LMFDB - Embedded newform 5610.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -6.00000 q^{29} +1.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +6.00000 q^{37} -4.00000 q^{38} -2.00000 q^{39} -1.00000 q^{40} -10.0000 q^{41} +4.00000 q^{43} +1.00000 q^{44} +1.00000 q^{45} +4.00000 q^{46} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} +2.00000 q^{52} +2.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -4.00000 q^{57} +6.00000 q^{58} -1.00000 q^{60} -10.0000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} +1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} +4.00000 q^{69} -4.00000 q^{71} -1.00000 q^{72} +6.00000 q^{73} -6.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +2.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +4.00000 q^{83} -1.00000 q^{85} -4.00000 q^{86} +6.00000 q^{87} -1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{90} -4.00000 q^{92} +8.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} +7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−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
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	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
$35$	0	0
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−4.00000	−0.648886
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	4.00000	0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	2.00000	0.277350
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	0	0
$57$	−4.00000	−0.529813
$58$	6.00000	0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−1.00000	−0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	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
$69$	4.00000	0.481543
$70$	0	0
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	−1.00000	−0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−6.00000	−0.697486
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	0	0
$78$	2.00000	0.226455
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	−1.00000	−0.108465
$86$	−4.00000	−0.431331
$87$	6.00000	0.643268
$88$	−1.00000	−0.106600
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−4.00000	−0.417029
$93$	8.00000	0.829561
$94$	0	0
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	7.00000	0.707107
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−1.00000	−0.0990148
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−2.00000	−0.194257
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−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
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	4.00000	0.374634
$115$	−4.00000	−0.373002
$116$	−6.00000	−0.557086
$117$	2.00000	0.184900
$118$	0	0
$119$	0	0
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	10.0000	0.905357
$123$	10.0000	0.901670
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	0	0
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−2.00000	−0.175412
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	4.00000	0.345547
$135$	−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	$0.472772\pi$
$138$	−4.00000	−0.340503
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	0	0
$142$	4.00000	0.335673
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−6.00000	−0.496564
$147$	7.00000	0.577350
$148$	6.00000	0.493197
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	1.00000	0.0816497
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	−4.00000	−0.324443
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−2.00000	−0.160128
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	8.00000	0.636446
$159$	−2.00000	−0.158610
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−10.0000	−0.780869
$165$	−1.00000	−0.0778499
$166$	−4.00000	−0.310460
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	1.00000	0.0766965
$171$	4.00000	0.305888
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−6.00000	−0.454859
$175$	0	0
$176$	1.00000	0.0753778
$177$	0	0
$178$	−2.00000	−0.149906
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	1.00000	0.0745356
$181$	22.0000	1.63525	0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000	1.63525	0.817624	+	0.575753i	$0.195291\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	4.00000	0.294884
$185$	6.00000	0.441129
$186$	−8.00000	−0.586588
$187$	−1.00000	−0.0731272
$188$	0	0
$189$	0	0
$190$	−4.00000	−0.290191
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	−1.00000	−0.0721688
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	−2.00000	−0.143592
$195$	−2.00000	−0.143223
$196$	−7.00000	−0.500000
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	−1.00000	−0.0710669
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.00000	−0.0707107
$201$	4.00000	0.282138
$202$	−10.0000	−0.703598
$203$	0	0
$204$	1.00000	0.0700140
$205$	−10.0000	−0.698430
$206$	8.00000	0.557386
$207$	−4.00000	−0.278019
$208$	2.00000	0.138675
$209$	4.00000	0.276686
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	2.00000	0.137361
$213$	4.00000	0.274075
$214$	4.00000	0.273434
$215$	4.00000	0.272798
$216$	1.00000	0.0680414
$217$	0	0
$218$	10.0000	0.677285
$219$	−6.00000	−0.405442
$220$	1.00000	0.0674200
$221$	−2.00000	−0.134535
$222$	6.00000	0.402694
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−4.00000	−0.264906
$229$	30.0000	1.98246	0.991228	−	0.132164i	$-0.0421925\pi$
$229$	30.0000	1.98246	0.991228	+	0.132164i	$0.0421925\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	6.00000	0.393919
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	0	0
$237$	8.00000	0.519656
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−1.00000	−0.0645497
$241$	6.00000	0.386494	0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−10.0000	−0.640184
$245$	−7.00000	−0.447214
$246$	−10.0000	−0.637577
$247$	8.00000	0.509028
$248$	8.00000	0.508001
$249$	−4.00000	−0.253490
$250$	−1.00000	−0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	−12.0000	−0.752947
$255$	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	$0.643834\pi$
$258$	4.00000	0.249029
$259$	0	0
$260$	2.00000	0.124035
$261$	−6.00000	−0.371391
$262$	12.0000	0.741362
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	1.00000	0.0615457
$265$	2.00000	0.122859
$266$	0	0
$267$	−2.00000	−0.122398
$268$	−4.00000	−0.244339
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	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
$273$	0	0
$274$	−2.00000	−0.120824
$275$	1.00000	0.0603023
$276$	4.00000	0.240772
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	8.00000	0.479808
$279$	−8.00000	−0.478947
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	−4.00000	−0.237356
$285$	−4.00000	−0.236940
$286$	−2.00000	−0.118262
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	−2.00000	−0.117242
$292$	6.00000	0.351123
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−7.00000	−0.408248
$295$	0	0
$296$	−6.00000	−0.348743
$297$	−1.00000	−0.0580259
$298$	−10.0000	−0.579284
$299$	−8.00000	−0.462652
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	−12.0000	−0.690522
$303$	−10.0000	−0.574485
$304$	4.00000	0.229416
$305$	−10.0000	−0.572598
$306$	1.00000	0.0571662
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	8.00000	0.454369
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	2.00000	0.113228
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	2.00000	0.112154
$319$	−6.00000	−0.335936
$320$	1.00000	0.0559017
$321$	4.00000	0.223258
$322$	0	0
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	−12.0000	−0.664619
$327$	10.0000	0.553001
$328$	10.0000	0.552158
$329$	0	0
$330$	1.00000	0.0550482
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	4.00000	0.219529
$333$	6.00000	0.328798
$334$	24.0000	1.31322
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	9.00000	0.489535
$339$	2.00000	0.108625
$340$	−1.00000	−0.0542326
$341$	−8.00000	−0.433224
$342$	−4.00000	−0.216295
$343$	0	0
$344$	−4.00000	−0.215666
$345$	4.00000	0.215353
$346$	6.00000	0.322562
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	6.00000	0.321634
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	−1.00000	−0.0533002
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	0	0
$355$	−4.00000	−0.212298
$356$	2.00000	0.106000
$357$	0	0
$358$	24.0000	1.26844
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−22.0000	−1.15629
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	6.00000	0.314054
$366$	−10.0000	−0.522708
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	−4.00000	−0.208514
$369$	−10.0000	−0.520579
$370$	−6.00000	−0.311925
$371$	0	0
$372$	8.00000	0.414781
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	−12.0000	−0.618031
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	4.00000	0.205196
$381$	−12.0000	−0.614779
$382$	24.0000	1.22795
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	18.0000	0.916176
$387$	4.00000	0.203331
$388$	2.00000	0.101535
$389$	34.0000	1.72387	0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000	1.72387	0.861934	+	0.507020i	$0.169253\pi$
$390$	2.00000	0.101274
$391$	4.00000	0.202289
$392$	7.00000	0.353553
$393$	12.0000	0.605320
$394$	−18.0000	−0.906827
$395$	−8.00000	−0.402524
$396$	1.00000	0.0502519
$397$	30.0000	1.50566	0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000	1.50566	0.752828	+	0.658217i	$0.228689\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	1.00000	0.0500000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	−4.00000	−0.199502
$403$	−16.0000	−0.797017
$404$	10.0000	0.497519
$405$	1.00000	0.0496904
$406$	0	0
$407$	6.00000	0.297409
$408$	−1.00000	−0.0495074
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	10.0000	0.493865
$411$	−2.00000	−0.0986527
$412$	−8.00000	−0.394132
$413$	0	0
$414$	4.00000	0.196589
$415$	4.00000	0.196352
$416$	−2.00000	−0.0980581
$417$	8.00000	0.391762
$418$	−4.00000	−0.195646
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	0	0
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	−1.00000	−0.0485071
$426$	−4.00000	−0.193801
$427$	0	0
$428$	−4.00000	−0.193347
$429$	−2.00000	−0.0965609
$430$	−4.00000	−0.192897
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	−1.00000	−0.0481125
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−10.0000	−0.478913
$437$	−16.0000	−0.765384
$438$	6.00000	0.286691
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	−1.00000	−0.0476731
$441$	−7.00000	−0.333333
$442$	2.00000	0.0951303
$443$	16.0000	0.760183	0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000	0.760183	0.380091	+	0.924949i	$0.375893\pi$
$444$	−6.00000	−0.284747
$445$	2.00000	0.0948091
$446$	−8.00000	−0.378811
$447$	−10.0000	−0.472984
$448$	0	0
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	−1.00000	−0.0471405
$451$	−10.0000	−0.470882
$452$	−2.00000	−0.0940721
$453$	−12.0000	−0.563809
$454$	−12.0000	−0.563188
$455$	0	0
$456$	4.00000	0.187317
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	−30.0000	−1.40181
$459$	1.00000	0.0466760
$460$	−4.00000	−0.186501
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	−6.00000	−0.278543
$465$	8.00000	0.370991
$466$	10.0000	0.463241
$467$	−24.0000	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	0	0
$471$	−6.00000	−0.276465
$472$	0	0
$473$	4.00000	0.183920
$474$	−8.00000	−0.367452
$475$	4.00000	0.183533
$476$	0	0
$477$	2.00000	0.0915737
$478$	0	0
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	1.00000	0.0456435
$481$	12.0000	0.547153
$482$	−6.00000	−0.273293
$483$	0	0
$484$	1.00000	0.0454545
$485$	2.00000	0.0908153
$486$	1.00000	0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	10.0000	0.452679
$489$	−12.0000	−0.542659
$490$	7.00000	0.316228
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	10.0000	0.450835
$493$	6.00000	0.270226
$494$	−8.00000	−0.359937
$495$	1.00000	0.0449467
$496$	−8.00000	−0.359211
$497$	0	0
$498$	4.00000	0.179244
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	1.00000	0.0447214
$501$	24.0000	1.07224
$502$	0	0
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	4.00000	0.177822
$507$	9.00000	0.399704
$508$	12.0000	0.532414
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	−1.00000	−0.0442807
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	14.0000	0.617514
$515$	−8.00000	−0.352522
$516$	−4.00000	−0.176090
$517$	0	0
$518$	0	0
$519$	6.00000	0.263371
$520$	−2.00000	−0.0877058
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	6.00000	0.262613
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	16.0000	0.697633
$527$	8.00000	0.348485
$528$	−1.00000	−0.0435194
$529$	−7.00000	−0.304348
$530$	−2.00000	−0.0868744
$531$	0	0
$532$	0	0
$533$	−20.0000	−0.866296
$534$	2.00000	0.0865485
$535$	−4.00000	−0.172935
$536$	4.00000	0.172774
$537$	24.0000	1.03568
$538$	10.0000	0.431131
$539$	−7.00000	−0.301511
$540$	−1.00000	−0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−20.0000	−0.859074
$543$	−22.0000	−0.944110
$544$	1.00000	0.0428746
$545$	−10.0000	−0.428353
$546$	0	0
$547$	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
$551$	−24.0000	−1.02243
$552$	−4.00000	−0.170251
$553$	0	0
$554$	2.00000	0.0849719
$555$	−6.00000	−0.254686
$556$	−8.00000	−0.339276
$557$	−14.0000	−0.593199	−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000	−0.593199	−0.296600	+	0.955002i	$0.595853\pi$
$558$	8.00000	0.338667
$559$	8.00000	0.338364
$560$	0	0
$561$	1.00000	0.0422200
$562$	−30.0000	−1.26547
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	−2.00000	−0.0841406
$566$	−16.0000	−0.672530
$567$	0	0
$568$	4.00000	0.167836
$569$	22.0000	0.922288	0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000	0.922288	0.461144	+	0.887325i	$0.347439\pi$
$570$	4.00000	0.167542
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	2.00000	0.0836242
$573$	24.0000	1.00261
$574$	0	0
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	−1.00000	−0.0415945
$579$	18.0000	0.748054
$580$	−6.00000	−0.249136
$581$	0	0
$582$	2.00000	0.0829027
$583$	2.00000	0.0828315
$584$	−6.00000	−0.248282
$585$	2.00000	0.0826898
$586$	6.00000	0.247858
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	7.00000	0.288675
$589$	−32.0000	−1.31854
$590$	0	0
$591$	−18.0000	−0.740421
$592$	6.00000	0.246598
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	10.0000	0.409616
$597$	16.0000	0.654836
$598$	8.00000	0.327144
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	1.00000	0.0408248
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	12.0000	0.488273
$605$	1.00000	0.0406558
$606$	10.0000	0.406222
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	10.0000	0.404888
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	4.00000	0.161427
$615$	10.0000	0.403239
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	−8.00000	−0.321807
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−8.00000	−0.321288
$621$	4.00000	0.160514
$622$	12.0000	0.481156
$623$	0	0
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−26.0000	−1.03917
$627$	−4.00000	−0.159745
$628$	6.00000	0.239426
$629$	−6.00000	−0.239236
$630$	0	0
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	10.0000	0.397151
$635$	12.0000	0.476205
$636$	−2.00000	−0.0793052
$637$	−14.0000	−0.554700
$638$	6.00000	0.237542
$639$	−4.00000	−0.158238
$640$	−1.00000	−0.0395285
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	−4.00000	−0.157867
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	4.00000	0.157378
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	12.0000	0.469956
$653$	−42.0000	−1.64359	−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000	−1.64359	−0.821794	+	0.569785i	$0.807026\pi$
$654$	−10.0000	−0.391031
$655$	−12.0000	−0.468879
$656$	−10.0000	−0.390434
$657$	6.00000	0.234082
$658$	0	0
$659$	−44.0000	−1.71400	−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000	−1.71400	−0.856998	+	0.515319i	$0.827673\pi$
$660$	−1.00000	−0.0389249
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	20.0000	0.777322
$663$	2.00000	0.0776736
$664$	−4.00000	−0.155230
$665$	0	0
$666$	−6.00000	−0.232495
$667$	24.0000	0.929284
$668$	−24.0000	−0.928588
$669$	−8.00000	−0.309298
$670$	4.00000	0.154533
$671$	−10.0000	−0.386046
$672$	0	0
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	18.0000	0.693334
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	1.00000	0.0383482
$681$	−12.0000	−0.459841
$682$	8.00000	0.306336
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	4.00000	0.152944
$685$	2.00000	0.0764161
$686$	0	0
$687$	−30.0000	−1.14457
$688$	4.00000	0.152499
$689$	4.00000	0.152388
$690$	−4.00000	−0.152277
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	−8.00000	−0.303457
$696$	−6.00000	−0.227429
$697$	10.0000	0.378777
$698$	−26.0000	−0.984115
$699$	10.0000	0.378235
$700$	0	0
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	2.00000	0.0754851
$703$	24.0000	0.905177
$704$	1.00000	0.0376889
$705$	0	0
$706$	14.0000	0.526897
$707$	0	0
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	4.00000	0.150117
$711$	−8.00000	−0.300023
$712$	−2.00000	−0.0749532
$713$	32.0000	1.19841
$714$	0	0
$715$	2.00000	0.0747958
$716$	−24.0000	−0.896922
$717$	0	0
$718$	16.0000	0.597115
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	3.00000	0.111648
$723$	−6.00000	−0.223142
$724$	22.0000	0.817624
$725$	−6.00000	−0.222834
$726$	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	$0.595887\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	−4.00000	−0.147945
$732$	10.0000	0.369611
$733$	50.0000	1.84679	0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000	1.84679	0.923396	+	0.383849i	$0.125402\pi$
$734$	32.0000	1.18114
$735$	7.00000	0.258199
$736$	4.00000	0.147442
$737$	−4.00000	−0.147342
$738$	10.0000	0.368105
$739$	−52.0000	−1.91285	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−52.0000	−1.91285	−0.956425	+	0.291977i	$0.905687\pi$
$740$	6.00000	0.220564
$741$	−8.00000	−0.293887
$742$	0	0
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	−8.00000	−0.293294
$745$	10.0000	0.366372
$746$	14.0000	0.512576
$747$	4.00000	0.146352
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	1.00000	0.0365148
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	0	0
$753$	0	0
$754$	12.0000	0.437014
$755$	12.0000	0.436725
$756$	0	0
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	20.0000	0.726433
$759$	4.00000	0.145191
$760$	−4.00000	−0.145095
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	12.0000	0.434714
$763$	0	0
$764$	−24.0000	−0.868290
$765$	−1.00000	−0.0361551
$766$	16.0000	0.578103
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−46.0000	−1.65880	−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000	−1.65880	−0.829401	+	0.558653i	$0.811318\pi$
$770$	0	0
$771$	14.0000	0.504198
$772$	−18.0000	−0.647834
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	−4.00000	−0.143777
$775$	−8.00000	−0.287368
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	−34.0000	−1.21896
$779$	−40.0000	−1.43315
$780$	−2.00000	−0.0716115
$781$	−4.00000	−0.143131
$782$	−4.00000	−0.143040
$783$	6.00000	0.214423
$784$	−7.00000	−0.250000
$785$	6.00000	0.214149
$786$	−12.0000	−0.428026
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	18.0000	0.641223
$789$	16.0000	0.569615
$790$	8.00000	0.284627
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	−20.0000	−0.710221
$794$	−30.0000	−1.06466
$795$	−2.00000	−0.0709327
$796$	−16.0000	−0.567105
$797$	50.0000	1.77109	0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000	1.77109	0.885545	+	0.464553i	$0.153785\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	2.00000	0.0706665
$802$	18.0000	0.635602
$803$	6.00000	0.211735
$804$	4.00000	0.141069
$805$	0	0
$806$	16.0000	0.563576
$807$	10.0000	0.352017
$808$	−10.0000	−0.351799
$809$	−42.0000	−1.47664	−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000	−1.47664	−0.738321	+	0.674450i	$0.764381\pi$
$810$	−1.00000	−0.0351364
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	0	0
$813$	−20.0000	−0.701431
$814$	−6.00000	−0.210300
$815$	12.0000	0.420342
$816$	1.00000	0.0350070
$817$	16.0000	0.559769
$818$	22.0000	0.769212
$819$	0	0
$820$	−10.0000	−0.349215
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	2.00000	0.0697580
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	8.00000	0.278693
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	−4.00000	−0.139094	−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000	−0.139094	−0.0695468	+	0.997579i	$0.522155\pi$
$828$	−4.00000	−0.139010
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−4.00000	−0.138842
$831$	2.00000	0.0693792
$832$	2.00000	0.0693375
$833$	7.00000	0.242536
$834$	−8.00000	−0.277017
$835$	−24.0000	−0.830554
$836$	4.00000	0.138343
$837$	8.00000	0.276520
$838$	20.0000	0.690889
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	10.0000	0.344623
$843$	−30.0000	−1.03325
$844$	0	0
$845$	−9.00000	−0.309609
$846$	0	0
$847$	0	0
$848$	2.00000	0.0686803
$849$	−16.0000	−0.549119
$850$	1.00000	0.0342997
$851$	−24.0000	−0.822709
$852$	4.00000	0.137038
$853$	6.00000	0.205436	0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000	0.205436	0.102718	+	0.994711i	$0.467246\pi$
$854$	0	0
$855$	4.00000	0.136797
$856$	4.00000	0.136717
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	2.00000	0.0682789
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	−8.00000	−0.272481
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	1.00000	0.0340207
$865$	−6.00000	−0.204006
$866$	30.0000	1.01944
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−8.00000	−0.271381
$870$	−6.00000	−0.203419
$871$	−8.00000	−0.271070
$872$	10.0000	0.338643
$873$	2.00000	0.0676897
$874$	16.0000	0.541208
$875$	0	0
$876$	−6.00000	−0.202721
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	−8.00000	−0.269987
$879$	6.00000	0.202375
$880$	1.00000	0.0337100
$881$	22.0000	0.741199	0.370599	−	0.928793i	$-0.379152\pi$
$881$	22.0000	0.741199	0.370599	+	0.928793i	$0.379152\pi$
$882$	7.00000	0.235702
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	−16.0000	−0.537531
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	6.00000	0.201347
$889$	0	0
$890$	−2.00000	−0.0670402
$891$	1.00000	0.0335013
$892$	8.00000	0.267860
$893$	0	0
$894$	10.0000	0.334450
$895$	−24.0000	−0.802232
$896$	0	0
$897$	8.00000	0.267112
$898$	34.0000	1.13459
$899$	48.0000	1.60089
$900$	1.00000	0.0333333
$901$	−2.00000	−0.0666297
$902$	10.0000	0.332964
$903$	0	0
$904$	2.00000	0.0665190
$905$	22.0000	0.731305
$906$	12.0000	0.398673
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	12.0000	0.398234
$909$	10.0000	0.331679
$910$	0	0
$911$	52.0000	1.72284	0.861418	−	0.507896i	$-0.169577\pi$
$911$	52.0000	1.72284	0.861418	+	0.507896i	$0.169577\pi$
$912$	−4.00000	−0.132453
$913$	4.00000	0.132381
$914$	22.0000	0.727695
$915$	10.0000	0.330590
$916$	30.0000	0.991228
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	4.00000	0.131876
$921$	4.00000	0.131804
$922$	14.0000	0.461065
$923$	−8.00000	−0.263323
$924$	0	0
$925$	6.00000	0.197279
$926$	−24.0000	−0.788689
$927$	−8.00000	−0.262754
$928$	6.00000	0.196960
$929$	38.0000	1.24674	0.623370	−	0.781927i	$-0.285763\pi$
$929$	38.0000	1.24674	0.623370	+	0.781927i	$0.285763\pi$
$930$	−8.00000	−0.262330
$931$	−28.0000	−0.917663
$932$	−10.0000	−0.327561
$933$	12.0000	0.392862
$934$	24.0000	0.785304
$935$	−1.00000	−0.0327035
$936$	−2.00000	−0.0653720
$937$	−14.0000	−0.457360	−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000	−0.457360	−0.228680	+	0.973502i	$0.573441\pi$
$938$	0	0
$939$	−26.0000	−0.848478
$940$	0	0
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	6.00000	0.195491
$943$	40.0000	1.30258
$944$	0	0
$945$	0	0
$946$	−4.00000	−0.130051
$947$	−60.0000	−1.94974	−0.974869	−	0.222779i	$-0.928487\pi$
$947$	−60.0000	−1.94974	−0.974869	+	0.222779i	$0.928487\pi$
$948$	8.00000	0.259828
$949$	12.0000	0.389536
$950$	−4.00000	−0.129777
$951$	10.0000	0.324272
$952$	0	0
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	−2.00000	−0.0647524
$955$	−24.0000	−0.776622
$956$	0	0
$957$	6.00000	0.193952
$958$	16.0000	0.516937
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	−12.0000	−0.386896
$963$	−4.00000	−0.128898
$964$	6.00000	0.193247
$965$	−18.0000	−0.579441
$966$	0	0
$967$	36.0000	1.15768	0.578841	−	0.815440i	$-0.303505\pi$
$967$	36.0000	1.15768	0.578841	+	0.815440i	$0.303505\pi$
$968$	−1.00000	−0.0321412
$969$	4.00000	0.128499
$970$	−2.00000	−0.0642161
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	16.0000	0.512673
$975$	−2.00000	−0.0640513
$976$	−10.0000	−0.320092
$977$	26.0000	0.831814	0.415907	−	0.909407i	$-0.363464\pi$
$977$	26.0000	0.831814	0.415907	+	0.909407i	$0.363464\pi$
$978$	12.0000	0.383718
$979$	2.00000	0.0639203
$980$	−7.00000	−0.223607
$981$	−10.0000	−0.319275
$982$	−20.0000	−0.638226
$983$	28.0000	0.893061	0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000	0.893061	0.446531	+	0.894768i	$0.352659\pi$
$984$	−10.0000	−0.318788
$985$	18.0000	0.573528
$986$	−6.00000	−0.191079
$987$	0	0
$988$	8.00000	0.254514
$989$	−16.0000	−0.508770
$990$	−1.00000	−0.0317821
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	8.00000	0.254000
$993$	20.0000	0.634681
$994$	0	0
$995$	−16.0000	−0.507234
$996$	−4.00000	−0.126745
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	−4.00000	−0.126618
$999$	−6.00000	−0.189832

Twists

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

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