LMFDB - Embedded newform 1900.3.g.d.949.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,3,Mod(949,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1900.949");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1900.g (of order $2$, degree $1$, 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:	$51.7712502285$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			949.16
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.d.949.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.284180 q^{3} -2.19606i q^{7} -8.91924 q^{9} +O(q^{10})$	$q+0.284180 q^{3} -2.19606i q^{7} -8.91924 q^{9} -2.14967 q^{11} +5.91448 q^{13} +21.3302i q^{17} +(12.8601 - 13.9863i) q^{19} -0.624075i q^{21} -9.06199i q^{23} -5.09229 q^{27} +33.2891i q^{29} -44.1498i q^{31} -0.610894 q^{33} -50.0133 q^{37} +1.68078 q^{39} +61.1061i q^{41} -5.39704i q^{43} -9.02253i q^{47} +44.1773 q^{49} +6.06161i q^{51} +62.0535 q^{53} +(3.65460 - 3.97463i) q^{57} +37.5680i q^{59} +58.0153 q^{61} +19.5871i q^{63} +121.549 q^{67} -2.57524i q^{69} +103.884i q^{71} -120.816i q^{73} +4.72080i q^{77} +57.1212i q^{79} +78.8260 q^{81} -47.3469i q^{83} +9.46009i q^{87} -68.2779i q^{89} -12.9885i q^{91} -12.5465i q^{93} -22.7712 q^{97} +19.1735 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 104 q^{9}+O(q^{10}) $ 28 * q + 104 * q^9	$ 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) $ 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$	0.284180			0.0947267			0.0473633	−	0.998878i	$-0.484918\pi$
$3$	0.284180			0.0947267			0.0473633	+	0.998878i	$0.484918\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	2.19606i		−	0.313722i	−0.987621	−	0.156861i	$-0.949863\pi$
$7$		−	2.19606i		−	0.313722i	0.987621	−	0.156861i	$-0.0501375\pi$
$8$		0			0
$9$	−8.91924			−0.991027
$10$		0			0
$11$	−2.14967			−0.195425			−0.0977124	−	0.995215i	$-0.531153\pi$
$11$	−2.14967			−0.195425			−0.0977124	+	0.995215i	$0.531153\pi$
$12$		0			0
$13$	5.91448			0.454960			0.227480	−	0.973783i	$-0.426951\pi$
$13$	5.91448			0.454960			0.227480	+	0.973783i	$0.426951\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			21.3302i			1.25472i	0.778731	+	0.627358i	$0.215864\pi$
$17$			21.3302i			1.25472i	−0.778731	+	0.627358i	$0.784136\pi$
$18$		0			0
$19$	12.8601	−	13.9863i	0.676850	−	0.736121i
$19$	12.8601	−	13.9863i	0.676850	−	0.736121i
$20$		0			0
$21$		−	0.624075i		−	0.0297178i
$22$		0			0
$23$		−	9.06199i		−	0.394000i	−0.980404	−	0.197000i	$-0.936880\pi$
$23$		−	9.06199i		−	0.394000i	0.980404	−	0.197000i	$-0.0631198\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.09229			−0.188603
$28$		0			0
$29$			33.2891i			1.14790i	0.818891	+	0.573950i	$0.194589\pi$
$29$			33.2891i			1.14790i	−0.818891	+	0.573950i	$0.805411\pi$
$30$		0			0
$31$		−	44.1498i		−	1.42419i	−0.702085	−	0.712093i	$-0.747747\pi$
$31$		−	44.1498i		−	1.42419i	0.702085	−	0.712093i	$-0.252253\pi$
$32$		0			0
$33$	−0.610894			−0.0185119
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−50.0133			−1.35171			−0.675855	−	0.737035i	$-0.736225\pi$
$37$	−50.0133			−1.35171			−0.675855	+	0.737035i	$0.736225\pi$
$38$		0			0
$39$	1.68078			0.0430968
$40$		0			0
$41$			61.1061i			1.49039i	0.666845	+	0.745196i	$0.267644\pi$
$41$			61.1061i			1.49039i	−0.666845	+	0.745196i	$0.732356\pi$
$42$		0			0
$43$		−	5.39704i		−	0.125513i	−0.998029	−	0.0627563i	$-0.980011\pi$
$43$		−	5.39704i		−	0.125513i	0.998029	−	0.0627563i	$-0.0199891\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	9.02253i		−	0.191969i	−0.995383	−	0.0959844i	$-0.969400\pi$
$47$		−	9.02253i		−	0.191969i	0.995383	−	0.0959844i	$-0.0305999\pi$
$48$		0			0
$49$	44.1773			0.901578
$50$		0			0
$51$			6.06161i			0.118855i
$52$		0			0
$53$	62.0535			1.17082			0.585411	−	0.810737i	$-0.300933\pi$
$53$	62.0535			1.17082			0.585411	+	0.810737i	$0.300933\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.65460	−	3.97463i	0.0641157	−	0.0697303i
$58$		0			0
$59$			37.5680i			0.636746i	0.947966	+	0.318373i	$0.103136\pi$
$59$			37.5680i			0.636746i	−0.947966	+	0.318373i	$0.896864\pi$
$60$		0			0
$61$	58.0153			0.951071			0.475535	−	0.879697i	$-0.342254\pi$
$61$	58.0153			0.951071			0.475535	+	0.879697i	$0.342254\pi$
$62$		0			0
$63$			19.5871i			0.310907i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	121.549			1.81416			0.907080	−	0.420958i	$-0.138306\pi$
$67$	121.549			1.81416			0.907080	+	0.420958i	$0.138306\pi$
$68$		0			0
$69$		−	2.57524i		−	0.0373223i
$70$		0			0
$71$			103.884i			1.46315i	0.681759	+	0.731576i	$0.261215\pi$
$71$			103.884i			1.46315i	−0.681759	+	0.731576i	$0.738785\pi$
$72$		0			0
$73$		−	120.816i		−	1.65501i	−0.561456	−	0.827507i	$-0.689759\pi$
$73$		−	120.816i		−	1.65501i	0.561456	−	0.827507i	$-0.310241\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			4.72080i			0.0613091i
$78$		0			0
$79$			57.1212i			0.723053i	0.932362	+	0.361526i	$0.117744\pi$
$79$			57.1212i			0.723053i	−0.932362	+	0.361526i	$0.882256\pi$
$80$		0			0
$81$	78.8260			0.973161
$82$		0			0
$83$		−	47.3469i		−	0.570445i	−0.958461	−	0.285222i	$-0.907933\pi$
$83$		−	47.3469i		−	0.570445i	0.958461	−	0.285222i	$-0.0920674\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			9.46009i			0.108737i
$88$		0			0
$89$		−	68.2779i		−	0.767168i	−0.923506	−	0.383584i	$-0.874690\pi$
$89$		−	68.2779i		−	0.767168i	0.923506	−	0.383584i	$-0.125310\pi$
$90$		0			0
$91$		−	12.9885i		−	0.142731i
$92$		0			0
$93$		−	12.5465i		−	0.134908i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−22.7712			−0.234755			−0.117378	−	0.993087i	$-0.537449\pi$
$97$	−22.7712			−0.234755			−0.117378	+	0.993087i	$0.537449\pi$
$98$		0			0
$99$	19.1735			0.193671
$100$		0			0
$101$	37.0879			0.367207			0.183603	−	0.983000i	$-0.441224\pi$
$101$	37.0879			0.367207			0.183603	+	0.983000i	$0.441224\pi$
$102$		0			0
$103$	167.221			1.62350			0.811752	−	0.584003i	$-0.198514\pi$
$103$	167.221			1.62350			0.811752	+	0.584003i	$0.198514\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−82.4568			−0.770624			−0.385312	−	0.922786i	$-0.625906\pi$
$107$	−82.4568			−0.770624			−0.385312	+	0.922786i	$0.625906\pi$
$108$		0			0
$109$			137.915i			1.26528i	0.774448	+	0.632638i	$0.218028\pi$
$109$			137.915i			1.26528i	−0.774448	+	0.632638i	$0.781972\pi$
$110$		0			0
$111$	−14.2128			−0.128043
$112$		0			0
$113$	156.892			1.38842			0.694211	−	0.719772i	$-0.255753\pi$
$113$	156.892			1.38842			0.694211	+	0.719772i	$0.255753\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−52.7527			−0.450877
$118$		0			0
$119$	46.8422			0.393632
$120$		0			0
$121$	−116.379			−0.961809
$122$		0			0
$123$			17.3651i			0.141180i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−160.978			−1.26754			−0.633771	−	0.773521i	$-0.718494\pi$
$127$	−160.978			−1.26754			−0.633771	+	0.773521i	$0.718494\pi$
$128$		0			0
$129$		−	1.53373i		−	0.0118894i
$130$		0			0
$131$	200.942			1.53391			0.766954	−	0.641703i	$-0.221772\pi$
$131$	200.942			1.53391			0.766954	+	0.641703i	$0.221772\pi$
$132$		0			0
$133$	−30.7147	−	28.2416i	−0.230938	−	0.212343i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			181.728i			1.32648i	0.748406	+	0.663240i	$0.230819\pi$
$137$			181.728i			1.32648i	−0.748406	+	0.663240i	$0.769181\pi$
$138$		0			0
$139$	49.6249			0.357013			0.178507	−	0.983939i	$-0.442873\pi$
$139$	49.6249			0.357013			0.178507	+	0.983939i	$0.442873\pi$
$140$		0			0
$141$		−	2.56402i		−	0.0181846i
$142$		0			0
$143$	−12.7142			−0.0889104
$144$		0			0
$145$		0			0
$146$		0			0
$147$	12.5543			0.0854035
$148$		0			0
$149$	197.358			1.32455			0.662276	−	0.749260i	$-0.269591\pi$
$149$	197.358			1.32455			0.662276	+	0.749260i	$0.269591\pi$
$150$		0			0
$151$			76.4718i			0.506436i	0.967409	+	0.253218i	$0.0814890\pi$
$151$			76.4718i			0.506436i	−0.967409	+	0.253218i	$0.918511\pi$
$152$		0			0
$153$		−	190.249i		−	1.24346i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			163.139i			1.03910i	0.854440	+	0.519550i	$0.173900\pi$
$157$			163.139i			1.03910i	−0.854440	+	0.519550i	$0.826100\pi$
$158$		0			0
$159$	17.6344			0.110908
$160$		0			0
$161$	−19.9006			−0.123606
$162$		0			0
$163$		−	287.890i		−	1.76620i	−0.469185	−	0.883100i	$-0.655452\pi$
$163$		−	287.890i		−	1.76620i	0.469185	−	0.883100i	$-0.344548\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−47.3144			−0.283320			−0.141660	−	0.989915i	$-0.545244\pi$
$167$	−47.3144			−0.283320			−0.141660	+	0.989915i	$0.545244\pi$
$168$		0			0
$169$	−134.019			−0.793012
$170$		0			0
$171$	−114.703	+	124.747i	−0.670776	+	0.729516i
$172$		0			0
$173$	64.2813			0.371568			0.185784	−	0.982591i	$-0.440518\pi$
$173$	64.2813			0.371568			0.185784	+	0.982591i	$0.440518\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			10.6761i			0.0603168i
$178$		0			0
$179$			276.531i			1.54487i	0.635097	+	0.772433i	$0.280960\pi$
$179$			276.531i			1.54487i	−0.635097	+	0.772433i	$0.719040\pi$
$180$		0			0
$181$			95.9988i			0.530380i	0.964196	+	0.265190i	$0.0854347\pi$
$181$			95.9988i			0.530380i	−0.964196	+	0.265190i	$0.914565\pi$
$182$		0			0
$183$	16.4868			0.0900918
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	45.8529i		−	0.245203i
$188$		0			0
$189$			11.1829i			0.0591690i
$190$		0			0
$191$	235.317			1.23203			0.616013	−	0.787736i	$-0.288747\pi$
$191$	235.317			1.23203			0.616013	+	0.787736i	$0.288747\pi$
$192$		0			0
$193$	311.842			1.61576			0.807882	−	0.589344i	$-0.200614\pi$
$193$	311.842			1.61576			0.807882	+	0.589344i	$0.200614\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	212.226i		−	1.07729i	−0.842533	−	0.538644i	$-0.818937\pi$
$197$		−	212.226i		−	1.07729i	0.842533	−	0.538644i	$-0.181063\pi$
$198$		0			0
$199$	63.8764			0.320987			0.160493	−	0.987037i	$-0.448691\pi$
$199$	63.8764			0.320987			0.160493	+	0.987037i	$0.448691\pi$
$200$		0			0
$201$	34.5417			0.171849
$202$		0			0
$203$	73.1046			0.360121
$204$		0			0
$205$		0			0
$206$		0			0
$207$			80.8261i			0.390464i
$208$		0			0
$209$	−27.6451	+	30.0660i	−0.132273	+	0.143856i
$210$		0			0
$211$			153.634i			0.728125i	0.931375	+	0.364063i	$0.118611\pi$
$211$			153.634i			0.728125i	−0.931375	+	0.364063i	$0.881389\pi$
$212$		0			0
$213$			29.5217i			0.138600i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−96.9553			−0.446799
$218$		0			0
$219$		−	34.3335i		−	0.156774i
$220$		0			0
$221$			126.157i			0.570845i
$222$		0			0
$223$	64.1517			0.287676			0.143838	−	0.989601i	$-0.454056\pi$
$223$	64.1517			0.287676			0.143838	+	0.989601i	$0.454056\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	185.129			0.815546			0.407773	−	0.913083i	$-0.366306\pi$
$227$	185.129			0.815546			0.407773	+	0.913083i	$0.366306\pi$
$228$		0			0
$229$	244.498			1.06768			0.533838	−	0.845587i	$-0.320749\pi$
$229$	244.498			1.06768			0.533838	+	0.845587i	$0.320749\pi$
$230$		0			0
$231$			1.34156i			0.00580761i
$232$		0			0
$233$		−	76.4331i		−	0.328039i	−0.986457	−	0.164019i	$-0.947554\pi$
$233$		−	76.4331i		−	0.328039i	0.986457	−	0.164019i	$-0.0524460\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			16.2327i			0.0684924i
$238$		0			0
$239$	221.151			0.925317			0.462659	−	0.886537i	$-0.346896\pi$
$239$	221.151			0.925317			0.462659	+	0.886537i	$0.346896\pi$
$240$		0			0
$241$		−	14.4423i		−	0.0599266i	−0.999551	−	0.0299633i	$-0.990461\pi$
$241$		−	14.4423i		−	0.0599266i	0.999551	−	0.0299633i	$-0.00953904\pi$
$242$		0			0
$243$	68.2314			0.280788
$244$		0			0
$245$		0			0
$246$		0			0
$247$	76.0610	−	82.7217i	0.307939	−	0.334906i
$248$		0			0
$249$		−	13.4550i		−	0.0540363i
$250$		0			0
$251$	120.711			0.480920			0.240460	−	0.970659i	$-0.422702\pi$
$251$	120.711			0.480920			0.240460	+	0.970659i	$0.422702\pi$
$252$		0			0
$253$			19.4803i			0.0769973i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−396.891			−1.54432			−0.772161	−	0.635426i	$-0.780824\pi$
$257$	−396.891			−1.54432			−0.772161	+	0.635426i	$0.780824\pi$
$258$		0			0
$259$			109.832i			0.424061i
$260$		0			0
$261$		−	296.913i		−	1.13760i
$262$		0			0
$263$		−	435.465i		−	1.65576i	−0.560905	−	0.827880i	$-0.689547\pi$
$263$		−	435.465i		−	1.65576i	0.560905	−	0.827880i	$-0.310453\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	19.4032i		−	0.0726713i
$268$		0			0
$269$		−	59.6306i		−	0.221675i	−0.993839	−	0.110838i	$-0.964647\pi$
$269$		−	59.6306i		−	0.221675i	0.993839	−	0.110838i	$-0.0353533\pi$
$270$		0			0
$271$	419.450			1.54779			0.773893	−	0.633317i	$-0.218307\pi$
$271$	419.450			1.54779			0.773893	+	0.633317i	$0.218307\pi$
$272$		0			0
$273$		−	3.69108i		−	0.0135204i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			262.373i			0.947196i	0.880741	+	0.473598i	$0.157045\pi$
$277$			262.373i			0.947196i	−0.880741	+	0.473598i	$0.842955\pi$
$278$		0			0
$279$			393.783i			1.41141i
$280$		0			0
$281$			223.815i			0.796495i	0.917278	+	0.398247i	$0.130381\pi$
$281$			223.815i			0.796495i	−0.917278	+	0.398247i	$0.869619\pi$
$282$		0			0
$283$			240.958i			0.851441i	0.904855	+	0.425721i	$0.139979\pi$
$283$			240.958i			0.851441i	−0.904855	+	0.425721i	$0.860021\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	134.192			0.467569
$288$		0			0
$289$	−165.976			−0.574312
$290$		0			0
$291$	−6.47113			−0.0222376
$292$		0			0
$293$	−418.683			−1.42895			−0.714476	−	0.699660i	$-0.753335\pi$
$293$	−418.683			−1.42895			−0.714476	+	0.699660i	$0.753335\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	10.9468			0.0368578
$298$		0			0
$299$		−	53.5969i		−	0.179254i
$300$		0			0
$301$	−11.8522			−0.0393761
$302$		0			0
$303$	10.5396			0.0347843
$304$		0			0
$305$		0			0
$306$		0			0
$307$	31.3393			0.102082			0.0510412	−	0.998697i	$-0.483746\pi$
$307$	31.3393			0.102082			0.0510412	+	0.998697i	$0.483746\pi$
$308$		0			0
$309$	47.5208			0.153789
$310$		0			0
$311$	−475.395			−1.52860			−0.764301	−	0.644860i	$-0.776916\pi$
$311$	−475.395			−1.52860			−0.764301	+	0.644860i	$0.776916\pi$
$312$		0			0
$313$			97.9348i			0.312891i	0.987687	+	0.156445i	$0.0500035\pi$
$313$			97.9348i			0.312891i	−0.987687	+	0.156445i	$0.949996\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	491.774			1.55134			0.775669	−	0.631140i	$-0.217413\pi$
$317$	491.774			1.55134			0.775669	+	0.631140i	$0.217413\pi$
$318$		0			0
$319$		−	71.5606i		−	0.224328i
$320$		0			0
$321$	−23.4326			−0.0729987
$322$		0			0
$323$	298.330	+	274.309i	0.923623	+	0.849254i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			39.1927i			0.119855i
$328$		0			0
$329$	−19.8140			−0.0602249
$330$		0			0
$331$			329.980i			0.996919i	0.866913	+	0.498460i	$0.166101\pi$
$331$			329.980i			0.996919i	−0.866913	+	0.498460i	$0.833899\pi$
$332$		0			0
$333$	446.080			1.33958
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−548.629			−1.62798			−0.813990	−	0.580879i	$-0.802709\pi$
$337$	−548.629			−1.62798			−0.813990	+	0.580879i	$0.802709\pi$
$338$		0			0
$339$	44.5855			0.131521
$340$		0			0
$341$			94.9076i			0.278321i
$342$		0			0
$343$		−	204.623i		−	0.596567i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	225.865i		−	0.650907i	−0.945558	−	0.325454i	$-0.894483\pi$
$347$		−	225.865i		−	0.650907i	0.945558	−	0.325454i	$-0.105517\pi$
$348$		0			0
$349$	−236.046			−0.676350			−0.338175	−	0.941083i	$-0.609810\pi$
$349$	−236.046			−0.676350			−0.338175	+	0.941083i	$0.609810\pi$
$350$		0			0
$351$	−30.1182			−0.0858069
$352$		0			0
$353$		−	205.291i		−	0.581560i	−0.956790	−	0.290780i	$-0.906085\pi$
$353$		−	205.291i		−	0.581560i	0.956790	−	0.290780i	$-0.0939147\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	13.3116			0.0372875
$358$		0			0
$359$	132.769			0.369830			0.184915	−	0.982755i	$-0.440799\pi$
$359$	132.769			0.369830			0.184915	+	0.982755i	$0.440799\pi$
$360$		0			0
$361$	−30.2334	−	359.732i	−0.0837490	−	0.996487i
$362$		0			0
$363$	−33.0726			−0.0911090
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	314.585i		−	0.857181i	−0.903499	−	0.428590i	$-0.859010\pi$
$367$		−	314.585i		−	0.857181i	0.903499	−	0.428590i	$-0.140990\pi$
$368$		0			0
$369$		−	545.020i		−	1.47702i
$370$		0			0
$371$		−	136.273i		−	0.367313i
$372$		0			0
$373$	79.5881			0.213373			0.106687	−	0.994293i	$-0.465976\pi$
$373$	79.5881			0.213373			0.106687	+	0.994293i	$0.465976\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			196.887i			0.522248i
$378$		0			0
$379$		−	212.412i		−	0.560454i	−0.959934	−	0.280227i	$-0.909590\pi$
$379$		−	212.412i		−	0.560454i	0.959934	−	0.280227i	$-0.0904098\pi$
$380$		0			0
$381$	−45.7467			−0.120070
$382$		0			0
$383$	−709.304			−1.85197			−0.925984	−	0.377563i	$-0.876762\pi$
$383$	−709.304			−1.85197			−0.925984	+	0.377563i	$0.876762\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			48.1375i			0.124386i
$388$		0			0
$389$	−604.145			−1.55307			−0.776536	−	0.630073i	$-0.783025\pi$
$389$	−604.145			−1.55307			−0.776536	+	0.630073i	$0.783025\pi$
$390$		0			0
$391$	193.294			0.494358
$392$		0			0
$393$	57.1036			0.145302
$394$		0			0
$395$		0			0
$396$		0			0
$397$			374.253i			0.942703i	0.881945	+	0.471352i	$0.156234\pi$
$397$			374.253i			0.942703i	−0.881945	+	0.471352i	$0.843766\pi$
$398$		0			0
$399$	−8.72850	−	8.02569i	−0.0218759	−	0.0201145i
$400$		0			0
$401$		−	298.430i		−	0.744215i	−0.928190	−	0.372108i	$-0.878635\pi$
$401$		−	298.430i		−	0.744215i	0.928190	−	0.372108i	$-0.121365\pi$
$402$		0			0
$403$		−	261.123i		−	0.647948i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	107.512			0.264158
$408$		0			0
$409$		−	290.042i		−	0.709150i	−0.935028	−	0.354575i	$-0.884626\pi$
$409$		−	290.042i		−	0.709150i	0.935028	−	0.354575i	$-0.115374\pi$
$410$		0			0
$411$			51.6434i			0.125653i
$412$		0			0
$413$	82.5014			0.199761
$414$		0			0
$415$		0			0
$416$		0			0
$417$	14.1024			0.0338187
$418$		0			0
$419$	44.1734			0.105426			0.0527129	−	0.998610i	$-0.483213\pi$
$419$	44.1734			0.105426			0.0527129	+	0.998610i	$0.483213\pi$
$420$		0			0
$421$		−	326.685i		−	0.775975i	−0.921665	−	0.387987i	$-0.873170\pi$
$421$		−	326.685i		−	0.775975i	0.921665	−	0.387987i	$-0.126830\pi$
$422$		0			0
$423$			80.4742i			0.190246i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	127.405i		−	0.298372i
$428$		0			0
$429$	−3.61312			−0.00842219
$430$		0			0
$431$			152.204i			0.353141i	0.984288	+	0.176571i	$0.0565004\pi$
$431$			152.204i			0.353141i	−0.984288	+	0.176571i	$0.943500\pi$
$432$		0			0
$433$	−223.747			−0.516736			−0.258368	−	0.966047i	$-0.583185\pi$
$433$	−223.747			−0.516736			−0.258368	+	0.966047i	$0.583185\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−126.744	−	116.539i	−0.290031	−	0.266679i
$438$		0			0
$439$			253.627i			0.577737i	0.957369	+	0.288869i	$0.0932791\pi$
$439$			253.627i			0.577737i	−0.957369	+	0.288869i	$0.906721\pi$
$440$		0			0
$441$	−394.028			−0.893488
$442$		0			0
$443$			471.418i			1.06415i	0.846697	+	0.532075i	$0.178587\pi$
$443$			471.418i			1.06415i	−0.846697	+	0.532075i	$0.821413\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	56.0852			0.125470
$448$		0			0
$449$			546.839i			1.21790i	0.793207	+	0.608952i	$0.208410\pi$
$449$			546.839i			1.21790i	−0.793207	+	0.608952i	$0.791590\pi$
$450$		0			0
$451$		−	131.358i		−	0.291260i
$452$		0			0
$453$			21.7318i			0.0479730i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			166.467i			0.364261i	0.983274	+	0.182130i	$0.0582993\pi$
$457$			166.467i			0.364261i	−0.983274	+	0.182130i	$0.941701\pi$
$458$		0			0
$459$		−	108.619i		−	0.236644i
$460$		0			0
$461$	−258.722			−0.561220			−0.280610	−	0.959822i	$-0.590537\pi$
$461$	−258.722			−0.561220			−0.280610	+	0.959822i	$0.590537\pi$
$462$		0			0
$463$			629.974i			1.36064i	0.732917	+	0.680318i	$0.238158\pi$
$463$			629.974i			1.36064i	−0.732917	+	0.680318i	$0.761842\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	151.843i		−	0.325145i	−0.986697	−	0.162573i	$-0.948021\pi$
$467$		−	151.843i		−	0.325145i	0.986697	−	0.162573i	$-0.0519792\pi$
$468$		0			0
$469$		−	266.928i		−	0.569142i
$470$		0			0
$471$			46.3608i			0.0984305i
$472$		0			0
$473$			11.6019i			0.0245283i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−553.470			−1.16032
$478$		0			0
$479$	15.2726			0.0318843			0.0159421	−	0.999873i	$-0.494925\pi$
$479$	15.2726			0.0318843			0.0159421	+	0.999873i	$0.494925\pi$
$480$		0			0
$481$	−295.802			−0.614974
$482$		0			0
$483$	−5.65536			−0.0117088
$484$		0			0
$485$		0			0
$486$		0			0
$487$	279.446			0.573812			0.286906	−	0.957959i	$-0.407373\pi$
$487$	279.446			0.573812			0.286906	+	0.957959i	$0.407373\pi$
$488$		0			0
$489$		−	81.8127i		−	0.167306i
$490$		0			0
$491$	641.107			1.30572			0.652859	−	0.757480i	$-0.273569\pi$
$491$	641.107			1.30572			0.652859	+	0.757480i	$0.273569\pi$
$492$		0			0
$493$	−710.062			−1.44029
$494$		0			0
$495$		0			0
$496$		0			0
$497$	228.135			0.459023
$498$		0			0
$499$	102.056			0.204521			0.102261	−	0.994758i	$-0.467392\pi$
$499$	102.056			0.204521			0.102261	+	0.994758i	$0.467392\pi$
$500$		0			0
$501$	−13.4458			−0.0268379
$502$		0			0
$503$			889.366i			1.76812i	0.467371	+	0.884061i	$0.345201\pi$
$503$			889.366i			1.76812i	−0.467371	+	0.884061i	$0.654799\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−38.0855			−0.0751193
$508$		0			0
$509$			35.5445i			0.0698320i	0.999390	+	0.0349160i	$0.0111164\pi$
$509$			35.5445i			0.0698320i	−0.999390	+	0.0349160i	$0.988884\pi$
$510$		0			0
$511$	−265.319			−0.519214
$512$		0			0
$513$	−65.4876	+	71.2223i	−0.127656	+	0.138835i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			19.3955i			0.0375155i
$518$		0			0
$519$	18.2674			0.0351974
$520$		0			0
$521$		−	747.135i		−	1.43404i	−0.697053	−	0.717020i	$-0.745506\pi$
$521$		−	747.135i		−	1.43404i	0.697053	−	0.717020i	$-0.254494\pi$
$522$		0			0
$523$	−677.562			−1.29553			−0.647765	−	0.761840i	$-0.724296\pi$
$523$	−677.562			−1.29553			−0.647765	+	0.761840i	$0.724296\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	941.722			1.78695
$528$		0			0
$529$	446.880			0.844764
$530$		0			0
$531$		−	335.078i		−	0.631032i
$532$		0			0
$533$			361.411i			0.678069i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			78.5845i			0.146340i
$538$		0			0
$539$	−94.9668			−0.176191
$540$		0			0
$541$	−362.237			−0.669569			−0.334784	−	0.942295i	$-0.608663\pi$
$541$	−362.237			−0.669569			−0.334784	+	0.942295i	$0.608663\pi$
$542$		0			0
$543$			27.2809i			0.0502411i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	585.353			1.07011			0.535057	−	0.844816i	$-0.320290\pi$
$547$	585.353			1.07011			0.535057	+	0.844816i	$0.320290\pi$
$548$		0			0
$549$	−517.453			−0.942537
$550$		0			0
$551$	465.591	+	428.102i	0.844993	+	0.776955i
$552$		0			0
$553$	125.441			0.226838
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1040.06i		−	1.86725i	−0.358257	−	0.933623i	$-0.616629\pi$
$557$		−	1040.06i		−	1.86725i	0.358257	−	0.933623i	$-0.383371\pi$
$558$		0			0
$559$		−	31.9207i		−	0.0571032i
$560$		0			0
$561$		−	13.0305i		−	0.0232272i
$562$		0			0
$563$	−421.015			−0.747807			−0.373903	−	0.927468i	$-0.621981\pi$
$563$	−421.015			−0.747807			−0.373903	+	0.927468i	$0.621981\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	173.106i		−	0.305302i
$568$		0			0
$569$			24.7446i			0.0434879i	0.999764	+	0.0217440i	$0.00692187\pi$
$569$			24.7446i			0.0434879i	−0.999764	+	0.0217440i	$0.993078\pi$
$570$		0			0
$571$	−283.521			−0.496534			−0.248267	−	0.968692i	$-0.579861\pi$
$571$	−283.521			−0.496534			−0.248267	+	0.968692i	$0.579861\pi$
$572$		0			0
$573$	66.8723			0.116706
$574$		0			0
$575$		0			0
$576$		0			0
$577$			147.592i			0.255792i	0.991788	+	0.127896i	$0.0408223\pi$
$577$			147.592i			0.255792i	−0.991788	+	0.127896i	$0.959178\pi$
$578$		0			0
$579$	88.6194			0.153056
$580$		0			0
$581$	−103.976			−0.178961
$582$		0			0
$583$	−133.395			−0.228808
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	876.849i		−	1.49378i	−0.664948	−	0.746890i	$-0.731546\pi$
$587$		−	876.849i		−	1.49378i	0.664948	−	0.746890i	$-0.268454\pi$
$588$		0			0
$589$	−617.492	−	567.772i	−1.04837	−	0.963960i
$590$		0			0
$591$		−	60.3103i		−	0.102048i
$592$		0			0
$593$		−	205.974i		−	0.347343i	−0.984804	−	0.173671i	$-0.944437\pi$
$593$		−	205.974i		−	0.347343i	0.984804	−	0.173671i	$-0.0555630\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18.1524			0.0304060
$598$		0			0
$599$			631.341i			1.05399i	0.849868	+	0.526996i	$0.176682\pi$
$599$			631.341i			1.05399i	−0.849868	+	0.526996i	$0.823318\pi$
$600$		0			0
$601$		−	139.903i		−	0.232784i	−0.993203	−	0.116392i	$-0.962867\pi$
$601$		−	139.903i		−	0.232784i	0.993203	−	0.116392i	$-0.0371328\pi$
$602$		0			0
$603$	−1084.12			−1.79788
$604$		0			0
$605$		0			0
$606$		0			0
$607$	18.9312			0.0311881			0.0155940	−	0.999878i	$-0.495036\pi$
$607$	18.9312			0.0311881			0.0155940	+	0.999878i	$0.495036\pi$
$608$		0			0
$609$	20.7749			0.0341131
$610$		0			0
$611$		−	53.3636i		−	0.0873381i
$612$		0			0
$613$			86.8754i			0.141722i	0.997486	+	0.0708608i	$0.0225746\pi$
$613$			86.8754i			0.141722i	−0.997486	+	0.0708608i	$0.977425\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			664.265i			1.07660i	0.842752	+	0.538302i	$0.180934\pi$
$617$			664.265i			1.07660i	−0.842752	+	0.538302i	$0.819066\pi$
$618$		0			0
$619$	−1120.54			−1.81024			−0.905122	−	0.425151i	$-0.860221\pi$
$619$	−1120.54			−1.81024			−0.905122	+	0.425151i	$0.860221\pi$
$620$		0			0
$621$			46.1463i			0.0743096i
$622$		0			0
$623$	−149.942			−0.240678
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.85618	+	8.54415i	−0.0125298	+	0.0136270i
$628$		0			0
$629$		−	1066.79i		−	1.69601i
$630$		0			0
$631$	−940.484			−1.49047			−0.745233	−	0.666804i	$-0.767662\pi$
$631$	−940.484			−1.49047			−0.745233	+	0.666804i	$0.767662\pi$
$632$		0			0
$633$			43.6598i			0.0689729i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	261.286			0.410182
$638$		0			0
$639$		−	926.565i		−	1.45002i
$640$		0			0
$641$			585.344i			0.913174i	0.889679	+	0.456587i	$0.150928\pi$
$641$			585.344i			0.913174i	−0.889679	+	0.456587i	$0.849072\pi$
$642$		0			0
$643$			562.853i			0.875354i	0.899132	+	0.437677i	$0.144199\pi$
$643$			562.853i			0.875354i	−0.899132	+	0.437677i	$0.855801\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	723.636i		−	1.11845i	−0.829017	−	0.559224i	$-0.811099\pi$
$647$		−	723.636i		−	1.11845i	0.829017	−	0.559224i	$-0.188901\pi$
$648$		0			0
$649$		−	80.7589i		−	0.124436i
$650$		0			0
$651$	−27.5528			−0.0423238
$652$		0			0
$653$			211.465i			0.323836i	0.986804	+	0.161918i	$0.0517680\pi$
$653$			211.465i			0.323836i	−0.986804	+	0.161918i	$0.948232\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			1077.59i			1.64016i
$658$		0			0
$659$		−	692.365i		−	1.05063i	−0.850908	−	0.525315i	$-0.823948\pi$
$659$		−	692.365i		−	1.05063i	0.850908	−	0.525315i	$-0.176052\pi$
$660$		0			0
$661$		−	1121.07i		−	1.69602i	−0.529978	−	0.848011i	$-0.677800\pi$
$661$		−	1121.07i		−	1.69602i	0.529978	−	0.848011i	$-0.322200\pi$
$662$		0			0
$663$			35.8512i			0.0540743i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	301.665			0.452272
$668$		0			0
$669$	18.2306			0.0272506
$670$		0			0
$671$	−124.714			−0.185863
$672$		0			0
$673$	536.583			0.797301			0.398650	−	0.917103i	$-0.369479\pi$
$673$	536.583			0.797301			0.398650	+	0.917103i	$0.369479\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−234.317			−0.346110			−0.173055	−	0.984912i	$-0.555364\pi$
$677$	−234.317			−0.346110			−0.173055	+	0.984912i	$0.555364\pi$
$678$		0			0
$679$			50.0069i			0.0736478i
$680$		0			0
$681$	52.6099			0.0772539
$682$		0			0
$683$	545.339			0.798447			0.399223	−	0.916854i	$-0.369280\pi$
$683$	545.339			0.798447			0.399223	+	0.916854i	$0.369280\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	69.4814			0.101137
$688$		0			0
$689$	367.014			0.532677
$690$		0			0
$691$	−225.173			−0.325865			−0.162933	−	0.986637i	$-0.552095\pi$
$691$	−225.173			−0.325865			−0.162933	+	0.986637i	$0.552095\pi$
$692$		0			0
$693$		−	42.1060i		−	0.0607590i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1303.40			−1.87002
$698$		0			0
$699$		−	21.7207i		−	0.0310740i
$700$		0			0
$701$	−517.342			−0.738005			−0.369003	−	0.929428i	$-0.620301\pi$
$701$	−517.342			−0.738005			−0.369003	+	0.929428i	$0.620301\pi$
$702$		0			0
$703$	−643.178	+	699.501i	−0.914905	+	0.995022i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	81.4471i		−	0.115201i
$708$		0			0
$709$	−272.183			−0.383897			−0.191948	−	0.981405i	$-0.561481\pi$
$709$	−272.183			−0.383897			−0.191948	+	0.981405i	$0.561481\pi$
$710$		0			0
$711$		−	509.478i		−	0.716565i
$712$		0			0
$713$	−400.085			−0.561129
$714$		0			0
$715$		0			0
$716$		0			0
$717$	62.8466			0.0876522
$718$		0			0
$719$	−547.539			−0.761528			−0.380764	−	0.924672i	$-0.624339\pi$
$719$	−547.539			−0.761528			−0.380764	+	0.924672i	$0.624339\pi$
$720$		0			0
$721$		−	367.226i		−	0.509329i
$722$		0			0
$723$		−	4.10421i		−	0.00567664i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	1211.49i		−	1.66642i	−0.552957	−	0.833210i	$-0.686501\pi$
$727$		−	1211.49i		−	1.66642i	0.552957	−	0.833210i	$-0.313499\pi$
$728$		0			0
$729$	−690.044			−0.946563
$730$		0			0
$731$	115.120			0.157483
$732$		0			0
$733$		−	3.28014i		−	0.00447495i	−0.999997	−	0.00223748i	$-0.999288\pi$
$733$		−	3.28014i		−	0.00447495i	0.999997	−	0.00223748i	$-0.000712211\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−261.290			−0.354532
$738$		0			0
$739$	848.413			1.14806			0.574028	−	0.818836i	$-0.305380\pi$
$739$	848.413			1.14806			0.574028	+	0.818836i	$0.305380\pi$
$740$		0			0
$741$	21.6150	−	23.5078i	0.0291701	−	0.0317245i
$742$		0			0
$743$	−620.675			−0.835363			−0.417682	−	0.908593i	$-0.637157\pi$
$743$	−620.675			−0.835363			−0.417682	+	0.908593i	$0.637157\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			422.298i			0.565326i
$748$		0			0
$749$			181.080i			0.241762i
$750$		0			0
$751$			88.8695i			0.118335i	0.998248	+	0.0591674i	$0.0188446\pi$
$751$			88.8695i			0.118335i	−0.998248	+	0.0591674i	$0.981155\pi$
$752$		0			0
$753$	34.3036			0.0455559
$754$		0			0
$755$		0			0
$756$		0			0
$757$			389.621i			0.514692i	0.966319	+	0.257346i	$0.0828479\pi$
$757$			389.621i			0.514692i	−0.966319	+	0.257346i	$0.917152\pi$
$758$		0			0
$759$			5.53592i			0.00729370i
$760$		0			0
$761$	183.315			0.240887			0.120444	−	0.992720i	$-0.461568\pi$
$761$	183.315			0.240887			0.120444	+	0.992720i	$0.461568\pi$
$762$		0			0
$763$	302.869			0.396945
$764$		0			0
$765$		0			0
$766$		0			0
$767$			222.195i			0.289694i
$768$		0			0
$769$	−839.391			−1.09154			−0.545768	−	0.837936i	$-0.683762\pi$
$769$	−839.391			−1.09154			−0.545768	+	0.837936i	$0.683762\pi$
$770$		0			0
$771$	−112.788			−0.146289
$772$		0			0
$773$	−1149.34			−1.48685			−0.743425	−	0.668819i	$-0.766800\pi$
$773$	−1149.34			−1.48685			−0.743425	+	0.668819i	$0.766800\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			31.2120i			0.0401699i
$778$		0			0
$779$	854.649	+	785.833i	1.09711	+	1.00877i
$780$		0			0
$781$		−	223.316i		−	0.285936i
$782$		0			0
$783$		−	169.518i		−	0.216498i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	500.800			0.636341			0.318170	−	0.948034i	$-0.396932\pi$
$787$	500.800			0.636341			0.318170	+	0.948034i	$0.396932\pi$
$788$		0			0
$789$		−	123.750i		−	0.156845i
$790$		0			0
$791$		−	344.543i		−	0.435579i
$792$		0			0
$793$	343.130			0.432699
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−481.090			−0.603626			−0.301813	−	0.953367i	$-0.597592\pi$
$797$	−481.090			−0.603626			−0.301813	+	0.953367i	$0.597592\pi$
$798$		0			0
$799$	192.452			0.240866
$800$		0			0
$801$			608.988i			0.760284i
$802$		0			0
$803$			259.715i			0.323431i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	16.9458i		−	0.0209985i
$808$		0			0
$809$	16.0970			0.0198974			0.00994869	−	0.999951i	$-0.496833\pi$
$809$	16.0970			0.0198974			0.00994869	+	0.999951i	$0.496833\pi$
$810$		0			0
$811$		−	744.398i		−	0.917876i	−0.888468	−	0.458938i	$-0.848230\pi$
$811$		−	744.398i		−	0.917876i	0.888468	−	0.458938i	$-0.151770\pi$
$812$		0			0
$813$	119.199			0.146617
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−75.4846	−	69.4067i	−0.0923925	−	0.0849531i
$818$		0			0
$819$			115.848i			0.141450i
$820$		0			0
$821$	−817.427			−0.995648			−0.497824	−	0.867278i	$-0.665868\pi$
$821$	−817.427			−0.995648			−0.497824	+	0.867278i	$0.665868\pi$
$822$		0			0
$823$		−	447.054i		−	0.543201i	−0.962410	−	0.271600i	$-0.912447\pi$
$823$		−	447.054i		−	0.543201i	0.962410	−	0.271600i	$-0.0875529\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1387.55			1.67782			0.838908	−	0.544274i	$-0.183195\pi$
$827$	1387.55			1.67782			0.838908	+	0.544274i	$0.183195\pi$
$828$		0			0
$829$		−	1076.73i		−	1.29883i	−0.760433	−	0.649416i	$-0.775013\pi$
$829$		−	1076.73i		−	1.29883i	0.760433	−	0.649416i	$-0.224987\pi$
$830$		0			0
$831$			74.5613i			0.0897247i
$832$		0			0
$833$			942.310i			1.13122i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			224.823i			0.268606i
$838$		0			0
$839$			606.394i			0.722758i	0.932419	+	0.361379i	$0.117694\pi$
$839$			606.394i			0.722758i	−0.932419	+	0.361379i	$0.882306\pi$
$840$		0			0
$841$	−267.163			−0.317673
$842$		0			0
$843$			63.6038i			0.0754493i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			255.574i			0.301741i
$848$		0			0
$849$			68.4754i			0.0806542i
$850$		0			0
$851$			453.220i			0.532573i
$852$		0			0
$853$			99.5618i			0.116720i	0.998296	+	0.0583598i	$0.0185871\pi$
$853$			99.5618i			0.116720i	−0.998296	+	0.0583598i	$0.981413\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1591.90			1.85753			0.928765	−	0.370669i	$-0.120872\pi$
$857$	1591.90			1.85753			0.928765	+	0.370669i	$0.120872\pi$
$858$		0			0
$859$	−974.586			−1.13456			−0.567279	−	0.823525i	$-0.692004\pi$
$859$	−974.586			−1.13456			−0.567279	+	0.823525i	$0.692004\pi$
$860$		0			0
$861$	38.1348			0.0442913
$862$		0			0
$863$	−270.696			−0.313669			−0.156834	−	0.987625i	$-0.550129\pi$
$863$	−270.696			−0.313669			−0.156834	+	0.987625i	$0.550129\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−47.1671			−0.0544027
$868$		0			0
$869$		−	122.792i		−	0.141302i
$870$		0			0
$871$	718.897			0.825370
$872$		0			0
$873$	203.102			0.232649
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−868.510			−0.990319			−0.495160	−	0.868802i	$-0.664890\pi$
$877$	−868.510			−0.990319			−0.495160	+	0.868802i	$0.664890\pi$
$878$		0			0
$879$	−118.981			−0.135360
$880$		0			0
$881$	916.787			1.04062			0.520311	−	0.853977i	$-0.325816\pi$
$881$	916.787			1.04062			0.520311	+	0.853977i	$0.325816\pi$
$882$		0			0
$883$		−	878.004i		−	0.994342i	−0.867653	−	0.497171i	$-0.834372\pi$
$883$		−	878.004i		−	0.994342i	0.867653	−	0.497171i	$-0.165628\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1351.53			1.52371			0.761856	−	0.647747i	$-0.224289\pi$
$887$	1351.53			1.52371			0.761856	+	0.647747i	$0.224289\pi$
$888$		0			0
$889$			353.516i			0.397656i
$890$		0			0
$891$	−169.450			−0.190180
$892$		0			0
$893$	−126.192	−	116.031i	−0.141312	−	0.129934i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	15.2312i		−	0.0169801i
$898$		0			0
$899$	1469.71			1.63482
$900$		0			0
$901$			1323.61i			1.46905i
$902$		0			0
$903$	−3.36816			−0.00372996
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−872.623			−0.962098			−0.481049	−	0.876694i	$-0.659744\pi$
$907$	−872.623			−0.962098			−0.481049	+	0.876694i	$0.659744\pi$
$908$		0			0
$909$	−330.796			−0.363912
$910$		0			0
$911$			885.104i			0.971574i	0.874077	+	0.485787i	$0.161467\pi$
$911$			885.104i			0.971574i	−0.874077	+	0.485787i	$0.838533\pi$
$912$		0			0
$913$			101.780i			0.111479i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	441.279i		−	0.481221i
$918$		0			0
$919$	446.590			0.485952			0.242976	−	0.970032i	$-0.421876\pi$
$919$	446.590			0.485952			0.242976	+	0.970032i	$0.421876\pi$
$920$		0			0
$921$	8.90600			0.00966992
$922$		0			0
$923$			614.419i			0.665676i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1491.48			−1.60894
$928$		0			0
$929$	−534.036			−0.574850			−0.287425	−	0.957803i	$-0.592799\pi$
$929$	−534.036			−0.574850			−0.287425	+	0.957803i	$0.592799\pi$
$930$		0			0
$931$	568.127	−	617.878i	0.610233	−	0.663671i
$932$		0			0
$933$	−135.098			−0.144799
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1157.99i		−	1.23585i	−0.786236	−	0.617926i	$-0.787973\pi$
$937$		−	1157.99i		−	1.23585i	0.786236	−	0.617926i	$-0.212027\pi$
$938$		0			0
$939$			27.8311i			0.0296391i
$940$		0			0
$941$		−	868.034i		−	0.922459i	−0.887281	−	0.461230i	$-0.847408\pi$
$941$		−	868.034i		−	0.922459i	0.887281	−	0.461230i	$-0.152592\pi$
$942$		0			0
$943$	553.743			0.587214
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	1754.37i		−	1.85255i	−0.376845	−	0.926276i	$-0.622991\pi$
$947$		−	1754.37i		−	1.85255i	0.376845	−	0.926276i	$-0.377009\pi$
$948$		0			0
$949$		−	714.563i		−	0.752965i
$950$		0			0
$951$	139.752			0.146953
$952$		0			0
$953$	−541.232			−0.567924			−0.283962	−	0.958836i	$-0.591649\pi$
$953$	−541.232			−0.567924			−0.283962	+	0.958836i	$0.591649\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	20.3361i		−	0.0212498i
$958$		0			0
$959$	399.084			0.416146
$960$		0			0
$961$	−988.203			−1.02831
$962$		0			0
$963$	735.452			0.763709
$964$		0			0
$965$		0			0
$966$		0			0
$967$			632.276i			0.653853i	0.945050	+	0.326927i	$0.106013\pi$
$967$			632.276i			0.653853i	−0.945050	+	0.326927i	$0.893987\pi$
$968$		0			0
$969$	84.7795	+	77.9531i	0.0874917	+	0.0804470i
$970$		0			0
$971$			1326.62i			1.36624i	0.730305	+	0.683122i	$0.239378\pi$
$971$			1326.62i			1.36624i	−0.730305	+	0.683122i	$0.760622\pi$
$972$		0			0
$973$		−	108.979i		−	0.112003i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−250.280			−0.256172			−0.128086	−	0.991763i	$-0.540883\pi$
$977$	−250.280			−0.256172			−0.128086	+	0.991763i	$0.540883\pi$
$978$		0			0
$979$			146.775i			0.149924i
$980$		0			0
$981$		−	1230.10i		−	1.25392i
$982$		0			0
$983$	1291.69			1.31403			0.657014	−	0.753879i	$-0.271819\pi$
$983$	1291.69			1.31403			0.657014	+	0.753879i	$0.271819\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.63074			−0.00570490
$988$		0			0
$989$	−48.9079			−0.0494519
$990$		0			0
$991$			468.338i			0.472592i	0.971681	+	0.236296i	$0.0759335\pi$
$991$			468.338i			0.472592i	−0.971681	+	0.236296i	$0.924067\pi$
$992$		0			0
$993$			93.7738i			0.0944348i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			1592.68i			1.59747i	0.601683	+	0.798735i	$0.294497\pi$
$997$			1592.68i			1.59747i	−0.601683	+	0.798735i	$0.705503\pi$
$998$		0			0
$999$	254.682			0.254937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.d.949.16		28
5.2	odd	4		1900.3.e.g.1101.7	✓	14
5.3	odd	4		1900.3.e.h.1101.8	yes	14
5.4	even	2	inner	1900.3.g.d.949.13		28
19.18	odd	2	inner	1900.3.g.d.949.14		28
95.18	even	4		1900.3.e.h.1101.7	yes	14
95.37	even	4		1900.3.e.g.1101.8	yes	14
95.94	odd	2	inner	1900.3.g.d.949.15		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.3.e.g.1101.7	✓	14	5.2	odd	4
1900.3.e.g.1101.8	yes	14	95.37	even	4
1900.3.e.h.1101.7	yes	14	95.18	even	4
1900.3.e.h.1101.8	yes	14	5.3	odd	4
1900.3.g.d.949.13		28	5.4	even	2	inner
1900.3.g.d.949.14		28	19.18	odd	2	inner
1900.3.g.d.949.15		28	95.94	odd	2	inner
1900.3.g.d.949.16		28	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1900.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.284180 q^{3} -2.19606i q^{7} -8.91924 q^{9} +O(q^{10})\)	\(q+0.284180 q^{3} -2.19606i q^{7} -8.91924 q^{9} -2.14967 q^{11} +5.91448 q^{13} +21.3302i q^{17} +(12.8601 - 13.9863i) q^{19} -0.624075i q^{21} -9.06199i q^{23} -5.09229 q^{27} +33.2891i q^{29} -44.1498i q^{31} -0.610894 q^{33} -50.0133 q^{37} +1.68078 q^{39} +61.1061i q^{41} -5.39704i q^{43} -9.02253i q^{47} +44.1773 q^{49} +6.06161i q^{51} +62.0535 q^{53} +(3.65460 - 3.97463i) q^{57} +37.5680i q^{59} +58.0153 q^{61} +19.5871i q^{63} +121.549 q^{67} -2.57524i q^{69} +103.884i q^{71} -120.816i q^{73} +4.72080i q^{77} +57.1212i q^{79} +78.8260 q^{81} -47.3469i q^{83} +9.46009i q^{87} -68.2779i q^{89} -12.9885i q^{91} -12.5465i q^{93} -22.7712 q^{97} +19.1735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 104 q^{9}+O(q^{10}) \) 28 * q + 104 * q^9	\( 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) \) 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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