LMFDB - Embedded newform 5.28.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,28,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, 28, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 28 $
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:	$23.0927787419$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 105406182x^{3} - 8285617904x^{2} + 1593173725628800x - 1939393055148057600 $ x^5 - 2x^4 - 105406182x^3 - 8285617904x^2 + 1593173725628800x - 1939393055148057600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{5}\cdot 5^{4}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3161.03$ 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)

$f(q)$	$=$	$q-2338.06 q^{2} +4.67850e6 q^{3} -1.28751e8 q^{4} -1.22070e9 q^{5} -1.09386e10 q^{6} -1.25721e10 q^{7} +6.14836e11 q^{8} +1.42627e13 q^{9} +O(q^{10})$	\(q-2338.06 q^{2} +4.67850e6 q^{3} -1.28751e8 q^{4} -1.22070e9 q^{5} -1.09386e10 q^{6} -1.25721e10 q^{7} +6.14836e11 q^{8} +1.42627e13 q^{9} +2.85407e12 q^{10} +1.89375e14 q^{11} -6.02362e14 q^{12} -1.22888e15 q^{13} +2.93943e13 q^{14} -5.71106e15 q^{15} +1.58432e16 q^{16} +5.96062e16 q^{17} -3.33471e16 q^{18} -8.38134e16 q^{19} +1.57167e17 q^{20} -5.88187e16 q^{21} -4.42769e17 q^{22} +3.90301e18 q^{23} +2.87651e18 q^{24} +1.49012e18 q^{25} +2.87320e18 q^{26} +3.10518e19 q^{27} +1.61868e18 q^{28} +1.17051e19 q^{29} +1.33528e19 q^{30} +1.03900e20 q^{31} -1.19564e20 q^{32} +8.85988e20 q^{33} -1.39363e20 q^{34} +1.53468e19 q^{35} -1.83634e21 q^{36} -7.26467e20 q^{37} +1.95961e20 q^{38} -5.74933e21 q^{39} -7.50533e20 q^{40} +7.01388e21 q^{41} +1.37521e20 q^{42} +1.02137e22 q^{43} -2.43822e22 q^{44} -1.74106e22 q^{45} -9.12546e21 q^{46} +6.70366e21 q^{47} +7.41222e22 q^{48} -6.55543e22 q^{49} -3.48398e21 q^{50} +2.78868e23 q^{51} +1.58220e23 q^{52} -1.41448e22 q^{53} -7.26010e22 q^{54} -2.31170e23 q^{55} -7.72980e21 q^{56} -3.92121e23 q^{57} -2.73673e22 q^{58} +3.39576e23 q^{59} +7.35305e23 q^{60} -1.55004e24 q^{61} -2.42923e23 q^{62} -1.79313e23 q^{63} -1.84689e24 q^{64} +1.50010e24 q^{65} -2.07149e24 q^{66} -5.04410e24 q^{67} -7.67437e24 q^{68} +1.82602e25 q^{69} -3.58818e22 q^{70} +6.00958e24 q^{71} +8.76925e24 q^{72} +1.39363e24 q^{73} +1.69852e24 q^{74} +6.97150e24 q^{75} +1.07911e25 q^{76} -2.38084e24 q^{77} +1.34423e25 q^{78} -6.12943e25 q^{79} -1.93398e25 q^{80} +3.65141e25 q^{81} -1.63988e25 q^{82} -1.45279e25 q^{83} +7.57297e24 q^{84} -7.27615e25 q^{85} -2.38802e25 q^{86} +5.47624e25 q^{87} +1.16434e26 q^{88} -3.13028e26 q^{89} +4.07069e25 q^{90} +1.54497e25 q^{91} -5.02517e26 q^{92} +4.86094e26 q^{93} -1.56735e25 q^{94} +1.02311e26 q^{95} -5.59381e26 q^{96} +8.31816e26 q^{97} +1.53270e26 q^{98} +2.70100e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9}+O(q^{10}) $ 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9	$ 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9} - 24311523437500 q^{10} - 34307841041440 q^{11} + 10\!\cdots\!96 q^{12}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9 - 24311523437500 * q^10 - 34307841041440 * q^11 + 1067087945485696 * q^12 + 1264965428684322 * q^13 - 1494481038585720 * q^14 - 5945656738281250 * q^15 + 50480141682449280 * q^16 + 11381432659133186 * q^17 + 199164599348648492 * q^18 - 177889284152803500 * q^19 - 306994921875000000 * q^20 + 15690874972867260 * q^21 + 1661117755714509952 * q^22 + 5314231426153528362 * q^23 + 25461226121295412800 * q^24 + 7450580596923828125 * q^25 + 64194207115665583160 * q^26 + 69831879763488728300 * q^27 + 74243491650979261568 * q^28 + 142675767255557016550 * q^29 - 48077371044921875000 * q^30 + 490757140558660526660 * q^31 + 709255558573159910656 * q^32 + 262404778486784711104 * q^33 - 823451155892216853320 * q^34 - 189997983649902343750 * q^35 + 364604386623731602880 * q^36 - 1594690133202798011054 * q^37 - 8102840491936976962000 * q^38 - 3725217775868438909980 * q^39 - 5913608024414062500000 * q^40 - 14453824011731896105490 * q^41 - 18735431399125775369328 * q^42 - 6456338188721923591758 * q^43 - 61776067586935488773120 * q^44 - 11299361297711181640625 * q^45 + 41662242513049160161560 * q^46 + 19960747396802751518726 * q^47 + 306904049567056770080512 * q^48 + 64529931934369352760065 * q^49 + 29677152633666992187500 * q^50 + 45124322296416065252260 * q^51 + 694364047806293961951616 * q^52 + 203485571063020242199082 * q^53 + 430355877536329740706000 * q^54 + 41879688771289062500000 * q^55 - 514718506150627561339200 * q^56 - 1075206797979440282527000 * q^57 - 568257469475936639738200 * q^58 - 1753694580358227494398300 * q^59 - 1302597589704218750000000 * q^60 - 1715799924029775655491390 * q^61 + 856653132512718918087792 * q^62 - 3772385601985154457719778 * q^63 + 2825791291455308901232640 * q^64 - 1544147251811916503906250 * q^65 - 14020757899728664042151680 * q^66 - 52283413307813388053914 * q^67 - 18798756173665084661988992 * q^68 + 17423855056223403670703220 * q^69 + 1824317674054833984375000 * q^70 + 13737346388576400396156460 * q^71 + 48990987369760413733351200 * q^72 + 52785881484144679283287962 * q^73 + 44617246831379823508169080 * q^74 + 7257881760597229003906250 * q^75 - 50943444226830794465542400 * q^76 + 40527442829187717880256832 * q^77 + 96469318519881413261089264 * q^78 - 18659027886608771061377800 * q^79 - 61621266702208593750000000 * q^80 - 18780471510820240351050695 * q^81 - 233045910890443727506605688 * q^82 - 49391953045615520178004398 * q^83 - 276316883591574899554456320 * q^84 - 13893350413980939941406250 * q^85 - 246095687260751641221151240 * q^86 - 67750867272390013078210900 * q^87 - 662199546636275930413900800 * q^88 + 180573322691431536135373650 * q^89 - 243120848814268178710937500 * q^90 + 317295677016426969579588460 * q^91 - 379021343242797571985691264 * q^92 + 1482223660602013833974435784 * q^93 - 34623503302055809185576920 * q^94 + 217150005069340209960937500 * q^95 + 2545248606864865567495170560 * q^96 + 1118012018325586896775804426 * q^97 - 243326561625995319625007012 * q^98 + 2661033543665827983852919520 * 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 $

$2$	−2338.06	−0.201813	−0.100907	−	0.994896i	$-0.532174\pi$
$2$	−2338.06	−0.201813	−0.100907	+	0.994896i	$0.532174\pi$
$3$	4.67850e6	1.69422	0.847109	−	0.531419i	$-0.178341\pi$
$3$	4.67850e6	1.69422	0.847109	+	0.531419i	$0.178341\pi$
$4$	−1.28751e8	−0.959271
$5$	−1.22070e9	−0.447214
$5$	−1.22070e9	−0.447214
$6$	−1.09386e10	−0.341916
$7$	−1.25721e10	−0.0490439	−0.0245220	−	0.999699i	$-0.507806\pi$
$7$	−1.25721e10	−0.0490439	−0.0245220	+	0.999699i	$0.507806\pi$
$8$	6.14836e11	0.395407
$9$	1.42627e13	1.87038
$10$	2.85407e12	0.0902537
$11$	1.89375e14	1.65394	0.826971	−	0.562244i	$-0.190062\pi$
$11$	1.89375e14	1.65394	0.826971	+	0.562244i	$0.190062\pi$
$12$	−6.02362e14	−1.62522
$13$	−1.22888e15	−1.12532	−0.562660	−	0.826689i	$-0.690222\pi$
$13$	−1.22888e15	−1.12532	−0.562660	+	0.826689i	$0.690222\pi$
$14$	2.93943e13	0.00989772
$15$	−5.71106e15	−0.757678
$16$	1.58432e16	0.879473
$17$	5.96062e16	1.45959	0.729795	−	0.683666i	$-0.239615\pi$
$17$	5.96062e16	1.45959	0.729795	+	0.683666i	$0.239615\pi$
$18$	−3.33471e16	−0.377467
$19$	−8.38134e16	−0.457236	−0.228618	−	0.973516i	$-0.573421\pi$
$19$	−8.38134e16	−0.457236	−0.228618	+	0.973516i	$0.573421\pi$
$20$	1.57167e17	0.428999
$21$	−5.88187e16	−0.0830911
$22$	−4.42769e17	−0.333788
$23$	3.90301e18	1.61463	0.807317	−	0.590119i	$-0.200919\pi$
$23$	3.90301e18	1.61463	0.807317	+	0.590119i	$0.200919\pi$
$24$	2.87651e18	0.669907
$25$	1.49012e18	0.200000
$26$	2.87320e18	0.227105
$27$	3.10518e19	1.47461
$28$	1.61868e18	0.0470464
$29$	1.17051e19	0.211838	0.105919	−	0.994375i	$-0.466222\pi$
$29$	1.17051e19	0.211838	0.105919	+	0.994375i	$0.466222\pi$
$30$	1.33528e19	0.152910
$31$	1.03900e20	0.764243	0.382121	−	0.924112i	$-0.375194\pi$
$31$	1.03900e20	0.764243	0.382121	+	0.924112i	$0.375194\pi$
$32$	−1.19564e20	−0.572897
$33$	8.85988e20	2.80214
$34$	−1.39363e20	−0.294565
$35$	1.53468e19	0.0219331
$36$	−1.83634e21	−1.79420
$37$	−7.26467e20	−0.490335	−0.245167	−	0.969481i	$-0.578843\pi$
$37$	−7.26467e20	−0.490335	−0.245167	+	0.969481i	$0.578843\pi$
$38$	1.95961e20	0.0922763
$39$	−5.74933e21	−1.90654
$40$	−7.50533e20	−0.176832
$41$	7.01388e21	1.18407	0.592033	−	0.805914i	$-0.298325\pi$
$41$	7.01388e21	1.18407	0.592033	+	0.805914i	$0.298325\pi$
$42$	1.37521e20	0.0167689
$43$	1.02137e22	0.906479	0.453240	−	0.891389i	$-0.350268\pi$
$43$	1.02137e22	0.906479	0.453240	+	0.891389i	$0.350268\pi$
$44$	−2.43822e22	−1.58658
$45$	−1.74106e22	−0.836458
$46$	−9.12546e21	−0.325855
$47$	6.70366e21	0.179057	0.0895284	−	0.995984i	$-0.471464\pi$
$47$	6.70366e21	0.179057	0.0895284	+	0.995984i	$0.471464\pi$
$48$	7.41222e22	1.49002
$49$	−6.55543e22	−0.997595
$50$	−3.48398e21	−0.0403627
$51$	2.78868e23	2.47287
$52$	1.58220e23	1.07949
$53$	−1.41448e22	−0.0746228	−0.0373114	−	0.999304i	$-0.511879\pi$
$53$	−1.41448e22	−0.0746228	−0.0373114	+	0.999304i	$0.511879\pi$
$54$	−7.26010e22	−0.297596
$55$	−2.31170e23	−0.739666
$56$	−7.72980e21	−0.0193923
$57$	−3.92121e23	−0.774657
$58$	−2.73673e22	−0.0427517
$59$	3.39576e23	0.421148	0.210574	−	0.977578i	$-0.432467\pi$
$59$	3.39576e23	0.421148	0.210574	+	0.977578i	$0.432467\pi$
$60$	7.35305e23	0.726818
$61$	−1.55004e24	−1.22572	−0.612859	−	0.790192i	$-0.709981\pi$
$61$	−1.55004e24	−1.22572	−0.612859	+	0.790192i	$0.709981\pi$
$62$	−2.42923e23	−0.154234
$63$	−1.79313e23	−0.0917306
$64$	−1.84689e24	−0.763854
$65$	1.50010e24	0.503258
$66$	−2.07149e24	−0.565510
$67$	−5.04410e24	−1.12402	−0.562010	−	0.827131i	$-0.689972\pi$
$67$	−5.04410e24	−1.12402	−0.562010	+	0.827131i	$0.689972\pi$
$68$	−7.67437e24	−1.40014
$69$	1.82602e25	2.73554
$70$	−3.58818e22	−0.00442640
$71$	6.00958e24	0.612148	0.306074	−	0.952008i	$-0.400985\pi$
$71$	6.00958e24	0.612148	0.306074	+	0.952008i	$0.400985\pi$
$72$	8.76925e24	0.739561
$73$	1.39363e24	0.0975642	0.0487821	−	0.998809i	$-0.484466\pi$
$73$	1.39363e24	0.0975642	0.0487821	+	0.998809i	$0.484466\pi$
$74$	1.69852e24	0.0989562
$75$	6.97150e24	0.338844
$76$	1.07911e25	0.438613
$77$	−2.38084e24	−0.0811158
$78$	1.34423e25	0.384765
$79$	−6.12943e25	−1.47725	−0.738625	−	0.674116i	$-0.764525\pi$
$79$	−6.12943e25	−1.47725	−0.738625	+	0.674116i	$0.764525\pi$
$80$	−1.93398e25	−0.393312
$81$	3.65141e25	0.627932
$82$	−1.63988e25	−0.238961
$83$	−1.45279e25	−0.179742	−0.0898710	−	0.995953i	$-0.528645\pi$
$83$	−1.45279e25	−0.179742	−0.0898710	+	0.995953i	$0.528645\pi$
$84$	7.57297e24	0.0797069
$85$	−7.27615e25	−0.652749
$86$	−2.38802e25	−0.182940
$87$	5.47624e25	0.358899
$88$	1.16434e26	0.653981
$89$	−3.13028e26	−1.50945	−0.754725	−	0.656042i	$-0.772230\pi$
$89$	−3.13028e26	−1.50945	−0.754725	+	0.656042i	$0.772230\pi$
$90$	4.07069e25	0.168808
$91$	1.54497e25	0.0551901
$92$	−5.02517e26	−1.54887
$93$	4.86094e26	1.29479
$94$	−1.56735e25	−0.0361361
$95$	1.02311e26	0.204482
$96$	−5.59381e26	−0.970612
$97$	8.31816e26	1.25490	0.627449	−	0.778657i	$-0.284099\pi$
$97$	8.31816e26	1.25490	0.627449	+	0.778657i	$0.284099\pi$
$98$	1.53270e26	0.201328
$99$	2.70100e27	3.09350
$100$	−1.91854e26	−0.191854
$101$	8.16586e26	0.713943	0.356971	−	0.934115i	$-0.383809\pi$
$101$	8.16586e26	0.713943	0.356971	+	0.934115i	$0.383809\pi$
$102$	−6.52008e26	−0.499058
$103$	−2.50605e27	−1.68147	−0.840733	−	0.541450i	$-0.817875\pi$
$103$	−2.50605e27	−1.68147	−0.840733	+	0.541450i	$0.817875\pi$
$104$	−7.55563e26	−0.444960
$105$	7.18001e25	0.0371595
$106$	3.30713e25	0.0150599
$107$	−1.58822e27	−0.637131	−0.318565	−	0.947901i	$-0.603201\pi$
$107$	−1.58822e27	−0.637131	−0.318565	+	0.947901i	$0.603201\pi$
$108$	−3.99796e27	−1.41455
$109$	3.49500e27	1.09192	0.545958	−	0.837813i	$-0.316166\pi$
$109$	3.49500e27	1.09192	0.545958	+	0.837813i	$0.316166\pi$
$110$	5.40489e26	0.149275
$111$	−3.39878e27	−0.830735
$112$	−1.99182e26	−0.0431328
$113$	9.45748e27	1.81642	0.908211	−	0.418513i	$-0.137449\pi$
$113$	9.45748e27	1.81642	0.908211	+	0.418513i	$0.137449\pi$
$114$	9.16801e26	0.156336
$115$	−4.76442e27	−0.722086
$116$	−1.50705e27	−0.203210
$117$	−1.75273e28	−2.10477
$118$	−7.93947e26	−0.0849933
$119$	−7.49377e26	−0.0715841
$120$	−3.51137e27	−0.299591
$121$	2.27527e28	1.73553
$122$	3.62409e27	0.247366
$123$	3.28144e28	2.00607
$124$	−1.33772e28	−0.733116
$125$	−1.81899e27	−0.0894427
$126$	4.19244e26	0.0185125
$127$	7.07707e27	0.280868	0.140434	−	0.990090i	$-0.455150\pi$
$127$	7.07707e27	0.280868	0.140434	+	0.990090i	$0.455150\pi$
$128$	2.03658e28	0.727053
$129$	4.77847e28	1.53577
$130$	−3.50733e27	−0.101564
$131$	−2.34691e28	−0.612822	−0.306411	−	0.951899i	$-0.599128\pi$
$131$	−2.34691e28	−0.612822	−0.306411	+	0.951899i	$0.599128\pi$
$132$	−1.14072e29	−2.68801
$133$	1.05371e27	0.0224246
$134$	1.17934e28	0.226842
$135$	−3.79051e28	−0.659465
$136$	3.66481e28	0.577133
$137$	−4.91561e28	−0.701213	−0.350606	−	0.936523i	$-0.614024\pi$
$137$	−4.91561e28	−0.701213	−0.350606	+	0.936523i	$0.614024\pi$
$138$	−4.26934e28	−0.552069
$139$	1.02675e29	1.20439	0.602195	−	0.798349i	$-0.294293\pi$
$139$	1.02675e29	1.20439	0.602195	+	0.798349i	$0.294293\pi$
$140$	−1.97592e27	−0.0210398
$141$	3.13631e28	0.303361
$142$	−1.40507e28	−0.123540
$143$	−2.32720e29	−1.86121
$144$	2.25967e29	1.64495
$145$	−1.42885e28	−0.0947367
$146$	−3.25840e27	−0.0196898
$147$	−3.06696e29	−1.69014
$148$	9.35336e28	0.470364
$149$	3.10118e29	1.42401	0.712003	−	0.702176i	$-0.247788\pi$
$149$	3.10118e29	1.42401	0.712003	+	0.702176i	$0.247788\pi$
$150$	−1.62998e28	−0.0683832
$151$	−4.76708e29	−1.82837	−0.914183	−	0.405301i	$-0.867167\pi$
$151$	−4.76708e29	−1.82837	−0.914183	+	0.405301i	$0.867167\pi$
$152$	−5.15315e28	−0.180794
$153$	8.50148e29	2.72998
$154$	5.56654e27	0.0163703
$155$	−1.26831e29	−0.341780
$156$	7.40234e29	1.82889
$157$	−1.65124e29	−0.374252	−0.187126	−	0.982336i	$-0.559917\pi$
$157$	−1.65124e29	−0.374252	−0.187126	+	0.982336i	$0.559917\pi$
$158$	1.43310e29	0.298129
$159$	−6.61763e28	−0.126427
$160$	1.45952e29	0.256207
$161$	−4.90691e28	−0.0791879
$162$	−8.53720e28	−0.126725
$163$	−3.99033e28	−0.0545100	−0.0272550	−	0.999629i	$-0.508677\pi$
$163$	−3.99033e28	−0.0545100	−0.0272550	+	0.999629i	$0.508677\pi$
$164$	−9.03045e29	−1.13584
$165$	−1.08153e30	−1.25316
$166$	3.39672e28	0.0362744
$167$	−1.93481e29	−0.190531	−0.0952654	−	0.995452i	$-0.530370\pi$
$167$	−1.93481e29	−0.190531	−0.0952654	+	0.995452i	$0.530370\pi$
$168$	−3.61639e28	−0.0328548
$169$	3.17624e29	0.266344
$170$	1.70121e29	0.131734
$171$	−1.19541e30	−0.855203
$172$	−1.31502e30	−0.869560
$173$	−2.66172e29	−0.162757	−0.0813786	−	0.996683i	$-0.525932\pi$
$173$	−2.66172e29	−0.162757	−0.0813786	+	0.996683i	$0.525932\pi$
$174$	−1.28038e29	−0.0724307
$175$	−1.87339e28	−0.00980878
$176$	3.00029e30	1.45460
$177$	1.58870e30	0.713516
$178$	7.31878e29	0.304627
$179$	5.57621e29	0.215191	0.107595	−	0.994195i	$-0.465685\pi$
$179$	5.57621e29	0.215191	0.107595	+	0.994195i	$0.465685\pi$
$180$	2.24163e30	0.802390
$181$	−1.28099e30	−0.425487	−0.212743	−	0.977108i	$-0.568240\pi$
$181$	−1.28099e30	−0.425487	−0.212743	+	0.977108i	$0.568240\pi$
$182$	−3.61223e28	−0.0111381
$183$	−7.25187e30	−2.07663
$184$	2.39971e30	0.638438
$185$	8.86801e29	0.219284
$186$	−1.13652e30	−0.261307
$187$	1.12879e31	2.41408
$188$	−8.63104e29	−0.171764
$189$	−3.90388e29	−0.0723206
$190$	−2.39210e29	−0.0412672
$191$	−4.20978e30	−0.676564	−0.338282	−	0.941045i	$-0.609846\pi$
$191$	−4.20978e30	−0.676564	−0.338282	+	0.941045i	$0.609846\pi$
$192$	−8.64065e30	−1.29414
$193$	9.07179e30	1.26669	0.633344	−	0.773871i	$-0.281682\pi$
$193$	9.07179e30	1.26669	0.633344	+	0.773871i	$0.281682\pi$
$194$	−1.94483e30	−0.253256
$195$	7.01823e30	0.852629
$196$	8.44020e30	0.956964
$197$	3.76946e30	0.399011	0.199506	−	0.979897i	$-0.436066\pi$
$197$	3.76946e30	0.399011	0.199506	+	0.979897i	$0.436066\pi$
$198$	−6.31509e30	−0.624309
$199$	−9.92066e30	−0.916271	−0.458135	−	0.888882i	$-0.651483\pi$
$199$	−9.92066e30	−0.916271	−0.458135	+	0.888882i	$0.651483\pi$
$200$	9.16178e29	0.0790815
$201$	−2.35988e31	−1.90433
$202$	−1.90922e30	−0.144083
$203$	−1.47158e29	−0.0103893
$204$	−3.59045e31	−2.37215
$205$	−8.56186e30	−0.529531
$206$	5.85930e30	0.339342
$207$	5.56676e31	3.01997
$208$	−1.94694e31	−0.989688
$209$	−1.58721e31	−0.756241
$210$	−1.67873e29	−0.00749928
$211$	4.29587e31	1.79986	0.899928	−	0.436038i	$-0.143619\pi$
$211$	4.29587e31	1.79986	0.899928	+	0.436038i	$0.143619\pi$
$212$	1.82116e30	0.0715836
$213$	2.81158e31	1.03711
$214$	3.71334e30	0.128582
$215$	−1.24679e31	−0.405390
$216$	1.90918e31	0.583071
$217$	−1.30624e30	−0.0374815
$218$	−8.17150e30	−0.220363
$219$	6.52012e30	0.165295
$220$	2.97634e31	0.709540
$221$	−7.32492e31	−1.64251
$222$	7.94653e30	0.167653
$223$	−2.42471e31	−0.481443	−0.240721	−	0.970594i	$-0.577384\pi$
$223$	−2.42471e31	−0.481443	−0.240721	+	0.970594i	$0.577384\pi$
$224$	1.50318e30	0.0280971
$225$	2.12531e31	0.374075
$226$	−2.21121e31	−0.366578
$227$	2.33494e31	0.364692	0.182346	−	0.983234i	$-0.441631\pi$
$227$	2.33494e31	0.364692	0.182346	+	0.983234i	$0.441631\pi$
$228$	5.04860e31	0.743106
$229$	9.82105e31	1.36263	0.681316	−	0.731989i	$-0.261408\pi$
$229$	9.82105e31	1.36263	0.681316	+	0.731989i	$0.261408\pi$
$230$	1.11395e31	0.145727
$231$	−1.11388e31	−0.137428
$232$	7.19674e30	0.0837622
$233$	−1.11061e32	−1.21971	−0.609855	−	0.792513i	$-0.708772\pi$
$233$	−1.11061e32	−1.21971	−0.609855	+	0.792513i	$0.708772\pi$
$234$	4.09797e31	0.424771
$235$	−8.18318e30	−0.0800766
$236$	−4.37208e31	−0.403995
$237$	−2.86765e32	−2.50279
$238$	1.75209e30	0.0144466
$239$	−8.63723e31	−0.672981	−0.336490	−	0.941687i	$-0.609240\pi$
$239$	−8.63723e31	−0.672981	−0.336490	+	0.941687i	$0.609240\pi$
$240$	−9.04812e31	−0.666357
$241$	9.34419e31	0.650596	0.325298	−	0.945612i	$-0.394535\pi$
$241$	9.34419e31	0.650596	0.325298	+	0.945612i	$0.394535\pi$
$242$	−5.31972e31	−0.350253
$243$	−6.59579e31	−0.410754
$244$	1.99570e32	1.17580
$245$	8.00223e31	0.446138
$246$	−7.67219e31	−0.404851
$247$	1.02997e32	0.514536
$248$	6.38813e31	0.302187
$249$	−6.79689e31	−0.304522
$250$	4.25290e30	0.0180507
$251$	2.88609e32	1.16068	0.580342	−	0.814373i	$-0.302919\pi$
$251$	2.88609e32	1.16068	0.580342	+	0.814373i	$0.302919\pi$
$252$	2.30868e31	0.0879945
$253$	7.39131e32	2.67051
$254$	−1.65466e31	−0.0566830
$255$	−3.40414e32	−1.10590
$256$	2.00269e32	0.617125
$257$	−3.13202e32	−0.915644	−0.457822	−	0.889044i	$-0.651370\pi$
$257$	−3.13202e32	−0.915644	−0.457822	+	0.889044i	$0.651370\pi$
$258$	−1.11723e32	−0.309940
$259$	9.13324e30	0.0240479
$260$	−1.93140e32	−0.482761
$261$	1.66947e32	0.396216
$262$	5.48721e31	0.123676
$263$	−3.91406e32	−0.837964	−0.418982	−	0.907995i	$-0.637613\pi$
$263$	−3.91406e32	−0.837964	−0.418982	+	0.907995i	$0.637613\pi$
$264$	5.44738e32	1.10799
$265$	1.72666e31	0.0333724
$266$	−2.46364e30	−0.00452559
$267$	−1.46450e33	−2.55734
$268$	6.49434e32	1.07824
$269$	−3.31255e32	−0.523005	−0.261503	−	0.965203i	$-0.584218\pi$
$269$	−3.31255e32	−0.523005	−0.261503	+	0.965203i	$0.584218\pi$
$270$	8.86243e31	0.133089
$271$	8.02382e31	0.114629	0.0573147	−	0.998356i	$-0.481746\pi$
$271$	8.02382e31	0.114629	0.0573147	+	0.998356i	$0.481746\pi$
$272$	9.44352e32	1.28367
$273$	7.22813e31	0.0935041
$274$	1.14930e32	0.141514
$275$	2.82190e32	0.330789
$276$	−2.35103e33	−2.62413
$277$	−3.39573e32	−0.360957	−0.180479	−	0.983579i	$-0.557765\pi$
$277$	−3.39573e32	−0.360957	−0.180479	+	0.983579i	$0.557765\pi$
$278$	−2.40061e32	−0.243062
$279$	1.48189e33	1.42942
$280$	9.43579e30	0.00867251
$281$	−4.90655e32	−0.429774	−0.214887	−	0.976639i	$-0.568938\pi$
$281$	−4.90655e32	−0.429774	−0.214887	+	0.976639i	$0.568938\pi$
$282$	−7.33286e31	−0.0612224
$283$	−9.12716e32	−0.726472	−0.363236	−	0.931697i	$-0.618328\pi$
$283$	−9.12716e32	−0.726472	−0.363236	+	0.931697i	$0.618328\pi$
$284$	−7.73740e32	−0.587216
$285$	4.78663e32	0.346437
$286$	5.44112e32	0.375618
$287$	−8.81793e31	−0.0580712
$288$	−1.70531e33	−1.07153
$289$	1.88519e33	1.13041
$290$	3.34073e31	0.0191191
$291$	3.89165e33	2.12607
$292$	−1.79432e32	−0.0935905
$293$	3.47574e32	0.173115	0.0865574	−	0.996247i	$-0.472413\pi$
$293$	3.47574e32	0.173115	0.0865574	+	0.996247i	$0.472413\pi$
$294$	7.17072e32	0.341094
$295$	−4.14521e32	−0.188343
$296$	−4.46659e32	−0.193882
$297$	5.88043e33	2.43892
$298$	−7.25073e32	−0.287384
$299$	−4.79635e33	−1.81698
$300$	−8.97590e32	−0.325043
$301$	−1.28408e32	−0.0444573
$302$	1.11457e33	0.368989
$303$	3.82039e33	1.20957
$304$	−1.32787e33	−0.402126
$305$	1.89214e33	0.548158
$306$	−1.98769e33	−0.550948
$307$	3.00880e32	0.0798041	0.0399020	−	0.999204i	$-0.487295\pi$
$307$	3.00880e32	0.0798041	0.0399020	+	0.999204i	$0.487295\pi$
$308$	3.06536e32	0.0778121
$309$	−1.17246e34	−2.84877
$310$	2.96537e32	0.0689757
$311$	−2.42501e33	−0.540068	−0.270034	−	0.962851i	$-0.587035\pi$
$311$	−2.42501e33	−0.540068	−0.270034	+	0.962851i	$0.587035\pi$
$312$	−3.53490e33	−0.753859
$313$	−1.63148e33	−0.333222	−0.166611	−	0.986023i	$-0.553282\pi$
$313$	−1.63148e33	−0.333222	−0.166611	+	0.986023i	$0.553282\pi$
$314$	3.86069e32	0.0755292
$315$	2.18888e32	0.0410232
$316$	7.89171e33	1.41708
$317$	3.45785e33	0.594984	0.297492	−	0.954724i	$-0.403850\pi$
$317$	3.45785e33	0.594984	0.297492	+	0.954724i	$0.403850\pi$
$318$	1.54724e32	0.0255148
$319$	2.21665e33	0.350367
$320$	2.25450e33	0.341606
$321$	−7.43046e33	−1.07944
$322$	1.14726e32	0.0159812
$323$	−4.99580e33	−0.667377
$324$	−4.70123e33	−0.602357
$325$	−1.83118e33	−0.225064
$326$	9.32963e31	0.0110009
$327$	1.63513e34	1.84994
$328$	4.31239e33	0.468189
$329$	−8.42793e31	−0.00878165
$330$	2.52868e33	0.252904
$331$	−6.39396e33	−0.613892	−0.306946	−	0.951727i	$-0.599307\pi$
$331$	−6.39396e33	−0.613892	−0.306946	+	0.951727i	$0.599307\pi$
$332$	1.87049e33	0.172421
$333$	−1.03614e34	−0.917111
$334$	4.52369e32	0.0384517
$335$	6.15735e33	0.502677
$336$	−9.31874e32	−0.0730764
$337$	−1.98144e34	−1.49272	−0.746358	−	0.665545i	$-0.768199\pi$
$337$	−1.98144e34	−1.49272	−0.746358	+	0.665545i	$0.768199\pi$
$338$	−7.42623e32	−0.0537518
$339$	4.42468e34	3.07741
$340$	9.36813e33	0.626163
$341$	1.96760e34	1.26401
$342$	2.79493e33	0.172591
$343$	1.65030e33	0.0979699
$344$	6.27974e33	0.358429
$345$	−2.22903e34	−1.22337
$346$	6.22326e32	0.0328466
$347$	1.11409e34	0.565554	0.282777	−	0.959186i	$-0.408744\pi$
$347$	1.11409e34	0.565554	0.282777	+	0.959186i	$0.408744\pi$
$348$	−7.05073e33	−0.344282
$349$	−2.04826e34	−0.962148	−0.481074	−	0.876680i	$-0.659753\pi$
$349$	−2.04826e34	−0.962148	−0.481074	+	0.876680i	$0.659753\pi$
$350$	4.38010e31	0.00197954
$351$	−3.81591e34	−1.65941
$352$	−2.26424e34	−0.947539
$353$	−2.46807e34	−0.994029	−0.497014	−	0.867742i	$-0.665570\pi$
$353$	−2.46807e34	−0.994029	−0.497014	+	0.867742i	$0.665570\pi$
$354$	−3.71448e33	−0.143997
$355$	−7.33591e33	−0.273761
$356$	4.03028e34	1.44797
$357$	−3.50596e33	−0.121279
$358$	−1.30375e33	−0.0434284
$359$	−4.62197e34	−1.48269	−0.741347	−	0.671121i	$-0.765813\pi$
$359$	−4.62197e34	−1.48269	−0.741347	+	0.671121i	$0.765813\pi$
$360$	−1.07047e34	−0.330742
$361$	−2.65759e34	−0.790936
$362$	2.99504e33	0.0858690
$363$	1.06449e35	2.94036
$364$	−1.98917e33	−0.0529423
$365$	−1.70121e33	−0.0436320
$366$	1.69553e34	0.419093
$367$	−6.43858e34	−1.53390	−0.766952	−	0.641704i	$-0.778228\pi$
$367$	−6.43858e34	−1.53390	−0.766952	+	0.641704i	$0.778228\pi$
$368$	6.18361e34	1.42003
$369$	1.00037e35	2.21465
$370$	−2.07339e33	−0.0442546
$371$	1.77830e32	0.00365980
$372$	−6.25852e34	−1.24206
$373$	−4.98993e33	−0.0955049	−0.0477524	−	0.998859i	$-0.515206\pi$
$373$	−4.98993e33	−0.0955049	−0.0477524	+	0.998859i	$0.515206\pi$
$374$	−2.63918e34	−0.487194
$375$	−8.51014e33	−0.151536
$376$	4.12165e33	0.0708004
$377$	−1.43843e34	−0.238385
$378$	9.12749e32	0.0145953
$379$	−3.23150e34	−0.498625	−0.249313	−	0.968423i	$-0.580205\pi$
$379$	−3.23150e34	−0.498625	−0.249313	+	0.968423i	$0.580205\pi$
$380$	−1.31727e34	−0.196154
$381$	3.31100e34	0.475853
$382$	9.84271e33	0.136540
$383$	−2.94215e34	−0.393987	−0.196993	−	0.980405i	$-0.563118\pi$
$383$	−2.94215e34	−0.393987	−0.196993	+	0.980405i	$0.563118\pi$
$384$	9.52812e34	1.23179
$385$	2.90630e33	0.0362761
$386$	−2.12104e34	−0.255635
$387$	1.45675e35	1.69546
$388$	−1.07097e35	−1.20379
$389$	1.32593e35	1.43946	0.719731	−	0.694253i	$-0.244265\pi$
$389$	1.32593e35	1.43946	0.719731	+	0.694253i	$0.244265\pi$
$390$	−1.64090e34	−0.172072
$391$	2.32644e35	2.35670
$392$	−4.03052e34	−0.394456
$393$	−1.09800e35	−1.03825
$394$	−8.81321e33	−0.0805259
$395$	7.48221e34	0.660647
$396$	−3.47757e35	−2.96750
$397$	−2.11665e35	−1.74573	−0.872866	−	0.487959i	$-0.837741\pi$
$397$	−2.11665e35	−1.74573	−0.872866	+	0.487959i	$0.837741\pi$
$398$	2.31951e34	0.184916
$399$	4.92979e33	0.0379922
$400$	2.36082e34	0.175895
$401$	6.91095e34	0.497839	0.248920	−	0.968524i	$-0.419925\pi$
$401$	6.91095e34	0.497839	0.248920	+	0.968524i	$0.419925\pi$
$402$	5.51753e34	0.384320
$403$	−1.27681e35	−0.860017
$404$	−1.05136e35	−0.684865
$405$	−4.45728e34	−0.280820
$406$	3.44065e32	0.00209671
$407$	−1.37574e35	−0.810986
$408$	1.71458e35	0.977790
$409$	−1.13393e35	−0.625638	−0.312819	−	0.949813i	$-0.601273\pi$
$409$	−1.13393e35	−0.625638	−0.312819	+	0.949813i	$0.601273\pi$
$410$	2.00181e34	0.106866
$411$	−2.29977e35	−1.18801
$412$	3.22658e35	1.61298
$413$	−4.26919e33	−0.0206547
$414$	−1.30154e35	−0.609471
$415$	1.77343e34	0.0803831
$416$	1.46931e35	0.644692
$417$	4.80367e35	2.04050
$418$	3.71100e34	0.152620
$419$	7.36925e34	0.293450	0.146725	−	0.989177i	$-0.453127\pi$
$419$	7.36925e34	0.293450	0.146725	+	0.989177i	$0.453127\pi$
$420$	−9.24435e33	−0.0356460
$421$	1.11727e35	0.417205	0.208603	−	0.978000i	$-0.433108\pi$
$421$	1.11727e35	0.417205	0.208603	+	0.978000i	$0.433108\pi$
$422$	−1.00440e35	−0.363235
$423$	9.56125e34	0.334904
$424$	−8.69672e33	−0.0295064
$425$	8.88202e34	0.291918
$426$	−6.57363e34	−0.209303
$427$	1.94873e34	0.0601140
$428$	2.04485e35	0.611181
$429$	−1.08878e36	−3.15330
$430$	2.91506e34	0.0818132
$431$	6.69272e35	1.82037	0.910184	−	0.414203i	$-0.135940\pi$
$431$	6.69272e35	1.82037	0.910184	+	0.414203i	$0.135940\pi$
$432$	4.91960e35	1.29688
$433$	2.91517e35	0.744864	0.372432	−	0.928060i	$-0.378524\pi$
$433$	2.91517e35	0.744864	0.372432	+	0.928060i	$0.378524\pi$
$434$	3.05406e33	0.00756426
$435$	−6.68486e34	−0.160505
$436$	−4.49985e35	−1.04744
$437$	−3.27125e35	−0.738268
$438$	−1.52444e34	−0.0333588
$439$	2.33996e35	0.496521	0.248260	−	0.968693i	$-0.420141\pi$
$439$	2.33996e35	0.496521	0.248260	+	0.968693i	$0.420141\pi$
$440$	−1.42132e35	−0.292469
$441$	−9.34984e35	−1.86588
$442$	1.71261e35	0.331480
$443$	−8.07938e35	−1.51680	−0.758399	−	0.651791i	$-0.774018\pi$
$443$	−8.07938e35	−1.51680	−0.758399	+	0.651791i	$0.774018\pi$
$444$	4.37597e35	0.796900
$445$	3.82115e35	0.675046
$446$	5.66912e34	0.0971616
$447$	1.45088e36	2.41258
$448$	2.32193e34	0.0374624
$449$	−6.87077e35	−1.07567	−0.537836	−	0.843049i	$-0.680758\pi$
$449$	−6.87077e35	−1.07567	−0.537836	+	0.843049i	$0.680758\pi$
$450$	−4.96910e34	−0.0754934
$451$	1.32825e36	1.95838
$452$	−1.21766e36	−1.74244
$453$	−2.23028e36	−3.09765
$454$	−5.45922e34	−0.0735998
$455$	−1.88595e34	−0.0246818
$456$	−2.41090e35	−0.306305
$457$	−8.17859e35	−1.00881	−0.504405	−	0.863467i	$-0.668288\pi$
$457$	−8.17859e35	−1.00881	−0.504405	+	0.863467i	$0.668288\pi$
$458$	−2.29622e35	−0.274998
$459$	1.85088e36	2.15232
$460$	6.13424e35	0.692676
$461$	−7.20617e35	−0.790209	−0.395105	−	0.918636i	$-0.629292\pi$
$461$	−7.20617e35	−0.790209	−0.395105	+	0.918636i	$0.629292\pi$
$462$	2.60431e34	0.0277348
$463$	5.62611e35	0.581922	0.290961	−	0.956735i	$-0.406025\pi$
$463$	5.62611e35	0.581922	0.290961	+	0.956735i	$0.406025\pi$
$464$	1.85446e35	0.186305
$465$	−5.93377e35	−0.579049
$466$	2.59667e35	0.246154
$467$	−6.98906e35	−0.643637	−0.321818	−	0.946801i	$-0.604294\pi$
$467$	−6.98906e35	−0.643637	−0.321818	+	0.946801i	$0.604294\pi$
$468$	2.25666e36	2.01905
$469$	6.34150e34	0.0551263
$470$	1.91327e34	0.0161605
$471$	−7.72532e35	−0.634065
$472$	2.08784e35	0.166525
$473$	1.93421e36	1.49926
$474$	6.70473e35	0.505096
$475$	−1.24892e35	−0.0914471
$476$	9.64832e34	0.0686685
$477$	−2.01743e35	−0.139573
$478$	2.01943e35	0.135817
$479$	8.45105e35	0.552562	0.276281	−	0.961077i	$-0.410898\pi$
$479$	8.45105e35	0.552562	0.276281	+	0.961077i	$0.410898\pi$
$480$	6.82838e35	0.434071
$481$	8.92745e35	0.551783
$482$	−2.18472e35	−0.131299
$483$	−2.29570e35	−0.134162
$484$	−2.92944e36	−1.66484
$485$	−1.01540e36	−0.561208
$486$	1.54213e35	0.0828958
$487$	3.42116e35	0.178868	0.0894341	−	0.995993i	$-0.471494\pi$
$487$	3.42116e35	0.178868	0.0894341	+	0.995993i	$0.471494\pi$
$488$	−9.53022e35	−0.484658
$489$	−1.86688e35	−0.0923519
$490$	−1.87097e35	−0.0900366
$491$	1.37697e36	0.644649	0.322325	−	0.946629i	$-0.395536\pi$
$491$	1.37697e36	0.644649	0.322325	+	0.946629i	$0.395536\pi$
$492$	−4.22489e36	−1.92436
$493$	6.97698e35	0.309196
$494$	−2.40813e35	−0.103840
$495$	−3.29712e36	−1.38345
$496$	1.64610e36	0.672131
$497$	−7.55532e34	−0.0300221
$498$	1.58915e35	0.0614567
$499$	3.06680e36	1.15432	0.577162	−	0.816630i	$-0.304160\pi$
$499$	3.06680e36	1.15432	0.577162	+	0.816630i	$0.304160\pi$
$500$	2.34197e35	0.0857998
$501$	−9.05198e35	−0.322801
$502$	−6.74784e35	−0.234242
$503$	2.35728e36	0.796604	0.398302	−	0.917254i	$-0.369600\pi$
$503$	2.35728e36	0.796604	0.398302	+	0.917254i	$0.369600\pi$
$504$	−1.10248e35	−0.0362710
$505$	−9.96809e35	−0.319285
$506$	−1.72813e36	−0.538945
$507$	1.48600e36	0.451245
$508$	−9.11181e35	−0.269429
$509$	1.92574e36	0.554508	0.277254	−	0.960797i	$-0.410576\pi$
$509$	1.92574e36	0.554508	0.277254	+	0.960797i	$0.410576\pi$
$510$	7.95909e35	0.223185
$511$	−1.75210e34	−0.00478493
$512$	−3.20169e36	−0.851597
$513$	−2.60256e36	−0.674243
$514$	7.32283e35	0.184789
$515$	3.05915e36	0.751974
$516$	−6.15233e36	−1.47322
$517$	1.26950e36	0.296150
$518$	−2.13540e34	−0.00485320
$519$	−1.24529e36	−0.275746
$520$	9.22318e35	0.198992
$521$	4.60123e36	0.967308	0.483654	−	0.875259i	$-0.339309\pi$
$521$	4.60123e36	0.967308	0.483654	+	0.875259i	$0.339309\pi$
$522$	−3.90332e35	−0.0799618
$523$	−8.48366e36	−1.69360	−0.846799	−	0.531913i	$-0.821473\pi$
$523$	−8.48366e36	−1.69360	−0.846799	+	0.531913i	$0.821473\pi$
$524$	3.02168e36	0.587862
$525$	−8.76466e34	−0.0166182
$526$	9.15130e35	0.169112
$527$	6.19307e36	1.11548
$528$	1.40369e37	2.46441
$529$	9.39028e36	1.60704
$530$	−4.03702e34	−0.00673499
$531$	4.84328e36	0.787705
$532$	−1.35667e35	−0.0215113
$533$	−8.61924e36	−1.33245
$534$	3.42409e36	0.516105
$535$	1.93874e36	0.284933
$536$	−3.10130e36	−0.444446
$537$	2.60883e36	0.364580
$538$	7.74492e35	0.105550
$539$	−1.24143e37	−1.64996
$540$	4.88033e36	0.632606
$541$	−9.76505e36	−1.23456	−0.617279	−	0.786745i	$-0.711765\pi$
$541$	−9.76505e36	−1.23456	−0.617279	+	0.786745i	$0.711765\pi$
$542$	−1.87601e35	−0.0231337
$543$	−5.99312e36	−0.720868
$544$	−7.12677e36	−0.836195
$545$	−4.26635e36	−0.488320
$546$	−1.68998e35	−0.0188704
$547$	−5.02160e36	−0.547032	−0.273516	−	0.961867i	$-0.588187\pi$
$547$	−5.02160e36	−0.547032	−0.273516	+	0.961867i	$0.588187\pi$
$548$	6.32891e36	0.672653
$549$	−2.21078e37	−2.29255
$550$	−6.59777e35	−0.0667576
$551$	−9.81047e35	−0.0968597
$552$	1.12270e37	1.08165
$553$	7.70600e35	0.0724502
$554$	7.93941e35	0.0728461
$555$	4.14890e36	0.371516
$556$	−1.32196e37	−1.15534
$557$	7.55160e36	0.644160	0.322080	−	0.946712i	$-0.395618\pi$
$557$	7.55160e36	0.644160	0.322080	+	0.946712i	$0.395618\pi$
$558$	−3.46475e36	−0.288477
$559$	−1.25514e37	−1.02008
$560$	2.43143e35	0.0192896
$561$	5.28104e37	4.08998
$562$	1.14718e36	0.0867343
$563$	3.10320e36	0.229058	0.114529	−	0.993420i	$-0.463464\pi$
$563$	3.10320e36	0.229058	0.114529	+	0.993420i	$0.463464\pi$
$564$	−4.03803e36	−0.291006
$565$	−1.15448e37	−0.812328
$566$	2.13398e36	0.146612
$567$	−4.59059e35	−0.0307962
$568$	3.69491e36	0.242048
$569$	−8.33926e36	−0.533472	−0.266736	−	0.963770i	$-0.585945\pi$
$569$	−8.33926e36	−0.533472	−0.266736	+	0.963770i	$0.585945\pi$
$570$	−1.11914e36	−0.0699157
$571$	−1.39387e37	−0.850422	−0.425211	−	0.905094i	$-0.639800\pi$
$571$	−1.39387e37	−0.850422	−0.425211	+	0.905094i	$0.639800\pi$
$572$	2.99629e37	1.78541
$573$	−1.96955e37	−1.14625
$574$	2.06168e35	0.0117196
$575$	5.81594e36	0.322927
$576$	−2.63417e37	−1.42870
$577$	1.48161e35	0.00784984	0.00392492	−	0.999992i	$-0.498751\pi$
$577$	1.48161e35	0.00784984	0.00392492	+	0.999992i	$0.498751\pi$
$578$	−4.40768e36	−0.228131
$579$	4.24424e37	2.14605
$580$	1.83966e36	0.0908782
$581$	1.82647e35	0.00881526
$582$	−9.09890e36	−0.429070
$583$	−2.67866e36	−0.123422
$584$	8.56858e35	0.0385776
$585$	2.13956e37	0.941282
$586$	−8.12647e35	−0.0349369
$587$	1.02226e37	0.429483	0.214742	−	0.976671i	$-0.431109\pi$
$587$	1.02226e37	0.429483	0.214742	+	0.976671i	$0.431109\pi$
$588$	3.94874e37	1.62131
$589$	−8.70819e36	−0.349439
$590$	9.69174e35	0.0380102
$591$	1.76354e37	0.676012
$592$	−1.15095e37	−0.431236
$593$	−1.29289e36	−0.0473504	−0.0236752	−	0.999720i	$-0.507537\pi$
$593$	−1.29289e36	−0.0473504	−0.0236752	+	0.999720i	$0.507537\pi$
$594$	−1.37488e37	−0.492206
$595$	9.14767e35	0.0320134
$596$	−3.99280e37	−1.36601
$597$	−4.64138e37	−1.55236
$598$	1.12141e37	0.366691
$599$	2.79596e37	0.893858	0.446929	−	0.894569i	$-0.352518\pi$
$599$	2.79596e37	0.893858	0.446929	+	0.894569i	$0.352518\pi$
$600$	4.28633e36	0.133981
$601$	−9.64209e36	−0.294690	−0.147345	−	0.989085i	$-0.547073\pi$
$601$	−9.64209e36	−0.294690	−0.147345	+	0.989085i	$0.547073\pi$
$602$	3.00224e35	0.00897208
$603$	−7.19427e37	−2.10234
$604$	6.13767e37	1.75390
$605$	−2.77743e37	−0.776151
$606$	−8.93230e36	−0.244109
$607$	6.28701e36	0.168034	0.0840169	−	0.996464i	$-0.473225\pi$
$607$	6.28701e36	0.168034	0.0840169	+	0.996464i	$0.473225\pi$
$608$	1.00211e37	0.261949
$609$	−6.88480e35	−0.0176018
$610$	−4.42393e36	−0.110626
$611$	−8.23802e36	−0.201496
$612$	−1.09458e38	−2.61880
$613$	−1.79780e37	−0.420751	−0.210375	−	0.977621i	$-0.567469\pi$
$613$	−1.79780e37	−0.420751	−0.210375	+	0.977621i	$0.567469\pi$
$614$	−7.03474e35	−0.0161055
$615$	−4.00566e37	−0.897140
$616$	−1.46383e36	−0.0320738
$617$	8.73695e37	1.87288	0.936440	−	0.350827i	$-0.114099\pi$
$617$	8.73695e37	1.87288	0.936440	+	0.350827i	$0.114099\pi$
$618$	2.74127e37	0.574920
$619$	4.71115e37	0.966725	0.483362	−	0.875420i	$-0.339415\pi$
$619$	4.71115e37	0.966725	0.483362	+	0.875420i	$0.339415\pi$
$620$	1.63296e37	0.327859
$621$	1.21196e38	2.38095
$622$	5.66982e36	0.108993
$623$	3.93543e36	0.0740293
$624$	−9.10877e37	−1.67675
$625$	2.22045e36	0.0400000
$626$	3.81449e36	0.0672486
$627$	−7.42577e37	−1.28124
$628$	2.12599e37	0.359010
$629$	−4.33020e37	−0.715689
$630$	−5.11772e35	−0.00827903
$631$	2.98089e37	0.472009	0.236004	−	0.971752i	$-0.424162\pi$
$631$	2.98089e37	0.472009	0.236004	+	0.971752i	$0.424162\pi$
$632$	−3.76860e37	−0.584116
$633$	2.00982e38	3.04935
$634$	−8.08464e36	−0.120076
$635$	−8.63900e36	−0.125608
$636$	8.52028e36	0.121278
$637$	8.05587e37	1.12261
$638$	−5.18266e36	−0.0707089
$639$	8.57130e37	1.14495
$640$	−2.48605e37	−0.325148
$641$	−6.10129e37	−0.781336	−0.390668	−	0.920532i	$-0.627756\pi$
$641$	−6.10129e37	−0.781336	−0.390668	+	0.920532i	$0.627756\pi$
$642$	1.73728e37	0.217845
$643$	−1.01555e38	−1.24696	−0.623479	−	0.781840i	$-0.714281\pi$
$643$	−1.01555e38	−1.24696	−0.623479	+	0.781840i	$0.714281\pi$
$644$	6.31771e36	0.0759627
$645$	−5.83309e37	−0.686819
$646$	1.16805e37	0.134686
$647$	−1.65349e38	−1.86722	−0.933608	−	0.358297i	$-0.883358\pi$
$647$	−1.65349e38	−1.86722	−0.933608	+	0.358297i	$0.883358\pi$
$648$	2.24502e37	0.248289
$649$	6.43070e37	0.696554
$650$	4.28141e36	0.0454209
$651$	−6.11124e36	−0.0635018
$652$	5.13760e36	0.0522899
$653$	5.82203e37	0.580425	0.290213	−	0.956962i	$-0.406274\pi$
$653$	5.82203e37	0.580425	0.290213	+	0.956962i	$0.406274\pi$
$654$	−3.82304e37	−0.373344
$655$	2.86488e37	0.274062
$656$	1.11122e38	1.04135
$657$	1.98770e37	0.182482
$658$	1.97050e35	0.00177226
$659$	4.05967e37	0.357716	0.178858	−	0.983875i	$-0.442760\pi$
$659$	4.05967e37	0.357716	0.178858	+	0.983875i	$0.442760\pi$
$660$	1.39248e38	1.20212
$661$	−1.76084e38	−1.48936	−0.744680	−	0.667422i	$-0.767398\pi$
$661$	−1.76084e38	−1.48936	−0.744680	+	0.667422i	$0.767398\pi$
$662$	1.49494e37	0.123892
$663$	−3.42696e38	−2.78276
$664$	−8.93231e36	−0.0710713
$665$	−1.28627e36	−0.0100286
$666$	2.42256e37	0.185085
$667$	4.56852e37	0.342040
$668$	2.49109e37	0.182771
$669$	−1.13440e38	−0.815669
$670$	−1.43962e37	−0.101447
$671$	−2.93538e38	−2.02727
$672$	7.03261e36	0.0476026
$673$	1.68442e38	1.11750	0.558749	−	0.829337i	$-0.311282\pi$
$673$	1.68442e38	1.11750	0.558749	+	0.829337i	$0.311282\pi$
$674$	4.63272e37	0.301250
$675$	4.62709e37	0.294922
$676$	−4.08945e37	−0.255496
$677$	1.57146e37	0.0962403	0.0481202	−	0.998842i	$-0.484677\pi$
$677$	1.57146e37	0.0962403	0.0481202	+	0.998842i	$0.484677\pi$
$678$	−1.03452e38	−0.621064
$679$	−1.04577e37	−0.0615452
$680$	−4.47364e37	−0.258102
$681$	1.09240e38	0.617868
$682$	−4.60035e37	−0.255095
$683$	−2.87974e38	−1.56557	−0.782786	−	0.622291i	$-0.786202\pi$
$683$	−2.87974e38	−1.56557	−0.782786	+	0.622291i	$0.786202\pi$
$684$	1.53910e38	0.820371
$685$	6.00050e37	0.313592
$686$	−3.85850e36	−0.0197716
$687$	4.59477e38	2.30860
$688$	1.61817e38	0.797224
$689$	1.73823e37	0.0839745
$690$	5.21160e37	0.246893
$691$	3.14097e38	1.45918	0.729592	−	0.683883i	$-0.239710\pi$
$691$	3.14097e38	1.45918	0.729592	+	0.683883i	$0.239710\pi$
$692$	3.42700e37	0.156128
$693$	−3.39573e37	−0.151717
$694$	−2.60482e37	−0.114136
$695$	−1.25336e38	−0.538619
$696$	3.36699e37	0.141911
$697$	4.18071e38	1.72825
$698$	4.78895e37	0.194174
$699$	−5.19599e38	−2.06646
$700$	2.41202e36	0.00940929
$701$	4.31670e38	1.65180	0.825902	−	0.563813i	$-0.190666\pi$
$701$	4.31670e38	1.65180	0.825902	+	0.563813i	$0.190666\pi$
$702$	8.92182e37	0.334890
$703$	6.08877e37	0.224199
$704$	−3.49753e38	−1.26337
$705$	−3.82850e37	−0.135667
$706$	5.77049e37	0.200608
$707$	−1.02662e37	−0.0350145
$708$	−2.04548e38	−0.684456
$709$	−3.18870e38	−1.04686	−0.523431	−	0.852068i	$-0.675348\pi$
$709$	−3.18870e38	−1.04686	−0.523431	+	0.852068i	$0.675348\pi$
$710$	1.71518e37	0.0552486
$711$	−8.74224e38	−2.76302
$712$	−1.92461e38	−0.596848
$713$	4.05521e38	1.23397
$714$	8.19713e36	0.0244757
$715$	2.84081e38	0.832360
$716$	−7.17944e37	−0.206426
$717$	−4.04092e38	−1.14018
$718$	1.08064e38	0.299228
$719$	3.00338e38	0.816152	0.408076	−	0.912948i	$-0.366200\pi$
$719$	3.00338e38	0.816152	0.408076	+	0.912948i	$0.366200\pi$
$720$	−2.75839e38	−0.735642
$721$	3.15064e37	0.0824657
$722$	6.21360e37	0.159621
$723$	4.37168e38	1.10225
$724$	1.64929e38	0.408157
$725$	1.74420e37	0.0423675
$726$	−2.48883e38	−0.593404
$727$	−2.84414e38	−0.665635	−0.332818	−	0.942991i	$-0.607999\pi$
$727$	−2.84414e38	−0.665635	−0.332818	+	0.942991i	$0.607999\pi$
$728$	9.49903e36	0.0218226
$729$	−5.87026e38	−1.32384
$730$	3.97754e36	0.00880553
$731$	6.08799e38	1.32309
$732$	9.33687e38	1.99206
$733$	−4.74505e38	−0.993887	−0.496943	−	0.867783i	$-0.665544\pi$
$733$	−4.74505e38	−0.993887	−0.496943	+	0.867783i	$0.665544\pi$
$734$	1.50538e38	0.309563
$735$	3.74384e38	0.755855
$736$	−4.66660e38	−0.925018
$737$	−9.55224e38	−1.85906
$738$	−2.33892e38	−0.446946
$739$	5.59489e38	1.04976	0.524882	−	0.851175i	$-0.324110\pi$
$739$	5.59489e38	1.04976	0.524882	+	0.851175i	$0.324110\pi$
$740$	−1.14177e38	−0.210353
$741$	4.81871e38	0.871737
$742$	−4.15776e35	−0.000738596 0
$743$	−3.42012e38	−0.596613	−0.298307	−	0.954470i	$-0.596422\pi$
$743$	−3.42012e38	−0.596613	−0.298307	+	0.954470i	$0.596422\pi$
$744$	2.98868e38	0.511971
$745$	−3.78562e38	−0.636835
$746$	1.16667e37	0.0192742
$747$	−2.07208e38	−0.336185
$748$	−1.45333e39	−2.31576
$749$	1.99672e37	0.0312474
$750$	1.98972e37	0.0305819
$751$	1.90162e38	0.287068	0.143534	−	0.989645i	$-0.454153\pi$
$751$	1.90162e38	0.287068	0.143534	+	0.989645i	$0.454153\pi$
$752$	1.06207e38	0.157476
$753$	1.35026e39	1.96645
$754$	3.36312e37	0.0481093
$755$	5.81919e38	0.817671
$756$	5.02629e37	0.0693750
$757$	−1.46622e38	−0.198795	−0.0993975	−	0.995048i	$-0.531692\pi$
$757$	−1.46622e38	−0.198795	−0.0993975	+	0.995048i	$0.531692\pi$
$758$	7.55542e37	0.100629
$759$	3.45802e39	4.52443
$760$	6.29047e37	0.0808537
$761$	1.57792e38	0.199247	0.0996236	−	0.995025i	$-0.468236\pi$
$761$	1.57792e38	0.199247	0.0996236	+	0.995025i	$0.468236\pi$
$762$	−7.74131e37	−0.0960335
$763$	−4.39395e37	−0.0535518
$764$	5.42015e38	0.649009
$765$	−1.03778e39	−1.22089
$766$	6.87892e37	0.0795119
$767$	−4.17299e38	−0.473926
$768$	9.36956e38	1.04555
$769$	−1.66271e39	−1.82310	−0.911551	−	0.411188i	$-0.865114\pi$
$769$	−1.66271e39	−1.82310	−0.911551	+	0.411188i	$0.865114\pi$
$770$	−6.79510e36	−0.00732101
$771$	−1.46531e39	−1.55130
$772$	−1.16800e39	−1.21510
$773$	3.33427e38	0.340861	0.170431	−	0.985370i	$-0.445484\pi$
$773$	3.33427e38	0.340861	0.170431	+	0.985370i	$0.445484\pi$
$774$	−3.40596e38	−0.342166
$775$	1.54823e38	0.152849
$776$	5.11431e38	0.496196
$777$	4.27298e37	0.0407425
$778$	−3.10010e38	−0.290503
$779$	−5.87857e38	−0.541397
$780$	−9.03605e38	−0.817903
$781$	1.13806e39	1.01246
$782$	−5.43934e38	−0.475615
$783$	3.63466e38	0.312378
$784$	−1.03859e39	−0.877357
$785$	2.01567e38	0.167371
$786$	2.56719e38	0.209534
$787$	−1.64160e39	−1.31707	−0.658536	−	0.752549i	$-0.728824\pi$
$787$	−1.64160e39	−1.31707	−0.658536	+	0.752549i	$0.728824\pi$
$788$	−4.85323e38	−0.382760
$789$	−1.83119e39	−1.41969
$790$	−1.74938e38	−0.133327
$791$	−1.18901e38	−0.0890844
$792$	1.66067e39	1.22319
$793$	1.90482e39	1.37932
$794$	4.94886e38	0.352312
$795$	8.07816e37	0.0565401
$796$	1.27730e39	0.878952
$797$	1.90150e39	1.28649	0.643247	−	0.765658i	$-0.277587\pi$
$797$	1.90150e39	1.28649	0.643247	+	0.765658i	$0.277587\pi$
$798$	−1.15261e37	−0.00766734
$799$	3.99580e38	0.261350
$800$	−1.78165e38	−0.114579
$801$	−4.46464e39	−2.82324
$802$	−1.61582e38	−0.100471
$803$	2.63919e38	0.161366
$804$	3.03837e39	1.82677
$805$	5.98988e37	0.0354139
$806$	2.98525e38	0.173563
$807$	−1.54977e39	−0.886085
$808$	5.02067e38	0.282298
$809$	−2.33558e39	−1.29149	−0.645744	−	0.763554i	$-0.723453\pi$
$809$	−2.33558e39	−1.29149	−0.645744	+	0.763554i	$0.723453\pi$
$810$	1.04214e38	0.0566732
$811$	−1.51609e39	−0.810854	−0.405427	−	0.914127i	$-0.632877\pi$
$811$	−1.51609e39	−0.810854	−0.405427	+	0.914127i	$0.632877\pi$
$812$	1.89468e37	0.00996621
$813$	3.75394e38	0.194207
$814$	3.21657e38	0.163668
$815$	4.87101e37	0.0243776
$816$	4.41815e39	2.17482
$817$	−8.56043e38	−0.414475
$818$	2.65120e38	0.126262
$819$	2.20355e38	0.103226
$820$	1.10235e39	0.507963
$821$	1.61094e39	0.730208	0.365104	−	0.930967i	$-0.381033\pi$
$821$	1.61094e39	0.730208	0.365104	+	0.930967i	$0.381033\pi$
$822$	5.37699e38	0.239756
$823$	6.64569e38	0.291502	0.145751	−	0.989321i	$-0.453440\pi$
$823$	6.64569e38	0.291502	0.145751	+	0.989321i	$0.453440\pi$
$824$	−1.54081e39	−0.664864
$825$	1.32023e39	0.560428
$826$	9.98161e36	0.00416840
$827$	3.77166e39	1.54956	0.774780	−	0.632231i	$-0.217861\pi$
$827$	3.77166e39	1.54956	0.774780	+	0.632231i	$0.217861\pi$
$828$	−7.16727e39	−2.89697
$829$	4.39675e39	1.74842	0.874210	−	0.485547i	$-0.161380\pi$
$829$	4.39675e39	1.74842	0.874210	+	0.485547i	$0.161380\pi$
$830$	−4.14638e37	−0.0162224
$831$	−1.58869e39	−0.611541
$832$	2.26961e39	0.859580
$833$	−3.90744e39	−1.45608
$834$	−1.12313e39	−0.411800
$835$	2.36182e38	0.0852079
$836$	2.04356e39	0.725441
$837$	3.22628e39	1.12696
$838$	−1.72297e38	−0.0592222
$839$	2.92220e39	0.988380	0.494190	−	0.869354i	$-0.335465\pi$
$839$	2.92220e39	0.988380	0.494190	+	0.869354i	$0.335465\pi$
$840$	4.41453e37	0.0146931
$841$	−2.91612e39	−0.955125
$842$	−2.61224e38	−0.0841977
$843$	−2.29553e39	−0.728132
$844$	−5.53098e39	−1.72655
$845$	−3.87725e38	−0.119113
$846$	−2.23548e38	−0.0675881
$847$	−2.86050e38	−0.0851170
$848$	−2.24098e38	−0.0656288
$849$	−4.27014e39	−1.23080
$850$	−2.07667e38	−0.0589130
$851$	−2.83541e39	−0.791711
$852$	−3.61994e39	−0.994872
$853$	4.42315e39	1.19652	0.598260	−	0.801302i	$-0.295859\pi$
$853$	4.42315e39	1.19652	0.598260	+	0.801302i	$0.295859\pi$
$854$	−4.55625e37	−0.0121318
$855$	1.45924e39	0.382458
$856$	−9.76493e38	−0.251926
$857$	−2.68356e39	−0.681506	−0.340753	−	0.940153i	$-0.610682\pi$
$857$	−2.68356e39	−0.681506	−0.340753	+	0.940153i	$0.610682\pi$
$858$	2.54562e39	0.636379
$859$	2.15068e39	0.529259	0.264629	−	0.964350i	$-0.414750\pi$
$859$	2.15068e39	0.529259	0.264629	+	0.964350i	$0.414750\pi$
$860$	1.60525e39	0.388879
$861$	−4.12547e38	−0.0983854
$862$	−1.56480e39	−0.367375
$863$	−1.28220e39	−0.296353	−0.148176	−	0.988961i	$-0.547340\pi$
$863$	−1.28220e39	−0.296353	−0.148176	+	0.988961i	$0.547340\pi$
$864$	−3.71269e39	−0.844798
$865$	3.24917e38	0.0727873
$866$	−6.81583e38	−0.150324
$867$	8.81986e39	1.91515
$868$	1.68180e38	0.0359549
$869$	−1.16076e40	−2.44329
$870$	1.56296e38	0.0323920
$871$	6.19862e39	1.26488
$872$	2.14885e39	0.431752
$873$	1.18640e40	2.34713
$874$	7.64836e38	0.148992
$875$	2.28686e37	0.00438662
$876$	−8.39473e38	−0.158563
$877$	3.36323e39	0.625550	0.312775	−	0.949827i	$-0.398741\pi$
$877$	3.36323e39	0.625550	0.312775	+	0.949827i	$0.398741\pi$
$878$	−5.47096e38	−0.100205
$879$	1.62612e39	0.293294
$880$	−3.66247e39	−0.650516
$881$	−2.76526e39	−0.483683	−0.241842	−	0.970316i	$-0.577751\pi$
$881$	−2.76526e39	−0.483683	−0.241842	+	0.970316i	$0.577751\pi$
$882$	2.18605e39	0.376559
$883$	−1.96736e39	−0.333745	−0.166873	−	0.985978i	$-0.553367\pi$
$883$	−1.96736e39	−0.333745	−0.166873	+	0.985978i	$0.553367\pi$
$884$	9.43092e39	1.57561
$885$	−1.93934e39	−0.319094
$886$	1.88901e39	0.306110
$887$	−9.60586e38	−0.153309	−0.0766545	−	0.997058i	$-0.524424\pi$
$887$	−9.60586e38	−0.153309	−0.0766545	+	0.997058i	$0.524424\pi$
$888$	−2.08969e39	−0.328479
$889$	−8.89738e37	−0.0137749
$890$	−8.93406e38	−0.136233
$891$	6.91484e39	1.03856
$892$	3.12185e39	0.461834
$893$	−5.61857e38	−0.0818711
$894$	−3.39225e39	−0.486891
$895$	−6.80690e38	−0.0962361
$896$	−2.56041e38	−0.0356575
$897$	−2.24397e40	−3.07836
$898$	1.60643e39	0.217085
$899$	1.21616e39	0.161895
$900$	−2.73637e39	−0.358840
$901$	−8.43117e38	−0.108919
$902$	−3.10552e39	−0.395227
$903$	−6.00755e38	−0.0753204
$904$	5.81481e39	0.718226
$905$	1.56371e39	0.190283
$906$	5.21451e39	0.625148
$907$	1.27730e40	1.50867	0.754337	−	0.656488i	$-0.227959\pi$
$907$	1.27730e40	1.50867	0.754337	+	0.656488i	$0.227959\pi$
$908$	−3.00626e39	−0.349839
$909$	1.16468e40	1.33534
$910$	4.40946e37	0.00498111
$911$	−8.44318e39	−0.939740	−0.469870	−	0.882735i	$-0.655699\pi$
$911$	−8.44318e39	−0.939740	−0.469870	+	0.882735i	$0.655699\pi$
$912$	−6.21244e39	−0.681290
$913$	−2.75122e39	−0.297283
$914$	1.91220e39	0.203592
$915$	8.85237e39	0.928699
$916$	−1.26447e40	−1.30713
$917$	2.95057e38	0.0300552
$918$	−4.32747e39	−0.434368
$919$	4.98439e39	0.493007	0.246503	−	0.969142i	$-0.420718\pi$
$919$	4.98439e39	0.493007	0.246503	+	0.969142i	$0.420718\pi$
$920$	−2.92934e39	−0.285518
$921$	1.40767e39	0.135206
$922$	1.68484e39	0.159475
$923$	−7.38508e39	−0.688862
$924$	1.43413e39	0.131831
$925$	−1.08252e39	−0.0980670
$926$	−1.31542e39	−0.117440
$927$	−3.57432e40	−3.14497
$928$	−1.39951e39	−0.121361
$929$	1.36968e40	1.17059	0.585297	−	0.810819i	$-0.300978\pi$
$929$	1.36968e40	1.17059	0.585297	+	0.810819i	$0.300978\pi$
$930$	1.38735e39	0.116860
$931$	5.49433e39	0.456136
$932$	1.42992e40	1.17003
$933$	−1.13454e40	−0.914994
$934$	1.63408e39	0.129895
$935$	−1.37792e40	−1.07961
$936$	−1.07764e40	−0.832242
$937$	−1.09933e40	−0.836844	−0.418422	−	0.908253i	$-0.637417\pi$
$937$	−1.09933e40	−0.836844	−0.418422	+	0.908253i	$0.637417\pi$
$938$	−1.48268e38	−0.0111252
$939$	−7.63287e39	−0.564550
$940$	1.05359e39	0.0768152
$941$	1.75764e40	1.26320	0.631599	−	0.775296i	$-0.282399\pi$
$941$	1.75764e40	1.26320	0.631599	+	0.775296i	$0.282399\pi$
$942$	1.80622e39	0.127963
$943$	2.73752e40	1.91183
$944$	5.37996e39	0.370388
$945$	4.76547e38	0.0323427
$946$	−4.52230e39	−0.302572
$947$	−7.60731e39	−0.501772	−0.250886	−	0.968017i	$-0.580722\pi$
$947$	−7.60731e39	−0.501772	−0.250886	+	0.968017i	$0.580722\pi$
$948$	3.69214e40	2.40085
$949$	−1.71262e39	−0.109791
$950$	2.92004e38	0.0184553
$951$	1.61775e40	1.00803
$952$	−4.60744e38	−0.0283049
$953$	1.16790e40	0.707379	0.353689	−	0.935363i	$-0.384927\pi$
$953$	1.16790e40	0.707379	0.353689	+	0.935363i	$0.384927\pi$
$954$	4.71687e38	0.0281677
$955$	5.13889e39	0.302569
$956$	1.11205e40	0.645571
$957$	1.03706e40	0.593599
$958$	−1.97590e39	−0.111515
$959$	6.17997e38	0.0343902
$960$	1.05477e40	0.578755
$961$	−7.68758e39	−0.415933
$962$	−2.08729e39	−0.111357
$963$	−2.26523e40	−1.19167
$964$	−1.20308e40	−0.624098
$965$	−1.10740e40	−0.566480
$966$	5.36747e38	0.0270756
$967$	−7.69495e38	−0.0382779	−0.0191390	−	0.999817i	$-0.506092\pi$
$967$	−7.69495e38	−0.0382779	−0.0191390	+	0.999817i	$0.506092\pi$
$968$	1.39892e40	0.686240
$969$	−2.33728e40	−1.13068
$970$	2.37406e39	0.113259
$971$	−1.59976e40	−0.752651	−0.376326	−	0.926487i	$-0.622813\pi$
$971$	−1.59976e40	−0.752651	−0.376326	+	0.926487i	$0.622813\pi$
$972$	8.49216e39	0.394025
$973$	−1.29085e39	−0.0590680
$974$	−7.99888e38	−0.0360980
$975$	−8.56717e39	−0.381307
$976$	−2.45576e40	−1.07799
$977$	3.49602e40	1.51355	0.756775	−	0.653675i	$-0.226774\pi$
$977$	3.49602e40	1.51355	0.756775	+	0.653675i	$0.226774\pi$
$978$	4.36486e38	0.0186379
$979$	−5.92796e40	−2.49654
$980$	−1.03030e40	−0.427967
$981$	4.98482e40	2.04229
$982$	−3.21943e39	−0.130099
$983$	−3.81223e40	−1.51952	−0.759760	−	0.650204i	$-0.774683\pi$
$983$	−3.81223e40	−1.51952	−0.759760	+	0.650204i	$0.774683\pi$
$984$	2.01755e40	0.793214
$985$	−4.60139e39	−0.178443
$986$	−1.63126e39	−0.0624000
$987$	−3.94300e38	−0.0148780
$988$	−1.32610e40	−0.493580
$989$	3.98641e40	1.46363
$990$	7.70885e39	0.279200
$991$	−7.70607e39	−0.275320	−0.137660	−	0.990480i	$-0.543958\pi$
$991$	−7.70607e39	−0.275320	−0.137660	+	0.990480i	$0.543958\pi$
$992$	−1.24227e40	−0.437832
$993$	−2.99141e40	−1.04007
$994$	1.76648e38	0.00605887
$995$	1.21102e40	0.409769
$996$	8.75108e39	0.292120
$997$	4.44428e40	1.46358	0.731790	−	0.681530i	$-0.238685\pi$
$997$	4.44428e40	1.46358	0.731790	+	0.681530i	$0.238685\pi$
$998$	−7.17034e39	−0.232958
$999$	−2.25582e40	−0.723052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.28.a.b.1.2	✓	5
3.2	odd	2		45.28.a.d.1.4		5
5.2	odd	4		25.28.b.c.24.4		10
5.3	odd	4		25.28.b.c.24.7		10
5.4	even	2		25.28.a.c.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.28.a.b.1.2	✓	5	1.1	even	1	trivial
25.28.a.c.1.4		5	5.4	even	2
25.28.b.c.24.4		10	5.2	odd	4
25.28.b.c.24.7		10	5.3	odd	4
45.28.a.d.1.4		5	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:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-2338.06 q^{2} +4.67850e6 q^{3} -1.28751e8 q^{4} -1.22070e9 q^{5} -1.09386e10 q^{6} -1.25721e10 q^{7} +6.14836e11 q^{8} +1.42627e13 q^{9} +O(q^{10})\)	\(q-2338.06 q^{2} +4.67850e6 q^{3} -1.28751e8 q^{4} -1.22070e9 q^{5} -1.09386e10 q^{6} -1.25721e10 q^{7} +6.14836e11 q^{8} +1.42627e13 q^{9} +2.85407e12 q^{10} +1.89375e14 q^{11} -6.02362e14 q^{12} -1.22888e15 q^{13} +2.93943e13 q^{14} -5.71106e15 q^{15} +1.58432e16 q^{16} +5.96062e16 q^{17} -3.33471e16 q^{18} -8.38134e16 q^{19} +1.57167e17 q^{20} -5.88187e16 q^{21} -4.42769e17 q^{22} +3.90301e18 q^{23} +2.87651e18 q^{24} +1.49012e18 q^{25} +2.87320e18 q^{26} +3.10518e19 q^{27} +1.61868e18 q^{28} +1.17051e19 q^{29} +1.33528e19 q^{30} +1.03900e20 q^{31} -1.19564e20 q^{32} +8.85988e20 q^{33} -1.39363e20 q^{34} +1.53468e19 q^{35} -1.83634e21 q^{36} -7.26467e20 q^{37} +1.95961e20 q^{38} -5.74933e21 q^{39} -7.50533e20 q^{40} +7.01388e21 q^{41} +1.37521e20 q^{42} +1.02137e22 q^{43} -2.43822e22 q^{44} -1.74106e22 q^{45} -9.12546e21 q^{46} +6.70366e21 q^{47} +7.41222e22 q^{48} -6.55543e22 q^{49} -3.48398e21 q^{50} +2.78868e23 q^{51} +1.58220e23 q^{52} -1.41448e22 q^{53} -7.26010e22 q^{54} -2.31170e23 q^{55} -7.72980e21 q^{56} -3.92121e23 q^{57} -2.73673e22 q^{58} +3.39576e23 q^{59} +7.35305e23 q^{60} -1.55004e24 q^{61} -2.42923e23 q^{62} -1.79313e23 q^{63} -1.84689e24 q^{64} +1.50010e24 q^{65} -2.07149e24 q^{66} -5.04410e24 q^{67} -7.67437e24 q^{68} +1.82602e25 q^{69} -3.58818e22 q^{70} +6.00958e24 q^{71} +8.76925e24 q^{72} +1.39363e24 q^{73} +1.69852e24 q^{74} +6.97150e24 q^{75} +1.07911e25 q^{76} -2.38084e24 q^{77} +1.34423e25 q^{78} -6.12943e25 q^{79} -1.93398e25 q^{80} +3.65141e25 q^{81} -1.63988e25 q^{82} -1.45279e25 q^{83} +7.57297e24 q^{84} -7.27615e25 q^{85} -2.38802e25 q^{86} +5.47624e25 q^{87} +1.16434e26 q^{88} -3.13028e26 q^{89} +4.07069e25 q^{90} +1.54497e25 q^{91} -5.02517e26 q^{92} +4.86094e26 q^{93} -1.56735e25 q^{94} +1.02311e26 q^{95} -5.59381e26 q^{96} +8.31816e26 q^{97} +1.53270e26 q^{98} +2.70100e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9}+O(q^{10}) \) 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9	\( 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9} - 24311523437500 q^{10} - 34307841041440 q^{11} + 10\!\cdots\!96 q^{12}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9 - 24311523437500 * q^10 - 34307841041440 * q^11 + 1067087945485696 * q^12 + 1264965428684322 * q^13 - 1494481038585720 * q^14 - 5945656738281250 * q^15 + 50480141682449280 * q^16 + 11381432659133186 * q^17 + 199164599348648492 * q^18 - 177889284152803500 * q^19 - 306994921875000000 * q^20 + 15690874972867260 * q^21 + 1661117755714509952 * q^22 + 5314231426153528362 * q^23 + 25461226121295412800 * q^24 + 7450580596923828125 * q^25 + 64194207115665583160 * q^26 + 69831879763488728300 * q^27 + 74243491650979261568 * q^28 + 142675767255557016550 * q^29 - 48077371044921875000 * q^30 + 490757140558660526660 * q^31 + 709255558573159910656 * q^32 + 262404778486784711104 * q^33 - 823451155892216853320 * q^34 - 189997983649902343750 * q^35 + 364604386623731602880 * q^36 - 1594690133202798011054 * q^37 - 8102840491936976962000 * q^38 - 3725217775868438909980 * q^39 - 5913608024414062500000 * q^40 - 14453824011731896105490 * q^41 - 18735431399125775369328 * q^42 - 6456338188721923591758 * q^43 - 61776067586935488773120 * q^44 - 11299361297711181640625 * q^45 + 41662242513049160161560 * q^46 + 19960747396802751518726 * q^47 + 306904049567056770080512 * q^48 + 64529931934369352760065 * q^49 + 29677152633666992187500 * q^50 + 45124322296416065252260 * q^51 + 694364047806293961951616 * q^52 + 203485571063020242199082 * q^53 + 430355877536329740706000 * q^54 + 41879688771289062500000 * q^55 - 514718506150627561339200 * q^56 - 1075206797979440282527000 * q^57 - 568257469475936639738200 * q^58 - 1753694580358227494398300 * q^59 - 1302597589704218750000000 * q^60 - 1715799924029775655491390 * q^61 + 856653132512718918087792 * q^62 - 3772385601985154457719778 * q^63 + 2825791291455308901232640 * q^64 - 1544147251811916503906250 * q^65 - 14020757899728664042151680 * q^66 - 52283413307813388053914 * q^67 - 18798756173665084661988992 * q^68 + 17423855056223403670703220 * q^69 + 1824317674054833984375000 * q^70 + 13737346388576400396156460 * q^71 + 48990987369760413733351200 * q^72 + 52785881484144679283287962 * q^73 + 44617246831379823508169080 * q^74 + 7257881760597229003906250 * q^75 - 50943444226830794465542400 * q^76 + 40527442829187717880256832 * q^77 + 96469318519881413261089264 * q^78 - 18659027886608771061377800 * q^79 - 61621266702208593750000000 * q^80 - 18780471510820240351050695 * q^81 - 233045910890443727506605688 * q^82 - 49391953045615520178004398 * q^83 - 276316883591574899554456320 * q^84 - 13893350413980939941406250 * q^85 - 246095687260751641221151240 * q^86 - 67750867272390013078210900 * q^87 - 662199546636275930413900800 * q^88 + 180573322691431536135373650 * q^89 - 243120848814268178710937500 * q^90 + 317295677016426969579588460 * q^91 - 379021343242797571985691264 * q^92 + 1482223660602013833974435784 * q^93 - 34623503302055809185576920 * q^94 + 217150005069340209960937500 * q^95 + 2545248606864865567495170560 * q^96 + 1118012018325586896775804426 * q^97 - 243326561625995319625007012 * q^98 + 2661033543665827983852919520 * q^99

Introduction

L-functions

Modular forms

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