LMFDB - Embedded newform 1900.2.i.g.501.4

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			501.4
Root			$0.628167 - 1.08802i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.g.201.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.628167 - 1.08802i) q^{3} -4.97100 q^{7} +(0.710812 - 1.23116i) q^{9} +O(q^{10})$	$q+(-0.628167 - 1.08802i) q^{3} -4.97100 q^{7} +(0.710812 - 1.23116i) q^{9} -3.85491 q^{11} +(1.33470 - 2.31178i) q^{13} +(-1.29521 - 2.24337i) q^{17} +(-1.24479 + 4.17738i) q^{19} +(3.12262 + 5.40854i) q^{21} +(1.08682 - 1.88243i) q^{23} -5.55504 q^{27} +(-1.29432 + 2.24183i) q^{29} +7.76610 q^{31} +(2.42153 + 4.19421i) q^{33} +2.75768 q^{37} -3.35367 q^{39} +(3.66243 + 6.34351i) q^{41} +(-0.895083 - 1.55033i) q^{43} +(-0.854141 + 1.47942i) q^{47} +17.7109 q^{49} +(-1.62722 + 2.81842i) q^{51} +(-3.98220 + 6.89738i) q^{53} +(5.32700 - 1.26974i) q^{57} +(0.127300 + 0.220490i) q^{59} +(-1.66702 + 2.88737i) q^{61} +(-3.53345 + 6.12011i) q^{63} +(-6.60237 + 11.4356i) q^{67} -2.73082 q^{69} +(3.85760 + 6.68156i) q^{71} +(2.25489 + 3.90558i) q^{73} +19.1628 q^{77} +(-5.52715 - 9.57330i) q^{79} +(1.35706 + 2.35050i) q^{81} +3.04360 q^{83} +3.25221 q^{87} +(-4.76212 + 8.24824i) q^{89} +(-6.63482 + 11.4918i) q^{91} +(-4.87841 - 8.44966i) q^{93} +(-5.61676 - 9.72851i) q^{97} +(-2.74011 + 4.74601i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

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

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
$3$	−0.628167	−	1.08802i	−0.362673	−	0.628167i	0.625727	−	0.780042i	$-0.284802\pi$
$3$	−0.628167	−	1.08802i	−0.362673	−	0.628167i	−0.988400	+	0.151875i	$0.951469\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.97100			−1.87886			−0.939432	−	0.342736i	$-0.888646\pi$
$7$	−4.97100			−1.87886			−0.939432	+	0.342736i	$0.888646\pi$
$8$		0			0
$9$	0.710812	−	1.23116i	0.236937	−	0.410387i
$10$		0			0
$11$	−3.85491			−1.16230			−0.581149	−	0.813797i	$-0.697397\pi$
$11$	−3.85491			−1.16230			−0.581149	+	0.813797i	$0.697397\pi$
$12$		0			0
$13$	1.33470	−	2.31178i	0.370180	−	0.641171i	−0.619413	−	0.785066i	$-0.712629\pi$
$13$	1.33470	−	2.31178i	0.370180	−	0.641171i	0.989593	+	0.143894i	$0.0459625\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.29521	−	2.24337i	−0.314135	−	0.544097i	0.665118	−	0.746738i	$-0.268381\pi$
$17$	−1.29521	−	2.24337i	−0.314135	−	0.544097i	−0.979253	+	0.202641i	$0.935048\pi$
$18$		0			0
$19$	−1.24479	+	4.17738i	−0.285574	+	0.958357i
$19$	−1.24479	+	4.17738i	−0.285574	+	0.958357i
$20$		0			0
$21$	3.12262	+	5.40854i	0.681412	+	1.18024i
$22$		0			0
$23$	1.08682	−	1.88243i	0.226618	−	0.392514i	−0.730186	−	0.683249i	$-0.760566\pi$
$23$	1.08682	−	1.88243i	0.226618	−	0.392514i	0.956804	+	0.290735i	$0.0938998\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.55504			−1.06907
$28$		0			0
$29$	−1.29432	+	2.24183i	−0.240350	+	0.416298i	−0.960814	−	0.277194i	$-0.910595\pi$
$29$	−1.29432	+	2.24183i	−0.240350	+	0.416298i	0.720464	+	0.693492i	$0.243929\pi$
$30$		0			0
$31$	7.76610			1.39483			0.697417	−	0.716666i	$-0.254333\pi$
$31$	7.76610			1.39483			0.697417	+	0.716666i	$0.254333\pi$
$32$		0			0
$33$	2.42153	+	4.19421i	0.421533	+	0.730117i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.75768			0.453359			0.226680	−	0.973969i	$-0.427213\pi$
$37$	2.75768			0.453359			0.226680	+	0.973969i	$0.427213\pi$
$38$		0			0
$39$	−3.35367			−0.537017
$40$		0			0
$41$	3.66243	+	6.34351i	0.571975	+	0.990690i	0.996363	+	0.0852097i	$0.0271560\pi$
$41$	3.66243	+	6.34351i	0.571975	+	0.990690i	−0.424388	+	0.905481i	$0.639511\pi$
$42$		0			0
$43$	−0.895083	−	1.55033i	−0.136499	−	0.236423i	0.789670	−	0.613532i	$-0.210252\pi$
$43$	−0.895083	−	1.55033i	−0.136499	−	0.236423i	−0.926169	+	0.377109i	$0.876918\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.854141	+	1.47942i	−0.124589	+	0.215795i	−0.921572	−	0.388207i	$-0.873095\pi$
$47$	−0.854141	+	1.47942i	−0.124589	+	0.215795i	0.796983	+	0.604002i	$0.206428\pi$
$48$		0			0
$49$	17.7109			2.53013
$50$		0			0
$51$	−1.62722	+	2.81842i	−0.227856	+	0.394658i
$52$		0			0
$53$	−3.98220	+	6.89738i	−0.546998	+	0.947428i	0.451480	+	0.892281i	$0.350896\pi$
$53$	−3.98220	+	6.89738i	−0.546998	+	0.947428i	−0.998478	+	0.0551469i	$0.982437\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.32700	−	1.26974i	0.705578	−	0.168182i
$58$		0			0
$59$	0.127300	+	0.220490i	0.0165730	+	0.0287053i	0.874193	−	0.485579i	$-0.161391\pi$
$59$	0.127300	+	0.220490i	0.0165730	+	0.0287053i	−0.857620	+	0.514284i	$0.828058\pi$
$60$		0			0
$61$	−1.66702	+	2.88737i	−0.213441	+	0.369690i	−0.952789	−	0.303633i	$-0.901800\pi$
$61$	−1.66702	+	2.88737i	−0.213441	+	0.369690i	0.739349	+	0.673323i	$0.235134\pi$
$62$		0			0
$63$	−3.53345	+	6.12011i	−0.445173	+	0.771062i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.60237	+	11.4356i	−0.806607	+	1.39708i	0.108593	+	0.994086i	$0.465365\pi$
$67$	−6.60237	+	11.4356i	−0.806607	+	1.39708i	−0.915201	+	0.402999i	$0.867968\pi$
$68$		0			0
$69$	−2.73082			−0.328752
$70$		0			0
$71$	3.85760	+	6.68156i	0.457813	+	0.792955i	0.998845	−	0.0480468i	$-0.0152997\pi$
$71$	3.85760	+	6.68156i	0.457813	+	0.792955i	−0.541032	+	0.841002i	$0.681966\pi$
$72$		0			0
$73$	2.25489	+	3.90558i	0.263915	+	0.457114i	0.967279	−	0.253716i	$-0.0816529\pi$
$73$	2.25489	+	3.90558i	0.263915	+	0.457114i	−0.703364	+	0.710830i	$0.748320\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	19.1628			2.18380
$78$		0			0
$79$	−5.52715	−	9.57330i	−0.621852	−	1.07708i	−0.989141	−	0.146973i	$-0.953047\pi$
$79$	−5.52715	−	9.57330i	−0.621852	−	1.07708i	0.367288	−	0.930107i	$-0.380286\pi$
$80$		0			0
$81$	1.35706	+	2.35050i	0.150784	+	0.261166i
$82$		0			0
$83$	3.04360			0.334079			0.167040	−	0.985950i	$-0.446579\pi$
$83$	3.04360			0.334079			0.167040	+	0.985950i	$0.446579\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.25221			0.348673
$88$		0			0
$89$	−4.76212	+	8.24824i	−0.504784	+	0.874311i	0.495201	+	0.868779i	$0.335094\pi$
$89$	−4.76212	+	8.24824i	−0.504784	+	0.874311i	−0.999985	+	0.00553277i	$0.998239\pi$
$90$		0			0
$91$	−6.63482	+	11.4918i	−0.695518	+	1.20467i
$92$		0			0
$93$	−4.87841	−	8.44966i	−0.505868	−	0.876189i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.61676	−	9.72851i	−0.570295	−	0.987780i	−0.996535	−	0.0831703i	$-0.973495\pi$
$97$	−5.61676	−	9.72851i	−0.570295	−	0.987780i	0.426240	−	0.904610i	$-0.359838\pi$
$98$		0			0
$99$	−2.74011	+	4.74601i	−0.275392	+	0.476992i
$100$		0			0
$101$	5.45345	−	9.44564i	0.542638	−	0.939877i	−0.456113	−	0.889922i	$-0.650759\pi$
$101$	5.45345	−	9.44564i	0.542638	−	0.939877i	0.998751	−	0.0499550i	$-0.0159078\pi$
$102$		0			0
$103$	−11.4532			−1.12852			−0.564260	−	0.825597i	$-0.690839\pi$
$103$	−11.4532			−1.12852			−0.564260	+	0.825597i	$0.690839\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	18.3401			1.77300			0.886502	−	0.462725i	$-0.153128\pi$
$107$	18.3401			1.77300			0.886502	+	0.462725i	$0.153128\pi$
$108$		0			0
$109$	6.55467	+	11.3530i	0.627824	+	1.08742i	0.987988	+	0.154533i	$0.0493874\pi$
$109$	6.55467	+	11.3530i	0.627824	+	1.08742i	−0.360164	+	0.932889i	$0.617279\pi$
$110$		0			0
$111$	−1.73228	−	3.00040i	−0.164421	−	0.284785i
$112$		0			0
$113$	−0.696954			−0.0655640			−0.0327820	−	0.999463i	$-0.510437\pi$
$113$	−0.696954			−0.0655640			−0.0327820	+	0.999463i	$0.510437\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.89745	−	3.28647i	−0.175419	−	0.303835i
$118$		0			0
$119$	6.43850	+	11.1518i	0.590216	+	1.02228i
$120$		0			0
$121$	3.86029			0.350936
$122$		0			0
$123$	4.60124	−	7.96957i	0.414879	−	0.718592i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.92636	+	11.9968i	−0.614615	+	1.06454i	0.375837	+	0.926686i	$0.377355\pi$
$127$	−6.92636	+	11.9968i	−0.614615	+	1.06454i	−0.990452	+	0.137859i	$0.955978\pi$
$128$		0			0
$129$	−1.12452	+	1.94773i	−0.0990088	+	0.171488i
$130$		0			0
$131$	6.11533	+	10.5921i	0.534299	+	0.925433i	0.999197	+	0.0400690i	$0.0127578\pi$
$131$	6.11533	+	10.5921i	0.534299	+	0.925433i	−0.464898	+	0.885364i	$0.653909\pi$
$132$		0			0
$133$	6.18785	−	20.7658i	0.536554	−	1.80062i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.59855	−	7.96493i	0.392881	−	0.680490i	−0.599947	−	0.800039i	$-0.704812\pi$
$137$	4.59855	−	7.96493i	0.392881	−	0.680490i	0.992828	+	0.119550i	$0.0381451\pi$
$138$		0			0
$139$	3.22178	−	5.58028i	0.273267	−	0.473313i	−0.696429	−	0.717626i	$-0.745229\pi$
$139$	3.22178	−	5.58028i	0.273267	−	0.473313i	0.969697	+	0.244312i	$0.0785623\pi$
$140$		0			0
$141$	2.14617			0.180741
$142$		0			0
$143$	−5.14516	+	8.91168i	−0.430260	+	0.745232i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.1254	−	19.2698i	−0.917608	−	1.58934i
$148$		0			0
$149$	−11.5381	−	19.9846i	−0.945239	−	1.63720i	−0.755272	−	0.655411i	$-0.772495\pi$
$149$	−11.5381	−	19.9846i	−0.945239	−	1.63720i	−0.189966	−	0.981791i	$-0.560838\pi$
$150$		0			0
$151$	20.1613			1.64071			0.820353	−	0.571858i	$-0.193777\pi$
$151$	20.1613			1.64071			0.820353	+	0.571858i	$0.193777\pi$
$152$		0			0
$153$	−3.68260			−0.297721
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.93532	+	10.2803i	0.473690	+	0.820456i	0.999546	−	0.0301179i	$-0.00958827\pi$
$157$	5.93532	+	10.2803i	0.473690	+	0.820456i	−0.525856	+	0.850574i	$0.676255\pi$
$158$		0			0
$159$	10.0060			0.793524
$160$		0			0
$161$	−5.40259	+	9.35757i	−0.425784	+	0.737480i
$162$		0			0
$163$	13.1763			1.03205			0.516023	−	0.856575i	$-0.327412\pi$
$163$	13.1763			1.03205			0.516023	+	0.856575i	$0.327412\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.83285	−	3.17459i	0.141830	−	0.245657i	−0.786356	−	0.617774i	$-0.788035\pi$
$167$	1.83285	−	3.17459i	0.141830	−	0.245657i	0.928186	+	0.372117i	$0.121368\pi$
$168$		0			0
$169$	2.93713	+	5.08726i	0.225933	+	0.391327i
$170$		0			0
$171$	4.25822	+	4.50186i	0.325634	+	0.344266i
$172$		0			0
$173$	0.0426855	+	0.0739334i	0.00324532	+	0.00562105i	0.867644	−	0.497187i	$-0.165634\pi$
$173$	0.0426855	+	0.0739334i	0.00324532	+	0.00562105i	−0.864398	+	0.502808i	$0.832300\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.159931	−	0.277009i	0.0120212	−	0.0208212i
$178$		0			0
$179$	−16.2256			−1.21276			−0.606380	−	0.795175i	$-0.707379\pi$
$179$	−16.2256			−1.21276			−0.606380	+	0.795175i	$0.707379\pi$
$180$		0			0
$181$	−10.1549	+	17.5888i	−0.754808	+	1.30737i	0.190662	+	0.981656i	$0.438937\pi$
$181$	−10.1549	+	17.5888i	−0.754808	+	1.30737i	−0.945470	+	0.325710i	$0.894397\pi$
$182$		0			0
$183$	4.18868			0.309636
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.99291	+	8.64798i	0.365118	+	0.632403i
$188$		0			0
$189$	27.6141			2.00863
$190$		0			0
$191$	−21.9157			−1.58576			−0.792881	−	0.609377i	$-0.791420\pi$
$191$	−21.9157			−1.58576			−0.792881	+	0.609377i	$0.791420\pi$
$192$		0			0
$193$	2.51480	+	4.35575i	0.181019	+	0.313534i	0.942228	−	0.334973i	$-0.108727\pi$
$193$	2.51480	+	4.35575i	0.181019	+	0.313534i	−0.761209	+	0.648507i	$0.775394\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.1189			−1.36217			−0.681084	−	0.732205i	$-0.738491\pi$
$197$	−19.1189			−1.36217			−0.681084	+	0.732205i	$0.738491\pi$
$198$		0			0
$199$	−9.04425	+	15.6651i	−0.641130	+	1.11047i	0.344051	+	0.938951i	$0.388201\pi$
$199$	−9.04425	+	15.6651i	−0.641130	+	1.11047i	−0.985181	+	0.171518i	$0.945133\pi$
$200$		0			0
$201$	16.5896			1.17014
$202$		0			0
$203$	6.43409	−	11.1442i	0.451584	−	0.782167i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.54505	−	2.67611i	−0.107388	−	0.186002i
$208$		0			0
$209$	4.79854	−	16.1034i	0.331922	−	1.11390i
$210$		0			0
$211$	−8.03757	−	13.9215i	−0.553329	−	0.958394i	−0.998031	−	0.0627157i	$-0.980024\pi$
$211$	−8.03757	−	13.9215i	−0.553329	−	0.958394i	0.444702	−	0.895678i	$-0.353309\pi$
$212$		0			0
$213$	4.84644	−	8.39427i	0.332072	−	0.575166i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−38.6053			−2.62070
$218$		0			0
$219$	2.83289	−	4.90672i	0.191429	−	0.331565i
$220$		0			0
$221$	−6.91489			−0.465146
$222$		0			0
$223$	8.66036	+	15.0002i	0.579941	+	1.00449i	0.995485	+	0.0949140i	$0.0302576\pi$
$223$	8.66036	+	15.0002i	0.579941	+	1.00449i	−0.415545	+	0.909573i	$0.636409\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	23.7579			1.57687			0.788434	−	0.615120i	$-0.210892\pi$
$227$	23.7579			1.57687			0.788434	+	0.615120i	$0.210892\pi$
$228$		0			0
$229$	0.732245			0.0483881			0.0241941	−	0.999707i	$-0.492298\pi$
$229$	0.732245			0.0483881			0.0241941	+	0.999707i	$0.492298\pi$
$230$		0			0
$231$	−12.0374	−	20.8494i	−0.792004	−	1.37179i
$232$		0			0
$233$	9.94933	+	17.2328i	0.651803	+	1.12896i	0.982685	+	0.185283i	$0.0593202\pi$
$233$	9.94933	+	17.2328i	0.651803	+	1.12896i	−0.330883	+	0.943672i	$0.607346\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.94394	+	12.0273i	−0.451058	+	0.781255i
$238$		0			0
$239$	−28.9063			−1.86979			−0.934897	−	0.354919i	$-0.884508\pi$
$239$	−28.9063			−1.86979			−0.934897	+	0.354919i	$0.884508\pi$
$240$		0			0
$241$	11.8979	−	20.6077i	0.766409	−	1.32746i	−0.173090	−	0.984906i	$-0.555375\pi$
$241$	11.8979	−	20.6077i	0.766409	−	1.32746i	0.939499	−	0.342553i	$-0.111292\pi$
$242$		0			0
$243$	−6.62764	+	11.4794i	−0.425163	+	0.736404i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.99574	+	8.45324i	0.508757	+	0.537867i
$248$		0			0
$249$	−1.91189	−	3.31150i	−0.121161	−	0.209858i
$250$		0			0
$251$	3.44694	−	5.97028i	0.217569	−	0.376840i	−0.736495	−	0.676443i	$-0.763521\pi$
$251$	3.44694	−	5.97028i	0.217569	−	0.376840i	0.954064	+	0.299602i	$0.0968540\pi$
$252$		0			0
$253$	−4.18959	+	7.25659i	−0.263397	+	0.456218i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.32874	+	10.9617i	−0.394776	+	0.683772i	−0.993073	−	0.117502i	$-0.962511\pi$
$257$	−6.32874	+	10.9617i	−0.394776	+	0.683772i	0.598296	+	0.801275i	$0.295845\pi$
$258$		0			0
$259$	−13.7084			−0.851800
$260$		0			0
$261$	1.84004	+	3.18704i	0.113896	+	0.197273i
$262$		0			0
$263$	12.4743	+	21.6062i	0.769200	+	1.33229i	0.937997	+	0.346643i	$0.112678\pi$
$263$	12.4743	+	21.6062i	0.769200	+	1.33229i	−0.168797	+	0.985651i	$0.553988\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	11.9656			0.732285
$268$		0			0
$269$	9.54155	+	16.5265i	0.581759	+	1.00764i	0.995271	+	0.0971371i	$0.0309685\pi$
$269$	9.54155	+	16.5265i	0.581759	+	1.00764i	−0.413512	+	0.910499i	$0.635698\pi$
$270$		0			0
$271$	−1.48490	−	2.57192i	−0.0902012	−	0.156233i	0.817395	−	0.576078i	$-0.195418\pi$
$271$	−1.48490	−	2.57192i	−0.0902012	−	0.156233i	−0.907596	+	0.419845i	$0.862084\pi$
$272$		0			0
$273$	16.6711			1.00898
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.51535			0.331385			0.165693	−	0.986177i	$-0.447014\pi$
$277$	5.51535			0.331385			0.165693	+	0.986177i	$0.447014\pi$
$278$		0			0
$279$	5.52024	−	9.56133i	0.330488	−	0.572422i
$280$		0			0
$281$	12.4800	−	21.6159i	0.744493	−	1.28950i	−0.205939	−	0.978565i	$-0.566025\pi$
$281$	12.4800	−	21.6159i	0.744493	−	1.28950i	0.950431	−	0.310934i	$-0.100642\pi$
$282$		0			0
$283$	−6.72761	−	11.6526i	−0.399915	−	0.692673i	0.593800	−	0.804613i	$-0.297627\pi$
$283$	−6.72761	−	11.6526i	−0.399915	−	0.692673i	−0.993715	+	0.111939i	$0.964294\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.2060	−	31.5336i	−1.07466	−	1.86137i
$288$		0			0
$289$	5.14486	−	8.91116i	0.302639	−	0.524186i
$290$		0			0
$291$	−7.05653	+	12.2223i	−0.413661	+	0.716482i
$292$		0			0
$293$	−23.7710			−1.38871			−0.694357	−	0.719630i	$-0.744311\pi$
$293$	−23.7710			−1.38871			−0.694357	+	0.719630i	$0.744311\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	21.4141			1.24257
$298$		0			0
$299$	−2.90117	−	5.02497i	−0.167779	−	0.290602i
$300$		0			0
$301$	4.44946	+	7.70670i	0.256463	+	0.444207i
$302$		0			0
$303$	−13.7027			−0.787200
$304$		0			0
$305$		0			0
$306$		0			0
$307$	3.37243	+	5.84122i	0.192475	+	0.333376i	0.946070	−	0.323963i	$-0.105015\pi$
$307$	3.37243	+	5.84122i	0.192475	+	0.333376i	−0.753595	+	0.657339i	$0.771682\pi$
$308$		0			0
$309$	7.19455	+	12.4613i	0.409284	+	0.708900i
$310$		0			0
$311$	−11.6908			−0.662924			−0.331462	−	0.943468i	$-0.607542\pi$
$311$	−11.6908			−0.662924			−0.331462	+	0.943468i	$0.607542\pi$
$312$		0			0
$313$	8.78157	−	15.2101i	0.496364	−	0.859727i	−0.503628	−	0.863921i	$-0.668002\pi$
$313$	8.78157	−	15.2101i	0.496364	−	0.859727i	0.999991	+	0.00419387i	$0.00133495\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.4775	+	28.5399i	−0.925469	+	1.60296i	−0.134663	+	0.990891i	$0.542995\pi$
$317$	−16.4775	+	28.5399i	−0.925469	+	1.60296i	−0.790806	+	0.612067i	$0.790338\pi$
$318$		0			0
$319$	4.98949	−	8.64206i	0.279358	−	0.483862i
$320$		0			0
$321$	−11.5206	−	19.9543i	−0.643020	−	1.11374i
$322$		0			0
$323$	10.9837	−	2.61807i	0.611148	−	0.145673i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.23486	−	14.2632i	0.455389	−	0.788757i
$328$		0			0
$329$	4.24594	−	7.35418i	0.234086	−	0.405449i
$330$		0			0
$331$	−4.54726			−0.249940			−0.124970	−	0.992161i	$-0.539883\pi$
$331$	−4.54726			−0.249940			−0.124970	+	0.992161i	$0.539883\pi$
$332$		0			0
$333$	1.96019	−	3.39515i	0.107418	−	0.186053i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−10.9801	−	19.0180i	−0.598122	−	1.03598i	−0.993098	−	0.117286i	$-0.962581\pi$
$337$	−10.9801	−	19.0180i	−0.598122	−	1.03598i	0.394976	−	0.918691i	$-0.370753\pi$
$338$		0			0
$339$	0.437804	+	0.758299i	0.0237783	+	0.0411851i
$340$		0			0
$341$	−29.9376			−1.62121
$342$		0			0
$343$	−53.2439			−2.87490
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.63104	+	6.28915i	0.194925	+	0.337619i	0.946876	−	0.321599i	$-0.104220\pi$
$347$	3.63104	+	6.28915i	0.194925	+	0.337619i	−0.751951	+	0.659219i	$0.770887\pi$
$348$		0			0
$349$	−16.0910			−0.861329			−0.430665	−	0.902512i	$-0.641721\pi$
$349$	−16.0910			−0.861329			−0.430665	+	0.902512i	$0.641721\pi$
$350$		0			0
$351$	−7.41433	+	12.8420i	−0.395748	+	0.685455i
$352$		0			0
$353$	−33.4331			−1.77947			−0.889733	−	0.456481i	$-0.849110\pi$
$353$	−33.4331			−1.77947			−0.889733	+	0.456481i	$0.849110\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.08891	−	14.0104i	0.428110	−	0.741509i
$358$		0			0
$359$	−9.97814	−	17.2826i	−0.526626	−	0.912143i	−0.999519	−	0.0310231i	$-0.990123\pi$
$359$	−9.97814	−	17.2826i	−0.526626	−	0.912143i	0.472893	−	0.881120i	$-0.343210\pi$
$360$		0			0
$361$	−15.9010	−	10.3999i	−0.836895	−	0.547363i
$362$		0			0
$363$	−2.42491	−	4.20007i	−0.127275	−	0.220446i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.81476	−	6.60735i	0.199129	−	0.344901i	−0.749117	−	0.662437i	$-0.769522\pi$
$367$	3.81476	−	6.60735i	0.199129	−	0.344901i	0.948246	+	0.317536i	$0.102856\pi$
$368$		0			0
$369$	10.4132			0.542089
$370$		0			0
$371$	19.7956	−	34.2869i	1.02773	−	1.78009i
$372$		0			0
$373$	2.22095			0.114996			0.0574982	−	0.998346i	$-0.481688\pi$
$373$	2.22095			0.114996			0.0574982	+	0.998346i	$0.481688\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.45508	+	5.98437i	0.177946	+	0.308211i
$378$		0			0
$379$	6.92717			0.355825			0.177912	−	0.984046i	$-0.443066\pi$
$379$	6.92717			0.355825			0.177912	+	0.984046i	$0.443066\pi$
$380$		0			0
$381$	17.4037			0.891616
$382$		0			0
$383$	−9.60631	−	16.6386i	−0.490859	−	0.850193i	0.509085	−	0.860716i	$-0.329984\pi$
$383$	−9.60631	−	16.6386i	−0.490859	−	0.850193i	−0.999945	+	0.0105227i	$0.996650\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.54494			−0.129367
$388$		0			0
$389$	−13.4261	+	23.2547i	−0.680730	+	1.17906i	0.294029	+	0.955797i	$0.405004\pi$
$389$	−13.4261	+	23.2547i	−0.680730	+	1.17906i	−0.974758	+	0.223262i	$0.928329\pi$
$390$		0			0
$391$	−5.63065			−0.284754
$392$		0			0
$393$	7.68291	−	13.3072i	0.387551	−	0.671259i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3.70839	+	6.42312i	0.186119	+	0.322367i	0.943953	−	0.330080i	$-0.107076\pi$
$397$	3.70839	+	6.42312i	0.186119	+	0.322367i	−0.757834	+	0.652447i	$0.773742\pi$
$398$		0			0
$399$	−26.4805	+	6.31190i	−1.32568	+	0.315990i
$400$		0			0
$401$	2.66556	+	4.61689i	0.133112	+	0.230557i	0.924875	−	0.380272i	$-0.124170\pi$
$401$	2.66556	+	4.61689i	0.133112	+	0.230557i	−0.791763	+	0.610829i	$0.790836\pi$
$402$		0			0
$403$	10.3655	−	17.9535i	0.516340	−	0.894327i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.6306			−0.526938
$408$		0			0
$409$	5.70960	−	9.88933i	0.282322	−	0.488996i	−0.689634	−	0.724158i	$-0.742229\pi$
$409$	5.70960	−	9.88933i	0.282322	−	0.488996i	0.971956	+	0.235162i	$0.0755621\pi$
$410$		0			0
$411$	−11.5546			−0.569948
$412$		0			0
$413$	−0.632807	−	1.09605i	−0.0311384	−	0.0539333i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.09526			−0.396426
$418$		0			0
$419$	−12.2311			−0.597529			−0.298765	−	0.954327i	$-0.596575\pi$
$419$	−12.2311			−0.597529			−0.298765	+	0.954327i	$0.596575\pi$
$420$		0			0
$421$	6.63359	+	11.4897i	0.323301	+	0.559974i	0.981167	−	0.193161i	$-0.0618739\pi$
$421$	6.63359	+	11.4897i	0.323301	+	0.559974i	−0.657866	+	0.753135i	$0.728541\pi$
$422$		0			0
$423$	1.21427	+	2.10317i	0.0590397	+	0.102260i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.28678	−	14.3531i	0.401026	−	0.694597i
$428$		0			0
$429$	12.9281			0.624174
$430$		0			0
$431$	−8.19094	+	14.1871i	−0.394544	+	0.683370i	−0.993043	−	0.117754i	$-0.962431\pi$
$431$	−8.19094	+	14.1871i	−0.394544	+	0.683370i	0.598499	+	0.801124i	$0.295764\pi$
$432$		0			0
$433$	−7.50864	+	13.0054i	−0.360842	+	0.624997i	−0.988100	−	0.153815i	$-0.950844\pi$
$433$	−7.50864	+	13.0054i	−0.360842	+	0.624997i	0.627257	+	0.778812i	$0.284177\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.51076	+	6.88329i	0.311452	+	0.329272i
$438$		0			0
$439$	−7.68192	−	13.3055i	−0.366638	−	0.635035i	0.622400	−	0.782700i	$-0.286158\pi$
$439$	−7.68192	−	13.3055i	−0.366638	−	0.635035i	−0.989038	+	0.147664i	$0.952825\pi$
$440$		0			0
$441$	12.5891	−	21.8050i	0.599481	−	1.03833i
$442$		0			0
$443$	−12.1180	+	20.9890i	−0.575745	+	0.997219i	0.420216	+	0.907424i	$0.361954\pi$
$443$	−12.1180	+	20.9890i	−0.575745	+	0.997219i	−0.995960	+	0.0897946i	$0.971379\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−14.4957	+	25.1073i	−0.685624	+	1.18754i
$448$		0			0
$449$	16.8854			0.796873			0.398436	−	0.917196i	$-0.369553\pi$
$449$	16.8854			0.796873			0.398436	+	0.917196i	$0.369553\pi$
$450$		0			0
$451$	−14.1183	−	24.4536i	−0.664805	−	1.15148i
$452$		0			0
$453$	−12.6647	−	21.9359i	−0.595039	−	1.03064i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	29.1914			1.36551			0.682757	−	0.730645i	$-0.260781\pi$
$457$	29.1914			1.36551			0.682757	+	0.730645i	$0.260781\pi$
$458$		0			0
$459$	7.19495	+	12.4620i	0.335831	+	0.581677i
$460$		0			0
$461$	−1.87254	−	3.24333i	−0.0872127	−	0.151057i	0.819119	−	0.573623i	$-0.194463\pi$
$461$	−1.87254	−	3.24333i	−0.0872127	−	0.151057i	−0.906332	+	0.422566i	$0.861129\pi$
$462$		0			0
$463$	21.4714			0.997860			0.498930	−	0.866642i	$-0.333727\pi$
$463$	21.4714			0.997860			0.498930	+	0.866642i	$0.333727\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−29.1079			−1.34695			−0.673476	−	0.739209i	$-0.735200\pi$
$467$	−29.1079			−1.34695			−0.673476	+	0.739209i	$0.735200\pi$
$468$		0			0
$469$	32.8204	−	56.8466i	1.51550	−	2.62493i
$470$		0			0
$471$	7.45675	−	12.9155i	0.343589	−	0.595114i
$472$		0			0
$473$	3.45046	+	5.97637i	0.158652	+	0.274794i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.66119	+	9.80547i	0.259208	+	0.448962i
$478$		0			0
$479$	0.258348	−	0.447471i	0.0118042	−	0.0204455i	−0.860063	−	0.510188i	$-0.829576\pi$
$479$	0.258348	−	0.447471i	0.0118042	−	0.0204455i	0.871867	+	0.489742i	$0.162909\pi$
$480$		0			0
$481$	3.68068	−	6.37513i	0.167825	−	0.290681i
$482$		0			0
$483$	13.5749			0.617681
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.6668			0.483358			0.241679	−	0.970356i	$-0.422302\pi$
$487$	10.6668			0.483358			0.241679	+	0.970356i	$0.422302\pi$
$488$		0			0
$489$	−8.27691	−	14.3360i	−0.374295	−	0.648298i
$490$		0			0
$491$	−12.0852	−	20.9322i	−0.545398	−	0.944656i	−0.998582	−	0.0532395i	$-0.983045\pi$
$491$	−12.0852	−	20.9322i	−0.545398	−	0.944656i	0.453184	−	0.891417i	$-0.350288\pi$
$492$		0			0
$493$	6.70569			0.302009
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.1761	−	33.2141i	−0.860168	−	1.48985i
$498$		0			0
$499$	2.38934	+	4.13846i	0.106962	+	0.185263i	0.914538	−	0.404500i	$-0.132554\pi$
$499$	2.38934	+	4.13846i	0.106962	+	0.185263i	−0.807576	+	0.589763i	$0.799221\pi$
$500$		0			0
$501$	−4.60535			−0.205752
$502$		0			0
$503$	8.92453	−	15.4577i	0.397925	−	0.689227i	−0.595545	−	0.803322i	$-0.703064\pi$
$503$	8.92453	−	15.4577i	0.397925	−	0.689227i	0.993470	+	0.114096i	$0.0363970\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.69002	−	6.39130i	0.163879	−	0.283847i
$508$		0			0
$509$	−3.57492	+	6.19194i	−0.158455	+	0.274453i	−0.934312	−	0.356457i	$-0.883985\pi$
$509$	−3.57492	+	6.19194i	−0.158455	+	0.274453i	0.775856	+	0.630909i	$0.217318\pi$
$510$		0			0
$511$	−11.2091	−	19.4147i	−0.495860	−	0.858854i
$512$		0			0
$513$	6.91484	−	23.2055i	0.305298	−	1.02455i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	3.29263	−	5.70301i	0.144810	−	0.250818i
$518$		0			0
$519$	0.0536272	−	0.0928851i	0.00235397	−	0.00407720i
$520$		0			0
$521$	−19.7280			−0.864301			−0.432151	−	0.901801i	$-0.642245\pi$
$521$	−19.7280			−0.864301			−0.432151	+	0.901801i	$0.642245\pi$
$522$		0			0
$523$	−18.1328	+	31.4070i	−0.792894	+	1.37333i	0.131274	+	0.991346i	$0.458093\pi$
$523$	−18.1328	+	31.4070i	−0.792894	+	1.37333i	−0.924168	+	0.381986i	$0.875240\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.0587	−	17.4222i	−0.438166	−	0.758925i
$528$		0			0
$529$	9.13764	+	15.8269i	0.397289	+	0.688124i
$530$		0			0
$531$	0.361944			0.0157070
$532$		0			0
$533$	19.5530			0.846936
$534$		0			0
$535$		0			0
$536$		0			0
$537$	10.1924	+	17.6538i	0.439835	+	0.761816i
$538$		0			0
$539$	−68.2738			−2.94076
$540$		0			0
$541$	11.4419	−	19.8180i	0.491927	−	0.852043i	−0.508029	−	0.861340i	$-0.669626\pi$
$541$	11.4419	−	19.8180i	0.491927	−	0.852043i	0.999957	+	0.00929658i	$0.00295924\pi$
$542$		0			0
$543$	25.5159			1.09499
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−6.35861	+	11.0134i	−0.271875	+	0.470901i	−0.969342	−	0.245716i	$-0.920977\pi$
$547$	−6.35861	+	11.0134i	−0.271875	+	0.470901i	0.697467	+	0.716617i	$0.254310\pi$
$548$		0			0
$549$	2.36988	+	4.10475i	0.101144	+	0.175187i
$550$		0			0
$551$	−7.75383	−	8.19749i	−0.330324	−	0.349225i
$552$		0			0
$553$	27.4755	+	47.5889i	1.16838	+	2.02369i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.1803	+	19.3648i	−0.473722	+	0.820511i	−0.999547	−	0.0300814i	$-0.990423\pi$
$557$	−11.1803	+	19.3648i	−0.473722	+	0.820511i	0.525825	+	0.850593i	$0.323757\pi$
$558$		0			0
$559$	−4.77869			−0.202117
$560$		0			0
$561$	6.27277	−	10.8648i	0.264837	−	0.458710i
$562$		0			0
$563$	−10.6447			−0.448619			−0.224310	−	0.974518i	$-0.572013\pi$
$563$	−10.6447			−0.448619			−0.224310	+	0.974518i	$0.572013\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.74595	−	11.6843i	−0.283303	−	0.490696i
$568$		0			0
$569$	−3.13498			−0.131425			−0.0657126	−	0.997839i	$-0.520932\pi$
$569$	−3.13498			−0.131425			−0.0657126	+	0.997839i	$0.520932\pi$
$570$		0			0
$571$	1.29260			0.0540938			0.0270469	−	0.999634i	$-0.491390\pi$
$571$	1.29260			0.0540938			0.0270469	+	0.999634i	$0.491390\pi$
$572$		0			0
$573$	13.7667	+	23.8446i	0.575112	+	0.996124i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.18544			0.340764			0.170382	−	0.985378i	$-0.445500\pi$
$577$	8.18544			0.340764			0.170382	+	0.985378i	$0.445500\pi$
$578$		0			0
$579$	3.15943	−	5.47229i	0.131301	−	0.227420i
$580$		0			0
$581$	−15.1298			−0.627689
$582$		0			0
$583$	15.3510	−	26.5887i	0.635774	−	1.10119i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.08512	+	15.7359i	0.374983	+	0.649490i	0.990325	−	0.138771i	$-0.0443151\pi$
$587$	9.08512	+	15.7359i	0.374983	+	0.649490i	−0.615341	+	0.788261i	$0.710982\pi$
$588$		0			0
$589$	−9.66715	+	32.4420i	−0.398328	+	1.33675i
$590$		0			0
$591$	12.0099	+	20.8017i	0.494021	+	0.855669i
$592$		0			0
$593$	−4.44341	+	7.69621i	−0.182469	+	0.316046i	−0.942721	−	0.333583i	$-0.891742\pi$
$593$	−4.44341	+	7.69621i	−0.182469	+	0.316046i	0.760252	+	0.649629i	$0.225076\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	22.7252			0.930081
$598$		0			0
$599$	2.18264	−	3.78044i	0.0891801	−	0.154465i	−0.817985	−	0.575240i	$-0.804909\pi$
$599$	2.18264	−	3.78044i	0.0891801	−	0.154465i	0.907165	+	0.420775i	$0.138242\pi$
$600$		0			0
$601$	−4.25303			−0.173485			−0.0867424	−	0.996231i	$-0.527646\pi$
$601$	−4.25303			−0.173485			−0.0867424	+	0.996231i	$0.527646\pi$
$602$		0			0
$603$	9.38608	+	16.2572i	0.382231	+	0.662043i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	23.5995			0.957876			0.478938	−	0.877849i	$-0.341022\pi$
$607$	23.5995			0.957876			0.478938	+	0.877849i	$0.341022\pi$
$608$		0			0
$609$	−16.1667			−0.655109
$610$		0			0
$611$	2.28005	+	3.94917i	0.0922410	+	0.159766i
$612$		0			0
$613$	10.1665	+	17.6090i	0.410623	+	0.711220i	0.994958	−	0.100293i	$-0.0319780\pi$
$613$	10.1665	+	17.6090i	0.410623	+	0.711220i	−0.584335	+	0.811512i	$0.698645\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.6422	+	27.0932i	−0.629733	+	1.09073i	0.357872	+	0.933771i	$0.383502\pi$
$617$	−15.6422	+	27.0932i	−0.629733	+	1.09073i	−0.987605	+	0.156959i	$0.949831\pi$
$618$		0			0
$619$	25.7635			1.03552			0.517761	−	0.855525i	$-0.326766\pi$
$619$	25.7635			1.03552			0.517761	+	0.855525i	$0.326766\pi$
$620$		0			0
$621$	−6.03733	+	10.4570i	−0.242270	+	0.419624i
$622$		0			0
$623$	23.6725	−	41.0020i	0.948420	−	1.64271i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−20.5351	+	4.89474i	−0.820092	+	0.195477i
$628$		0			0
$629$	−3.57177	−	6.18649i	−0.142416	−	0.246671i
$630$		0			0
$631$	−10.6458	+	18.4391i	−0.423804	+	0.734050i	−0.996308	−	0.0858517i	$-0.972639\pi$
$631$	−10.6458	+	18.4391i	−0.423804	+	0.734050i	0.572504	+	0.819902i	$0.305972\pi$
$632$		0			0
$633$	−10.0979	+	17.4900i	−0.401355	+	0.695167i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	23.6388	−	40.9436i	0.936603	−	1.62224i
$638$		0			0
$639$	10.9681			0.433891
$640$		0			0
$641$	16.5525	+	28.6698i	0.653785	+	1.13239i	0.982197	+	0.187854i	$0.0601533\pi$
$641$	16.5525	+	28.6698i	0.653785	+	1.13239i	−0.328412	+	0.944535i	$0.606513\pi$
$642$		0			0
$643$	15.0702	+	26.1024i	0.594311	+	1.02938i	0.993644	+	0.112570i	$0.0359084\pi$
$643$	15.0702	+	26.1024i	0.594311	+	1.02938i	−0.399333	+	0.916806i	$0.630758\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.5273			−0.413870			−0.206935	−	0.978355i	$-0.566349\pi$
$647$	−10.5273			−0.413870			−0.206935	+	0.978355i	$0.566349\pi$
$648$		0			0
$649$	−0.490728	−	0.849966i	−0.0192628	−	0.0333641i
$650$		0			0
$651$	24.2506	+	42.0033i	0.950456	+	1.64624i
$652$		0			0
$653$	−14.9511			−0.585081			−0.292540	−	0.956253i	$-0.594501\pi$
$653$	−14.9511			−0.585081			−0.292540	+	0.956253i	$0.594501\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.41120			0.250125
$658$		0			0
$659$	16.6909	−	28.9094i	0.650184	−	1.12615i	−0.332894	−	0.942964i	$-0.608025\pi$
$659$	16.6909	−	28.9094i	0.650184	−	1.12615i	0.983078	−	0.183187i	$-0.0586414\pi$
$660$		0			0
$661$	−12.7433	+	22.0720i	−0.495655	+	0.858501i	−0.999987	−	0.00500935i	$-0.998405\pi$
$661$	−12.7433	+	22.0720i	−0.495655	+	0.858501i	0.504332	+	0.863510i	$0.331739\pi$
$662$		0			0
$663$	4.34371	+	7.52353i	0.168696	+	0.292190i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.81340	+	4.87295i	0.108935	+	0.188681i
$668$		0			0
$669$	10.8803	−	18.8453i	0.420657	−	0.728600i
$670$		0			0
$671$	6.42622	−	11.1305i	0.248081	−	0.429690i
$672$		0			0
$673$	−9.87133			−0.380512			−0.190256	−	0.981735i	$-0.560932\pi$
$673$	−9.87133			−0.380512			−0.190256	+	0.981735i	$0.560932\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.8367			−0.454922			−0.227461	−	0.973787i	$-0.573042\pi$
$677$	−11.8367			−0.454922			−0.227461	+	0.973787i	$0.573042\pi$
$678$		0			0
$679$	27.9209	+	48.3605i	1.07151	+	1.85590i
$680$		0			0
$681$	−14.9239	−	25.8490i	−0.571887	−	0.990537i
$682$		0			0
$683$	29.6716			1.13535			0.567675	−	0.823253i	$-0.307843\pi$
$683$	29.6716			1.13535			0.567675	+	0.823253i	$0.307843\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.459972	−	0.796696i	−0.0175490	−	0.0303958i
$688$		0			0
$689$	10.6301	+	18.4119i	0.404976	+	0.701438i
$690$		0			0
$691$	9.73437			0.370313			0.185156	−	0.982709i	$-0.440721\pi$
$691$	9.73437			0.370313			0.185156	+	0.982709i	$0.440721\pi$
$692$		0			0
$693$	13.6211	−	23.5924i	0.517423	−	0.896203i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.48723	−	16.4324i	0.359355	−	0.622420i
$698$		0			0
$699$	12.4997	−	21.6501i	0.472782	−	0.818882i
$700$		0			0
$701$	10.3345	+	17.8999i	0.390329	+	0.676070i	0.992493	−	0.122303i	$-0.0390279\pi$
$701$	10.3345	+	17.8999i	0.390329	+	0.676070i	−0.602164	+	0.798373i	$0.705695\pi$
$702$		0			0
$703$	−3.43272	+	11.5199i	−0.129468	+	0.434480i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−27.1091	+	46.9543i	−1.01954	+	1.76590i
$708$		0			0
$709$	−10.0066	+	17.3319i	−0.375806	+	0.650915i	−0.990447	−	0.137892i	$-0.955967\pi$
$709$	−10.0066	+	17.3319i	−0.375806	+	0.650915i	0.614641	+	0.788807i	$0.289301\pi$
$710$		0			0
$711$	−15.7150			−0.589360
$712$		0			0
$713$	8.44037	−	14.6191i	0.316094	−	0.547491i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	18.1580	+	31.4506i	0.678123	+	1.17454i
$718$		0			0
$719$	−11.2807	−	19.5387i	−0.420698	−	0.728671i	0.575309	−	0.817936i	$-0.304882\pi$
$719$	−11.2807	−	19.5387i	−0.420698	−	0.728671i	−0.996008	+	0.0892647i	$0.971548\pi$
$720$		0			0
$721$	56.9341			2.12034
$722$		0			0
$723$	−29.8954			−1.11182
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.77735	−	4.81051i	−0.103006	−	0.178412i	0.809916	−	0.586546i	$-0.199513\pi$
$727$	−2.77735	−	4.81051i	−0.103006	−	0.178412i	−0.912922	+	0.408134i	$0.866179\pi$
$728$		0			0
$729$	24.7954			0.918349
$730$		0			0
$731$	−2.31864	+	4.01601i	−0.0857581	+	0.148537i
$732$		0			0
$733$	−45.3490			−1.67500			−0.837501	−	0.546436i	$-0.815984\pi$
$733$	−45.3490			−1.67500			−0.837501	+	0.546436i	$0.815984\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.4515	−	44.0833i	0.937518	−	1.62383i
$738$		0			0
$739$	9.01081	+	15.6072i	0.331468	+	0.574119i	0.982800	−	0.184674i	$-0.0591228\pi$
$739$	9.01081	+	15.6072i	0.331468	+	0.574119i	−0.651332	+	0.758793i	$0.725789\pi$
$740$		0			0
$741$	4.17461	−	14.0096i	0.153358	−	0.514654i
$742$		0			0
$743$	−21.3235	−	36.9333i	−0.782282	−	1.35495i	−0.930610	−	0.366013i	$-0.880723\pi$
$743$	−21.3235	−	36.9333i	−0.782282	−	1.35495i	0.148328	−	0.988938i	$-0.452611\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.16343	−	3.74717i	0.0791557	−	0.137102i
$748$		0			0
$749$	−91.1687			−3.33123
$750$		0			0
$751$	−2.45338	+	4.24938i	−0.0895252	+	0.155062i	−0.907311	−	0.420461i	$-0.861868\pi$
$751$	−2.45338	+	4.24938i	−0.0895252	+	0.155062i	0.817785	+	0.575523i	$0.195202\pi$
$752$		0			0
$753$	−8.66102			−0.315625
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−13.9842	−	24.2213i	−0.508264	−	0.880339i	−0.999954	−	0.00956884i	$-0.996954\pi$
$757$	−13.9842	−	24.2213i	−0.508264	−	0.880339i	0.491690	−	0.870770i	$-0.336379\pi$
$758$		0			0
$759$	10.5271			0.382108
$760$		0			0
$761$	−11.7443			−0.425731			−0.212866	−	0.977081i	$-0.568280\pi$
$761$	−11.7443			−0.425731			−0.212866	+	0.977081i	$0.568280\pi$
$762$		0			0
$763$	−32.5833	−	56.4359i	−1.17959	−	2.04312i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.679630			0.0245400
$768$		0			0
$769$	−8.22905	+	14.2531i	−0.296747	+	0.513981i	−0.975390	−	0.220488i	$-0.929235\pi$
$769$	−8.22905	+	14.2531i	−0.296747	+	0.513981i	0.678643	+	0.734469i	$0.262568\pi$
$770$		0			0
$771$	15.9020			0.572698
$772$		0			0
$773$	−22.9542	+	39.7578i	−0.825605	+	1.42999i	0.0758511	+	0.997119i	$0.475833\pi$
$773$	−22.9542	+	39.7578i	−0.825605	+	1.42999i	−0.901456	+	0.432871i	$0.857501\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	8.61118	+	14.9150i	0.308924	+	0.535073i
$778$		0			0
$779$	−31.0582	+	7.40303i	−1.11278	+	0.265241i
$780$		0			0
$781$	−14.8707	−	25.7568i	−0.532115	−	0.921650i
$782$		0			0
$783$	7.19002	−	12.4535i	0.256950	−	0.445051i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	28.1763			1.00438			0.502189	−	0.864758i	$-0.332528\pi$
$787$	28.1763			1.00438			0.502189	+	0.864758i	$0.332528\pi$
$788$		0			0
$789$	15.6719	−	27.1446i	0.557936	−	0.966373i
$790$		0			0
$791$	3.46456			0.123186
$792$		0			0
$793$	4.44997	+	7.70757i	0.158023	+	0.273704i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.18117			−0.0418394			−0.0209197	−	0.999781i	$-0.506659\pi$
$797$	−1.18117			−0.0418394			−0.0209197	+	0.999781i	$0.506659\pi$
$798$		0			0
$799$	4.42517			0.156551
$800$		0			0
$801$	6.76994	+	11.7259i	0.239204	+	0.414314i
$802$		0			0
$803$	−8.69238	−	15.0556i	−0.306747	−	0.531302i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.9874	−	20.7628i	0.421976	−	0.730884i
$808$		0			0
$809$	4.72471			0.166112			0.0830561	−	0.996545i	$-0.473532\pi$
$809$	4.72471			0.166112			0.0830561	+	0.996545i	$0.473532\pi$
$810$		0			0
$811$	18.7800	−	32.5280i	0.659456	−	1.14221i	−0.321301	−	0.946977i	$-0.604120\pi$
$811$	18.7800	−	32.5280i	0.659456	−	1.14221i	0.980757	−	0.195234i	$-0.0625465\pi$
$812$		0			0
$813$	−1.86553	+	3.23119i	−0.0654270	+	0.113323i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.59050	−	1.80927i	0.265558	−	0.0632984i
$818$		0			0
$819$	9.43222	+	16.3371i	0.329588	+	0.570864i
$820$		0			0
$821$	−17.3453	+	30.0430i	−0.605357	+	1.04851i	0.386638	+	0.922231i	$0.373636\pi$
$821$	−17.3453	+	30.0430i	−0.605357	+	1.04851i	−0.991995	+	0.126277i	$0.959697\pi$
$822$		0			0
$823$	−1.26478	+	2.19067i	−0.0440876	+	0.0763620i	−0.887227	−	0.461333i	$-0.847371\pi$
$823$	−1.26478	+	2.19067i	−0.0440876	+	0.0763620i	0.843140	+	0.537695i	$0.180705\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.4339	−	18.0721i	0.362823	−	0.628428i	−0.625601	−	0.780143i	$-0.715146\pi$
$827$	10.4339	−	18.0721i	0.362823	−	0.628428i	0.988424	+	0.151715i	$0.0484797\pi$
$828$		0			0
$829$	26.1170			0.907081			0.453540	−	0.891236i	$-0.350161\pi$
$829$	26.1170			0.907081			0.453540	+	0.891236i	$0.350161\pi$
$830$		0			0
$831$	−3.46456	−	6.00080i	−0.120184	−	0.208165i
$832$		0			0
$833$	−22.9393	−	39.7321i	−0.794801	−	1.37664i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−43.1410			−1.49117
$838$		0			0
$839$	5.69792	+	9.86908i	0.196714	+	0.340719i	0.947461	−	0.319871i	$-0.103640\pi$
$839$	5.69792	+	9.86908i	0.196714	+	0.340719i	−0.750747	+	0.660590i	$0.770306\pi$
$840$		0			0
$841$	11.1495	+	19.3114i	0.384464	+	0.665911i
$842$		0			0
$843$	−31.3580			−1.08003
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−19.1895			−0.659360
$848$		0			0
$849$	−8.45213	+	14.6395i	−0.290077	+	0.502427i
$850$		0			0
$851$	2.99710	−	5.19113i	0.102739	−	0.177950i
$852$		0			0
$853$	3.11493	+	5.39521i	0.106653	+	0.184728i	0.914412	−	0.404784i	$-0.132653\pi$
$853$	3.11493	+	5.39521i	0.106653	+	0.184728i	−0.807759	+	0.589512i	$0.799320\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.3807	+	43.9606i	0.866987	+	1.50166i	0.865061	+	0.501667i	$0.167280\pi$
$857$	25.3807	+	43.9606i	0.866987	+	1.50166i	0.00192568	+	0.999998i	$0.499387\pi$
$858$		0			0
$859$	4.07445	−	7.05715i	0.139018	−	0.240787i	−0.788107	−	0.615538i	$-0.788939\pi$
$859$	4.07445	−	7.05715i	0.139018	−	0.240787i	0.927125	+	0.374751i	$0.122272\pi$
$860$		0			0
$861$	−22.8728	+	39.6168i	−0.779502	+	1.35014i
$862$		0			0
$863$	1.20591			0.0410498			0.0205249	−	0.999789i	$-0.493466\pi$
$863$	1.20591			0.0410498			0.0205249	+	0.999789i	$0.493466\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−12.9273			−0.439035
$868$		0			0
$869$	21.3066	+	36.9041i	0.722778	+	1.25189i
$870$		0			0
$871$	17.6244	+	30.5264i	0.597180	+	1.03435i
$872$		0			0
$873$	−15.9698			−0.540497
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.25368	−	14.2958i	−0.278707	−	0.482735i	0.692357	−	0.721555i	$-0.256572\pi$
$877$	−8.25368	−	14.2958i	−0.278707	−	0.482735i	−0.971064	+	0.238821i	$0.923239\pi$
$878$		0			0
$879$	14.9321	+	25.8632i	0.503649	+	0.872345i
$880$		0			0
$881$	−22.9549			−0.773370			−0.386685	−	0.922212i	$-0.626380\pi$
$881$	−22.9549			−0.773370			−0.386685	+	0.922212i	$0.626380\pi$
$882$		0			0
$883$	−14.3895	+	24.9234i	−0.484246	+	0.838739i	−0.999836	−	0.0180963i	$-0.994239\pi$
$883$	−14.3895	+	24.9234i	−0.484246	+	0.838739i	0.515590	+	0.856835i	$0.327573\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.2699	−	26.4482i	0.512712	−	0.888044i	−0.487179	−	0.873302i	$-0.661974\pi$
$887$	15.2699	−	26.4482i	0.512712	−	0.888044i	0.999891	−	0.0147418i	$-0.00469263\pi$
$888$		0			0
$889$	34.4310	−	59.6362i	1.15478	−	2.00013i
$890$		0			0
$891$	−5.23133	−	9.06094i	−0.175256	−	0.303553i
$892$		0			0
$893$	−5.11686	−	5.40963i	−0.171229	−	0.181026i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.64484	+	6.31305i	−0.121698	+	0.210787i
$898$		0			0
$899$	−10.0518	+	17.4103i	−0.335248	+	0.580666i
$900$		0			0
$901$	20.6312			0.687324
$902$		0			0
$903$	5.59001	−	9.68219i	0.186024	−	0.322203i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	8.76481	+	15.1811i	0.291031	+	0.504080i	0.974054	−	0.226317i	$-0.0726685\pi$
$907$	8.76481	+	15.1811i	0.291031	+	0.504080i	−0.683023	+	0.730397i	$0.739335\pi$
$908$		0			0
$909$	−7.75274	−	13.4281i	−0.257142	−	0.445383i
$910$		0			0
$911$	1.25152			0.0414648			0.0207324	−	0.999785i	$-0.493400\pi$
$911$	1.25152			0.0414648			0.0207324	+	0.999785i	$0.493400\pi$
$912$		0			0
$913$	−11.7328			−0.388299
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−30.3994	−	52.6532i	−1.00388	−	1.73876i
$918$		0			0
$919$	17.4588			0.575912			0.287956	−	0.957644i	$-0.407024\pi$
$919$	17.4588			0.575912			0.287956	+	0.957644i	$0.407024\pi$
$920$		0			0
$921$	4.23690	−	7.33853i	0.139611	−	0.241813i
$922$		0			0
$923$	20.5950			0.677893
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−8.14109	+	14.1008i	−0.267389	+	0.463131i
$928$		0			0
$929$	−28.6100	−	49.5540i	−0.938665	−	1.62582i	−0.767964	−	0.640493i	$-0.778730\pi$
$929$	−28.6100	−	49.5540i	−0.938665	−	1.62582i	−0.170701	−	0.985323i	$-0.554603\pi$
$930$		0			0
$931$	−22.0463	+	73.9851i	−0.722538	+	2.42476i
$932$		0			0
$933$	7.34378	+	12.7198i	0.240425	+	0.416428i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−4.83820	+	8.38001i	−0.158057	+	0.273763i	−0.934168	−	0.356834i	$-0.883856\pi$
$937$	−4.83820	+	8.38001i	−0.158057	+	0.273763i	0.776111	+	0.630596i	$0.217190\pi$
$938$		0			0
$939$	−22.0652			−0.720070
$940$		0			0
$941$	−14.0336	+	24.3069i	−0.457482	+	0.792383i	−0.998827	−	0.0484179i	$-0.984582\pi$
$941$	−14.0336	+	24.3069i	−0.457482	+	0.792383i	0.541345	+	0.840801i	$0.317915\pi$
$942$		0			0
$943$	15.9216			0.518479
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.1397	+	26.2228i	0.491975	+	0.852125i	0.999957	−	0.00924220i	$-0.00294193\pi$
$947$	15.1397	+	26.2228i	0.491975	+	0.852125i	−0.507983	+	0.861367i	$0.669609\pi$
$948$		0			0
$949$	12.0384			0.390784
$950$		0			0
$951$	41.4025			1.34257
$952$		0			0
$953$	3.36029	+	5.82020i	0.108851	+	0.188535i	0.915305	−	0.402762i	$-0.131950\pi$
$953$	3.36029	+	5.82020i	0.108851	+	0.188535i	−0.806454	+	0.591296i	$0.798616\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−12.5369			−0.405262
$958$		0			0
$959$	−22.8594	+	39.5937i	−0.738169	+	1.27855i
$960$		0			0
$961$	29.3124			0.945560
$962$		0			0
$963$	13.0364	−	22.5796i	0.420091	−	0.727618i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	19.8585	+	34.3960i	0.638607	+	1.10610i	0.985739	+	0.168284i	$0.0538226\pi$
$967$	19.8585	+	34.3960i	0.638607	+	1.10610i	−0.347131	+	0.937817i	$0.612844\pi$
$968$		0			0
$969$	−9.74809	−	10.3058i	−0.313154	−	0.331072i
$970$		0			0
$971$	−7.09379	−	12.2868i	−0.227651	−	0.394302i	0.729461	−	0.684023i	$-0.239771\pi$
$971$	−7.09379	−	12.2868i	−0.227651	−	0.394302i	−0.957111	+	0.289720i	$0.906438\pi$
$972$		0			0
$973$	−16.0155	+	27.7396i	−0.513432	+	0.889291i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.49394			0.175767			0.0878833	−	0.996131i	$-0.471990\pi$
$977$	5.49394			0.175767			0.0878833	+	0.996131i	$0.471990\pi$
$978$		0			0
$979$	18.3575	−	31.7962i	0.586709	−	1.01621i
$980$		0			0
$981$	18.6365			0.595019
$982$		0			0
$983$	−18.9275	−	32.7834i	−0.603695	−	1.04563i	−0.992256	−	0.124207i	$-0.960361\pi$
$983$	−18.9275	−	32.7834i	−0.603695	−	1.04563i	0.388562	−	0.921423i	$-0.372972\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.6686			−0.339587
$988$		0			0
$989$	−3.89118			−0.123732
$990$		0			0
$991$	22.6116	+	39.1645i	0.718282	+	1.24410i	0.961680	+	0.274175i	$0.0884047\pi$
$991$	22.6116	+	39.1645i	0.718282	+	1.24410i	−0.243398	+	0.969927i	$0.578262\pi$
$992$		0			0
$993$	2.85644	+	4.94750i	0.0906464	+	0.157004i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	24.7184	−	42.8135i	0.782840	−	1.35592i	−0.147441	−	0.989071i	$-0.547104\pi$
$997$	24.7184	−	42.8135i	0.782840	−	1.35592i	0.930281	−	0.366848i	$-0.119563\pi$
$998$		0			0
$999$	−15.3190			−0.484672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.g.501.4		20
5.2	odd	4		380.2.r.a.349.4	yes	20
5.3	odd	4		380.2.r.a.349.7	yes	20
5.4	even	2	inner	1900.2.i.g.501.7		20
15.2	even	4		3420.2.bj.c.2629.2		20
15.8	even	4		3420.2.bj.c.2629.9		20
19.11	even	3	inner	1900.2.i.g.201.4		20
95.49	even	6	inner	1900.2.i.g.201.7		20
95.68	odd	12		380.2.r.a.49.4	✓	20
95.87	odd	12		380.2.r.a.49.7	yes	20
285.68	even	12		3420.2.bj.c.1189.2		20
285.182	even	12		3420.2.bj.c.1189.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.4	✓	20	95.68	odd	12
380.2.r.a.49.7	yes	20	95.87	odd	12
380.2.r.a.349.4	yes	20	5.2	odd	4
380.2.r.a.349.7	yes	20	5.3	odd	4
1900.2.i.g.201.4		20	19.11	even	3	inner
1900.2.i.g.201.7		20	95.49	even	6	inner
1900.2.i.g.501.4		20	1.1	even	1	trivial
1900.2.i.g.501.7		20	5.4	even	2	inner
3420.2.bj.c.1189.2		20	285.68	even	12
3420.2.bj.c.1189.9		20	285.182	even	12
3420.2.bj.c.2629.2		20	15.2	even	4
3420.2.bj.c.2629.9		20	15.8	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.628167 - 1.08802i) q^{3} -4.97100 q^{7} +(0.710812 - 1.23116i) q^{9} +O(q^{10})\)	\(q+(-0.628167 - 1.08802i) q^{3} -4.97100 q^{7} +(0.710812 - 1.23116i) q^{9} -3.85491 q^{11} +(1.33470 - 2.31178i) q^{13} +(-1.29521 - 2.24337i) q^{17} +(-1.24479 + 4.17738i) q^{19} +(3.12262 + 5.40854i) q^{21} +(1.08682 - 1.88243i) q^{23} -5.55504 q^{27} +(-1.29432 + 2.24183i) q^{29} +7.76610 q^{31} +(2.42153 + 4.19421i) q^{33} +2.75768 q^{37} -3.35367 q^{39} +(3.66243 + 6.34351i) q^{41} +(-0.895083 - 1.55033i) q^{43} +(-0.854141 + 1.47942i) q^{47} +17.7109 q^{49} +(-1.62722 + 2.81842i) q^{51} +(-3.98220 + 6.89738i) q^{53} +(5.32700 - 1.26974i) q^{57} +(0.127300 + 0.220490i) q^{59} +(-1.66702 + 2.88737i) q^{61} +(-3.53345 + 6.12011i) q^{63} +(-6.60237 + 11.4356i) q^{67} -2.73082 q^{69} +(3.85760 + 6.68156i) q^{71} +(2.25489 + 3.90558i) q^{73} +19.1628 q^{77} +(-5.52715 - 9.57330i) q^{79} +(1.35706 + 2.35050i) q^{81} +3.04360 q^{83} +3.25221 q^{87} +(-4.76212 + 8.24824i) q^{89} +(-6.63482 + 11.4918i) q^{91} +(-4.87841 - 8.44966i) q^{93} +(-5.61676 - 9.72851i) q^{97} +(-2.74011 + 4.74601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more