LMFDB - Embedded newform 1900.2.i.e.201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 $ x^12 - 3x^11 + 15x^10 - 16x^9 + 79x^8 - 65x^7 + 298x^6 + 13x^5 + 233x^4 + 14x^3 + 145x^2 + 33*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.4
Root			$0.430479 - 0.745611i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.e.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0695210 + 0.120414i) q^{3} -3.40785 q^{7} +(1.49033 + 2.58133i) q^{9} +O(q^{10})$	\(q+(-0.0695210 + 0.120414i) q^{3} -3.40785 q^{7} +(1.49033 + 2.58133i) q^{9} +0.185690 q^{11} +(-1.17736 - 2.03925i) q^{13} +(3.35663 - 5.81385i) q^{17} +(-2.14437 + 3.79495i) q^{19} +(0.236918 - 0.410353i) q^{21} +(-0.463767 - 0.803267i) q^{23} -0.831564 q^{27} +(0.677360 + 1.17322i) q^{29} -9.46158 q^{31} +(-0.0129094 + 0.0223597i) q^{33} -1.62862 q^{37} +0.327405 q^{39} +(4.29573 - 7.44043i) q^{41} +(3.80076 - 6.58312i) q^{43} +(4.09639 + 7.09515i) q^{47} +4.61347 q^{49} +(0.466712 + 0.808369i) q^{51} +(-6.70168 - 11.6077i) q^{53} +(-0.307887 - 0.522041i) q^{57} +(2.02981 - 3.51573i) q^{59} +(-6.31247 - 10.9335i) q^{61} +(-5.07884 - 8.79681i) q^{63} +(-1.62613 - 2.81654i) q^{67} +0.128966 q^{69} +(6.59887 - 11.4296i) q^{71} +(2.45260 - 4.24802i) q^{73} -0.632805 q^{77} +(-2.98245 + 5.16576i) q^{79} +(-4.41319 + 7.64387i) q^{81} +1.30480 q^{83} -0.188363 q^{87} +(1.95584 + 3.38761i) q^{89} +(4.01227 + 6.94946i) q^{91} +(0.657779 - 1.13931i) q^{93} +(7.25291 - 12.5624i) q^{97} +(0.276740 + 0.479328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 3 * q^9	$ 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 3 * q^9 + 2 * q^11 - 7 * q^13 + q^17 + q^21 + 2 * q^23 + 24 * q^27 + q^29 + 2 * q^31 - 10 * q^33 - 20 * q^37 + 36 * q^39 - 7 * q^41 - 19 * q^43 + 14 * q^47 + 8 * q^49 + 11 * q^51 - 6 * q^53 + 28 * q^57 - 5 * q^61 + 11 * q^63 - 14 * q^67 - 14 * q^69 + 8 * q^71 + 9 * q^73 - 2 * q^77 + q^79 + 2 * q^81 + 26 * q^83 - 30 * q^87 - 8 * q^89 + 3 * q^91 - 9 * q^93 + 11 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0695210	+	0.120414i	−0.0401380	+	0.0695210i	−0.885397	−	0.464837i	$-0.846113\pi$
$3$	−0.0695210	+	0.120414i	−0.0401380	+	0.0695210i	0.845259	+	0.534358i	$0.179446\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.40785			−1.28805			−0.644024	−	0.765005i	$-0.722736\pi$
$7$	−3.40785			−1.28805			−0.644024	+	0.765005i	$0.722736\pi$
$8$		0			0
$9$	1.49033	+	2.58133i	0.496778	+	0.860445i
$10$		0			0
$11$	0.185690			0.0559876			0.0279938	−	0.999608i	$-0.491088\pi$
$11$	0.185690			0.0559876			0.0279938	+	0.999608i	$0.491088\pi$
$12$		0			0
$13$	−1.17736	−	2.03925i	−0.326541	−	0.565586i	0.655282	−	0.755384i	$-0.272550\pi$
$13$	−1.17736	−	2.03925i	−0.326541	−	0.565586i	−0.981823	+	0.189799i	$0.939216\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.35663	−	5.81385i	0.814102	−	1.41007i	−0.0958696	−	0.995394i	$-0.530563\pi$
$17$	3.35663	−	5.81385i	0.814102	−	1.41007i	0.909971	−	0.414671i	$-0.136103\pi$
$18$		0			0
$19$	−2.14437	+	3.79495i	−0.491952	+	0.870622i
$19$	−2.14437	+	3.79495i	−0.491952	+	0.870622i
$20$		0			0
$21$	0.236918	−	0.410353i	0.0516996	−	0.0895464i
$22$		0			0
$23$	−0.463767	−	0.803267i	−0.0967020	−	0.167493i	0.813616	−	0.581403i	$-0.197496\pi$
$23$	−0.463767	−	0.803267i	−0.0967020	−	0.167493i	−0.910318	+	0.413910i	$0.864163\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.831564			−0.160035
$28$		0			0
$29$	0.677360	+	1.17322i	0.125783	+	0.217862i	0.922039	−	0.387098i	$-0.126522\pi$
$29$	0.677360	+	1.17322i	0.125783	+	0.217862i	−0.796256	+	0.604960i	$0.793189\pi$
$30$		0			0
$31$	−9.46158			−1.69935			−0.849675	−	0.527306i	$-0.823202\pi$
$31$	−9.46158			−1.69935			−0.849675	+	0.527306i	$0.823202\pi$
$32$		0			0
$33$	−0.0129094	+	0.0223597i	−0.00224723	+	0.00389232i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.62862			−0.267743			−0.133872	−	0.990999i	$-0.542741\pi$
$37$	−1.62862			−0.267743			−0.133872	+	0.990999i	$0.542741\pi$
$38$		0			0
$39$	0.327405			0.0524268
$40$		0			0
$41$	4.29573	−	7.44043i	0.670881	−	1.16200i	−0.306774	−	0.951782i	$-0.599250\pi$
$41$	4.29573	−	7.44043i	0.670881	−	1.16200i	0.977655	−	0.210217i	$-0.0674171\pi$
$42$		0			0
$43$	3.80076	−	6.58312i	0.579611	−	1.00392i	−0.415913	−	0.909405i	$-0.636538\pi$
$43$	3.80076	−	6.58312i	0.579611	−	1.00392i	0.995524	−	0.0945112i	$-0.0301288\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.09639	+	7.09515i	0.597519	+	1.03493i	0.993186	+	0.116540i	$0.0371802\pi$
$47$	4.09639	+	7.09515i	0.597519	+	1.03493i	−0.395667	+	0.918394i	$0.629486\pi$
$48$		0			0
$49$	4.61347			0.659067
$50$		0			0
$51$	0.466712	+	0.808369i	0.0653528	+	0.113194i
$52$		0			0
$53$	−6.70168	−	11.6077i	−0.920547	−	1.59443i	−0.798571	−	0.601901i	$-0.794410\pi$
$53$	−6.70168	−	11.6077i	−0.920547	−	1.59443i	−0.121976	−	0.992533i	$-0.538923\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.307887	−	0.522041i	−0.0407806	−	0.0691460i
$58$		0			0
$59$	2.02981	−	3.51573i	0.264259	−	0.457710i	−0.703110	−	0.711081i	$-0.748206\pi$
$59$	2.02981	−	3.51573i	0.264259	−	0.457710i	0.967369	+	0.253371i	$0.0815394\pi$
$60$		0			0
$61$	−6.31247	−	10.9335i	−0.808228	−	1.39989i	−0.914090	−	0.405512i	$-0.867093\pi$
$61$	−6.31247	−	10.9335i	−0.808228	−	1.39989i	0.105861	−	0.994381i	$-0.466240\pi$
$62$		0			0
$63$	−5.07884	−	8.79681i	−0.639874	−	1.10829i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.62613	−	2.81654i	−0.198664	−	0.344096i	0.749432	−	0.662082i	$-0.230327\pi$
$67$	−1.62613	−	2.81654i	−0.198664	−	0.344096i	−0.948095	+	0.317986i	$0.896993\pi$
$68$		0			0
$69$	0.128966			0.0155257
$70$		0			0
$71$	6.59887	−	11.4296i	0.783142	−	1.35644i	−0.146961	−	0.989142i	$-0.546949\pi$
$71$	6.59887	−	11.4296i	0.783142	−	1.35644i	0.930103	−	0.367300i	$-0.119718\pi$
$72$		0			0
$73$	2.45260	−	4.24802i	0.287055	−	0.497193i	−0.686051	−	0.727554i	$-0.740657\pi$
$73$	2.45260	−	4.24802i	0.287055	−	0.497193i	0.973105	+	0.230360i	$0.0739905\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.632805			−0.0721148
$78$		0			0
$79$	−2.98245	+	5.16576i	−0.335552	+	0.581194i	−0.983591	−	0.180414i	$-0.942256\pi$
$79$	−2.98245	+	5.16576i	−0.335552	+	0.581194i	0.648038	+	0.761608i	$0.275590\pi$
$80$		0			0
$81$	−4.41319	+	7.64387i	−0.490354	+	0.849319i
$82$		0			0
$83$	1.30480			0.143221			0.0716105	−	0.997433i	$-0.477186\pi$
$83$	1.30480			0.143221			0.0716105	+	0.997433i	$0.477186\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.188363			−0.0201946
$88$		0			0
$89$	1.95584	+	3.38761i	0.207319	+	0.359086i	0.950869	−	0.309594i	$-0.100193\pi$
$89$	1.95584	+	3.38761i	0.207319	+	0.359086i	−0.743550	+	0.668680i	$0.766860\pi$
$90$		0			0
$91$	4.01227	+	6.94946i	0.420600	+	0.728501i
$92$		0			0
$93$	0.657779	−	1.13931i	0.0682085	−	0.118141i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.25291	−	12.5624i	0.736421	−	1.27552i	−0.217676	−	0.976021i	$-0.569848\pi$
$97$	7.25291	−	12.5624i	0.736421	−	1.27552i	0.954097	−	0.299498i	$-0.0968192\pi$
$98$		0			0
$99$	0.276740	+	0.479328i	0.0278134	+	0.0481743i
$100$		0			0
$101$	−0.348049	−	0.602838i	−0.0346321	−	0.0599846i	0.848190	−	0.529692i	$-0.177693\pi$
$101$	−0.348049	−	0.602838i	−0.0346321	−	0.0599846i	−0.882822	+	0.469708i	$0.844359\pi$
$102$		0			0
$103$	−10.5016			−1.03476			−0.517378	−	0.855757i	$-0.673092\pi$
$103$	−10.5016			−1.03476			−0.517378	+	0.855757i	$0.673092\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.1627			−1.46583			−0.732915	−	0.680320i	$-0.761841\pi$
$107$	−15.1627			−1.46583			−0.732915	+	0.680320i	$0.761841\pi$
$108$		0			0
$109$	−0.0595573	+	0.103156i	−0.00570456	+	0.00988058i	−0.868864	−	0.495052i	$-0.835149\pi$
$109$	−0.0595573	+	0.103156i	−0.00570456	+	0.00988058i	0.863159	+	0.504932i	$0.168482\pi$
$110$		0			0
$111$	0.113223	−	0.196109i	0.0107467	−	0.0186138i
$112$		0			0
$113$	−10.1268			−0.952648			−0.476324	−	0.879270i	$-0.658031\pi$
$113$	−10.1268			−0.952648			−0.476324	+	0.879270i	$0.658031\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.50932	−	6.07832i	0.324437	−	0.561941i
$118$		0			0
$119$	−11.4389	+	19.8127i	−1.04860	+	1.81623i
$120$		0			0
$121$	−10.9655			−0.996865
$122$		0			0
$123$	0.597288	+	1.03453i	0.0538556	+	0.0932806i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.85268	−	3.20894i	−0.164399	−	0.284748i	0.772043	−	0.635571i	$-0.219235\pi$
$127$	−1.85268	−	3.20894i	−0.164399	−	0.284748i	−0.936442	+	0.350823i	$0.885902\pi$
$128$		0			0
$129$	0.528466	+	0.915330i	0.0465288	+	0.0805903i
$130$		0			0
$131$	10.7555	−	18.6291i	0.939713	−	1.62763i	0.173707	−	0.984797i	$-0.444425\pi$
$131$	10.7555	−	18.6291i	0.939713	−	1.62763i	0.766006	−	0.642833i	$-0.222241\pi$
$132$		0			0
$133$	7.30770	−	12.9327i	0.633658	−	1.12140i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.88852	−	11.9313i	−0.588526	−	1.01936i	−0.994426	−	0.105439i	$-0.966375\pi$
$137$	−6.88852	−	11.9313i	−0.588526	−	1.01936i	0.405900	−	0.913918i	$-0.366958\pi$
$138$		0			0
$139$	9.25188	+	16.0247i	0.784734	+	1.35920i	0.929158	+	0.369683i	$0.120534\pi$
$139$	9.25188	+	16.0247i	0.784734	+	1.35920i	−0.144424	+	0.989516i	$0.546133\pi$
$140$		0			0
$141$	−1.13914			−0.0959329
$142$		0			0
$143$	−0.218624	−	0.378668i	−0.0182823	−	0.0316658i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.320733	+	0.555526i	−0.0264536	+	0.0458190i
$148$		0			0
$149$	3.40386	−	5.89565i	0.278855	−	0.482991i	−0.692246	−	0.721662i	$-0.743379\pi$
$149$	3.40386	−	5.89565i	0.278855	−	0.482991i	0.971100	+	0.238671i	$0.0767119\pi$
$150$		0			0
$151$	3.67527			0.299089			0.149545	−	0.988755i	$-0.452219\pi$
$151$	3.67527			0.299089			0.149545	+	0.988755i	$0.452219\pi$
$152$		0			0
$153$	20.0100			1.61771
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.05638	+	12.2220i	−0.563160	+	0.975422i	0.434058	+	0.900885i	$0.357081\pi$
$157$	−7.05638	+	12.2220i	−0.563160	+	0.975422i	−0.997218	+	0.0745372i	$0.976252\pi$
$158$		0			0
$159$	1.86363			0.147796
$160$		0			0
$161$	1.58045	+	2.73742i	0.124557	+	0.215739i
$162$		0			0
$163$	−5.63660			−0.441493			−0.220746	−	0.975331i	$-0.570849\pi$
$163$	−5.63660			−0.441493			−0.220746	+	0.975331i	$0.570849\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.73880	+	6.47579i	0.289317	+	0.501112i	0.973647	−	0.228061i	$-0.0732385\pi$
$167$	3.73880	+	6.47579i	0.289317	+	0.501112i	−0.684330	+	0.729173i	$0.739905\pi$
$168$		0			0
$169$	3.72765	−	6.45647i	0.286742	−	0.496652i
$170$		0			0
$171$	−12.9919	+	0.120414i	−0.993513	+	0.00920829i
$172$		0			0
$173$	−11.6888	+	20.2457i	−0.888686	+	1.53925i	−0.0472554	+	0.998883i	$0.515047\pi$
$173$	−11.6888	+	20.2457i	−0.888686	+	1.53925i	−0.841430	+	0.540366i	$0.818286\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.282229	+	0.488835i	0.0212136	+	0.0367431i
$178$		0			0
$179$	10.0035			0.747698			0.373849	−	0.927490i	$-0.378038\pi$
$179$	10.0035			0.747698			0.373849	+	0.927490i	$0.378038\pi$
$180$		0			0
$181$	7.13969	+	12.3663i	0.530689	+	0.919180i	0.999359	+	0.0358064i	$0.0114000\pi$
$181$	7.13969	+	12.3663i	0.530689	+	0.919180i	−0.468670	+	0.883373i	$0.655267\pi$
$182$		0			0
$183$	1.75540			0.129763
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.623292	−	1.07957i	0.0455796	−	0.0789462i
$188$		0			0
$189$	2.83385			0.206132
$190$		0			0
$191$	−5.36977			−0.388543			−0.194271	−	0.980948i	$-0.562234\pi$
$191$	−5.36977			−0.388543			−0.194271	+	0.980948i	$0.562234\pi$
$192$		0			0
$193$	7.54615	−	13.0703i	0.543184	−	0.940822i	−0.455535	−	0.890218i	$-0.650552\pi$
$193$	7.54615	−	13.0703i	0.543184	−	0.940822i	0.998719	−	0.0506044i	$-0.0161148\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.4610			0.745315			0.372657	−	0.927969i	$-0.378447\pi$
$197$	10.4610			0.745315			0.372657	+	0.927969i	$0.378447\pi$
$198$		0			0
$199$	−8.36446	−	14.4877i	−0.592941	−	1.02700i	−0.993834	−	0.110879i	$-0.964633\pi$
$199$	−8.36446	−	14.4877i	−0.592941	−	1.02700i	0.400893	−	0.916125i	$-0.368700\pi$
$200$		0			0
$201$	0.452202			0.0318958
$202$		0			0
$203$	−2.30835	−	3.99817i	−0.162014	−	0.280617i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.38233	−	2.39427i	0.0960789	−	0.166413i
$208$		0			0
$209$	−0.398188	+	0.704685i	−0.0275432	+	0.0487441i
$210$		0			0
$211$	9.00494	−	15.5970i	0.619926	−	1.07374i	−0.369573	−	0.929202i	$-0.620496\pi$
$211$	9.00494	−	15.5970i	0.619926	−	1.07374i	0.989499	−	0.144541i	$-0.0461706\pi$
$212$		0			0
$213$	0.917521	+	1.58919i	0.0628675	+	0.108890i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	32.2437			2.18884
$218$		0			0
$219$	0.341014	+	0.590654i	0.0230436	+	0.0399127i
$220$		0			0
$221$	−15.8078			−1.06335
$222$		0			0
$223$	−3.96313	+	6.86434i	−0.265391	+	0.459670i	−0.967666	−	0.252235i	$-0.918834\pi$
$223$	−3.96313	+	6.86434i	−0.265391	+	0.459670i	0.702275	+	0.711906i	$0.252168\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.4260			−0.957487			−0.478743	−	0.877955i	$-0.658908\pi$
$227$	−14.4260			−0.957487			−0.478743	+	0.877955i	$0.658908\pi$
$228$		0			0
$229$	1.27578			0.0843061			0.0421530	−	0.999111i	$-0.486578\pi$
$229$	1.27578			0.0843061			0.0421530	+	0.999111i	$0.486578\pi$
$230$		0			0
$231$	0.0439932	−	0.0761985i	0.00289454	−	0.00501349i
$232$		0			0
$233$	1.59603	−	2.76441i	0.104560	−	0.181102i	−0.808999	−	0.587811i	$-0.799990\pi$
$233$	1.59603	−	2.76441i	0.104560	−	0.181102i	0.913558	+	0.406708i	$0.133323\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.414687	−	0.718258i	−0.0269368	−	0.0466559i
$238$		0			0
$239$	−11.9921			−0.775705			−0.387853	−	0.921721i	$-0.626783\pi$
$239$	−11.9921			−0.775705			−0.387853	+	0.921721i	$0.626783\pi$
$240$		0			0
$241$	12.9988	+	22.5145i	0.837323	+	1.45029i	0.892125	+	0.451789i	$0.149214\pi$
$241$	12.9988	+	22.5145i	0.837323	+	1.45029i	−0.0548017	+	0.998497i	$0.517453\pi$
$242$		0			0
$243$	−1.86097	−	3.22329i	−0.119381	−	0.206774i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.2635	−	0.0951268i	0.653054	−	0.00605277i
$248$		0			0
$249$	−0.0907114	+	0.157117i	−0.00574860	+	0.00995687i
$250$		0			0
$251$	−5.22437	−	9.04887i	−0.329759	−	0.571160i	0.652705	−	0.757612i	$-0.273634\pi$
$251$	−5.22437	−	9.04887i	−0.329759	−	0.571160i	−0.982464	+	0.186453i	$0.940301\pi$
$252$		0			0
$253$	−0.0861168	−	0.149159i	−0.00541412	−	0.00937753i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.28137	+	10.8797i	0.391821	+	0.678655i	0.992690	−	0.120693i	$-0.0385118\pi$
$257$	6.28137	+	10.8797i	0.391821	+	0.678655i	−0.600868	+	0.799348i	$0.705178\pi$
$258$		0			0
$259$	5.55010			0.344866
$260$		0			0
$261$	−2.01899	+	3.49699i	−0.124972	+	0.216458i
$262$		0			0
$263$	−1.47801	+	2.55999i	−0.0911381	+	0.157856i	−0.907990	−	0.418991i	$-0.862384\pi$
$263$	−1.47801	+	2.55999i	−0.0911381	+	0.157856i	0.816852	+	0.576847i	$0.195717\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.543888			−0.0332854
$268$		0			0
$269$	−1.93417	+	3.35007i	−0.117928	+	0.204258i	−0.918946	−	0.394382i	$-0.870959\pi$
$269$	−1.93417	+	3.35007i	−0.117928	+	0.204258i	0.801018	+	0.598640i	$0.204292\pi$
$270$		0			0
$271$	3.47998	−	6.02749i	0.211393	−	0.366144i	−0.740757	−	0.671773i	$-0.765533\pi$
$271$	3.47998	−	6.02749i	0.211393	−	0.366144i	0.952151	+	0.305628i	$0.0988665\pi$
$272$		0			0
$273$	−1.11575			−0.0675282
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.1698			−1.09172			−0.545858	−	0.837878i	$-0.683796\pi$
$277$	−18.1698			−1.09172			−0.545858	+	0.837878i	$0.683796\pi$
$278$		0			0
$279$	−14.1009	−	24.4235i	−0.844200	−	1.46220i
$280$		0			0
$281$	1.08306	+	1.87591i	0.0646099	+	0.111908i	0.896521	−	0.443001i	$-0.146086\pi$
$281$	1.08306	+	1.87591i	0.0646099	+	0.111908i	−0.831911	+	0.554909i	$0.812753\pi$
$282$		0			0
$283$	−9.13750	+	15.8266i	−0.543168	+	0.940794i	0.455552	+	0.890209i	$0.349442\pi$
$283$	−9.13750	+	15.8266i	−0.543168	+	0.940794i	−0.998720	+	0.0505849i	$0.983891\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.6392	+	25.3559i	−0.864127	+	1.49671i
$288$		0			0
$289$	−14.0339	−	24.3074i	−0.825523	−	1.42985i
$290$		0			0
$291$	1.00846	+	1.74670i	0.0591169	+	0.102394i
$292$		0			0
$293$	4.01486			0.234550			0.117275	−	0.993099i	$-0.462584\pi$
$293$	4.01486			0.234550			0.117275	+	0.993099i	$0.462584\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.154413			−0.00895996
$298$		0			0
$299$	−1.09204	+	1.89147i	−0.0631544	+	0.109387i
$300$		0			0
$301$	−12.9524	+	22.4343i	−0.746567	+	1.29309i
$302$		0			0
$303$	0.0967868			0.00556026
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.91354	+	11.9746i	−0.394577	+	0.683427i	−0.993047	−	0.117718i	$-0.962442\pi$
$307$	−6.91354	+	11.9746i	−0.394577	+	0.683427i	0.598470	+	0.801145i	$0.295775\pi$
$308$		0			0
$309$	0.730084	−	1.26454i	0.0415330	−	0.0719373i
$310$		0			0
$311$	22.4425			1.27260			0.636299	−	0.771443i	$-0.280464\pi$
$311$	22.4425			1.27260			0.636299	+	0.771443i	$0.280464\pi$
$312$		0			0
$313$	10.4976	+	18.1823i	0.593357	+	1.02772i	0.993776	+	0.111393i	$0.0355312\pi$
$313$	10.4976	+	18.1823i	0.593357	+	1.02772i	−0.400419	+	0.916332i	$0.631136\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.40192	−	9.35641i	−0.303402	−	0.525508i	0.673502	−	0.739185i	$-0.264789\pi$
$317$	−5.40192	−	9.35641i	−0.303402	−	0.525508i	−0.976904	+	0.213677i	$0.931456\pi$
$318$		0			0
$319$	0.125779	+	0.217856i	0.00704227	+	0.0121976i
$320$		0			0
$321$	1.05412	−	1.82580i	0.0588355	−	0.101906i
$322$		0			0
$323$	14.8654	+	25.2053i	0.827135	+	1.40246i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.00828097	−	0.0143431i	−0.000457939	−	0.000793173i
$328$		0			0
$329$	−13.9599	−	24.1792i	−0.769633	−	1.33304i
$330$		0			0
$331$	7.71526			0.424069			0.212035	−	0.977262i	$-0.431991\pi$
$331$	7.71526			0.424069			0.212035	+	0.977262i	$0.431991\pi$
$332$		0			0
$333$	−2.42719	−	4.20401i	−0.133009	−	0.230378i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.29656	−	5.70981i	0.179575	−	0.311033i	−0.762160	−	0.647389i	$-0.775861\pi$
$337$	3.29656	−	5.70981i	0.179575	−	0.311033i	0.941735	+	0.336355i	$0.109194\pi$
$338$		0			0
$339$	0.704025	−	1.21941i	0.0382374	−	0.0662291i
$340$		0			0
$341$	−1.75692			−0.0951426
$342$		0			0
$343$	8.13294			0.439138
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.4385	+	21.5441i	−0.667732	+	1.15655i	0.310805	+	0.950474i	$0.399402\pi$
$347$	−12.4385	+	21.5441i	−0.667732	+	1.15655i	−0.978537	+	0.206072i	$0.933932\pi$
$348$		0			0
$349$	20.9351			1.12063			0.560316	−	0.828279i	$-0.310680\pi$
$349$	20.9351			1.12063			0.560316	+	0.828279i	$0.310680\pi$
$350$		0			0
$351$	0.979051	+	1.69577i	0.0522579	+	0.0905133i
$352$		0			0
$353$	18.6926			0.994907			0.497454	−	0.867491i	$-0.334268\pi$
$353$	18.6926			0.994907			0.497454	+	0.867491i	$0.334268\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.59049	−	2.75481i	−0.0841775	−	0.145800i
$358$		0			0
$359$	−6.92376	+	11.9923i	−0.365422	+	0.632929i	−0.988844	−	0.148956i	$-0.952409\pi$
$359$	−6.92376	+	11.9923i	−0.365422	+	0.632929i	0.623422	+	0.781886i	$0.285742\pi$
$360$		0			0
$361$	−9.80336	−	16.2756i	−0.515966	−	0.856609i
$362$		0			0
$363$	0.762334	−	1.32040i	0.0400122	−	0.0693031i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.15058	−	15.8493i	−0.477656	−	0.827325i	0.522016	−	0.852936i	$-0.325180\pi$
$367$	−9.15058	−	15.8493i	−0.477656	−	0.827325i	−0.999672	+	0.0256108i	$0.991847\pi$
$368$		0			0
$369$	25.6083			1.33311
$370$		0			0
$371$	22.8384	+	39.5572i	1.18571	+	2.05371i
$372$		0			0
$373$	−12.9735			−0.671743			−0.335872	−	0.941908i	$-0.609031\pi$
$373$	−12.9735			−0.671743			−0.335872	+	0.941908i	$0.609031\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.59499	−	2.76261i	0.0821464	−	0.142282i
$378$		0			0
$379$	−17.4091			−0.894243			−0.447122	−	0.894473i	$-0.647551\pi$
$379$	−17.4091			−0.894243			−0.447122	+	0.894473i	$0.647551\pi$
$380$		0			0
$381$	0.515202			0.0263946
$382$		0			0
$383$	−6.66235	+	11.5395i	−0.340430	+	0.589642i	−0.984513	−	0.175314i	$-0.943906\pi$
$383$	−6.66235	+	11.5395i	−0.340430	+	0.589642i	0.644082	+	0.764956i	$0.277239\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	22.6576			1.15175
$388$		0			0
$389$	13.9471	+	24.1572i	0.707148	+	1.22482i	0.965911	+	0.258875i	$0.0833519\pi$
$389$	13.9471	+	24.1572i	0.707148	+	1.22482i	−0.258763	+	0.965941i	$0.583315\pi$
$390$		0			0
$391$	−6.22677			−0.314901
$392$		0			0
$393$	1.49547	+	2.59023i	0.0754364	+	0.130660i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.7453	−	25.5397i	0.740048	−	1.28180i	−0.212425	−	0.977177i	$-0.568136\pi$
$397$	14.7453	−	25.5397i	0.740048	−	1.28180i	0.952473	−	0.304623i	$-0.0985305\pi$
$398$		0			0
$399$	1.04923	+	1.77904i	0.0525273	+	0.0890634i
$400$		0			0
$401$	−14.8616	+	25.7411i	−0.742154	+	1.28545i	0.209359	+	0.977839i	$0.432862\pi$
$401$	−14.8616	+	25.7411i	−0.742154	+	1.28545i	−0.951513	+	0.307609i	$0.900471\pi$
$402$		0			0
$403$	11.1397	+	19.2945i	0.554908	+	0.961128i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.302418			−0.0149903
$408$		0			0
$409$	−3.66752	−	6.35233i	−0.181347	−	0.314102i	0.760992	−	0.648761i	$-0.224712\pi$
$409$	−3.66752	−	6.35233i	−0.181347	−	0.314102i	−0.942340	+	0.334658i	$0.891379\pi$
$410$		0			0
$411$	1.91559			0.0944890
$412$		0			0
$413$	−6.91730	+	11.9811i	−0.340378	+	0.589552i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.57280			−0.125991
$418$		0			0
$419$	−13.9330			−0.680671			−0.340336	−	0.940304i	$-0.610541\pi$
$419$	−13.9330			−0.680671			−0.340336	+	0.940304i	$0.610541\pi$
$420$		0			0
$421$	−11.7615	+	20.3715i	−0.573219	+	0.992845i	0.423014	+	0.906123i	$0.360972\pi$
$421$	−11.7615	+	20.3715i	−0.573219	+	0.992845i	−0.996233	+	0.0867212i	$0.972361\pi$
$422$		0			0
$423$	−12.2100	+	21.1483i	−0.593669	+	1.02826i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	21.5120	+	37.2598i	1.04104	+	1.80313i
$428$		0			0
$429$	0.0607959			0.00293525
$430$		0			0
$431$	6.02358	+	10.4331i	0.290146	+	0.502547i	0.973844	−	0.227218i	$-0.0729629\pi$
$431$	6.02358	+	10.4331i	0.290146	+	0.502547i	−0.683698	+	0.729765i	$0.739630\pi$
$432$		0			0
$433$	15.4837	+	26.8186i	0.744101	+	1.28882i	0.950613	+	0.310377i	$0.100455\pi$
$433$	15.4837	+	26.8186i	0.744101	+	1.28882i	−0.206512	+	0.978444i	$0.566211\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.04285	−	0.0374708i	0.193396	−	0.00179247i
$438$		0			0
$439$	14.4121	−	24.9625i	0.687852	−	1.19139i	−0.284680	−	0.958623i	$-0.591887\pi$
$439$	14.4121	−	24.9625i	0.687852	−	1.19139i	0.972531	−	0.232771i	$-0.0747794\pi$
$440$		0			0
$441$	6.87561	+	11.9089i	0.327410	+	0.567091i
$442$		0			0
$443$	10.6001	+	18.3599i	0.503624	+	0.872303i	0.999991	+	0.00419027i	$0.00133381\pi$
$443$	10.6001	+	18.3599i	0.503624	+	0.872303i	−0.496367	+	0.868113i	$0.665333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.473279	+	0.819743i	0.0223853	+	0.0387725i
$448$		0			0
$449$	−27.5158			−1.29855			−0.649275	−	0.760553i	$-0.724928\pi$
$449$	−27.5158			−1.29855			−0.649275	+	0.760553i	$0.724928\pi$
$450$		0			0
$451$	0.797675	−	1.38161i	0.0375610	−	0.0650576i
$452$		0			0
$453$	−0.255508	+	0.442554i	−0.0120048	+	0.0207930i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.5615			0.821492			0.410746	−	0.911750i	$-0.365268\pi$
$457$	17.5615			0.821492			0.410746	+	0.911750i	$0.365268\pi$
$458$		0			0
$459$	−2.79125	+	4.83459i	−0.130284	+	0.225659i
$460$		0			0
$461$	17.9075	−	31.0167i	0.834036	−	1.44459i	−0.0607773	−	0.998151i	$-0.519358\pi$
$461$	17.9075	−	31.0167i	0.834036	−	1.44459i	0.894813	−	0.446441i	$-0.147309\pi$
$462$		0			0
$463$	2.10186			0.0976817			0.0488409	−	0.998807i	$-0.484447\pi$
$463$	2.10186			0.0976817			0.0488409	+	0.998807i	$0.484447\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.3019			−0.800637			−0.400319	−	0.916376i	$-0.631101\pi$
$467$	−17.3019			−0.800637			−0.400319	+	0.916376i	$0.631101\pi$
$468$		0			0
$469$	5.54162	+	9.59837i	0.255888	+	0.443212i
$470$		0			0
$471$	−0.981133	−	1.69937i	−0.0452082	−	0.0783030i
$472$		0			0
$473$	0.705764	−	1.22242i	0.0324511	−	0.0562069i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	19.9755	−	34.5985i	0.914614	−	1.58416i
$478$		0			0
$479$	14.5267	+	25.1610i	0.663743	+	1.14964i	0.979625	+	0.200837i	$0.0643663\pi$
$479$	14.5267	+	25.1610i	0.663743	+	1.14964i	−0.315882	+	0.948799i	$0.602300\pi$
$480$		0			0
$481$	1.91747	+	3.32116i	0.0874292	+	0.151432i
$482$		0			0
$483$	−0.439498			−0.0199978
$484$		0			0
$485$		0			0
$486$		0			0
$487$	13.0964			0.593456			0.296728	−	0.954962i	$-0.404105\pi$
$487$	13.0964			0.593456			0.296728	+	0.954962i	$0.404105\pi$
$488$		0			0
$489$	0.391862	−	0.678726i	0.0177206	−	0.0306930i
$490$		0			0
$491$	−3.11779	+	5.40016i	−0.140704	+	0.243706i	−0.927762	−	0.373173i	$-0.878270\pi$
$491$	−3.11779	+	5.40016i	−0.140704	+	0.243706i	0.787058	+	0.616879i	$0.211603\pi$
$492$		0			0
$493$	9.09458			0.409599
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−22.4880	+	38.9504i	−1.00872	+	1.74716i
$498$		0			0
$499$	5.67610	−	9.83130i	0.254097	−	0.440109i	−0.710553	−	0.703644i	$-0.751555\pi$
$499$	5.67610	−	9.83130i	0.254097	−	0.440109i	0.964650	+	0.263535i	$0.0848883\pi$
$500$		0			0
$501$	−1.03970			−0.0464504
$502$		0			0
$503$	8.99758	+	15.5843i	0.401182	+	0.694868i	0.993869	−	0.110565i	$-0.0352661\pi$
$503$	8.99758	+	15.5843i	0.401182	+	0.694868i	−0.592687	+	0.805433i	$0.701933\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.518300	+	0.897721i	0.0230185	+	0.0398692i
$508$		0			0
$509$	−12.8639	−	22.2810i	−0.570184	−	0.987587i	−0.996547	−	0.0830350i	$-0.973539\pi$
$509$	−12.8639	−	22.2810i	−0.570184	−	0.987587i	0.426363	−	0.904552i	$-0.359795\pi$
$510$		0			0
$511$	−8.35809	+	14.4766i	−0.369740	+	0.640409i
$512$		0			0
$513$	1.78318	−	3.15575i	0.0787294	−	0.139330i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.760658	+	1.31750i	0.0334537	+	0.0579435i
$518$		0			0
$519$	−1.62524	−	2.81500i	−0.0713401	−	0.123565i
$520$		0			0
$521$	13.7913			0.604206			0.302103	−	0.953275i	$-0.402311\pi$
$521$	13.7913			0.604206			0.302103	+	0.953275i	$0.402311\pi$
$522$		0			0
$523$	−11.0625	−	19.1607i	−0.483728	−	0.837841i	0.516098	−	0.856530i	$-0.327384\pi$
$523$	−11.0625	−	19.1607i	−0.483728	−	0.837841i	−0.999825	+	0.0186889i	$0.994051\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−31.7590	+	55.0082i	−1.38344	+	2.39620i
$528$		0			0
$529$	11.0698	−	19.1735i	0.481297	−	0.833632i
$530$		0			0
$531$	12.1004			0.525112
$532$		0			0
$533$	−20.2305			−0.876280
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.695455	+	1.20456i	−0.0300111	+	0.0519808i
$538$		0			0
$539$	0.856676			0.0368996
$540$		0			0
$541$	−14.7284	−	25.5104i	−0.633224	−	1.09678i	−0.986888	−	0.161404i	$-0.948398\pi$
$541$	−14.7284	−	25.5104i	−0.633224	−	1.09678i	0.353664	−	0.935372i	$-0.384936\pi$
$542$		0			0
$543$	−1.98543			−0.0852031
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.2421	−	35.0604i	−0.865491	−	1.49908i	−0.866558	−	0.499076i	$-0.833673\pi$
$547$	−20.2421	−	35.0604i	−0.865491	−	1.49908i	0.00106707	−	0.999999i	$-0.499660\pi$
$548$		0			0
$549$	18.8154	−	32.5892i	0.803020	−	1.39087i
$550$		0			0
$551$	−5.90484	+	0.0547284i	−0.251554	+	0.00233151i
$552$		0			0
$553$	10.1638	−	17.6042i	0.432208	−	0.748605i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.1035	+	17.4998i	0.428099	+	0.741490i	0.996704	−	0.0811209i	$-0.0258500\pi$
$557$	10.1035	+	17.4998i	0.428099	+	0.741490i	−0.568605	+	0.822611i	$0.692517\pi$
$558$		0			0
$559$	−17.8995			−0.757067
$560$		0			0
$561$	0.0866638	+	0.150106i	0.00365895	+	0.00633749i
$562$		0			0
$563$	25.1900			1.06163			0.530816	−	0.847487i	$-0.321885\pi$
$563$	25.1900			1.06163			0.530816	+	0.847487i	$0.321885\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	15.0395	−	26.0492i	0.631600	−	1.09396i
$568$		0			0
$569$	−32.6378			−1.36825			−0.684124	−	0.729366i	$-0.739815\pi$
$569$	−32.6378			−1.36825			−0.684124	+	0.729366i	$0.739815\pi$
$570$		0			0
$571$	−30.4795			−1.27553			−0.637764	−	0.770232i	$-0.720141\pi$
$571$	−30.4795			−1.27553			−0.637764	+	0.770232i	$0.720141\pi$
$572$		0			0
$573$	0.373312	−	0.646595i	0.0155953	−	0.0270119i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	18.3407			0.763533			0.381766	−	0.924259i	$-0.375316\pi$
$577$	18.3407			0.763533			0.381766	+	0.924259i	$0.375316\pi$
$578$		0			0
$579$	1.04923	+	1.81732i	0.0436046	+	0.0755254i
$580$		0			0
$581$	−4.44658			−0.184475
$582$		0			0
$583$	−1.24444	−	2.15543i	−0.0515392	−	0.0892686i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.16010	+	14.1337i	−0.336804	+	0.583361i	−0.983830	−	0.179107i	$-0.942679\pi$
$587$	−8.16010	+	14.1337i	−0.336804	+	0.583361i	0.647026	+	0.762468i	$0.276012\pi$
$588$		0			0
$589$	20.2891	−	35.9063i	0.835999	−	1.47949i
$590$		0			0
$591$	−0.727259	+	1.25965i	−0.0299154	+	0.0518150i
$592$		0			0
$593$	−4.27547	−	7.40534i	−0.175573	−	0.304101i	0.764787	−	0.644284i	$-0.222844\pi$
$593$	−4.27547	−	7.40534i	−0.175573	−	0.304101i	−0.940359	+	0.340183i	$0.889511\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.32602			0.0951978
$598$		0			0
$599$	−7.09169	−	12.2832i	−0.289758	−	0.501876i	0.683994	−	0.729488i	$-0.260242\pi$
$599$	−7.09169	−	12.2832i	−0.289758	−	0.501876i	−0.973752	+	0.227612i	$0.926908\pi$
$600$		0			0
$601$	21.3129			0.869370			0.434685	−	0.900583i	$-0.356860\pi$
$601$	21.3129			0.869370			0.434685	+	0.900583i	$0.356860\pi$
$602$		0			0
$603$	4.84696	−	8.39518i	0.197383	−	0.341878i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−28.4812			−1.15602			−0.578009	−	0.816031i	$-0.696170\pi$
$607$	−28.4812			−1.15602			−0.578009	+	0.816031i	$0.696170\pi$
$608$		0			0
$609$	0.641914			0.0260117
$610$		0			0
$611$	9.64584	−	16.7071i	0.390229	−	0.675896i
$612$		0			0
$613$	−12.9742	+	22.4720i	−0.524025	+	0.907638i	0.475584	+	0.879670i	$0.342237\pi$
$613$	−12.9742	+	22.4720i	−0.524025	+	0.907638i	−0.999609	+	0.0279673i	$0.991097\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.71585	+	11.6322i	0.270370	+	0.468295i	0.968957	−	0.247231i	$-0.0795206\pi$
$617$	6.71585	+	11.6322i	0.270370	+	0.468295i	−0.698587	+	0.715526i	$0.746187\pi$
$618$		0			0
$619$	−23.9017			−0.960690			−0.480345	−	0.877080i	$-0.659489\pi$
$619$	−23.9017			−0.960690			−0.480345	+	0.877080i	$0.659489\pi$
$620$		0			0
$621$	0.385652	+	0.667968i	0.0154757	+	0.0268047i
$622$		0			0
$623$	−6.66521	−	11.5445i	−0.267036	−	0.462520i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.0571715	−	0.0969378i	−0.00228321	−	0.00387132i
$628$		0			0
$629$	−5.46667	+	9.46855i	−0.217970	+	0.377536i
$630$		0			0
$631$	12.0962	+	20.9512i	0.481541	+	0.834054i	0.999776	−	0.0211849i	$-0.00674387\pi$
$631$	12.0962	+	20.9512i	0.481541	+	0.834054i	−0.518234	+	0.855239i	$0.673411\pi$
$632$		0			0
$633$	1.25207	+	2.16864i	0.0497651	+	0.0861957i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.43172	−	9.40801i	−0.215213	−	0.372759i
$638$		0			0
$639$	39.3381			1.55619
$640$		0			0
$641$	11.7338	−	20.3235i	0.463456	−	0.802729i	−0.535675	−	0.844424i	$-0.679943\pi$
$641$	11.7338	−	20.3235i	0.463456	−	0.802729i	0.999130	+	0.0416956i	$0.0132760\pi$
$642$		0			0
$643$	0.497264	−	0.861287i	0.0196102	−	0.0339658i	−0.856054	−	0.516887i	$-0.827091\pi$
$643$	0.497264	−	0.861287i	0.0196102	−	0.0339658i	0.875664	+	0.482921i	$0.160424\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.24679			0.0883306			0.0441653	−	0.999024i	$-0.485937\pi$
$647$	2.24679			0.0883306			0.0441653	+	0.999024i	$0.485937\pi$
$648$		0			0
$649$	0.376915	−	0.652837i	0.0147952	−	0.0256261i
$650$		0			0
$651$	−2.24162	+	3.88259i	−0.0878558	+	0.152171i
$652$		0			0
$653$	−16.9500			−0.663307			−0.331653	−	0.943401i	$-0.607606\pi$
$653$	−16.9500			−0.663307			−0.331653	+	0.943401i	$0.607606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	14.6207			0.570410
$658$		0			0
$659$	−16.1670	−	28.0020i	−0.629775	−	1.09080i	−0.987597	−	0.157013i	$-0.949814\pi$
$659$	−16.1670	−	28.0020i	−0.629775	−	1.09080i	0.357821	−	0.933790i	$-0.383520\pi$
$660$		0			0
$661$	9.67075	+	16.7502i	0.376149	+	0.651509i	0.990498	−	0.137525i	$-0.0439149\pi$
$661$	9.67075	+	16.7502i	0.376149	+	0.651509i	−0.614350	+	0.789034i	$0.710582\pi$
$662$		0			0
$663$	1.09898	−	1.90348i	0.0426807	−	0.0739252i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.628274	−	1.08820i	0.0243269	−	0.0421354i
$668$		0			0
$669$	−0.551042	−	0.954432i	−0.0213045	−	0.0369005i
$670$		0			0
$671$	−1.17216	−	2.03024i	−0.0452508	−	0.0783767i
$672$		0			0
$673$	22.4887			0.866875			0.433438	−	0.901184i	$-0.357300\pi$
$673$	22.4887			0.866875			0.433438	+	0.901184i	$0.357300\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.8477			0.724377			0.362188	−	0.932105i	$-0.382030\pi$
$677$	18.8477			0.724377			0.362188	+	0.932105i	$0.382030\pi$
$678$		0			0
$679$	−24.7169	+	42.8109i	−0.948546	+	1.64293i
$680$		0			0
$681$	1.00291	−	1.73709i	0.0384316	−	0.0665655i
$682$		0			0
$683$	−44.8197			−1.71498			−0.857489	−	0.514502i	$-0.827977\pi$
$683$	−44.8197			−1.71498			−0.857489	+	0.514502i	$0.827977\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.0886937	+	0.153622i	−0.00338388	+	0.00586105i
$688$		0			0
$689$	−15.7806	+	27.3328i	−0.601192	+	1.04130i
$690$		0			0
$691$	1.57873			0.0600578			0.0300289	−	0.999549i	$-0.490440\pi$
$691$	1.57873			0.0600578			0.0300289	+	0.999549i	$0.490440\pi$
$692$		0			0
$693$	−0.943090	−	1.63348i	−0.0358250	−	0.0620508i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−28.8383	−	49.9495i	−1.09233	−	1.89197i
$698$		0			0
$699$	0.221916	+	0.384369i	0.00839362	+	0.0145382i
$700$		0			0
$701$	−17.2140	+	29.8155i	−0.650163	+	1.12611i	0.332920	+	0.942955i	$0.391966\pi$
$701$	−17.2140	+	29.8155i	−0.650163	+	1.12611i	−0.983083	+	0.183160i	$0.941367\pi$
$702$		0			0
$703$	3.49236	−	6.18054i	0.131717	−	0.233103i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.18610	+	2.05438i	0.0446078	+	0.0772630i
$708$		0			0
$709$	11.3751	+	19.7023i	0.427202	+	0.739936i	0.996623	−	0.0821102i	$-0.0261659\pi$
$709$	11.3751	+	19.7023i	0.427202	+	0.739936i	−0.569421	+	0.822046i	$0.692833\pi$
$710$		0			0
$711$	−17.7794			−0.666780
$712$		0			0
$713$	4.38797	+	7.60018i	0.164331	+	0.284629i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.833704	−	1.44402i	0.0311352	−	0.0539278i
$718$		0			0
$719$	−15.0042	+	25.9880i	−0.559561	+	0.969188i	0.437972	+	0.898989i	$0.355697\pi$
$719$	−15.0042	+	25.9880i	−0.559561	+	0.969188i	−0.997533	+	0.0701994i	$0.977636\pi$
$720$		0			0
$721$	35.7880			1.33282
$722$		0			0
$723$	−3.61475			−0.134434
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−12.0504	+	20.8719i	−0.446924	+	0.774096i	−0.998184	−	0.0602381i	$-0.980814\pi$
$727$	−12.0504	+	20.8719i	−0.446924	+	0.774096i	0.551260	+	0.834334i	$0.314147\pi$
$728$		0			0
$729$	−25.9616			−0.961542
$730$		0			0
$731$	−25.5155	−	44.1941i	−0.943724	−	1.63458i
$732$		0			0
$733$	−12.5801			−0.464657			−0.232329	−	0.972637i	$-0.574635\pi$
$733$	−12.5801			−0.464657			−0.232329	+	0.972637i	$0.574635\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.301957	−	0.523004i	−0.0111227	−	0.0192651i
$738$		0			0
$739$	3.54647	−	6.14266i	0.130459	−	0.225961i	−0.793395	−	0.608708i	$-0.791688\pi$
$739$	3.54647	−	6.14266i	0.130459	−	0.225961i	0.923854	+	0.382746i	$0.125022\pi$
$740$		0			0
$741$	−0.702078	+	1.24249i	−0.0257915	+	0.0456439i
$742$		0			0
$743$	17.1507	−	29.7060i	0.629200	−	1.08981i	−0.358513	−	0.933525i	$-0.616716\pi$
$743$	17.1507	−	29.7060i	0.629200	−	1.08981i	0.987713	−	0.156281i	$-0.0499506\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.94459	+	3.36814i	0.0711490	+	0.123234i
$748$		0			0
$749$	51.6722			1.88806
$750$		0			0
$751$	−19.0760	−	33.0406i	−0.696094	−	1.20567i	−0.969811	−	0.243860i	$-0.921586\pi$
$751$	−19.0760	−	33.0406i	−0.696094	−	1.20567i	0.273717	−	0.961810i	$-0.411747\pi$
$752$		0			0
$753$	1.45281			0.0529435
$754$		0			0
$755$		0			0
$756$		0			0
$757$	14.2143	−	24.6200i	0.516629	−	0.894828i	−0.483185	−	0.875519i	$-0.660520\pi$
$757$	14.2143	−	24.6200i	0.516629	−	0.894828i	0.999814	−	0.0193092i	$-0.00614669\pi$
$758$		0			0
$759$	0.0239477			0.000869247
$760$		0			0
$761$	−3.88441			−0.140810			−0.0704048	−	0.997519i	$-0.522429\pi$
$761$	−3.88441			−0.140810			−0.0704048	+	0.997519i	$0.522429\pi$
$762$		0			0
$763$	0.202963	−	0.351542i	0.00734774	−	0.0127267i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.55927			−0.345165
$768$		0			0
$769$	17.8289	+	30.8806i	0.642928	+	1.11358i	0.984776	+	0.173829i	$0.0556140\pi$
$769$	17.8289	+	30.8806i	0.642928	+	1.11358i	−0.341847	+	0.939755i	$0.611053\pi$
$770$		0			0
$771$	−1.74675			−0.0629077
$772$		0			0
$773$	−15.0060	−	25.9912i	−0.539729	−	0.934839i	−0.998918	−	0.0465000i	$-0.985193\pi$
$773$	−15.0060	−	25.9912i	−0.539729	−	0.934839i	0.459189	−	0.888339i	$-0.348140\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.385849	+	0.668309i	−0.0138422	+	0.0239755i
$778$		0			0
$779$	19.0244	+	32.2571i	0.681621	+	1.15573i
$780$		0			0
$781$	1.22534	−	2.12236i	0.0438463	−	0.0759440i
$782$		0			0
$783$	−0.563269	−	0.975610i	−0.0201296	−	0.0348654i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	40.9891			1.46110			0.730552	−	0.682857i	$-0.239263\pi$
$787$	40.9891			1.46110			0.730552	+	0.682857i	$0.239263\pi$
$788$		0			0
$789$	−0.205506	−	0.355947i	−0.00731620	−	0.0126720i
$790$		0			0
$791$	34.5106			1.22706
$792$		0			0
$793$	−14.8641	+	25.7454i	−0.527839	+	0.914245i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−46.6104			−1.65103			−0.825513	−	0.564383i	$-0.809114\pi$
$797$	−46.6104			−1.65103			−0.825513	+	0.564383i	$0.809114\pi$
$798$		0			0
$799$	55.0001			1.94577
$800$		0			0
$801$	−5.82971	+	10.0973i	−0.205983	+	0.356772i
$802$		0			0
$803$	0.455423	−	0.788815i	0.0160715	−	0.0278367i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.268930	−	0.465801i	−0.00946680	−	0.0163970i
$808$		0			0
$809$	15.1137			0.531371			0.265686	−	0.964060i	$-0.414402\pi$
$809$	15.1137			0.531371			0.265686	+	0.964060i	$0.414402\pi$
$810$		0			0
$811$	−1.57195	−	2.72270i	−0.0551986	−	0.0956068i	0.837106	−	0.547041i	$-0.184246\pi$
$811$	−1.57195	−	2.72270i	−0.0551986	−	0.0956068i	−0.892304	+	0.451434i	$0.850913\pi$
$812$		0			0
$813$	0.483863	+	0.838075i	0.0169698	+	0.0293926i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.8324	+	28.5404i	0.588890	+	0.998501i
$818$		0			0
$819$	−11.9592	+	20.7140i	−0.417890	+	0.723807i
$820$		0			0
$821$	0.406694	+	0.704414i	0.0141937	+	0.0245842i	0.873035	−	0.487658i	$-0.162149\pi$
$821$	0.406694	+	0.704414i	0.0141937	+	0.0245842i	−0.858841	+	0.512242i	$0.828815\pi$
$822$		0			0
$823$	4.80912	+	8.32963i	0.167635	+	0.290353i	0.937588	−	0.347748i	$-0.113054\pi$
$823$	4.80912	+	8.32963i	0.167635	+	0.290353i	−0.769953	+	0.638101i	$0.779720\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.1356	−	40.0720i	−0.804503	−	1.39344i	−0.916626	−	0.399745i	$-0.869099\pi$
$827$	−23.1356	−	40.0720i	−0.804503	−	1.39344i	0.112124	−	0.993694i	$-0.464235\pi$
$828$		0			0
$829$	−14.2046			−0.493345			−0.246672	−	0.969099i	$-0.579337\pi$
$829$	−14.2046			−0.493345			−0.246672	+	0.969099i	$0.579337\pi$
$830$		0			0
$831$	1.26318	−	2.18789i	0.0438193	−	0.0758972i
$832$		0			0
$833$	15.4857	−	26.8220i	0.536548	−	0.929328i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	7.86791			0.271955
$838$		0			0
$839$	7.79460	−	13.5006i	0.269099	−	0.466094i	−0.699530	−	0.714603i	$-0.746607\pi$
$839$	7.79460	−	13.5006i	0.269099	−	0.466094i	0.968629	+	0.248509i	$0.0799407\pi$
$840$		0			0
$841$	13.5824	−	23.5253i	0.468357	−	0.811219i
$842$		0			0
$843$	−0.301182			−0.0103732
$844$		0			0
$845$		0			0
$846$		0			0
$847$	37.3689			1.28401
$848$		0			0
$849$	−1.27050	−	2.20056i	−0.0436033	−	0.0755232i
$850$		0			0
$851$	0.755300	+	1.30822i	0.0258913	+	0.0448451i
$852$		0			0
$853$	20.8821	−	36.1689i	0.714991	−	1.23840i	−0.247973	−	0.968767i	$-0.579764\pi$
$853$	20.8821	−	36.1689i	0.714991	−	1.23840i	0.962963	−	0.269633i	$-0.0869024\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.460667	−	0.797898i	0.0157361	−	0.0272557i	−0.858050	−	0.513566i	$-0.828324\pi$
$857$	0.460667	−	0.797898i	0.0157361	−	0.0272557i	0.873786	+	0.486310i	$0.161658\pi$
$858$		0			0
$859$	−1.54335	−	2.67315i	−0.0526583	−	0.0912068i	0.838495	−	0.544910i	$-0.183436\pi$
$859$	−1.54335	−	2.67315i	−0.0526583	−	0.0912068i	−0.891153	+	0.453703i	$0.850103\pi$
$860$		0			0
$861$	−2.03547	−	3.52554i	−0.0693686	−	0.120150i
$862$		0			0
$863$	51.8011			1.76333			0.881666	−	0.471875i	$-0.156423\pi$
$863$	51.8011			1.76333			0.881666	+	0.471875i	$0.156423\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.90260			0.132539
$868$		0			0
$869$	−0.553812	+	0.959231i	−0.0187868	+	0.0325397i
$870$		0			0
$871$	−3.82909	+	6.63217i	−0.129744	+	0.224723i
$872$		0			0
$873$	43.2370			1.46335
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.72507	−	13.3802i	0.260857	−	0.451818i	−0.705613	−	0.708598i	$-0.749328\pi$
$877$	7.72507	−	13.3802i	0.260857	−	0.451818i	0.966470	+	0.256780i	$0.0826615\pi$
$878$		0			0
$879$	−0.279117	+	0.483445i	−0.00941438	+	0.0163062i
$880$		0			0
$881$	−41.6529			−1.40332			−0.701661	−	0.712511i	$-0.747558\pi$
$881$	−41.6529			−1.40332			−0.701661	+	0.712511i	$0.747558\pi$
$882$		0			0
$883$	−26.7799	−	46.3841i	−0.901215	−	1.56095i	−0.825919	−	0.563788i	$-0.809343\pi$
$883$	−26.7799	−	46.3841i	−0.901215	−	1.56095i	−0.0752955	−	0.997161i	$-0.523990\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.4140	−	38.8223i	−0.752590	−	1.30352i	−0.946563	−	0.322518i	$-0.895471\pi$
$887$	−22.4140	−	38.8223i	−0.752590	−	1.30352i	0.193973	−	0.981007i	$-0.437862\pi$
$888$		0			0
$889$	6.31368	+	10.9356i	0.211754	+	0.366769i
$890$		0			0
$891$	−0.819485	+	1.41939i	−0.0274538	+	0.0475514i
$892$		0			0
$893$	−35.7099	+	0.330974i	−1.19499	+	0.0110756i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.151840	−	0.262994i	−0.00506978	−	0.00878111i
$898$		0			0
$899$	−6.40890	−	11.1005i	−0.213749	−	0.370224i
$900$		0			0
$901$	−89.9802			−2.99767
$902$		0			0
$903$	−1.80094	−	3.11931i	−0.0599314	−	0.103804i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.20013	−	10.7389i	0.205872	−	0.356581i	−0.744538	−	0.667580i	$-0.767330\pi$
$907$	6.20013	−	10.7389i	0.205872	−	0.356581i	0.950410	+	0.310999i	$0.100664\pi$
$908$		0			0
$909$	1.03742	−	1.79686i	0.0344090	−	0.0595981i
$910$		0			0
$911$	25.5512			0.846548			0.423274	−	0.906002i	$-0.360881\pi$
$911$	25.5512			0.846548			0.423274	+	0.906002i	$0.360881\pi$
$912$		0			0
$913$	0.242289			0.00801860
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−36.6532	+	63.4852i	−1.21040	+	2.09647i
$918$		0			0
$919$	21.4055			0.706101			0.353051	−	0.935604i	$-0.385144\pi$
$919$	21.4055			0.706101			0.353051	+	0.935604i	$0.385144\pi$
$920$		0			0
$921$	−0.961273	−	1.66497i	−0.0316750	−	0.0548628i
$922$		0			0
$923$	−31.0770			−1.02291
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−15.6509	−	27.1082i	−0.514044	−	0.890351i
$928$		0			0
$929$	−27.9411	+	48.3954i	−0.916717	+	1.58780i	−0.112349	+	0.993669i	$0.535837\pi$
$929$	−27.9411	+	48.3954i	−0.916717	+	1.58780i	−0.804368	+	0.594131i	$0.797496\pi$
$930$		0			0
$931$	−9.89299	+	17.5079i	−0.324230	+	0.573799i
$932$		0			0
$933$	−1.56023	+	2.70239i	−0.0510795	+	0.0884723i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−11.4266	−	19.7914i	−0.373289	−	0.646556i	0.616780	−	0.787136i	$-0.288437\pi$
$937$	−11.4266	−	19.7914i	−0.373289	−	0.646556i	−0.990069	+	0.140579i	$0.955103\pi$
$938$		0			0
$939$	−2.91920			−0.0952646
$940$		0			0
$941$	−29.0459	−	50.3089i	−0.946868	−	1.64002i	−0.751967	−	0.659200i	$-0.770895\pi$
$941$	−29.0459	−	50.3089i	−0.946868	−	1.64002i	−0.194901	−	0.980823i	$-0.562438\pi$
$942$		0			0
$943$	−7.96887			−0.259502
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.9088	−	25.8228i	0.484472	−	0.839130i	−0.515369	−	0.856968i	$-0.672345\pi$
$947$	14.9088	−	25.8228i	0.484472	−	0.839130i	0.999841	+	0.0178386i	$0.00567850\pi$
$948$		0			0
$949$	−11.5504			−0.374940
$950$		0			0
$951$	1.50219			0.0487118
$952$		0			0
$953$	−26.1390	+	45.2741i	−0.846725	+	1.46657i	0.0373888	+	0.999301i	$0.488096\pi$
$953$	−26.1390	+	45.2741i	−0.846725	+	1.46657i	−0.884114	+	0.467271i	$0.845237\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.0349772			−0.00113065
$958$		0			0
$959$	23.4751	+	40.6600i	0.758050	+	1.31298i
$960$		0			0
$961$	58.5216			1.88779
$962$		0			0
$963$	−22.5974	−	39.1399i	−0.728192	−	1.26127i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.0586	+	17.4220i	−0.323463	+	0.560254i	−0.981200	−	0.192994i	$-0.938180\pi$
$967$	−10.0586	+	17.4220i	−0.323463	+	0.560254i	0.657737	+	0.753247i	$0.271514\pi$
$968$		0			0
$969$	−4.06853	+	0.0377088i	−0.130700	+	0.00121138i
$970$		0			0
$971$	8.91867	−	15.4476i	0.286214	−	0.495737i	−0.686689	−	0.726951i	$-0.740937\pi$
$971$	8.91867	−	15.4476i	0.286214	−	0.495737i	0.972903	+	0.231215i	$0.0742700\pi$
$972$		0			0
$973$	−31.5290	−	54.6099i	−1.01077	−	1.75071i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.7616			0.376287			0.188143	−	0.982142i	$-0.439753\pi$
$977$	11.7616			0.376287			0.188143	+	0.982142i	$0.439753\pi$
$978$		0			0
$979$	0.363180	+	0.629046i	0.0116073	+	0.0201044i
$980$		0			0
$981$	−0.355041			−0.0113356
$982$		0			0
$983$	16.3241	−	28.2742i	0.520659	−	0.901807i	−0.479053	−	0.877786i	$-0.659020\pi$
$983$	16.3241	−	28.2742i	0.520659	−	0.901807i	0.999711	−	0.0240213i	$-0.00764694\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.88202			0.123566
$988$		0			0
$989$	−7.05067			−0.224198
$990$		0			0
$991$	26.7049	−	46.2543i	0.848310	−	1.46932i	−0.0344052	−	0.999408i	$-0.510954\pi$
$991$	26.7049	−	46.2543i	0.848310	−	1.46932i	0.882715	−	0.469908i	$-0.155713\pi$
$992$		0			0
$993$	−0.536373	+	0.929025i	−0.0170213	+	0.0294817i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	5.83999	+	10.1152i	0.184954	+	0.320350i	0.943561	−	0.331198i	$-0.107453\pi$
$997$	5.83999	+	10.1152i	0.184954	+	0.320350i	−0.758607	+	0.651549i	$0.774120\pi$
$998$		0			0
$999$	1.35430			0.0428482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.e.201.4	✓	12
5.2	odd	4		1900.2.s.e.49.7		24
5.3	odd	4		1900.2.s.e.49.6		24
5.4	even	2		1900.2.i.f.201.3	yes	12
19.7	even	3	inner	1900.2.i.e.501.4	yes	12
95.7	odd	12		1900.2.s.e.349.6		24
95.64	even	6		1900.2.i.f.501.3	yes	12
95.83	odd	12		1900.2.s.e.349.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.4	✓	12	1.1	even	1	trivial
1900.2.i.e.501.4	yes	12	19.7	even	3	inner
1900.2.i.f.201.3	yes	12	5.4	even	2
1900.2.i.f.501.3	yes	12	95.64	even	6
1900.2.s.e.49.6		24	5.3	odd	4
1900.2.s.e.49.7		24	5.2	odd	4
1900.2.s.e.349.6		24	95.7	odd	12
1900.2.s.e.349.7		24	95.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0695210 + 0.120414i) q^{3} -3.40785 q^{7} +(1.49033 + 2.58133i) q^{9} +O(q^{10})\)	\(q+(-0.0695210 + 0.120414i) q^{3} -3.40785 q^{7} +(1.49033 + 2.58133i) q^{9} +0.185690 q^{11} +(-1.17736 - 2.03925i) q^{13} +(3.35663 - 5.81385i) q^{17} +(-2.14437 + 3.79495i) q^{19} +(0.236918 - 0.410353i) q^{21} +(-0.463767 - 0.803267i) q^{23} -0.831564 q^{27} +(0.677360 + 1.17322i) q^{29} -9.46158 q^{31} +(-0.0129094 + 0.0223597i) q^{33} -1.62862 q^{37} +0.327405 q^{39} +(4.29573 - 7.44043i) q^{41} +(3.80076 - 6.58312i) q^{43} +(4.09639 + 7.09515i) q^{47} +4.61347 q^{49} +(0.466712 + 0.808369i) q^{51} +(-6.70168 - 11.6077i) q^{53} +(-0.307887 - 0.522041i) q^{57} +(2.02981 - 3.51573i) q^{59} +(-6.31247 - 10.9335i) q^{61} +(-5.07884 - 8.79681i) q^{63} +(-1.62613 - 2.81654i) q^{67} +0.128966 q^{69} +(6.59887 - 11.4296i) q^{71} +(2.45260 - 4.24802i) q^{73} -0.632805 q^{77} +(-2.98245 + 5.16576i) q^{79} +(-4.41319 + 7.64387i) q^{81} +1.30480 q^{83} -0.188363 q^{87} +(1.95584 + 3.38761i) q^{89} +(4.01227 + 6.94946i) q^{91} +(0.657779 - 1.13931i) q^{93} +(7.25291 - 12.5624i) q^{97} +(0.276740 + 0.479328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 3 * q^9	\( 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 3 * q^9 + 2 * q^11 - 7 * q^13 + q^17 + q^21 + 2 * q^23 + 24 * q^27 + q^29 + 2 * q^31 - 10 * q^33 - 20 * q^37 + 36 * q^39 - 7 * q^41 - 19 * q^43 + 14 * q^47 + 8 * q^49 + 11 * q^51 - 6 * q^53 + 28 * q^57 - 5 * q^61 + 11 * q^63 - 14 * q^67 - 14 * q^69 + 8 * q^71 + 9 * q^73 - 2 * q^77 + q^79 + 2 * q^81 + 26 * q^83 - 30 * q^87 - 8 * q^89 + 3 * q^91 - 9 * q^93 + 11 * q^97 - 18 * q^99

Introduction

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