LMFDB - Embedded newform 5610.2.a.bb.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -2.00000 q^{19} +1.00000 q^{20} +2.00000 q^{21} +1.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} -2.00000 q^{29} -1.00000 q^{30} -8.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} -2.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} +2.00000 q^{42} -6.00000 q^{43} +1.00000 q^{44} +1.00000 q^{45} +6.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} -4.00000 q^{52} -1.00000 q^{54} +1.00000 q^{55} -2.00000 q^{56} +2.00000 q^{57} -2.00000 q^{58} +10.0000 q^{59} -1.00000 q^{60} -6.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -1.00000 q^{66} -8.00000 q^{67} +1.00000 q^{68} -6.00000 q^{69} -2.00000 q^{70} -10.0000 q^{71} +1.00000 q^{72} +12.0000 q^{73} -6.00000 q^{74} -1.00000 q^{75} -2.00000 q^{76} -2.00000 q^{77} +4.00000 q^{78} -6.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +4.00000 q^{83} +2.00000 q^{84} +1.00000 q^{85} -6.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} -18.0000 q^{89} +1.00000 q^{90} +8.00000 q^{91} +6.00000 q^{92} +8.00000 q^{93} +8.00000 q^{94} -2.00000 q^{95} -1.00000 q^{96} -2.00000 q^{97} -3.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	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
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.00000	−0.534522
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	1.00000	0.223607
$21$	2.00000	0.436436
$22$	1.00000	0.213201
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	−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
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−2.00000	−0.324443
$39$	4.00000	0.640513
$40$	1.00000	0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	2.00000	0.308607
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	6.00000	0.884652
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	−4.00000	−0.554700
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−2.00000	−0.267261
$57$	2.00000	0.264906
$58$	−2.00000	−0.262613
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	−1.00000	−0.129099
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−8.00000	−1.01600
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	−1.00000	−0.123091
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	1.00000	0.121268
$69$	−6.00000	−0.722315
$70$	−2.00000	−0.239046
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	1.00000	0.117851
$73$	12.0000	1.40449	0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000	1.40449	0.702247	+	0.711934i	$0.252180\pi$
$74$	−6.00000	−0.697486
$75$	−1.00000	−0.115470
$76$	−2.00000	−0.229416
$77$	−2.00000	−0.227921
$78$	4.00000	0.452911
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	2.00000	0.218218
$85$	1.00000	0.108465
$86$	−6.00000	−0.646997
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	1.00000	0.105409
$91$	8.00000	0.838628
$92$	6.00000	0.625543
$93$	8.00000	0.829561
$94$	8.00000	0.825137
$95$	−2.00000	−0.205196
$96$	−1.00000	−0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−3.00000	−0.303046
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	−1.00000	−0.0990148
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	−4.00000	−0.392232
$105$	2.00000	0.195180
$106$	0	0
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	−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
$111$	6.00000	0.569495
$112$	−2.00000	−0.188982
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	2.00000	0.187317
$115$	6.00000	0.559503
$116$	−2.00000	−0.185695
$117$	−4.00000	−0.369800
$118$	10.0000	0.920575
$119$	−2.00000	−0.183340
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−6.00000	−0.543214
$123$	−2.00000	−0.180334
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	−2.00000	−0.178174
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000	0.0883883
$129$	6.00000	0.528271
$130$	−4.00000	−0.350823
$131$	20.0000	1.74741	0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000	1.74741	0.873704	+	0.486458i	$0.161711\pi$
$132$	−1.00000	−0.0870388
$133$	4.00000	0.346844
$134$	−8.00000	−0.691095
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−6.00000	−0.510754
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	−2.00000	−0.169031
$141$	−8.00000	−0.673722
$142$	−10.0000	−0.839181
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	12.0000	0.993127
$147$	3.00000	0.247436
$148$	−6.00000	−0.493197
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−1.00000	−0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−2.00000	−0.162221
$153$	1.00000	0.0808452
$154$	−2.00000	−0.161165
$155$	−8.00000	−0.642575
$156$	4.00000	0.320256
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−6.00000	−0.477334
$159$	0	0
$160$	1.00000	0.0790569
$161$	−12.0000	−0.945732
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	−1.00000	−0.0778499
$166$	4.00000	0.310460
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	1.00000	0.0766965
$171$	−2.00000	−0.152944
$172$	−6.00000	−0.457496
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	2.00000	0.151620
$175$	−2.00000	−0.151186
$176$	1.00000	0.0753778
$177$	−10.0000	−0.751646
$178$	−18.0000	−1.34916
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	1.00000	0.0745356
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	8.00000	0.592999
$183$	6.00000	0.443533
$184$	6.00000	0.442326
$185$	−6.00000	−0.441129
$186$	8.00000	0.586588
$187$	1.00000	0.0731272
$188$	8.00000	0.583460
$189$	2.00000	0.145479
$190$	−2.00000	−0.145095
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	−1.00000	−0.0721688
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	−2.00000	−0.143592
$195$	4.00000	0.286446
$196$	−3.00000	−0.214286
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	1.00000	0.0710669
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	1.00000	0.0707107
$201$	8.00000	0.564276
$202$	−10.0000	−0.703598
$203$	4.00000	0.280745
$204$	−1.00000	−0.0700140
$205$	2.00000	0.139686
$206$	−16.0000	−1.11477
$207$	6.00000	0.417029
$208$	−4.00000	−0.277350
$209$	−2.00000	−0.138343
$210$	2.00000	0.138013
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	0	0
$213$	10.0000	0.685189
$214$	12.0000	0.820303
$215$	−6.00000	−0.409197
$216$	−1.00000	−0.0680414
$217$	16.0000	1.08615
$218$	−10.0000	−0.677285
$219$	−12.0000	−0.810885
$220$	1.00000	0.0674200
$221$	−4.00000	−0.269069
$222$	6.00000	0.402694
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	−2.00000	−0.133631
$225$	1.00000	0.0666667
$226$	−4.00000	−0.266076
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	2.00000	0.132453
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	6.00000	0.395628
$231$	2.00000	0.131590
$232$	−2.00000	−0.131306
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−4.00000	−0.261488
$235$	8.00000	0.521862
$236$	10.0000	0.650945
$237$	6.00000	0.389742
$238$	−2.00000	−0.129641
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	−1.00000	−0.0645497
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−6.00000	−0.384111
$245$	−3.00000	−0.191663
$246$	−2.00000	−0.127515
$247$	8.00000	0.509028
$248$	−8.00000	−0.508001
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	−2.00000	−0.125988
$253$	6.00000	0.377217
$254$	0	0
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	6.00000	0.373544
$259$	12.0000	0.745644
$260$	−4.00000	−0.248069
$261$	−2.00000	−0.123797
$262$	20.0000	1.23560
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	−1.00000	−0.0615457
$265$	0	0
$266$	4.00000	0.245256
$267$	18.0000	1.10158
$268$	−8.00000	−0.488678
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	−1.00000	−0.0608581
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	1.00000	0.0606339
$273$	−8.00000	−0.484182
$274$	−6.00000	−0.362473
$275$	1.00000	0.0603023
$276$	−6.00000	−0.361158
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	−2.00000	−0.119523
$281$	−26.0000	−1.55103	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000	−1.55103	−0.775515	+	0.631329i	$0.782510\pi$
$282$	−8.00000	−0.476393
$283$	32.0000	1.90220	0.951101	−	0.308879i	$-0.0999539\pi$
$283$	32.0000	1.90220	0.951101	+	0.308879i	$0.0999539\pi$
$284$	−10.0000	−0.593391
$285$	2.00000	0.118470
$286$	−4.00000	−0.236525
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	2.00000	0.117242
$292$	12.0000	0.702247
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	3.00000	0.174964
$295$	10.0000	0.582223
$296$	−6.00000	−0.348743
$297$	−1.00000	−0.0580259
$298$	−6.00000	−0.347571
$299$	−24.0000	−1.38796
$300$	−1.00000	−0.0577350
$301$	12.0000	0.691669
$302$	−4.00000	−0.230174
$303$	10.0000	0.574485
$304$	−2.00000	−0.114708
$305$	−6.00000	−0.343559
$306$	1.00000	0.0571662
$307$	6.00000	0.342438	0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000	0.342438	0.171219	+	0.985233i	$0.445229\pi$
$308$	−2.00000	−0.113961
$309$	16.0000	0.910208
$310$	−8.00000	−0.454369
$311$	−26.0000	−1.47432	−0.737162	−	0.675716i	$-0.763835\pi$
$311$	−26.0000	−1.47432	−0.737162	+	0.675716i	$0.763835\pi$
$312$	4.00000	0.226455
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	−2.00000	−0.112867
$315$	−2.00000	−0.112687
$316$	−6.00000	−0.337526
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	−2.00000	−0.111979
$320$	1.00000	0.0559017
$321$	−12.0000	−0.669775
$322$	−12.0000	−0.668734
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−4.00000	−0.221540
$327$	10.0000	0.553001
$328$	2.00000	0.110432
$329$	−16.0000	−0.882109
$330$	−1.00000	−0.0550482
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	4.00000	0.219529
$333$	−6.00000	−0.328798
$334$	−16.0000	−0.875481
$335$	−8.00000	−0.437087
$336$	2.00000	0.109109
$337$	−36.0000	−1.96104	−0.980522	−	0.196407i	$-0.937073\pi$
$337$	−36.0000	−1.96104	−0.980522	+	0.196407i	$0.937073\pi$
$338$	3.00000	0.163178
$339$	4.00000	0.217250
$340$	1.00000	0.0542326
$341$	−8.00000	−0.433224
$342$	−2.00000	−0.108148
$343$	20.0000	1.07990
$344$	−6.00000	−0.323498
$345$	−6.00000	−0.323029
$346$	18.0000	0.967686
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	2.00000	0.107211
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	−2.00000	−0.106904
$351$	4.00000	0.213504
$352$	1.00000	0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	−10.0000	−0.531494
$355$	−10.0000	−0.530745
$356$	−18.0000	−0.953998
$357$	2.00000	0.105851
$358$	−10.0000	−0.528516
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	1.00000	0.0527046
$361$	−15.0000	−0.789474
$362$	−22.0000	−1.15629
$363$	−1.00000	−0.0524864
$364$	8.00000	0.419314
$365$	12.0000	0.628109
$366$	6.00000	0.313625
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	6.00000	0.312772
$369$	2.00000	0.104116
$370$	−6.00000	−0.311925
$371$	0	0
$372$	8.00000	0.414781
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	8.00000	0.412568
$377$	8.00000	0.412021
$378$	2.00000	0.102869
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	−2.00000	−0.102598
$381$	0	0
$382$	−12.0000	−0.613973
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	−1.00000	−0.0510310
$385$	−2.00000	−0.101929
$386$	−16.0000	−0.814379
$387$	−6.00000	−0.304997
$388$	−2.00000	−0.101535
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	4.00000	0.202548
$391$	6.00000	0.303433
$392$	−3.00000	−0.151523
$393$	−20.0000	−1.00887
$394$	−2.00000	−0.100759
$395$	−6.00000	−0.301893
$396$	1.00000	0.0502519
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	0	0
$399$	−4.00000	−0.200250
$400$	1.00000	0.0500000
$401$	−16.0000	−0.799002	−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000	−0.799002	−0.399501	+	0.916733i	$0.630817\pi$
$402$	8.00000	0.399004
$403$	32.0000	1.59403
$404$	−10.0000	−0.497519
$405$	1.00000	0.0496904
$406$	4.00000	0.198517
$407$	−6.00000	−0.297409
$408$	−1.00000	−0.0495074
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	2.00000	0.0987730
$411$	6.00000	0.295958
$412$	−16.0000	−0.788263
$413$	−20.0000	−0.984136
$414$	6.00000	0.294884
$415$	4.00000	0.196352
$416$	−4.00000	−0.196116
$417$	0	0
$418$	−2.00000	−0.0978232
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	2.00000	0.0975900
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−8.00000	−0.389434
$423$	8.00000	0.388973
$424$	0	0
$425$	1.00000	0.0485071
$426$	10.0000	0.484502
$427$	12.0000	0.580721
$428$	12.0000	0.580042
$429$	4.00000	0.193122
$430$	−6.00000	−0.289346
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	−1.00000	−0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	16.0000	0.768025
$435$	2.00000	0.0958927
$436$	−10.0000	−0.478913
$437$	−12.0000	−0.574038
$438$	−12.0000	−0.573382
$439$	−6.00000	−0.286364	−0.143182	−	0.989696i	$-0.545733\pi$
$439$	−6.00000	−0.286364	−0.143182	+	0.989696i	$0.545733\pi$
$440$	1.00000	0.0476731
$441$	−3.00000	−0.142857
$442$	−4.00000	−0.190261
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	6.00000	0.284747
$445$	−18.0000	−0.853282
$446$	−8.00000	−0.378811
$447$	6.00000	0.283790
$448$	−2.00000	−0.0944911
$449$	20.0000	0.943858	0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000	0.943858	0.471929	+	0.881636i	$0.343558\pi$
$450$	1.00000	0.0471405
$451$	2.00000	0.0941763
$452$	−4.00000	−0.188144
$453$	4.00000	0.187936
$454$	20.0000	0.938647
$455$	8.00000	0.375046
$456$	2.00000	0.0936586
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	2.00000	0.0934539
$459$	−1.00000	−0.0466760
$460$	6.00000	0.279751
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	2.00000	0.0930484
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	−2.00000	−0.0928477
$465$	8.00000	0.370991
$466$	6.00000	0.277945
$467$	14.0000	0.647843	0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000	0.647843	0.323921	+	0.946084i	$0.394999\pi$
$468$	−4.00000	−0.184900
$469$	16.0000	0.738811
$470$	8.00000	0.369012
$471$	2.00000	0.0921551
$472$	10.0000	0.460287
$473$	−6.00000	−0.275880
$474$	6.00000	0.275589
$475$	−2.00000	−0.0917663
$476$	−2.00000	−0.0916698
$477$	0	0
$478$	8.00000	0.365911
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	−1.00000	−0.0456435
$481$	24.0000	1.09431
$482$	4.00000	0.182195
$483$	12.0000	0.546019
$484$	1.00000	0.0454545
$485$	−2.00000	−0.0908153
$486$	−1.00000	−0.0453609
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−6.00000	−0.271607
$489$	4.00000	0.180886
$490$	−3.00000	−0.135526
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	−2.00000	−0.0901670
$493$	−2.00000	−0.0900755
$494$	8.00000	0.359937
$495$	1.00000	0.0449467
$496$	−8.00000	−0.359211
$497$	20.0000	0.897123
$498$	−4.00000	−0.179244
$499$	−12.0000	−0.537194	−0.268597	−	0.963253i	$-0.586560\pi$
$499$	−12.0000	−0.537194	−0.268597	+	0.963253i	$0.586560\pi$
$500$	1.00000	0.0447214
$501$	16.0000	0.714827
$502$	6.00000	0.267793
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	−2.00000	−0.0890871
$505$	−10.0000	−0.444994
$506$	6.00000	0.266733
$507$	−3.00000	−0.133235
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	−1.00000	−0.0442807
$511$	−24.0000	−1.06170
$512$	1.00000	0.0441942
$513$	2.00000	0.0883022
$514$	−14.0000	−0.617514
$515$	−16.0000	−0.705044
$516$	6.00000	0.264135
$517$	8.00000	0.351840
$518$	12.0000	0.527250
$519$	−18.0000	−0.790112
$520$	−4.00000	−0.175412
$521$	8.00000	0.350486	0.175243	−	0.984525i	$-0.443929\pi$
$521$	8.00000	0.350486	0.175243	+	0.984525i	$0.443929\pi$
$522$	−2.00000	−0.0875376
$523$	14.0000	0.612177	0.306089	−	0.952003i	$-0.400980\pi$
$523$	14.0000	0.612177	0.306089	+	0.952003i	$0.400980\pi$
$524$	20.0000	0.873704
$525$	2.00000	0.0872872
$526$	24.0000	1.04645
$527$	−8.00000	−0.348485
$528$	−1.00000	−0.0435194
$529$	13.0000	0.565217
$530$	0	0
$531$	10.0000	0.433963
$532$	4.00000	0.173422
$533$	−8.00000	−0.346518
$534$	18.0000	0.778936
$535$	12.0000	0.518805
$536$	−8.00000	−0.345547
$537$	10.0000	0.431532
$538$	14.0000	0.603583
$539$	−3.00000	−0.129219
$540$	−1.00000	−0.0430331
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	0	0
$543$	22.0000	0.944110
$544$	1.00000	0.0428746
$545$	−10.0000	−0.428353
$546$	−8.00000	−0.342368
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	−6.00000	−0.256307
$549$	−6.00000	−0.256074
$550$	1.00000	0.0426401
$551$	4.00000	0.170406
$552$	−6.00000	−0.255377
$553$	12.0000	0.510292
$554$	−2.00000	−0.0849719
$555$	6.00000	0.254686
$556$	0	0
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	−8.00000	−0.338667
$559$	24.0000	1.01509
$560$	−2.00000	−0.0845154
$561$	−1.00000	−0.0422200
$562$	−26.0000	−1.09674
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	−8.00000	−0.336861
$565$	−4.00000	−0.168281
$566$	32.0000	1.34506
$567$	−2.00000	−0.0839921
$568$	−10.0000	−0.419591
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	2.00000	0.0837708
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	−4.00000	−0.167248
$573$	12.0000	0.501307
$574$	−4.00000	−0.166957
$575$	6.00000	0.250217
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	1.00000	0.0415945
$579$	16.0000	0.664937
$580$	−2.00000	−0.0830455
$581$	−8.00000	−0.331896
$582$	2.00000	0.0829027
$583$	0	0
$584$	12.0000	0.496564
$585$	−4.00000	−0.165380
$586$	22.0000	0.908812
$587$	−2.00000	−0.0825488	−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000	−0.0825488	−0.0412744	+	0.999148i	$0.513142\pi$
$588$	3.00000	0.123718
$589$	16.0000	0.659269
$590$	10.0000	0.411693
$591$	2.00000	0.0822690
$592$	−6.00000	−0.246598
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	−1.00000	−0.0410305
$595$	−2.00000	−0.0819920
$596$	−6.00000	−0.245770
$597$	0	0
$598$	−24.0000	−0.981433
$599$	−44.0000	−1.79779	−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000	−1.79779	−0.898896	+	0.438163i	$0.855629\pi$
$600$	−1.00000	−0.0408248
$601$	32.0000	1.30531	0.652654	−	0.757656i	$-0.273656\pi$
$601$	32.0000	1.30531	0.652654	+	0.757656i	$0.273656\pi$
$602$	12.0000	0.489083
$603$	−8.00000	−0.325785
$604$	−4.00000	−0.162758
$605$	1.00000	0.0406558
$606$	10.0000	0.406222
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	−2.00000	−0.0811107
$609$	−4.00000	−0.162088
$610$	−6.00000	−0.242933
$611$	−32.0000	−1.29458
$612$	1.00000	0.0404226
$613$	4.00000	0.161558	0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000	0.161558	0.0807792	+	0.996732i	$0.474259\pi$
$614$	6.00000	0.242140
$615$	−2.00000	−0.0806478
$616$	−2.00000	−0.0805823
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	16.0000	0.643614
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	−8.00000	−0.321288
$621$	−6.00000	−0.240772
$622$	−26.0000	−1.04251
$623$	36.0000	1.44231
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	2.00000	0.0798723
$628$	−2.00000	−0.0798087
$629$	−6.00000	−0.239236
$630$	−2.00000	−0.0796819
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.00000	−0.238667
$633$	8.00000	0.317971
$634$	−6.00000	−0.238290
$635$	0	0
$636$	0	0
$637$	12.0000	0.475457
$638$	−2.00000	−0.0791808
$639$	−10.0000	−0.395594
$640$	1.00000	0.0395285
$641$	16.0000	0.631962	0.315981	−	0.948766i	$-0.397666\pi$
$641$	16.0000	0.631962	0.315981	+	0.948766i	$0.397666\pi$
$642$	−12.0000	−0.473602
$643$	36.0000	1.41970	0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000	1.41970	0.709851	+	0.704352i	$0.248762\pi$
$644$	−12.0000	−0.472866
$645$	6.00000	0.236250
$646$	−2.00000	−0.0786889
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	1.00000	0.0392837
$649$	10.0000	0.392534
$650$	−4.00000	−0.156893
$651$	−16.0000	−0.627089
$652$	−4.00000	−0.156652
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	10.0000	0.391031
$655$	20.0000	0.781465
$656$	2.00000	0.0780869
$657$	12.0000	0.468165
$658$	−16.0000	−0.623745
$659$	28.0000	1.09073	0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000	1.09073	0.545363	+	0.838200i	$0.316392\pi$
$660$	−1.00000	−0.0389249
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	−28.0000	−1.08825
$663$	4.00000	0.155347
$664$	4.00000	0.155230
$665$	4.00000	0.155113
$666$	−6.00000	−0.232495
$667$	−12.0000	−0.464642
$668$	−16.0000	−0.619059
$669$	8.00000	0.309298
$670$	−8.00000	−0.309067
$671$	−6.00000	−0.231627
$672$	2.00000	0.0771517
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	−36.0000	−1.38667
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	−2.00000	−0.0768662	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000	−0.0768662	−0.0384331	+	0.999261i	$0.512237\pi$
$678$	4.00000	0.153619
$679$	4.00000	0.153506
$680$	1.00000	0.0383482
$681$	−20.0000	−0.766402
$682$	−8.00000	−0.306336
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−2.00000	−0.0764719
$685$	−6.00000	−0.229248
$686$	20.0000	0.763604
$687$	−2.00000	−0.0763048
$688$	−6.00000	−0.228748
$689$	0	0
$690$	−6.00000	−0.228416
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	18.0000	0.684257
$693$	−2.00000	−0.0759737
$694$	−12.0000	−0.455514
$695$	0	0
$696$	2.00000	0.0758098
$697$	2.00000	0.0757554
$698$	8.00000	0.302804
$699$	−6.00000	−0.226941
$700$	−2.00000	−0.0755929
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	4.00000	0.150970
$703$	12.0000	0.452589
$704$	1.00000	0.0376889
$705$	−8.00000	−0.301297
$706$	−6.00000	−0.225813
$707$	20.0000	0.752177
$708$	−10.0000	−0.375823
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	−10.0000	−0.375293
$711$	−6.00000	−0.225018
$712$	−18.0000	−0.674579
$713$	−48.0000	−1.79761
$714$	2.00000	0.0748481
$715$	−4.00000	−0.149592
$716$	−10.0000	−0.373718
$717$	−8.00000	−0.298765
$718$	−8.00000	−0.298557
$719$	34.0000	1.26799	0.633993	−	0.773339i	$-0.281415\pi$
$719$	34.0000	1.26799	0.633993	+	0.773339i	$0.281415\pi$
$720$	1.00000	0.0372678
$721$	32.0000	1.19174
$722$	−15.0000	−0.558242
$723$	−4.00000	−0.148762
$724$	−22.0000	−0.817624
$725$	−2.00000	−0.0742781
$726$	−1.00000	−0.0371135
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	12.0000	0.444140
$731$	−6.00000	−0.221918
$732$	6.00000	0.221766
$733$	28.0000	1.03420	0.517102	−	0.855924i	$-0.327011\pi$
$733$	28.0000	1.03420	0.517102	+	0.855924i	$0.327011\pi$
$734$	12.0000	0.442928
$735$	3.00000	0.110657
$736$	6.00000	0.221163
$737$	−8.00000	−0.294684
$738$	2.00000	0.0736210
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	−6.00000	−0.220564
$741$	−8.00000	−0.293887
$742$	0	0
$743$	52.0000	1.90769	0.953847	−	0.300291i	$-0.0970839\pi$
$743$	52.0000	1.90769	0.953847	+	0.300291i	$0.0970839\pi$
$744$	8.00000	0.293294
$745$	−6.00000	−0.219823
$746$	4.00000	0.146450
$747$	4.00000	0.146352
$748$	1.00000	0.0365636
$749$	−24.0000	−0.876941
$750$	−1.00000	−0.0365148
$751$	−20.0000	−0.729810	−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000	−0.729810	−0.364905	+	0.931045i	$0.618899\pi$
$752$	8.00000	0.291730
$753$	−6.00000	−0.218652
$754$	8.00000	0.291343
$755$	−4.00000	−0.145575
$756$	2.00000	0.0727393
$757$	26.0000	0.944986	0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000	0.944986	0.472493	+	0.881334i	$0.343354\pi$
$758$	−12.0000	−0.435860
$759$	−6.00000	−0.217786
$760$	−2.00000	−0.0725476
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	20.0000	0.724049
$764$	−12.0000	−0.434145
$765$	1.00000	0.0361551
$766$	36.0000	1.30073
$767$	−40.0000	−1.44432
$768$	−1.00000	−0.0360844
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	−2.00000	−0.0720750
$771$	14.0000	0.504198
$772$	−16.0000	−0.575853
$773$	−4.00000	−0.143870	−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000	−0.143870	−0.0719350	+	0.997409i	$0.522917\pi$
$774$	−6.00000	−0.215666
$775$	−8.00000	−0.287368
$776$	−2.00000	−0.0717958
$777$	−12.0000	−0.430498
$778$	0	0
$779$	−4.00000	−0.143315
$780$	4.00000	0.143223
$781$	−10.0000	−0.357828
$782$	6.00000	0.214560
$783$	2.00000	0.0714742
$784$	−3.00000	−0.107143
$785$	−2.00000	−0.0713831
$786$	−20.0000	−0.713376
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−2.00000	−0.0712470
$789$	−24.0000	−0.854423
$790$	−6.00000	−0.213470
$791$	8.00000	0.284447
$792$	1.00000	0.0355335
$793$	24.0000	0.852265
$794$	−34.0000	−1.20661
$795$	0	0
$796$	0	0
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	−4.00000	−0.141598
$799$	8.00000	0.283020
$800$	1.00000	0.0353553
$801$	−18.0000	−0.635999
$802$	−16.0000	−0.564980
$803$	12.0000	0.423471
$804$	8.00000	0.282138
$805$	−12.0000	−0.422944
$806$	32.0000	1.12715
$807$	−14.0000	−0.492823
$808$	−10.0000	−0.351799
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	1.00000	0.0351364
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	4.00000	0.140372
$813$	0	0
$814$	−6.00000	−0.210300
$815$	−4.00000	−0.140114
$816$	−1.00000	−0.0350070
$817$	12.0000	0.419827
$818$	22.0000	0.769212
$819$	8.00000	0.279543
$820$	2.00000	0.0698430
$821$	−38.0000	−1.32621	−0.663105	−	0.748527i	$-0.730762\pi$
$821$	−38.0000	−1.32621	−0.663105	+	0.748527i	$0.730762\pi$
$822$	6.00000	0.209274
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	−16.0000	−0.557386
$825$	−1.00000	−0.0348155
$826$	−20.0000	−0.695889
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	6.00000	0.208514
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	4.00000	0.138842
$831$	2.00000	0.0693792
$832$	−4.00000	−0.138675
$833$	−3.00000	−0.103944
$834$	0	0
$835$	−16.0000	−0.553703
$836$	−2.00000	−0.0691714
$837$	8.00000	0.276520
$838$	4.00000	0.138178
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	2.00000	0.0690066
$841$	−25.0000	−0.862069
$842$	−10.0000	−0.344623
$843$	26.0000	0.895488
$844$	−8.00000	−0.275371
$845$	3.00000	0.103203
$846$	8.00000	0.275046
$847$	−2.00000	−0.0687208
$848$	0	0
$849$	−32.0000	−1.09824
$850$	1.00000	0.0342997
$851$	−36.0000	−1.23406
$852$	10.0000	0.342594
$853$	54.0000	1.84892	0.924462	−	0.381273i	$-0.124514\pi$
$853$	54.0000	1.84892	0.924462	+	0.381273i	$0.124514\pi$
$854$	12.0000	0.410632
$855$	−2.00000	−0.0683986
$856$	12.0000	0.410152
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	4.00000	0.136558
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	−6.00000	−0.204598
$861$	4.00000	0.136320
$862$	16.0000	0.544962
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	−1.00000	−0.0340207
$865$	18.0000	0.612018
$866$	−2.00000	−0.0679628
$867$	−1.00000	−0.0339618
$868$	16.0000	0.543075
$869$	−6.00000	−0.203536
$870$	2.00000	0.0678064
$871$	32.0000	1.08428
$872$	−10.0000	−0.338643
$873$	−2.00000	−0.0676897
$874$	−12.0000	−0.405906
$875$	−2.00000	−0.0676123
$876$	−12.0000	−0.405442
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	−6.00000	−0.202490
$879$	−22.0000	−0.742042
$880$	1.00000	0.0337100
$881$	44.0000	1.48240	0.741199	−	0.671286i	$-0.234258\pi$
$881$	44.0000	1.48240	0.741199	+	0.671286i	$0.234258\pi$
$882$	−3.00000	−0.101015
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	−4.00000	−0.134535
$885$	−10.0000	−0.336146
$886$	−18.0000	−0.604722
$887$	−16.0000	−0.537227	−0.268614	−	0.963248i	$-0.586566\pi$
$887$	−16.0000	−0.537227	−0.268614	+	0.963248i	$0.586566\pi$
$888$	6.00000	0.201347
$889$	0	0
$890$	−18.0000	−0.603361
$891$	1.00000	0.0335013
$892$	−8.00000	−0.267860
$893$	−16.0000	−0.535420
$894$	6.00000	0.200670
$895$	−10.0000	−0.334263
$896$	−2.00000	−0.0668153
$897$	24.0000	0.801337
$898$	20.0000	0.667409
$899$	16.0000	0.533630
$900$	1.00000	0.0333333
$901$	0	0
$902$	2.00000	0.0665927
$903$	−12.0000	−0.399335
$904$	−4.00000	−0.133038
$905$	−22.0000	−0.731305
$906$	4.00000	0.132891
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	20.0000	0.663723
$909$	−10.0000	−0.331679
$910$	8.00000	0.265197
$911$	54.0000	1.78910	0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000	1.78910	0.894550	+	0.446968i	$0.147496\pi$
$912$	2.00000	0.0662266
$913$	4.00000	0.132381
$914$	−18.0000	−0.595387
$915$	6.00000	0.198354
$916$	2.00000	0.0660819
$917$	−40.0000	−1.32092
$918$	−1.00000	−0.0330049
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	6.00000	0.197814
$921$	−6.00000	−0.197707
$922$	−30.0000	−0.987997
$923$	40.0000	1.31662
$924$	2.00000	0.0657952
$925$	−6.00000	−0.197279
$926$	−40.0000	−1.31448
$927$	−16.0000	−0.525509
$928$	−2.00000	−0.0656532
$929$	36.0000	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$930$	8.00000	0.262330
$931$	6.00000	0.196642
$932$	6.00000	0.196537
$933$	26.0000	0.851202
$934$	14.0000	0.458094
$935$	1.00000	0.0327035
$936$	−4.00000	−0.130744
$937$	−42.0000	−1.37208	−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000	−1.37208	−0.686040	+	0.727564i	$0.740653\pi$
$938$	16.0000	0.522419
$939$	−6.00000	−0.195803
$940$	8.00000	0.260931
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	2.00000	0.0651635
$943$	12.0000	0.390774
$944$	10.0000	0.325472
$945$	2.00000	0.0650600
$946$	−6.00000	−0.195077
$947$	40.0000	1.29983	0.649913	−	0.760009i	$-0.274805\pi$
$947$	40.0000	1.29983	0.649913	+	0.760009i	$0.274805\pi$
$948$	6.00000	0.194871
$949$	−48.0000	−1.55815
$950$	−2.00000	−0.0648886
$951$	6.00000	0.194563
$952$	−2.00000	−0.0648204
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	0	0
$955$	−12.0000	−0.388311
$956$	8.00000	0.258738
$957$	2.00000	0.0646508
$958$	−20.0000	−0.646171
$959$	12.0000	0.387500
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	24.0000	0.773791
$963$	12.0000	0.386695
$964$	4.00000	0.128831
$965$	−16.0000	−0.515058
$966$	12.0000	0.386094
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	1.00000	0.0321412
$969$	2.00000	0.0642493
$970$	−2.00000	−0.0642161
$971$	−22.0000	−0.706014	−0.353007	−	0.935621i	$-0.614841\pi$
$971$	−22.0000	−0.706014	−0.353007	+	0.935621i	$0.614841\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−4.00000	−0.128168
$975$	4.00000	0.128103
$976$	−6.00000	−0.192055
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	4.00000	0.127906
$979$	−18.0000	−0.575282
$980$	−3.00000	−0.0958315
$981$	−10.0000	−0.319275
$982$	36.0000	1.14881
$983$	−10.0000	−0.318950	−0.159475	−	0.987202i	$-0.550980\pi$
$983$	−10.0000	−0.318950	−0.159475	+	0.987202i	$0.550980\pi$
$984$	−2.00000	−0.0637577
$985$	−2.00000	−0.0637253
$986$	−2.00000	−0.0636930
$987$	16.0000	0.509286
$988$	8.00000	0.254514
$989$	−36.0000	−1.14473
$990$	1.00000	0.0317821
$991$	60.0000	1.90596	0.952981	−	0.303029i	$-0.0979978\pi$
$991$	60.0000	1.90596	0.952981	+	0.303029i	$0.0979978\pi$
$992$	−8.00000	−0.254000
$993$	28.0000	0.888553
$994$	20.0000	0.634361
$995$	0	0
$996$	−4.00000	−0.126745
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	−12.0000	−0.379853
$999$	6.00000	0.189832

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bb.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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