LMFDB - Embedded newform 5610.2.a.z.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} -1.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} -1.00000 q^{29} +1.00000 q^{30} +9.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -8.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +8.00000 q^{41} +1.00000 q^{42} +1.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +1.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +8.00000 q^{53} -1.00000 q^{54} +1.00000 q^{55} -1.00000 q^{56} +8.00000 q^{57} -1.00000 q^{58} +10.0000 q^{59} +1.00000 q^{60} -2.00000 q^{61} +9.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} -1.00000 q^{69} +1.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} +14.0000 q^{73} -2.00000 q^{74} -1.00000 q^{75} -8.00000 q^{76} +1.00000 q^{77} -4.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} +8.00000 q^{82} -4.00000 q^{83} +1.00000 q^{84} +1.00000 q^{85} +1.00000 q^{86} +1.00000 q^{87} -1.00000 q^{88} -4.00000 q^{89} -1.00000 q^{90} -4.00000 q^{91} +1.00000 q^{92} -9.00000 q^{93} -8.00000 q^{94} +8.00000 q^{95} -1.00000 q^{96} -1.00000 q^{97} -6.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−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
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	−1.00000	−0.213201
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	1.00000	0.182574
$31$	9.00000	1.61645	0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000	1.61645	0.808224	+	0.588875i	$0.200429\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−8.00000	−1.29777
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	1.00000	0.154303
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	8.00000	1.09888	0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000	1.09888	0.549442	+	0.835532i	$0.314840\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−1.00000	−0.133631
$57$	8.00000	1.05963
$58$	−1.00000	−0.131306
$59$	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
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	9.00000	1.14300
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	1.00000	0.123091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	−0.121268
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	1.00000	0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−8.00000	−0.917663
$77$	1.00000	0.113961
$78$	−4.00000	−0.452911
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	1.00000	0.109109
$85$	1.00000	0.108465
$86$	1.00000	0.107833
$87$	1.00000	0.107211
$88$	−1.00000	−0.106600
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	−1.00000	−0.105409
$91$	−4.00000	−0.419314
$92$	1.00000	0.104257
$93$	−9.00000	−0.933257
$94$	−8.00000	−0.825137
$95$	8.00000	0.820783
$96$	−1.00000	−0.102062
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−6.00000	−0.606092
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	1.00000	0.0990148
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	4.00000	0.392232
$105$	−1.00000	−0.0975900
$106$	8.00000	0.777029
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	−1.00000	−0.0962250
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	1.00000	0.0953463
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	8.00000	0.749269
$115$	−1.00000	−0.0932505
$116$	−1.00000	−0.0928477
$117$	4.00000	0.369800
$118$	10.0000	0.920575
$119$	1.00000	0.0916698
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−8.00000	−0.721336
$124$	9.00000	0.808224
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	−1.00000	−0.0880451
$130$	−4.00000	−0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	1.00000	0.0870388
$133$	8.00000	0.693688
$134$	−4.00000	−0.345547
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	21.0000	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$138$	−1.00000	−0.0851257
$139$	21.0000	1.78120	0.890598	−	0.454791i	$-0.150286\pi$
$139$	21.0000	1.78120	0.890598	+	0.454791i	$0.150286\pi$
$140$	1.00000	0.0845154
$141$	8.00000	0.673722
$142$	6.00000	0.503509
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	1.00000	0.0830455
$146$	14.0000	1.15865
$147$	6.00000	0.494872
$148$	−2.00000	−0.164399
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	−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	$0.552039\pi$
$152$	−8.00000	−0.648886
$153$	−1.00000	−0.0808452
$154$	1.00000	0.0805823
$155$	−9.00000	−0.722897
$156$	−4.00000	−0.320256
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	0	0
$159$	−8.00000	−0.634441
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	−15.0000	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$163$	−15.0000	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$164$	8.00000	0.624695
$165$	−1.00000	−0.0778499
$166$	−4.00000	−0.310460
$167$	10.0000	0.773823	0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000	0.773823	0.386912	+	0.922117i	$0.373542\pi$
$168$	1.00000	0.0771517
$169$	3.00000	0.230769
$170$	1.00000	0.0766965
$171$	−8.00000	−0.611775
$172$	1.00000	0.0762493
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	1.00000	0.0758098
$175$	−1.00000	−0.0755929
$176$	−1.00000	−0.0753778
$177$	−10.0000	−0.751646
$178$	−4.00000	−0.299813
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	−1.00000	−0.0745356
$181$	5.00000	0.371647	0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000	0.371647	0.185824	+	0.982583i	$0.440505\pi$
$182$	−4.00000	−0.296500
$183$	2.00000	0.147844
$184$	1.00000	0.0737210
$185$	2.00000	0.147043
$186$	−9.00000	−0.659912
$187$	1.00000	0.0731272
$188$	−8.00000	−0.583460
$189$	1.00000	0.0727393
$190$	8.00000	0.580381
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−1.00000	−0.0717958
$195$	4.00000	0.286446
$196$	−6.00000	−0.428571
$197$	24.0000	1.70993	0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000	1.70993	0.854965	+	0.518686i	$0.173579\pi$
$198$	−1.00000	−0.0710669
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	1.00000	0.0707107
$201$	4.00000	0.282138
$202$	2.00000	0.140720
$203$	1.00000	0.0701862
$204$	1.00000	0.0700140
$205$	−8.00000	−0.558744
$206$	−1.00000	−0.0696733
$207$	1.00000	0.0695048
$208$	4.00000	0.277350
$209$	8.00000	0.553372
$210$	−1.00000	−0.0690066
$211$	3.00000	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$212$	8.00000	0.549442
$213$	−6.00000	−0.411113
$214$	−3.00000	−0.205076
$215$	−1.00000	−0.0681994
$216$	−1.00000	−0.0680414
$217$	−9.00000	−0.610960
$218$	0	0
$219$	−14.0000	−0.946032
$220$	1.00000	0.0674200
$221$	−4.00000	−0.269069
$222$	2.00000	0.134231
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	18.0000	1.19734
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	8.00000	0.529813
$229$	16.0000	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$230$	−1.00000	−0.0659380
$231$	−1.00000	−0.0657952
$232$	−1.00000	−0.0656532
$233$	11.0000	0.720634	0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000	0.720634	0.360317	+	0.932830i	$0.382669\pi$
$234$	4.00000	0.261488
$235$	8.00000	0.521862
$236$	10.0000	0.650945
$237$	0	0
$238$	1.00000	0.0648204
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	1.00000	0.0645497
$241$	−9.00000	−0.579741	−0.289870	−	0.957066i	$-0.593612\pi$
$241$	−9.00000	−0.579741	−0.289870	+	0.957066i	$0.593612\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	6.00000	0.383326
$246$	−8.00000	−0.510061
$247$	−32.0000	−2.03611
$248$	9.00000	0.571501
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	−1.00000	−0.0629941
$253$	−1.00000	−0.0628695
$254$	−2.00000	−0.125491
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	19.0000	1.18519	0.592594	−	0.805502i	$-0.298104\pi$
$257$	19.0000	1.18519	0.592594	+	0.805502i	$0.298104\pi$
$258$	−1.00000	−0.0622573
$259$	2.00000	0.124274
$260$	−4.00000	−0.248069
$261$	−1.00000	−0.0618984
$262$	0	0
$263$	21.0000	1.29492	0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000	1.29492	0.647458	+	0.762101i	$0.275832\pi$
$264$	1.00000	0.0615457
$265$	−8.00000	−0.491436
$266$	8.00000	0.490511
$267$	4.00000	0.244796
$268$	−4.00000	−0.244339
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	1.00000	0.0608581
$271$	13.0000	0.789694	0.394847	−	0.918747i	$-0.370798\pi$
$271$	13.0000	0.789694	0.394847	+	0.918747i	$0.370798\pi$
$272$	−1.00000	−0.0606339
$273$	4.00000	0.242091
$274$	21.0000	1.26866
$275$	−1.00000	−0.0603023
$276$	−1.00000	−0.0601929
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	21.0000	1.25950
$279$	9.00000	0.538816
$280$	1.00000	0.0597614
$281$	−17.0000	−1.01413	−0.507067	−	0.861906i	$-0.669271\pi$
$281$	−17.0000	−1.01413	−0.507067	+	0.861906i	$0.669271\pi$
$282$	8.00000	0.476393
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	6.00000	0.356034
$285$	−8.00000	−0.473879
$286$	−4.00000	−0.236525
$287$	−8.00000	−0.472225
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	1.00000	0.0587220
$291$	1.00000	0.0586210
$292$	14.0000	0.819288
$293$	7.00000	0.408944	0.204472	−	0.978872i	$-0.434452\pi$
$293$	7.00000	0.408944	0.204472	+	0.978872i	$0.434452\pi$
$294$	6.00000	0.349927
$295$	−10.0000	−0.582223
$296$	−2.00000	−0.116248
$297$	1.00000	0.0580259
$298$	12.0000	0.695141
$299$	4.00000	0.231326
$300$	−1.00000	−0.0577350
$301$	−1.00000	−0.0576390
$302$	−4.00000	−0.230174
$303$	−2.00000	−0.114897
$304$	−8.00000	−0.458831
$305$	2.00000	0.114520
$306$	−1.00000	−0.0571662
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	1.00000	0.0569803
$309$	1.00000	0.0568880
$310$	−9.00000	−0.511166
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	−4.00000	−0.226455
$313$	−7.00000	−0.395663	−0.197832	−	0.980236i	$-0.563390\pi$
$313$	−7.00000	−0.395663	−0.197832	+	0.980236i	$0.563390\pi$
$314$	−14.0000	−0.790066
$315$	1.00000	0.0563436
$316$	0	0
$317$	27.0000	1.51647	0.758236	−	0.651981i	$-0.226062\pi$
$317$	27.0000	1.51647	0.758236	+	0.651981i	$0.226062\pi$
$318$	−8.00000	−0.448618
$319$	1.00000	0.0559893
$320$	−1.00000	−0.0559017
$321$	3.00000	0.167444
$322$	−1.00000	−0.0557278
$323$	8.00000	0.445132
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−15.0000	−0.830773
$327$	0	0
$328$	8.00000	0.441726
$329$	8.00000	0.441054
$330$	−1.00000	−0.0550482
$331$	−7.00000	−0.384755	−0.192377	−	0.981321i	$-0.561620\pi$
$331$	−7.00000	−0.384755	−0.192377	+	0.981321i	$0.561620\pi$
$332$	−4.00000	−0.219529
$333$	−2.00000	−0.109599
$334$	10.0000	0.547176
$335$	4.00000	0.218543
$336$	1.00000	0.0545545
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	3.00000	0.163178
$339$	−18.0000	−0.977626
$340$	1.00000	0.0542326
$341$	−9.00000	−0.487377
$342$	−8.00000	−0.432590
$343$	13.0000	0.701934
$344$	1.00000	0.0539164
$345$	1.00000	0.0538382
$346$	−14.0000	−0.752645
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	1.00000	0.0536056
$349$	−34.0000	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$350$	−1.00000	−0.0534522
$351$	−4.00000	−0.213504
$352$	−1.00000	−0.0533002
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	−10.0000	−0.531494
$355$	−6.00000	−0.318447
$356$	−4.00000	−0.212000
$357$	−1.00000	−0.0529256
$358$	6.00000	0.317110
$359$	−34.0000	−1.79445	−0.897226	−	0.441572i	$-0.854421\pi$
$359$	−34.0000	−1.79445	−0.897226	+	0.441572i	$0.854421\pi$
$360$	−1.00000	−0.0527046
$361$	45.0000	2.36842
$362$	5.00000	0.262794
$363$	−1.00000	−0.0524864
$364$	−4.00000	−0.209657
$365$	−14.0000	−0.732793
$366$	2.00000	0.104542
$367$	−26.0000	−1.35719	−0.678594	−	0.734513i	$-0.737411\pi$
$367$	−26.0000	−1.35719	−0.678594	+	0.734513i	$0.737411\pi$
$368$	1.00000	0.0521286
$369$	8.00000	0.416463
$370$	2.00000	0.103975
$371$	−8.00000	−0.415339
$372$	−9.00000	−0.466628
$373$	2.00000	0.103556	0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000	0.103556	0.0517780	+	0.998659i	$0.483511\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−8.00000	−0.412568
$377$	−4.00000	−0.206010
$378$	1.00000	0.0514344
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	8.00000	0.410391
$381$	2.00000	0.102463
$382$	−15.0000	−0.767467
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	−1.00000	−0.0510310
$385$	−1.00000	−0.0509647
$386$	22.0000	1.11977
$387$	1.00000	0.0508329
$388$	−1.00000	−0.0507673
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	4.00000	0.202548
$391$	−1.00000	−0.0505722
$392$	−6.00000	−0.303046
$393$	0	0
$394$	24.0000	1.20910
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	−10.0000	−0.501886	−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000	−0.501886	−0.250943	+	0.968002i	$0.580741\pi$
$398$	16.0000	0.802008
$399$	−8.00000	−0.400501
$400$	1.00000	0.0500000
$401$	15.0000	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$402$	4.00000	0.199502
$403$	36.0000	1.79329
$404$	2.00000	0.0995037
$405$	−1.00000	−0.0496904
$406$	1.00000	0.0496292
$407$	2.00000	0.0991363
$408$	1.00000	0.0495074
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	−8.00000	−0.395092
$411$	−21.0000	−1.03585
$412$	−1.00000	−0.0492665
$413$	−10.0000	−0.492068
$414$	1.00000	0.0491473
$415$	4.00000	0.196352
$416$	4.00000	0.196116
$417$	−21.0000	−1.02837
$418$	8.00000	0.391293
$419$	−31.0000	−1.51445	−0.757225	−	0.653155i	$-0.773445\pi$
$419$	−31.0000	−1.51445	−0.757225	+	0.653155i	$0.773445\pi$
$420$	−1.00000	−0.0487950
$421$	−28.0000	−1.36464	−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000	−1.36464	−0.682318	+	0.731055i	$0.739028\pi$
$422$	3.00000	0.146038
$423$	−8.00000	−0.388973
$424$	8.00000	0.388514
$425$	−1.00000	−0.0485071
$426$	−6.00000	−0.290701
$427$	2.00000	0.0967868
$428$	−3.00000	−0.145010
$429$	4.00000	0.193122
$430$	−1.00000	−0.0482243
$431$	−19.0000	−0.915198	−0.457599	−	0.889159i	$-0.651290\pi$
$431$	−19.0000	−0.915198	−0.457599	+	0.889159i	$0.651290\pi$
$432$	−1.00000	−0.0481125
$433$	8.00000	0.384455	0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000	0.384455	0.192228	+	0.981350i	$0.438429\pi$
$434$	−9.00000	−0.432014
$435$	−1.00000	−0.0479463
$436$	0	0
$437$	−8.00000	−0.382692
$438$	−14.0000	−0.668946
$439$	−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
$441$	−6.00000	−0.285714
$442$	−4.00000	−0.190261
$443$	37.0000	1.75792	0.878962	−	0.476893i	$-0.158237\pi$
$443$	37.0000	1.75792	0.878962	+	0.476893i	$0.158237\pi$
$444$	2.00000	0.0949158
$445$	4.00000	0.189618
$446$	−1.00000	−0.0473514
$447$	−12.0000	−0.567581
$448$	−1.00000	−0.0472456
$449$	13.0000	0.613508	0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000	0.613508	0.306754	+	0.951789i	$0.400757\pi$
$450$	1.00000	0.0471405
$451$	−8.00000	−0.376705
$452$	18.0000	0.846649
$453$	4.00000	0.187936
$454$	−3.00000	−0.140797
$455$	4.00000	0.187523
$456$	8.00000	0.374634
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	16.0000	0.747631
$459$	1.00000	0.0466760
$460$	−1.00000	−0.0466252
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	−1.00000	−0.0465242
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	−1.00000	−0.0464238
$465$	9.00000	0.417365
$466$	11.0000	0.509565
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	4.00000	0.184900
$469$	4.00000	0.184703
$470$	8.00000	0.369012
$471$	14.0000	0.645086
$472$	10.0000	0.460287
$473$	−1.00000	−0.0459800
$474$	0	0
$475$	−8.00000	−0.367065
$476$	1.00000	0.0458349
$477$	8.00000	0.366295
$478$	30.0000	1.37217
$479$	−13.0000	−0.593985	−0.296993	−	0.954880i	$-0.595984\pi$
$479$	−13.0000	−0.593985	−0.296993	+	0.954880i	$0.595984\pi$
$480$	1.00000	0.0456435
$481$	−8.00000	−0.364769
$482$	−9.00000	−0.409939
$483$	1.00000	0.0455016
$484$	1.00000	0.0454545
$485$	1.00000	0.0454077
$486$	−1.00000	−0.0453609
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	−2.00000	−0.0905357
$489$	15.0000	0.678323
$490$	6.00000	0.271052
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	−8.00000	−0.360668
$493$	1.00000	0.0450377
$494$	−32.0000	−1.43975
$495$	1.00000	0.0449467
$496$	9.00000	0.404112
$497$	−6.00000	−0.269137
$498$	4.00000	0.179244
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	−1.00000	−0.0447214
$501$	−10.0000	−0.446767
$502$	−8.00000	−0.357057
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	−1.00000	−0.0445435
$505$	−2.00000	−0.0889988
$506$	−1.00000	−0.0444554
$507$	−3.00000	−0.133235
$508$	−2.00000	−0.0887357
$509$	−14.0000	−0.620539	−0.310270	−	0.950649i	$-0.600419\pi$
$509$	−14.0000	−0.620539	−0.310270	+	0.950649i	$0.600419\pi$
$510$	−1.00000	−0.0442807
$511$	−14.0000	−0.619324
$512$	1.00000	0.0441942
$513$	8.00000	0.353209
$514$	19.0000	0.838054
$515$	1.00000	0.0440653
$516$	−1.00000	−0.0440225
$517$	8.00000	0.351840
$518$	2.00000	0.0878750
$519$	14.0000	0.614532
$520$	−4.00000	−0.175412
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	−1.00000	−0.0437688
$523$	33.0000	1.44299	0.721495	−	0.692420i	$-0.243455\pi$
$523$	33.0000	1.44299	0.721495	+	0.692420i	$0.243455\pi$
$524$	0	0
$525$	1.00000	0.0436436
$526$	21.0000	0.915644
$527$	−9.00000	−0.392046
$528$	1.00000	0.0435194
$529$	−22.0000	−0.956522
$530$	−8.00000	−0.347498
$531$	10.0000	0.433963
$532$	8.00000	0.346844
$533$	32.0000	1.38607
$534$	4.00000	0.173097
$535$	3.00000	0.129701
$536$	−4.00000	−0.172774
$537$	−6.00000	−0.258919
$538$	10.0000	0.431131
$539$	6.00000	0.258438
$540$	1.00000	0.0430331
$541$	8.00000	0.343947	0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000	0.343947	0.171973	+	0.985102i	$0.444986\pi$
$542$	13.0000	0.558398
$543$	−5.00000	−0.214571
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	4.00000	0.171184
$547$	18.0000	0.769624	0.384812	−	0.922995i	$-0.374266\pi$
$547$	18.0000	0.769624	0.384812	+	0.922995i	$0.374266\pi$
$548$	21.0000	0.897076
$549$	−2.00000	−0.0853579
$550$	−1.00000	−0.0426401
$551$	8.00000	0.340811
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	10.0000	0.424859
$555$	−2.00000	−0.0848953
$556$	21.0000	0.890598
$557$	41.0000	1.73723	0.868613	−	0.495491i	$-0.165012\pi$
$557$	41.0000	1.73723	0.868613	+	0.495491i	$0.165012\pi$
$558$	9.00000	0.381000
$559$	4.00000	0.169182
$560$	1.00000	0.0422577
$561$	−1.00000	−0.0422200
$562$	−17.0000	−0.717102
$563$	−44.0000	−1.85438	−0.927189	−	0.374593i	$-0.877783\pi$
$563$	−44.0000	−1.85438	−0.927189	+	0.374593i	$0.877783\pi$
$564$	8.00000	0.336861
$565$	−18.0000	−0.757266
$566$	14.0000	0.588464
$567$	−1.00000	−0.0419961
$568$	6.00000	0.251754
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	−8.00000	−0.335083
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	−4.00000	−0.167248
$573$	15.0000	0.626634
$574$	−8.00000	−0.333914
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	1.00000	0.0415945
$579$	−22.0000	−0.914289
$580$	1.00000	0.0415227
$581$	4.00000	0.165948
$582$	1.00000	0.0414513
$583$	−8.00000	−0.331326
$584$	14.0000	0.579324
$585$	−4.00000	−0.165380
$586$	7.00000	0.289167
$587$	11.0000	0.454019	0.227009	−	0.973893i	$-0.427105\pi$
$587$	11.0000	0.454019	0.227009	+	0.973893i	$0.427105\pi$
$588$	6.00000	0.247436
$589$	−72.0000	−2.96671
$590$	−10.0000	−0.411693
$591$	−24.0000	−0.987228
$592$	−2.00000	−0.0821995
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	1.00000	0.0410305
$595$	−1.00000	−0.0409960
$596$	12.0000	0.491539
$597$	−16.0000	−0.654836
$598$	4.00000	0.163572
$599$	−9.00000	−0.367730	−0.183865	−	0.982952i	$-0.558861\pi$
$599$	−9.00000	−0.367730	−0.183865	+	0.982952i	$0.558861\pi$
$600$	−1.00000	−0.0408248
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	−1.00000	−0.0407570
$603$	−4.00000	−0.162893
$604$	−4.00000	−0.162758
$605$	−1.00000	−0.0406558
$606$	−2.00000	−0.0812444
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	−8.00000	−0.324443
$609$	−1.00000	−0.0405220
$610$	2.00000	0.0809776
$611$	−32.0000	−1.29458
$612$	−1.00000	−0.0404226
$613$	−30.0000	−1.21169	−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000	−1.21169	−0.605844	+	0.795583i	$0.707165\pi$
$614$	28.0000	1.12999
$615$	8.00000	0.322591
$616$	1.00000	0.0402911
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	1.00000	0.0402259
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	−9.00000	−0.361449
$621$	−1.00000	−0.0401286
$622$	−4.00000	−0.160385
$623$	4.00000	0.160257
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−7.00000	−0.279776
$627$	−8.00000	−0.319489
$628$	−14.0000	−0.558661
$629$	2.00000	0.0797452
$630$	1.00000	0.0398410
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	0	0
$633$	−3.00000	−0.119239
$634$	27.0000	1.07231
$635$	2.00000	0.0793676
$636$	−8.00000	−0.317221
$637$	−24.0000	−0.950915
$638$	1.00000	0.0395904
$639$	6.00000	0.237356
$640$	−1.00000	−0.0395285
$641$	25.0000	0.987441	0.493720	−	0.869621i	$-0.335637\pi$
$641$	25.0000	0.987441	0.493720	+	0.869621i	$0.335637\pi$
$642$	3.00000	0.118401
$643$	7.00000	0.276053	0.138027	−	0.990429i	$-0.455924\pi$
$643$	7.00000	0.276053	0.138027	+	0.990429i	$0.455924\pi$
$644$	−1.00000	−0.0394055
$645$	1.00000	0.0393750
$646$	8.00000	0.314756
$647$	22.0000	0.864909	0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000	0.864909	0.432455	+	0.901656i	$0.357648\pi$
$648$	1.00000	0.0392837
$649$	−10.0000	−0.392534
$650$	4.00000	0.156893
$651$	9.00000	0.352738
$652$	−15.0000	−0.587445
$653$	−5.00000	−0.195665	−0.0978326	−	0.995203i	$-0.531191\pi$
$653$	−5.00000	−0.195665	−0.0978326	+	0.995203i	$0.531191\pi$
$654$	0	0
$655$	0	0
$656$	8.00000	0.312348
$657$	14.0000	0.546192
$658$	8.00000	0.311872
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	−1.00000	−0.0389249
$661$	36.0000	1.40024	0.700119	−	0.714026i	$-0.253130\pi$
$661$	36.0000	1.40024	0.700119	+	0.714026i	$0.253130\pi$
$662$	−7.00000	−0.272063
$663$	4.00000	0.155347
$664$	−4.00000	−0.155230
$665$	−8.00000	−0.310227
$666$	−2.00000	−0.0774984
$667$	−1.00000	−0.0387202
$668$	10.0000	0.386912
$669$	1.00000	0.0386622
$670$	4.00000	0.154533
$671$	2.00000	0.0772091
$672$	1.00000	0.0385758
$673$	−4.00000	−0.154189	−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000	−0.154189	−0.0770943	+	0.997024i	$0.524564\pi$
$674$	18.0000	0.693334
$675$	−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	$0.638940\pi$
$678$	−18.0000	−0.691286
$679$	1.00000	0.0383765
$680$	1.00000	0.0383482
$681$	3.00000	0.114960
$682$	−9.00000	−0.344628
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	−8.00000	−0.305888
$685$	−21.0000	−0.802369
$686$	13.0000	0.496342
$687$	−16.0000	−0.610438
$688$	1.00000	0.0381246
$689$	32.0000	1.21910
$690$	1.00000	0.0380693
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	−14.0000	−0.532200
$693$	1.00000	0.0379869
$694$	4.00000	0.151838
$695$	−21.0000	−0.796575
$696$	1.00000	0.0379049
$697$	−8.00000	−0.303022
$698$	−34.0000	−1.28692
$699$	−11.0000	−0.416058
$700$	−1.00000	−0.0377964
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	−4.00000	−0.150970
$703$	16.0000	0.603451
$704$	−1.00000	−0.0376889
$705$	−8.00000	−0.301297
$706$	−3.00000	−0.112906
$707$	−2.00000	−0.0752177
$708$	−10.0000	−0.375823
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	−6.00000	−0.225176
$711$	0	0
$712$	−4.00000	−0.149906
$713$	9.00000	0.337053
$714$	−1.00000	−0.0374241
$715$	4.00000	0.149592
$716$	6.00000	0.224231
$717$	−30.0000	−1.12037
$718$	−34.0000	−1.26887
$719$	26.0000	0.969636	0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000	0.969636	0.484818	+	0.874615i	$0.338886\pi$
$720$	−1.00000	−0.0372678
$721$	1.00000	0.0372419
$722$	45.0000	1.67473
$723$	9.00000	0.334714
$724$	5.00000	0.185824
$725$	−1.00000	−0.0371391
$726$	−1.00000	−0.0371135
$727$	39.0000	1.44643	0.723215	−	0.690623i	$-0.242664\pi$
$727$	39.0000	1.44643	0.723215	+	0.690623i	$0.242664\pi$
$728$	−4.00000	−0.148250
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	−1.00000	−0.0369863
$732$	2.00000	0.0739221
$733$	−4.00000	−0.147743	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000	−0.147743	−0.0738717	+	0.997268i	$0.523536\pi$
$734$	−26.0000	−0.959678
$735$	−6.00000	−0.221313
$736$	1.00000	0.0368605
$737$	4.00000	0.147342
$738$	8.00000	0.294484
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	2.00000	0.0735215
$741$	32.0000	1.17555
$742$	−8.00000	−0.293689
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−9.00000	−0.329956
$745$	−12.0000	−0.439646
$746$	2.00000	0.0732252
$747$	−4.00000	−0.146352
$748$	1.00000	0.0365636
$749$	3.00000	0.109618
$750$	1.00000	0.0365148
$751$	−1.00000	−0.0364905	−0.0182453	−	0.999834i	$-0.505808\pi$
$751$	−1.00000	−0.0364905	−0.0182453	+	0.999834i	$0.505808\pi$
$752$	−8.00000	−0.291730
$753$	8.00000	0.291536
$754$	−4.00000	−0.145671
$755$	4.00000	0.145575
$756$	1.00000	0.0363696
$757$	−17.0000	−0.617876	−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000	−0.617876	−0.308938	+	0.951082i	$0.599973\pi$
$758$	−20.0000	−0.726433
$759$	1.00000	0.0362977
$760$	8.00000	0.290191
$761$	−39.0000	−1.41375	−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000	−1.41375	−0.706874	+	0.707339i	$0.749895\pi$
$762$	2.00000	0.0724524
$763$	0	0
$764$	−15.0000	−0.542681
$765$	1.00000	0.0361551
$766$	16.0000	0.578103
$767$	40.0000	1.44432
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	−1.00000	−0.0360375
$771$	−19.0000	−0.684268
$772$	22.0000	0.791797
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	1.00000	0.0359443
$775$	9.00000	0.323290
$776$	−1.00000	−0.0358979
$777$	−2.00000	−0.0717496
$778$	−6.00000	−0.215110
$779$	−64.0000	−2.29304
$780$	4.00000	0.143223
$781$	−6.00000	−0.214697
$782$	−1.00000	−0.0357599
$783$	1.00000	0.0357371
$784$	−6.00000	−0.214286
$785$	14.0000	0.499681
$786$	0	0
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	24.0000	0.854965
$789$	−21.0000	−0.747620
$790$	0	0
$791$	−18.0000	−0.640006
$792$	−1.00000	−0.0355335
$793$	−8.00000	−0.284088
$794$	−10.0000	−0.354887
$795$	8.00000	0.283731
$796$	16.0000	0.567105
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	−8.00000	−0.283197
$799$	8.00000	0.283020
$800$	1.00000	0.0353553
$801$	−4.00000	−0.141333
$802$	15.0000	0.529668
$803$	−14.0000	−0.494049
$804$	4.00000	0.141069
$805$	1.00000	0.0352454
$806$	36.0000	1.26805
$807$	−10.0000	−0.352017
$808$	2.00000	0.0703598
$809$	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
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	1.00000	0.0350931
$813$	−13.0000	−0.455930
$814$	2.00000	0.0701000
$815$	15.0000	0.525427
$816$	1.00000	0.0350070
$817$	−8.00000	−0.279885
$818$	−20.0000	−0.699284
$819$	−4.00000	−0.139771
$820$	−8.00000	−0.279372
$821$	−3.00000	−0.104701	−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000	−0.104701	−0.0523504	+	0.998629i	$0.516671\pi$
$822$	−21.0000	−0.732459
$823$	22.0000	0.766872	0.383436	−	0.923567i	$-0.374741\pi$
$823$	22.0000	0.766872	0.383436	+	0.923567i	$0.374741\pi$
$824$	−1.00000	−0.0348367
$825$	1.00000	0.0348155
$826$	−10.0000	−0.347945
$827$	−53.0000	−1.84299	−0.921495	−	0.388390i	$-0.873032\pi$
$827$	−53.0000	−1.84299	−0.921495	+	0.388390i	$0.873032\pi$
$828$	1.00000	0.0347524
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	4.00000	0.138842
$831$	−10.0000	−0.346896
$832$	4.00000	0.138675
$833$	6.00000	0.207888
$834$	−21.0000	−0.727171
$835$	−10.0000	−0.346064
$836$	8.00000	0.276686
$837$	−9.00000	−0.311086
$838$	−31.0000	−1.07088
$839$	−34.0000	−1.17381	−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000	−1.17381	−0.586905	+	0.809656i	$0.699654\pi$
$840$	−1.00000	−0.0345033
$841$	−28.0000	−0.965517
$842$	−28.0000	−0.964944
$843$	17.0000	0.585511
$844$	3.00000	0.103264
$845$	−3.00000	−0.103203
$846$	−8.00000	−0.275046
$847$	−1.00000	−0.0343604
$848$	8.00000	0.274721
$849$	−14.0000	−0.480479
$850$	−1.00000	−0.0342997
$851$	−2.00000	−0.0685591
$852$	−6.00000	−0.205557
$853$	−21.0000	−0.719026	−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000	−0.719026	−0.359513	+	0.933140i	$0.617057\pi$
$854$	2.00000	0.0684386
$855$	8.00000	0.273594
$856$	−3.00000	−0.102538
$857$	−11.0000	−0.375753	−0.187876	−	0.982193i	$-0.560160\pi$
$857$	−11.0000	−0.375753	−0.187876	+	0.982193i	$0.560160\pi$
$858$	4.00000	0.136558
$859$	39.0000	1.33066	0.665331	−	0.746548i	$-0.268290\pi$
$859$	39.0000	1.33066	0.665331	+	0.746548i	$0.268290\pi$
$860$	−1.00000	−0.0340997
$861$	8.00000	0.272639
$862$	−19.0000	−0.647143
$863$	20.0000	0.680808	0.340404	−	0.940279i	$-0.389436\pi$
$863$	20.0000	0.680808	0.340404	+	0.940279i	$0.389436\pi$
$864$	−1.00000	−0.0340207
$865$	14.0000	0.476014
$866$	8.00000	0.271851
$867$	−1.00000	−0.0339618
$868$	−9.00000	−0.305480
$869$	0	0
$870$	−1.00000	−0.0339032
$871$	−16.0000	−0.542139
$872$	0	0
$873$	−1.00000	−0.0338449
$874$	−8.00000	−0.270604
$875$	1.00000	0.0338062
$876$	−14.0000	−0.473016
$877$	19.0000	0.641584	0.320792	−	0.947150i	$-0.396051\pi$
$877$	19.0000	0.641584	0.320792	+	0.947150i	$0.396051\pi$
$878$	−6.00000	−0.202490
$879$	−7.00000	−0.236104
$880$	1.00000	0.0337100
$881$	39.0000	1.31394	0.656972	−	0.753915i	$-0.271837\pi$
$881$	39.0000	1.31394	0.656972	+	0.753915i	$0.271837\pi$
$882$	−6.00000	−0.202031
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	−4.00000	−0.134535
$885$	10.0000	0.336146
$886$	37.0000	1.24304
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	2.00000	0.0671156
$889$	2.00000	0.0670778
$890$	4.00000	0.134080
$891$	−1.00000	−0.0335013
$892$	−1.00000	−0.0334825
$893$	64.0000	2.14168
$894$	−12.0000	−0.401340
$895$	−6.00000	−0.200558
$896$	−1.00000	−0.0334077
$897$	−4.00000	−0.133556
$898$	13.0000	0.433816
$899$	−9.00000	−0.300167
$900$	1.00000	0.0333333
$901$	−8.00000	−0.266519
$902$	−8.00000	−0.266371
$903$	1.00000	0.0332779
$904$	18.0000	0.598671
$905$	−5.00000	−0.166206
$906$	4.00000	0.132891
$907$	31.0000	1.02934	0.514669	−	0.857389i	$-0.327915\pi$
$907$	31.0000	1.02934	0.514669	+	0.857389i	$0.327915\pi$
$908$	−3.00000	−0.0995585
$909$	2.00000	0.0663358
$910$	4.00000	0.132599
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	8.00000	0.264906
$913$	4.00000	0.132381
$914$	−22.0000	−0.727695
$915$	−2.00000	−0.0661180
$916$	16.0000	0.528655
$917$	0	0
$918$	1.00000	0.0330049
$919$	−13.0000	−0.428830	−0.214415	−	0.976743i	$-0.568785\pi$
$919$	−13.0000	−0.428830	−0.214415	+	0.976743i	$0.568785\pi$
$920$	−1.00000	−0.0329690
$921$	−28.0000	−0.922631
$922$	−30.0000	−0.987997
$923$	24.0000	0.789970
$924$	−1.00000	−0.0328976
$925$	−2.00000	−0.0657596
$926$	−32.0000	−1.05159
$927$	−1.00000	−0.0328443
$928$	−1.00000	−0.0328266
$929$	−35.0000	−1.14831	−0.574156	−	0.818746i	$-0.694670\pi$
$929$	−35.0000	−1.14831	−0.574156	+	0.818746i	$0.694670\pi$
$930$	9.00000	0.295122
$931$	48.0000	1.57314
$932$	11.0000	0.360317
$933$	4.00000	0.130954
$934$	−36.0000	−1.17796
$935$	−1.00000	−0.0327035
$936$	4.00000	0.130744
$937$	−54.0000	−1.76410	−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000	−1.76410	−0.882052	+	0.471153i	$0.843838\pi$
$938$	4.00000	0.130605
$939$	7.00000	0.228436
$940$	8.00000	0.260931
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	14.0000	0.456145
$943$	8.00000	0.260516
$944$	10.0000	0.325472
$945$	−1.00000	−0.0325300
$946$	−1.00000	−0.0325128
$947$	14.0000	0.454939	0.227469	−	0.973785i	$-0.426955\pi$
$947$	14.0000	0.454939	0.227469	+	0.973785i	$0.426955\pi$
$948$	0	0
$949$	56.0000	1.81784
$950$	−8.00000	−0.259554
$951$	−27.0000	−0.875535
$952$	1.00000	0.0324102
$953$	38.0000	1.23094	0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000	1.23094	0.615470	+	0.788160i	$0.288966\pi$
$954$	8.00000	0.259010
$955$	15.0000	0.485389
$956$	30.0000	0.970269
$957$	−1.00000	−0.0323254
$958$	−13.0000	−0.420011
$959$	−21.0000	−0.678125
$960$	1.00000	0.0322749
$961$	50.0000	1.61290
$962$	−8.00000	−0.257930
$963$	−3.00000	−0.0966736
$964$	−9.00000	−0.289870
$965$	−22.0000	−0.708205
$966$	1.00000	0.0321745
$967$	2.00000	0.0643157	0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000	0.0643157	0.0321578	+	0.999483i	$0.489762\pi$
$968$	1.00000	0.0321412
$969$	−8.00000	−0.256997
$970$	1.00000	0.0321081
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	−1.00000	−0.0320750
$973$	−21.0000	−0.673229
$974$	2.00000	0.0640841
$975$	−4.00000	−0.128103
$976$	−2.00000	−0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	15.0000	0.479647
$979$	4.00000	0.127841
$980$	6.00000	0.191663
$981$	0	0
$982$	−8.00000	−0.255290
$983$	−7.00000	−0.223265	−0.111633	−	0.993750i	$-0.535608\pi$
$983$	−7.00000	−0.223265	−0.111633	+	0.993750i	$0.535608\pi$
$984$	−8.00000	−0.255031
$985$	−24.0000	−0.764704
$986$	1.00000	0.0318465
$987$	−8.00000	−0.254643
$988$	−32.0000	−1.01806
$989$	1.00000	0.0317982
$990$	1.00000	0.0317821
$991$	−45.0000	−1.42947	−0.714736	−	0.699394i	$-0.753453\pi$
$991$	−45.0000	−1.42947	−0.714736	+	0.699394i	$0.753453\pi$
$992$	9.00000	0.285750
$993$	7.00000	0.222138
$994$	−6.00000	−0.190308
$995$	−16.0000	−0.507234
$996$	4.00000	0.126745
$997$	−55.0000	−1.74187	−0.870934	−	0.491400i	$-0.836485\pi$
$997$	−55.0000	−1.74187	−0.870934	+	0.491400i	$0.836485\pi$
$998$	0	0
$999$	2.00000	0.0632772

Twists

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

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