LMFDB - Embedded newform 47.20.a.a.1.6

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			1.6
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)

$f(q)$	$=$	$q-1022.36 q^{2} -52765.0 q^{3} +520940. q^{4} -4.07696e6 q^{5} +5.39451e7 q^{6} +1.19233e8 q^{7} +3.42261e6 q^{8} +1.62189e9 q^{9} +O(q^{10})$	\(q-1022.36 q^{2} -52765.0 q^{3} +520940. q^{4} -4.07696e6 q^{5} +5.39451e7 q^{6} +1.19233e8 q^{7} +3.42261e6 q^{8} +1.62189e9 q^{9} +4.16814e9 q^{10} -9.12712e9 q^{11} -2.74874e10 q^{12} +9.45308e9 q^{13} -1.21900e11 q^{14} +2.15121e11 q^{15} -2.76622e11 q^{16} -4.24458e11 q^{17} -1.65816e12 q^{18} -1.41285e12 q^{19} -2.12385e12 q^{20} -6.29135e12 q^{21} +9.33124e12 q^{22} +9.72475e12 q^{23} -1.80594e11 q^{24} -2.45186e12 q^{25} -9.66449e12 q^{26} -2.42523e13 q^{27} +6.21134e13 q^{28} +1.35675e13 q^{29} -2.19932e14 q^{30} -2.05294e14 q^{31} +2.81014e14 q^{32} +4.81593e14 q^{33} +4.33951e14 q^{34} -4.86110e14 q^{35} +8.44907e14 q^{36} -1.99365e14 q^{37} +1.44445e15 q^{38} -4.98792e14 q^{39} -1.39538e13 q^{40} -1.34394e15 q^{41} +6.43205e15 q^{42} +2.40405e15 q^{43} -4.75468e15 q^{44} -6.61238e15 q^{45} -9.94223e15 q^{46} +1.11913e15 q^{47} +1.45960e16 q^{48} +2.81769e15 q^{49} +2.50670e15 q^{50} +2.23966e16 q^{51} +4.92449e15 q^{52} +4.20458e16 q^{53} +2.47946e16 q^{54} +3.72109e16 q^{55} +4.08089e14 q^{56} +7.45491e16 q^{57} -1.38709e16 q^{58} +1.78370e16 q^{59} +1.12065e17 q^{60} +3.15780e16 q^{61} +2.09886e17 q^{62} +1.93383e17 q^{63} -1.42269e17 q^{64} -3.85399e16 q^{65} -4.92363e17 q^{66} -2.10855e17 q^{67} -2.21117e17 q^{68} -5.13127e17 q^{69} +4.96981e17 q^{70} +3.81493e17 q^{71} +5.55109e15 q^{72} +1.99595e15 q^{73} +2.03823e17 q^{74} +1.29373e17 q^{75} -7.36011e17 q^{76} -1.08826e18 q^{77} +5.09947e17 q^{78} -9.21491e17 q^{79} +1.12778e18 q^{80} -6.05387e17 q^{81} +1.37399e18 q^{82} +3.32892e18 q^{83} -3.27742e18 q^{84} +1.73050e18 q^{85} -2.45781e18 q^{86} -7.15891e17 q^{87} -3.12386e16 q^{88} +2.81299e18 q^{89} +6.76026e18 q^{90} +1.12712e18 q^{91} +5.06601e18 q^{92} +1.08324e19 q^{93} -1.14416e18 q^{94} +5.76014e18 q^{95} -1.48277e19 q^{96} -1.69262e17 q^{97} -2.88070e18 q^{98} -1.48032e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1022.36	−1.41195	−0.705977	−	0.708235i	$-0.749492\pi$
$2$	−1022.36	−1.41195	−0.705977	+	0.708235i	$0.749492\pi$
$3$	−52765.0	−1.54773	−0.773864	−	0.633352i	$-0.781678\pi$
$3$	−52765.0	−1.54773	−0.773864	+	0.633352i	$0.781678\pi$
$4$	520940.	0.993615
$5$	−4.07696e6	−0.933516	−0.466758	−	0.884385i	$-0.654578\pi$
$5$	−4.07696e6	−0.933516	−0.466758	+	0.884385i	$0.654578\pi$
$6$	5.39451e7	2.18532
$7$	1.19233e8	1.11678	0.558388	−	0.829580i	$-0.311420\pi$
$7$	1.19233e8	1.11678	0.558388	+	0.829580i	$0.311420\pi$
$8$	3.42261e6	0.00901576
$9$	1.62189e9	1.39546
$10$	4.16814e9	1.31808
$11$	−9.12712e9	−1.16709	−0.583543	−	0.812082i	$-0.698334\pi$
$11$	−9.12712e9	−1.16709	−0.583543	+	0.812082i	$0.698334\pi$
$12$	−2.74874e10	−1.53784
$13$	9.45308e9	0.247236	0.123618	−	0.992330i	$-0.460550\pi$
$13$	9.45308e9	0.247236	0.123618	+	0.992330i	$0.460550\pi$
$14$	−1.21900e11	−1.57684
$15$	2.15121e11	1.44483
$16$	−2.76622e11	−1.00634
$17$	−4.24458e11	−0.868101	−0.434051	−	0.900888i	$-0.642916\pi$
$17$	−4.24458e11	−0.868101	−0.434051	+	0.900888i	$0.642916\pi$
$18$	−1.65816e12	−1.97032
$19$	−1.41285e12	−1.00447	−0.502235	−	0.864731i	$-0.667489\pi$
$19$	−1.41285e12	−1.00447	−0.502235	+	0.864731i	$0.667489\pi$
$20$	−2.12385e12	−0.927555
$21$	−6.29135e12	−1.72847
$22$	9.33124e12	1.64787
$23$	9.72475e12	1.12581	0.562904	−	0.826523i	$-0.309684\pi$
$23$	9.72475e12	1.12581	0.562904	+	0.826523i	$0.309684\pi$
$24$	−1.80594e11	−0.0139539
$25$	−2.45186e12	−0.128548
$26$	−9.66449e12	−0.349086
$27$	−2.42523e13	−0.612063
$28$	6.21134e13	1.10965
$29$	1.35675e13	0.173668	0.0868339	−	0.996223i	$-0.472325\pi$
$29$	1.35675e13	0.173668	0.0868339	+	0.996223i	$0.472325\pi$
$30$	−2.19932e14	−2.04003
$31$	−2.05294e14	−1.39457	−0.697286	−	0.716793i	$-0.745609\pi$
$31$	−2.05294e14	−1.39457	−0.697286	+	0.716793i	$0.745609\pi$
$32$	2.81014e14	1.41190
$33$	4.81593e14	1.80633
$34$	4.33951e14	1.22572
$35$	−4.86110e14	−1.04253
$36$	8.44907e14	1.38655
$37$	−1.99365e14	−0.252193	−0.126096	−	0.992018i	$-0.540245\pi$
$37$	−1.99365e14	−0.252193	−0.126096	+	0.992018i	$0.540245\pi$
$38$	1.44445e15	1.41827
$39$	−4.98792e14	−0.382654
$40$	−1.39538e13	−0.00841635
$41$	−1.34394e15	−0.641109	−0.320554	−	0.947230i	$-0.603869\pi$
$41$	−1.34394e15	−0.641109	−0.320554	+	0.947230i	$0.603869\pi$
$42$	6.43205e15	2.44051
$43$	2.40405e15	0.729445	0.364723	−	0.931116i	$-0.381164\pi$
$43$	2.40405e15	0.729445	0.364723	+	0.931116i	$0.381164\pi$
$44$	−4.75468e15	−1.15963
$45$	−6.61238e15	−1.30268
$46$	−9.94223e15	−1.58959
$47$	1.11913e15	0.145865
$47$	1.11913e15	0.145865
$48$	1.45960e16	1.55755
$49$	2.81769e15	0.247190
$50$	2.50670e15	0.181504
$51$	2.23966e16	1.34358
$52$	4.92449e15	0.245657
$53$	4.20458e16	1.75026	0.875129	−	0.483890i	$-0.160777\pi$
$53$	4.20458e16	1.75026	0.875129	+	0.483890i	$0.160777\pi$
$54$	2.47946e16	0.864206
$55$	3.72109e16	1.08949
$56$	4.08089e14	0.0100686
$57$	7.45491e16	1.55465
$58$	−1.38709e16	−0.245211
$59$	1.78370e16	0.268057	0.134029	−	0.990977i	$-0.457209\pi$
$59$	1.78370e16	0.268057	0.134029	+	0.990977i	$0.457209\pi$
$60$	1.12065e17	1.43560
$61$	3.15780e16	0.345741	0.172871	−	0.984945i	$-0.444696\pi$
$61$	3.15780e16	0.345741	0.172871	+	0.984945i	$0.444696\pi$
$62$	2.09886e17	1.96907
$63$	1.93383e17	1.55842
$64$	−1.42269e17	−0.987189
$65$	−3.85399e16	−0.230799
$66$	−4.92363e17	−2.55046
$67$	−2.10855e17	−0.946834	−0.473417	−	0.880839i	$-0.656980\pi$
$67$	−2.10855e17	−0.946834	−0.473417	+	0.880839i	$0.656980\pi$
$68$	−2.21117e17	−0.862558
$69$	−5.13127e17	−1.74244
$70$	4.96981e17	1.47200
$71$	3.81493e17	0.987490	0.493745	−	0.869607i	$-0.335628\pi$
$71$	3.81493e17	0.987490	0.493745	+	0.869607i	$0.335628\pi$
$72$	5.55109e15	0.0125811
$73$	1.99595e15	0.00396809	0.00198405	−	0.999998i	$-0.499368\pi$
$73$	1.99595e15	0.00396809	0.00198405	+	0.999998i	$0.499368\pi$
$74$	2.03823e17	0.356084
$75$	1.29373e17	0.198958
$76$	−7.36011e17	−0.998056
$77$	−1.08826e18	−1.30338
$78$	5.09947e17	0.540290
$79$	−9.21491e17	−0.865035	−0.432518	−	0.901625i	$-0.642375\pi$
$79$	−9.21491e17	−0.865035	−0.432518	+	0.901625i	$0.642375\pi$
$80$	1.12778e18	0.939438
$81$	−6.05387e17	−0.448152
$82$	1.37399e18	0.905216
$83$	3.32892e18	1.95461	0.977307	−	0.211826i	$-0.0679411\pi$
$83$	3.32892e18	1.95461	0.977307	+	0.211826i	$0.0679411\pi$
$84$	−3.27742e18	−1.71743
$85$	1.73050e18	0.810386
$86$	−2.45781e18	−1.02994
$87$	−7.15891e17	−0.268790
$88$	−3.12386e16	−0.0105222
$89$	2.81299e18	0.851066	0.425533	−	0.904943i	$-0.360087\pi$
$89$	2.81299e18	0.851066	0.425533	+	0.904943i	$0.360087\pi$
$90$	6.76026e18	1.83933
$91$	1.12712e18	0.276107
$92$	5.06601e18	1.11862
$93$	1.08324e19	2.15842
$94$	−1.14416e18	−0.205955
$95$	5.76014e18	0.937688
$96$	−1.48277e19	−2.18523
$97$	−1.69262e17	−0.0226062	−0.0113031	−	0.999936i	$-0.503598\pi$
$97$	−1.69262e17	−0.0226062	−0.0113031	+	0.999936i	$0.503598\pi$
$98$	−2.88070e18	−0.349020
$99$	−1.48032e19	−1.62862
$100$	−1.27727e18	−0.127727
$101$	1.47590e19	1.34278	0.671389	−	0.741105i	$-0.265698\pi$
$101$	1.47590e19	1.34278	0.671389	+	0.741105i	$0.265698\pi$
$102$	−2.28974e19	−1.89708
$103$	−2.16124e19	−1.63211	−0.816055	−	0.577974i	$-0.803843\pi$
$103$	−2.16124e19	−1.63211	−0.816055	+	0.577974i	$0.803843\pi$
$104$	3.23542e16	0.00222902
$105$	2.56496e19	1.61355
$106$	−4.29861e19	−2.47128
$107$	−8.57553e18	−0.450936	−0.225468	−	0.974251i	$-0.572391\pi$
$107$	−8.57553e18	−0.450936	−0.225468	+	0.974251i	$0.572391\pi$
$108$	−1.26340e19	−0.608155
$109$	−5.04994e18	−0.222707	−0.111354	−	0.993781i	$-0.535519\pi$
$109$	−5.04994e18	−0.222707	−0.111354	+	0.993781i	$0.535519\pi$
$110$	−3.80431e19	−1.53832
$111$	1.05195e19	0.390325
$112$	−3.29825e19	−1.12386
$113$	1.74404e19	0.546150	0.273075	−	0.961993i	$-0.411959\pi$
$113$	1.74404e19	0.546150	0.273075	+	0.961993i	$0.411959\pi$
$114$	−7.62163e19	−2.19509
$115$	−3.96474e19	−1.05096
$116$	7.06787e18	0.172559
$117$	1.53318e19	0.345008
$118$	−1.82359e19	−0.378485
$119$	−5.06096e19	−0.969475
$120$	7.36275e17	0.0130262
$121$	2.21452e19	0.362092
$122$	−3.22842e19	−0.488171
$123$	7.09128e19	0.992261
$124$	−1.06946e20	−1.38567
$125$	8.77580e19	1.05352
$126$	−1.97708e20	−2.20041
$127$	−4.53351e19	−0.468057	−0.234029	−	0.972230i	$-0.575191\pi$
$127$	−4.53351e19	−0.468057	−0.234029	+	0.972230i	$0.575191\pi$
$128$	−1.88156e18	−0.0180312
$129$	−1.26850e20	−1.12898
$130$	3.94018e19	0.325877
$131$	4.76462e19	0.366396	0.183198	−	0.983076i	$-0.441355\pi$
$131$	4.76462e19	0.366396	0.183198	+	0.983076i	$0.441355\pi$
$132$	2.50881e20	1.79480
$133$	−1.68459e20	−1.12177
$134$	2.15571e20	1.33689
$135$	9.88755e19	0.571371
$136$	−1.45275e18	−0.00782659
$137$	−2.02806e20	−1.01914	−0.509571	−	0.860429i	$-0.670196\pi$
$137$	−2.02806e20	−1.01914	−0.509571	+	0.860429i	$0.670196\pi$
$138$	5.24602e20	2.46025
$139$	−3.80169e19	−0.166470	−0.0832350	−	0.996530i	$-0.526525\pi$
$139$	−3.80169e19	−0.166470	−0.0832350	+	0.996530i	$0.526525\pi$
$140$	−2.53234e20	−1.03587
$141$	−5.90510e19	−0.225759
$142$	−3.90025e20	−1.39429
$143$	−8.62794e19	−0.288546
$144$	−4.48650e20	−1.40431
$145$	−5.53143e19	−0.162122
$146$	−2.04059e18	−0.00560277
$147$	−1.48676e20	−0.382582
$148$	−1.03857e20	−0.250582
$149$	2.86503e20	0.648426	0.324213	−	0.945984i	$-0.394901\pi$
$149$	2.86503e20	0.648426	0.324213	+	0.945984i	$0.394901\pi$
$150$	−1.32266e20	−0.280919
$151$	7.40062e20	1.47566	0.737832	−	0.674985i	$-0.235850\pi$
$151$	7.40062e20	1.47566	0.737832	+	0.674985i	$0.235850\pi$
$152$	−4.83563e18	−0.00905606
$153$	−6.88424e20	−1.21140
$154$	1.11259e21	1.84031
$155$	8.36978e20	1.30186
$156$	−2.59841e20	−0.380210
$157$	1.44417e21	1.98872	0.994358	−	0.106077i	$-0.0338291\pi$
$157$	1.44417e21	1.98872	0.994358	+	0.106077i	$0.0338291\pi$
$158$	9.42099e20	1.22139
$159$	−2.21855e21	−2.70892
$160$	−1.14568e21	−1.31803
$161$	1.15951e21	1.25727
$162$	6.18926e20	0.632770
$163$	1.70511e21	1.64426	0.822128	−	0.569303i	$-0.192787\pi$
$163$	1.70511e21	1.64426	0.822128	+	0.569303i	$0.192787\pi$
$164$	−7.00110e20	−0.637015
$165$	−1.96344e21	−1.68624
$166$	−3.40337e21	−2.75983
$167$	1.66096e21	1.27219	0.636096	−	0.771610i	$-0.280548\pi$
$167$	1.66096e21	1.27219	0.636096	+	0.771610i	$0.280548\pi$
$168$	−2.15328e19	−0.0155834
$169$	−1.37256e21	−0.938874
$170$	−1.76920e21	−1.14423
$171$	−2.29149e21	−1.40170
$172$	1.25237e21	0.724788
$173$	−1.84123e21	−1.00849	−0.504244	−	0.863561i	$-0.668229\pi$
$173$	−1.84123e21	−1.00849	−0.504244	+	0.863561i	$0.668229\pi$
$174$	7.31901e20	0.379520
$175$	−2.92344e20	−0.143560
$176$	2.52476e21	1.17449
$177$	−9.41170e20	−0.414880
$178$	−2.87590e21	−1.20167
$179$	−2.02644e21	−0.802843	−0.401421	−	0.915893i	$-0.631484\pi$
$179$	−2.02644e21	−0.802843	−0.401421	+	0.915893i	$0.631484\pi$
$180$	−3.44465e21	−1.29437
$181$	4.62493e21	1.64877	0.824383	−	0.566033i	$-0.191522\pi$
$181$	4.62493e21	1.64877	0.824383	+	0.566033i	$0.191522\pi$
$182$	−1.15233e21	−0.389851
$183$	−1.66621e21	−0.535113
$184$	3.32840e19	0.0101500
$185$	8.12803e20	0.235426
$186$	−1.10746e22	−3.04759
$187$	3.87408e21	1.01315
$188$	5.83000e20	0.144934
$189$	−2.89168e21	−0.683538
$190$	−5.88896e21	−1.32397
$191$	3.16078e21	0.676047	0.338024	−	0.941138i	$-0.390242\pi$
$191$	3.16078e21	0.676047	0.338024	+	0.941138i	$0.390242\pi$
$192$	7.50683e21	1.52790
$193$	−4.26557e21	−0.826385	−0.413192	−	0.910644i	$-0.635586\pi$
$193$	−4.26557e21	−0.826385	−0.413192	+	0.910644i	$0.635586\pi$
$194$	1.73047e20	0.0319190
$195$	2.03356e21	0.357213
$196$	1.46785e21	0.245611
$197$	−5.80179e20	−0.0924981	−0.0462491	−	0.998930i	$-0.514727\pi$
$197$	−5.80179e20	−0.0924981	−0.0462491	+	0.998930i	$0.514727\pi$
$198$	1.51342e22	2.29954
$199$	8.62529e21	1.24931	0.624654	−	0.780902i	$-0.285240\pi$
$199$	8.62529e21	1.24931	0.624654	+	0.780902i	$0.285240\pi$
$200$	−8.39177e18	−0.00115896
$201$	1.11258e22	1.46544
$202$	−1.50891e22	−1.89594
$203$	1.61770e21	0.193948
$204$	1.16673e22	1.33500
$205$	5.47917e21	0.598485
$206$	2.20957e22	2.30447
$207$	1.57725e22	1.57102
$208$	−2.61493e21	−0.248805
$209$	1.28953e22	1.17230
$210$	−2.62232e22	−2.27826
$211$	1.08491e21	0.0900970	0.0450485	−	0.998985i	$-0.485656\pi$
$211$	1.08491e21	0.0900970	0.0450485	+	0.998985i	$0.485656\pi$
$212$	2.19034e22	1.73908
$213$	−2.01295e22	−1.52837
$214$	8.76732e21	0.636701
$215$	−9.80121e21	−0.680949
$216$	−8.30060e19	−0.00551822
$217$	−2.44779e22	−1.55743
$218$	5.16287e21	0.314452
$219$	−1.05316e20	−0.00614153
$220$	1.93847e22	1.08254
$221$	−4.01244e21	−0.214626
$222$	−1.07548e22	−0.551121
$223$	2.97238e22	1.45951	0.729757	−	0.683707i	$-0.239633\pi$
$223$	2.97238e22	1.45951	0.729757	+	0.683707i	$0.239633\pi$
$224$	3.35062e22	1.57677
$225$	−3.97665e21	−0.179384
$226$	−1.78305e22	−0.771138
$227$	−1.86274e22	−0.772516	−0.386258	−	0.922391i	$-0.626233\pi$
$227$	−1.86274e22	−0.772516	−0.386258	+	0.922391i	$0.626233\pi$
$228$	3.88356e22	1.54472
$229$	1.36090e22	0.519265	0.259632	−	0.965708i	$-0.416399\pi$
$229$	1.36090e22	0.519265	0.259632	+	0.965708i	$0.416399\pi$
$230$	4.05341e22	1.48391
$231$	5.74219e22	2.01727
$232$	4.64363e19	0.00156575
$233$	−1.36758e22	−0.442661	−0.221330	−	0.975199i	$-0.571040\pi$
$233$	−1.36758e22	−0.442661	−0.221330	+	0.975199i	$0.571040\pi$
$234$	−1.56747e22	−0.487135
$235$	−4.56265e21	−0.136167
$236$	9.29201e21	0.266346
$237$	4.86225e22	1.33884
$238$	5.17414e22	1.36885
$239$	9.74817e21	0.247824	0.123912	−	0.992293i	$-0.460456\pi$
$239$	9.74817e21	0.247824	0.123912	+	0.992293i	$0.460456\pi$
$240$	−5.95072e22	−1.45399
$241$	−9.39627e21	−0.220696	−0.110348	−	0.993893i	$-0.535196\pi$
$241$	−9.39627e21	−0.220696	−0.110348	+	0.993893i	$0.535196\pi$
$242$	−2.26404e22	−0.511257
$243$	6.01308e22	1.30568
$244$	1.64503e22	0.343534
$245$	−1.14876e22	−0.230755
$246$	−7.24987e22	−1.40103
$247$	−1.33558e22	−0.248341
$248$	−7.02643e20	−0.0125731
$249$	−1.75650e23	−3.02521
$250$	−8.97207e22	−1.48752
$251$	−6.15359e22	−0.982264	−0.491132	−	0.871085i	$-0.663417\pi$
$251$	−6.15359e22	−0.982264	−0.491132	+	0.871085i	$0.663417\pi$
$252$	1.00741e23	1.54847
$253$	−8.87589e22	−1.31391
$254$	4.63490e22	0.660875
$255$	−9.13100e22	−1.25426
$256$	7.65135e22	1.01265
$257$	−3.20774e22	−0.409104	−0.204552	−	0.978856i	$-0.565574\pi$
$257$	−3.20774e22	−0.409104	−0.204552	+	0.978856i	$0.565574\pi$
$258$	1.29687e23	1.59407
$259$	−2.37709e22	−0.281643
$260$	−2.00770e22	−0.229325
$261$	2.20050e22	0.242346
$262$	−4.87118e22	−0.517335
$263$	−2.36609e22	−0.242355	−0.121177	−	0.992631i	$-0.538667\pi$
$263$	−2.36609e22	−0.242355	−0.121177	+	0.992631i	$0.538667\pi$
$264$	1.64830e21	0.0162855
$265$	−1.71419e23	−1.63389
$266$	1.72226e23	1.58389
$267$	−1.48428e23	−1.31722
$268$	−1.09843e23	−0.940788
$269$	2.24891e23	1.85919	0.929597	−	0.368577i	$-0.120155\pi$
$269$	2.24891e23	1.85919	0.929597	+	0.368577i	$0.120155\pi$
$270$	−1.01087e23	−0.806750
$271$	−2.07753e23	−1.60081	−0.800403	−	0.599462i	$-0.795381\pi$
$271$	−2.07753e23	−1.60081	−0.800403	+	0.599462i	$0.795381\pi$
$272$	1.17414e23	0.873609
$273$	−5.94727e22	−0.427339
$274$	2.07341e23	1.43898
$275$	2.23785e22	0.150027
$276$	−2.67308e23	−1.73132
$277$	−2.37132e23	−1.48400	−0.741999	−	0.670401i	$-0.766122\pi$
$277$	−2.37132e23	−1.48400	−0.741999	+	0.670401i	$0.766122\pi$
$278$	3.88671e22	0.235048
$279$	−3.32965e23	−1.94607
$280$	−1.66376e21	−0.00939919
$281$	3.28612e22	0.179462	0.0897311	−	0.995966i	$-0.471399\pi$
$281$	3.28612e22	0.179462	0.0897311	+	0.995966i	$0.471399\pi$
$282$	6.03716e22	0.318762
$283$	3.24747e23	1.65796	0.828980	−	0.559278i	$-0.188922\pi$
$283$	3.24747e23	1.65796	0.828980	+	0.559278i	$0.188922\pi$
$284$	1.98735e23	0.981185
$285$	−3.03934e23	−1.45129
$286$	8.82090e22	0.407413
$287$	−1.60242e23	−0.715975
$288$	4.55773e23	1.97024
$289$	−5.89075e22	−0.246400
$290$	5.65513e22	0.228908
$291$	8.93112e21	0.0349883
$292$	1.03977e21	0.00394276
$293$	1.43863e23	0.528090	0.264045	−	0.964510i	$-0.414943\pi$
$293$	1.43863e23	0.528090	0.264045	+	0.964510i	$0.414943\pi$
$294$	1.52000e23	0.540189
$295$	−7.27208e22	−0.250236
$296$	−6.82348e20	−0.00227371
$297$	2.21353e23	0.714331
$298$	−2.92911e23	−0.915547
$299$	9.19289e22	0.278340
$300$	6.73955e22	0.197687
$301$	2.86643e23	0.814627
$302$	−7.56613e23	−2.08357
$303$	−7.78760e23	−2.07825
$304$	3.90825e23	1.01084
$305$	−1.28742e23	−0.322755
$306$	7.03820e23	1.71044
$307$	−1.33002e23	−0.313359	−0.156680	−	0.987649i	$-0.550079\pi$
$307$	−1.33002e23	−0.313359	−0.156680	+	0.987649i	$0.550079\pi$
$308$	−5.66917e23	−1.29505
$309$	1.14038e24	2.52606
$310$	−8.55696e23	−1.83816
$311$	−4.77314e23	−0.994444	−0.497222	−	0.867623i	$-0.665647\pi$
$311$	−4.77314e23	−0.994444	−0.497222	+	0.867623i	$0.665647\pi$
$312$	−1.70717e21	−0.00344991
$313$	4.77240e23	0.935547	0.467774	−	0.883848i	$-0.345056\pi$
$313$	4.77240e23	0.935547	0.467774	+	0.883848i	$0.345056\pi$
$314$	−1.47647e24	−2.80798
$315$	−7.88416e23	−1.45481
$316$	−4.80042e23	−0.859512
$317$	−6.75533e23	−1.17377	−0.586886	−	0.809670i	$-0.699646\pi$
$317$	−6.75533e23	−1.17377	−0.586886	+	0.809670i	$0.699646\pi$
$318$	2.26816e24	3.82487
$319$	−1.23832e23	−0.202685
$320$	5.80025e23	0.921556
$321$	4.52488e23	0.697926
$322$	−1.18545e24	−1.77521
$323$	5.99696e23	0.871981
$324$	−3.15371e23	−0.445291
$325$	−2.31777e22	−0.0317818
$326$	−1.74324e24	−2.32161
$327$	2.66460e23	0.344690
$328$	−4.59976e21	−0.00578008
$329$	1.33438e23	0.162899
$330$	2.00735e24	2.38089
$331$	−1.25064e24	−1.44134	−0.720668	−	0.693280i	$-0.756165\pi$
$331$	−1.25064e24	−1.44134	−0.720668	+	0.693280i	$0.756165\pi$
$332$	1.73417e24	1.94213
$333$	−3.23348e23	−0.351925
$334$	−1.69811e24	−1.79628
$335$	8.59649e23	0.883884
$336$	1.74033e24	1.73943
$337$	3.11062e23	0.302248	0.151124	−	0.988515i	$-0.451711\pi$
$337$	3.11062e23	0.302248	0.151124	+	0.988515i	$0.451711\pi$
$338$	1.40326e24	1.32565
$339$	−9.20244e23	−0.845291
$340$	9.01488e23	0.805212
$341$	1.87375e24	1.62759
$342$	2.34273e24	1.97913
$343$	−1.02317e24	−0.840721
$344$	8.22812e21	0.00657650
$345$	2.09200e24	1.62660
$346$	1.88241e24	1.42394
$347$	−6.56980e23	−0.483529	−0.241764	−	0.970335i	$-0.577726\pi$
$347$	−6.56980e23	−0.483529	−0.241764	+	0.970335i	$0.577726\pi$
$348$	−3.72936e23	−0.267074
$349$	−1.79836e24	−1.25324	−0.626620	−	0.779325i	$-0.715562\pi$
$349$	−1.79836e24	−1.25324	−0.626620	+	0.779325i	$0.715562\pi$
$350$	2.98882e23	0.202700
$351$	−2.29259e23	−0.151324
$352$	−2.56485e24	−1.64781
$353$	−2.53352e24	−1.58440	−0.792199	−	0.610262i	$-0.791064\pi$
$353$	−2.53352e24	−1.58440	−0.792199	+	0.610262i	$0.791064\pi$
$354$	9.62219e23	0.585791
$355$	−1.55533e24	−0.921838
$356$	1.46540e24	0.845632
$357$	2.67042e24	1.50048
$358$	2.07176e24	1.13358
$359$	−3.10246e24	−1.65314	−0.826569	−	0.562835i	$-0.809711\pi$
$359$	−3.10246e24	−1.65314	−0.826569	+	0.562835i	$0.809711\pi$
$360$	−2.26316e22	−0.0117447
$361$	1.77260e22	0.00895967
$362$	−4.72836e24	−2.32798
$363$	−1.16849e24	−0.560419
$364$	5.87163e23	0.274344
$365$	−8.13740e21	−0.00370428
$366$	1.70348e24	0.755555
$367$	2.34349e24	1.01283	0.506415	−	0.862290i	$-0.330971\pi$
$367$	2.34349e24	1.01283	0.506415	+	0.862290i	$0.330971\pi$
$368$	−2.69008e24	−1.13295
$369$	−2.17971e24	−0.894641
$370$	−8.30981e23	−0.332410
$371$	5.01326e24	1.95465
$372$	5.64302e24	2.14464
$373$	−2.78800e24	−1.03290	−0.516451	−	0.856317i	$-0.672747\pi$
$373$	−2.78800e24	−1.03290	−0.516451	+	0.856317i	$0.672747\pi$
$374$	−3.96072e24	−1.43052
$375$	−4.63056e24	−1.63056
$376$	3.83035e21	0.00131508
$377$	1.28255e23	0.0429369
$378$	2.95635e24	0.965124
$379$	7.75429e23	0.246871	0.123435	−	0.992353i	$-0.460609\pi$
$379$	7.75429e23	0.246871	0.123435	+	0.992353i	$0.460609\pi$
$380$	3.00069e24	0.931701
$381$	2.39211e24	0.724425
$382$	−3.23147e24	−0.954548
$383$	2.54571e24	0.733536	0.366768	−	0.930313i	$-0.380464\pi$
$383$	2.54571e24	0.733536	0.366768	+	0.930313i	$0.380464\pi$
$384$	9.92806e22	0.0279073
$385$	4.43678e24	1.21672
$386$	4.36096e24	1.16682
$387$	3.89910e24	1.01791
$388$	−8.81754e22	−0.0224619
$389$	4.16817e24	1.03615	0.518076	−	0.855334i	$-0.326648\pi$
$389$	4.16817e24	1.03615	0.518076	+	0.855334i	$0.326648\pi$
$390$	−2.07904e24	−0.504369
$391$	−4.12775e24	−0.977315
$392$	9.64385e21	0.00222860
$393$	−2.51405e24	−0.567081
$394$	5.93154e23	0.130603
$395$	3.75688e24	0.807524
$396$	−7.71157e24	−1.61822
$397$	−1.31063e24	−0.268515	−0.134258	−	0.990946i	$-0.542865\pi$
$397$	−1.31063e24	−0.268515	−0.134258	+	0.990946i	$0.542865\pi$
$398$	−8.81819e24	−1.76397
$399$	8.88874e24	1.73619
$400$	6.78239e23	0.129364
$401$	−2.75964e24	−0.514021	−0.257011	−	0.966409i	$-0.582738\pi$
$401$	−2.75964e24	−0.514021	−0.257011	+	0.966409i	$0.582738\pi$
$402$	−1.13746e25	−2.06913
$403$	−1.94067e24	−0.344788
$404$	7.68856e24	1.33420
$405$	2.46814e24	0.418357
$406$	−1.65388e24	−0.273846
$407$	1.81963e24	0.294331
$408$	7.66547e22	0.0121134
$409$	2.90954e24	0.449213	0.224607	−	0.974450i	$-0.427890\pi$
$409$	2.90954e24	0.449213	0.224607	+	0.974450i	$0.427890\pi$
$410$	−5.60171e24	−0.845034
$411$	1.07011e25	1.57735
$412$	−1.12588e25	−1.62169
$413$	2.12677e24	0.299360
$414$	−1.61252e25	−2.21821
$415$	−1.35719e25	−1.82466
$416$	2.65645e24	0.349072
$417$	2.00596e24	0.257650
$418$	−1.31836e25	−1.65524
$419$	7.30269e24	0.896293	0.448146	−	0.893960i	$-0.352084\pi$
$419$	7.30269e24	0.896293	0.448146	+	0.893960i	$0.352084\pi$
$420$	1.33619e25	1.60325
$421$	1.62240e25	1.90317	0.951586	−	0.307384i	$-0.0994536\pi$
$421$	1.62240e25	1.90317	0.951586	+	0.307384i	$0.0994536\pi$
$422$	−1.10917e24	−0.127213
$423$	1.81511e24	0.203549
$424$	1.43906e23	0.0157799
$425$	1.04071e24	0.111593
$426$	2.05797e25	2.15798
$427$	3.76515e24	0.386116
$428$	−4.46734e24	−0.448057
$429$	4.55254e24	0.446590
$430$	1.00204e25	0.961468
$431$	−4.05288e24	−0.380391	−0.190195	−	0.981746i	$-0.560912\pi$
$431$	−4.05288e24	−0.380391	−0.190195	+	0.981746i	$0.560912\pi$
$432$	6.70871e24	0.615947
$433$	1.94227e25	1.74451	0.872256	−	0.489050i	$-0.162656\pi$
$433$	1.94227e25	1.74451	0.872256	+	0.489050i	$0.162656\pi$
$434$	2.50254e25	2.19901
$435$	2.91866e24	0.250920
$436$	−2.63072e24	−0.221285
$437$	−1.37396e25	−1.13084
$438$	1.07672e23	0.00867156
$439$	−2.19289e24	−0.172824	−0.0864119	−	0.996259i	$-0.527540\pi$
$439$	−2.19289e24	−0.172824	−0.0864119	+	0.996259i	$0.527540\pi$
$440$	1.27358e23	0.00982262
$441$	4.56998e24	0.344943
$442$	4.10217e24	0.303042
$443$	−1.73819e25	−1.25679	−0.628394	−	0.777895i	$-0.716287\pi$
$443$	−1.73819e25	−1.25679	−0.628394	+	0.777895i	$0.716287\pi$
$444$	5.48003e24	0.387833
$445$	−1.14685e25	−0.794483
$446$	−3.03885e25	−2.06077
$447$	−1.51174e25	−1.00359
$448$	−1.69632e25	−1.10247
$449$	−1.15401e25	−0.734296	−0.367148	−	0.930163i	$-0.619666\pi$
$449$	−1.15401e25	−0.734296	−0.367148	+	0.930163i	$0.619666\pi$
$450$	4.06559e24	0.253282
$451$	1.22663e25	0.748230
$452$	9.08542e24	0.542662
$453$	−3.90494e25	−2.28392
$454$	1.90440e25	1.09076
$455$	−4.59524e24	−0.257750
$456$	2.55152e23	0.0140163
$457$	2.89229e25	1.55610	0.778051	−	0.628201i	$-0.216208\pi$
$457$	2.89229e25	1.55610	0.778051	+	0.628201i	$0.216208\pi$
$458$	−1.39133e25	−0.733178
$459$	1.02941e25	0.531333
$460$	−2.06539e25	−1.04425
$461$	1.76621e25	0.874750	0.437375	−	0.899279i	$-0.355908\pi$
$461$	1.76621e25	0.874750	0.437375	+	0.899279i	$0.355908\pi$
$462$	−5.87061e25	−2.84829
$463$	−2.52585e25	−1.20057	−0.600287	−	0.799785i	$-0.704947\pi$
$463$	−2.52585e25	−1.20057	−0.600287	+	0.799785i	$0.704947\pi$
$464$	−3.75307e24	−0.174770
$465$	−4.41632e25	−2.01492
$466$	1.39816e25	0.625016
$467$	2.80601e24	0.122908	0.0614538	−	0.998110i	$-0.480426\pi$
$467$	2.80601e24	0.122908	0.0614538	+	0.998110i	$0.480426\pi$
$468$	7.98698e24	0.342805
$469$	−2.51410e25	−1.05740
$470$	4.66469e24	0.192262
$471$	−7.62019e25	−3.07799
$472$	6.10491e22	0.00241674
$473$	−2.19420e25	−0.851326
$474$	−4.97099e25	−1.89038
$475$	3.46412e24	0.129123
$476$	−2.63646e25	−0.963285
$477$	6.81936e25	2.44241
$478$	−9.96617e24	−0.349916
$479$	−5.19468e25	−1.78801	−0.894007	−	0.448052i	$-0.852118\pi$
$479$	−5.19468e25	−1.78801	−0.894007	+	0.448052i	$0.852118\pi$
$480$	6.04520e25	2.03995
$481$	−1.88461e24	−0.0623511
$482$	9.60641e24	0.311612
$483$	−6.11818e25	−1.94592
$484$	1.15363e25	0.359779
$485$	6.90075e23	0.0211033
$486$	−6.14755e25	−1.84356
$487$	8.41218e24	0.247391	0.123695	−	0.992320i	$-0.460525\pi$
$487$	8.41218e24	0.247391	0.123695	+	0.992320i	$0.460525\pi$
$488$	1.08079e23	0.00311712
$489$	−8.99700e25	−2.54486
$490$	1.17445e25	0.325816
$491$	−1.14815e25	−0.312411	−0.156205	−	0.987725i	$-0.549926\pi$
$491$	−1.14815e25	−0.312411	−0.156205	+	0.987725i	$0.549926\pi$
$492$	3.69413e25	0.985926
$493$	−5.75885e24	−0.150761
$494$	1.36545e25	0.350646
$495$	6.03520e25	1.52034
$496$	5.67889e25	1.40342
$497$	4.54867e25	1.10281
$498$	1.79579e26	4.27146
$499$	1.81507e25	0.423583	0.211792	−	0.977315i	$-0.432070\pi$
$499$	1.81507e25	0.423583	0.211792	+	0.977315i	$0.432070\pi$
$500$	4.57167e25	1.04679
$501$	−8.76406e25	−1.96901
$502$	6.29121e25	1.38691
$503$	2.02505e25	0.438066	0.219033	−	0.975717i	$-0.429710\pi$
$503$	2.02505e25	0.438066	0.219033	+	0.975717i	$0.429710\pi$
$504$	6.61875e23	0.0140503
$505$	−6.01719e25	−1.25350
$506$	9.07439e25	1.85519
$507$	7.24232e25	1.45312
$508$	−2.36169e25	−0.465069
$509$	1.67341e25	0.323432	0.161716	−	0.986837i	$-0.448297\pi$
$509$	1.67341e25	0.323432	0.161716	+	0.986837i	$0.448297\pi$
$510$	9.33520e25	1.77095
$511$	2.37983e23	0.00443147
$512$	−7.72382e25	−1.41178
$513$	3.42648e25	0.614799
$514$	3.27948e25	0.577637
$515$	8.81130e25	1.52360
$516$	−6.60811e25	−1.12177
$517$	−1.02144e25	−0.170237
$518$	2.43026e25	0.397667
$519$	9.71527e25	1.56086
$520$	−1.31907e23	−0.00208083
$521$	−3.89807e25	−0.603798	−0.301899	−	0.953340i	$-0.597621\pi$
$521$	−3.89807e25	−0.603798	−0.301899	+	0.953340i	$0.597621\pi$
$522$	−2.24971e25	−0.342182
$523$	7.86738e25	1.17507	0.587535	−	0.809199i	$-0.300098\pi$
$523$	7.86738e25	1.17507	0.587535	+	0.809199i	$0.300098\pi$
$524$	2.48208e25	0.364057
$525$	1.54255e25	0.222191
$526$	2.41900e25	0.342193
$527$	8.71389e25	1.21063
$528$	−1.33219e26	−1.81779
$529$	1.99553e25	0.267442
$530$	1.75253e26	2.30698
$531$	2.89296e25	0.374063
$532$	−8.77570e25	−1.11461
$533$	−1.27043e25	−0.158505
$534$	1.51747e26	1.85985
$535$	3.49621e25	0.420956
$536$	−7.21675e23	−0.00853643
$537$	1.06925e26	1.24258
$538$	−2.29920e26	−2.62510
$539$	−2.57174e25	−0.288492
$540$	5.15083e25	0.567723
$541$	−1.78053e26	−1.92831	−0.964154	−	0.265343i	$-0.914515\pi$
$541$	−1.78053e26	−1.92831	−0.964154	+	0.265343i	$0.914515\pi$
$542$	2.12399e26	2.26026
$543$	−2.44035e26	−2.55184
$544$	−1.19279e26	−1.22567
$545$	2.05884e25	0.207901
$546$	6.08027e25	0.603383
$547$	1.17678e24	0.0114767	0.00573834	−	0.999984i	$-0.498173\pi$
$547$	1.17678e24	0.0114767	0.00573834	+	0.999984i	$0.498173\pi$
$548$	−1.05650e26	−1.01263
$549$	5.12160e25	0.482468
$550$	−2.28789e25	−0.211831
$551$	−1.91689e25	−0.174444
$552$	−1.75623e24	−0.0157094
$553$	−1.09872e26	−0.966051
$554$	2.42436e26	2.09534
$555$	−4.28876e25	−0.364375
$556$	−1.98045e25	−0.165407
$557$	−1.82726e26	−1.50029	−0.750146	−	0.661272i	$-0.770017\pi$
$557$	−1.82726e26	−1.50029	−0.750146	+	0.661272i	$0.770017\pi$
$558$	3.40411e26	2.74776
$559$	2.27257e25	0.180345
$560$	1.34469e26	1.04914
$561$	−2.04416e26	−1.56808
$562$	−3.35961e25	−0.253392
$563$	4.27666e25	0.317157	0.158579	−	0.987346i	$-0.449309\pi$
$563$	4.27666e25	0.317157	0.158579	+	0.987346i	$0.449309\pi$
$564$	−3.07620e25	−0.224318
$565$	−7.11039e25	−0.509839
$566$	−3.32010e26	−2.34096
$567$	−7.21823e25	−0.500486
$568$	1.30570e24	0.00890298
$569$	1.21390e26	0.813985	0.406993	−	0.913431i	$-0.366577\pi$
$569$	1.21390e26	0.813985	0.406993	+	0.913431i	$0.366577\pi$
$570$	3.10731e26	2.04915
$571$	−1.74823e26	−1.13385	−0.566926	−	0.823769i	$-0.691868\pi$
$571$	−1.74823e26	−1.13385	−0.566926	+	0.823769i	$0.691868\pi$
$572$	−4.49464e25	−0.286703
$573$	−1.66779e26	−1.04634
$574$	1.63826e26	1.01092
$575$	−2.38438e25	−0.144721
$576$	−2.30744e26	−1.37758
$577$	−2.42907e26	−1.42649	−0.713246	−	0.700914i	$-0.752776\pi$
$577$	−2.42907e26	−1.42649	−0.713246	+	0.700914i	$0.752776\pi$
$578$	6.02249e25	0.347906
$579$	2.25073e26	1.27902
$580$	−2.88154e25	−0.161086
$581$	3.96918e26	2.18287
$582$	−9.13086e24	−0.0494018
$583$	−3.83757e26	−2.04270
$584$	6.83135e21	3.57754e−5 0
$585$	−6.25074e25	−0.322070
$586$	−1.47081e26	−0.745638
$587$	2.12853e26	1.06174	0.530871	−	0.847453i	$-0.321865\pi$
$587$	2.12853e26	1.06174	0.530871	+	0.847453i	$0.321865\pi$
$588$	−7.74511e25	−0.380139
$589$	2.90050e26	1.40081
$590$	7.43471e25	0.353322
$591$	3.06132e25	0.143162
$592$	5.51487e25	0.253793
$593$	2.17532e26	0.985155	0.492577	−	0.870269i	$-0.336055\pi$
$593$	2.17532e26	0.985155	0.492577	+	0.870269i	$0.336055\pi$
$594$	−2.26304e26	−1.00860
$595$	2.06333e26	0.905020
$596$	1.49251e26	0.644285
$597$	−4.55114e26	−1.93359
$598$	−9.39848e25	−0.393003
$599$	−4.28569e26	−1.76387	−0.881934	−	0.471373i	$-0.843759\pi$
$599$	−4.28569e26	−1.76387	−0.881934	+	0.471373i	$0.843759\pi$
$600$	4.42792e23	0.00179376
$601$	−2.71265e26	−1.08165	−0.540823	−	0.841136i	$-0.681887\pi$
$601$	−2.71265e26	−1.08165	−0.540823	+	0.841136i	$0.681887\pi$
$602$	−2.93053e26	−1.15022
$603$	−3.41984e26	−1.32127
$604$	3.85528e26	1.46624
$605$	−9.02851e25	−0.338018
$606$	7.96176e26	2.93440
$607$	1.86771e26	0.677668	0.338834	−	0.940846i	$-0.389967\pi$
$607$	1.86771e26	0.677668	0.338834	+	0.940846i	$0.389967\pi$
$608$	−3.97030e26	−1.41821
$609$	−8.53580e25	−0.300179
$610$	1.31622e26	0.455715
$611$	1.05792e25	0.0360631
$612$	−3.58628e26	−1.20366
$613$	−3.82072e26	−1.26261	−0.631307	−	0.775533i	$-0.717481\pi$
$613$	−3.82072e26	−1.26261	−0.631307	+	0.775533i	$0.717481\pi$
$614$	1.35976e26	0.442449
$615$	−2.89109e26	−0.926292
$616$	−3.72468e24	−0.0117509
$617$	−1.43625e26	−0.446192	−0.223096	−	0.974796i	$-0.571616\pi$
$617$	−1.43625e26	−0.446192	−0.223096	+	0.974796i	$0.571616\pi$
$618$	−1.16588e27	−3.56668
$619$	−1.75252e25	−0.0527960	−0.0263980	−	0.999652i	$-0.508404\pi$
$619$	−1.75252e25	−0.0527960	−0.0263980	+	0.999652i	$0.508404\pi$
$620$	4.36015e26	1.29354
$621$	−2.35847e26	−0.689065
$622$	4.87989e26	1.40411
$623$	3.35402e26	0.950450
$624$	1.37977e26	0.385082
$625$	−3.11021e26	−0.854927
$626$	−4.87913e26	−1.32095
$627$	−6.80418e26	−1.81441
$628$	7.52328e26	1.97602
$629$	8.46221e25	0.218929
$630$	8.06048e26	2.05412
$631$	9.12083e25	0.228958	0.114479	−	0.993426i	$-0.463480\pi$
$631$	9.12083e25	0.228958	0.114479	+	0.993426i	$0.463480\pi$
$632$	−3.15390e24	−0.00779895
$633$	−5.72453e25	−0.139446
$634$	6.90641e26	1.65731
$635$	1.84829e26	0.436939
$636$	−1.15573e27	−2.69162
$637$	2.66358e25	0.0611142
$638$	1.26602e26	0.286183
$639$	6.18740e26	1.37800
$640$	7.67105e24	0.0168324
$641$	8.20783e26	1.77450	0.887252	−	0.461285i	$-0.152611\pi$
$641$	8.20783e26	1.77450	0.887252	+	0.461285i	$0.152611\pi$
$642$	−4.62608e26	−0.985440
$643$	−8.98468e26	−1.88581	−0.942906	−	0.333059i	$-0.891919\pi$
$643$	−8.98468e26	−1.88581	−0.942906	+	0.333059i	$0.891919\pi$
$644$	6.04038e26	1.24925
$645$	5.17161e26	1.05392
$646$	−6.13108e26	−1.23120
$647$	6.64670e26	1.31527	0.657636	−	0.753336i	$-0.271557\pi$
$647$	6.64670e26	1.31527	0.657636	+	0.753336i	$0.271557\pi$
$648$	−2.07200e24	−0.00404043
$649$	−1.62800e26	−0.312846
$650$	2.36960e25	0.0448744
$651$	1.29158e27	2.41047
$652$	8.88259e26	1.63376
$653$	−8.73959e25	−0.158422	−0.0792111	−	0.996858i	$-0.525240\pi$
$653$	−8.73959e25	−0.158422	−0.0792111	+	0.996858i	$0.525240\pi$
$654$	−2.72419e26	−0.486686
$655$	−1.94252e26	−0.342037
$656$	3.71762e26	0.645176
$657$	3.23721e24	0.00553732
$658$	−1.36422e26	−0.230005
$659$	−3.51957e26	−0.584895	−0.292447	−	0.956282i	$-0.594470\pi$
$659$	−3.51957e26	−0.584895	−0.292447	+	0.956282i	$0.594470\pi$
$660$	−1.02283e27	−1.67547
$661$	−1.15754e26	−0.186905	−0.0934524	−	0.995624i	$-0.529790\pi$
$661$	−1.15754e26	−0.186905	−0.0934524	+	0.995624i	$0.529790\pi$
$662$	1.27861e27	2.03510
$663$	2.11717e26	0.332182
$664$	1.13936e25	0.0176223
$665$	6.86800e26	1.04719
$666$	3.30579e26	0.496901
$667$	1.31941e26	0.195516
$668$	8.65261e26	1.26407
$669$	−1.56838e27	−2.25893
$670$	−8.78874e26	−1.24800
$671$	−2.88216e26	−0.403510
$672$	−1.76796e27	−2.44041
$673$	−7.77854e26	−1.05866	−0.529328	−	0.848417i	$-0.677556\pi$
$673$	−7.77854e26	−1.05866	−0.529328	+	0.848417i	$0.677556\pi$
$674$	−3.18019e26	−0.426760
$675$	5.94633e25	0.0786797
$676$	−7.15022e26	−0.932879
$677$	−4.02240e26	−0.517479	−0.258740	−	0.965947i	$-0.583307\pi$
$677$	−4.02240e26	−0.517479	−0.258740	+	0.965947i	$0.583307\pi$
$678$	9.40825e26	1.19351
$679$	−2.01817e25	−0.0252461
$680$	5.92283e24	0.00730625
$681$	9.82878e26	1.19564
$682$	−1.91565e27	−2.29808
$683$	5.35798e26	0.633877	0.316938	−	0.948446i	$-0.397345\pi$
$683$	5.35798e26	0.633877	0.316938	+	0.948446i	$0.397345\pi$
$684$	−1.19373e27	−1.39275
$685$	8.26831e26	0.951385
$686$	1.04605e27	1.18706
$687$	−7.18079e26	−0.803680
$688$	−6.65012e26	−0.734073
$689$	3.97462e26	0.432727
$690$	−2.13878e27	−2.29668
$691$	1.57716e27	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$691$	1.57716e27	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$692$	−9.59172e26	−1.00205
$693$	−1.76503e27	−1.81881
$694$	6.71673e26	0.682721
$695$	1.54993e26	0.155402
$696$	−2.45021e24	−0.00242335
$697$	5.70445e26	0.556547
$698$	1.83858e27	1.76952
$699$	7.21603e26	0.685118
$700$	−1.52294e26	−0.142643
$701$	−1.93886e26	−0.179153	−0.0895767	−	0.995980i	$-0.528551\pi$
$701$	−1.93886e26	−0.179153	−0.0895767	+	0.995980i	$0.528551\pi$
$702$	2.34386e26	0.213663
$703$	2.81673e26	0.253320
$704$	1.29851e27	1.15214
$705$	2.40749e26	0.210750
$706$	2.59018e27	2.23710
$707$	1.75977e27	1.49958
$708$	−4.90294e26	−0.412231
$709$	8.31005e26	0.689389	0.344695	−	0.938715i	$-0.387982\pi$
$709$	8.31005e26	0.689389	0.344695	+	0.938715i	$0.387982\pi$
$710$	1.59012e27	1.30159
$711$	−1.49456e27	−1.20712
$712$	9.62777e24	0.00767301
$713$	−1.99644e27	−1.57002
$714$	−2.73014e27	−2.11861
$715$	3.51758e26	0.269362
$716$	−1.05566e27	−0.797717
$717$	−5.14362e26	−0.383563
$718$	3.17185e27	2.33416
$719$	3.30261e26	0.239846	0.119923	−	0.992783i	$-0.461735\pi$
$719$	3.30261e26	0.239846	0.119923	+	0.992783i	$0.461735\pi$
$720$	1.82913e27	1.31095
$721$	−2.57692e27	−1.82270
$722$	−1.81224e25	−0.0126506
$723$	4.95795e26	0.341577
$724$	2.40931e27	1.63824
$725$	−3.32657e25	−0.0223247
$726$	1.19462e27	0.791286
$727$	−2.64923e27	−1.73198	−0.865990	−	0.500061i	$-0.833311\pi$
$727$	−2.64923e27	−1.73198	−0.865990	+	0.500061i	$0.833311\pi$
$728$	3.85770e24	0.00248932
$729$	−2.46918e27	−1.57269
$730$	8.31939e24	0.00523027
$731$	−1.02042e27	−0.633232
$732$	−8.67998e26	−0.531696
$733$	−2.59756e27	−1.57064	−0.785321	−	0.619089i	$-0.787502\pi$
$733$	−2.59756e27	−1.57064	−0.785321	+	0.619089i	$0.787502\pi$
$734$	−2.39590e27	−1.43007
$735$	6.06144e26	0.357146
$736$	2.73279e27	1.58952
$737$	1.92450e27	1.10504
$738$	2.22846e27	1.26319
$739$	6.91158e26	0.386772	0.193386	−	0.981123i	$-0.438053\pi$
$739$	6.91158e26	0.386772	0.193386	+	0.981123i	$0.438053\pi$
$740$	4.23422e26	0.233922
$741$	7.04719e26	0.384364
$742$	−5.12538e27	−2.75987
$743$	2.31326e27	1.22979	0.614896	−	0.788608i	$-0.289198\pi$
$743$	2.31326e27	1.22979	0.614896	+	0.788608i	$0.289198\pi$
$744$	3.70750e25	0.0194598
$745$	−1.16806e27	−0.605316
$746$	2.85035e27	1.45841
$747$	5.39913e27	2.72759
$748$	2.01817e27	1.00668
$749$	−1.02249e27	−0.503595
$750$	4.73412e27	2.30227
$751$	3.17303e26	0.152368	0.0761841	−	0.997094i	$-0.475726\pi$
$751$	3.17303e26	0.152368	0.0761841	+	0.997094i	$0.475726\pi$
$752$	−3.09576e26	−0.146790
$753$	3.24694e27	1.52028
$754$	−1.31123e26	−0.0606250
$755$	−3.01721e27	−1.37755
$756$	−1.50639e27	−0.679173
$757$	2.08781e27	0.929567	0.464783	−	0.885424i	$-0.346132\pi$
$757$	2.08781e27	0.929567	0.464783	+	0.885424i	$0.346132\pi$
$758$	−7.92771e26	−0.348570
$759$	4.68337e27	2.03358
$760$	1.97147e25	0.00845397
$761$	1.98452e27	0.840431	0.420216	−	0.907424i	$-0.361954\pi$
$761$	1.98452e27	0.840431	0.420216	+	0.907424i	$0.361954\pi$
$762$	−2.44560e27	−1.02285
$763$	−6.02121e26	−0.248714
$764$	1.64658e27	0.671731
$765$	2.80668e27	1.13086
$766$	−2.60265e27	−1.03572
$767$	1.68615e26	0.0662734
$768$	−4.03724e27	−1.56730
$769$	−3.35525e27	−1.28654	−0.643272	−	0.765638i	$-0.722424\pi$
$769$	−3.35525e27	−1.28654	−0.643272	+	0.765638i	$0.722424\pi$
$770$	−4.53601e27	−1.71795
$771$	1.69256e27	0.633182
$772$	−2.22211e27	−0.821108
$773$	−3.65384e27	−1.33366	−0.666828	−	0.745211i	$-0.732349\pi$
$773$	−3.65384e27	−1.33366	−0.666828	+	0.745211i	$0.732349\pi$
$774$	−3.98630e27	−1.43724
$775$	5.03354e26	0.179270
$776$	−5.79318e23	−0.000203812 0
$777$	1.25427e27	0.435906
$778$	−4.26138e27	−1.46300
$779$	1.89878e27	0.643974
$780$	1.05936e27	0.354932
$781$	−3.48194e27	−1.15249
$782$	4.22006e27	1.37992
$783$	−3.29043e26	−0.106296
$784$	−7.79434e26	−0.248758
$785$	−5.88784e27	−1.85650
$786$	2.57028e27	0.800693
$787$	4.87753e27	1.50121	0.750603	−	0.660754i	$-0.229763\pi$
$787$	4.87753e27	1.50121	0.750603	+	0.660754i	$0.229763\pi$
$788$	−3.02239e26	−0.0919075
$789$	1.24847e27	0.375099
$790$	−3.84090e27	−1.14019
$791$	2.07948e27	0.609927
$792$	−5.06655e25	−0.0146833
$793$	2.98509e26	0.0854797
$794$	1.33994e27	0.379132
$795$	9.04494e27	2.52882
$796$	4.49326e27	1.24133
$797$	−3.54591e26	−0.0967997	−0.0483998	−	0.998828i	$-0.515412\pi$
$797$	−3.54591e26	−0.0967997	−0.0483998	+	0.998828i	$0.515412\pi$
$798$	−9.08753e27	−2.45142
$799$	−4.75024e26	−0.126626
$800$	−6.89008e26	−0.181497
$801$	4.56236e27	1.18763
$802$	2.82136e27	0.725775
$803$	−1.82173e25	−0.00463111
$804$	5.79587e27	1.45608
$805$	−4.72730e27	−1.17369
$806$	1.98407e27	0.486825
$807$	−1.18664e28	−2.87753
$808$	5.05143e25	0.0121062
$809$	−5.26665e27	−1.24745	−0.623726	−	0.781643i	$-0.714382\pi$
$809$	−5.26665e27	−1.24745	−0.623726	+	0.781643i	$0.714382\pi$
$810$	−2.52334e27	−0.590701
$811$	−2.41107e27	−0.557842	−0.278921	−	0.960314i	$-0.589977\pi$
$811$	−2.41107e27	−0.557842	−0.278921	+	0.960314i	$0.589977\pi$
$812$	8.42725e26	0.192710
$813$	1.09621e28	2.47761
$814$	−1.86032e27	−0.415581
$815$	−6.95166e27	−1.53494
$816$	−6.19538e27	−1.35211
$817$	−3.39656e27	−0.732706
$818$	−2.97461e27	−0.634269
$819$	1.82807e27	0.385297
$820$	2.85432e27	0.594664
$821$	6.93833e27	1.42888	0.714439	−	0.699698i	$-0.246682\pi$
$821$	6.93833e27	1.42888	0.714439	+	0.699698i	$0.246682\pi$
$822$	−1.09404e28	−2.22715
$823$	7.20527e27	1.44995	0.724973	−	0.688778i	$-0.241852\pi$
$823$	7.20527e27	1.44995	0.724973	+	0.688778i	$0.241852\pi$
$824$	−7.39708e25	−0.0147147
$825$	−1.18080e27	−0.232201
$826$	−2.17433e27	−0.422683
$827$	6.73740e27	1.29476	0.647382	−	0.762166i	$-0.275864\pi$
$827$	6.73740e27	1.29476	0.647382	+	0.762166i	$0.275864\pi$
$828$	8.21651e27	1.56099
$829$	−5.87295e27	−1.10303	−0.551517	−	0.834164i	$-0.685951\pi$
$829$	−5.87295e27	−1.10303	−0.551517	+	0.834164i	$0.685951\pi$
$830$	1.38754e28	2.57634
$831$	1.25123e28	2.29682
$832$	−1.34488e27	−0.244069
$833$	−1.19599e27	−0.214586
$834$	−2.05082e27	−0.363790
$835$	−6.77167e27	−1.18761
$836$	6.71765e27	1.16482
$837$	4.97885e27	0.853567
$838$	−7.46601e27	−1.26552
$839$	−3.34939e27	−0.561342	−0.280671	−	0.959804i	$-0.590557\pi$
$839$	−3.34939e27	−0.561342	−0.280671	+	0.959804i	$0.590557\pi$
$840$	8.77886e25	0.0145474
$841$	−5.91918e27	−0.969839
$842$	−1.65868e28	−2.68719
$843$	−1.73392e27	−0.277759
$844$	5.65173e26	0.0895217
$845$	5.59587e27	0.876454
$846$	−1.85570e27	−0.287401
$847$	2.64044e27	0.404375
$848$	−1.16308e28	−1.76136
$849$	−1.71353e28	−2.56607
$850$	−1.06399e27	−0.157564
$851$	−1.93877e27	−0.283920
$852$	−1.04863e28	−1.51861
$853$	−5.84630e27	−0.837270	−0.418635	−	0.908155i	$-0.637491\pi$
$853$	−5.84630e27	−0.837270	−0.418635	+	0.908155i	$0.637491\pi$
$854$	−3.84935e27	−0.545178
$855$	9.34230e27	1.30851
$856$	−2.93507e25	−0.00406553
$857$	−6.41678e27	−0.879021	−0.439510	−	0.898238i	$-0.644848\pi$
$857$	−6.41678e27	−0.879021	−0.439510	+	0.898238i	$0.644848\pi$
$858$	−4.65435e27	−0.630565
$859$	8.80913e27	1.18032	0.590158	−	0.807288i	$-0.299066\pi$
$859$	8.80913e27	1.18032	0.590158	+	0.807288i	$0.299066\pi$
$860$	−5.10585e27	−0.676601
$861$	8.45517e27	1.10813
$862$	4.14352e27	0.537095
$863$	9.11753e27	1.16889	0.584446	−	0.811432i	$-0.301312\pi$
$863$	9.11753e27	1.16889	0.584446	+	0.811432i	$0.301312\pi$
$864$	−6.81522e27	−0.864170
$865$	7.50664e27	0.941439
$866$	−1.98570e28	−2.46317
$867$	3.10826e27	0.381360
$868$	−1.27515e28	−1.54748
$869$	8.41056e27	1.00957
$870$	−2.98393e27	−0.354288
$871$	−1.99323e27	−0.234091
$872$	−1.72840e25	−0.00200787
$873$	−2.74524e26	−0.0315461
$874$	1.40469e28	1.59669
$875$	1.04637e28	1.17654
$876$	−5.48635e25	−0.00610231
$877$	8.47767e27	0.932783	0.466391	−	0.884578i	$-0.345554\pi$
$877$	8.47767e27	0.932783	0.466391	+	0.884578i	$0.345554\pi$
$878$	2.24193e27	0.244019
$879$	−7.59095e27	−0.817339
$880$	−1.02934e28	−1.09641
$881$	2.54848e27	0.268541	0.134270	−	0.990945i	$-0.457131\pi$
$881$	2.54848e27	0.268541	0.134270	+	0.990945i	$0.457131\pi$
$882$	−4.67218e27	−0.487044
$883$	1.31906e26	0.0136031	0.00680157	−	0.999977i	$-0.497835\pi$
$883$	1.31906e26	0.0136031	0.00680157	+	0.999977i	$0.497835\pi$
$884$	−2.09024e27	−0.213255
$885$	3.83712e27	0.387297
$886$	1.77706e28	1.77453
$887$	−7.23189e27	−0.714460	−0.357230	−	0.934017i	$-0.616279\pi$
$887$	−7.23189e27	−0.714460	−0.357230	+	0.934017i	$0.616279\pi$
$888$	3.60041e25	0.00351908
$889$	−5.40545e27	−0.522715
$890$	1.17249e28	1.12177
$891$	5.52544e27	0.523033
$892$	1.54843e28	1.45019
$893$	−1.58116e27	−0.146517
$894$	1.54555e28	1.41702
$895$	8.26173e27	0.749467
$896$	−2.24345e26	−0.0201368
$897$	−4.85063e27	−0.430794
$898$	1.17982e28	1.03679
$899$	−2.78534e27	−0.242192
$900$	−2.07160e27	−0.178239
$901$	−1.78467e28	−1.51940
$902$	−1.25406e28	−1.05647
$903$	−1.51247e28	−1.26082
$904$	5.96917e25	0.00492395
$905$	−1.88557e28	−1.53915
$906$	3.99227e28	3.22480
$907$	2.18059e27	0.174303	0.0871514	−	0.996195i	$-0.472224\pi$
$907$	2.18059e27	0.174303	0.0871514	+	0.996195i	$0.472224\pi$
$908$	−9.70378e27	−0.767583
$909$	2.39375e28	1.87379
$910$	4.69800e27	0.363932
$911$	1.78840e27	0.137101	0.0685503	−	0.997648i	$-0.478163\pi$
$911$	1.78840e27	0.137101	0.0685503	+	0.997648i	$0.478163\pi$
$912$	−2.06219e28	−1.56451
$913$	−3.03834e28	−2.28120
$914$	−2.95697e28	−2.19714
$915$	6.79310e27	0.499537
$916$	7.08947e27	0.515949
$917$	5.68102e27	0.409183
$918$	−1.05243e28	−0.750218
$919$	2.43828e28	1.72023	0.860116	−	0.510098i	$-0.170391\pi$
$919$	2.43828e28	1.72023	0.860116	+	0.510098i	$0.170391\pi$
$920$	−1.35698e26	−0.00947519
$921$	7.01784e27	0.484994
$922$	−1.80571e28	−1.23511
$923$	3.60629e27	0.244143
$924$	2.99134e28	2.00439
$925$	4.88816e26	0.0324189
$926$	2.58234e28	1.69515
$927$	−3.50529e28	−2.27754
$928$	3.81266e27	0.245201
$929$	−4.66745e27	−0.297119	−0.148560	−	0.988903i	$-0.547464\pi$
$929$	−4.66745e27	−0.297119	−0.148560	+	0.988903i	$0.547464\pi$
$930$	4.51508e28	2.84497
$931$	−3.98097e27	−0.248295
$932$	−7.12426e27	−0.439834
$933$	2.51855e28	1.53913
$934$	−2.86876e27	−0.173540
$935$	−1.57945e28	−0.945791
$936$	5.24749e25	0.00311051
$937$	1.35542e27	0.0795333	0.0397667	−	0.999209i	$-0.487339\pi$
$937$	1.35542e27	0.0795333	0.0397667	+	0.999209i	$0.487339\pi$
$938$	2.57032e28	1.49300
$939$	−2.51816e28	−1.44797
$940$	−2.37687e27	−0.135298
$941$	1.10910e28	0.624987	0.312493	−	0.949920i	$-0.398836\pi$
$941$	1.10910e28	0.624987	0.312493	+	0.949920i	$0.398836\pi$
$942$	7.79061e28	4.34598
$943$	−1.30694e28	−0.721765
$944$	−4.93411e27	−0.269758
$945$	1.17893e28	0.638094
$946$	2.24327e28	1.20203
$947$	−2.26188e28	−1.19990	−0.599949	−	0.800039i	$-0.704812\pi$
$947$	−2.26188e28	−1.19990	−0.599949	+	0.800039i	$0.704812\pi$
$948$	2.53294e28	1.33029
$949$	1.88679e25	0.000981056 0
$950$	−3.54159e27	−0.182316
$951$	3.56445e28	1.81668
$952$	−1.73217e26	−0.00874055
$953$	−1.97093e28	−0.984667	−0.492334	−	0.870407i	$-0.663856\pi$
$953$	−1.97093e28	−0.984667	−0.492334	+	0.870407i	$0.663856\pi$
$954$	−6.97187e28	−3.44858
$955$	−1.28864e28	−0.631101
$956$	5.07821e27	0.246241
$957$	6.53402e27	0.313702
$958$	5.31085e28	2.52460
$959$	−2.41812e28	−1.13815
$960$	−3.06050e28	−1.42632
$961$	2.04751e28	0.944832
$962$	1.92676e27	0.0880368
$963$	−1.39086e28	−0.629263
$964$	−4.89490e27	−0.219286
$965$	1.73906e28	0.771443
$966$	6.25501e28	2.74755
$967$	−9.50650e27	−0.413494	−0.206747	−	0.978394i	$-0.566288\pi$
$967$	−9.50650e27	−0.413494	−0.206747	+	0.978394i	$0.566288\pi$
$968$	7.57943e25	0.00326453
$969$	−3.16430e28	−1.34959
$970$	−7.05508e26	−0.0297969
$971$	2.91165e28	1.21775	0.608873	−	0.793268i	$-0.291622\pi$
$971$	2.91165e28	1.21775	0.608873	+	0.793268i	$0.291622\pi$
$972$	3.13245e28	1.29734
$973$	−4.53288e27	−0.185910
$974$	−8.60031e27	−0.349304
$975$	1.22297e27	0.0491895
$976$	−8.73517e27	−0.347935
$977$	2.70418e28	1.06669	0.533343	−	0.845899i	$-0.320935\pi$
$977$	2.70418e28	1.06669	0.533343	+	0.845899i	$0.320935\pi$
$978$	9.19821e28	3.59322
$979$	−2.56745e28	−0.993268
$980$	−5.98436e27	−0.229282
$981$	−8.19044e27	−0.310779
$982$	1.17383e28	0.441109
$983$	4.53466e28	1.68766	0.843832	−	0.536607i	$-0.180294\pi$
$983$	4.53466e28	1.68766	0.843832	+	0.536607i	$0.180294\pi$
$984$	2.42707e26	0.00894599
$985$	2.36537e27	0.0863485
$986$	5.88764e27	0.212868
$987$	−7.04084e27	−0.252123
$988$	−6.95757e27	−0.246755
$989$	2.33788e28	0.821215
$990$	−6.17017e28	−2.14666
$991$	4.02149e28	1.38576	0.692879	−	0.721054i	$-0.256342\pi$
$991$	4.02149e28	1.38576	0.692879	+	0.721054i	$0.256342\pi$
$992$	−5.76906e28	−1.96899
$993$	6.59899e28	2.23080
$994$	−4.65040e28	−1.55711
$995$	−3.51650e28	−1.16625
$996$	−9.15034e28	−3.00589
$997$	−2.67636e28	−0.870845	−0.435423	−	0.900226i	$-0.643401\pi$
$997$	−2.67636e28	−0.870845	−0.435423	+	0.900226i	$0.643401\pi$
$998$	−1.85567e28	−0.598081
$999$	4.83505e27	0.154358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.a.1.6	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1022.36 q^{2} -52765.0 q^{3} +520940. q^{4} -4.07696e6 q^{5} +5.39451e7 q^{6} +1.19233e8 q^{7} +3.42261e6 q^{8} +1.62189e9 q^{9} +O(q^{10})\)	\(q-1022.36 q^{2} -52765.0 q^{3} +520940. q^{4} -4.07696e6 q^{5} +5.39451e7 q^{6} +1.19233e8 q^{7} +3.42261e6 q^{8} +1.62189e9 q^{9} +4.16814e9 q^{10} -9.12712e9 q^{11} -2.74874e10 q^{12} +9.45308e9 q^{13} -1.21900e11 q^{14} +2.15121e11 q^{15} -2.76622e11 q^{16} -4.24458e11 q^{17} -1.65816e12 q^{18} -1.41285e12 q^{19} -2.12385e12 q^{20} -6.29135e12 q^{21} +9.33124e12 q^{22} +9.72475e12 q^{23} -1.80594e11 q^{24} -2.45186e12 q^{25} -9.66449e12 q^{26} -2.42523e13 q^{27} +6.21134e13 q^{28} +1.35675e13 q^{29} -2.19932e14 q^{30} -2.05294e14 q^{31} +2.81014e14 q^{32} +4.81593e14 q^{33} +4.33951e14 q^{34} -4.86110e14 q^{35} +8.44907e14 q^{36} -1.99365e14 q^{37} +1.44445e15 q^{38} -4.98792e14 q^{39} -1.39538e13 q^{40} -1.34394e15 q^{41} +6.43205e15 q^{42} +2.40405e15 q^{43} -4.75468e15 q^{44} -6.61238e15 q^{45} -9.94223e15 q^{46} +1.11913e15 q^{47} +1.45960e16 q^{48} +2.81769e15 q^{49} +2.50670e15 q^{50} +2.23966e16 q^{51} +4.92449e15 q^{52} +4.20458e16 q^{53} +2.47946e16 q^{54} +3.72109e16 q^{55} +4.08089e14 q^{56} +7.45491e16 q^{57} -1.38709e16 q^{58} +1.78370e16 q^{59} +1.12065e17 q^{60} +3.15780e16 q^{61} +2.09886e17 q^{62} +1.93383e17 q^{63} -1.42269e17 q^{64} -3.85399e16 q^{65} -4.92363e17 q^{66} -2.10855e17 q^{67} -2.21117e17 q^{68} -5.13127e17 q^{69} +4.96981e17 q^{70} +3.81493e17 q^{71} +5.55109e15 q^{72} +1.99595e15 q^{73} +2.03823e17 q^{74} +1.29373e17 q^{75} -7.36011e17 q^{76} -1.08826e18 q^{77} +5.09947e17 q^{78} -9.21491e17 q^{79} +1.12778e18 q^{80} -6.05387e17 q^{81} +1.37399e18 q^{82} +3.32892e18 q^{83} -3.27742e18 q^{84} +1.73050e18 q^{85} -2.45781e18 q^{86} -7.15891e17 q^{87} -3.12386e16 q^{88} +2.81299e18 q^{89} +6.76026e18 q^{90} +1.12712e18 q^{91} +5.06601e18 q^{92} +1.08324e19 q^{93} -1.14416e18 q^{94} +5.76014e18 q^{95} -1.48277e19 q^{96} -1.69262e17 q^{97} -2.88070e18 q^{98} -1.48032e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) \) 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

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Groups

Database

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