LMFDB - Embedded newform 258.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [258,2,Mod(1,258)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(258, 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("258.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 258 = 2 \cdot 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	258.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:	$2.06014037215$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	258.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +5.00000 q^{11} +1.00000 q^{12} -7.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +5.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} -7.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -5.00000 q^{29} -1.00000 q^{30} -10.0000 q^{31} +1.00000 q^{32} +5.00000 q^{33} +4.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} -7.00000 q^{39} -1.00000 q^{40} +1.00000 q^{42} +1.00000 q^{43} +5.00000 q^{44} -1.00000 q^{45} -4.00000 q^{46} -1.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -4.00000 q^{50} +4.00000 q^{51} -7.00000 q^{52} +12.0000 q^{53} +1.00000 q^{54} -5.00000 q^{55} +1.00000 q^{56} -1.00000 q^{57} -5.00000 q^{58} +4.00000 q^{59} -1.00000 q^{60} -8.00000 q^{61} -10.0000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +7.00000 q^{65} +5.00000 q^{66} -2.00000 q^{67} +4.00000 q^{68} -4.00000 q^{69} -1.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} +4.00000 q^{73} +10.0000 q^{74} -4.00000 q^{75} -1.00000 q^{76} +5.00000 q^{77} -7.00000 q^{78} +10.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.00000 q^{83} +1.00000 q^{84} -4.00000 q^{85} +1.00000 q^{86} -5.00000 q^{87} +5.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -7.00000 q^{91} -4.00000 q^{92} -10.0000 q^{93} -1.00000 q^{94} +1.00000 q^{95} +1.00000 q^{96} -7.00000 q^{97} -6.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	1.00000	0.288675
$13$	−7.00000	−1.94145	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000	−1.94145	−0.970725	+	0.240192i	$0.922790\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	5.00000	1.06600
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	−7.00000	−1.37281
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	−1.00000	−0.182574
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	1.00000	0.176777
$33$	5.00000	0.870388
$34$	4.00000	0.685994
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−1.00000	−0.162221
$39$	−7.00000	−1.12090
$40$	−1.00000	−0.158114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	1.00000	0.154303
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.00000	0.753778
$45$	−1.00000	−0.149071
$46$	−4.00000	−0.589768
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	−4.00000	−0.565685
$51$	4.00000	0.560112
$52$	−7.00000	−0.970725
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	1.00000	0.136083
$55$	−5.00000	−0.674200
$56$	1.00000	0.133631
$57$	−1.00000	−0.132453
$58$	−5.00000	−0.656532
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−1.00000	−0.129099
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	−10.0000	−1.27000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	7.00000	0.868243
$66$	5.00000	0.615457
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	4.00000	0.485071
$69$	−4.00000	−0.481543
$70$	−1.00000	−0.119523
$71$	−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
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	10.0000	1.16248
$75$	−4.00000	−0.461880
$76$	−1.00000	−0.114708
$77$	5.00000	0.569803
$78$	−7.00000	−0.792594
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	0	0
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	1.00000	0.109109
$85$	−4.00000	−0.433861
$86$	1.00000	0.107833
$87$	−5.00000	−0.536056
$88$	5.00000	0.533002
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−0.105409
$91$	−7.00000	−0.733799
$92$	−4.00000	−0.417029
$93$	−10.0000	−1.03695
$94$	−1.00000	−0.103142
$95$	1.00000	0.102598
$96$	1.00000	0.102062
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	−6.00000	−0.606092
$99$	5.00000	0.502519
$100$	−4.00000	−0.400000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	4.00000	0.396059
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−7.00000	−0.686406
$105$	−1.00000	−0.0975900
$106$	12.0000	1.16554
$107$	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
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	−5.00000	−0.476731
$111$	10.0000	0.949158
$112$	1.00000	0.0944911
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	−1.00000	−0.0936586
$115$	4.00000	0.373002
$116$	−5.00000	−0.464238
$117$	−7.00000	−0.647150
$118$	4.00000	0.368230
$119$	4.00000	0.366679
$120$	−1.00000	−0.0912871
$121$	14.0000	1.27273
$122$	−8.00000	−0.724286
$123$	0	0
$124$	−10.0000	−0.898027
$125$	9.00000	0.804984
$126$	1.00000	0.0890871
$127$	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
$129$	1.00000	0.0880451
$130$	7.00000	0.613941
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	5.00000	0.435194
$133$	−1.00000	−0.0867110
$134$	−2.00000	−0.172774
$135$	−1.00000	−0.0860663
$136$	4.00000	0.342997
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	−4.00000	−0.340503
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	−1.00000	−0.0845154
$141$	−1.00000	−0.0842152
$142$	−12.0000	−1.00702
$143$	−35.0000	−2.92685
$144$	1.00000	0.0833333
$145$	5.00000	0.415227
$146$	4.00000	0.331042
$147$	−6.00000	−0.494872
$148$	10.0000	0.821995
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	−4.00000	−0.326599
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	−1.00000	−0.0811107
$153$	4.00000	0.323381
$154$	5.00000	0.402911
$155$	10.0000	0.803219
$156$	−7.00000	−0.560449
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	10.0000	0.795557
$159$	12.0000	0.951662
$160$	−1.00000	−0.0790569
$161$	−4.00000	−0.315244
$162$	1.00000	0.0785674
$163$	3.00000	0.234978	0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000	0.234978	0.117489	+	0.993074i	$0.462515\pi$
$164$	0	0
$165$	−5.00000	−0.389249
$166$	−7.00000	−0.543305
$167$	7.00000	0.541676	0.270838	−	0.962625i	$-0.412699\pi$
$167$	7.00000	0.541676	0.270838	+	0.962625i	$0.412699\pi$
$168$	1.00000	0.0771517
$169$	36.0000	2.76923
$170$	−4.00000	−0.306786
$171$	−1.00000	−0.0764719
$172$	1.00000	0.0762493
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−5.00000	−0.379049
$175$	−4.00000	−0.302372
$176$	5.00000	0.376889
$177$	4.00000	0.300658
$178$	6.00000	0.449719
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	−1.00000	−0.0745356
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	−7.00000	−0.518875
$183$	−8.00000	−0.591377
$184$	−4.00000	−0.294884
$185$	−10.0000	−0.735215
$186$	−10.0000	−0.733236
$187$	20.0000	1.46254
$188$	−1.00000	−0.0729325
$189$	1.00000	0.0727393
$190$	1.00000	0.0725476
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.00000	0.0721688
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−7.00000	−0.502571
$195$	7.00000	0.501280
$196$	−6.00000	−0.428571
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	5.00000	0.355335
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−4.00000	−0.282843
$201$	−2.00000	−0.141069
$202$	18.0000	1.26648
$203$	−5.00000	−0.350931
$204$	4.00000	0.280056
$205$	0	0
$206$	6.00000	0.418040
$207$	−4.00000	−0.278019
$208$	−7.00000	−0.485363
$209$	−5.00000	−0.345857
$210$	−1.00000	−0.0690066
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	12.0000	0.824163
$213$	−12.0000	−0.822226
$214$	3.00000	0.205076
$215$	−1.00000	−0.0681994
$216$	1.00000	0.0680414
$217$	−10.0000	−0.678844
$218$	5.00000	0.338643
$219$	4.00000	0.270295
$220$	−5.00000	−0.337100
$221$	−28.0000	−1.88348
$222$	10.0000	0.671156
$223$	7.00000	0.468755	0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000	0.468755	0.234377	+	0.972146i	$0.424695\pi$
$224$	1.00000	0.0668153
$225$	−4.00000	−0.266667
$226$	9.00000	0.598671
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	−1.00000	−0.0662266
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	4.00000	0.263752
$231$	5.00000	0.328976
$232$	−5.00000	−0.328266
$233$	−25.0000	−1.63780	−0.818902	−	0.573933i	$-0.805417\pi$
$233$	−25.0000	−1.63780	−0.818902	+	0.573933i	$0.805417\pi$
$234$	−7.00000	−0.457604
$235$	1.00000	0.0652328
$236$	4.00000	0.260378
$237$	10.0000	0.649570
$238$	4.00000	0.259281
$239$	−5.00000	−0.323423	−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000	−0.323423	−0.161712	+	0.986838i	$0.551701\pi$
$240$	−1.00000	−0.0645497
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	14.0000	0.899954
$243$	1.00000	0.0641500
$244$	−8.00000	−0.512148
$245$	6.00000	0.383326
$246$	0	0
$247$	7.00000	0.445399
$248$	−10.0000	−0.635001
$249$	−7.00000	−0.443607
$250$	9.00000	0.569210
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	1.00000	0.0629941
$253$	−20.0000	−1.25739
$254$	16.0000	1.00393
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	−15.0000	−0.935674	−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000	−0.935674	−0.467837	+	0.883815i	$0.654967\pi$
$258$	1.00000	0.0622573
$259$	10.0000	0.621370
$260$	7.00000	0.434122
$261$	−5.00000	−0.309492
$262$	6.00000	0.370681
$263$	−2.00000	−0.123325	−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000	−0.123325	−0.0616626	+	0.998097i	$0.519640\pi$
$264$	5.00000	0.307729
$265$	−12.0000	−0.737154
$266$	−1.00000	−0.0613139
$267$	6.00000	0.367194
$268$	−2.00000	−0.122169
$269$	4.00000	0.243884	0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000	0.243884	0.121942	+	0.992537i	$0.461088\pi$
$270$	−1.00000	−0.0608581
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	4.00000	0.242536
$273$	−7.00000	−0.423659
$274$	−9.00000	−0.543710
$275$	−20.0000	−1.20605
$276$	−4.00000	−0.240772
$277$	−30.0000	−1.80253	−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−30.0000	−1.80253	−0.901263	+	0.433273i	$0.857359\pi$
$278$	−14.0000	−0.839664
$279$	−10.0000	−0.598684
$280$	−1.00000	−0.0597614
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	−1.00000	−0.0595491
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−12.0000	−0.712069
$285$	1.00000	0.0592349
$286$	−35.0000	−2.06959
$287$	0	0
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	5.00000	0.293610
$291$	−7.00000	−0.410347
$292$	4.00000	0.234082
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	−6.00000	−0.349927
$295$	−4.00000	−0.232889
$296$	10.0000	0.581238
$297$	5.00000	0.290129
$298$	10.0000	0.579284
$299$	28.0000	1.61928
$300$	−4.00000	−0.230940
$301$	1.00000	0.0576390
$302$	−16.0000	−0.920697
$303$	18.0000	1.03407
$304$	−1.00000	−0.0573539
$305$	8.00000	0.458079
$306$	4.00000	0.228665
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	5.00000	0.284901
$309$	6.00000	0.341328
$310$	10.0000	0.567962
$311$	−31.0000	−1.75785	−0.878924	−	0.476961i	$-0.841738\pi$
$311$	−31.0000	−1.75785	−0.878924	+	0.476961i	$0.841738\pi$
$312$	−7.00000	−0.396297
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	18.0000	1.01580
$315$	−1.00000	−0.0563436
$316$	10.0000	0.562544
$317$	24.0000	1.34797	0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000	1.34797	0.673987	+	0.738743i	$0.264580\pi$
$318$	12.0000	0.672927
$319$	−25.0000	−1.39973
$320$	−1.00000	−0.0559017
$321$	3.00000	0.167444
$322$	−4.00000	−0.222911
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	28.0000	1.55316
$326$	3.00000	0.166155
$327$	5.00000	0.276501
$328$	0	0
$329$	−1.00000	−0.0551318
$330$	−5.00000	−0.275241
$331$	17.0000	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	−7.00000	−0.384175
$333$	10.0000	0.547997
$334$	7.00000	0.383023
$335$	2.00000	0.109272
$336$	1.00000	0.0545545
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	36.0000	1.95814
$339$	9.00000	0.488813
$340$	−4.00000	−0.216930
$341$	−50.0000	−2.70765
$342$	−1.00000	−0.0540738
$343$	−13.0000	−0.701934
$344$	1.00000	0.0539164
$345$	4.00000	0.215353
$346$	6.00000	0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−5.00000	−0.268028
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	−4.00000	−0.213809
$351$	−7.00000	−0.373632
$352$	5.00000	0.266501
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	4.00000	0.212598
$355$	12.0000	0.636894
$356$	6.00000	0.317999
$357$	4.00000	0.211702
$358$	−16.0000	−0.845626
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	−1.00000	−0.0527046
$361$	−18.0000	−0.947368
$362$	7.00000	0.367912
$363$	14.0000	0.734809
$364$	−7.00000	−0.366900
$365$	−4.00000	−0.209370
$366$	−8.00000	−0.418167
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	−10.0000	−0.519875
$371$	12.0000	0.623009
$372$	−10.0000	−0.518476
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	20.0000	1.03418
$375$	9.00000	0.464758
$376$	−1.00000	−0.0515711
$377$	35.0000	1.80259
$378$	1.00000	0.0514344
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	1.00000	0.0512989
$381$	16.0000	0.819705
$382$	−18.0000	−0.920960
$383$	−36.0000	−1.83951	−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000	−1.83951	−0.919757	+	0.392488i	$0.871614\pi$
$384$	1.00000	0.0510310
$385$	−5.00000	−0.254824
$386$	−2.00000	−0.101797
$387$	1.00000	0.0508329
$388$	−7.00000	−0.355371
$389$	5.00000	0.253510	0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000	0.253510	0.126755	+	0.991934i	$0.459544\pi$
$390$	7.00000	0.354459
$391$	−16.0000	−0.809155
$392$	−6.00000	−0.303046
$393$	6.00000	0.302660
$394$	2.00000	0.100759
$395$	−10.0000	−0.503155
$396$	5.00000	0.251259
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	4.00000	0.200502
$399$	−1.00000	−0.0500626
$400$	−4.00000	−0.200000
$401$	38.0000	1.89763	0.948815	−	0.315833i	$-0.102284\pi$
$401$	38.0000	1.89763	0.948815	+	0.315833i	$0.102284\pi$
$402$	−2.00000	−0.0997509
$403$	70.0000	3.48695
$404$	18.0000	0.895533
$405$	−1.00000	−0.0496904
$406$	−5.00000	−0.248146
$407$	50.0000	2.47841
$408$	4.00000	0.198030
$409$	32.0000	1.58230	0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000	1.58230	0.791149	+	0.611623i	$0.209483\pi$
$410$	0	0
$411$	−9.00000	−0.443937
$412$	6.00000	0.295599
$413$	4.00000	0.196827
$414$	−4.00000	−0.196589
$415$	7.00000	0.343616
$416$	−7.00000	−0.343203
$417$	−14.0000	−0.685583
$418$	−5.00000	−0.244558
$419$	28.0000	1.36789	0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000	1.36789	0.683945	+	0.729534i	$0.260263\pi$
$420$	−1.00000	−0.0487950
$421$	16.0000	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$422$	−5.00000	−0.243396
$423$	−1.00000	−0.0486217
$424$	12.0000	0.582772
$425$	−16.0000	−0.776114
$426$	−12.0000	−0.581402
$427$	−8.00000	−0.387147
$428$	3.00000	0.145010
$429$	−35.0000	−1.68982
$430$	−1.00000	−0.0482243
$431$	19.0000	0.915198	0.457599	−	0.889159i	$-0.348710\pi$
$431$	19.0000	0.915198	0.457599	+	0.889159i	$0.348710\pi$
$432$	1.00000	0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−10.0000	−0.480015
$435$	5.00000	0.239732
$436$	5.00000	0.239457
$437$	4.00000	0.191346
$438$	4.00000	0.191127
$439$	−22.0000	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$440$	−5.00000	−0.238366
$441$	−6.00000	−0.285714
$442$	−28.0000	−1.33182
$443$	−39.0000	−1.85295	−0.926473	−	0.376361i	$-0.877175\pi$
$443$	−39.0000	−1.85295	−0.926473	+	0.376361i	$0.877175\pi$
$444$	10.0000	0.474579
$445$	−6.00000	−0.284427
$446$	7.00000	0.331460
$447$	10.0000	0.472984
$448$	1.00000	0.0472456
$449$	−19.0000	−0.896665	−0.448333	−	0.893867i	$-0.647982\pi$
$449$	−19.0000	−0.896665	−0.448333	+	0.893867i	$0.647982\pi$
$450$	−4.00000	−0.188562
$451$	0	0
$452$	9.00000	0.423324
$453$	−16.0000	−0.751746
$454$	18.0000	0.844782
$455$	7.00000	0.328165
$456$	−1.00000	−0.0468293
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−22.0000	−1.02799
$459$	4.00000	0.186704
$460$	4.00000	0.186501
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	5.00000	0.232621
$463$	23.0000	1.06890	0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000	1.06890	0.534450	+	0.845200i	$0.320519\pi$
$464$	−5.00000	−0.232119
$465$	10.0000	0.463739
$466$	−25.0000	−1.15810
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	−7.00000	−0.323575
$469$	−2.00000	−0.0923514
$470$	1.00000	0.0461266
$471$	18.0000	0.829396
$472$	4.00000	0.184115
$473$	5.00000	0.229900
$474$	10.0000	0.459315
$475$	4.00000	0.183533
$476$	4.00000	0.183340
$477$	12.0000	0.549442
$478$	−5.00000	−0.228695
$479$	11.0000	0.502603	0.251301	−	0.967909i	$-0.419141\pi$
$479$	11.0000	0.502603	0.251301	+	0.967909i	$0.419141\pi$
$480$	−1.00000	−0.0456435
$481$	−70.0000	−3.19173
$482$	−10.0000	−0.455488
$483$	−4.00000	−0.182006
$484$	14.0000	0.636364
$485$	7.00000	0.317854
$486$	1.00000	0.0453609
$487$	12.0000	0.543772	0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000	0.543772	0.271886	+	0.962329i	$0.412353\pi$
$488$	−8.00000	−0.362143
$489$	3.00000	0.135665
$490$	6.00000	0.271052
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	0	0
$493$	−20.0000	−0.900755
$494$	7.00000	0.314945
$495$	−5.00000	−0.224733
$496$	−10.0000	−0.449013
$497$	−12.0000	−0.538274
$498$	−7.00000	−0.313678
$499$	−25.0000	−1.11915	−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000	−1.11915	−0.559577	+	0.828778i	$0.689036\pi$
$500$	9.00000	0.402492
$501$	7.00000	0.312737
$502$	−21.0000	−0.937276
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	1.00000	0.0445435
$505$	−18.0000	−0.800989
$506$	−20.0000	−0.889108
$507$	36.0000	1.59882
$508$	16.0000	0.709885
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	−4.00000	−0.177123
$511$	4.00000	0.176950
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−15.0000	−0.661622
$515$	−6.00000	−0.264392
$516$	1.00000	0.0440225
$517$	−5.00000	−0.219900
$518$	10.0000	0.439375
$519$	6.00000	0.263371
$520$	7.00000	0.306970
$521$	−31.0000	−1.35813	−0.679067	−	0.734076i	$-0.737616\pi$
$521$	−31.0000	−1.35813	−0.679067	+	0.734076i	$0.737616\pi$
$522$	−5.00000	−0.218844
$523$	−1.00000	−0.0437269	−0.0218635	−	0.999761i	$-0.506960\pi$
$523$	−1.00000	−0.0437269	−0.0218635	+	0.999761i	$0.506960\pi$
$524$	6.00000	0.262111
$525$	−4.00000	−0.174574
$526$	−2.00000	−0.0872041
$527$	−40.0000	−1.74243
$528$	5.00000	0.217597
$529$	−7.00000	−0.304348
$530$	−12.0000	−0.521247
$531$	4.00000	0.173585
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	6.00000	0.259645
$535$	−3.00000	−0.129701
$536$	−2.00000	−0.0863868
$537$	−16.0000	−0.690451
$538$	4.00000	0.172452
$539$	−30.0000	−1.29219
$540$	−1.00000	−0.0430331
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	−8.00000	−0.343629
$543$	7.00000	0.300399
$544$	4.00000	0.171499
$545$	−5.00000	−0.214176
$546$	−7.00000	−0.299572
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	−9.00000	−0.384461
$549$	−8.00000	−0.341432
$550$	−20.0000	−0.852803
$551$	5.00000	0.213007
$552$	−4.00000	−0.170251
$553$	10.0000	0.425243
$554$	−30.0000	−1.27458
$555$	−10.0000	−0.424476
$556$	−14.0000	−0.593732
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−10.0000	−0.423334
$559$	−7.00000	−0.296068
$560$	−1.00000	−0.0422577
$561$	20.0000	0.844401
$562$	30.0000	1.26547
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	−1.00000	−0.0421076
$565$	−9.00000	−0.378633
$566$	4.00000	0.168133
$567$	1.00000	0.0419961
$568$	−12.0000	−0.503509
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	1.00000	0.0418854
$571$	−23.0000	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$572$	−35.0000	−1.46342
$573$	−18.0000	−0.751961
$574$	0	0
$575$	16.0000	0.667246
$576$	1.00000	0.0416667
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	−1.00000	−0.0415945
$579$	−2.00000	−0.0831172
$580$	5.00000	0.207614
$581$	−7.00000	−0.290409
$582$	−7.00000	−0.290159
$583$	60.0000	2.48495
$584$	4.00000	0.165521
$585$	7.00000	0.289414
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	−6.00000	−0.247436
$589$	10.0000	0.412043
$590$	−4.00000	−0.164677
$591$	2.00000	0.0822690
$592$	10.0000	0.410997
$593$	−22.0000	−0.903432	−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000	−0.903432	−0.451716	+	0.892162i	$0.649188\pi$
$594$	5.00000	0.205152
$595$	−4.00000	−0.163984
$596$	10.0000	0.409616
$597$	4.00000	0.163709
$598$	28.0000	1.14501
$599$	19.0000	0.776319	0.388159	−	0.921592i	$-0.373111\pi$
$599$	19.0000	0.776319	0.388159	+	0.921592i	$0.373111\pi$
$600$	−4.00000	−0.163299
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	1.00000	0.0407570
$603$	−2.00000	−0.0814463
$604$	−16.0000	−0.651031
$605$	−14.0000	−0.569181
$606$	18.0000	0.731200
$607$	−1.00000	−0.0405887	−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000	−0.0405887	−0.0202944	+	0.999794i	$0.506460\pi$
$608$	−1.00000	−0.0405554
$609$	−5.00000	−0.202610
$610$	8.00000	0.323911
$611$	7.00000	0.283190
$612$	4.00000	0.161690
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	5.00000	0.201456
$617$	16.0000	0.644136	0.322068	−	0.946717i	$-0.395622\pi$
$617$	16.0000	0.644136	0.322068	+	0.946717i	$0.395622\pi$
$618$	6.00000	0.241355
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	10.0000	0.401610
$621$	−4.00000	−0.160514
$622$	−31.0000	−1.24299
$623$	6.00000	0.240385
$624$	−7.00000	−0.280224
$625$	11.0000	0.440000
$626$	−8.00000	−0.319744
$627$	−5.00000	−0.199681
$628$	18.0000	0.718278
$629$	40.0000	1.59490
$630$	−1.00000	−0.0398410
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	10.0000	0.397779
$633$	−5.00000	−0.198732
$634$	24.0000	0.953162
$635$	−16.0000	−0.634941
$636$	12.0000	0.475831
$637$	42.0000	1.66410
$638$	−25.0000	−0.989759
$639$	−12.0000	−0.474713
$640$	−1.00000	−0.0395285
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	3.00000	0.118401
$643$	42.0000	1.65632	0.828159	−	0.560493i	$-0.189388\pi$
$643$	42.0000	1.65632	0.828159	+	0.560493i	$0.189388\pi$
$644$	−4.00000	−0.157622
$645$	−1.00000	−0.0393750
$646$	−4.00000	−0.157378
$647$	−10.0000	−0.393141	−0.196570	−	0.980490i	$-0.562980\pi$
$647$	−10.0000	−0.393141	−0.196570	+	0.980490i	$0.562980\pi$
$648$	1.00000	0.0392837
$649$	20.0000	0.785069
$650$	28.0000	1.09825
$651$	−10.0000	−0.391931
$652$	3.00000	0.117489
$653$	17.0000	0.665261	0.332631	−	0.943057i	$-0.392064\pi$
$653$	17.0000	0.665261	0.332631	+	0.943057i	$0.392064\pi$
$654$	5.00000	0.195515
$655$	−6.00000	−0.234439
$656$	0	0
$657$	4.00000	0.156055
$658$	−1.00000	−0.0389841
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	−5.00000	−0.194625
$661$	11.0000	0.427850	0.213925	−	0.976850i	$-0.431375\pi$
$661$	11.0000	0.427850	0.213925	+	0.976850i	$0.431375\pi$
$662$	17.0000	0.660724
$663$	−28.0000	−1.08743
$664$	−7.00000	−0.271653
$665$	1.00000	0.0387783
$666$	10.0000	0.387492
$667$	20.0000	0.774403
$668$	7.00000	0.270838
$669$	7.00000	0.270636
$670$	2.00000	0.0772667
$671$	−40.0000	−1.54418
$672$	1.00000	0.0385758
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	−5.00000	−0.192593
$675$	−4.00000	−0.153960
$676$	36.0000	1.38462
$677$	34.0000	1.30673	0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000	1.30673	0.653363	+	0.757045i	$0.273358\pi$
$678$	9.00000	0.345643
$679$	−7.00000	−0.268635
$680$	−4.00000	−0.153393
$681$	18.0000	0.689761
$682$	−50.0000	−1.91460
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−1.00000	−0.0382360
$685$	9.00000	0.343872
$686$	−13.0000	−0.496342
$687$	−22.0000	−0.839352
$688$	1.00000	0.0381246
$689$	−84.0000	−3.20015
$690$	4.00000	0.152277
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	6.00000	0.228086
$693$	5.00000	0.189934
$694$	12.0000	0.455514
$695$	14.0000	0.531050
$696$	−5.00000	−0.189525
$697$	0	0
$698$	−28.0000	−1.05982
$699$	−25.0000	−0.945587
$700$	−4.00000	−0.151186
$701$	16.0000	0.604312	0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000	0.604312	0.302156	+	0.953259i	$0.402294\pi$
$702$	−7.00000	−0.264198
$703$	−10.0000	−0.377157
$704$	5.00000	0.188445
$705$	1.00000	0.0376622
$706$	4.00000	0.150542
$707$	18.0000	0.676960
$708$	4.00000	0.150329
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	12.0000	0.450352
$711$	10.0000	0.375029
$712$	6.00000	0.224860
$713$	40.0000	1.49801
$714$	4.00000	0.149696
$715$	35.0000	1.30893
$716$	−16.0000	−0.597948
$717$	−5.00000	−0.186728
$718$	24.0000	0.895672
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	−1.00000	−0.0372678
$721$	6.00000	0.223452
$722$	−18.0000	−0.669891
$723$	−10.0000	−0.371904
$724$	7.00000	0.260153
$725$	20.0000	0.742781
$726$	14.0000	0.519589
$727$	−7.00000	−0.259616	−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000	−0.259616	−0.129808	+	0.991539i	$0.541436\pi$
$728$	−7.00000	−0.259437
$729$	1.00000	0.0370370
$730$	−4.00000	−0.148047
$731$	4.00000	0.147945
$732$	−8.00000	−0.295689
$733$	−36.0000	−1.32969	−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000	−1.32969	−0.664845	+	0.746981i	$0.731502\pi$
$734$	−10.0000	−0.369107
$735$	6.00000	0.221313
$736$	−4.00000	−0.147442
$737$	−10.0000	−0.368355
$738$	0	0
$739$	−51.0000	−1.87607	−0.938033	−	0.346547i	$-0.887354\pi$
$739$	−51.0000	−1.87607	−0.938033	+	0.346547i	$0.887354\pi$
$740$	−10.0000	−0.367607
$741$	7.00000	0.257151
$742$	12.0000	0.440534
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	−10.0000	−0.366618
$745$	−10.0000	−0.366372
$746$	10.0000	0.366126
$747$	−7.00000	−0.256117
$748$	20.0000	0.731272
$749$	3.00000	0.109618
$750$	9.00000	0.328634
$751$	−25.0000	−0.912263	−0.456131	−	0.889912i	$-0.650765\pi$
$751$	−25.0000	−0.912263	−0.456131	+	0.889912i	$0.650765\pi$
$752$	−1.00000	−0.0364662
$753$	−21.0000	−0.765283
$754$	35.0000	1.27462
$755$	16.0000	0.582300
$756$	1.00000	0.0363696
$757$	30.0000	1.09037	0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000	1.09037	0.545184	+	0.838316i	$0.316460\pi$
$758$	−12.0000	−0.435860
$759$	−20.0000	−0.725954
$760$	1.00000	0.0362738
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	16.0000	0.579619
$763$	5.00000	0.181012
$764$	−18.0000	−0.651217
$765$	−4.00000	−0.144620
$766$	−36.0000	−1.30073
$767$	−28.0000	−1.01102
$768$	1.00000	0.0360844
$769$	−21.0000	−0.757279	−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000	−0.757279	−0.378640	+	0.925544i	$0.623608\pi$
$770$	−5.00000	−0.180187
$771$	−15.0000	−0.540212
$772$	−2.00000	−0.0719816
$773$	−45.0000	−1.61854	−0.809269	−	0.587439i	$-0.800136\pi$
$773$	−45.0000	−1.61854	−0.809269	+	0.587439i	$0.800136\pi$
$774$	1.00000	0.0359443
$775$	40.0000	1.43684
$776$	−7.00000	−0.251285
$777$	10.0000	0.358748
$778$	5.00000	0.179259
$779$	0	0
$780$	7.00000	0.250640
$781$	−60.0000	−2.14697
$782$	−16.0000	−0.572159
$783$	−5.00000	−0.178685
$784$	−6.00000	−0.214286
$785$	−18.0000	−0.642448
$786$	6.00000	0.214013
$787$	46.0000	1.63972	0.819861	−	0.572562i	$-0.194050\pi$
$787$	46.0000	1.63972	0.819861	+	0.572562i	$0.194050\pi$
$788$	2.00000	0.0712470
$789$	−2.00000	−0.0712019
$790$	−10.0000	−0.355784
$791$	9.00000	0.320003
$792$	5.00000	0.177667
$793$	56.0000	1.98862
$794$	−1.00000	−0.0354887
$795$	−12.0000	−0.425596
$796$	4.00000	0.141776
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	−1.00000	−0.0353996
$799$	−4.00000	−0.141510
$800$	−4.00000	−0.141421
$801$	6.00000	0.212000
$802$	38.0000	1.34183
$803$	20.0000	0.705785
$804$	−2.00000	−0.0705346
$805$	4.00000	0.140981
$806$	70.0000	2.46564
$807$	4.00000	0.140807
$808$	18.0000	0.633238
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	−1.00000	−0.0351364
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	−5.00000	−0.175466
$813$	−8.00000	−0.280572
$814$	50.0000	1.75250
$815$	−3.00000	−0.105085
$816$	4.00000	0.140028
$817$	−1.00000	−0.0349856
$818$	32.0000	1.11885
$819$	−7.00000	−0.244600
$820$	0	0
$821$	24.0000	0.837606	0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000	0.837606	0.418803	+	0.908077i	$0.362450\pi$
$822$	−9.00000	−0.313911
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	6.00000	0.209020
$825$	−20.0000	−0.696311
$826$	4.00000	0.139178
$827$	23.0000	0.799788	0.399894	−	0.916561i	$-0.369047\pi$
$827$	23.0000	0.799788	0.399894	+	0.916561i	$0.369047\pi$
$828$	−4.00000	−0.139010
$829$	−38.0000	−1.31979	−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000	−1.31979	−0.659897	+	0.751356i	$0.729400\pi$
$830$	7.00000	0.242974
$831$	−30.0000	−1.04069
$832$	−7.00000	−0.242681
$833$	−24.0000	−0.831551
$834$	−14.0000	−0.484780
$835$	−7.00000	−0.242245
$836$	−5.00000	−0.172929
$837$	−10.0000	−0.345651
$838$	28.0000	0.967244
$839$	−14.0000	−0.483334	−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000	−0.483334	−0.241667	+	0.970359i	$0.577694\pi$
$840$	−1.00000	−0.0345033
$841$	−4.00000	−0.137931
$842$	16.0000	0.551396
$843$	30.0000	1.03325
$844$	−5.00000	−0.172107
$845$	−36.0000	−1.23844
$846$	−1.00000	−0.0343807
$847$	14.0000	0.481046
$848$	12.0000	0.412082
$849$	4.00000	0.137280
$850$	−16.0000	−0.548795
$851$	−40.0000	−1.37118
$852$	−12.0000	−0.411113
$853$	−21.0000	−0.719026	−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000	−0.719026	−0.359513	+	0.933140i	$0.617057\pi$
$854$	−8.00000	−0.273754
$855$	1.00000	0.0341993
$856$	3.00000	0.102538
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	−35.0000	−1.19488
$859$	−15.0000	−0.511793	−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000	−0.511793	−0.255897	+	0.966704i	$0.582371\pi$
$860$	−1.00000	−0.0340997
$861$	0	0
$862$	19.0000	0.647143
$863$	10.0000	0.340404	0.170202	−	0.985409i	$-0.445558\pi$
$863$	10.0000	0.340404	0.170202	+	0.985409i	$0.445558\pi$
$864$	1.00000	0.0340207
$865$	−6.00000	−0.204006
$866$	14.0000	0.475739
$867$	−1.00000	−0.0339618
$868$	−10.0000	−0.339422
$869$	50.0000	1.69613
$870$	5.00000	0.169516
$871$	14.0000	0.474372
$872$	5.00000	0.169321
$873$	−7.00000	−0.236914
$874$	4.00000	0.135302
$875$	9.00000	0.304256
$876$	4.00000	0.135147
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	−22.0000	−0.742464
$879$	0	0
$880$	−5.00000	−0.168550
$881$	28.0000	0.943344	0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000	0.943344	0.471672	+	0.881774i	$0.343651\pi$
$882$	−6.00000	−0.202031
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	−28.0000	−0.941742
$885$	−4.00000	−0.134459
$886$	−39.0000	−1.31023
$887$	−22.0000	−0.738688	−0.369344	−	0.929293i	$-0.620418\pi$
$887$	−22.0000	−0.738688	−0.369344	+	0.929293i	$0.620418\pi$
$888$	10.0000	0.335578
$889$	16.0000	0.536623
$890$	−6.00000	−0.201120
$891$	5.00000	0.167506
$892$	7.00000	0.234377
$893$	1.00000	0.0334637
$894$	10.0000	0.334450
$895$	16.0000	0.534821
$896$	1.00000	0.0334077
$897$	28.0000	0.934893
$898$	−19.0000	−0.634038
$899$	50.0000	1.66759
$900$	−4.00000	−0.133333
$901$	48.0000	1.59911
$902$	0	0
$903$	1.00000	0.0332779
$904$	9.00000	0.299336
$905$	−7.00000	−0.232688
$906$	−16.0000	−0.531564
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	18.0000	0.597351
$909$	18.0000	0.597022
$910$	7.00000	0.232048
$911$	−54.0000	−1.78910	−0.894550	−	0.446968i	$-0.852504\pi$
$911$	−54.0000	−1.78910	−0.894550	+	0.446968i	$0.852504\pi$
$912$	−1.00000	−0.0331133
$913$	−35.0000	−1.15833
$914$	10.0000	0.330771
$915$	8.00000	0.264472
$916$	−22.0000	−0.726900
$917$	6.00000	0.198137
$918$	4.00000	0.132020
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	4.00000	0.131876
$921$	28.0000	0.922631
$922$	−14.0000	−0.461065
$923$	84.0000	2.76489
$924$	5.00000	0.164488
$925$	−40.0000	−1.31519
$926$	23.0000	0.755827
$927$	6.00000	0.197066
$928$	−5.00000	−0.164133
$929$	27.0000	0.885841	0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000	0.885841	0.442921	+	0.896561i	$0.353942\pi$
$930$	10.0000	0.327913
$931$	6.00000	0.196642
$932$	−25.0000	−0.818902
$933$	−31.0000	−1.01489
$934$	6.00000	0.196326
$935$	−20.0000	−0.654070
$936$	−7.00000	−0.228802
$937$	−28.0000	−0.914720	−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000	−0.914720	−0.457360	+	0.889282i	$0.651205\pi$
$938$	−2.00000	−0.0653023
$939$	−8.00000	−0.261070
$940$	1.00000	0.0326164
$941$	46.0000	1.49956	0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000	1.49956	0.749779	+	0.661689i	$0.230160\pi$
$942$	18.0000	0.586472
$943$	0	0
$944$	4.00000	0.130189
$945$	−1.00000	−0.0325300
$946$	5.00000	0.162564
$947$	−53.0000	−1.72227	−0.861134	−	0.508378i	$-0.830245\pi$
$947$	−53.0000	−1.72227	−0.861134	+	0.508378i	$0.830245\pi$
$948$	10.0000	0.324785
$949$	−28.0000	−0.908918
$950$	4.00000	0.129777
$951$	24.0000	0.778253
$952$	4.00000	0.129641
$953$	9.00000	0.291539	0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000	0.291539	0.145769	+	0.989319i	$0.453434\pi$
$954$	12.0000	0.388514
$955$	18.0000	0.582466
$956$	−5.00000	−0.161712
$957$	−25.0000	−0.808135
$958$	11.0000	0.355394
$959$	−9.00000	−0.290625
$960$	−1.00000	−0.0322749
$961$	69.0000	2.22581
$962$	−70.0000	−2.25689
$963$	3.00000	0.0966736
$964$	−10.0000	−0.322078
$965$	2.00000	0.0643823
$966$	−4.00000	−0.128698
$967$	−54.0000	−1.73652	−0.868261	−	0.496107i	$-0.834762\pi$
$967$	−54.0000	−1.73652	−0.868261	+	0.496107i	$0.834762\pi$
$968$	14.0000	0.449977
$969$	−4.00000	−0.128499
$970$	7.00000	0.224756
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	1.00000	0.0320750
$973$	−14.0000	−0.448819
$974$	12.0000	0.384505
$975$	28.0000	0.896718
$976$	−8.00000	−0.256074
$977$	−16.0000	−0.511885	−0.255943	−	0.966692i	$-0.582386\pi$
$977$	−16.0000	−0.511885	−0.255943	+	0.966692i	$0.582386\pi$
$978$	3.00000	0.0959294
$979$	30.0000	0.958804
$980$	6.00000	0.191663
$981$	5.00000	0.159638
$982$	30.0000	0.957338
$983$	18.0000	0.574111	0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000	0.574111	0.287055	+	0.957914i	$0.407324\pi$
$984$	0	0
$985$	−2.00000	−0.0637253
$986$	−20.0000	−0.636930
$987$	−1.00000	−0.0318304
$988$	7.00000	0.222700
$989$	−4.00000	−0.127193
$990$	−5.00000	−0.158910
$991$	−23.0000	−0.730619	−0.365310	−	0.930886i	$-0.619037\pi$
$991$	−23.0000	−0.730619	−0.365310	+	0.930886i	$0.619037\pi$
$992$	−10.0000	−0.317500
$993$	17.0000	0.539479
$994$	−12.0000	−0.380617
$995$	−4.00000	−0.126809
$996$	−7.00000	−0.221803
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−25.0000	−0.791361
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	258.2.a.f.1.1	✓	1
3.2	odd	2		774.2.a.c.1.1		1
4.3	odd	2		2064.2.a.c.1.1		1
5.4	even	2		6450.2.a.e.1.1		1
8.3	odd	2		8256.2.a.bl.1.1		1
8.5	even	2		8256.2.a.n.1.1		1
12.11	even	2		6192.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
258.2.a.f.1.1	✓	1	1.1	even	1	trivial
774.2.a.c.1.1		1	3.2	odd	2
2064.2.a.c.1.1		1	4.3	odd	2
6192.2.a.n.1.1		1	12.11	even	2
6450.2.a.e.1.1		1	5.4	even	2
8256.2.a.n.1.1		1	8.5	even	2
8256.2.a.bl.1.1		1	8.3	odd	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:	\( N \)	\(=\)	\( 258 = 2 \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	258.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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