LMFDB - Embedded newform 2006.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
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	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +3.00000 q^{10} +1.00000 q^{12} -4.00000 q^{13} +1.00000 q^{14} -3.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +2.00000 q^{18} -1.00000 q^{19} -3.00000 q^{20} -1.00000 q^{21} +6.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} +4.00000 q^{26} -5.00000 q^{27} -1.00000 q^{28} -9.00000 q^{29} +3.00000 q^{30} +8.00000 q^{31} -1.00000 q^{32} -1.00000 q^{34} +3.00000 q^{35} -2.00000 q^{36} +8.00000 q^{37} +1.00000 q^{38} -4.00000 q^{39} +3.00000 q^{40} -3.00000 q^{41} +1.00000 q^{42} +8.00000 q^{43} +6.00000 q^{45} -6.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -4.00000 q^{50} +1.00000 q^{51} -4.00000 q^{52} +3.00000 q^{53} +5.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} +9.00000 q^{58} -1.00000 q^{59} -3.00000 q^{60} +2.00000 q^{61} -8.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +12.0000 q^{65} +8.00000 q^{67} +1.00000 q^{68} +6.00000 q^{69} -3.00000 q^{70} -12.0000 q^{71} +2.00000 q^{72} +2.00000 q^{73} -8.00000 q^{74} +4.00000 q^{75} -1.00000 q^{76} +4.00000 q^{78} +17.0000 q^{79} -3.00000 q^{80} +1.00000 q^{81} +3.00000 q^{82} +12.0000 q^{83} -1.00000 q^{84} -3.00000 q^{85} -8.00000 q^{86} -9.00000 q^{87} -6.00000 q^{90} +4.00000 q^{91} +6.00000 q^{92} +8.00000 q^{93} -6.00000 q^{94} +3.00000 q^{95} -1.00000 q^{96} -16.0000 q^{97} +6.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	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	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	3.00000	0.948683
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.00000	0.267261
$15$	−3.00000	−0.774597
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.00000	0.471405
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−3.00000	−0.670820
$21$	−1.00000	−0.218218
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	4.00000	0.800000
$26$	4.00000	0.784465
$27$	−5.00000	−0.962250
$28$	−1.00000	−0.188982
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	3.00000	0.547723
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−1.00000	−0.171499
$35$	3.00000	0.507093
$36$	−2.00000	−0.333333
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	1.00000	0.162221
$39$	−4.00000	−0.640513
$40$	3.00000	0.474342
$41$	−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
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	0	0
$45$	6.00000	0.894427
$46$	−6.00000	−0.884652
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	−4.00000	−0.565685
$51$	1.00000	0.140028
$52$	−4.00000	−0.554700
$53$	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
$55$	0	0
$56$	1.00000	0.133631
$57$	−1.00000	−0.132453
$58$	9.00000	1.18176
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.00000	−0.387298
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	12.0000	1.48842
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	1.00000	0.121268
$69$	6.00000	0.722315
$70$	−3.00000	−0.358569
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	2.00000	0.235702
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−8.00000	−0.929981
$75$	4.00000	0.461880
$76$	−1.00000	−0.114708
$77$	0	0
$78$	4.00000	0.452911
$79$	17.0000	1.91265	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	17.0000	1.91265	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	3.00000	0.331295
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	−1.00000	−0.109109
$85$	−3.00000	−0.325396
$86$	−8.00000	−0.862662
$87$	−9.00000	−0.964901
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−6.00000	−0.632456
$91$	4.00000	0.419314
$92$	6.00000	0.625543
$93$	8.00000	0.829561
$94$	−6.00000	−0.618853
$95$	3.00000	0.307794
$96$	−1.00000	−0.102062
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	4.00000	0.400000
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	−1.00000	−0.0990148
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	4.00000	0.392232
$105$	3.00000	0.292770
$106$	−3.00000	−0.291386
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	−5.00000	−0.481125
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−1.00000	−0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	0.0936586
$115$	−18.0000	−1.67851
$116$	−9.00000	−0.835629
$117$	8.00000	0.739600
$118$	1.00000	0.0920575
$119$	−1.00000	−0.0916698
$120$	3.00000	0.273861
$121$	−11.0000	−1.00000
$122$	−2.00000	−0.181071
$123$	−3.00000	−0.270501
$124$	8.00000	0.718421
$125$	3.00000	0.268328
$126$	−2.00000	−0.178174
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	−12.0000	−1.05247
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	−8.00000	−0.691095
$135$	15.0000	1.29099
$136$	−1.00000	−0.0857493
$137$	−21.0000	−1.79415	−0.897076	−	0.441877i	$-0.854313\pi$
$137$	−21.0000	−1.79415	−0.897076	+	0.441877i	$0.854313\pi$
$138$	−6.00000	−0.510754
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	3.00000	0.253546
$141$	6.00000	0.505291
$142$	12.0000	1.00702
$143$	0	0
$144$	−2.00000	−0.166667
$145$	27.0000	2.24223
$146$	−2.00000	−0.165521
$147$	−6.00000	−0.494872
$148$	8.00000	0.657596
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−4.00000	−0.326599
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	1.00000	0.0811107
$153$	−2.00000	−0.161690
$154$	0	0
$155$	−24.0000	−1.92773
$156$	−4.00000	−0.320256
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−17.0000	−1.35245
$159$	3.00000	0.237915
$160$	3.00000	0.237171
$161$	−6.00000	−0.472866
$162$	−1.00000	−0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	−3.00000	−0.234261
$165$	0	0
$166$	−12.0000	−0.931381
$167$	−21.0000	−1.62503	−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000	−1.62503	−0.812514	+	0.582941i	$0.801902\pi$
$168$	1.00000	0.0771517
$169$	3.00000	0.230769
$170$	3.00000	0.230089
$171$	2.00000	0.152944
$172$	8.00000	0.609994
$173$	−24.0000	−1.82469	−0.912343	−	0.409426i	$-0.865729\pi$
$173$	−24.0000	−1.82469	−0.912343	+	0.409426i	$0.865729\pi$
$174$	9.00000	0.682288
$175$	−4.00000	−0.302372
$176$	0	0
$177$	−1.00000	−0.0751646
$178$	0	0
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	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	$0.173687\pi$
$182$	−4.00000	−0.296500
$183$	2.00000	0.147844
$184$	−6.00000	−0.442326
$185$	−24.0000	−1.76452
$186$	−8.00000	−0.586588
$187$	0	0
$188$	6.00000	0.437595
$189$	5.00000	0.363696
$190$	−3.00000	−0.217643
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	1.00000	0.0721688
$193$	−7.00000	−0.503871	−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000	−0.503871	−0.251936	+	0.967744i	$0.581067\pi$
$194$	16.0000	1.14873
$195$	12.0000	0.859338
$196$	−6.00000	−0.428571
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	−4.00000	−0.282843
$201$	8.00000	0.564276
$202$	−12.0000	−0.844317
$203$	9.00000	0.631676
$204$	1.00000	0.0700140
$205$	9.00000	0.628587
$206$	−8.00000	−0.557386
$207$	−12.0000	−0.834058
$208$	−4.00000	−0.277350
$209$	0	0
$210$	−3.00000	−0.207020
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	3.00000	0.206041
$213$	−12.0000	−0.822226
$214$	−9.00000	−0.615227
$215$	−24.0000	−1.63679
$216$	5.00000	0.340207
$217$	−8.00000	−0.543075
$218$	−2.00000	−0.135457
$219$	2.00000	0.135147
$220$	0	0
$221$	−4.00000	−0.269069
$222$	−8.00000	−0.536925
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	1.00000	0.0668153
$225$	−8.00000	−0.533333
$226$	6.00000	0.399114
$227$	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	$0.759040\pi$
$230$	18.0000	1.18688
$231$	0	0
$232$	9.00000	0.590879
$233$	−12.0000	−0.786146	−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000	−0.786146	−0.393073	+	0.919507i	$0.628588\pi$
$234$	−8.00000	−0.522976
$235$	−18.0000	−1.17419
$236$	−1.00000	−0.0650945
$237$	17.0000	1.10427
$238$	1.00000	0.0648204
$239$	9.00000	0.582162	0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000	0.582162	0.291081	+	0.956698i	$0.405985\pi$
$240$	−3.00000	−0.193649
$241$	−1.00000	−0.0644157	−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000	−0.0644157	−0.0322078	+	0.999481i	$0.510254\pi$
$242$	11.0000	0.707107
$243$	16.0000	1.02640
$244$	2.00000	0.128037
$245$	18.0000	1.14998
$246$	3.00000	0.191273
$247$	4.00000	0.254514
$248$	−8.00000	−0.508001
$249$	12.0000	0.760469
$250$	−3.00000	−0.189737
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	13.0000	0.815693
$255$	−3.00000	−0.187867
$256$	1.00000	0.0625000
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	−8.00000	−0.498058
$259$	−8.00000	−0.497096
$260$	12.0000	0.744208
$261$	18.0000	1.11417
$262$	−6.00000	−0.370681
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	−9.00000	−0.552866
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	8.00000	0.488678
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−15.0000	−0.912871
$271$	23.0000	1.39715	0.698575	−	0.715537i	$-0.253818\pi$
$271$	23.0000	1.39715	0.698575	+	0.715537i	$0.253818\pi$
$272$	1.00000	0.0606339
$273$	4.00000	0.242091
$274$	21.0000	1.26866
$275$	0	0
$276$	6.00000	0.361158
$277$	17.0000	1.02143	0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000	1.02143	0.510716	+	0.859750i	$0.329381\pi$
$278$	−20.0000	−1.19952
$279$	−16.0000	−0.957895
$280$	−3.00000	−0.179284
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	−6.00000	−0.357295
$283$	26.0000	1.54554	0.772770	−	0.634686i	$-0.218871\pi$
$283$	26.0000	1.54554	0.772770	+	0.634686i	$0.218871\pi$
$284$	−12.0000	−0.712069
$285$	3.00000	0.177705
$286$	0	0
$287$	3.00000	0.177084
$288$	2.00000	0.117851
$289$	1.00000	0.0588235
$290$	−27.0000	−1.58549
$291$	−16.0000	−0.937937
$292$	2.00000	0.117041
$293$	33.0000	1.92788	0.963940	−	0.266119i	$-0.0857413\pi$
$293$	33.0000	1.92788	0.963940	+	0.266119i	$0.0857413\pi$
$294$	6.00000	0.349927
$295$	3.00000	0.174667
$296$	−8.00000	−0.464991
$297$	0	0
$298$	−6.00000	−0.347571
$299$	−24.0000	−1.38796
$300$	4.00000	0.230940
$301$	−8.00000	−0.461112
$302$	−20.0000	−1.15087
$303$	12.0000	0.689382
$304$	−1.00000	−0.0573539
$305$	−6.00000	−0.343559
$306$	2.00000	0.114332
$307$	−7.00000	−0.399511	−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000	−0.399511	−0.199756	+	0.979846i	$0.564015\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	24.0000	1.36311
$311$	−21.0000	−1.19080	−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000	−1.19080	−0.595400	+	0.803429i	$0.703007\pi$
$312$	4.00000	0.226455
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−14.0000	−0.790066
$315$	−6.00000	−0.338062
$316$	17.0000	0.956325
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−3.00000	−0.168232
$319$	0	0
$320$	−3.00000	−0.167705
$321$	9.00000	0.502331
$322$	6.00000	0.334367
$323$	−1.00000	−0.0556415
$324$	1.00000	0.0555556
$325$	−16.0000	−0.887520
$326$	16.0000	0.886158
$327$	2.00000	0.110600
$328$	3.00000	0.165647
$329$	−6.00000	−0.330791
$330$	0	0
$331$	−1.00000	−0.0549650	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	−1.00000	−0.0549650	−0.0274825	+	0.999622i	$0.508749\pi$
$332$	12.0000	0.658586
$333$	−16.0000	−0.876795
$334$	21.0000	1.14907
$335$	−24.0000	−1.31126
$336$	−1.00000	−0.0545545
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−3.00000	−0.163178
$339$	−6.00000	−0.325875
$340$	−3.00000	−0.162698
$341$	0	0
$342$	−2.00000	−0.108148
$343$	13.0000	0.701934
$344$	−8.00000	−0.431331
$345$	−18.0000	−0.969087
$346$	24.0000	1.29025
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−9.00000	−0.482451
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	4.00000	0.213809
$351$	20.0000	1.06752
$352$	0	0
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	1.00000	0.0531494
$355$	36.0000	1.91068
$356$	0	0
$357$	−1.00000	−0.0529256
$358$	−6.00000	−0.317110
$359$	−9.00000	−0.475002	−0.237501	−	0.971387i	$-0.576328\pi$
$359$	−9.00000	−0.475002	−0.237501	+	0.971387i	$0.576328\pi$
$360$	−6.00000	−0.316228
$361$	−18.0000	−0.947368
$362$	−23.0000	−1.20885
$363$	−11.0000	−0.577350
$364$	4.00000	0.209657
$365$	−6.00000	−0.314054
$366$	−2.00000	−0.104542
$367$	20.0000	1.04399	0.521996	−	0.852948i	$-0.325188\pi$
$367$	20.0000	1.04399	0.521996	+	0.852948i	$0.325188\pi$
$368$	6.00000	0.312772
$369$	6.00000	0.312348
$370$	24.0000	1.24770
$371$	−3.00000	−0.155752
$372$	8.00000	0.414781
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	0	0
$375$	3.00000	0.154919
$376$	−6.00000	−0.309426
$377$	36.0000	1.85409
$378$	−5.00000	−0.257172
$379$	−13.0000	−0.667765	−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000	−0.667765	−0.333883	+	0.942615i	$0.608359\pi$
$380$	3.00000	0.153897
$381$	−13.0000	−0.666010
$382$	6.00000	0.306987
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	7.00000	0.356291
$387$	−16.0000	−0.813326
$388$	−16.0000	−0.812277
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	−12.0000	−0.607644
$391$	6.00000	0.303433
$392$	6.00000	0.303046
$393$	6.00000	0.302660
$394$	6.00000	0.302276
$395$	−51.0000	−2.56609
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−11.0000	−0.551380
$399$	1.00000	0.0500626
$400$	4.00000	0.200000
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	−8.00000	−0.399004
$403$	−32.0000	−1.59403
$404$	12.0000	0.597022
$405$	−3.00000	−0.149071
$406$	−9.00000	−0.446663
$407$	0	0
$408$	−1.00000	−0.0495074
$409$	−28.0000	−1.38451	−0.692255	−	0.721653i	$-0.743383\pi$
$409$	−28.0000	−1.38451	−0.692255	+	0.721653i	$0.743383\pi$
$410$	−9.00000	−0.444478
$411$	−21.0000	−1.03585
$412$	8.00000	0.394132
$413$	1.00000	0.0492068
$414$	12.0000	0.589768
$415$	−36.0000	−1.76717
$416$	4.00000	0.196116
$417$	20.0000	0.979404
$418$	0	0
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	3.00000	0.146385
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	−20.0000	−0.973585
$423$	−12.0000	−0.583460
$424$	−3.00000	−0.145693
$425$	4.00000	0.194029
$426$	12.0000	0.581402
$427$	−2.00000	−0.0967868
$428$	9.00000	0.435031
$429$	0	0
$430$	24.0000	1.15738
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	−5.00000	−0.240563
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	8.00000	0.384012
$435$	27.0000	1.29455
$436$	2.00000	0.0957826
$437$	−6.00000	−0.287019
$438$	−2.00000	−0.0955637
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	4.00000	0.190261
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	−8.00000	−0.378811
$447$	6.00000	0.283790
$448$	−1.00000	−0.0472456
$449$	−21.0000	−0.991051	−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000	−0.991051	−0.495526	+	0.868593i	$0.665025\pi$
$450$	8.00000	0.377124
$451$	0	0
$452$	−6.00000	−0.282216
$453$	20.0000	0.939682
$454$	−18.0000	−0.844782
$455$	−12.0000	−0.562569
$456$	1.00000	0.0468293
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	22.0000	1.02799
$459$	−5.00000	−0.233380
$460$	−18.0000	−0.839254
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	−22.0000	−1.02243	−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000	−1.02243	−0.511213	+	0.859454i	$0.670804\pi$
$464$	−9.00000	−0.417815
$465$	−24.0000	−1.11297
$466$	12.0000	0.555889
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	8.00000	0.369800
$469$	−8.00000	−0.369406
$470$	18.0000	0.830278
$471$	14.0000	0.645086
$472$	1.00000	0.0460287
$473$	0	0
$474$	−17.0000	−0.780836
$475$	−4.00000	−0.183533
$476$	−1.00000	−0.0458349
$477$	−6.00000	−0.274721
$478$	−9.00000	−0.411650
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	3.00000	0.136931
$481$	−32.0000	−1.45907
$482$	1.00000	0.0455488
$483$	−6.00000	−0.273009
$484$	−11.0000	−0.500000
$485$	48.0000	2.17957
$486$	−16.0000	−0.725775
$487$	−13.0000	−0.589086	−0.294543	−	0.955638i	$-0.595167\pi$
$487$	−13.0000	−0.589086	−0.294543	+	0.955638i	$0.595167\pi$
$488$	−2.00000	−0.0905357
$489$	−16.0000	−0.723545
$490$	−18.0000	−0.813157
$491$	−39.0000	−1.76005	−0.880023	−	0.474932i	$-0.842473\pi$
$491$	−39.0000	−1.76005	−0.880023	+	0.474932i	$0.842473\pi$
$492$	−3.00000	−0.135250
$493$	−9.00000	−0.405340
$494$	−4.00000	−0.179969
$495$	0	0
$496$	8.00000	0.359211
$497$	12.0000	0.538274
$498$	−12.0000	−0.537733
$499$	−31.0000	−1.38775	−0.693875	−	0.720095i	$-0.744098\pi$
$499$	−31.0000	−1.38775	−0.693875	+	0.720095i	$0.744098\pi$
$500$	3.00000	0.134164
$501$	−21.0000	−0.938211
$502$	−9.00000	−0.401690
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	−2.00000	−0.0890871
$505$	−36.0000	−1.60198
$506$	0	0
$507$	3.00000	0.133235
$508$	−13.0000	−0.576782
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	3.00000	0.132842
$511$	−2.00000	−0.0884748
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	3.00000	0.132324
$515$	−24.0000	−1.05757
$516$	8.00000	0.352180
$517$	0	0
$518$	8.00000	0.351500
$519$	−24.0000	−1.05348
$520$	−12.0000	−0.526235
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	−18.0000	−0.787839
$523$	−7.00000	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$523$	−7.00000	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$524$	6.00000	0.262111
$525$	−4.00000	−0.174574
$526$	−9.00000	−0.392419
$527$	8.00000	0.348485
$528$	0	0
$529$	13.0000	0.565217
$530$	9.00000	0.390935
$531$	2.00000	0.0867926
$532$	1.00000	0.0433555
$533$	12.0000	0.519778
$534$	0	0
$535$	−27.0000	−1.16731
$536$	−8.00000	−0.345547
$537$	6.00000	0.258919
$538$	18.0000	0.776035
$539$	0	0
$540$	15.0000	0.645497
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−23.0000	−0.987935
$543$	23.0000	0.987024
$544$	−1.00000	−0.0428746
$545$	−6.00000	−0.257012
$546$	−4.00000	−0.171184
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−21.0000	−0.897076
$549$	−4.00000	−0.170716
$550$	0	0
$551$	9.00000	0.383413
$552$	−6.00000	−0.255377
$553$	−17.0000	−0.722914
$554$	−17.0000	−0.722261
$555$	−24.0000	−1.01874
$556$	20.0000	0.848189
$557$	−9.00000	−0.381342	−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000	−0.381342	−0.190671	+	0.981654i	$0.561066\pi$
$558$	16.0000	0.677334
$559$	−32.0000	−1.35346
$560$	3.00000	0.126773
$561$	0	0
$562$	−15.0000	−0.632737
$563$	−18.0000	−0.758610	−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000	−0.758610	−0.379305	+	0.925272i	$0.623837\pi$
$564$	6.00000	0.252646
$565$	18.0000	0.757266
$566$	−26.0000	−1.09286
$567$	−1.00000	−0.0419961
$568$	12.0000	0.503509
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	−3.00000	−0.125656
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	0	0
$573$	−6.00000	−0.250654
$574$	−3.00000	−0.125218
$575$	24.0000	1.00087
$576$	−2.00000	−0.0833333
$577$	−31.0000	−1.29055	−0.645273	−	0.763952i	$-0.723257\pi$
$577$	−31.0000	−1.29055	−0.645273	+	0.763952i	$0.723257\pi$
$578$	−1.00000	−0.0415945
$579$	−7.00000	−0.290910
$580$	27.0000	1.12111
$581$	−12.0000	−0.497844
$582$	16.0000	0.663221
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	−24.0000	−0.992278
$586$	−33.0000	−1.36322
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−6.00000	−0.247436
$589$	−8.00000	−0.329634
$590$	−3.00000	−0.123508
$591$	−6.00000	−0.246807
$592$	8.00000	0.328798
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	0	0
$595$	3.00000	0.122988
$596$	6.00000	0.245770
$597$	11.0000	0.450200
$598$	24.0000	0.981433
$599$	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
$601$	44.0000	1.79480	0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000	1.79480	0.897399	+	0.441221i	$0.145454\pi$
$602$	8.00000	0.326056
$603$	−16.0000	−0.651570
$604$	20.0000	0.813788
$605$	33.0000	1.34164
$606$	−12.0000	−0.487467
$607$	−13.0000	−0.527654	−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000	−0.527654	−0.263827	+	0.964570i	$0.584985\pi$
$608$	1.00000	0.0405554
$609$	9.00000	0.364698
$610$	6.00000	0.242933
$611$	−24.0000	−0.970936
$612$	−2.00000	−0.0808452
$613$	−40.0000	−1.61558	−0.807792	−	0.589467i	$-0.799338\pi$
$613$	−40.0000	−1.61558	−0.807792	+	0.589467i	$0.799338\pi$
$614$	7.00000	0.282497
$615$	9.00000	0.362915
$616$	0	0
$617$	27.0000	1.08698	0.543490	−	0.839416i	$-0.317103\pi$
$617$	27.0000	1.08698	0.543490	+	0.839416i	$0.317103\pi$
$618$	−8.00000	−0.321807
$619$	35.0000	1.40677	0.703384	−	0.710810i	$-0.251671\pi$
$619$	35.0000	1.40677	0.703384	+	0.710810i	$0.251671\pi$
$620$	−24.0000	−0.963863
$621$	−30.0000	−1.20386
$622$	21.0000	0.842023
$623$	0	0
$624$	−4.00000	−0.160128
$625$	−29.0000	−1.16000
$626$	−26.0000	−1.03917
$627$	0	0
$628$	14.0000	0.558661
$629$	8.00000	0.318981
$630$	6.00000	0.239046
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	−17.0000	−0.676224
$633$	20.0000	0.794929
$634$	−18.0000	−0.714871
$635$	39.0000	1.54767
$636$	3.00000	0.118958
$637$	24.0000	0.950915
$638$	0	0
$639$	24.0000	0.949425
$640$	3.00000	0.118585
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−9.00000	−0.355202
$643$	29.0000	1.14365	0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000	1.14365	0.571824	+	0.820376i	$0.306236\pi$
$644$	−6.00000	−0.236433
$645$	−24.0000	−0.944999
$646$	1.00000	0.0393445
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	16.0000	0.627572
$651$	−8.00000	−0.313545
$652$	−16.0000	−0.626608
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	−2.00000	−0.0782062
$655$	−18.0000	−0.703318
$656$	−3.00000	−0.117130
$657$	−4.00000	−0.156055
$658$	6.00000	0.233904
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	0	0
$661$	−1.00000	−0.0388955	−0.0194477	−	0.999811i	$-0.506191\pi$
$661$	−1.00000	−0.0388955	−0.0194477	+	0.999811i	$0.506191\pi$
$662$	1.00000	0.0388661
$663$	−4.00000	−0.155347
$664$	−12.0000	−0.465690
$665$	−3.00000	−0.116335
$666$	16.0000	0.619987
$667$	−54.0000	−2.09089
$668$	−21.0000	−0.812514
$669$	8.00000	0.309298
$670$	24.0000	0.927201
$671$	0	0
$672$	1.00000	0.0385758
$673$	44.0000	1.69608	0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000	1.69608	0.848038	+	0.529936i	$0.177784\pi$
$674$	22.0000	0.847408
$675$	−20.0000	−0.769800
$676$	3.00000	0.115385
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	6.00000	0.230429
$679$	16.0000	0.614024
$680$	3.00000	0.115045
$681$	18.0000	0.689761
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	2.00000	0.0764719
$685$	63.0000	2.40711
$686$	−13.0000	−0.496342
$687$	−22.0000	−0.839352
$688$	8.00000	0.304997
$689$	−12.0000	−0.457164
$690$	18.0000	0.685248
$691$	−22.0000	−0.836919	−0.418460	−	0.908235i	$-0.637430\pi$
$691$	−22.0000	−0.836919	−0.418460	+	0.908235i	$0.637430\pi$
$692$	−24.0000	−0.912343
$693$	0	0
$694$	0	0
$695$	−60.0000	−2.27593
$696$	9.00000	0.341144
$697$	−3.00000	−0.113633
$698$	−26.0000	−0.984115
$699$	−12.0000	−0.453882
$700$	−4.00000	−0.151186
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	−20.0000	−0.754851
$703$	−8.00000	−0.301726
$704$	0	0
$705$	−18.0000	−0.677919
$706$	24.0000	0.903252
$707$	−12.0000	−0.451306
$708$	−1.00000	−0.0375823
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	−36.0000	−1.35106
$711$	−34.0000	−1.27510
$712$	0	0
$713$	48.0000	1.79761
$714$	1.00000	0.0374241
$715$	0	0
$716$	6.00000	0.224231
$717$	9.00000	0.336111
$718$	9.00000	0.335877
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	6.00000	0.223607
$721$	−8.00000	−0.297936
$722$	18.0000	0.669891
$723$	−1.00000	−0.0371904
$724$	23.0000	0.854788
$725$	−36.0000	−1.33701
$726$	11.0000	0.408248
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	−4.00000	−0.148250
$729$	13.0000	0.481481
$730$	6.00000	0.222070
$731$	8.00000	0.295891
$732$	2.00000	0.0739221
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	−20.0000	−0.738213
$735$	18.0000	0.663940
$736$	−6.00000	−0.221163
$737$	0	0
$738$	−6.00000	−0.220863
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−24.0000	−0.882258
$741$	4.00000	0.146944
$742$	3.00000	0.110133
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−8.00000	−0.293294
$745$	−18.0000	−0.659469
$746$	22.0000	0.805477
$747$	−24.0000	−0.878114
$748$	0	0
$749$	−9.00000	−0.328853
$750$	−3.00000	−0.109545
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	6.00000	0.218797
$753$	9.00000	0.327978
$754$	−36.0000	−1.31104
$755$	−60.0000	−2.18362
$756$	5.00000	0.181848
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	13.0000	0.472181
$759$	0	0
$760$	−3.00000	−0.108821
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	13.0000	0.470940
$763$	−2.00000	−0.0724049
$764$	−6.00000	−0.217072
$765$	6.00000	0.216930
$766$	24.0000	0.867155
$767$	4.00000	0.144432
$768$	1.00000	0.0360844
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	−3.00000	−0.108042
$772$	−7.00000	−0.251936
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	16.0000	0.575108
$775$	32.0000	1.14947
$776$	16.0000	0.574367
$777$	−8.00000	−0.286998
$778$	−18.0000	−0.645331
$779$	3.00000	0.107486
$780$	12.0000	0.429669
$781$	0	0
$782$	−6.00000	−0.214560
$783$	45.0000	1.60817
$784$	−6.00000	−0.214286
$785$	−42.0000	−1.49904
$786$	−6.00000	−0.214013
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−6.00000	−0.213741
$789$	9.00000	0.320408
$790$	51.0000	1.81450
$791$	6.00000	0.213335
$792$	0	0
$793$	−8.00000	−0.284088
$794$	−2.00000	−0.0709773
$795$	−9.00000	−0.319197
$796$	11.0000	0.389885
$797$	36.0000	1.27519	0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000	1.27519	0.637593	+	0.770374i	$0.279930\pi$
$798$	−1.00000	−0.0353996
$799$	6.00000	0.212265
$800$	−4.00000	−0.141421
$801$	0	0
$802$	−24.0000	−0.847469
$803$	0	0
$804$	8.00000	0.282138
$805$	18.0000	0.634417
$806$	32.0000	1.12715
$807$	−18.0000	−0.633630
$808$	−12.0000	−0.422159
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	3.00000	0.105409
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	9.00000	0.315838
$813$	23.0000	0.806645
$814$	0	0
$815$	48.0000	1.68137
$816$	1.00000	0.0350070
$817$	−8.00000	−0.279885
$818$	28.0000	0.978997
$819$	−8.00000	−0.279543
$820$	9.00000	0.314294
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	21.0000	0.732459
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	−1.00000	−0.0347945
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	−12.0000	−0.417029
$829$	−19.0000	−0.659897	−0.329949	−	0.943999i	$-0.607031\pi$
$829$	−19.0000	−0.659897	−0.329949	+	0.943999i	$0.607031\pi$
$830$	36.0000	1.24958
$831$	17.0000	0.589723
$832$	−4.00000	−0.138675
$833$	−6.00000	−0.207888
$834$	−20.0000	−0.692543
$835$	63.0000	2.18020
$836$	0	0
$837$	−40.0000	−1.38260
$838$	36.0000	1.24360
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	−3.00000	−0.103510
$841$	52.0000	1.79310
$842$	−20.0000	−0.689246
$843$	15.0000	0.516627
$844$	20.0000	0.688428
$845$	−9.00000	−0.309609
$846$	12.0000	0.412568
$847$	11.0000	0.377964
$848$	3.00000	0.103020
$849$	26.0000	0.892318
$850$	−4.00000	−0.137199
$851$	48.0000	1.64542
$852$	−12.0000	−0.411113
$853$	−1.00000	−0.0342393	−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000	−0.0342393	−0.0171197	+	0.999853i	$0.505450\pi$
$854$	2.00000	0.0684386
$855$	−6.00000	−0.205196
$856$	−9.00000	−0.307614
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	0	0
$859$	38.0000	1.29654	0.648272	−	0.761409i	$-0.275492\pi$
$859$	38.0000	1.29654	0.648272	+	0.761409i	$0.275492\pi$
$860$	−24.0000	−0.818393
$861$	3.00000	0.102240
$862$	−12.0000	−0.408722
$863$	54.0000	1.83818	0.919091	−	0.394046i	$-0.128925\pi$
$863$	54.0000	1.83818	0.919091	+	0.394046i	$0.128925\pi$
$864$	5.00000	0.170103
$865$	72.0000	2.44807
$866$	1.00000	0.0339814
$867$	1.00000	0.0339618
$868$	−8.00000	−0.271538
$869$	0	0
$870$	−27.0000	−0.915386
$871$	−32.0000	−1.08428
$872$	−2.00000	−0.0677285
$873$	32.0000	1.08304
$874$	6.00000	0.202953
$875$	−3.00000	−0.101419
$876$	2.00000	0.0675737
$877$	59.0000	1.99229	0.996144	−	0.0877308i	$-0.0279615\pi$
$877$	59.0000	1.99229	0.996144	+	0.0877308i	$0.0279615\pi$
$878$	−32.0000	−1.07995
$879$	33.0000	1.11306
$880$	0	0
$881$	−12.0000	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$882$	−12.0000	−0.404061
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	−4.00000	−0.134535
$885$	3.00000	0.100844
$886$	24.0000	0.806296
$887$	−42.0000	−1.41022	−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000	−1.41022	−0.705111	+	0.709097i	$0.749103\pi$
$888$	−8.00000	−0.268462
$889$	13.0000	0.436006
$890$	0	0
$891$	0	0
$892$	8.00000	0.267860
$893$	−6.00000	−0.200782
$894$	−6.00000	−0.200670
$895$	−18.0000	−0.601674
$896$	1.00000	0.0334077
$897$	−24.0000	−0.801337
$898$	21.0000	0.700779
$899$	−72.0000	−2.40133
$900$	−8.00000	−0.266667
$901$	3.00000	0.0999445
$902$	0	0
$903$	−8.00000	−0.266223
$904$	6.00000	0.199557
$905$	−69.0000	−2.29364
$906$	−20.0000	−0.664455
$907$	−43.0000	−1.42779	−0.713896	−	0.700252i	$-0.753071\pi$
$907$	−43.0000	−1.42779	−0.713896	+	0.700252i	$0.753071\pi$
$908$	18.0000	0.597351
$909$	−24.0000	−0.796030
$910$	12.0000	0.397796
$911$	15.0000	0.496972	0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000	0.496972	0.248486	+	0.968635i	$0.420067\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	28.0000	0.926158
$915$	−6.00000	−0.198354
$916$	−22.0000	−0.726900
$917$	−6.00000	−0.198137
$918$	5.00000	0.165025
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	18.0000	0.593442
$921$	−7.00000	−0.230658
$922$	30.0000	0.987997
$923$	48.0000	1.57994
$924$	0	0
$925$	32.0000	1.05215
$926$	22.0000	0.722965
$927$	−16.0000	−0.525509
$928$	9.00000	0.295439
$929$	48.0000	1.57483	0.787414	−	0.616424i	$-0.211419\pi$
$929$	48.0000	1.57483	0.787414	+	0.616424i	$0.211419\pi$
$930$	24.0000	0.786991
$931$	6.00000	0.196642
$932$	−12.0000	−0.393073
$933$	−21.0000	−0.687509
$934$	6.00000	0.196326
$935$	0	0
$936$	−8.00000	−0.261488
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	8.00000	0.261209
$939$	26.0000	0.848478
$940$	−18.0000	−0.587095
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	−14.0000	−0.456145
$943$	−18.0000	−0.586161
$944$	−1.00000	−0.0325472
$945$	−15.0000	−0.487950
$946$	0	0
$947$	−3.00000	−0.0974869	−0.0487435	−	0.998811i	$-0.515522\pi$
$947$	−3.00000	−0.0974869	−0.0487435	+	0.998811i	$0.515522\pi$
$948$	17.0000	0.552134
$949$	−8.00000	−0.259691
$950$	4.00000	0.129777
$951$	18.0000	0.583690
$952$	1.00000	0.0324102
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	6.00000	0.194257
$955$	18.0000	0.582466
$956$	9.00000	0.291081
$957$	0	0
$958$	−24.0000	−0.775405
$959$	21.0000	0.678125
$960$	−3.00000	−0.0968246
$961$	33.0000	1.06452
$962$	32.0000	1.03172
$963$	−18.0000	−0.580042
$964$	−1.00000	−0.0322078
$965$	21.0000	0.676014
$966$	6.00000	0.193047
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	11.0000	0.353553
$969$	−1.00000	−0.0321246
$970$	−48.0000	−1.54119
$971$	−3.00000	−0.0962746	−0.0481373	−	0.998841i	$-0.515328\pi$
$971$	−3.00000	−0.0962746	−0.0481373	+	0.998841i	$0.515328\pi$
$972$	16.0000	0.513200
$973$	−20.0000	−0.641171
$974$	13.0000	0.416547
$975$	−16.0000	−0.512410
$976$	2.00000	0.0640184
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	16.0000	0.511624
$979$	0	0
$980$	18.0000	0.574989
$981$	−4.00000	−0.127710
$982$	39.0000	1.24454
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	3.00000	0.0956365
$985$	18.0000	0.573528
$986$	9.00000	0.286618
$987$	−6.00000	−0.190982
$988$	4.00000	0.127257
$989$	48.0000	1.52631
$990$	0	0
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	−8.00000	−0.254000
$993$	−1.00000	−0.0317340
$994$	−12.0000	−0.380617
$995$	−33.0000	−1.04617
$996$	12.0000	0.380235
$997$	−13.0000	−0.411714	−0.205857	−	0.978582i	$-0.565998\pi$
$997$	−13.0000	−0.411714	−0.205857	+	0.978582i	$0.565998\pi$
$998$	31.0000	0.981288
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.e.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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