LMFDB - Embedded newform 930.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(1,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
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	$\chi$	$=$	930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} +6.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.00000 q^{26} -1.00000 q^{27} +2.00000 q^{29} -1.00000 q^{30} -1.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} +4.00000 q^{38} -6.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} -1.00000 q^{45} +4.00000 q^{46} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} -2.00000 q^{51} +6.00000 q^{52} +2.00000 q^{53} +1.00000 q^{54} +4.00000 q^{55} +4.00000 q^{57} -2.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} -6.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} -4.00000 q^{66} +16.0000 q^{67} +2.00000 q^{68} +4.00000 q^{69} -12.0000 q^{71} -1.00000 q^{72} -6.00000 q^{73} +2.00000 q^{74} -1.00000 q^{75} -4.00000 q^{76} +6.00000 q^{78} -16.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -12.0000 q^{83} -2.00000 q^{85} +4.00000 q^{86} -2.00000 q^{87} +4.00000 q^{88} -18.0000 q^{89} +1.00000 q^{90} -4.00000 q^{92} +1.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} -14.0000 q^{97} +7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	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
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	4.00000	0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.00000	−0.182574
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	−2.00000	−0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−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
$39$	−6.00000	−0.960769
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	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
$45$	−1.00000	−0.149071
$46$	4.00000	0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	−2.00000	−0.280056
$52$	6.00000	0.832050
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	1.00000	0.136083
$55$	4.00000	0.539360
$56$	0	0
$57$	4.00000	0.529813
$58$	−2.00000	−0.262613
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	1.00000	0.129099
$61$	−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
$65$	−6.00000	−0.744208
$66$	−4.00000	−0.492366
$67$	16.0000	1.95471	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	16.0000	1.95471	0.977356	+	0.211604i	$0.0678686\pi$
$68$	2.00000	0.242536
$69$	4.00000	0.481543
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.00000	0.232495
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	0	0
$78$	6.00000	0.679366
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	4.00000	0.431331
$87$	−2.00000	−0.214423
$88$	4.00000	0.426401
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−4.00000	−0.417029
$93$	1.00000	0.103695
$94$	0	0
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	7.00000	0.707107
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	2.00000	0.198030
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−2.00000	−0.194257
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−1.00000	−0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−4.00000	−0.381385
$111$	2.00000	0.189832
$112$	0	0
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	−4.00000	−0.374634
$115$	4.00000	0.373002
$116$	2.00000	0.185695
$117$	6.00000	0.554700
$118$	4.00000	0.368230
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	6.00000	0.543214
$123$	6.00000	0.541002
$124$	−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
$129$	4.00000	0.352180
$130$	6.00000	0.526235
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	−16.0000	−1.38219
$135$	1.00000	0.0860663
$136$	−2.00000	−0.171499
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	−4.00000	−0.340503
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	0	0
$142$	12.0000	1.00702
$143$	−24.0000	−2.00698
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	6.00000	0.496564
$147$	7.00000	0.577350
$148$	−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	$0.365663\pi$
$150$	1.00000	0.0816497
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	4.00000	0.324443
$153$	2.00000	0.161690
$154$	0	0
$155$	1.00000	0.0803219
$156$	−6.00000	−0.480384
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	16.0000	1.27289
$159$	−2.00000	−0.158610
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	−6.00000	−0.468521
$165$	−4.00000	−0.311400
$166$	12.0000	0.931381
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	2.00000	0.153393
$171$	−4.00000	−0.305888
$172$	−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	$0.678635\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−4.00000	−0.301511
$177$	4.00000	0.300658
$178$	18.0000	1.34916
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	−1.00000	−0.0745356
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	4.00000	0.294884
$185$	2.00000	0.147043
$186$	−1.00000	−0.0733236
$187$	−8.00000	−0.585018
$188$	0	0
$189$	0	0
$190$	−4.00000	−0.290191
$191$	4.00000	0.289430	0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000	0.289430	0.144715	+	0.989473i	$0.453773\pi$
$192$	−1.00000	−0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	14.0000	1.00514
$195$	6.00000	0.429669
$196$	−7.00000	−0.500000
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	4.00000	0.284268
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.00000	−0.0707107
$201$	−16.0000	−1.12855
$202$	−2.00000	−0.140720
$203$	0	0
$204$	−2.00000	−0.140028
$205$	6.00000	0.419058
$206$	−8.00000	−0.557386
$207$	−4.00000	−0.278019
$208$	6.00000	0.416025
$209$	16.0000	1.10674
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	2.00000	0.137361
$213$	12.0000	0.822226
$214$	−4.00000	−0.273434
$215$	4.00000	0.272798
$216$	1.00000	0.0680414
$217$	0	0
$218$	−6.00000	−0.406371
$219$	6.00000	0.405442
$220$	4.00000	0.269680
$221$	12.0000	0.807207
$222$	−2.00000	−0.134231
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	10.0000	0.665190
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	4.00000	0.264906
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−2.00000	−0.131306
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−4.00000	−0.260378
$237$	16.0000	1.03931
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	1.00000	0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−5.00000	−0.321412
$243$	−1.00000	−0.0641500
$244$	−6.00000	−0.384111
$245$	7.00000	0.447214
$246$	−6.00000	−0.382546
$247$	−24.0000	−1.52708
$248$	1.00000	0.0635001
$249$	12.0000	0.760469
$250$	1.00000	0.0632456
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	8.00000	0.501965
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	−6.00000	−0.372104
$261$	2.00000	0.123797
$262$	4.00000	0.247121
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−4.00000	−0.246183
$265$	−2.00000	−0.122859
$266$	0	0
$267$	18.0000	1.10158
$268$	16.0000	0.977356
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	−1.00000	−0.0608581
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	−18.0000	−1.08742
$275$	−4.00000	−0.241209
$276$	4.00000	0.240772
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	−8.00000	−0.479808
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−12.0000	−0.712069
$285$	−4.00000	−0.236940
$286$	24.0000	1.41915
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	2.00000	0.117444
$291$	14.0000	0.820695
$292$	−6.00000	−0.351123
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−7.00000	−0.408248
$295$	4.00000	0.232889
$296$	2.00000	0.116248
$297$	4.00000	0.232104
$298$	−10.0000	−0.579284
$299$	−24.0000	−1.38796
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	−16.0000	−0.920697
$303$	−2.00000	−0.114897
$304$	−4.00000	−0.229416
$305$	6.00000	0.343559
$306$	−2.00000	−0.114332
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−1.00000	−0.0567962
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	6.00000	0.339683
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	−16.0000	−0.900070
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	2.00000	0.112154
$319$	−8.00000	−0.447914
$320$	−1.00000	−0.0559017
$321$	−4.00000	−0.223258
$322$	0	0
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	6.00000	0.332820
$326$	24.0000	1.32924
$327$	−6.00000	−0.331801
$328$	6.00000	0.331295
$329$	0	0
$330$	4.00000	0.220193
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−12.0000	−0.658586
$333$	−2.00000	−0.109599
$334$	−12.0000	−0.656611
$335$	−16.0000	−0.874173
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−23.0000	−1.25104
$339$	10.0000	0.543125
$340$	−2.00000	−0.108465
$341$	4.00000	0.216612
$342$	4.00000	0.216295
$343$	0	0
$344$	4.00000	0.215666
$345$	−4.00000	−0.215353
$346$	14.0000	0.752645
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	−2.00000	−0.107211
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	−6.00000	−0.320256
$352$	4.00000	0.213201
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	−4.00000	−0.212598
$355$	12.0000	0.636894
$356$	−18.0000	−0.953998
$357$	0	0
$358$	4.00000	0.211407
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	6.00000	0.315353
$363$	−5.00000	−0.262432
$364$	0	0
$365$	6.00000	0.314054
$366$	−6.00000	−0.313625
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	−4.00000	−0.208514
$369$	−6.00000	−0.312348
$370$	−2.00000	−0.103975
$371$	0	0
$372$	1.00000	0.0518476
$373$	−38.0000	−1.96757	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−38.0000	−1.96757	−0.983783	+	0.179364i	$0.942596\pi$
$374$	8.00000	0.413670
$375$	1.00000	0.0516398
$376$	0	0
$377$	12.0000	0.618031
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	4.00000	0.205196
$381$	8.00000	0.409852
$382$	−4.00000	−0.204658
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−4.00000	−0.203331
$388$	−14.0000	−0.710742
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−6.00000	−0.303822
$391$	−8.00000	−0.404577
$392$	7.00000	0.353553
$393$	4.00000	0.201773
$394$	−2.00000	−0.100759
$395$	16.0000	0.805047
$396$	−4.00000	−0.201008
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	1.00000	0.0500000
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	16.0000	0.798007
$403$	−6.00000	−0.298881
$404$	2.00000	0.0995037
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	8.00000	0.396545
$408$	2.00000	0.0990148
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	−6.00000	−0.296319
$411$	−18.0000	−0.887875
$412$	8.00000	0.394132
$413$	0	0
$414$	4.00000	0.196589
$415$	12.0000	0.589057
$416$	−6.00000	−0.294174
$417$	−8.00000	−0.391762
$418$	−16.0000	−0.782586
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	2.00000	0.0970143
$426$	−12.0000	−0.581402
$427$	0	0
$428$	4.00000	0.193347
$429$	24.0000	1.15873
$430$	−4.00000	−0.192897
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	−1.00000	−0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	2.00000	0.0958927
$436$	6.00000	0.287348
$437$	16.0000	0.765384
$438$	−6.00000	−0.286691
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	−4.00000	−0.190693
$441$	−7.00000	−0.333333
$442$	−12.0000	−0.570782
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	2.00000	0.0949158
$445$	18.0000	0.853282
$446$	8.00000	0.378811
$447$	−10.0000	−0.472984
$448$	0	0
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	−1.00000	−0.0471405
$451$	24.0000	1.13012
$452$	−10.0000	−0.470360
$453$	−16.0000	−0.751746
$454$	−20.0000	−0.938647
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	−10.0000	−0.467269
$459$	−2.00000	−0.0933520
$460$	4.00000	0.186501
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	2.00000	0.0928477
$465$	−1.00000	−0.0463739
$466$	−22.0000	−1.01913
$467$	−4.00000	−0.185098	−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000	−0.185098	−0.0925490	+	0.995708i	$0.529501\pi$
$468$	6.00000	0.277350
$469$	0	0
$470$	0	0
$471$	−18.0000	−0.829396
$472$	4.00000	0.184115
$473$	16.0000	0.735681
$474$	−16.0000	−0.734904
$475$	−4.00000	−0.183533
$476$	0	0
$477$	2.00000	0.0915737
$478$	0	0
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	−1.00000	−0.0456435
$481$	−12.0000	−0.547153
$482$	14.0000	0.637683
$483$	0	0
$484$	5.00000	0.227273
$485$	14.0000	0.635707
$486$	1.00000	0.0453609
$487$	−40.0000	−1.81257	−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000	−1.81257	−0.906287	+	0.422664i	$0.861095\pi$
$488$	6.00000	0.271607
$489$	24.0000	1.08532
$490$	−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	$0.350963\pi$
$492$	6.00000	0.270501
$493$	4.00000	0.180151
$494$	24.0000	1.07981
$495$	4.00000	0.179787
$496$	−1.00000	−0.0449013
$497$	0	0
$498$	−12.0000	−0.537733
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	−1.00000	−0.0447214
$501$	−12.0000	−0.536120
$502$	−20.0000	−0.892644
$503$	32.0000	1.42681	0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000	1.42681	0.713405	+	0.700752i	$0.247152\pi$
$504$	0	0
$505$	−2.00000	−0.0889988
$506$	−16.0000	−0.711287
$507$	−23.0000	−1.02147
$508$	−8.00000	−0.354943
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	−2.00000	−0.0885615
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	4.00000	0.176604
$514$	−22.0000	−0.970378
$515$	−8.00000	−0.352522
$516$	4.00000	0.176090
$517$	0	0
$518$	0	0
$519$	14.0000	0.614532
$520$	6.00000	0.263117
$521$	−14.0000	−0.613351	−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000	−0.613351	−0.306676	+	0.951814i	$0.599217\pi$
$522$	−2.00000	−0.0875376
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	12.0000	0.523225
$527$	−2.00000	−0.0871214
$528$	4.00000	0.174078
$529$	−7.00000	−0.304348
$530$	2.00000	0.0868744
$531$	−4.00000	−0.173585
$532$	0	0
$533$	−36.0000	−1.55933
$534$	−18.0000	−0.778936
$535$	−4.00000	−0.172935
$536$	−16.0000	−0.691095
$537$	4.00000	0.172613
$538$	−18.0000	−0.776035
$539$	28.0000	1.20605
$540$	1.00000	0.0430331
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	8.00000	0.343629
$543$	6.00000	0.257485
$544$	−2.00000	−0.0857493
$545$	−6.00000	−0.257012
$546$	0	0
$547$	16.0000	0.684111	0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000	0.684111	0.342055	+	0.939680i	$0.388877\pi$
$548$	18.0000	0.768922
$549$	−6.00000	−0.256074
$550$	4.00000	0.170561
$551$	−8.00000	−0.340811
$552$	−4.00000	−0.170251
$553$	0	0
$554$	−6.00000	−0.254916
$555$	−2.00000	−0.0848953
$556$	8.00000	0.339276
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	1.00000	0.0423334
$559$	−24.0000	−1.01509
$560$	0	0
$561$	8.00000	0.337760
$562$	−10.0000	−0.421825
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	0	0
$565$	10.0000	0.420703
$566$	0	0
$567$	0	0
$568$	12.0000	0.503509
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	4.00000	0.167542
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	−24.0000	−1.00349
$573$	−4.00000	−0.167102
$574$	0	0
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	13.0000	0.540729
$579$	22.0000	0.914289
$580$	−2.00000	−0.0830455
$581$	0	0
$582$	−14.0000	−0.580319
$583$	−8.00000	−0.331326
$584$	6.00000	0.248282
$585$	−6.00000	−0.248069
$586$	6.00000	0.247858
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	7.00000	0.288675
$589$	4.00000	0.164817
$590$	−4.00000	−0.164677
$591$	−2.00000	−0.0822690
$592$	−2.00000	−0.0821995
$593$	14.0000	0.574911	0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000	0.574911	0.287456	+	0.957794i	$0.407191\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	10.0000	0.409616
$597$	−16.0000	−0.654836
$598$	24.0000	0.981433
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	1.00000	0.0408248
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	16.0000	0.651570
$604$	16.0000	0.651031
$605$	−5.00000	−0.203279
$606$	2.00000	0.0812444
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	−6.00000	−0.242933
$611$	0	0
$612$	2.00000	0.0808452
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	16.0000	0.645707
$615$	−6.00000	−0.241943
$616$	0	0
$617$	46.0000	1.85189	0.925945	−	0.377658i	$-0.123271\pi$
$617$	46.0000	1.85189	0.925945	+	0.377658i	$0.123271\pi$
$618$	8.00000	0.321807
$619$	32.0000	1.28619	0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000	1.28619	0.643094	+	0.765787i	$0.277650\pi$
$620$	1.00000	0.0401610
$621$	4.00000	0.160514
$622$	28.0000	1.12270
$623$	0	0
$624$	−6.00000	−0.240192
$625$	1.00000	0.0400000
$626$	−26.0000	−1.03917
$627$	−16.0000	−0.638978
$628$	18.0000	0.718278
$629$	−4.00000	−0.159490
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	16.0000	0.636446
$633$	4.00000	0.158986
$634$	−2.00000	−0.0794301
$635$	8.00000	0.317470
$636$	−2.00000	−0.0793052
$637$	−42.0000	−1.66410
$638$	8.00000	0.316723
$639$	−12.0000	−0.474713
$640$	1.00000	0.0395285
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	4.00000	0.157867
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	8.00000	0.314756
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	−1.00000	−0.0392837
$649$	16.0000	0.628055
$650$	−6.00000	−0.235339
$651$	0	0
$652$	−24.0000	−0.939913
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	6.00000	0.234619
$655$	4.00000	0.156293
$656$	−6.00000	−0.234261
$657$	−6.00000	−0.234082
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	−4.00000	−0.155700
$661$	−34.0000	−1.32245	−0.661223	−	0.750189i	$-0.729962\pi$
$661$	−34.0000	−1.32245	−0.661223	+	0.750189i	$0.729962\pi$
$662$	−24.0000	−0.932786
$663$	−12.0000	−0.466041
$664$	12.0000	0.465690
$665$	0	0
$666$	2.00000	0.0774984
$667$	−8.00000	−0.309761
$668$	12.0000	0.464294
$669$	8.00000	0.309298
$670$	16.0000	0.618134
$671$	24.0000	0.926510
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	−2.00000	−0.0770371
$675$	−1.00000	−0.0384900
$676$	23.0000	0.884615
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	−10.0000	−0.384048
$679$	0	0
$680$	2.00000	0.0766965
$681$	−20.0000	−0.766402
$682$	−4.00000	−0.153168
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−4.00000	−0.152944
$685$	−18.0000	−0.687745
$686$	0	0
$687$	−10.0000	−0.381524
$688$	−4.00000	−0.152499
$689$	12.0000	0.457164
$690$	4.00000	0.152277
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	4.00000	0.151838
$695$	−8.00000	−0.303457
$696$	2.00000	0.0758098
$697$	−12.0000	−0.454532
$698$	2.00000	0.0757011
$699$	−22.0000	−0.832116
$700$	0	0
$701$	−38.0000	−1.43524	−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000	−1.43524	−0.717620	+	0.696435i	$0.754769\pi$
$702$	6.00000	0.226455
$703$	8.00000	0.301726
$704$	−4.00000	−0.150756
$705$	0	0
$706$	6.00000	0.225813
$707$	0	0
$708$	4.00000	0.150329
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	−12.0000	−0.450352
$711$	−16.0000	−0.600047
$712$	18.0000	0.674579
$713$	4.00000	0.149801
$714$	0	0
$715$	24.0000	0.897549
$716$	−4.00000	−0.149487
$717$	0	0
$718$	20.0000	0.746393
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	3.00000	0.111648
$723$	14.0000	0.520666
$724$	−6.00000	−0.222988
$725$	2.00000	0.0742781
$726$	5.00000	0.185567
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	−8.00000	−0.295891
$732$	6.00000	0.221766
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	−16.0000	−0.590571
$735$	−7.00000	−0.258199
$736$	4.00000	0.147442
$737$	−64.0000	−2.35747
$738$	6.00000	0.220863
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	2.00000	0.0735215
$741$	24.0000	0.881662
$742$	0	0
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	−1.00000	−0.0366618
$745$	−10.0000	−0.366372
$746$	38.0000	1.39128
$747$	−12.0000	−0.439057
$748$	−8.00000	−0.292509
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	0	0
$753$	−20.0000	−0.728841
$754$	−12.0000	−0.437014
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	20.0000	0.726433
$759$	−16.0000	−0.580763
$760$	−4.00000	−0.145095
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	−8.00000	−0.289809
$763$	0	0
$764$	4.00000	0.144715
$765$	−2.00000	−0.0723102
$766$	−4.00000	−0.144526
$767$	−24.0000	−0.866590
$768$	−1.00000	−0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	−22.0000	−0.792311
$772$	−22.0000	−0.791797
$773$	50.0000	1.79838	0.899188	−	0.437564i	$-0.144158\pi$
$773$	50.0000	1.79838	0.899188	+	0.437564i	$0.144158\pi$
$774$	4.00000	0.143777
$775$	−1.00000	−0.0359211
$776$	14.0000	0.502571
$777$	0	0
$778$	6.00000	0.215110
$779$	24.0000	0.859889
$780$	6.00000	0.214834
$781$	48.0000	1.71758
$782$	8.00000	0.286079
$783$	−2.00000	−0.0714742
$784$	−7.00000	−0.250000
$785$	−18.0000	−0.642448
$786$	−4.00000	−0.142675
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	2.00000	0.0712470
$789$	12.0000	0.427211
$790$	−16.0000	−0.569254
$791$	0	0
$792$	4.00000	0.142134
$793$	−36.0000	−1.27840
$794$	14.0000	0.496841
$795$	2.00000	0.0709327
$796$	16.0000	0.567105
$797$	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
$801$	−18.0000	−0.635999
$802$	−14.0000	−0.494357
$803$	24.0000	0.846942
$804$	−16.0000	−0.564276
$805$	0	0
$806$	6.00000	0.211341
$807$	−18.0000	−0.633630
$808$	−2.00000	−0.0703598
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	1.00000	0.0351364
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	−8.00000	−0.280400
$815$	24.0000	0.840683
$816$	−2.00000	−0.0700140
$817$	16.0000	0.559769
$818$	6.00000	0.209785
$819$	0	0
$820$	6.00000	0.209529
$821$	−22.0000	−0.767805	−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000	−0.767805	−0.383903	+	0.923374i	$0.625420\pi$
$822$	18.0000	0.627822
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	−8.00000	−0.278693
$825$	4.00000	0.139262
$826$	0	0
$827$	52.0000	1.80822	0.904109	−	0.427303i	$-0.140536\pi$
$827$	52.0000	1.80822	0.904109	+	0.427303i	$0.140536\pi$
$828$	−4.00000	−0.139010
$829$	50.0000	1.73657	0.868286	−	0.496064i	$-0.165222\pi$
$829$	50.0000	1.73657	0.868286	+	0.496064i	$0.165222\pi$
$830$	−12.0000	−0.416526
$831$	−6.00000	−0.208138
$832$	6.00000	0.208013
$833$	−14.0000	−0.485071
$834$	8.00000	0.277017
$835$	−12.0000	−0.415277
$836$	16.0000	0.553372
$837$	1.00000	0.0345651
$838$	12.0000	0.414533
$839$	28.0000	0.966667	0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000	0.966667	0.483334	+	0.875436i	$0.339426\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−14.0000	−0.482472
$843$	−10.0000	−0.344418
$844$	−4.00000	−0.137686
$845$	−23.0000	−0.791224
$846$	0	0
$847$	0	0
$848$	2.00000	0.0686803
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	8.00000	0.274236
$852$	12.0000	0.411113
$853$	58.0000	1.98588	0.992941	−	0.118609i	$-0.0378434\pi$
$853$	58.0000	1.98588	0.992941	+	0.118609i	$0.0378434\pi$
$854$	0	0
$855$	4.00000	0.136797
$856$	−4.00000	−0.136717
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	−24.0000	−0.819346
$859$	48.0000	1.63774	0.818869	−	0.573980i	$-0.194601\pi$
$859$	48.0000	1.63774	0.818869	+	0.573980i	$0.194601\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	12.0000	0.408722
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	1.00000	0.0340207
$865$	14.0000	0.476014
$866$	−2.00000	−0.0679628
$867$	13.0000	0.441503
$868$	0	0
$869$	64.0000	2.17105
$870$	−2.00000	−0.0678064
$871$	96.0000	3.25284
$872$	−6.00000	−0.203186
$873$	−14.0000	−0.473828
$874$	−16.0000	−0.541208
$875$	0	0
$876$	6.00000	0.202721
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	32.0000	1.07995
$879$	6.00000	0.202375
$880$	4.00000	0.134840
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	7.00000	0.235702
$883$	52.0000	1.74994	0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000	1.74994	0.874970	+	0.484178i	$0.160881\pi$
$884$	12.0000	0.403604
$885$	−4.00000	−0.134459
$886$	4.00000	0.134383
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	−2.00000	−0.0671156
$889$	0	0
$890$	−18.0000	−0.603361
$891$	−4.00000	−0.134005
$892$	−8.00000	−0.267860
$893$	0	0
$894$	10.0000	0.334450
$895$	4.00000	0.133705
$896$	0	0
$897$	24.0000	0.801337
$898$	18.0000	0.600668
$899$	−2.00000	−0.0667037
$900$	1.00000	0.0333333
$901$	4.00000	0.133259
$902$	−24.0000	−0.799113
$903$	0	0
$904$	10.0000	0.332595
$905$	6.00000	0.199447
$906$	16.0000	0.531564
$907$	−56.0000	−1.85945	−0.929725	−	0.368255i	$-0.879955\pi$
$907$	−56.0000	−1.85945	−0.929725	+	0.368255i	$0.879955\pi$
$908$	20.0000	0.663723
$909$	2.00000	0.0663358
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	4.00000	0.132453
$913$	48.0000	1.58857
$914$	22.0000	0.727695
$915$	−6.00000	−0.198354
$916$	10.0000	0.330409
$917$	0	0
$918$	2.00000	0.0660098
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	−4.00000	−0.131876
$921$	16.0000	0.527218
$922$	14.0000	0.461065
$923$	−72.0000	−2.36991
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	24.0000	0.788689
$927$	8.00000	0.262754
$928$	−2.00000	−0.0656532
$929$	−42.0000	−1.37798	−0.688988	−	0.724773i	$-0.741945\pi$
$929$	−42.0000	−1.37798	−0.688988	+	0.724773i	$0.741945\pi$
$930$	1.00000	0.0327913
$931$	28.0000	0.917663
$932$	22.0000	0.720634
$933$	28.0000	0.916679
$934$	4.00000	0.130884
$935$	8.00000	0.261628
$936$	−6.00000	−0.196116
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	0	0
$939$	−26.0000	−0.848478
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	18.0000	0.586472
$943$	24.0000	0.781548
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−16.0000	−0.520205
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	16.0000	0.519656
$949$	−36.0000	−1.16861
$950$	4.00000	0.129777
$951$	−2.00000	−0.0648544
$952$	0	0
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	−2.00000	−0.0647524
$955$	−4.00000	−0.129437
$956$	0	0
$957$	8.00000	0.258603
$958$	−36.0000	−1.16311
$959$	0	0
$960$	1.00000	0.0322749
$961$	1.00000	0.0322581
$962$	12.0000	0.386896
$963$	4.00000	0.128898
$964$	−14.0000	−0.450910
$965$	22.0000	0.708205
$966$	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
$969$	8.00000	0.256997
$970$	−14.0000	−0.449513
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	40.0000	1.28168
$975$	−6.00000	−0.192154
$976$	−6.00000	−0.192055
$977$	22.0000	0.703842	0.351921	−	0.936030i	$-0.385529\pi$
$977$	22.0000	0.703842	0.351921	+	0.936030i	$0.385529\pi$
$978$	−24.0000	−0.767435
$979$	72.0000	2.30113
$980$	7.00000	0.223607
$981$	6.00000	0.191565
$982$	−20.0000	−0.638226
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−6.00000	−0.191273
$985$	−2.00000	−0.0637253
$986$	−4.00000	−0.127386
$987$	0	0
$988$	−24.0000	−0.763542
$989$	16.0000	0.508770
$990$	−4.00000	−0.127128
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	1.00000	0.0317500
$993$	−24.0000	−0.761617
$994$	0	0
$995$	−16.0000	−0.507234
$996$	12.0000	0.380235
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−16.0000	−0.506471
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.a.b.1.1	✓	1
3.2	odd	2		2790.2.a.ba.1.1		1
4.3	odd	2		7440.2.a.q.1.1		1
5.2	odd	4		4650.2.d.o.3349.1		2
5.3	odd	4		4650.2.d.o.3349.2		2
5.4	even	2		4650.2.a.bp.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.b.1.1	✓	1	1.1	even	1	trivial
2790.2.a.ba.1.1		1	3.2	odd	2
4650.2.a.bp.1.1		1	5.4	even	2
4650.2.d.o.3349.1		2	5.2	odd	4
4650.2.d.o.3349.2		2	5.3	odd	4
7440.2.a.q.1.1		1	4.3	odd	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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