LMFDB - Embedded newform 1900.2.i.g.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(201,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.i (of order $3$, degree $2$, 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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + \cdots + 4096 $ x^20 + 20x^18 + 261x^16 + 1994x^14 + 11074x^12 + 39211x^10 + 99376x^8 + 134299x^6 + 124617x^4 + 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.3
Root			$1.00667 + 1.74361i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.g.501.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00667 + 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 - 0.912416i) q^{9} +O(q^{10})$	\(q+(-1.00667 + 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 - 0.912416i) q^{9} +5.25594 q^{11} +(-1.21773 - 2.10918i) q^{13} +(0.679914 - 1.17765i) q^{17} +(-2.89815 - 3.25587i) q^{19} +(1.35300 - 2.34346i) q^{21} +(-4.07329 - 7.05514i) q^{23} -3.91884 q^{27} +(1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(-5.29102 + 9.16431i) q^{33} -5.57175 q^{37} +4.90344 q^{39} +(2.70353 - 4.68265i) q^{41} +(6.36221 - 11.0197i) q^{43} +(-1.63266 - 2.82785i) q^{47} -5.19359 q^{49} +(1.36890 + 2.37101i) q^{51} +(5.88276 + 10.1892i) q^{53} +(8.59447 - 1.77564i) q^{57} +(-0.0175979 + 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(0.708011 + 1.22631i) q^{63} +(-0.383377 - 0.664028i) q^{67} +16.4019 q^{69} +(5.68450 - 9.84583i) q^{71} +(1.07635 - 1.86429i) q^{73} -7.06413 q^{77} +(6.48576 - 11.2337i) q^{79} +(5.52535 - 9.57019i) q^{81} +4.20304 q^{83} -4.17153 q^{87} +(3.65426 + 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(0.516632 - 0.894833i) q^{93} +(0.416683 - 0.721716i) q^{97} +(-2.76875 - 4.79561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^9	$ 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) $ 20 * q - 10 * q^9 - 14 * q^19 - 8 * q^21 + 16 * q^29 + 8 * q^31 + 8 * q^39 + 26 * q^41 + 44 * q^49 + 26 * q^51 - 4 * q^59 + 2 * q^61 - 48 * q^69 - 2 * q^71 + 16 * q^79 + 26 * q^81 + 40 * q^89 - 4 * q^91 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−1.00667	+	1.74361i	−0.581203	+	1.00667i	0.414134	+	0.910216i	$0.364085\pi$
$3$	−1.00667	+	1.74361i	−0.581203	+	1.00667i	−0.995337	+	0.0964577i	$0.969249\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.34403			−0.507994			−0.253997	−	0.967205i	$-0.581745\pi$
$7$	−1.34403			−0.507994			−0.253997	+	0.967205i	$0.581745\pi$
$8$		0			0
$9$	−0.526784	−	0.912416i	−0.175595	−	0.304139i
$10$		0			0
$11$	5.25594			1.58473			0.792363	−	0.610050i	$-0.208851\pi$
$11$	5.25594			1.58473			0.792363	+	0.610050i	$0.208851\pi$
$12$		0			0
$13$	−1.21773	−	2.10918i	−0.337738	−	0.584980i	0.646269	−	0.763110i	$-0.276329\pi$
$13$	−1.21773	−	2.10918i	−0.337738	−	0.584980i	−0.984007	+	0.178130i	$0.942995\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.679914	−	1.17765i	0.164903	−	0.285621i	−0.771718	−	0.635965i	$-0.780602\pi$
$17$	0.679914	−	1.17765i	0.164903	−	0.285621i	0.936621	+	0.350344i	$0.113935\pi$
$18$		0			0
$19$	−2.89815	−	3.25587i	−0.664882	−	0.746949i
$19$	−2.89815	−	3.25587i	−0.664882	−	0.746949i
$20$		0			0
$21$	1.35300	−	2.34346i	0.295248	−	0.511384i
$22$		0			0
$23$	−4.07329	−	7.05514i	−0.849339	−	1.47110i	−0.881799	−	0.471625i	$-0.843668\pi$
$23$	−4.07329	−	7.05514i	−0.849339	−	1.47110i	0.0324603	−	0.999473i	$-0.489666\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.91884			−0.754182
$28$		0			0
$29$	1.03597	+	1.79435i	0.192375	+	0.333203i	0.946037	−	0.324059i	$-0.105048\pi$
$29$	1.03597	+	1.79435i	0.192375	+	0.333203i	−0.753662	+	0.657262i	$0.771714\pi$
$30$		0			0
$31$	−0.513207			−0.0921747			−0.0460873	−	0.998937i	$-0.514675\pi$
$31$	−0.513207			−0.0921747			−0.0460873	+	0.998937i	$0.514675\pi$
$32$		0			0
$33$	−5.29102	+	9.16431i	−0.921048	+	1.59530i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.57175			−0.915991			−0.457995	−	0.888955i	$-0.651432\pi$
$37$	−5.57175			−0.915991			−0.457995	+	0.888955i	$0.651432\pi$
$38$		0			0
$39$	4.90344			0.785179
$40$		0			0
$41$	2.70353	−	4.68265i	0.422220	−	0.731307i	−0.573936	−	0.818900i	$-0.694584\pi$
$41$	2.70353	−	4.68265i	0.422220	−	0.731307i	0.996156	+	0.0875933i	$0.0279176\pi$
$42$		0			0
$43$	6.36221	−	11.0197i	0.970228	−	1.68048i	0.275369	−	0.961339i	$-0.411200\pi$
$43$	6.36221	−	11.0197i	0.970228	−	1.68048i	0.694859	−	0.719146i	$-0.255467\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.63266	−	2.82785i	−0.238148	−	0.412485i	0.722035	−	0.691857i	$-0.243207\pi$
$47$	−1.63266	−	2.82785i	−0.238148	−	0.412485i	−0.960183	+	0.279372i	$0.909874\pi$
$48$		0			0
$49$	−5.19359			−0.741942
$50$		0			0
$51$	1.36890	+	2.37101i	0.191685	+	0.332008i
$52$		0			0
$53$	5.88276	+	10.1892i	0.808060	+	1.39960i	0.914206	+	0.405250i	$0.132815\pi$
$53$	5.88276	+	10.1892i	0.808060	+	1.39960i	−0.106146	+	0.994351i	$0.533851\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	8.59447	−	1.77564i	1.13837	−	0.235190i
$58$		0			0
$59$	−0.0175979	+	0.0304805i	−0.00229105	+	0.00396822i	−0.867169	−	0.498015i	$-0.834063\pi$
$59$	−0.0175979	+	0.0304805i	−0.00229105	+	0.00396822i	0.864878	+	0.501983i	$0.167396\pi$
$60$		0			0
$61$	0.518372	+	0.897846i	0.0663707	+	0.114957i	0.897301	−	0.441419i	$-0.145525\pi$
$61$	0.518372	+	0.897846i	0.0663707	+	0.114957i	−0.830930	+	0.556376i	$0.812191\pi$
$62$		0			0
$63$	0.708011	+	1.22631i	0.0892010	+	0.154501i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.383377	−	0.664028i	−0.0468369	−	0.0811239i	0.841657	−	0.540013i	$-0.181581\pi$
$67$	−0.383377	−	0.664028i	−0.0468369	−	0.0811239i	−0.888493	+	0.458889i	$0.848247\pi$
$68$		0			0
$69$	16.4019			1.97455
$70$		0			0
$71$	5.68450	−	9.84583i	0.674625	−	1.16849i	−0.301953	−	0.953323i	$-0.597638\pi$
$71$	5.68450	−	9.84583i	0.674625	−	1.16849i	0.976578	−	0.215163i	$-0.0690282\pi$
$72$		0			0
$73$	1.07635	−	1.86429i	0.125977	−	0.218199i	−0.796137	−	0.605116i	$-0.793127\pi$
$73$	1.07635	−	1.86429i	0.125977	−	0.218199i	0.922115	+	0.386917i	$0.126460\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.06413			−0.805032
$78$		0			0
$79$	6.48576	−	11.2337i	0.729705	−	1.26389i	−0.227302	−	0.973824i	$-0.572991\pi$
$79$	6.48576	−	11.2337i	0.729705	−	1.26389i	0.957008	−	0.290062i	$-0.0936761\pi$
$80$		0			0
$81$	5.52535	−	9.57019i	0.613928	−	1.06335i
$82$		0			0
$83$	4.20304			0.461343			0.230672	−	0.973032i	$-0.425908\pi$
$83$	4.20304			0.461343			0.230672	+	0.973032i	$0.425908\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.17153			−0.447235
$88$		0			0
$89$	3.65426	+	6.32937i	0.387351	+	0.670912i	0.992092	−	0.125510i	$-0.0400568\pi$
$89$	3.65426	+	6.32937i	0.387351	+	0.670912i	−0.604741	+	0.796422i	$0.706723\pi$
$90$		0			0
$91$	1.63667	+	2.83479i	0.171569	+	0.297166i
$92$		0			0
$93$	0.516632	−	0.894833i	0.0535722	−	0.0927898i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.416683	−	0.721716i	0.0423077	−	0.0732791i	−0.844096	−	0.536192i	$-0.819862\pi$
$97$	0.416683	−	0.721716i	0.0423077	−	0.0732791i	0.886404	+	0.462913i	$0.153196\pi$
$98$		0			0
$99$	−2.76875	−	4.79561i	−0.278269	−	0.481977i
$100$		0			0
$101$	−7.40992	−	12.8344i	−0.737315	−	1.27707i	−0.953700	−	0.300759i	$-0.902760\pi$
$101$	−7.40992	−	12.8344i	−0.737315	−	1.27707i	0.216385	−	0.976308i	$-0.430573\pi$
$102$		0			0
$103$	−9.40773			−0.926971			−0.463486	−	0.886104i	$-0.653401\pi$
$103$	−9.40773			−0.926971			−0.463486	+	0.886104i	$0.653401\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.8130			1.23868			0.619338	−	0.785124i	$-0.287401\pi$
$107$	12.8130			1.23868			0.619338	+	0.785124i	$0.287401\pi$
$108$		0			0
$109$	−0.996875	+	1.72664i	−0.0954833	+	0.165382i	−0.909810	−	0.415025i	$-0.863773\pi$
$109$	−0.996875	+	1.72664i	−0.0954833	+	0.165382i	0.814327	+	0.580406i	$0.197106\pi$
$110$		0			0
$111$	5.60894	−	9.71497i	0.532377	−	0.922104i
$112$		0			0
$113$	8.34647			0.785170			0.392585	−	0.919716i	$-0.371581\pi$
$113$	8.34647			0.785170			0.392585	+	0.919716i	$0.371581\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.28296	+	2.22216i	−0.118610	+	0.205439i
$118$		0			0
$119$	−0.913823	+	1.58279i	−0.0837700	+	0.145094i
$120$		0			0
$121$	16.6249			1.51136
$122$		0			0
$123$	5.44314	+	9.42780i	0.490791	+	0.850076i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	10.2907	+	17.8240i	0.913153	+	1.58163i	0.809583	+	0.587005i	$0.199693\pi$
$127$	10.2907	+	17.8240i	0.913153	+	1.58163i	0.103569	+	0.994622i	$0.466974\pi$
$128$		0			0
$129$	12.8093	+	22.1864i	1.12780	+	1.95341i
$130$		0			0
$131$	−5.36554	+	9.29339i	−0.468790	+	0.811967i	−0.999364	−	0.0356712i	$-0.988643\pi$
$131$	−5.36554	+	9.29339i	−0.468790	+	0.811967i	0.530574	+	0.847639i	$0.321976\pi$
$132$		0			0
$133$	3.89519	+	4.37598i	0.337756	+	0.379446i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.58931	+	14.8771i	0.733834	+	1.27104i	0.955233	+	0.295855i	$0.0956045\pi$
$137$	8.58931	+	14.8771i	0.733834	+	1.27104i	−0.221399	+	0.975183i	$0.571062\pi$
$138$		0			0
$139$	−3.66394	−	6.34613i	−0.310771	−	0.538272i	0.667758	−	0.744378i	$-0.267254\pi$
$139$	−3.66394	−	6.34613i	−0.310771	−	0.538272i	−0.978530	+	0.206106i	$0.933921\pi$
$140$		0			0
$141$	6.57423			0.553650
$142$		0			0
$143$	−6.40033	−	11.0857i	−0.535223	−	0.927033i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.22825	−	9.05560i	0.431219	−	0.746893i
$148$		0			0
$149$	6.12292	−	10.6052i	0.501609	−	0.868812i	−0.498389	−	0.866953i	$-0.666075\pi$
$149$	6.12292	−	10.6052i	0.501609	−	0.868812i	0.999998	−	0.00185904i	$-0.000591751\pi$
$150$		0			0
$151$	−11.5577			−0.940549			−0.470274	−	0.882520i	$-0.655845\pi$
$151$	−11.5577			−0.940549			−0.470274	+	0.882520i	$0.655845\pi$
$152$		0			0
$153$	−1.43267			−0.115825
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.06996	−	3.58528i	0.165201	−	0.286137i	−0.771526	−	0.636198i	$-0.780506\pi$
$157$	2.06996	−	3.58528i	0.165201	−	0.286137i	0.936727	+	0.350062i	$0.113839\pi$
$158$		0			0
$159$	−23.6881			−1.87859
$160$		0			0
$161$	5.47460	+	9.48229i	0.431459	+	0.747309i
$162$		0			0
$163$	−9.41672			−0.737575			−0.368787	−	0.929514i	$-0.620227\pi$
$163$	−9.41672			−0.737575			−0.368787	+	0.929514i	$0.620227\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.83551	−	11.8395i	−0.528948	−	0.916164i	−0.999430	−	0.0337550i	$-0.989253\pi$
$167$	−6.83551	−	11.8395i	−0.528948	−	0.916164i	0.470482	−	0.882409i	$-0.344080\pi$
$168$		0			0
$169$	3.53425	−	6.12151i	0.271866	−	0.470885i
$170$		0			0
$171$	−1.44401	+	4.35946i	−0.110426	+	0.333376i
$172$		0			0
$173$	5.88891	−	10.1999i	0.447726	−	0.775484i	−0.550512	−	0.834827i	$-0.685567\pi$
$173$	5.88891	−	10.1999i	0.447726	−	0.775484i	0.998238	+	0.0593437i	$0.0189008\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.0354307	−	0.0613678i	−0.00266314	−	0.00461269i
$178$		0			0
$179$	−16.5727			−1.23870			−0.619350	−	0.785115i	$-0.712604\pi$
$179$	−16.5727			−1.23870			−0.619350	+	0.785115i	$0.712604\pi$
$180$		0			0
$181$	7.19552	+	12.4630i	0.534839	+	0.926368i	0.999171	+	0.0407069i	$0.0129610\pi$
$181$	7.19552	+	12.4630i	0.534839	+	0.926368i	−0.464332	+	0.885661i	$0.653706\pi$
$182$		0			0
$183$	−2.08733			−0.154300
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.57359	−	6.18964i	0.261327	−	0.452631i
$188$		0			0
$189$	5.26703			0.383120
$190$		0			0
$191$	−5.97170			−0.432097			−0.216049	−	0.976383i	$-0.569317\pi$
$191$	−5.97170			−0.432097			−0.216049	+	0.976383i	$0.569317\pi$
$192$		0			0
$193$	−8.14331	+	14.1046i	−0.586168	+	1.01527i	0.408560	+	0.912731i	$0.366031\pi$
$193$	−8.14331	+	14.1046i	−0.586168	+	1.01527i	−0.994729	+	0.102542i	$0.967302\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.5233			0.820998			0.410499	−	0.911861i	$-0.365355\pi$
$197$	11.5233			0.820998			0.410499	+	0.911861i	$0.365355\pi$
$198$		0			0
$199$	−4.79943	−	8.31285i	−0.340222	−	0.589283i	0.644251	−	0.764814i	$-0.277169\pi$
$199$	−4.79943	−	8.31285i	−0.340222	−	0.589283i	−0.984474	+	0.175531i	$0.943836\pi$
$200$		0			0
$201$	1.54374			0.108887
$202$		0			0
$203$	−1.39237	−	2.41166i	−0.0977253	−	0.169265i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.29148	+	7.43307i	−0.298279	+	0.516634i
$208$		0			0
$209$	−15.2325	−	17.1127i	−1.05366	−	1.18371i
$210$		0			0
$211$	7.28207	−	12.6129i	0.501318	−	0.868308i	−0.498681	−	0.866786i	$-0.666182\pi$
$211$	7.28207	−	12.6129i	0.501318	−	0.868308i	0.999999	−	0.00152265i	$-0.000484675\pi$
$212$		0			0
$213$	11.4449	+	19.8231i	0.784189	+	1.35826i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.689764			0.0468242
$218$		0			0
$219$	2.16707	+	3.75347i	0.146437	+	0.253636i
$220$		0			0
$221$	−3.31182			−0.222777
$222$		0			0
$223$	3.78635	−	6.55816i	0.253553	−	0.439167i	−0.710949	−	0.703244i	$-0.751734\pi$
$223$	3.78635	−	6.55816i	0.253553	−	0.439167i	0.964501	+	0.264077i	$0.0850675\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.86640			0.455739			0.227869	−	0.973692i	$-0.426824\pi$
$227$	6.86640			0.455739			0.227869	+	0.973692i	$0.426824\pi$
$228$		0			0
$229$	22.1011			1.46048			0.730240	−	0.683191i	$-0.239408\pi$
$229$	22.1011			1.46048			0.730240	+	0.683191i	$0.239408\pi$
$230$		0			0
$231$	7.11127	−	12.3171i	0.467887	−	0.810404i
$232$		0			0
$233$	−1.48844	+	2.57806i	−0.0975111	+	0.168894i	−0.910654	−	0.413170i	$-0.864421\pi$
$233$	−1.48844	+	2.57806i	−0.0975111	+	0.168894i	0.813143	+	0.582064i	$0.197755\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	13.0581	+	22.6173i	0.848214	+	1.46915i
$238$		0			0
$239$	−9.71289			−0.628275			−0.314137	−	0.949378i	$-0.601715\pi$
$239$	−9.71289			−0.628275			−0.314137	+	0.949378i	$0.601715\pi$
$240$		0			0
$241$	9.34287	+	16.1823i	0.601827	+	1.04239i	0.992544	+	0.121884i	$0.0388937\pi$
$241$	9.34287	+	16.1823i	0.601827	+	1.04239i	−0.390717	+	0.920511i	$0.627773\pi$
$242$		0			0
$243$	5.24618	+	9.08665i	0.336543	+	0.582909i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.33803	+	10.0775i	−0.212394	+	0.641216i
$248$		0			0
$249$	−4.23109	+	7.32846i	−0.268134	+	0.464422i
$250$		0			0
$251$	2.10091	+	3.63888i	0.132608	+	0.229684i	0.924681	−	0.380742i	$-0.124332\pi$
$251$	2.10091	+	3.63888i	0.132608	+	0.229684i	−0.792073	+	0.610426i	$0.790998\pi$
$252$		0			0
$253$	−21.4090	−	37.0814i	−1.34597	−	2.33129i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.0842	−	24.3946i	−0.878548	−	1.52169i	−0.852934	−	0.522018i	$-0.825179\pi$
$257$	−14.0842	−	24.3946i	−0.878548	−	1.52169i	−0.0256140	−	0.999672i	$-0.508154\pi$
$258$		0			0
$259$	7.48859			0.465318
$260$		0			0
$261$	1.09146	−	1.89047i	0.0675599	−	0.117017i
$262$		0			0
$263$	−1.35425	+	2.34563i	−0.0835065	+	0.144637i	−0.904754	−	0.425935i	$-0.859945\pi$
$263$	−1.35425	+	2.34563i	−0.0835065	+	0.144637i	0.821247	+	0.570572i	$0.193279\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−14.7146			−0.900519
$268$		0			0
$269$	−5.64101	+	9.77052i	−0.343938	+	0.595719i	−0.985160	−	0.171637i	$-0.945094\pi$
$269$	−5.64101	+	9.77052i	−0.343938	+	0.595719i	0.641222	+	0.767356i	$0.278428\pi$
$270$		0			0
$271$	−3.16690	+	5.48523i	−0.192375	+	0.333204i	−0.946037	−	0.324059i	$-0.894952\pi$
$271$	−3.16690	+	5.48523i	−0.192375	+	0.333204i	0.753662	+	0.657263i	$0.228286\pi$
$272$		0			0
$273$	−6.59035			−0.398866
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.1435			−0.669549			−0.334774	−	0.942298i	$-0.608660\pi$
$277$	−11.1435			−0.669549			−0.334774	+	0.942298i	$0.608660\pi$
$278$		0			0
$279$	0.270349	+	0.468258i	0.0161854	+	0.0280339i
$280$		0			0
$281$	−12.9061	−	22.3541i	−0.769916	−	1.33353i	−0.937608	−	0.347694i	$-0.886965\pi$
$281$	−12.9061	−	22.3541i	−0.769916	−	1.33353i	0.167693	−	0.985839i	$-0.446368\pi$
$282$		0			0
$283$	14.4304	−	24.9942i	0.857799	−	1.48575i	−0.0162249	−	0.999868i	$-0.505165\pi$
$283$	14.4304	−	24.9942i	0.857799	−	1.48575i	0.874024	−	0.485883i	$-0.161502\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.63361	+	6.29360i	−0.214485	+	0.371500i
$288$		0			0
$289$	7.57543	+	13.1210i	0.445614	+	0.771826i
$290$		0			0
$291$	0.838927	+	1.45306i	0.0491788	+	0.0851801i
$292$		0			0
$293$	−22.7742			−1.33048			−0.665242	−	0.746628i	$-0.731672\pi$
$293$	−22.7742			−1.33048			−0.665242	+	0.746628i	$0.731672\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−20.5972			−1.19517
$298$		0			0
$299$	−9.92035	+	17.1825i	−0.573709	+	0.993692i
$300$		0			0
$301$	−8.55098	+	14.8107i	−0.492870	+	0.853676i
$302$		0			0
$303$	29.8375			1.71412
$304$		0			0
$305$		0			0
$306$		0			0
$307$	8.09880	−	14.0275i	0.462223	−	0.800593i	−0.536849	−	0.843679i	$-0.680385\pi$
$307$	8.09880	−	14.0275i	0.462223	−	0.800593i	0.999071	+	0.0430854i	$0.0137187\pi$
$308$		0			0
$309$	9.47052	−	16.4034i	0.538759	−	0.933158i
$310$		0			0
$311$	−28.3483			−1.60749			−0.803743	−	0.594977i	$-0.797161\pi$
$311$	−28.3483			−1.60749			−0.803743	+	0.594977i	$0.797161\pi$
$312$		0			0
$313$	1.54464	+	2.67539i	0.0873081	+	0.151222i	0.906372	−	0.422480i	$-0.138840\pi$
$313$	1.54464	+	2.67539i	0.0873081	+	0.151222i	−0.819064	+	0.573702i	$0.805507\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.0225	−	20.8236i	−0.675251	−	1.16957i	−0.976395	−	0.215991i	$-0.930702\pi$
$317$	−12.0225	−	20.8236i	−0.675251	−	1.16957i	0.301144	−	0.953579i	$-0.402632\pi$
$318$		0			0
$319$	5.44500	+	9.43101i	0.304861	+	0.528035i
$320$		0			0
$321$	−12.8985	+	22.3408i	−0.719923	+	1.24694i
$322$		0			0
$323$	−5.80476	+	1.19928i	−0.322986	+	0.0667298i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.00706	−	3.47632i	−0.110990	−	0.192241i
$328$		0			0
$329$	2.19434	+	3.80071i	0.120978	+	0.209540i
$330$		0			0
$331$	−20.7717			−1.14171			−0.570857	−	0.821049i	$-0.693389\pi$
$331$	−20.7717			−1.14171			−0.570857	+	0.821049i	$0.693389\pi$
$332$		0			0
$333$	2.93511	+	5.08376i	0.160843	+	0.278588i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.21324	+	2.10139i	−0.0660892	+	0.114470i	−0.897177	−	0.441672i	$-0.854386\pi$
$337$	−1.21324	+	2.10139i	−0.0660892	+	0.114470i	0.831087	+	0.556142i	$0.187719\pi$
$338$		0			0
$339$	−8.40217	+	14.5530i	−0.456343	+	0.790410i
$340$		0			0
$341$	−2.69739			−0.146072
$342$		0			0
$343$	16.3885			0.884896
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.43664	−	2.48834i	0.0771230	−	0.133581i	−0.824885	−	0.565301i	$-0.808760\pi$
$347$	1.43664	−	2.48834i	0.0771230	−	0.133581i	0.902008	+	0.431720i	$0.142093\pi$
$348$		0			0
$349$	−5.89385			−0.315490			−0.157745	−	0.987480i	$-0.550422\pi$
$349$	−5.89385			−0.315490			−0.157745	+	0.987480i	$0.550422\pi$
$350$		0			0
$351$	4.77211	+	8.26553i	0.254716	+	0.441181i
$352$		0			0
$353$	−12.0238			−0.639962			−0.319981	−	0.947424i	$-0.603676\pi$
$353$	−12.0238			−0.639962			−0.319981	+	0.947424i	$0.603676\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.83984	−	3.18670i	−0.0973748	−	0.168658i
$358$		0			0
$359$	2.26590	−	3.92466i	0.119590	−	0.207136i	−0.800015	−	0.599979i	$-0.795175\pi$
$359$	2.26590	−	3.92466i	0.119590	−	0.207136i	0.919605	+	0.392844i	$0.128509\pi$
$360$		0			0
$361$	−2.20143	+	18.8720i	−0.115865	+	0.993265i
$362$		0			0
$363$	−16.7359	+	28.9874i	−0.878406	+	1.52144i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−17.2710	−	29.9143i	−0.901539	−	1.56151i	−0.825496	−	0.564407i	$-0.809105\pi$
$367$	−17.2710	−	29.9143i	−0.901539	−	1.56151i	−0.0760429	−	0.997105i	$-0.524229\pi$
$368$		0			0
$369$	−5.69670			−0.296558
$370$		0			0
$371$	−7.90659	−	13.6946i	−0.410490	−	0.710989i
$372$		0			0
$373$	24.0801			1.24682			0.623411	−	0.781894i	$-0.285746\pi$
$373$	24.0801			1.24682			0.623411	+	0.781894i	$0.285746\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.52307	−	4.37008i	0.129945	−	0.225071i
$378$		0			0
$379$	30.1565			1.54904			0.774518	−	0.632552i	$-0.217992\pi$
$379$	30.1565			1.54904			0.774518	+	0.632552i	$0.217992\pi$
$380$		0			0
$381$	−41.4375			−2.12291
$382$		0			0
$383$	−19.4101	+	33.6192i	−0.991809	+	1.71786i	−0.385286	+	0.922797i	$0.625897\pi$
$383$	−19.4101	+	33.6192i	−0.991809	+	1.71786i	−0.606522	+	0.795066i	$0.707436\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−13.4060			−0.681467
$388$		0			0
$389$	−18.6935	−	32.3781i	−0.947799	−	1.64164i	−0.750048	−	0.661383i	$-0.769970\pi$
$389$	−18.6935	−	32.3781i	−0.947799	−	1.64164i	−0.197750	−	0.980252i	$-0.563364\pi$
$390$		0			0
$391$	−11.0779			−0.560236
$392$		0			0
$393$	−10.8027	−	18.7108i	−0.544924	−	0.943836i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.78211	+	13.4790i	−0.390573	+	0.676492i	−0.992525	−	0.122040i	$-0.961056\pi$
$397$	−7.78211	+	13.4790i	−0.390573	+	0.676492i	0.601952	+	0.798532i	$0.294390\pi$
$398$		0			0
$399$	−11.5512	+	2.38651i	−0.578283	+	0.119475i
$400$		0			0
$401$	−11.3113	+	19.5918i	−0.564860	+	0.978366i	0.432203	+	0.901777i	$0.357737\pi$
$401$	−11.3113	+	19.5918i	−0.564860	+	0.978366i	−0.997063	+	0.0765898i	$0.975597\pi$
$402$		0			0
$403$	0.624949	+	1.08244i	0.0311309	+	0.0539203i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−29.2848			−1.45159
$408$		0			0
$409$	18.1239	+	31.3915i	0.896169	+	1.55221i	0.832351	+	0.554249i	$0.186995\pi$
$409$	18.1239	+	31.3915i	0.896169	+	1.55221i	0.0638187	+	0.997962i	$0.479672\pi$
$410$		0			0
$411$	−34.5865			−1.70603
$412$		0			0
$413$	0.0236521	−	0.0409666i	0.00116384	−	0.00201583i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	14.7536			0.722486
$418$		0			0
$419$	−14.5598			−0.711293			−0.355647	−	0.934621i	$-0.615739\pi$
$419$	−14.5598			−0.711293			−0.355647	+	0.934621i	$0.615739\pi$
$420$		0			0
$421$	−0.784161	+	1.35821i	−0.0382177	+	0.0661950i	−0.884502	−	0.466537i	$-0.845501\pi$
$421$	−0.784161	+	1.35821i	−0.0382177	+	0.0661950i	0.846284	+	0.532732i	$0.178835\pi$
$422$		0			0
$423$	−1.72012	+	2.97934i	−0.0836351	+	0.144860i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.696705	−	1.20673i	−0.0337159	−	0.0583977i
$428$		0			0
$429$	25.7722			1.24429
$430$		0			0
$431$	12.7303	+	22.0495i	0.613197	+	1.06209i	0.990698	+	0.136080i	$0.0434503\pi$
$431$	12.7303	+	22.0495i	0.613197	+	1.06209i	−0.377500	+	0.926009i	$0.623216\pi$
$432$		0			0
$433$	8.44155	+	14.6212i	0.405675	+	0.702650i	0.994400	−	0.105684i	$-0.0337031\pi$
$433$	8.44155	+	14.6212i	0.405675	+	0.702650i	−0.588725	+	0.808334i	$0.700370\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.1656	+	33.7090i	−0.534125	+	1.61252i
$438$		0			0
$439$	−9.93240	+	17.2034i	−0.474048	+	0.821075i	−0.999558	−	0.0297121i	$-0.990541\pi$
$439$	−9.93240	+	17.2034i	−0.474048	+	0.821075i	0.525511	+	0.850787i	$0.323874\pi$
$440$		0			0
$441$	2.73590	+	4.73872i	0.130281	+	0.225653i
$442$		0			0
$443$	2.57742	+	4.46422i	0.122457	+	0.212101i	0.920736	−	0.390186i	$-0.127589\pi$
$443$	2.57742	+	4.46422i	0.122457	+	0.212101i	−0.798279	+	0.602288i	$0.794256\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.3276	+	21.3520i	0.583074	+	1.00991i
$448$		0			0
$449$	−33.2207			−1.56778			−0.783892	−	0.620897i	$-0.786768\pi$
$449$	−33.2207			−1.56778			−0.783892	+	0.620897i	$0.786768\pi$
$450$		0			0
$451$	14.2096	−	24.6117i	0.669103	−	1.15892i
$452$		0			0
$453$	11.6348	−	20.1520i	0.546650	−	0.946826i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.7126			0.547894			0.273947	−	0.961745i	$-0.411671\pi$
$457$	11.7126			0.547894			0.273947	+	0.961745i	$0.411671\pi$
$458$		0			0
$459$	−2.66448	+	4.61501i	−0.124367	+	0.215410i
$460$		0			0
$461$	3.68501	−	6.38263i	0.171628	−	0.297269i	−0.767361	−	0.641215i	$-0.778431\pi$
$461$	3.68501	−	6.38263i	0.171628	−	0.297269i	0.938989	+	0.343947i	$0.111764\pi$
$462$		0			0
$463$	−28.8020			−1.33854			−0.669271	−	0.743019i	$-0.733393\pi$
$463$	−28.8020			−1.33854			−0.669271	+	0.743019i	$0.733393\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	34.1251			1.57912			0.789561	−	0.613673i	$-0.210309\pi$
$467$	34.1251			1.57912			0.789561	+	0.613673i	$0.210309\pi$
$468$		0			0
$469$	0.515268	+	0.892471i	0.0237929	+	0.0412105i
$470$		0			0
$471$	4.16756	+	7.21842i	0.192031	+	0.332607i
$472$		0			0
$473$	33.4394	−	57.9188i	1.53755	−	2.66311i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.19789	−	10.7351i	0.283782	−	0.491525i
$478$		0			0
$479$	−14.4130	−	24.9640i	−0.658546	−	1.14064i	−0.980992	−	0.194048i	$-0.937838\pi$
$479$	−14.4130	−	24.9640i	−0.658546	−	1.14064i	0.322446	−	0.946588i	$-0.395495\pi$
$480$		0			0
$481$	6.78491	+	11.7518i	0.309365	+	0.535836i
$482$		0			0
$483$	−22.0446			−1.00306
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.5796			0.751294			0.375647	−	0.926763i	$-0.377421\pi$
$487$	16.5796			0.751294			0.375647	+	0.926763i	$0.377421\pi$
$488$		0			0
$489$	9.47957	−	16.4191i	0.428681	−	0.742497i
$490$		0			0
$491$	−4.94615	+	8.56698i	−0.223217	+	0.386623i	−0.955783	−	0.294073i	$-0.904989\pi$
$491$	−4.94615	+	8.56698i	−0.223217	+	0.386623i	0.732566	+	0.680696i	$0.238322\pi$
$492$		0			0
$493$	2.81748			0.126893
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.64011	+	13.2331i	−0.342706	+	0.593584i
$498$		0			0
$499$	15.4949	−	26.8380i	0.693649	−	1.20144i	−0.276985	−	0.960874i	$-0.589335\pi$
$499$	15.4949	−	26.8380i	0.693649	−	1.20144i	0.970634	−	0.240561i	$-0.0773315\pi$
$500$		0			0
$501$	27.5245			1.22970
$502$		0			0
$503$	6.43203	+	11.1406i	0.286790	+	0.496735i	0.973042	−	0.230629i	$-0.0740784\pi$
$503$	6.43203	+	11.1406i	0.286790	+	0.496735i	−0.686252	+	0.727364i	$0.740745\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.11568	+	12.3247i	0.316018	+	0.547360i
$508$		0			0
$509$	7.35312	+	12.7360i	0.325921	+	0.564512i	0.981698	−	0.190442i	$-0.0609922\pi$
$509$	7.35312	+	12.7360i	0.325921	+	0.564512i	−0.655777	+	0.754955i	$0.727659\pi$
$510$		0			0
$511$	−1.44664	+	2.50566i	−0.0639957	+	0.110844i
$512$		0			0
$513$	11.3574	+	12.7593i	0.501442	+	0.563335i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−8.58118	−	14.8630i	−0.377400	−	0.653676i
$518$		0			0
$519$	11.8564	+	20.5359i	0.520439	+	0.901427i
$520$		0			0
$521$	5.35528			0.234619			0.117310	−	0.993095i	$-0.462573\pi$
$521$	5.35528			0.234619			0.117310	+	0.993095i	$0.462573\pi$
$522$		0			0
$523$	−7.98981	−	13.8388i	−0.349370	−	0.605127i	0.636768	−	0.771056i	$-0.280271\pi$
$523$	−7.98981	−	13.8388i	−0.349370	−	0.605127i	−0.986138	+	0.165929i	$0.946938\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.348937	+	0.604376i	−0.0151999	+	0.0263270i
$528$		0			0
$529$	−21.6833	+	37.5566i	−0.942753	+	1.63290i
$530$		0			0
$531$	0.0370812			0.00160919
$532$		0			0
$533$	−13.1687			−0.570400
$534$		0			0
$535$		0			0
$536$		0			0
$537$	16.6833	−	28.8963i	0.719937	−	1.24697i
$538$		0			0
$539$	−27.2972			−1.17577
$540$		0			0
$541$	−17.9500	−	31.0904i	−0.771732	−	1.33668i	−0.936613	−	0.350366i	$-0.886057\pi$
$541$	−17.9500	−	31.0904i	−0.771732	−	1.33668i	0.164881	−	0.986313i	$-0.447276\pi$
$542$		0			0
$543$	−28.9742			−1.24340
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.0754	+	22.6473i	0.559064	+	0.968327i	0.997575	+	0.0696011i	$0.0221727\pi$
$547$	13.0754	+	22.6473i	0.559064	+	0.968327i	−0.438511	+	0.898726i	$0.644494\pi$
$548$		0			0
$549$	0.546140	−	0.945942i	0.0233087	−	0.0403718i
$550$		0			0
$551$	2.83979	−	8.57329i	0.120979	−	0.365235i
$552$		0			0
$553$	−8.71704	+	15.0983i	−0.370686	+	0.642047i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.10412	+	3.64444i	0.0891543	+	0.154420i	0.907154	−	0.420799i	$-0.138250\pi$
$557$	2.10412	+	3.64444i	0.0891543	+	0.154420i	−0.818000	+	0.575219i	$0.804917\pi$
$558$		0			0
$559$	−30.9899			−1.31073
$560$		0			0
$561$	7.19488	+	12.4619i	0.303768	+	0.526142i
$562$		0			0
$563$	40.5225			1.70782			0.853909	−	0.520422i	$-0.174225\pi$
$563$	40.5225			1.70782			0.853909	+	0.520422i	$0.174225\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.42622	+	12.8626i	−0.311872	+	0.540178i
$568$		0			0
$569$	23.9522			1.00413			0.502064	−	0.864831i	$-0.332574\pi$
$569$	23.9522			1.00413			0.502064	+	0.864831i	$0.332574\pi$
$570$		0			0
$571$	−7.78949			−0.325980			−0.162990	−	0.986628i	$-0.552114\pi$
$571$	−7.78949			−0.325980			−0.162990	+	0.986628i	$0.552114\pi$
$572$		0			0
$573$	6.01155	−	10.4123i	0.251136	−	0.434981i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	34.1385			1.42121			0.710603	−	0.703593i	$-0.248422\pi$
$577$	34.1385			1.42121			0.710603	+	0.703593i	$0.248422\pi$
$578$		0			0
$579$	−16.3953	−	28.3975i	−0.681366	−	1.18016i
$580$		0			0
$581$	−5.64899			−0.234360
$582$		0			0
$583$	30.9195	+	53.5541i	1.28055	+	2.21798i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.0700	−	19.1737i	0.456906	−	0.791384i	−0.541890	−	0.840450i	$-0.682291\pi$
$587$	11.0700	−	19.1737i	0.456906	−	0.791384i	0.998796	+	0.0490654i	$0.0156243\pi$
$588$		0			0
$589$	1.48735	+	1.67094i	0.0612853	+	0.0688498i
$590$		0			0
$591$	−11.6002	+	20.0921i	−0.477167	+	0.826477i
$592$		0			0
$593$	−20.6767	−	35.8131i	−0.849089	−	1.47067i	−0.882022	−	0.471208i	$-0.843818\pi$
$593$	−20.6767	−	35.8131i	−0.849089	−	1.47067i	0.0329325	−	0.999458i	$-0.489515\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	19.3258			0.790954
$598$		0			0
$599$	−16.8243	−	29.1406i	−0.687423	−	1.19065i	−0.972669	−	0.232197i	$-0.925409\pi$
$599$	−16.8243	−	29.1406i	−0.687423	−	1.19065i	0.285246	−	0.958454i	$-0.407925\pi$
$600$		0			0
$601$	38.4939			1.57020			0.785100	−	0.619369i	$-0.212611\pi$
$601$	38.4939			1.57020			0.785100	+	0.619369i	$0.212611\pi$
$602$		0			0
$603$	−0.403913	+	0.699598i	−0.0164486	+	0.0284899i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−22.1827			−0.900367			−0.450183	−	0.892936i	$-0.648641\pi$
$607$	−22.1827			−0.900367			−0.450183	+	0.892936i	$0.648641\pi$
$608$		0			0
$609$	5.60665			0.227193
$610$		0			0
$611$	−3.97629	+	6.88714i	−0.160864	+	0.278624i
$612$		0			0
$613$	−2.38703	+	4.13445i	−0.0964111	+	0.166989i	−0.910197	−	0.414176i	$-0.864070\pi$
$613$	−2.38703	+	4.13445i	−0.0964111	+	0.166989i	0.813786	+	0.581165i	$0.197403\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.09317	+	14.0178i	0.325819	+	0.564335i	0.981678	−	0.190549i	$-0.0610267\pi$
$617$	8.09317	+	14.0178i	0.325819	+	0.564335i	−0.655859	+	0.754883i	$0.727693\pi$
$618$		0			0
$619$	13.4892			0.542176			0.271088	−	0.962555i	$-0.412617\pi$
$619$	13.4892			0.542176			0.271088	+	0.962555i	$0.412617\pi$
$620$		0			0
$621$	15.9626	+	27.6480i	0.640556	+	1.10948i
$622$		0			0
$623$	−4.91143	−	8.50684i	−0.196772	−	0.340819i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	45.1720	−	9.33268i	1.80400	−	0.372711i
$628$		0			0
$629$	−3.78832	+	6.56156i	−0.151050	+	0.261626i
$630$		0			0
$631$	13.2207	+	22.8989i	0.526308	+	0.911592i	0.999530	+	0.0306488i	$0.00975735\pi$
$631$	13.2207	+	22.8989i	0.526308	+	0.911592i	−0.473222	+	0.880943i	$0.656909\pi$
$632$		0			0
$633$	14.6613	+	25.3942i	0.582735	+	1.00933i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	6.32441	+	10.9542i	0.250582	+	0.434021i
$638$		0			0
$639$	−11.9780			−0.473842
$640$		0			0
$641$	−4.27817	+	7.41000i	−0.168977	+	0.292677i	−0.938061	−	0.346471i	$-0.887380\pi$
$641$	−4.27817	+	7.41000i	−0.168977	+	0.292677i	0.769083	+	0.639149i	$0.220713\pi$
$642$		0			0
$643$	14.0112	−	24.2681i	0.552548	−	0.957042i	−0.445541	−	0.895261i	$-0.646989\pi$
$643$	14.0112	−	24.2681i	0.552548	−	0.957042i	0.998090	−	0.0617804i	$-0.0196779\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.57376			−0.376383			−0.188192	−	0.982132i	$-0.560263\pi$
$647$	−9.57376			−0.376383			−0.188192	+	0.982132i	$0.560263\pi$
$648$		0			0
$649$	−0.0924936	+	0.160204i	−0.00363069	+	0.00628854i
$650$		0			0
$651$	−0.694367	+	1.20268i	−0.0272144	+	0.0471367i
$652$		0			0
$653$	16.4168			0.642439			0.321219	−	0.947005i	$-0.395907\pi$
$653$	16.4168			0.642439			0.321219	+	0.947005i	$0.395907\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.26801			−0.0884837
$658$		0			0
$659$	−7.08162	−	12.2657i	−0.275861	−	0.477805i	0.694491	−	0.719501i	$-0.255629\pi$
$659$	−7.08162	−	12.2657i	−0.275861	−	0.477805i	−0.970352	+	0.241697i	$0.922296\pi$
$660$		0			0
$661$	−18.5170	−	32.0724i	−0.720229	−	1.24747i	−0.960908	−	0.276868i	$-0.910704\pi$
$661$	−18.5170	−	32.0724i	−0.720229	−	1.24747i	0.240679	−	0.970605i	$-0.422630\pi$
$662$		0			0
$663$	3.33392	−	5.77452i	0.129479	−	0.224264i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.43960	−	14.6178i	0.326783	−	0.566004i
$668$		0			0
$669$	7.62324	+	13.2038i	0.294732	+	0.510490i
$670$		0			0
$671$	2.72453	+	4.71903i	0.105179	+	0.182176i
$672$		0			0
$673$	−42.3293			−1.63167			−0.815837	−	0.578282i	$-0.803723\pi$
$673$	−42.3293			−1.63167			−0.815837	+	0.578282i	$0.803723\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.9856			−0.537510			−0.268755	−	0.963209i	$-0.586612\pi$
$677$	−13.9856			−0.537510			−0.268755	+	0.963209i	$0.586612\pi$
$678$		0			0
$679$	−0.560033	+	0.970005i	−0.0214921	+	0.0372254i
$680$		0			0
$681$	−6.91222	+	11.9723i	−0.264877	+	0.458780i
$682$		0			0
$683$	11.6668			0.446416			0.223208	−	0.974771i	$-0.428347\pi$
$683$	11.6668			0.446416			0.223208	+	0.974771i	$0.428347\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−22.2486	+	38.5356i	−0.848835	+	1.47023i
$688$		0			0
$689$	14.3273	−	24.8156i	0.545825	−	0.945397i
$690$		0			0
$691$	−15.7886			−0.600627			−0.300313	−	0.953841i	$-0.597091\pi$
$691$	−15.7886			−0.600627			−0.300313	+	0.953841i	$0.597091\pi$
$692$		0			0
$693$	3.72127	+	6.44542i	0.141359	+	0.244841i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−3.67633	−	6.36760i	−0.139251	−	0.241190i
$698$		0			0
$699$	−2.99675	−	5.19053i	−0.113348	−	0.196324i
$700$		0			0
$701$	2.64450	−	4.58042i	0.0998816	−	0.173000i	−0.811754	−	0.584000i	$-0.801487\pi$
$701$	2.64450	−	4.58042i	0.0998816	−	0.173000i	0.911635	+	0.411000i	$0.134820\pi$
$702$		0			0
$703$	16.1478	+	18.1409i	0.609025	+	0.684198i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.95913	+	17.2497i	0.374552	+	0.648743i
$708$		0			0
$709$	12.2529	+	21.2226i	0.460166	+	0.797031i	0.998969	−	0.0454011i	$-0.0144566\pi$
$709$	12.2529	+	21.2226i	0.460166	+	0.797031i	−0.538803	+	0.842432i	$0.681123\pi$
$710$		0			0
$711$	−13.6664			−0.512529
$712$		0			0
$713$	2.09044	+	3.62075i	0.0782875	+	0.135598i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.77771	−	16.9355i	0.365155	−	0.632467i
$718$		0			0
$719$	−22.4239	+	38.8393i	−0.836269	+	1.44846i	0.0567236	+	0.998390i	$0.481935\pi$
$719$	−22.4239	+	38.8393i	−0.836269	+	1.44846i	−0.892993	+	0.450071i	$0.851399\pi$
$720$		0			0
$721$	12.6442			0.470896
$722$		0			0
$723$	−37.6209			−1.39914
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−16.2453	+	28.1376i	−0.602504	+	1.04357i	0.389937	+	0.920842i	$0.372497\pi$
$727$	−16.2453	+	28.1376i	−0.602504	+	1.04357i	−0.992441	+	0.122726i	$0.960836\pi$
$728$		0			0
$729$	12.0273			0.445457
$730$		0			0
$731$	−8.65152	−	14.9849i	−0.319988	−	0.554235i
$732$		0			0
$733$	−11.1969			−0.413568			−0.206784	−	0.978387i	$-0.566300\pi$
$733$	−11.1969			−0.413568			−0.206784	+	0.978387i	$0.566300\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.01501	−	3.49009i	−0.0742237	−	0.128559i
$738$		0			0
$739$	−0.466361	+	0.807761i	−0.0171554	+	0.0297140i	−0.874476	−	0.485069i	$-0.838794\pi$
$739$	−0.466361	+	0.807761i	−0.0171554	+	0.0297140i	0.857320	+	0.514783i	$0.172128\pi$
$740$		0			0
$741$	−14.2109	−	15.9650i	−0.522051	−	0.586488i
$742$		0			0
$743$	13.4736	−	23.3370i	0.494300	−	0.856153i	−0.505678	−	0.862722i	$-0.668758\pi$
$743$	13.4736	−	23.3370i	0.494300	−	0.856153i	0.999978	+	0.00656939i	$0.00209112\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.21409	−	3.83492i	−0.0810094	−	0.140312i
$748$		0			0
$749$	−17.2210			−0.629240
$750$		0			0
$751$	2.33645	+	4.04686i	0.0852584	+	0.147672i	0.905501	−	0.424343i	$-0.139495\pi$
$751$	2.33645	+	4.04686i	0.0852584	+	0.147672i	−0.820243	+	0.572015i	$0.806162\pi$
$752$		0			0
$753$	−8.45971			−0.308289
$754$		0			0
$755$		0			0
$756$		0			0
$757$	21.4140	−	37.0902i	0.778306	−	1.34807i	−0.154612	−	0.987975i	$-0.549413\pi$
$757$	21.4140	−	37.0902i	0.778306	−	1.34807i	0.932918	−	0.360090i	$-0.117254\pi$
$758$		0			0
$759$	86.2073			3.12913
$760$		0			0
$761$	−16.7169			−0.605987			−0.302994	−	0.952993i	$-0.597986\pi$
$761$	−16.7169			−0.605987			−0.302994	+	0.952993i	$0.597986\pi$
$762$		0			0
$763$	1.33983	−	2.32065i	0.0485050	−	0.0840131i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.0857182			0.00309511
$768$		0			0
$769$	7.70852	+	13.3516i	0.277976	+	0.481469i	0.970882	−	0.239559i	$-0.0770029\pi$
$769$	7.70852	+	13.3516i	0.277976	+	0.481469i	−0.692905	+	0.721029i	$0.743670\pi$
$770$		0			0
$771$	56.7128			2.04246
$772$		0			0
$773$	16.5897	+	28.7343i	0.596691	+	1.03350i	0.993306	+	0.115514i	$0.0368516\pi$
$773$	16.5897	+	28.7343i	0.596691	+	1.03350i	−0.396615	+	0.917985i	$0.629815\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.53856	+	13.0572i	−0.270444	+	0.468423i
$778$		0			0
$779$	−23.0813	+	4.76868i	−0.826975	+	0.170856i
$780$		0			0
$781$	29.8774	−	51.7491i	1.06910	−	1.85173i
$782$		0			0
$783$	−4.05980	−	7.03179i	−0.145086	−	0.251296i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−12.8318			−0.457405			−0.228702	−	0.973496i	$-0.573448\pi$
$787$	−12.8318			−0.457405			−0.228702	+	0.973496i	$0.573448\pi$
$788$		0			0
$789$	−2.72657	−	4.72256i	−0.0970685	−	0.168128i
$790$		0			0
$791$	−11.2179			−0.398862
$792$		0			0
$793$	1.26248	−	2.18667i	0.0448319	−	0.0776511i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.28485			−0.0809336			−0.0404668	−	0.999181i	$-0.512885\pi$
$797$	−2.28485			−0.0809336			−0.0404668	+	0.999181i	$0.512885\pi$
$798$		0			0
$799$	−4.44028			−0.157086
$800$		0			0
$801$	3.85001	−	6.66842i	0.136034	−	0.235617i
$802$		0			0
$803$	5.65723	−	9.79861i	0.199639	−	0.345786i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.3573	−	19.6714i	−0.399796	−	0.692468i
$808$		0			0
$809$	17.3304			0.609305			0.304652	−	0.952464i	$-0.401460\pi$
$809$	17.3304			0.609305			0.304652	+	0.952464i	$0.401460\pi$
$810$		0			0
$811$	−24.7926	−	42.9420i	−0.870586	−	1.50790i	−0.861392	−	0.507941i	$-0.830407\pi$
$811$	−24.7926	−	42.9420i	−0.870586	−	1.50790i	−0.00919378	−	0.999958i	$-0.502927\pi$
$812$		0			0
$813$	−6.37606	−	11.0437i	−0.223618	−	0.387318i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−54.3173	+	11.2221i	−1.90032	+	0.392612i
$818$		0			0
$819$	1.72434	−	2.98664i	0.0602532	−	0.104362i
$820$		0			0
$821$	−11.1029	−	19.2308i	−0.387495	−	0.671160i	0.604617	−	0.796516i	$-0.293326\pi$
$821$	−11.1029	−	19.2308i	−0.387495	−	0.671160i	−0.992112	+	0.125356i	$0.959993\pi$
$822$		0			0
$823$	−9.56519	−	16.5674i	−0.333422	−	0.577503i	0.649759	−	0.760141i	$-0.274870\pi$
$823$	−9.56519	−	16.5674i	−0.333422	−	0.577503i	−0.983180	+	0.182637i	$0.941537\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.52461	−	13.0330i	−0.261656	−	0.453202i	0.705026	−	0.709182i	$-0.250935\pi$
$827$	−7.52461	−	13.0330i	−0.261656	−	0.453202i	−0.966682	+	0.255980i	$0.917602\pi$
$828$		0			0
$829$	3.62995			0.126074			0.0630368	−	0.998011i	$-0.479921\pi$
$829$	3.62995			0.126074			0.0630368	+	0.998011i	$0.479921\pi$
$830$		0			0
$831$	11.2179	−	19.4299i	0.389144	−	0.674017i
$832$		0			0
$833$	−3.53120	+	6.11621i	−0.122349	+	0.211914i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.01118			0.0695165
$838$		0			0
$839$	9.47453	−	16.4104i	0.327097	−	0.566549i	−0.654838	−	0.755770i	$-0.727263\pi$
$839$	9.47453	−	16.4104i	0.327097	−	0.566549i	0.981935	+	0.189221i	$0.0605963\pi$
$840$		0			0
$841$	12.3535	−	21.3969i	0.425984	−	0.737826i
$842$		0			0
$843$	51.9691			1.78991
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−22.3443			−0.767761
$848$		0			0
$849$	29.0534	+	50.3220i	0.997111	+	1.72705i
$850$		0			0
$851$	22.6954	+	39.3095i	0.777987	+	1.34751i
$852$		0			0
$853$	−21.3785	+	37.0287i	−0.731987	+	1.26784i	0.224045	+	0.974579i	$0.428074\pi$
$853$	−21.3785	+	37.0287i	−0.731987	+	1.26784i	−0.956033	+	0.293260i	$0.905260\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.57024	+	2.71973i	−0.0536383	+	0.0929043i	−0.891598	−	0.452828i	$-0.850415\pi$
$857$	−1.57024	+	2.71973i	−0.0536383	+	0.0929043i	0.837960	+	0.545732i	$0.183748\pi$
$858$		0			0
$859$	−3.53437	−	6.12170i	−0.120591	−	0.208870i	0.799410	−	0.600786i	$-0.205146\pi$
$859$	−3.53437	−	6.12170i	−0.120591	−	0.208870i	−0.920001	+	0.391916i	$0.871812\pi$
$860$		0			0
$861$	−7.31572	−	12.6712i	−0.249319	−	0.431834i
$862$		0			0
$863$	−0.464328			−0.0158059			−0.00790296	−	0.999969i	$-0.502516\pi$
$863$	−0.464328			−0.0158059			−0.00790296	+	0.999969i	$0.502516\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−30.5040			−1.03597
$868$		0			0
$869$	34.0888	−	59.0435i	1.15638	−	2.00291i
$870$		0			0
$871$	−0.933701	+	1.61722i	−0.0316373	+	0.0547973i
$872$		0			0
$873$	−0.878007			−0.0297160
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.463552	−	0.802896i	0.0156530	−	0.0271119i	−0.858093	−	0.513495i	$-0.828351\pi$
$877$	0.463552	−	0.802896i	0.0156530	−	0.0271119i	0.873746	+	0.486383i	$0.161684\pi$
$878$		0			0
$879$	22.9262	−	39.7094i	0.773282	−	1.33936i
$880$		0			0
$881$	4.50850			0.151895			0.0759477	−	0.997112i	$-0.475802\pi$
$881$	4.50850			0.151895			0.0759477	+	0.997112i	$0.475802\pi$
$882$		0			0
$883$	17.1245	+	29.6605i	0.576286	+	0.998156i	0.995901	+	0.0904542i	$0.0288319\pi$
$883$	17.1245	+	29.6605i	0.576286	+	0.998156i	−0.419615	+	0.907702i	$0.637835\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.2791	+	24.7321i	0.479445	+	0.830423i	0.999722	−	0.0235747i	$-0.00750474\pi$
$887$	14.2791	+	24.7321i	0.479445	+	0.830423i	−0.520277	+	0.853997i	$0.674171\pi$
$888$		0			0
$889$	−13.8310	−	23.9560i	−0.463876	−	0.803457i
$890$		0			0
$891$	29.0409	−	50.3003i	0.972907	−	1.68512i
$892$		0			0
$893$	−4.47544	+	13.5113i	−0.149765	+	0.452138i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−19.9731	−	34.5944i	−0.666883	−	1.15507i
$898$		0			0
$899$	−0.531667	−	0.920874i	−0.0177321	−	0.0307129i
$900$		0			0
$901$	15.9991			0.533007
$902$		0			0
$903$	−17.2161	−	29.8191i	−0.572916	−	0.992319i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	7.85765	−	13.6098i	0.260909	−	0.451907i	−0.705575	−	0.708635i	$-0.749311\pi$
$907$	7.85765	−	13.6098i	0.260909	−	0.451907i	0.966484	+	0.256728i	$0.0826445\pi$
$908$		0			0
$909$	−7.80686	+	13.5219i	−0.258937	+	0.448492i
$910$		0			0
$911$	20.7125			0.686237			0.343119	−	0.939292i	$-0.388517\pi$
$911$	20.7125			0.686237			0.343119	+	0.939292i	$0.388517\pi$
$912$		0			0
$913$	22.0909			0.731103
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.21143	−	12.4906i	0.238142	−	0.412475i
$918$		0			0
$919$	30.6628			1.01147			0.505737	−	0.862688i	$-0.331221\pi$
$919$	30.6628			1.01147			0.505737	+	0.862688i	$0.331221\pi$
$920$		0			0
$921$	16.3057	+	28.2423i	0.537291	+	0.930615i
$922$		0			0
$923$	−27.6888			−0.911388
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.95584	+	8.58377i	0.162771	+	0.281928i
$928$		0			0
$929$	7.65011	−	13.2504i	0.250992	−	0.434731i	−0.712807	−	0.701360i	$-0.752577\pi$
$929$	7.65011	−	13.2504i	0.250992	−	0.434731i	0.963799	+	0.266629i	$0.0859099\pi$
$930$		0			0
$931$	15.0518	+	16.9097i	0.493303	+	0.554193i
$932$		0			0
$933$	28.5375	−	49.4284i	0.934276	−	1.61821i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.21623	−	3.83862i	−0.0724011	−	0.125402i	0.827552	−	0.561389i	$-0.189733\pi$
$937$	−2.21623	−	3.83862i	−0.0724011	−	0.125402i	−0.899953	+	0.435987i	$0.856399\pi$
$938$		0			0
$939$	−6.21978			−0.202975
$940$		0			0
$941$	−17.3400	−	30.0338i	−0.565268	−	0.979073i	−0.997025	−	0.0770825i	$-0.975440\pi$
$941$	−17.3400	−	30.0338i	−0.565268	−	0.979073i	0.431757	−	0.901990i	$-0.357894\pi$
$942$		0			0
$943$	−44.0490			−1.43443
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.603945	+	1.04606i	−0.0196256	+	0.0339925i	−0.875671	−	0.482907i	$-0.839581\pi$
$947$	−0.603945	+	1.04606i	−0.0196256	+	0.0339925i	0.856046	+	0.516900i	$0.172914\pi$
$948$		0			0
$949$	−5.24283			−0.170189
$950$		0			0
$951$	48.4110			1.56983
$952$		0			0
$953$	−29.6627	+	51.3773i	−0.960868	+	1.66427i	−0.240540	+	0.970639i	$0.577324\pi$
$953$	−29.6627	+	51.3773i	−0.960868	+	1.66427i	−0.720329	+	0.693633i	$0.756009\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−21.9253			−0.708746
$958$		0			0
$959$	−11.5443	−	19.9952i	−0.372784	−	0.645680i
$960$		0			0
$961$	−30.7366			−0.991504
$962$		0			0
$963$	−6.74966	−	11.6908i	−0.217505	−	0.376729i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	22.7736	−	39.4450i	0.732350	−	1.26847i	−0.223527	−	0.974698i	$-0.571757\pi$
$967$	22.7736	−	39.4450i	0.732350	−	1.26847i	0.955876	−	0.293769i	$-0.0949097\pi$
$968$		0			0
$969$	3.75242	−	11.3285i	0.120545	−	0.363925i
$970$		0			0
$971$	−0.738715	+	1.27949i	−0.0237065	+	0.0410608i	−0.877635	−	0.479329i	$-0.840880\pi$
$971$	−0.738715	+	1.27949i	−0.0237065	+	0.0410608i	0.853929	+	0.520390i	$0.174213\pi$
$972$		0			0
$973$	4.92443	+	8.52937i	0.157870	+	0.273439i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−46.8443			−1.49868			−0.749341	−	0.662184i	$-0.769630\pi$
$977$	−46.8443			−1.49868			−0.749341	+	0.662184i	$0.769630\pi$
$978$		0			0
$979$	19.2066	+	33.2668i	0.613846	+	1.06321i
$980$		0			0
$981$	2.10055			0.0670654
$982$		0			0
$983$	−10.0466	+	17.4012i	−0.320436	+	0.555011i	−0.980578	−	0.196130i	$-0.937163\pi$
$983$	−10.0466	+	17.4012i	−0.320436	+	0.555011i	0.660142	+	0.751141i	$0.270496\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−8.83595			−0.281251
$988$		0			0
$989$	−103.660			−3.29621
$990$		0			0
$991$	−8.95274	+	15.5066i	−0.284393	+	0.492583i	−0.972462	−	0.233062i	$-0.925125\pi$
$991$	−8.95274	+	15.5066i	−0.284393	+	0.492583i	0.688069	+	0.725646i	$0.258459\pi$
$992$		0			0
$993$	20.9103	−	36.2177i	0.663568	−	1.14933i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.989838	−	1.71445i	−0.0313485	−	0.0542972i	0.849926	−	0.526903i	$-0.176647\pi$
$997$	−0.989838	−	1.71445i	−0.0313485	−	0.0542972i	−0.881274	+	0.472606i	$0.843314\pi$
$998$		0			0
$999$	21.8348			0.690824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.g.201.3		20
5.2	odd	4		380.2.r.a.49.8	yes	20
5.3	odd	4		380.2.r.a.49.3	✓	20
5.4	even	2	inner	1900.2.i.g.201.8		20
15.2	even	4		3420.2.bj.c.1189.6		20
15.8	even	4		3420.2.bj.c.1189.8		20
19.7	even	3	inner	1900.2.i.g.501.3		20
95.7	odd	12		380.2.r.a.349.3	yes	20
95.64	even	6	inner	1900.2.i.g.501.8		20
95.83	odd	12		380.2.r.a.349.8	yes	20
285.83	even	12		3420.2.bj.c.2629.6		20
285.197	even	12		3420.2.bj.c.2629.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.3	✓	20	5.3	odd	4
380.2.r.a.49.8	yes	20	5.2	odd	4
380.2.r.a.349.3	yes	20	95.7	odd	12
380.2.r.a.349.8	yes	20	95.83	odd	12
1900.2.i.g.201.3		20	1.1	even	1	trivial
1900.2.i.g.201.8		20	5.4	even	2	inner
1900.2.i.g.501.3		20	19.7	even	3	inner
1900.2.i.g.501.8		20	95.64	even	6	inner
3420.2.bj.c.1189.6		20	15.2	even	4
3420.2.bj.c.1189.8		20	15.8	even	4
3420.2.bj.c.2629.6		20	285.83	even	12
3420.2.bj.c.2629.8		20	285.197	even	12

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00667 + 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 - 0.912416i) q^{9} +O(q^{10})\)	\(q+(-1.00667 + 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 - 0.912416i) q^{9} +5.25594 q^{11} +(-1.21773 - 2.10918i) q^{13} +(0.679914 - 1.17765i) q^{17} +(-2.89815 - 3.25587i) q^{19} +(1.35300 - 2.34346i) q^{21} +(-4.07329 - 7.05514i) q^{23} -3.91884 q^{27} +(1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(-5.29102 + 9.16431i) q^{33} -5.57175 q^{37} +4.90344 q^{39} +(2.70353 - 4.68265i) q^{41} +(6.36221 - 11.0197i) q^{43} +(-1.63266 - 2.82785i) q^{47} -5.19359 q^{49} +(1.36890 + 2.37101i) q^{51} +(5.88276 + 10.1892i) q^{53} +(8.59447 - 1.77564i) q^{57} +(-0.0175979 + 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(0.708011 + 1.22631i) q^{63} +(-0.383377 - 0.664028i) q^{67} +16.4019 q^{69} +(5.68450 - 9.84583i) q^{71} +(1.07635 - 1.86429i) q^{73} -7.06413 q^{77} +(6.48576 - 11.2337i) q^{79} +(5.52535 - 9.57019i) q^{81} +4.20304 q^{83} -4.17153 q^{87} +(3.65426 + 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(0.516632 - 0.894833i) q^{93} +(0.416683 - 0.721716i) q^{97} +(-2.76875 - 4.79561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^9	\( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) \) 20 * q - 10 * q^9 - 14 * q^19 - 8 * q^21 + 16 * q^29 + 8 * q^31 + 8 * q^39 + 26 * q^41 + 44 * q^49 + 26 * q^51 - 4 * q^59 + 2 * q^61 - 48 * q^69 - 2 * q^71 + 16 * q^79 + 26 * q^81 + 40 * q^89 - 4 * q^91 + 20 * q^99

Introduction

L-functions

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