LMFDB - Embedded newform 47.20.a.a.1.15

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			1.15
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)

$f(q)$	$=$	$q-368.710 q^{2} +20882.6 q^{3} -388341. q^{4} +2.99874e6 q^{5} -7.69963e6 q^{6} -1.36719e8 q^{7} +3.36495e8 q^{8} -7.26177e8 q^{9} +O(q^{10})$	\(q-368.710 q^{2} +20882.6 q^{3} -388341. q^{4} +2.99874e6 q^{5} -7.69963e6 q^{6} -1.36719e8 q^{7} +3.36495e8 q^{8} -7.26177e8 q^{9} -1.10566e9 q^{10} -1.22365e9 q^{11} -8.10958e9 q^{12} +3.71174e10 q^{13} +5.04095e10 q^{14} +6.26215e10 q^{15} +7.95334e10 q^{16} +1.80130e11 q^{17} +2.67749e11 q^{18} -5.57279e11 q^{19} -1.16453e12 q^{20} -2.85504e12 q^{21} +4.51173e11 q^{22} +1.69151e13 q^{23} +7.02691e12 q^{24} -1.00811e13 q^{25} -1.36856e13 q^{26} -3.94356e13 q^{27} +5.30934e13 q^{28} +6.33151e12 q^{29} -2.30892e13 q^{30} +1.33570e14 q^{31} -2.05745e14 q^{32} -2.55531e13 q^{33} -6.64157e13 q^{34} -4.09983e14 q^{35} +2.82004e14 q^{36} -8.74697e14 q^{37} +2.05474e14 q^{38} +7.75109e14 q^{39} +1.00906e15 q^{40} +3.65413e15 q^{41} +1.05268e15 q^{42} -2.22927e15 q^{43} +4.75195e14 q^{44} -2.17761e15 q^{45} -6.23677e15 q^{46} +1.11913e15 q^{47} +1.66087e15 q^{48} +7.29306e15 q^{49} +3.71699e15 q^{50} +3.76159e15 q^{51} -1.44142e16 q^{52} -4.31371e16 q^{53} +1.45403e16 q^{54} -3.66941e15 q^{55} -4.60051e16 q^{56} -1.16375e16 q^{57} -2.33449e15 q^{58} -3.97026e16 q^{59} -2.43185e16 q^{60} +1.37240e17 q^{61} -4.92487e16 q^{62} +9.92819e16 q^{63} +3.41619e16 q^{64} +1.11305e17 q^{65} +9.42168e15 q^{66} +1.80393e17 q^{67} -6.99518e16 q^{68} +3.53232e17 q^{69} +1.51165e17 q^{70} +5.23868e17 q^{71} -2.44355e17 q^{72} +1.58892e17 q^{73} +3.22510e17 q^{74} -2.10519e17 q^{75} +2.16414e17 q^{76} +1.67296e17 q^{77} -2.85790e17 q^{78} -1.12947e18 q^{79} +2.38499e17 q^{80} +2.04893e16 q^{81} -1.34731e18 q^{82} -4.45706e17 q^{83} +1.10873e18 q^{84} +5.40162e17 q^{85} +8.21952e17 q^{86} +1.32219e17 q^{87} -4.11754e17 q^{88} +2.18459e18 q^{89} +8.02907e17 q^{90} -5.07464e18 q^{91} -6.56883e18 q^{92} +2.78930e18 q^{93} -4.12634e17 q^{94} -1.67113e18 q^{95} -4.29650e18 q^{96} -4.57058e18 q^{97} -2.68902e18 q^{98} +8.88589e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−368.710	−0.509213	−0.254607	−	0.967045i	$-0.581946\pi$
$2$	−368.710	−0.509213	−0.254607	+	0.967045i	$0.581946\pi$
$3$	20882.6	0.612538	0.306269	−	0.951945i	$-0.400919\pi$
$3$	20882.6	0.612538	0.306269	+	0.951945i	$0.400919\pi$
$4$	−388341.	−0.740702
$5$	2.99874e6	0.686630	0.343315	−	0.939220i	$-0.388450\pi$
$5$	2.99874e6	0.686630	0.343315	+	0.939220i	$0.388450\pi$
$6$	−7.69963e6	−0.311913
$7$	−1.36719e8	−1.28055	−0.640274	−	0.768146i	$-0.721179\pi$
$7$	−1.36719e8	−1.28055	−0.640274	+	0.768146i	$0.721179\pi$
$8$	3.36495e8	0.886389
$9$	−7.26177e8	−0.624797
$10$	−1.10566e9	−0.349641
$11$	−1.22365e9	−0.156469	−0.0782344	−	0.996935i	$-0.524928\pi$
$11$	−1.22365e9	−0.156469	−0.0782344	+	0.996935i	$0.524928\pi$
$12$	−8.10958e9	−0.453708
$13$	3.71174e10	0.970769	0.485384	−	0.874301i	$-0.338680\pi$
$13$	3.71174e10	0.970769	0.485384	+	0.874301i	$0.338680\pi$
$14$	5.04095e10	0.652072
$15$	6.26215e10	0.420588
$16$	7.95334e10	0.289341
$17$	1.80130e11	0.368401	0.184201	−	0.982889i	$-0.441030\pi$
$17$	1.80130e11	0.368401	0.184201	+	0.982889i	$0.441030\pi$
$18$	2.67749e11	0.318155
$19$	−5.57279e11	−0.396199	−0.198100	−	0.980182i	$-0.563477\pi$
$19$	−5.57279e11	−0.396199	−0.198100	+	0.980182i	$0.563477\pi$
$20$	−1.16453e12	−0.508588
$21$	−2.85504e12	−0.784385
$22$	4.51173e11	0.0796760
$23$	1.69151e13	1.95821	0.979107	−	0.203344i	$-0.0651811\pi$
$23$	1.69151e13	1.95821	0.979107	+	0.203344i	$0.0651811\pi$
$24$	7.02691e12	0.542947
$25$	−1.00811e13	−0.528539
$26$	−1.36856e13	−0.494328
$27$	−3.94356e13	−0.995250
$28$	5.30934e13	0.948504
$29$	6.33151e12	0.0810450	0.0405225	−	0.999179i	$-0.487098\pi$
$29$	6.33151e12	0.0810450	0.0405225	+	0.999179i	$0.487098\pi$
$30$	−2.30892e13	−0.214169
$31$	1.33570e14	0.907348	0.453674	−	0.891168i	$-0.350113\pi$
$31$	1.33570e14	0.907348	0.453674	+	0.891168i	$0.350113\pi$
$32$	−2.05745e14	−1.03372
$33$	−2.55531e13	−0.0958432
$34$	−6.64157e13	−0.187595
$35$	−4.09983e14	−0.879263
$36$	2.82004e14	0.462788
$37$	−8.74697e14	−1.10647	−0.553237	−	0.833024i	$-0.686608\pi$
$37$	−8.74697e14	−1.10647	−0.553237	+	0.833024i	$0.686608\pi$
$38$	2.05474e14	0.201750
$39$	7.75109e14	0.594633
$40$	1.00906e15	0.608621
$41$	3.65413e15	1.74316	0.871579	−	0.490255i	$-0.163096\pi$
$41$	3.65413e15	1.74316	0.871579	+	0.490255i	$0.163096\pi$
$42$	1.05268e15	0.399419
$43$	−2.22927e15	−0.676412	−0.338206	−	0.941072i	$-0.609820\pi$
$43$	−2.22927e15	−0.676412	−0.338206	+	0.941072i	$0.609820\pi$
$44$	4.75195e14	0.115897
$45$	−2.17761e15	−0.429004
$46$	−6.23677e15	−0.997149
$47$	1.11913e15	0.145865
$47$	1.11913e15	0.145865
$48$	1.66087e15	0.177232
$49$	7.29306e15	0.639804
$50$	3.71699e15	0.269139
$51$	3.76159e15	0.225660
$52$	−1.44142e16	−0.719050
$53$	−4.31371e16	−1.79569	−0.897843	−	0.440315i	$-0.854867\pi$
$53$	−4.31371e16	−1.79569	−0.897843	+	0.440315i	$0.854867\pi$
$54$	1.45403e16	0.506795
$55$	−3.66941e15	−0.107436
$56$	−4.60051e16	−1.13506
$57$	−1.16375e16	−0.242687
$58$	−2.33449e15	−0.0412692
$59$	−3.97026e16	−0.596657	−0.298328	−	0.954463i	$-0.596429\pi$
$59$	−3.97026e16	−0.596657	−0.298328	+	0.954463i	$0.596429\pi$
$60$	−2.43185e16	−0.311530
$61$	1.37240e17	1.50262	0.751309	−	0.659951i	$-0.229423\pi$
$61$	1.37240e17	1.50262	0.751309	+	0.659951i	$0.229423\pi$
$62$	−4.92487e16	−0.462034
$63$	9.92819e16	0.800082
$64$	3.41619e16	0.237046
$65$	1.11305e17	0.666559
$66$	9.42168e15	0.0488046
$67$	1.80393e17	0.810043	0.405021	−	0.914307i	$-0.367264\pi$
$67$	1.80393e17	0.810043	0.405021	+	0.914307i	$0.367264\pi$
$68$	−6.99518e16	−0.272875
$69$	3.53232e17	1.19948
$70$	1.51165e17	0.447733
$71$	5.23868e17	1.35603	0.678013	−	0.735050i	$-0.262841\pi$
$71$	5.23868e17	1.35603	0.678013	+	0.735050i	$0.262841\pi$
$72$	−2.44355e17	−0.553813
$73$	1.58892e17	0.315890	0.157945	−	0.987448i	$-0.449513\pi$
$73$	1.58892e17	0.315890	0.157945	+	0.987448i	$0.449513\pi$
$74$	3.22510e17	0.563432
$75$	−2.10519e17	−0.323750
$76$	2.16414e17	0.293465
$77$	1.67296e17	0.200366
$78$	−2.85790e17	−0.302795
$79$	−1.12947e18	−1.06027	−0.530137	−	0.847912i	$-0.677860\pi$
$79$	−1.12947e18	−1.06027	−0.530137	+	0.847912i	$0.677860\pi$
$80$	2.38499e17	0.198670
$81$	2.04893e16	0.0151677
$82$	−1.34731e18	−0.887640
$83$	−4.45706e17	−0.261702	−0.130851	−	0.991402i	$-0.541771\pi$
$83$	−4.45706e17	−0.261702	−0.130851	+	0.991402i	$0.541771\pi$
$84$	1.10873e18	0.580995
$85$	5.40162e17	0.252955
$86$	8.21952e17	0.344438
$87$	1.32219e17	0.0496432
$88$	−4.11754e17	−0.138692
$89$	2.18459e18	0.660945	0.330473	−	0.943816i	$-0.392792\pi$
$89$	2.18459e18	0.660945	0.330473	+	0.943816i	$0.392792\pi$
$90$	8.02907e17	0.218455
$91$	−5.07464e18	−1.24312
$92$	−6.56883e18	−1.45045
$93$	2.78930e18	0.555785
$94$	−4.12634e17	−0.0742764
$95$	−1.67113e18	−0.272043
$96$	−4.29650e18	−0.633196
$97$	−4.57058e18	−0.610436	−0.305218	−	0.952282i	$-0.598729\pi$
$97$	−4.57058e18	−0.610436	−0.305218	+	0.952282i	$0.598729\pi$
$98$	−2.68902e18	−0.325797
$99$	8.88589e17	0.0977612
$100$	3.91489e18	0.391489
$101$	−1.91450e19	−1.74181	−0.870907	−	0.491448i	$-0.836468\pi$
$101$	−1.91450e19	−1.74181	−0.870907	+	0.491448i	$0.836468\pi$
$102$	−1.38693e18	−0.114909
$103$	−2.04633e19	−1.54533	−0.772665	−	0.634814i	$-0.781077\pi$
$103$	−2.04633e19	−1.54533	−0.772665	+	0.634814i	$0.781077\pi$
$104$	1.24898e19	0.860478
$105$	−8.56152e18	−0.538583
$106$	1.59051e19	0.914388
$107$	−2.73287e19	−1.43705	−0.718526	−	0.695500i	$-0.755183\pi$
$107$	−2.73287e19	−1.43705	−0.718526	+	0.695500i	$0.755183\pi$
$108$	1.53144e19	0.737184
$109$	6.56619e18	0.289575	0.144788	−	0.989463i	$-0.453750\pi$
$109$	6.56619e18	0.289575	0.144788	+	0.989463i	$0.453750\pi$
$110$	1.35295e18	0.0547080
$111$	−1.82660e19	−0.677758
$112$	−1.08737e19	−0.370515
$113$	9.05182e18	0.283459	0.141730	−	0.989905i	$-0.454734\pi$
$113$	9.05182e18	0.283459	0.141730	+	0.989905i	$0.454734\pi$
$114$	4.29085e18	0.123580
$115$	5.07239e19	1.34457
$116$	−2.45878e18	−0.0600301
$117$	−2.69538e19	−0.606533
$118$	1.46387e19	0.303826
$119$	−2.46271e19	−0.471756
$120$	2.10718e19	0.372804
$121$	−5.96618e19	−0.975517
$122$	−5.06019e19	−0.765153
$123$	7.63078e19	1.06775
$124$	−5.18708e19	−0.672074
$125$	−8.74268e19	−1.04954
$126$	−3.66062e19	−0.407413
$127$	−1.00658e20	−1.03923	−0.519616	−	0.854400i	$-0.673925\pi$
$127$	−1.00658e20	−1.03923	−0.519616	+	0.854400i	$0.673925\pi$
$128$	9.52739e19	0.913018
$129$	−4.65529e19	−0.414328
$130$	−4.10393e19	−0.339421
$131$	−2.42528e20	−1.86502	−0.932512	−	0.361139i	$-0.882388\pi$
$131$	−2.42528e20	−1.86502	−0.932512	+	0.361139i	$0.882388\pi$
$132$	9.92332e18	0.0709912
$133$	7.61904e19	0.507352
$134$	−6.65125e19	−0.412485
$135$	−1.18257e20	−0.683369
$136$	6.06129e19	0.326547
$137$	−1.05755e20	−0.531440	−0.265720	−	0.964050i	$-0.585610\pi$
$137$	−1.05755e20	−0.531440	−0.265720	+	0.964050i	$0.585610\pi$
$138$	−1.30240e20	−0.610792
$139$	−6.26015e19	−0.274122	−0.137061	−	0.990563i	$-0.543766\pi$
$139$	−6.26015e19	−0.274122	−0.137061	+	0.990563i	$0.543766\pi$
$140$	1.59213e20	0.651272
$141$	2.33704e19	0.0893479
$142$	−1.93155e20	−0.690506
$143$	−4.54188e19	−0.151895
$144$	−5.77553e19	−0.180779
$145$	1.89865e19	0.0556479
$146$	−5.85852e19	−0.160856
$147$	1.52298e20	0.391905
$148$	3.39681e20	0.819568
$149$	−5.68491e20	−1.28663	−0.643315	−	0.765601i	$-0.722442\pi$
$149$	−5.68491e20	−1.28663	−0.643315	+	0.765601i	$0.722442\pi$
$150$	7.76206e19	0.164858
$151$	7.30142e20	1.45588	0.727942	−	0.685639i	$-0.240477\pi$
$151$	7.30142e20	1.45588	0.727942	+	0.685639i	$0.240477\pi$
$152$	−1.87522e20	−0.351187
$153$	−1.30806e20	−0.230176
$154$	−6.16837e19	−0.102029
$155$	4.00542e20	0.623013
$156$	−3.01007e20	−0.440446
$157$	−2.66306e19	−0.0366720	−0.0183360	−	0.999832i	$-0.505837\pi$
$157$	−2.66306e19	−0.0366720	−0.0183360	+	0.999832i	$0.505837\pi$
$158$	4.16448e20	0.539906
$159$	−9.00817e20	−1.09993
$160$	−6.16975e20	−0.709787
$161$	−2.31261e21	−2.50759
$162$	−7.55460e18	−0.00772358
$163$	1.32567e21	1.27836	0.639182	−	0.769055i	$-0.279273\pi$
$163$	1.32567e21	1.27836	0.639182	+	0.769055i	$0.279273\pi$
$164$	−1.41905e21	−1.29116
$165$	−7.66270e19	−0.0658088
$166$	1.64336e20	0.133262
$167$	−7.57823e20	−0.580445	−0.290223	−	0.956959i	$-0.593729\pi$
$167$	−7.57823e20	−0.580445	−0.290223	+	0.956959i	$0.593729\pi$
$168$	−9.60709e20	−0.695270
$169$	−8.42188e19	−0.0576084
$170$	−1.99163e20	−0.128808
$171$	4.04683e20	0.247544
$172$	8.65715e20	0.501020
$173$	1.17653e21	0.644413	0.322207	−	0.946669i	$-0.395575\pi$
$173$	1.17653e21	0.644413	0.322207	+	0.946669i	$0.395575\pi$
$174$	−4.87503e19	−0.0252790
$175$	1.37827e21	0.676819
$176$	−9.73213e19	−0.0452728
$177$	−8.29094e20	−0.365475
$178$	−8.05481e20	−0.336562
$179$	−3.03763e21	−1.20346	−0.601729	−	0.798700i	$-0.705521\pi$
$179$	−3.03763e21	−1.20346	−0.601729	+	0.798700i	$0.705521\pi$
$180$	8.45656e20	0.317764
$181$	2.24789e20	0.0801361	0.0400680	−	0.999197i	$-0.487243\pi$
$181$	2.24789e20	0.0801361	0.0400680	+	0.999197i	$0.487243\pi$
$182$	1.87107e21	0.633011
$183$	2.86594e21	0.920411
$184$	5.69185e21	1.73574
$185$	−2.62299e21	−0.759739
$186$	−1.02844e21	−0.283013
$187$	−2.20417e20	−0.0576433
$188$	−4.34604e20	−0.108042
$189$	5.39157e21	1.27447
$190$	6.16163e20	0.138528
$191$	−4.27247e21	−0.913824	−0.456912	−	0.889512i	$-0.651045\pi$
$191$	−4.27247e21	−0.913824	−0.456912	+	0.889512i	$0.651045\pi$
$192$	7.13391e20	0.145200
$193$	−5.36963e21	−1.04028	−0.520139	−	0.854081i	$-0.674120\pi$
$193$	−5.36963e21	−1.04028	−0.520139	+	0.854081i	$0.674120\pi$
$194$	1.68522e21	0.310842
$195$	2.32435e21	0.408293
$196$	−2.83219e21	−0.473904
$197$	1.13368e21	0.180743	0.0903714	−	0.995908i	$-0.471195\pi$
$197$	1.13368e21	0.180743	0.0903714	+	0.995908i	$0.471195\pi$
$198$	−3.27632e20	−0.0497813
$199$	−9.64479e21	−1.39698	−0.698488	−	0.715622i	$-0.746143\pi$
$199$	−9.64479e21	−1.39698	−0.698488	+	0.715622i	$0.746143\pi$
$200$	−3.39223e21	−0.468491
$201$	3.76707e21	0.496182
$202$	7.05894e21	0.886955
$203$	−8.65634e20	−0.103782
$204$	−1.46078e21	−0.167147
$205$	1.09578e22	1.19691
$206$	7.54501e21	0.786903
$207$	−1.22834e22	−1.22349
$208$	2.95207e21	0.280883
$209$	6.81917e20	0.0619928
$210$	3.15672e21	0.274254
$211$	1.76816e22	1.46838	0.734189	−	0.678945i	$-0.237562\pi$
$211$	1.76816e22	1.46838	0.734189	+	0.678945i	$0.237562\pi$
$212$	1.67519e22	1.33007
$213$	1.09397e22	0.830618
$214$	1.00764e22	0.731766
$215$	−6.68498e21	−0.464445
$216$	−1.32699e22	−0.882179
$217$	−1.82615e22	−1.16190
$218$	−2.42102e21	−0.147456
$219$	3.31809e21	0.193495
$220$	1.42498e21	0.0795782
$221$	6.68595e21	0.357632
$222$	6.73485e21	0.345124
$223$	1.96934e22	0.966996	0.483498	−	0.875346i	$-0.339366\pi$
$223$	1.96934e22	0.966996	0.483498	+	0.875346i	$0.339366\pi$
$224$	2.81292e22	1.32373
$225$	7.32065e21	0.330229
$226$	−3.33749e21	−0.144341
$227$	2.26172e22	0.937979	0.468989	−	0.883204i	$-0.344618\pi$
$227$	2.26172e22	0.937979	0.468989	+	0.883204i	$0.344618\pi$
$228$	4.51930e21	0.179759
$229$	1.50436e22	0.574005	0.287003	−	0.957930i	$-0.407341\pi$
$229$	1.50436e22	0.574005	0.287003	+	0.957930i	$0.407341\pi$
$230$	−1.87024e22	−0.684673
$231$	3.49358e21	0.122732
$232$	2.13052e21	0.0718373
$233$	−5.50604e22	−1.78221	−0.891104	−	0.453800i	$-0.850068\pi$
$233$	−5.50604e22	−1.78221	−0.891104	+	0.453800i	$0.850068\pi$
$234$	9.93814e21	0.308855
$235$	3.35598e21	0.100155
$236$	1.54181e22	0.441945
$237$	−2.35864e22	−0.649459
$238$	9.08025e21	0.240224
$239$	−1.56111e22	−0.396876	−0.198438	−	0.980113i	$-0.563587\pi$
$239$	−1.56111e22	−0.396876	−0.198438	+	0.980113i	$0.563587\pi$
$240$	4.98050e21	0.121693
$241$	8.14186e22	1.91233	0.956163	−	0.292836i	$-0.0945989\pi$
$241$	8.14186e22	1.91233	0.956163	+	0.292836i	$0.0945989\pi$
$242$	2.19979e22	0.496747
$243$	4.62623e22	1.00454
$244$	−5.32961e22	−1.11299
$245$	2.18700e22	0.439309
$246$	−2.81354e22	−0.543713
$247$	−2.06848e22	−0.384618
$248$	4.49458e22	0.804263
$249$	−9.30752e21	−0.160302
$250$	3.22351e22	0.534440
$251$	−1.01836e23	−1.62555	−0.812774	−	0.582579i	$-0.802044\pi$
$251$	−1.01836e23	−1.62555	−0.812774	+	0.582579i	$0.802044\pi$
$252$	−3.85552e22	−0.592622
$253$	−2.06982e22	−0.306400
$254$	3.71136e22	0.529191
$255$	1.12800e22	0.154945
$256$	−5.30391e22	−0.701967
$257$	−5.47947e22	−0.698834	−0.349417	−	0.936967i	$-0.613620\pi$
$257$	−5.47947e22	−0.698834	−0.349417	+	0.936967i	$0.613620\pi$
$258$	1.71645e22	0.210982
$259$	1.19587e23	1.41689
$260$	−4.32244e22	−0.493722
$261$	−4.59780e21	−0.0506366
$262$	8.94224e22	0.949695
$263$	−1.27515e22	−0.130611	−0.0653057	−	0.997865i	$-0.520802\pi$
$263$	−1.27515e22	−0.130611	−0.0653057	+	0.997865i	$0.520802\pi$
$264$	−8.59850e21	−0.0849543
$265$	−1.29357e23	−1.23297
$266$	−2.80922e22	−0.258351
$267$	4.56201e22	0.404854
$268$	−7.00538e22	−0.600000
$269$	−1.61571e22	−0.133573	−0.0667864	−	0.997767i	$-0.521275\pi$
$269$	−1.61571e22	−0.133573	−0.0667864	+	0.997767i	$0.521275\pi$
$270$	4.36025e22	0.347981
$271$	−4.26126e22	−0.328345	−0.164172	−	0.986432i	$-0.552495\pi$
$271$	−4.26126e22	−0.328345	−0.164172	+	0.986432i	$0.552495\pi$
$272$	1.43263e22	0.106593
$273$	−1.05972e23	−0.761456
$274$	3.89928e22	0.270616
$275$	1.23357e22	0.0826998
$276$	−1.37174e23	−0.888458
$277$	−3.05769e23	−1.91353	−0.956765	−	0.290863i	$-0.906058\pi$
$277$	−3.05769e23	−1.91353	−0.956765	+	0.290863i	$0.906058\pi$
$278$	2.30818e22	0.139587
$279$	−9.69957e22	−0.566908
$280$	−1.37957e23	−0.779369
$281$	2.44760e23	1.33669	0.668345	−	0.743852i	$-0.267003\pi$
$281$	2.44760e23	1.33669	0.668345	+	0.743852i	$0.267003\pi$
$282$	−8.61689e21	−0.0454972
$283$	2.75613e23	1.40711	0.703556	−	0.710640i	$-0.251595\pi$
$283$	2.75613e23	1.40711	0.703556	+	0.710640i	$0.251595\pi$
$284$	−2.03440e23	−1.00441
$285$	−3.48977e22	−0.166636
$286$	1.67464e22	0.0773470
$287$	−4.99587e23	−2.23220
$288$	1.49407e23	0.645868
$289$	−2.06626e23	−0.864281
$290$	−7.00051e21	−0.0283367
$291$	−9.54458e22	−0.373916
$292$	−6.17045e22	−0.233980
$293$	−4.28700e22	−0.157366	−0.0786830	−	0.996900i	$-0.525071\pi$
$293$	−4.28700e22	−0.157366	−0.0786830	+	0.996900i	$0.525071\pi$
$294$	−5.61539e22	−0.199563
$295$	−1.19058e23	−0.409683
$296$	−2.94332e23	−0.980767
$297$	4.82555e22	0.155726
$298$	2.09608e23	0.655170
$299$	6.27845e23	1.90097
$300$	8.17533e22	0.239802
$301$	3.04782e23	0.866179
$302$	−2.69211e23	−0.741355
$303$	−3.99798e23	−1.06693
$304$	−4.43223e22	−0.114637
$305$	4.11548e23	1.03174
$306$	4.82295e22	0.117209
$307$	−2.46489e23	−0.580742	−0.290371	−	0.956914i	$-0.593779\pi$
$307$	−2.46489e23	−0.580742	−0.290371	+	0.956914i	$0.593779\pi$
$308$	−6.49679e22	−0.148411
$309$	−4.27327e23	−0.946574
$310$	−1.47684e23	−0.317246
$311$	−9.55842e22	−0.199142	−0.0995708	−	0.995030i	$-0.531747\pi$
$311$	−9.55842e22	−0.199142	−0.0995708	+	0.995030i	$0.531747\pi$
$312$	2.60821e23	0.527076
$313$	6.53463e23	1.28100	0.640501	−	0.767958i	$-0.278727\pi$
$313$	6.53463e23	1.28100	0.640501	+	0.767958i	$0.278727\pi$
$314$	9.81898e21	0.0186739
$315$	2.97720e23	0.549361
$316$	4.38620e23	0.785347
$317$	−6.82945e23	−1.18665	−0.593325	−	0.804963i	$-0.702185\pi$
$317$	−6.82945e23	−1.18665	−0.593325	+	0.804963i	$0.702185\pi$
$318$	3.32140e23	0.560098
$319$	−7.74757e21	−0.0126810
$320$	1.02443e23	0.162763
$321$	−5.70695e23	−0.880250
$322$	8.52682e23	1.27690
$323$	−1.00383e23	−0.145960
$324$	−7.95683e21	−0.0112347
$325$	−3.74183e23	−0.513089
$326$	−4.88789e23	−0.650960
$327$	1.37119e23	0.177376
$328$	1.22960e24	1.54512
$329$	−1.53006e23	−0.186787
$330$	2.82531e22	0.0335107
$331$	−5.49691e23	−0.633509	−0.316755	−	0.948508i	$-0.602593\pi$
$331$	−5.49691e23	−0.633509	−0.316755	+	0.948508i	$0.602593\pi$
$332$	1.73086e23	0.193843
$333$	6.35185e23	0.691322
$334$	2.79417e23	0.295570
$335$	5.40949e23	0.556200
$336$	−2.27071e23	−0.226955
$337$	−9.38423e23	−0.911832	−0.455916	−	0.890023i	$-0.650688\pi$
$337$	−9.38423e23	−0.911832	−0.455916	+	0.890023i	$0.650688\pi$
$338$	3.10523e22	0.0293349
$339$	1.89026e23	0.173630
$340$	−2.09767e23	−0.187365
$341$	−1.63444e23	−0.141972
$342$	−1.49211e23	−0.126053
$343$	5.61344e23	0.461248
$344$	−7.50138e23	−0.599564
$345$	1.05925e24	0.823601
$346$	−4.33798e23	−0.328144
$347$	1.45869e24	1.07358	0.536789	−	0.843716i	$-0.319637\pi$
$347$	1.45869e24	1.07358	0.536789	+	0.843716i	$0.319637\pi$
$348$	−5.13459e22	−0.0367708
$349$	−5.71663e23	−0.398381	−0.199191	−	0.979961i	$-0.563831\pi$
$349$	−5.71663e23	−0.398381	−0.199191	+	0.979961i	$0.563831\pi$
$350$	−5.08182e23	−0.344645
$351$	−1.46375e24	−0.966158
$352$	2.51761e23	0.161746
$353$	−4.57945e23	−0.286387	−0.143194	−	0.989695i	$-0.545737\pi$
$353$	−4.57945e23	−0.286387	−0.143194	+	0.989695i	$0.545737\pi$
$354$	3.05695e23	0.186105
$355$	1.57094e24	0.931088
$356$	−8.48367e23	−0.489563
$357$	−5.14278e23	−0.288968
$358$	1.12000e24	0.612817
$359$	1.86898e24	0.995880	0.497940	−	0.867211i	$-0.334090\pi$
$359$	1.86898e24	0.995880	0.497940	+	0.867211i	$0.334090\pi$
$360$	−7.32757e23	−0.380265
$361$	−1.66786e24	−0.843026
$362$	−8.28819e22	−0.0408064
$363$	−1.24589e24	−0.597542
$364$	1.97069e24	0.920778
$365$	4.76476e23	0.216900
$366$	−1.05670e24	−0.468686
$367$	1.02478e24	0.442896	0.221448	−	0.975172i	$-0.428922\pi$
$367$	1.02478e24	0.442896	0.221448	+	0.975172i	$0.428922\pi$
$368$	1.34532e24	0.566591
$369$	−2.65354e24	−1.08912
$370$	9.67121e23	0.386869
$371$	5.89765e24	2.29946
$372$	−1.08320e24	−0.411671
$373$	−6.61882e23	−0.245215	−0.122607	−	0.992455i	$-0.539126\pi$
$373$	−6.61882e23	−0.245215	−0.122607	+	0.992455i	$0.539126\pi$
$374$	8.12698e22	0.0293527
$375$	−1.82570e24	−0.642884
$376$	3.76582e23	0.129293
$377$	2.35009e23	0.0786759
$378$	−1.98793e24	−0.648975
$379$	5.02285e24	1.59911	0.799554	−	0.600595i	$-0.205069\pi$
$379$	5.02285e24	1.59911	0.799554	+	0.600595i	$0.205069\pi$
$380$	6.48969e23	0.201502
$381$	−2.10200e24	−0.636570
$382$	1.57530e24	0.465331
$383$	−1.07097e24	−0.308596	−0.154298	−	0.988024i	$-0.549312\pi$
$383$	−1.07097e24	−0.308596	−0.154298	+	0.988024i	$0.549312\pi$
$384$	1.98957e24	0.559259
$385$	5.01677e23	0.137577
$386$	1.97983e24	0.529724
$387$	1.61884e24	0.422620
$388$	1.77495e24	0.452151
$389$	−3.26874e24	−0.812566	−0.406283	−	0.913747i	$-0.633175\pi$
$389$	−3.26874e24	−0.812566	−0.406283	+	0.913747i	$0.633175\pi$
$390$	−8.57010e23	−0.207908
$391$	3.04692e24	0.721409
$392$	2.45408e24	0.567115
$393$	−5.06462e24	−1.14240
$394$	−4.17999e23	−0.0920367
$395$	−3.38699e24	−0.728016
$396$	−3.45076e23	−0.0724119
$397$	8.56504e23	0.175477	0.0877383	−	0.996144i	$-0.472036\pi$
$397$	8.56504e23	0.175477	0.0877383	+	0.996144i	$0.472036\pi$
$398$	3.55613e24	0.711359
$399$	1.59106e24	0.310773
$400$	−8.01782e23	−0.152928
$401$	−7.38898e23	−0.137630	−0.0688150	−	0.997629i	$-0.521922\pi$
$401$	−7.38898e23	−0.137630	−0.0688150	+	0.997629i	$0.521922\pi$
$402$	−1.38896e24	−0.252663
$403$	4.95778e24	0.880825
$404$	7.43478e24	1.29016
$405$	6.14419e22	0.0104146
$406$	3.19168e23	0.0528472
$407$	1.07033e24	0.173129
$408$	1.26576e24	0.200022
$409$	3.53625e24	0.545974	0.272987	−	0.962018i	$-0.411988\pi$
$409$	3.53625e24	0.545974	0.272987	+	0.962018i	$0.411988\pi$
$410$	−4.04023e24	−0.609480
$411$	−2.20843e24	−0.325527
$412$	7.94673e24	1.14463
$413$	5.42808e24	0.764048
$414$	4.52900e24	0.623016
$415$	−1.33656e24	−0.179692
$416$	−7.63673e24	−1.00351
$417$	−1.30728e24	−0.167910
$418$	−2.51429e23	−0.0315676
$419$	4.57623e24	0.561661	0.280831	−	0.959757i	$-0.409390\pi$
$419$	4.57623e24	0.561661	0.280831	+	0.959757i	$0.409390\pi$
$420$	3.32479e24	0.398929
$421$	−5.99871e24	−0.703685	−0.351842	−	0.936059i	$-0.614445\pi$
$421$	−5.99871e24	−0.703685	−0.351842	+	0.936059i	$0.614445\pi$
$422$	−6.51938e24	−0.747718
$423$	−8.12687e23	−0.0911360
$424$	−1.45154e25	−1.59168
$425$	−1.81590e24	−0.194714
$426$	−4.03359e24	−0.422962
$427$	−1.87633e25	−1.92417
$428$	1.06128e25	1.06443
$429$	−9.48465e23	−0.0930415
$430$	2.46482e24	0.236502
$431$	−8.27044e24	−0.776238	−0.388119	−	0.921609i	$-0.626875\pi$
$431$	−8.27044e24	−0.776238	−0.388119	+	0.921609i	$0.626875\pi$
$432$	−3.13644e24	−0.287966
$433$	−1.54449e25	−1.38723	−0.693616	−	0.720345i	$-0.743984\pi$
$433$	−1.54449e25	−1.38723	−0.693616	+	0.720345i	$0.743984\pi$
$434$	6.73321e24	0.591657
$435$	3.96488e23	0.0340865
$436$	−2.54992e24	−0.214489
$437$	−9.42644e24	−0.775843
$438$	−1.22341e24	−0.0985302
$439$	−2.50336e25	−1.97292	−0.986462	−	0.163989i	$-0.947564\pi$
$439$	−2.50336e25	−1.97292	−0.986462	+	0.163989i	$0.947564\pi$
$440$	−1.23474e24	−0.0952303
$441$	−5.29605e24	−0.399748
$442$	−2.46518e24	−0.182111
$443$	7.51024e24	0.543023	0.271511	−	0.962435i	$-0.412477\pi$
$443$	7.51024e24	0.543023	0.271511	+	0.962435i	$0.412477\pi$
$444$	7.09343e24	0.502017
$445$	6.55102e24	0.453825
$446$	−7.26115e24	−0.492407
$447$	−1.18716e25	−0.788111
$448$	−4.67057e24	−0.303549
$449$	1.81713e25	1.15624	0.578118	−	0.815953i	$-0.303787\pi$
$449$	1.81713e25	1.15624	0.578118	+	0.815953i	$0.303787\pi$
$450$	−2.69919e24	−0.168157
$451$	−4.47138e24	−0.272750
$452$	−3.51519e24	−0.209959
$453$	1.52473e25	0.891785
$454$	−8.33918e24	−0.477631
$455$	−1.52175e25	−0.853561
$456$	−3.91595e24	−0.215115
$457$	1.10823e25	0.596245	0.298123	−	0.954528i	$-0.403640\pi$
$457$	1.10823e25	0.596245	0.298123	+	0.954528i	$0.403640\pi$
$458$	−5.54674e24	−0.292291
$459$	−7.10352e24	−0.366651
$460$	−1.96982e25	−0.995925
$461$	2.72916e25	1.35167	0.675835	−	0.737053i	$-0.263783\pi$
$461$	2.72916e25	1.35167	0.675835	+	0.737053i	$0.263783\pi$
$462$	−1.28812e24	−0.0624967
$463$	−4.13349e24	−0.196471	−0.0982353	−	0.995163i	$-0.531320\pi$
$463$	−4.13349e24	−0.196471	−0.0982353	+	0.995163i	$0.531320\pi$
$464$	5.03566e23	0.0234496
$465$	8.36437e24	0.381619
$466$	2.03013e25	0.907524
$467$	2.91382e25	1.27630	0.638149	−	0.769913i	$-0.279700\pi$
$467$	2.91382e25	1.27630	0.638149	+	0.769913i	$0.279700\pi$
$468$	1.04673e25	0.449260
$469$	−2.46630e25	−1.03730
$470$	−1.23738e24	−0.0510004
$471$	−5.56118e23	−0.0224630
$472$	−1.33597e25	−0.528870
$473$	2.72785e24	0.105837
$474$	8.69652e24	0.330713
$475$	5.61797e24	0.209407
$476$	9.56371e24	0.349430
$477$	3.13252e25	1.12194
$478$	5.75598e24	0.202094
$479$	−2.04027e24	−0.0702265	−0.0351132	−	0.999383i	$-0.511179\pi$
$479$	−2.04027e24	−0.0702265	−0.0351132	+	0.999383i	$0.511179\pi$
$480$	−1.28841e25	−0.434772
$481$	−3.24665e25	−1.07413
$482$	−3.00198e25	−0.973782
$483$	−4.82933e25	−1.53599
$484$	2.31691e25	0.722567
$485$	−1.37060e25	−0.419144
$486$	−1.70574e25	−0.511526
$487$	1.89167e24	0.0556314	0.0278157	−	0.999613i	$-0.491145\pi$
$487$	1.89167e24	0.0556314	0.0278157	+	0.999613i	$0.491145\pi$
$488$	4.61807e25	1.33190
$489$	2.76836e25	0.783047
$490$	−8.06367e24	−0.223702
$491$	2.30493e25	0.627166	0.313583	−	0.949561i	$-0.398471\pi$
$491$	2.30493e25	0.627166	0.313583	+	0.949561i	$0.398471\pi$
$492$	−2.96334e25	−0.790885
$493$	1.14049e24	0.0298571
$494$	7.62668e24	0.195853
$495$	2.66464e24	0.0671258
$496$	1.06233e25	0.262533
$497$	−7.16225e25	−1.73646
$498$	3.43177e24	0.0816282
$499$	2.54085e24	0.0592958	0.0296479	−	0.999560i	$-0.490561\pi$
$499$	2.54085e24	0.0592958	0.0296479	+	0.999560i	$0.490561\pi$
$500$	3.39514e25	0.777397
$501$	−1.58253e25	−0.355545
$502$	3.75479e25	0.827751
$503$	4.14707e25	0.897109	0.448554	−	0.893756i	$-0.351939\pi$
$503$	4.14707e25	0.897109	0.448554	+	0.893756i	$0.351939\pi$
$504$	3.34079e25	0.709184
$505$	−5.74107e25	−1.19598
$506$	7.63164e24	0.156023
$507$	−1.75871e24	−0.0352873
$508$	3.90896e25	0.769761
$509$	−7.04233e25	−1.36112	−0.680562	−	0.732691i	$-0.738264\pi$
$509$	−7.04233e25	−1.36112	−0.680562	+	0.732691i	$0.738264\pi$
$510$	−4.15905e24	−0.0789000
$511$	−2.17235e25	−0.404513
$512$	−3.03949e25	−0.555567
$513$	2.19766e25	0.394317
$514$	2.02033e25	0.355856
$515$	−6.13639e25	−1.06107
$516$	1.80784e25	0.306894
$517$	−1.36943e24	−0.0228233
$518$	−4.40930e25	−0.721502
$519$	2.45690e25	0.394728
$520$	3.74537e25	0.590831
$521$	−4.88527e25	−0.756711	−0.378356	−	0.925660i	$-0.623510\pi$
$521$	−4.88527e25	−0.756711	−0.378356	+	0.925660i	$0.623510\pi$
$522$	1.69525e24	0.0257849
$523$	5.67262e24	0.0847261	0.0423631	−	0.999102i	$-0.486511\pi$
$523$	5.67262e24	0.0847261	0.0423631	+	0.999102i	$0.486511\pi$
$524$	9.41835e25	1.38143
$525$	2.87819e25	0.414578
$526$	4.70160e24	0.0665091
$527$	2.40600e25	0.334268
$528$	−2.03232e24	−0.0277313
$529$	2.11505e26	2.83460
$530$	4.76951e25	0.627846
$531$	2.88311e25	0.372789
$532$	−2.95879e25	−0.375797
$533$	1.35632e26	1.69220
$534$	−1.68206e25	−0.206157
$535$	−8.19515e25	−0.986724
$536$	6.07012e25	0.718013
$537$	−6.34337e25	−0.737165
$538$	5.95730e24	0.0680170
$539$	−8.92418e24	−0.100109
$540$	4.59240e25	0.506173
$541$	1.25703e26	1.36135	0.680675	−	0.732585i	$-0.261686\pi$
$541$	1.25703e26	1.36135	0.680675	+	0.732585i	$0.261686\pi$
$542$	1.57117e25	0.167198
$543$	4.69418e24	0.0490864
$544$	−3.70609e25	−0.380825
$545$	1.96903e25	0.198831
$546$	3.90728e25	0.387744
$547$	−1.08302e26	−1.05623	−0.528115	−	0.849173i	$-0.677101\pi$
$547$	−1.08302e26	−1.05623	−0.528115	+	0.849173i	$0.677101\pi$
$548$	4.10688e25	0.393638
$549$	−9.96608e25	−0.938831
$550$	−4.54831e24	−0.0421119
$551$	−3.52842e24	−0.0321100
$552$	1.18861e26	1.06321
$553$	1.54420e26	1.35773
$554$	1.12740e26	0.974395
$555$	−5.47748e25	−0.465369
$556$	2.43107e25	0.203043
$557$	−2.81368e25	−0.231020	−0.115510	−	0.993306i	$-0.536850\pi$
$557$	−2.81368e25	−0.231020	−0.115510	+	0.993306i	$0.536850\pi$
$558$	3.57633e25	0.288677
$559$	−8.27445e25	−0.656640
$560$	−3.26073e25	−0.254407
$561$	−4.60288e24	−0.0353087
$562$	−9.02454e25	−0.680660
$563$	1.41262e26	1.04760	0.523802	−	0.851840i	$-0.324513\pi$
$563$	1.41262e26	1.04760	0.523802	+	0.851840i	$0.324513\pi$
$564$	−9.07568e24	−0.0661801
$565$	2.71440e25	0.194632
$566$	−1.01621e26	−0.716520
$567$	−2.80126e24	−0.0194229
$568$	1.76279e26	1.20197
$569$	−2.75626e26	−1.84822	−0.924109	−	0.382128i	$-0.875191\pi$
$569$	−2.75626e26	−1.84822	−0.924109	+	0.382128i	$0.875191\pi$
$570$	1.28671e25	0.0848535
$571$	−2.21165e26	−1.43441	−0.717205	−	0.696862i	$-0.754579\pi$
$571$	−2.21165e26	−1.43441	−0.717205	+	0.696862i	$0.754579\pi$
$572$	1.76380e25	0.112509
$573$	−8.92205e25	−0.559752
$574$	1.84203e26	1.13667
$575$	−1.70522e26	−1.03499
$576$	−2.48076e25	−0.148105
$577$	−1.46920e26	−0.862803	−0.431401	−	0.902160i	$-0.641981\pi$
$577$	−1.46920e26	−0.862803	−0.431401	+	0.902160i	$0.641981\pi$
$578$	7.61849e25	0.440103
$579$	−1.12132e26	−0.637210
$580$	−7.37324e24	−0.0412185
$581$	6.09363e25	0.335122
$582$	3.51918e25	0.190403
$583$	5.27849e25	0.280969
$584$	5.34666e25	0.280002
$585$	−8.08273e25	−0.416464
$586$	1.58066e25	0.0801328
$587$	9.66990e25	0.482347	0.241174	−	0.970482i	$-0.422468\pi$
$587$	9.66990e25	0.482347	0.241174	+	0.970482i	$0.422468\pi$
$588$	−5.91437e25	−0.290284
$589$	−7.44360e25	−0.359491
$590$	4.38977e25	0.208616
$591$	2.36742e25	0.110712
$592$	−6.95676e25	−0.320148
$593$	−5.25294e25	−0.237894	−0.118947	−	0.992901i	$-0.537952\pi$
$593$	−5.25294e25	−0.237894	−0.118947	+	0.992901i	$0.537952\pi$
$594$	−1.77923e25	−0.0792976
$595$	−7.38501e25	−0.323922
$596$	2.20768e26	0.953009
$597$	−2.01409e26	−0.855701
$598$	−2.31493e26	−0.968001
$599$	7.20968e25	0.296730	0.148365	−	0.988933i	$-0.452599\pi$
$599$	7.20968e25	0.296730	0.148365	+	0.988933i	$0.452599\pi$
$600$	−7.08388e25	−0.286969
$601$	2.56924e26	1.02447	0.512233	−	0.858847i	$-0.328819\pi$
$601$	2.56924e26	1.02447	0.512233	+	0.858847i	$0.328819\pi$
$602$	−1.12376e26	−0.441070
$603$	−1.30997e26	−0.506112
$604$	−2.83544e26	−1.07838
$605$	−1.78910e26	−0.669820
$606$	1.47409e26	0.543294
$607$	1.81263e26	0.657684	0.328842	−	0.944385i	$-0.393342\pi$
$607$	1.81263e26	0.657684	0.328842	+	0.944385i	$0.393342\pi$
$608$	1.14658e26	0.409561
$609$	−1.80767e25	−0.0635705
$610$	−1.51742e26	−0.525377
$611$	4.15392e25	0.141601
$612$	5.07974e25	0.170492
$613$	−5.58771e26	−1.84654	−0.923271	−	0.384150i	$-0.874494\pi$
$613$	−5.58771e26	−1.84654	−0.923271	+	0.384150i	$0.874494\pi$
$614$	9.08830e25	0.295722
$615$	2.28827e26	0.733151
$616$	5.62944e25	0.177602
$617$	2.41931e26	0.751594	0.375797	−	0.926702i	$-0.377369\pi$
$617$	2.41931e26	0.751594	0.375797	+	0.926702i	$0.377369\pi$
$618$	1.57560e26	0.482008
$619$	2.57586e26	0.776000	0.388000	−	0.921659i	$-0.373166\pi$
$619$	2.57586e26	0.776000	0.388000	+	0.921659i	$0.373166\pi$
$620$	−1.55547e26	−0.461467
$621$	−6.67057e26	−1.94891
$622$	3.52428e25	0.101406
$623$	−2.98674e26	−0.846373
$624$	6.16470e25	0.172052
$625$	−6.98886e25	−0.192108
$626$	−2.40938e26	−0.652303
$627$	1.42402e25	0.0379730
$628$	1.03418e25	0.0271630
$629$	−1.57559e26	−0.407627
$630$	−1.09772e26	−0.279742
$631$	−1.71380e26	−0.430212	−0.215106	−	0.976591i	$-0.569010\pi$
$631$	−1.71380e26	−0.430212	−0.215106	+	0.976591i	$0.569010\pi$
$632$	−3.80062e26	−0.939815
$633$	3.69238e26	0.899438
$634$	2.51809e26	0.604258
$635$	−3.01847e26	−0.713569
$636$	3.49824e26	0.814718
$637$	2.70699e26	0.621102
$638$	2.85661e24	0.00645734
$639$	−3.80421e26	−0.847240
$640$	2.85701e26	0.626906
$641$	8.10829e25	0.175298	0.0876492	−	0.996151i	$-0.472065\pi$
$641$	8.10829e25	0.175298	0.0876492	+	0.996151i	$0.472065\pi$
$642$	2.10421e26	0.448235
$643$	−7.84136e26	−1.64584	−0.822919	−	0.568159i	$-0.807656\pi$
$643$	−7.84136e26	−1.64584	−0.822919	+	0.568159i	$0.807656\pi$
$644$	8.98081e26	1.85738
$645$	−1.39600e26	−0.284491
$646$	3.70121e25	0.0743249
$647$	−1.51739e26	−0.300265	−0.150133	−	0.988666i	$-0.547970\pi$
$647$	−1.51739e26	−0.300265	−0.150133	+	0.988666i	$0.547970\pi$
$648$	6.89455e24	0.0134445
$649$	4.85822e25	0.0933582
$650$	1.37965e26	0.261272
$651$	−3.81349e26	−0.711710
$652$	−5.14814e26	−0.946887
$653$	−2.77586e26	−0.503179	−0.251590	−	0.967834i	$-0.580953\pi$
$653$	−2.77586e26	−0.503179	−0.251590	+	0.967834i	$0.580953\pi$
$654$	−5.05573e25	−0.0903223
$655$	−7.27277e26	−1.28058
$656$	2.90625e26	0.504367
$657$	−1.15384e26	−0.197367
$658$	5.64148e25	0.0951145
$659$	4.01360e26	0.666995	0.333497	−	0.942751i	$-0.391771\pi$
$659$	4.01360e26	0.666995	0.333497	+	0.942751i	$0.391771\pi$
$660$	2.97574e25	0.0487447
$661$	3.51032e26	0.566805	0.283402	−	0.959001i	$-0.408537\pi$
$661$	3.51032e26	0.566805	0.283402	+	0.959001i	$0.408537\pi$
$662$	2.02677e26	0.322591
$663$	1.39620e26	0.219064
$664$	−1.49978e26	−0.231970
$665$	2.28475e26	0.348364
$666$	−2.34199e26	−0.352030
$667$	1.07098e26	0.158703
$668$	2.94294e26	0.429937
$669$	4.11250e26	0.592322
$670$	−1.99453e26	−0.283224
$671$	−1.67935e26	−0.235113
$672$	5.87411e26	0.810838
$673$	4.06871e26	0.553750	0.276875	−	0.960906i	$-0.410701\pi$
$673$	4.06871e26	0.553750	0.276875	+	0.960906i	$0.410701\pi$
$674$	3.46006e26	0.464317
$675$	3.97553e26	0.526028
$676$	3.27056e25	0.0426706
$677$	2.91591e26	0.375130	0.187565	−	0.982252i	$-0.439940\pi$
$677$	2.91591e26	0.375130	0.187565	+	0.982252i	$0.439940\pi$
$678$	−6.96957e25	−0.0884145
$679$	6.24884e26	0.781693
$680$	1.81762e26	0.224217
$681$	4.72306e26	0.574548
$682$	6.02633e25	0.0722939
$683$	−5.63827e25	−0.0667036	−0.0333518	−	0.999444i	$-0.510618\pi$
$683$	−5.63827e25	−0.0667036	−0.0333518	+	0.999444i	$0.510618\pi$
$684$	−1.57155e26	−0.183356
$685$	−3.17130e26	−0.364903
$686$	−2.06973e26	−0.234874
$687$	3.14151e26	0.351600
$688$	−1.77301e26	−0.195714
$689$	−1.60114e27	−1.74320
$690$	−3.90556e26	−0.419388
$691$	−1.38173e27	−1.46346	−0.731729	−	0.681595i	$-0.761286\pi$
$691$	−1.38173e27	−1.46346	−0.731729	+	0.681595i	$0.761286\pi$
$692$	−4.56894e26	−0.477318
$693$	−1.21487e26	−0.125188
$694$	−5.37835e26	−0.546681
$695$	−1.87725e26	−0.188221
$696$	4.44909e25	0.0440031
$697$	6.58217e26	0.642182
$698$	2.10778e26	0.202861
$699$	−1.14981e27	−1.09167
$700$	−5.35239e26	−0.501321
$701$	4.54973e26	0.420401	0.210201	−	0.977658i	$-0.432588\pi$
$701$	4.54973e26	0.420401	0.210201	+	0.977658i	$0.432588\pi$
$702$	5.39698e26	0.491981
$703$	4.87451e26	0.438384
$704$	−4.18023e25	−0.0370903
$705$	7.00816e25	0.0613490
$706$	1.68849e26	0.145832
$707$	2.61747e27	2.23048
$708$	3.21971e26	0.270708
$709$	−7.63206e26	−0.633144	−0.316572	−	0.948568i	$-0.602532\pi$
$709$	−7.63206e26	−0.633144	−0.316572	+	0.948568i	$0.602532\pi$
$710$	−5.79222e26	−0.474123
$711$	8.20197e26	0.662456
$712$	7.35106e26	0.585855
$713$	2.25936e27	1.77678
$714$	1.89620e26	0.147147
$715$	−1.36199e26	−0.104296
$716$	1.17964e27	0.891404
$717$	−3.26002e26	−0.243102
$718$	−6.89111e26	−0.507116
$719$	−2.17695e27	−1.58097	−0.790486	−	0.612481i	$-0.790172\pi$
$719$	−2.17695e27	−1.58097	−0.790486	+	0.612481i	$0.790172\pi$
$720$	−1.73193e26	−0.124128
$721$	2.79771e27	1.97887
$722$	6.14956e26	0.429280
$723$	1.70023e27	1.17137
$724$	−8.72947e25	−0.0593569
$725$	−6.38284e25	−0.0428354
$726$	4.59374e26	0.304276
$727$	2.95232e27	1.93013	0.965064	−	0.262016i	$-0.0843873\pi$
$727$	2.95232e27	1.93013	0.965064	+	0.262016i	$0.0843873\pi$
$728$	−1.70759e27	−1.10188
$729$	9.42265e26	0.600152
$730$	−1.75682e26	−0.110448
$731$	−4.01557e26	−0.249191
$732$	−1.11296e27	−0.681750
$733$	−1.58903e27	−0.960828	−0.480414	−	0.877042i	$-0.659514\pi$
$733$	−1.58903e27	−0.960828	−0.480414	+	0.877042i	$0.659514\pi$
$734$	−3.77845e26	−0.225528
$735$	4.56702e26	0.269094
$736$	−3.48020e27	−2.02426
$737$	−2.20738e26	−0.126746
$738$	9.78388e26	0.554594
$739$	6.01246e26	0.336458	0.168229	−	0.985748i	$-0.446195\pi$
$739$	6.01246e26	0.336458	0.168229	+	0.985748i	$0.446195\pi$
$740$	1.01861e27	0.562740
$741$	−4.31952e26	−0.235593
$742$	−2.17452e27	−1.17092
$743$	−1.61229e27	−0.857137	−0.428568	−	0.903509i	$-0.640982\pi$
$743$	−1.61229e27	−0.857137	−0.428568	+	0.903509i	$0.640982\pi$
$744$	9.38586e26	0.492642
$745$	−1.70475e27	−0.883440
$746$	2.44042e26	0.124867
$747$	3.23662e26	0.163510
$748$	8.55968e25	0.0426965
$749$	3.73634e27	1.84022
$750$	6.73154e26	0.327365
$751$	−4.82056e26	−0.231483	−0.115741	−	0.993279i	$-0.536924\pi$
$751$	−4.82056e26	−0.231483	−0.115741	+	0.993279i	$0.536924\pi$
$752$	8.90082e25	0.0422047
$753$	−2.12660e27	−0.995711
$754$	−8.66502e25	−0.0400628
$755$	2.18950e27	0.999654
$756$	−2.09377e27	−0.943999
$757$	2.15752e27	0.960604	0.480302	−	0.877103i	$-0.340527\pi$
$757$	2.15752e27	0.960604	0.480302	+	0.877103i	$0.340527\pi$
$758$	−1.85197e27	−0.814287
$759$	−4.32233e26	−0.187682
$760$	−5.62328e26	−0.241135
$761$	1.55283e27	0.657611	0.328806	−	0.944398i	$-0.393354\pi$
$761$	1.55283e27	0.657611	0.328806	+	0.944398i	$0.393354\pi$
$762$	7.75029e26	0.324150
$763$	−8.97720e26	−0.370815
$764$	1.65918e27	0.676871
$765$	−3.92253e26	−0.158046
$766$	3.94878e26	0.157141
$767$	−1.47366e27	−0.579216
$768$	−1.10760e27	−0.429982
$769$	2.12486e27	0.814760	0.407380	−	0.913259i	$-0.366443\pi$
$769$	2.12486e27	0.814760	0.407380	+	0.913259i	$0.366443\pi$
$770$	−1.84973e26	−0.0700562
$771$	−1.14426e27	−0.428063
$772$	2.08525e27	0.770536
$773$	1.86964e27	0.682421	0.341211	−	0.939987i	$-0.389163\pi$
$773$	1.86964e27	0.682421	0.341211	+	0.939987i	$0.389163\pi$
$774$	−5.96883e26	−0.215204
$775$	−1.34653e27	−0.479568
$776$	−1.53798e27	−0.541084
$777$	2.49730e27	0.867902
$778$	1.20522e27	0.413770
$779$	−2.03637e27	−0.690638
$780$	−9.02639e26	−0.302423
$781$	−6.41033e26	−0.212176
$782$	−1.12343e27	−0.367351
$783$	−2.49687e26	−0.0806600
$784$	5.80042e26	0.185121
$785$	−7.98582e25	−0.0251801
$786$	1.86738e27	0.581725
$787$	5.41737e27	1.66736	0.833678	−	0.552251i	$-0.186231\pi$
$787$	5.41737e27	1.66736	0.833678	+	0.552251i	$0.186231\pi$
$788$	−4.40254e26	−0.133877
$789$	−2.66284e26	−0.0800045
$790$	1.24882e27	0.370716
$791$	−1.23755e27	−0.362983
$792$	2.99006e26	0.0866544
$793$	5.09401e27	1.45869
$794$	−3.15801e26	−0.0893551
$795$	−2.70131e27	−0.755243
$796$	3.74547e27	1.03474
$797$	4.95500e27	1.35266	0.676331	−	0.736598i	$-0.263569\pi$
$797$	4.95500e27	1.35266	0.676331	+	0.736598i	$0.263569\pi$
$798$	−5.86638e26	−0.158250
$799$	2.01589e26	0.0537368
$800$	2.07413e27	0.546363
$801$	−1.58640e27	−0.412957
$802$	2.72439e26	0.0700830
$803$	−1.94429e26	−0.0494270
$804$	−1.46291e27	−0.367523
$805$	−6.93490e27	−1.72179
$806$	−1.82798e27	−0.448528
$807$	−3.37404e26	−0.0818184
$808$	−6.44220e27	−1.54392
$809$	−3.63670e27	−0.861383	−0.430691	−	0.902499i	$-0.641730\pi$
$809$	−3.63670e27	−0.861383	−0.430691	+	0.902499i	$0.641730\pi$
$810$	−2.26542e25	−0.00530325
$811$	−5.72899e27	−1.32550	−0.662751	−	0.748840i	$-0.730611\pi$
$811$	−5.72899e27	−1.32550	−0.662751	+	0.748840i	$0.730611\pi$
$812$	3.36161e26	0.0768715
$813$	−8.89864e26	−0.201124
$814$	−3.94640e26	−0.0881595
$815$	3.97535e27	0.877764
$816$	2.99172e26	0.0652926
$817$	1.24232e27	0.267994
$818$	−1.30385e27	−0.278017
$819$	3.68508e27	0.776695
$820$	−4.25535e27	−0.886550
$821$	6.89682e27	1.42033	0.710164	−	0.704036i	$-0.248621\pi$
$821$	6.89682e27	1.42033	0.710164	+	0.704036i	$0.248621\pi$
$822$	8.14272e26	0.165763
$823$	−4.64707e25	−0.00935149	−0.00467575	−	0.999989i	$-0.501488\pi$
$823$	−4.64707e25	−0.00935149	−0.00467575	+	0.999989i	$0.501488\pi$
$824$	−6.88580e27	−1.36976
$825$	2.57603e26	0.0506568
$826$	−2.00139e27	−0.389063
$827$	−9.26519e27	−1.78054	−0.890271	−	0.455431i	$-0.849485\pi$
$827$	−9.26519e27	−1.78054	−0.890271	+	0.455431i	$0.849485\pi$
$828$	4.77013e27	0.906238
$829$	−2.92837e27	−0.549994	−0.274997	−	0.961445i	$-0.588677\pi$
$829$	−2.92837e27	−0.549994	−0.274997	+	0.961445i	$0.588677\pi$
$830$	4.92801e26	0.0915018
$831$	−6.38525e27	−1.17211
$832$	1.26800e27	0.230117
$833$	1.31370e27	0.235705
$834$	4.82009e26	0.0855022
$835$	−2.27251e27	−0.398551
$836$	−2.64816e26	−0.0459182
$837$	−5.26742e27	−0.903038
$838$	−1.68730e27	−0.286005
$839$	−5.71687e27	−0.958119	−0.479060	−	0.877782i	$-0.659022\pi$
$839$	−5.71687e27	−0.958119	−0.479060	+	0.877782i	$0.659022\pi$
$840$	−2.88091e27	−0.477394
$841$	−6.06317e27	−0.993432
$842$	2.21178e27	0.358326
$843$	5.11123e27	0.818774
$844$	−6.86649e27	−1.08763
$845$	−2.52550e26	−0.0395556
$846$	2.99646e26	0.0464077
$847$	8.15687e27	1.24920
$848$	−3.43084e27	−0.519565
$849$	5.75552e27	0.861910
$850$	6.69541e26	0.0991511
$851$	−1.47956e28	−2.16671
$852$	−4.24835e27	−0.615240
$853$	2.99596e27	0.429063	0.214531	−	0.976717i	$-0.431178\pi$
$853$	2.99596e27	0.429063	0.214531	+	0.976717i	$0.431178\pi$
$854$	6.91821e27	0.979815
$855$	1.21354e27	0.169971
$856$	−9.19597e27	−1.27379
$857$	−1.49271e27	−0.204484	−0.102242	−	0.994760i	$-0.532602\pi$
$857$	−1.49271e27	−0.204484	−0.102242	+	0.994760i	$0.532602\pi$
$858$	3.49708e26	0.0473780
$859$	−5.73808e27	−0.768832	−0.384416	−	0.923160i	$-0.625597\pi$
$859$	−5.73808e27	−0.768832	−0.384416	+	0.923160i	$0.625597\pi$
$860$	2.59605e27	0.344015
$861$	−1.04327e28	−1.36731
$862$	3.04939e27	0.395271
$863$	2.34691e27	0.300880	0.150440	−	0.988619i	$-0.451931\pi$
$863$	2.34691e27	0.300880	0.150440	+	0.988619i	$0.451931\pi$
$864$	8.11368e27	1.02882
$865$	3.52810e27	0.442474
$866$	5.69468e27	0.706397
$867$	−4.31489e27	−0.529405
$868$	7.09170e27	0.860623
$869$	1.38208e27	0.165900
$870$	−1.46189e26	−0.0173573
$871$	6.69570e27	0.786364
$872$	2.20949e27	0.256676
$873$	3.31905e27	0.381399
$874$	3.47562e27	0.395070
$875$	1.19529e28	1.34399
$876$	−1.28855e27	−0.143322
$877$	−1.09751e28	−1.20757	−0.603785	−	0.797148i	$-0.706341\pi$
$877$	−1.09751e28	−1.20757	−0.603785	+	0.797148i	$0.706341\pi$
$878$	9.23014e27	1.00464
$879$	−8.95237e26	−0.0963927
$880$	−2.91841e26	−0.0310857
$881$	9.97103e27	1.05068	0.525338	−	0.850894i	$-0.323939\pi$
$881$	9.97103e27	1.05068	0.525338	+	0.850894i	$0.323939\pi$
$882$	1.95271e27	0.203557
$883$	5.32334e27	0.548981	0.274491	−	0.961590i	$-0.411491\pi$
$883$	5.32334e27	0.548981	0.274491	+	0.961590i	$0.411491\pi$
$884$	−2.59643e27	−0.264899
$885$	−2.48623e27	−0.250946
$886$	−2.76910e27	−0.276515
$887$	−1.56399e28	−1.54511	−0.772556	−	0.634946i	$-0.781022\pi$
$887$	−1.56399e28	−1.54511	−0.772556	+	0.634946i	$0.781022\pi$
$888$	−6.14642e27	−0.600757
$889$	1.37618e28	1.33079
$890$	−2.41543e27	−0.231094
$891$	−2.50718e25	−0.00237327
$892$	−7.64776e27	−0.716255
$893$	−6.23668e26	−0.0577916
$894$	4.37717e27	0.401316
$895$	−9.10905e27	−0.826331
$896$	−1.30257e28	−1.16916
$897$	1.31111e28	1.16442
$898$	−6.69995e27	−0.588771
$899$	8.45701e26	0.0735360
$900$	−2.84291e27	−0.244601
$901$	−7.77029e27	−0.661533
$902$	1.64864e27	0.138888
$903$	6.36465e27	0.530568
$904$	3.04589e27	0.251255
$905$	6.74082e26	0.0550239
$906$	−5.62183e27	−0.454109
$907$	1.14409e28	0.914515	0.457257	−	0.889334i	$-0.348832\pi$
$907$	1.14409e28	0.914515	0.457257	+	0.889334i	$0.348832\pi$
$908$	−8.78318e27	−0.694763
$909$	1.39026e28	1.08828
$910$	5.61084e27	0.434645
$911$	−9.54682e27	−0.731870	−0.365935	−	0.930640i	$-0.619251\pi$
$911$	−9.54682e27	−0.731870	−0.365935	+	0.930640i	$0.619251\pi$
$912$	−9.25566e26	−0.0702193
$913$	5.45390e26	0.0409482
$914$	−4.08614e27	−0.303616
$915$	8.59420e27	0.631982
$916$	−5.84206e27	−0.425167
$917$	3.31581e28	2.38825
$918$	2.61914e27	0.186704
$919$	−3.46912e27	−0.244749	−0.122375	−	0.992484i	$-0.539051\pi$
$919$	−3.46912e27	−0.244749	−0.122375	+	0.992484i	$0.539051\pi$
$920$	1.70684e28	1.19181
$921$	−5.14734e27	−0.355727
$922$	−1.00627e28	−0.688289
$923$	1.94446e28	1.31639
$924$	−1.35670e27	−0.0909077
$925$	8.81789e27	0.584815
$926$	1.52406e27	0.100045
$927$	1.48600e28	0.965518
$928$	−1.30268e27	−0.0837782
$929$	1.87970e28	1.19658	0.598288	−	0.801281i	$-0.295848\pi$
$929$	1.87970e28	1.19658	0.598288	+	0.801281i	$0.295848\pi$
$930$	−3.08403e27	−0.194326
$931$	−4.06427e27	−0.253490
$932$	2.13822e28	1.32008
$933$	−1.99605e27	−0.121982
$934$	−1.07435e28	−0.649908
$935$	−6.60971e26	−0.0395797
$936$	−9.06983e27	−0.537624
$937$	−3.16610e28	−1.85780	−0.928900	−	0.370330i	$-0.879245\pi$
$937$	−3.16610e28	−1.85780	−0.928900	+	0.370330i	$0.879245\pi$
$938$	9.09349e27	0.528206
$939$	1.36460e28	0.784663
$940$	−1.30326e27	−0.0741852
$941$	7.79945e27	0.439504	0.219752	−	0.975556i	$-0.429475\pi$
$941$	7.79945e27	0.439504	0.219752	+	0.975556i	$0.429475\pi$
$942$	2.05046e26	0.0114385
$943$	6.18099e28	3.41348
$944$	−3.15768e27	−0.172637
$945$	1.61679e28	0.875087
$946$	−1.00578e27	−0.0538939
$947$	1.40516e28	0.745418	0.372709	−	0.927948i	$-0.378429\pi$
$947$	1.40516e28	0.745418	0.372709	+	0.927948i	$0.378429\pi$
$948$	9.15955e27	0.481055
$949$	5.89768e27	0.306656
$950$	−2.07140e27	−0.106633
$951$	−1.42617e28	−0.726869
$952$	−8.28690e27	−0.418159
$953$	−2.16654e28	−1.08239	−0.541195	−	0.840897i	$-0.682028\pi$
$953$	−2.16654e28	−1.08239	−0.541195	+	0.840897i	$0.682028\pi$
$954$	−1.15499e28	−0.571306
$955$	−1.28120e28	−0.627459
$956$	6.06245e27	0.293967
$957$	−1.61790e26	−0.00776761
$958$	7.52269e26	0.0357603
$959$	1.44586e28	0.680534
$960$	2.13927e27	0.0996985
$961$	−3.82964e27	−0.176720
$962$	1.19707e28	0.546962
$963$	1.98455e28	0.897866
$964$	−3.16182e28	−1.41646
$965$	−1.61021e28	−0.714287
$966$	1.78062e28	0.782149
$967$	8.99589e27	0.391285	0.195642	−	0.980675i	$-0.437321\pi$
$967$	8.99589e27	0.391285	0.195642	+	0.980675i	$0.437321\pi$
$968$	−2.00759e28	−0.864688
$969$	−2.09625e27	−0.0894063
$970$	5.05353e27	0.213434
$971$	−3.76835e28	−1.57604	−0.788022	−	0.615647i	$-0.788895\pi$
$971$	−3.76835e28	−1.57604	−0.788022	+	0.615647i	$0.788895\pi$
$972$	−1.79656e28	−0.744065
$973$	8.55878e27	0.351027
$974$	−6.97477e26	−0.0283282
$975$	−7.81393e27	−0.314287
$976$	1.09152e28	0.434768
$977$	−4.33141e28	−1.70856	−0.854281	−	0.519811i	$-0.826002\pi$
$977$	−4.33141e28	−1.70856	−0.854281	+	0.519811i	$0.826002\pi$
$978$	−1.02072e28	−0.398738
$979$	−2.67319e27	−0.103417
$980$	−8.49300e27	−0.325397
$981$	−4.76822e27	−0.180926
$982$	−8.49849e27	−0.319362
$983$	2.67918e27	0.0997111	0.0498555	−	0.998756i	$-0.484124\pi$
$983$	2.67918e27	0.0997111	0.0498555	+	0.998756i	$0.484124\pi$
$984$	2.56772e28	0.946443
$985$	3.39960e27	0.124104
$986$	−4.20511e26	−0.0152036
$987$	−3.19517e27	−0.114414
$988$	8.03274e27	0.284887
$989$	−3.77083e28	−1.32456
$990$	−9.82480e26	−0.0341814
$991$	4.85085e28	1.67154	0.835772	−	0.549076i	$-0.185020\pi$
$991$	4.85085e28	1.67154	0.835772	+	0.549076i	$0.185020\pi$
$992$	−2.74815e28	−0.937948
$993$	−1.14790e28	−0.388049
$994$	2.64079e28	0.884227
$995$	−2.89222e28	−0.959206
$996$	3.61449e27	0.118736
$997$	−4.36029e28	−1.41877	−0.709384	−	0.704822i	$-0.751027\pi$
$997$	−4.36029e28	−1.41877	−0.709384	+	0.704822i	$0.751027\pi$
$998$	−9.36836e26	−0.0301942
$999$	3.44942e28	1.10122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.a.1.15	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.a.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-368.710 q^{2} +20882.6 q^{3} -388341. q^{4} +2.99874e6 q^{5} -7.69963e6 q^{6} -1.36719e8 q^{7} +3.36495e8 q^{8} -7.26177e8 q^{9} +O(q^{10})\)	\(q-368.710 q^{2} +20882.6 q^{3} -388341. q^{4} +2.99874e6 q^{5} -7.69963e6 q^{6} -1.36719e8 q^{7} +3.36495e8 q^{8} -7.26177e8 q^{9} -1.10566e9 q^{10} -1.22365e9 q^{11} -8.10958e9 q^{12} +3.71174e10 q^{13} +5.04095e10 q^{14} +6.26215e10 q^{15} +7.95334e10 q^{16} +1.80130e11 q^{17} +2.67749e11 q^{18} -5.57279e11 q^{19} -1.16453e12 q^{20} -2.85504e12 q^{21} +4.51173e11 q^{22} +1.69151e13 q^{23} +7.02691e12 q^{24} -1.00811e13 q^{25} -1.36856e13 q^{26} -3.94356e13 q^{27} +5.30934e13 q^{28} +6.33151e12 q^{29} -2.30892e13 q^{30} +1.33570e14 q^{31} -2.05745e14 q^{32} -2.55531e13 q^{33} -6.64157e13 q^{34} -4.09983e14 q^{35} +2.82004e14 q^{36} -8.74697e14 q^{37} +2.05474e14 q^{38} +7.75109e14 q^{39} +1.00906e15 q^{40} +3.65413e15 q^{41} +1.05268e15 q^{42} -2.22927e15 q^{43} +4.75195e14 q^{44} -2.17761e15 q^{45} -6.23677e15 q^{46} +1.11913e15 q^{47} +1.66087e15 q^{48} +7.29306e15 q^{49} +3.71699e15 q^{50} +3.76159e15 q^{51} -1.44142e16 q^{52} -4.31371e16 q^{53} +1.45403e16 q^{54} -3.66941e15 q^{55} -4.60051e16 q^{56} -1.16375e16 q^{57} -2.33449e15 q^{58} -3.97026e16 q^{59} -2.43185e16 q^{60} +1.37240e17 q^{61} -4.92487e16 q^{62} +9.92819e16 q^{63} +3.41619e16 q^{64} +1.11305e17 q^{65} +9.42168e15 q^{66} +1.80393e17 q^{67} -6.99518e16 q^{68} +3.53232e17 q^{69} +1.51165e17 q^{70} +5.23868e17 q^{71} -2.44355e17 q^{72} +1.58892e17 q^{73} +3.22510e17 q^{74} -2.10519e17 q^{75} +2.16414e17 q^{76} +1.67296e17 q^{77} -2.85790e17 q^{78} -1.12947e18 q^{79} +2.38499e17 q^{80} +2.04893e16 q^{81} -1.34731e18 q^{82} -4.45706e17 q^{83} +1.10873e18 q^{84} +5.40162e17 q^{85} +8.21952e17 q^{86} +1.32219e17 q^{87} -4.11754e17 q^{88} +2.18459e18 q^{89} +8.02907e17 q^{90} -5.07464e18 q^{91} -6.56883e18 q^{92} +2.78930e18 q^{93} -4.12634e17 q^{94} -1.67113e18 q^{95} -4.29650e18 q^{96} -4.57058e18 q^{97} -2.68902e18 q^{98} +8.88589e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) \) 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