LMFDB - Embedded newform 560.6.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,6,Mod(1,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("560.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	560.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:	$89.8149390953$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	560.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+12.0000 q^{3} +25.0000 q^{5} +49.0000 q^{7} -99.0000 q^{9} +O(q^{10})$

$q+12.0000 q^{3} +25.0000 q^{5} +49.0000 q^{7} -99.0000 q^{9} -556.000 q^{11} -354.000 q^{13} +300.000 q^{15} +770.000 q^{17} +2684.00 q^{19} +588.000 q^{21} +1528.00 q^{23} +625.000 q^{25} -4104.00 q^{27} -2418.00 q^{29} -7840.00 q^{31} -6672.00 q^{33} +1225.00 q^{35} -314.000 q^{37} -4248.00 q^{39} -17878.0 q^{41} -16476.0 q^{43} -2475.00 q^{45} -5376.00 q^{47} +2401.00 q^{49} +9240.00 q^{51} +1654.00 q^{53} -13900.0 q^{55} +32208.0 q^{57} +29492.0 q^{59} +27630.0 q^{61} -4851.00 q^{63} -8850.00 q^{65} -57716.0 q^{67} +18336.0 q^{69} -70648.0 q^{71} +74202.0 q^{73} +7500.00 q^{75} -27244.0 q^{77} -74336.0 q^{79} -25191.0 q^{81} -44068.0 q^{83} +19250.0 q^{85} -29016.0 q^{87} +129306. q^{89} -17346.0 q^{91} -94080.0 q^{93} +67100.0 q^{95} -137646. q^{97} +55044.0 q^{99} +O(q^{100})$

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
$3$	12.0000	0.769800	0.384900	−	0.922958i	$-0.374236\pi$
$3$	12.0000	0.769800	0.384900	+	0.922958i	$0.374236\pi$
$4$	0	0
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	0	0
$9$	−99.0000	−0.407407
$10$	0	0
$11$	−556.000	−1.38546	−0.692729	−	0.721198i	$-0.743592\pi$
$11$	−556.000	−1.38546	−0.692729	+	0.721198i	$0.743592\pi$
$12$	0	0
$13$	−354.000	−0.580958	−0.290479	−	0.956881i	$-0.593815\pi$
$13$	−354.000	−0.580958	−0.290479	+	0.956881i	$0.593815\pi$
$14$	0	0
$15$	300.000	0.344265
$16$	0	0
$17$	770.000	0.646202	0.323101	−	0.946364i	$-0.395275\pi$
$17$	770.000	0.646202	0.323101	+	0.946364i	$0.395275\pi$
$18$	0	0
$19$	2684.00	1.70568	0.852842	−	0.522169i	$-0.174877\pi$
$19$	2684.00	1.70568	0.852842	+	0.522169i	$0.174877\pi$
$20$	0	0
$21$	588.000	0.290957
$22$	0	0
$23$	1528.00	0.602287	0.301144	−	0.953579i	$-0.402632\pi$
$23$	1528.00	0.602287	0.301144	+	0.953579i	$0.402632\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	−4104.00	−1.08342
$28$	0	0
$29$	−2418.00	−0.533902	−0.266951	−	0.963710i	$-0.586016\pi$
$29$	−2418.00	−0.533902	−0.266951	+	0.963710i	$0.586016\pi$
$30$	0	0
$31$	−7840.00	−1.46525	−0.732625	−	0.680632i	$-0.761705\pi$
$31$	−7840.00	−1.46525	−0.732625	+	0.680632i	$0.761705\pi$
$32$	0	0
$33$	−6672.00	−1.06653
$34$	0	0
$35$	1225.00	0.169031
$36$	0	0
$37$	−314.000	−0.0377073	−0.0188536	−	0.999822i	$-0.506002\pi$
$37$	−314.000	−0.0377073	−0.0188536	+	0.999822i	$0.506002\pi$
$38$	0	0
$39$	−4248.00	−0.447222
$40$	0	0
$41$	−17878.0	−1.66096	−0.830480	−	0.557048i	$-0.811934\pi$
$41$	−17878.0	−1.66096	−0.830480	+	0.557048i	$0.811934\pi$
$42$	0	0
$43$	−16476.0	−1.35888	−0.679439	−	0.733732i	$-0.737777\pi$
$43$	−16476.0	−1.35888	−0.679439	+	0.733732i	$0.737777\pi$
$44$	0	0
$45$	−2475.00	−0.182198
$46$	0	0
$47$	−5376.00	−0.354989	−0.177494	−	0.984122i	$-0.556799\pi$
$47$	−5376.00	−0.354989	−0.177494	+	0.984122i	$0.556799\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	9240.00	0.497447
$52$	0	0
$53$	1654.00	0.0808809	0.0404404	−	0.999182i	$-0.487124\pi$
$53$	1654.00	0.0808809	0.0404404	+	0.999182i	$0.487124\pi$
$54$	0	0
$55$	−13900.0	−0.619595
$56$	0	0
$57$	32208.0	1.31304
$58$	0	0
$59$	29492.0	1.10300	0.551498	−	0.834176i	$-0.314056\pi$
$59$	29492.0	1.10300	0.551498	+	0.834176i	$0.314056\pi$
$60$	0	0
$61$	27630.0	0.950728	0.475364	−	0.879789i	$-0.342316\pi$
$61$	27630.0	0.950728	0.475364	+	0.879789i	$0.342316\pi$
$62$	0	0
$63$	−4851.00	−0.153986
$64$	0	0
$65$	−8850.00	−0.259812
$66$	0	0
$67$	−57716.0	−1.57076	−0.785379	−	0.619015i	$-0.787532\pi$
$67$	−57716.0	−1.57076	−0.785379	+	0.619015i	$0.787532\pi$
$68$	0	0
$69$	18336.0	0.463641
$70$	0	0
$71$	−70648.0	−1.66324	−0.831618	−	0.555348i	$-0.812585\pi$
$71$	−70648.0	−1.66324	−0.831618	+	0.555348i	$0.812585\pi$
$72$	0	0
$73$	74202.0	1.62970	0.814851	−	0.579670i	$-0.196818\pi$
$73$	74202.0	1.62970	0.814851	+	0.579670i	$0.196818\pi$
$74$	0	0
$75$	7500.00	0.153960
$76$	0	0
$77$	−27244.0	−0.523654
$78$	0	0
$79$	−74336.0	−1.34008	−0.670041	−	0.742324i	$-0.733724\pi$
$79$	−74336.0	−1.34008	−0.670041	+	0.742324i	$0.733724\pi$
$80$	0	0
$81$	−25191.0	−0.426612
$82$	0	0
$83$	−44068.0	−0.702147	−0.351074	−	0.936348i	$-0.614183\pi$
$83$	−44068.0	−0.702147	−0.351074	+	0.936348i	$0.614183\pi$
$84$	0	0
$85$	19250.0	0.288990
$86$	0	0
$87$	−29016.0	−0.410998
$88$	0	0
$89$	129306.	1.73039	0.865194	−	0.501437i	$-0.167195\pi$
$89$	129306.	1.73039	0.865194	+	0.501437i	$0.167195\pi$
$90$	0	0
$91$	−17346.0	−0.219582
$92$	0	0
$93$	−94080.0	−1.12795
$94$	0	0
$95$	67100.0	0.762805
$96$	0	0
$97$	−137646.	−1.48537	−0.742684	−	0.669642i	$-0.766448\pi$
$97$	−137646.	−1.48537	−0.742684	+	0.669642i	$0.766448\pi$
$98$	0	0
$99$	55044.0	0.564445
$100$	0	0
$101$	52086.0	0.508063	0.254032	−	0.967196i	$-0.418243\pi$
$101$	52086.0	0.508063	0.254032	+	0.967196i	$0.418243\pi$
$102$	0	0
$103$	−128216.	−1.19083	−0.595414	−	0.803419i	$-0.703012\pi$
$103$	−128216.	−1.19083	−0.595414	+	0.803419i	$0.703012\pi$
$104$	0	0
$105$	14700.0	0.130120
$106$	0	0
$107$	−113340.	−0.957026	−0.478513	−	0.878080i	$-0.658824\pi$
$107$	−113340.	−0.957026	−0.478513	+	0.878080i	$0.658824\pi$
$108$	0	0
$109$	−138946.	−1.12016	−0.560080	−	0.828439i	$-0.689229\pi$
$109$	−138946.	−1.12016	−0.560080	+	0.828439i	$0.689229\pi$
$110$	0	0
$111$	−3768.00	−0.0290271
$112$	0	0
$113$	−28046.0	−0.206621	−0.103311	−	0.994649i	$-0.532944\pi$
$113$	−28046.0	−0.206621	−0.103311	+	0.994649i	$0.532944\pi$
$114$	0	0
$115$	38200.0	0.269351
$116$	0	0
$117$	35046.0	0.236687
$118$	0	0
$119$	37730.0	0.244241
$120$	0	0
$121$	148085.	0.919491
$122$	0	0
$123$	−214536.	−1.27861
$124$	0	0
$125$	15625.0	0.0894427
$126$	0	0
$127$	26704.0	0.146915	0.0734576	−	0.997298i	$-0.476597\pi$
$127$	26704.0	0.146915	0.0734576	+	0.997298i	$0.476597\pi$
$128$	0	0
$129$	−197712.	−1.04607
$130$	0	0
$131$	−7028.00	−0.0357811	−0.0178905	−	0.999840i	$-0.505695\pi$
$131$	−7028.00	−0.0357811	−0.0178905	+	0.999840i	$0.505695\pi$
$132$	0	0
$133$	131516.	0.644688
$134$	0	0
$135$	−102600.	−0.484521
$136$	0	0
$137$	140202.	0.638194	0.319097	−	0.947722i	$-0.396620\pi$
$137$	140202.	0.638194	0.319097	+	0.947722i	$0.396620\pi$
$138$	0	0
$139$	95876.0	0.420894	0.210447	−	0.977605i	$-0.432508\pi$
$139$	95876.0	0.420894	0.210447	+	0.977605i	$0.432508\pi$
$140$	0	0
$141$	−64512.0	−0.273270
$142$	0	0
$143$	196824.	0.804893
$144$	0	0
$145$	−60450.0	−0.238768
$146$	0	0
$147$	28812.0	0.109971
$148$	0	0
$149$	−347002.	−1.28046	−0.640230	−	0.768183i	$-0.721161\pi$
$149$	−347002.	−1.28046	−0.640230	+	0.768183i	$0.721161\pi$
$150$	0	0
$151$	270328.	0.964825	0.482413	−	0.875944i	$-0.339761\pi$
$151$	270328.	0.964825	0.482413	+	0.875944i	$0.339761\pi$
$152$	0	0
$153$	−76230.0	−0.263268
$154$	0	0
$155$	−196000.	−0.655280
$156$	0	0
$157$	−151186.	−0.489511	−0.244755	−	0.969585i	$-0.578708\pi$
$157$	−151186.	−0.489511	−0.244755	+	0.969585i	$0.578708\pi$
$158$	0	0
$159$	19848.0	0.0622621
$160$	0	0
$161$	74872.0	0.227643
$162$	0	0
$163$	−588148.	−1.73387	−0.866937	−	0.498417i	$-0.833915\pi$
$163$	−588148.	−1.73387	−0.866937	+	0.498417i	$0.833915\pi$
$164$	0	0
$165$	−166800.	−0.476965
$166$	0	0
$167$	−61912.0	−0.171784	−0.0858922	−	0.996304i	$-0.527374\pi$
$167$	−61912.0	−0.171784	−0.0858922	+	0.996304i	$0.527374\pi$
$168$	0	0
$169$	−245977.	−0.662488
$170$	0	0
$171$	−265716.	−0.694908
$172$	0	0
$173$	4862.00	0.0123509	0.00617547	−	0.999981i	$-0.498034\pi$
$173$	4862.00	0.0123509	0.00617547	+	0.999981i	$0.498034\pi$
$174$	0	0
$175$	30625.0	0.0755929
$176$	0	0
$177$	353904.	0.849087
$178$	0	0
$179$	17964.0	0.0419054	0.0209527	−	0.999780i	$-0.493330\pi$
$179$	17964.0	0.0419054	0.0209527	+	0.999780i	$0.493330\pi$
$180$	0	0
$181$	228422.	0.518253	0.259126	−	0.965843i	$-0.416565\pi$
$181$	228422.	0.518253	0.259126	+	0.965843i	$0.416565\pi$
$182$	0	0
$183$	331560.	0.731871
$184$	0	0
$185$	−7850.00	−0.0168632
$186$	0	0
$187$	−428120.	−0.895285
$188$	0	0
$189$	−201096.	−0.409495
$190$	0	0
$191$	357840.	0.709750	0.354875	−	0.934914i	$-0.384523\pi$
$191$	357840.	0.709750	0.354875	+	0.934914i	$0.384523\pi$
$192$	0	0
$193$	−494174.	−0.954963	−0.477482	−	0.878642i	$-0.658450\pi$
$193$	−494174.	−0.954963	−0.477482	+	0.878642i	$0.658450\pi$
$194$	0	0
$195$	−106200.	−0.200004
$196$	0	0
$197$	595302.	1.09288	0.546439	−	0.837499i	$-0.315983\pi$
$197$	595302.	1.09288	0.546439	+	0.837499i	$0.315983\pi$
$198$	0	0
$199$	261208.	0.467578	0.233789	−	0.972287i	$-0.424888\pi$
$199$	261208.	0.467578	0.233789	+	0.972287i	$0.424888\pi$
$200$	0	0
$201$	−692592.	−1.20917
$202$	0	0
$203$	−118482.	−0.201796
$204$	0	0
$205$	−446950.	−0.742804
$206$	0	0
$207$	−151272.	−0.245376
$208$	0	0
$209$	−1.49230e6	−2.36315
$210$	0	0
$211$	−788564.	−1.21936	−0.609678	−	0.792649i	$-0.708701\pi$
$211$	−788564.	−1.21936	−0.609678	+	0.792649i	$0.708701\pi$
$212$	0	0
$213$	−847776.	−1.28036
$214$	0	0
$215$	−411900.	−0.607709
$216$	0	0
$217$	−384160.	−0.553813
$218$	0	0
$219$	890424.	1.25455
$220$	0	0
$221$	−272580.	−0.375416
$222$	0	0
$223$	1.35842e6	1.82924	0.914620	−	0.404315i	$-0.132490\pi$
$223$	1.35842e6	1.82924	0.914620	+	0.404315i	$0.132490\pi$
$224$	0	0
$225$	−61875.0	−0.0814815
$226$	0	0
$227$	461068.	0.593882	0.296941	−	0.954896i	$-0.404033\pi$
$227$	461068.	0.593882	0.296941	+	0.954896i	$0.404033\pi$
$228$	0	0
$229$	1.25509e6	1.58157	0.790783	−	0.612096i	$-0.209673\pi$
$229$	1.25509e6	1.58157	0.790783	+	0.612096i	$0.209673\pi$
$230$	0	0
$231$	−326928.	−0.403109
$232$	0	0
$233$	503914.	0.608088	0.304044	−	0.952658i	$-0.401663\pi$
$233$	503914.	0.608088	0.304044	+	0.952658i	$0.401663\pi$
$234$	0	0
$235$	−134400.	−0.158756
$236$	0	0
$237$	−892032.	−1.03160
$238$	0	0
$239$	−1.50902e6	−1.70884	−0.854420	−	0.519583i	$-0.826087\pi$
$239$	−1.50902e6	−1.70884	−0.854420	+	0.519583i	$0.826087\pi$
$240$	0	0
$241$	−63022.0	−0.0698956	−0.0349478	−	0.999389i	$-0.511126\pi$
$241$	−63022.0	−0.0698956	−0.0349478	+	0.999389i	$0.511126\pi$
$242$	0	0
$243$	694980.	0.755017
$244$	0	0
$245$	60025.0	0.0638877
$246$	0	0
$247$	−950136.	−0.990931
$248$	0	0
$249$	−528816.	−0.540513
$250$	0	0
$251$	964820.	0.966634	0.483317	−	0.875445i	$-0.339432\pi$
$251$	964820.	0.966634	0.483317	+	0.875445i	$0.339432\pi$
$252$	0	0
$253$	−849568.	−0.834443
$254$	0	0
$255$	231000.	0.222465
$256$	0	0
$257$	−495150.	−0.467632	−0.233816	−	0.972281i	$-0.575121\pi$
$257$	−495150.	−0.467632	−0.233816	+	0.972281i	$0.575121\pi$
$258$	0	0
$259$	−15386.0	−0.0142520
$260$	0	0
$261$	239382.	0.217516
$262$	0	0
$263$	−2.18092e6	−1.94424	−0.972121	−	0.234479i	$-0.924661\pi$
$263$	−2.18092e6	−1.94424	−0.972121	+	0.234479i	$0.924661\pi$
$264$	0	0
$265$	41350.0	0.0361710
$266$	0	0
$267$	1.55167e6	1.33205
$268$	0	0
$269$	−473346.	−0.398839	−0.199420	−	0.979914i	$-0.563906\pi$
$269$	−473346.	−0.398839	−0.199420	+	0.979914i	$0.563906\pi$
$270$	0	0
$271$	2.19234e6	1.81336	0.906680	−	0.421820i	$-0.138609\pi$
$271$	2.19234e6	1.81336	0.906680	+	0.421820i	$0.138609\pi$
$272$	0	0
$273$	−208152.	−0.169034
$274$	0	0
$275$	−347500.	−0.277091
$276$	0	0
$277$	388502.	0.304224	0.152112	−	0.988363i	$-0.451393\pi$
$277$	388502.	0.304224	0.152112	+	0.988363i	$0.451393\pi$
$278$	0	0
$279$	776160.	0.596954
$280$	0	0
$281$	−75462.0	−0.0570115	−0.0285058	−	0.999594i	$-0.509075\pi$
$281$	−75462.0	−0.0570115	−0.0285058	+	0.999594i	$0.509075\pi$
$282$	0	0
$283$	−2.17272e6	−1.61264	−0.806319	−	0.591481i	$-0.798543\pi$
$283$	−2.17272e6	−1.61264	−0.806319	+	0.591481i	$0.798543\pi$
$284$	0	0
$285$	805200.	0.587208
$286$	0	0
$287$	−876022.	−0.627784
$288$	0	0
$289$	−826957.	−0.582423
$290$	0	0
$291$	−1.65175e6	−1.14344
$292$	0	0
$293$	142902.	0.0972454	0.0486227	−	0.998817i	$-0.484517\pi$
$293$	142902.	0.0972454	0.0486227	+	0.998817i	$0.484517\pi$
$294$	0	0
$295$	737300.	0.493275
$296$	0	0
$297$	2.28182e6	1.50104
$298$	0	0
$299$	−540912.	−0.349904
$300$	0	0
$301$	−807324.	−0.513608
$302$	0	0
$303$	625032.	0.391107
$304$	0	0
$305$	690750.	0.425178
$306$	0	0
$307$	−1.05277e6	−0.637512	−0.318756	−	0.947837i	$-0.603265\pi$
$307$	−1.05277e6	−0.637512	−0.318756	+	0.947837i	$0.603265\pi$
$308$	0	0
$309$	−1.53859e6	−0.916700
$310$	0	0
$311$	3.11214e6	1.82456	0.912279	−	0.409570i	$-0.134321\pi$
$311$	3.11214e6	1.82456	0.912279	+	0.409570i	$0.134321\pi$
$312$	0	0
$313$	−1.95676e6	−1.12895	−0.564477	−	0.825449i	$-0.690922\pi$
$313$	−1.95676e6	−1.12895	−0.564477	+	0.825449i	$0.690922\pi$
$314$	0	0
$315$	−121275.	−0.0688644
$316$	0	0
$317$	2.74800e6	1.53592	0.767959	−	0.640499i	$-0.221272\pi$
$317$	2.74800e6	1.53592	0.767959	+	0.640499i	$0.221272\pi$
$318$	0	0
$319$	1.34441e6	0.739698
$320$	0	0
$321$	−1.36008e6	−0.736719
$322$	0	0
$323$	2.06668e6	1.10222
$324$	0	0
$325$	−221250.	−0.116192
$326$	0	0
$327$	−1.66735e6	−0.862299
$328$	0	0
$329$	−263424.	−0.134173
$330$	0	0
$331$	−2.23019e6	−1.11885	−0.559425	−	0.828881i	$-0.688978\pi$
$331$	−2.23019e6	−1.11885	−0.559425	+	0.828881i	$0.688978\pi$
$332$	0	0
$333$	31086.0	0.0153622
$334$	0	0
$335$	−1.44290e6	−0.702464
$336$	0	0
$337$	3.13439e6	1.50341	0.751706	−	0.659499i	$-0.229231\pi$
$337$	3.13439e6	1.50341	0.751706	+	0.659499i	$0.229231\pi$
$338$	0	0
$339$	−336552.	−0.159057
$340$	0	0
$341$	4.35904e6	2.03004
$342$	0	0
$343$	117649.	0.0539949
$344$	0	0
$345$	458400.	0.207347
$346$	0	0
$347$	−2.43003e6	−1.08340	−0.541698	−	0.840573i	$-0.682219\pi$
$347$	−2.43003e6	−1.08340	−0.541698	+	0.840573i	$0.682219\pi$
$348$	0	0
$349$	3.46062e6	1.52086	0.760432	−	0.649417i	$-0.224987\pi$
$349$	3.46062e6	1.52086	0.760432	+	0.649417i	$0.224987\pi$
$350$	0	0
$351$	1.45282e6	0.629423
$352$	0	0
$353$	−1.25627e6	−0.536595	−0.268297	−	0.963336i	$-0.586461\pi$
$353$	−1.25627e6	−0.536595	−0.268297	+	0.963336i	$0.586461\pi$
$354$	0	0
$355$	−1.76620e6	−0.743822
$356$	0	0
$357$	452760.	0.188017
$358$	0	0
$359$	−878712.	−0.359841	−0.179920	−	0.983681i	$-0.557584\pi$
$359$	−878712.	−0.359841	−0.179920	+	0.983681i	$0.557584\pi$
$360$	0	0
$361$	4.72776e6	1.90936
$362$	0	0
$363$	1.77702e6	0.707825
$364$	0	0
$365$	1.85505e6	0.728825
$366$	0	0
$367$	−234880.	−0.0910292	−0.0455146	−	0.998964i	$-0.514493\pi$
$367$	−234880.	−0.0910292	−0.0455146	+	0.998964i	$0.514493\pi$
$368$	0	0
$369$	1.76992e6	0.676688
$370$	0	0
$371$	81046.0	0.0305701
$372$	0	0
$373$	97430.0	0.0362594	0.0181297	−	0.999836i	$-0.494229\pi$
$373$	97430.0	0.0362594	0.0181297	+	0.999836i	$0.494229\pi$
$374$	0	0
$375$	187500.	0.0688530
$376$	0	0
$377$	855972.	0.310175
$378$	0	0
$379$	1.99722e6	0.714213	0.357107	−	0.934064i	$-0.383763\pi$
$379$	1.99722e6	0.714213	0.357107	+	0.934064i	$0.383763\pi$
$380$	0	0
$381$	320448.	0.113095
$382$	0	0
$383$	−119664.	−0.0416837	−0.0208419	−	0.999783i	$-0.506635\pi$
$383$	−119664.	−0.0416837	−0.0208419	+	0.999783i	$0.506635\pi$
$384$	0	0
$385$	−681100.	−0.234185
$386$	0	0
$387$	1.63112e6	0.553617
$388$	0	0
$389$	327670.	0.109790	0.0548950	−	0.998492i	$-0.482518\pi$
$389$	327670.	0.109790	0.0548950	+	0.998492i	$0.482518\pi$
$390$	0	0
$391$	1.17656e6	0.389199
$392$	0	0
$393$	−84336.0	−0.0275443
$394$	0	0
$395$	−1.85840e6	−0.599303
$396$	0	0
$397$	4.46653e6	1.42231	0.711154	−	0.703036i	$-0.248173\pi$
$397$	4.46653e6	1.42231	0.711154	+	0.703036i	$0.248173\pi$
$398$	0	0
$399$	1.57819e6	0.496281
$400$	0	0
$401$	−1.83249e6	−0.569091	−0.284545	−	0.958663i	$-0.591843\pi$
$401$	−1.83249e6	−0.569091	−0.284545	+	0.958663i	$0.591843\pi$
$402$	0	0
$403$	2.77536e6	0.851249
$404$	0	0
$405$	−629775.	−0.190787
$406$	0	0
$407$	174584.	0.0522418
$408$	0	0
$409$	−5.59393e6	−1.65352	−0.826758	−	0.562558i	$-0.809817\pi$
$409$	−5.59393e6	−1.65352	−0.826758	+	0.562558i	$0.809817\pi$
$410$	0	0
$411$	1.68242e6	0.491282
$412$	0	0
$413$	1.44511e6	0.416894
$414$	0	0
$415$	−1.10170e6	−0.314010
$416$	0	0
$417$	1.15051e6	0.324004
$418$	0	0
$419$	−562772.	−0.156602	−0.0783010	−	0.996930i	$-0.524950\pi$
$419$	−562772.	−0.156602	−0.0783010	+	0.996930i	$0.524950\pi$
$420$	0	0
$421$	679158.	0.186752	0.0933761	−	0.995631i	$-0.470234\pi$
$421$	679158.	0.186752	0.0933761	+	0.995631i	$0.470234\pi$
$422$	0	0
$423$	532224.	0.144625
$424$	0	0
$425$	481250.	0.129240
$426$	0	0
$427$	1.35387e6	0.359341
$428$	0	0
$429$	2.36189e6	0.619607
$430$	0	0
$431$	−5.89466e6	−1.52850	−0.764250	−	0.644920i	$-0.776891\pi$
$431$	−5.89466e6	−1.52850	−0.764250	+	0.644920i	$0.776891\pi$
$432$	0	0
$433$	−1.64499e6	−0.421642	−0.210821	−	0.977525i	$-0.567614\pi$
$433$	−1.64499e6	−0.421642	−0.210821	+	0.977525i	$0.567614\pi$
$434$	0	0
$435$	−725400.	−0.183804
$436$	0	0
$437$	4.10115e6	1.02731
$438$	0	0
$439$	4.20138e6	1.04047	0.520237	−	0.854022i	$-0.325844\pi$
$439$	4.20138e6	1.04047	0.520237	+	0.854022i	$0.325844\pi$
$440$	0	0
$441$	−237699.	−0.0582011
$442$	0	0
$443$	565684.	0.136951	0.0684754	−	0.997653i	$-0.478187\pi$
$443$	565684.	0.136951	0.0684754	+	0.997653i	$0.478187\pi$
$444$	0	0
$445$	3.23265e6	0.773853
$446$	0	0
$447$	−4.16402e6	−0.985699
$448$	0	0
$449$	648386.	0.151781	0.0758906	−	0.997116i	$-0.475820\pi$
$449$	648386.	0.151781	0.0758906	+	0.997116i	$0.475820\pi$
$450$	0	0
$451$	9.94017e6	2.30119
$452$	0	0
$453$	3.24394e6	0.742723
$454$	0	0
$455$	−433650.	−0.0981999
$456$	0	0
$457$	−1.74713e6	−0.391322	−0.195661	−	0.980672i	$-0.562685\pi$
$457$	−1.74713e6	−0.391322	−0.195661	+	0.980672i	$0.562685\pi$
$458$	0	0
$459$	−3.16008e6	−0.700110
$460$	0	0
$461$	−317378.	−0.0695544	−0.0347772	−	0.999395i	$-0.511072\pi$
$461$	−317378.	−0.0695544	−0.0347772	+	0.999395i	$0.511072\pi$
$462$	0	0
$463$	5.84678e6	1.26755	0.633774	−	0.773518i	$-0.281505\pi$
$463$	5.84678e6	1.26755	0.633774	+	0.773518i	$0.281505\pi$
$464$	0	0
$465$	−2.35200e6	−0.504435
$466$	0	0
$467$	3.67257e6	0.779252	0.389626	−	0.920973i	$-0.372604\pi$
$467$	3.67257e6	0.779252	0.389626	+	0.920973i	$0.372604\pi$
$468$	0	0
$469$	−2.82808e6	−0.593691
$470$	0	0
$471$	−1.81423e6	−0.376826
$472$	0	0
$473$	9.16066e6	1.88267
$474$	0	0
$475$	1.67750e6	0.341137
$476$	0	0
$477$	−163746.	−0.0329515
$478$	0	0
$479$	1.66333e6	0.331237	0.165619	−	0.986190i	$-0.447038\pi$
$479$	1.66333e6	0.331237	0.165619	+	0.986190i	$0.447038\pi$
$480$	0	0
$481$	111156.	0.0219064
$482$	0	0
$483$	898464.	0.175240
$484$	0	0
$485$	−3.44115e6	−0.664277
$486$	0	0
$487$	−4.34505e6	−0.830180	−0.415090	−	0.909780i	$-0.636250\pi$
$487$	−4.34505e6	−0.830180	−0.415090	+	0.909780i	$0.636250\pi$
$488$	0	0
$489$	−7.05778e6	−1.33474
$490$	0	0
$491$	6.65016e6	1.24488	0.622442	−	0.782666i	$-0.286141\pi$
$491$	6.65016e6	1.24488	0.622442	+	0.782666i	$0.286141\pi$
$492$	0	0
$493$	−1.86186e6	−0.345008
$494$	0	0
$495$	1.37610e6	0.252428
$496$	0	0
$497$	−3.46175e6	−0.628644
$498$	0	0
$499$	−742996.	−0.133578	−0.0667890	−	0.997767i	$-0.521275\pi$
$499$	−742996.	−0.133578	−0.0667890	+	0.997767i	$0.521275\pi$
$500$	0	0
$501$	−742944.	−0.132240
$502$	0	0
$503$	5.57126e6	0.981823	0.490911	−	0.871209i	$-0.336664\pi$
$503$	5.57126e6	0.981823	0.490911	+	0.871209i	$0.336664\pi$
$504$	0	0
$505$	1.30215e6	0.227213
$506$	0	0
$507$	−2.95172e6	−0.509983
$508$	0	0
$509$	−5.91247e6	−1.01152	−0.505760	−	0.862674i	$-0.668788\pi$
$509$	−5.91247e6	−1.01152	−0.505760	+	0.862674i	$0.668788\pi$
$510$	0	0
$511$	3.63590e6	0.615970
$512$	0	0
$513$	−1.10151e7	−1.84798
$514$	0	0
$515$	−3.20540e6	−0.532555
$516$	0	0
$517$	2.98906e6	0.491822
$518$	0	0
$519$	58344.0	0.00950775
$520$	0	0
$521$	6.34065e6	1.02339	0.511693	−	0.859168i	$-0.329019\pi$
$521$	6.34065e6	1.02339	0.511693	+	0.859168i	$0.329019\pi$
$522$	0	0
$523$	−118300.	−0.0189117	−0.00945585	−	0.999955i	$-0.503010\pi$
$523$	−118300.	−0.0189117	−0.00945585	+	0.999955i	$0.503010\pi$
$524$	0	0
$525$	367500.	0.0581914
$526$	0	0
$527$	−6.03680e6	−0.946848
$528$	0	0
$529$	−4.10156e6	−0.637250
$530$	0	0
$531$	−2.91971e6	−0.449369
$532$	0	0
$533$	6.32881e6	0.964949
$534$	0	0
$535$	−2.83350e6	−0.427995
$536$	0	0
$537$	215568.	0.0322588
$538$	0	0
$539$	−1.33496e6	−0.197922
$540$	0	0
$541$	5.36248e6	0.787721	0.393860	−	0.919170i	$-0.371139\pi$
$541$	5.36248e6	0.787721	0.393860	+	0.919170i	$0.371139\pi$
$542$	0	0
$543$	2.74106e6	0.398951
$544$	0	0
$545$	−3.47365e6	−0.500950
$546$	0	0
$547$	579116.	0.0827556	0.0413778	−	0.999144i	$-0.486825\pi$
$547$	579116.	0.0827556	0.0413778	+	0.999144i	$0.486825\pi$
$548$	0	0
$549$	−2.73537e6	−0.387334
$550$	0	0
$551$	−6.48991e6	−0.910667
$552$	0	0
$553$	−3.64246e6	−0.506503
$554$	0	0
$555$	−94200.0	−0.0129813
$556$	0	0
$557$	6.61880e6	0.903943	0.451972	−	0.892032i	$-0.350721\pi$
$557$	6.61880e6	0.903943	0.451972	+	0.892032i	$0.350721\pi$
$558$	0	0
$559$	5.83250e6	0.789452
$560$	0	0
$561$	−5.13744e6	−0.689191
$562$	0	0
$563$	2.65907e6	0.353556	0.176778	−	0.984251i	$-0.443433\pi$
$563$	2.65907e6	0.353556	0.176778	+	0.984251i	$0.443433\pi$
$564$	0	0
$565$	−701150.	−0.0924038
$566$	0	0
$567$	−1.23436e6	−0.161244
$568$	0	0
$569$	−1.12650e7	−1.45865	−0.729324	−	0.684169i	$-0.760165\pi$
$569$	−1.12650e7	−1.45865	−0.729324	+	0.684169i	$0.760165\pi$
$570$	0	0
$571$	4.05242e6	0.520145	0.260072	−	0.965589i	$-0.416254\pi$
$571$	4.05242e6	0.520145	0.260072	+	0.965589i	$0.416254\pi$
$572$	0	0
$573$	4.29408e6	0.546366
$574$	0	0
$575$	955000.	0.120457
$576$	0	0
$577$	−5.07566e6	−0.634678	−0.317339	−	0.948312i	$-0.602789\pi$
$577$	−5.07566e6	−0.634678	−0.317339	+	0.948312i	$0.602789\pi$
$578$	0	0
$579$	−5.93009e6	−0.735131
$580$	0	0
$581$	−2.15933e6	−0.265387
$582$	0	0
$583$	−919624.	−0.112057
$584$	0	0
$585$	876150.	0.105849
$586$	0	0
$587$	9.07079e6	1.08655	0.543275	−	0.839555i	$-0.317184\pi$
$587$	9.07079e6	1.08655	0.543275	+	0.839555i	$0.317184\pi$
$588$	0	0
$589$	−2.10426e7	−2.49925
$590$	0	0
$591$	7.14362e6	0.841298
$592$	0	0
$593$	1.47793e7	1.72590	0.862951	−	0.505288i	$-0.168614\pi$
$593$	1.47793e7	1.72590	0.862951	+	0.505288i	$0.168614\pi$
$594$	0	0
$595$	943250.	0.109228
$596$	0	0
$597$	3.13450e6	0.359941
$598$	0	0
$599$	−9.06212e6	−1.03196	−0.515980	−	0.856601i	$-0.672572\pi$
$599$	−9.06212e6	−1.03196	−0.515980	+	0.856601i	$0.672572\pi$
$600$	0	0
$601$	−2.65482e6	−0.299812	−0.149906	−	0.988700i	$-0.547897\pi$
$601$	−2.65482e6	−0.299812	−0.149906	+	0.988700i	$0.547897\pi$
$602$	0	0
$603$	5.71388e6	0.639938
$604$	0	0
$605$	3.70212e6	0.411209
$606$	0	0
$607$	−1.52930e7	−1.68470	−0.842349	−	0.538932i	$-0.818828\pi$
$607$	−1.52930e7	−1.68470	−0.842349	+	0.538932i	$0.818828\pi$
$608$	0	0
$609$	−1.42178e6	−0.155343
$610$	0	0
$611$	1.90310e6	0.206234
$612$	0	0
$613$	1.49070e7	1.60228	0.801139	−	0.598479i	$-0.204228\pi$
$613$	1.49070e7	1.60228	0.801139	+	0.598479i	$0.204228\pi$
$614$	0	0
$615$	−5.36340e6	−0.571811
$616$	0	0
$617$	5.12030e6	0.541480	0.270740	−	0.962653i	$-0.412732\pi$
$617$	5.12030e6	0.541480	0.270740	+	0.962653i	$0.412732\pi$
$618$	0	0
$619$	4.83140e6	0.506811	0.253405	−	0.967360i	$-0.418449\pi$
$619$	4.83140e6	0.506811	0.253405	+	0.967360i	$0.418449\pi$
$620$	0	0
$621$	−6.27091e6	−0.652532
$622$	0	0
$623$	6.33599e6	0.654025
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	−1.79076e7	−1.81915
$628$	0	0
$629$	−241780.	−0.0243665
$630$	0	0
$631$	−5.78212e6	−0.578114	−0.289057	−	0.957312i	$-0.593342\pi$
$631$	−5.78212e6	−0.578114	−0.289057	+	0.957312i	$0.593342\pi$
$632$	0	0
$633$	−9.46277e6	−0.938661
$634$	0	0
$635$	667600.	0.0657025
$636$	0	0
$637$	−849954.	−0.0829940
$638$	0	0
$639$	6.99415e6	0.677615
$640$	0	0
$641$	−1.65691e7	−1.59277	−0.796386	−	0.604789i	$-0.793257\pi$
$641$	−1.65691e7	−1.59277	−0.796386	+	0.604789i	$0.793257\pi$
$642$	0	0
$643$	9.28491e6	0.885626	0.442813	−	0.896614i	$-0.353981\pi$
$643$	9.28491e6	0.885626	0.442813	+	0.896614i	$0.353981\pi$
$644$	0	0
$645$	−4.94280e6	−0.467815
$646$	0	0
$647$	1.31505e7	1.23504	0.617519	−	0.786556i	$-0.288138\pi$
$647$	1.31505e7	1.23504	0.617519	+	0.786556i	$0.288138\pi$
$648$	0	0
$649$	−1.63976e7	−1.52815
$650$	0	0
$651$	−4.60992e6	−0.426325
$652$	0	0
$653$	−6.28207e6	−0.576527	−0.288263	−	0.957551i	$-0.593078\pi$
$653$	−6.28207e6	−0.576527	−0.288263	+	0.957551i	$0.593078\pi$
$654$	0	0
$655$	−175700.	−0.0160018
$656$	0	0
$657$	−7.34600e6	−0.663953
$658$	0	0
$659$	2.16007e7	1.93756	0.968779	−	0.247927i	$-0.0797492\pi$
$659$	2.16007e7	1.93756	0.968779	+	0.247927i	$0.0797492\pi$
$660$	0	0
$661$	−5.79235e6	−0.515645	−0.257823	−	0.966192i	$-0.583005\pi$
$661$	−5.79235e6	−0.515645	−0.257823	+	0.966192i	$0.583005\pi$
$662$	0	0
$663$	−3.27096e6	−0.288996
$664$	0	0
$665$	3.28790e6	0.288313
$666$	0	0
$667$	−3.69470e6	−0.321562
$668$	0	0
$669$	1.63010e7	1.40815
$670$	0	0
$671$	−1.53623e7	−1.31719
$672$	0	0
$673$	1.45071e7	1.23465	0.617324	−	0.786709i	$-0.288217\pi$
$673$	1.45071e7	1.23465	0.617324	+	0.786709i	$0.288217\pi$
$674$	0	0
$675$	−2.56500e6	−0.216685
$676$	0	0
$677$	1.66775e7	1.39849	0.699243	−	0.714884i	$-0.253520\pi$
$677$	1.66775e7	1.39849	0.699243	+	0.714884i	$0.253520\pi$
$678$	0	0
$679$	−6.74465e6	−0.561417
$680$	0	0
$681$	5.53282e6	0.457171
$682$	0	0
$683$	−3.35555e6	−0.275240	−0.137620	−	0.990485i	$-0.543945\pi$
$683$	−3.35555e6	−0.275240	−0.137620	+	0.990485i	$0.543945\pi$
$684$	0	0
$685$	3.50505e6	0.285409
$686$	0	0
$687$	1.50611e7	1.21749
$688$	0	0
$689$	−585516.	−0.0469884
$690$	0	0
$691$	−80036.0	−0.00637662	−0.00318831	−	0.999995i	$-0.501015\pi$
$691$	−80036.0	−0.00637662	−0.00318831	+	0.999995i	$0.501015\pi$
$692$	0	0
$693$	2.69716e6	0.213340
$694$	0	0
$695$	2.39690e6	0.188230
$696$	0	0
$697$	−1.37661e7	−1.07332
$698$	0	0
$699$	6.04697e6	0.468107
$700$	0	0
$701$	1.26403e7	0.971544	0.485772	−	0.874086i	$-0.338539\pi$
$701$	1.26403e7	0.971544	0.485772	+	0.874086i	$0.338539\pi$
$702$	0	0
$703$	−842776.	−0.0643167
$704$	0	0
$705$	−1.61280e6	−0.122210
$706$	0	0
$707$	2.55221e6	0.192030
$708$	0	0
$709$	1.03203e7	0.771043	0.385521	−	0.922699i	$-0.374022\pi$
$709$	1.03203e7	0.771043	0.385521	+	0.922699i	$0.374022\pi$
$710$	0	0
$711$	7.35926e6	0.545959
$712$	0	0
$713$	−1.19795e7	−0.882502
$714$	0	0
$715$	4.92060e6	0.359959
$716$	0	0
$717$	−1.81083e7	−1.31547
$718$	0	0
$719$	−1.32330e7	−0.954630	−0.477315	−	0.878732i	$-0.658390\pi$
$719$	−1.32330e7	−0.954630	−0.477315	+	0.878732i	$0.658390\pi$
$720$	0	0
$721$	−6.28258e6	−0.450091
$722$	0	0
$723$	−756264.	−0.0538056
$724$	0	0
$725$	−1.51125e6	−0.106780
$726$	0	0
$727$	−1.89447e6	−0.132939	−0.0664695	−	0.997788i	$-0.521173\pi$
$727$	−1.89447e6	−0.132939	−0.0664695	+	0.997788i	$0.521173\pi$
$728$	0	0
$729$	1.44612e7	1.00782
$730$	0	0
$731$	−1.26865e7	−0.878110
$732$	0	0
$733$	−3.25023e6	−0.223436	−0.111718	−	0.993740i	$-0.535635\pi$
$733$	−3.25023e6	−0.223436	−0.111718	+	0.993740i	$0.535635\pi$
$734$	0	0
$735$	720300.	0.0491807
$736$	0	0
$737$	3.20901e7	2.17622
$738$	0	0
$739$	−2.56366e7	−1.72683	−0.863415	−	0.504495i	$-0.831679\pi$
$739$	−2.56366e7	−1.72683	−0.863415	+	0.504495i	$0.831679\pi$
$740$	0	0
$741$	−1.14016e7	−0.762819
$742$	0	0
$743$	1.10332e7	0.733209	0.366605	−	0.930377i	$-0.380520\pi$
$743$	1.10332e7	0.733209	0.366605	+	0.930377i	$0.380520\pi$
$744$	0	0
$745$	−8.67505e6	−0.572640
$746$	0	0
$747$	4.36273e6	0.286060
$748$	0	0
$749$	−5.55366e6	−0.361722
$750$	0	0
$751$	−1.75977e7	−1.13856	−0.569279	−	0.822144i	$-0.692778\pi$
$751$	−1.75977e7	−1.13856	−0.569279	+	0.822144i	$0.692778\pi$
$752$	0	0
$753$	1.15778e7	0.744115
$754$	0	0
$755$	6.75820e6	0.431483
$756$	0	0
$757$	−9.25444e6	−0.586963	−0.293481	−	0.955965i	$-0.594814\pi$
$757$	−9.25444e6	−0.586963	−0.293481	+	0.955965i	$0.594814\pi$
$758$	0	0
$759$	−1.01948e7	−0.642355
$760$	0	0
$761$	1.36640e7	0.855293	0.427647	−	0.903946i	$-0.359343\pi$
$761$	1.36640e7	0.855293	0.427647	+	0.903946i	$0.359343\pi$
$762$	0	0
$763$	−6.80835e6	−0.423380
$764$	0	0
$765$	−1.90575e6	−0.117737
$766$	0	0
$767$	−1.04402e7	−0.640795
$768$	0	0
$769$	−2.98498e7	−1.82023	−0.910114	−	0.414357i	$-0.864006\pi$
$769$	−2.98498e7	−1.82023	−0.910114	+	0.414357i	$0.864006\pi$
$770$	0	0
$771$	−5.94180e6	−0.359983
$772$	0	0
$773$	2.32878e7	1.40178	0.700891	−	0.713269i	$-0.252786\pi$
$773$	2.32878e7	1.40178	0.700891	+	0.713269i	$0.252786\pi$
$774$	0	0
$775$	−4.90000e6	−0.293050
$776$	0	0
$777$	−184632.	−0.0109712
$778$	0	0
$779$	−4.79846e7	−2.83307
$780$	0	0
$781$	3.92803e7	2.30434
$782$	0	0
$783$	9.92347e6	0.578441
$784$	0	0
$785$	−3.77965e6	−0.218916
$786$	0	0
$787$	1.01691e7	0.585259	0.292629	−	0.956226i	$-0.405470\pi$
$787$	1.01691e7	0.585259	0.292629	+	0.956226i	$0.405470\pi$
$788$	0	0
$789$	−2.61710e7	−1.49668
$790$	0	0
$791$	−1.37425e6	−0.0780955
$792$	0	0
$793$	−9.78102e6	−0.552333
$794$	0	0
$795$	496200.	0.0278445
$796$	0	0
$797$	2.43192e6	0.135614	0.0678068	−	0.997698i	$-0.478400\pi$
$797$	2.43192e6	0.135614	0.0678068	+	0.997698i	$0.478400\pi$
$798$	0	0
$799$	−4.13952e6	−0.229395
$800$	0	0
$801$	−1.28013e7	−0.704973
$802$	0	0
$803$	−4.12563e7	−2.25788
$804$	0	0
$805$	1.87180e6	0.101805
$806$	0	0
$807$	−5.68015e6	−0.307027
$808$	0	0
$809$	1.41960e7	0.762595	0.381298	−	0.924452i	$-0.375477\pi$
$809$	1.41960e7	0.762595	0.381298	+	0.924452i	$0.375477\pi$
$810$	0	0
$811$	−1.75548e6	−0.0937227	−0.0468613	−	0.998901i	$-0.514922\pi$
$811$	−1.75548e6	−0.0937227	−0.0468613	+	0.998901i	$0.514922\pi$
$812$	0	0
$813$	2.63080e7	1.39592
$814$	0	0
$815$	−1.47037e7	−0.775412
$816$	0	0
$817$	−4.42216e7	−2.31782
$818$	0	0
$819$	1.71725e6	0.0894592
$820$	0	0
$821$	1.69715e7	0.878742	0.439371	−	0.898306i	$-0.355201\pi$
$821$	1.69715e7	0.878742	0.439371	+	0.898306i	$0.355201\pi$
$822$	0	0
$823$	8.85241e6	0.455577	0.227789	−	0.973711i	$-0.426851\pi$
$823$	8.85241e6	0.455577	0.227789	+	0.973711i	$0.426851\pi$
$824$	0	0
$825$	−4.17000e6	−0.213305
$826$	0	0
$827$	−2.48418e7	−1.26304	−0.631522	−	0.775358i	$-0.717570\pi$
$827$	−2.48418e7	−1.26304	−0.631522	+	0.775358i	$0.717570\pi$
$828$	0	0
$829$	3.55691e6	0.179757	0.0898787	−	0.995953i	$-0.471352\pi$
$829$	3.55691e6	0.179757	0.0898787	+	0.995953i	$0.471352\pi$
$830$	0	0
$831$	4.66202e6	0.234192
$832$	0	0
$833$	1.84877e6	0.0923146
$834$	0	0
$835$	−1.54780e6	−0.0768243
$836$	0	0
$837$	3.21754e7	1.58749
$838$	0	0
$839$	−2.51401e7	−1.23300	−0.616499	−	0.787356i	$-0.711449\pi$
$839$	−2.51401e7	−1.23300	−0.616499	+	0.787356i	$0.711449\pi$
$840$	0	0
$841$	−1.46644e7	−0.714949
$842$	0	0
$843$	−905544.	−0.0438875
$844$	0	0
$845$	−6.14942e6	−0.296273
$846$	0	0
$847$	7.25616e6	0.347535
$848$	0	0
$849$	−2.60726e7	−1.24141
$850$	0	0
$851$	−479792.	−0.0227106
$852$	0	0
$853$	−1.01242e7	−0.476419	−0.238209	−	0.971214i	$-0.576560\pi$
$853$	−1.01242e7	−0.476419	−0.238209	+	0.971214i	$0.576560\pi$
$854$	0	0
$855$	−6.64290e6	−0.310772
$856$	0	0
$857$	−1.05522e7	−0.490784	−0.245392	−	0.969424i	$-0.578917\pi$
$857$	−1.05522e7	−0.490784	−0.245392	+	0.969424i	$0.578917\pi$
$858$	0	0
$859$	−3.37758e7	−1.56179	−0.780894	−	0.624663i	$-0.785236\pi$
$859$	−3.37758e7	−1.56179	−0.780894	+	0.624663i	$0.785236\pi$
$860$	0	0
$861$	−1.05123e7	−0.483268
$862$	0	0
$863$	3.12652e7	1.42901	0.714503	−	0.699633i	$-0.246653\pi$
$863$	3.12652e7	1.42901	0.714503	+	0.699633i	$0.246653\pi$
$864$	0	0
$865$	121550.	0.00552350
$866$	0	0
$867$	−9.92348e6	−0.448349
$868$	0	0
$869$	4.13308e7	1.85663
$870$	0	0
$871$	2.04315e7	0.912545
$872$	0	0
$873$	1.36270e7	0.605150
$874$	0	0
$875$	765625.	0.0338062
$876$	0	0
$877$	−2.89921e7	−1.27286	−0.636430	−	0.771334i	$-0.719590\pi$
$877$	−2.89921e7	−1.27286	−0.636430	+	0.771334i	$0.719590\pi$
$878$	0	0
$879$	1.71482e6	0.0748596
$880$	0	0
$881$	−6.43211e6	−0.279199	−0.139599	−	0.990208i	$-0.544581\pi$
$881$	−6.43211e6	−0.279199	−0.139599	+	0.990208i	$0.544581\pi$
$882$	0	0
$883$	2.41164e7	1.04090	0.520452	−	0.853891i	$-0.325764\pi$
$883$	2.41164e7	1.04090	0.520452	+	0.853891i	$0.325764\pi$
$884$	0	0
$885$	8.84760e6	0.379723
$886$	0	0
$887$	−4.16359e6	−0.177688	−0.0888442	−	0.996046i	$-0.528317\pi$
$887$	−4.16359e6	−0.177688	−0.0888442	+	0.996046i	$0.528317\pi$
$888$	0	0
$889$	1.30850e6	0.0555288
$890$	0	0
$891$	1.40062e7	0.591052
$892$	0	0
$893$	−1.44292e7	−0.605499
$894$	0	0
$895$	449100.	0.0187407
$896$	0	0
$897$	−6.49094e6	−0.269356
$898$	0	0
$899$	1.89571e7	0.782300
$900$	0	0
$901$	1.27358e6	0.0522654
$902$	0	0
$903$	−9.68789e6	−0.395375
$904$	0	0
$905$	5.71055e6	0.231770
$906$	0	0
$907$	4.18248e7	1.68817	0.844083	−	0.536212i	$-0.180145\pi$
$907$	4.18248e7	1.68817	0.844083	+	0.536212i	$0.180145\pi$
$908$	0	0
$909$	−5.15651e6	−0.206989
$910$	0	0
$911$	2.96323e6	0.118296	0.0591480	−	0.998249i	$-0.481162\pi$
$911$	2.96323e6	0.118296	0.0591480	+	0.998249i	$0.481162\pi$
$912$	0	0
$913$	2.45018e7	0.972795
$914$	0	0
$915$	8.28900e6	0.327303
$916$	0	0
$917$	−344372.	−0.0135240
$918$	0	0
$919$	−2.22355e7	−0.868476	−0.434238	−	0.900798i	$-0.642982\pi$
$919$	−2.22355e7	−0.868476	−0.434238	+	0.900798i	$0.642982\pi$
$920$	0	0
$921$	−1.26333e7	−0.490757
$922$	0	0
$923$	2.50094e7	0.966271
$924$	0	0
$925$	−196250.	−0.00754146
$926$	0	0
$927$	1.26934e7	0.485152
$928$	0	0
$929$	−9.65046e6	−0.366867	−0.183434	−	0.983032i	$-0.558721\pi$
$929$	−9.65046e6	−0.366867	−0.183434	+	0.983032i	$0.558721\pi$
$930$	0	0
$931$	6.44428e6	0.243669
$932$	0	0
$933$	3.73456e7	1.40455
$934$	0	0
$935$	−1.07030e7	−0.400384
$936$	0	0
$937$	−4.45116e7	−1.65624	−0.828122	−	0.560548i	$-0.810590\pi$
$937$	−4.45116e7	−1.65624	−0.828122	+	0.560548i	$0.810590\pi$
$938$	0	0
$939$	−2.34811e7	−0.869069
$940$	0	0
$941$	1.08983e7	0.401223	0.200612	−	0.979671i	$-0.435707\pi$
$941$	1.08983e7	0.401223	0.200612	+	0.979671i	$0.435707\pi$
$942$	0	0
$943$	−2.73176e7	−1.00038
$944$	0	0
$945$	−5.02740e6	−0.183132
$946$	0	0
$947$	1.37370e7	0.497757	0.248879	−	0.968535i	$-0.419938\pi$
$947$	1.37370e7	0.497757	0.248879	+	0.968535i	$0.419938\pi$
$948$	0	0
$949$	−2.62675e7	−0.946789
$950$	0	0
$951$	3.29760e7	1.18235
$952$	0	0
$953$	−2.78867e7	−0.994639	−0.497319	−	0.867568i	$-0.665682\pi$
$953$	−2.78867e7	−0.994639	−0.497319	+	0.867568i	$0.665682\pi$
$954$	0	0
$955$	8.94600e6	0.317410
$956$	0	0
$957$	1.61329e7	0.569420
$958$	0	0
$959$	6.86990e6	0.241215
$960$	0	0
$961$	3.28364e7	1.14696
$962$	0	0
$963$	1.12207e7	0.389900
$964$	0	0
$965$	−1.23543e7	−0.427073
$966$	0	0
$967$	−7.36444e6	−0.253264	−0.126632	−	0.991950i	$-0.540417\pi$
$967$	−7.36444e6	−0.253264	−0.126632	+	0.991950i	$0.540417\pi$
$968$	0	0
$969$	2.48002e7	0.848487
$970$	0	0
$971$	8.71508e6	0.296635	0.148318	−	0.988940i	$-0.452614\pi$
$971$	8.71508e6	0.296635	0.148318	+	0.988940i	$0.452614\pi$
$972$	0	0
$973$	4.69792e6	0.159083
$974$	0	0
$975$	−2.65500e6	−0.0894444
$976$	0	0
$977$	−1.60032e7	−0.536377	−0.268188	−	0.963366i	$-0.586425\pi$
$977$	−1.60032e7	−0.536377	−0.268188	+	0.963366i	$0.586425\pi$
$978$	0	0
$979$	−7.18941e7	−2.39738
$980$	0	0
$981$	1.37557e7	0.456361
$982$	0	0
$983$	3.81746e7	1.26006	0.630030	−	0.776571i	$-0.283043\pi$
$983$	3.81746e7	1.26006	0.630030	+	0.776571i	$0.283043\pi$
$984$	0	0
$985$	1.48826e7	0.488750
$986$	0	0
$987$	−3.16109e6	−0.103287
$988$	0	0
$989$	−2.51753e7	−0.818435
$990$	0	0
$991$	3.76979e7	1.21936	0.609681	−	0.792647i	$-0.291298\pi$
$991$	3.76979e7	1.21936	0.609681	+	0.792647i	$0.291298\pi$
$992$	0	0
$993$	−2.67623e7	−0.861290
$994$	0	0
$995$	6.53020e6	0.209107
$996$	0	0
$997$	4.40251e7	1.40269	0.701347	−	0.712820i	$-0.252582\pi$
$997$	4.40251e7	1.40269	0.701347	+	0.712820i	$0.252582\pi$
$998$	0	0
$999$	1.28866e6	0.0408529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.6.a.g.1.1		1
4.3	odd	2		280.6.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.6.a.a.1.1	✓	1	4.3	odd	2
560.6.a.g.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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	560.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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