LMFDB - Embedded newform 1900.3.g.c.949.2

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:	$24$
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			949.2
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.c.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.83157 q^{3} -3.72856i q^{7} +14.3441 q^{9} +O(q^{10})$	$q-4.83157 q^{3} -3.72856i q^{7} +14.3441 q^{9} -13.8938 q^{11} +4.10699 q^{13} -15.3087i q^{17} +(16.4588 + 9.49250i) q^{19} +18.0148i q^{21} -17.4452i q^{23} -25.8203 q^{27} +16.3924i q^{29} -15.9121i q^{31} +67.1291 q^{33} -5.14304 q^{37} -19.8432 q^{39} +42.2785i q^{41} -1.56664i q^{43} -54.5821i q^{47} +35.0979 q^{49} +73.9649i q^{51} +55.9822 q^{53} +(-79.5219 - 45.8637i) q^{57} +101.822i q^{59} +80.5719 q^{61} -53.4827i q^{63} -24.8838 q^{67} +84.2876i q^{69} -121.245i q^{71} +33.9798i q^{73} +51.8040i q^{77} +102.623i q^{79} -4.34417 q^{81} -80.3324i q^{83} -79.2009i q^{87} -12.0884i q^{89} -15.3131i q^{91} +76.8802i q^{93} +161.837 q^{97} -199.294 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 32 q^{9}+O(q^{10}) $ 24 * q + 32 * q^9	$ 24 q + 32 q^{9} - 64 q^{11} - 48 q^{19} - 248 q^{39} + 48 q^{49} + 304 q^{61} - 936 q^{81} - 784 q^{99}+O(q^{100}) $ 24 * q + 32 * q^9 - 64 * q^11 - 48 * q^19 - 248 * q^39 + 48 * q^49 + 304 * q^61 - 936 * q^81 - 784 * 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
$3$	−4.83157			−1.61052			−0.805262	−	0.592919i	$-0.797975\pi$
$3$	−4.83157			−1.61052			−0.805262	+	0.592919i	$0.797975\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	3.72856i		−	0.532651i	−0.963883	−	0.266326i	$-0.914190\pi$
$7$		−	3.72856i		−	0.532651i	0.963883	−	0.266326i	$-0.0858096\pi$
$8$		0			0
$9$	14.3441			1.59379
$10$		0			0
$11$	−13.8938			−1.26308			−0.631539	−	0.775344i	$-0.717576\pi$
$11$	−13.8938			−1.26308			−0.631539	+	0.775344i	$0.717576\pi$
$12$		0			0
$13$	4.10699			0.315922			0.157961	−	0.987445i	$-0.449508\pi$
$13$	4.10699			0.315922			0.157961	+	0.987445i	$0.449508\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	15.3087i		−	0.900510i	−0.892900	−	0.450255i	$-0.851333\pi$
$17$		−	15.3087i		−	0.900510i	0.892900	−	0.450255i	$-0.148667\pi$
$18$		0			0
$19$	16.4588	+	9.49250i	0.866253	+	0.499605i
$19$	16.4588	+	9.49250i	0.866253	+	0.499605i
$20$		0			0
$21$			18.0148i			0.857847i
$22$		0			0
$23$		−	17.4452i		−	0.758486i	−0.925297	−	0.379243i	$-0.876184\pi$
$23$		−	17.4452i		−	0.758486i	0.925297	−	0.379243i	$-0.123816\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−25.8203			−0.956307
$28$		0			0
$29$			16.3924i			0.565254i	0.959230	+	0.282627i	$0.0912059\pi$
$29$			16.3924i			0.565254i	−0.959230	+	0.282627i	$0.908794\pi$
$30$		0			0
$31$		−	15.9121i		−	0.513292i	−0.966505	−	0.256646i	$-0.917383\pi$
$31$		−	15.9121i		−	0.513292i	0.966505	−	0.256646i	$-0.0826175\pi$
$32$		0			0
$33$	67.1291			2.03422
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.14304			−0.139001			−0.0695005	−	0.997582i	$-0.522141\pi$
$37$	−5.14304			−0.139001			−0.0695005	+	0.997582i	$0.522141\pi$
$38$		0			0
$39$	−19.8432			−0.508800
$40$		0			0
$41$			42.2785i			1.03118i	0.856835	+	0.515591i	$0.172428\pi$
$41$			42.2785i			1.03118i	−0.856835	+	0.515591i	$0.827572\pi$
$42$		0			0
$43$		−	1.56664i		−	0.0364334i	−0.999834	−	0.0182167i	$-0.994201\pi$
$43$		−	1.56664i		−	0.0364334i	0.999834	−	0.0182167i	$-0.00579888\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	54.5821i		−	1.16132i	−0.814146	−	0.580660i	$-0.802794\pi$
$47$		−	54.5821i		−	1.16132i	0.814146	−	0.580660i	$-0.197206\pi$
$48$		0			0
$49$	35.0979			0.716283
$50$		0			0
$51$			73.9649i			1.45029i
$52$		0			0
$53$	55.9822			1.05627			0.528134	−	0.849161i	$-0.322892\pi$
$53$	55.9822			1.05627			0.528134	+	0.849161i	$0.322892\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−79.5219	−	45.8637i	−1.39512	−	0.804626i
$58$		0			0
$59$			101.822i			1.72580i	0.505376	+	0.862899i	$0.331354\pi$
$59$			101.822i			1.72580i	−0.505376	+	0.862899i	$0.668646\pi$
$60$		0			0
$61$	80.5719			1.32085			0.660426	−	0.750892i	$-0.270376\pi$
$61$	80.5719			1.32085			0.660426	+	0.750892i	$0.270376\pi$
$62$		0			0
$63$		−	53.4827i		−	0.848932i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−24.8838			−0.371400			−0.185700	−	0.982606i	$-0.559455\pi$
$67$	−24.8838			−0.371400			−0.185700	+	0.982606i	$0.559455\pi$
$68$		0			0
$69$			84.2876i			1.22156i
$70$		0			0
$71$		−	121.245i		−	1.70767i	−0.520545	−	0.853835i	$-0.674271\pi$
$71$		−	121.245i		−	1.70767i	0.520545	−	0.853835i	$-0.325729\pi$
$72$		0			0
$73$			33.9798i			0.465476i	0.972539	+	0.232738i	$0.0747685\pi$
$73$			33.9798i			0.465476i	−0.972539	+	0.232738i	$0.925231\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			51.8040i			0.672779i
$78$		0			0
$79$			102.623i			1.29902i	0.760351	+	0.649512i	$0.225027\pi$
$79$			102.623i			1.29902i	−0.760351	+	0.649512i	$0.774973\pi$
$80$		0			0
$81$	−4.34417			−0.0536317
$82$		0			0
$83$		−	80.3324i		−	0.967860i	−0.875107	−	0.483930i	$-0.839209\pi$
$83$		−	80.3324i		−	0.967860i	0.875107	−	0.483930i	$-0.160791\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	79.2009i		−	0.910355i
$88$		0			0
$89$		−	12.0884i		−	0.135824i	−0.997691	−	0.0679121i	$-0.978366\pi$
$89$		−	12.0884i		−	0.135824i	0.997691	−	0.0679121i	$-0.0216338\pi$
$90$		0			0
$91$		−	15.3131i		−	0.168276i
$92$		0			0
$93$			76.8802i			0.826669i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	161.837			1.66842			0.834210	−	0.551447i	$-0.185924\pi$
$97$	161.837			1.66842			0.834210	+	0.551447i	$0.185924\pi$
$98$		0			0
$99$	−199.294			−2.01308
$100$		0			0
$101$	−6.07921			−0.0601901			−0.0300951	−	0.999547i	$-0.509581\pi$
$101$	−6.07921			−0.0601901			−0.0300951	+	0.999547i	$0.509581\pi$
$102$		0			0
$103$	27.8929			0.270805			0.135402	−	0.990791i	$-0.456767\pi$
$103$	27.8929			0.270805			0.135402	+	0.990791i	$0.456767\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−61.4652			−0.574441			−0.287220	−	0.957865i	$-0.592731\pi$
$107$	−61.4652			−0.574441			−0.287220	+	0.957865i	$0.592731\pi$
$108$		0			0
$109$		−	30.2310i		−	0.277348i	−0.990338	−	0.138674i	$-0.955716\pi$
$109$		−	30.2310i		−	0.277348i	0.990338	−	0.138674i	$-0.0442841\pi$
$110$		0			0
$111$	24.8489			0.223864
$112$		0			0
$113$	−178.939			−1.58353			−0.791765	−	0.610826i	$-0.790837\pi$
$113$	−178.939			−1.58353			−0.791765	+	0.610826i	$0.790837\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	58.9109			0.503512
$118$		0			0
$119$	−57.0793			−0.479658
$120$		0			0
$121$	72.0390			0.595364
$122$		0			0
$123$		−	204.272i		−	1.66074i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−53.4071			−0.420528			−0.210264	−	0.977645i	$-0.567432\pi$
$127$	−53.4071			−0.420528			−0.210264	+	0.977645i	$0.567432\pi$
$128$		0			0
$129$			7.56932i			0.0586769i
$130$		0			0
$131$	−109.035			−0.832327			−0.416163	−	0.909290i	$-0.636626\pi$
$131$	−109.035			−0.832327			−0.416163	+	0.909290i	$0.636626\pi$
$132$		0			0
$133$	35.3933	−	61.3676i	0.266115	−	0.461411i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	24.9987i		−	0.182472i	−0.995829	−	0.0912362i	$-0.970918\pi$
$137$		−	24.9987i		−	0.182472i	0.995829	−	0.0912362i	$-0.0290818\pi$
$138$		0			0
$139$	−115.083			−0.827936			−0.413968	−	0.910291i	$-0.635857\pi$
$139$	−115.083			−0.827936			−0.413968	+	0.910291i	$0.635857\pi$
$140$		0			0
$141$			263.717i			1.87033i
$142$		0			0
$143$	−57.0619			−0.399034
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−169.578			−1.15359
$148$		0			0
$149$	141.364			0.948750			0.474375	−	0.880323i	$-0.342674\pi$
$149$	141.364			0.948750			0.474375	+	0.880323i	$0.342674\pi$
$150$		0			0
$151$		−	250.107i		−	1.65634i	−0.560478	−	0.828169i	$-0.689383\pi$
$151$		−	250.107i		−	1.65634i	0.560478	−	0.828169i	$-0.310617\pi$
$152$		0			0
$153$		−	219.589i		−	1.43522i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	14.5947i		−	0.0929601i	−0.998919	−	0.0464801i	$-0.985200\pi$
$157$		−	14.5947i		−	0.0929601i	0.998919	−	0.0464801i	$-0.0148004\pi$
$158$		0			0
$159$	−270.482			−1.70115
$160$		0			0
$161$	−65.0454			−0.404009
$162$		0			0
$163$			9.57924i			0.0587684i	0.999568	+	0.0293842i	$0.00935462\pi$
$163$			9.57924i			0.0587684i	−0.999568	+	0.0293842i	$0.990645\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−302.815			−1.81326			−0.906631	−	0.421923i	$-0.861355\pi$
$167$	−302.815			−1.81326			−0.906631	+	0.421923i	$0.861355\pi$
$168$		0			0
$169$	−152.133			−0.900193
$170$		0			0
$171$	236.086	+	136.161i	1.38062	+	0.796264i
$172$		0			0
$173$	−111.084			−0.642102			−0.321051	−	0.947062i	$-0.604036\pi$
$173$	−111.084			−0.642102			−0.321051	+	0.947062i	$0.604036\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	491.961i		−	2.77944i
$178$		0			0
$179$		−	247.724i		−	1.38393i	−0.721929	−	0.691967i	$-0.756744\pi$
$179$		−	247.724i		−	1.38393i	0.721929	−	0.691967i	$-0.243256\pi$
$180$		0			0
$181$		−	234.560i		−	1.29591i	−0.761678	−	0.647956i	$-0.775624\pi$
$181$		−	234.560i		−	1.29591i	0.761678	−	0.647956i	$-0.224376\pi$
$182$		0			0
$183$	−389.289			−2.12726
$184$		0			0
$185$		0			0
$186$		0			0
$187$			212.696i			1.13741i
$188$		0			0
$189$			96.2724i			0.509378i
$190$		0			0
$191$	−250.384			−1.31091			−0.655455	−	0.755235i	$-0.727523\pi$
$191$	−250.384			−1.31091			−0.655455	+	0.755235i	$0.727523\pi$
$192$		0			0
$193$	−122.208			−0.633204			−0.316602	−	0.948558i	$-0.602542\pi$
$193$	−122.208			−0.633204			−0.316602	+	0.948558i	$0.602542\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	343.177i		−	1.74201i	−0.491271	−	0.871007i	$-0.663467\pi$
$197$		−	343.177i		−	1.74201i	0.491271	−	0.871007i	$-0.336533\pi$
$198$		0			0
$199$	−297.583			−1.49539			−0.747696	−	0.664042i	$-0.768840\pi$
$199$	−297.583			−1.49539			−0.747696	+	0.664042i	$0.768840\pi$
$200$		0			0
$201$	120.228			0.598148
$202$		0			0
$203$	61.1199			0.301083
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	250.235i		−	1.20886i
$208$		0			0
$209$	−228.676	−	131.887i	−1.09414	−	0.631040i
$210$		0			0
$211$		−	237.792i		−	1.12698i	−0.826124	−	0.563488i	$-0.809459\pi$
$211$		−	237.792i		−	1.12698i	0.826124	−	0.563488i	$-0.190541\pi$
$212$		0			0
$213$			585.801i			2.75024i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−59.3290			−0.273406
$218$		0			0
$219$		−	164.176i		−	0.749661i
$220$		0			0
$221$		−	62.8725i		−	0.284491i
$222$		0			0
$223$	−152.390			−0.683365			−0.341682	−	0.939815i	$-0.610997\pi$
$223$	−152.390			−0.683365			−0.341682	+	0.939815i	$0.610997\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	205.814			0.906670			0.453335	−	0.891340i	$-0.350234\pi$
$227$	205.814			0.906670			0.453335	+	0.891340i	$0.350234\pi$
$228$		0			0
$229$	−135.060			−0.589783			−0.294892	−	0.955531i	$-0.595284\pi$
$229$	−135.060			−0.589783			−0.294892	+	0.955531i	$0.595284\pi$
$230$		0			0
$231$		−	250.295i		−	1.08353i
$232$		0			0
$233$		−	100.593i		−	0.431728i	−0.976423	−	0.215864i	$-0.930743\pi$
$233$		−	100.593i		−	0.431728i	0.976423	−	0.215864i	$-0.0692567\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	495.830i		−	2.09211i
$238$		0			0
$239$	328.565			1.37475			0.687373	−	0.726304i	$-0.258764\pi$
$239$	328.565			1.37475			0.687373	+	0.726304i	$0.258764\pi$
$240$		0			0
$241$			144.249i			0.598543i	0.954168	+	0.299272i	$0.0967437\pi$
$241$			144.249i			0.598543i	−0.954168	+	0.299272i	$0.903256\pi$
$242$		0			0
$243$	253.372			1.04268
$244$		0			0
$245$		0			0
$246$		0			0
$247$	67.5961	+	38.9856i	0.273669	+	0.157836i
$248$		0			0
$249$			388.132i			1.55876i
$250$		0			0
$251$	66.0565			0.263173			0.131587	−	0.991305i	$-0.457993\pi$
$251$	66.0565			0.263173			0.131587	+	0.991305i	$0.457993\pi$
$252$		0			0
$253$			242.381i			0.958027i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−268.255			−1.04379			−0.521896	−	0.853009i	$-0.674775\pi$
$257$	−268.255			−1.04379			−0.521896	+	0.853009i	$0.674775\pi$
$258$		0			0
$259$			19.1761i			0.0740390i
$260$		0			0
$261$			235.133i			0.900895i
$262$		0			0
$263$			241.131i			0.916848i	0.888734	+	0.458424i	$0.151586\pi$
$263$			241.131i			0.916848i	−0.888734	+	0.458424i	$0.848414\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			58.4058i			0.218748i
$268$		0			0
$269$		−	270.274i		−	1.00473i	−0.864654	−	0.502367i	$-0.832462\pi$
$269$		−	270.274i		−	1.00473i	0.864654	−	0.502367i	$-0.167538\pi$
$270$		0			0
$271$	159.872			0.589934			0.294967	−	0.955507i	$-0.404691\pi$
$271$	159.872			0.589934			0.294967	+	0.955507i	$0.404691\pi$
$272$		0			0
$273$			73.9865i			0.271013i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			480.862i			1.73596i	0.496597	+	0.867981i	$0.334583\pi$
$277$			480.862i			1.73596i	−0.496597	+	0.867981i	$0.665417\pi$
$278$		0			0
$279$		−	228.244i		−	0.818078i
$280$		0			0
$281$		−	125.506i		−	0.446639i	−0.974745	−	0.223320i	$-0.928311\pi$
$281$		−	125.506i		−	0.446639i	0.974745	−	0.223320i	$-0.0716894\pi$
$282$		0			0
$283$			169.824i			0.600086i	0.953926	+	0.300043i	$0.0970011\pi$
$283$			169.824i			0.600086i	−0.953926	+	0.300043i	$0.902999\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	157.638			0.549261
$288$		0			0
$289$	54.6445			0.189081
$290$		0			0
$291$	−781.925			−2.68703
$292$		0			0
$293$	103.213			0.352263			0.176131	−	0.984367i	$-0.443642\pi$
$293$	103.213			0.352263			0.176131	+	0.984367i	$0.443642\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	358.743			1.20789
$298$		0			0
$299$		−	71.6472i		−	0.239623i
$300$		0			0
$301$	−5.84130			−0.0194063
$302$		0			0
$303$	29.3721			0.0969377
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−470.447			−1.53240			−0.766200	−	0.642602i	$-0.777855\pi$
$307$	−470.447			−1.53240			−0.766200	+	0.642602i	$0.777855\pi$
$308$		0			0
$309$	−134.767			−0.436138
$310$		0			0
$311$	−104.966			−0.337511			−0.168756	−	0.985658i	$-0.553975\pi$
$311$	−104.966			−0.337511			−0.168756	+	0.985658i	$0.553975\pi$
$312$		0			0
$313$		−	358.845i		−	1.14647i	−0.819392	−	0.573234i	$-0.805689\pi$
$313$		−	358.845i		−	1.14647i	0.819392	−	0.573234i	$-0.194311\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−367.285			−1.15863			−0.579314	−	0.815104i	$-0.696680\pi$
$317$	−367.285			−1.15863			−0.579314	+	0.815104i	$0.696680\pi$
$318$		0			0
$319$		−	227.753i		−	0.713960i
$320$		0			0
$321$	296.973			0.925150
$322$		0			0
$323$	145.318	−	251.963i	0.449900	−	0.780070i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			146.063i			0.446676i
$328$		0			0
$329$	−203.512			−0.618579
$330$		0			0
$331$			496.428i			1.49978i	0.661561	+	0.749892i	$0.269894\pi$
$331$			496.428i			1.49978i	−0.661561	+	0.749892i	$0.730106\pi$
$332$		0			0
$333$	−73.7721			−0.221538
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−52.5036			−0.155797			−0.0778986	−	0.996961i	$-0.524821\pi$
$337$	−52.5036			−0.155797			−0.0778986	+	0.996961i	$0.524821\pi$
$338$		0			0
$339$	864.556			2.55031
$340$		0			0
$341$			221.080i			0.648328i
$342$		0			0
$343$		−	313.564i		−	0.914180i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			409.556i			1.18028i	0.807302	+	0.590138i	$0.200927\pi$
$347$			409.556i			1.18028i	−0.807302	+	0.590138i	$0.799073\pi$
$348$		0			0
$349$	−562.063			−1.61050			−0.805248	−	0.592938i	$-0.797968\pi$
$349$	−562.063			−1.61050			−0.805248	+	0.592938i	$0.797968\pi$
$350$		0			0
$351$	−106.044			−0.302118
$352$		0			0
$353$		−	252.453i		−	0.715165i	−0.933881	−	0.357583i	$-0.883601\pi$
$353$		−	252.453i		−	0.715165i	0.933881	−	0.357583i	$-0.116399\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	275.783			0.772500
$358$		0			0
$359$	119.344			0.332433			0.166217	−	0.986089i	$-0.446845\pi$
$359$	119.344			0.332433			0.166217	+	0.986089i	$0.446845\pi$
$360$		0			0
$361$	180.785	+	312.470i	0.500789	+	0.865569i
$362$		0			0
$363$	−348.062			−0.958848
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	690.635i		−	1.88184i	−0.338629	−	0.940920i	$-0.609963\pi$
$367$		−	690.635i		−	1.88184i	0.338629	−	0.940920i	$-0.390037\pi$
$368$		0			0
$369$			606.446i			1.64349i
$370$		0			0
$371$		−	208.733i		−	0.562623i
$372$		0			0
$373$	491.052			1.31649			0.658246	−	0.752803i	$-0.271299\pi$
$373$	491.052			1.31649			0.658246	+	0.752803i	$0.271299\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			67.3233i			0.178576i
$378$		0			0
$379$			691.775i			1.82526i	0.408782	+	0.912632i	$0.365954\pi$
$379$			691.775i			1.82526i	−0.408782	+	0.912632i	$0.634046\pi$
$380$		0			0
$381$	258.040			0.677271
$382$		0			0
$383$	−252.889			−0.660285			−0.330142	−	0.943931i	$-0.607097\pi$
$383$	−252.889			−0.660285			−0.330142	+	0.943931i	$0.607097\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	22.4720i		−	0.0580671i
$388$		0			0
$389$	504.764			1.29759			0.648797	−	0.760961i	$-0.275272\pi$
$389$	504.764			1.29759			0.648797	+	0.760961i	$0.275272\pi$
$390$		0			0
$391$	−267.063			−0.683025
$392$		0			0
$393$	526.809			1.34048
$394$		0			0
$395$		0			0
$396$		0			0
$397$			313.581i			0.789876i	0.918708	+	0.394938i	$0.129234\pi$
$397$			313.581i			0.789876i	−0.918708	+	0.394938i	$0.870766\pi$
$398$		0			0
$399$	−171.005	+	296.502i	−0.428585	+	0.743113i
$400$		0			0
$401$			561.838i			1.40109i	0.713607	+	0.700546i	$0.247060\pi$
$401$			561.838i			1.40109i	−0.713607	+	0.700546i	$0.752940\pi$
$402$		0			0
$403$		−	65.3506i		−	0.162160i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	71.4566			0.175569
$408$		0			0
$409$			165.613i			0.404921i	0.979290	+	0.202460i	$0.0648937\pi$
$409$			165.613i			0.404921i	−0.979290	+	0.202460i	$0.935106\pi$
$410$		0			0
$411$			120.783i			0.293876i
$412$		0			0
$413$	379.650			0.919249
$414$		0			0
$415$		0			0
$416$		0			0
$417$	556.032			1.33341
$418$		0			0
$419$	440.399			1.05107			0.525536	−	0.850771i	$-0.323865\pi$
$419$	440.399			1.05107			0.525536	+	0.850771i	$0.323865\pi$
$420$		0			0
$421$		−	786.831i		−	1.86896i	−0.356018	−	0.934479i	$-0.615866\pi$
$421$		−	786.831i		−	1.86896i	0.356018	−	0.934479i	$-0.384134\pi$
$422$		0			0
$423$		−	782.929i		−	1.85090i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	300.417i		−	0.703553i
$428$		0			0
$429$	275.698			0.642654
$430$		0			0
$431$		−	219.539i		−	0.509372i	−0.967024	−	0.254686i	$-0.918028\pi$
$431$		−	219.539i		−	0.509372i	0.967024	−	0.254686i	$-0.0819721\pi$
$432$		0			0
$433$	−450.900			−1.04134			−0.520670	−	0.853758i	$-0.674318\pi$
$433$	−450.900			−1.04134			−0.520670	+	0.853758i	$0.674318\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	165.598	−	287.127i	0.378944	−	0.657041i
$438$		0			0
$439$		−	319.069i		−	0.726808i	−0.931632	−	0.363404i	$-0.881615\pi$
$439$		−	319.069i		−	0.726808i	0.931632	−	0.363404i	$-0.118385\pi$
$440$		0			0
$441$	503.446			1.14160
$442$		0			0
$443$		−	780.776i		−	1.76247i	−0.472674	−	0.881237i	$-0.656711\pi$
$443$		−	780.776i		−	1.76247i	0.472674	−	0.881237i	$-0.343289\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−683.009			−1.52798
$448$		0			0
$449$			523.244i			1.16535i	0.812704	+	0.582677i	$0.197995\pi$
$449$			523.244i			1.16535i	−0.812704	+	0.582677i	$0.802005\pi$
$450$		0			0
$451$		−	587.411i		−	1.30246i
$452$		0			0
$453$			1208.41i			2.66757i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			874.643i			1.91388i	0.290285	+	0.956940i	$0.406250\pi$
$457$			874.643i			1.91388i	−0.290285	+	0.956940i	$0.593750\pi$
$458$		0			0
$459$			395.274i			0.861164i
$460$		0			0
$461$	120.368			0.261102			0.130551	−	0.991442i	$-0.458325\pi$
$461$	120.368			0.261102			0.130551	+	0.991442i	$0.458325\pi$
$462$		0			0
$463$		−	256.911i		−	0.554883i	−0.960743	−	0.277441i	$-0.910514\pi$
$463$		−	256.911i		−	0.554883i	0.960743	−	0.277441i	$-0.0894864\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			490.911i			1.05120i	0.850731	+	0.525601i	$0.176160\pi$
$467$			490.911i			1.05120i	−0.850731	+	0.525601i	$0.823840\pi$
$468$		0			0
$469$			92.7807i			0.197827i
$470$		0			0
$471$			70.5155i			0.149714i
$472$		0			0
$473$			21.7666i			0.0460182i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	803.014			1.68347
$478$		0			0
$479$	−545.752			−1.13936			−0.569679	−	0.821868i	$-0.692932\pi$
$479$	−545.752			−1.13936			−0.569679	+	0.821868i	$0.692932\pi$
$480$		0			0
$481$	−21.1224			−0.0439135
$482$		0			0
$483$	314.271			0.650665
$484$		0			0
$485$		0			0
$486$		0			0
$487$	243.032			0.499039			0.249519	−	0.968370i	$-0.419727\pi$
$487$	243.032			0.499039			0.249519	+	0.968370i	$0.419727\pi$
$488$		0			0
$489$		−	46.2828i		−	0.0946479i
$490$		0			0
$491$	−555.332			−1.13102			−0.565511	−	0.824740i	$-0.691321\pi$
$491$	−555.332			−1.13102			−0.565511	+	0.824740i	$0.691321\pi$
$492$		0			0
$493$	250.946			0.509017
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−452.067			−0.909592
$498$		0			0
$499$	231.235			0.463397			0.231698	−	0.972788i	$-0.425572\pi$
$499$	231.235			0.463397			0.231698	+	0.972788i	$0.425572\pi$
$500$		0			0
$501$	1463.07			2.92030
$502$		0			0
$503$			206.048i			0.409638i	0.978800	+	0.204819i	$0.0656605\pi$
$503$			206.048i			0.409638i	−0.978800	+	0.204819i	$0.934340\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	735.040			1.44978
$508$		0			0
$509$		−	398.832i		−	0.783560i	−0.920059	−	0.391780i	$-0.871859\pi$
$509$		−	398.832i		−	0.783560i	0.920059	−	0.391780i	$-0.128141\pi$
$510$		0			0
$511$	126.696			0.247936
$512$		0			0
$513$	−424.971	−	245.099i	−0.828404	−	0.477776i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			758.355i			1.46684i
$518$		0			0
$519$	536.708			1.03412
$520$		0			0
$521$		−	262.617i		−	0.504064i	−0.967719	−	0.252032i	$-0.918901\pi$
$521$		−	262.617i		−	0.504064i	0.967719	−	0.252032i	$-0.0810988\pi$
$522$		0			0
$523$	814.031			1.55646			0.778232	−	0.627977i	$-0.216117\pi$
$523$	814.031			1.55646			0.778232	+	0.627977i	$0.216117\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−243.592			−0.462225
$528$		0			0
$529$	224.666			0.424699
$530$		0			0
$531$			1460.54i			2.75055i
$532$		0			0
$533$			173.637i			0.325773i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			1196.90i			2.22886i
$538$		0			0
$539$	−487.644			−0.904720
$540$		0			0
$541$	−196.753			−0.363684			−0.181842	−	0.983328i	$-0.558206\pi$
$541$	−196.753			−0.363684			−0.181842	+	0.983328i	$0.558206\pi$
$542$		0			0
$543$			1133.29i			2.08710i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−759.052			−1.38766			−0.693832	−	0.720137i	$-0.744079\pi$
$547$	−759.052			−1.38766			−0.693832	+	0.720137i	$0.744079\pi$
$548$		0			0
$549$	1155.73			2.10515
$550$		0			0
$551$	−155.605	+	269.799i	−0.282404	+	0.489653i
$552$		0			0
$553$	382.636			0.691927
$554$		0			0
$555$		0			0
$556$		0			0
$557$			705.968i			1.26745i	0.773560	+	0.633723i	$0.218474\pi$
$557$			705.968i			1.26745i	−0.773560	+	0.633723i	$0.781526\pi$
$558$		0			0
$559$		−	6.43416i		−	0.0115101i
$560$		0			0
$561$		−	1027.66i		−	1.83183i
$562$		0			0
$563$	357.744			0.635424			0.317712	−	0.948187i	$-0.397086\pi$
$563$	357.744			0.635424			0.317712	+	0.948187i	$0.397086\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			16.1975i			0.0285670i
$568$		0			0
$569$		−	448.411i		−	0.788069i	−0.919096	−	0.394034i	$-0.871079\pi$
$569$		−	448.411i		−	0.788069i	0.919096	−	0.394034i	$-0.128921\pi$
$570$		0			0
$571$	203.672			0.356694			0.178347	−	0.983968i	$-0.442925\pi$
$571$	203.672			0.356694			0.178347	+	0.983968i	$0.442925\pi$
$572$		0			0
$573$	1209.75			2.11125
$574$		0			0
$575$		0			0
$576$		0			0
$577$			232.447i			0.402854i	0.979504	+	0.201427i	$0.0645579\pi$
$577$			232.447i			0.402854i	−0.979504	+	0.201427i	$0.935442\pi$
$578$		0			0
$579$	590.458			1.01979
$580$		0			0
$581$	−299.524			−0.515532
$582$		0			0
$583$	−777.809			−1.33415
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	1101.80i		−	1.87701i	−0.345271	−	0.938503i	$-0.612213\pi$
$587$		−	1101.80i		−	1.87701i	0.345271	−	0.938503i	$-0.387787\pi$
$588$		0			0
$589$	151.045	−	261.894i	0.256443	−	0.444641i
$590$		0			0
$591$			1658.08i			2.80555i
$592$		0			0
$593$			387.409i			0.653303i	0.945145	+	0.326651i	$0.105920\pi$
$593$			387.409i			0.653303i	−0.945145	+	0.326651i	$0.894080\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1437.79			2.40836
$598$		0			0
$599$		−	649.288i		−	1.08395i	−0.840393	−	0.541977i	$-0.817676\pi$
$599$		−	649.288i		−	1.08395i	0.840393	−	0.541977i	$-0.182324\pi$
$600$		0			0
$601$		−	564.191i		−	0.938754i	−0.882998	−	0.469377i	$-0.844479\pi$
$601$		−	564.191i		−	0.938754i	0.882998	−	0.469377i	$-0.155521\pi$
$602$		0			0
$603$	−356.935			−0.591932
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−431.505			−0.710882			−0.355441	−	0.934699i	$-0.615669\pi$
$607$	−431.505			−0.710882			−0.355441	+	0.934699i	$0.615669\pi$
$608$		0			0
$609$	−295.305			−0.484902
$610$		0			0
$611$		−	224.168i		−	0.366887i
$612$		0			0
$613$		−	360.161i		−	0.587539i	−0.955876	−	0.293769i	$-0.905090\pi$
$613$		−	360.161i		−	0.587539i	0.955876	−	0.293769i	$-0.0949098\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	255.900i		−	0.414749i	−0.978262	−	0.207375i	$-0.933508\pi$
$617$		−	255.900i		−	0.414749i	0.978262	−	0.207375i	$-0.0664919\pi$
$618$		0			0
$619$	231.220			0.373538			0.186769	−	0.982404i	$-0.440198\pi$
$619$	231.220			0.373538			0.186769	+	0.982404i	$0.440198\pi$
$620$		0			0
$621$			450.440i			0.725346i
$622$		0			0
$623$	−45.0722			−0.0723470
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1104.87	+	637.223i	1.76215	+	1.01630i
$628$		0			0
$629$			78.7331i			0.125172i
$630$		0			0
$631$	55.6688			0.0882232			0.0441116	−	0.999027i	$-0.485954\pi$
$631$	55.6688			0.0882232			0.0441116	+	0.999027i	$0.485954\pi$
$632$		0			0
$633$			1148.91i			1.81502i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	144.146			0.226290
$638$		0			0
$639$		−	1739.14i		−	2.72166i
$640$		0			0
$641$		−	1086.58i		−	1.69513i	−0.530692	−	0.847565i	$-0.678068\pi$
$641$		−	1086.58i		−	1.69513i	0.530692	−	0.847565i	$-0.321932\pi$
$642$		0			0
$643$		−	132.021i		−	0.205320i	−0.994717	−	0.102660i	$-0.967265\pi$
$643$		−	132.021i		−	0.205320i	0.994717	−	0.102660i	$-0.0327353\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			139.001i			0.214840i	0.994214	+	0.107420i	$0.0342589\pi$
$647$			139.001i			0.214840i	−0.994214	+	0.107420i	$0.965741\pi$
$648$		0			0
$649$		−	1414.70i		−	2.17982i
$650$		0			0
$651$	286.652			0.440326
$652$		0			0
$653$			2.61433i			0.00400356i	0.999998	+	0.00200178i	$0.000637187\pi$
$653$			2.61433i			0.00400356i	−0.999998	+	0.00200178i	$0.999363\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			487.408i			0.741870i
$658$		0			0
$659$			1115.25i			1.69234i	0.532911	+	0.846171i	$0.321098\pi$
$659$			1115.25i			1.69234i	−0.532911	+	0.846171i	$0.678902\pi$
$660$		0			0
$661$		−	1032.56i		−	1.56212i	−0.624453	−	0.781062i	$-0.714678\pi$
$661$		−	1032.56i		−	1.56212i	0.624453	−	0.781062i	$-0.285322\pi$
$662$		0			0
$663$			303.773i			0.458180i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	285.968			0.428738
$668$		0			0
$669$	736.285			1.10058
$670$		0			0
$671$	−1119.45			−1.66834
$672$		0			0
$673$	−923.804			−1.37267			−0.686333	−	0.727288i	$-0.740781\pi$
$673$	−923.804			−1.37267			−0.686333	+	0.727288i	$0.740781\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1144.25			−1.69017			−0.845086	−	0.534631i	$-0.820451\pi$
$677$	−1144.25			−1.69017			−0.845086	+	0.534631i	$0.820451\pi$
$678$		0			0
$679$		−	603.417i		−	0.888686i
$680$		0			0
$681$	−994.406			−1.46021
$682$		0			0
$683$	−686.997			−1.00585			−0.502926	−	0.864330i	$-0.667743\pi$
$683$	−686.997			−1.00585			−0.502926	+	0.864330i	$0.667743\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	652.554			0.949860
$688$		0			0
$689$	229.918			0.333699
$690$		0			0
$691$	−1216.77			−1.76088			−0.880442	−	0.474154i	$-0.842754\pi$
$691$	−1216.77			−1.76088			−0.880442	+	0.474154i	$0.842754\pi$
$692$		0			0
$693$			743.081i			1.07227i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	647.228			0.928591
$698$		0			0
$699$			486.020i			0.695308i
$700$		0			0
$701$	−1082.00			−1.54351			−0.771753	−	0.635922i	$-0.780620\pi$
$701$	−1082.00			−1.54351			−0.771753	+	0.635922i	$0.780620\pi$
$702$		0			0
$703$	−84.6482	−	48.8203i	−0.120410	−	0.0694456i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			22.6667i			0.0320604i
$708$		0			0
$709$	639.509			0.901987			0.450994	−	0.892527i	$-0.351070\pi$
$709$	639.509			0.901987			0.450994	+	0.892527i	$0.351070\pi$
$710$		0			0
$711$			1472.03i			2.07037i
$712$		0			0
$713$	−277.589			−0.389325
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1587.48			−2.21406
$718$		0			0
$719$	95.9878			0.133502			0.0667509	−	0.997770i	$-0.478737\pi$
$719$	95.9878			0.133502			0.0667509	+	0.997770i	$0.478737\pi$
$720$		0			0
$721$		−	104.000i		−	0.144245i
$722$		0			0
$723$		−	696.949i		−	0.963968i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	368.875i		−	0.507394i	−0.967284	−	0.253697i	$-0.918353\pi$
$727$		−	368.875i		−	0.507394i	0.967284	−	0.253697i	$-0.0816466\pi$
$728$		0			0
$729$	−1185.09			−1.62563
$730$		0			0
$731$	−23.9831			−0.0328087
$732$		0			0
$733$			865.251i			1.18042i	0.807248	+	0.590212i	$0.200956\pi$
$733$			865.251i			1.18042i	−0.807248	+	0.590212i	$0.799044\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	345.732			0.469107
$738$		0			0
$739$	934.331			1.26432			0.632159	−	0.774839i	$-0.282169\pi$
$739$	934.331			1.26432			0.632159	+	0.774839i	$0.282169\pi$
$740$		0			0
$741$	−326.595	−	188.362i	−0.440750	−	0.254199i
$742$		0			0
$743$	−235.551			−0.317027			−0.158514	−	0.987357i	$-0.550670\pi$
$743$	−235.551			−0.317027			−0.158514	+	0.987357i	$0.550670\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	1152.29i		−	1.54256i
$748$		0			0
$749$			229.176i			0.305976i
$750$		0			0
$751$		−	971.042i		−	1.29300i	−0.762915	−	0.646499i	$-0.776232\pi$
$751$		−	971.042i		−	1.29300i	0.762915	−	0.646499i	$-0.223768\pi$
$752$		0			0
$753$	−319.156			−0.423847
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	177.074i		−	0.233916i	−0.993137	−	0.116958i	$-0.962686\pi$
$757$		−	177.074i		−	0.233916i	0.993137	−	0.116958i	$-0.0373143\pi$
$758$		0			0
$759$		−	1171.08i		−	1.54292i
$760$		0			0
$761$	−159.521			−0.209621			−0.104810	−	0.994492i	$-0.533424\pi$
$761$	−159.521			−0.209621			−0.104810	+	0.994492i	$0.533424\pi$
$762$		0			0
$763$	−112.718			−0.147730
$764$		0			0
$765$		0			0
$766$		0			0
$767$			418.182i			0.545218i
$768$		0			0
$769$	−707.134			−0.919551			−0.459775	−	0.888035i	$-0.652070\pi$
$769$	−707.134			−0.919551			−0.459775	+	0.888035i	$0.652070\pi$
$770$		0			0
$771$	1296.09			1.68105
$772$		0			0
$773$	−799.572			−1.03438			−0.517188	−	0.855872i	$-0.673021\pi$
$773$	−799.572			−1.03438			−0.517188	+	0.855872i	$0.673021\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	92.6507i		−	0.119242i
$778$		0			0
$779$	−401.329	+	695.854i	−0.515184	+	0.893265i
$780$		0			0
$781$			1684.55i			2.15692i
$782$		0			0
$783$		−	423.256i		−	0.540557i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1366.97			1.73693			0.868466	−	0.495749i	$-0.165107\pi$
$787$	1366.97			1.73693			0.868466	+	0.495749i	$0.165107\pi$
$788$		0			0
$789$		−	1165.04i		−	1.47661i
$790$		0			0
$791$			667.184i			0.843469i
$792$		0			0
$793$	330.908			0.417286
$794$		0			0
$795$		0			0
$796$		0			0
$797$	121.258			0.152143			0.0760717	−	0.997102i	$-0.475762\pi$
$797$	121.258			0.152143			0.0760717	+	0.997102i	$0.475762\pi$
$798$		0			0
$799$	−835.579			−1.04578
$800$		0			0
$801$		−	173.396i		−	0.216475i
$802$		0			0
$803$		−	472.110i		−	0.587933i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			1305.85i			1.61815i
$808$		0			0
$809$	−820.488			−1.01420			−0.507100	−	0.861887i	$-0.669283\pi$
$809$	−820.488			−1.01420			−0.507100	+	0.861887i	$0.669283\pi$
$810$		0			0
$811$			537.722i			0.663036i	0.943449	+	0.331518i	$0.107561\pi$
$811$			537.722i			0.663036i	−0.943449	+	0.331518i	$0.892439\pi$
$812$		0			0
$813$	−772.434			−0.950103
$814$		0			0
$815$		0			0
$816$		0			0
$817$	14.8713	−	25.7850i	0.0182023	−	0.0315606i
$818$		0			0
$819$		−	219.653i		−	0.268196i
$820$		0			0
$821$	−54.0424			−0.0658250			−0.0329125	−	0.999458i	$-0.510478\pi$
$821$	−54.0424			−0.0658250			−0.0329125	+	0.999458i	$0.510478\pi$
$822$		0			0
$823$			599.052i			0.727889i	0.931421	+	0.363944i	$0.118570\pi$
$823$			599.052i			0.727889i	−0.931421	+	0.363944i	$0.881430\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−620.339			−0.750108			−0.375054	−	0.927003i	$-0.622376\pi$
$827$	−620.339			−0.750108			−0.375054	+	0.927003i	$0.622376\pi$
$828$		0			0
$829$		−	36.8107i		−	0.0444038i	−0.999754	−	0.0222019i	$-0.992932\pi$
$829$		−	36.8107i		−	0.0444038i	0.999754	−	0.0222019i	$-0.00706766\pi$
$830$		0			0
$831$		−	2323.32i		−	2.79581i
$832$		0			0
$833$		−	537.302i		−	0.645020i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			410.854i			0.490865i
$838$		0			0
$839$		−	531.549i		−	0.633551i	−0.948501	−	0.316776i	$-0.897400\pi$
$839$		−	531.549i		−	0.633551i	0.948501	−	0.316776i	$-0.102600\pi$
$840$		0			0
$841$	572.290			0.680488
$842$		0			0
$843$			606.389i			0.719323i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	268.602i		−	0.317121i
$848$		0			0
$849$		−	820.519i		−	0.966453i
$850$		0			0
$851$			89.7212i			0.105430i
$852$		0			0
$853$		−	16.6518i		−	0.0195214i	−0.999952	−	0.00976072i	$-0.996893\pi$
$853$		−	16.6518i		−	0.0195214i	0.999952	−	0.00976072i	$-0.00310698\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−656.701			−0.766279			−0.383139	−	0.923691i	$-0.625157\pi$
$857$	−656.701			−0.766279			−0.383139	+	0.923691i	$0.625157\pi$
$858$		0			0
$859$	7.72122			0.00898862			0.00449431	−	0.999990i	$-0.498569\pi$
$859$	7.72122			0.00898862			0.00449431	+	0.999990i	$0.498569\pi$
$860$		0			0
$861$	−761.638			−0.884597
$862$		0			0
$863$	−1132.71			−1.31253			−0.656266	−	0.754530i	$-0.727865\pi$
$863$	−1132.71			−1.31253			−0.656266	+	0.754530i	$0.727865\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−264.019			−0.304520
$868$		0			0
$869$		−	1425.83i		−	1.64077i
$870$		0			0
$871$	−102.197			−0.117333
$872$		0			0
$873$	2321.40			2.65910
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−826.040			−0.941893			−0.470947	−	0.882162i	$-0.656088\pi$
$877$	−826.040			−0.941893			−0.470947	+	0.882162i	$0.656088\pi$
$878$		0			0
$879$	−498.681			−0.567327
$880$		0			0
$881$	691.162			0.784520			0.392260	−	0.919854i	$-0.371693\pi$
$881$	691.162			0.784520			0.392260	+	0.919854i	$0.371693\pi$
$882$		0			0
$883$			1339.08i			1.51651i	0.651958	+	0.758255i	$0.273948\pi$
$883$			1339.08i			1.51651i	−0.651958	+	0.758255i	$0.726052\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1263.16			1.42408			0.712040	−	0.702139i	$-0.247772\pi$
$887$	1263.16			1.42408			0.712040	+	0.702139i	$0.247772\pi$
$888$		0			0
$889$			199.131i			0.223995i
$890$		0			0
$891$	60.3572			0.0677409
$892$		0			0
$893$	518.120	−	898.356i	0.580202	−	1.00600i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			346.168i			0.385918i
$898$		0			0
$899$	260.836			0.290141
$900$		0			0
$901$		−	857.014i		−	0.951181i
$902$		0			0
$903$	28.2227			0.0312543
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−531.490			−0.585987			−0.292994	−	0.956114i	$-0.594651\pi$
$907$	−531.490			−0.585987			−0.292994	+	0.956114i	$0.594651\pi$
$908$		0			0
$909$	−87.2006			−0.0959302
$910$		0			0
$911$		−	214.421i		−	0.235368i	−0.993051	−	0.117684i	$-0.962453\pi$
$911$		−	214.421i		−	0.235368i	0.993051	−	0.117684i	$-0.0375471\pi$
$912$		0			0
$913$			1116.13i			1.22248i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			406.542i			0.443340i
$918$		0			0
$919$	1523.80			1.65811			0.829055	−	0.559167i	$-0.188879\pi$
$919$	1523.80			1.65811			0.829055	+	0.559167i	$0.188879\pi$
$920$		0			0
$921$	2273.00			2.46797
$922$		0			0
$923$		−	497.950i		−	0.539490i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	400.098			0.431605
$928$		0			0
$929$	269.533			0.290132			0.145066	−	0.989422i	$-0.453661\pi$
$929$	269.533			0.290132			0.145066	+	0.989422i	$0.453661\pi$
$930$		0			0
$931$	577.669	+	333.166i	0.620482	+	0.357859i
$932$		0			0
$933$	507.151			0.543570
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	492.223i		−	0.525318i	−0.964889	−	0.262659i	$-0.915401\pi$
$937$		−	492.223i		−	0.525318i	0.964889	−	0.262659i	$-0.0845995\pi$
$938$		0			0
$939$			1733.78i			1.84641i
$940$		0			0
$941$		−	1364.05i		−	1.44958i	−0.688972	−	0.724788i	$-0.741938\pi$
$941$		−	1364.05i		−	1.44958i	0.688972	−	0.724788i	$-0.258062\pi$
$942$		0			0
$943$	737.556			0.782138
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	1082.40i		−	1.14298i	−0.820609	−	0.571490i	$-0.806366\pi$
$947$		−	1082.40i		−	1.14298i	0.820609	−	0.571490i	$-0.193634\pi$
$948$		0			0
$949$			139.554i			0.147054i
$950$		0			0
$951$	1774.56			1.86600
$952$		0			0
$953$	196.828			0.206535			0.103268	−	0.994654i	$-0.467070\pi$
$953$	196.828			0.206535			0.103268	+	0.994654i	$0.467070\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			1100.41i			1.14985i
$958$		0			0
$959$	−93.2092			−0.0971941
$960$		0			0
$961$	707.806			0.736531
$962$		0			0
$963$	−881.661			−0.915536
$964$		0			0
$965$		0			0
$966$		0			0
$967$			1381.14i			1.42828i	0.700005	+	0.714138i	$0.253181\pi$
$967$			1381.14i			1.42828i	−0.700005	+	0.714138i	$0.746819\pi$
$968$		0			0
$969$	−702.112	+	1217.37i	−0.724574	+	1.25632i
$970$		0			0
$971$			1116.21i			1.14954i	0.818314	+	0.574771i	$0.194909\pi$
$971$			1116.21i			1.14954i	−0.818314	+	0.574771i	$0.805091\pi$
$972$		0			0
$973$			429.094i			0.441001i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1784.43			1.82644			0.913218	−	0.407471i	$-0.133589\pi$
$977$	1784.43			1.82644			0.913218	+	0.407471i	$0.133589\pi$
$978$		0			0
$979$			167.954i			0.171557i
$980$		0			0
$981$		−	433.635i		−	0.442034i
$982$		0			0
$983$	−600.203			−0.610583			−0.305291	−	0.952259i	$-0.598754\pi$
$983$	−600.203			−0.610583			−0.305291	+	0.952259i	$0.598754\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	983.285			0.996236
$988$		0			0
$989$	−27.3303			−0.0276343
$990$		0			0
$991$			14.0179i			0.0141452i	0.999975	+	0.00707259i	$0.00225129\pi$
$991$			14.0179i			0.0141452i	−0.999975	+	0.00707259i	$0.997749\pi$
$992$		0			0
$993$		−	2398.53i		−	2.41544i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			137.727i			0.138142i	0.997612	+	0.0690708i	$0.0220034\pi$
$997$			137.727i			0.138142i	−0.997612	+	0.0690708i	$0.977997\pi$
$998$		0			0
$999$	132.795			0.132928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.c.949.2		24
5.2	odd	4		1900.3.e.f.1101.12		12
5.3	odd	4		380.3.e.a.341.1	✓	12
5.4	even	2	inner	1900.3.g.c.949.23		24
15.8	even	4		3420.3.o.a.721.4		12
19.18	odd	2	inner	1900.3.g.c.949.24		24
20.3	even	4		1520.3.h.b.721.12		12
95.18	even	4		380.3.e.a.341.12	yes	12
95.37	even	4		1900.3.e.f.1101.1		12
95.94	odd	2	inner	1900.3.g.c.949.1		24
285.113	odd	4		3420.3.o.a.721.3		12
380.303	odd	4		1520.3.h.b.721.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.e.a.341.1	✓	12	5.3	odd	4
380.3.e.a.341.12	yes	12	95.18	even	4
1520.3.h.b.721.1		12	380.303	odd	4
1520.3.h.b.721.12		12	20.3	even	4
1900.3.e.f.1101.1		12	95.37	even	4
1900.3.e.f.1101.12		12	5.2	odd	4
1900.3.g.c.949.1		24	95.94	odd	2	inner
1900.3.g.c.949.2		24	1.1	even	1	trivial
1900.3.g.c.949.23		24	5.4	even	2	inner
1900.3.g.c.949.24		24	19.18	odd	2	inner
3420.3.o.a.721.3		12	285.113	odd	4
3420.3.o.a.721.4		12	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q-4.83157 q^{3} -3.72856i q^{7} +14.3441 q^{9} +O(q^{10})\)	\(q-4.83157 q^{3} -3.72856i q^{7} +14.3441 q^{9} -13.8938 q^{11} +4.10699 q^{13} -15.3087i q^{17} +(16.4588 + 9.49250i) q^{19} +18.0148i q^{21} -17.4452i q^{23} -25.8203 q^{27} +16.3924i q^{29} -15.9121i q^{31} +67.1291 q^{33} -5.14304 q^{37} -19.8432 q^{39} +42.2785i q^{41} -1.56664i q^{43} -54.5821i q^{47} +35.0979 q^{49} +73.9649i q^{51} +55.9822 q^{53} +(-79.5219 - 45.8637i) q^{57} +101.822i q^{59} +80.5719 q^{61} -53.4827i q^{63} -24.8838 q^{67} +84.2876i q^{69} -121.245i q^{71} +33.9798i q^{73} +51.8040i q^{77} +102.623i q^{79} -4.34417 q^{81} -80.3324i q^{83} -79.2009i q^{87} -12.0884i q^{89} -15.3131i q^{91} +76.8802i q^{93} +161.837 q^{97} -199.294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 32 q^{9}+O(q^{10}) \) 24 * q + 32 * q^9	\( 24 q + 32 q^{9} - 64 q^{11} - 48 q^{19} - 248 q^{39} + 48 q^{49} + 304 q^{61} - 936 q^{81} - 784 q^{99}+O(q^{100}) \) 24 * q + 32 * q^9 - 64 * q^11 - 48 * q^19 - 248 * q^39 + 48 * q^49 + 304 * q^61 - 936 * q^81 - 784 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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