LMFDB - Embedded newform 2790.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(1,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2790.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.a (trivial)

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:	yes
Analytic conductor:	$22.2782621639$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2790.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -5.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -5.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +1.00000 q^{11} -4.00000 q^{13} -5.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +3.00000 q^{19} -1.00000 q^{20} +1.00000 q^{22} +7.00000 q^{23} +1.00000 q^{25} -4.00000 q^{26} -5.00000 q^{28} -8.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +5.00000 q^{35} +8.00000 q^{37} +3.00000 q^{38} -1.00000 q^{40} +1.00000 q^{43} +1.00000 q^{44} +7.00000 q^{46} +18.0000 q^{49} +1.00000 q^{50} -4.00000 q^{52} -1.00000 q^{53} -1.00000 q^{55} -5.00000 q^{56} -8.00000 q^{58} +8.00000 q^{59} +2.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +10.0000 q^{67} +6.00000 q^{68} +5.00000 q^{70} -9.00000 q^{71} +11.0000 q^{73} +8.00000 q^{74} +3.00000 q^{76} -5.00000 q^{77} +3.00000 q^{79} -1.00000 q^{80} +2.00000 q^{83} -6.00000 q^{85} +1.00000 q^{86} +1.00000 q^{88} +9.00000 q^{89} +20.0000 q^{91} +7.00000 q^{92} -3.00000 q^{95} +16.0000 q^{97} +18.0000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−5.00000	−1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	7.00000	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	0	0
$28$	−5.00000	−0.944911
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	5.00000	0.845154
$36$	0	0
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	3.00000	0.486664
$39$	0	0
$40$	−1.00000	−0.158114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	7.00000	1.03209
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	1.00000	0.141421
$51$	0	0
$52$	−4.00000	−0.554700
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	−5.00000	−0.668153
$57$	0	0
$58$	−8.00000	−1.05045
$59$	8.00000	1.04151	0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000	1.04151	0.520756	+	0.853706i	$0.325650\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	5.00000	0.597614
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	0	0
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	3.00000	0.344124
$77$	−5.00000	−0.569803
$78$	0	0
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	0	0
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	1.00000	0.107833
$87$	0	0
$88$	1.00000	0.106600
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	20.0000	2.09657
$92$	7.00000	0.729800
$93$	0	0
$94$	0	0
$95$	−3.00000	−0.307794
$96$	0	0
$97$	16.0000	1.62455	0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000	1.62455	0.812277	+	0.583272i	$0.198228\pi$
$98$	18.0000	1.81827
$99$	0	0
$100$	1.00000	0.100000
$101$	−15.0000	−1.49256	−0.746278	−	0.665635i	$-0.768161\pi$
$101$	−15.0000	−1.49256	−0.746278	+	0.665635i	$0.768161\pi$
$102$	0	0
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	−1.00000	−0.0971286
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	0	0
$109$	−12.0000	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$110$	−1.00000	−0.0953463
$111$	0	0
$112$	−5.00000	−0.472456
$113$	15.0000	1.41108	0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000	1.41108	0.705541	+	0.708669i	$0.250704\pi$
$114$	0	0
$115$	−7.00000	−0.652753
$116$	−8.00000	−0.742781
$117$	0	0
$118$	8.00000	0.736460
$119$	−30.0000	−2.75010
$120$	0	0
$121$	−10.0000	−0.909091
$122$	2.00000	0.181071
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	−15.0000	−1.30066
$134$	10.0000	0.863868
$135$	0	0
$136$	6.00000	0.514496
$137$	−20.0000	−1.70872	−0.854358	−	0.519685i	$-0.826049\pi$
$137$	−20.0000	−1.70872	−0.854358	+	0.519685i	$0.826049\pi$
$138$	0	0
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	5.00000	0.422577
$141$	0	0
$142$	−9.00000	−0.755263
$143$	−4.00000	−0.334497
$144$	0	0
$145$	8.00000	0.664364
$146$	11.0000	0.910366
$147$	0	0
$148$	8.00000	0.657596
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	3.00000	0.243332
$153$	0	0
$154$	−5.00000	−0.402911
$155$	1.00000	0.0803219
$156$	0	0
$157$	3.00000	0.239426	0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000	0.239426	0.119713	+	0.992809i	$0.461803\pi$
$158$	3.00000	0.238667
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	−35.0000	−2.75839
$162$	0	0
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	0	0
$165$	0	0
$166$	2.00000	0.155230
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	−6.00000	−0.460179
$171$	0	0
$172$	1.00000	0.0762493
$173$	−4.00000	−0.304114	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−4.00000	−0.304114	−0.152057	+	0.988372i	$0.548590\pi$
$174$	0	0
$175$	−5.00000	−0.377964
$176$	1.00000	0.0753778
$177$	0	0
$178$	9.00000	0.674579
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	20.0000	1.48250
$183$	0	0
$184$	7.00000	0.516047
$185$	−8.00000	−0.588172
$186$	0	0
$187$	6.00000	0.438763
$188$	0	0
$189$	0	0
$190$	−3.00000	−0.217643
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	16.0000	1.14873
$195$	0	0
$196$	18.0000	1.28571
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	19.0000	1.34687	0.673437	−	0.739244i	$-0.264817\pi$
$199$	19.0000	1.34687	0.673437	+	0.739244i	$0.264817\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	−15.0000	−1.05540
$203$	40.0000	2.80745
$204$	0	0
$205$	0	0
$206$	16.0000	1.11477
$207$	0	0
$208$	−4.00000	−0.277350
$209$	3.00000	0.207514
$210$	0	0
$211$	3.00000	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$212$	−1.00000	−0.0686803
$213$	0	0
$214$	9.00000	0.615227
$215$	−1.00000	−0.0681994
$216$	0	0
$217$	5.00000	0.339422
$218$	−12.0000	−0.812743
$219$	0	0
$220$	−1.00000	−0.0674200
$221$	−24.0000	−1.61441
$222$	0	0
$223$	12.0000	0.803579	0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000	0.803579	0.401790	+	0.915732i	$0.368388\pi$
$224$	−5.00000	−0.334077
$225$	0	0
$226$	15.0000	0.997785
$227$	21.0000	1.39382	0.696909	−	0.717159i	$-0.254558\pi$
$227$	21.0000	1.39382	0.696909	+	0.717159i	$0.254558\pi$
$228$	0	0
$229$	7.00000	0.462573	0.231287	−	0.972886i	$-0.425707\pi$
$229$	7.00000	0.462573	0.231287	+	0.972886i	$0.425707\pi$
$230$	−7.00000	−0.461566
$231$	0	0
$232$	−8.00000	−0.525226
$233$	−15.0000	−0.982683	−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000	−0.982683	−0.491341	+	0.870967i	$0.663493\pi$
$234$	0	0
$235$	0	0
$236$	8.00000	0.520756
$237$	0	0
$238$	−30.0000	−1.94461
$239$	26.0000	1.68180	0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000	1.68180	0.840900	+	0.541190i	$0.182026\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−10.0000	−0.642824
$243$	0	0
$244$	2.00000	0.128037
$245$	−18.0000	−1.14998
$246$	0	0
$247$	−12.0000	−0.763542
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	7.00000	0.440086
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−13.0000	−0.810918	−0.405459	−	0.914113i	$-0.632888\pi$
$257$	−13.0000	−0.810918	−0.405459	+	0.914113i	$0.632888\pi$
$258$	0	0
$259$	−40.0000	−2.48548
$260$	4.00000	0.248069
$261$	0	0
$262$	6.00000	0.370681
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	1.00000	0.0614295
$266$	−15.0000	−0.919709
$267$	0	0
$268$	10.0000	0.610847
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	29.0000	1.76162	0.880812	−	0.473466i	$-0.156997\pi$
$271$	29.0000	1.76162	0.880812	+	0.473466i	$0.156997\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−20.0000	−1.20824
$275$	1.00000	0.0603023
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−22.0000	−1.31947
$279$	0	0
$280$	5.00000	0.298807
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−9.00000	−0.534052
$285$	0	0
$286$	−4.00000	−0.236525
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	8.00000	0.469776
$291$	0	0
$292$	11.0000	0.643726
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	8.00000	0.464991
$297$	0	0
$298$	15.0000	0.868927
$299$	−28.0000	−1.61928
$300$	0	0
$301$	−5.00000	−0.288195
$302$	−16.0000	−0.920697
$303$	0	0
$304$	3.00000	0.172062
$305$	−2.00000	−0.114520
$306$	0	0
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	−5.00000	−0.284901
$309$	0	0
$310$	1.00000	0.0567962
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	0	0
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	3.00000	0.169300
$315$	0	0
$316$	3.00000	0.168763
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	−8.00000	−0.447914
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	−35.0000	−1.95047
$323$	18.0000	1.00155
$324$	0	0
$325$	−4.00000	−0.221880
$326$	−8.00000	−0.443079
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	10.0000	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$332$	2.00000	0.109764
$333$	0	0
$334$	3.00000	0.164153
$335$	−10.0000	−0.546358
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	−6.00000	−0.325396
$341$	−1.00000	−0.0541530
$342$	0	0
$343$	−55.0000	−2.96972
$344$	1.00000	0.0539164
$345$	0	0
$346$	−4.00000	−0.215041
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	34.0000	1.81998	0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000	1.81998	0.909989	+	0.414632i	$0.136090\pi$
$350$	−5.00000	−0.267261
$351$	0	0
$352$	1.00000	0.0533002
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	0	0
$355$	9.00000	0.477670
$356$	9.00000	0.476999
$357$	0	0
$358$	−20.0000	−1.05703
$359$	11.0000	0.580558	0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000	0.580558	0.290279	+	0.956942i	$0.406252\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−5.00000	−0.262794
$363$	0	0
$364$	20.0000	1.04828
$365$	−11.0000	−0.575766
$366$	0	0
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	7.00000	0.364900
$369$	0	0
$370$	−8.00000	−0.415900
$371$	5.00000	0.259587
$372$	0	0
$373$	−21.0000	−1.08734	−0.543669	−	0.839299i	$-0.682965\pi$
$373$	−21.0000	−1.08734	−0.543669	+	0.839299i	$0.682965\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	0	0
$377$	32.0000	1.64808
$378$	0	0
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	−3.00000	−0.153897
$381$	0	0
$382$	16.0000	0.818631
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	5.00000	0.254824
$386$	−10.0000	−0.508987
$387$	0	0
$388$	16.0000	0.812277
$389$	4.00000	0.202808	0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000	0.202808	0.101404	+	0.994845i	$0.467667\pi$
$390$	0	0
$391$	42.0000	2.12403
$392$	18.0000	0.909137
$393$	0	0
$394$	−10.0000	−0.503793
$395$	−3.00000	−0.150946
$396$	0	0
$397$	19.0000	0.953583	0.476791	−	0.879017i	$-0.341800\pi$
$397$	19.0000	0.953583	0.476791	+	0.879017i	$0.341800\pi$
$398$	19.0000	0.952384
$399$	0	0
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376	0.0249688	−	0.999688i	$-0.492051\pi$
$401$	1.00000	0.0499376	0.0249688	+	0.999688i	$0.492051\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	−15.0000	−0.746278
$405$	0	0
$406$	40.0000	1.98517
$407$	8.00000	0.396545
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	0	0
$411$	0	0
$412$	16.0000	0.788263
$413$	−40.0000	−1.96827
$414$	0	0
$415$	−2.00000	−0.0981761
$416$	−4.00000	−0.196116
$417$	0	0
$418$	3.00000	0.146735
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	3.00000	0.146038
$423$	0	0
$424$	−1.00000	−0.0485643
$425$	6.00000	0.291043
$426$	0	0
$427$	−10.0000	−0.483934
$428$	9.00000	0.435031
$429$	0	0
$430$	−1.00000	−0.0482243
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	5.00000	0.240008
$435$	0	0
$436$	−12.0000	−0.574696
$437$	21.0000	1.00457
$438$	0	0
$439$	−34.0000	−1.62273	−0.811366	−	0.584539i	$-0.801275\pi$
$439$	−34.0000	−1.62273	−0.811366	+	0.584539i	$0.801275\pi$
$440$	−1.00000	−0.0476731
$441$	0	0
$442$	−24.0000	−1.14156
$443$	31.0000	1.47285	0.736427	−	0.676517i	$-0.236511\pi$
$443$	31.0000	1.47285	0.736427	+	0.676517i	$0.236511\pi$
$444$	0	0
$445$	−9.00000	−0.426641
$446$	12.0000	0.568216
$447$	0	0
$448$	−5.00000	−0.236228
$449$	−2.00000	−0.0943858	−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000	−0.0943858	−0.0471929	+	0.998886i	$0.515028\pi$
$450$	0	0
$451$	0	0
$452$	15.0000	0.705541
$453$	0	0
$454$	21.0000	0.985579
$455$	−20.0000	−0.937614
$456$	0	0
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	7.00000	0.327089
$459$	0	0
$460$	−7.00000	−0.326377
$461$	−24.0000	−1.11779	−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000	−1.11779	−0.558896	+	0.829238i	$0.688775\pi$
$462$	0	0
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	−15.0000	−0.694862
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	−50.0000	−2.30879
$470$	0	0
$471$	0	0
$472$	8.00000	0.368230
$473$	1.00000	0.0459800
$474$	0	0
$475$	3.00000	0.137649
$476$	−30.0000	−1.37505
$477$	0	0
$478$	26.0000	1.18921
$479$	27.0000	1.23366	0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000	1.23366	0.616831	+	0.787096i	$0.288416\pi$
$480$	0	0
$481$	−32.0000	−1.45907
$482$	−10.0000	−0.455488
$483$	0	0
$484$	−10.0000	−0.454545
$485$	−16.0000	−0.726523
$486$	0	0
$487$	24.0000	1.08754	0.543772	−	0.839233i	$-0.316996\pi$
$487$	24.0000	1.08754	0.543772	+	0.839233i	$0.316996\pi$
$488$	2.00000	0.0905357
$489$	0	0
$490$	−18.0000	−0.813157
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	0	0
$493$	−48.0000	−2.16181
$494$	−12.0000	−0.539906
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	45.0000	2.01853
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−4.00000	−0.178529
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	0	0
$505$	15.0000	0.667491
$506$	7.00000	0.311188
$507$	0	0
$508$	16.0000	0.709885
$509$	10.0000	0.443242	0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000	0.443242	0.221621	+	0.975133i	$0.428865\pi$
$510$	0	0
$511$	−55.0000	−2.43306
$512$	1.00000	0.0441942
$513$	0	0
$514$	−13.0000	−0.573405
$515$	−16.0000	−0.705044
$516$	0	0
$517$	0	0
$518$	−40.0000	−1.75750
$519$	0	0
$520$	4.00000	0.175412
$521$	44.0000	1.92767	0.963837	−	0.266491i	$-0.0858642\pi$
$521$	44.0000	1.92767	0.963837	+	0.266491i	$0.0858642\pi$
$522$	0	0
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	−24.0000	−1.04645
$527$	−6.00000	−0.261364
$528$	0	0
$529$	26.0000	1.13043
$530$	1.00000	0.0434372
$531$	0	0
$532$	−15.0000	−0.650332
$533$	0	0
$534$	0	0
$535$	−9.00000	−0.389104
$536$	10.0000	0.431934
$537$	0	0
$538$	−18.0000	−0.776035
$539$	18.0000	0.775315
$540$	0	0
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	29.0000	1.24566
$543$	0	0
$544$	6.00000	0.257248
$545$	12.0000	0.514024
$546$	0	0
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	−20.0000	−0.854358
$549$	0	0
$550$	1.00000	0.0426401
$551$	−24.0000	−1.02243
$552$	0	0
$553$	−15.0000	−0.637865
$554$	8.00000	0.339887
$555$	0	0
$556$	−22.0000	−0.933008
$557$	7.00000	0.296600	0.148300	−	0.988942i	$-0.452620\pi$
$557$	7.00000	0.296600	0.148300	+	0.988942i	$0.452620\pi$
$558$	0	0
$559$	−4.00000	−0.169182
$560$	5.00000	0.211289
$561$	0	0
$562$	−12.0000	−0.506189
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	−15.0000	−0.631055
$566$	−4.00000	−0.168133
$567$	0	0
$568$	−9.00000	−0.377632
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	0	0
$571$	30.0000	1.25546	0.627730	−	0.778431i	$-0.283984\pi$
$571$	30.0000	1.25546	0.627730	+	0.778431i	$0.283984\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	0	0
$575$	7.00000	0.291920
$576$	0	0
$577$	−8.00000	−0.333044	−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000	−0.333044	−0.166522	+	0.986038i	$0.553254\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	8.00000	0.332182
$581$	−10.0000	−0.414870
$582$	0	0
$583$	−1.00000	−0.0414158
$584$	11.0000	0.455183
$585$	0	0
$586$	−24.0000	−0.991431
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	−3.00000	−0.123613
$590$	−8.00000	−0.329355
$591$	0	0
$592$	8.00000	0.328798
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	0	0
$595$	30.0000	1.22988
$596$	15.0000	0.614424
$597$	0	0
$598$	−28.0000	−1.14501
$599$	17.0000	0.694601	0.347301	−	0.937754i	$-0.387098\pi$
$599$	17.0000	0.694601	0.347301	+	0.937754i	$0.387098\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−5.00000	−0.203785
$603$	0	0
$604$	−16.0000	−0.651031
$605$	10.0000	0.406558
$606$	0	0
$607$	31.0000	1.25825	0.629126	−	0.777304i	$-0.283413\pi$
$607$	31.0000	1.25825	0.629126	+	0.777304i	$0.283413\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	0	0
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	12.0000	0.484281
$615$	0	0
$616$	−5.00000	−0.201456
$617$	−33.0000	−1.32853	−0.664265	−	0.747497i	$-0.731255\pi$
$617$	−33.0000	−1.32853	−0.664265	+	0.747497i	$0.731255\pi$
$618$	0	0
$619$	6.00000	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$619$	6.00000	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$620$	1.00000	0.0401610
$621$	0	0
$622$	−16.0000	−0.641542
$623$	−45.0000	−1.80289
$624$	0	0
$625$	1.00000	0.0400000
$626$	18.0000	0.719425
$627$	0	0
$628$	3.00000	0.119713
$629$	48.0000	1.91389
$630$	0	0
$631$	13.0000	0.517522	0.258761	−	0.965941i	$-0.416686\pi$
$631$	13.0000	0.517522	0.258761	+	0.965941i	$0.416686\pi$
$632$	3.00000	0.119334
$633$	0	0
$634$	18.0000	0.714871
$635$	−16.0000	−0.634941
$636$	0	0
$637$	−72.0000	−2.85274
$638$	−8.00000	−0.316723
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	−25.0000	−0.985904	−0.492952	−	0.870057i	$-0.664082\pi$
$643$	−25.0000	−0.985904	−0.492952	+	0.870057i	$0.664082\pi$
$644$	−35.0000	−1.37919
$645$	0	0
$646$	18.0000	0.708201
$647$	−15.0000	−0.589711	−0.294855	−	0.955542i	$-0.595271\pi$
$647$	−15.0000	−0.589711	−0.294855	+	0.955542i	$0.595271\pi$
$648$	0	0
$649$	8.00000	0.314027
$650$	−4.00000	−0.156893
$651$	0	0
$652$	−8.00000	−0.313304
$653$	−38.0000	−1.48705	−0.743527	−	0.668705i	$-0.766849\pi$
$653$	−38.0000	−1.48705	−0.743527	+	0.668705i	$0.766849\pi$
$654$	0	0
$655$	−6.00000	−0.234439
$656$	0	0
$657$	0	0
$658$	0	0
$659$	16.0000	0.623272	0.311636	−	0.950202i	$-0.399123\pi$
$659$	16.0000	0.623272	0.311636	+	0.950202i	$0.399123\pi$
$660$	0	0
$661$	16.0000	0.622328	0.311164	−	0.950356i	$-0.399281\pi$
$661$	16.0000	0.622328	0.311164	+	0.950356i	$0.399281\pi$
$662$	10.0000	0.388661
$663$	0	0
$664$	2.00000	0.0776151
$665$	15.0000	0.581675
$666$	0	0
$667$	−56.0000	−2.16833
$668$	3.00000	0.116073
$669$	0	0
$670$	−10.0000	−0.386334
$671$	2.00000	0.0772091
$672$	0	0
$673$	−42.0000	−1.61898	−0.809491	−	0.587133i	$-0.800257\pi$
$673$	−42.0000	−1.61898	−0.809491	+	0.587133i	$0.800257\pi$
$674$	−14.0000	−0.539260
$675$	0	0
$676$	3.00000	0.115385
$677$	15.0000	0.576497	0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000	0.576497	0.288248	+	0.957556i	$0.406927\pi$
$678$	0	0
$679$	−80.0000	−3.07012
$680$	−6.00000	−0.230089
$681$	0	0
$682$	−1.00000	−0.0382920
$683$	−19.0000	−0.727015	−0.363507	−	0.931591i	$-0.618421\pi$
$683$	−19.0000	−0.727015	−0.363507	+	0.931591i	$0.618421\pi$
$684$	0	0
$685$	20.0000	0.764161
$686$	−55.0000	−2.09991
$687$	0	0
$688$	1.00000	0.0381246
$689$	4.00000	0.152388
$690$	0	0
$691$	−33.0000	−1.25538	−0.627690	−	0.778464i	$-0.715999\pi$
$691$	−33.0000	−1.25538	−0.627690	+	0.778464i	$0.715999\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	0	0
$695$	22.0000	0.834508
$696$	0	0
$697$	0	0
$698$	34.0000	1.28692
$699$	0	0
$700$	−5.00000	−0.188982
$701$	−35.0000	−1.32193	−0.660966	−	0.750416i	$-0.729853\pi$
$701$	−35.0000	−1.32193	−0.660966	+	0.750416i	$0.729853\pi$
$702$	0	0
$703$	24.0000	0.905177
$704$	1.00000	0.0376889
$705$	0	0
$706$	−26.0000	−0.978523
$707$	75.0000	2.82067
$708$	0	0
$709$	1.00000	0.0375558	0.0187779	−	0.999824i	$-0.494022\pi$
$709$	1.00000	0.0375558	0.0187779	+	0.999824i	$0.494022\pi$
$710$	9.00000	0.337764
$711$	0	0
$712$	9.00000	0.337289
$713$	−7.00000	−0.262152
$714$	0	0
$715$	4.00000	0.149592
$716$	−20.0000	−0.747435
$717$	0	0
$718$	11.0000	0.410516
$719$	−4.00000	−0.149175	−0.0745874	−	0.997214i	$-0.523764\pi$
$719$	−4.00000	−0.149175	−0.0745874	+	0.997214i	$0.523764\pi$
$720$	0	0
$721$	−80.0000	−2.97936
$722$	−10.0000	−0.372161
$723$	0	0
$724$	−5.00000	−0.185824
$725$	−8.00000	−0.297113
$726$	0	0
$727$	11.0000	0.407967	0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000	0.407967	0.203984	+	0.978974i	$0.434611\pi$
$728$	20.0000	0.741249
$729$	0	0
$730$	−11.0000	−0.407128
$731$	6.00000	0.221918
$732$	0	0
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	12.0000	0.442928
$735$	0	0
$736$	7.00000	0.258023
$737$	10.0000	0.368355
$738$	0	0
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	5.00000	0.183556
$743$	21.0000	0.770415	0.385208	−	0.922830i	$-0.374130\pi$
$743$	21.0000	0.770415	0.385208	+	0.922830i	$0.374130\pi$
$744$	0	0
$745$	−15.0000	−0.549557
$746$	−21.0000	−0.768865
$747$	0	0
$748$	6.00000	0.219382
$749$	−45.0000	−1.64426
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	0	0
$753$	0	0
$754$	32.0000	1.16537
$755$	16.0000	0.582300
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−15.0000	−0.544825
$759$	0	0
$760$	−3.00000	−0.108821
$761$	−43.0000	−1.55875	−0.779374	−	0.626559i	$-0.784463\pi$
$761$	−43.0000	−1.55875	−0.779374	+	0.626559i	$0.784463\pi$
$762$	0	0
$763$	60.0000	2.17215
$764$	16.0000	0.578860
$765$	0	0
$766$	0	0
$767$	−32.0000	−1.15545
$768$	0	0
$769$	−35.0000	−1.26213	−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000	−1.26213	−0.631066	+	0.775729i	$0.717382\pi$
$770$	5.00000	0.180187
$771$	0	0
$772$	−10.0000	−0.359908
$773$	1.00000	0.0359675	0.0179838	−	0.999838i	$-0.494275\pi$
$773$	1.00000	0.0359675	0.0179838	+	0.999838i	$0.494275\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	16.0000	0.574367
$777$	0	0
$778$	4.00000	0.143407
$779$	0	0
$780$	0	0
$781$	−9.00000	−0.322045
$782$	42.0000	1.50192
$783$	0	0
$784$	18.0000	0.642857
$785$	−3.00000	−0.107075
$786$	0	0
$787$	21.0000	0.748569	0.374285	−	0.927314i	$-0.377888\pi$
$787$	21.0000	0.748569	0.374285	+	0.927314i	$0.377888\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	−3.00000	−0.106735
$791$	−75.0000	−2.66669
$792$	0	0
$793$	−8.00000	−0.284088
$794$	19.0000	0.674285
$795$	0	0
$796$	19.0000	0.673437
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	0	0
$802$	1.00000	0.0353112
$803$	11.0000	0.388182
$804$	0	0
$805$	35.0000	1.23359
$806$	4.00000	0.140894
$807$	0	0
$808$	−15.0000	−0.527698
$809$	45.0000	1.58212	0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000	1.58212	0.791058	+	0.611741i	$0.209531\pi$
$810$	0	0
$811$	39.0000	1.36948	0.684738	−	0.728790i	$-0.259917\pi$
$811$	39.0000	1.36948	0.684738	+	0.728790i	$0.259917\pi$
$812$	40.0000	1.40372
$813$	0	0
$814$	8.00000	0.280400
$815$	8.00000	0.280228
$816$	0	0
$817$	3.00000	0.104957
$818$	34.0000	1.18878
$819$	0	0
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	16.0000	0.557386
$825$	0	0
$826$	−40.0000	−1.39178
$827$	−38.0000	−1.32139	−0.660695	−	0.750655i	$-0.729738\pi$
$827$	−38.0000	−1.32139	−0.660695	+	0.750655i	$0.729738\pi$
$828$	0	0
$829$	47.0000	1.63238	0.816189	−	0.577785i	$-0.196083\pi$
$829$	47.0000	1.63238	0.816189	+	0.577785i	$0.196083\pi$
$830$	−2.00000	−0.0694210
$831$	0	0
$832$	−4.00000	−0.138675
$833$	108.000	3.74198
$834$	0	0
$835$	−3.00000	−0.103819
$836$	3.00000	0.103757
$837$	0	0
$838$	20.0000	0.690889
$839$	−41.0000	−1.41548	−0.707739	−	0.706474i	$-0.750285\pi$
$839$	−41.0000	−1.41548	−0.707739	+	0.706474i	$0.750285\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	28.0000	0.964944
$843$	0	0
$844$	3.00000	0.103264
$845$	−3.00000	−0.103203
$846$	0	0
$847$	50.0000	1.71802
$848$	−1.00000	−0.0343401
$849$	0	0
$850$	6.00000	0.205798
$851$	56.0000	1.91966
$852$	0	0
$853$	15.0000	0.513590	0.256795	−	0.966466i	$-0.417333\pi$
$853$	15.0000	0.513590	0.256795	+	0.966466i	$0.417333\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	9.00000	0.307614
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−1.00000	−0.0340997
$861$	0	0
$862$	0	0
$863$	53.0000	1.80414	0.902070	−	0.431589i	$-0.142047\pi$
$863$	53.0000	1.80414	0.902070	+	0.431589i	$0.142047\pi$
$864$	0	0
$865$	4.00000	0.136004
$866$	−11.0000	−0.373795
$867$	0	0
$868$	5.00000	0.169711
$869$	3.00000	0.101768
$870$	0	0
$871$	−40.0000	−1.35535
$872$	−12.0000	−0.406371
$873$	0	0
$874$	21.0000	0.710336
$875$	5.00000	0.169031
$876$	0	0
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	−34.0000	−1.14744
$879$	0	0
$880$	−1.00000	−0.0337100
$881$	−34.0000	−1.14549	−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000	−1.14549	−0.572745	+	0.819734i	$0.694121\pi$
$882$	0	0
$883$	3.00000	0.100958	0.0504790	−	0.998725i	$-0.483925\pi$
$883$	3.00000	0.100958	0.0504790	+	0.998725i	$0.483925\pi$
$884$	−24.0000	−0.807207
$885$	0	0
$886$	31.0000	1.04147
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	0	0
$889$	−80.0000	−2.68311
$890$	−9.00000	−0.301681
$891$	0	0
$892$	12.0000	0.401790
$893$	0	0
$894$	0	0
$895$	20.0000	0.668526
$896$	−5.00000	−0.167038
$897$	0	0
$898$	−2.00000	−0.0667409
$899$	8.00000	0.266815
$900$	0	0
$901$	−6.00000	−0.199889
$902$	0	0
$903$	0	0
$904$	15.0000	0.498893
$905$	5.00000	0.166206
$906$	0	0
$907$	−54.0000	−1.79304	−0.896520	−	0.443003i	$-0.853913\pi$
$907$	−54.0000	−1.79304	−0.896520	+	0.443003i	$0.853913\pi$
$908$	21.0000	0.696909
$909$	0	0
$910$	−20.0000	−0.662994
$911$	−42.0000	−1.39152	−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000	−1.39152	−0.695761	+	0.718273i	$0.744933\pi$
$912$	0	0
$913$	2.00000	0.0661903
$914$	26.0000	0.860004
$915$	0	0
$916$	7.00000	0.231287
$917$	−30.0000	−0.990687
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	−7.00000	−0.230783
$921$	0	0
$922$	−24.0000	−0.790398
$923$	36.0000	1.18495
$924$	0	0
$925$	8.00000	0.263038
$926$	−20.0000	−0.657241
$927$	0	0
$928$	−8.00000	−0.262613
$929$	−1.00000	−0.0328089	−0.0164045	−	0.999865i	$-0.505222\pi$
$929$	−1.00000	−0.0328089	−0.0164045	+	0.999865i	$0.505222\pi$
$930$	0	0
$931$	54.0000	1.76978
$932$	−15.0000	−0.491341
$933$	0	0
$934$	12.0000	0.392652
$935$	−6.00000	−0.196221
$936$	0	0
$937$	−50.0000	−1.63343	−0.816714	−	0.577042i	$-0.804207\pi$
$937$	−50.0000	−1.63343	−0.816714	+	0.577042i	$0.804207\pi$
$938$	−50.0000	−1.63256
$939$	0	0
$940$	0	0
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	0	0
$943$	0	0
$944$	8.00000	0.260378
$945$	0	0
$946$	1.00000	0.0325128
$947$	−38.0000	−1.23483	−0.617417	−	0.786636i	$-0.711821\pi$
$947$	−38.0000	−1.23483	−0.617417	+	0.786636i	$0.711821\pi$
$948$	0	0
$949$	−44.0000	−1.42830
$950$	3.00000	0.0973329
$951$	0	0
$952$	−30.0000	−0.972306
$953$	40.0000	1.29573	0.647864	−	0.761756i	$-0.275663\pi$
$953$	40.0000	1.29573	0.647864	+	0.761756i	$0.275663\pi$
$954$	0	0
$955$	−16.0000	−0.517748
$956$	26.0000	0.840900
$957$	0	0
$958$	27.0000	0.872330
$959$	100.000	3.22917
$960$	0	0
$961$	1.00000	0.0322581
$962$	−32.0000	−1.03172
$963$	0	0
$964$	−10.0000	−0.322078
$965$	10.0000	0.321911
$966$	0	0
$967$	30.0000	0.964735	0.482367	−	0.875969i	$-0.339777\pi$
$967$	30.0000	0.964735	0.482367	+	0.875969i	$0.339777\pi$
$968$	−10.0000	−0.321412
$969$	0	0
$970$	−16.0000	−0.513729
$971$	−50.0000	−1.60458	−0.802288	−	0.596937i	$-0.796384\pi$
$971$	−50.0000	−1.60458	−0.802288	+	0.596937i	$0.796384\pi$
$972$	0	0
$973$	110.000	3.52644
$974$	24.0000	0.769010
$975$	0	0
$976$	2.00000	0.0640184
$977$	−22.0000	−0.703842	−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000	−0.703842	−0.351921	+	0.936030i	$0.614471\pi$
$978$	0	0
$979$	9.00000	0.287641
$980$	−18.0000	−0.574989
$981$	0	0
$982$	−15.0000	−0.478669
$983$	20.0000	0.637901	0.318950	−	0.947771i	$-0.396670\pi$
$983$	20.0000	0.637901	0.318950	+	0.947771i	$0.396670\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	−48.0000	−1.52863
$987$	0	0
$988$	−12.0000	−0.381771
$989$	7.00000	0.222587
$990$	0	0
$991$	−17.0000	−0.540023	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	−17.0000	−0.540023	−0.270011	+	0.962857i	$0.587027\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	45.0000	1.42731
$995$	−19.0000	−0.602340
$996$	0	0
$997$	−26.0000	−0.823428	−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000	−0.823428	−0.411714	+	0.911313i	$0.635070\pi$
$998$	−4.00000	−0.126618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.a.n.1.1	yes	1
3.2	odd	2		2790.2.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2790.2.a.d.1.1	✓	1	3.2	odd	2
2790.2.a.n.1.1	yes	1	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:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more