LMFDB - Embedded newform 6018.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$2$
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	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{10} -2.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +2.00000 q^{14} +4.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} -4.00000 q^{20} +2.00000 q^{21} +2.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +11.0000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} -4.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} -1.00000 q^{34} +8.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +4.00000 q^{38} -2.00000 q^{39} +4.00000 q^{40} -10.0000 q^{41} -2.00000 q^{42} +4.00000 q^{43} -2.00000 q^{44} -4.00000 q^{45} +8.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -11.0000 q^{50} -1.00000 q^{51} +2.00000 q^{52} -2.00000 q^{53} +1.00000 q^{54} +8.00000 q^{55} +2.00000 q^{56} +4.00000 q^{57} -1.00000 q^{59} +4.00000 q^{60} -10.0000 q^{61} +4.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -8.00000 q^{65} -2.00000 q^{66} +8.00000 q^{67} +1.00000 q^{68} +8.00000 q^{69} -8.00000 q^{70} +6.00000 q^{71} -1.00000 q^{72} -16.0000 q^{73} +2.00000 q^{74} -11.0000 q^{75} -4.00000 q^{76} +4.00000 q^{77} +2.00000 q^{78} +10.0000 q^{79} -4.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -12.0000 q^{83} +2.00000 q^{84} -4.00000 q^{85} -4.00000 q^{86} +2.00000 q^{88} -14.0000 q^{89} +4.00000 q^{90} -4.00000 q^{91} -8.00000 q^{92} +4.00000 q^{93} +8.00000 q^{94} +16.0000 q^{95} +1.00000 q^{96} -16.0000 q^{97} +3.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
$5$	−4.00000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−4.00000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.00000	1.26491
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−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	$0.410544\pi$
$14$	2.00000	0.534522
$15$	4.00000	1.03280
$16$	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	$0.651732\pi$
$20$	−4.00000	−0.894427
$21$	2.00000	0.436436
$22$	2.00000	0.426401
$23$	−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
$25$	11.0000	2.20000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−4.00000	−0.730297
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	−1.00000	−0.171499
$35$	8.00000	1.35225
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	4.00000	0.648886
$39$	−2.00000	−0.320256
$40$	4.00000	0.632456
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	−2.00000	−0.308607
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−0.301511
$45$	−4.00000	−0.596285
$46$	8.00000	1.17954
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	−11.0000	−1.55563
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	1.00000	0.136083
$55$	8.00000	1.07872
$56$	2.00000	0.267261
$57$	4.00000	0.529813
$58$	0	0
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	4.00000	0.516398
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	4.00000	0.508001
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	−8.00000	−0.992278
$66$	−2.00000	−0.246183
$67$	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
$69$	8.00000	0.963087
$70$	−8.00000	−0.956183
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−1.00000	−0.117851
$73$	−16.0000	−1.87266	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000	−1.87266	−0.936329	+	0.351123i	$0.885800\pi$
$74$	2.00000	0.232495
$75$	−11.0000	−1.27017
$76$	−4.00000	−0.458831
$77$	4.00000	0.455842
$78$	2.00000	0.226455
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	2.00000	0.218218
$85$	−4.00000	−0.433861
$86$	−4.00000	−0.431331
$87$	0	0
$88$	2.00000	0.213201
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	4.00000	0.421637
$91$	−4.00000	−0.419314
$92$	−8.00000	−0.834058
$93$	4.00000	0.414781
$94$	8.00000	0.825137
$95$	16.0000	1.64157
$96$	1.00000	0.102062
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	3.00000	0.303046
$99$	−2.00000	−0.201008
$100$	11.0000	1.10000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	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
$105$	−8.00000	−0.780720
$106$	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	$0.658969\pi$
$110$	−8.00000	−0.762770
$111$	2.00000	0.189832
$112$	−2.00000	−0.188982
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−4.00000	−0.374634
$115$	32.0000	2.98402
$116$	0	0
$117$	2.00000	0.184900
$118$	1.00000	0.0920575
$119$	−2.00000	−0.183340
$120$	−4.00000	−0.365148
$121$	−7.00000	−0.636364
$122$	10.0000	0.905357
$123$	10.0000	0.901670
$124$	−4.00000	−0.359211
$125$	−24.0000	−2.14663
$126$	2.00000	0.178174
$127$	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
$130$	8.00000	0.701646
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	2.00000	0.174078
$133$	8.00000	0.693688
$134$	−8.00000	−0.691095
$135$	4.00000	0.344265
$136$	−1.00000	−0.0857493
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	−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	$0.669953\pi$
$140$	8.00000	0.676123
$141$	8.00000	0.673722
$142$	−6.00000	−0.503509
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	0	0
$146$	16.0000	1.32417
$147$	3.00000	0.247436
$148$	−2.00000	−0.164399
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	11.0000	0.898146
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	4.00000	0.324443
$153$	1.00000	0.0808452
$154$	−4.00000	−0.322329
$155$	16.0000	1.28515
$156$	−2.00000	−0.160128
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−10.0000	−0.795557
$159$	2.00000	0.158610
$160$	4.00000	0.316228
$161$	16.0000	1.26098
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−10.0000	−0.780869
$165$	−8.00000	−0.622799
$166$	12.0000	0.931381
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	−2.00000	−0.154303
$169$	−9.00000	−0.692308
$170$	4.00000	0.306786
$171$	−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	$0.426753\pi$
$174$	0	0
$175$	−22.0000	−1.66304
$176$	−2.00000	−0.150756
$177$	1.00000	0.0751646
$178$	14.0000	1.04934
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	−4.00000	−0.298142
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	4.00000	0.296500
$183$	10.0000	0.739221
$184$	8.00000	0.589768
$185$	8.00000	0.588172
$186$	−4.00000	−0.293294
$187$	−2.00000	−0.146254
$188$	−8.00000	−0.583460
$189$	2.00000	0.145479
$190$	−16.0000	−1.16076
$191$	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	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	16.0000	1.14873
$195$	8.00000	0.572892
$196$	−3.00000	−0.214286
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	2.00000	0.142134
$199$	22.0000	1.55954	0.779769	−	0.626067i	$-0.215336\pi$
$199$	22.0000	1.55954	0.779769	+	0.626067i	$0.215336\pi$
$200$	−11.0000	−0.777817
$201$	−8.00000	−0.564276
$202$	10.0000	0.703598
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	40.0000	2.79372
$206$	8.00000	0.557386
$207$	−8.00000	−0.556038
$208$	2.00000	0.138675
$209$	8.00000	0.553372
$210$	8.00000	0.552052
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	−2.00000	−0.137361
$213$	−6.00000	−0.411113
$214$	4.00000	0.273434
$215$	−16.0000	−1.09119
$216$	1.00000	0.0680414
$217$	8.00000	0.543075
$218$	10.0000	0.677285
$219$	16.0000	1.08118
$220$	8.00000	0.539360
$221$	2.00000	0.134535
$222$	−2.00000	−0.134231
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	2.00000	0.133631
$225$	11.0000	0.733333
$226$	0	0
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	4.00000	0.264906
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	−32.0000	−2.11002
$231$	−4.00000	−0.263181
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	−2.00000	−0.130744
$235$	32.0000	2.08745
$236$	−1.00000	−0.0650945
$237$	−10.0000	−0.649570
$238$	2.00000	0.129641
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	4.00000	0.258199
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	7.00000	0.449977
$243$	−1.00000	−0.0641500
$244$	−10.0000	−0.640184
$245$	12.0000	0.766652
$246$	−10.0000	−0.637577
$247$	−8.00000	−0.509028
$248$	4.00000	0.254000
$249$	12.0000	0.760469
$250$	24.0000	1.51789
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	−2.00000	−0.125988
$253$	16.0000	1.00591
$254$	−12.0000	−0.752947
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	4.00000	0.249029
$259$	4.00000	0.248548
$260$	−8.00000	−0.496139
$261$	0	0
$262$	−6.00000	−0.370681
$263$	4.00000	0.246651	0.123325	−	0.992366i	$-0.460644\pi$
$263$	4.00000	0.246651	0.123325	+	0.992366i	$0.460644\pi$
$264$	−2.00000	−0.123091
$265$	8.00000	0.491436
$266$	−8.00000	−0.490511
$267$	14.0000	0.856786
$268$	8.00000	0.488678
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	−4.00000	−0.243432
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	1.00000	0.0606339
$273$	4.00000	0.242091
$274$	−6.00000	−0.362473
$275$	−22.0000	−1.32665
$276$	8.00000	0.481543
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	12.0000	0.719712
$279$	−4.00000	−0.239474
$280$	−8.00000	−0.478091
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	−8.00000	−0.476393
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	6.00000	0.356034
$285$	−16.0000	−0.947758
$286$	4.00000	0.236525
$287$	20.0000	1.18056
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	16.0000	0.937937
$292$	−16.0000	−0.936329
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	−3.00000	−0.174964
$295$	4.00000	0.232889
$296$	2.00000	0.116248
$297$	2.00000	0.116052
$298$	22.0000	1.27443
$299$	−16.0000	−0.925304
$300$	−11.0000	−0.635085
$301$	−8.00000	−0.461112
$302$	−8.00000	−0.460348
$303$	10.0000	0.574485
$304$	−4.00000	−0.229416
$305$	40.0000	2.29039
$306$	−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
$310$	−16.0000	−0.908739
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	2.00000	0.113228
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	2.00000	0.112867
$315$	8.00000	0.450749
$316$	10.0000	0.562544
$317$	4.00000	0.224662	0.112331	−	0.993671i	$-0.464168\pi$
$317$	4.00000	0.224662	0.112331	+	0.993671i	$0.464168\pi$
$318$	−2.00000	−0.112154
$319$	0	0
$320$	−4.00000	−0.223607
$321$	4.00000	0.223258
$322$	−16.0000	−0.891645
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	22.0000	1.22034
$326$	4.00000	0.221540
$327$	10.0000	0.553001
$328$	10.0000	0.552158
$329$	16.0000	0.882109
$330$	8.00000	0.440386
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−12.0000	−0.658586
$333$	−2.00000	−0.109599
$334$	2.00000	0.109435
$335$	−32.0000	−1.74835
$336$	2.00000	0.109109
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	−4.00000	−0.216930
$341$	8.00000	0.433224
$342$	4.00000	0.216295
$343$	20.0000	1.07990
$344$	−4.00000	−0.215666
$345$	−32.0000	−1.72282
$346$	−6.00000	−0.322562
$347$	−10.0000	−0.536828	−0.268414	−	0.963304i	$-0.586500\pi$
$347$	−10.0000	−0.536828	−0.268414	+	0.963304i	$0.586500\pi$
$348$	0	0
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	22.0000	1.17595
$351$	−2.00000	−0.106752
$352$	2.00000	0.106600
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	−1.00000	−0.0531494
$355$	−24.0000	−1.27379
$356$	−14.0000	−0.741999
$357$	2.00000	0.105851
$358$	16.0000	0.845626
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	4.00000	0.210819
$361$	−3.00000	−0.157895
$362$	−16.0000	−0.840941
$363$	7.00000	0.367405
$364$	−4.00000	−0.209657
$365$	64.0000	3.34991
$366$	−10.0000	−0.522708
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−8.00000	−0.417029
$369$	−10.0000	−0.520579
$370$	−8.00000	−0.415900
$371$	4.00000	0.207670
$372$	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	$0.549645\pi$
$374$	2.00000	0.103418
$375$	24.0000	1.23935
$376$	8.00000	0.412568
$377$	0	0
$378$	−2.00000	−0.102869
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	16.0000	0.820783
$381$	−12.0000	−0.614779
$382$	0	0
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	1.00000	0.0510310
$385$	−16.0000	−0.815436
$386$	2.00000	0.101797
$387$	4.00000	0.203331
$388$	−16.0000	−0.812277
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	−8.00000	−0.405096
$391$	−8.00000	−0.404577
$392$	3.00000	0.151523
$393$	−6.00000	−0.302660
$394$	12.0000	0.604551
$395$	−40.0000	−2.01262
$396$	−2.00000	−0.100504
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−22.0000	−1.10276
$399$	−8.00000	−0.400501
$400$	11.0000	0.550000
$401$	−24.0000	−1.19850	−0.599251	−	0.800561i	$-0.704535\pi$
$401$	−24.0000	−1.19850	−0.599251	+	0.800561i	$0.704535\pi$
$402$	8.00000	0.399004
$403$	−8.00000	−0.398508
$404$	−10.0000	−0.497519
$405$	−4.00000	−0.198762
$406$	0	0
$407$	4.00000	0.198273
$408$	1.00000	0.0495074
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	−40.0000	−1.97546
$411$	−6.00000	−0.295958
$412$	−8.00000	−0.394132
$413$	2.00000	0.0984136
$414$	8.00000	0.393179
$415$	48.0000	2.35623
$416$	−2.00000	−0.0980581
$417$	12.0000	0.587643
$418$	−8.00000	−0.391293
$419$	−34.0000	−1.66101	−0.830504	−	0.557012i	$-0.811948\pi$
$419$	−34.0000	−1.66101	−0.830504	+	0.557012i	$0.811948\pi$
$420$	−8.00000	−0.390360
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	14.0000	0.681509
$423$	−8.00000	−0.388973
$424$	2.00000	0.0971286
$425$	11.0000	0.533578
$426$	6.00000	0.290701
$427$	20.0000	0.967868
$428$	−4.00000	−0.193347
$429$	4.00000	0.193122
$430$	16.0000	0.771589
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	−1.00000	−0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	−10.0000	−0.478913
$437$	32.0000	1.53077
$438$	−16.0000	−0.764510
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	−8.00000	−0.381385
$441$	−3.00000	−0.142857
$442$	−2.00000	−0.0951303
$443$	28.0000	1.33032	0.665160	−	0.746701i	$-0.268363\pi$
$443$	28.0000	1.33032	0.665160	+	0.746701i	$0.268363\pi$
$444$	2.00000	0.0949158
$445$	56.0000	2.65465
$446$	−8.00000	−0.378811
$447$	22.0000	1.04056
$448$	−2.00000	−0.0944911
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	−11.0000	−0.518545
$451$	20.0000	0.941763
$452$	0	0
$453$	−8.00000	−0.375873
$454$	−2.00000	−0.0938647
$455$	16.0000	0.750092
$456$	−4.00000	−0.187317
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	10.0000	0.467269
$459$	−1.00000	−0.0466760
$460$	32.0000	1.49201
$461$	−34.0000	−1.58354	−0.791769	−	0.610821i	$-0.790840\pi$
$461$	−34.0000	−1.58354	−0.791769	+	0.610821i	$0.790840\pi$
$462$	4.00000	0.186097
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	0	0
$465$	−16.0000	−0.741982
$466$	0	0
$467$	−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
$469$	−16.0000	−0.738811
$470$	−32.0000	−1.47605
$471$	2.00000	0.0921551
$472$	1.00000	0.0460287
$473$	−8.00000	−0.367840
$474$	10.0000	0.459315
$475$	−44.0000	−2.01886
$476$	−2.00000	−0.0916698
$477$	−2.00000	−0.0915737
$478$	−24.0000	−1.09773
$479$	22.0000	1.00521	0.502603	−	0.864517i	$-0.332376\pi$
$479$	22.0000	1.00521	0.502603	+	0.864517i	$0.332376\pi$
$480$	−4.00000	−0.182574
$481$	−4.00000	−0.182384
$482$	−10.0000	−0.455488
$483$	−16.0000	−0.728025
$484$	−7.00000	−0.318182
$485$	64.0000	2.90609
$486$	1.00000	0.0453609
$487$	14.0000	0.634401	0.317200	−	0.948359i	$-0.397257\pi$
$487$	14.0000	0.634401	0.317200	+	0.948359i	$0.397257\pi$
$488$	10.0000	0.452679
$489$	4.00000	0.180886
$490$	−12.0000	−0.542105
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	10.0000	0.450835
$493$	0	0
$494$	8.00000	0.359937
$495$	8.00000	0.359573
$496$	−4.00000	−0.179605
$497$	−12.0000	−0.538274
$498$	−12.0000	−0.537733
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	−24.0000	−1.07331
$501$	2.00000	0.0893534
$502$	4.00000	0.178529
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	2.00000	0.0890871
$505$	40.0000	1.77998
$506$	−16.0000	−0.711287
$507$	9.00000	0.399704
$508$	12.0000	0.532414
$509$	34.0000	1.50702	0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000	1.50702	0.753512	+	0.657434i	$0.228358\pi$
$510$	−4.00000	−0.177123
$511$	32.0000	1.41560
$512$	−1.00000	−0.0441942
$513$	4.00000	0.176604
$514$	6.00000	0.264649
$515$	32.0000	1.41009
$516$	−4.00000	−0.176090
$517$	16.0000	0.703679
$518$	−4.00000	−0.175750
$519$	−6.00000	−0.263371
$520$	8.00000	0.350823
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	6.00000	0.262111
$525$	22.0000	0.960159
$526$	−4.00000	−0.174408
$527$	−4.00000	−0.174243
$528$	2.00000	0.0870388
$529$	41.0000	1.78261
$530$	−8.00000	−0.347498
$531$	−1.00000	−0.0433963
$532$	8.00000	0.346844
$533$	−20.0000	−0.866296
$534$	−14.0000	−0.605839
$535$	16.0000	0.691740
$536$	−8.00000	−0.345547
$537$	16.0000	0.690451
$538$	−6.00000	−0.258678
$539$	6.00000	0.258438
$540$	4.00000	0.172133
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−16.0000	−0.687259
$543$	−16.0000	−0.686626
$544$	−1.00000	−0.0428746
$545$	40.0000	1.71341
$546$	−4.00000	−0.171184
$547$	16.0000	0.684111	0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000	0.684111	0.342055	+	0.939680i	$0.388877\pi$
$548$	6.00000	0.256307
$549$	−10.0000	−0.426790
$550$	22.0000	0.938083
$551$	0	0
$552$	−8.00000	−0.340503
$553$	−20.0000	−0.850487
$554$	−8.00000	−0.339887
$555$	−8.00000	−0.339581
$556$	−12.0000	−0.508913
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	4.00000	0.169334
$559$	8.00000	0.338364
$560$	8.00000	0.338062
$561$	2.00000	0.0844401
$562$	−14.0000	−0.590554
$563$	−40.0000	−1.68580	−0.842900	−	0.538071i	$-0.819153\pi$
$563$	−40.0000	−1.68580	−0.842900	+	0.538071i	$0.819153\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	−6.00000	−0.252199
$567$	−2.00000	−0.0839921
$568$	−6.00000	−0.251754
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	16.0000	0.670166
$571$	2.00000	0.0836974	0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000	0.0836974	0.0418487	+	0.999124i	$0.486675\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	−20.0000	−0.834784
$575$	−88.0000	−3.66985
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−1.00000	−0.0415945
$579$	2.00000	0.0831172
$580$	0	0
$581$	24.0000	0.995688
$582$	−16.0000	−0.663221
$583$	4.00000	0.165663
$584$	16.0000	0.662085
$585$	−8.00000	−0.330759
$586$	−18.0000	−0.743573
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	3.00000	0.123718
$589$	16.0000	0.659269
$590$	−4.00000	−0.164677
$591$	12.0000	0.493614
$592$	−2.00000	−0.0821995
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	−2.00000	−0.0820610
$595$	8.00000	0.327968
$596$	−22.0000	−0.901155
$597$	−22.0000	−0.900400
$598$	16.0000	0.654289
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	11.0000	0.449073
$601$	28.0000	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$602$	8.00000	0.326056
$603$	8.00000	0.325785
$604$	8.00000	0.325515
$605$	28.0000	1.13836
$606$	−10.0000	−0.406222
$607$	46.0000	1.86708	0.933541	−	0.358470i	$-0.116702\pi$
$607$	46.0000	1.86708	0.933541	+	0.358470i	$0.116702\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	−40.0000	−1.61955
$611$	−16.0000	−0.647291
$612$	1.00000	0.0404226
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	−20.0000	−0.807134
$615$	−40.0000	−1.61296
$616$	−4.00000	−0.161165
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	−8.00000	−0.321807
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	16.0000	0.642575
$621$	8.00000	0.321029
$622$	18.0000	0.721734
$623$	28.0000	1.12180
$624$	−2.00000	−0.0800641
$625$	41.0000	1.64000
$626$	0	0
$627$	−8.00000	−0.319489
$628$	−2.00000	−0.0798087
$629$	−2.00000	−0.0797452
$630$	−8.00000	−0.318728
$631$	−28.0000	−1.11466	−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000	−1.11466	−0.557331	+	0.830290i	$0.688175\pi$
$632$	−10.0000	−0.397779
$633$	14.0000	0.556450
$634$	−4.00000	−0.158860
$635$	−48.0000	−1.90482
$636$	2.00000	0.0793052
$637$	−6.00000	−0.237729
$638$	0	0
$639$	6.00000	0.237356
$640$	4.00000	0.158114
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	−4.00000	−0.157867
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	16.0000	0.630488
$645$	16.0000	0.629999
$646$	4.00000	0.157378
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	−1.00000	−0.0392837
$649$	2.00000	0.0785069
$650$	−22.0000	−0.862911
$651$	−8.00000	−0.313545
$652$	−4.00000	−0.156652
$653$	28.0000	1.09572	0.547862	−	0.836569i	$-0.315442\pi$
$653$	28.0000	1.09572	0.547862	+	0.836569i	$0.315442\pi$
$654$	−10.0000	−0.391031
$655$	−24.0000	−0.937758
$656$	−10.0000	−0.390434
$657$	−16.0000	−0.624219
$658$	−16.0000	−0.623745
$659$	40.0000	1.55818	0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000	1.55818	0.779089	+	0.626913i	$0.215682\pi$
$660$	−8.00000	−0.311400
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	12.0000	0.466393
$663$	−2.00000	−0.0776736
$664$	12.0000	0.465690
$665$	−32.0000	−1.24091
$666$	2.00000	0.0774984
$667$	0	0
$668$	−2.00000	−0.0773823
$669$	−8.00000	−0.309298
$670$	32.0000	1.23627
$671$	20.0000	0.772091
$672$	−2.00000	−0.0771517
$673$	−12.0000	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$674$	4.00000	0.154074
$675$	−11.0000	−0.423390
$676$	−9.00000	−0.346154
$677$	−28.0000	−1.07613	−0.538064	−	0.842904i	$-0.680844\pi$
$677$	−28.0000	−1.07613	−0.538064	+	0.842904i	$0.680844\pi$
$678$	0	0
$679$	32.0000	1.22805
$680$	4.00000	0.153393
$681$	−2.00000	−0.0766402
$682$	−8.00000	−0.306336
$683$	38.0000	1.45403	0.727015	−	0.686622i	$-0.240907\pi$
$683$	38.0000	1.45403	0.727015	+	0.686622i	$0.240907\pi$
$684$	−4.00000	−0.152944
$685$	−24.0000	−0.916993
$686$	−20.0000	−0.763604
$687$	10.0000	0.381524
$688$	4.00000	0.152499
$689$	−4.00000	−0.152388
$690$	32.0000	1.21822
$691$	−34.0000	−1.29342	−0.646710	−	0.762736i	$-0.723856\pi$
$691$	−34.0000	−1.29342	−0.646710	+	0.762736i	$0.723856\pi$
$692$	6.00000	0.228086
$693$	4.00000	0.151947
$694$	10.0000	0.379595
$695$	48.0000	1.82074
$696$	0	0
$697$	−10.0000	−0.378777
$698$	14.0000	0.529908
$699$	0	0
$700$	−22.0000	−0.831522
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	2.00000	0.0754851
$703$	8.00000	0.301726
$704$	−2.00000	−0.0753778
$705$	−32.0000	−1.20519
$706$	10.0000	0.376355
$707$	20.0000	0.752177
$708$	1.00000	0.0375823
$709$	44.0000	1.65245	0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000	1.65245	0.826227	+	0.563337i	$0.190483\pi$
$710$	24.0000	0.900704
$711$	10.0000	0.375029
$712$	14.0000	0.524672
$713$	32.0000	1.19841
$714$	−2.00000	−0.0748481
$715$	16.0000	0.598366
$716$	−16.0000	−0.597948
$717$	−24.0000	−0.896296
$718$	4.00000	0.149279
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	−4.00000	−0.149071
$721$	16.0000	0.595871
$722$	3.00000	0.111648
$723$	−10.0000	−0.371904
$724$	16.0000	0.594635
$725$	0	0
$726$	−7.00000	−0.259794
$727$	52.0000	1.92857	0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000	1.92857	0.964287	+	0.264861i	$0.0853260\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	−64.0000	−2.36875
$731$	4.00000	0.147945
$732$	10.0000	0.369611
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	−8.00000	−0.295285
$735$	−12.0000	−0.442627
$736$	8.00000	0.294884
$737$	−16.0000	−0.589368
$738$	10.0000	0.368105
$739$	−24.0000	−0.882854	−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000	−0.882854	−0.441427	+	0.897297i	$0.645528\pi$
$740$	8.00000	0.294086
$741$	8.00000	0.293887
$742$	−4.00000	−0.146845
$743$	14.0000	0.513610	0.256805	−	0.966463i	$-0.417330\pi$
$743$	14.0000	0.513610	0.256805	+	0.966463i	$0.417330\pi$
$744$	−4.00000	−0.146647
$745$	88.0000	3.22407
$746$	6.00000	0.219676
$747$	−12.0000	−0.439057
$748$	−2.00000	−0.0731272
$749$	8.00000	0.292314
$750$	−24.0000	−0.876356
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	−8.00000	−0.291730
$753$	4.00000	0.145768
$754$	0	0
$755$	−32.0000	−1.16460
$756$	2.00000	0.0727393
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	4.00000	0.145287
$759$	−16.0000	−0.580763
$760$	−16.0000	−0.580381
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	12.0000	0.434714
$763$	20.0000	0.724049
$764$	0	0
$765$	−4.00000	−0.144620
$766$	−36.0000	−1.30073
$767$	−2.00000	−0.0722158
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	16.0000	0.576600
$771$	6.00000	0.216085
$772$	−2.00000	−0.0719816
$773$	26.0000	0.935155	0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000	0.935155	0.467578	+	0.883952i	$0.345127\pi$
$774$	−4.00000	−0.143777
$775$	−44.0000	−1.58053
$776$	16.0000	0.574367
$777$	−4.00000	−0.143499
$778$	−18.0000	−0.645331
$779$	40.0000	1.43315
$780$	8.00000	0.286446
$781$	−12.0000	−0.429394
$782$	8.00000	0.286079
$783$	0	0
$784$	−3.00000	−0.107143
$785$	8.00000	0.285532
$786$	6.00000	0.214013
$787$	24.0000	0.855508	0.427754	−	0.903895i	$-0.359305\pi$
$787$	24.0000	0.855508	0.427754	+	0.903895i	$0.359305\pi$
$788$	−12.0000	−0.427482
$789$	−4.00000	−0.142404
$790$	40.0000	1.42314
$791$	0	0
$792$	2.00000	0.0710669
$793$	−20.0000	−0.710221
$794$	22.0000	0.780751
$795$	−8.00000	−0.283731
$796$	22.0000	0.779769
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	8.00000	0.283197
$799$	−8.00000	−0.283020
$800$	−11.0000	−0.388909
$801$	−14.0000	−0.494666
$802$	24.0000	0.847469
$803$	32.0000	1.12926
$804$	−8.00000	−0.282138
$805$	−64.0000	−2.25570
$806$	8.00000	0.281788
$807$	−6.00000	−0.211210
$808$	10.0000	0.351799
$809$	−12.0000	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$810$	4.00000	0.140546
$811$	−14.0000	−0.491606	−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000	−0.491606	−0.245803	+	0.969320i	$0.579052\pi$
$812$	0	0
$813$	−16.0000	−0.561144
$814$	−4.00000	−0.140200
$815$	16.0000	0.560456
$816$	−1.00000	−0.0350070
$817$	−16.0000	−0.559769
$818$	−10.0000	−0.349642
$819$	−4.00000	−0.139771
$820$	40.0000	1.39686
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	6.00000	0.209274
$823$	−20.0000	−0.697156	−0.348578	−	0.937280i	$-0.613335\pi$
$823$	−20.0000	−0.697156	−0.348578	+	0.937280i	$0.613335\pi$
$824$	8.00000	0.278693
$825$	22.0000	0.765942
$826$	−2.00000	−0.0695889
$827$	20.0000	0.695468	0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000	0.695468	0.347734	+	0.937593i	$0.386951\pi$
$828$	−8.00000	−0.278019
$829$	−42.0000	−1.45872	−0.729360	−	0.684130i	$-0.760182\pi$
$829$	−42.0000	−1.45872	−0.729360	+	0.684130i	$0.760182\pi$
$830$	−48.0000	−1.66610
$831$	−8.00000	−0.277517
$832$	2.00000	0.0693375
$833$	−3.00000	−0.103944
$834$	−12.0000	−0.415526
$835$	8.00000	0.276851
$836$	8.00000	0.276686
$837$	4.00000	0.138260
$838$	34.0000	1.17451
$839$	28.0000	0.966667	0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000	0.966667	0.483334	+	0.875436i	$0.339426\pi$
$840$	8.00000	0.276026
$841$	−29.0000	−1.00000
$842$	26.0000	0.896019
$843$	−14.0000	−0.482186
$844$	−14.0000	−0.481900
$845$	36.0000	1.23844
$846$	8.00000	0.275046
$847$	14.0000	0.481046
$848$	−2.00000	−0.0686803
$849$	−6.00000	−0.205919
$850$	−11.0000	−0.377297
$851$	16.0000	0.548473
$852$	−6.00000	−0.205557
$853$	−44.0000	−1.50653	−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000	−1.50653	−0.753266	+	0.657716i	$0.771523\pi$
$854$	−20.0000	−0.684386
$855$	16.0000	0.547188
$856$	4.00000	0.136717
$857$	28.0000	0.956462	0.478231	−	0.878234i	$-0.341278\pi$
$857$	28.0000	0.956462	0.478231	+	0.878234i	$0.341278\pi$
$858$	−4.00000	−0.136558
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−16.0000	−0.545595
$861$	−20.0000	−0.681598
$862$	20.0000	0.681203
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	1.00000	0.0340207
$865$	−24.0000	−0.816024
$866$	2.00000	0.0679628
$867$	−1.00000	−0.0339618
$868$	8.00000	0.271538
$869$	−20.0000	−0.678454
$870$	0	0
$871$	16.0000	0.542139
$872$	10.0000	0.338643
$873$	−16.0000	−0.541518
$874$	−32.0000	−1.08242
$875$	48.0000	1.62270
$876$	16.0000	0.540590
$877$	−44.0000	−1.48577	−0.742887	−	0.669417i	$-0.766544\pi$
$877$	−44.0000	−1.48577	−0.742887	+	0.669417i	$0.766544\pi$
$878$	−10.0000	−0.337484
$879$	−18.0000	−0.607125
$880$	8.00000	0.269680
$881$	48.0000	1.61716	0.808581	−	0.588386i	$-0.200236\pi$
$881$	48.0000	1.61716	0.808581	+	0.588386i	$0.200236\pi$
$882$	3.00000	0.101015
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	2.00000	0.0672673
$885$	−4.00000	−0.134459
$886$	−28.0000	−0.940678
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	−2.00000	−0.0671156
$889$	−24.0000	−0.804934
$890$	−56.0000	−1.87712
$891$	−2.00000	−0.0670025
$892$	8.00000	0.267860
$893$	32.0000	1.07084
$894$	−22.0000	−0.735790
$895$	64.0000	2.13928
$896$	2.00000	0.0668153
$897$	16.0000	0.534224
$898$	14.0000	0.467186
$899$	0	0
$900$	11.0000	0.366667
$901$	−2.00000	−0.0666297
$902$	−20.0000	−0.665927
$903$	8.00000	0.266223
$904$	0	0
$905$	−64.0000	−2.12743
$906$	8.00000	0.265782
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	2.00000	0.0663723
$909$	−10.0000	−0.331679
$910$	−16.0000	−0.530395
$911$	42.0000	1.39152	0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000	1.39152	0.695761	+	0.718273i	$0.255067\pi$
$912$	4.00000	0.132453
$913$	24.0000	0.794284
$914$	−2.00000	−0.0661541
$915$	−40.0000	−1.32236
$916$	−10.0000	−0.330409
$917$	−12.0000	−0.396275
$918$	1.00000	0.0330049
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	−32.0000	−1.05501
$921$	−20.0000	−0.659022
$922$	34.0000	1.11973
$923$	12.0000	0.394985
$924$	−4.00000	−0.131590
$925$	−22.0000	−0.723356
$926$	−16.0000	−0.525793
$927$	−8.00000	−0.262754
$928$	0	0
$929$	−16.0000	−0.524943	−0.262471	−	0.964940i	$-0.584538\pi$
$929$	−16.0000	−0.524943	−0.262471	+	0.964940i	$0.584538\pi$
$930$	16.0000	0.524661
$931$	12.0000	0.393284
$932$	0	0
$933$	18.0000	0.589294
$934$	24.0000	0.785304
$935$	8.00000	0.261628
$936$	−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	$0.426559\pi$
$938$	16.0000	0.522419
$939$	0	0
$940$	32.0000	1.04372
$941$	−58.0000	−1.89075	−0.945373	−	0.325991i	$-0.894302\pi$
$941$	−58.0000	−1.89075	−0.945373	+	0.325991i	$0.894302\pi$
$942$	−2.00000	−0.0651635
$943$	80.0000	2.60516
$944$	−1.00000	−0.0325472
$945$	−8.00000	−0.260240
$946$	8.00000	0.260102
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	−10.0000	−0.324785
$949$	−32.0000	−1.03876
$950$	44.0000	1.42755
$951$	−4.00000	−0.129709
$952$	2.00000	0.0648204
$953$	−50.0000	−1.61966	−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000	−1.61966	−0.809829	+	0.586665i	$0.800440\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	24.0000	0.776215
$957$	0	0
$958$	−22.0000	−0.710788
$959$	−12.0000	−0.387500
$960$	4.00000	0.129099
$961$	−15.0000	−0.483871
$962$	4.00000	0.128965
$963$	−4.00000	−0.128898
$964$	10.0000	0.322078
$965$	8.00000	0.257529
$966$	16.0000	0.514792
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	7.00000	0.224989
$969$	4.00000	0.128499
$970$	−64.0000	−2.05492
$971$	−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
$973$	24.0000	0.769405
$974$	−14.0000	−0.448589
$975$	−22.0000	−0.704564
$976$	−10.0000	−0.320092
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−4.00000	−0.127906
$979$	28.0000	0.894884
$980$	12.0000	0.383326
$981$	−10.0000	−0.319275
$982$	12.0000	0.382935
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	−10.0000	−0.318788
$985$	48.0000	1.52941
$986$	0	0
$987$	−16.0000	−0.509286
$988$	−8.00000	−0.254514
$989$	−32.0000	−1.01754
$990$	−8.00000	−0.254257
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	4.00000	0.127000
$993$	12.0000	0.380808
$994$	12.0000	0.380617
$995$	−88.0000	−2.78979
$996$	12.0000	0.380235
$997$	16.0000	0.506725	0.253363	−	0.967371i	$-0.418463\pi$
$997$	16.0000	0.506725	0.253363	+	0.967371i	$0.418463\pi$
$998$	40.0000	1.26618
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.a.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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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