LMFDB - Embedded newform 6018.2.a.e.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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -7.00000 q^{19} +2.00000 q^{20} -1.00000 q^{21} +2.00000 q^{22} -5.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +4.00000 q^{29} -2.00000 q^{30} +10.0000 q^{31} -1.00000 q^{32} -2.00000 q^{33} -1.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} +7.00000 q^{38} -2.00000 q^{39} -2.00000 q^{40} -3.00000 q^{41} +1.00000 q^{42} -6.00000 q^{43} -2.00000 q^{44} +2.00000 q^{45} +5.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} -2.00000 q^{52} +9.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} -7.00000 q^{57} -4.00000 q^{58} -1.00000 q^{59} +2.00000 q^{60} -2.00000 q^{61} -10.0000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} +2.00000 q^{66} -10.0000 q^{67} +1.00000 q^{68} -5.00000 q^{69} +2.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} +7.00000 q^{73} -8.00000 q^{74} -1.00000 q^{75} -7.00000 q^{76} +2.00000 q^{77} +2.00000 q^{78} +2.00000 q^{80} +1.00000 q^{81} +3.00000 q^{82} -9.00000 q^{83} -1.00000 q^{84} +2.00000 q^{85} +6.00000 q^{86} +4.00000 q^{87} +2.00000 q^{88} -11.0000 q^{89} -2.00000 q^{90} +2.00000 q^{91} -5.00000 q^{92} +10.0000 q^{93} -4.00000 q^{94} -14.0000 q^{95} -1.00000 q^{96} -5.00000 q^{97} +6.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−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
$10$	−2.00000	−0.632456
$11$	−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	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	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	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	2.00000	0.447214
$21$	−1.00000	−0.218218
$22$	2.00000	0.426401
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	−1.00000	−0.204124
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	−2.00000	−0.365148
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−1.00000	−0.171499
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	7.00000	1.13555
$39$	−2.00000	−0.320256
$40$	−2.00000	−0.316228
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	1.00000	0.154303
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−2.00000	−0.301511
$45$	2.00000	0.298142
$46$	5.00000	0.737210
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−2.00000	−0.277350
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	−1.00000	−0.136083
$55$	−4.00000	−0.539360
$56$	1.00000	0.133631
$57$	−7.00000	−0.927173
$58$	−4.00000	−0.525226
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.00000	0.258199
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−10.0000	−1.27000
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	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
$69$	−5.00000	−0.601929
$70$	2.00000	0.239046
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−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	$0.365653\pi$
$74$	−8.00000	−0.929981
$75$	−1.00000	−0.115470
$76$	−7.00000	−0.802955
$77$	2.00000	0.227921
$78$	2.00000	0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	3.00000	0.331295
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	−1.00000	−0.109109
$85$	2.00000	0.216930
$86$	6.00000	0.646997
$87$	4.00000	0.428845
$88$	2.00000	0.213201
$89$	−11.0000	−1.16600	−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000	−1.16600	−0.582999	+	0.812473i	$0.698121\pi$
$90$	−2.00000	−0.210819
$91$	2.00000	0.209657
$92$	−5.00000	−0.521286
$93$	10.0000	1.03695
$94$	−4.00000	−0.412568
$95$	−14.0000	−1.43637
$96$	−1.00000	−0.102062
$97$	−5.00000	−0.507673	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000	−0.507673	−0.253837	+	0.967247i	$0.581693\pi$
$98$	6.00000	0.606092
$99$	−2.00000	−0.201008
$100$	−1.00000	−0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−1.00000	−0.0990148
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	2.00000	0.196116
$105$	−2.00000	−0.195180
$106$	−9.00000	−0.874157
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	1.00000	0.0962250
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	4.00000	0.381385
$111$	8.00000	0.759326
$112$	−1.00000	−0.0944911
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	7.00000	0.655610
$115$	−10.0000	−0.932505
$116$	4.00000	0.371391
$117$	−2.00000	−0.184900
$118$	1.00000	0.0920575
$119$	−1.00000	−0.0916698
$120$	−2.00000	−0.182574
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	−3.00000	−0.270501
$124$	10.0000	0.898027
$125$	−12.0000	−1.07331
$126$	1.00000	0.0890871
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	−6.00000	−0.528271
$130$	4.00000	0.350823
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	−2.00000	−0.174078
$133$	7.00000	0.606977
$134$	10.0000	0.863868
$135$	2.00000	0.172133
$136$	−1.00000	−0.0857493
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	5.00000	0.425628
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	−2.00000	−0.169031
$141$	4.00000	0.336861
$142$	6.00000	0.503509
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	8.00000	0.664364
$146$	−7.00000	−0.579324
$147$	−6.00000	−0.494872
$148$	8.00000	0.657596
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	1.00000	0.0816497
$151$	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
$155$	20.0000	1.60644
$156$	−2.00000	−0.160128
$157$	23.0000	1.83560	0.917800	−	0.397043i	$-0.129964\pi$
$157$	23.0000	1.83560	0.917800	+	0.397043i	$0.129964\pi$
$158$	0	0
$159$	9.00000	0.713746
$160$	−2.00000	−0.158114
$161$	5.00000	0.394055
$162$	−1.00000	−0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	−3.00000	−0.234261
$165$	−4.00000	−0.311400
$166$	9.00000	0.698535
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	−7.00000	−0.535303
$172$	−6.00000	−0.457496
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	−4.00000	−0.303239
$175$	1.00000	0.0755929
$176$	−2.00000	−0.150756
$177$	−1.00000	−0.0751646
$178$	11.0000	0.824485
$179$	−19.0000	−1.42013	−0.710063	−	0.704138i	$-0.751334\pi$
$179$	−19.0000	−1.42013	−0.710063	+	0.704138i	$0.751334\pi$
$180$	2.00000	0.149071
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	−2.00000	−0.148250
$183$	−2.00000	−0.147844
$184$	5.00000	0.368605
$185$	16.0000	1.17634
$186$	−10.0000	−0.733236
$187$	−2.00000	−0.146254
$188$	4.00000	0.291730
$189$	−1.00000	−0.0727393
$190$	14.0000	1.01567
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	1.00000	0.0721688
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	5.00000	0.358979
$195$	−4.00000	−0.286446
$196$	−6.00000	−0.428571
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	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	$0.556711\pi$
$200$	1.00000	0.0707107
$201$	−10.0000	−0.705346
$202$	6.00000	0.422159
$203$	−4.00000	−0.280745
$204$	1.00000	0.0700140
$205$	−6.00000	−0.419058
$206$	1.00000	0.0696733
$207$	−5.00000	−0.347524
$208$	−2.00000	−0.138675
$209$	14.0000	0.968400
$210$	2.00000	0.138013
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	9.00000	0.618123
$213$	−6.00000	−0.411113
$214$	−3.00000	−0.205076
$215$	−12.0000	−0.818393
$216$	−1.00000	−0.0680414
$217$	−10.0000	−0.678844
$218$	4.00000	0.270914
$219$	7.00000	0.473016
$220$	−4.00000	−0.269680
$221$	−2.00000	−0.134535
$222$	−8.00000	−0.536925
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	1.00000	0.0668153
$225$	−1.00000	−0.0666667
$226$	14.0000	0.931266
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−7.00000	−0.463586
$229$	1.00000	0.0660819	0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000	0.0660819	0.0330409	+	0.999454i	$0.489481\pi$
$230$	10.0000	0.659380
$231$	2.00000	0.131590
$232$	−4.00000	−0.262613
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	2.00000	0.130744
$235$	8.00000	0.521862
$236$	−1.00000	−0.0650945
$237$	0	0
$238$	1.00000	0.0648204
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	2.00000	0.129099
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	−12.0000	−0.766652
$246$	3.00000	0.191273
$247$	14.0000	0.890799
$248$	−10.0000	−0.635001
$249$	−9.00000	−0.570352
$250$	12.0000	0.758947
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	−1.00000	−0.0629941
$253$	10.0000	0.628695
$254$	4.00000	0.250982
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	6.00000	0.373544
$259$	−8.00000	−0.497096
$260$	−4.00000	−0.248069
$261$	4.00000	0.247594
$262$	10.0000	0.617802
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	2.00000	0.123091
$265$	18.0000	1.10573
$266$	−7.00000	−0.429198
$267$	−11.0000	−0.673189
$268$	−10.0000	−0.610847
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	−2.00000	−0.121716
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	1.00000	0.0606339
$273$	2.00000	0.121046
$274$	0	0
$275$	2.00000	0.120605
$276$	−5.00000	−0.300965
$277$	−9.00000	−0.540758	−0.270379	−	0.962754i	$-0.587149\pi$
$277$	−9.00000	−0.540758	−0.270379	+	0.962754i	$0.587149\pi$
$278$	20.0000	1.19952
$279$	10.0000	0.598684
$280$	2.00000	0.119523
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	−4.00000	−0.238197
$283$	11.0000	0.653882	0.326941	−	0.945045i	$-0.393982\pi$
$283$	11.0000	0.653882	0.326941	+	0.945045i	$0.393982\pi$
$284$	−6.00000	−0.356034
$285$	−14.0000	−0.829288
$286$	−4.00000	−0.236525
$287$	3.00000	0.177084
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−8.00000	−0.469776
$291$	−5.00000	−0.293105
$292$	7.00000	0.409644
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	6.00000	0.349927
$295$	−2.00000	−0.116445
$296$	−8.00000	−0.464991
$297$	−2.00000	−0.116052
$298$	−12.0000	−0.695141
$299$	10.0000	0.578315
$300$	−1.00000	−0.0577350
$301$	6.00000	0.345834
$302$	−17.0000	−0.978240
$303$	−6.00000	−0.344691
$304$	−7.00000	−0.401478
$305$	−4.00000	−0.229039
$306$	−1.00000	−0.0571662
$307$	−5.00000	−0.285365	−0.142683	−	0.989769i	$-0.545573\pi$
$307$	−5.00000	−0.285365	−0.142683	+	0.989769i	$0.545573\pi$
$308$	2.00000	0.113961
$309$	−1.00000	−0.0568880
$310$	−20.0000	−1.13592
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	2.00000	0.113228
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−23.0000	−1.29797
$315$	−2.00000	−0.112687
$316$	0	0
$317$	−24.0000	−1.34797	−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000	−1.34797	−0.673987	+	0.738743i	$0.735420\pi$
$318$	−9.00000	−0.504695
$319$	−8.00000	−0.447914
$320$	2.00000	0.111803
$321$	3.00000	0.167444
$322$	−5.00000	−0.278639
$323$	−7.00000	−0.389490
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	20.0000	1.10770
$327$	−4.00000	−0.221201
$328$	3.00000	0.165647
$329$	−4.00000	−0.220527
$330$	4.00000	0.220193
$331$	21.0000	1.15426	0.577132	−	0.816651i	$-0.304172\pi$
$331$	21.0000	1.15426	0.577132	+	0.816651i	$0.304172\pi$
$332$	−9.00000	−0.493939
$333$	8.00000	0.438397
$334$	24.0000	1.31322
$335$	−20.0000	−1.09272
$336$	−1.00000	−0.0545545
$337$	25.0000	1.36184	0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000	1.36184	0.680918	+	0.732359i	$0.261581\pi$
$338$	9.00000	0.489535
$339$	−14.0000	−0.760376
$340$	2.00000	0.108465
$341$	−20.0000	−1.08306
$342$	7.00000	0.378517
$343$	13.0000	0.701934
$344$	6.00000	0.323498
$345$	−10.0000	−0.538382
$346$	−2.00000	−0.107521
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	4.00000	0.214423
$349$	27.0000	1.44528	0.722638	−	0.691226i	$-0.242929\pi$
$349$	27.0000	1.44528	0.722638	+	0.691226i	$0.242929\pi$
$350$	−1.00000	−0.0534522
$351$	−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
$355$	−12.0000	−0.636894
$356$	−11.0000	−0.582999
$357$	−1.00000	−0.0529256
$358$	19.0000	1.00418
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	−2.00000	−0.105409
$361$	30.0000	1.57895
$362$	6.00000	0.315353
$363$	−7.00000	−0.367405
$364$	2.00000	0.104828
$365$	14.0000	0.732793
$366$	2.00000	0.104542
$367$	−20.0000	−1.04399	−0.521996	−	0.852948i	$-0.674812\pi$
$367$	−20.0000	−1.04399	−0.521996	+	0.852948i	$0.674812\pi$
$368$	−5.00000	−0.260643
$369$	−3.00000	−0.156174
$370$	−16.0000	−0.831800
$371$	−9.00000	−0.467257
$372$	10.0000	0.518476
$373$	36.0000	1.86401	0.932005	−	0.362446i	$-0.118058\pi$
$373$	36.0000	1.86401	0.932005	+	0.362446i	$0.118058\pi$
$374$	2.00000	0.103418
$375$	−12.0000	−0.619677
$376$	−4.00000	−0.206284
$377$	−8.00000	−0.412021
$378$	1.00000	0.0514344
$379$	30.0000	1.54100	0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000	1.54100	0.770498	+	0.637442i	$0.220007\pi$
$380$	−14.0000	−0.718185
$381$	−4.00000	−0.204926
$382$	−6.00000	−0.306987
$383$	1.00000	0.0510976	0.0255488	−	0.999674i	$-0.491867\pi$
$383$	1.00000	0.0510976	0.0255488	+	0.999674i	$0.491867\pi$
$384$	−1.00000	−0.0510310
$385$	4.00000	0.203859
$386$	0	0
$387$	−6.00000	−0.304997
$388$	−5.00000	−0.253837
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	4.00000	0.202548
$391$	−5.00000	−0.252861
$392$	6.00000	0.303046
$393$	−10.0000	−0.504433
$394$	22.0000	1.10834
$395$	0	0
$396$	−2.00000	−0.100504
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	5.00000	0.250627
$399$	7.00000	0.350438
$400$	−1.00000	−0.0500000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	10.0000	0.498755
$403$	−20.0000	−0.996271
$404$	−6.00000	−0.298511
$405$	2.00000	0.0993808
$406$	4.00000	0.198517
$407$	−16.0000	−0.793091
$408$	−1.00000	−0.0495074
$409$	18.0000	0.890043	0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000	0.890043	0.445021	+	0.895520i	$0.353196\pi$
$410$	6.00000	0.296319
$411$	0	0
$412$	−1.00000	−0.0492665
$413$	1.00000	0.0492068
$414$	5.00000	0.245737
$415$	−18.0000	−0.883585
$416$	2.00000	0.0980581
$417$	−20.0000	−0.979404
$418$	−14.0000	−0.684762
$419$	18.0000	0.879358	0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000	0.879358	0.439679	+	0.898155i	$0.355092\pi$
$420$	−2.00000	−0.0975900
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	8.00000	0.389434
$423$	4.00000	0.194487
$424$	−9.00000	−0.437079
$425$	−1.00000	−0.0485071
$426$	6.00000	0.290701
$427$	2.00000	0.0967868
$428$	3.00000	0.145010
$429$	4.00000	0.193122
$430$	12.0000	0.578691
$431$	−39.0000	−1.87856	−0.939282	−	0.343146i	$-0.888507\pi$
$431$	−39.0000	−1.87856	−0.939282	+	0.343146i	$0.888507\pi$
$432$	1.00000	0.0481125
$433$	−39.0000	−1.87422	−0.937110	−	0.349034i	$-0.886510\pi$
$433$	−39.0000	−1.87422	−0.937110	+	0.349034i	$0.886510\pi$
$434$	10.0000	0.480015
$435$	8.00000	0.383571
$436$	−4.00000	−0.191565
$437$	35.0000	1.67428
$438$	−7.00000	−0.334473
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	4.00000	0.190693
$441$	−6.00000	−0.285714
$442$	2.00000	0.0951303
$443$	33.0000	1.56788	0.783939	−	0.620838i	$-0.213208\pi$
$443$	33.0000	1.56788	0.783939	+	0.620838i	$0.213208\pi$
$444$	8.00000	0.379663
$445$	−22.0000	−1.04290
$446$	4.00000	0.189405
$447$	12.0000	0.567581
$448$	−1.00000	−0.0472456
$449$	15.0000	0.707894	0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000	0.707894	0.353947	+	0.935266i	$0.384839\pi$
$450$	1.00000	0.0471405
$451$	6.00000	0.282529
$452$	−14.0000	−0.658505
$453$	17.0000	0.798730
$454$	12.0000	0.563188
$455$	4.00000	0.187523
$456$	7.00000	0.327805
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−1.00000	−0.0467269
$459$	1.00000	0.0466760
$460$	−10.0000	−0.466252
$461$	−1.00000	−0.0465746	−0.0232873	−	0.999729i	$-0.507413\pi$
$461$	−1.00000	−0.0465746	−0.0232873	+	0.999729i	$0.507413\pi$
$462$	−2.00000	−0.0930484
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	4.00000	0.185695
$465$	20.0000	0.927478
$466$	6.00000	0.277945
$467$	24.0000	1.11059	0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000	1.11059	0.555294	+	0.831654i	$0.312606\pi$
$468$	−2.00000	−0.0924500
$469$	10.0000	0.461757
$470$	−8.00000	−0.369012
$471$	23.0000	1.05978
$472$	1.00000	0.0460287
$473$	12.0000	0.551761
$474$	0	0
$475$	7.00000	0.321182
$476$	−1.00000	−0.0458349
$477$	9.00000	0.412082
$478$	4.00000	0.182956
$479$	−42.0000	−1.91903	−0.959514	−	0.281659i	$-0.909115\pi$
$479$	−42.0000	−1.91903	−0.959514	+	0.281659i	$0.909115\pi$
$480$	−2.00000	−0.0912871
$481$	−16.0000	−0.729537
$482$	−4.00000	−0.182195
$483$	5.00000	0.227508
$484$	−7.00000	−0.318182
$485$	−10.0000	−0.454077
$486$	−1.00000	−0.0453609
$487$	1.00000	0.0453143	0.0226572	−	0.999743i	$-0.492787\pi$
$487$	1.00000	0.0453143	0.0226572	+	0.999743i	$0.492787\pi$
$488$	2.00000	0.0905357
$489$	−20.0000	−0.904431
$490$	12.0000	0.542105
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	−3.00000	−0.135250
$493$	4.00000	0.180151
$494$	−14.0000	−0.629890
$495$	−4.00000	−0.179787
$496$	10.0000	0.449013
$497$	6.00000	0.269137
$498$	9.00000	0.403300
$499$	34.0000	1.52205	0.761025	−	0.648723i	$-0.224697\pi$
$499$	34.0000	1.52205	0.761025	+	0.648723i	$0.224697\pi$
$500$	−12.0000	−0.536656
$501$	−24.0000	−1.07224
$502$	−6.00000	−0.267793
$503$	21.0000	0.936344	0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000	0.936344	0.468172	+	0.883637i	$0.344913\pi$
$504$	1.00000	0.0445435
$505$	−12.0000	−0.533993
$506$	−10.0000	−0.444554
$507$	−9.00000	−0.399704
$508$	−4.00000	−0.177471
$509$	38.0000	1.68432	0.842160	−	0.539227i	$-0.181284\pi$
$509$	38.0000	1.68432	0.842160	+	0.539227i	$0.181284\pi$
$510$	−2.00000	−0.0885615
$511$	−7.00000	−0.309662
$512$	−1.00000	−0.0441942
$513$	−7.00000	−0.309058
$514$	18.0000	0.793946
$515$	−2.00000	−0.0881305
$516$	−6.00000	−0.264135
$517$	−8.00000	−0.351840
$518$	8.00000	0.351500
$519$	2.00000	0.0877903
$520$	4.00000	0.175412
$521$	−39.0000	−1.70862	−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000	−1.70862	−0.854311	+	0.519763i	$0.826020\pi$
$522$	−4.00000	−0.175075
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	−10.0000	−0.436852
$525$	1.00000	0.0436436
$526$	9.00000	0.392419
$527$	10.0000	0.435607
$528$	−2.00000	−0.0870388
$529$	2.00000	0.0869565
$530$	−18.0000	−0.781870
$531$	−1.00000	−0.0433963
$532$	7.00000	0.303488
$533$	6.00000	0.259889
$534$	11.0000	0.476017
$535$	6.00000	0.259403
$536$	10.0000	0.431934
$537$	−19.0000	−0.819911
$538$	3.00000	0.129339
$539$	12.0000	0.516877
$540$	2.00000	0.0860663
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	−32.0000	−1.37452
$543$	−6.00000	−0.257485
$544$	−1.00000	−0.0428746
$545$	−8.00000	−0.342682
$546$	−2.00000	−0.0855921
$547$	−42.0000	−1.79579	−0.897895	−	0.440209i	$-0.854904\pi$
$547$	−42.0000	−1.79579	−0.897895	+	0.440209i	$0.854904\pi$
$548$	0	0
$549$	−2.00000	−0.0853579
$550$	−2.00000	−0.0852803
$551$	−28.0000	−1.19284
$552$	5.00000	0.212814
$553$	0	0
$554$	9.00000	0.382373
$555$	16.0000	0.679162
$556$	−20.0000	−0.848189
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−10.0000	−0.423334
$559$	12.0000	0.507546
$560$	−2.00000	−0.0845154
$561$	−2.00000	−0.0844401
$562$	−6.00000	−0.253095
$563$	−29.0000	−1.22220	−0.611102	−	0.791552i	$-0.709274\pi$
$563$	−29.0000	−1.22220	−0.611102	+	0.791552i	$0.709274\pi$
$564$	4.00000	0.168430
$565$	−28.0000	−1.17797
$566$	−11.0000	−0.462364
$567$	−1.00000	−0.0419961
$568$	6.00000	0.251754
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	14.0000	0.586395
$571$	−13.0000	−0.544033	−0.272017	−	0.962293i	$-0.587691\pi$
$571$	−13.0000	−0.544033	−0.272017	+	0.962293i	$0.587691\pi$
$572$	4.00000	0.167248
$573$	6.00000	0.250654
$574$	−3.00000	−0.125218
$575$	5.00000	0.208514
$576$	1.00000	0.0416667
$577$	22.0000	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	8.00000	0.332182
$581$	9.00000	0.373383
$582$	5.00000	0.207257
$583$	−18.0000	−0.745484
$584$	−7.00000	−0.289662
$585$	−4.00000	−0.165380
$586$	−6.00000	−0.247858
$587$	−35.0000	−1.44460	−0.722302	−	0.691577i	$-0.756916\pi$
$587$	−35.0000	−1.44460	−0.722302	+	0.691577i	$0.756916\pi$
$588$	−6.00000	−0.247436
$589$	−70.0000	−2.88430
$590$	2.00000	0.0823387
$591$	−22.0000	−0.904959
$592$	8.00000	0.328798
$593$	−20.0000	−0.821302	−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000	−0.821302	−0.410651	+	0.911793i	$0.634698\pi$
$594$	2.00000	0.0820610
$595$	−2.00000	−0.0819920
$596$	12.0000	0.491539
$597$	−5.00000	−0.204636
$598$	−10.0000	−0.408930
$599$	13.0000	0.531166	0.265583	−	0.964088i	$-0.414436\pi$
$599$	13.0000	0.531166	0.265583	+	0.964088i	$0.414436\pi$
$600$	1.00000	0.0408248
$601$	15.0000	0.611863	0.305931	−	0.952054i	$-0.401032\pi$
$601$	15.0000	0.611863	0.305931	+	0.952054i	$0.401032\pi$
$602$	−6.00000	−0.244542
$603$	−10.0000	−0.407231
$604$	17.0000	0.691720
$605$	−14.0000	−0.569181
$606$	6.00000	0.243733
$607$	17.0000	0.690009	0.345004	−	0.938601i	$-0.387877\pi$
$607$	17.0000	0.690009	0.345004	+	0.938601i	$0.387877\pi$
$608$	7.00000	0.283887
$609$	−4.00000	−0.162088
$610$	4.00000	0.161955
$611$	−8.00000	−0.323645
$612$	1.00000	0.0404226
$613$	−11.0000	−0.444286	−0.222143	−	0.975014i	$-0.571305\pi$
$613$	−11.0000	−0.444286	−0.222143	+	0.975014i	$0.571305\pi$
$614$	5.00000	0.201784
$615$	−6.00000	−0.241943
$616$	−2.00000	−0.0805823
$617$	21.0000	0.845428	0.422714	−	0.906263i	$-0.361077\pi$
$617$	21.0000	0.845428	0.422714	+	0.906263i	$0.361077\pi$
$618$	1.00000	0.0402259
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	20.0000	0.803219
$621$	−5.00000	−0.200643
$622$	−30.0000	−1.20289
$623$	11.0000	0.440706
$624$	−2.00000	−0.0800641
$625$	−19.0000	−0.760000
$626$	−26.0000	−1.03917
$627$	14.0000	0.559106
$628$	23.0000	0.917800
$629$	8.00000	0.318981
$630$	2.00000	0.0796819
$631$	24.0000	0.955425	0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000	0.955425	0.477712	+	0.878516i	$0.341466\pi$
$632$	0	0
$633$	−8.00000	−0.317971
$634$	24.0000	0.953162
$635$	−8.00000	−0.317470
$636$	9.00000	0.356873
$637$	12.0000	0.475457
$638$	8.00000	0.316723
$639$	−6.00000	−0.237356
$640$	−2.00000	−0.0790569
$641$	17.0000	0.671460	0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000	0.671460	0.335730	+	0.941958i	$0.391017\pi$
$642$	−3.00000	−0.118401
$643$	34.0000	1.34083	0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000	1.34083	0.670415	+	0.741987i	$0.266116\pi$
$644$	5.00000	0.197028
$645$	−12.0000	−0.472500
$646$	7.00000	0.275411
$647$	27.0000	1.06148	0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000	1.06148	0.530740	+	0.847535i	$0.321914\pi$
$648$	−1.00000	−0.0392837
$649$	2.00000	0.0785069
$650$	−2.00000	−0.0784465
$651$	−10.0000	−0.391931
$652$	−20.0000	−0.783260
$653$	26.0000	1.01746	0.508729	−	0.860927i	$-0.330115\pi$
$653$	26.0000	1.01746	0.508729	+	0.860927i	$0.330115\pi$
$654$	4.00000	0.156412
$655$	−20.0000	−0.781465
$656$	−3.00000	−0.117130
$657$	7.00000	0.273096
$658$	4.00000	0.155936
$659$	−9.00000	−0.350590	−0.175295	−	0.984516i	$-0.556088\pi$
$659$	−9.00000	−0.350590	−0.175295	+	0.984516i	$0.556088\pi$
$660$	−4.00000	−0.155700
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	−21.0000	−0.816188
$663$	−2.00000	−0.0776736
$664$	9.00000	0.349268
$665$	14.0000	0.542897
$666$	−8.00000	−0.309994
$667$	−20.0000	−0.774403
$668$	−24.0000	−0.928588
$669$	−4.00000	−0.154649
$670$	20.0000	0.772667
$671$	4.00000	0.154418
$672$	1.00000	0.0385758
$673$	15.0000	0.578208	0.289104	−	0.957298i	$-0.406643\pi$
$673$	15.0000	0.578208	0.289104	+	0.957298i	$0.406643\pi$
$674$	−25.0000	−0.962964
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	14.0000	0.537667
$679$	5.00000	0.191882
$680$	−2.00000	−0.0766965
$681$	−12.0000	−0.459841
$682$	20.0000	0.765840
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−7.00000	−0.267652
$685$	0	0
$686$	−13.0000	−0.496342
$687$	1.00000	0.0381524
$688$	−6.00000	−0.228748
$689$	−18.0000	−0.685745
$690$	10.0000	0.380693
$691$	49.0000	1.86405	0.932024	−	0.362397i	$-0.118041\pi$
$691$	49.0000	1.86405	0.932024	+	0.362397i	$0.118041\pi$
$692$	2.00000	0.0760286
$693$	2.00000	0.0759737
$694$	−12.0000	−0.455514
$695$	−40.0000	−1.51729
$696$	−4.00000	−0.151620
$697$	−3.00000	−0.113633
$698$	−27.0000	−1.02197
$699$	−6.00000	−0.226941
$700$	1.00000	0.0377964
$701$	4.00000	0.151078	0.0755390	−	0.997143i	$-0.475932\pi$
$701$	4.00000	0.151078	0.0755390	+	0.997143i	$0.475932\pi$
$702$	2.00000	0.0754851
$703$	−56.0000	−2.11208
$704$	−2.00000	−0.0753778
$705$	8.00000	0.301297
$706$	9.00000	0.338719
$707$	6.00000	0.225653
$708$	−1.00000	−0.0375823
$709$	−2.00000	−0.0751116	−0.0375558	−	0.999295i	$-0.511957\pi$
$709$	−2.00000	−0.0751116	−0.0375558	+	0.999295i	$0.511957\pi$
$710$	12.0000	0.450352
$711$	0	0
$712$	11.0000	0.412242
$713$	−50.0000	−1.87251
$714$	1.00000	0.0374241
$715$	8.00000	0.299183
$716$	−19.0000	−0.710063
$717$	−4.00000	−0.149383
$718$	21.0000	0.783713
$719$	−32.0000	−1.19340	−0.596699	−	0.802465i	$-0.703521\pi$
$719$	−32.0000	−1.19340	−0.596699	+	0.802465i	$0.703521\pi$
$720$	2.00000	0.0745356
$721$	1.00000	0.0372419
$722$	−30.0000	−1.11648
$723$	4.00000	0.148762
$724$	−6.00000	−0.222988
$725$	−4.00000	−0.148556
$726$	7.00000	0.259794
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	−6.00000	−0.221918
$732$	−2.00000	−0.0739221
$733$	−24.0000	−0.886460	−0.443230	−	0.896408i	$-0.646168\pi$
$733$	−24.0000	−0.886460	−0.443230	+	0.896408i	$0.646168\pi$
$734$	20.0000	0.738213
$735$	−12.0000	−0.442627
$736$	5.00000	0.184302
$737$	20.0000	0.736709
$738$	3.00000	0.110432
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	16.0000	0.588172
$741$	14.0000	0.514303
$742$	9.00000	0.330400
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	−10.0000	−0.366618
$745$	24.0000	0.879292
$746$	−36.0000	−1.31805
$747$	−9.00000	−0.329293
$748$	−2.00000	−0.0731272
$749$	−3.00000	−0.109618
$750$	12.0000	0.438178
$751$	50.0000	1.82453	0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000	1.82453	0.912263	+	0.409605i	$0.134333\pi$
$752$	4.00000	0.145865
$753$	6.00000	0.218652
$754$	8.00000	0.291343
$755$	34.0000	1.23739
$756$	−1.00000	−0.0363696
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−30.0000	−1.08965
$759$	10.0000	0.362977
$760$	14.0000	0.507833
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	4.00000	0.144905
$763$	4.00000	0.144810
$764$	6.00000	0.217072
$765$	2.00000	0.0723102
$766$	−1.00000	−0.0361315
$767$	2.00000	0.0722158
$768$	1.00000	0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	−4.00000	−0.144150
$771$	−18.0000	−0.648254
$772$	0	0
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	6.00000	0.215666
$775$	−10.0000	−0.359211
$776$	5.00000	0.179490
$777$	−8.00000	−0.286998
$778$	−30.0000	−1.07555
$779$	21.0000	0.752403
$780$	−4.00000	−0.143223
$781$	12.0000	0.429394
$782$	5.00000	0.178800
$783$	4.00000	0.142948
$784$	−6.00000	−0.214286
$785$	46.0000	1.64181
$786$	10.0000	0.356688
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−22.0000	−0.783718
$789$	−9.00000	−0.320408
$790$	0	0
$791$	14.0000	0.497783
$792$	2.00000	0.0710669
$793$	4.00000	0.142044
$794$	2.00000	0.0709773
$795$	18.0000	0.638394
$796$	−5.00000	−0.177220
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	−7.00000	−0.247797
$799$	4.00000	0.141510
$800$	1.00000	0.0353553
$801$	−11.0000	−0.388666
$802$	22.0000	0.776847
$803$	−14.0000	−0.494049
$804$	−10.0000	−0.352673
$805$	10.0000	0.352454
$806$	20.0000	0.704470
$807$	−3.00000	−0.105605
$808$	6.00000	0.211079
$809$	−14.0000	−0.492214	−0.246107	−	0.969243i	$-0.579151\pi$
$809$	−14.0000	−0.492214	−0.246107	+	0.969243i	$0.579151\pi$
$810$	−2.00000	−0.0702728
$811$	7.00000	0.245803	0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000	0.245803	0.122902	+	0.992419i	$0.460780\pi$
$812$	−4.00000	−0.140372
$813$	32.0000	1.12229
$814$	16.0000	0.560800
$815$	−40.0000	−1.40114
$816$	1.00000	0.0350070
$817$	42.0000	1.46939
$818$	−18.0000	−0.629355
$819$	2.00000	0.0698857
$820$	−6.00000	−0.209529
$821$	11.0000	0.383903	0.191951	−	0.981404i	$-0.438518\pi$
$821$	11.0000	0.383903	0.191951	+	0.981404i	$0.438518\pi$
$822$	0	0
$823$	38.0000	1.32460	0.662298	−	0.749240i	$-0.269581\pi$
$823$	38.0000	1.32460	0.662298	+	0.749240i	$0.269581\pi$
$824$	1.00000	0.0348367
$825$	2.00000	0.0696311
$826$	−1.00000	−0.0347945
$827$	−15.0000	−0.521601	−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000	−0.521601	−0.260801	+	0.965393i	$0.583986\pi$
$828$	−5.00000	−0.173762
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	18.0000	0.624789
$831$	−9.00000	−0.312207
$832$	−2.00000	−0.0693375
$833$	−6.00000	−0.207888
$834$	20.0000	0.692543
$835$	−48.0000	−1.66111
$836$	14.0000	0.484200
$837$	10.0000	0.345651
$838$	−18.0000	−0.621800
$839$	−8.00000	−0.276191	−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000	−0.276191	−0.138095	+	0.990419i	$0.544098\pi$
$840$	2.00000	0.0690066
$841$	−13.0000	−0.448276
$842$	−17.0000	−0.585859
$843$	6.00000	0.206651
$844$	−8.00000	−0.275371
$845$	−18.0000	−0.619219
$846$	−4.00000	−0.137523
$847$	7.00000	0.240523
$848$	9.00000	0.309061
$849$	11.0000	0.377519
$850$	1.00000	0.0342997
$851$	−40.0000	−1.37118
$852$	−6.00000	−0.205557
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	−2.00000	−0.0684386
$855$	−14.0000	−0.478790
$856$	−3.00000	−0.102538
$857$	50.0000	1.70797	0.853984	−	0.520300i	$-0.174180\pi$
$857$	50.0000	1.70797	0.853984	+	0.520300i	$0.174180\pi$
$858$	−4.00000	−0.136558
$859$	22.0000	0.750630	0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000	0.750630	0.375315	+	0.926897i	$0.377534\pi$
$860$	−12.0000	−0.409197
$861$	3.00000	0.102240
$862$	39.0000	1.32835
$863$	−28.0000	−0.953131	−0.476566	−	0.879139i	$-0.658119\pi$
$863$	−28.0000	−0.953131	−0.476566	+	0.879139i	$0.658119\pi$
$864$	−1.00000	−0.0340207
$865$	4.00000	0.136004
$866$	39.0000	1.32527
$867$	1.00000	0.0339618
$868$	−10.0000	−0.339422
$869$	0	0
$870$	−8.00000	−0.271225
$871$	20.0000	0.677674
$872$	4.00000	0.135457
$873$	−5.00000	−0.169224
$874$	−35.0000	−1.18389
$875$	12.0000	0.405674
$876$	7.00000	0.236508
$877$	31.0000	1.04680	0.523398	−	0.852088i	$-0.324664\pi$
$877$	31.0000	1.04680	0.523398	+	0.852088i	$0.324664\pi$
$878$	32.0000	1.07995
$879$	6.00000	0.202375
$880$	−4.00000	−0.134840
$881$	−36.0000	−1.21287	−0.606435	−	0.795133i	$-0.707401\pi$
$881$	−36.0000	−1.21287	−0.606435	+	0.795133i	$0.707401\pi$
$882$	6.00000	0.202031
$883$	−41.0000	−1.37976	−0.689880	−	0.723924i	$-0.742337\pi$
$883$	−41.0000	−1.37976	−0.689880	+	0.723924i	$0.742337\pi$
$884$	−2.00000	−0.0672673
$885$	−2.00000	−0.0672293
$886$	−33.0000	−1.10866
$887$	−11.0000	−0.369344	−0.184672	−	0.982800i	$-0.559122\pi$
$887$	−11.0000	−0.369344	−0.184672	+	0.982800i	$0.559122\pi$
$888$	−8.00000	−0.268462
$889$	4.00000	0.134156
$890$	22.0000	0.737442
$891$	−2.00000	−0.0670025
$892$	−4.00000	−0.133930
$893$	−28.0000	−0.936984
$894$	−12.0000	−0.401340
$895$	−38.0000	−1.27020
$896$	1.00000	0.0334077
$897$	10.0000	0.333890
$898$	−15.0000	−0.500556
$899$	40.0000	1.33407
$900$	−1.00000	−0.0333333
$901$	9.00000	0.299833
$902$	−6.00000	−0.199778
$903$	6.00000	0.199667
$904$	14.0000	0.465633
$905$	−12.0000	−0.398893
$906$	−17.0000	−0.564787
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−12.0000	−0.398234
$909$	−6.00000	−0.199007
$910$	−4.00000	−0.132599
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	−7.00000	−0.231793
$913$	18.0000	0.595713
$914$	−10.0000	−0.330771
$915$	−4.00000	−0.132236
$916$	1.00000	0.0330409
$917$	10.0000	0.330229
$918$	−1.00000	−0.0330049
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	10.0000	0.329690
$921$	−5.00000	−0.164756
$922$	1.00000	0.0329332
$923$	12.0000	0.394985
$924$	2.00000	0.0657952
$925$	−8.00000	−0.263038
$926$	8.00000	0.262896
$927$	−1.00000	−0.0328443
$928$	−4.00000	−0.131306
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	−20.0000	−0.655826
$931$	42.0000	1.37649
$932$	−6.00000	−0.196537
$933$	30.0000	0.982156
$934$	−24.0000	−0.785304
$935$	−4.00000	−0.130814
$936$	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	$0.324926\pi$
$938$	−10.0000	−0.326512
$939$	26.0000	0.848478
$940$	8.00000	0.260931
$941$	−7.00000	−0.228193	−0.114097	−	0.993470i	$-0.536397\pi$
$941$	−7.00000	−0.228193	−0.114097	+	0.993470i	$0.536397\pi$
$942$	−23.0000	−0.749380
$943$	15.0000	0.488467
$944$	−1.00000	−0.0325472
$945$	−2.00000	−0.0650600
$946$	−12.0000	−0.390154
$947$	−7.00000	−0.227469	−0.113735	−	0.993511i	$-0.536281\pi$
$947$	−7.00000	−0.227469	−0.113735	+	0.993511i	$0.536281\pi$
$948$	0	0
$949$	−14.0000	−0.454459
$950$	−7.00000	−0.227110
$951$	−24.0000	−0.778253
$952$	1.00000	0.0324102
$953$	10.0000	0.323932	0.161966	−	0.986796i	$-0.448217\pi$
$953$	10.0000	0.323932	0.161966	+	0.986796i	$0.448217\pi$
$954$	−9.00000	−0.291386
$955$	12.0000	0.388311
$956$	−4.00000	−0.129369
$957$	−8.00000	−0.258603
$958$	42.0000	1.35696
$959$	0	0
$960$	2.00000	0.0645497
$961$	69.0000	2.22581
$962$	16.0000	0.515861
$963$	3.00000	0.0966736
$964$	4.00000	0.128831
$965$	0	0
$966$	−5.00000	−0.160872
$967$	−1.00000	−0.0321578	−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000	−0.0321578	−0.0160789	+	0.999871i	$0.505118\pi$
$968$	7.00000	0.224989
$969$	−7.00000	−0.224872
$970$	10.0000	0.321081
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	1.00000	0.0320750
$973$	20.0000	0.641171
$974$	−1.00000	−0.0320421
$975$	2.00000	0.0640513
$976$	−2.00000	−0.0640184
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	20.0000	0.639529
$979$	22.0000	0.703123
$980$	−12.0000	−0.383326
$981$	−4.00000	−0.127710
$982$	2.00000	0.0638226
$983$	35.0000	1.11633	0.558163	−	0.829731i	$-0.311506\pi$
$983$	35.0000	1.11633	0.558163	+	0.829731i	$0.311506\pi$
$984$	3.00000	0.0956365
$985$	−44.0000	−1.40196
$986$	−4.00000	−0.127386
$987$	−4.00000	−0.127321
$988$	14.0000	0.445399
$989$	30.0000	0.953945
$990$	4.00000	0.127128
$991$	−56.0000	−1.77890	−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000	−1.77890	−0.889449	+	0.457034i	$0.848912\pi$
$992$	−10.0000	−0.317500
$993$	21.0000	0.666415
$994$	−6.00000	−0.190308
$995$	−10.0000	−0.317021
$996$	−9.00000	−0.285176
$997$	61.0000	1.93189	0.965945	−	0.258749i	$-0.0833101\pi$
$997$	61.0000	1.93189	0.965945	+	0.258749i	$0.0833101\pi$
$998$	−34.0000	−1.07625
$999$	8.00000	0.253109

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.e.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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