LMFDB - Embedded newform 1890.2.a.x.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1890.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.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:	$15.0917259820$
Analytic rank:	$0$
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	$\chi$	$=$	1890.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{10} +3.00000 q^{11} +5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -7.00000 q^{19} +1.00000 q^{20} +3.00000 q^{22} +6.00000 q^{23} +1.00000 q^{25} +5.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{35} +2.00000 q^{37} -7.00000 q^{38} +1.00000 q^{40} -3.00000 q^{41} -1.00000 q^{43} +3.00000 q^{44} +6.00000 q^{46} +3.00000 q^{47} +1.00000 q^{49} +1.00000 q^{50} +5.00000 q^{52} +9.00000 q^{53} +3.00000 q^{55} +1.00000 q^{56} -6.00000 q^{58} +6.00000 q^{59} +8.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +5.00000 q^{65} -13.0000 q^{67} +1.00000 q^{70} -7.00000 q^{73} +2.00000 q^{74} -7.00000 q^{76} +3.00000 q^{77} +8.00000 q^{79} +1.00000 q^{80} -3.00000 q^{82} +3.00000 q^{83} -1.00000 q^{86} +3.00000 q^{88} +9.00000 q^{89} +5.00000 q^{91} +6.00000 q^{92} +3.00000 q^{94} -7.00000 q^{95} -10.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	1.00000	0.316228
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	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	$0.5\pi$
$18$	0	0
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	3.00000	0.639602
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	5.00000	0.980581
$27$	0	0
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	0	0
$35$	1.00000	0.169031
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−7.00000	−1.13555
$39$	0	0
$40$	1.00000	0.158114
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	6.00000	0.884652
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0	0
$52$	5.00000	0.693375
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	0	0
$55$	3.00000	0.404520
$56$	1.00000	0.133631
$57$	0	0
$58$	−6.00000	−0.787839
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	5.00000	0.620174
$66$	0	0
$67$	−13.0000	−1.58820	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000	−1.58820	−0.794101	+	0.607785i	$0.792058\pi$
$68$	0	0
$69$	0	0
$70$	1.00000	0.119523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−7.00000	−0.802955
$77$	3.00000	0.341882
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	−3.00000	−0.331295
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	0	0
$85$	0	0
$86$	−1.00000	−0.107833
$87$	0	0
$88$	3.00000	0.319801
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	6.00000	0.625543
$93$	0	0
$94$	3.00000	0.309426
$95$	−7.00000	−0.718185
$96$	0	0
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	5.00000	0.490290
$105$	0	0
$106$	9.00000	0.874157
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	3.00000	0.286039
$111$	0	0
$112$	1.00000	0.0944911
$113$	15.0000	1.41108	0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000	1.41108	0.705541	+	0.708669i	$0.250704\pi$
$114$	0	0
$115$	6.00000	0.559503
$116$	−6.00000	−0.557086
$117$	0	0
$118$	6.00000	0.552345
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	8.00000	0.724286
$123$	0	0
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	5.00000	0.438529
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	−7.00000	−0.606977
$134$	−13.0000	−1.12303
$135$	0	0
$136$	0	0
$137$	−15.0000	−1.28154	−0.640768	−	0.767734i	$-0.721384\pi$
$137$	−15.0000	−1.28154	−0.640768	+	0.767734i	$0.721384\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	0	0
$143$	15.0000	1.25436
$144$	0	0
$145$	−6.00000	−0.498273
$146$	−7.00000	−0.579324
$147$	0	0
$148$	2.00000	0.164399
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	−7.00000	−0.567775
$153$	0	0
$154$	3.00000	0.241747
$155$	−4.00000	−0.321288
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	1.00000	0.0790569
$161$	6.00000	0.472866
$162$	0	0
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	−3.00000	−0.234261
$165$	0	0
$166$	3.00000	0.232845
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	3.00000	0.226134
$177$	0	0
$178$	9.00000	0.674579
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	5.00000	0.370625
$183$	0	0
$184$	6.00000	0.442326
$185$	2.00000	0.147043
$186$	0	0
$187$	0	0
$188$	3.00000	0.218797
$189$	0	0
$190$	−7.00000	−0.507833
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	0	0
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	27.0000	1.92367	0.961835	−	0.273629i	$-0.0882242\pi$
$197$	27.0000	1.92367	0.961835	+	0.273629i	$0.0882242\pi$
$198$	0	0
$199$	−25.0000	−1.77220	−0.886102	−	0.463491i	$-0.846597\pi$
$199$	−25.0000	−1.77220	−0.886102	+	0.463491i	$0.846597\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	3.00000	0.211079
$203$	−6.00000	−0.421117
$204$	0	0
$205$	−3.00000	−0.209529
$206$	−4.00000	−0.278693
$207$	0	0
$208$	5.00000	0.346688
$209$	−21.0000	−1.45260
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	9.00000	0.618123
$213$	0	0
$214$	0	0
$215$	−1.00000	−0.0681994
$216$	0	0
$217$	−4.00000	−0.271538
$218$	11.0000	0.745014
$219$	0	0
$220$	3.00000	0.202260
$221$	0	0
$222$	0	0
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	15.0000	0.997785
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	0	0
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	−6.00000	−0.393919
$233$	27.0000	1.76883	0.884414	−	0.466702i	$-0.154558\pi$
$233$	27.0000	1.76883	0.884414	+	0.466702i	$0.154558\pi$
$234$	0	0
$235$	3.00000	0.195698
$236$	6.00000	0.390567
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	−2.00000	−0.128565
$243$	0	0
$244$	8.00000	0.512148
$245$	1.00000	0.0638877
$246$	0	0
$247$	−35.0000	−2.22700
$248$	−4.00000	−0.254000
$249$	0	0
$250$	1.00000	0.0632456
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	0	0
$253$	18.0000	1.13165
$254$	−7.00000	−0.439219
$255$	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	$0.622107\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	5.00000	0.310087
$261$	0	0
$262$	−12.0000	−0.741362
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	−7.00000	−0.429198
$267$	0	0
$268$	−13.0000	−0.794101
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	29.0000	1.76162	0.880812	−	0.473466i	$-0.156997\pi$
$271$	29.0000	1.76162	0.880812	+	0.473466i	$0.156997\pi$
$272$	0	0
$273$	0	0
$274$	−15.0000	−0.906183
$275$	3.00000	0.180907
$276$	0	0
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	1.00000	0.0597614
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	0	0
$285$	0	0
$286$	15.0000	0.886969
$287$	−3.00000	−0.177084
$288$	0	0
$289$	−17.0000	−1.00000
$290$	−6.00000	−0.352332
$291$	0	0
$292$	−7.00000	−0.409644
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	0	0
$295$	6.00000	0.349334
$296$	2.00000	0.116248
$297$	0	0
$298$	6.00000	0.347571
$299$	30.0000	1.73494
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	−10.0000	−0.575435
$303$	0	0
$304$	−7.00000	−0.401478
$305$	8.00000	0.458079
$306$	0	0
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	−4.00000	−0.227185
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	0	0
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	8.00000	0.450035
$317$	−15.0000	−0.842484	−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000	−0.842484	−0.421242	+	0.906948i	$0.638406\pi$
$318$	0	0
$319$	−18.0000	−1.00781
$320$	1.00000	0.0559017
$321$	0	0
$322$	6.00000	0.334367
$323$	0	0
$324$	0	0
$325$	5.00000	0.277350
$326$	−16.0000	−0.886158
$327$	0	0
$328$	−3.00000	−0.165647
$329$	3.00000	0.165395
$330$	0	0
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	3.00000	0.164646
$333$	0	0
$334$	−12.0000	−0.656611
$335$	−13.0000	−0.710266
$336$	0	0
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	−12.0000	−0.649836
$342$	0	0
$343$	1.00000	0.0539949
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	3.00000	0.159901
$353$	12.0000	0.638696	0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000	0.638696	0.319348	+	0.947638i	$0.396536\pi$
$354$	0	0
$355$	0	0
$356$	9.00000	0.476999
$357$	0	0
$358$	9.00000	0.475665
$359$	9.00000	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	2.00000	0.105118
$363$	0	0
$364$	5.00000	0.262071
$365$	−7.00000	−0.366397
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	2.00000	0.103975
$371$	9.00000	0.467257
$372$	0	0
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	0	0
$375$	0	0
$376$	3.00000	0.154713
$377$	−30.0000	−1.54508
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	−7.00000	−0.359092
$381$	0	0
$382$	3.00000	0.153493
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	3.00000	0.152894
$386$	−22.0000	−1.11977
$387$	0	0
$388$	−10.0000	−0.507673
$389$	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
$392$	1.00000	0.0505076
$393$	0	0
$394$	27.0000	1.36024
$395$	8.00000	0.402524
$396$	0	0
$397$	38.0000	1.90717	0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000	1.90717	0.953583	+	0.301131i	$0.0973643\pi$
$398$	−25.0000	−1.25314
$399$	0	0
$400$	1.00000	0.0500000
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	0	0
$403$	−20.0000	−0.996271
$404$	3.00000	0.149256
$405$	0	0
$406$	−6.00000	−0.297775
$407$	6.00000	0.297409
$408$	0	0
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	−3.00000	−0.148159
$411$	0	0
$412$	−4.00000	−0.197066
$413$	6.00000	0.295241
$414$	0	0
$415$	3.00000	0.147264
$416$	5.00000	0.245145
$417$	0	0
$418$	−21.0000	−1.02714
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	0	0
$421$	35.0000	1.70580	0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000	1.70580	0.852898	+	0.522078i	$0.174843\pi$
$422$	14.0000	0.681509
$423$	0	0
$424$	9.00000	0.437079
$425$	0	0
$426$	0	0
$427$	8.00000	0.387147
$428$	0	0
$429$	0	0
$430$	−1.00000	−0.0482243
$431$	−9.00000	−0.433515	−0.216757	−	0.976226i	$-0.569548\pi$
$431$	−9.00000	−0.433515	−0.216757	+	0.976226i	$0.569548\pi$
$432$	0	0
$433$	11.0000	0.528626	0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000	0.528626	0.264313	+	0.964437i	$0.414855\pi$
$434$	−4.00000	−0.192006
$435$	0	0
$436$	11.0000	0.526804
$437$	−42.0000	−2.00913
$438$	0	0
$439$	−19.0000	−0.906821	−0.453410	−	0.891302i	$-0.649793\pi$
$439$	−19.0000	−0.906821	−0.453410	+	0.891302i	$0.649793\pi$
$440$	3.00000	0.143019
$441$	0	0
$442$	0	0
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	0	0
$445$	9.00000	0.426641
$446$	26.0000	1.23114
$447$	0	0
$448$	1.00000	0.0472456
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	−9.00000	−0.423793
$452$	15.0000	0.705541
$453$	0	0
$454$	3.00000	0.140797
$455$	5.00000	0.234404
$456$	0	0
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	−22.0000	−1.02799
$459$	0	0
$460$	6.00000	0.279751
$461$	3.00000	0.139724	0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000	0.139724	0.0698620	+	0.997557i	$0.477744\pi$
$462$	0	0
$463$	−13.0000	−0.604161	−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000	−0.604161	−0.302081	+	0.953282i	$0.597681\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	27.0000	1.25075
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	0	0
$469$	−13.0000	−0.600284
$470$	3.00000	0.138380
$471$	0	0
$472$	6.00000	0.276172
$473$	−3.00000	−0.137940
$474$	0	0
$475$	−7.00000	−0.321182
$476$	0	0
$477$	0	0
$478$	24.0000	1.09773
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	8.00000	0.364390
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−10.0000	−0.454077
$486$	0	0
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	8.00000	0.362143
$489$	0	0
$490$	1.00000	0.0451754
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0	0
$493$	0	0
$494$	−35.0000	−1.57472
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−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	$0.435696\pi$
$504$	0	0
$505$	3.00000	0.133498
$506$	18.0000	0.800198
$507$	0	0
$508$	−7.00000	−0.310575
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	−7.00000	−0.309662
$512$	1.00000	0.0441942
$513$	0	0
$514$	−12.0000	−0.529297
$515$	−4.00000	−0.176261
$516$	0	0
$517$	9.00000	0.395820
$518$	2.00000	0.0878750
$519$	0	0
$520$	5.00000	0.219265
$521$	−27.0000	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$522$	0	0
$523$	38.0000	1.66162	0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000	1.66162	0.830812	+	0.556553i	$0.187876\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−24.0000	−1.04645
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	9.00000	0.390935
$531$	0	0
$532$	−7.00000	−0.303488
$533$	−15.0000	−0.649722
$534$	0	0
$535$	0	0
$536$	−13.0000	−0.561514
$537$	0	0
$538$	−18.0000	−0.776035
$539$	3.00000	0.129219
$540$	0	0
$541$	29.0000	1.24681	0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000	1.24681	0.623404	+	0.781900i	$0.285749\pi$
$542$	29.0000	1.24566
$543$	0	0
$544$	0	0
$545$	11.0000	0.471188
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−15.0000	−0.640768
$549$	0	0
$550$	3.00000	0.127920
$551$	42.0000	1.78926
$552$	0	0
$553$	8.00000	0.340195
$554$	26.0000	1.10463
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	0	0
$559$	−5.00000	−0.211477
$560$	1.00000	0.0422577
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−21.0000	−0.885044	−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000	−0.885044	−0.442522	+	0.896758i	$0.645916\pi$
$564$	0	0
$565$	15.0000	0.631055
$566$	−22.0000	−0.924729
$567$	0	0
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	15.0000	0.627182
$573$	0	0
$574$	−3.00000	−0.125218
$575$	6.00000	0.250217
$576$	0	0
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	−17.0000	−0.707107
$579$	0	0
$580$	−6.00000	−0.249136
$581$	3.00000	0.124461
$582$	0	0
$583$	27.0000	1.11823
$584$	−7.00000	−0.289662
$585$	0	0
$586$	−30.0000	−1.23929
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	28.0000	1.15372
$590$	6.00000	0.247016
$591$	0	0
$592$	2.00000	0.0821995
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	0	0
$595$	0	0
$596$	6.00000	0.245770
$597$	0	0
$598$	30.0000	1.22679
$599$	−39.0000	−1.59350	−0.796748	−	0.604311i	$-0.793448\pi$
$599$	−39.0000	−1.59350	−0.796748	+	0.604311i	$0.793448\pi$
$600$	0	0
$601$	44.0000	1.79480	0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000	1.79480	0.897399	+	0.441221i	$0.145454\pi$
$602$	−1.00000	−0.0407570
$603$	0	0
$604$	−10.0000	−0.406894
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	−7.00000	−0.283887
$609$	0	0
$610$	8.00000	0.323911
$611$	15.0000	0.606835
$612$	0	0
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	3.00000	0.120873
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	0	0
$619$	−1.00000	−0.0401934	−0.0200967	−	0.999798i	$-0.506397\pi$
$619$	−1.00000	−0.0401934	−0.0200967	+	0.999798i	$0.506397\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	−30.0000	−1.20289
$623$	9.00000	0.360577
$624$	0	0
$625$	1.00000	0.0400000
$626$	−1.00000	−0.0399680
$627$	0	0
$628$	−22.0000	−0.877896
$629$	0	0
$630$	0	0
$631$	−34.0000	−1.35352	−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000	−1.35352	−0.676759	+	0.736204i	$0.736616\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	−15.0000	−0.595726
$635$	−7.00000	−0.277787
$636$	0	0
$637$	5.00000	0.198107
$638$	−18.0000	−0.712627
$639$	0	0
$640$	1.00000	0.0395285
$641$	−24.0000	−0.947943	−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000	−0.947943	−0.473972	+	0.880540i	$0.657180\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	0	0
$647$	27.0000	1.06148	0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000	1.06148	0.530740	+	0.847535i	$0.321914\pi$
$648$	0	0
$649$	18.0000	0.706562
$650$	5.00000	0.196116
$651$	0	0
$652$	−16.0000	−0.626608
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	−3.00000	−0.117130
$657$	0	0
$658$	3.00000	0.116952
$659$	48.0000	1.86981	0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000	1.86981	0.934907	+	0.354892i	$0.115482\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−10.0000	−0.388661
$663$	0	0
$664$	3.00000	0.116423
$665$	−7.00000	−0.271448
$666$	0	0
$667$	−36.0000	−1.39393
$668$	−12.0000	−0.464294
$669$	0	0
$670$	−13.0000	−0.502234
$671$	24.0000	0.926510
$672$	0	0
$673$	8.00000	0.308377	0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000	0.308377	0.154189	+	0.988041i	$0.450724\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	12.0000	0.461538
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	−10.0000	−0.383765
$680$	0	0
$681$	0	0
$682$	−12.0000	−0.459504
$683$	−18.0000	−0.688751	−0.344375	−	0.938832i	$-0.611909\pi$
$683$	−18.0000	−0.688751	−0.344375	+	0.938832i	$0.611909\pi$
$684$	0	0
$685$	−15.0000	−0.573121
$686$	1.00000	0.0381802
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	45.0000	1.71436
$690$	0	0
$691$	17.0000	0.646710	0.323355	−	0.946278i	$-0.395189\pi$
$691$	17.0000	0.646710	0.323355	+	0.946278i	$0.395189\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−30.0000	−1.13878
$695$	−4.00000	−0.151729
$696$	0	0
$697$	0	0
$698$	−10.0000	−0.378506
$699$	0	0
$700$	1.00000	0.0377964
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−14.0000	−0.528020
$704$	3.00000	0.113067
$705$	0	0
$706$	12.0000	0.451626
$707$	3.00000	0.112827
$708$	0	0
$709$	−19.0000	−0.713560	−0.356780	−	0.934188i	$-0.616125\pi$
$709$	−19.0000	−0.713560	−0.356780	+	0.934188i	$0.616125\pi$
$710$	0	0
$711$	0	0
$712$	9.00000	0.337289
$713$	−24.0000	−0.898807
$714$	0	0
$715$	15.0000	0.560968
$716$	9.00000	0.336346
$717$	0	0
$718$	9.00000	0.335877
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	30.0000	1.11648
$723$	0	0
$724$	2.00000	0.0743294
$725$	−6.00000	−0.222834
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	5.00000	0.185312
$729$	0	0
$730$	−7.00000	−0.259082
$731$	0	0
$732$	0	0
$733$	5.00000	0.184679	0.0923396	−	0.995728i	$-0.470565\pi$
$733$	5.00000	0.184679	0.0923396	+	0.995728i	$0.470565\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	6.00000	0.221163
$737$	−39.0000	−1.43658
$738$	0	0
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	9.00000	0.330400
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	−4.00000	−0.146450
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	14.0000	0.510867	0.255434	−	0.966827i	$-0.417782\pi$
$751$	14.0000	0.510867	0.255434	+	0.966827i	$0.417782\pi$
$752$	3.00000	0.109399
$753$	0	0
$754$	−30.0000	−1.09254
$755$	−10.0000	−0.363937
$756$	0	0
$757$	−52.0000	−1.88997	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000	−1.88997	−0.944986	+	0.327111i	$0.893925\pi$
$758$	−16.0000	−0.581146
$759$	0	0
$760$	−7.00000	−0.253917
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	11.0000	0.398227
$764$	3.00000	0.108536
$765$	0	0
$766$	24.0000	0.867155
$767$	30.0000	1.08324
$768$	0	0
$769$	32.0000	1.15395	0.576975	−	0.816762i	$-0.304233\pi$
$769$	32.0000	1.15395	0.576975	+	0.816762i	$0.304233\pi$
$770$	3.00000	0.108112
$771$	0	0
$772$	−22.0000	−0.791797
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	0	0
$775$	−4.00000	−0.143684
$776$	−10.0000	−0.358979
$777$	0	0
$778$	30.0000	1.07555
$779$	21.0000	0.752403
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	−22.0000	−0.785214
$786$	0	0
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	27.0000	0.961835
$789$	0	0
$790$	8.00000	0.284627
$791$	15.0000	0.533339
$792$	0	0
$793$	40.0000	1.42044
$794$	38.0000	1.34857
$795$	0	0
$796$	−25.0000	−0.886102
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	0	0
$802$	24.0000	0.847469
$803$	−21.0000	−0.741074
$804$	0	0
$805$	6.00000	0.211472
$806$	−20.0000	−0.704470
$807$	0	0
$808$	3.00000	0.105540
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	0	0
$811$	−7.00000	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	6.00000	0.210300
$815$	−16.0000	−0.560456
$816$	0	0
$817$	7.00000	0.244899
$818$	14.0000	0.489499
$819$	0	0
$820$	−3.00000	−0.104765
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	−49.0000	−1.70803	−0.854016	−	0.520246i	$-0.825840\pi$
$823$	−49.0000	−1.70803	−0.854016	+	0.520246i	$0.825840\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	6.00000	0.208767
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	0	0
$829$	−52.0000	−1.80603	−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000	−1.80603	−0.903017	+	0.429604i	$0.858653\pi$
$830$	3.00000	0.104132
$831$	0	0
$832$	5.00000	0.173344
$833$	0	0
$834$	0	0
$835$	−12.0000	−0.415277
$836$	−21.0000	−0.726300
$837$	0	0
$838$	−30.0000	−1.03633
$839$	−42.0000	−1.45000	−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000	−1.45000	−0.725001	+	0.688748i	$0.758161\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	35.0000	1.20618
$843$	0	0
$844$	14.0000	0.481900
$845$	12.0000	0.412813
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	9.00000	0.309061
$849$	0	0
$850$	0	0
$851$	12.0000	0.411355
$852$	0	0
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	0	0
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	0	0
$859$	41.0000	1.39890	0.699451	−	0.714681i	$-0.253428\pi$
$859$	41.0000	1.39890	0.699451	+	0.714681i	$0.253428\pi$
$860$	−1.00000	−0.0340997
$861$	0	0
$862$	−9.00000	−0.306541
$863$	18.0000	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	11.0000	0.373795
$867$	0	0
$868$	−4.00000	−0.135769
$869$	24.0000	0.814144
$870$	0	0
$871$	−65.0000	−2.20244
$872$	11.0000	0.372507
$873$	0	0
$874$	−42.0000	−1.42067
$875$	1.00000	0.0338062
$876$	0	0
$877$	−40.0000	−1.35070	−0.675352	−	0.737496i	$-0.736008\pi$
$877$	−40.0000	−1.35070	−0.675352	+	0.737496i	$0.736008\pi$
$878$	−19.0000	−0.641219
$879$	0	0
$880$	3.00000	0.101130
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	0	0
$885$	0	0
$886$	−24.0000	−0.806296
$887$	15.0000	0.503651	0.251825	−	0.967773i	$-0.418969\pi$
$887$	15.0000	0.503651	0.251825	+	0.967773i	$0.418969\pi$
$888$	0	0
$889$	−7.00000	−0.234772
$890$	9.00000	0.301681
$891$	0	0
$892$	26.0000	0.870544
$893$	−21.0000	−0.702738
$894$	0	0
$895$	9.00000	0.300837
$896$	1.00000	0.0334077
$897$	0	0
$898$	0	0
$899$	24.0000	0.800445
$900$	0	0
$901$	0	0
$902$	−9.00000	−0.299667
$903$	0	0
$904$	15.0000	0.498893
$905$	2.00000	0.0664822
$906$	0	0
$907$	−1.00000	−0.0332045	−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000	−0.0332045	−0.0166022	+	0.999862i	$0.505285\pi$
$908$	3.00000	0.0995585
$909$	0	0
$910$	5.00000	0.165748
$911$	57.0000	1.88849	0.944247	−	0.329238i	$-0.106792\pi$
$911$	57.0000	1.88849	0.944247	+	0.329238i	$0.106792\pi$
$912$	0	0
$913$	9.00000	0.297857
$914$	−28.0000	−0.926158
$915$	0	0
$916$	−22.0000	−0.726900
$917$	−12.0000	−0.396275
$918$	0	0
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	6.00000	0.197814
$921$	0	0
$922$	3.00000	0.0987997
$923$	0	0
$924$	0	0
$925$	2.00000	0.0657596
$926$	−13.0000	−0.427207
$927$	0	0
$928$	−6.00000	−0.196960
$929$	3.00000	0.0984268	0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000	0.0984268	0.0492134	+	0.998788i	$0.484329\pi$
$930$	0	0
$931$	−7.00000	−0.229416
$932$	27.0000	0.884414
$933$	0	0
$934$	−36.0000	−1.17796
$935$	0	0
$936$	0	0
$937$	−7.00000	−0.228680	−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000	−0.228680	−0.114340	+	0.993442i	$0.536475\pi$
$938$	−13.0000	−0.424465
$939$	0	0
$940$	3.00000	0.0978492
$941$	−3.00000	−0.0977972	−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000	−0.0977972	−0.0488986	+	0.998804i	$0.515571\pi$
$942$	0	0
$943$	−18.0000	−0.586161
$944$	6.00000	0.195283
$945$	0	0
$946$	−3.00000	−0.0975384
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	−35.0000	−1.13615
$950$	−7.00000	−0.227110
$951$	0	0
$952$	0	0
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	0	0
$955$	3.00000	0.0970777
$956$	24.0000	0.776215
$957$	0	0
$958$	−24.0000	−0.775405
$959$	−15.0000	−0.484375
$960$	0	0
$961$	−15.0000	−0.483871
$962$	10.0000	0.322413
$963$	0	0
$964$	8.00000	0.257663
$965$	−22.0000	−0.708205
$966$	0	0
$967$	23.0000	0.739630	0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000	0.739630	0.369815	+	0.929105i	$0.379421\pi$
$968$	−2.00000	−0.0642824
$969$	0	0
$970$	−10.0000	−0.321081
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	−7.00000	−0.224294
$975$	0	0
$976$	8.00000	0.256074
$977$	15.0000	0.479893	0.239946	−	0.970786i	$-0.422870\pi$
$977$	15.0000	0.479893	0.239946	+	0.970786i	$0.422870\pi$
$978$	0	0
$979$	27.0000	0.862924
$980$	1.00000	0.0319438
$981$	0	0
$982$	−12.0000	−0.382935
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	0	0
$985$	27.0000	0.860292
$986$	0	0
$987$	0	0
$988$	−35.0000	−1.11350
$989$	−6.00000	−0.190789
$990$	0	0
$991$	20.0000	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	−25.0000	−0.792553
$996$	0	0
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	14.0000	0.443162
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.a.x.1.1	yes	1
3.2	odd	2		1890.2.a.c.1.1	✓	1
5.4	even	2		9450.2.a.u.1.1		1
15.14	odd	2		9450.2.a.ce.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.c.1.1	✓	1	3.2	odd	2
1890.2.a.x.1.1	yes	1	1.1	even	1	trivial
9450.2.a.u.1.1		1	5.4	even	2
9450.2.a.ce.1.1		1	15.14	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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