LMFDB - Embedded newform 5610.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
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	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.00000 q^{19} -1.00000 q^{20} -3.00000 q^{21} -1.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -3.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +1.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +3.00000 q^{35} +1.00000 q^{36} +5.00000 q^{37} +3.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} +6.00000 q^{41} +3.00000 q^{42} +1.00000 q^{44} -1.00000 q^{45} +1.00000 q^{46} -10.0000 q^{47} +1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} -1.00000 q^{51} +1.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} -1.00000 q^{55} +3.00000 q^{56} -3.00000 q^{57} -6.00000 q^{58} -4.00000 q^{59} -1.00000 q^{60} +5.00000 q^{61} -1.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.00000 q^{66} -7.00000 q^{67} -1.00000 q^{68} -1.00000 q^{69} -3.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} +4.00000 q^{73} -5.00000 q^{74} +1.00000 q^{75} -3.00000 q^{76} -3.00000 q^{77} -1.00000 q^{78} -10.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +3.00000 q^{83} -3.00000 q^{84} +1.00000 q^{85} +6.00000 q^{87} -1.00000 q^{88} -14.0000 q^{89} +1.00000 q^{90} -3.00000 q^{91} -1.00000 q^{92} +1.00000 q^{93} +10.0000 q^{94} +3.00000 q^{95} -1.00000 q^{96} -15.0000 q^{97} -2.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	3.00000	0.801784
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−1.00000	−0.223607
$21$	−3.00000	−0.654654
$22$	−1.00000	−0.213201
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−3.00000	−0.566947
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	3.00000	0.507093
$36$	1.00000	0.166667
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	3.00000	0.486664
$39$	1.00000	0.160128
$40$	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	$0.344787\pi$
$42$	3.00000	0.462910
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	1.00000	0.144338
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	1.00000	0.138675
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	3.00000	0.400892
$57$	−3.00000	−0.397360
$58$	−6.00000	−0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.00000	−0.129099
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−1.00000	−0.127000
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−1.00000	−0.123091
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	−1.00000	−0.121268
$69$	−1.00000	−0.120386
$70$	−3.00000	−0.358569
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.00000	−0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−5.00000	−0.581238
$75$	1.00000	0.115470
$76$	−3.00000	−0.344124
$77$	−3.00000	−0.341882
$78$	−1.00000	−0.113228
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	−3.00000	−0.327327
$85$	1.00000	0.108465
$86$	0	0
$87$	6.00000	0.643268
$88$	−1.00000	−0.106600
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	1.00000	0.105409
$91$	−3.00000	−0.314485
$92$	−1.00000	−0.104257
$93$	1.00000	0.103695
$94$	10.0000	1.03142
$95$	3.00000	0.307794
$96$	−1.00000	−0.102062
$97$	−15.0000	−1.52302	−0.761510	−	0.648154i	$-0.775541\pi$
$97$	−15.0000	−1.52302	−0.761510	+	0.648154i	$0.775541\pi$
$98$	−2.00000	−0.202031
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	1.00000	0.0990148
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−1.00000	−0.0980581
$105$	3.00000	0.292770
$106$	−2.00000	−0.194257
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	1.00000	0.0962250
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	1.00000	0.0953463
$111$	5.00000	0.474579
$112$	−3.00000	−0.283473
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	3.00000	0.280976
$115$	1.00000	0.0932505
$116$	6.00000	0.557086
$117$	1.00000	0.0924500
$118$	4.00000	0.368230
$119$	3.00000	0.275010
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−5.00000	−0.452679
$123$	6.00000	0.541002
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	3.00000	0.267261
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	1.00000	0.0877058
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	1.00000	0.0870388
$133$	9.00000	0.780399
$134$	7.00000	0.604708
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−21.0000	−1.79415	−0.897076	−	0.441877i	$-0.854313\pi$
$137$	−21.0000	−1.79415	−0.897076	+	0.441877i	$0.854313\pi$
$138$	1.00000	0.0851257
$139$	6.00000	0.508913	0.254457	−	0.967084i	$-0.418103\pi$
$139$	6.00000	0.508913	0.254457	+	0.967084i	$0.418103\pi$
$140$	3.00000	0.253546
$141$	−10.0000	−0.842152
$142$	6.00000	0.503509
$143$	1.00000	0.0836242
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−4.00000	−0.331042
$147$	2.00000	0.164957
$148$	5.00000	0.410997
$149$	7.00000	0.573462	0.286731	−	0.958011i	$-0.407431\pi$
$149$	7.00000	0.573462	0.286731	+	0.958011i	$0.407431\pi$
$150$	−1.00000	−0.0816497
$151$	−17.0000	−1.38344	−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000	−1.38344	−0.691720	+	0.722166i	$0.743147\pi$
$152$	3.00000	0.243332
$153$	−1.00000	−0.0808452
$154$	3.00000	0.241747
$155$	−1.00000	−0.0803219
$156$	1.00000	0.0800641
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	10.0000	0.795557
$159$	2.00000	0.158610
$160$	1.00000	0.0790569
$161$	3.00000	0.236433
$162$	−1.00000	−0.0785674
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	6.00000	0.468521
$165$	−1.00000	−0.0778499
$166$	−3.00000	−0.232845
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	3.00000	0.231455
$169$	−12.0000	−0.923077
$170$	−1.00000	−0.0766965
$171$	−3.00000	−0.229416
$172$	0	0
$173$	−7.00000	−0.532200	−0.266100	−	0.963945i	$-0.585735\pi$
$173$	−7.00000	−0.532200	−0.266100	+	0.963945i	$0.585735\pi$
$174$	−6.00000	−0.454859
$175$	−3.00000	−0.226779
$176$	1.00000	0.0753778
$177$	−4.00000	−0.300658
$178$	14.0000	1.04934
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	−1.00000	−0.0745356
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	3.00000	0.222375
$183$	5.00000	0.369611
$184$	1.00000	0.0737210
$185$	−5.00000	−0.367607
$186$	−1.00000	−0.0733236
$187$	−1.00000	−0.0731272
$188$	−10.0000	−0.729325
$189$	−3.00000	−0.218218
$190$	−3.00000	−0.217643
$191$	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
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	15.0000	1.07694
$195$	−1.00000	−0.0716115
$196$	2.00000	0.142857
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	−1.00000	−0.0710669
$199$	1.00000	0.0708881	0.0354441	−	0.999372i	$-0.488715\pi$
$199$	1.00000	0.0708881	0.0354441	+	0.999372i	$0.488715\pi$
$200$	−1.00000	−0.0707107
$201$	−7.00000	−0.493742
$202$	−18.0000	−1.26648
$203$	−18.0000	−1.26335
$204$	−1.00000	−0.0700140
$205$	−6.00000	−0.419058
$206$	7.00000	0.487713
$207$	−1.00000	−0.0695048
$208$	1.00000	0.0693375
$209$	−3.00000	−0.207514
$210$	−3.00000	−0.207020
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	2.00000	0.137361
$213$	−6.00000	−0.411113
$214$	−18.0000	−1.23045
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−3.00000	−0.203653
$218$	−7.00000	−0.474100
$219$	4.00000	0.270295
$220$	−1.00000	−0.0674200
$221$	−1.00000	−0.0672673
$222$	−5.00000	−0.335578
$223$	23.0000	1.54019	0.770097	−	0.637927i	$-0.220208\pi$
$223$	23.0000	1.54019	0.770097	+	0.637927i	$0.220208\pi$
$224$	3.00000	0.200446
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	−3.00000	−0.198680
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	−1.00000	−0.0659380
$231$	−3.00000	−0.197386
$232$	−6.00000	−0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−1.00000	−0.0653720
$235$	10.0000	0.652328
$236$	−4.00000	−0.260378
$237$	−10.0000	−0.649570
$238$	−3.00000	−0.194461
$239$	−26.0000	−1.68180	−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000	−1.68180	−0.840900	+	0.541190i	$0.817974\pi$
$240$	−1.00000	−0.0645497
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	5.00000	0.320092
$245$	−2.00000	−0.127775
$246$	−6.00000	−0.382546
$247$	−3.00000	−0.190885
$248$	−1.00000	−0.0635001
$249$	3.00000	0.190117
$250$	1.00000	0.0632456
$251$	−11.0000	−0.694314	−0.347157	−	0.937807i	$-0.612853\pi$
$251$	−11.0000	−0.694314	−0.347157	+	0.937807i	$0.612853\pi$
$252$	−3.00000	−0.188982
$253$	−1.00000	−0.0628695
$254$	20.0000	1.25491
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−10.0000	−0.623783	−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000	−0.623783	−0.311891	+	0.950118i	$0.600963\pi$
$258$	0	0
$259$	−15.0000	−0.932055
$260$	−1.00000	−0.0620174
$261$	6.00000	0.371391
$262$	−3.00000	−0.185341
$263$	15.0000	0.924940	0.462470	−	0.886635i	$-0.346963\pi$
$263$	15.0000	0.924940	0.462470	+	0.886635i	$0.346963\pi$
$264$	−1.00000	−0.0615457
$265$	−2.00000	−0.122859
$266$	−9.00000	−0.551825
$267$	−14.0000	−0.856786
$268$	−7.00000	−0.427593
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	1.00000	0.0608581
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	−1.00000	−0.0606339
$273$	−3.00000	−0.181568
$274$	21.0000	1.26866
$275$	1.00000	0.0603023
$276$	−1.00000	−0.0601929
$277$	−24.0000	−1.44202	−0.721010	−	0.692925i	$-0.756322\pi$
$277$	−24.0000	−1.44202	−0.721010	+	0.692925i	$0.756322\pi$
$278$	−6.00000	−0.359856
$279$	1.00000	0.0598684
$280$	−3.00000	−0.179284
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	10.0000	0.595491
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−6.00000	−0.356034
$285$	3.00000	0.177705
$286$	−1.00000	−0.0591312
$287$	−18.0000	−1.06251
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	−15.0000	−0.879316
$292$	4.00000	0.234082
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	−2.00000	−0.116642
$295$	4.00000	0.232889
$296$	−5.00000	−0.290619
$297$	1.00000	0.0580259
$298$	−7.00000	−0.405499
$299$	−1.00000	−0.0578315
$300$	1.00000	0.0577350
$301$	0	0
$302$	17.0000	0.978240
$303$	18.0000	1.03407
$304$	−3.00000	−0.172062
$305$	−5.00000	−0.286299
$306$	1.00000	0.0571662
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	−3.00000	−0.170941
$309$	−7.00000	−0.398216
$310$	1.00000	0.0567962
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	−1.00000	−0.0566139
$313$	15.0000	0.847850	0.423925	−	0.905697i	$-0.360652\pi$
$313$	15.0000	0.847850	0.423925	+	0.905697i	$0.360652\pi$
$314$	0	0
$315$	3.00000	0.169031
$316$	−10.0000	−0.562544
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−2.00000	−0.112154
$319$	6.00000	0.335936
$320$	−1.00000	−0.0559017
$321$	18.0000	1.00466
$322$	−3.00000	−0.167183
$323$	3.00000	0.166924
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	24.0000	1.32924
$327$	7.00000	0.387101
$328$	−6.00000	−0.331295
$329$	30.0000	1.65395
$330$	1.00000	0.0550482
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	3.00000	0.164646
$333$	5.00000	0.273998
$334$	8.00000	0.437741
$335$	7.00000	0.382451
$336$	−3.00000	−0.163663
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	12.0000	0.652714
$339$	−2.00000	−0.108625
$340$	1.00000	0.0542326
$341$	1.00000	0.0541530
$342$	3.00000	0.162221
$343$	15.0000	0.809924
$344$	0	0
$345$	1.00000	0.0538382
$346$	7.00000	0.376322
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	6.00000	0.321634
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	3.00000	0.160357
$351$	1.00000	0.0533761
$352$	−1.00000	−0.0533002
$353$	13.0000	0.691920	0.345960	−	0.938249i	$-0.387553\pi$
$353$	13.0000	0.691920	0.345960	+	0.938249i	$0.387553\pi$
$354$	4.00000	0.212598
$355$	6.00000	0.318447
$356$	−14.0000	−0.741999
$357$	3.00000	0.158777
$358$	−9.00000	−0.475665
$359$	14.0000	0.738892	0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000	0.738892	0.369446	+	0.929252i	$0.379548\pi$
$360$	1.00000	0.0527046
$361$	−10.0000	−0.526316
$362$	20.0000	1.05118
$363$	1.00000	0.0524864
$364$	−3.00000	−0.157243
$365$	−4.00000	−0.209370
$366$	−5.00000	−0.261354
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	−1.00000	−0.0521286
$369$	6.00000	0.312348
$370$	5.00000	0.259938
$371$	−6.00000	−0.311504
$372$	1.00000	0.0518476
$373$	−34.0000	−1.76045	−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000	−1.76045	−0.880227	+	0.474554i	$0.842610\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	10.0000	0.515711
$377$	6.00000	0.309016
$378$	3.00000	0.154303
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	3.00000	0.153897
$381$	−20.0000	−1.02463
$382$	−8.00000	−0.409316
$383$	2.00000	0.102195	0.0510976	−	0.998694i	$-0.483728\pi$
$383$	2.00000	0.102195	0.0510976	+	0.998694i	$0.483728\pi$
$384$	−1.00000	−0.0510310
$385$	3.00000	0.152894
$386$	4.00000	0.203595
$387$	0	0
$388$	−15.0000	−0.761510
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	1.00000	0.0506370
$391$	1.00000	0.0505722
$392$	−2.00000	−0.101015
$393$	3.00000	0.151330
$394$	−21.0000	−1.05796
$395$	10.0000	0.503155
$396$	1.00000	0.0502519
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	−1.00000	−0.0501255
$399$	9.00000	0.450564
$400$	1.00000	0.0500000
$401$	5.00000	0.249688	0.124844	−	0.992176i	$-0.460157\pi$
$401$	5.00000	0.249688	0.124844	+	0.992176i	$0.460157\pi$
$402$	7.00000	0.349128
$403$	1.00000	0.0498135
$404$	18.0000	0.895533
$405$	−1.00000	−0.0496904
$406$	18.0000	0.893325
$407$	5.00000	0.247841
$408$	1.00000	0.0495074
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	6.00000	0.296319
$411$	−21.0000	−1.03585
$412$	−7.00000	−0.344865
$413$	12.0000	0.590481
$414$	1.00000	0.0491473
$415$	−3.00000	−0.147264
$416$	−1.00000	−0.0490290
$417$	6.00000	0.293821
$418$	3.00000	0.146735
$419$	32.0000	1.56330	0.781651	−	0.623716i	$-0.214378\pi$
$419$	32.0000	1.56330	0.781651	+	0.623716i	$0.214378\pi$
$420$	3.00000	0.146385
$421$	35.0000	1.70580	0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000	1.70580	0.852898	+	0.522078i	$0.174843\pi$
$422$	10.0000	0.486792
$423$	−10.0000	−0.486217
$424$	−2.00000	−0.0971286
$425$	−1.00000	−0.0485071
$426$	6.00000	0.290701
$427$	−15.0000	−0.725901
$428$	18.0000	0.870063
$429$	1.00000	0.0482805
$430$	0	0
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	1.00000	0.0481125
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	3.00000	0.144005
$435$	−6.00000	−0.287678
$436$	7.00000	0.335239
$437$	3.00000	0.143509
$438$	−4.00000	−0.191127
$439$	−22.0000	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$440$	1.00000	0.0476731
$441$	2.00000	0.0952381
$442$	1.00000	0.0475651
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	5.00000	0.237289
$445$	14.0000	0.663664
$446$	−23.0000	−1.08908
$447$	7.00000	0.331089
$448$	−3.00000	−0.141737
$449$	−33.0000	−1.55737	−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000	−1.55737	−0.778683	+	0.627417i	$0.784112\pi$
$450$	−1.00000	−0.0471405
$451$	6.00000	0.282529
$452$	−2.00000	−0.0940721
$453$	−17.0000	−0.798730
$454$	18.0000	0.844782
$455$	3.00000	0.140642
$456$	3.00000	0.140488
$457$	15.0000	0.701670	0.350835	−	0.936437i	$-0.385898\pi$
$457$	15.0000	0.701670	0.350835	+	0.936437i	$0.385898\pi$
$458$	13.0000	0.607450
$459$	−1.00000	−0.0466760
$460$	1.00000	0.0466252
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	3.00000	0.139573
$463$	3.00000	0.139422	0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000	0.139422	0.0697109	+	0.997567i	$0.477792\pi$
$464$	6.00000	0.278543
$465$	−1.00000	−0.0463739
$466$	6.00000	0.277945
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	1.00000	0.0462250
$469$	21.0000	0.969690
$470$	−10.0000	−0.461266
$471$	0	0
$472$	4.00000	0.184115
$473$	0	0
$474$	10.0000	0.459315
$475$	−3.00000	−0.137649
$476$	3.00000	0.137505
$477$	2.00000	0.0915737
$478$	26.0000	1.18921
$479$	−15.0000	−0.685367	−0.342684	−	0.939451i	$-0.611336\pi$
$479$	−15.0000	−0.685367	−0.342684	+	0.939451i	$0.611336\pi$
$480$	1.00000	0.0456435
$481$	5.00000	0.227980
$482$	17.0000	0.774329
$483$	3.00000	0.136505
$484$	1.00000	0.0454545
$485$	15.0000	0.681115
$486$	−1.00000	−0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−5.00000	−0.226339
$489$	−24.0000	−1.08532
$490$	2.00000	0.0903508
$491$	22.0000	0.992846	0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000	0.992846	0.496423	+	0.868081i	$0.334646\pi$
$492$	6.00000	0.270501
$493$	−6.00000	−0.270226
$494$	3.00000	0.134976
$495$	−1.00000	−0.0449467
$496$	1.00000	0.0449013
$497$	18.0000	0.807410
$498$	−3.00000	−0.134433
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	−1.00000	−0.0447214
$501$	−8.00000	−0.357414
$502$	11.0000	0.490954
$503$	40.0000	1.78351	0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000	1.78351	0.891756	+	0.452517i	$0.149474\pi$
$504$	3.00000	0.133631
$505$	−18.0000	−0.800989
$506$	1.00000	0.0444554
$507$	−12.0000	−0.532939
$508$	−20.0000	−0.887357
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	−1.00000	−0.0442807
$511$	−12.0000	−0.530849
$512$	−1.00000	−0.0441942
$513$	−3.00000	−0.132453
$514$	10.0000	0.441081
$515$	7.00000	0.308457
$516$	0	0
$517$	−10.0000	−0.439799
$518$	15.0000	0.659062
$519$	−7.00000	−0.307266
$520$	1.00000	0.0438529
$521$	−19.0000	−0.832405	−0.416203	−	0.909272i	$-0.636639\pi$
$521$	−19.0000	−0.832405	−0.416203	+	0.909272i	$0.636639\pi$
$522$	−6.00000	−0.262613
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	3.00000	0.131056
$525$	−3.00000	−0.130931
$526$	−15.0000	−0.654031
$527$	−1.00000	−0.0435607
$528$	1.00000	0.0435194
$529$	−22.0000	−0.956522
$530$	2.00000	0.0868744
$531$	−4.00000	−0.173585
$532$	9.00000	0.390199
$533$	6.00000	0.259889
$534$	14.0000	0.605839
$535$	−18.0000	−0.778208
$536$	7.00000	0.302354
$537$	9.00000	0.388379
$538$	−15.0000	−0.646696
$539$	2.00000	0.0861461
$540$	−1.00000	−0.0430331
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	−12.0000	−0.515444
$543$	−20.0000	−0.858282
$544$	1.00000	0.0428746
$545$	−7.00000	−0.299847
$546$	3.00000	0.128388
$547$	−41.0000	−1.75303	−0.876517	−	0.481371i	$-0.840139\pi$
$547$	−41.0000	−1.75303	−0.876517	+	0.481371i	$0.840139\pi$
$548$	−21.0000	−0.897076
$549$	5.00000	0.213395
$550$	−1.00000	−0.0426401
$551$	−18.0000	−0.766826
$552$	1.00000	0.0425628
$553$	30.0000	1.27573
$554$	24.0000	1.01966
$555$	−5.00000	−0.212238
$556$	6.00000	0.254457
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	−1.00000	−0.0423334
$559$	0	0
$560$	3.00000	0.126773
$561$	−1.00000	−0.0422200
$562$	−10.0000	−0.421825
$563$	33.0000	1.39078	0.695392	−	0.718631i	$-0.255231\pi$
$563$	33.0000	1.39078	0.695392	+	0.718631i	$0.255231\pi$
$564$	−10.0000	−0.421076
$565$	2.00000	0.0841406
$566$	4.00000	0.168133
$567$	−3.00000	−0.125988
$568$	6.00000	0.251754
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	−3.00000	−0.125656
$571$	26.0000	1.08807	0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000	1.08807	0.544033	+	0.839064i	$0.316897\pi$
$572$	1.00000	0.0418121
$573$	8.00000	0.334205
$574$	18.0000	0.751305
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	6.00000	0.249783	0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000	0.249783	0.124892	+	0.992170i	$0.460142\pi$
$578$	−1.00000	−0.0415945
$579$	−4.00000	−0.166234
$580$	−6.00000	−0.249136
$581$	−9.00000	−0.373383
$582$	15.0000	0.621770
$583$	2.00000	0.0828315
$584$	−4.00000	−0.165521
$585$	−1.00000	−0.0413449
$586$	12.0000	0.495715
$587$	14.0000	0.577842	0.288921	−	0.957353i	$-0.406704\pi$
$587$	14.0000	0.577842	0.288921	+	0.957353i	$0.406704\pi$
$588$	2.00000	0.0824786
$589$	−3.00000	−0.123613
$590$	−4.00000	−0.164677
$591$	21.0000	0.863825
$592$	5.00000	0.205499
$593$	−10.0000	−0.410651	−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000	−0.410651	−0.205325	+	0.978694i	$0.565825\pi$
$594$	−1.00000	−0.0410305
$595$	−3.00000	−0.122988
$596$	7.00000	0.286731
$597$	1.00000	0.0409273
$598$	1.00000	0.0408930
$599$	−21.0000	−0.858037	−0.429018	−	0.903296i	$-0.641140\pi$
$599$	−21.0000	−0.858037	−0.429018	+	0.903296i	$0.641140\pi$
$600$	−1.00000	−0.0408248
$601$	−41.0000	−1.67242	−0.836212	−	0.548406i	$-0.815235\pi$
$601$	−41.0000	−1.67242	−0.836212	+	0.548406i	$0.815235\pi$
$602$	0	0
$603$	−7.00000	−0.285062
$604$	−17.0000	−0.691720
$605$	−1.00000	−0.0406558
$606$	−18.0000	−0.731200
$607$	−27.0000	−1.09590	−0.547948	−	0.836512i	$-0.684591\pi$
$607$	−27.0000	−1.09590	−0.547948	+	0.836512i	$0.684591\pi$
$608$	3.00000	0.121666
$609$	−18.0000	−0.729397
$610$	5.00000	0.202444
$611$	−10.0000	−0.404557
$612$	−1.00000	−0.0404226
$613$	42.0000	1.69636	0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000	1.69636	0.848182	+	0.529705i	$0.177697\pi$
$614$	32.0000	1.29141
$615$	−6.00000	−0.241943
$616$	3.00000	0.120873
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	7.00000	0.281581
$619$	−9.00000	−0.361741	−0.180870	−	0.983507i	$-0.557891\pi$
$619$	−9.00000	−0.361741	−0.180870	+	0.983507i	$0.557891\pi$
$620$	−1.00000	−0.0401610
$621$	−1.00000	−0.0401286
$622$	−14.0000	−0.561349
$623$	42.0000	1.68269
$624$	1.00000	0.0400320
$625$	1.00000	0.0400000
$626$	−15.0000	−0.599521
$627$	−3.00000	−0.119808
$628$	0	0
$629$	−5.00000	−0.199363
$630$	−3.00000	−0.119523
$631$	−26.0000	−1.03504	−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000	−1.03504	−0.517522	+	0.855670i	$0.673145\pi$
$632$	10.0000	0.397779
$633$	−10.0000	−0.397464
$634$	18.0000	0.714871
$635$	20.0000	0.793676
$636$	2.00000	0.0793052
$637$	2.00000	0.0792429
$638$	−6.00000	−0.237542
$639$	−6.00000	−0.237356
$640$	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	$0.671640\pi$
$642$	−18.0000	−0.710403
$643$	−8.00000	−0.315489	−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000	−0.315489	−0.157745	+	0.987480i	$0.550422\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−3.00000	−0.118033
$647$	22.0000	0.864909	0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000	0.864909	0.432455	+	0.901656i	$0.357648\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	−1.00000	−0.0392232
$651$	−3.00000	−0.117579
$652$	−24.0000	−0.939913
$653$	−48.0000	−1.87839	−0.939193	−	0.343391i	$-0.888424\pi$
$653$	−48.0000	−1.87839	−0.939193	+	0.343391i	$0.888424\pi$
$654$	−7.00000	−0.273722
$655$	−3.00000	−0.117220
$656$	6.00000	0.234261
$657$	4.00000	0.156055
$658$	−30.0000	−1.16952
$659$	34.0000	1.32445	0.662226	−	0.749304i	$-0.269612\pi$
$659$	34.0000	1.32445	0.662226	+	0.749304i	$0.269612\pi$
$660$	−1.00000	−0.0389249
$661$	−3.00000	−0.116686	−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000	−0.116686	−0.0583432	+	0.998297i	$0.518582\pi$
$662$	−12.0000	−0.466393
$663$	−1.00000	−0.0388368
$664$	−3.00000	−0.116423
$665$	−9.00000	−0.349005
$666$	−5.00000	−0.193746
$667$	−6.00000	−0.232321
$668$	−8.00000	−0.309529
$669$	23.0000	0.889231
$670$	−7.00000	−0.270434
$671$	5.00000	0.193023
$672$	3.00000	0.115728
$673$	−36.0000	−1.38770	−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000	−1.38770	−0.693849	+	0.720121i	$0.744086\pi$
$674$	−4.00000	−0.154074
$675$	1.00000	0.0384900
$676$	−12.0000	−0.461538
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	2.00000	0.0768095
$679$	45.0000	1.72694
$680$	−1.00000	−0.0383482
$681$	−18.0000	−0.689761
$682$	−1.00000	−0.0382920
$683$	3.00000	0.114792	0.0573959	−	0.998351i	$-0.481720\pi$
$683$	3.00000	0.114792	0.0573959	+	0.998351i	$0.481720\pi$
$684$	−3.00000	−0.114708
$685$	21.0000	0.802369
$686$	−15.0000	−0.572703
$687$	−13.0000	−0.495981
$688$	0	0
$689$	2.00000	0.0761939
$690$	−1.00000	−0.0380693
$691$	−13.0000	−0.494543	−0.247272	−	0.968946i	$-0.579534\pi$
$691$	−13.0000	−0.494543	−0.247272	+	0.968946i	$0.579534\pi$
$692$	−7.00000	−0.266100
$693$	−3.00000	−0.113961
$694$	6.00000	0.227757
$695$	−6.00000	−0.227593
$696$	−6.00000	−0.227429
$697$	−6.00000	−0.227266
$698$	−18.0000	−0.681310
$699$	−6.00000	−0.226941
$700$	−3.00000	−0.113389
$701$	26.0000	0.982006	0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000	0.982006	0.491003	+	0.871158i	$0.336630\pi$
$702$	−1.00000	−0.0377426
$703$	−15.0000	−0.565736
$704$	1.00000	0.0376889
$705$	10.0000	0.376622
$706$	−13.0000	−0.489261
$707$	−54.0000	−2.03088
$708$	−4.00000	−0.150329
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	−6.00000	−0.225176
$711$	−10.0000	−0.375029
$712$	14.0000	0.524672
$713$	−1.00000	−0.0374503
$714$	−3.00000	−0.112272
$715$	−1.00000	−0.0373979
$716$	9.00000	0.336346
$717$	−26.0000	−0.970988
$718$	−14.0000	−0.522475
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	−1.00000	−0.0372678
$721$	21.0000	0.782081
$722$	10.0000	0.372161
$723$	−17.0000	−0.632237
$724$	−20.0000	−0.743294
$725$	6.00000	0.222834
$726$	−1.00000	−0.0371135
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	3.00000	0.111187
$729$	1.00000	0.0370370
$730$	4.00000	0.148047
$731$	0	0
$732$	5.00000	0.184805
$733$	19.0000	0.701781	0.350891	−	0.936416i	$-0.385879\pi$
$733$	19.0000	0.701781	0.350891	+	0.936416i	$0.385879\pi$
$734$	28.0000	1.03350
$735$	−2.00000	−0.0737711
$736$	1.00000	0.0368605
$737$	−7.00000	−0.257848
$738$	−6.00000	−0.220863
$739$	11.0000	0.404642	0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000	0.404642	0.202321	+	0.979319i	$0.435152\pi$
$740$	−5.00000	−0.183804
$741$	−3.00000	−0.110208
$742$	6.00000	0.220267
$743$	−52.0000	−1.90769	−0.953847	−	0.300291i	$-0.902916\pi$
$743$	−52.0000	−1.90769	−0.953847	+	0.300291i	$0.902916\pi$
$744$	−1.00000	−0.0366618
$745$	−7.00000	−0.256460
$746$	34.0000	1.24483
$747$	3.00000	0.109764
$748$	−1.00000	−0.0365636
$749$	−54.0000	−1.97312
$750$	1.00000	0.0365148
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	−10.0000	−0.364662
$753$	−11.0000	−0.400862
$754$	−6.00000	−0.218507
$755$	17.0000	0.618693
$756$	−3.00000	−0.109109
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	15.0000	0.544825
$759$	−1.00000	−0.0362977
$760$	−3.00000	−0.108821
$761$	−31.0000	−1.12375	−0.561875	−	0.827222i	$-0.689920\pi$
$761$	−31.0000	−1.12375	−0.561875	+	0.827222i	$0.689920\pi$
$762$	20.0000	0.724524
$763$	−21.0000	−0.760251
$764$	8.00000	0.289430
$765$	1.00000	0.0361551
$766$	−2.00000	−0.0722629
$767$	−4.00000	−0.144432
$768$	1.00000	0.0360844
$769$	40.0000	1.44244	0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000	1.44244	0.721218	+	0.692708i	$0.243582\pi$
$770$	−3.00000	−0.108112
$771$	−10.0000	−0.360141
$772$	−4.00000	−0.143963
$773$	1.00000	0.0359675	0.0179838	−	0.999838i	$-0.494275\pi$
$773$	1.00000	0.0359675	0.0179838	+	0.999838i	$0.494275\pi$
$774$	0	0
$775$	1.00000	0.0359211
$776$	15.0000	0.538469
$777$	−15.0000	−0.538122
$778$	−12.0000	−0.430221
$779$	−18.0000	−0.644917
$780$	−1.00000	−0.0358057
$781$	−6.00000	−0.214697
$782$	−1.00000	−0.0357599
$783$	6.00000	0.214423
$784$	2.00000	0.0714286
$785$	0	0
$786$	−3.00000	−0.107006
$787$	37.0000	1.31891	0.659454	−	0.751745i	$-0.270788\pi$
$787$	37.0000	1.31891	0.659454	+	0.751745i	$0.270788\pi$
$788$	21.0000	0.748094
$789$	15.0000	0.534014
$790$	−10.0000	−0.355784
$791$	6.00000	0.213335
$792$	−1.00000	−0.0355335
$793$	5.00000	0.177555
$794$	−18.0000	−0.638796
$795$	−2.00000	−0.0709327
$796$	1.00000	0.0354441
$797$	3.00000	0.106265	0.0531327	−	0.998587i	$-0.483079\pi$
$797$	3.00000	0.106265	0.0531327	+	0.998587i	$0.483079\pi$
$798$	−9.00000	−0.318597
$799$	10.0000	0.353775
$800$	−1.00000	−0.0353553
$801$	−14.0000	−0.494666
$802$	−5.00000	−0.176556
$803$	4.00000	0.141157
$804$	−7.00000	−0.246871
$805$	−3.00000	−0.105736
$806$	−1.00000	−0.0352235
$807$	15.0000	0.528025
$808$	−18.0000	−0.633238
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	1.00000	0.0351364
$811$	−46.0000	−1.61528	−0.807639	−	0.589677i	$-0.799255\pi$
$811$	−46.0000	−1.61528	−0.807639	+	0.589677i	$0.799255\pi$
$812$	−18.0000	−0.631676
$813$	12.0000	0.420858
$814$	−5.00000	−0.175250
$815$	24.0000	0.840683
$816$	−1.00000	−0.0350070
$817$	0	0
$818$	−10.0000	−0.349642
$819$	−3.00000	−0.104828
$820$	−6.00000	−0.209529
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	21.0000	0.732459
$823$	6.00000	0.209147	0.104573	−	0.994517i	$-0.466652\pi$
$823$	6.00000	0.209147	0.104573	+	0.994517i	$0.466652\pi$
$824$	7.00000	0.243857
$825$	1.00000	0.0348155
$826$	−12.0000	−0.417533
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	−1.00000	−0.0347524
$829$	35.0000	1.21560	0.607800	−	0.794090i	$-0.292052\pi$
$829$	35.0000	1.21560	0.607800	+	0.794090i	$0.292052\pi$
$830$	3.00000	0.104132
$831$	−24.0000	−0.832551
$832$	1.00000	0.0346688
$833$	−2.00000	−0.0692959
$834$	−6.00000	−0.207763
$835$	8.00000	0.276851
$836$	−3.00000	−0.103757
$837$	1.00000	0.0345651
$838$	−32.0000	−1.10542
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	−3.00000	−0.103510
$841$	7.00000	0.241379
$842$	−35.0000	−1.20618
$843$	10.0000	0.344418
$844$	−10.0000	−0.344214
$845$	12.0000	0.412813
$846$	10.0000	0.343807
$847$	−3.00000	−0.103081
$848$	2.00000	0.0686803
$849$	−4.00000	−0.137280
$850$	1.00000	0.0342997
$851$	−5.00000	−0.171398
$852$	−6.00000	−0.205557
$853$	4.00000	0.136957	0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000	0.136957	0.0684787	+	0.997653i	$0.478185\pi$
$854$	15.0000	0.513289
$855$	3.00000	0.102598
$856$	−18.0000	−0.615227
$857$	33.0000	1.12726	0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000	1.12726	0.563629	+	0.826028i	$0.309405\pi$
$858$	−1.00000	−0.0341394
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	0	0
$861$	−18.0000	−0.613438
$862$	8.00000	0.272481
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	−1.00000	−0.0340207
$865$	7.00000	0.238007
$866$	6.00000	0.203888
$867$	1.00000	0.0339618
$868$	−3.00000	−0.101827
$869$	−10.0000	−0.339227
$870$	6.00000	0.203419
$871$	−7.00000	−0.237186
$872$	−7.00000	−0.237050
$873$	−15.0000	−0.507673
$874$	−3.00000	−0.101477
$875$	3.00000	0.101419
$876$	4.00000	0.135147
$877$	4.00000	0.135070	0.0675352	−	0.997717i	$-0.478487\pi$
$877$	4.00000	0.135070	0.0675352	+	0.997717i	$0.478487\pi$
$878$	22.0000	0.742464
$879$	−12.0000	−0.404750
$880$	−1.00000	−0.0337100
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	−2.00000	−0.0673435
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−1.00000	−0.0336336
$885$	4.00000	0.134459
$886$	26.0000	0.873487
$887$	−32.0000	−1.07445	−0.537227	−	0.843437i	$-0.680528\pi$
$887$	−32.0000	−1.07445	−0.537227	+	0.843437i	$0.680528\pi$
$888$	−5.00000	−0.167789
$889$	60.0000	2.01234
$890$	−14.0000	−0.469281
$891$	1.00000	0.0335013
$892$	23.0000	0.770097
$893$	30.0000	1.00391
$894$	−7.00000	−0.234115
$895$	−9.00000	−0.300837
$896$	3.00000	0.100223
$897$	−1.00000	−0.0333890
$898$	33.0000	1.10122
$899$	6.00000	0.200111
$900$	1.00000	0.0333333
$901$	−2.00000	−0.0666297
$902$	−6.00000	−0.199778
$903$	0	0
$904$	2.00000	0.0665190
$905$	20.0000	0.664822
$906$	17.0000	0.564787
$907$	16.0000	0.531271	0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000	0.531271	0.265636	+	0.964073i	$0.414418\pi$
$908$	−18.0000	−0.597351
$909$	18.0000	0.597022
$910$	−3.00000	−0.0994490
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	−3.00000	−0.0993399
$913$	3.00000	0.0992855
$914$	−15.0000	−0.496156
$915$	−5.00000	−0.165295
$916$	−13.0000	−0.429532
$917$	−9.00000	−0.297206
$918$	1.00000	0.0330049
$919$	3.00000	0.0989609	0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000	0.0989609	0.0494804	+	0.998775i	$0.484243\pi$
$920$	−1.00000	−0.0329690
$921$	−32.0000	−1.05444
$922$	30.0000	0.987997
$923$	−6.00000	−0.197492
$924$	−3.00000	−0.0986928
$925$	5.00000	0.164399
$926$	−3.00000	−0.0985861
$927$	−7.00000	−0.229910
$928$	−6.00000	−0.196960
$929$	3.00000	0.0984268	0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000	0.0984268	0.0492134	+	0.998788i	$0.484329\pi$
$930$	1.00000	0.0327913
$931$	−6.00000	−0.196642
$932$	−6.00000	−0.196537
$933$	14.0000	0.458339
$934$	−4.00000	−0.130884
$935$	1.00000	0.0327035
$936$	−1.00000	−0.0326860
$937$	−49.0000	−1.60076	−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000	−1.60076	−0.800380	+	0.599493i	$0.795369\pi$
$938$	−21.0000	−0.685674
$939$	15.0000	0.489506
$940$	10.0000	0.326164
$941$	28.0000	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$942$	0	0
$943$	−6.00000	−0.195387
$944$	−4.00000	−0.130189
$945$	3.00000	0.0975900
$946$	0	0
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	−10.0000	−0.324785
$949$	4.00000	0.129845
$950$	3.00000	0.0973329
$951$	−18.0000	−0.583690
$952$	−3.00000	−0.0972306
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	−2.00000	−0.0647524
$955$	−8.00000	−0.258874
$956$	−26.0000	−0.840900
$957$	6.00000	0.193952
$958$	15.0000	0.484628
$959$	63.0000	2.03438
$960$	−1.00000	−0.0322749
$961$	−30.0000	−0.967742
$962$	−5.00000	−0.161206
$963$	18.0000	0.580042
$964$	−17.0000	−0.547533
$965$	4.00000	0.128765
$966$	−3.00000	−0.0965234
$967$	6.00000	0.192947	0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000	0.192947	0.0964735	+	0.995336i	$0.469244\pi$
$968$	−1.00000	−0.0321412
$969$	3.00000	0.0963739
$970$	−15.0000	−0.481621
$971$	11.0000	0.353007	0.176503	−	0.984300i	$-0.443521\pi$
$971$	11.0000	0.353007	0.176503	+	0.984300i	$0.443521\pi$
$972$	1.00000	0.0320750
$973$	−18.0000	−0.577054
$974$	16.0000	0.512673
$975$	1.00000	0.0320256
$976$	5.00000	0.160046
$977$	33.0000	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$978$	24.0000	0.767435
$979$	−14.0000	−0.447442
$980$	−2.00000	−0.0638877
$981$	7.00000	0.223493
$982$	−22.0000	−0.702048
$983$	20.0000	0.637901	0.318950	−	0.947771i	$-0.396670\pi$
$983$	20.0000	0.637901	0.318950	+	0.947771i	$0.396670\pi$
$984$	−6.00000	−0.191273
$985$	−21.0000	−0.669116
$986$	6.00000	0.191079
$987$	30.0000	0.954911
$988$	−3.00000	−0.0954427
$989$	0	0
$990$	1.00000	0.0317821
$991$	3.00000	0.0952981	0.0476491	−	0.998864i	$-0.484827\pi$
$991$	3.00000	0.0952981	0.0476491	+	0.998864i	$0.484827\pi$
$992$	−1.00000	−0.0317500
$993$	12.0000	0.380808
$994$	−18.0000	−0.570925
$995$	−1.00000	−0.0317021
$996$	3.00000	0.0950586
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	28.0000	0.886325
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.l.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.l.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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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