LMFDB - Embedded newform 6018.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +7.00000 q^{19} -4.00000 q^{20} -1.00000 q^{21} -2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +11.0000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} -4.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} -1.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +7.00000 q^{38} +2.00000 q^{39} -4.00000 q^{40} -7.00000 q^{41} -1.00000 q^{42} -10.0000 q^{43} -2.00000 q^{44} -4.00000 q^{45} -1.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +11.0000 q^{50} -1.00000 q^{51} +2.00000 q^{52} +3.00000 q^{53} +1.00000 q^{54} +8.00000 q^{55} -1.00000 q^{56} +7.00000 q^{57} -2.00000 q^{58} -1.00000 q^{59} -4.00000 q^{60} -2.00000 q^{61} +2.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -8.00000 q^{65} -2.00000 q^{66} -1.00000 q^{68} -1.00000 q^{69} +4.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} +7.00000 q^{73} -2.00000 q^{74} +11.0000 q^{75} +7.00000 q^{76} +2.00000 q^{77} +2.00000 q^{78} +16.0000 q^{79} -4.00000 q^{80} +1.00000 q^{81} -7.00000 q^{82} -11.0000 q^{83} -1.00000 q^{84} +4.00000 q^{85} -10.0000 q^{86} -2.00000 q^{87} -2.00000 q^{88} +9.00000 q^{89} -4.00000 q^{90} -2.00000 q^{91} -1.00000 q^{92} +2.00000 q^{93} -6.00000 q^{94} -28.0000 q^{95} +1.00000 q^{96} -17.0000 q^{97} -6.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−4.00000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−4.00000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	1.00000	0.408248
$7$	−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
$9$	1.00000	0.333333
$10$	−4.00000	−1.26491
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	−4.00000	−0.894427
$21$	−1.00000	−0.218218
$22$	−2.00000	−0.426401
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	1.00000	0.204124
$25$	11.0000	2.20000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−4.00000	−0.730297
$31$	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
$33$	−2.00000	−0.348155
$34$	−1.00000	−0.171499
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	7.00000	1.13555
$39$	2.00000	0.320256
$40$	−4.00000	−0.632456
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	−1.00000	−0.154303
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−2.00000	−0.301511
$45$	−4.00000	−0.596285
$46$	−1.00000	−0.147442
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	11.0000	1.55563
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	1.00000	0.136083
$55$	8.00000	1.07872
$56$	−1.00000	−0.133631
$57$	7.00000	0.927173
$58$	−2.00000	−0.262613
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.00000	−0.516398
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.00000	0.254000
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−8.00000	−0.992278
$66$	−2.00000	−0.246183
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−1.00000	−0.121268
$69$	−1.00000	−0.120386
$70$	4.00000	0.478091
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−2.00000	−0.232495
$75$	11.0000	1.27017
$76$	7.00000	0.802955
$77$	2.00000	0.227921
$78$	2.00000	0.226455
$79$	16.0000	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	−7.00000	−0.773021
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	−1.00000	−0.109109
$85$	4.00000	0.433861
$86$	−10.0000	−1.07833
$87$	−2.00000	−0.214423
$88$	−2.00000	−0.213201
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	−4.00000	−0.421637
$91$	−2.00000	−0.209657
$92$	−1.00000	−0.104257
$93$	2.00000	0.207390
$94$	−6.00000	−0.618853
$95$	−28.0000	−2.87274
$96$	1.00000	0.102062
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	−6.00000	−0.606092
$99$	−2.00000	−0.201008
$100$	11.0000	1.10000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−1.00000	−0.0990148
$103$	−13.0000	−1.28093	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000	−1.28093	−0.640464	+	0.767988i	$0.721258\pi$
$104$	2.00000	0.196116
$105$	4.00000	0.390360
$106$	3.00000	0.291386
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	1.00000	0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	8.00000	0.762770
$111$	−2.00000	−0.189832
$112$	−1.00000	−0.0944911
$113$	−16.0000	−1.50515	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000	−1.50515	−0.752577	+	0.658505i	$0.771189\pi$
$114$	7.00000	0.655610
$115$	4.00000	0.373002
$116$	−2.00000	−0.185695
$117$	2.00000	0.184900
$118$	−1.00000	−0.0920575
$119$	1.00000	0.0916698
$120$	−4.00000	−0.365148
$121$	−7.00000	−0.636364
$122$	−2.00000	−0.181071
$123$	−7.00000	−0.631169
$124$	2.00000	0.179605
$125$	−24.0000	−2.14663
$126$	−1.00000	−0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	−10.0000	−0.880451
$130$	−8.00000	−0.701646
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	−2.00000	−0.174078
$133$	−7.00000	−0.606977
$134$	0	0
$135$	−4.00000	−0.344265
$136$	−1.00000	−0.0857493
$137$	−22.0000	−1.87959	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−22.0000	−1.87959	−0.939793	+	0.341743i	$0.888983\pi$
$138$	−1.00000	−0.0851257
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	4.00000	0.338062
$141$	−6.00000	−0.505291
$142$	−12.0000	−1.00702
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	8.00000	0.664364
$146$	7.00000	0.579324
$147$	−6.00000	−0.494872
$148$	−2.00000	−0.164399
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	11.0000	0.898146
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	7.00000	0.567775
$153$	−1.00000	−0.0808452
$154$	2.00000	0.161165
$155$	−8.00000	−0.642575
$156$	2.00000	0.160128
$157$	9.00000	0.718278	0.359139	−	0.933284i	$-0.383070\pi$
$157$	9.00000	0.718278	0.359139	+	0.933284i	$0.383070\pi$
$158$	16.0000	1.27289
$159$	3.00000	0.237915
$160$	−4.00000	−0.316228
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	−7.00000	−0.546608
$165$	8.00000	0.622799
$166$	−11.0000	−0.853766
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	4.00000	0.306786
$171$	7.00000	0.535303
$172$	−10.0000	−0.762493
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−2.00000	−0.151620
$175$	−11.0000	−0.831522
$176$	−2.00000	−0.150756
$177$	−1.00000	−0.0751646
$178$	9.00000	0.674579
$179$	−13.0000	−0.971666	−0.485833	−	0.874052i	$-0.661484\pi$
$179$	−13.0000	−0.971666	−0.485833	+	0.874052i	$0.661484\pi$
$180$	−4.00000	−0.298142
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.00000	−0.148250
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	8.00000	0.588172
$186$	2.00000	0.146647
$187$	2.00000	0.146254
$188$	−6.00000	−0.437595
$189$	−1.00000	−0.0727393
$190$	−28.0000	−2.03133
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−17.0000	−1.22053
$195$	−8.00000	−0.572892
$196$	−6.00000	−0.428571
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	−2.00000	−0.142134
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	11.0000	0.777817
$201$	0	0
$202$	0	0
$203$	2.00000	0.140372
$204$	−1.00000	−0.0700140
$205$	28.0000	1.95560
$206$	−13.0000	−0.905753
$207$	−1.00000	−0.0695048
$208$	2.00000	0.138675
$209$	−14.0000	−0.968400
$210$	4.00000	0.276026
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	3.00000	0.206041
$213$	−12.0000	−0.822226
$214$	13.0000	0.888662
$215$	40.0000	2.72798
$216$	1.00000	0.0680414
$217$	−2.00000	−0.135769
$218$	4.00000	0.270914
$219$	7.00000	0.473016
$220$	8.00000	0.539360
$221$	−2.00000	−0.134535
$222$	−2.00000	−0.134231
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	−1.00000	−0.0668153
$225$	11.0000	0.733333
$226$	−16.0000	−1.06430
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	7.00000	0.463586
$229$	23.0000	1.51988	0.759941	−	0.649992i	$-0.225228\pi$
$229$	23.0000	1.51988	0.759941	+	0.649992i	$0.225228\pi$
$230$	4.00000	0.263752
$231$	2.00000	0.131590
$232$	−2.00000	−0.131306
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	2.00000	0.130744
$235$	24.0000	1.56559
$236$	−1.00000	−0.0650945
$237$	16.0000	1.03931
$238$	1.00000	0.0648204
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−4.00000	−0.258199
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	−7.00000	−0.449977
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	24.0000	1.53330
$246$	−7.00000	−0.446304
$247$	14.0000	0.890799
$248$	2.00000	0.127000
$249$	−11.0000	−0.697097
$250$	−24.0000	−1.51789
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	−1.00000	−0.0629941
$253$	2.00000	0.125739
$254$	−2.00000	−0.125491
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	−10.0000	−0.622573
$259$	2.00000	0.124274
$260$	−8.00000	−0.496139
$261$	−2.00000	−0.123797
$262$	−20.0000	−1.23560
$263$	27.0000	1.66489	0.832446	−	0.554107i	$-0.186940\pi$
$263$	27.0000	1.66489	0.832446	+	0.554107i	$0.186940\pi$
$264$	−2.00000	−0.123091
$265$	−12.0000	−0.737154
$266$	−7.00000	−0.429198
$267$	9.00000	0.550791
$268$	0	0
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	−4.00000	−0.243432
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	−1.00000	−0.0606339
$273$	−2.00000	−0.121046
$274$	−22.0000	−1.32907
$275$	−22.0000	−1.32665
$276$	−1.00000	−0.0601929
$277$	−11.0000	−0.660926	−0.330463	−	0.943819i	$-0.607205\pi$
$277$	−11.0000	−0.660926	−0.330463	+	0.943819i	$0.607205\pi$
$278$	−10.0000	−0.599760
$279$	2.00000	0.119737
$280$	4.00000	0.239046
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	−6.00000	−0.357295
$283$	−27.0000	−1.60498	−0.802492	−	0.596663i	$-0.796493\pi$
$283$	−27.0000	−1.60498	−0.802492	+	0.596663i	$0.796493\pi$
$284$	−12.0000	−0.712069
$285$	−28.0000	−1.65858
$286$	−4.00000	−0.236525
$287$	7.00000	0.413197
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	8.00000	0.469776
$291$	−17.0000	−0.996558
$292$	7.00000	0.409644
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	−6.00000	−0.349927
$295$	4.00000	0.232889
$296$	−2.00000	−0.116248
$297$	−2.00000	−0.116052
$298$	0	0
$299$	−2.00000	−0.115663
$300$	11.0000	0.635085
$301$	10.0000	0.576390
$302$	17.0000	0.978240
$303$	0	0
$304$	7.00000	0.401478
$305$	8.00000	0.458079
$306$	−1.00000	−0.0571662
$307$	17.0000	0.970241	0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000	0.970241	0.485121	+	0.874447i	$0.338776\pi$
$308$	2.00000	0.113961
$309$	−13.0000	−0.739544
$310$	−8.00000	−0.454369
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	2.00000	0.113228
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	9.00000	0.507899
$315$	4.00000	0.225374
$316$	16.0000	0.900070
$317$	−32.0000	−1.79730	−0.898650	−	0.438667i	$-0.855451\pi$
$317$	−32.0000	−1.79730	−0.898650	+	0.438667i	$0.855451\pi$
$318$	3.00000	0.168232
$319$	4.00000	0.223957
$320$	−4.00000	−0.223607
$321$	13.0000	0.725589
$322$	1.00000	0.0557278
$323$	−7.00000	−0.389490
$324$	1.00000	0.0555556
$325$	22.0000	1.22034
$326$	−18.0000	−0.996928
$327$	4.00000	0.221201
$328$	−7.00000	−0.386510
$329$	6.00000	0.330791
$330$	8.00000	0.440386
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	−11.0000	−0.603703
$333$	−2.00000	−0.109599
$334$	16.0000	0.875481
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	−3.00000	−0.163420	−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000	−0.163420	−0.0817102	+	0.996656i	$0.526038\pi$
$338$	−9.00000	−0.489535
$339$	−16.0000	−0.869001
$340$	4.00000	0.216930
$341$	−4.00000	−0.216612
$342$	7.00000	0.378517
$343$	13.0000	0.701934
$344$	−10.0000	−0.539164
$345$	4.00000	0.215353
$346$	6.00000	0.322562
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	−2.00000	−0.107211
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	−11.0000	−0.587975
$351$	2.00000	0.106752
$352$	−2.00000	−0.106600
$353$	−9.00000	−0.479022	−0.239511	−	0.970894i	$-0.576987\pi$
$353$	−9.00000	−0.479022	−0.239511	+	0.970894i	$0.576987\pi$
$354$	−1.00000	−0.0531494
$355$	48.0000	2.54758
$356$	9.00000	0.476999
$357$	1.00000	0.0529256
$358$	−13.0000	−0.687071
$359$	19.0000	1.00278	0.501391	−	0.865221i	$-0.332822\pi$
$359$	19.0000	1.00278	0.501391	+	0.865221i	$0.332822\pi$
$360$	−4.00000	−0.210819
$361$	30.0000	1.57895
$362$	−10.0000	−0.525588
$363$	−7.00000	−0.367405
$364$	−2.00000	−0.104828
$365$	−28.0000	−1.46559
$366$	−2.00000	−0.104542
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−1.00000	−0.0521286
$369$	−7.00000	−0.364405
$370$	8.00000	0.415900
$371$	−3.00000	−0.155752
$372$	2.00000	0.103695
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	2.00000	0.103418
$375$	−24.0000	−1.23935
$376$	−6.00000	−0.309426
$377$	−4.00000	−0.206010
$378$	−1.00000	−0.0514344
$379$	−26.0000	−1.33553	−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000	−1.33553	−0.667765	+	0.744372i	$0.732749\pi$
$380$	−28.0000	−1.43637
$381$	−2.00000	−0.102463
$382$	8.00000	0.409316
$383$	33.0000	1.68622	0.843111	−	0.537740i	$-0.180722\pi$
$383$	33.0000	1.68622	0.843111	+	0.537740i	$0.180722\pi$
$384$	1.00000	0.0510310
$385$	−8.00000	−0.407718
$386$	−22.0000	−1.11977
$387$	−10.0000	−0.508329
$388$	−17.0000	−0.863044
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	−8.00000	−0.405096
$391$	1.00000	0.0505722
$392$	−6.00000	−0.303046
$393$	−20.0000	−1.00887
$394$	18.0000	0.906827
$395$	−64.0000	−3.22019
$396$	−2.00000	−0.100504
$397$	28.0000	1.40528	0.702640	−	0.711546i	$-0.252005\pi$
$397$	28.0000	1.40528	0.702640	+	0.711546i	$0.252005\pi$
$398$	−5.00000	−0.250627
$399$	−7.00000	−0.350438
$400$	11.0000	0.550000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	0	0
$405$	−4.00000	−0.198762
$406$	2.00000	0.0992583
$407$	4.00000	0.198273
$408$	−1.00000	−0.0495074
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	28.0000	1.38282
$411$	−22.0000	−1.08518
$412$	−13.0000	−0.640464
$413$	1.00000	0.0492068
$414$	−1.00000	−0.0491473
$415$	44.0000	2.15988
$416$	2.00000	0.0980581
$417$	−10.0000	−0.489702
$418$	−14.0000	−0.684762
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	4.00000	0.195180
$421$	23.0000	1.12095	0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000	1.12095	0.560476	+	0.828171i	$0.310618\pi$
$422$	0	0
$423$	−6.00000	−0.291730
$424$	3.00000	0.145693
$425$	−11.0000	−0.533578
$426$	−12.0000	−0.581402
$427$	2.00000	0.0967868
$428$	13.0000	0.628379
$429$	−4.00000	−0.193122
$430$	40.0000	1.92897
$431$	21.0000	1.01153	0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000	1.01153	0.505767	+	0.862670i	$0.331209\pi$
$432$	1.00000	0.0481125
$433$	41.0000	1.97033	0.985167	−	0.171598i	$-0.0548929\pi$
$433$	41.0000	1.97033	0.985167	+	0.171598i	$0.0548929\pi$
$434$	−2.00000	−0.0960031
$435$	8.00000	0.383571
$436$	4.00000	0.191565
$437$	−7.00000	−0.334855
$438$	7.00000	0.334473
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	8.00000	0.381385
$441$	−6.00000	−0.285714
$442$	−2.00000	−0.0951303
$443$	−37.0000	−1.75792	−0.878962	−	0.476893i	$-0.841763\pi$
$443$	−37.0000	−1.75792	−0.878962	+	0.476893i	$0.841763\pi$
$444$	−2.00000	−0.0949158
$445$	−36.0000	−1.70656
$446$	−14.0000	−0.662919
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	11.0000	0.519122	0.259561	−	0.965727i	$-0.416422\pi$
$449$	11.0000	0.519122	0.259561	+	0.965727i	$0.416422\pi$
$450$	11.0000	0.518545
$451$	14.0000	0.659234
$452$	−16.0000	−0.752577
$453$	17.0000	0.798730
$454$	−6.00000	−0.281594
$455$	8.00000	0.375046
$456$	7.00000	0.327805
$457$	24.0000	1.12267	0.561336	−	0.827588i	$-0.310287\pi$
$457$	24.0000	1.12267	0.561336	+	0.827588i	$0.310287\pi$
$458$	23.0000	1.07472
$459$	−1.00000	−0.0466760
$460$	4.00000	0.186501
$461$	5.00000	0.232873	0.116437	−	0.993198i	$-0.462853\pi$
$461$	5.00000	0.232873	0.116437	+	0.993198i	$0.462853\pi$
$462$	2.00000	0.0930484
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	−2.00000	−0.0928477
$465$	−8.00000	−0.370991
$466$	−10.0000	−0.463241
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	24.0000	1.10704
$471$	9.00000	0.414698
$472$	−1.00000	−0.0460287
$473$	20.0000	0.919601
$474$	16.0000	0.734904
$475$	77.0000	3.53300
$476$	1.00000	0.0458349
$477$	3.00000	0.137361
$478$	0	0
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	−4.00000	−0.182574
$481$	−4.00000	−0.182384
$482$	14.0000	0.637683
$483$	1.00000	0.0455016
$484$	−7.00000	−0.318182
$485$	68.0000	3.08772
$486$	1.00000	0.0453609
$487$	−23.0000	−1.04223	−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000	−1.04223	−0.521115	+	0.853487i	$0.674484\pi$
$488$	−2.00000	−0.0905357
$489$	−18.0000	−0.813988
$490$	24.0000	1.08421
$491$	16.0000	0.722070	0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000	0.722070	0.361035	+	0.932552i	$0.382424\pi$
$492$	−7.00000	−0.315584
$493$	2.00000	0.0900755
$494$	14.0000	0.629890
$495$	8.00000	0.359573
$496$	2.00000	0.0898027
$497$	12.0000	0.538274
$498$	−11.0000	−0.492922
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−24.0000	−1.07331
$501$	16.0000	0.714827
$502$	−4.00000	−0.178529
$503$	1.00000	0.0445878	0.0222939	−	0.999751i	$-0.492903\pi$
$503$	1.00000	0.0445878	0.0222939	+	0.999751i	$0.492903\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	2.00000	0.0889108
$507$	−9.00000	−0.399704
$508$	−2.00000	−0.0887357
$509$	10.0000	0.443242	0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000	0.443242	0.221621	+	0.975133i	$0.428865\pi$
$510$	4.00000	0.177123
$511$	−7.00000	−0.309662
$512$	1.00000	0.0441942
$513$	7.00000	0.309058
$514$	−24.0000	−1.05859
$515$	52.0000	2.29139
$516$	−10.0000	−0.440225
$517$	12.0000	0.527759
$518$	2.00000	0.0878750
$519$	6.00000	0.263371
$520$	−8.00000	−0.350823
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−2.00000	−0.0875376
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−20.0000	−0.873704
$525$	−11.0000	−0.480079
$526$	27.0000	1.17726
$527$	−2.00000	−0.0871214
$528$	−2.00000	−0.0870388
$529$	−22.0000	−0.956522
$530$	−12.0000	−0.521247
$531$	−1.00000	−0.0433963
$532$	−7.00000	−0.303488
$533$	−14.0000	−0.606407
$534$	9.00000	0.389468
$535$	−52.0000	−2.24816
$536$	0	0
$537$	−13.0000	−0.560991
$538$	−21.0000	−0.905374
$539$	12.0000	0.516877
$540$	−4.00000	−0.172133
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	−20.0000	−0.859074
$543$	−10.0000	−0.429141
$544$	−1.00000	−0.0428746
$545$	−16.0000	−0.685365
$546$	−2.00000	−0.0855921
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	−22.0000	−0.939793
$549$	−2.00000	−0.0853579
$550$	−22.0000	−0.938083
$551$	−14.0000	−0.596420
$552$	−1.00000	−0.0425628
$553$	−16.0000	−0.680389
$554$	−11.0000	−0.467345
$555$	8.00000	0.339581
$556$	−10.0000	−0.424094
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	2.00000	0.0846668
$559$	−20.0000	−0.845910
$560$	4.00000	0.169031
$561$	2.00000	0.0844401
$562$	24.0000	1.01238
$563$	−23.0000	−0.969334	−0.484667	−	0.874699i	$-0.661059\pi$
$563$	−23.0000	−0.969334	−0.484667	+	0.874699i	$0.661059\pi$
$564$	−6.00000	−0.252646
$565$	64.0000	2.69250
$566$	−27.0000	−1.13489
$567$	−1.00000	−0.0419961
$568$	−12.0000	−0.503509
$569$	29.0000	1.21574	0.607872	−	0.794035i	$-0.292024\pi$
$569$	29.0000	1.21574	0.607872	+	0.794035i	$0.292024\pi$
$570$	−28.0000	−1.17279
$571$	−43.0000	−1.79949	−0.899747	−	0.436412i	$-0.856249\pi$
$571$	−43.0000	−1.79949	−0.899747	+	0.436412i	$0.856249\pi$
$572$	−4.00000	−0.167248
$573$	8.00000	0.334205
$574$	7.00000	0.292174
$575$	−11.0000	−0.458732
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	1.00000	0.0415945
$579$	−22.0000	−0.914289
$580$	8.00000	0.332182
$581$	11.0000	0.456357
$582$	−17.0000	−0.704673
$583$	−6.00000	−0.248495
$584$	7.00000	0.289662
$585$	−8.00000	−0.330759
$586$	18.0000	0.743573
$587$	19.0000	0.784214	0.392107	−	0.919920i	$-0.371746\pi$
$587$	19.0000	0.784214	0.392107	+	0.919920i	$0.371746\pi$
$588$	−6.00000	−0.247436
$589$	14.0000	0.576860
$590$	4.00000	0.164677
$591$	18.0000	0.740421
$592$	−2.00000	−0.0821995
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	−2.00000	−0.0820610
$595$	−4.00000	−0.163984
$596$	0	0
$597$	−5.00000	−0.204636
$598$	−2.00000	−0.0817861
$599$	41.0000	1.67521	0.837607	−	0.546273i	$-0.183954\pi$
$599$	41.0000	1.67521	0.837607	+	0.546273i	$0.183954\pi$
$600$	11.0000	0.449073
$601$	35.0000	1.42768	0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000	1.42768	0.713840	+	0.700309i	$0.246954\pi$
$602$	10.0000	0.407570
$603$	0	0
$604$	17.0000	0.691720
$605$	28.0000	1.13836
$606$	0	0
$607$	29.0000	1.17707	0.588537	−	0.808470i	$-0.299704\pi$
$607$	29.0000	1.17707	0.588537	+	0.808470i	$0.299704\pi$
$608$	7.00000	0.283887
$609$	2.00000	0.0810441
$610$	8.00000	0.323911
$611$	−12.0000	−0.485468
$612$	−1.00000	−0.0404226
$613$	−9.00000	−0.363507	−0.181753	−	0.983344i	$-0.558177\pi$
$613$	−9.00000	−0.363507	−0.181753	+	0.983344i	$0.558177\pi$
$614$	17.0000	0.686064
$615$	28.0000	1.12907
$616$	2.00000	0.0805823
$617$	1.00000	0.0402585	0.0201292	−	0.999797i	$-0.493592\pi$
$617$	1.00000	0.0402585	0.0201292	+	0.999797i	$0.493592\pi$
$618$	−13.0000	−0.522937
$619$	18.0000	0.723481	0.361741	−	0.932279i	$-0.382183\pi$
$619$	18.0000	0.723481	0.361741	+	0.932279i	$0.382183\pi$
$620$	−8.00000	−0.321288
$621$	−1.00000	−0.0401286
$622$	12.0000	0.481156
$623$	−9.00000	−0.360577
$624$	2.00000	0.0800641
$625$	41.0000	1.64000
$626$	10.0000	0.399680
$627$	−14.0000	−0.559106
$628$	9.00000	0.359139
$629$	2.00000	0.0797452
$630$	4.00000	0.159364
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	16.0000	0.636446
$633$	0	0
$634$	−32.0000	−1.27088
$635$	8.00000	0.317470
$636$	3.00000	0.118958
$637$	−12.0000	−0.475457
$638$	4.00000	0.158362
$639$	−12.0000	−0.474713
$640$	−4.00000	−0.158114
$641$	9.00000	0.355479	0.177739	−	0.984078i	$-0.443122\pi$
$641$	9.00000	0.355479	0.177739	+	0.984078i	$0.443122\pi$
$642$	13.0000	0.513069
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	1.00000	0.0394055
$645$	40.0000	1.57500
$646$	−7.00000	−0.275411
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	1.00000	0.0392837
$649$	2.00000	0.0785069
$650$	22.0000	0.862911
$651$	−2.00000	−0.0783862
$652$	−18.0000	−0.704934
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	4.00000	0.156412
$655$	80.0000	3.12586
$656$	−7.00000	−0.273304
$657$	7.00000	0.273096
$658$	6.00000	0.233904
$659$	−15.0000	−0.584317	−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000	−0.584317	−0.292159	+	0.956370i	$0.594373\pi$
$660$	8.00000	0.311400
$661$	−32.0000	−1.24466	−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000	−1.24466	−0.622328	+	0.782757i	$0.713813\pi$
$662$	−17.0000	−0.660724
$663$	−2.00000	−0.0776736
$664$	−11.0000	−0.426883
$665$	28.0000	1.08579
$666$	−2.00000	−0.0774984
$667$	2.00000	0.0774403
$668$	16.0000	0.619059
$669$	−14.0000	−0.541271
$670$	0	0
$671$	4.00000	0.154418
$672$	−1.00000	−0.0385758
$673$	−13.0000	−0.501113	−0.250557	−	0.968102i	$-0.580614\pi$
$673$	−13.0000	−0.501113	−0.250557	+	0.968102i	$0.580614\pi$
$674$	−3.00000	−0.115556
$675$	11.0000	0.423390
$676$	−9.00000	−0.346154
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	−16.0000	−0.614476
$679$	17.0000	0.652400
$680$	4.00000	0.153393
$681$	−6.00000	−0.229920
$682$	−4.00000	−0.153168
$683$	26.0000	0.994862	0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000	0.994862	0.497431	+	0.867503i	$0.334277\pi$
$684$	7.00000	0.267652
$685$	88.0000	3.36231
$686$	13.0000	0.496342
$687$	23.0000	0.877505
$688$	−10.0000	−0.381246
$689$	6.00000	0.228582
$690$	4.00000	0.152277
$691$	−37.0000	−1.40755	−0.703773	−	0.710425i	$-0.748503\pi$
$691$	−37.0000	−1.40755	−0.703773	+	0.710425i	$0.748503\pi$
$692$	6.00000	0.228086
$693$	2.00000	0.0759737
$694$	18.0000	0.683271
$695$	40.0000	1.51729
$696$	−2.00000	−0.0758098
$697$	7.00000	0.265144
$698$	5.00000	0.189253
$699$	−10.0000	−0.378235
$700$	−11.0000	−0.415761
$701$	−40.0000	−1.51078	−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000	−1.51078	−0.755390	+	0.655276i	$0.772552\pi$
$702$	2.00000	0.0754851
$703$	−14.0000	−0.528020
$704$	−2.00000	−0.0753778
$705$	24.0000	0.903892
$706$	−9.00000	−0.338719
$707$	0	0
$708$	−1.00000	−0.0375823
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	48.0000	1.80141
$711$	16.0000	0.600047
$712$	9.00000	0.337289
$713$	−2.00000	−0.0749006
$714$	1.00000	0.0374241
$715$	16.0000	0.598366
$716$	−13.0000	−0.485833
$717$	0	0
$718$	19.0000	0.709074
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	−4.00000	−0.149071
$721$	13.0000	0.484145
$722$	30.0000	1.11648
$723$	14.0000	0.520666
$724$	−10.0000	−0.371647
$725$	−22.0000	−0.817059
$726$	−7.00000	−0.259794
$727$	−46.0000	−1.70605	−0.853023	−	0.521874i	$-0.825233\pi$
$727$	−46.0000	−1.70605	−0.853023	+	0.521874i	$0.825233\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−28.0000	−1.03633
$731$	10.0000	0.369863
$732$	−2.00000	−0.0739221
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	0	0
$735$	24.0000	0.885253
$736$	−1.00000	−0.0368605
$737$	0	0
$738$	−7.00000	−0.257674
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	8.00000	0.294086
$741$	14.0000	0.514303
$742$	−3.00000	−0.110133
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	2.00000	0.0733236
$745$	0	0
$746$	10.0000	0.366126
$747$	−11.0000	−0.402469
$748$	2.00000	0.0731272
$749$	−13.0000	−0.475010
$750$	−24.0000	−0.876356
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−6.00000	−0.218797
$753$	−4.00000	−0.145768
$754$	−4.00000	−0.145671
$755$	−68.0000	−2.47477
$756$	−1.00000	−0.0363696
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−26.0000	−0.944363
$759$	2.00000	0.0725954
$760$	−28.0000	−1.01567
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	−2.00000	−0.0724524
$763$	−4.00000	−0.144810
$764$	8.00000	0.289430
$765$	4.00000	0.144620
$766$	33.0000	1.19234
$767$	−2.00000	−0.0722158
$768$	1.00000	0.0360844
$769$	36.0000	1.29819	0.649097	−	0.760706i	$-0.275147\pi$
$769$	36.0000	1.29819	0.649097	+	0.760706i	$0.275147\pi$
$770$	−8.00000	−0.288300
$771$	−24.0000	−0.864339
$772$	−22.0000	−0.791797
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	−10.0000	−0.359443
$775$	22.0000	0.790263
$776$	−17.0000	−0.610264
$777$	2.00000	0.0717496
$778$	−30.0000	−1.07555
$779$	−49.0000	−1.75561
$780$	−8.00000	−0.286446
$781$	24.0000	0.858788
$782$	1.00000	0.0357599
$783$	−2.00000	−0.0714742
$784$	−6.00000	−0.214286
$785$	−36.0000	−1.28490
$786$	−20.0000	−0.713376
$787$	44.0000	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$788$	18.0000	0.641223
$789$	27.0000	0.961225
$790$	−64.0000	−2.27702
$791$	16.0000	0.568895
$792$	−2.00000	−0.0710669
$793$	−4.00000	−0.142044
$794$	28.0000	0.993683
$795$	−12.0000	−0.425596
$796$	−5.00000	−0.177220
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	−7.00000	−0.247797
$799$	6.00000	0.212265
$800$	11.0000	0.388909
$801$	9.00000	0.317999
$802$	−12.0000	−0.423735
$803$	−14.0000	−0.494049
$804$	0	0
$805$	−4.00000	−0.140981
$806$	4.00000	0.140894
$807$	−21.0000	−0.739235
$808$	0	0
$809$	−8.00000	−0.281265	−0.140633	−	0.990062i	$-0.544914\pi$
$809$	−8.00000	−0.281265	−0.140633	+	0.990062i	$0.544914\pi$
$810$	−4.00000	−0.140546
$811$	45.0000	1.58016	0.790082	−	0.613001i	$-0.210038\pi$
$811$	45.0000	1.58016	0.790082	+	0.613001i	$0.210038\pi$
$812$	2.00000	0.0701862
$813$	−20.0000	−0.701431
$814$	4.00000	0.140200
$815$	72.0000	2.52205
$816$	−1.00000	−0.0350070
$817$	−70.0000	−2.44899
$818$	34.0000	1.18878
$819$	−2.00000	−0.0698857
$820$	28.0000	0.977802
$821$	−3.00000	−0.104701	−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000	−0.104701	−0.0523504	+	0.998629i	$0.516671\pi$
$822$	−22.0000	−0.767338
$823$	46.0000	1.60346	0.801730	−	0.597687i	$-0.203913\pi$
$823$	46.0000	1.60346	0.801730	+	0.597687i	$0.203913\pi$
$824$	−13.0000	−0.452876
$825$	−22.0000	−0.765942
$826$	1.00000	0.0347945
$827$	27.0000	0.938882	0.469441	−	0.882964i	$-0.344455\pi$
$827$	27.0000	0.938882	0.469441	+	0.882964i	$0.344455\pi$
$828$	−1.00000	−0.0347524
$829$	24.0000	0.833554	0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000	0.833554	0.416777	+	0.909009i	$0.363160\pi$
$830$	44.0000	1.52726
$831$	−11.0000	−0.381586
$832$	2.00000	0.0693375
$833$	6.00000	0.207888
$834$	−10.0000	−0.346272
$835$	−64.0000	−2.21481
$836$	−14.0000	−0.484200
$837$	2.00000	0.0691301
$838$	20.0000	0.690889
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	4.00000	0.138013
$841$	−25.0000	−0.862069
$842$	23.0000	0.792632
$843$	24.0000	0.826604
$844$	0	0
$845$	36.0000	1.23844
$846$	−6.00000	−0.206284
$847$	7.00000	0.240523
$848$	3.00000	0.103020
$849$	−27.0000	−0.926638
$850$	−11.0000	−0.377297
$851$	2.00000	0.0685591
$852$	−12.0000	−0.411113
$853$	−42.0000	−1.43805	−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000	−1.43805	−0.719026	+	0.694983i	$0.755412\pi$
$854$	2.00000	0.0684386
$855$	−28.0000	−0.957580
$856$	13.0000	0.444331
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	−4.00000	−0.136558
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	40.0000	1.36399
$861$	7.00000	0.238559
$862$	21.0000	0.715263
$863$	−26.0000	−0.885050	−0.442525	−	0.896756i	$-0.645917\pi$
$863$	−26.0000	−0.885050	−0.442525	+	0.896756i	$0.645917\pi$
$864$	1.00000	0.0340207
$865$	−24.0000	−0.816024
$866$	41.0000	1.39324
$867$	1.00000	0.0339618
$868$	−2.00000	−0.0678844
$869$	−32.0000	−1.08553
$870$	8.00000	0.271225
$871$	0	0
$872$	4.00000	0.135457
$873$	−17.0000	−0.575363
$874$	−7.00000	−0.236779
$875$	24.0000	0.811348
$876$	7.00000	0.236508
$877$	−15.0000	−0.506514	−0.253257	−	0.967399i	$-0.581502\pi$
$877$	−15.0000	−0.506514	−0.253257	+	0.967399i	$0.581502\pi$
$878$	−28.0000	−0.944954
$879$	18.0000	0.607125
$880$	8.00000	0.269680
$881$	−8.00000	−0.269527	−0.134763	−	0.990878i	$-0.543027\pi$
$881$	−8.00000	−0.269527	−0.134763	+	0.990878i	$0.543027\pi$
$882$	−6.00000	−0.202031
$883$	45.0000	1.51437	0.757185	−	0.653200i	$-0.226574\pi$
$883$	45.0000	1.51437	0.757185	+	0.653200i	$0.226574\pi$
$884$	−2.00000	−0.0672673
$885$	4.00000	0.134459
$886$	−37.0000	−1.24304
$887$	21.0000	0.705111	0.352555	−	0.935791i	$-0.385313\pi$
$887$	21.0000	0.705111	0.352555	+	0.935791i	$0.385313\pi$
$888$	−2.00000	−0.0671156
$889$	2.00000	0.0670778
$890$	−36.0000	−1.20672
$891$	−2.00000	−0.0670025
$892$	−14.0000	−0.468755
$893$	−42.0000	−1.40548
$894$	0	0
$895$	52.0000	1.73817
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	11.0000	0.367075
$899$	−4.00000	−0.133407
$900$	11.0000	0.366667
$901$	−3.00000	−0.0999445
$902$	14.0000	0.466149
$903$	10.0000	0.332779
$904$	−16.0000	−0.532152
$905$	40.0000	1.32964
$906$	17.0000	0.564787
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	−6.00000	−0.199117
$909$	0	0
$910$	8.00000	0.265197
$911$	34.0000	1.12647	0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000	1.12647	0.563235	+	0.826297i	$0.309557\pi$
$912$	7.00000	0.231793
$913$	22.0000	0.728094
$914$	24.0000	0.793849
$915$	8.00000	0.264472
$916$	23.0000	0.759941
$917$	20.0000	0.660458
$918$	−1.00000	−0.0330049
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	4.00000	0.131876
$921$	17.0000	0.560169
$922$	5.00000	0.164666
$923$	−24.0000	−0.789970
$924$	2.00000	0.0657952
$925$	−22.0000	−0.723356
$926$	−20.0000	−0.657241
$927$	−13.0000	−0.426976
$928$	−2.00000	−0.0656532
$929$	26.0000	0.853032	0.426516	−	0.904480i	$-0.359741\pi$
$929$	26.0000	0.853032	0.426516	+	0.904480i	$0.359741\pi$
$930$	−8.00000	−0.262330
$931$	−42.0000	−1.37649
$932$	−10.0000	−0.327561
$933$	12.0000	0.392862
$934$	12.0000	0.392652
$935$	−8.00000	−0.261628
$936$	2.00000	0.0653720
$937$	32.0000	1.04539	0.522697	−	0.852518i	$-0.324926\pi$
$937$	32.0000	1.04539	0.522697	+	0.852518i	$0.324926\pi$
$938$	0	0
$939$	10.0000	0.326338
$940$	24.0000	0.782794
$941$	−53.0000	−1.72775	−0.863875	−	0.503706i	$-0.831970\pi$
$941$	−53.0000	−1.72775	−0.863875	+	0.503706i	$0.831970\pi$
$942$	9.00000	0.293236
$943$	7.00000	0.227951
$944$	−1.00000	−0.0325472
$945$	4.00000	0.130120
$946$	20.0000	0.650256
$947$	−25.0000	−0.812391	−0.406195	−	0.913786i	$-0.633145\pi$
$947$	−25.0000	−0.812391	−0.406195	+	0.913786i	$0.633145\pi$
$948$	16.0000	0.519656
$949$	14.0000	0.454459
$950$	77.0000	2.49821
$951$	−32.0000	−1.03767
$952$	1.00000	0.0324102
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	3.00000	0.0971286
$955$	−32.0000	−1.03550
$956$	0	0
$957$	4.00000	0.129302
$958$	−30.0000	−0.969256
$959$	22.0000	0.710417
$960$	−4.00000	−0.129099
$961$	−27.0000	−0.870968
$962$	−4.00000	−0.128965
$963$	13.0000	0.418919
$964$	14.0000	0.450910
$965$	88.0000	2.83282
$966$	1.00000	0.0321745
$967$	−37.0000	−1.18984	−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000	−1.18984	−0.594920	+	0.803785i	$0.702816\pi$
$968$	−7.00000	−0.224989
$969$	−7.00000	−0.224872
$970$	68.0000	2.18335
$971$	−18.0000	−0.577647	−0.288824	−	0.957382i	$-0.593264\pi$
$971$	−18.0000	−0.577647	−0.288824	+	0.957382i	$0.593264\pi$
$972$	1.00000	0.0320750
$973$	10.0000	0.320585
$974$	−23.0000	−0.736968
$975$	22.0000	0.704564
$976$	−2.00000	−0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−18.0000	−0.575577
$979$	−18.0000	−0.575282
$980$	24.0000	0.766652
$981$	4.00000	0.127710
$982$	16.0000	0.510581
$983$	−17.0000	−0.542216	−0.271108	−	0.962549i	$-0.587390\pi$
$983$	−17.0000	−0.542216	−0.271108	+	0.962549i	$0.587390\pi$
$984$	−7.00000	−0.223152
$985$	−72.0000	−2.29411
$986$	2.00000	0.0636930
$987$	6.00000	0.190982
$988$	14.0000	0.445399
$989$	10.0000	0.317982
$990$	8.00000	0.254257
$991$	38.0000	1.20711	0.603555	−	0.797321i	$-0.293750\pi$
$991$	38.0000	1.20711	0.603555	+	0.797321i	$0.293750\pi$
$992$	2.00000	0.0635001
$993$	−17.0000	−0.539479
$994$	12.0000	0.380617
$995$	20.0000	0.634043
$996$	−11.0000	−0.348548
$997$	−17.0000	−0.538395	−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000	−0.538395	−0.269198	+	0.963085i	$0.586759\pi$
$998$	−4.00000	−0.126618
$999$	−2.00000	−0.0632772

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.j.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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