LMFDB - Embedded newform 2850.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(1,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, 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("2850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.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:	$22.7573645761$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -4.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} +2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{29} -6.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -1.00000 q^{38} -2.00000 q^{39} -6.00000 q^{43} -4.00000 q^{44} +6.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} +6.00000 q^{51} +2.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} +1.00000 q^{57} -2.00000 q^{58} +2.00000 q^{59} -6.00000 q^{61} -6.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} +8.00000 q^{67} -6.00000 q^{68} -6.00000 q^{69} -12.0000 q^{71} +1.00000 q^{72} -16.0000 q^{73} -10.0000 q^{74} -1.00000 q^{76} -2.00000 q^{78} -14.0000 q^{79} +1.00000 q^{81} +12.0000 q^{83} -6.00000 q^{86} +2.00000 q^{87} -4.00000 q^{88} +4.00000 q^{89} +6.00000 q^{92} +6.00000 q^{93} +6.00000 q^{94} -1.00000 q^{96} -10.0000 q^{97} -7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	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	$0.759367\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	0	0
$22$	−4.00000	−0.852803
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000	0.176777
$33$	4.00000	0.696311
$34$	−6.00000	−1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−1.00000	−0.162221
$39$	−2.00000	−0.320256
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	6.00000	0.884652
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	0	0
$51$	6.00000	0.840168
$52$	2.00000	0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	1.00000	0.132453
$58$	−2.00000	−0.262613
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−6.00000	−0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	4.00000	0.492366
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−6.00000	−0.727607
$69$	−6.00000	−0.722315
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	−16.0000	−1.87266	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000	−1.87266	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	0	0
$86$	−6.00000	−0.646997
$87$	2.00000	0.214423
$88$	−4.00000	−0.426401
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	0	0
$92$	6.00000	0.625543
$93$	6.00000	0.622171
$94$	6.00000	0.618853
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	−7.00000	−0.707107
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	6.00000	0.594089
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	0.196116
$105$	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	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−2.00000	−0.185695
$117$	2.00000	0.184900
$118$	2.00000	0.184115
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	−6.00000	−0.543214
$123$	0	0
$124$	−6.00000	−0.538816
$125$	0	0
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	0	0
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	8.00000	0.691095
$135$	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	$0.417494\pi$
$138$	−6.00000	−0.510754
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	−12.0000	−1.00702
$143$	−8.00000	−0.668994
$144$	1.00000	0.0833333
$145$	0	0
$146$	−16.0000	−1.32417
$147$	7.00000	0.577350
$148$	−10.0000	−0.821995
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	−1.00000	−0.0811107
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	−2.00000	−0.160128
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−14.0000	−1.11378
$159$	−10.0000	−0.793052
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	0	0
$165$	0	0
$166$	12.0000	0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	−6.00000	−0.457496
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−2.00000	−0.150329
$178$	4.00000	0.299813
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	0	0
$181$	−4.00000	−0.297318	−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000	−0.297318	−0.148659	+	0.988889i	$0.547496\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	6.00000	0.442326
$185$	0	0
$186$	6.00000	0.439941
$187$	24.0000	1.75505
$188$	6.00000	0.437595
$189$	0	0
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	−7.00000	−0.500000
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	−4.00000	−0.284268
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	−18.0000	−1.26648
$203$	0	0
$204$	6.00000	0.420084
$205$	0	0
$206$	8.00000	0.557386
$207$	6.00000	0.417029
$208$	2.00000	0.138675
$209$	4.00000	0.276686
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	10.0000	0.686803
$213$	12.0000	0.822226
$214$	−4.00000	−0.273434
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	4.00000	0.270914
$219$	16.0000	1.08118
$220$	0	0
$221$	−12.0000	−0.807207
$222$	10.0000	0.671156
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	0	0
$226$	2.00000	0.133038
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	1.00000	0.0662266
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	−2.00000	−0.131306
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	2.00000	0.130189
$237$	14.0000	0.909398
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	−6.00000	−0.384111
$245$	0	0
$246$	0	0
$247$	−2.00000	−0.127257
$248$	−6.00000	−0.381000
$249$	−12.0000	−0.760469
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	−24.0000	−1.50887
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	6.00000	0.373544
$259$	0	0
$260$	0	0
$261$	−2.00000	−0.123797
$262$	−8.00000	−0.494242
$263$	−2.00000	−0.123325	−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000	−0.123325	−0.0616626	+	0.998097i	$0.519640\pi$
$264$	4.00000	0.246183
$265$	0	0
$266$	0	0
$267$	−4.00000	−0.244796
$268$	8.00000	0.488678
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	−6.00000	−0.361158
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	12.0000	0.719712
$279$	−6.00000	−0.359211
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	−6.00000	−0.357295
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−8.00000	−0.473050
$287$	0	0
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	10.0000	0.586210
$292$	−16.0000	−0.936329
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	7.00000	0.408248
$295$	0	0
$296$	−10.0000	−0.581238
$297$	4.00000	0.232104
$298$	−6.00000	−0.347571
$299$	12.0000	0.693978
$300$	0	0
$301$	0	0
$302$	10.0000	0.575435
$303$	18.0000	1.03407
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−6.00000	−0.342997
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	−2.00000	−0.113228
$313$	28.0000	1.58265	0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000	1.58265	0.791327	+	0.611393i	$0.209391\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	−14.0000	−0.787562
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−10.0000	−0.560772
$319$	8.00000	0.447914
$320$	0	0
$321$	4.00000	0.223258
$322$	0	0
$323$	6.00000	0.333849
$324$	1.00000	0.0555556
$325$	0	0
$326$	−10.0000	−0.553849
$327$	−4.00000	−0.221201
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	12.0000	0.658586
$333$	−10.0000	−0.547997
$334$	0	0
$335$	0	0
$336$	0	0
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	−9.00000	−0.489535
$339$	−2.00000	−0.108625
$340$	0	0
$341$	24.0000	1.29967
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−14.0000	−0.752645
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	2.00000	0.107211
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	−4.00000	−0.213201
$353$	−2.00000	−0.106449	−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000	−0.106449	−0.0532246	+	0.998583i	$0.516950\pi$
$354$	−2.00000	−0.106299
$355$	0	0
$356$	4.00000	0.212000
$357$	0	0
$358$	−18.0000	−0.951330
$359$	−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
$362$	−4.00000	−0.210235
$363$	−5.00000	−0.262432
$364$	0	0
$365$	0	0
$366$	6.00000	0.313625
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	0	0
$372$	6.00000	0.311086
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	6.00000	0.309426
$377$	−4.00000	−0.206010
$378$	0	0
$379$	24.0000	1.23280	0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000	1.23280	0.616399	+	0.787434i	$0.288591\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	24.0000	1.22795
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	14.0000	0.712581
$387$	−6.00000	−0.304997
$388$	−10.0000	−0.507673
$389$	38.0000	1.92668	0.963338	−	0.268290i	$-0.0864585\pi$
$389$	38.0000	1.92668	0.963338	+	0.268290i	$0.0864585\pi$
$390$	0	0
$391$	−36.0000	−1.82060
$392$	−7.00000	−0.353553
$393$	8.00000	0.403547
$394$	8.00000	0.403034
$395$	0	0
$396$	−4.00000	−0.201008
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	0	0
$401$	16.0000	0.799002	0.399501	−	0.916733i	$-0.369183\pi$
$401$	16.0000	0.799002	0.399501	+	0.916733i	$0.369183\pi$
$402$	−8.00000	−0.399004
$403$	−12.0000	−0.597763
$404$	−18.0000	−0.895533
$405$	0	0
$406$	0	0
$407$	40.0000	1.98273
$408$	6.00000	0.297044
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	0	0
$411$	−6.00000	−0.295958
$412$	8.00000	0.394132
$413$	0	0
$414$	6.00000	0.294884
$415$	0	0
$416$	2.00000	0.0980581
$417$	−12.0000	−0.587643
$418$	4.00000	0.195646
$419$	8.00000	0.390826	0.195413	−	0.980721i	$-0.437395\pi$
$419$	8.00000	0.390826	0.195413	+	0.980721i	$0.437395\pi$
$420$	0	0
$421$	16.0000	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$422$	−8.00000	−0.389434
$423$	6.00000	0.291730
$424$	10.0000	0.485643
$425$	0	0
$426$	12.0000	0.581402
$427$	0	0
$428$	−4.00000	−0.193347
$429$	8.00000	0.386244
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	−1.00000	−0.0481125
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	0	0
$435$	0	0
$436$	4.00000	0.191565
$437$	−6.00000	−0.287019
$438$	16.0000	0.764510
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	−12.0000	−0.570782
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	10.0000	0.474579
$445$	0	0
$446$	−8.00000	−0.378811
$447$	6.00000	0.283790
$448$	0	0
$449$	4.00000	0.188772	0.0943858	−	0.995536i	$-0.469911\pi$
$449$	4.00000	0.188772	0.0943858	+	0.995536i	$0.469911\pi$
$450$	0	0
$451$	0	0
$452$	2.00000	0.0940721
$453$	−10.0000	−0.469841
$454$	−12.0000	−0.563188
$455$	0	0
$456$	1.00000	0.0468293
$457$	16.0000	0.748448	0.374224	−	0.927338i	$-0.377909\pi$
$457$	16.0000	0.748448	0.374224	+	0.927338i	$0.377909\pi$
$458$	−10.0000	−0.467269
$459$	6.00000	0.280056
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	14.0000	0.648537
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	0	0
$471$	18.0000	0.829396
$472$	2.00000	0.0920575
$473$	24.0000	1.10352
$474$	14.0000	0.643041
$475$	0	0
$476$	0	0
$477$	10.0000	0.457869
$478$	−8.00000	−0.365911
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	−10.0000	−0.455488
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	24.0000	1.08754	0.543772	−	0.839233i	$-0.316996\pi$
$487$	24.0000	1.08754	0.543772	+	0.839233i	$0.316996\pi$
$488$	−6.00000	−0.271607
$489$	10.0000	0.452216
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	−2.00000	−0.0899843
$495$	0	0
$496$	−6.00000	−0.269408
$497$	0	0
$498$	−12.0000	−0.537733
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	−14.0000	−0.624229	−0.312115	−	0.950044i	$-0.601037\pi$
$503$	−14.0000	−0.624229	−0.312115	+	0.950044i	$0.601037\pi$
$504$	0	0
$505$	0	0
$506$	−24.0000	−1.06693
$507$	9.00000	0.399704
$508$	8.00000	0.354943
$509$	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
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	22.0000	0.970378
$515$	0	0
$516$	6.00000	0.264135
$517$	−24.0000	−1.05552
$518$	0	0
$519$	14.0000	0.614532
$520$	0	0
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	−2.00000	−0.0875376
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	−2.00000	−0.0872041
$527$	36.0000	1.56818
$528$	4.00000	0.174078
$529$	13.0000	0.565217
$530$	0	0
$531$	2.00000	0.0867926
$532$	0	0
$533$	0	0
$534$	−4.00000	−0.173097
$535$	0	0
$536$	8.00000	0.345547
$537$	18.0000	0.776757
$538$	−14.0000	−0.603583
$539$	28.0000	1.20605
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	32.0000	1.37452
$543$	4.00000	0.171656
$544$	−6.00000	−0.257248
$545$	0	0
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	6.00000	0.256307
$549$	−6.00000	−0.256074
$550$	0	0
$551$	2.00000	0.0852029
$552$	−6.00000	−0.255377
$553$	0	0
$554$	−26.0000	−1.10463
$555$	0	0
$556$	12.0000	0.508913
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	−6.00000	−0.254000
$559$	−12.0000	−0.507546
$560$	0	0
$561$	−24.0000	−1.01328
$562$	0	0
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	22.0000	0.924729
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−28.0000	−1.17382	−0.586911	−	0.809652i	$-0.699656\pi$
$569$	−28.0000	−1.17382	−0.586911	+	0.809652i	$0.699656\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	−8.00000	−0.334497
$573$	−24.0000	−1.00261
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−8.00000	−0.333044	−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000	−0.333044	−0.166522	+	0.986038i	$0.553254\pi$
$578$	19.0000	0.790296
$579$	−14.0000	−0.581820
$580$	0	0
$581$	0	0
$582$	10.0000	0.414513
$583$	−40.0000	−1.65663
$584$	−16.0000	−0.662085
$585$	0	0
$586$	2.00000	0.0826192
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	7.00000	0.288675
$589$	6.00000	0.247226
$590$	0	0
$591$	−8.00000	−0.329076
$592$	−10.0000	−0.410997
$593$	−46.0000	−1.88899	−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000	−1.88899	−0.944497	+	0.328521i	$0.893450\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−6.00000	−0.245770
$597$	16.0000	0.654836
$598$	12.0000	0.490716
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	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
$603$	8.00000	0.325785
$604$	10.0000	0.406894
$605$	0	0
$606$	18.0000	0.731200
$607$	−24.0000	−0.974130	−0.487065	−	0.873366i	$-0.661933\pi$
$607$	−24.0000	−0.974130	−0.487065	+	0.873366i	$0.661933\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	12.0000	0.485468
$612$	−6.00000	−0.242536
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−8.00000	−0.321807
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	0	0
$621$	−6.00000	−0.240772
$622$	24.0000	0.962312
$623$	0	0
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	28.0000	1.11911
$627$	−4.00000	−0.159745
$628$	−18.0000	−0.718278
$629$	60.0000	2.39236
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	−14.0000	−0.556890
$633$	8.00000	0.317971
$634$	6.00000	0.238290
$635$	0	0
$636$	−10.0000	−0.396526
$637$	−14.0000	−0.554700
$638$	8.00000	0.316723
$639$	−12.0000	−0.474713
$640$	0	0
$641$	48.0000	1.89589	0.947943	−	0.318440i	$-0.103159\pi$
$641$	48.0000	1.89589	0.947943	+	0.318440i	$0.103159\pi$
$642$	4.00000	0.157867
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	0	0
$645$	0	0
$646$	6.00000	0.236067
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	1.00000	0.0392837
$649$	−8.00000	−0.314027
$650$	0	0
$651$	0	0
$652$	−10.0000	−0.391630
$653$	48.0000	1.87839	0.939193	−	0.343391i	$-0.111576\pi$
$653$	48.0000	1.87839	0.939193	+	0.343391i	$0.111576\pi$
$654$	−4.00000	−0.156412
$655$	0	0
$656$	0	0
$657$	−16.0000	−0.624219
$658$	0	0
$659$	46.0000	1.79191	0.895953	−	0.444149i	$-0.146494\pi$
$659$	46.0000	1.79191	0.895953	+	0.444149i	$0.146494\pi$
$660$	0	0
$661$	−8.00000	−0.311164	−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000	−0.311164	−0.155582	+	0.987823i	$0.549725\pi$
$662$	−4.00000	−0.155464
$663$	12.0000	0.466041
$664$	12.0000	0.465690
$665$	0	0
$666$	−10.0000	−0.387492
$667$	−12.0000	−0.464642
$668$	0	0
$669$	8.00000	0.309298
$670$	0	0
$671$	24.0000	0.926510
$672$	0	0
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	6.00000	0.231111
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	0	0
$681$	12.0000	0.459841
$682$	24.0000	0.919007
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	0	0
$687$	10.0000	0.381524
$688$	−6.00000	−0.228748
$689$	20.0000	0.761939
$690$	0	0
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	20.0000	0.759190
$695$	0	0
$696$	2.00000	0.0758098
$697$	0	0
$698$	−26.0000	−0.984115
$699$	−14.0000	−0.529529
$700$	0	0
$701$	−22.0000	−0.830929	−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000	−0.830929	−0.415464	+	0.909610i	$0.636381\pi$
$702$	−2.00000	−0.0754851
$703$	10.0000	0.377157
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−2.00000	−0.0752710
$707$	0	0
$708$	−2.00000	−0.0751646
$709$	−2.00000	−0.0751116	−0.0375558	−	0.999295i	$-0.511957\pi$
$709$	−2.00000	−0.0751116	−0.0375558	+	0.999295i	$0.511957\pi$
$710$	0	0
$711$	−14.0000	−0.525041
$712$	4.00000	0.149906
$713$	−36.0000	−1.34821
$714$	0	0
$715$	0	0
$716$	−18.0000	−0.672692
$717$	8.00000	0.298765
$718$	−8.00000	−0.298557
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	0	0
$721$	0	0
$722$	1.00000	0.0372161
$723$	10.0000	0.371904
$724$	−4.00000	−0.148659
$725$	0	0
$726$	−5.00000	−0.185567
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	36.0000	1.33151
$732$	6.00000	0.221766
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	12.0000	0.442928
$735$	0	0
$736$	6.00000	0.221163
$737$	−32.0000	−1.17874
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	2.00000	0.0734718
$742$	0	0
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	6.00000	0.219971
$745$	0	0
$746$	6.00000	0.219676
$747$	12.0000	0.439057
$748$	24.0000	0.877527
$749$	0	0
$750$	0	0
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	6.00000	0.218797
$753$	−12.0000	−0.437304
$754$	−4.00000	−0.145671
$755$	0	0
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	24.0000	0.871719
$759$	24.0000	0.871145
$760$	0	0
$761$	30.0000	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$762$	−8.00000	−0.289809
$763$	0	0
$764$	24.0000	0.868290
$765$	0	0
$766$	36.0000	1.30073
$767$	4.00000	0.144432
$768$	−1.00000	−0.0360844
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	0	0
$771$	−22.0000	−0.792311
$772$	14.0000	0.503871
$773$	−50.0000	−1.79838	−0.899188	−	0.437564i	$-0.855842\pi$
$773$	−50.0000	−1.79838	−0.899188	+	0.437564i	$0.855842\pi$
$774$	−6.00000	−0.215666
$775$	0	0
$776$	−10.0000	−0.358979
$777$	0	0
$778$	38.0000	1.36237
$779$	0	0
$780$	0	0
$781$	48.0000	1.71758
$782$	−36.0000	−1.28736
$783$	2.00000	0.0714742
$784$	−7.00000	−0.250000
$785$	0	0
$786$	8.00000	0.285351
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	8.00000	0.284988
$789$	2.00000	0.0712019
$790$	0	0
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−12.0000	−0.426132
$794$	−30.0000	−1.06466
$795$	0	0
$796$	−16.0000	−0.567105
$797$	−54.0000	−1.91278	−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000	−1.91278	−0.956389	+	0.292096i	$0.905647\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	0	0
$801$	4.00000	0.141333
$802$	16.0000	0.564980
$803$	64.0000	2.25851
$804$	−8.00000	−0.282138
$805$	0	0
$806$	−12.0000	−0.422682
$807$	14.0000	0.492823
$808$	−18.0000	−0.633238
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0	0
$813$	−32.0000	−1.12229
$814$	40.0000	1.40200
$815$	0	0
$816$	6.00000	0.210042
$817$	6.00000	0.209913
$818$	26.0000	0.909069
$819$	0	0
$820$	0	0
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	−6.00000	−0.209274
$823$	−12.0000	−0.418294	−0.209147	−	0.977884i	$-0.567069\pi$
$823$	−12.0000	−0.418294	−0.209147	+	0.977884i	$0.567069\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	6.00000	0.208514
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	0	0
$831$	26.0000	0.901930
$832$	2.00000	0.0693375
$833$	42.0000	1.45521
$834$	−12.0000	−0.415526
$835$	0	0
$836$	4.00000	0.138343
$837$	6.00000	0.207390
$838$	8.00000	0.276355
$839$	44.0000	1.51905	0.759524	−	0.650479i	$-0.225432\pi$
$839$	44.0000	1.51905	0.759524	+	0.650479i	$0.225432\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	16.0000	0.551396
$843$	0	0
$844$	−8.00000	−0.275371
$845$	0	0
$846$	6.00000	0.206284
$847$	0	0
$848$	10.0000	0.343401
$849$	−22.0000	−0.755038
$850$	0	0
$851$	−60.0000	−2.05677
$852$	12.0000	0.411113
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	0	0
$855$	0	0
$856$	−4.00000	−0.136717
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	8.00000	0.273115
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	0	0
$861$	0	0
$862$	−24.0000	−0.817443
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	6.00000	0.203888
$867$	−19.0000	−0.645274
$868$	0	0
$869$	56.0000	1.89967
$870$	0	0
$871$	16.0000	0.542139
$872$	4.00000	0.135457
$873$	−10.0000	−0.338449
$874$	−6.00000	−0.202953
$875$	0	0
$876$	16.0000	0.540590
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	−14.0000	−0.472477
$879$	−2.00000	−0.0674583
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	−7.00000	−0.235702
$883$	10.0000	0.336527	0.168263	−	0.985742i	$-0.446184\pi$
$883$	10.0000	0.336527	0.168263	+	0.985742i	$0.446184\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	0	0
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	0	0
$891$	−4.00000	−0.134005
$892$	−8.00000	−0.267860
$893$	−6.00000	−0.200782
$894$	6.00000	0.200670
$895$	0	0
$896$	0	0
$897$	−12.0000	−0.400668
$898$	4.00000	0.133482
$899$	12.0000	0.400222
$900$	0	0
$901$	−60.0000	−1.99889
$902$	0	0
$903$	0	0
$904$	2.00000	0.0665190
$905$	0	0
$906$	−10.0000	−0.332228
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	−12.0000	−0.398234
$909$	−18.0000	−0.597022
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	1.00000	0.0331133
$913$	−48.0000	−1.58857
$914$	16.0000	0.529233
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	6.00000	0.198030
$919$	28.0000	0.923635	0.461817	−	0.886975i	$-0.347198\pi$
$919$	28.0000	0.923635	0.461817	+	0.886975i	$0.347198\pi$
$920$	0	0
$921$	12.0000	0.395413
$922$	−18.0000	−0.592798
$923$	−24.0000	−0.789970
$924$	0	0
$925$	0	0
$926$	−8.00000	−0.262896
$927$	8.00000	0.262754
$928$	−2.00000	−0.0656532
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	0	0
$931$	7.00000	0.229416
$932$	14.0000	0.458585
$933$	−24.0000	−0.785725
$934$	0	0
$935$	0	0
$936$	2.00000	0.0653720
$937$	−44.0000	−1.43742	−0.718709	−	0.695311i	$-0.755266\pi$
$937$	−44.0000	−1.43742	−0.718709	+	0.695311i	$0.755266\pi$
$938$	0	0
$939$	−28.0000	−0.913745
$940$	0	0
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	18.0000	0.586472
$943$	0	0
$944$	2.00000	0.0650945
$945$	0	0
$946$	24.0000	0.780307
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	14.0000	0.454699
$949$	−32.0000	−1.03876
$950$	0	0
$951$	−6.00000	−0.194563
$952$	0	0
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	10.0000	0.323762
$955$	0	0
$956$	−8.00000	−0.258738
$957$	−8.00000	−0.258603
$958$	−16.0000	−0.516937
$959$	0	0
$960$	0	0
$961$	5.00000	0.161290
$962$	−20.0000	−0.644826
$963$	−4.00000	−0.128898
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	5.00000	0.160706
$969$	−6.00000	−0.192748
$970$	0	0
$971$	−58.0000	−1.86131	−0.930654	−	0.365900i	$-0.880761\pi$
$971$	−58.0000	−1.86131	−0.930654	+	0.365900i	$0.880761\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	24.0000	0.769010
$975$	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	$0.636536\pi$
$978$	10.0000	0.319765
$979$	−16.0000	−0.511362
$980$	0	0
$981$	4.00000	0.127710
$982$	0	0
$983$	56.0000	1.78612	0.893061	−	0.449935i	$-0.148553\pi$
$983$	56.0000	1.78612	0.893061	+	0.449935i	$0.148553\pi$
$984$	0	0
$985$	0	0
$986$	12.0000	0.382158
$987$	0	0
$988$	−2.00000	−0.0636285
$989$	−36.0000	−1.14473
$990$	0	0
$991$	−6.00000	−0.190596	−0.0952981	−	0.995449i	$-0.530380\pi$
$991$	−6.00000	−0.190596	−0.0952981	+	0.995449i	$0.530380\pi$
$992$	−6.00000	−0.190500
$993$	4.00000	0.126936
$994$	0	0
$995$	0	0
$996$	−12.0000	−0.380235
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	20.0000	0.633089
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.t.1.1		1
3.2	odd	2		8550.2.a.k.1.1		1
5.2	odd	4		570.2.d.a.229.2	yes	2
5.3	odd	4		570.2.d.a.229.1	✓	2
5.4	even	2		2850.2.a.i.1.1		1
15.2	even	4		1710.2.d.b.1369.1		2
15.8	even	4		1710.2.d.b.1369.2		2
15.14	odd	2		8550.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.a.229.1	✓	2	5.3	odd	4
570.2.d.a.229.2	yes	2	5.2	odd	4
1710.2.d.b.1369.1		2	15.2	even	4
1710.2.d.b.1369.2		2	15.8	even	4
2850.2.a.i.1.1		1	5.4	even	2
2850.2.a.t.1.1		1	1.1	even	1	trivial
8550.2.a.k.1.1		1	3.2	odd	2
8550.2.a.bb.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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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