LMFDB - Embedded newform 430.2.a.a.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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{28} -5.00000 q^{29} -9.00000 q^{31} -1.00000 q^{32} -1.00000 q^{35} -3.00000 q^{36} +4.00000 q^{37} -1.00000 q^{38} +1.00000 q^{40} -7.00000 q^{41} -1.00000 q^{43} -4.00000 q^{44} +3.00000 q^{45} +4.00000 q^{46} +6.00000 q^{47} -6.00000 q^{49} -1.00000 q^{50} -1.00000 q^{52} -2.00000 q^{53} +4.00000 q^{55} -1.00000 q^{56} +5.00000 q^{58} -7.00000 q^{61} +9.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} +15.0000 q^{67} +1.00000 q^{70} -6.00000 q^{71} +3.00000 q^{72} -5.00000 q^{73} -4.00000 q^{74} +1.00000 q^{76} -4.00000 q^{77} +9.00000 q^{79} -1.00000 q^{80} +9.00000 q^{81} +7.00000 q^{82} +1.00000 q^{86} +4.00000 q^{88} -3.00000 q^{90} -1.00000 q^{91} -4.00000 q^{92} -6.00000 q^{94} -1.00000 q^{95} -2.00000 q^{97} +6.00000 q^{98} +12.0000 q^{99} +O(q^{100})\)

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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	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	$0.706037\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	3.00000	0.707107
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	−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	$0.636929\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	−9.00000	−1.61645	−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000	−1.61645	−0.808224	+	0.588875i	$0.799571\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0	0
$35$	−1.00000	−0.169031
$36$	−3.00000	−0.500000
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−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
$44$	−4.00000	−0.603023
$45$	3.00000	0.447214
$46$	4.00000	0.589768
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	4.00000	0.539360
$56$	−1.00000	−0.133631
$57$	0	0
$58$	5.00000	0.656532
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	9.00000	1.14300
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0	0
$67$	15.0000	1.83254	0.916271	−	0.400559i	$-0.131184\pi$
$67$	15.0000	1.83254	0.916271	+	0.400559i	$0.131184\pi$
$68$	0	0
$69$	0	0
$70$	1.00000	0.119523
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	3.00000	0.353553
$73$	−5.00000	−0.585206	−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000	−0.585206	−0.292603	+	0.956234i	$0.594521\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	1.00000	0.114708
$77$	−4.00000	−0.455842
$78$	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
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	1.00000	0.107833
$87$	0	0
$88$	4.00000	0.426401
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−3.00000	−0.316228
$91$	−1.00000	−0.104828
$92$	−4.00000	−0.417029
$93$	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	$0.532375\pi$
$98$	6.00000	0.606092
$99$	12.0000	1.20605
$100$	1.00000	0.100000
$101$	16.0000	1.59206	0.796030	−	0.605257i	$-0.206930\pi$
$101$	16.0000	1.59206	0.796030	+	0.605257i	$0.206930\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	2.00000	0.194257
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	0	0
$109$	8.00000	0.766261	0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000	0.766261	0.383131	+	0.923694i	$0.374846\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	1.00000	0.0944911
$113$	−19.0000	−1.78737	−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000	−1.78737	−0.893685	+	0.448695i	$0.851889\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	−5.00000	−0.464238
$117$	3.00000	0.277350
$118$	0	0
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	7.00000	0.633750
$123$	0	0
$124$	−9.00000	−0.808224
$125$	−1.00000	−0.0894427
$126$	3.00000	0.267261
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−1.00000	−0.0877058
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	−15.0000	−1.29580
$135$	0	0
$136$	0	0
$137$	1.00000	0.0854358	0.0427179	−	0.999087i	$-0.486398\pi$
$137$	1.00000	0.0854358	0.0427179	+	0.999087i	$0.486398\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	6.00000	0.503509
$143$	4.00000	0.334497
$144$	−3.00000	−0.250000
$145$	5.00000	0.415227
$146$	5.00000	0.413803
$147$	0	0
$148$	4.00000	0.328798
$149$	−11.0000	−0.901155	−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000	−0.901155	−0.450578	+	0.892737i	$0.648782\pi$
$150$	0	0
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	4.00000	0.322329
$155$	9.00000	0.722897
$156$	0	0
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−9.00000	−0.716002
$159$	0	0
$160$	1.00000	0.0790569
$161$	−4.00000	−0.315244
$162$	−9.00000	−0.707107
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	−7.00000	−0.546608
$165$	0	0
$166$	0	0
$167$	−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
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−3.00000	−0.229416
$172$	−1.00000	−0.0762493
$173$	−13.0000	−0.988372	−0.494186	−	0.869356i	$-0.664534\pi$
$173$	−13.0000	−0.988372	−0.494186	+	0.869356i	$0.664534\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	−4.00000	−0.301511
$177$	0	0
$178$	0	0
$179$	−1.00000	−0.0747435	−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000	−0.0747435	−0.0373718	+	0.999301i	$0.511899\pi$
$180$	3.00000	0.223607
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	1.00000	0.0741249
$183$	0	0
$184$	4.00000	0.294884
$185$	−4.00000	−0.294086
$186$	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
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−1.00000	−0.0712470	−0.0356235	−	0.999365i	$-0.511342\pi$
$197$	−1.00000	−0.0712470	−0.0356235	+	0.999365i	$0.511342\pi$
$198$	−12.0000	−0.852803
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−16.0000	−1.12576
$203$	−5.00000	−0.350931
$204$	0	0
$205$	7.00000	0.488901
$206$	−6.00000	−0.418040
$207$	12.0000	0.834058
$208$	−1.00000	−0.0693375
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	−15.0000	−1.02538
$215$	1.00000	0.0681994
$216$	0	0
$217$	−9.00000	−0.610960
$218$	−8.00000	−0.541828
$219$	0	0
$220$	4.00000	0.269680
$221$	0	0
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−1.00000	−0.0668153
$225$	−3.00000	−0.200000
$226$	19.0000	1.26386
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	5.00000	0.328266
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	−3.00000	−0.196116
$235$	−6.00000	−0.391397
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−3.00000	−0.194054	−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000	−0.194054	−0.0970269	+	0.995282i	$0.530933\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−5.00000	−0.321412
$243$	0	0
$244$	−7.00000	−0.448129
$245$	6.00000	0.383326
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	9.00000	0.571501
$249$	0	0
$250$	1.00000	0.0632456
$251$	−10.0000	−0.631194	−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000	−0.631194	−0.315597	+	0.948893i	$0.602205\pi$
$252$	−3.00000	−0.188982
$253$	16.0000	1.00591
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−27.0000	−1.68421	−0.842107	−	0.539311i	$-0.818685\pi$
$257$	−27.0000	−1.68421	−0.842107	+	0.539311i	$0.818685\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	1.00000	0.0620174
$261$	15.0000	0.928477
$262$	−16.0000	−0.988483
$263$	15.0000	0.924940	0.462470	−	0.886635i	$-0.346963\pi$
$263$	15.0000	0.924940	0.462470	+	0.886635i	$0.346963\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	15.0000	0.916271
$269$	4.00000	0.243884	0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000	0.243884	0.121942	+	0.992537i	$0.461088\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	0	0
$273$	0	0
$274$	−1.00000	−0.0604122
$275$	−4.00000	−0.241209
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	0	0
$279$	27.0000	1.61645
$280$	1.00000	0.0597614
$281$	−15.0000	−0.894825	−0.447412	−	0.894328i	$-0.647654\pi$
$281$	−15.0000	−0.894825	−0.447412	+	0.894328i	$0.647654\pi$
$282$	0	0
$283$	−19.0000	−1.12943	−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000	−1.12943	−0.564716	+	0.825285i	$0.691014\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	−4.00000	−0.236525
$287$	−7.00000	−0.413197
$288$	3.00000	0.176777
$289$	−17.0000	−1.00000
$290$	−5.00000	−0.293610
$291$	0	0
$292$	−5.00000	−0.292603
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	0	0
$295$	0	0
$296$	−4.00000	−0.232495
$297$	0	0
$298$	11.0000	0.637213
$299$	4.00000	0.231326
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	−6.00000	−0.345261
$303$	0	0
$304$	1.00000	0.0573539
$305$	7.00000	0.400819
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	−4.00000	−0.227921
$309$	0	0
$310$	−9.00000	−0.511166
$311$	3.00000	0.170114	0.0850572	−	0.996376i	$-0.472893\pi$
$311$	3.00000	0.170114	0.0850572	+	0.996376i	$0.472893\pi$
$312$	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
$315$	3.00000	0.169031
$316$	9.00000	0.506290
$317$	−1.00000	−0.0561656	−0.0280828	−	0.999606i	$-0.508940\pi$
$317$	−1.00000	−0.0561656	−0.0280828	+	0.999606i	$0.508940\pi$
$318$	0	0
$319$	20.0000	1.11979
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	4.00000	0.222911
$323$	0	0
$324$	9.00000	0.500000
$325$	−1.00000	−0.0554700
$326$	8.00000	0.443079
$327$	0	0
$328$	7.00000	0.386510
$329$	6.00000	0.330791
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	0	0
$333$	−12.0000	−0.657596
$334$	16.0000	0.875481
$335$	−15.0000	−0.819538
$336$	0	0
$337$	−30.0000	−1.63420	−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000	−1.63420	−0.817102	+	0.576493i	$0.804421\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	36.0000	1.94951
$342$	3.00000	0.162221
$343$	−13.0000	−0.701934
$344$	1.00000	0.0539164
$345$	0	0
$346$	13.0000	0.698884
$347$	−22.0000	−1.18102	−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000	−1.18102	−0.590511	+	0.807030i	$0.701074\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	4.00000	0.213201
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	6.00000	0.318447
$356$	0	0
$357$	0	0
$358$	1.00000	0.0528516
$359$	−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
$362$	20.0000	1.05118
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	5.00000	0.261712
$366$	0	0
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	−4.00000	−0.208514
$369$	21.0000	1.09322
$370$	4.00000	0.207950
$371$	−2.00000	−0.103835
$372$	0	0
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	0	0
$375$	0	0
$376$	−6.00000	−0.309426
$377$	5.00000	0.257513
$378$	0	0
$379$	34.0000	1.74646	0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000	1.74646	0.873231	+	0.487306i	$0.162020\pi$
$380$	−1.00000	−0.0512989
$381$	0	0
$382$	−6.00000	−0.306987
$383$	37.0000	1.89061	0.945306	−	0.326185i	$-0.105763\pi$
$383$	37.0000	1.89061	0.945306	+	0.326185i	$0.105763\pi$
$384$	0	0
$385$	4.00000	0.203859
$386$	−4.00000	−0.203595
$387$	3.00000	0.152499
$388$	−2.00000	−0.101535
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	0	0
$392$	6.00000	0.303046
$393$	0	0
$394$	1.00000	0.0503793
$395$	−9.00000	−0.452839
$396$	12.0000	0.603023
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	10.0000	0.501255
$399$	0	0
$400$	1.00000	0.0500000
$401$	27.0000	1.34832	0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000	1.34832	0.674158	+	0.738587i	$0.264507\pi$
$402$	0	0
$403$	9.00000	0.448322
$404$	16.0000	0.796030
$405$	−9.00000	−0.447214
$406$	5.00000	0.248146
$407$	−16.0000	−0.793091
$408$	0	0
$409$	−24.0000	−1.18672	−0.593362	−	0.804936i	$-0.702200\pi$
$409$	−24.0000	−1.18672	−0.593362	+	0.804936i	$0.702200\pi$
$410$	−7.00000	−0.345705
$411$	0	0
$412$	6.00000	0.295599
$413$	0	0
$414$	−12.0000	−0.589768
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	4.00000	0.195646
$419$	1.00000	0.0488532	0.0244266	−	0.999702i	$-0.492224\pi$
$419$	1.00000	0.0488532	0.0244266	+	0.999702i	$0.492224\pi$
$420$	0	0
$421$	−33.0000	−1.60832	−0.804161	−	0.594412i	$-0.797385\pi$
$421$	−33.0000	−1.60832	−0.804161	+	0.594412i	$0.797385\pi$
$422$	20.0000	0.973585
$423$	−18.0000	−0.875190
$424$	2.00000	0.0971286
$425$	0	0
$426$	0	0
$427$	−7.00000	−0.338754
$428$	15.0000	0.725052
$429$	0	0
$430$	−1.00000	−0.0482243
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	7.00000	0.336399	0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000	0.336399	0.168199	+	0.985753i	$0.446205\pi$
$434$	9.00000	0.432014
$435$	0	0
$436$	8.00000	0.383131
$437$	−4.00000	−0.191346
$438$	0	0
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	−4.00000	−0.190693
$441$	18.0000	0.857143
$442$	0	0
$443$	1.00000	0.0475114	0.0237557	−	0.999718i	$-0.492438\pi$
$443$	1.00000	0.0475114	0.0237557	+	0.999718i	$0.492438\pi$
$444$	0	0
$445$	0	0
$446$	−8.00000	−0.378811
$447$	0	0
$448$	1.00000	0.0472456
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	3.00000	0.141421
$451$	28.0000	1.31847
$452$	−19.0000	−0.893685
$453$	0	0
$454$	−4.00000	−0.187729
$455$	1.00000	0.0468807
$456$	0	0
$457$	−30.0000	−1.40334	−0.701670	−	0.712502i	$-0.747562\pi$
$457$	−30.0000	−1.40334	−0.701670	+	0.712502i	$0.747562\pi$
$458$	−22.0000	−1.02799
$459$	0	0
$460$	4.00000	0.186501
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	0	0
$463$	19.0000	0.883005	0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000	0.883005	0.441502	+	0.897260i	$0.354446\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	14.0000	0.648537
$467$	20.0000	0.925490	0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000	0.925490	0.462745	+	0.886492i	$0.346865\pi$
$468$	3.00000	0.138675
$469$	15.0000	0.692636
$470$	6.00000	0.276759
$471$	0	0
$472$	0	0
$473$	4.00000	0.183920
$474$	0	0
$475$	1.00000	0.0458831
$476$	0	0
$477$	6.00000	0.274721
$478$	3.00000	0.137217
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	−10.0000	−0.455488
$483$	0	0
$484$	5.00000	0.227273
$485$	2.00000	0.0908153
$486$	0	0
$487$	−18.0000	−0.815658	−0.407829	−	0.913058i	$-0.633714\pi$
$487$	−18.0000	−0.815658	−0.407829	+	0.913058i	$0.633714\pi$
$488$	7.00000	0.316875
$489$	0	0
$490$	−6.00000	−0.271052
$491$	−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
$493$	0	0
$494$	1.00000	0.0449921
$495$	−12.0000	−0.539360
$496$	−9.00000	−0.404112
$497$	−6.00000	−0.269137
$498$	0	0
$499$	13.0000	0.581960	0.290980	−	0.956729i	$-0.406019\pi$
$499$	13.0000	0.581960	0.290980	+	0.956729i	$0.406019\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	10.0000	0.446322
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	3.00000	0.133631
$505$	−16.0000	−0.711991
$506$	−16.0000	−0.711287
$507$	0	0
$508$	8.00000	0.354943
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	0	0
$511$	−5.00000	−0.221187
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	27.0000	1.19092
$515$	−6.00000	−0.264392
$516$	0	0
$517$	−24.0000	−1.05552
$518$	−4.00000	−0.175750
$519$	0	0
$520$	−1.00000	−0.0438529
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	−15.0000	−0.656532
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	16.0000	0.698963
$525$	0	0
$526$	−15.0000	−0.654031
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−2.00000	−0.0868744
$531$	0	0
$532$	1.00000	0.0433555
$533$	7.00000	0.303204
$534$	0	0
$535$	−15.0000	−0.648507
$536$	−15.0000	−0.647901
$537$	0	0
$538$	−4.00000	−0.172452
$539$	24.0000	1.03375
$540$	0	0
$541$	−14.0000	−0.601907	−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000	−0.601907	−0.300954	+	0.953639i	$0.597305\pi$
$542$	−5.00000	−0.214768
$543$	0	0
$544$	0	0
$545$	−8.00000	−0.342682
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	1.00000	0.0427179
$549$	21.0000	0.896258
$550$	4.00000	0.170561
$551$	−5.00000	−0.213007
$552$	0	0
$553$	9.00000	0.382719
$554$	−8.00000	−0.339887
$555$	0	0
$556$	0	0
$557$	−3.00000	−0.127114	−0.0635570	−	0.997978i	$-0.520244\pi$
$557$	−3.00000	−0.127114	−0.0635570	+	0.997978i	$0.520244\pi$
$558$	−27.0000	−1.14300
$559$	1.00000	0.0422955
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	15.0000	0.632737
$563$	−41.0000	−1.72794	−0.863972	−	0.503540i	$-0.832031\pi$
$563$	−41.0000	−1.72794	−0.863972	+	0.503540i	$0.832031\pi$
$564$	0	0
$565$	19.0000	0.799336
$566$	19.0000	0.798630
$567$	9.00000	0.377964
$568$	6.00000	0.251754
$569$	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
$571$	−23.0000	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	7.00000	0.292174
$575$	−4.00000	−0.166812
$576$	−3.00000	−0.125000
$577$	−27.0000	−1.12402	−0.562012	−	0.827129i	$-0.689973\pi$
$577$	−27.0000	−1.12402	−0.562012	+	0.827129i	$0.689973\pi$
$578$	17.0000	0.707107
$579$	0	0
$580$	5.00000	0.207614
$581$	0	0
$582$	0	0
$583$	8.00000	0.331326
$584$	5.00000	0.206901
$585$	−3.00000	−0.124035
$586$	−26.0000	−1.07405
$587$	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
$589$	−9.00000	−0.370839
$590$	0	0
$591$	0	0
$592$	4.00000	0.164399
$593$	9.00000	0.369586	0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000	0.369586	0.184793	+	0.982777i	$0.440839\pi$
$594$	0	0
$595$	0	0
$596$	−11.0000	−0.450578
$597$	0	0
$598$	−4.00000	−0.163572
$599$	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
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	1.00000	0.0407570
$603$	−45.0000	−1.83254
$604$	6.00000	0.244137
$605$	−5.00000	−0.203279
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−7.00000	−0.283422
$611$	−6.00000	−0.242734
$612$	0	0
$613$	31.0000	1.25208	0.626039	−	0.779792i	$-0.284675\pi$
$613$	31.0000	1.25208	0.626039	+	0.779792i	$0.284675\pi$
$614$	11.0000	0.443924
$615$	0	0
$616$	4.00000	0.161165
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	0	0
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	9.00000	0.361449
$621$	0	0
$622$	−3.00000	−0.120289
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	−4.00000	−0.159617
$629$	0	0
$630$	−3.00000	−0.119523
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	−9.00000	−0.358001
$633$	0	0
$634$	1.00000	0.0397151
$635$	−8.00000	−0.317470
$636$	0	0
$637$	6.00000	0.237729
$638$	−20.0000	−0.791808
$639$	18.0000	0.712069
$640$	1.00000	0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	33.0000	1.30139	0.650696	−	0.759338i	$-0.274477\pi$
$643$	33.0000	1.30139	0.650696	+	0.759338i	$0.274477\pi$
$644$	−4.00000	−0.157622
$645$	0	0
$646$	0	0
$647$	11.0000	0.432455	0.216227	−	0.976343i	$-0.430625\pi$
$647$	11.0000	0.432455	0.216227	+	0.976343i	$0.430625\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	1.00000	0.0392232
$651$	0	0
$652$	−8.00000	−0.313304
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	−16.0000	−0.625172
$656$	−7.00000	−0.273304
$657$	15.0000	0.585206
$658$	−6.00000	−0.233904
$659$	−28.0000	−1.09073	−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000	−1.09073	−0.545363	+	0.838200i	$0.683608\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	12.0000	0.466393
$663$	0	0
$664$	0	0
$665$	−1.00000	−0.0387783
$666$	12.0000	0.464991
$667$	20.0000	0.774403
$668$	−16.0000	−0.619059
$669$	0	0
$670$	15.0000	0.579501
$671$	28.0000	1.08093
$672$	0	0
$673$	−17.0000	−0.655302	−0.327651	−	0.944799i	$-0.606257\pi$
$673$	−17.0000	−0.655302	−0.327651	+	0.944799i	$0.606257\pi$
$674$	30.0000	1.15556
$675$	0	0
$676$	−12.0000	−0.461538
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	0	0
$682$	−36.0000	−1.37851
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	−3.00000	−0.114708
$685$	−1.00000	−0.0382080
$686$	13.0000	0.496342
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	2.00000	0.0761939
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−13.0000	−0.494186
$693$	12.0000	0.455842
$694$	22.0000	0.835109
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−10.0000	−0.378506
$699$	0	0
$700$	1.00000	0.0377964
$701$	48.0000	1.81293	0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000	1.81293	0.906467	+	0.422276i	$0.138769\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−14.0000	−0.526897
$707$	16.0000	0.601742
$708$	0	0
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	−6.00000	−0.225176
$711$	−27.0000	−1.01258
$712$	0	0
$713$	36.0000	1.34821
$714$	0	0
$715$	−4.00000	−0.149592
$716$	−1.00000	−0.0373718
$717$	0	0
$718$	21.0000	0.783713
$719$	−28.0000	−1.04422	−0.522112	−	0.852877i	$-0.674856\pi$
$719$	−28.0000	−1.04422	−0.522112	+	0.852877i	$0.674856\pi$
$720$	3.00000	0.111803
$721$	6.00000	0.223452
$722$	18.0000	0.669891
$723$	0	0
$724$	−20.0000	−0.743294
$725$	−5.00000	−0.185695
$726$	0	0
$727$	48.0000	1.78022	0.890111	−	0.455744i	$-0.150627\pi$
$727$	48.0000	1.78022	0.890111	+	0.455744i	$0.150627\pi$
$728$	1.00000	0.0370625
$729$	−27.0000	−1.00000
$730$	−5.00000	−0.185058
$731$	0	0
$732$	0	0
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	4.00000	0.147442
$737$	−60.0000	−2.21013
$738$	−21.0000	−0.773021
$739$	1.00000	0.0367856	0.0183928	−	0.999831i	$-0.494145\pi$
$739$	1.00000	0.0367856	0.0183928	+	0.999831i	$0.494145\pi$
$740$	−4.00000	−0.147043
$741$	0	0
$742$	2.00000	0.0734223
$743$	−21.0000	−0.770415	−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000	−0.770415	−0.385208	+	0.922830i	$0.625870\pi$
$744$	0	0
$745$	11.0000	0.403009
$746$	36.0000	1.31805
$747$	0	0
$748$	0	0
$749$	15.0000	0.548088
$750$	0	0
$751$	−20.0000	−0.729810	−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000	−0.729810	−0.364905	+	0.931045i	$0.618899\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	−5.00000	−0.182089
$755$	−6.00000	−0.218362
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−34.0000	−1.23494
$759$	0	0
$760$	1.00000	0.0362738
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	0	0
$763$	8.00000	0.289619
$764$	6.00000	0.217072
$765$	0	0
$766$	−37.0000	−1.33686
$767$	0	0
$768$	0	0
$769$	−41.0000	−1.47850	−0.739249	−	0.673432i	$-0.764819\pi$
$769$	−41.0000	−1.47850	−0.739249	+	0.673432i	$0.764819\pi$
$770$	−4.00000	−0.144150
$771$	0	0
$772$	4.00000	0.143963
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	−3.00000	−0.107833
$775$	−9.00000	−0.323290
$776$	2.00000	0.0717958
$777$	0	0
$778$	−30.0000	−1.07555
$779$	−7.00000	−0.250801
$780$	0	0
$781$	24.0000	0.858788
$782$	0	0
$783$	0	0
$784$	−6.00000	−0.214286
$785$	4.00000	0.142766
$786$	0	0
$787$	11.0000	0.392108	0.196054	−	0.980593i	$-0.437187\pi$
$787$	11.0000	0.392108	0.196054	+	0.980593i	$0.437187\pi$
$788$	−1.00000	−0.0356235
$789$	0	0
$790$	9.00000	0.320206
$791$	−19.0000	−0.675562
$792$	−12.0000	−0.426401
$793$	7.00000	0.248577
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−10.0000	−0.354441
$797$	−1.00000	−0.0354218	−0.0177109	−	0.999843i	$-0.505638\pi$
$797$	−1.00000	−0.0354218	−0.0177109	+	0.999843i	$0.505638\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−27.0000	−0.953403
$803$	20.0000	0.705785
$804$	0	0
$805$	4.00000	0.140981
$806$	−9.00000	−0.317011
$807$	0	0
$808$	−16.0000	−0.562878
$809$	−19.0000	−0.668004	−0.334002	−	0.942572i	$-0.608399\pi$
$809$	−19.0000	−0.668004	−0.334002	+	0.942572i	$0.608399\pi$
$810$	9.00000	0.316228
$811$	3.00000	0.105344	0.0526721	−	0.998612i	$-0.483226\pi$
$811$	3.00000	0.105344	0.0526721	+	0.998612i	$0.483226\pi$
$812$	−5.00000	−0.175466
$813$	0	0
$814$	16.0000	0.560800
$815$	8.00000	0.280228
$816$	0	0
$817$	−1.00000	−0.0349856
$818$	24.0000	0.839140
$819$	3.00000	0.104828
$820$	7.00000	0.244451
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	0	0
$823$	−26.0000	−0.906303	−0.453152	−	0.891434i	$-0.649700\pi$
$823$	−26.0000	−0.906303	−0.453152	+	0.891434i	$0.649700\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	0	0
$827$	57.0000	1.98208	0.991042	−	0.133550i	$-0.0426376\pi$
$827$	57.0000	1.98208	0.991042	+	0.133550i	$0.0426376\pi$
$828$	12.0000	0.417029
$829$	13.0000	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$829$	13.0000	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	0	0
$835$	16.0000	0.553703
$836$	−4.00000	−0.138343
$837$	0	0
$838$	−1.00000	−0.0345444
$839$	42.0000	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	33.0000	1.13726
$843$	0	0
$844$	−20.0000	−0.688428
$845$	12.0000	0.412813
$846$	18.0000	0.618853
$847$	5.00000	0.171802
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	0	0
$851$	−16.0000	−0.548473
$852$	0	0
$853$	22.0000	0.753266	0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000	0.753266	0.376633	+	0.926363i	$0.377082\pi$
$854$	7.00000	0.239535
$855$	3.00000	0.102598
$856$	−15.0000	−0.512689
$857$	48.0000	1.63965	0.819824	−	0.572615i	$-0.194071\pi$
$857$	48.0000	1.63965	0.819824	+	0.572615i	$0.194071\pi$
$858$	0	0
$859$	−49.0000	−1.67186	−0.835929	−	0.548837i	$-0.815071\pi$
$859$	−49.0000	−1.67186	−0.835929	+	0.548837i	$0.815071\pi$
$860$	1.00000	0.0340997
$861$	0	0
$862$	0	0
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	0	0
$865$	13.0000	0.442013
$866$	−7.00000	−0.237870
$867$	0	0
$868$	−9.00000	−0.305480
$869$	−36.0000	−1.22122
$870$	0	0
$871$	−15.0000	−0.508256
$872$	−8.00000	−0.270914
$873$	6.00000	0.203069
$874$	4.00000	0.135302
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	24.0000	0.809961
$879$	0	0
$880$	4.00000	0.134840
$881$	43.0000	1.44871	0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000	1.44871	0.724353	+	0.689429i	$0.242138\pi$
$882$	−18.0000	−0.606092
$883$	39.0000	1.31245	0.656227	−	0.754563i	$-0.272151\pi$
$883$	39.0000	1.31245	0.656227	+	0.754563i	$0.272151\pi$
$884$	0	0
$885$	0	0
$886$	−1.00000	−0.0335957
$887$	−19.0000	−0.637958	−0.318979	−	0.947762i	$-0.603340\pi$
$887$	−19.0000	−0.637958	−0.318979	+	0.947762i	$0.603340\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	−36.0000	−1.20605
$892$	8.00000	0.267860
$893$	6.00000	0.200782
$894$	0	0
$895$	1.00000	0.0334263
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	24.0000	0.800890
$899$	45.0000	1.50083
$900$	−3.00000	−0.100000
$901$	0	0
$902$	−28.0000	−0.932298
$903$	0	0
$904$	19.0000	0.631931
$905$	20.0000	0.664822
$906$	0	0
$907$	13.0000	0.431658	0.215829	−	0.976431i	$-0.430755\pi$
$907$	13.0000	0.431658	0.215829	+	0.976431i	$0.430755\pi$
$908$	4.00000	0.132745
$909$	−48.0000	−1.59206
$910$	−1.00000	−0.0331497
$911$	10.0000	0.331315	0.165657	−	0.986183i	$-0.447025\pi$
$911$	10.0000	0.331315	0.165657	+	0.986183i	$0.447025\pi$
$912$	0	0
$913$	0	0
$914$	30.0000	0.992312
$915$	0	0
$916$	22.0000	0.726900
$917$	16.0000	0.528367
$918$	0	0
$919$	25.0000	0.824674	0.412337	−	0.911031i	$-0.364713\pi$
$919$	25.0000	0.824674	0.412337	+	0.911031i	$0.364713\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	12.0000	0.395199
$923$	6.00000	0.197492
$924$	0	0
$925$	4.00000	0.131519
$926$	−19.0000	−0.624379
$927$	−18.0000	−0.591198
$928$	5.00000	0.164133
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−14.0000	−0.458585
$933$	0	0
$934$	−20.0000	−0.654420
$935$	0	0
$936$	−3.00000	−0.0980581
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−15.0000	−0.489767
$939$	0	0
$940$	−6.00000	−0.195698
$941$	26.0000	0.847576	0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000	0.847576	0.423788	+	0.905761i	$0.360700\pi$
$942$	0	0
$943$	28.0000	0.911805
$944$	0	0
$945$	0	0
$946$	−4.00000	−0.130051
$947$	29.0000	0.942373	0.471187	−	0.882034i	$-0.343826\pi$
$947$	29.0000	0.942373	0.471187	+	0.882034i	$0.343826\pi$
$948$	0	0
$949$	5.00000	0.162307
$950$	−1.00000	−0.0324443
$951$	0	0
$952$	0	0
$953$	35.0000	1.13376	0.566881	−	0.823800i	$-0.308150\pi$
$953$	35.0000	1.13376	0.566881	+	0.823800i	$0.308150\pi$
$954$	−6.00000	−0.194257
$955$	−6.00000	−0.194155
$956$	−3.00000	−0.0970269
$957$	0	0
$958$	20.0000	0.646171
$959$	1.00000	0.0322917
$960$	0	0
$961$	50.0000	1.61290
$962$	4.00000	0.128965
$963$	−45.0000	−1.45010
$964$	10.0000	0.322078
$965$	−4.00000	−0.128765
$966$	0	0
$967$	−18.0000	−0.578841	−0.289420	−	0.957202i	$-0.593463\pi$
$967$	−18.0000	−0.578841	−0.289420	+	0.957202i	$0.593463\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	−2.00000	−0.0642161
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	18.0000	0.576757
$975$	0	0
$976$	−7.00000	−0.224065
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	0	0
$979$	0	0
$980$	6.00000	0.191663
$981$	−24.0000	−0.766261
$982$	24.0000	0.765871
$983$	−1.00000	−0.0318950	−0.0159475	−	0.999873i	$-0.505076\pi$
$983$	−1.00000	−0.0318950	−0.0159475	+	0.999873i	$0.505076\pi$
$984$	0	0
$985$	1.00000	0.0318626
$986$	0	0
$987$	0	0
$988$	−1.00000	−0.0318142
$989$	4.00000	0.127193
$990$	12.0000	0.381385
$991$	52.0000	1.65183	0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000	1.65183	0.825917	+	0.563791i	$0.190658\pi$
$992$	9.00000	0.285750
$993$	0	0
$994$	6.00000	0.190308
$995$	10.0000	0.317021
$996$	0	0
$997$	−40.0000	−1.26681	−0.633406	−	0.773819i	$-0.718344\pi$
$997$	−40.0000	−1.26681	−0.633406	+	0.773819i	$0.718344\pi$
$998$	−13.0000	−0.411508
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.a.1.1	✓	1	1.1	even	1	trivial
2150.2.a.n.1.1		1	5.4	even	2
2150.2.b.f.1549.1		2	5.2	odd	4
2150.2.b.f.1549.2		2	5.3	odd	4
3440.2.a.a.1.1		1	4.3	odd	2
3870.2.a.y.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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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