LMFDB - Embedded newform 5610.2.a.s.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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -5.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -1.00000 q^{22} -5.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} -1.00000 q^{30} -9.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} -7.00000 q^{37} +5.00000 q^{38} +5.00000 q^{39} -1.00000 q^{40} -10.0000 q^{41} +1.00000 q^{42} -12.0000 q^{43} +1.00000 q^{44} +1.00000 q^{45} +5.00000 q^{46} -2.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} +5.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +1.00000 q^{55} +1.00000 q^{56} -5.00000 q^{57} +2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +13.0000 q^{61} +9.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.00000 q^{65} -1.00000 q^{66} -5.00000 q^{67} +1.00000 q^{68} -5.00000 q^{69} +1.00000 q^{70} -2.00000 q^{71} -1.00000 q^{72} -12.0000 q^{73} +7.00000 q^{74} +1.00000 q^{75} -5.00000 q^{76} -1.00000 q^{77} -5.00000 q^{78} -2.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +15.0000 q^{83} -1.00000 q^{84} +1.00000 q^{85} +12.0000 q^{86} -2.00000 q^{87} -1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{90} -5.00000 q^{91} -5.00000 q^{92} -9.00000 q^{93} +2.00000 q^{94} -5.00000 q^{95} -1.00000 q^{96} +13.0000 q^{97} +6.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−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
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	−1.00000	−0.213201
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−5.00000	−0.980581
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−0.182574
$31$	−9.00000	−1.61645	−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000	−1.61645	−0.808224	+	0.588875i	$0.799571\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	5.00000	0.811107
$39$	5.00000	0.800641
$40$	−1.00000	−0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	1.00000	0.154303
$43$	−12.0000	−1.82998	−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000	−1.82998	−0.914991	+	0.403473i	$0.867803\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	5.00000	0.737210
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	5.00000	0.693375
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	1.00000	0.133631
$57$	−5.00000	−0.662266
$58$	2.00000	0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	1.00000	0.129099
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	9.00000	1.14300
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	5.00000	0.620174
$66$	−1.00000	−0.123091
$67$	−5.00000	−0.610847	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000	−0.610847	−0.305424	+	0.952217i	$0.598798\pi$
$68$	1.00000	0.121268
$69$	−5.00000	−0.601929
$70$	1.00000	0.119523
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	−1.00000	−0.117851
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	7.00000	0.813733
$75$	1.00000	0.115470
$76$	−5.00000	−0.573539
$77$	−1.00000	−0.113961
$78$	−5.00000	−0.566139
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	15.0000	1.64646	0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000	1.64646	0.823232	+	0.567705i	$0.192169\pi$
$84$	−1.00000	−0.109109
$85$	1.00000	0.108465
$86$	12.0000	1.29399
$87$	−2.00000	−0.214423
$88$	−1.00000	−0.106600
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−1.00000	−0.105409
$91$	−5.00000	−0.524142
$92$	−5.00000	−0.521286
$93$	−9.00000	−0.933257
$94$	2.00000	0.206284
$95$	−5.00000	−0.512989
$96$	−1.00000	−0.102062
$97$	13.0000	1.31995	0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000	1.31995	0.659975	+	0.751288i	$0.270567\pi$
$98$	6.00000	0.606092
$99$	1.00000	0.100504
$100$	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
$103$	−5.00000	−0.492665	−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000	−0.492665	−0.246332	+	0.969185i	$0.579225\pi$
$104$	−5.00000	−0.490290
$105$	−1.00000	−0.0975900
$106$	10.0000	0.971286
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	1.00000	0.0962250
$109$	15.0000	1.43674	0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000	1.43674	0.718370	+	0.695662i	$0.244889\pi$
$110$	−1.00000	−0.0953463
$111$	−7.00000	−0.664411
$112$	−1.00000	−0.0944911
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	5.00000	0.468293
$115$	−5.00000	−0.466252
$116$	−2.00000	−0.185695
$117$	5.00000	0.462250
$118$	−4.00000	−0.368230
$119$	−1.00000	−0.0916698
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−13.0000	−1.17696
$123$	−10.0000	−0.901670
$124$	−9.00000	−0.808224
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000	−0.0883883
$129$	−12.0000	−1.05654
$130$	−5.00000	−0.438529
$131$	11.0000	0.961074	0.480537	−	0.876974i	$-0.340442\pi$
$131$	11.0000	0.961074	0.480537	+	0.876974i	$0.340442\pi$
$132$	1.00000	0.0870388
$133$	5.00000	0.433555
$134$	5.00000	0.431934
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	1.00000	0.0854358	0.0427179	−	0.999087i	$-0.486398\pi$
$137$	1.00000	0.0854358	0.0427179	+	0.999087i	$0.486398\pi$
$138$	5.00000	0.425628
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	−1.00000	−0.0845154
$141$	−2.00000	−0.168430
$142$	2.00000	0.167836
$143$	5.00000	0.418121
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	12.0000	0.993127
$147$	−6.00000	−0.494872
$148$	−7.00000	−0.575396
$149$	−7.00000	−0.573462	−0.286731	−	0.958011i	$-0.592569\pi$
$149$	−7.00000	−0.573462	−0.286731	+	0.958011i	$0.592569\pi$
$150$	−1.00000	−0.0816497
$151$	−23.0000	−1.87171	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−23.0000	−1.87171	−0.935857	+	0.352381i	$0.885372\pi$
$152$	5.00000	0.405554
$153$	1.00000	0.0808452
$154$	1.00000	0.0805823
$155$	−9.00000	−0.722897
$156$	5.00000	0.400320
$157$	24.0000	1.91541	0.957704	−	0.287754i	$-0.0929087\pi$
$157$	24.0000	1.91541	0.957704	+	0.287754i	$0.0929087\pi$
$158$	2.00000	0.159111
$159$	−10.0000	−0.793052
$160$	−1.00000	−0.0790569
$161$	5.00000	0.394055
$162$	−1.00000	−0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−10.0000	−0.780869
$165$	1.00000	0.0778499
$166$	−15.0000	−1.16423
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	1.00000	0.0771517
$169$	12.0000	0.923077
$170$	−1.00000	−0.0766965
$171$	−5.00000	−0.382360
$172$	−12.0000	−0.914991
$173$	3.00000	0.228086	0.114043	−	0.993476i	$-0.463620\pi$
$173$	3.00000	0.228086	0.114043	+	0.993476i	$0.463620\pi$
$174$	2.00000	0.151620
$175$	−1.00000	−0.0755929
$176$	1.00000	0.0753778
$177$	4.00000	0.300658
$178$	−2.00000	−0.149906
$179$	−7.00000	−0.523205	−0.261602	−	0.965176i	$-0.584251\pi$
$179$	−7.00000	−0.523205	−0.261602	+	0.965176i	$0.584251\pi$
$180$	1.00000	0.0745356
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	5.00000	0.370625
$183$	13.0000	0.960988
$184$	5.00000	0.368605
$185$	−7.00000	−0.514650
$186$	9.00000	0.659912
$187$	1.00000	0.0731272
$188$	−2.00000	−0.145865
$189$	−1.00000	−0.0727393
$190$	5.00000	0.362738
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	1.00000	0.0721688
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	−13.0000	−0.933346
$195$	5.00000	0.358057
$196$	−6.00000	−0.428571
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	−1.00000	−0.0710669
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	−1.00000	−0.0707107
$201$	−5.00000	−0.352673
$202$	−6.00000	−0.422159
$203$	2.00000	0.140372
$204$	1.00000	0.0700140
$205$	−10.0000	−0.698430
$206$	5.00000	0.348367
$207$	−5.00000	−0.347524
$208$	5.00000	0.346688
$209$	−5.00000	−0.345857
$210$	1.00000	0.0690066
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	−10.0000	−0.686803
$213$	−2.00000	−0.137038
$214$	2.00000	0.136717
$215$	−12.0000	−0.818393
$216$	−1.00000	−0.0680414
$217$	9.00000	0.610960
$218$	−15.0000	−1.01593
$219$	−12.0000	−0.810885
$220$	1.00000	0.0674200
$221$	5.00000	0.336336
$222$	7.00000	0.469809
$223$	−19.0000	−1.27233	−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000	−1.27233	−0.636167	+	0.771551i	$0.719481\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	26.0000	1.72568	0.862840	−	0.505477i	$-0.168683\pi$
$227$	26.0000	1.72568	0.862840	+	0.505477i	$0.168683\pi$
$228$	−5.00000	−0.331133
$229$	−21.0000	−1.38772	−0.693860	−	0.720110i	$-0.744091\pi$
$229$	−21.0000	−1.38772	−0.693860	+	0.720110i	$0.744091\pi$
$230$	5.00000	0.329690
$231$	−1.00000	−0.0657952
$232$	2.00000	0.131306
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	−5.00000	−0.326860
$235$	−2.00000	−0.130466
$236$	4.00000	0.260378
$237$	−2.00000	−0.129914
$238$	1.00000	0.0648204
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	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
$244$	13.0000	0.832240
$245$	−6.00000	−0.383326
$246$	10.0000	0.637577
$247$	−25.0000	−1.59071
$248$	9.00000	0.571501
$249$	15.0000	0.950586
$250$	−1.00000	−0.0632456
$251$	−27.0000	−1.70422	−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000	−1.70422	−0.852112	+	0.523359i	$0.824679\pi$
$252$	−1.00000	−0.0629941
$253$	−5.00000	−0.314347
$254$	−12.0000	−0.752947
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	12.0000	0.747087
$259$	7.00000	0.434959
$260$	5.00000	0.310087
$261$	−2.00000	−0.123797
$262$	−11.0000	−0.679582
$263$	3.00000	0.184988	0.0924940	−	0.995713i	$-0.470516\pi$
$263$	3.00000	0.184988	0.0924940	+	0.995713i	$0.470516\pi$
$264$	−1.00000	−0.0615457
$265$	−10.0000	−0.614295
$266$	−5.00000	−0.306570
$267$	2.00000	0.122398
$268$	−5.00000	−0.305424
$269$	−7.00000	−0.426798	−0.213399	−	0.976965i	$-0.568453\pi$
$269$	−7.00000	−0.426798	−0.213399	+	0.976965i	$0.568453\pi$
$270$	−1.00000	−0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	1.00000	0.0606339
$273$	−5.00000	−0.302614
$274$	−1.00000	−0.0604122
$275$	1.00000	0.0603023
$276$	−5.00000	−0.300965
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	14.0000	0.839664
$279$	−9.00000	−0.538816
$280$	1.00000	0.0597614
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	2.00000	0.119098
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−2.00000	−0.118678
$285$	−5.00000	−0.296174
$286$	−5.00000	−0.295656
$287$	10.0000	0.590281
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	2.00000	0.117444
$291$	13.0000	0.762073
$292$	−12.0000	−0.702247
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	6.00000	0.349927
$295$	4.00000	0.232889
$296$	7.00000	0.406867
$297$	1.00000	0.0580259
$298$	7.00000	0.405499
$299$	−25.0000	−1.44579
$300$	1.00000	0.0577350
$301$	12.0000	0.691669
$302$	23.0000	1.32350
$303$	6.00000	0.344691
$304$	−5.00000	−0.286770
$305$	13.0000	0.744378
$306$	−1.00000	−0.0571662
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−1.00000	−0.0569803
$309$	−5.00000	−0.284440
$310$	9.00000	0.511166
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	−5.00000	−0.283069
$313$	−21.0000	−1.18699	−0.593495	−	0.804838i	$-0.702252\pi$
$313$	−21.0000	−1.18699	−0.593495	+	0.804838i	$0.702252\pi$
$314$	−24.0000	−1.35440
$315$	−1.00000	−0.0563436
$316$	−2.00000	−0.112509
$317$	26.0000	1.46031	0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000	1.46031	0.730153	+	0.683284i	$0.239449\pi$
$318$	10.0000	0.560772
$319$	−2.00000	−0.111979
$320$	1.00000	0.0559017
$321$	−2.00000	−0.111629
$322$	−5.00000	−0.278639
$323$	−5.00000	−0.278207
$324$	1.00000	0.0555556
$325$	5.00000	0.277350
$326$	12.0000	0.664619
$327$	15.0000	0.829502
$328$	10.0000	0.552158
$329$	2.00000	0.110264
$330$	−1.00000	−0.0550482
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	15.0000	0.823232
$333$	−7.00000	−0.383598
$334$	16.0000	0.875481
$335$	−5.00000	−0.273179
$336$	−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	$0.223908\pi$
$338$	−12.0000	−0.652714
$339$	6.00000	0.325875
$340$	1.00000	0.0542326
$341$	−9.00000	−0.487377
$342$	5.00000	0.270369
$343$	13.0000	0.701934
$344$	12.0000	0.646997
$345$	−5.00000	−0.269191
$346$	−3.00000	−0.161281
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	−2.00000	−0.107211
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	1.00000	0.0534522
$351$	5.00000	0.266880
$352$	−1.00000	−0.0533002
$353$	−1.00000	−0.0532246	−0.0266123	−	0.999646i	$-0.508472\pi$
$353$	−1.00000	−0.0532246	−0.0266123	+	0.999646i	$0.508472\pi$
$354$	−4.00000	−0.212598
$355$	−2.00000	−0.106149
$356$	2.00000	0.106000
$357$	−1.00000	−0.0529256
$358$	7.00000	0.369961
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	−1.00000	−0.0527046
$361$	6.00000	0.315789
$362$	16.0000	0.840941
$363$	1.00000	0.0524864
$364$	−5.00000	−0.262071
$365$	−12.0000	−0.628109
$366$	−13.0000	−0.679521
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	−5.00000	−0.260643
$369$	−10.0000	−0.520579
$370$	7.00000	0.363913
$371$	10.0000	0.519174
$372$	−9.00000	−0.466628
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	2.00000	0.103142
$377$	−10.0000	−0.515026
$378$	1.00000	0.0514344
$379$	7.00000	0.359566	0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000	0.359566	0.179783	+	0.983706i	$0.442460\pi$
$380$	−5.00000	−0.256495
$381$	12.0000	0.614779
$382$	0	0
$383$	26.0000	1.32854	0.664269	−	0.747494i	$-0.268743\pi$
$383$	26.0000	1.32854	0.664269	+	0.747494i	$0.268743\pi$
$384$	−1.00000	−0.0510310
$385$	−1.00000	−0.0509647
$386$	0	0
$387$	−12.0000	−0.609994
$388$	13.0000	0.659975
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	−5.00000	−0.253185
$391$	−5.00000	−0.252861
$392$	6.00000	0.303046
$393$	11.0000	0.554877
$394$	−15.0000	−0.755689
$395$	−2.00000	−0.100631
$396$	1.00000	0.0502519
$397$	10.0000	0.501886	0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000	0.501886	0.250943	+	0.968002i	$0.419259\pi$
$398$	17.0000	0.852133
$399$	5.00000	0.250313
$400$	1.00000	0.0500000
$401$	19.0000	0.948815	0.474407	−	0.880305i	$-0.342662\pi$
$401$	19.0000	0.948815	0.474407	+	0.880305i	$0.342662\pi$
$402$	5.00000	0.249377
$403$	−45.0000	−2.24161
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−2.00000	−0.0992583
$407$	−7.00000	−0.346977
$408$	−1.00000	−0.0495074
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	10.0000	0.493865
$411$	1.00000	0.0493264
$412$	−5.00000	−0.246332
$413$	−4.00000	−0.196827
$414$	5.00000	0.245737
$415$	15.0000	0.736321
$416$	−5.00000	−0.245145
$417$	−14.0000	−0.685583
$418$	5.00000	0.244558
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	−1.00000	−0.0487950
$421$	−29.0000	−1.41337	−0.706687	−	0.707527i	$-0.749811\pi$
$421$	−29.0000	−1.41337	−0.706687	+	0.707527i	$0.749811\pi$
$422$	−14.0000	−0.681509
$423$	−2.00000	−0.0972433
$424$	10.0000	0.485643
$425$	1.00000	0.0485071
$426$	2.00000	0.0969003
$427$	−13.0000	−0.629114
$428$	−2.00000	−0.0966736
$429$	5.00000	0.241402
$430$	12.0000	0.578691
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	1.00000	0.0481125
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	−9.00000	−0.432014
$435$	−2.00000	−0.0958927
$436$	15.0000	0.718370
$437$	25.0000	1.19591
$438$	12.0000	0.573382
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	−1.00000	−0.0476731
$441$	−6.00000	−0.285714
$442$	−5.00000	−0.237826
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	−7.00000	−0.332205
$445$	2.00000	0.0948091
$446$	19.0000	0.899676
$447$	−7.00000	−0.331089
$448$	−1.00000	−0.0472456
$449$	25.0000	1.17982	0.589911	−	0.807468i	$-0.299163\pi$
$449$	25.0000	1.17982	0.589911	+	0.807468i	$0.299163\pi$
$450$	−1.00000	−0.0471405
$451$	−10.0000	−0.470882
$452$	6.00000	0.282216
$453$	−23.0000	−1.08063
$454$	−26.0000	−1.22024
$455$	−5.00000	−0.234404
$456$	5.00000	0.234146
$457$	−29.0000	−1.35656	−0.678281	−	0.734802i	$-0.737275\pi$
$457$	−29.0000	−1.35656	−0.678281	+	0.734802i	$0.737275\pi$
$458$	21.0000	0.981266
$459$	1.00000	0.0466760
$460$	−5.00000	−0.233126
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	1.00000	0.0465242
$463$	−23.0000	−1.06890	−0.534450	−	0.845200i	$-0.679481\pi$
$463$	−23.0000	−1.06890	−0.534450	+	0.845200i	$0.679481\pi$
$464$	−2.00000	−0.0928477
$465$	−9.00000	−0.417365
$466$	−22.0000	−1.01913
$467$	32.0000	1.48078	0.740392	−	0.672176i	$-0.234640\pi$
$467$	32.0000	1.48078	0.740392	+	0.672176i	$0.234640\pi$
$468$	5.00000	0.231125
$469$	5.00000	0.230879
$470$	2.00000	0.0922531
$471$	24.0000	1.10586
$472$	−4.00000	−0.184115
$473$	−12.0000	−0.551761
$474$	2.00000	0.0918630
$475$	−5.00000	−0.229416
$476$	−1.00000	−0.0458349
$477$	−10.0000	−0.457869
$478$	−6.00000	−0.274434
$479$	−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
$481$	−35.0000	−1.59586
$482$	17.0000	0.774329
$483$	5.00000	0.227508
$484$	1.00000	0.0454545
$485$	13.0000	0.590300
$486$	−1.00000	−0.0453609
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	−13.0000	−0.588482
$489$	−12.0000	−0.542659
$490$	6.00000	0.271052
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	−10.0000	−0.450835
$493$	−2.00000	−0.0900755
$494$	25.0000	1.12480
$495$	1.00000	0.0449467
$496$	−9.00000	−0.404112
$497$	2.00000	0.0897123
$498$	−15.0000	−0.672166
$499$	−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
$501$	−16.0000	−0.714827
$502$	27.0000	1.20507
$503$	4.00000	0.178351	0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000	0.178351	0.0891756	+	0.996016i	$0.471577\pi$
$504$	1.00000	0.0445435
$505$	6.00000	0.266996
$506$	5.00000	0.222277
$507$	12.0000	0.532939
$508$	12.0000	0.532414
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	−1.00000	−0.0442807
$511$	12.0000	0.530849
$512$	−1.00000	−0.0441942
$513$	−5.00000	−0.220755
$514$	6.00000	0.264649
$515$	−5.00000	−0.220326
$516$	−12.0000	−0.528271
$517$	−2.00000	−0.0879599
$518$	−7.00000	−0.307562
$519$	3.00000	0.131685
$520$	−5.00000	−0.219265
$521$	−29.0000	−1.27051	−0.635257	−	0.772301i	$-0.719106\pi$
$521$	−29.0000	−1.27051	−0.635257	+	0.772301i	$0.719106\pi$
$522$	2.00000	0.0875376
$523$	−32.0000	−1.39926	−0.699631	−	0.714504i	$-0.746652\pi$
$523$	−32.0000	−1.39926	−0.699631	+	0.714504i	$0.746652\pi$
$524$	11.0000	0.480537
$525$	−1.00000	−0.0436436
$526$	−3.00000	−0.130806
$527$	−9.00000	−0.392046
$528$	1.00000	0.0435194
$529$	2.00000	0.0869565
$530$	10.0000	0.434372
$531$	4.00000	0.173585
$532$	5.00000	0.216777
$533$	−50.0000	−2.16574
$534$	−2.00000	−0.0865485
$535$	−2.00000	−0.0864675
$536$	5.00000	0.215967
$537$	−7.00000	−0.302072
$538$	7.00000	0.301791
$539$	−6.00000	−0.258438
$540$	1.00000	0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−20.0000	−0.859074
$543$	−16.0000	−0.686626
$544$	−1.00000	−0.0428746
$545$	15.0000	0.642529
$546$	5.00000	0.213980
$547$	−27.0000	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$547$	−27.0000	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$548$	1.00000	0.0427179
$549$	13.0000	0.554826
$550$	−1.00000	−0.0426401
$551$	10.0000	0.426014
$552$	5.00000	0.212814
$553$	2.00000	0.0850487
$554$	−4.00000	−0.169944
$555$	−7.00000	−0.297133
$556$	−14.0000	−0.593732
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	9.00000	0.381000
$559$	−60.0000	−2.53773
$560$	−1.00000	−0.0422577
$561$	1.00000	0.0422200
$562$	18.0000	0.759284
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	−2.00000	−0.0842152
$565$	6.00000	0.252422
$566$	−4.00000	−0.168133
$567$	−1.00000	−0.0419961
$568$	2.00000	0.0839181
$569$	7.00000	0.293455	0.146728	−	0.989177i	$-0.453126\pi$
$569$	7.00000	0.293455	0.146728	+	0.989177i	$0.453126\pi$
$570$	5.00000	0.209427
$571$	42.0000	1.75765	0.878823	−	0.477149i	$-0.158330\pi$
$571$	42.0000	1.75765	0.878823	+	0.477149i	$0.158330\pi$
$572$	5.00000	0.209061
$573$	0	0
$574$	−10.0000	−0.417392
$575$	−5.00000	−0.208514
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	−2.00000	−0.0830455
$581$	−15.0000	−0.622305
$582$	−13.0000	−0.538867
$583$	−10.0000	−0.414158
$584$	12.0000	0.496564
$585$	5.00000	0.206725
$586$	24.0000	0.991431
$587$	−2.00000	−0.0825488	−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000	−0.0825488	−0.0412744	+	0.999148i	$0.513142\pi$
$588$	−6.00000	−0.247436
$589$	45.0000	1.85419
$590$	−4.00000	−0.164677
$591$	15.0000	0.617018
$592$	−7.00000	−0.287698
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	−1.00000	−0.0410305
$595$	−1.00000	−0.0409960
$596$	−7.00000	−0.286731
$597$	−17.0000	−0.695764
$598$	25.0000	1.02233
$599$	−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
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	−12.0000	−0.489083
$603$	−5.00000	−0.203616
$604$	−23.0000	−0.935857
$605$	1.00000	0.0406558
$606$	−6.00000	−0.243733
$607$	7.00000	0.284121	0.142061	−	0.989858i	$-0.454627\pi$
$607$	7.00000	0.284121	0.142061	+	0.989858i	$0.454627\pi$
$608$	5.00000	0.202777
$609$	2.00000	0.0810441
$610$	−13.0000	−0.526355
$611$	−10.0000	−0.404557
$612$	1.00000	0.0404226
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	20.0000	0.807134
$615$	−10.0000	−0.403239
$616$	1.00000	0.0402911
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	5.00000	0.201129
$619$	17.0000	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$620$	−9.00000	−0.361449
$621$	−5.00000	−0.200643
$622$	6.00000	0.240578
$623$	−2.00000	−0.0801283
$624$	5.00000	0.200160
$625$	1.00000	0.0400000
$626$	21.0000	0.839329
$627$	−5.00000	−0.199681
$628$	24.0000	0.957704
$629$	−7.00000	−0.279108
$630$	1.00000	0.0398410
$631$	−10.0000	−0.398094	−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000	−0.398094	−0.199047	+	0.979990i	$0.563785\pi$
$632$	2.00000	0.0795557
$633$	14.0000	0.556450
$634$	−26.0000	−1.03259
$635$	12.0000	0.476205
$636$	−10.0000	−0.396526
$637$	−30.0000	−1.18864
$638$	2.00000	0.0791808
$639$	−2.00000	−0.0791188
$640$	−1.00000	−0.0395285
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	2.00000	0.0789337
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	5.00000	0.197028
$645$	−12.0000	−0.472500
$646$	5.00000	0.196722
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	−1.00000	−0.0392837
$649$	4.00000	0.157014
$650$	−5.00000	−0.196116
$651$	9.00000	0.352738
$652$	−12.0000	−0.469956
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	−15.0000	−0.586546
$655$	11.0000	0.429806
$656$	−10.0000	−0.390434
$657$	−12.0000	−0.468165
$658$	−2.00000	−0.0779681
$659$	−42.0000	−1.63609	−0.818044	−	0.575156i	$-0.804941\pi$
$659$	−42.0000	−1.63609	−0.818044	+	0.575156i	$0.804941\pi$
$660$	1.00000	0.0389249
$661$	−11.0000	−0.427850	−0.213925	−	0.976850i	$-0.568625\pi$
$661$	−11.0000	−0.427850	−0.213925	+	0.976850i	$0.568625\pi$
$662$	12.0000	0.466393
$663$	5.00000	0.194184
$664$	−15.0000	−0.582113
$665$	5.00000	0.193892
$666$	7.00000	0.271244
$667$	10.0000	0.387202
$668$	−16.0000	−0.619059
$669$	−19.0000	−0.734582
$670$	5.00000	0.193167
$671$	13.0000	0.501859
$672$	1.00000	0.0385758
$673$	−28.0000	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$674$	−28.0000	−1.07852
$675$	1.00000	0.0384900
$676$	12.0000	0.461538
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	−6.00000	−0.230429
$679$	−13.0000	−0.498894
$680$	−1.00000	−0.0383482
$681$	26.0000	0.996322
$682$	9.00000	0.344628
$683$	39.0000	1.49229	0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000	1.49229	0.746147	+	0.665782i	$0.231902\pi$
$684$	−5.00000	−0.191180
$685$	1.00000	0.0382080
$686$	−13.0000	−0.496342
$687$	−21.0000	−0.801200
$688$	−12.0000	−0.457496
$689$	−50.0000	−1.90485
$690$	5.00000	0.190347
$691$	−27.0000	−1.02713	−0.513564	−	0.858051i	$-0.671675\pi$
$691$	−27.0000	−1.02713	−0.513564	+	0.858051i	$0.671675\pi$
$692$	3.00000	0.114043
$693$	−1.00000	−0.0379869
$694$	−30.0000	−1.13878
$695$	−14.0000	−0.531050
$696$	2.00000	0.0758098
$697$	−10.0000	−0.378777
$698$	−10.0000	−0.378506
$699$	22.0000	0.832116
$700$	−1.00000	−0.0377964
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−5.00000	−0.188713
$703$	35.0000	1.32005
$704$	1.00000	0.0376889
$705$	−2.00000	−0.0753244
$706$	1.00000	0.0376355
$707$	−6.00000	−0.225653
$708$	4.00000	0.150329
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	2.00000	0.0750587
$711$	−2.00000	−0.0750059
$712$	−2.00000	−0.0749532
$713$	45.0000	1.68526
$714$	1.00000	0.0374241
$715$	5.00000	0.186989
$716$	−7.00000	−0.261602
$717$	6.00000	0.224074
$718$	−10.0000	−0.373197
$719$	−30.0000	−1.11881	−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000	−1.11881	−0.559406	+	0.828894i	$0.688971\pi$
$720$	1.00000	0.0372678
$721$	5.00000	0.186210
$722$	−6.00000	−0.223297
$723$	−17.0000	−0.632237
$724$	−16.0000	−0.594635
$725$	−2.00000	−0.0742781
$726$	−1.00000	−0.0371135
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	5.00000	0.185312
$729$	1.00000	0.0370370
$730$	12.0000	0.444140
$731$	−12.0000	−0.443836
$732$	13.0000	0.480494
$733$	15.0000	0.554038	0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000	0.554038	0.277019	+	0.960864i	$0.410654\pi$
$734$	−28.0000	−1.03350
$735$	−6.00000	−0.221313
$736$	5.00000	0.184302
$737$	−5.00000	−0.184177
$738$	10.0000	0.368105
$739$	−43.0000	−1.58178	−0.790890	−	0.611958i	$-0.790382\pi$
$739$	−43.0000	−1.58178	−0.790890	+	0.611958i	$0.790382\pi$
$740$	−7.00000	−0.257325
$741$	−25.0000	−0.918398
$742$	−10.0000	−0.367112
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	9.00000	0.329956
$745$	−7.00000	−0.256460
$746$	−6.00000	−0.219676
$747$	15.0000	0.548821
$748$	1.00000	0.0365636
$749$	2.00000	0.0730784
$750$	−1.00000	−0.0365148
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	−2.00000	−0.0729325
$753$	−27.0000	−0.983935
$754$	10.0000	0.364179
$755$	−23.0000	−0.837056
$756$	−1.00000	−0.0363696
$757$	−6.00000	−0.218074	−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000	−0.218074	−0.109037	+	0.994038i	$0.534777\pi$
$758$	−7.00000	−0.254251
$759$	−5.00000	−0.181489
$760$	5.00000	0.181369
$761$	31.0000	1.12375	0.561875	−	0.827222i	$-0.310080\pi$
$761$	31.0000	1.12375	0.561875	+	0.827222i	$0.310080\pi$
$762$	−12.0000	−0.434714
$763$	−15.0000	−0.543036
$764$	0	0
$765$	1.00000	0.0361551
$766$	−26.0000	−0.939418
$767$	20.0000	0.722158
$768$	1.00000	0.0360844
$769$	4.00000	0.144244	0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000	0.144244	0.0721218	+	0.997396i	$0.477023\pi$
$770$	1.00000	0.0360375
$771$	−6.00000	−0.216085
$772$	0	0
$773$	27.0000	0.971123	0.485561	−	0.874203i	$-0.338615\pi$
$773$	27.0000	0.971123	0.485561	+	0.874203i	$0.338615\pi$
$774$	12.0000	0.431331
$775$	−9.00000	−0.323290
$776$	−13.0000	−0.466673
$777$	7.00000	0.251124
$778$	−12.0000	−0.430221
$779$	50.0000	1.79144
$780$	5.00000	0.179029
$781$	−2.00000	−0.0715656
$782$	5.00000	0.178800
$783$	−2.00000	−0.0714742
$784$	−6.00000	−0.214286
$785$	24.0000	0.856597
$786$	−11.0000	−0.392357
$787$	7.00000	0.249523	0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000	0.249523	0.124762	+	0.992187i	$0.460183\pi$
$788$	15.0000	0.534353
$789$	3.00000	0.106803
$790$	2.00000	0.0711568
$791$	−6.00000	−0.213335
$792$	−1.00000	−0.0355335
$793$	65.0000	2.30822
$794$	−10.0000	−0.354887
$795$	−10.0000	−0.354663
$796$	−17.0000	−0.602549
$797$	33.0000	1.16892	0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000	1.16892	0.584460	+	0.811423i	$0.301306\pi$
$798$	−5.00000	−0.176998
$799$	−2.00000	−0.0707549
$800$	−1.00000	−0.0353553
$801$	2.00000	0.0706665
$802$	−19.0000	−0.670913
$803$	−12.0000	−0.423471
$804$	−5.00000	−0.176336
$805$	5.00000	0.176227
$806$	45.0000	1.58506
$807$	−7.00000	−0.246412
$808$	−6.00000	−0.211079
$809$	−2.00000	−0.0703163	−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000	−0.0703163	−0.0351581	+	0.999382i	$0.511193\pi$
$810$	−1.00000	−0.0351364
$811$	46.0000	1.61528	0.807639	−	0.589677i	$-0.200745\pi$
$811$	46.0000	1.61528	0.807639	+	0.589677i	$0.200745\pi$
$812$	2.00000	0.0701862
$813$	20.0000	0.701431
$814$	7.00000	0.245350
$815$	−12.0000	−0.420342
$816$	1.00000	0.0350070
$817$	60.0000	2.09913
$818$	2.00000	0.0699284
$819$	−5.00000	−0.174714
$820$	−10.0000	−0.349215
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	−1.00000	−0.0348790
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	5.00000	0.174183
$825$	1.00000	0.0348155
$826$	4.00000	0.139178
$827$	−2.00000	−0.0695468	−0.0347734	−	0.999395i	$-0.511071\pi$
$827$	−2.00000	−0.0695468	−0.0347734	+	0.999395i	$0.511071\pi$
$828$	−5.00000	−0.173762
$829$	−13.0000	−0.451509	−0.225754	−	0.974184i	$-0.572485\pi$
$829$	−13.0000	−0.451509	−0.225754	+	0.974184i	$0.572485\pi$
$830$	−15.0000	−0.520658
$831$	4.00000	0.138758
$832$	5.00000	0.173344
$833$	−6.00000	−0.207888
$834$	14.0000	0.484780
$835$	−16.0000	−0.553703
$836$	−5.00000	−0.172929
$837$	−9.00000	−0.311086
$838$	−20.0000	−0.690889
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	1.00000	0.0345033
$841$	−25.0000	−0.862069
$842$	29.0000	0.999406
$843$	−18.0000	−0.619953
$844$	14.0000	0.481900
$845$	12.0000	0.412813
$846$	2.00000	0.0687614
$847$	−1.00000	−0.0343604
$848$	−10.0000	−0.343401
$849$	4.00000	0.137280
$850$	−1.00000	−0.0342997
$851$	35.0000	1.19978
$852$	−2.00000	−0.0685189
$853$	−28.0000	−0.958702	−0.479351	−	0.877623i	$-0.659128\pi$
$853$	−28.0000	−0.958702	−0.479351	+	0.877623i	$0.659128\pi$
$854$	13.0000	0.444851
$855$	−5.00000	−0.170996
$856$	2.00000	0.0683586
$857$	11.0000	0.375753	0.187876	−	0.982193i	$-0.439840\pi$
$857$	11.0000	0.375753	0.187876	+	0.982193i	$0.439840\pi$
$858$	−5.00000	−0.170697
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	−12.0000	−0.409197
$861$	10.0000	0.340799
$862$	32.0000	1.08992
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	−1.00000	−0.0340207
$865$	3.00000	0.102003
$866$	30.0000	1.01944
$867$	1.00000	0.0339618
$868$	9.00000	0.305480
$869$	−2.00000	−0.0678454
$870$	2.00000	0.0678064
$871$	−25.0000	−0.847093
$872$	−15.0000	−0.507964
$873$	13.0000	0.439983
$874$	−25.0000	−0.845638
$875$	−1.00000	−0.0338062
$876$	−12.0000	−0.405442
$877$	12.0000	0.405211	0.202606	−	0.979260i	$-0.435059\pi$
$877$	12.0000	0.405211	0.202606	+	0.979260i	$0.435059\pi$
$878$	14.0000	0.472477
$879$	−24.0000	−0.809500
$880$	1.00000	0.0337100
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	6.00000	0.202031
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	5.00000	0.168168
$885$	4.00000	0.134459
$886$	−18.0000	−0.604722
$887$	−20.0000	−0.671534	−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000	−0.671534	−0.335767	+	0.941945i	$0.608996\pi$
$888$	7.00000	0.234905
$889$	−12.0000	−0.402467
$890$	−2.00000	−0.0670402
$891$	1.00000	0.0335013
$892$	−19.0000	−0.636167
$893$	10.0000	0.334637
$894$	7.00000	0.234115
$895$	−7.00000	−0.233984
$896$	1.00000	0.0334077
$897$	−25.0000	−0.834726
$898$	−25.0000	−0.834261
$899$	18.0000	0.600334
$900$	1.00000	0.0333333
$901$	−10.0000	−0.333148
$902$	10.0000	0.332964
$903$	12.0000	0.399335
$904$	−6.00000	−0.199557
$905$	−16.0000	−0.531858
$906$	23.0000	0.764124
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	26.0000	0.862840
$909$	6.00000	0.199007
$910$	5.00000	0.165748
$911$	−28.0000	−0.927681	−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000	−0.927681	−0.463841	+	0.885919i	$0.653529\pi$
$912$	−5.00000	−0.165567
$913$	15.0000	0.496428
$914$	29.0000	0.959235
$915$	13.0000	0.429767
$916$	−21.0000	−0.693860
$917$	−11.0000	−0.363252
$918$	−1.00000	−0.0330049
$919$	−11.0000	−0.362857	−0.181428	−	0.983404i	$-0.558072\pi$
$919$	−11.0000	−0.362857	−0.181428	+	0.983404i	$0.558072\pi$
$920$	5.00000	0.164845
$921$	−20.0000	−0.659022
$922$	−30.0000	−0.987997
$923$	−10.0000	−0.329154
$924$	−1.00000	−0.0328976
$925$	−7.00000	−0.230159
$926$	23.0000	0.755827
$927$	−5.00000	−0.164222
$928$	2.00000	0.0656532
$929$	−19.0000	−0.623370	−0.311685	−	0.950186i	$-0.600893\pi$
$929$	−19.0000	−0.623370	−0.311685	+	0.950186i	$0.600893\pi$
$930$	9.00000	0.295122
$931$	30.0000	0.983210
$932$	22.0000	0.720634
$933$	−6.00000	−0.196431
$934$	−32.0000	−1.04707
$935$	1.00000	0.0327035
$936$	−5.00000	−0.163430
$937$	−29.0000	−0.947389	−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000	−0.947389	−0.473694	+	0.880689i	$0.657080\pi$
$938$	−5.00000	−0.163256
$939$	−21.0000	−0.685309
$940$	−2.00000	−0.0652328
$941$	28.0000	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$942$	−24.0000	−0.781962
$943$	50.0000	1.62822
$944$	4.00000	0.130189
$945$	−1.00000	−0.0325300
$946$	12.0000	0.390154
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	−2.00000	−0.0649570
$949$	−60.0000	−1.94768
$950$	5.00000	0.162221
$951$	26.0000	0.843108
$952$	1.00000	0.0324102
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	10.0000	0.323762
$955$	0	0
$956$	6.00000	0.194054
$957$	−2.00000	−0.0646508
$958$	15.0000	0.484628
$959$	−1.00000	−0.0322917
$960$	1.00000	0.0322749
$961$	50.0000	1.61290
$962$	35.0000	1.12845
$963$	−2.00000	−0.0644491
$964$	−17.0000	−0.547533
$965$	0	0
$966$	−5.00000	−0.160872
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	−1.00000	−0.0321412
$969$	−5.00000	−0.160623
$970$	−13.0000	−0.417405
$971$	−61.0000	−1.95758	−0.978792	−	0.204859i	$-0.934327\pi$
$971$	−61.0000	−1.95758	−0.978792	+	0.204859i	$0.934327\pi$
$972$	1.00000	0.0320750
$973$	14.0000	0.448819
$974$	−40.0000	−1.28168
$975$	5.00000	0.160128
$976$	13.0000	0.416120
$977$	−53.0000	−1.69562	−0.847810	−	0.530300i	$-0.822079\pi$
$977$	−53.0000	−1.69562	−0.847810	+	0.530300i	$0.822079\pi$
$978$	12.0000	0.383718
$979$	2.00000	0.0639203
$980$	−6.00000	−0.191663
$981$	15.0000	0.478913
$982$	−6.00000	−0.191468
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	10.0000	0.318788
$985$	15.0000	0.477940
$986$	2.00000	0.0636930
$987$	2.00000	0.0636607
$988$	−25.0000	−0.795356
$989$	60.0000	1.90789
$990$	−1.00000	−0.0317821
$991$	21.0000	0.667087	0.333543	−	0.942735i	$-0.391756\pi$
$991$	21.0000	0.667087	0.333543	+	0.942735i	$0.391756\pi$
$992$	9.00000	0.285750
$993$	−12.0000	−0.380808
$994$	−2.00000	−0.0634361
$995$	−17.0000	−0.538936
$996$	15.0000	0.475293
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	28.0000	0.886325
$999$	−7.00000	−0.221470

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.s.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
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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