LMFDB - Embedded newform 4730.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
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	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +5.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} +5.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} +7.00000 q^{19} +1.00000 q^{20} +5.00000 q^{21} +1.00000 q^{22} +8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -5.00000 q^{27} +5.00000 q^{28} -5.00000 q^{29} +1.00000 q^{30} -11.0000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +5.00000 q^{35} -2.00000 q^{36} -7.00000 q^{37} +7.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} -12.0000 q^{41} +5.00000 q^{42} -1.00000 q^{43} +1.00000 q^{44} -2.00000 q^{45} +8.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +18.0000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} -13.0000 q^{53} -5.00000 q^{54} +1.00000 q^{55} +5.00000 q^{56} +7.00000 q^{57} -5.00000 q^{58} -8.00000 q^{59} +1.00000 q^{60} +5.00000 q^{61} -11.0000 q^{62} -10.0000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} -12.0000 q^{67} +1.00000 q^{68} +8.00000 q^{69} +5.00000 q^{70} +1.00000 q^{71} -2.00000 q^{72} -10.0000 q^{73} -7.00000 q^{74} +1.00000 q^{75} +7.00000 q^{76} +5.00000 q^{77} +4.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} +4.00000 q^{83} +5.00000 q^{84} +1.00000 q^{85} -1.00000 q^{86} -5.00000 q^{87} +1.00000 q^{88} -9.00000 q^{89} -2.00000 q^{90} +20.0000 q^{91} +8.00000 q^{92} -11.0000 q^{93} +6.00000 q^{94} +7.00000 q^{95} +1.00000 q^{96} -8.00000 q^{97} +18.0000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	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	$0.312833\pi$
$14$	5.00000	1.33631
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	−2.00000	−0.471405
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	1.00000	0.223607
$21$	5.00000	1.09109
$22$	1.00000	0.213201
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	−5.00000	−0.962250
$28$	5.00000	0.944911
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	1.00000	0.182574
$31$	−11.0000	−1.97566	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−11.0000	−1.97566	−0.987829	+	0.155543i	$0.950287\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	5.00000	0.845154
$36$	−2.00000	−0.333333
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	7.00000	1.13555
$39$	4.00000	0.640513
$40$	1.00000	0.158114
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	5.00000	0.771517
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−2.00000	−0.298142
$46$	8.00000	1.17954
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	18.0000	2.57143
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	−13.0000	−1.78569	−0.892844	−	0.450367i	$-0.851293\pi$
$53$	−13.0000	−1.78569	−0.892844	+	0.450367i	$0.851293\pi$
$54$	−5.00000	−0.680414
$55$	1.00000	0.134840
$56$	5.00000	0.668153
$57$	7.00000	0.927173
$58$	−5.00000	−0.656532
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	1.00000	0.129099
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−11.0000	−1.39700
$63$	−10.0000	−1.25988
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	1.00000	0.123091
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	1.00000	0.121268
$69$	8.00000	0.963087
$70$	5.00000	0.597614
$71$	1.00000	0.118678	0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000	0.118678	0.0593391	+	0.998238i	$0.481101\pi$
$72$	−2.00000	−0.235702
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−7.00000	−0.813733
$75$	1.00000	0.115470
$76$	7.00000	0.802955
$77$	5.00000	0.569803
$78$	4.00000	0.452911
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−12.0000	−1.32518
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	5.00000	0.545545
$85$	1.00000	0.108465
$86$	−1.00000	−0.107833
$87$	−5.00000	−0.536056
$88$	1.00000	0.106600
$89$	−9.00000	−0.953998	−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000	−0.953998	−0.476999	+	0.878904i	$0.658275\pi$
$90$	−2.00000	−0.210819
$91$	20.0000	2.09657
$92$	8.00000	0.834058
$93$	−11.0000	−1.14065
$94$	6.00000	0.618853
$95$	7.00000	0.718185
$96$	1.00000	0.102062
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	18.0000	1.81827
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	1.00000	0.0990148
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	4.00000	0.392232
$105$	5.00000	0.487950
$106$	−13.0000	−1.26267
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−5.00000	−0.481125
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	1.00000	0.0953463
$111$	−7.00000	−0.664411
$112$	5.00000	0.472456
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	7.00000	0.655610
$115$	8.00000	0.746004
$116$	−5.00000	−0.464238
$117$	−8.00000	−0.739600
$118$	−8.00000	−0.736460
$119$	5.00000	0.458349
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	5.00000	0.452679
$123$	−12.0000	−1.08200
$124$	−11.0000	−0.987829
$125$	1.00000	0.0894427
$126$	−10.0000	−0.890871
$127$	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
$129$	−1.00000	−0.0880451
$130$	4.00000	0.350823
$131$	15.0000	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$132$	1.00000	0.0870388
$133$	35.0000	3.03488
$134$	−12.0000	−1.03664
$135$	−5.00000	−0.430331
$136$	1.00000	0.0857493
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	8.00000	0.681005
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	5.00000	0.422577
$141$	6.00000	0.505291
$142$	1.00000	0.0839181
$143$	4.00000	0.334497
$144$	−2.00000	−0.166667
$145$	−5.00000	−0.415227
$146$	−10.0000	−0.827606
$147$	18.0000	1.48461
$148$	−7.00000	−0.575396
$149$	−3.00000	−0.245770	−0.122885	−	0.992421i	$-0.539215\pi$
$149$	−3.00000	−0.245770	−0.122885	+	0.992421i	$0.539215\pi$
$150$	1.00000	0.0816497
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	7.00000	0.567775
$153$	−2.00000	−0.161690
$154$	5.00000	0.402911
$155$	−11.0000	−0.883541
$156$	4.00000	0.320256
$157$	−7.00000	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$158$	8.00000	0.636446
$159$	−13.0000	−1.03097
$160$	1.00000	0.0790569
$161$	40.0000	3.15244
$162$	1.00000	0.0785674
$163$	1.00000	0.0783260	0.0391630	−	0.999233i	$-0.487531\pi$
$163$	1.00000	0.0783260	0.0391630	+	0.999233i	$0.487531\pi$
$164$	−12.0000	−0.937043
$165$	1.00000	0.0778499
$166$	4.00000	0.310460
$167$	19.0000	1.47026	0.735132	−	0.677924i	$-0.237120\pi$
$167$	19.0000	1.47026	0.735132	+	0.677924i	$0.237120\pi$
$168$	5.00000	0.385758
$169$	3.00000	0.230769
$170$	1.00000	0.0766965
$171$	−14.0000	−1.07061
$172$	−1.00000	−0.0762493
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−5.00000	−0.379049
$175$	5.00000	0.377964
$176$	1.00000	0.0753778
$177$	−8.00000	−0.601317
$178$	−9.00000	−0.674579
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	−2.00000	−0.149071
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	20.0000	1.48250
$183$	5.00000	0.369611
$184$	8.00000	0.589768
$185$	−7.00000	−0.514650
$186$	−11.0000	−0.806559
$187$	1.00000	0.0731272
$188$	6.00000	0.437595
$189$	−25.0000	−1.81848
$190$	7.00000	0.507833
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	1.00000	0.0721688
$193$	9.00000	0.647834	0.323917	−	0.946085i	$-0.395000\pi$
$193$	9.00000	0.647834	0.323917	+	0.946085i	$0.395000\pi$
$194$	−8.00000	−0.574367
$195$	4.00000	0.286446
$196$	18.0000	1.28571
$197$	−4.00000	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$198$	−2.00000	−0.142134
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	1.00000	0.0707107
$201$	−12.0000	−0.846415
$202$	6.00000	0.422159
$203$	−25.0000	−1.75466
$204$	1.00000	0.0700140
$205$	−12.0000	−0.838116
$206$	0	0
$207$	−16.0000	−1.11208
$208$	4.00000	0.277350
$209$	7.00000	0.484200
$210$	5.00000	0.345033
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	−13.0000	−0.892844
$213$	1.00000	0.0685189
$214$	4.00000	0.273434
$215$	−1.00000	−0.0681994
$216$	−5.00000	−0.340207
$217$	−55.0000	−3.73364
$218$	−10.0000	−0.677285
$219$	−10.0000	−0.675737
$220$	1.00000	0.0674200
$221$	4.00000	0.269069
$222$	−7.00000	−0.469809
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	5.00000	0.334077
$225$	−2.00000	−0.133333
$226$	−12.0000	−0.798228
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	7.00000	0.463586
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	8.00000	0.527504
$231$	5.00000	0.328976
$232$	−5.00000	−0.328266
$233$	−25.0000	−1.63780	−0.818902	−	0.573933i	$-0.805417\pi$
$233$	−25.0000	−1.63780	−0.818902	+	0.573933i	$0.805417\pi$
$234$	−8.00000	−0.522976
$235$	6.00000	0.391397
$236$	−8.00000	−0.520756
$237$	8.00000	0.519656
$238$	5.00000	0.324102
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	1.00000	0.0645497
$241$	16.0000	1.03065	0.515325	−	0.856995i	$-0.327671\pi$
$241$	16.0000	1.03065	0.515325	+	0.856995i	$0.327671\pi$
$242$	1.00000	0.0642824
$243$	16.0000	1.02640
$244$	5.00000	0.320092
$245$	18.0000	1.14998
$246$	−12.0000	−0.765092
$247$	28.0000	1.78160
$248$	−11.0000	−0.698501
$249$	4.00000	0.253490
$250$	1.00000	0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−10.0000	−0.629941
$253$	8.00000	0.502956
$254$	12.0000	0.752947
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	−1.00000	−0.0622573
$259$	−35.0000	−2.17479
$260$	4.00000	0.248069
$261$	10.0000	0.618984
$262$	15.0000	0.926703
$263$	−5.00000	−0.308313	−0.154157	−	0.988046i	$-0.549266\pi$
$263$	−5.00000	−0.308313	−0.154157	+	0.988046i	$0.549266\pi$
$264$	1.00000	0.0615457
$265$	−13.0000	−0.798584
$266$	35.0000	2.14599
$267$	−9.00000	−0.550791
$268$	−12.0000	−0.733017
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−5.00000	−0.304290
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	1.00000	0.0606339
$273$	20.0000	1.21046
$274$	10.0000	0.604122
$275$	1.00000	0.0603023
$276$	8.00000	0.481543
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	16.0000	0.959616
$279$	22.0000	1.31711
$280$	5.00000	0.298807
$281$	16.0000	0.954480	0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000	0.954480	0.477240	+	0.878773i	$0.341637\pi$
$282$	6.00000	0.357295
$283$	−18.0000	−1.06999	−0.534994	−	0.844856i	$-0.679686\pi$
$283$	−18.0000	−1.06999	−0.534994	+	0.844856i	$0.679686\pi$
$284$	1.00000	0.0593391
$285$	7.00000	0.414644
$286$	4.00000	0.236525
$287$	−60.0000	−3.54169
$288$	−2.00000	−0.117851
$289$	−16.0000	−0.941176
$290$	−5.00000	−0.293610
$291$	−8.00000	−0.468968
$292$	−10.0000	−0.585206
$293$	4.00000	0.233682	0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000	0.233682	0.116841	+	0.993151i	$0.462723\pi$
$294$	18.0000	1.04978
$295$	−8.00000	−0.465778
$296$	−7.00000	−0.406867
$297$	−5.00000	−0.290129
$298$	−3.00000	−0.173785
$299$	32.0000	1.85061
$300$	1.00000	0.0577350
$301$	−5.00000	−0.288195
$302$	20.0000	1.15087
$303$	6.00000	0.344691
$304$	7.00000	0.401478
$305$	5.00000	0.286299
$306$	−2.00000	−0.114332
$307$	10.0000	0.570730	0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000	0.570730	0.285365	+	0.958419i	$0.407885\pi$
$308$	5.00000	0.284901
$309$	0	0
$310$	−11.0000	−0.624758
$311$	−35.0000	−1.98467	−0.992334	−	0.123585i	$-0.960561\pi$
$311$	−35.0000	−1.98467	−0.992334	+	0.123585i	$0.960561\pi$
$312$	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	$0.237274\pi$
$314$	−7.00000	−0.395033
$315$	−10.0000	−0.563436
$316$	8.00000	0.450035
$317$	−15.0000	−0.842484	−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000	−0.842484	−0.421242	+	0.906948i	$0.638406\pi$
$318$	−13.0000	−0.729004
$319$	−5.00000	−0.279946
$320$	1.00000	0.0559017
$321$	4.00000	0.223258
$322$	40.0000	2.22911
$323$	7.00000	0.389490
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	1.00000	0.0553849
$327$	−10.0000	−0.553001
$328$	−12.0000	−0.662589
$329$	30.0000	1.65395
$330$	1.00000	0.0550482
$331$	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
$333$	14.0000	0.767195
$334$	19.0000	1.03963
$335$	−12.0000	−0.655630
$336$	5.00000	0.272772
$337$	7.00000	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$338$	3.00000	0.163178
$339$	−12.0000	−0.651751
$340$	1.00000	0.0542326
$341$	−11.0000	−0.595683
$342$	−14.0000	−0.757033
$343$	55.0000	2.96972
$344$	−1.00000	−0.0539164
$345$	8.00000	0.430706
$346$	−2.00000	−0.107521
$347$	−14.0000	−0.751559	−0.375780	−	0.926709i	$-0.622625\pi$
$347$	−14.0000	−0.751559	−0.375780	+	0.926709i	$0.622625\pi$
$348$	−5.00000	−0.268028
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	5.00000	0.267261
$351$	−20.0000	−1.06752
$352$	1.00000	0.0533002
$353$	−28.0000	−1.49029	−0.745145	−	0.666903i	$-0.767620\pi$
$353$	−28.0000	−1.49029	−0.745145	+	0.666903i	$0.767620\pi$
$354$	−8.00000	−0.425195
$355$	1.00000	0.0530745
$356$	−9.00000	−0.476999
$357$	5.00000	0.264628
$358$	−20.0000	−1.05703
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	−2.00000	−0.105409
$361$	30.0000	1.57895
$362$	−10.0000	−0.525588
$363$	1.00000	0.0524864
$364$	20.0000	1.04828
$365$	−10.0000	−0.523424
$366$	5.00000	0.261354
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	8.00000	0.417029
$369$	24.0000	1.24939
$370$	−7.00000	−0.363913
$371$	−65.0000	−3.37463
$372$	−11.0000	−0.570323
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	6.00000	0.309426
$377$	−20.0000	−1.03005
$378$	−25.0000	−1.28586
$379$	24.0000	1.23280	0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000	1.23280	0.616399	+	0.787434i	$0.288591\pi$
$380$	7.00000	0.359092
$381$	12.0000	0.614779
$382$	−4.00000	−0.204658
$383$	−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
$385$	5.00000	0.254824
$386$	9.00000	0.458088
$387$	2.00000	0.101666
$388$	−8.00000	−0.406138
$389$	4.00000	0.202808	0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000	0.202808	0.101404	+	0.994845i	$0.467667\pi$
$390$	4.00000	0.202548
$391$	8.00000	0.404577
$392$	18.0000	0.909137
$393$	15.0000	0.756650
$394$	−4.00000	−0.201517
$395$	8.00000	0.402524
$396$	−2.00000	−0.100504
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−7.00000	−0.350878
$399$	35.0000	1.75219
$400$	1.00000	0.0500000
$401$	−17.0000	−0.848939	−0.424470	−	0.905442i	$-0.639539\pi$
$401$	−17.0000	−0.848939	−0.424470	+	0.905442i	$0.639539\pi$
$402$	−12.0000	−0.598506
$403$	−44.0000	−2.19180
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−25.0000	−1.24073
$407$	−7.00000	−0.346977
$408$	1.00000	0.0495074
$409$	−8.00000	−0.395575	−0.197787	−	0.980245i	$-0.563376\pi$
$409$	−8.00000	−0.395575	−0.197787	+	0.980245i	$0.563376\pi$
$410$	−12.0000	−0.592638
$411$	10.0000	0.493264
$412$	0	0
$413$	−40.0000	−1.96827
$414$	−16.0000	−0.786357
$415$	4.00000	0.196352
$416$	4.00000	0.196116
$417$	16.0000	0.783523
$418$	7.00000	0.342381
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	5.00000	0.243975
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	23.0000	1.11962
$423$	−12.0000	−0.583460
$424$	−13.0000	−0.631336
$425$	1.00000	0.0485071
$426$	1.00000	0.0484502
$427$	25.0000	1.20983
$428$	4.00000	0.193347
$429$	4.00000	0.193122
$430$	−1.00000	−0.0482243
$431$	−6.00000	−0.289010	−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000	−0.289010	−0.144505	+	0.989504i	$0.546159\pi$
$432$	−5.00000	−0.240563
$433$	−20.0000	−0.961139	−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000	−0.961139	−0.480569	+	0.876957i	$0.659570\pi$
$434$	−55.0000	−2.64008
$435$	−5.00000	−0.239732
$436$	−10.0000	−0.478913
$437$	56.0000	2.67884
$438$	−10.0000	−0.477818
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	1.00000	0.0476731
$441$	−36.0000	−1.71429
$442$	4.00000	0.190261
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−7.00000	−0.332205
$445$	−9.00000	−0.426641
$446$	−16.0000	−0.757622
$447$	−3.00000	−0.141895
$448$	5.00000	0.236228
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	−2.00000	−0.0942809
$451$	−12.0000	−0.565058
$452$	−12.0000	−0.564433
$453$	20.0000	0.939682
$454$	2.00000	0.0938647
$455$	20.0000	0.937614
$456$	7.00000	0.327805
$457$	−3.00000	−0.140334	−0.0701670	−	0.997535i	$-0.522353\pi$
$457$	−3.00000	−0.140334	−0.0701670	+	0.997535i	$0.522353\pi$
$458$	−14.0000	−0.654177
$459$	−5.00000	−0.233380
$460$	8.00000	0.373002
$461$	35.0000	1.63011	0.815056	−	0.579382i	$-0.196706\pi$
$461$	35.0000	1.63011	0.815056	+	0.579382i	$0.196706\pi$
$462$	5.00000	0.232621
$463$	22.0000	1.02243	0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000	1.02243	0.511213	+	0.859454i	$0.329196\pi$
$464$	−5.00000	−0.232119
$465$	−11.0000	−0.510113
$466$	−25.0000	−1.15810
$467$	13.0000	0.601568	0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$468$	−8.00000	−0.369800
$469$	−60.0000	−2.77054
$470$	6.00000	0.276759
$471$	−7.00000	−0.322543
$472$	−8.00000	−0.368230
$473$	−1.00000	−0.0459800
$474$	8.00000	0.367452
$475$	7.00000	0.321182
$476$	5.00000	0.229175
$477$	26.0000	1.19046
$478$	−6.00000	−0.274434
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	1.00000	0.0456435
$481$	−28.0000	−1.27669
$482$	16.0000	0.728780
$483$	40.0000	1.82006
$484$	1.00000	0.0454545
$485$	−8.00000	−0.363261
$486$	16.0000	0.725775
$487$	−10.0000	−0.453143	−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000	−0.453143	−0.226572	+	0.973995i	$0.572752\pi$
$488$	5.00000	0.226339
$489$	1.00000	0.0452216
$490$	18.0000	0.813157
$491$	27.0000	1.21849	0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000	1.21849	0.609246	+	0.792981i	$0.291472\pi$
$492$	−12.0000	−0.541002
$493$	−5.00000	−0.225189
$494$	28.0000	1.25978
$495$	−2.00000	−0.0898933
$496$	−11.0000	−0.493915
$497$	5.00000	0.224281
$498$	4.00000	0.179244
$499$	6.00000	0.268597	0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000	0.268597	0.134298	+	0.990941i	$0.457122\pi$
$500$	1.00000	0.0447214
$501$	19.0000	0.848857
$502$	12.0000	0.535586
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	−10.0000	−0.445435
$505$	6.00000	0.266996
$506$	8.00000	0.355643
$507$	3.00000	0.133235
$508$	12.0000	0.532414
$509$	−12.0000	−0.531891	−0.265945	−	0.963988i	$-0.585684\pi$
$509$	−12.0000	−0.531891	−0.265945	+	0.963988i	$0.585684\pi$
$510$	1.00000	0.0442807
$511$	−50.0000	−2.21187
$512$	1.00000	0.0441942
$513$	−35.0000	−1.54529
$514$	14.0000	0.617514
$515$	0	0
$516$	−1.00000	−0.0440225
$517$	6.00000	0.263880
$518$	−35.0000	−1.53781
$519$	−2.00000	−0.0877903
$520$	4.00000	0.175412
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	10.0000	0.437688
$523$	30.0000	1.31181	0.655904	−	0.754844i	$-0.272288\pi$
$523$	30.0000	1.31181	0.655904	+	0.754844i	$0.272288\pi$
$524$	15.0000	0.655278
$525$	5.00000	0.218218
$526$	−5.00000	−0.218010
$527$	−11.0000	−0.479168
$528$	1.00000	0.0435194
$529$	41.0000	1.78261
$530$	−13.0000	−0.564684
$531$	16.0000	0.694341
$532$	35.0000	1.51744
$533$	−48.0000	−2.07911
$534$	−9.00000	−0.389468
$535$	4.00000	0.172935
$536$	−12.0000	−0.518321
$537$	−20.0000	−0.863064
$538$	−18.0000	−0.776035
$539$	18.0000	0.775315
$540$	−5.00000	−0.215166
$541$	−39.0000	−1.67674	−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000	−1.67674	−0.838370	+	0.545101i	$0.816491\pi$
$542$	22.0000	0.944981
$543$	−10.0000	−0.429141
$544$	1.00000	0.0428746
$545$	−10.0000	−0.428353
$546$	20.0000	0.855921
$547$	44.0000	1.88130	0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000	1.88130	0.940652	+	0.339372i	$0.110215\pi$
$548$	10.0000	0.427179
$549$	−10.0000	−0.426790
$550$	1.00000	0.0426401
$551$	−35.0000	−1.49105
$552$	8.00000	0.340503
$553$	40.0000	1.70097
$554$	−22.0000	−0.934690
$555$	−7.00000	−0.297133
$556$	16.0000	0.678551
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	22.0000	0.931334
$559$	−4.00000	−0.169182
$560$	5.00000	0.211289
$561$	1.00000	0.0422200
$562$	16.0000	0.674919
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	6.00000	0.252646
$565$	−12.0000	−0.504844
$566$	−18.0000	−0.756596
$567$	5.00000	0.209980
$568$	1.00000	0.0419591
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	7.00000	0.293198
$571$	−39.0000	−1.63210	−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000	−1.63210	−0.816050	+	0.577982i	$0.803840\pi$
$572$	4.00000	0.167248
$573$	−4.00000	−0.167102
$574$	−60.0000	−2.50435
$575$	8.00000	0.333623
$576$	−2.00000	−0.0833333
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	−16.0000	−0.665512
$579$	9.00000	0.374027
$580$	−5.00000	−0.207614
$581$	20.0000	0.829740
$582$	−8.00000	−0.331611
$583$	−13.0000	−0.538405
$584$	−10.0000	−0.413803
$585$	−8.00000	−0.330759
$586$	4.00000	0.165238
$587$	−33.0000	−1.36206	−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000	−1.36206	−0.681028	+	0.732257i	$0.738467\pi$
$588$	18.0000	0.742307
$589$	−77.0000	−3.17273
$590$	−8.00000	−0.329355
$591$	−4.00000	−0.164538
$592$	−7.00000	−0.287698
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	−5.00000	−0.205152
$595$	5.00000	0.204980
$596$	−3.00000	−0.122885
$597$	−7.00000	−0.286491
$598$	32.0000	1.30858
$599$	17.0000	0.694601	0.347301	−	0.937754i	$-0.387098\pi$
$599$	17.0000	0.694601	0.347301	+	0.937754i	$0.387098\pi$
$600$	1.00000	0.0408248
$601$	20.0000	0.815817	0.407909	−	0.913023i	$-0.366258\pi$
$601$	20.0000	0.815817	0.407909	+	0.913023i	$0.366258\pi$
$602$	−5.00000	−0.203785
$603$	24.0000	0.977356
$604$	20.0000	0.813788
$605$	1.00000	0.0406558
$606$	6.00000	0.243733
$607$	−1.00000	−0.0405887	−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000	−0.0405887	−0.0202944	+	0.999794i	$0.506460\pi$
$608$	7.00000	0.283887
$609$	−25.0000	−1.01305
$610$	5.00000	0.202444
$611$	24.0000	0.970936
$612$	−2.00000	−0.0808452
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	10.0000	0.403567
$615$	−12.0000	−0.483887
$616$	5.00000	0.201456
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	−11.0000	−0.441771
$621$	−40.0000	−1.60514
$622$	−35.0000	−1.40337
$623$	−45.0000	−1.80289
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	26.0000	1.03917
$627$	7.00000	0.279553
$628$	−7.00000	−0.279330
$629$	−7.00000	−0.279108
$630$	−10.0000	−0.398410
$631$	17.0000	0.676759	0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000	0.676759	0.338380	+	0.941010i	$0.390121\pi$
$632$	8.00000	0.318223
$633$	23.0000	0.914168
$634$	−15.0000	−0.595726
$635$	12.0000	0.476205
$636$	−13.0000	−0.515484
$637$	72.0000	2.85274
$638$	−5.00000	−0.197952
$639$	−2.00000	−0.0791188
$640$	1.00000	0.0395285
$641$	9.00000	0.355479	0.177739	−	0.984078i	$-0.443122\pi$
$641$	9.00000	0.355479	0.177739	+	0.984078i	$0.443122\pi$
$642$	4.00000	0.157867
$643$	35.0000	1.38027	0.690133	−	0.723683i	$-0.257552\pi$
$643$	35.0000	1.38027	0.690133	+	0.723683i	$0.257552\pi$
$644$	40.0000	1.57622
$645$	−1.00000	−0.0393750
$646$	7.00000	0.275411
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	1.00000	0.0392837
$649$	−8.00000	−0.314027
$650$	4.00000	0.156893
$651$	−55.0000	−2.15562
$652$	1.00000	0.0391630
$653$	39.0000	1.52619	0.763094	−	0.646288i	$-0.223679\pi$
$653$	39.0000	1.52619	0.763094	+	0.646288i	$0.223679\pi$
$654$	−10.0000	−0.391031
$655$	15.0000	0.586098
$656$	−12.0000	−0.468521
$657$	20.0000	0.780274
$658$	30.0000	1.16952
$659$	−41.0000	−1.59713	−0.798567	−	0.601906i	$-0.794408\pi$
$659$	−41.0000	−1.59713	−0.798567	+	0.601906i	$0.794408\pi$
$660$	1.00000	0.0389249
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	36.0000	1.39918
$663$	4.00000	0.155347
$664$	4.00000	0.155230
$665$	35.0000	1.35724
$666$	14.0000	0.542489
$667$	−40.0000	−1.54881
$668$	19.0000	0.735132
$669$	−16.0000	−0.618596
$670$	−12.0000	−0.463600
$671$	5.00000	0.193023
$672$	5.00000	0.192879
$673$	−37.0000	−1.42625	−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000	−1.42625	−0.713123	+	0.701039i	$0.752720\pi$
$674$	7.00000	0.269630
$675$	−5.00000	−0.192450
$676$	3.00000	0.115385
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−12.0000	−0.460857
$679$	−40.0000	−1.53506
$680$	1.00000	0.0383482
$681$	2.00000	0.0766402
$682$	−11.0000	−0.421212
$683$	21.0000	0.803543	0.401771	−	0.915740i	$-0.368395\pi$
$683$	21.0000	0.803543	0.401771	+	0.915740i	$0.368395\pi$
$684$	−14.0000	−0.535303
$685$	10.0000	0.382080
$686$	55.0000	2.09991
$687$	−14.0000	−0.534133
$688$	−1.00000	−0.0381246
$689$	−52.0000	−1.98104
$690$	8.00000	0.304555
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	−2.00000	−0.0760286
$693$	−10.0000	−0.379869
$694$	−14.0000	−0.531433
$695$	16.0000	0.606915
$696$	−5.00000	−0.189525
$697$	−12.0000	−0.454532
$698$	10.0000	0.378506
$699$	−25.0000	−0.945587
$700$	5.00000	0.188982
$701$	23.0000	0.868698	0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000	0.868698	0.434349	+	0.900745i	$0.356978\pi$
$702$	−20.0000	−0.754851
$703$	−49.0000	−1.84807
$704$	1.00000	0.0376889
$705$	6.00000	0.225973
$706$	−28.0000	−1.05379
$707$	30.0000	1.12827
$708$	−8.00000	−0.300658
$709$	−12.0000	−0.450669	−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000	−0.450669	−0.225335	+	0.974281i	$0.572348\pi$
$710$	1.00000	0.0375293
$711$	−16.0000	−0.600047
$712$	−9.00000	−0.337289
$713$	−88.0000	−3.29563
$714$	5.00000	0.187120
$715$	4.00000	0.149592
$716$	−20.0000	−0.747435
$717$	−6.00000	−0.224074
$718$	−4.00000	−0.149279
$719$	13.0000	0.484818	0.242409	−	0.970174i	$-0.422062\pi$
$719$	13.0000	0.484818	0.242409	+	0.970174i	$0.422062\pi$
$720$	−2.00000	−0.0745356
$721$	0	0
$722$	30.0000	1.11648
$723$	16.0000	0.595046
$724$	−10.0000	−0.371647
$725$	−5.00000	−0.185695
$726$	1.00000	0.0371135
$727$	18.0000	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$728$	20.0000	0.741249
$729$	13.0000	0.481481
$730$	−10.0000	−0.370117
$731$	−1.00000	−0.0369863
$732$	5.00000	0.184805
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	18.0000	0.664392
$735$	18.0000	0.663940
$736$	8.00000	0.294884
$737$	−12.0000	−0.442026
$738$	24.0000	0.883452
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	−7.00000	−0.257325
$741$	28.0000	1.02861
$742$	−65.0000	−2.38623
$743$	−31.0000	−1.13728	−0.568640	−	0.822587i	$-0.692530\pi$
$743$	−31.0000	−1.13728	−0.568640	+	0.822587i	$0.692530\pi$
$744$	−11.0000	−0.403280
$745$	−3.00000	−0.109911
$746$	0	0
$747$	−8.00000	−0.292705
$748$	1.00000	0.0365636
$749$	20.0000	0.730784
$750$	1.00000	0.0365148
$751$	−25.0000	−0.912263	−0.456131	−	0.889912i	$-0.650765\pi$
$751$	−25.0000	−0.912263	−0.456131	+	0.889912i	$0.650765\pi$
$752$	6.00000	0.218797
$753$	12.0000	0.437304
$754$	−20.0000	−0.728357
$755$	20.0000	0.727875
$756$	−25.0000	−0.909241
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	24.0000	0.871719
$759$	8.00000	0.290382
$760$	7.00000	0.253917
$761$	32.0000	1.16000	0.580000	−	0.814617i	$-0.303053\pi$
$761$	32.0000	1.16000	0.580000	+	0.814617i	$0.303053\pi$
$762$	12.0000	0.434714
$763$	−50.0000	−1.81012
$764$	−4.00000	−0.144715
$765$	−2.00000	−0.0723102
$766$	−24.0000	−0.867155
$767$	−32.0000	−1.15545
$768$	1.00000	0.0360844
$769$	6.00000	0.216366	0.108183	−	0.994131i	$-0.465497\pi$
$769$	6.00000	0.216366	0.108183	+	0.994131i	$0.465497\pi$
$770$	5.00000	0.180187
$771$	14.0000	0.504198
$772$	9.00000	0.323917
$773$	−11.0000	−0.395643	−0.197821	−	0.980238i	$-0.563387\pi$
$773$	−11.0000	−0.395643	−0.197821	+	0.980238i	$0.563387\pi$
$774$	2.00000	0.0718885
$775$	−11.0000	−0.395132
$776$	−8.00000	−0.287183
$777$	−35.0000	−1.25562
$778$	4.00000	0.143407
$779$	−84.0000	−3.00961
$780$	4.00000	0.143223
$781$	1.00000	0.0357828
$782$	8.00000	0.286079
$783$	25.0000	0.893427
$784$	18.0000	0.642857
$785$	−7.00000	−0.249841
$786$	15.0000	0.535032
$787$	8.00000	0.285169	0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000	0.285169	0.142585	+	0.989783i	$0.454459\pi$
$788$	−4.00000	−0.142494
$789$	−5.00000	−0.178005
$790$	8.00000	0.284627
$791$	−60.0000	−2.13335
$792$	−2.00000	−0.0710669
$793$	20.0000	0.710221
$794$	−2.00000	−0.0709773
$795$	−13.0000	−0.461062
$796$	−7.00000	−0.248108
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	35.0000	1.23899
$799$	6.00000	0.212265
$800$	1.00000	0.0353553
$801$	18.0000	0.635999
$802$	−17.0000	−0.600291
$803$	−10.0000	−0.352892
$804$	−12.0000	−0.423207
$805$	40.0000	1.40981
$806$	−44.0000	−1.54983
$807$	−18.0000	−0.633630
$808$	6.00000	0.211079
$809$	−36.0000	−1.26569	−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000	−1.26569	−0.632846	+	0.774277i	$0.718114\pi$
$810$	1.00000	0.0351364
$811$	−23.0000	−0.807639	−0.403820	−	0.914839i	$-0.632318\pi$
$811$	−23.0000	−0.807639	−0.403820	+	0.914839i	$0.632318\pi$
$812$	−25.0000	−0.877328
$813$	22.0000	0.771574
$814$	−7.00000	−0.245350
$815$	1.00000	0.0350285
$816$	1.00000	0.0350070
$817$	−7.00000	−0.244899
$818$	−8.00000	−0.279713
$819$	−40.0000	−1.39771
$820$	−12.0000	−0.419058
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	10.0000	0.348790
$823$	−22.0000	−0.766872	−0.383436	−	0.923567i	$-0.625259\pi$
$823$	−22.0000	−0.766872	−0.383436	+	0.923567i	$0.625259\pi$
$824$	0	0
$825$	1.00000	0.0348155
$826$	−40.0000	−1.39178
$827$	20.0000	0.695468	0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000	0.695468	0.347734	+	0.937593i	$0.386951\pi$
$828$	−16.0000	−0.556038
$829$	−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
$831$	−22.0000	−0.763172
$832$	4.00000	0.138675
$833$	18.0000	0.623663
$834$	16.0000	0.554035
$835$	19.0000	0.657522
$836$	7.00000	0.242100
$837$	55.0000	1.90108
$838$	−6.00000	−0.207267
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	5.00000	0.172516
$841$	−4.00000	−0.137931
$842$	28.0000	0.964944
$843$	16.0000	0.551069
$844$	23.0000	0.791693
$845$	3.00000	0.103203
$846$	−12.0000	−0.412568
$847$	5.00000	0.171802
$848$	−13.0000	−0.446422
$849$	−18.0000	−0.617758
$850$	1.00000	0.0342997
$851$	−56.0000	−1.91966
$852$	1.00000	0.0342594
$853$	4.00000	0.136957	0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000	0.136957	0.0684787	+	0.997653i	$0.478185\pi$
$854$	25.0000	0.855482
$855$	−14.0000	−0.478790
$856$	4.00000	0.136717
$857$	−27.0000	−0.922302	−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000	−0.922302	−0.461151	+	0.887322i	$0.652563\pi$
$858$	4.00000	0.136558
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	−1.00000	−0.0340997
$861$	−60.0000	−2.04479
$862$	−6.00000	−0.204361
$863$	−14.0000	−0.476566	−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000	−0.476566	−0.238283	+	0.971196i	$0.576585\pi$
$864$	−5.00000	−0.170103
$865$	−2.00000	−0.0680020
$866$	−20.0000	−0.679628
$867$	−16.0000	−0.543388
$868$	−55.0000	−1.86682
$869$	8.00000	0.271381
$870$	−5.00000	−0.169516
$871$	−48.0000	−1.62642
$872$	−10.0000	−0.338643
$873$	16.0000	0.541518
$874$	56.0000	1.89423
$875$	5.00000	0.169031
$876$	−10.0000	−0.337869
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	22.0000	0.742464
$879$	4.00000	0.134917
$880$	1.00000	0.0337100
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	−36.0000	−1.21218
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	4.00000	0.134535
$885$	−8.00000	−0.268917
$886$	12.0000	0.403148
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	−7.00000	−0.234905
$889$	60.0000	2.01234
$890$	−9.00000	−0.301681
$891$	1.00000	0.0335013
$892$	−16.0000	−0.535720
$893$	42.0000	1.40548
$894$	−3.00000	−0.100335
$895$	−20.0000	−0.668526
$896$	5.00000	0.167038
$897$	32.0000	1.06845
$898$	18.0000	0.600668
$899$	55.0000	1.83435
$900$	−2.00000	−0.0666667
$901$	−13.0000	−0.433093
$902$	−12.0000	−0.399556
$903$	−5.00000	−0.166390
$904$	−12.0000	−0.399114
$905$	−10.0000	−0.332411
$906$	20.0000	0.664455
$907$	−9.00000	−0.298840	−0.149420	−	0.988774i	$-0.547741\pi$
$907$	−9.00000	−0.298840	−0.149420	+	0.988774i	$0.547741\pi$
$908$	2.00000	0.0663723
$909$	−12.0000	−0.398015
$910$	20.0000	0.662994
$911$	−15.0000	−0.496972	−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000	−0.496972	−0.248486	+	0.968635i	$0.579933\pi$
$912$	7.00000	0.231793
$913$	4.00000	0.132381
$914$	−3.00000	−0.0992312
$915$	5.00000	0.165295
$916$	−14.0000	−0.462573
$917$	75.0000	2.47672
$918$	−5.00000	−0.165025
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	8.00000	0.263752
$921$	10.0000	0.329511
$922$	35.0000	1.15266
$923$	4.00000	0.131662
$924$	5.00000	0.164488
$925$	−7.00000	−0.230159
$926$	22.0000	0.722965
$927$	0	0
$928$	−5.00000	−0.164133
$929$	13.0000	0.426516	0.213258	−	0.976996i	$-0.431592\pi$
$929$	13.0000	0.426516	0.213258	+	0.976996i	$0.431592\pi$
$930$	−11.0000	−0.360704
$931$	126.000	4.12948
$932$	−25.0000	−0.818902
$933$	−35.0000	−1.14585
$934$	13.0000	0.425373
$935$	1.00000	0.0327035
$936$	−8.00000	−0.261488
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	−60.0000	−1.95907
$939$	26.0000	0.848478
$940$	6.00000	0.195698
$941$	33.0000	1.07577	0.537885	−	0.843018i	$-0.319224\pi$
$941$	33.0000	1.07577	0.537885	+	0.843018i	$0.319224\pi$
$942$	−7.00000	−0.228072
$943$	−96.0000	−3.12619
$944$	−8.00000	−0.260378
$945$	−25.0000	−0.813250
$946$	−1.00000	−0.0325128
$947$	−39.0000	−1.26733	−0.633665	−	0.773608i	$-0.718450\pi$
$947$	−39.0000	−1.26733	−0.633665	+	0.773608i	$0.718450\pi$
$948$	8.00000	0.259828
$949$	−40.0000	−1.29845
$950$	7.00000	0.227110
$951$	−15.0000	−0.486408
$952$	5.00000	0.162051
$953$	−11.0000	−0.356325	−0.178162	−	0.984001i	$-0.557015\pi$
$953$	−11.0000	−0.356325	−0.178162	+	0.984001i	$0.557015\pi$
$954$	26.0000	0.841781
$955$	−4.00000	−0.129437
$956$	−6.00000	−0.194054
$957$	−5.00000	−0.161627
$958$	0	0
$959$	50.0000	1.61458
$960$	1.00000	0.0322749
$961$	90.0000	2.90323
$962$	−28.0000	−0.902756
$963$	−8.00000	−0.257796
$964$	16.0000	0.515325
$965$	9.00000	0.289720
$966$	40.0000	1.28698
$967$	−19.0000	−0.610999	−0.305499	−	0.952192i	$-0.598823\pi$
$967$	−19.0000	−0.610999	−0.305499	+	0.952192i	$0.598823\pi$
$968$	1.00000	0.0321412
$969$	7.00000	0.224872
$970$	−8.00000	−0.256865
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	16.0000	0.513200
$973$	80.0000	2.56468
$974$	−10.0000	−0.320421
$975$	4.00000	0.128103
$976$	5.00000	0.160046
$977$	−36.0000	−1.15174	−0.575871	−	0.817541i	$-0.695337\pi$
$977$	−36.0000	−1.15174	−0.575871	+	0.817541i	$0.695337\pi$
$978$	1.00000	0.0319765
$979$	−9.00000	−0.287641
$980$	18.0000	0.574989
$981$	20.0000	0.638551
$982$	27.0000	0.861605
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−12.0000	−0.382546
$985$	−4.00000	−0.127451
$986$	−5.00000	−0.159232
$987$	30.0000	0.954911
$988$	28.0000	0.890799
$989$	−8.00000	−0.254385
$990$	−2.00000	−0.0635642
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	−11.0000	−0.349250
$993$	36.0000	1.14243
$994$	5.00000	0.158590
$995$	−7.00000	−0.221915
$996$	4.00000	0.126745
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	6.00000	0.189927
$999$	35.0000	1.10735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.j.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.j.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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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