LMFDB - Embedded newform 434.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [434,2,Mod(1,434)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(434, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("434.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 434 = 2 \cdot 7 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	434.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:	$3.46550744772$
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	$\chi$	$=$	434.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -2.00000 q^{11} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +3.00000 q^{18} -6.00000 q^{19} +2.00000 q^{22} -5.00000 q^{25} +2.00000 q^{26} -1.00000 q^{28} +8.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} -2.00000 q^{34} -3.00000 q^{36} -8.00000 q^{37} +6.00000 q^{38} -10.0000 q^{41} -6.00000 q^{43} -2.00000 q^{44} -4.00000 q^{47} +1.00000 q^{49} +5.00000 q^{50} -2.00000 q^{52} +4.00000 q^{53} +1.00000 q^{56} -8.00000 q^{58} +6.00000 q^{59} +6.00000 q^{61} +1.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -4.00000 q^{67} +2.00000 q^{68} -8.00000 q^{71} +3.00000 q^{72} +14.0000 q^{73} +8.00000 q^{74} -6.00000 q^{76} +2.00000 q^{77} -16.0000 q^{79} +9.00000 q^{81} +10.0000 q^{82} +8.00000 q^{83} +6.00000 q^{86} +2.00000 q^{88} -6.00000 q^{89} +2.00000 q^{91} +4.00000 q^{94} +14.0000 q^{97} -1.00000 q^{98} +6.00000 q^{99} +O(q^{100})$

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
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	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	$0.422021\pi$
$18$	3.00000	0.707107
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	2.00000	0.392232
$27$	0	0
$28$	−1.00000	−0.188982
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	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
$36$	−3.00000	−0.500000
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	0	0
$41$	−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
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	0	0
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	5.00000	0.707107
$51$	0	0
$52$	−2.00000	−0.277350
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−8.00000	−1.05045
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	1.00000	0.127000
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	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
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	3.00000	0.353553
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	−6.00000	−0.688247
$77$	2.00000	0.227921
$78$	0	0
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	10.0000	1.10432
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	0	0
$85$	0	0
$86$	6.00000	0.646997
$87$	0	0
$88$	2.00000	0.213201
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	0	0
$93$	0	0
$94$	4.00000	0.412568
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−1.00000	−0.101015
$99$	6.00000	0.603023
$100$	−5.00000	−0.500000
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−4.00000	−0.388514
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	0	0
$116$	8.00000	0.742781
$117$	6.00000	0.554700
$118$	−6.00000	−0.552345
$119$	−2.00000	−0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−6.00000	−0.543214
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	−3.00000	−0.267261
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−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
$133$	6.00000	0.520266
$134$	4.00000	0.345547
$135$	0	0
$136$	−2.00000	−0.171499
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	0	0
$142$	8.00000	0.671345
$143$	4.00000	0.334497
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−14.0000	−1.15865
$147$	0	0
$148$	−8.00000	−0.657596
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	6.00000	0.486664
$153$	−6.00000	−0.485071
$154$	−2.00000	−0.161165
$155$	0	0
$156$	0	0
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	16.0000	1.27289
$159$	0	0
$160$	0	0
$161$	0	0
$162$	−9.00000	−0.707107
$163$	−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
$166$	−8.00000	−0.620920
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	18.0000	1.37649
$172$	−6.00000	−0.457496
$173$	16.0000	1.21646	0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000	1.21646	0.608229	+	0.793762i	$0.291880\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	−2.00000	−0.150756
$177$	0	0
$178$	6.00000	0.449719
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	−2.00000	−0.148250
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−4.00000	−0.292509
$188$	−4.00000	−0.291730
$189$	0	0
$190$	0	0
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	0	0
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	1.00000	0.0714286
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	−6.00000	−0.426401
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	5.00000	0.353553
$201$	0	0
$202$	−8.00000	−0.562878
$203$	−8.00000	−0.561490
$204$	0	0
$205$	0	0
$206$	−8.00000	−0.557386
$207$	0	0
$208$	−2.00000	−0.138675
$209$	12.0000	0.830057
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	4.00000	0.274721
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	1.00000	0.0678844
$218$	6.00000	0.406371
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	1.00000	0.0668153
$225$	15.0000	1.00000
$226$	−18.0000	−1.19734
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	−8.00000	−0.525226
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	6.00000	0.390567
$237$	0	0
$238$	2.00000	0.129641
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	6.00000	0.384111
$245$	0	0
$246$	0	0
$247$	12.0000	0.763542
$248$	1.00000	0.0635001
$249$	0	0
$250$	0	0
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	3.00000	0.188982
$253$	0	0
$254$	−4.00000	−0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	0	0
$261$	−24.0000	−1.48556
$262$	−10.0000	−0.617802
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	0	0
$266$	−6.00000	−0.367884
$267$	0	0
$268$	−4.00000	−0.244339
$269$	26.0000	1.58525	0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000	1.58525	0.792624	+	0.609711i	$0.208714\pi$
$270$	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
$274$	−14.0000	−0.845771
$275$	10.0000	0.603023
$276$	0	0
$277$	−12.0000	−0.721010	−0.360505	−	0.932757i	$-0.617396\pi$
$277$	−12.0000	−0.721010	−0.360505	+	0.932757i	$0.617396\pi$
$278$	20.0000	1.19952
$279$	3.00000	0.179605
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	−4.00000	−0.236525
$287$	10.0000	0.590281
$288$	3.00000	0.176777
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	14.0000	0.819288
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	0	0
$296$	8.00000	0.464991
$297$	0	0
$298$	14.0000	0.810998
$299$	0	0
$300$	0	0
$301$	6.00000	0.345834
$302$	−4.00000	−0.230174
$303$	0	0
$304$	−6.00000	−0.344124
$305$	0	0
$306$	6.00000	0.342997
$307$	14.0000	0.799022	0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000	0.799022	0.399511	+	0.916728i	$0.369180\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	0	0
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−8.00000	−0.451466
$315$	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	$0.482113\pi$
$318$	0	0
$319$	−16.0000	−0.895828
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−12.0000	−0.667698
$324$	9.00000	0.500000
$325$	10.0000	0.554700
$326$	4.00000	0.221540
$327$	0	0
$328$	10.0000	0.552158
$329$	4.00000	0.220527
$330$	0	0
$331$	22.0000	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$331$	22.0000	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$332$	8.00000	0.439057
$333$	24.0000	1.31519
$334$	16.0000	0.875481
$335$	0	0
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	0	0
$341$	2.00000	0.108306
$342$	−18.0000	−0.973329
$343$	−1.00000	−0.0539949
$344$	6.00000	0.323498
$345$	0	0
$346$	−16.0000	−0.860165
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	0	0
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	−5.00000	−0.267261
$351$	0	0
$352$	2.00000	0.106600
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	0	0
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−6.00000	−0.317110
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	6.00000	0.315353
$363$	0	0
$364$	2.00000	0.104828
$365$	0	0
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	0	0
$369$	30.0000	1.56174
$370$	0	0
$371$	−4.00000	−0.207670
$372$	0	0
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	4.00000	0.206284
$377$	−16.0000	−0.824042
$378$	0	0
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	0	0
$381$	0	0
$382$	16.0000	0.818631
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	18.0000	0.916176
$387$	18.0000	0.914991
$388$	14.0000	0.710742
$389$	−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
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	12.0000	0.604551
$395$	0	0
$396$	6.00000	0.301511
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−5.00000	−0.250000
$401$	−2.00000	−0.0998752	−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000	−0.0998752	−0.0499376	+	0.998752i	$0.515902\pi$
$402$	0	0
$403$	2.00000	0.0996271
$404$	8.00000	0.398015
$405$	0	0
$406$	8.00000	0.397033
$407$	16.0000	0.793091
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	0	0
$412$	8.00000	0.394132
$413$	−6.00000	−0.295241
$414$	0	0
$415$	0	0
$416$	2.00000	0.0980581
$417$	0	0
$418$	−12.0000	−0.586939
$419$	26.0000	1.27018	0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000	1.27018	0.635092	+	0.772437i	$0.280962\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	8.00000	0.389434
$423$	12.0000	0.583460
$424$	−4.00000	−0.194257
$425$	−10.0000	−0.485071
$426$	0	0
$427$	−6.00000	−0.290360
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	−1.00000	−0.0480015
$435$	0	0
$436$	−6.00000	−0.287348
$437$	0	0
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	4.00000	0.190261
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	0	0
$445$	0	0
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−42.0000	−1.98210	−0.991051	−	0.133482i	$-0.957384\pi$
$449$	−42.0000	−1.98210	−0.991051	+	0.133482i	$0.957384\pi$
$450$	−15.0000	−0.707107
$451$	20.0000	0.941763
$452$	18.0000	0.846649
$453$	0	0
$454$	18.0000	0.844782
$455$	0	0
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	8.00000	0.371391
$465$	0	0
$466$	−14.0000	−0.648537
$467$	14.0000	0.647843	0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000	0.647843	0.323921	+	0.946084i	$0.394999\pi$
$468$	6.00000	0.277350
$469$	4.00000	0.184703
$470$	0	0
$471$	0	0
$472$	−6.00000	−0.276172
$473$	12.0000	0.551761
$474$	0	0
$475$	30.0000	1.37649
$476$	−2.00000	−0.0916698
$477$	−12.0000	−0.549442
$478$	12.0000	0.548867
$479$	−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
$481$	16.0000	0.729537
$482$	−14.0000	−0.637683
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−28.0000	−1.26880	−0.634401	−	0.773004i	$-0.718753\pi$
$487$	−28.0000	−1.26880	−0.634401	+	0.773004i	$0.718753\pi$
$488$	−6.00000	−0.271607
$489$	0	0
$490$	0	0
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	0	0
$493$	16.0000	0.720604
$494$	−12.0000	−0.539906
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	8.00000	0.358849
$498$	0	0
$499$	26.0000	1.16392	0.581960	−	0.813217i	$-0.302286\pi$
$499$	26.0000	1.16392	0.581960	+	0.813217i	$0.302286\pi$
$500$	0	0
$501$	0	0
$502$	−8.00000	−0.357057
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	0	0
$507$	0	0
$508$	4.00000	0.177471
$509$	−38.0000	−1.68432	−0.842160	−	0.539227i	$-0.818716\pi$
$509$	−38.0000	−1.68432	−0.842160	+	0.539227i	$0.818716\pi$
$510$	0	0
$511$	−14.0000	−0.619324
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	14.0000	0.617514
$515$	0	0
$516$	0	0
$517$	8.00000	0.351840
$518$	−8.00000	−0.351500
$519$	0	0
$520$	0	0
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	24.0000	1.05045
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	24.0000	1.04645
$527$	−2.00000	−0.0871214
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−18.0000	−0.781133
$532$	6.00000	0.260133
$533$	20.0000	0.866296
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	−26.0000	−1.12094
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	−26.0000	−1.11783	−0.558914	−	0.829226i	$-0.688782\pi$
$541$	−26.0000	−1.11783	−0.558914	+	0.829226i	$0.688782\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	14.0000	0.598050
$549$	−18.0000	−0.768221
$550$	−10.0000	−0.426401
$551$	−48.0000	−2.04487
$552$	0	0
$553$	16.0000	0.680389
$554$	12.0000	0.509831
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	−3.00000	−0.127000
$559$	12.0000	0.507546
$560$	0	0
$561$	0	0
$562$	6.00000	0.253095
$563$	−42.0000	−1.77009	−0.885044	−	0.465506i	$-0.845872\pi$
$563$	−42.0000	−1.77009	−0.885044	+	0.465506i	$0.845872\pi$
$564$	0	0
$565$	0	0
$566$	−6.00000	−0.252199
$567$	−9.00000	−0.377964
$568$	8.00000	0.335673
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	−30.0000	−1.25546	−0.627730	−	0.778431i	$-0.716016\pi$
$571$	−30.0000	−1.25546	−0.627730	+	0.778431i	$0.716016\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	−10.0000	−0.417392
$575$	0	0
$576$	−3.00000	−0.125000
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	0	0
$581$	−8.00000	−0.331896
$582$	0	0
$583$	−8.00000	−0.331326
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−12.0000	−0.495715
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	6.00000	0.247226
$590$	0	0
$591$	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
$595$	0	0
$596$	−14.0000	−0.573462
$597$	0	0
$598$	0	0
$599$	8.00000	0.326871	0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000	0.326871	0.163436	+	0.986554i	$0.447742\pi$
$600$	0	0
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	−6.00000	−0.244542
$603$	12.0000	0.488678
$604$	4.00000	0.162758
$605$	0	0
$606$	0	0
$607$	−4.00000	−0.162355	−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000	−0.162355	−0.0811775	+	0.996700i	$0.525868\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	0	0
$611$	8.00000	0.323645
$612$	−6.00000	−0.242536
$613$	4.00000	0.161558	0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000	0.161558	0.0807792	+	0.996732i	$0.474259\pi$
$614$	−14.0000	−0.564994
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	0	0
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	0	0
$621$	0	0
$622$	20.0000	0.801927
$623$	6.00000	0.240385
$624$	0	0
$625$	25.0000	1.00000
$626$	−22.0000	−0.879297
$627$	0	0
$628$	8.00000	0.319235
$629$	−16.0000	−0.637962
$630$	0	0
$631$	24.0000	0.955425	0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000	0.955425	0.477712	+	0.878516i	$0.341466\pi$
$632$	16.0000	0.636446
$633$	0	0
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	16.0000	0.633446
$639$	24.0000	0.949425
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	0	0
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	0	0
$645$	0	0
$646$	12.0000	0.472134
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	−9.00000	−0.353553
$649$	−12.0000	−0.471041
$650$	−10.0000	−0.392232
$651$	0	0
$652$	−4.00000	−0.156652
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	0	0
$655$	0	0
$656$	−10.0000	−0.390434
$657$	−42.0000	−1.63858
$658$	−4.00000	−0.155936
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	4.00000	0.155582	0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000	0.155582	0.0777910	+	0.996970i	$0.475213\pi$
$662$	−22.0000	−0.855054
$663$	0	0
$664$	−8.00000	−0.310460
$665$	0	0
$666$	−24.0000	−0.929981
$667$	0	0
$668$	−16.0000	−0.619059
$669$	0	0
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	−14.0000	−0.537271
$680$	0	0
$681$	0	0
$682$	−2.00000	−0.0765840
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	18.0000	0.688247
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−6.00000	−0.228748
$689$	−8.00000	−0.304776
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	16.0000	0.608229
$693$	−6.00000	−0.227921
$694$	30.0000	1.13878
$695$	0	0
$696$	0	0
$697$	−20.0000	−0.757554
$698$	−20.0000	−0.757011
$699$	0	0
$700$	5.00000	0.188982
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	0	0
$703$	48.0000	1.81035
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	10.0000	0.376355
$707$	−8.00000	−0.300871
$708$	0	0
$709$	−28.0000	−1.05156	−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000	−1.05156	−0.525781	+	0.850620i	$0.676227\pi$
$710$	0	0
$711$	48.0000	1.80014
$712$	6.00000	0.224860
$713$	0	0
$714$	0	0
$715$	0	0
$716$	6.00000	0.224231
$717$	0	0
$718$	0	0
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	−17.0000	−0.632674
$723$	0	0
$724$	−6.00000	−0.222988
$725$	−40.0000	−1.48556
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	−2.00000	−0.0741249
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−12.0000	−0.443836
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	0	0
$737$	8.00000	0.294684
$738$	−30.0000	−1.10432
$739$	6.00000	0.220714	0.110357	−	0.993892i	$-0.464801\pi$
$739$	6.00000	0.220714	0.110357	+	0.993892i	$0.464801\pi$
$740$	0	0
$741$	0	0
$742$	4.00000	0.146845
$743$	4.00000	0.146746	0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000	0.146746	0.0733729	+	0.997305i	$0.476624\pi$
$744$	0	0
$745$	0	0
$746$	−6.00000	−0.219676
$747$	−24.0000	−0.878114
$748$	−4.00000	−0.146254
$749$	0	0
$750$	0	0
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	−4.00000	−0.145865
$753$	0	0
$754$	16.0000	0.582686
$755$	0	0
$756$	0	0
$757$	−20.0000	−0.726912	−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000	−0.726912	−0.363456	+	0.931611i	$0.618403\pi$
$758$	−36.0000	−1.30758
$759$	0	0
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	0	0
$763$	6.00000	0.217215
$764$	−16.0000	−0.578860
$765$	0	0
$766$	0	0
$767$	−12.0000	−0.433295
$768$	0	0
$769$	38.0000	1.37032	0.685158	−	0.728395i	$-0.259733\pi$
$769$	38.0000	1.37032	0.685158	+	0.728395i	$0.259733\pi$
$770$	0	0
$771$	0	0
$772$	−18.0000	−0.647834
$773$	−10.0000	−0.359675	−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000	−0.359675	−0.179838	+	0.983696i	$0.557557\pi$
$774$	−18.0000	−0.646997
$775$	5.00000	0.179605
$776$	−14.0000	−0.502571
$777$	0	0
$778$	24.0000	0.860442
$779$	60.0000	2.14972
$780$	0	0
$781$	16.0000	0.572525
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	−12.0000	−0.427482
$789$	0	0
$790$	0	0
$791$	−18.0000	−0.640006
$792$	−6.00000	−0.213201
$793$	−12.0000	−0.426132
$794$	20.0000	0.709773
$795$	0	0
$796$	−16.0000	−0.567105
$797$	−34.0000	−1.20434	−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000	−1.20434	−0.602171	+	0.798367i	$0.705697\pi$
$798$	0	0
$799$	−8.00000	−0.283020
$800$	5.00000	0.176777
$801$	18.0000	0.635999
$802$	2.00000	0.0706225
$803$	−28.0000	−0.988099
$804$	0	0
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	0	0
$808$	−8.00000	−0.281439
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	−26.0000	−0.912983	−0.456492	−	0.889728i	$-0.650894\pi$
$811$	−26.0000	−0.912983	−0.456492	+	0.889728i	$0.650894\pi$
$812$	−8.00000	−0.280745
$813$	0	0
$814$	−16.0000	−0.560800
$815$	0	0
$816$	0	0
$817$	36.0000	1.25948
$818$	26.0000	0.909069
$819$	−6.00000	−0.209657
$820$	0	0
$821$	−4.00000	−0.139601	−0.0698005	−	0.997561i	$-0.522236\pi$
$821$	−4.00000	−0.139601	−0.0698005	+	0.997561i	$0.522236\pi$
$822$	0	0
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	6.00000	0.208767
$827$	−10.0000	−0.347734	−0.173867	−	0.984769i	$-0.555626\pi$
$827$	−10.0000	−0.347734	−0.173867	+	0.984769i	$0.555626\pi$
$828$	0	0
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	0	0
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	2.00000	0.0692959
$834$	0	0
$835$	0	0
$836$	12.0000	0.415029
$837$	0	0
$838$	−26.0000	−0.898155
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	−10.0000	−0.344623
$843$	0	0
$844$	−8.00000	−0.275371
$845$	0	0
$846$	−12.0000	−0.412568
$847$	7.00000	0.240523
$848$	4.00000	0.137361
$849$	0	0
$850$	10.0000	0.342997
$851$	0	0
$852$	0	0
$853$	28.0000	0.958702	0.479351	−	0.877623i	$-0.340872\pi$
$853$	28.0000	0.958702	0.479351	+	0.877623i	$0.340872\pi$
$854$	6.00000	0.205316
$855$	0	0
$856$	0	0
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	0	0
$865$	0	0
$866$	18.0000	0.611665
$867$	0	0
$868$	1.00000	0.0339422
$869$	32.0000	1.08553
$870$	0	0
$871$	8.00000	0.271070
$872$	6.00000	0.203186
$873$	−42.0000	−1.42148
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−10.0000	−0.337676	−0.168838	−	0.985644i	$-0.554001\pi$
$877$	−10.0000	−0.337676	−0.168838	+	0.985644i	$0.554001\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	0	0
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	3.00000	0.101015
$883$	34.0000	1.14419	0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000	1.14419	0.572096	+	0.820187i	$0.306131\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−12.0000	−0.403148
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	0	0
$889$	−4.00000	−0.134156
$890$	0	0
$891$	−18.0000	−0.603023
$892$	16.0000	0.535720
$893$	24.0000	0.803129
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	42.0000	1.40156
$899$	−8.00000	−0.266815
$900$	15.0000	0.500000
$901$	8.00000	0.266519
$902$	−20.0000	−0.665927
$903$	0	0
$904$	−18.0000	−0.598671
$905$	0	0
$906$	0	0
$907$	56.0000	1.85945	0.929725	−	0.368255i	$-0.120045\pi$
$907$	56.0000	1.85945	0.929725	+	0.368255i	$0.120045\pi$
$908$	−18.0000	−0.597351
$909$	−24.0000	−0.796030
$910$	0	0
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	10.0000	0.330771
$915$	0	0
$916$	−10.0000	−0.330409
$917$	−10.0000	−0.330229
$918$	0	0
$919$	48.0000	1.58337	0.791687	−	0.610927i	$-0.209203\pi$
$919$	48.0000	1.58337	0.791687	+	0.610927i	$0.209203\pi$
$920$	0	0
$921$	0	0
$922$	−18.0000	−0.592798
$923$	16.0000	0.526646
$924$	0	0
$925$	40.0000	1.31519
$926$	−4.00000	−0.131448
$927$	−24.0000	−0.788263
$928$	−8.00000	−0.262613
$929$	46.0000	1.50921	0.754606	−	0.656179i	$-0.227828\pi$
$929$	46.0000	1.50921	0.754606	+	0.656179i	$0.227828\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	14.0000	0.458585
$933$	0	0
$934$	−14.0000	−0.458094
$935$	0	0
$936$	−6.00000	−0.196116
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	−4.00000	−0.130605
$939$	0	0
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	0	0
$943$	0	0
$944$	6.00000	0.195283
$945$	0	0
$946$	−12.0000	−0.390154
$947$	34.0000	1.10485	0.552426	−	0.833562i	$-0.313702\pi$
$947$	34.0000	1.10485	0.552426	+	0.833562i	$0.313702\pi$
$948$	0	0
$949$	−28.0000	−0.908918
$950$	−30.0000	−0.973329
$951$	0	0
$952$	2.00000	0.0648204
$953$	−10.0000	−0.323932	−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000	−0.323932	−0.161966	+	0.986796i	$0.551783\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	24.0000	0.775405
$959$	−14.0000	−0.452084
$960$	0	0
$961$	1.00000	0.0322581
$962$	−16.0000	−0.515861
$963$	0	0
$964$	14.0000	0.450910
$965$	0	0
$966$	0	0
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	0	0
$971$	−14.0000	−0.449281	−0.224641	−	0.974442i	$-0.572121\pi$
$971$	−14.0000	−0.449281	−0.224641	+	0.974442i	$0.572121\pi$
$972$	0	0
$973$	20.0000	0.641171
$974$	28.0000	0.897178
$975$	0	0
$976$	6.00000	0.192055
$977$	10.0000	0.319928	0.159964	−	0.987123i	$-0.448862\pi$
$977$	10.0000	0.319928	0.159964	+	0.987123i	$0.448862\pi$
$978$	0	0
$979$	12.0000	0.383522
$980$	0	0
$981$	18.0000	0.574696
$982$	−2.00000	−0.0638226
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	0	0
$985$	0	0
$986$	−16.0000	−0.509544
$987$	0	0
$988$	12.0000	0.381771
$989$	0	0
$990$	0	0
$991$	−36.0000	−1.14358	−0.571789	−	0.820401i	$-0.693750\pi$
$991$	−36.0000	−1.14358	−0.571789	+	0.820401i	$0.693750\pi$
$992$	1.00000	0.0317500
$993$	0	0
$994$	−8.00000	−0.253745
$995$	0	0
$996$	0	0
$997$	52.0000	1.64686	0.823428	−	0.567420i	$-0.192059\pi$
$997$	52.0000	1.64686	0.823428	+	0.567420i	$0.192059\pi$
$998$	−26.0000	−0.823016
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	434.2.a.a.1.1	✓	1
3.2	odd	2		3906.2.a.q.1.1		1
4.3	odd	2		3472.2.a.d.1.1		1
7.6	odd	2		3038.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
434.2.a.a.1.1	✓	1	1.1	even	1	trivial
3038.2.a.b.1.1		1	7.6	odd	2
3472.2.a.d.1.1		1	4.3	odd	2
3906.2.a.q.1.1		1	3.2	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:	\( N \)	\(=\)	\( 434 = 2 \cdot 7 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	434.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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