LMFDB - Embedded newform 4830.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.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:	$38.5677441763$
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	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -10.0000 q^{29} +1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} -2.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -1.00000 q^{42} -8.00000 q^{43} -1.00000 q^{45} -1.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} +2.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +1.00000 q^{56} +4.00000 q^{57} -10.0000 q^{58} +12.0000 q^{59} +1.00000 q^{60} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} -8.00000 q^{67} -2.00000 q^{68} +1.00000 q^{69} -1.00000 q^{70} +8.00000 q^{71} +1.00000 q^{72} +10.0000 q^{73} -6.00000 q^{74} -1.00000 q^{75} -4.00000 q^{76} -2.00000 q^{78} -8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} -4.00000 q^{83} -1.00000 q^{84} +2.00000 q^{85} -8.00000 q^{86} +10.0000 q^{87} +14.0000 q^{89} -1.00000 q^{90} +2.00000 q^{91} -1.00000 q^{92} +4.00000 q^{93} +12.0000 q^{94} +4.00000 q^{95} -1.00000 q^{96} -18.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	1.00000	0.182574
$31$	−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
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−4.00000	−0.648886
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−1.00000	−0.154303
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	2.00000	0.280056
$52$	2.00000	0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	−10.0000	−1.31306
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.00000	−0.508001
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−2.00000	−0.242536
$69$	1.00000	0.120386
$70$	−1.00000	−0.119523
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	1.00000	0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−6.00000	−0.697486
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	−1.00000	−0.109109
$85$	2.00000	0.216930
$86$	−8.00000	−0.862662
$87$	10.0000	1.07211
$88$	0	0
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	−1.00000	−0.105409
$91$	2.00000	0.209657
$92$	−1.00000	−0.104257
$93$	4.00000	0.414781
$94$	12.0000	1.23771
$95$	4.00000	0.410391
$96$	−1.00000	−0.102062
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	2.00000	0.198030
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	2.00000	0.196116
$105$	1.00000	0.0975900
$106$	−6.00000	−0.582772
$107$	−16.0000	−1.54678	−0.773389	−	0.633932i	$-0.781440\pi$
$107$	−16.0000	−1.54678	−0.773389	+	0.633932i	$0.781440\pi$
$108$	−1.00000	−0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	1.00000	0.0944911
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	4.00000	0.374634
$115$	1.00000	0.0932505
$116$	−10.0000	−0.928477
$117$	2.00000	0.184900
$118$	12.0000	1.10469
$119$	−2.00000	−0.183340
$120$	1.00000	0.0912871
$121$	−11.0000	−1.00000
$122$	2.00000	0.181071
$123$	−2.00000	−0.180334
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	1.00000	0.0890871
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	−2.00000	−0.175412
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	−8.00000	−0.691095
$135$	1.00000	0.0860663
$136$	−2.00000	−0.171499
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	1.00000	0.0851257
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	−1.00000	−0.0845154
$141$	−12.0000	−1.01058
$142$	8.00000	0.671345
$143$	0	0
$144$	1.00000	0.0833333
$145$	10.0000	0.830455
$146$	10.0000	0.827606
$147$	−1.00000	−0.0824786
$148$	−6.00000	−0.493197
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	−1.00000	−0.0816497
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−4.00000	−0.324443
$153$	−2.00000	−0.161690
$154$	0	0
$155$	4.00000	0.321288
$156$	−2.00000	−0.160128
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	−8.00000	−0.636446
$159$	6.00000	0.475831
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−4.00000	−0.310460
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	2.00000	0.153393
$171$	−4.00000	−0.305888
$172$	−8.00000	−0.609994
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	10.0000	0.758098
$175$	1.00000	0.0755929
$176$	0	0
$177$	−12.0000	−0.901975
$178$	14.0000	1.04934
$179$	−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
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	2.00000	0.148250
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	6.00000	0.441129
$186$	4.00000	0.293294
$187$	0	0
$188$	12.0000	0.875190
$189$	−1.00000	−0.0727393
$190$	4.00000	0.290191
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−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	$0.275675\pi$
$194$	−18.0000	−1.29232
$195$	2.00000	0.143223
$196$	1.00000	0.0714286
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	0	0
$199$	−24.0000	−1.70131	−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000	−1.70131	−0.850657	+	0.525720i	$0.823796\pi$
$200$	1.00000	0.0707107
$201$	8.00000	0.564276
$202$	−6.00000	−0.422159
$203$	−10.0000	−0.701862
$204$	2.00000	0.140028
$205$	−2.00000	−0.139686
$206$	−8.00000	−0.557386
$207$	−1.00000	−0.0695048
$208$	2.00000	0.138675
$209$	0	0
$210$	1.00000	0.0690066
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−6.00000	−0.412082
$213$	−8.00000	−0.548151
$214$	−16.0000	−1.09374
$215$	8.00000	0.545595
$216$	−1.00000	−0.0680414
$217$	−4.00000	−0.271538
$218$	2.00000	0.135457
$219$	−10.0000	−0.675737
$220$	0	0
$221$	−4.00000	−0.269069
$222$	6.00000	0.402694
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	10.0000	0.665190
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	4.00000	0.264906
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	−10.0000	−0.656532
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	2.00000	0.130744
$235$	−12.0000	−0.782794
$236$	12.0000	0.781133
$237$	8.00000	0.519656
$238$	−2.00000	−0.129641
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	1.00000	0.0645497
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	−11.0000	−0.707107
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	−1.00000	−0.0638877
$246$	−2.00000	−0.127515
$247$	−8.00000	−0.509028
$248$	−4.00000	−0.254000
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	1.00000	0.0629941
$253$	0	0
$254$	−8.00000	−0.501965
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	8.00000	0.498058
$259$	−6.00000	−0.372822
$260$	−2.00000	−0.124035
$261$	−10.0000	−0.618984
$262$	−12.0000	−0.741362
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−4.00000	−0.245256
$267$	−14.0000	−0.856786
$268$	−8.00000	−0.488678
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	1.00000	0.0608581
$271$	−28.0000	−1.70088	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000	−1.70088	−0.850439	+	0.526073i	$0.823664\pi$
$272$	−2.00000	−0.121268
$273$	−2.00000	−0.121046
$274$	−14.0000	−0.845771
$275$	0	0
$276$	1.00000	0.0601929
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−12.0000	−0.719712
$279$	−4.00000	−0.239474
$280$	−1.00000	−0.0597614
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−12.0000	−0.714590
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	8.00000	0.474713
$285$	−4.00000	−0.236940
$286$	0	0
$287$	2.00000	0.118056
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	10.0000	0.587220
$291$	18.0000	1.05518
$292$	10.0000	0.585206
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−1.00000	−0.0583212
$295$	−12.0000	−0.698667
$296$	−6.00000	−0.348743
$297$	0	0
$298$	−14.0000	−0.810998
$299$	−2.00000	−0.115663
$300$	−1.00000	−0.0577350
$301$	−8.00000	−0.461112
$302$	−8.00000	−0.460348
$303$	6.00000	0.344691
$304$	−4.00000	−0.229416
$305$	−2.00000	−0.114520
$306$	−2.00000	−0.114332
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	4.00000	0.227185
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−2.00000	−0.113228
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	2.00000	0.112867
$315$	−1.00000	−0.0563436
$316$	−8.00000	−0.450035
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	6.00000	0.336463
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	16.0000	0.893033
$322$	−1.00000	−0.0557278
$323$	8.00000	0.445132
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	−4.00000	−0.221540
$327$	−2.00000	−0.110600
$328$	2.00000	0.110432
$329$	12.0000	0.661581
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	−4.00000	−0.219529
$333$	−6.00000	−0.328798
$334$	12.0000	0.656611
$335$	8.00000	0.437087
$336$	−1.00000	−0.0545545
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−9.00000	−0.489535
$339$	−10.0000	−0.543125
$340$	2.00000	0.108465
$341$	0	0
$342$	−4.00000	−0.216295
$343$	1.00000	0.0539949
$344$	−8.00000	−0.431331
$345$	−1.00000	−0.0538382
$346$	−6.00000	−0.322562
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	10.0000	0.536056
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	1.00000	0.0534522
$351$	−2.00000	−0.106752
$352$	0	0
$353$	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
$355$	−8.00000	−0.424596
$356$	14.0000	0.741999
$357$	2.00000	0.105851
$358$	−12.0000	−0.634220
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	10.0000	0.525588
$363$	11.0000	0.577350
$364$	2.00000	0.104828
$365$	−10.0000	−0.523424
$366$	−2.00000	−0.104542
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−1.00000	−0.0521286
$369$	2.00000	0.104116
$370$	6.00000	0.311925
$371$	−6.00000	−0.311504
$372$	4.00000	0.207390
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	12.0000	0.618853
$377$	−20.0000	−1.03005
$378$	−1.00000	−0.0514344
$379$	32.0000	1.64373	0.821865	−	0.569683i	$-0.192934\pi$
$379$	32.0000	1.64373	0.821865	+	0.569683i	$0.192934\pi$
$380$	4.00000	0.205196
$381$	8.00000	0.409852
$382$	0	0
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	18.0000	0.916176
$387$	−8.00000	−0.406663
$388$	−18.0000	−0.913812
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	2.00000	0.101274
$391$	2.00000	0.101144
$392$	1.00000	0.0505076
$393$	12.0000	0.605320
$394$	−2.00000	−0.100759
$395$	8.00000	0.402524
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−24.0000	−1.20301
$399$	4.00000	0.200250
$400$	1.00000	0.0500000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	8.00000	0.399004
$403$	−8.00000	−0.398508
$404$	−6.00000	−0.298511
$405$	−1.00000	−0.0496904
$406$	−10.0000	−0.496292
$407$	0	0
$408$	2.00000	0.0990148
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	−2.00000	−0.0987730
$411$	14.0000	0.690569
$412$	−8.00000	−0.394132
$413$	12.0000	0.590481
$414$	−1.00000	−0.0491473
$415$	4.00000	0.196352
$416$	2.00000	0.0980581
$417$	12.0000	0.587643
$418$	0	0
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	1.00000	0.0487950
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	−4.00000	−0.194717
$423$	12.0000	0.583460
$424$	−6.00000	−0.291386
$425$	−2.00000	−0.0970143
$426$	−8.00000	−0.387601
$427$	2.00000	0.0967868
$428$	−16.0000	−0.773389
$429$	0	0
$430$	8.00000	0.385794
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−1.00000	−0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−4.00000	−0.192006
$435$	−10.0000	−0.479463
$436$	2.00000	0.0957826
$437$	4.00000	0.191346
$438$	−10.0000	−0.477818
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−4.00000	−0.190261
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	6.00000	0.284747
$445$	−14.0000	−0.663664
$446$	−4.00000	−0.189405
$447$	14.0000	0.662177
$448$	1.00000	0.0472456
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	10.0000	0.470360
$453$	8.00000	0.375873
$454$	12.0000	0.563188
$455$	−2.00000	−0.0937614
$456$	4.00000	0.187317
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	−6.00000	−0.280362
$459$	2.00000	0.0933520
$460$	1.00000	0.0466252
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−10.0000	−0.464238
$465$	−4.00000	−0.185496
$466$	26.0000	1.20443
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	2.00000	0.0924500
$469$	−8.00000	−0.369406
$470$	−12.0000	−0.553519
$471$	−2.00000	−0.0921551
$472$	12.0000	0.552345
$473$	0	0
$474$	8.00000	0.367452
$475$	−4.00000	−0.183533
$476$	−2.00000	−0.0916698
$477$	−6.00000	−0.274721
$478$	−24.0000	−1.09773
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	−12.0000	−0.547153
$482$	14.0000	0.637683
$483$	1.00000	0.0455016
$484$	−11.0000	−0.500000
$485$	18.0000	0.817338
$486$	−1.00000	−0.0453609
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	2.00000	0.0905357
$489$	4.00000	0.180886
$490$	−1.00000	−0.0451754
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	−2.00000	−0.0901670
$493$	20.0000	0.900755
$494$	−8.00000	−0.359937
$495$	0	0
$496$	−4.00000	−0.179605
$497$	8.00000	0.358849
$498$	4.00000	0.179244
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	−1.00000	−0.0447214
$501$	−12.0000	−0.536120
$502$	20.0000	0.892644
$503$	−40.0000	−1.78351	−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000	−1.78351	−0.891756	+	0.452517i	$0.850526\pi$
$504$	1.00000	0.0445435
$505$	6.00000	0.266996
$506$	0	0
$507$	9.00000	0.399704
$508$	−8.00000	−0.354943
$509$	42.0000	1.86162	0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000	1.86162	0.930809	+	0.365507i	$0.119104\pi$
$510$	−2.00000	−0.0885615
$511$	10.0000	0.442374
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	−22.0000	−0.970378
$515$	8.00000	0.352522
$516$	8.00000	0.352180
$517$	0	0
$518$	−6.00000	−0.263625
$519$	6.00000	0.263371
$520$	−2.00000	−0.0877058
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	−10.0000	−0.437688
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−12.0000	−0.524222
$525$	−1.00000	−0.0436436
$526$	24.0000	1.04645
$527$	8.00000	0.348485
$528$	0	0
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	12.0000	0.520756
$532$	−4.00000	−0.173422
$533$	4.00000	0.173259
$534$	−14.0000	−0.605839
$535$	16.0000	0.691740
$536$	−8.00000	−0.345547
$537$	12.0000	0.517838
$538$	−6.00000	−0.258678
$539$	0	0
$540$	1.00000	0.0430331
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−28.0000	−1.20270
$543$	−10.0000	−0.429141
$544$	−2.00000	−0.0857493
$545$	−2.00000	−0.0856706
$546$	−2.00000	−0.0855921
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	−14.0000	−0.598050
$549$	2.00000	0.0853579
$550$	0	0
$551$	40.0000	1.70406
$552$	1.00000	0.0425628
$553$	−8.00000	−0.340195
$554$	22.0000	0.934690
$555$	−6.00000	−0.254686
$556$	−12.0000	−0.508913
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	−4.00000	−0.169334
$559$	−16.0000	−0.676728
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−12.0000	−0.505291
$565$	−10.0000	−0.420703
$566$	12.0000	0.504398
$567$	1.00000	0.0419961
$568$	8.00000	0.335673
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	−4.00000	−0.167542
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	0	0
$573$	0	0
$574$	2.00000	0.0834784
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	−13.0000	−0.540729
$579$	−18.0000	−0.748054
$580$	10.0000	0.415227
$581$	−4.00000	−0.165948
$582$	18.0000	0.746124
$583$	0	0
$584$	10.0000	0.413803
$585$	−2.00000	−0.0826898
$586$	−6.00000	−0.247858
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	−1.00000	−0.0412393
$589$	16.0000	0.659269
$590$	−12.0000	−0.494032
$591$	2.00000	0.0822690
$592$	−6.00000	−0.246598
$593$	10.0000	0.410651	0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000	0.410651	0.205325	+	0.978694i	$0.434175\pi$
$594$	0	0
$595$	2.00000	0.0819920
$596$	−14.0000	−0.573462
$597$	24.0000	0.982255
$598$	−2.00000	−0.0817861
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	−1.00000	−0.0408248
$601$	18.0000	0.734235	0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000	0.734235	0.367118	+	0.930175i	$0.380345\pi$
$602$	−8.00000	−0.326056
$603$	−8.00000	−0.325785
$604$	−8.00000	−0.325515
$605$	11.0000	0.447214
$606$	6.00000	0.243733
$607$	20.0000	0.811775	0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000	0.811775	0.405887	+	0.913923i	$0.366962\pi$
$608$	−4.00000	−0.162221
$609$	10.0000	0.405220
$610$	−2.00000	−0.0809776
$611$	24.0000	0.970936
$612$	−2.00000	−0.0808452
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	−12.0000	−0.484281
$615$	2.00000	0.0806478
$616$	0	0
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	8.00000	0.321807
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	4.00000	0.160644
$621$	1.00000	0.0401286
$622$	4.00000	0.160385
$623$	14.0000	0.560898
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	0	0
$628$	2.00000	0.0798087
$629$	12.0000	0.478471
$630$	−1.00000	−0.0398410
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−8.00000	−0.318223
$633$	4.00000	0.158986
$634$	22.0000	0.873732
$635$	8.00000	0.317470
$636$	6.00000	0.237915
$637$	2.00000	0.0792429
$638$	0	0
$639$	8.00000	0.316475
$640$	−1.00000	−0.0395285
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	16.0000	0.631470
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	−1.00000	−0.0394055
$645$	−8.00000	−0.315000
$646$	8.00000	0.314756
$647$	−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
$649$	0	0
$650$	2.00000	0.0784465
$651$	4.00000	0.156772
$652$	−4.00000	−0.156652
$653$	38.0000	1.48705	0.743527	−	0.668705i	$-0.233151\pi$
$653$	38.0000	1.48705	0.743527	+	0.668705i	$0.233151\pi$
$654$	−2.00000	−0.0782062
$655$	12.0000	0.468879
$656$	2.00000	0.0780869
$657$	10.0000	0.390137
$658$	12.0000	0.467809
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	0	0
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	28.0000	1.08825
$663$	4.00000	0.155347
$664$	−4.00000	−0.155230
$665$	4.00000	0.155113
$666$	−6.00000	−0.232495
$667$	10.0000	0.387202
$668$	12.0000	0.464294
$669$	4.00000	0.154649
$670$	8.00000	0.309067
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	26.0000	1.00148
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−38.0000	−1.46046	−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000	−1.46046	−0.730229	+	0.683202i	$0.760587\pi$
$678$	−10.0000	−0.384048
$679$	−18.0000	−0.690777
$680$	2.00000	0.0766965
$681$	−12.0000	−0.459841
$682$	0	0
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	−4.00000	−0.152944
$685$	14.0000	0.534913
$686$	1.00000	0.0381802
$687$	6.00000	0.228914
$688$	−8.00000	−0.304997
$689$	−12.0000	−0.457164
$690$	−1.00000	−0.0380693
$691$	12.0000	0.456502	0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000	0.456502	0.228251	+	0.973602i	$0.426699\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−4.00000	−0.151838
$695$	12.0000	0.455186
$696$	10.0000	0.379049
$697$	−4.00000	−0.151511
$698$	−30.0000	−1.13552
$699$	−26.0000	−0.983410
$700$	1.00000	0.0377964
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	−2.00000	−0.0754851
$703$	24.0000	0.905177
$704$	0	0
$705$	12.0000	0.451946
$706$	18.0000	0.677439
$707$	−6.00000	−0.225653
$708$	−12.0000	−0.450988
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	−8.00000	−0.300235
$711$	−8.00000	−0.300023
$712$	14.0000	0.524672
$713$	4.00000	0.149801
$714$	2.00000	0.0748481
$715$	0	0
$716$	−12.0000	−0.448461
$717$	24.0000	0.896296
$718$	−8.00000	−0.298557
$719$	−12.0000	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$720$	−1.00000	−0.0372678
$721$	−8.00000	−0.297936
$722$	−3.00000	−0.111648
$723$	−14.0000	−0.520666
$724$	10.0000	0.371647
$725$	−10.0000	−0.371391
$726$	11.0000	0.408248
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	2.00000	0.0741249
$729$	1.00000	0.0370370
$730$	−10.0000	−0.370117
$731$	16.0000	0.591781
$732$	−2.00000	−0.0739221
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	8.00000	0.295285
$735$	1.00000	0.0368856
$736$	−1.00000	−0.0368605
$737$	0	0
$738$	2.00000	0.0736210
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	6.00000	0.220564
$741$	8.00000	0.293887
$742$	−6.00000	−0.220267
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	4.00000	0.146647
$745$	14.0000	0.512920
$746$	−6.00000	−0.219676
$747$	−4.00000	−0.146352
$748$	0	0
$749$	−16.0000	−0.584627
$750$	1.00000	0.0365148
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	12.0000	0.437595
$753$	−20.0000	−0.728841
$754$	−20.0000	−0.728357
$755$	8.00000	0.291150
$756$	−1.00000	−0.0363696
$757$	−46.0000	−1.67190	−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000	−1.67190	−0.835949	+	0.548807i	$0.815082\pi$
$758$	32.0000	1.16229
$759$	0	0
$760$	4.00000	0.145095
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	8.00000	0.289809
$763$	2.00000	0.0724049
$764$	0	0
$765$	2.00000	0.0723102
$766$	8.00000	0.289052
$767$	24.0000	0.866590
$768$	−1.00000	−0.0360844
$769$	−50.0000	−1.80305	−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000	−1.80305	−0.901523	+	0.432731i	$0.857550\pi$
$770$	0	0
$771$	22.0000	0.792311
$772$	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
$775$	−4.00000	−0.143684
$776$	−18.0000	−0.646162
$777$	6.00000	0.215249
$778$	10.0000	0.358517
$779$	−8.00000	−0.286630
$780$	2.00000	0.0716115
$781$	0	0
$782$	2.00000	0.0715199
$783$	10.0000	0.357371
$784$	1.00000	0.0357143
$785$	−2.00000	−0.0713831
$786$	12.0000	0.428026
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−2.00000	−0.0712470
$789$	−24.0000	−0.854423
$790$	8.00000	0.284627
$791$	10.0000	0.355559
$792$	0	0
$793$	4.00000	0.142044
$794$	2.00000	0.0709773
$795$	−6.00000	−0.212798
$796$	−24.0000	−0.850657
$797$	50.0000	1.77109	0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000	1.77109	0.885545	+	0.464553i	$0.153785\pi$
$798$	4.00000	0.141598
$799$	−24.0000	−0.849059
$800$	1.00000	0.0353553
$801$	14.0000	0.494666
$802$	−6.00000	−0.211867
$803$	0	0
$804$	8.00000	0.282138
$805$	1.00000	0.0352454
$806$	−8.00000	−0.281788
$807$	6.00000	0.211210
$808$	−6.00000	−0.211079
$809$	42.0000	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$810$	−1.00000	−0.0351364
$811$	−4.00000	−0.140459	−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000	−0.140459	−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−10.0000	−0.350931
$813$	28.0000	0.982003
$814$	0	0
$815$	4.00000	0.140114
$816$	2.00000	0.0700140
$817$	32.0000	1.11954
$818$	−6.00000	−0.209785
$819$	2.00000	0.0698857
$820$	−2.00000	−0.0698430
$821$	46.0000	1.60541	0.802706	−	0.596376i	$-0.203393\pi$
$821$	46.0000	1.60541	0.802706	+	0.596376i	$0.203393\pi$
$822$	14.0000	0.488306
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	12.0000	0.417533
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	−1.00000	−0.0347524
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	4.00000	0.138842
$831$	−22.0000	−0.763172
$832$	2.00000	0.0693375
$833$	−2.00000	−0.0692959
$834$	12.0000	0.415526
$835$	−12.0000	−0.415277
$836$	0	0
$837$	4.00000	0.138260
$838$	−20.0000	−0.690889
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	1.00000	0.0345033
$841$	71.0000	2.44828
$842$	−14.0000	−0.482472
$843$	6.00000	0.206651
$844$	−4.00000	−0.137686
$845$	9.00000	0.309609
$846$	12.0000	0.412568
$847$	−11.0000	−0.377964
$848$	−6.00000	−0.206041
$849$	−12.0000	−0.411839
$850$	−2.00000	−0.0685994
$851$	6.00000	0.205677
$852$	−8.00000	−0.274075
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	2.00000	0.0684386
$855$	4.00000	0.136797
$856$	−16.0000	−0.546869
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	8.00000	0.272798
$861$	−2.00000	−0.0681598
$862$	24.0000	0.817443
$863$	−56.0000	−1.90626	−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000	−1.90626	−0.953131	+	0.302558i	$0.902160\pi$
$864$	−1.00000	−0.0340207
$865$	6.00000	0.204006
$866$	14.0000	0.475739
$867$	13.0000	0.441503
$868$	−4.00000	−0.135769
$869$	0	0
$870$	−10.0000	−0.339032
$871$	−16.0000	−0.542139
$872$	2.00000	0.0677285
$873$	−18.0000	−0.609208
$874$	4.00000	0.135302
$875$	−1.00000	−0.0338062
$876$	−10.0000	−0.337869
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	20.0000	0.674967
$879$	6.00000	0.202375
$880$	0	0
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	1.00000	0.0336718
$883$	−28.0000	−0.942275	−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000	−0.942275	−0.471138	+	0.882060i	$0.656156\pi$
$884$	−4.00000	−0.134535
$885$	12.0000	0.403376
$886$	−4.00000	−0.134383
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	6.00000	0.201347
$889$	−8.00000	−0.268311
$890$	−14.0000	−0.469281
$891$	0	0
$892$	−4.00000	−0.133930
$893$	−48.0000	−1.60626
$894$	14.0000	0.468230
$895$	12.0000	0.401116
$896$	1.00000	0.0334077
$897$	2.00000	0.0667781
$898$	−14.0000	−0.467186
$899$	40.0000	1.33407
$900$	1.00000	0.0333333
$901$	12.0000	0.399778
$902$	0	0
$903$	8.00000	0.266223
$904$	10.0000	0.332595
$905$	−10.0000	−0.332411
$906$	8.00000	0.265782
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	12.0000	0.398234
$909$	−6.00000	−0.199007
$910$	−2.00000	−0.0662994
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	2.00000	0.0661541
$915$	2.00000	0.0661180
$916$	−6.00000	−0.198246
$917$	−12.0000	−0.396275
$918$	2.00000	0.0660098
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	1.00000	0.0329690
$921$	12.0000	0.395413
$922$	10.0000	0.329332
$923$	16.0000	0.526646
$924$	0	0
$925$	−6.00000	−0.197279
$926$	−16.0000	−0.525793
$927$	−8.00000	−0.262754
$928$	−10.0000	−0.328266
$929$	−22.0000	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$930$	−4.00000	−0.131165
$931$	−4.00000	−0.131095
$932$	26.0000	0.851658
$933$	−4.00000	−0.130954
$934$	−12.0000	−0.392652
$935$	0	0
$936$	2.00000	0.0653720
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	−8.00000	−0.261209
$939$	18.0000	0.587408
$940$	−12.0000	−0.391397
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−2.00000	−0.0651635
$943$	−2.00000	−0.0651290
$944$	12.0000	0.390567
$945$	1.00000	0.0325300
$946$	0	0
$947$	20.0000	0.649913	0.324956	−	0.945729i	$-0.394650\pi$
$947$	20.0000	0.649913	0.324956	+	0.945729i	$0.394650\pi$
$948$	8.00000	0.259828
$949$	20.0000	0.649227
$950$	−4.00000	−0.129777
$951$	−22.0000	−0.713399
$952$	−2.00000	−0.0648204
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	−24.0000	−0.776215
$957$	0	0
$958$	−24.0000	−0.775405
$959$	−14.0000	−0.452084
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	−12.0000	−0.386896
$963$	−16.0000	−0.515593
$964$	14.0000	0.450910
$965$	−18.0000	−0.579441
$966$	1.00000	0.0321745
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−11.0000	−0.353553
$969$	−8.00000	−0.256997
$970$	18.0000	0.577945
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−1.00000	−0.0320750
$973$	−12.0000	−0.384702
$974$	40.0000	1.28168
$975$	−2.00000	−0.0640513
$976$	2.00000	0.0640184
$977$	26.0000	0.831814	0.415907	−	0.909407i	$-0.363464\pi$
$977$	26.0000	0.831814	0.415907	+	0.909407i	$0.363464\pi$
$978$	4.00000	0.127906
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	2.00000	0.0638551
$982$	−12.0000	−0.382935
$983$	−56.0000	−1.78612	−0.893061	−	0.449935i	$-0.851447\pi$
$983$	−56.0000	−1.78612	−0.893061	+	0.449935i	$0.851447\pi$
$984$	−2.00000	−0.0637577
$985$	2.00000	0.0637253
$986$	20.0000	0.636930
$987$	−12.0000	−0.381964
$988$	−8.00000	−0.254514
$989$	8.00000	0.254385
$990$	0	0
$991$	−32.0000	−1.01651	−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000	−1.01651	−0.508257	+	0.861206i	$0.669710\pi$
$992$	−4.00000	−0.127000
$993$	−28.0000	−0.888553
$994$	8.00000	0.253745
$995$	24.0000	0.760851
$996$	4.00000	0.126745
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	4.00000	0.126618
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.t.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.t.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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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