LMFDB - Embedded newform 65.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(1,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("65.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.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:	$10.4249482878$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{2} +6.00000 q^{3} -7.00000 q^{4} -25.0000 q^{5} +30.0000 q^{6} -244.000 q^{7} -195.000 q^{8} -207.000 q^{9} +O(q^{10})$

\(q+5.00000 q^{2} +6.00000 q^{3} -7.00000 q^{4} -25.0000 q^{5} +30.0000 q^{6} -244.000 q^{7} -195.000 q^{8} -207.000 q^{9} -125.000 q^{10} +794.000 q^{11} -42.0000 q^{12} -169.000 q^{13} -1220.00 q^{14} -150.000 q^{15} -751.000 q^{16} -1534.00 q^{17} -1035.00 q^{18} +2706.00 q^{19} +175.000 q^{20} -1464.00 q^{21} +3970.00 q^{22} -702.000 q^{23} -1170.00 q^{24} +625.000 q^{25} -845.000 q^{26} -2700.00 q^{27} +1708.00 q^{28} -5038.00 q^{29} -750.000 q^{30} -3634.00 q^{31} +2485.00 q^{32} +4764.00 q^{33} -7670.00 q^{34} +6100.00 q^{35} +1449.00 q^{36} -7058.00 q^{37} +13530.0 q^{38} -1014.00 q^{39} +4875.00 q^{40} -294.000 q^{41} -7320.00 q^{42} +7618.00 q^{43} -5558.00 q^{44} +5175.00 q^{45} -3510.00 q^{46} -3020.00 q^{47} -4506.00 q^{48} +42729.0 q^{49} +3125.00 q^{50} -9204.00 q^{51} +1183.00 q^{52} +626.000 q^{53} -13500.0 q^{54} -19850.0 q^{55} +47580.0 q^{56} +16236.0 q^{57} -25190.0 q^{58} -30066.0 q^{59} +1050.00 q^{60} -5806.00 q^{61} -18170.0 q^{62} +50508.0 q^{63} +36457.0 q^{64} +4225.00 q^{65} +23820.0 q^{66} -12436.0 q^{67} +10738.0 q^{68} -4212.00 q^{69} +30500.0 q^{70} +4734.00 q^{71} +40365.0 q^{72} -14694.0 q^{73} -35290.0 q^{74} +3750.00 q^{75} -18942.0 q^{76} -193736. q^{77} -5070.00 q^{78} -39804.0 q^{79} +18775.0 q^{80} +34101.0 q^{81} -1470.00 q^{82} -41776.0 q^{83} +10248.0 q^{84} +38350.0 q^{85} +38090.0 q^{86} -30228.0 q^{87} -154830. q^{88} +7970.00 q^{89} +25875.0 q^{90} +41236.0 q^{91} +4914.00 q^{92} -21804.0 q^{93} -15100.0 q^{94} -67650.0 q^{95} +14910.0 q^{96} -78050.0 q^{97} +213645. q^{98} -164358. q^{99} +O(q^{100})\)

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 $

$2$	5.00000	0.883883	0.441942	−	0.897044i	$-0.354290\pi$
$2$	5.00000	0.883883	0.441942	+	0.897044i	$0.354290\pi$
$3$	6.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	6.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	−7.00000	−0.218750
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	30.0000	0.340207
$7$	−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
$9$	−207.000	−0.851852
$10$	−125.000	−0.395285
$11$	794.000	1.97851	0.989256	−	0.146192i	$-0.0467017\pi$
$11$	794.000	1.97851	0.989256	+	0.146192i	$0.0467017\pi$
$12$	−42.0000	−0.0841969
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	−1220.00	−1.66356
$15$	−150.000	−0.172133
$16$	−751.000	−0.733398
$17$	−1534.00	−1.28737	−0.643685	−	0.765291i	$-0.722595\pi$
$17$	−1534.00	−1.28737	−0.643685	+	0.765291i	$0.722595\pi$
$18$	−1035.00	−0.752938
$19$	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
$21$	−1464.00	−0.724424
$22$	3970.00	1.74877
$23$	−702.000	−0.276705	−0.138353	−	0.990383i	$-0.544181\pi$
$23$	−702.000	−0.276705	−0.138353	+	0.990383i	$0.544181\pi$
$24$	−1170.00	−0.414627
$25$	625.000	0.200000
$26$	−845.000	−0.245145
$27$	−2700.00	−0.712778
$28$	1708.00	0.411711
$29$	−5038.00	−1.11241	−0.556203	−	0.831047i	$-0.687742\pi$
$29$	−5038.00	−1.11241	−0.556203	+	0.831047i	$0.687742\pi$
$30$	−750.000	−0.152145
$31$	−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
$33$	4764.00	0.761530
$34$	−7670.00	−1.13788
$35$	6100.00	0.841705
$36$	1449.00	0.186343
$37$	−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
$39$	−1014.00	−0.106752
$40$	4875.00	0.481753
$41$	−294.000	−0.0273141	−0.0136571	−	0.999907i	$-0.504347\pi$
$41$	−294.000	−0.0273141	−0.0136571	+	0.999907i	$0.504347\pi$
$42$	−7320.00	−0.640306
$43$	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
$45$	5175.00	0.380960
$46$	−3510.00	−0.244575
$47$	−3020.00	−0.199417	−0.0997085	−	0.995017i	$-0.531791\pi$
$47$	−3020.00	−0.199417	−0.0997085	+	0.995017i	$0.531791\pi$
$48$	−4506.00	−0.282285
$49$	42729.0	2.54233
$50$	3125.00	0.176777
$51$	−9204.00	−0.495509
$52$	1183.00	0.0606703
$53$	626.000	0.0306115	0.0153058	−	0.999883i	$-0.495128\pi$
$53$	626.000	0.0306115	0.0153058	+	0.999883i	$0.495128\pi$
$54$	−13500.0	−0.630013
$55$	−19850.0	−0.884818
$56$	47580.0	2.02747
$57$	16236.0	0.661899
$58$	−25190.0	−0.983237
$59$	−30066.0	−1.12446	−0.562232	−	0.826979i	$-0.690057\pi$
$59$	−30066.0	−1.12446	−0.562232	+	0.826979i	$0.690057\pi$
$60$	1050.00	0.0376540
$61$	−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
$63$	50508.0	1.60328
$64$	36457.0	1.11258
$65$	4225.00	0.124035
$66$	23820.0	0.673104
$67$	−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
$69$	−4212.00	−0.106504
$70$	30500.0	0.743969
$71$	4734.00	0.111451	0.0557253	−	0.998446i	$-0.482253\pi$
$71$	4734.00	0.111451	0.0557253	+	0.998446i	$0.482253\pi$
$72$	40365.0	0.917643
$73$	−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
$75$	3750.00	0.0769800
$76$	−18942.0	−0.376177
$77$	−193736.	−3.72378
$78$	−5070.00	−0.0943564
$79$	−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
$81$	34101.0	0.577503
$82$	−1470.00	−0.0241425
$83$	−41776.0	−0.665628	−0.332814	−	0.942992i	$-0.607998\pi$
$83$	−41776.0	−0.665628	−0.332814	+	0.942992i	$0.607998\pi$
$84$	10248.0	0.158468
$85$	38350.0	0.575729
$86$	38090.0	0.555348
$87$	−30228.0	−0.428165
$88$	−154830.	−2.13132
$89$	7970.00	0.106656	0.0533278	−	0.998577i	$-0.483017\pi$
$89$	7970.00	0.106656	0.0533278	+	0.998577i	$0.483017\pi$
$90$	25875.0	0.336724
$91$	41236.0	0.522003
$92$	4914.00	0.0605293
$93$	−21804.0	−0.261414
$94$	−15100.0	−0.176261
$95$	−67650.0	−0.769057
$96$	14910.0	0.165120
$97$	−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
$99$	−164358.	−1.68540
$100$	−4375.00	−0.0437500
$101$	−23010.0	−0.224447	−0.112223	−	0.993683i	$-0.535797\pi$
$101$	−23010.0	−0.224447	−0.112223	+	0.993683i	$0.535797\pi$
$102$	−46020.0	−0.437972
$103$	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
$105$	36600.0	0.323972
$106$	3130.00	0.0270570
$107$	−70142.0	−0.592269	−0.296134	−	0.955146i	$-0.595698\pi$
$107$	−70142.0	−0.592269	−0.296134	+	0.955146i	$0.595698\pi$
$108$	18900.0	0.155920
$109$	−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
$111$	−42348.0	−0.326231
$112$	183244.	1.38034
$113$	−100238.	−0.738476	−0.369238	−	0.929335i	$-0.620381\pi$
$113$	−100238.	−0.738476	−0.369238	+	0.929335i	$0.620381\pi$
$114$	81180.0	0.585042
$115$	17550.0	0.123746
$116$	35266.0	0.243339
$117$	34983.0	0.236261
$118$	−150330.	−0.993895
$119$	374296.	2.42297
$120$	29250.0	0.185427
$121$	469385.	2.91451
$122$	−29030.0	−0.176582
$123$	−1764.00	−0.0105132
$124$	25438.0	0.148569
$125$	−15625.0	−0.0894427
$126$	252540.	1.41711
$127$	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
$129$	45708.0	0.241834
$130$	21125.0	0.109632
$131$	211460.	1.07659	0.538295	−	0.842757i	$-0.319069\pi$
$131$	211460.	1.07659	0.538295	+	0.842757i	$0.319069\pi$
$132$	−33348.0	−0.166585
$133$	−660264.	−3.23660
$134$	−62180.0	−0.299150
$135$	67500.0	0.318764
$136$	299130.	1.38680
$137$	26302.0	0.119726	0.0598628	−	0.998207i	$-0.480934\pi$
$137$	26302.0	0.119726	0.0598628	+	0.998207i	$0.480934\pi$
$138$	−21060.0	−0.0941371
$139$	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
$141$	−18120.0	−0.0767557
$142$	23670.0	0.0985093
$143$	−134186.	−0.548741
$144$	155457.	0.624747
$145$	125950.	0.497483
$146$	−73470.0	−0.285251
$147$	256374.	0.978545
$148$	49406.0	0.185407
$149$	−49086.0	−0.181131	−0.0905653	−	0.995891i	$-0.528867\pi$
$149$	−49086.0	−0.181131	−0.0905653	+	0.995891i	$0.528867\pi$
$150$	18750.0	0.0680414
$151$	−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
$153$	317538.	1.09665
$154$	−968680.	−3.29138
$155$	90850.0	0.303736
$156$	7098.00	0.0233520
$157$	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
$159$	3756.00	0.0117824
$160$	−62125.0	−0.191852
$161$	171288.	0.520790
$162$	170505.	0.510446
$163$	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
$165$	−119100.	−0.340566
$166$	−208880.	−0.588338
$167$	212772.	0.590369	0.295184	−	0.955440i	$-0.404619\pi$
$167$	212772.	0.590369	0.295184	+	0.955440i	$0.404619\pi$
$168$	285480.	0.780373
$169$	28561.0	0.0769231
$170$	191750.	0.508877
$171$	−560142.	−1.46490
$172$	−53326.0	−0.137442
$173$	503178.	1.27822	0.639111	−	0.769114i	$-0.279302\pi$
$173$	503178.	1.27822	0.639111	+	0.769114i	$0.279302\pi$
$174$	−151140.	−0.378448
$175$	−152500.	−0.376422
$176$	−596294.	−1.45104
$177$	−180396.	−0.432806
$178$	39850.0	0.0942710
$179$	581724.	1.35701	0.678507	−	0.734594i	$-0.262627\pi$
$179$	581724.	1.35701	0.678507	+	0.734594i	$0.262627\pi$
$180$	−36225.0	−0.0833349
$181$	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
$183$	−34836.0	−0.0768954
$184$	136890.	0.298076
$185$	176450.	0.379046
$186$	−109020.	−0.231059
$187$	−1.21800e6	−2.54708
$188$	21140.0	0.0436225
$189$	658800.	1.34153
$190$	−338250.	−0.679757
$191$	−340608.	−0.675572	−0.337786	−	0.941223i	$-0.609678\pi$
$191$	−340608.	−0.675572	−0.337786	+	0.941223i	$0.609678\pi$
$192$	218742.	0.428232
$193$	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
$195$	25350.0	0.0477410
$196$	−299103.	−0.556135
$197$	538218.	0.988081	0.494041	−	0.869439i	$-0.335519\pi$
$197$	538218.	0.988081	0.494041	+	0.869439i	$0.335519\pi$
$198$	−821790.	−1.48970
$199$	−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
$201$	−74616.0	−0.130269
$202$	−115050.	−0.198385
$203$	1.22927e6	2.09367
$204$	64428.0	0.108392
$205$	7350.00	0.0122153
$206$	608530.	0.999111
$207$	145314.	0.235712
$208$	126919.	0.203408
$209$	2.14856e6	3.40238
$210$	183000.	0.286354
$211$	−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
$213$	28404.0	0.0428974
$214$	−350710.	−0.523496
$215$	−190450.	−0.280986
$216$	526500.	0.767828
$217$	886696.	1.27828
$218$	−979390.	−1.39577
$219$	−88164.0	−0.124217
$220$	138950.	0.193554
$221$	259246.	0.357052
$222$	−211740.	−0.288350
$223$	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
$225$	−129375.	−0.170370
$226$	−501190.	−0.652727
$227$	−880748.	−1.13445	−0.567227	−	0.823561i	$-0.691984\pi$
$227$	−880748.	−1.13445	−0.567227	+	0.823561i	$0.691984\pi$
$228$	−113652.	−0.144790
$229$	−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
$231$	−1.16242e6	−1.43328
$232$	982410.	1.19832
$233$	−1.20700e6	−1.45652	−0.728260	−	0.685300i	$-0.759671\pi$
$233$	−1.20700e6	−1.45652	−0.728260	+	0.685300i	$0.759671\pi$
$234$	174915.	0.208827
$235$	75500.0	0.0891820
$236$	210462.	0.245977
$237$	−238824.	−0.276189
$238$	1.87148e6	2.14162
$239$	−187038.	−0.211804	−0.105902	−	0.994377i	$-0.533773\pi$
$239$	−187038.	−0.211804	−0.105902	+	0.994377i	$0.533773\pi$
$240$	112650.	0.126242
$241$	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
$243$	860706.	0.935059
$244$	40642.0	0.0437019
$245$	−1.06822e6	−1.13697
$246$	−8820.00	−0.00929246
$247$	−457314.	−0.476949
$248$	708630.	0.731628
$249$	−250656.	−0.256200
$250$	−78125.0	−0.0790569
$251$	102648.	0.102841	0.0514205	−	0.998677i	$-0.483625\pi$
$251$	102648.	0.102841	0.0514205	+	0.998677i	$0.483625\pi$
$252$	−353556.	−0.350717
$253$	−557388.	−0.547465
$254$	196430.	0.191040
$255$	230100.	0.221598
$256$	−652799.	−0.622558
$257$	−221182.	−0.208890	−0.104445	−	0.994531i	$-0.533307\pi$
$257$	−221182.	−0.208890	−0.104445	+	0.994531i	$0.533307\pi$
$258$	228540.	0.213753
$259$	1.72215e6	1.59523
$260$	−29575.0	−0.0271326
$261$	1.04287e6	0.947605
$262$	1.05730e6	0.951579
$263$	1.40317e6	1.25090	0.625449	−	0.780265i	$-0.284916\pi$
$263$	1.40317e6	1.25090	0.625449	+	0.780265i	$0.284916\pi$
$264$	−928980.	−0.820345
$265$	−15650.0	−0.0136899
$266$	−3.30132e6	−2.86077
$267$	47820.0	0.0410517
$268$	87052.0	0.0740358
$269$	−582954.	−0.491195	−0.245597	−	0.969372i	$-0.578984\pi$
$269$	−582954.	−0.491195	−0.245597	+	0.969372i	$0.578984\pi$
$270$	337500.	0.281750
$271$	−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
$273$	247416.	0.200919
$274$	131510.	0.105824
$275$	496250.	0.395702
$276$	29484.0	0.0232977
$277$	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
$279$	752238.	0.578555
$280$	−1.18950e6	−0.906712
$281$	908826.	0.686618	0.343309	−	0.939223i	$-0.388452\pi$
$281$	908826.	0.686618	0.343309	+	0.939223i	$0.388452\pi$
$282$	−90600.0	−0.0678431
$283$	−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
$285$	−405900.	−0.296010
$286$	−670930.	−0.485023
$287$	71736.0	0.0514082
$288$	−514395.	−0.365440
$289$	933299.	0.657319
$290$	629750.	0.439717
$291$	−468300.	−0.324184
$292$	102858.	0.0705961
$293$	−1.96083e6	−1.33435	−0.667175	−	0.744901i	$-0.732497\pi$
$293$	−1.96083e6	−1.33435	−0.667175	+	0.744901i	$0.732497\pi$
$294$	1.28187e6	0.864919
$295$	751650.	0.502876
$296$	1.37631e6	0.913034
$297$	−2.14380e6	−1.41024
$298$	−245430.	−0.160098
$299$	118638.	0.0767442
$300$	−26250.0	−0.0168394
$301$	−1.85879e6	−1.18254
$302$	−1.78999e6	−1.12936
$303$	−138060.	−0.0863896
$304$	−2.03221e6	−1.26120
$305$	145150.	0.0893444
$306$	1.58769e6	0.969309
$307$	−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
$309$	730236.	0.435078
$310$	454250.	0.268467
$311$	2.41233e6	1.41428	0.707141	−	0.707072i	$-0.249985\pi$
$311$	2.41233e6	1.41428	0.707141	+	0.707072i	$0.249985\pi$
$312$	197730.	0.114997
$313$	−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
$315$	−1.26270e6	−0.717008
$316$	278628.	0.156967
$317$	2.59616e6	1.45105	0.725526	−	0.688195i	$-0.241597\pi$
$317$	2.59616e6	1.45105	0.725526	+	0.688195i	$0.241597\pi$
$318$	18780.0	0.0104142
$319$	−4.00017e6	−2.20091
$320$	−911425.	−0.497561
$321$	−420852.	−0.227964
$322$	856440.	0.460317
$323$	−4.15100e6	−2.21384
$324$	−238707.	−0.126329
$325$	−105625.	−0.0554700
$326$	29460.0	0.0153528
$327$	−1.17527e6	−0.607810
$328$	57330.0	0.0294237
$329$	736880.	0.375325
$330$	−595500.	−0.301021
$331$	−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
$333$	1.46101e6	0.722007
$334$	1.06386e6	0.521817
$335$	310900.	0.151359
$336$	1.09946e6	0.531291
$337$	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
$339$	−601428.	−0.284239
$340$	−268450.	−0.125941
$341$	−2.88540e6	−1.34375
$342$	−2.80071e6	−1.29480
$343$	−6.32497e6	−2.90284
$344$	−1.48551e6	−0.676830
$345$	105300.	0.0476300
$346$	2.51589e6	1.12980
$347$	3.41808e6	1.52391	0.761954	−	0.647631i	$-0.224240\pi$
$347$	3.41808e6	1.52391	0.761954	+	0.647631i	$0.224240\pi$
$348$	211596.	0.0936611
$349$	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
$351$	456300.	0.197689
$352$	1.97309e6	0.848770
$353$	−3.76395e6	−1.60771	−0.803854	−	0.594827i	$-0.797221\pi$
$353$	−3.76395e6	−1.60771	−0.803854	+	0.594827i	$0.797221\pi$
$354$	−901980.	−0.382550
$355$	−118350.	−0.0498422
$356$	−55790.0	−0.0233309
$357$	2.24578e6	0.932601
$358$	2.90862e6	1.19944
$359$	3.28216e6	1.34407	0.672037	−	0.740517i	$-0.265419\pi$
$359$	3.28216e6	1.34407	0.672037	+	0.740517i	$0.265419\pi$
$360$	−1.00913e6	−0.410382
$361$	4.84634e6	1.95725
$362$	1.01101e6	0.405494
$363$	2.81631e6	1.12180
$364$	−288652.	−0.114188
$365$	367350.	0.144327
$366$	−174180.	−0.0679666
$367$	−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
$369$	60858.0	0.0232676
$370$	882250.	0.335033
$371$	−152744.	−0.0576142
$372$	152628.	0.0571843
$373$	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
$375$	−93750.0	−0.0344265
$376$	588900.	0.214819
$377$	851422.	0.308526
$378$	3.29400e6	1.18575
$379$	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
$381$	235716.	0.0831911
$382$	−1.70304e6	−0.597127
$383$	−475044.	−0.165477	−0.0827384	−	0.996571i	$-0.526367\pi$
$383$	−475044.	−0.165477	−0.0827384	+	0.996571i	$0.526367\pi$
$384$	616590.	0.213387
$385$	4.84340e6	1.66532
$386$	1.37807e6	0.470764
$387$	−1.57693e6	−0.535222
$388$	546350.	0.184243
$389$	150566.	0.0504490	0.0252245	−	0.999682i	$-0.491970\pi$
$389$	150566.	0.0504490	0.0252245	+	0.999682i	$0.491970\pi$
$390$	126750.	0.0421975
$391$	1.07687e6	0.356222
$392$	−8.33216e6	−2.73869
$393$	1.26876e6	0.414379
$394$	2.69109e6	0.873349
$395$	995100.	0.320903
$396$	1.15051e6	0.368681
$397$	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
$399$	−3.96158e6	−1.24577
$400$	−469375.	−0.146680
$401$	−3.19679e6	−0.992780	−0.496390	−	0.868100i	$-0.665341\pi$
$401$	−3.19679e6	−0.992780	−0.496390	+	0.868100i	$0.665341\pi$
$402$	−373080.	−0.115143
$403$	614146.	0.188369
$404$	161070.	0.0490977
$405$	−852525.	−0.258267
$406$	6.14636e6	1.85056
$407$	−5.60405e6	−1.67693
$408$	1.79478e6	0.533778
$409$	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
$411$	157812.	0.0460824
$412$	−851942.	−0.247267
$413$	7.33610e6	2.11636
$414$	726570.	0.208342
$415$	1.04440e6	0.297678
$416$	−419965.	−0.118982
$417$	8064.00	0.00227096
$418$	1.07428e7	3.00731
$419$	−1.13159e6	−0.314887	−0.157444	−	0.987528i	$-0.550325\pi$
$419$	−1.13159e6	−0.314887	−0.157444	+	0.987528i	$0.550325\pi$
$420$	−256200.	−0.0708689
$421$	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
$423$	625140.	0.169874
$424$	−122070.	−0.0329757
$425$	−958750.	−0.257474
$426$	142020.	0.0379163
$427$	1.41666e6	0.376008
$428$	490994.	0.129559
$429$	−805116.	−0.211210
$430$	−952250.	−0.248359
$431$	3.41044e6	0.884335	0.442168	−	0.896932i	$-0.354210\pi$
$431$	3.41044e6	0.884335	0.442168	+	0.896932i	$0.354210\pi$
$432$	2.02770e6	0.522750
$433$	−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
$435$	755700.	0.191481
$436$	1.37115e6	0.345436
$437$	−1.89961e6	−0.475840
$438$	−440820.	−0.109793
$439$	−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
$441$	−8.84490e6	−2.16569
$442$	1.29623e6	0.315592
$443$	−8.23508e6	−1.99369	−0.996847	−	0.0793445i	$-0.974717\pi$
$443$	−8.23508e6	−1.99369	−0.996847	+	0.0793445i	$0.974717\pi$
$444$	296436.	0.0713631
$445$	−199250.	−0.0476978
$446$	106820.	0.0254282
$447$	−294516.	−0.0697172
$448$	−8.89551e6	−2.09400
$449$	−1.29601e6	−0.303383	−0.151691	−	0.988428i	$-0.548472\pi$
$449$	−1.29601e6	−0.303383	−0.151691	+	0.988428i	$0.548472\pi$
$450$	−646875.	−0.150588
$451$	−233436.	−0.0540414
$452$	701666.	0.161542
$453$	−2.14799e6	−0.491798
$454$	−4.40374e6	−1.00273
$455$	−1.03090e6	−0.233447
$456$	−3.16602e6	−0.713020
$457$	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
$459$	4.14180e6	0.917608
$460$	−122850.	−0.0270695
$461$	−3.20663e6	−0.702743	−0.351372	−	0.936236i	$-0.614285\pi$
$461$	−3.20663e6	−0.702743	−0.351372	+	0.936236i	$0.614285\pi$
$462$	−5.81208e6	−1.26685
$463$	−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
$465$	545100.	0.116908
$466$	−6.03499e6	−1.28739
$467$	−8.26813e6	−1.75435	−0.877173	−	0.480175i	$-0.840573\pi$
$467$	−8.26813e6	−1.75435	−0.877173	+	0.480175i	$0.840573\pi$
$468$	−244881.	−0.0516821
$469$	3.03438e6	0.636999
$470$	377500.	0.0788265
$471$	272700.	0.0566413
$472$	5.86287e6	1.21131
$473$	6.04869e6	1.24311
$474$	−1.19412e6	−0.244119
$475$	1.69125e6	0.343933
$476$	−2.62007e6	−0.530024
$477$	−129582.	−0.0260765
$478$	−935190.	−0.187210
$479$	3.65468e6	0.727797	0.363899	−	0.931439i	$-0.381445\pi$
$479$	3.65468e6	0.727797	0.363899	+	0.931439i	$0.381445\pi$
$480$	−372750.	−0.0738439
$481$	1.19280e6	0.235075
$482$	1.35845e6	0.266334
$483$	1.02773e6	0.200452
$484$	−3.28570e6	−0.637549
$485$	1.95125e6	0.376668
$486$	4.30353e6	0.826483
$487$	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
$489$	35352.0	0.00668562
$490$	−5.34113e6	−1.00495
$491$	5.72551e6	1.07179	0.535896	−	0.844284i	$-0.319974\pi$
$491$	5.72551e6	1.07179	0.535896	+	0.844284i	$0.319974\pi$
$492$	12348.0	0.00229977
$493$	7.72829e6	1.43208
$494$	−2.28657e6	−0.421568
$495$	4.10895e6	0.753734
$496$	2.72913e6	0.498105
$497$	−1.15510e6	−0.209762
$498$	−1.25328e6	−0.226451
$499$	−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
$501$	1.27663e6	0.227233
$502$	513240.	0.0908994
$503$	−2.90611e6	−0.512143	−0.256072	−	0.966658i	$-0.582428\pi$
$503$	−2.90611e6	−0.512143	−0.256072	+	0.966658i	$0.582428\pi$
$504$	−9.84906e6	−1.72710
$505$	575250.	0.100376
$506$	−2.78694e6	−0.483895
$507$	171366.	0.0296077
$508$	−275002.	−0.0472799
$509$	−8.37125e6	−1.43217	−0.716087	−	0.698011i	$-0.754069\pi$
$509$	−8.37125e6	−1.43217	−0.716087	+	0.698011i	$0.754069\pi$
$510$	1.15050e6	0.195867
$511$	3.58534e6	0.607404
$512$	−6.55248e6	−1.10466
$513$	−7.30620e6	−1.22574
$514$	−1.10591e6	−0.184634
$515$	−3.04265e6	−0.505515
$516$	−319956.	−0.0529013
$517$	−2.39788e6	−0.394549
$518$	8.61076e6	1.40999
$519$	3.01907e6	0.491988
$520$	−823875.	−0.133614
$521$	5.37332e6	0.867258	0.433629	−	0.901092i	$-0.357233\pi$
$521$	5.37332e6	0.867258	0.433629	+	0.901092i	$0.357233\pi$
$522$	5.21433e6	0.837572
$523$	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
$525$	−915000.	−0.144885
$526$	7.01587e6	1.10565
$527$	5.57456e6	0.874347
$528$	−3.57776e6	−0.558505
$529$	−5.94354e6	−0.923434
$530$	−78250.0	−0.0121003
$531$	6.22366e6	0.957877
$532$	4.62185e6	0.708005
$533$	49686.0	0.00757558
$534$	239100.	0.0362849
$535$	1.75355e6	0.264871
$536$	2.42502e6	0.364589
$537$	3.49034e6	0.522315
$538$	−2.91477e6	−0.434159
$539$	3.39268e7	5.03004
$540$	−472500.	−0.0697296
$541$	−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
$543$	1.21321e6	0.176578
$544$	−3.81199e6	−0.552274
$545$	4.89695e6	0.706211
$546$	1.23708e6	0.177589
$547$	−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
$549$	1.20184e6	0.170183
$550$	2.48125e6	0.349755
$551$	−1.36328e7	−1.91296
$552$	821340.	0.114730
$553$	9.71218e6	1.35053
$554$	5.52305e6	0.764548
$555$	1.05870e6	0.145895
$556$	−9408.00	−0.00129066
$557$	−5.88545e6	−0.803788	−0.401894	−	0.915686i	$-0.631648\pi$
$557$	−5.88545e6	−0.803788	−0.401894	+	0.915686i	$0.631648\pi$
$558$	3.76119e6	0.511375
$559$	−1.28744e6	−0.174260
$560$	−4.58110e6	−0.617305
$561$	−7.30798e6	−0.980370
$562$	4.54413e6	0.606890
$563$	−3.91526e6	−0.520583	−0.260291	−	0.965530i	$-0.583819\pi$
$563$	−3.91526e6	−0.520583	−0.260291	+	0.965530i	$0.583819\pi$
$564$	126840.	0.0167903
$565$	2.50595e6	0.330256
$566$	−2.24627e6	−0.294728
$567$	−8.32064e6	−1.08692
$568$	−923130.	−0.120058
$569$	9.78180e6	1.26660	0.633298	−	0.773908i	$-0.281701\pi$
$569$	9.78180e6	1.26660	0.633298	+	0.773908i	$0.281701\pi$
$570$	−2.02950e6	−0.261639
$571$	−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
$573$	−2.04365e6	−0.260028
$574$	358680.	0.0454389
$575$	−438750.	−0.0553411
$576$	−7.54660e6	−0.947753
$577$	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
$579$	1.65368e6	0.205001
$580$	−881650.	−0.108824
$581$	1.01933e7	1.25278
$582$	−2.34150e6	−0.286541
$583$	497044.	0.0605652
$584$	2.86533e6	0.347650
$585$	−874575.	−0.105659
$586$	−9.80413e6	−1.17941
$587$	1.22649e7	1.46916	0.734578	−	0.678525i	$-0.237380\pi$
$587$	1.22649e7	1.46916	0.734578	+	0.678525i	$0.237380\pi$
$588$	−1.79462e6	−0.214057
$589$	−9.83360e6	−1.16795
$590$	3.75825e6	0.444483
$591$	3.22931e6	0.380313
$592$	5.30056e6	0.621609
$593$	−1.54878e7	−1.80864	−0.904320	−	0.426856i	$-0.859621\pi$
$593$	−1.54878e7	−1.80864	−0.904320	+	0.426856i	$0.859621\pi$
$594$	−1.07190e7	−1.24649
$595$	−9.35740e6	−1.08358
$596$	343602.	0.0396223
$597$	−5.12304e6	−0.588291
$598$	593190.	0.0678330
$599$	9.75710e6	1.11110	0.555551	−	0.831483i	$-0.312507\pi$
$599$	9.75710e6	1.11110	0.555551	+	0.831483i	$0.312507\pi$
$600$	−731250.	−0.0829254
$601$	−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
$603$	2.57425e6	0.288309
$604$	2.50599e6	0.279503
$605$	−1.17346e7	−1.30341
$606$	−690300.	−0.0763583
$607$	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
$609$	7.37563e6	0.805853
$610$	725750.	0.0789701
$611$	510380.	0.0553083
$612$	−2.22277e6	−0.239892
$613$	−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
$615$	44100.0	0.00470166
$616$	3.77785e7	4.01137
$617$	8.55509e6	0.904715	0.452358	−	0.891837i	$-0.350583\pi$
$617$	8.55509e6	0.904715	0.452358	+	0.891837i	$0.350583\pi$
$618$	3.65118e6	0.384558
$619$	−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
$621$	1.89540e6	0.197230
$622$	1.20617e7	1.25006
$623$	−1.94468e6	−0.200737
$624$	761514.	0.0782918
$625$	390625.	0.0400000
$626$	−1.07718e7	−1.09863
$627$	1.28914e7	1.30958
$628$	−318150.	−0.0321909
$629$	1.08270e7	1.09114
$630$	−6.31350e6	−0.633751
$631$	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
$633$	−6.00674e6	−0.595840
$634$	1.29808e7	1.28256
$635$	−982150.	−0.0966593
$636$	−26292.0	−0.00257739
$637$	−7.22120e6	−0.705116
$638$	−2.00009e7	−1.94535
$639$	−979938.	−0.0949394
$640$	−2.56912e6	−0.247934
$641$	9.96437e6	0.957866	0.478933	−	0.877851i	$-0.341024\pi$
$641$	9.96437e6	0.957866	0.478933	+	0.877851i	$0.341024\pi$
$642$	−2.10426e6	−0.201494
$643$	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
$645$	−1.14270e6	−0.108152
$646$	−2.07550e7	−1.95678
$647$	844766.	0.0793370	0.0396685	−	0.999213i	$-0.487370\pi$
$647$	844766.	0.0793370	0.0396685	+	0.999213i	$0.487370\pi$
$648$	−6.64969e6	−0.622106
$649$	−2.38724e7	−2.22477
$650$	−528125.	−0.0490290
$651$	5.32018e6	0.492010
$652$	−41244.0	−0.00379963
$653$	5.79681e6	0.531993	0.265997	−	0.963974i	$-0.414299\pi$
$653$	5.79681e6	0.531993	0.265997	+	0.963974i	$0.414299\pi$
$654$	−5.87634e6	−0.537233
$655$	−5.28650e6	−0.481465
$656$	220794.	0.0200322
$657$	3.04166e6	0.274914
$658$	3.68440e6	0.331743
$659$	−1.12406e7	−1.00827	−0.504136	−	0.863624i	$-0.668189\pi$
$659$	−1.12406e7	−1.00827	−0.504136	+	0.863624i	$0.668189\pi$
$660$	833700.	0.0744989
$661$	−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
$663$	1.55548e6	0.137429
$664$	8.14632e6	0.717037
$665$	1.65066e7	1.44745
$666$	7.30503e6	0.638170
$667$	3.53668e6	0.307809
$668$	−1.48940e6	−0.129143
$669$	128184.	0.0110731
$670$	1.55450e6	0.133784
$671$	−4.60996e6	−0.395268
$672$	−3.63804e6	−0.310774
$673$	−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
$675$	−1.68750e6	−0.142556
$676$	−199927.	−0.0168269
$677$	−7.57359e6	−0.635082	−0.317541	−	0.948244i	$-0.602857\pi$
$677$	−7.57359e6	−0.635082	−0.317541	+	0.948244i	$0.602857\pi$
$678$	−3.00714e6	−0.251235
$679$	1.90442e7	1.58522
$680$	−7.47825e6	−0.620194
$681$	−5.28449e6	−0.436652
$682$	−1.44270e7	−1.18772
$683$	−1.65552e7	−1.35794	−0.678972	−	0.734164i	$-0.737574\pi$
$683$	−1.65552e7	−1.35794	−0.678972	+	0.734164i	$0.737574\pi$
$684$	3.92099e6	0.320447
$685$	−657550.	−0.0535430
$686$	−3.16248e7	−2.56577
$687$	−78180.0	−0.00631981
$688$	−5.72112e6	−0.460797
$689$	−105794.	−0.00849010
$690$	526500.	0.0420994
$691$	−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
$693$	4.01034e7	3.17211
$694$	1.70904e7	1.34696
$695$	−33600.0	−0.00263862
$696$	5.89446e6	0.461234
$697$	450996.	0.0351634
$698$	1.17846e7	0.915535
$699$	−7.24199e6	−0.560615
$700$	1.06750e6	0.0823423
$701$	1.52050e7	1.16867	0.584334	−	0.811514i	$-0.301356\pi$
$701$	1.52050e7	1.16867	0.584334	+	0.811514i	$0.301356\pi$
$702$	2.28150e6	0.174734
$703$	−1.90989e7	−1.45754
$704$	2.89469e7	2.20125
$705$	453000.	0.0343262
$706$	−1.88198e7	−1.42103
$707$	5.61444e6	0.422433
$708$	1.26277e6	0.0946764
$709$	−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
$711$	8.23943e6	0.611256
$712$	−1.55415e6	−0.114893
$713$	2.55107e6	0.187931
$714$	1.12289e7	0.824311
$715$	3.35465e6	0.245404
$716$	−4.07207e6	−0.296847
$717$	−1.12223e6	−0.0815236
$718$	1.64108e7	1.18801
$719$	−2.08096e7	−1.50121	−0.750604	−	0.660752i	$-0.770237\pi$
$719$	−2.08096e7	−1.50121	−0.750604	+	0.660752i	$0.770237\pi$
$720$	−3.88643e6	−0.279395
$721$	−2.96963e7	−2.12747
$722$	2.42317e7	1.72998
$723$	1.63014e6	0.115979
$724$	−1.41541e6	−0.100355
$725$	−3.14875e6	−0.222481
$726$	1.40816e7	0.991537
$727$	−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
$729$	−3.12231e6	−0.217599
$730$	1.83675e6	0.127568
$731$	−1.16860e7	−0.808859
$732$	243852.	0.0168209
$733$	−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
$735$	−6.40935e6	−0.437618
$736$	−1.74447e6	−0.118705
$737$	−9.87418e6	−0.669626
$738$	304290.	0.0205659
$739$	−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
$741$	−2.74388e6	−0.183578
$742$	−763720.	−0.0509242
$743$	5.57725e6	0.370637	0.185318	−	0.982679i	$-0.440668\pi$
$743$	5.57725e6	0.370637	0.185318	+	0.982679i	$0.440668\pi$
$744$	4.25178e6	0.281604
$745$	1.22715e6	0.0810041
$746$	1.40318e7	0.923135
$747$	8.64763e6	0.567016
$748$	8.52597e6	0.557173
$749$	1.71146e7	1.11471
$750$	−468750.	−0.0304290
$751$	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
$753$	615888.	0.0395835
$754$	4.25711e6	0.272701
$755$	8.94995e6	0.571417
$756$	−4.61160e6	−0.293459
$757$	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
$759$	−3.34433e6	−0.210719
$760$	1.31918e7	0.828454
$761$	−2.10490e7	−1.31756	−0.658780	−	0.752335i	$-0.728927\pi$
$761$	−2.10490e7	−1.31756	−0.658780	+	0.752335i	$0.728927\pi$
$762$	1.17858e6	0.0735312
$763$	4.77942e7	2.97210
$764$	2.38426e6	0.147781
$765$	−7.93845e6	−0.490436
$766$	−2.37522e6	−0.146262
$767$	5.08115e6	0.311870
$768$	−3.91679e6	−0.239623
$769$	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
$771$	−1.32709e6	−0.0804017
$772$	−1.92930e6	−0.116508
$773$	1.15053e7	0.692545	0.346272	−	0.938134i	$-0.387447\pi$
$773$	1.15053e7	0.692545	0.346272	+	0.938134i	$0.387447\pi$
$774$	−7.88463e6	−0.473074
$775$	−2.27125e6	−0.135835
$776$	1.52198e7	0.907305
$777$	1.03329e7	0.614003
$778$	752830.	0.0445911
$779$	−795564.	−0.0469712
$780$	−177450.	−0.0104433
$781$	3.75880e6	0.220506
$782$	5.38434e6	0.314859
$783$	1.36026e7	0.792898
$784$	−3.20895e7	−1.86454
$785$	−1.13625e6	−0.0658112
$786$	6.34380e6	0.366263
$787$	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
$789$	8.41904e6	0.481471
$790$	4.97550e6	0.283641
$791$	2.44581e7	1.38989
$792$	3.20498e7	1.81557
$793$	981214.	0.0554091
$794$	1.20843e6	0.0680253
$795$	−93900.0	−0.00526924
$796$	5.97688e6	0.334343
$797$	−2.85072e7	−1.58968	−0.794838	−	0.606821i	$-0.792444\pi$
$797$	−2.85072e7	−1.58968	−0.794838	+	0.606821i	$0.792444\pi$
$798$	−1.98079e7	−1.10111
$799$	4.63268e6	0.256723
$800$	1.55313e6	0.0857988
$801$	−1.64979e6	−0.0908547
$802$	−1.59840e7	−0.877502
$803$	−1.16670e7	−0.638516
$804$	522312.	0.0284964
$805$	−4.28220e6	−0.232904
$806$	3.07073e6	0.166496
$807$	−3.49772e6	−0.189061
$808$	4.48695e6	0.241781
$809$	1.08912e7	0.585065	0.292533	−	0.956256i	$-0.405502\pi$
$809$	1.08912e7	0.585065	0.292533	+	0.956256i	$0.405502\pi$
$810$	−4.26262e6	−0.228278
$811$	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
$813$	−6.28141e6	−0.333297
$814$	−2.80203e7	−1.48221
$815$	−147300.	−0.00776799
$816$	6.91220e6	0.363405
$817$	2.06143e7	1.08047
$818$	2.11641e6	0.110590
$819$	−8.53585e6	−0.444669
$820$	−51450.0	−0.00267209
$821$	−9.60605e6	−0.497378	−0.248689	−	0.968583i	$-0.580000\pi$
$821$	−9.60605e6	−0.497378	−0.248689	+	0.968583i	$0.580000\pi$
$822$	789060.	0.0407315
$823$	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
$825$	2.97750e6	0.152306
$826$	3.66805e7	1.87062
$827$	2.40317e7	1.22186	0.610930	−	0.791685i	$-0.290796\pi$
$827$	2.40317e7	1.22186	0.610930	+	0.791685i	$0.290796\pi$
$828$	−1.01720e6	−0.0515620
$829$	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
$831$	6.62766e6	0.332934
$832$	−6.16123e6	−0.308574
$833$	−6.55463e7	−3.27292
$834$	40320.0	0.00200727
$835$	−5.31930e6	−0.264021
$836$	−1.50399e7	−0.744270
$837$	9.81180e6	0.484100
$838$	−5.65796e6	−0.278323
$839$	−6.89303e6	−0.338069	−0.169034	−	0.985610i	$-0.554065\pi$
$839$	−6.89303e6	−0.338069	−0.169034	+	0.985610i	$0.554065\pi$
$840$	−7.13700e6	−0.348994
$841$	4.87030e6	0.237446
$842$	1.73849e7	0.845070
$843$	5.45296e6	0.264279
$844$	7.00787e6	0.338633
$845$	−714025.	−0.0344010
$846$	3.12570e6	0.150149
$847$	−1.14530e8	−5.48543
$848$	−470126.	−0.0224504
$849$	−2.69552e6	−0.128344
$850$	−4.79375e6	−0.227577
$851$	4.95472e6	0.234528
$852$	−198828.	−0.00938380
$853$	−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
$855$	1.40035e7	0.655123
$856$	1.36777e7	0.638011
$857$	−7.89742e6	−0.367310	−0.183655	−	0.982991i	$-0.558793\pi$
$857$	−7.89742e6	−0.367310	−0.183655	+	0.982991i	$0.558793\pi$
$858$	−4.02558e6	−0.186685
$859$	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
$861$	430416.	0.0197870
$862$	1.70522e7	0.781649
$863$	1.76565e7	0.807007	0.403503	−	0.914978i	$-0.367792\pi$
$863$	1.76565e7	0.807007	0.403503	+	0.914978i	$0.367792\pi$
$864$	−6.70950e6	−0.305778
$865$	−1.25794e7	−0.571638
$866$	−1.70361e7	−0.771926
$867$	5.59979e6	0.253002
$868$	−6.20687e6	−0.279623
$869$	−3.16044e7	−1.41970
$870$	3.77850e6	0.169247
$871$	2.10168e6	0.0938690
$872$	3.81962e7	1.70110
$873$	1.61564e7	0.717476
$874$	−9.49806e6	−0.420587
$875$	3.81250e6	0.168341
$876$	617148.	0.0271725
$877$	−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
$879$	−1.17650e7	−0.513592
$880$	1.49074e7	0.648924
$881$	−1.14571e7	−0.497318	−0.248659	−	0.968591i	$-0.579990\pi$
$881$	−1.14571e7	−0.497318	−0.248659	+	0.968591i	$0.579990\pi$
$882$	−4.42245e7	−1.91422
$883$	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
$885$	4.50990e6	0.193557
$886$	−4.11754e7	−1.76219
$887$	8.66087e6	0.369617	0.184809	−	0.982775i	$-0.440833\pi$
$887$	8.66087e6	0.369617	0.184809	+	0.982775i	$0.440833\pi$
$888$	8.25786e6	0.351427
$889$	−9.58578e6	−0.406793
$890$	−996250.	−0.0421593
$891$	2.70762e7	1.14260
$892$	−149548.	−0.00629316
$893$	−8.17212e6	−0.342930
$894$	−1.47258e6	−0.0616219
$895$	−1.45431e7	−0.606875
$896$	−2.50747e7	−1.04343
$897$	711828.	0.0295389
$898$	−6.48003e6	−0.268155
$899$	1.83081e7	0.755516
$900$	905625.	0.0372685
$901$	−960284.	−0.0394083
$902$	−1.16718e6	−0.0477663
$903$	−1.11528e7	−0.455159
$904$	1.95464e7	0.795511
$905$	−5.05505e6	−0.205165
$906$	−1.07399e7	−0.434692
$907$	−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
$909$	4.76307e6	0.191195
$910$	−5.15450e6	−0.206340
$911$	−942576.	−0.0376288	−0.0188144	−	0.999823i	$-0.505989\pi$
$911$	−942576.	−0.0376288	−0.0188144	+	0.999823i	$0.505989\pi$
$912$	−1.21932e7	−0.485436
$913$	−3.31701e7	−1.31695
$914$	8.40979e6	0.332981
$915$	870900.	0.0343887
$916$	91210.0	0.00359173
$917$	−5.15962e7	−2.02626
$918$	2.07090e7	0.811059
$919$	−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
$921$	−1.07631e7	−0.418107
$922$	−1.60332e7	−0.621143
$923$	−800046.	−0.0309108
$924$	8.13691e6	0.313530
$925$	−4.41125e6	−0.169515
$926$	−2.63185e7	−1.00863
$927$	−2.51931e7	−0.962904
$928$	−1.25194e7	−0.477216
$929$	1.10181e7	0.418858	0.209429	−	0.977824i	$-0.432840\pi$
$929$	1.10181e7	0.418858	0.209429	+	0.977824i	$0.432840\pi$
$930$	2.72550e6	0.103333
$931$	1.15625e8	4.37196
$932$	8.44899e6	0.318614
$933$	1.44740e7	0.544358
$934$	−4.13406e7	−1.55064
$935$	3.04499e7	1.13909
$936$	−6.82168e6	−0.254508
$937$	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
$939$	−1.29261e7	−0.478415
$940$	−528500.	−0.0195086
$941$	1.28845e7	0.474345	0.237172	−	0.971468i	$-0.423779\pi$
$941$	1.28845e7	0.474345	0.237172	+	0.971468i	$0.423779\pi$
$942$	1.36350e6	0.0500643
$943$	206388.	0.00755797
$944$	2.25796e7	0.824680
$945$	−1.64700e7	−0.599949
$946$	3.02435e7	1.09876
$947$	−1.18911e7	−0.430871	−0.215436	−	0.976518i	$-0.569117\pi$
$947$	−1.18911e7	−0.430871	−0.215436	+	0.976518i	$0.569117\pi$
$948$	1.67177e6	0.0604164
$949$	2.48329e6	0.0895079
$950$	8.45625e6	0.303997
$951$	1.55769e7	0.558510
$952$	−7.29877e7	−2.61010
$953$	4.40094e7	1.56969	0.784844	−	0.619694i	$-0.212743\pi$
$953$	4.40094e7	1.56969	0.784844	+	0.619694i	$0.212743\pi$
$954$	−647910.	−0.0230486
$955$	8.51520e6	0.302125
$956$	1.30927e6	0.0463322
$957$	−2.40010e7	−0.847130
$958$	1.82734e7	0.643288
$959$	−6.41769e6	−0.225337
$960$	−5.46855e6	−0.191511
$961$	−1.54232e7	−0.538723
$962$	5.96401e6	0.207779
$963$	1.45194e7	0.504525
$964$	−1.90183e6	−0.0659142
$965$	−6.89035e6	−0.238190
$966$	5.13864e6	0.177176
$967$	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
$969$	−2.49060e7	−0.852109
$970$	9.75625e6	0.332931
$971$	2.44293e7	0.831502	0.415751	−	0.909478i	$-0.363519\pi$
$971$	2.44293e7	0.831502	0.415751	+	0.909478i	$0.363519\pi$
$972$	−6.02494e6	−0.204544
$973$	−327936.	−0.0111047
$974$	3.56542e7	1.20424
$975$	−633750.	−0.0213504
$976$	4.36031e6	0.146518
$977$	5.15549e7	1.72796	0.863980	−	0.503527i	$-0.167964\pi$
$977$	5.15549e7	1.72796	0.863980	+	0.503527i	$0.167964\pi$
$978$	176760.	0.00590931
$979$	6.32818e6	0.211019
$980$	7.47758e6	0.248711
$981$	4.05467e7	1.34519
$982$	2.86276e7	0.947339
$983$	−1.38938e7	−0.458604	−0.229302	−	0.973355i	$-0.573644\pi$
$983$	−1.38938e7	−0.458604	−0.229302	+	0.973355i	$0.573644\pi$
$984$	343980.	0.0113252
$985$	−1.34554e7	−0.441883
$986$	3.86415e7	1.26579
$987$	4.42128e6	0.144463
$988$	3.20120e6	0.104333
$989$	−5.34784e6	−0.173855
$990$	2.05448e7	0.666213
$991$	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
$993$	−5.50336e6	−0.177115
$994$	−5.77548e6	−0.185405
$995$	2.13460e7	0.683532
$996$	1.75459e6	0.0560438
$997$	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
$999$	1.90566e7	0.604132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.a.a.1.1	✓	1
3.2	odd	2		585.6.a.a.1.1		1
4.3	odd	2		1040.6.a.a.1.1		1
5.2	odd	4		325.6.b.a.274.2		2
5.3	odd	4		325.6.b.a.274.1		2
5.4	even	2		325.6.a.a.1.1		1
13.12	even	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	1.1	even	1	trivial
325.6.a.a.1.1		1	5.4	even	2
325.6.b.a.274.1		2	5.3	odd	4
325.6.b.a.274.2		2	5.2	odd	4
585.6.a.a.1.1		1	3.2	odd	2
845.6.a.a.1.1		1	13.12	even	2
1040.6.a.a.1.1		1	4.3	odd	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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