0			0
$696$		−	1.90702i		−	0.0722855i
$697$	−4.73205	−	1.26795i	−0.179239	−	0.0480270i
$698$	−27.9143	+	7.47961i	−1.05657	+	0.283107i
$699$	4.24264	+	7.34847i	0.160471	+	0.277945i
$700$		0			0
$701$	2.67423	−	4.63191i	0.101004	−	0.174945i	−0.811094	−	0.584915i	$-0.801128\pi$
$701$	2.67423	−	4.63191i	0.101004	−	0.174945i	0.912099	+	0.409971i	$0.134461\pi$
$702$		0			0
$703$	−1.13625	−	2.11355i	−0.0428546	−	0.0797141i
$704$			3.44949i			0.130008i
$705$		0			0
$706$	20.0227	+	11.5601i	0.753564	+	0.435071i
$707$	19.7080	−	73.5514i	0.741197	−	2.76619i
$708$	−2.19615	−	8.19615i	−0.0825365	−	0.308030i
$709$	−2.33562	+	1.34847i	−0.0877159	+	0.0506428i	−0.543216	−	0.839593i	$-0.682794\pi$
$709$	−2.33562	+	1.34847i	−0.0877159	+	0.0506428i	0.455500	+	0.890236i	$0.349460\pi$
$710$		0			0
$711$		−	35.8481i		−	1.34441i
$712$	−0.851289	+	3.17705i	−0.0319034	+	0.119065i
$713$	−10.3645	+	38.6809i	−0.388154	+	1.44861i
$714$		−	31.5959i		−	1.18245i
$715$		0			0
$716$	−5.17423	+	2.98735i	−0.193370	+	0.111642i
$717$	3.67576	+	13.7181i	0.137274	+	0.512313i
$718$	1.08757	−	4.05886i	0.0405877	−	0.151475i
$719$	1.51775	+	0.876276i	0.0566027	+	0.0326796i	0.528034	−	0.849223i	$-0.322929\pi$
$719$	1.51775	+	0.876276i	0.0566027	+	0.0326796i	−0.471432	+	0.881903i	$0.656263\pi$
$720$		0			0
$721$			36.0231i			1.34157i
$722$	6.02082	−	18.0208i	0.224072	−	0.670665i
$723$	11.3939	−	11.3939i	0.423743	−	0.423743i
$724$	−6.53893	+	11.3258i	−0.243018	+	0.420919i
$725$		0			0
$726$	−1.10102	−	1.90702i	−0.0408627	−	0.0707763i
$727$	6.96812	−	1.86710i	0.258433	−	0.0692470i	−0.127276	−	0.991867i	$-0.540623\pi$
$727$	6.96812	−	1.86710i	0.258433	−	0.0692470i	0.385709	+	0.922620i	$0.373957\pi$
$728$	−21.5804	−	5.78245i	−0.799823	−	0.214312i
$729$			27.0000i			1.00000i
$730$		0			0
$731$	5.10102	+	8.83523i	0.188668	+	0.326783i
$732$	18.9282	+	5.07180i	0.699607	+	0.187459i
$733$	10.0227	−	10.0227i	0.370197	−	0.370197i	−0.497352	−	0.867549i	$-0.665694\pi$
$733$	10.0227	−	10.0227i	0.370197	−	0.370197i	0.867549	+	0.497352i	$0.165694\pi$
$734$	26.4415			0.975972
$735$		0			0
$736$	4.50000	+	2.59808i	0.165872	+	0.0957664i
$737$	−31.8218	−	8.52663i	−1.17217	−	0.314083i
$738$	−1.34486	−	5.01910i	−0.0495051	−	0.184756i
$739$	−25.6790	−	14.8258i	−0.944617	−	0.545375i	−0.0532120	−	0.998583i	$-0.516946\pi$
$739$	−25.6790	−	14.8258i	−0.944617	−	0.545375i	−0.891404	+	0.453209i	$0.850279\pi$
$740$		0			0
$741$	50.0908	+	15.0635i	1.84013	+	0.553373i
$742$	−33.3712	−	33.3712i	−1.22509	−	1.22509i
$743$	18.6355	−	4.99336i	0.683669	−	0.183189i	0.0997647	−	0.995011i	$-0.468191\pi$
$743$	18.6355	−	4.99336i	0.683669	−	0.183189i	0.583904	+	0.811822i	$0.301524\pi$
$744$	−9.43879	+	16.3485i	−0.346043	+	0.599364i
$745$		0			0
$746$	8.97219	−	15.5403i	0.328495	−	0.568971i
$747$	2.57880	−	9.62421i	0.0943533	−	0.352131i
$748$	−6.89898	+	6.89898i	−0.252252	+	0.252252i
$749$	−55.8542			−2.04087
$750$		0			0
$751$	−15.9773	+	9.22450i	−0.583020	+	0.336607i	−0.762333	−	0.647185i	$-0.775946\pi$
$751$	−15.9773	+	9.22450i	−0.583020	+	0.336607i	0.179313	+	0.983792i	$0.442613\pi$
$752$	−4.89898	−	4.89898i	−0.178647	−	0.178647i
$753$	15.4135	+	15.4135i	0.561699	+	0.561699i
$754$	−1.90702	−	3.30306i	−0.0694497	−	0.120290i
$755$		0			0
$756$		0			0
$757$	−36.1617	+	9.68950i	−1.31432	+	0.352171i	−0.846847	−	0.531837i	$-0.821502\pi$
$757$	−36.1617	+	9.68950i	−1.31432	+	0.352171i	−0.467472	+	0.884008i	$0.654835\pi$
$758$	−5.69188	−	21.2424i	−0.206738	−	0.771558i
$759$	−43.9048			−1.59364
$760$		0			0
$761$	10.7980			0.391426			0.195713	−	0.980661i	$-0.437298\pi$
$761$	10.7980			0.391426			0.195713	+	0.980661i	$0.437298\pi$
$762$	2.59994	+	9.70312i	0.0941860	+	0.351507i
$763$		0			0
$764$	−7.14250	+	4.12372i	−0.258407	+	0.149191i
$765$		0			0
$766$	−4.89898	−	8.48528i	−0.177007	−	0.306586i
$767$	−12.0000	−	12.0000i	−0.433295	−	0.433295i
$768$	1.73205	+	1.73205i	0.0625000	+	0.0625000i
$769$	−3.81405	+	2.20204i	−0.137538	+	0.0794076i	−0.567190	−	0.823587i	$-0.691970\pi$
$769$	−3.81405	+	2.20204i	−0.137538	+	0.0794076i	0.429652	+	0.902995i	$0.358636\pi$
$770$		0			0
$771$	35.3939			1.27468
$772$	−0.953512	+	0.953512i	−0.0343176	+	0.0343176i
$773$	5.78421	−	21.5870i	0.208044	−	0.776429i	−0.780457	−	0.625210i	$-0.785013\pi$
$773$	5.78421	−	21.5870i	0.208044	−	0.776429i	0.988500	−	0.151219i	$-0.0483200\pi$
$774$	−5.41045	+	9.37117i	−0.194475	+	0.336840i
$775$		0			0
$776$	4.77526	−	8.27098i	0.171422	−	0.296911i
$777$	−5.94012	+	1.59165i	−0.213101	+	0.0571001i
$778$	−4.87832	−	4.87832i	−0.174896	−	0.174896i
$779$	−5.49794	+	5.17423i	−0.196984	+	0.185386i
$780$		0			0
$781$	−10.3485	−	5.97469i	−0.370297	−	0.213791i
$782$	3.80385	+	14.1962i	0.136025	+	0.507653i
$783$		0			0
$784$	11.9494	+	6.89898i	0.426764	+	0.246392i
$785$		0			0
$786$	−42.2474			−1.50692
$787$	7.88171	−	7.88171i	0.280953	−	0.280953i	−0.552536	−	0.833489i	$-0.686340\pi$
$787$	7.88171	−	7.88171i	0.280953	−	0.280953i	0.833489	+	0.552536i	$0.186340\pi$
$788$	17.3133	+	4.63909i	0.616762	+	0.165261i
$789$	−35.2839	−	61.1135i	−1.25614	−	2.17570i
$790$		0			0
$791$		−	28.4914i		−	1.01304i
$792$	−9.99585	−	2.67838i	−0.355187	−	0.0951721i
$793$	37.8564	−	10.1436i	1.34432	−	0.360210i
$794$	5.81577	+	10.0732i	0.206394	+	0.357485i
$795$		0			0
$796$	4.89898	−	8.48528i	0.173640	−	0.300753i
$797$	−20.0454	+	20.0454i	−0.710044	+	0.710044i	−0.966544	−	0.256500i	$-0.917431\pi$
$797$	−20.0454	+	20.0454i	−0.710044	+	0.710044i	0.256500	+	0.966544i	$0.417431\pi$
$798$	−41.4115	−	25.6136i	−1.46595	−	0.906710i
$799$		−	19.5959i		−	0.693254i
$800$		0			0
$801$	−8.54541	−	4.93369i	−0.301937	−	0.174323i
$802$	4.48288	−	16.7303i	0.158296	−	0.590768i
$803$	1.95768	+	7.30614i	0.0690849	+	0.257828i
$804$	−20.2597	+	11.6969i	−0.714504	+	0.412519i
$805$		0			0
$806$			37.7552i			1.32987i
$807$	−4.39230	+	16.3923i	−0.154616	+	0.577036i
$808$	−4.32149	+	16.1280i	−0.152029	+	0.567381i
$809$		−	37.7980i		−	1.32891i	−0.747330	−	0.664453i	$-0.768665\pi$
$809$		−	37.7980i		−	1.32891i	0.747330	−	0.664453i	$-0.231335\pi$
$810$		0			0
$811$	−15.5227	+	8.96204i	−0.545076	+	0.314700i	−0.747134	−	0.664674i	$-0.768570\pi$
$811$	−15.5227	+	8.96204i	−0.545076	+	0.314700i	0.202058	+	0.979374i	$0.435237\pi$
$812$	0.918940	+	3.42953i	0.0322485	+	0.120353i
$813$	20.7290	−	77.3618i	0.726999	−	2.71320i
$814$	1.64456	+	0.949490i	0.0576420	+	0.0332796i
$815$		0			0
$816$			6.92820i			0.242536i
$817$	15.7152	+	0.476662i	0.549804	+	0.0166763i
$818$	−11.0227	+	11.0227i	−0.385400	+	0.385400i
$819$	33.5125	−	58.0454i	1.17102	−	2.02827i
$820$		0			0
$821$	−23.2474	−	40.2658i	−0.811342	−	1.40528i	−0.911925	−	0.410356i	$-0.865404\pi$
$821$	−23.2474	−	40.2658i	−0.811342	−	1.40528i	0.100584	−	0.994929i	$-0.467929\pi$
$822$	6.69213	−	1.79315i	0.233415	−	0.0625433i
$823$	15.3333	+	4.10854i	0.534485	+	0.143215i	0.515958	−	0.856614i	$-0.327436\pi$
$823$	15.3333	+	4.10854i	0.534485	+	0.143215i	0.0185263	+	0.999828i	$0.494103\pi$
$824$		−	7.89898i		−	0.275174i
$825$		0			0
$826$	7.89898	+	13.6814i	0.274841	+	0.476038i
$827$	−46.0180	−	12.3305i	−1.60020	−	0.428773i	−0.655099	−	0.755543i	$-0.727373\pi$
$827$	−46.0180	−	12.3305i	−1.60020	−	0.428773i	−0.945104	+	0.326771i	$0.894040\pi$
$828$	−11.0227	+	11.0227i	−0.383065	+	0.383065i
$829$	−41.5692			−1.44376			−0.721879	−	0.692019i	$-0.756721\pi$
$829$	−41.5692			−1.44376			−0.721879	+	0.692019i	$0.756721\pi$
$830$		0			0
$831$	−17.3939	−	10.0424i	−0.603387	−	0.348366i
$832$	4.73205	+	1.26795i	0.164054	+	0.0439582i
$833$	10.1008	+	37.6967i	0.349972	+	1.30611i
$834$	15.0635	+	8.69694i	0.521608	+	0.301150i
$835$		0			0
$836$	3.44949	+	14.6349i	0.119303	+	0.506160i
$837$		0			0
$838$	−6.13215	+	1.64310i	−0.211832	+	0.0567601i
$839$	20.2204	−	35.0227i	0.698085	−	1.20912i	−0.271045	−	0.962567i	$-0.587369\pi$
$839$	20.2204	−	35.0227i	0.698085	−	1.20912i	0.969130	−	0.246551i	$-0.0792974\pi$
$840$		0			0
$841$	14.1969	−	24.5898i	0.489550	−	0.847925i
$842$	−4.68438	+	17.4823i	−0.161434	+	0.602481i
$843$	21.0000	−	21.0000i	0.723278	−	0.723278i
$844$	−26.7593			−0.921093
$845$		0			0
$846$	18.0000	−	10.3923i	0.618853	−	0.357295i
$847$	2.89898	+	2.89898i	0.0996101	+	0.0996101i
$848$	7.31747	+	7.31747i	0.251283	+	0.251283i
$849$	−7.70674	−	13.3485i	−0.264495	−	0.458118i
$850$		0			0
$851$	2.47730	−	1.43027i	0.0849206	−	0.0490289i
$852$	−8.19615	+	2.19615i	−0.280796	+	0.0752389i
$853$	−13.6871	−	51.0810i	−0.468638	−	1.74898i	−0.644539	−	0.764572i	$-0.722951\pi$
$853$	−13.6871	−	51.0810i	−0.468638	−	1.74898i	0.175901	−	0.984408i	$-0.443716\pi$
$854$	−36.4838			−1.24845
$855$		0			0
$856$	12.2474			0.418609
$857$	−2.40781	−	8.98607i	−0.0822492	−	0.306958i	0.912530	−	0.409010i	$-0.134126\pi$
$857$	−2.40781	−	8.98607i	−0.0822492	−	0.306958i	−0.994779	+	0.102052i	$0.967459\pi$
$858$	−39.9834	+	10.7135i	−1.36501	+	0.365754i
$859$	21.0864	−	12.1742i	0.719458	−	0.415380i	−0.0950949	−	0.995468i	$-0.530315\pi$
$859$	21.0864	−	12.1742i	0.719458	−	0.415380i	0.814553	+	0.580089i	$0.196982\pi$
$860$		0			0
$861$	9.67423	+	16.7563i	0.329697	+	0.571052i
$862$	−1.65153	−	1.65153i	−0.0562514	−	0.0562514i
$863$	7.92104	+	7.92104i	0.269635	+	0.269635i	0.828953	−	0.559318i	$-0.188937\pi$
$863$	7.92104	+	7.92104i	0.269635	+	0.269635i	−0.559318	+	0.828953i	$0.688937\pi$
$864$		0			0
$865$		0			0
$866$	−4.65153			−0.158065
$867$	15.5885	−	15.5885i	0.529412	−	0.529412i
$868$	9.09656	−	33.9488i	0.308758	−	1.15230i
$869$	20.6096	−	35.6969i	0.699134	−	1.21094i
$870$		0			0
$871$	−23.3939	+	40.5194i	−0.792671	+	1.37295i
$872$		0			0
$873$	20.2597	+	20.2597i	0.685687	+	0.685687i
$874$	21.6900	+	6.52270i	0.733674	+	0.220634i
$875$		0			0
$876$	4.65153	+	2.68556i	0.157161	+	0.0907367i
$877$	−9.30309	−	34.7196i	−0.314143	−	1.17240i	−0.924785	−	0.380491i	$-0.875755\pi$
$877$	−9.30309	−	34.7196i	−0.314143	−	1.17240i	0.610642	−	0.791907i	$-0.290912\pi$
$878$	30.5286	+	8.18011i	1.03029	+	0.276065i
$879$	5.83904	+	3.37117i	0.196946	+	0.113707i
$880$		0			0
$881$	−23.2929			−0.784756			−0.392378	−	0.919804i	$-0.628348\pi$
$881$	−23.2929			−0.784756			−0.392378	+	0.919804i	$0.628348\pi$
$882$	−29.2699	+	29.2699i	−0.985568	+	0.985568i
$883$	−32.6466	−	8.74763i	−1.09865	−	0.294381i	−0.336433	−	0.941707i	$-0.609221\pi$
$883$	−32.6466	−	8.74763i	−1.09865	−	0.294381i	−0.762213	+	0.647326i	$0.775887\pi$
$884$	6.92820	+	12.0000i	0.233021	+	0.403604i
$885$		0			0
$886$		−	30.8270i		−	1.03565i
$887$	−52.6380	−	14.1043i	−1.76741	−	0.473577i	−0.779214	−	0.626758i	$-0.784381\pi$
$887$	−52.6380	−	14.1043i	−1.76741	−	0.473577i	−0.988198	+	0.153181i	$0.951048\pi$
$888$	1.30252	−	0.349010i	0.0437098	−	0.0117120i
$889$	−9.35131	−	16.1969i	−0.313633	−	0.543228i
$890$		0			0
$891$	−15.5227	+	26.8861i	−0.520030	+	0.900719i
$892$	12.5136	−	12.5136i	0.418987	−	0.418987i
$893$	−25.6836	−	15.8856i	−0.859469	−	0.531592i
$894$			3.79796i			0.127023i
$895$		0			0
$896$	−3.94949	−	2.28024i	−0.131943	−	0.0761774i
$897$	−16.1384	+	60.2292i	−0.538844	+	2.01099i
$898$	−2.24144	−	8.36516i	−0.0747978	−	0.279149i
$899$	5.19615	−	3.00000i	0.173301	−	0.100056i
$900$		0			0
$901$			29.2699i			0.975121i
$902$	1.54636	−	5.77111i	0.0514883	−	0.192157i
$903$	10.4286	−	38.9199i	0.347041	−	1.29517i
$904$			6.24745i			0.207787i
$905$		0			0
$906$	18.0000	−	10.3923i	0.598010	−	0.345261i
$907$	14.1684	+	52.8770i	0.470453	+	1.75575i	0.638147	+	0.769914i	$0.279701\pi$
$907$	14.1684	+	52.8770i	0.470453	+	1.75575i	−0.167694	+	0.985839i	$0.553632\pi$
$908$	−5.29272	+	19.7527i	−0.175645	+	0.655516i
$909$	−43.3799	−	25.0454i	−1.43882	−	0.830704i
$910$		0			0
$911$		−	22.6916i		−	0.751807i	−0.926659	−	0.375904i	$-0.877332\pi$
$911$		−	22.6916i		−	0.751807i	0.926659	−	0.375904i	$-0.122668\pi$
$912$	9.08052	+	5.61642i	0.300686	+	0.185978i
$913$	8.10102	−	8.10102i	0.268105	−	0.268105i
$914$	3.71051	−	6.42679i	0.122733	−	0.212579i
$915$		0			0
$916$	−10.2247	−	17.7098i	−0.337835	−	0.585148i
$917$	75.9765	−	20.3578i	2.50896	−	0.672275i
$918$		0			0
$919$		−	54.0908i		−	1.78429i	−0.451748	−	0.892146i	$-0.649199\pi$
$919$		−	54.0908i		−	1.78429i	0.451748	−	0.892146i	$-0.350801\pi$
$920$		0			0
$921$	−1.65153	−	2.86054i	−0.0544198	−	0.0942578i
$922$	34.5782	+	9.26519i	1.13877	+	0.305133i
$923$	−12.0000	+	12.0000i	−0.394985	+	0.394985i
$924$	38.5337			1.26767
$925$		0			0
$926$	10.7474	+	6.20504i	0.353183	+	0.203910i
$927$	22.8895	+	6.13322i	0.751789	+	0.201441i
$928$	−0.201501	−	0.752011i	−0.00661459	−	0.0246860i
$929$	9.00136	+	5.19694i	0.295325	+	0.170506i	0.640341	−	0.768091i	$-0.278793\pi$
$929$	9.00136	+	5.19694i	0.295325	+	0.170506i	−0.345016	+	0.938597i	$0.612126\pi$
$930$		0			0
$931$	57.5959	+	17.3205i	1.88763	+	0.567657i
$932$	2.44949	+	2.44949i	0.0802357	+	0.0802357i
$933$	−14.6742	+	3.93194i	−0.480411	+	0.128726i
$934$	13.1172	−	22.7196i	0.429208	−	0.743409i
$935$		0			0
$936$	−7.34847	+	12.7279i	−0.240192	+	0.416025i
$937$	11.5483	−	43.0988i	0.377266	−	1.40798i	−0.472739	−	0.881202i	$-0.656735\pi$
$937$	11.5483	−	43.0988i	0.377266	−	1.40798i	0.850005	−	0.526774i	$-0.176599\pi$
$938$	30.7980	−	30.7980i	1.00559	−	1.00559i
$939$	79.8316			2.60521
$940$		0			0
$941$	45.3712	−	26.1951i	1.47906	−	0.853935i	0.479339	−	0.877630i	$-0.340877\pi$
$941$	45.3712	−	26.1951i	1.47906	−	0.853935i	0.999719	+	0.0236955i	$0.00754320\pi$
$942$	−6.55051	−	6.55051i	−0.213427	−	0.213427i
$943$	−6.36396	−	6.36396i	−0.207239	−	0.207239i
$944$	−1.73205	−	3.00000i	−0.0563735	−	0.0976417i
$945$		0			0
$946$	−10.7753	+	6.22110i	−0.350334	+	0.202265i
$947$	10.9282	−	2.92820i	0.355119	−	0.0951538i	−0.0768492	−	0.997043i	$-0.524486\pi$
$947$	10.9282	−	2.92820i	0.355119	−	0.0951538i	0.431968	+	0.901889i	$0.357819\pi$
$948$	−7.57561	−	28.2725i	−0.246044	−	0.918250i
$949$	10.7423			0.348708
$950$		0			0
$951$	22.6515			0.734526
$952$	−3.33850	−	12.4595i	−0.108201	−	0.403813i
$953$	30.5193	−	8.17763i	0.988618	−	0.264899i	0.271948	−	0.962312i	$-0.412332\pi$
$953$	30.5193	−	8.17763i	0.988618	−	0.264899i	0.716670	+	0.697413i	$0.245666\pi$
$954$	−26.8861	+	15.5227i	−0.870470	+	0.502566i
$955$		0			0
$956$	2.89898	+	5.02118i	0.0937597	+	0.162397i
$957$	4.65153	+	4.65153i	0.150363	+	0.150363i
$958$	−22.1988	−	22.1988i	−0.717211	−	0.717211i
$959$	−11.1708	+	6.44949i	−0.360725	+	0.208265i
$960$		0			0
$961$	−28.3939			−0.915932
$962$	1.90702	−	1.90702i	0.0614849	−	0.0614849i
$963$	−9.50962	+	35.4904i	−0.306443	+	1.14366i
$964$	3.28913	−	5.69694i	0.105936	−	0.183486i
$965$		0			0
$966$	29.0227	−	50.2688i	0.933790	−	1.61737i
$967$	−2.73205	+	0.732051i	−0.0878568	+	0.0235412i	−0.302480	−	0.953156i	$-0.597814\pi$
$967$	−2.73205	+	0.732051i	−0.0878568	+	0.0235412i	0.214623	+	0.976697i	$0.431148\pi$
$968$	−0.635674	−	0.635674i	−0.0204314	−	0.0204314i
$969$	6.92820	+	29.3939i	0.222566	+	0.944267i
$970$		0			0
$971$	−28.0454	−	16.1920i	−0.900020	−	0.519627i	−0.0228133	−	0.999740i	$-0.507262\pi$
$971$	−28.0454	−	16.1920i	−0.900020	−	0.519627i	−0.877207	+	0.480113i	$0.840596\pi$
$972$	5.70577	+	21.2942i	0.183013	+	0.683013i
$973$	−31.2806	−	8.38161i	−1.00281	−	0.268702i
$974$	−37.0641	−	21.3990i	−1.18761	−	0.685668i
$975$		0			0
$976$	8.00000			0.256074
$977$	8.31031	−	8.31031i	0.265870	−	0.265870i	−0.561563	−	0.827434i	$-0.689800\pi$
$977$	8.31031	−	8.31031i	0.265870	−	0.265870i	0.827434	+	0.561563i	$0.189800\pi$
$978$	17.8963	+	4.79531i	0.572261	+	0.153337i
$979$	−5.67291	−	9.82577i	−0.181307	−	0.314033i
$980$		0			0
$981$		0			0
$982$	−5.45896	−	1.46272i	−0.174202	−	0.0466774i
$983$	−9.17137	+	2.45746i	−0.292521	+	0.0783808i	−0.402095	−	0.915598i	$-0.631718\pi$
$983$	−9.17137	+	2.45746i	−0.292521	+	0.0783808i	0.109574	+	0.993979i	$0.465051\pi$
$984$	−2.12132	−	3.67423i	−0.0676252	−	0.117130i
$985$		0			0
$986$	1.10102	−	1.90702i	0.0350636	−	0.0607320i
$987$	−54.7257	+	54.7257i	−1.74194	+	1.74194i
$988$	21.3443	+	0.647402i	0.679054	+	0.0205966i
$989$			18.7423i			0.595972i
$990$		0			0
$991$	−18.9773	−	10.9565i	−0.602834	−	0.348046i	0.167322	−	0.985902i	$-0.446488\pi$
$991$	−18.9773	−	10.9565i	−0.602834	−	0.348046i	−0.770156	+	0.637856i	$0.779821\pi$
$992$	−1.99465	+	7.44414i	−0.0633303	+	0.236352i
$993$	13.5596	+	50.6050i	0.430300	+	1.60590i
$994$	13.6814	−	7.89898i	0.433949	−	0.250540i
$995$		0			0
$996$		−	8.13534i		−	0.257778i
$997$	1.06941	−	3.99109i	0.0338686	−	0.126399i	−0.946922	−	0.321464i	$-0.895825\pi$
$997$	1.06941	−	3.99109i	0.0338686	−	0.126399i	0.980790	+	0.195065i	$0.0624917\pi$
$998$	−0.840502	+	3.13679i	−0.0266056	+	0.0992935i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.a.407.2		8
5.2	odd	4		190.2.m.a.103.1	yes	8
5.3	odd	4	inner	950.2.q.a.293.2		8
5.4	even	2		190.2.m.a.27.1	✓	8
19.12	odd	6	inner	950.2.q.a.107.2		8
95.12	even	12		190.2.m.a.183.1	yes	8
95.69	odd	6		190.2.m.a.107.1	yes	8
95.88	even	12	inner	950.2.q.a.943.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.a.27.1	✓	8	5.4	even	2
190.2.m.a.103.1	yes	8	5.2	odd	4
190.2.m.a.107.1	yes	8	95.69	odd	6
190.2.m.a.183.1	yes	8	95.12	even	12
950.2.q.a.107.2		8	19.12	odd	6	inner
950.2.q.a.293.2		8	5.3	odd	4	inner
950.2.q.a.407.2		8	1.1	even	1	trivial
950.2.q.a.943.2		8	95.88	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.22474 - 2.12132i) q^{6} +(3.22474 + 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.22474 - 2.12132i) q^{6} +(3.22474 + 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +3.44949 q^{11} +(1.73205 - 1.73205i) q^{12} +(1.26795 - 4.73205i) q^{13} +(-2.28024 + 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.73205 - 0.732051i) q^{17} +(2.12132 + 2.12132i) q^{18} +(1.25529 - 4.17423i) q^{19} +(-9.67423 - 5.58542i) q^{21} +(0.892794 + 3.33195i) q^{22} +(5.01910 + 1.34486i) q^{23} +(2.12132 + 1.22474i) q^{24} +4.89898 q^{26} +(-4.40508 - 1.18034i) q^{28} +(-0.389270 - 0.674235i) q^{29} +7.70674i q^{31} +(0.965926 + 0.258819i) q^{32} +(-8.16158 + 2.18689i) q^{33} +(1.41421 + 2.44949i) q^{34} +(-1.50000 + 2.59808i) q^{36} +(0.389270 - 0.389270i) q^{37} +(4.35690 + 0.132150i) q^{38} +12.0000i q^{39} +(-1.50000 - 0.866025i) q^{41} +(2.89123 - 10.7902i) q^{42} +(0.933552 + 3.48406i) q^{43} +(-2.98735 + 1.72474i) q^{44} +5.19615i q^{46} +(1.79315 - 6.69213i) q^{47} +(-0.633975 + 2.36603i) q^{48} +13.7980i q^{49} +(-6.00000 + 3.46410i) q^{51} +(1.26795 + 4.73205i) q^{52} +(-2.67838 + 9.99585i) q^{53} -4.56048i q^{56} +(-0.323701 + 10.6722i) q^{57} +(0.550510 - 0.550510i) q^{58} +(1.73205 - 3.00000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-7.44414 + 1.99465i) q^{62} +(13.2153 + 3.54102i) q^{63} +1.00000i q^{64} +(-4.22474 - 7.31747i) q^{66} +(-9.22508 - 2.47185i) q^{67} +(-2.00000 + 2.00000i) q^{68} -12.7279 q^{69} +(-3.00000 - 1.73205i) q^{71} +(-2.89778 - 0.776457i) q^{72} +(0.567526 + 2.11804i) q^{73} +(0.476756 + 0.275255i) q^{74} +(1.00000 + 4.24264i) q^{76} +(11.1237 + 11.1237i) q^{77} +(-11.5911 + 3.10583i) q^{78} +(5.97469 - 10.3485i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(0.448288 - 1.67303i) q^{82} +(2.34847 - 2.34847i) q^{83} +11.1708 q^{84} +(-3.12372 + 1.80348i) q^{86} +(1.34847 + 1.34847i) q^{87} +(-2.43916 - 2.43916i) q^{88} +(-1.64456 - 2.84847i) q^{89} +(19.3485 - 11.1708i) q^{91} +(-5.01910 + 1.34486i) q^{92} +(-4.88588 - 18.2343i) q^{93} +6.92820 q^{94} -2.44949 q^{96} +(2.47185 + 9.22508i) q^{97} +(-13.3278 + 3.57117i) q^{98} +(8.96204 - 5.17423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 16 q^{7}+O(q^{10}) \) 8 * q - 12 * q^3 + 16 * q^7	\( 8 q - 12 q^{3} + 16 q^{7} + 8 q^{11} + 24 q^{13} + 4 q^{16} + 8 q^{17} - 48 q^{21} + 12 q^{22} - 8 q^{28} - 12 q^{33} - 12 q^{36} + 12 q^{38} - 12 q^{41} - 12 q^{42} - 20 q^{43} - 12 q^{48} - 48 q^{51} + 24 q^{52} - 36 q^{53} + 12 q^{57} + 24 q^{58} + 32 q^{61} - 12 q^{62} + 24 q^{63} - 24 q^{66} + 12 q^{67} - 16 q^{68} - 24 q^{71} - 16 q^{73} + 8 q^{76} + 40 q^{77} - 36 q^{81} - 40 q^{83} + 24 q^{86} - 48 q^{87} + 96 q^{91} + 24 q^{93} - 12 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 12 * q^3 + 16 * q^7 + 8 * q^11 + 24 * q^13 + 4 * q^16 + 8 * q^17 - 48 * q^21 + 12 * q^22 - 8 * q^28 - 12 * q^33 - 12 * q^36 + 12 * q^38 - 12 * q^41 - 12 * q^42 - 20 * q^43 - 12 * q^48 - 48 * q^51 + 24 * q^52 - 36 * q^53 + 12 * q^57 + 24 * q^58 + 32 * q^61 - 12 * q^62 + 24 * q^63 - 24 * q^66 + 12 * q^67 - 16 * q^68 - 24 * q^71 - 16 * q^73 + 8 * q^76 + 40 * q^77 - 36 * q^81 - 40 * q^83 + 24 * q^86 - 48 * q^87 + 96 * q^91 + 24 * q^93 - 12 * q^97 - 48 * q^98

Introduction

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