LMFDB - Embedded newform 1710.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, 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("1710.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.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:	$13.6544187456$
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	$\chi$	$=$	1710.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{22} -8.00000 q^{23} +1.00000 q^{25} -4.00000 q^{26} -2.00000 q^{28} +6.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} +2.00000 q^{35} -8.00000 q^{37} +1.00000 q^{38} -1.00000 q^{40} +12.0000 q^{41} +2.00000 q^{44} -8.00000 q^{46} -3.00000 q^{49} +1.00000 q^{50} -4.00000 q^{52} -10.0000 q^{53} -2.00000 q^{55} -2.00000 q^{56} +6.00000 q^{58} +6.00000 q^{59} -6.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +12.0000 q^{67} -6.00000 q^{68} +2.00000 q^{70} -12.0000 q^{71} -10.0000 q^{73} -8.00000 q^{74} +1.00000 q^{76} -4.00000 q^{77} -8.00000 q^{79} -1.00000 q^{80} +12.0000 q^{82} +8.00000 q^{83} +6.00000 q^{85} +2.00000 q^{88} +8.00000 q^{89} +8.00000 q^{91} -8.00000 q^{92} -1.00000 q^{95} -14.0000 q^{97} -3.00000 q^{98} +O(q^{100})$

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
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.00000	−0.223607
$21$	0	0
$22$	2.00000	0.426401
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	0	0
$28$	−2.00000	−0.377964
$29$	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
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	2.00000	0.338062
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−1.00000	−0.158114
$41$	12.0000	1.87409	0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000	1.87409	0.937043	+	0.349215i	$0.113552\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−8.00000	−1.17954
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	0	0
$52$	−4.00000	−0.554700
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	−2.00000	−0.267261
$57$	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
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	2.00000	0.239046
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	1.00000	0.114708
$77$	−4.00000	−0.455842
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	12.0000	1.32518
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	0	0
$87$	0	0
$88$	2.00000	0.213201
$89$	8.00000	0.847998	0.423999	−	0.905663i	$-0.360626\pi$
$89$	8.00000	0.847998	0.423999	+	0.905663i	$0.360626\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	−8.00000	−0.834058
$93$	0	0
$94$	0	0
$95$	−1.00000	−0.102598
$96$	0	0
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−3.00000	−0.303046
$99$	0	0
$100$	1.00000	0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	−10.0000	−0.971286
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	−2.00000	−0.188982
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	8.00000	0.746004
$116$	6.00000	0.557086
$117$	0	0
$118$	6.00000	0.552345
$119$	12.0000	1.10004
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−6.00000	−0.543214
$123$	0	0
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	−2.00000	−0.174741	−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000	−0.174741	−0.0873704	+	0.996176i	$0.527846\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	12.0000	1.03664
$135$	0	0
$136$	−6.00000	−0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	−12.0000	−1.00702
$143$	−8.00000	−0.668994
$144$	0	0
$145$	−6.00000	−0.498273
$146$	−10.0000	−0.827606
$147$	0	0
$148$	−8.00000	−0.657596
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	−4.00000	−0.322329
$155$	8.00000	0.642575
$156$	0	0
$157$	24.0000	1.91541	0.957704	−	0.287754i	$-0.0929087\pi$
$157$	24.0000	1.91541	0.957704	+	0.287754i	$0.0929087\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	16.0000	1.26098
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	8.00000	0.620920
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	6.00000	0.460179
$171$	0	0
$172$	0	0
$173$	−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
$175$	−2.00000	−0.151186
$176$	2.00000	0.150756
$177$	0	0
$178$	8.00000	0.599625
$179$	−2.00000	−0.149487	−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000	−0.149487	−0.0747435	+	0.997203i	$0.523814\pi$
$180$	0	0
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	8.00000	0.592999
$183$	0	0
$184$	−8.00000	−0.589768
$185$	8.00000	0.588172
$186$	0	0
$187$	−12.0000	−0.877527
$188$	0	0
$189$	0	0
$190$	−1.00000	−0.0725476
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	−3.00000	−0.214286
$197$	26.0000	1.85242	0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000	1.85242	0.926212	+	0.377004i	$0.123046\pi$
$198$	0	0
$199$	−24.0000	−1.70131	−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000	−1.70131	−0.850657	+	0.525720i	$0.823796\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	−2.00000	−0.140720
$203$	−12.0000	−0.842235
$204$	0	0
$205$	−12.0000	−0.838116
$206$	−14.0000	−0.975426
$207$	0	0
$208$	−4.00000	−0.277350
$209$	2.00000	0.138343
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	−4.00000	−0.273434
$215$	0	0
$216$	0	0
$217$	16.0000	1.08615
$218$	−2.00000	−0.135457
$219$	0	0
$220$	−2.00000	−0.134840
$221$	24.0000	1.61441
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	18.0000	1.19734
$227$	−16.0000	−1.06196	−0.530979	−	0.847385i	$-0.678176\pi$
$227$	−16.0000	−1.06196	−0.530979	+	0.847385i	$0.678176\pi$
$228$	0	0
$229$	30.0000	1.98246	0.991228	−	0.132164i	$-0.0421925\pi$
$229$	30.0000	1.98246	0.991228	+	0.132164i	$0.0421925\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	6.00000	0.393919
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	0	0
$235$	0	0
$236$	6.00000	0.390567
$237$	0	0
$238$	12.0000	0.777844
$239$	28.0000	1.81117	0.905585	−	0.424165i	$-0.139432\pi$
$239$	28.0000	1.81117	0.905585	+	0.424165i	$0.139432\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	−6.00000	−0.384111
$245$	3.00000	0.191663
$246$	0	0
$247$	−4.00000	−0.254514
$248$	−8.00000	−0.508001
$249$	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
$253$	−16.0000	−1.00591
$254$	18.0000	1.12942
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.0000	0.623783	0.311891	−	0.950118i	$-0.399037\pi$
$257$	10.0000	0.623783	0.311891	+	0.950118i	$0.399037\pi$
$258$	0	0
$259$	16.0000	0.994192
$260$	4.00000	0.248069
$261$	0	0
$262$	−2.00000	−0.123560
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	10.0000	0.614295
$266$	−2.00000	−0.122628
$267$	0	0
$268$	12.0000	0.733017
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	6.00000	0.362473
$275$	2.00000	0.120605
$276$	0	0
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	2.00000	0.119523
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−8.00000	−0.473050
$287$	−24.0000	−1.41668
$288$	0	0
$289$	19.0000	1.11765
$290$	−6.00000	−0.352332
$291$	0	0
$292$	−10.0000	−0.585206
$293$	−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
$296$	−8.00000	−0.464991
$297$	0	0
$298$	2.00000	0.115857
$299$	32.0000	1.85061
$300$	0	0
$301$	0	0
$302$	20.0000	1.15087
$303$	0	0
$304$	1.00000	0.0573539
$305$	6.00000	0.343559
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	−4.00000	−0.227921
$309$	0	0
$310$	8.00000	0.454369
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	24.0000	1.35440
$315$	0	0
$316$	−8.00000	−0.450035
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	16.0000	0.891645
$323$	−6.00000	−0.333849
$324$	0	0
$325$	−4.00000	−0.221880
$326$	4.00000	0.221540
$327$	0	0
$328$	12.0000	0.662589
$329$	0	0
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	8.00000	0.439057
$333$	0	0
$334$	16.0000	0.875481
$335$	−12.0000	−0.655630
$336$	0	0
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	6.00000	0.325396
$341$	−16.0000	−0.866449
$342$	0	0
$343$	20.0000	1.07990
$344$	0	0
$345$	0	0
$346$	−2.00000	−0.107521
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	−2.00000	−0.106904
$351$	0	0
$352$	2.00000	0.106600
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	0	0
$355$	12.0000	0.636894
$356$	8.00000	0.423999
$357$	0	0
$358$	−2.00000	−0.105703
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	14.0000	0.735824
$363$	0	0
$364$	8.00000	0.419314
$365$	10.0000	0.523424
$366$	0	0
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	−8.00000	−0.417029
$369$	0	0
$370$	8.00000	0.415900
$371$	20.0000	1.03835
$372$	0	0
$373$	28.0000	1.44979	0.724893	−	0.688862i	$-0.241889\pi$
$373$	28.0000	1.44979	0.724893	+	0.688862i	$0.241889\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	0	0
$377$	−24.0000	−1.23606
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	−1.00000	−0.0512989
$381$	0	0
$382$	−12.0000	−0.613973
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	4.00000	0.203859
$386$	−2.00000	−0.101797
$387$	0	0
$388$	−14.0000	−0.710742
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	0	0
$391$	48.0000	2.42746
$392$	−3.00000	−0.151523
$393$	0	0
$394$	26.0000	1.30986
$395$	8.00000	0.402524
$396$	0	0
$397$	20.0000	1.00377	0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000	1.00377	0.501886	+	0.864934i	$0.332640\pi$
$398$	−24.0000	−1.20301
$399$	0	0
$400$	1.00000	0.0500000
$401$	−24.0000	−1.19850	−0.599251	−	0.800561i	$-0.704535\pi$
$401$	−24.0000	−1.19850	−0.599251	+	0.800561i	$0.704535\pi$
$402$	0	0
$403$	32.0000	1.59403
$404$	−2.00000	−0.0995037
$405$	0	0
$406$	−12.0000	−0.595550
$407$	−16.0000	−0.793091
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−12.0000	−0.592638
$411$	0	0
$412$	−14.0000	−0.689730
$413$	−12.0000	−0.590481
$414$	0	0
$415$	−8.00000	−0.392705
$416$	−4.00000	−0.196116
$417$	0	0
$418$	2.00000	0.0978232
$419$	−10.0000	−0.488532	−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000	−0.488532	−0.244266	+	0.969708i	$0.578547\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	−10.0000	−0.485643
$425$	−6.00000	−0.291043
$426$	0	0
$427$	12.0000	0.580721
$428$	−4.00000	−0.193347
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	−8.00000	−0.382692
$438$	0	0
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	24.0000	1.14156
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	0	0
$445$	−8.00000	−0.379236
$446$	−14.0000	−0.662919
$447$	0	0
$448$	−2.00000	−0.0944911
$449$	8.00000	0.377543	0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000	0.377543	0.188772	+	0.982021i	$0.439549\pi$
$450$	0	0
$451$	24.0000	1.13012
$452$	18.0000	0.846649
$453$	0	0
$454$	−16.0000	−0.750917
$455$	−8.00000	−0.375046
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	30.0000	1.40181
$459$	0	0
$460$	8.00000	0.373002
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	10.0000	0.464739	0.232370	−	0.972628i	$-0.425352\pi$
$463$	10.0000	0.464739	0.232370	+	0.972628i	$0.425352\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	10.0000	0.463241
$467$	−32.0000	−1.48078	−0.740392	−	0.672176i	$-0.765360\pi$
$467$	−32.0000	−1.48078	−0.740392	+	0.672176i	$0.765360\pi$
$468$	0	0
$469$	−24.0000	−1.10822
$470$	0	0
$471$	0	0
$472$	6.00000	0.276172
$473$	0	0
$474$	0	0
$475$	1.00000	0.0458831
$476$	12.0000	0.550019
$477$	0	0
$478$	28.0000	1.28069
$479$	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
$481$	32.0000	1.45907
$482$	−18.0000	−0.819878
$483$	0	0
$484$	−7.00000	−0.318182
$485$	14.0000	0.635707
$486$	0	0
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	−6.00000	−0.271607
$489$	0	0
$490$	3.00000	0.135526
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	0	0
$493$	−36.0000	−1.62136
$494$	−4.00000	−0.179969
$495$	0	0
$496$	−8.00000	−0.359211
$497$	24.0000	1.07655
$498$	0	0
$499$	−12.0000	−0.537194	−0.268597	−	0.963253i	$-0.586560\pi$
$499$	−12.0000	−0.537194	−0.268597	+	0.963253i	$0.586560\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−18.0000	−0.803379
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	−16.0000	−0.711287
$507$	0	0
$508$	18.0000	0.798621
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	0	0
$511$	20.0000	0.884748
$512$	1.00000	0.0441942
$513$	0	0
$514$	10.0000	0.441081
$515$	14.0000	0.616914
$516$	0	0
$517$	0	0
$518$	16.0000	0.703000
$519$	0	0
$520$	4.00000	0.175412
$521$	24.0000	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$522$	0	0
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	−2.00000	−0.0873704
$525$	0	0
$526$	−16.0000	−0.697633
$527$	48.0000	2.09091
$528$	0	0
$529$	41.0000	1.78261
$530$	10.0000	0.434372
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	−48.0000	−2.07911
$534$	0	0
$535$	4.00000	0.172935
$536$	12.0000	0.518321
$537$	0	0
$538$	−10.0000	−0.431131
$539$	−6.00000	−0.258438
$540$	0	0
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	0	0
$543$	0	0
$544$	−6.00000	−0.257248
$545$	2.00000	0.0856706
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	2.00000	0.0852803
$551$	6.00000	0.255609
$552$	0	0
$553$	16.0000	0.680389
$554$	4.00000	0.169944
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−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
$559$	0	0
$560$	2.00000	0.0845154
$561$	0	0
$562$	0	0
$563$	−16.0000	−0.674320	−0.337160	−	0.941447i	$-0.609466\pi$
$563$	−16.0000	−0.674320	−0.337160	+	0.941447i	$0.609466\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	−20.0000	−0.840663
$567$	0	0
$568$	−12.0000	−0.503509
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	−8.00000	−0.334497
$573$	0	0
$574$	−24.0000	−1.00174
$575$	−8.00000	−0.333623
$576$	0	0
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	−6.00000	−0.249136
$581$	−16.0000	−0.663792
$582$	0	0
$583$	−20.0000	−0.828315
$584$	−10.0000	−0.413803
$585$	0	0
$586$	−30.0000	−1.23929
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	−8.00000	−0.329634
$590$	−6.00000	−0.247016
$591$	0	0
$592$	−8.00000	−0.328798
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	0	0
$595$	−12.0000	−0.491952
$596$	2.00000	0.0819232
$597$	0	0
$598$	32.0000	1.30858
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	0	0
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	0	0
$603$	0	0
$604$	20.0000	0.813788
$605$	7.00000	0.284590
$606$	0	0
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	6.00000	0.242933
$611$	0	0
$612$	0	0
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	−4.00000	−0.161165
$617$	−22.0000	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$618$	0	0
$619$	−12.0000	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	−20.0000	−0.801927
$623$	−16.0000	−0.641026
$624$	0	0
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	24.0000	0.957704
$629$	48.0000	1.91389
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	18.0000	0.714871
$635$	−18.0000	−0.714308
$636$	0	0
$637$	12.0000	0.475457
$638$	12.0000	0.475085
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−28.0000	−1.10593	−0.552967	−	0.833203i	$-0.686504\pi$
$641$	−28.0000	−1.10593	−0.552967	+	0.833203i	$0.686504\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	16.0000	0.630488
$645$	0	0
$646$	−6.00000	−0.236067
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	0	0
$649$	12.0000	0.471041
$650$	−4.00000	−0.156893
$651$	0	0
$652$	4.00000	0.156652
$653$	2.00000	0.0782660	0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000	0.0782660	0.0391330	+	0.999234i	$0.487540\pi$
$654$	0	0
$655$	2.00000	0.0781465
$656$	12.0000	0.468521
$657$	0	0
$658$	0	0
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	0	0
$661$	−18.0000	−0.700119	−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000	−0.700119	−0.350059	+	0.936727i	$0.613839\pi$
$662$	−28.0000	−1.08825
$663$	0	0
$664$	8.00000	0.310460
$665$	2.00000	0.0775567
$666$	0	0
$667$	−48.0000	−1.85857
$668$	16.0000	0.619059
$669$	0	0
$670$	−12.0000	−0.463600
$671$	−12.0000	−0.463255
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	6.00000	0.231111
$675$	0	0
$676$	3.00000	0.115385
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	28.0000	1.07454
$680$	6.00000	0.230089
$681$	0	0
$682$	−16.0000	−0.612672
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	0	0
$685$	−6.00000	−0.229248
$686$	20.0000	0.763604
$687$	0	0
$688$	0	0
$689$	40.0000	1.52388
$690$	0	0
$691$	−36.0000	−1.36950	−0.684752	−	0.728776i	$-0.740090\pi$
$691$	−36.0000	−1.36950	−0.684752	+	0.728776i	$0.740090\pi$
$692$	−2.00000	−0.0760286
$693$	0	0
$694$	12.0000	0.455514
$695$	20.0000	0.758643
$696$	0	0
$697$	−72.0000	−2.72719
$698$	−22.0000	−0.832712
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	0	0
$703$	−8.00000	−0.301726
$704$	2.00000	0.0753778
$705$	0	0
$706$	10.0000	0.376355
$707$	4.00000	0.150435
$708$	0	0
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	12.0000	0.450352
$711$	0	0
$712$	8.00000	0.299813
$713$	64.0000	2.39682
$714$	0	0
$715$	8.00000	0.299183
$716$	−2.00000	−0.0747435
$717$	0	0
$718$	−8.00000	−0.298557
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	28.0000	1.04277
$722$	1.00000	0.0372161
$723$	0	0
$724$	14.0000	0.520306
$725$	6.00000	0.222834
$726$	0	0
$727$	−22.0000	−0.815935	−0.407967	−	0.912996i	$-0.633762\pi$
$727$	−22.0000	−0.815935	−0.407967	+	0.912996i	$0.633762\pi$
$728$	8.00000	0.296500
$729$	0	0
$730$	10.0000	0.370117
$731$	0	0
$732$	0	0
$733$	36.0000	1.32969	0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000	1.32969	0.664845	+	0.746981i	$0.268498\pi$
$734$	14.0000	0.516749
$735$	0	0
$736$	−8.00000	−0.294884
$737$	24.0000	0.884051
$738$	0	0
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	8.00000	0.294086
$741$	0	0
$742$	20.0000	0.734223
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	−2.00000	−0.0732743
$746$	28.0000	1.02515
$747$	0	0
$748$	−12.0000	−0.438763
$749$	8.00000	0.292314
$750$	0	0
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	0	0
$753$	0	0
$754$	−24.0000	−0.874028
$755$	−20.0000	−0.727875
$756$	0	0
$757$	−36.0000	−1.30844	−0.654221	−	0.756303i	$-0.727003\pi$
$757$	−36.0000	−1.30844	−0.654221	+	0.756303i	$0.727003\pi$
$758$	12.0000	0.435860
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	−28.0000	−1.01500	−0.507500	−	0.861652i	$-0.669430\pi$
$761$	−28.0000	−1.01500	−0.507500	+	0.861652i	$0.669430\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−16.0000	−0.578103
$767$	−24.0000	−0.866590
$768$	0	0
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	4.00000	0.144150
$771$	0	0
$772$	−2.00000	−0.0719816
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	−8.00000	−0.287368
$776$	−14.0000	−0.502571
$777$	0	0
$778$	26.0000	0.932145
$779$	12.0000	0.429945
$780$	0	0
$781$	−24.0000	−0.858788
$782$	48.0000	1.71648
$783$	0	0
$784$	−3.00000	−0.107143
$785$	−24.0000	−0.856597
$786$	0	0
$787$	−12.0000	−0.427754	−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000	−0.427754	−0.213877	+	0.976861i	$0.568609\pi$
$788$	26.0000	0.926212
$789$	0	0
$790$	8.00000	0.284627
$791$	−36.0000	−1.28001
$792$	0	0
$793$	24.0000	0.852265
$794$	20.0000	0.709773
$795$	0	0
$796$	−24.0000	−0.850657
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	0	0
$802$	−24.0000	−0.847469
$803$	−20.0000	−0.705785
$804$	0	0
$805$	−16.0000	−0.563926
$806$	32.0000	1.12715
$807$	0	0
$808$	−2.00000	−0.0703598
$809$	16.0000	0.562530	0.281265	−	0.959630i	$-0.409246\pi$
$809$	16.0000	0.562530	0.281265	+	0.959630i	$0.409246\pi$
$810$	0	0
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	−12.0000	−0.421117
$813$	0	0
$814$	−16.0000	−0.560800
$815$	−4.00000	−0.140114
$816$	0	0
$817$	0	0
$818$	10.0000	0.349642
$819$	0	0
$820$	−12.0000	−0.419058
$821$	38.0000	1.32621	0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000	1.32621	0.663105	+	0.748527i	$0.269238\pi$
$822$	0	0
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	0	0
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	−8.00000	−0.277684
$831$	0	0
$832$	−4.00000	−0.138675
$833$	18.0000	0.623663
$834$	0	0
$835$	−16.0000	−0.553703
$836$	2.00000	0.0691714
$837$	0	0
$838$	−10.0000	−0.345444
$839$	−16.0000	−0.552381	−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000	−0.552381	−0.276191	+	0.961103i	$0.589072\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	10.0000	0.344623
$843$	0	0
$844$	4.00000	0.137686
$845$	−3.00000	−0.103203
$846$	0	0
$847$	14.0000	0.481046
$848$	−10.0000	−0.343401
$849$	0	0
$850$	−6.00000	−0.205798
$851$	64.0000	2.19389
$852$	0	0
$853$	−12.0000	−0.410872	−0.205436	−	0.978671i	$-0.565861\pi$
$853$	−12.0000	−0.410872	−0.205436	+	0.978671i	$0.565861\pi$
$854$	12.0000	0.410632
$855$	0	0
$856$	−4.00000	−0.136717
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−40.0000	−1.36162	−0.680808	−	0.732462i	$-0.738371\pi$
$863$	−40.0000	−1.36162	−0.680808	+	0.732462i	$0.738371\pi$
$864$	0	0
$865$	2.00000	0.0680020
$866$	−34.0000	−1.15537
$867$	0	0
$868$	16.0000	0.543075
$869$	−16.0000	−0.542763
$870$	0	0
$871$	−48.0000	−1.62642
$872$	−2.00000	−0.0677285
$873$	0	0
$874$	−8.00000	−0.270604
$875$	2.00000	0.0676123
$876$	0	0
$877$	12.0000	0.405211	0.202606	−	0.979260i	$-0.435059\pi$
$877$	12.0000	0.405211	0.202606	+	0.979260i	$0.435059\pi$
$878$	−28.0000	−0.944954
$879$	0	0
$880$	−2.00000	−0.0674200
$881$	52.0000	1.75192	0.875962	−	0.482380i	$-0.160227\pi$
$881$	52.0000	1.75192	0.875962	+	0.482380i	$0.160227\pi$
$882$	0	0
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	−12.0000	−0.403148
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	0	0
$889$	−36.0000	−1.20740
$890$	−8.00000	−0.268161
$891$	0	0
$892$	−14.0000	−0.468755
$893$	0	0
$894$	0	0
$895$	2.00000	0.0668526
$896$	−2.00000	−0.0668153
$897$	0	0
$898$	8.00000	0.266963
$899$	−48.0000	−1.60089
$900$	0	0
$901$	60.0000	1.99889
$902$	24.0000	0.799113
$903$	0	0
$904$	18.0000	0.598671
$905$	−14.0000	−0.465376
$906$	0	0
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	−16.0000	−0.530979
$909$	0	0
$910$	−8.00000	−0.265197
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	16.0000	0.529523
$914$	10.0000	0.330771
$915$	0	0
$916$	30.0000	0.991228
$917$	4.00000	0.132092
$918$	0	0
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	8.00000	0.263752
$921$	0	0
$922$	−30.0000	−0.987997
$923$	48.0000	1.57994
$924$	0	0
$925$	−8.00000	−0.263038
$926$	10.0000	0.328620
$927$	0	0
$928$	6.00000	0.196960
$929$	−36.0000	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	10.0000	0.327561
$933$	0	0
$934$	−32.0000	−1.04707
$935$	12.0000	0.392442
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−24.0000	−0.783628
$939$	0	0
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	0	0
$943$	−96.0000	−3.12619
$944$	6.00000	0.195283
$945$	0	0
$946$	0	0
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	40.0000	1.29845
$950$	1.00000	0.0324443
$951$	0	0
$952$	12.0000	0.388922
$953$	18.0000	0.583077	0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000	0.583077	0.291539	+	0.956559i	$0.405833\pi$
$954$	0	0
$955$	12.0000	0.388311
$956$	28.0000	0.905585
$957$	0	0
$958$	12.0000	0.387702
$959$	−12.0000	−0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	32.0000	1.03172
$963$	0	0
$964$	−18.0000	−0.579741
$965$	2.00000	0.0643823
$966$	0	0
$967$	−2.00000	−0.0643157	−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000	−0.0643157	−0.0321578	+	0.999483i	$0.510238\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	14.0000	0.449513
$971$	10.0000	0.320915	0.160458	−	0.987043i	$-0.448703\pi$
$971$	10.0000	0.320915	0.160458	+	0.987043i	$0.448703\pi$
$972$	0	0
$973$	40.0000	1.28234
$974$	−26.0000	−0.833094
$975$	0	0
$976$	−6.00000	−0.192055
$977$	−26.0000	−0.831814	−0.415907	−	0.909407i	$-0.636536\pi$
$977$	−26.0000	−0.831814	−0.415907	+	0.909407i	$0.636536\pi$
$978$	0	0
$979$	16.0000	0.511362
$980$	3.00000	0.0958315
$981$	0	0
$982$	−18.0000	−0.574403
$983$	−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
$985$	−26.0000	−0.828429
$986$	−36.0000	−1.14647
$987$	0	0
$988$	−4.00000	−0.127257
$989$	0	0
$990$	0	0
$991$	−60.0000	−1.90596	−0.952981	−	0.303029i	$-0.902002\pi$
$991$	−60.0000	−1.90596	−0.952981	+	0.303029i	$0.902002\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	24.0000	0.761234
$995$	24.0000	0.760851
$996$	0	0
$997$	−56.0000	−1.77354	−0.886769	−	0.462213i	$-0.847056\pi$
$997$	−56.0000	−1.77354	−0.886769	+	0.462213i	$0.847056\pi$
$998$	−12.0000	−0.379853
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.a.m.1.1	yes	1
3.2	odd	2		1710.2.a.h.1.1	✓	1
5.4	even	2		8550.2.a.p.1.1		1
15.14	odd	2		8550.2.a.bg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.a.h.1.1	✓	1	3.2	odd	2
1710.2.a.m.1.1	yes	1	1.1	even	1	trivial
8550.2.a.p.1.1		1	5.4	even	2
8550.2.a.bg.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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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