LMFDB - Embedded newform 598.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [598,2,Mod(1,598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(598, 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("598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 598 = 2 \cdot 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	598.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:	$4.77505404087$
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	$\chi$	$=$	598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +3.00000 q^{10} +2.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.00000 q^{14} -3.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.00000 q^{18} -4.00000 q^{19} +3.00000 q^{20} -3.00000 q^{21} +2.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} +3.00000 q^{28} -3.00000 q^{30} +8.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} -1.00000 q^{34} +9.00000 q^{35} -2.00000 q^{36} +3.00000 q^{37} -4.00000 q^{38} +1.00000 q^{39} +3.00000 q^{40} -2.00000 q^{41} -3.00000 q^{42} -1.00000 q^{43} +2.00000 q^{44} -6.00000 q^{45} -1.00000 q^{46} -3.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +4.00000 q^{50} +1.00000 q^{51} -1.00000 q^{52} -2.00000 q^{53} +5.00000 q^{54} +6.00000 q^{55} +3.00000 q^{56} +4.00000 q^{57} -3.00000 q^{60} -4.00000 q^{61} +8.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -3.00000 q^{65} -2.00000 q^{66} -10.0000 q^{67} -1.00000 q^{68} +1.00000 q^{69} +9.00000 q^{70} +3.00000 q^{71} -2.00000 q^{72} -12.0000 q^{73} +3.00000 q^{74} -4.00000 q^{75} -4.00000 q^{76} +6.00000 q^{77} +1.00000 q^{78} +8.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +6.00000 q^{83} -3.00000 q^{84} -3.00000 q^{85} -1.00000 q^{86} +2.00000 q^{88} -14.0000 q^{89} -6.00000 q^{90} -3.00000 q^{91} -1.00000 q^{92} -8.00000 q^{93} -3.00000 q^{94} -12.0000 q^{95} -1.00000 q^{96} -12.0000 q^{97} +2.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	−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
$10$	3.00000	0.948683
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.00000	0.801784
$15$	−3.00000	−0.774597
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	−2.00000	−0.471405
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	3.00000	0.670820
$21$	−3.00000	−0.654654
$22$	2.00000	0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	4.00000	0.800000
$26$	−1.00000	−0.196116
$27$	5.00000	0.962250
$28$	3.00000	0.566947
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−3.00000	−0.547723
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	−1.00000	−0.171499
$35$	9.00000	1.52128
$36$	−2.00000	−0.333333
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−4.00000	−0.648886
$39$	1.00000	0.160128
$40$	3.00000	0.474342
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−3.00000	−0.462910
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	2.00000	0.301511
$45$	−6.00000	−0.894427
$46$	−1.00000	−0.147442
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	4.00000	0.565685
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	5.00000	0.680414
$55$	6.00000	0.809040
$56$	3.00000	0.400892
$57$	4.00000	0.529813
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−3.00000	−0.387298
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	8.00000	1.01600
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	−2.00000	−0.246183
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−1.00000	−0.121268
$69$	1.00000	0.120386
$70$	9.00000	1.07571
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	−2.00000	−0.235702
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	3.00000	0.348743
$75$	−4.00000	−0.461880
$76$	−4.00000	−0.458831
$77$	6.00000	0.683763
$78$	1.00000	0.113228
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−3.00000	−0.327327
$85$	−3.00000	−0.325396
$86$	−1.00000	−0.107833
$87$	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	$0.766122\pi$
$90$	−6.00000	−0.632456
$91$	−3.00000	−0.314485
$92$	−1.00000	−0.104257
$93$	−8.00000	−0.829561
$94$	−3.00000	−0.309426
$95$	−12.0000	−1.23117
$96$	−1.00000	−0.102062
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	2.00000	0.202031
$99$	−4.00000	−0.402015
$100$	4.00000	0.400000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	1.00000	0.0990148
$103$	10.0000	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$104$	−1.00000	−0.0980581
$105$	−9.00000	−0.878310
$106$	−2.00000	−0.194257
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	5.00000	0.481125
$109$	−17.0000	−1.62830	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−17.0000	−1.62830	−0.814152	+	0.580651i	$0.802798\pi$
$110$	6.00000	0.572078
$111$	−3.00000	−0.284747
$112$	3.00000	0.283473
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	4.00000	0.374634
$115$	−3.00000	−0.279751
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	−3.00000	−0.275010
$120$	−3.00000	−0.273861
$121$	−7.00000	−0.636364
$122$	−4.00000	−0.362143
$123$	2.00000	0.180334
$124$	8.00000	0.718421
$125$	−3.00000	−0.268328
$126$	−6.00000	−0.534522
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	1.00000	0.0883883
$129$	1.00000	0.0880451
$130$	−3.00000	−0.263117
$131$	1.00000	0.0873704	0.0436852	−	0.999045i	$-0.486090\pi$
$131$	1.00000	0.0873704	0.0436852	+	0.999045i	$0.486090\pi$
$132$	−2.00000	−0.174078
$133$	−12.0000	−1.04053
$134$	−10.0000	−0.863868
$135$	15.0000	1.29099
$136$	−1.00000	−0.0857493
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	1.00000	0.0851257
$139$	−19.0000	−1.61156	−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000	−1.61156	−0.805779	+	0.592216i	$0.798253\pi$
$140$	9.00000	0.760639
$141$	3.00000	0.252646
$142$	3.00000	0.251754
$143$	−2.00000	−0.167248
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−12.0000	−0.993127
$147$	−2.00000	−0.164957
$148$	3.00000	0.246598
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−4.00000	−0.326599
$151$	−1.00000	−0.0813788	−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000	−0.0813788	−0.0406894	+	0.999172i	$0.512955\pi$
$152$	−4.00000	−0.324443
$153$	2.00000	0.161690
$154$	6.00000	0.483494
$155$	24.0000	1.92773
$156$	1.00000	0.0800641
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	8.00000	0.636446
$159$	2.00000	0.158610
$160$	3.00000	0.237171
$161$	−3.00000	−0.236433
$162$	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	$0.550070\pi$
$164$	−2.00000	−0.156174
$165$	−6.00000	−0.467099
$166$	6.00000	0.465690
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−3.00000	−0.231455
$169$	1.00000	0.0769231
$170$	−3.00000	−0.230089
$171$	8.00000	0.611775
$172$	−1.00000	−0.0762493
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	0	0
$175$	12.0000	0.907115
$176$	2.00000	0.150756
$177$	0	0
$178$	−14.0000	−1.04934
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	−6.00000	−0.447214
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	−3.00000	−0.222375
$183$	4.00000	0.295689
$184$	−1.00000	−0.0737210
$185$	9.00000	0.661693
$186$	−8.00000	−0.586588
$187$	−2.00000	−0.146254
$188$	−3.00000	−0.218797
$189$	15.0000	1.09109
$190$	−12.0000	−0.870572
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−1.00000	−0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−12.0000	−0.861550
$195$	3.00000	0.214834
$196$	2.00000	0.142857
$197$	7.00000	0.498729	0.249365	−	0.968410i	$-0.419778\pi$
$197$	7.00000	0.498729	0.249365	+	0.968410i	$0.419778\pi$
$198$	−4.00000	−0.284268
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	4.00000	0.282843
$201$	10.0000	0.705346
$202$	10.0000	0.703598
$203$	0	0
$204$	1.00000	0.0700140
$205$	−6.00000	−0.419058
$206$	10.0000	0.696733
$207$	2.00000	0.139010
$208$	−1.00000	−0.0693375
$209$	−8.00000	−0.553372
$210$	−9.00000	−0.621059
$211$	−23.0000	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$212$	−2.00000	−0.137361
$213$	−3.00000	−0.205557
$214$	4.00000	0.273434
$215$	−3.00000	−0.204598
$216$	5.00000	0.340207
$217$	24.0000	1.62923
$218$	−17.0000	−1.15139
$219$	12.0000	0.810885
$220$	6.00000	0.404520
$221$	1.00000	0.0672673
$222$	−3.00000	−0.201347
$223$	−5.00000	−0.334825	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	−5.00000	−0.334825	−0.167412	+	0.985887i	$0.553541\pi$
$224$	3.00000	0.200446
$225$	−8.00000	−0.533333
$226$	−18.0000	−1.19734
$227$	22.0000	1.46019	0.730096	−	0.683345i	$-0.239475\pi$
$227$	22.0000	1.46019	0.730096	+	0.683345i	$0.239475\pi$
$228$	4.00000	0.264906
$229$	17.0000	1.12339	0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000	1.12339	0.561696	+	0.827344i	$0.310149\pi$
$230$	−3.00000	−0.197814
$231$	−6.00000	−0.394771
$232$	0	0
$233$	13.0000	0.851658	0.425829	−	0.904804i	$-0.359982\pi$
$233$	13.0000	0.851658	0.425829	+	0.904804i	$0.359982\pi$
$234$	2.00000	0.130744
$235$	−9.00000	−0.587095
$236$	0	0
$237$	−8.00000	−0.519656
$238$	−3.00000	−0.194461
$239$	17.0000	1.09964	0.549819	−	0.835284i	$-0.314697\pi$
$239$	17.0000	1.09964	0.549819	+	0.835284i	$0.314697\pi$
$240$	−3.00000	−0.193649
$241$	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
$243$	−16.0000	−1.02640
$244$	−4.00000	−0.256074
$245$	6.00000	0.383326
$246$	2.00000	0.127515
$247$	4.00000	0.254514
$248$	8.00000	0.508001
$249$	−6.00000	−0.380235
$250$	−3.00000	−0.189737
$251$	−28.0000	−1.76734	−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000	−1.76734	−0.883672	+	0.468106i	$0.844936\pi$
$252$	−6.00000	−0.377964
$253$	−2.00000	−0.125739
$254$	18.0000	1.12942
$255$	3.00000	0.187867
$256$	1.00000	0.0625000
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	1.00000	0.0622573
$259$	9.00000	0.559233
$260$	−3.00000	−0.186052
$261$	0	0
$262$	1.00000	0.0617802
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	−2.00000	−0.123091
$265$	−6.00000	−0.368577
$266$	−12.0000	−0.735767
$267$	14.0000	0.856786
$268$	−10.0000	−0.610847
$269$	−8.00000	−0.487769	−0.243884	−	0.969804i	$-0.578422\pi$
$269$	−8.00000	−0.487769	−0.243884	+	0.969804i	$0.578422\pi$
$270$	15.0000	0.912871
$271$	−31.0000	−1.88312	−0.941558	−	0.336851i	$-0.890638\pi$
$271$	−31.0000	−1.88312	−0.941558	+	0.336851i	$0.890638\pi$
$272$	−1.00000	−0.0606339
$273$	3.00000	0.181568
$274$	−2.00000	−0.120824
$275$	8.00000	0.482418
$276$	1.00000	0.0601929
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	−19.0000	−1.13954
$279$	−16.0000	−0.957895
$280$	9.00000	0.537853
$281$	32.0000	1.90896	0.954480	−	0.298275i	$-0.0964112\pi$
$281$	32.0000	1.90896	0.954480	+	0.298275i	$0.0964112\pi$
$282$	3.00000	0.178647
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	3.00000	0.178017
$285$	12.0000	0.710819
$286$	−2.00000	−0.118262
$287$	−6.00000	−0.354169
$288$	−2.00000	−0.117851
$289$	−16.0000	−0.941176
$290$	0	0
$291$	12.0000	0.703452
$292$	−12.0000	−0.702247
$293$	19.0000	1.10999	0.554996	−	0.831853i	$-0.312720\pi$
$293$	19.0000	1.10999	0.554996	+	0.831853i	$0.312720\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	3.00000	0.174371
$297$	10.0000	0.580259
$298$	−2.00000	−0.115857
$299$	1.00000	0.0578315
$300$	−4.00000	−0.230940
$301$	−3.00000	−0.172917
$302$	−1.00000	−0.0575435
$303$	−10.0000	−0.574485
$304$	−4.00000	−0.229416
$305$	−12.0000	−0.687118
$306$	2.00000	0.114332
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	6.00000	0.341882
$309$	−10.0000	−0.568880
$310$	24.0000	1.36311
$311$	32.0000	1.81455	0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000	1.81455	0.907277	+	0.420534i	$0.138157\pi$
$312$	1.00000	0.0566139
$313$	−31.0000	−1.75222	−0.876112	−	0.482108i	$-0.839871\pi$
$313$	−31.0000	−1.75222	−0.876112	+	0.482108i	$0.839871\pi$
$314$	4.00000	0.225733
$315$	−18.0000	−1.01419
$316$	8.00000	0.450035
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	2.00000	0.112154
$319$	0	0
$320$	3.00000	0.167705
$321$	−4.00000	−0.223258
$322$	−3.00000	−0.167183
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−4.00000	−0.221540
$327$	17.0000	0.940102
$328$	−2.00000	−0.110432
$329$	−9.00000	−0.496186
$330$	−6.00000	−0.330289
$331$	−2.00000	−0.109930	−0.0549650	−	0.998488i	$-0.517505\pi$
$331$	−2.00000	−0.109930	−0.0549650	+	0.998488i	$0.517505\pi$
$332$	6.00000	0.329293
$333$	−6.00000	−0.328798
$334$	0	0
$335$	−30.0000	−1.63908
$336$	−3.00000	−0.163663
$337$	13.0000	0.708155	0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000	0.708155	0.354078	+	0.935216i	$0.384795\pi$
$338$	1.00000	0.0543928
$339$	18.0000	0.977626
$340$	−3.00000	−0.162698
$341$	16.0000	0.866449
$342$	8.00000	0.432590
$343$	−15.0000	−0.809924
$344$	−1.00000	−0.0539164
$345$	3.00000	0.161515
$346$	−2.00000	−0.107521
$347$	1.00000	0.0536828	0.0268414	−	0.999640i	$-0.491455\pi$
$347$	1.00000	0.0536828	0.0268414	+	0.999640i	$0.491455\pi$
$348$	0	0
$349$	−35.0000	−1.87351	−0.936754	−	0.349990i	$-0.886185\pi$
$349$	−35.0000	−1.87351	−0.936754	+	0.349990i	$0.886185\pi$
$350$	12.0000	0.641427
$351$	−5.00000	−0.266880
$352$	2.00000	0.106600
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	0	0
$355$	9.00000	0.477670
$356$	−14.0000	−0.741999
$357$	3.00000	0.158777
$358$	−3.00000	−0.158555
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	−6.00000	−0.316228
$361$	−3.00000	−0.157895
$362$	16.0000	0.840941
$363$	7.00000	0.367405
$364$	−3.00000	−0.157243
$365$	−36.0000	−1.88433
$366$	4.00000	0.209083
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	−1.00000	−0.0521286
$369$	4.00000	0.208232
$370$	9.00000	0.467888
$371$	−6.00000	−0.311504
$372$	−8.00000	−0.414781
$373$	20.0000	1.03556	0.517780	−	0.855514i	$-0.326758\pi$
$373$	20.0000	1.03556	0.517780	+	0.855514i	$0.326758\pi$
$374$	−2.00000	−0.103418
$375$	3.00000	0.154919
$376$	−3.00000	−0.154713
$377$	0	0
$378$	15.0000	0.771517
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	−12.0000	−0.615587
$381$	−18.0000	−0.922168
$382$	16.0000	0.818631
$383$	9.00000	0.459879	0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000	0.459879	0.229939	+	0.973205i	$0.426147\pi$
$384$	−1.00000	−0.0510310
$385$	18.0000	0.917365
$386$	14.0000	0.712581
$387$	2.00000	0.101666
$388$	−12.0000	−0.609208
$389$	8.00000	0.405616	0.202808	−	0.979219i	$-0.434993\pi$
$389$	8.00000	0.405616	0.202808	+	0.979219i	$0.434993\pi$
$390$	3.00000	0.151911
$391$	1.00000	0.0505722
$392$	2.00000	0.101015
$393$	−1.00000	−0.0504433
$394$	7.00000	0.352655
$395$	24.0000	1.20757
$396$	−4.00000	−0.201008
$397$	30.0000	1.50566	0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000	1.50566	0.752828	+	0.658217i	$0.228689\pi$
$398$	−4.00000	−0.200502
$399$	12.0000	0.600751
$400$	4.00000	0.200000
$401$	32.0000	1.59800	0.799002	−	0.601329i	$-0.205362\pi$
$401$	32.0000	1.59800	0.799002	+	0.601329i	$0.205362\pi$
$402$	10.0000	0.498755
$403$	−8.00000	−0.398508
$404$	10.0000	0.497519
$405$	3.00000	0.149071
$406$	0	0
$407$	6.00000	0.297409
$408$	1.00000	0.0495074
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	−6.00000	−0.296319
$411$	2.00000	0.0986527
$412$	10.0000	0.492665
$413$	0	0
$414$	2.00000	0.0982946
$415$	18.0000	0.883585
$416$	−1.00000	−0.0490290
$417$	19.0000	0.930434
$418$	−8.00000	−0.391293
$419$	−35.0000	−1.70986	−0.854931	−	0.518742i	$-0.826401\pi$
$419$	−35.0000	−1.70986	−0.854931	+	0.518742i	$0.826401\pi$
$420$	−9.00000	−0.439155
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	−23.0000	−1.11962
$423$	6.00000	0.291730
$424$	−2.00000	−0.0971286
$425$	−4.00000	−0.194029
$426$	−3.00000	−0.145350
$427$	−12.0000	−0.580721
$428$	4.00000	0.193347
$429$	2.00000	0.0965609
$430$	−3.00000	−0.144673
$431$	3.00000	0.144505	0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000	0.144505	0.0722525	+	0.997386i	$0.476981\pi$
$432$	5.00000	0.240563
$433$	37.0000	1.77811	0.889053	−	0.457804i	$-0.151364\pi$
$433$	37.0000	1.77811	0.889053	+	0.457804i	$0.151364\pi$
$434$	24.0000	1.15204
$435$	0	0
$436$	−17.0000	−0.814152
$437$	4.00000	0.191346
$438$	12.0000	0.573382
$439$	18.0000	0.859093	0.429547	−	0.903045i	$-0.358673\pi$
$439$	18.0000	0.859093	0.429547	+	0.903045i	$0.358673\pi$
$440$	6.00000	0.286039
$441$	−4.00000	−0.190476
$442$	1.00000	0.0475651
$443$	39.0000	1.85295	0.926473	−	0.376361i	$-0.122825\pi$
$443$	39.0000	1.85295	0.926473	+	0.376361i	$0.122825\pi$
$444$	−3.00000	−0.142374
$445$	−42.0000	−1.99099
$446$	−5.00000	−0.236757
$447$	2.00000	0.0945968
$448$	3.00000	0.141737
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	−8.00000	−0.377124
$451$	−4.00000	−0.188353
$452$	−18.0000	−0.846649
$453$	1.00000	0.0469841
$454$	22.0000	1.03251
$455$	−9.00000	−0.421927
$456$	4.00000	0.187317
$457$	−12.0000	−0.561336	−0.280668	−	0.959805i	$-0.590556\pi$
$457$	−12.0000	−0.561336	−0.280668	+	0.959805i	$0.590556\pi$
$458$	17.0000	0.794358
$459$	−5.00000	−0.233380
$460$	−3.00000	−0.139876
$461$	−7.00000	−0.326023	−0.163011	−	0.986624i	$-0.552121\pi$
$461$	−7.00000	−0.326023	−0.163011	+	0.986624i	$0.552121\pi$
$462$	−6.00000	−0.279145
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	0	0
$465$	−24.0000	−1.11297
$466$	13.0000	0.602213
$467$	−4.00000	−0.185098	−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000	−0.185098	−0.0925490	+	0.995708i	$0.529501\pi$
$468$	2.00000	0.0924500
$469$	−30.0000	−1.38527
$470$	−9.00000	−0.415139
$471$	−4.00000	−0.184310
$472$	0	0
$473$	−2.00000	−0.0919601
$474$	−8.00000	−0.367452
$475$	−16.0000	−0.734130
$476$	−3.00000	−0.137505
$477$	4.00000	0.183147
$478$	17.0000	0.777562
$479$	−1.00000	−0.0456912	−0.0228456	−	0.999739i	$-0.507273\pi$
$479$	−1.00000	−0.0456912	−0.0228456	+	0.999739i	$0.507273\pi$
$480$	−3.00000	−0.136931
$481$	−3.00000	−0.136788
$482$	10.0000	0.455488
$483$	3.00000	0.136505
$484$	−7.00000	−0.318182
$485$	−36.0000	−1.63468
$486$	−16.0000	−0.725775
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	−4.00000	−0.181071
$489$	4.00000	0.180886
$490$	6.00000	0.271052
$491$	−23.0000	−1.03798	−0.518988	−	0.854782i	$-0.673691\pi$
$491$	−23.0000	−1.03798	−0.518988	+	0.854782i	$0.673691\pi$
$492$	2.00000	0.0901670
$493$	0	0
$494$	4.00000	0.179969
$495$	−12.0000	−0.539360
$496$	8.00000	0.359211
$497$	9.00000	0.403705
$498$	−6.00000	−0.268866
$499$	−8.00000	−0.358129	−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000	−0.358129	−0.179065	+	0.983837i	$0.557307\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	−28.0000	−1.24970
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−6.00000	−0.267261
$505$	30.0000	1.33498
$506$	−2.00000	−0.0889108
$507$	−1.00000	−0.0444116
$508$	18.0000	0.798621
$509$	−34.0000	−1.50702	−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000	−1.50702	−0.753512	+	0.657434i	$0.771642\pi$
$510$	3.00000	0.132842
$511$	−36.0000	−1.59255
$512$	1.00000	0.0441942
$513$	−20.0000	−0.883022
$514$	−3.00000	−0.132324
$515$	30.0000	1.32196
$516$	1.00000	0.0440225
$517$	−6.00000	−0.263880
$518$	9.00000	0.395437
$519$	2.00000	0.0877903
$520$	−3.00000	−0.131559
$521$	−27.0000	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$522$	0	0
$523$	−28.0000	−1.22435	−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000	−1.22435	−0.612177	+	0.790721i	$0.709706\pi$
$524$	1.00000	0.0436852
$525$	−12.0000	−0.523723
$526$	18.0000	0.784837
$527$	−8.00000	−0.348485
$528$	−2.00000	−0.0870388
$529$	1.00000	0.0434783
$530$	−6.00000	−0.260623
$531$	0	0
$532$	−12.0000	−0.520266
$533$	2.00000	0.0866296
$534$	14.0000	0.605839
$535$	12.0000	0.518805
$536$	−10.0000	−0.431934
$537$	3.00000	0.129460
$538$	−8.00000	−0.344904
$539$	4.00000	0.172292
$540$	15.0000	0.645497
$541$	−45.0000	−1.93470	−0.967351	−	0.253442i	$-0.918437\pi$
$541$	−45.0000	−1.93470	−0.967351	+	0.253442i	$0.918437\pi$
$542$	−31.0000	−1.33156
$543$	−16.0000	−0.686626
$544$	−1.00000	−0.0428746
$545$	−51.0000	−2.18460
$546$	3.00000	0.128388
$547$	39.0000	1.66752	0.833760	−	0.552127i	$-0.186184\pi$
$547$	39.0000	1.66752	0.833760	+	0.552127i	$0.186184\pi$
$548$	−2.00000	−0.0854358
$549$	8.00000	0.341432
$550$	8.00000	0.341121
$551$	0	0
$552$	1.00000	0.0425628
$553$	24.0000	1.02058
$554$	4.00000	0.169944
$555$	−9.00000	−0.382029
$556$	−19.0000	−0.805779
$557$	5.00000	0.211857	0.105928	−	0.994374i	$-0.466219\pi$
$557$	5.00000	0.211857	0.105928	+	0.994374i	$0.466219\pi$
$558$	−16.0000	−0.677334
$559$	1.00000	0.0422955
$560$	9.00000	0.380319
$561$	2.00000	0.0844401
$562$	32.0000	1.34984
$563$	39.0000	1.64365	0.821827	−	0.569737i	$-0.192955\pi$
$563$	39.0000	1.64365	0.821827	+	0.569737i	$0.192955\pi$
$564$	3.00000	0.126323
$565$	−54.0000	−2.27180
$566$	−4.00000	−0.168133
$567$	3.00000	0.125988
$568$	3.00000	0.125877
$569$	33.0000	1.38343	0.691716	−	0.722170i	$-0.256855\pi$
$569$	33.0000	1.38343	0.691716	+	0.722170i	$0.256855\pi$
$570$	12.0000	0.502625
$571$	−3.00000	−0.125546	−0.0627730	−	0.998028i	$-0.519994\pi$
$571$	−3.00000	−0.125546	−0.0627730	+	0.998028i	$0.519994\pi$
$572$	−2.00000	−0.0836242
$573$	−16.0000	−0.668410
$574$	−6.00000	−0.250435
$575$	−4.00000	−0.166812
$576$	−2.00000	−0.0833333
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−16.0000	−0.665512
$579$	−14.0000	−0.581820
$580$	0	0
$581$	18.0000	0.746766
$582$	12.0000	0.497416
$583$	−4.00000	−0.165663
$584$	−12.0000	−0.496564
$585$	6.00000	0.248069
$586$	19.0000	0.784883
$587$	−2.00000	−0.0825488	−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000	−0.0825488	−0.0412744	+	0.999148i	$0.513142\pi$
$588$	−2.00000	−0.0824786
$589$	−32.0000	−1.31854
$590$	0	0
$591$	−7.00000	−0.287942
$592$	3.00000	0.123299
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	10.0000	0.410305
$595$	−9.00000	−0.368964
$596$	−2.00000	−0.0819232
$597$	4.00000	0.163709
$598$	1.00000	0.0408930
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−4.00000	−0.163299
$601$	−7.00000	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$602$	−3.00000	−0.122271
$603$	20.0000	0.814463
$604$	−1.00000	−0.0406894
$605$	−21.0000	−0.853771
$606$	−10.0000	−0.406222
$607$	−28.0000	−1.13648	−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000	−1.13648	−0.568242	+	0.822861i	$0.692376\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	−12.0000	−0.485866
$611$	3.00000	0.121367
$612$	2.00000	0.0808452
$613$	46.0000	1.85792	0.928961	−	0.370177i	$-0.120703\pi$
$613$	46.0000	1.85792	0.928961	+	0.370177i	$0.120703\pi$
$614$	−20.0000	−0.807134
$615$	6.00000	0.241943
$616$	6.00000	0.241747
$617$	4.00000	0.161034	0.0805170	−	0.996753i	$-0.474343\pi$
$617$	4.00000	0.161034	0.0805170	+	0.996753i	$0.474343\pi$
$618$	−10.0000	−0.402259
$619$	18.0000	0.723481	0.361741	−	0.932279i	$-0.382183\pi$
$619$	18.0000	0.723481	0.361741	+	0.932279i	$0.382183\pi$
$620$	24.0000	0.963863
$621$	−5.00000	−0.200643
$622$	32.0000	1.28308
$623$	−42.0000	−1.68269
$624$	1.00000	0.0400320
$625$	−29.0000	−1.16000
$626$	−31.0000	−1.23901
$627$	8.00000	0.319489
$628$	4.00000	0.159617
$629$	−3.00000	−0.119618
$630$	−18.0000	−0.717137
$631$	25.0000	0.995234	0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000	0.995234	0.497617	+	0.867397i	$0.334208\pi$
$632$	8.00000	0.318223
$633$	23.0000	0.914168
$634$	10.0000	0.397151
$635$	54.0000	2.14292
$636$	2.00000	0.0793052
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	−6.00000	−0.237356
$640$	3.00000	0.118585
$641$	14.0000	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$642$	−4.00000	−0.157867
$643$	−38.0000	−1.49857	−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000	−1.49857	−0.749287	+	0.662246i	$0.769604\pi$
$644$	−3.00000	−0.118217
$645$	3.00000	0.118125
$646$	4.00000	0.157378
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−4.00000	−0.156893
$651$	−24.0000	−0.940634
$652$	−4.00000	−0.156652
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	17.0000	0.664753
$655$	3.00000	0.117220
$656$	−2.00000	−0.0780869
$657$	24.0000	0.936329
$658$	−9.00000	−0.350857
$659$	−44.0000	−1.71400	−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000	−1.71400	−0.856998	+	0.515319i	$0.827673\pi$
$660$	−6.00000	−0.233550
$661$	−50.0000	−1.94477	−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−50.0000	−1.94477	−0.972387	+	0.233373i	$0.925024\pi$
$662$	−2.00000	−0.0777322
$663$	−1.00000	−0.0388368
$664$	6.00000	0.232845
$665$	−36.0000	−1.39602
$666$	−6.00000	−0.232495
$667$	0	0
$668$	0	0
$669$	5.00000	0.193311
$670$	−30.0000	−1.15900
$671$	−8.00000	−0.308837
$672$	−3.00000	−0.115728
$673$	13.0000	0.501113	0.250557	−	0.968102i	$-0.419386\pi$
$673$	13.0000	0.501113	0.250557	+	0.968102i	$0.419386\pi$
$674$	13.0000	0.500741
$675$	20.0000	0.769800
$676$	1.00000	0.0384615
$677$	−2.00000	−0.0768662	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000	−0.0768662	−0.0384331	+	0.999261i	$0.512237\pi$
$678$	18.0000	0.691286
$679$	−36.0000	−1.38155
$680$	−3.00000	−0.115045
$681$	−22.0000	−0.843042
$682$	16.0000	0.612672
$683$	−26.0000	−0.994862	−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000	−0.994862	−0.497431	+	0.867503i	$0.665723\pi$
$684$	8.00000	0.305888
$685$	−6.00000	−0.229248
$686$	−15.0000	−0.572703
$687$	−17.0000	−0.648590
$688$	−1.00000	−0.0381246
$689$	2.00000	0.0761939
$690$	3.00000	0.114208
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	−2.00000	−0.0760286
$693$	−12.0000	−0.455842
$694$	1.00000	0.0379595
$695$	−57.0000	−2.16213
$696$	0	0
$697$	2.00000	0.0757554
$698$	−35.0000	−1.32477
$699$	−13.0000	−0.491705
$700$	12.0000	0.453557
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	−5.00000	−0.188713
$703$	−12.0000	−0.452589
$704$	2.00000	0.0753778
$705$	9.00000	0.338960
$706$	10.0000	0.376355
$707$	30.0000	1.12827
$708$	0	0
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	9.00000	0.337764
$711$	−16.0000	−0.600047
$712$	−14.0000	−0.524672
$713$	−8.00000	−0.299602
$714$	3.00000	0.112272
$715$	−6.00000	−0.224387
$716$	−3.00000	−0.112115
$717$	−17.0000	−0.634877
$718$	32.0000	1.19423
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	−6.00000	−0.223607
$721$	30.0000	1.11726
$722$	−3.00000	−0.111648
$723$	−10.0000	−0.371904
$724$	16.0000	0.594635
$725$	0	0
$726$	7.00000	0.259794
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	−3.00000	−0.111187
$729$	13.0000	0.481481
$730$	−36.0000	−1.33242
$731$	1.00000	0.0369863
$732$	4.00000	0.147844
$733$	−11.0000	−0.406294	−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000	−0.406294	−0.203147	+	0.979148i	$0.565117\pi$
$734$	12.0000	0.442928
$735$	−6.00000	−0.221313
$736$	−1.00000	−0.0368605
$737$	−20.0000	−0.736709
$738$	4.00000	0.147242
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	9.00000	0.330847
$741$	−4.00000	−0.146944
$742$	−6.00000	−0.220267
$743$	−9.00000	−0.330178	−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000	−0.330178	−0.165089	+	0.986279i	$0.552791\pi$
$744$	−8.00000	−0.293294
$745$	−6.00000	−0.219823
$746$	20.0000	0.732252
$747$	−12.0000	−0.439057
$748$	−2.00000	−0.0731272
$749$	12.0000	0.438470
$750$	3.00000	0.109545
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	−3.00000	−0.109399
$753$	28.0000	1.02038
$754$	0	0
$755$	−3.00000	−0.109181
$756$	15.0000	0.545545
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	4.00000	0.145287
$759$	2.00000	0.0725954
$760$	−12.0000	−0.435286
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	−18.0000	−0.652071
$763$	−51.0000	−1.84632
$764$	16.0000	0.578860
$765$	6.00000	0.216930
$766$	9.00000	0.325183
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	18.0000	0.648675
$771$	3.00000	0.108042
$772$	14.0000	0.503871
$773$	3.00000	0.107903	0.0539513	−	0.998544i	$-0.482818\pi$
$773$	3.00000	0.107903	0.0539513	+	0.998544i	$0.482818\pi$
$774$	2.00000	0.0718885
$775$	32.0000	1.14947
$776$	−12.0000	−0.430775
$777$	−9.00000	−0.322873
$778$	8.00000	0.286814
$779$	8.00000	0.286630
$780$	3.00000	0.107417
$781$	6.00000	0.214697
$782$	1.00000	0.0357599
$783$	0	0
$784$	2.00000	0.0714286
$785$	12.0000	0.428298
$786$	−1.00000	−0.0356688
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	7.00000	0.249365
$789$	−18.0000	−0.640817
$790$	24.0000	0.853882
$791$	−54.0000	−1.92002
$792$	−4.00000	−0.142134
$793$	4.00000	0.142044
$794$	30.0000	1.06466
$795$	6.00000	0.212798
$796$	−4.00000	−0.141776
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	12.0000	0.424795
$799$	3.00000	0.106132
$800$	4.00000	0.141421
$801$	28.0000	0.989331
$802$	32.0000	1.12996
$803$	−24.0000	−0.846942
$804$	10.0000	0.352673
$805$	−9.00000	−0.317208
$806$	−8.00000	−0.281788
$807$	8.00000	0.281613
$808$	10.0000	0.351799
$809$	43.0000	1.51180	0.755900	−	0.654687i	$-0.227200\pi$
$809$	43.0000	1.51180	0.755900	+	0.654687i	$0.227200\pi$
$810$	3.00000	0.105409
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	31.0000	1.08722
$814$	6.00000	0.210300
$815$	−12.0000	−0.420342
$816$	1.00000	0.0350070
$817$	4.00000	0.139942
$818$	6.00000	0.209785
$819$	6.00000	0.209657
$820$	−6.00000	−0.209529
$821$	41.0000	1.43091	0.715455	−	0.698659i	$-0.246219\pi$
$821$	41.0000	1.43091	0.715455	+	0.698659i	$0.246219\pi$
$822$	2.00000	0.0697580
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	10.0000	0.348367
$825$	−8.00000	−0.278524
$826$	0	0
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	2.00000	0.0695048
$829$	24.0000	0.833554	0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000	0.833554	0.416777	+	0.909009i	$0.363160\pi$
$830$	18.0000	0.624789
$831$	−4.00000	−0.138758
$832$	−1.00000	−0.0346688
$833$	−2.00000	−0.0692959
$834$	19.0000	0.657916
$835$	0	0
$836$	−8.00000	−0.276686
$837$	40.0000	1.38260
$838$	−35.0000	−1.20905
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	−9.00000	−0.310530
$841$	−29.0000	−1.00000
$842$	−17.0000	−0.585859
$843$	−32.0000	−1.10214
$844$	−23.0000	−0.791693
$845$	3.00000	0.103203
$846$	6.00000	0.206284
$847$	−21.0000	−0.721569
$848$	−2.00000	−0.0686803
$849$	4.00000	0.137280
$850$	−4.00000	−0.137199
$851$	−3.00000	−0.102839
$852$	−3.00000	−0.102778
$853$	−33.0000	−1.12990	−0.564949	−	0.825126i	$-0.691104\pi$
$853$	−33.0000	−1.12990	−0.564949	+	0.825126i	$0.691104\pi$
$854$	−12.0000	−0.410632
$855$	24.0000	0.820783
$856$	4.00000	0.136717
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	2.00000	0.0682789
$859$	36.0000	1.22830	0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000	1.22830	0.614152	+	0.789188i	$0.289498\pi$
$860$	−3.00000	−0.102299
$861$	6.00000	0.204479
$862$	3.00000	0.102180
$863$	−11.0000	−0.374444	−0.187222	−	0.982318i	$-0.559948\pi$
$863$	−11.0000	−0.374444	−0.187222	+	0.982318i	$0.559948\pi$
$864$	5.00000	0.170103
$865$	−6.00000	−0.204006
$866$	37.0000	1.25731
$867$	16.0000	0.543388
$868$	24.0000	0.814613
$869$	16.0000	0.542763
$870$	0	0
$871$	10.0000	0.338837
$872$	−17.0000	−0.575693
$873$	24.0000	0.812277
$874$	4.00000	0.135302
$875$	−9.00000	−0.304256
$876$	12.0000	0.405442
$877$	−17.0000	−0.574049	−0.287025	−	0.957923i	$-0.592666\pi$
$877$	−17.0000	−0.574049	−0.287025	+	0.957923i	$0.592666\pi$
$878$	18.0000	0.607471
$879$	−19.0000	−0.640854
$880$	6.00000	0.202260
$881$	−49.0000	−1.65085	−0.825426	−	0.564510i	$-0.809065\pi$
$881$	−49.0000	−1.65085	−0.825426	+	0.564510i	$0.809065\pi$
$882$	−4.00000	−0.134687
$883$	43.0000	1.44707	0.723533	−	0.690290i	$-0.242517\pi$
$883$	43.0000	1.44707	0.723533	+	0.690290i	$0.242517\pi$
$884$	1.00000	0.0336336
$885$	0	0
$886$	39.0000	1.31023
$887$	22.0000	0.738688	0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000	0.738688	0.369344	+	0.929293i	$0.379582\pi$
$888$	−3.00000	−0.100673
$889$	54.0000	1.81110
$890$	−42.0000	−1.40784
$891$	2.00000	0.0670025
$892$	−5.00000	−0.167412
$893$	12.0000	0.401565
$894$	2.00000	0.0668900
$895$	−9.00000	−0.300837
$896$	3.00000	0.100223
$897$	−1.00000	−0.0333890
$898$	12.0000	0.400445
$899$	0	0
$900$	−8.00000	−0.266667
$901$	2.00000	0.0666297
$902$	−4.00000	−0.133185
$903$	3.00000	0.0998337
$904$	−18.0000	−0.598671
$905$	48.0000	1.59557
$906$	1.00000	0.0332228
$907$	39.0000	1.29497	0.647487	−	0.762077i	$-0.275820\pi$
$907$	39.0000	1.29497	0.647487	+	0.762077i	$0.275820\pi$
$908$	22.0000	0.730096
$909$	−20.0000	−0.663358
$910$	−9.00000	−0.298347
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	4.00000	0.132453
$913$	12.0000	0.397142
$914$	−12.0000	−0.396925
$915$	12.0000	0.396708
$916$	17.0000	0.561696
$917$	3.00000	0.0990687
$918$	−5.00000	−0.165025
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	−3.00000	−0.0989071
$921$	20.0000	0.659022
$922$	−7.00000	−0.230533
$923$	−3.00000	−0.0987462
$924$	−6.00000	−0.197386
$925$	12.0000	0.394558
$926$	−20.0000	−0.657241
$927$	−20.0000	−0.656886
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	−24.0000	−0.786991
$931$	−8.00000	−0.262189
$932$	13.0000	0.425829
$933$	−32.0000	−1.04763
$934$	−4.00000	−0.130884
$935$	−6.00000	−0.196221
$936$	2.00000	0.0653720
$937$	−54.0000	−1.76410	−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000	−1.76410	−0.882052	+	0.471153i	$0.843838\pi$
$938$	−30.0000	−0.979535
$939$	31.0000	1.01165
$940$	−9.00000	−0.293548
$941$	5.00000	0.162995	0.0814977	−	0.996674i	$-0.474030\pi$
$941$	5.00000	0.162995	0.0814977	+	0.996674i	$0.474030\pi$
$942$	−4.00000	−0.130327
$943$	2.00000	0.0651290
$944$	0	0
$945$	45.0000	1.46385
$946$	−2.00000	−0.0650256
$947$	−2.00000	−0.0649913	−0.0324956	−	0.999472i	$-0.510346\pi$
$947$	−2.00000	−0.0649913	−0.0324956	+	0.999472i	$0.510346\pi$
$948$	−8.00000	−0.259828
$949$	12.0000	0.389536
$950$	−16.0000	−0.519109
$951$	−10.0000	−0.324272
$952$	−3.00000	−0.0972306
$953$	29.0000	0.939402	0.469701	−	0.882826i	$-0.344362\pi$
$953$	29.0000	0.939402	0.469701	+	0.882826i	$0.344362\pi$
$954$	4.00000	0.129505
$955$	48.0000	1.55324
$956$	17.0000	0.549819
$957$	0	0
$958$	−1.00000	−0.0323085
$959$	−6.00000	−0.193750
$960$	−3.00000	−0.0968246
$961$	33.0000	1.06452
$962$	−3.00000	−0.0967239
$963$	−8.00000	−0.257796
$964$	10.0000	0.322078
$965$	42.0000	1.35203
$966$	3.00000	0.0965234
$967$	−21.0000	−0.675314	−0.337657	−	0.941269i	$-0.609634\pi$
$967$	−21.0000	−0.675314	−0.337657	+	0.941269i	$0.609634\pi$
$968$	−7.00000	−0.224989
$969$	−4.00000	−0.128499
$970$	−36.0000	−1.15589
$971$	1.00000	0.0320915	0.0160458	−	0.999871i	$-0.494892\pi$
$971$	1.00000	0.0320915	0.0160458	+	0.999871i	$0.494892\pi$
$972$	−16.0000	−0.513200
$973$	−57.0000	−1.82734
$974$	32.0000	1.02535
$975$	4.00000	0.128103
$976$	−4.00000	−0.128037
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	4.00000	0.127906
$979$	−28.0000	−0.894884
$980$	6.00000	0.191663
$981$	34.0000	1.08554
$982$	−23.0000	−0.733959
$983$	7.00000	0.223265	0.111633	−	0.993750i	$-0.464392\pi$
$983$	7.00000	0.223265	0.111633	+	0.993750i	$0.464392\pi$
$984$	2.00000	0.0637577
$985$	21.0000	0.669116
$986$	0	0
$987$	9.00000	0.286473
$988$	4.00000	0.127257
$989$	1.00000	0.0317982
$990$	−12.0000	−0.381385
$991$	10.0000	0.317660	0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000	0.317660	0.158830	+	0.987306i	$0.449228\pi$
$992$	8.00000	0.254000
$993$	2.00000	0.0634681
$994$	9.00000	0.285463
$995$	−12.0000	−0.380426
$996$	−6.00000	−0.190117
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	−8.00000	−0.253236
$999$	15.0000	0.474579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	598.2.a.d.1.1	✓	1
3.2	odd	2		5382.2.a.a.1.1		1
4.3	odd	2		4784.2.a.f.1.1		1
13.12	even	2		7774.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
598.2.a.d.1.1	✓	1	1.1	even	1	trivial
4784.2.a.f.1.1		1	4.3	odd	2
5382.2.a.a.1.1		1	3.2	odd	2
7774.2.a.a.1.1		1	13.12	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:	\( N \)	\(=\)	\( 598 = 2 \cdot 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	598.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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