LMFDB - Embedded newform 585.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,6,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("585.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	585.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:	$93.8245345906$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-5.00000 q^{2} -7.00000 q^{4} +25.0000 q^{5} -244.000 q^{7} +195.000 q^{8} +O(q^{10})$

\(q-5.00000 q^{2} -7.00000 q^{4} +25.0000 q^{5} -244.000 q^{7} +195.000 q^{8} -125.000 q^{10} -794.000 q^{11} -169.000 q^{13} +1220.00 q^{14} -751.000 q^{16} +1534.00 q^{17} +2706.00 q^{19} -175.000 q^{20} +3970.00 q^{22} +702.000 q^{23} +625.000 q^{25} +845.000 q^{26} +1708.00 q^{28} +5038.00 q^{29} -3634.00 q^{31} -2485.00 q^{32} -7670.00 q^{34} -6100.00 q^{35} -7058.00 q^{37} -13530.0 q^{38} +4875.00 q^{40} +294.000 q^{41} +7618.00 q^{43} +5558.00 q^{44} -3510.00 q^{46} +3020.00 q^{47} +42729.0 q^{49} -3125.00 q^{50} +1183.00 q^{52} -626.000 q^{53} -19850.0 q^{55} -47580.0 q^{56} -25190.0 q^{58} +30066.0 q^{59} -5806.00 q^{61} +18170.0 q^{62} +36457.0 q^{64} -4225.00 q^{65} -12436.0 q^{67} -10738.0 q^{68} +30500.0 q^{70} -4734.00 q^{71} -14694.0 q^{73} +35290.0 q^{74} -18942.0 q^{76} +193736. q^{77} -39804.0 q^{79} -18775.0 q^{80} -1470.00 q^{82} +41776.0 q^{83} +38350.0 q^{85} -38090.0 q^{86} -154830. q^{88} -7970.00 q^{89} +41236.0 q^{91} -4914.00 q^{92} -15100.0 q^{94} +67650.0 q^{95} -78050.0 q^{97} -213645. q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.00000	−0.883883	−0.441942	−	0.897044i	$-0.645710\pi$
$2$	−5.00000	−0.883883	−0.441942	+	0.897044i	$0.645710\pi$
$3$	0	0
$3$	0	0
$4$	−7.00000	−0.218750
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	−244.000	−1.88211	−0.941054	−	0.338255i	$-0.890163\pi$
$7$	−244.000	−1.88211	−0.941054	+	0.338255i	$0.890163\pi$
$8$	195.000	1.07723
$9$	0	0
$10$	−125.000	−0.395285
$11$	−794.000	−1.97851	−0.989256	−	0.146192i	$-0.953298\pi$
$11$	−794.000	−1.97851	−0.989256	+	0.146192i	$0.953298\pi$
$12$	0	0
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	1220.00	1.66356
$15$	0	0
$16$	−751.000	−0.733398
$17$	1534.00	1.28737	0.643685	−	0.765291i	$-0.277405\pi$
$17$	1534.00	1.28737	0.643685	+	0.765291i	$0.277405\pi$
$18$	0	0
$19$	2706.00	1.71966	0.859832	−	0.510576i	$-0.170568\pi$
$19$	2706.00	1.71966	0.859832	+	0.510576i	$0.170568\pi$
$20$	−175.000	−0.0978280
$21$	0	0
$22$	3970.00	1.74877
$23$	702.000	0.276705	0.138353	−	0.990383i	$-0.455819\pi$
$23$	702.000	0.276705	0.138353	+	0.990383i	$0.455819\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	845.000	0.245145
$27$	0	0
$28$	1708.00	0.411711
$29$	5038.00	1.11241	0.556203	−	0.831047i	$-0.312258\pi$
$29$	5038.00	1.11241	0.556203	+	0.831047i	$0.312258\pi$
$30$	0	0
$31$	−3634.00	−0.679173	−0.339587	−	0.940575i	$-0.610287\pi$
$31$	−3634.00	−0.679173	−0.339587	+	0.940575i	$0.610287\pi$
$32$	−2485.00	−0.428994
$33$	0	0
$34$	−7670.00	−1.13788
$35$	−6100.00	−0.841705
$36$	0	0
$37$	−7058.00	−0.847573	−0.423787	−	0.905762i	$-0.639299\pi$
$37$	−7058.00	−0.847573	−0.423787	+	0.905762i	$0.639299\pi$
$38$	−13530.0	−1.51998
$39$	0	0
$40$	4875.00	0.481753
$41$	294.000	0.0273141	0.0136571	−	0.999907i	$-0.495653\pi$
$41$	294.000	0.0273141	0.0136571	+	0.999907i	$0.495653\pi$
$42$	0	0
$43$	7618.00	0.628304	0.314152	−	0.949373i	$-0.398280\pi$
$43$	7618.00	0.628304	0.314152	+	0.949373i	$0.398280\pi$
$44$	5558.00	0.432800
$45$	0	0
$46$	−3510.00	−0.244575
$47$	3020.00	0.199417	0.0997085	−	0.995017i	$-0.468209\pi$
$47$	3020.00	0.199417	0.0997085	+	0.995017i	$0.468209\pi$
$48$	0	0
$49$	42729.0	2.54233
$50$	−3125.00	−0.176777
$51$	0	0
$52$	1183.00	0.0606703
$53$	−626.000	−0.0306115	−0.0153058	−	0.999883i	$-0.504872\pi$
$53$	−626.000	−0.0306115	−0.0153058	+	0.999883i	$0.504872\pi$
$54$	0	0
$55$	−19850.0	−0.884818
$56$	−47580.0	−2.02747
$57$	0	0
$58$	−25190.0	−0.983237
$59$	30066.0	1.12446	0.562232	−	0.826979i	$-0.309943\pi$
$59$	30066.0	1.12446	0.562232	+	0.826979i	$0.309943\pi$
$60$	0	0
$61$	−5806.00	−0.199780	−0.0998901	−	0.994998i	$-0.531849\pi$
$61$	−5806.00	−0.199780	−0.0998901	+	0.994998i	$0.531849\pi$
$62$	18170.0	0.600310
$63$	0	0
$64$	36457.0	1.11258
$65$	−4225.00	−0.124035
$66$	0	0
$67$	−12436.0	−0.338449	−0.169225	−	0.985577i	$-0.554126\pi$
$67$	−12436.0	−0.338449	−0.169225	+	0.985577i	$0.554126\pi$
$68$	−10738.0	−0.281612
$69$	0	0
$70$	30500.0	0.743969
$71$	−4734.00	−0.111451	−0.0557253	−	0.998446i	$-0.517747\pi$
$71$	−4734.00	−0.111451	−0.0557253	+	0.998446i	$0.517747\pi$
$72$	0	0
$73$	−14694.0	−0.322725	−0.161363	−	0.986895i	$-0.551589\pi$
$73$	−14694.0	−0.322725	−0.161363	+	0.986895i	$0.551589\pi$
$74$	35290.0	0.749156
$75$	0	0
$76$	−18942.0	−0.376177
$77$	193736.	3.72378
$78$	0	0
$79$	−39804.0	−0.717561	−0.358781	−	0.933422i	$-0.616807\pi$
$79$	−39804.0	−0.717561	−0.358781	+	0.933422i	$0.616807\pi$
$80$	−18775.0	−0.327986
$81$	0	0
$82$	−1470.00	−0.0241425
$83$	41776.0	0.665628	0.332814	−	0.942992i	$-0.392002\pi$
$83$	41776.0	0.665628	0.332814	+	0.942992i	$0.392002\pi$
$84$	0	0
$85$	38350.0	0.575729
$86$	−38090.0	−0.555348
$87$	0	0
$88$	−154830.	−2.13132
$89$	−7970.00	−0.106656	−0.0533278	−	0.998577i	$-0.516983\pi$
$89$	−7970.00	−0.106656	−0.0533278	+	0.998577i	$0.516983\pi$
$90$	0	0
$91$	41236.0	0.522003
$92$	−4914.00	−0.0605293
$93$	0	0
$94$	−15100.0	−0.176261
$95$	67650.0	0.769057
$96$	0	0
$97$	−78050.0	−0.842255	−0.421127	−	0.907001i	$-0.638366\pi$
$97$	−78050.0	−0.842255	−0.421127	+	0.907001i	$0.638366\pi$
$98$	−213645.	−2.24713
$99$	0	0
$100$	−4375.00	−0.0437500
$101$	23010.0	0.224447	0.112223	−	0.993683i	$-0.464203\pi$
$101$	23010.0	0.224447	0.112223	+	0.993683i	$0.464203\pi$
$102$	0	0
$103$	121706.	1.13037	0.565183	−	0.824966i	$-0.308806\pi$
$103$	121706.	1.13037	0.565183	+	0.824966i	$0.308806\pi$
$104$	−32955.0	−0.298771
$105$	0	0
$106$	3130.00	0.0270570
$107$	70142.0	0.592269	0.296134	−	0.955146i	$-0.404302\pi$
$107$	70142.0	0.592269	0.296134	+	0.955146i	$0.404302\pi$
$108$	0	0
$109$	−195878.	−1.57914	−0.789568	−	0.613663i	$-0.789695\pi$
$109$	−195878.	−1.57914	−0.789568	+	0.613663i	$0.789695\pi$
$110$	99250.0	0.782076
$111$	0	0
$112$	183244.	1.38034
$113$	100238.	0.738476	0.369238	−	0.929335i	$-0.379619\pi$
$113$	100238.	0.738476	0.369238	+	0.929335i	$0.379619\pi$
$114$	0	0
$115$	17550.0	0.123746
$116$	−35266.0	−0.243339
$117$	0	0
$118$	−150330.	−0.993895
$119$	−374296.	−2.42297
$120$	0	0
$121$	469385.	2.91451
$122$	29030.0	0.176582
$123$	0	0
$124$	25438.0	0.148569
$125$	15625.0	0.0894427
$126$	0	0
$127$	39286.0	0.216137	0.108068	−	0.994143i	$-0.465533\pi$
$127$	39286.0	0.216137	0.108068	+	0.994143i	$0.465533\pi$
$128$	−102765.	−0.554396
$129$	0	0
$130$	21125.0	0.109632
$131$	−211460.	−1.07659	−0.538295	−	0.842757i	$-0.680931\pi$
$131$	−211460.	−1.07659	−0.538295	+	0.842757i	$0.680931\pi$
$132$	0	0
$133$	−660264.	−3.23660
$134$	62180.0	0.299150
$135$	0	0
$136$	299130.	1.38680
$137$	−26302.0	−0.119726	−0.0598628	−	0.998207i	$-0.519066\pi$
$137$	−26302.0	−0.119726	−0.0598628	+	0.998207i	$0.519066\pi$
$138$	0	0
$139$	1344.00	0.00590014	0.00295007	−	0.999996i	$-0.499061\pi$
$139$	1344.00	0.00590014	0.00295007	+	0.999996i	$0.499061\pi$
$140$	42700.0	0.184123
$141$	0	0
$142$	23670.0	0.0985093
$143$	134186.	0.548741
$144$	0	0
$145$	125950.	0.497483
$146$	73470.0	0.285251
$147$	0	0
$148$	49406.0	0.185407
$149$	49086.0	0.181131	0.0905653	−	0.995891i	$-0.471133\pi$
$149$	49086.0	0.181131	0.0905653	+	0.995891i	$0.471133\pi$
$150$	0	0
$151$	−357998.	−1.27773	−0.638864	−	0.769320i	$-0.720595\pi$
$151$	−357998.	−1.27773	−0.638864	+	0.769320i	$0.720595\pi$
$152$	527670.	1.85248
$153$	0	0
$154$	−968680.	−3.29138
$155$	−90850.0	−0.303736
$156$	0	0
$157$	45450.0	0.147158	0.0735791	−	0.997289i	$-0.476558\pi$
$157$	45450.0	0.147158	0.0735791	+	0.997289i	$0.476558\pi$
$158$	199020.	0.634241
$159$	0	0
$160$	−62125.0	−0.191852
$161$	−171288.	−0.520790
$162$	0	0
$163$	5892.00	0.0173698	0.00868488	−	0.999962i	$-0.497235\pi$
$163$	5892.00	0.0173698	0.00868488	+	0.999962i	$0.497235\pi$
$164$	−2058.00	−0.00597497
$165$	0	0
$166$	−208880.	−0.588338
$167$	−212772.	−0.590369	−0.295184	−	0.955440i	$-0.595381\pi$
$167$	−212772.	−0.590369	−0.295184	+	0.955440i	$0.595381\pi$
$168$	0	0
$169$	28561.0	0.0769231
$170$	−191750.	−0.508877
$171$	0	0
$172$	−53326.0	−0.137442
$173$	−503178.	−1.27822	−0.639111	−	0.769114i	$-0.720698\pi$
$173$	−503178.	−1.27822	−0.639111	+	0.769114i	$0.720698\pi$
$174$	0	0
$175$	−152500.	−0.376422
$176$	596294.	1.45104
$177$	0	0
$178$	39850.0	0.0942710
$179$	−581724.	−1.35701	−0.678507	−	0.734594i	$-0.737373\pi$
$179$	−581724.	−1.35701	−0.678507	+	0.734594i	$0.737373\pi$
$180$	0	0
$181$	202202.	0.458764	0.229382	−	0.973337i	$-0.426330\pi$
$181$	202202.	0.458764	0.229382	+	0.973337i	$0.426330\pi$
$182$	−206180.	−0.461390
$183$	0	0
$184$	136890.	0.298076
$185$	−176450.	−0.379046
$186$	0	0
$187$	−1.21800e6	−2.54708
$188$	−21140.0	−0.0436225
$189$	0	0
$190$	−338250.	−0.679757
$191$	340608.	0.675572	0.337786	−	0.941223i	$-0.390322\pi$
$191$	340608.	0.675572	0.337786	+	0.941223i	$0.390322\pi$
$192$	0	0
$193$	275614.	0.532608	0.266304	−	0.963889i	$-0.414197\pi$
$193$	275614.	0.532608	0.266304	+	0.963889i	$0.414197\pi$
$194$	390250.	0.744455
$195$	0	0
$196$	−299103.	−0.556135
$197$	−538218.	−0.988081	−0.494041	−	0.869439i	$-0.664481\pi$
$197$	−538218.	−0.988081	−0.494041	+	0.869439i	$0.664481\pi$
$198$	0	0
$199$	−853840.	−1.52842	−0.764212	−	0.644965i	$-0.776872\pi$
$199$	−853840.	−1.52842	−0.764212	+	0.644965i	$0.776872\pi$
$200$	121875.	0.215447
$201$	0	0
$202$	−115050.	−0.198385
$203$	−1.22927e6	−2.09367
$204$	0	0
$205$	7350.00	0.0122153
$206$	−608530.	−0.999111
$207$	0	0
$208$	126919.	0.203408
$209$	−2.14856e6	−3.40238
$210$	0	0
$211$	−1.00112e6	−1.54804	−0.774019	−	0.633162i	$-0.781757\pi$
$211$	−1.00112e6	−1.54804	−0.774019	+	0.633162i	$0.781757\pi$
$212$	4382.00	0.00669627
$213$	0	0
$214$	−350710.	−0.523496
$215$	190450.	0.280986
$216$	0	0
$217$	886696.	1.27828
$218$	979390.	1.39577
$219$	0	0
$220$	138950.	0.193554
$221$	−259246.	−0.357052
$222$	0	0
$223$	21364.0	0.0287687	0.0143844	−	0.999897i	$-0.495421\pi$
$223$	21364.0	0.0287687	0.0143844	+	0.999897i	$0.495421\pi$
$224$	606340.	0.807414
$225$	0	0
$226$	−501190.	−0.652727
$227$	880748.	1.13445	0.567227	−	0.823561i	$-0.308016\pi$
$227$	880748.	1.13445	0.567227	+	0.823561i	$0.308016\pi$
$228$	0	0
$229$	−13030.0	−0.0164193	−0.00820967	−	0.999966i	$-0.502613\pi$
$229$	−13030.0	−0.0164193	−0.00820967	+	0.999966i	$0.502613\pi$
$230$	−87750.0	−0.109377
$231$	0	0
$232$	982410.	1.19832
$233$	1.20700e6	1.45652	0.728260	−	0.685300i	$-0.240329\pi$
$233$	1.20700e6	1.45652	0.728260	+	0.685300i	$0.240329\pi$
$234$	0	0
$235$	75500.0	0.0891820
$236$	−210462.	−0.245977
$237$	0	0
$238$	1.87148e6	2.14162
$239$	187038.	0.211804	0.105902	−	0.994377i	$-0.466227\pi$
$239$	187038.	0.211804	0.105902	+	0.994377i	$0.466227\pi$
$240$	0	0
$241$	271690.	0.301322	0.150661	−	0.988585i	$-0.451860\pi$
$241$	271690.	0.301322	0.150661	+	0.988585i	$0.451860\pi$
$242$	−2.34692e6	−2.57609
$243$	0	0
$244$	40642.0	0.0437019
$245$	1.06822e6	1.13697
$246$	0	0
$247$	−457314.	−0.476949
$248$	−708630.	−0.731628
$249$	0	0
$250$	−78125.0	−0.0790569
$251$	−102648.	−0.102841	−0.0514205	−	0.998677i	$-0.516375\pi$
$251$	−102648.	−0.102841	−0.0514205	+	0.998677i	$0.516375\pi$
$252$	0	0
$253$	−557388.	−0.547465
$254$	−196430.	−0.191040
$255$	0	0
$256$	−652799.	−0.622558
$257$	221182.	0.208890	0.104445	−	0.994531i	$-0.466693\pi$
$257$	221182.	0.208890	0.104445	+	0.994531i	$0.466693\pi$
$258$	0	0
$259$	1.72215e6	1.59523
$260$	29575.0	0.0271326
$261$	0	0
$262$	1.05730e6	0.951579
$263$	−1.40317e6	−1.25090	−0.625449	−	0.780265i	$-0.715084\pi$
$263$	−1.40317e6	−1.25090	−0.625449	+	0.780265i	$0.715084\pi$
$264$	0	0
$265$	−15650.0	−0.0136899
$266$	3.30132e6	2.86077
$267$	0	0
$268$	87052.0	0.0740358
$269$	582954.	0.491195	0.245597	−	0.969372i	$-0.421016\pi$
$269$	582954.	0.491195	0.245597	+	0.969372i	$0.421016\pi$
$270$	0	0
$271$	−1.04690e6	−0.865930	−0.432965	−	0.901411i	$-0.642533\pi$
$271$	−1.04690e6	−0.865930	−0.432965	+	0.901411i	$0.642533\pi$
$272$	−1.15203e6	−0.944154
$273$	0	0
$274$	131510.	0.105824
$275$	−496250.	−0.395702
$276$	0	0
$277$	1.10461e6	0.864987	0.432493	−	0.901637i	$-0.357634\pi$
$277$	1.10461e6	0.864987	0.432493	+	0.901637i	$0.357634\pi$
$278$	−6720.00	−0.00521504
$279$	0	0
$280$	−1.18950e6	−0.906712
$281$	−908826.	−0.686618	−0.343309	−	0.939223i	$-0.611548\pi$
$281$	−908826.	−0.686618	−0.343309	+	0.939223i	$0.611548\pi$
$282$	0	0
$283$	−449254.	−0.333446	−0.166723	−	0.986004i	$-0.553319\pi$
$283$	−449254.	−0.333446	−0.166723	+	0.986004i	$0.553319\pi$
$284$	33138.0	0.0243798
$285$	0	0
$286$	−670930.	−0.485023
$287$	−71736.0	−0.0514082
$288$	0	0
$289$	933299.	0.657319
$290$	−629750.	−0.439717
$291$	0	0
$292$	102858.	0.0705961
$293$	1.96083e6	1.33435	0.667175	−	0.744901i	$-0.267503\pi$
$293$	1.96083e6	1.33435	0.667175	+	0.744901i	$0.267503\pi$
$294$	0	0
$295$	751650.	0.502876
$296$	−1.37631e6	−0.913034
$297$	0	0
$298$	−245430.	−0.160098
$299$	−118638.	−0.0767442
$300$	0	0
$301$	−1.85879e6	−1.18254
$302$	1.78999e6	1.12936
$303$	0	0
$304$	−2.03221e6	−1.26120
$305$	−145150.	−0.0893444
$306$	0	0
$307$	−1.79385e6	−1.08627	−0.543137	−	0.839644i	$-0.682764\pi$
$307$	−1.79385e6	−1.08627	−0.543137	+	0.839644i	$0.682764\pi$
$308$	−1.35615e6	−0.814576
$309$	0	0
$310$	454250.	0.268467
$311$	−2.41233e6	−1.41428	−0.707141	−	0.707072i	$-0.750015\pi$
$311$	−2.41233e6	−1.41428	−0.707141	+	0.707072i	$0.750015\pi$
$312$	0	0
$313$	−2.15436e6	−1.24296	−0.621480	−	0.783430i	$-0.713468\pi$
$313$	−2.15436e6	−1.24296	−0.621480	+	0.783430i	$0.713468\pi$
$314$	−227250.	−0.130071
$315$	0	0
$316$	278628.	0.156967
$317$	−2.59616e6	−1.45105	−0.725526	−	0.688195i	$-0.758403\pi$
$317$	−2.59616e6	−1.45105	−0.725526	+	0.688195i	$0.758403\pi$
$318$	0	0
$319$	−4.00017e6	−2.20091
$320$	911425.	0.497561
$321$	0	0
$322$	856440.	0.460317
$323$	4.15100e6	2.21384
$324$	0	0
$325$	−105625.	−0.0554700
$326$	−29460.0	−0.0153528
$327$	0	0
$328$	57330.0	0.0294237
$329$	−736880.	−0.375325
$330$	0	0
$331$	−917226.	−0.460157	−0.230079	−	0.973172i	$-0.573898\pi$
$331$	−917226.	−0.460157	−0.230079	+	0.973172i	$0.573898\pi$
$332$	−292432.	−0.145606
$333$	0	0
$334$	1.06386e6	0.521817
$335$	−310900.	−0.151359
$336$	0	0
$337$	2.23894e6	1.07391	0.536954	−	0.843611i	$-0.319575\pi$
$337$	2.23894e6	1.07391	0.536954	+	0.843611i	$0.319575\pi$
$338$	−142805.	−0.0679910
$339$	0	0
$340$	−268450.	−0.125941
$341$	2.88540e6	1.34375
$342$	0	0
$343$	−6.32497e6	−2.90284
$344$	1.48551e6	0.676830
$345$	0	0
$346$	2.51589e6	1.12980
$347$	−3.41808e6	−1.52391	−0.761954	−	0.647631i	$-0.775760\pi$
$347$	−3.41808e6	−1.52391	−0.761954	+	0.647631i	$0.775760\pi$
$348$	0	0
$349$	2.35691e6	1.03581	0.517905	−	0.855438i	$-0.326712\pi$
$349$	2.35691e6	1.03581	0.517905	+	0.855438i	$0.326712\pi$
$350$	762500.	0.332713
$351$	0	0
$352$	1.97309e6	0.848770
$353$	3.76395e6	1.60771	0.803854	−	0.594827i	$-0.202779\pi$
$353$	3.76395e6	1.60771	0.803854	+	0.594827i	$0.202779\pi$
$354$	0	0
$355$	−118350.	−0.0498422
$356$	55790.0	0.0233309
$357$	0	0
$358$	2.90862e6	1.19944
$359$	−3.28216e6	−1.34407	−0.672037	−	0.740517i	$-0.734581\pi$
$359$	−3.28216e6	−1.34407	−0.672037	+	0.740517i	$0.734581\pi$
$360$	0	0
$361$	4.84634e6	1.95725
$362$	−1.01101e6	−0.405494
$363$	0	0
$364$	−288652.	−0.114188
$365$	−367350.	−0.144327
$366$	0	0
$367$	−2.42605e6	−0.940233	−0.470116	−	0.882604i	$-0.655788\pi$
$367$	−2.42605e6	−0.940233	−0.470116	+	0.882604i	$0.655788\pi$
$368$	−527202.	−0.202935
$369$	0	0
$370$	882250.	0.335033
$371$	152744.	0.0576142
$372$	0	0
$373$	2.80635e6	1.04441	0.522204	−	0.852820i	$-0.325110\pi$
$373$	2.80635e6	1.04441	0.522204	+	0.852820i	$0.325110\pi$
$374$	6.08998e6	2.25132
$375$	0	0
$376$	588900.	0.214819
$377$	−851422.	−0.308526
$378$	0	0
$379$	3.15392e6	1.12785	0.563927	−	0.825825i	$-0.309290\pi$
$379$	3.15392e6	1.12785	0.563927	+	0.825825i	$0.309290\pi$
$380$	−473550.	−0.168231
$381$	0	0
$382$	−1.70304e6	−0.597127
$383$	475044.	0.165477	0.0827384	−	0.996571i	$-0.473633\pi$
$383$	475044.	0.165477	0.0827384	+	0.996571i	$0.473633\pi$
$384$	0	0
$385$	4.84340e6	1.66532
$386$	−1.37807e6	−0.470764
$387$	0	0
$388$	546350.	0.184243
$389$	−150566.	−0.0504490	−0.0252245	−	0.999682i	$-0.508030\pi$
$389$	−150566.	−0.0504490	−0.0252245	+	0.999682i	$0.508030\pi$
$390$	0	0
$391$	1.07687e6	0.356222
$392$	8.33216e6	2.73869
$393$	0	0
$394$	2.69109e6	0.873349
$395$	−995100.	−0.320903
$396$	0	0
$397$	241686.	0.0769618	0.0384809	−	0.999259i	$-0.487748\pi$
$397$	241686.	0.0769618	0.0384809	+	0.999259i	$0.487748\pi$
$398$	4.26920e6	1.35095
$399$	0	0
$400$	−469375.	−0.146680
$401$	3.19679e6	0.992780	0.496390	−	0.868100i	$-0.334659\pi$
$401$	3.19679e6	0.992780	0.496390	+	0.868100i	$0.334659\pi$
$402$	0	0
$403$	614146.	0.188369
$404$	−161070.	−0.0490977
$405$	0	0
$406$	6.14636e6	1.85056
$407$	5.60405e6	1.67693
$408$	0	0
$409$	423282.	0.125119	0.0625593	−	0.998041i	$-0.480074\pi$
$409$	423282.	0.125119	0.0625593	+	0.998041i	$0.480074\pi$
$410$	−36750.0	−0.0107969
$411$	0	0
$412$	−851942.	−0.247267
$413$	−7.33610e6	−2.11636
$414$	0	0
$415$	1.04440e6	0.297678
$416$	419965.	0.118982
$417$	0	0
$418$	1.07428e7	3.00731
$419$	1.13159e6	0.314887	0.157444	−	0.987528i	$-0.449675\pi$
$419$	1.13159e6	0.314887	0.157444	+	0.987528i	$0.449675\pi$
$420$	0	0
$421$	3.47699e6	0.956088	0.478044	−	0.878336i	$-0.341346\pi$
$421$	3.47699e6	0.956088	0.478044	+	0.878336i	$0.341346\pi$
$422$	5.00562e6	1.36829
$423$	0	0
$424$	−122070.	−0.0329757
$425$	958750.	0.257474
$426$	0	0
$427$	1.41666e6	0.376008
$428$	−490994.	−0.129559
$429$	0	0
$430$	−952250.	−0.248359
$431$	−3.41044e6	−0.884335	−0.442168	−	0.896932i	$-0.645790\pi$
$431$	−3.41044e6	−0.884335	−0.442168	+	0.896932i	$0.645790\pi$
$432$	0	0
$433$	−3.40722e6	−0.873335	−0.436667	−	0.899623i	$-0.643841\pi$
$433$	−3.40722e6	−0.873335	−0.436667	+	0.899623i	$0.643841\pi$
$434$	−4.43348e6	−1.12985
$435$	0	0
$436$	1.37115e6	0.345436
$437$	1.89961e6	0.475840
$438$	0	0
$439$	−7.09114e6	−1.75612	−0.878061	−	0.478549i	$-0.841163\pi$
$439$	−7.09114e6	−1.75612	−0.878061	+	0.478549i	$0.841163\pi$
$440$	−3.87075e6	−0.953155
$441$	0	0
$442$	1.29623e6	0.315592
$443$	8.23508e6	1.99369	0.996847	−	0.0793445i	$-0.0252827\pi$
$443$	8.23508e6	1.99369	0.996847	+	0.0793445i	$0.0252827\pi$
$444$	0	0
$445$	−199250.	−0.0476978
$446$	−106820.	−0.0254282
$447$	0	0
$448$	−8.89551e6	−2.09400
$449$	1.29601e6	0.303383	0.151691	−	0.988428i	$-0.451528\pi$
$449$	1.29601e6	0.303383	0.151691	+	0.988428i	$0.451528\pi$
$450$	0	0
$451$	−233436.	−0.0540414
$452$	−701666.	−0.161542
$453$	0	0
$454$	−4.40374e6	−1.00273
$455$	1.03090e6	0.233447
$456$	0	0
$457$	1.68196e6	0.376725	0.188363	−	0.982100i	$-0.439682\pi$
$457$	1.68196e6	0.376725	0.188363	+	0.982100i	$0.439682\pi$
$458$	65150.0	0.0145128
$459$	0	0
$460$	−122850.	−0.0270695
$461$	3.20663e6	0.702743	0.351372	−	0.936236i	$-0.385715\pi$
$461$	3.20663e6	0.702743	0.351372	+	0.936236i	$0.385715\pi$
$462$	0	0
$463$	−5.26370e6	−1.14114	−0.570570	−	0.821249i	$-0.693278\pi$
$463$	−5.26370e6	−1.14114	−0.570570	+	0.821249i	$0.693278\pi$
$464$	−3.78354e6	−0.815837
$465$	0	0
$466$	−6.03499e6	−1.28739
$467$	8.26813e6	1.75435	0.877173	−	0.480175i	$-0.159427\pi$
$467$	8.26813e6	1.75435	0.877173	+	0.480175i	$0.159427\pi$
$468$	0	0
$469$	3.03438e6	0.636999
$470$	−377500.	−0.0788265
$471$	0	0
$472$	5.86287e6	1.21131
$473$	−6.04869e6	−1.24311
$474$	0	0
$475$	1.69125e6	0.343933
$476$	2.62007e6	0.530024
$477$	0	0
$478$	−935190.	−0.187210
$479$	−3.65468e6	−0.727797	−0.363899	−	0.931439i	$-0.618555\pi$
$479$	−3.65468e6	−0.727797	−0.363899	+	0.931439i	$0.618555\pi$
$480$	0	0
$481$	1.19280e6	0.235075
$482$	−1.35845e6	−0.266334
$483$	0	0
$484$	−3.28570e6	−0.637549
$485$	−1.95125e6	−0.376668
$486$	0	0
$487$	7.13084e6	1.36244	0.681221	−	0.732077i	$-0.261449\pi$
$487$	7.13084e6	1.36244	0.681221	+	0.732077i	$0.261449\pi$
$488$	−1.13217e6	−0.215210
$489$	0	0
$490$	−5.34113e6	−1.00495
$491$	−5.72551e6	−1.07179	−0.535896	−	0.844284i	$-0.680026\pi$
$491$	−5.72551e6	−1.07179	−0.535896	+	0.844284i	$0.680026\pi$
$492$	0	0
$493$	7.72829e6	1.43208
$494$	2.28657e6	0.421568
$495$	0	0
$496$	2.72913e6	0.498105
$497$	1.15510e6	0.209762
$498$	0	0
$499$	−7.17251e6	−1.28950	−0.644748	−	0.764395i	$-0.723038\pi$
$499$	−7.17251e6	−1.28950	−0.644748	+	0.764395i	$0.723038\pi$
$500$	−109375.	−0.0195656
$501$	0	0
$502$	513240.	0.0908994
$503$	2.90611e6	0.512143	0.256072	−	0.966658i	$-0.417572\pi$
$503$	2.90611e6	0.512143	0.256072	+	0.966658i	$0.417572\pi$
$504$	0	0
$505$	575250.	0.100376
$506$	2.78694e6	0.483895
$507$	0	0
$508$	−275002.	−0.0472799
$509$	8.37125e6	1.43217	0.716087	−	0.698011i	$-0.245931\pi$
$509$	8.37125e6	1.43217	0.716087	+	0.698011i	$0.245931\pi$
$510$	0	0
$511$	3.58534e6	0.607404
$512$	6.55248e6	1.10466
$513$	0	0
$514$	−1.10591e6	−0.184634
$515$	3.04265e6	0.505515
$516$	0	0
$517$	−2.39788e6	−0.394549
$518$	−8.61076e6	−1.40999
$519$	0	0
$520$	−823875.	−0.133614
$521$	−5.37332e6	−0.867258	−0.433629	−	0.901092i	$-0.642767\pi$
$521$	−5.37332e6	−0.867258	−0.433629	+	0.901092i	$0.642767\pi$
$522$	0	0
$523$	5.26875e6	0.842274	0.421137	−	0.906997i	$-0.361631\pi$
$523$	5.26875e6	0.842274	0.421137	+	0.906997i	$0.361631\pi$
$524$	1.48022e6	0.235504
$525$	0	0
$526$	7.01587e6	1.10565
$527$	−5.57456e6	−0.874347
$528$	0	0
$529$	−5.94354e6	−0.923434
$530$	78250.0	0.0121003
$531$	0	0
$532$	4.62185e6	0.708005
$533$	−49686.0	−0.00757558
$534$	0	0
$535$	1.75355e6	0.264871
$536$	−2.42502e6	−0.364589
$537$	0	0
$538$	−2.91477e6	−0.434159
$539$	−3.39268e7	−5.03004
$540$	0	0
$541$	−6.07956e6	−0.893056	−0.446528	−	0.894770i	$-0.647340\pi$
$541$	−6.07956e6	−0.893056	−0.446528	+	0.894770i	$0.647340\pi$
$542$	5.23451e6	0.765381
$543$	0	0
$544$	−3.81199e6	−0.552274
$545$	−4.89695e6	−0.706211
$546$	0	0
$547$	−7.88715e6	−1.12707	−0.563536	−	0.826091i	$-0.690559\pi$
$547$	−7.88715e6	−1.12707	−0.563536	+	0.826091i	$0.690559\pi$
$548$	184114.	0.0261900
$549$	0	0
$550$	2.48125e6	0.349755
$551$	1.36328e7	1.91296
$552$	0	0
$553$	9.71218e6	1.35053
$554$	−5.52305e6	−0.764548
$555$	0	0
$556$	−9408.00	−0.00129066
$557$	5.88545e6	0.803788	0.401894	−	0.915686i	$-0.368352\pi$
$557$	5.88545e6	0.803788	0.401894	+	0.915686i	$0.368352\pi$
$558$	0	0
$559$	−1.28744e6	−0.174260
$560$	4.58110e6	0.617305
$561$	0	0
$562$	4.54413e6	0.606890
$563$	3.91526e6	0.520583	0.260291	−	0.965530i	$-0.416181\pi$
$563$	3.91526e6	0.520583	0.260291	+	0.965530i	$0.416181\pi$
$564$	0	0
$565$	2.50595e6	0.330256
$566$	2.24627e6	0.294728
$567$	0	0
$568$	−923130.	−0.120058
$569$	−9.78180e6	−1.26660	−0.633298	−	0.773908i	$-0.718299\pi$
$569$	−9.78180e6	−1.26660	−0.633298	+	0.773908i	$0.718299\pi$
$570$	0	0
$571$	−1.08198e7	−1.38877	−0.694386	−	0.719603i	$-0.744324\pi$
$571$	−1.08198e7	−1.38877	−0.694386	+	0.719603i	$0.744324\pi$
$572$	−939302.	−0.120037
$573$	0	0
$574$	358680.	0.0454389
$575$	438750.	0.0553411
$576$	0	0
$577$	1.48792e7	1.86055	0.930274	−	0.366865i	$-0.119569\pi$
$577$	1.48792e7	1.86055	0.930274	+	0.366865i	$0.119569\pi$
$578$	−4.66650e6	−0.580993
$579$	0	0
$580$	−881650.	−0.108824
$581$	−1.01933e7	−1.25278
$582$	0	0
$583$	497044.	0.0605652
$584$	−2.86533e6	−0.347650
$585$	0	0
$586$	−9.80413e6	−1.17941
$587$	−1.22649e7	−1.46916	−0.734578	−	0.678525i	$-0.762620\pi$
$587$	−1.22649e7	−1.46916	−0.734578	+	0.678525i	$0.762620\pi$
$588$	0	0
$589$	−9.83360e6	−1.16795
$590$	−3.75825e6	−0.444483
$591$	0	0
$592$	5.30056e6	0.621609
$593$	1.54878e7	1.80864	0.904320	−	0.426856i	$-0.140379\pi$
$593$	1.54878e7	1.80864	0.904320	+	0.426856i	$0.140379\pi$
$594$	0	0
$595$	−9.35740e6	−1.08358
$596$	−343602.	−0.0396223
$597$	0	0
$598$	593190.	0.0678330
$599$	−9.75710e6	−1.11110	−0.555551	−	0.831483i	$-0.687493\pi$
$599$	−9.75710e6	−1.11110	−0.555551	+	0.831483i	$0.687493\pi$
$600$	0	0
$601$	−7.57967e6	−0.855981	−0.427990	−	0.903783i	$-0.640778\pi$
$601$	−7.57967e6	−0.855981	−0.427990	+	0.903783i	$0.640778\pi$
$602$	9.29396e6	1.04522
$603$	0	0
$604$	2.50599e6	0.279503
$605$	1.17346e7	1.30341
$606$	0	0
$607$	1.36231e7	1.50073	0.750367	−	0.661022i	$-0.229877\pi$
$607$	1.36231e7	1.50073	0.750367	+	0.661022i	$0.229877\pi$
$608$	−6.72441e6	−0.737726
$609$	0	0
$610$	725750.	0.0789701
$611$	−510380.	−0.0553083
$612$	0	0
$613$	−1.20366e7	−1.29376	−0.646880	−	0.762592i	$-0.723927\pi$
$613$	−1.20366e7	−1.29376	−0.646880	+	0.762592i	$0.723927\pi$
$614$	8.96924e6	0.960140
$615$	0	0
$616$	3.77785e7	4.01137
$617$	−8.55509e6	−0.904715	−0.452358	−	0.891837i	$-0.649417\pi$
$617$	−8.55509e6	−0.904715	−0.452358	+	0.891837i	$0.649417\pi$
$618$	0	0
$619$	−1.33018e7	−1.39535	−0.697675	−	0.716414i	$-0.745782\pi$
$619$	−1.33018e7	−1.39535	−0.697675	+	0.716414i	$0.745782\pi$
$620$	635950.	0.0664422
$621$	0	0
$622$	1.20617e7	1.25006
$623$	1.94468e6	0.200737
$624$	0	0
$625$	390625.	0.0400000
$626$	1.07718e7	1.09863
$627$	0	0
$628$	−318150.	−0.0321909
$629$	−1.08270e7	−1.09114
$630$	0	0
$631$	9.16681e6	0.916526	0.458263	−	0.888817i	$-0.348472\pi$
$631$	9.16681e6	0.916526	0.458263	+	0.888817i	$0.348472\pi$
$632$	−7.76178e6	−0.772981
$633$	0	0
$634$	1.29808e7	1.28256
$635$	982150.	0.0966593
$636$	0	0
$637$	−7.22120e6	−0.705116
$638$	2.00009e7	1.94535
$639$	0	0
$640$	−2.56912e6	−0.247934
$641$	−9.96437e6	−0.957866	−0.478933	−	0.877851i	$-0.658976\pi$
$641$	−9.96437e6	−0.957866	−0.478933	+	0.877851i	$0.658976\pi$
$642$	0	0
$643$	6.64194e6	0.633530	0.316765	−	0.948504i	$-0.397403\pi$
$643$	6.64194e6	0.633530	0.316765	+	0.948504i	$0.397403\pi$
$644$	1.19902e6	0.113923
$645$	0	0
$646$	−2.07550e7	−1.95678
$647$	−844766.	−0.0793370	−0.0396685	−	0.999213i	$-0.512630\pi$
$647$	−844766.	−0.0793370	−0.0396685	+	0.999213i	$0.512630\pi$
$648$	0	0
$649$	−2.38724e7	−2.22477
$650$	528125.	0.0490290
$651$	0	0
$652$	−41244.0	−0.00379963
$653$	−5.79681e6	−0.531993	−0.265997	−	0.963974i	$-0.585701\pi$
$653$	−5.79681e6	−0.531993	−0.265997	+	0.963974i	$0.585701\pi$
$654$	0	0
$655$	−5.28650e6	−0.481465
$656$	−220794.	−0.0200322
$657$	0	0
$658$	3.68440e6	0.331743
$659$	1.12406e7	1.00827	0.504136	−	0.863624i	$-0.331811\pi$
$659$	1.12406e7	1.00827	0.504136	+	0.863624i	$0.331811\pi$
$660$	0	0
$661$	−1.54928e7	−1.37920	−0.689599	−	0.724191i	$-0.742213\pi$
$661$	−1.54928e7	−1.37920	−0.689599	+	0.724191i	$0.742213\pi$
$662$	4.58613e6	0.406725
$663$	0	0
$664$	8.14632e6	0.717037
$665$	−1.65066e7	−1.44745
$666$	0	0
$667$	3.53668e6	0.307809
$668$	1.48940e6	0.129143
$669$	0	0
$670$	1.55450e6	0.133784
$671$	4.60996e6	0.395268
$672$	0	0
$673$	−723294.	−0.0615570	−0.0307785	−	0.999526i	$-0.509799\pi$
$673$	−723294.	−0.0615570	−0.0307785	+	0.999526i	$0.509799\pi$
$674$	−1.11947e7	−0.949210
$675$	0	0
$676$	−199927.	−0.0168269
$677$	7.57359e6	0.635082	0.317541	−	0.948244i	$-0.397143\pi$
$677$	7.57359e6	0.635082	0.317541	+	0.948244i	$0.397143\pi$
$678$	0	0
$679$	1.90442e7	1.58522
$680$	7.47825e6	0.620194
$681$	0	0
$682$	−1.44270e7	−1.18772
$683$	1.65552e7	1.35794	0.678972	−	0.734164i	$-0.262426\pi$
$683$	1.65552e7	1.35794	0.678972	+	0.734164i	$0.262426\pi$
$684$	0	0
$685$	−657550.	−0.0535430
$686$	3.16248e7	2.56577
$687$	0	0
$688$	−5.72112e6	−0.460797
$689$	105794.	0.00849010
$690$	0	0
$691$	−2.04593e7	−1.63003	−0.815016	−	0.579438i	$-0.803272\pi$
$691$	−2.04593e7	−1.63003	−0.815016	+	0.579438i	$0.803272\pi$
$692$	3.52225e6	0.279611
$693$	0	0
$694$	1.70904e7	1.34696
$695$	33600.0	0.00263862
$696$	0	0
$697$	450996.	0.0351634
$698$	−1.17846e7	−0.915535
$699$	0	0
$700$	1.06750e6	0.0823423
$701$	−1.52050e7	−1.16867	−0.584334	−	0.811514i	$-0.698644\pi$
$701$	−1.52050e7	−1.16867	−0.584334	+	0.811514i	$0.698644\pi$
$702$	0	0
$703$	−1.90989e7	−1.45754
$704$	−2.89469e7	−2.20125
$705$	0	0
$706$	−1.88198e7	−1.42103
$707$	−5.61444e6	−0.422433
$708$	0	0
$709$	−1.80833e7	−1.35102	−0.675509	−	0.737351i	$-0.736076\pi$
$709$	−1.80833e7	−1.35102	−0.675509	+	0.737351i	$0.736076\pi$
$710$	591750.	0.0440547
$711$	0	0
$712$	−1.55415e6	−0.114893
$713$	−2.55107e6	−0.187931
$714$	0	0
$715$	3.35465e6	0.245404
$716$	4.07207e6	0.296847
$717$	0	0
$718$	1.64108e7	1.18801
$719$	2.08096e7	1.50121	0.750604	−	0.660752i	$-0.229763\pi$
$719$	2.08096e7	1.50121	0.750604	+	0.660752i	$0.229763\pi$
$720$	0	0
$721$	−2.96963e7	−2.12747
$722$	−2.42317e7	−1.72998
$723$	0	0
$724$	−1.41541e6	−0.100355
$725$	3.14875e6	0.222481
$726$	0	0
$727$	−2.59006e7	−1.81750	−0.908749	−	0.417344i	$-0.862961\pi$
$727$	−2.59006e7	−1.81750	−0.908749	+	0.417344i	$0.862961\pi$
$728$	8.04102e6	0.562319
$729$	0	0
$730$	1.83675e6	0.127568
$731$	1.16860e7	0.808859
$732$	0	0
$733$	−1.96307e7	−1.34951	−0.674754	−	0.738043i	$-0.735750\pi$
$733$	−1.96307e7	−1.34951	−0.674754	+	0.738043i	$0.735750\pi$
$734$	1.21303e7	0.831056
$735$	0	0
$736$	−1.74447e6	−0.118705
$737$	9.87418e6	0.669626
$738$	0	0
$739$	−1.67436e7	−1.12781	−0.563906	−	0.825839i	$-0.690702\pi$
$739$	−1.67436e7	−1.12781	−0.563906	+	0.825839i	$0.690702\pi$
$740$	1.23515e6	0.0829164
$741$	0	0
$742$	−763720.	−0.0509242
$743$	−5.57725e6	−0.370637	−0.185318	−	0.982679i	$-0.559332\pi$
$743$	−5.57725e6	−0.370637	−0.185318	+	0.982679i	$0.559332\pi$
$744$	0	0
$745$	1.22715e6	0.0810041
$746$	−1.40318e7	−0.923135
$747$	0	0
$748$	8.52597e6	0.557173
$749$	−1.71146e7	−1.11471
$750$	0	0
$751$	1.24035e7	0.802499	0.401250	−	0.915969i	$-0.368576\pi$
$751$	1.24035e7	0.802499	0.401250	+	0.915969i	$0.368576\pi$
$752$	−2.26802e6	−0.146252
$753$	0	0
$754$	4.25711e6	0.272701
$755$	−8.94995e6	−0.571417
$756$	0	0
$757$	4.37170e6	0.277275	0.138637	−	0.990343i	$-0.455728\pi$
$757$	4.37170e6	0.277275	0.138637	+	0.990343i	$0.455728\pi$
$758$	−1.57696e7	−0.996892
$759$	0	0
$760$	1.31918e7	0.828454
$761$	2.10490e7	1.31756	0.658780	−	0.752335i	$-0.271073\pi$
$761$	2.10490e7	1.31756	0.658780	+	0.752335i	$0.271073\pi$
$762$	0	0
$763$	4.77942e7	2.97210
$764$	−2.38426e6	−0.147781
$765$	0	0
$766$	−2.37522e6	−0.146262
$767$	−5.08115e6	−0.311870
$768$	0	0
$769$	2.26551e7	1.38150	0.690748	−	0.723096i	$-0.257282\pi$
$769$	2.26551e7	1.38150	0.690748	+	0.723096i	$0.257282\pi$
$770$	−2.42170e7	−1.47195
$771$	0	0
$772$	−1.92930e6	−0.116508
$773$	−1.15053e7	−0.692545	−0.346272	−	0.938134i	$-0.612553\pi$
$773$	−1.15053e7	−0.692545	−0.346272	+	0.938134i	$0.612553\pi$
$774$	0	0
$775$	−2.27125e6	−0.135835
$776$	−1.52198e7	−0.907305
$777$	0	0
$778$	752830.	0.0445911
$779$	795564.	0.0469712
$780$	0	0
$781$	3.75880e6	0.220506
$782$	−5.38434e6	−0.314859
$783$	0	0
$784$	−3.20895e7	−1.86454
$785$	1.13625e6	0.0658112
$786$	0	0
$787$	967112.	0.0556596	0.0278298	−	0.999613i	$-0.491140\pi$
$787$	967112.	0.0556596	0.0278298	+	0.999613i	$0.491140\pi$
$788$	3.76753e6	0.216143
$789$	0	0
$790$	4.97550e6	0.283641
$791$	−2.44581e7	−1.38989
$792$	0	0
$793$	981214.	0.0554091
$794$	−1.20843e6	−0.0680253
$795$	0	0
$796$	5.97688e6	0.334343
$797$	2.85072e7	1.58968	0.794838	−	0.606821i	$-0.207556\pi$
$797$	2.85072e7	1.58968	0.794838	+	0.606821i	$0.207556\pi$
$798$	0	0
$799$	4.63268e6	0.256723
$800$	−1.55313e6	−0.0857988
$801$	0	0
$802$	−1.59840e7	−0.877502
$803$	1.16670e7	0.638516
$804$	0	0
$805$	−4.28220e6	−0.232904
$806$	−3.07073e6	−0.166496
$807$	0	0
$808$	4.48695e6	0.241781
$809$	−1.08912e7	−0.585065	−0.292533	−	0.956256i	$-0.594498\pi$
$809$	−1.08912e7	−0.585065	−0.292533	+	0.956256i	$0.594498\pi$
$810$	0	0
$811$	1.28535e7	0.686228	0.343114	−	0.939294i	$-0.388518\pi$
$811$	1.28535e7	0.686228	0.343114	+	0.939294i	$0.388518\pi$
$812$	8.60490e6	0.457990
$813$	0	0
$814$	−2.80203e7	−1.48221
$815$	147300.	0.00776799
$816$	0	0
$817$	2.06143e7	1.08047
$818$	−2.11641e6	−0.110590
$819$	0	0
$820$	−51450.0	−0.00267209
$821$	9.60605e6	0.497378	0.248689	−	0.968583i	$-0.420000\pi$
$821$	9.60605e6	0.497378	0.248689	+	0.968583i	$0.420000\pi$
$822$	0	0
$823$	1.42909e7	0.735460	0.367730	−	0.929933i	$-0.380135\pi$
$823$	1.42909e7	0.735460	0.367730	+	0.929933i	$0.380135\pi$
$824$	2.37327e7	1.21767
$825$	0	0
$826$	3.66805e7	1.87062
$827$	−2.40317e7	−1.22186	−0.610930	−	0.791685i	$-0.709204\pi$
$827$	−2.40317e7	−1.22186	−0.610930	+	0.791685i	$0.709204\pi$
$828$	0	0
$829$	1.10830e7	0.560107	0.280053	−	0.959984i	$-0.409648\pi$
$829$	1.10830e7	0.560107	0.280053	+	0.959984i	$0.409648\pi$
$830$	−5.22200e6	−0.263113
$831$	0	0
$832$	−6.16123e6	−0.308574
$833$	6.55463e7	3.27292
$834$	0	0
$835$	−5.31930e6	−0.264021
$836$	1.50399e7	0.744270
$837$	0	0
$838$	−5.65796e6	−0.278323
$839$	6.89303e6	0.338069	0.169034	−	0.985610i	$-0.445935\pi$
$839$	6.89303e6	0.338069	0.169034	+	0.985610i	$0.445935\pi$
$840$	0	0
$841$	4.87030e6	0.237446
$842$	−1.73849e7	−0.845070
$843$	0	0
$844$	7.00787e6	0.338633
$845$	714025.	0.0344010
$846$	0	0
$847$	−1.14530e8	−5.48543
$848$	470126.	0.0224504
$849$	0	0
$850$	−4.79375e6	−0.227577
$851$	−4.95472e6	−0.234528
$852$	0	0
$853$	−683466.	−0.0321621	−0.0160810	−	0.999871i	$-0.505119\pi$
$853$	−683466.	−0.0321621	−0.0160810	+	0.999871i	$0.505119\pi$
$854$	−7.08332e6	−0.332347
$855$	0	0
$856$	1.36777e7	0.638011
$857$	7.89742e6	0.367310	0.183655	−	0.982991i	$-0.441207\pi$
$857$	7.89742e6	0.367310	0.183655	+	0.982991i	$0.441207\pi$
$858$	0	0
$859$	3.52556e7	1.63021	0.815107	−	0.579310i	$-0.196678\pi$
$859$	3.52556e7	1.63021	0.815107	+	0.579310i	$0.196678\pi$
$860$	−1.33315e6	−0.0614657
$861$	0	0
$862$	1.70522e7	0.781649
$863$	−1.76565e7	−0.807007	−0.403503	−	0.914978i	$-0.632208\pi$
$863$	−1.76565e7	−0.807007	−0.403503	+	0.914978i	$0.632208\pi$
$864$	0	0
$865$	−1.25794e7	−0.571638
$866$	1.70361e7	0.771926
$867$	0	0
$868$	−6.20687e6	−0.279623
$869$	3.16044e7	1.41970
$870$	0	0
$871$	2.10168e6	0.0938690
$872$	−3.81962e7	−1.70110
$873$	0	0
$874$	−9.49806e6	−0.420587
$875$	−3.81250e6	−0.168341
$876$	0	0
$877$	−6.40016e6	−0.280991	−0.140495	−	0.990081i	$-0.544869\pi$
$877$	−6.40016e6	−0.280991	−0.140495	+	0.990081i	$0.544869\pi$
$878$	3.54557e7	1.55221
$879$	0	0
$880$	1.49074e7	0.648924
$881$	1.14571e7	0.497318	0.248659	−	0.968591i	$-0.420010\pi$
$881$	1.14571e7	0.497318	0.248659	+	0.968591i	$0.420010\pi$
$882$	0	0
$883$	2.42296e7	1.04579	0.522896	−	0.852397i	$-0.324852\pi$
$883$	2.42296e7	1.04579	0.522896	+	0.852397i	$0.324852\pi$
$884$	1.81472e6	0.0781051
$885$	0	0
$886$	−4.11754e7	−1.76219
$887$	−8.66087e6	−0.369617	−0.184809	−	0.982775i	$-0.559167\pi$
$887$	−8.66087e6	−0.369617	−0.184809	+	0.982775i	$0.559167\pi$
$888$	0	0
$889$	−9.58578e6	−0.406793
$890$	996250.	0.0421593
$891$	0	0
$892$	−149548.	−0.00629316
$893$	8.17212e6	0.342930
$894$	0	0
$895$	−1.45431e7	−0.606875
$896$	2.50747e7	1.04343
$897$	0	0
$898$	−6.48003e6	−0.268155
$899$	−1.83081e7	−0.755516
$900$	0	0
$901$	−960284.	−0.0394083
$902$	1.16718e6	0.0477663
$903$	0	0
$904$	1.95464e7	0.795511
$905$	5.05505e6	0.205165
$906$	0	0
$907$	−7.84287e6	−0.316561	−0.158280	−	0.987394i	$-0.550595\pi$
$907$	−7.84287e6	−0.316561	−0.158280	+	0.987394i	$0.550595\pi$
$908$	−6.16524e6	−0.248162
$909$	0	0
$910$	−5.15450e6	−0.206340
$911$	942576.	0.0376288	0.0188144	−	0.999823i	$-0.494011\pi$
$911$	942576.	0.0376288	0.0188144	+	0.999823i	$0.494011\pi$
$912$	0	0
$913$	−3.31701e7	−1.31695
$914$	−8.40979e6	−0.332981
$915$	0	0
$916$	91210.0	0.00359173
$917$	5.15962e7	2.02626
$918$	0	0
$919$	−2.00734e7	−0.784030	−0.392015	−	0.919959i	$-0.628222\pi$
$919$	−2.00734e7	−0.784030	−0.392015	+	0.919959i	$0.628222\pi$
$920$	3.42225e6	0.133304
$921$	0	0
$922$	−1.60332e7	−0.621143
$923$	800046.	0.0309108
$924$	0	0
$925$	−4.41125e6	−0.169515
$926$	2.63185e7	1.00863
$927$	0	0
$928$	−1.25194e7	−0.477216
$929$	−1.10181e7	−0.418858	−0.209429	−	0.977824i	$-0.567160\pi$
$929$	−1.10181e7	−0.418858	−0.209429	+	0.977824i	$0.567160\pi$
$930$	0	0
$931$	1.15625e8	4.37196
$932$	−8.44899e6	−0.318614
$933$	0	0
$934$	−4.13406e7	−1.55064
$935$	−3.04499e7	−1.13909
$936$	0	0
$937$	3.59532e7	1.33779	0.668896	−	0.743356i	$-0.266767\pi$
$937$	3.59532e7	1.33779	0.668896	+	0.743356i	$0.266767\pi$
$938$	−1.51719e7	−0.563032
$939$	0	0
$940$	−528500.	−0.0195086
$941$	−1.28845e7	−0.474345	−0.237172	−	0.971468i	$-0.576221\pi$
$941$	−1.28845e7	−0.474345	−0.237172	+	0.971468i	$0.576221\pi$
$942$	0	0
$943$	206388.	0.00755797
$944$	−2.25796e7	−0.824680
$945$	0	0
$946$	3.02435e7	1.09876
$947$	1.18911e7	0.430871	0.215436	−	0.976518i	$-0.430883\pi$
$947$	1.18911e7	0.430871	0.215436	+	0.976518i	$0.430883\pi$
$948$	0	0
$949$	2.48329e6	0.0895079
$950$	−8.45625e6	−0.303997
$951$	0	0
$952$	−7.29877e7	−2.61010
$953$	−4.40094e7	−1.56969	−0.784844	−	0.619694i	$-0.787257\pi$
$953$	−4.40094e7	−1.56969	−0.784844	+	0.619694i	$0.787257\pi$
$954$	0	0
$955$	8.51520e6	0.302125
$956$	−1.30927e6	−0.0463322
$957$	0	0
$958$	1.82734e7	0.643288
$959$	6.41769e6	0.225337
$960$	0	0
$961$	−1.54232e7	−0.538723
$962$	−5.96401e6	−0.207779
$963$	0	0
$964$	−1.90183e6	−0.0659142
$965$	6.89035e6	0.238190
$966$	0	0
$967$	2.11144e7	0.726128	0.363064	−	0.931764i	$-0.381731\pi$
$967$	2.11144e7	0.726128	0.363064	+	0.931764i	$0.381731\pi$
$968$	9.15301e7	3.13961
$969$	0	0
$970$	9.75625e6	0.332931
$971$	−2.44293e7	−0.831502	−0.415751	−	0.909478i	$-0.636481\pi$
$971$	−2.44293e7	−0.831502	−0.415751	+	0.909478i	$0.636481\pi$
$972$	0	0
$973$	−327936.	−0.0111047
$974$	−3.56542e7	−1.20424
$975$	0	0
$976$	4.36031e6	0.146518
$977$	−5.15549e7	−1.72796	−0.863980	−	0.503527i	$-0.832036\pi$
$977$	−5.15549e7	−1.72796	−0.863980	+	0.503527i	$0.832036\pi$
$978$	0	0
$979$	6.32818e6	0.211019
$980$	−7.47758e6	−0.248711
$981$	0	0
$982$	2.86276e7	0.947339
$983$	1.38938e7	0.458604	0.229302	−	0.973355i	$-0.426356\pi$
$983$	1.38938e7	0.458604	0.229302	+	0.973355i	$0.426356\pi$
$984$	0	0
$985$	−1.34554e7	−0.441883
$986$	−3.86415e7	−1.26579
$987$	0	0
$988$	3.20120e6	0.104333
$989$	5.34784e6	0.173855
$990$	0	0
$991$	3.31496e7	1.07225	0.536123	−	0.844140i	$-0.319888\pi$
$991$	3.31496e7	1.07225	0.536123	+	0.844140i	$0.319888\pi$
$992$	9.03049e6	0.291361
$993$	0	0
$994$	−5.77548e6	−0.185405
$995$	−2.13460e7	−0.683532
$996$	0	0
$997$	9.45871e6	0.301366	0.150683	−	0.988582i	$-0.451853\pi$
$997$	9.45871e6	0.301366	0.150683	+	0.988582i	$0.451853\pi$
$998$	3.58626e7	1.13976
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.6.a.a.1.1		1
3.2	odd	2		65.6.a.a.1.1	✓	1
12.11	even	2		1040.6.a.a.1.1		1
15.2	even	4		325.6.b.a.274.2		2
15.8	even	4		325.6.b.a.274.1		2
15.14	odd	2		325.6.a.a.1.1		1
39.38	odd	2		845.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.a.a.1.1	✓	1	3.2	odd	2
325.6.a.a.1.1		1	15.14	odd	2
325.6.b.a.274.1		2	15.8	even	4
325.6.b.a.274.2		2	15.2	even	4
585.6.a.a.1.1		1	1.1	even	1	trivial
845.6.a.a.1.1		1	39.38	odd	2
1040.6.a.a.1.1		1	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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