LMFDB - Embedded newform 1900.2.i.g.501.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1900.201"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

gp:f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			501.6
Root			$-0.226426 + 0.392182i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.g.201.6

$q$-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 $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

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

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
$3$	0.226426	+	0.392182i	0.130727	+	0.226426i	0.923957	−	0.382496i	$-0.124935\pi$
$3$	0.226426	+	0.392182i	0.130727	+	0.226426i	−0.793230	+	0.608922i	$0.791602\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.54366			−0.961414			−0.480707	−	0.876881i	$-0.659620\pi$
$7$	−2.54366			−0.961414			−0.480707	+	0.876881i	$0.659620\pi$
$8$		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	−0.289812	+	0.957084i	$0.593593\pi$
$13$	−3.51096	+	6.08116i	−0.973765	+	1.68661i	−0.683953	+	0.729526i	$0.739741\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.27878	−	2.21492i	−0.310151	−	0.537197i	0.668244	−	0.743942i	$-0.267046\pi$
$17$	−1.27878	−	2.21492i	−0.310151	−	0.537197i	−0.978395	+	0.206745i	$0.933713\pi$
$18$		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	−0.0552521	−	0.998472i	$-0.517596\pi$
$23$	4.01448	−	6.95328i	0.837076	−	1.44986i	0.892329	−	0.451387i	$-0.149070\pi$
$24$		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	−0.765243	−	0.643742i	$-0.777381\pi$
$29$	0.941734	−	1.63113i	0.174876	−	0.302893i	0.940118	+	0.340849i	$0.110714\pi$
$30$		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	$-0.424433\pi$
$37$	2.86105			0.470353			0.235177	+	0.971953i	$0.424433\pi$
$38$		0			0
$39$	−3.17989			−0.509190
$40$		0			0
$41$	−3.67524	−	6.36571i	−0.573977	−	0.994157i	−0.996152	−	0.0876426i	$-0.972067\pi$
$41$	−3.67524	−	6.36571i	−0.573977	−	0.994157i	0.422175	−	0.906514i	$-0.361267\pi$
$42$		0			0
$43$	1.84706	+	3.19919i	0.281673	+	0.487873i	0.971797	−	0.235819i	$-0.0757772\pi$
$43$	1.84706	+	3.19919i	0.281673	+	0.487873i	−0.690124	+	0.723691i	$0.742444\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.36448	−	4.09540i	0.344895	−	0.597376i	−0.640440	−	0.768008i	$-0.721248\pi$
$47$	2.36448	−	4.09540i	0.344895	−	0.597376i	0.985335	+	0.170633i	$0.0545812\pi$
$48$		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	−0.259255	−	0.965809i	$-0.583477\pi$
$53$	5.14549	−	8.91226i	0.706788	−	1.22419i	0.966042	−	0.258383i	$-0.0831898\pi$
$54$		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	0.999879	−	0.0155515i	$-0.00495040\pi$
$59$	3.73666	+	6.47208i	0.486472	+	0.842593i	−0.513408	+	0.858145i	$0.671617\pi$
$60$		0			0
$61$	4.17839	−	7.23719i	0.534988	−	0.926627i	−0.464176	−	0.885743i	$-0.653649\pi$
$61$	4.17839	−	7.23719i	0.534988	−	0.926627i	0.999164	−	0.0408838i	$-0.0130174\pi$
$62$		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	0.190368	+	0.981713i	$0.439032\pi$
$67$	−6.17997	+	10.7040i	−0.755004	+	1.30771i	−0.945372	+	0.325993i	$0.894302\pi$
$68$		0			0
$69$	3.63593			0.437715
$70$		0			0
$71$	−4.13931	−	7.16950i	−0.491246	−	0.850863i	0.508703	−	0.860942i	$-0.330125\pi$
$71$	−4.13931	−	7.16950i	−0.491246	−	0.850863i	−0.999949	+	0.0100790i	$0.996792\pi$
$72$		0			0
$73$	−6.32134	−	10.9489i	−0.739857	−	1.28147i	−0.952559	−	0.304352i	$-0.901560\pi$
$73$	−6.32134	−	10.9489i	−0.739857	−	1.28147i	0.212703	−	0.977117i	$-0.431773\pi$
$74$		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	0.960634	−	0.277818i	$-0.0896112\pi$
$79$	2.13067	+	3.69043i	0.239719	+	0.415206i	−0.720914	+	0.693024i	$0.756278\pi$
$80$		0			0
$81$	−3.59819	−	6.23225i	−0.399799	−	0.692472i
$82$		0			0
$83$	−14.7613			−1.62026			−0.810132	−	0.586248i	$-0.800604\pi$
$83$	−14.7613			−1.62026			−0.810132	+	0.586248i	$0.800604\pi$
$84$		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	−0.178958	−	0.983857i	$-0.557273\pi$
$89$	7.19403	−	12.4604i	0.762566	−	1.32080i	0.941524	−	0.336946i	$-0.109394\pi$
$90$		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	$-0.262306\pi$
$97$	−2.91488	−	5.04871i	−0.295961	−	0.512619i	−0.975208	+	0.221291i	$0.928973\pi$
$98$		0			0
$99$	3.10763	−	5.38258i	0.312329	−	0.540969i
$100$		0			0
$101$	6.47686	−	11.2183i	0.644472	−	1.11626i	−0.339951	−	0.940443i	$-0.610411\pi$
$101$	6.47686	−	11.2183i	0.644472	−	1.11626i	0.984423	−	0.175815i	$-0.0562560\pi$
$102$		0			0
$103$	16.6116			1.63679			0.818394	−	0.574658i	$-0.194865\pi$
$103$	16.6116			1.63679			0.818394	+	0.574658i	$0.194865\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.59275			0.443998			0.221999	−	0.975047i	$-0.428742\pi$
$107$	4.59275			0.443998			0.221999	+	0.975047i	$0.428742\pi$
$108$		0			0
$109$	1.30902	+	2.26728i	0.125381	+	0.217166i	0.921882	−	0.387471i	$-0.126651\pi$
$109$	1.30902	+	2.26728i	0.125381	+	0.217166i	−0.796501	+	0.604637i	$0.793318\pi$
$110$		0			0
$111$	0.647816	+	1.12205i	0.0614880	+	0.106500i
$112$		0			0
$113$	0.509357			0.0479163			0.0239581	−	0.999713i	$-0.492373\pi$
$113$	0.509357			0.0479163			0.0239581	+	0.999713i	$0.492373\pi$
$114$		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	$-0.843708\pi$
$127$	−0.367242	+	0.636081i	−0.0325874	+	0.0564431i	0.849272	+	0.527956i	$0.177041\pi$
$128$		0			0
$129$	−0.836444	+	1.44876i	−0.0736448	+	0.127556i
$130$		0			0
$131$	2.84274	+	4.92377i	0.248371	+	0.430192i	0.963074	−	0.269236i	$-0.0867713\pi$
$131$	2.84274	+	4.92377i	0.248371	+	0.430192i	−0.714703	+	0.699428i	$0.753438\pi$
$132$		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	−0.114482	−	0.993425i	$-0.536521\pi$
$137$	9.39993	−	16.2812i	0.803091	−	1.39099i	0.917573	−	0.397568i	$-0.130146\pi$
$138$		0			0
$139$	−2.05362	+	3.55697i	−0.174186	+	0.301698i	−0.939879	−	0.341507i	$-0.889063\pi$
$139$	−2.05362	+	3.55697i	−0.174186	+	0.301698i	0.765694	+	0.643206i	$0.222396\pi$
$140$		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	0.938610	−	0.344980i	$-0.112114\pi$
$149$	2.08175	+	3.60570i	0.170544	+	0.295391i	−0.768066	+	0.640370i	$0.778781\pi$
$150$		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	$-0.0449660\pi$
$157$	4.67476	+	8.09693i	0.373087	+	0.646205i	−0.616952	+	0.787001i	$0.711633\pi$
$158$		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	$-0.519361\pi$
$163$	−1.55215			−0.121574			−0.0607869	+	0.998151i	$0.519361\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.05980	+	7.03177i	−0.314157	+	0.544135i	−0.979258	−	0.202618i	$-0.935055\pi$
$167$	−4.05980	+	7.03177i	−0.314157	+	0.544135i	0.665101	+	0.746753i	$0.268388\pi$
$168$		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	$-0.175518\pi$
$173$	−0.365686	−	0.633386i	−0.0278026	−	0.0481555i	−0.879592	+	0.475729i	$0.842184\pi$
$174$		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	−0.745492	−	0.666515i	$-0.767785\pi$
$181$	2.75090	−	4.76469i	0.204473	−	0.354157i	0.949965	+	0.312358i	$0.101119\pi$
$182$		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	$-0.0301138\pi$
$193$	5.77864	+	10.0089i	0.415956	+	0.720457i	−0.579572	+	0.814921i	$0.696780\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.11825			−0.364660			−0.182330	−	0.983237i	$-0.558364\pi$
$197$	−5.11825			−0.364660			−0.182330	+	0.983237i	$0.558364\pi$
$198$		0			0
$199$	−6.71897	+	11.6376i	−0.476295	+	0.824968i	−0.999631	−	0.0271588i	$-0.991354\pi$
$199$	−6.71897	+	11.6376i	−0.476295	+	0.824968i	0.523336	+	0.852127i	$0.324687\pi$
$200$		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	0.940128	−	0.340821i	$-0.110705\pi$
$211$	2.54063	+	4.40050i	0.174904	+	0.302943i	−0.765224	+	0.643764i	$0.777372\pi$
$212$		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	−0.923916	−	0.382595i	$-0.875030\pi$
$223$	−11.8464	−	20.5186i	−0.793295	−	1.37403i	0.130621	−	0.991432i	$-0.458303\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.0306			−1.26310			−0.631551	−	0.775334i	$-0.717582\pi$
$227$	−19.0306			−1.26310			−0.631551	+	0.775334i	$0.717582\pi$
$228$		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	$-0.0130732\pi$
$233$	7.08296	+	12.2680i	0.464020	+	0.803706i	−0.535137	+	0.844765i	$0.679740\pi$
$234$		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	0.444321	+	0.895868i	$0.353445\pi$
$241$	−8.59549	+	14.8878i	−0.553684	+	0.959009i	−0.998005	+	0.0631409i	$0.979888\pi$
$242$		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	0.197534	+	0.980296i	$0.436707\pi$
$251$	−11.8853	+	20.5860i	−0.750195	+	1.29938i	−0.947728	+	0.319079i	$0.896626\pi$
$252$		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	$-0.819104\pi$
$257$	0.716409	−	1.24086i	0.0446884	−	0.0774026i	0.887504	+	0.460799i	$0.152437\pi$
$258$		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	$-0.0961163\pi$
$263$	3.56505	+	6.17484i	0.219830	+	0.380757i	−0.734926	+	0.678148i	$0.762783\pi$
$264$		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	0.997750	+	0.0670494i	$0.0213585\pi$
$269$	9.13452	+	15.8214i	0.556941	+	0.964651i	−0.440808	+	0.897601i	$0.645308\pi$
$270$		0			0
$271$	2.90265	+	5.02754i	0.176324	+	0.305401i	0.940619	−	0.339465i	$-0.110246\pi$
$271$	2.90265	+	5.02754i	0.176324	+	0.305401i	−0.764295	+	0.644867i	$0.776913\pi$
$272$		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	$-0.445008\pi$
$277$	5.72209			0.343807			0.171904	+	0.985114i	$0.445008\pi$
$278$		0			0
$279$	8.35838	−	14.4771i	0.500403	−	0.866724i
$280$		0			0
$281$	3.07155	−	5.32009i	0.183233	−	0.317370i	−0.759746	−	0.650220i	$-0.774677\pi$
$281$	3.07155	−	5.32009i	0.183233	−	0.317370i	0.942980	+	0.332850i	$0.108010\pi$
$282$		0			0
$283$	−8.22632	−	14.2484i	−0.489004	−	0.846980i	0.510916	−	0.859631i	$-0.329306\pi$
$283$	−8.22632	−	14.2484i	−0.489004	−	0.846980i	−0.999920	+	0.0126510i	$0.995973\pi$
$284$		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	$-0.693677\pi$
$293$	−19.5684			−1.14320			−0.571599	+	0.820533i	$0.693677\pi$
$294$		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	−0.904327	−	0.426839i	$-0.859627\pi$
$307$	−14.3994	−	24.9405i	−0.821817	−	1.42343i	0.0825100	−	0.996590i	$-0.473706\pi$
$308$		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	$-0.921143\pi$
$313$	−4.81885	+	8.34649i	−0.272377	+	0.471772i	0.697093	+	0.716981i	$0.254477\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.115348	−	0.199789i	0.00647860	−	0.0112213i	−0.862768	−	0.505600i	$-0.831271\pi$
$317$	0.115348	−	0.199789i	0.00647860	−	0.0112213i	0.869247	+	0.494379i	$0.164604\pi$
$318$		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	$-0.0685226\pi$
$337$	5.57090	+	9.64909i	0.303466	+	0.525619i	−0.673452	+	0.739231i	$0.735189\pi$
$338$		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	$-0.117865\pi$
$347$	2.84478	+	4.92730i	0.152716	+	0.264511i	−0.779509	+	0.626391i	$0.784532\pi$
$348$		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	$-0.484142\pi$
$353$	1.87124			0.0995962			0.0497981	+	0.998759i	$0.484142\pi$
$354$		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	0.998219	−	0.0596485i	$-0.0189980\pi$
$359$	8.47802	+	14.6844i	0.447453	+	0.775011i	−0.550767	+	0.834659i	$0.685665\pi$
$360$		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	$-0.864828\pi$
$367$	−1.89237	+	3.27769i	−0.0987812	+	0.171094i	0.812399	+	0.583102i	$0.198161\pi$
$368$		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	$-0.537268\pi$
$373$	−4.51203			−0.233624			−0.116812	+	0.993154i	$0.537268\pi$
$374$		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	$-0.282941\pi$
$383$	−6.99088	−	12.1086i	−0.357218	−	0.618719i	−0.987495	+	0.157651i	$0.949608\pi$
$384$		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	−0.948364	−	0.317185i	$-0.897263\pi$
$389$	−3.93460	+	6.81492i	−0.199492	+	0.345530i	0.748872	+	0.662715i	$0.230596\pi$
$390$		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	$-0.306696\pi$
$397$	−8.48528	−	14.6969i	−0.425864	−	0.737618i	−0.996501	+	0.0835846i	$0.973363\pi$
$398$		0			0
$399$	−1.85184	+	4.66706i	−0.0927078	+	0.233645i
$400$		0			0
$401$	−7.16651	−	12.4128i	−0.357878	−	0.619864i	0.629728	−	0.776816i	$-0.283166\pi$
$401$	−7.16651	−	12.4128i	−0.357878	−	0.619864i	−0.987606	+	0.156952i	$0.949833\pi$
$402$		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	−0.862980	−	0.505238i	$-0.831405\pi$
$409$	0.122530	−	0.212228i	0.00605872	−	0.0104940i	0.869039	+	0.494744i	$0.164738\pi$
$410$		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	0.782785	−	0.622292i	$-0.213798\pi$
$421$	−3.02703	−	5.24297i	−0.147529	−	0.255527i	−0.930313	+	0.366765i	$0.880465\pi$
$422$		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	0.464484	+	0.885581i	$0.346240\pi$
$431$	−11.1005	+	19.2267i	−0.534694	+	0.926117i	−0.999178	+	0.0405356i	$0.987094\pi$
$432$		0			0
$433$	−12.1298	+	21.0094i	−0.582920	+	1.00965i	0.412211	+	0.911089i	$0.364757\pi$
$433$	−12.1298	+	21.0094i	−0.582920	+	1.00965i	−0.995131	+	0.0985593i	$0.968577\pi$
$434$		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	0.996537	+	0.0831509i	$0.0264983\pi$
$439$	11.9487	+	20.6957i	0.570279	+	0.987753i	−0.426258	+	0.904602i	$0.640168\pi$
$440$		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	$-0.669944\pi$
$443$	10.3356	−	17.9017i	0.491057	−	0.850536i	0.999947	+	0.0102958i	$0.00327733\pi$
$444$		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	$-0.608897\pi$
$457$	−14.3433			−0.670952			−0.335476	+	0.942049i	$0.608897\pi$
$458$		0			0
$459$	−3.35584	−	5.81249i	−0.156637	−	0.271304i
$460$		0			0
$461$	13.3682	+	23.1544i	0.622618	+	1.07841i	0.988996	+	0.147940i	$0.0472643\pi$
$461$	13.3682	+	23.1544i	0.622618	+	1.07841i	−0.366378	+	0.930466i	$0.619402\pi$
$462$		0			0
$463$	12.0950			0.562101			0.281051	−	0.959693i	$-0.409317\pi$
$463$	12.0950			0.562101			0.281051	+	0.959693i	$0.409317\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	27.3169			1.26408			0.632038	−	0.774938i	$-0.282219\pi$
$467$	27.3169			1.26408			0.632038	+	0.774938i	$0.282219\pi$
$468$		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	−0.938028	−	0.346559i	$-0.887350\pi$
$479$	−3.69624	+	6.40208i	−0.168886	+	0.292519i	0.769143	+	0.639077i	$0.220684\pi$
$480$		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	$-0.594733\pi$
$487$	−12.9424			−0.586477			−0.293239	+	0.956039i	$0.594733\pi$
$488$		0			0
$489$	−0.351447	−	0.608725i	−0.0158930	−	0.0275275i
$490$		0			0
$491$	5.59974	+	9.69903i	0.252713	+	0.437711i	0.964272	−	0.264915i	$-0.0853439\pi$
$491$	5.59974	+	9.69903i	0.252713	+	0.437711i	−0.711559	+	0.702626i	$0.752011\pi$
$492$		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	0.995407	+	0.0957335i	$0.0305196\pi$
$499$	12.9699	+	22.4645i	0.580611	+	1.00565i	−0.414796	+	0.909914i	$0.636147\pi$
$500$		0			0
$501$	−3.67698			−0.164275
$502$		0			0
$503$	−13.6300	+	23.6079i	−0.607733	+	1.05262i	0.383881	+	0.923383i	$0.374587\pi$
$503$	−13.6300	+	23.6079i	−0.607733	+	1.05262i	−0.991613	+	0.129241i	$0.958746\pi$
$504$		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	0.438161	+	0.898896i	$0.355630\pi$
$509$	−12.6203	+	21.8591i	−0.559386	+	0.968885i	−0.997548	+	0.0699892i	$0.977704\pi$
$510$		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	$-0.790324\pi$
$523$	3.08063	−	5.33581i	0.134706	−	0.233318i	0.925485	+	0.378784i	$0.123658\pi$
$524$		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	−0.927782	−	0.373122i	$-0.878287\pi$
$541$	−3.27394	+	5.67063i	−0.140758	+	0.243799i	0.787025	+	0.616922i	$0.211620\pi$
$542$		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	$-0.993484\pi$
$547$	−11.2770	+	19.5323i	−0.482169	+	0.835141i	0.517621	+	0.855610i	$0.326818\pi$
$548$		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	$-0.721492\pi$
$557$	8.12281	−	14.0691i	0.344175	−	0.596128i	0.985203	+	0.171389i	$0.0548254\pi$
$558$		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	$-0.260250\pi$
$563$	32.4581			1.36795			0.683974	+	0.729506i	$0.260250\pi$
$564$		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	$-0.121496\pi$
$577$	44.5844			1.85607			0.928037	+	0.372489i	$0.121496\pi$
$578$		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	$-0.0693988\pi$
$587$	7.28884	+	12.6246i	0.300842	+	0.521074i	−0.675485	+	0.737374i	$0.736065\pi$
$588$		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	$-0.671328\pi$
$593$	11.8657	−	20.5520i	0.487265	−	0.843968i	0.999893	+	0.0146433i	$0.00466126\pi$
$594$		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	−0.591140	−	0.806569i	$-0.701322\pi$
$599$	9.86173	−	17.0810i	0.402939	−	0.697911i	0.994079	+	0.108658i	$0.0346552\pi$
$600$		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	$-0.453050\pi$
$607$	7.24160			0.293928			0.146964	+	0.989142i	$0.453050\pi$
$608$		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	−0.950947	−	0.309352i	$-0.899888\pi$
$613$	−18.4052	−	31.8788i	−0.743381	−	1.28757i	0.207567	−	0.978221i	$-0.433446\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.3448	−	31.7741i	0.738533	−	1.27918i	−0.214623	−	0.976697i	$-0.568852\pi$
$617$	18.3448	−	31.7741i	0.738533	−	1.27918i	0.953156	−	0.302479i	$-0.0978143\pi$
$618$		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	−0.972158	−	0.234325i	$-0.924712\pi$
$631$	−7.11258	+	12.3193i	−0.283147	+	0.490426i	0.689011	+	0.724751i	$0.258045\pi$
$632$		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	0.993994	−	0.109437i	$-0.0349048\pi$
$641$	10.1834	+	17.6382i	0.402222	+	0.696668i	−0.591772	+	0.806105i	$0.701571\pi$
$642$		0			0
$643$	5.77586	+	10.0041i	0.227778	+	0.394523i	0.957149	−	0.289595i	$-0.0935207\pi$
$643$	5.77586	+	10.0041i	0.227778	+	0.394523i	−0.729371	+	0.684118i	$0.760187\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.1233			0.515932			0.257966	−	0.966154i	$-0.416948\pi$
$647$	13.1233			0.515932			0.257966	+	0.966154i	$0.416948\pi$
$648$		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	$-0.624208\pi$
$653$	−19.4406			−0.760769			−0.380385	+	0.924828i	$0.624208\pi$
$654$		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	−0.462086	−	0.886835i	$-0.652899\pi$
$659$	13.7848	−	23.8759i	0.536979	−	0.930074i	0.999065	−	0.0432391i	$-0.0137677\pi$
$660$		0			0
$661$	3.88006	−	6.72046i	0.150917	−	0.261396i	−0.780648	−	0.624971i	$-0.785111\pi$
$661$	3.88006	−	6.72046i	0.150917	−	0.261396i	0.931565	+	0.363575i	$0.118444\pi$
$662$		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	$-0.654885\pi$
$673$	−24.2617			−0.935220			−0.467610	+	0.883935i	$0.654885\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.88851			0.187881			0.0939403	−	0.995578i	$-0.470054\pi$
$677$	4.88851			0.187881			0.0939403	+	0.995578i	$0.470054\pi$
$678$		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	$-0.496589\pi$
$683$	0.560031			0.0214290			0.0107145	+	0.999943i	$0.496589\pi$
$684$		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	0.888479	−	0.458916i	$-0.151762\pi$
$701$	1.23926	+	2.14647i	0.0468064	+	0.0810710i	−0.841673	+	0.539987i	$0.818429\pi$
$702$		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	−0.383249	−	0.923645i	$-0.625195\pi$
$709$	16.1966	−	28.0533i	0.608276	−	1.05356i	0.991525	−	0.129919i	$-0.0414718\pi$
$710$		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	0.658617	−	0.752478i	$-0.271142\pi$
$719$	−8.64373	−	14.9714i	−0.322357	−	0.558338i	−0.980974	+	0.194140i	$0.937808\pi$
$720$		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	$-0.280905\pi$
$727$	−9.47034	−	16.4031i	−0.351236	−	0.608358i	−0.986466	+	0.163965i	$0.947572\pi$
$728$		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	$-0.496813\pi$
$733$	0.542118			0.0200236			0.0100118	+	0.999950i	$0.496813\pi$
$734$		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	0.913978	−	0.405764i	$-0.132995\pi$
$739$	2.87033	+	4.97156i	0.105587	+	0.182882i	−0.808391	+	0.588646i	$0.799661\pi$
$740$		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	$-0.305379\pi$
$743$	−11.5060	−	19.9290i	−0.422115	−	0.731125i	−0.996146	+	0.0877087i	$0.972046\pi$
$744$		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	0.197368	−	0.980330i	$-0.436761\pi$
$751$	25.9704	−	44.9821i	0.947674	−	1.64142i	0.750306	−	0.661090i	$-0.229906\pi$
$752$		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	$-0.240966\pi$
$757$	−6.36406	−	11.0229i	−0.231306	−	0.400633i	−0.958193	+	0.286124i	$0.907633\pi$
$758$		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	−0.992419	−	0.122898i	$-0.960781\pi$
$769$	−10.8089	+	18.7215i	−0.389777	+	0.675114i	0.602642	+	0.798012i	$0.294115\pi$
$770$		0			0
$771$	0.648856			0.0233680
$772$		0			0
$773$	−21.6637	+	37.5227i	−0.779190	+	1.34960i	0.153220	+	0.988192i	$0.451036\pi$
$773$	−21.6637	+	37.5227i	−0.779190	+	1.34960i	−0.932409	+	0.361404i	$0.882298\pi$
$774$		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	$-0.327067\pi$
$787$	29.0046			1.03390			0.516950	+	0.856015i	$0.327067\pi$
$788$		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	$-0.419051\pi$
$797$	14.2045			0.503150			0.251575	+	0.967838i	$0.419051\pi$
$798$		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	−0.239300	−	0.970946i	$-0.576918\pi$
$811$	20.5388	−	35.5742i	0.721214	−	1.24918i	0.960513	−	0.278233i	$-0.0897489\pi$
$812$		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	−0.196160	−	0.980572i	$-0.562847\pi$
$821$	21.5219	−	37.2771i	0.751120	−	1.30098i	0.947280	−	0.320407i	$-0.103820\pi$
$822$		0			0
$823$	−7.18105	+	12.4379i	−0.250316	+	0.433559i	−0.963613	−	0.267302i	$-0.913868\pi$
$823$	−7.18105	+	12.4379i	−0.250316	+	0.433559i	0.713297	+	0.700862i	$0.247201\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.1891	−	38.4326i	0.771590	−	1.33643i	−0.165101	−	0.986277i	$-0.552795\pi$
$827$	22.1891	−	38.4326i	0.771590	−	1.33643i	0.936691	−	0.350157i	$-0.113872\pi$
$828$		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	0.957322	+	0.289022i	$0.0933301\pi$
$839$	21.1147	+	36.5718i	0.728962	+	1.26260i	−0.228361	+	0.973577i	$0.573337\pi$
$840$		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	$-0.0564821\pi$
$853$	9.90917	+	17.1632i	0.339284	+	0.587656i	−0.645015	+	0.764170i	$0.723149\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.7082	+	44.5279i	0.878175	+	1.52104i	0.853342	+	0.521352i	$0.174572\pi$
$857$	25.7082	+	44.5279i	0.878175	+	1.52104i	0.0248328	+	0.999692i	$0.492095\pi$
$858$		0			0
$859$	10.5243	−	18.2286i	0.359084	−	0.621951i	−0.628724	−	0.777628i	$-0.716423\pi$
$859$	10.5243	−	18.2286i	0.359084	−	0.621951i	0.987808	+	0.155677i	$0.0497559\pi$
$860$		0			0
$861$	−4.23353	+	7.33268i	−0.144278	+	0.249897i
$862$		0			0
$863$	38.8358			1.32199			0.660994	−	0.750391i	$-0.270135\pi$
$863$	38.8358			1.32199			0.660994	+	0.750391i	$0.270135\pi$
$864$		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	$-0.0215533\pi$
$877$	13.0379	+	22.5823i	0.440259	+	0.762551i	−0.557450	+	0.830211i	$0.688220\pi$
$878$		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	−0.445053	−	0.895504i	$-0.646815\pi$
$883$	16.4326	−	28.4622i	0.553003	−	0.957828i	0.998056	−	0.0623244i	$-0.0198513\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.11165	−	12.3177i	0.238786	−	0.413589i	−0.721580	−	0.692331i	$-0.756584\pi$
$887$	7.11165	−	12.3177i	0.238786	−	0.413589i	0.960366	+	0.278741i	$0.0899173\pi$
$888$		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	0.949842	+	0.312729i	$0.101243\pi$
$907$	22.4594	+	38.9008i	0.745752	+	1.29168i	−0.204090	+	0.978952i	$0.565424\pi$
$908$		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	0.831981	−	0.554804i	$-0.187207\pi$
$929$	−1.96542	−	3.40421i	−0.0644834	−	0.111689i	−0.896465	+	0.443115i	$0.853873\pi$
$930$		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	0.0381558	−	0.999272i	$-0.487852\pi$
$937$	27.0741	−	46.8937i	0.884473	−	1.53195i	0.846317	−	0.532680i	$-0.178815\pi$
$938$		0			0
$939$	−4.36445			−0.142429
$940$		0			0
$941$	14.9969	−	25.9755i	0.488886	−	0.846776i	−0.511032	−	0.859562i	$-0.670737\pi$
$941$	14.9969	−	25.9755i	0.488886	−	0.846776i	0.999918	+	0.0127858i	$0.00406997\pi$
$942$		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	−0.985328	−	0.170674i	$-0.945406\pi$
$947$	−19.7095	−	34.1378i	−0.640472	−	1.10933i	0.344856	−	0.938656i	$-0.387928\pi$
$948$		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	$-0.173505\pi$
$953$	−0.663142	−	1.14860i	−0.0214813	−	0.0372067i	−0.876566	+	0.481281i	$0.840172\pi$
$954$		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	$-0.130038\pi$
$967$	3.57052	+	6.18431i	0.114820	+	0.198874i	−0.802888	+	0.596130i	$0.796704\pi$
$968$		0			0
$969$	−4.99487	+	0.733782i	−0.160458	+	0.0235725i
$970$		0			0
$971$	−12.5252	−	21.6943i	−0.401953	−	0.696202i	0.592009	−	0.805931i	$-0.298335\pi$
$971$	−12.5252	−	21.6943i	−0.401953	−	0.696202i	−0.993962	+	0.109729i	$0.965002\pi$
$972$		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	$-0.500021\pi$
$977$	−0.00409135			−0.000130894			−6.54469e−5		1.00000i	$0.500021\pi$
$978$		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	−0.965586	−	0.260084i	$-0.916250\pi$
$983$	−22.1988	−	38.4495i	−0.708033	−	1.22635i	0.257553	−	0.966264i	$-0.417084\pi$
$984$		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	0.945435	+	0.325810i	$0.105637\pi$
$991$	23.7636	+	41.1598i	0.754877	+	1.30749i	−0.190558	+	0.981676i	$0.561030\pi$
$992$		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	$-0.988643\pi$
$997$	−14.8021	+	25.6381i	−0.468788	+	0.811965i	0.530575	+	0.847638i	$0.321976\pi$
$998$		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.501.6		20
5.2	odd	4		380.2.r.a.349.6	yes	20
5.3	odd	4		380.2.r.a.349.5	yes	20
5.4	even	2	inner	1900.2.i.g.501.5		20
15.2	even	4		3420.2.bj.c.2629.5		20
15.8	even	4		3420.2.bj.c.2629.3		20
19.11	even	3	inner	1900.2.i.g.201.6		20
95.49	even	6	inner	1900.2.i.g.201.5		20
95.68	odd	12		380.2.r.a.49.6	yes	20
95.87	odd	12		380.2.r.a.49.5	✓	20
285.68	even	12		3420.2.bj.c.1189.5		20
285.182	even	12		3420.2.bj.c.1189.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.5	✓	20	95.87	odd	12
380.2.r.a.49.6	yes	20	95.68	odd	12
380.2.r.a.349.5	yes	20	5.3	odd	4
380.2.r.a.349.6	yes	20	5.2	odd	4
1900.2.i.g.201.5		20	95.49	even	6	inner
1900.2.i.g.201.6		20	19.11	even	3	inner
1900.2.i.g.501.5		20	5.4	even	2	inner
1900.2.i.g.501.6		20	1.1	even	1	trivial
3420.2.bj.c.1189.3		20	285.182	even	12
3420.2.bj.c.1189.5		20	285.68	even	12
3420.2.bj.c.2629.3		20	15.8	even	4
3420.2.bj.c.2629.5		20	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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