LMFDB - Embedded newform 4598.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
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	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +2.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} +2.00000 q^{12} +6.00000 q^{13} +4.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.00000 q^{20} +8.00000 q^{21} +8.00000 q^{23} +2.00000 q^{24} -1.00000 q^{25} +6.00000 q^{26} -4.00000 q^{27} +4.00000 q^{28} -6.00000 q^{29} -4.00000 q^{30} -10.0000 q^{31} +1.00000 q^{32} +4.00000 q^{34} -8.00000 q^{35} +1.00000 q^{36} +6.00000 q^{37} -1.00000 q^{38} +12.0000 q^{39} -2.00000 q^{40} -6.00000 q^{41} +8.00000 q^{42} +8.00000 q^{43} -2.00000 q^{45} +8.00000 q^{46} +2.00000 q^{48} +9.00000 q^{49} -1.00000 q^{50} +8.00000 q^{51} +6.00000 q^{52} +6.00000 q^{53} -4.00000 q^{54} +4.00000 q^{56} -2.00000 q^{57} -6.00000 q^{58} -14.0000 q^{59} -4.00000 q^{60} -12.0000 q^{61} -10.0000 q^{62} +4.00000 q^{63} +1.00000 q^{64} -12.0000 q^{65} +14.0000 q^{67} +4.00000 q^{68} +16.0000 q^{69} -8.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} +4.00000 q^{73} +6.00000 q^{74} -2.00000 q^{75} -1.00000 q^{76} +12.0000 q^{78} -2.00000 q^{80} -11.0000 q^{81} -6.00000 q^{82} +8.00000 q^{84} -8.00000 q^{85} +8.00000 q^{86} -12.0000 q^{87} -14.0000 q^{89} -2.00000 q^{90} +24.0000 q^{91} +8.00000 q^{92} -20.0000 q^{93} +2.00000 q^{95} +2.00000 q^{96} -2.00000 q^{97} +9.00000 q^{98} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	2.00000	0.816497
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	0	0
$11$	0	0
$12$	2.00000	0.577350
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	4.00000	1.06904
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.00000	−0.447214
$21$	8.00000	1.74574
$22$	0	0
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	2.00000	0.408248
$25$	−1.00000	−0.200000
$26$	6.00000	1.17670
$27$	−4.00000	−0.769800
$28$	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	$0.688081\pi$
$30$	−4.00000	−0.730297
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	−8.00000	−1.35225
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−1.00000	−0.162221
$39$	12.0000	1.92154
$40$	−2.00000	−0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	8.00000	1.23443
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	8.00000	1.17954
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	2.00000	0.288675
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	8.00000	1.12022
$52$	6.00000	0.832050
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	4.00000	0.534522
$57$	−2.00000	−0.264906
$58$	−6.00000	−0.787839
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	−4.00000	−0.516398
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−10.0000	−1.27000
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	−12.0000	−1.48842
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	4.00000	0.485071
$69$	16.0000	1.92617
$70$	−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
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	6.00000	0.697486
$75$	−2.00000	−0.230940
$76$	−1.00000	−0.114708
$77$	0	0
$78$	12.0000	1.35873
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−2.00000	−0.223607
$81$	−11.0000	−1.22222
$82$	−6.00000	−0.662589
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	8.00000	0.872872
$85$	−8.00000	−0.867722
$86$	8.00000	0.862662
$87$	−12.0000	−1.28654
$88$	0	0
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	−2.00000	−0.210819
$91$	24.0000	2.51588
$92$	8.00000	0.834058
$93$	−20.0000	−2.07390
$94$	0	0
$95$	2.00000	0.205196
$96$	2.00000	0.204124
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−8.00000	−0.796030	−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000	−0.796030	−0.398015	+	0.917379i	$0.630301\pi$
$102$	8.00000	0.792118
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	6.00000	0.588348
$105$	−16.0000	−1.56144
$106$	6.00000	0.582772
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−4.00000	−0.384900
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	0	0
$111$	12.0000	1.13899
$112$	4.00000	0.377964
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−2.00000	−0.187317
$115$	−16.0000	−1.49201
$116$	−6.00000	−0.557086
$117$	6.00000	0.554700
$118$	−14.0000	−1.28880
$119$	16.0000	1.46672
$120$	−4.00000	−0.365148
$121$	0	0
$122$	−12.0000	−1.08643
$123$	−12.0000	−1.08200
$124$	−10.0000	−0.898027
$125$	12.0000	1.07331
$126$	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
$129$	16.0000	1.40872
$130$	−12.0000	−1.05247
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	14.0000	1.20942
$135$	8.00000	0.688530
$136$	4.00000	0.342997
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	16.0000	1.36201
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−8.00000	−0.676123
$141$	0	0
$142$	6.00000	0.503509
$143$	0	0
$144$	1.00000	0.0833333
$145$	12.0000	0.996546
$146$	4.00000	0.331042
$147$	18.0000	1.48461
$148$	6.00000	0.493197
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	−2.00000	−0.163299
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.00000	−0.0811107
$153$	4.00000	0.323381
$154$	0	0
$155$	20.0000	1.60644
$156$	12.0000	0.960769
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	0	0
$159$	12.0000	0.951662
$160$	−2.00000	−0.158114
$161$	32.0000	2.52195
$162$	−11.0000	−0.864242
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	8.00000	0.617213
$169$	23.0000	1.76923
$170$	−8.00000	−0.613572
$171$	−1.00000	−0.0764719
$172$	8.00000	0.609994
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−12.0000	−0.909718
$175$	−4.00000	−0.302372
$176$	0	0
$177$	−28.0000	−2.10461
$178$	−14.0000	−1.04934
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	−2.00000	−0.149071
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	24.0000	1.77900
$183$	−24.0000	−1.77413
$184$	8.00000	0.589768
$185$	−12.0000	−0.882258
$186$	−20.0000	−1.46647
$187$	0	0
$188$	0	0
$189$	−16.0000	−1.16383
$190$	2.00000	0.145095
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	2.00000	0.144338
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−2.00000	−0.143592
$195$	−24.0000	−1.71868
$196$	9.00000	0.642857
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−1.00000	−0.0707107
$201$	28.0000	1.97497
$202$	−8.00000	−0.562878
$203$	−24.0000	−1.68447
$204$	8.00000	0.560112
$205$	12.0000	0.838116
$206$	14.0000	0.975426
$207$	8.00000	0.556038
$208$	6.00000	0.416025
$209$	0	0
$210$	−16.0000	−1.10410
$211$	−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
$213$	12.0000	0.822226
$214$	−4.00000	−0.273434
$215$	−16.0000	−1.09119
$216$	−4.00000	−0.272166
$217$	−40.0000	−2.71538
$218$	18.0000	1.21911
$219$	8.00000	0.540590
$220$	0	0
$221$	24.0000	1.61441
$222$	12.0000	0.805387
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	4.00000	0.267261
$225$	−1.00000	−0.0666667
$226$	6.00000	0.399114
$227$	−28.0000	−1.85843	−0.929213	−	0.369546i	$-0.879513\pi$
$227$	−28.0000	−1.85843	−0.929213	+	0.369546i	$0.879513\pi$
$228$	−2.00000	−0.132453
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−16.0000	−1.05501
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−8.00000	−0.524097	−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000	−0.524097	−0.262049	+	0.965055i	$0.584398\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	−14.0000	−0.911322
$237$	0	0
$238$	16.0000	1.03713
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	−4.00000	−0.258199
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	−12.0000	−0.768221
$245$	−18.0000	−1.14998
$246$	−12.0000	−0.765092
$247$	−6.00000	−0.381771
$248$	−10.0000	−0.635001
$249$	0	0
$250$	12.0000	0.758947
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	4.00000	0.251976
$253$	0	0
$254$	−16.0000	−1.00393
$255$	−16.0000	−1.00196
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	16.0000	0.996116
$259$	24.0000	1.49129
$260$	−12.0000	−0.744208
$261$	−6.00000	−0.371391
$262$	8.00000	0.494242
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	−12.0000	−0.737154
$266$	−4.00000	−0.245256
$267$	−28.0000	−1.71357
$268$	14.0000	0.855186
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	8.00000	0.486864
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	4.00000	0.242536
$273$	48.0000	2.90509
$274$	6.00000	0.362473
$275$	0	0
$276$	16.0000	0.963087
$277$	24.0000	1.44202	0.721010	−	0.692925i	$-0.243678\pi$
$277$	24.0000	1.44202	0.721010	+	0.692925i	$0.243678\pi$
$278$	4.00000	0.239904
$279$	−10.0000	−0.598684
$280$	−8.00000	−0.478091
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	6.00000	0.356034
$285$	4.00000	0.236940
$286$	0	0
$287$	−24.0000	−1.41668
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	12.0000	0.704664
$291$	−4.00000	−0.234484
$292$	4.00000	0.234082
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	18.0000	1.04978
$295$	28.0000	1.63022
$296$	6.00000	0.348743
$297$	0	0
$298$	0	0
$299$	48.0000	2.77591
$300$	−2.00000	−0.115470
$301$	32.0000	1.84445
$302$	−8.00000	−0.460348
$303$	−16.0000	−0.919176
$304$	−1.00000	−0.0573539
$305$	24.0000	1.37424
$306$	4.00000	0.228665
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	28.0000	1.59286
$310$	20.0000	1.13592
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	12.0000	0.679366
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	2.00000	0.112867
$315$	−8.00000	−0.450749
$316$	0	0
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	12.0000	0.672927
$319$	0	0
$320$	−2.00000	−0.111803
$321$	−8.00000	−0.446516
$322$	32.0000	1.78329
$323$	−4.00000	−0.222566
$324$	−11.0000	−0.611111
$325$	−6.00000	−0.332820
$326$	12.0000	0.664619
$327$	36.0000	1.99080
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	−26.0000	−1.42909	−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000	−1.42909	−0.714545	+	0.699590i	$0.753366\pi$
$332$	0	0
$333$	6.00000	0.328798
$334$	0	0
$335$	−28.0000	−1.52980
$336$	8.00000	0.436436
$337$	10.0000	0.544735	0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000	0.544735	0.272367	+	0.962193i	$0.412193\pi$
$338$	23.0000	1.25104
$339$	12.0000	0.651751
$340$	−8.00000	−0.433861
$341$	0	0
$342$	−1.00000	−0.0540738
$343$	8.00000	0.431959
$344$	8.00000	0.431331
$345$	−32.0000	−1.72282
$346$	−2.00000	−0.107521
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−12.0000	−0.643268
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	−4.00000	−0.213809
$351$	−24.0000	−1.28103
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	−28.0000	−1.48818
$355$	−12.0000	−0.636894
$356$	−14.0000	−0.741999
$357$	32.0000	1.69362
$358$	−6.00000	−0.317110
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−2.00000	−0.105409
$361$	1.00000	0.0526316
$362$	−10.0000	−0.525588
$363$	0	0
$364$	24.0000	1.25794
$365$	−8.00000	−0.418739
$366$	−24.0000	−1.25450
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	8.00000	0.417029
$369$	−6.00000	−0.312348
$370$	−12.0000	−0.623850
$371$	24.0000	1.24602
$372$	−20.0000	−1.03695
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	0	0
$375$	24.0000	1.23935
$376$	0	0
$377$	−36.0000	−1.85409
$378$	−16.0000	−0.822951
$379$	−34.0000	−1.74646	−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000	−1.74646	−0.873231	+	0.487306i	$0.837980\pi$
$380$	2.00000	0.102598
$381$	−32.0000	−1.63941
$382$	8.00000	0.409316
$383$	−30.0000	−1.53293	−0.766464	−	0.642287i	$-0.777986\pi$
$383$	−30.0000	−1.53293	−0.766464	+	0.642287i	$0.777986\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−22.0000	−1.11977
$387$	8.00000	0.406663
$388$	−2.00000	−0.101535
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−24.0000	−1.21529
$391$	32.0000	1.61831
$392$	9.00000	0.454569
$393$	16.0000	0.807093
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	4.00000	0.200502
$399$	−8.00000	−0.400501
$400$	−1.00000	−0.0500000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	28.0000	1.39651
$403$	−60.0000	−2.98881
$404$	−8.00000	−0.398015
$405$	22.0000	1.09319
$406$	−24.0000	−1.19110
$407$	0	0
$408$	8.00000	0.396059
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	12.0000	0.592638
$411$	12.0000	0.591916
$412$	14.0000	0.689730
$413$	−56.0000	−2.75558
$414$	8.00000	0.393179
$415$	0	0
$416$	6.00000	0.294174
$417$	8.00000	0.391762
$418$	0	0
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	−16.0000	−0.780720
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	6.00000	0.291386
$425$	−4.00000	−0.194029
$426$	12.0000	0.581402
$427$	−48.0000	−2.32288
$428$	−4.00000	−0.193347
$429$	0	0
$430$	−16.0000	−0.771589
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−4.00000	−0.192450
$433$	22.0000	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$434$	−40.0000	−1.92006
$435$	24.0000	1.15071
$436$	18.0000	0.862044
$437$	−8.00000	−0.382692
$438$	8.00000	0.382255
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	24.0000	1.14156
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	12.0000	0.569495
$445$	28.0000	1.32733
$446$	10.0000	0.473514
$447$	0	0
$448$	4.00000	0.188982
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	6.00000	0.282216
$453$	−16.0000	−0.751746
$454$	−28.0000	−1.31411
$455$	−48.0000	−2.25027
$456$	−2.00000	−0.0936586
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	10.0000	0.467269
$459$	−16.0000	−0.746816
$460$	−16.0000	−0.746004
$461$	−40.0000	−1.86299	−0.931493	−	0.363760i	$-0.881493\pi$
$461$	−40.0000	−1.86299	−0.931493	+	0.363760i	$0.881493\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−6.00000	−0.278543
$465$	40.0000	1.85496
$466$	−8.00000	−0.370593
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	6.00000	0.277350
$469$	56.0000	2.58584
$470$	0	0
$471$	4.00000	0.184310
$472$	−14.0000	−0.644402
$473$	0	0
$474$	0	0
$475$	1.00000	0.0458831
$476$	16.0000	0.733359
$477$	6.00000	0.274721
$478$	8.00000	0.365911
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	−4.00000	−0.182574
$481$	36.0000	1.64146
$482$	14.0000	0.637683
$483$	64.0000	2.91210
$484$	0	0
$485$	4.00000	0.181631
$486$	−10.0000	−0.453609
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	−12.0000	−0.543214
$489$	24.0000	1.08532
$490$	−18.0000	−0.813157
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	−12.0000	−0.541002
$493$	−24.0000	−1.08091
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−10.0000	−0.449013
$497$	24.0000	1.07655
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	−12.0000	−0.535586
$503$	−44.0000	−1.96186	−0.980932	−	0.194354i	$-0.937739\pi$
$503$	−44.0000	−1.96186	−0.980932	+	0.194354i	$0.937739\pi$
$504$	4.00000	0.178174
$505$	16.0000	0.711991
$506$	0	0
$507$	46.0000	2.04293
$508$	−16.0000	−0.709885
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	−16.0000	−0.708492
$511$	16.0000	0.707798
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	−22.0000	−0.970378
$515$	−28.0000	−1.23383
$516$	16.0000	0.704361
$517$	0	0
$518$	24.0000	1.05450
$519$	−4.00000	−0.175581
$520$	−12.0000	−0.526235
$521$	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
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	8.00000	0.349482
$525$	−8.00000	−0.349149
$526$	8.00000	0.348817
$527$	−40.0000	−1.74243
$528$	0	0
$529$	41.0000	1.78261
$530$	−12.0000	−0.521247
$531$	−14.0000	−0.607548
$532$	−4.00000	−0.173422
$533$	−36.0000	−1.55933
$534$	−28.0000	−1.21168
$535$	8.00000	0.345870
$536$	14.0000	0.604708
$537$	−12.0000	−0.517838
$538$	−18.0000	−0.776035
$539$	0	0
$540$	8.00000	0.344265
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	−16.0000	−0.687259
$543$	−20.0000	−0.858282
$544$	4.00000	0.171499
$545$	−36.0000	−1.54207
$546$	48.0000	2.05421
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	6.00000	0.256307
$549$	−12.0000	−0.512148
$550$	0	0
$551$	6.00000	0.255609
$552$	16.0000	0.681005
$553$	0	0
$554$	24.0000	1.01966
$555$	−24.0000	−1.01874
$556$	4.00000	0.169638
$557$	8.00000	0.338971	0.169485	−	0.985533i	$-0.445789\pi$
$557$	8.00000	0.338971	0.169485	+	0.985533i	$0.445789\pi$
$558$	−10.0000	−0.423334
$559$	48.0000	2.03018
$560$	−8.00000	−0.338062
$561$	0	0
$562$	6.00000	0.253095
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	−12.0000	−0.504844
$566$	−12.0000	−0.504398
$567$	−44.0000	−1.84783
$568$	6.00000	0.251754
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	4.00000	0.167542
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	0	0
$573$	16.0000	0.668410
$574$	−24.0000	−1.00174
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	10.0000	0.416305	0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000	0.416305	0.208153	+	0.978096i	$0.433255\pi$
$578$	−1.00000	−0.0415945
$579$	−44.0000	−1.82858
$580$	12.0000	0.498273
$581$	0	0
$582$	−4.00000	−0.165805
$583$	0	0
$584$	4.00000	0.165521
$585$	−12.0000	−0.496139
$586$	−6.00000	−0.247858
$587$	−16.0000	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$588$	18.0000	0.742307
$589$	10.0000	0.412043
$590$	28.0000	1.15274
$591$	24.0000	0.987228
$592$	6.00000	0.246598
$593$	8.00000	0.328521	0.164260	−	0.986417i	$-0.447476\pi$
$593$	8.00000	0.328521	0.164260	+	0.986417i	$0.447476\pi$
$594$	0	0
$595$	−32.0000	−1.31187
$596$	0	0
$597$	8.00000	0.327418
$598$	48.0000	1.96287
$599$	−18.0000	−0.735460	−0.367730	−	0.929933i	$-0.619865\pi$
$599$	−18.0000	−0.735460	−0.367730	+	0.929933i	$0.619865\pi$
$600$	−2.00000	−0.0816497
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	32.0000	1.30422
$603$	14.0000	0.570124
$604$	−8.00000	−0.325515
$605$	0	0
$606$	−16.0000	−0.649956
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	−1.00000	−0.0405554
$609$	−48.0000	−1.94506
$610$	24.0000	0.971732
$611$	0	0
$612$	4.00000	0.161690
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	−12.0000	−0.484281
$615$	24.0000	0.967773
$616$	0	0
$617$	26.0000	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$618$	28.0000	1.12633
$619$	24.0000	0.964641	0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000	0.964641	0.482321	+	0.875995i	$0.339794\pi$
$620$	20.0000	0.803219
$621$	−32.0000	−1.28412
$622$	−12.0000	−0.481156
$623$	−56.0000	−2.24359
$624$	12.0000	0.480384
$625$	−19.0000	−0.760000
$626$	14.0000	0.559553
$627$	0	0
$628$	2.00000	0.0798087
$629$	24.0000	0.956943
$630$	−8.00000	−0.318728
$631$	−36.0000	−1.43314	−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000	−1.43314	−0.716569	+	0.697517i	$0.754288\pi$
$632$	0	0
$633$	−40.0000	−1.58986
$634$	18.0000	0.714871
$635$	32.0000	1.26988
$636$	12.0000	0.475831
$637$	54.0000	2.13956
$638$	0	0
$639$	6.00000	0.237356
$640$	−2.00000	−0.0790569
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−8.00000	−0.315735
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	32.0000	1.26098
$645$	−32.0000	−1.26000
$646$	−4.00000	−0.157378
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	−11.0000	−0.432121
$649$	0	0
$650$	−6.00000	−0.235339
$651$	−80.0000	−3.13545
$652$	12.0000	0.469956
$653$	34.0000	1.33052	0.665261	−	0.746611i	$-0.268320\pi$
$653$	34.0000	1.33052	0.665261	+	0.746611i	$0.268320\pi$
$654$	36.0000	1.40771
$655$	−16.0000	−0.625172
$656$	−6.00000	−0.234261
$657$	4.00000	0.156055
$658$	0	0
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−26.0000	−1.01052
$663$	48.0000	1.86417
$664$	0	0
$665$	8.00000	0.310227
$666$	6.00000	0.232495
$667$	−48.0000	−1.85857
$668$	0	0
$669$	20.0000	0.773245
$670$	−28.0000	−1.08173
$671$	0	0
$672$	8.00000	0.308607
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	10.0000	0.385186
$675$	4.00000	0.153960
$676$	23.0000	0.884615
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	12.0000	0.460857
$679$	−8.00000	−0.307012
$680$	−8.00000	−0.306786
$681$	−56.0000	−2.14592
$682$	0	0
$683$	−14.0000	−0.535695	−0.267848	−	0.963461i	$-0.586312\pi$
$683$	−14.0000	−0.535695	−0.267848	+	0.963461i	$0.586312\pi$
$684$	−1.00000	−0.0382360
$685$	−12.0000	−0.458496
$686$	8.00000	0.305441
$687$	20.0000	0.763048
$688$	8.00000	0.304997
$689$	36.0000	1.37149
$690$	−32.0000	−1.21822
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	−2.00000	−0.0760286
$693$	0	0
$694$	12.0000	0.455514
$695$	−8.00000	−0.303457
$696$	−12.0000	−0.454859
$697$	−24.0000	−0.909065
$698$	0	0
$699$	−16.0000	−0.605176
$700$	−4.00000	−0.151186
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	−24.0000	−0.905822
$703$	−6.00000	−0.226294
$704$	0	0
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−32.0000	−1.20348
$708$	−28.0000	−1.05230
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	−12.0000	−0.450352
$711$	0	0
$712$	−14.0000	−0.524672
$713$	−80.0000	−2.99602
$714$	32.0000	1.19757
$715$	0	0
$716$	−6.00000	−0.224231
$717$	16.0000	0.597531
$718$	0	0
$719$	−28.0000	−1.04422	−0.522112	−	0.852877i	$-0.674856\pi$
$719$	−28.0000	−1.04422	−0.522112	+	0.852877i	$0.674856\pi$
$720$	−2.00000	−0.0745356
$721$	56.0000	2.08555
$722$	1.00000	0.0372161
$723$	28.0000	1.04133
$724$	−10.0000	−0.371647
$725$	6.00000	0.222834
$726$	0	0
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	24.0000	0.889499
$729$	13.0000	0.481481
$730$	−8.00000	−0.296093
$731$	32.0000	1.18356
$732$	−24.0000	−0.887066
$733$	−36.0000	−1.32969	−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000	−1.32969	−0.664845	+	0.746981i	$0.731502\pi$
$734$	24.0000	0.885856
$735$	−36.0000	−1.32788
$736$	8.00000	0.294884
$737$	0	0
$738$	−6.00000	−0.220863
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	−12.0000	−0.441129
$741$	−12.0000	−0.440831
$742$	24.0000	0.881068
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	−20.0000	−0.733236
$745$	0	0
$746$	−26.0000	−0.951928
$747$	0	0
$748$	0	0
$749$	−16.0000	−0.584627
$750$	24.0000	0.876356
$751$	6.00000	0.218943	0.109472	−	0.993990i	$-0.465084\pi$
$751$	6.00000	0.218943	0.109472	+	0.993990i	$0.465084\pi$
$752$	0	0
$753$	−24.0000	−0.874609
$754$	−36.0000	−1.31104
$755$	16.0000	0.582300
$756$	−16.0000	−0.581914
$757$	30.0000	1.09037	0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000	1.09037	0.545184	+	0.838316i	$0.316460\pi$
$758$	−34.0000	−1.23494
$759$	0	0
$760$	2.00000	0.0725476
$761$	20.0000	0.724999	0.362500	−	0.931984i	$-0.381923\pi$
$761$	20.0000	0.724999	0.362500	+	0.931984i	$0.381923\pi$
$762$	−32.0000	−1.15924
$763$	72.0000	2.60658
$764$	8.00000	0.289430
$765$	−8.00000	−0.289241
$766$	−30.0000	−1.08394
$767$	−84.0000	−3.03306
$768$	2.00000	0.0721688
$769$	24.0000	0.865462	0.432731	−	0.901523i	$-0.357550\pi$
$769$	24.0000	0.865462	0.432731	+	0.901523i	$0.357550\pi$
$770$	0	0
$771$	−44.0000	−1.58462
$772$	−22.0000	−0.791797
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	8.00000	0.287554
$775$	10.0000	0.359211
$776$	−2.00000	−0.0717958
$777$	48.0000	1.72199
$778$	−6.00000	−0.215110
$779$	6.00000	0.214972
$780$	−24.0000	−0.859338
$781$	0	0
$782$	32.0000	1.14432
$783$	24.0000	0.857690
$784$	9.00000	0.321429
$785$	−4.00000	−0.142766
$786$	16.0000	0.570701
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	12.0000	0.427482
$789$	16.0000	0.569615
$790$	0	0
$791$	24.0000	0.853342
$792$	0	0
$793$	−72.0000	−2.55679
$794$	−14.0000	−0.496841
$795$	−24.0000	−0.851192
$796$	4.00000	0.141776
$797$	10.0000	0.354218	0.177109	−	0.984191i	$-0.443325\pi$
$797$	10.0000	0.354218	0.177109	+	0.984191i	$0.443325\pi$
$798$	−8.00000	−0.283197
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−14.0000	−0.494666
$802$	−18.0000	−0.635602
$803$	0	0
$804$	28.0000	0.987484
$805$	−64.0000	−2.25570
$806$	−60.0000	−2.11341
$807$	−36.0000	−1.26726
$808$	−8.00000	−0.281439
$809$	−40.0000	−1.40633	−0.703163	−	0.711029i	$-0.748229\pi$
$809$	−40.0000	−1.40633	−0.703163	+	0.711029i	$0.748229\pi$
$810$	22.0000	0.773001
$811$	36.0000	1.26413	0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000	1.26413	0.632065	+	0.774915i	$0.282207\pi$
$812$	−24.0000	−0.842235
$813$	−32.0000	−1.12229
$814$	0	0
$815$	−24.0000	−0.840683
$816$	8.00000	0.280056
$817$	−8.00000	−0.279885
$818$	14.0000	0.489499
$819$	24.0000	0.838628
$820$	12.0000	0.419058
$821$	−40.0000	−1.39601	−0.698005	−	0.716093i	$-0.745929\pi$
$821$	−40.0000	−1.39601	−0.698005	+	0.716093i	$0.745929\pi$
$822$	12.0000	0.418548
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	−56.0000	−1.94849
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	8.00000	0.278019
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	0	0
$831$	48.0000	1.66510
$832$	6.00000	0.208013
$833$	36.0000	1.24733
$834$	8.00000	0.277017
$835$	0	0
$836$	0	0
$837$	40.0000	1.38260
$838$	−36.0000	−1.24360
$839$	−38.0000	−1.31191	−0.655953	−	0.754802i	$-0.727733\pi$
$839$	−38.0000	−1.31191	−0.655953	+	0.754802i	$0.727733\pi$
$840$	−16.0000	−0.552052
$841$	7.00000	0.241379
$842$	2.00000	0.0689246
$843$	12.0000	0.413302
$844$	−20.0000	−0.688428
$845$	−46.0000	−1.58245
$846$	0	0
$847$	0	0
$848$	6.00000	0.206041
$849$	−24.0000	−0.823678
$850$	−4.00000	−0.137199
$851$	48.0000	1.64542
$852$	12.0000	0.411113
$853$	4.00000	0.136957	0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000	0.136957	0.0684787	+	0.997653i	$0.478185\pi$
$854$	−48.0000	−1.64253
$855$	2.00000	0.0683986
$856$	−4.00000	−0.136717
$857$	−10.0000	−0.341593	−0.170797	−	0.985306i	$-0.554634\pi$
$857$	−10.0000	−0.341593	−0.170797	+	0.985306i	$0.554634\pi$
$858$	0	0
$859$	24.0000	0.818869	0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000	0.818869	0.409435	+	0.912339i	$0.365726\pi$
$860$	−16.0000	−0.545595
$861$	−48.0000	−1.63584
$862$	0	0
$863$	30.0000	1.02121	0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000	1.02121	0.510606	+	0.859815i	$0.329421\pi$
$864$	−4.00000	−0.136083
$865$	4.00000	0.136004
$866$	22.0000	0.747590
$867$	−2.00000	−0.0679236
$868$	−40.0000	−1.35769
$869$	0	0
$870$	24.0000	0.813676
$871$	84.0000	2.84623
$872$	18.0000	0.609557
$873$	−2.00000	−0.0676897
$874$	−8.00000	−0.270604
$875$	48.0000	1.62270
$876$	8.00000	0.270295
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	16.0000	0.539974
$879$	−12.0000	−0.404750
$880$	0	0
$881$	46.0000	1.54978	0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$882$	9.00000	0.303046
$883$	−24.0000	−0.807664	−0.403832	−	0.914833i	$-0.632322\pi$
$883$	−24.0000	−0.807664	−0.403832	+	0.914833i	$0.632322\pi$
$884$	24.0000	0.807207
$885$	56.0000	1.88242
$886$	24.0000	0.806296
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	12.0000	0.402694
$889$	−64.0000	−2.14649
$890$	28.0000	0.938562
$891$	0	0
$892$	10.0000	0.334825
$893$	0	0
$894$	0	0
$895$	12.0000	0.401116
$896$	4.00000	0.133631
$897$	96.0000	3.20535
$898$	2.00000	0.0667409
$899$	60.0000	2.00111
$900$	−1.00000	−0.0333333
$901$	24.0000	0.799556
$902$	0	0
$903$	64.0000	2.12979
$904$	6.00000	0.199557
$905$	20.0000	0.664822
$906$	−16.0000	−0.531564
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	−28.0000	−0.929213
$909$	−8.00000	−0.265343
$910$	−48.0000	−1.59118
$911$	46.0000	1.52405	0.762024	−	0.647549i	$-0.224206\pi$
$911$	46.0000	1.52405	0.762024	+	0.647549i	$0.224206\pi$
$912$	−2.00000	−0.0662266
$913$	0	0
$914$	8.00000	0.264616
$915$	48.0000	1.58683
$916$	10.0000	0.330409
$917$	32.0000	1.05673
$918$	−16.0000	−0.528079
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	−16.0000	−0.527504
$921$	−24.0000	−0.790827
$922$	−40.0000	−1.31733
$923$	36.0000	1.18495
$924$	0	0
$925$	−6.00000	−0.197279
$926$	−4.00000	−0.131448
$927$	14.0000	0.459820
$928$	−6.00000	−0.196960
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	40.0000	1.31165
$931$	−9.00000	−0.294963
$932$	−8.00000	−0.262049
$933$	−24.0000	−0.785725
$934$	12.0000	0.392652
$935$	0	0
$936$	6.00000	0.196116
$937$	−12.0000	−0.392023	−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000	−0.392023	−0.196011	+	0.980602i	$0.562799\pi$
$938$	56.0000	1.82846
$939$	28.0000	0.913745
$940$	0	0
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	4.00000	0.130327
$943$	−48.0000	−1.56310
$944$	−14.0000	−0.455661
$945$	32.0000	1.04096
$946$	0	0
$947$	−40.0000	−1.29983	−0.649913	−	0.760009i	$-0.725195\pi$
$947$	−40.0000	−1.29983	−0.649913	+	0.760009i	$0.725195\pi$
$948$	0	0
$949$	24.0000	0.779073
$950$	1.00000	0.0324443
$951$	36.0000	1.16738
$952$	16.0000	0.518563
$953$	−38.0000	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$954$	6.00000	0.194257
$955$	−16.0000	−0.517748
$956$	8.00000	0.258738
$957$	0	0
$958$	−12.0000	−0.387702
$959$	24.0000	0.775000
$960$	−4.00000	−0.129099
$961$	69.0000	2.22581
$962$	36.0000	1.16069
$963$	−4.00000	−0.128898
$964$	14.0000	0.450910
$965$	44.0000	1.41641
$966$	64.0000	2.05917
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	0	0
$969$	−8.00000	−0.256997
$970$	4.00000	0.128432
$971$	50.0000	1.60458	0.802288	−	0.596937i	$-0.203616\pi$
$971$	50.0000	1.60458	0.802288	+	0.596937i	$0.203616\pi$
$972$	−10.0000	−0.320750
$973$	16.0000	0.512936
$974$	2.00000	0.0640841
$975$	−12.0000	−0.384308
$976$	−12.0000	−0.384111
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	24.0000	0.767435
$979$	0	0
$980$	−18.0000	−0.574989
$981$	18.0000	0.574696
$982$	−8.00000	−0.255290
$983$	−18.0000	−0.574111	−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000	−0.574111	−0.287055	+	0.957914i	$0.592676\pi$
$984$	−12.0000	−0.382546
$985$	−24.0000	−0.764704
$986$	−24.0000	−0.764316
$987$	0	0
$988$	−6.00000	−0.190885
$989$	64.0000	2.03508
$990$	0	0
$991$	−54.0000	−1.71537	−0.857683	−	0.514178i	$-0.828097\pi$
$991$	−54.0000	−1.71537	−0.857683	+	0.514178i	$0.828097\pi$
$992$	−10.0000	−0.317500
$993$	−52.0000	−1.65017
$994$	24.0000	0.761234
$995$	−8.00000	−0.253617
$996$	0	0
$997$	8.00000	0.253363	0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000	0.253363	0.126681	+	0.991943i	$0.459567\pi$
$998$	−4.00000	−0.126618
$999$	−24.0000	−0.759326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.r.1.1	yes	1
11.10	odd	2		4598.2.a.i.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.i.1.1	✓	1	11.10	odd	2
4598.2.a.r.1.1	yes	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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