LMFDB - Embedded newform 2790.2.a.x.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:	$1$
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)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -3.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{10} -5.00000 q^{11} -3.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{19} +1.00000 q^{20} -5.00000 q^{22} +7.00000 q^{23} +1.00000 q^{25} -3.00000 q^{28} +4.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} -3.00000 q^{35} -8.00000 q^{37} -1.00000 q^{38} +1.00000 q^{40} -12.0000 q^{41} -1.00000 q^{43} -5.00000 q^{44} +7.00000 q^{46} -12.0000 q^{47} +2.00000 q^{49} +1.00000 q^{50} -5.00000 q^{53} -5.00000 q^{55} -3.00000 q^{56} +4.00000 q^{58} -8.00000 q^{59} -6.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} -2.00000 q^{68} -3.00000 q^{70} -3.00000 q^{71} -15.0000 q^{73} -8.00000 q^{74} -1.00000 q^{76} +15.0000 q^{77} -1.00000 q^{79} +1.00000 q^{80} -12.0000 q^{82} +6.00000 q^{83} -2.00000 q^{85} -1.00000 q^{86} -5.00000 q^{88} +15.0000 q^{89} +7.00000 q^{92} -12.0000 q^{94} -1.00000 q^{95} +16.0000 q^{97} +2.00000 q^{98} +O(q^{100})$

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
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	1.00000	0.316228
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−5.00000	−1.06600
$23$	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
$26$	0	0
$27$	0	0
$28$	−3.00000	−0.566947
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−3.00000	−0.507093
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	1.00000	0.158114
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	7.00000	1.03209
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	1.00000	0.141421
$51$	0	0
$52$	0	0
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	−3.00000	−0.400892
$57$	0	0
$58$	4.00000	0.525226
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	−3.00000	−0.358569
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	0	0
$73$	−15.0000	−1.75562	−0.877809	−	0.479012i	$-0.840995\pi$
$73$	−15.0000	−1.75562	−0.877809	+	0.479012i	$0.840995\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−1.00000	−0.114708
$77$	15.0000	1.70941
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	−12.0000	−1.32518
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−1.00000	−0.107833
$87$	0	0
$88$	−5.00000	−0.533002
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	0	0
$92$	7.00000	0.729800
$93$	0	0
$94$	−12.0000	−1.23771
$95$	−1.00000	−0.102598
$96$	0	0
$97$	16.0000	1.62455	0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000	1.62455	0.812277	+	0.583272i	$0.198228\pi$
$98$	2.00000	0.202031
$99$	0	0
$100$	1.00000	0.100000
$101$	7.00000	0.696526	0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000	0.696526	0.348263	+	0.937397i	$0.386772\pi$
$102$	0	0
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	0	0
$105$	0	0
$106$	−5.00000	−0.485643
$107$	−7.00000	−0.676716	−0.338358	−	0.941018i	$-0.609871\pi$
$107$	−7.00000	−0.676716	−0.338358	+	0.941018i	$0.609871\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	−5.00000	−0.476731
$111$	0	0
$112$	−3.00000	−0.283473
$113$	19.0000	1.78737	0.893685	−	0.448695i	$-0.148111\pi$
$113$	19.0000	1.78737	0.893685	+	0.448695i	$0.148111\pi$
$114$	0	0
$115$	7.00000	0.652753
$116$	4.00000	0.371391
$117$	0	0
$118$	−8.00000	−0.736460
$119$	6.00000	0.550019
$120$	0	0
$121$	14.0000	1.27273
$122$	−6.00000	−0.543214
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	−2.00000	−0.172774
$135$	0	0
$136$	−2.00000	−0.171499
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	−3.00000	−0.253546
$141$	0	0
$142$	−3.00000	−0.251754
$143$	0	0
$144$	0	0
$145$	4.00000	0.332182
$146$	−15.0000	−1.24141
$147$	0	0
$148$	−8.00000	−0.657596
$149$	−7.00000	−0.573462	−0.286731	−	0.958011i	$-0.592569\pi$
$149$	−7.00000	−0.573462	−0.286731	+	0.958011i	$0.592569\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	15.0000	1.20873
$155$	−1.00000	−0.0803219
$156$	0	0
$157$	9.00000	0.718278	0.359139	−	0.933284i	$-0.383070\pi$
$157$	9.00000	0.718278	0.359139	+	0.933284i	$0.383070\pi$
$158$	−1.00000	−0.0795557
$159$	0	0
$160$	1.00000	0.0790569
$161$	−21.0000	−1.65503
$162$	0	0
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−12.0000	−0.937043
$165$	0	0
$166$	6.00000	0.465690
$167$	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
$169$	−13.0000	−1.00000
$170$	−2.00000	−0.153393
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	20.0000	1.52057	0.760286	−	0.649589i	$-0.225059\pi$
$173$	20.0000	1.52057	0.760286	+	0.649589i	$0.225059\pi$
$174$	0	0
$175$	−3.00000	−0.226779
$176$	−5.00000	−0.376889
$177$	0	0
$178$	15.0000	1.12430
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	0	0
$181$	−21.0000	−1.56092	−0.780459	−	0.625207i	$-0.785014\pi$
$181$	−21.0000	−1.56092	−0.780459	+	0.625207i	$0.785014\pi$
$182$	0	0
$183$	0	0
$184$	7.00000	0.516047
$185$	−8.00000	−0.588172
$186$	0	0
$187$	10.0000	0.731272
$188$	−12.0000	−0.875190
$189$	0	0
$190$	−1.00000	−0.0725476
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	26.0000	1.87152	0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000	1.87152	0.935760	+	0.352636i	$0.114715\pi$
$194$	16.0000	1.14873
$195$	0	0
$196$	2.00000	0.142857
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	0	0
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	7.00000	0.492518
$203$	−12.0000	−0.842235
$204$	0	0
$205$	−12.0000	−0.838116
$206$	−16.0000	−1.11477
$207$	0	0
$208$	0	0
$209$	5.00000	0.345857
$210$	0	0
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	−5.00000	−0.343401
$213$	0	0
$214$	−7.00000	−0.478510
$215$	−1.00000	−0.0681994
$216$	0	0
$217$	3.00000	0.203653
$218$	0	0
$219$	0	0
$220$	−5.00000	−0.337100
$221$	0	0
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	19.0000	1.26386
$227$	−11.0000	−0.730096	−0.365048	−	0.930989i	$-0.618947\pi$
$227$	−11.0000	−0.730096	−0.365048	+	0.930989i	$0.618947\pi$
$228$	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
$232$	4.00000	0.262613
$233$	5.00000	0.327561	0.163780	−	0.986497i	$-0.447631\pi$
$233$	5.00000	0.327561	0.163780	+	0.986497i	$0.447631\pi$
$234$	0	0
$235$	−12.0000	−0.782794
$236$	−8.00000	−0.520756
$237$	0	0
$238$	6.00000	0.388922
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	−6.00000	−0.384111
$245$	2.00000	0.127775
$246$	0	0
$247$	0	0
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	1.00000	0.0632456
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	0	0
$253$	−35.0000	−2.20043
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−1.00000	−0.0623783	−0.0311891	−	0.999514i	$-0.509929\pi$
$257$	−1.00000	−0.0623783	−0.0311891	+	0.999514i	$0.509929\pi$
$258$	0	0
$259$	24.0000	1.49129
$260$	0	0
$261$	0	0
$262$	10.0000	0.617802
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	−5.00000	−0.307148
$266$	3.00000	0.183942
$267$	0	0
$268$	−2.00000	−0.122169
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−23.0000	−1.39715	−0.698575	−	0.715537i	$-0.746182\pi$
$271$	−23.0000	−1.39715	−0.698575	+	0.715537i	$0.746182\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	12.0000	0.724947
$275$	−5.00000	−0.301511
$276$	0	0
$277$	12.0000	0.721010	0.360505	−	0.932757i	$-0.382604\pi$
$277$	12.0000	0.721010	0.360505	+	0.932757i	$0.382604\pi$
$278$	−10.0000	−0.599760
$279$	0	0
$280$	−3.00000	−0.179284
$281$	20.0000	1.19310	0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000	1.19310	0.596550	+	0.802576i	$0.296538\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−3.00000	−0.178017
$285$	0	0
$286$	0	0
$287$	36.0000	2.12501
$288$	0	0
$289$	−13.0000	−0.764706
$290$	4.00000	0.234888
$291$	0	0
$292$	−15.0000	−0.877809
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	−8.00000	−0.464991
$297$	0	0
$298$	−7.00000	−0.405499
$299$	0	0
$300$	0	0
$301$	3.00000	0.172917
$302$	−8.00000	−0.460348
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	−6.00000	−0.343559
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	15.0000	0.854704
$309$	0	0
$310$	−1.00000	−0.0567962
$311$	−32.0000	−1.81455	−0.907277	−	0.420534i	$-0.861843\pi$
$311$	−32.0000	−1.81455	−0.907277	+	0.420534i	$0.861843\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	9.00000	0.507899
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	0	0
$319$	−20.0000	−1.11979
$320$	1.00000	0.0559017
$321$	0	0
$322$	−21.0000	−1.17028
$323$	2.00000	0.111283
$324$	0	0
$325$	0	0
$326$	−12.0000	−0.664619
$327$	0	0
$328$	−12.0000	−0.662589
$329$	36.0000	1.98474
$330$	0	0
$331$	−30.0000	−1.64895	−0.824475	−	0.565899i	$-0.808529\pi$
$331$	−30.0000	−1.64895	−0.824475	+	0.565899i	$0.808529\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	3.00000	0.164153
$335$	−2.00000	−0.109272
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	−13.0000	−0.707107
$339$	0	0
$340$	−2.00000	−0.108465
$341$	5.00000	0.270765
$342$	0	0
$343$	15.0000	0.809924
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	20.0000	1.07521
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	0	0
$349$	34.0000	1.81998	0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000	1.81998	0.909989	+	0.414632i	$0.136090\pi$
$350$	−3.00000	−0.160357
$351$	0	0
$352$	−5.00000	−0.266501
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−3.00000	−0.159223
$356$	15.0000	0.794998
$357$	0	0
$358$	4.00000	0.211407
$359$	17.0000	0.897226	0.448613	−	0.893726i	$-0.351918\pi$
$359$	17.0000	0.897226	0.448613	+	0.893726i	$0.351918\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	−21.0000	−1.10374
$363$	0	0
$364$	0	0
$365$	−15.0000	−0.785136
$366$	0	0
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	7.00000	0.364900
$369$	0	0
$370$	−8.00000	−0.415900
$371$	15.0000	0.778761
$372$	0	0
$373$	1.00000	0.0517780	0.0258890	−	0.999665i	$-0.491758\pi$
$373$	1.00000	0.0517780	0.0258890	+	0.999665i	$0.491758\pi$
$374$	10.0000	0.517088
$375$	0	0
$376$	−12.0000	−0.618853
$377$	0	0
$378$	0	0
$379$	13.0000	0.667765	0.333883	−	0.942615i	$-0.391641\pi$
$379$	13.0000	0.667765	0.333883	+	0.942615i	$0.391641\pi$
$380$	−1.00000	−0.0512989
$381$	0	0
$382$	8.00000	0.409316
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	15.0000	0.764471
$386$	26.0000	1.32337
$387$	0	0
$388$	16.0000	0.812277
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	0	0
$391$	−14.0000	−0.708010
$392$	2.00000	0.101015
$393$	0	0
$394$	22.0000	1.10834
$395$	−1.00000	−0.0503155
$396$	0	0
$397$	−23.0000	−1.15434	−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000	−1.15434	−0.577168	+	0.816625i	$0.695842\pi$
$398$	−17.0000	−0.852133
$399$	0	0
$400$	1.00000	0.0500000
$401$	−17.0000	−0.848939	−0.424470	−	0.905442i	$-0.639539\pi$
$401$	−17.0000	−0.848939	−0.424470	+	0.905442i	$0.639539\pi$
$402$	0	0
$403$	0	0
$404$	7.00000	0.348263
$405$	0	0
$406$	−12.0000	−0.595550
$407$	40.0000	1.98273
$408$	0	0
$409$	−30.0000	−1.48340	−0.741702	−	0.670729i	$-0.765981\pi$
$409$	−30.0000	−1.48340	−0.741702	+	0.670729i	$0.765981\pi$
$410$	−12.0000	−0.592638
$411$	0	0
$412$	−16.0000	−0.788263
$413$	24.0000	1.18096
$414$	0	0
$415$	6.00000	0.294528
$416$	0	0
$417$	0	0
$418$	5.00000	0.244558
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−4.00000	−0.194948	−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000	−0.194948	−0.0974740	+	0.995238i	$0.531076\pi$
$422$	23.0000	1.11962
$423$	0	0
$424$	−5.00000	−0.242821
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	18.0000	0.871081
$428$	−7.00000	−0.338358
$429$	0	0
$430$	−1.00000	−0.0482243
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	3.00000	0.144005
$435$	0	0
$436$	0	0
$437$	−7.00000	−0.334855
$438$	0	0
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	−5.00000	−0.238366
$441$	0	0
$442$	0	0
$443$	−41.0000	−1.94797	−0.973984	−	0.226615i	$-0.927234\pi$
$443$	−41.0000	−1.94797	−0.973984	+	0.226615i	$0.927234\pi$
$444$	0	0
$445$	15.0000	0.711068
$446$	−8.00000	−0.378811
$447$	0	0
$448$	−3.00000	−0.141737
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	0	0
$451$	60.0000	2.82529
$452$	19.0000	0.893685
$453$	0	0
$454$	−11.0000	−0.516256
$455$	0	0
$456$	0	0
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	7.00000	0.327089
$459$	0	0
$460$	7.00000	0.326377
$461$	−16.0000	−0.745194	−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000	−0.745194	−0.372597	+	0.927993i	$0.621533\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	5.00000	0.231621
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	0	0
$469$	6.00000	0.277054
$470$	−12.0000	−0.553519
$471$	0	0
$472$	−8.00000	−0.368230
$473$	5.00000	0.229900
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	6.00000	0.275010
$477$	0	0
$478$	−6.00000	−0.274434
$479$	33.0000	1.50781	0.753904	−	0.656984i	$-0.228168\pi$
$479$	33.0000	1.50781	0.753904	+	0.656984i	$0.228168\pi$
$480$	0	0
$481$	0	0
$482$	10.0000	0.455488
$483$	0	0
$484$	14.0000	0.636364
$485$	16.0000	0.726523
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	−6.00000	−0.271607
$489$	0	0
$490$	2.00000	0.0903508
$491$	−5.00000	−0.225647	−0.112823	−	0.993615i	$-0.535989\pi$
$491$	−5.00000	−0.225647	−0.112823	+	0.993615i	$0.535989\pi$
$492$	0	0
$493$	−8.00000	−0.360302
$494$	0	0
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	9.00000	0.403705
$498$	0	0
$499$	−32.0000	−1.43252	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000	−1.43252	−0.716258	+	0.697835i	$0.754147\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	4.00000	0.178529
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	0	0
$505$	7.00000	0.311496
$506$	−35.0000	−1.55594
$507$	0	0
$508$	−8.00000	−0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	45.0000	1.99068
$512$	1.00000	0.0441942
$513$	0	0
$514$	−1.00000	−0.0441081
$515$	−16.0000	−0.705044
$516$	0	0
$517$	60.0000	2.63880
$518$	24.0000	1.05450
$519$	0	0
$520$	0	0
$521$	−16.0000	−0.700973	−0.350486	−	0.936568i	$-0.613984\pi$
$521$	−16.0000	−0.700973	−0.350486	+	0.936568i	$0.613984\pi$
$522$	0	0
$523$	11.0000	0.480996	0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000	0.480996	0.240498	+	0.970650i	$0.422689\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	0	0
$527$	2.00000	0.0871214
$528$	0	0
$529$	26.0000	1.13043
$530$	−5.00000	−0.217186
$531$	0	0
$532$	3.00000	0.130066
$533$	0	0
$534$	0	0
$535$	−7.00000	−0.302636
$536$	−2.00000	−0.0863868
$537$	0	0
$538$	−6.00000	−0.258678
$539$	−10.0000	−0.430730
$540$	0	0
$541$	−4.00000	−0.171973	−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000	−0.171973	−0.0859867	+	0.996296i	$0.527404\pi$
$542$	−23.0000	−0.987935
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	0	0
$547$	10.0000	0.427569	0.213785	−	0.976881i	$-0.431421\pi$
$547$	10.0000	0.427569	0.213785	+	0.976881i	$0.431421\pi$
$548$	12.0000	0.512615
$549$	0	0
$550$	−5.00000	−0.213201
$551$	−4.00000	−0.170406
$552$	0	0
$553$	3.00000	0.127573
$554$	12.0000	0.509831
$555$	0	0
$556$	−10.0000	−0.424094
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	0	0
$559$	0	0
$560$	−3.00000	−0.126773
$561$	0	0
$562$	20.0000	0.843649
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	19.0000	0.799336
$566$	0	0
$567$	0	0
$568$	−3.00000	−0.125877
$569$	−33.0000	−1.38343	−0.691716	−	0.722170i	$-0.743145\pi$
$569$	−33.0000	−1.38343	−0.691716	+	0.722170i	$0.743145\pi$
$570$	0	0
$571$	46.0000	1.92504	0.962520	−	0.271211i	$-0.0874240\pi$
$571$	46.0000	1.92504	0.962520	+	0.271211i	$0.0874240\pi$
$572$	0	0
$573$	0	0
$574$	36.0000	1.50261
$575$	7.00000	0.291920
$576$	0	0
$577$	−12.0000	−0.499567	−0.249783	−	0.968302i	$-0.580359\pi$
$577$	−12.0000	−0.499567	−0.249783	+	0.968302i	$0.580359\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	4.00000	0.166091
$581$	−18.0000	−0.746766
$582$	0	0
$583$	25.0000	1.03539
$584$	−15.0000	−0.620704
$585$	0	0
$586$	24.0000	0.991431
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	1.00000	0.0412043
$590$	−8.00000	−0.329355
$591$	0	0
$592$	−8.00000	−0.328798
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	6.00000	0.245976
$596$	−7.00000	−0.286731
$597$	0	0
$598$	0	0
$599$	−5.00000	−0.204294	−0.102147	−	0.994769i	$-0.532571\pi$
$599$	−5.00000	−0.204294	−0.102147	+	0.994769i	$0.532571\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	3.00000	0.122271
$603$	0	0
$604$	−8.00000	−0.325515
$605$	14.0000	0.569181
$606$	0	0
$607$	9.00000	0.365299	0.182649	−	0.983178i	$-0.441533\pi$
$607$	9.00000	0.365299	0.182649	+	0.983178i	$0.441533\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−6.00000	−0.242933
$611$	0	0
$612$	0	0
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	15.0000	0.604367
$617$	11.0000	0.442843	0.221422	−	0.975178i	$-0.428930\pi$
$617$	11.0000	0.442843	0.221422	+	0.975178i	$0.428930\pi$
$618$	0	0
$619$	2.00000	0.0803868	0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000	0.0803868	0.0401934	+	0.999192i	$0.487203\pi$
$620$	−1.00000	−0.0401610
$621$	0	0
$622$	−32.0000	−1.28308
$623$	−45.0000	−1.80289
$624$	0	0
$625$	1.00000	0.0400000
$626$	−10.0000	−0.399680
$627$	0	0
$628$	9.00000	0.359139
$629$	16.0000	0.637962
$630$	0	0
$631$	41.0000	1.63218	0.816092	−	0.577922i	$-0.196136\pi$
$631$	41.0000	1.63218	0.816092	+	0.577922i	$0.196136\pi$
$632$	−1.00000	−0.0397779
$633$	0	0
$634$	22.0000	0.873732
$635$	−8.00000	−0.317470
$636$	0	0
$637$	0	0
$638$	−20.0000	−0.791808
$639$	0	0
$640$	1.00000	0.0395285
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	0	0
$643$	1.00000	0.0394362	0.0197181	−	0.999806i	$-0.493723\pi$
$643$	1.00000	0.0394362	0.0197181	+	0.999806i	$0.493723\pi$
$644$	−21.0000	−0.827516
$645$	0	0
$646$	2.00000	0.0786889
$647$	33.0000	1.29736	0.648682	−	0.761060i	$-0.275321\pi$
$647$	33.0000	1.29736	0.648682	+	0.761060i	$0.275321\pi$
$648$	0	0
$649$	40.0000	1.57014
$650$	0	0
$651$	0	0
$652$	−12.0000	−0.469956
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	10.0000	0.390732
$656$	−12.0000	−0.468521
$657$	0	0
$658$	36.0000	1.40343
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−28.0000	−1.08907	−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000	−1.08907	−0.544537	+	0.838737i	$0.683295\pi$
$662$	−30.0000	−1.16598
$663$	0	0
$664$	6.00000	0.232845
$665$	3.00000	0.116335
$666$	0	0
$667$	28.0000	1.08416
$668$	3.00000	0.116073
$669$	0	0
$670$	−2.00000	−0.0772667
$671$	30.0000	1.15814
$672$	0	0
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	−13.0000	−0.500000
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	0	0
$679$	−48.0000	−1.84207
$680$	−2.00000	−0.0766965
$681$	0	0
$682$	5.00000	0.191460
$683$	−27.0000	−1.03313	−0.516563	−	0.856249i	$-0.672789\pi$
$683$	−27.0000	−1.03313	−0.516563	+	0.856249i	$0.672789\pi$
$684$	0	0
$685$	12.0000	0.458496
$686$	15.0000	0.572703
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	0	0
$690$	0	0
$691$	19.0000	0.722794	0.361397	−	0.932412i	$-0.382300\pi$
$691$	19.0000	0.722794	0.361397	+	0.932412i	$0.382300\pi$
$692$	20.0000	0.760286
$693$	0	0
$694$	4.00000	0.151838
$695$	−10.0000	−0.379322
$696$	0	0
$697$	24.0000	0.909065
$698$	34.0000	1.28692
$699$	0	0
$700$	−3.00000	−0.113389
$701$	11.0000	0.415464	0.207732	−	0.978186i	$-0.433392\pi$
$701$	11.0000	0.415464	0.207732	+	0.978186i	$0.433392\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	−5.00000	−0.188445
$705$	0	0
$706$	−6.00000	−0.225813
$707$	−21.0000	−0.789786
$708$	0	0
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	−3.00000	−0.112588
$711$	0	0
$712$	15.0000	0.562149
$713$	−7.00000	−0.262152
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	17.0000	0.634434
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	0	0
$721$	48.0000	1.78761
$722$	−18.0000	−0.669891
$723$	0	0
$724$	−21.0000	−0.780459
$725$	4.00000	0.148556
$726$	0	0
$727$	37.0000	1.37225	0.686127	−	0.727482i	$-0.259309\pi$
$727$	37.0000	1.37225	0.686127	+	0.727482i	$0.259309\pi$
$728$	0	0
$729$	0	0
$730$	−15.0000	−0.555175
$731$	2.00000	0.0739727
$732$	0	0
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	28.0000	1.03350
$735$	0	0
$736$	7.00000	0.258023
$737$	10.0000	0.368355
$738$	0	0
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	15.0000	0.550667
$743$	−51.0000	−1.87101	−0.935504	−	0.353315i	$-0.885054\pi$
$743$	−51.0000	−1.87101	−0.935504	+	0.353315i	$0.885054\pi$
$744$	0	0
$745$	−7.00000	−0.256460
$746$	1.00000	0.0366126
$747$	0	0
$748$	10.0000	0.365636
$749$	21.0000	0.767323
$750$	0	0
$751$	12.0000	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$752$	−12.0000	−0.437595
$753$	0	0
$754$	0	0
$755$	−8.00000	−0.291150
$756$	0	0
$757$	−30.0000	−1.09037	−0.545184	−	0.838316i	$-0.683540\pi$
$757$	−30.0000	−1.09037	−0.545184	+	0.838316i	$0.683540\pi$
$758$	13.0000	0.472181
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	−13.0000	−0.471250	−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000	−0.471250	−0.235625	+	0.971844i	$0.575714\pi$
$762$	0	0
$763$	0	0
$764$	8.00000	0.289430
$765$	0	0
$766$	−16.0000	−0.578103
$767$	0	0
$768$	0	0
$769$	−35.0000	−1.26213	−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000	−1.26213	−0.631066	+	0.775729i	$0.717382\pi$
$770$	15.0000	0.540562
$771$	0	0
$772$	26.0000	0.935760
$773$	−11.0000	−0.395643	−0.197821	−	0.980238i	$-0.563387\pi$
$773$	−11.0000	−0.395643	−0.197821	+	0.980238i	$0.563387\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	16.0000	0.574367
$777$	0	0
$778$	−24.0000	−0.860442
$779$	12.0000	0.429945
$780$	0	0
$781$	15.0000	0.536742
$782$	−14.0000	−0.500639
$783$	0	0
$784$	2.00000	0.0714286
$785$	9.00000	0.321224
$786$	0	0
$787$	−53.0000	−1.88925	−0.944623	−	0.328158i	$-0.893572\pi$
$787$	−53.0000	−1.88925	−0.944623	+	0.328158i	$0.893572\pi$
$788$	22.0000	0.783718
$789$	0	0
$790$	−1.00000	−0.0355784
$791$	−57.0000	−2.02669
$792$	0	0
$793$	0	0
$794$	−23.0000	−0.816239
$795$	0	0
$796$	−17.0000	−0.602549
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	0	0
$799$	24.0000	0.849059
$800$	1.00000	0.0353553
$801$	0	0
$802$	−17.0000	−0.600291
$803$	75.0000	2.64669
$804$	0	0
$805$	−21.0000	−0.740153
$806$	0	0
$807$	0	0
$808$	7.00000	0.246259
$809$	19.0000	0.668004	0.334002	−	0.942572i	$-0.391601\pi$
$809$	19.0000	0.668004	0.334002	+	0.942572i	$0.391601\pi$
$810$	0	0
$811$	−45.0000	−1.58016	−0.790082	−	0.613001i	$-0.789962\pi$
$811$	−45.0000	−1.58016	−0.790082	+	0.613001i	$0.789962\pi$
$812$	−12.0000	−0.421117
$813$	0	0
$814$	40.0000	1.40200
$815$	−12.0000	−0.420342
$816$	0	0
$817$	1.00000	0.0349856
$818$	−30.0000	−1.04893
$819$	0	0
$820$	−12.0000	−0.419058
$821$	−50.0000	−1.74501	−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−50.0000	−1.74501	−0.872506	+	0.488603i	$0.837507\pi$
$822$	0	0
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	−16.0000	−0.557386
$825$	0	0
$826$	24.0000	0.835067
$827$	38.0000	1.32139	0.660695	−	0.750655i	$-0.270262\pi$
$827$	38.0000	1.32139	0.660695	+	0.750655i	$0.270262\pi$
$828$	0	0
$829$	−49.0000	−1.70184	−0.850920	−	0.525295i	$-0.823955\pi$
$829$	−49.0000	−1.70184	−0.850920	+	0.525295i	$0.823955\pi$
$830$	6.00000	0.208263
$831$	0	0
$832$	0	0
$833$	−4.00000	−0.138592
$834$	0	0
$835$	3.00000	0.103819
$836$	5.00000	0.172929
$837$	0	0
$838$	0	0
$839$	5.00000	0.172619	0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000	0.172619	0.0863096	+	0.996268i	$0.472493\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	−4.00000	−0.137849
$843$	0	0
$844$	23.0000	0.791693
$845$	−13.0000	−0.447214
$846$	0	0
$847$	−42.0000	−1.44314
$848$	−5.00000	−0.171701
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	−56.0000	−1.91966
$852$	0	0
$853$	13.0000	0.445112	0.222556	−	0.974920i	$-0.428560\pi$
$853$	13.0000	0.445112	0.222556	+	0.974920i	$0.428560\pi$
$854$	18.0000	0.615947
$855$	0	0
$856$	−7.00000	−0.239255
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	0	0
$859$	−12.0000	−0.409435	−0.204717	−	0.978821i	$-0.565628\pi$
$859$	−12.0000	−0.409435	−0.204717	+	0.978821i	$0.565628\pi$
$860$	−1.00000	−0.0340997
$861$	0	0
$862$	−24.0000	−0.817443
$863$	45.0000	1.53182	0.765909	−	0.642949i	$-0.222289\pi$
$863$	45.0000	1.53182	0.765909	+	0.642949i	$0.222289\pi$
$864$	0	0
$865$	20.0000	0.680020
$866$	−1.00000	−0.0339814
$867$	0	0
$868$	3.00000	0.101827
$869$	5.00000	0.169613
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	−7.00000	−0.236779
$875$	−3.00000	−0.101419
$876$	0	0
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	10.0000	0.337484
$879$	0	0
$880$	−5.00000	−0.168550
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	0	0
$883$	37.0000	1.24515	0.622575	−	0.782560i	$-0.286087\pi$
$883$	37.0000	1.24515	0.622575	+	0.782560i	$0.286087\pi$
$884$	0	0
$885$	0	0
$886$	−41.0000	−1.37742
$887$	30.0000	1.00730	0.503651	−	0.863907i	$-0.331990\pi$
$887$	30.0000	1.00730	0.503651	+	0.863907i	$0.331990\pi$
$888$	0	0
$889$	24.0000	0.804934
$890$	15.0000	0.502801
$891$	0	0
$892$	−8.00000	−0.267860
$893$	12.0000	0.401565
$894$	0	0
$895$	4.00000	0.133705
$896$	−3.00000	−0.100223
$897$	0	0
$898$	18.0000	0.600668
$899$	−4.00000	−0.133407
$900$	0	0
$901$	10.0000	0.333148
$902$	60.0000	1.99778
$903$	0	0
$904$	19.0000	0.631931
$905$	−21.0000	−0.698064
$906$	0	0
$907$	−50.0000	−1.66022	−0.830111	−	0.557598i	$-0.811723\pi$
$907$	−50.0000	−1.66022	−0.830111	+	0.557598i	$0.811723\pi$
$908$	−11.0000	−0.365048
$909$	0	0
$910$	0	0
$911$	−18.0000	−0.596367	−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000	−0.596367	−0.298183	+	0.954509i	$0.596381\pi$
$912$	0	0
$913$	−30.0000	−0.992855
$914$	−34.0000	−1.12462
$915$	0	0
$916$	7.00000	0.231287
$917$	−30.0000	−0.990687
$918$	0	0
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	7.00000	0.230783
$921$	0	0
$922$	−16.0000	−0.526932
$923$	0	0
$924$	0	0
$925$	−8.00000	−0.263038
$926$	−24.0000	−0.788689
$927$	0	0
$928$	4.00000	0.131306
$929$	−39.0000	−1.27955	−0.639774	−	0.768563i	$-0.720972\pi$
$929$	−39.0000	−1.27955	−0.639774	+	0.768563i	$0.720972\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	5.00000	0.163780
$933$	0	0
$934$	4.00000	0.130884
$935$	10.0000	0.327035
$936$	0	0
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	6.00000	0.195907
$939$	0	0
$940$	−12.0000	−0.391397
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	0	0
$943$	−84.0000	−2.73542
$944$	−8.00000	−0.260378
$945$	0	0
$946$	5.00000	0.162564
$947$	−46.0000	−1.49480	−0.747400	−	0.664375i	$-0.768698\pi$
$947$	−46.0000	−1.49480	−0.747400	+	0.664375i	$0.768698\pi$
$948$	0	0
$949$	0	0
$950$	−1.00000	−0.0324443
$951$	0	0
$952$	6.00000	0.194461
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	0	0
$955$	8.00000	0.258874
$956$	−6.00000	−0.194054
$957$	0	0
$958$	33.0000	1.06618
$959$	−36.0000	−1.16250
$960$	0	0
$961$	1.00000	0.0322581
$962$	0	0
$963$	0	0
$964$	10.0000	0.322078
$965$	26.0000	0.836970
$966$	0	0
$967$	34.0000	1.09337	0.546683	−	0.837340i	$-0.315890\pi$
$967$	34.0000	1.09337	0.546683	+	0.837340i	$0.315890\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	16.0000	0.513729
$971$	−6.00000	−0.192549	−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000	−0.192549	−0.0962746	+	0.995355i	$0.530693\pi$
$972$	0	0
$973$	30.0000	0.961756
$974$	8.00000	0.256337
$975$	0	0
$976$	−6.00000	−0.192055
$977$	−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
$979$	−75.0000	−2.39701
$980$	2.00000	0.0638877
$981$	0	0
$982$	−5.00000	−0.159556
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	22.0000	0.700978
$986$	−8.00000	−0.254772
$987$	0	0
$988$	0	0
$989$	−7.00000	−0.222587
$990$	0	0
$991$	−13.0000	−0.412959	−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000	−0.412959	−0.206479	+	0.978451i	$0.566201\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	9.00000	0.285463
$995$	−17.0000	−0.538936
$996$	0	0
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−32.0000	−1.01294
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2790.2.a.a.1.1	✓	1	3.2	odd	2
2790.2.a.x.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

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