LMFDB - Embedded newform 1900.2.i.g.201.5

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			201.5
Root			$0.226426 + 0.392182i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.g.501.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.226426 + 0.392182i) q^{3} +2.54366 q^{7} +(1.39746 + 2.42048i) q^{9} +2.22377 q^{11} +(3.51096 + 6.08116i) q^{13} +(1.27878 - 2.21492i) q^{17} +(-2.70498 + 3.41805i) q^{19} +(-0.575952 + 0.997578i) q^{21} +(-4.01448 - 6.95328i) q^{23} -2.62425 q^{27} +(0.941734 + 1.63113i) q^{29} +5.98111 q^{31} +(-0.503519 + 0.872121i) q^{33} -2.86105 q^{37} -3.17989 q^{39} +(-3.67524 + 6.36571i) q^{41} +(-1.84706 + 3.19919i) q^{43} +(-2.36448 - 4.09540i) q^{47} -0.529782 q^{49} +(0.579100 + 1.00303i) q^{51} +(-5.14549 - 8.91226i) q^{53} +(-0.728020 - 1.83478i) q^{57} +(3.73666 - 6.47208i) q^{59} +(4.17839 + 7.23719i) q^{61} +(3.55467 + 6.15687i) q^{63} +(6.17997 + 10.7040i) q^{67} +3.63593 q^{69} +(-4.13931 + 7.16950i) q^{71} +(6.32134 - 10.9489i) q^{73} +5.65651 q^{77} +(2.13067 - 3.69043i) q^{79} +(-3.59819 + 6.23225i) q^{81} +14.7613 q^{83} -0.852933 q^{87} +(7.19403 + 12.4604i) q^{89} +(8.93069 + 15.4684i) q^{91} +(-1.35428 + 2.34568i) q^{93} +(2.91488 - 5.04871i) q^{97} +(3.10763 + 5.38258i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.226426	+	0.392182i	−0.130727	+	0.226426i	−0.923957	−	0.382496i	$-0.875065\pi$
$3$	−0.226426	+	0.392182i	−0.130727	+	0.226426i	0.793230	+	0.608922i	$0.208398\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.54366			0.961414			0.480707	−	0.876881i	$-0.340380\pi$
$7$	2.54366			0.961414			0.480707	+	0.876881i	$0.340380\pi$
$8$		0			0
$9$	1.39746	+	2.42048i	0.465821	+	0.806825i
$10$		0			0
$11$	2.22377			0.670491			0.335246	−	0.942131i	$-0.391181\pi$
$11$	2.22377			0.670491			0.335246	+	0.942131i	$0.391181\pi$
$12$		0			0
$13$	3.51096	+	6.08116i	0.973765	+	1.68661i	0.683953	+	0.729526i	$0.260259\pi$
$13$	3.51096	+	6.08116i	0.973765	+	1.68661i	0.289812	+	0.957084i	$0.406407\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.27878	−	2.21492i	0.310151	−	0.537197i	−0.668244	−	0.743942i	$-0.732954\pi$
$17$	1.27878	−	2.21492i	0.310151	−	0.537197i	0.978395	+	0.206745i	$0.0662872\pi$
$18$		0			0
$19$	−2.70498	+	3.41805i	−0.620565	+	0.784155i
$19$	−2.70498	+	3.41805i	−0.620565	+	0.784155i
$20$		0			0
$21$	−0.575952	+	0.997578i	−0.125683	+	0.217689i
$22$		0			0
$23$	−4.01448	−	6.95328i	−0.837076	−	1.44986i	−0.892329	−	0.451387i	$-0.850930\pi$
$23$	−4.01448	−	6.95328i	−0.837076	−	1.44986i	0.0552521	−	0.998472i	$-0.482404\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.62425			−0.505036
$28$		0			0
$29$	0.941734	+	1.63113i	0.174876	+	0.302893i	0.940118	−	0.340849i	$-0.110714\pi$
$29$	0.941734	+	1.63113i	0.174876	+	0.302893i	−0.765243	+	0.643742i	$0.777381\pi$
$30$		0			0
$31$	5.98111			1.07424			0.537120	−	0.843506i	$-0.319512\pi$
$31$	5.98111			1.07424			0.537120	+	0.843506i	$0.319512\pi$
$32$		0			0
$33$	−0.503519	+	0.872121i	−0.0876515	+	0.151817i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.86105			−0.470353			−0.235177	−	0.971953i	$-0.575567\pi$
$37$	−2.86105			−0.470353			−0.235177	+	0.971953i	$0.575567\pi$
$38$		0			0
$39$	−3.17989			−0.509190
$40$		0			0
$41$	−3.67524	+	6.36571i	−0.573977	+	0.994157i	0.422175	+	0.906514i	$0.361267\pi$
$41$	−3.67524	+	6.36571i	−0.573977	+	0.994157i	−0.996152	+	0.0876426i	$0.972067\pi$
$42$		0			0
$43$	−1.84706	+	3.19919i	−0.281673	+	0.487873i	−0.971797	−	0.235819i	$-0.924223\pi$
$43$	−1.84706	+	3.19919i	−0.281673	+	0.487873i	0.690124	+	0.723691i	$0.257556\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.36448	−	4.09540i	−0.344895	−	0.597376i	0.640440	−	0.768008i	$-0.278752\pi$
$47$	−2.36448	−	4.09540i	−0.344895	−	0.597376i	−0.985335	+	0.170633i	$0.945419\pi$
$48$		0			0
$49$	−0.529782			−0.0756832
$50$		0			0
$51$	0.579100	+	1.00303i	0.0810903	+	0.140453i
$52$		0			0
$53$	−5.14549	−	8.91226i	−0.706788	−	1.22419i	−0.966042	−	0.258383i	$-0.916810\pi$
$53$	−5.14549	−	8.91226i	−0.706788	−	1.22419i	0.259255	−	0.965809i	$-0.416523\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.728020	−	1.83478i	−0.0964286	−	0.243023i
$58$		0			0
$59$	3.73666	−	6.47208i	0.486472	−	0.842593i	−0.513408	−	0.858145i	$-0.671617\pi$
$59$	3.73666	−	6.47208i	0.486472	−	0.842593i	0.999879	+	0.0155515i	$0.00495040\pi$
$60$		0			0
$61$	4.17839	+	7.23719i	0.534988	+	0.926627i	0.999164	+	0.0408838i	$0.0130174\pi$
$61$	4.17839	+	7.23719i	0.534988	+	0.926627i	−0.464176	+	0.885743i	$0.653649\pi$
$62$		0			0
$63$	3.55467	+	6.15687i	0.447847	+	0.775693i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.17997	+	10.7040i	0.755004	+	1.30771i	0.945372	+	0.325993i	$0.105698\pi$
$67$	6.17997	+	10.7040i	0.755004	+	1.30771i	−0.190368	+	0.981713i	$0.560968\pi$
$68$		0			0
$69$	3.63593			0.437715
$70$		0			0
$71$	−4.13931	+	7.16950i	−0.491246	+	0.850863i	−0.999949	−	0.0100790i	$-0.996792\pi$
$71$	−4.13931	+	7.16950i	−0.491246	+	0.850863i	0.508703	+	0.860942i	$0.330125\pi$
$72$		0			0
$73$	6.32134	−	10.9489i	0.739857	−	1.28147i	−0.212703	−	0.977117i	$-0.568227\pi$
$73$	6.32134	−	10.9489i	0.739857	−	1.28147i	0.952559	−	0.304352i	$-0.0984401\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.65651			0.644620
$78$		0			0
$79$	2.13067	−	3.69043i	0.239719	−	0.415206i	−0.720914	−	0.693024i	$-0.756278\pi$
$79$	2.13067	−	3.69043i	0.239719	−	0.415206i	0.960634	+	0.277818i	$0.0896112\pi$
$80$		0			0
$81$	−3.59819	+	6.23225i	−0.399799	+	0.692472i
$82$		0			0
$83$	14.7613			1.62026			0.810132	−	0.586248i	$-0.199396\pi$
$83$	14.7613			1.62026			0.810132	+	0.586248i	$0.199396\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.852933			−0.0914440
$88$		0			0
$89$	7.19403	+	12.4604i	0.762566	+	1.32080i	0.941524	+	0.336946i	$0.109394\pi$
$89$	7.19403	+	12.4604i	0.762566	+	1.32080i	−0.178958	+	0.983857i	$0.557273\pi$
$90$		0			0
$91$	8.93069	+	15.4684i	0.936191	+	1.62153i
$92$		0			0
$93$	−1.35428	+	2.34568i	−0.140432	+	0.243236i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.91488	−	5.04871i	0.295961	−	0.512619i	−0.679247	−	0.733910i	$-0.737694\pi$
$97$	2.91488	−	5.04871i	0.295961	−	0.512619i	0.975208	+	0.221291i	$0.0710269\pi$
$98$		0			0
$99$	3.10763	+	5.38258i	0.312329	+	0.540969i
$100$		0			0
$101$	6.47686	+	11.2183i	0.644472	+	1.11626i	0.984423	+	0.175815i	$0.0562560\pi$
$101$	6.47686	+	11.2183i	0.644472	+	1.11626i	−0.339951	+	0.940443i	$0.610411\pi$
$102$		0			0
$103$	−16.6116			−1.63679			−0.818394	−	0.574658i	$-0.805135\pi$
$103$	−16.6116			−1.63679			−0.818394	+	0.574658i	$0.805135\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.59275			−0.443998			−0.221999	−	0.975047i	$-0.571258\pi$
$107$	−4.59275			−0.443998			−0.221999	+	0.975047i	$0.571258\pi$
$108$		0			0
$109$	1.30902	−	2.26728i	0.125381	−	0.217166i	−0.796501	−	0.604637i	$-0.793318\pi$
$109$	1.30902	−	2.26728i	0.125381	−	0.217166i	0.921882	+	0.387471i	$0.126651\pi$
$110$		0			0
$111$	0.647816	−	1.12205i	0.0614880	−	0.106500i
$112$		0			0
$113$	−0.509357			−0.0479163			−0.0239581	−	0.999713i	$-0.507627\pi$
$113$	−0.509357			−0.0479163			−0.0239581	+	0.999713i	$0.507627\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−9.81286	+	16.9964i	−0.907200	+	1.57132i
$118$		0			0
$119$	3.25279	−	5.63401i	0.298183	−	0.516468i
$120$		0			0
$121$	−6.05486			−0.550441
$122$		0			0
$123$	−1.66434	−	2.88273i	−0.150069	−	0.259927i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.367242	+	0.636081i	0.0325874	+	0.0564431i	0.881859	−	0.471513i	$-0.156292\pi$
$127$	0.367242	+	0.636081i	0.0325874	+	0.0564431i	−0.849272	+	0.527956i	$0.822959\pi$
$128$		0			0
$129$	−0.836444	−	1.44876i	−0.0736448	−	0.127556i
$130$		0			0
$131$	2.84274	−	4.92377i	0.248371	−	0.430192i	−0.714703	−	0.699428i	$-0.753438\pi$
$131$	2.84274	−	4.92377i	0.248371	−	0.430192i	0.963074	+	0.269236i	$0.0867713\pi$
$132$		0			0
$133$	−6.88055	+	8.69437i	−0.596620	+	0.753898i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.39993	−	16.2812i	−0.803091	−	1.39099i	−0.917573	−	0.397568i	$-0.869854\pi$
$137$	−9.39993	−	16.2812i	−0.803091	−	1.39099i	0.114482	−	0.993425i	$-0.463479\pi$
$138$		0			0
$139$	−2.05362	−	3.55697i	−0.174186	−	0.301698i	0.765694	−	0.643206i	$-0.222396\pi$
$139$	−2.05362	−	3.55697i	−0.174186	−	0.301698i	−0.939879	+	0.341507i	$0.889063\pi$
$140$		0			0
$141$	2.14152			0.180349
$142$		0			0
$143$	7.80756	+	13.5231i	0.652901	+	1.13086i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.119957	−	0.207771i	0.00989385	−	0.0171367i
$148$		0			0
$149$	2.08175	−	3.60570i	0.170544	−	0.295391i	−0.768066	−	0.640370i	$-0.778781\pi$
$149$	2.08175	−	3.60570i	0.170544	−	0.295391i	0.938610	+	0.344980i	$0.112114\pi$
$150$		0			0
$151$	17.7955			1.44818			0.724090	−	0.689706i	$-0.242260\pi$
$151$	17.7955			1.44818			0.724090	+	0.689706i	$0.242260\pi$
$152$		0			0
$153$	7.14821			0.577899
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.67476	+	8.09693i	−0.373087	+	0.646205i	−0.990039	−	0.140796i	$-0.955034\pi$
$157$	−4.67476	+	8.09693i	−0.373087	+	0.646205i	0.616952	+	0.787001i	$0.288367\pi$
$158$		0			0
$159$	4.66030			0.369586
$160$		0			0
$161$	−10.2115	−	17.6868i	−0.804777	−	1.39391i
$162$		0			0
$163$	1.55215			0.121574			0.0607869	−	0.998151i	$-0.480639\pi$
$163$	1.55215			0.121574			0.0607869	+	0.998151i	$0.480639\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.05980	+	7.03177i	0.314157	+	0.544135i	0.979258	−	0.202618i	$-0.0649450\pi$
$167$	4.05980	+	7.03177i	0.314157	+	0.544135i	−0.665101	+	0.746753i	$0.731612\pi$
$168$		0			0
$169$	−18.1537	+	31.4431i	−1.39644	+	2.41870i
$170$		0			0
$171$	−12.0534	−	1.77073i	−0.921748	−	0.135411i
$172$		0			0
$173$	0.365686	−	0.633386i	0.0278026	−	0.0481555i	−0.851789	−	0.523884i	$-0.824482\pi$
$173$	0.365686	−	0.633386i	0.0278026	−	0.0481555i	0.879592	+	0.475729i	$0.157816\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.69216	+	2.93090i	0.127190	+	0.220300i
$178$		0			0
$179$	2.68858			0.200954			0.100477	−	0.994939i	$-0.467963\pi$
$179$	2.68858			0.200954			0.100477	+	0.994939i	$0.467963\pi$
$180$		0			0
$181$	2.75090	+	4.76469i	0.204473	+	0.354157i	0.949965	−	0.312358i	$-0.101119\pi$
$181$	2.75090	+	4.76469i	0.204473	+	0.354157i	−0.745492	+	0.666515i	$0.767785\pi$
$182$		0			0
$183$	−3.78439			−0.279750
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.84372	−	4.92547i	0.207953	−	0.360186i
$188$		0			0
$189$	−6.67520			−0.485549
$190$		0			0
$191$	9.39845			0.680048			0.340024	−	0.940417i	$-0.389565\pi$
$191$	9.39845			0.680048			0.340024	+	0.940417i	$0.389565\pi$
$192$		0			0
$193$	−5.77864	+	10.0089i	−0.415956	+	0.720457i	−0.995528	−	0.0944641i	$-0.969886\pi$
$193$	−5.77864	+	10.0089i	−0.415956	+	0.720457i	0.579572	+	0.814921i	$0.303220\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.11825			0.364660			0.182330	−	0.983237i	$-0.441636\pi$
$197$	5.11825			0.364660			0.182330	+	0.983237i	$0.441636\pi$
$198$		0			0
$199$	−6.71897	−	11.6376i	−0.476295	−	0.824968i	0.523336	−	0.852127i	$-0.324687\pi$
$199$	−6.71897	−	11.6376i	−0.476295	−	0.824968i	−0.999631	+	0.0271588i	$0.991354\pi$
$200$		0			0
$201$	−5.59723			−0.394798
$202$		0			0
$203$	2.39545	+	4.14905i	0.168128	+	0.291206i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	11.2202	−	19.4339i	0.779855	−	1.35075i
$208$		0			0
$209$	−6.01524	+	7.60096i	−0.416083	+	0.525769i
$210$		0			0
$211$	2.54063	−	4.40050i	0.174904	−	0.302943i	−0.765224	−	0.643764i	$-0.777372\pi$
$211$	2.54063	−	4.40050i	0.174904	−	0.302943i	0.940128	+	0.340821i	$0.110705\pi$
$212$		0			0
$213$	−1.87450	−	3.24673i	−0.128438	−	0.222462i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	15.2139			1.03279
$218$		0			0
$219$	2.86263	+	4.95823i	0.193439	+	0.335046i
$220$		0			0
$221$	17.9590			1.20806
$222$		0			0
$223$	11.8464	−	20.5186i	0.793295	−	1.37403i	−0.130621	−	0.991432i	$-0.541697\pi$
$223$	11.8464	−	20.5186i	0.793295	−	1.37403i	0.923916	−	0.382595i	$-0.124970\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	19.0306			1.26310			0.631551	−	0.775334i	$-0.282418\pi$
$227$	19.0306			1.26310			0.631551	+	0.775334i	$0.282418\pi$
$228$		0			0
$229$	−27.9233			−1.84523			−0.922613	−	0.385727i	$-0.873951\pi$
$229$	−27.9233			−1.84523			−0.922613	+	0.385727i	$0.873951\pi$
$230$		0			0
$231$	−1.28078	+	2.21838i	−0.0842694	+	0.145959i
$232$		0			0
$233$	−7.08296	+	12.2680i	−0.464020	+	0.803706i	−0.999157	−	0.0410592i	$-0.986927\pi$
$233$	−7.08296	+	12.2680i	−0.464020	+	0.803706i	0.535137	+	0.844765i	$0.320260\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.964881	+	1.67122i	0.0626757	+	0.108558i
$238$		0			0
$239$	17.0237			1.10117			0.550585	−	0.834779i	$-0.314405\pi$
$239$	17.0237			1.10117			0.550585	+	0.834779i	$0.314405\pi$
$240$		0			0
$241$	−8.59549	−	14.8878i	−0.553684	−	0.959009i	−0.998005	−	0.0631409i	$-0.979888\pi$
$241$	−8.59549	−	14.8878i	−0.553684	−	0.959009i	0.444321	−	0.895868i	$-0.353445\pi$
$242$		0			0
$243$	−5.56582	−	9.64028i	−0.357047	−	0.618424i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−30.2828	−	4.44876i	−1.92685	−	0.283068i
$248$		0			0
$249$	−3.34235	+	5.78911i	−0.211813	+	0.366870i
$250$		0			0
$251$	−11.8853	−	20.5860i	−0.750195	−	1.29938i	−0.947728	−	0.319079i	$-0.896626\pi$
$251$	−11.8853	−	20.5860i	−0.750195	−	1.29938i	0.197534	−	0.980296i	$-0.436707\pi$
$252$		0			0
$253$	−8.92727	−	15.4625i	−0.561252	−	0.972118i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.716409	−	1.24086i	−0.0446884	−	0.0774026i	0.842816	−	0.538202i	$-0.180896\pi$
$257$	−0.716409	−	1.24086i	−0.0446884	−	0.0774026i	−0.887504	+	0.460799i	$0.847563\pi$
$258$		0			0
$259$	−7.27754			−0.452204
$260$		0			0
$261$	−2.63208	+	4.55889i	−0.162921	+	0.282188i
$262$		0			0
$263$	−3.56505	+	6.17484i	−0.219830	+	0.380757i	−0.954756	−	0.297390i	$-0.903884\pi$
$263$	−3.56505	+	6.17484i	−0.219830	+	0.380757i	0.734926	+	0.678148i	$0.237217\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.51567			−0.398753
$268$		0			0
$269$	9.13452	−	15.8214i	0.556941	−	0.964651i	−0.440808	−	0.897601i	$-0.645308\pi$
$269$	9.13452	−	15.8214i	0.556941	−	0.964651i	0.997750	−	0.0670494i	$-0.0213585\pi$
$270$		0			0
$271$	2.90265	−	5.02754i	0.176324	−	0.305401i	−0.764295	−	0.644867i	$-0.776913\pi$
$271$	2.90265	−	5.02754i	0.176324	−	0.305401i	0.940619	+	0.339465i	$0.110246\pi$
$272$		0			0
$273$	−8.08857			−0.489543
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.72209			−0.343807			−0.171904	−	0.985114i	$-0.554992\pi$
$277$	−5.72209			−0.343807			−0.171904	+	0.985114i	$0.554992\pi$
$278$		0			0
$279$	8.35838	+	14.4771i	0.500403	+	0.866724i
$280$		0			0
$281$	3.07155	+	5.32009i	0.183233	+	0.317370i	0.942980	−	0.332850i	$-0.108010\pi$
$281$	3.07155	+	5.32009i	0.183233	+	0.317370i	−0.759746	+	0.650220i	$0.774677\pi$
$282$		0			0
$283$	8.22632	−	14.2484i	0.489004	−	0.846980i	−0.510916	−	0.859631i	$-0.670694\pi$
$283$	8.22632	−	14.2484i	0.489004	−	0.846980i	0.999920	+	0.0126510i	$0.00402704\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.34858	+	16.1922i	−0.551829	+	0.955796i
$288$		0			0
$289$	5.22942	+	9.05763i	0.307613	+	0.532801i
$290$		0			0
$291$	1.32001	+	2.28632i	0.0773803	+	0.134027i
$292$		0			0
$293$	19.5684			1.14320			0.571599	−	0.820533i	$-0.306323\pi$
$293$	19.5684			1.14320			0.571599	+	0.820533i	$0.306323\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.83571			−0.338622
$298$		0			0
$299$	28.1893	−	48.8253i	1.63023	−	2.82364i
$300$		0			0
$301$	−4.69829	+	8.13767i	−0.270805	+	0.469047i
$302$		0			0
$303$	−5.86613			−0.337000
$304$		0			0
$305$		0			0
$306$		0			0
$307$	14.3994	−	24.9405i	0.821817	−	1.42343i	−0.0825100	−	0.996590i	$-0.526294\pi$
$307$	14.3994	−	24.9405i	0.821817	−	1.42343i	0.904327	−	0.426839i	$-0.140373\pi$
$308$		0			0
$309$	3.76130	−	6.51476i	0.213973	−	0.370612i
$310$		0			0
$311$	−19.4309			−1.10182			−0.550911	−	0.834564i	$-0.685720\pi$
$311$	−19.4309			−1.10182			−0.550911	+	0.834564i	$0.685720\pi$
$312$		0			0
$313$	4.81885	+	8.34649i	0.272377	+	0.471772i	0.969470	−	0.245209i	$-0.0788567\pi$
$313$	4.81885	+	8.34649i	0.272377	+	0.471772i	−0.697093	+	0.716981i	$0.745523\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.115348	−	0.199789i	−0.00647860	−	0.0112213i	0.862768	−	0.505600i	$-0.168729\pi$
$317$	−0.115348	−	0.199789i	−0.00647860	−	0.0112213i	−0.869247	+	0.494379i	$0.835396\pi$
$318$		0			0
$319$	2.09420	+	3.62726i	0.117253	+	0.203087i
$320$		0			0
$321$	1.03992	−	1.80119i	0.0580427	−	0.100533i
$322$		0			0
$323$	4.11163	+	10.3623i	0.228777	+	0.576572i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.592791	+	1.02674i	0.0327814	+	0.0567791i
$328$		0			0
$329$	−6.01444	−	10.4173i	−0.331587	−	0.574325i
$330$		0			0
$331$	−12.1135			−0.665820			−0.332910	−	0.942959i	$-0.608031\pi$
$331$	−12.1135			−0.665820			−0.332910	+	0.942959i	$0.608031\pi$
$332$		0			0
$333$	−3.99821	−	6.92510i	−0.219100	−	0.379493i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.57090	+	9.64909i	−0.303466	+	0.525619i	−0.976919	−	0.213611i	$-0.931477\pi$
$337$	−5.57090	+	9.64909i	−0.303466	+	0.525619i	0.673452	+	0.739231i	$0.264811\pi$
$338$		0			0
$339$	0.115332	−	0.199761i	0.00626396	−	0.0108495i
$340$		0			0
$341$	13.3006			0.720268
$342$		0			0
$343$	−19.1532			−1.03418
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.84478	+	4.92730i	−0.152716	+	0.264511i	−0.932225	−	0.361880i	$-0.882135\pi$
$347$	−2.84478	+	4.92730i	−0.152716	+	0.264511i	0.779509	+	0.626391i	$0.215468\pi$
$348$		0			0
$349$	0.369374			0.0197722			0.00988608	−	0.999951i	$-0.496853\pi$
$349$	0.369374			0.0197722			0.00988608	+	0.999951i	$0.496853\pi$
$350$		0			0
$351$	−9.21362	−	15.9585i	−0.491787	−	0.851799i
$352$		0			0
$353$	−1.87124			−0.0995962			−0.0497981	−	0.998759i	$-0.515858\pi$
$353$	−1.87124			−0.0995962			−0.0497981	+	0.998759i	$0.515858\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.47304	+	2.55137i	0.0779613	+	0.135033i
$358$		0			0
$359$	8.47802	−	14.6844i	0.447453	−	0.775011i	−0.550767	−	0.834659i	$-0.685665\pi$
$359$	8.47802	−	14.6844i	0.447453	−	0.775011i	0.998219	+	0.0596485i	$0.0189980\pi$
$360$		0			0
$361$	−4.36618	−	18.4915i	−0.229799	−	0.973238i
$362$		0			0
$363$	1.37098	−	2.37460i	0.0719577	−	0.124634i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.89237	+	3.27769i	0.0987812	+	0.171094i	0.911180	−	0.412008i	$-0.135172\pi$
$367$	1.89237	+	3.27769i	0.0987812	+	0.171094i	−0.812399	+	0.583102i	$0.801839\pi$
$368$		0			0
$369$	−20.5441			−1.06948
$370$		0			0
$371$	−13.0884	−	22.6698i	−0.679516	−	1.17696i
$372$		0			0
$373$	4.51203			0.233624			0.116812	−	0.993154i	$-0.462732\pi$
$373$	4.51203			0.233624			0.116812	+	0.993154i	$0.462732\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.61278	+	11.4537i	−0.340575	+	0.589894i
$378$		0			0
$379$	4.64242			0.238465			0.119233	−	0.992866i	$-0.461957\pi$
$379$	4.64242			0.238465			0.119233	+	0.992866i	$0.461957\pi$
$380$		0			0
$381$	−0.332612			−0.0170403
$382$		0			0
$383$	6.99088	−	12.1086i	0.357218	−	0.618719i	−0.630277	−	0.776370i	$-0.717059\pi$
$383$	6.99088	−	12.1086i	0.357218	−	0.618719i	0.987495	+	0.157651i	$0.0503922\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.3248			−0.524837
$388$		0			0
$389$	−3.93460	−	6.81492i	−0.199492	−	0.345530i	0.748872	−	0.662715i	$-0.230596\pi$
$389$	−3.93460	−	6.81492i	−0.199492	−	0.345530i	−0.948364	+	0.317185i	$0.897263\pi$
$390$		0			0
$391$	−20.5346			−1.03848
$392$		0			0
$393$	1.28734	+	2.22974i	0.0649378	+	0.112476i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.48528	−	14.6969i	0.425864	−	0.737618i	−0.570637	−	0.821203i	$-0.693304\pi$
$397$	8.48528	−	14.6969i	0.425864	−	0.737618i	0.996501	+	0.0835846i	$0.0266369\pi$
$398$		0			0
$399$	−1.85184	−	4.66706i	−0.0927078	−	0.233645i
$400$		0			0
$401$	−7.16651	+	12.4128i	−0.357878	+	0.619864i	−0.987606	−	0.156952i	$-0.949833\pi$
$401$	−7.16651	+	12.4128i	−0.357878	+	0.619864i	0.629728	+	0.776816i	$0.283166\pi$
$402$		0			0
$403$	20.9994	+	36.3721i	1.04606	+	1.81182i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.36231			−0.315368
$408$		0			0
$409$	0.122530	+	0.212228i	0.00605872	+	0.0104940i	0.869039	−	0.494744i	$-0.164738\pi$
$409$	0.122530	+	0.212228i	0.00605872	+	0.0104940i	−0.862980	+	0.505238i	$0.831405\pi$
$410$		0			0
$411$	8.51357			0.419943
$412$		0			0
$413$	9.50480	−	16.4628i	0.467701	−	0.810081i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.85997			0.0910832
$418$		0			0
$419$	−25.4690			−1.24424			−0.622122	−	0.782920i	$-0.713729\pi$
$419$	−25.4690			−1.24424			−0.622122	+	0.782920i	$0.713729\pi$
$420$		0			0
$421$	−3.02703	+	5.24297i	−0.147529	+	0.255527i	−0.930313	−	0.366765i	$-0.880465\pi$
$421$	−3.02703	+	5.24297i	−0.147529	+	0.255527i	0.782785	+	0.622292i	$0.213798\pi$
$422$		0			0
$423$	6.60855	−	11.4463i	0.321318	−	0.556540i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	10.6284	+	18.4090i	0.514345	+	0.890872i
$428$		0			0
$429$	−7.07134			−0.341408
$430$		0			0
$431$	−11.1005	−	19.2267i	−0.534694	−	0.926117i	−0.999178	−	0.0405356i	$-0.987094\pi$
$431$	−11.1005	−	19.2267i	−0.534694	−	0.926117i	0.464484	−	0.885581i	$-0.346240\pi$
$432$		0			0
$433$	12.1298	+	21.0094i	0.582920	+	1.00965i	0.995131	+	0.0985593i	$0.0314234\pi$
$433$	12.1298	+	21.0094i	0.582920	+	1.00965i	−0.412211	+	0.911089i	$0.635243\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	34.6258	+	5.08677i	1.65637	+	0.243333i
$438$		0			0
$439$	11.9487	−	20.6957i	0.570279	−	0.987753i	−0.426258	−	0.904602i	$-0.640168\pi$
$439$	11.9487	−	20.6957i	0.570279	−	0.987753i	0.996537	−	0.0831509i	$-0.0264983\pi$
$440$		0			0
$441$	−0.740350	−	1.28232i	−0.0352548	−	0.0610631i
$442$		0			0
$443$	−10.3356	−	17.9017i	−0.491057	−	0.850536i	0.508890	−	0.860832i	$-0.330056\pi$
$443$	−10.3356	−	17.9017i	−0.491057	−	0.850536i	−0.999947	+	0.0102958i	$0.996723\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.942727	+	1.63285i	0.0445895	+	0.0772312i
$448$		0			0
$449$	−6.64143			−0.313429			−0.156714	−	0.987644i	$-0.550090\pi$
$449$	−6.64143			−0.313429			−0.156714	+	0.987644i	$0.550090\pi$
$450$		0			0
$451$	−8.17289	+	14.1559i	−0.384846	+	0.666573i
$452$		0			0
$453$	−4.02937	+	6.97908i	−0.189316	+	0.327906i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.3433			0.670952			0.335476	−	0.942049i	$-0.391103\pi$
$457$	14.3433			0.670952			0.335476	+	0.942049i	$0.391103\pi$
$458$		0			0
$459$	−3.35584	+	5.81249i	−0.156637	+	0.271304i
$460$		0			0
$461$	13.3682	−	23.1544i	0.622618	−	1.07841i	−0.366378	−	0.930466i	$-0.619402\pi$
$461$	13.3682	−	23.1544i	0.622618	−	1.07841i	0.988996	−	0.147940i	$-0.0472643\pi$
$462$		0			0
$463$	−12.0950			−0.562101			−0.281051	−	0.959693i	$-0.590683\pi$
$463$	−12.0950			−0.562101			−0.281051	+	0.959693i	$0.590683\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−27.3169			−1.26408			−0.632038	−	0.774938i	$-0.717781\pi$
$467$	−27.3169			−1.26408			−0.632038	+	0.774938i	$0.717781\pi$
$468$		0			0
$469$	15.7198	+	27.2274i	0.725871	+	1.25725i
$470$		0			0
$471$	−2.11698	−	3.66671i	−0.0975452	−	0.168953i
$472$		0			0
$473$	−4.10742	+	7.11427i	−0.188860	+	0.327114i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	14.3813	−	24.9091i	0.658473	−	1.14051i
$478$		0			0
$479$	−3.69624	−	6.40208i	−0.168886	−	0.292519i	0.769143	−	0.639077i	$-0.220684\pi$
$479$	−3.69624	−	6.40208i	−0.168886	−	0.292519i	−0.938028	+	0.346559i	$0.887350\pi$
$480$		0			0
$481$	−10.0450	−	17.3985i	−0.458013	−	0.793302i
$482$		0			0
$483$	9.24858			0.420825
$484$		0			0
$485$		0			0
$486$		0			0
$487$	12.9424			0.586477			0.293239	−	0.956039i	$-0.405267\pi$
$487$	12.9424			0.586477			0.293239	+	0.956039i	$0.405267\pi$
$488$		0			0
$489$	−0.351447	+	0.608725i	−0.0158930	+	0.0275275i
$490$		0			0
$491$	5.59974	−	9.69903i	0.252713	−	0.437711i	−0.711559	−	0.702626i	$-0.752011\pi$
$491$	5.59974	−	9.69903i	0.252713	−	0.437711i	0.964272	+	0.264915i	$0.0853439\pi$
$492$		0			0
$493$	4.81710			0.216951
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.5290	+	18.2368i	−0.472291	+	0.818032i
$498$		0			0
$499$	12.9699	−	22.4645i	0.580611	−	1.00565i	−0.414796	−	0.909914i	$-0.636147\pi$
$499$	12.9699	−	22.4645i	0.580611	−	1.00565i	0.995407	−	0.0957335i	$-0.0305196\pi$
$500$		0			0
$501$	−3.67698			−0.164275
$502$		0			0
$503$	13.6300	+	23.6079i	0.607733	+	1.05262i	0.991613	+	0.129241i	$0.0412541\pi$
$503$	13.6300	+	23.6079i	0.607733	+	1.05262i	−0.383881	+	0.923383i	$0.625413\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.22093	−	14.2391i	−0.365104	−	0.632379i
$508$		0			0
$509$	−12.6203	−	21.8591i	−0.559386	−	0.968885i	−0.997548	−	0.0699892i	$-0.977704\pi$
$509$	−12.6203	−	21.8591i	−0.559386	−	0.968885i	0.438161	−	0.898896i	$-0.355630\pi$
$510$		0			0
$511$	16.0794	−	27.8503i	0.711309	−	1.23202i
$512$		0			0
$513$	7.09853	−	8.96981i	0.313408	−	0.396027i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−5.25806	−	9.10722i	−0.231249	−	0.400535i
$518$		0			0
$519$	0.165602	+	0.286831i	0.00726911	+	0.0125905i
$520$		0			0
$521$	−24.8142			−1.08713			−0.543565	−	0.839367i	$-0.682926\pi$
$521$	−24.8142			−1.08713			−0.543565	+	0.839367i	$0.682926\pi$
$522$		0			0
$523$	−3.08063	−	5.33581i	−0.134706	−	0.233318i	0.790779	−	0.612102i	$-0.209676\pi$
$523$	−3.08063	−	5.33581i	−0.134706	−	0.233318i	−0.925485	+	0.378784i	$0.876342\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.64855	−	13.2477i	0.333176	−	0.577078i
$528$		0			0
$529$	−20.7321	+	35.9090i	−0.901394	+	1.56126i
$530$		0			0
$531$	20.8874			0.906434
$532$		0			0
$533$	−51.6145			−2.23567
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.608765	+	1.05441i	−0.0262702	+	0.0455013i
$538$		0			0
$539$	−1.17811			−0.0507449
$540$		0			0
$541$	−3.27394	−	5.67063i	−0.140758	−	0.243799i	0.787025	−	0.616922i	$-0.211620\pi$
$541$	−3.27394	−	5.67063i	−0.140758	−	0.243799i	−0.927782	+	0.373122i	$0.878287\pi$
$542$		0			0
$543$	−2.49150			−0.106921
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.2770	+	19.5323i	0.482169	+	0.835141i	0.999791	−	0.0204683i	$-0.00651572\pi$
$547$	11.2770	+	19.5323i	0.482169	+	0.835141i	−0.517621	+	0.855610i	$0.673182\pi$
$548$		0			0
$549$	−11.6783	+	20.2274i	−0.498417	+	0.863284i
$550$		0			0
$551$	−8.12266	−	1.19328i	−0.346037	−	0.0508353i
$552$		0			0
$553$	5.41971	−	9.38722i	0.230470	−	0.399185i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.12281	−	14.0691i	−0.344175	−	0.596128i	0.641029	−	0.767517i	$-0.278508\pi$
$557$	−8.12281	−	14.0691i	−0.344175	−	0.596128i	−0.985203	+	0.171389i	$0.945175\pi$
$558$		0			0
$559$	−25.9397			−1.09713
$560$		0			0
$561$	1.28779	+	2.23051i	0.0543703	+	0.0941722i
$562$		0			0
$563$	−32.4581			−1.36795			−0.683974	−	0.729506i	$-0.739750\pi$
$563$	−32.4581			−1.36795			−0.683974	+	0.729506i	$0.739750\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−9.15258	+	15.8527i	−0.384372	+	0.665752i
$568$		0			0
$569$	25.5422			1.07078			0.535392	−	0.844604i	$-0.320164\pi$
$569$	25.5422			1.07078			0.535392	+	0.844604i	$0.320164\pi$
$570$		0			0
$571$	25.9974			1.08796			0.543979	−	0.839099i	$-0.316917\pi$
$571$	25.9974			1.08796			0.543979	+	0.839099i	$0.316917\pi$
$572$		0			0
$573$	−2.12806	+	3.68590i	−0.0889008	+	0.153981i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−44.5844			−1.85607			−0.928037	−	0.372489i	$-0.878504\pi$
$577$	−44.5844			−1.85607			−0.928037	+	0.372489i	$0.878504\pi$
$578$		0			0
$579$	−2.61687	−	4.53256i	−0.108754	−	0.188367i
$580$		0			0
$581$	37.5478			1.55774
$582$		0			0
$583$	−11.4424	−	19.8188i	−0.473895	−	0.820810i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.28884	+	12.6246i	−0.300842	+	0.521074i	−0.976327	−	0.216300i	$-0.930601\pi$
$587$	−7.28884	+	12.6246i	−0.300842	+	0.521074i	0.675485	+	0.737374i	$0.263935\pi$
$588$		0			0
$589$	−16.1788	+	20.4438i	−0.666635	+	0.842371i
$590$		0			0
$591$	−1.15891	+	2.00728i	−0.0476710	+	0.0825686i
$592$		0			0
$593$	−11.8657	−	20.5520i	−0.487265	−	0.843968i	0.512628	−	0.858611i	$-0.328672\pi$
$593$	−11.8657	−	20.5520i	−0.487265	−	0.843968i	−0.999893	+	0.0146433i	$0.995339\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.08541			0.249059
$598$		0			0
$599$	9.86173	+	17.0810i	0.402939	+	0.697911i	0.994079	−	0.108658i	$-0.0346552\pi$
$599$	9.86173	+	17.0810i	0.402939	+	0.697911i	−0.591140	+	0.806569i	$0.701322\pi$
$600$		0			0
$601$	−45.0351			−1.83702			−0.918509	−	0.395400i	$-0.870606\pi$
$601$	−45.0351			−1.83702			−0.918509	+	0.395400i	$0.870606\pi$
$602$		0			0
$603$	−17.2726	+	29.9170i	−0.703393	+	1.21831i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−7.24160			−0.293928			−0.146964	−	0.989142i	$-0.546950\pi$
$607$	−7.24160			−0.293928			−0.146964	+	0.989142i	$0.546950\pi$
$608$		0			0
$609$	−2.16957			−0.0879156
$610$		0			0
$611$	16.6032	−	28.7576i	0.671693	−	1.16341i
$612$		0			0
$613$	18.4052	−	31.8788i	0.743381	−	1.28757i	−0.207567	−	0.978221i	$-0.566554\pi$
$613$	18.4052	−	31.8788i	0.743381	−	1.28757i	0.950947	−	0.309352i	$-0.100112\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.3448	−	31.7741i	−0.738533	−	1.27918i	−0.953156	−	0.302479i	$-0.902186\pi$
$617$	−18.3448	−	31.7741i	−0.738533	−	1.27918i	0.214623	−	0.976697i	$-0.431148\pi$
$618$		0			0
$619$	24.1569			0.970948			0.485474	−	0.874251i	$-0.338647\pi$
$619$	24.1569			0.970948			0.485474	+	0.874251i	$0.338647\pi$
$620$		0			0
$621$	10.5350	+	18.2471i	0.422754	+	0.732231i
$622$		0			0
$623$	18.2992	+	31.6951i	0.733142	+	1.26984i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.61895	−	4.08013i	−0.0646545	−	0.162945i
$628$		0			0
$629$	−3.65866	+	6.33699i	−0.145880	+	0.252672i
$630$		0			0
$631$	−7.11258	−	12.3193i	−0.283147	−	0.490426i	0.689011	−	0.724751i	$-0.258045\pi$
$631$	−7.11258	−	12.3193i	−0.283147	−	0.490426i	−0.972158	+	0.234325i	$0.924712\pi$
$632$		0			0
$633$	1.15053	+	1.99278i	0.0457295	+	0.0792058i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.86004	−	3.22169i	−0.0736976	−	0.127648i
$638$		0			0
$639$	−23.1381			−0.915330
$640$		0			0
$641$	10.1834	−	17.6382i	0.402222	−	0.696668i	−0.591772	−	0.806105i	$-0.701571\pi$
$641$	10.1834	−	17.6382i	0.402222	−	0.696668i	0.993994	+	0.109437i	$0.0349048\pi$
$642$		0			0
$643$	−5.77586	+	10.0041i	−0.227778	+	0.394523i	−0.957149	−	0.289595i	$-0.906479\pi$
$643$	−5.77586	+	10.0041i	−0.227778	+	0.394523i	0.729371	+	0.684118i	$0.239813\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.1233			−0.515932			−0.257966	−	0.966154i	$-0.583052\pi$
$647$	−13.1233			−0.515932			−0.257966	+	0.966154i	$0.583052\pi$
$648$		0			0
$649$	8.30946	−	14.3924i	0.326175	−	0.564952i
$650$		0			0
$651$	−3.44483	+	5.96663i	−0.135014	+	0.233851i
$652$		0			0
$653$	19.4406			0.760769			0.380385	−	0.924828i	$-0.375792\pi$
$653$	19.4406			0.760769			0.380385	+	0.924828i	$0.375792\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	35.3353			1.37856
$658$		0			0
$659$	13.7848	+	23.8759i	0.536979	+	0.930074i	0.999065	+	0.0432391i	$0.0137677\pi$
$659$	13.7848	+	23.8759i	0.536979	+	0.930074i	−0.462086	+	0.886835i	$0.652899\pi$
$660$		0			0
$661$	3.88006	+	6.72046i	0.150917	+	0.261396i	0.931565	−	0.363575i	$-0.118444\pi$
$661$	3.88006	+	6.72046i	0.150917	+	0.261396i	−0.780648	+	0.624971i	$0.785111\pi$
$662$		0			0
$663$	−4.06640	+	7.04320i	−0.157926	+	0.273535i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.56114	−	13.0963i	0.292769	−	0.507090i
$668$		0			0
$669$	5.36468	+	9.29190i	0.207411	+	0.359246i
$670$		0			0
$671$	9.29178	+	16.0938i	0.358705	+	0.621295i
$672$		0			0
$673$	24.2617			0.935220			0.467610	−	0.883935i	$-0.345115\pi$
$673$	24.2617			0.935220			0.467610	+	0.883935i	$0.345115\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.88851			−0.187881			−0.0939403	−	0.995578i	$-0.529946\pi$
$677$	−4.88851			−0.187881			−0.0939403	+	0.995578i	$0.529946\pi$
$678$		0			0
$679$	7.41446	−	12.8422i	0.284541	−	0.492839i
$680$		0			0
$681$	−4.30902	+	7.46344i	−0.165122	+	0.286000i
$682$		0			0
$683$	−0.560031			−0.0214290			−0.0107145	−	0.999943i	$-0.503411\pi$
$683$	−0.560031			−0.0214290			−0.0107145	+	0.999943i	$0.503411\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	6.32257	−	10.9510i	0.241221	−	0.417807i
$688$		0			0
$689$	36.1312	−	62.5811i	1.37649	−	2.38415i
$690$		0			0
$691$	−14.5255			−0.552576			−0.276288	−	0.961075i	$-0.589104\pi$
$691$	−14.5255			−0.552576			−0.276288	+	0.961075i	$0.589104\pi$
$692$		0			0
$693$	7.90477	+	13.6915i	0.300277	+	0.520095i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.39969	+	16.2807i	0.356039	+	0.616677i
$698$		0			0
$699$	−3.20754	−	5.55561i	−0.121320	−	0.210133i
$700$		0			0
$701$	1.23926	−	2.14647i	0.0468064	−	0.0810710i	−0.841673	−	0.539987i	$-0.818429\pi$
$701$	1.23926	−	2.14647i	0.0468064	−	0.0810710i	0.888479	+	0.458916i	$0.151762\pi$
$702$		0			0
$703$	7.73907	−	9.77921i	0.291885	−	0.368830i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.4749	+	28.5354i	0.619604	+	1.07319i
$708$		0			0
$709$	16.1966	+	28.0533i	0.608276	+	1.05356i	0.991525	+	0.129919i	$0.0414718\pi$
$709$	16.1966	+	28.0533i	0.608276	+	1.05356i	−0.383249	+	0.923645i	$0.625195\pi$
$710$		0			0
$711$	11.9101			0.446665
$712$		0			0
$713$	−24.0110	−	41.5884i	−0.899221	−	1.55750i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.85461	+	6.67637i	−0.143953	+	0.249334i
$718$		0			0
$719$	−8.64373	+	14.9714i	−0.322357	+	0.558338i	−0.980974	−	0.194140i	$-0.937808\pi$
$719$	−8.64373	+	14.9714i	−0.322357	+	0.558338i	0.658617	+	0.752478i	$0.271142\pi$
$720$		0			0
$721$	−42.2542			−1.57363
$722$		0			0
$723$	7.78497			0.289526
$724$		0			0
$725$		0			0
$726$		0			0
$727$	9.47034	−	16.4031i	0.351236	−	0.608358i	−0.635231	−	0.772323i	$-0.719095\pi$
$727$	9.47034	−	16.4031i	0.351236	−	0.608358i	0.986466	+	0.163965i	$0.0524283\pi$
$728$		0			0
$729$	−16.5481			−0.612894
$730$		0			0
$731$	4.72397	+	8.18216i	0.174722	+	0.302628i
$732$		0			0
$733$	−0.542118			−0.0200236			−0.0100118	−	0.999950i	$-0.503187\pi$
$733$	−0.542118			−0.0200236			−0.0100118	+	0.999950i	$0.503187\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.7428	+	23.8033i	0.506224	+	0.876805i
$738$		0			0
$739$	2.87033	−	4.97156i	0.105587	−	0.182882i	−0.808391	−	0.588646i	$-0.799661\pi$
$739$	2.87033	−	4.97156i	0.105587	−	0.182882i	0.913978	+	0.405764i	$0.132995\pi$
$740$		0			0
$741$	8.60154	−	10.8690i	0.315985	−	0.399284i
$742$		0			0
$743$	11.5060	−	19.9290i	0.422115	−	0.731125i	−0.574031	−	0.818834i	$-0.694621\pi$
$743$	11.5060	−	19.9290i	0.422115	−	0.731125i	0.996146	+	0.0877087i	$0.0279545\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	20.6284	+	35.7294i	0.754752	+	1.30727i
$748$		0			0
$749$	−11.6824			−0.426866
$750$		0			0
$751$	25.9704	+	44.9821i	0.947674	+	1.64142i	0.750306	+	0.661090i	$0.229906\pi$
$751$	25.9704	+	44.9821i	0.947674	+	1.64142i	0.197368	+	0.980330i	$0.436761\pi$
$752$		0			0
$753$	10.7646			0.392283
$754$		0			0
$755$		0			0
$756$		0			0
$757$	6.36406	−	11.0229i	0.231306	−	0.400633i	−0.726887	−	0.686757i	$-0.759034\pi$
$757$	6.36406	−	11.0229i	0.231306	−	0.400633i	0.958193	+	0.286124i	$0.0923669\pi$
$758$		0			0
$759$	8.08547			0.293484
$760$		0			0
$761$	−10.6089			−0.384573			−0.192287	−	0.981339i	$-0.561590\pi$
$761$	−10.6089			−0.384573			−0.192287	+	0.981339i	$0.561590\pi$
$762$		0			0
$763$	3.32969	−	5.76720i	0.120543	−	0.208787i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	52.4770			1.89484
$768$		0			0
$769$	−10.8089	−	18.7215i	−0.389777	−	0.675114i	0.602642	−	0.798012i	$-0.294115\pi$
$769$	−10.8089	−	18.7215i	−0.389777	−	0.675114i	−0.992419	+	0.122898i	$0.960781\pi$
$770$		0			0
$771$	0.648856			0.0233680
$772$		0			0
$773$	21.6637	+	37.5227i	0.779190	+	1.34960i	0.932409	+	0.361404i	$0.117702\pi$
$773$	21.6637	+	37.5227i	0.779190	+	1.34960i	−0.153220	+	0.988192i	$0.548964\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.64783	−	2.85412i	0.0591154	−	0.102391i
$778$		0			0
$779$	−11.8169	−	29.7813i	−0.423384	−	1.06703i
$780$		0			0
$781$	−9.20487	+	15.9433i	−0.329376	+	0.570496i
$782$		0			0
$783$	−2.47134	−	4.28049i	−0.0883185	−	0.152972i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−29.0046			−1.03390			−0.516950	−	0.856015i	$-0.672933\pi$
$787$	−29.0046			−1.03390			−0.516950	+	0.856015i	$0.672933\pi$
$788$		0			0
$789$	−1.61444	−	2.79629i	−0.0574756	−	0.0995507i
$790$		0			0
$791$	−1.29563			−0.0460674
$792$		0			0
$793$	−29.3403	+	50.8189i	−1.04191	+	1.80463i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.2045			−0.503150			−0.251575	−	0.967838i	$-0.580949\pi$
$797$	−14.2045			−0.503150			−0.251575	+	0.967838i	$0.580949\pi$
$798$		0			0
$799$	−12.0946			−0.427878
$800$		0			0
$801$	−20.1068	+	34.8260i	−0.710438	+	1.23052i
$802$		0			0
$803$	14.0572	−	24.3478i	0.496067	−	0.859214i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.13659	+	7.16478i	0.145615	+	0.252212i
$808$		0			0
$809$	14.9781			0.526603			0.263301	−	0.964714i	$-0.415189\pi$
$809$	14.9781			0.526603			0.263301	+	0.964714i	$0.415189\pi$
$810$		0			0
$811$	20.5388	+	35.5742i	0.721214	+	1.24918i	0.960513	+	0.278233i	$0.0897489\pi$
$811$	20.5388	+	35.5742i	0.721214	+	1.24918i	−0.239300	+	0.970946i	$0.576918\pi$
$812$		0			0
$813$	1.31447	+	2.27674i	0.0461006	+	0.0798486i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.93877	−	14.9671i	−0.207771	−	0.523632i
$818$		0			0
$819$	−24.9606	+	43.2330i	−0.872194	+	1.51068i
$820$		0			0
$821$	21.5219	+	37.2771i	0.751120	+	1.30098i	0.947280	+	0.320407i	$0.103820\pi$
$821$	21.5219	+	37.2771i	0.751120	+	1.30098i	−0.196160	+	0.980572i	$0.562847\pi$
$822$		0			0
$823$	7.18105	+	12.4379i	0.250316	+	0.433559i	0.963613	−	0.267302i	$-0.0861323\pi$
$823$	7.18105	+	12.4379i	0.250316	+	0.433559i	−0.713297	+	0.700862i	$0.752799\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.1891	−	38.4326i	−0.771590	−	1.33643i	−0.936691	−	0.350157i	$-0.886128\pi$
$827$	−22.1891	−	38.4326i	−0.771590	−	1.33643i	0.165101	−	0.986277i	$-0.447205\pi$
$828$		0			0
$829$	35.6112			1.23683			0.618413	−	0.785853i	$-0.287776\pi$
$829$	35.6112			1.23683			0.618413	+	0.785853i	$0.287776\pi$
$830$		0			0
$831$	1.29563	−	2.24410i	0.0449450	−	0.0778470i
$832$		0			0
$833$	−0.677477	+	1.17342i	−0.0234732	+	0.0406567i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−15.6959			−0.542530
$838$		0			0
$839$	21.1147	−	36.5718i	0.728962	−	1.26260i	−0.228361	−	0.973577i	$-0.573337\pi$
$839$	21.1147	−	36.5718i	0.728962	−	1.26260i	0.957322	−	0.289022i	$-0.0933301\pi$
$840$		0			0
$841$	12.7263	−	22.0426i	0.438837	−	0.760088i
$842$		0			0
$843$	−2.78192			−0.0958144
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−15.4015			−0.529202
$848$		0			0
$849$	3.72531	+	6.45242i	0.127852	+	0.221447i
$850$		0			0
$851$	11.4856	+	19.8937i	0.393722	+	0.681946i
$852$		0			0
$853$	−9.90917	+	17.1632i	−0.339284	+	0.587656i	−0.984298	−	0.176514i	$-0.943518\pi$
$853$	−9.90917	+	17.1632i	−0.339284	+	0.587656i	0.645015	+	0.764170i	$0.276851\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.7082	+	44.5279i	−0.878175	+	1.52104i	−0.0248328	+	0.999692i	$0.507905\pi$
$857$	−25.7082	+	44.5279i	−0.878175	+	1.52104i	−0.853342	+	0.521352i	$0.825428\pi$
$858$		0			0
$859$	10.5243	+	18.2286i	0.359084	+	0.621951i	0.987808	−	0.155677i	$-0.0497559\pi$
$859$	10.5243	+	18.2286i	0.359084	+	0.621951i	−0.628724	+	0.777628i	$0.716423\pi$
$860$		0			0
$861$	−4.23353	−	7.33268i	−0.144278	−	0.249897i
$862$		0			0
$863$	−38.8358			−1.32199			−0.660994	−	0.750391i	$-0.729865\pi$
$863$	−38.8358			−1.32199			−0.660994	+	0.750391i	$0.729865\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.73631			−0.160854
$868$		0			0
$869$	4.73812	−	8.20667i	0.160730	−	0.278392i
$870$		0			0
$871$	−43.3953	+	75.1628i	−1.47039	+	2.54679i
$872$		0			0
$873$	16.2937			0.551459
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.0379	+	22.5823i	−0.440259	+	0.762551i	−0.997708	−	0.0676600i	$-0.978447\pi$
$877$	−13.0379	+	22.5823i	−0.440259	+	0.762551i	0.557450	+	0.830211i	$0.311780\pi$
$878$		0			0
$879$	−4.43080	+	7.67437i	−0.149447	+	0.258850i
$880$		0			0
$881$	8.23096			0.277308			0.138654	−	0.990341i	$-0.455722\pi$
$881$	8.23096			0.277308			0.138654	+	0.990341i	$0.455722\pi$
$882$		0			0
$883$	−16.4326	−	28.4622i	−0.553003	−	0.957828i	−0.998056	−	0.0623244i	$-0.980149\pi$
$883$	−16.4326	−	28.4622i	−0.553003	−	0.957828i	0.445053	−	0.895504i	$-0.353185\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.11165	−	12.3177i	−0.238786	−	0.413589i	0.721580	−	0.692331i	$-0.243416\pi$
$887$	−7.11165	−	12.3177i	−0.238786	−	0.413589i	−0.960366	+	0.278741i	$0.910083\pi$
$888$		0			0
$889$	0.934139	+	1.61798i	0.0313300	+	0.0542652i
$890$		0			0
$891$	−8.00154	+	13.8591i	−0.268062	+	0.464296i
$892$		0			0
$893$	20.3942	+	2.99605i	0.682465	+	0.100259i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	12.7656	+	22.1107i	0.426231	+	0.738254i
$898$		0			0
$899$	5.63262	+	9.75598i	0.187858	+	0.325380i
$900$		0			0
$901$	−26.3199			−0.876843
$902$		0			0
$903$	−2.12763	−	3.68516i	−0.0708031	−	0.122635i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−22.4594	+	38.9008i	−0.745752	+	1.29168i	0.204090	+	0.978952i	$0.434576\pi$
$907$	−22.4594	+	38.9008i	−0.745752	+	1.29168i	−0.949842	+	0.312729i	$0.898757\pi$
$908$		0			0
$909$	−18.1023	+	31.3542i	−0.600417	+	1.03995i
$910$		0			0
$911$	38.3516			1.27064			0.635322	−	0.772247i	$-0.280867\pi$
$911$	38.3516			1.27064			0.635322	+	0.772247i	$0.280867\pi$
$912$		0			0
$913$	32.8257			1.08637
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.23097	−	12.5244i	0.238788	−	0.413593i
$918$		0			0
$919$	−36.3727			−1.19983			−0.599913	−	0.800065i	$-0.704798\pi$
$919$	−36.3727			−1.19983			−0.599913	+	0.800065i	$0.704798\pi$
$920$		0			0
$921$	6.52081	+	11.2944i	0.214868	+	0.372162i
$922$		0			0
$923$	−58.1318			−1.91343
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−23.2140	−	40.2079i	−0.762449	−	1.32060i
$928$		0			0
$929$	−1.96542	+	3.40421i	−0.0644834	+	0.111689i	−0.896465	−	0.443115i	$-0.853873\pi$
$929$	−1.96542	+	3.40421i	−0.0644834	+	0.111689i	0.831981	+	0.554804i	$0.187207\pi$
$930$		0			0
$931$	1.43305	−	1.81082i	0.0469663	−	0.0593473i
$932$		0			0
$933$	4.39966	−	7.62043i	0.144038	−	0.249482i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−27.0741	−	46.8937i	−0.884473	−	1.53195i	−0.846317	−	0.532680i	$-0.821185\pi$
$937$	−27.0741	−	46.8937i	−0.884473	−	1.53195i	−0.0381558	−	0.999272i	$-0.512148\pi$
$938$		0			0
$939$	−4.36445			−0.142429
$940$		0			0
$941$	14.9969	+	25.9755i	0.488886	+	0.846776i	0.999918	−	0.0127858i	$-0.00406997\pi$
$941$	14.9969	+	25.9755i	0.488886	+	0.846776i	−0.511032	+	0.859562i	$0.670737\pi$
$942$		0			0
$943$	59.0167			1.92185
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.7095	−	34.1378i	0.640472	−	1.10933i	−0.344856	−	0.938656i	$-0.612072\pi$
$947$	19.7095	−	34.1378i	0.640472	−	1.10933i	0.985328	−	0.170674i	$-0.0545945\pi$
$948$		0			0
$949$	88.7758			2.88179
$950$		0			0
$951$	0.104471			0.00338772
$952$		0			0
$953$	0.663142	−	1.14860i	0.0214813	−	0.0372067i	−0.855085	−	0.518488i	$-0.826495\pi$
$953$	0.663142	−	1.14860i	0.0214813	−	0.0372067i	0.876566	+	0.481281i	$0.159828\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.89673			−0.0613124
$958$		0			0
$959$	−23.9103	−	41.4138i	−0.772102	−	1.33732i
$960$		0			0
$961$	4.77372			0.153991
$962$		0			0
$963$	−6.41820	−	11.1167i	−0.206824	−	0.358229i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−3.57052	+	6.18431i	−0.114820	+	0.198874i	−0.917708	−	0.397256i	$-0.869962\pi$
$967$	−3.57052	+	6.18431i	−0.114820	+	0.198874i	0.802888	+	0.596130i	$0.203296\pi$
$968$		0			0
$969$	−4.99487	−	0.733782i	−0.160458	−	0.0235725i
$970$		0			0
$971$	−12.5252	+	21.6943i	−0.401953	+	0.696202i	−0.993962	−	0.109729i	$-0.965002\pi$
$971$	−12.5252	+	21.6943i	−0.401953	+	0.696202i	0.592009	+	0.805931i	$0.298335\pi$
$972$		0			0
$973$	−5.22371	−	9.04773i	−0.167464	−	0.290057i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.00409135			0.000130894			6.54469e−5	−	1.00000i	$-0.499979\pi$
$977$	0.00409135			0.000130894			6.54469e−5		1.00000i	$0.499979\pi$
$978$		0			0
$979$	15.9979	+	27.7091i	0.511294	+	0.885587i
$980$		0			0
$981$	7.31720			0.233620
$982$		0			0
$983$	22.1988	−	38.4495i	0.708033	−	1.22635i	−0.257553	−	0.966264i	$-0.582916\pi$
$983$	22.1988	−	38.4495i	0.708033	−	1.22635i	0.965586	−	0.260084i	$-0.0837504\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	5.44731			0.173390
$988$		0			0
$989$	29.6599			0.943128
$990$		0			0
$991$	23.7636	−	41.1598i	0.754877	−	1.30749i	−0.190558	−	0.981676i	$-0.561030\pi$
$991$	23.7636	−	41.1598i	0.754877	−	1.30749i	0.945435	−	0.325810i	$-0.105637\pi$
$992$		0			0
$993$	2.74282	−	4.75071i	0.0870408	−	0.150759i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	14.8021	+	25.6381i	0.468788	+	0.811965i	0.999364	−	0.0356725i	$-0.0113573\pi$
$997$	14.8021	+	25.6381i	0.468788	+	0.811965i	−0.530575	+	0.847638i	$0.678024\pi$
$998$		0			0
$999$	7.50809			0.237545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.g.201.5		20
5.2	odd	4		380.2.r.a.49.6	yes	20
5.3	odd	4		380.2.r.a.49.5	✓	20
5.4	even	2	inner	1900.2.i.g.201.6		20
15.2	even	4		3420.2.bj.c.1189.5		20
15.8	even	4		3420.2.bj.c.1189.3		20
19.7	even	3	inner	1900.2.i.g.501.5		20
95.7	odd	12		380.2.r.a.349.5	yes	20
95.64	even	6	inner	1900.2.i.g.501.6		20
95.83	odd	12		380.2.r.a.349.6	yes	20
285.83	even	12		3420.2.bj.c.2629.5		20
285.197	even	12		3420.2.bj.c.2629.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.5	✓	20	5.3	odd	4
380.2.r.a.49.6	yes	20	5.2	odd	4
380.2.r.a.349.5	yes	20	95.7	odd	12
380.2.r.a.349.6	yes	20	95.83	odd	12
1900.2.i.g.201.5		20	1.1	even	1	trivial
1900.2.i.g.201.6		20	5.4	even	2	inner
1900.2.i.g.501.5		20	19.7	even	3	inner
1900.2.i.g.501.6		20	95.64	even	6	inner
3420.2.bj.c.1189.3		20	15.8	even	4
3420.2.bj.c.1189.5		20	15.2	even	4
3420.2.bj.c.2629.3		20	285.197	even	12
3420.2.bj.c.2629.5		20	285.83	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(-0.226426 + 0.392182i) q^{3} +2.54366 q^{7} +(1.39746 + 2.42048i) q^{9} +2.22377 q^{11} +(3.51096 + 6.08116i) q^{13} +(1.27878 - 2.21492i) q^{17} +(-2.70498 + 3.41805i) q^{19} +(-0.575952 + 0.997578i) q^{21} +(-4.01448 - 6.95328i) q^{23} -2.62425 q^{27} +(0.941734 + 1.63113i) q^{29} +5.98111 q^{31} +(-0.503519 + 0.872121i) q^{33} -2.86105 q^{37} -3.17989 q^{39} +(-3.67524 + 6.36571i) q^{41} +(-1.84706 + 3.19919i) q^{43} +(-2.36448 - 4.09540i) q^{47} -0.529782 q^{49} +(0.579100 + 1.00303i) q^{51} +(-5.14549 - 8.91226i) q^{53} +(-0.728020 - 1.83478i) q^{57} +(3.73666 - 6.47208i) q^{59} +(4.17839 + 7.23719i) q^{61} +(3.55467 + 6.15687i) q^{63} +(6.17997 + 10.7040i) q^{67} +3.63593 q^{69} +(-4.13931 + 7.16950i) q^{71} +(6.32134 - 10.9489i) q^{73} +5.65651 q^{77} +(2.13067 - 3.69043i) q^{79} +(-3.59819 + 6.23225i) q^{81} +14.7613 q^{83} -0.852933 q^{87} +(7.19403 + 12.4604i) q^{89} +(8.93069 + 15.4684i) q^{91} +(-1.35428 + 2.34568i) q^{93} +(2.91488 - 5.04871i) q^{97} +(3.10763 + 5.38258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) \) 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

Fields

Representations

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Database

Properties

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