LMFDB - Embedded newform 4598.2.a.j.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)

$f(q)$

$=$

$q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -3.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -3.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +6.00000 q^{9} +2.00000 q^{10} +3.00000 q^{12} +7.00000 q^{13} +1.00000 q^{14} -6.00000 q^{15} +1.00000 q^{16} +3.00000 q^{17} -6.00000 q^{18} -1.00000 q^{19} -2.00000 q^{20} -3.00000 q^{21} +3.00000 q^{23} -3.00000 q^{24} -1.00000 q^{25} -7.00000 q^{26} +9.00000 q^{27} -1.00000 q^{28} -1.00000 q^{29} +6.00000 q^{30} +2.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +2.00000 q^{35} +6.00000 q^{36} -6.00000 q^{37} +1.00000 q^{38} +21.0000 q^{39} +2.00000 q^{40} +2.00000 q^{41} +3.00000 q^{42} -4.00000 q^{43} -12.0000 q^{45} -3.00000 q^{46} +3.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} +9.00000 q^{51} +7.00000 q^{52} +3.00000 q^{53} -9.00000 q^{54} +1.00000 q^{56} -3.00000 q^{57} +1.00000 q^{58} +7.00000 q^{59} -6.00000 q^{60} +12.0000 q^{61} -2.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -14.0000 q^{65} +15.0000 q^{67} +3.00000 q^{68} +9.00000 q^{69} -2.00000 q^{70} +6.00000 q^{71} -6.00000 q^{72} +9.00000 q^{73} +6.00000 q^{74} -3.00000 q^{75} -1.00000 q^{76} -21.0000 q^{78} +8.00000 q^{79} -2.00000 q^{80} +9.00000 q^{81} -2.00000 q^{82} -16.0000 q^{83} -3.00000 q^{84} -6.00000 q^{85} +4.00000 q^{86} -3.00000 q^{87} -16.0000 q^{89} +12.0000 q^{90} -7.00000 q^{91} +3.00000 q^{92} +6.00000 q^{93} +2.00000 q^{95} -3.00000 q^{96} +8.00000 q^{97} +6.00000 q^{98} +O(q^{100})\)

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
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	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	$0.647584\pi$
$6$	−3.00000	−1.22474
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000	−0.353553
$9$	6.00000	2.00000
$10$	2.00000	0.632456
$11$	0	0
$11$	0	0
$12$	3.00000	0.866025
$13$	7.00000	1.94145	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000	1.94145	0.970725	+	0.240192i	$0.0772105\pi$
$14$	1.00000	0.267261
$15$	−6.00000	−1.54919
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−6.00000	−1.41421
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.00000	−0.447214
$21$	−3.00000	−0.654654
$22$	0	0
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	−3.00000	−0.612372
$25$	−1.00000	−0.200000
$26$	−7.00000	−1.37281
$27$	9.00000	1.73205
$28$	−1.00000	−0.188982
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	6.00000	1.09545
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	2.00000	0.338062
$36$	6.00000	1.00000
$37$	−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
$39$	21.0000	3.36269
$40$	2.00000	0.316228
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	3.00000	0.462910
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−12.0000	−1.78885
$46$	−3.00000	−0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	3.00000	0.433013
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	9.00000	1.26025
$52$	7.00000	0.970725
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	−9.00000	−1.22474
$55$	0	0
$56$	1.00000	0.133631
$57$	−3.00000	−0.397360
$58$	1.00000	0.131306
$59$	7.00000	0.911322	0.455661	−	0.890153i	$-0.349403\pi$
$59$	7.00000	0.911322	0.455661	+	0.890153i	$0.349403\pi$
$60$	−6.00000	−0.774597
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	−2.00000	−0.254000
$63$	−6.00000	−0.755929
$64$	1.00000	0.125000
$65$	−14.0000	−1.73649
$66$	0	0
$67$	15.0000	1.83254	0.916271	−	0.400559i	$-0.131184\pi$
$67$	15.0000	1.83254	0.916271	+	0.400559i	$0.131184\pi$
$68$	3.00000	0.363803
$69$	9.00000	1.08347
$70$	−2.00000	−0.239046
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−6.00000	−0.707107
$73$	9.00000	1.05337	0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000	1.05337	0.526685	+	0.850060i	$0.323435\pi$
$74$	6.00000	0.697486
$75$	−3.00000	−0.346410
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−21.0000	−2.37778
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−2.00000	−0.223607
$81$	9.00000	1.00000
$82$	−2.00000	−0.220863
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	−3.00000	−0.327327
$85$	−6.00000	−0.650791
$86$	4.00000	0.431331
$87$	−3.00000	−0.321634
$88$	0	0
$89$	−16.0000	−1.69600	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−16.0000	−1.69600	−0.847998	+	0.529999i	$0.822192\pi$
$90$	12.0000	1.26491
$91$	−7.00000	−0.733799
$92$	3.00000	0.312772
$93$	6.00000	0.622171
$94$	0	0
$95$	2.00000	0.205196
$96$	−3.00000	−0.306186
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	−1.00000	−0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	−9.00000	−0.891133
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	−7.00000	−0.686406
$105$	6.00000	0.585540
$106$	−3.00000	−0.291386
$107$	−11.0000	−1.06341	−0.531705	−	0.846930i	$-0.678449\pi$
$107$	−11.0000	−1.06341	−0.531705	+	0.846930i	$0.678449\pi$
$108$	9.00000	0.866025
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	−18.0000	−1.70848
$112$	−1.00000	−0.0944911
$113$	20.0000	1.88144	0.940721	−	0.339182i	$-0.110150\pi$
$113$	20.0000	1.88144	0.940721	+	0.339182i	$0.110150\pi$
$114$	3.00000	0.280976
$115$	−6.00000	−0.559503
$116$	−1.00000	−0.0928477
$117$	42.0000	3.88290
$118$	−7.00000	−0.644402
$119$	−3.00000	−0.275010
$120$	6.00000	0.547723
$121$	0	0
$122$	−12.0000	−1.08643
$123$	6.00000	0.541002
$124$	2.00000	0.179605
$125$	12.0000	1.07331
$126$	6.00000	0.534522
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	−12.0000	−1.05654
$130$	14.0000	1.22788
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	−15.0000	−1.29580
$135$	−18.0000	−1.54919
$136$	−3.00000	−0.257248
$137$	−17.0000	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$137$	−17.0000	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$138$	−9.00000	−0.766131
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	−6.00000	−0.503509
$143$	0	0
$144$	6.00000	0.500000
$145$	2.00000	0.166091
$146$	−9.00000	−0.744845
$147$	−18.0000	−1.48461
$148$	−6.00000	−0.493197
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	3.00000	0.244949
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	1.00000	0.0811107
$153$	18.0000	1.45521
$154$	0	0
$155$	−4.00000	−0.321288
$156$	21.0000	1.68135
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	−8.00000	−0.636446
$159$	9.00000	0.713746
$160$	2.00000	0.158114
$161$	−3.00000	−0.236433
$162$	−9.00000	−0.707107
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	16.0000	1.24184
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	3.00000	0.231455
$169$	36.0000	2.76923
$170$	6.00000	0.460179
$171$	−6.00000	−0.458831
$172$	−4.00000	−0.304997
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	3.00000	0.227429
$175$	1.00000	0.0755929
$176$	0	0
$177$	21.0000	1.57846
$178$	16.0000	1.19925
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	−12.0000	−0.894427
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	7.00000	0.518875
$183$	36.0000	2.66120
$184$	−3.00000	−0.221163
$185$	12.0000	0.882258
$186$	−6.00000	−0.439941
$187$	0	0
$188$	0	0
$189$	−9.00000	−0.654654
$190$	−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	$0.465384\pi$
$192$	3.00000	0.216506
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−8.00000	−0.574367
$195$	−42.0000	−3.00768
$196$	−6.00000	−0.428571
$197$	28.0000	1.99492	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	28.0000	1.99492	0.997459	+	0.0712470i	$0.0226979\pi$
$198$	0	0
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	1.00000	0.0707107
$201$	45.0000	3.17406
$202$	−2.00000	−0.140720
$203$	1.00000	0.0701862
$204$	9.00000	0.630126
$205$	−4.00000	−0.279372
$206$	12.0000	0.836080
$207$	18.0000	1.25109
$208$	7.00000	0.485363
$209$	0	0
$210$	−6.00000	−0.414039
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	3.00000	0.206041
$213$	18.0000	1.23334
$214$	11.0000	0.751945
$215$	8.00000	0.545595
$216$	−9.00000	−0.612372
$217$	−2.00000	−0.135769
$218$	11.0000	0.745014
$219$	27.0000	1.82449
$220$	0	0
$221$	21.0000	1.41261
$222$	18.0000	1.20808
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	1.00000	0.0668153
$225$	−6.00000	−0.400000
$226$	−20.0000	−1.33038
$227$	−25.0000	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$227$	−25.0000	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$228$	−3.00000	−0.198680
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	1.00000	0.0656532
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−42.0000	−2.74563
$235$	0	0
$236$	7.00000	0.455661
$237$	24.0000	1.55897
$238$	3.00000	0.194461
$239$	−13.0000	−0.840900	−0.420450	−	0.907316i	$-0.638128\pi$
$239$	−13.0000	−0.840900	−0.420450	+	0.907316i	$0.638128\pi$
$240$	−6.00000	−0.387298
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	0	0
$243$	0	0
$244$	12.0000	0.768221
$245$	12.0000	0.766652
$246$	−6.00000	−0.382546
$247$	−7.00000	−0.445399
$248$	−2.00000	−0.127000
$249$	−48.0000	−3.04188
$250$	−12.0000	−0.758947
$251$	−30.0000	−1.89358	−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000	−1.89358	−0.946792	+	0.321847i	$0.895696\pi$
$252$	−6.00000	−0.377964
$253$	0	0
$254$	−16.0000	−1.00393
$255$	−18.0000	−1.12720
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	12.0000	0.747087
$259$	6.00000	0.372822
$260$	−14.0000	−0.868243
$261$	−6.00000	−0.371391
$262$	−14.0000	−0.864923
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−1.00000	−0.0613139
$267$	−48.0000	−2.93755
$268$	15.0000	0.916271
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	18.0000	1.09545
$271$	3.00000	0.182237	0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000	0.182237	0.0911185	+	0.995840i	$0.470956\pi$
$272$	3.00000	0.181902
$273$	−21.0000	−1.27098
$274$	17.0000	1.02701
$275$	0	0
$276$	9.00000	0.541736
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	10.0000	0.599760
$279$	12.0000	0.718421
$280$	−2.00000	−0.119523
$281$	16.0000	0.954480	0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000	0.954480	0.477240	+	0.878773i	$0.341637\pi$
$282$	0	0
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	6.00000	0.356034
$285$	6.00000	0.355409
$286$	0	0
$287$	−2.00000	−0.118056
$288$	−6.00000	−0.353553
$289$	−8.00000	−0.470588
$290$	−2.00000	−0.117444
$291$	24.0000	1.40690
$292$	9.00000	0.526685
$293$	−15.0000	−0.876309	−0.438155	−	0.898900i	$-0.644368\pi$
$293$	−15.0000	−0.876309	−0.438155	+	0.898900i	$0.644368\pi$
$294$	18.0000	1.04978
$295$	−14.0000	−0.815112
$296$	6.00000	0.348743
$297$	0	0
$298$	14.0000	0.810998
$299$	21.0000	1.21446
$300$	−3.00000	−0.173205
$301$	4.00000	0.230556
$302$	−12.0000	−0.690522
$303$	6.00000	0.344691
$304$	−1.00000	−0.0573539
$305$	−24.0000	−1.37424
$306$	−18.0000	−1.02899
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	0	0
$309$	−36.0000	−2.04797
$310$	4.00000	0.227185
$311$	11.0000	0.623753	0.311876	−	0.950123i	$-0.399043\pi$
$311$	11.0000	0.623753	0.311876	+	0.950123i	$0.399043\pi$
$312$	−21.0000	−1.18889
$313$	−27.0000	−1.52613	−0.763065	−	0.646322i	$-0.776306\pi$
$313$	−27.0000	−1.52613	−0.763065	+	0.646322i	$0.776306\pi$
$314$	−18.0000	−1.01580
$315$	12.0000	0.676123
$316$	8.00000	0.450035
$317$	1.00000	0.0561656	0.0280828	−	0.999606i	$-0.491060\pi$
$317$	1.00000	0.0561656	0.0280828	+	0.999606i	$0.491060\pi$
$318$	−9.00000	−0.504695
$319$	0	0
$320$	−2.00000	−0.111803
$321$	−33.0000	−1.84188
$322$	3.00000	0.167183
$323$	−3.00000	−0.166924
$324$	9.00000	0.500000
$325$	−7.00000	−0.388290
$326$	−14.0000	−0.775388
$327$	−33.0000	−1.82490
$328$	−2.00000	−0.110432
$329$	0	0
$330$	0	0
$331$	17.0000	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	−16.0000	−0.878114
$333$	−36.0000	−1.97279
$334$	18.0000	0.984916
$335$	−30.0000	−1.63908
$336$	−3.00000	−0.163663
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	−36.0000	−1.95814
$339$	60.0000	3.25875
$340$	−6.00000	−0.325396
$341$	0	0
$342$	6.00000	0.324443
$343$	13.0000	0.701934
$344$	4.00000	0.215666
$345$	−18.0000	−0.969087
$346$	−2.00000	−0.107521
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	−3.00000	−0.160817
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	−1.00000	−0.0534522
$351$	63.0000	3.36269
$352$	0	0
$353$	−31.0000	−1.64996	−0.824982	−	0.565159i	$-0.808815\pi$
$353$	−31.0000	−1.64996	−0.824982	+	0.565159i	$0.808815\pi$
$354$	−21.0000	−1.11614
$355$	−12.0000	−0.636894
$356$	−16.0000	−0.847998
$357$	−9.00000	−0.476331
$358$	4.00000	0.211407
$359$	−27.0000	−1.42501	−0.712503	−	0.701669i	$-0.752438\pi$
$359$	−27.0000	−1.42501	−0.712503	+	0.701669i	$0.752438\pi$
$360$	12.0000	0.632456
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	0	0
$364$	−7.00000	−0.366900
$365$	−18.0000	−0.942163
$366$	−36.0000	−1.88175
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	3.00000	0.156386
$369$	12.0000	0.624695
$370$	−12.0000	−0.623850
$371$	−3.00000	−0.155752
$372$	6.00000	0.311086
$373$	13.0000	0.673114	0.336557	−	0.941663i	$-0.390737\pi$
$373$	13.0000	0.673114	0.336557	+	0.941663i	$0.390737\pi$
$374$	0	0
$375$	36.0000	1.85903
$376$	0	0
$377$	−7.00000	−0.360518
$378$	9.00000	0.462910
$379$	−1.00000	−0.0513665	−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000	−0.0513665	−0.0256833	+	0.999670i	$0.508176\pi$
$380$	2.00000	0.102598
$381$	48.0000	2.45911
$382$	−3.00000	−0.153493
$383$	26.0000	1.32854	0.664269	−	0.747494i	$-0.268743\pi$
$383$	26.0000	1.32854	0.664269	+	0.747494i	$0.268743\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	4.00000	0.203595
$387$	−24.0000	−1.21999
$388$	8.00000	0.406138
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	42.0000	2.12675
$391$	9.00000	0.455150
$392$	6.00000	0.303046
$393$	42.0000	2.11862
$394$	−28.0000	−1.41062
$395$	−16.0000	−0.805047
$396$	0	0
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	−7.00000	−0.350878
$399$	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	$0.515902\pi$
$402$	−45.0000	−2.24440
$403$	14.0000	0.697390
$404$	2.00000	0.0995037
$405$	−18.0000	−0.894427
$406$	−1.00000	−0.0496292
$407$	0	0
$408$	−9.00000	−0.445566
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	4.00000	0.197546
$411$	−51.0000	−2.51564
$412$	−12.0000	−0.591198
$413$	−7.00000	−0.344447
$414$	−18.0000	−0.884652
$415$	32.0000	1.57082
$416$	−7.00000	−0.343203
$417$	−30.0000	−1.46911
$418$	0	0
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	6.00000	0.292770
$421$	3.00000	0.146211	0.0731055	−	0.997324i	$-0.476709\pi$
$421$	3.00000	0.146211	0.0731055	+	0.997324i	$0.476709\pi$
$422$	−23.0000	−1.11962
$423$	0	0
$424$	−3.00000	−0.145693
$425$	−3.00000	−0.145521
$426$	−18.0000	−0.872103
$427$	−12.0000	−0.580721
$428$	−11.0000	−0.531705
$429$	0	0
$430$	−8.00000	−0.385794
$431$	22.0000	1.05970	0.529851	−	0.848091i	$-0.322248\pi$
$431$	22.0000	1.05970	0.529851	+	0.848091i	$0.322248\pi$
$432$	9.00000	0.433013
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	2.00000	0.0960031
$435$	6.00000	0.287678
$436$	−11.0000	−0.526804
$437$	−3.00000	−0.143509
$438$	−27.0000	−1.29011
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	0	0
$441$	−36.0000	−1.71429
$442$	−21.0000	−0.998868
$443$	−14.0000	−0.665160	−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000	−0.665160	−0.332580	+	0.943075i	$0.607919\pi$
$444$	−18.0000	−0.854242
$445$	32.0000	1.51695
$446$	−2.00000	−0.0947027
$447$	−42.0000	−1.98653
$448$	−1.00000	−0.0472456
$449$	−32.0000	−1.51017	−0.755087	−	0.655625i	$-0.772405\pi$
$449$	−32.0000	−1.51017	−0.755087	+	0.655625i	$0.772405\pi$
$450$	6.00000	0.282843
$451$	0	0
$452$	20.0000	0.940721
$453$	36.0000	1.69143
$454$	25.0000	1.17331
$455$	14.0000	0.656330
$456$	3.00000	0.140488
$457$	−23.0000	−1.07589	−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000	−1.07589	−0.537947	+	0.842978i	$0.680800\pi$
$458$	−20.0000	−0.934539
$459$	27.0000	1.26025
$460$	−6.00000	−0.279751
$461$	40.0000	1.86299	0.931493	−	0.363760i	$-0.118507\pi$
$461$	40.0000	1.86299	0.931493	+	0.363760i	$0.118507\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	−1.00000	−0.0464238
$465$	−12.0000	−0.556487
$466$	6.00000	0.277945
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	42.0000	1.94145
$469$	−15.0000	−0.692636
$470$	0	0
$471$	54.0000	2.48819
$472$	−7.00000	−0.322201
$473$	0	0
$474$	−24.0000	−1.10236
$475$	1.00000	0.0458831
$476$	−3.00000	−0.137505
$477$	18.0000	0.824163
$478$	13.0000	0.594606
$479$	−28.0000	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$479$	−28.0000	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$480$	6.00000	0.273861
$481$	−42.0000	−1.91504
$482$	−20.0000	−0.910975
$483$	−9.00000	−0.409514
$484$	0	0
$485$	−16.0000	−0.726523
$486$	0	0
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	−12.0000	−0.543214
$489$	42.0000	1.89931
$490$	−12.0000	−0.542105
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	6.00000	0.270501
$493$	−3.00000	−0.135113
$494$	7.00000	0.314945
$495$	0	0
$496$	2.00000	0.0898027
$497$	−6.00000	−0.269137
$498$	48.0000	2.15093
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	12.0000	0.536656
$501$	−54.0000	−2.41254
$502$	30.0000	1.33897
$503$	23.0000	1.02552	0.512760	−	0.858532i	$-0.328623\pi$
$503$	23.0000	1.02552	0.512760	+	0.858532i	$0.328623\pi$
$504$	6.00000	0.267261
$505$	−4.00000	−0.177998
$506$	0	0
$507$	108.000	4.79645
$508$	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	$0.630614\pi$
$510$	18.0000	0.797053
$511$	−9.00000	−0.398137
$512$	−1.00000	−0.0441942
$513$	−9.00000	−0.397360
$514$	−18.0000	−0.793946
$515$	24.0000	1.05757
$516$	−12.0000	−0.528271
$517$	0	0
$518$	−6.00000	−0.263625
$519$	6.00000	0.263371
$520$	14.0000	0.613941
$521$	−4.00000	−0.175243	−0.0876216	−	0.996154i	$-0.527927\pi$
$521$	−4.00000	−0.175243	−0.0876216	+	0.996154i	$0.527927\pi$
$522$	6.00000	0.262613
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	14.0000	0.611593
$525$	3.00000	0.130931
$526$	12.0000	0.523225
$527$	6.00000	0.261364
$528$	0	0
$529$	−14.0000	−0.608696
$530$	6.00000	0.260623
$531$	42.0000	1.82264
$532$	1.00000	0.0433555
$533$	14.0000	0.606407
$534$	48.0000	2.07716
$535$	22.0000	0.951143
$536$	−15.0000	−0.647901
$537$	−12.0000	−0.517838
$538$	−18.0000	−0.776035
$539$	0	0
$540$	−18.0000	−0.774597
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	−3.00000	−0.128861
$543$	−6.00000	−0.257485
$544$	−3.00000	−0.128624
$545$	22.0000	0.942376
$546$	21.0000	0.898717
$547$	−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
$549$	72.0000	3.07289
$550$	0	0
$551$	1.00000	0.0426014
$552$	−9.00000	−0.383065
$553$	−8.00000	−0.340195
$554$	−8.00000	−0.339887
$555$	36.0000	1.52811
$556$	−10.0000	−0.424094
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	−12.0000	−0.508001
$559$	−28.0000	−1.18427
$560$	2.00000	0.0845154
$561$	0	0
$562$	−16.0000	−0.674919
$563$	8.00000	0.337160	0.168580	−	0.985688i	$-0.446082\pi$
$563$	8.00000	0.337160	0.168580	+	0.985688i	$0.446082\pi$
$564$	0	0
$565$	−40.0000	−1.68281
$566$	−22.0000	−0.924729
$567$	−9.00000	−0.377964
$568$	−6.00000	−0.251754
$569$	−4.00000	−0.167689	−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000	−0.167689	−0.0838444	+	0.996479i	$0.526720\pi$
$570$	−6.00000	−0.251312
$571$	−2.00000	−0.0836974	−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000	−0.0836974	−0.0418487	+	0.999124i	$0.513325\pi$
$572$	0	0
$573$	9.00000	0.375980
$574$	2.00000	0.0834784
$575$	−3.00000	−0.125109
$576$	6.00000	0.250000
$577$	−17.0000	−0.707719	−0.353860	−	0.935299i	$-0.615131\pi$
$577$	−17.0000	−0.707719	−0.353860	+	0.935299i	$0.615131\pi$
$578$	8.00000	0.332756
$579$	−12.0000	−0.498703
$580$	2.00000	0.0830455
$581$	16.0000	0.663792
$582$	−24.0000	−0.994832
$583$	0	0
$584$	−9.00000	−0.372423
$585$	−84.0000	−3.47297
$586$	15.0000	0.619644
$587$	20.0000	0.825488	0.412744	−	0.910847i	$-0.364570\pi$
$587$	20.0000	0.825488	0.412744	+	0.910847i	$0.364570\pi$
$588$	−18.0000	−0.742307
$589$	−2.00000	−0.0824086
$590$	14.0000	0.576371
$591$	84.0000	3.45530
$592$	−6.00000	−0.246598
$593$	−26.0000	−1.06769	−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000	−1.06769	−0.533846	+	0.845582i	$0.679254\pi$
$594$	0	0
$595$	6.00000	0.245976
$596$	−14.0000	−0.573462
$597$	21.0000	0.859473
$598$	−21.0000	−0.858754
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	3.00000	0.122474
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	−4.00000	−0.163028
$603$	90.0000	3.66508
$604$	12.0000	0.488273
$605$	0	0
$606$	−6.00000	−0.243733
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	1.00000	0.0405554
$609$	3.00000	0.121566
$610$	24.0000	0.971732
$611$	0	0
$612$	18.0000	0.727607
$613$	−28.0000	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$613$	−28.0000	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$614$	16.0000	0.645707
$615$	−12.0000	−0.483887
$616$	0	0
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	36.0000	1.44813
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−4.00000	−0.160644
$621$	27.0000	1.08347
$622$	−11.0000	−0.441060
$623$	16.0000	0.641026
$624$	21.0000	0.840673
$625$	−19.0000	−0.760000
$626$	27.0000	1.07914
$627$	0	0
$628$	18.0000	0.718278
$629$	−18.0000	−0.717707
$630$	−12.0000	−0.478091
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	−0.318223
$633$	69.0000	2.74250
$634$	−1.00000	−0.0397151
$635$	−32.0000	−1.26988
$636$	9.00000	0.356873
$637$	−42.0000	−1.66410
$638$	0	0
$639$	36.0000	1.42414
$640$	2.00000	0.0790569
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	33.0000	1.30241
$643$	−34.0000	−1.34083	−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000	−1.34083	−0.670415	+	0.741987i	$0.733884\pi$
$644$	−3.00000	−0.118217
$645$	24.0000	0.944999
$646$	3.00000	0.118033
$647$	3.00000	0.117942	0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000	0.117942	0.0589711	+	0.998260i	$0.481218\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	7.00000	0.274563
$651$	−6.00000	−0.235159
$652$	14.0000	0.548282
$653$	12.0000	0.469596	0.234798	−	0.972044i	$-0.424557\pi$
$653$	12.0000	0.469596	0.234798	+	0.972044i	$0.424557\pi$
$654$	33.0000	1.29040
$655$	−28.0000	−1.09405
$656$	2.00000	0.0780869
$657$	54.0000	2.10674
$658$	0	0
$659$	−27.0000	−1.05177	−0.525885	−	0.850555i	$-0.676266\pi$
$659$	−27.0000	−1.05177	−0.525885	+	0.850555i	$0.676266\pi$
$660$	0	0
$661$	25.0000	0.972387	0.486194	−	0.873851i	$-0.338385\pi$
$661$	25.0000	0.972387	0.486194	+	0.873851i	$0.338385\pi$
$662$	−17.0000	−0.660724
$663$	63.0000	2.44672
$664$	16.0000	0.620920
$665$	−2.00000	−0.0775567
$666$	36.0000	1.39497
$667$	−3.00000	−0.116160
$668$	−18.0000	−0.696441
$669$	6.00000	0.231973
$670$	30.0000	1.15900
$671$	0	0
$672$	3.00000	0.115728
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	4.00000	0.154074
$675$	−9.00000	−0.346410
$676$	36.0000	1.38462
$677$	−27.0000	−1.03769	−0.518847	−	0.854867i	$-0.673639\pi$
$677$	−27.0000	−1.03769	−0.518847	+	0.854867i	$0.673639\pi$
$678$	−60.0000	−2.30429
$679$	−8.00000	−0.307012
$680$	6.00000	0.230089
$681$	−75.0000	−2.87401
$682$	0	0
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	−6.00000	−0.229416
$685$	34.0000	1.29907
$686$	−13.0000	−0.496342
$687$	60.0000	2.28914
$688$	−4.00000	−0.152499
$689$	21.0000	0.800036
$690$	18.0000	0.685248
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	6.00000	0.227757
$695$	20.0000	0.758643
$696$	3.00000	0.113715
$697$	6.00000	0.227266
$698$	10.0000	0.378506
$699$	−18.0000	−0.680823
$700$	1.00000	0.0377964
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	−63.0000	−2.37778
$703$	6.00000	0.226294
$704$	0	0
$705$	0	0
$706$	31.0000	1.16670
$707$	−2.00000	−0.0752177
$708$	21.0000	0.789228
$709$	−50.0000	−1.87779	−0.938895	−	0.344204i	$-0.888149\pi$
$709$	−50.0000	−1.87779	−0.938895	+	0.344204i	$0.888149\pi$
$710$	12.0000	0.450352
$711$	48.0000	1.80014
$712$	16.0000	0.599625
$713$	6.00000	0.224702
$714$	9.00000	0.336817
$715$	0	0
$716$	−4.00000	−0.149487
$717$	−39.0000	−1.45648
$718$	27.0000	1.00763
$719$	−25.0000	−0.932343	−0.466171	−	0.884694i	$-0.654367\pi$
$719$	−25.0000	−0.932343	−0.466171	+	0.884694i	$0.654367\pi$
$720$	−12.0000	−0.447214
$721$	12.0000	0.446903
$722$	−1.00000	−0.0372161
$723$	60.0000	2.23142
$724$	−2.00000	−0.0743294
$725$	1.00000	0.0371391
$726$	0	0
$727$	23.0000	0.853023	0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000	0.853023	0.426511	+	0.904482i	$0.359742\pi$
$728$	7.00000	0.259437
$729$	−27.0000	−1.00000
$730$	18.0000	0.666210
$731$	−12.0000	−0.443836
$732$	36.0000	1.33060
$733$	6.00000	0.221615	0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000	0.221615	0.110808	+	0.993842i	$0.464656\pi$
$734$	−16.0000	−0.590571
$735$	36.0000	1.32788
$736$	−3.00000	−0.110581
$737$	0	0
$738$	−12.0000	−0.441726
$739$	−52.0000	−1.91285	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−52.0000	−1.91285	−0.956425	+	0.291977i	$0.905687\pi$
$740$	12.0000	0.441129
$741$	−21.0000	−0.771454
$742$	3.00000	0.110133
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	−6.00000	−0.219971
$745$	28.0000	1.02584
$746$	−13.0000	−0.475964
$747$	−96.0000	−3.51246
$748$	0	0
$749$	11.0000	0.401931
$750$	−36.0000	−1.31453
$751$	−34.0000	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$751$	−34.0000	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$752$	0	0
$753$	−90.0000	−3.27978
$754$	7.00000	0.254925
$755$	−24.0000	−0.873449
$756$	−9.00000	−0.327327
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	1.00000	0.0363216
$759$	0	0
$760$	−2.00000	−0.0725476
$761$	15.0000	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$762$	−48.0000	−1.73886
$763$	11.0000	0.398227
$764$	3.00000	0.108536
$765$	−36.0000	−1.30158
$766$	−26.0000	−0.939418
$767$	49.0000	1.76929
$768$	3.00000	0.108253
$769$	37.0000	1.33425	0.667127	−	0.744944i	$-0.267524\pi$
$769$	37.0000	1.33425	0.667127	+	0.744944i	$0.267524\pi$
$770$	0	0
$771$	54.0000	1.94476
$772$	−4.00000	−0.143963
$773$	−19.0000	−0.683383	−0.341691	−	0.939812i	$-0.611000\pi$
$773$	−19.0000	−0.683383	−0.341691	+	0.939812i	$0.611000\pi$
$774$	24.0000	0.862662
$775$	−2.00000	−0.0718421
$776$	−8.00000	−0.287183
$777$	18.0000	0.645746
$778$	14.0000	0.501924
$779$	−2.00000	−0.0716574
$780$	−42.0000	−1.50384
$781$	0	0
$782$	−9.00000	−0.321839
$783$	−9.00000	−0.321634
$784$	−6.00000	−0.214286
$785$	−36.0000	−1.28490
$786$	−42.0000	−1.49809
$787$	−41.0000	−1.46149	−0.730746	−	0.682649i	$-0.760828\pi$
$787$	−41.0000	−1.46149	−0.730746	+	0.682649i	$0.760828\pi$
$788$	28.0000	0.997459
$789$	−36.0000	−1.28163
$790$	16.0000	0.569254
$791$	−20.0000	−0.711118
$792$	0	0
$793$	84.0000	2.98293
$794$	30.0000	1.06466
$795$	−18.0000	−0.638394
$796$	7.00000	0.248108
$797$	−33.0000	−1.16892	−0.584460	−	0.811423i	$-0.698694\pi$
$797$	−33.0000	−1.16892	−0.584460	+	0.811423i	$0.698694\pi$
$798$	−3.00000	−0.106199
$799$	0	0
$800$	1.00000	0.0353553
$801$	−96.0000	−3.39199
$802$	2.00000	0.0706225
$803$	0	0
$804$	45.0000	1.58703
$805$	6.00000	0.211472
$806$	−14.0000	−0.493129
$807$	54.0000	1.90089
$808$	−2.00000	−0.0703598
$809$	17.0000	0.597688	0.298844	−	0.954302i	$-0.403399\pi$
$809$	17.0000	0.597688	0.298844	+	0.954302i	$0.403399\pi$
$810$	18.0000	0.632456
$811$	25.0000	0.877869	0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000	0.877869	0.438934	+	0.898519i	$0.355356\pi$
$812$	1.00000	0.0350931
$813$	9.00000	0.315644
$814$	0	0
$815$	−28.0000	−0.980797
$816$	9.00000	0.315063
$817$	4.00000	0.139942
$818$	−14.0000	−0.489499
$819$	−42.0000	−1.46760
$820$	−4.00000	−0.139686
$821$	8.00000	0.279202	0.139601	−	0.990208i	$-0.455418\pi$
$821$	8.00000	0.279202	0.139601	+	0.990208i	$0.455418\pi$
$822$	51.0000	1.77883
$823$	53.0000	1.84746	0.923732	−	0.383040i	$-0.125123\pi$
$823$	53.0000	1.84746	0.923732	+	0.383040i	$0.125123\pi$
$824$	12.0000	0.418040
$825$	0	0
$826$	7.00000	0.243561
$827$	−13.0000	−0.452054	−0.226027	−	0.974121i	$-0.572574\pi$
$827$	−13.0000	−0.452054	−0.226027	+	0.974121i	$0.572574\pi$
$828$	18.0000	0.625543
$829$	53.0000	1.84077	0.920383	−	0.391018i	$-0.127877\pi$
$829$	53.0000	1.84077	0.920383	+	0.391018i	$0.127877\pi$
$830$	−32.0000	−1.11074
$831$	24.0000	0.832551
$832$	7.00000	0.242681
$833$	−18.0000	−0.623663
$834$	30.0000	1.03882
$835$	36.0000	1.24583
$836$	0	0
$837$	18.0000	0.622171
$838$	6.00000	0.207267
$839$	32.0000	1.10476	0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000	1.10476	0.552381	+	0.833592i	$0.313719\pi$
$840$	−6.00000	−0.207020
$841$	−28.0000	−0.965517
$842$	−3.00000	−0.103387
$843$	48.0000	1.65321
$844$	23.0000	0.791693
$845$	−72.0000	−2.47688
$846$	0	0
$847$	0	0
$848$	3.00000	0.103020
$849$	66.0000	2.26511
$850$	3.00000	0.102899
$851$	−18.0000	−0.617032
$852$	18.0000	0.616670
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	12.0000	0.410632
$855$	12.0000	0.410391
$856$	11.0000	0.375972
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	0	0
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	8.00000	0.272798
$861$	−6.00000	−0.204479
$862$	−22.0000	−0.749323
$863$	−38.0000	−1.29354	−0.646768	−	0.762687i	$-0.723880\pi$
$863$	−38.0000	−1.29354	−0.646768	+	0.762687i	$0.723880\pi$
$864$	−9.00000	−0.306186
$865$	−4.00000	−0.136004
$866$	0	0
$867$	−24.0000	−0.815083
$868$	−2.00000	−0.0678844
$869$	0	0
$870$	−6.00000	−0.203419
$871$	105.000	3.55779
$872$	11.0000	0.372507
$873$	48.0000	1.62455
$874$	3.00000	0.101477
$875$	−12.0000	−0.405674
$876$	27.0000	0.912245
$877$	−27.0000	−0.911725	−0.455863	−	0.890050i	$-0.650669\pi$
$877$	−27.0000	−0.911725	−0.455863	+	0.890050i	$0.650669\pi$
$878$	−22.0000	−0.742464
$879$	−45.0000	−1.51781
$880$	0	0
$881$	−38.0000	−1.28025	−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000	−1.28025	−0.640126	+	0.768270i	$0.721118\pi$
$882$	36.0000	1.21218
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	21.0000	0.706306
$885$	−42.0000	−1.41181
$886$	14.0000	0.470339
$887$	20.0000	0.671534	0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000	0.671534	0.335767	+	0.941945i	$0.391004\pi$
$888$	18.0000	0.604040
$889$	−16.0000	−0.536623
$890$	−32.0000	−1.07264
$891$	0	0
$892$	2.00000	0.0669650
$893$	0	0
$894$	42.0000	1.40469
$895$	8.00000	0.267411
$896$	1.00000	0.0334077
$897$	63.0000	2.10351
$898$	32.0000	1.06785
$899$	−2.00000	−0.0667037
$900$	−6.00000	−0.200000
$901$	9.00000	0.299833
$902$	0	0
$903$	12.0000	0.399335
$904$	−20.0000	−0.665190
$905$	4.00000	0.132964
$906$	−36.0000	−1.19602
$907$	1.00000	0.0332045	0.0166022	−	0.999862i	$-0.494715\pi$
$907$	1.00000	0.0332045	0.0166022	+	0.999862i	$0.494715\pi$
$908$	−25.0000	−0.829654
$909$	12.0000	0.398015
$910$	−14.0000	−0.464095
$911$	−30.0000	−0.993944	−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000	−0.993944	−0.496972	+	0.867766i	$0.665555\pi$
$912$	−3.00000	−0.0993399
$913$	0	0
$914$	23.0000	0.760772
$915$	−72.0000	−2.38025
$916$	20.0000	0.660819
$917$	−14.0000	−0.462321
$918$	−27.0000	−0.891133
$919$	−39.0000	−1.28649	−0.643246	−	0.765660i	$-0.722413\pi$
$919$	−39.0000	−1.28649	−0.643246	+	0.765660i	$0.722413\pi$
$920$	6.00000	0.197814
$921$	−48.0000	−1.58165
$922$	−40.0000	−1.31733
$923$	42.0000	1.38245
$924$	0	0
$925$	6.00000	0.197279
$926$	32.0000	1.05159
$927$	−72.0000	−2.36479
$928$	1.00000	0.0328266
$929$	−51.0000	−1.67326	−0.836628	−	0.547772i	$-0.815476\pi$
$929$	−51.0000	−1.67326	−0.836628	+	0.547772i	$0.815476\pi$
$930$	12.0000	0.393496
$931$	6.00000	0.196642
$932$	−6.00000	−0.196537
$933$	33.0000	1.08037
$934$	12.0000	0.392652
$935$	0	0
$936$	−42.0000	−1.37281
$937$	41.0000	1.33941	0.669706	−	0.742627i	$-0.266420\pi$
$937$	41.0000	1.33941	0.669706	+	0.742627i	$0.266420\pi$
$938$	15.0000	0.489767
$939$	−81.0000	−2.64334
$940$	0	0
$941$	15.0000	0.488986	0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000	0.488986	0.244493	+	0.969651i	$0.421378\pi$
$942$	−54.0000	−1.75942
$943$	6.00000	0.195387
$944$	7.00000	0.227831
$945$	18.0000	0.585540
$946$	0	0
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	24.0000	0.779484
$949$	63.0000	2.04507
$950$	−1.00000	−0.0324443
$951$	3.00000	0.0972817
$952$	3.00000	0.0972306
$953$	−4.00000	−0.129573	−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000	−0.129573	−0.0647864	+	0.997899i	$0.520637\pi$
$954$	−18.0000	−0.582772
$955$	−6.00000	−0.194155
$956$	−13.0000	−0.420450
$957$	0	0
$958$	28.0000	0.904639
$959$	17.0000	0.548959
$960$	−6.00000	−0.193649
$961$	−27.0000	−0.870968
$962$	42.0000	1.35413
$963$	−66.0000	−2.12682
$964$	20.0000	0.644157
$965$	8.00000	0.257529
$966$	9.00000	0.289570
$967$	−56.0000	−1.80084	−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000	−1.80084	−0.900419	+	0.435023i	$0.856740\pi$
$968$	0	0
$969$	−9.00000	−0.289122
$970$	16.0000	0.513729
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	0	0
$973$	10.0000	0.320585
$974$	20.0000	0.640841
$975$	−21.0000	−0.672538
$976$	12.0000	0.384111
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	−42.0000	−1.34301
$979$	0	0
$980$	12.0000	0.383326
$981$	−66.0000	−2.10722
$982$	−6.00000	−0.191468
$983$	50.0000	1.59475	0.797376	−	0.603483i	$-0.206221\pi$
$983$	50.0000	1.59475	0.797376	+	0.603483i	$0.206221\pi$
$984$	−6.00000	−0.191273
$985$	−56.0000	−1.78431
$986$	3.00000	0.0955395
$987$	0	0
$988$	−7.00000	−0.222700
$989$	−12.0000	−0.381578
$990$	0	0
$991$	−44.0000	−1.39771	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000	−1.39771	−0.698853	+	0.715265i	$0.746306\pi$
$992$	−2.00000	−0.0635001
$993$	51.0000	1.61844
$994$	6.00000	0.190308
$995$	−14.0000	−0.443830
$996$	−48.0000	−1.52094
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	20.0000	0.633089
$999$	−54.0000	−1.70848

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.c.1.1	✓	1	11.10	odd	2
3344.2.a.a.1.1		1	44.43	even	2
3762.2.a.j.1.1		1	33.32	even	2
4598.2.a.j.1.1		1	1.1	even	1	trivial
7942.2.a.a.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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