LMFDB - Embedded newform 430.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(1,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, 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("430.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
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	$\chi$	$=$	430.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -3.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -3.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{10} -3.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} +3.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} +1.00000 q^{25} +3.00000 q^{26} -3.00000 q^{28} -3.00000 q^{29} +7.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} -3.00000 q^{35} -3.00000 q^{36} -8.00000 q^{37} +1.00000 q^{38} -1.00000 q^{40} -7.00000 q^{41} +1.00000 q^{43} -3.00000 q^{45} -6.00000 q^{47} +2.00000 q^{49} -1.00000 q^{50} -3.00000 q^{52} -6.00000 q^{53} +3.00000 q^{56} +3.00000 q^{58} -4.00000 q^{59} +7.00000 q^{61} -7.00000 q^{62} +9.00000 q^{63} +1.00000 q^{64} -3.00000 q^{65} +5.00000 q^{67} -4.00000 q^{68} +3.00000 q^{70} +2.00000 q^{71} +3.00000 q^{72} -1.00000 q^{73} +8.00000 q^{74} -1.00000 q^{76} +9.00000 q^{79} +1.00000 q^{80} +9.00000 q^{81} +7.00000 q^{82} +8.00000 q^{83} -4.00000 q^{85} -1.00000 q^{86} +4.00000 q^{89} +3.00000 q^{90} +9.00000 q^{91} +6.00000 q^{94} -1.00000 q^{95} -2.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	−1.00000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	3.00000	0.707107
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	3.00000	0.588348
$27$	0	0
$28$	−3.00000	−0.566947
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	−3.00000	−0.507093
$36$	−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	$0.728427\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	0	0
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0	0
$45$	−3.00000	−0.447214
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−3.00000	−0.416025
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	3.00000	0.400892
$57$	0	0
$58$	3.00000	0.393919
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	7.00000	0.896258	0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000	0.896258	0.448129	+	0.893969i	$0.352090\pi$
$62$	−7.00000	−0.889001
$63$	9.00000	1.13389
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	0	0
$67$	5.00000	0.610847	0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000	0.610847	0.305424	+	0.952217i	$0.401202\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	3.00000	0.358569
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	3.00000	0.353553
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	0	0
$79$	9.00000	1.01258	0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000	1.01258	0.506290	+	0.862364i	$0.331017\pi$
$80$	1.00000	0.111803
$81$	9.00000	1.00000
$82$	7.00000	0.773021
$83$	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
$85$	−4.00000	−0.433861
$86$	−1.00000	−0.107833
$87$	0	0
$88$	0	0
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	3.00000	0.316228
$91$	9.00000	0.943456
$92$	0	0
$93$	0	0
$94$	6.00000	0.618853
$95$	−1.00000	−0.102598
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	1.00000	0.100000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	18.0000	1.77359	0.886796	−	0.462160i	$-0.152926\pi$
$103$	18.0000	1.77359	0.886796	+	0.462160i	$0.152926\pi$
$104$	3.00000	0.294174
$105$	0	0
$106$	6.00000	0.582772
$107$	−19.0000	−1.83680	−0.918400	−	0.395654i	$-0.870518\pi$
$107$	−19.0000	−1.83680	−0.918400	+	0.395654i	$0.870518\pi$
$108$	0	0
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	0	0
$111$	0	0
$112$	−3.00000	−0.283473
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	9.00000	0.832050
$118$	4.00000	0.368230
$119$	12.0000	1.10004
$120$	0	0
$121$	−11.0000	−1.00000
$122$	−7.00000	−0.633750
$123$	0	0
$124$	7.00000	0.628619
$125$	1.00000	0.0894427
$126$	−9.00000	−0.801784
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	3.00000	0.263117
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	−5.00000	−0.431934
$135$	0	0
$136$	4.00000	0.342997
$137$	5.00000	0.427179	0.213589	−	0.976924i	$-0.431485\pi$
$137$	5.00000	0.427179	0.213589	+	0.976924i	$0.431485\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	−3.00000	−0.253546
$141$	0	0
$142$	−2.00000	−0.167836
$143$	0	0
$144$	−3.00000	−0.250000
$145$	−3.00000	−0.249136
$146$	1.00000	0.0827606
$147$	0	0
$148$	−8.00000	−0.657596
$149$	−5.00000	−0.409616	−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000	−0.409616	−0.204808	+	0.978802i	$0.565657\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	1.00000	0.0811107
$153$	12.0000	0.970143
$154$	0	0
$155$	7.00000	0.562254
$156$	0	0
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	−9.00000	−0.716002
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−9.00000	−0.707107
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	−7.00000	−0.546608
$165$	0	0
$166$	−8.00000	−0.620920
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	4.00000	0.306786
$171$	3.00000	0.229416
$172$	1.00000	0.0762493
$173$	1.00000	0.0760286	0.0380143	−	0.999277i	$-0.487897\pi$
$173$	1.00000	0.0760286	0.0380143	+	0.999277i	$0.487897\pi$
$174$	0	0
$175$	−3.00000	−0.226779
$176$	0	0
$177$	0	0
$178$	−4.00000	−0.299813
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	−3.00000	−0.223607
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−9.00000	−0.667124
$183$	0	0
$184$	0	0
$185$	−8.00000	−0.588172
$186$	0	0
$187$	0	0
$188$	−6.00000	−0.437595
$189$	0	0
$190$	1.00000	0.0725476
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	0	0
$193$	−24.0000	−1.72756	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−24.0000	−1.72756	−0.863779	+	0.503871i	$0.831909\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	2.00000	0.142857
$197$	−11.0000	−0.783718	−0.391859	−	0.920025i	$-0.628168\pi$
$197$	−11.0000	−0.783718	−0.391859	+	0.920025i	$0.628168\pi$
$198$	0	0
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	12.0000	0.844317
$203$	9.00000	0.631676
$204$	0	0
$205$	−7.00000	−0.488901
$206$	−18.0000	−1.25412
$207$	0	0
$208$	−3.00000	−0.208013
$209$	0	0
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	19.0000	1.29881
$215$	1.00000	0.0681994
$216$	0	0
$217$	−21.0000	−1.42557
$218$	−16.0000	−1.08366
$219$	0	0
$220$	0	0
$221$	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	$0.679960\pi$
$224$	3.00000	0.200446
$225$	−3.00000	−0.200000
$226$	−9.00000	−0.598671
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	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
$232$	3.00000	0.196960
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−9.00000	−0.588348
$235$	−6.00000	−0.391397
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−12.0000	−0.777844
$239$	−11.0000	−0.711531	−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000	−0.711531	−0.355765	+	0.934575i	$0.615780\pi$
$240$	0	0
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	11.0000	0.707107
$243$	0	0
$244$	7.00000	0.448129
$245$	2.00000	0.127775
$246$	0	0
$247$	3.00000	0.190885
$248$	−7.00000	−0.444500
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	9.00000	0.566947
$253$	0	0
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	9.00000	0.561405	0.280702	−	0.959795i	$-0.409433\pi$
$257$	9.00000	0.561405	0.280702	+	0.959795i	$0.409433\pi$
$258$	0	0
$259$	24.0000	1.49129
$260$	−3.00000	−0.186052
$261$	9.00000	0.557086
$262$	0	0
$263$	11.0000	0.678289	0.339145	−	0.940734i	$-0.389862\pi$
$263$	11.0000	0.678289	0.339145	+	0.940734i	$0.389862\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−3.00000	−0.183942
$267$	0	0
$268$	5.00000	0.305424
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	0	0
$271$	13.0000	0.789694	0.394847	−	0.918747i	$-0.370798\pi$
$271$	13.0000	0.789694	0.394847	+	0.918747i	$0.370798\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	−5.00000	−0.302061
$275$	0	0
$276$	0	0
$277$	24.0000	1.44202	0.721010	−	0.692925i	$-0.243678\pi$
$277$	24.0000	1.44202	0.721010	+	0.692925i	$0.243678\pi$
$278$	12.0000	0.719712
$279$	−21.0000	−1.25724
$280$	3.00000	0.179284
$281$	−23.0000	−1.37206	−0.686032	−	0.727571i	$-0.740649\pi$
$281$	−23.0000	−1.37206	−0.686032	+	0.727571i	$0.740649\pi$
$282$	0	0
$283$	−25.0000	−1.48610	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000	−1.48610	−0.743048	+	0.669238i	$0.766621\pi$
$284$	2.00000	0.118678
$285$	0	0
$286$	0	0
$287$	21.0000	1.23959
$288$	3.00000	0.176777
$289$	−1.00000	−0.0588235
$290$	3.00000	0.176166
$291$	0	0
$292$	−1.00000	−0.0585206
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	0	0
$295$	−4.00000	−0.232889
$296$	8.00000	0.464991
$297$	0	0
$298$	5.00000	0.289642
$299$	0	0
$300$	0	0
$301$	−3.00000	−0.172917
$302$	−2.00000	−0.115087
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	7.00000	0.400819
$306$	−12.0000	−0.685994
$307$	15.0000	0.856095	0.428048	−	0.903756i	$-0.359202\pi$
$307$	15.0000	0.856095	0.428048	+	0.903756i	$0.359202\pi$
$308$	0	0
$309$	0	0
$310$	−7.00000	−0.397573
$311$	−13.0000	−0.737162	−0.368581	−	0.929596i	$-0.620156\pi$
$311$	−13.0000	−0.737162	−0.368581	+	0.929596i	$0.620156\pi$
$312$	0	0
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−4.00000	−0.225733
$315$	9.00000	0.507093
$316$	9.00000	0.506290
$317$	13.0000	0.730153	0.365076	−	0.930978i	$-0.381043\pi$
$317$	13.0000	0.730153	0.365076	+	0.930978i	$0.381043\pi$
$318$	0	0
$319$	0	0
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	4.00000	0.222566
$324$	9.00000	0.500000
$325$	−3.00000	−0.166410
$326$	−20.0000	−1.10770
$327$	0	0
$328$	7.00000	0.386510
$329$	18.0000	0.992372
$330$	0	0
$331$	36.0000	1.97874	0.989369	−	0.145424i	$-0.0464545\pi$
$331$	36.0000	1.97874	0.989369	+	0.145424i	$0.0464545\pi$
$332$	8.00000	0.439057
$333$	24.0000	1.31519
$334$	8.00000	0.437741
$335$	5.00000	0.273179
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	4.00000	0.217571
$339$	0	0
$340$	−4.00000	−0.216930
$341$	0	0
$342$	−3.00000	−0.162221
$343$	15.0000	0.809924
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−1.00000	−0.0537603
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	−34.0000	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$350$	3.00000	0.160357
$351$	0	0
$352$	0	0
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	0	0
$355$	2.00000	0.106149
$356$	4.00000	0.212000
$357$	0	0
$358$	15.0000	0.792775
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	3.00000	0.158114
$361$	−18.0000	−0.947368
$362$	−12.0000	−0.630706
$363$	0	0
$364$	9.00000	0.471728
$365$	−1.00000	−0.0523424
$366$	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
$369$	21.0000	1.09322
$370$	8.00000	0.415900
$371$	18.0000	0.934513
$372$	0	0
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	0	0
$375$	0	0
$376$	6.00000	0.309426
$377$	9.00000	0.463524
$378$	0	0
$379$	−30.0000	−1.54100	−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000	−1.54100	−0.770498	+	0.637442i	$0.779993\pi$
$380$	−1.00000	−0.0512989
$381$	0	0
$382$	−6.00000	−0.306987
$383$	−23.0000	−1.17525	−0.587623	−	0.809135i	$-0.699936\pi$
$383$	−23.0000	−1.17525	−0.587623	+	0.809135i	$0.699936\pi$
$384$	0	0
$385$	0	0
$386$	24.0000	1.22157
$387$	−3.00000	−0.152499
$388$	−2.00000	−0.101535
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	0	0
$392$	−2.00000	−0.101015
$393$	0	0
$394$	11.0000	0.554172
$395$	9.00000	0.452839
$396$	0	0
$397$	26.0000	1.30490	0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000	1.30490	0.652451	+	0.757831i	$0.273741\pi$
$398$	−10.0000	−0.501255
$399$	0	0
$400$	1.00000	0.0500000
$401$	−37.0000	−1.84769	−0.923846	−	0.382765i	$-0.874972\pi$
$401$	−37.0000	−1.84769	−0.923846	+	0.382765i	$0.874972\pi$
$402$	0	0
$403$	−21.0000	−1.04608
$404$	−12.0000	−0.597022
$405$	9.00000	0.447214
$406$	−9.00000	−0.446663
$407$	0	0
$408$	0	0
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	7.00000	0.345705
$411$	0	0
$412$	18.0000	0.886796
$413$	12.0000	0.590481
$414$	0	0
$415$	8.00000	0.392705
$416$	3.00000	0.147087
$417$	0	0
$418$	0	0
$419$	15.0000	0.732798	0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000	0.732798	0.366399	+	0.930458i	$0.380591\pi$
$420$	0	0
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	4.00000	0.194717
$423$	18.0000	0.875190
$424$	6.00000	0.291386
$425$	−4.00000	−0.194029
$426$	0	0
$427$	−21.0000	−1.01626
$428$	−19.0000	−0.918400
$429$	0	0
$430$	−1.00000	−0.0482243
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	0	0
$433$	−29.0000	−1.39365	−0.696826	−	0.717241i	$-0.745405\pi$
$433$	−29.0000	−1.39365	−0.696826	+	0.717241i	$0.745405\pi$
$434$	21.0000	1.00803
$435$	0	0
$436$	16.0000	0.766261
$437$	0	0
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−12.0000	−0.570782
$443$	−21.0000	−0.997740	−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000	−0.997740	−0.498870	+	0.866677i	$0.666252\pi$
$444$	0	0
$445$	4.00000	0.189618
$446$	16.0000	0.757622
$447$	0	0
$448$	−3.00000	−0.141737
$449$	−8.00000	−0.377543	−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000	−0.377543	−0.188772	+	0.982021i	$0.560451\pi$
$450$	3.00000	0.141421
$451$	0	0
$452$	9.00000	0.423324
$453$	0	0
$454$	−24.0000	−1.12638
$455$	9.00000	0.421927
$456$	0	0
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	0	0
$461$	16.0000	0.745194	0.372597	−	0.927993i	$-0.378467\pi$
$461$	16.0000	0.745194	0.372597	+	0.927993i	$0.378467\pi$
$462$	0	0
$463$	−17.0000	−0.790057	−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000	−0.790057	−0.395029	+	0.918669i	$0.629265\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	6.00000	0.277945
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	9.00000	0.416025
$469$	−15.0000	−0.692636
$470$	6.00000	0.276759
$471$	0	0
$472$	4.00000	0.184115
$473$	0	0
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	12.0000	0.550019
$477$	18.0000	0.824163
$478$	11.0000	0.503128
$479$	28.0000	1.27935	0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000	1.27935	0.639676	+	0.768644i	$0.279068\pi$
$480$	0	0
$481$	24.0000	1.09431
$482$	26.0000	1.18427
$483$	0	0
$484$	−11.0000	−0.500000
$485$	−2.00000	−0.0908153
$486$	0	0
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	−7.00000	−0.316875
$489$	0	0
$490$	−2.00000	−0.0903508
$491$	−24.0000	−1.08310	−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000	−1.08310	−0.541552	+	0.840667i	$0.682163\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	−3.00000	−0.134976
$495$	0	0
$496$	7.00000	0.314309
$497$	−6.00000	−0.269137
$498$	0	0
$499$	−21.0000	−0.940089	−0.470045	−	0.882643i	$-0.655762\pi$
$499$	−21.0000	−0.940089	−0.470045	+	0.882643i	$0.655762\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	14.0000	0.624851
$503$	−32.0000	−1.42681	−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000	−1.42681	−0.713405	+	0.700752i	$0.752848\pi$
$504$	−9.00000	−0.400892
$505$	−12.0000	−0.533993
$506$	0	0
$507$	0	0
$508$	−8.00000	−0.354943
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	3.00000	0.132712
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−9.00000	−0.396973
$515$	18.0000	0.793175
$516$	0	0
$517$	0	0
$518$	−24.0000	−1.05450
$519$	0	0
$520$	3.00000	0.131559
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	−9.00000	−0.393919
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	0	0
$525$	0	0
$526$	−11.0000	−0.479623
$527$	−28.0000	−1.21970
$528$	0	0
$529$	−23.0000	−1.00000
$530$	6.00000	0.260623
$531$	12.0000	0.520756
$532$	3.00000	0.130066
$533$	21.0000	0.909611
$534$	0	0
$535$	−19.0000	−0.821442
$536$	−5.00000	−0.215967
$537$	0	0
$538$	12.0000	0.517357
$539$	0	0
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−13.0000	−0.558398
$543$	0	0
$544$	4.00000	0.171499
$545$	16.0000	0.685365
$546$	0	0
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	5.00000	0.213589
$549$	−21.0000	−0.896258
$550$	0	0
$551$	3.00000	0.127804
$552$	0	0
$553$	−27.0000	−1.14816
$554$	−24.0000	−1.01966
$555$	0	0
$556$	−12.0000	−0.508913
$557$	7.00000	0.296600	0.148300	−	0.988942i	$-0.452620\pi$
$557$	7.00000	0.296600	0.148300	+	0.988942i	$0.452620\pi$
$558$	21.0000	0.889001
$559$	−3.00000	−0.126886
$560$	−3.00000	−0.126773
$561$	0	0
$562$	23.0000	0.970196
$563$	−27.0000	−1.13791	−0.568957	−	0.822367i	$-0.692653\pi$
$563$	−27.0000	−1.13791	−0.568957	+	0.822367i	$0.692653\pi$
$564$	0	0
$565$	9.00000	0.378633
$566$	25.0000	1.05083
$567$	−27.0000	−1.13389
$568$	−2.00000	−0.0839181
$569$	13.0000	0.544988	0.272494	−	0.962157i	$-0.412151\pi$
$569$	13.0000	0.544988	0.272494	+	0.962157i	$0.412151\pi$
$570$	0	0
$571$	−17.0000	−0.711428	−0.355714	−	0.934595i	$-0.615762\pi$
$571$	−17.0000	−0.711428	−0.355714	+	0.934595i	$0.615762\pi$
$572$	0	0
$573$	0	0
$574$	−21.0000	−0.876523
$575$	0	0
$576$	−3.00000	−0.125000
$577$	17.0000	0.707719	0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000	0.707719	0.353860	+	0.935299i	$0.384869\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	−3.00000	−0.124568
$581$	−24.0000	−0.995688
$582$	0	0
$583$	0	0
$584$	1.00000	0.0413803
$585$	9.00000	0.372104
$586$	10.0000	0.413096
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	−7.00000	−0.288430
$590$	4.00000	0.164677
$591$	0	0
$592$	−8.00000	−0.328798
$593$	45.0000	1.84793	0.923964	−	0.382479i	$-0.124930\pi$
$593$	45.0000	1.84793	0.923964	+	0.382479i	$0.124930\pi$
$594$	0	0
$595$	12.0000	0.491952
$596$	−5.00000	−0.204808
$597$	0	0
$598$	0	0
$599$	−40.0000	−1.63436	−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000	−1.63436	−0.817178	+	0.576386i	$0.804463\pi$
$600$	0	0
$601$	28.0000	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$602$	3.00000	0.122271
$603$	−15.0000	−0.610847
$604$	2.00000	0.0813788
$605$	−11.0000	−0.447214
$606$	0	0
$607$	−4.00000	−0.162355	−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000	−0.162355	−0.0811775	+	0.996700i	$0.525868\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−7.00000	−0.283422
$611$	18.0000	0.728202
$612$	12.0000	0.485071
$613$	37.0000	1.49442	0.747208	−	0.664590i	$-0.231394\pi$
$613$	37.0000	1.49442	0.747208	+	0.664590i	$0.231394\pi$
$614$	−15.0000	−0.605351
$615$	0	0
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	7.00000	0.281127
$621$	0	0
$622$	13.0000	0.521253
$623$	−12.0000	−0.480770
$624$	0	0
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	4.00000	0.159617
$629$	32.0000	1.27592
$630$	−9.00000	−0.358569
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	−9.00000	−0.358001
$633$	0	0
$634$	−13.0000	−0.516296
$635$	−8.00000	−0.317470
$636$	0	0
$637$	−6.00000	−0.237729
$638$	0	0
$639$	−6.00000	−0.237356
$640$	−1.00000	−0.0395285
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	0	0
$643$	3.00000	0.118308	0.0591542	−	0.998249i	$-0.481160\pi$
$643$	3.00000	0.118308	0.0591542	+	0.998249i	$0.481160\pi$
$644$	0	0
$645$	0	0
$646$	−4.00000	−0.157378
$647$	−25.0000	−0.982851	−0.491426	−	0.870919i	$-0.663524\pi$
$647$	−25.0000	−0.982851	−0.491426	+	0.870919i	$0.663524\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	3.00000	0.117670
$651$	0	0
$652$	20.0000	0.783260
$653$	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
$656$	−7.00000	−0.273304
$657$	3.00000	0.117041
$658$	−18.0000	−0.701713
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	−36.0000	−1.39918
$663$	0	0
$664$	−8.00000	−0.310460
$665$	3.00000	0.116335
$666$	−24.0000	−0.929981
$667$	0	0
$668$	−8.00000	−0.309529
$669$	0	0
$670$	−5.00000	−0.193167
$671$	0	0
$672$	0	0
$673$	−29.0000	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−4.00000	−0.153846
$677$	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
$679$	6.00000	0.230259
$680$	4.00000	0.153393
$681$	0	0
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	3.00000	0.114708
$685$	5.00000	0.191040
$686$	−15.0000	−0.572703
$687$	0	0
$688$	1.00000	0.0381246
$689$	18.0000	0.685745
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	1.00000	0.0380143
$693$	0	0
$694$	−18.0000	−0.683271
$695$	−12.0000	−0.455186
$696$	0	0
$697$	28.0000	1.06058
$698$	34.0000	1.28692
$699$	0	0
$700$	−3.00000	−0.113389
$701$	−12.0000	−0.453234	−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000	−0.453234	−0.226617	+	0.973984i	$0.572767\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	0	0
$705$	0	0
$706$	−30.0000	−1.12906
$707$	36.0000	1.35392
$708$	0	0
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	−2.00000	−0.0750587
$711$	−27.0000	−1.01258
$712$	−4.00000	−0.149906
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−15.0000	−0.560576
$717$	0	0
$718$	21.0000	0.783713
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	−3.00000	−0.111803
$721$	−54.0000	−2.01107
$722$	18.0000	0.669891
$723$	0	0
$724$	12.0000	0.445976
$725$	−3.00000	−0.111417
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−9.00000	−0.333562
$729$	−27.0000	−1.00000
$730$	1.00000	0.0370117
$731$	−4.00000	−0.147945
$732$	0	0
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−21.0000	−0.773021
$739$	−17.0000	−0.625355	−0.312678	−	0.949859i	$-0.601226\pi$
$739$	−17.0000	−0.625355	−0.312678	+	0.949859i	$0.601226\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	−18.0000	−0.660801
$743$	−25.0000	−0.917161	−0.458581	−	0.888653i	$-0.651642\pi$
$743$	−25.0000	−0.917161	−0.458581	+	0.888653i	$0.651642\pi$
$744$	0	0
$745$	−5.00000	−0.183186
$746$	−16.0000	−0.585802
$747$	−24.0000	−0.878114
$748$	0	0
$749$	57.0000	2.08273
$750$	0	0
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	−9.00000	−0.327761
$755$	2.00000	0.0727875
$756$	0	0
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	30.0000	1.08965
$759$	0	0
$760$	1.00000	0.0362738
$761$	30.0000	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$762$	0	0
$763$	−48.0000	−1.73772
$764$	6.00000	0.217072
$765$	12.0000	0.433861
$766$	23.0000	0.831024
$767$	12.0000	0.433295
$768$	0	0
$769$	−25.0000	−0.901523	−0.450762	−	0.892644i	$-0.648848\pi$
$769$	−25.0000	−0.901523	−0.450762	+	0.892644i	$0.648848\pi$
$770$	0	0
$771$	0	0
$772$	−24.0000	−0.863779
$773$	16.0000	0.575480	0.287740	−	0.957709i	$-0.407096\pi$
$773$	16.0000	0.575480	0.287740	+	0.957709i	$0.407096\pi$
$774$	3.00000	0.107833
$775$	7.00000	0.251447
$776$	2.00000	0.0717958
$777$	0	0
$778$	6.00000	0.215110
$779$	7.00000	0.250801
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	2.00000	0.0714286
$785$	4.00000	0.142766
$786$	0	0
$787$	−15.0000	−0.534692	−0.267346	−	0.963601i	$-0.586147\pi$
$787$	−15.0000	−0.534692	−0.267346	+	0.963601i	$0.586147\pi$
$788$	−11.0000	−0.391859
$789$	0	0
$790$	−9.00000	−0.320206
$791$	−27.0000	−0.960009
$792$	0	0
$793$	−21.0000	−0.745732
$794$	−26.0000	−0.922705
$795$	0	0
$796$	10.0000	0.354441
$797$	13.0000	0.460484	0.230242	−	0.973133i	$-0.426048\pi$
$797$	13.0000	0.460484	0.230242	+	0.973133i	$0.426048\pi$
$798$	0	0
$799$	24.0000	0.849059
$800$	−1.00000	−0.0353553
$801$	−12.0000	−0.423999
$802$	37.0000	1.30652
$803$	0	0
$804$	0	0
$805$	0	0
$806$	21.0000	0.739693
$807$	0	0
$808$	12.0000	0.422159
$809$	29.0000	1.01959	0.509793	−	0.860297i	$-0.329722\pi$
$809$	29.0000	1.01959	0.509793	+	0.860297i	$0.329722\pi$
$810$	−9.00000	−0.316228
$811$	29.0000	1.01833	0.509164	−	0.860670i	$-0.329955\pi$
$811$	29.0000	1.01833	0.509164	+	0.860670i	$0.329955\pi$
$812$	9.00000	0.315838
$813$	0	0
$814$	0	0
$815$	20.0000	0.700569
$816$	0	0
$817$	−1.00000	−0.0349856
$818$	20.0000	0.699284
$819$	−27.0000	−0.943456
$820$	−7.00000	−0.244451
$821$	−22.0000	−0.767805	−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000	−0.767805	−0.383903	+	0.923374i	$0.625420\pi$
$822$	0	0
$823$	18.0000	0.627441	0.313720	−	0.949515i	$-0.398425\pi$
$823$	18.0000	0.627441	0.313720	+	0.949515i	$0.398425\pi$
$824$	−18.0000	−0.627060
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−45.0000	−1.56480	−0.782402	−	0.622774i	$-0.786006\pi$
$827$	−45.0000	−1.56480	−0.782402	+	0.622774i	$0.786006\pi$
$828$	0	0
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	−8.00000	−0.277684
$831$	0	0
$832$	−3.00000	−0.104006
$833$	−8.00000	−0.277184
$834$	0	0
$835$	−8.00000	−0.276851
$836$	0	0
$837$	0	0
$838$	−15.0000	−0.518166
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−17.0000	−0.585859
$843$	0	0
$844$	−4.00000	−0.137686
$845$	−4.00000	−0.137604
$846$	−18.0000	−0.618853
$847$	33.0000	1.13389
$848$	−6.00000	−0.206041
$849$	0	0
$850$	4.00000	0.137199
$851$	0	0
$852$	0	0
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	21.0000	0.718605
$855$	3.00000	0.102598
$856$	19.0000	0.649407
$857$	16.0000	0.546550	0.273275	−	0.961936i	$-0.411893\pi$
$857$	16.0000	0.546550	0.273275	+	0.961936i	$0.411893\pi$
$858$	0	0
$859$	25.0000	0.852989	0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000	0.852989	0.426494	+	0.904490i	$0.359748\pi$
$860$	1.00000	0.0340997
$861$	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
$865$	1.00000	0.0340010
$866$	29.0000	0.985460
$867$	0	0
$868$	−21.0000	−0.712786
$869$	0	0
$870$	0	0
$871$	−15.0000	−0.508256
$872$	−16.0000	−0.541828
$873$	6.00000	0.203069
$874$	0	0
$875$	−3.00000	−0.101419
$876$	0	0
$877$	30.0000	1.01303	0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000	1.01303	0.506514	+	0.862232i	$0.330934\pi$
$878$	8.00000	0.269987
$879$	0	0
$880$	0	0
$881$	35.0000	1.17918	0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000	1.17918	0.589590	+	0.807703i	$0.299289\pi$
$882$	6.00000	0.202031
$883$	−11.0000	−0.370179	−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000	−0.370179	−0.185090	+	0.982722i	$0.559258\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	21.0000	0.705509
$887$	25.0000	0.839418	0.419709	−	0.907659i	$-0.362132\pi$
$887$	25.0000	0.839418	0.419709	+	0.907659i	$0.362132\pi$
$888$	0	0
$889$	24.0000	0.804934
$890$	−4.00000	−0.134080
$891$	0	0
$892$	−16.0000	−0.535720
$893$	6.00000	0.200782
$894$	0	0
$895$	−15.0000	−0.501395
$896$	3.00000	0.100223
$897$	0	0
$898$	8.00000	0.266963
$899$	−21.0000	−0.700389
$900$	−3.00000	−0.100000
$901$	24.0000	0.799556
$902$	0	0
$903$	0	0
$904$	−9.00000	−0.299336
$905$	12.0000	0.398893
$906$	0	0
$907$	−17.0000	−0.564476	−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000	−0.564476	−0.282238	+	0.959344i	$0.591077\pi$
$908$	24.0000	0.796468
$909$	36.0000	1.19404
$910$	−9.00000	−0.298347
$911$	30.0000	0.993944	0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000	0.993944	0.496972	+	0.867766i	$0.334445\pi$
$912$	0	0
$913$	0	0
$914$	−18.0000	−0.595387
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	9.00000	0.296883	0.148441	−	0.988921i	$-0.452574\pi$
$919$	9.00000	0.296883	0.148441	+	0.988921i	$0.452574\pi$
$920$	0	0
$921$	0	0
$922$	−16.0000	−0.526932
$923$	−6.00000	−0.197492
$924$	0	0
$925$	−8.00000	−0.263038
$926$	17.0000	0.558655
$927$	−54.0000	−1.77359
$928$	3.00000	0.0984798
$929$	22.0000	0.721797	0.360898	−	0.932605i	$-0.382470\pi$
$929$	22.0000	0.721797	0.360898	+	0.932605i	$0.382470\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	−6.00000	−0.196537
$933$	0	0
$934$	8.00000	0.261768
$935$	0	0
$936$	−9.00000	−0.294174
$937$	46.0000	1.50275	0.751377	−	0.659873i	$-0.229390\pi$
$937$	46.0000	1.50275	0.751377	+	0.659873i	$0.229390\pi$
$938$	15.0000	0.489767
$939$	0	0
$940$	−6.00000	−0.195698
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	0	0
$943$	0	0
$944$	−4.00000	−0.130189
$945$	0	0
$946$	0	0
$947$	15.0000	0.487435	0.243717	−	0.969846i	$-0.421633\pi$
$947$	15.0000	0.487435	0.243717	+	0.969846i	$0.421633\pi$
$948$	0	0
$949$	3.00000	0.0973841
$950$	1.00000	0.0324443
$951$	0	0
$952$	−12.0000	−0.388922
$953$	−41.0000	−1.32812	−0.664060	−	0.747679i	$-0.731168\pi$
$953$	−41.0000	−1.32812	−0.664060	+	0.747679i	$0.731168\pi$
$954$	−18.0000	−0.582772
$955$	6.00000	0.194155
$956$	−11.0000	−0.355765
$957$	0	0
$958$	−28.0000	−0.904639
$959$	−15.0000	−0.484375
$960$	0	0
$961$	18.0000	0.580645
$962$	−24.0000	−0.773791
$963$	57.0000	1.83680
$964$	−26.0000	−0.837404
$965$	−24.0000	−0.772587
$966$	0	0
$967$	−30.0000	−0.964735	−0.482367	−	0.875969i	$-0.660223\pi$
$967$	−30.0000	−0.964735	−0.482367	+	0.875969i	$0.660223\pi$
$968$	11.0000	0.353553
$969$	0	0
$970$	2.00000	0.0642161
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	0	0
$973$	36.0000	1.15411
$974$	26.0000	0.833094
$975$	0	0
$976$	7.00000	0.224065
$977$	30.0000	0.959785	0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000	0.959785	0.479893	+	0.877327i	$0.340676\pi$
$978$	0	0
$979$	0	0
$980$	2.00000	0.0638877
$981$	−48.0000	−1.53252
$982$	24.0000	0.765871
$983$	51.0000	1.62665	0.813324	−	0.581811i	$-0.197656\pi$
$983$	51.0000	1.62665	0.813324	+	0.581811i	$0.197656\pi$
$984$	0	0
$985$	−11.0000	−0.350489
$986$	−12.0000	−0.382158
$987$	0	0
$988$	3.00000	0.0954427
$989$	0	0
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	−7.00000	−0.222250
$993$	0	0
$994$	6.00000	0.190308
$995$	10.0000	0.317021
$996$	0	0
$997$	−20.0000	−0.633406	−0.316703	−	0.948525i	$-0.602576\pi$
$997$	−20.0000	−0.633406	−0.316703	+	0.948525i	$0.602576\pi$
$998$	21.0000	0.664743
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.a.b.1.1	✓	1
3.2	odd	2		3870.2.a.n.1.1		1
4.3	odd	2		3440.2.a.c.1.1		1
5.2	odd	4		2150.2.b.g.1549.1		2
5.3	odd	4		2150.2.b.g.1549.2		2
5.4	even	2		2150.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.b.1.1	✓	1	1.1	even	1	trivial
2150.2.a.o.1.1		1	5.4	even	2
2150.2.b.g.1549.1		2	5.2	odd	4
2150.2.b.g.1549.2		2	5.3	odd	4
3440.2.a.c.1.1		1	4.3	odd	2
3870.2.a.n.1.1		1	3.2	odd	2

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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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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