LMFDB - Embedded newform 5.24.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,24,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	5.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:	$16.7602018673$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 215756x + 18660756 $ x^3 - x^2 - 215756*x + 18660756
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$89.8102$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+758.861 q^{2} +360571. q^{3} -7.81274e6 q^{4} +4.88281e7 q^{5} +2.73623e8 q^{6} -1.00441e10 q^{7} -1.22946e10 q^{8} +3.58682e10 q^{9} +O(q^{10})$	\(q+758.861 q^{2} +360571. q^{3} -7.81274e6 q^{4} +4.88281e7 q^{5} +2.73623e8 q^{6} -1.00441e10 q^{7} -1.22946e10 q^{8} +3.58682e10 q^{9} +3.70538e10 q^{10} +9.30325e11 q^{11} -2.81705e12 q^{12} -4.62648e12 q^{13} -7.62211e12 q^{14} +1.76060e13 q^{15} +5.62081e13 q^{16} -2.57225e14 q^{17} +2.72190e13 q^{18} -4.24898e14 q^{19} -3.81481e14 q^{20} -3.62163e15 q^{21} +7.05988e14 q^{22} +1.18528e15 q^{23} -4.43307e15 q^{24} +2.38419e15 q^{25} -3.51085e15 q^{26} -2.10123e16 q^{27} +7.84723e16 q^{28} -6.04141e16 q^{29} +1.33605e16 q^{30} +1.71978e17 q^{31} +1.45789e17 q^{32} +3.35448e17 q^{33} -1.95198e17 q^{34} -4.90437e17 q^{35} -2.80229e17 q^{36} +5.78331e17 q^{37} -3.22438e17 q^{38} -1.66817e18 q^{39} -6.00321e17 q^{40} +1.88124e18 q^{41} -2.74831e18 q^{42} -4.22624e18 q^{43} -7.26839e18 q^{44} +1.75138e18 q^{45} +8.99461e17 q^{46} +6.75282e18 q^{47} +2.02670e19 q^{48} +7.35161e19 q^{49} +1.80927e18 q^{50} -9.27480e19 q^{51} +3.61455e19 q^{52} -3.81753e19 q^{53} -1.59454e19 q^{54} +4.54260e19 q^{55} +1.23488e20 q^{56} -1.53206e20 q^{57} -4.58459e19 q^{58} -6.41344e18 q^{59} -1.37551e20 q^{60} -1.14535e20 q^{61} +1.30507e20 q^{62} -3.60266e20 q^{63} -3.60875e20 q^{64} -2.25902e20 q^{65} +2.54559e20 q^{66} +2.51375e20 q^{67} +2.00963e21 q^{68} +4.27377e20 q^{69} -3.72173e20 q^{70} +6.24114e20 q^{71} -4.40985e20 q^{72} +1.44534e21 q^{73} +4.38873e20 q^{74} +8.59668e20 q^{75} +3.31962e21 q^{76} -9.34432e21 q^{77} -1.26591e21 q^{78} -1.52724e21 q^{79} +2.74454e21 q^{80} -1.09532e22 q^{81} +1.42760e21 q^{82} -8.73110e21 q^{83} +2.82948e22 q^{84} -1.25598e22 q^{85} -3.20713e21 q^{86} -2.17836e22 q^{87} -1.14379e22 q^{88} +1.90405e22 q^{89} +1.32905e21 q^{90} +4.64690e22 q^{91} -9.26026e21 q^{92} +6.20102e22 q^{93} +5.12446e21 q^{94} -2.07470e22 q^{95} +5.25671e22 q^{96} -8.82090e22 q^{97} +5.57885e22 q^{98} +3.33691e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9}+O(q^{10}) $ 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9	$ 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9} + 32519531250 q^{10} - 165286030404 q^{11} - 2460925191744 q^{12} - 3554970733998 q^{13} + 1638464466408 q^{14} - 6808007812500 q^{15} - 68987884476912 q^{16} - 416105769269514 q^{17} - 302723670254238 q^{18} - 975704043068460 q^{19} - 463062304687500 q^{20} - 51\!\cdots\!84 q^{21}+ \cdots + 19\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9 + 32519531250 * q^10 - 165286030404 * q^11 - 2460925191744 * q^12 - 3554970733998 * q^13 + 1638464466408 * q^14 - 6808007812500 * q^15 - 68987884476912 * q^16 - 416105769269514 * q^17 - 302723670254238 * q^18 - 975704043068460 * q^19 - 463062304687500 * q^20 - 5102384337991584 * q^21 - 5786145456383688 * q^22 - 4979666912332368 * q^23 - 10409810708926080 * q^24 + 7152557373046875 * q^25 - 17675137590787524 * q^26 + 20047178078003160 * q^27 + 71220956974215888 * q^28 + 95526863867406210 * q^29 + 46870059375000000 * q^30 + 203997528720796176 * q^31 + 170287635059993376 * q^32 + 322079222096408304 * q^33 + 716918393922501108 * q^34 - 118783366406250000 * q^35 - 220893376245027372 * q^36 - 483030177185234454 * q^37 - 3922824866561525640 * q^38 - 2555750058791490648 * q^39 - 626973708984375000 * q^40 - 4358124871734570834 * q^41 - 2559620302421551488 * q^42 - 5324153686845536508 * q^43 - 5745533240877106512 * q^44 + 82670114794921875 * q^45 + 10292691411163504536 * q^46 + 12258262539323374776 * q^47 + 52185334595839679232 * q^48 + 53865950980476272379 * q^49 + 1587867736816406250 * q^50 - 13305294839256933384 * q^51 + 36561029094508759896 * q^52 + 71640983942760085722 * q^53 - 8722300088406303360 * q^54 - 8070606953320312500 * q^55 + 32773217861089510560 * q^56 - 174702718819675136880 * q^57 - 258910443213048121860 * q^58 - 420843416438104506180 * q^59 - 120162362878125000000 * q^60 - 581725337824220015454 * q^61 - 6386866856435690928 * q^62 - 701377962769300673808 * q^63 + 910193477718092702784 * q^64 - 173582555370996093750 * q^65 + 1527698529319557146112 * q^66 - 1399668543169120673364 * q^67 + 2058346167335115118728 * q^68 + 2368452906957113559072 * q^69 + 80003147773828125000 * q^70 - 409151675006970497064 * q^71 + 2624939937107847919080 * q^72 + 3254958507976741960782 * q^73 + 5024018202030699806508 * q^74 - 332422256469726562500 * q^75 + 4116463921392566297520 * q^76 - 17679177187365753067008 * q^77 + 2659161203582354699904 * q^78 - 10163548547854309111440 * q^79 - 3368549046724218750000 * q^80 - 17599804703176322735397 * q^81 - 12650907933669059897148 * q^82 - 14365350009027465650388 * q^83 + 29520686861588838037248 * q^84 - 20317664515112988281250 * q^85 + 26606188682127536075856 * q^86 - 69805465343858969988120 * q^87 + 49185500030908263850080 * q^88 + 55263110999125019200830 * q^89 - 14781429211632714843750 * q^90 + 41561600612192918902176 * q^91 - 4955822257768756710864 * q^92 + 48060187726233171700224 * q^93 + 160261789932669635237208 * q^94 - 47641798977952148437500 * q^95 + 56188621559544366859776 * q^96 - 231524977804298299798074 * q^97 + 129877246807137874291338 * q^98 + 195725739081953651557932 * q^99

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 $

$2$	758.861	0.262010	0.131005	−	0.991382i	$-0.458180\pi$
$2$	758.861	0.262010	0.131005	+	0.991382i	$0.458180\pi$
$3$	360571.	1.17516	0.587579	−	0.809167i	$-0.300081\pi$
$3$	360571.	1.17516	0.587579	+	0.809167i	$0.300081\pi$
$4$	−7.81274e6	−0.931351
$5$	4.88281e7	0.447214
$5$	4.88281e7	0.447214
$6$	2.73623e8	0.307903
$7$	−1.00441e10	−1.91993	−0.959965	−	0.280120i	$-0.909626\pi$
$7$	−1.00441e10	−1.91993	−0.959965	+	0.280120i	$0.909626\pi$
$8$	−1.22946e10	−0.506033
$9$	3.58682e10	0.380997
$10$	3.70538e10	0.117174
$11$	9.30325e11	0.983148	0.491574	−	0.870836i	$-0.336422\pi$
$11$	9.30325e11	0.983148	0.491574	+	0.870836i	$0.336422\pi$
$12$	−2.81705e12	−1.09448
$13$	−4.62648e12	−0.715982	−0.357991	−	0.933725i	$-0.616538\pi$
$13$	−4.62648e12	−0.715982	−0.357991	+	0.933725i	$0.616538\pi$
$14$	−7.62211e12	−0.503040
$15$	1.76060e13	0.525547
$16$	5.62081e13	0.798765
$17$	−2.57225e14	−1.82033	−0.910167	−	0.414241i	$-0.864047\pi$
$17$	−2.57225e14	−1.82033	−0.910167	+	0.414241i	$0.864047\pi$
$18$	2.72190e13	0.0998248
$19$	−4.24898e14	−0.836793	−0.418397	−	0.908264i	$-0.637408\pi$
$19$	−4.24898e14	−0.836793	−0.418397	+	0.908264i	$0.637408\pi$
$20$	−3.81481e14	−0.416513
$21$	−3.62163e15	−2.25622
$22$	7.05988e14	0.257594
$23$	1.18528e15	0.259388	0.129694	−	0.991554i	$-0.458600\pi$
$23$	1.18528e15	0.259388	0.129694	+	0.991554i	$0.458600\pi$
$24$	−4.43307e15	−0.594668
$25$	2.38419e15	0.200000
$26$	−3.51085e15	−0.187594
$27$	−2.10123e16	−0.727427
$28$	7.84723e16	1.78813
$29$	−6.04141e16	−0.919521	−0.459760	−	0.888043i	$-0.652065\pi$
$29$	−6.04141e16	−0.919521	−0.459760	+	0.888043i	$0.652065\pi$
$30$	1.33605e16	0.137698
$31$	1.71978e17	1.21566	0.607831	−	0.794066i	$-0.292040\pi$
$31$	1.71978e17	1.21566	0.607831	+	0.794066i	$0.292040\pi$
$32$	1.45789e17	0.715317
$33$	3.35448e17	1.15535
$34$	−1.95198e17	−0.476945
$35$	−4.90437e17	−0.858619
$36$	−2.80229e17	−0.354842
$37$	5.78331e17	0.534388	0.267194	−	0.963643i	$-0.413904\pi$
$37$	5.78331e17	0.534388	0.267194	+	0.963643i	$0.413904\pi$
$38$	−3.22438e17	−0.219248
$39$	−1.66817e18	−0.841392
$40$	−6.00321e17	−0.226305
$41$	1.88124e18	0.533864	0.266932	−	0.963715i	$-0.413990\pi$
$41$	1.88124e18	0.533864	0.266932	+	0.963715i	$0.413990\pi$
$42$	−2.74831e18	−0.591152
$43$	−4.22624e18	−0.693533	−0.346766	−	0.937952i	$-0.612720\pi$
$43$	−4.22624e18	−0.693533	−0.346766	+	0.937952i	$0.612720\pi$
$44$	−7.26839e18	−0.915656
$45$	1.75138e18	0.170387
$46$	8.99461e17	0.0679622
$47$	6.75282e18	0.398437	0.199219	−	0.979955i	$-0.436160\pi$
$47$	6.75282e18	0.398437	0.199219	+	0.979955i	$0.436160\pi$
$48$	2.02670e19	0.938676
$49$	7.35161e19	2.68613
$50$	1.80927e18	0.0524019
$51$	−9.27480e19	−2.13918
$52$	3.61455e19	0.666830
$53$	−3.81753e19	−0.565730	−0.282865	−	0.959160i	$-0.591285\pi$
$53$	−3.81753e19	−0.565730	−0.282865	+	0.959160i	$0.591285\pi$
$54$	−1.59454e19	−0.190593
$55$	4.54260e19	0.439677
$56$	1.23488e20	0.971547
$57$	−1.53206e20	−0.983364
$58$	−4.58459e19	−0.240923
$59$	−6.41344e18	−0.0276881	−0.0138440	−	0.999904i	$-0.504407\pi$
$59$	−6.41344e18	−0.0276881	−0.0138440	+	0.999904i	$0.504407\pi$
$60$	−1.37551e20	−0.489468
$61$	−1.14535e20	−0.337012	−0.168506	−	0.985701i	$-0.553894\pi$
$61$	−1.14535e20	−0.337012	−0.168506	+	0.985701i	$0.553894\pi$
$62$	1.30507e20	0.318515
$63$	−3.60266e20	−0.731487
$64$	−3.60875e20	−0.611345
$65$	−2.25902e20	−0.320197
$66$	2.54559e20	0.302714
$67$	2.51375e20	0.251456	0.125728	−	0.992065i	$-0.459873\pi$
$67$	2.51375e20	0.251456	0.125728	+	0.992065i	$0.459873\pi$
$68$	2.00963e21	1.69537
$69$	4.27377e20	0.304822
$70$	−3.72173e20	−0.224966
$71$	6.24114e20	0.320474	0.160237	−	0.987079i	$-0.448774\pi$
$71$	6.24114e20	0.320474	0.160237	+	0.987079i	$0.448774\pi$
$72$	−4.40985e20	−0.192797
$73$	1.44534e21	0.539209	0.269605	−	0.962971i	$-0.413107\pi$
$73$	1.44534e21	0.539209	0.269605	+	0.962971i	$0.413107\pi$
$74$	4.38873e20	0.140015
$75$	8.59668e20	0.235032
$76$	3.31962e21	0.779348
$77$	−9.34432e21	−1.88758
$78$	−1.26591e21	−0.220453
$79$	−1.52724e21	−0.229719	−0.114859	−	0.993382i	$-0.536642\pi$
$79$	−1.52724e21	−0.229719	−0.114859	+	0.993382i	$0.536642\pi$
$80$	2.74454e21	0.357219
$81$	−1.09532e22	−1.23584
$82$	1.42760e21	0.139878
$83$	−8.73110e21	−0.744168	−0.372084	−	0.928199i	$-0.621357\pi$
$83$	−8.73110e21	−0.744168	−0.372084	+	0.928199i	$0.621357\pi$
$84$	2.82948e22	2.10133
$85$	−1.25598e22	−0.814078
$86$	−3.20713e21	−0.181712
$87$	−2.17836e22	−1.08058
$88$	−1.14379e22	−0.497505
$89$	1.90405e22	0.727265	0.363633	−	0.931542i	$-0.381536\pi$
$89$	1.90405e22	0.727265	0.363633	+	0.931542i	$0.381536\pi$
$90$	1.32905e21	0.0446430
$91$	4.64690e22	1.37464
$92$	−9.26026e21	−0.241581
$93$	6.20102e22	1.42860
$94$	5.12446e21	0.104394
$95$	−2.07470e22	−0.374225
$96$	5.25671e22	0.840611
$97$	−8.82090e22	−1.25210	−0.626048	−	0.779784i	$-0.715329\pi$
$97$	−8.82090e22	−1.25210	−0.626048	+	0.779784i	$0.715329\pi$
$98$	5.57885e22	0.703792
$99$	3.33691e22	0.374576
$100$	−1.86270e22	−0.186270
$101$	−1.98900e23	−1.77394	−0.886972	−	0.461823i	$-0.847196\pi$
$101$	−1.98900e23	−1.77394	−0.886972	+	0.461823i	$0.847196\pi$
$102$	−7.03829e22	−0.560486
$103$	1.13722e23	0.809497	0.404749	−	0.914428i	$-0.367359\pi$
$103$	1.13722e23	0.809497	0.404749	+	0.914428i	$0.367359\pi$
$104$	5.68806e22	0.362310
$105$	−1.76837e23	−1.00901
$106$	−2.89697e22	−0.148227
$107$	−1.71410e23	−0.787269	−0.393635	−	0.919267i	$-0.628783\pi$
$107$	−1.71410e23	−0.787269	−0.393635	+	0.919267i	$0.628783\pi$
$108$	1.64163e23	0.677490
$109$	2.98025e23	1.10624	0.553119	−	0.833103i	$-0.313438\pi$
$109$	2.98025e23	1.10624	0.553119	+	0.833103i	$0.313438\pi$
$110$	3.44720e22	0.115200
$111$	2.08529e23	0.627990
$112$	−5.64562e23	−1.53357
$113$	−4.55638e23	−1.11742	−0.558712	−	0.829362i	$-0.688704\pi$
$113$	−4.55638e23	−1.11742	−0.558712	+	0.829362i	$0.688704\pi$
$114$	−1.16262e23	−0.257651
$115$	5.78749e22	0.116002
$116$	4.72000e23	0.856396
$117$	−1.65944e23	−0.272787
$118$	−4.86691e21	−0.00725455
$119$	2.58361e24	3.49492
$120$	−2.16458e23	−0.265944
$121$	−2.99256e22	−0.0334203
$122$	−8.69162e22	−0.0883004
$123$	6.78322e23	0.627375
$124$	−1.34362e24	−1.13221
$125$	1.16415e23	0.0894427
$126$	−2.73392e23	−0.191657
$127$	1.72179e23	0.110214	0.0551071	−	0.998480i	$-0.482450\pi$
$127$	1.72179e23	0.110214	0.0551071	+	0.998480i	$0.482450\pi$
$128$	−1.49682e24	−0.875495
$129$	−1.52386e24	−0.815011
$130$	−1.71428e23	−0.0838947
$131$	−2.25026e24	−1.00835	−0.504176	−	0.863601i	$-0.668204\pi$
$131$	−2.25026e24	−1.00835	−0.504176	+	0.863601i	$0.668204\pi$
$132$	−2.62077e24	−1.07604
$133$	4.26773e24	1.60658
$134$	1.90759e23	0.0658839
$135$	−1.02599e24	−0.325315
$136$	3.16248e24	0.921149
$137$	1.22984e24	0.329278	0.164639	−	0.986354i	$-0.447354\pi$
$137$	1.22984e24	0.329278	0.164639	+	0.986354i	$0.447354\pi$
$138$	3.24320e23	0.0798663
$139$	−7.62746e24	−1.72866	−0.864331	−	0.502924i	$-0.832257\pi$
$139$	−7.62746e24	−1.72866	−0.864331	+	0.502924i	$0.832257\pi$
$140$	3.83165e24	0.799675
$141$	2.43487e24	0.468227
$142$	4.73616e23	0.0839673
$143$	−4.30413e24	−0.703916
$144$	2.01609e24	0.304327
$145$	−2.94991e24	−0.411222
$146$	1.09681e24	0.141278
$147$	2.65078e25	3.15663
$148$	−4.51835e24	−0.497703
$149$	5.54742e24	0.565522	0.282761	−	0.959190i	$-0.408750\pi$
$149$	5.54742e24	0.565522	0.282761	+	0.959190i	$0.408750\pi$
$150$	6.52369e23	0.0615806
$151$	−1.93105e25	−1.68873	−0.844364	−	0.535771i	$-0.820021\pi$
$151$	−1.93105e25	−1.68873	−0.844364	+	0.535771i	$0.820021\pi$
$152$	5.22394e24	0.423445
$153$	−9.22622e24	−0.693541
$154$	−7.09104e24	−0.494563
$155$	8.39735e24	0.543661
$156$	1.30330e25	0.783631
$157$	−9.91604e24	−0.553978	−0.276989	−	0.960873i	$-0.589336\pi$
$157$	−9.91604e24	−0.553978	−0.276989	+	0.960873i	$0.589336\pi$
$158$	−1.15897e24	−0.0601885
$159$	−1.37649e25	−0.664823
$160$	7.11858e24	0.319899
$161$	−1.19051e25	−0.498007
$162$	−8.31193e24	−0.323802
$163$	−3.90038e25	−1.41563	−0.707814	−	0.706399i	$-0.750319\pi$
$163$	−3.90038e25	−1.41563	−0.707814	+	0.706399i	$0.750319\pi$
$164$	−1.46977e25	−0.497215
$165$	1.63793e25	0.516690
$166$	−6.62569e24	−0.194979
$167$	4.09537e25	1.12474	0.562371	−	0.826885i	$-0.309889\pi$
$167$	4.09537e25	1.12474	0.562371	+	0.826885i	$0.309889\pi$
$168$	4.45263e25	1.14172
$169$	−2.03496e25	−0.487370
$170$	−9.53117e24	−0.213296
$171$	−1.52403e25	−0.318815
$172$	3.30185e25	0.645922
$173$	4.19622e25	0.767942	0.383971	−	0.923345i	$-0.374556\pi$
$173$	4.19622e25	0.767942	0.383971	+	0.923345i	$0.374556\pi$
$174$	−1.65307e25	−0.283123
$175$	−2.39471e25	−0.383986
$176$	5.22918e25	0.785305
$177$	−2.31250e24	−0.0325379
$178$	1.44491e25	0.190551
$179$	−1.69981e25	−0.210179	−0.105090	−	0.994463i	$-0.533513\pi$
$179$	−1.69981e25	−0.210179	−0.105090	+	0.994463i	$0.533513\pi$
$180$	−1.36831e25	−0.158690
$181$	6.85498e25	0.745937	0.372969	−	0.927844i	$-0.378340\pi$
$181$	6.85498e25	0.745937	0.372969	+	0.927844i	$0.378340\pi$
$182$	3.52635e25	0.360168
$183$	−4.12980e25	−0.396042
$184$	−1.45725e25	−0.131259
$185$	2.82388e25	0.238986
$186$	4.70571e25	0.374306
$187$	−2.39303e26	−1.78966
$188$	−5.27580e25	−0.371085
$189$	2.11050e26	1.39661
$190$	−1.57441e25	−0.0980507
$191$	7.25063e25	0.425101	0.212550	−	0.977150i	$-0.431823\pi$
$191$	7.25063e25	0.425101	0.212550	+	0.977150i	$0.431823\pi$
$192$	−1.30121e26	−0.718428
$193$	−7.25769e25	−0.377476	−0.188738	−	0.982027i	$-0.560440\pi$
$193$	−7.25769e25	−0.377476	−0.188738	+	0.982027i	$0.560440\pi$
$194$	−6.69384e25	−0.328061
$195$	−8.14538e25	−0.376282
$196$	−5.74362e26	−2.50173
$197$	−7.40066e25	−0.304025	−0.152012	−	0.988379i	$-0.548575\pi$
$197$	−7.40066e25	−0.304025	−0.152012	+	0.988379i	$0.548575\pi$
$198$	2.53225e25	0.0981426
$199$	3.37269e26	1.23358	0.616788	−	0.787129i	$-0.288433\pi$
$199$	3.37269e26	1.23358	0.616788	+	0.787129i	$0.288433\pi$
$200$	−2.93125e25	−0.101207
$201$	9.06385e25	0.295500
$202$	−1.50938e26	−0.464791
$203$	6.06808e26	1.76542
$204$	7.24616e26	1.99233
$205$	9.18576e25	0.238751
$206$	8.62990e25	0.212096
$207$	4.25138e25	0.0988260
$208$	−2.60046e26	−0.571902
$209$	−3.95293e26	−0.822691
$210$	−1.34195e26	−0.264371
$211$	2.49981e26	0.466294	0.233147	−	0.972442i	$-0.425098\pi$
$211$	2.49981e26	0.466294	0.233147	+	0.972442i	$0.425098\pi$
$212$	2.98253e26	0.526893
$213$	2.25037e26	0.376607
$214$	−1.30077e26	−0.206272
$215$	−2.06359e26	−0.310157
$216$	2.58337e26	0.368102
$217$	−1.72737e27	−2.33399
$218$	2.26160e26	0.289845
$219$	5.21148e26	0.633656
$220$	−3.54902e26	−0.409494
$221$	1.19005e27	1.30333
$222$	1.58245e26	0.164540
$223$	−7.51993e26	−0.742519	−0.371260	−	0.928529i	$-0.621074\pi$
$223$	−7.51993e26	−0.742519	−0.371260	+	0.928529i	$0.621074\pi$
$224$	−1.46432e27	−1.37336
$225$	8.55165e25	0.0761993
$226$	−3.45766e26	−0.292776
$227$	1.68449e27	1.35572	0.677861	−	0.735190i	$-0.262907\pi$
$227$	1.68449e27	1.35572	0.677861	+	0.735190i	$0.262907\pi$
$228$	1.19696e27	0.915857
$229$	−5.66583e26	−0.412245	−0.206123	−	0.978526i	$-0.566085\pi$
$229$	−5.66583e26	−0.412245	−0.206123	+	0.978526i	$0.566085\pi$
$230$	4.39190e25	0.0303936
$231$	−3.36929e27	−2.21820
$232$	7.42766e26	0.465307
$233$	−2.23006e27	−1.32961	−0.664805	−	0.747017i	$-0.731485\pi$
$233$	−2.23006e27	−1.32961	−0.664805	+	0.747017i	$0.731485\pi$
$234$	−1.25928e26	−0.0714728
$235$	3.29728e26	0.178187
$236$	5.01065e25	0.0257873
$237$	−5.50679e26	−0.269956
$238$	1.96060e27	0.915702
$239$	1.14941e27	0.511564	0.255782	−	0.966734i	$-0.417667\pi$
$239$	1.14941e27	0.511564	0.255782	+	0.966734i	$0.417667\pi$
$240$	9.89600e26	0.419789
$241$	4.88621e27	1.97595	0.987976	−	0.154609i	$-0.0494118\pi$
$241$	4.88621e27	1.97595	0.987976	+	0.154609i	$0.0494118\pi$
$242$	−2.27094e25	−0.00875645
$243$	−1.97123e27	−0.724879
$244$	8.94832e26	0.313876
$245$	3.58965e27	1.20127
$246$	5.14752e26	0.164378
$247$	1.96578e27	0.599129
$248$	−2.11439e27	−0.615165
$249$	−3.14818e27	−0.874515
$250$	8.83431e25	0.0234349
$251$	−7.40407e27	−1.87596	−0.937978	−	0.346696i	$-0.887304\pi$
$251$	−7.40407e27	−1.87596	−0.937978	+	0.346696i	$0.887304\pi$
$252$	2.81466e27	0.681271
$253$	1.10269e27	0.255017
$254$	1.30660e26	0.0288772
$255$	−4.52871e27	−0.956671
$256$	1.89136e27	0.381957
$257$	7.82304e27	1.51058	0.755291	−	0.655389i	$-0.227495\pi$
$257$	7.82304e27	1.51058	0.755291	+	0.655389i	$0.227495\pi$
$258$	−1.15640e27	−0.213541
$259$	−5.80884e27	−1.02599
$260$	1.76492e27	0.298216
$261$	−2.16695e27	−0.350334
$262$	−1.70763e27	−0.264198
$263$	−5.68078e27	−0.841234	−0.420617	−	0.907238i	$-0.638186\pi$
$263$	−5.68078e27	−0.841234	−0.420617	+	0.907238i	$0.638186\pi$
$264$	−4.12419e27	−0.584647
$265$	−1.86403e27	−0.253002
$266$	3.23862e27	0.420941
$267$	6.86544e27	0.854652
$268$	−1.96393e27	−0.234194
$269$	−4.10203e27	−0.468649	−0.234325	−	0.972158i	$-0.575288\pi$
$269$	−4.10203e27	−0.468649	−0.234325	+	0.972158i	$0.575288\pi$
$270$	−7.78583e26	−0.0852357
$271$	2.16887e27	0.227555	0.113778	−	0.993506i	$-0.463705\pi$
$271$	2.16887e27	0.227555	0.113778	+	0.993506i	$0.463705\pi$
$272$	−1.44582e28	−1.45402
$273$	1.67554e28	1.61541
$274$	9.33280e26	0.0862741
$275$	2.21807e27	0.196630
$276$	−3.33898e27	−0.283896
$277$	5.62858e27	0.459073	0.229536	−	0.973300i	$-0.426279\pi$
$277$	5.62858e27	0.459073	0.229536	+	0.973300i	$0.426279\pi$
$278$	−5.78818e27	−0.452926
$279$	6.16854e27	0.463163
$280$	6.02971e27	0.434489
$281$	1.51342e28	1.04673	0.523366	−	0.852108i	$-0.324676\pi$
$281$	1.51342e28	1.04673	0.523366	+	0.852108i	$0.324676\pi$
$282$	1.84773e27	0.122680
$283$	2.00594e28	1.27871	0.639357	−	0.768910i	$-0.279201\pi$
$283$	2.00594e28	1.27871	0.639357	+	0.768910i	$0.279201\pi$
$284$	−4.87604e27	−0.298474
$285$	−7.48075e27	−0.439774
$286$	−3.26624e27	−0.184433
$287$	−1.88955e28	−1.02498
$288$	5.22918e27	0.272533
$289$	4.61973e28	2.31362
$290$	−2.23857e27	−0.107744
$291$	−3.18056e28	−1.47141
$292$	−1.12921e28	−0.502193
$293$	−2.93035e28	−1.25297	−0.626487	−	0.779432i	$-0.715508\pi$
$293$	−2.93035e28	−1.25297	−0.626487	+	0.779432i	$0.715508\pi$
$294$	2.01157e28	0.827067
$295$	−3.13156e26	−0.0123825
$296$	−7.11033e27	−0.270418
$297$	−1.95482e28	−0.715168
$298$	4.20972e27	0.148172
$299$	−5.48366e27	−0.185717
$300$	−6.71636e27	−0.218897
$301$	4.24490e28	1.33153
$302$	−1.46540e28	−0.442463
$303$	−7.17177e28	−2.08467
$304$	−2.38827e28	−0.668401
$305$	−5.59253e27	−0.150716
$306$	−7.00142e27	−0.181715
$307$	−3.91936e28	−0.979769	−0.489885	−	0.871787i	$-0.662961\pi$
$307$	−3.91936e28	−0.979769	−0.489885	+	0.871787i	$0.662961\pi$
$308$	7.30047e28	1.75799
$309$	4.10047e28	0.951287
$310$	6.37242e27	0.142444
$311$	5.67033e28	1.22142	0.610709	−	0.791855i	$-0.290885\pi$
$311$	5.67033e28	1.22142	0.610709	+	0.791855i	$0.290885\pi$
$312$	2.05095e28	0.425772
$313$	4.03638e28	0.807666	0.403833	−	0.914833i	$-0.367678\pi$
$313$	4.03638e28	0.807666	0.403833	+	0.914833i	$0.367678\pi$
$314$	−7.52490e27	−0.145148
$315$	−1.75911e28	−0.327131
$316$	1.19319e28	0.213949
$317$	−2.70069e28	−0.466974	−0.233487	−	0.972360i	$-0.575014\pi$
$317$	−2.70069e28	−0.466974	−0.233487	+	0.972360i	$0.575014\pi$
$318$	−1.04456e28	−0.174190
$319$	−5.62048e28	−0.904025
$320$	−1.76208e28	−0.273402
$321$	−6.18056e28	−0.925166
$322$	−9.03432e27	−0.130483
$323$	1.09295e29	1.52324
$324$	8.55741e28	1.15100
$325$	−1.10304e28	−0.143196
$326$	−2.95985e28	−0.370908
$327$	1.07459e29	1.30000
$328$	−2.31291e28	−0.270153
$329$	−6.78263e28	−0.764972
$330$	1.24296e28	0.135378
$331$	2.49547e28	0.262501	0.131250	−	0.991349i	$-0.458101\pi$
$331$	2.49547e28	0.262501	0.131250	+	0.991349i	$0.458101\pi$
$332$	6.82138e28	0.693081
$333$	2.07437e28	0.203600
$334$	3.10781e28	0.294694
$335$	1.22742e28	0.112454
$336$	−2.03565e29	−1.80219
$337$	2.29016e28	0.195940	0.0979699	−	0.995189i	$-0.468765\pi$
$337$	2.29016e28	0.195940	0.0979699	+	0.995189i	$0.468765\pi$
$338$	−1.54425e28	−0.127696
$339$	−1.64290e29	−1.31315
$340$	9.81267e28	0.758193
$341$	1.59995e29	1.19518
$342$	−1.15653e28	−0.0835327
$343$	−4.63510e29	−3.23725
$344$	5.19598e28	0.350950
$345$	2.08680e28	0.136321
$346$	3.18435e28	0.201208
$347$	−2.92855e29	−1.79004	−0.895021	−	0.446025i	$-0.852839\pi$
$347$	−2.92855e29	−1.79004	−0.895021	+	0.446025i	$0.852839\pi$
$348$	1.70189e29	1.00640
$349$	−1.01511e29	−0.580792	−0.290396	−	0.956907i	$-0.593787\pi$
$349$	−1.01511e29	−0.580792	−0.290396	+	0.956907i	$0.593787\pi$
$350$	−1.81725e28	−0.100608
$351$	9.72127e28	0.520824
$352$	1.35631e29	0.703262
$353$	−1.38730e29	−0.696245	−0.348123	−	0.937449i	$-0.613181\pi$
$353$	−1.38730e29	−0.696245	−0.348123	+	0.937449i	$0.613181\pi$
$354$	−1.75487e27	−0.00852524
$355$	3.04743e28	0.143320
$356$	−1.48758e29	−0.677339
$357$	9.31574e29	4.10708
$358$	−1.28992e28	−0.0550690
$359$	2.44824e29	1.01220	0.506102	−	0.862474i	$-0.331086\pi$
$359$	2.44824e29	1.01220	0.506102	+	0.862474i	$0.331086\pi$
$360$	−2.15325e28	−0.0862213
$361$	−7.72914e28	−0.299777
$362$	5.20198e28	0.195443
$363$	−1.07903e28	−0.0392742
$364$	−3.63050e29	−1.28027
$365$	7.05733e28	0.241142
$366$	−3.13395e28	−0.103767
$367$	−3.82777e29	−1.22825	−0.614124	−	0.789209i	$-0.710491\pi$
$367$	−3.82777e29	−1.22825	−0.614124	+	0.789209i	$0.710491\pi$
$368$	6.66222e28	0.207190
$369$	6.74769e28	0.203400
$370$	2.14293e28	0.0626165
$371$	3.83438e29	1.08616
$372$	−4.84469e29	−1.33052
$373$	6.27342e29	1.67052	0.835262	−	0.549853i	$-0.185316\pi$
$373$	6.27342e29	1.67052	0.835262	+	0.549853i	$0.185316\pi$
$374$	−1.81598e29	−0.468908
$375$	4.19760e28	0.105109
$376$	−8.30231e28	−0.201622
$377$	2.79505e29	0.658360
$378$	1.60158e29	0.365925
$379$	−5.48022e29	−1.21464	−0.607319	−	0.794458i	$-0.707755\pi$
$379$	−5.48022e29	−1.21464	−0.607319	+	0.794458i	$0.707755\pi$
$380$	1.62091e29	0.348535
$381$	6.20828e28	0.129519
$382$	5.50222e28	0.111381
$383$	−6.72727e29	−1.32146	−0.660728	−	0.750625i	$-0.729752\pi$
$383$	−6.72727e29	−1.32146	−0.660728	+	0.750625i	$0.729752\pi$
$384$	−5.39709e29	−1.02885
$385$	−4.56265e29	−0.844149
$386$	−5.50758e28	−0.0989023
$387$	−1.51588e29	−0.264234
$388$	6.89153e29	1.16614
$389$	9.14527e29	1.50237	0.751183	−	0.660094i	$-0.229483\pi$
$389$	9.14527e29	1.50237	0.751183	+	0.660094i	$0.229483\pi$
$390$	−6.18121e28	−0.0985895
$391$	−3.04884e29	−0.472173
$392$	−9.03848e29	−1.35927
$393$	−8.11378e29	−1.18497
$394$	−5.61608e28	−0.0796574
$395$	−7.45724e28	−0.102733
$396$	−2.60704e29	−0.348862
$397$	2.68927e29	0.349578	0.174789	−	0.984606i	$-0.444076\pi$
$397$	2.68927e29	0.349578	0.174789	+	0.984606i	$0.444076\pi$
$398$	2.55940e29	0.323209
$399$	1.53882e30	1.88799
$400$	1.34011e29	0.159753
$401$	−1.73566e28	−0.0201050	−0.0100525	−	0.999949i	$-0.503200\pi$
$401$	−1.73566e28	−0.0201050	−0.0100525	+	0.999949i	$0.503200\pi$
$402$	6.87820e28	0.0774240
$403$	−7.95651e29	−0.870392
$404$	1.55396e30	1.65216
$405$	−5.34822e29	−0.552684
$406$	4.60483e29	0.462556
$407$	5.38036e29	0.525382
$408$	1.14030e30	1.08250
$409$	6.80964e29	0.628501	0.314250	−	0.949340i	$-0.398247\pi$
$409$	6.80964e29	0.628501	0.314250	+	0.949340i	$0.398247\pi$
$410$	6.97071e28	0.0625551
$411$	4.43445e29	0.386954
$412$	−8.88478e29	−0.753926
$413$	6.44175e28	0.0531592
$414$	3.22621e28	0.0258934
$415$	−4.26323e29	−0.332802
$416$	−6.74487e29	−0.512154
$417$	−2.75024e30	−2.03145
$418$	−2.99973e29	−0.215553
$419$	−1.32309e30	−0.924971	−0.462485	−	0.886627i	$-0.653042\pi$
$419$	−1.32309e30	−0.924971	−0.462485	+	0.886627i	$0.653042\pi$
$420$	1.38158e30	0.939745
$421$	1.34073e30	0.887357	0.443678	−	0.896186i	$-0.353673\pi$
$421$	1.34073e30	0.887357	0.443678	+	0.896186i	$0.353673\pi$
$422$	1.89701e29	0.122173
$423$	2.42212e29	0.151803
$424$	4.69348e29	0.286278
$425$	−6.13273e29	−0.364067
$426$	1.70772e29	0.0986748
$427$	1.15041e30	0.647039
$428$	1.33918e30	0.733224
$429$	−1.55194e30	−0.827213
$430$	−1.56598e29	−0.0812642
$431$	−1.78765e30	−0.903219	−0.451609	−	0.892216i	$-0.649150\pi$
$431$	−1.78765e30	−0.903219	−0.451609	+	0.892216i	$0.649150\pi$
$432$	−1.18106e30	−0.581043
$433$	6.16261e29	0.295226	0.147613	−	0.989045i	$-0.452841\pi$
$433$	6.16261e29	0.295226	0.147613	+	0.989045i	$0.452841\pi$
$434$	−1.31083e30	−0.611527
$435$	−1.06365e30	−0.483251
$436$	−2.32839e30	−1.03029
$437$	−5.03622e29	−0.217054
$438$	3.95479e29	0.166024
$439$	2.52366e30	1.03202	0.516012	−	0.856582i	$-0.327416\pi$
$439$	2.52366e30	1.03202	0.516012	+	0.856582i	$0.327416\pi$
$440$	−5.58494e29	−0.222491
$441$	2.63689e30	1.02341
$442$	9.03081e29	0.341484
$443$	−1.42696e30	−0.525736	−0.262868	−	0.964832i	$-0.584668\pi$
$443$	−1.42696e30	−0.525736	−0.262868	+	0.964832i	$0.584668\pi$
$444$	−1.62919e30	−0.584879
$445$	9.29711e29	0.325243
$446$	−5.70658e29	−0.194547
$447$	2.00024e30	0.664577
$448$	3.62468e30	1.17374
$449$	−5.62825e30	−1.77640	−0.888199	−	0.459458i	$-0.848044\pi$
$449$	−5.62825e30	−1.77640	−0.888199	+	0.459458i	$0.848044\pi$
$450$	6.48952e28	0.0199650
$451$	1.75017e30	0.524867
$452$	3.55978e30	1.04071
$453$	−6.96282e30	−1.98452
$454$	1.27829e30	0.355212
$455$	2.26899e30	0.614755
$456$	1.88360e30	0.497614
$457$	1.68594e30	0.434317	0.217159	−	0.976136i	$-0.430321\pi$
$457$	1.68594e30	0.434317	0.217159	+	0.976136i	$0.430321\pi$
$458$	−4.29958e29	−0.108012
$459$	5.40488e30	1.32416
$460$	−4.52161e29	−0.108038
$461$	6.50532e30	1.51603	0.758015	−	0.652237i	$-0.226169\pi$
$461$	6.50532e30	1.51603	0.758015	+	0.652237i	$0.226169\pi$
$462$	−2.55682e30	−0.581190
$463$	−2.36769e30	−0.524981	−0.262491	−	0.964935i	$-0.584544\pi$
$463$	−2.36769e30	−0.524981	−0.262491	+	0.964935i	$0.584544\pi$
$464$	−3.39576e30	−0.734481
$465$	3.02784e30	0.638887
$466$	−1.69231e30	−0.348371
$467$	7.29810e30	1.46577	0.732885	−	0.680353i	$-0.238173\pi$
$467$	7.29810e30	1.46577	0.732885	+	0.680353i	$0.238173\pi$
$468$	1.29647e30	0.254060
$469$	−2.52485e30	−0.482778
$470$	2.50218e29	0.0466866
$471$	−3.57544e30	−0.651011
$472$	7.88505e28	0.0140111
$473$	−3.93178e30	−0.681845
$474$	−4.17889e29	−0.0707311
$475$	−1.01304e30	−0.167359
$476$	−2.01851e31	−3.25499
$477$	−1.36928e30	−0.215541
$478$	8.72245e29	0.134035
$479$	3.89580e30	0.584438	0.292219	−	0.956351i	$-0.405606\pi$
$479$	3.89580e30	0.584438	0.292219	+	0.956351i	$0.405606\pi$
$480$	2.56675e30	0.375932
$481$	−2.67564e30	−0.382612
$482$	3.70796e30	0.517718
$483$	−4.29263e30	−0.585237
$484$	2.33801e29	0.0311261
$485$	−4.30708e30	−0.559955
$486$	−1.49589e30	−0.189925
$487$	7.12105e30	0.883000	0.441500	−	0.897261i	$-0.354447\pi$
$487$	7.12105e30	0.883000	0.441500	+	0.897261i	$0.354447\pi$
$488$	1.40816e30	0.170539
$489$	−1.40636e31	−1.66359
$490$	2.72405e30	0.314746
$491$	1.28795e31	1.45366	0.726828	−	0.686820i	$-0.240994\pi$
$491$	1.28795e31	1.45366	0.726828	+	0.686820i	$0.240994\pi$
$492$	−5.29955e30	−0.584306
$493$	1.55400e31	1.67384
$494$	1.49175e30	0.156978
$495$	1.62935e30	0.167516
$496$	9.66655e30	0.971029
$497$	−6.26869e30	−0.615287
$498$	−2.38903e30	−0.229131
$499$	−3.70590e30	−0.347326	−0.173663	−	0.984805i	$-0.555560\pi$
$499$	−3.70590e30	−0.347326	−0.173663	+	0.984805i	$0.555560\pi$
$500$	−9.09522e29	−0.0833026
$501$	1.47667e31	1.32175
$502$	−5.61866e30	−0.491518
$503$	1.98479e30	0.169700	0.0848501	−	0.996394i	$-0.472959\pi$
$503$	1.98479e30	0.169700	0.0848501	+	0.996394i	$0.472959\pi$
$504$	4.42931e30	0.370156
$505$	−9.71194e30	−0.793332
$506$	8.36791e29	0.0668169
$507$	−7.33748e30	−0.572737
$508$	−1.34519e30	−0.102648
$509$	3.33830e30	0.249041	0.124521	−	0.992217i	$-0.460261\pi$
$509$	3.33830e30	0.249041	0.124521	+	0.992217i	$0.460261\pi$
$510$	−3.43666e30	−0.250657
$511$	−1.45172e31	−1.03524
$512$	1.39915e31	0.975572
$513$	8.92806e30	0.608706
$514$	5.93660e30	0.395787
$515$	5.55282e30	0.362018
$516$	1.19055e31	0.759061
$517$	6.28232e30	0.391723
$518$	−4.40810e30	−0.268819
$519$	1.51304e31	0.902453
$520$	2.77737e30	0.162030
$521$	−9.63803e30	−0.549989	−0.274995	−	0.961446i	$-0.588676\pi$
$521$	−9.63803e30	−0.549989	−0.274995	+	0.961446i	$0.588676\pi$
$522$	−1.64441e30	−0.0917910
$523$	−2.08719e31	−1.13971	−0.569854	−	0.821746i	$-0.693000\pi$
$523$	−2.08719e31	−1.13971	−0.569854	+	0.821746i	$0.693000\pi$
$524$	1.75807e31	0.939130
$525$	−8.63463e30	−0.451244
$526$	−4.31093e30	−0.220412
$527$	−4.42370e31	−2.21291
$528$	1.88549e31	0.922857
$529$	−1.94756e31	−0.932718
$530$	−1.41454e30	−0.0662891
$531$	−2.30039e29	−0.0105491
$532$	−3.33427e31	−1.49629
$533$	−8.70353e30	−0.382237
$534$	5.20992e30	0.223927
$535$	−8.36964e30	−0.352078
$536$	−3.09055e30	−0.127245
$537$	−6.12901e30	−0.246994
$538$	−3.11287e30	−0.122791
$539$	6.83938e31	2.64086
$540$	8.01578e30	0.302983
$541$	−2.79922e31	−1.03578	−0.517891	−	0.855447i	$-0.673283\pi$
$541$	−2.79922e31	−1.03578	−0.517891	+	0.855447i	$0.673283\pi$
$542$	1.64587e30	0.0596216
$543$	2.47171e31	0.876594
$544$	−3.75005e31	−1.30212
$545$	1.45520e31	0.494724
$546$	1.27150e31	0.423254
$547$	6.46852e30	0.210839	0.105419	−	0.994428i	$-0.466381\pi$
$547$	6.46852e30	0.210839	0.105419	+	0.994428i	$0.466381\pi$
$548$	−9.60844e30	−0.306673
$549$	−4.10817e30	−0.128400
$550$	1.68321e30	0.0515189
$551$	2.56698e31	0.769449
$552$	−5.25441e30	−0.154250
$553$	1.53398e31	0.441044
$554$	4.27131e30	0.120282
$555$	1.01821e31	0.280846
$556$	5.95914e31	1.60999
$557$	5.00469e30	0.132447	0.0662235	−	0.997805i	$-0.478905\pi$
$557$	5.00469e30	0.132447	0.0662235	+	0.997805i	$0.478905\pi$
$558$	4.68106e30	0.121353
$559$	1.95526e31	0.496557
$560$	−2.75665e31	−0.685835
$561$	−8.62858e31	−2.10313
$562$	1.14847e31	0.274254
$563$	−1.43472e31	−0.335677	−0.167838	−	0.985815i	$-0.553679\pi$
$563$	−1.43472e31	−0.335677	−0.167838	+	0.985815i	$0.553679\pi$
$564$	−1.90230e31	−0.436084
$565$	−2.22480e31	−0.499727
$566$	1.52223e31	0.335035
$567$	1.10015e32	2.37272
$568$	−7.67321e30	−0.162170
$569$	−5.00718e31	−1.03706	−0.518528	−	0.855061i	$-0.673520\pi$
$569$	−5.00718e31	−1.03706	−0.518528	+	0.855061i	$0.673520\pi$
$570$	−5.67685e30	−0.115225
$571$	−1.18729e31	−0.236180	−0.118090	−	0.993003i	$-0.537677\pi$
$571$	−1.18729e31	−0.236180	−0.118090	+	0.993003i	$0.537677\pi$
$572$	3.36270e31	0.655593
$573$	2.61437e31	0.499561
$574$	−1.43390e31	−0.268555
$575$	2.82592e30	0.0518776
$576$	−1.29439e31	−0.232921
$577$	−1.53638e30	−0.0271004	−0.0135502	−	0.999908i	$-0.504313\pi$
$577$	−1.53638e30	−0.0271004	−0.0135502	+	0.999908i	$0.504313\pi$
$578$	3.50574e31	0.606190
$579$	−2.61691e31	−0.443594
$580$	2.30469e31	0.382992
$581$	8.76964e31	1.42875
$582$	−2.41360e31	−0.385524
$583$	−3.55154e31	−0.556197
$584$	−1.77698e31	−0.272857
$585$	−8.10272e30	−0.121994
$586$	−2.22373e31	−0.328292
$587$	−1.10866e32	−1.60494	−0.802470	−	0.596693i	$-0.796481\pi$
$587$	−1.10866e32	−1.60494	−0.802470	+	0.596693i	$0.796481\pi$
$588$	−2.07098e32	−2.93993
$589$	−7.30730e31	−1.01726
$590$	−2.37642e29	−0.00324433
$591$	−2.66846e31	−0.357277
$592$	3.25069e31	0.426851
$593$	1.30676e32	1.68293	0.841464	−	0.540314i	$-0.181694\pi$
$593$	1.30676e32	1.68293	0.841464	+	0.540314i	$0.181694\pi$
$594$	−1.48344e31	−0.187381
$595$	1.26153e32	1.56297
$596$	−4.33406e31	−0.526699
$597$	1.21609e32	1.44965
$598$	−4.16134e30	−0.0486597
$599$	−1.27032e32	−1.45716	−0.728578	−	0.684963i	$-0.759818\pi$
$599$	−1.27032e32	−1.45716	−0.728578	+	0.684963i	$0.759818\pi$
$600$	−1.05693e31	−0.118934
$601$	−1.38042e31	−0.152390	−0.0761949	−	0.997093i	$-0.524277\pi$
$601$	−1.38042e31	−0.152390	−0.0761949	+	0.997093i	$0.524277\pi$
$602$	3.22129e31	0.348875
$603$	9.01637e30	0.0958038
$604$	1.50868e32	1.57280
$605$	−1.46121e30	−0.0149460
$606$	−5.44238e31	−0.546202
$607$	−2.71714e31	−0.267573	−0.133786	−	0.991010i	$-0.542714\pi$
$607$	−2.71714e31	−0.267573	−0.133786	+	0.991010i	$0.542714\pi$
$608$	−6.19452e31	−0.598572
$609$	2.18797e32	2.07464
$610$	−4.24395e30	−0.0394891
$611$	−3.12418e31	−0.285274
$612$	7.20820e31	0.645930
$613$	5.86458e31	0.515753	0.257876	−	0.966178i	$-0.416977\pi$
$613$	5.86458e31	0.515753	0.257876	+	0.966178i	$0.416977\pi$
$614$	−2.97425e31	−0.256709
$615$	3.31212e31	0.280570
$616$	1.14884e32	0.955175
$617$	9.71399e31	0.792717	0.396358	−	0.918096i	$-0.370274\pi$
$617$	9.71399e31	0.792717	0.396358	+	0.918096i	$0.370274\pi$
$618$	3.11169e31	0.249246
$619$	−1.70197e31	−0.133817	−0.0669083	−	0.997759i	$-0.521313\pi$
$619$	−1.70197e31	−0.133817	−0.0669083	+	0.997759i	$0.521313\pi$
$620$	−6.56063e31	−0.506339
$621$	−2.49054e31	−0.188686
$622$	4.30299e31	0.320023
$623$	−1.91245e32	−1.39630
$624$	−9.37649e31	−0.672075
$625$	5.68434e30	0.0400000
$626$	3.06305e31	0.211616
$627$	−1.42531e32	−0.966793
$628$	7.74714e31	0.515948
$629$	−1.48761e32	−0.972765
$630$	−1.33492e31	−0.0857115
$631$	2.89593e31	0.182579	0.0912896	−	0.995824i	$-0.470901\pi$
$631$	2.89593e31	0.182579	0.0912896	+	0.995824i	$0.470901\pi$
$632$	1.87768e31	0.116245
$633$	9.01361e31	0.547969
$634$	−2.04945e31	−0.122352
$635$	8.40718e30	0.0492893
$636$	1.07541e32	0.619183
$637$	−3.40120e32	−1.92322
$638$	−4.26516e31	−0.236863
$639$	2.23859e31	0.122099
$640$	−7.30867e31	−0.391533
$641$	1.99297e32	1.04866	0.524328	−	0.851516i	$-0.324316\pi$
$641$	1.99297e32	1.04866	0.524328	+	0.851516i	$0.324316\pi$
$642$	−4.69018e31	−0.242402
$643$	−3.63319e30	−0.0184443	−0.00922213	−	0.999957i	$-0.502936\pi$
$643$	−3.63319e30	−0.0184443	−0.00922213	+	0.999957i	$0.502936\pi$
$644$	9.30114e31	0.463819
$645$	−7.44072e31	−0.364484
$646$	8.29394e31	0.399105
$647$	−2.61307e32	−1.23524	−0.617621	−	0.786476i	$-0.711904\pi$
$647$	−2.61307e32	−1.23524	−0.617621	+	0.786476i	$0.711904\pi$
$648$	1.34664e32	0.625375
$649$	−5.96659e30	−0.0272215
$650$	−8.37053e30	−0.0375188
$651$	−6.22839e32	−2.74280
$652$	3.04726e32	1.31845
$653$	9.99691e31	0.424976	0.212488	−	0.977164i	$-0.431843\pi$
$653$	9.99691e31	0.424976	0.212488	+	0.977164i	$0.431843\pi$
$654$	8.15466e31	0.340614
$655$	−1.09876e32	−0.450949
$656$	1.05741e32	0.426432
$657$	5.18418e31	0.205437
$658$	−5.14708e31	−0.200430
$659$	3.45610e32	1.32253	0.661263	−	0.750154i	$-0.270021\pi$
$659$	3.45610e32	1.32253	0.661263	+	0.750154i	$0.270021\pi$
$660$	−1.27967e32	−0.481220
$661$	−9.50782e31	−0.351370	−0.175685	−	0.984446i	$-0.556214\pi$
$661$	−9.50782e31	−0.351370	−0.175685	+	0.984446i	$0.556214\pi$
$662$	1.89372e31	0.0687777
$663$	4.29097e32	1.53161
$664$	1.07345e32	0.376573
$665$	2.08385e32	0.718486
$666$	1.57416e31	0.0533452
$667$	−7.16075e31	−0.238513
$668$	−3.19960e32	−1.04753
$669$	−2.71147e32	−0.872577
$670$	9.31439e30	0.0294642
$671$	−1.06555e32	−0.331333
$672$	−5.27991e32	−1.61391
$673$	5.54839e32	1.66722	0.833611	−	0.552351i	$-0.186269\pi$
$673$	5.54839e32	1.66722	0.833611	+	0.552351i	$0.186269\pi$
$674$	1.73792e31	0.0513381
$675$	−5.00971e31	−0.145485
$676$	1.58986e32	0.453913
$677$	1.25812e32	0.353145	0.176572	−	0.984288i	$-0.443499\pi$
$677$	1.25812e32	0.353145	0.176572	+	0.984288i	$0.443499\pi$
$678$	−1.24673e32	−0.344058
$679$	8.85983e32	2.40394
$680$	1.54418e32	0.411950
$681$	6.07378e32	1.59319
$682$	1.21414e32	0.313148
$683$	−4.46032e32	−1.13117	−0.565585	−	0.824690i	$-0.691349\pi$
$683$	−4.46032e32	−1.13117	−0.565585	+	0.824690i	$0.691349\pi$
$684$	1.19069e32	0.296929
$685$	6.00509e31	0.147258
$686$	−3.51740e32	−0.848192
$687$	−2.04293e32	−0.484453
$688$	−2.37549e32	−0.553970
$689$	1.76617e32	0.405053
$690$	1.58359e31	0.0357173
$691$	−2.97447e32	−0.659799	−0.329900	−	0.944016i	$-0.607015\pi$
$691$	−2.97447e32	−0.659799	−0.329900	+	0.944016i	$0.607015\pi$
$692$	−3.27840e32	−0.715223
$693$	−3.35164e32	−0.719160
$694$	−2.22236e32	−0.469008
$695$	−3.72435e32	−0.773081
$696$	2.67820e32	0.546810
$697$	−4.83903e32	−0.971811
$698$	−7.70327e31	−0.152173
$699$	−8.04096e32	−1.56250
$700$	1.87092e32	0.357626
$701$	2.99071e32	0.562364	0.281182	−	0.959654i	$-0.409274\pi$
$701$	2.99071e32	0.562364	0.281182	+	0.959654i	$0.409274\pi$
$702$	7.37710e31	0.136461
$703$	−2.45732e32	−0.447172
$704$	−3.35731e32	−0.601043
$705$	1.18890e32	0.209397
$706$	−1.05277e32	−0.182423
$707$	1.99778e33	3.40585
$708$	1.80670e31	0.0303042
$709$	−8.26923e32	−1.36469	−0.682344	−	0.731031i	$-0.739039\pi$
$709$	−8.26923e32	−1.36469	−0.682344	+	0.731031i	$0.739039\pi$
$710$	2.31258e31	0.0375513
$711$	−5.47795e31	−0.0875221
$712$	−2.34095e32	−0.368020
$713$	2.03841e32	0.315328
$714$	7.06935e32	1.07609
$715$	−2.10163e32	−0.314801
$716$	1.32801e32	0.195750
$717$	4.14445e32	0.601169
$718$	1.85787e32	0.265207
$719$	−7.08875e32	−0.995836	−0.497918	−	0.867224i	$-0.665902\pi$
$719$	−7.08875e32	−0.995836	−0.497918	+	0.867224i	$0.665902\pi$
$720$	9.84417e31	0.136099
$721$	−1.14224e33	−1.55418
$722$	−5.86535e31	−0.0785445
$723$	1.76183e33	2.32206
$724$	−5.35561e32	−0.694730
$725$	−1.44038e32	−0.183904
$726$	−8.18833e30	−0.0102902
$727$	8.60076e31	0.106388	0.0531938	−	0.998584i	$-0.483060\pi$
$727$	8.60076e31	0.106388	0.0531938	+	0.998584i	$0.483060\pi$
$728$	−5.71317e32	−0.695610
$729$	3.20397e32	0.383991
$730$	5.35553e31	0.0631815
$731$	1.08710e33	1.26246
$732$	3.22651e32	0.368854
$733$	−7.60327e32	−0.855667	−0.427834	−	0.903858i	$-0.640723\pi$
$733$	−7.60327e32	−0.855667	−0.427834	+	0.903858i	$0.640723\pi$
$734$	−2.90475e32	−0.321813
$735$	1.29432e33	1.41169
$736$	1.72800e32	0.185545
$737$	2.33860e32	0.247218
$738$	5.12056e31	0.0532929
$739$	−6.71232e32	−0.687799	−0.343899	−	0.939007i	$-0.611748\pi$
$739$	−6.71232e32	−0.687799	−0.343899	+	0.939007i	$0.611748\pi$
$740$	−2.20622e32	−0.222579
$741$	7.08803e32	0.704071
$742$	2.90976e32	0.284585
$743$	−3.30401e32	−0.318178	−0.159089	−	0.987264i	$-0.550856\pi$
$743$	−3.30401e32	−0.318178	−0.159089	+	0.987264i	$0.550856\pi$
$744$	−7.62389e32	−0.722916
$745$	2.70870e32	0.252909
$746$	4.76065e32	0.437693
$747$	−3.13169e32	−0.283525
$748$	1.86961e33	1.66680
$749$	1.72167e33	1.51150
$750$	3.18539e31	0.0275397
$751$	−1.43043e33	−1.21789	−0.608943	−	0.793214i	$-0.708406\pi$
$751$	−1.43043e33	−1.21789	−0.608943	+	0.793214i	$0.708406\pi$
$752$	3.79564e32	0.318258
$753$	−2.66969e33	−2.20454
$754$	2.12105e32	0.172497
$755$	−9.42897e32	−0.755222
$756$	−1.64888e33	−1.30073
$757$	6.80968e32	0.529083	0.264542	−	0.964374i	$-0.414779\pi$
$757$	6.80968e32	0.529083	0.264542	+	0.964374i	$0.414779\pi$
$758$	−4.15872e32	−0.318247
$759$	3.97599e32	0.299685
$760$	2.55075e32	0.189370
$761$	−2.12463e33	−1.55368	−0.776838	−	0.629700i	$-0.783178\pi$
$761$	−2.12463e33	−1.55368	−0.776838	+	0.629700i	$0.783178\pi$
$762$	4.71122e31	0.0339353
$763$	−2.99341e33	−2.12390
$764$	−5.66473e32	−0.395918
$765$	−4.50499e32	−0.310161
$766$	−5.10506e32	−0.346234
$767$	2.96717e31	0.0198242
$768$	6.81970e32	0.448860
$769$	9.49480e32	0.615649	0.307824	−	0.951443i	$-0.400399\pi$
$769$	9.49480e32	0.615649	0.307824	+	0.951443i	$0.400399\pi$
$770$	−3.46242e32	−0.221175
$771$	2.82076e33	1.77517
$772$	5.67024e32	0.351563
$773$	1.26831e33	0.774750	0.387375	−	0.921922i	$-0.373382\pi$
$773$	1.26831e33	0.774750	0.387375	+	0.921922i	$0.373382\pi$
$774$	−1.15034e32	−0.0692318
$775$	4.10027e32	0.243132
$776$	1.08449e33	0.633602
$777$	−2.09450e33	−1.20570
$778$	6.93999e32	0.393635
$779$	−7.99336e32	−0.446734
$780$	6.36377e32	0.350450
$781$	5.80629e32	0.315073
$782$	−2.31364e32	−0.123714
$783$	1.26944e33	0.668884
$784$	4.13220e33	2.14559
$785$	−4.84182e32	−0.247746
$786$	−6.15723e32	−0.310475
$787$	−2.42724e33	−1.20615	−0.603077	−	0.797683i	$-0.706059\pi$
$787$	−2.42724e33	−1.20615	−0.603077	+	0.797683i	$0.706059\pi$
$788$	5.78194e32	0.283154
$789$	−2.04833e33	−0.988584
$790$	−5.65901e31	−0.0269171
$791$	4.57650e33	2.14538
$792$	−4.10259e32	−0.189548
$793$	5.29894e32	0.241294
$794$	2.04078e32	0.0915928
$795$	−6.72114e32	−0.297318
$796$	−2.63499e33	−1.14889
$797$	−1.29113e31	−0.00554880	−0.00277440	−	0.999996i	$-0.500883\pi$
$797$	−1.29113e31	−0.00554880	−0.00277440	+	0.999996i	$0.500883\pi$
$798$	1.16775e33	0.494672
$799$	−1.73700e33	−0.725289
$800$	3.47587e32	0.143063
$801$	6.82948e32	0.277086
$802$	−1.31713e31	−0.00526771
$803$	1.34464e33	0.530122
$804$	−7.08135e32	−0.275215
$805$	−5.81304e32	−0.222716
$806$	−6.03789e32	−0.228051
$807$	−1.47907e33	−0.550737
$808$	2.44540e33	0.897674
$809$	3.84511e33	1.39156	0.695779	−	0.718256i	$-0.255059\pi$
$809$	3.84511e33	1.39156	0.695779	+	0.718256i	$0.255059\pi$
$810$	−4.05856e32	−0.144808
$811$	1.61036e33	0.566479	0.283240	−	0.959049i	$-0.408591\pi$
$811$	1.61036e33	0.566479	0.283240	+	0.959049i	$0.408591\pi$
$812$	−4.74083e33	−1.64422
$813$	7.82031e32	0.267413
$814$	4.08294e32	0.137655
$815$	−1.90448e33	−0.633088
$816$	−5.21319e33	−1.70870
$817$	1.79572e33	0.580343
$818$	5.16757e32	0.164673
$819$	1.66676e33	0.523731
$820$	−7.17659e32	−0.222361
$821$	−7.83861e32	−0.239493	−0.119747	−	0.992804i	$-0.538208\pi$
$821$	−7.83861e32	−0.239493	−0.119747	+	0.992804i	$0.538208\pi$
$822$	3.36513e32	0.101386
$823$	2.88308e33	0.856563	0.428282	−	0.903645i	$-0.359119\pi$
$823$	2.88308e33	0.856563	0.428282	+	0.903645i	$0.359119\pi$
$824$	−1.39816e33	−0.409632
$825$	7.99771e32	0.231071
$826$	4.88840e31	0.0139282
$827$	5.24220e32	0.147299	0.0736496	−	0.997284i	$-0.476535\pi$
$827$	5.24220e32	0.147299	0.0736496	+	0.997284i	$0.476535\pi$
$828$	−3.32149e32	−0.0920417
$829$	−2.14168e33	−0.585300	−0.292650	−	0.956220i	$-0.594537\pi$
$829$	−2.14168e33	−0.585300	−0.292650	+	0.956220i	$0.594537\pi$
$830$	−3.23520e32	−0.0871973
$831$	2.02950e33	0.539483
$832$	1.66958e33	0.437712
$833$	−1.89102e34	−4.88966
$834$	−2.08705e33	−0.532260
$835$	1.99969e33	0.503000
$836$	3.08832e33	0.766214
$837$	−3.61364e33	−0.884305
$838$	−1.00404e33	−0.242351
$839$	6.92143e33	1.64791	0.823954	−	0.566656i	$-0.191763\pi$
$839$	6.92143e33	1.64791	0.823954	+	0.566656i	$0.191763\pi$
$840$	2.17414e33	0.510593
$841$	−6.66855e32	−0.154482
$842$	1.01743e33	0.232496
$843$	5.45694e33	1.23008
$844$	−1.95304e33	−0.434283
$845$	−9.93633e32	−0.217959
$846$	1.83805e32	0.0397739
$847$	3.00577e32	0.0641647
$848$	−2.14576e33	−0.451886
$849$	7.23283e33	1.50269
$850$	−4.65389e32	−0.0953891
$851$	6.85483e32	0.138614
$852$	−1.75816e33	−0.350754
$853$	8.64503e33	1.70158	0.850791	−	0.525504i	$-0.176123\pi$
$853$	8.64503e33	1.70158	0.850791	+	0.525504i	$0.176123\pi$
$854$	8.72999e32	0.169531
$855$	−7.44157e32	−0.142579
$856$	2.10742e33	0.398384
$857$	7.96732e33	1.48605	0.743024	−	0.669265i	$-0.233391\pi$
$857$	7.96732e33	1.48605	0.743024	+	0.669265i	$0.233391\pi$
$858$	−1.17771e33	−0.216738
$859$	−5.84690e33	−1.06171	−0.530853	−	0.847464i	$-0.678128\pi$
$859$	−5.84690e33	−1.06171	−0.530853	+	0.847464i	$0.678128\pi$
$860$	1.61223e33	0.288865
$861$	−6.81316e33	−1.20452
$862$	−1.35658e33	−0.236652
$863$	−7.34050e33	−1.26358	−0.631788	−	0.775141i	$-0.717679\pi$
$863$	−7.34050e33	−1.26358	−0.631788	+	0.775141i	$0.717679\pi$
$864$	−3.06334e33	−0.520341
$865$	2.04894e33	0.343434
$866$	4.67657e32	0.0773520
$867$	1.66574e34	2.71887
$868$	1.34955e34	2.17376
$869$	−1.42083e33	−0.225848
$870$	−8.07164e32	−0.126616
$871$	−1.16298e33	−0.180038
$872$	−3.66409e33	−0.559792
$873$	−3.16390e33	−0.477045
$874$	−3.82179e32	−0.0568703
$875$	−1.16929e33	−0.171724
$876$	−4.07159e33	−0.590156
$877$	−1.49405e33	−0.213732	−0.106866	−	0.994273i	$-0.534082\pi$
$877$	−1.49405e33	−0.213732	−0.106866	+	0.994273i	$0.534082\pi$
$878$	1.91511e33	0.270400
$879$	−1.05660e34	−1.47244
$880$	2.55331e33	0.351199
$881$	−3.45598e32	−0.0469189	−0.0234595	−	0.999725i	$-0.507468\pi$
$881$	−3.45598e32	−0.0469189	−0.0234595	+	0.999725i	$0.507468\pi$
$882$	2.00103e33	0.268143
$883$	−3.79462e33	−0.501903	−0.250952	−	0.968000i	$-0.580744\pi$
$883$	−3.79462e33	−0.501903	−0.250952	+	0.968000i	$0.580744\pi$
$884$	−9.29753e33	−1.21385
$885$	−1.12915e32	−0.0145514
$886$	−1.08286e33	−0.137748
$887$	8.19992e32	0.102965	0.0514823	−	0.998674i	$-0.483605\pi$
$887$	8.19992e32	0.102965	0.0514823	+	0.998674i	$0.483605\pi$
$888$	−2.56378e33	−0.317784
$889$	−1.72939e33	−0.211604
$890$	7.05522e32	0.0852168
$891$	−1.01900e34	−1.21501
$892$	5.87512e33	0.691546
$893$	−2.86926e33	−0.333410
$894$	1.51790e33	0.174126
$895$	−8.29983e32	−0.0939949
$896$	1.50342e34	1.68089
$897$	−1.97725e33	−0.218247
$898$	−4.27106e33	−0.465434
$899$	−1.03899e34	−1.11783
$900$	−6.68118e32	−0.0709683
$901$	9.81964e33	1.02982
$902$	1.32813e33	0.137520
$903$	1.53059e34	1.56476
$904$	5.60188e33	0.565453
$905$	3.34716e33	0.333593
$906$	−5.28381e33	−0.519964
$907$	−1.79718e34	−1.74625	−0.873126	−	0.487494i	$-0.837911\pi$
$907$	−1.79718e34	−1.74625	−0.873126	+	0.487494i	$0.837911\pi$
$908$	−1.31605e34	−1.26265
$909$	−7.13421e33	−0.675867
$910$	1.72185e33	0.161072
$911$	1.84010e34	1.69973	0.849867	−	0.526997i	$-0.176682\pi$
$911$	1.84010e34	1.69973	0.849867	+	0.526997i	$0.176682\pi$
$912$	−8.61141e33	−0.785477
$913$	−8.12276e33	−0.731627
$914$	1.27940e33	0.113795
$915$	−2.01650e33	−0.177116
$916$	4.42657e33	0.383945
$917$	2.26019e34	1.93597
$918$	4.10156e33	0.346943
$919$	5.47044e33	0.456977	0.228488	−	0.973547i	$-0.426622\pi$
$919$	5.47044e33	0.456977	0.228488	+	0.973547i	$0.426622\pi$
$920$	−7.11547e32	−0.0587007
$921$	−1.41321e34	−1.15138
$922$	4.93663e33	0.397214
$923$	−2.88745e33	−0.229453
$924$	2.63234e34	2.06592
$925$	1.37885e33	0.106878
$926$	−1.79675e33	−0.137550
$927$	4.07900e33	0.308416
$928$	−8.80768e33	−0.657749
$929$	9.70929e33	0.716154	0.358077	−	0.933692i	$-0.383432\pi$
$929$	9.70929e33	0.716154	0.358077	+	0.933692i	$0.383432\pi$
$930$	2.29771e33	0.167395
$931$	−3.12368e34	−2.24774
$932$	1.74229e34	1.23833
$933$	2.04456e34	1.43536
$934$	5.53825e33	0.384046
$935$	−1.16847e34	−0.800359
$936$	2.04021e33	0.138039
$937$	−2.61062e34	−1.74477	−0.872384	−	0.488820i	$-0.837427\pi$
$937$	−2.61062e34	−1.74477	−0.872384	+	0.488820i	$0.837427\pi$
$938$	−1.91601e33	−0.126492
$939$	1.45540e34	0.949135
$940$	−2.57608e33	−0.165954
$941$	2.92896e34	1.86394	0.931971	−	0.362533i	$-0.118088\pi$
$941$	2.92896e34	1.86394	0.931971	+	0.362533i	$0.118088\pi$
$942$	−2.71326e33	−0.170571
$943$	2.22980e33	0.138478
$944$	−3.60488e32	−0.0221163
$945$	1.03052e34	0.624582
$946$	−2.98367e33	−0.178650
$947$	−2.04861e34	−1.21181	−0.605905	−	0.795537i	$-0.707189\pi$
$947$	−2.04861e34	−1.21181	−0.605905	+	0.795537i	$0.707189\pi$
$948$	4.30231e33	0.251424
$949$	−6.68684e33	−0.386064
$950$	−7.68753e32	−0.0438496
$951$	−9.73789e33	−0.548768
$952$	−3.17644e34	−1.76854
$953$	−5.96330e33	−0.328033	−0.164017	−	0.986458i	$-0.552445\pi$
$953$	−5.96330e33	−0.328033	−0.164017	+	0.986458i	$0.552445\pi$
$954$	−1.03909e33	−0.0564739
$955$	3.54035e33	0.190111
$956$	−8.98006e33	−0.476446
$957$	−2.02658e34	−1.06237
$958$	2.95637e33	0.153128
$959$	−1.23527e34	−0.632191
$960$	−6.35356e33	−0.321291
$961$	9.56304e33	0.477834
$962$	−2.03044e33	−0.100248
$963$	−6.14818e33	−0.299947
$964$	−3.81747e34	−1.84030
$965$	−3.54379e33	−0.168812
$966$	−3.25751e33	−0.153338
$967$	2.05474e34	0.955768	0.477884	−	0.878423i	$-0.341404\pi$
$967$	2.05474e34	0.955768	0.477884	+	0.878423i	$0.341404\pi$
$968$	3.67922e32	0.0169118
$969$	3.94084e34	1.79005
$970$	−3.26847e33	−0.146714
$971$	7.44883e33	0.330421	0.165210	−	0.986258i	$-0.447170\pi$
$971$	7.44883e33	0.330421	0.165210	+	0.986258i	$0.447170\pi$
$972$	1.54007e34	0.675116
$973$	7.66113e34	3.31891
$974$	5.40388e33	0.231355
$975$	−3.97724e33	−0.168278
$976$	−6.43780e33	−0.269193
$977$	−1.03566e34	−0.427987	−0.213994	−	0.976835i	$-0.568647\pi$
$977$	−1.03566e34	−0.427987	−0.213994	+	0.976835i	$0.568647\pi$
$978$	−1.06723e34	−0.435876
$979$	1.77138e34	0.715009
$980$	−2.80450e34	−1.11881
$981$	1.06896e34	0.421473
$982$	9.77375e33	0.380872
$983$	−2.48660e34	−0.957723	−0.478862	−	0.877890i	$-0.658950\pi$
$983$	−2.48660e34	−0.957723	−0.478862	+	0.877890i	$0.658950\pi$
$984$	−8.33967e33	−0.317472
$985$	−3.61360e33	−0.135964
$986$	1.17927e34	0.438561
$987$	−2.44562e34	−0.898963
$988$	−1.53581e34	−0.557999
$989$	−5.00927e33	−0.179894
$990$	1.23645e33	0.0438907
$991$	−4.22694e34	−1.48313	−0.741565	−	0.670881i	$-0.765916\pi$
$991$	−4.22694e34	−1.48313	−0.741565	+	0.670881i	$0.765916\pi$
$992$	2.50724e34	0.869584
$993$	8.99794e33	0.308480
$994$	−4.75706e33	−0.161211
$995$	1.64682e34	0.551672
$996$	2.45959e34	0.814480
$997$	2.73309e33	0.0894662	0.0447331	−	0.998999i	$-0.485756\pi$
$997$	2.73309e33	0.0894662	0.0447331	+	0.998999i	$0.485756\pi$
$998$	−2.81226e33	−0.0910027
$999$	−1.21520e34	−0.388728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.24.a.a.1.2	✓	3
3.2	odd	2		45.24.a.a.1.2		3
5.2	odd	4		25.24.b.b.24.4		6
5.3	odd	4		25.24.b.b.24.3		6
5.4	even	2		25.24.a.b.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.a.a.1.2	✓	3	1.1	even	1	trivial
25.24.a.b.1.2		3	5.4	even	2
25.24.b.b.24.3		6	5.3	odd	4
25.24.b.b.24.4		6	5.2	odd	4
45.24.a.a.1.2		3	3.2	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+758.861 q^{2} +360571. q^{3} -7.81274e6 q^{4} +4.88281e7 q^{5} +2.73623e8 q^{6} -1.00441e10 q^{7} -1.22946e10 q^{8} +3.58682e10 q^{9} +O(q^{10})\)	\(q+758.861 q^{2} +360571. q^{3} -7.81274e6 q^{4} +4.88281e7 q^{5} +2.73623e8 q^{6} -1.00441e10 q^{7} -1.22946e10 q^{8} +3.58682e10 q^{9} +3.70538e10 q^{10} +9.30325e11 q^{11} -2.81705e12 q^{12} -4.62648e12 q^{13} -7.62211e12 q^{14} +1.76060e13 q^{15} +5.62081e13 q^{16} -2.57225e14 q^{17} +2.72190e13 q^{18} -4.24898e14 q^{19} -3.81481e14 q^{20} -3.62163e15 q^{21} +7.05988e14 q^{22} +1.18528e15 q^{23} -4.43307e15 q^{24} +2.38419e15 q^{25} -3.51085e15 q^{26} -2.10123e16 q^{27} +7.84723e16 q^{28} -6.04141e16 q^{29} +1.33605e16 q^{30} +1.71978e17 q^{31} +1.45789e17 q^{32} +3.35448e17 q^{33} -1.95198e17 q^{34} -4.90437e17 q^{35} -2.80229e17 q^{36} +5.78331e17 q^{37} -3.22438e17 q^{38} -1.66817e18 q^{39} -6.00321e17 q^{40} +1.88124e18 q^{41} -2.74831e18 q^{42} -4.22624e18 q^{43} -7.26839e18 q^{44} +1.75138e18 q^{45} +8.99461e17 q^{46} +6.75282e18 q^{47} +2.02670e19 q^{48} +7.35161e19 q^{49} +1.80927e18 q^{50} -9.27480e19 q^{51} +3.61455e19 q^{52} -3.81753e19 q^{53} -1.59454e19 q^{54} +4.54260e19 q^{55} +1.23488e20 q^{56} -1.53206e20 q^{57} -4.58459e19 q^{58} -6.41344e18 q^{59} -1.37551e20 q^{60} -1.14535e20 q^{61} +1.30507e20 q^{62} -3.60266e20 q^{63} -3.60875e20 q^{64} -2.25902e20 q^{65} +2.54559e20 q^{66} +2.51375e20 q^{67} +2.00963e21 q^{68} +4.27377e20 q^{69} -3.72173e20 q^{70} +6.24114e20 q^{71} -4.40985e20 q^{72} +1.44534e21 q^{73} +4.38873e20 q^{74} +8.59668e20 q^{75} +3.31962e21 q^{76} -9.34432e21 q^{77} -1.26591e21 q^{78} -1.52724e21 q^{79} +2.74454e21 q^{80} -1.09532e22 q^{81} +1.42760e21 q^{82} -8.73110e21 q^{83} +2.82948e22 q^{84} -1.25598e22 q^{85} -3.20713e21 q^{86} -2.17836e22 q^{87} -1.14379e22 q^{88} +1.90405e22 q^{89} +1.32905e21 q^{90} +4.64690e22 q^{91} -9.26026e21 q^{92} +6.20102e22 q^{93} +5.12446e21 q^{94} -2.07470e22 q^{95} +5.25671e22 q^{96} -8.82090e22 q^{97} +5.57885e22 q^{98} +3.33691e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9}+O(q^{10}) \) 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9	\( 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9} + 32519531250 q^{10} - 165286030404 q^{11} - 2460925191744 q^{12} - 3554970733998 q^{13} + 1638464466408 q^{14} - 6808007812500 q^{15} - 68987884476912 q^{16} - 416105769269514 q^{17} - 302723670254238 q^{18} - 975704043068460 q^{19} - 463062304687500 q^{20} - 51\!\cdots\!84 q^{21}+ \cdots + 19\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9 + 32519531250 * q^10 - 165286030404 * q^11 - 2460925191744 * q^12 - 3554970733998 * q^13 + 1638464466408 * q^14 - 6808007812500 * q^15 - 68987884476912 * q^16 - 416105769269514 * q^17 - 302723670254238 * q^18 - 975704043068460 * q^19 - 463062304687500 * q^20 - 5102384337991584 * q^21 - 5786145456383688 * q^22 - 4979666912332368 * q^23 - 10409810708926080 * q^24 + 7152557373046875 * q^25 - 17675137590787524 * q^26 + 20047178078003160 * q^27 + 71220956974215888 * q^28 + 95526863867406210 * q^29 + 46870059375000000 * q^30 + 203997528720796176 * q^31 + 170287635059993376 * q^32 + 322079222096408304 * q^33 + 716918393922501108 * q^34 - 118783366406250000 * q^35 - 220893376245027372 * q^36 - 483030177185234454 * q^37 - 3922824866561525640 * q^38 - 2555750058791490648 * q^39 - 626973708984375000 * q^40 - 4358124871734570834 * q^41 - 2559620302421551488 * q^42 - 5324153686845536508 * q^43 - 5745533240877106512 * q^44 + 82670114794921875 * q^45 + 10292691411163504536 * q^46 + 12258262539323374776 * q^47 + 52185334595839679232 * q^48 + 53865950980476272379 * q^49 + 1587867736816406250 * q^50 - 13305294839256933384 * q^51 + 36561029094508759896 * q^52 + 71640983942760085722 * q^53 - 8722300088406303360 * q^54 - 8070606953320312500 * q^55 + 32773217861089510560 * q^56 - 174702718819675136880 * q^57 - 258910443213048121860 * q^58 - 420843416438104506180 * q^59 - 120162362878125000000 * q^60 - 581725337824220015454 * q^61 - 6386866856435690928 * q^62 - 701377962769300673808 * q^63 + 910193477718092702784 * q^64 - 173582555370996093750 * q^65 + 1527698529319557146112 * q^66 - 1399668543169120673364 * q^67 + 2058346167335115118728 * q^68 + 2368452906957113559072 * q^69 + 80003147773828125000 * q^70 - 409151675006970497064 * q^71 + 2624939937107847919080 * q^72 + 3254958507976741960782 * q^73 + 5024018202030699806508 * q^74 - 332422256469726562500 * q^75 + 4116463921392566297520 * q^76 - 17679177187365753067008 * q^77 + 2659161203582354699904 * q^78 - 10163548547854309111440 * q^79 - 3368549046724218750000 * q^80 - 17599804703176322735397 * q^81 - 12650907933669059897148 * q^82 - 14365350009027465650388 * q^83 + 29520686861588838037248 * q^84 - 20317664515112988281250 * q^85 + 26606188682127536075856 * q^86 - 69805465343858969988120 * q^87 + 49185500030908263850080 * q^88 + 55263110999125019200830 * q^89 - 14781429211632714843750 * q^90 + 41561600612192918902176 * q^91 - 4955822257768756710864 * q^92 + 48060187726233171700224 * q^93 + 160261789932669635237208 * q^94 - 47641798977952148437500 * q^95 + 56188621559544366859776 * q^96 - 231524977804298299798074 * q^97 + 129877246807137874291338 * q^98 + 195725739081953651557932 * q^99

Introduction

L-functions

Modular forms

Varieties

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