LMFDB - Embedded newform 5610.2.a.c.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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -6.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} -1.00000 q^{20} +1.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} +6.00000 q^{29} -1.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} -8.00000 q^{38} +6.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} -4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +8.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -6.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -8.00000 q^{57} -6.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} +14.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} -1.00000 q^{66} +4.00000 q^{67} -1.00000 q^{68} +8.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} -10.0000 q^{74} -1.00000 q^{75} +8.00000 q^{76} -6.00000 q^{78} -16.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +4.00000 q^{83} +1.00000 q^{85} +4.00000 q^{86} -6.00000 q^{87} +1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{90} -8.00000 q^{92} -4.00000 q^{93} -4.00000 q^{94} -8.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} +7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	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
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	6.00000	1.17670
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−1.00000	−0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−8.00000	−1.29777
$39$	6.00000	0.960769
$40$	1.00000	0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	8.00000	1.17954
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	−6.00000	−0.832050
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	0	0
$57$	−8.00000	−1.05963
$58$	−6.00000	−0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	1.00000	0.129099
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	−1.00000	−0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−1.00000	−0.121268
$69$	8.00000	0.963087
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−1.00000	−0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−10.0000	−1.16248
$75$	−1.00000	−0.115470
$76$	8.00000	0.917663
$77$	0	0
$78$	−6.00000	−0.679366
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	1.00000	0.108465
$86$	4.00000	0.431331
$87$	−6.00000	−0.643268
$88$	1.00000	0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−8.00000	−0.834058
$93$	−4.00000	−0.414781
$94$	−4.00000	−0.412568
$95$	−8.00000	−0.820783
$96$	1.00000	0.102062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	7.00000	0.707107
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−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	$0.628955\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	6.00000	0.582772
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	−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
$111$	−10.0000	−0.949158
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	8.00000	0.749269
$115$	8.00000	0.746004
$116$	6.00000	0.557086
$117$	−6.00000	−0.554700
$118$	4.00000	0.368230
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−14.0000	−1.26750
$123$	−2.00000	−0.180334
$124$	4.00000	0.359211
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	4.00000	0.352180
$130$	−6.00000	−0.526235
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	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	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−8.00000	−0.681005
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	−4.00000	−0.336861
$142$	−8.00000	−0.671345
$143$	6.00000	0.501745
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−2.00000	−0.165521
$147$	7.00000	0.577350
$148$	10.0000	0.821995
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	1.00000	0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−8.00000	−0.648886
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−4.00000	−0.321288
$156$	6.00000	0.480384
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	16.0000	1.27289
$159$	6.00000	0.475831
$160$	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	$0.344270\pi$
$164$	2.00000	0.156174
$165$	−1.00000	−0.0778499
$166$	−4.00000	−0.310460
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−1.00000	−0.0766965
$171$	8.00000	0.611775
$172$	−4.00000	−0.304997
$173$	−22.0000	−1.67263	−0.836315	−	0.548250i	$-0.815294\pi$
$173$	−22.0000	−1.67263	−0.836315	+	0.548250i	$0.815294\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	4.00000	0.300658
$178$	6.00000	0.449719
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.00000	−0.0745356
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	−14.0000	−1.03491
$184$	8.00000	0.589768
$185$	−10.0000	−0.735215
$186$	4.00000	0.293294
$187$	1.00000	0.0731272
$188$	4.00000	0.291730
$189$	0	0
$190$	8.00000	0.580381
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.00000	−0.0721688
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	10.0000	0.717958
$195$	−6.00000	−0.429669
$196$	−7.00000	−0.500000
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	1.00000	0.0710669
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00000	−0.282138
$202$	6.00000	0.422159
$203$	0	0
$204$	1.00000	0.0700140
$205$	−2.00000	−0.139686
$206$	8.00000	0.557386
$207$	−8.00000	−0.556038
$208$	−6.00000	−0.416025
$209$	−8.00000	−0.553372
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−6.00000	−0.412082
$213$	−8.00000	−0.548151
$214$	−8.00000	−0.546869
$215$	4.00000	0.272798
$216$	1.00000	0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	−2.00000	−0.135147
$220$	1.00000	0.0674200
$221$	6.00000	0.403604
$222$	10.0000	0.671156
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	−8.00000	−0.529813
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	−8.00000	−0.527504
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	6.00000	0.392232
$235$	−4.00000	−0.260931
$236$	−4.00000	−0.260378
$237$	16.0000	1.03931
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	1.00000	0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	14.0000	0.896258
$245$	7.00000	0.447214
$246$	2.00000	0.127515
$247$	−48.0000	−3.05417
$248$	−4.00000	−0.254000
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	−16.0000	−1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	6.00000	0.372104
$261$	6.00000	0.371391
$262$	4.00000	0.247121
$263$	−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
$265$	6.00000	0.368577
$266$	0	0
$267$	6.00000	0.367194
$268$	4.00000	0.244339
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	−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
$276$	8.00000	0.481543
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	12.0000	0.719712
$279$	4.00000	0.239474
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	4.00000	0.238197
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	8.00000	0.474713
$285$	8.00000	0.473879
$286$	−6.00000	−0.354787
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	10.0000	0.586210
$292$	2.00000	0.117041
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	−7.00000	−0.408248
$295$	4.00000	0.232889
$296$	−10.0000	−0.581238
$297$	1.00000	0.0580259
$298$	6.00000	0.347571
$299$	48.0000	2.77591
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	4.00000	0.230174
$303$	6.00000	0.344691
$304$	8.00000	0.458831
$305$	−14.0000	−0.801638
$306$	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	$0.205351\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	4.00000	0.227185
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	−6.00000	−0.339683
$313$	30.0000	1.69570	0.847850	−	0.530236i	$-0.177897\pi$
$313$	30.0000	1.69570	0.847850	+	0.530236i	$0.177897\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	−16.0000	−0.900070
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	−6.00000	−0.336463
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	−8.00000	−0.446516
$322$	0	0
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	−6.00000	−0.332820
$326$	−12.0000	−0.664619
$327$	2.00000	0.110600
$328$	−2.00000	−0.110432
$329$	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
$333$	10.0000	0.547997
$334$	−12.0000	−0.656611
$335$	−4.00000	−0.218543
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−23.0000	−1.25104
$339$	2.00000	0.108625
$340$	1.00000	0.0542326
$341$	−4.00000	−0.216612
$342$	−8.00000	−0.432590
$343$	0	0
$344$	4.00000	0.215666
$345$	−8.00000	−0.430706
$346$	22.0000	1.18273
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	−6.00000	−0.321634
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	6.00000	0.320256
$352$	1.00000	0.0533002
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	−4.00000	−0.212598
$355$	−8.00000	−0.424596
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−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
$361$	45.0000	2.36842
$362$	2.00000	0.105118
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−2.00000	−0.104685
$366$	14.0000	0.731792
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	−8.00000	−0.417029
$369$	2.00000	0.104116
$370$	10.0000	0.519875
$371$	0	0
$372$	−4.00000	−0.207390
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	−4.00000	−0.206284
$377$	−36.0000	−1.85409
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	−8.00000	−0.410391
$381$	−16.0000	−0.819705
$382$	8.00000	0.409316
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−10.0000	−0.508987
$387$	−4.00000	−0.203331
$388$	−10.0000	−0.507673
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	6.00000	0.303822
$391$	8.00000	0.404577
$392$	7.00000	0.353553
$393$	4.00000	0.201773
$394$	−2.00000	−0.100759
$395$	16.0000	0.805047
$396$	−1.00000	−0.0502519
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−20.0000	−1.00251
$399$	0	0
$400$	1.00000	0.0500000
$401$	−34.0000	−1.69788	−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000	−1.69788	−0.848939	+	0.528490i	$0.822758\pi$
$402$	4.00000	0.199502
$403$	−24.0000	−1.19553
$404$	−6.00000	−0.298511
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−10.0000	−0.495682
$408$	−1.00000	−0.0495074
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	2.00000	0.0987730
$411$	2.00000	0.0986527
$412$	−8.00000	−0.394132
$413$	0	0
$414$	8.00000	0.393179
$415$	−4.00000	−0.196352
$416$	6.00000	0.294174
$417$	12.0000	0.587643
$418$	8.00000	0.391293
$419$	−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
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	20.0000	0.973585
$423$	4.00000	0.194487
$424$	6.00000	0.291386
$425$	−1.00000	−0.0485071
$426$	8.00000	0.387601
$427$	0	0
$428$	8.00000	0.386695
$429$	−6.00000	−0.289683
$430$	−4.00000	−0.192897
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−1.00000	−0.0481125
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−2.00000	−0.0957826
$437$	−64.0000	−3.06154
$438$	2.00000	0.0955637
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	−1.00000	−0.0476731
$441$	−7.00000	−0.333333
$442$	−6.00000	−0.285391
$443$	−40.0000	−1.90046	−0.950229	−	0.311553i	$-0.899151\pi$
$443$	−40.0000	−1.90046	−0.950229	+	0.311553i	$0.899151\pi$
$444$	−10.0000	−0.474579
$445$	6.00000	0.284427
$446$	−16.0000	−0.757622
$447$	6.00000	0.283790
$448$	0	0
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	−1.00000	−0.0471405
$451$	−2.00000	−0.0941763
$452$	−2.00000	−0.0940721
$453$	4.00000	0.187936
$454$	8.00000	0.375459
$455$	0	0
$456$	8.00000	0.374634
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	−6.00000	−0.280362
$459$	1.00000	0.0466760
$460$	8.00000	0.373002
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	6.00000	0.278543
$465$	4.00000	0.185496
$466$	26.0000	1.20443
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−6.00000	−0.277350
$469$	0	0
$470$	4.00000	0.184506
$471$	2.00000	0.0921551
$472$	4.00000	0.184115
$473$	4.00000	0.183920
$474$	−16.0000	−0.734904
$475$	8.00000	0.367065
$476$	0	0
$477$	−6.00000	−0.274721
$478$	8.00000	0.365911
$479$	−32.0000	−1.46212	−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000	−1.46212	−0.731059	+	0.682315i	$0.760973\pi$
$480$	−1.00000	−0.0456435
$481$	−60.0000	−2.73576
$482$	14.0000	0.637683
$483$	0	0
$484$	1.00000	0.0454545
$485$	10.0000	0.454077
$486$	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	$0.618082\pi$
$488$	−14.0000	−0.633750
$489$	−12.0000	−0.542659
$490$	−7.00000	−0.316228
$491$	−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
$493$	−6.00000	−0.270226
$494$	48.0000	2.15962
$495$	1.00000	0.0449467
$496$	4.00000	0.179605
$497$	0	0
$498$	4.00000	0.179244
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	−1.00000	−0.0447214
$501$	−12.0000	−0.536120
$502$	20.0000	0.892644
$503$	−4.00000	−0.178351	−0.0891756	−	0.996016i	$-0.528423\pi$
$503$	−4.00000	−0.178351	−0.0891756	+	0.996016i	$0.528423\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	−8.00000	−0.355643
$507$	−23.0000	−1.02147
$508$	16.0000	0.709885
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	1.00000	0.0442807
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	−6.00000	−0.264649
$515$	8.00000	0.352522
$516$	4.00000	0.176090
$517$	−4.00000	−0.175920
$518$	0	0
$519$	22.0000	0.965693
$520$	−6.00000	−0.263117
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	−6.00000	−0.262613
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	24.0000	1.04645
$527$	−4.00000	−0.174243
$528$	1.00000	0.0435194
$529$	41.0000	1.78261
$530$	−6.00000	−0.260623
$531$	−4.00000	−0.173585
$532$	0	0
$533$	−12.0000	−0.519778
$534$	−6.00000	−0.259645
$535$	−8.00000	−0.345870
$536$	−4.00000	−0.172774
$537$	−12.0000	−0.517838
$538$	30.0000	1.29339
$539$	7.00000	0.301511
$540$	1.00000	0.0430331
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−20.0000	−0.859074
$543$	2.00000	0.0858282
$544$	1.00000	0.0428746
$545$	2.00000	0.0856706
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	−2.00000	−0.0854358
$549$	14.0000	0.597505
$550$	1.00000	0.0426401
$551$	48.0000	2.04487
$552$	−8.00000	−0.340503
$553$	0	0
$554$	10.0000	0.424859
$555$	10.0000	0.424476
$556$	−12.0000	−0.508913
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	−4.00000	−0.169334
$559$	24.0000	1.01509
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	18.0000	0.759284
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	−4.00000	−0.168430
$565$	2.00000	0.0841406
$566$	28.0000	1.17693
$567$	0	0
$568$	−8.00000	−0.335673
$569$	38.0000	1.59304	0.796521	−	0.604610i	$-0.206671\pi$
$569$	38.0000	1.59304	0.796521	+	0.604610i	$0.206671\pi$
$570$	−8.00000	−0.335083
$571$	−44.0000	−1.84134	−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000	−1.84134	−0.920671	+	0.390339i	$0.872358\pi$
$572$	6.00000	0.250873
$573$	8.00000	0.334205
$574$	0	0
$575$	−8.00000	−0.333623
$576$	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
$579$	−10.0000	−0.415586
$580$	−6.00000	−0.249136
$581$	0	0
$582$	−10.0000	−0.414513
$583$	6.00000	0.248495
$584$	−2.00000	−0.0827606
$585$	6.00000	0.248069
$586$	−26.0000	−1.07405
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	7.00000	0.288675
$589$	32.0000	1.31854
$590$	−4.00000	−0.164677
$591$	−2.00000	−0.0822690
$592$	10.0000	0.410997
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−6.00000	−0.245770
$597$	−20.0000	−0.818546
$598$	−48.0000	−1.96287
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	1.00000	0.0408248
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	−4.00000	−0.162758
$605$	−1.00000	−0.0406558
$606$	−6.00000	−0.243733
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	−8.00000	−0.324443
$609$	0	0
$610$	14.0000	0.566843
$611$	−24.0000	−0.970936
$612$	−1.00000	−0.0404226
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	−28.0000	−1.12999
$615$	2.00000	0.0806478
$616$	0	0
$617$	−26.0000	−1.04672	−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000	−1.04672	−0.523360	+	0.852111i	$0.675322\pi$
$618$	−8.00000	−0.321807
$619$	−40.0000	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$620$	−4.00000	−0.160644
$621$	8.00000	0.321029
$622$	8.00000	0.320771
$623$	0	0
$624$	6.00000	0.240192
$625$	1.00000	0.0400000
$626$	−30.0000	−1.19904
$627$	8.00000	0.319489
$628$	−2.00000	−0.0798087
$629$	−10.0000	−0.398726
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	16.0000	0.636446
$633$	20.0000	0.794929
$634$	−2.00000	−0.0794301
$635$	−16.0000	−0.634941
$636$	6.00000	0.237915
$637$	42.0000	1.66410
$638$	6.00000	0.237542
$639$	8.00000	0.316475
$640$	1.00000	0.0395285
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	8.00000	0.315735
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	8.00000	0.314756
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	−1.00000	−0.0392837
$649$	4.00000	0.157014
$650$	6.00000	0.235339
$651$	0	0
$652$	12.0000	0.469956
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	−2.00000	−0.0782062
$655$	4.00000	0.156293
$656$	2.00000	0.0780869
$657$	2.00000	0.0780274
$658$	0	0
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	−1.00000	−0.0389249
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	20.0000	0.777322
$663$	−6.00000	−0.233021
$664$	−4.00000	−0.155230
$665$	0	0
$666$	−10.0000	−0.387492
$667$	−48.0000	−1.85857
$668$	12.0000	0.464294
$669$	−16.0000	−0.618596
$670$	4.00000	0.154533
$671$	−14.0000	−0.540464
$672$	0	0
$673$	−38.0000	−1.46479	−0.732396	−	0.680879i	$-0.761598\pi$
$673$	−38.0000	−1.46479	−0.732396	+	0.680879i	$0.761598\pi$
$674$	−26.0000	−1.00148
$675$	−1.00000	−0.0384900
$676$	23.0000	0.884615
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	−1.00000	−0.0383482
$681$	8.00000	0.306561
$682$	4.00000	0.153168
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	8.00000	0.305888
$685$	2.00000	0.0764161
$686$	0	0
$687$	−6.00000	−0.228914
$688$	−4.00000	−0.152499
$689$	36.0000	1.37149
$690$	8.00000	0.304555
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−22.0000	−0.836315
$693$	0	0
$694$	24.0000	0.911028
$695$	12.0000	0.455186
$696$	6.00000	0.227429
$697$	−2.00000	−0.0757554
$698$	10.0000	0.378506
$699$	26.0000	0.983410
$700$	0	0
$701$	26.0000	0.982006	0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000	0.982006	0.491003	+	0.871158i	$0.336630\pi$
$702$	−6.00000	−0.226455
$703$	80.0000	3.01726
$704$	−1.00000	−0.0376889
$705$	4.00000	0.150649
$706$	18.0000	0.677439
$707$	0	0
$708$	4.00000	0.150329
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	8.00000	0.300235
$711$	−16.0000	−0.600047
$712$	6.00000	0.224860
$713$	−32.0000	−1.19841
$714$	0	0
$715$	−6.00000	−0.224387
$716$	12.0000	0.448461
$717$	8.00000	0.298765
$718$	16.0000	0.597115
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−45.0000	−1.67473
$723$	14.0000	0.520666
$724$	−2.00000	−0.0743294
$725$	6.00000	0.222834
$726$	1.00000	0.0371135
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	4.00000	0.147945
$732$	−14.0000	−0.517455
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	16.0000	0.590571
$735$	−7.00000	−0.258199
$736$	8.00000	0.294884
$737$	−4.00000	−0.147342
$738$	−2.00000	−0.0736210
$739$	−48.0000	−1.76571	−0.882854	−	0.469647i	$-0.844381\pi$
$739$	−48.0000	−1.76571	−0.882854	+	0.469647i	$0.844381\pi$
$740$	−10.0000	−0.367607
$741$	48.0000	1.76332
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	4.00000	0.146647
$745$	6.00000	0.219823
$746$	6.00000	0.219676
$747$	4.00000	0.146352
$748$	1.00000	0.0365636
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	4.00000	0.145865
$753$	20.0000	0.728841
$754$	36.0000	1.31104
$755$	4.00000	0.145575
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	0	0
$759$	−8.00000	−0.290382
$760$	8.00000	0.290191
$761$	54.0000	1.95750	0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000	1.95750	0.978749	+	0.205061i	$0.0657392\pi$
$762$	16.0000	0.579619
$763$	0	0
$764$	−8.00000	−0.289430
$765$	1.00000	0.0361551
$766$	4.00000	0.144526
$767$	24.0000	0.866590
$768$	−1.00000	−0.0360844
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	10.0000	0.359908
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	4.00000	0.143777
$775$	4.00000	0.143684
$776$	10.0000	0.358979
$777$	0	0
$778$	−30.0000	−1.07555
$779$	16.0000	0.573259
$780$	−6.00000	−0.214834
$781$	−8.00000	−0.286263
$782$	−8.00000	−0.286079
$783$	−6.00000	−0.214423
$784$	−7.00000	−0.250000
$785$	2.00000	0.0713831
$786$	−4.00000	−0.142675
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	2.00000	0.0712470
$789$	24.0000	0.854423
$790$	−16.0000	−0.569254
$791$	0	0
$792$	1.00000	0.0355335
$793$	−84.0000	−2.98293
$794$	22.0000	0.780751
$795$	−6.00000	−0.212798
$796$	20.0000	0.708881
$797$	−22.0000	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$798$	0	0
$799$	−4.00000	−0.141510
$800$	−1.00000	−0.0353553
$801$	−6.00000	−0.212000
$802$	34.0000	1.20058
$803$	−2.00000	−0.0705785
$804$	−4.00000	−0.141069
$805$	0	0
$806$	24.0000	0.845364
$807$	30.0000	1.05605
$808$	6.00000	0.211079
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	1.00000	0.0351364
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	−20.0000	−0.701431
$814$	10.0000	0.350500
$815$	−12.0000	−0.420342
$816$	1.00000	0.0350070
$817$	−32.0000	−1.11954
$818$	14.0000	0.489499
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	−2.00000	−0.0697580
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	8.00000	0.278693
$825$	1.00000	0.0348155
$826$	0	0
$827$	−32.0000	−1.11275	−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000	−1.11275	−0.556375	+	0.830932i	$0.687808\pi$
$828$	−8.00000	−0.278019
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	4.00000	0.138842
$831$	10.0000	0.346896
$832$	−6.00000	−0.208013
$833$	7.00000	0.242536
$834$	−12.0000	−0.415526
$835$	−12.0000	−0.415277
$836$	−8.00000	−0.276686
$837$	−4.00000	−0.138260
$838$	20.0000	0.690889
$839$	16.0000	0.552381	0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000	0.552381	0.276191	+	0.961103i	$0.410928\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	26.0000	0.896019
$843$	18.0000	0.619953
$844$	−20.0000	−0.688428
$845$	−23.0000	−0.791224
$846$	−4.00000	−0.137523
$847$	0	0
$848$	−6.00000	−0.206041
$849$	28.0000	0.960958
$850$	1.00000	0.0342997
$851$	−80.0000	−2.74236
$852$	−8.00000	−0.274075
$853$	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
$855$	−8.00000	−0.273594
$856$	−8.00000	−0.273434
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	6.00000	0.204837
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	−24.0000	−0.817443
$863$	4.00000	0.136162	0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000	0.136162	0.0680808	+	0.997680i	$0.478312\pi$
$864$	1.00000	0.0340207
$865$	22.0000	0.748022
$866$	−26.0000	−0.883516
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	16.0000	0.542763
$870$	−6.00000	−0.203419
$871$	−24.0000	−0.813209
$872$	2.00000	0.0677285
$873$	−10.0000	−0.338449
$874$	64.0000	2.16483
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	40.0000	1.34993
$879$	−26.0000	−0.876958
$880$	1.00000	0.0337100
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	7.00000	0.235702
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	6.00000	0.201802
$885$	−4.00000	−0.134459
$886$	40.0000	1.34383
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	−6.00000	−0.201120
$891$	−1.00000	−0.0335013
$892$	16.0000	0.535720
$893$	32.0000	1.07084
$894$	−6.00000	−0.200670
$895$	−12.0000	−0.401116
$896$	0	0
$897$	−48.0000	−1.60267
$898$	−6.00000	−0.200223
$899$	24.0000	0.800445
$900$	1.00000	0.0333333
$901$	6.00000	0.199889
$902$	2.00000	0.0665927
$903$	0	0
$904$	2.00000	0.0665190
$905$	2.00000	0.0664822
$906$	−4.00000	−0.132891
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	−8.00000	−0.265489
$909$	−6.00000	−0.199007
$910$	0	0
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	−8.00000	−0.264906
$913$	−4.00000	−0.132381
$914$	−22.0000	−0.727695
$915$	14.0000	0.462826
$916$	6.00000	0.198246
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	−60.0000	−1.97922	−0.989609	−	0.143787i	$-0.954072\pi$
$919$	−60.0000	−1.97922	−0.989609	+	0.143787i	$0.954072\pi$
$920$	−8.00000	−0.263752
$921$	−28.0000	−0.922631
$922$	6.00000	0.197599
$923$	−48.0000	−1.57994
$924$	0	0
$925$	10.0000	0.328798
$926$	−16.0000	−0.525793
$927$	−8.00000	−0.262754
$928$	−6.00000	−0.196960
$929$	−10.0000	−0.328089	−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000	−0.328089	−0.164045	+	0.986453i	$0.552454\pi$
$930$	−4.00000	−0.131165
$931$	−56.0000	−1.83533
$932$	−26.0000	−0.851658
$933$	8.00000	0.261908
$934$	8.00000	0.261768
$935$	−1.00000	−0.0327035
$936$	6.00000	0.196116
$937$	−34.0000	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$938$	0	0
$939$	−30.0000	−0.979013
$940$	−4.00000	−0.130466
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	−2.00000	−0.0651635
$943$	−16.0000	−0.521032
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−4.00000	−0.130051
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	16.0000	0.519656
$949$	−12.0000	−0.389536
$950$	−8.00000	−0.259554
$951$	−2.00000	−0.0648544
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	6.00000	0.194257
$955$	8.00000	0.258874
$956$	−8.00000	−0.258738
$957$	6.00000	0.193952
$958$	32.0000	1.03387
$959$	0	0
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	60.0000	1.93448
$963$	8.00000	0.257796
$964$	−14.0000	−0.450910
$965$	−10.0000	−0.321911
$966$	0	0
$967$	16.0000	0.514525	0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000	0.514525	0.257263	+	0.966342i	$0.417179\pi$
$968$	−1.00000	−0.0321412
$969$	8.00000	0.256997
$970$	−10.0000	−0.321081
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	16.0000	0.512673
$975$	6.00000	0.192154
$976$	14.0000	0.448129
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	12.0000	0.383718
$979$	6.00000	0.191761
$980$	7.00000	0.223607
$981$	−2.00000	−0.0638551
$982$	12.0000	0.382935
$983$	8.00000	0.255160	0.127580	−	0.991828i	$-0.459279\pi$
$983$	8.00000	0.255160	0.127580	+	0.991828i	$0.459279\pi$
$984$	2.00000	0.0637577
$985$	−2.00000	−0.0637253
$986$	6.00000	0.191079
$987$	0	0
$988$	−48.0000	−1.52708
$989$	32.0000	1.01754
$990$	−1.00000	−0.0317821
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	−4.00000	−0.127000
$993$	20.0000	0.634681
$994$	0	0
$995$	−20.0000	−0.634043
$996$	−4.00000	−0.126745
$997$	54.0000	1.71020	0.855099	−	0.518465i	$-0.173497\pi$
$997$	54.0000	1.71020	0.855099	+	0.518465i	$0.173497\pi$
$998$	−8.00000	−0.253236
$999$	−10.0000	−0.316386

Twists

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

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