LMFDB - Embedded newform 4830.2.a.z.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -6.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} -1.00000 q^{30} +1.00000 q^{32} -6.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +6.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} -1.00000 q^{42} -8.00000 q^{43} +1.00000 q^{45} +1.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +6.00000 q^{51} -6.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +1.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} -4.00000 q^{59} -1.00000 q^{60} +14.0000 q^{61} +1.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} -16.0000 q^{67} -6.00000 q^{68} -1.00000 q^{69} +1.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} -14.0000 q^{73} -10.0000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +6.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +4.00000 q^{83} -1.00000 q^{84} -6.00000 q^{85} -8.00000 q^{86} +6.00000 q^{87} +14.0000 q^{89} +1.00000 q^{90} -6.00000 q^{91} +1.00000 q^{92} +8.00000 q^{94} +4.00000 q^{95} -1.00000 q^{96} +14.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	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
$26$	−6.00000	−1.17670
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−0.182574
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	0.648886
$39$	6.00000	0.960769
$40$	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
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	6.00000	0.840168
$52$	−6.00000	−0.832050
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.00000	0.133631
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	−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
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	0	0
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	0	0
$67$	−16.0000	−1.95471	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−16.0000	−1.95471	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−6.00000	−0.727607
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	−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
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	−10.0000	−1.16248
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	0	0
$78$	6.00000	0.679366
$79$	−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	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−1.00000	−0.109109
$85$	−6.00000	−0.650791
$86$	−8.00000	−0.862662
$87$	6.00000	0.643268
$88$	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
$91$	−6.00000	−0.628971
$92$	1.00000	0.104257
$93$	0	0
$94$	8.00000	0.825137
$95$	4.00000	0.410391
$96$	−1.00000	−0.102062
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	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	$0.468274\pi$
$102$	6.00000	0.594089
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−6.00000	−0.588348
$105$	−1.00000	−0.0975900
$106$	−10.0000	−0.971286
$107$	20.0000	1.93347	0.966736	−	0.255774i	$-0.0823304\pi$
$107$	20.0000	1.93347	0.966736	+	0.255774i	$0.0823304\pi$
$108$	−1.00000	−0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	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
$116$	−6.00000	−0.557086
$117$	−6.00000	−0.554700
$118$	−4.00000	−0.368230
$119$	−6.00000	−0.550019
$120$	−1.00000	−0.0912871
$121$	−11.0000	−1.00000
$122$	14.0000	1.26750
$123$	−2.00000	−0.180334
$124$	0	0
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	−6.00000	−0.526235
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	−16.0000	−1.38219
$135$	−1.00000	−0.0860663
$136$	−6.00000	−0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−1.00000	−0.0851257
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	1.00000	0.0845154
$141$	−8.00000	−0.673722
$142$	−12.0000	−1.00702
$143$	0	0
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−14.0000	−1.15865
$147$	−1.00000	−0.0824786
$148$	−10.0000	−0.821995
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−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
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	6.00000	0.480384
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−8.00000	−0.636446
$159$	10.0000	0.793052
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	4.00000	0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	−1.00000	−0.0771517
$169$	23.0000	1.76923
$170$	−6.00000	−0.460179
$171$	4.00000	0.305888
$172$	−8.00000	−0.609994
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	6.00000	0.454859
$175$	1.00000	0.0755929
$176$	0	0
$177$	4.00000	0.300658
$178$	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
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	−6.00000	−0.444750
$183$	−14.0000	−1.03491
$184$	1.00000	0.0737210
$185$	−10.0000	−0.735215
$186$	0	0
$187$	0	0
$188$	8.00000	0.583460
$189$	−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	$0.275675\pi$
$194$	14.0000	1.00514
$195$	6.00000	0.429669
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	1.00000	0.0707107
$201$	16.0000	1.12855
$202$	2.00000	0.140720
$203$	−6.00000	−0.421117
$204$	6.00000	0.420084
$205$	2.00000	0.139686
$206$	8.00000	0.557386
$207$	1.00000	0.0695048
$208$	−6.00000	−0.416025
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−10.0000	−0.686803
$213$	12.0000	0.822226
$214$	20.0000	1.36717
$215$	−8.00000	−0.545595
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−2.00000	−0.135457
$219$	14.0000	0.946032
$220$	0	0
$221$	36.0000	2.42162
$222$	10.0000	0.671156
$223$	−12.0000	−0.803579	−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000	−0.803579	−0.401790	+	0.915732i	$0.631612\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−14.0000	−0.931266
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	−4.00000	−0.264906
$229$	−26.0000	−1.71813	−0.859064	−	0.511868i	$-0.828954\pi$
$229$	−26.0000	−1.71813	−0.859064	+	0.511868i	$0.828954\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−6.00000	−0.392232
$235$	8.00000	0.521862
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	−6.00000	−0.388922
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	−1.00000	−0.0645497
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−11.0000	−0.707107
$243$	−1.00000	−0.0641500
$244$	14.0000	0.896258
$245$	1.00000	0.0638877
$246$	−2.00000	−0.127515
$247$	−24.0000	−1.52708
$248$	0	0
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	−24.0000	−1.51487	−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000	−1.51487	−0.757433	+	0.652913i	$0.773547\pi$
$252$	1.00000	0.0629941
$253$	0	0
$254$	12.0000	0.752947
$255$	6.00000	0.375735
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	8.00000	0.498058
$259$	−10.0000	−0.621370
$260$	−6.00000	−0.372104
$261$	−6.00000	−0.371391
$262$	−4.00000	−0.247121
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	−10.0000	−0.614295
$266$	4.00000	0.245256
$267$	−14.0000	−0.856786
$268$	−16.0000	−0.977356
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	−1.00000	−0.0608581
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−6.00000	−0.363803
$273$	6.00000	0.363137
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	1.00000	0.0597614
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	−8.00000	−0.476393
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	−12.0000	−0.712069
$285$	−4.00000	−0.236940
$286$	0	0
$287$	2.00000	0.118056
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	−6.00000	−0.352332
$291$	−14.0000	−0.820695
$292$	−14.0000	−0.819288
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−1.00000	−0.0583212
$295$	−4.00000	−0.232889
$296$	−10.0000	−0.581238
$297$	0	0
$298$	6.00000	0.347571
$299$	−6.00000	−0.346989
$300$	−1.00000	−0.0577350
$301$	−8.00000	−0.461112
$302$	0	0
$303$	−2.00000	−0.114897
$304$	4.00000	0.229416
$305$	14.0000	0.801638
$306$	−6.00000	−0.342997
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	0	0
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	6.00000	0.339683
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−18.0000	−1.01580
$315$	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	$0.288015\pi$
$318$	10.0000	0.560772
$319$	0	0
$320$	1.00000	0.0559017
$321$	−20.0000	−1.11629
$322$	1.00000	0.0557278
$323$	−24.0000	−1.33540
$324$	1.00000	0.0555556
$325$	−6.00000	−0.332820
$326$	4.00000	0.221540
$327$	2.00000	0.110600
$328$	2.00000	0.110432
$329$	8.00000	0.441054
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	4.00000	0.219529
$333$	−10.0000	−0.547997
$334$	−8.00000	−0.437741
$335$	−16.0000	−0.874173
$336$	−1.00000	−0.0545545
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	23.0000	1.25104
$339$	14.0000	0.760376
$340$	−6.00000	−0.325396
$341$	0	0
$342$	4.00000	0.216295
$343$	1.00000	0.0539949
$344$	−8.00000	−0.431331
$345$	−1.00000	−0.0538382
$346$	−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	$0.395612\pi$
$348$	6.00000	0.321634
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	1.00000	0.0534522
$351$	6.00000	0.320256
$352$	0	0
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	4.00000	0.212598
$355$	−12.0000	−0.636894
$356$	14.0000	0.741999
$357$	6.00000	0.317554
$358$	−12.0000	−0.634220
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	6.00000	0.315353
$363$	11.0000	0.577350
$364$	−6.00000	−0.314485
$365$	−14.0000	−0.732793
$366$	−14.0000	−0.731792
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	1.00000	0.0521286
$369$	2.00000	0.104116
$370$	−10.0000	−0.519875
$371$	−10.0000	−0.519174
$372$	0	0
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	8.00000	0.412568
$377$	36.0000	1.85409
$378$	−1.00000	−0.0514344
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	4.00000	0.205196
$381$	−12.0000	−0.614779
$382$	0	0
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	18.0000	0.916176
$387$	−8.00000	−0.406663
$388$	14.0000	0.710742
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	6.00000	0.303822
$391$	−6.00000	−0.303433
$392$	1.00000	0.0505076
$393$	4.00000	0.201773
$394$	−10.0000	−0.503793
$395$	−8.00000	−0.402524
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	8.00000	0.401004
$399$	−4.00000	−0.200250
$400$	1.00000	0.0500000
$401$	−2.00000	−0.0998752	−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000	−0.0998752	−0.0499376	+	0.998752i	$0.515902\pi$
$402$	16.0000	0.798007
$403$	0	0
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	−6.00000	−0.297775
$407$	0	0
$408$	6.00000	0.297044
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	2.00000	0.0987730
$411$	6.00000	0.295958
$412$	8.00000	0.394132
$413$	−4.00000	−0.196827
$414$	1.00000	0.0491473
$415$	4.00000	0.196352
$416$	−6.00000	−0.294174
$417$	−4.00000	−0.195881
$418$	0	0
$419$	−8.00000	−0.390826	−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000	−0.390826	−0.195413	+	0.980721i	$0.562605\pi$
$420$	−1.00000	−0.0487950
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	−20.0000	−0.973585
$423$	8.00000	0.388973
$424$	−10.0000	−0.485643
$425$	−6.00000	−0.291043
$426$	12.0000	0.581402
$427$	14.0000	0.677507
$428$	20.0000	0.966736
$429$	0	0
$430$	−8.00000	−0.385794
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	−1.00000	−0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−2.00000	−0.0957826
$437$	4.00000	0.191346
$438$	14.0000	0.668946
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	36.0000	1.71235
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	10.0000	0.474579
$445$	14.0000	0.663664
$446$	−12.0000	−0.568216
$447$	−6.00000	−0.283790
$448$	1.00000	0.0472456
$449$	26.0000	1.22702	0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000	1.22702	0.613508	+	0.789689i	$0.289758\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−14.0000	−0.658505
$453$	0	0
$454$	−4.00000	−0.187729
$455$	−6.00000	−0.281284
$456$	−4.00000	−0.187317
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	−26.0000	−1.21490
$459$	6.00000	0.280056
$460$	1.00000	0.0466252
$461$	42.0000	1.95614	0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000	1.95614	0.978068	+	0.208288i	$0.0667892\pi$
$462$	0	0
$463$	20.0000	0.929479	0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000	0.929479	0.464739	+	0.885448i	$0.346148\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−6.00000	−0.277945
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	−6.00000	−0.277350
$469$	−16.0000	−0.738811
$470$	8.00000	0.369012
$471$	18.0000	0.829396
$472$	−4.00000	−0.184115
$473$	0	0
$474$	8.00000	0.367452
$475$	4.00000	0.183533
$476$	−6.00000	−0.275010
$477$	−10.0000	−0.457869
$478$	12.0000	0.548867
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	−1.00000	−0.0456435
$481$	60.0000	2.73576
$482$	2.00000	0.0910975
$483$	−1.00000	−0.0455016
$484$	−11.0000	−0.500000
$485$	14.0000	0.635707
$486$	−1.00000	−0.0453609
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	14.0000	0.633750
$489$	−4.00000	−0.180886
$490$	1.00000	0.0451754
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	−2.00000	−0.0901670
$493$	36.0000	1.62136
$494$	−24.0000	−1.07981
$495$	0	0
$496$	0	0
$497$	−12.0000	−0.538274
$498$	−4.00000	−0.179244
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	1.00000	0.0447214
$501$	8.00000	0.357414
$502$	−24.0000	−1.07117
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	1.00000	0.0445435
$505$	2.00000	0.0889988
$506$	0	0
$507$	−23.0000	−1.02147
$508$	12.0000	0.532414
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	6.00000	0.265684
$511$	−14.0000	−0.619324
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	18.0000	0.793946
$515$	8.00000	0.352522
$516$	8.00000	0.352180
$517$	0	0
$518$	−10.0000	−0.439375
$519$	18.0000	0.790112
$520$	−6.00000	−0.263117
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	−6.00000	−0.262613
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−4.00000	−0.174741
$525$	−1.00000	−0.0436436
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	−10.0000	−0.434372
$531$	−4.00000	−0.173585
$532$	4.00000	0.173422
$533$	−12.0000	−0.519778
$534$	−14.0000	−0.605839
$535$	20.0000	0.864675
$536$	−16.0000	−0.691095
$537$	12.0000	0.517838
$538$	18.0000	0.776035
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−26.0000	−1.11783	−0.558914	−	0.829226i	$-0.688782\pi$
$541$	−26.0000	−1.11783	−0.558914	+	0.829226i	$0.688782\pi$
$542$	−16.0000	−0.687259
$543$	−6.00000	−0.257485
$544$	−6.00000	−0.257248
$545$	−2.00000	−0.0856706
$546$	6.00000	0.256776
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	−6.00000	−0.256307
$549$	14.0000	0.597505
$550$	0	0
$551$	−24.0000	−1.02243
$552$	−1.00000	−0.0425628
$553$	−8.00000	−0.340195
$554$	18.0000	0.764747
$555$	10.0000	0.424476
$556$	4.00000	0.169638
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	0	0
$559$	48.0000	2.03018
$560$	1.00000	0.0422577
$561$	0	0
$562$	−2.00000	−0.0843649
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	−8.00000	−0.336861
$565$	−14.0000	−0.588984
$566$	−16.0000	−0.672530
$567$	1.00000	0.0419961
$568$	−12.0000	−0.503509
$569$	22.0000	0.922288	0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000	0.922288	0.461144	+	0.887325i	$0.347439\pi$
$570$	−4.00000	−0.167542
$571$	36.0000	1.50655	0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000	1.50655	0.753277	+	0.657704i	$0.228472\pi$
$572$	0	0
$573$	0	0
$574$	2.00000	0.0834784
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	26.0000	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$577$	26.0000	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$578$	19.0000	0.790296
$579$	−18.0000	−0.748054
$580$	−6.00000	−0.249136
$581$	4.00000	0.165948
$582$	−14.0000	−0.580319
$583$	0	0
$584$	−14.0000	−0.579324
$585$	−6.00000	−0.248069
$586$	6.00000	0.247858
$587$	−20.0000	−0.825488	−0.412744	−	0.910847i	$-0.635430\pi$
$587$	−20.0000	−0.825488	−0.412744	+	0.910847i	$0.635430\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	−4.00000	−0.164677
$591$	10.0000	0.411345
$592$	−10.0000	−0.410997
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	−6.00000	−0.245976
$596$	6.00000	0.245770
$597$	−8.00000	−0.327418
$598$	−6.00000	−0.245358
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	−1.00000	−0.0408248
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	−8.00000	−0.326056
$603$	−16.0000	−0.651570
$604$	0	0
$605$	−11.0000	−0.447214
$606$	−2.00000	−0.0812444
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	4.00000	0.162221
$609$	6.00000	0.243132
$610$	14.0000	0.566843
$611$	−48.0000	−1.94187
$612$	−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	$0.512860\pi$
$614$	12.0000	0.484281
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	34.0000	1.36879	0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000	1.36879	0.684394	+	0.729112i	$0.260067\pi$
$618$	−8.00000	−0.321807
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	4.00000	0.160385
$623$	14.0000	0.560898
$624$	6.00000	0.240192
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	−18.0000	−0.718278
$629$	60.0000	2.39236
$630$	1.00000	0.0398410
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−8.00000	−0.318223
$633$	20.0000	0.794929
$634$	22.0000	0.873732
$635$	12.0000	0.476205
$636$	10.0000	0.396526
$637$	−6.00000	−0.237729
$638$	0	0
$639$	−12.0000	−0.474713
$640$	1.00000	0.0395285
$641$	−10.0000	−0.394976	−0.197488	−	0.980305i	$-0.563278\pi$
$641$	−10.0000	−0.394976	−0.197488	+	0.980305i	$0.563278\pi$
$642$	−20.0000	−0.789337
$643$	−24.0000	−0.946468	−0.473234	−	0.880937i	$-0.656913\pi$
$643$	−24.0000	−0.946468	−0.473234	+	0.880937i	$0.656913\pi$
$644$	1.00000	0.0394055
$645$	8.00000	0.315000
$646$	−24.0000	−0.944267
$647$	−16.0000	−0.629025	−0.314512	−	0.949253i	$-0.601841\pi$
$647$	−16.0000	−0.629025	−0.314512	+	0.949253i	$0.601841\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−6.00000	−0.235339
$651$	0	0
$652$	4.00000	0.156652
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	2.00000	0.0782062
$655$	−4.00000	−0.156293
$656$	2.00000	0.0780869
$657$	−14.0000	−0.546192
$658$	8.00000	0.311872
$659$	−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
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−28.0000	−1.08825
$663$	−36.0000	−1.39812
$664$	4.00000	0.155230
$665$	4.00000	0.155113
$666$	−10.0000	−0.387492
$667$	−6.00000	−0.232321
$668$	−8.00000	−0.309529
$669$	12.0000	0.463947
$670$	−16.0000	−0.618134
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	−22.0000	−0.848038	−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000	−0.848038	−0.424019	+	0.905653i	$0.639381\pi$
$674$	−26.0000	−1.00148
$675$	−1.00000	−0.0384900
$676$	23.0000	0.884615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	14.0000	0.537667
$679$	14.0000	0.537271
$680$	−6.00000	−0.230089
$681$	4.00000	0.153280
$682$	0	0
$683$	44.0000	1.68361	0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000	1.68361	0.841807	+	0.539779i	$0.181492\pi$
$684$	4.00000	0.152944
$685$	−6.00000	−0.229248
$686$	1.00000	0.0381802
$687$	26.0000	0.991962
$688$	−8.00000	−0.304997
$689$	60.0000	2.28582
$690$	−1.00000	−0.0380693
$691$	4.00000	0.152167	0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000	0.152167	0.0760836	+	0.997101i	$0.475758\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	12.0000	0.455514
$695$	4.00000	0.151729
$696$	6.00000	0.227429
$697$	−12.0000	−0.454532
$698$	−10.0000	−0.378506
$699$	6.00000	0.226941
$700$	1.00000	0.0377964
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	6.00000	0.226455
$703$	−40.0000	−1.50863
$704$	0	0
$705$	−8.00000	−0.301297
$706$	18.0000	0.677439
$707$	2.00000	0.0752177
$708$	4.00000	0.150329
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	−12.0000	−0.450352
$711$	−8.00000	−0.300023
$712$	14.0000	0.524672
$713$	0	0
$714$	6.00000	0.224544
$715$	0	0
$716$	−12.0000	−0.448461
$717$	−12.0000	−0.448148
$718$	8.00000	0.298557
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	1.00000	0.0372678
$721$	8.00000	0.297936
$722$	−3.00000	−0.111648
$723$	−2.00000	−0.0743808
$724$	6.00000	0.222988
$725$	−6.00000	−0.222834
$726$	11.0000	0.408248
$727$	−48.0000	−1.78022	−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000	−1.78022	−0.890111	+	0.455744i	$0.849373\pi$
$728$	−6.00000	−0.222375
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	48.0000	1.77534
$732$	−14.0000	−0.517455
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−32.0000	−1.18114
$735$	−1.00000	−0.0368856
$736$	1.00000	0.0368605
$737$	0	0
$738$	2.00000	0.0736210
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	−10.0000	−0.367607
$741$	24.0000	0.881662
$742$	−10.0000	−0.367112
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	−10.0000	−0.366126
$747$	4.00000	0.146352
$748$	0	0
$749$	20.0000	0.730784
$750$	−1.00000	−0.0365148
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	8.00000	0.291730
$753$	24.0000	0.874609
$754$	36.0000	1.31104
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	46.0000	1.67190	0.835949	−	0.548807i	$-0.184918\pi$
$757$	46.0000	1.67190	0.835949	+	0.548807i	$0.184918\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	4.00000	0.145095
$761$	26.0000	0.942499	0.471250	−	0.882000i	$-0.343803\pi$
$761$	26.0000	0.942499	0.471250	+	0.882000i	$0.343803\pi$
$762$	−12.0000	−0.434714
$763$	−2.00000	−0.0724049
$764$	0	0
$765$	−6.00000	−0.216930
$766$	−24.0000	−0.867155
$767$	24.0000	0.866590
$768$	−1.00000	−0.0360844
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	18.0000	0.647834
$773$	22.0000	0.791285	0.395643	−	0.918405i	$-0.370522\pi$
$773$	22.0000	0.791285	0.395643	+	0.918405i	$0.370522\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	14.0000	0.502571
$777$	10.0000	0.358748
$778$	−18.0000	−0.645331
$779$	8.00000	0.286630
$780$	6.00000	0.214834
$781$	0	0
$782$	−6.00000	−0.214560
$783$	6.00000	0.214423
$784$	1.00000	0.0357143
$785$	−18.0000	−0.642448
$786$	4.00000	0.142675
$787$	8.00000	0.285169	0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000	0.285169	0.142585	+	0.989783i	$0.454459\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	−8.00000	−0.284627
$791$	−14.0000	−0.497783
$792$	0	0
$793$	−84.0000	−2.98293
$794$	−22.0000	−0.780751
$795$	10.0000	0.354663
$796$	8.00000	0.283552
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	−4.00000	−0.141598
$799$	−48.0000	−1.69812
$800$	1.00000	0.0353553
$801$	14.0000	0.494666
$802$	−2.00000	−0.0706225
$803$	0	0
$804$	16.0000	0.564276
$805$	1.00000	0.0352454
$806$	0	0
$807$	−18.0000	−0.633630
$808$	2.00000	0.0703598
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	1.00000	0.0351364
$811$	−52.0000	−1.82597	−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000	−1.82597	−0.912983	+	0.407997i	$0.866228\pi$
$812$	−6.00000	−0.210559
$813$	16.0000	0.561144
$814$	0	0
$815$	4.00000	0.140114
$816$	6.00000	0.210042
$817$	−32.0000	−1.11954
$818$	−22.0000	−0.769212
$819$	−6.00000	−0.209657
$820$	2.00000	0.0698430
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	6.00000	0.209274
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−4.00000	−0.139178
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	1.00000	0.0347524
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	4.00000	0.138842
$831$	−18.0000	−0.624413
$832$	−6.00000	−0.208013
$833$	−6.00000	−0.207888
$834$	−4.00000	−0.138509
$835$	−8.00000	−0.276851
$836$	0	0
$837$	0	0
$838$	−8.00000	−0.276355
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	−1.00000	−0.0345033
$841$	7.00000	0.241379
$842$	6.00000	0.206774
$843$	2.00000	0.0688837
$844$	−20.0000	−0.688428
$845$	23.0000	0.791224
$846$	8.00000	0.275046
$847$	−11.0000	−0.377964
$848$	−10.0000	−0.343401
$849$	16.0000	0.549119
$850$	−6.00000	−0.205798
$851$	−10.0000	−0.342796
$852$	12.0000	0.411113
$853$	18.0000	0.616308	0.308154	−	0.951336i	$-0.400289\pi$
$853$	18.0000	0.616308	0.308154	+	0.951336i	$0.400289\pi$
$854$	14.0000	0.479070
$855$	4.00000	0.136797
$856$	20.0000	0.683586
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	−8.00000	−0.272798
$861$	−2.00000	−0.0681598
$862$	−32.0000	−1.08992
$863$	−8.00000	−0.272323	−0.136162	−	0.990687i	$-0.543477\pi$
$863$	−8.00000	−0.272323	−0.136162	+	0.990687i	$0.543477\pi$
$864$	−1.00000	−0.0340207
$865$	−18.0000	−0.612018
$866$	−2.00000	−0.0679628
$867$	−19.0000	−0.645274
$868$	0	0
$869$	0	0
$870$	6.00000	0.203419
$871$	96.0000	3.25284
$872$	−2.00000	−0.0677285
$873$	14.0000	0.473828
$874$	4.00000	0.135302
$875$	1.00000	0.0338062
$876$	14.0000	0.473016
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	16.0000	0.539974
$879$	−6.00000	−0.202375
$880$	0	0
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	1.00000	0.0336718
$883$	4.00000	0.134611	0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000	0.134611	0.0673054	+	0.997732i	$0.478560\pi$
$884$	36.0000	1.21081
$885$	4.00000	0.134459
$886$	−4.00000	−0.134383
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	10.0000	0.335578
$889$	12.0000	0.402467
$890$	14.0000	0.469281
$891$	0	0
$892$	−12.0000	−0.401790
$893$	32.0000	1.07084
$894$	−6.00000	−0.200670
$895$	−12.0000	−0.401116
$896$	1.00000	0.0334077
$897$	6.00000	0.200334
$898$	26.0000	0.867631
$899$	0	0
$900$	1.00000	0.0333333
$901$	60.0000	1.99889
$902$	0	0
$903$	8.00000	0.266223
$904$	−14.0000	−0.465633
$905$	6.00000	0.199447
$906$	0	0
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	−4.00000	−0.132745
$909$	2.00000	0.0663358
$910$	−6.00000	−0.198898
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	22.0000	0.727695
$915$	−14.0000	−0.462826
$916$	−26.0000	−0.859064
$917$	−4.00000	−0.132092
$918$	6.00000	0.198030
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	1.00000	0.0329690
$921$	−12.0000	−0.395413
$922$	42.0000	1.38320
$923$	72.0000	2.36991
$924$	0	0
$925$	−10.0000	−0.328798
$926$	20.0000	0.657241
$927$	8.00000	0.262754
$928$	−6.00000	−0.196960
$929$	10.0000	0.328089	0.164045	−	0.986453i	$-0.447546\pi$
$929$	10.0000	0.328089	0.164045	+	0.986453i	$0.447546\pi$
$930$	0	0
$931$	4.00000	0.131095
$932$	−6.00000	−0.196537
$933$	−4.00000	−0.130954
$934$	36.0000	1.17796
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	−16.0000	−0.522419
$939$	−14.0000	−0.456873
$940$	8.00000	0.260931
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	18.0000	0.586472
$943$	2.00000	0.0651290
$944$	−4.00000	−0.130189
$945$	−1.00000	−0.0325300
$946$	0	0
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	8.00000	0.259828
$949$	84.0000	2.72676
$950$	4.00000	0.129777
$951$	−22.0000	−0.713399
$952$	−6.00000	−0.194461
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−10.0000	−0.323762
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	0	0
$959$	−6.00000	−0.193750
$960$	−1.00000	−0.0322749
$961$	−31.0000	−1.00000
$962$	60.0000	1.93448
$963$	20.0000	0.644491
$964$	2.00000	0.0644157
$965$	18.0000	0.579441
$966$	−1.00000	−0.0321745
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	−11.0000	−0.353553
$969$	24.0000	0.770991
$970$	14.0000	0.449513
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	−1.00000	−0.0320750
$973$	4.00000	0.128234
$974$	−20.0000	−0.640841
$975$	6.00000	0.192154
$976$	14.0000	0.448129
$977$	−22.0000	−0.703842	−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000	−0.703842	−0.351921	+	0.936030i	$0.614471\pi$
$978$	−4.00000	−0.127906
$979$	0	0
$980$	1.00000	0.0319438
$981$	−2.00000	−0.0638551
$982$	20.0000	0.638226
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	−2.00000	−0.0637577
$985$	−10.0000	−0.318626
$986$	36.0000	1.14647
$987$	−8.00000	−0.254643
$988$	−24.0000	−0.763542
$989$	−8.00000	−0.254385
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	0	0
$993$	28.0000	0.888553
$994$	−12.0000	−0.380617
$995$	8.00000	0.253617
$996$	−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	$0.407995\pi$
$998$	28.0000	0.886325
$999$	10.0000	0.316386

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.z.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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