LMFDB - Embedded newform 406.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(1,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, 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("406.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.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:	$3.24192632206$
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	$\chi$	$=$	406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} -2.00000 q^{18} -4.00000 q^{19} -3.00000 q^{20} +1.00000 q^{21} -1.00000 q^{22} -2.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} -1.00000 q^{28} +1.00000 q^{29} +3.00000 q^{30} -1.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} -4.00000 q^{34} +3.00000 q^{35} -2.00000 q^{36} +6.00000 q^{37} -4.00000 q^{38} +1.00000 q^{39} -3.00000 q^{40} +1.00000 q^{42} +3.00000 q^{43} -1.00000 q^{44} +6.00000 q^{45} -2.00000 q^{46} -9.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} +4.00000 q^{51} -1.00000 q^{52} +3.00000 q^{53} +5.00000 q^{54} +3.00000 q^{55} -1.00000 q^{56} +4.00000 q^{57} +1.00000 q^{58} +3.00000 q^{60} +6.00000 q^{61} -1.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +3.00000 q^{65} +1.00000 q^{66} +2.00000 q^{67} -4.00000 q^{68} +2.00000 q^{69} +3.00000 q^{70} -8.00000 q^{71} -2.00000 q^{72} +6.00000 q^{74} -4.00000 q^{75} -4.00000 q^{76} +1.00000 q^{77} +1.00000 q^{78} -13.0000 q^{79} -3.00000 q^{80} +1.00000 q^{81} +1.00000 q^{84} +12.0000 q^{85} +3.00000 q^{86} -1.00000 q^{87} -1.00000 q^{88} -14.0000 q^{89} +6.00000 q^{90} +1.00000 q^{91} -2.00000 q^{92} +1.00000 q^{93} -9.00000 q^{94} +12.0000 q^{95} -1.00000 q^{96} +16.0000 q^{97} +1.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	−3.00000	−0.948683
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.00000	−0.267261
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	−2.00000	−0.471405
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−3.00000	−0.670820
$21$	1.00000	0.218218
$22$	−1.00000	−0.213201
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	−1.00000	−0.204124
$25$	4.00000	0.800000
$26$	−1.00000	−0.196116
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.00000	0.547723
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−4.00000	−0.685994
$35$	3.00000	0.507093
$36$	−2.00000	−0.333333
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−4.00000	−0.648886
$39$	1.00000	0.160128
$40$	−3.00000	−0.474342
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	1.00000	0.154303
$43$	3.00000	0.457496	0.228748	−	0.973486i	$-0.426537\pi$
$43$	3.00000	0.457496	0.228748	+	0.973486i	$0.426537\pi$
$44$	−1.00000	−0.150756
$45$	6.00000	0.894427
$46$	−2.00000	−0.294884
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	4.00000	0.560112
$52$	−1.00000	−0.138675
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	5.00000	0.680414
$55$	3.00000	0.404520
$56$	−1.00000	−0.133631
$57$	4.00000	0.529813
$58$	1.00000	0.131306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	3.00000	0.387298
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−1.00000	−0.127000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	1.00000	0.123091
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	−4.00000	−0.485071
$69$	2.00000	0.240772
$70$	3.00000	0.358569
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	−2.00000	−0.235702
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	6.00000	0.697486
$75$	−4.00000	−0.461880
$76$	−4.00000	−0.458831
$77$	1.00000	0.113961
$78$	1.00000	0.113228
$79$	−13.0000	−1.46261	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−13.0000	−1.46261	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	1.00000	0.109109
$85$	12.0000	1.30158
$86$	3.00000	0.323498
$87$	−1.00000	−0.107211
$88$	−1.00000	−0.106600
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	6.00000	0.632456
$91$	1.00000	0.104828
$92$	−2.00000	−0.208514
$93$	1.00000	0.103695
$94$	−9.00000	−0.928279
$95$	12.0000	1.23117
$96$	−1.00000	−0.102062
$97$	16.0000	1.62455	0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000	1.62455	0.812277	+	0.583272i	$0.198228\pi$
$98$	1.00000	0.101015
$99$	2.00000	0.201008
$100$	4.00000	0.400000
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	4.00000	0.396059
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−1.00000	−0.0980581
$105$	−3.00000	−0.292770
$106$	3.00000	0.291386
$107$	−14.0000	−1.35343	−0.676716	−	0.736245i	$-0.736597\pi$
$107$	−14.0000	−1.35343	−0.676716	+	0.736245i	$0.736597\pi$
$108$	5.00000	0.481125
$109$	15.0000	1.43674	0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000	1.43674	0.718370	+	0.695662i	$0.244889\pi$
$110$	3.00000	0.286039
$111$	−6.00000	−0.569495
$112$	−1.00000	−0.0944911
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	4.00000	0.374634
$115$	6.00000	0.559503
$116$	1.00000	0.0928477
$117$	2.00000	0.184900
$118$	0	0
$119$	4.00000	0.366679
$120$	3.00000	0.273861
$121$	−10.0000	−0.909091
$122$	6.00000	0.543214
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	3.00000	0.268328
$126$	2.00000	0.178174
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	−3.00000	−0.264135
$130$	3.00000	0.263117
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	1.00000	0.0870388
$133$	4.00000	0.346844
$134$	2.00000	0.172774
$135$	−15.0000	−1.29099
$136$	−4.00000	−0.342997
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	2.00000	0.170251
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	3.00000	0.253546
$141$	9.00000	0.757937
$142$	−8.00000	−0.671345
$143$	1.00000	0.0836242
$144$	−2.00000	−0.166667
$145$	−3.00000	−0.249136
$146$	0	0
$147$	−1.00000	−0.0824786
$148$	6.00000	0.493197
$149$	−11.0000	−0.901155	−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000	−0.901155	−0.450578	+	0.892737i	$0.648782\pi$
$150$	−4.00000	−0.326599
$151$	14.0000	1.13930	0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000	1.13930	0.569652	+	0.821886i	$0.307078\pi$
$152$	−4.00000	−0.324443
$153$	8.00000	0.646762
$154$	1.00000	0.0805823
$155$	3.00000	0.240966
$156$	1.00000	0.0800641
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	−13.0000	−1.03422
$159$	−3.00000	−0.237915
$160$	−3.00000	−0.237171
$161$	2.00000	0.157622
$162$	1.00000	0.0785674
$163$	−21.0000	−1.64485	−0.822423	−	0.568876i	$-0.807379\pi$
$163$	−21.0000	−1.64485	−0.822423	+	0.568876i	$0.807379\pi$
$164$	0	0
$165$	−3.00000	−0.233550
$166$	0	0
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	1.00000	0.0771517
$169$	−12.0000	−0.923077
$170$	12.0000	0.920358
$171$	8.00000	0.611775
$172$	3.00000	0.228748
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	−1.00000	−0.0758098
$175$	−4.00000	−0.302372
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−14.0000	−1.04934
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	6.00000	0.447214
$181$	23.0000	1.70958	0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000	1.70958	0.854788	+	0.518977i	$0.173687\pi$
$182$	1.00000	0.0741249
$183$	−6.00000	−0.443533
$184$	−2.00000	−0.147442
$185$	−18.0000	−1.32339
$186$	1.00000	0.0733236
$187$	4.00000	0.292509
$188$	−9.00000	−0.656392
$189$	−5.00000	−0.363696
$190$	12.0000	0.870572
$191$	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
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	16.0000	1.14873
$195$	−3.00000	−0.214834
$196$	1.00000	0.0714286
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	2.00000	0.142134
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	4.00000	0.282843
$201$	−2.00000	−0.141069
$202$	−4.00000	−0.281439
$203$	−1.00000	−0.0701862
$204$	4.00000	0.280056
$205$	0	0
$206$	4.00000	0.278693
$207$	4.00000	0.278019
$208$	−1.00000	−0.0693375
$209$	4.00000	0.276686
$210$	−3.00000	−0.207020
$211$	−9.00000	−0.619586	−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000	−0.619586	−0.309793	+	0.950804i	$0.600260\pi$
$212$	3.00000	0.206041
$213$	8.00000	0.548151
$214$	−14.0000	−0.957020
$215$	−9.00000	−0.613795
$216$	5.00000	0.340207
$217$	1.00000	0.0678844
$218$	15.0000	1.01593
$219$	0	0
$220$	3.00000	0.202260
$221$	4.00000	0.269069
$222$	−6.00000	−0.402694
$223$	−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
$225$	−8.00000	−0.533333
$226$	0	0
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	4.00000	0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	6.00000	0.395628
$231$	−1.00000	−0.0657952
$232$	1.00000	0.0656532
$233$	11.0000	0.720634	0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000	0.720634	0.360317	+	0.932830i	$0.382669\pi$
$234$	2.00000	0.130744
$235$	27.0000	1.76129
$236$	0	0
$237$	13.0000	0.844441
$238$	4.00000	0.259281
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	3.00000	0.193649
$241$	−29.0000	−1.86805	−0.934027	−	0.357202i	$-0.883731\pi$
$241$	−29.0000	−1.86805	−0.934027	+	0.357202i	$0.883731\pi$
$242$	−10.0000	−0.642824
$243$	−16.0000	−1.02640
$244$	6.00000	0.384111
$245$	−3.00000	−0.191663
$246$	0	0
$247$	4.00000	0.254514
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	3.00000	0.189737
$251$	−17.0000	−1.07303	−0.536515	−	0.843891i	$-0.680260\pi$
$251$	−17.0000	−1.07303	−0.536515	+	0.843891i	$0.680260\pi$
$252$	2.00000	0.125988
$253$	2.00000	0.125739
$254$	−16.0000	−1.00393
$255$	−12.0000	−0.751469
$256$	1.00000	0.0625000
$257$	−9.00000	−0.561405	−0.280702	−	0.959795i	$-0.590567\pi$
$257$	−9.00000	−0.561405	−0.280702	+	0.959795i	$0.590567\pi$
$258$	−3.00000	−0.186772
$259$	−6.00000	−0.372822
$260$	3.00000	0.186052
$261$	−2.00000	−0.123797
$262$	0	0
$263$	5.00000	0.308313	0.154157	−	0.988046i	$-0.450734\pi$
$263$	5.00000	0.308313	0.154157	+	0.988046i	$0.450734\pi$
$264$	1.00000	0.0615457
$265$	−9.00000	−0.552866
$266$	4.00000	0.245256
$267$	14.0000	0.856786
$268$	2.00000	0.122169
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	−15.0000	−0.912871
$271$	25.0000	1.51864	0.759321	−	0.650716i	$-0.225531\pi$
$271$	25.0000	1.51864	0.759321	+	0.650716i	$0.225531\pi$
$272$	−4.00000	−0.242536
$273$	−1.00000	−0.0605228
$274$	−10.0000	−0.604122
$275$	−4.00000	−0.241209
$276$	2.00000	0.120386
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	−14.0000	−0.839664
$279$	2.00000	0.119737
$280$	3.00000	0.179284
$281$	−21.0000	−1.25275	−0.626377	−	0.779520i	$-0.715463\pi$
$281$	−21.0000	−1.25275	−0.626377	+	0.779520i	$0.715463\pi$
$282$	9.00000	0.535942
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	−8.00000	−0.474713
$285$	−12.0000	−0.710819
$286$	1.00000	0.0591312
$287$	0	0
$288$	−2.00000	−0.117851
$289$	−1.00000	−0.0588235
$290$	−3.00000	−0.176166
$291$	−16.0000	−0.937937
$292$	0	0
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	−1.00000	−0.0583212
$295$	0	0
$296$	6.00000	0.348743
$297$	−5.00000	−0.290129
$298$	−11.0000	−0.637213
$299$	2.00000	0.115663
$300$	−4.00000	−0.230940
$301$	−3.00000	−0.172917
$302$	14.0000	0.805609
$303$	4.00000	0.229794
$304$	−4.00000	−0.229416
$305$	−18.0000	−1.03068
$306$	8.00000	0.457330
$307$	9.00000	0.513657	0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000	0.513657	0.256829	+	0.966457i	$0.417322\pi$
$308$	1.00000	0.0569803
$309$	−4.00000	−0.227552
$310$	3.00000	0.170389
$311$	20.0000	1.13410	0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000	1.13410	0.567048	+	0.823685i	$0.308085\pi$
$312$	1.00000	0.0566139
$313$	−5.00000	−0.282617	−0.141308	−	0.989966i	$-0.545131\pi$
$313$	−5.00000	−0.282617	−0.141308	+	0.989966i	$0.545131\pi$
$314$	−12.0000	−0.677199
$315$	−6.00000	−0.338062
$316$	−13.0000	−0.731307
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	−3.00000	−0.168232
$319$	−1.00000	−0.0559893
$320$	−3.00000	−0.167705
$321$	14.0000	0.781404
$322$	2.00000	0.111456
$323$	16.0000	0.890264
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−21.0000	−1.16308
$327$	−15.0000	−0.829502
$328$	0	0
$329$	9.00000	0.496186
$330$	−3.00000	−0.165145
$331$	27.0000	1.48405	0.742027	−	0.670370i	$-0.233865\pi$
$331$	27.0000	1.48405	0.742027	+	0.670370i	$0.233865\pi$
$332$	0	0
$333$	−12.0000	−0.657596
$334$	12.0000	0.656611
$335$	−6.00000	−0.327815
$336$	1.00000	0.0545545
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	12.0000	0.650791
$341$	1.00000	0.0541530
$342$	8.00000	0.432590
$343$	−1.00000	−0.0539949
$344$	3.00000	0.161749
$345$	−6.00000	−0.323029
$346$	14.0000	0.752645
$347$	10.0000	0.536828	0.268414	−	0.963304i	$-0.413500\pi$
$347$	10.0000	0.536828	0.268414	+	0.963304i	$0.413500\pi$
$348$	−1.00000	−0.0536056
$349$	−3.00000	−0.160586	−0.0802932	−	0.996771i	$-0.525586\pi$
$349$	−3.00000	−0.160586	−0.0802932	+	0.996771i	$0.525586\pi$
$350$	−4.00000	−0.213809
$351$	−5.00000	−0.266880
$352$	−1.00000	−0.0533002
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	0	0
$355$	24.0000	1.27379
$356$	−14.0000	−0.741999
$357$	−4.00000	−0.211702
$358$	−24.0000	−1.26844
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	6.00000	0.316228
$361$	−3.00000	−0.157895
$362$	23.0000	1.20885
$363$	10.0000	0.524864
$364$	1.00000	0.0524142
$365$	0	0
$366$	−6.00000	−0.313625
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	−2.00000	−0.104257
$369$	0	0
$370$	−18.0000	−0.935775
$371$	−3.00000	−0.155752
$372$	1.00000	0.0518476
$373$	17.0000	0.880227	0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000	0.880227	0.440113	+	0.897942i	$0.354938\pi$
$374$	4.00000	0.206835
$375$	−3.00000	−0.154919
$376$	−9.00000	−0.464140
$377$	−1.00000	−0.0515026
$378$	−5.00000	−0.257172
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	12.0000	0.615587
$381$	16.0000	0.819705
$382$	8.00000	0.409316
$383$	30.0000	1.53293	0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000	1.53293	0.766464	+	0.642287i	$0.222014\pi$
$384$	−1.00000	−0.0510310
$385$	−3.00000	−0.152894
$386$	12.0000	0.610784
$387$	−6.00000	−0.304997
$388$	16.0000	0.812277
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	−3.00000	−0.151911
$391$	8.00000	0.404577
$392$	1.00000	0.0505076
$393$	0	0
$394$	−2.00000	−0.100759
$395$	39.0000	1.96230
$396$	2.00000	0.100504
$397$	11.0000	0.552074	0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000	0.552074	0.276037	+	0.961147i	$0.410979\pi$
$398$	−20.0000	−1.00251
$399$	−4.00000	−0.200250
$400$	4.00000	0.200000
$401$	39.0000	1.94757	0.973784	−	0.227477i	$-0.0730475\pi$
$401$	39.0000	1.94757	0.973784	+	0.227477i	$0.0730475\pi$
$402$	−2.00000	−0.0997509
$403$	1.00000	0.0498135
$404$	−4.00000	−0.199007
$405$	−3.00000	−0.149071
$406$	−1.00000	−0.0496292
$407$	−6.00000	−0.297409
$408$	4.00000	0.198030
$409$	28.0000	1.38451	0.692255	−	0.721653i	$-0.256617\pi$
$409$	28.0000	1.38451	0.692255	+	0.721653i	$0.256617\pi$
$410$	0	0
$411$	10.0000	0.493264
$412$	4.00000	0.197066
$413$	0	0
$414$	4.00000	0.196589
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	14.0000	0.685583
$418$	4.00000	0.195646
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	−3.00000	−0.146385
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−9.00000	−0.438113
$423$	18.0000	0.875190
$424$	3.00000	0.145693
$425$	−16.0000	−0.776114
$426$	8.00000	0.387601
$427$	−6.00000	−0.290360
$428$	−14.0000	−0.676716
$429$	−1.00000	−0.0482805
$430$	−9.00000	−0.434019
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	5.00000	0.240563
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	1.00000	0.0480015
$435$	3.00000	0.143839
$436$	15.0000	0.718370
$437$	8.00000	0.382692
$438$	0	0
$439$	2.00000	0.0954548	0.0477274	−	0.998860i	$-0.484802\pi$
$439$	2.00000	0.0954548	0.0477274	+	0.998860i	$0.484802\pi$
$440$	3.00000	0.143019
$441$	−2.00000	−0.0952381
$442$	4.00000	0.190261
$443$	20.0000	0.950229	0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000	0.950229	0.475114	+	0.879924i	$0.342407\pi$
$444$	−6.00000	−0.284747
$445$	42.0000	1.99099
$446$	−4.00000	−0.189405
$447$	11.0000	0.520282
$448$	−1.00000	−0.0472456
$449$	−16.0000	−0.755087	−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000	−0.755087	−0.377543	+	0.925992i	$0.623231\pi$
$450$	−8.00000	−0.377124
$451$	0	0
$452$	0	0
$453$	−14.0000	−0.657777
$454$	14.0000	0.657053
$455$	−3.00000	−0.140642
$456$	4.00000	0.187317
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	14.0000	0.654177
$459$	−20.0000	−0.933520
$460$	6.00000	0.279751
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	−1.00000	−0.0465242
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	1.00000	0.0464238
$465$	−3.00000	−0.139122
$466$	11.0000	0.509565
$467$	13.0000	0.601568	0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$468$	2.00000	0.0924500
$469$	−2.00000	−0.0923514
$470$	27.0000	1.24542
$471$	12.0000	0.552931
$472$	0	0
$473$	−3.00000	−0.137940
$474$	13.0000	0.597110
$475$	−16.0000	−0.734130
$476$	4.00000	0.183340
$477$	−6.00000	−0.274721
$478$	−12.0000	−0.548867
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	3.00000	0.136931
$481$	−6.00000	−0.273576
$482$	−29.0000	−1.32091
$483$	−2.00000	−0.0910032
$484$	−10.0000	−0.454545
$485$	−48.0000	−2.17957
$486$	−16.0000	−0.725775
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	6.00000	0.271607
$489$	21.0000	0.949653
$490$	−3.00000	−0.135526
$491$	9.00000	0.406164	0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000	0.406164	0.203082	+	0.979162i	$0.434904\pi$
$492$	0	0
$493$	−4.00000	−0.180151
$494$	4.00000	0.179969
$495$	−6.00000	−0.269680
$496$	−1.00000	−0.0449013
$497$	8.00000	0.358849
$498$	0	0
$499$	−38.0000	−1.70111	−0.850557	−	0.525883i	$-0.823735\pi$
$499$	−38.0000	−1.70111	−0.850557	+	0.525883i	$0.823735\pi$
$500$	3.00000	0.134164
$501$	−12.0000	−0.536120
$502$	−17.0000	−0.758747
$503$	−11.0000	−0.490466	−0.245233	−	0.969464i	$-0.578864\pi$
$503$	−11.0000	−0.490466	−0.245233	+	0.969464i	$0.578864\pi$
$504$	2.00000	0.0890871
$505$	12.0000	0.533993
$506$	2.00000	0.0889108
$507$	12.0000	0.532939
$508$	−16.0000	−0.709885
$509$	−7.00000	−0.310270	−0.155135	−	0.987893i	$-0.549581\pi$
$509$	−7.00000	−0.310270	−0.155135	+	0.987893i	$0.549581\pi$
$510$	−12.0000	−0.531369
$511$	0	0
$512$	1.00000	0.0441942
$513$	−20.0000	−0.883022
$514$	−9.00000	−0.396973
$515$	−12.0000	−0.528783
$516$	−3.00000	−0.132068
$517$	9.00000	0.395820
$518$	−6.00000	−0.263625
$519$	−14.0000	−0.614532
$520$	3.00000	0.131559
$521$	25.0000	1.09527	0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000	1.09527	0.547635	+	0.836717i	$0.315528\pi$
$522$	−2.00000	−0.0875376
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	0	0
$525$	4.00000	0.174574
$526$	5.00000	0.218010
$527$	4.00000	0.174243
$528$	1.00000	0.0435194
$529$	−19.0000	−0.826087
$530$	−9.00000	−0.390935
$531$	0	0
$532$	4.00000	0.173422
$533$	0	0
$534$	14.0000	0.605839
$535$	42.0000	1.81582
$536$	2.00000	0.0863868
$537$	24.0000	1.03568
$538$	−28.0000	−1.20717
$539$	−1.00000	−0.0430730
$540$	−15.0000	−0.645497
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	25.0000	1.07384
$543$	−23.0000	−0.987024
$544$	−4.00000	−0.171499
$545$	−45.0000	−1.92759
$546$	−1.00000	−0.0427960
$547$	−14.0000	−0.598597	−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000	−0.598597	−0.299298	+	0.954160i	$0.596753\pi$
$548$	−10.0000	−0.427179
$549$	−12.0000	−0.512148
$550$	−4.00000	−0.170561
$551$	−4.00000	−0.170406
$552$	2.00000	0.0851257
$553$	13.0000	0.552816
$554$	10.0000	0.424859
$555$	18.0000	0.764057
$556$	−14.0000	−0.593732
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	2.00000	0.0846668
$559$	−3.00000	−0.126886
$560$	3.00000	0.126773
$561$	−4.00000	−0.168880
$562$	−21.0000	−0.885832
$563$	9.00000	0.379305	0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000	0.379305	0.189652	+	0.981851i	$0.439264\pi$
$564$	9.00000	0.378968
$565$	0	0
$566$	−2.00000	−0.0840663
$567$	−1.00000	−0.0419961
$568$	−8.00000	−0.335673
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	−12.0000	−0.502625
$571$	18.0000	0.753277	0.376638	−	0.926360i	$-0.377080\pi$
$571$	18.0000	0.753277	0.376638	+	0.926360i	$0.377080\pi$
$572$	1.00000	0.0418121
$573$	−8.00000	−0.334205
$574$	0	0
$575$	−8.00000	−0.333623
$576$	−2.00000	−0.0833333
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−1.00000	−0.0415945
$579$	−12.0000	−0.498703
$580$	−3.00000	−0.124568
$581$	0	0
$582$	−16.0000	−0.663221
$583$	−3.00000	−0.124247
$584$	0	0
$585$	−6.00000	−0.248069
$586$	18.0000	0.743573
$587$	30.0000	1.23823	0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000	1.23823	0.619116	+	0.785299i	$0.287491\pi$
$588$	−1.00000	−0.0412393
$589$	4.00000	0.164817
$590$	0	0
$591$	2.00000	0.0822690
$592$	6.00000	0.246598
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	−5.00000	−0.205152
$595$	−12.0000	−0.491952
$596$	−11.0000	−0.450578
$597$	20.0000	0.818546
$598$	2.00000	0.0817861
$599$	15.0000	0.612883	0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000	0.612883	0.306442	+	0.951889i	$0.400862\pi$
$600$	−4.00000	−0.163299
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	−3.00000	−0.122271
$603$	−4.00000	−0.162893
$604$	14.0000	0.569652
$605$	30.0000	1.21967
$606$	4.00000	0.162489
$607$	−7.00000	−0.284121	−0.142061	−	0.989858i	$-0.545373\pi$
$607$	−7.00000	−0.284121	−0.142061	+	0.989858i	$0.545373\pi$
$608$	−4.00000	−0.162221
$609$	1.00000	0.0405220
$610$	−18.0000	−0.728799
$611$	9.00000	0.364101
$612$	8.00000	0.323381
$613$	−29.0000	−1.17130	−0.585649	−	0.810564i	$-0.699160\pi$
$613$	−29.0000	−1.17130	−0.585649	+	0.810564i	$0.699160\pi$
$614$	9.00000	0.363210
$615$	0	0
$616$	1.00000	0.0402911
$617$	−36.0000	−1.44931	−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000	−1.44931	−0.724653	+	0.689114i	$0.758000\pi$
$618$	−4.00000	−0.160904
$619$	−3.00000	−0.120580	−0.0602901	−	0.998181i	$-0.519203\pi$
$619$	−3.00000	−0.120580	−0.0602901	+	0.998181i	$0.519203\pi$
$620$	3.00000	0.120483
$621$	−10.0000	−0.401286
$622$	20.0000	0.801927
$623$	14.0000	0.560898
$624$	1.00000	0.0400320
$625$	−29.0000	−1.16000
$626$	−5.00000	−0.199840
$627$	−4.00000	−0.159745
$628$	−12.0000	−0.478852
$629$	−24.0000	−0.956943
$630$	−6.00000	−0.239046
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	−13.0000	−0.517112
$633$	9.00000	0.357718
$634$	22.0000	0.873732
$635$	48.0000	1.90482
$636$	−3.00000	−0.118958
$637$	−1.00000	−0.0396214
$638$	−1.00000	−0.0395904
$639$	16.0000	0.632950
$640$	−3.00000	−0.118585
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	14.0000	0.552536
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	2.00000	0.0788110
$645$	9.00000	0.354375
$646$	16.0000	0.629512
$647$	−20.0000	−0.786281	−0.393141	−	0.919478i	$-0.628611\pi$
$647$	−20.0000	−0.786281	−0.393141	+	0.919478i	$0.628611\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−4.00000	−0.156893
$651$	−1.00000	−0.0391931
$652$	−21.0000	−0.822423
$653$	20.0000	0.782660	0.391330	−	0.920250i	$-0.372015\pi$
$653$	20.0000	0.782660	0.391330	+	0.920250i	$0.372015\pi$
$654$	−15.0000	−0.586546
$655$	0	0
$656$	0	0
$657$	0	0
$658$	9.00000	0.350857
$659$	−43.0000	−1.67504	−0.837521	−	0.546405i	$-0.815996\pi$
$659$	−43.0000	−1.67504	−0.837521	+	0.546405i	$0.815996\pi$
$660$	−3.00000	−0.116775
$661$	−2.00000	−0.0777910	−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000	−0.0777910	−0.0388955	+	0.999243i	$0.512384\pi$
$662$	27.0000	1.04938
$663$	−4.00000	−0.155347
$664$	0	0
$665$	−12.0000	−0.465340
$666$	−12.0000	−0.464991
$667$	−2.00000	−0.0774403
$668$	12.0000	0.464294
$669$	4.00000	0.154649
$670$	−6.00000	−0.231800
$671$	−6.00000	−0.231627
$672$	1.00000	0.0385758
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	26.0000	1.00148
$675$	20.0000	0.769800
$676$	−12.0000	−0.461538
$677$	40.0000	1.53732	0.768662	−	0.639655i	$-0.220923\pi$
$677$	40.0000	1.53732	0.768662	+	0.639655i	$0.220923\pi$
$678$	0	0
$679$	−16.0000	−0.614024
$680$	12.0000	0.460179
$681$	−14.0000	−0.536481
$682$	1.00000	0.0382920
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	8.00000	0.305888
$685$	30.0000	1.14624
$686$	−1.00000	−0.0381802
$687$	−14.0000	−0.534133
$688$	3.00000	0.114374
$689$	−3.00000	−0.114291
$690$	−6.00000	−0.228416
$691$	−48.0000	−1.82601	−0.913003	−	0.407953i	$-0.866243\pi$
$691$	−48.0000	−1.82601	−0.913003	+	0.407953i	$0.866243\pi$
$692$	14.0000	0.532200
$693$	−2.00000	−0.0759737
$694$	10.0000	0.379595
$695$	42.0000	1.59315
$696$	−1.00000	−0.0379049
$697$	0	0
$698$	−3.00000	−0.113552
$699$	−11.0000	−0.416058
$700$	−4.00000	−0.151186
$701$	−35.0000	−1.32193	−0.660966	−	0.750416i	$-0.729853\pi$
$701$	−35.0000	−1.32193	−0.660966	+	0.750416i	$0.729853\pi$
$702$	−5.00000	−0.188713
$703$	−24.0000	−0.905177
$704$	−1.00000	−0.0376889
$705$	−27.0000	−1.01688
$706$	−34.0000	−1.27961
$707$	4.00000	0.150435
$708$	0	0
$709$	9.00000	0.338002	0.169001	−	0.985616i	$-0.445946\pi$
$709$	9.00000	0.338002	0.169001	+	0.985616i	$0.445946\pi$
$710$	24.0000	0.900704
$711$	26.0000	0.975076
$712$	−14.0000	−0.524672
$713$	2.00000	0.0749006
$714$	−4.00000	−0.149696
$715$	−3.00000	−0.112194
$716$	−24.0000	−0.896922
$717$	12.0000	0.448148
$718$	−21.0000	−0.783713
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	6.00000	0.223607
$721$	−4.00000	−0.148968
$722$	−3.00000	−0.111648
$723$	29.0000	1.07852
$724$	23.0000	0.854788
$725$	4.00000	0.148556
$726$	10.0000	0.371135
$727$	12.0000	0.445055	0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000	0.445055	0.222528	+	0.974926i	$0.428569\pi$
$728$	1.00000	0.0370625
$729$	13.0000	0.481481
$730$	0	0
$731$	−12.0000	−0.443836
$732$	−6.00000	−0.221766
$733$	−38.0000	−1.40356	−0.701781	−	0.712393i	$-0.747612\pi$
$733$	−38.0000	−1.40356	−0.701781	+	0.712393i	$0.747612\pi$
$734$	16.0000	0.590571
$735$	3.00000	0.110657
$736$	−2.00000	−0.0737210
$737$	−2.00000	−0.0736709
$738$	0	0
$739$	−47.0000	−1.72892	−0.864461	−	0.502699i	$-0.832340\pi$
$739$	−47.0000	−1.72892	−0.864461	+	0.502699i	$0.832340\pi$
$740$	−18.0000	−0.661693
$741$	−4.00000	−0.146944
$742$	−3.00000	−0.110133
$743$	−20.0000	−0.733729	−0.366864	−	0.930274i	$-0.619569\pi$
$743$	−20.0000	−0.733729	−0.366864	+	0.930274i	$0.619569\pi$
$744$	1.00000	0.0366618
$745$	33.0000	1.20903
$746$	17.0000	0.622414
$747$	0	0
$748$	4.00000	0.146254
$749$	14.0000	0.511549
$750$	−3.00000	−0.109545
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	−9.00000	−0.328196
$753$	17.0000	0.619514
$754$	−1.00000	−0.0364179
$755$	−42.0000	−1.52854
$756$	−5.00000	−0.181848
$757$	−28.0000	−1.01768	−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000	−1.01768	−0.508839	+	0.860862i	$0.669925\pi$
$758$	36.0000	1.30758
$759$	−2.00000	−0.0725954
$760$	12.0000	0.435286
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	16.0000	0.579619
$763$	−15.0000	−0.543036
$764$	8.00000	0.289430
$765$	−24.0000	−0.867722
$766$	30.0000	1.08394
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	4.00000	0.144244	0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000	0.144244	0.0721218	+	0.997396i	$0.477023\pi$
$770$	−3.00000	−0.108112
$771$	9.00000	0.324127
$772$	12.0000	0.431889
$773$	−20.0000	−0.719350	−0.359675	−	0.933078i	$-0.617112\pi$
$773$	−20.0000	−0.719350	−0.359675	+	0.933078i	$0.617112\pi$
$774$	−6.00000	−0.215666
$775$	−4.00000	−0.143684
$776$	16.0000	0.574367
$777$	6.00000	0.215249
$778$	−4.00000	−0.143407
$779$	0	0
$780$	−3.00000	−0.107417
$781$	8.00000	0.286263
$782$	8.00000	0.286079
$783$	5.00000	0.178685
$784$	1.00000	0.0357143
$785$	36.0000	1.28490
$786$	0	0
$787$	−12.0000	−0.427754	−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000	−0.427754	−0.213877	+	0.976861i	$0.568609\pi$
$788$	−2.00000	−0.0712470
$789$	−5.00000	−0.178005
$790$	39.0000	1.38756
$791$	0	0
$792$	2.00000	0.0710669
$793$	−6.00000	−0.213066
$794$	11.0000	0.390375
$795$	9.00000	0.319197
$796$	−20.0000	−0.708881
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	−4.00000	−0.141598
$799$	36.0000	1.27359
$800$	4.00000	0.141421
$801$	28.0000	0.989331
$802$	39.0000	1.37714
$803$	0	0
$804$	−2.00000	−0.0705346
$805$	−6.00000	−0.211472
$806$	1.00000	0.0352235
$807$	28.0000	0.985647
$808$	−4.00000	−0.140720
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	−3.00000	−0.105409
$811$	−30.0000	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$812$	−1.00000	−0.0350931
$813$	−25.0000	−0.876788
$814$	−6.00000	−0.210300
$815$	63.0000	2.20679
$816$	4.00000	0.140028
$817$	−12.0000	−0.419827
$818$	28.0000	0.978997
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	53.0000	1.84971	0.924856	−	0.380317i	$-0.124185\pi$
$821$	53.0000	1.84971	0.924856	+	0.380317i	$0.124185\pi$
$822$	10.0000	0.348790
$823$	−8.00000	−0.278862	−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000	−0.278862	−0.139431	+	0.990232i	$0.544527\pi$
$824$	4.00000	0.139347
$825$	4.00000	0.139262
$826$	0	0
$827$	47.0000	1.63435	0.817175	−	0.576390i	$-0.195539\pi$
$827$	47.0000	1.63435	0.817175	+	0.576390i	$0.195539\pi$
$828$	4.00000	0.139010
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	−1.00000	−0.0346688
$833$	−4.00000	−0.138592
$834$	14.0000	0.484780
$835$	−36.0000	−1.24583
$836$	4.00000	0.138343
$837$	−5.00000	−0.172825
$838$	−16.0000	−0.552711
$839$	−21.0000	−0.725001	−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000	−0.725001	−0.362500	+	0.931984i	$0.618077\pi$
$840$	−3.00000	−0.103510
$841$	1.00000	0.0344828
$842$	26.0000	0.896019
$843$	21.0000	0.723278
$844$	−9.00000	−0.309793
$845$	36.0000	1.23844
$846$	18.0000	0.618853
$847$	10.0000	0.343604
$848$	3.00000	0.103020
$849$	2.00000	0.0686398
$850$	−16.0000	−0.548795
$851$	−12.0000	−0.411355
$852$	8.00000	0.274075
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	−6.00000	−0.205316
$855$	−24.0000	−0.820783
$856$	−14.0000	−0.478510
$857$	−41.0000	−1.40053	−0.700267	−	0.713881i	$-0.746936\pi$
$857$	−41.0000	−1.40053	−0.700267	+	0.713881i	$0.746936\pi$
$858$	−1.00000	−0.0341394
$859$	31.0000	1.05771	0.528853	−	0.848713i	$-0.322622\pi$
$859$	31.0000	1.05771	0.528853	+	0.848713i	$0.322622\pi$
$860$	−9.00000	−0.306897
$861$	0	0
$862$	−24.0000	−0.817443
$863$	58.0000	1.97434	0.987171	−	0.159664i	$-0.0510410\pi$
$863$	58.0000	1.97434	0.987171	+	0.159664i	$0.0510410\pi$
$864$	5.00000	0.170103
$865$	−42.0000	−1.42804
$866$	34.0000	1.15537
$867$	1.00000	0.0339618
$868$	1.00000	0.0339422
$869$	13.0000	0.440995
$870$	3.00000	0.101710
$871$	−2.00000	−0.0677674
$872$	15.0000	0.507964
$873$	−32.0000	−1.08304
$874$	8.00000	0.270604
$875$	−3.00000	−0.101419
$876$	0	0
$877$	31.0000	1.04680	0.523398	−	0.852088i	$-0.324664\pi$
$877$	31.0000	1.04680	0.523398	+	0.852088i	$0.324664\pi$
$878$	2.00000	0.0674967
$879$	−18.0000	−0.607125
$880$	3.00000	0.101130
$881$	−26.0000	−0.875962	−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000	−0.875962	−0.437981	+	0.898984i	$0.644306\pi$
$882$	−2.00000	−0.0673435
$883$	−6.00000	−0.201916	−0.100958	−	0.994891i	$-0.532191\pi$
$883$	−6.00000	−0.201916	−0.100958	+	0.994891i	$0.532191\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	20.0000	0.671913
$887$	3.00000	0.100730	0.0503651	−	0.998731i	$-0.483962\pi$
$887$	3.00000	0.100730	0.0503651	+	0.998731i	$0.483962\pi$
$888$	−6.00000	−0.201347
$889$	16.0000	0.536623
$890$	42.0000	1.40784
$891$	−1.00000	−0.0335013
$892$	−4.00000	−0.133930
$893$	36.0000	1.20469
$894$	11.0000	0.367895
$895$	72.0000	2.40669
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	−16.0000	−0.533927
$899$	−1.00000	−0.0333519
$900$	−8.00000	−0.266667
$901$	−12.0000	−0.399778
$902$	0	0
$903$	3.00000	0.0998337
$904$	0	0
$905$	−69.0000	−2.29364
$906$	−14.0000	−0.465119
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	14.0000	0.464606
$909$	8.00000	0.265343
$910$	−3.00000	−0.0994490
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	−26.0000	−0.860004
$915$	18.0000	0.595062
$916$	14.0000	0.462573
$917$	0	0
$918$	−20.0000	−0.660098
$919$	10.0000	0.329870	0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000	0.329870	0.164935	+	0.986304i	$0.447259\pi$
$920$	6.00000	0.197814
$921$	−9.00000	−0.296560
$922$	−28.0000	−0.922131
$923$	8.00000	0.263323
$924$	−1.00000	−0.0328976
$925$	24.0000	0.789115
$926$	−20.0000	−0.657241
$927$	−8.00000	−0.262754
$928$	1.00000	0.0328266
$929$	54.0000	1.77168	0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000	1.77168	0.885841	+	0.463988i	$0.153582\pi$
$930$	−3.00000	−0.0983739
$931$	−4.00000	−0.131095
$932$	11.0000	0.360317
$933$	−20.0000	−0.654771
$934$	13.0000	0.425373
$935$	−12.0000	−0.392442
$936$	2.00000	0.0653720
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−2.00000	−0.0653023
$939$	5.00000	0.163169
$940$	27.0000	0.880643
$941$	−27.0000	−0.880175	−0.440087	−	0.897955i	$-0.645053\pi$
$941$	−27.0000	−0.880175	−0.440087	+	0.897955i	$0.645053\pi$
$942$	12.0000	0.390981
$943$	0	0
$944$	0	0
$945$	15.0000	0.487950
$946$	−3.00000	−0.0975384
$947$	19.0000	0.617417	0.308709	−	0.951157i	$-0.400103\pi$
$947$	19.0000	0.617417	0.308709	+	0.951157i	$0.400103\pi$
$948$	13.0000	0.422220
$949$	0	0
$950$	−16.0000	−0.519109
$951$	−22.0000	−0.713399
$952$	4.00000	0.129641
$953$	47.0000	1.52248	0.761240	−	0.648471i	$-0.224591\pi$
$953$	47.0000	1.52248	0.761240	+	0.648471i	$0.224591\pi$
$954$	−6.00000	−0.194257
$955$	−24.0000	−0.776622
$956$	−12.0000	−0.388108
$957$	1.00000	0.0323254
$958$	21.0000	0.678479
$959$	10.0000	0.322917
$960$	3.00000	0.0968246
$961$	−30.0000	−0.967742
$962$	−6.00000	−0.193448
$963$	28.0000	0.902287
$964$	−29.0000	−0.934027
$965$	−36.0000	−1.15888
$966$	−2.00000	−0.0643489
$967$	−31.0000	−0.996893	−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000	−0.996893	−0.498446	+	0.866921i	$0.666096\pi$
$968$	−10.0000	−0.321412
$969$	−16.0000	−0.513994
$970$	−48.0000	−1.54119
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−16.0000	−0.513200
$973$	14.0000	0.448819
$974$	−20.0000	−0.640841
$975$	4.00000	0.128103
$976$	6.00000	0.192055
$977$	53.0000	1.69562	0.847810	−	0.530300i	$-0.177921\pi$
$977$	53.0000	1.69562	0.847810	+	0.530300i	$0.177921\pi$
$978$	21.0000	0.671506
$979$	14.0000	0.447442
$980$	−3.00000	−0.0958315
$981$	−30.0000	−0.957826
$982$	9.00000	0.287202
$983$	39.0000	1.24391	0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000	1.24391	0.621953	+	0.783054i	$0.286339\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	−4.00000	−0.127386
$987$	−9.00000	−0.286473
$988$	4.00000	0.127257
$989$	−6.00000	−0.190789
$990$	−6.00000	−0.190693
$991$	−2.00000	−0.0635321	−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000	−0.0635321	−0.0317660	+	0.999495i	$0.510113\pi$
$992$	−1.00000	−0.0317500
$993$	−27.0000	−0.856819
$994$	8.00000	0.253745
$995$	60.0000	1.90213
$996$	0	0
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	−38.0000	−1.20287
$999$	30.0000	0.949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.a.d.1.1	✓	1
3.2	odd	2		3654.2.a.l.1.1		1
4.3	odd	2		3248.2.a.k.1.1		1
7.6	odd	2		2842.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.d.1.1	✓	1	1.1	even	1	trivial
2842.2.a.f.1.1		1	7.6	odd	2
3248.2.a.k.1.1		1	4.3	odd	2
3654.2.a.l.1.1		1	3.2	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:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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