LMFDB - Embedded newform 3950.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3950,2,Mod(1,3950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3950 = 2 \cdot 5^{2} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3950.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:	$31.5409087984$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 158)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +2.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +2.00000 q^{18} -3.00000 q^{21} -2.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} -1.00000 q^{26} -5.00000 q^{27} -3.00000 q^{28} -10.0000 q^{29} +2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} -2.00000 q^{34} -2.00000 q^{36} +2.00000 q^{37} +1.00000 q^{39} +2.00000 q^{41} +3.00000 q^{42} -4.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} -3.00000 q^{47} +1.00000 q^{48} +2.00000 q^{49} +2.00000 q^{51} +1.00000 q^{52} -4.00000 q^{53} +5.00000 q^{54} +3.00000 q^{56} +10.0000 q^{58} +5.00000 q^{59} +12.0000 q^{61} -2.00000 q^{62} +6.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -8.00000 q^{67} +2.00000 q^{68} +6.00000 q^{69} -13.0000 q^{71} +2.00000 q^{72} +6.00000 q^{73} -2.00000 q^{74} -6.00000 q^{77} -1.00000 q^{78} -1.00000 q^{79} +1.00000 q^{81} -2.00000 q^{82} +6.00000 q^{83} -3.00000 q^{84} +4.00000 q^{86} -10.0000 q^{87} -2.00000 q^{88} -15.0000 q^{89} -3.00000 q^{91} +6.00000 q^{92} +2.00000 q^{93} +3.00000 q^{94} -1.00000 q^{96} -13.0000 q^{97} -2.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	2.00000	0.471405
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	−2.00000	−0.426401
$23$	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
$26$	−1.00000	−0.196116
$27$	−5.00000	−0.962250
$28$	−3.00000	−0.566947
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	−2.00000	−0.342997
$35$	0	0
$36$	−2.00000	−0.333333
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	3.00000	0.462910
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−6.00000	−0.884652
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	1.00000	0.144338
$49$	2.00000	0.285714
$50$	0	0
$51$	2.00000	0.280056
$52$	1.00000	0.138675
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	3.00000	0.400892
$57$	0	0
$58$	10.0000	1.31306
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0	0
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	−2.00000	−0.254000
$63$	6.00000	0.755929
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	2.00000	0.242536
$69$	6.00000	0.722315
$70$	0	0
$71$	−13.0000	−1.54282	−0.771408	−	0.636341i	$-0.780447\pi$
$71$	−13.0000	−1.54282	−0.771408	+	0.636341i	$0.780447\pi$
$72$	2.00000	0.235702
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	0	0
$77$	−6.00000	−0.683763
$78$	−1.00000	−0.113228
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−3.00000	−0.327327
$85$	0	0
$86$	4.00000	0.431331
$87$	−10.0000	−1.07211
$88$	−2.00000	−0.213201
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	6.00000	0.625543
$93$	2.00000	0.207390
$94$	3.00000	0.309426
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−13.0000	−1.31995	−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000	−1.31995	−0.659975	+	0.751288i	$0.729433\pi$
$98$	−2.00000	−0.202031
$99$	−4.00000	−0.402015
$100$	0	0
$101$	7.00000	0.696526	0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000	0.696526	0.348263	+	0.937397i	$0.386772\pi$
$102$	−2.00000	−0.198030
$103$	−19.0000	−1.87213	−0.936063	−	0.351833i	$-0.885559\pi$
$103$	−19.0000	−1.87213	−0.936063	+	0.351833i	$0.885559\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	4.00000	0.388514
$107$	−13.0000	−1.25676	−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000	−1.25676	−0.628379	+	0.777908i	$0.716281\pi$
$108$	−5.00000	−0.481125
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	−3.00000	−0.283473
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	0	0
$116$	−10.0000	−0.928477
$117$	−2.00000	−0.184900
$118$	−5.00000	−0.460287
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−12.0000	−1.08643
$123$	2.00000	0.180334
$124$	2.00000	0.179605
$125$	0	0
$126$	−6.00000	−0.534522
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	8.00000	0.691095
$135$	0	0
$136$	−2.00000	−0.171499
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	−6.00000	−0.510754
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	0	0
$141$	−3.00000	−0.252646
$142$	13.0000	1.09094
$143$	2.00000	0.167248
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−6.00000	−0.496564
$147$	2.00000	0.164957
$148$	2.00000	0.164399
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	0	0
$153$	−4.00000	−0.323381
$154$	6.00000	0.483494
$155$	0	0
$156$	1.00000	0.0800641
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	1.00000	0.0795557
$159$	−4.00000	−0.317221
$160$	0	0
$161$	−18.0000	−1.41860
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−6.00000	−0.465690
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	3.00000	0.231455
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−4.00000	−0.304997
$173$	−4.00000	−0.304114	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−4.00000	−0.304114	−0.152057	+	0.988372i	$0.548590\pi$
$174$	10.0000	0.758098
$175$	0	0
$176$	2.00000	0.150756
$177$	5.00000	0.375823
$178$	15.0000	1.12430
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	0	0
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	3.00000	0.222375
$183$	12.0000	0.887066
$184$	−6.00000	−0.442326
$185$	0	0
$186$	−2.00000	−0.146647
$187$	4.00000	0.292509
$188$	−3.00000	−0.218797
$189$	15.0000	1.09109
$190$	0	0
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	1.00000	0.0721688
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	13.0000	0.933346
$195$	0	0
$196$	2.00000	0.142857
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	4.00000	0.284268
$199$	15.0000	1.06332	0.531661	−	0.846957i	$-0.321568\pi$
$199$	15.0000	1.06332	0.531661	+	0.846957i	$0.321568\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	−7.00000	−0.492518
$203$	30.0000	2.10559
$204$	2.00000	0.140028
$205$	0	0
$206$	19.0000	1.32379
$207$	−12.0000	−0.834058
$208$	1.00000	0.0693375
$209$	0	0
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−4.00000	−0.274721
$213$	−13.0000	−0.890745
$214$	13.0000	0.888662
$215$	0	0
$216$	5.00000	0.340207
$217$	−6.00000	−0.407307
$218$	−10.0000	−0.677285
$219$	6.00000	0.405442
$220$	0	0
$221$	2.00000	0.134535
$222$	−2.00000	−0.134231
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	3.00000	0.200446
$225$	0	0
$226$	4.00000	0.266076
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	0	0
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	0	0
$231$	−6.00000	−0.394771
$232$	10.0000	0.656532
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	5.00000	0.325472
$237$	−1.00000	−0.0649570
$238$	6.00000	0.388922
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	7.00000	0.449977
$243$	16.0000	1.02640
$244$	12.0000	0.768221
$245$	0	0
$246$	−2.00000	−0.127515
$247$	0	0
$248$	−2.00000	−0.127000
$249$	6.00000	0.380235
$250$	0	0
$251$	27.0000	1.70422	0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000	1.70422	0.852112	+	0.523359i	$0.175321\pi$
$252$	6.00000	0.377964
$253$	12.0000	0.754434
$254$	−7.00000	−0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	4.00000	0.249029
$259$	−6.00000	−0.372822
$260$	0	0
$261$	20.0000	1.23797
$262$	18.0000	1.11204
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	0	0
$267$	−15.0000	−0.917985
$268$	−8.00000	−0.488678
$269$	25.0000	1.52428	0.762138	−	0.647414i	$-0.224150\pi$
$269$	25.0000	1.52428	0.762138	+	0.647414i	$0.224150\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.00000	0.121268
$273$	−3.00000	−0.181568
$274$	−12.0000	−0.724947
$275$	0	0
$276$	6.00000	0.361158
$277$	17.0000	1.02143	0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000	1.02143	0.510716	+	0.859750i	$0.329381\pi$
$278$	5.00000	0.299880
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−33.0000	−1.96861	−0.984307	−	0.176462i	$-0.943535\pi$
$281$	−33.0000	−1.96861	−0.984307	+	0.176462i	$0.943535\pi$
$282$	3.00000	0.178647
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−13.0000	−0.771408
$285$	0	0
$286$	−2.00000	−0.118262
$287$	−6.00000	−0.354169
$288$	2.00000	0.117851
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−13.0000	−0.762073
$292$	6.00000	0.351123
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	−2.00000	−0.116248
$297$	−10.0000	−0.580259
$298$	10.0000	0.579284
$299$	6.00000	0.346989
$300$	0	0
$301$	12.0000	0.691669
$302$	−2.00000	−0.115087
$303$	7.00000	0.402139
$304$	0	0
$305$	0	0
$306$	4.00000	0.228665
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	−6.00000	−0.341882
$309$	−19.0000	−1.08087
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−1.00000	−0.0566139
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	18.0000	1.01580
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	−3.00000	−0.168497	−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000	−0.168497	−0.0842484	+	0.996445i	$0.526849\pi$
$318$	4.00000	0.224309
$319$	−20.0000	−1.11979
$320$	0	0
$321$	−13.0000	−0.725589
$322$	18.0000	1.00310
$323$	0	0
$324$	1.00000	0.0555556
$325$	0	0
$326$	4.00000	0.221540
$327$	10.0000	0.553001
$328$	−2.00000	−0.110432
$329$	9.00000	0.496186
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	6.00000	0.329293
$333$	−4.00000	−0.219199
$334$	−2.00000	−0.109435
$335$	0	0
$336$	−3.00000	−0.163663
$337$	−23.0000	−1.25289	−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000	−1.25289	−0.626445	+	0.779466i	$0.715491\pi$
$338$	12.0000	0.652714
$339$	−4.00000	−0.217250
$340$	0	0
$341$	4.00000	0.216612
$342$	0	0
$343$	15.0000	0.809924
$344$	4.00000	0.215666
$345$	0	0
$346$	4.00000	0.215041
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	−10.0000	−0.536056
$349$	−20.0000	−1.07058	−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000	−1.07058	−0.535288	+	0.844670i	$0.679797\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	−2.00000	−0.106600
$353$	36.0000	1.91609	0.958043	−	0.286623i	$-0.0925328\pi$
$353$	36.0000	1.91609	0.958043	+	0.286623i	$0.0925328\pi$
$354$	−5.00000	−0.265747
$355$	0	0
$356$	−15.0000	−0.794998
$357$	−6.00000	−0.317554
$358$	−20.0000	−1.05703
$359$	25.0000	1.31945	0.659725	−	0.751507i	$-0.270673\pi$
$359$	25.0000	1.31945	0.659725	+	0.751507i	$0.270673\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	18.0000	0.946059
$363$	−7.00000	−0.367405
$364$	−3.00000	−0.157243
$365$	0	0
$366$	−12.0000	−0.627250
$367$	22.0000	1.14839	0.574195	−	0.818718i	$-0.305315\pi$
$367$	22.0000	1.14839	0.574195	+	0.818718i	$0.305315\pi$
$368$	6.00000	0.312772
$369$	−4.00000	−0.208232
$370$	0	0
$371$	12.0000	0.623009
$372$	2.00000	0.103695
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	3.00000	0.154713
$377$	−10.0000	−0.515026
$378$	−15.0000	−0.771517
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	0	0
$381$	7.00000	0.358621
$382$	3.00000	0.153493
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	14.0000	0.712581
$387$	8.00000	0.406663
$388$	−13.0000	−0.659975
$389$	−5.00000	−0.253510	−0.126755	−	0.991934i	$-0.540456\pi$
$389$	−5.00000	−0.253510	−0.126755	+	0.991934i	$0.540456\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	−2.00000	−0.101015
$393$	−18.0000	−0.907980
$394$	18.0000	0.906827
$395$	0	0
$396$	−4.00000	−0.201008
$397$	37.0000	1.85698	0.928488	−	0.371361i	$-0.121109\pi$
$397$	37.0000	1.85698	0.928488	+	0.371361i	$0.121109\pi$
$398$	−15.0000	−0.751882
$399$	0	0
$400$	0	0
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	8.00000	0.399004
$403$	2.00000	0.0996271
$404$	7.00000	0.348263
$405$	0	0
$406$	−30.0000	−1.48888
$407$	4.00000	0.198273
$408$	−2.00000	−0.0990148
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	−19.0000	−0.936063
$413$	−15.0000	−0.738102
$414$	12.0000	0.589768
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	−5.00000	−0.244851
$418$	0	0
$419$	25.0000	1.22133	0.610665	−	0.791889i	$-0.290902\pi$
$419$	25.0000	1.22133	0.610665	+	0.791889i	$0.290902\pi$
$420$	0	0
$421$	7.00000	0.341159	0.170580	−	0.985344i	$-0.445436\pi$
$421$	7.00000	0.341159	0.170580	+	0.985344i	$0.445436\pi$
$422$	28.0000	1.36302
$423$	6.00000	0.291730
$424$	4.00000	0.194257
$425$	0	0
$426$	13.0000	0.629852
$427$	−36.0000	−1.74216
$428$	−13.0000	−0.628379
$429$	2.00000	0.0965609
$430$	0	0
$431$	32.0000	1.54139	0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000	1.54139	0.770693	+	0.637207i	$0.219910\pi$
$432$	−5.00000	−0.240563
$433$	11.0000	0.528626	0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000	0.528626	0.264313	+	0.964437i	$0.414855\pi$
$434$	6.00000	0.288009
$435$	0	0
$436$	10.0000	0.478913
$437$	0	0
$438$	−6.00000	−0.286691
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	−2.00000	−0.0951303
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	14.0000	0.662919
$447$	−10.0000	−0.472984
$448$	−3.00000	−0.141737
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	0	0
$451$	4.00000	0.188353
$452$	−4.00000	−0.188144
$453$	2.00000	0.0939682
$454$	8.00000	0.375459
$455$	0	0
$456$	0	0
$457$	−23.0000	−1.07589	−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000	−1.07589	−0.537947	+	0.842978i	$0.680800\pi$
$458$	−20.0000	−0.934539
$459$	−10.0000	−0.466760
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	6.00000	0.279145
$463$	31.0000	1.44069	0.720346	−	0.693615i	$-0.243983\pi$
$463$	31.0000	1.44069	0.720346	+	0.693615i	$0.243983\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−6.00000	−0.277945
$467$	42.0000	1.94353	0.971764	−	0.235954i	$-0.0758216\pi$
$467$	42.0000	1.94353	0.971764	+	0.235954i	$0.0758216\pi$
$468$	−2.00000	−0.0924500
$469$	24.0000	1.10822
$470$	0	0
$471$	−18.0000	−0.829396
$472$	−5.00000	−0.230144
$473$	−8.00000	−0.367840
$474$	1.00000	0.0459315
$475$	0	0
$476$	−6.00000	−0.275010
$477$	8.00000	0.366295
$478$	0	0
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	−17.0000	−0.774329
$483$	−18.0000	−0.819028
$484$	−7.00000	−0.318182
$485$	0	0
$486$	−16.0000	−0.725775
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	−12.0000	−0.543214
$489$	−4.00000	−0.180886
$490$	0	0
$491$	−3.00000	−0.135388	−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000	−0.135388	−0.0676941	+	0.997706i	$0.521564\pi$
$492$	2.00000	0.0901670
$493$	−20.0000	−0.900755
$494$	0	0
$495$	0	0
$496$	2.00000	0.0898027
$497$	39.0000	1.74939
$498$	−6.00000	−0.268866
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	0	0
$501$	2.00000	0.0893534
$502$	−27.0000	−1.20507
$503$	−39.0000	−1.73892	−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000	−1.73892	−0.869462	+	0.494000i	$0.835534\pi$
$504$	−6.00000	−0.267261
$505$	0	0
$506$	−12.0000	−0.533465
$507$	−12.0000	−0.532939
$508$	7.00000	0.310575
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	−4.00000	−0.176090
$517$	−6.00000	−0.263880
$518$	6.00000	0.263625
$519$	−4.00000	−0.175581
$520$	0	0
$521$	12.0000	0.525730	0.262865	−	0.964833i	$-0.415333\pi$
$521$	12.0000	0.525730	0.262865	+	0.964833i	$0.415333\pi$
$522$	−20.0000	−0.875376
$523$	26.0000	1.13690	0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000	1.13690	0.568450	+	0.822718i	$0.307543\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	−6.00000	−0.261612
$527$	4.00000	0.174243
$528$	2.00000	0.0870388
$529$	13.0000	0.565217
$530$	0	0
$531$	−10.0000	−0.433963
$532$	0	0
$533$	2.00000	0.0866296
$534$	15.0000	0.649113
$535$	0	0
$536$	8.00000	0.345547
$537$	20.0000	0.863064
$538$	−25.0000	−1.07783
$539$	4.00000	0.172292
$540$	0	0
$541$	7.00000	0.300954	0.150477	−	0.988614i	$-0.451919\pi$
$541$	7.00000	0.300954	0.150477	+	0.988614i	$0.451919\pi$
$542$	8.00000	0.343629
$543$	−18.0000	−0.772454
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	3.00000	0.128388
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	12.0000	0.512615
$549$	−24.0000	−1.02430
$550$	0	0
$551$	0	0
$552$	−6.00000	−0.255377
$553$	3.00000	0.127573
$554$	−17.0000	−0.722261
$555$	0	0
$556$	−5.00000	−0.212047
$557$	7.00000	0.296600	0.148300	−	0.988942i	$-0.452620\pi$
$557$	7.00000	0.296600	0.148300	+	0.988942i	$0.452620\pi$
$558$	4.00000	0.169334
$559$	−4.00000	−0.169182
$560$	0	0
$561$	4.00000	0.168880
$562$	33.0000	1.39202
$563$	−14.0000	−0.590030	−0.295015	−	0.955493i	$-0.595325\pi$
$563$	−14.0000	−0.590030	−0.295015	+	0.955493i	$0.595325\pi$
$564$	−3.00000	−0.126323
$565$	0	0
$566$	4.00000	0.168133
$567$	−3.00000	−0.125988
$568$	13.0000	0.545468
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	22.0000	0.920671	0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000	0.920671	0.460336	+	0.887745i	$0.347729\pi$
$572$	2.00000	0.0836242
$573$	−3.00000	−0.125327
$574$	6.00000	0.250435
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	12.0000	0.499567	0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000	0.499567	0.249783	+	0.968302i	$0.419641\pi$
$578$	13.0000	0.540729
$579$	−14.0000	−0.581820
$580$	0	0
$581$	−18.0000	−0.746766
$582$	13.0000	0.538867
$583$	−8.00000	−0.331326
$584$	−6.00000	−0.248282
$585$	0	0
$586$	24.0000	0.991431
$587$	7.00000	0.288921	0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000	0.288921	0.144460	+	0.989511i	$0.453855\pi$
$588$	2.00000	0.0824786
$589$	0	0
$590$	0	0
$591$	−18.0000	−0.740421
$592$	2.00000	0.0821995
$593$	21.0000	0.862367	0.431183	−	0.902264i	$-0.358096\pi$
$593$	21.0000	0.862367	0.431183	+	0.902264i	$0.358096\pi$
$594$	10.0000	0.410305
$595$	0	0
$596$	−10.0000	−0.409616
$597$	15.0000	0.613909
$598$	−6.00000	−0.245358
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	0	0
$601$	12.0000	0.489490	0.244745	−	0.969587i	$-0.421296\pi$
$601$	12.0000	0.489490	0.244745	+	0.969587i	$0.421296\pi$
$602$	−12.0000	−0.489083
$603$	16.0000	0.651570
$604$	2.00000	0.0813788
$605$	0	0
$606$	−7.00000	−0.284356
$607$	−33.0000	−1.33943	−0.669714	−	0.742619i	$-0.733583\pi$
$607$	−33.0000	−1.33943	−0.669714	+	0.742619i	$0.733583\pi$
$608$	0	0
$609$	30.0000	1.21566
$610$	0	0
$611$	−3.00000	−0.121367
$612$	−4.00000	−0.161690
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	6.00000	0.241747
$617$	27.0000	1.08698	0.543490	−	0.839416i	$-0.317103\pi$
$617$	27.0000	1.08698	0.543490	+	0.839416i	$0.317103\pi$
$618$	19.0000	0.764292
$619$	−35.0000	−1.40677	−0.703384	−	0.710810i	$-0.748329\pi$
$619$	−35.0000	−1.40677	−0.703384	+	0.710810i	$0.748329\pi$
$620$	0	0
$621$	−30.0000	−1.20386
$622$	−12.0000	−0.481156
$623$	45.0000	1.80289
$624$	1.00000	0.0400320
$625$	0	0
$626$	14.0000	0.559553
$627$	0	0
$628$	−18.0000	−0.718278
$629$	4.00000	0.159490
$630$	0	0
$631$	37.0000	1.47295	0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000	1.47295	0.736473	+	0.676467i	$0.236490\pi$
$632$	1.00000	0.0397779
$633$	−28.0000	−1.11290
$634$	3.00000	0.119145
$635$	0	0
$636$	−4.00000	−0.158610
$637$	2.00000	0.0792429
$638$	20.0000	0.791808
$639$	26.0000	1.02854
$640$	0	0
$641$	−33.0000	−1.30342	−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000	−1.30342	−0.651711	+	0.758468i	$0.725948\pi$
$642$	13.0000	0.513069
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−18.0000	−0.709299
$645$	0	0
$646$	0	0
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	−1.00000	−0.0392837
$649$	10.0000	0.392534
$650$	0	0
$651$	−6.00000	−0.235159
$652$	−4.00000	−0.156652
$653$	11.0000	0.430463	0.215232	−	0.976563i	$-0.430949\pi$
$653$	11.0000	0.430463	0.215232	+	0.976563i	$0.430949\pi$
$654$	−10.0000	−0.391031
$655$	0	0
$656$	2.00000	0.0780869
$657$	−12.0000	−0.468165
$658$	−9.00000	−0.350857
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	28.0000	1.08825
$663$	2.00000	0.0776736
$664$	−6.00000	−0.232845
$665$	0	0
$666$	4.00000	0.154997
$667$	−60.0000	−2.32321
$668$	2.00000	0.0773823
$669$	−14.0000	−0.541271
$670$	0	0
$671$	24.0000	0.926510
$672$	3.00000	0.115728
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	23.0000	0.885927
$675$	0	0
$676$	−12.0000	−0.461538
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	4.00000	0.153619
$679$	39.0000	1.49668
$680$	0	0
$681$	−8.00000	−0.306561
$682$	−4.00000	−0.153168
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	0	0
$685$	0	0
$686$	−15.0000	−0.572703
$687$	20.0000	0.763048
$688$	−4.00000	−0.152499
$689$	−4.00000	−0.152388
$690$	0	0
$691$	17.0000	0.646710	0.323355	−	0.946278i	$-0.395189\pi$
$691$	17.0000	0.646710	0.323355	+	0.946278i	$0.395189\pi$
$692$	−4.00000	−0.152057
$693$	12.0000	0.455842
$694$	18.0000	0.683271
$695$	0	0
$696$	10.0000	0.379049
$697$	4.00000	0.151511
$698$	20.0000	0.757011
$699$	6.00000	0.226941
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	5.00000	0.188713
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	−36.0000	−1.35488
$707$	−21.0000	−0.789786
$708$	5.00000	0.187912
$709$	−50.0000	−1.87779	−0.938895	−	0.344204i	$-0.888149\pi$
$709$	−50.0000	−1.87779	−0.938895	+	0.344204i	$0.888149\pi$
$710$	0	0
$711$	2.00000	0.0750059
$712$	15.0000	0.562149
$713$	12.0000	0.449404
$714$	6.00000	0.224544
$715$	0	0
$716$	20.0000	0.747435
$717$	0	0
$718$	−25.0000	−0.932992
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	0	0
$721$	57.0000	2.12279
$722$	19.0000	0.707107
$723$	17.0000	0.632237
$724$	−18.0000	−0.668965
$725$	0	0
$726$	7.00000	0.259794
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	3.00000	0.111187
$729$	13.0000	0.481481
$730$	0	0
$731$	−8.00000	−0.295891
$732$	12.0000	0.443533
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	−22.0000	−0.812035
$735$	0	0
$736$	−6.00000	−0.221163
$737$	−16.0000	−0.589368
$738$	4.00000	0.147242
$739$	−5.00000	−0.183928	−0.0919640	−	0.995762i	$-0.529314\pi$
$739$	−5.00000	−0.183928	−0.0919640	+	0.995762i	$0.529314\pi$
$740$	0	0
$741$	0	0
$742$	−12.0000	−0.440534
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−2.00000	−0.0733236
$745$	0	0
$746$	14.0000	0.512576
$747$	−12.0000	−0.439057
$748$	4.00000	0.146254
$749$	39.0000	1.42503
$750$	0	0
$751$	42.0000	1.53260	0.766301	−	0.642482i	$-0.222095\pi$
$751$	42.0000	1.53260	0.766301	+	0.642482i	$0.222095\pi$
$752$	−3.00000	−0.109399
$753$	27.0000	0.983935
$754$	10.0000	0.364179
$755$	0	0
$756$	15.0000	0.545545
$757$	37.0000	1.34479	0.672394	−	0.740193i	$-0.265266\pi$
$757$	37.0000	1.34479	0.672394	+	0.740193i	$0.265266\pi$
$758$	15.0000	0.544825
$759$	12.0000	0.435572
$760$	0	0
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	−7.00000	−0.253583
$763$	−30.0000	−1.08607
$764$	−3.00000	−0.108536
$765$	0	0
$766$	−6.00000	−0.216789
$767$	5.00000	0.180540
$768$	1.00000	0.0360844
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	−14.0000	−0.503871
$773$	−34.0000	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	13.0000	0.466673
$777$	−6.00000	−0.215249
$778$	5.00000	0.179259
$779$	0	0
$780$	0	0
$781$	−26.0000	−0.930353
$782$	−12.0000	−0.429119
$783$	50.0000	1.78685
$784$	2.00000	0.0714286
$785$	0	0
$786$	18.0000	0.642039
$787$	−18.0000	−0.641631	−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000	−0.641631	−0.320815	+	0.947142i	$0.603957\pi$
$788$	−18.0000	−0.641223
$789$	6.00000	0.213606
$790$	0	0
$791$	12.0000	0.426671
$792$	4.00000	0.142134
$793$	12.0000	0.426132
$794$	−37.0000	−1.31308
$795$	0	0
$796$	15.0000	0.531661
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	−6.00000	−0.212265
$800$	0	0
$801$	30.0000	1.06000
$802$	−2.00000	−0.0706225
$803$	12.0000	0.423471
$804$	−8.00000	−0.282138
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	25.0000	0.880042
$808$	−7.00000	−0.246259
$809$	15.0000	0.527372	0.263686	−	0.964609i	$-0.415062\pi$
$809$	15.0000	0.527372	0.263686	+	0.964609i	$0.415062\pi$
$810$	0	0
$811$	22.0000	0.772524	0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000	0.772524	0.386262	+	0.922389i	$0.373766\pi$
$812$	30.0000	1.05279
$813$	−8.00000	−0.280572
$814$	−4.00000	−0.140200
$815$	0	0
$816$	2.00000	0.0700140
$817$	0	0
$818$	20.0000	0.699284
$819$	6.00000	0.209657
$820$	0	0
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	−12.0000	−0.418548
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	19.0000	0.661896
$825$	0	0
$826$	15.0000	0.521917
$827$	−23.0000	−0.799788	−0.399894	−	0.916561i	$-0.630953\pi$
$827$	−23.0000	−0.799788	−0.399894	+	0.916561i	$0.630953\pi$
$828$	−12.0000	−0.417029
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	17.0000	0.589723
$832$	1.00000	0.0346688
$833$	4.00000	0.138592
$834$	5.00000	0.173136
$835$	0	0
$836$	0	0
$837$	−10.0000	−0.345651
$838$	−25.0000	−0.863611
$839$	20.0000	0.690477	0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000	0.690477	0.345238	+	0.938515i	$0.387798\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	−7.00000	−0.241236
$843$	−33.0000	−1.13658
$844$	−28.0000	−0.963800
$845$	0	0
$846$	−6.00000	−0.206284
$847$	21.0000	0.721569
$848$	−4.00000	−0.137361
$849$	−4.00000	−0.137280
$850$	0	0
$851$	12.0000	0.411355
$852$	−13.0000	−0.445373
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	36.0000	1.23189
$855$	0	0
$856$	13.0000	0.444331
$857$	−33.0000	−1.12726	−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000	−1.12726	−0.563629	+	0.826028i	$0.690595\pi$
$858$	−2.00000	−0.0682789
$859$	−35.0000	−1.19418	−0.597092	−	0.802173i	$-0.703677\pi$
$859$	−35.0000	−1.19418	−0.597092	+	0.802173i	$0.703677\pi$
$860$	0	0
$861$	−6.00000	−0.204479
$862$	−32.0000	−1.08992
$863$	46.0000	1.56586	0.782929	−	0.622111i	$-0.213725\pi$
$863$	46.0000	1.56586	0.782929	+	0.622111i	$0.213725\pi$
$864$	5.00000	0.170103
$865$	0	0
$866$	−11.0000	−0.373795
$867$	−13.0000	−0.441503
$868$	−6.00000	−0.203653
$869$	−2.00000	−0.0678454
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−10.0000	−0.338643
$873$	26.0000	0.879967
$874$	0	0
$875$	0	0
$876$	6.00000	0.202721
$877$	−58.0000	−1.95852	−0.979260	−	0.202606i	$-0.935059\pi$
$877$	−58.0000	−1.95852	−0.979260	+	0.202606i	$0.935059\pi$
$878$	40.0000	1.34993
$879$	−24.0000	−0.809500
$880$	0	0
$881$	12.0000	0.404290	0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000	0.404290	0.202145	+	0.979356i	$0.435209\pi$
$882$	4.00000	0.134687
$883$	1.00000	0.0336527	0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000	0.0336527	0.0168263	+	0.999858i	$0.494644\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	4.00000	0.134383
$887$	22.0000	0.738688	0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000	0.738688	0.369344	+	0.929293i	$0.379582\pi$
$888$	−2.00000	−0.0671156
$889$	−21.0000	−0.704317
$890$	0	0
$891$	2.00000	0.0670025
$892$	−14.0000	−0.468755
$893$	0	0
$894$	10.0000	0.334450
$895$	0	0
$896$	3.00000	0.100223
$897$	6.00000	0.200334
$898$	10.0000	0.333704
$899$	−20.0000	−0.667037
$900$	0	0
$901$	−8.00000	−0.266519
$902$	−4.00000	−0.133185
$903$	12.0000	0.399335
$904$	4.00000	0.133038
$905$	0	0
$906$	−2.00000	−0.0664455
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	−8.00000	−0.265489
$909$	−14.0000	−0.464351
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	23.0000	0.760772
$915$	0	0
$916$	20.0000	0.660819
$917$	54.0000	1.78324
$918$	10.0000	0.330049
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	12.0000	0.395413
$922$	18.0000	0.592798
$923$	−13.0000	−0.427900
$924$	−6.00000	−0.197386
$925$	0	0
$926$	−31.0000	−1.01872
$927$	38.0000	1.24808
$928$	10.0000	0.328266
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	12.0000	0.392862
$934$	−42.0000	−1.37428
$935$	0	0
$936$	2.00000	0.0653720
$937$	12.0000	0.392023	0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000	0.392023	0.196011	+	0.980602i	$0.437201\pi$
$938$	−24.0000	−0.783628
$939$	−14.0000	−0.456873
$940$	0	0
$941$	−38.0000	−1.23876	−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000	−1.23876	−0.619382	+	0.785090i	$0.712617\pi$
$942$	18.0000	0.586472
$943$	12.0000	0.390774
$944$	5.00000	0.162736
$945$	0	0
$946$	8.00000	0.260102
$947$	32.0000	1.03986	0.519930	−	0.854209i	$-0.325958\pi$
$947$	32.0000	1.03986	0.519930	+	0.854209i	$0.325958\pi$
$948$	−1.00000	−0.0324785
$949$	6.00000	0.194768
$950$	0	0
$951$	−3.00000	−0.0972817
$952$	6.00000	0.194461
$953$	31.0000	1.00419	0.502094	−	0.864813i	$-0.332563\pi$
$953$	31.0000	1.00419	0.502094	+	0.864813i	$0.332563\pi$
$954$	−8.00000	−0.259010
$955$	0	0
$956$	0	0
$957$	−20.0000	−0.646508
$958$	20.0000	0.646171
$959$	−36.0000	−1.16250
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−2.00000	−0.0644826
$963$	26.0000	0.837838
$964$	17.0000	0.547533
$965$	0	0
$966$	18.0000	0.579141
$967$	52.0000	1.67221	0.836104	−	0.548572i	$-0.184828\pi$
$967$	52.0000	1.67221	0.836104	+	0.548572i	$0.184828\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	0	0
$971$	22.0000	0.706014	0.353007	−	0.935621i	$-0.385159\pi$
$971$	22.0000	0.706014	0.353007	+	0.935621i	$0.385159\pi$
$972$	16.0000	0.513200
$973$	15.0000	0.480878
$974$	38.0000	1.21760
$975$	0	0
$976$	12.0000	0.384111
$977$	−58.0000	−1.85558	−0.927792	−	0.373097i	$-0.878296\pi$
$977$	−58.0000	−1.85558	−0.927792	+	0.373097i	$0.878296\pi$
$978$	4.00000	0.127906
$979$	−30.0000	−0.958804
$980$	0	0
$981$	−20.0000	−0.638551
$982$	3.00000	0.0957338
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	−2.00000	−0.0637577
$985$	0	0
$986$	20.0000	0.636930
$987$	9.00000	0.286473
$988$	0	0
$989$	−24.0000	−0.763156
$990$	0	0
$991$	−13.0000	−0.412959	−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000	−0.412959	−0.206479	+	0.978451i	$0.566201\pi$
$992$	−2.00000	−0.0635001
$993$	−28.0000	−0.888553
$994$	−39.0000	−1.23700
$995$	0	0
$996$	6.00000	0.190117
$997$	22.0000	0.696747	0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000	0.696747	0.348373	+	0.937356i	$0.386734\pi$
$998$	10.0000	0.316544
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3950.2.a.d.1.1		1
5.4	even	2		158.2.a.d.1.1	✓	1
15.14	odd	2		1422.2.a.a.1.1		1
20.19	odd	2		1264.2.a.f.1.1		1
35.34	odd	2		7742.2.a.m.1.1		1
40.19	odd	2		5056.2.a.e.1.1		1
40.29	even	2		5056.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.a.d.1.1	✓	1	5.4	even	2
1264.2.a.f.1.1		1	20.19	odd	2
1422.2.a.a.1.1		1	15.14	odd	2
3950.2.a.d.1.1		1	1.1	even	1	trivial
5056.2.a.e.1.1		1	40.19	odd	2
5056.2.a.m.1.1		1	40.29	even	2
7742.2.a.m.1.1		1	35.34	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:	\( N \)	\(=\)	\( 3950 = 2 \cdot 5^{2} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more