LMFDB - Embedded newform 4830.2.a.s.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} -4.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +2.00000 q^{29} +1.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +6.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} -1.00000 q^{42} +4.00000 q^{43} -4.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} -12.0000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} -2.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +4.00000 q^{55} +1.00000 q^{56} +4.00000 q^{57} +2.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} -14.0000 q^{61} +4.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +4.00000 q^{66} -12.0000 q^{67} +6.00000 q^{68} +1.00000 q^{69} -1.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} +10.0000 q^{73} -6.00000 q^{74} -1.00000 q^{75} -4.00000 q^{76} -4.00000 q^{77} +2.00000 q^{78} -8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -4.00000 q^{83} -1.00000 q^{84} -6.00000 q^{85} +4.00000 q^{86} -2.00000 q^{87} -4.00000 q^{88} -6.00000 q^{89} -1.00000 q^{90} -2.00000 q^{91} -1.00000 q^{92} -4.00000 q^{93} -12.0000 q^{94} +4.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} +1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	1.00000	0.235702
$19$	−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
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	1.00000	0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	4.00000	0.696311
$34$	6.00000	1.02899
$35$	−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
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−1.00000	−0.154303
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−4.00000	−0.603023
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	−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
$55$	4.00000	0.539360
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	2.00000	0.262613
$59$	−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	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	4.00000	0.508001
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	4.00000	0.492366
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	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
$73$	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
$77$	−4.00000	−0.455842
$78$	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
$82$	10.0000	1.10432
$83$	−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
$85$	−6.00000	−0.650791
$86$	4.00000	0.431331
$87$	−2.00000	−0.214423
$88$	−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
$93$	−4.00000	−0.414781
$94$	−12.0000	−1.23771
$95$	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
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	−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	$0.371045\pi$
$104$	−2.00000	−0.196116
$105$	1.00000	0.0975900
$106$	−6.00000	−0.582772
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	−1.00000	−0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	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
$116$	2.00000	0.185695
$117$	−2.00000	−0.184900
$118$	−4.00000	−0.368230
$119$	6.00000	0.550019
$120$	1.00000	0.0912871
$121$	5.00000	0.454545
$122$	−14.0000	−1.26750
$123$	−10.0000	−0.901670
$124$	4.00000	0.359211
$125$	−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
$129$	−4.00000	−0.352180
$130$	2.00000	0.175412
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	4.00000	0.348155
$133$	−4.00000	−0.346844
$134$	−12.0000	−1.03664
$135$	1.00000	0.0860663
$136$	6.00000	0.514496
$137$	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
$141$	12.0000	1.01058
$142$	−12.0000	−1.00702
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	10.0000	0.827606
$147$	−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
$153$	6.00000	0.485071
$154$	−4.00000	−0.322329
$155$	−4.00000	−0.321288
$156$	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	$0.688685\pi$
$158$	−8.00000	−0.636446
$159$	6.00000	0.475831
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	10.0000	0.780869
$165$	−4.00000	−0.311400
$166$	−4.00000	−0.310460
$167$	−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
$170$	−6.00000	−0.460179
$171$	−4.00000	−0.305888
$172$	4.00000	0.304997
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	−2.00000	−0.151620
$175$	1.00000	0.0755929
$176$	−4.00000	−0.301511
$177$	4.00000	0.300658
$178$	−6.00000	−0.449719
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	−1.00000	−0.0745356
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	−2.00000	−0.148250
$183$	14.0000	1.03491
$184$	−1.00000	−0.0737210
$185$	6.00000	0.441129
$186$	−4.00000	−0.293294
$187$	−24.0000	−1.75505
$188$	−12.0000	−0.875190
$189$	−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
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	2.00000	0.143592
$195$	−2.00000	−0.143223
$196$	1.00000	0.0714286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	−4.00000	−0.284268
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	1.00000	0.0707107
$201$	12.0000	0.846415
$202$	14.0000	0.985037
$203$	2.00000	0.140372
$204$	−6.00000	−0.420084
$205$	−10.0000	−0.698430
$206$	8.00000	0.557386
$207$	−1.00000	−0.0695048
$208$	−2.00000	−0.138675
$209$	16.0000	1.10674
$210$	1.00000	0.0690066
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−6.00000	−0.412082
$213$	12.0000	0.822226
$214$	0	0
$215$	−4.00000	−0.272798
$216$	−1.00000	−0.0680414
$217$	4.00000	0.271538
$218$	−6.00000	−0.406371
$219$	−10.0000	−0.675737
$220$	4.00000	0.269680
$221$	−12.0000	−0.807207
$222$	6.00000	0.402694
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−14.0000	−0.931266
$227$	−28.0000	−1.85843	−0.929213	−	0.369546i	$-0.879513\pi$
$227$	−28.0000	−1.85843	−0.929213	+	0.369546i	$0.879513\pi$
$228$	4.00000	0.264906
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	1.00000	0.0659380
$231$	4.00000	0.263181
$232$	2.00000	0.131306
$233$	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
$236$	−4.00000	−0.260378
$237$	8.00000	0.519656
$238$	6.00000	0.388922
$239$	−28.0000	−1.81117	−0.905585	−	0.424165i	$-0.860568\pi$
$239$	−28.0000	−1.81117	−0.905585	+	0.424165i	$0.860568\pi$
$240$	1.00000	0.0645497
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	−14.0000	−0.896258
$245$	−1.00000	−0.0638877
$246$	−10.0000	−0.637577
$247$	8.00000	0.509028
$248$	4.00000	0.254000
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	1.00000	0.0629941
$253$	4.00000	0.251478
$254$	−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	$0.310261\pi$
$258$	−4.00000	−0.249029
$259$	−6.00000	−0.372822
$260$	2.00000	0.124035
$261$	2.00000	0.123797
$262$	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
$265$	6.00000	0.368577
$266$	−4.00000	−0.245256
$267$	6.00000	0.367194
$268$	−12.0000	−0.733017
$269$	−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
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	6.00000	0.363803
$273$	2.00000	0.121046
$274$	10.0000	0.604122
$275$	−4.00000	−0.241209
$276$	1.00000	0.0601929
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	−4.00000	−0.239904
$279$	4.00000	0.239474
$280$	−1.00000	−0.0597614
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	12.0000	0.714590
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−12.0000	−0.712069
$285$	−4.00000	−0.236940
$286$	8.00000	0.473050
$287$	10.0000	0.590281
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	−2.00000	−0.117444
$291$	−2.00000	−0.117242
$292$	10.0000	0.585206
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	−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
$301$	4.00000	0.230556
$302$	0	0
$303$	−14.0000	−0.804279
$304$	−4.00000	−0.229416
$305$	14.0000	0.801638
$306$	6.00000	0.342997
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	−4.00000	−0.227921
$309$	−8.00000	−0.455104
$310$	−4.00000	−0.227185
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	2.00000	0.113228
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−14.0000	−0.790066
$315$	−1.00000	−0.0563436
$316$	−8.00000	−0.450035
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	6.00000	0.336463
$319$	−8.00000	−0.447914
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	−24.0000	−1.33540
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	12.0000	0.664619
$327$	6.00000	0.331801
$328$	10.0000	0.552158
$329$	−12.0000	−0.661581
$330$	−4.00000	−0.220193
$331$	−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
$333$	−6.00000	−0.328798
$334$	−20.0000	−1.09435
$335$	12.0000	0.655630
$336$	−1.00000	−0.0545545
$337$	30.0000	1.63420	0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000	1.63420	0.817102	+	0.576493i	$0.195579\pi$
$338$	−9.00000	−0.489535
$339$	14.0000	0.760376
$340$	−6.00000	−0.325396
$341$	−16.0000	−0.866449
$342$	−4.00000	−0.216295
$343$	1.00000	0.0539949
$344$	4.00000	0.215666
$345$	−1.00000	−0.0538382
$346$	10.0000	0.537603
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	−2.00000	−0.107211
$349$	−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
$352$	−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
$357$	−6.00000	−0.317554
$358$	4.00000	0.211407
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−22.0000	−1.15629
$363$	−5.00000	−0.262432
$364$	−2.00000	−0.104828
$365$	−10.0000	−0.523424
$366$	14.0000	0.731792
$367$	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
$369$	10.0000	0.520579
$370$	6.00000	0.311925
$371$	−6.00000	−0.311504
$372$	−4.00000	−0.207390
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	−24.0000	−1.24101
$375$	1.00000	0.0516398
$376$	−12.0000	−0.618853
$377$	−4.00000	−0.206010
$378$	−1.00000	−0.0514344
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	4.00000	0.205196
$381$	12.0000	0.614779
$382$	8.00000	0.409316
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−1.00000	−0.0510310
$385$	4.00000	0.203859
$386$	−14.0000	−0.712581
$387$	4.00000	0.203331
$388$	2.00000	0.101535
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	−2.00000	−0.101274
$391$	−6.00000	−0.303433
$392$	1.00000	0.0505076
$393$	−12.0000	−0.605320
$394$	−18.0000	−0.906827
$395$	8.00000	0.402524
$396$	−4.00000	−0.201008
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	24.0000	1.20301
$399$	4.00000	0.200250
$400$	1.00000	0.0500000
$401$	−34.0000	−1.69788	−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000	−1.69788	−0.848939	+	0.528490i	$0.822758\pi$
$402$	12.0000	0.598506
$403$	−8.00000	−0.398508
$404$	14.0000	0.696526
$405$	−1.00000	−0.0496904
$406$	2.00000	0.0992583
$407$	24.0000	1.18964
$408$	−6.00000	−0.297044
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−10.0000	−0.493865
$411$	−10.0000	−0.493264
$412$	8.00000	0.394132
$413$	−4.00000	−0.196827
$414$	−1.00000	−0.0491473
$415$	4.00000	0.196352
$416$	−2.00000	−0.0980581
$417$	4.00000	0.195881
$418$	16.0000	0.782586
$419$	−40.0000	−1.95413	−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000	−1.95413	−0.977064	+	0.212946i	$0.931694\pi$
$420$	1.00000	0.0487950
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−28.0000	−1.36302
$423$	−12.0000	−0.583460
$424$	−6.00000	−0.291386
$425$	6.00000	0.291043
$426$	12.0000	0.581402
$427$	−14.0000	−0.677507
$428$	0	0
$429$	−8.00000	−0.386244
$430$	−4.00000	−0.192897
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	4.00000	0.192006
$435$	2.00000	0.0958927
$436$	−6.00000	−0.287348
$437$	4.00000	0.191346
$438$	−10.0000	−0.477818
$439$	36.0000	1.71819	0.859093	−	0.511819i	$-0.171028\pi$
$439$	36.0000	1.71819	0.859093	+	0.511819i	$0.171028\pi$
$440$	4.00000	0.190693
$441$	1.00000	0.0476190
$442$	−12.0000	−0.570782
$443$	−20.0000	−0.950229	−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000	−0.950229	−0.475114	+	0.879924i	$0.657593\pi$
$444$	6.00000	0.284747
$445$	6.00000	0.284427
$446$	−16.0000	−0.757622
$447$	−10.0000	−0.472984
$448$	1.00000	0.0472456
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	1.00000	0.0471405
$451$	−40.0000	−1.88353
$452$	−14.0000	−0.658505
$453$	0	0
$454$	−28.0000	−1.31411
$455$	2.00000	0.0937614
$456$	4.00000	0.187317
$457$	14.0000	0.654892	0.327446	−	0.944870i	$-0.393812\pi$
$457$	14.0000	0.654892	0.327446	+	0.944870i	$0.393812\pi$
$458$	−22.0000	−1.02799
$459$	−6.00000	−0.280056
$460$	1.00000	0.0466252
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	4.00000	0.186097
$463$	36.0000	1.67306	0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000	1.67306	0.836531	+	0.547920i	$0.184580\pi$
$464$	2.00000	0.0928477
$465$	4.00000	0.185496
$466$	26.0000	1.20443
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	−2.00000	−0.0924500
$469$	−12.0000	−0.554109
$470$	12.0000	0.553519
$471$	14.0000	0.645086
$472$	−4.00000	−0.184115
$473$	−16.0000	−0.735681
$474$	8.00000	0.367452
$475$	−4.00000	−0.183533
$476$	6.00000	0.275010
$477$	−6.00000	−0.274721
$478$	−28.0000	−1.28069
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	1.00000	0.0456435
$481$	12.0000	0.547153
$482$	−18.0000	−0.819878
$483$	1.00000	0.0455016
$484$	5.00000	0.227273
$485$	−2.00000	−0.0908153
$486$	−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
$489$	−12.0000	−0.542659
$490$	−1.00000	−0.0451754
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	−10.0000	−0.450835
$493$	12.0000	0.540453
$494$	8.00000	0.359937
$495$	4.00000	0.179787
$496$	4.00000	0.179605
$497$	−12.0000	−0.538274
$498$	4.00000	0.179244
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	−1.00000	−0.0447214
$501$	20.0000	0.893534
$502$	24.0000	1.07117
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	1.00000	0.0445435
$505$	−14.0000	−0.622992
$506$	4.00000	0.177822
$507$	9.00000	0.399704
$508$	−12.0000	−0.532414
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	6.00000	0.265684
$511$	10.0000	0.442374
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	18.0000	0.793946
$515$	−8.00000	−0.352522
$516$	−4.00000	−0.176090
$517$	48.0000	2.11104
$518$	−6.00000	−0.263625
$519$	−10.0000	−0.438951
$520$	2.00000	0.0877058
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	2.00000	0.0875376
$523$	−32.0000	−1.39926	−0.699631	−	0.714504i	$-0.746652\pi$
$523$	−32.0000	−1.39926	−0.699631	+	0.714504i	$0.746652\pi$
$524$	12.0000	0.524222
$525$	−1.00000	−0.0436436
$526$	−16.0000	−0.697633
$527$	24.0000	1.04546
$528$	4.00000	0.174078
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	−4.00000	−0.173585
$532$	−4.00000	−0.173422
$533$	−20.0000	−0.866296
$534$	6.00000	0.259645
$535$	0	0
$536$	−12.0000	−0.518321
$537$	−4.00000	−0.172613
$538$	−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	$0.402695\pi$
$542$	−20.0000	−0.859074
$543$	22.0000	0.944110
$544$	6.00000	0.257248
$545$	6.00000	0.257012
$546$	2.00000	0.0855921
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	10.0000	0.427179
$549$	−14.0000	−0.597505
$550$	−4.00000	−0.170561
$551$	−8.00000	−0.340811
$552$	1.00000	0.0425628
$553$	−8.00000	−0.340195
$554$	−14.0000	−0.594803
$555$	−6.00000	−0.254686
$556$	−4.00000	−0.169638
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	4.00000	0.169334
$559$	−8.00000	−0.338364
$560$	−1.00000	−0.0422577
$561$	24.0000	1.01328
$562$	6.00000	0.253095
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	12.0000	0.505291
$565$	14.0000	0.588984
$566$	24.0000	1.00880
$567$	1.00000	0.0419961
$568$	−12.0000	−0.503509
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	−4.00000	−0.167542
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	8.00000	0.334497
$573$	−8.00000	−0.334205
$574$	10.0000	0.417392
$575$	−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	$0.486745\pi$
$578$	19.0000	0.790296
$579$	14.0000	0.581820
$580$	−2.00000	−0.0830455
$581$	−4.00000	−0.165948
$582$	−2.00000	−0.0829027
$583$	24.0000	0.993978
$584$	10.0000	0.413803
$585$	2.00000	0.0826898
$586$	26.0000	1.07405
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−1.00000	−0.0412393
$589$	−16.0000	−0.659269
$590$	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
$595$	−6.00000	−0.245976
$596$	10.0000	0.409616
$597$	−24.0000	−0.982255
$598$	2.00000	0.0817861
$599$	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
$601$	−14.0000	−0.571072	−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000	−0.571072	−0.285536	+	0.958368i	$0.592172\pi$
$602$	4.00000	0.163028
$603$	−12.0000	−0.488678
$604$	0	0
$605$	−5.00000	−0.203279
$606$	−14.0000	−0.568711
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	−4.00000	−0.162221
$609$	−2.00000	−0.0810441
$610$	14.0000	0.566843
$611$	24.0000	0.970936
$612$	6.00000	0.242536
$613$	42.0000	1.69636	0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000	1.69636	0.848182	+	0.529705i	$0.177697\pi$
$614$	20.0000	0.807134
$615$	10.0000	0.403239
$616$	−4.00000	−0.161165
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	−8.00000	−0.321807
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	−4.00000	−0.160644
$621$	1.00000	0.0401286
$622$	24.0000	0.962312
$623$	−6.00000	−0.240385
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	−16.0000	−0.638978
$628$	−14.0000	−0.558661
$629$	−36.0000	−1.43541
$630$	−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
$633$	28.0000	1.11290
$634$	−18.0000	−0.714871
$635$	12.0000	0.476205
$636$	6.00000	0.237915
$637$	−2.00000	−0.0792429
$638$	−8.00000	−0.316723
$639$	−12.0000	−0.474713
$640$	−1.00000	−0.0395285
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	24.0000	0.946468	0.473234	−	0.880937i	$-0.343087\pi$
$643$	24.0000	0.946468	0.473234	+	0.880937i	$0.343087\pi$
$644$	−1.00000	−0.0394055
$645$	4.00000	0.157500
$646$	−24.0000	−0.944267
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	1.00000	0.0392837
$649$	16.0000	0.628055
$650$	−2.00000	−0.0784465
$651$	−4.00000	−0.156772
$652$	12.0000	0.469956
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	6.00000	0.234619
$655$	−12.0000	−0.468879
$656$	10.0000	0.390434
$657$	10.0000	0.390137
$658$	−12.0000	−0.467809
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	−4.00000	−0.155700
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	−28.0000	−1.08825
$663$	12.0000	0.466041
$664$	−4.00000	−0.155230
$665$	4.00000	0.155113
$666$	−6.00000	−0.232495
$667$	−2.00000	−0.0774403
$668$	−20.0000	−0.773823
$669$	16.0000	0.618596
$670$	12.0000	0.463600
$671$	56.0000	2.16186
$672$	−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	$0.438264\pi$
$674$	30.0000	1.15556
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	26.0000	0.999261	0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000	0.999261	0.499631	+	0.866239i	$0.333469\pi$
$678$	14.0000	0.537667
$679$	2.00000	0.0767530
$680$	−6.00000	−0.230089
$681$	28.0000	1.07296
$682$	−16.0000	−0.612672
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−4.00000	−0.152944
$685$	−10.0000	−0.382080
$686$	1.00000	0.0381802
$687$	22.0000	0.839352
$688$	4.00000	0.152499
$689$	12.0000	0.457164
$690$	−1.00000	−0.0380693
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	10.0000	0.380143
$693$	−4.00000	−0.151947
$694$	28.0000	1.06287
$695$	4.00000	0.151729
$696$	−2.00000	−0.0758098
$697$	60.0000	2.27266
$698$	−30.0000	−1.13552
$699$	−26.0000	−0.983410
$700$	1.00000	0.0377964
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	2.00000	0.0754851
$703$	24.0000	0.905177
$704$	−4.00000	−0.150756
$705$	−12.0000	−0.451946
$706$	26.0000	0.978523
$707$	14.0000	0.526524
$708$	4.00000	0.150329
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	12.0000	0.450352
$711$	−8.00000	−0.300023
$712$	−6.00000	−0.224860
$713$	−4.00000	−0.149801
$714$	−6.00000	−0.224544
$715$	−8.00000	−0.299183
$716$	4.00000	0.149487
$717$	28.0000	1.04568
$718$	−32.0000	−1.19423
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	−1.00000	−0.0372678
$721$	8.00000	0.297936
$722$	−3.00000	−0.111648
$723$	18.0000	0.669427
$724$	−22.0000	−0.817624
$725$	2.00000	0.0742781
$726$	−5.00000	−0.185567
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−10.0000	−0.370117
$731$	24.0000	0.887672
$732$	14.0000	0.517455
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	8.00000	0.295285
$735$	1.00000	0.0368856
$736$	−1.00000	−0.0368605
$737$	48.0000	1.76810
$738$	10.0000	0.368105
$739$	36.0000	1.32428	0.662141	−	0.749380i	$-0.269648\pi$
$739$	36.0000	1.32428	0.662141	+	0.749380i	$0.269648\pi$
$740$	6.00000	0.220564
$741$	−8.00000	−0.293887
$742$	−6.00000	−0.220267
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	−4.00000	−0.146647
$745$	−10.0000	−0.366372
$746$	−22.0000	−0.805477
$747$	−4.00000	−0.146352
$748$	−24.0000	−0.877527
$749$	0	0
$750$	1.00000	0.0365148
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	−12.0000	−0.437595
$753$	−24.0000	−0.874609
$754$	−4.00000	−0.145671
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	−8.00000	−0.290573
$759$	−4.00000	−0.145191
$760$	4.00000	0.145095
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	12.0000	0.434714
$763$	−6.00000	−0.217215
$764$	8.00000	0.289430
$765$	−6.00000	−0.216930
$766$	0	0
$767$	8.00000	0.288863
$768$	−1.00000	−0.0360844
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	4.00000	0.144150
$771$	−18.0000	−0.648254
$772$	−14.0000	−0.503871
$773$	−54.0000	−1.94225	−0.971123	−	0.238581i	$-0.923318\pi$
$773$	−54.0000	−1.94225	−0.971123	+	0.238581i	$0.923318\pi$
$774$	4.00000	0.143777
$775$	4.00000	0.143684
$776$	2.00000	0.0717958
$777$	6.00000	0.215249
$778$	26.0000	0.932145
$779$	−40.0000	−1.43315
$780$	−2.00000	−0.0716115
$781$	48.0000	1.71758
$782$	−6.00000	−0.214560
$783$	−2.00000	−0.0714742
$784$	1.00000	0.0357143
$785$	14.0000	0.499681
$786$	−12.0000	−0.428026
$787$	8.00000	0.285169	0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000	0.285169	0.142585	+	0.989783i	$0.454459\pi$
$788$	−18.0000	−0.641223
$789$	16.0000	0.569615
$790$	8.00000	0.284627
$791$	−14.0000	−0.497783
$792$	−4.00000	−0.142134
$793$	28.0000	0.994309
$794$	−2.00000	−0.0709773
$795$	−6.00000	−0.212798
$796$	24.0000	0.850657
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	4.00000	0.141598
$799$	−72.0000	−2.54718
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	−34.0000	−1.20058
$803$	−40.0000	−1.41157
$804$	12.0000	0.423207
$805$	1.00000	0.0352454
$806$	−8.00000	−0.281788
$807$	10.0000	0.352017
$808$	14.0000	0.492518
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	−1.00000	−0.0351364
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	2.00000	0.0701862
$813$	20.0000	0.701431
$814$	24.0000	0.841200
$815$	−12.0000	−0.420342
$816$	−6.00000	−0.210042
$817$	−16.0000	−0.559769
$818$	10.0000	0.349642
$819$	−2.00000	−0.0698857
$820$	−10.0000	−0.349215
$821$	2.00000	0.0698005	0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000	0.0698005	0.0349002	+	0.999391i	$0.488889\pi$
$822$	−10.0000	−0.348790
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	8.00000	0.278693
$825$	4.00000	0.139262
$826$	−4.00000	−0.139178
$827$	16.0000	0.556375	0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000	0.556375	0.278187	+	0.960527i	$0.410266\pi$
$828$	−1.00000	−0.0347524
$829$	−38.0000	−1.31979	−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000	−1.31979	−0.659897	+	0.751356i	$0.729400\pi$
$830$	4.00000	0.138842
$831$	14.0000	0.485655
$832$	−2.00000	−0.0693375
$833$	6.00000	0.207888
$834$	4.00000	0.138509
$835$	20.0000	0.692129
$836$	16.0000	0.553372
$837$	−4.00000	−0.138260
$838$	−40.0000	−1.38178
$839$	32.0000	1.10476	0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000	1.10476	0.552381	+	0.833592i	$0.313719\pi$
$840$	1.00000	0.0345033
$841$	−25.0000	−0.862069
$842$	26.0000	0.896019
$843$	−6.00000	−0.206651
$844$	−28.0000	−0.963800
$845$	9.00000	0.309609
$846$	−12.0000	−0.412568
$847$	5.00000	0.171802
$848$	−6.00000	−0.206041
$849$	−24.0000	−0.823678
$850$	6.00000	0.205798
$851$	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	$0.377082\pi$
$854$	−14.0000	−0.479070
$855$	4.00000	0.136797
$856$	0	0
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	−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	$0.710502\pi$
$860$	−4.00000	−0.136399
$861$	−10.0000	−0.340799
$862$	0	0
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	−1.00000	−0.0340207
$865$	−10.0000	−0.340010
$866$	−30.0000	−1.01944
$867$	−19.0000	−0.645274
$868$	4.00000	0.135769
$869$	32.0000	1.08553
$870$	2.00000	0.0678064
$871$	24.0000	0.813209
$872$	−6.00000	−0.203186
$873$	2.00000	0.0676897
$874$	4.00000	0.135302
$875$	−1.00000	−0.0338062
$876$	−10.0000	−0.337869
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	36.0000	1.21494
$879$	−26.0000	−0.876958
$880$	4.00000	0.134840
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	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	$0.656156\pi$
$884$	−12.0000	−0.403604
$885$	−4.00000	−0.134459
$886$	−20.0000	−0.671913
$887$	4.00000	0.134307	0.0671534	−	0.997743i	$-0.478608\pi$
$887$	4.00000	0.134307	0.0671534	+	0.997743i	$0.478608\pi$
$888$	6.00000	0.201347
$889$	−12.0000	−0.402467
$890$	6.00000	0.201120
$891$	−4.00000	−0.134005
$892$	−16.0000	−0.535720
$893$	48.0000	1.60626
$894$	−10.0000	−0.334450
$895$	−4.00000	−0.133705
$896$	1.00000	0.0334077
$897$	−2.00000	−0.0667781
$898$	−22.0000	−0.734150
$899$	8.00000	0.266815
$900$	1.00000	0.0333333
$901$	−36.0000	−1.19933
$902$	−40.0000	−1.33185
$903$	−4.00000	−0.133112
$904$	−14.0000	−0.465633
$905$	22.0000	0.731305
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−28.0000	−0.929213
$909$	14.0000	0.464351
$910$	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
$913$	16.0000	0.529523
$914$	14.0000	0.463079
$915$	−14.0000	−0.462826
$916$	−22.0000	−0.726900
$917$	12.0000	0.396275
$918$	−6.00000	−0.198030
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	1.00000	0.0329690
$921$	−20.0000	−0.659022
$922$	30.0000	0.987997
$923$	24.0000	0.789970
$924$	4.00000	0.131590
$925$	−6.00000	−0.197279
$926$	36.0000	1.18303
$927$	8.00000	0.262754
$928$	2.00000	0.0656532
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	4.00000	0.131165
$931$	−4.00000	−0.131095
$932$	26.0000	0.851658
$933$	−24.0000	−0.785725
$934$	4.00000	0.130884
$935$	24.0000	0.784884
$936$	−2.00000	−0.0653720
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	−12.0000	−0.391814
$939$	−10.0000	−0.326338
$940$	12.0000	0.391397
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	14.0000	0.456145
$943$	−10.0000	−0.325645
$944$	−4.00000	−0.130189
$945$	1.00000	0.0325300
$946$	−16.0000	−0.520205
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	8.00000	0.259828
$949$	−20.0000	−0.649227
$950$	−4.00000	−0.129777
$951$	18.0000	0.583690
$952$	6.00000	0.194461
$953$	18.0000	0.583077	0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000	0.583077	0.291539	+	0.956559i	$0.405833\pi$
$954$	−6.00000	−0.194257
$955$	−8.00000	−0.258874
$956$	−28.0000	−0.905585
$957$	8.00000	0.258603
$958$	24.0000	0.775405
$959$	10.0000	0.322917
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	12.0000	0.386896
$963$	0	0
$964$	−18.0000	−0.579741
$965$	14.0000	0.450676
$966$	1.00000	0.0321745
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	5.00000	0.160706
$969$	24.0000	0.770991
$970$	−2.00000	−0.0642161
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	−1.00000	−0.0320750
$973$	−4.00000	−0.128234
$974$	−20.0000	−0.640841
$975$	2.00000	0.0640513
$976$	−14.0000	−0.448129
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	−12.0000	−0.383718
$979$	24.0000	0.767043
$980$	−1.00000	−0.0319438
$981$	−6.00000	−0.191565
$982$	28.0000	0.893516
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	−10.0000	−0.318788
$985$	18.0000	0.573528
$986$	12.0000	0.382158
$987$	12.0000	0.381964
$988$	8.00000	0.254514
$989$	−4.00000	−0.127193
$990$	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	$0.151088\pi$
$992$	4.00000	0.127000
$993$	28.0000	0.888553
$994$	−12.0000	−0.380617
$995$	−24.0000	−0.760851
$996$	4.00000	0.126745
$997$	−18.0000	−0.570066	−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000	−0.570066	−0.285033	+	0.958518i	$0.592005\pi$
$998$	−20.0000	−0.633089
$999$	6.00000	0.189832

Twists

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

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