LMFDB - Embedded newform 80.10.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,10,Mod(1,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("80.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	80.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:	$41.2028668931$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	80.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+204.000 q^{3} +625.000 q^{5} -5432.00 q^{7} +21933.0 q^{9} +O(q^{10})$

$q+204.000 q^{3} +625.000 q^{5} -5432.00 q^{7} +21933.0 q^{9} -73932.0 q^{11} -114514. q^{13} +127500. q^{15} +41682.0 q^{17} -1.05746e6 q^{19} -1.10813e6 q^{21} -1.59934e6 q^{23} +390625. q^{25} +459000. q^{27} +2.18451e6 q^{29} +9.61965e6 q^{31} -1.50821e7 q^{33} -3.39500e6 q^{35} +4.79994e6 q^{37} -2.33609e7 q^{39} +9.53188e6 q^{41} +1.34645e7 q^{43} +1.37081e7 q^{45} -1.14420e7 q^{47} -1.08470e7 q^{49} +8.50313e6 q^{51} +5.36158e7 q^{53} -4.62075e7 q^{55} -2.15722e8 q^{57} -8.18626e7 q^{59} -1.04691e8 q^{61} -1.19140e8 q^{63} -7.15712e7 q^{65} -1.40571e8 q^{67} -3.26265e8 q^{69} -9.70988e7 q^{71} +1.71849e8 q^{73} +7.96875e7 q^{75} +4.01599e8 q^{77} +1.17380e8 q^{79} -3.38071e8 q^{81} -3.23638e8 q^{83} +2.60512e7 q^{85} +4.45640e8 q^{87} -8.94379e8 q^{89} +6.22040e8 q^{91} +1.96241e9 q^{93} -6.60912e8 q^{95} +2.32679e8 q^{97} -1.62155e9 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	204.000	1.45407	0.727034	−	0.686602i	$-0.240898\pi$
$3$	204.000	1.45407	0.727034	+	0.686602i	$0.240898\pi$
$4$	0	0
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	0	0
$7$	−5432.00	−0.855103	−0.427552	−	0.903991i	$-0.640624\pi$
$7$	−5432.00	−0.855103	−0.427552	+	0.903991i	$0.640624\pi$
$8$	0	0
$9$	21933.0	1.11431
$10$	0	0
$11$	−73932.0	−1.52253	−0.761264	−	0.648442i	$-0.775421\pi$
$11$	−73932.0	−1.52253	−0.761264	+	0.648442i	$0.775421\pi$
$12$	0	0
$13$	−114514.	−1.11202	−0.556011	−	0.831175i	$-0.687669\pi$
$13$	−114514.	−1.11202	−0.556011	+	0.831175i	$0.687669\pi$
$14$	0	0
$15$	127500.	0.650279
$16$	0	0
$17$	41682.0	0.121040	0.0605199	−	0.998167i	$-0.480724\pi$
$17$	41682.0	0.121040	0.0605199	+	0.998167i	$0.480724\pi$
$18$	0	0
$19$	−1.05746e6	−1.86154	−0.930771	−	0.365603i	$-0.880863\pi$
$19$	−1.05746e6	−1.86154	−0.930771	+	0.365603i	$0.880863\pi$
$20$	0	0
$21$	−1.10813e6	−1.24338
$22$	0	0
$23$	−1.59934e6	−1.19169	−0.595847	−	0.803098i	$-0.703183\pi$
$23$	−1.59934e6	−1.19169	−0.595847	+	0.803098i	$0.703183\pi$
$24$	0	0
$25$	390625.	0.200000
$26$	0	0
$27$	459000.	0.166217
$28$	0	0
$29$	2.18451e6	0.573539	0.286770	−	0.958000i	$-0.407419\pi$
$29$	2.18451e6	0.573539	0.286770	+	0.958000i	$0.407419\pi$
$30$	0	0
$31$	9.61965e6	1.87082	0.935409	−	0.353567i	$-0.115032\pi$
$31$	9.61965e6	1.87082	0.935409	+	0.353567i	$0.115032\pi$
$32$	0	0
$33$	−1.50821e7	−2.21386
$34$	0	0
$35$	−3.39500e6	−0.382414
$36$	0	0
$37$	4.79994e6	0.421045	0.210522	−	0.977589i	$-0.432484\pi$
$37$	4.79994e6	0.421045	0.210522	+	0.977589i	$0.432484\pi$
$38$	0	0
$39$	−2.33609e7	−1.61696
$40$	0	0
$41$	9.53188e6	0.526807	0.263403	−	0.964686i	$-0.415155\pi$
$41$	9.53188e6	0.526807	0.263403	+	0.964686i	$0.415155\pi$
$42$	0	0
$43$	1.34645e7	0.600595	0.300297	−	0.953846i	$-0.402914\pi$
$43$	1.34645e7	0.600595	0.300297	+	0.953846i	$0.402914\pi$
$44$	0	0
$45$	1.37081e7	0.498335
$46$	0	0
$47$	−1.14420e7	−0.342027	−0.171013	−	0.985269i	$-0.554704\pi$
$47$	−1.14420e7	−0.342027	−0.171013	+	0.985269i	$0.554704\pi$
$48$	0	0
$49$	−1.08470e7	−0.268798
$50$	0	0
$51$	8.50313e6	0.176000
$52$	0	0
$53$	5.36158e7	0.933364	0.466682	−	0.884425i	$-0.345449\pi$
$53$	5.36158e7	0.933364	0.466682	+	0.884425i	$0.345449\pi$
$54$	0	0
$55$	−4.62075e7	−0.680895
$56$	0	0
$57$	−2.15722e8	−2.70681
$58$	0	0
$59$	−8.18626e7	−0.879532	−0.439766	−	0.898112i	$-0.644939\pi$
$59$	−8.18626e7	−0.879532	−0.439766	+	0.898112i	$0.644939\pi$
$60$	0	0
$61$	−1.04691e8	−0.968114	−0.484057	−	0.875037i	$-0.660837\pi$
$61$	−1.04691e8	−0.968114	−0.484057	+	0.875037i	$0.660837\pi$
$62$	0	0
$63$	−1.19140e8	−0.952852
$64$	0	0
$65$	−7.15712e7	−0.497311
$66$	0	0
$67$	−1.40571e8	−0.852235	−0.426118	−	0.904668i	$-0.640119\pi$
$67$	−1.40571e8	−0.852235	−0.426118	+	0.904668i	$0.640119\pi$
$68$	0	0
$69$	−3.26265e8	−1.73280
$70$	0	0
$71$	−9.70988e7	−0.453473	−0.226736	−	0.973956i	$-0.572806\pi$
$71$	−9.70988e7	−0.453473	−0.226736	+	0.973956i	$0.572806\pi$
$72$	0	0
$73$	1.71849e8	0.708262	0.354131	−	0.935196i	$-0.384777\pi$
$73$	1.71849e8	0.708262	0.354131	+	0.935196i	$0.384777\pi$
$74$	0	0
$75$	7.96875e7	0.290813
$76$	0	0
$77$	4.01599e8	1.30192
$78$	0	0
$79$	1.17380e8	0.339057	0.169528	−	0.985525i	$-0.445776\pi$
$79$	1.17380e8	0.339057	0.169528	+	0.985525i	$0.445776\pi$
$80$	0	0
$81$	−3.38071e8	−0.872621
$82$	0	0
$83$	−3.23638e8	−0.748527	−0.374264	−	0.927322i	$-0.622104\pi$
$83$	−3.23638e8	−0.748527	−0.374264	+	0.927322i	$0.622104\pi$
$84$	0	0
$85$	2.60512e7	0.0541307
$86$	0	0
$87$	4.45640e8	0.833965
$88$	0	0
$89$	−8.94379e8	−1.51101	−0.755504	−	0.655144i	$-0.772608\pi$
$89$	−8.94379e8	−1.51101	−0.755504	+	0.655144i	$0.772608\pi$
$90$	0	0
$91$	6.22040e8	0.950894
$92$	0	0
$93$	1.96241e9	2.72030
$94$	0	0
$95$	−6.60912e8	−0.832507
$96$	0	0
$97$	2.32679e8	0.266860	0.133430	−	0.991058i	$-0.457401\pi$
$97$	2.32679e8	0.266860	0.133430	+	0.991058i	$0.457401\pi$
$98$	0	0
$99$	−1.62155e9	−1.69657
$100$	0	0
$101$	6.51288e8	0.622769	0.311384	−	0.950284i	$-0.399207\pi$
$101$	6.51288e8	0.622769	0.311384	+	0.950284i	$0.399207\pi$
$102$	0	0
$103$	1.71129e9	1.49815	0.749076	−	0.662484i	$-0.230498\pi$
$103$	1.71129e9	1.49815	0.749076	+	0.662484i	$0.230498\pi$
$104$	0	0
$105$	−6.92580e8	−0.556055
$106$	0	0
$107$	1.31553e9	0.970228	0.485114	−	0.874451i	$-0.338778\pi$
$107$	1.31553e9	0.970228	0.485114	+	0.874451i	$0.338778\pi$
$108$	0	0
$109$	3.10670e8	0.210805	0.105402	−	0.994430i	$-0.466387\pi$
$109$	3.10670e8	0.210805	0.105402	+	0.994430i	$0.466387\pi$
$110$	0	0
$111$	9.79188e8	0.612227
$112$	0	0
$113$	−2.74850e9	−1.58578	−0.792889	−	0.609366i	$-0.791424\pi$
$113$	−2.74850e9	−1.58578	−0.792889	+	0.609366i	$0.791424\pi$
$114$	0	0
$115$	−9.99585e8	−0.532941
$116$	0	0
$117$	−2.51164e9	−1.23914
$118$	0	0
$119$	−2.26417e8	−0.103502
$120$	0	0
$121$	3.10799e9	1.31809
$122$	0	0
$123$	1.94450e9	0.766012
$124$	0	0
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	−2.64323e9	−0.901608	−0.450804	−	0.892623i	$-0.648863\pi$
$127$	−2.64323e9	−0.901608	−0.450804	+	0.892623i	$0.648863\pi$
$128$	0	0
$129$	2.74675e9	0.873305
$130$	0	0
$131$	2.63724e9	0.782401	0.391201	−	0.920305i	$-0.372060\pi$
$131$	2.63724e9	0.782401	0.391201	+	0.920305i	$0.372060\pi$
$132$	0	0
$133$	5.74412e9	1.59181
$134$	0	0
$135$	2.86875e8	0.0743346
$136$	0	0
$137$	5.16539e9	1.25274	0.626370	−	0.779526i	$-0.284540\pi$
$137$	5.16539e9	1.25274	0.626370	+	0.779526i	$0.284540\pi$
$138$	0	0
$139$	−2.76751e9	−0.628815	−0.314407	−	0.949288i	$-0.601806\pi$
$139$	−2.76751e9	−0.628815	−0.314407	+	0.949288i	$0.601806\pi$
$140$	0	0
$141$	−2.33416e9	−0.497330
$142$	0	0
$143$	8.46625e9	1.69309
$144$	0	0
$145$	1.36532e9	0.256494
$146$	0	0
$147$	−2.21278e9	−0.390851
$148$	0	0
$149$	−6.04151e9	−1.00417	−0.502085	−	0.864818i	$-0.667434\pi$
$149$	−6.04151e9	−1.00417	−0.502085	+	0.864818i	$0.667434\pi$
$150$	0	0
$151$	−4.07206e8	−0.0637408	−0.0318704	−	0.999492i	$-0.510146\pi$
$151$	−4.07206e8	−0.0637408	−0.0318704	+	0.999492i	$0.510146\pi$
$152$	0	0
$153$	9.14211e8	0.134876
$154$	0	0
$155$	6.01228e9	0.836655
$156$	0	0
$157$	1.80938e8	0.0237674	0.0118837	−	0.999929i	$-0.496217\pi$
$157$	1.80938e8	0.0237674	0.0118837	+	0.999929i	$0.496217\pi$
$158$	0	0
$159$	1.09376e10	1.35717
$160$	0	0
$161$	8.68759e9	1.01902
$162$	0	0
$163$	−5.88002e9	−0.652432	−0.326216	−	0.945295i	$-0.605774\pi$
$163$	−5.88002e9	−0.652432	−0.326216	+	0.945295i	$0.605774\pi$
$164$	0	0
$165$	−9.42633e9	−0.990068
$166$	0	0
$167$	−1.36197e9	−0.135501	−0.0677507	−	0.997702i	$-0.521582\pi$
$167$	−1.36197e9	−0.135501	−0.0677507	+	0.997702i	$0.521582\pi$
$168$	0	0
$169$	2.50896e9	0.236594
$170$	0	0
$171$	−2.31933e10	−2.07434
$172$	0	0
$173$	−1.41778e10	−1.20338	−0.601688	−	0.798731i	$-0.705505\pi$
$173$	−1.41778e10	−1.20338	−0.601688	+	0.798731i	$0.705505\pi$
$174$	0	0
$175$	−2.12188e9	−0.171021
$176$	0	0
$177$	−1.67000e10	−1.27890
$178$	0	0
$179$	−2.66456e9	−0.193993	−0.0969967	−	0.995285i	$-0.530924\pi$
$179$	−2.66456e9	−0.193993	−0.0969967	+	0.995285i	$0.530924\pi$
$180$	0	0
$181$	−4.05446e9	−0.280789	−0.140394	−	0.990096i	$-0.544837\pi$
$181$	−4.05446e9	−0.280789	−0.140394	+	0.990096i	$0.544837\pi$
$182$	0	0
$183$	−2.13570e10	−1.40770
$184$	0	0
$185$	2.99996e9	0.188297
$186$	0	0
$187$	−3.08163e9	−0.184287
$188$	0	0
$189$	−2.49329e9	−0.142133
$190$	0	0
$191$	1.01385e10	0.551216	0.275608	−	0.961270i	$-0.411121\pi$
$191$	1.01385e10	0.551216	0.275608	+	0.961270i	$0.411121\pi$
$192$	0	0
$193$	−7.57686e9	−0.393080	−0.196540	−	0.980496i	$-0.562971\pi$
$193$	−7.57686e9	−0.393080	−0.196540	+	0.980496i	$0.562971\pi$
$194$	0	0
$195$	−1.46005e10	−0.723124
$196$	0	0
$197$	−2.20768e8	−0.0104433	−0.00522166	−	0.999986i	$-0.501662\pi$
$197$	−2.20768e8	−0.0104433	−0.00522166	+	0.999986i	$0.501662\pi$
$198$	0	0
$199$	2.99296e10	1.35289	0.676445	−	0.736493i	$-0.263519\pi$
$199$	2.99296e10	1.35289	0.676445	+	0.736493i	$0.263519\pi$
$200$	0	0
$201$	−2.86765e10	−1.23921
$202$	0	0
$203$	−1.18663e10	−0.490435
$204$	0	0
$205$	5.95743e9	0.235595
$206$	0	0
$207$	−3.50782e10	−1.32792
$208$	0	0
$209$	7.81801e10	2.83425
$210$	0	0
$211$	−2.92533e10	−1.01602	−0.508012	−	0.861350i	$-0.669619\pi$
$211$	−2.92533e10	−1.01602	−0.508012	+	0.861350i	$0.669619\pi$
$212$	0	0
$213$	−1.98082e10	−0.659380
$214$	0	0
$215$	8.41530e9	0.268594
$216$	0	0
$217$	−5.22539e10	−1.59974
$218$	0	0
$219$	3.50572e10	1.02986
$220$	0	0
$221$	−4.77317e9	−0.134599
$222$	0	0
$223$	5.18482e10	1.40398	0.701991	−	0.712186i	$-0.252295\pi$
$223$	5.18482e10	1.40398	0.701991	+	0.712186i	$0.252295\pi$
$224$	0	0
$225$	8.56758e9	0.222862
$226$	0	0
$227$	−4.56273e10	−1.14053	−0.570267	−	0.821460i	$-0.693160\pi$
$227$	−4.56273e10	−1.14053	−0.570267	+	0.821460i	$0.693160\pi$
$228$	0	0
$229$	6.21495e10	1.49341	0.746703	−	0.665158i	$-0.231636\pi$
$229$	6.21495e10	1.49341	0.746703	+	0.665158i	$0.231636\pi$
$230$	0	0
$231$	8.19261e10	1.89308
$232$	0	0
$233$	−3.72165e9	−0.0827245	−0.0413623	−	0.999144i	$-0.513170\pi$
$233$	−3.72165e9	−0.0827245	−0.0413623	+	0.999144i	$0.513170\pi$
$234$	0	0
$235$	−7.15122e9	−0.152959
$236$	0	0
$237$	2.39455e10	0.493011
$238$	0	0
$239$	−3.62221e9	−0.0718098	−0.0359049	−	0.999355i	$-0.511431\pi$
$239$	−3.62221e9	−0.0718098	−0.0359049	+	0.999355i	$0.511431\pi$
$240$	0	0
$241$	−3.36556e10	−0.642660	−0.321330	−	0.946967i	$-0.604130\pi$
$241$	−3.36556e10	−0.642660	−0.321330	+	0.946967i	$0.604130\pi$
$242$	0	0
$243$	−7.80010e10	−1.43507
$244$	0	0
$245$	−6.77936e9	−0.120210
$246$	0	0
$247$	1.21094e11	2.07008
$248$	0	0
$249$	−6.60221e10	−1.08841
$250$	0	0
$251$	5.88110e10	0.935248	0.467624	−	0.883928i	$-0.345110\pi$
$251$	5.88110e10	0.935248	0.467624	+	0.883928i	$0.345110\pi$
$252$	0	0
$253$	1.18242e11	1.81439
$254$	0	0
$255$	5.31446e9	0.0787096
$256$	0	0
$257$	−7.52072e10	−1.07538	−0.537688	−	0.843144i	$-0.680702\pi$
$257$	−7.52072e10	−1.07538	−0.537688	+	0.843144i	$0.680702\pi$
$258$	0	0
$259$	−2.60733e10	−0.360037
$260$	0	0
$261$	4.79129e10	0.639101
$262$	0	0
$263$	1.16316e10	0.149913	0.0749565	−	0.997187i	$-0.476118\pi$
$263$	1.16316e10	0.149913	0.0749565	+	0.997187i	$0.476118\pi$
$264$	0	0
$265$	3.35099e10	0.417413
$266$	0	0
$267$	−1.82453e11	−2.19711
$268$	0	0
$269$	2.83871e10	0.330549	0.165275	−	0.986248i	$-0.447149\pi$
$269$	2.83871e10	0.330549	0.165275	+	0.986248i	$0.447149\pi$
$270$	0	0
$271$	−1.47987e11	−1.66672	−0.833361	−	0.552729i	$-0.813586\pi$
$271$	−1.47987e11	−1.66672	−0.833361	+	0.552729i	$0.813586\pi$
$272$	0	0
$273$	1.26896e11	1.38266
$274$	0	0
$275$	−2.88797e10	−0.304506
$276$	0	0
$277$	−7.58857e10	−0.774464	−0.387232	−	0.921982i	$-0.626569\pi$
$277$	−7.58857e10	−0.774464	−0.387232	+	0.921982i	$0.626569\pi$
$278$	0	0
$279$	2.10988e11	2.08467
$280$	0	0
$281$	1.72151e11	1.64714	0.823570	−	0.567215i	$-0.191979\pi$
$281$	1.72151e11	1.64714	0.823570	+	0.567215i	$0.191979\pi$
$282$	0	0
$283$	1.49932e11	1.38949	0.694745	−	0.719256i	$-0.255517\pi$
$283$	1.49932e11	1.38949	0.694745	+	0.719256i	$0.255517\pi$
$284$	0	0
$285$	−1.34826e11	−1.21052
$286$	0	0
$287$	−5.17772e10	−0.450474
$288$	0	0
$289$	−1.16850e11	−0.985349
$290$	0	0
$291$	4.74664e10	0.388032
$292$	0	0
$293$	9.51745e9	0.0754426	0.0377213	−	0.999288i	$-0.487990\pi$
$293$	9.51745e9	0.0754426	0.0377213	+	0.999288i	$0.487990\pi$
$294$	0	0
$295$	−5.11641e10	−0.393339
$296$	0	0
$297$	−3.39348e10	−0.253070
$298$	0	0
$299$	1.83146e11	1.32519
$300$	0	0
$301$	−7.31391e10	−0.513571
$302$	0	0
$303$	1.32863e11	0.905547
$304$	0	0
$305$	−6.54321e10	−0.432954
$306$	0	0
$307$	−9.05900e10	−0.582046	−0.291023	−	0.956716i	$-0.593996\pi$
$307$	−9.05900e10	−0.582046	−0.291023	+	0.956716i	$0.593996\pi$
$308$	0	0
$309$	3.49103e11	2.17841
$310$	0	0
$311$	2.81285e11	1.70500	0.852501	−	0.522726i	$-0.175085\pi$
$311$	2.81285e11	1.70500	0.852501	+	0.522726i	$0.175085\pi$
$312$	0	0
$313$	−9.11248e10	−0.536645	−0.268323	−	0.963329i	$-0.586469\pi$
$313$	−9.11248e10	−0.536645	−0.268323	+	0.963329i	$0.586469\pi$
$314$	0	0
$315$	−7.44625e10	−0.426128
$316$	0	0
$317$	1.03167e11	0.573819	0.286909	−	0.957958i	$-0.407372\pi$
$317$	1.03167e11	0.573819	0.286909	+	0.957958i	$0.407372\pi$
$318$	0	0
$319$	−1.61505e11	−0.873230
$320$	0	0
$321$	2.68368e11	1.41078
$322$	0	0
$323$	−4.40770e10	−0.225321
$324$	0	0
$325$	−4.47320e10	−0.222404
$326$	0	0
$327$	6.33767e10	0.306524
$328$	0	0
$329$	6.21527e10	0.292468
$330$	0	0
$331$	−2.51080e11	−1.14970	−0.574851	−	0.818258i	$-0.694940\pi$
$331$	−2.51080e11	−1.14970	−0.574851	+	0.818258i	$0.694940\pi$
$332$	0	0
$333$	1.05277e11	0.469175
$334$	0	0
$335$	−8.78569e10	−0.381131
$336$	0	0
$337$	−4.04967e11	−1.71035	−0.855175	−	0.518339i	$-0.826550\pi$
$337$	−4.04967e11	−1.71035	−0.855175	+	0.518339i	$0.826550\pi$
$338$	0	0
$339$	−5.60694e11	−2.30583
$340$	0	0
$341$	−7.11200e11	−2.84837
$342$	0	0
$343$	2.78122e11	1.08495
$344$	0	0
$345$	−2.03915e11	−0.774933
$346$	0	0
$347$	−4.20848e11	−1.55827	−0.779134	−	0.626857i	$-0.784341\pi$
$347$	−4.20848e11	−1.55827	−0.779134	+	0.626857i	$0.784341\pi$
$348$	0	0
$349$	−3.99383e11	−1.44104	−0.720518	−	0.693436i	$-0.756096\pi$
$349$	−3.99383e11	−1.44104	−0.720518	+	0.693436i	$0.756096\pi$
$350$	0	0
$351$	−5.25619e10	−0.184837
$352$	0	0
$353$	−7.88806e10	−0.270386	−0.135193	−	0.990819i	$-0.543165\pi$
$353$	−7.88806e10	−0.270386	−0.135193	+	0.990819i	$0.543165\pi$
$354$	0	0
$355$	−6.06867e10	−0.202799
$356$	0	0
$357$	−4.61890e10	−0.150498
$358$	0	0
$359$	−1.39842e11	−0.444337	−0.222168	−	0.975008i	$-0.571314\pi$
$359$	−1.39842e11	−0.444337	−0.222168	+	0.975008i	$0.571314\pi$
$360$	0	0
$361$	7.95534e11	2.46534
$362$	0	0
$363$	6.34031e11	1.91660
$364$	0	0
$365$	1.07406e11	0.316744
$366$	0	0
$367$	−5.08662e11	−1.46363	−0.731816	−	0.681502i	$-0.761327\pi$
$367$	−5.08662e11	−1.46363	−0.731816	+	0.681502i	$0.761327\pi$
$368$	0	0
$369$	2.09063e11	0.587027
$370$	0	0
$371$	−2.91241e11	−0.798123
$372$	0	0
$373$	−2.96761e11	−0.793810	−0.396905	−	0.917860i	$-0.629916\pi$
$373$	−2.96761e11	−0.793810	−0.396905	+	0.917860i	$0.629916\pi$
$374$	0	0
$375$	4.98047e10	0.130056
$376$	0	0
$377$	−2.50157e11	−0.637788
$378$	0	0
$379$	4.53918e11	1.13006	0.565030	−	0.825071i	$-0.308865\pi$
$379$	4.53918e11	1.13006	0.565030	+	0.825071i	$0.308865\pi$
$380$	0	0
$381$	−5.39219e11	−1.31100
$382$	0	0
$383$	−2.67567e11	−0.635387	−0.317694	−	0.948193i	$-0.602908\pi$
$383$	−2.67567e11	−0.635387	−0.317694	+	0.948193i	$0.602908\pi$
$384$	0	0
$385$	2.50999e11	0.582236
$386$	0	0
$387$	2.95317e11	0.669250
$388$	0	0
$389$	3.34750e11	0.741221	0.370610	−	0.928788i	$-0.379148\pi$
$389$	3.34750e11	0.741221	0.370610	+	0.928788i	$0.379148\pi$
$390$	0	0
$391$	−6.66635e10	−0.144242
$392$	0	0
$393$	5.37998e11	1.13766
$394$	0	0
$395$	7.33626e10	0.151631
$396$	0	0
$397$	−4.55573e11	−0.920451	−0.460226	−	0.887802i	$-0.652231\pi$
$397$	−4.55573e11	−0.920451	−0.460226	+	0.887802i	$0.652231\pi$
$398$	0	0
$399$	1.17180e12	2.31460
$400$	0	0
$401$	2.18973e11	0.422904	0.211452	−	0.977388i	$-0.432181\pi$
$401$	2.18973e11	0.422904	0.211452	+	0.977388i	$0.432181\pi$
$402$	0	0
$403$	−1.10158e12	−2.08039
$404$	0	0
$405$	−2.11295e11	−0.390248
$406$	0	0
$407$	−3.54869e11	−0.641053
$408$	0	0
$409$	−3.63048e11	−0.641519	−0.320760	−	0.947161i	$-0.603938\pi$
$409$	−3.63048e11	−0.641519	−0.320760	+	0.947161i	$0.603938\pi$
$410$	0	0
$411$	1.05374e12	1.82157
$412$	0	0
$413$	4.44678e11	0.752091
$414$	0	0
$415$	−2.02274e11	−0.334752
$416$	0	0
$417$	−5.64572e11	−0.914339
$418$	0	0
$419$	1.14340e12	1.81232	0.906158	−	0.422939i	$-0.139001\pi$
$419$	1.14340e12	1.81232	0.906158	+	0.422939i	$0.139001\pi$
$420$	0	0
$421$	6.58288e11	1.02128	0.510642	−	0.859793i	$-0.329408\pi$
$421$	6.58288e11	1.02128	0.510642	+	0.859793i	$0.329408\pi$
$422$	0	0
$423$	−2.50956e11	−0.381124
$424$	0	0
$425$	1.62820e10	0.0242080
$426$	0	0
$427$	5.68683e11	0.827837
$428$	0	0
$429$	1.72711e12	2.46186
$430$	0	0
$431$	1.27825e11	0.178430	0.0892152	−	0.996012i	$-0.471564\pi$
$431$	1.27825e11	0.178430	0.0892152	+	0.996012i	$0.471564\pi$
$432$	0	0
$433$	−5.76786e10	−0.0788531	−0.0394266	−	0.999222i	$-0.512553\pi$
$433$	−5.76786e10	−0.0788531	−0.0394266	+	0.999222i	$0.512553\pi$
$434$	0	0
$435$	2.78525e11	0.372960
$436$	0	0
$437$	1.69123e12	2.21839
$438$	0	0
$439$	−4.11418e11	−0.528681	−0.264340	−	0.964429i	$-0.585154\pi$
$439$	−4.11418e11	−0.528681	−0.264340	+	0.964429i	$0.585154\pi$
$440$	0	0
$441$	−2.37907e11	−0.299525
$442$	0	0
$443$	−1.17254e11	−0.144647	−0.0723237	−	0.997381i	$-0.523041\pi$
$443$	−1.17254e11	−0.144647	−0.0723237	+	0.997381i	$0.523041\pi$
$444$	0	0
$445$	−5.58987e11	−0.675743
$446$	0	0
$447$	−1.23247e12	−1.46013
$448$	0	0
$449$	9.15676e10	0.106325	0.0531623	−	0.998586i	$-0.483070\pi$
$449$	9.15676e10	0.106325	0.0531623	+	0.998586i	$0.483070\pi$
$450$	0	0
$451$	−7.04711e11	−0.802078
$452$	0	0
$453$	−8.30700e10	−0.0926834
$454$	0	0
$455$	3.88775e11	0.425253
$456$	0	0
$457$	−1.55029e12	−1.66261	−0.831305	−	0.555816i	$-0.812406\pi$
$457$	−1.55029e12	−1.66261	−0.831305	+	0.555816i	$0.812406\pi$
$458$	0	0
$459$	1.91320e10	0.0201189
$460$	0	0
$461$	−1.61825e12	−1.66875	−0.834374	−	0.551198i	$-0.814171\pi$
$461$	−1.61825e12	−1.66875	−0.834374	+	0.551198i	$0.814171\pi$
$462$	0	0
$463$	−9.04370e11	−0.914601	−0.457301	−	0.889312i	$-0.651184\pi$
$463$	−9.04370e11	−0.914601	−0.457301	+	0.889312i	$0.651184\pi$
$464$	0	0
$465$	1.22651e12	1.21655
$466$	0	0
$467$	1.28255e12	1.24781	0.623903	−	0.781502i	$-0.285546\pi$
$467$	1.28255e12	1.24781	0.623903	+	0.781502i	$0.285546\pi$
$468$	0	0
$469$	7.63582e11	0.728749
$470$	0	0
$471$	3.69113e10	0.0345594
$472$	0	0
$473$	−9.95456e11	−0.914423
$474$	0	0
$475$	−4.13070e11	−0.372308
$476$	0	0
$477$	1.17595e12	1.04006
$478$	0	0
$479$	5.31423e11	0.461244	0.230622	−	0.973043i	$-0.425924\pi$
$479$	5.31423e11	0.461244	0.230622	+	0.973043i	$0.425924\pi$
$480$	0	0
$481$	−5.49661e11	−0.468211
$482$	0	0
$483$	1.77227e12	1.48172
$484$	0	0
$485$	1.45424e11	0.119343
$486$	0	0
$487$	1.10916e12	0.893539	0.446770	−	0.894649i	$-0.352574\pi$
$487$	1.10916e12	0.893539	0.446770	+	0.894649i	$0.352574\pi$
$488$	0	0
$489$	−1.19953e12	−0.948679
$490$	0	0
$491$	9.04143e11	0.702054	0.351027	−	0.936365i	$-0.385832\pi$
$491$	9.04143e11	0.702054	0.351027	+	0.936365i	$0.385832\pi$
$492$	0	0
$493$	9.10547e10	0.0694211
$494$	0	0
$495$	−1.01347e12	−0.758730
$496$	0	0
$497$	5.27441e11	0.387766
$498$	0	0
$499$	−1.01146e12	−0.730290	−0.365145	−	0.930951i	$-0.618981\pi$
$499$	−1.01146e12	−0.730290	−0.365145	+	0.930951i	$0.618981\pi$
$500$	0	0
$501$	−2.77842e11	−0.197028
$502$	0	0
$503$	−1.26417e11	−0.0880538	−0.0440269	−	0.999030i	$-0.514019\pi$
$503$	−1.26417e11	−0.0880538	−0.0440269	+	0.999030i	$0.514019\pi$
$504$	0	0
$505$	4.07055e11	0.278511
$506$	0	0
$507$	5.11827e11	0.344023
$508$	0	0
$509$	−4.08226e11	−0.269569	−0.134785	−	0.990875i	$-0.543034\pi$
$509$	−4.08226e11	−0.269569	−0.134785	+	0.990875i	$0.543034\pi$
$510$	0	0
$511$	−9.33483e11	−0.605637
$512$	0	0
$513$	−4.85374e11	−0.309420
$514$	0	0
$515$	1.06956e12	0.669994
$516$	0	0
$517$	8.45926e11	0.520745
$518$	0	0
$519$	−2.89227e12	−1.74979
$520$	0	0
$521$	2.96958e12	1.76573	0.882867	−	0.469624i	$-0.155610\pi$
$521$	2.96958e12	1.76573	0.882867	+	0.469624i	$0.155610\pi$
$522$	0	0
$523$	4.01653e11	0.234743	0.117372	−	0.993088i	$-0.462553\pi$
$523$	4.01653e11	0.234743	0.117372	+	0.993088i	$0.462553\pi$
$524$	0	0
$525$	−4.32862e11	−0.248676
$526$	0	0
$527$	4.00966e11	0.226444
$528$	0	0
$529$	7.56723e11	0.420133
$530$	0	0
$531$	−1.79549e12	−0.980073
$532$	0	0
$533$	−1.09153e12	−0.585821
$534$	0	0
$535$	8.22206e11	0.433899
$536$	0	0
$537$	−5.43571e11	−0.282080
$538$	0	0
$539$	8.01939e11	0.409253
$540$	0	0
$541$	−6.35088e11	−0.318747	−0.159374	−	0.987218i	$-0.550947\pi$
$541$	−6.35088e11	−0.318747	−0.159374	+	0.987218i	$0.550947\pi$
$542$	0	0
$543$	−8.27110e11	−0.408285
$544$	0	0
$545$	1.94169e11	0.0942747
$546$	0	0
$547$	−2.74387e12	−1.31045	−0.655224	−	0.755434i	$-0.727426\pi$
$547$	−2.74387e12	−1.31045	−0.655224	+	0.755434i	$0.727426\pi$
$548$	0	0
$549$	−2.29619e12	−1.07878
$550$	0	0
$551$	−2.31003e12	−1.06767
$552$	0	0
$553$	−6.37609e11	−0.289929
$554$	0	0
$555$	6.11993e11	0.273796
$556$	0	0
$557$	−1.31358e12	−0.578238	−0.289119	−	0.957293i	$-0.593362\pi$
$557$	−1.31358e12	−0.578238	−0.289119	+	0.957293i	$0.593362\pi$
$558$	0	0
$559$	−1.54187e12	−0.667875
$560$	0	0
$561$	−6.28653e11	−0.267965
$562$	0	0
$563$	3.11100e12	1.30500	0.652502	−	0.757787i	$-0.273719\pi$
$563$	3.11100e12	1.30500	0.652502	+	0.757787i	$0.273719\pi$
$564$	0	0
$565$	−1.71781e12	−0.709182
$566$	0	0
$567$	1.83640e12	0.746181
$568$	0	0
$569$	−1.45889e12	−0.583470	−0.291735	−	0.956499i	$-0.594233\pi$
$569$	−1.45889e12	−0.583470	−0.291735	+	0.956499i	$0.594233\pi$
$570$	0	0
$571$	3.94710e12	1.55387	0.776936	−	0.629579i	$-0.216773\pi$
$571$	3.94710e12	1.55387	0.776936	+	0.629579i	$0.216773\pi$
$572$	0	0
$573$	2.06824e12	0.801505
$574$	0	0
$575$	−6.24741e11	−0.238339
$576$	0	0
$577$	−5.27904e11	−0.198273	−0.0991365	−	0.995074i	$-0.531608\pi$
$577$	−5.27904e11	−0.198273	−0.0991365	+	0.995074i	$0.531608\pi$
$578$	0	0
$579$	−1.54568e12	−0.571565
$580$	0	0
$581$	1.75800e12	0.640068
$582$	0	0
$583$	−3.96392e12	−1.42107
$584$	0	0
$585$	−1.56977e12	−0.554160
$586$	0	0
$587$	−4.56943e12	−1.58851	−0.794255	−	0.607584i	$-0.792139\pi$
$587$	−4.56943e12	−1.58851	−0.794255	+	0.607584i	$0.792139\pi$
$588$	0	0
$589$	−1.01724e13	−3.48261
$590$	0	0
$591$	−4.50367e10	−0.0151853
$592$	0	0
$593$	3.19168e12	1.05992	0.529960	−	0.848022i	$-0.322207\pi$
$593$	3.19168e12	1.05992	0.529960	+	0.848022i	$0.322207\pi$
$594$	0	0
$595$	−1.41510e11	−0.0462873
$596$	0	0
$597$	6.10565e12	1.96719
$598$	0	0
$599$	−2.72611e12	−0.865211	−0.432605	−	0.901583i	$-0.642406\pi$
$599$	−2.72611e12	−0.865211	−0.432605	+	0.901583i	$0.642406\pi$
$600$	0	0
$601$	1.16094e11	0.0362974	0.0181487	−	0.999835i	$-0.494223\pi$
$601$	1.16094e11	0.0362974	0.0181487	+	0.999835i	$0.494223\pi$
$602$	0	0
$603$	−3.08315e12	−0.949656
$604$	0	0
$605$	1.94250e12	0.589469
$606$	0	0
$607$	3.81951e12	1.14198	0.570990	−	0.820957i	$-0.306559\pi$
$607$	3.81951e12	1.14198	0.570990	+	0.820957i	$0.306559\pi$
$608$	0	0
$609$	−2.42072e12	−0.713126
$610$	0	0
$611$	1.31026e12	0.380341
$612$	0	0
$613$	−3.74021e12	−1.06985	−0.534926	−	0.844899i	$-0.679660\pi$
$613$	−3.74021e12	−1.06985	−0.534926	+	0.844899i	$0.679660\pi$
$614$	0	0
$615$	1.21531e12	0.342571
$616$	0	0
$617$	6.24435e12	1.73462	0.867310	−	0.497769i	$-0.165847\pi$
$617$	6.24435e12	1.73462	0.867310	+	0.497769i	$0.165847\pi$
$618$	0	0
$619$	−4.46634e12	−1.22277	−0.611383	−	0.791335i	$-0.709387\pi$
$619$	−4.46634e12	−1.22277	−0.611383	+	0.791335i	$0.709387\pi$
$620$	0	0
$621$	−7.34095e11	−0.198080
$622$	0	0
$623$	4.85827e12	1.29207
$624$	0	0
$625$	1.52588e11	0.0400000
$626$	0	0
$627$	1.59487e13	4.12119
$628$	0	0
$629$	2.00071e11	0.0509632
$630$	0	0
$631$	3.08003e12	0.773434	0.386717	−	0.922198i	$-0.373609\pi$
$631$	3.08003e12	0.773434	0.386717	+	0.922198i	$0.373609\pi$
$632$	0	0
$633$	−5.96767e12	−1.47737
$634$	0	0
$635$	−1.65202e12	−0.403212
$636$	0	0
$637$	1.24213e12	0.298910
$638$	0	0
$639$	−2.12967e12	−0.505310
$640$	0	0
$641$	7.87684e12	1.84285	0.921427	−	0.388552i	$-0.127025\pi$
$641$	7.87684e12	1.84285	0.921427	+	0.388552i	$0.127025\pi$
$642$	0	0
$643$	2.80833e12	0.647886	0.323943	−	0.946077i	$-0.394991\pi$
$643$	2.80833e12	0.647886	0.323943	+	0.946077i	$0.394991\pi$
$644$	0	0
$645$	1.71672e12	0.390554
$646$	0	0
$647$	−2.03365e12	−0.456254	−0.228127	−	0.973631i	$-0.573260\pi$
$647$	−2.03365e12	−0.456254	−0.228127	+	0.973631i	$0.573260\pi$
$648$	0	0
$649$	6.05227e12	1.33911
$650$	0	0
$651$	−1.06598e13	−2.32613
$652$	0	0
$653$	5.29056e12	1.13865	0.569327	−	0.822111i	$-0.307204\pi$
$653$	5.29056e12	1.13865	0.569327	+	0.822111i	$0.307204\pi$
$654$	0	0
$655$	1.64828e12	0.349900
$656$	0	0
$657$	3.76916e12	0.789225
$658$	0	0
$659$	5.06766e12	1.04670	0.523351	−	0.852117i	$-0.324682\pi$
$659$	5.06766e12	1.04670	0.523351	+	0.852117i	$0.324682\pi$
$660$	0	0
$661$	−6.05804e12	−1.23431	−0.617157	−	0.786840i	$-0.711716\pi$
$661$	−6.05804e12	−1.23431	−0.617157	+	0.786840i	$0.711716\pi$
$662$	0	0
$663$	−9.73727e11	−0.195716
$664$	0	0
$665$	3.59008e12	0.711879
$666$	0	0
$667$	−3.49377e12	−0.683483
$668$	0	0
$669$	1.05770e13	2.04149
$670$	0	0
$671$	7.74004e12	1.47398
$672$	0	0
$673$	5.03218e12	0.945559	0.472779	−	0.881181i	$-0.343251\pi$
$673$	5.03218e12	0.945559	0.472779	+	0.881181i	$0.343251\pi$
$674$	0	0
$675$	1.79297e11	0.0332434
$676$	0	0
$677$	−8.61276e12	−1.57577	−0.787886	−	0.615821i	$-0.788824\pi$
$677$	−8.61276e12	−1.57577	−0.787886	+	0.615821i	$0.788824\pi$
$678$	0	0
$679$	−1.26391e12	−0.228193
$680$	0	0
$681$	−9.30796e12	−1.65841
$682$	0	0
$683$	3.37706e11	0.0593807	0.0296903	−	0.999559i	$-0.490548\pi$
$683$	3.37706e11	0.0593807	0.0296903	+	0.999559i	$0.490548\pi$
$684$	0	0
$685$	3.22837e12	0.560242
$686$	0	0
$687$	1.26785e13	2.17151
$688$	0	0
$689$	−6.13976e12	−1.03792
$690$	0	0
$691$	−1.74896e11	−0.0291830	−0.0145915	−	0.999894i	$-0.504645\pi$
$691$	−1.74896e11	−0.0291830	−0.0145915	+	0.999894i	$0.504645\pi$
$692$	0	0
$693$	8.80826e12	1.45074
$694$	0	0
$695$	−1.72969e12	−0.281214
$696$	0	0
$697$	3.97308e11	0.0637646
$698$	0	0
$699$	−7.59217e11	−0.120287
$700$	0	0
$701$	−5.36577e12	−0.839269	−0.419634	−	0.907693i	$-0.637842\pi$
$701$	−5.36577e12	−0.839269	−0.419634	+	0.907693i	$0.637842\pi$
$702$	0	0
$703$	−5.07575e12	−0.783792
$704$	0	0
$705$	−1.45885e12	−0.222413
$706$	0	0
$707$	−3.53779e12	−0.532531
$708$	0	0
$709$	5.45452e12	0.810679	0.405339	−	0.914166i	$-0.367153\pi$
$709$	5.45452e12	0.810679	0.405339	+	0.914166i	$0.367153\pi$
$710$	0	0
$711$	2.57450e12	0.377815
$712$	0	0
$713$	−1.53850e13	−2.22944
$714$	0	0
$715$	5.29141e12	0.757171
$716$	0	0
$717$	−7.38932e11	−0.104416
$718$	0	0
$719$	6.60953e12	0.922339	0.461169	−	0.887312i	$-0.347430\pi$
$719$	6.60953e12	0.922339	0.461169	+	0.887312i	$0.347430\pi$
$720$	0	0
$721$	−9.29572e12	−1.28107
$722$	0	0
$723$	−6.86575e12	−0.934471
$724$	0	0
$725$	8.53324e11	0.114708
$726$	0	0
$727$	−1.12652e13	−1.49566	−0.747832	−	0.663888i	$-0.768905\pi$
$727$	−1.12652e13	−1.49566	−0.747832	+	0.663888i	$0.768905\pi$
$728$	0	0
$729$	−9.25795e12	−1.21406
$730$	0	0
$731$	5.61227e11	0.0726959
$732$	0	0
$733$	−1.55010e13	−1.98332	−0.991659	−	0.128890i	$-0.958859\pi$
$733$	−1.55010e13	−1.98332	−0.991659	+	0.128890i	$0.958859\pi$
$734$	0	0
$735$	−1.38299e12	−0.174794
$736$	0	0
$737$	1.03927e13	1.29755
$738$	0	0
$739$	−8.86702e12	−1.09365	−0.546824	−	0.837247i	$-0.684163\pi$
$739$	−8.86702e12	−1.09365	−0.546824	+	0.837247i	$0.684163\pi$
$740$	0	0
$741$	2.47032e13	3.01003
$742$	0	0
$743$	−1.04586e13	−1.25900	−0.629500	−	0.777001i	$-0.716740\pi$
$743$	−1.04586e13	−1.25900	−0.629500	+	0.777001i	$0.716740\pi$
$744$	0	0
$745$	−3.77595e12	−0.449079
$746$	0	0
$747$	−7.09834e12	−0.834093
$748$	0	0
$749$	−7.14596e12	−0.829645
$750$	0	0
$751$	−3.37332e11	−0.0386971	−0.0193485	−	0.999813i	$-0.506159\pi$
$751$	−3.37332e11	−0.0386971	−0.0193485	+	0.999813i	$0.506159\pi$
$752$	0	0
$753$	1.19974e13	1.35991
$754$	0	0
$755$	−2.54504e11	−0.0285058
$756$	0	0
$757$	1.61864e12	0.179151	0.0895756	−	0.995980i	$-0.471449\pi$
$757$	1.61864e12	0.179151	0.0895756	+	0.995980i	$0.471449\pi$
$758$	0	0
$759$	2.41214e13	2.63824
$760$	0	0
$761$	−3.16676e12	−0.342282	−0.171141	−	0.985247i	$-0.554745\pi$
$761$	−3.16676e12	−0.342282	−0.171141	+	0.985247i	$0.554745\pi$
$762$	0	0
$763$	−1.68756e12	−0.180260
$764$	0	0
$765$	5.71382e11	0.0603184
$766$	0	0
$767$	9.37442e12	0.978059
$768$	0	0
$769$	9.41136e12	0.970474	0.485237	−	0.874383i	$-0.338733\pi$
$769$	9.41136e12	0.970474	0.485237	+	0.874383i	$0.338733\pi$
$770$	0	0
$771$	−1.53423e13	−1.56367
$772$	0	0
$773$	−3.00421e12	−0.302638	−0.151319	−	0.988485i	$-0.548352\pi$
$773$	−3.00421e12	−0.302638	−0.151319	+	0.988485i	$0.548352\pi$
$774$	0	0
$775$	3.75768e12	0.374164
$776$	0	0
$777$	−5.31895e12	−0.523518
$778$	0	0
$779$	−1.00796e13	−0.980673
$780$	0	0
$781$	7.17871e12	0.690425
$782$	0	0
$783$	1.00269e12	0.0953320
$784$	0	0
$785$	1.13086e11	0.0106291
$786$	0	0
$787$	−4.78765e12	−0.444873	−0.222436	−	0.974947i	$-0.571401\pi$
$787$	−4.78765e12	−0.444873	−0.222436	+	0.974947i	$0.571401\pi$
$788$	0	0
$789$	2.37285e12	0.217983
$790$	0	0
$791$	1.49298e13	1.35600
$792$	0	0
$793$	1.19886e13	1.07656
$794$	0	0
$795$	6.83601e12	0.606947
$796$	0	0
$797$	−8.82657e12	−0.774871	−0.387436	−	0.921897i	$-0.626639\pi$
$797$	−8.82657e12	−0.774871	−0.387436	+	0.921897i	$0.626639\pi$
$798$	0	0
$799$	−4.76923e11	−0.0413988
$800$	0	0
$801$	−1.96164e13	−1.68373
$802$	0	0
$803$	−1.27051e13	−1.07835
$804$	0	0
$805$	5.42975e12	0.455720
$806$	0	0
$807$	5.79097e12	0.480641
$808$	0	0
$809$	−4.75875e12	−0.390593	−0.195296	−	0.980744i	$-0.562567\pi$
$809$	−4.75875e12	−0.390593	−0.195296	+	0.980744i	$0.562567\pi$
$810$	0	0
$811$	−1.32270e13	−1.07366	−0.536831	−	0.843690i	$-0.680379\pi$
$811$	−1.32270e13	−1.07366	−0.536831	+	0.843690i	$0.680379\pi$
$812$	0	0
$813$	−3.01894e13	−2.42353
$814$	0	0
$815$	−3.67502e12	−0.291776
$816$	0	0
$817$	−1.42382e13	−1.11803
$818$	0	0
$819$	1.36432e13	1.05959
$820$	0	0
$821$	1.96204e13	1.50717	0.753587	−	0.657348i	$-0.228322\pi$
$821$	1.96204e13	1.50717	0.753587	+	0.657348i	$0.228322\pi$
$822$	0	0
$823$	−1.44369e12	−0.109692	−0.0548461	−	0.998495i	$-0.517467\pi$
$823$	−1.44369e12	−0.109692	−0.0548461	+	0.998495i	$0.517467\pi$
$824$	0	0
$825$	−5.89146e12	−0.442772
$826$	0	0
$827$	6.15968e12	0.457913	0.228957	−	0.973437i	$-0.426469\pi$
$827$	6.15968e12	0.457913	0.228957	+	0.973437i	$0.426469\pi$
$828$	0	0
$829$	−7.89482e12	−0.580560	−0.290280	−	0.956942i	$-0.593748\pi$
$829$	−7.89482e12	−0.580560	−0.290280	+	0.956942i	$0.593748\pi$
$830$	0	0
$831$	−1.54807e13	−1.12612
$832$	0	0
$833$	−4.52124e11	−0.0325353
$834$	0	0
$835$	−8.51232e11	−0.0605981
$836$	0	0
$837$	4.41542e12	0.310962
$838$	0	0
$839$	−1.39455e13	−0.971642	−0.485821	−	0.874058i	$-0.661479\pi$
$839$	−1.39455e13	−0.971642	−0.485821	+	0.874058i	$0.661479\pi$
$840$	0	0
$841$	−9.73506e12	−0.671053
$842$	0	0
$843$	3.51188e13	2.39505
$844$	0	0
$845$	1.56810e12	0.105808
$846$	0	0
$847$	−1.68826e13	−1.12711
$848$	0	0
$849$	3.05861e13	2.02041
$850$	0	0
$851$	−7.67672e12	−0.501756
$852$	0	0
$853$	2.06868e12	0.133789	0.0668947	−	0.997760i	$-0.478691\pi$
$853$	2.06868e12	0.133789	0.0668947	+	0.997760i	$0.478691\pi$
$854$	0	0
$855$	−1.44958e13	−0.927672
$856$	0	0
$857$	1.27749e13	0.808989	0.404494	−	0.914540i	$-0.367447\pi$
$857$	1.27749e13	0.808989	0.404494	+	0.914540i	$0.367447\pi$
$858$	0	0
$859$	−2.44751e13	−1.53376	−0.766878	−	0.641793i	$-0.778191\pi$
$859$	−2.44751e13	−1.53376	−0.766878	+	0.641793i	$0.778191\pi$
$860$	0	0
$861$	−1.05625e13	−0.655020
$862$	0	0
$863$	3.04987e13	1.87169	0.935843	−	0.352417i	$-0.114640\pi$
$863$	3.04987e13	1.87169	0.935843	+	0.352417i	$0.114640\pi$
$864$	0	0
$865$	−8.86113e12	−0.538167
$866$	0	0
$867$	−2.38375e13	−1.43276
$868$	0	0
$869$	−8.67814e12	−0.516224
$870$	0	0
$871$	1.60974e13	0.947704
$872$	0	0
$873$	5.10334e12	0.297365
$874$	0	0
$875$	−1.32617e12	−0.0764828
$876$	0	0
$877$	−3.32305e13	−1.89688	−0.948439	−	0.316960i	$-0.897338\pi$
$877$	−3.32305e13	−1.89688	−0.948439	+	0.316960i	$0.897338\pi$
$878$	0	0
$879$	1.94156e12	0.109699
$880$	0	0
$881$	1.65219e13	0.923995	0.461998	−	0.886881i	$-0.347133\pi$
$881$	1.65219e13	0.923995	0.461998	+	0.886881i	$0.347133\pi$
$882$	0	0
$883$	2.19061e13	1.21267	0.606333	−	0.795211i	$-0.292640\pi$
$883$	2.19061e13	1.21267	0.606333	+	0.795211i	$0.292640\pi$
$884$	0	0
$885$	−1.04375e13	−0.571941
$886$	0	0
$887$	−1.63192e13	−0.885203	−0.442601	−	0.896718i	$-0.645944\pi$
$887$	−1.63192e13	−0.885203	−0.442601	+	0.896718i	$0.645944\pi$
$888$	0	0
$889$	1.43580e13	0.770968
$890$	0	0
$891$	2.49943e13	1.32859
$892$	0	0
$893$	1.20994e13	0.636697
$894$	0	0
$895$	−1.66535e12	−0.0867565
$896$	0	0
$897$	3.73619e13	1.92691
$898$	0	0
$899$	2.10142e13	1.07299
$900$	0	0
$901$	2.23481e12	0.112974
$902$	0	0
$903$	−1.49204e13	−0.746766
$904$	0	0
$905$	−2.53404e12	−0.125572
$906$	0	0
$907$	1.98103e12	0.0971980	0.0485990	−	0.998818i	$-0.484524\pi$
$907$	1.98103e12	0.0971980	0.0485990	+	0.998818i	$0.484524\pi$
$908$	0	0
$909$	1.42847e13	0.693958
$910$	0	0
$911$	1.60376e12	0.0771446	0.0385723	−	0.999256i	$-0.487719\pi$
$911$	1.60376e12	0.0771446	0.0385723	+	0.999256i	$0.487719\pi$
$912$	0	0
$913$	2.39272e13	1.13965
$914$	0	0
$915$	−1.33481e13	−0.629544
$916$	0	0
$917$	−1.43255e13	−0.669034
$918$	0	0
$919$	2.81428e13	1.30151	0.650755	−	0.759288i	$-0.274452\pi$
$919$	2.81428e13	1.30151	0.650755	+	0.759288i	$0.274452\pi$
$920$	0	0
$921$	−1.84804e13	−0.846335
$922$	0	0
$923$	1.11192e13	0.504272
$924$	0	0
$925$	1.87498e12	0.0842089
$926$	0	0
$927$	3.75337e13	1.66941
$928$	0	0
$929$	−5.39418e12	−0.237605	−0.118802	−	0.992918i	$-0.537905\pi$
$929$	−5.39418e12	−0.237605	−0.118802	+	0.992918i	$0.537905\pi$
$930$	0	0
$931$	1.14703e13	0.500379
$932$	0	0
$933$	5.73821e13	2.47919
$934$	0	0
$935$	−1.92602e12	−0.0824155
$936$	0	0
$937$	−1.25051e13	−0.529978	−0.264989	−	0.964251i	$-0.585368\pi$
$937$	−1.25051e13	−0.529978	−0.264989	+	0.964251i	$0.585368\pi$
$938$	0	0
$939$	−1.85895e13	−0.780318
$940$	0	0
$941$	9.23095e12	0.383789	0.191895	−	0.981416i	$-0.438537\pi$
$941$	9.23095e12	0.383789	0.191895	+	0.981416i	$0.438537\pi$
$942$	0	0
$943$	−1.52447e13	−0.627792
$944$	0	0
$945$	−1.55830e12	−0.0635637
$946$	0	0
$947$	−4.13417e13	−1.67037	−0.835186	−	0.549967i	$-0.814640\pi$
$947$	−4.13417e13	−1.67037	−0.835186	+	0.549967i	$0.814640\pi$
$948$	0	0
$949$	−1.96791e13	−0.787603
$950$	0	0
$951$	2.10461e13	0.834371
$952$	0	0
$953$	1.05715e13	0.415162	0.207581	−	0.978218i	$-0.433441\pi$
$953$	1.05715e13	0.415162	0.207581	+	0.978218i	$0.433441\pi$
$954$	0	0
$955$	6.33653e12	0.246511
$956$	0	0
$957$	−3.29471e13	−1.26973
$958$	0	0
$959$	−2.80584e13	−1.07122
$960$	0	0
$961$	6.60980e13	2.49996
$962$	0	0
$963$	2.88535e13	1.08114
$964$	0	0
$965$	−4.73553e12	−0.175791
$966$	0	0
$967$	4.28128e13	1.57454	0.787271	−	0.616607i	$-0.211493\pi$
$967$	4.28128e13	1.57454	0.787271	+	0.616607i	$0.211493\pi$
$968$	0	0
$969$	−8.99172e12	−0.327632
$970$	0	0
$971$	−5.22930e12	−0.188780	−0.0943902	−	0.995535i	$-0.530090\pi$
$971$	−5.22930e12	−0.188780	−0.0943902	+	0.995535i	$0.530090\pi$
$972$	0	0
$973$	1.50331e13	0.537702
$974$	0	0
$975$	−9.12533e12	−0.323391
$976$	0	0
$977$	3.56421e12	0.125152	0.0625760	−	0.998040i	$-0.480068\pi$
$977$	3.56421e12	0.125152	0.0625760	+	0.998040i	$0.480068\pi$
$978$	0	0
$979$	6.61232e13	2.30055
$980$	0	0
$981$	6.81393e12	0.234902
$982$	0	0
$983$	−1.92286e13	−0.656837	−0.328418	−	0.944532i	$-0.606516\pi$
$983$	−1.92286e13	−0.656837	−0.328418	+	0.944532i	$0.606516\pi$
$984$	0	0
$985$	−1.37980e11	−0.00467039
$986$	0	0
$987$	1.26791e13	0.425268
$988$	0	0
$989$	−2.15342e13	−0.715725
$990$	0	0
$991$	3.28794e13	1.08291	0.541454	−	0.840730i	$-0.317874\pi$
$991$	3.28794e13	1.08291	0.541454	+	0.840730i	$0.317874\pi$
$992$	0	0
$993$	−5.12203e13	−1.67175
$994$	0	0
$995$	1.87060e13	0.605031
$996$	0	0
$997$	1.66280e13	0.532982	0.266491	−	0.963837i	$-0.414136\pi$
$997$	1.66280e13	0.532982	0.266491	+	0.963837i	$0.414136\pi$
$998$	0	0
$999$	2.20317e12	0.0699848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.10.a.e.1.1		1
4.3	odd	2		10.10.a.a.1.1	✓	1
5.2	odd	4		400.10.c.b.49.1		2
5.3	odd	4		400.10.c.b.49.2		2
5.4	even	2		400.10.a.a.1.1		1
8.3	odd	2		320.10.a.j.1.1		1
8.5	even	2		320.10.a.a.1.1		1
12.11	even	2		90.10.a.g.1.1		1
20.3	even	4		50.10.b.e.49.2		2
20.7	even	4		50.10.b.e.49.1		2
20.19	odd	2		50.10.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.10.a.a.1.1	✓	1	4.3	odd	2
50.10.a.f.1.1		1	20.19	odd	2
50.10.b.e.49.1		2	20.7	even	4
50.10.b.e.49.2		2	20.3	even	4
80.10.a.e.1.1		1	1.1	even	1	trivial
90.10.a.g.1.1		1	12.11	even	2
320.10.a.a.1.1		1	8.5	even	2
320.10.a.j.1.1		1	8.3	odd	2
400.10.a.a.1.1		1	5.4	even	2
400.10.c.b.49.1		2	5.2	odd	4
400.10.c.b.49.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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