LMFDB - Embedded newform 1900.2.i.g.501.2

Error: no document with id 279330818 found in table mf_hecke_traces.

Error: no document with id 206982620 found in table mf_hecke_traces.

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1900,2,Mod(201,1900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			501.2
Root			$1.21562 - 2.10552i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.g.201.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21562 - 2.10552i) q^{3} +0.663818 q^{7} +(-1.45548 + 2.52097i) q^{9} -1.80905 q^{11} +(1.15197 - 1.99526i) q^{13} +(-2.18033 - 3.77643i) q^{17} +(4.21168 + 1.12329i) q^{19} +(-0.806953 - 1.39768i) q^{21} +(1.04716 - 1.81374i) q^{23} -0.216466 q^{27} +(-0.974621 + 1.68809i) q^{29} -9.52527 q^{31} +(2.19913 + 3.80900i) q^{33} +2.97461 q^{37} -5.60143 q^{39} +(-0.247657 - 0.428954i) q^{41} +(-3.93588 - 6.81715i) q^{43} +(3.28772 - 5.69449i) q^{47} -6.55935 q^{49} +(-5.30091 + 9.18145i) q^{51} +(1.15225 - 1.99575i) q^{53} +(-2.75471 - 10.2333i) q^{57} +(-3.88559 - 6.73003i) q^{59} +(-5.36021 + 9.28415i) q^{61} +(-0.966176 + 1.67347i) q^{63} +(-2.29199 + 3.96984i) q^{67} -5.09182 q^{69} +(-2.95914 - 5.12538i) q^{71} +(2.80773 + 4.86313i) q^{73} -1.20088 q^{77} +(2.99810 + 5.19286i) q^{79} +(4.62959 + 8.01868i) q^{81} -6.20090 q^{83} +4.73909 q^{87} +(6.65028 - 11.5186i) q^{89} +(0.764696 - 1.32449i) q^{91} +(11.5791 + 20.0557i) q^{93} +(5.08470 + 8.80695i) q^{97} +(2.63305 - 4.56057i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

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

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
$3$	−1.21562	−	2.10552i	−0.701841	−	1.21562i	−0.967820	−	0.251645i	$-0.919028\pi$
$3$	−1.21562	−	2.10552i	−0.701841	−	1.21562i	0.265979	−	0.963979i	$-0.414305\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.663818			0.250900			0.125450	−	0.992100i	$-0.459963\pi$
$7$	0.663818			0.250900			0.125450	+	0.992100i	$0.459963\pi$
$8$		0			0
$9$	−1.45548	+	2.52097i	−0.485161	+	0.840323i
$10$		0			0
$11$	−1.80905			−0.545450			−0.272725	−	0.962092i	$-0.587925\pi$
$11$	−1.80905			−0.545450			−0.272725	+	0.962092i	$0.587925\pi$
$12$		0			0
$13$	1.15197	−	1.99526i	0.319498	−	0.553386i	−0.660886	−	0.750487i	$-0.729819\pi$
$13$	1.15197	−	1.99526i	0.319498	−	0.553386i	0.980383	+	0.197100i	$0.0631525\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.18033	−	3.77643i	−0.528807	−	0.915920i	−0.999436	−	0.0335887i	$-0.989306\pi$
$17$	−2.18033	−	3.77643i	−0.528807	−	0.915920i	0.470629	−	0.882331i	$-0.344027\pi$
$18$		0			0
$19$	4.21168	+	1.12329i	0.966225	+	0.257699i
$19$	4.21168	+	1.12329i	0.966225	+	0.257699i
$20$		0			0
$21$	−0.806953	−	1.39768i	−0.176092	−	0.305000i
$22$		0			0
$23$	1.04716	−	1.81374i	0.218349	−	0.378191i	−0.735955	−	0.677031i	$-0.763266\pi$
$23$	1.04716	−	1.81374i	0.218349	−	0.378191i	0.954303	+	0.298840i	$0.0965997\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.216466			−0.0416588
$28$		0			0
$29$	−0.974621	+	1.68809i	−0.180983	+	0.313471i	−0.942215	−	0.335008i	$-0.891261\pi$
$29$	−0.974621	+	1.68809i	−0.180983	+	0.313471i	0.761233	+	0.648479i	$0.224594\pi$
$30$		0			0
$31$	−9.52527			−1.71079			−0.855394	−	0.517977i	$-0.826685\pi$
$31$	−9.52527			−1.71079			−0.855394	+	0.517977i	$0.826685\pi$
$32$		0			0
$33$	2.19913	+	3.80900i	0.382819	+	0.663062i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.97461			0.489023			0.244511	−	0.969646i	$-0.421372\pi$
$37$	2.97461			0.489023			0.244511	+	0.969646i	$0.421372\pi$
$38$		0			0
$39$	−5.60143			−0.896946
$40$		0			0
$41$	−0.247657	−	0.428954i	−0.0386775	−	0.0669914i	0.846039	−	0.533122i	$-0.178981\pi$
$41$	−0.247657	−	0.428954i	−0.0386775	−	0.0669914i	−0.884716	+	0.466130i	$0.845648\pi$
$42$		0			0
$43$	−3.93588	−	6.81715i	−0.600216	−	1.03960i	−0.992788	−	0.119884i	$-0.961748\pi$
$43$	−3.93588	−	6.81715i	−0.600216	−	1.03960i	0.392572	−	0.919721i	$-0.371585\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.28772	−	5.69449i	0.479563	−	0.830627i	−0.520163	−	0.854067i	$-0.674129\pi$
$47$	3.28772	−	5.69449i	0.479563	−	0.830627i	0.999725	+	0.0234403i	$0.00746198\pi$
$48$		0			0
$49$	−6.55935			−0.937049
$50$		0			0
$51$	−5.30091	+	9.18145i	−0.742276	+	1.28566i
$52$		0			0
$53$	1.15225	−	1.99575i	0.158273	−	0.274137i	−0.775973	−	0.630766i	$-0.782741\pi$
$53$	1.15225	−	1.99575i	0.158273	−	0.274137i	0.934246	+	0.356629i	$0.116074\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.75471	−	10.2333i	−0.364871	−	1.35543i
$58$		0			0
$59$	−3.88559	−	6.73003i	−0.505860	−	0.876176i	−0.999977	−	0.00678007i	$-0.997842\pi$
$59$	−3.88559	−	6.73003i	−0.505860	−	0.876176i	0.494117	−	0.869396i	$-0.335492\pi$
$60$		0			0
$61$	−5.36021	+	9.28415i	−0.686304	+	1.18871i	0.286721	+	0.958014i	$0.407435\pi$
$61$	−5.36021	+	9.28415i	−0.686304	+	1.18871i	−0.973025	+	0.230700i	$0.925899\pi$
$62$		0			0
$63$	−0.966176	+	1.67347i	−0.121727	+	0.210837i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.29199	+	3.96984i	−0.280011	+	0.484993i	−0.971387	−	0.237502i	$-0.923671\pi$
$67$	−2.29199	+	3.96984i	−0.280011	+	0.484993i	0.691376	+	0.722495i	$0.257005\pi$
$68$		0			0
$69$	−5.09182			−0.612984
$70$		0			0
$71$	−2.95914	−	5.12538i	−0.351185	−	0.608270i	0.635272	−	0.772288i	$-0.280888\pi$
$71$	−2.95914	−	5.12538i	−0.351185	−	0.608270i	−0.986457	+	0.164018i	$0.947554\pi$
$72$		0			0
$73$	2.80773	+	4.86313i	0.328620	+	0.569187i	0.982238	−	0.187638i	$-0.0600831\pi$
$73$	2.80773	+	4.86313i	0.328620	+	0.569187i	−0.653618	+	0.756824i	$0.726750\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.20088			−0.136853
$78$		0			0
$79$	2.99810	+	5.19286i	0.337312	+	0.584242i	0.983926	−	0.178575i	$-0.0571488\pi$
$79$	2.99810	+	5.19286i	0.337312	+	0.584242i	−0.646614	+	0.762817i	$0.723815\pi$
$80$		0			0
$81$	4.62959	+	8.01868i	0.514399	+	0.890965i
$82$		0			0
$83$	−6.20090			−0.680638			−0.340319	−	0.940310i	$-0.610535\pi$
$83$	−6.20090			−0.680638			−0.340319	+	0.940310i	$0.610535\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.73909			0.508084
$88$		0			0
$89$	6.65028	−	11.5186i	0.704928	−	1.22097i	−0.261789	−	0.965125i	$-0.584312\pi$
$89$	6.65028	−	11.5186i	0.704928	−	1.22097i	0.966717	−	0.255847i	$-0.0823542\pi$
$90$		0			0
$91$	0.764696	−	1.32449i	0.0801619	−	0.138844i
$92$		0			0
$93$	11.5791	+	20.0557i	1.20070	+	2.07968i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.08470	+	8.80695i	0.516273	+	0.894211i	0.999822	+	0.0188932i	$0.00601425\pi$
$97$	5.08470	+	8.80695i	0.516273	+	0.894211i	−0.483549	+	0.875317i	$0.660652\pi$
$98$		0			0
$99$	2.63305	−	4.56057i	0.264631	−	0.458354i
$100$		0			0
$101$	−7.48770	+	12.9691i	−0.745054	+	1.29047i	0.205116	+	0.978738i	$0.434243\pi$
$101$	−7.48770	+	12.9691i	−0.745054	+	1.29047i	−0.950170	+	0.311733i	$0.899091\pi$
$102$		0			0
$103$	−18.1501			−1.78839			−0.894193	−	0.447681i	$-0.852250\pi$
$103$	−18.1501			−1.78839			−0.894193	+	0.447681i	$0.852250\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.9698			−1.35051			−0.675256	−	0.737584i	$-0.735967\pi$
$107$	−13.9698			−1.35051			−0.675256	+	0.737584i	$0.735967\pi$
$108$		0			0
$109$	9.20544	+	15.9443i	0.881721	+	1.52719i	0.849426	+	0.527707i	$0.176948\pi$
$109$	9.20544	+	15.9443i	0.881721	+	1.52719i	0.0322945	+	0.999478i	$0.489719\pi$
$110$		0			0
$111$	−3.61601	−	6.26311i	−0.343216	−	0.594468i
$112$		0			0
$113$	10.8946			1.02487			0.512437	−	0.858725i	$-0.328743\pi$
$113$	10.8946			1.02487			0.512437	+	0.858725i	$0.328743\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.35333	+	5.80814i	0.310016	+	0.536963i
$118$		0			0
$119$	−1.44734	−	2.50687i	−0.132677	−	0.229804i
$120$		0			0
$121$	−7.72733			−0.702484
$122$		0			0
$123$	−0.602115	+	1.04289i	−0.0542909	+	0.0940346i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.65262	−	2.86242i	0.146646	−	0.253998i	−0.783340	−	0.621594i	$-0.786486\pi$
$127$	1.65262	−	2.86242i	0.146646	−	0.253998i	0.929986	+	0.367595i	$0.119819\pi$
$128$		0			0
$129$	−9.56910	+	16.5742i	−0.842512	+	1.45927i
$130$		0			0
$131$	−0.646627	−	1.11999i	−0.0564961	−	0.0978541i	0.836394	−	0.548128i	$-0.184660\pi$
$131$	−0.646627	−	1.11999i	−0.0564961	−	0.0978541i	−0.892890	+	0.450274i	$0.851326\pi$
$132$		0			0
$133$	2.79579	+	0.745658i	0.242426	+	0.0646567i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.29920	+	12.6426i	−0.623613	+	1.08013i	0.365195	+	0.930931i	$0.381002\pi$
$137$	−7.29920	+	12.6426i	−0.623613	+	1.08013i	−0.988807	+	0.149197i	$0.952331\pi$
$138$		0			0
$139$	1.87915	−	3.25478i	0.159387	−	0.276067i	−0.775261	−	0.631641i	$-0.782382\pi$
$139$	1.87915	−	3.25478i	0.159387	−	0.276067i	0.934648	+	0.355575i	$0.115715\pi$
$140$		0			0
$141$	−15.9865			−1.34631
$142$		0			0
$143$	−2.08397	+	3.60954i	−0.174270	+	0.301844i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.97370	+	13.8108i	0.657659	+	1.13910i
$148$		0			0
$149$	−3.83653	−	6.64507i	−0.314301	−	0.544385i	0.664988	−	0.746854i	$-0.268437\pi$
$149$	−3.83653	−	6.64507i	−0.314301	−	0.544385i	−0.979289	+	0.202469i	$0.935103\pi$
$150$		0			0
$151$	1.62643			0.132357			0.0661785	−	0.997808i	$-0.478919\pi$
$151$	1.62643			0.132357			0.0661785	+	0.997808i	$0.478919\pi$
$152$		0			0
$153$	12.6937			1.02622
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.32729	+	2.29893i	0.105929	+	0.183474i	0.914117	−	0.405450i	$-0.132885\pi$
$157$	1.32729	+	2.29893i	0.105929	+	0.183474i	−0.808188	+	0.588924i	$0.799552\pi$
$158$		0			0
$159$	−5.60279			−0.444331
$160$		0			0
$161$	0.695126	−	1.20399i	0.0547836	−	0.0948880i
$162$		0			0
$163$	−19.8052			−1.55127			−0.775633	−	0.631184i	$-0.782569\pi$
$163$	−19.8052			−1.55127			−0.775633	+	0.631184i	$0.782569\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.0448558	+	0.0776925i	−0.00347105	+	0.00601203i	−0.867756	−	0.496991i	$-0.834438\pi$
$167$	−0.0448558	+	0.0776925i	−0.00347105	+	0.00601203i	0.864285	+	0.503003i	$0.167772\pi$
$168$		0			0
$169$	3.84595	+	6.66139i	0.295842	+	0.512414i
$170$		0			0
$171$	−8.96179	+	8.98259i	−0.685325	+	0.686916i
$172$		0			0
$173$	−7.91662	−	13.7120i	−0.601889	−	1.04250i	−0.992535	−	0.121962i	$-0.961082\pi$
$173$	−7.91662	−	13.7120i	−0.601889	−	1.04250i	0.390646	−	0.920541i	$-0.372252\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.44682	+	16.3624i	−0.710067	+	1.22987i
$178$		0			0
$179$	−13.5051			−1.00942			−0.504709	−	0.863290i	$-0.668400\pi$
$179$	−13.5051			−1.00942			−0.504709	+	0.863290i	$0.668400\pi$
$180$		0			0
$181$	4.78591	−	8.28945i	0.355734	−	0.616150i	−0.631509	−	0.775368i	$-0.717564\pi$
$181$	4.78591	−	8.28945i	0.355734	−	0.616150i	0.987243	+	0.159219i	$0.0508975\pi$
$182$		0			0
$183$	26.0640			1.92670
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.94432	+	6.83177i	0.288438	+	0.499588i
$188$		0			0
$189$	−0.143694			−0.0104522
$190$		0			0
$191$	26.9010			1.94649			0.973243	−	0.229778i	$-0.0738000\pi$
$191$	26.9010			1.94649			0.973243	+	0.229778i	$0.0738000\pi$
$192$		0			0
$193$	−11.4137	−	19.7692i	−0.821579	−	1.42302i	−0.904506	−	0.426461i	$-0.859760\pi$
$193$	−11.4137	−	19.7692i	−0.821579	−	1.42302i	0.0829272	−	0.996556i	$-0.473573\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.4172			0.742192			0.371096	−	0.928594i	$-0.378982\pi$
$197$	10.4172			0.742192			0.371096	+	0.928594i	$0.378982\pi$
$198$		0			0
$199$	−0.782081	+	1.35460i	−0.0554403	+	0.0960254i	−0.892414	−	0.451218i	$-0.850990\pi$
$199$	−0.782081	+	1.35460i	−0.0554403	+	0.0960254i	0.836973	+	0.547244i	$0.184323\pi$
$200$		0			0
$201$	11.1448			0.786092
$202$		0			0
$203$	−0.646971	+	1.12059i	−0.0454085	+	0.0786498i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.04825	+	5.27973i	0.211868	+	0.366967i
$208$		0			0
$209$	−7.61915	−	2.03208i	−0.527028	−	0.140562i
$210$		0			0
$211$	−10.4253	−	18.0571i	−0.717704	−	1.24310i	−0.961907	−	0.273376i	$-0.911860\pi$
$211$	−10.4253	−	18.0571i	−0.717704	−	1.24310i	0.244203	−	0.969724i	$-0.421474\pi$
$212$		0			0
$213$	−7.19439	+	12.4611i	−0.492952	+	0.853818i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.32305			−0.429236
$218$		0			0
$219$	6.82629	−	11.8235i	0.461278	−	0.798957i
$220$		0			0
$221$	−10.0466			−0.675810
$222$		0			0
$223$	−11.2856	−	19.5472i	−0.755740	−	1.30898i	−0.945006	−	0.327054i	$-0.893944\pi$
$223$	−11.2856	−	19.5472i	−0.755740	−	1.30898i	0.189266	−	0.981926i	$-0.439389\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.4187			−0.757883			−0.378941	−	0.925421i	$-0.623712\pi$
$227$	−11.4187			−0.757883			−0.378941	+	0.925421i	$0.623712\pi$
$228$		0			0
$229$	−15.8237			−1.04566			−0.522829	−	0.852438i	$-0.675123\pi$
$229$	−15.8237			−1.04566			−0.522829	+	0.852438i	$0.675123\pi$
$230$		0			0
$231$	1.45982	+	2.52849i	0.0960492	+	0.166362i
$232$		0			0
$233$	6.73314	+	11.6621i	0.441103	+	0.764013i	0.997772	−	0.0667219i	$-0.0212540\pi$
$233$	6.73314	+	11.6621i	0.441103	+	0.764013i	−0.556669	+	0.830735i	$0.687921\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	7.28912	−	12.6251i	0.473479	−	0.820090i
$238$		0			0
$239$	19.7437			1.27711			0.638557	−	0.769574i	$-0.279532\pi$
$239$	19.7437			1.27711			0.638557	+	0.769574i	$0.279532\pi$
$240$		0			0
$241$	2.69793	−	4.67295i	0.173789	−	0.301011i	−0.765953	−	0.642897i	$-0.777732\pi$
$241$	2.69793	−	4.67295i	0.173789	−	0.301011i	0.939742	+	0.341886i	$0.111066\pi$
$242$		0			0
$243$	10.9310	−	18.9330i	0.701223	−	1.21455i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.09296	−	7.10942i	0.451314	−	0.452361i
$248$		0			0
$249$	7.53797	+	13.0561i	0.477699	+	0.827399i
$250$		0			0
$251$	1.78646	−	3.09424i	0.112760	−	0.195306i	−0.804122	−	0.594464i	$-0.797364\pi$
$251$	1.78646	−	3.09424i	0.112760	−	0.195306i	0.916882	+	0.399158i	$0.130697\pi$
$252$		0			0
$253$	−1.89437	+	3.28115i	−0.119098	+	0.206284i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.26649	−	16.0500i	0.578028	−	1.00117i	−0.417678	−	0.908595i	$-0.637156\pi$
$257$	9.26649	−	16.0500i	0.578028	−	1.00117i	0.995705	−	0.0925780i	$-0.0295107\pi$
$258$		0			0
$259$	1.97460			0.122696
$260$		0			0
$261$	−2.83709	−	4.91398i	−0.175611	−	0.304168i
$262$		0			0
$263$	5.37288	+	9.30609i	0.331306	+	0.573838i	0.982768	−	0.184843i	$-0.0591775\pi$
$263$	5.37288	+	9.30609i	0.331306	+	0.573838i	−0.651462	+	0.758681i	$0.725844\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−32.3370			−1.97899
$268$		0			0
$269$	6.05027	+	10.4794i	0.368892	+	0.638939i	0.989393	−	0.145267i	$-0.0464040\pi$
$269$	6.05027	+	10.4794i	0.368892	+	0.638939i	−0.620501	+	0.784206i	$0.713071\pi$
$270$		0			0
$271$	9.34472	+	16.1855i	0.567651	+	0.983201i	0.996798	+	0.0799661i	$0.0254812\pi$
$271$	9.34472	+	16.1855i	0.567651	+	0.983201i	−0.429146	+	0.903235i	$0.641185\pi$
$272$		0			0
$273$	−3.71833			−0.225044
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.94922			0.357454			0.178727	−	0.983899i	$-0.442802\pi$
$277$	5.94922			0.357454			0.178727	+	0.983899i	$0.442802\pi$
$278$		0			0
$279$	13.8639	−	24.0129i	0.830008	−	1.43762i
$280$		0			0
$281$	8.78943	−	15.2237i	0.524333	−	0.908172i	−0.475265	−	0.879843i	$-0.657648\pi$
$281$	8.78943	−	15.2237i	0.524333	−	0.908172i	0.999599	−	0.0283294i	$-0.00901874\pi$
$282$		0			0
$283$	15.7056	+	27.2029i	0.933603	+	1.61705i	0.777107	+	0.629368i	$0.216686\pi$
$283$	15.7056	+	27.2029i	0.933603	+	1.61705i	0.156495	+	0.987679i	$0.449980\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.164399	−	0.284748i	−0.00970418	−	0.0168081i
$288$		0			0
$289$	−1.00764	+	1.74528i	−0.0592727	+	0.102663i
$290$		0			0
$291$	12.3622	−	21.4119i	0.724682	−	1.25519i
$292$		0			0
$293$	−28.1435			−1.64416			−0.822080	−	0.569372i	$-0.807186\pi$
$293$	−28.1435			−1.64416			−0.822080	+	0.569372i	$0.807186\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.391598			0.0227228
$298$		0			0
$299$	−2.41259	−	4.17873i	−0.139524	−	0.241662i
$300$		0			0
$301$	−2.61271	−	4.52535i	−0.150594	−	0.260837i
$302$		0			0
$303$	36.4089			2.09164
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−13.4862	−	23.3588i	−0.769698	−	1.33316i	−0.937727	−	0.347374i	$-0.887073\pi$
$307$	−13.4862	−	23.3588i	−0.769698	−	1.33316i	0.168028	−	0.985782i	$-0.446260\pi$
$308$		0			0
$309$	22.0637	+	38.2155i	1.25516	+	2.17401i
$310$		0			0
$311$	−4.99721			−0.283366			−0.141683	−	0.989912i	$-0.545251\pi$
$311$	−4.99721			−0.283366			−0.141683	+	0.989912i	$0.545251\pi$
$312$		0			0
$313$	13.0761	−	22.6484i	0.739104	−	1.28017i	−0.213795	−	0.976878i	$-0.568583\pi$
$313$	13.0761	−	22.6484i	0.739104	−	1.28017i	0.952899	−	0.303287i	$-0.0980841\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.0085	−	22.5314i	0.730632	−	1.26549i	−0.225982	−	0.974131i	$-0.572559\pi$
$317$	13.0085	−	22.5314i	0.730632	−	1.26549i	0.956614	−	0.291359i	$-0.0941076\pi$
$318$		0			0
$319$	1.76314	−	3.05385i	0.0987169	−	0.170983i
$320$		0			0
$321$	16.9820	+	29.4137i	0.947844	+	1.64171i
$322$		0			0
$323$	−4.94081	−	18.3543i	−0.274914	−	1.02126i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	22.3807	−	38.7645i	1.23766	−	2.14368i
$328$		0			0
$329$	2.18245	−	3.78011i	0.120322	−	0.208404i
$330$		0			0
$331$	7.97402			0.438292			0.219146	−	0.975692i	$-0.429673\pi$
$331$	7.97402			0.438292			0.219146	+	0.975692i	$0.429673\pi$
$332$		0			0
$333$	−4.32949	+	7.49890i	−0.237255	+	0.410937i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.97951	+	3.42862i	0.107831	+	0.186769i	0.914891	−	0.403700i	$-0.132276\pi$
$337$	1.97951	+	3.42862i	0.107831	+	0.186769i	−0.807060	+	0.590469i	$0.798943\pi$
$338$		0			0
$339$	−13.2437	−	22.9387i	−0.719299	−	1.24586i
$340$		0			0
$341$	17.2317			0.933150
$342$		0			0
$343$	−9.00094			−0.486005
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.40205	−	4.16047i	−0.128949	−	0.223345i	0.794321	−	0.607498i	$-0.207827\pi$
$347$	−2.40205	−	4.16047i	−0.128949	−	0.223345i	−0.923269	+	0.384153i	$0.874494\pi$
$348$		0			0
$349$	9.02058			0.482861			0.241430	−	0.970418i	$-0.422383\pi$
$349$	9.02058			0.482861			0.241430	+	0.970418i	$0.422383\pi$
$350$		0			0
$351$	−0.249361	+	0.431906i	−0.0133099	+	0.0230534i
$352$		0			0
$353$	−18.0910			−0.962889			−0.481444	−	0.876477i	$-0.659888\pi$
$353$	−18.0910			−0.962889			−0.481444	+	0.876477i	$0.659888\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.51884	+	6.09481i	−0.186237	+	0.322572i
$358$		0			0
$359$	−17.4849	−	30.2848i	−0.922820	−	1.59837i	−0.795030	−	0.606571i	$-0.792545\pi$
$359$	−17.4849	−	30.2848i	−0.922820	−	1.59837i	−0.127791	−	0.991801i	$-0.540789\pi$
$360$		0			0
$361$	16.4765	+	9.46183i	0.867182	+	0.497991i
$362$		0			0
$363$	9.39352	+	16.2701i	0.493032	+	0.853957i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.93819	−	8.55319i	0.257771	−	0.446473i	−0.707873	−	0.706339i	$-0.750345\pi$
$367$	4.93819	−	8.55319i	0.257771	−	0.446473i	0.965645	+	0.259866i	$0.0836786\pi$
$368$		0			0
$369$	1.44184			0.0750593
$370$		0			0
$371$	0.764883	−	1.32482i	0.0397107	−	0.0687810i
$372$		0			0
$373$	−18.9698			−0.982220			−0.491110	−	0.871098i	$-0.663409\pi$
$373$	−18.9698			−0.982220			−0.491110	+	0.871098i	$0.663409\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.24546	+	3.88925i	0.115647	+	0.200306i
$378$		0			0
$379$	8.93773			0.459101			0.229550	−	0.973297i	$-0.426274\pi$
$379$	8.93773			0.459101			0.229550	+	0.973297i	$0.426274\pi$
$380$		0			0
$381$	−8.03584			−0.411689
$382$		0			0
$383$	−8.06230	−	13.9643i	−0.411964	−	0.713543i	0.583140	−	0.812371i	$-0.301824\pi$
$383$	−8.06230	−	13.9643i	−0.411964	−	0.713543i	−0.995104	+	0.0988287i	$0.968490\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	22.9144			1.16481
$388$		0			0
$389$	10.0603	−	17.4249i	0.510075	−	0.883476i	−0.489857	−	0.871803i	$-0.662951\pi$
$389$	10.0603	−	17.4249i	0.510075	−	0.883476i	0.999932	−	0.0116730i	$-0.00371573\pi$
$390$		0			0
$391$	−9.13262			−0.461857
$392$		0			0
$393$	−1.57211	+	2.72298i	−0.0793025	+	0.137356i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.00633	−	13.8674i	−0.401826	−	0.695983i	0.592120	−	0.805850i	$-0.298291\pi$
$397$	−8.00633	−	13.8674i	−0.401826	−	0.695983i	−0.993946	+	0.109866i	$0.964958\pi$
$398$		0			0
$399$	−1.82863	−	6.79304i	−0.0915460	−	0.340077i
$400$		0			0
$401$	6.83602	+	11.8403i	0.341375	+	0.591278i	0.984688	−	0.174324i	$-0.0557741\pi$
$401$	6.83602	+	11.8403i	0.341375	+	0.591278i	−0.643313	+	0.765603i	$0.722441\pi$
$402$		0			0
$403$	−10.9728	+	19.0054i	−0.546593	+	0.946727i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.38123			−0.266738
$408$		0			0
$409$	−3.03518	+	5.25709i	−0.150080	+	0.259946i	−0.931257	−	0.364364i	$-0.881287\pi$
$409$	−3.03518	+	5.25709i	−0.150080	+	0.259946i	0.781177	+	0.624310i	$0.214620\pi$
$410$		0			0
$411$	35.4923			1.75071
$412$		0			0
$413$	−2.57932	−	4.46752i	−0.126920	−	0.219832i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.13735			−0.447458
$418$		0			0
$419$	−6.33985			−0.309722			−0.154861	−	0.987936i	$-0.549493\pi$
$419$	−6.33985			−0.309722			−0.154861	+	0.987936i	$0.549493\pi$
$420$		0			0
$421$	3.52768	+	6.11011i	0.171928	+	0.297789i	0.939094	−	0.343660i	$-0.111667\pi$
$421$	3.52768	+	6.11011i	0.171928	+	0.297789i	−0.767166	+	0.641449i	$0.778334\pi$
$422$		0			0
$423$	9.57043	+	16.5765i	0.465330	+	0.805975i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.55820	+	6.16299i	−0.172194	+	0.298248i
$428$		0			0
$429$	10.1333			0.489239
$430$		0			0
$431$	13.0390	−	22.5843i	0.628069	−	1.08785i	−0.359870	−	0.933002i	$-0.617179\pi$
$431$	13.0390	−	22.5843i	0.628069	−	1.08785i	0.987939	−	0.154845i	$-0.0494877\pi$
$432$		0			0
$433$	17.1278	−	29.6662i	0.823109	−	1.42567i	−0.0802463	−	0.996775i	$-0.525571\pi$
$433$	17.1278	−	29.6662i	0.823109	−	1.42567i	0.903356	−	0.428892i	$-0.141096\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.44766	−	6.46262i	0.308433	−	0.309149i
$438$		0			0
$439$	−3.13427	−	5.42872i	−0.149591	−	0.259099i	0.781485	−	0.623923i	$-0.214462\pi$
$439$	−3.13427	−	5.42872i	−0.149591	−	0.259099i	−0.931076	+	0.364825i	$0.881129\pi$
$440$		0			0
$441$	9.54701	−	16.5359i	0.454620	−	0.787424i
$442$		0			0
$443$	−16.3447	+	28.3099i	−0.776561	+	1.34504i	0.157352	+	0.987543i	$0.449704\pi$
$443$	−16.3447	+	28.3099i	−0.776561	+	1.34504i	−0.933913	+	0.357500i	$0.883629\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−9.32756	+	16.1558i	−0.441178	+	0.764143i
$448$		0			0
$449$	−23.0822			−1.08932			−0.544659	−	0.838658i	$-0.683341\pi$
$449$	−23.0822			−1.08932			−0.544659	+	0.838658i	$0.683341\pi$
$450$		0			0
$451$	0.448025	+	0.776001i	0.0210967	+	0.0365405i
$452$		0			0
$453$	−1.97713	−	3.42448i	−0.0928935	−	0.160896i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.9166			−0.931661			−0.465830	−	0.884874i	$-0.654244\pi$
$457$	−19.9166			−0.931661			−0.465830	+	0.884874i	$0.654244\pi$
$458$		0			0
$459$	0.471966	+	0.817468i	0.0220295	+	0.0381562i
$460$		0			0
$461$	−21.2586	−	36.8209i	−0.990111	−	1.71492i	−0.616548	−	0.787317i	$-0.711470\pi$
$461$	−21.2586	−	36.8209i	−0.990111	−	1.71492i	−0.373562	−	0.927605i	$-0.621864\pi$
$462$		0			0
$463$	27.2843			1.26801			0.634005	−	0.773329i	$-0.281410\pi$
$463$	27.2843			1.26801			0.634005	+	0.773329i	$0.281410\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−39.5912			−1.83206			−0.916031	−	0.401107i	$-0.868625\pi$
$467$	−39.5912			−1.83206			−0.916031	+	0.401107i	$0.868625\pi$
$468$		0			0
$469$	−1.52146	+	2.63525i	−0.0702547	+	0.121685i
$470$		0			0
$471$	3.22696	−	5.58927i	0.148691	−	0.257540i
$472$		0			0
$473$	7.12022	+	12.3326i	0.327388	+	0.567053i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.35415	+	5.80956i	0.153576	+	0.266001i
$478$		0			0
$479$	13.7954	−	23.8943i	0.630326	−	1.09176i	−0.357159	−	0.934044i	$-0.616255\pi$
$479$	13.7954	−	23.8943i	0.630326	−	1.09176i	0.987485	−	0.157713i	$-0.0504121\pi$
$480$		0			0
$481$	3.42665	−	5.93513i	0.156242	−	0.270618i
$482$		0			0
$483$	−3.38005			−0.153797
$484$		0			0
$485$		0			0
$486$		0			0
$487$	29.9289			1.35621			0.678104	−	0.734966i	$-0.262802\pi$
$487$	29.9289			1.35621			0.678104	+	0.734966i	$0.262802\pi$
$488$		0			0
$489$	24.0757	+	41.7004i	1.08874	+	1.88576i
$490$		0			0
$491$	−7.23550	−	12.5323i	−0.326534	−	0.565573i	0.655288	−	0.755379i	$-0.272547\pi$
$491$	−7.23550	−	12.5323i	−0.326534	−	0.565573i	−0.981822	+	0.189806i	$0.939214\pi$
$492$		0			0
$493$	8.49996			0.382819
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.96433	−	3.40232i	−0.0881122	−	0.152615i
$498$		0			0
$499$	9.06799	+	15.7062i	0.405939	+	0.703107i	0.994430	−	0.105396i	$-0.0336111\pi$
$499$	9.06799	+	15.7062i	0.405939	+	0.703107i	−0.588491	+	0.808504i	$0.700278\pi$
$500$		0			0
$501$	0.218111			0.00974449
$502$		0			0
$503$	8.48833	−	14.7022i	0.378476	−	0.655539i	−0.612365	−	0.790575i	$-0.709782\pi$
$503$	8.48833	−	14.7022i	0.378476	−	0.655539i	0.990841	+	0.135036i	$0.0431150\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.35046	−	16.1955i	0.415269	−	0.719266i
$508$		0			0
$509$	16.6888	−	28.9058i	0.739717	−	1.28123i	−0.212906	−	0.977073i	$-0.568293\pi$
$509$	16.6888	−	28.9058i	0.739717	−	1.28123i	0.952623	−	0.304155i	$-0.0983739\pi$
$510$		0			0
$511$	1.86382	+	3.22824i	0.0824507	+	0.142809i
$512$		0			0
$513$	−0.911684	−	0.243153i	−0.0402518	−	0.0107355i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−5.94765	+	10.3016i	−0.261577	+	0.453065i
$518$		0			0
$519$	−19.2473	+	33.3372i	−0.844861	+	1.46334i
$520$		0			0
$521$	1.09359			0.0479110			0.0239555	−	0.999713i	$-0.492374\pi$
$521$	1.09359			0.0479110			0.0239555	+	0.999713i	$0.492374\pi$
$522$		0			0
$523$	−2.02994	+	3.51597i	−0.0887633	+	0.153742i	−0.906989	−	0.421155i	$-0.861625\pi$
$523$	−2.02994	+	3.51597i	−0.0887633	+	0.153742i	0.818225	+	0.574898i	$0.194958\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.7682	+	35.9715i	0.904676	+	1.56695i
$528$		0			0
$529$	9.30690	+	16.1200i	0.404648	+	0.700871i
$530$		0			0
$531$	22.6216			0.981694
$532$		0			0
$533$	−1.14117			−0.0494295
$534$		0			0
$535$		0			0
$536$		0			0
$537$	16.4171	+	28.4352i	0.708450	+	1.22707i
$538$		0			0
$539$	11.8662			0.511114
$540$		0			0
$541$	−6.65097	+	11.5198i	−0.285947	+	0.495275i	−0.972838	−	0.231485i	$-0.925642\pi$
$541$	−6.65097	+	11.5198i	−0.285947	+	0.495275i	0.686891	+	0.726760i	$0.258975\pi$
$542$		0			0
$543$	−23.2715			−0.998675
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.1362	+	29.6808i	−0.732692	+	1.26906i	0.223036	+	0.974810i	$0.428403\pi$
$547$	−17.1362	+	29.6808i	−0.732692	+	1.26906i	−0.955729	+	0.294250i	$0.904930\pi$
$548$		0			0
$549$	−15.6034	−	27.0258i	−0.665936	−	1.15343i
$550$		0			0
$551$	−6.00100	+	6.01493i	−0.255651	+	0.256244i
$552$		0			0
$553$	1.99019	+	3.44712i	0.0846316	+	0.146586i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.3255	+	35.2047i	−0.861217	+	1.49167i	0.00953795	+	0.999955i	$0.496964\pi$
$557$	−20.3255	+	35.2047i	−0.861217	+	1.49167i	−0.870755	+	0.491717i	$0.836369\pi$
$558$		0			0
$559$	−18.1360			−0.767071
$560$		0			0
$561$	9.58963	−	16.6097i	0.404874	−	0.701263i
$562$		0			0
$563$	20.7137			0.872980			0.436490	−	0.899709i	$-0.356221\pi$
$563$	20.7137			0.872980			0.436490	+	0.899709i	$0.356221\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.07321	+	5.32295i	0.129063	+	0.223543i
$568$		0			0
$569$	34.0551			1.42766			0.713831	−	0.700318i	$-0.246958\pi$
$569$	34.0551			1.42766			0.713831	+	0.700318i	$0.246958\pi$
$570$		0			0
$571$	18.5413			0.775929			0.387965	−	0.921674i	$-0.373178\pi$
$571$	18.5413			0.775929			0.387965	+	0.921674i	$0.373178\pi$
$572$		0			0
$573$	−32.7015	−	56.6406i	−1.36612	−	2.36620i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.96818			0.123567			0.0617834	−	0.998090i	$-0.480321\pi$
$577$	2.96818			0.123567			0.0617834	+	0.998090i	$0.480321\pi$
$578$		0			0
$579$	−27.7496	+	48.0638i	−1.15324	+	1.99746i
$580$		0			0
$581$	−4.11627			−0.170772
$582$		0			0
$583$	−2.08448	+	3.61042i	−0.0863302	+	0.149528i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.0138	+	32.9328i	0.784781	+	1.35928i	0.929130	+	0.369754i	$0.120558\pi$
$587$	19.0138	+	32.9328i	0.784781	+	1.35928i	−0.144348	+	0.989527i	$0.546108\pi$
$588$		0			0
$589$	−40.1174	−	10.6996i	−1.65301	−	0.440869i
$590$		0			0
$591$	−12.6634	−	21.9336i	−0.520901	−	0.902227i
$592$		0			0
$593$	21.9428	−	38.0060i	0.901081	−	1.56072i	0.0749876	−	0.997184i	$-0.476108\pi$
$593$	21.9428	−	38.0060i	0.901081	−	1.56072i	0.826093	−	0.563533i	$-0.190558\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.80287			0.155641
$598$		0			0
$599$	17.4883	−	30.2906i	0.714552	−	1.23764i	−0.248581	−	0.968611i	$-0.579964\pi$
$599$	17.4883	−	30.2906i	0.714552	−	1.23764i	0.963132	−	0.269029i	$-0.0867026\pi$
$600$		0			0
$601$	31.9988			1.30526			0.652630	−	0.757677i	$-0.273666\pi$
$601$	31.9988			1.30526			0.652630	+	0.757677i	$0.273666\pi$
$602$		0			0
$603$	−6.67190	−	11.5561i	−0.271701	−	0.470599i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	2.10357			0.0853814			0.0426907	−	0.999088i	$-0.486407\pi$
$607$	2.10357			0.0853814			0.0426907	+	0.999088i	$0.486407\pi$
$608$		0			0
$609$	3.14589			0.127478
$610$		0			0
$611$	−7.57467	−	13.1197i	−0.306438	−	0.530767i
$612$		0			0
$613$	17.4127	+	30.1598i	0.703294	+	1.21814i	0.967304	+	0.253621i	$0.0816216\pi$
$613$	17.4127	+	30.1598i	0.703294	+	1.21814i	−0.264010	+	0.964520i	$0.585045\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.16726	−	15.8782i	0.369060	−	0.639231i	−0.620359	−	0.784318i	$-0.713013\pi$
$617$	9.16726	−	15.8782i	0.369060	−	0.639231i	0.989419	+	0.145087i	$0.0463463\pi$
$618$		0			0
$619$	32.4325			1.30357			0.651786	−	0.758403i	$-0.274020\pi$
$619$	32.4325			1.30357			0.651786	+	0.758403i	$0.274020\pi$
$620$		0			0
$621$	−0.226675	+	0.392612i	−0.00909615	+	0.0157550i
$622$		0			0
$623$	4.41458	−	7.64628i	0.176866	−	0.306342i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	4.98342	+	18.5125i	0.199019	+	0.739319i
$628$		0			0
$629$	−6.48562	−	11.2334i	−0.258598	−	0.447906i
$630$		0			0
$631$	−7.25551	+	12.5669i	−0.288837	+	0.500281i	−0.973532	−	0.228549i	$-0.926602\pi$
$631$	−7.25551	+	12.5669i	−0.288837	+	0.500281i	0.684695	+	0.728830i	$0.259935\pi$
$632$		0			0
$633$	−25.3464	+	43.9012i	−1.00743	+	1.74492i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−7.55614	+	13.0876i	−0.299385	+	0.518550i
$638$		0			0
$639$	17.2279			0.681525
$640$		0			0
$641$	13.8849	+	24.0494i	0.548421	+	0.949892i	0.998383	+	0.0568449i	$0.0181041\pi$
$641$	13.8849	+	24.0494i	0.548421	+	0.949892i	−0.449962	+	0.893048i	$0.648563\pi$
$642$		0			0
$643$	5.61539	+	9.72615i	0.221450	+	0.383562i	0.955248	−	0.295805i	$-0.0955879\pi$
$643$	5.61539	+	9.72615i	0.221450	+	0.383562i	−0.733799	+	0.679367i	$0.762255\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.00223			0.0787157			0.0393578	−	0.999225i	$-0.487469\pi$
$647$	2.00223			0.0787157			0.0393578	+	0.999225i	$0.487469\pi$
$648$		0			0
$649$	7.02923	+	12.1750i	0.275921	+	0.477910i
$650$		0			0
$651$	7.68645	+	13.3133i	0.301256	+	0.521790i
$652$		0			0
$653$	−3.23945			−0.126770			−0.0633848	−	0.997989i	$-0.520190\pi$
$653$	−3.23945			−0.126770			−0.0633848	+	0.997989i	$0.520190\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−16.3464			−0.637734
$658$		0			0
$659$	3.14745	−	5.45154i	0.122607	−	0.212362i	−0.798188	−	0.602409i	$-0.794208\pi$
$659$	3.14745	−	5.45154i	0.122607	−	0.212362i	0.920795	+	0.390047i	$0.127541\pi$
$660$		0			0
$661$	−0.196536	+	0.340410i	−0.00764435	+	0.0132404i	−0.869822	−	0.493365i	$-0.835767\pi$
$661$	−0.196536	+	0.340410i	−0.00764435	+	0.0132404i	0.862178	+	0.506606i	$0.169100\pi$
$662$		0			0
$663$	12.2129	+	21.1534i	0.474311	+	0.821530i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.04117	+	3.53542i	0.0790346	+	0.136892i
$668$		0			0
$669$	−27.4381	+	47.5242i	−1.06082	+	1.83739i
$670$		0			0
$671$	9.69690	−	16.7955i	0.374345	−	0.648384i
$672$		0			0
$673$	−43.1041			−1.66154			−0.830770	−	0.556616i	$-0.812100\pi$
$673$	−43.1041			−1.66154			−0.830770	+	0.556616i	$0.812100\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.3727			−0.475522			−0.237761	−	0.971324i	$-0.576413\pi$
$677$	−12.3727			−0.475522			−0.237761	+	0.971324i	$0.576413\pi$
$678$		0			0
$679$	3.37532	+	5.84622i	0.129533	+	0.224357i
$680$		0			0
$681$	13.8808	+	24.0422i	0.531913	+	0.921300i
$682$		0			0
$683$	32.8415			1.25664			0.628322	−	0.777954i	$-0.283742\pi$
$683$	32.8415			1.25664			0.628322	+	0.777954i	$0.283742\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	19.2356	+	33.3171i	0.733885	+	1.27113i
$688$		0			0
$689$	−2.65470	−	4.59807i	−0.101136	−	0.175172i
$690$		0			0
$691$	−16.6704			−0.634171			−0.317085	−	0.948397i	$-0.602704\pi$
$691$	−16.6704			−0.634171			−0.317085	+	0.948397i	$0.602704\pi$
$692$		0			0
$693$	1.74786	−	3.02739i	0.0663959	−	0.115001i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.07995	+	1.87052i	−0.0409059	+	0.0708510i
$698$		0			0
$699$	16.3699	−	28.3536i	0.619168	−	1.07243i
$700$		0			0
$701$	−15.9399	−	27.6087i	−0.602041	−	1.04277i	−0.992512	−	0.122151i	$-0.961021\pi$
$701$	−15.9399	−	27.6087i	−0.602041	−	1.04277i	0.390470	−	0.920616i	$-0.372312\pi$
$702$		0			0
$703$	12.5281	+	3.34134i	0.472506	+	0.126021i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.97047	+	8.60911i	−0.186934	+	0.323779i
$708$		0			0
$709$	2.99202	−	5.18233i	0.112368	−	0.194626i	−0.804357	−	0.594147i	$-0.797490\pi$
$709$	2.99202	−	5.18233i	0.112368	−	0.194626i	0.916724	+	0.399520i	$0.130823\pi$
$710$		0			0
$711$	−17.4547			−0.654603
$712$		0			0
$713$	−9.97451	+	17.2764i	−0.373548	+	0.647004i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−24.0009	−	41.5708i	−0.896331	−	1.55249i
$718$		0			0
$719$	0.345920	+	0.599151i	0.0129006	+	0.0223446i	0.872404	−	0.488786i	$-0.162560\pi$
$719$	0.345920	+	0.599151i	0.0129006	+	0.0223446i	−0.859503	+	0.511131i	$0.829227\pi$
$720$		0			0
$721$	−12.0484			−0.448706
$722$		0			0
$723$	−13.1187			−0.487889
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−11.0511	−	19.1410i	−0.409862	−	0.709902i	0.585012	−	0.811025i	$-0.301090\pi$
$727$	−11.0511	−	19.1410i	−0.409862	−	0.709902i	−0.994874	+	0.101123i	$0.967756\pi$
$728$		0			0
$729$	−25.3743			−0.939789
$730$		0			0
$731$	−17.1630	+	29.7272i	−0.634796	+	1.09950i
$732$		0			0
$733$	19.0945			0.705271			0.352635	−	0.935761i	$-0.385286\pi$
$733$	19.0945			0.705271			0.352635	+	0.935761i	$0.385286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.14633	−	7.18165i	0.152732	−	0.264540i
$738$		0			0
$739$	−6.05045	−	10.4797i	−0.222569	−	0.385501i	0.733018	−	0.680209i	$-0.238111\pi$
$739$	−6.05045	−	10.4797i	−0.222569	−	0.385501i	−0.955587	+	0.294708i	$0.904778\pi$
$740$		0			0
$741$	−23.5914	−	6.29200i	−0.866652	−	0.231142i
$742$		0			0
$743$	−7.89364	−	13.6722i	−0.289590	−	0.501584i	0.684122	−	0.729368i	$-0.260186\pi$
$743$	−7.89364	−	13.6722i	−0.289590	−	0.501584i	−0.973712	+	0.227783i	$0.926852\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	9.02531	−	15.6323i	0.330219	−	0.571956i
$748$		0			0
$749$	−9.27341			−0.338843
$750$		0			0
$751$	−17.5848	+	30.4578i	−0.641678	+	1.11142i	0.343380	+	0.939197i	$0.388428\pi$
$751$	−17.5848	+	30.4578i	−0.641678	+	1.11142i	−0.985058	+	0.172223i	$0.944905\pi$
$752$		0			0
$753$	−8.68664			−0.316559
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.35917	−	12.7465i	−0.267473	−	0.463278i	0.700735	−	0.713421i	$-0.252855\pi$
$757$	−7.35917	−	12.7465i	−0.267473	−	0.463278i	−0.968209	+	0.250144i	$0.919522\pi$
$758$		0			0
$759$	9.21138			0.334352
$760$		0			0
$761$	−39.9486			−1.44814			−0.724068	−	0.689728i	$-0.757730\pi$
$761$	−39.9486			−1.44814			−0.724068	+	0.689728i	$0.757730\pi$
$762$		0			0
$763$	6.11074	+	10.5841i	0.221224	+	0.383170i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.9042			−0.646485
$768$		0			0
$769$	−24.9729	+	43.2544i	−0.900547	+	1.55979i	−0.0737605	+	0.997276i	$0.523500\pi$
$769$	−24.9729	+	43.2544i	−0.900547	+	1.55979i	−0.826786	+	0.562516i	$0.809833\pi$
$770$		0			0
$771$	−45.0583			−1.62273
$772$		0			0
$773$	−11.6269	+	20.1384i	−0.418190	+	0.724327i	−0.995757	−	0.0920165i	$-0.970669\pi$
$773$	−11.6269	+	20.1384i	−0.418190	+	0.724327i	0.577567	+	0.816343i	$0.304002\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.40037	−	4.15757i	−0.0861129	−	0.149152i
$778$		0			0
$779$	−0.561213	−	2.08481i	−0.0201075	−	0.0746960i
$780$		0			0
$781$	5.35324	+	9.27208i	0.191554	+	0.331781i
$782$		0			0
$783$	0.210972	−	0.365414i	0.00753952	−	0.0130588i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−19.5711			−0.697636			−0.348818	−	0.937191i	$-0.613417\pi$
$787$	−19.5711			−0.697636			−0.348818	+	0.937191i	$0.613417\pi$
$788$		0			0
$789$	13.0628	−	22.6254i	0.465048	−	0.805486i
$790$		0			0
$791$	7.23201			0.257141
$792$		0			0
$793$	12.3495	+	21.3900i	0.438545	+	0.759582i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	47.6782			1.68885			0.844424	−	0.535676i	$-0.179943\pi$
$797$	47.6782			1.68885			0.844424	+	0.535676i	$0.179943\pi$
$798$		0			0
$799$	−28.6732			−1.01438
$800$		0			0
$801$	19.3587	+	33.5303i	0.684007	+	1.18474i
$802$		0			0
$803$	−5.07933	−	8.79767i	−0.179246	−	0.310463i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.7097	−	25.4780i	0.517806	−	0.896867i
$808$		0			0
$809$	−24.4485			−0.859565			−0.429782	−	0.902933i	$-0.641410\pi$
$809$	−24.4485			−0.859565			−0.429782	+	0.902933i	$0.641410\pi$
$810$		0			0
$811$	5.38004	−	9.31850i	0.188919	−	0.327217i	−0.755971	−	0.654605i	$-0.772835\pi$
$811$	5.38004	−	9.31850i	0.188919	−	0.327217i	0.944890	+	0.327388i	$0.106168\pi$
$812$		0			0
$813$	22.7193	−	39.3510i	0.796802	−	1.38010i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−8.91906	−	33.1327i	−0.312038	−	1.15917i
$818$		0			0
$819$	2.22600	+	3.85555i	0.0777828	+	0.134724i
$820$		0			0
$821$	3.60434	−	6.24289i	0.125792	−	0.217879i	−0.796250	−	0.604968i	$-0.793186\pi$
$821$	3.60434	−	6.24289i	0.125792	−	0.217879i	0.922042	+	0.387089i	$0.126519\pi$
$822$		0			0
$823$	3.87075	−	6.70433i	0.134926	−	0.233698i	−0.790643	−	0.612277i	$-0.790254\pi$
$823$	3.87075	−	6.70433i	0.134926	−	0.233698i	0.925569	+	0.378579i	$0.123587\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.3140	−	23.0605i	0.462972	−	0.801891i	−0.536136	−	0.844132i	$-0.680116\pi$
$827$	13.3140	−	23.0605i	0.462972	−	0.801891i	0.999107	+	0.0422411i	$0.0134498\pi$
$828$		0			0
$829$	−12.1093			−0.420572			−0.210286	−	0.977640i	$-0.567439\pi$
$829$	−12.1093			−0.420572			−0.210286	+	0.977640i	$0.567439\pi$
$830$		0			0
$831$	−7.23201	−	12.5262i	−0.250876	−	0.434530i
$832$		0			0
$833$	14.3015	+	24.7709i	0.495518	+	0.858262i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.06189			0.0712695
$838$		0			0
$839$	1.20591	+	2.08869i	0.0416325	+	0.0721096i	0.886091	−	0.463512i	$-0.153411\pi$
$839$	1.20591	+	2.08869i	0.0416325	+	0.0721096i	−0.844458	+	0.535621i	$0.820077\pi$
$840$		0			0
$841$	12.6002	+	21.8242i	0.434491	+	0.752560i
$842$		0			0
$843$	−42.7386			−1.47199
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.12954			−0.176253
$848$		0			0
$849$	38.1843	−	66.1371i	1.31048	−	2.26982i
$850$		0			0
$851$	3.11490	−	5.39517i	0.106777	−	0.184944i
$852$		0			0
$853$	13.8401	+	23.9717i	0.473875	+	0.820775i	0.999553	−	0.0299085i	$-0.00952159\pi$
$853$	13.8401	+	23.9717i	0.473875	+	0.820775i	−0.525678	+	0.850684i	$0.676188\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.20245	−	14.2071i	−0.280190	−	0.485304i	0.691241	−	0.722624i	$-0.257064\pi$
$857$	−8.20245	−	14.2071i	−0.280190	−	0.485304i	−0.971431	+	0.237320i	$0.923731\pi$
$858$		0			0
$859$	17.4715	−	30.2616i	0.596121	−	1.03251i	−0.397267	−	0.917703i	$-0.630041\pi$
$859$	17.4715	−	30.2616i	0.596121	−	1.03251i	0.993388	−	0.114808i	$-0.0366254\pi$
$860$		0			0
$861$	−0.399695	+	0.692293i	−0.0136216	+	0.0235933i
$862$		0			0
$863$	−18.6243			−0.633979			−0.316990	−	0.948429i	$-0.602672\pi$
$863$	−18.6243			−0.633979			−0.316990	+	0.948429i	$0.602672\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.89962			0.166400
$868$		0			0
$869$	−5.42372	−	9.39416i	−0.183987	−	0.318675i
$870$		0			0
$871$	5.28058	+	9.14624i	0.178926	+	0.309908i
$872$		0			0
$873$	−29.6028			−1.00190
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.1893	−	26.3087i	−0.512907	−	0.888381i	−0.999888	−	0.0149683i	$-0.995235\pi$
$877$	−15.1893	−	26.3087i	−0.512907	−	0.888381i	0.486981	−	0.873413i	$-0.338098\pi$
$878$		0			0
$879$	34.2119	+	59.2567i	1.15394	+	1.99868i
$880$		0			0
$881$	−26.3772			−0.888670			−0.444335	−	0.895861i	$-0.646560\pi$
$881$	−26.3772			−0.888670			−0.444335	+	0.895861i	$0.646560\pi$
$882$		0			0
$883$	14.5598	−	25.2183i	0.489977	−	0.848664i	−0.509957	−	0.860200i	$-0.670339\pi$
$883$	14.5598	−	25.2183i	0.489977	−	0.848664i	0.999933	+	0.0115356i	$0.00367198\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.0100	−	17.3379i	0.336104	−	0.582148i	−0.647593	−	0.761987i	$-0.724224\pi$
$887$	10.0100	−	17.3379i	0.336104	−	0.582148i	0.983696	+	0.179838i	$0.0575574\pi$
$888$		0			0
$889$	1.09704	−	1.90012i	0.0367935	−	0.0637281i
$890$		0			0
$891$	−8.37517	−	14.5062i	−0.280579	−	0.485977i
$892$		0			0
$893$	20.2433	−	20.2903i	0.677418	−	0.678990i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−5.86560	+	10.1595i	−0.195847	+	0.339217i
$898$		0			0
$899$	9.28352	−	16.0795i	0.309623	−	0.536283i
$900$		0			0
$901$	−10.0491			−0.334784
$902$		0			0
$903$	−6.35215	+	11.0022i	−0.211386	+	0.366132i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.75370	−	6.50159i	−0.124639	−	0.215882i	0.796952	−	0.604042i	$-0.206444\pi$
$907$	−3.75370	−	6.50159i	−0.124639	−	0.215882i	−0.921592	+	0.388160i	$0.873111\pi$
$908$		0			0
$909$	−21.7964	−	37.7525i	−0.722942	−	1.25217i
$910$		0			0
$911$	38.3882			1.27186			0.635929	−	0.771748i	$-0.280617\pi$
$911$	38.3882			1.27186			0.635929	+	0.771748i	$0.280617\pi$
$912$		0			0
$913$	11.2178			0.371254
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.429243	−	0.743471i	−0.0141749	−	0.0245516i
$918$		0			0
$919$	−37.8811			−1.24958			−0.624791	−	0.780792i	$-0.714816\pi$
$919$	−37.8811			−1.24958			−0.624791	+	0.780792i	$0.714816\pi$
$920$		0			0
$921$	−32.7883	+	56.7910i	−1.08041	+	1.87133i
$922$		0			0
$923$	−13.6353			−0.448811
$924$		0			0
$925$		0			0
$926$		0			0
$927$	26.4172	−	45.7560i	0.867655	−	1.50282i
$928$		0			0
$929$	5.96821	+	10.3372i	0.195811	+	0.339154i	0.947166	−	0.320744i	$-0.103933\pi$
$929$	5.96821	+	10.3372i	0.195811	+	0.339154i	−0.751355	+	0.659898i	$0.770600\pi$
$930$		0			0
$931$	−27.6258	−	7.36802i	−0.905401	−	0.241477i
$932$		0			0
$933$	6.07473	+	10.5217i	0.198878	+	0.344466i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	6.77228	−	11.7299i	0.221241	−	0.383200i	−0.733944	−	0.679210i	$-0.762323\pi$
$937$	6.77228	−	11.7299i	0.221241	−	0.383200i	0.955185	+	0.296010i	$0.0956561\pi$
$938$		0			0
$939$	−63.5824			−2.07493
$940$		0			0
$941$	−7.04614	+	12.2043i	−0.229698	+	0.397848i	−0.957718	−	0.287707i	$-0.907107\pi$
$941$	−7.04614	+	12.2043i	−0.229698	+	0.397848i	0.728021	+	0.685555i	$0.240440\pi$
$942$		0			0
$943$	−1.03735			−0.0337807
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.53567	+	9.58806i	0.179885	+	0.311570i	0.941841	−	0.336059i	$-0.109094\pi$
$947$	5.53567	+	9.58806i	0.179885	+	0.311570i	−0.761956	+	0.647629i	$0.775761\pi$
$948$		0			0
$949$	12.9376			0.419973
$950$		0			0
$951$	−63.2539			−2.05115
$952$		0			0
$953$	−3.69507	−	6.40004i	−0.119695	−	0.207318i	0.799952	−	0.600064i	$-0.204858\pi$
$953$	−3.69507	−	6.40004i	−0.119695	−	0.207318i	−0.919647	+	0.392747i	$0.871525\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−8.57326			−0.277134
$958$		0			0
$959$	−4.84534	+	8.39238i	−0.156464	+	0.271004i
$960$		0			0
$961$	59.7307			1.92680
$962$		0			0
$963$	20.3328	−	35.2174i	0.655215	−	1.13487i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.760861	+	1.31785i	0.0244676	+	0.0423792i	0.878000	−	0.478661i	$-0.158878\pi$
$967$	0.760861	+	1.31785i	0.0244676	+	0.0423792i	−0.853532	+	0.521040i	$0.825544\pi$
$968$		0			0
$969$	−32.6391	+	32.7149i	−1.04852	+	1.05095i
$970$		0			0
$971$	27.2897	+	47.2671i	0.875768	+	1.51687i	0.855942	+	0.517071i	$0.172978\pi$
$971$	27.2897	+	47.2671i	0.875768	+	1.51687i	0.0198254	+	0.999803i	$0.493689\pi$
$972$		0			0
$973$	1.24741	−	2.16058i	0.0399902	−	0.0692651i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.0130			0.416321			0.208161	−	0.978095i	$-0.433252\pi$
$977$	13.0130			0.416321			0.208161	+	0.978095i	$0.433252\pi$
$978$		0			0
$979$	−12.0307	+	20.8378i	−0.384503	+	0.665979i
$980$		0			0
$981$	−53.5934			−1.71111
$982$		0			0
$983$	10.1709	+	17.6166i	0.324402	+	0.561882i	0.981391	−	0.192019i	$-0.0615034\pi$
$983$	10.1709	+	17.6166i	0.324402	+	0.561882i	−0.656989	+	0.753900i	$0.728170\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.6121			−0.337788
$988$		0			0
$989$	−16.4860			−0.524225
$990$		0			0
$991$	−16.9449	−	29.3495i	−0.538274	−	0.932318i	−0.998997	−	0.0447741i	$-0.985743\pi$
$991$	−16.9449	−	29.3495i	−0.538274	−	0.932318i	0.460723	−	0.887544i	$-0.347590\pi$
$992$		0			0
$993$	−9.69341	−	16.7895i	−0.307611	−	0.532798i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.76185	+	3.05162i	−0.0557985	+	0.0966458i	−0.892575	−	0.450898i	$-0.851104\pi$
$997$	−1.76185	+	3.05162i	−0.0557985	+	0.0966458i	0.836777	+	0.547544i	$0.184437\pi$
$998$		0			0
$999$	−0.643901			−0.0203721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.g.501.2		20
5.2	odd	4		380.2.r.a.349.2	yes	20
5.3	odd	4		380.2.r.a.349.9	yes	20
5.4	even	2	inner	1900.2.i.g.501.9		20
15.2	even	4		3420.2.bj.c.2629.7		20
15.8	even	4		3420.2.bj.c.2629.1		20
19.11	even	3	inner	1900.2.i.g.201.2		20
95.49	even	6	inner	1900.2.i.g.201.9		20
95.68	odd	12		380.2.r.a.49.2	✓	20
95.87	odd	12		380.2.r.a.49.9	yes	20
285.68	even	12		3420.2.bj.c.1189.7		20
285.182	even	12		3420.2.bj.c.1189.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.2	✓	20	95.68	odd	12
380.2.r.a.49.9	yes	20	95.87	odd	12
380.2.r.a.349.2	yes	20	5.2	odd	4
380.2.r.a.349.9	yes	20	5.3	odd	4
1900.2.i.g.201.2		20	19.11	even	3	inner
1900.2.i.g.201.9		20	95.49	even	6	inner
1900.2.i.g.501.2		20	1.1	even	1	trivial
1900.2.i.g.501.9		20	5.4	even	2	inner
3420.2.bj.c.1189.1		20	285.182	even	12
3420.2.bj.c.1189.7		20	285.68	even	12
3420.2.bj.c.2629.1		20	15.8	even	4
3420.2.bj.c.2629.7		20	15.2	even	4

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.21562 - 2.10552i) q^{3} +0.663818 q^{7} +(-1.45548 + 2.52097i) q^{9} -1.80905 q^{11} +(1.15197 - 1.99526i) q^{13} +(-2.18033 - 3.77643i) q^{17} +(4.21168 + 1.12329i) q^{19} +(-0.806953 - 1.39768i) q^{21} +(1.04716 - 1.81374i) q^{23} -0.216466 q^{27} +(-0.974621 + 1.68809i) q^{29} -9.52527 q^{31} +(2.19913 + 3.80900i) q^{33} +2.97461 q^{37} -5.60143 q^{39} +(-0.247657 - 0.428954i) q^{41} +(-3.93588 - 6.81715i) q^{43} +(3.28772 - 5.69449i) q^{47} -6.55935 q^{49} +(-5.30091 + 9.18145i) q^{51} +(1.15225 - 1.99575i) q^{53} +(-2.75471 - 10.2333i) q^{57} +(-3.88559 - 6.73003i) q^{59} +(-5.36021 + 9.28415i) q^{61} +(-0.966176 + 1.67347i) q^{63} +(-2.29199 + 3.96984i) q^{67} -5.09182 q^{69} +(-2.95914 - 5.12538i) q^{71} +(2.80773 + 4.86313i) q^{73} -1.20088 q^{77} +(2.99810 + 5.19286i) q^{79} +(4.62959 + 8.01868i) q^{81} -6.20090 q^{83} +4.73909 q^{87} +(6.65028 - 11.5186i) q^{89} +(0.764696 - 1.32449i) q^{91} +(11.5791 + 20.0557i) q^{93} +(5.08470 + 8.80695i) q^{97} +(2.63305 - 4.56057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

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Representations

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Database

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