LMFDB - Embedded newform 1900.2.s.e.349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(49,1900)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.s (of order $6$, degree $2$, not 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.7
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.e.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.120414 - 0.0695210i) q^{3} +3.40785i q^{7} +(-1.49033 + 2.58133i) q^{9} +O(q^{10})$	\(q+(0.120414 - 0.0695210i) q^{3} +3.40785i q^{7} +(-1.49033 + 2.58133i) q^{9} +0.185690 q^{11} +(-2.03925 - 1.17736i) q^{13} +(5.81385 - 3.35663i) q^{17} +(2.14437 + 3.79495i) q^{19} +(0.236918 + 0.410353i) q^{21} +(-0.803267 - 0.463767i) q^{23} +0.831564i q^{27} +(-0.677360 + 1.17322i) q^{29} -9.46158 q^{31} +(0.0223597 - 0.0129094i) q^{33} +1.62862i q^{37} -0.327405 q^{39} +(4.29573 + 7.44043i) q^{41} +(-6.58312 + 3.80076i) q^{43} +(-7.09515 - 4.09639i) q^{47} -4.61347 q^{49} +(0.466712 - 0.808369i) q^{51} +(-11.6077 - 6.70168i) q^{53} +(0.522041 + 0.307887i) q^{57} +(-2.02981 - 3.51573i) q^{59} +(-6.31247 + 10.9335i) q^{61} +(-8.79681 - 5.07884i) q^{63} +(2.81654 + 1.62613i) q^{67} -0.128966 q^{69} +(6.59887 + 11.4296i) q^{71} +(-4.24802 + 2.45260i) q^{73} +0.632805i q^{77} +(2.98245 + 5.16576i) q^{79} +(-4.41319 - 7.64387i) q^{81} +1.30480i q^{83} +0.188363i q^{87} +(-1.95584 + 3.38761i) q^{89} +(4.01227 - 6.94946i) q^{91} +(-1.13931 + 0.657779i) q^{93} +(12.5624 - 7.25291i) q^{97} +(-0.276740 + 0.479328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} + 4 q^{11} + 2 q^{21} - 2 q^{29} + 4 q^{31} - 72 q^{39} - 14 q^{41} - 16 q^{49} + 22 q^{51} - 10 q^{61} + 28 q^{69} + 16 q^{71} - 2 q^{79} + 4 q^{81} + 16 q^{89} + 6 q^{91} + 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 + 4 * q^11 + 2 * q^21 - 2 * q^29 + 4 * q^31 - 72 * q^39 - 14 * q^41 - 16 * q^49 + 22 * q^51 - 10 * q^61 + 28 * q^69 + 16 * q^71 - 2 * q^79 + 4 * q^81 + 16 * q^89 + 6 * q^91 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.120414	−	0.0695210i	0.0695210	−	0.0401380i	−0.464837	−	0.885397i	$-0.653887\pi$
$3$	0.120414	−	0.0695210i	0.0695210	−	0.0401380i	0.534358	+	0.845259i	$0.320554\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.40785i			1.28805i	0.765005	+	0.644024i	$0.222736\pi$
$7$			3.40785i			1.28805i	−0.765005	+	0.644024i	$0.777264\pi$
$8$		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
$13$	−2.03925	−	1.17736i	−0.565586	−	0.326541i	0.189799	−	0.981823i	$-0.439216\pi$
$13$	−2.03925	−	1.17736i	−0.565586	−	0.326541i	−0.755384	+	0.655282i	$0.772550\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.81385	−	3.35663i	1.41007	−	0.814102i	0.414671	−	0.909971i	$-0.363897\pi$
$17$	5.81385	−	3.35663i	1.41007	−	0.814102i	0.995394	+	0.0958696i	$0.0305632\pi$
$18$		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
$23$	−0.803267	−	0.463767i	−0.167493	−	0.0967020i	0.413910	−	0.910318i	$-0.364163\pi$
$23$	−0.803267	−	0.463767i	−0.167493	−	0.0967020i	−0.581403	+	0.813616i	$0.697496\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			0.831564i			0.160035i
$28$		0			0
$29$	−0.677360	+	1.17322i	−0.125783	+	0.217862i	−0.922039	−	0.387098i	$-0.873478\pi$
$29$	−0.677360	+	1.17322i	−0.125783	+	0.217862i	0.796256	+	0.604960i	$0.206811\pi$
$30$		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
$33$	0.0223597	−	0.0129094i	0.00389232	−	0.00224723i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			1.62862i			0.267743i	0.990999	+	0.133872i	$0.0427410\pi$
$37$			1.62862i			0.267743i	−0.990999	+	0.133872i	$0.957259\pi$
$38$		0			0
$39$	−0.327405			−0.0524268
$40$		0			0
$41$	4.29573	+	7.44043i	0.670881	+	1.16200i	0.977655	+	0.210217i	$0.0674171\pi$
$41$	4.29573	+	7.44043i	0.670881	+	1.16200i	−0.306774	+	0.951782i	$0.599250\pi$
$42$		0			0
$43$	−6.58312	+	3.80076i	−1.00392	+	0.579611i	−0.909405	−	0.415913i	$-0.863462\pi$
$43$	−6.58312	+	3.80076i	−1.00392	+	0.579611i	−0.0945112	+	0.995524i	$0.530129\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.09515	−	4.09639i	−1.03493	−	0.597519i	−0.116540	−	0.993186i	$-0.537180\pi$
$47$	−7.09515	−	4.09639i	−1.03493	−	0.597519i	−0.918394	+	0.395667i	$0.870514\pi$
$48$		0			0
$49$	−4.61347			−0.659067
$50$		0			0
$51$	0.466712	−	0.808369i	0.0653528	−	0.113194i
$52$		0			0
$53$	−11.6077	−	6.70168i	−1.59443	−	0.920547i	−0.992533	−	0.121976i	$-0.961077\pi$
$53$	−11.6077	−	6.70168i	−1.59443	−	0.920547i	−0.601901	−	0.798571i	$-0.705590\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.522041	+	0.307887i	0.0691460	+	0.0407806i
$58$		0			0
$59$	−2.02981	−	3.51573i	−0.264259	−	0.457710i	0.703110	−	0.711081i	$-0.251794\pi$
$59$	−2.02981	−	3.51573i	−0.264259	−	0.457710i	−0.967369	+	0.253371i	$0.918461\pi$
$60$		0			0
$61$	−6.31247	+	10.9335i	−0.808228	+	1.39989i	0.105861	+	0.994381i	$0.466240\pi$
$61$	−6.31247	+	10.9335i	−0.808228	+	1.39989i	−0.914090	+	0.405512i	$0.867093\pi$
$62$		0			0
$63$	−8.79681	−	5.07884i	−1.10829	−	0.639874i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.81654	+	1.62613i	0.344096	+	0.198664i	0.662082	−	0.749432i	$-0.269673\pi$
$67$	2.81654	+	1.62613i	0.344096	+	0.198664i	−0.317986	+	0.948095i	$0.603007\pi$
$68$		0			0
$69$	−0.128966			−0.0155257
$70$		0			0
$71$	6.59887	+	11.4296i	0.783142	+	1.35644i	0.930103	+	0.367300i	$0.119718\pi$
$71$	6.59887	+	11.4296i	0.783142	+	1.35644i	−0.146961	+	0.989142i	$0.546949\pi$
$72$		0			0
$73$	−4.24802	+	2.45260i	−0.497193	+	0.287055i	−0.727554	−	0.686051i	$-0.759343\pi$
$73$	−4.24802	+	2.45260i	−0.497193	+	0.287055i	0.230360	+	0.973105i	$0.426009\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			0.632805i			0.0721148i
$78$		0			0
$79$	2.98245	+	5.16576i	0.335552	+	0.581194i	0.983591	−	0.180414i	$-0.0577437\pi$
$79$	2.98245	+	5.16576i	0.335552	+	0.581194i	−0.648038	+	0.761608i	$0.724410\pi$
$80$		0			0
$81$	−4.41319	−	7.64387i	−0.490354	−	0.849319i
$82$		0			0
$83$			1.30480i			0.143221i	0.997433	+	0.0716105i	$0.0228138\pi$
$83$			1.30480i			0.143221i	−0.997433	+	0.0716105i	$0.977186\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			0.188363i			0.0201946i
$88$		0			0
$89$	−1.95584	+	3.38761i	−0.207319	+	0.359086i	−0.950869	−	0.309594i	$-0.899807\pi$
$89$	−1.95584	+	3.38761i	−0.207319	+	0.359086i	0.743550	+	0.668680i	$0.233140\pi$
$90$		0			0
$91$	4.01227	−	6.94946i	0.420600	−	0.728501i
$92$		0			0
$93$	−1.13931	+	0.657779i	−0.118141	+	0.0682085i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.5624	−	7.25291i	1.27552	−	0.736421i	0.299498	−	0.954097i	$-0.403181\pi$
$97$	12.5624	−	7.25291i	1.27552	−	0.736421i	0.976021	+	0.217676i	$0.0698475\pi$
$98$		0			0
$99$	−0.276740	+	0.479328i	−0.0278134	+	0.0481743i
$100$		0			0
$101$	−0.348049	+	0.602838i	−0.0346321	+	0.0599846i	−0.882822	−	0.469708i	$-0.844359\pi$
$101$	−0.348049	+	0.602838i	−0.0346321	+	0.0599846i	0.848190	+	0.529692i	$0.177693\pi$
$102$		0			0
$103$		−	10.5016i		−	1.03476i	−0.855757	−	0.517378i	$-0.826908\pi$
$103$		−	10.5016i		−	1.03476i	0.855757	−	0.517378i	$-0.173092\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			15.1627i			1.46583i	0.680320	+	0.732915i	$0.261841\pi$
$107$			15.1627i			1.46583i	−0.680320	+	0.732915i	$0.738159\pi$
$108$		0			0
$109$	0.0595573	+	0.103156i	0.00570456	+	0.00988058i	0.868864	−	0.495052i	$-0.164851\pi$
$109$	0.0595573	+	0.103156i	0.00570456	+	0.00988058i	−0.863159	+	0.504932i	$0.831518\pi$
$110$		0			0
$111$	0.113223	+	0.196109i	0.0107467	+	0.0186138i
$112$		0			0
$113$		−	10.1268i		−	0.952648i	−0.879270	−	0.476324i	$-0.841969\pi$
$113$		−	10.1268i		−	0.952648i	0.879270	−	0.476324i	$-0.158031\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.07832	−	3.50932i	0.561941	−	0.324437i
$118$		0			0
$119$	11.4389	+	19.8127i	1.04860	+	1.81623i
$120$		0			0
$121$	−10.9655			−0.996865
$122$		0			0
$123$	1.03453	+	0.597288i	0.0932806	+	0.0538556i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.20894	+	1.85268i	0.284748	+	0.164399i	0.635571	−	0.772043i	$-0.280765\pi$
$127$	3.20894	+	1.85268i	0.284748	+	0.164399i	−0.350823	+	0.936442i	$0.614098\pi$
$128$		0			0
$129$	−0.528466	+	0.915330i	−0.0465288	+	0.0805903i
$130$		0			0
$131$	10.7555	+	18.6291i	0.939713	+	1.62763i	0.766006	+	0.642833i	$0.222241\pi$
$131$	10.7555	+	18.6291i	0.939713	+	1.62763i	0.173707	+	0.984797i	$0.444425\pi$
$132$		0			0
$133$	−12.9327	+	7.30770i	−1.12140	+	0.633658i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.9313	+	6.88852i	1.01936	+	0.588526i	0.913918	−	0.405900i	$-0.133042\pi$
$137$	11.9313	+	6.88852i	1.01936	+	0.588526i	0.105439	+	0.994426i	$0.466375\pi$
$138$		0			0
$139$	−9.25188	+	16.0247i	−0.784734	+	1.35920i	0.144424	+	0.989516i	$0.453867\pi$
$139$	−9.25188	+	16.0247i	−0.784734	+	1.35920i	−0.929158	+	0.369683i	$0.879466\pi$
$140$		0			0
$141$	−1.13914			−0.0959329
$142$		0			0
$143$	−0.378668	−	0.218624i	−0.0316658	−	0.0182823i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.555526	+	0.320733i	−0.0458190	+	0.0264536i
$148$		0			0
$149$	−3.40386	−	5.89565i	−0.278855	−	0.482991i	0.692246	−	0.721662i	$-0.256621\pi$
$149$	−3.40386	−	5.89565i	−0.278855	−	0.482991i	−0.971100	+	0.238671i	$0.923288\pi$
$150$		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
$153$			20.0100i			1.61771i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.2220	+	7.05638i	−0.975422	+	0.563160i	−0.900885	−	0.434058i	$-0.857081\pi$
$157$	−12.2220	+	7.05638i	−0.975422	+	0.563160i	−0.0745372	+	0.997218i	$0.523748\pi$
$158$		0			0
$159$	−1.86363			−0.147796
$160$		0			0
$161$	1.58045	−	2.73742i	0.124557	−	0.215739i
$162$		0			0
$163$		−	5.63660i		−	0.441493i	−0.975331	−	0.220746i	$-0.929151\pi$
$163$		−	5.63660i		−	0.441493i	0.975331	−	0.220746i	$-0.0708493\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.47579	−	3.73880i	−0.501112	−	0.289317i	0.228061	−	0.973647i	$-0.426762\pi$
$167$	−6.47579	−	3.73880i	−0.501112	−	0.289317i	−0.729173	+	0.684330i	$0.760095\pi$
$168$		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
$173$	20.2457	−	11.6888i	1.53925	−	0.888686i	0.540366	−	0.841430i	$-0.318286\pi$
$173$	20.2457	−	11.6888i	1.53925	−	0.888686i	0.998883	−	0.0472554i	$-0.0150475\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.488835	−	0.282229i	−0.0367431	−	0.0212136i
$178$		0			0
$179$	−10.0035			−0.747698			−0.373849	−	0.927490i	$-0.621962\pi$
$179$	−10.0035			−0.747698			−0.373849	+	0.927490i	$0.621962\pi$
$180$		0			0
$181$	7.13969	−	12.3663i	0.530689	−	0.919180i	−0.468670	−	0.883373i	$-0.655267\pi$
$181$	7.13969	−	12.3663i	0.530689	−	0.919180i	0.999359	−	0.0358064i	$-0.0114000\pi$
$182$		0			0
$183$			1.75540i			0.129763i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.07957	−	0.623292i	0.0789462	−	0.0455796i
$188$		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
$193$	−13.0703	+	7.54615i	−0.940822	+	0.543184i	−0.890218	−	0.455535i	$-0.849448\pi$
$193$	−13.0703	+	7.54615i	−0.940822	+	0.543184i	−0.0506044	+	0.998719i	$0.516115\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	10.4610i		−	0.745315i	−0.927969	−	0.372657i	$-0.878447\pi$
$197$		−	10.4610i		−	0.745315i	0.927969	−	0.372657i	$-0.121553\pi$
$198$		0			0
$199$	8.36446	−	14.4877i	0.592941	−	1.02700i	−0.400893	−	0.916125i	$-0.631300\pi$
$199$	8.36446	−	14.4877i	0.592941	−	1.02700i	0.993834	−	0.110879i	$-0.0353666\pi$
$200$		0			0
$201$	0.452202			0.0318958
$202$		0			0
$203$	−3.99817	−	2.30835i	−0.280617	−	0.162014i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.39427	−	1.38233i	0.166413	−	0.0960789i
$208$		0			0
$209$	0.398188	+	0.704685i	0.0275432	+	0.0487441i
$210$		0			0
$211$	9.00494	+	15.5970i	0.619926	+	1.07374i	0.989499	+	0.144541i	$0.0461706\pi$
$211$	9.00494	+	15.5970i	0.619926	+	1.07374i	−0.369573	+	0.929202i	$0.620496\pi$
$212$		0			0
$213$	1.58919	+	0.917521i	0.108890	+	0.0628675i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	32.2437i		−	2.18884i
$218$		0			0
$219$	−0.341014	+	0.590654i	−0.0230436	+	0.0399127i
$220$		0			0
$221$	−15.8078			−1.06335
$222$		0			0
$223$	6.86434	−	3.96313i	0.459670	−	0.265391i	−0.252235	−	0.967666i	$-0.581166\pi$
$223$	6.86434	−	3.96313i	0.459670	−	0.265391i	0.711906	+	0.702275i	$0.247832\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			14.4260i			0.957487i	0.877955	+	0.478743i	$0.158908\pi$
$227$			14.4260i			0.957487i	−0.877955	+	0.478743i	$0.841092\pi$
$228$		0			0
$229$	−1.27578			−0.0843061			−0.0421530	−	0.999111i	$-0.513422\pi$
$229$	−1.27578			−0.0843061			−0.0421530	+	0.999111i	$0.513422\pi$
$230$		0			0
$231$	0.0439932	+	0.0761985i	0.00289454	+	0.00501349i
$232$		0			0
$233$	−2.76441	+	1.59603i	−0.181102	+	0.104560i	−0.587811	−	0.808999i	$-0.700010\pi$
$233$	−2.76441	+	1.59603i	−0.181102	+	0.104560i	0.406708	+	0.913558i	$0.366677\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.718258	+	0.414687i	0.0466559	+	0.0269368i
$238$		0			0
$239$	11.9921			0.775705			0.387853	−	0.921721i	$-0.373217\pi$
$239$	11.9921			0.775705			0.387853	+	0.921721i	$0.373217\pi$
$240$		0			0
$241$	12.9988	−	22.5145i	0.837323	−	1.45029i	−0.0548017	−	0.998497i	$-0.517453\pi$
$241$	12.9988	−	22.5145i	0.837323	−	1.45029i	0.892125	−	0.451789i	$-0.149214\pi$
$242$		0			0
$243$	−3.22329	−	1.86097i	−0.206774	−	0.119381i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.0951268	−	10.2635i	0.00605277	−	0.653054i
$248$		0			0
$249$	0.0907114	+	0.157117i	0.00574860	+	0.00995687i
$250$		0			0
$251$	−5.22437	+	9.04887i	−0.329759	+	0.571160i	−0.982464	−	0.186453i	$-0.940301\pi$
$251$	−5.22437	+	9.04887i	−0.329759	+	0.571160i	0.652705	+	0.757612i	$0.273634\pi$
$252$		0			0
$253$	−0.149159	−	0.0861168i	−0.00937753	−	0.00541412i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.8797	−	6.28137i	−0.678655	−	0.391821i	0.120693	−	0.992690i	$-0.461488\pi$
$257$	−10.8797	−	6.28137i	−0.678655	−	0.391821i	−0.799348	+	0.600868i	$0.794822\pi$
$258$		0			0
$259$	−5.55010			−0.344866
$260$		0			0
$261$	−2.01899	−	3.49699i	−0.124972	−	0.216458i
$262$		0			0
$263$	2.55999	−	1.47801i	0.157856	−	0.0911381i	−0.418991	−	0.907990i	$-0.637616\pi$
$263$	2.55999	−	1.47801i	0.157856	−	0.0911381i	0.576847	+	0.816852i	$0.304283\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			0.543888i			0.0332854i
$268$		0			0
$269$	1.93417	+	3.35007i	0.117928	+	0.204258i	0.918946	−	0.394382i	$-0.129041\pi$
$269$	1.93417	+	3.35007i	0.117928	+	0.204258i	−0.801018	+	0.598640i	$0.795708\pi$
$270$		0			0
$271$	3.47998	+	6.02749i	0.211393	+	0.366144i	0.952151	−	0.305628i	$-0.0988665\pi$
$271$	3.47998	+	6.02749i	0.211393	+	0.366144i	−0.740757	+	0.671773i	$0.765533\pi$
$272$		0			0
$273$		−	1.11575i		−	0.0675282i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			18.1698i			1.09172i	0.837878	+	0.545858i	$0.183796\pi$
$277$			18.1698i			1.09172i	−0.837878	+	0.545858i	$0.816204\pi$
$278$		0			0
$279$	14.1009	−	24.4235i	0.844200	−	1.46220i
$280$		0			0
$281$	1.08306	−	1.87591i	0.0646099	−	0.111908i	−0.831911	−	0.554909i	$-0.812753\pi$
$281$	1.08306	−	1.87591i	0.0646099	−	0.111908i	0.896521	+	0.443001i	$0.146086\pi$
$282$		0			0
$283$	15.8266	−	9.13750i	0.940794	−	0.543168i	0.0505849	−	0.998720i	$-0.483891\pi$
$283$	15.8266	−	9.13750i	0.940794	−	0.543168i	0.890209	+	0.455552i	$0.150558\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−25.3559	+	14.6392i	−1.49671	+	0.864127i
$288$		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
$293$			4.01486i			0.234550i	0.993099	+	0.117275i	$0.0374160\pi$
$293$			4.01486i			0.234550i	−0.993099	+	0.117275i	$0.962584\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			0.154413i			0.00895996i
$298$		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
$303$			0.0967868i			0.00556026i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.9746	+	6.91354i	−0.683427	+	0.394577i	−0.801145	−	0.598470i	$-0.795775\pi$
$307$	−11.9746	+	6.91354i	−0.683427	+	0.394577i	0.117718	+	0.993047i	$0.462442\pi$
$308$		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
$313$	18.1823	+	10.4976i	1.02772	+	0.593357i	0.916332	−	0.400419i	$-0.131136\pi$
$313$	18.1823	+	10.4976i	1.02772	+	0.593357i	0.111393	+	0.993776i	$0.464469\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.35641	+	5.40192i	0.525508	+	0.303402i	0.739185	−	0.673502i	$-0.235211\pi$
$317$	9.35641	+	5.40192i	0.525508	+	0.303402i	−0.213677	+	0.976904i	$0.568544\pi$
$318$		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
$323$	25.2053	+	14.8654i	1.40246	+	0.827135i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.0143431	+	0.00828097i	0.000793173	+	0.000457939i
$328$		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
$333$	−4.20401	−	2.42719i	−0.230378	−	0.133009i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.70981	−	3.29656i	0.311033	−	0.179575i	−0.336355	−	0.941735i	$-0.609194\pi$
$337$	5.70981	−	3.29656i	0.311033	−	0.179575i	0.647389	+	0.762160i	$0.275861\pi$
$338$		0			0
$339$	−0.704025	−	1.21941i	−0.0382374	−	0.0662291i
$340$		0			0
$341$	−1.75692			−0.0951426
$342$		0			0
$343$			8.13294i			0.439138i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−21.5441	+	12.4385i	−1.15655	+	0.667732i	−0.950474	−	0.310805i	$-0.899402\pi$
$347$	−21.5441	+	12.4385i	−1.15655	+	0.667732i	−0.206072	+	0.978537i	$0.566068\pi$
$348$		0			0
$349$	−20.9351			−1.12063			−0.560316	−	0.828279i	$-0.689320\pi$
$349$	−20.9351			−1.12063			−0.560316	+	0.828279i	$0.689320\pi$
$350$		0			0
$351$	0.979051	−	1.69577i	0.0522579	−	0.0905133i
$352$		0			0
$353$			18.6926i			0.994907i	0.867491	+	0.497454i	$0.165732\pi$
$353$			18.6926i			0.994907i	−0.867491	+	0.497454i	$0.834268\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.75481	+	1.59049i	0.145800	+	0.0841775i
$358$		0			0
$359$	6.92376	+	11.9923i	0.365422	+	0.632929i	0.988844	−	0.148956i	$-0.0475914\pi$
$359$	6.92376	+	11.9923i	0.365422	+	0.632929i	−0.623422	+	0.781886i	$0.714258\pi$
$360$		0			0
$361$	−9.80336	+	16.2756i	−0.515966	+	0.856609i
$362$		0			0
$363$	−1.32040	+	0.762334i	−0.0693031	+	0.0400122i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	15.8493	+	9.15058i	0.827325	+	0.477656i	0.852936	−	0.522016i	$-0.174820\pi$
$367$	15.8493	+	9.15058i	0.827325	+	0.477656i	−0.0256108	+	0.999672i	$0.508153\pi$
$368$		0			0
$369$	−25.6083			−1.33311
$370$		0			0
$371$	22.8384	−	39.5572i	1.18571	−	2.05371i
$372$		0			0
$373$		−	12.9735i		−	0.671743i	−0.941908	−	0.335872i	$-0.890969\pi$
$373$		−	12.9735i		−	0.671743i	0.941908	−	0.335872i	$-0.109031\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.76261	−	1.59499i	0.142282	−	0.0821464i
$378$		0			0
$379$	17.4091			0.894243			0.447122	−	0.894473i	$-0.352449\pi$
$379$	17.4091			0.894243			0.447122	+	0.894473i	$0.352449\pi$
$380$		0			0
$381$	0.515202			0.0263946
$382$		0			0
$383$	11.5395	−	6.66235i	0.589642	−	0.340430i	−0.175314	−	0.984513i	$-0.556094\pi$
$383$	11.5395	−	6.66235i	0.589642	−	0.340430i	0.764956	+	0.644082i	$0.222761\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	22.6576i		−	1.15175i
$388$		0			0
$389$	−13.9471	+	24.1572i	−0.707148	+	1.22482i	0.258763	+	0.965941i	$0.416685\pi$
$389$	−13.9471	+	24.1572i	−0.707148	+	1.22482i	−0.965911	+	0.258875i	$0.916648\pi$
$390$		0			0
$391$	−6.22677			−0.314901
$392$		0			0
$393$	2.59023	+	1.49547i	0.130660	+	0.0754364i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	25.5397	−	14.7453i	1.28180	−	0.740048i	0.304623	−	0.952473i	$-0.401469\pi$
$397$	25.5397	−	14.7453i	1.28180	−	0.740048i	0.977177	+	0.212425i	$0.0681362\pi$
$398$		0			0
$399$	−1.04923	+	1.77904i	−0.0525273	+	0.0890634i
$400$		0			0
$401$	−14.8616	−	25.7411i	−0.742154	−	1.28545i	−0.951513	−	0.307609i	$-0.900471\pi$
$401$	−14.8616	−	25.7411i	−0.742154	−	1.28545i	0.209359	−	0.977839i	$-0.432862\pi$
$402$		0			0
$403$	19.2945	+	11.1397i	0.961128	+	0.554908i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			0.302418i			0.0149903i
$408$		0			0
$409$	3.66752	−	6.35233i	0.181347	−	0.314102i	−0.760992	−	0.648761i	$-0.775288\pi$
$409$	3.66752	−	6.35233i	0.181347	−	0.314102i	0.942340	+	0.334658i	$0.108621\pi$
$410$		0			0
$411$	1.91559			0.0944890
$412$		0			0
$413$	11.9811	−	6.91730i	0.589552	−	0.340378i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			2.57280i			0.125991i
$418$		0			0
$419$	13.9330			0.680671			0.340336	−	0.940304i	$-0.389459\pi$
$419$	13.9330			0.680671			0.340336	+	0.940304i	$0.389459\pi$
$420$		0			0
$421$	−11.7615	−	20.3715i	−0.573219	−	0.992845i	−0.996233	−	0.0867212i	$-0.972361\pi$
$421$	−11.7615	−	20.3715i	−0.573219	−	0.992845i	0.423014	−	0.906123i	$-0.360972\pi$
$422$		0			0
$423$	21.1483	−	12.2100i	1.02826	−	0.593669i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−37.2598	−	21.5120i	−1.80313	−	1.04104i
$428$		0			0
$429$	−0.0607959			−0.00293525
$430$		0			0
$431$	6.02358	−	10.4331i	0.290146	−	0.502547i	−0.683698	−	0.729765i	$-0.739630\pi$
$431$	6.02358	−	10.4331i	0.290146	−	0.502547i	0.973844	+	0.227218i	$0.0729629\pi$
$432$		0			0
$433$	26.8186	+	15.4837i	1.28882	+	0.744101i	0.978444	−	0.206512i	$-0.0662112\pi$
$433$	26.8186	+	15.4837i	1.28882	+	0.744101i	0.310377	+	0.950613i	$0.399545\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.0374708	−	4.04285i	0.00179247	−	0.193396i
$438$		0			0
$439$	−14.4121	−	24.9625i	−0.687852	−	1.19139i	−0.972531	−	0.232771i	$-0.925221\pi$
$439$	−14.4121	−	24.9625i	−0.687852	−	1.19139i	0.284680	−	0.958623i	$-0.408113\pi$
$440$		0			0
$441$	6.87561	−	11.9089i	0.327410	−	0.567091i
$442$		0			0
$443$	18.3599	+	10.6001i	0.872303	+	0.503624i	0.868113	−	0.496367i	$-0.165333\pi$
$443$	18.3599	+	10.6001i	0.872303	+	0.503624i	0.00419027	+	0.999991i	$0.498666\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.819743	−	0.473279i	−0.0387725	−	0.0223853i
$448$		0			0
$449$	27.5158			1.29855			0.649275	−	0.760553i	$-0.275072\pi$
$449$	27.5158			1.29855			0.649275	+	0.760553i	$0.275072\pi$
$450$		0			0
$451$	0.797675	+	1.38161i	0.0375610	+	0.0650576i
$452$		0			0
$453$	0.442554	−	0.255508i	0.0207930	−	0.0120048i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	17.5615i		−	0.821492i	−0.911750	−	0.410746i	$-0.865268\pi$
$457$		−	17.5615i		−	0.821492i	0.911750	−	0.410746i	$-0.134732\pi$
$458$		0			0
$459$	2.79125	+	4.83459i	0.130284	+	0.225659i
$460$		0			0
$461$	17.9075	+	31.0167i	0.834036	+	1.44459i	0.894813	+	0.446441i	$0.147309\pi$
$461$	17.9075	+	31.0167i	0.834036	+	1.44459i	−0.0607773	+	0.998151i	$0.519358\pi$
$462$		0			0
$463$			2.10186i			0.0976817i	0.998807	+	0.0488409i	$0.0155527\pi$
$463$			2.10186i			0.0976817i	−0.998807	+	0.0488409i	$0.984447\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			17.3019i			0.800637i	0.916376	+	0.400319i	$0.131101\pi$
$467$			17.3019i			0.800637i	−0.916376	+	0.400319i	$0.868899\pi$
$468$		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
$473$	−1.22242	+	0.705764i	−0.0562069	+	0.0324511i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	34.5985	−	19.9755i	1.58416	−	0.914614i
$478$		0			0
$479$	−14.5267	+	25.1610i	−0.663743	+	1.14964i	0.315882	+	0.948799i	$0.397700\pi$
$479$	−14.5267	+	25.1610i	−0.663743	+	1.14964i	−0.979625	+	0.200837i	$0.935634\pi$
$480$		0			0
$481$	1.91747	−	3.32116i	0.0874292	−	0.151432i
$482$		0			0
$483$		−	0.439498i		−	0.0199978i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	13.0964i		−	0.593456i	−0.954962	−	0.296728i	$-0.904105\pi$
$487$		−	13.0964i		−	0.593456i	0.954962	−	0.296728i	$-0.0958954\pi$
$488$		0			0
$489$	−0.391862	−	0.678726i	−0.0177206	−	0.0306930i
$490$		0			0
$491$	−3.11779	−	5.40016i	−0.140704	−	0.243706i	0.787058	−	0.616879i	$-0.211603\pi$
$491$	−3.11779	−	5.40016i	−0.140704	−	0.243706i	−0.927762	+	0.373173i	$0.878270\pi$
$492$		0			0
$493$			9.09458i			0.409599i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−38.9504	+	22.4880i	−1.74716	+	1.00872i
$498$		0			0
$499$	−5.67610	−	9.83130i	−0.254097	−	0.440109i	0.710553	−	0.703644i	$-0.248445\pi$
$499$	−5.67610	−	9.83130i	−0.254097	−	0.440109i	−0.964650	+	0.263535i	$0.915112\pi$
$500$		0			0
$501$	−1.03970			−0.0464504
$502$		0			0
$503$	15.5843	+	8.99758i	0.694868	+	0.401182i	0.805433	−	0.592687i	$-0.201933\pi$
$503$	15.5843	+	8.99758i	0.694868	+	0.401182i	−0.110565	+	0.993869i	$0.535266\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.897721	−	0.518300i	−0.0398692	−	0.0230185i
$508$		0			0
$509$	12.8639	−	22.2810i	0.570184	−	0.987587i	−0.426363	−	0.904552i	$-0.640205\pi$
$509$	12.8639	−	22.2810i	0.570184	−	0.987587i	0.996547	−	0.0830350i	$-0.0264613\pi$
$510$		0			0
$511$	−8.35809	−	14.4766i	−0.369740	−	0.640409i
$512$		0			0
$513$	−3.15575	+	1.78318i	−0.139330	+	0.0787294i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.31750	−	0.760658i	−0.0579435	−	0.0334537i
$518$		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
$523$	−19.1607	−	11.0625i	−0.837841	−	0.483728i	0.0186889	−	0.999825i	$-0.494051\pi$
$523$	−19.1607	−	11.0625i	−0.837841	−	0.483728i	−0.856530	+	0.516098i	$0.827384\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−55.0082	+	31.7590i	−2.39620	+	1.38344i
$528$		0			0
$529$	−11.0698	−	19.1735i	−0.481297	−	0.833632i
$530$		0			0
$531$	12.1004			0.525112
$532$		0			0
$533$		−	20.2305i		−	0.876280i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.20456	+	0.695455i	−0.0519808	+	0.0300111i
$538$		0			0
$539$	−0.856676			−0.0368996
$540$		0			0
$541$	−14.7284	+	25.5104i	−0.633224	+	1.09678i	0.353664	+	0.935372i	$0.384936\pi$
$541$	−14.7284	+	25.5104i	−0.633224	+	1.09678i	−0.986888	+	0.161404i	$0.948398\pi$
$542$		0			0
$543$		−	1.98543i		−	0.0852031i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	35.0604	+	20.2421i	1.49908	+	0.865491i	0.999999	−	0.00106707i	$-0.000339660\pi$
$547$	35.0604	+	20.2421i	1.49908	+	0.865491i	0.499076	+	0.866558i	$0.333673\pi$
$548$		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
$553$	−17.6042	+	10.1638i	−0.748605	+	0.432208i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.4998	−	10.1035i	−0.741490	−	0.428099i	0.0811209	−	0.996704i	$-0.474150\pi$
$557$	−17.4998	−	10.1035i	−0.741490	−	0.428099i	−0.822611	+	0.568605i	$0.807483\pi$
$558$		0			0
$559$	17.8995			0.757067
$560$		0			0
$561$	0.0866638	−	0.150106i	0.00365895	−	0.00633749i
$562$		0			0
$563$			25.1900i			1.06163i	0.847487	+	0.530816i	$0.178115\pi$
$563$			25.1900i			1.06163i	−0.847487	+	0.530816i	$0.821885\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	26.0492	−	15.0395i	1.09396	−	0.631600i
$568$		0			0
$569$	32.6378			1.36825			0.684124	−	0.729366i	$-0.260185\pi$
$569$	32.6378			1.36825			0.684124	+	0.729366i	$0.260185\pi$
$570$		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
$573$	−0.646595	+	0.373312i	−0.0270119	+	0.0155953i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	18.3407i		−	0.763533i	−0.924259	−	0.381766i	$-0.875316\pi$
$577$		−	18.3407i		−	0.763533i	0.924259	−	0.381766i	$-0.124684\pi$
$578$		0			0
$579$	−1.04923	+	1.81732i	−0.0436046	+	0.0755254i
$580$		0			0
$581$	−4.44658			−0.184475
$582$		0			0
$583$	−2.15543	−	1.24444i	−0.0892686	−	0.0515392i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.1337	+	8.16010i	−0.583361	+	0.336804i	−0.762468	−	0.647026i	$-0.776012\pi$
$587$	−14.1337	+	8.16010i	−0.583361	+	0.336804i	0.179107	+	0.983830i	$0.442679\pi$
$588$		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
$593$	−7.40534	−	4.27547i	−0.304101	−	0.175573i	0.340183	−	0.940359i	$-0.389511\pi$
$593$	−7.40534	−	4.27547i	−0.304101	−	0.175573i	−0.644284	+	0.764787i	$0.722844\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	2.32602i		−	0.0951978i
$598$		0			0
$599$	7.09169	−	12.2832i	0.289758	−	0.501876i	−0.683994	−	0.729488i	$-0.739758\pi$
$599$	7.09169	−	12.2832i	0.289758	−	0.501876i	0.973752	+	0.227612i	$0.0730917\pi$
$600$		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
$603$	−8.39518	+	4.84696i	−0.341878	+	0.197383i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			28.4812i			1.15602i	0.816031	+	0.578009i	$0.196170\pi$
$607$			28.4812i			1.15602i	−0.816031	+	0.578009i	$0.803830\pi$
$608$		0			0
$609$	−0.641914			−0.0260117
$610$		0			0
$611$	9.64584	+	16.7071i	0.390229	+	0.675896i
$612$		0			0
$613$	22.4720	−	12.9742i	0.907638	−	0.524025i	0.0279673	−	0.999609i	$-0.491097\pi$
$613$	22.4720	−	12.9742i	0.907638	−	0.524025i	0.879670	+	0.475584i	$0.157763\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.6322	−	6.71585i	−0.468295	−	0.270370i	0.247231	−	0.968957i	$-0.420479\pi$
$617$	−11.6322	−	6.71585i	−0.468295	−	0.270370i	−0.715526	+	0.698587i	$0.753813\pi$
$618$		0			0
$619$	23.9017			0.960690			0.480345	−	0.877080i	$-0.340511\pi$
$619$	23.9017			0.960690			0.480345	+	0.877080i	$0.340511\pi$
$620$		0			0
$621$	0.385652	−	0.667968i	0.0154757	−	0.0268047i
$622$		0			0
$623$	−11.5445	−	6.66521i	−0.462520	−	0.267036i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.0969378	+	0.0571715i	0.00387132	+	0.00228321i
$628$		0			0
$629$	5.46667	+	9.46855i	0.217970	+	0.377536i
$630$		0			0
$631$	12.0962	−	20.9512i	0.481541	−	0.834054i	−0.518234	−	0.855239i	$-0.673411\pi$
$631$	12.0962	−	20.9512i	0.481541	−	0.834054i	0.999776	+	0.0211849i	$0.00674387\pi$
$632$		0			0
$633$	2.16864	+	1.25207i	0.0861957	+	0.0497651i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.40801	+	5.43172i	0.372759	+	0.215213i
$638$		0			0
$639$	−39.3381			−1.55619
$640$		0			0
$641$	11.7338	+	20.3235i	0.463456	+	0.802729i	0.999130	−	0.0416956i	$-0.0132760\pi$
$641$	11.7338	+	20.3235i	0.463456	+	0.802729i	−0.535675	+	0.844424i	$0.679943\pi$
$642$		0			0
$643$	−0.861287	+	0.497264i	−0.0339658	+	0.0196102i	−0.516887	−	0.856054i	$-0.672909\pi$
$643$	−0.861287	+	0.497264i	−0.0339658	+	0.0196102i	0.482921	+	0.875664i	$0.339576\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	2.24679i		−	0.0883306i	−0.999024	−	0.0441653i	$-0.985937\pi$
$647$		−	2.24679i		−	0.0883306i	0.999024	−	0.0441653i	$-0.0140628\pi$
$648$		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
$653$		−	16.9500i		−	0.663307i	−0.943401	−	0.331653i	$-0.892394\pi$
$653$		−	16.9500i		−	0.663307i	0.943401	−	0.331653i	$-0.107606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	14.6207i		−	0.570410i
$658$		0			0
$659$	16.1670	−	28.0020i	0.629775	−	1.09080i	−0.357821	−	0.933790i	$-0.616480\pi$
$659$	16.1670	−	28.0020i	0.629775	−	1.09080i	0.987597	−	0.157013i	$-0.0501864\pi$
$660$		0			0
$661$	9.67075	−	16.7502i	0.376149	−	0.651509i	−0.614350	−	0.789034i	$-0.710582\pi$
$661$	9.67075	−	16.7502i	0.376149	−	0.651509i	0.990498	+	0.137525i	$0.0439149\pi$
$662$		0			0
$663$	−1.90348	+	1.09898i	−0.0739252	+	0.0426807i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.08820	−	0.628274i	0.0421354	−	0.0243269i
$668$		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
$673$			22.4887i			0.866875i	0.901184	+	0.433438i	$0.142700\pi$
$673$			22.4887i			0.866875i	−0.901184	+	0.433438i	$0.857300\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	18.8477i		−	0.724377i	−0.932105	−	0.362188i	$-0.882030\pi$
$677$		−	18.8477i		−	0.724377i	0.932105	−	0.362188i	$-0.117970\pi$
$678$		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
$683$		−	44.8197i		−	1.71498i	−0.514502	−	0.857489i	$-0.672023\pi$
$683$		−	44.8197i		−	1.71498i	0.514502	−	0.857489i	$-0.327977\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.153622	+	0.0886937i	−0.00586105	+	0.00338388i
$688$		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
$693$	−1.63348	−	0.943090i	−0.0620508	−	0.0358250i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	49.9495	+	28.8383i	1.89197	+	1.09233i
$698$		0			0
$699$	−0.221916	+	0.384369i	−0.00839362	+	0.0145382i
$700$		0			0
$701$	−17.2140	−	29.8155i	−0.650163	−	1.12611i	−0.983083	−	0.183160i	$-0.941367\pi$
$701$	−17.2140	−	29.8155i	−0.650163	−	1.12611i	0.332920	−	0.942955i	$-0.391966\pi$
$702$		0			0
$703$	−6.18054	+	3.49236i	−0.233103	+	0.131717i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.05438	−	1.18610i	−0.0772630	−	0.0446078i
$708$		0			0
$709$	−11.3751	+	19.7023i	−0.427202	+	0.739936i	−0.996623	−	0.0821102i	$-0.973834\pi$
$709$	−11.3751	+	19.7023i	−0.427202	+	0.739936i	0.569421	+	0.822046i	$0.307167\pi$
$710$		0			0
$711$	−17.7794			−0.666780
$712$		0			0
$713$	7.60018	+	4.38797i	0.284629	+	0.164331i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.44402	−	0.833704i	0.0539278	−	0.0311352i
$718$		0			0
$719$	15.0042	+	25.9880i	0.559561	+	0.969188i	0.997533	+	0.0701994i	$0.0223636\pi$
$719$	15.0042	+	25.9880i	0.559561	+	0.969188i	−0.437972	+	0.898989i	$0.644303\pi$
$720$		0			0
$721$	35.7880			1.33282
$722$		0			0
$723$		−	3.61475i		−	0.134434i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−20.8719	+	12.0504i	−0.774096	+	0.446924i	−0.834334	−	0.551260i	$-0.814147\pi$
$727$	−20.8719	+	12.0504i	−0.774096	+	0.446924i	0.0602381	+	0.998184i	$0.480814\pi$
$728$		0			0
$729$	25.9616			0.961542
$730$		0			0
$731$	−25.5155	+	44.1941i	−0.943724	+	1.63458i
$732$		0			0
$733$		−	12.5801i		−	0.464657i	−0.972637	−	0.232329i	$-0.925365\pi$
$733$		−	12.5801i		−	0.464657i	0.972637	−	0.232329i	$-0.0746345\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.523004	+	0.301957i	0.0192651	+	0.0111227i
$738$		0			0
$739$	−3.54647	−	6.14266i	−0.130459	−	0.225961i	0.793395	−	0.608708i	$-0.208312\pi$
$739$	−3.54647	−	6.14266i	−0.130459	−	0.225961i	−0.923854	+	0.382746i	$0.874978\pi$
$740$		0			0
$741$	−0.702078	−	1.24249i	−0.0257915	−	0.0456439i
$742$		0			0
$743$	−29.7060	+	17.1507i	−1.08981	+	0.629200i	−0.933525	−	0.358513i	$-0.883284\pi$
$743$	−29.7060	+	17.1507i	−1.08981	+	0.629200i	−0.156281	+	0.987713i	$0.549951\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.36814	−	1.94459i	−0.123234	−	0.0711490i
$748$		0			0
$749$	−51.6722			−1.88806
$750$		0			0
$751$	−19.0760	+	33.0406i	−0.696094	+	1.20567i	0.273717	+	0.961810i	$0.411747\pi$
$751$	−19.0760	+	33.0406i	−0.696094	+	1.20567i	−0.969811	+	0.243860i	$0.921586\pi$
$752$		0			0
$753$			1.45281i			0.0529435i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	24.6200	−	14.2143i	0.894828	−	0.516629i	0.0193092	−	0.999814i	$-0.493853\pi$
$757$	24.6200	−	14.2143i	0.894828	−	0.516629i	0.875519	+	0.483185i	$0.160520\pi$
$758$		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
$763$	−0.351542	+	0.202963i	−0.0127267	+	0.00734774i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			9.55927i			0.345165i
$768$		0			0
$769$	−17.8289	+	30.8806i	−0.642928	+	1.11358i	0.341847	+	0.939755i	$0.388947\pi$
$769$	−17.8289	+	30.8806i	−0.642928	+	1.11358i	−0.984776	+	0.173829i	$0.944386\pi$
$770$		0			0
$771$	−1.74675			−0.0629077
$772$		0			0
$773$	−25.9912	−	15.0060i	−0.934839	−	0.539729i	−0.0465000	−	0.998918i	$-0.514807\pi$
$773$	−25.9912	−	15.0060i	−0.934839	−	0.539729i	−0.888339	+	0.459189i	$0.848140\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.668309	+	0.385849i	−0.0239755	+	0.0138422i
$778$		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
$783$	−0.975610	−	0.563269i	−0.0348654	−	0.0201296i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	40.9891i		−	1.46110i	−0.682857	−	0.730552i	$-0.739263\pi$
$787$		−	40.9891i		−	1.46110i	0.682857	−	0.730552i	$-0.260737\pi$
$788$		0			0
$789$	0.205506	−	0.355947i	0.00731620	−	0.0126720i
$790$		0			0
$791$	34.5106			1.22706
$792$		0			0
$793$	25.7454	−	14.8641i	0.914245	−	0.527839i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			46.6104i			1.65103i	0.564383	+	0.825513i	$0.309114\pi$
$797$			46.6104i			1.65103i	−0.564383	+	0.825513i	$0.690886\pi$
$798$		0			0
$799$	−55.0001			−1.94577
$800$		0			0
$801$	−5.82971	−	10.0973i	−0.205983	−	0.356772i
$802$		0			0
$803$	−0.788815	+	0.455423i	−0.0278367	+	0.0160715i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.465801	+	0.268930i	0.0163970	+	0.00946680i
$808$		0			0
$809$	−15.1137			−0.531371			−0.265686	−	0.964060i	$-0.585598\pi$
$809$	−15.1137			−0.531371			−0.265686	+	0.964060i	$0.585598\pi$
$810$		0			0
$811$	−1.57195	+	2.72270i	−0.0551986	+	0.0956068i	−0.892304	−	0.451434i	$-0.850913\pi$
$811$	−1.57195	+	2.72270i	−0.0551986	+	0.0956068i	0.837106	+	0.547041i	$0.184246\pi$
$812$		0			0
$813$	0.838075	+	0.483863i	0.0293926	+	0.0169698i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−28.5404	−	16.8324i	−0.998501	−	0.588890i
$818$		0			0
$819$	11.9592	+	20.7140i	0.417890	+	0.723807i
$820$		0			0
$821$	0.406694	−	0.704414i	0.0141937	−	0.0245842i	−0.858841	−	0.512242i	$-0.828815\pi$
$821$	0.406694	−	0.704414i	0.0141937	−	0.0245842i	0.873035	+	0.487658i	$0.162149\pi$
$822$		0			0
$823$	8.32963	+	4.80912i	0.290353	+	0.167635i	0.638101	−	0.769953i	$-0.279720\pi$
$823$	8.32963	+	4.80912i	0.290353	+	0.167635i	−0.347748	+	0.937588i	$0.613054\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	40.0720	+	23.1356i	1.39344	+	0.804503i	0.993694	−	0.112124i	$-0.0357653\pi$
$827$	40.0720	+	23.1356i	1.39344	+	0.804503i	0.399745	+	0.916626i	$0.369099\pi$
$828$		0			0
$829$	14.2046			0.493345			0.246672	−	0.969099i	$-0.420663\pi$
$829$	14.2046			0.493345			0.246672	+	0.969099i	$0.420663\pi$
$830$		0			0
$831$	1.26318	+	2.18789i	0.0438193	+	0.0758972i
$832$		0			0
$833$	−26.8220	+	15.4857i	−0.929328	+	0.536548i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	7.86791i		−	0.271955i
$838$		0			0
$839$	−7.79460	−	13.5006i	−0.269099	−	0.466094i	0.699530	−	0.714603i	$-0.253393\pi$
$839$	−7.79460	−	13.5006i	−0.269099	−	0.466094i	−0.968629	+	0.248509i	$0.920059\pi$
$840$		0			0
$841$	13.5824	+	23.5253i	0.468357	+	0.811219i
$842$		0			0
$843$		−	0.301182i		−	0.0103732i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	37.3689i		−	1.28401i
$848$		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
$853$	−36.1689	+	20.8821i	−1.23840	+	0.714991i	−0.968767	−	0.247973i	$-0.920236\pi$
$853$	−36.1689	+	20.8821i	−1.23840	+	0.714991i	−0.269633	+	0.962963i	$0.586902\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.797898	−	0.460667i	0.0272557	−	0.0157361i	−0.486310	−	0.873786i	$-0.661658\pi$
$857$	0.797898	−	0.460667i	0.0272557	−	0.0157361i	0.513566	+	0.858050i	$0.328324\pi$
$858$		0			0
$859$	1.54335	−	2.67315i	0.0526583	−	0.0912068i	−0.838495	−	0.544910i	$-0.816564\pi$
$859$	1.54335	−	2.67315i	0.0526583	−	0.0912068i	0.891153	+	0.453703i	$0.149897\pi$
$860$		0			0
$861$	−2.03547	+	3.52554i	−0.0693686	+	0.120150i
$862$		0			0
$863$			51.8011i			1.76333i	0.471875	+	0.881666i	$0.343577\pi$
$863$			51.8011i			1.76333i	−0.471875	+	0.881666i	$0.656423\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	3.90260i		−	0.132539i
$868$		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
$873$			43.2370i			1.46335i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	13.3802	−	7.72507i	0.451818	−	0.260857i	−0.256780	−	0.966470i	$-0.582661\pi$
$877$	13.3802	−	7.72507i	0.451818	−	0.260857i	0.708598	+	0.705613i	$0.249328\pi$
$878$		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
$883$	−46.3841	−	26.7799i	−1.56095	−	0.901215i	−0.997161	−	0.0752955i	$-0.976010\pi$
$883$	−46.3841	−	26.7799i	−1.56095	−	0.901215i	−0.563788	−	0.825919i	$-0.690657\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	38.8223	+	22.4140i	1.30352	+	0.752590i	0.981007	−	0.193973i	$-0.0621375\pi$
$887$	38.8223	+	22.4140i	1.30352	+	0.752590i	0.322518	+	0.946563i	$0.395471\pi$
$888$		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
$893$	0.330974	−	35.7099i	0.0110756	−	1.19499i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.262994	+	0.151840i	0.00878111	+	0.00506978i
$898$		0			0
$899$	6.40890	−	11.1005i	0.213749	−	0.370224i
$900$		0			0
$901$	−89.9802			−2.99767
$902$		0			0
$903$	−3.11931	−	1.80094i	−0.103804	−	0.0599314i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	10.7389	−	6.20013i	0.356581	−	0.205872i	−0.310999	−	0.950410i	$-0.600664\pi$
$907$	10.7389	−	6.20013i	0.356581	−	0.205872i	0.667580	+	0.744538i	$0.267330\pi$
$908$		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
$913$			0.242289i			0.00801860i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−63.4852	+	36.6532i	−2.09647	+	1.21040i
$918$		0			0
$919$	−21.4055			−0.706101			−0.353051	−	0.935604i	$-0.614856\pi$
$919$	−21.4055			−0.706101			−0.353051	+	0.935604i	$0.614856\pi$
$920$		0			0
$921$	−0.961273	+	1.66497i	−0.0316750	+	0.0548628i
$922$		0			0
$923$		−	31.0770i		−	1.02291i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	27.1082	+	15.6509i	0.890351	+	0.514044i
$928$		0			0
$929$	27.9411	+	48.3954i	0.916717	+	1.58780i	0.804368	+	0.594131i	$0.202504\pi$
$929$	27.9411	+	48.3954i	0.916717	+	1.58780i	0.112349	+	0.993669i	$0.464163\pi$
$930$		0			0
$931$	−9.89299	−	17.5079i	−0.324230	−	0.573799i
$932$		0			0
$933$	2.70239	−	1.56023i	0.0884723	−	0.0510795i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.7914	+	11.4266i	0.646556	+	0.373289i	0.787136	−	0.616780i	$-0.211563\pi$
$937$	19.7914	+	11.4266i	0.646556	+	0.373289i	−0.140579	+	0.990069i	$0.544897\pi$
$938$		0			0
$939$	2.91920			0.0952646
$940$		0			0
$941$	−29.0459	+	50.3089i	−0.946868	+	1.64002i	−0.194901	+	0.980823i	$0.562438\pi$
$941$	−29.0459	+	50.3089i	−0.946868	+	1.64002i	−0.751967	+	0.659200i	$0.770895\pi$
$942$		0			0
$943$		−	7.96887i		−	0.259502i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.8228	−	14.9088i	0.839130	−	0.484472i	−0.0178386	−	0.999841i	$-0.505679\pi$
$947$	25.8228	−	14.9088i	0.839130	−	0.484472i	0.856968	+	0.515369i	$0.172345\pi$
$948$		0			0
$949$	11.5504			0.374940
$950$		0			0
$951$	1.50219			0.0487118
$952$		0			0
$953$	45.2741	−	26.1390i	1.46657	−	0.846725i	0.467271	−	0.884114i	$-0.345237\pi$
$953$	45.2741	−	26.1390i	1.46657	−	0.846725i	0.999301	+	0.0373888i	$0.0119040\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			0.0349772i			0.00113065i
$958$		0			0
$959$	−23.4751	+	40.6600i	−0.758050	+	1.31298i
$960$		0			0
$961$	58.5216			1.88779
$962$		0			0
$963$	−39.1399	−	22.5974i	−1.26127	−	0.728192i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−17.4220	+	10.0586i	−0.560254	+	0.323463i	−0.753247	−	0.657737i	$-0.771514\pi$
$967$	−17.4220	+	10.0586i	−0.560254	+	0.323463i	0.192994	+	0.981200i	$0.438180\pi$
$968$		0			0
$969$	4.06853	+	0.0377088i	0.130700	+	0.00121138i
$970$		0			0
$971$	8.91867	+	15.4476i	0.286214	+	0.495737i	0.972903	−	0.231215i	$-0.0742700\pi$
$971$	8.91867	+	15.4476i	0.286214	+	0.495737i	−0.686689	+	0.726951i	$0.740937\pi$
$972$		0			0
$973$	−54.6099	−	31.5290i	−1.75071	−	1.01077i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	11.7616i		−	0.376287i	−0.982142	−	0.188143i	$-0.939753\pi$
$977$		−	11.7616i		−	0.376287i	0.982142	−	0.188143i	$-0.0602470\pi$
$978$		0			0
$979$	−0.363180	+	0.629046i	−0.0116073	+	0.0201044i
$980$		0			0
$981$	−0.355041			−0.0113356
$982$		0			0
$983$	−28.2742	+	16.3241i	−0.901807	+	0.520659i	−0.877786	−	0.479053i	$-0.840980\pi$
$983$	−28.2742	+	16.3241i	−0.901807	+	0.520659i	−0.0240213	+	0.999711i	$0.507647\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	3.88202i		−	0.123566i
$988$		0			0
$989$	7.05067			0.224198
$990$		0			0
$991$	26.7049	+	46.2543i	0.848310	+	1.46932i	0.882715	+	0.469908i	$0.155713\pi$
$991$	26.7049	+	46.2543i	0.848310	+	1.46932i	−0.0344052	+	0.999408i	$0.510954\pi$
$992$		0			0
$993$	0.929025	−	0.536373i	0.0294817	−	0.0170213i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.1152	−	5.83999i	−0.320350	−	0.184954i	0.331198	−	0.943561i	$-0.392547\pi$
$997$	−10.1152	−	5.83999i	−0.320350	−	0.184954i	−0.651549	+	0.758607i	$0.725880\pi$
$998$		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.s.e.349.7		24
5.2	odd	4		1900.2.i.e.501.4	yes	12
5.3	odd	4		1900.2.i.f.501.3	yes	12
5.4	even	2	inner	1900.2.s.e.349.6		24
19.11	even	3	inner	1900.2.s.e.49.6		24
95.49	even	6	inner	1900.2.s.e.49.7		24
95.68	odd	12		1900.2.i.f.201.3	yes	12
95.87	odd	12		1900.2.i.e.201.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.4	✓	12	95.87	odd	12
1900.2.i.e.501.4	yes	12	5.2	odd	4
1900.2.i.f.201.3	yes	12	95.68	odd	12
1900.2.i.f.501.3	yes	12	5.3	odd	4
1900.2.s.e.49.6		24	19.11	even	3	inner
1900.2.s.e.49.7		24	95.49	even	6	inner
1900.2.s.e.349.6		24	5.4	even	2	inner
1900.2.s.e.349.7		24	1.1	even	1	trivial

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.120414 - 0.0695210i) q^{3} +3.40785i q^{7} +(-1.49033 + 2.58133i) q^{9} +O(q^{10})\)	\(q+(0.120414 - 0.0695210i) q^{3} +3.40785i q^{7} +(-1.49033 + 2.58133i) q^{9} +0.185690 q^{11} +(-2.03925 - 1.17736i) q^{13} +(5.81385 - 3.35663i) q^{17} +(2.14437 + 3.79495i) q^{19} +(0.236918 + 0.410353i) q^{21} +(-0.803267 - 0.463767i) q^{23} +0.831564i q^{27} +(-0.677360 + 1.17322i) q^{29} -9.46158 q^{31} +(0.0223597 - 0.0129094i) q^{33} +1.62862i q^{37} -0.327405 q^{39} +(4.29573 + 7.44043i) q^{41} +(-6.58312 + 3.80076i) q^{43} +(-7.09515 - 4.09639i) q^{47} -4.61347 q^{49} +(0.466712 - 0.808369i) q^{51} +(-11.6077 - 6.70168i) q^{53} +(0.522041 + 0.307887i) q^{57} +(-2.02981 - 3.51573i) q^{59} +(-6.31247 + 10.9335i) q^{61} +(-8.79681 - 5.07884i) q^{63} +(2.81654 + 1.62613i) q^{67} -0.128966 q^{69} +(6.59887 + 11.4296i) q^{71} +(-4.24802 + 2.45260i) q^{73} +0.632805i q^{77} +(2.98245 + 5.16576i) q^{79} +(-4.41319 - 7.64387i) q^{81} +1.30480i q^{83} +0.188363i q^{87} +(-1.95584 + 3.38761i) q^{89} +(4.01227 - 6.94946i) q^{91} +(-1.13931 + 0.657779i) q^{93} +(12.5624 - 7.25291i) q^{97} +(-0.276740 + 0.479328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} + 4 q^{11} + 2 q^{21} - 2 q^{29} + 4 q^{31} - 72 q^{39} - 14 q^{41} - 16 q^{49} + 22 q^{51} - 10 q^{61} + 28 q^{69} + 16 q^{71} - 2 q^{79} + 4 q^{81} + 16 q^{89} + 6 q^{91} + 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 + 4 * q^11 + 2 * q^21 - 2 * q^29 + 4 * q^31 - 72 * q^39 - 14 * q^41 - 16 * q^49 + 22 * q^51 - 10 * q^61 + 28 * q^69 + 16 * q^71 - 2 * q^79 + 4 * q^81 + 16 * q^89 + 6 * q^91 + 36 * q^99

Introduction

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Modular forms

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Database

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