LMFDB - Embedded newform 1890.2.a.f.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:	$1$
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	$\chi$	$=$	1890.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} -1.00000 q^{11} +3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -8.00000 q^{17} -3.00000 q^{19} +1.00000 q^{20} +1.00000 q^{22} +6.00000 q^{23} +1.00000 q^{25} -3.00000 q^{26} -1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} +8.00000 q^{34} -1.00000 q^{35} +2.00000 q^{37} +3.00000 q^{38} -1.00000 q^{40} -11.0000 q^{41} +1.00000 q^{43} -1.00000 q^{44} -6.00000 q^{46} +1.00000 q^{47} +1.00000 q^{49} -1.00000 q^{50} +3.00000 q^{52} -1.00000 q^{53} -1.00000 q^{55} +1.00000 q^{56} +6.00000 q^{58} -10.0000 q^{59} +4.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +3.00000 q^{65} -3.00000 q^{67} -8.00000 q^{68} +1.00000 q^{70} -8.00000 q^{71} +11.0000 q^{73} -2.00000 q^{74} -3.00000 q^{76} +1.00000 q^{77} +4.00000 q^{79} +1.00000 q^{80} +11.0000 q^{82} -11.0000 q^{83} -8.00000 q^{85} -1.00000 q^{86} +1.00000 q^{88} -7.00000 q^{89} -3.00000 q^{91} +6.00000 q^{92} -1.00000 q^{94} -3.00000 q^{95} +2.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	0	0
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−8.00000	−1.94029	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−8.00000	−1.94029	−0.970143	+	0.242536i	$0.922021\pi$
$18$	0	0
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	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
$26$	−3.00000	−0.588348
$27$	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
$34$	8.00000	1.37199
$35$	−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	$0.447432\pi$
$38$	3.00000	0.486664
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−11.0000	−1.71791	−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000	−1.71791	−0.858956	+	0.512050i	$0.828886\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−6.00000	−0.884652
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	3.00000	0.416025
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	1.00000	0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	−8.00000	−0.970143
$69$	0	0
$70$	1.00000	0.119523
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−3.00000	−0.344124
$77$	1.00000	0.113961
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	11.0000	1.21475
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	0	0
$85$	−8.00000	−0.867722
$86$	−1.00000	−0.107833
$87$	0	0
$88$	1.00000	0.106600
$89$	−7.00000	−0.741999	−0.370999	−	0.928633i	$-0.620985\pi$
$89$	−7.00000	−0.741999	−0.370999	+	0.928633i	$0.620985\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	6.00000	0.625543
$93$	0	0
$94$	−1.00000	−0.103142
$95$	−3.00000	−0.307794
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	15.0000	1.49256	0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000	1.49256	0.746278	+	0.665635i	$0.231839\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	1.00000	0.0971286
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	−9.00000	−0.862044	−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000	−0.862044	−0.431022	+	0.902342i	$0.641847\pi$
$110$	1.00000	0.0953463
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	13.0000	1.22294	0.611469	−	0.791269i	$-0.290579\pi$
$113$	13.0000	1.22294	0.611469	+	0.791269i	$0.290579\pi$
$114$	0	0
$115$	6.00000	0.559503
$116$	−6.00000	−0.557086
$117$	0	0
$118$	10.0000	0.920575
$119$	8.00000	0.733359
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−4.00000	−0.362143
$123$	0	0
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	−5.00000	−0.443678	−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000	−0.443678	−0.221839	+	0.975083i	$0.571206\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−3.00000	−0.263117
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	3.00000	0.259161
$135$	0	0
$136$	8.00000	0.685994
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	8.00000	0.671345
$143$	−3.00000	−0.250873
$144$	0	0
$145$	−6.00000	−0.498273
$146$	−11.0000	−0.910366
$147$	0	0
$148$	2.00000	0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	3.00000	0.243332
$153$	0	0
$154$	−1.00000	−0.0805823
$155$	−4.00000	−0.321288
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	−4.00000	−0.318223
$159$	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	$0.715557\pi$
$164$	−11.0000	−0.858956
$165$	0	0
$166$	11.0000	0.853766
$167$	−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
$169$	−4.00000	−0.307692
$170$	8.00000	0.613572
$171$	0	0
$172$	1.00000	0.0762493
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	7.00000	0.524672
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	3.00000	0.222375
$183$	0	0
$184$	−6.00000	−0.442326
$185$	2.00000	0.147043
$186$	0	0
$187$	8.00000	0.585018
$188$	1.00000	0.0729325
$189$	0	0
$190$	3.00000	0.217643
$191$	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
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	−11.0000	−0.783718	−0.391859	−	0.920025i	$-0.628168\pi$
$197$	−11.0000	−0.783718	−0.391859	+	0.920025i	$0.628168\pi$
$198$	0	0
$199$	23.0000	1.63043	0.815213	−	0.579161i	$-0.196620\pi$
$199$	23.0000	1.63043	0.815213	+	0.579161i	$0.196620\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−15.0000	−1.05540
$203$	6.00000	0.421117
$204$	0	0
$205$	−11.0000	−0.768273
$206$	8.00000	0.557386
$207$	0	0
$208$	3.00000	0.208013
$209$	3.00000	0.207514
$210$	0	0
$211$	−26.0000	−1.78991	−0.894957	−	0.446153i	$-0.852794\pi$
$211$	−26.0000	−1.78991	−0.894957	+	0.446153i	$0.852794\pi$
$212$	−1.00000	−0.0686803
$213$	0	0
$214$	12.0000	0.820303
$215$	1.00000	0.0681994
$216$	0	0
$217$	4.00000	0.271538
$218$	9.00000	0.609557
$219$	0	0
$220$	−1.00000	−0.0674200
$221$	−24.0000	−1.61441
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−13.0000	−0.864747
$227$	−11.0000	−0.730096	−0.365048	−	0.930989i	$-0.618947\pi$
$227$	−11.0000	−0.730096	−0.365048	+	0.930989i	$0.618947\pi$
$228$	0	0
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	−6.00000	−0.395628
$231$	0	0
$232$	6.00000	0.393919
$233$	9.00000	0.589610	0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000	0.589610	0.294805	+	0.955557i	$0.404745\pi$
$234$	0	0
$235$	1.00000	0.0652328
$236$	−10.0000	−0.650945
$237$	0	0
$238$	−8.00000	−0.518563
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	0	0
$241$	−20.0000	−1.28831	−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000	−1.28831	−0.644157	+	0.764894i	$0.722792\pi$
$242$	10.0000	0.642824
$243$	0	0
$244$	4.00000	0.256074
$245$	1.00000	0.0638877
$246$	0	0
$247$	−9.00000	−0.572656
$248$	4.00000	0.254000
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	−30.0000	−1.89358	−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000	−1.89358	−0.946792	+	0.321847i	$0.895696\pi$
$252$	0	0
$253$	−6.00000	−0.377217
$254$	5.00000	0.313728
$255$	0	0
$256$	1.00000	0.0625000
$257$	−20.0000	−1.24757	−0.623783	−	0.781598i	$-0.714405\pi$
$257$	−20.0000	−1.24757	−0.623783	+	0.781598i	$0.714405\pi$
$258$	0	0
$259$	−2.00000	−0.124274
$260$	3.00000	0.186052
$261$	0	0
$262$	−4.00000	−0.247121
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	−1.00000	−0.0614295
$266$	−3.00000	−0.183942
$267$	0	0
$268$	−3.00000	−0.183254
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	−27.0000	−1.64013	−0.820067	−	0.572268i	$-0.806064\pi$
$271$	−27.0000	−1.64013	−0.820067	+	0.572268i	$0.806064\pi$
$272$	−8.00000	−0.485071
$273$	0	0
$274$	−3.00000	−0.181237
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	20.0000	1.19952
$279$	0	0
$280$	1.00000	0.0597614
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	3.00000	0.177394
$287$	11.0000	0.649309
$288$	0	0
$289$	47.0000	2.76471
$290$	6.00000	0.352332
$291$	0	0
$292$	11.0000	0.643726
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	0	0
$295$	−10.0000	−0.582223
$296$	−2.00000	−0.116248
$297$	0	0
$298$	−18.0000	−1.04271
$299$	18.0000	1.04097
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	10.0000	0.575435
$303$	0	0
$304$	−3.00000	−0.172062
$305$	4.00000	0.229039
$306$	0	0
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	1.00000	0.0569803
$309$	0	0
$310$	4.00000	0.227185
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	29.0000	1.63918	0.819588	−	0.572953i	$-0.194202\pi$
$313$	29.0000	1.63918	0.819588	+	0.572953i	$0.194202\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	4.00000	0.225018
$317$	23.0000	1.29181	0.645904	−	0.763418i	$-0.276480\pi$
$317$	23.0000	1.29181	0.645904	+	0.763418i	$0.276480\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	1.00000	0.0559017
$321$	0	0
$322$	6.00000	0.334367
$323$	24.0000	1.33540
$324$	0	0
$325$	3.00000	0.166410
$326$	16.0000	0.886158
$327$	0	0
$328$	11.0000	0.607373
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	34.0000	1.86881	0.934405	−	0.356214i	$-0.115932\pi$
$331$	34.0000	1.86881	0.934405	+	0.356214i	$0.115932\pi$
$332$	−11.0000	−0.603703
$333$	0	0
$334$	12.0000	0.656611
$335$	−3.00000	−0.163908
$336$	0	0
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	4.00000	0.217571
$339$	0	0
$340$	−8.00000	−0.433861
$341$	4.00000	0.216612
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	2.00000	0.107521
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	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
$352$	1.00000	0.0533002
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	−7.00000	−0.370999
$357$	0	0
$358$	3.00000	0.158555
$359$	1.00000	0.0527780	0.0263890	−	0.999652i	$-0.491599\pi$
$359$	1.00000	0.0527780	0.0263890	+	0.999652i	$0.491599\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	14.0000	0.735824
$363$	0	0
$364$	−3.00000	−0.157243
$365$	11.0000	0.575766
$366$	0	0
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	−2.00000	−0.103975
$371$	1.00000	0.0519174
$372$	0	0
$373$	32.0000	1.65690	0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000	1.65690	0.828449	+	0.560065i	$0.189224\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	−1.00000	−0.0515711
$377$	−18.0000	−0.927047
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	−3.00000	−0.153897
$381$	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
$385$	1.00000	0.0509647
$386$	10.0000	0.508987
$387$	0	0
$388$	2.00000	0.101535
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	−48.0000	−2.42746
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	11.0000	0.554172
$395$	4.00000	0.201262
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	−23.0000	−1.15289
$399$	0	0
$400$	1.00000	0.0500000
$401$	20.0000	0.998752	0.499376	−	0.866385i	$-0.333563\pi$
$401$	20.0000	0.998752	0.499376	+	0.866385i	$0.333563\pi$
$402$	0	0
$403$	−12.0000	−0.597763
$404$	15.0000	0.746278
$405$	0	0
$406$	−6.00000	−0.297775
$407$	−2.00000	−0.0991363
$408$	0	0
$409$	−18.0000	−0.890043	−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000	−0.890043	−0.445021	+	0.895520i	$0.646804\pi$
$410$	11.0000	0.543251
$411$	0	0
$412$	−8.00000	−0.394132
$413$	10.0000	0.492068
$414$	0	0
$415$	−11.0000	−0.539969
$416$	−3.00000	−0.147087
$417$	0	0
$418$	−3.00000	−0.146735
$419$	18.0000	0.879358	0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000	0.879358	0.439679	+	0.898155i	$0.355092\pi$
$420$	0	0
$421$	−1.00000	−0.0487370	−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000	−0.0487370	−0.0243685	+	0.999703i	$0.507758\pi$
$422$	26.0000	1.26566
$423$	0	0
$424$	1.00000	0.0485643
$425$	−8.00000	−0.388057
$426$	0	0
$427$	−4.00000	−0.193574
$428$	−12.0000	−0.580042
$429$	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
$433$	−7.00000	−0.336399	−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000	−0.336399	−0.168199	+	0.985753i	$0.553795\pi$
$434$	−4.00000	−0.192006
$435$	0	0
$436$	−9.00000	−0.431022
$437$	−18.0000	−0.861057
$438$	0	0
$439$	−11.0000	−0.525001	−0.262501	−	0.964932i	$-0.584547\pi$
$439$	−11.0000	−0.525001	−0.262501	+	0.964932i	$0.584547\pi$
$440$	1.00000	0.0476731
$441$	0	0
$442$	24.0000	1.14156
$443$	−16.0000	−0.760183	−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000	−0.760183	−0.380091	+	0.924949i	$0.624107\pi$
$444$	0	0
$445$	−7.00000	−0.331832
$446$	2.00000	0.0947027
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	36.0000	1.69895	0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000	1.69895	0.849473	+	0.527633i	$0.176920\pi$
$450$	0	0
$451$	11.0000	0.517970
$452$	13.0000	0.611469
$453$	0	0
$454$	11.0000	0.516256
$455$	−3.00000	−0.140642
$456$	0	0
$457$	16.0000	0.748448	0.374224	−	0.927338i	$-0.377909\pi$
$457$	16.0000	0.748448	0.374224	+	0.927338i	$0.377909\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	6.00000	0.279751
$461$	−1.00000	−0.0465746	−0.0232873	−	0.999729i	$-0.507413\pi$
$461$	−1.00000	−0.0465746	−0.0232873	+	0.999729i	$0.507413\pi$
$462$	0	0
$463$	17.0000	0.790057	0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000	0.790057	0.395029	+	0.918669i	$0.370735\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−9.00000	−0.416917
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	3.00000	0.138527
$470$	−1.00000	−0.0461266
$471$	0	0
$472$	10.0000	0.460287
$473$	−1.00000	−0.0459800
$474$	0	0
$475$	−3.00000	−0.137649
$476$	8.00000	0.366679
$477$	0	0
$478$	−8.00000	−0.365911
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	20.0000	0.910975
$483$	0	0
$484$	−10.0000	−0.454545
$485$	2.00000	0.0908153
$486$	0	0
$487$	11.0000	0.498458	0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000	0.498458	0.249229	+	0.968445i	$0.419823\pi$
$488$	−4.00000	−0.181071
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	48.0000	2.16181
$494$	9.00000	0.404929
$495$	0	0
$496$	−4.00000	−0.179605
$497$	8.00000	0.358849
$498$	0	0
$499$	18.0000	0.805791	0.402895	−	0.915246i	$-0.368004\pi$
$499$	18.0000	0.805791	0.402895	+	0.915246i	$0.368004\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	30.0000	1.33897
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	15.0000	0.667491
$506$	6.00000	0.266733
$507$	0	0
$508$	−5.00000	−0.221839
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	−11.0000	−0.486611
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	20.0000	0.882162
$515$	−8.00000	−0.352522
$516$	0	0
$517$	−1.00000	−0.0439799
$518$	2.00000	0.0878750
$519$	0	0
$520$	−3.00000	−0.131559
$521$	−35.0000	−1.53338	−0.766689	−	0.642019i	$-0.778097\pi$
$521$	−35.0000	−1.53338	−0.766689	+	0.642019i	$0.778097\pi$
$522$	0	0
$523$	−26.0000	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$523$	−26.0000	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	−16.0000	−0.697633
$527$	32.0000	1.39394
$528$	0	0
$529$	13.0000	0.565217
$530$	1.00000	0.0434372
$531$	0	0
$532$	3.00000	0.130066
$533$	−33.0000	−1.42939
$534$	0	0
$535$	−12.0000	−0.518805
$536$	3.00000	0.129580
$537$	0	0
$538$	−6.00000	−0.258678
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	9.00000	0.386940	0.193470	−	0.981106i	$-0.438026\pi$
$541$	9.00000	0.386940	0.193470	+	0.981106i	$0.438026\pi$
$542$	27.0000	1.15975
$543$	0	0
$544$	8.00000	0.342997
$545$	−9.00000	−0.385518
$546$	0	0
$547$	−24.0000	−1.02617	−0.513083	−	0.858339i	$-0.671497\pi$
$547$	−24.0000	−1.02617	−0.513083	+	0.858339i	$0.671497\pi$
$548$	3.00000	0.128154
$549$	0	0
$550$	1.00000	0.0426401
$551$	18.0000	0.766826
$552$	0	0
$553$	−4.00000	−0.170097
$554$	−18.0000	−0.764747
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−46.0000	−1.94908	−0.974541	−	0.224208i	$-0.928020\pi$
$557$	−46.0000	−1.94908	−0.974541	+	0.224208i	$0.928020\pi$
$558$	0	0
$559$	3.00000	0.126886
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−10.0000	−0.421825
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	0	0
$565$	13.0000	0.546914
$566$	22.0000	0.924729
$567$	0	0
$568$	8.00000	0.335673
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	36.0000	1.50655	0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000	1.50655	0.753277	+	0.657704i	$0.228472\pi$
$572$	−3.00000	−0.125436
$573$	0	0
$574$	−11.0000	−0.459131
$575$	6.00000	0.250217
$576$	0	0
$577$	25.0000	1.04076	0.520382	−	0.853934i	$-0.325790\pi$
$577$	25.0000	1.04076	0.520382	+	0.853934i	$0.325790\pi$
$578$	−47.0000	−1.95494
$579$	0	0
$580$	−6.00000	−0.249136
$581$	11.0000	0.456357
$582$	0	0
$583$	1.00000	0.0414158
$584$	−11.0000	−0.455183
$585$	0	0
$586$	−14.0000	−0.578335
$587$	−20.0000	−0.825488	−0.412744	−	0.910847i	$-0.635430\pi$
$587$	−20.0000	−0.825488	−0.412744	+	0.910847i	$0.635430\pi$
$588$	0	0
$589$	12.0000	0.494451
$590$	10.0000	0.411693
$591$	0	0
$592$	2.00000	0.0821995
$593$	48.0000	1.97112	0.985562	−	0.169316i	$-0.0541557\pi$
$593$	48.0000	1.97112	0.985562	+	0.169316i	$0.0541557\pi$
$594$	0	0
$595$	8.00000	0.327968
$596$	18.0000	0.737309
$597$	0	0
$598$	−18.0000	−0.736075
$599$	9.00000	0.367730	0.183865	−	0.982952i	$-0.441139\pi$
$599$	9.00000	0.367730	0.183865	+	0.982952i	$0.441139\pi$
$600$	0	0
$601$	12.0000	0.489490	0.244745	−	0.969587i	$-0.421296\pi$
$601$	12.0000	0.489490	0.244745	+	0.969587i	$0.421296\pi$
$602$	1.00000	0.0407570
$603$	0	0
$604$	−10.0000	−0.406894
$605$	−10.0000	−0.406558
$606$	0	0
$607$	34.0000	1.38002	0.690009	−	0.723801i	$-0.257607\pi$
$607$	34.0000	1.38002	0.690009	+	0.723801i	$0.257607\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	−4.00000	−0.161955
$611$	3.00000	0.121367
$612$	0	0
$613$	−36.0000	−1.45403	−0.727013	−	0.686624i	$-0.759092\pi$
$613$	−36.0000	−1.45403	−0.727013	+	0.686624i	$0.759092\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	0	0
$619$	11.0000	0.442127	0.221064	−	0.975259i	$-0.429047\pi$
$619$	11.0000	0.442127	0.221064	+	0.975259i	$0.429047\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	−18.0000	−0.721734
$623$	7.00000	0.280449
$624$	0	0
$625$	1.00000	0.0400000
$626$	−29.0000	−1.15907
$627$	0	0
$628$	22.0000	0.877896
$629$	−16.0000	−0.637962
$630$	0	0
$631$	−34.0000	−1.35352	−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000	−1.35352	−0.676759	+	0.736204i	$0.736616\pi$
$632$	−4.00000	−0.159111
$633$	0	0
$634$	−23.0000	−0.913447
$635$	−5.00000	−0.198419
$636$	0	0
$637$	3.00000	0.118864
$638$	−6.00000	−0.237542
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	28.0000	1.10593	0.552967	−	0.833203i	$-0.313496\pi$
$641$	28.0000	1.10593	0.552967	+	0.833203i	$0.313496\pi$
$642$	0	0
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	−24.0000	−0.944267
$647$	−7.00000	−0.275198	−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000	−0.275198	−0.137599	+	0.990488i	$0.543939\pi$
$648$	0	0
$649$	10.0000	0.392534
$650$	−3.00000	−0.117670
$651$	0	0
$652$	−16.0000	−0.626608
$653$	22.0000	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$653$	22.0000	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$654$	0	0
$655$	4.00000	0.156293
$656$	−11.0000	−0.429478
$657$	0	0
$658$	1.00000	0.0389841
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−34.0000	−1.32145
$663$	0	0
$664$	11.0000	0.426883
$665$	3.00000	0.116335
$666$	0	0
$667$	−36.0000	−1.39393
$668$	−12.0000	−0.464294
$669$	0	0
$670$	3.00000	0.115900
$671$	−4.00000	−0.154418
$672$	0	0
$673$	−32.0000	−1.23351	−0.616755	−	0.787155i	$-0.711553\pi$
$673$	−32.0000	−1.23351	−0.616755	+	0.787155i	$0.711553\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	−4.00000	−0.153846
$677$	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
$679$	−2.00000	−0.0767530
$680$	8.00000	0.306786
$681$	0	0
$682$	−4.00000	−0.153168
$683$	−2.00000	−0.0765279	−0.0382639	−	0.999268i	$-0.512183\pi$
$683$	−2.00000	−0.0765279	−0.0382639	+	0.999268i	$0.512183\pi$
$684$	0	0
$685$	3.00000	0.114624
$686$	1.00000	0.0381802
$687$	0	0
$688$	1.00000	0.0381246
$689$	−3.00000	−0.114291
$690$	0	0
$691$	−35.0000	−1.33146	−0.665731	−	0.746191i	$-0.731880\pi$
$691$	−35.0000	−1.33146	−0.665731	+	0.746191i	$0.731880\pi$
$692$	−2.00000	−0.0760286
$693$	0	0
$694$	−2.00000	−0.0759190
$695$	−20.0000	−0.758643
$696$	0	0
$697$	88.0000	3.33324
$698$	−10.0000	−0.378506
$699$	0	0
$700$	−1.00000	−0.0377964
$701$	32.0000	1.20862	0.604312	−	0.796748i	$-0.293448\pi$
$701$	32.0000	1.20862	0.604312	+	0.796748i	$0.293448\pi$
$702$	0	0
$703$	−6.00000	−0.226294
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	0	0
$707$	−15.0000	−0.564133
$708$	0	0
$709$	25.0000	0.938895	0.469447	−	0.882960i	$-0.344453\pi$
$709$	25.0000	0.938895	0.469447	+	0.882960i	$0.344453\pi$
$710$	8.00000	0.300235
$711$	0	0
$712$	7.00000	0.262336
$713$	−24.0000	−0.898807
$714$	0	0
$715$	−3.00000	−0.112194
$716$	−3.00000	−0.112115
$717$	0	0
$718$	−1.00000	−0.0373197
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	10.0000	0.372161
$723$	0	0
$724$	−14.0000	−0.520306
$725$	−6.00000	−0.222834
$726$	0	0
$727$	−24.0000	−0.890111	−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000	−0.890111	−0.445055	+	0.895503i	$0.646816\pi$
$728$	3.00000	0.111187
$729$	0	0
$730$	−11.0000	−0.407128
$731$	−8.00000	−0.295891
$732$	0	0
$733$	−5.00000	−0.184679	−0.0923396	−	0.995728i	$-0.529435\pi$
$733$	−5.00000	−0.184679	−0.0923396	+	0.995728i	$0.529435\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	−6.00000	−0.221163
$737$	3.00000	0.110506
$738$	0	0
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	−1.00000	−0.0367112
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	0	0
$745$	18.0000	0.659469
$746$	−32.0000	−1.17160
$747$	0	0
$748$	8.00000	0.292509
$749$	12.0000	0.438470
$750$	0	0
$751$	−34.0000	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$751$	−34.0000	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$752$	1.00000	0.0364662
$753$	0	0
$754$	18.0000	0.655521
$755$	−10.0000	−0.363937
$756$	0	0
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	3.00000	0.108821
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	9.00000	0.325822
$764$	3.00000	0.108536
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−30.0000	−1.08324
$768$	0	0
$769$	4.00000	0.144244	0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000	0.144244	0.0721218	+	0.997396i	$0.477023\pi$
$770$	−1.00000	−0.0360375
$771$	0	0
$772$	−10.0000	−0.359908
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	−4.00000	−0.143684
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	26.0000	0.932145
$779$	33.0000	1.18235
$780$	0	0
$781$	8.00000	0.286263
$782$	48.0000	1.71648
$783$	0	0
$784$	1.00000	0.0357143
$785$	22.0000	0.785214
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−11.0000	−0.391859
$789$	0	0
$790$	−4.00000	−0.142314
$791$	−13.0000	−0.462227
$792$	0	0
$793$	12.0000	0.426132
$794$	14.0000	0.496841
$795$	0	0
$796$	23.0000	0.815213
$797$	−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
$799$	−8.00000	−0.283020
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−20.0000	−0.706225
$803$	−11.0000	−0.388182
$804$	0	0
$805$	−6.00000	−0.211472
$806$	12.0000	0.422682
$807$	0	0
$808$	−15.0000	−0.527698
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	29.0000	1.01833	0.509164	−	0.860670i	$-0.329955\pi$
$811$	29.0000	1.01833	0.509164	+	0.860670i	$0.329955\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	2.00000	0.0701000
$815$	−16.0000	−0.560456
$816$	0	0
$817$	−3.00000	−0.104957
$818$	18.0000	0.629355
$819$	0	0
$820$	−11.0000	−0.384137
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	0	0
$823$	37.0000	1.28974	0.644869	−	0.764293i	$-0.276912\pi$
$823$	37.0000	1.28974	0.644869	+	0.764293i	$0.276912\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−10.0000	−0.347945
$827$	−32.0000	−1.11275	−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000	−1.11275	−0.556375	+	0.830932i	$0.687808\pi$
$828$	0	0
$829$	−16.0000	−0.555703	−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000	−0.555703	−0.277851	+	0.960624i	$0.589622\pi$
$830$	11.0000	0.381816
$831$	0	0
$832$	3.00000	0.104006
$833$	−8.00000	−0.277184
$834$	0	0
$835$	−12.0000	−0.415277
$836$	3.00000	0.103757
$837$	0	0
$838$	−18.0000	−0.621800
$839$	−50.0000	−1.72619	−0.863096	−	0.505040i	$-0.831478\pi$
$839$	−50.0000	−1.72619	−0.863096	+	0.505040i	$0.831478\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	1.00000	0.0344623
$843$	0	0
$844$	−26.0000	−0.894957
$845$	−4.00000	−0.137604
$846$	0	0
$847$	10.0000	0.343604
$848$	−1.00000	−0.0343401
$849$	0	0
$850$	8.00000	0.274398
$851$	12.0000	0.411355
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	4.00000	0.136877
$855$	0	0
$856$	12.0000	0.410152
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	0	0
$859$	−3.00000	−0.102359	−0.0511793	−	0.998689i	$-0.516298\pi$
$859$	−3.00000	−0.102359	−0.0511793	+	0.998689i	$0.516298\pi$
$860$	1.00000	0.0340997
$861$	0	0
$862$	9.00000	0.306541
$863$	14.0000	0.476566	0.238283	−	0.971196i	$-0.423415\pi$
$863$	14.0000	0.476566	0.238283	+	0.971196i	$0.423415\pi$
$864$	0	0
$865$	−2.00000	−0.0680020
$866$	7.00000	0.237870
$867$	0	0
$868$	4.00000	0.135769
$869$	−4.00000	−0.135691
$870$	0	0
$871$	−9.00000	−0.304953
$872$	9.00000	0.304778
$873$	0	0
$874$	18.0000	0.608859
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−28.0000	−0.945493	−0.472746	−	0.881199i	$-0.656737\pi$
$877$	−28.0000	−0.945493	−0.472746	+	0.881199i	$0.656737\pi$
$878$	11.0000	0.371232
$879$	0	0
$880$	−1.00000	−0.0337100
$881$	−50.0000	−1.68454	−0.842271	−	0.539054i	$-0.818782\pi$
$881$	−50.0000	−1.68454	−0.842271	+	0.539054i	$0.818782\pi$
$882$	0	0
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	−24.0000	−0.807207
$885$	0	0
$886$	16.0000	0.537531
$887$	37.0000	1.24234	0.621169	−	0.783676i	$-0.286658\pi$
$887$	37.0000	1.24234	0.621169	+	0.783676i	$0.286658\pi$
$888$	0	0
$889$	5.00000	0.167695
$890$	7.00000	0.234641
$891$	0	0
$892$	−2.00000	−0.0669650
$893$	−3.00000	−0.100391
$894$	0	0
$895$	−3.00000	−0.100279
$896$	1.00000	0.0334077
$897$	0	0
$898$	−36.0000	−1.20134
$899$	24.0000	0.800445
$900$	0	0
$901$	8.00000	0.266519
$902$	−11.0000	−0.366260
$903$	0	0
$904$	−13.0000	−0.432374
$905$	−14.0000	−0.465376
$906$	0	0
$907$	17.0000	0.564476	0.282238	−	0.959344i	$-0.408923\pi$
$907$	17.0000	0.564476	0.282238	+	0.959344i	$0.408923\pi$
$908$	−11.0000	−0.365048
$909$	0	0
$910$	3.00000	0.0994490
$911$	33.0000	1.09334	0.546669	−	0.837349i	$-0.315895\pi$
$911$	33.0000	1.09334	0.546669	+	0.837349i	$0.315895\pi$
$912$	0	0
$913$	11.0000	0.364047
$914$	−16.0000	−0.529233
$915$	0	0
$916$	−14.0000	−0.462573
$917$	−4.00000	−0.132092
$918$	0	0
$919$	−28.0000	−0.923635	−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000	−0.923635	−0.461817	+	0.886975i	$0.652802\pi$
$920$	−6.00000	−0.197814
$921$	0	0
$922$	1.00000	0.0329332
$923$	−24.0000	−0.789970
$924$	0	0
$925$	2.00000	0.0657596
$926$	−17.0000	−0.558655
$927$	0	0
$928$	6.00000	0.196960
$929$	35.0000	1.14831	0.574156	−	0.818746i	$-0.305330\pi$
$929$	35.0000	1.14831	0.574156	+	0.818746i	$0.305330\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	9.00000	0.294805
$933$	0	0
$934$	−28.0000	−0.916188
$935$	8.00000	0.261628
$936$	0	0
$937$	−37.0000	−1.20874	−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000	−1.20874	−0.604369	+	0.796705i	$0.706575\pi$
$938$	−3.00000	−0.0979535
$939$	0	0
$940$	1.00000	0.0326164
$941$	−23.0000	−0.749779	−0.374889	−	0.927070i	$-0.622319\pi$
$941$	−23.0000	−0.749779	−0.374889	+	0.927070i	$0.622319\pi$
$942$	0	0
$943$	−66.0000	−2.14926
$944$	−10.0000	−0.325472
$945$	0	0
$946$	1.00000	0.0325128
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	0	0
$949$	33.0000	1.07123
$950$	3.00000	0.0973329
$951$	0	0
$952$	−8.00000	−0.259281
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	0	0
$955$	3.00000	0.0970777
$956$	8.00000	0.258738
$957$	0	0
$958$	−12.0000	−0.387702
$959$	−3.00000	−0.0968751
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−6.00000	−0.193448
$963$	0	0
$964$	−20.0000	−0.644157
$965$	−10.0000	−0.321911
$966$	0	0
$967$	−35.0000	−1.12552	−0.562762	−	0.826619i	$-0.690261\pi$
$967$	−35.0000	−1.12552	−0.562762	+	0.826619i	$0.690261\pi$
$968$	10.0000	0.321412
$969$	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
$973$	20.0000	0.641171
$974$	−11.0000	−0.352463
$975$	0	0
$976$	4.00000	0.128037
$977$	−3.00000	−0.0959785	−0.0479893	−	0.998848i	$-0.515281\pi$
$977$	−3.00000	−0.0959785	−0.0479893	+	0.998848i	$0.515281\pi$
$978$	0	0
$979$	7.00000	0.223721
$980$	1.00000	0.0319438
$981$	0	0
$982$	−36.0000	−1.14881
$983$	−56.0000	−1.78612	−0.893061	−	0.449935i	$-0.851447\pi$
$983$	−56.0000	−1.78612	−0.893061	+	0.449935i	$0.851447\pi$
$984$	0	0
$985$	−11.0000	−0.350489
$986$	−48.0000	−1.52863
$987$	0	0
$988$	−9.00000	−0.286328
$989$	6.00000	0.190789
$990$	0	0
$991$	−44.0000	−1.39771	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000	−1.39771	−0.698853	+	0.715265i	$0.746306\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	−8.00000	−0.253745
$995$	23.0000	0.729149
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−18.0000	−0.569780
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.a.f.1.1	✓	1
3.2	odd	2		1890.2.a.p.1.1	yes	1
5.4	even	2		9450.2.a.dj.1.1		1
15.14	odd	2		9450.2.a.bp.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.f.1.1	✓	1	1.1	even	1	trivial
1890.2.a.p.1.1	yes	1	3.2	odd	2
9450.2.a.bp.1.1		1	15.14	odd	2
9450.2.a.dj.1.1		1	5.4	even	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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