LMFDB - Embedded newform 6026.2.a.c.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)

$f(q)$

$=$

$q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{10} -1.00000 q^{11} -2.00000 q^{12} -6.00000 q^{13} +2.00000 q^{14} -6.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -2.00000 q^{19} +3.00000 q^{20} -4.00000 q^{21} -1.00000 q^{22} -1.00000 q^{23} -2.00000 q^{24} +4.00000 q^{25} -6.00000 q^{26} +4.00000 q^{27} +2.00000 q^{28} -2.00000 q^{29} -6.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{34} +6.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -2.00000 q^{38} +12.0000 q^{39} +3.00000 q^{40} -9.00000 q^{41} -4.00000 q^{42} -5.00000 q^{43} -1.00000 q^{44} +3.00000 q^{45} -1.00000 q^{46} -10.0000 q^{47} -2.00000 q^{48} -3.00000 q^{49} +4.00000 q^{50} -2.00000 q^{51} -6.00000 q^{52} -2.00000 q^{53} +4.00000 q^{54} -3.00000 q^{55} +2.00000 q^{56} +4.00000 q^{57} -2.00000 q^{58} +6.00000 q^{59} -6.00000 q^{60} -7.00000 q^{61} -4.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -18.0000 q^{65} +2.00000 q^{66} -6.00000 q^{67} +1.00000 q^{68} +2.00000 q^{69} +6.00000 q^{70} +2.00000 q^{71} +1.00000 q^{72} +4.00000 q^{73} +2.00000 q^{74} -8.00000 q^{75} -2.00000 q^{76} -2.00000 q^{77} +12.0000 q^{78} -4.00000 q^{79} +3.00000 q^{80} -11.0000 q^{81} -9.00000 q^{82} -4.00000 q^{84} +3.00000 q^{85} -5.00000 q^{86} +4.00000 q^{87} -1.00000 q^{88} +3.00000 q^{90} -12.0000 q^{91} -1.00000 q^{92} +8.00000 q^{93} -10.0000 q^{94} -6.00000 q^{95} -2.00000 q^{96} +2.00000 q^{97} -3.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	−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
$10$	3.00000	0.948683
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−2.00000	−0.577350
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	2.00000	0.534522
$15$	−6.00000	−1.54919
$16$	1.00000	0.250000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	1.00000	0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	3.00000	0.670820
$21$	−4.00000	−0.872872
$22$	−1.00000	−0.213201
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.00000	−0.408248
$25$	4.00000	0.800000
$26$	−6.00000	−1.17670
$27$	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	$0.559454\pi$
$30$	−6.00000	−1.09545
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	2.00000	0.348155
$34$	1.00000	0.171499
$35$	6.00000	1.01419
$36$	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	$0.447432\pi$
$38$	−2.00000	−0.324443
$39$	12.0000	1.92154
$40$	3.00000	0.474342
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	−4.00000	−0.617213
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−1.00000	−0.150756
$45$	3.00000	0.447214
$46$	−1.00000	−0.147442
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	−2.00000	−0.288675
$49$	−3.00000	−0.428571
$50$	4.00000	0.565685
$51$	−2.00000	−0.280056
$52$	−6.00000	−0.832050
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	4.00000	0.544331
$55$	−3.00000	−0.404520
$56$	2.00000	0.267261
$57$	4.00000	0.529813
$58$	−2.00000	−0.262613
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	−6.00000	−0.774597
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	−4.00000	−0.508001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	−18.0000	−2.23263
$66$	2.00000	0.246183
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	1.00000	0.121268
$69$	2.00000	0.240772
$70$	6.00000	0.717137
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	1.00000	0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	2.00000	0.232495
$75$	−8.00000	−0.923760
$76$	−2.00000	−0.229416
$77$	−2.00000	−0.227921
$78$	12.0000	1.35873
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	3.00000	0.335410
$81$	−11.0000	−1.22222
$82$	−9.00000	−0.993884
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−4.00000	−0.436436
$85$	3.00000	0.325396
$86$	−5.00000	−0.539164
$87$	4.00000	0.428845
$88$	−1.00000	−0.106600
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	3.00000	0.316228
$91$	−12.0000	−1.25794
$92$	−1.00000	−0.104257
$93$	8.00000	0.829561
$94$	−10.0000	−1.03142
$95$	−6.00000	−0.615587
$96$	−2.00000	−0.204124
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−3.00000	−0.303046
$99$	−1.00000	−0.100504
$100$	4.00000	0.400000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−2.00000	−0.198030
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	−6.00000	−0.588348
$105$	−12.0000	−1.17108
$106$	−2.00000	−0.194257
$107$	−7.00000	−0.676716	−0.338358	−	0.941018i	$-0.609871\pi$
$107$	−7.00000	−0.676716	−0.338358	+	0.941018i	$0.609871\pi$
$108$	4.00000	0.384900
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	−3.00000	−0.286039
$111$	−4.00000	−0.379663
$112$	2.00000	0.188982
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	4.00000	0.374634
$115$	−3.00000	−0.279751
$116$	−2.00000	−0.185695
$117$	−6.00000	−0.554700
$118$	6.00000	0.552345
$119$	2.00000	0.183340
$120$	−6.00000	−0.547723
$121$	−10.0000	−0.909091
$122$	−7.00000	−0.633750
$123$	18.0000	1.62301
$124$	−4.00000	−0.359211
$125$	−3.00000	−0.268328
$126$	2.00000	0.178174
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.00000	0.0883883
$129$	10.0000	0.880451
$130$	−18.0000	−1.57870
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	2.00000	0.174078
$133$	−4.00000	−0.346844
$134$	−6.00000	−0.518321
$135$	12.0000	1.03280
$136$	1.00000	0.0857493
$137$	−3.00000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	2.00000	0.170251
$139$	19.0000	1.61156	0.805779	−	0.592216i	$-0.201747\pi$
$139$	19.0000	1.61156	0.805779	+	0.592216i	$0.201747\pi$
$140$	6.00000	0.507093
$141$	20.0000	1.68430
$142$	2.00000	0.167836
$143$	6.00000	0.501745
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	4.00000	0.331042
$147$	6.00000	0.494872
$148$	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	$0.634337\pi$
$150$	−8.00000	−0.653197
$151$	−3.00000	−0.244137	−0.122068	−	0.992522i	$-0.538953\pi$
$151$	−3.00000	−0.244137	−0.122068	+	0.992522i	$0.538953\pi$
$152$	−2.00000	−0.162221
$153$	1.00000	0.0808452
$154$	−2.00000	−0.161165
$155$	−12.0000	−0.963863
$156$	12.0000	0.960769
$157$	−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
$159$	4.00000	0.317221
$160$	3.00000	0.237171
$161$	−2.00000	−0.157622
$162$	−11.0000	−0.864242
$163$	−15.0000	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$163$	−15.0000	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$164$	−9.00000	−0.702782
$165$	6.00000	0.467099
$166$	0	0
$167$	−7.00000	−0.541676	−0.270838	−	0.962625i	$-0.587301\pi$
$167$	−7.00000	−0.541676	−0.270838	+	0.962625i	$0.587301\pi$
$168$	−4.00000	−0.308607
$169$	23.0000	1.76923
$170$	3.00000	0.230089
$171$	−2.00000	−0.152944
$172$	−5.00000	−0.381246
$173$	5.00000	0.380143	0.190071	−	0.981770i	$-0.439128\pi$
$173$	5.00000	0.380143	0.190071	+	0.981770i	$0.439128\pi$
$174$	4.00000	0.303239
$175$	8.00000	0.604743
$176$	−1.00000	−0.0753778
$177$	−12.0000	−0.901975
$178$	0	0
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	3.00000	0.223607
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−12.0000	−0.889499
$183$	14.0000	1.03491
$184$	−1.00000	−0.0737210
$185$	6.00000	0.441129
$186$	8.00000	0.586588
$187$	−1.00000	−0.0731272
$188$	−10.0000	−0.729325
$189$	8.00000	0.581914
$190$	−6.00000	−0.435286
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	−2.00000	−0.144338
$193$	15.0000	1.07972	0.539862	−	0.841754i	$-0.318476\pi$
$193$	15.0000	1.07972	0.539862	+	0.841754i	$0.318476\pi$
$194$	2.00000	0.143592
$195$	36.0000	2.57801
$196$	−3.00000	−0.214286
$197$	−11.0000	−0.783718	−0.391859	−	0.920025i	$-0.628168\pi$
$197$	−11.0000	−0.783718	−0.391859	+	0.920025i	$0.628168\pi$
$198$	−1.00000	−0.0710669
$199$	25.0000	1.77220	0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000	1.77220	0.886102	+	0.463491i	$0.153403\pi$
$200$	4.00000	0.282843
$201$	12.0000	0.846415
$202$	0	0
$203$	−4.00000	−0.280745
$204$	−2.00000	−0.140028
$205$	−27.0000	−1.88576
$206$	13.0000	0.905753
$207$	−1.00000	−0.0695048
$208$	−6.00000	−0.416025
$209$	2.00000	0.138343
$210$	−12.0000	−0.828079
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	−2.00000	−0.137361
$213$	−4.00000	−0.274075
$214$	−7.00000	−0.478510
$215$	−15.0000	−1.02299
$216$	4.00000	0.272166
$217$	−8.00000	−0.543075
$218$	5.00000	0.338643
$219$	−8.00000	−0.540590
$220$	−3.00000	−0.202260
$221$	−6.00000	−0.403604
$222$	−4.00000	−0.268462
$223$	−26.0000	−1.74109	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000	−1.74109	−0.870544	+	0.492090i	$0.836233\pi$
$224$	2.00000	0.133631
$225$	4.00000	0.266667
$226$	0	0
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	4.00000	0.264906
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	−3.00000	−0.197814
$231$	4.00000	0.263181
$232$	−2.00000	−0.131306
$233$	−21.0000	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$234$	−6.00000	−0.392232
$235$	−30.0000	−1.95698
$236$	6.00000	0.390567
$237$	8.00000	0.519656
$238$	2.00000	0.129641
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	−6.00000	−0.387298
$241$	15.0000	0.966235	0.483117	−	0.875556i	$-0.339504\pi$
$241$	15.0000	0.966235	0.483117	+	0.875556i	$0.339504\pi$
$242$	−10.0000	−0.642824
$243$	10.0000	0.641500
$244$	−7.00000	−0.448129
$245$	−9.00000	−0.574989
$246$	18.0000	1.14764
$247$	12.0000	0.763542
$248$	−4.00000	−0.254000
$249$	0	0
$250$	−3.00000	−0.189737
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	2.00000	0.125988
$253$	1.00000	0.0628695
$254$	−4.00000	−0.250982
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	10.0000	0.622573
$259$	4.00000	0.248548
$260$	−18.0000	−1.11631
$261$	−2.00000	−0.123797
$262$	1.00000	0.0617802
$263$	26.0000	1.60323	0.801614	−	0.597841i	$-0.203975\pi$
$263$	26.0000	1.60323	0.801614	+	0.597841i	$0.203975\pi$
$264$	2.00000	0.123091
$265$	−6.00000	−0.368577
$266$	−4.00000	−0.245256
$267$	0	0
$268$	−6.00000	−0.366508
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	12.0000	0.730297
$271$	−9.00000	−0.546711	−0.273356	−	0.961913i	$-0.588134\pi$
$271$	−9.00000	−0.546711	−0.273356	+	0.961913i	$0.588134\pi$
$272$	1.00000	0.0606339
$273$	24.0000	1.45255
$274$	−3.00000	−0.181237
$275$	−4.00000	−0.241209
$276$	2.00000	0.120386
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	19.0000	1.13954
$279$	−4.00000	−0.239474
$280$	6.00000	0.358569
$281$	−3.00000	−0.178965	−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000	−0.178965	−0.0894825	+	0.995988i	$0.528521\pi$
$282$	20.0000	1.19098
$283$	−8.00000	−0.475551	−0.237775	−	0.971320i	$-0.576418\pi$
$283$	−8.00000	−0.475551	−0.237775	+	0.971320i	$0.576418\pi$
$284$	2.00000	0.118678
$285$	12.0000	0.710819
$286$	6.00000	0.354787
$287$	−18.0000	−1.06251
$288$	1.00000	0.0589256
$289$	−16.0000	−0.941176
$290$	−6.00000	−0.352332
$291$	−4.00000	−0.234484
$292$	4.00000	0.234082
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	6.00000	0.349927
$295$	18.0000	1.04800
$296$	2.00000	0.116248
$297$	−4.00000	−0.232104
$298$	−10.0000	−0.579284
$299$	6.00000	0.346989
$300$	−8.00000	−0.461880
$301$	−10.0000	−0.576390
$302$	−3.00000	−0.172631
$303$	0	0
$304$	−2.00000	−0.114708
$305$	−21.0000	−1.20246
$306$	1.00000	0.0571662
$307$	34.0000	1.94048	0.970241	−	0.242140i	$-0.0778494\pi$
$307$	34.0000	1.94048	0.970241	+	0.242140i	$0.0778494\pi$
$308$	−2.00000	−0.113961
$309$	−26.0000	−1.47909
$310$	−12.0000	−0.681554
$311$	19.0000	1.07739	0.538696	−	0.842500i	$-0.318917\pi$
$311$	19.0000	1.07739	0.538696	+	0.842500i	$0.318917\pi$
$312$	12.0000	0.679366
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−10.0000	−0.564333
$315$	6.00000	0.338062
$316$	−4.00000	−0.225018
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	4.00000	0.224309
$319$	2.00000	0.111979
$320$	3.00000	0.167705
$321$	14.0000	0.781404
$322$	−2.00000	−0.111456
$323$	−2.00000	−0.111283
$324$	−11.0000	−0.611111
$325$	−24.0000	−1.33128
$326$	−15.0000	−0.830773
$327$	−10.0000	−0.553001
$328$	−9.00000	−0.496942
$329$	−20.0000	−1.10264
$330$	6.00000	0.330289
$331$	16.0000	0.879440	0.439720	−	0.898135i	$-0.355078\pi$
$331$	16.0000	0.879440	0.439720	+	0.898135i	$0.355078\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	−7.00000	−0.383023
$335$	−18.0000	−0.983445
$336$	−4.00000	−0.218218
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	23.0000	1.25104
$339$	0	0
$340$	3.00000	0.162698
$341$	4.00000	0.216612
$342$	−2.00000	−0.108148
$343$	−20.0000	−1.07990
$344$	−5.00000	−0.269582
$345$	6.00000	0.323029
$346$	5.00000	0.268802
$347$	−13.0000	−0.697877	−0.348938	−	0.937146i	$-0.613458\pi$
$347$	−13.0000	−0.697877	−0.348938	+	0.937146i	$0.613458\pi$
$348$	4.00000	0.214423
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	8.00000	0.427618
$351$	−24.0000	−1.28103
$352$	−1.00000	−0.0533002
$353$	9.00000	0.479022	0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000	0.479022	0.239511	+	0.970894i	$0.423013\pi$
$354$	−12.0000	−0.637793
$355$	6.00000	0.318447
$356$	0	0
$357$	−4.00000	−0.211702
$358$	20.0000	1.05703
$359$	−15.0000	−0.791670	−0.395835	−	0.918322i	$-0.629545\pi$
$359$	−15.0000	−0.791670	−0.395835	+	0.918322i	$0.629545\pi$
$360$	3.00000	0.158114
$361$	−15.0000	−0.789474
$362$	12.0000	0.630706
$363$	20.0000	1.04973
$364$	−12.0000	−0.628971
$365$	12.0000	0.628109
$366$	14.0000	0.731792
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	−1.00000	−0.0521286
$369$	−9.00000	−0.468521
$370$	6.00000	0.311925
$371$	−4.00000	−0.207670
$372$	8.00000	0.414781
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	−1.00000	−0.0517088
$375$	6.00000	0.309839
$376$	−10.0000	−0.515711
$377$	12.0000	0.618031
$378$	8.00000	0.411476
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	−6.00000	−0.307794
$381$	8.00000	0.409852
$382$	18.0000	0.920960
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	−2.00000	−0.102062
$385$	−6.00000	−0.305788
$386$	15.0000	0.763480
$387$	−5.00000	−0.254164
$388$	2.00000	0.101535
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	36.0000	1.82293
$391$	−1.00000	−0.0505722
$392$	−3.00000	−0.151523
$393$	−2.00000	−0.100887
$394$	−11.0000	−0.554172
$395$	−12.0000	−0.603786
$396$	−1.00000	−0.0502519
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	25.0000	1.25314
$399$	8.00000	0.400501
$400$	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	$0.685111\pi$
$402$	12.0000	0.598506
$403$	24.0000	1.19553
$404$	0	0
$405$	−33.0000	−1.63978
$406$	−4.00000	−0.198517
$407$	−2.00000	−0.0991363
$408$	−2.00000	−0.0990148
$409$	1.00000	0.0494468	0.0247234	−	0.999694i	$-0.492129\pi$
$409$	1.00000	0.0494468	0.0247234	+	0.999694i	$0.492129\pi$
$410$	−27.0000	−1.33343
$411$	6.00000	0.295958
$412$	13.0000	0.640464
$413$	12.0000	0.590481
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−6.00000	−0.294174
$417$	−38.0000	−1.86087
$418$	2.00000	0.0978232
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	−12.0000	−0.585540
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	−10.0000	−0.486792
$423$	−10.0000	−0.486217
$424$	−2.00000	−0.0971286
$425$	4.00000	0.194029
$426$	−4.00000	−0.193801
$427$	−14.0000	−0.677507
$428$	−7.00000	−0.338358
$429$	−12.0000	−0.579365
$430$	−15.0000	−0.723364
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	4.00000	0.192450
$433$	−25.0000	−1.20142	−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000	−1.20142	−0.600712	+	0.799466i	$0.705116\pi$
$434$	−8.00000	−0.384012
$435$	12.0000	0.575356
$436$	5.00000	0.239457
$437$	2.00000	0.0956730
$438$	−8.00000	−0.382255
$439$	−27.0000	−1.28864	−0.644320	−	0.764756i	$-0.722859\pi$
$439$	−27.0000	−1.28864	−0.644320	+	0.764756i	$0.722859\pi$
$440$	−3.00000	−0.143019
$441$	−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
$445$	0	0
$446$	−26.0000	−1.23114
$447$	20.0000	0.945968
$448$	2.00000	0.0944911
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	4.00000	0.188562
$451$	9.00000	0.423793
$452$	0	0
$453$	6.00000	0.281905
$454$	18.0000	0.844782
$455$	−36.0000	−1.68771
$456$	4.00000	0.187317
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	0	0
$459$	4.00000	0.186704
$460$	−3.00000	−0.139876
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	4.00000	0.186097
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	−2.00000	−0.0928477
$465$	24.0000	1.11297
$466$	−21.0000	−0.972806
$467$	25.0000	1.15686	0.578431	−	0.815731i	$-0.303665\pi$
$467$	25.0000	1.15686	0.578431	+	0.815731i	$0.303665\pi$
$468$	−6.00000	−0.277350
$469$	−12.0000	−0.554109
$470$	−30.0000	−1.38380
$471$	20.0000	0.921551
$472$	6.00000	0.276172
$473$	5.00000	0.229900
$474$	8.00000	0.367452
$475$	−8.00000	−0.367065
$476$	2.00000	0.0916698
$477$	−2.00000	−0.0915737
$478$	−12.0000	−0.548867
$479$	−11.0000	−0.502603	−0.251301	−	0.967909i	$-0.580859\pi$
$479$	−11.0000	−0.502603	−0.251301	+	0.967909i	$0.580859\pi$
$480$	−6.00000	−0.273861
$481$	−12.0000	−0.547153
$482$	15.0000	0.683231
$483$	4.00000	0.182006
$484$	−10.0000	−0.454545
$485$	6.00000	0.272446
$486$	10.0000	0.453609
$487$	−31.0000	−1.40474	−0.702372	−	0.711810i	$-0.747876\pi$
$487$	−31.0000	−1.40474	−0.702372	+	0.711810i	$0.747876\pi$
$488$	−7.00000	−0.316875
$489$	30.0000	1.35665
$490$	−9.00000	−0.406579
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	18.0000	0.811503
$493$	−2.00000	−0.0900755
$494$	12.0000	0.539906
$495$	−3.00000	−0.134840
$496$	−4.00000	−0.179605
$497$	4.00000	0.179425
$498$	0	0
$499$	21.0000	0.940089	0.470045	−	0.882643i	$-0.344238\pi$
$499$	21.0000	0.940089	0.470045	+	0.882643i	$0.344238\pi$
$500$	−3.00000	−0.134164
$501$	14.0000	0.625474
$502$	12.0000	0.535586
$503$	−3.00000	−0.133763	−0.0668817	−	0.997761i	$-0.521305\pi$
$503$	−3.00000	−0.133763	−0.0668817	+	0.997761i	$0.521305\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	1.00000	0.0444554
$507$	−46.0000	−2.04293
$508$	−4.00000	−0.177471
$509$	9.00000	0.398918	0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000	0.398918	0.199459	+	0.979906i	$0.436082\pi$
$510$	−6.00000	−0.265684
$511$	8.00000	0.353899
$512$	1.00000	0.0441942
$513$	−8.00000	−0.353209
$514$	−24.0000	−1.05859
$515$	39.0000	1.71855
$516$	10.0000	0.440225
$517$	10.0000	0.439799
$518$	4.00000	0.175750
$519$	−10.0000	−0.438951
$520$	−18.0000	−0.789352
$521$	−17.0000	−0.744784	−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000	−0.744784	−0.372392	+	0.928076i	$0.621462\pi$
$522$	−2.00000	−0.0875376
$523$	18.0000	0.787085	0.393543	−	0.919306i	$-0.371249\pi$
$523$	18.0000	0.787085	0.393543	+	0.919306i	$0.371249\pi$
$524$	1.00000	0.0436852
$525$	−16.0000	−0.698297
$526$	26.0000	1.13365
$527$	−4.00000	−0.174243
$528$	2.00000	0.0870388
$529$	1.00000	0.0434783
$530$	−6.00000	−0.260623
$531$	6.00000	0.260378
$532$	−4.00000	−0.173422
$533$	54.0000	2.33900
$534$	0	0
$535$	−21.0000	−0.907909
$536$	−6.00000	−0.259161
$537$	−40.0000	−1.72613
$538$	−14.0000	−0.603583
$539$	3.00000	0.129219
$540$	12.0000	0.516398
$541$	15.0000	0.644900	0.322450	−	0.946586i	$-0.395494\pi$
$541$	15.0000	0.644900	0.322450	+	0.946586i	$0.395494\pi$
$542$	−9.00000	−0.386583
$543$	−24.0000	−1.02994
$544$	1.00000	0.0428746
$545$	15.0000	0.642529
$546$	24.0000	1.02711
$547$	−5.00000	−0.213785	−0.106892	−	0.994271i	$-0.534090\pi$
$547$	−5.00000	−0.213785	−0.106892	+	0.994271i	$0.534090\pi$
$548$	−3.00000	−0.128154
$549$	−7.00000	−0.298753
$550$	−4.00000	−0.170561
$551$	4.00000	0.170406
$552$	2.00000	0.0851257
$553$	−8.00000	−0.340195
$554$	2.00000	0.0849719
$555$	−12.0000	−0.509372
$556$	19.0000	0.805779
$557$	9.00000	0.381342	0.190671	−	0.981654i	$-0.438934\pi$
$557$	9.00000	0.381342	0.190671	+	0.981654i	$0.438934\pi$
$558$	−4.00000	−0.169334
$559$	30.0000	1.26886
$560$	6.00000	0.253546
$561$	2.00000	0.0844401
$562$	−3.00000	−0.126547
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	20.0000	0.842152
$565$	0	0
$566$	−8.00000	−0.336265
$567$	−22.0000	−0.923913
$568$	2.00000	0.0839181
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	12.0000	0.502625
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	6.00000	0.250873
$573$	−36.0000	−1.50392
$574$	−18.0000	−0.751305
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−1.00000	−0.0416305	−0.0208153	−	0.999783i	$-0.506626\pi$
$577$	−1.00000	−0.0416305	−0.0208153	+	0.999783i	$0.506626\pi$
$578$	−16.0000	−0.665512
$579$	−30.0000	−1.24676
$580$	−6.00000	−0.249136
$581$	0	0
$582$	−4.00000	−0.165805
$583$	2.00000	0.0828315
$584$	4.00000	0.165521
$585$	−18.0000	−0.744208
$586$	−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
$589$	8.00000	0.329634
$590$	18.0000	0.741048
$591$	22.0000	0.904959
$592$	2.00000	0.0821995
$593$	8.00000	0.328521	0.164260	−	0.986417i	$-0.447476\pi$
$593$	8.00000	0.328521	0.164260	+	0.986417i	$0.447476\pi$
$594$	−4.00000	−0.164122
$595$	6.00000	0.245976
$596$	−10.0000	−0.409616
$597$	−50.0000	−2.04636
$598$	6.00000	0.245358
$599$	−27.0000	−1.10319	−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000	−1.10319	−0.551595	+	0.834112i	$0.685981\pi$
$600$	−8.00000	−0.326599
$601$	35.0000	1.42768	0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000	1.42768	0.713840	+	0.700309i	$0.246954\pi$
$602$	−10.0000	−0.407570
$603$	−6.00000	−0.244339
$604$	−3.00000	−0.122068
$605$	−30.0000	−1.21967
$606$	0	0
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	−2.00000	−0.0811107
$609$	8.00000	0.324176
$610$	−21.0000	−0.850265
$611$	60.0000	2.42734
$612$	1.00000	0.0404226
$613$	−7.00000	−0.282727	−0.141364	−	0.989958i	$-0.545149\pi$
$613$	−7.00000	−0.282727	−0.141364	+	0.989958i	$0.545149\pi$
$614$	34.0000	1.37213
$615$	54.0000	2.17749
$616$	−2.00000	−0.0805823
$617$	1.00000	0.0402585	0.0201292	−	0.999797i	$-0.493592\pi$
$617$	1.00000	0.0402585	0.0201292	+	0.999797i	$0.493592\pi$
$618$	−26.0000	−1.04587
$619$	34.0000	1.36658	0.683288	−	0.730149i	$-0.260549\pi$
$619$	34.0000	1.36658	0.683288	+	0.730149i	$0.260549\pi$
$620$	−12.0000	−0.481932
$621$	−4.00000	−0.160514
$622$	19.0000	0.761831
$623$	0	0
$624$	12.0000	0.480384
$625$	−29.0000	−1.16000
$626$	10.0000	0.399680
$627$	−4.00000	−0.159745
$628$	−10.0000	−0.399043
$629$	2.00000	0.0797452
$630$	6.00000	0.239046
$631$	26.0000	1.03504	0.517522	−	0.855670i	$-0.326855\pi$
$631$	26.0000	1.03504	0.517522	+	0.855670i	$0.326855\pi$
$632$	−4.00000	−0.159111
$633$	20.0000	0.794929
$634$	−12.0000	−0.476581
$635$	−12.0000	−0.476205
$636$	4.00000	0.158610
$637$	18.0000	0.713186
$638$	2.00000	0.0791808
$639$	2.00000	0.0791188
$640$	3.00000	0.118585
$641$	28.0000	1.10593	0.552967	−	0.833203i	$-0.313496\pi$
$641$	28.0000	1.10593	0.552967	+	0.833203i	$0.313496\pi$
$642$	14.0000	0.552536
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	−2.00000	−0.0788110
$645$	30.0000	1.18125
$646$	−2.00000	−0.0786889
$647$	11.0000	0.432455	0.216227	−	0.976343i	$-0.430625\pi$
$647$	11.0000	0.432455	0.216227	+	0.976343i	$0.430625\pi$
$648$	−11.0000	−0.432121
$649$	−6.00000	−0.235521
$650$	−24.0000	−0.941357
$651$	16.0000	0.627089
$652$	−15.0000	−0.587445
$653$	16.0000	0.626128	0.313064	−	0.949732i	$-0.398644\pi$
$653$	16.0000	0.626128	0.313064	+	0.949732i	$0.398644\pi$
$654$	−10.0000	−0.391031
$655$	3.00000	0.117220
$656$	−9.00000	−0.351391
$657$	4.00000	0.156055
$658$	−20.0000	−0.779681
$659$	27.0000	1.05177	0.525885	−	0.850555i	$-0.323734\pi$
$659$	27.0000	1.05177	0.525885	+	0.850555i	$0.323734\pi$
$660$	6.00000	0.233550
$661$	28.0000	1.08907	0.544537	−	0.838737i	$-0.316705\pi$
$661$	28.0000	1.08907	0.544537	+	0.838737i	$0.316705\pi$
$662$	16.0000	0.621858
$663$	12.0000	0.466041
$664$	0	0
$665$	−12.0000	−0.465340
$666$	2.00000	0.0774984
$667$	2.00000	0.0774403
$668$	−7.00000	−0.270838
$669$	52.0000	2.01044
$670$	−18.0000	−0.695401
$671$	7.00000	0.270232
$672$	−4.00000	−0.154303
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	8.00000	0.308148
$675$	16.0000	0.615840
$676$	23.0000	0.884615
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	4.00000	0.153506
$680$	3.00000	0.115045
$681$	−36.0000	−1.37952
$682$	4.00000	0.153168
$683$	14.0000	0.535695	0.267848	−	0.963461i	$-0.413688\pi$
$683$	14.0000	0.535695	0.267848	+	0.963461i	$0.413688\pi$
$684$	−2.00000	−0.0764719
$685$	−9.00000	−0.343872
$686$	−20.0000	−0.763604
$687$	0	0
$688$	−5.00000	−0.190623
$689$	12.0000	0.457164
$690$	6.00000	0.228416
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	5.00000	0.190071
$693$	−2.00000	−0.0759737
$694$	−13.0000	−0.493473
$695$	57.0000	2.16213
$696$	4.00000	0.151620
$697$	−9.00000	−0.340899
$698$	−26.0000	−0.984115
$699$	42.0000	1.58859
$700$	8.00000	0.302372
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	−24.0000	−0.905822
$703$	−4.00000	−0.150863
$704$	−1.00000	−0.0376889
$705$	60.0000	2.25973
$706$	9.00000	0.338719
$707$	0	0
$708$	−12.0000	−0.450988
$709$	−42.0000	−1.57734	−0.788672	−	0.614815i	$-0.789231\pi$
$709$	−42.0000	−1.57734	−0.788672	+	0.614815i	$0.789231\pi$
$710$	6.00000	0.225176
$711$	−4.00000	−0.150012
$712$	0	0
$713$	4.00000	0.149801
$714$	−4.00000	−0.149696
$715$	18.0000	0.673162
$716$	20.0000	0.747435
$717$	24.0000	0.896296
$718$	−15.0000	−0.559795
$719$	−43.0000	−1.60363	−0.801815	−	0.597573i	$-0.796132\pi$
$719$	−43.0000	−1.60363	−0.801815	+	0.597573i	$0.796132\pi$
$720$	3.00000	0.111803
$721$	26.0000	0.968291
$722$	−15.0000	−0.558242
$723$	−30.0000	−1.11571
$724$	12.0000	0.445976
$725$	−8.00000	−0.297113
$726$	20.0000	0.742270
$727$	−19.0000	−0.704671	−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000	−0.704671	−0.352335	+	0.935874i	$0.614612\pi$
$728$	−12.0000	−0.444750
$729$	13.0000	0.481481
$730$	12.0000	0.444140
$731$	−5.00000	−0.184932
$732$	14.0000	0.517455
$733$	8.00000	0.295487	0.147743	−	0.989026i	$-0.452799\pi$
$733$	8.00000	0.295487	0.147743	+	0.989026i	$0.452799\pi$
$734$	−22.0000	−0.812035
$735$	18.0000	0.663940
$736$	−1.00000	−0.0368605
$737$	6.00000	0.221013
$738$	−9.00000	−0.331295
$739$	10.0000	0.367856	0.183928	−	0.982940i	$-0.441119\pi$
$739$	10.0000	0.367856	0.183928	+	0.982940i	$0.441119\pi$
$740$	6.00000	0.220564
$741$	−24.0000	−0.881662
$742$	−4.00000	−0.146845
$743$	51.0000	1.87101	0.935504	−	0.353315i	$-0.114946\pi$
$743$	51.0000	1.87101	0.935504	+	0.353315i	$0.114946\pi$
$744$	8.00000	0.293294
$745$	−30.0000	−1.09911
$746$	12.0000	0.439351
$747$	0	0
$748$	−1.00000	−0.0365636
$749$	−14.0000	−0.511549
$750$	6.00000	0.219089
$751$	19.0000	0.693320	0.346660	−	0.937991i	$-0.387316\pi$
$751$	19.0000	0.693320	0.346660	+	0.937991i	$0.387316\pi$
$752$	−10.0000	−0.364662
$753$	−24.0000	−0.874609
$754$	12.0000	0.437014
$755$	−9.00000	−0.327544
$756$	8.00000	0.290957
$757$	−11.0000	−0.399802	−0.199901	−	0.979816i	$-0.564062\pi$
$757$	−11.0000	−0.399802	−0.199901	+	0.979816i	$0.564062\pi$
$758$	5.00000	0.181608
$759$	−2.00000	−0.0725954
$760$	−6.00000	−0.217643
$761$	−50.0000	−1.81250	−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000	−1.81250	−0.906249	+	0.422744i	$0.861067\pi$
$762$	8.00000	0.289809
$763$	10.0000	0.362024
$764$	18.0000	0.651217
$765$	3.00000	0.108465
$766$	6.00000	0.216789
$767$	−36.0000	−1.29988
$768$	−2.00000	−0.0721688
$769$	28.0000	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$769$	28.0000	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$770$	−6.00000	−0.216225
$771$	48.0000	1.72868
$772$	15.0000	0.539862
$773$	−14.0000	−0.503545	−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000	−0.503545	−0.251773	+	0.967786i	$0.581013\pi$
$774$	−5.00000	−0.179721
$775$	−16.0000	−0.574737
$776$	2.00000	0.0717958
$777$	−8.00000	−0.286998
$778$	−12.0000	−0.430221
$779$	18.0000	0.644917
$780$	36.0000	1.28901
$781$	−2.00000	−0.0715656
$782$	−1.00000	−0.0357599
$783$	−8.00000	−0.285897
$784$	−3.00000	−0.107143
$785$	−30.0000	−1.07075
$786$	−2.00000	−0.0713376
$787$	7.00000	0.249523	0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000	0.249523	0.124762	+	0.992187i	$0.460183\pi$
$788$	−11.0000	−0.391859
$789$	−52.0000	−1.85125
$790$	−12.0000	−0.426941
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	42.0000	1.49146
$794$	−8.00000	−0.283909
$795$	12.0000	0.425596
$796$	25.0000	0.886102
$797$	7.00000	0.247953	0.123976	−	0.992285i	$-0.460435\pi$
$797$	7.00000	0.247953	0.123976	+	0.992285i	$0.460435\pi$
$798$	8.00000	0.283197
$799$	−10.0000	−0.353775
$800$	4.00000	0.141421
$801$	0	0
$802$	−22.0000	−0.776847
$803$	−4.00000	−0.141157
$804$	12.0000	0.423207
$805$	−6.00000	−0.211472
$806$	24.0000	0.845364
$807$	28.0000	0.985647
$808$	0	0
$809$	−36.0000	−1.26569	−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000	−1.26569	−0.632846	+	0.774277i	$0.718114\pi$
$810$	−33.0000	−1.15950
$811$	−50.0000	−1.75574	−0.877869	−	0.478901i	$-0.841035\pi$
$811$	−50.0000	−1.75574	−0.877869	+	0.478901i	$0.841035\pi$
$812$	−4.00000	−0.140372
$813$	18.0000	0.631288
$814$	−2.00000	−0.0701000
$815$	−45.0000	−1.57628
$816$	−2.00000	−0.0700140
$817$	10.0000	0.349856
$818$	1.00000	0.0349642
$819$	−12.0000	−0.419314
$820$	−27.0000	−0.942881
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	6.00000	0.209274
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	13.0000	0.452876
$825$	8.00000	0.278524
$826$	12.0000	0.417533
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	−1.00000	−0.0347524
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	0	0
$831$	−4.00000	−0.138758
$832$	−6.00000	−0.208013
$833$	−3.00000	−0.103944
$834$	−38.0000	−1.31583
$835$	−21.0000	−0.726735
$836$	2.00000	0.0691714
$837$	−16.0000	−0.553041
$838$	−12.0000	−0.414533
$839$	10.0000	0.345238	0.172619	−	0.984989i	$-0.444777\pi$
$839$	10.0000	0.345238	0.172619	+	0.984989i	$0.444777\pi$
$840$	−12.0000	−0.414039
$841$	−25.0000	−0.862069
$842$	6.00000	0.206774
$843$	6.00000	0.206651
$844$	−10.0000	−0.344214
$845$	69.0000	2.37367
$846$	−10.0000	−0.343807
$847$	−20.0000	−0.687208
$848$	−2.00000	−0.0686803
$849$	16.0000	0.549119
$850$	4.00000	0.137199
$851$	−2.00000	−0.0685591
$852$	−4.00000	−0.137038
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	−14.0000	−0.479070
$855$	−6.00000	−0.205196
$856$	−7.00000	−0.239255
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	−12.0000	−0.409673
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	−15.0000	−0.511496
$861$	36.0000	1.22688
$862$	−36.0000	−1.22616
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	4.00000	0.136083
$865$	15.0000	0.510015
$866$	−25.0000	−0.849535
$867$	32.0000	1.08678
$868$	−8.00000	−0.271538
$869$	4.00000	0.135691
$870$	12.0000	0.406838
$871$	36.0000	1.21981
$872$	5.00000	0.169321
$873$	2.00000	0.0676897
$874$	2.00000	0.0676510
$875$	−6.00000	−0.202837
$876$	−8.00000	−0.270295
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	−27.0000	−0.911206
$879$	36.0000	1.21425
$880$	−3.00000	−0.101130
$881$	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
$883$	−27.0000	−0.908622	−0.454311	−	0.890843i	$-0.650115\pi$
$883$	−27.0000	−0.908622	−0.454311	+	0.890843i	$0.650115\pi$
$884$	−6.00000	−0.201802
$885$	−36.0000	−1.21013
$886$	12.0000	0.403148
$887$	−41.0000	−1.37665	−0.688323	−	0.725405i	$-0.741653\pi$
$887$	−41.0000	−1.37665	−0.688323	+	0.725405i	$0.741653\pi$
$888$	−4.00000	−0.134231
$889$	−8.00000	−0.268311
$890$	0	0
$891$	11.0000	0.368514
$892$	−26.0000	−0.870544
$893$	20.0000	0.669274
$894$	20.0000	0.668900
$895$	60.0000	2.00558
$896$	2.00000	0.0668153
$897$	−12.0000	−0.400668
$898$	−30.0000	−1.00111
$899$	8.00000	0.266815
$900$	4.00000	0.133333
$901$	−2.00000	−0.0666297
$902$	9.00000	0.299667
$903$	20.0000	0.665558
$904$	0	0
$905$	36.0000	1.19668
$906$	6.00000	0.199337
$907$	−1.00000	−0.0332045	−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000	−0.0332045	−0.0166022	+	0.999862i	$0.505285\pi$
$908$	18.0000	0.597351
$909$	0	0
$910$	−36.0000	−1.19339
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	−4.00000	−0.132308
$915$	42.0000	1.38848
$916$	0	0
$917$	2.00000	0.0660458
$918$	4.00000	0.132020
$919$	−25.0000	−0.824674	−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000	−0.824674	−0.412337	+	0.911031i	$0.635287\pi$
$920$	−3.00000	−0.0989071
$921$	−68.0000	−2.24068
$922$	−37.0000	−1.21853
$923$	−12.0000	−0.394985
$924$	4.00000	0.131590
$925$	8.00000	0.263038
$926$	24.0000	0.788689
$927$	13.0000	0.426976
$928$	−2.00000	−0.0656532
$929$	25.0000	0.820223	0.410112	−	0.912035i	$-0.365490\pi$
$929$	25.0000	0.820223	0.410112	+	0.912035i	$0.365490\pi$
$930$	24.0000	0.786991
$931$	6.00000	0.196642
$932$	−21.0000	−0.687878
$933$	−38.0000	−1.24406
$934$	25.0000	0.818025
$935$	−3.00000	−0.0981105
$936$	−6.00000	−0.196116
$937$	50.0000	1.63343	0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000	1.63343	0.816714	+	0.577042i	$0.195793\pi$
$938$	−12.0000	−0.391814
$939$	−20.0000	−0.652675
$940$	−30.0000	−0.978492
$941$	−22.0000	−0.717180	−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000	−0.717180	−0.358590	+	0.933495i	$0.616742\pi$
$942$	20.0000	0.651635
$943$	9.00000	0.293080
$944$	6.00000	0.195283
$945$	24.0000	0.780720
$946$	5.00000	0.162564
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	8.00000	0.259828
$949$	−24.0000	−0.779073
$950$	−8.00000	−0.259554
$951$	24.0000	0.778253
$952$	2.00000	0.0648204
$953$	−12.0000	−0.388718	−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000	−0.388718	−0.194359	+	0.980930i	$0.562263\pi$
$954$	−2.00000	−0.0647524
$955$	54.0000	1.74740
$956$	−12.0000	−0.388108
$957$	−4.00000	−0.129302
$958$	−11.0000	−0.355394
$959$	−6.00000	−0.193750
$960$	−6.00000	−0.193649
$961$	−15.0000	−0.483871
$962$	−12.0000	−0.386896
$963$	−7.00000	−0.225572
$964$	15.0000	0.483117
$965$	45.0000	1.44860
$966$	4.00000	0.128698
$967$	−20.0000	−0.643157	−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000	−0.643157	−0.321578	+	0.946883i	$0.604213\pi$
$968$	−10.0000	−0.321412
$969$	4.00000	0.128499
$970$	6.00000	0.192648
$971$	40.0000	1.28366	0.641831	−	0.766846i	$-0.278175\pi$
$971$	40.0000	1.28366	0.641831	+	0.766846i	$0.278175\pi$
$972$	10.0000	0.320750
$973$	38.0000	1.21822
$974$	−31.0000	−0.993304
$975$	48.0000	1.53723
$976$	−7.00000	−0.224065
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	30.0000	0.959294
$979$	0	0
$980$	−9.00000	−0.287494
$981$	5.00000	0.159638
$982$	−15.0000	−0.478669
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	18.0000	0.573819
$985$	−33.0000	−1.05147
$986$	−2.00000	−0.0636930
$987$	40.0000	1.27321
$988$	12.0000	0.381771
$989$	5.00000	0.158991
$990$	−3.00000	−0.0953463
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	−4.00000	−0.127000
$993$	−32.0000	−1.01549
$994$	4.00000	0.126872
$995$	75.0000	2.37766
$996$	0	0
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	21.0000	0.664743
$999$	8.00000	0.253109

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.c.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

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