LMFDB - Embedded newform 4830.2.a.e.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)

$f(q)$

$=$

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

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

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
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	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
$22$	−2.00000	−0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	−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
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−6.00000	−1.02899
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	4.00000	0.648886
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−1.00000	−0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	2.00000	0.301511
$45$	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
$52$	4.00000	0.554700
$53$	−8.00000	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$54$	1.00000	0.136083
$55$	2.00000	0.269680
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	−2.00000	−0.262613
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	−1.00000	−0.129099
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−2.00000	−0.254000
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	2.00000	0.246183
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	6.00000	0.727607
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	−1.00000	−0.117851
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	−8.00000	−0.929981
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	−2.00000	−0.227921
$78$	4.00000	0.452911
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−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
$86$	0	0
$87$	−2.00000	−0.214423
$88$	−2.00000	−0.213201
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−0.105409
$91$	−4.00000	−0.419314
$92$	−1.00000	−0.104257
$93$	−2.00000	−0.207390
$94$	−8.00000	−0.825137
$95$	−4.00000	−0.410391
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.00000	−0.101015
$99$	2.00000	0.201008
$100$	1.00000	0.100000
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	6.00000	0.594089
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−4.00000	−0.392232
$105$	1.00000	0.0975900
$106$	8.00000	0.777029
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−2.00000	−0.190693
$111$	−8.00000	−0.759326
$112$	−1.00000	−0.0944911
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	−4.00000	−0.374634
$115$	−1.00000	−0.0932505
$116$	2.00000	0.185695
$117$	4.00000	0.369800
$118$	14.0000	1.28880
$119$	−6.00000	−0.550019
$120$	1.00000	0.0912871
$121$	−7.00000	−0.636364
$122$	6.00000	0.543214
$123$	−6.00000	−0.541002
$124$	2.00000	0.179605
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−4.00000	−0.350823
$131$	−14.0000	−1.22319	−0.611593	−	0.791173i	$-0.709471\pi$
$131$	−14.0000	−1.22319	−0.611593	+	0.791173i	$0.709471\pi$
$132$	−2.00000	−0.174078
$133$	4.00000	0.346844
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	−6.00000	−0.514496
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	−1.00000	−0.0851257
$139$	10.0000	0.848189	0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000	0.848189	0.424094	+	0.905618i	$0.360592\pi$
$140$	−1.00000	−0.0845154
$141$	−8.00000	−0.673722
$142$	−4.00000	−0.335673
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	−8.00000	−0.662085
$147$	−1.00000	−0.0824786
$148$	8.00000	0.657596
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	1.00000	0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	4.00000	0.324443
$153$	6.00000	0.485071
$154$	2.00000	0.161165
$155$	2.00000	0.160644
$156$	−4.00000	−0.320256
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	−10.0000	−0.795557
$159$	8.00000	0.634441
$160$	−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	$0.449930\pi$
$164$	6.00000	0.468521
$165$	−2.00000	−0.155700
$166$	4.00000	0.310460
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	−1.00000	−0.0771517
$169$	3.00000	0.230769
$170$	−6.00000	−0.460179
$171$	−4.00000	−0.305888
$172$	0	0
$173$	16.0000	1.21646	0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000	1.21646	0.608229	+	0.793762i	$0.291880\pi$
$174$	2.00000	0.151620
$175$	−1.00000	−0.0755929
$176$	2.00000	0.150756
$177$	14.0000	1.05230
$178$	−6.00000	−0.449719
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	1.00000	0.0745356
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	4.00000	0.296500
$183$	6.00000	0.443533
$184$	1.00000	0.0737210
$185$	8.00000	0.588172
$186$	2.00000	0.146647
$187$	12.0000	0.877527
$188$	8.00000	0.583460
$189$	1.00000	0.0727393
$190$	4.00000	0.290191
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	2.00000	0.143592
$195$	−4.00000	−0.286446
$196$	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	$0.615940\pi$
$198$	−2.00000	−0.142134
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	−1.00000	−0.0707107
$201$	4.00000	0.282138
$202$	14.0000	0.985037
$203$	−2.00000	−0.140372
$204$	−6.00000	−0.420084
$205$	6.00000	0.419058
$206$	8.00000	0.557386
$207$	−1.00000	−0.0695048
$208$	4.00000	0.277350
$209$	−8.00000	−0.553372
$210$	−1.00000	−0.0690066
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	−8.00000	−0.549442
$213$	−4.00000	−0.274075
$214$	4.00000	0.273434
$215$	0	0
$216$	1.00000	0.0680414
$217$	−2.00000	−0.135769
$218$	−10.0000	−0.677285
$219$	−8.00000	−0.540590
$220$	2.00000	0.134840
$221$	24.0000	1.61441
$222$	8.00000	0.536925
$223$	−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
$226$	−8.00000	−0.532152
$227$	−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	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	1.00000	0.0659380
$231$	2.00000	0.131590
$232$	−2.00000	−0.131306
$233$	−30.0000	−1.96537	−0.982683	−	0.185296i	$-0.940675\pi$
$233$	−30.0000	−1.96537	−0.982683	+	0.185296i	$0.940675\pi$
$234$	−4.00000	−0.261488
$235$	8.00000	0.521862
$236$	−14.0000	−0.911322
$237$	−10.0000	−0.649570
$238$	6.00000	0.388922
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	−1.00000	−0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	7.00000	0.449977
$243$	−1.00000	−0.0641500
$244$	−6.00000	−0.384111
$245$	1.00000	0.0638877
$246$	6.00000	0.382546
$247$	−16.0000	−1.01806
$248$	−2.00000	−0.127000
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	−1.00000	−0.0629941
$253$	−2.00000	−0.125739
$254$	−8.00000	−0.501965
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	−12.0000	−0.748539	−0.374270	−	0.927320i	$-0.622107\pi$
$257$	−12.0000	−0.748539	−0.374270	+	0.927320i	$0.622107\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	4.00000	0.248069
$261$	2.00000	0.123797
$262$	14.0000	0.864923
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	2.00000	0.123091
$265$	−8.00000	−0.491436
$266$	−4.00000	−0.245256
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	1.00000	0.0608581
$271$	−14.0000	−0.850439	−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000	−0.850439	−0.425220	+	0.905090i	$0.639803\pi$
$272$	6.00000	0.363803
$273$	4.00000	0.242091
$274$	−12.0000	−0.724947
$275$	2.00000	0.120605
$276$	1.00000	0.0601929
$277$	−6.00000	−0.360505	−0.180253	−	0.983620i	$-0.557691\pi$
$277$	−6.00000	−0.360505	−0.180253	+	0.983620i	$0.557691\pi$
$278$	−10.0000	−0.599760
$279$	2.00000	0.119737
$280$	1.00000	0.0597614
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	8.00000	0.476393
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	4.00000	0.237356
$285$	4.00000	0.236940
$286$	−8.00000	−0.473050
$287$	−6.00000	−0.354169
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	−2.00000	−0.117444
$291$	2.00000	0.117242
$292$	8.00000	0.468165
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	1.00000	0.0583212
$295$	−14.0000	−0.815112
$296$	−8.00000	−0.464991
$297$	−2.00000	−0.116052
$298$	22.0000	1.27443
$299$	−4.00000	−0.231326
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	4.00000	0.230174
$303$	14.0000	0.804279
$304$	−4.00000	−0.229416
$305$	−6.00000	−0.343559
$306$	−6.00000	−0.342997
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−2.00000	−0.113961
$309$	8.00000	0.455104
$310$	−2.00000	−0.113592
$311$	34.0000	1.92796	0.963982	−	0.265969i	$-0.0856919\pi$
$311$	34.0000	1.92796	0.963982	+	0.265969i	$0.0856919\pi$
$312$	4.00000	0.226455
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−22.0000	−1.24153
$315$	−1.00000	−0.0563436
$316$	10.0000	0.562544
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−8.00000	−0.448618
$319$	4.00000	0.223957
$320$	1.00000	0.0559017
$321$	4.00000	0.223258
$322$	−1.00000	−0.0557278
$323$	−24.0000	−1.33540
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−4.00000	−0.221540
$327$	−10.0000	−0.553001
$328$	−6.00000	−0.331295
$329$	−8.00000	−0.441054
$330$	2.00000	0.110096
$331$	36.0000	1.97874	0.989369	−	0.145424i	$-0.0464545\pi$
$331$	36.0000	1.97874	0.989369	+	0.145424i	$0.0464545\pi$
$332$	−4.00000	−0.219529
$333$	8.00000	0.438397
$334$	−16.0000	−0.875481
$335$	−4.00000	−0.218543
$336$	1.00000	0.0545545
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	−3.00000	−0.163178
$339$	−8.00000	−0.434500
$340$	6.00000	0.325396
$341$	4.00000	0.216612
$342$	4.00000	0.216295
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	1.00000	0.0538382
$346$	−16.0000	−0.860165
$347$	36.0000	1.93258	0.966291	−	0.257454i	$-0.0828835\pi$
$347$	36.0000	1.93258	0.966291	+	0.257454i	$0.0828835\pi$
$348$	−2.00000	−0.107211
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	1.00000	0.0534522
$351$	−4.00000	−0.213504
$352$	−2.00000	−0.106600
$353$	−16.0000	−0.851594	−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−16.0000	−0.851594	−0.425797	+	0.904819i	$0.640006\pi$
$354$	−14.0000	−0.744092
$355$	4.00000	0.212298
$356$	6.00000	0.317999
$357$	6.00000	0.317554
$358$	16.0000	0.845626
$359$	−34.0000	−1.79445	−0.897226	−	0.441572i	$-0.854421\pi$
$359$	−34.0000	−1.79445	−0.897226	+	0.441572i	$0.854421\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	2.00000	0.105118
$363$	7.00000	0.367405
$364$	−4.00000	−0.209657
$365$	8.00000	0.418739
$366$	−6.00000	−0.313625
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	−1.00000	−0.0521286
$369$	6.00000	0.312348
$370$	−8.00000	−0.415900
$371$	8.00000	0.415339
$372$	−2.00000	−0.103695
$373$	−24.0000	−1.24267	−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000	−1.24267	−0.621336	+	0.783544i	$0.713410\pi$
$374$	−12.0000	−0.620505
$375$	−1.00000	−0.0516398
$376$	−8.00000	−0.412568
$377$	8.00000	0.412021
$378$	−1.00000	−0.0514344
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	−4.00000	−0.205196
$381$	−8.00000	−0.409852
$382$	−2.00000	−0.102329
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.00000	0.0510310
$385$	−2.00000	−0.101929
$386$	−14.0000	−0.712581
$387$	0	0
$388$	−2.00000	−0.101535
$389$	34.0000	1.72387	0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000	1.72387	0.861934	+	0.507020i	$0.169253\pi$
$390$	4.00000	0.202548
$391$	−6.00000	−0.303433
$392$	−1.00000	−0.0505076
$393$	14.0000	0.706207
$394$	10.0000	0.503793
$395$	10.0000	0.503155
$396$	2.00000	0.100504
$397$	32.0000	1.60603	0.803017	−	0.595956i	$-0.203227\pi$
$397$	32.0000	1.60603	0.803017	+	0.595956i	$0.203227\pi$
$398$	8.00000	0.401004
$399$	−4.00000	−0.200250
$400$	1.00000	0.0500000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	−4.00000	−0.199502
$403$	8.00000	0.398508
$404$	−14.0000	−0.696526
$405$	1.00000	0.0496904
$406$	2.00000	0.0992583
$407$	16.0000	0.793091
$408$	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	$0.683059\pi$
$410$	−6.00000	−0.296319
$411$	−12.0000	−0.591916
$412$	−8.00000	−0.394132
$413$	14.0000	0.688895
$414$	1.00000	0.0491473
$415$	−4.00000	−0.196352
$416$	−4.00000	−0.196116
$417$	−10.0000	−0.489702
$418$	8.00000	0.391293
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	1.00000	0.0487950
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	−16.0000	−0.778868
$423$	8.00000	0.388973
$424$	8.00000	0.388514
$425$	6.00000	0.291043
$426$	4.00000	0.193801
$427$	6.00000	0.290360
$428$	−4.00000	−0.193347
$429$	−8.00000	−0.386244
$430$	0	0
$431$	−10.0000	−0.481683	−0.240842	−	0.970564i	$-0.577423\pi$
$431$	−10.0000	−0.481683	−0.240842	+	0.970564i	$0.577423\pi$
$432$	−1.00000	−0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	2.00000	0.0960031
$435$	−2.00000	−0.0958927
$436$	10.0000	0.478913
$437$	4.00000	0.191346
$438$	8.00000	0.382255
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	−2.00000	−0.0953463
$441$	1.00000	0.0476190
$442$	−24.0000	−1.14156
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	−8.00000	−0.379663
$445$	6.00000	0.284427
$446$	16.0000	0.757622
$447$	22.0000	1.04056
$448$	−1.00000	−0.0472456
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	−1.00000	−0.0471405
$451$	12.0000	0.565058
$452$	8.00000	0.376288
$453$	4.00000	0.187936
$454$	4.00000	0.187729
$455$	−4.00000	−0.187523
$456$	−4.00000	−0.187317
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	−26.0000	−1.21490
$459$	−6.00000	−0.280056
$460$	−1.00000	−0.0466252
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	−2.00000	−0.0930484
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	2.00000	0.0928477
$465$	−2.00000	−0.0927478
$466$	30.0000	1.38972
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	4.00000	0.184900
$469$	4.00000	0.184703
$470$	−8.00000	−0.369012
$471$	−22.0000	−1.01371
$472$	14.0000	0.644402
$473$	0	0
$474$	10.0000	0.459315
$475$	−4.00000	−0.183533
$476$	−6.00000	−0.275010
$477$	−8.00000	−0.366295
$478$	4.00000	0.182956
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	1.00000	0.0456435
$481$	32.0000	1.45907
$482$	14.0000	0.637683
$483$	−1.00000	−0.0455016
$484$	−7.00000	−0.318182
$485$	−2.00000	−0.0908153
$486$	1.00000	0.0453609
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	6.00000	0.271607
$489$	−4.00000	−0.180886
$490$	−1.00000	−0.0451754
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	−6.00000	−0.270501
$493$	12.0000	0.540453
$494$	16.0000	0.719874
$495$	2.00000	0.0898933
$496$	2.00000	0.0898027
$497$	−4.00000	−0.179425
$498$	−4.00000	−0.179244
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	1.00000	0.0447214
$501$	−16.0000	−0.714827
$502$	8.00000	0.357057
$503$	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
$506$	2.00000	0.0889108
$507$	−3.00000	−0.133235
$508$	8.00000	0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	6.00000	0.265684
$511$	−8.00000	−0.353899
$512$	−1.00000	−0.0441942
$513$	4.00000	0.176604
$514$	12.0000	0.529297
$515$	−8.00000	−0.352522
$516$	0	0
$517$	16.0000	0.703679
$518$	8.00000	0.351500
$519$	−16.0000	−0.702322
$520$	−4.00000	−0.175412
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	−2.00000	−0.0875376
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−14.0000	−0.611593
$525$	1.00000	0.0436436
$526$	−28.0000	−1.22086
$527$	12.0000	0.522728
$528$	−2.00000	−0.0870388
$529$	1.00000	0.0434783
$530$	8.00000	0.347498
$531$	−14.0000	−0.607548
$532$	4.00000	0.173422
$533$	24.0000	1.03956
$534$	6.00000	0.259645
$535$	−4.00000	−0.172935
$536$	4.00000	0.172774
$537$	16.0000	0.690451
$538$	6.00000	0.258678
$539$	2.00000	0.0861461
$540$	−1.00000	−0.0430331
$541$	34.0000	1.46177	0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000	1.46177	0.730887	+	0.682498i	$0.239107\pi$
$542$	14.0000	0.601351
$543$	2.00000	0.0858282
$544$	−6.00000	−0.257248
$545$	10.0000	0.428353
$546$	−4.00000	−0.171184
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	12.0000	0.512615
$549$	−6.00000	−0.256074
$550$	−2.00000	−0.0852803
$551$	−8.00000	−0.340811
$552$	−1.00000	−0.0425628
$553$	−10.0000	−0.425243
$554$	6.00000	0.254916
$555$	−8.00000	−0.339581
$556$	10.0000	0.424094
$557$	16.0000	0.677942	0.338971	−	0.940797i	$-0.389921\pi$
$557$	16.0000	0.677942	0.338971	+	0.940797i	$0.389921\pi$
$558$	−2.00000	−0.0846668
$559$	0	0
$560$	−1.00000	−0.0422577
$561$	−12.0000	−0.506640
$562$	10.0000	0.421825
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−8.00000	−0.336861
$565$	8.00000	0.336563
$566$	−20.0000	−0.840663
$567$	−1.00000	−0.0419961
$568$	−4.00000	−0.167836
$569$	−14.0000	−0.586911	−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000	−0.586911	−0.293455	+	0.955973i	$0.594805\pi$
$570$	−4.00000	−0.167542
$571$	18.0000	0.753277	0.376638	−	0.926360i	$-0.377080\pi$
$571$	18.0000	0.753277	0.376638	+	0.926360i	$0.377080\pi$
$572$	8.00000	0.334497
$573$	−2.00000	−0.0835512
$574$	6.00000	0.250435
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	−19.0000	−0.790296
$579$	−14.0000	−0.581820
$580$	2.00000	0.0830455
$581$	4.00000	0.165948
$582$	−2.00000	−0.0829027
$583$	−16.0000	−0.662652
$584$	−8.00000	−0.331042
$585$	4.00000	0.165380
$586$	−14.0000	−0.578335
$587$	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
$589$	−8.00000	−0.329634
$590$	14.0000	0.576371
$591$	10.0000	0.411345
$592$	8.00000	0.328798
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	2.00000	0.0820610
$595$	−6.00000	−0.245976
$596$	−22.0000	−0.901155
$597$	8.00000	0.327418
$598$	4.00000	0.163572
$599$	32.0000	1.30748	0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000	1.30748	0.653742	+	0.756717i	$0.273198\pi$
$600$	1.00000	0.0408248
$601$	46.0000	1.87638	0.938190	−	0.346122i	$-0.112502\pi$
$601$	46.0000	1.87638	0.938190	+	0.346122i	$0.112502\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	−4.00000	−0.162758
$605$	−7.00000	−0.284590
$606$	−14.0000	−0.568711
$607$	−36.0000	−1.46119	−0.730597	−	0.682808i	$-0.760758\pi$
$607$	−36.0000	−1.46119	−0.730597	+	0.682808i	$0.760758\pi$
$608$	4.00000	0.162221
$609$	2.00000	0.0810441
$610$	6.00000	0.242933
$611$	32.0000	1.29458
$612$	6.00000	0.242536
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	−4.00000	−0.161427
$615$	−6.00000	−0.241943
$616$	2.00000	0.0805823
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	−8.00000	−0.321807
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	2.00000	0.0803219
$621$	1.00000	0.0401286
$622$	−34.0000	−1.36328
$623$	−6.00000	−0.240385
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−26.0000	−1.03917
$627$	8.00000	0.319489
$628$	22.0000	0.877896
$629$	48.0000	1.91389
$630$	1.00000	0.0398410
$631$	10.0000	0.398094	0.199047	−	0.979990i	$-0.436215\pi$
$631$	10.0000	0.398094	0.199047	+	0.979990i	$0.436215\pi$
$632$	−10.0000	−0.397779
$633$	−16.0000	−0.635943
$634$	−6.00000	−0.238290
$635$	8.00000	0.317470
$636$	8.00000	0.317221
$637$	4.00000	0.158486
$638$	−4.00000	−0.158362
$639$	4.00000	0.158238
$640$	−1.00000	−0.0395285
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	−4.00000	−0.157867
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	24.0000	0.944267
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	−1.00000	−0.0392837
$649$	−28.0000	−1.09910
$650$	−4.00000	−0.156893
$651$	2.00000	0.0783862
$652$	4.00000	0.156652
$653$	−42.0000	−1.64359	−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000	−1.64359	−0.821794	+	0.569785i	$0.807026\pi$
$654$	10.0000	0.391031
$655$	−14.0000	−0.547025
$656$	6.00000	0.234261
$657$	8.00000	0.312110
$658$	8.00000	0.311872
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	−2.00000	−0.0778499
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	−36.0000	−1.39918
$663$	−24.0000	−0.932083
$664$	4.00000	0.155230
$665$	4.00000	0.155113
$666$	−8.00000	−0.309994
$667$	−2.00000	−0.0774403
$668$	16.0000	0.619059
$669$	16.0000	0.618596
$670$	4.00000	0.154533
$671$	−12.0000	−0.463255
$672$	−1.00000	−0.0385758
$673$	38.0000	1.46479	0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000	1.46479	0.732396	+	0.680879i	$0.238402\pi$
$674$	−28.0000	−1.07852
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	8.00000	0.307238
$679$	2.00000	0.0767530
$680$	−6.00000	−0.230089
$681$	4.00000	0.153280
$682$	−4.00000	−0.153168
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−4.00000	−0.152944
$685$	12.0000	0.458496
$686$	1.00000	0.0381802
$687$	−26.0000	−0.991962
$688$	0	0
$689$	−32.0000	−1.21910
$690$	−1.00000	−0.0380693
$691$	26.0000	0.989087	0.494543	−	0.869153i	$-0.335335\pi$
$691$	26.0000	0.989087	0.494543	+	0.869153i	$0.335335\pi$
$692$	16.0000	0.608229
$693$	−2.00000	−0.0759737
$694$	−36.0000	−1.36654
$695$	10.0000	0.379322
$696$	2.00000	0.0758098
$697$	36.0000	1.36360
$698$	−6.00000	−0.227103
$699$	30.0000	1.13470
$700$	−1.00000	−0.0377964
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	4.00000	0.150970
$703$	−32.0000	−1.20690
$704$	2.00000	0.0753778
$705$	−8.00000	−0.301297
$706$	16.0000	0.602168
$707$	14.0000	0.526524
$708$	14.0000	0.526152
$709$	−50.0000	−1.87779	−0.938895	−	0.344204i	$-0.888149\pi$
$709$	−50.0000	−1.87779	−0.938895	+	0.344204i	$0.888149\pi$
$710$	−4.00000	−0.150117
$711$	10.0000	0.375029
$712$	−6.00000	−0.224860
$713$	−2.00000	−0.0749006
$714$	−6.00000	−0.224544
$715$	8.00000	0.299183
$716$	−16.0000	−0.597948
$717$	4.00000	0.149383
$718$	34.0000	1.26887
$719$	−50.0000	−1.86469	−0.932343	−	0.361576i	$-0.882239\pi$
$719$	−50.0000	−1.86469	−0.932343	+	0.361576i	$0.882239\pi$
$720$	1.00000	0.0372678
$721$	8.00000	0.297936
$722$	3.00000	0.111648
$723$	14.0000	0.520666
$724$	−2.00000	−0.0743294
$725$	2.00000	0.0742781
$726$	−7.00000	−0.259794
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	−8.00000	−0.296093
$731$	0	0
$732$	6.00000	0.221766
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	−24.0000	−0.885856
$735$	−1.00000	−0.0368856
$736$	1.00000	0.0368605
$737$	−8.00000	−0.294684
$738$	−6.00000	−0.220863
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	8.00000	0.294086
$741$	16.0000	0.587775
$742$	−8.00000	−0.293689
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	2.00000	0.0733236
$745$	−22.0000	−0.806018
$746$	24.0000	0.878702
$747$	−4.00000	−0.146352
$748$	12.0000	0.438763
$749$	4.00000	0.146157
$750$	1.00000	0.0365148
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	8.00000	0.291730
$753$	8.00000	0.291536
$754$	−8.00000	−0.291343
$755$	−4.00000	−0.145575
$756$	1.00000	0.0363696
$757$	−20.0000	−0.726912	−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000	−0.726912	−0.363456	+	0.931611i	$0.618403\pi$
$758$	−2.00000	−0.0726433
$759$	2.00000	0.0725954
$760$	4.00000	0.145095
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	8.00000	0.289809
$763$	−10.0000	−0.362024
$764$	2.00000	0.0723575
$765$	6.00000	0.216930
$766$	0	0
$767$	−56.0000	−2.02204
$768$	−1.00000	−0.0360844
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	2.00000	0.0720750
$771$	12.0000	0.432169
$772$	14.0000	0.503871
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	2.00000	0.0718421
$776$	2.00000	0.0717958
$777$	8.00000	0.286998
$778$	−34.0000	−1.21896
$779$	−24.0000	−0.859889
$780$	−4.00000	−0.143223
$781$	8.00000	0.286263
$782$	6.00000	0.214560
$783$	−2.00000	−0.0714742
$784$	1.00000	0.0357143
$785$	22.0000	0.785214
$786$	−14.0000	−0.499363
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−10.0000	−0.356235
$789$	−28.0000	−0.996826
$790$	−10.0000	−0.355784
$791$	−8.00000	−0.284447
$792$	−2.00000	−0.0710669
$793$	−24.0000	−0.852265
$794$	−32.0000	−1.13564
$795$	8.00000	0.283731
$796$	−8.00000	−0.283552
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	4.00000	0.141598
$799$	48.0000	1.69812
$800$	−1.00000	−0.0353553
$801$	6.00000	0.212000
$802$	22.0000	0.776847
$803$	16.0000	0.564628
$804$	4.00000	0.141069
$805$	1.00000	0.0352454
$806$	−8.00000	−0.281788
$807$	6.00000	0.211210
$808$	14.0000	0.492518
$809$	−54.0000	−1.89854	−0.949269	−	0.314464i	$-0.898175\pi$
$809$	−54.0000	−1.89854	−0.949269	+	0.314464i	$0.898175\pi$
$810$	−1.00000	−0.0351364
$811$	−30.0000	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$812$	−2.00000	−0.0701862
$813$	14.0000	0.491001
$814$	−16.0000	−0.560800
$815$	4.00000	0.140114
$816$	−6.00000	−0.210042
$817$	0	0
$818$	22.0000	0.769212
$819$	−4.00000	−0.139771
$820$	6.00000	0.209529
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	12.0000	0.418548
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	8.00000	0.278693
$825$	−2.00000	−0.0696311
$826$	−14.0000	−0.487122
$827$	−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
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	4.00000	0.138842
$831$	6.00000	0.208138
$832$	4.00000	0.138675
$833$	6.00000	0.207888
$834$	10.0000	0.346272
$835$	16.0000	0.553703
$836$	−8.00000	−0.276686
$837$	−2.00000	−0.0691301
$838$	−36.0000	−1.24360
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	−1.00000	−0.0345033
$841$	−25.0000	−0.862069
$842$	18.0000	0.620321
$843$	10.0000	0.344418
$844$	16.0000	0.550743
$845$	3.00000	0.103203
$846$	−8.00000	−0.275046
$847$	7.00000	0.240523
$848$	−8.00000	−0.274721
$849$	−20.0000	−0.686398
$850$	−6.00000	−0.205798
$851$	−8.00000	−0.274236
$852$	−4.00000	−0.137038
$853$	−16.0000	−0.547830	−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000	−0.547830	−0.273915	+	0.961754i	$0.588319\pi$
$854$	−6.00000	−0.205316
$855$	−4.00000	−0.136797
$856$	4.00000	0.136717
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	8.00000	0.273115
$859$	−22.0000	−0.750630	−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000	−0.750630	−0.375315	+	0.926897i	$0.622466\pi$
$860$	0	0
$861$	6.00000	0.204479
$862$	10.0000	0.340601
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	1.00000	0.0340207
$865$	16.0000	0.544016
$866$	−14.0000	−0.475739
$867$	−19.0000	−0.645274
$868$	−2.00000	−0.0678844
$869$	20.0000	0.678454
$870$	2.00000	0.0678064
$871$	−16.0000	−0.542139
$872$	−10.0000	−0.338643
$873$	−2.00000	−0.0676897
$874$	−4.00000	−0.135302
$875$	−1.00000	−0.0338062
$876$	−8.00000	−0.270295
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	−22.0000	−0.742464
$879$	−14.0000	−0.472208
$880$	2.00000	0.0674200
$881$	−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
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	24.0000	0.807207
$885$	14.0000	0.470605
$886$	28.0000	0.940678
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	8.00000	0.268462
$889$	−8.00000	−0.268311
$890$	−6.00000	−0.201120
$891$	2.00000	0.0670025
$892$	−16.0000	−0.535720
$893$	−32.0000	−1.07084
$894$	−22.0000	−0.735790
$895$	−16.0000	−0.534821
$896$	1.00000	0.0334077
$897$	4.00000	0.133556
$898$	−30.0000	−1.00111
$899$	4.00000	0.133407
$900$	1.00000	0.0333333
$901$	−48.0000	−1.59911
$902$	−12.0000	−0.399556
$903$	0	0
$904$	−8.00000	−0.266076
$905$	−2.00000	−0.0664822
$906$	−4.00000	−0.132891
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	−4.00000	−0.132745
$909$	−14.0000	−0.464351
$910$	4.00000	0.132599
$911$	30.0000	0.993944	0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000	0.993944	0.496972	+	0.867766i	$0.334445\pi$
$912$	4.00000	0.132453
$913$	−8.00000	−0.264761
$914$	8.00000	0.264616
$915$	6.00000	0.198354
$916$	26.0000	0.859064
$917$	14.0000	0.462321
$918$	6.00000	0.198030
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	1.00000	0.0329690
$921$	−4.00000	−0.131804
$922$	6.00000	0.197599
$923$	16.0000	0.526646
$924$	2.00000	0.0657952
$925$	8.00000	0.263038
$926$	−8.00000	−0.262896
$927$	−8.00000	−0.262754
$928$	−2.00000	−0.0656532
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	2.00000	0.0655826
$931$	−4.00000	−0.131095
$932$	−30.0000	−0.982683
$933$	−34.0000	−1.11311
$934$	−12.0000	−0.392652
$935$	12.0000	0.392442
$936$	−4.00000	−0.130744
$937$	54.0000	1.76410	0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000	1.76410	0.882052	+	0.471153i	$0.156162\pi$
$938$	−4.00000	−0.130605
$939$	−26.0000	−0.848478
$940$	8.00000	0.260931
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	22.0000	0.716799
$943$	−6.00000	−0.195387
$944$	−14.0000	−0.455661
$945$	1.00000	0.0325300
$946$	0	0
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	−10.0000	−0.324785
$949$	32.0000	1.03876
$950$	4.00000	0.129777
$951$	−6.00000	−0.194563
$952$	6.00000	0.194461
$953$	44.0000	1.42530	0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000	1.42530	0.712650	+	0.701520i	$0.247495\pi$
$954$	8.00000	0.259010
$955$	2.00000	0.0647185
$956$	−4.00000	−0.129369
$957$	−4.00000	−0.129302
$958$	−12.0000	−0.387702
$959$	−12.0000	−0.387500
$960$	−1.00000	−0.0322749
$961$	−27.0000	−0.870968
$962$	−32.0000	−1.03172
$963$	−4.00000	−0.128898
$964$	−14.0000	−0.450910
$965$	14.0000	0.450676
$966$	1.00000	0.0321745
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	7.00000	0.224989
$969$	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
$973$	−10.0000	−0.320585
$974$	−8.00000	−0.256337
$975$	−4.00000	−0.128103
$976$	−6.00000	−0.192055
$977$	16.0000	0.511885	0.255943	−	0.966692i	$-0.417614\pi$
$977$	16.0000	0.511885	0.255943	+	0.966692i	$0.417614\pi$
$978$	4.00000	0.127906
$979$	12.0000	0.383522
$980$	1.00000	0.0319438
$981$	10.0000	0.319275
$982$	0	0
$983$	−48.0000	−1.53096	−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000	−1.53096	−0.765481	+	0.643458i	$0.777499\pi$
$984$	6.00000	0.191273
$985$	−10.0000	−0.318626
$986$	−12.0000	−0.382158
$987$	8.00000	0.254643
$988$	−16.0000	−0.509028
$989$	0	0
$990$	−2.00000	−0.0635642
$991$	28.0000	0.889449	0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000	0.889449	0.444725	+	0.895667i	$0.353302\pi$
$992$	−2.00000	−0.0635001
$993$	−36.0000	−1.14243
$994$	4.00000	0.126872
$995$	−8.00000	−0.253617
$996$	4.00000	0.126745
$997$	4.00000	0.126681	0.0633406	−	0.997992i	$-0.479825\pi$
$997$	4.00000	0.126681	0.0633406	+	0.997992i	$0.479825\pi$
$998$	−8.00000	−0.253236
$999$	−8.00000	−0.253109

Twists

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

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