LMFDB - Embedded newform 47.20.a.a.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [47,20,Mod(1,47)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(47, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("47.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	47.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:	$107.543847381$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+867.376 q^{2} -46891.0 q^{3} +228052. q^{4} -6.21584e6 q^{5} -4.06721e7 q^{6} +1.08010e8 q^{7} -2.56948e8 q^{8} +1.03650e9 q^{9} +O(q^{10})$	\(q+867.376 q^{2} -46891.0 q^{3} +228052. q^{4} -6.21584e6 q^{5} -4.06721e7 q^{6} +1.08010e8 q^{7} -2.56948e8 q^{8} +1.03650e9 q^{9} -5.39147e9 q^{10} +1.80571e9 q^{11} -1.06936e10 q^{12} +2.66015e10 q^{13} +9.36848e10 q^{14} +2.91467e11 q^{15} -3.42435e11 q^{16} -3.93292e11 q^{17} +8.99037e11 q^{18} +1.72955e12 q^{19} -1.41754e12 q^{20} -5.06467e12 q^{21} +1.56623e12 q^{22} +9.57883e12 q^{23} +1.20485e13 q^{24} +1.95632e13 q^{25} +2.30735e13 q^{26} +5.89693e12 q^{27} +2.46318e13 q^{28} +5.53399e13 q^{29} +2.52811e14 q^{30} -9.26869e13 q^{31} -1.62305e14 q^{32} -8.46714e13 q^{33} -3.41132e14 q^{34} -6.71370e14 q^{35} +2.36377e14 q^{36} +6.10772e14 q^{37} +1.50017e15 q^{38} -1.24737e15 q^{39} +1.59714e15 q^{40} +8.08946e14 q^{41} -4.39297e15 q^{42} -3.26437e15 q^{43} +4.11796e14 q^{44} -6.44274e15 q^{45} +8.30844e15 q^{46} +1.11913e15 q^{47} +1.60571e16 q^{48} +2.67167e14 q^{49} +1.69686e16 q^{50} +1.84419e16 q^{51} +6.06653e15 q^{52} -3.46454e15 q^{53} +5.11486e15 q^{54} -1.12240e16 q^{55} -2.77528e16 q^{56} -8.11004e16 q^{57} +4.80005e16 q^{58} +4.77881e16 q^{59} +6.64697e16 q^{60} -1.80870e17 q^{61} -8.03943e16 q^{62} +1.11952e17 q^{63} +3.87549e16 q^{64} -1.65350e17 q^{65} -7.34419e16 q^{66} -2.98219e17 q^{67} -8.96913e16 q^{68} -4.49161e17 q^{69} -5.82330e17 q^{70} -6.99366e17 q^{71} -2.66327e17 q^{72} -1.26648e17 q^{73} +5.29769e17 q^{74} -9.17336e17 q^{75} +3.94429e17 q^{76} +1.95034e17 q^{77} -1.08194e18 q^{78} +1.04635e18 q^{79} +2.12852e18 q^{80} -1.48120e18 q^{81} +7.01660e17 q^{82} -1.69272e18 q^{83} -1.15501e18 q^{84} +2.44464e18 q^{85} -2.83143e18 q^{86} -2.59494e18 q^{87} -4.63972e17 q^{88} +4.34956e18 q^{89} -5.58827e18 q^{90} +2.87321e18 q^{91} +2.18448e18 q^{92} +4.34618e18 q^{93} +9.70706e17 q^{94} -1.07506e19 q^{95} +7.61066e18 q^{96} +2.70199e18 q^{97} +2.31734e17 q^{98} +1.87162e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) $ 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9	$ 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9} - 10197084160 q^{10} - 7963915630 q^{11} - 12629269764 q^{12} - 159160177690 q^{13} + 404118350082 q^{14} - 59651276056 q^{15} + 1400499411089 q^{16} - 2004886737784 q^{17} - 4449273908039 q^{18} - 1058821844658 q^{19} + 5114247081432 q^{20} + 2403861756792 q^{21} - 3900401557590 q^{22} - 17333732320340 q^{23} + 32877217250016 q^{24} + 85478486158774 q^{25} - 52056718761868 q^{26} - 137248515015920 q^{27} - 361374372214712 q^{28} - 66840103484258 q^{29} - 884984566401484 q^{30} - 481560705870844 q^{31} - 19\!\cdots\!67 q^{32}+ \cdots + 10\!\cdots\!22 q^{99}+O(q^{100}) $ 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9 - 10197084160 * q^10 - 7963915630 * q^11 - 12629269764 * q^12 - 159160177690 * q^13 + 404118350082 * q^14 - 59651276056 * q^15 + 1400499411089 * q^16 - 2004886737784 * q^17 - 4449273908039 * q^18 - 1058821844658 * q^19 + 5114247081432 * q^20 + 2403861756792 * q^21 - 3900401557590 * q^22 - 17333732320340 * q^23 + 32877217250016 * q^24 + 85478486158774 * q^25 - 52056718761868 * q^26 - 137248515015920 * q^27 - 361374372214712 * q^28 - 66840103484258 * q^29 - 884984566401484 * q^30 - 481560705870844 * q^31 - 1956224504349967 * q^32 - 1089319960511632 * q^33 - 1024355370607462 * q^34 - 368682962835736 * q^35 - 447128934368887 * q^36 - 2062248173433492 * q^37 - 1576879945450998 * q^38 - 2078450045289336 * q^39 - 6293443543679952 * q^40 + 1056258166827256 * q^41 + 3982705476758466 * q^42 - 3467551217747682 * q^43 - 3212244140107742 * q^44 + 4912736475062322 * q^45 + 5810353662475960 * q^46 + 38050436085494078 * q^47 + 57514374310072968 * q^48 + 47238885151375334 * q^49 + 14878200688182597 * q^50 - 29591098904130220 * q^51 - 21974217154008420 * q^52 - 72013726688940684 * q^53 + 172899128132785018 * q^54 + 93309162211316908 * q^55 + 475212376185711512 * q^56 + 64982196426903912 * q^57 + 191264232277219708 * q^58 + 76501047180767180 * q^59 + 400074650609834880 * q^60 - 93578930877721460 * q^61 + 57387957390004612 * q^62 - 383255174667133284 * q^63 + 259127393615024481 * q^64 - 901725390399661584 * q^65 - 254413721370645848 * q^66 - 1182341009802075686 * q^67 - 925231639360979526 * q^68 - 947344752044875104 * q^69 - 363789978732097444 * q^70 - 848931219817628416 * q^71 - 2149287430983690291 * q^72 - 2671220396145181732 * q^73 - 3011451157682875714 * q^74 - 17689756878445192 * q^75 - 3177271521326582258 * q^76 - 1684143788069292280 * q^77 - 224568865304519456 * q^78 + 707599882299569300 * q^79 - 715147860460459392 * q^80 + 3538237990220919930 * q^81 + 1087170674699769934 * q^82 + 3231397917214389292 * q^83 - 5938450004747482572 * q^84 - 1954320626223684628 * q^85 - 1629641946563167526 * q^86 + 7707422320592255560 * q^87 - 5131462381092863934 * q^88 - 6860870532479969712 * q^89 - 8661425364016769956 * q^90 - 2927652813879512704 * q^91 - 26818660612119538580 * q^92 - 19098581600812512 * q^93 - 1657432230665197927 * q^94 - 5345445300954569692 * q^95 - 59798491695034221784 * q^96 - 7217040872018076624 * q^97 - 44647529467669017809 * q^98 + 10120380184661285522 * 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 $

$2$	867.376	1.19790	0.598952	−	0.800785i	$-0.295584\pi$
$2$	867.376	1.19790	0.598952	+	0.800785i	$0.295584\pi$
$3$	−46891.0	−1.37543	−0.687713	−	0.725982i	$-0.741385\pi$
$3$	−46891.0	−1.37543	−0.687713	+	0.725982i	$0.741385\pi$
$4$	228052.	0.434975
$5$	−6.21584e6	−1.42326	−0.711631	−	0.702554i	$-0.752043\pi$
$5$	−6.21584e6	−1.42326	−0.711631	+	0.702554i	$0.752043\pi$
$6$	−4.06721e7	−1.64763
$7$	1.08010e8	1.01165	0.505826	−	0.862636i	$-0.331188\pi$
$7$	1.08010e8	1.01165	0.505826	+	0.862636i	$0.331188\pi$
$8$	−2.56948e8	−0.676845
$9$	1.03650e9	0.891799
$10$	−5.39147e9	−1.70493
$11$	1.80571e9	0.230896	0.115448	−	0.993314i	$-0.463170\pi$
$11$	1.80571e9	0.230896	0.115448	+	0.993314i	$0.463170\pi$
$12$	−1.06936e10	−0.598277
$13$	2.66015e10	0.695734	0.347867	−	0.937544i	$-0.386906\pi$
$13$	2.66015e10	0.695734	0.347867	+	0.937544i	$0.386906\pi$
$14$	9.36848e10	1.21186
$15$	2.91467e11	1.95759
$16$	−3.42435e11	−1.24577
$17$	−3.93292e11	−0.804360	−0.402180	−	0.915561i	$-0.631747\pi$
$17$	−3.93292e11	−0.804360	−0.402180	+	0.915561i	$0.631747\pi$
$18$	8.99037e11	1.06829
$19$	1.72955e12	1.22963	0.614815	−	0.788671i	$-0.289231\pi$
$19$	1.72955e12	1.22963	0.614815	+	0.788671i	$0.289231\pi$
$20$	−1.41754e12	−0.619084
$21$	−5.06467e12	−1.39145
$22$	1.56623e12	0.276592
$23$	9.57883e12	1.10891	0.554457	−	0.832212i	$-0.312926\pi$
$23$	9.57883e12	1.10891	0.554457	+	0.832212i	$0.312926\pi$
$24$	1.20485e13	0.930951
$25$	1.95632e13	1.02567
$26$	2.30735e13	0.833424
$27$	5.89693e12	0.148823
$28$	2.46318e13	0.440043
$29$	5.53399e13	0.708365	0.354183	−	0.935176i	$-0.384759\pi$
$29$	5.53399e13	0.708365	0.354183	+	0.935176i	$0.384759\pi$
$30$	2.52811e14	2.34501
$31$	−9.26869e13	−0.629625	−0.314813	−	0.949154i	$-0.601942\pi$
$31$	−9.26869e13	−0.629625	−0.314813	+	0.949154i	$0.601942\pi$
$32$	−1.62305e14	−0.815470
$33$	−8.46714e13	−0.317581
$34$	−3.41132e14	−0.963547
$35$	−6.71370e14	−1.43984
$36$	2.36377e14	0.387911
$37$	6.10772e14	0.772615	0.386307	−	0.922370i	$-0.373750\pi$
$37$	6.10772e14	0.772615	0.386307	+	0.922370i	$0.373750\pi$
$38$	1.50017e15	1.47298
$39$	−1.24737e15	−0.956932
$40$	1.59714e15	0.963328
$41$	8.08946e14	0.385898	0.192949	−	0.981209i	$-0.438195\pi$
$41$	8.08946e14	0.385898	0.192949	+	0.981209i	$0.438195\pi$
$42$	−4.39297e15	−1.66683
$43$	−3.26437e15	−0.990487	−0.495244	−	0.868754i	$-0.664921\pi$
$43$	−3.26437e15	−0.990487	−0.495244	+	0.868754i	$0.664921\pi$
$44$	4.11796e14	0.100434
$45$	−6.44274e15	−1.26926
$46$	8.30844e15	1.32837
$47$	1.11913e15	0.145865
$47$	1.11913e15	0.145865
$48$	1.60571e16	1.71347
$49$	2.67167e14	0.0234379
$50$	1.69686e16	1.22866
$51$	1.84419e16	1.10634
$52$	6.06653e15	0.302627
$53$	−3.46454e15	−0.144220	−0.0721099	−	0.997397i	$-0.522973\pi$
$53$	−3.46454e15	−0.144220	−0.0721099	+	0.997397i	$0.522973\pi$
$54$	5.11486e15	0.178276
$55$	−1.12240e16	−0.328626
$56$	−2.77528e16	−0.684731
$57$	−8.11004e16	−1.69127
$58$	4.80005e16	0.848554
$59$	4.77881e16	0.718168	0.359084	−	0.933305i	$-0.383089\pi$
$59$	4.77881e16	0.718168	0.359084	+	0.933305i	$0.383089\pi$
$60$	6.64697e16	0.851504
$61$	−1.80870e17	−1.98031	−0.990154	−	0.139982i	$-0.955295\pi$
$61$	−1.80870e17	−1.98031	−0.990154	+	0.139982i	$0.955295\pi$
$62$	−8.03943e16	−0.754231
$63$	1.11952e17	0.902189
$64$	3.87549e16	0.268916
$65$	−1.65350e17	−0.990212
$66$	−7.34419e16	−0.380432
$67$	−2.98219e17	−1.33913	−0.669567	−	0.742752i	$-0.733520\pi$
$67$	−2.98219e17	−1.33913	−0.669567	+	0.742752i	$0.733520\pi$
$68$	−8.96913e16	−0.349877
$69$	−4.49161e17	−1.52523
$70$	−5.82330e17	−1.72480
$71$	−6.99366e17	−1.81030	−0.905149	−	0.425094i	$-0.860241\pi$
$71$	−6.99366e17	−1.81030	−0.905149	+	0.425094i	$0.860241\pi$
$72$	−2.66327e17	−0.603610
$73$	−1.26648e17	−0.251785	−0.125893	−	0.992044i	$-0.540179\pi$
$73$	−1.26648e17	−0.251785	−0.125893	+	0.992044i	$0.540179\pi$
$74$	5.29769e17	0.925519
$75$	−9.17336e17	−1.41074
$76$	3.94429e17	0.534859
$77$	1.95034e17	0.233586
$78$	−1.08194e18	−1.14631
$79$	1.04635e18	0.982241	0.491120	−	0.871092i	$-0.336588\pi$
$79$	1.04635e18	0.982241	0.491120	+	0.871092i	$0.336588\pi$
$80$	2.12852e18	1.77306
$81$	−1.48120e18	−1.09649
$82$	7.01660e17	0.462269
$83$	−1.69272e18	−0.993903	−0.496952	−	0.867778i	$-0.665547\pi$
$83$	−1.69272e18	−0.993903	−0.496952	+	0.867778i	$0.665547\pi$
$84$	−1.15501e18	−0.605247
$85$	2.44464e18	1.14482
$86$	−2.83143e18	−1.18651
$87$	−2.59494e18	−0.974305
$88$	−4.63972e17	−0.156281
$89$	4.34956e18	1.31595	0.657977	−	0.753038i	$-0.271412\pi$
$89$	4.34956e18	1.31595	0.657977	+	0.753038i	$0.271412\pi$
$90$	−5.58827e18	−1.52046
$91$	2.87321e18	0.703841
$92$	2.18448e18	0.482351
$93$	4.34618e18	0.866003
$94$	9.70706e17	0.174732
$95$	−1.07506e19	−1.75008
$96$	7.61066e18	1.12162
$97$	2.70199e18	0.360872	0.180436	−	0.983587i	$-0.442249\pi$
$97$	2.70199e18	0.360872	0.180436	+	0.983587i	$0.442249\pi$
$98$	2.31734e17	0.0280764
$99$	1.87162e18	0.205913
$100$	4.46143e18	0.446143
$101$	−1.38338e18	−0.125860	−0.0629301	−	0.998018i	$-0.520045\pi$
$101$	−1.38338e18	−0.125860	−0.0629301	+	0.998018i	$0.520045\pi$
$102$	1.59960e19	1.32529
$103$	1.70792e19	1.28978	0.644888	−	0.764277i	$-0.276904\pi$
$103$	1.70792e19	1.28978	0.644888	+	0.764277i	$0.276904\pi$
$104$	−6.83518e18	−0.470905
$105$	3.14812e19	1.98040
$106$	−3.00506e18	−0.172762
$107$	−5.98939e18	−0.314947	−0.157473	−	0.987523i	$-0.550335\pi$
$107$	−5.98939e18	−0.314947	−0.157473	+	0.987523i	$0.550335\pi$
$108$	1.34481e18	0.0647344
$109$	1.78856e19	0.788771	0.394386	−	0.918945i	$-0.370957\pi$
$109$	1.78856e19	0.788771	0.394386	+	0.918945i	$0.370957\pi$
$110$	−9.73541e18	−0.393662
$111$	−2.86397e19	−1.06267
$112$	−3.69863e19	−1.26029
$113$	8.24628e18	0.258234	0.129117	−	0.991629i	$-0.458786\pi$
$113$	8.24628e18	0.258234	0.129117	+	0.991629i	$0.458786\pi$
$114$	−7.03445e19	−2.02598
$115$	−5.95405e19	−1.57828
$116$	1.26204e19	0.308122
$117$	2.75725e19	0.620455
$118$	4.14502e19	0.860296
$119$	−4.24793e19	−0.813732
$120$	−7.48917e19	−1.32499
$121$	−5.78985e19	−0.946687
$122$	−1.56882e20	−2.37222
$123$	−3.79323e19	−0.530775
$124$	−2.11375e19	−0.273871
$125$	−3.04374e18	−0.0365395
$126$	9.71046e19	1.08074
$127$	−4.39376e19	−0.453629	−0.226814	−	0.973938i	$-0.572831\pi$
$127$	−4.39376e19	−0.453629	−0.226814	+	0.973938i	$0.572831\pi$
$128$	1.18710e20	1.13761
$129$	1.53070e20	1.36234
$130$	−1.43421e20	−1.18618
$131$	1.68264e20	1.29394	0.646969	−	0.762517i	$-0.276036\pi$
$131$	1.68264e20	1.29394	0.646969	+	0.762517i	$0.276036\pi$
$132$	−1.93095e19	−0.138140
$133$	1.86808e20	1.24396
$134$	−2.58668e20	−1.60416
$135$	−3.66544e19	−0.211814
$136$	1.01055e20	0.544428
$137$	2.17398e20	1.09247	0.546235	−	0.837632i	$-0.316061\pi$
$137$	2.17398e20	1.09247	0.546235	+	0.837632i	$0.316061\pi$
$138$	−3.89591e20	−1.82708
$139$	−1.87061e20	−0.819109	−0.409555	−	0.912286i	$-0.634316\pi$
$139$	−1.87061e20	−0.819109	−0.409555	+	0.912286i	$0.634316\pi$
$140$	−1.53108e20	−0.626297
$141$	−5.24771e19	−0.200627
$142$	−6.06613e20	−2.16856
$143$	4.80344e19	0.160642
$144$	−3.54935e20	−1.11098
$145$	−3.43984e20	−1.00819
$146$	−1.09851e20	−0.301615
$147$	−1.25277e19	−0.0322372
$148$	1.39288e20	0.336068
$149$	−2.82917e20	−0.640310	−0.320155	−	0.947365i	$-0.603735\pi$
$149$	−2.82917e20	−0.640310	−0.320155	+	0.947365i	$0.603735\pi$
$150$	−7.95675e20	−1.68993
$151$	−1.74244e20	−0.347438	−0.173719	−	0.984795i	$-0.555578\pi$
$151$	−1.74244e20	−0.347438	−0.173719	+	0.984795i	$0.555578\pi$
$152$	−4.44404e20	−0.832269
$153$	−4.07649e20	−0.717327
$154$	1.69167e20	0.279814
$155$	5.76127e20	0.896121
$156$	−2.84465e20	−0.416242
$157$	6.15346e20	0.847369	0.423684	−	0.905810i	$-0.360737\pi$
$157$	6.15346e20	0.847369	0.423684	+	0.905810i	$0.360737\pi$
$158$	9.07575e20	1.17663
$159$	1.62456e20	0.198364
$160$	1.00886e21	1.16063
$161$	1.03461e21	1.12183
$162$	−1.28476e21	−1.31350
$163$	−1.64518e21	−1.58646	−0.793232	−	0.608920i	$-0.791603\pi$
$163$	−1.64518e21	−1.58646	−0.793232	+	0.608920i	$0.791603\pi$
$164$	1.84482e20	0.167856
$165$	5.26304e20	0.452001
$166$	−1.46823e21	−1.19060
$167$	−2.13855e21	−1.63800	−0.819000	−	0.573794i	$-0.805471\pi$
$167$	−2.13855e21	−1.63800	−0.819000	+	0.573794i	$0.805471\pi$
$168$	1.30136e21	0.941798
$169$	−7.54283e20	−0.515954
$170$	2.12042e21	1.37138
$171$	1.79269e21	1.09658
$172$	−7.44447e20	−0.430838
$173$	3.68982e20	0.202100	0.101050	−	0.994881i	$-0.467780\pi$
$173$	3.68982e20	0.202100	0.101050	+	0.994881i	$0.467780\pi$
$174$	−2.25079e21	−1.16712
$175$	2.11301e21	1.03762
$176$	−6.18338e20	−0.287644
$177$	−2.24083e21	−0.987787
$178$	3.77271e21	1.57639
$179$	−6.55011e20	−0.259504	−0.129752	−	0.991546i	$-0.541418\pi$
$179$	−6.55011e20	−0.259504	−0.129752	+	0.991546i	$0.541418\pi$
$180$	−1.46928e21	−0.552098
$181$	−2.72757e21	−0.972366	−0.486183	−	0.873857i	$-0.661611\pi$
$181$	−2.72757e21	−0.972366	−0.486183	+	0.873857i	$0.661611\pi$
$182$	2.49215e21	0.843134
$183$	8.48117e21	2.72377
$184$	−2.46126e21	−0.750564
$185$	−3.79646e21	−1.09963
$186$	3.76977e21	1.03739
$187$	−7.10171e20	−0.185724
$188$	2.55220e20	0.0634477
$189$	6.36925e20	0.150557
$190$	−9.32482e21	−2.09643
$191$	3.23124e21	0.691118	0.345559	−	0.938397i	$-0.387689\pi$
$191$	3.23124e21	0.691118	0.345559	+	0.938397i	$0.387689\pi$
$192$	−1.81726e21	−0.369874
$193$	3.58557e19	0.00694647	0.00347323	−	0.999994i	$-0.498894\pi$
$193$	3.58557e19	0.00694647	0.00347323	+	0.999994i	$0.498894\pi$
$194$	2.34364e21	0.432290
$195$	7.75344e21	1.36196
$196$	6.09280e19	0.0101949
$197$	1.46193e21	0.233077	0.116538	−	0.993186i	$-0.462820\pi$
$197$	1.46193e21	0.233077	0.116538	+	0.993186i	$0.462820\pi$
$198$	1.62340e21	0.246664
$199$	−8.98993e21	−1.30212	−0.651062	−	0.759025i	$-0.725676\pi$
$199$	−8.98993e21	−1.30212	−0.651062	+	0.759025i	$0.725676\pi$
$200$	−5.02671e21	−0.694222
$201$	1.39838e22	1.84188
$202$	−1.19991e21	−0.150769
$203$	5.97724e21	0.716619
$204$	4.20571e21	0.481230
$205$	−5.02828e21	−0.549234
$206$	1.48141e22	1.54503
$207$	9.92849e21	0.988928
$208$	−9.10927e21	−0.866726
$209$	3.12307e21	0.283917
$210$	2.73060e22	2.37233
$211$	−1.91522e22	−1.59051	−0.795253	−	0.606278i	$-0.792662\pi$
$211$	−1.91522e22	−1.59051	−0.795253	+	0.606278i	$0.792662\pi$
$212$	−7.90097e20	−0.0627321
$213$	3.27940e22	2.48993
$214$	−5.19505e21	−0.377276
$215$	2.02908e22	1.40972
$216$	−1.51520e21	−0.100730
$217$	−1.00111e22	−0.636961
$218$	1.55135e22	0.944873
$219$	5.93864e21	0.346312
$220$	−2.55966e21	−0.142944
$221$	−1.04621e22	−0.559621
$222$	−2.48414e22	−1.27298
$223$	−1.31218e22	−0.644316	−0.322158	−	0.946686i	$-0.604408\pi$
$223$	−1.31218e22	−0.644316	−0.322158	+	0.946686i	$0.604408\pi$
$224$	−1.75305e22	−0.824971
$225$	2.02773e22	0.914694
$226$	7.15262e21	0.309339
$227$	3.34516e22	1.38730	0.693651	−	0.720311i	$-0.256001\pi$
$227$	3.34516e22	1.38730	0.693651	+	0.720311i	$0.256001\pi$
$228$	−1.84951e22	−0.735659
$229$	1.36372e22	0.520341	0.260171	−	0.965563i	$-0.416221\pi$
$229$	1.36372e22	0.520341	0.260171	+	0.965563i	$0.416221\pi$
$230$	−5.16439e22	−1.89062
$231$	−9.14532e21	−0.321281
$232$	−1.42194e22	−0.479454
$233$	−3.84387e21	−0.124419	−0.0622097	−	0.998063i	$-0.519815\pi$
$233$	−3.84387e21	−0.124419	−0.0622097	+	0.998063i	$0.519815\pi$
$234$	2.39157e22	0.743246
$235$	−6.95633e21	−0.207604
$236$	1.08982e22	0.312385
$237$	−4.90642e22	−1.35100
$238$	−3.68455e22	−0.974773
$239$	−4.48741e21	−0.114082	−0.0570408	−	0.998372i	$-0.518166\pi$
$239$	−4.48741e21	−0.114082	−0.0570408	+	0.998372i	$0.518166\pi$
$240$	−9.98085e22	−2.43871
$241$	5.78103e22	1.35782	0.678912	−	0.734220i	$-0.262452\pi$
$241$	5.78103e22	1.35782	0.678912	+	0.734220i	$0.262452\pi$
$242$	−5.02198e22	−1.13404
$243$	6.26012e22	1.35932
$244$	−4.12478e22	−0.861385
$245$	−1.66066e21	−0.0333583
$246$	−3.29015e22	−0.635817
$247$	4.60086e22	0.855496
$248$	2.38157e22	0.426159
$249$	7.93735e22	1.36704
$250$	−2.64006e21	−0.0437708
$251$	9.50014e22	1.51646	0.758228	−	0.651990i	$-0.226066\pi$
$251$	9.50014e22	1.51646	0.758228	+	0.651990i	$0.226066\pi$
$252$	2.55310e22	0.392430
$253$	1.72966e22	0.256044
$254$	−3.81104e22	−0.543404
$255$	−1.14632e23	−1.57461
$256$	8.26473e22	1.09383
$257$	−1.01342e23	−1.29249	−0.646243	−	0.763132i	$-0.723661\pi$
$257$	−1.01342e23	−1.29249	−0.646243	+	0.763132i	$0.723661\pi$
$258$	1.32769e23	1.63196
$259$	6.59692e22	0.781616
$260$	−3.77085e22	−0.430718
$261$	5.73600e22	0.631719
$262$	1.45948e23	1.55001
$263$	1.75126e22	0.179379	0.0896895	−	0.995970i	$-0.471413\pi$
$263$	1.75126e22	0.179379	0.0896895	+	0.995970i	$0.471413\pi$
$264$	2.17561e22	0.214953
$265$	2.15350e22	0.205262
$266$	1.62033e23	1.49014
$267$	−2.03955e23	−1.81000
$268$	−6.80095e22	−0.582491
$269$	7.96301e22	0.658310	0.329155	−	0.944276i	$-0.393236\pi$
$269$	7.96301e22	0.658310	0.329155	+	0.944276i	$0.393236\pi$
$270$	−3.17931e22	−0.253733
$271$	−6.36562e22	−0.490493	−0.245246	−	0.969461i	$-0.578869\pi$
$271$	−6.36562e22	−0.490493	−0.245246	+	0.969461i	$0.578869\pi$
$272$	1.34677e23	1.00205
$273$	−1.34728e23	−0.968081
$274$	1.88565e23	1.30868
$275$	3.53253e22	0.236824
$276$	−1.02432e23	−0.663438
$277$	−2.48953e23	−1.55797	−0.778986	−	0.627041i	$-0.784266\pi$
$277$	−2.48953e23	−1.55797	−0.778986	+	0.627041i	$0.784266\pi$
$278$	−1.62252e23	−0.981215
$279$	−9.60702e22	−0.561499
$280$	1.72507e23	0.974552
$281$	−1.07944e23	−0.589507	−0.294753	−	0.955573i	$-0.595237\pi$
$281$	−1.07944e23	−0.589507	−0.294753	+	0.955573i	$0.595237\pi$
$282$	−4.55174e22	−0.240332
$283$	−2.42254e22	−0.123680	−0.0618401	−	0.998086i	$-0.519697\pi$
$283$	−2.42254e22	−0.123680	−0.0618401	+	0.998086i	$0.519697\pi$
$284$	−1.59492e23	−0.787435
$285$	5.04107e23	2.40711
$286$	4.16639e22	0.192434
$287$	8.73739e22	0.390394
$288$	−1.68230e23	−0.727235
$289$	−8.43936e22	−0.353004
$290$	−2.98363e23	−1.20771
$291$	−1.26699e23	−0.496353
$292$	−2.88823e22	−0.109520
$293$	1.41996e23	0.521234	0.260617	−	0.965442i	$-0.416074\pi$
$293$	1.41996e23	0.521234	0.260617	+	0.965442i	$0.416074\pi$
$294$	−1.08662e22	−0.0386170
$295$	−2.97043e23	−1.02214
$296$	−1.56936e23	−0.522941
$297$	1.06481e22	0.0343627
$298$	−2.45396e23	−0.767030
$299$	2.54811e23	0.771510
$300$	−2.09201e23	−0.613636
$301$	−3.52583e23	−1.00203
$302$	−1.51135e23	−0.416197
$303$	6.48681e22	0.173112
$304$	−5.92259e23	−1.53184
$305$	1.12426e24	2.81850
$306$	−3.53585e23	−0.859290
$307$	−6.01961e23	−1.41825	−0.709126	−	0.705081i	$-0.750910\pi$
$307$	−6.01961e23	−1.41825	−0.709126	+	0.705081i	$0.750910\pi$
$308$	4.44779e22	0.101604
$309$	−8.00862e23	−1.77399
$310$	4.99718e23	1.07347
$311$	−3.16273e23	−0.658929	−0.329465	−	0.944168i	$-0.606868\pi$
$311$	−3.16273e23	−0.658929	−0.329465	+	0.944168i	$0.606868\pi$
$312$	3.20508e23	0.647695
$313$	−7.85003e23	−1.53886	−0.769432	−	0.638729i	$-0.779460\pi$
$313$	−7.85003e23	−1.53886	−0.769432	+	0.638729i	$0.779460\pi$
$314$	5.33736e23	1.01507
$315$	−6.95877e23	−1.28405
$316$	2.38622e23	0.427251
$317$	3.36671e23	0.584982	0.292491	−	0.956268i	$-0.405516\pi$
$317$	3.36671e23	0.584982	0.292491	+	0.956268i	$0.405516\pi$
$318$	1.40910e23	0.237621
$319$	9.99277e22	0.163559
$320$	−2.40894e23	−0.382738
$321$	2.80849e23	0.433186
$322$	8.97391e23	1.34385
$323$	−6.80220e23	−0.989066
$324$	−3.37791e23	−0.476948
$325$	5.20409e23	0.713596
$326$	−1.42699e24	−1.90043
$327$	−8.38672e23	−1.08490
$328$	−2.07857e23	−0.261193
$329$	1.20877e23	0.147564
$330$	4.56503e23	0.541454
$331$	−3.44715e23	−0.397277	−0.198639	−	0.980073i	$-0.563652\pi$
$331$	−3.44715e23	−0.397277	−0.198639	+	0.980073i	$0.563652\pi$
$332$	−3.86030e23	−0.432324
$333$	6.33067e23	0.689017
$334$	−1.85493e24	−1.96217
$335$	1.85368e24	1.90594
$336$	1.73432e24	1.73343
$337$	−9.64620e23	−0.937287	−0.468643	−	0.883388i	$-0.655257\pi$
$337$	−9.64620e23	−0.937287	−0.468643	+	0.883388i	$0.655257\pi$
$338$	−6.54247e23	−0.618063
$339$	−3.86676e23	−0.355181
$340$	5.57506e23	0.497967
$341$	−1.67365e23	−0.145378
$342$	1.55493e24	1.31360
$343$	−1.20233e24	−0.987940
$344$	8.38772e23	0.670407
$345$	2.79191e24	2.17080
$346$	3.20046e23	0.242097
$347$	−1.49574e24	−1.10084	−0.550422	−	0.834886i	$-0.685533\pi$
$347$	−1.49574e24	−1.10084	−0.550422	+	0.834886i	$0.685533\pi$
$348$	−5.91783e23	−0.423799
$349$	3.98597e22	0.0277775	0.0138887	−	0.999904i	$-0.495579\pi$
$349$	3.98597e22	0.0277775	0.0138887	+	0.999904i	$0.495579\pi$
$350$	1.83277e24	1.24297
$351$	1.56867e23	0.103541
$352$	−2.93076e23	−0.188289
$353$	1.77339e24	1.10903	0.554517	−	0.832172i	$-0.312903\pi$
$353$	1.77339e24	1.10903	0.554517	+	0.832172i	$0.312903\pi$
$354$	−1.94364e24	−1.18327
$355$	4.34715e24	2.57653
$356$	9.91929e23	0.572408
$357$	1.99190e24	1.11923
$358$	−5.68141e23	−0.310862
$359$	2.03419e24	1.08391	0.541957	−	0.840406i	$-0.317684\pi$
$359$	2.03419e24	1.08391	0.541957	+	0.840406i	$0.317684\pi$
$360$	1.65544e24	0.859095
$361$	1.01293e24	0.511990
$362$	−2.36583e24	−1.16480
$363$	2.71492e24	1.30210
$364$	6.55243e23	0.306153
$365$	7.87222e23	0.358356
$366$	7.35636e24	3.26281
$367$	−1.85065e24	−0.799827	−0.399914	−	0.916553i	$-0.630960\pi$
$367$	−1.85065e24	−0.799827	−0.399914	+	0.916553i	$0.630960\pi$
$368$	−3.28013e24	−1.38145
$369$	8.38475e23	0.344143
$370$	−3.29296e24	−1.31725
$371$	−3.74203e23	−0.145900
$372$	9.91156e23	0.376690
$373$	4.74865e24	1.75928	0.879642	−	0.475637i	$-0.157782\pi$
$373$	4.74865e24	1.75928	0.879642	+	0.475637i	$0.157782\pi$
$374$	−6.15985e23	−0.222479
$375$	1.42724e23	0.0502574
$376$	−2.87558e23	−0.0987281
$377$	1.47212e24	0.492834
$378$	5.52453e23	0.180353
$379$	4.58320e24	1.45914	0.729568	−	0.683908i	$-0.239721\pi$
$379$	4.58320e24	1.45914	0.729568	+	0.683908i	$0.239721\pi$
$380$	−2.45170e24	−0.761244
$381$	2.06028e24	0.623933
$382$	2.80270e24	0.827894
$383$	−3.51015e23	−0.101143	−0.0505717	−	0.998720i	$-0.516104\pi$
$383$	−3.51015e23	−0.101143	−0.0505717	+	0.998720i	$0.516104\pi$
$384$	−5.56642e24	−1.56469
$385$	−1.21230e24	−0.332455
$386$	3.11004e22	0.00832120
$387$	−3.38353e24	−0.883315
$388$	6.16196e23	0.156970
$389$	−2.95614e24	−0.734858	−0.367429	−	0.930052i	$-0.619762\pi$
$389$	−2.95614e24	−0.734858	−0.367429	+	0.930052i	$0.619762\pi$
$390$	6.72514e24	1.63150
$391$	−3.76728e24	−0.891967
$392$	−6.86478e22	−0.0158639
$393$	−7.89005e24	−1.77972
$394$	1.26805e24	0.279204
$395$	−6.50392e24	−1.39799
$396$	4.26828e23	0.0895671
$397$	−3.35791e24	−0.687954	−0.343977	−	0.938978i	$-0.611774\pi$
$397$	−3.35791e24	−0.687954	−0.343977	+	0.938978i	$0.611774\pi$
$398$	−7.79764e24	−1.55982
$399$	−8.75962e24	−1.71097
$400$	−6.69911e24	−1.27775
$401$	−1.00872e25	−1.87889	−0.939443	−	0.342704i	$-0.888657\pi$
$401$	−1.00872e25	−1.87889	−0.939443	+	0.342704i	$0.888657\pi$
$402$	1.21292e25	2.20640
$403$	−2.46560e24	−0.438052
$404$	−3.15483e23	−0.0547461
$405$	9.20690e24	1.56060
$406$	5.18451e24	0.858441
$407$	1.10288e24	0.178394
$408$	−4.73859e24	−0.748820
$409$	−1.25329e25	−1.93500	−0.967500	−	0.252870i	$-0.918625\pi$
$409$	−1.25329e25	−1.93500	−0.967500	+	0.252870i	$0.918625\pi$
$410$	−4.36140e24	−0.657930
$411$	−1.01940e25	−1.50261
$412$	3.89496e24	0.561021
$413$	5.16157e24	0.726535
$414$	8.61173e24	1.18464
$415$	1.05217e25	1.41458
$416$	−4.31756e24	−0.567351
$417$	8.77146e24	1.12662
$418$	2.70887e24	0.340105
$419$	5.18528e24	0.636412	0.318206	−	0.948022i	$-0.396920\pi$
$419$	5.18528e24	0.636412	0.318206	+	0.948022i	$0.396920\pi$
$420$	7.17936e24	0.861425
$421$	4.26585e24	0.500410	0.250205	−	0.968193i	$-0.419502\pi$
$421$	4.26585e24	0.500410	0.250205	+	0.968193i	$0.419502\pi$
$422$	−1.66121e25	−1.90527
$423$	1.15998e24	0.130082
$424$	8.90205e23	0.0976145
$425$	−7.69404e24	−0.825011
$426$	2.84447e25	2.98270
$427$	−1.95357e25	−2.00338
$428$	−1.36590e24	−0.136994
$429$	−2.25238e24	−0.220952
$430$	1.75997e25	1.68871
$431$	−1.62111e25	−1.52152	−0.760761	−	0.649032i	$-0.775174\pi$
$431$	−1.62111e25	−1.52152	−0.760761	+	0.649032i	$0.775174\pi$
$432$	−2.01932e24	−0.185400
$433$	1.79221e24	0.160973	0.0804864	−	0.996756i	$-0.474353\pi$
$433$	1.79221e24	0.160973	0.0804864	+	0.996756i	$0.474353\pi$
$434$	−8.68335e24	−0.763018
$435$	1.61297e25	1.38669
$436$	4.07885e24	0.343096
$437$	1.65671e25	1.36355
$438$	5.15103e24	0.414849
$439$	−2.37966e25	−1.87543	−0.937716	−	0.347402i	$-0.887064\pi$
$439$	−2.37966e25	−1.87543	−0.937716	+	0.347402i	$0.887064\pi$
$440$	2.88398e24	0.222429
$441$	2.76919e23	0.0209019
$442$	−9.07461e24	−0.670373
$443$	−2.29791e25	−1.66149	−0.830746	−	0.556651i	$-0.812086\pi$
$443$	−2.29791e25	−1.66149	−0.830746	+	0.556651i	$0.812086\pi$
$444$	−6.53136e24	−0.462237
$445$	−2.70362e25	−1.87295
$446$	−1.13816e25	−0.771829
$447$	1.32663e25	0.880699
$448$	4.18590e24	0.272049
$449$	−1.30364e25	−0.829499	−0.414749	−	0.909936i	$-0.636131\pi$
$449$	−1.30364e25	−0.829499	−0.414749	+	0.909936i	$0.636131\pi$
$450$	1.75880e25	1.09572
$451$	1.46072e24	0.0891024
$452$	1.88058e24	0.112325
$453$	8.17048e24	0.477875
$454$	2.90151e25	1.66186
$455$	−1.78594e25	−1.00175
$456$	2.08385e25	1.14473
$457$	2.40851e25	1.29582	0.647909	−	0.761718i	$-0.275644\pi$
$457$	2.40851e25	1.29582	0.647909	+	0.761718i	$0.275644\pi$
$458$	1.18286e25	0.623319
$459$	−2.31922e24	−0.119707
$460$	−1.35783e25	−0.686511
$461$	1.13153e25	0.560413	0.280206	−	0.959940i	$-0.409597\pi$
$461$	1.13153e25	0.560413	0.280206	+	0.959940i	$0.409597\pi$
$462$	−7.93243e24	−0.384864
$463$	−2.75259e25	−1.30835	−0.654173	−	0.756345i	$-0.726983\pi$
$463$	−2.75259e25	−1.30835	−0.654173	+	0.756345i	$0.726983\pi$
$464$	−1.89503e25	−0.882462
$465$	−2.70151e25	−1.23255
$466$	−3.33408e24	−0.149042
$467$	1.52699e25	0.668848	0.334424	−	0.942423i	$-0.391458\pi$
$467$	1.52699e25	0.668848	0.334424	+	0.942423i	$0.391458\pi$
$468$	6.28797e24	0.269883
$469$	−3.22105e25	−1.35474
$470$	−6.03375e24	−0.248690
$471$	−2.88542e25	−1.16549
$472$	−1.22790e25	−0.486089
$473$	−5.89450e24	−0.228700
$474$	−4.25571e25	−1.61837
$475$	3.38355e25	1.26120
$476$	−9.68751e24	−0.353954
$477$	−3.59101e24	−0.128615
$478$	−3.89227e24	−0.136659
$479$	−6.01023e24	−0.206873	−0.103437	−	0.994636i	$-0.532984\pi$
$479$	−6.01023e24	−0.206873	−0.103437	+	0.994636i	$0.532984\pi$
$480$	−4.73066e25	−1.59636
$481$	1.62474e25	0.537535
$482$	5.01432e25	1.62654
$483$	−4.85137e25	−1.54300
$484$	−1.32039e25	−0.411786
$485$	−1.67952e25	−0.513615
$486$	5.42987e25	1.62834
$487$	1.31006e25	0.385272	0.192636	−	0.981270i	$-0.438296\pi$
$487$	1.31006e25	0.385272	0.192636	+	0.981270i	$0.438296\pi$
$488$	4.64741e25	1.34036
$489$	7.71439e25	2.18206
$490$	−1.44042e24	−0.0399601
$491$	3.44205e25	0.936576	0.468288	−	0.883576i	$-0.344871\pi$
$491$	3.44205e25	0.936576	0.468288	+	0.883576i	$0.344871\pi$
$492$	−8.65055e24	−0.230874
$493$	−2.17648e25	−0.569781
$494$	3.99067e25	1.02480
$495$	−1.16337e25	−0.293068
$496$	3.17392e25	0.784369
$497$	−7.55382e25	−1.83139
$498$	6.88466e25	1.63758
$499$	−1.19681e25	−0.279300	−0.139650	−	0.990201i	$-0.544598\pi$
$499$	−1.19681e25	−0.279300	−0.139650	+	0.990201i	$0.544598\pi$
$500$	−6.94132e23	−0.0158938
$501$	1.00279e26	2.25295
$502$	8.24019e25	1.81657
$503$	9.51180e24	0.205763	0.102881	−	0.994694i	$-0.467194\pi$
$503$	9.51180e24	0.205763	0.102881	+	0.994694i	$0.467194\pi$
$504$	−2.87658e25	−0.610643
$505$	8.59887e24	0.179132
$506$	1.50026e25	0.306717
$507$	3.53691e25	0.709656
$508$	−1.00201e25	−0.197317
$509$	−9.73568e25	−1.88169	−0.940844	−	0.338841i	$-0.889965\pi$
$509$	−9.73568e25	−1.88169	−0.940844	+	0.338841i	$0.889965\pi$
$510$	−9.94287e25	−1.88623
$511$	−1.36792e25	−0.254719
$512$	9.44810e24	0.172695
$513$	1.01991e25	0.182997
$514$	−8.79017e25	−1.54827
$515$	−1.06162e26	−1.83569
$516$	3.49079e25	0.592586
$517$	2.02082e24	0.0336797
$518$	5.72201e25	0.936302
$519$	−1.73019e25	−0.277974
$520$	4.24864e25	0.670221
$521$	−2.16082e25	−0.334704	−0.167352	−	0.985897i	$-0.553522\pi$
$521$	−2.16082e25	−0.334704	−0.167352	+	0.985897i	$0.553522\pi$
$522$	4.97526e25	0.756739
$523$	5.60889e25	0.837743	0.418871	−	0.908046i	$-0.362426\pi$
$523$	5.60889e25	0.837743	0.418871	+	0.908046i	$0.362426\pi$
$524$	3.83730e25	0.562831
$525$	−9.90810e25	−1.42717
$526$	1.51900e25	0.214879
$527$	3.64530e25	0.506446
$528$	2.89945e25	0.395633
$529$	1.71385e25	0.229691
$530$	1.86790e25	0.245885
$531$	4.95325e25	0.640461
$532$	4.26020e25	0.541091
$533$	2.15191e25	0.268483
$534$	−1.76906e26	−2.16821
$535$	3.72291e25	0.448251
$536$	7.66265e25	0.906387
$537$	3.07141e25	0.356929
$538$	6.90692e25	0.788592
$539$	4.82425e23	0.00541173
$540$	−8.35912e24	−0.0921340
$541$	−1.73640e26	−1.88051	−0.940255	−	0.340471i	$-0.889413\pi$
$541$	−1.73640e26	−1.88051	−0.940255	+	0.340471i	$0.889413\pi$
$542$	−5.52139e25	−0.587564
$543$	1.27899e26	1.33742
$544$	6.38335e25	0.655932
$545$	−1.11174e26	−1.12263
$546$	−1.16860e26	−1.15967
$547$	1.21853e26	1.18838	0.594192	−	0.804323i	$-0.297472\pi$
$547$	1.21853e26	1.18838	0.594192	+	0.804323i	$0.297472\pi$
$548$	4.95781e25	0.475198
$549$	−1.87472e26	−1.76604
$550$	3.06403e25	0.283693
$551$	9.57132e25	0.871027
$552$	1.15411e26	1.03235
$553$	1.13015e26	0.993685
$554$	−2.15936e26	−1.86630
$555$	1.78020e26	1.51246
$556$	−4.26596e25	−0.356292
$557$	5.48692e25	0.450510	0.225255	−	0.974300i	$-0.427678\pi$
$557$	5.48692e25	0.450510	0.225255	+	0.974300i	$0.427678\pi$
$558$	−8.33290e25	−0.672622
$559$	−8.68370e25	−0.689116
$560$	2.29901e26	1.79372
$561$	3.33006e25	0.255449
$562$	−9.36281e25	−0.706173
$563$	−2.07339e26	−1.53763	−0.768815	−	0.639471i	$-0.779153\pi$
$563$	−2.07339e26	−1.53763	−0.768815	+	0.639471i	$0.779153\pi$
$564$	−1.19675e25	−0.0872677
$565$	−5.12575e25	−0.367534
$566$	−2.10125e25	−0.148157
$567$	−1.59984e26	−1.10927
$568$	1.79700e26	1.22529
$569$	1.81712e26	1.21848	0.609238	−	0.792987i	$-0.291475\pi$
$569$	1.81712e26	1.21848	0.609238	+	0.792987i	$0.291475\pi$
$570$	4.37250e26	2.88349
$571$	−8.01699e25	−0.519958	−0.259979	−	0.965614i	$-0.583716\pi$
$571$	−8.01699e25	−0.519958	−0.259979	+	0.965614i	$0.583716\pi$
$572$	1.09544e25	0.0698755
$573$	−1.51516e26	−0.950583
$574$	7.57860e25	0.467655
$575$	1.87392e26	1.13738
$576$	4.01696e25	0.239819
$577$	1.25572e25	0.0737431	0.0368715	−	0.999320i	$-0.488261\pi$
$577$	1.25572e25	0.0737431	0.0368715	+	0.999320i	$0.488261\pi$
$578$	−7.32010e25	−0.422866
$579$	−1.68131e24	−0.00955435
$580$	−7.84464e25	−0.438538
$581$	−1.82830e26	−1.00548
$582$	−1.09896e26	−0.594583
$583$	−6.25595e24	−0.0332998
$584$	3.25418e25	0.170420
$585$	−1.71386e26	−0.883070
$586$	1.23164e26	0.624389
$587$	8.05884e25	0.401986	0.200993	−	0.979593i	$-0.435583\pi$
$587$	8.05884e25	0.401986	0.200993	+	0.979593i	$0.435583\pi$
$588$	−2.85697e24	−0.0140224
$589$	−1.60307e26	−0.774206
$590$	−2.57648e26	−1.22443
$591$	−6.85515e25	−0.320580
$592$	−2.09150e26	−0.962501
$593$	−1.78007e26	−0.806155	−0.403077	−	0.915166i	$-0.632059\pi$
$593$	−1.78007e26	−0.806155	−0.403077	+	0.915166i	$0.632059\pi$
$594$	9.23594e24	0.0411633
$595$	2.64045e26	1.15815
$596$	−6.45200e25	−0.278519
$597$	4.21547e26	1.79097
$598$	2.21017e26	0.924195
$599$	1.20491e26	0.495908	0.247954	−	0.968772i	$-0.420242\pi$
$599$	1.20491e26	0.495908	0.247954	+	0.968772i	$0.420242\pi$
$600$	2.35707e26	0.954852
$601$	1.40717e26	0.561100	0.280550	−	0.959839i	$-0.409483\pi$
$601$	1.40717e26	0.561100	0.280550	+	0.959839i	$0.409483\pi$
$602$	−3.05822e26	−1.20033
$603$	−3.09105e26	−1.19424
$604$	−3.97368e25	−0.151127
$605$	3.59888e26	1.34738
$606$	5.62650e25	0.207371
$607$	1.15624e25	0.0419523	0.0209761	−	0.999780i	$-0.493323\pi$
$607$	1.15624e25	0.0419523	0.0209761	+	0.999780i	$0.493323\pi$
$608$	−2.80716e26	−1.00273
$609$	−2.80279e26	−0.985656
$610$	9.75154e26	3.37629
$611$	2.97705e25	0.101483
$612$	−9.29653e25	−0.312020
$613$	−2.74343e26	−0.906608	−0.453304	−	0.891356i	$-0.649755\pi$
$613$	−2.74343e26	−0.906608	−0.453304	+	0.891356i	$0.649755\pi$
$614$	−5.22126e26	−1.69893
$615$	2.35781e26	0.755431
$616$	−5.01134e25	−0.158102
$617$	7.07896e25	0.219918	0.109959	−	0.993936i	$-0.464928\pi$
$617$	7.07896e25	0.219918	0.109959	+	0.993936i	$0.464928\pi$
$618$	−6.94648e26	−2.12507
$619$	5.46136e26	1.64528	0.822640	−	0.568563i	$-0.192500\pi$
$619$	5.46136e26	1.64528	0.822640	+	0.568563i	$0.192500\pi$
$620$	1.31387e26	0.389791
$621$	5.64857e25	0.165032
$622$	−2.74328e26	−0.789335
$623$	4.69795e26	1.33129
$624$	4.27143e26	1.19212
$625$	−3.54218e26	−0.973668
$626$	−6.80892e26	−1.84341
$627$	−1.46444e26	−0.390507
$628$	1.40331e26	0.368585
$629$	−2.40212e26	−0.621461
$630$	−6.03587e26	−1.53817
$631$	−6.50291e26	−1.63241	−0.816204	−	0.577764i	$-0.803926\pi$
$631$	−6.50291e26	−1.63241	−0.816204	+	0.577764i	$0.803926\pi$
$632$	−2.68856e26	−0.664825
$633$	8.98065e26	2.18762
$634$	2.92020e26	0.700753
$635$	2.73109e26	0.645633
$636$	3.70484e25	0.0862834
$637$	7.10702e24	0.0163066
$638$	8.66748e25	0.195928
$639$	−7.24895e26	−1.61442
$640$	−7.37881e26	−1.61911
$641$	4.23871e26	0.916394	0.458197	−	0.888851i	$-0.348495\pi$
$641$	4.23871e26	0.916394	0.458197	+	0.888851i	$0.348495\pi$
$642$	2.43601e26	0.518915
$643$	3.08686e26	0.647907	0.323953	−	0.946073i	$-0.394988\pi$
$643$	3.08686e26	0.647907	0.323953	+	0.946073i	$0.394988\pi$
$644$	2.35944e26	0.487971
$645$	−9.51455e26	−1.93897
$646$	−5.90006e26	−1.18481
$647$	−8.96012e26	−1.77306	−0.886530	−	0.462672i	$-0.846891\pi$
$647$	−8.96012e26	−1.77306	−0.886530	+	0.462672i	$0.846891\pi$
$648$	3.80591e26	0.742157
$649$	8.62914e25	0.165822
$650$	4.51390e26	0.854820
$651$	4.69429e26	0.876093
$652$	−3.75186e26	−0.690073
$653$	−4.59469e26	−0.832878	−0.416439	−	0.909164i	$-0.636722\pi$
$653$	−4.59469e26	−0.832878	−0.416439	+	0.909164i	$0.636722\pi$
$654$	−7.27444e26	−1.29960
$655$	−1.04590e27	−1.84161
$656$	−2.77011e26	−0.480741
$657$	−1.31271e26	−0.224542
$658$	1.04846e26	0.176768
$659$	−1.00071e27	−1.66302	−0.831509	−	0.555511i	$-0.812523\pi$
$659$	−1.00071e27	−1.66302	−0.831509	+	0.555511i	$0.812523\pi$
$660$	1.20025e26	0.196609
$661$	4.57973e26	0.739479	0.369739	−	0.929135i	$-0.379447\pi$
$661$	4.57973e26	0.739479	0.369739	+	0.929135i	$0.379447\pi$
$662$	−2.98997e26	−0.475900
$663$	4.90580e26	0.769718
$664$	4.34941e26	0.672719
$665$	−1.16117e27	−1.77048
$666$	5.49107e26	0.825376
$667$	5.30091e26	0.785517
$668$	−4.87702e26	−0.712490
$669$	6.15296e26	0.886209
$670$	1.60784e27	2.28313
$671$	−3.26598e26	−0.457246
$672$	8.22024e26	1.13469
$673$	9.65494e26	1.31403	0.657017	−	0.753876i	$-0.271818\pi$
$673$	9.65494e26	1.31403	0.657017	+	0.753876i	$0.271818\pi$
$674$	−8.36688e26	−1.12278
$675$	1.15363e26	0.152644
$676$	−1.72016e26	−0.224427
$677$	7.63793e26	0.982615	0.491307	−	0.870986i	$-0.336519\pi$
$677$	7.63793e26	0.982615	0.491307	+	0.870986i	$0.336519\pi$
$678$	−3.35393e26	−0.425473
$679$	2.91841e26	0.365076
$680$	−6.28145e26	−0.774863
$681$	−1.56858e27	−1.90813
$682$	−1.45169e26	−0.174149
$683$	1.20799e27	1.42912	0.714558	−	0.699576i	$-0.246628\pi$
$683$	1.20799e27	1.42912	0.714558	+	0.699576i	$0.246628\pi$
$684$	4.08826e26	0.476986
$685$	−1.35131e27	−1.55487
$686$	−1.04287e27	−1.18346
$687$	−6.39462e26	−0.715691
$688$	1.11783e27	1.23392
$689$	−9.21618e25	−0.100339
$690$	2.42164e27	2.60041
$691$	3.32434e26	0.352098	0.176049	−	0.984381i	$-0.443668\pi$
$691$	3.32434e26	0.352098	0.176049	+	0.984381i	$0.443668\pi$
$692$	8.41471e25	0.0879086
$693$	2.02153e26	0.208312
$694$	−1.29737e27	−1.31871
$695$	1.16274e27	1.16581
$696$	6.66764e26	0.659454
$697$	−3.18152e26	−0.310401
$698$	3.45734e25	0.0332748
$699$	1.80243e26	0.171130
$700$	4.81877e26	0.451341
$701$	−2.11074e27	−1.95035	−0.975177	−	0.221426i	$-0.928929\pi$
$701$	−2.11074e27	−1.95035	−0.975177	+	0.221426i	$0.928929\pi$
$702$	1.36063e26	0.124033
$703$	1.05636e27	0.950030
$704$	6.99800e25	0.0620917
$705$	3.26189e26	0.285544
$706$	1.53820e27	1.32852
$707$	−1.49418e26	−0.127327
$708$	−5.11027e26	−0.429663
$709$	−2.36248e27	−1.95988	−0.979938	−	0.199303i	$-0.936132\pi$
$709$	−2.36248e27	−1.95988	−0.979938	+	0.199303i	$0.936132\pi$
$710$	3.77061e27	3.08643
$711$	1.08454e27	0.875961
$712$	−1.11761e27	−0.890698
$713$	−8.87832e26	−0.698200
$714$	1.72772e27	1.34073
$715$	−2.98574e26	−0.228636
$716$	−1.49377e26	−0.112878
$717$	2.10419e26	0.156911
$718$	1.76441e27	1.29843
$719$	7.09586e26	0.515324	0.257662	−	0.966235i	$-0.417048\pi$
$719$	7.09586e26	0.515324	0.257662	+	0.966235i	$0.417048\pi$
$720$	2.20622e27	1.58121
$721$	1.84472e27	1.30480
$722$	8.78591e26	0.613315
$723$	−2.71078e27	−1.86759
$724$	−6.22029e26	−0.422955
$725$	1.08262e27	0.726551
$726$	2.35485e27	1.55979
$727$	1.08097e27	0.706704	0.353352	−	0.935490i	$-0.385042\pi$
$727$	1.08097e27	0.706704	0.353352	+	0.935490i	$0.385042\pi$
$728$	−7.38264e26	−0.476391
$729$	−1.21389e27	−0.773156
$730$	6.82817e26	0.429277
$731$	1.28385e27	0.796709
$732$	1.93415e27	1.18477
$733$	3.37569e26	0.204115	0.102057	−	0.994779i	$-0.467457\pi$
$733$	3.37569e26	0.204115	0.102057	+	0.994779i	$0.467457\pi$
$734$	−1.60521e27	−0.958117
$735$	7.78702e25	0.0458819
$736$	−1.55470e27	−0.904287
$737$	−5.38496e26	−0.309201
$738$	7.27273e26	0.412251
$739$	2.56582e27	1.43583	0.717916	−	0.696129i	$-0.245096\pi$
$739$	2.56582e27	1.43583	0.717916	+	0.696129i	$0.245096\pi$
$740$	−8.65792e26	−0.478313
$741$	−2.15739e27	−1.17667
$742$	−3.24575e26	−0.174774
$743$	−3.26302e27	−1.73471	−0.867354	−	0.497692i	$-0.834181\pi$
$743$	−3.26302e27	−1.73471	−0.867354	+	0.497692i	$0.834181\pi$
$744$	−1.11674e27	−0.586150
$745$	1.75857e27	0.911328
$746$	4.11886e27	2.10745
$747$	−1.75451e27	−0.886362
$748$	−1.61956e26	−0.0807853
$749$	−6.46912e26	−0.318616
$750$	1.23795e26	0.0602035
$751$	3.12820e27	1.50216	0.751079	−	0.660213i	$-0.229534\pi$
$751$	3.12820e27	1.50216	0.751079	+	0.660213i	$0.229534\pi$
$752$	−3.83230e26	−0.181714
$753$	−4.45471e27	−2.08577
$754$	1.27688e27	0.590368
$755$	1.08307e27	0.494495
$756$	1.45252e26	0.0654887
$757$	−1.07887e27	−0.480348	−0.240174	−	0.970730i	$-0.577205\pi$
$757$	−1.07887e27	−0.480348	−0.240174	+	0.970730i	$0.577205\pi$
$758$	3.97535e27	1.74791
$759$	−8.11053e26	−0.352170
$760$	2.76234e27	1.18454
$761$	−1.52236e27	−0.644708	−0.322354	−	0.946619i	$-0.604474\pi$
$761$	−1.52236e27	−0.644708	−0.322354	+	0.946619i	$0.604474\pi$
$762$	1.78703e27	0.747413
$763$	1.93181e27	0.797961
$764$	7.36893e26	0.300620
$765$	2.53388e27	1.02094
$766$	−3.04462e26	−0.121160
$767$	1.27123e27	0.499654
$768$	−3.87541e27	−1.50448
$769$	−2.98682e27	−1.14527	−0.572636	−	0.819810i	$-0.694079\pi$
$769$	−2.98682e27	−1.14527	−0.572636	+	0.819810i	$0.694079\pi$
$770$	−1.05152e27	−0.398249
$771$	4.75203e27	1.77772
$772$	8.17698e24	0.00302154
$773$	−6.35136e26	−0.231826	−0.115913	−	0.993259i	$-0.536979\pi$
$773$	−6.35136e26	−0.231826	−0.115913	+	0.993259i	$0.536979\pi$
$774$	−2.93479e27	−1.05813
$775$	−1.81325e27	−0.645790
$776$	−6.94271e26	−0.244254
$777$	−3.09336e27	−1.07506
$778$	−2.56408e27	−0.880290
$779$	1.39911e27	0.474512
$780$	1.76819e27	0.592421
$781$	−1.26285e27	−0.417991
$782$	−3.26765e27	−1.06849
$783$	3.26336e26	0.105421
$784$	−9.14872e25	−0.0291983
$785$	−3.82489e27	−1.20603
$786$	−6.84364e27	−2.13193
$787$	−6.81826e26	−0.209852	−0.104926	−	0.994480i	$-0.533461\pi$
$787$	−6.81826e26	−0.209852	−0.104926	+	0.994480i	$0.533461\pi$
$788$	3.33398e26	0.101383
$789$	−8.21184e26	−0.246723
$790$	−5.64134e27	−1.67465
$791$	8.90677e26	0.261242
$792$	−4.80908e26	−0.139371
$793$	−4.81140e27	−1.37777
$794$	−2.91257e27	−0.824104
$795$	−1.00980e27	−0.282323
$796$	−2.05018e27	−0.566392
$797$	1.58329e27	0.432223	0.216111	−	0.976369i	$-0.430663\pi$
$797$	1.58329e27	0.432223	0.216111	+	0.976369i	$0.430663\pi$
$798$	−7.59788e27	−2.04958
$799$	−4.40145e26	−0.117328
$800$	−3.17521e27	−0.836406
$801$	4.50834e27	1.17357
$802$	−8.74942e27	−2.25073
$803$	−2.28689e26	−0.0581363
$804$	3.18903e27	0.801173
$805$	−6.43094e27	−1.59666
$806$	−2.13861e27	−0.524744
$807$	−3.73393e27	−0.905457
$808$	3.55456e26	0.0851880
$809$	8.24887e27	1.95382	0.976908	−	0.213660i	$-0.0685386\pi$
$809$	8.24887e27	1.95382	0.976908	+	0.213660i	$0.0685386\pi$
$810$	7.98584e27	1.86945
$811$	4.87889e27	1.12882	0.564408	−	0.825496i	$-0.309105\pi$
$811$	4.87889e27	1.12882	0.564408	+	0.825496i	$0.309105\pi$
$812$	1.36312e27	0.311712
$813$	2.98490e27	0.674637
$814$	9.56608e26	0.213699
$815$	1.02261e28	2.25795
$816$	−6.31514e27	−1.37825
$817$	−5.64590e27	−1.21793
$818$	−1.08708e28	−2.31795
$819$	2.97809e27	0.627684
$820$	−1.14671e27	−0.238903
$821$	3.18212e27	0.655324	0.327662	−	0.944795i	$-0.393739\pi$
$821$	3.18212e27	0.655324	0.327662	+	0.944795i	$0.393739\pi$
$822$	−8.84202e27	−1.79999
$823$	6.85596e26	0.137965	0.0689827	−	0.997618i	$-0.478025\pi$
$823$	6.85596e26	0.137965	0.0689827	+	0.997618i	$0.478025\pi$
$824$	−4.38846e27	−0.872979
$825$	−1.65644e27	−0.325734
$826$	4.47702e27	0.870320
$827$	3.40606e27	0.654560	0.327280	−	0.944927i	$-0.393868\pi$
$827$	3.40606e27	0.654560	0.327280	+	0.944927i	$0.393868\pi$
$828$	2.26422e27	0.430160
$829$	5.50774e27	1.03444	0.517220	−	0.855852i	$-0.326967\pi$
$829$	5.50774e27	1.03444	0.517220	+	0.855852i	$0.326967\pi$
$830$	9.12626e27	1.69454
$831$	1.16737e28	2.14288
$832$	1.03094e27	0.187094
$833$	−1.05075e26	−0.0188525
$834$	7.60815e27	1.34959
$835$	1.32929e28	2.33130
$836$	7.12223e26	0.123497
$837$	−5.46568e26	−0.0937028
$838$	4.49758e27	0.762361
$839$	1.02546e28	1.71862	0.859310	−	0.511455i	$-0.170893\pi$
$839$	1.02546e28	1.71862	0.859310	+	0.511455i	$0.170893\pi$
$840$	−8.08901e27	−1.34042
$841$	−3.04076e27	−0.498218
$842$	3.70009e27	0.599443
$843$	5.06160e27	0.810823
$844$	−4.36771e27	−0.691831
$845$	4.68850e27	0.734337
$846$	1.00614e27	0.155826
$847$	−6.25359e27	−0.957717
$848$	1.18638e27	0.179665
$849$	1.13595e27	0.170113
$850$	−6.67362e27	−0.988284
$851$	5.85048e27	0.856763
$852$	7.47874e27	1.08306
$853$	9.78663e26	0.140158	0.0700789	−	0.997541i	$-0.477675\pi$
$853$	9.78663e26	0.140158	0.0700789	+	0.997541i	$0.477675\pi$
$854$	−1.69448e28	−2.39986
$855$	−1.11430e28	−1.56072
$856$	1.53896e27	0.213170
$857$	−3.03352e27	−0.415556	−0.207778	−	0.978176i	$-0.566623\pi$
$857$	−3.03352e27	−0.415556	−0.207778	+	0.978176i	$0.566623\pi$
$858$	−1.95366e27	−0.264679
$859$	1.11406e27	0.149271	0.0746353	−	0.997211i	$-0.476221\pi$
$859$	1.11406e27	0.149271	0.0746353	+	0.997211i	$0.476221\pi$
$860$	4.62736e27	0.613195
$861$	−4.09705e27	−0.536959
$862$	−1.40611e28	−1.82264
$863$	−1.10662e28	−1.41872	−0.709360	−	0.704846i	$-0.751016\pi$
$863$	−1.10662e28	−1.41872	−0.709360	+	0.704846i	$0.751016\pi$
$864$	−9.57104e26	−0.121361
$865$	−2.29353e27	−0.287641
$866$	1.55452e27	0.192830
$867$	3.95730e27	0.485532
$868$	−2.28305e27	−0.277062
$869$	1.88939e27	0.226796
$870$	1.39905e28	1.66112
$871$	−7.93305e27	−0.931682
$872$	−4.59565e27	−0.533876
$873$	2.80063e27	0.321825
$874$	1.43699e28	1.63341
$875$	−3.28753e26	−0.0369652
$876$	1.35432e27	0.150637
$877$	1.17438e28	1.29215	0.646076	−	0.763273i	$-0.276409\pi$
$877$	1.17438e28	1.29215	0.646076	+	0.763273i	$0.276409\pi$
$878$	−2.06406e28	−2.24659
$879$	−6.65832e27	−0.716920
$880$	3.84349e27	0.409393
$881$	4.29749e27	0.452839	0.226419	−	0.974030i	$-0.427298\pi$
$881$	4.29749e27	0.452839	0.226419	+	0.974030i	$0.427298\pi$
$882$	2.40193e26	0.0250385
$883$	−1.06760e28	−1.10099	−0.550495	−	0.834839i	$-0.685561\pi$
$883$	−1.06760e28	−1.10099	−0.550495	+	0.834839i	$0.685561\pi$
$884$	−2.38592e27	−0.243422
$885$	1.39286e28	1.40588
$886$	−1.99315e28	−1.99031
$887$	2.78218e25	0.00274859	0.00137430	−	0.999999i	$-0.499563\pi$
$887$	2.78218e25	0.00274859	0.00137430	+	0.999999i	$0.499563\pi$
$888$	7.35890e27	0.719267
$889$	−4.74568e27	−0.458914
$890$	−2.34505e28	−2.24361
$891$	−2.67462e27	−0.253176
$892$	−2.99247e27	−0.280262
$893$	1.93559e27	0.179360
$894$	1.15068e28	1.05499
$895$	4.07144e27	0.369343
$896$	1.28218e28	1.15086
$897$	−1.19483e28	−1.06116
$898$	−1.13074e28	−0.993661
$899$	−5.12928e27	−0.446005
$900$	4.62428e27	0.397869
$901$	1.36258e27	0.116005
$902$	1.26699e27	0.106736
$903$	1.65330e28	1.37822
$904$	−2.11886e27	−0.174784
$905$	1.69541e28	1.38393
$906$	7.08687e27	0.572449
$907$	−1.15797e28	−0.925607	−0.462804	−	0.886461i	$-0.653157\pi$
$907$	−1.15797e28	−0.925607	−0.462804	+	0.886461i	$0.653157\pi$
$908$	7.62871e27	0.603442
$909$	−1.43388e27	−0.112242
$910$	−1.54908e28	−1.20000
$911$	1.83381e28	1.40582	0.702908	−	0.711280i	$-0.251884\pi$
$911$	1.83381e28	1.40582	0.702908	+	0.711280i	$0.251884\pi$
$912$	2.77716e28	2.10693
$913$	−3.05656e27	−0.229489
$914$	2.08908e28	1.55227
$915$	−5.27176e28	−3.87663
$916$	3.11000e27	0.226336
$917$	1.81741e28	1.30901
$918$	−2.01163e27	−0.143398
$919$	3.60918e27	0.254631	0.127315	−	0.991862i	$-0.459364\pi$
$919$	3.60918e27	0.254631	0.127315	+	0.991862i	$0.459364\pi$
$920$	1.52988e28	1.06825
$921$	2.82265e28	1.95070
$922$	9.81463e27	0.671321
$923$	−1.86042e28	−1.25949
$924$	−2.08561e27	−0.139749
$925$	1.19486e28	0.792450
$926$	−2.38753e28	−1.56727
$927$	1.77027e28	1.15022
$928$	−8.98196e27	−0.577651
$929$	4.85587e27	0.309114	0.154557	−	0.987984i	$-0.450605\pi$
$929$	4.85587e27	0.309114	0.154557	+	0.987984i	$0.450605\pi$
$930$	−2.34323e28	−1.47648
$931$	4.62078e26	0.0288200
$932$	−8.76605e26	−0.0541193
$933$	1.48304e28	0.906309
$934$	1.32448e28	0.801216
$935$	4.41431e27	0.264334
$936$	−7.08468e27	−0.419952
$937$	−2.57103e28	−1.50862	−0.754311	−	0.656517i	$-0.772029\pi$
$937$	−2.57103e28	−1.50862	−0.754311	+	0.656517i	$0.772029\pi$
$938$	−2.79386e28	−1.62285
$939$	3.68096e28	2.11659
$940$	−1.58641e27	−0.0903027
$941$	3.00712e28	1.69453	0.847265	−	0.531171i	$-0.178248\pi$
$941$	3.00712e28	1.69453	0.847265	+	0.531171i	$0.178248\pi$
$942$	−2.50274e28	−1.39615
$943$	7.74875e27	0.427928
$944$	−1.63643e28	−0.894673
$945$	−3.95902e27	−0.214282
$946$	−5.11274e27	−0.273961
$947$	−1.55758e28	−0.826277	−0.413139	−	0.910668i	$-0.635568\pi$
$947$	−1.55758e28	−0.826277	−0.413139	+	0.910668i	$0.635568\pi$
$948$	−1.11892e28	−0.587652
$949$	−3.36901e27	−0.175176
$950$	2.93481e28	1.51080
$951$	−1.57868e28	−0.804600
$952$	1.09150e28	0.550771
$953$	−2.51922e28	−1.25859	−0.629294	−	0.777167i	$-0.716656\pi$
$953$	−2.51922e28	−1.25859	−0.629294	+	0.777167i	$0.716656\pi$
$954$	−3.11475e27	−0.154069
$955$	−2.00849e28	−0.983642
$956$	−1.02336e27	−0.0496227
$957$	−4.68571e27	−0.224963
$958$	−5.21313e27	−0.247814
$959$	2.34810e28	1.10520
$960$	1.12958e28	0.526428
$961$	−1.30798e28	−0.603572
$962$	1.40926e28	0.643915
$963$	−6.20802e27	−0.280869
$964$	1.31838e28	0.590620
$965$	−2.22873e26	−0.00988664
$966$	−4.20796e28	−1.84837
$967$	4.41895e28	1.92206	0.961031	−	0.276441i	$-0.0891551\pi$
$967$	4.41895e28	1.92206	0.961031	+	0.276441i	$0.0891551\pi$
$968$	1.48769e28	0.640761
$969$	3.18962e28	1.36039
$970$	−1.45677e28	−0.615262
$971$	−2.41886e28	−1.01164	−0.505822	−	0.862638i	$-0.668811\pi$
$971$	−2.41886e28	−1.01164	−0.505822	+	0.862638i	$0.668811\pi$
$972$	1.42764e28	0.591273
$973$	−2.02043e28	−0.828653
$974$	1.13632e28	0.461519
$975$	−2.44025e28	−0.981499
$976$	6.19362e28	2.46701
$977$	1.48453e28	0.585585	0.292793	−	0.956176i	$-0.405415\pi$
$977$	1.48453e28	0.585585	0.292793	+	0.956176i	$0.405415\pi$
$978$	6.69128e28	2.61391
$979$	7.85404e27	0.303849
$980$	−3.78718e26	−0.0145100
$981$	1.85384e28	0.703425
$982$	2.98555e28	1.12193
$983$	−1.00480e28	−0.373956	−0.186978	−	0.982364i	$-0.559869\pi$
$983$	−1.00480e28	−0.373956	−0.186978	+	0.982364i	$0.559869\pi$
$984$	9.74660e27	0.359252
$985$	−9.08715e27	−0.331729
$986$	−1.88782e28	−0.682543
$987$	−5.66803e27	−0.202964
$988$	1.04924e28	0.372120
$989$	−3.12688e28	−1.09837
$990$	−1.00908e28	−0.351067
$991$	−2.07434e28	−0.714791	−0.357396	−	0.933953i	$-0.616335\pi$
$991$	−2.07434e28	−0.714791	−0.357396	+	0.933953i	$0.616335\pi$
$992$	1.50436e28	0.513441
$993$	1.61640e28	0.546426
$994$	−6.55200e28	−2.19383
$995$	5.58799e28	1.85326
$996$	1.81013e28	0.594629
$997$	5.01662e28	1.63233	0.816163	−	0.577822i	$-0.196097\pi$
$997$	5.01662e28	1.63233	0.816163	+	0.577822i	$0.196097\pi$
$998$	−1.03809e28	−0.334575
$999$	3.60168e27	0.114983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.a.1.26	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.a.1.26	✓	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	47.a (trivial)

\(f(q)\)	\(=\)	\(q+867.376 q^{2} -46891.0 q^{3} +228052. q^{4} -6.21584e6 q^{5} -4.06721e7 q^{6} +1.08010e8 q^{7} -2.56948e8 q^{8} +1.03650e9 q^{9} +O(q^{10})\)	\(q+867.376 q^{2} -46891.0 q^{3} +228052. q^{4} -6.21584e6 q^{5} -4.06721e7 q^{6} +1.08010e8 q^{7} -2.56948e8 q^{8} +1.03650e9 q^{9} -5.39147e9 q^{10} +1.80571e9 q^{11} -1.06936e10 q^{12} +2.66015e10 q^{13} +9.36848e10 q^{14} +2.91467e11 q^{15} -3.42435e11 q^{16} -3.93292e11 q^{17} +8.99037e11 q^{18} +1.72955e12 q^{19} -1.41754e12 q^{20} -5.06467e12 q^{21} +1.56623e12 q^{22} +9.57883e12 q^{23} +1.20485e13 q^{24} +1.95632e13 q^{25} +2.30735e13 q^{26} +5.89693e12 q^{27} +2.46318e13 q^{28} +5.53399e13 q^{29} +2.52811e14 q^{30} -9.26869e13 q^{31} -1.62305e14 q^{32} -8.46714e13 q^{33} -3.41132e14 q^{34} -6.71370e14 q^{35} +2.36377e14 q^{36} +6.10772e14 q^{37} +1.50017e15 q^{38} -1.24737e15 q^{39} +1.59714e15 q^{40} +8.08946e14 q^{41} -4.39297e15 q^{42} -3.26437e15 q^{43} +4.11796e14 q^{44} -6.44274e15 q^{45} +8.30844e15 q^{46} +1.11913e15 q^{47} +1.60571e16 q^{48} +2.67167e14 q^{49} +1.69686e16 q^{50} +1.84419e16 q^{51} +6.06653e15 q^{52} -3.46454e15 q^{53} +5.11486e15 q^{54} -1.12240e16 q^{55} -2.77528e16 q^{56} -8.11004e16 q^{57} +4.80005e16 q^{58} +4.77881e16 q^{59} +6.64697e16 q^{60} -1.80870e17 q^{61} -8.03943e16 q^{62} +1.11952e17 q^{63} +3.87549e16 q^{64} -1.65350e17 q^{65} -7.34419e16 q^{66} -2.98219e17 q^{67} -8.96913e16 q^{68} -4.49161e17 q^{69} -5.82330e17 q^{70} -6.99366e17 q^{71} -2.66327e17 q^{72} -1.26648e17 q^{73} +5.29769e17 q^{74} -9.17336e17 q^{75} +3.94429e17 q^{76} +1.95034e17 q^{77} -1.08194e18 q^{78} +1.04635e18 q^{79} +2.12852e18 q^{80} -1.48120e18 q^{81} +7.01660e17 q^{82} -1.69272e18 q^{83} -1.15501e18 q^{84} +2.44464e18 q^{85} -2.83143e18 q^{86} -2.59494e18 q^{87} -4.63972e17 q^{88} +4.34956e18 q^{89} -5.58827e18 q^{90} +2.87321e18 q^{91} +2.18448e18 q^{92} +4.34618e18 q^{93} +9.70706e17 q^{94} -1.07506e19 q^{95} +7.61066e18 q^{96} +2.70199e18 q^{97} +2.31734e17 q^{98} +1.87162e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) \) 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9} - 10197084160 q^{10} - 7963915630 q^{11} - 12629269764 q^{12} - 159160177690 q^{13} + 404118350082 q^{14} - 59651276056 q^{15} + 1400499411089 q^{16} - 2004886737784 q^{17} - 4449273908039 q^{18} - 1058821844658 q^{19} + 5114247081432 q^{20} + 2403861756792 q^{21} - 3900401557590 q^{22} - 17333732320340 q^{23} + 32877217250016 q^{24} + 85478486158774 q^{25} - 52056718761868 q^{26} - 137248515015920 q^{27} - 361374372214712 q^{28} - 66840103484258 q^{29} - 884984566401484 q^{30} - 481560705870844 q^{31} - 19\!\cdots\!67 q^{32}+ \cdots + 10\!\cdots\!22 q^{99}+O(q^{100}) \) 34 * q - 1481 * q^2 - 74552 * q^3 + 8752837 * q^4 + 28914 * q^5 - 43599872 * q^6 - 203565056 * q^7 - 994215087 * q^8 + 10020983718 * q^9 - 10197084160 * q^10 - 7963915630 * q^11 - 12629269764 * q^12 - 159160177690 * q^13 + 404118350082 * q^14 - 59651276056 * q^15 + 1400499411089 * q^16 - 2004886737784 * q^17 - 4449273908039 * q^18 - 1058821844658 * q^19 + 5114247081432 * q^20 + 2403861756792 * q^21 - 3900401557590 * q^22 - 17333732320340 * q^23 + 32877217250016 * q^24 + 85478486158774 * q^25 - 52056718761868 * q^26 - 137248515015920 * q^27 - 361374372214712 * q^28 - 66840103484258 * q^29 - 884984566401484 * q^30 - 481560705870844 * q^31 - 1956224504349967 * q^32 - 1089319960511632 * q^33 - 1024355370607462 * q^34 - 368682962835736 * q^35 - 447128934368887 * q^36 - 2062248173433492 * q^37 - 1576879945450998 * q^38 - 2078450045289336 * q^39 - 6293443543679952 * q^40 + 1056258166827256 * q^41 + 3982705476758466 * q^42 - 3467551217747682 * q^43 - 3212244140107742 * q^44 + 4912736475062322 * q^45 + 5810353662475960 * q^46 + 38050436085494078 * q^47 + 57514374310072968 * q^48 + 47238885151375334 * q^49 + 14878200688182597 * q^50 - 29591098904130220 * q^51 - 21974217154008420 * q^52 - 72013726688940684 * q^53 + 172899128132785018 * q^54 + 93309162211316908 * q^55 + 475212376185711512 * q^56 + 64982196426903912 * q^57 + 191264232277219708 * q^58 + 76501047180767180 * q^59 + 400074650609834880 * q^60 - 93578930877721460 * q^61 + 57387957390004612 * q^62 - 383255174667133284 * q^63 + 259127393615024481 * q^64 - 901725390399661584 * q^65 - 254413721370645848 * q^66 - 1182341009802075686 * q^67 - 925231639360979526 * q^68 - 947344752044875104 * q^69 - 363789978732097444 * q^70 - 848931219817628416 * q^71 - 2149287430983690291 * q^72 - 2671220396145181732 * q^73 - 3011451157682875714 * q^74 - 17689756878445192 * q^75 - 3177271521326582258 * q^76 - 1684143788069292280 * q^77 - 224568865304519456 * q^78 + 707599882299569300 * q^79 - 715147860460459392 * q^80 + 3538237990220919930 * q^81 + 1087170674699769934 * q^82 + 3231397917214389292 * q^83 - 5938450004747482572 * q^84 - 1954320626223684628 * q^85 - 1629641946563167526 * q^86 + 7707422320592255560 * q^87 - 5131462381092863934 * q^88 - 6860870532479969712 * q^89 - 8661425364016769956 * q^90 - 2927652813879512704 * q^91 - 26818660612119538580 * q^92 - 19098581600812512 * q^93 - 1657432230665197927 * q^94 - 5345445300954569692 * q^95 - 59798491695034221784 * q^96 - 7217040872018076624 * q^97 - 44647529467669017809 * q^98 + 10120380184661285522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more