LMFDB - Embedded newform 6026.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
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	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.00000 q^{11} +2.00000 q^{12} -2.00000 q^{13} +2.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} -1.00000 q^{20} +4.00000 q^{21} -5.00000 q^{22} -1.00000 q^{23} +2.00000 q^{24} -4.00000 q^{25} -2.00000 q^{26} -4.00000 q^{27} +2.00000 q^{28} -2.00000 q^{29} -2.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -10.0000 q^{33} -3.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -6.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +7.00000 q^{41} +4.00000 q^{42} -1.00000 q^{43} -5.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} -6.00000 q^{47} +2.00000 q^{48} -3.00000 q^{49} -4.00000 q^{50} -6.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} -4.00000 q^{54} +5.00000 q^{55} +2.00000 q^{56} -12.0000 q^{57} -2.00000 q^{58} +10.0000 q^{59} -2.00000 q^{60} -3.00000 q^{61} +4.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -10.0000 q^{66} -10.0000 q^{67} -3.00000 q^{68} -2.00000 q^{69} -2.00000 q^{70} -2.00000 q^{71} +1.00000 q^{72} -16.0000 q^{73} +2.00000 q^{74} -8.00000 q^{75} -6.00000 q^{76} -10.0000 q^{77} -4.00000 q^{78} +4.00000 q^{79} -1.00000 q^{80} -11.0000 q^{81} +7.00000 q^{82} -12.0000 q^{83} +4.00000 q^{84} +3.00000 q^{85} -1.00000 q^{86} -4.00000 q^{87} -5.00000 q^{88} -16.0000 q^{89} -1.00000 q^{90} -4.00000 q^{91} -1.00000 q^{92} +8.00000 q^{93} -6.00000 q^{94} +6.00000 q^{95} +2.00000 q^{96} +10.0000 q^{97} -3.00000 q^{98} -5.00000 q^{99} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	2.00000	0.816497
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	2.00000	0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	2.00000	0.534522
$15$	−2.00000	−0.516398
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.00000	0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−1.00000	−0.223607
$21$	4.00000	0.872872
$22$	−5.00000	−1.06600
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.00000	0.408248
$25$	−4.00000	−0.800000
$26$	−2.00000	−0.392232
$27$	−4.00000	−0.769800
$28$	2.00000	0.377964
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−2.00000	−0.365148
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	−10.0000	−1.74078
$34$	−3.00000	−0.514496
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−6.00000	−0.973329
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	4.00000	0.617213
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−5.00000	−0.753778
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	2.00000	0.288675
$49$	−3.00000	−0.428571
$50$	−4.00000	−0.565685
$51$	−6.00000	−0.840168
$52$	−2.00000	−0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−4.00000	−0.544331
$55$	5.00000	0.674200
$56$	2.00000	0.267261
$57$	−12.0000	−1.58944
$58$	−2.00000	−0.262613
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	−2.00000	−0.258199
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	4.00000	0.508001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−10.0000	−1.23091
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−3.00000	−0.363803
$69$	−2.00000	−0.240772
$70$	−2.00000	−0.239046
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	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	$0.885800\pi$
$74$	2.00000	0.232495
$75$	−8.00000	−0.923760
$76$	−6.00000	−0.688247
$77$	−10.0000	−1.13961
$78$	−4.00000	−0.452911
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−1.00000	−0.111803
$81$	−11.0000	−1.22222
$82$	7.00000	0.773021
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	4.00000	0.436436
$85$	3.00000	0.325396
$86$	−1.00000	−0.107833
$87$	−4.00000	−0.428845
$88$	−5.00000	−0.533002
$89$	−16.0000	−1.69600	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−16.0000	−1.69600	−0.847998	+	0.529999i	$0.822192\pi$
$90$	−1.00000	−0.105409
$91$	−4.00000	−0.419314
$92$	−1.00000	−0.104257
$93$	8.00000	0.829561
$94$	−6.00000	−0.618853
$95$	6.00000	0.615587
$96$	2.00000	0.204124
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	−3.00000	−0.303046
$99$	−5.00000	−0.502519
$100$	−4.00000	−0.400000
$101$	16.0000	1.59206	0.796030	−	0.605257i	$-0.206930\pi$
$101$	16.0000	1.59206	0.796030	+	0.605257i	$0.206930\pi$
$102$	−6.00000	−0.594089
$103$	1.00000	0.0985329	0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000	0.0985329	0.0492665	+	0.998786i	$0.484312\pi$
$104$	−2.00000	−0.196116
$105$	−4.00000	−0.390360
$106$	6.00000	0.582772
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	−4.00000	−0.384900
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	5.00000	0.476731
$111$	4.00000	0.379663
$112$	2.00000	0.188982
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	−12.0000	−1.12390
$115$	1.00000	0.0932505
$116$	−2.00000	−0.185695
$117$	−2.00000	−0.184900
$118$	10.0000	0.920575
$119$	−6.00000	−0.550019
$120$	−2.00000	−0.182574
$121$	14.0000	1.27273
$122$	−3.00000	−0.271607
$123$	14.0000	1.26234
$124$	4.00000	0.359211
$125$	9.00000	0.804984
$126$	2.00000	0.178174
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	−2.00000	−0.176090
$130$	2.00000	0.175412
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−10.0000	−0.870388
$133$	−12.0000	−1.04053
$134$	−10.0000	−0.863868
$135$	4.00000	0.344265
$136$	−3.00000	−0.257248
$137$	1.00000	0.0854358	0.0427179	−	0.999087i	$-0.486398\pi$
$137$	1.00000	0.0854358	0.0427179	+	0.999087i	$0.486398\pi$
$138$	−2.00000	−0.170251
$139$	3.00000	0.254457	0.127228	−	0.991873i	$-0.459392\pi$
$139$	3.00000	0.254457	0.127228	+	0.991873i	$0.459392\pi$
$140$	−2.00000	−0.169031
$141$	−12.0000	−1.01058
$142$	−2.00000	−0.167836
$143$	10.0000	0.836242
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	−16.0000	−1.32417
$147$	−6.00000	−0.494872
$148$	2.00000	0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−8.00000	−0.653197
$151$	−11.0000	−0.895167	−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000	−0.895167	−0.447584	+	0.894242i	$0.647715\pi$
$152$	−6.00000	−0.486664
$153$	−3.00000	−0.242536
$154$	−10.0000	−0.805823
$155$	−4.00000	−0.321288
$156$	−4.00000	−0.320256
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	4.00000	0.318223
$159$	12.0000	0.951662
$160$	−1.00000	−0.0790569
$161$	−2.00000	−0.157622
$162$	−11.0000	−0.864242
$163$	1.00000	0.0783260	0.0391630	−	0.999233i	$-0.487531\pi$
$163$	1.00000	0.0783260	0.0391630	+	0.999233i	$0.487531\pi$
$164$	7.00000	0.546608
$165$	10.0000	0.778499
$166$	−12.0000	−0.931381
$167$	9.00000	0.696441	0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000	0.696441	0.348220	+	0.937413i	$0.386786\pi$
$168$	4.00000	0.308607
$169$	−9.00000	−0.692308
$170$	3.00000	0.230089
$171$	−6.00000	−0.458831
$172$	−1.00000	−0.0762493
$173$	21.0000	1.59660	0.798300	−	0.602260i	$-0.205733\pi$
$173$	21.0000	1.59660	0.798300	+	0.602260i	$0.205733\pi$
$174$	−4.00000	−0.303239
$175$	−8.00000	−0.604743
$176$	−5.00000	−0.376889
$177$	20.0000	1.50329
$178$	−16.0000	−1.19925
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	−0.0745356
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	−4.00000	−0.296500
$183$	−6.00000	−0.443533
$184$	−1.00000	−0.0737210
$185$	−2.00000	−0.147043
$186$	8.00000	0.586588
$187$	15.0000	1.09691
$188$	−6.00000	−0.437595
$189$	−8.00000	−0.581914
$190$	6.00000	0.435286
$191$	14.0000	1.01300	0.506502	−	0.862239i	$-0.330938\pi$
$191$	14.0000	1.01300	0.506502	+	0.862239i	$0.330938\pi$
$192$	2.00000	0.144338
$193$	23.0000	1.65558	0.827788	−	0.561041i	$-0.189599\pi$
$193$	23.0000	1.65558	0.827788	+	0.561041i	$0.189599\pi$
$194$	10.0000	0.717958
$195$	4.00000	0.286446
$196$	−3.00000	−0.214286
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	−5.00000	−0.355335
$199$	−3.00000	−0.212664	−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000	−0.212664	−0.106332	+	0.994331i	$0.533911\pi$
$200$	−4.00000	−0.282843
$201$	−20.0000	−1.41069
$202$	16.0000	1.12576
$203$	−4.00000	−0.280745
$204$	−6.00000	−0.420084
$205$	−7.00000	−0.488901
$206$	1.00000	0.0696733
$207$	−1.00000	−0.0695048
$208$	−2.00000	−0.138675
$209$	30.0000	2.07514
$210$	−4.00000	−0.276026
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	6.00000	0.412082
$213$	−4.00000	−0.274075
$214$	13.0000	0.888662
$215$	1.00000	0.0681994
$216$	−4.00000	−0.272166
$217$	8.00000	0.543075
$218$	1.00000	0.0677285
$219$	−32.0000	−2.16236
$220$	5.00000	0.337100
$221$	6.00000	0.403604
$222$	4.00000	0.268462
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	2.00000	0.133631
$225$	−4.00000	−0.266667
$226$	−12.0000	−0.798228
$227$	10.0000	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$228$	−12.0000	−0.794719
$229$	16.0000	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$230$	1.00000	0.0659380
$231$	−20.0000	−1.31590
$232$	−2.00000	−0.131306
$233$	−5.00000	−0.327561	−0.163780	−	0.986497i	$-0.552369\pi$
$233$	−5.00000	−0.327561	−0.163780	+	0.986497i	$0.552369\pi$
$234$	−2.00000	−0.130744
$235$	6.00000	0.391397
$236$	10.0000	0.650945
$237$	8.00000	0.519656
$238$	−6.00000	−0.388922
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	−2.00000	−0.129099
$241$	11.0000	0.708572	0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000	0.708572	0.354286	+	0.935137i	$0.384724\pi$
$242$	14.0000	0.899954
$243$	−10.0000	−0.641500
$244$	−3.00000	−0.192055
$245$	3.00000	0.191663
$246$	14.0000	0.892607
$247$	12.0000	0.763542
$248$	4.00000	0.254000
$249$	−24.0000	−1.52094
$250$	9.00000	0.569210
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	2.00000	0.125988
$253$	5.00000	0.314347
$254$	16.0000	1.00393
$255$	6.00000	0.375735
$256$	1.00000	0.0625000
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	−2.00000	−0.124515
$259$	4.00000	0.248548
$260$	2.00000	0.124035
$261$	−2.00000	−0.123797
$262$	1.00000	0.0617802
$263$	−10.0000	−0.616626	−0.308313	−	0.951285i	$-0.599764\pi$
$263$	−10.0000	−0.616626	−0.308313	+	0.951285i	$0.599764\pi$
$264$	−10.0000	−0.615457
$265$	−6.00000	−0.368577
$266$	−12.0000	−0.735767
$267$	−32.0000	−1.95837
$268$	−10.0000	−0.610847
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	4.00000	0.243432
$271$	7.00000	0.425220	0.212610	−	0.977137i	$-0.431804\pi$
$271$	7.00000	0.425220	0.212610	+	0.977137i	$0.431804\pi$
$272$	−3.00000	−0.181902
$273$	−8.00000	−0.484182
$274$	1.00000	0.0604122
$275$	20.0000	1.20605
$276$	−2.00000	−0.120386
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	3.00000	0.179928
$279$	4.00000	0.239474
$280$	−2.00000	−0.119523
$281$	1.00000	0.0596550	0.0298275	−	0.999555i	$-0.490504\pi$
$281$	1.00000	0.0596550	0.0298275	+	0.999555i	$0.490504\pi$
$282$	−12.0000	−0.714590
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	−2.00000	−0.118678
$285$	12.0000	0.710819
$286$	10.0000	0.591312
$287$	14.0000	0.826394
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	2.00000	0.117444
$291$	20.0000	1.17242
$292$	−16.0000	−0.936329
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	−6.00000	−0.349927
$295$	−10.0000	−0.582223
$296$	2.00000	0.116248
$297$	20.0000	1.16052
$298$	−6.00000	−0.347571
$299$	2.00000	0.115663
$300$	−8.00000	−0.461880
$301$	−2.00000	−0.115278
$302$	−11.0000	−0.632979
$303$	32.0000	1.83835
$304$	−6.00000	−0.344124
$305$	3.00000	0.171780
$306$	−3.00000	−0.171499
$307$	6.00000	0.342438	0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000	0.342438	0.171219	+	0.985233i	$0.445229\pi$
$308$	−10.0000	−0.569803
$309$	2.00000	0.113776
$310$	−4.00000	−0.227185
$311$	−5.00000	−0.283524	−0.141762	−	0.989901i	$-0.545277\pi$
$311$	−5.00000	−0.283524	−0.141762	+	0.989901i	$0.545277\pi$
$312$	−4.00000	−0.226455
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−10.0000	−0.564333
$315$	−2.00000	−0.112687
$316$	4.00000	0.225018
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	12.0000	0.672927
$319$	10.0000	0.559893
$320$	−1.00000	−0.0559017
$321$	26.0000	1.45118
$322$	−2.00000	−0.111456
$323$	18.0000	1.00155
$324$	−11.0000	−0.611111
$325$	8.00000	0.443760
$326$	1.00000	0.0553849
$327$	2.00000	0.110600
$328$	7.00000	0.386510
$329$	−12.0000	−0.661581
$330$	10.0000	0.550482
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	−12.0000	−0.658586
$333$	2.00000	0.109599
$334$	9.00000	0.492458
$335$	10.0000	0.546358
$336$	4.00000	0.218218
$337$	−28.0000	−1.52526	−0.762629	−	0.646837i	$-0.776092\pi$
$337$	−28.0000	−1.52526	−0.762629	+	0.646837i	$0.776092\pi$
$338$	−9.00000	−0.489535
$339$	−24.0000	−1.30350
$340$	3.00000	0.162698
$341$	−20.0000	−1.08306
$342$	−6.00000	−0.324443
$343$	−20.0000	−1.07990
$344$	−1.00000	−0.0539164
$345$	2.00000	0.107676
$346$	21.0000	1.12897
$347$	27.0000	1.44944	0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000	1.44944	0.724718	+	0.689046i	$0.241970\pi$
$348$	−4.00000	−0.214423
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−8.00000	−0.427618
$351$	8.00000	0.427008
$352$	−5.00000	−0.266501
$353$	−23.0000	−1.22417	−0.612083	−	0.790793i	$-0.709668\pi$
$353$	−23.0000	−1.22417	−0.612083	+	0.790793i	$0.709668\pi$
$354$	20.0000	1.06299
$355$	2.00000	0.106149
$356$	−16.0000	−0.847998
$357$	−12.0000	−0.635107
$358$	−12.0000	−0.634220
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	−1.00000	−0.0527046
$361$	17.0000	0.894737
$362$	−20.0000	−1.05118
$363$	28.0000	1.46962
$364$	−4.00000	−0.209657
$365$	16.0000	0.837478
$366$	−6.00000	−0.313625
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	−1.00000	−0.0521286
$369$	7.00000	0.364405
$370$	−2.00000	−0.103975
$371$	12.0000	0.623009
$372$	8.00000	0.414781
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	15.0000	0.775632
$375$	18.0000	0.929516
$376$	−6.00000	−0.309426
$377$	4.00000	0.206010
$378$	−8.00000	−0.411476
$379$	−23.0000	−1.18143	−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000	−1.18143	−0.590715	+	0.806880i	$0.701154\pi$
$380$	6.00000	0.307794
$381$	32.0000	1.63941
$382$	14.0000	0.716302
$383$	−26.0000	−1.32854	−0.664269	−	0.747494i	$-0.731257\pi$
$383$	−26.0000	−1.32854	−0.664269	+	0.747494i	$0.731257\pi$
$384$	2.00000	0.102062
$385$	10.0000	0.509647
$386$	23.0000	1.17067
$387$	−1.00000	−0.0508329
$388$	10.0000	0.507673
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	4.00000	0.202548
$391$	3.00000	0.151717
$392$	−3.00000	−0.151523
$393$	2.00000	0.100887
$394$	21.0000	1.05796
$395$	−4.00000	−0.201262
$396$	−5.00000	−0.251259
$397$	−36.0000	−1.80679	−0.903394	−	0.428811i	$-0.858933\pi$
$397$	−36.0000	−1.80679	−0.903394	+	0.428811i	$0.858933\pi$
$398$	−3.00000	−0.150376
$399$	−24.0000	−1.20150
$400$	−4.00000	−0.200000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	−20.0000	−0.997509
$403$	−8.00000	−0.398508
$404$	16.0000	0.796030
$405$	11.0000	0.546594
$406$	−4.00000	−0.198517
$407$	−10.0000	−0.495682
$408$	−6.00000	−0.297044
$409$	9.00000	0.445021	0.222511	−	0.974930i	$-0.428575\pi$
$409$	9.00000	0.445021	0.222511	+	0.974930i	$0.428575\pi$
$410$	−7.00000	−0.345705
$411$	2.00000	0.0986527
$412$	1.00000	0.0492665
$413$	20.0000	0.984136
$414$	−1.00000	−0.0491473
$415$	12.0000	0.589057
$416$	−2.00000	−0.0980581
$417$	6.00000	0.293821
$418$	30.0000	1.46735
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	−4.00000	−0.195180
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−14.0000	−0.681509
$423$	−6.00000	−0.291730
$424$	6.00000	0.291386
$425$	12.0000	0.582086
$426$	−4.00000	−0.193801
$427$	−6.00000	−0.290360
$428$	13.0000	0.628379
$429$	20.0000	0.965609
$430$	1.00000	0.0482243
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−4.00000	−0.192450
$433$	19.0000	0.913082	0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000	0.913082	0.456541	+	0.889702i	$0.349088\pi$
$434$	8.00000	0.384012
$435$	4.00000	0.191785
$436$	1.00000	0.0478913
$437$	6.00000	0.287019
$438$	−32.0000	−1.52902
$439$	−19.0000	−0.906821	−0.453410	−	0.891302i	$-0.649793\pi$
$439$	−19.0000	−0.906821	−0.453410	+	0.891302i	$0.649793\pi$
$440$	5.00000	0.238366
$441$	−3.00000	−0.142857
$442$	6.00000	0.285391
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	4.00000	0.189832
$445$	16.0000	0.758473
$446$	14.0000	0.662919
$447$	−12.0000	−0.567581
$448$	2.00000	0.0944911
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	−4.00000	−0.188562
$451$	−35.0000	−1.64809
$452$	−12.0000	−0.564433
$453$	−22.0000	−1.03365
$454$	10.0000	0.469323
$455$	4.00000	0.187523
$456$	−12.0000	−0.561951
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	16.0000	0.747631
$459$	12.0000	0.560112
$460$	1.00000	0.0466252
$461$	−21.0000	−0.978068	−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000	−0.978068	−0.489034	+	0.872265i	$0.662651\pi$
$462$	−20.0000	−0.930484
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	−2.00000	−0.0928477
$465$	−8.00000	−0.370991
$466$	−5.00000	−0.231621
$467$	−3.00000	−0.138823	−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000	−0.138823	−0.0694117	+	0.997588i	$0.522112\pi$
$468$	−2.00000	−0.0924500
$469$	−20.0000	−0.923514
$470$	6.00000	0.276759
$471$	−20.0000	−0.921551
$472$	10.0000	0.460287
$473$	5.00000	0.229900
$474$	8.00000	0.367452
$475$	24.0000	1.10120
$476$	−6.00000	−0.275010
$477$	6.00000	0.274721
$478$	−12.0000	−0.548867
$479$	−39.0000	−1.78196	−0.890978	−	0.454047i	$-0.849980\pi$
$479$	−39.0000	−1.78196	−0.890978	+	0.454047i	$0.849980\pi$
$480$	−2.00000	−0.0912871
$481$	−4.00000	−0.182384
$482$	11.0000	0.501036
$483$	−4.00000	−0.182006
$484$	14.0000	0.636364
$485$	−10.0000	−0.454077
$486$	−10.0000	−0.453609
$487$	17.0000	0.770344	0.385172	−	0.922845i	$-0.374142\pi$
$487$	17.0000	0.770344	0.385172	+	0.922845i	$0.374142\pi$
$488$	−3.00000	−0.135804
$489$	2.00000	0.0904431
$490$	3.00000	0.135526
$491$	−7.00000	−0.315906	−0.157953	−	0.987447i	$-0.550489\pi$
$491$	−7.00000	−0.315906	−0.157953	+	0.987447i	$0.550489\pi$
$492$	14.0000	0.631169
$493$	6.00000	0.270226
$494$	12.0000	0.539906
$495$	5.00000	0.224733
$496$	4.00000	0.179605
$497$	−4.00000	−0.179425
$498$	−24.0000	−1.07547
$499$	29.0000	1.29822	0.649109	−	0.760695i	$-0.275142\pi$
$499$	29.0000	1.29822	0.649109	+	0.760695i	$0.275142\pi$
$500$	9.00000	0.402492
$501$	18.0000	0.804181
$502$	0	0
$503$	−39.0000	−1.73892	−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000	−1.73892	−0.869462	+	0.494000i	$0.835534\pi$
$504$	2.00000	0.0890871
$505$	−16.0000	−0.711991
$506$	5.00000	0.222277
$507$	−18.0000	−0.799408
$508$	16.0000	0.709885
$509$	25.0000	1.10811	0.554053	−	0.832482i	$-0.313081\pi$
$509$	25.0000	1.10811	0.554053	+	0.832482i	$0.313081\pi$
$510$	6.00000	0.265684
$511$	−32.0000	−1.41560
$512$	1.00000	0.0441942
$513$	24.0000	1.05963
$514$	−8.00000	−0.352865
$515$	−1.00000	−0.0440653
$516$	−2.00000	−0.0880451
$517$	30.0000	1.31940
$518$	4.00000	0.175750
$519$	42.0000	1.84360
$520$	2.00000	0.0877058
$521$	35.0000	1.53338	0.766689	−	0.642019i	$-0.221903\pi$
$521$	35.0000	1.53338	0.766689	+	0.642019i	$0.221903\pi$
$522$	−2.00000	−0.0875376
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	1.00000	0.0436852
$525$	−16.0000	−0.698297
$526$	−10.0000	−0.436021
$527$	−12.0000	−0.522728
$528$	−10.0000	−0.435194
$529$	1.00000	0.0434783
$530$	−6.00000	−0.260623
$531$	10.0000	0.433963
$532$	−12.0000	−0.520266
$533$	−14.0000	−0.606407
$534$	−32.0000	−1.38478
$535$	−13.0000	−0.562039
$536$	−10.0000	−0.431934
$537$	−24.0000	−1.03568
$538$	6.00000	0.258678
$539$	15.0000	0.646096
$540$	4.00000	0.172133
$541$	−9.00000	−0.386940	−0.193470	−	0.981106i	$-0.561974\pi$
$541$	−9.00000	−0.386940	−0.193470	+	0.981106i	$0.561974\pi$
$542$	7.00000	0.300676
$543$	−40.0000	−1.71656
$544$	−3.00000	−0.128624
$545$	−1.00000	−0.0428353
$546$	−8.00000	−0.342368
$547$	−29.0000	−1.23995	−0.619975	−	0.784621i	$-0.712857\pi$
$547$	−29.0000	−1.23995	−0.619975	+	0.784621i	$0.712857\pi$
$548$	1.00000	0.0427179
$549$	−3.00000	−0.128037
$550$	20.0000	0.852803
$551$	12.0000	0.511217
$552$	−2.00000	−0.0851257
$553$	8.00000	0.340195
$554$	−14.0000	−0.594803
$555$	−4.00000	−0.169791
$556$	3.00000	0.127228
$557$	5.00000	0.211857	0.105928	−	0.994374i	$-0.466219\pi$
$557$	5.00000	0.211857	0.105928	+	0.994374i	$0.466219\pi$
$558$	4.00000	0.169334
$559$	2.00000	0.0845910
$560$	−2.00000	−0.0845154
$561$	30.0000	1.26660
$562$	1.00000	0.0421825
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	−12.0000	−0.505291
$565$	12.0000	0.504844
$566$	−16.0000	−0.672530
$567$	−22.0000	−0.923913
$568$	−2.00000	−0.0839181
$569$	40.0000	1.67689	0.838444	−	0.544988i	$-0.183466\pi$
$569$	40.0000	1.67689	0.838444	+	0.544988i	$0.183466\pi$
$570$	12.0000	0.502625
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	10.0000	0.418121
$573$	28.0000	1.16972
$574$	14.0000	0.584349
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	23.0000	0.957503	0.478751	−	0.877951i	$-0.341090\pi$
$577$	23.0000	0.957503	0.478751	+	0.877951i	$0.341090\pi$
$578$	−8.00000	−0.332756
$579$	46.0000	1.91169
$580$	2.00000	0.0830455
$581$	−24.0000	−0.995688
$582$	20.0000	0.829027
$583$	−30.0000	−1.24247
$584$	−16.0000	−0.662085
$585$	2.00000	0.0826898
$586$	18.0000	0.743573
$587$	30.0000	1.23823	0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000	1.23823	0.619116	+	0.785299i	$0.287491\pi$
$588$	−6.00000	−0.247436
$589$	−24.0000	−0.988903
$590$	−10.0000	−0.411693
$591$	42.0000	1.72765
$592$	2.00000	0.0821995
$593$	44.0000	1.80686	0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000	1.80686	0.903432	+	0.428732i	$0.141040\pi$
$594$	20.0000	0.820610
$595$	6.00000	0.245976
$596$	−6.00000	−0.245770
$597$	−6.00000	−0.245564
$598$	2.00000	0.0817861
$599$	45.0000	1.83865	0.919325	−	0.393499i	$-0.128735\pi$
$599$	45.0000	1.83865	0.919325	+	0.393499i	$0.128735\pi$
$600$	−8.00000	−0.326599
$601$	3.00000	0.122373	0.0611863	−	0.998126i	$-0.480512\pi$
$601$	3.00000	0.122373	0.0611863	+	0.998126i	$0.480512\pi$
$602$	−2.00000	−0.0815139
$603$	−10.0000	−0.407231
$604$	−11.0000	−0.447584
$605$	−14.0000	−0.569181
$606$	32.0000	1.29991
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	−6.00000	−0.243332
$609$	−8.00000	−0.324176
$610$	3.00000	0.121466
$611$	12.0000	0.485468
$612$	−3.00000	−0.121268
$613$	−3.00000	−0.121169	−0.0605844	−	0.998163i	$-0.519296\pi$
$613$	−3.00000	−0.121169	−0.0605844	+	0.998163i	$0.519296\pi$
$614$	6.00000	0.242140
$615$	−14.0000	−0.564534
$616$	−10.0000	−0.402911
$617$	−27.0000	−1.08698	−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000	−1.08698	−0.543490	+	0.839416i	$0.682897\pi$
$618$	2.00000	0.0804518
$619$	−2.00000	−0.0803868	−0.0401934	−	0.999192i	$-0.512797\pi$
$619$	−2.00000	−0.0803868	−0.0401934	+	0.999192i	$0.512797\pi$
$620$	−4.00000	−0.160644
$621$	4.00000	0.160514
$622$	−5.00000	−0.200482
$623$	−32.0000	−1.28205
$624$	−4.00000	−0.160128
$625$	11.0000	0.440000
$626$	−22.0000	−0.879297
$627$	60.0000	2.39617
$628$	−10.0000	−0.399043
$629$	−6.00000	−0.239236
$630$	−2.00000	−0.0796819
$631$	−30.0000	−1.19428	−0.597141	−	0.802137i	$-0.703697\pi$
$631$	−30.0000	−1.19428	−0.597141	+	0.802137i	$0.703697\pi$
$632$	4.00000	0.159111
$633$	−28.0000	−1.11290
$634$	0	0
$635$	−16.0000	−0.634941
$636$	12.0000	0.475831
$637$	6.00000	0.237729
$638$	10.0000	0.395904
$639$	−2.00000	−0.0791188
$640$	−1.00000	−0.0395285
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	26.0000	1.02614
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	−2.00000	−0.0788110
$645$	2.00000	0.0787499
$646$	18.0000	0.708201
$647$	3.00000	0.117942	0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000	0.117942	0.0589711	+	0.998260i	$0.481218\pi$
$648$	−11.0000	−0.432121
$649$	−50.0000	−1.96267
$650$	8.00000	0.313786
$651$	16.0000	0.627089
$652$	1.00000	0.0391630
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	2.00000	0.0782062
$655$	−1.00000	−0.0390732
$656$	7.00000	0.273304
$657$	−16.0000	−0.624219
$658$	−12.0000	−0.467809
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	10.0000	0.389249
$661$	−8.00000	−0.311164	−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000	−0.311164	−0.155582	+	0.987823i	$0.549725\pi$
$662$	−16.0000	−0.621858
$663$	12.0000	0.466041
$664$	−12.0000	−0.465690
$665$	12.0000	0.465340
$666$	2.00000	0.0774984
$667$	2.00000	0.0774403
$668$	9.00000	0.348220
$669$	28.0000	1.08254
$670$	10.0000	0.386334
$671$	15.0000	0.579069
$672$	4.00000	0.154303
$673$	−46.0000	−1.77317	−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000	−1.77317	−0.886585	+	0.462566i	$0.846929\pi$
$674$	−28.0000	−1.07852
$675$	16.0000	0.615840
$676$	−9.00000	−0.346154
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−24.0000	−0.921714
$679$	20.0000	0.767530
$680$	3.00000	0.115045
$681$	20.0000	0.766402
$682$	−20.0000	−0.765840
$683$	2.00000	0.0765279	0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000	0.0765279	0.0382639	+	0.999268i	$0.487817\pi$
$684$	−6.00000	−0.229416
$685$	−1.00000	−0.0382080
$686$	−20.0000	−0.763604
$687$	32.0000	1.22088
$688$	−1.00000	−0.0381246
$689$	−12.0000	−0.457164
$690$	2.00000	0.0761387
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	21.0000	0.798300
$693$	−10.0000	−0.379869
$694$	27.0000	1.02491
$695$	−3.00000	−0.113796
$696$	−4.00000	−0.151620
$697$	−21.0000	−0.795432
$698$	−2.00000	−0.0757011
$699$	−10.0000	−0.378235
$700$	−8.00000	−0.302372
$701$	26.0000	0.982006	0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000	0.982006	0.491003	+	0.871158i	$0.336630\pi$
$702$	8.00000	0.301941
$703$	−12.0000	−0.452589
$704$	−5.00000	−0.188445
$705$	12.0000	0.451946
$706$	−23.0000	−0.865616
$707$	32.0000	1.20348
$708$	20.0000	0.751646
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	2.00000	0.0750587
$711$	4.00000	0.150012
$712$	−16.0000	−0.599625
$713$	−4.00000	−0.149801
$714$	−12.0000	−0.449089
$715$	−10.0000	−0.373979
$716$	−12.0000	−0.448461
$717$	−24.0000	−0.896296
$718$	−11.0000	−0.410516
$719$	−43.0000	−1.60363	−0.801815	−	0.597573i	$-0.796132\pi$
$719$	−43.0000	−1.60363	−0.801815	+	0.597573i	$0.796132\pi$
$720$	−1.00000	−0.0372678
$721$	2.00000	0.0744839
$722$	17.0000	0.632674
$723$	22.0000	0.818189
$724$	−20.0000	−0.743294
$725$	8.00000	0.297113
$726$	28.0000	1.03918
$727$	−7.00000	−0.259616	−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000	−0.259616	−0.129808	+	0.991539i	$0.541436\pi$
$728$	−4.00000	−0.148250
$729$	13.0000	0.481481
$730$	16.0000	0.592187
$731$	3.00000	0.110959
$732$	−6.00000	−0.221766
$733$	−8.00000	−0.295487	−0.147743	−	0.989026i	$-0.547201\pi$
$733$	−8.00000	−0.295487	−0.147743	+	0.989026i	$0.547201\pi$
$734$	14.0000	0.516749
$735$	6.00000	0.221313
$736$	−1.00000	−0.0368605
$737$	50.0000	1.84177
$738$	7.00000	0.257674
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	−2.00000	−0.0735215
$741$	24.0000	0.881662
$742$	12.0000	0.440534
$743$	39.0000	1.43077	0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000	1.43077	0.715386	+	0.698730i	$0.246251\pi$
$744$	8.00000	0.293294
$745$	6.00000	0.219823
$746$	−16.0000	−0.585802
$747$	−12.0000	−0.439057
$748$	15.0000	0.548454
$749$	26.0000	0.950019
$750$	18.0000	0.657267
$751$	7.00000	0.255434	0.127717	−	0.991811i	$-0.459235\pi$
$751$	7.00000	0.255434	0.127717	+	0.991811i	$0.459235\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	4.00000	0.145671
$755$	11.0000	0.400331
$756$	−8.00000	−0.290957
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	−23.0000	−0.835398
$759$	10.0000	0.362977
$760$	6.00000	0.217643
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	32.0000	1.15924
$763$	2.00000	0.0724049
$764$	14.0000	0.506502
$765$	3.00000	0.108465
$766$	−26.0000	−0.939418
$767$	−20.0000	−0.722158
$768$	2.00000	0.0721688
$769$	−20.0000	−0.721218	−0.360609	−	0.932717i	$-0.617431\pi$
$769$	−20.0000	−0.721218	−0.360609	+	0.932717i	$0.617431\pi$
$770$	10.0000	0.360375
$771$	−16.0000	−0.576226
$772$	23.0000	0.827788
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	−1.00000	−0.0359443
$775$	−16.0000	−0.574737
$776$	10.0000	0.358979
$777$	8.00000	0.286998
$778$	24.0000	0.860442
$779$	−42.0000	−1.50481
$780$	4.00000	0.143223
$781$	10.0000	0.357828
$782$	3.00000	0.107280
$783$	8.00000	0.285897
$784$	−3.00000	−0.107143
$785$	10.0000	0.356915
$786$	2.00000	0.0713376
$787$	43.0000	1.53278	0.766392	−	0.642373i	$-0.222050\pi$
$787$	43.0000	1.53278	0.766392	+	0.642373i	$0.222050\pi$
$788$	21.0000	0.748094
$789$	−20.0000	−0.712019
$790$	−4.00000	−0.142314
$791$	−24.0000	−0.853342
$792$	−5.00000	−0.177667
$793$	6.00000	0.213066
$794$	−36.0000	−1.27759
$795$	−12.0000	−0.425596
$796$	−3.00000	−0.106332
$797$	−29.0000	−1.02723	−0.513616	−	0.858020i	$-0.671695\pi$
$797$	−29.0000	−1.02723	−0.513616	+	0.858020i	$0.671695\pi$
$798$	−24.0000	−0.849591
$799$	18.0000	0.636794
$800$	−4.00000	−0.141421
$801$	−16.0000	−0.565332
$802$	−22.0000	−0.776847
$803$	80.0000	2.82314
$804$	−20.0000	−0.705346
$805$	2.00000	0.0704907
$806$	−8.00000	−0.281788
$807$	12.0000	0.422420
$808$	16.0000	0.562878
$809$	24.0000	0.843795	0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000	0.843795	0.421898	+	0.906644i	$0.361364\pi$
$810$	11.0000	0.386501
$811$	−10.0000	−0.351147	−0.175574	−	0.984466i	$-0.556178\pi$
$811$	−10.0000	−0.351147	−0.175574	+	0.984466i	$0.556178\pi$
$812$	−4.00000	−0.140372
$813$	14.0000	0.491001
$814$	−10.0000	−0.350500
$815$	−1.00000	−0.0350285
$816$	−6.00000	−0.210042
$817$	6.00000	0.209913
$818$	9.00000	0.314678
$819$	−4.00000	−0.139771
$820$	−7.00000	−0.244451
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	2.00000	0.0697580
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	1.00000	0.0348367
$825$	40.0000	1.39262
$826$	20.0000	0.695889
$827$	−52.0000	−1.80822	−0.904109	−	0.427303i	$-0.859464\pi$
$827$	−52.0000	−1.80822	−0.904109	+	0.427303i	$0.859464\pi$
$828$	−1.00000	−0.0347524
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	12.0000	0.416526
$831$	−28.0000	−0.971309
$832$	−2.00000	−0.0693375
$833$	9.00000	0.311832
$834$	6.00000	0.207763
$835$	−9.00000	−0.311458
$836$	30.0000	1.03757
$837$	−16.0000	−0.553041
$838$	−16.0000	−0.552711
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	−4.00000	−0.138013
$841$	−25.0000	−0.862069
$842$	22.0000	0.758170
$843$	2.00000	0.0688837
$844$	−14.0000	−0.481900
$845$	9.00000	0.309609
$846$	−6.00000	−0.206284
$847$	28.0000	0.962091
$848$	6.00000	0.206041
$849$	−32.0000	−1.09824
$850$	12.0000	0.411597
$851$	−2.00000	−0.0685591
$852$	−4.00000	−0.137038
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	−6.00000	−0.205316
$855$	6.00000	0.205196
$856$	13.0000	0.444331
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	20.0000	0.682789
$859$	56.0000	1.91070	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	56.0000	1.91070	0.955348	+	0.295484i	$0.0954809\pi$
$860$	1.00000	0.0340997
$861$	28.0000	0.954237
$862$	−16.0000	−0.544962
$863$	−32.0000	−1.08929	−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000	−1.08929	−0.544646	+	0.838666i	$0.683336\pi$
$864$	−4.00000	−0.136083
$865$	−21.0000	−0.714021
$866$	19.0000	0.645646
$867$	−16.0000	−0.543388
$868$	8.00000	0.271538
$869$	−20.0000	−0.678454
$870$	4.00000	0.135613
$871$	20.0000	0.677674
$872$	1.00000	0.0338643
$873$	10.0000	0.338449
$874$	6.00000	0.202953
$875$	18.0000	0.608511
$876$	−32.0000	−1.08118
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	−19.0000	−0.641219
$879$	36.0000	1.21425
$880$	5.00000	0.168550
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−3.00000	−0.101015
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	6.00000	0.201802
$885$	−20.0000	−0.672293
$886$	12.0000	0.403148
$887$	47.0000	1.57811	0.789053	−	0.614325i	$-0.210572\pi$
$887$	47.0000	1.57811	0.789053	+	0.614325i	$0.210572\pi$
$888$	4.00000	0.134231
$889$	32.0000	1.07325
$890$	16.0000	0.536321
$891$	55.0000	1.84257
$892$	14.0000	0.468755
$893$	36.0000	1.20469
$894$	−12.0000	−0.401340
$895$	12.0000	0.401116
$896$	2.00000	0.0668153
$897$	4.00000	0.133556
$898$	−22.0000	−0.734150
$899$	−8.00000	−0.266815
$900$	−4.00000	−0.133333
$901$	−18.0000	−0.599667
$902$	−35.0000	−1.16537
$903$	−4.00000	−0.133112
$904$	−12.0000	−0.399114
$905$	20.0000	0.664822
$906$	−22.0000	−0.730901
$907$	−29.0000	−0.962929	−0.481465	−	0.876466i	$-0.659895\pi$
$907$	−29.0000	−0.962929	−0.481465	+	0.876466i	$0.659895\pi$
$908$	10.0000	0.331862
$909$	16.0000	0.530687
$910$	4.00000	0.132599
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	−12.0000	−0.397360
$913$	60.0000	1.98571
$914$	−28.0000	−0.926158
$915$	6.00000	0.198354
$916$	16.0000	0.528655
$917$	2.00000	0.0660458
$918$	12.0000	0.396059
$919$	51.0000	1.68233	0.841167	−	0.540775i	$-0.181869\pi$
$919$	51.0000	1.68233	0.841167	+	0.540775i	$0.181869\pi$
$920$	1.00000	0.0329690
$921$	12.0000	0.395413
$922$	−21.0000	−0.691598
$923$	4.00000	0.131662
$924$	−20.0000	−0.657952
$925$	−8.00000	−0.263038
$926$	32.0000	1.05159
$927$	1.00000	0.0328443
$928$	−2.00000	−0.0656532
$929$	41.0000	1.34517	0.672583	−	0.740022i	$-0.265185\pi$
$929$	41.0000	1.34517	0.672583	+	0.740022i	$0.265185\pi$
$930$	−8.00000	−0.262330
$931$	18.0000	0.589926
$932$	−5.00000	−0.163780
$933$	−10.0000	−0.327385
$934$	−3.00000	−0.0981630
$935$	−15.0000	−0.490552
$936$	−2.00000	−0.0653720
$937$	−14.0000	−0.457360	−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000	−0.457360	−0.228680	+	0.973502i	$0.573441\pi$
$938$	−20.0000	−0.653023
$939$	−44.0000	−1.43589
$940$	6.00000	0.195698
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	−20.0000	−0.651635
$943$	−7.00000	−0.227951
$944$	10.0000	0.325472
$945$	8.00000	0.260240
$946$	5.00000	0.162564
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	8.00000	0.259828
$949$	32.0000	1.03876
$950$	24.0000	0.778663
$951$	0	0
$952$	−6.00000	−0.194461
$953$	−12.0000	−0.388718	−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000	−0.388718	−0.194359	+	0.980930i	$0.562263\pi$
$954$	6.00000	0.194257
$955$	−14.0000	−0.453029
$956$	−12.0000	−0.388108
$957$	20.0000	0.646508
$958$	−39.0000	−1.26003
$959$	2.00000	0.0645834
$960$	−2.00000	−0.0645497
$961$	−15.0000	−0.483871
$962$	−4.00000	−0.128965
$963$	13.0000	0.418919
$964$	11.0000	0.354286
$965$	−23.0000	−0.740396
$966$	−4.00000	−0.128698
$967$	−12.0000	−0.385894	−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000	−0.385894	−0.192947	+	0.981209i	$0.561805\pi$
$968$	14.0000	0.449977
$969$	36.0000	1.15649
$970$	−10.0000	−0.321081
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	−10.0000	−0.320750
$973$	6.00000	0.192351
$974$	17.0000	0.544715
$975$	16.0000	0.512410
$976$	−3.00000	−0.0960277
$977$	−58.0000	−1.85558	−0.927792	−	0.373097i	$-0.878296\pi$
$977$	−58.0000	−1.85558	−0.927792	+	0.373097i	$0.878296\pi$
$978$	2.00000	0.0639529
$979$	80.0000	2.55681
$980$	3.00000	0.0958315
$981$	1.00000	0.0319275
$982$	−7.00000	−0.223379
$983$	−48.0000	−1.53096	−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000	−1.53096	−0.765481	+	0.643458i	$0.777499\pi$
$984$	14.0000	0.446304
$985$	−21.0000	−0.669116
$986$	6.00000	0.191079
$987$	−24.0000	−0.763928
$988$	12.0000	0.381771
$989$	1.00000	0.0317982
$990$	5.00000	0.158910
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	4.00000	0.127000
$993$	−32.0000	−1.01549
$994$	−4.00000	−0.126872
$995$	3.00000	0.0951064
$996$	−24.0000	−0.760469
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	29.0000	0.917979
$999$	−8.00000	−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.d.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more