LMFDB - Embedded newform 1890.2.a.s.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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +3.00000 q^{11} -1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{19} -1.00000 q^{20} +3.00000 q^{22} +6.00000 q^{23} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{35} +2.00000 q^{37} -1.00000 q^{38} -1.00000 q^{40} +3.00000 q^{41} -1.00000 q^{43} +3.00000 q^{44} +6.00000 q^{46} +9.00000 q^{47} +1.00000 q^{49} +1.00000 q^{50} -1.00000 q^{52} -3.00000 q^{53} -3.00000 q^{55} +1.00000 q^{56} +6.00000 q^{58} +6.00000 q^{59} -4.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +1.00000 q^{65} +11.0000 q^{67} -1.00000 q^{70} -1.00000 q^{73} +2.00000 q^{74} -1.00000 q^{76} +3.00000 q^{77} -4.00000 q^{79} -1.00000 q^{80} +3.00000 q^{82} -3.00000 q^{83} -1.00000 q^{86} +3.00000 q^{88} -9.00000 q^{89} -1.00000 q^{91} +6.00000 q^{92} +9.00000 q^{94} +1.00000 q^{95} +2.00000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$11$	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
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	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
$26$	−1.00000	−0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	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	$0.447432\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	−1.00000	−0.158114
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	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
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	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
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0	0
$67$	11.0000	1.34386	0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000	1.34386	0.671932	+	0.740613i	$0.265465\pi$
$68$	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
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	3.00000	0.341882
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	3.00000	0.331295
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	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	$-0.658275\pi$
$89$	−9.00000	−0.953998	−0.476999	+	0.878904i	$0.658275\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	6.00000	0.625543
$93$	0	0
$94$	9.00000	0.928279
$95$	1.00000	0.102598
$96$	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
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−3.00000	−0.291386
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	−3.00000	−0.286039
$111$	0	0
$112$	1.00000	0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	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
$122$	−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	$-0.428794\pi$
$127$	5.00000	0.443678	0.221839	+	0.975083i	$0.428794\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	1.00000	0.0877058
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	11.0000	0.950255
$135$	0	0
$136$	0	0
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	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
$143$	−3.00000	−0.250873
$144$	0	0
$145$	−6.00000	−0.498273
$146$	−1.00000	−0.0827606
$147$	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
$151$	−22.0000	−1.79033	−0.895167	−	0.445730i	$-0.852944\pi$
$151$	−22.0000	−1.79033	−0.895167	+	0.445730i	$0.852944\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	3.00000	0.241747
$155$	4.00000	0.321288
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	−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	$0.715557\pi$
$164$	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
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−1.00000	−0.0741249
$183$	0	0
$184$	6.00000	0.442326
$185$	−2.00000	−0.147043
$186$	0	0
$187$	0	0
$188$	9.00000	0.656392
$189$	0	0
$190$	1.00000	0.0725476
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	−9.00000	−0.641223	−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000	−0.641223	−0.320612	+	0.947211i	$0.603888\pi$
$198$	0	0
$199$	−19.0000	−1.34687	−0.673437	−	0.739244i	$-0.735183\pi$
$199$	−19.0000	−1.34687	−0.673437	+	0.739244i	$0.735183\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	9.00000	0.633238
$203$	6.00000	0.421117
$204$	0	0
$205$	−3.00000	−0.209529
$206$	8.00000	0.557386
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−3.00000	−0.207514
$210$	0	0
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	−3.00000	−0.206041
$213$	0	0
$214$	12.0000	0.820303
$215$	1.00000	0.0681994
$216$	0	0
$217$	−4.00000	−0.271538
$218$	−1.00000	−0.0677285
$219$	0	0
$220$	−3.00000	−0.202260
$221$	0	0
$222$	0	0
$223$	−22.0000	−1.47323	−0.736614	−	0.676313i	$-0.763577\pi$
$223$	−22.0000	−1.47323	−0.736614	+	0.676313i	$0.763577\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−9.00000	−0.598671
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	−6.00000	−0.395628
$231$	0	0
$232$	6.00000	0.393919
$233$	3.00000	0.196537	0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000	0.196537	0.0982683	+	0.995160i	$0.468670\pi$
$234$	0	0
$235$	−9.00000	−0.587095
$236$	6.00000	0.390567
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	−2.00000	−0.128565
$243$	0	0
$244$	−4.00000	−0.256074
$245$	−1.00000	−0.0638877
$246$	0	0
$247$	1.00000	0.0636285
$248$	−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
$253$	18.0000	1.13165
$254$	5.00000	0.313728
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	1.00000	0.0620174
$261$	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
$265$	3.00000	0.184289
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	11.0000	0.671932
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−25.0000	−1.51864	−0.759321	−	0.650716i	$-0.774469\pi$
$271$	−25.0000	−1.51864	−0.759321	+	0.650716i	$0.774469\pi$
$272$	0	0
$273$	0	0
$274$	9.00000	0.543710
$275$	3.00000	0.180907
$276$	0	0
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	−1.00000	−0.0597614
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−10.0000	−0.594438	−0.297219	−	0.954809i	$-0.596059\pi$
$283$	−10.0000	−0.594438	−0.297219	+	0.954809i	$0.596059\pi$
$284$	0	0
$285$	0	0
$286$	−3.00000	−0.177394
$287$	3.00000	0.177084
$288$	0	0
$289$	−17.0000	−1.00000
$290$	−6.00000	−0.352332
$291$	0	0
$292$	−1.00000	−0.0585206
$293$	−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
$299$	−6.00000	−0.346989
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	−22.0000	−1.26596
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	4.00000	0.229039
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	4.00000	0.227185
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	17.0000	0.960897	0.480448	−	0.877023i	$-0.340474\pi$
$313$	17.0000	0.960897	0.480448	+	0.877023i	$0.340474\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−4.00000	−0.225018
$317$	21.0000	1.17948	0.589739	−	0.807594i	$-0.299231\pi$
$317$	21.0000	1.17948	0.589739	+	0.807594i	$0.299231\pi$
$318$	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
$325$	−1.00000	−0.0554700
$326$	−16.0000	−0.886158
$327$	0	0
$328$	3.00000	0.165647
$329$	9.00000	0.496186
$330$	0	0
$331$	−34.0000	−1.86881	−0.934405	−	0.356214i	$-0.884068\pi$
$331$	−34.0000	−1.86881	−0.934405	+	0.356214i	$0.884068\pi$
$332$	−3.00000	−0.164646
$333$	0	0
$334$	−12.0000	−0.656611
$335$	−11.0000	−0.600994
$336$	0	0
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	−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
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	3.00000	0.159901
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	0	0
$355$	0	0
$356$	−9.00000	−0.476999
$357$	0	0
$358$	−15.0000	−0.792775
$359$	−3.00000	−0.158334	−0.0791670	−	0.996861i	$-0.525226\pi$
$359$	−3.00000	−0.158334	−0.0791670	+	0.996861i	$0.525226\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	2.00000	0.105118
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	1.00000	0.0523424
$366$	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
$371$	−3.00000	−0.155752
$372$	0	0
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	0	0
$375$	0	0
$376$	9.00000	0.464140
$377$	−6.00000	−0.309016
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	1.00000	0.0512989
$381$	0	0
$382$	15.0000	0.767467
$383$	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
$386$	14.0000	0.712581
$387$	0	0
$388$	2.00000	0.101535
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	0	0
$392$	1.00000	0.0505076
$393$	0	0
$394$	−9.00000	−0.453413
$395$	4.00000	0.201262
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−19.0000	−0.952384
$399$	0	0
$400$	1.00000	0.0500000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	9.00000	0.447767
$405$	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
$412$	8.00000	0.394132
$413$	6.00000	0.295241
$414$	0	0
$415$	3.00000	0.147264
$416$	−1.00000	−0.0490290
$417$	0	0
$418$	−3.00000	−0.146735
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−1.00000	−0.0487370	−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000	−0.0487370	−0.0243685	+	0.999703i	$0.507758\pi$
$422$	2.00000	0.0973585
$423$	0	0
$424$	−3.00000	−0.145693
$425$	0	0
$426$	0	0
$427$	−4.00000	−0.193574
$428$	12.0000	0.580042
$429$	0	0
$430$	1.00000	0.0482243
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	0	0
$433$	29.0000	1.39365	0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000	1.39365	0.696826	+	0.717241i	$0.254595\pi$
$434$	−4.00000	−0.192006
$435$	0	0
$436$	−1.00000	−0.0478913
$437$	−6.00000	−0.287019
$438$	0	0
$439$	−1.00000	−0.0477274	−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000	−0.0477274	−0.0238637	+	0.999715i	$0.507597\pi$
$440$	−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
$446$	−22.0000	−1.04173
$447$	0	0
$448$	1.00000	0.0472456
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	−9.00000	−0.423324
$453$	0	0
$454$	−3.00000	−0.140797
$455$	1.00000	0.0468807
$456$	0	0
$457$	32.0000	1.49690	0.748448	−	0.663193i	$-0.230799\pi$
$457$	32.0000	1.49690	0.748448	+	0.663193i	$0.230799\pi$
$458$	26.0000	1.21490
$459$	0	0
$460$	−6.00000	−0.279751
$461$	−15.0000	−0.698620	−0.349310	−	0.937007i	$-0.613584\pi$
$461$	−15.0000	−0.698620	−0.349310	+	0.937007i	$0.613584\pi$
$462$	0	0
$463$	−1.00000	−0.0464739	−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000	−0.0464739	−0.0232370	+	0.999730i	$0.507397\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	3.00000	0.138972
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	11.0000	0.507933
$470$	−9.00000	−0.415139
$471$	0	0
$472$	6.00000	0.276172
$473$	−3.00000	−0.137940
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	−28.0000	−1.27537
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−2.00000	−0.0908153
$486$	0	0
$487$	−43.0000	−1.94852	−0.974258	−	0.225436i	$-0.927619\pi$
$487$	−43.0000	−1.94852	−0.974258	+	0.225436i	$0.927619\pi$
$488$	−4.00000	−0.181071
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	0	0
$494$	1.00000	0.0449921
$495$	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
$502$	−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
$505$	−9.00000	−0.400495
$506$	18.0000	0.800198
$507$	0	0
$508$	5.00000	0.221839
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	−1.00000	−0.0442374
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.0000	0.529297
$515$	−8.00000	−0.352522
$516$	0	0
$517$	27.0000	1.18746
$518$	2.00000	0.0878750
$519$	0	0
$520$	1.00000	0.0438529
$521$	−21.0000	−0.920027	−0.460013	−	0.887912i	$-0.652155\pi$
$521$	−21.0000	−0.920027	−0.460013	+	0.887912i	$0.652155\pi$
$522$	0	0
$523$	2.00000	0.0874539	0.0437269	−	0.999044i	$-0.486077\pi$
$523$	2.00000	0.0874539	0.0437269	+	0.999044i	$0.486077\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−24.0000	−1.04645
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	3.00000	0.130312
$531$	0	0
$532$	−1.00000	−0.0433555
$533$	−3.00000	−0.129944
$534$	0	0
$535$	−12.0000	−0.518805
$536$	11.0000	0.475128
$537$	0	0
$538$	−6.00000	−0.258678
$539$	3.00000	0.129219
$540$	0	0
$541$	−7.00000	−0.300954	−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000	−0.300954	−0.150477	+	0.988614i	$0.548081\pi$
$542$	−25.0000	−1.07384
$543$	0	0
$544$	0	0
$545$	1.00000	0.0428353
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	9.00000	0.384461
$549$	0	0
$550$	3.00000	0.127920
$551$	−6.00000	−0.255609
$552$	0	0
$553$	−4.00000	−0.170097
$554$	2.00000	0.0849719
$555$	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
$559$	1.00000	0.0422955
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	30.0000	1.26547
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	0	0
$565$	9.00000	0.378633
$566$	−10.0000	−0.420331
$567$	0	0
$568$	0	0
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−3.00000	−0.125436
$573$	0	0
$574$	3.00000	0.125218
$575$	6.00000	0.250217
$576$	0	0
$577$	29.0000	1.20729	0.603643	−	0.797255i	$-0.293715\pi$
$577$	29.0000	1.20729	0.603643	+	0.797255i	$0.293715\pi$
$578$	−17.0000	−0.707107
$579$	0	0
$580$	−6.00000	−0.249136
$581$	−3.00000	−0.124461
$582$	0	0
$583$	−9.00000	−0.372742
$584$	−1.00000	−0.0413803
$585$	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
$589$	4.00000	0.164817
$590$	−6.00000	−0.247016
$591$	0	0
$592$	2.00000	0.0821995
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	6.00000	0.245770
$597$	0	0
$598$	−6.00000	−0.245358
$599$	−27.0000	−1.10319	−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000	−1.10319	−0.551595	+	0.834112i	$0.685981\pi$
$600$	0	0
$601$	−4.00000	−0.163163	−0.0815817	−	0.996667i	$-0.525997\pi$
$601$	−4.00000	−0.163163	−0.0815817	+	0.996667i	$0.525997\pi$
$602$	−1.00000	−0.0407570
$603$	0	0
$604$	−22.0000	−0.895167
$605$	2.00000	0.0813116
$606$	0	0
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	4.00000	0.161955
$611$	−9.00000	−0.364101
$612$	0	0
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	3.00000	0.120873
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	17.0000	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$620$	4.00000	0.160644
$621$	0	0
$622$	−6.00000	−0.240578
$623$	−9.00000	−0.360577
$624$	0	0
$625$	1.00000	0.0400000
$626$	17.0000	0.679457
$627$	0	0
$628$	−10.0000	−0.399043
$629$	0	0
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	−4.00000	−0.159111
$633$	0	0
$634$	21.0000	0.834017
$635$	−5.00000	−0.198419
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	18.0000	0.712627
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	0	0
$647$	−39.0000	−1.53325	−0.766624	−	0.642096i	$-0.778065\pi$
$647$	−39.0000	−1.53325	−0.766624	+	0.642096i	$0.778065\pi$
$648$	0	0
$649$	18.0000	0.706562
$650$	−1.00000	−0.0392232
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	3.00000	0.117130
$657$	0	0
$658$	9.00000	0.350857
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	−34.0000	−1.32145
$663$	0	0
$664$	−3.00000	−0.116423
$665$	1.00000	0.0387783
$666$	0	0
$667$	36.0000	1.39393
$668$	−12.0000	−0.464294
$669$	0	0
$670$	−11.0000	−0.424967
$671$	−12.0000	−0.463255
$672$	0	0
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	32.0000	1.23259
$675$	0	0
$676$	−12.0000	−0.461538
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	0	0
$681$	0	0
$682$	−12.0000	−0.459504
$683$	30.0000	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$684$	0	0
$685$	−9.00000	−0.343872
$686$	1.00000	0.0381802
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	3.00000	0.114291
$690$	0	0
$691$	23.0000	0.874961	0.437481	−	0.899228i	$-0.355871\pi$
$691$	23.0000	0.874961	0.437481	+	0.899228i	$0.355871\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	18.0000	0.683271
$695$	4.00000	0.151729
$696$	0	0
$697$	0	0
$698$	26.0000	0.984115
$699$	0	0
$700$	1.00000	0.0377964
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	3.00000	0.113067
$705$	0	0
$706$	−24.0000	−0.903252
$707$	9.00000	0.338480
$708$	0	0
$709$	−7.00000	−0.262891	−0.131445	−	0.991323i	$-0.541962\pi$
$709$	−7.00000	−0.262891	−0.131445	+	0.991323i	$0.541962\pi$
$710$	0	0
$711$	0	0
$712$	−9.00000	−0.337289
$713$	−24.0000	−0.898807
$714$	0	0
$715$	3.00000	0.112194
$716$	−15.0000	−0.560576
$717$	0	0
$718$	−3.00000	−0.111959
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	−18.0000	−0.669891
$723$	0	0
$724$	2.00000	0.0743294
$725$	6.00000	0.222834
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	−1.00000	−0.0370625
$729$	0	0
$730$	1.00000	0.0370117
$731$	0	0
$732$	0	0
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	6.00000	0.221163
$737$	33.0000	1.21557
$738$	0	0
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	−3.00000	−0.110133
$743$	42.0000	1.54083	0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000	1.54083	0.770415	+	0.637542i	$0.220049\pi$
$744$	0	0
$745$	−6.00000	−0.219823
$746$	−16.0000	−0.585802
$747$	0	0
$748$	0	0
$749$	12.0000	0.438470
$750$	0	0
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	9.00000	0.328196
$753$	0	0
$754$	−6.00000	−0.218507
$755$	22.0000	0.800662
$756$	0	0
$757$	44.0000	1.59921	0.799604	−	0.600528i	$-0.205043\pi$
$757$	44.0000	1.59921	0.799604	+	0.600528i	$0.205043\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	1.00000	0.0362738
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	0	0
$763$	−1.00000	−0.0362024
$764$	15.0000	0.542681
$765$	0	0
$766$	24.0000	0.867155
$767$	−6.00000	−0.216647
$768$	0	0
$769$	−4.00000	−0.144244	−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000	−0.144244	−0.0721218	+	0.997396i	$0.522977\pi$
$770$	−3.00000	−0.108112
$771$	0	0
$772$	14.0000	0.503871
$773$	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
$776$	2.00000	0.0717958
$777$	0	0
$778$	−30.0000	−1.07555
$779$	−3.00000	−0.107486
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	10.0000	0.356915
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	−9.00000	−0.320612
$789$	0	0
$790$	4.00000	0.142314
$791$	−9.00000	−0.320003
$792$	0	0
$793$	4.00000	0.142044
$794$	2.00000	0.0709773
$795$	0	0
$796$	−19.0000	−0.673437
$797$	−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
$802$	−12.0000	−0.423735
$803$	−3.00000	−0.105868
$804$	0	0
$805$	−6.00000	−0.211472
$806$	4.00000	0.140894
$807$	0	0
$808$	9.00000	0.316619
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	−1.00000	−0.0351147	−0.0175574	−	0.999846i	$-0.505589\pi$
$811$	−1.00000	−0.0351147	−0.0175574	+	0.999846i	$0.505589\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	6.00000	0.210300
$815$	16.0000	0.560456
$816$	0	0
$817$	1.00000	0.0349856
$818$	14.0000	0.489499
$819$	0	0
$820$	−3.00000	−0.104765
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	11.0000	0.383436	0.191718	−	0.981450i	$-0.438594\pi$
$823$	11.0000	0.383436	0.191718	+	0.981450i	$0.438594\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	6.00000	0.208767
$827$	−24.0000	−0.834562	−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000	−0.834562	−0.417281	+	0.908778i	$0.637017\pi$
$828$	0	0
$829$	32.0000	1.11141	0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000	1.11141	0.555703	+	0.831381i	$0.312449\pi$
$830$	3.00000	0.104132
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	0	0
$835$	12.0000	0.415277
$836$	−3.00000	−0.103757
$837$	0	0
$838$	−6.00000	−0.207267
$839$	−18.0000	−0.621429	−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000	−0.621429	−0.310715	+	0.950503i	$0.600568\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−1.00000	−0.0344623
$843$	0	0
$844$	2.00000	0.0688428
$845$	12.0000	0.412813
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	−3.00000	−0.103020
$849$	0	0
$850$	0	0
$851$	12.0000	0.411355
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	−4.00000	−0.136877
$855$	0	0
$856$	12.0000	0.410152
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	0	0
$859$	23.0000	0.784750	0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000	0.784750	0.392375	+	0.919805i	$0.371654\pi$
$860$	1.00000	0.0340997
$861$	0	0
$862$	−21.0000	−0.715263
$863$	54.0000	1.83818	0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000	1.83818	0.919091	+	0.394046i	$0.128925\pi$
$864$	0	0
$865$	6.00000	0.204006
$866$	29.0000	0.985460
$867$	0	0
$868$	−4.00000	−0.135769
$869$	−12.0000	−0.407072
$870$	0	0
$871$	−11.0000	−0.372721
$872$	−1.00000	−0.0338643
$873$	0	0
$874$	−6.00000	−0.202953
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−4.00000	−0.135070	−0.0675352	−	0.997717i	$-0.521513\pi$
$877$	−4.00000	−0.135070	−0.0675352	+	0.997717i	$0.521513\pi$
$878$	−1.00000	−0.0337484
$879$	0	0
$880$	−3.00000	−0.101130
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	0	0
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	0	0
$885$	0	0
$886$	−24.0000	−0.806296
$887$	45.0000	1.51095	0.755476	−	0.655176i	$-0.227406\pi$
$887$	45.0000	1.51095	0.755476	+	0.655176i	$0.227406\pi$
$888$	0	0
$889$	5.00000	0.167695
$890$	9.00000	0.301681
$891$	0	0
$892$	−22.0000	−0.736614
$893$	−9.00000	−0.301174
$894$	0	0
$895$	15.0000	0.501395
$896$	1.00000	0.0334077
$897$	0	0
$898$	−12.0000	−0.400445
$899$	−24.0000	−0.800445
$900$	0	0
$901$	0	0
$902$	9.00000	0.299667
$903$	0	0
$904$	−9.00000	−0.299336
$905$	−2.00000	−0.0664822
$906$	0	0
$907$	23.0000	0.763702	0.381851	−	0.924224i	$-0.375287\pi$
$907$	23.0000	0.763702	0.381851	+	0.924224i	$0.375287\pi$
$908$	−3.00000	−0.0995585
$909$	0	0
$910$	1.00000	0.0331497
$911$	45.0000	1.49092	0.745458	−	0.666552i	$-0.232231\pi$
$911$	45.0000	1.49092	0.745458	+	0.666552i	$0.232231\pi$
$912$	0	0
$913$	−9.00000	−0.297857
$914$	32.0000	1.05847
$915$	0	0
$916$	26.0000	0.859064
$917$	12.0000	0.396275
$918$	0	0
$919$	−52.0000	−1.71532	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000	−1.71532	−0.857661	+	0.514216i	$0.828083\pi$
$920$	−6.00000	−0.197814
$921$	0	0
$922$	−15.0000	−0.493999
$923$	0	0
$924$	0	0
$925$	2.00000	0.0657596
$926$	−1.00000	−0.0328620
$927$	0	0
$928$	6.00000	0.196960
$929$	−3.00000	−0.0984268	−0.0492134	−	0.998788i	$-0.515671\pi$
$929$	−3.00000	−0.0984268	−0.0492134	+	0.998788i	$0.515671\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	3.00000	0.0982683
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	0	0
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	11.0000	0.359163
$939$	0	0
$940$	−9.00000	−0.293548
$941$	39.0000	1.27136	0.635682	−	0.771951i	$-0.280719\pi$
$941$	39.0000	1.27136	0.635682	+	0.771951i	$0.280719\pi$
$942$	0	0
$943$	18.0000	0.586161
$944$	6.00000	0.195283
$945$	0	0
$946$	−3.00000	−0.0975384
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	0	0
$949$	1.00000	0.0324614
$950$	−1.00000	−0.0324443
$951$	0	0
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	−15.0000	−0.485389
$956$	0	0
$957$	0	0
$958$	−36.0000	−1.16311
$959$	9.00000	0.290625
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−2.00000	−0.0644826
$963$	0	0
$964$	−28.0000	−0.901819
$965$	−14.0000	−0.450676
$966$	0	0
$967$	−37.0000	−1.18984	−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000	−1.18984	−0.594920	+	0.803785i	$0.702816\pi$
$968$	−2.00000	−0.0642824
$969$	0	0
$970$	−2.00000	−0.0642161
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	−43.0000	−1.37781
$975$	0	0
$976$	−4.00000	−0.128037
$977$	−33.0000	−1.05576	−0.527882	−	0.849318i	$-0.677014\pi$
$977$	−33.0000	−1.05576	−0.527882	+	0.849318i	$0.677014\pi$
$978$	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
$985$	9.00000	0.286764
$986$	0	0
$987$	0	0
$988$	1.00000	0.0318142
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−52.0000	−1.65183	−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000	−1.65183	−0.825917	+	0.563791i	$0.809342\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	19.0000	0.602340
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	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.s.1.1	yes	1
3.2	odd	2		1890.2.a.j.1.1	✓	1
5.4	even	2		9450.2.a.v.1.1		1
15.14	odd	2		9450.2.a.cf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.j.1.1	✓	1	3.2	odd	2
1890.2.a.s.1.1	yes	1	1.1	even	1	trivial
9450.2.a.v.1.1		1	5.4	even	2
9450.2.a.cf.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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