LMFDB - Embedded newform 2790.2.a.c.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:	no (minimal twist has level 930)
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)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{8} +1.00000 q^{10} +4.00000 q^{11} +6.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} +4.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} +8.00000 q^{23} +1.00000 q^{25} -6.00000 q^{26} -6.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} -2.00000 q^{37} -4.00000 q^{38} +1.00000 q^{40} -10.0000 q^{41} -4.00000 q^{43} +4.00000 q^{44} -8.00000 q^{46} -7.00000 q^{49} -1.00000 q^{50} +6.00000 q^{52} +10.0000 q^{53} -4.00000 q^{55} +6.00000 q^{58} +12.0000 q^{59} -2.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} -4.00000 q^{67} -2.00000 q^{68} +2.00000 q^{73} +2.00000 q^{74} +4.00000 q^{76} -1.00000 q^{80} +10.0000 q^{82} -4.00000 q^{83} +2.00000 q^{85} +4.00000 q^{86} -4.00000 q^{88} +14.0000 q^{89} +8.00000 q^{92} -4.00000 q^{95} +18.0000 q^{97} +7.00000 q^{98} +O(q^{100})$

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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	1.00000	0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	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
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	0	0
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	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
$35$	0	0
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−4.00000	−0.648886
$39$	0	0
$40$	1.00000	0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−8.00000	−1.17954
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	0	0
$52$	6.00000	0.832050
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	0	0
$55$	−4.00000	−0.539360
$56$	0	0
$57$	0	0
$58$	6.00000	0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	1.00000	0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	4.00000	0.458831
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	10.0000	1.10432
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	4.00000	0.431331
$87$	0	0
$88$	−4.00000	−0.426401
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	0	0
$92$	8.00000	0.834058
$93$	0	0
$94$	0	0
$95$	−4.00000	−0.410391
$96$	0	0
$97$	18.0000	1.82762	0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000	1.82762	0.913812	+	0.406138i	$0.133125\pi$
$98$	7.00000	0.707107
$99$	0	0
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−10.0000	−0.971286
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	0	0
$109$	−18.0000	−1.72409	−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000	−1.72409	−0.862044	+	0.506834i	$0.830816\pi$
$110$	4.00000	0.381385
$111$	0	0
$112$	0	0
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	0	0
$115$	−8.00000	−0.746004
$116$	−6.00000	−0.557086
$117$	0	0
$118$	−12.0000	−1.10469
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	6.00000	0.526235
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	2.00000	0.171499
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	24.0000	2.00698
$144$	0	0
$145$	6.00000	0.498273
$146$	−2.00000	−0.165521
$147$	0	0
$148$	−2.00000	−0.164399
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−4.00000	−0.324443
$153$	0	0
$154$	0	0
$155$	1.00000	0.0803219
$156$	0	0
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	0	0
$159$	0	0
$160$	1.00000	0.0790569
$161$	0	0
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	4.00000	0.310460
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−2.00000	−0.153393
$171$	0	0
$172$	−4.00000	−0.304997
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	−14.0000	−1.04934
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	0	0
$184$	−8.00000	−0.589768
$185$	2.00000	0.147043
$186$	0	0
$187$	−8.00000	−0.585018
$188$	0	0
$189$	0	0
$190$	4.00000	0.290191
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−18.0000	−1.29232
$195$	0	0
$196$	−7.00000	−0.500000
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	6.00000	0.422159
$203$	0	0
$204$	0	0
$205$	10.0000	0.698430
$206$	−16.0000	−1.11477
$207$	0	0
$208$	6.00000	0.416025
$209$	16.0000	1.10674
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	−4.00000	−0.273434
$215$	4.00000	0.272798
$216$	0	0
$217$	0	0
$218$	18.0000	1.21911
$219$	0	0
$220$	−4.00000	−0.269680
$221$	−12.0000	−0.807207
$222$	0	0
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	0	0
$225$	0	0
$226$	−14.0000	−0.931266
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	6.00000	0.393919
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	0	0
$236$	12.0000	0.781133
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	−5.00000	−0.321412
$243$	0	0
$244$	−2.00000	−0.128037
$245$	7.00000	0.447214
$246$	0	0
$247$	24.0000	1.52708
$248$	1.00000	0.0635001
$249$	0	0
$250$	1.00000	0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	32.0000	2.01182
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	0	0
$260$	−6.00000	−0.372104
$261$	0	0
$262$	−4.00000	−0.247121
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	−10.0000	−0.614295
$266$	0	0
$267$	0	0
$268$	−4.00000	−0.244339
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−22.0000	−1.32907
$275$	4.00000	0.241209
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	0	0
$285$	0	0
$286$	−24.0000	−1.41915
$287$	0	0
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−6.00000	−0.352332
$291$	0	0
$292$	2.00000	0.117041
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	0	0
$295$	−12.0000	−0.698667
$296$	2.00000	0.116248
$297$	0	0
$298$	−10.0000	−0.579284
$299$	48.0000	2.77591
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	0	0
$304$	4.00000	0.229416
$305$	2.00000	0.114520
$306$	0	0
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	0	0
$310$	−1.00000	−0.0567962
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	0	0
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	0	0
$319$	−24.0000	−1.34374
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	0	0
$323$	−8.00000	−0.445132
$324$	0	0
$325$	6.00000	0.332820
$326$	4.00000	0.221540
$327$	0	0
$328$	10.0000	0.552158
$329$	0	0
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	24.0000	1.31322
$335$	4.00000	0.218543
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−23.0000	−1.25104
$339$	0	0
$340$	2.00000	0.108465
$341$	−4.00000	−0.216612
$342$	0	0
$343$	0	0
$344$	4.00000	0.215666
$345$	0	0
$346$	14.0000	0.752645
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	0	0
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	0	0
$351$	0	0
$352$	−4.00000	−0.213201
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	0	0
$356$	14.0000	0.741999
$357$	0	0
$358$	4.00000	0.211407
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	10.0000	0.525588
$363$	0	0
$364$	0	0
$365$	−2.00000	−0.104685
$366$	0	0
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	8.00000	0.417029
$369$	0	0
$370$	−2.00000	−0.103975
$371$	0	0
$372$	0	0
$373$	38.0000	1.96757	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	38.0000	1.96757	0.983783	+	0.179364i	$0.0574041\pi$
$374$	8.00000	0.413670
$375$	0	0
$376$	0	0
$377$	−36.0000	−1.85409
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	−4.00000	−0.205196
$381$	0	0
$382$	−24.0000	−1.22795
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	0	0
$385$	0	0
$386$	14.0000	0.712581
$387$	0	0
$388$	18.0000	0.913812
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	7.00000	0.353553
$393$	0	0
$394$	−10.0000	−0.503793
$395$	0	0
$396$	0	0
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	1.00000	0.0500000
$401$	−26.0000	−1.29838	−0.649189	−	0.760627i	$-0.724892\pi$
$401$	−26.0000	−1.29838	−0.649189	+	0.760627i	$0.724892\pi$
$402$	0	0
$403$	−6.00000	−0.298881
$404$	−6.00000	−0.298511
$405$	0	0
$406$	0	0
$407$	−8.00000	−0.396545
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−10.0000	−0.493865
$411$	0	0
$412$	16.0000	0.788263
$413$	0	0
$414$	0	0
$415$	4.00000	0.196352
$416$	−6.00000	−0.294174
$417$	0	0
$418$	−16.0000	−0.782586
$419$	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
$421$	38.0000	1.85201	0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000	1.85201	0.926003	+	0.377515i	$0.123221\pi$
$422$	−4.00000	−0.194717
$423$	0	0
$424$	−10.0000	−0.485643
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	0	0
$428$	4.00000	0.193347
$429$	0	0
$430$	−4.00000	−0.192897
$431$	−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
$433$	−22.0000	−1.05725	−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000	−1.05725	−0.528626	+	0.848855i	$0.677293\pi$
$434$	0	0
$435$	0	0
$436$	−18.0000	−0.862044
$437$	32.0000	1.53077
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	4.00000	0.190693
$441$	0	0
$442$	12.0000	0.570782
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	0	0
$445$	−14.0000	−0.663664
$446$	16.0000	0.757622
$447$	0	0
$448$	0	0
$449$	−42.0000	−1.98210	−0.991051	−	0.133482i	$-0.957384\pi$
$449$	−42.0000	−1.98210	−0.991051	+	0.133482i	$0.957384\pi$
$450$	0	0
$451$	−40.0000	−1.88353
$452$	14.0000	0.658505
$453$	0	0
$454$	4.00000	0.187729
$455$	0	0
$456$	0	0
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	−8.00000	−0.373002
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	10.0000	0.463241
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−12.0000	−0.552345
$473$	−16.0000	−0.735681
$474$	0	0
$475$	4.00000	0.183533
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	−18.0000	−0.819878
$483$	0	0
$484$	5.00000	0.227273
$485$	−18.0000	−0.817338
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	2.00000	0.0905357
$489$	0	0
$490$	−7.00000	−0.316228
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	−24.0000	−1.07981
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	0	0
$498$	0	0
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	12.0000	0.535586
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	−32.0000	−1.42257
$507$	0	0
$508$	0	0
$509$	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
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	2.00000	0.0882162
$515$	−16.0000	−0.705044
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	6.00000	0.263117
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	−8.00000	−0.348817
$527$	2.00000	0.0871214
$528$	0	0
$529$	41.0000	1.78261
$530$	10.0000	0.434372
$531$	0	0
$532$	0	0
$533$	−60.0000	−2.59889
$534$	0	0
$535$	−4.00000	−0.172935
$536$	4.00000	0.172774
$537$	0	0
$538$	−10.0000	−0.431131
$539$	−28.0000	−1.20605
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	2.00000	0.0857493
$545$	18.0000	0.771035
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	22.0000	0.939793
$549$	0	0
$550$	−4.00000	−0.170561
$551$	−24.0000	−1.02243
$552$	0	0
$553$	0	0
$554$	2.00000	0.0849719
$555$	0	0
$556$	−4.00000	−0.169638
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	−24.0000	−1.01509
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	−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
$565$	−14.0000	−0.588984
$566$	−20.0000	−0.840663
$567$	0	0
$568$	0	0
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	24.0000	1.00349
$573$	0	0
$574$	0	0
$575$	8.00000	0.333623
$576$	0	0
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	6.00000	0.249136
$581$	0	0
$582$	0	0
$583$	40.0000	1.65663
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	−26.0000	−1.07405
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	−4.00000	−0.164817
$590$	12.0000	0.494032
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	0	0
$595$	0	0
$596$	10.0000	0.409616
$597$	0	0
$598$	−48.0000	−1.96287
$599$	32.0000	1.30748	0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000	1.30748	0.653742	+	0.756717i	$0.273198\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	0	0
$604$	8.00000	0.325515
$605$	−5.00000	−0.203279
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	0	0
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	0	0
$617$	22.0000	0.885687	0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000	0.885687	0.442843	+	0.896599i	$0.353970\pi$
$618$	0	0
$619$	12.0000	0.482321	0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000	0.482321	0.241160	+	0.970485i	$0.422472\pi$
$620$	1.00000	0.0401610
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	0	0
$628$	14.0000	0.558661
$629$	4.00000	0.159490
$630$	0	0
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	0	0
$633$	0	0
$634$	30.0000	1.19145
$635$	0	0
$636$	0	0
$637$	−42.0000	−1.66410
$638$	24.0000	0.950169
$639$	0	0
$640$	1.00000	0.0395285
$641$	−10.0000	−0.394976	−0.197488	−	0.980305i	$-0.563278\pi$
$641$	−10.0000	−0.394976	−0.197488	+	0.980305i	$0.563278\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	0	0
$646$	8.00000	0.314756
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	0	0
$649$	48.0000	1.88416
$650$	−6.00000	−0.235339
$651$	0	0
$652$	−4.00000	−0.156652
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	−4.00000	−0.156293
$656$	−10.0000	−0.390434
$657$	0	0
$658$	0	0
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	4.00000	0.155230
$665$	0	0
$666$	0	0
$667$	−48.0000	−1.85857
$668$	−24.0000	−0.928588
$669$	0	0
$670$	−4.00000	−0.154533
$671$	−8.00000	−0.308837
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	23.0000	0.884615
$677$	26.0000	0.999261	0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000	0.999261	0.499631	+	0.866239i	$0.333469\pi$
$678$	0	0
$679$	0	0
$680$	−2.00000	−0.0766965
$681$	0	0
$682$	4.00000	0.153168
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	0	0
$685$	−22.0000	−0.840577
$686$	0	0
$687$	0	0
$688$	−4.00000	−0.152499
$689$	60.0000	2.28582
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	28.0000	1.06287
$695$	4.00000	0.151729
$696$	0	0
$697$	20.0000	0.757554
$698$	−30.0000	−1.13552
$699$	0	0
$700$	0	0
$701$	50.0000	1.88847	0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000	1.88847	0.944237	+	0.329267i	$0.106802\pi$
$702$	0	0
$703$	−8.00000	−0.301726
$704$	4.00000	0.150756
$705$	0	0
$706$	−14.0000	−0.526897
$707$	0	0
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	0	0
$712$	−14.0000	−0.524672
$713$	−8.00000	−0.299602
$714$	0	0
$715$	−24.0000	−0.897549
$716$	−4.00000	−0.149487
$717$	0	0
$718$	−16.0000	−0.597115
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	0	0
$721$	0	0
$722$	3.00000	0.111648
$723$	0	0
$724$	−10.0000	−0.371647
$725$	−6.00000	−0.222834
$726$	0	0
$727$	−48.0000	−1.78022	−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000	−1.78022	−0.890111	+	0.455744i	$0.849373\pi$
$728$	0	0
$729$	0	0
$730$	2.00000	0.0740233
$731$	8.00000	0.295891
$732$	0	0
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−32.0000	−1.18114
$735$	0	0
$736$	−8.00000	−0.294884
$737$	−16.0000	−0.589368
$738$	0	0
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	−38.0000	−1.39128
$747$	0	0
$748$	−8.00000	−0.292509
$749$	0	0
$750$	0	0
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	0	0
$753$	0	0
$754$	36.0000	1.31104
$755$	−8.00000	−0.291150
$756$	0	0
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	4.00000	0.145095
$761$	−2.00000	−0.0724999	−0.0362500	−	0.999343i	$-0.511541\pi$
$761$	−2.00000	−0.0724999	−0.0362500	+	0.999343i	$0.511541\pi$
$762$	0	0
$763$	0	0
$764$	24.0000	0.868290
$765$	0	0
$766$	−32.0000	−1.15621
$767$	72.0000	2.59977
$768$	0	0
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	0	0
$771$	0	0
$772$	−14.0000	−0.503871
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	−18.0000	−0.646162
$777$	0	0
$778$	−18.0000	−0.645331
$779$	−40.0000	−1.43315
$780$	0	0
$781$	0	0
$782$	16.0000	0.572159
$783$	0	0
$784$	−7.00000	−0.250000
$785$	−14.0000	−0.499681
$786$	0	0
$787$	−12.0000	−0.427754	−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000	−0.427754	−0.213877	+	0.976861i	$0.568609\pi$
$788$	10.0000	0.356235
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−12.0000	−0.426132
$794$	18.0000	0.638796
$795$	0	0
$796$	−8.00000	−0.283552
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	26.0000	0.918092
$803$	8.00000	0.282314
$804$	0	0
$805$	0	0
$806$	6.00000	0.211341
$807$	0	0
$808$	6.00000	0.211079
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	−4.00000	−0.140459	−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000	−0.140459	−0.0702295	+	0.997531i	$0.522373\pi$
$812$	0	0
$813$	0	0
$814$	8.00000	0.280400
$815$	4.00000	0.140114
$816$	0	0
$817$	−16.0000	−0.559769
$818$	−10.0000	−0.349642
$819$	0	0
$820$	10.0000	0.349215
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	−16.0000	−0.557386
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−4.00000	−0.138842
$831$	0	0
$832$	6.00000	0.208013
$833$	14.0000	0.485071
$834$	0	0
$835$	24.0000	0.830554
$836$	16.0000	0.553372
$837$	0	0
$838$	−20.0000	−0.690889
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−38.0000	−1.30957
$843$	0	0
$844$	4.00000	0.137686
$845$	−23.0000	−0.791224
$846$	0	0
$847$	0	0
$848$	10.0000	0.343401
$849$	0	0
$850$	2.00000	0.0685994
$851$	−16.0000	−0.548473
$852$	0	0
$853$	22.0000	0.753266	0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000	0.753266	0.376633	+	0.926363i	$0.377082\pi$
$854$	0	0
$855$	0	0
$856$	−4.00000	−0.136717
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	0	0
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	24.0000	0.817443
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	14.0000	0.476014
$866$	22.0000	0.747590
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−24.0000	−0.813209
$872$	18.0000	0.609557
$873$	0	0
$874$	−32.0000	−1.08242
$875$	0	0
$876$	0	0
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	8.00000	0.269987
$879$	0	0
$880$	−4.00000	−0.134840
$881$	22.0000	0.741199	0.370599	−	0.928793i	$-0.379152\pi$
$881$	22.0000	0.741199	0.370599	+	0.928793i	$0.379152\pi$
$882$	0	0
$883$	−44.0000	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	28.0000	0.940678
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	0	0
$890$	14.0000	0.469281
$891$	0	0
$892$	−16.0000	−0.535720
$893$	0	0
$894$	0	0
$895$	4.00000	0.133705
$896$	0	0
$897$	0	0
$898$	42.0000	1.40156
$899$	6.00000	0.200111
$900$	0	0
$901$	−20.0000	−0.666297
$902$	40.0000	1.33185
$903$	0	0
$904$	−14.0000	−0.465633
$905$	10.0000	0.332411
$906$	0	0
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	−4.00000	−0.132745
$909$	0	0
$910$	0	0
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	−56.0000	−1.84727	−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000	−1.84727	−0.923635	+	0.383274i	$0.874797\pi$
$920$	8.00000	0.263752
$921$	0	0
$922$	6.00000	0.197599
$923$	0	0
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	16.0000	0.525793
$927$	0	0
$928$	6.00000	0.196960
$929$	38.0000	1.24674	0.623370	−	0.781927i	$-0.285763\pi$
$929$	38.0000	1.24674	0.623370	+	0.781927i	$0.285763\pi$
$930$	0	0
$931$	−28.0000	−0.917663
$932$	−10.0000	−0.327561
$933$	0	0
$934$	36.0000	1.17796
$935$	8.00000	0.261628
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−22.0000	−0.717180	−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000	−0.717180	−0.358590	+	0.933495i	$0.616742\pi$
$942$	0	0
$943$	−80.0000	−2.60516
$944$	12.0000	0.390567
$945$	0	0
$946$	16.0000	0.520205
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	−4.00000	−0.129777
$951$	0	0
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	−24.0000	−0.776622
$956$	0	0
$957$	0	0
$958$	24.0000	0.775405
$959$	0	0
$960$	0	0
$961$	1.00000	0.0322581
$962$	12.0000	0.386896
$963$	0	0
$964$	18.0000	0.579741
$965$	14.0000	0.450676
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	18.0000	0.577945
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	0	0
$973$	0	0
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	56.0000	1.78977
$980$	7.00000	0.223607
$981$	0	0
$982$	−20.0000	−0.638226
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	0	0
$985$	−10.0000	−0.318626
$986$	−12.0000	−0.382158
$987$	0	0
$988$	24.0000	0.763542
$989$	−32.0000	−1.01754
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	1.00000	0.0317500
$993$	0	0
$994$	0	0
$995$	8.00000	0.253617
$996$	0	0
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	−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.c.1.1		1
3.2	odd	2		930.2.a.o.1.1	✓	1
12.11	even	2		7440.2.a.j.1.1		1
15.2	even	4		4650.2.d.n.3349.2		2
15.8	even	4		4650.2.d.n.3349.1		2
15.14	odd	2		4650.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.o.1.1	✓	1	3.2	odd	2
2790.2.a.c.1.1		1	1.1	even	1	trivial
4650.2.a.h.1.1		1	15.14	odd	2
4650.2.d.n.3349.1		2	15.8	even	4
4650.2.d.n.3349.2		2	15.2	even	4
7440.2.a.j.1.1		1	12.11	even	2

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)

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