LMFDB - Embedded newform 4598.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
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	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} +1.00000 q^{21} -9.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} -2.00000 q^{26} -5.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +8.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} -2.00000 q^{36} -7.00000 q^{37} -1.00000 q^{38} -2.00000 q^{39} +1.00000 q^{42} +10.0000 q^{43} -9.00000 q^{46} +9.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -5.00000 q^{50} -6.00000 q^{51} -2.00000 q^{52} -9.00000 q^{53} -5.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} -3.00000 q^{58} -9.00000 q^{59} -8.00000 q^{61} +8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{67} -6.00000 q^{68} -9.00000 q^{69} +12.0000 q^{71} -2.00000 q^{72} -2.00000 q^{73} -7.00000 q^{74} -5.00000 q^{75} -1.00000 q^{76} -2.00000 q^{78} -14.0000 q^{79} +1.00000 q^{81} +12.0000 q^{83} +1.00000 q^{84} +10.0000 q^{86} -3.00000 q^{87} +6.00000 q^{89} -2.00000 q^{91} -9.00000 q^{92} +8.00000 q^{93} +9.00000 q^{94} +1.00000 q^{96} -16.0000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	1.00000	0.408248
$7$	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
$9$	−2.00000	−0.666667
$10$	0	0
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	−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
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−2.00000	−0.471405
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	1.00000	0.218218
$22$	0	0
$23$	−9.00000	−1.87663	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000	−1.87663	−0.938315	+	0.345782i	$0.887614\pi$
$24$	1.00000	0.204124
$25$	−5.00000	−1.00000
$26$	−2.00000	−0.392232
$27$	−5.00000	−0.962250
$28$	1.00000	0.188982
$29$	−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
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	−1.00000	−0.162221
$39$	−2.00000	−0.320256
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	1.00000	0.154303
$43$	10.0000	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$44$	0	0
$45$	0	0
$46$	−9.00000	−1.32698
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	−5.00000	−0.707107
$51$	−6.00000	−0.840168
$52$	−2.00000	−0.277350
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	−1.00000	−0.132453
$58$	−3.00000	−0.393919
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	8.00000	1.01600
$63$	−2.00000	−0.251976
$64$	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	$0.578571\pi$
$68$	−6.00000	−0.727607
$69$	−9.00000	−1.08347
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	−2.00000	−0.235702
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−7.00000	−0.813733
$75$	−5.00000	−0.577350
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	10.0000	1.07833
$87$	−3.00000	−0.321634
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	−9.00000	−0.938315
$93$	8.00000	0.829561
$94$	9.00000	0.928279
$95$	0	0
$96$	1.00000	0.102062
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−5.00000	−0.500000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−6.00000	−0.594089
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−9.00000	−0.874157
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	−5.00000	−0.481125
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	1.00000	0.0944911
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−3.00000	−0.278543
$117$	4.00000	0.369800
$118$	−9.00000	−0.828517
$119$	−6.00000	−0.550019
$120$	0	0
$121$	0	0
$122$	−8.00000	−0.724286
$123$	0	0
$124$	8.00000	0.718421
$125$	0	0
$126$	−2.00000	−0.178174
$127$	−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
$129$	10.0000	0.880451
$130$	0	0
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−6.00000	−0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−9.00000	−0.766131
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	12.0000	1.00702
$143$	0	0
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−2.00000	−0.165521
$147$	−6.00000	−0.494872
$148$	−7.00000	−0.575396
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	−5.00000	−0.408248
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	−1.00000	−0.0811107
$153$	12.0000	0.970143
$154$	0	0
$155$	0	0
$156$	−2.00000	−0.160128
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	−14.0000	−1.11378
$159$	−9.00000	−0.713746
$160$	0	0
$161$	−9.00000	−0.709299
$162$	1.00000	0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	0	0
$165$	0	0
$166$	12.0000	0.931381
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	0	0
$171$	2.00000	0.152944
$172$	10.0000	0.762493
$173$	−3.00000	−0.228086	−0.114043	−	0.993476i	$-0.536380\pi$
$173$	−3.00000	−0.228086	−0.114043	+	0.993476i	$0.536380\pi$
$174$	−3.00000	−0.227429
$175$	−5.00000	−0.377964
$176$	0	0
$177$	−9.00000	−0.676481
$178$	6.00000	0.449719
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	−2.00000	−0.148250
$183$	−8.00000	−0.591377
$184$	−9.00000	−0.663489
$185$	0	0
$186$	8.00000	0.586588
$187$	0	0
$188$	9.00000	0.656392
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	1.00000	0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−16.0000	−1.14873
$195$	0	0
$196$	−6.00000	−0.428571
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−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
$201$	−4.00000	−0.282138
$202$	0	0
$203$	−3.00000	−0.210559
$204$	−6.00000	−0.420084
$205$	0	0
$206$	14.0000	0.975426
$207$	18.0000	1.25109
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	−9.00000	−0.618123
$213$	12.0000	0.822226
$214$	15.0000	1.02538
$215$	0	0
$216$	−5.00000	−0.340207
$217$	8.00000	0.543075
$218$	19.0000	1.28684
$219$	−2.00000	−0.135147
$220$	0	0
$221$	12.0000	0.807207
$222$	−7.00000	−0.469809
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	1.00000	0.0668153
$225$	10.0000	0.666667
$226$	12.0000	0.798228
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−1.00000	−0.0662266
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	0	0
$231$	0	0
$232$	−3.00000	−0.196960
$233$	−27.0000	−1.76883	−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000	−1.76883	−0.884414	+	0.466702i	$0.845442\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	−9.00000	−0.585850
$237$	−14.0000	−0.909398
$238$	−6.00000	−0.388922
$239$	−9.00000	−0.582162	−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000	−0.582162	−0.291081	+	0.956698i	$0.594015\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	−8.00000	−0.512148
$245$	0	0
$246$	0	0
$247$	2.00000	0.127257
$248$	8.00000	0.508001
$249$	12.0000	0.760469
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−12.0000	−0.748539	−0.374270	−	0.927320i	$-0.622107\pi$
$257$	−12.0000	−0.748539	−0.374270	+	0.927320i	$0.622107\pi$
$258$	10.0000	0.622573
$259$	−7.00000	−0.434959
$260$	0	0
$261$	6.00000	0.371391
$262$	18.0000	1.11204
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	6.00000	0.367194
$268$	−4.00000	−0.244339
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	−6.00000	−0.363803
$273$	−2.00000	−0.121046
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−9.00000	−0.541736
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	−8.00000	−0.479808
$279$	−16.0000	−0.957895
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	9.00000	0.535942
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	0	0
$287$	0	0
$288$	−2.00000	−0.117851
$289$	19.0000	1.11765
$290$	0	0
$291$	−16.0000	−0.937937
$292$	−2.00000	−0.117041
$293$	−33.0000	−1.92788	−0.963940	−	0.266119i	$-0.914259\pi$
$293$	−33.0000	−1.92788	−0.963940	+	0.266119i	$0.914259\pi$
$294$	−6.00000	−0.349927
$295$	0	0
$296$	−7.00000	−0.406867
$297$	0	0
$298$	12.0000	0.695141
$299$	18.0000	1.04097
$300$	−5.00000	−0.288675
$301$	10.0000	0.576390
$302$	10.0000	0.575435
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	12.0000	0.685994
$307$	−17.0000	−0.970241	−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000	−0.970241	−0.485121	+	0.874447i	$0.661224\pi$
$308$	0	0
$309$	14.0000	0.796432
$310$	0	0
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	−2.00000	−0.113228
$313$	17.0000	0.960897	0.480448	−	0.877023i	$-0.340474\pi$
$313$	17.0000	0.960897	0.480448	+	0.877023i	$0.340474\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	−14.0000	−0.787562
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−9.00000	−0.504695
$319$	0	0
$320$	0	0
$321$	15.0000	0.837218
$322$	−9.00000	−0.501550
$323$	6.00000	0.333849
$324$	1.00000	0.0555556
$325$	10.0000	0.554700
$326$	−10.0000	−0.553849
$327$	19.0000	1.05070
$328$	0	0
$329$	9.00000	0.496186
$330$	0	0
$331$	5.00000	0.274825	0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000	0.274825	0.137412	+	0.990514i	$0.456121\pi$
$332$	12.0000	0.658586
$333$	14.0000	0.767195
$334$	−6.00000	−0.328305
$335$	0	0
$336$	1.00000	0.0545545
$337$	−32.0000	−1.74315	−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−32.0000	−1.74315	−0.871576	+	0.490261i	$0.836901\pi$
$338$	−9.00000	−0.489535
$339$	12.0000	0.651751
$340$	0	0
$341$	0	0
$342$	2.00000	0.108148
$343$	−13.0000	−0.701934
$344$	10.0000	0.539164
$345$	0	0
$346$	−3.00000	−0.161281
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−3.00000	−0.160817
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−5.00000	−0.267261
$351$	10.0000	0.533761
$352$	0	0
$353$	−15.0000	−0.798369	−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000	−0.798369	−0.399185	+	0.916871i	$0.630707\pi$
$354$	−9.00000	−0.478345
$355$	0	0
$356$	6.00000	0.317999
$357$	−6.00000	−0.317554
$358$	15.0000	0.792775
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−22.0000	−1.15629
$363$	0	0
$364$	−2.00000	−0.104828
$365$	0	0
$366$	−8.00000	−0.418167
$367$	23.0000	1.20059	0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000	1.20059	0.600295	+	0.799779i	$0.295050\pi$
$368$	−9.00000	−0.469157
$369$	0	0
$370$	0	0
$371$	−9.00000	−0.467257
$372$	8.00000	0.414781
$373$	19.0000	0.983783	0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000	0.983783	0.491891	+	0.870657i	$0.336306\pi$
$374$	0	0
$375$	0	0
$376$	9.00000	0.464140
$377$	6.00000	0.309016
$378$	−5.00000	−0.257172
$379$	−13.0000	−0.667765	−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000	−0.667765	−0.333883	+	0.942615i	$0.608359\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	−9.00000	−0.460480
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−20.0000	−1.01666
$388$	−16.0000	−0.812277
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	54.0000	2.73090
$392$	−6.00000	−0.303046
$393$	18.0000	0.907980
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−16.0000	−0.802008
$399$	−1.00000	−0.0500626
$400$	−5.00000	−0.250000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	−4.00000	−0.199502
$403$	−16.0000	−0.797017
$404$	0	0
$405$	0	0
$406$	−3.00000	−0.148888
$407$	0	0
$408$	−6.00000	−0.297044
$409$	4.00000	0.197787	0.0988936	−	0.995098i	$-0.468470\pi$
$409$	4.00000	0.197787	0.0988936	+	0.995098i	$0.468470\pi$
$410$	0	0
$411$	−6.00000	−0.295958
$412$	14.0000	0.689730
$413$	−9.00000	−0.442861
$414$	18.0000	0.884652
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	−8.00000	−0.391762
$418$	0	0
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	−1.00000	−0.0487370	−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000	−0.0487370	−0.0243685	+	0.999703i	$0.507758\pi$
$422$	−5.00000	−0.243396
$423$	−18.0000	−0.875190
$424$	−9.00000	−0.437079
$425$	30.0000	1.45521
$426$	12.0000	0.581402
$427$	−8.00000	−0.387147
$428$	15.0000	0.725052
$429$	0	0
$430$	0	0
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	−5.00000	−0.240563
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	19.0000	0.909935
$437$	9.00000	0.430528
$438$	−2.00000	−0.0955637
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	12.0000	0.570782
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	−7.00000	−0.332205
$445$	0	0
$446$	−16.0000	−0.757622
$447$	12.0000	0.567581
$448$	1.00000	0.0472456
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	10.0000	0.471405
$451$	0	0
$452$	12.0000	0.564433
$453$	10.0000	0.469841
$454$	−12.0000	−0.563188
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−17.0000	−0.795226	−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000	−0.795226	−0.397613	+	0.917553i	$0.630161\pi$
$458$	−4.00000	−0.186908
$459$	30.0000	1.40028
$460$	0	0
$461$	−24.0000	−1.11779	−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000	−1.11779	−0.558896	+	0.829238i	$0.688775\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	−27.0000	−1.25075
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	4.00000	0.184900
$469$	−4.00000	−0.184703
$470$	0	0
$471$	−22.0000	−1.01371
$472$	−9.00000	−0.414259
$473$	0	0
$474$	−14.0000	−0.643041
$475$	5.00000	0.229416
$476$	−6.00000	−0.275010
$477$	18.0000	0.824163
$478$	−9.00000	−0.411650
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	0	0
$481$	14.0000	0.638345
$482$	−2.00000	−0.0910975
$483$	−9.00000	−0.409514
$484$	0	0
$485$	0	0
$486$	16.0000	0.725775
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	−8.00000	−0.362143
$489$	−10.0000	−0.452216
$490$	0	0
$491$	−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
$493$	18.0000	0.810679
$494$	2.00000	0.0899843
$495$	0	0
$496$	8.00000	0.359211
$497$	12.0000	0.538274
$498$	12.0000	0.537733
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	0	0
$501$	−6.00000	−0.268060
$502$	18.0000	0.803379
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	−8.00000	−0.354943
$509$	−27.0000	−1.19675	−0.598377	−	0.801215i	$-0.704187\pi$
$509$	−27.0000	−1.19675	−0.598377	+	0.801215i	$0.704187\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	1.00000	0.0441942
$513$	5.00000	0.220755
$514$	−12.0000	−0.529297
$515$	0	0
$516$	10.0000	0.440225
$517$	0	0
$518$	−7.00000	−0.307562
$519$	−3.00000	−0.131685
$520$	0	0
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	6.00000	0.262613
$523$	7.00000	0.306089	0.153044	−	0.988219i	$-0.451092\pi$
$523$	7.00000	0.306089	0.153044	+	0.988219i	$0.451092\pi$
$524$	18.0000	0.786334
$525$	−5.00000	−0.218218
$526$	24.0000	1.04645
$527$	−48.0000	−2.09091
$528$	0	0
$529$	58.0000	2.52174
$530$	0	0
$531$	18.0000	0.781133
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	6.00000	0.259645
$535$	0	0
$536$	−4.00000	−0.172774
$537$	15.0000	0.647298
$538$	−3.00000	−0.129339
$539$	0	0
$540$	0	0
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	16.0000	0.687259
$543$	−22.0000	−0.944110
$544$	−6.00000	−0.257248
$545$	0	0
$546$	−2.00000	−0.0855921
$547$	−23.0000	−0.983409	−0.491704	−	0.870762i	$-0.663626\pi$
$547$	−23.0000	−0.983409	−0.491704	+	0.870762i	$0.663626\pi$
$548$	−6.00000	−0.256307
$549$	16.0000	0.682863
$550$	0	0
$551$	3.00000	0.127804
$552$	−9.00000	−0.383065
$553$	−14.0000	−0.595341
$554$	4.00000	0.169944
$555$	0	0
$556$	−8.00000	−0.339276
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−16.0000	−0.677334
$559$	−20.0000	−0.845910
$560$	0	0
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−9.00000	−0.379305	−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000	−0.379305	−0.189652	+	0.981851i	$0.560736\pi$
$564$	9.00000	0.378968
$565$	0	0
$566$	16.0000	0.672530
$567$	1.00000	0.0419961
$568$	12.0000	0.503509
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	−38.0000	−1.59025	−0.795125	−	0.606445i	$-0.792595\pi$
$571$	−38.0000	−1.59025	−0.795125	+	0.606445i	$0.792595\pi$
$572$	0	0
$573$	−9.00000	−0.375980
$574$	0	0
$575$	45.0000	1.87663
$576$	−2.00000	−0.0833333
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	19.0000	0.790296
$579$	22.0000	0.914289
$580$	0	0
$581$	12.0000	0.497844
$582$	−16.0000	−0.663221
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	−33.0000	−1.36322
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	−6.00000	−0.247436
$589$	−8.00000	−0.329634
$590$	0	0
$591$	12.0000	0.493614
$592$	−7.00000	−0.287698
$593$	−15.0000	−0.615976	−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000	−0.615976	−0.307988	+	0.951390i	$0.599656\pi$
$594$	0	0
$595$	0	0
$596$	12.0000	0.491539
$597$	−16.0000	−0.654836
$598$	18.0000	0.736075
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	−5.00000	−0.204124
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	10.0000	0.407570
$603$	8.00000	0.325785
$604$	10.0000	0.406894
$605$	0	0
$606$	0	0
$607$	10.0000	0.405887	0.202944	−	0.979190i	$-0.434949\pi$
$607$	10.0000	0.405887	0.202944	+	0.979190i	$0.434949\pi$
$608$	−1.00000	−0.0405554
$609$	−3.00000	−0.121566
$610$	0	0
$611$	−18.0000	−0.728202
$612$	12.0000	0.485071
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−17.0000	−0.686064
$615$	0	0
$616$	0	0
$617$	45.0000	1.81163	0.905816	−	0.423672i	$-0.139259\pi$
$617$	45.0000	1.81163	0.905816	+	0.423672i	$0.139259\pi$
$618$	14.0000	0.563163
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	0	0
$621$	45.0000	1.80579
$622$	−12.0000	−0.481156
$623$	6.00000	0.240385
$624$	−2.00000	−0.0800641
$625$	25.0000	1.00000
$626$	17.0000	0.679457
$627$	0	0
$628$	−22.0000	−0.877896
$629$	42.0000	1.67465
$630$	0	0
$631$	35.0000	1.39333	0.696664	−	0.717398i	$-0.254667\pi$
$631$	35.0000	1.39333	0.696664	+	0.717398i	$0.254667\pi$
$632$	−14.0000	−0.556890
$633$	−5.00000	−0.198732
$634$	−18.0000	−0.714871
$635$	0	0
$636$	−9.00000	−0.356873
$637$	12.0000	0.475457
$638$	0	0
$639$	−24.0000	−0.949425
$640$	0	0
$641$	24.0000	0.947943	0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000	0.947943	0.473972	+	0.880540i	$0.342820\pi$
$642$	15.0000	0.592003
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	−9.00000	−0.354650
$645$	0	0
$646$	6.00000	0.236067
$647$	45.0000	1.76913	0.884566	−	0.466415i	$-0.154454\pi$
$647$	45.0000	1.76913	0.884566	+	0.466415i	$0.154454\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	10.0000	0.392232
$651$	8.00000	0.313545
$652$	−10.0000	−0.391630
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	19.0000	0.742959
$655$	0	0
$656$	0	0
$657$	4.00000	0.156055
$658$	9.00000	0.350857
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−19.0000	−0.739014	−0.369507	−	0.929228i	$-0.620473\pi$
$661$	−19.0000	−0.739014	−0.369507	+	0.929228i	$0.620473\pi$
$662$	5.00000	0.194331
$663$	12.0000	0.466041
$664$	12.0000	0.465690
$665$	0	0
$666$	14.0000	0.542489
$667$	27.0000	1.04544
$668$	−6.00000	−0.232147
$669$	−16.0000	−0.618596
$670$	0	0
$671$	0	0
$672$	1.00000	0.0385758
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	−32.0000	−1.23259
$675$	25.0000	0.962250
$676$	−9.00000	−0.346154
$677$	3.00000	0.115299	0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000	0.115299	0.0576497	+	0.998337i	$0.481639\pi$
$678$	12.0000	0.460857
$679$	−16.0000	−0.614024
$680$	0	0
$681$	−12.0000	−0.459841
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	−13.0000	−0.496342
$687$	−4.00000	−0.152610
$688$	10.0000	0.381246
$689$	18.0000	0.685745
$690$	0	0
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	−3.00000	−0.114043
$693$	0	0
$694$	12.0000	0.455514
$695$	0	0
$696$	−3.00000	−0.113715
$697$	0	0
$698$	10.0000	0.378506
$699$	−27.0000	−1.02123
$700$	−5.00000	−0.188982
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	10.0000	0.377426
$703$	7.00000	0.264010
$704$	0	0
$705$	0	0
$706$	−15.0000	−0.564532
$707$	0	0
$708$	−9.00000	−0.338241
$709$	−16.0000	−0.600893	−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000	−0.600893	−0.300446	+	0.953799i	$0.597136\pi$
$710$	0	0
$711$	28.0000	1.05008
$712$	6.00000	0.224860
$713$	−72.0000	−2.69642
$714$	−6.00000	−0.224544
$715$	0	0
$716$	15.0000	0.560576
$717$	−9.00000	−0.336111
$718$	12.0000	0.447836
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	14.0000	0.521387
$722$	1.00000	0.0372161
$723$	−2.00000	−0.0743808
$724$	−22.0000	−0.817624
$725$	15.0000	0.557086
$726$	0	0
$727$	−19.0000	−0.704671	−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000	−0.704671	−0.352335	+	0.935874i	$0.614612\pi$
$728$	−2.00000	−0.0741249
$729$	13.0000	0.481481
$730$	0	0
$731$	−60.0000	−2.21918
$732$	−8.00000	−0.295689
$733$	4.00000	0.147743	0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000	0.147743	0.0738717	+	0.997268i	$0.476464\pi$
$734$	23.0000	0.848945
$735$	0	0
$736$	−9.00000	−0.331744
$737$	0	0
$738$	0	0
$739$	−14.0000	−0.514998	−0.257499	−	0.966279i	$-0.582898\pi$
$739$	−14.0000	−0.514998	−0.257499	+	0.966279i	$0.582898\pi$
$740$	0	0
$741$	2.00000	0.0734718
$742$	−9.00000	−0.330400
$743$	−30.0000	−1.10059	−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000	−1.10059	−0.550297	+	0.834969i	$0.685485\pi$
$744$	8.00000	0.293294
$745$	0	0
$746$	19.0000	0.695639
$747$	−24.0000	−0.878114
$748$	0	0
$749$	15.0000	0.548088
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	9.00000	0.328196
$753$	18.0000	0.655956
$754$	6.00000	0.218507
$755$	0	0
$756$	−5.00000	−0.181848
$757$	−46.0000	−1.67190	−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000	−1.67190	−0.835949	+	0.548807i	$0.815082\pi$
$758$	−13.0000	−0.472181
$759$	0	0
$760$	0	0
$761$	21.0000	0.761249	0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000	0.761249	0.380625	+	0.924730i	$0.375709\pi$
$762$	−8.00000	−0.289809
$763$	19.0000	0.687846
$764$	−9.00000	−0.325609
$765$	0	0
$766$	−12.0000	−0.433578
$767$	18.0000	0.649942
$768$	1.00000	0.0360844
$769$	7.00000	0.252426	0.126213	−	0.992003i	$-0.459718\pi$
$769$	7.00000	0.252426	0.126213	+	0.992003i	$0.459718\pi$
$770$	0	0
$771$	−12.0000	−0.432169
$772$	22.0000	0.791797
$773$	21.0000	0.755318	0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000	0.755318	0.377659	+	0.925945i	$0.376729\pi$
$774$	−20.0000	−0.718885
$775$	−40.0000	−1.43684
$776$	−16.0000	−0.574367
$777$	−7.00000	−0.251124
$778$	6.00000	0.215110
$779$	0	0
$780$	0	0
$781$	0	0
$782$	54.0000	1.93104
$783$	15.0000	0.536056
$784$	−6.00000	−0.214286
$785$	0	0
$786$	18.0000	0.642039
$787$	7.00000	0.249523	0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000	0.249523	0.124762	+	0.992187i	$0.460183\pi$
$788$	12.0000	0.427482
$789$	24.0000	0.854423
$790$	0	0
$791$	12.0000	0.426671
$792$	0	0
$793$	16.0000	0.568177
$794$	−34.0000	−1.20661
$795$	0	0
$796$	−16.0000	−0.567105
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	−1.00000	−0.0353996
$799$	−54.0000	−1.91038
$800$	−5.00000	−0.176777
$801$	−12.0000	−0.423999
$802$	−12.0000	−0.423735
$803$	0	0
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−16.0000	−0.563576
$807$	−3.00000	−0.105605
$808$	0	0
$809$	−45.0000	−1.58212	−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000	−1.58212	−0.791058	+	0.611741i	$0.790469\pi$
$810$	0	0
$811$	−35.0000	−1.22902	−0.614508	−	0.788911i	$-0.710645\pi$
$811$	−35.0000	−1.22902	−0.614508	+	0.788911i	$0.710645\pi$
$812$	−3.00000	−0.105279
$813$	16.0000	0.561144
$814$	0	0
$815$	0	0
$816$	−6.00000	−0.210042
$817$	−10.0000	−0.349856
$818$	4.00000	0.139857
$819$	4.00000	0.139771
$820$	0	0
$821$	48.0000	1.67521	0.837606	−	0.546275i	$-0.183955\pi$
$821$	48.0000	1.67521	0.837606	+	0.546275i	$0.183955\pi$
$822$	−6.00000	−0.209274
$823$	23.0000	0.801730	0.400865	−	0.916137i	$-0.368710\pi$
$823$	23.0000	0.801730	0.400865	+	0.916137i	$0.368710\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	−9.00000	−0.313150
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	18.0000	0.625543
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	0	0
$831$	4.00000	0.138758
$832$	−2.00000	−0.0693375
$833$	36.0000	1.24733
$834$	−8.00000	−0.277017
$835$	0	0
$836$	0	0
$837$	−40.0000	−1.38260
$838$	24.0000	0.829066
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−1.00000	−0.0344623
$843$	−6.00000	−0.206651
$844$	−5.00000	−0.172107
$845$	0	0
$846$	−18.0000	−0.618853
$847$	0	0
$848$	−9.00000	−0.309061
$849$	16.0000	0.549119
$850$	30.0000	1.02899
$851$	63.0000	2.15961
$852$	12.0000	0.411113
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	15.0000	0.512689
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	0	0
$861$	0	0
$862$	18.0000	0.613082
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−34.0000	−1.15537
$867$	19.0000	0.645274
$868$	8.00000	0.271538
$869$	0	0
$870$	0	0
$871$	8.00000	0.271070
$872$	19.0000	0.643421
$873$	32.0000	1.08304
$874$	9.00000	0.304430
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	16.0000	0.539974
$879$	−33.0000	−1.11306
$880$	0	0
$881$	45.0000	1.51609	0.758044	−	0.652203i	$-0.226155\pi$
$881$	45.0000	1.51609	0.758044	+	0.652203i	$0.226155\pi$
$882$	12.0000	0.404061
$883$	−10.0000	−0.336527	−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000	−0.336527	−0.168263	+	0.985742i	$0.553816\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	−6.00000	−0.201574
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	−7.00000	−0.234905
$889$	−8.00000	−0.268311
$890$	0	0
$891$	0	0
$892$	−16.0000	−0.535720
$893$	−9.00000	−0.301174
$894$	12.0000	0.401340
$895$	0	0
$896$	1.00000	0.0334077
$897$	18.0000	0.601003
$898$	6.00000	0.200223
$899$	−24.0000	−0.800445
$900$	10.0000	0.333333
$901$	54.0000	1.79900
$902$	0	0
$903$	10.0000	0.332779
$904$	12.0000	0.399114
$905$	0	0
$906$	10.0000	0.332228
$907$	−19.0000	−0.630885	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	−19.0000	−0.630885	−0.315442	+	0.948945i	$0.602153\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	0	0
$911$	18.0000	0.596367	0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000	0.596367	0.298183	+	0.954509i	$0.403619\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	−17.0000	−0.562310
$915$	0	0
$916$	−4.00000	−0.132164
$917$	18.0000	0.594412
$918$	30.0000	0.990148
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	0	0
$921$	−17.0000	−0.560169
$922$	−24.0000	−0.790398
$923$	−24.0000	−0.789970
$924$	0	0
$925$	35.0000	1.15079
$926$	−16.0000	−0.525793
$927$	−28.0000	−0.919641
$928$	−3.00000	−0.0984798
$929$	45.0000	1.47640	0.738201	−	0.674581i	$-0.235676\pi$
$929$	45.0000	1.47640	0.738201	+	0.674581i	$0.235676\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	−27.0000	−0.884414
$933$	−12.0000	−0.392862
$934$	−6.00000	−0.196326
$935$	0	0
$936$	4.00000	0.130744
$937$	19.0000	0.620703	0.310351	−	0.950622i	$-0.399553\pi$
$937$	19.0000	0.620703	0.310351	+	0.950622i	$0.399553\pi$
$938$	−4.00000	−0.130605
$939$	17.0000	0.554774
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−22.0000	−0.716799
$943$	0	0
$944$	−9.00000	−0.292925
$945$	0	0
$946$	0	0
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	−14.0000	−0.454699
$949$	4.00000	0.129845
$950$	5.00000	0.162221
$951$	−18.0000	−0.583690
$952$	−6.00000	−0.194461
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	18.0000	0.582772
$955$	0	0
$956$	−9.00000	−0.291081
$957$	0	0
$958$	21.0000	0.678479
$959$	−6.00000	−0.193750
$960$	0	0
$961$	33.0000	1.06452
$962$	14.0000	0.451378
$963$	−30.0000	−0.966736
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	−9.00000	−0.289570
$967$	−59.0000	−1.89731	−0.948656	−	0.316310i	$-0.897556\pi$
$967$	−59.0000	−1.89731	−0.948656	+	0.316310i	$0.897556\pi$
$968$	0	0
$969$	6.00000	0.192748
$970$	0	0
$971$	39.0000	1.25157	0.625785	−	0.779996i	$-0.284779\pi$
$971$	39.0000	1.25157	0.625785	+	0.779996i	$0.284779\pi$
$972$	16.0000	0.513200
$973$	−8.00000	−0.256468
$974$	2.00000	0.0640841
$975$	10.0000	0.320256
$976$	−8.00000	−0.256074
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	−10.0000	−0.319765
$979$	0	0
$980$	0	0
$981$	−38.0000	−1.21325
$982$	−24.0000	−0.765871
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	18.0000	0.573237
$987$	9.00000	0.286473
$988$	2.00000	0.0636285
$989$	−90.0000	−2.86183
$990$	0	0
$991$	−28.0000	−0.889449	−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000	−0.889449	−0.444725	+	0.895667i	$0.646698\pi$
$992$	8.00000	0.254000
$993$	5.00000	0.158670
$994$	12.0000	0.380617
$995$	0	0
$996$	12.0000	0.380235
$997$	52.0000	1.64686	0.823428	−	0.567420i	$-0.192059\pi$
$997$	52.0000	1.64686	0.823428	+	0.567420i	$0.192059\pi$
$998$	−10.0000	−0.316544
$999$	35.0000	1.10735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.q.1.1	yes	1
11.10	odd	2		4598.2.a.h.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.h.1.1	✓	1	11.10	odd	2
4598.2.a.q.1.1	yes	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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