LMFDB - Embedded newform 8015.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
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	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -3.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} +6.00000 q^{6} +1.00000 q^{7} +6.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -3.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} +6.00000 q^{6} +1.00000 q^{7} +6.00000 q^{9} -2.00000 q^{10} +5.00000 q^{11} -6.00000 q^{12} -1.00000 q^{13} -2.00000 q^{14} -3.00000 q^{15} -4.00000 q^{16} +3.00000 q^{17} -12.0000 q^{18} +2.00000 q^{19} +2.00000 q^{20} -3.00000 q^{21} -10.0000 q^{22} +6.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -9.00000 q^{27} +2.00000 q^{28} +5.00000 q^{29} +6.00000 q^{30} +2.00000 q^{31} +8.00000 q^{32} -15.0000 q^{33} -6.00000 q^{34} +1.00000 q^{35} +12.0000 q^{36} -8.00000 q^{37} -4.00000 q^{38} +3.00000 q^{39} +6.00000 q^{41} +6.00000 q^{42} -4.00000 q^{43} +10.0000 q^{44} +6.00000 q^{45} -12.0000 q^{46} -1.00000 q^{47} +12.0000 q^{48} +1.00000 q^{49} -2.00000 q^{50} -9.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} +18.0000 q^{54} +5.00000 q^{55} -6.00000 q^{57} -10.0000 q^{58} -6.00000 q^{60} +10.0000 q^{61} -4.00000 q^{62} +6.00000 q^{63} -8.00000 q^{64} -1.00000 q^{65} +30.0000 q^{66} +8.00000 q^{67} +6.00000 q^{68} -18.0000 q^{69} -2.00000 q^{70} +12.0000 q^{71} -10.0000 q^{73} +16.0000 q^{74} -3.00000 q^{75} +4.00000 q^{76} +5.00000 q^{77} -6.00000 q^{78} +9.00000 q^{79} -4.00000 q^{80} +9.00000 q^{81} -12.0000 q^{82} +4.00000 q^{83} -6.00000 q^{84} +3.00000 q^{85} +8.00000 q^{86} -15.0000 q^{87} +12.0000 q^{89} -12.0000 q^{90} -1.00000 q^{91} +12.0000 q^{92} -6.00000 q^{93} +2.00000 q^{94} +2.00000 q^{95} -24.0000 q^{96} +11.0000 q^{97} -2.00000 q^{98} +30.0000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	6.00000	2.44949
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	6.00000	2.00000
$10$	−2.00000	−0.632456
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	−6.00000	−1.73205
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−2.00000	−0.534522
$15$	−3.00000	−0.774597
$16$	−4.00000	−1.00000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−12.0000	−2.82843
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	2.00000	0.447214
$21$	−3.00000	−0.654654
$22$	−10.0000	−2.13201
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−9.00000	−1.73205
$28$	2.00000	0.377964
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	6.00000	1.09545
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	8.00000	1.41421
$33$	−15.0000	−2.61116
$34$	−6.00000	−1.02899
$35$	1.00000	0.169031
$36$	12.0000	2.00000
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−4.00000	−0.648886
$39$	3.00000	0.480384
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	6.00000	0.925820
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	10.0000	1.50756
$45$	6.00000	0.894427
$46$	−12.0000	−1.76930
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	12.0000	1.73205
$49$	1.00000	0.142857
$50$	−2.00000	−0.282843
$51$	−9.00000	−1.26025
$52$	−2.00000	−0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	18.0000	2.44949
$55$	5.00000	0.674200
$56$	0	0
$57$	−6.00000	−0.794719
$58$	−10.0000	−1.31306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−6.00000	−0.774597
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−4.00000	−0.508001
$63$	6.00000	0.755929
$64$	−8.00000	−1.00000
$65$	−1.00000	−0.124035
$66$	30.0000	3.69274
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	6.00000	0.727607
$69$	−18.0000	−2.16695
$70$	−2.00000	−0.239046
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	16.0000	1.85996
$75$	−3.00000	−0.346410
$76$	4.00000	0.458831
$77$	5.00000	0.569803
$78$	−6.00000	−0.679366
$79$	9.00000	1.01258	0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000	1.01258	0.506290	+	0.862364i	$0.331017\pi$
$80$	−4.00000	−0.447214
$81$	9.00000	1.00000
$82$	−12.0000	−1.32518
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−6.00000	−0.654654
$85$	3.00000	0.325396
$86$	8.00000	0.862662
$87$	−15.0000	−1.60817
$88$	0	0
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	−12.0000	−1.26491
$91$	−1.00000	−0.104828
$92$	12.0000	1.25109
$93$	−6.00000	−0.622171
$94$	2.00000	0.206284
$95$	2.00000	0.205196
$96$	−24.0000	−2.44949
$97$	11.0000	1.11688	0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000	1.11688	0.558440	+	0.829545i	$0.311400\pi$
$98$	−2.00000	−0.202031
$99$	30.0000	3.01511
$100$	2.00000	0.200000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	18.0000	1.78227
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	0	0
$105$	−3.00000	−0.292770
$106$	−12.0000	−1.16554
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−18.0000	−1.73205
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	−10.0000	−0.953463
$111$	24.0000	2.27798
$112$	−4.00000	−0.377964
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	12.0000	1.12390
$115$	6.00000	0.559503
$116$	10.0000	0.928477
$117$	−6.00000	−0.554700
$118$	0	0
$119$	3.00000	0.275010
$120$	0	0
$121$	14.0000	1.27273
$122$	−20.0000	−1.81071
$123$	−18.0000	−1.62301
$124$	4.00000	0.359211
$125$	1.00000	0.0894427
$126$	−12.0000	−1.06904
$127$	−10.0000	−0.887357	−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000	−0.887357	−0.443678	+	0.896186i	$0.646327\pi$
$128$	0	0
$129$	12.0000	1.05654
$130$	2.00000	0.175412
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	−30.0000	−2.61116
$133$	2.00000	0.173422
$134$	−16.0000	−1.38219
$135$	−9.00000	−0.774597
$136$	0	0
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	36.0000	3.06452
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	2.00000	0.169031
$141$	3.00000	0.252646
$142$	−24.0000	−2.01404
$143$	−5.00000	−0.418121
$144$	−24.0000	−2.00000
$145$	5.00000	0.415227
$146$	20.0000	1.65521
$147$	−3.00000	−0.247436
$148$	−16.0000	−1.31519
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	6.00000	0.489898
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	0	0
$153$	18.0000	1.45521
$154$	−10.0000	−0.805823
$155$	2.00000	0.160644
$156$	6.00000	0.480384
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	−18.0000	−1.43200
$159$	−18.0000	−1.42749
$160$	8.00000	0.632456
$161$	6.00000	0.472866
$162$	−18.0000	−1.41421
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	12.0000	0.937043
$165$	−15.0000	−1.16775
$166$	−8.00000	−0.620920
$167$	−19.0000	−1.47026	−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000	−1.47026	−0.735132	+	0.677924i	$0.762880\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	−6.00000	−0.460179
$171$	12.0000	0.917663
$172$	−8.00000	−0.609994
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	30.0000	2.27429
$175$	1.00000	0.0755929
$176$	−20.0000	−1.50756
$177$	0	0
$178$	−24.0000	−1.79888
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	12.0000	0.894427
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	2.00000	0.148250
$183$	−30.0000	−2.21766
$184$	0	0
$185$	−8.00000	−0.588172
$186$	12.0000	0.879883
$187$	15.0000	1.09691
$188$	−2.00000	−0.145865
$189$	−9.00000	−0.654654
$190$	−4.00000	−0.290191
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	24.0000	1.73205
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−22.0000	−1.57951
$195$	3.00000	0.214834
$196$	2.00000	0.142857
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	−60.0000	−4.26401
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	0	0
$201$	−24.0000	−1.69283
$202$	24.0000	1.68863
$203$	5.00000	0.350931
$204$	−18.0000	−1.26025
$205$	6.00000	0.419058
$206$	−26.0000	−1.81151
$207$	36.0000	2.50217
$208$	4.00000	0.277350
$209$	10.0000	0.691714
$210$	6.00000	0.414039
$211$	17.0000	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$212$	12.0000	0.824163
$213$	−36.0000	−2.46668
$214$	−12.0000	−0.820303
$215$	−4.00000	−0.272798
$216$	0	0
$217$	2.00000	0.135769
$218$	−14.0000	−0.948200
$219$	30.0000	2.02721
$220$	10.0000	0.674200
$221$	−3.00000	−0.201802
$222$	−48.0000	−3.22155
$223$	−9.00000	−0.602685	−0.301342	−	0.953516i	$-0.597435\pi$
$223$	−9.00000	−0.602685	−0.301342	+	0.953516i	$0.597435\pi$
$224$	8.00000	0.534522
$225$	6.00000	0.400000
$226$	−24.0000	−1.59646
$227$	−21.0000	−1.39382	−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000	−1.39382	−0.696909	+	0.717159i	$0.745442\pi$
$228$	−12.0000	−0.794719
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−12.0000	−0.791257
$231$	−15.0000	−0.986928
$232$	0	0
$233$	4.00000	0.262049	0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000	0.262049	0.131024	+	0.991379i	$0.458173\pi$
$234$	12.0000	0.784465
$235$	−1.00000	−0.0652328
$236$	0	0
$237$	−27.0000	−1.75384
$238$	−6.00000	−0.388922
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	12.0000	0.774597
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	−28.0000	−1.79991
$243$	0	0
$244$	20.0000	1.28037
$245$	1.00000	0.0638877
$246$	36.0000	2.29528
$247$	−2.00000	−0.127257
$248$	0	0
$249$	−12.0000	−0.760469
$250$	−2.00000	−0.126491
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	12.0000	0.755929
$253$	30.0000	1.88608
$254$	20.0000	1.25491
$255$	−9.00000	−0.563602
$256$	16.0000	1.00000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	−24.0000	−1.49417
$259$	−8.00000	−0.497096
$260$	−2.00000	−0.124035
$261$	30.0000	1.85695
$262$	−28.0000	−1.72985
$263$	−26.0000	−1.60323	−0.801614	−	0.597841i	$-0.796025\pi$
$263$	−26.0000	−1.60323	−0.801614	+	0.597841i	$0.796025\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−4.00000	−0.245256
$267$	−36.0000	−2.20316
$268$	16.0000	0.977356
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	18.0000	1.09545
$271$	−6.00000	−0.364474	−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000	−0.364474	−0.182237	+	0.983255i	$0.558334\pi$
$272$	−12.0000	−0.727607
$273$	3.00000	0.181568
$274$	−32.0000	−1.93319
$275$	5.00000	0.301511
$276$	−36.0000	−2.16695
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	20.0000	1.19952
$279$	12.0000	0.718421
$280$	0	0
$281$	9.00000	0.536895	0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000	0.536895	0.268447	+	0.963294i	$0.413489\pi$
$282$	−6.00000	−0.357295
$283$	−31.0000	−1.84276	−0.921379	−	0.388664i	$-0.872937\pi$
$283$	−31.0000	−1.84276	−0.921379	+	0.388664i	$0.872937\pi$
$284$	24.0000	1.42414
$285$	−6.00000	−0.355409
$286$	10.0000	0.591312
$287$	6.00000	0.354169
$288$	48.0000	2.82843
$289$	−8.00000	−0.470588
$290$	−10.0000	−0.587220
$291$	−33.0000	−1.93449
$292$	−20.0000	−1.17041
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	0	0
$297$	−45.0000	−2.61116
$298$	−4.00000	−0.231714
$299$	−6.00000	−0.346989
$300$	−6.00000	−0.346410
$301$	−4.00000	−0.230556
$302$	18.0000	1.03578
$303$	36.0000	2.06815
$304$	−8.00000	−0.458831
$305$	10.0000	0.572598
$306$	−36.0000	−2.05798
$307$	−21.0000	−1.19853	−0.599267	−	0.800549i	$-0.704541\pi$
$307$	−21.0000	−1.19853	−0.599267	+	0.800549i	$0.704541\pi$
$308$	10.0000	0.569803
$309$	−39.0000	−2.21863
$310$	−4.00000	−0.227185
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	11.0000	0.621757	0.310878	−	0.950450i	$-0.399377\pi$
$313$	11.0000	0.621757	0.310878	+	0.950450i	$0.399377\pi$
$314$	12.0000	0.677199
$315$	6.00000	0.338062
$316$	18.0000	1.01258
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	36.0000	2.01878
$319$	25.0000	1.39973
$320$	−8.00000	−0.447214
$321$	−18.0000	−1.00466
$322$	−12.0000	−0.668734
$323$	6.00000	0.333849
$324$	18.0000	1.00000
$325$	−1.00000	−0.0554700
$326$	16.0000	0.886158
$327$	−21.0000	−1.16130
$328$	0	0
$329$	−1.00000	−0.0551318
$330$	30.0000	1.65145
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	8.00000	0.439057
$333$	−48.0000	−2.63038
$334$	38.0000	2.07927
$335$	8.00000	0.437087
$336$	12.0000	0.654654
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	24.0000	1.30543
$339$	−36.0000	−1.95525
$340$	6.00000	0.325396
$341$	10.0000	0.541530
$342$	−24.0000	−1.29777
$343$	1.00000	0.0539949
$344$	0	0
$345$	−18.0000	−0.969087
$346$	−22.0000	−1.18273
$347$	22.0000	1.18102	0.590511	−	0.807030i	$-0.298926\pi$
$347$	22.0000	1.18102	0.590511	+	0.807030i	$0.298926\pi$
$348$	−30.0000	−1.60817
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−2.00000	−0.106904
$351$	9.00000	0.480384
$352$	40.0000	2.13201
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	12.0000	0.636894
$356$	24.0000	1.27200
$357$	−9.00000	−0.476331
$358$	−24.0000	−1.26844
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−12.0000	−0.630706
$363$	−42.0000	−2.20443
$364$	−2.00000	−0.104828
$365$	−10.0000	−0.523424
$366$	60.0000	3.13625
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	−24.0000	−1.25109
$369$	36.0000	1.87409
$370$	16.0000	0.831800
$371$	6.00000	0.311504
$372$	−12.0000	−0.622171
$373$	32.0000	1.65690	0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000	1.65690	0.828449	+	0.560065i	$0.189224\pi$
$374$	−30.0000	−1.55126
$375$	−3.00000	−0.154919
$376$	0	0
$377$	−5.00000	−0.257513
$378$	18.0000	0.925820
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	4.00000	0.205196
$381$	30.0000	1.53695
$382$	−6.00000	−0.306987
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	5.00000	0.254824
$386$	−8.00000	−0.407189
$387$	−24.0000	−1.21999
$388$	22.0000	1.11688
$389$	31.0000	1.57176	0.785881	−	0.618378i	$-0.212210\pi$
$389$	31.0000	1.57176	0.785881	+	0.618378i	$0.212210\pi$
$390$	−6.00000	−0.303822
$391$	18.0000	0.910299
$392$	0	0
$393$	−42.0000	−2.11862
$394$	20.0000	1.00759
$395$	9.00000	0.452839
$396$	60.0000	3.01511
$397$	15.0000	0.752828	0.376414	−	0.926451i	$-0.377157\pi$
$397$	15.0000	0.752828	0.376414	+	0.926451i	$0.377157\pi$
$398$	8.00000	0.401004
$399$	−6.00000	−0.300376
$400$	−4.00000	−0.200000
$401$	25.0000	1.24844	0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000	1.24844	0.624220	+	0.781248i	$0.285417\pi$
$402$	48.0000	2.39402
$403$	−2.00000	−0.0996271
$404$	−24.0000	−1.19404
$405$	9.00000	0.447214
$406$	−10.0000	−0.496292
$407$	−40.0000	−1.98273
$408$	0	0
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	−12.0000	−0.592638
$411$	−48.0000	−2.36767
$412$	26.0000	1.28093
$413$	0	0
$414$	−72.0000	−3.53861
$415$	4.00000	0.196352
$416$	−8.00000	−0.392232
$417$	30.0000	1.46911
$418$	−20.0000	−0.978232
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	−6.00000	−0.292770
$421$	−11.0000	−0.536107	−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000	−0.536107	−0.268054	+	0.963404i	$0.586380\pi$
$422$	−34.0000	−1.65509
$423$	−6.00000	−0.291730
$424$	0	0
$425$	3.00000	0.145521
$426$	72.0000	3.48841
$427$	10.0000	0.483934
$428$	12.0000	0.580042
$429$	15.0000	0.724207
$430$	8.00000	0.385794
$431$	21.0000	1.01153	0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000	1.01153	0.505767	+	0.862670i	$0.331209\pi$
$432$	36.0000	1.73205
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	−4.00000	−0.192006
$435$	−15.0000	−0.719195
$436$	14.0000	0.670478
$437$	12.0000	0.574038
$438$	−60.0000	−2.86691
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	0	0
$441$	6.00000	0.285714
$442$	6.00000	0.285391
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	48.0000	2.27798
$445$	12.0000	0.568855
$446$	18.0000	0.852325
$447$	−6.00000	−0.283790
$448$	−8.00000	−0.377964
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	−12.0000	−0.565685
$451$	30.0000	1.41264
$452$	24.0000	1.12887
$453$	27.0000	1.26857
$454$	42.0000	1.97116
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	−2.00000	−0.0934539
$459$	−27.0000	−1.26025
$460$	12.0000	0.559503
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	30.0000	1.39573
$463$	−14.0000	−0.650635	−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000	−0.650635	−0.325318	+	0.945605i	$0.605471\pi$
$464$	−20.0000	−0.928477
$465$	−6.00000	−0.278243
$466$	−8.00000	−0.370593
$467$	−21.0000	−0.971764	−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000	−0.971764	−0.485882	+	0.874024i	$0.661502\pi$
$468$	−12.0000	−0.554700
$469$	8.00000	0.369406
$470$	2.00000	0.0922531
$471$	18.0000	0.829396
$472$	0	0
$473$	−20.0000	−0.919601
$474$	54.0000	2.48030
$475$	2.00000	0.0917663
$476$	6.00000	0.275010
$477$	36.0000	1.64833
$478$	30.0000	1.37217
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	−24.0000	−1.09545
$481$	8.00000	0.364769
$482$	−36.0000	−1.63976
$483$	−18.0000	−0.819028
$484$	28.0000	1.27273
$485$	11.0000	0.499484
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	0	0
$489$	24.0000	1.08532
$490$	−2.00000	−0.0903508
$491$	−13.0000	−0.586682	−0.293341	−	0.956008i	$-0.594767\pi$
$491$	−13.0000	−0.586682	−0.293341	+	0.956008i	$0.594767\pi$
$492$	−36.0000	−1.62301
$493$	15.0000	0.675566
$494$	4.00000	0.179969
$495$	30.0000	1.34840
$496$	−8.00000	−0.359211
$497$	12.0000	0.538274
$498$	24.0000	1.07547
$499$	−5.00000	−0.223831	−0.111915	−	0.993718i	$-0.535699\pi$
$499$	−5.00000	−0.223831	−0.111915	+	0.993718i	$0.535699\pi$
$500$	2.00000	0.0894427
$501$	57.0000	2.54657
$502$	36.0000	1.60676
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	−60.0000	−2.66733
$507$	36.0000	1.59882
$508$	−20.0000	−0.887357
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	18.0000	0.797053
$511$	−10.0000	−0.442374
$512$	−32.0000	−1.41421
$513$	−18.0000	−0.794719
$514$	44.0000	1.94076
$515$	13.0000	0.572848
$516$	24.0000	1.05654
$517$	−5.00000	−0.219900
$518$	16.0000	0.703000
$519$	−33.0000	−1.44854
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	−60.0000	−2.62613
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	28.0000	1.22319
$525$	−3.00000	−0.130931
$526$	52.0000	2.26731
$527$	6.00000	0.261364
$528$	60.0000	2.61116
$529$	13.0000	0.565217
$530$	−12.0000	−0.521247
$531$	0	0
$532$	4.00000	0.173422
$533$	−6.00000	−0.259889
$534$	72.0000	3.11574
$535$	6.00000	0.259403
$536$	0	0
$537$	−36.0000	−1.55351
$538$	56.0000	2.41433
$539$	5.00000	0.215365
$540$	−18.0000	−0.774597
$541$	43.0000	1.84871	0.924357	−	0.381528i	$-0.124602\pi$
$541$	43.0000	1.84871	0.924357	+	0.381528i	$0.124602\pi$
$542$	12.0000	0.515444
$543$	−18.0000	−0.772454
$544$	24.0000	1.02899
$545$	7.00000	0.299847
$546$	−6.00000	−0.256776
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	32.0000	1.36697
$549$	60.0000	2.56074
$550$	−10.0000	−0.426401
$551$	10.0000	0.426014
$552$	0	0
$553$	9.00000	0.382719
$554$	52.0000	2.20927
$555$	24.0000	1.01874
$556$	−20.0000	−0.848189
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	−24.0000	−1.01600
$559$	4.00000	0.169182
$560$	−4.00000	−0.169031
$561$	−45.0000	−1.89990
$562$	−18.0000	−0.759284
$563$	−20.0000	−0.842900	−0.421450	−	0.906852i	$-0.638479\pi$
$563$	−20.0000	−0.842900	−0.421450	+	0.906852i	$0.638479\pi$
$564$	6.00000	0.252646
$565$	12.0000	0.504844
$566$	62.0000	2.60605
$567$	9.00000	0.377964
$568$	0	0
$569$	38.0000	1.59304	0.796521	−	0.604610i	$-0.206671\pi$
$569$	38.0000	1.59304	0.796521	+	0.604610i	$0.206671\pi$
$570$	12.0000	0.502625
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	−10.0000	−0.418121
$573$	−9.00000	−0.375980
$574$	−12.0000	−0.500870
$575$	6.00000	0.250217
$576$	−48.0000	−2.00000
$577$	−1.00000	−0.0416305	−0.0208153	−	0.999783i	$-0.506626\pi$
$577$	−1.00000	−0.0416305	−0.0208153	+	0.999783i	$0.506626\pi$
$578$	16.0000	0.665512
$579$	−12.0000	−0.498703
$580$	10.0000	0.415227
$581$	4.00000	0.165948
$582$	66.0000	2.73579
$583$	30.0000	1.24247
$584$	0	0
$585$	−6.00000	−0.248069
$586$	42.0000	1.73500
$587$	−4.00000	−0.165098	−0.0825488	−	0.996587i	$-0.526306\pi$
$587$	−4.00000	−0.165098	−0.0825488	+	0.996587i	$0.526306\pi$
$588$	−6.00000	−0.247436
$589$	4.00000	0.164817
$590$	0	0
$591$	30.0000	1.23404
$592$	32.0000	1.31519
$593$	45.0000	1.84793	0.923964	−	0.382479i	$-0.124930\pi$
$593$	45.0000	1.84793	0.923964	+	0.382479i	$0.124930\pi$
$594$	90.0000	3.69274
$595$	3.00000	0.122988
$596$	4.00000	0.163846
$597$	12.0000	0.491127
$598$	12.0000	0.490716
$599$	−33.0000	−1.34834	−0.674172	−	0.738575i	$-0.735499\pi$
$599$	−33.0000	−1.34834	−0.674172	+	0.738575i	$0.735499\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	8.00000	0.326056
$603$	48.0000	1.95471
$604$	−18.0000	−0.732410
$605$	14.0000	0.569181
$606$	−72.0000	−2.92480
$607$	27.0000	1.09590	0.547948	−	0.836512i	$-0.315409\pi$
$607$	27.0000	1.09590	0.547948	+	0.836512i	$0.315409\pi$
$608$	16.0000	0.648886
$609$	−15.0000	−0.607831
$610$	−20.0000	−0.809776
$611$	1.00000	0.0404557
$612$	36.0000	1.45521
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	42.0000	1.69498
$615$	−18.0000	−0.725830
$616$	0	0
$617$	−36.0000	−1.44931	−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000	−1.44931	−0.724653	+	0.689114i	$0.758000\pi$
$618$	78.0000	3.13762
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	4.00000	0.160644
$621$	−54.0000	−2.16695
$622$	−48.0000	−1.92462
$623$	12.0000	0.480770
$624$	−12.0000	−0.480384
$625$	1.00000	0.0400000
$626$	−22.0000	−0.879297
$627$	−30.0000	−1.19808
$628$	−12.0000	−0.478852
$629$	−24.0000	−0.956943
$630$	−12.0000	−0.478091
$631$	25.0000	0.995234	0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000	0.995234	0.497617	+	0.867397i	$0.334208\pi$
$632$	0	0
$633$	−51.0000	−2.02707
$634$	−36.0000	−1.42974
$635$	−10.0000	−0.396838
$636$	−36.0000	−1.42749
$637$	−1.00000	−0.0396214
$638$	−50.0000	−1.97952
$639$	72.0000	2.84828
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	36.0000	1.42081
$643$	−7.00000	−0.276053	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	−7.00000	−0.276053	−0.138027	+	0.990429i	$0.544076\pi$
$644$	12.0000	0.472866
$645$	12.0000	0.472500
$646$	−12.0000	−0.472134
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	2.00000	0.0784465
$651$	−6.00000	−0.235159
$652$	−16.0000	−0.626608
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	42.0000	1.64233
$655$	14.0000	0.547025
$656$	−24.0000	−0.937043
$657$	−60.0000	−2.34082
$658$	2.00000	0.0779681
$659$	7.00000	0.272681	0.136341	−	0.990662i	$-0.456466\pi$
$659$	7.00000	0.272681	0.136341	+	0.990662i	$0.456466\pi$
$660$	−30.0000	−1.16775
$661$	−32.0000	−1.24466	−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000	−1.24466	−0.622328	+	0.782757i	$0.713813\pi$
$662$	16.0000	0.621858
$663$	9.00000	0.349531
$664$	0	0
$665$	2.00000	0.0775567
$666$	96.0000	3.71992
$667$	30.0000	1.16160
$668$	−38.0000	−1.47026
$669$	27.0000	1.04388
$670$	−16.0000	−0.618134
$671$	50.0000	1.93023
$672$	−24.0000	−0.925820
$673$	−44.0000	−1.69608	−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000	−1.69608	−0.848038	+	0.529936i	$0.822216\pi$
$674$	−16.0000	−0.616297
$675$	−9.00000	−0.346410
$676$	−24.0000	−0.923077
$677$	−33.0000	−1.26829	−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000	−1.26829	−0.634147	+	0.773213i	$0.718648\pi$
$678$	72.0000	2.76514
$679$	11.0000	0.422141
$680$	0	0
$681$	63.0000	2.41417
$682$	−20.0000	−0.765840
$683$	44.0000	1.68361	0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000	1.68361	0.841807	+	0.539779i	$0.181492\pi$
$684$	24.0000	0.917663
$685$	16.0000	0.611329
$686$	−2.00000	−0.0763604
$687$	−3.00000	−0.114457
$688$	16.0000	0.609994
$689$	−6.00000	−0.228582
$690$	36.0000	1.37050
$691$	−30.0000	−1.14125	−0.570627	−	0.821209i	$-0.693300\pi$
$691$	−30.0000	−1.14125	−0.570627	+	0.821209i	$0.693300\pi$
$692$	22.0000	0.836315
$693$	30.0000	1.13961
$694$	−44.0000	−1.67022
$695$	−10.0000	−0.379322
$696$	0	0
$697$	18.0000	0.681799
$698$	−4.00000	−0.151402
$699$	−12.0000	−0.453882
$700$	2.00000	0.0755929
$701$	−9.00000	−0.339925	−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000	−0.339925	−0.169963	+	0.985451i	$0.554365\pi$
$702$	−18.0000	−0.679366
$703$	−16.0000	−0.603451
$704$	−40.0000	−1.50756
$705$	3.00000	0.112987
$706$	−42.0000	−1.58069
$707$	−12.0000	−0.451306
$708$	0	0
$709$	−19.0000	−0.713560	−0.356780	−	0.934188i	$-0.616125\pi$
$709$	−19.0000	−0.713560	−0.356780	+	0.934188i	$0.616125\pi$
$710$	−24.0000	−0.900704
$711$	54.0000	2.02516
$712$	0	0
$713$	12.0000	0.449404
$714$	18.0000	0.673633
$715$	−5.00000	−0.186989
$716$	24.0000	0.896922
$717$	45.0000	1.68056
$718$	48.0000	1.79134
$719$	−10.0000	−0.372937	−0.186469	−	0.982461i	$-0.559704\pi$
$719$	−10.0000	−0.372937	−0.186469	+	0.982461i	$0.559704\pi$
$720$	−24.0000	−0.894427
$721$	13.0000	0.484145
$722$	30.0000	1.11648
$723$	−54.0000	−2.00828
$724$	12.0000	0.445976
$725$	5.00000	0.185695
$726$	84.0000	3.11753
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	20.0000	0.740233
$731$	−12.0000	−0.443836
$732$	−60.0000	−2.21766
$733$	−19.0000	−0.701781	−0.350891	−	0.936416i	$-0.614121\pi$
$733$	−19.0000	−0.701781	−0.350891	+	0.936416i	$0.614121\pi$
$734$	−34.0000	−1.25496
$735$	−3.00000	−0.110657
$736$	48.0000	1.76930
$737$	40.0000	1.47342
$738$	−72.0000	−2.65036
$739$	−29.0000	−1.06678	−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000	−1.06678	−0.533391	+	0.845869i	$0.679083\pi$
$740$	−16.0000	−0.588172
$741$	6.00000	0.220416
$742$	−12.0000	−0.440534
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	−64.0000	−2.34321
$747$	24.0000	0.878114
$748$	30.0000	1.09691
$749$	6.00000	0.219235
$750$	6.00000	0.219089
$751$	15.0000	0.547358	0.273679	−	0.961821i	$-0.411759\pi$
$751$	15.0000	0.547358	0.273679	+	0.961821i	$0.411759\pi$
$752$	4.00000	0.145865
$753$	54.0000	1.96787
$754$	10.0000	0.364179
$755$	−9.00000	−0.327544
$756$	−18.0000	−0.654654
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−8.00000	−0.290573
$759$	−90.0000	−3.26679
$760$	0	0
$761$	30.0000	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$762$	−60.0000	−2.17357
$763$	7.00000	0.253417
$764$	6.00000	0.217072
$765$	18.0000	0.650791
$766$	32.0000	1.15621
$767$	0	0
$768$	−48.0000	−1.73205
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	−10.0000	−0.360375
$771$	66.0000	2.37693
$772$	8.00000	0.287926
$773$	31.0000	1.11499	0.557496	−	0.830179i	$-0.311762\pi$
$773$	31.0000	1.11499	0.557496	+	0.830179i	$0.311762\pi$
$774$	48.0000	1.72532
$775$	2.00000	0.0718421
$776$	0	0
$777$	24.0000	0.860995
$778$	−62.0000	−2.22281
$779$	12.0000	0.429945
$780$	6.00000	0.214834
$781$	60.0000	2.14697
$782$	−36.0000	−1.28736
$783$	−45.0000	−1.60817
$784$	−4.00000	−0.142857
$785$	−6.00000	−0.214149
$786$	84.0000	2.99618
$787$	−7.00000	−0.249523	−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000	−0.249523	−0.124762	+	0.992187i	$0.539817\pi$
$788$	−20.0000	−0.712470
$789$	78.0000	2.77687
$790$	−18.0000	−0.640411
$791$	12.0000	0.426671
$792$	0	0
$793$	−10.0000	−0.355110
$794$	−30.0000	−1.06466
$795$	−18.0000	−0.638394
$796$	−8.00000	−0.283552
$797$	−39.0000	−1.38145	−0.690725	−	0.723117i	$-0.742709\pi$
$797$	−39.0000	−1.38145	−0.690725	+	0.723117i	$0.742709\pi$
$798$	12.0000	0.424795
$799$	−3.00000	−0.106132
$800$	8.00000	0.282843
$801$	72.0000	2.54399
$802$	−50.0000	−1.76556
$803$	−50.0000	−1.76446
$804$	−48.0000	−1.69283
$805$	6.00000	0.211472
$806$	4.00000	0.140894
$807$	84.0000	2.95694
$808$	0	0
$809$	27.0000	0.949269	0.474635	−	0.880183i	$-0.342580\pi$
$809$	27.0000	0.949269	0.474635	+	0.880183i	$0.342580\pi$
$810$	−18.0000	−0.632456
$811$	38.0000	1.33436	0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000	1.33436	0.667180	+	0.744896i	$0.267501\pi$
$812$	10.0000	0.350931
$813$	18.0000	0.631288
$814$	80.0000	2.80400
$815$	−8.00000	−0.280228
$816$	36.0000	1.26025
$817$	−8.00000	−0.279885
$818$	8.00000	0.279713
$819$	−6.00000	−0.209657
$820$	12.0000	0.419058
$821$	45.0000	1.57051	0.785255	−	0.619172i	$-0.212532\pi$
$821$	45.0000	1.57051	0.785255	+	0.619172i	$0.212532\pi$
$822$	96.0000	3.34838
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	−15.0000	−0.522233
$826$	0	0
$827$	−14.0000	−0.486828	−0.243414	−	0.969923i	$-0.578267\pi$
$827$	−14.0000	−0.486828	−0.243414	+	0.969923i	$0.578267\pi$
$828$	72.0000	2.50217
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	−8.00000	−0.277684
$831$	78.0000	2.70579
$832$	8.00000	0.277350
$833$	3.00000	0.103944
$834$	−60.0000	−2.07763
$835$	−19.0000	−0.657522
$836$	20.0000	0.691714
$837$	−18.0000	−0.622171
$838$	32.0000	1.10542
$839$	−30.0000	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	22.0000	0.758170
$843$	−27.0000	−0.929929
$844$	34.0000	1.17033
$845$	−12.0000	−0.412813
$846$	12.0000	0.412568
$847$	14.0000	0.481046
$848$	−24.0000	−0.824163
$849$	93.0000	3.19175
$850$	−6.00000	−0.205798
$851$	−48.0000	−1.64542
$852$	−72.0000	−2.46668
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	−20.0000	−0.684386
$855$	12.0000	0.410391
$856$	0	0
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	−30.0000	−1.02418
$859$	−48.0000	−1.63774	−0.818869	−	0.573980i	$-0.805399\pi$
$859$	−48.0000	−1.63774	−0.818869	+	0.573980i	$0.805399\pi$
$860$	−8.00000	−0.272798
$861$	−18.0000	−0.613438
$862$	−42.0000	−1.43053
$863$	−40.0000	−1.36162	−0.680808	−	0.732462i	$-0.738371\pi$
$863$	−40.0000	−1.36162	−0.680808	+	0.732462i	$0.738371\pi$
$864$	−72.0000	−2.44949
$865$	11.0000	0.374011
$866$	−68.0000	−2.31073
$867$	24.0000	0.815083
$868$	4.00000	0.135769
$869$	45.0000	1.52652
$870$	30.0000	1.01710
$871$	−8.00000	−0.271070
$872$	0	0
$873$	66.0000	2.23376
$874$	−24.0000	−0.811812
$875$	1.00000	0.0338062
$876$	60.0000	2.02721
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	28.0000	0.944954
$879$	63.0000	2.12494
$880$	−20.0000	−0.674200
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	−12.0000	−0.404061
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	−36.0000	−1.20944
$887$	16.0000	0.537227	0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000	0.537227	0.268614	+	0.963248i	$0.413434\pi$
$888$	0	0
$889$	−10.0000	−0.335389
$890$	−24.0000	−0.804482
$891$	45.0000	1.50756
$892$	−18.0000	−0.602685
$893$	−2.00000	−0.0669274
$894$	12.0000	0.401340
$895$	12.0000	0.401116
$896$	0	0
$897$	18.0000	0.601003
$898$	18.0000	0.600668
$899$	10.0000	0.333519
$900$	12.0000	0.400000
$901$	18.0000	0.599667
$902$	−60.0000	−1.99778
$903$	12.0000	0.399335
$904$	0	0
$905$	6.00000	0.199447
$906$	−54.0000	−1.79403
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	−42.0000	−1.39382
$909$	−72.0000	−2.38809
$910$	2.00000	0.0662994
$911$	−20.0000	−0.662630	−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000	−0.662630	−0.331315	+	0.943520i	$0.607492\pi$
$912$	24.0000	0.794719
$913$	20.0000	0.661903
$914$	−44.0000	−1.45539
$915$	−30.0000	−0.991769
$916$	2.00000	0.0660819
$917$	14.0000	0.462321
$918$	54.0000	1.78227
$919$	23.0000	0.758700	0.379350	−	0.925253i	$-0.376148\pi$
$919$	23.0000	0.758700	0.379350	+	0.925253i	$0.376148\pi$
$920$	0	0
$921$	63.0000	2.07592
$922$	28.0000	0.922131
$923$	−12.0000	−0.394985
$924$	−30.0000	−0.986928
$925$	−8.00000	−0.263038
$926$	28.0000	0.920137
$927$	78.0000	2.56186
$928$	40.0000	1.31306
$929$	16.0000	0.524943	0.262471	−	0.964940i	$-0.415462\pi$
$929$	16.0000	0.524943	0.262471	+	0.964940i	$0.415462\pi$
$930$	12.0000	0.393496
$931$	2.00000	0.0655474
$932$	8.00000	0.262049
$933$	−72.0000	−2.35717
$934$	42.0000	1.37428
$935$	15.0000	0.490552
$936$	0	0
$937$	17.0000	0.555366	0.277683	−	0.960673i	$-0.410434\pi$
$937$	17.0000	0.555366	0.277683	+	0.960673i	$0.410434\pi$
$938$	−16.0000	−0.522419
$939$	−33.0000	−1.07691
$940$	−2.00000	−0.0652328
$941$	−12.0000	−0.391189	−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000	−0.391189	−0.195594	+	0.980685i	$0.562664\pi$
$942$	−36.0000	−1.17294
$943$	36.0000	1.17232
$944$	0	0
$945$	−9.00000	−0.292770
$946$	40.0000	1.30051
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	−54.0000	−1.75384
$949$	10.0000	0.324614
$950$	−4.00000	−0.129777
$951$	−54.0000	−1.75107
$952$	0	0
$953$	−14.0000	−0.453504	−0.226752	−	0.973952i	$-0.572811\pi$
$953$	−14.0000	−0.453504	−0.226752	+	0.973952i	$0.572811\pi$
$954$	−72.0000	−2.33109
$955$	3.00000	0.0970777
$956$	−30.0000	−0.970269
$957$	−75.0000	−2.42441
$958$	72.0000	2.32621
$959$	16.0000	0.516667
$960$	24.0000	0.774597
$961$	−27.0000	−0.870968
$962$	−16.0000	−0.515861
$963$	36.0000	1.16008
$964$	36.0000	1.15948
$965$	4.00000	0.128765
$966$	36.0000	1.15828
$967$	22.0000	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$968$	0	0
$969$	−18.0000	−0.578243
$970$	−22.0000	−0.706377
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	0	0
$973$	−10.0000	−0.320585
$974$	16.0000	0.512673
$975$	3.00000	0.0960769
$976$	−40.0000	−1.28037
$977$	−32.0000	−1.02377	−0.511885	−	0.859054i	$-0.671053\pi$
$977$	−32.0000	−1.02377	−0.511885	+	0.859054i	$0.671053\pi$
$978$	−48.0000	−1.53487
$979$	60.0000	1.91761
$980$	2.00000	0.0638877
$981$	42.0000	1.34096
$982$	26.0000	0.829693
$983$	53.0000	1.69044	0.845219	−	0.534421i	$-0.179470\pi$
$983$	53.0000	1.69044	0.845219	+	0.534421i	$0.179470\pi$
$984$	0	0
$985$	−10.0000	−0.318626
$986$	−30.0000	−0.955395
$987$	3.00000	0.0954911
$988$	−4.00000	−0.127257
$989$	−24.0000	−0.763156
$990$	−60.0000	−1.90693
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	16.0000	0.508001
$993$	24.0000	0.761617
$994$	−24.0000	−0.761234
$995$	−4.00000	−0.126809
$996$	−24.0000	−0.760469
$997$	19.0000	0.601736	0.300868	−	0.953666i	$-0.402724\pi$
$997$	19.0000	0.601736	0.300868	+	0.953666i	$0.402724\pi$
$998$	10.0000	0.316544
$999$	72.0000	2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.a.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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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