LMFDB - Embedded newform 5610.2.a.i.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +1.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} +2.00000 q^{29} +1.00000 q^{30} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +6.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} +2.00000 q^{42} -2.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +6.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -4.00000 q^{52} -4.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -2.00000 q^{56} +6.00000 q^{57} -2.00000 q^{58} +14.0000 q^{59} -1.00000 q^{60} +10.0000 q^{61} +2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -1.00000 q^{66} +8.00000 q^{67} -1.00000 q^{68} +6.00000 q^{69} -2.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} +4.00000 q^{73} +6.00000 q^{74} -1.00000 q^{75} -6.00000 q^{76} -2.00000 q^{77} -4.00000 q^{78} +14.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} -2.00000 q^{84} -1.00000 q^{85} +2.00000 q^{86} -2.00000 q^{87} +1.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -8.00000 q^{91} -6.00000 q^{92} -8.00000 q^{94} -6.00000 q^{95} +1.00000 q^{96} +14.0000 q^{97} +3.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−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
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.00000	0.223607
$21$	−2.00000	−0.436436
$22$	1.00000	0.213201
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	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	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	1.00000	0.182574
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−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	$0.664172\pi$
$38$	6.00000	0.973329
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	2.00000	0.308607
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	−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
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	−2.00000	−0.267261
$57$	6.00000	0.794719
$58$	−2.00000	−0.262613
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	−1.00000	−0.129099
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	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	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−1.00000	−0.121268
$69$	6.00000	0.722315
$70$	−2.00000	−0.239046
$71$	−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	$0.424791\pi$
$74$	6.00000	0.697486
$75$	−1.00000	−0.115470
$76$	−6.00000	−0.688247
$77$	−2.00000	−0.227921
$78$	−4.00000	−0.452911
$79$	14.0000	1.57512	0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000	1.57512	0.787562	+	0.616236i	$0.211343\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	−2.00000	−0.218218
$85$	−1.00000	−0.108465
$86$	2.00000	0.215666
$87$	−2.00000	−0.214423
$88$	1.00000	0.106600
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−0.105409
$91$	−8.00000	−0.838628
$92$	−6.00000	−0.625543
$93$	0	0
$94$	−8.00000	−0.825137
$95$	−6.00000	−0.615587
$96$	1.00000	0.102062
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	3.00000	0.303046
$99$	−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
$103$	−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
$106$	4.00000	0.388514
$107$	20.0000	1.93347	0.966736	−	0.255774i	$-0.0823304\pi$
$107$	20.0000	1.93347	0.966736	+	0.255774i	$0.0823304\pi$
$108$	−1.00000	−0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.00000	0.0953463
$111$	6.00000	0.569495
$112$	2.00000	0.188982
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−6.00000	−0.561951
$115$	−6.00000	−0.559503
$116$	2.00000	0.185695
$117$	−4.00000	−0.369800
$118$	−14.0000	−1.28880
$119$	−2.00000	−0.183340
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−10.0000	−0.905357
$123$	2.00000	0.180334
$124$	0	0
$125$	1.00000	0.0894427
$126$	−2.00000	−0.178174
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−1.00000	−0.0883883
$129$	2.00000	0.176090
$130$	4.00000	0.350823
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	1.00000	0.0870388
$133$	−12.0000	−1.04053
$134$	−8.00000	−0.691095
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−6.00000	−0.510754
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.00000	0.169031
$141$	−8.00000	−0.673722
$142$	6.00000	0.503509
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	−4.00000	−0.331042
$147$	3.00000	0.247436
$148$	−6.00000	−0.493197
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	1.00000	0.0816497
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	6.00000	0.486664
$153$	−1.00000	−0.0808452
$154$	2.00000	0.161165
$155$	0	0
$156$	4.00000	0.320256
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−14.0000	−1.11378
$159$	4.00000	0.317221
$160$	−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
$166$	−12.0000	−0.931381
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	1.00000	0.0766965
$171$	−6.00000	−0.458831
$172$	−2.00000	−0.152499
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	2.00000	0.151620
$175$	2.00000	0.151186
$176$	−1.00000	−0.0753778
$177$	−14.0000	−1.05230
$178$	−6.00000	−0.449719
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	1.00000	0.0745356
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	8.00000	0.592999
$183$	−10.0000	−0.739221
$184$	6.00000	0.442326
$185$	−6.00000	−0.441129
$186$	0	0
$187$	1.00000	0.0731272
$188$	8.00000	0.583460
$189$	−2.00000	−0.145479
$190$	6.00000	0.435286
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	−1.00000	−0.0721688
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	−14.0000	−1.00514
$195$	4.00000	0.286446
$196$	−3.00000	−0.214286
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	1.00000	0.0710669
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	−1.00000	−0.0707107
$201$	−8.00000	−0.564276
$202$	−18.0000	−1.26648
$203$	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
$209$	6.00000	0.415029
$210$	2.00000	0.138013
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−4.00000	−0.274721
$213$	6.00000	0.411113
$214$	−20.0000	−1.36717
$215$	−2.00000	−0.136399
$216$	1.00000	0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	−4.00000	−0.270295
$220$	−1.00000	−0.0674200
$221$	4.00000	0.269069
$222$	−6.00000	−0.402694
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	−2.00000	−0.133631
$225$	1.00000	0.0666667
$226$	0	0
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	6.00000	0.397360
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	6.00000	0.395628
$231$	2.00000	0.131590
$232$	−2.00000	−0.131306
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	4.00000	0.261488
$235$	8.00000	0.521862
$236$	14.0000	0.911322
$237$	−14.0000	−0.909398
$238$	2.00000	0.129641
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	−1.00000	−0.0645497
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	10.0000	0.640184
$245$	−3.00000	−0.191663
$246$	−2.00000	−0.127515
$247$	24.0000	1.52708
$248$	0	0
$249$	−12.0000	−0.760469
$250$	−1.00000	−0.0632456
$251$	10.0000	0.631194	0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000	0.631194	0.315597	+	0.948893i	$0.397795\pi$
$252$	2.00000	0.125988
$253$	6.00000	0.377217
$254$	−4.00000	−0.250982
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	−2.00000	−0.124515
$259$	−12.0000	−0.745644
$260$	−4.00000	−0.248069
$261$	2.00000	0.123797
$262$	−12.0000	−0.741362
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−1.00000	−0.0615457
$265$	−4.00000	−0.245718
$266$	12.0000	0.735767
$267$	−6.00000	−0.367194
$268$	8.00000	0.488678
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	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
$273$	8.00000	0.484182
$274$	−2.00000	−0.120824
$275$	−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	$0.519137\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	−2.00000	−0.119523
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	8.00000	0.476393
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	−6.00000	−0.356034
$285$	6.00000	0.355409
$286$	−4.00000	−0.236525
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	−14.0000	−0.820695
$292$	4.00000	0.234082
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	−3.00000	−0.174964
$295$	14.0000	0.815112
$296$	6.00000	0.348743
$297$	1.00000	0.0580259
$298$	−6.00000	−0.347571
$299$	24.0000	1.38796
$300$	−1.00000	−0.0577350
$301$	−4.00000	−0.230556
$302$	8.00000	0.460348
$303$	−18.0000	−1.03407
$304$	−6.00000	−0.344124
$305$	10.0000	0.572598
$306$	1.00000	0.0571662
$307$	−30.0000	−1.71219	−0.856095	−	0.516818i	$-0.827116\pi$
$307$	−30.0000	−1.71219	−0.856095	+	0.516818i	$0.827116\pi$
$308$	−2.00000	−0.113961
$309$	16.0000	0.910208
$310$	0	0
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	−4.00000	−0.226455
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	18.0000	1.01580
$315$	2.00000	0.112687
$316$	14.0000	0.787562
$317$	34.0000	1.90963	0.954815	−	0.297200i	$-0.0960529\pi$
$317$	34.0000	1.90963	0.954815	+	0.297200i	$0.0960529\pi$
$318$	−4.00000	−0.224309
$319$	−2.00000	−0.111979
$320$	1.00000	0.0559017
$321$	−20.0000	−1.11629
$322$	12.0000	0.668734
$323$	6.00000	0.333849
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	4.00000	0.221540
$327$	2.00000	0.110600
$328$	2.00000	0.110432
$329$	16.0000	0.882109
$330$	−1.00000	−0.0550482
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	12.0000	0.658586
$333$	−6.00000	−0.328798
$334$	−8.00000	−0.437741
$335$	8.00000	0.437087
$336$	−2.00000	−0.109109
$337$	−12.0000	−0.653682	−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000	−0.653682	−0.326841	+	0.945079i	$0.605984\pi$
$338$	−3.00000	−0.163178
$339$	0	0
$340$	−1.00000	−0.0542326
$341$	0	0
$342$	6.00000	0.324443
$343$	−20.0000	−1.07990
$344$	2.00000	0.107833
$345$	6.00000	0.323029
$346$	−14.0000	−0.752645
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−2.00000	−0.107211
$349$	16.0000	0.856460	0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000	0.856460	0.428230	+	0.903670i	$0.359137\pi$
$350$	−2.00000	−0.106904
$351$	4.00000	0.213504
$352$	1.00000	0.0533002
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	14.0000	0.744092
$355$	−6.00000	−0.318447
$356$	6.00000	0.317999
$357$	2.00000	0.105851
$358$	6.00000	0.317110
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−1.00000	−0.0527046
$361$	17.0000	0.894737
$362$	−10.0000	−0.525588
$363$	−1.00000	−0.0524864
$364$	−8.00000	−0.419314
$365$	4.00000	0.209370
$366$	10.0000	0.522708
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	−6.00000	−0.312772
$369$	−2.00000	−0.104116
$370$	6.00000	0.311925
$371$	−8.00000	−0.415339
$372$	0	0
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	−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	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	−6.00000	−0.307794
$381$	−4.00000	−0.204926
$382$	4.00000	0.204658
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	1.00000	0.0510310
$385$	−2.00000	−0.101929
$386$	16.0000	0.814379
$387$	−2.00000	−0.101666
$388$	14.0000	0.710742
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	−4.00000	−0.202548
$391$	6.00000	0.303433
$392$	3.00000	0.151523
$393$	−12.0000	−0.605320
$394$	22.0000	1.10834
$395$	14.0000	0.704416
$396$	−1.00000	−0.0502519
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	−8.00000	−0.401004
$399$	12.0000	0.600751
$400$	1.00000	0.0500000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	8.00000	0.399004
$403$	0	0
$404$	18.0000	0.895533
$405$	1.00000	0.0496904
$406$	−4.00000	−0.198517
$407$	6.00000	0.297409
$408$	−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	$0.515746\pi$
$410$	2.00000	0.0987730
$411$	−2.00000	−0.0986527
$412$	−16.0000	−0.788263
$413$	28.0000	1.37779
$414$	6.00000	0.294884
$415$	12.0000	0.589057
$416$	4.00000	0.196116
$417$	4.00000	0.195881
$418$	−6.00000	−0.293470
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	−2.00000	−0.0975900
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−20.0000	−0.973585
$423$	8.00000	0.388973
$424$	4.00000	0.194257
$425$	−1.00000	−0.0485071
$426$	−6.00000	−0.290701
$427$	20.0000	0.967868
$428$	20.0000	0.966736
$429$	−4.00000	−0.193122
$430$	2.00000	0.0964486
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	−2.00000	−0.0957826
$437$	36.0000	1.72211
$438$	4.00000	0.191127
$439$	6.00000	0.286364	0.143182	−	0.989696i	$-0.454267\pi$
$439$	6.00000	0.286364	0.143182	+	0.989696i	$0.454267\pi$
$440$	1.00000	0.0476731
$441$	−3.00000	−0.142857
$442$	−4.00000	−0.190261
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	6.00000	0.284747
$445$	6.00000	0.284427
$446$	−16.0000	−0.757622
$447$	−6.00000	−0.283790
$448$	2.00000	0.0944911
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	−1.00000	−0.0471405
$451$	2.00000	0.0941763
$452$	0	0
$453$	8.00000	0.375873
$454$	4.00000	0.187729
$455$	−8.00000	−0.375046
$456$	−6.00000	−0.280976
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	14.0000	0.654177
$459$	1.00000	0.0466760
$460$	−6.00000	−0.279751
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	−2.00000	−0.0930484
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	22.0000	1.01913
$467$	2.00000	0.0925490	0.0462745	−	0.998929i	$-0.485265\pi$
$467$	2.00000	0.0925490	0.0462745	+	0.998929i	$0.485265\pi$
$468$	−4.00000	−0.184900
$469$	16.0000	0.738811
$470$	−8.00000	−0.369012
$471$	18.0000	0.829396
$472$	−14.0000	−0.644402
$473$	2.00000	0.0919601
$474$	14.0000	0.643041
$475$	−6.00000	−0.275299
$476$	−2.00000	−0.0916698
$477$	−4.00000	−0.183147
$478$	−16.0000	−0.731823
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	1.00000	0.0456435
$481$	24.0000	1.09431
$482$	4.00000	0.182195
$483$	12.0000	0.546019
$484$	1.00000	0.0454545
$485$	14.0000	0.635707
$486$	1.00000	0.0453609
$487$	−28.0000	−1.26880	−0.634401	−	0.773004i	$-0.718753\pi$
$487$	−28.0000	−1.26880	−0.634401	+	0.773004i	$0.718753\pi$
$488$	−10.0000	−0.452679
$489$	4.00000	0.180886
$490$	3.00000	0.135526
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	2.00000	0.0901670
$493$	−2.00000	−0.0900755
$494$	−24.0000	−1.07981
$495$	−1.00000	−0.0449467
$496$	0	0
$497$	−12.0000	−0.538274
$498$	12.0000	0.537733
$499$	−36.0000	−1.61158	−0.805791	−	0.592200i	$-0.798259\pi$
$499$	−36.0000	−1.61158	−0.805791	+	0.592200i	$0.798259\pi$
$500$	1.00000	0.0447214
$501$	−8.00000	−0.357414
$502$	−10.0000	−0.446322
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	−2.00000	−0.0890871
$505$	18.0000	0.800989
$506$	−6.00000	−0.266733
$507$	−3.00000	−0.133235
$508$	4.00000	0.177471
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	−1.00000	−0.0442807
$511$	8.00000	0.353899
$512$	−1.00000	−0.0441942
$513$	6.00000	0.264906
$514$	−18.0000	−0.793946
$515$	−16.0000	−0.705044
$516$	2.00000	0.0880451
$517$	−8.00000	−0.351840
$518$	12.0000	0.527250
$519$	−14.0000	−0.614532
$520$	4.00000	0.175412
$521$	12.0000	0.525730	0.262865	−	0.964833i	$-0.415333\pi$
$521$	12.0000	0.525730	0.262865	+	0.964833i	$0.415333\pi$
$522$	−2.00000	−0.0875376
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	12.0000	0.524222
$525$	−2.00000	−0.0872872
$526$	24.0000	1.04645
$527$	0	0
$528$	1.00000	0.0435194
$529$	13.0000	0.565217
$530$	4.00000	0.173749
$531$	14.0000	0.607548
$532$	−12.0000	−0.520266
$533$	8.00000	0.346518
$534$	6.00000	0.259645
$535$	20.0000	0.864675
$536$	−8.00000	−0.345547
$537$	6.00000	0.258919
$538$	−6.00000	−0.258678
$539$	3.00000	0.129219
$540$	−1.00000	−0.0430331
$541$	42.0000	1.80572	0.902861	−	0.429934i	$-0.141463\pi$
$541$	42.0000	1.80572	0.902861	+	0.429934i	$0.141463\pi$
$542$	−20.0000	−0.859074
$543$	−10.0000	−0.429141
$544$	1.00000	0.0428746
$545$	−2.00000	−0.0856706
$546$	−8.00000	−0.342368
$547$	32.0000	1.36822	0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000	1.36822	0.684111	+	0.729378i	$0.260191\pi$
$548$	2.00000	0.0854358
$549$	10.0000	0.426790
$550$	1.00000	0.0426401
$551$	−12.0000	−0.511217
$552$	−6.00000	−0.255377
$553$	28.0000	1.19068
$554$	2.00000	0.0849719
$555$	6.00000	0.254686
$556$	−4.00000	−0.169638
$557$	10.0000	0.423714	0.211857	−	0.977301i	$-0.432049\pi$
$557$	10.0000	0.423714	0.211857	+	0.977301i	$0.432049\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	2.00000	0.0845154
$561$	−1.00000	−0.0422200
$562$	−18.0000	−0.759284
$563$	28.0000	1.18006	0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000	1.18006	0.590030	+	0.807382i	$0.299116\pi$
$564$	−8.00000	−0.336861
$565$	0	0
$566$	−28.0000	−1.17693
$567$	2.00000	0.0839921
$568$	6.00000	0.251754
$569$	14.0000	0.586911	0.293455	−	0.955973i	$-0.405195\pi$
$569$	14.0000	0.586911	0.293455	+	0.955973i	$0.405195\pi$
$570$	−6.00000	−0.251312
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	4.00000	0.167248
$573$	4.00000	0.167102
$574$	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
$581$	24.0000	0.995688
$582$	14.0000	0.580319
$583$	4.00000	0.165663
$584$	−4.00000	−0.165521
$585$	−4.00000	−0.165380
$586$	−2.00000	−0.0826192
$587$	2.00000	0.0825488	0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000	0.0825488	0.0412744	+	0.999148i	$0.486858\pi$
$588$	3.00000	0.123718
$589$	0	0
$590$	−14.0000	−0.576371
$591$	22.0000	0.904959
$592$	−6.00000	−0.246598
$593$	−46.0000	−1.88899	−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000	−1.88899	−0.944497	+	0.328521i	$0.893450\pi$
$594$	−1.00000	−0.0410305
$595$	−2.00000	−0.0819920
$596$	6.00000	0.245770
$597$	−8.00000	−0.327418
$598$	−24.0000	−0.981433
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	1.00000	0.0408248
$601$	−16.0000	−0.652654	−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000	−0.652654	−0.326327	+	0.945257i	$0.605811\pi$
$602$	4.00000	0.163028
$603$	8.00000	0.325785
$604$	−8.00000	−0.325515
$605$	1.00000	0.0406558
$606$	18.0000	0.731200
$607$	−30.0000	−1.21766	−0.608831	−	0.793300i	$-0.708361\pi$
$607$	−30.0000	−1.21766	−0.608831	+	0.793300i	$0.708361\pi$
$608$	6.00000	0.243332
$609$	−4.00000	−0.162088
$610$	−10.0000	−0.404888
$611$	−32.0000	−1.29458
$612$	−1.00000	−0.0404226
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	30.0000	1.21070
$615$	2.00000	0.0806478
$616$	2.00000	0.0805823
$617$	4.00000	0.161034	0.0805170	−	0.996753i	$-0.474343\pi$
$617$	4.00000	0.161034	0.0805170	+	0.996753i	$0.474343\pi$
$618$	−16.0000	−0.643614
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	0	0
$621$	6.00000	0.240772
$622$	30.0000	1.20289
$623$	12.0000	0.480770
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	18.0000	0.719425
$627$	−6.00000	−0.239617
$628$	−18.0000	−0.718278
$629$	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	$0.449096\pi$
$632$	−14.0000	−0.556890
$633$	−20.0000	−0.794929
$634$	−34.0000	−1.35031
$635$	4.00000	0.158735
$636$	4.00000	0.158610
$637$	12.0000	0.475457
$638$	2.00000	0.0791808
$639$	−6.00000	−0.237356
$640$	−1.00000	−0.0395285
$641$	28.0000	1.10593	0.552967	−	0.833203i	$-0.313496\pi$
$641$	28.0000	1.10593	0.552967	+	0.833203i	$0.313496\pi$
$642$	20.0000	0.789337
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−12.0000	−0.472866
$645$	2.00000	0.0787499
$646$	−6.00000	−0.236067
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	−1.00000	−0.0392837
$649$	−14.0000	−0.549548
$650$	4.00000	0.156893
$651$	0	0
$652$	−4.00000	−0.156652
$653$	−34.0000	−1.33052	−0.665261	−	0.746611i	$-0.731680\pi$
$653$	−34.0000	−1.33052	−0.665261	+	0.746611i	$0.731680\pi$
$654$	−2.00000	−0.0782062
$655$	12.0000	0.468879
$656$	−2.00000	−0.0780869
$657$	4.00000	0.156055
$658$	−16.0000	−0.623745
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	1.00000	0.0389249
$661$	−6.00000	−0.233373	−0.116686	−	0.993169i	$-0.537227\pi$
$661$	−6.00000	−0.233373	−0.116686	+	0.993169i	$0.537227\pi$
$662$	−4.00000	−0.155464
$663$	−4.00000	−0.155347
$664$	−12.0000	−0.465690
$665$	−12.0000	−0.465340
$666$	6.00000	0.232495
$667$	−12.0000	−0.464642
$668$	8.00000	0.309529
$669$	−16.0000	−0.618596
$670$	−8.00000	−0.309067
$671$	−10.0000	−0.386046
$672$	2.00000	0.0771517
$673$	32.0000	1.23351	0.616755	−	0.787155i	$-0.288447\pi$
$673$	32.0000	1.23351	0.616755	+	0.787155i	$0.288447\pi$
$674$	12.0000	0.462223
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	0	0
$679$	28.0000	1.07454
$680$	1.00000	0.0383482
$681$	4.00000	0.153280
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−6.00000	−0.229416
$685$	2.00000	0.0764161
$686$	20.0000	0.763604
$687$	14.0000	0.534133
$688$	−2.00000	−0.0762493
$689$	16.0000	0.609551
$690$	−6.00000	−0.228416
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	14.0000	0.532200
$693$	−2.00000	−0.0759737
$694$	−12.0000	−0.455514
$695$	−4.00000	−0.151729
$696$	2.00000	0.0758098
$697$	2.00000	0.0757554
$698$	−16.0000	−0.605609
$699$	22.0000	0.832116
$700$	2.00000	0.0755929
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	−4.00000	−0.150970
$703$	36.0000	1.35777
$704$	−1.00000	−0.0376889
$705$	−8.00000	−0.301297
$706$	−10.0000	−0.376355
$707$	36.0000	1.35392
$708$	−14.0000	−0.526152
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	6.00000	0.225176
$711$	14.0000	0.525041
$712$	−6.00000	−0.224860
$713$	0	0
$714$	−2.00000	−0.0748481
$715$	4.00000	0.149592
$716$	−6.00000	−0.224231
$717$	−16.0000	−0.597531
$718$	−24.0000	−0.895672
$719$	14.0000	0.522112	0.261056	−	0.965324i	$-0.415929\pi$
$719$	14.0000	0.522112	0.261056	+	0.965324i	$0.415929\pi$
$720$	1.00000	0.0372678
$721$	−32.0000	−1.19174
$722$	−17.0000	−0.632674
$723$	4.00000	0.148762
$724$	10.0000	0.371647
$725$	2.00000	0.0742781
$726$	1.00000	0.0371135
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	−4.00000	−0.148047
$731$	2.00000	0.0739727
$732$	−10.0000	−0.369611
$733$	−36.0000	−1.32969	−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000	−1.32969	−0.664845	+	0.746981i	$0.731502\pi$
$734$	28.0000	1.03350
$735$	3.00000	0.110657
$736$	6.00000	0.221163
$737$	−8.00000	−0.294684
$738$	2.00000	0.0736210
$739$	50.0000	1.83928	0.919640	−	0.392763i	$-0.128481\pi$
$739$	50.0000	1.83928	0.919640	+	0.392763i	$0.128481\pi$
$740$	−6.00000	−0.220564
$741$	−24.0000	−0.881662
$742$	8.00000	0.293689
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	−12.0000	−0.439351
$747$	12.0000	0.439057
$748$	1.00000	0.0365636
$749$	40.0000	1.46157
$750$	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
$753$	−10.0000	−0.364420
$754$	8.00000	0.291343
$755$	−8.00000	−0.291150
$756$	−2.00000	−0.0727393
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−12.0000	−0.435860
$759$	−6.00000	−0.217786
$760$	6.00000	0.217643
$761$	−38.0000	−1.37750	−0.688749	−	0.724999i	$-0.741840\pi$
$761$	−38.0000	−1.37750	−0.688749	+	0.724999i	$0.741840\pi$
$762$	4.00000	0.144905
$763$	−4.00000	−0.144810
$764$	−4.00000	−0.144715
$765$	−1.00000	−0.0361551
$766$	12.0000	0.433578
$767$	−56.0000	−2.02204
$768$	−1.00000	−0.0360844
$769$	−38.0000	−1.37032	−0.685158	−	0.728395i	$-0.740267\pi$
$769$	−38.0000	−1.37032	−0.685158	+	0.728395i	$0.740267\pi$
$770$	2.00000	0.0720750
$771$	−18.0000	−0.648254
$772$	−16.0000	−0.575853
$773$	−32.0000	−1.15096	−0.575480	−	0.817816i	$-0.695185\pi$
$773$	−32.0000	−1.15096	−0.575480	+	0.817816i	$0.695185\pi$
$774$	2.00000	0.0718885
$775$	0	0
$776$	−14.0000	−0.502571
$777$	12.0000	0.430498
$778$	−12.0000	−0.430221
$779$	12.0000	0.429945
$780$	4.00000	0.143223
$781$	6.00000	0.214697
$782$	−6.00000	−0.214560
$783$	−2.00000	−0.0714742
$784$	−3.00000	−0.107143
$785$	−18.0000	−0.642448
$786$	12.0000	0.428026
$787$	48.0000	1.71102	0.855508	−	0.517790i	$-0.173245\pi$
$787$	48.0000	1.71102	0.855508	+	0.517790i	$0.173245\pi$
$788$	−22.0000	−0.783718
$789$	24.0000	0.854423
$790$	−14.0000	−0.498098
$791$	0	0
$792$	1.00000	0.0355335
$793$	−40.0000	−1.42044
$794$	18.0000	0.638796
$795$	4.00000	0.141865
$796$	8.00000	0.283552
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	−12.0000	−0.424795
$799$	−8.00000	−0.283020
$800$	−1.00000	−0.0353553
$801$	6.00000	0.212000
$802$	12.0000	0.423735
$803$	−4.00000	−0.141157
$804$	−8.00000	−0.282138
$805$	−12.0000	−0.422944
$806$	0	0
$807$	−6.00000	−0.211210
$808$	−18.0000	−0.633238
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	−1.00000	−0.0351364
$811$	−32.0000	−1.12367	−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000	−1.12367	−0.561836	+	0.827249i	$0.689905\pi$
$812$	4.00000	0.140372
$813$	−20.0000	−0.701431
$814$	−6.00000	−0.210300
$815$	−4.00000	−0.140114
$816$	1.00000	0.0350070
$817$	12.0000	0.419827
$818$	2.00000	0.0699284
$819$	−8.00000	−0.279543
$820$	−2.00000	−0.0698430
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	2.00000	0.0697580
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	16.0000	0.557386
$825$	1.00000	0.0348155
$826$	−28.0000	−0.974245
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−6.00000	−0.208514
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	−12.0000	−0.416526
$831$	2.00000	0.0693792
$832$	−4.00000	−0.138675
$833$	3.00000	0.103944
$834$	−4.00000	−0.138509
$835$	8.00000	0.276851
$836$	6.00000	0.207514
$837$	0	0
$838$	−20.0000	−0.690889
$839$	−22.0000	−0.759524	−0.379762	−	0.925084i	$-0.623994\pi$
$839$	−22.0000	−0.759524	−0.379762	+	0.925084i	$0.623994\pi$
$840$	2.00000	0.0690066
$841$	−25.0000	−0.862069
$842$	2.00000	0.0689246
$843$	−18.0000	−0.619953
$844$	20.0000	0.688428
$845$	3.00000	0.103203
$846$	−8.00000	−0.275046
$847$	2.00000	0.0687208
$848$	−4.00000	−0.137361
$849$	−28.0000	−0.960958
$850$	1.00000	0.0342997
$851$	36.0000	1.23406
$852$	6.00000	0.205557
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	−20.0000	−0.684386
$855$	−6.00000	−0.205196
$856$	−20.0000	−0.683586
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	4.00000	0.136558
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	−2.00000	−0.0681994
$861$	4.00000	0.136320
$862$	0	0
$863$	52.0000	1.77010	0.885050	−	0.465495i	$-0.154124\pi$
$863$	52.0000	1.77010	0.885050	+	0.465495i	$0.154124\pi$
$864$	1.00000	0.0340207
$865$	14.0000	0.476014
$866$	18.0000	0.611665
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−14.0000	−0.474917
$870$	2.00000	0.0678064
$871$	−32.0000	−1.08428
$872$	2.00000	0.0677285
$873$	14.0000	0.473828
$874$	−36.0000	−1.21772
$875$	2.00000	0.0676123
$876$	−4.00000	−0.135147
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	−6.00000	−0.202490
$879$	−2.00000	−0.0674583
$880$	−1.00000	−0.0337100
$881$	24.0000	0.808581	0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000	0.808581	0.404290	+	0.914631i	$0.367519\pi$
$882$	3.00000	0.101015
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	4.00000	0.134535
$885$	−14.0000	−0.470605
$886$	−18.0000	−0.604722
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	−6.00000	−0.201347
$889$	8.00000	0.268311
$890$	−6.00000	−0.201120
$891$	−1.00000	−0.0335013
$892$	16.0000	0.535720
$893$	−48.0000	−1.60626
$894$	6.00000	0.200670
$895$	−6.00000	−0.200558
$896$	−2.00000	−0.0668153
$897$	−24.0000	−0.801337
$898$	24.0000	0.800890
$899$	0	0
$900$	1.00000	0.0333333
$901$	4.00000	0.133259
$902$	−2.00000	−0.0665927
$903$	4.00000	0.133112
$904$	0	0
$905$	10.0000	0.332411
$906$	−8.00000	−0.265782
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−4.00000	−0.132745
$909$	18.0000	0.597022
$910$	8.00000	0.265197
$911$	−22.0000	−0.728893	−0.364446	−	0.931224i	$-0.618742\pi$
$911$	−22.0000	−0.728893	−0.364446	+	0.931224i	$0.618742\pi$
$912$	6.00000	0.198680
$913$	−12.0000	−0.397142
$914$	2.00000	0.0661541
$915$	−10.0000	−0.330590
$916$	−14.0000	−0.462573
$917$	24.0000	0.792550
$918$	−1.00000	−0.0330049
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	6.00000	0.197814
$921$	30.0000	0.988534
$922$	−14.0000	−0.461065
$923$	24.0000	0.789970
$924$	2.00000	0.0657952
$925$	−6.00000	−0.197279
$926$	−16.0000	−0.525793
$927$	−16.0000	−0.525509
$928$	−2.00000	−0.0656532
$929$	−32.0000	−1.04989	−0.524943	−	0.851137i	$-0.675913\pi$
$929$	−32.0000	−1.04989	−0.524943	+	0.851137i	$0.675913\pi$
$930$	0	0
$931$	18.0000	0.589926
$932$	−22.0000	−0.720634
$933$	30.0000	0.982156
$934$	−2.00000	−0.0654420
$935$	1.00000	0.0327035
$936$	4.00000	0.130744
$937$	−18.0000	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$938$	−16.0000	−0.522419
$939$	18.0000	0.587408
$940$	8.00000	0.260931
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	−18.0000	−0.586472
$943$	12.0000	0.390774
$944$	14.0000	0.455661
$945$	−2.00000	−0.0650600
$946$	−2.00000	−0.0650256
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	−14.0000	−0.454699
$949$	−16.0000	−0.519382
$950$	6.00000	0.194666
$951$	−34.0000	−1.10253
$952$	2.00000	0.0648204
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	4.00000	0.129505
$955$	−4.00000	−0.129437
$956$	16.0000	0.517477
$957$	2.00000	0.0646508
$958$	−4.00000	−0.129234
$959$	4.00000	0.129167
$960$	−1.00000	−0.0322749
$961$	−31.0000	−1.00000
$962$	−24.0000	−0.773791
$963$	20.0000	0.644491
$964$	−4.00000	−0.128831
$965$	−16.0000	−0.515058
$966$	−12.0000	−0.386094
$967$	−52.0000	−1.67221	−0.836104	−	0.548572i	$-0.815172\pi$
$967$	−52.0000	−1.67221	−0.836104	+	0.548572i	$0.815172\pi$
$968$	−1.00000	−0.0321412
$969$	−6.00000	−0.192748
$970$	−14.0000	−0.449513
$971$	−2.00000	−0.0641831	−0.0320915	−	0.999485i	$-0.510217\pi$
$971$	−2.00000	−0.0641831	−0.0320915	+	0.999485i	$0.510217\pi$
$972$	−1.00000	−0.0320750
$973$	−8.00000	−0.256468
$974$	28.0000	0.897178
$975$	4.00000	0.128103
$976$	10.0000	0.320092
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	−4.00000	−0.127906
$979$	−6.00000	−0.191761
$980$	−3.00000	−0.0958315
$981$	−2.00000	−0.0638551
$982$	12.0000	0.382935
$983$	−6.00000	−0.191370	−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000	−0.191370	−0.0956851	+	0.995412i	$0.530504\pi$
$984$	−2.00000	−0.0637577
$985$	−22.0000	−0.700978
$986$	2.00000	0.0636930
$987$	−16.0000	−0.509286
$988$	24.0000	0.763542
$989$	12.0000	0.381578
$990$	1.00000	0.0317821
$991$	28.0000	0.889449	0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000	0.889449	0.444725	+	0.895667i	$0.353302\pi$
$992$	0	0
$993$	−4.00000	−0.126936
$994$	12.0000	0.380617
$995$	8.00000	0.253617
$996$	−12.0000	−0.380235
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	36.0000	1.13956
$999$	6.00000	0.189832

Twists

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

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