LMFDB - Embedded newform 4598.2.a.b.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:	no (minimal twist has level 418)
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)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +2.00000 q^{10} -1.00000 q^{12} -1.00000 q^{13} -3.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +7.00000 q^{17} +2.00000 q^{18} -1.00000 q^{19} -2.00000 q^{20} -3.00000 q^{21} -5.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} +5.00000 q^{27} +3.00000 q^{28} -1.00000 q^{29} -2.00000 q^{30} +10.0000 q^{31} -1.00000 q^{32} -7.00000 q^{34} -6.00000 q^{35} -2.00000 q^{36} -6.00000 q^{37} +1.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} -6.00000 q^{41} +3.00000 q^{42} +4.00000 q^{43} +4.00000 q^{45} +5.00000 q^{46} -1.00000 q^{48} +2.00000 q^{49} +1.00000 q^{50} -7.00000 q^{51} -1.00000 q^{52} -1.00000 q^{53} -5.00000 q^{54} -3.00000 q^{56} +1.00000 q^{57} +1.00000 q^{58} +3.00000 q^{59} +2.00000 q^{60} +12.0000 q^{61} -10.0000 q^{62} -6.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +3.00000 q^{67} +7.00000 q^{68} +5.00000 q^{69} +6.00000 q^{70} -10.0000 q^{71} +2.00000 q^{72} -3.00000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} -1.00000 q^{78} -8.00000 q^{79} -2.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -8.00000 q^{83} -3.00000 q^{84} -14.0000 q^{85} -4.00000 q^{86} +1.00000 q^{87} -8.00000 q^{89} -4.00000 q^{90} -3.00000 q^{91} -5.00000 q^{92} -10.0000 q^{93} +2.00000 q^{95} +1.00000 q^{96} +8.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	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	$0.647584\pi$
$6$	1.00000	0.408248
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	2.00000	0.632456
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−3.00000	−0.801784
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	2.00000	0.471405
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.00000	−0.447214
$21$	−3.00000	−0.654654
$22$	0	0
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	5.00000	0.962250
$28$	3.00000	0.566947
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−2.00000	−0.365148
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.00000	−1.20049
$35$	−6.00000	−1.01419
$36$	−2.00000	−0.333333
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	1.00000	0.162221
$39$	1.00000	0.160128
$40$	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	$0.655213\pi$
$42$	3.00000	0.462910
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	4.00000	0.596285
$46$	5.00000	0.737210
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	1.00000	0.141421
$51$	−7.00000	−0.980196
$52$	−1.00000	−0.138675
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−3.00000	−0.400892
$57$	1.00000	0.132453
$58$	1.00000	0.131306
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	2.00000	0.258199
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	−10.0000	−1.27000
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	7.00000	0.848875
$69$	5.00000	0.601929
$70$	6.00000	0.717137
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	2.00000	0.235702
$73$	−3.00000	−0.351123	−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000	−0.351123	−0.175562	+	0.984468i	$0.556174\pi$
$74$	6.00000	0.697486
$75$	1.00000	0.115470
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	−3.00000	−0.327327
$85$	−14.0000	−1.51851
$86$	−4.00000	−0.431331
$87$	1.00000	0.107211
$88$	0	0
$89$	−8.00000	−0.847998	−0.423999	−	0.905663i	$-0.639374\pi$
$89$	−8.00000	−0.847998	−0.423999	+	0.905663i	$0.639374\pi$
$90$	−4.00000	−0.421637
$91$	−3.00000	−0.314485
$92$	−5.00000	−0.521286
$93$	−10.0000	−1.03695
$94$	0	0
$95$	2.00000	0.205196
$96$	1.00000	0.102062
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	7.00000	0.693103
$103$	12.0000	1.18240	0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000	1.18240	0.591198	+	0.806527i	$0.298655\pi$
$104$	1.00000	0.0980581
$105$	6.00000	0.585540
$106$	1.00000	0.0971286
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	5.00000	0.481125
$109$	13.0000	1.24517	0.622587	−	0.782551i	$-0.286082\pi$
$109$	13.0000	1.24517	0.622587	+	0.782551i	$0.286082\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	3.00000	0.283473
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	−1.00000	−0.0936586
$115$	10.0000	0.932505
$116$	−1.00000	−0.0928477
$117$	2.00000	0.184900
$118$	−3.00000	−0.276172
$119$	21.0000	1.92507
$120$	−2.00000	−0.182574
$121$	0	0
$122$	−12.0000	−1.08643
$123$	6.00000	0.541002
$124$	10.0000	0.898027
$125$	12.0000	1.07331
$126$	6.00000	0.534522
$127$	−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
$131$	22.0000	1.92215	0.961074	−	0.276289i	$-0.0891049\pi$
$131$	22.0000	1.92215	0.961074	+	0.276289i	$0.0891049\pi$
$132$	0	0
$133$	−3.00000	−0.260133
$134$	−3.00000	−0.259161
$135$	−10.0000	−0.860663
$136$	−7.00000	−0.600245
$137$	−17.0000	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$137$	−17.0000	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$138$	−5.00000	−0.425628
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	−6.00000	−0.507093
$141$	0	0
$142$	10.0000	0.839181
$143$	0	0
$144$	−2.00000	−0.166667
$145$	2.00000	0.166091
$146$	3.00000	0.248282
$147$	−2.00000	−0.164957
$148$	−6.00000	−0.493197
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−1.00000	−0.0816497
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	1.00000	0.0811107
$153$	−14.0000	−1.13183
$154$	0	0
$155$	−20.0000	−1.60644
$156$	1.00000	0.0800641
$157$	−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
$159$	1.00000	0.0793052
$160$	2.00000	0.158114
$161$	−15.0000	−1.18217
$162$	−1.00000	−0.0785674
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	8.00000	0.620920
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	3.00000	0.231455
$169$	−12.0000	−0.923077
$170$	14.0000	1.07375
$171$	2.00000	0.152944
$172$	4.00000	0.304997
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−1.00000	−0.0758098
$175$	−3.00000	−0.226779
$176$	0	0
$177$	−3.00000	−0.225494
$178$	8.00000	0.599625
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	4.00000	0.298142
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	3.00000	0.222375
$183$	−12.0000	−0.887066
$184$	5.00000	0.368605
$185$	12.0000	0.882258
$186$	10.0000	0.733236
$187$	0	0
$188$	0	0
$189$	15.0000	1.09109
$190$	−2.00000	−0.145095
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	−1.00000	−0.0721688
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−8.00000	−0.574367
$195$	−2.00000	−0.143223
$196$	2.00000	0.142857
$197$	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
$199$	23.0000	1.63043	0.815213	−	0.579161i	$-0.196620\pi$
$199$	23.0000	1.63043	0.815213	+	0.579161i	$0.196620\pi$
$200$	1.00000	0.0707107
$201$	−3.00000	−0.211604
$202$	6.00000	0.422159
$203$	−3.00000	−0.210559
$204$	−7.00000	−0.490098
$205$	12.0000	0.838116
$206$	−12.0000	−0.836080
$207$	10.0000	0.695048
$208$	−1.00000	−0.0693375
$209$	0	0
$210$	−6.00000	−0.414039
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	−1.00000	−0.0686803
$213$	10.0000	0.685189
$214$	−13.0000	−0.888662
$215$	−8.00000	−0.545595
$216$	−5.00000	−0.340207
$217$	30.0000	2.03653
$218$	−13.0000	−0.880471
$219$	3.00000	0.202721
$220$	0	0
$221$	−7.00000	−0.470871
$222$	−6.00000	−0.402694
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	−3.00000	−0.200446
$225$	2.00000	0.133333
$226$	12.0000	0.798228
$227$	15.0000	0.995585	0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000	0.995585	0.497792	+	0.867296i	$0.334144\pi$
$228$	1.00000	0.0662266
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	−10.0000	−0.659380
$231$	0	0
$232$	1.00000	0.0656532
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	3.00000	0.195283
$237$	8.00000	0.519656
$238$	−21.0000	−1.36123
$239$	−25.0000	−1.61712	−0.808558	−	0.588417i	$-0.799751\pi$
$239$	−25.0000	−1.61712	−0.808558	+	0.588417i	$0.799751\pi$
$240$	2.00000	0.129099
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	12.0000	0.768221
$245$	−4.00000	−0.255551
$246$	−6.00000	−0.382546
$247$	1.00000	0.0636285
$248$	−10.0000	−0.635001
$249$	8.00000	0.506979
$250$	−12.0000	−0.758947
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	−6.00000	−0.377964
$253$	0	0
$254$	16.0000	1.00393
$255$	14.0000	0.876714
$256$	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	$0.740706\pi$
$258$	4.00000	0.249029
$259$	−18.0000	−1.11847
$260$	2.00000	0.124035
$261$	2.00000	0.123797
$262$	−22.0000	−1.35916
$263$	−4.00000	−0.246651	−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000	−0.246651	−0.123325	+	0.992366i	$0.539356\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	3.00000	0.183942
$267$	8.00000	0.489592
$268$	3.00000	0.183254
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	10.0000	0.608581
$271$	15.0000	0.911185	0.455593	−	0.890188i	$-0.349427\pi$
$271$	15.0000	0.911185	0.455593	+	0.890188i	$0.349427\pi$
$272$	7.00000	0.424437
$273$	3.00000	0.181568
$274$	17.0000	1.02701
$275$	0	0
$276$	5.00000	0.300965
$277$	16.0000	0.961347	0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000	0.961347	0.480673	+	0.876900i	$0.340392\pi$
$278$	−14.0000	−0.839664
$279$	−20.0000	−1.19737
$280$	6.00000	0.358569
$281$	−16.0000	−0.954480	−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000	−0.954480	−0.477240	+	0.878773i	$0.658363\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−10.0000	−0.593391
$285$	−2.00000	−0.118470
$286$	0	0
$287$	−18.0000	−1.06251
$288$	2.00000	0.117851
$289$	32.0000	1.88235
$290$	−2.00000	−0.117444
$291$	−8.00000	−0.468968
$292$	−3.00000	−0.175562
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	2.00000	0.116642
$295$	−6.00000	−0.349334
$296$	6.00000	0.348743
$297$	0	0
$298$	−18.0000	−1.04271
$299$	5.00000	0.289157
$300$	1.00000	0.0577350
$301$	12.0000	0.691669
$302$	12.0000	0.690522
$303$	6.00000	0.344691
$304$	−1.00000	−0.0573539
$305$	−24.0000	−1.37424
$306$	14.0000	0.800327
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	20.0000	1.13592
$311$	3.00000	0.170114	0.0850572	−	0.996376i	$-0.472893\pi$
$311$	3.00000	0.170114	0.0850572	+	0.996376i	$0.472893\pi$
$312$	−1.00000	−0.0566139
$313$	21.0000	1.18699	0.593495	−	0.804838i	$-0.297748\pi$
$313$	21.0000	1.18699	0.593495	+	0.804838i	$0.297748\pi$
$314$	22.0000	1.24153
$315$	12.0000	0.676123
$316$	−8.00000	−0.450035
$317$	21.0000	1.17948	0.589739	−	0.807594i	$-0.299231\pi$
$317$	21.0000	1.17948	0.589739	+	0.807594i	$0.299231\pi$
$318$	−1.00000	−0.0560772
$319$	0	0
$320$	−2.00000	−0.111803
$321$	−13.0000	−0.725589
$322$	15.0000	0.835917
$323$	−7.00000	−0.389490
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	2.00000	0.110770
$327$	−13.0000	−0.718902
$328$	6.00000	0.331295
$329$	0	0
$330$	0	0
$331$	29.0000	1.59398	0.796992	−	0.603990i	$-0.206423\pi$
$331$	29.0000	1.59398	0.796992	+	0.603990i	$0.206423\pi$
$332$	−8.00000	−0.439057
$333$	12.0000	0.657596
$334$	−22.0000	−1.20379
$335$	−6.00000	−0.327815
$336$	−3.00000	−0.163663
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	12.0000	0.652714
$339$	12.0000	0.651751
$340$	−14.0000	−0.759257
$341$	0	0
$342$	−2.00000	−0.108148
$343$	−15.0000	−0.809924
$344$	−4.00000	−0.215666
$345$	−10.0000	−0.538382
$346$	14.0000	0.752645
$347$	26.0000	1.39575	0.697877	−	0.716218i	$-0.254128\pi$
$347$	26.0000	1.39575	0.697877	+	0.716218i	$0.254128\pi$
$348$	1.00000	0.0536056
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	3.00000	0.160357
$351$	−5.00000	−0.266880
$352$	0	0
$353$	1.00000	0.0532246	0.0266123	−	0.999646i	$-0.491528\pi$
$353$	1.00000	0.0532246	0.0266123	+	0.999646i	$0.491528\pi$
$354$	3.00000	0.159448
$355$	20.0000	1.06149
$356$	−8.00000	−0.423999
$357$	−21.0000	−1.11144
$358$	−4.00000	−0.211407
$359$	17.0000	0.897226	0.448613	−	0.893726i	$-0.351918\pi$
$359$	17.0000	0.897226	0.448613	+	0.893726i	$0.351918\pi$
$360$	−4.00000	−0.210819
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	0	0
$364$	−3.00000	−0.157243
$365$	6.00000	0.314054
$366$	12.0000	0.627250
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	−5.00000	−0.260643
$369$	12.0000	0.624695
$370$	−12.0000	−0.623850
$371$	−3.00000	−0.155752
$372$	−10.0000	−0.518476
$373$	−11.0000	−0.569558	−0.284779	−	0.958593i	$-0.591920\pi$
$373$	−11.0000	−0.569558	−0.284779	+	0.958593i	$0.591920\pi$
$374$	0	0
$375$	−12.0000	−0.619677
$376$	0	0
$377$	1.00000	0.0515026
$378$	−15.0000	−0.771517
$379$	−5.00000	−0.256833	−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000	−0.256833	−0.128416	+	0.991720i	$0.540989\pi$
$380$	2.00000	0.102598
$381$	16.0000	0.819705
$382$	−3.00000	−0.153493
$383$	2.00000	0.102195	0.0510976	−	0.998694i	$-0.483728\pi$
$383$	2.00000	0.102195	0.0510976	+	0.998694i	$0.483728\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−4.00000	−0.203595
$387$	−8.00000	−0.406663
$388$	8.00000	0.406138
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	2.00000	0.101274
$391$	−35.0000	−1.77003
$392$	−2.00000	−0.101015
$393$	−22.0000	−1.10975
$394$	−12.0000	−0.604551
$395$	16.0000	0.805047
$396$	0	0
$397$	34.0000	1.70641	0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000	1.70641	0.853206	+	0.521575i	$0.174655\pi$
$398$	−23.0000	−1.15289
$399$	3.00000	0.150188
$400$	−1.00000	−0.0500000
$401$	−2.00000	−0.0998752	−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000	−0.0998752	−0.0499376	+	0.998752i	$0.515902\pi$
$402$	3.00000	0.149626
$403$	−10.0000	−0.498135
$404$	−6.00000	−0.298511
$405$	−2.00000	−0.0993808
$406$	3.00000	0.148888
$407$	0	0
$408$	7.00000	0.346552
$409$	−34.0000	−1.68119	−0.840596	−	0.541663i	$-0.817795\pi$
$409$	−34.0000	−1.68119	−0.840596	+	0.541663i	$0.817795\pi$
$410$	−12.0000	−0.592638
$411$	17.0000	0.838548
$412$	12.0000	0.591198
$413$	9.00000	0.442861
$414$	−10.0000	−0.491473
$415$	16.0000	0.785409
$416$	1.00000	0.0490290
$417$	−14.0000	−0.685583
$418$	0	0
$419$	10.0000	0.488532	0.244266	−	0.969708i	$-0.421453\pi$
$419$	10.0000	0.488532	0.244266	+	0.969708i	$0.421453\pi$
$420$	6.00000	0.292770
$421$	15.0000	0.731055	0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000	0.731055	0.365528	+	0.930800i	$0.380889\pi$
$422$	1.00000	0.0486792
$423$	0	0
$424$	1.00000	0.0485643
$425$	−7.00000	−0.339550
$426$	−10.0000	−0.484502
$427$	36.0000	1.74216
$428$	13.0000	0.628379
$429$	0	0
$430$	8.00000	0.385794
$431$	−34.0000	−1.63772	−0.818861	−	0.573992i	$-0.805394\pi$
$431$	−34.0000	−1.63772	−0.818861	+	0.573992i	$0.805394\pi$
$432$	5.00000	0.240563
$433$	24.0000	1.15337	0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000	1.15337	0.576683	+	0.816968i	$0.304347\pi$
$434$	−30.0000	−1.44005
$435$	−2.00000	−0.0958927
$436$	13.0000	0.622587
$437$	5.00000	0.239182
$438$	−3.00000	−0.143346
$439$	14.0000	0.668184	0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000	0.668184	0.334092	+	0.942541i	$0.391570\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	7.00000	0.332956
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	6.00000	0.284747
$445$	16.0000	0.758473
$446$	−10.0000	−0.473514
$447$	−18.0000	−0.851371
$448$	3.00000	0.141737
$449$	24.0000	1.13263	0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000	1.13263	0.566315	+	0.824189i	$0.308369\pi$
$450$	−2.00000	−0.0942809
$451$	0	0
$452$	−12.0000	−0.564433
$453$	12.0000	0.563809
$454$	−15.0000	−0.703985
$455$	6.00000	0.281284
$456$	−1.00000	−0.0468293
$457$	37.0000	1.73079	0.865393	−	0.501093i	$-0.167069\pi$
$457$	37.0000	1.73079	0.865393	+	0.501093i	$0.167069\pi$
$458$	−20.0000	−0.934539
$459$	35.0000	1.63366
$460$	10.0000	0.466252
$461$	8.00000	0.372597	0.186299	−	0.982493i	$-0.440351\pi$
$461$	8.00000	0.372597	0.186299	+	0.982493i	$0.440351\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−1.00000	−0.0464238
$465$	20.0000	0.927478
$466$	−10.0000	−0.463241
$467$	20.0000	0.925490	0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000	0.925490	0.462745	+	0.886492i	$0.346865\pi$
$468$	2.00000	0.0924500
$469$	9.00000	0.415581
$470$	0	0
$471$	22.0000	1.01371
$472$	−3.00000	−0.138086
$473$	0	0
$474$	−8.00000	−0.367452
$475$	1.00000	0.0458831
$476$	21.0000	0.962533
$477$	2.00000	0.0915737
$478$	25.0000	1.14347
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	−2.00000	−0.0912871
$481$	6.00000	0.273576
$482$	−4.00000	−0.182195
$483$	15.0000	0.682524
$484$	0	0
$485$	−16.0000	−0.726523
$486$	16.0000	0.725775
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	−12.0000	−0.543214
$489$	2.00000	0.0904431
$490$	4.00000	0.180702
$491$	−10.0000	−0.451294	−0.225647	−	0.974209i	$-0.572450\pi$
$491$	−10.0000	−0.451294	−0.225647	+	0.974209i	$0.572450\pi$
$492$	6.00000	0.270501
$493$	−7.00000	−0.315264
$494$	−1.00000	−0.0449921
$495$	0	0
$496$	10.0000	0.449013
$497$	−30.0000	−1.34568
$498$	−8.00000	−0.358489
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	12.0000	0.536656
$501$	−22.0000	−0.982888
$502$	6.00000	0.267793
$503$	19.0000	0.847168	0.423584	−	0.905857i	$-0.360772\pi$
$503$	19.0000	0.847168	0.423584	+	0.905857i	$0.360772\pi$
$504$	6.00000	0.267261
$505$	12.0000	0.533993
$506$	0	0
$507$	12.0000	0.532939
$508$	−16.0000	−0.709885
$509$	−34.0000	−1.50702	−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000	−1.50702	−0.753512	+	0.657434i	$0.771642\pi$
$510$	−14.0000	−0.619930
$511$	−9.00000	−0.398137
$512$	−1.00000	−0.0441942
$513$	−5.00000	−0.220755
$514$	22.0000	0.970378
$515$	−24.0000	−1.05757
$516$	−4.00000	−0.176090
$517$	0	0
$518$	18.0000	0.790875
$519$	14.0000	0.614532
$520$	−2.00000	−0.0877058
$521$	−20.0000	−0.876216	−0.438108	−	0.898922i	$-0.644351\pi$
$521$	−20.0000	−0.876216	−0.438108	+	0.898922i	$0.644351\pi$
$522$	−2.00000	−0.0875376
$523$	21.0000	0.918266	0.459133	−	0.888368i	$-0.348160\pi$
$523$	21.0000	0.918266	0.459133	+	0.888368i	$0.348160\pi$
$524$	22.0000	0.961074
$525$	3.00000	0.130931
$526$	4.00000	0.174408
$527$	70.0000	3.04925
$528$	0	0
$529$	2.00000	0.0869565
$530$	−2.00000	−0.0868744
$531$	−6.00000	−0.260378
$532$	−3.00000	−0.130066
$533$	6.00000	0.259889
$534$	−8.00000	−0.346194
$535$	−26.0000	−1.12408
$536$	−3.00000	−0.129580
$537$	−4.00000	−0.172613
$538$	−18.0000	−0.776035
$539$	0	0
$540$	−10.0000	−0.430331
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	−15.0000	−0.644305
$543$	2.00000	0.0858282
$544$	−7.00000	−0.300123
$545$	−26.0000	−1.11372
$546$	−3.00000	−0.128388
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	−17.0000	−0.726204
$549$	−24.0000	−1.02430
$550$	0	0
$551$	1.00000	0.0426014
$552$	−5.00000	−0.212814
$553$	−24.0000	−1.02058
$554$	−16.0000	−0.679775
$555$	−12.0000	−0.509372
$556$	14.0000	0.593732
$557$	6.00000	0.254228	0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000	0.254228	0.127114	+	0.991888i	$0.459429\pi$
$558$	20.0000	0.846668
$559$	−4.00000	−0.169182
$560$	−6.00000	−0.253546
$561$	0	0
$562$	16.0000	0.674919
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	24.0000	1.00969
$566$	−14.0000	−0.588464
$567$	3.00000	0.125988
$568$	10.0000	0.419591
$569$	12.0000	0.503066	0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000	0.503066	0.251533	+	0.967849i	$0.419065\pi$
$570$	2.00000	0.0837708
$571$	14.0000	0.585882	0.292941	−	0.956131i	$-0.405366\pi$
$571$	14.0000	0.585882	0.292941	+	0.956131i	$0.405366\pi$
$572$	0	0
$573$	−3.00000	−0.125327
$574$	18.0000	0.751305
$575$	5.00000	0.208514
$576$	−2.00000	−0.0833333
$577$	23.0000	0.957503	0.478751	−	0.877951i	$-0.341090\pi$
$577$	23.0000	0.957503	0.478751	+	0.877951i	$0.341090\pi$
$578$	−32.0000	−1.33102
$579$	−4.00000	−0.166234
$580$	2.00000	0.0830455
$581$	−24.0000	−0.995688
$582$	8.00000	0.331611
$583$	0	0
$584$	3.00000	0.124141
$585$	−4.00000	−0.165380
$586$	−9.00000	−0.371787
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	−2.00000	−0.0824786
$589$	−10.0000	−0.412043
$590$	6.00000	0.247016
$591$	−12.0000	−0.493614
$592$	−6.00000	−0.246598
$593$	−42.0000	−1.72473	−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000	−1.72473	−0.862367	+	0.506284i	$0.831019\pi$
$594$	0	0
$595$	−42.0000	−1.72183
$596$	18.0000	0.737309
$597$	−23.0000	−0.941327
$598$	−5.00000	−0.204465
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	−1.00000	−0.0408248
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	−12.0000	−0.489083
$603$	−6.00000	−0.244339
$604$	−12.0000	−0.488273
$605$	0	0
$606$	−6.00000	−0.243733
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	1.00000	0.0405554
$609$	3.00000	0.121566
$610$	24.0000	0.971732
$611$	0	0
$612$	−14.0000	−0.565916
$613$	28.0000	1.13091	0.565455	−	0.824779i	$-0.308701\pi$
$613$	28.0000	1.13091	0.565455	+	0.824779i	$0.308701\pi$
$614$	−16.0000	−0.645707
$615$	−12.0000	−0.483887
$616$	0	0
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	12.0000	0.482711
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−20.0000	−0.803219
$621$	−25.0000	−1.00322
$622$	−3.00000	−0.120289
$623$	−24.0000	−0.961540
$624$	1.00000	0.0400320
$625$	−19.0000	−0.760000
$626$	−21.0000	−0.839329
$627$	0	0
$628$	−22.0000	−0.877896
$629$	−42.0000	−1.67465
$630$	−12.0000	−0.478091
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	8.00000	0.318223
$633$	1.00000	0.0397464
$634$	−21.0000	−0.834017
$635$	32.0000	1.26988
$636$	1.00000	0.0396526
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	20.0000	0.791188
$640$	2.00000	0.0790569
$641$	40.0000	1.57991	0.789953	−	0.613168i	$-0.210105\pi$
$641$	40.0000	1.57991	0.789953	+	0.613168i	$0.210105\pi$
$642$	13.0000	0.513069
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	−15.0000	−0.591083
$645$	8.00000	0.315000
$646$	7.00000	0.275411
$647$	3.00000	0.117942	0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000	0.117942	0.0589711	+	0.998260i	$0.481218\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−1.00000	−0.0392232
$651$	−30.0000	−1.17579
$652$	−2.00000	−0.0783260
$653$	4.00000	0.156532	0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000	0.156532	0.0782660	+	0.996933i	$0.475062\pi$
$654$	13.0000	0.508340
$655$	−44.0000	−1.71922
$656$	−6.00000	−0.234261
$657$	6.00000	0.234082
$658$	0	0
$659$	−11.0000	−0.428499	−0.214250	−	0.976779i	$-0.568731\pi$
$659$	−11.0000	−0.428499	−0.214250	+	0.976779i	$0.568731\pi$
$660$	0	0
$661$	29.0000	1.12797	0.563985	−	0.825785i	$-0.309268\pi$
$661$	29.0000	1.12797	0.563985	+	0.825785i	$0.309268\pi$
$662$	−29.0000	−1.12712
$663$	7.00000	0.271857
$664$	8.00000	0.310460
$665$	6.00000	0.232670
$666$	−12.0000	−0.464991
$667$	5.00000	0.193601
$668$	22.0000	0.851206
$669$	−10.0000	−0.386622
$670$	6.00000	0.231800
$671$	0	0
$672$	3.00000	0.115728
$673$	24.0000	0.925132	0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000	0.925132	0.462566	+	0.886585i	$0.346929\pi$
$674$	−20.0000	−0.770371
$675$	−5.00000	−0.192450
$676$	−12.0000	−0.461538
$677$	29.0000	1.11456	0.557280	−	0.830324i	$-0.311845\pi$
$677$	29.0000	1.11456	0.557280	+	0.830324i	$0.311845\pi$
$678$	−12.0000	−0.460857
$679$	24.0000	0.921035
$680$	14.0000	0.536875
$681$	−15.0000	−0.574801
$682$	0	0
$683$	−8.00000	−0.306111	−0.153056	−	0.988218i	$-0.548911\pi$
$683$	−8.00000	−0.306111	−0.153056	+	0.988218i	$0.548911\pi$
$684$	2.00000	0.0764719
$685$	34.0000	1.29907
$686$	15.0000	0.572703
$687$	−20.0000	−0.763048
$688$	4.00000	0.152499
$689$	1.00000	0.0380970
$690$	10.0000	0.380693
$691$	−14.0000	−0.532585	−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000	−0.532585	−0.266293	+	0.963892i	$0.585799\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	−26.0000	−0.986947
$695$	−28.0000	−1.06210
$696$	−1.00000	−0.0379049
$697$	−42.0000	−1.59086
$698$	10.0000	0.378506
$699$	−10.0000	−0.378235
$700$	−3.00000	−0.113389
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	5.00000	0.188713
$703$	6.00000	0.226294
$704$	0	0
$705$	0	0
$706$	−1.00000	−0.0376355
$707$	−18.0000	−0.676960
$708$	−3.00000	−0.112747
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	−20.0000	−0.750587
$711$	16.0000	0.600047
$712$	8.00000	0.299813
$713$	−50.0000	−1.87251
$714$	21.0000	0.785905
$715$	0	0
$716$	4.00000	0.149487
$717$	25.0000	0.933642
$718$	−17.0000	−0.634434
$719$	−33.0000	−1.23069	−0.615346	−	0.788257i	$-0.710984\pi$
$719$	−33.0000	−1.23069	−0.615346	+	0.788257i	$0.710984\pi$
$720$	4.00000	0.149071
$721$	36.0000	1.34071
$722$	−1.00000	−0.0372161
$723$	−4.00000	−0.148762
$724$	−2.00000	−0.0743294
$725$	1.00000	0.0371391
$726$	0	0
$727$	47.0000	1.74313	0.871567	−	0.490277i	$-0.163104\pi$
$727$	47.0000	1.74313	0.871567	+	0.490277i	$0.163104\pi$
$728$	3.00000	0.111187
$729$	13.0000	0.481481
$730$	−6.00000	−0.222070
$731$	28.0000	1.03562
$732$	−12.0000	−0.443533
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−16.0000	−0.590571
$735$	4.00000	0.147542
$736$	5.00000	0.184302
$737$	0	0
$738$	−12.0000	−0.441726
$739$	28.0000	1.03000	0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000	1.03000	0.514998	+	0.857191i	$0.327793\pi$
$740$	12.0000	0.441129
$741$	−1.00000	−0.0367359
$742$	3.00000	0.110133
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	10.0000	0.366618
$745$	−36.0000	−1.31894
$746$	11.0000	0.402739
$747$	16.0000	0.585409
$748$	0	0
$749$	39.0000	1.42503
$750$	12.0000	0.438178
$751$	−50.0000	−1.82453	−0.912263	−	0.409605i	$-0.865667\pi$
$751$	−50.0000	−1.82453	−0.912263	+	0.409605i	$0.865667\pi$
$752$	0	0
$753$	6.00000	0.218652
$754$	−1.00000	−0.0364179
$755$	24.0000	0.873449
$756$	15.0000	0.545545
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	5.00000	0.181608
$759$	0	0
$760$	−2.00000	−0.0725476
$761$	11.0000	0.398750	0.199375	−	0.979923i	$-0.436109\pi$
$761$	11.0000	0.398750	0.199375	+	0.979923i	$0.436109\pi$
$762$	−16.0000	−0.579619
$763$	39.0000	1.41189
$764$	3.00000	0.108536
$765$	28.0000	1.01234
$766$	−2.00000	−0.0722629
$767$	−3.00000	−0.108324
$768$	−1.00000	−0.0360844
$769$	49.0000	1.76699	0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000	1.76699	0.883493	+	0.468445i	$0.155186\pi$
$770$	0	0
$771$	22.0000	0.792311
$772$	4.00000	0.143963
$773$	−23.0000	−0.827253	−0.413626	−	0.910447i	$-0.635738\pi$
$773$	−23.0000	−0.827253	−0.413626	+	0.910447i	$0.635738\pi$
$774$	8.00000	0.287554
$775$	−10.0000	−0.359211
$776$	−8.00000	−0.287183
$777$	18.0000	0.645746
$778$	−18.0000	−0.645331
$779$	6.00000	0.214972
$780$	−2.00000	−0.0716115
$781$	0	0
$782$	35.0000	1.25160
$783$	−5.00000	−0.178685
$784$	2.00000	0.0714286
$785$	44.0000	1.57043
$786$	22.0000	0.784714
$787$	−49.0000	−1.74666	−0.873331	−	0.487128i	$-0.838045\pi$
$787$	−49.0000	−1.74666	−0.873331	+	0.487128i	$0.838045\pi$
$788$	12.0000	0.427482
$789$	4.00000	0.142404
$790$	−16.0000	−0.569254
$791$	−36.0000	−1.28001
$792$	0	0
$793$	−12.0000	−0.426132
$794$	−34.0000	−1.20661
$795$	−2.00000	−0.0709327
$796$	23.0000	0.815213
$797$	19.0000	0.673015	0.336507	−	0.941681i	$-0.390754\pi$
$797$	19.0000	0.673015	0.336507	+	0.941681i	$0.390754\pi$
$798$	−3.00000	−0.106199
$799$	0	0
$800$	1.00000	0.0353553
$801$	16.0000	0.565332
$802$	2.00000	0.0706225
$803$	0	0
$804$	−3.00000	−0.105802
$805$	30.0000	1.05736
$806$	10.0000	0.352235
$807$	−18.0000	−0.633630
$808$	6.00000	0.211079
$809$	13.0000	0.457056	0.228528	−	0.973537i	$-0.426609\pi$
$809$	13.0000	0.457056	0.228528	+	0.973537i	$0.426609\pi$
$810$	2.00000	0.0702728
$811$	25.0000	0.877869	0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000	0.877869	0.438934	+	0.898519i	$0.355356\pi$
$812$	−3.00000	−0.105279
$813$	−15.0000	−0.526073
$814$	0	0
$815$	4.00000	0.140114
$816$	−7.00000	−0.245049
$817$	−4.00000	−0.139942
$818$	34.0000	1.18878
$819$	6.00000	0.209657
$820$	12.0000	0.419058
$821$	16.0000	0.558404	0.279202	−	0.960232i	$-0.409930\pi$
$821$	16.0000	0.558404	0.279202	+	0.960232i	$0.409930\pi$
$822$	−17.0000	−0.592943
$823$	−43.0000	−1.49889	−0.749443	−	0.662069i	$-0.769679\pi$
$823$	−43.0000	−1.49889	−0.749443	+	0.662069i	$0.769679\pi$
$824$	−12.0000	−0.418040
$825$	0	0
$826$	−9.00000	−0.313150
$827$	−37.0000	−1.28662	−0.643308	−	0.765607i	$-0.722439\pi$
$827$	−37.0000	−1.28662	−0.643308	+	0.765607i	$0.722439\pi$
$828$	10.0000	0.347524
$829$	25.0000	0.868286	0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000	0.868286	0.434143	+	0.900844i	$0.357051\pi$
$830$	−16.0000	−0.555368
$831$	−16.0000	−0.555034
$832$	−1.00000	−0.0346688
$833$	14.0000	0.485071
$834$	14.0000	0.484780
$835$	−44.0000	−1.52268
$836$	0	0
$837$	50.0000	1.72825
$838$	−10.0000	−0.345444
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	−6.00000	−0.207020
$841$	−28.0000	−0.965517
$842$	−15.0000	−0.516934
$843$	16.0000	0.551069
$844$	−1.00000	−0.0344214
$845$	24.0000	0.825625
$846$	0	0
$847$	0	0
$848$	−1.00000	−0.0343401
$849$	−14.0000	−0.480479
$850$	7.00000	0.240098
$851$	30.0000	1.02839
$852$	10.0000	0.342594
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	−36.0000	−1.23189
$855$	−4.00000	−0.136797
$856$	−13.0000	−0.444331
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	0	0
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	−8.00000	−0.272798
$861$	18.0000	0.613438
$862$	34.0000	1.15804
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	−5.00000	−0.170103
$865$	28.0000	0.952029
$866$	−24.0000	−0.815553
$867$	−32.0000	−1.08678
$868$	30.0000	1.01827
$869$	0	0
$870$	2.00000	0.0678064
$871$	−3.00000	−0.101651
$872$	−13.0000	−0.440236
$873$	−16.0000	−0.541518
$874$	−5.00000	−0.169128
$875$	36.0000	1.21702
$876$	3.00000	0.101361
$877$	−27.0000	−0.911725	−0.455863	−	0.890050i	$-0.650669\pi$
$877$	−27.0000	−0.911725	−0.455863	+	0.890050i	$0.650669\pi$
$878$	−14.0000	−0.472477
$879$	−9.00000	−0.303562
$880$	0	0
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	4.00000	0.134687
$883$	−44.0000	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$884$	−7.00000	−0.235435
$885$	6.00000	0.201688
$886$	−18.0000	−0.604722
$887$	4.00000	0.134307	0.0671534	−	0.997743i	$-0.478608\pi$
$887$	4.00000	0.134307	0.0671534	+	0.997743i	$0.478608\pi$
$888$	−6.00000	−0.201347
$889$	−48.0000	−1.60987
$890$	−16.0000	−0.536321
$891$	0	0
$892$	10.0000	0.334825
$893$	0	0
$894$	18.0000	0.602010
$895$	−8.00000	−0.267411
$896$	−3.00000	−0.100223
$897$	−5.00000	−0.166945
$898$	−24.0000	−0.800890
$899$	−10.0000	−0.333519
$900$	2.00000	0.0666667
$901$	−7.00000	−0.233204
$902$	0	0
$903$	−12.0000	−0.399335
$904$	12.0000	0.399114
$905$	4.00000	0.132964
$906$	−12.0000	−0.398673
$907$	13.0000	0.431658	0.215829	−	0.976431i	$-0.430755\pi$
$907$	13.0000	0.431658	0.215829	+	0.976431i	$0.430755\pi$
$908$	15.0000	0.497792
$909$	12.0000	0.398015
$910$	−6.00000	−0.198898
$911$	−6.00000	−0.198789	−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000	−0.198789	−0.0993944	+	0.995048i	$0.531691\pi$
$912$	1.00000	0.0331133
$913$	0	0
$914$	−37.0000	−1.22385
$915$	24.0000	0.793416
$916$	20.0000	0.660819
$917$	66.0000	2.17951
$918$	−35.0000	−1.15517
$919$	−3.00000	−0.0989609	−0.0494804	−	0.998775i	$-0.515757\pi$
$919$	−3.00000	−0.0989609	−0.0494804	+	0.998775i	$0.515757\pi$
$920$	−10.0000	−0.329690
$921$	−16.0000	−0.527218
$922$	−8.00000	−0.263466
$923$	10.0000	0.329154
$924$	0	0
$925$	6.00000	0.197279
$926$	−16.0000	−0.525793
$927$	−24.0000	−0.788263
$928$	1.00000	0.0328266
$929$	29.0000	0.951459	0.475730	−	0.879592i	$-0.342184\pi$
$929$	29.0000	0.951459	0.475730	+	0.879592i	$0.342184\pi$
$930$	−20.0000	−0.655826
$931$	−2.00000	−0.0655474
$932$	10.0000	0.327561
$933$	−3.00000	−0.0982156
$934$	−20.0000	−0.654420
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	5.00000	0.163343	0.0816714	−	0.996659i	$-0.473974\pi$
$937$	5.00000	0.163343	0.0816714	+	0.996659i	$0.473974\pi$
$938$	−9.00000	−0.293860
$939$	−21.0000	−0.685309
$940$	0	0
$941$	−33.0000	−1.07577	−0.537885	−	0.843018i	$-0.680776\pi$
$941$	−33.0000	−1.07577	−0.537885	+	0.843018i	$0.680776\pi$
$942$	−22.0000	−0.716799
$943$	30.0000	0.976934
$944$	3.00000	0.0976417
$945$	−30.0000	−0.975900
$946$	0	0
$947$	−48.0000	−1.55979	−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000	−1.55979	−0.779895	+	0.625910i	$0.784728\pi$
$948$	8.00000	0.259828
$949$	3.00000	0.0973841
$950$	−1.00000	−0.0324443
$951$	−21.0000	−0.680972
$952$	−21.0000	−0.680614
$953$	−60.0000	−1.94359	−0.971795	−	0.235826i	$-0.924220\pi$
$953$	−60.0000	−1.94359	−0.971795	+	0.235826i	$0.924220\pi$
$954$	−2.00000	−0.0647524
$955$	−6.00000	−0.194155
$956$	−25.0000	−0.808558
$957$	0	0
$958$	−12.0000	−0.387702
$959$	−51.0000	−1.64688
$960$	2.00000	0.0645497
$961$	69.0000	2.22581
$962$	−6.00000	−0.193448
$963$	−26.0000	−0.837838
$964$	4.00000	0.128831
$965$	−8.00000	−0.257529
$966$	−15.0000	−0.482617
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	0	0
$969$	7.00000	0.224872
$970$	16.0000	0.513729
$971$	−44.0000	−1.41203	−0.706014	−	0.708198i	$-0.749508\pi$
$971$	−44.0000	−1.41203	−0.706014	+	0.708198i	$0.749508\pi$
$972$	−16.0000	−0.513200
$973$	42.0000	1.34646
$974$	12.0000	0.384505
$975$	−1.00000	−0.0320256
$976$	12.0000	0.384111
$977$	−60.0000	−1.91957	−0.959785	−	0.280736i	$-0.909421\pi$
$977$	−60.0000	−1.91957	−0.959785	+	0.280736i	$0.909421\pi$
$978$	−2.00000	−0.0639529
$979$	0	0
$980$	−4.00000	−0.127775
$981$	−26.0000	−0.830116
$982$	10.0000	0.319113
$983$	−46.0000	−1.46717	−0.733586	−	0.679597i	$-0.762155\pi$
$983$	−46.0000	−1.46717	−0.733586	+	0.679597i	$0.762155\pi$
$984$	−6.00000	−0.191273
$985$	−24.0000	−0.764704
$986$	7.00000	0.222925
$987$	0	0
$988$	1.00000	0.0318142
$989$	−20.0000	−0.635963
$990$	0	0
$991$	44.0000	1.39771	0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000	1.39771	0.698853	+	0.715265i	$0.253694\pi$
$992$	−10.0000	−0.317500
$993$	−29.0000	−0.920287
$994$	30.0000	0.951542
$995$	−46.0000	−1.45830
$996$	8.00000	0.253490
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	28.0000	0.886325
$999$	−30.0000	−0.949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.b.1.1		1
11.10	odd	2		418.2.a.a.1.1	✓	1
33.32	even	2		3762.2.a.g.1.1		1
44.43	even	2		3344.2.a.h.1.1		1
209.208	even	2		7942.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.a.1.1	✓	1	11.10	odd	2
3344.2.a.h.1.1		1	44.43	even	2
3762.2.a.g.1.1		1	33.32	even	2
4598.2.a.b.1.1		1	1.1	even	1	trivial
7942.2.a.i.1.1		1	209.208	even	2

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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