LMFDB - Embedded newform 5610.2.a.q.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)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +4.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +1.00000 q^{20} -4.00000 q^{21} -1.00000 q^{22} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} -6.00000 q^{29} -1.00000 q^{30} +8.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} +6.00000 q^{41} +4.00000 q^{42} -4.00000 q^{43} +1.00000 q^{44} +1.00000 q^{45} +12.0000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{50} -1.00000 q^{51} +2.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} +1.00000 q^{55} +4.00000 q^{56} -4.00000 q^{57} +6.00000 q^{58} +12.0000 q^{59} +1.00000 q^{60} +2.00000 q^{61} -8.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -1.00000 q^{66} +8.00000 q^{67} -1.00000 q^{68} +4.00000 q^{70} -12.0000 q^{71} -1.00000 q^{72} +2.00000 q^{73} +10.0000 q^{74} +1.00000 q^{75} -4.00000 q^{76} -4.00000 q^{77} -2.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -12.0000 q^{83} -4.00000 q^{84} -1.00000 q^{85} +4.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} -6.00000 q^{89} -1.00000 q^{90} -8.00000 q^{91} +8.00000 q^{93} -12.0000 q^{94} -4.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} -9.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−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	$0.410544\pi$
$14$	4.00000	1.06904
$15$	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	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	1.00000	0.223607
$21$	−4.00000	−0.872872
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	−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	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	−4.00000	−0.676123
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	0.648886
$39$	2.00000	0.320256
$40$	−1.00000	−0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	4.00000	0.617213
$43$	−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
$46$	0	0
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	4.00000	0.534522
$57$	−4.00000	−0.529813
$58$	6.00000	0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−1.00000	−0.123091
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−1.00000	−0.121268
$69$	0	0
$70$	4.00000	0.478091
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−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
$76$	−4.00000	−0.458831
$77$	−4.00000	−0.455842
$78$	−2.00000	−0.226455
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−4.00000	−0.436436
$85$	−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
$91$	−8.00000	−0.838628
$92$	0	0
$93$	8.00000	0.829561
$94$	−12.0000	−1.23771
$95$	−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	$0.467625\pi$
$98$	−9.00000	−0.909137
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	1.00000	0.0990148
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−2.00000	−0.196116
$105$	−4.00000	−0.390360
$106$	−6.00000	−0.582772
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	1.00000	0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.00000	−0.0953463
$111$	−10.0000	−0.949158
$112$	−4.00000	−0.377964
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	−6.00000	−0.557086
$117$	2.00000	0.184900
$118$	−12.0000	−1.10469
$119$	4.00000	0.366679
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	6.00000	0.541002
$124$	8.00000	0.718421
$125$	1.00000	0.0894427
$126$	4.00000	0.356348
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−2.00000	−0.175412
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	1.00000	0.0870388
$133$	16.0000	1.38738
$134$	−8.00000	−0.691095
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	−4.00000	−0.338062
$141$	12.0000	1.01058
$142$	12.0000	1.00702
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−2.00000	−0.165521
$147$	9.00000	0.742307
$148$	−10.0000	−0.821995
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−1.00000	−0.0816497
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	4.00000	0.324443
$153$	−1.00000	−0.0808452
$154$	4.00000	0.322329
$155$	8.00000	0.642575
$156$	2.00000	0.160128
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	−8.00000	−0.636446
$159$	6.00000	0.475831
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	6.00000	0.468521
$165$	1.00000	0.0778499
$166$	12.0000	0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	4.00000	0.308607
$169$	−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	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	6.00000	0.454859
$175$	−4.00000	−0.302372
$176$	1.00000	0.0753778
$177$	12.0000	0.901975
$178$	6.00000	0.449719
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	0.0745356
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	8.00000	0.592999
$183$	2.00000	0.147844
$184$	0	0
$185$	−10.0000	−0.735215
$186$	−8.00000	−0.586588
$187$	−1.00000	−0.0731272
$188$	12.0000	0.875190
$189$	−4.00000	−0.290957
$190$	4.00000	0.290191
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	1.00000	0.0721688
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−2.00000	−0.143592
$195$	2.00000	0.143223
$196$	9.00000	0.642857
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	−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
$201$	8.00000	0.564276
$202$	−6.00000	−0.422159
$203$	24.0000	1.68447
$204$	−1.00000	−0.0700140
$205$	6.00000	0.419058
$206$	−8.00000	−0.557386
$207$	0	0
$208$	2.00000	0.138675
$209$	−4.00000	−0.276686
$210$	4.00000	0.276026
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	6.00000	0.412082
$213$	−12.0000	−0.822226
$214$	0	0
$215$	−4.00000	−0.272798
$216$	−1.00000	−0.0680414
$217$	−32.0000	−2.17230
$218$	−2.00000	−0.135457
$219$	2.00000	0.135147
$220$	1.00000	0.0674200
$221$	−2.00000	−0.134535
$222$	10.0000	0.671156
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	4.00000	0.267261
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	−4.00000	−0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	−4.00000	−0.263181
$232$	6.00000	0.393919
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−2.00000	−0.130744
$235$	12.0000	0.782794
$236$	12.0000	0.781133
$237$	8.00000	0.519656
$238$	−4.00000	−0.259281
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	1.00000	0.0645497
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	9.00000	0.574989
$246$	−6.00000	−0.382546
$247$	−8.00000	−0.509028
$248$	−8.00000	−0.508001
$249$	−12.0000	−0.760469
$250$	−1.00000	−0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	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
$259$	40.0000	2.48548
$260$	2.00000	0.124035
$261$	−6.00000	−0.371391
$262$	−12.0000	−0.741362
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−1.00000	−0.0615457
$265$	6.00000	0.368577
$266$	−16.0000	−0.981023
$267$	−6.00000	−0.367194
$268$	8.00000	0.488678
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−1.00000	−0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.00000	−0.0606339
$273$	−8.00000	−0.484182
$274$	18.0000	1.08742
$275$	1.00000	0.0603023
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−20.0000	−1.19952
$279$	8.00000	0.478947
$280$	4.00000	0.239046
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	−12.0000	−0.714590
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	−12.0000	−0.712069
$285$	−4.00000	−0.236940
$286$	−2.00000	−0.118262
$287$	−24.0000	−1.41668
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	2.00000	0.117242
$292$	2.00000	0.117041
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−9.00000	−0.524891
$295$	12.0000	0.698667
$296$	10.0000	0.581238
$297$	1.00000	0.0580259
$298$	−6.00000	−0.347571
$299$	0	0
$300$	1.00000	0.0577350
$301$	16.0000	0.922225
$302$	−20.0000	−1.15087
$303$	6.00000	0.344691
$304$	−4.00000	−0.229416
$305$	2.00000	0.114520
$306$	1.00000	0.0571662
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	−4.00000	−0.227921
$309$	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	$0.237274\pi$
$314$	22.0000	1.24153
$315$	−4.00000	−0.225374
$316$	8.00000	0.450035
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−6.00000	−0.336463
$319$	−6.00000	−0.335936
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	−20.0000	−1.10770
$327$	2.00000	0.110600
$328$	−6.00000	−0.331295
$329$	−48.0000	−2.64633
$330$	−1.00000	−0.0550482
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−12.0000	−0.658586
$333$	−10.0000	−0.547997
$334$	0	0
$335$	8.00000	0.437087
$336$	−4.00000	−0.218218
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	9.00000	0.489535
$339$	18.0000	0.977626
$340$	−1.00000	−0.0542326
$341$	8.00000	0.433224
$342$	4.00000	0.216295
$343$	−8.00000	−0.431959
$344$	4.00000	0.215666
$345$	0	0
$346$	−6.00000	−0.322562
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−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	$0.255017\pi$
$350$	4.00000	0.213809
$351$	2.00000	0.106752
$352$	−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	$0.659008\pi$
$354$	−12.0000	−0.637793
$355$	−12.0000	−0.636894
$356$	−6.00000	−0.317999
$357$	4.00000	0.211702
$358$	12.0000	0.634220
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−26.0000	−1.36653
$363$	1.00000	0.0524864
$364$	−8.00000	−0.419314
$365$	2.00000	0.104685
$366$	−2.00000	−0.104542
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	0	0
$369$	6.00000	0.312348
$370$	10.0000	0.519875
$371$	−24.0000	−1.24602
$372$	8.00000	0.414781
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−12.0000	−0.618853
$377$	−12.0000	−0.618031
$378$	4.00000	0.205738
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	−4.00000	−0.205196
$381$	−16.0000	−0.819705
$382$	0	0
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	−1.00000	−0.0510310
$385$	−4.00000	−0.203859
$386$	−2.00000	−0.101797
$387$	−4.00000	−0.203331
$388$	2.00000	0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	−2.00000	−0.101274
$391$	0	0
$392$	−9.00000	−0.454569
$393$	12.0000	0.605320
$394$	−6.00000	−0.302276
$395$	8.00000	0.402524
$396$	1.00000	0.0502519
$397$	38.0000	1.90717	0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000	1.90717	0.953583	+	0.301131i	$0.0973643\pi$
$398$	16.0000	0.802008
$399$	16.0000	0.801002
$400$	1.00000	0.0500000
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	−8.00000	−0.399004
$403$	16.0000	0.797017
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−24.0000	−1.19110
$407$	−10.0000	−0.495682
$408$	1.00000	0.0495074
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	−6.00000	−0.296319
$411$	−18.0000	−0.887875
$412$	8.00000	0.394132
$413$	−48.0000	−2.36193
$414$	0	0
$415$	−12.0000	−0.589057
$416$	−2.00000	−0.0980581
$417$	20.0000	0.979404
$418$	4.00000	0.195646
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	−4.00000	−0.195180
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	−20.0000	−0.973585
$423$	12.0000	0.583460
$424$	−6.00000	−0.291386
$425$	−1.00000	−0.0485071
$426$	12.0000	0.581402
$427$	−8.00000	−0.387147
$428$	0	0
$429$	2.00000	0.0965609
$430$	4.00000	0.192897
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	32.0000	1.53605
$435$	−6.00000	−0.287678
$436$	2.00000	0.0957826
$437$	0	0
$438$	−2.00000	−0.0955637
$439$	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
$441$	9.00000	0.428571
$442$	2.00000	0.0951303
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	−10.0000	−0.474579
$445$	−6.00000	−0.284427
$446$	−8.00000	−0.378811
$447$	6.00000	0.283790
$448$	−4.00000	−0.188982
$449$	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
$451$	6.00000	0.282529
$452$	18.0000	0.846649
$453$	20.0000	0.939682
$454$	0	0
$455$	−8.00000	−0.375046
$456$	4.00000	0.187317
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−14.0000	−0.654177
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−42.0000	−1.95614	−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000	−1.95614	−0.978068	+	0.208288i	$0.933211\pi$
$462$	4.00000	0.186097
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−6.00000	−0.278543
$465$	8.00000	0.370991
$466$	−6.00000	−0.277945
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	2.00000	0.0924500
$469$	−32.0000	−1.47762
$470$	−12.0000	−0.553519
$471$	−22.0000	−1.01371
$472$	−12.0000	−0.552345
$473$	−4.00000	−0.183920
$474$	−8.00000	−0.367452
$475$	−4.00000	−0.183533
$476$	4.00000	0.183340
$477$	6.00000	0.274721
$478$	−24.0000	−1.09773
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	−1.00000	−0.0456435
$481$	−20.0000	−0.911922
$482$	10.0000	0.455488
$483$	0	0
$484$	1.00000	0.0454545
$485$	2.00000	0.0908153
$486$	−1.00000	−0.0453609
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	−2.00000	−0.0905357
$489$	20.0000	0.904431
$490$	−9.00000	−0.406579
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	6.00000	0.270501
$493$	6.00000	0.270226
$494$	8.00000	0.359937
$495$	1.00000	0.0449467
$496$	8.00000	0.359211
$497$	48.0000	2.15309
$498$	12.0000	0.537733
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−12.0000	−0.535586
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	4.00000	0.178174
$505$	6.00000	0.266996
$506$	0	0
$507$	−9.00000	−0.399704
$508$	−16.0000	−0.709885
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	1.00000	0.0442807
$511$	−8.00000	−0.353899
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	−6.00000	−0.264649
$515$	8.00000	0.352522
$516$	−4.00000	−0.176090
$517$	12.0000	0.527759
$518$	−40.0000	−1.75750
$519$	6.00000	0.263371
$520$	−2.00000	−0.0877058
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	6.00000	0.262613
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	12.0000	0.524222
$525$	−4.00000	−0.174574
$526$	24.0000	1.04645
$527$	−8.00000	−0.348485
$528$	1.00000	0.0435194
$529$	−23.0000	−1.00000
$530$	−6.00000	−0.260623
$531$	12.0000	0.520756
$532$	16.0000	0.693688
$533$	12.0000	0.519778
$534$	6.00000	0.259645
$535$	0	0
$536$	−8.00000	−0.345547
$537$	−12.0000	−0.517838
$538$	18.0000	0.776035
$539$	9.00000	0.387657
$540$	1.00000	0.0430331
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−20.0000	−0.859074
$543$	26.0000	1.11577
$544$	1.00000	0.0428746
$545$	2.00000	0.0856706
$546$	8.00000	0.342368
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−18.0000	−0.768922
$549$	2.00000	0.0853579
$550$	−1.00000	−0.0426401
$551$	24.0000	1.02243
$552$	0	0
$553$	−32.0000	−1.36078
$554$	22.0000	0.934690
$555$	−10.0000	−0.424476
$556$	20.0000	0.848189
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	−8.00000	−0.338667
$559$	−8.00000	−0.338364
$560$	−4.00000	−0.169031
$561$	−1.00000	−0.0422200
$562$	−6.00000	−0.253095
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	12.0000	0.505291
$565$	18.0000	0.757266
$566$	−20.0000	−0.840663
$567$	−4.00000	−0.167984
$568$	12.0000	0.503509
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	4.00000	0.167542
$571$	44.0000	1.84134	0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000	1.84134	0.920671	+	0.390339i	$0.127642\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	24.0000	1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	26.0000	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$577$	26.0000	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$578$	−1.00000	−0.0415945
$579$	2.00000	0.0831172
$580$	−6.00000	−0.249136
$581$	48.0000	1.99138
$582$	−2.00000	−0.0829027
$583$	6.00000	0.248495
$584$	−2.00000	−0.0827606
$585$	2.00000	0.0826898
$586$	6.00000	0.247858
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	9.00000	0.371154
$589$	−32.0000	−1.31854
$590$	−12.0000	−0.494032
$591$	6.00000	0.246807
$592$	−10.0000	−0.410997
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	−1.00000	−0.0410305
$595$	4.00000	0.163984
$596$	6.00000	0.245770
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	−1.00000	−0.0408248
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−16.0000	−0.652111
$603$	8.00000	0.325785
$604$	20.0000	0.813788
$605$	1.00000	0.0406558
$606$	−6.00000	−0.243733
$607$	20.0000	0.811775	0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000	0.811775	0.405887	+	0.913923i	$0.366962\pi$
$608$	4.00000	0.162221
$609$	24.0000	0.972529
$610$	−2.00000	−0.0809776
$611$	24.0000	0.970936
$612$	−1.00000	−0.0404226
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	−20.0000	−0.807134
$615$	6.00000	0.241943
$616$	4.00000	0.161165
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	−8.00000	−0.321807
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	12.0000	0.481156
$623$	24.0000	0.961540
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	−26.0000	−1.03917
$627$	−4.00000	−0.159745
$628$	−22.0000	−0.877896
$629$	10.0000	0.398726
$630$	4.00000	0.159364
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−8.00000	−0.318223
$633$	20.0000	0.794929
$634$	18.0000	0.714871
$635$	−16.0000	−0.634941
$636$	6.00000	0.237915
$637$	18.0000	0.713186
$638$	6.00000	0.237542
$639$	−12.0000	−0.474713
$640$	−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	$0.462194\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	−4.00000	−0.157378
$647$	36.0000	1.41531	0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000	1.41531	0.707653	+	0.706560i	$0.249754\pi$
$648$	−1.00000	−0.0392837
$649$	12.0000	0.471041
$650$	−2.00000	−0.0784465
$651$	−32.0000	−1.25418
$652$	20.0000	0.783260
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	−2.00000	−0.0782062
$655$	12.0000	0.468879
$656$	6.00000	0.234261
$657$	2.00000	0.0780274
$658$	48.0000	1.87123
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	1.00000	0.0389249
$661$	−34.0000	−1.32245	−0.661223	−	0.750189i	$-0.729962\pi$
$661$	−34.0000	−1.32245	−0.661223	+	0.750189i	$0.729962\pi$
$662$	−20.0000	−0.777322
$663$	−2.00000	−0.0776736
$664$	12.0000	0.465690
$665$	16.0000	0.620453
$666$	10.0000	0.387492
$667$	0	0
$668$	0	0
$669$	8.00000	0.309298
$670$	−8.00000	−0.309067
$671$	2.00000	0.0772091
$672$	4.00000	0.154303
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	22.0000	0.847408
$675$	1.00000	0.0384900
$676$	−9.00000	−0.346154
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	−18.0000	−0.691286
$679$	−8.00000	−0.307012
$680$	1.00000	0.0383482
$681$	0	0
$682$	−8.00000	−0.306336
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−4.00000	−0.152944
$685$	−18.0000	−0.687745
$686$	8.00000	0.305441
$687$	14.0000	0.534133
$688$	−4.00000	−0.152499
$689$	12.0000	0.457164
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	6.00000	0.228086
$693$	−4.00000	−0.151947
$694$	0	0
$695$	20.0000	0.758643
$696$	6.00000	0.227429
$697$	−6.00000	−0.227266
$698$	−26.0000	−0.984115
$699$	6.00000	0.226941
$700$	−4.00000	−0.151186
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	−2.00000	−0.0754851
$703$	40.0000	1.50863
$704$	1.00000	0.0376889
$705$	12.0000	0.451946
$706$	18.0000	0.677439
$707$	−24.0000	−0.902613
$708$	12.0000	0.450988
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	12.0000	0.450352
$711$	8.00000	0.300023
$712$	6.00000	0.224860
$713$	0	0
$714$	−4.00000	−0.149696
$715$	2.00000	0.0747958
$716$	−12.0000	−0.448461
$717$	24.0000	0.896296
$718$	0	0
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	1.00000	0.0372678
$721$	−32.0000	−1.19174
$722$	3.00000	0.111648
$723$	−10.0000	−0.371904
$724$	26.0000	0.966282
$725$	−6.00000	−0.222834
$726$	−1.00000	−0.0371135
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	−2.00000	−0.0740233
$731$	4.00000	0.147945
$732$	2.00000	0.0739221
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	−32.0000	−1.18114
$735$	9.00000	0.331970
$736$	0	0
$737$	8.00000	0.294684
$738$	−6.00000	−0.220863
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−10.0000	−0.367607
$741$	−8.00000	−0.293887
$742$	24.0000	0.881068
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−8.00000	−0.293294
$745$	6.00000	0.219823
$746$	22.0000	0.805477
$747$	−12.0000	−0.439057
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	12.0000	0.437595
$753$	12.0000	0.437304
$754$	12.0000	0.437014
$755$	20.0000	0.727875
$756$	−4.00000	−0.145479
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	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	$0.465315\pi$
$762$	16.0000	0.579619
$763$	−8.00000	−0.289619
$764$	0	0
$765$	−1.00000	−0.0361551
$766$	12.0000	0.433578
$767$	24.0000	0.866590
$768$	1.00000	0.0360844
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	4.00000	0.144150
$771$	6.00000	0.216085
$772$	2.00000	0.0719816
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	4.00000	0.143777
$775$	8.00000	0.287368
$776$	−2.00000	−0.0717958
$777$	40.0000	1.43499
$778$	−6.00000	−0.215110
$779$	−24.0000	−0.859889
$780$	2.00000	0.0716115
$781$	−12.0000	−0.429394
$782$	0	0
$783$	−6.00000	−0.214423
$784$	9.00000	0.321429
$785$	−22.0000	−0.785214
$786$	−12.0000	−0.428026
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	6.00000	0.213741
$789$	−24.0000	−0.854423
$790$	−8.00000	−0.284627
$791$	−72.0000	−2.56003
$792$	−1.00000	−0.0355335
$793$	4.00000	0.142044
$794$	−38.0000	−1.34857
$795$	6.00000	0.212798
$796$	−16.0000	−0.567105
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	−16.0000	−0.566394
$799$	−12.0000	−0.424529
$800$	−1.00000	−0.0353553
$801$	−6.00000	−0.212000
$802$	−6.00000	−0.211867
$803$	2.00000	0.0705785
$804$	8.00000	0.282138
$805$	0	0
$806$	−16.0000	−0.563576
$807$	−18.0000	−0.633630
$808$	−6.00000	−0.211079
$809$	−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
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	24.0000	0.842235
$813$	20.0000	0.701431
$814$	10.0000	0.350500
$815$	20.0000	0.700569
$816$	−1.00000	−0.0350070
$817$	16.0000	0.559769
$818$	−26.0000	−0.909069
$819$	−8.00000	−0.279543
$820$	6.00000	0.209529
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	18.0000	0.627822
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	−8.00000	−0.278693
$825$	1.00000	0.0348155
$826$	48.0000	1.67013
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	0	0
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	12.0000	0.416526
$831$	−22.0000	−0.763172
$832$	2.00000	0.0693375
$833$	−9.00000	−0.311832
$834$	−20.0000	−0.692543
$835$	0	0
$836$	−4.00000	−0.138343
$837$	8.00000	0.276520
$838$	12.0000	0.414533
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	4.00000	0.138013
$841$	7.00000	0.241379
$842$	34.0000	1.17172
$843$	6.00000	0.206651
$844$	20.0000	0.688428
$845$	−9.00000	−0.309609
$846$	−12.0000	−0.412568
$847$	−4.00000	−0.137442
$848$	6.00000	0.206041
$849$	20.0000	0.686398
$850$	1.00000	0.0342997
$851$	0	0
$852$	−12.0000	−0.411113
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	8.00000	0.273754
$855$	−4.00000	−0.136797
$856$	0	0
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	−2.00000	−0.0682789
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	−4.00000	−0.136399
$861$	−24.0000	−0.817918
$862$	24.0000	0.817443
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	−1.00000	−0.0340207
$865$	6.00000	0.204006
$866$	−2.00000	−0.0679628
$867$	1.00000	0.0339618
$868$	−32.0000	−1.08615
$869$	8.00000	0.271381
$870$	6.00000	0.203419
$871$	16.0000	0.542139
$872$	−2.00000	−0.0677285
$873$	2.00000	0.0676897
$874$	0	0
$875$	−4.00000	−0.135225
$876$	2.00000	0.0675737
$877$	−22.0000	−0.742887	−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000	−0.742887	−0.371444	+	0.928456i	$0.621137\pi$
$878$	−8.00000	−0.269987
$879$	−6.00000	−0.202375
$880$	1.00000	0.0337100
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	−9.00000	−0.303046
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	−2.00000	−0.0672673
$885$	12.0000	0.403376
$886$	12.0000	0.403148
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	10.0000	0.335578
$889$	64.0000	2.14649
$890$	6.00000	0.201120
$891$	1.00000	0.0335013
$892$	8.00000	0.267860
$893$	−48.0000	−1.60626
$894$	−6.00000	−0.200670
$895$	−12.0000	−0.401116
$896$	4.00000	0.133631
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−48.0000	−1.60089
$900$	1.00000	0.0333333
$901$	−6.00000	−0.199889
$902$	−6.00000	−0.199778
$903$	16.0000	0.532447
$904$	−18.0000	−0.598671
$905$	26.0000	0.864269
$906$	−20.0000	−0.664455
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	0	0
$909$	6.00000	0.199007
$910$	8.00000	0.265197
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−4.00000	−0.132453
$913$	−12.0000	−0.397142
$914$	10.0000	0.330771
$915$	2.00000	0.0661180
$916$	14.0000	0.462573
$917$	−48.0000	−1.58510
$918$	1.00000	0.0330049
$919$	−52.0000	−1.71532	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000	−1.71532	−0.857661	+	0.514216i	$0.828083\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	42.0000	1.38320
$923$	−24.0000	−0.789970
$924$	−4.00000	−0.131590
$925$	−10.0000	−0.328798
$926$	−8.00000	−0.262896
$927$	8.00000	0.262754
$928$	6.00000	0.196960
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	−8.00000	−0.262330
$931$	−36.0000	−1.17985
$932$	6.00000	0.196537
$933$	−12.0000	−0.392862
$934$	36.0000	1.17796
$935$	−1.00000	−0.0327035
$936$	−2.00000	−0.0653720
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	32.0000	1.04484
$939$	26.0000	0.848478
$940$	12.0000	0.391397
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	22.0000	0.716799
$943$	0	0
$944$	12.0000	0.390567
$945$	−4.00000	−0.130120
$946$	4.00000	0.130051
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	8.00000	0.259828
$949$	4.00000	0.129845
$950$	4.00000	0.129777
$951$	−18.0000	−0.583690
$952$	−4.00000	−0.129641
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	24.0000	0.776215
$957$	−6.00000	−0.193952
$958$	−24.0000	−0.775405
$959$	72.0000	2.32500
$960$	1.00000	0.0322749
$961$	33.0000	1.06452
$962$	20.0000	0.644826
$963$	0	0
$964$	−10.0000	−0.322078
$965$	2.00000	0.0643823
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−1.00000	−0.0321412
$969$	4.00000	0.128499
$970$	−2.00000	−0.0642161
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	1.00000	0.0320750
$973$	−80.0000	−2.56468
$974$	−8.00000	−0.256337
$975$	2.00000	0.0640513
$976$	2.00000	0.0640184
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−20.0000	−0.639529
$979$	−6.00000	−0.191761
$980$	9.00000	0.287494
$981$	2.00000	0.0638551
$982$	0	0
$983$	−48.0000	−1.53096	−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000	−1.53096	−0.765481	+	0.643458i	$0.777499\pi$
$984$	−6.00000	−0.191273
$985$	6.00000	0.191176
$986$	−6.00000	−0.191079
$987$	−48.0000	−1.52786
$988$	−8.00000	−0.254514
$989$	0	0
$990$	−1.00000	−0.0317821
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	−8.00000	−0.254000
$993$	20.0000	0.634681
$994$	−48.0000	−1.52247
$995$	−16.0000	−0.507234
$996$	−12.0000	−0.380235
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−32.0000	−1.01294
$999$	−10.0000	−0.316386

Twists

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

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