LMFDB - Embedded newform 4026.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
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	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +4.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} +2.00000 q^{20} -4.00000 q^{21} +1.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +4.00000 q^{28} -2.00000 q^{29} -2.00000 q^{30} +10.0000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +6.00000 q^{34} +8.00000 q^{35} +1.00000 q^{36} +6.00000 q^{37} -6.00000 q^{38} -2.00000 q^{39} +2.00000 q^{40} -8.00000 q^{41} -4.00000 q^{42} -8.00000 q^{43} +1.00000 q^{44} +2.00000 q^{45} +4.00000 q^{46} -1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{50} -6.00000 q^{51} +2.00000 q^{52} -1.00000 q^{54} +2.00000 q^{55} +4.00000 q^{56} +6.00000 q^{57} -2.00000 q^{58} -12.0000 q^{59} -2.00000 q^{60} +1.00000 q^{61} +10.0000 q^{62} +4.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -1.00000 q^{66} +2.00000 q^{67} +6.00000 q^{68} -4.00000 q^{69} +8.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} -10.0000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -6.00000 q^{76} +4.00000 q^{77} -2.00000 q^{78} +2.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} +8.00000 q^{83} -4.00000 q^{84} +12.0000 q^{85} -8.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} +12.0000 q^{89} +2.00000 q^{90} +8.00000 q^{91} +4.00000 q^{92} -10.0000 q^{93} -12.0000 q^{95} -1.00000 q^{96} -2.00000 q^{97} +9.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−1.00000	−0.408248
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	4.00000	1.06904
$15$	−2.00000	−0.516398
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	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	$0.741620\pi$
$20$	2.00000	0.447214
$21$	−4.00000	−0.872872
$22$	1.00000	0.213201
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	−1.00000	−0.204124
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	4.00000	0.755929
$29$	−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
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	6.00000	1.02899
$35$	8.00000	1.35225
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−6.00000	−0.973329
$39$	−2.00000	−0.320256
$40$	2.00000	0.316228
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−4.00000	−0.617213
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	1.00000	0.150756
$45$	2.00000	0.298142
$46$	4.00000	0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	−6.00000	−0.840168
$52$	2.00000	0.277350
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	−1.00000	−0.136083
$55$	2.00000	0.269680
$56$	4.00000	0.534522
$57$	6.00000	0.794719
$58$	−2.00000	−0.262613
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	−2.00000	−0.258199
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	10.0000	1.27000
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	−1.00000	−0.123091
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	6.00000	0.727607
$69$	−4.00000	−0.481543
$70$	8.00000	0.956183
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	6.00000	0.697486
$75$	1.00000	0.115470
$76$	−6.00000	−0.688247
$77$	4.00000	0.455842
$78$	−2.00000	−0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	−8.00000	−0.883452
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	−4.00000	−0.436436
$85$	12.0000	1.30158
$86$	−8.00000	−0.862662
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	2.00000	0.210819
$91$	8.00000	0.838628
$92$	4.00000	0.417029
$93$	−10.0000	−1.03695
$94$	0	0
$95$	−12.0000	−1.23117
$96$	−1.00000	−0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	9.00000	0.909137
$99$	1.00000	0.100504
$100$	−1.00000	−0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	−6.00000	−0.594089
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.00000	0.196116
$105$	−8.00000	−0.780720
$106$	0	0
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	2.00000	0.190693
$111$	−6.00000	−0.569495
$112$	4.00000	0.377964
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	6.00000	0.561951
$115$	8.00000	0.746004
$116$	−2.00000	−0.185695
$117$	2.00000	0.184900
$118$	−12.0000	−1.10469
$119$	24.0000	2.20008
$120$	−2.00000	−0.182574
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	8.00000	0.721336
$124$	10.0000	0.898027
$125$	−12.0000	−1.07331
$126$	4.00000	0.356348
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	4.00000	0.350823
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−1.00000	−0.0870388
$133$	−24.0000	−2.08106
$134$	2.00000	0.172774
$135$	−2.00000	−0.172133
$136$	6.00000	0.514496
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	−4.00000	−0.340503
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	8.00000	0.676123
$141$	0	0
$142$	−12.0000	−1.00702
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	−4.00000	−0.332182
$146$	−10.0000	−0.827606
$147$	−9.00000	−0.742307
$148$	6.00000	0.493197
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	1.00000	0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−6.00000	−0.486664
$153$	6.00000	0.485071
$154$	4.00000	0.322329
$155$	20.0000	1.60644
$156$	−2.00000	−0.160128
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	0	0
$159$	0	0
$160$	2.00000	0.158114
$161$	16.0000	1.26098
$162$	1.00000	0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−8.00000	−0.624695
$165$	−2.00000	−0.155700
$166$	8.00000	0.620920
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	−4.00000	−0.308607
$169$	−9.00000	−0.692308
$170$	12.0000	0.920358
$171$	−6.00000	−0.458831
$172$	−8.00000	−0.609994
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	2.00000	0.151620
$175$	−4.00000	−0.302372
$176$	1.00000	0.0753778
$177$	12.0000	0.901975
$178$	12.0000	0.899438
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	2.00000	0.149071
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	8.00000	0.592999
$183$	−1.00000	−0.0739221
$184$	4.00000	0.294884
$185$	12.0000	0.882258
$186$	−10.0000	−0.733236
$187$	6.00000	0.438763
$188$	0	0
$189$	−4.00000	−0.290957
$190$	−12.0000	−0.870572
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	−1.00000	−0.0721688
$193$	18.0000	1.29567	0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000	1.29567	0.647834	+	0.761781i	$0.275675\pi$
$194$	−2.00000	−0.143592
$195$	−4.00000	−0.286446
$196$	9.00000	0.642857
$197$	16.0000	1.13995	0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000	1.13995	0.569976	+	0.821661i	$0.306952\pi$
$198$	1.00000	0.0710669
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−1.00000	−0.0707107
$201$	−2.00000	−0.141069
$202$	−10.0000	−0.703598
$203$	−8.00000	−0.561490
$204$	−6.00000	−0.420084
$205$	−16.0000	−1.11749
$206$	−4.00000	−0.278693
$207$	4.00000	0.278019
$208$	2.00000	0.138675
$209$	−6.00000	−0.415029
$210$	−8.00000	−0.552052
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	0	0
$213$	12.0000	0.822226
$214$	−4.00000	−0.273434
$215$	−16.0000	−1.09119
$216$	−1.00000	−0.0680414
$217$	40.0000	2.71538
$218$	−6.00000	−0.406371
$219$	10.0000	0.675737
$220$	2.00000	0.134840
$221$	12.0000	0.807207
$222$	−6.00000	−0.402694
$223$	18.0000	1.20537	0.602685	−	0.797980i	$-0.294098\pi$
$223$	18.0000	1.20537	0.602685	+	0.797980i	$0.294098\pi$
$224$	4.00000	0.267261
$225$	−1.00000	−0.0666667
$226$	2.00000	0.133038
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	6.00000	0.397360
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	8.00000	0.527504
$231$	−4.00000	−0.263181
$232$	−2.00000	−0.131306
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−12.0000	−0.781133
$237$	0	0
$238$	24.0000	1.55569
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	−2.00000	−0.129099
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	18.0000	1.14998
$246$	8.00000	0.510061
$247$	−12.0000	−0.763542
$248$	10.0000	0.635001
$249$	−8.00000	−0.506979
$250$	−12.0000	−0.758947
$251$	−16.0000	−1.00991	−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000	−1.00991	−0.504956	+	0.863145i	$0.668491\pi$
$252$	4.00000	0.251976
$253$	4.00000	0.251478
$254$	−14.0000	−0.878438
$255$	−12.0000	−0.751469
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	8.00000	0.498058
$259$	24.0000	1.49129
$260$	4.00000	0.248069
$261$	−2.00000	−0.123797
$262$	−12.0000	−0.741362
$263$	−4.00000	−0.246651	−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000	−0.246651	−0.123325	+	0.992366i	$0.539356\pi$
$264$	−1.00000	−0.0615457
$265$	0	0
$266$	−24.0000	−1.47153
$267$	−12.0000	−0.734388
$268$	2.00000	0.122169
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−2.00000	−0.121716
$271$	−30.0000	−1.82237	−0.911185	−	0.411997i	$-0.864831\pi$
$271$	−30.0000	−1.82237	−0.911185	+	0.411997i	$0.864831\pi$
$272$	6.00000	0.363803
$273$	−8.00000	−0.484182
$274$	18.0000	1.08742
$275$	−1.00000	−0.0603023
$276$	−4.00000	−0.240772
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−12.0000	−0.719712
$279$	10.0000	0.598684
$280$	8.00000	0.478091
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	0	0
$283$	10.0000	0.594438	0.297219	−	0.954809i	$-0.403941\pi$
$283$	10.0000	0.594438	0.297219	+	0.954809i	$0.403941\pi$
$284$	−12.0000	−0.712069
$285$	12.0000	0.710819
$286$	2.00000	0.118262
$287$	−32.0000	−1.88890
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	−4.00000	−0.234888
$291$	2.00000	0.117242
$292$	−10.0000	−0.585206
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	−9.00000	−0.524891
$295$	−24.0000	−1.39733
$296$	6.00000	0.348743
$297$	−1.00000	−0.0580259
$298$	0	0
$299$	8.00000	0.462652
$300$	1.00000	0.0577350
$301$	−32.0000	−1.84445
$302$	−4.00000	−0.230174
$303$	10.0000	0.574485
$304$	−6.00000	−0.344124
$305$	2.00000	0.114520
$306$	6.00000	0.342997
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	4.00000	0.227921
$309$	4.00000	0.227552
$310$	20.0000	1.13592
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	−2.00000	−0.113228
$313$	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
$315$	8.00000	0.450749
$316$	0	0
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	0	0
$319$	−2.00000	−0.111979
$320$	2.00000	0.111803
$321$	4.00000	0.223258
$322$	16.0000	0.891645
$323$	−36.0000	−2.00309
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	12.0000	0.664619
$327$	6.00000	0.331801
$328$	−8.00000	−0.441726
$329$	0	0
$330$	−2.00000	−0.110096
$331$	30.0000	1.64895	0.824475	−	0.565899i	$-0.191471\pi$
$331$	30.0000	1.64895	0.824475	+	0.565899i	$0.191471\pi$
$332$	8.00000	0.439057
$333$	6.00000	0.328798
$334$	24.0000	1.31322
$335$	4.00000	0.218543
$336$	−4.00000	−0.218218
$337$	30.0000	1.63420	0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000	1.63420	0.817102	+	0.576493i	$0.195579\pi$
$338$	−9.00000	−0.489535
$339$	−2.00000	−0.108625
$340$	12.0000	0.650791
$341$	10.0000	0.541530
$342$	−6.00000	−0.324443
$343$	8.00000	0.431959
$344$	−8.00000	−0.431331
$345$	−8.00000	−0.430706
$346$	18.0000	0.967686
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	2.00000	0.107211
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−4.00000	−0.213809
$351$	−2.00000	−0.106752
$352$	1.00000	0.0533002
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	12.0000	0.637793
$355$	−24.0000	−1.27379
$356$	12.0000	0.635999
$357$	−24.0000	−1.27021
$358$	−4.00000	−0.211407
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	2.00000	0.105409
$361$	17.0000	0.894737
$362$	10.0000	0.525588
$363$	−1.00000	−0.0524864
$364$	8.00000	0.419314
$365$	−20.0000	−1.04685
$366$	−1.00000	−0.0522708
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	4.00000	0.208514
$369$	−8.00000	−0.416463
$370$	12.0000	0.623850
$371$	0	0
$372$	−10.0000	−0.518476
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	6.00000	0.310253
$375$	12.0000	0.619677
$376$	0	0
$377$	−4.00000	−0.206010
$378$	−4.00000	−0.205738
$379$	−36.0000	−1.84920	−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000	−1.84920	−0.924598	+	0.380945i	$0.875599\pi$
$380$	−12.0000	−0.615587
$381$	14.0000	0.717242
$382$	8.00000	0.409316
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	−1.00000	−0.0510310
$385$	8.00000	0.407718
$386$	18.0000	0.916176
$387$	−8.00000	−0.406663
$388$	−2.00000	−0.101535
$389$	−16.0000	−0.811232	−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000	−0.811232	−0.405616	+	0.914044i	$0.632943\pi$
$390$	−4.00000	−0.202548
$391$	24.0000	1.21373
$392$	9.00000	0.454569
$393$	12.0000	0.605320
$394$	16.0000	0.806068
$395$	0	0
$396$	1.00000	0.0502519
$397$	6.00000	0.301131	0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000	0.301131	0.150566	+	0.988600i	$0.451890\pi$
$398$	−4.00000	−0.200502
$399$	24.0000	1.20150
$400$	−1.00000	−0.0500000
$401$	−4.00000	−0.199750	−0.0998752	−	0.995000i	$-0.531844\pi$
$401$	−4.00000	−0.199750	−0.0998752	+	0.995000i	$0.531844\pi$
$402$	−2.00000	−0.0997509
$403$	20.0000	0.996271
$404$	−10.0000	−0.497519
$405$	2.00000	0.0993808
$406$	−8.00000	−0.397033
$407$	6.00000	0.297409
$408$	−6.00000	−0.297044
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	−16.0000	−0.790184
$411$	−18.0000	−0.887875
$412$	−4.00000	−0.197066
$413$	−48.0000	−2.36193
$414$	4.00000	0.196589
$415$	16.0000	0.785409
$416$	2.00000	0.0980581
$417$	12.0000	0.587643
$418$	−6.00000	−0.293470
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	−8.00000	−0.390360
$421$	−38.0000	−1.85201	−0.926003	−	0.377515i	$-0.876779\pi$
$421$	−38.0000	−1.85201	−0.926003	+	0.377515i	$0.876779\pi$
$422$	−12.0000	−0.584151
$423$	0	0
$424$	0	0
$425$	−6.00000	−0.291043
$426$	12.0000	0.581402
$427$	4.00000	0.193574
$428$	−4.00000	−0.193347
$429$	−2.00000	−0.0965609
$430$	−16.0000	−0.771589
$431$	4.00000	0.192673	0.0963366	−	0.995349i	$-0.469287\pi$
$431$	4.00000	0.192673	0.0963366	+	0.995349i	$0.469287\pi$
$432$	−1.00000	−0.0481125
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	40.0000	1.92006
$435$	4.00000	0.191785
$436$	−6.00000	−0.287348
$437$	−24.0000	−1.14808
$438$	10.0000	0.477818
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	2.00000	0.0953463
$441$	9.00000	0.428571
$442$	12.0000	0.570782
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	−6.00000	−0.284747
$445$	24.0000	1.13771
$446$	18.0000	0.852325
$447$	0	0
$448$	4.00000	0.188982
$449$	38.0000	1.79333	0.896665	−	0.442709i	$-0.145982\pi$
$449$	38.0000	1.79333	0.896665	+	0.442709i	$0.145982\pi$
$450$	−1.00000	−0.0471405
$451$	−8.00000	−0.376705
$452$	2.00000	0.0940721
$453$	4.00000	0.187936
$454$	12.0000	0.563188
$455$	16.0000	0.750092
$456$	6.00000	0.280976
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	−6.00000	−0.280362
$459$	−6.00000	−0.280056
$460$	8.00000	0.373002
$461$	−8.00000	−0.372597	−0.186299	−	0.982493i	$-0.559649\pi$
$461$	−8.00000	−0.372597	−0.186299	+	0.982493i	$0.559649\pi$
$462$	−4.00000	−0.186097
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−2.00000	−0.0928477
$465$	−20.0000	−0.927478
$466$	−18.0000	−0.833834
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	2.00000	0.0924500
$469$	8.00000	0.369406
$470$	0	0
$471$	10.0000	0.460776
$472$	−12.0000	−0.552345
$473$	−8.00000	−0.367840
$474$	0	0
$475$	6.00000	0.275299
$476$	24.0000	1.10004
$477$	0	0
$478$	8.00000	0.365911
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	−2.00000	−0.0912871
$481$	12.0000	0.547153
$482$	22.0000	1.00207
$483$	−16.0000	−0.728025
$484$	1.00000	0.0454545
$485$	−4.00000	−0.181631
$486$	−1.00000	−0.0453609
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	1.00000	0.0452679
$489$	−12.0000	−0.542659
$490$	18.0000	0.813157
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	8.00000	0.360668
$493$	−12.0000	−0.540453
$494$	−12.0000	−0.539906
$495$	2.00000	0.0898933
$496$	10.0000	0.449013
$497$	−48.0000	−2.15309
$498$	−8.00000	−0.358489
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	−12.0000	−0.536656
$501$	−24.0000	−1.07224
$502$	−16.0000	−0.714115
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	4.00000	0.178174
$505$	−20.0000	−0.889988
$506$	4.00000	0.177822
$507$	9.00000	0.399704
$508$	−14.0000	−0.621150
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	−12.0000	−0.531369
$511$	−40.0000	−1.76950
$512$	1.00000	0.0441942
$513$	6.00000	0.264906
$514$	6.00000	0.264649
$515$	−8.00000	−0.352522
$516$	8.00000	0.352180
$517$	0	0
$518$	24.0000	1.05450
$519$	−18.0000	−0.790112
$520$	4.00000	0.175412
$521$	16.0000	0.700973	0.350486	−	0.936568i	$-0.386016\pi$
$521$	16.0000	0.700973	0.350486	+	0.936568i	$0.386016\pi$
$522$	−2.00000	−0.0875376
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−12.0000	−0.524222
$525$	4.00000	0.174574
$526$	−4.00000	−0.174408
$527$	60.0000	2.61364
$528$	−1.00000	−0.0435194
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−12.0000	−0.520756
$532$	−24.0000	−1.04053
$533$	−16.0000	−0.693037
$534$	−12.0000	−0.519291
$535$	−8.00000	−0.345870
$536$	2.00000	0.0863868
$537$	4.00000	0.172613
$538$	−10.0000	−0.431131
$539$	9.00000	0.387657
$540$	−2.00000	−0.0860663
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−30.0000	−1.28861
$543$	−10.0000	−0.429141
$544$	6.00000	0.257248
$545$	−12.0000	−0.514024
$546$	−8.00000	−0.342368
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	18.0000	0.768922
$549$	1.00000	0.0426790
$550$	−1.00000	−0.0426401
$551$	12.0000	0.511217
$552$	−4.00000	−0.170251
$553$	0	0
$554$	−10.0000	−0.424859
$555$	−12.0000	−0.509372
$556$	−12.0000	−0.508913
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	10.0000	0.423334
$559$	−16.0000	−0.676728
$560$	8.00000	0.338062
$561$	−6.00000	−0.253320
$562$	−14.0000	−0.590554
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	4.00000	0.168281
$566$	10.0000	0.420331
$567$	4.00000	0.167984
$568$	−12.0000	−0.503509
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	12.0000	0.502625
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	2.00000	0.0836242
$573$	−8.00000	−0.334205
$574$	−32.0000	−1.33565
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	19.0000	0.790296
$579$	−18.0000	−0.748054
$580$	−4.00000	−0.166091
$581$	32.0000	1.32758
$582$	2.00000	0.0829027
$583$	0	0
$584$	−10.0000	−0.413803
$585$	4.00000	0.165380
$586$	24.0000	0.991431
$587$	32.0000	1.32078	0.660391	−	0.750922i	$-0.270391\pi$
$587$	32.0000	1.32078	0.660391	+	0.750922i	$0.270391\pi$
$588$	−9.00000	−0.371154
$589$	−60.0000	−2.47226
$590$	−24.0000	−0.988064
$591$	−16.0000	−0.658152
$592$	6.00000	0.246598
$593$	−22.0000	−0.903432	−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000	−0.903432	−0.451716	+	0.892162i	$0.649188\pi$
$594$	−1.00000	−0.0410305
$595$	48.0000	1.96781
$596$	0	0
$597$	4.00000	0.163709
$598$	8.00000	0.327144
$599$	44.0000	1.79779	0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000	1.79779	0.898896	+	0.438163i	$0.144371\pi$
$600$	1.00000	0.0408248
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	−32.0000	−1.30422
$603$	2.00000	0.0814463
$604$	−4.00000	−0.162758
$605$	2.00000	0.0813116
$606$	10.0000	0.406222
$607$	26.0000	1.05531	0.527654	−	0.849460i	$-0.323072\pi$
$607$	26.0000	1.05531	0.527654	+	0.849460i	$0.323072\pi$
$608$	−6.00000	−0.243332
$609$	8.00000	0.324176
$610$	2.00000	0.0809776
$611$	0	0
$612$	6.00000	0.242536
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	0	0
$615$	16.0000	0.645182
$616$	4.00000	0.161165
$617$	40.0000	1.61034	0.805170	−	0.593045i	$-0.202074\pi$
$617$	40.0000	1.61034	0.805170	+	0.593045i	$0.202074\pi$
$618$	4.00000	0.160904
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	20.0000	0.803219
$621$	−4.00000	−0.160514
$622$	−16.0000	−0.641542
$623$	48.0000	1.92308
$624$	−2.00000	−0.0800641
$625$	−19.0000	−0.760000
$626$	10.0000	0.399680
$627$	6.00000	0.239617
$628$	−10.0000	−0.399043
$629$	36.0000	1.43541
$630$	8.00000	0.318728
$631$	−46.0000	−1.83123	−0.915616	−	0.402055i	$-0.868296\pi$
$631$	−46.0000	−1.83123	−0.915616	+	0.402055i	$0.868296\pi$
$632$	0	0
$633$	12.0000	0.476957
$634$	14.0000	0.556011
$635$	−28.0000	−1.11115
$636$	0	0
$637$	18.0000	0.713186
$638$	−2.00000	−0.0791808
$639$	−12.0000	−0.474713
$640$	2.00000	0.0790569
$641$	−20.0000	−0.789953	−0.394976	−	0.918691i	$-0.629247\pi$
$641$	−20.0000	−0.789953	−0.394976	+	0.918691i	$0.629247\pi$
$642$	4.00000	0.157867
$643$	−50.0000	−1.97181	−0.985904	−	0.167313i	$-0.946491\pi$
$643$	−50.0000	−1.97181	−0.985904	+	0.167313i	$0.946491\pi$
$644$	16.0000	0.630488
$645$	16.0000	0.629999
$646$	−36.0000	−1.41640
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	1.00000	0.0392837
$649$	−12.0000	−0.471041
$650$	−2.00000	−0.0784465
$651$	−40.0000	−1.56772
$652$	12.0000	0.469956
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	6.00000	0.234619
$655$	−24.0000	−0.937758
$656$	−8.00000	−0.312348
$657$	−10.0000	−0.390137
$658$	0	0
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	−2.00000	−0.0778499
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	30.0000	1.16598
$663$	−12.0000	−0.466041
$664$	8.00000	0.310460
$665$	−48.0000	−1.86136
$666$	6.00000	0.232495
$667$	−8.00000	−0.309761
$668$	24.0000	0.928588
$669$	−18.0000	−0.695920
$670$	4.00000	0.154533
$671$	1.00000	0.0386046
$672$	−4.00000	−0.154303
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	30.0000	1.15556
$675$	1.00000	0.0384900
$676$	−9.00000	−0.346154
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−2.00000	−0.0768095
$679$	−8.00000	−0.307012
$680$	12.0000	0.460179
$681$	−12.0000	−0.459841
$682$	10.0000	0.382920
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	−6.00000	−0.229416
$685$	36.0000	1.37549
$686$	8.00000	0.305441
$687$	6.00000	0.228914
$688$	−8.00000	−0.304997
$689$	0	0
$690$	−8.00000	−0.304555
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	18.0000	0.684257
$693$	4.00000	0.151947
$694$	12.0000	0.455514
$695$	−24.0000	−0.910372
$696$	2.00000	0.0758098
$697$	−48.0000	−1.81813
$698$	2.00000	0.0757011
$699$	18.0000	0.680823
$700$	−4.00000	−0.151186
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	−2.00000	−0.0754851
$703$	−36.0000	−1.35777
$704$	1.00000	0.0376889
$705$	0	0
$706$	18.0000	0.677439
$707$	−40.0000	−1.50435
$708$	12.0000	0.450988
$709$	−30.0000	−1.12667	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000	−1.12667	−0.563337	+	0.826227i	$0.690483\pi$
$710$	−24.0000	−0.900704
$711$	0	0
$712$	12.0000	0.449719
$713$	40.0000	1.49801
$714$	−24.0000	−0.898177
$715$	4.00000	0.149592
$716$	−4.00000	−0.149487
$717$	−8.00000	−0.298765
$718$	24.0000	0.895672
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	2.00000	0.0745356
$721$	−16.0000	−0.595871
$722$	17.0000	0.632674
$723$	−22.0000	−0.818189
$724$	10.0000	0.371647
$725$	2.00000	0.0742781
$726$	−1.00000	−0.0371135
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	−20.0000	−0.740233
$731$	−48.0000	−1.77534
$732$	−1.00000	−0.0369611
$733$	26.0000	0.960332	0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000	0.960332	0.480166	+	0.877178i	$0.340576\pi$
$734$	−28.0000	−1.03350
$735$	−18.0000	−0.663940
$736$	4.00000	0.147442
$737$	2.00000	0.0736709
$738$	−8.00000	−0.294484
$739$	28.0000	1.03000	0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000	1.03000	0.514998	+	0.857191i	$0.327793\pi$
$740$	12.0000	0.441129
$741$	12.0000	0.440831
$742$	0	0
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	−10.0000	−0.366618
$745$	0	0
$746$	−14.0000	−0.512576
$747$	8.00000	0.292705
$748$	6.00000	0.219382
$749$	−16.0000	−0.584627
$750$	12.0000	0.438178
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	0	0
$753$	16.0000	0.583072
$754$	−4.00000	−0.145671
$755$	−8.00000	−0.291150
$756$	−4.00000	−0.145479
$757$	42.0000	1.52652	0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000	1.52652	0.763258	+	0.646094i	$0.223599\pi$
$758$	−36.0000	−1.30758
$759$	−4.00000	−0.145191
$760$	−12.0000	−0.435286
$761$	−14.0000	−0.507500	−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000	−0.507500	−0.253750	+	0.967270i	$0.581664\pi$
$762$	14.0000	0.507166
$763$	−24.0000	−0.868858
$764$	8.00000	0.289430
$765$	12.0000	0.433861
$766$	36.0000	1.30073
$767$	−24.0000	−0.866590
$768$	−1.00000	−0.0360844
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	8.00000	0.288300
$771$	−6.00000	−0.216085
$772$	18.0000	0.647834
$773$	26.0000	0.935155	0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000	0.935155	0.467578	+	0.883952i	$0.345127\pi$
$774$	−8.00000	−0.287554
$775$	−10.0000	−0.359211
$776$	−2.00000	−0.0717958
$777$	−24.0000	−0.860995
$778$	−16.0000	−0.573628
$779$	48.0000	1.71978
$780$	−4.00000	−0.143223
$781$	−12.0000	−0.429394
$782$	24.0000	0.858238
$783$	2.00000	0.0714742
$784$	9.00000	0.321429
$785$	−20.0000	−0.713831
$786$	12.0000	0.428026
$787$	−16.0000	−0.570338	−0.285169	−	0.958477i	$-0.592050\pi$
$787$	−16.0000	−0.570338	−0.285169	+	0.958477i	$0.592050\pi$
$788$	16.0000	0.569976
$789$	4.00000	0.142404
$790$	0	0
$791$	8.00000	0.284447
$792$	1.00000	0.0355335
$793$	2.00000	0.0710221
$794$	6.00000	0.212932
$795$	0	0
$796$	−4.00000	−0.141776
$797$	−22.0000	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$798$	24.0000	0.849591
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	12.0000	0.423999
$802$	−4.00000	−0.141245
$803$	−10.0000	−0.352892
$804$	−2.00000	−0.0705346
$805$	32.0000	1.12785
$806$	20.0000	0.704470
$807$	10.0000	0.352017
$808$	−10.0000	−0.351799
$809$	28.0000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$809$	28.0000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$810$	2.00000	0.0702728
$811$	−52.0000	−1.82597	−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000	−1.82597	−0.912983	+	0.407997i	$0.866228\pi$
$812$	−8.00000	−0.280745
$813$	30.0000	1.05215
$814$	6.00000	0.210300
$815$	24.0000	0.840683
$816$	−6.00000	−0.210042
$817$	48.0000	1.67931
$818$	−10.0000	−0.349642
$819$	8.00000	0.279543
$820$	−16.0000	−0.558744
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	−18.0000	−0.627822
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	−4.00000	−0.139347
$825$	1.00000	0.0348155
$826$	−48.0000	−1.67013
$827$	40.0000	1.39094	0.695468	−	0.718557i	$-0.255197\pi$
$827$	40.0000	1.39094	0.695468	+	0.718557i	$0.255197\pi$
$828$	4.00000	0.139010
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	16.0000	0.555368
$831$	10.0000	0.346896
$832$	2.00000	0.0693375
$833$	54.0000	1.87099
$834$	12.0000	0.415526
$835$	48.0000	1.66111
$836$	−6.00000	−0.207514
$837$	−10.0000	−0.345651
$838$	−12.0000	−0.414533
$839$	8.00000	0.276191	0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000	0.276191	0.138095	+	0.990419i	$0.455902\pi$
$840$	−8.00000	−0.276026
$841$	−25.0000	−0.862069
$842$	−38.0000	−1.30957
$843$	14.0000	0.482186
$844$	−12.0000	−0.413057
$845$	−18.0000	−0.619219
$846$	0	0
$847$	4.00000	0.137442
$848$	0	0
$849$	−10.0000	−0.343199
$850$	−6.00000	−0.205798
$851$	24.0000	0.822709
$852$	12.0000	0.411113
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	4.00000	0.136877
$855$	−12.0000	−0.410391
$856$	−4.00000	−0.136717
$857$	−4.00000	−0.136637	−0.0683187	−	0.997664i	$-0.521763\pi$
$857$	−4.00000	−0.136637	−0.0683187	+	0.997664i	$0.521763\pi$
$858$	−2.00000	−0.0682789
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	−16.0000	−0.545595
$861$	32.0000	1.09056
$862$	4.00000	0.136241
$863$	−32.0000	−1.08929	−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000	−1.08929	−0.544646	+	0.838666i	$0.683336\pi$
$864$	−1.00000	−0.0340207
$865$	36.0000	1.22404
$866$	−38.0000	−1.29129
$867$	−19.0000	−0.645274
$868$	40.0000	1.35769
$869$	0	0
$870$	4.00000	0.135613
$871$	4.00000	0.135535
$872$	−6.00000	−0.203186
$873$	−2.00000	−0.0676897
$874$	−24.0000	−0.811812
$875$	−48.0000	−1.62270
$876$	10.0000	0.337869
$877$	26.0000	0.877958	0.438979	−	0.898497i	$-0.355340\pi$
$877$	26.0000	0.877958	0.438979	+	0.898497i	$0.355340\pi$
$878$	−26.0000	−0.877457
$879$	−24.0000	−0.809500
$880$	2.00000	0.0674200
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	9.00000	0.303046
$883$	42.0000	1.41341	0.706706	−	0.707507i	$-0.250180\pi$
$883$	42.0000	1.41341	0.706706	+	0.707507i	$0.250180\pi$
$884$	12.0000	0.403604
$885$	24.0000	0.806751
$886$	−36.0000	−1.20944
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	−6.00000	−0.201347
$889$	−56.0000	−1.87818
$890$	24.0000	0.804482
$891$	1.00000	0.0335013
$892$	18.0000	0.602685
$893$	0	0
$894$	0	0
$895$	−8.00000	−0.267411
$896$	4.00000	0.133631
$897$	−8.00000	−0.267112
$898$	38.0000	1.26808
$899$	−20.0000	−0.667037
$900$	−1.00000	−0.0333333
$901$	0	0
$902$	−8.00000	−0.266371
$903$	32.0000	1.06489
$904$	2.00000	0.0665190
$905$	20.0000	0.664822
$906$	4.00000	0.132891
$907$	−34.0000	−1.12895	−0.564476	−	0.825450i	$-0.690922\pi$
$907$	−34.0000	−1.12895	−0.564476	+	0.825450i	$0.690922\pi$
$908$	12.0000	0.398234
$909$	−10.0000	−0.331679
$910$	16.0000	0.530395
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	6.00000	0.198680
$913$	8.00000	0.264761
$914$	22.0000	0.727695
$915$	−2.00000	−0.0661180
$916$	−6.00000	−0.198246
$917$	−48.0000	−1.58510
$918$	−6.00000	−0.198030
$919$	10.0000	0.329870	0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000	0.329870	0.164935	+	0.986304i	$0.447259\pi$
$920$	8.00000	0.263752
$921$	0	0
$922$	−8.00000	−0.263466
$923$	−24.0000	−0.789970
$924$	−4.00000	−0.131590
$925$	−6.00000	−0.197279
$926$	−24.0000	−0.788689
$927$	−4.00000	−0.131377
$928$	−2.00000	−0.0656532
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	−20.0000	−0.655826
$931$	−54.0000	−1.76978
$932$	−18.0000	−0.589610
$933$	16.0000	0.523816
$934$	12.0000	0.392652
$935$	12.0000	0.392442
$936$	2.00000	0.0653720
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	8.00000	0.261209
$939$	−10.0000	−0.326338
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	10.0000	0.325818
$943$	−32.0000	−1.04206
$944$	−12.0000	−0.390567
$945$	−8.00000	−0.260240
$946$	−8.00000	−0.260102
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	0	0
$949$	−20.0000	−0.649227
$950$	6.00000	0.194666
$951$	−14.0000	−0.453981
$952$	24.0000	0.777844
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	16.0000	0.517748
$956$	8.00000	0.258738
$957$	2.00000	0.0646508
$958$	−24.0000	−0.775405
$959$	72.0000	2.32500
$960$	−2.00000	−0.0645497
$961$	69.0000	2.22581
$962$	12.0000	0.386896
$963$	−4.00000	−0.128898
$964$	22.0000	0.708572
$965$	36.0000	1.15888
$966$	−16.0000	−0.514792
$967$	−42.0000	−1.35063	−0.675314	−	0.737530i	$-0.735992\pi$
$967$	−42.0000	−1.35063	−0.675314	+	0.737530i	$0.735992\pi$
$968$	1.00000	0.0321412
$969$	36.0000	1.15649
$970$	−4.00000	−0.128432
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−1.00000	−0.0320750
$973$	−48.0000	−1.53881
$974$	16.0000	0.512673
$975$	2.00000	0.0640513
$976$	1.00000	0.0320092
$977$	46.0000	1.47167	0.735835	−	0.677161i	$-0.236790\pi$
$977$	46.0000	1.47167	0.735835	+	0.677161i	$0.236790\pi$
$978$	−12.0000	−0.383718
$979$	12.0000	0.383522
$980$	18.0000	0.574989
$981$	−6.00000	−0.191565
$982$	−8.00000	−0.255290
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	8.00000	0.255031
$985$	32.0000	1.01960
$986$	−12.0000	−0.382158
$987$	0	0
$988$	−12.0000	−0.381771
$989$	−32.0000	−1.01754
$990$	2.00000	0.0635642
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	10.0000	0.317500
$993$	−30.0000	−0.952021
$994$	−48.0000	−1.52247
$995$	−8.00000	−0.253617
$996$	−8.00000	−0.253490
$997$	−62.0000	−1.96356	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000	−1.96356	−0.981780	+	0.190022i	$0.939144\pi$
$998$	−14.0000	−0.443162
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.g.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.g.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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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