LMFDB - Embedded newform 4830.2.a.c.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:	$0$
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	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

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

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−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
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−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
$22$	4.00000	0.852803
$23$	−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
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	−1.00000	−0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	0	0
$35$	−1.00000	−0.169031
$36$	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	$0.335828\pi$
$38$	4.00000	0.648886
$39$	2.00000	0.320256
$40$	1.00000	0.158114
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	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	$0.708828\pi$
$44$	−4.00000	−0.603023
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	1.00000	0.136083
$55$	4.00000	0.539360
$56$	−1.00000	−0.133631
$57$	4.00000	0.529813
$58$	−8.00000	−1.05045
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	1.00000	0.129099
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	8.00000	1.01600
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−4.00000	−0.492366
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	0	0
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.00000	−0.117851
$73$	16.0000	1.87266	0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000	1.87266	0.936329	+	0.351123i	$0.114200\pi$
$74$	−6.00000	−0.697486
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	−4.00000	−0.455842
$78$	−2.00000	−0.226455
$79$	16.0000	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	8.00000	0.862662
$87$	−8.00000	−0.857690
$88$	4.00000	0.426401
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	0.105409
$91$	−2.00000	−0.209657
$92$	−1.00000	−0.104257
$93$	8.00000	0.829561
$94$	0	0
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.00000	−0.101015
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	0	0
$103$	20.0000	1.97066	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	20.0000	1.97066	0.985329	+	0.170664i	$0.0545913\pi$
$104$	2.00000	0.196116
$105$	1.00000	0.0975900
$106$	12.0000	1.16554
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−1.00000	−0.0962250
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	−4.00000	−0.381385
$111$	−6.00000	−0.569495
$112$	1.00000	0.0944911
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−4.00000	−0.374634
$115$	1.00000	0.0932505
$116$	8.00000	0.742781
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	−10.0000	−0.905357
$123$	8.00000	0.721336
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	−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	$0.675644\pi$
$132$	4.00000	0.348155
$133$	−4.00000	−0.346844
$134$	0	0
$135$	1.00000	0.0860663
$136$	0	0
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	−1.00000	−0.0851257
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	−12.0000	−1.00702
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	−8.00000	−0.664364
$146$	−16.0000	−1.32417
$147$	−1.00000	−0.0824786
$148$	6.00000	0.493197
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	1.00000	0.0816497
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	4.00000	0.324443
$153$	0	0
$154$	4.00000	0.322329
$155$	8.00000	0.642575
$156$	2.00000	0.160128
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−16.0000	−1.27289
$159$	12.0000	0.951662
$160$	1.00000	0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	−8.00000	−0.624695
$165$	−4.00000	−0.311400
$166$	16.0000	1.24184
$167$	−20.0000	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$167$	−20.0000	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−4.00000	−0.305888
$172$	−8.00000	−0.609994
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	8.00000	0.606478
$175$	1.00000	0.0755929
$176$	−4.00000	−0.301511
$177$	4.00000	0.300658
$178$	6.00000	0.449719
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	−1.00000	−0.0745356
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	2.00000	0.148250
$183$	−10.0000	−0.739221
$184$	1.00000	0.0737210
$185$	−6.00000	−0.441129
$186$	−8.00000	−0.586588
$187$	0	0
$188$	0	0
$189$	−1.00000	−0.0727393
$190$	−4.00000	−0.290191
$191$	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
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−2.00000	−0.143592
$195$	−2.00000	−0.143223
$196$	1.00000	0.0714286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	4.00000	0.284268
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−2.00000	−0.140720
$203$	8.00000	0.561490
$204$	0	0
$205$	8.00000	0.558744
$206$	−20.0000	−1.39347
$207$	−1.00000	−0.0695048
$208$	−2.00000	−0.138675
$209$	16.0000	1.10674
$210$	−1.00000	−0.0690066
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	−12.0000	−0.824163
$213$	−12.0000	−0.822226
$214$	6.00000	0.410152
$215$	8.00000	0.545595
$216$	1.00000	0.0680414
$217$	−8.00000	−0.543075
$218$	−12.0000	−0.812743
$219$	−16.0000	−1.08118
$220$	4.00000	0.269680
$221$	0	0
$222$	6.00000	0.402694
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	14.0000	0.931266
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	4.00000	0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	−1.00000	−0.0659380
$231$	4.00000	0.263181
$232$	−8.00000	−0.525226
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−4.00000	−0.260378
$237$	−16.0000	−1.03931
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	1.00000	0.0645497
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	−5.00000	−0.321412
$243$	−1.00000	−0.0641500
$244$	10.0000	0.640184
$245$	−1.00000	−0.0638877
$246$	−8.00000	−0.510061
$247$	8.00000	0.509028
$248$	8.00000	0.508001
$249$	16.0000	1.01396
$250$	1.00000	0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	1.00000	0.0629941
$253$	4.00000	0.251478
$254$	12.0000	0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	−8.00000	−0.498058
$259$	6.00000	0.372822
$260$	2.00000	0.124035
$261$	8.00000	0.495188
$262$	12.0000	0.741362
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	−4.00000	−0.246183
$265$	12.0000	0.737154
$266$	4.00000	0.245256
$267$	6.00000	0.367194
$268$	0	0
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−1.00000	−0.0608581
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	0	0
$273$	2.00000	0.121046
$274$	−10.0000	−0.604122
$275$	−4.00000	−0.241209
$276$	1.00000	0.0601929
$277$	−20.0000	−1.20168	−0.600842	−	0.799368i	$-0.705168\pi$
$277$	−20.0000	−1.20168	−0.600842	+	0.799368i	$0.705168\pi$
$278$	4.00000	0.239904
$279$	−8.00000	−0.478947
$280$	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	$0.557275\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	12.0000	0.712069
$285$	−4.00000	−0.236940
$286$	−8.00000	−0.473050
$287$	−8.00000	−0.472225
$288$	−1.00000	−0.0589256
$289$	−17.0000	−1.00000
$290$	8.00000	0.469776
$291$	−2.00000	−0.117242
$292$	16.0000	0.936329
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	1.00000	0.0583212
$295$	4.00000	0.232889
$296$	−6.00000	−0.348743
$297$	4.00000	0.232104
$298$	−10.0000	−0.579284
$299$	2.00000	0.115663
$300$	−1.00000	−0.0577350
$301$	−8.00000	−0.461112
$302$	0	0
$303$	−2.00000	−0.114897
$304$	−4.00000	−0.229416
$305$	−10.0000	−0.572598
$306$	0	0
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	−4.00000	−0.227921
$309$	−20.0000	−1.13776
$310$	−8.00000	−0.454369
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	−2.00000	−0.113228
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	14.0000	0.790066
$315$	−1.00000	−0.0563436
$316$	16.0000	0.900070
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	−12.0000	−0.672927
$319$	−32.0000	−1.79166
$320$	−1.00000	−0.0559017
$321$	6.00000	0.334887
$322$	1.00000	0.0557278
$323$	0	0
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	18.0000	0.996928
$327$	−12.0000	−0.663602
$328$	8.00000	0.441726
$329$	0	0
$330$	4.00000	0.220193
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−16.0000	−0.878114
$333$	6.00000	0.328798
$334$	20.0000	1.09435
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	9.00000	0.489535
$339$	14.0000	0.760376
$340$	0	0
$341$	32.0000	1.73290
$342$	4.00000	0.216295
$343$	1.00000	0.0539949
$344$	8.00000	0.431331
$345$	−1.00000	−0.0538382
$346$	14.0000	0.752645
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	−8.00000	−0.428845
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	−1.00000	−0.0534522
$351$	2.00000	0.106752
$352$	4.00000	0.213201
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	−4.00000	−0.212598
$355$	−12.0000	−0.636894
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−10.0000	−0.528516
$359$	−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
$362$	−14.0000	−0.735824
$363$	−5.00000	−0.262432
$364$	−2.00000	−0.104828
$365$	−16.0000	−0.837478
$366$	10.0000	0.522708
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	−1.00000	−0.0521286
$369$	−8.00000	−0.416463
$370$	6.00000	0.311925
$371$	−12.0000	−0.623009
$372$	8.00000	0.414781
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0	0
$377$	−16.0000	−0.824042
$378$	1.00000	0.0514344
$379$	34.0000	1.74646	0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000	1.74646	0.873231	+	0.487306i	$0.162020\pi$
$380$	4.00000	0.205196
$381$	12.0000	0.614779
$382$	−8.00000	−0.409316
$383$	18.0000	0.919757	0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000	0.919757	0.459879	+	0.887982i	$0.347893\pi$
$384$	1.00000	0.0510310
$385$	4.00000	0.203859
$386$	−22.0000	−1.11977
$387$	−8.00000	−0.406663
$388$	2.00000	0.101535
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	2.00000	0.101274
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	12.0000	0.605320
$394$	−18.0000	−0.906827
$395$	−16.0000	−0.805047
$396$	−4.00000	−0.201008
$397$	−26.0000	−1.30490	−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000	−1.30490	−0.652451	+	0.757831i	$0.726259\pi$
$398$	−18.0000	−0.902258
$399$	4.00000	0.200250
$400$	1.00000	0.0500000
$401$	38.0000	1.89763	0.948815	−	0.315833i	$-0.102284\pi$
$401$	38.0000	1.89763	0.948815	+	0.315833i	$0.102284\pi$
$402$	0	0
$403$	16.0000	0.797017
$404$	2.00000	0.0995037
$405$	−1.00000	−0.0496904
$406$	−8.00000	−0.397033
$407$	−24.0000	−1.18964
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−8.00000	−0.395092
$411$	−10.0000	−0.493264
$412$	20.0000	0.985329
$413$	−4.00000	−0.196827
$414$	1.00000	0.0491473
$415$	16.0000	0.785409
$416$	2.00000	0.0980581
$417$	4.00000	0.195881
$418$	−16.0000	−0.782586
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	1.00000	0.0487950
$421$	−16.0000	−0.779792	−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000	−0.779792	−0.389896	+	0.920859i	$0.627489\pi$
$422$	−8.00000	−0.389434
$423$	0	0
$424$	12.0000	0.582772
$425$	0	0
$426$	12.0000	0.581402
$427$	10.0000	0.483934
$428$	−6.00000	−0.290021
$429$	−8.00000	−0.386244
$430$	−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
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	8.00000	0.384012
$435$	8.00000	0.383571
$436$	12.0000	0.574696
$437$	4.00000	0.191346
$438$	16.0000	0.764510
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	−4.00000	−0.190693
$441$	1.00000	0.0476190
$442$	0	0
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	−6.00000	−0.284747
$445$	6.00000	0.284427
$446$	−2.00000	−0.0947027
$447$	−10.0000	−0.472984
$448$	1.00000	0.0472456
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	−1.00000	−0.0471405
$451$	32.0000	1.50682
$452$	−14.0000	−0.658505
$453$	0	0
$454$	−20.0000	−0.938647
$455$	2.00000	0.0937614
$456$	−4.00000	−0.187317
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	−14.0000	−0.654177
$459$	0	0
$460$	1.00000	0.0466252
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	−4.00000	−0.186097
$463$	12.0000	0.557687	0.278844	−	0.960337i	$-0.410049\pi$
$463$	12.0000	0.557687	0.278844	+	0.960337i	$0.410049\pi$
$464$	8.00000	0.371391
$465$	−8.00000	−0.370991
$466$	−2.00000	−0.0926482
$467$	−20.0000	−0.925490	−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000	−0.925490	−0.462745	+	0.886492i	$0.653135\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	0	0
$471$	14.0000	0.645086
$472$	4.00000	0.184115
$473$	32.0000	1.47136
$474$	16.0000	0.734904
$475$	−4.00000	−0.183533
$476$	0	0
$477$	−12.0000	−0.549442
$478$	−20.0000	−0.914779
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	−1.00000	−0.0456435
$481$	−12.0000	−0.547153
$482$	12.0000	0.546585
$483$	1.00000	0.0455016
$484$	5.00000	0.227273
$485$	−2.00000	−0.0908153
$486$	1.00000	0.0453609
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	−10.0000	−0.452679
$489$	18.0000	0.813988
$490$	1.00000	0.0451754
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	8.00000	0.360668
$493$	0	0
$494$	−8.00000	−0.359937
$495$	4.00000	0.179787
$496$	−8.00000	−0.359211
$497$	12.0000	0.538274
$498$	−16.0000	−0.716977
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	−1.00000	−0.0447214
$501$	20.0000	0.893534
$502$	−12.0000	−0.535586
$503$	18.0000	0.802580	0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000	0.802580	0.401290	+	0.915951i	$0.368562\pi$
$504$	−1.00000	−0.0445435
$505$	−2.00000	−0.0889988
$506$	−4.00000	−0.177822
$507$	9.00000	0.399704
$508$	−12.0000	−0.532414
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	0	0
$511$	16.0000	0.707798
$512$	−1.00000	−0.0441942
$513$	4.00000	0.176604
$514$	6.00000	0.264649
$515$	−20.0000	−0.881305
$516$	8.00000	0.352180
$517$	0	0
$518$	−6.00000	−0.263625
$519$	14.0000	0.614532
$520$	−2.00000	−0.0877058
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	−8.00000	−0.350150
$523$	−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
$525$	−1.00000	−0.0436436
$526$	16.0000	0.697633
$527$	0	0
$528$	4.00000	0.174078
$529$	1.00000	0.0434783
$530$	−12.0000	−0.521247
$531$	−4.00000	−0.173585
$532$	−4.00000	−0.173422
$533$	16.0000	0.693037
$534$	−6.00000	−0.259645
$535$	6.00000	0.259403
$536$	0	0
$537$	−10.0000	−0.431532
$538$	10.0000	0.431131
$539$	−4.00000	−0.172292
$540$	1.00000	0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−16.0000	−0.687259
$543$	−14.0000	−0.600798
$544$	0	0
$545$	−12.0000	−0.514024
$546$	−2.00000	−0.0855921
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	10.0000	0.427179
$549$	10.0000	0.426790
$550$	4.00000	0.170561
$551$	−32.0000	−1.36325
$552$	−1.00000	−0.0425628
$553$	16.0000	0.680389
$554$	20.0000	0.849719
$555$	6.00000	0.254686
$556$	−4.00000	−0.169638
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	8.00000	0.338667
$559$	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	$0.581374\pi$
$564$	0	0
$565$	14.0000	0.588984
$566$	12.0000	0.504398
$567$	1.00000	0.0419961
$568$	−12.0000	−0.503509
$569$	14.0000	0.586911	0.293455	−	0.955973i	$-0.405195\pi$
$569$	14.0000	0.586911	0.293455	+	0.955973i	$0.405195\pi$
$570$	4.00000	0.167542
$571$	−22.0000	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$572$	8.00000	0.334497
$573$	−8.00000	−0.334205
$574$	8.00000	0.333914
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	−4.00000	−0.166522	−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000	−0.166522	−0.0832611	+	0.996528i	$0.526534\pi$
$578$	17.0000	0.707107
$579$	−22.0000	−0.914289
$580$	−8.00000	−0.332182
$581$	−16.0000	−0.663792
$582$	2.00000	0.0829027
$583$	48.0000	1.98796
$584$	−16.0000	−0.662085
$585$	2.00000	0.0826898
$586$	−2.00000	−0.0826192
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	−1.00000	−0.0412393
$589$	32.0000	1.31854
$590$	−4.00000	−0.164677
$591$	−18.0000	−0.740421
$592$	6.00000	0.246598
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	10.0000	0.409616
$597$	−18.0000	−0.736691
$598$	−2.00000	−0.0817861
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	1.00000	0.0408248
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	8.00000	0.326056
$603$	0	0
$604$	0	0
$605$	−5.00000	−0.203279
$606$	2.00000	0.0812444
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	4.00000	0.162221
$609$	−8.00000	−0.324176
$610$	10.0000	0.404888
$611$	0	0
$612$	0	0
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	−8.00000	−0.322854
$615$	−8.00000	−0.322591
$616$	4.00000	0.161165
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	20.0000	0.804518
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	8.00000	0.321288
$621$	1.00000	0.0401286
$622$	−18.0000	−0.721734
$623$	−6.00000	−0.240385
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	−22.0000	−0.879297
$627$	−16.0000	−0.638978
$628$	−14.0000	−0.558661
$629$	0	0
$630$	1.00000	0.0398410
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	−16.0000	−0.636446
$633$	−8.00000	−0.317971
$634$	−30.0000	−1.19145
$635$	12.0000	0.476205
$636$	12.0000	0.475831
$637$	−2.00000	−0.0792429
$638$	32.0000	1.26689
$639$	12.0000	0.474713
$640$	1.00000	0.0395285
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	−6.00000	−0.236801
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	−1.00000	−0.0394055
$645$	−8.00000	−0.315000
$646$	0	0
$647$	−36.0000	−1.41531	−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000	−1.41531	−0.707653	+	0.706560i	$0.750246\pi$
$648$	−1.00000	−0.0392837
$649$	16.0000	0.628055
$650$	2.00000	0.0784465
$651$	8.00000	0.313545
$652$	−18.0000	−0.704934
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	12.0000	0.469237
$655$	12.0000	0.468879
$656$	−8.00000	−0.312348
$657$	16.0000	0.624219
$658$	0	0
$659$	40.0000	1.55818	0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000	1.55818	0.779089	+	0.626913i	$0.215682\pi$
$660$	−4.00000	−0.155700
$661$	50.0000	1.94477	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000	1.94477	0.972387	+	0.233373i	$0.0749763\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	16.0000	0.620920
$665$	4.00000	0.155113
$666$	−6.00000	−0.232495
$667$	−8.00000	−0.309761
$668$	−20.0000	−0.773823
$669$	−2.00000	−0.0773245
$670$	0	0
$671$	−40.0000	−1.54418
$672$	1.00000	0.0385758
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	18.0000	0.693334
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	−14.0000	−0.537667
$679$	2.00000	0.0767530
$680$	0	0
$681$	−20.0000	−0.766402
$682$	−32.0000	−1.22534
$683$	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
$685$	−10.0000	−0.382080
$686$	−1.00000	−0.0381802
$687$	−14.0000	−0.534133
$688$	−8.00000	−0.304997
$689$	24.0000	0.914327
$690$	1.00000	0.0380693
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−14.0000	−0.532200
$693$	−4.00000	−0.151947
$694$	−28.0000	−1.06287
$695$	4.00000	0.151729
$696$	8.00000	0.303239
$697$	0	0
$698$	−30.0000	−1.13552
$699$	−2.00000	−0.0756469
$700$	1.00000	0.0377964
$701$	−34.0000	−1.28416	−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000	−1.28416	−0.642081	+	0.766637i	$0.721929\pi$
$702$	−2.00000	−0.0754851
$703$	−24.0000	−0.905177
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−26.0000	−0.978523
$707$	2.00000	0.0752177
$708$	4.00000	0.150329
$709$	44.0000	1.65245	0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000	1.65245	0.826227	+	0.563337i	$0.190483\pi$
$710$	12.0000	0.450352
$711$	16.0000	0.600047
$712$	6.00000	0.224860
$713$	8.00000	0.299602
$714$	0	0
$715$	−8.00000	−0.299183
$716$	10.0000	0.373718
$717$	−20.0000	−0.746914
$718$	8.00000	0.298557
$719$	2.00000	0.0745874	0.0372937	−	0.999304i	$-0.488126\pi$
$719$	2.00000	0.0745874	0.0372937	+	0.999304i	$0.488126\pi$
$720$	−1.00000	−0.0372678
$721$	20.0000	0.744839
$722$	3.00000	0.111648
$723$	12.0000	0.446285
$724$	14.0000	0.520306
$725$	8.00000	0.297113
$726$	5.00000	0.185567
$727$	−52.0000	−1.92857	−0.964287	−	0.264861i	$-0.914674\pi$
$727$	−52.0000	−1.92857	−0.964287	+	0.264861i	$0.914674\pi$
$728$	2.00000	0.0741249
$729$	1.00000	0.0370370
$730$	16.0000	0.592187
$731$	0	0
$732$	−10.0000	−0.369611
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−32.0000	−1.18114
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	0	0
$738$	8.00000	0.294484
$739$	−48.0000	−1.76571	−0.882854	−	0.469647i	$-0.844381\pi$
$739$	−48.0000	−1.76571	−0.882854	+	0.469647i	$0.844381\pi$
$740$	−6.00000	−0.220564
$741$	−8.00000	−0.293887
$742$	12.0000	0.440534
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	−8.00000	−0.293294
$745$	−10.0000	−0.366372
$746$	−26.0000	−0.951928
$747$	−16.0000	−0.585409
$748$	0	0
$749$	−6.00000	−0.219235
$750$	−1.00000	−0.0365148
$751$	36.0000	1.31366	0.656829	−	0.754039i	$-0.271897\pi$
$751$	36.0000	1.31366	0.656829	+	0.754039i	$0.271897\pi$
$752$	0	0
$753$	−12.0000	−0.437304
$754$	16.0000	0.582686
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	−50.0000	−1.81728	−0.908640	−	0.417579i	$-0.862879\pi$
$757$	−50.0000	−1.81728	−0.908640	+	0.417579i	$0.862879\pi$
$758$	−34.0000	−1.23494
$759$	−4.00000	−0.145191
$760$	−4.00000	−0.145095
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	−12.0000	−0.434714
$763$	12.0000	0.434429
$764$	8.00000	0.289430
$765$	0	0
$766$	−18.0000	−0.650366
$767$	8.00000	0.288863
$768$	−1.00000	−0.0360844
$769$	−32.0000	−1.15395	−0.576975	−	0.816762i	$-0.695767\pi$
$769$	−32.0000	−1.15395	−0.576975	+	0.816762i	$0.695767\pi$
$770$	−4.00000	−0.144150
$771$	6.00000	0.216085
$772$	22.0000	0.791797
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	8.00000	0.287554
$775$	−8.00000	−0.287368
$776$	−2.00000	−0.0717958
$777$	−6.00000	−0.215249
$778$	10.0000	0.358517
$779$	32.0000	1.14652
$780$	−2.00000	−0.0716115
$781$	−48.0000	−1.71758
$782$	0	0
$783$	−8.00000	−0.285897
$784$	1.00000	0.0357143
$785$	14.0000	0.499681
$786$	−12.0000	−0.428026
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	18.0000	0.641223
$789$	16.0000	0.569615
$790$	16.0000	0.569254
$791$	−14.0000	−0.497783
$792$	4.00000	0.142134
$793$	−20.0000	−0.710221
$794$	26.0000	0.922705
$795$	−12.0000	−0.425596
$796$	18.0000	0.637993
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	−4.00000	−0.141598
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−6.00000	−0.212000
$802$	−38.0000	−1.34183
$803$	−64.0000	−2.25851
$804$	0	0
$805$	1.00000	0.0352454
$806$	−16.0000	−0.563576
$807$	10.0000	0.352017
$808$	−2.00000	−0.0703598
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	1.00000	0.0351364
$811$	−44.0000	−1.54505	−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000	−1.54505	−0.772524	+	0.634985i	$0.781006\pi$
$812$	8.00000	0.280745
$813$	−16.0000	−0.561144
$814$	24.0000	0.841200
$815$	18.0000	0.630512
$816$	0	0
$817$	32.0000	1.11954
$818$	−10.0000	−0.349642
$819$	−2.00000	−0.0698857
$820$	8.00000	0.279372
$821$	8.00000	0.279202	0.139601	−	0.990208i	$-0.455418\pi$
$821$	8.00000	0.279202	0.139601	+	0.990208i	$0.455418\pi$
$822$	10.0000	0.348790
$823$	28.0000	0.976019	0.488009	−	0.872838i	$-0.337723\pi$
$823$	28.0000	0.976019	0.488009	+	0.872838i	$0.337723\pi$
$824$	−20.0000	−0.696733
$825$	4.00000	0.139262
$826$	4.00000	0.139178
$827$	−50.0000	−1.73867	−0.869335	−	0.494223i	$-0.835453\pi$
$827$	−50.0000	−1.73867	−0.869335	+	0.494223i	$0.835453\pi$
$828$	−1.00000	−0.0347524
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	−16.0000	−0.555368
$831$	20.0000	0.693792
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	−4.00000	−0.138509
$835$	20.0000	0.692129
$836$	16.0000	0.553372
$837$	8.00000	0.276520
$838$	4.00000	0.138178
$839$	−4.00000	−0.138095	−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000	−0.138095	−0.0690477	+	0.997613i	$0.521996\pi$
$840$	−1.00000	−0.0345033
$841$	35.0000	1.20690
$842$	16.0000	0.551396
$843$	6.00000	0.206651
$844$	8.00000	0.275371
$845$	9.00000	0.309609
$846$	0	0
$847$	5.00000	0.171802
$848$	−12.0000	−0.412082
$849$	12.0000	0.411839
$850$	0	0
$851$	−6.00000	−0.205677
$852$	−12.0000	−0.411113
$853$	22.0000	0.753266	0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000	0.753266	0.376633	+	0.926363i	$0.377082\pi$
$854$	−10.0000	−0.342193
$855$	4.00000	0.136797
$856$	6.00000	0.205076
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	8.00000	0.273115
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	8.00000	0.272798
$861$	8.00000	0.272639
$862$	−24.0000	−0.817443
$863$	32.0000	1.08929	0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000	1.08929	0.544646	+	0.838666i	$0.316664\pi$
$864$	1.00000	0.0340207
$865$	14.0000	0.476014
$866$	6.00000	0.203888
$867$	17.0000	0.577350
$868$	−8.00000	−0.271538
$869$	−64.0000	−2.17105
$870$	−8.00000	−0.271225
$871$	0	0
$872$	−12.0000	−0.406371
$873$	2.00000	0.0676897
$874$	−4.00000	−0.135302
$875$	−1.00000	−0.0338062
$876$	−16.0000	−0.540590
$877$	24.0000	0.810422	0.405211	−	0.914223i	$-0.367198\pi$
$877$	24.0000	0.810422	0.405211	+	0.914223i	$0.367198\pi$
$878$	0	0
$879$	−2.00000	−0.0674583
$880$	4.00000	0.134840
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	−1.00000	−0.0336718
$883$	−10.0000	−0.336527	−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000	−0.336527	−0.168263	+	0.985742i	$0.553816\pi$
$884$	0	0
$885$	−4.00000	−0.134459
$886$	−4.00000	−0.134383
$887$	40.0000	1.34307	0.671534	−	0.740973i	$-0.265636\pi$
$887$	40.0000	1.34307	0.671534	+	0.740973i	$0.265636\pi$
$888$	6.00000	0.201347
$889$	−12.0000	−0.402467
$890$	−6.00000	−0.201120
$891$	−4.00000	−0.134005
$892$	2.00000	0.0669650
$893$	0	0
$894$	10.0000	0.334450
$895$	−10.0000	−0.334263
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	10.0000	0.333704
$899$	−64.0000	−2.13452
$900$	1.00000	0.0333333
$901$	0	0
$902$	−32.0000	−1.06548
$903$	8.00000	0.266223
$904$	14.0000	0.465633
$905$	−14.0000	−0.465376
$906$	0	0
$907$	16.0000	0.531271	0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000	0.531271	0.265636	+	0.964073i	$0.414418\pi$
$908$	20.0000	0.663723
$909$	2.00000	0.0663358
$910$	−2.00000	−0.0662994
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	4.00000	0.132453
$913$	64.0000	2.11809
$914$	−38.0000	−1.25693
$915$	10.0000	0.330590
$916$	14.0000	0.462573
$917$	−12.0000	−0.396275
$918$	0	0
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	−1.00000	−0.0329690
$921$	−8.00000	−0.263609
$922$	−6.00000	−0.197599
$923$	−24.0000	−0.789970
$924$	4.00000	0.131590
$925$	6.00000	0.197279
$926$	−12.0000	−0.394344
$927$	20.0000	0.656886
$928$	−8.00000	−0.262613
$929$	12.0000	0.393707	0.196854	−	0.980433i	$-0.436928\pi$
$929$	12.0000	0.393707	0.196854	+	0.980433i	$0.436928\pi$
$930$	8.00000	0.262330
$931$	−4.00000	−0.131095
$932$	2.00000	0.0655122
$933$	−18.0000	−0.589294
$934$	20.0000	0.654420
$935$	0	0
$936$	2.00000	0.0653720
$937$	22.0000	0.718709	0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000	0.718709	0.359354	+	0.933201i	$0.382997\pi$
$938$	0	0
$939$	−22.0000	−0.717943
$940$	0	0
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	−14.0000	−0.456145
$943$	8.00000	0.260516
$944$	−4.00000	−0.130189
$945$	1.00000	0.0325300
$946$	−32.0000	−1.04041
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	−16.0000	−0.519656
$949$	−32.0000	−1.03876
$950$	4.00000	0.129777
$951$	−30.0000	−0.972817
$952$	0	0
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	12.0000	0.388514
$955$	−8.00000	−0.258874
$956$	20.0000	0.646846
$957$	32.0000	1.03441
$958$	0	0
$959$	10.0000	0.322917
$960$	1.00000	0.0322749
$961$	33.0000	1.06452
$962$	12.0000	0.386896
$963$	−6.00000	−0.193347
$964$	−12.0000	−0.386494
$965$	−22.0000	−0.708205
$966$	−1.00000	−0.0321745
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	2.00000	0.0642161
$971$	60.0000	1.92549	0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000	1.92549	0.962746	+	0.270408i	$0.0871586\pi$
$972$	−1.00000	−0.0320750
$973$	−4.00000	−0.128234
$974$	32.0000	1.02535
$975$	2.00000	0.0640513
$976$	10.0000	0.320092
$977$	−62.0000	−1.98356	−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−62.0000	−1.98356	−0.991778	+	0.127971i	$0.959153\pi$
$978$	−18.0000	−0.575577
$979$	24.0000	0.767043
$980$	−1.00000	−0.0319438
$981$	12.0000	0.383131
$982$	2.00000	0.0638226
$983$	−22.0000	−0.701691	−0.350846	−	0.936433i	$-0.614106\pi$
$983$	−22.0000	−0.701691	−0.350846	+	0.936433i	$0.614106\pi$
$984$	−8.00000	−0.255031
$985$	−18.0000	−0.573528
$986$	0	0
$987$	0	0
$988$	8.00000	0.254514
$989$	8.00000	0.254385
$990$	−4.00000	−0.127128
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	8.00000	0.254000
$993$	−20.0000	−0.634681
$994$	−12.0000	−0.380617
$995$	−18.0000	−0.570638
$996$	16.0000	0.506979
$997$	−6.00000	−0.190022	−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000	−0.190022	−0.0950110	+	0.995476i	$0.530289\pi$
$998$	−16.0000	−0.506471
$999$	−6.00000	−0.189832

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
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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