LMFDB - Embedded newform 47.20.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-1322.20 q^{2} -58648.5 q^{3} +1.22393e6 q^{4} -2.69135e6 q^{5} +7.75453e7 q^{6} -1.70403e8 q^{7} -9.25073e8 q^{8} +2.27739e9 q^{9} +O(q^{10})$	\(q-1322.20 q^{2} -58648.5 q^{3} +1.22393e6 q^{4} -2.69135e6 q^{5} +7.75453e7 q^{6} -1.70403e8 q^{7} -9.25073e8 q^{8} +2.27739e9 q^{9} +3.55852e9 q^{10} +2.84119e9 q^{11} -7.17819e10 q^{12} -4.77789e9 q^{13} +2.25308e11 q^{14} +1.57844e11 q^{15} +5.81441e11 q^{16} -4.56694e11 q^{17} -3.01117e12 q^{18} -8.99169e11 q^{19} -3.29404e12 q^{20} +9.99391e12 q^{21} -3.75664e12 q^{22} -1.55266e13 q^{23} +5.42542e13 q^{24} -1.18301e13 q^{25} +6.31735e12 q^{26} -6.54007e13 q^{27} -2.08562e14 q^{28} -9.23856e13 q^{29} -2.08702e14 q^{30} -6.23321e13 q^{31} -2.83778e14 q^{32} -1.66632e14 q^{33} +6.03842e14 q^{34} +4.58616e14 q^{35} +2.78737e15 q^{36} +2.05351e14 q^{37} +1.18888e15 q^{38} +2.80216e14 q^{39} +2.48970e15 q^{40} +2.83265e15 q^{41} -1.32140e16 q^{42} -1.74023e15 q^{43} +3.47743e15 q^{44} -6.12926e15 q^{45} +2.05294e16 q^{46} +1.11913e15 q^{47} -3.41007e16 q^{48} +1.76384e16 q^{49} +1.56418e16 q^{50} +2.67844e16 q^{51} -5.84782e15 q^{52} -1.80802e16 q^{53} +8.64730e16 q^{54} -7.64666e15 q^{55} +1.57636e17 q^{56} +5.27350e16 q^{57} +1.22153e17 q^{58} +6.22662e16 q^{59} +1.93190e17 q^{60} -1.45257e17 q^{61} +8.24157e16 q^{62} -3.88075e17 q^{63} +7.03700e16 q^{64} +1.28590e16 q^{65} +2.20321e17 q^{66} +3.92212e17 q^{67} -5.58962e17 q^{68} +9.10614e17 q^{69} -6.06383e17 q^{70} +5.02750e17 q^{71} -2.10675e18 q^{72} -9.66948e17 q^{73} -2.71515e17 q^{74} +6.93818e17 q^{75} -1.10052e18 q^{76} -4.84149e17 q^{77} -3.70503e17 q^{78} +1.46449e18 q^{79} -1.56486e18 q^{80} +1.18873e18 q^{81} -3.74534e18 q^{82} +5.27599e17 q^{83} +1.22319e19 q^{84} +1.22912e18 q^{85} +2.30093e18 q^{86} +5.41828e18 q^{87} -2.62831e18 q^{88} +2.55481e18 q^{89} +8.10413e18 q^{90} +8.14169e17 q^{91} -1.90036e19 q^{92} +3.65569e18 q^{93} -1.47972e18 q^{94} +2.41998e18 q^{95} +1.66432e19 q^{96} +1.02912e19 q^{97} -2.33216e19 q^{98} +6.47051e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1322.20	−1.82605	−0.913026	−	0.407901i	$-0.866261\pi$
$2$	−1322.20	−1.82605	−0.913026	+	0.407901i	$0.866261\pi$
$3$	−58648.5	−1.72030	−0.860152	−	0.510037i	$-0.829632\pi$
$3$	−58648.5	−1.72030	−0.860152	+	0.510037i	$0.829632\pi$
$4$	1.22393e6	2.33447
$5$	−2.69135e6	−0.616248	−0.308124	−	0.951346i	$-0.599701\pi$
$5$	−2.69135e6	−0.616248	−0.308124	+	0.951346i	$0.599701\pi$
$6$	7.75453e7	3.14137
$7$	−1.70403e8	−1.59605	−0.798026	−	0.602623i	$-0.794122\pi$
$7$	−1.70403e8	−1.59605	−0.798026	+	0.602623i	$0.794122\pi$
$8$	−9.25073e8	−2.43681
$9$	2.27739e9	1.95945
$10$	3.55852e9	1.12530
$11$	2.84119e9	0.363304	0.181652	−	0.983363i	$-0.441856\pi$
$11$	2.84119e9	0.363304	0.181652	+	0.983363i	$0.441856\pi$
$12$	−7.17819e10	−4.01599
$13$	−4.77789e9	−0.124961	−0.0624805	−	0.998046i	$-0.519901\pi$
$13$	−4.77789e9	−0.124961	−0.0624805	+	0.998046i	$0.519901\pi$
$14$	2.25308e11	2.91447
$15$	1.57844e11	1.06013
$16$	5.81441e11	2.11527
$17$	−4.56694e11	−0.934029	−0.467014	−	0.884250i	$-0.654670\pi$
$17$	−4.56694e11	−0.934029	−0.467014	+	0.884250i	$0.654670\pi$
$18$	−3.01117e12	−3.57805
$19$	−8.99169e11	−0.639267	−0.319633	−	0.947541i	$-0.603560\pi$
$19$	−8.99169e11	−0.639267	−0.319633	+	0.947541i	$0.603560\pi$
$20$	−3.29404e12	−1.43861
$21$	9.99391e12	2.74569
$22$	−3.75664e12	−0.663413
$23$	−1.55266e13	−1.79747	−0.898737	−	0.438488i	$-0.855514\pi$
$23$	−1.55266e13	−1.79747	−0.898737	+	0.438488i	$0.855514\pi$
$24$	5.42542e13	4.19205
$25$	−1.18301e13	−0.620238
$26$	6.31735e12	0.228185
$27$	−6.54007e13	−1.65054
$28$	−2.08562e14	−3.72593
$29$	−9.23856e13	−1.18256	−0.591280	−	0.806466i	$-0.701377\pi$
$29$	−9.23856e13	−1.18256	−0.591280	+	0.806466i	$0.701377\pi$
$30$	−2.08702e14	−1.93586
$31$	−6.23321e13	−0.423424	−0.211712	−	0.977332i	$-0.567904\pi$
$31$	−6.23321e13	−0.423424	−0.211712	+	0.977332i	$0.567904\pi$
$32$	−2.83778e14	−1.42579
$33$	−1.66632e14	−0.624994
$34$	6.03842e14	1.70559
$35$	4.58616e14	0.983564
$36$	2.78737e15	4.57427
$37$	2.05351e14	0.259764	0.129882	−	0.991529i	$-0.458540\pi$
$37$	2.05351e14	0.259764	0.129882	+	0.991529i	$0.458540\pi$
$38$	1.18888e15	1.16733
$39$	2.80216e14	0.214971
$40$	2.48970e15	1.50168
$41$	2.83265e15	1.35128	0.675642	−	0.737230i	$-0.263867\pi$
$41$	2.83265e15	1.35128	0.675642	+	0.737230i	$0.263867\pi$
$42$	−1.32140e16	−5.01378
$43$	−1.74023e15	−0.528027	−0.264013	−	0.964519i	$-0.585046\pi$
$43$	−1.74023e15	−0.528027	−0.264013	+	0.964519i	$0.585046\pi$
$44$	3.47743e15	0.848122
$45$	−6.12926e15	−1.20751
$46$	2.05294e16	3.28228
$47$	1.11913e15	0.145865
$47$	1.11913e15	0.145865
$48$	−3.41007e16	−3.63891
$49$	1.76384e16	1.54738
$50$	1.56418e16	1.13259
$51$	2.67844e16	1.60681
$52$	−5.84782e15	−0.291717
$53$	−1.80802e16	−0.752631	−0.376315	−	0.926492i	$-0.622809\pi$
$53$	−1.80802e16	−0.752631	−0.376315	+	0.926492i	$0.622809\pi$
$54$	8.64730e16	3.01397
$55$	−7.64666e15	−0.223886
$56$	1.57636e17	3.88927
$57$	5.27350e16	1.09973
$58$	1.22153e17	2.15942
$59$	6.22662e16	0.935746	0.467873	−	0.883796i	$-0.345020\pi$
$59$	6.22662e16	0.935746	0.467873	+	0.883796i	$0.345020\pi$
$60$	1.93190e17	2.47485
$61$	−1.45257e17	−1.59039	−0.795197	−	0.606351i	$-0.792633\pi$
$61$	−1.45257e17	−1.59039	−0.795197	+	0.606351i	$0.792633\pi$
$62$	8.24157e16	0.773195
$63$	−3.88075e17	−3.12738
$64$	7.03700e16	0.488290
$65$	1.28590e16	0.0770070
$66$	2.20321e17	1.14127
$67$	3.92212e17	1.76121	0.880603	−	0.473855i	$-0.157138\pi$
$67$	3.92212e17	1.76121	0.880603	+	0.473855i	$0.157138\pi$
$68$	−5.58962e17	−2.18046
$69$	9.10614e17	3.09220
$70$	−6.06383e17	−1.79604
$71$	5.02750e17	1.30136	0.650681	−	0.759352i	$-0.274484\pi$
$71$	5.02750e17	1.30136	0.650681	+	0.759352i	$0.274484\pi$
$72$	−2.10675e18	−4.77479
$73$	−9.66948e17	−1.92237	−0.961183	−	0.275911i	$-0.911021\pi$
$73$	−9.66948e17	−1.92237	−0.961183	+	0.275911i	$0.911021\pi$
$74$	−2.71515e17	−0.474343
$75$	6.93818e17	1.06700
$76$	−1.10052e18	−1.49235
$77$	−4.84149e17	−0.579852
$78$	−3.70503e17	−0.392548
$79$	1.46449e18	1.37476	0.687382	−	0.726296i	$-0.258760\pi$
$79$	1.46449e18	1.37476	0.687382	+	0.726296i	$0.258760\pi$
$80$	−1.56486e18	−1.30353
$81$	1.18873e18	0.879986
$82$	−3.74534e18	−2.46751
$83$	5.27599e17	0.309786	0.154893	−	0.987931i	$-0.450497\pi$
$83$	5.27599e17	0.309786	0.154893	+	0.987931i	$0.450497\pi$
$84$	1.22319e19	6.40973
$85$	1.22912e18	0.575594
$86$	2.30093e18	0.964204
$87$	5.41828e18	2.03436
$88$	−2.62831e18	−0.885302
$89$	2.55481e18	0.772955	0.386477	−	0.922299i	$-0.373692\pi$
$89$	2.55481e18	0.772955	0.386477	+	0.922299i	$0.373692\pi$
$90$	8.10413e18	2.20497
$91$	8.14169e17	0.199444
$92$	−1.90036e19	−4.19614
$93$	3.65569e18	0.728419
$94$	−1.47972e18	−0.266357
$95$	2.41998e18	0.393947
$96$	1.66432e19	2.45279
$97$	1.02912e19	1.37447	0.687236	−	0.726434i	$-0.258824\pi$
$97$	1.02912e19	1.37447	0.687236	+	0.726434i	$0.258824\pi$
$98$	−2.33216e19	−2.82560
$99$	6.47051e18	0.711876
$100$	−1.44793e19	−1.44793
$101$	−1.84934e19	−1.68253	−0.841265	−	0.540622i	$-0.818189\pi$
$101$	−1.84934e19	−1.68253	−0.841265	+	0.540622i	$0.818189\pi$
$102$	−3.54144e19	−2.93413
$103$	2.05794e19	1.55410	0.777052	−	0.629436i	$-0.216714\pi$
$103$	2.05794e19	1.55410	0.777052	+	0.629436i	$0.216714\pi$
$104$	4.41990e18	0.304506
$105$	−2.68972e19	−1.69203
$106$	2.39057e19	1.37434
$107$	2.33782e19	1.22932	0.614660	−	0.788792i	$-0.289293\pi$
$107$	2.33782e19	1.22932	0.614660	+	0.788792i	$0.289293\pi$
$108$	−8.00460e19	−3.85313
$109$	−5.65107e18	−0.249218	−0.124609	−	0.992206i	$-0.539768\pi$
$109$	−5.65107e18	−0.249218	−0.124609	+	0.992206i	$0.539768\pi$
$110$	1.01104e19	0.408827
$111$	−1.20435e19	−0.446874
$112$	−9.90795e19	−3.37608
$113$	−1.30671e19	−0.409199	−0.204599	−	0.978846i	$-0.565589\pi$
$113$	−1.30671e19	−0.409199	−0.204599	+	0.978846i	$0.565589\pi$
$114$	−6.97263e19	−2.00817
$115$	4.17876e19	1.10769
$116$	−1.13074e20	−2.76065
$117$	−1.08811e19	−0.244855
$118$	−8.23285e19	−1.70872
$119$	7.78222e19	1.49076
$120$	−1.46017e20	−2.58334
$121$	−5.30867e19	−0.868010
$122$	1.92060e20	2.90414
$123$	−1.66131e20	−2.32462
$124$	−7.62904e19	−0.988470
$125$	8.31725e19	0.998469
$126$	5.13114e20	5.71076
$127$	−4.94029e19	−0.510055	−0.255028	−	0.966934i	$-0.582085\pi$
$127$	−4.94029e19	−0.510055	−0.255028	+	0.966934i	$0.582085\pi$
$128$	5.57381e19	0.534143
$129$	1.02062e20	0.908366
$130$	−1.70022e19	−0.140619
$131$	−4.90716e19	−0.377357	−0.188679	−	0.982039i	$-0.560420\pi$
$131$	−4.90716e19	−0.377357	−0.188679	+	0.982039i	$0.560420\pi$
$132$	−2.03946e20	−1.45903
$133$	1.53221e20	1.02030
$134$	−5.18584e20	−3.21605
$135$	1.76016e20	1.01714
$136$	4.22475e20	2.27605
$137$	7.58339e19	0.381081	0.190541	−	0.981679i	$-0.438976\pi$
$137$	7.58339e19	0.381081	0.190541	+	0.981679i	$0.438976\pi$
$138$	−1.20402e21	−5.64652
$139$	−3.12924e20	−1.37024	−0.685122	−	0.728429i	$-0.740251\pi$
$139$	−3.12924e20	−1.37024	−0.685122	+	0.728429i	$0.740251\pi$
$140$	5.61315e20	2.29610
$141$	−6.56354e19	−0.250932
$142$	−6.64738e20	−2.37635
$143$	−1.35749e19	−0.0453989
$144$	1.32417e21	4.14476
$145$	2.48642e20	0.728751
$146$	1.27850e21	3.51034
$147$	−1.03447e21	−2.66197
$148$	2.51335e20	0.606411
$149$	3.98820e19	0.0902625	0.0451312	−	0.998981i	$-0.485629\pi$
$149$	3.98820e19	0.0902625	0.0451312	+	0.998981i	$0.485629\pi$
$150$	−9.17369e20	−1.94839
$151$	−3.53199e20	−0.704268	−0.352134	−	0.935950i	$-0.614544\pi$
$151$	−3.53199e20	−0.704268	−0.352134	+	0.935950i	$0.614544\pi$
$152$	8.31797e20	1.55777
$153$	−1.04007e21	−1.83018
$154$	6.40144e20	1.05884
$155$	1.67758e20	0.260935
$156$	3.42966e20	0.501843
$157$	7.79631e20	1.07360	0.536800	−	0.843710i	$-0.319633\pi$
$157$	7.79631e20	1.07360	0.536800	+	0.843710i	$0.319633\pi$
$158$	−1.93635e21	−2.51039
$159$	1.06038e21	1.29475
$160$	7.63747e20	0.878638
$161$	2.64579e21	2.86886
$162$	−1.57174e21	−1.60690
$163$	4.08379e20	0.393805	0.196902	−	0.980423i	$-0.436912\pi$
$163$	4.08379e20	0.393805	0.196902	+	0.980423i	$0.436912\pi$
$164$	3.46698e21	3.15453
$165$	4.48465e20	0.385151
$166$	−6.97593e20	−0.565686
$167$	−6.36067e20	−0.487188	−0.243594	−	0.969877i	$-0.578326\pi$
$167$	−6.36067e20	−0.487188	−0.243594	+	0.969877i	$0.578326\pi$
$168$	−9.24510e21	−6.69073
$169$	−1.43909e21	−0.984385
$170$	−1.62515e21	−1.05106
$171$	−2.04776e21	−1.25261
$172$	−2.12992e21	−1.23266
$173$	3.54433e21	1.94132	0.970659	−	0.240461i	$-0.0772987\pi$
$173$	3.54433e21	1.94132	0.970659	+	0.240461i	$0.0772987\pi$
$174$	−7.16407e21	−3.71485
$175$	2.01589e21	0.989932
$176$	1.65199e21	0.768486
$177$	−3.65182e21	−1.60977
$178$	−3.37798e21	−1.41146
$179$	−4.67429e19	−0.0185188	−0.00925938	−	0.999957i	$-0.502947\pi$
$179$	−4.67429e19	−0.0185188	−0.00925938	+	0.999957i	$0.502947\pi$
$180$	−7.50181e21	−2.81888
$181$	2.13871e21	0.762439	0.381219	−	0.924485i	$-0.375504\pi$
$181$	2.13871e21	0.762439	0.381219	+	0.924485i	$0.375504\pi$
$182$	−1.07650e21	−0.364196
$183$	8.51913e21	2.73596
$184$	1.43633e22	4.38010
$185$	−5.52671e20	−0.160079
$186$	−4.83356e21	−1.33013
$187$	−1.29756e21	−0.339337
$188$	1.36974e21	0.340517
$189$	1.11445e22	2.63435
$190$	−3.19971e21	−0.719368
$191$	1.01335e21	0.216743	0.108371	−	0.994110i	$-0.465436\pi$
$191$	1.01335e21	0.216743	0.108371	+	0.994110i	$0.465436\pi$
$192$	−4.12710e21	−0.840007
$193$	−7.21040e21	−1.39690	−0.698449	−	0.715660i	$-0.746126\pi$
$193$	−7.21040e21	−1.39690	−0.698449	+	0.715660i	$0.746126\pi$
$194$	−1.36071e22	−2.50986
$195$	−7.54162e20	−0.132476
$196$	2.15883e22	3.61231
$197$	3.23089e21	0.515102	0.257551	−	0.966265i	$-0.417085\pi$
$197$	3.23089e21	0.515102	0.257551	+	0.966265i	$0.417085\pi$
$198$	−8.55533e21	−1.29992
$199$	8.80627e21	1.27552	0.637761	−	0.770235i	$-0.279861\pi$
$199$	8.80627e21	1.27552	0.637761	+	0.770235i	$0.279861\pi$
$200$	1.09437e22	1.51140
$201$	−2.30027e22	−3.02981
$202$	2.44520e22	3.07239
$203$	1.57428e22	1.88743
$204$	3.27823e22	3.75105
$205$	−7.62367e21	−0.832726
$206$	−2.72102e22	−2.83788
$207$	−3.53602e22	−3.52206
$208$	−2.77806e21	−0.264326
$209$	−2.55471e21	−0.232248
$210$	3.55635e22	3.08973
$211$	6.06241e21	0.503456	0.251728	−	0.967798i	$-0.419001\pi$
$211$	6.06241e21	0.503456	0.251728	+	0.967798i	$0.419001\pi$
$212$	−2.21289e22	−1.75699
$213$	−2.94856e22	−2.23874
$214$	−3.09107e22	−2.24480
$215$	4.68357e21	0.325395
$216$	6.05004e22	4.02205
$217$	1.06216e22	0.675807
$218$	7.47186e21	0.455084
$219$	5.67101e22	3.30706
$220$	−9.35900e21	−0.522654
$221$	2.18203e21	0.116717
$222$	1.59240e22	0.816015
$223$	−3.15141e22	−1.54742	−0.773710	−	0.633540i	$-0.781601\pi$
$223$	−3.15141e22	−1.54742	−0.773710	+	0.633540i	$0.781601\pi$
$224$	4.83568e22	2.27563
$225$	−2.69418e22	−1.21532
$226$	1.72774e22	0.747219
$227$	1.20611e22	0.500197	0.250098	−	0.968220i	$-0.419537\pi$
$227$	1.20611e22	0.500197	0.250098	+	0.968220i	$0.419537\pi$
$228$	6.45440e22	2.56729
$229$	2.72200e22	1.03860	0.519302	−	0.854591i	$-0.326192\pi$
$229$	2.72200e22	1.03860	0.519302	+	0.854591i	$0.326192\pi$
$230$	−5.52517e22	−2.02270
$231$	2.83946e22	0.997523
$232$	8.54634e22	2.88167
$233$	−2.37504e21	−0.0768758	−0.0384379	−	0.999261i	$-0.512238\pi$
$233$	−2.37504e21	−0.0768758	−0.0384379	+	0.999261i	$0.512238\pi$
$234$	1.43871e22	0.447117
$235$	−3.01198e21	−0.0898890
$236$	7.62096e22	2.18447
$237$	−8.58901e22	−2.36501
$238$	−1.02897e23	−2.72220
$239$	6.11619e22	1.55489	0.777447	−	0.628949i	$-0.216515\pi$
$239$	6.11619e22	1.55489	0.777447	+	0.628949i	$0.216515\pi$
$240$	9.17769e22	2.24247
$241$	−6.69064e21	−0.157147	−0.0785735	−	0.996908i	$-0.525037\pi$
$241$	−6.69064e21	−0.157147	−0.0785735	+	0.996908i	$0.525037\pi$
$242$	7.01914e22	1.58503
$243$	6.29533e21	0.136697
$244$	−1.77785e23	−3.71272
$245$	−4.74713e22	−0.953571
$246$	2.19659e23	4.24488
$247$	4.29613e21	0.0798834
$248$	5.76618e22	1.03180
$249$	−3.09429e22	−0.532927
$250$	−1.09971e23	−1.82326
$251$	−2.38196e22	−0.380219	−0.190109	−	0.981763i	$-0.560884\pi$
$251$	−2.38196e22	−0.380219	−0.190109	+	0.981763i	$0.560884\pi$
$252$	−4.74978e23	−7.30076
$253$	−4.41142e22	−0.653030
$254$	6.53207e22	0.931388
$255$	−7.20863e22	−0.990196
$256$	−1.10591e23	−1.46366
$257$	−4.69045e21	−0.0598205	−0.0299102	−	0.999553i	$-0.509522\pi$
$257$	−4.69045e21	−0.0598205	−0.0299102	+	0.999553i	$0.509522\pi$
$258$	−1.34946e23	−1.65872
$259$	−3.49924e22	−0.414597
$260$	1.57386e22	0.179770
$261$	−2.10398e23	−2.31716
$262$	6.48826e22	0.689074
$263$	1.60562e23	1.64461	0.822303	−	0.569049i	$-0.192689\pi$
$263$	1.60562e23	1.64461	0.822303	+	0.569049i	$0.192689\pi$
$264$	1.54147e23	1.52299
$265$	4.86601e22	0.463807
$266$	−2.02590e23	−1.86313
$267$	−1.49836e23	−1.32972
$268$	4.80041e23	4.11148
$269$	−4.37427e22	−0.361626	−0.180813	−	0.983518i	$-0.557873\pi$
$269$	−4.37427e22	−0.361626	−0.180813	+	0.983518i	$0.557873\pi$
$270$	−2.32729e23	−1.85736
$271$	−2.05602e22	−0.158423	−0.0792117	−	0.996858i	$-0.525240\pi$
$271$	−2.05602e22	−0.158423	−0.0792117	+	0.996858i	$0.525240\pi$
$272$	−2.65540e23	−1.97572
$273$	−4.77498e22	−0.343105
$274$	−1.00268e23	−0.695875
$275$	−3.36116e22	−0.225335
$276$	1.11453e24	7.21865
$277$	−2.73950e23	−1.71440	−0.857202	−	0.514980i	$-0.827799\pi$
$277$	−2.73950e23	−1.71440	−0.857202	+	0.514980i	$0.827799\pi$
$278$	4.13749e23	2.50214
$279$	−1.41955e23	−0.829678
$280$	−4.24253e23	−2.39676
$281$	1.26702e23	0.691947	0.345973	−	0.938244i	$-0.387549\pi$
$281$	1.26702e23	0.691947	0.345973	+	0.938244i	$0.387549\pi$
$282$	8.67833e22	0.458215
$283$	1.68047e23	0.857948	0.428974	−	0.903317i	$-0.358875\pi$
$283$	1.68047e23	0.857948	0.428974	+	0.903317i	$0.358875\pi$
$284$	6.15332e23	3.03798
$285$	−1.41928e23	−0.677709
$286$	1.79488e22	0.0829007
$287$	−4.82694e23	−2.15672
$288$	−6.46274e23	−2.79375
$289$	−3.05033e22	−0.127590
$290$	−3.28756e23	−1.33074
$291$	−6.03566e23	−2.36451
$292$	−1.18348e24	−4.48770
$293$	2.99058e22	0.109778	0.0548888	−	0.998492i	$-0.482520\pi$
$293$	2.99058e22	0.109778	0.0548888	+	0.998492i	$0.482520\pi$
$294$	1.36778e24	4.86089
$295$	−1.67580e23	−0.576652
$296$	−1.89964e23	−0.632996
$297$	−1.85816e23	−0.599649
$298$	−5.27321e22	−0.164824
$299$	7.41846e22	0.224614
$300$	8.49187e23	2.49087
$301$	2.96541e23	0.842758
$302$	4.67000e23	1.28603
$303$	1.08461e24	2.89447
$304$	−5.22814e23	−1.35222
$305$	3.90939e23	0.980077
$306$	1.37518e24	3.34200
$307$	−4.63550e23	−1.09215	−0.546074	−	0.837737i	$-0.683878\pi$
$307$	−4.63550e23	−1.09215	−0.546074	+	0.837737i	$0.683878\pi$
$308$	−5.92566e23	−1.35365
$309$	−1.20695e24	−2.67353
$310$	−2.21810e23	−0.476480
$311$	8.89663e23	1.85354	0.926770	−	0.375630i	$-0.122574\pi$
$311$	8.89663e23	1.85354	0.926770	+	0.375630i	$0.122574\pi$
$312$	−2.59221e23	−0.523843
$313$	−3.71088e23	−0.727454	−0.363727	−	0.931506i	$-0.618496\pi$
$313$	−3.71088e23	−0.727454	−0.363727	+	0.931506i	$0.618496\pi$
$314$	−1.03083e24	−1.96045
$315$	1.04445e24	1.92724
$316$	1.79244e24	3.20934
$317$	3.52777e23	0.612967	0.306483	−	0.951876i	$-0.400848\pi$
$317$	3.52777e23	0.612967	0.306483	+	0.951876i	$0.400848\pi$
$318$	−1.40203e24	−2.36429
$319$	−2.62485e23	−0.429629
$320$	−1.89391e23	−0.300908
$321$	−1.37110e24	−2.11480
$322$	−3.49827e24	−5.23869
$323$	4.10645e23	0.597094
$324$	1.45493e24	2.05430
$325$	5.65230e22	0.0775056
$326$	−5.39960e23	−0.719108
$327$	3.31427e23	0.428730
$328$	−2.62041e24	−3.29282
$329$	−1.90704e23	−0.232808
$330$	−5.92962e23	−0.703307
$331$	−1.28705e24	−1.48330	−0.741650	−	0.670787i	$-0.765957\pi$
$331$	−1.28705e24	−1.48330	−0.741650	+	0.670787i	$0.765957\pi$
$332$	6.45746e23	0.723186
$333$	4.67663e23	0.508995
$334$	8.41010e23	0.889631
$335$	−1.05558e24	−1.08534
$336$	5.81087e24	5.80788
$337$	1.61437e24	1.56862	0.784311	−	0.620368i	$-0.213017\pi$
$337$	1.61437e24	1.56862	0.784311	+	0.620368i	$0.213017\pi$
$338$	1.90277e24	1.79754
$339$	7.66367e23	0.703947
$340$	1.50437e24	1.34370
$341$	−1.77098e23	−0.153832
$342$	2.70755e24	2.28733
$343$	−1.06324e24	−0.873648
$344$	1.60984e24	1.28670
$345$	−2.45078e24	−1.90556
$346$	−4.68633e24	−3.54495
$347$	−2.17772e23	−0.160277	−0.0801387	−	0.996784i	$-0.525536\pi$
$347$	−2.17772e23	−0.160277	−0.0801387	+	0.996784i	$0.525536\pi$
$348$	6.63161e24	4.74915
$349$	−2.32960e24	−1.62345	−0.811727	−	0.584037i	$-0.801472\pi$
$349$	−2.32960e24	−1.62345	−0.811727	+	0.584037i	$0.801472\pi$
$350$	−2.66542e24	−1.80767
$351$	3.12477e23	0.206253
$352$	−8.06269e23	−0.517994
$353$	5.69515e23	0.356160	0.178080	−	0.984016i	$-0.443011\pi$
$353$	5.69515e23	0.356160	0.178080	+	0.984016i	$0.443011\pi$
$354$	4.82845e24	2.93952
$355$	−1.35308e24	−0.801961
$356$	3.12692e24	1.80444
$357$	−4.56416e24	−2.56456
$358$	6.18036e22	0.0338162
$359$	1.74335e23	0.0928937	0.0464469	−	0.998921i	$-0.485210\pi$
$359$	1.74335e23	0.0928937	0.0464469	+	0.998921i	$0.485210\pi$
$360$	5.67001e24	2.94246
$361$	−1.16991e24	−0.591338
$362$	−2.82781e24	−1.39225
$363$	3.11346e24	1.49324
$364$	9.96489e23	0.465596
$365$	2.60240e24	1.18465
$366$	−1.12640e25	−4.99601
$367$	1.48756e24	0.642907	0.321454	−	0.946925i	$-0.395829\pi$
$367$	1.48756e24	0.642907	0.321454	+	0.946925i	$0.395829\pi$
$368$	−9.02781e24	−3.80214
$369$	6.45105e24	2.64777
$370$	7.30743e23	0.292313
$371$	3.08092e24	1.20124
$372$	4.47432e24	1.70047
$373$	−2.27107e24	−0.841390	−0.420695	−	0.907202i	$-0.638214\pi$
$373$	−2.27107e24	−0.841390	−0.420695	+	0.907202i	$0.638214\pi$
$374$	1.71563e24	0.619646
$375$	−4.87794e24	−1.71767
$376$	−1.03528e24	−0.355445
$377$	4.41408e23	0.147774
$378$	−1.47353e25	−4.81046
$379$	1.06621e24	0.339445	0.169723	−	0.985492i	$-0.445713\pi$
$379$	1.06621e24	0.339445	0.169723	+	0.985492i	$0.445713\pi$
$380$	2.96190e24	0.919656
$381$	2.89741e24	0.877450
$382$	−1.33986e24	−0.395783
$383$	−1.11067e24	−0.320034	−0.160017	−	0.987114i	$-0.551155\pi$
$383$	−1.11067e24	−0.320034	−0.160017	+	0.987114i	$0.551155\pi$
$384$	−3.26896e24	−0.918888
$385$	1.30302e24	0.357333
$386$	9.53361e24	2.55081
$387$	−3.96318e24	−1.03464
$388$	1.25958e25	3.20866
$389$	3.99560e24	0.993255	0.496627	−	0.867964i	$-0.334572\pi$
$389$	3.99560e24	0.993255	0.496627	+	0.867964i	$0.334572\pi$
$390$	9.97155e23	0.241907
$391$	7.09091e24	1.67889
$392$	−1.63168e25	−3.77067
$393$	2.87798e24	0.649169
$394$	−4.27189e24	−0.940602
$395$	−3.94145e24	−0.847196
$396$	7.91947e24	1.66185
$397$	7.01228e24	1.43664	0.718322	−	0.695711i	$-0.244910\pi$
$397$	7.01228e24	1.43664	0.718322	+	0.695711i	$0.244910\pi$
$398$	−1.16437e25	−2.32917
$399$	−8.98622e24	−1.75523
$400$	−6.87850e24	−1.31197
$401$	3.42848e24	0.638602	0.319301	−	0.947653i	$-0.396552\pi$
$401$	3.42848e24	0.638602	0.319301	+	0.947653i	$0.396552\pi$
$402$	3.04142e25	5.53259
$403$	2.97816e23	0.0529116
$404$	−2.26346e25	−3.92781
$405$	−3.19930e24	−0.542290
$406$	−2.08152e25	−3.44654
$407$	5.83441e23	0.0943735
$408$	−2.47775e25	−3.91549
$409$	7.94943e24	1.22734	0.613670	−	0.789563i	$-0.289693\pi$
$409$	7.94943e24	1.22734	0.613670	+	0.789563i	$0.289693\pi$
$410$	1.00800e25	1.52060
$411$	−4.44755e24	−0.655576
$412$	2.51879e25	3.62800
$413$	−1.06104e25	−1.49350
$414$	4.67533e25	6.43146
$415$	−1.41996e24	−0.190905
$416$	1.35586e24	0.178168
$417$	1.83525e25	2.35724
$418$	3.37785e24	0.424098
$419$	4.64557e24	0.570171	0.285086	−	0.958502i	$-0.407978\pi$
$419$	4.64557e24	0.570171	0.285086	+	0.958502i	$0.407978\pi$
$420$	−3.29203e25	−3.94999
$421$	−1.17976e25	−1.38393	−0.691965	−	0.721931i	$-0.743255\pi$
$421$	−1.17976e25	−1.38393	−0.691965	+	0.721931i	$0.743255\pi$
$422$	−8.01573e24	−0.919337
$423$	2.54870e24	0.285815
$424$	1.67255e25	1.83402
$425$	5.40273e24	0.579320
$426$	3.89859e25	4.08805
$427$	2.47524e25	2.53835
$428$	2.86133e25	2.86981
$429$	7.96150e23	0.0780999
$430$	−6.19263e24	−0.594189
$431$	8.47412e24	0.795354	0.397677	−	0.917525i	$-0.369816\pi$
$431$	8.47412e24	0.795354	0.397677	+	0.917525i	$0.369816\pi$
$432$	−3.80266e25	−3.49134
$433$	−8.51618e24	−0.764909	−0.382455	−	0.923974i	$-0.624921\pi$
$433$	−8.51618e24	−0.764909	−0.382455	+	0.923974i	$0.624921\pi$
$434$	−1.40439e25	−1.23406
$435$	−1.45825e25	−1.25367
$436$	−6.91653e24	−0.581790
$437$	1.39611e25	1.14907
$438$	−7.49823e25	−6.03886
$439$	−6.00148e24	−0.472983	−0.236492	−	0.971634i	$-0.575998\pi$
$439$	−6.00148e24	−0.472983	−0.236492	+	0.971634i	$0.575998\pi$
$440$	7.07372e24	0.545566
$441$	4.01696e25	3.03201
$442$	−2.88509e24	−0.213132
$443$	−1.75866e25	−1.27159	−0.635795	−	0.771858i	$-0.719328\pi$
$443$	−1.75866e25	−1.27159	−0.635795	+	0.771858i	$0.719328\pi$
$444$	−1.47405e25	−1.04321
$445$	−6.87590e24	−0.476332
$446$	4.16680e25	2.82567
$447$	−2.33902e24	−0.155279
$448$	−1.19913e25	−0.779336
$449$	1.04881e25	0.667352	0.333676	−	0.942688i	$-0.391711\pi$
$449$	1.04881e25	0.667352	0.333676	+	0.942688i	$0.391711\pi$
$450$	3.56225e25	2.21924
$451$	8.04811e24	0.490927
$452$	−1.59933e25	−0.955261
$453$	2.07146e25	1.21156
$454$	−1.59472e25	−0.913385
$455$	−2.19122e24	−0.122907
$456$	−4.87837e25	−2.67984
$457$	−1.92079e25	−1.03342	−0.516710	−	0.856161i	$-0.672843\pi$
$457$	−1.92079e25	−1.03342	−0.516710	+	0.856161i	$0.672843\pi$
$458$	−3.59903e25	−1.89655
$459$	2.98681e25	1.54165
$460$	5.11453e25	2.58587
$461$	3.39478e22	0.00168133	0.000840666	−	1.00000i	$-0.499732\pi$
$461$	3.39478e22	0.00168133	0.000840666		1.00000i	$0.499732\pi$
$462$	−3.75435e25	−1.82153
$463$	−4.51089e24	−0.214409	−0.107205	−	0.994237i	$-0.534190\pi$
$463$	−4.51089e24	−0.214409	−0.107205	+	0.994237i	$0.534190\pi$
$464$	−5.37167e25	−2.50143
$465$	−9.83875e24	−0.448887
$466$	3.14029e24	0.140379
$467$	−2.71051e25	−1.18725	−0.593623	−	0.804743i	$-0.702303\pi$
$467$	−2.71051e25	−1.18725	−0.593623	+	0.804743i	$0.702303\pi$
$468$	−1.33178e25	−0.571605
$469$	−6.68343e25	−2.81098
$470$	3.98244e24	0.164142
$471$	−4.57242e25	−1.84692
$472$	−5.76008e25	−2.28023
$473$	−4.94433e24	−0.191834
$474$	1.13564e26	4.31864
$475$	1.06373e25	0.396498
$476$	9.52491e25	3.48013
$477$	−4.11756e25	−1.47474
$478$	−8.08684e25	−2.83932
$479$	6.93873e23	0.0238832	0.0119416	−	0.999929i	$-0.496199\pi$
$479$	6.93873e23	0.0238832	0.0119416	+	0.999929i	$0.496199\pi$
$480$	−4.47927e25	−1.51152
$481$	−9.81143e23	−0.0324604
$482$	8.84639e24	0.286959
$483$	−1.55172e26	−4.93532
$484$	−6.49746e25	−2.02634
$485$	−2.76974e25	−0.847016
$486$	−8.32371e24	−0.249616
$487$	2.07702e25	0.610823	0.305412	−	0.952220i	$-0.401206\pi$
$487$	2.07702e25	0.610823	0.305412	+	0.952220i	$0.401206\pi$
$488$	1.34374e26	3.87548
$489$	−2.39508e25	−0.677464
$490$	6.27666e25	1.74127
$491$	6.25793e24	0.170277	0.0851386	−	0.996369i	$-0.472867\pi$
$491$	6.25793e24	0.170277	0.0851386	+	0.996369i	$0.472867\pi$
$492$	−2.03333e26	−5.42675
$493$	4.21919e25	1.10455
$494$	−5.68036e24	−0.145871
$495$	−1.74144e25	−0.438692
$496$	−3.62424e25	−0.895657
$497$	−8.56703e25	−2.07704
$498$	4.09128e25	0.973152
$499$	5.68771e25	1.32734	0.663670	−	0.748025i	$-0.268998\pi$
$499$	5.68771e25	1.32734	0.663670	+	0.748025i	$0.268998\pi$
$500$	1.01798e26	2.33089
$501$	3.73044e25	0.838111
$502$	3.14943e25	0.694299
$503$	3.93303e25	0.850808	0.425404	−	0.905003i	$-0.360132\pi$
$503$	3.93303e25	0.850808	0.425404	+	0.905003i	$0.360132\pi$
$504$	3.58998e26	7.62082
$505$	4.97722e25	1.03686
$506$	5.83279e25	1.19247
$507$	8.44006e25	1.69344
$508$	−6.04659e25	−1.19071
$509$	−4.33876e25	−0.838585	−0.419292	−	0.907851i	$-0.637722\pi$
$509$	−4.33876e25	−0.838585	−0.419292	+	0.907851i	$0.637722\pi$
$510$	9.53128e25	1.80815
$511$	1.64771e26	3.06820
$512$	1.17001e26	2.13858
$513$	5.88063e25	1.05514
$514$	6.20173e24	0.109235
$515$	−5.53866e25	−0.957714
$516$	1.24917e26	2.12055
$517$	3.17967e24	0.0529934
$518$	4.62671e25	0.757076
$519$	−2.07870e26	−3.33966
$520$	−1.18955e25	−0.187651
$521$	−8.39328e25	−1.30009	−0.650045	−	0.759896i	$-0.725250\pi$
$521$	−8.39328e25	−1.30009	−0.650045	+	0.759896i	$0.725250\pi$
$522$	2.78189e26	4.23126
$523$	4.20105e25	0.627468	0.313734	−	0.949511i	$-0.398420\pi$
$523$	4.20105e25	0.627468	0.313734	+	0.949511i	$0.398420\pi$
$524$	−6.00603e25	−0.880928
$525$	−1.18229e26	−1.70298
$526$	−2.12295e26	−3.00314
$527$	2.84667e25	0.395491
$528$	−9.68866e25	−1.32203
$529$	1.66461e26	2.23091
$530$	−6.43386e25	−0.846936
$531$	1.41804e26	1.83355
$532$	1.87533e26	2.38186
$533$	−1.35341e25	−0.168858
$534$	1.98114e26	2.42813
$535$	−6.29189e25	−0.757566
$536$	−3.62825e26	−4.29172
$537$	2.74140e24	0.0318579
$538$	5.78368e25	0.660348
$539$	5.01142e25	0.562170
$540$	2.15432e26	2.37449
$541$	2.48081e25	0.268670	0.134335	−	0.990936i	$-0.457110\pi$
$541$	2.48081e25	0.268670	0.134335	+	0.990936i	$0.457110\pi$
$542$	2.71848e25	0.289290
$543$	−1.25432e26	−1.31163
$544$	1.29600e26	1.33172
$545$	1.52090e25	0.153580
$546$	6.31350e25	0.626527
$547$	−1.72124e26	−1.67865	−0.839327	−	0.543626i	$-0.817051\pi$
$547$	−1.72124e26	−1.67865	−0.839327	+	0.543626i	$0.817051\pi$
$548$	9.28156e25	0.889622
$549$	−3.30808e26	−3.11629
$550$	4.44414e25	0.411474
$551$	8.30703e25	0.755971
$552$	−8.42384e26	−7.53510
$553$	−2.49554e26	−2.19420
$554$	3.62217e26	3.13059
$555$	3.24134e25	0.275385
$556$	−3.82998e26	−3.19879
$557$	1.17024e26	0.960843	0.480421	−	0.877038i	$-0.340484\pi$
$557$	1.17024e26	0.960843	0.480421	+	0.877038i	$0.340484\pi$
$558$	1.87693e26	1.51504
$559$	8.31462e24	0.0659827
$560$	2.66658e26	2.08050
$561$	7.60997e25	0.583762
$562$	−1.67525e26	−1.26353
$563$	−2.68438e26	−1.99074	−0.995368	−	0.0961344i	$-0.969352\pi$
$563$	−2.68438e26	−1.99074	−0.995368	+	0.0961344i	$0.969352\pi$
$564$	−8.03333e25	−0.585793
$565$	3.51682e25	0.252168
$566$	−2.22193e26	−1.56666
$567$	−2.02564e26	−1.40450
$568$	−4.65080e26	−3.17117
$569$	−1.61116e25	−0.108037	−0.0540184	−	0.998540i	$-0.517203\pi$
$569$	−1.61116e25	−0.108037	−0.0540184	+	0.998540i	$0.517203\pi$
$570$	1.87658e26	1.23753
$571$	−2.06594e26	−1.33991	−0.669953	−	0.742403i	$-0.733686\pi$
$571$	−2.06594e26	−1.33991	−0.669953	+	0.742403i	$0.733686\pi$
$572$	−1.66148e25	−0.105982
$573$	−5.94317e25	−0.372863
$574$	6.38219e26	3.93828
$575$	1.83682e26	1.11486
$576$	1.60260e26	0.956778
$577$	9.57142e25	0.562090	0.281045	−	0.959695i	$-0.409319\pi$
$577$	9.57142e25	0.562090	0.281045	+	0.959695i	$0.409319\pi$
$578$	4.03316e25	0.232987
$579$	4.22879e26	2.40309
$580$	3.04322e26	1.70124
$581$	−8.99047e25	−0.494435
$582$	7.98037e26	4.31772
$583$	−5.13693e25	−0.273434
$584$	8.94498e26	4.68444
$585$	2.92850e25	0.150891
$586$	−3.95416e25	−0.200460
$587$	3.14607e25	0.156930	0.0784651	−	0.996917i	$-0.474998\pi$
$587$	3.14607e25	0.156930	0.0784651	+	0.996917i	$0.474998\pi$
$588$	−1.26612e27	−6.21427
$589$	5.60471e25	0.270681
$590$	2.21575e26	1.05300
$591$	−1.89487e26	−0.886132
$592$	1.19399e26	0.549472
$593$	−6.01991e25	−0.272628	−0.136314	−	0.990666i	$-0.543526\pi$
$593$	−6.01991e25	−0.272628	−0.136314	+	0.990666i	$0.543526\pi$
$594$	2.45687e26	1.09499
$595$	−2.09447e26	−0.918677
$596$	4.88129e25	0.210715
$597$	−5.16475e26	−2.19428
$598$	−9.80871e25	−0.410157
$599$	−3.12461e26	−1.28600	−0.643000	−	0.765866i	$-0.722310\pi$
$599$	−3.12461e26	−1.28600	−0.643000	+	0.765866i	$0.722310\pi$
$600$	−6.41832e26	−2.60007
$601$	9.39020e24	0.0374427	0.0187214	−	0.999825i	$-0.494040\pi$
$601$	9.39020e24	0.0374427	0.0187214	+	0.999825i	$0.494040\pi$
$602$	−3.92087e26	−1.53892
$603$	8.93220e26	3.45099
$604$	−4.32291e26	−1.64409
$605$	1.42875e26	0.534910
$606$	−1.43407e27	−5.28544
$607$	4.26351e26	1.54695	0.773473	−	0.633830i	$-0.218518\pi$
$607$	4.26351e26	1.54695	0.773473	+	0.633830i	$0.218518\pi$
$608$	2.55165e26	0.911457
$609$	−9.23293e26	−3.24695
$610$	−5.16901e26	−1.78967
$611$	−5.34709e24	−0.0182274
$612$	−1.27298e27	−4.27249
$613$	−4.29268e26	−1.41858	−0.709291	−	0.704916i	$-0.750985\pi$
$613$	−4.29268e26	−1.41858	−0.709291	+	0.704916i	$0.750985\pi$
$614$	6.12907e26	1.99432
$615$	4.47117e26	1.43254
$616$	4.47873e26	1.41299
$617$	−2.23620e26	−0.694706	−0.347353	−	0.937735i	$-0.612919\pi$
$617$	−2.23620e26	−0.694706	−0.347353	+	0.937735i	$0.612919\pi$
$618$	1.59584e27	4.88201
$619$	−4.50989e26	−1.35864	−0.679321	−	0.733841i	$-0.737726\pi$
$619$	−4.50989e26	−1.35864	−0.679321	+	0.733841i	$0.737726\pi$
$620$	2.05324e26	0.609143
$621$	1.01545e27	2.96681
$622$	−1.17631e27	−3.38466
$623$	−4.35349e26	−1.23368
$624$	1.62929e26	0.454722
$625$	1.79474e24	0.00493335
$626$	4.90653e26	1.32837
$627$	1.49830e26	0.399538
$628$	9.54216e26	2.50628
$629$	−9.37823e25	−0.242627
$630$	−1.38097e27	−3.51924
$631$	−1.55016e26	−0.389133	−0.194566	−	0.980889i	$-0.562330\pi$
$631$	−1.55016e26	−0.389133	−0.194566	+	0.980889i	$0.562330\pi$
$632$	−1.35476e27	−3.35004
$633$	−3.55551e26	−0.866098
$634$	−4.66443e26	−1.11931
$635$	1.32961e26	0.314321
$636$	1.29783e27	3.02256
$637$	−8.42745e25	−0.193362
$638$	3.47059e26	0.784525
$639$	1.14496e27	2.54995
$640$	−1.50011e26	−0.329164
$641$	−5.61369e26	−1.21366	−0.606830	−	0.794832i	$-0.707559\pi$
$641$	−5.61369e26	−1.21366	−0.606830	+	0.794832i	$0.707559\pi$
$642$	1.81287e27	3.86174
$643$	4.02825e26	0.845496	0.422748	−	0.906247i	$-0.361065\pi$
$643$	4.02825e26	0.845496	0.422748	+	0.906247i	$0.361065\pi$
$644$	3.23827e27	6.69726
$645$	−2.74684e26	−0.559779
$646$	−5.42956e26	−1.09032
$647$	−5.60723e26	−1.10958	−0.554789	−	0.831991i	$-0.687201\pi$
$647$	−5.60723e26	−1.10958	−0.554789	+	0.831991i	$0.687201\pi$
$648$	−1.09966e27	−2.14436
$649$	1.76910e26	0.339961
$650$	−7.47348e25	−0.141529
$651$	−6.22942e26	−1.16259
$652$	4.99828e26	0.919324
$653$	4.04392e26	0.733039	0.366520	−	0.930410i	$-0.380549\pi$
$653$	4.04392e26	0.733039	0.366520	+	0.930410i	$0.380549\pi$
$654$	−4.38214e26	−0.782884
$655$	1.32069e26	0.232546
$656$	1.64702e27	2.85833
$657$	−2.20212e27	−3.76678
$658$	2.52149e26	0.425120
$659$	1.30756e26	0.217294	0.108647	−	0.994080i	$-0.465348\pi$
$659$	1.30756e26	0.217294	0.108647	+	0.994080i	$0.465348\pi$
$660$	5.48892e26	0.899123
$661$	3.84863e26	0.621430	0.310715	−	0.950503i	$-0.399432\pi$
$661$	3.84863e26	0.621430	0.310715	+	0.950503i	$0.399432\pi$
$662$	1.70174e27	2.70858
$663$	−1.27973e26	−0.200789
$664$	−4.88067e26	−0.754889
$665$	−4.12373e26	−0.628760
$666$	−6.18346e26	−0.929451
$667$	1.43444e27	2.12562
$668$	−7.78504e26	−1.13732
$669$	1.84825e27	2.66203
$670$	1.39569e27	1.98189
$671$	−4.12704e26	−0.577797
$672$	−2.83605e27	−3.91477
$673$	2.55951e26	0.348348	0.174174	−	0.984715i	$-0.444274\pi$
$673$	2.55951e26	0.348348	0.174174	+	0.984715i	$0.444274\pi$
$674$	−2.13452e27	−2.86439
$675$	7.73697e26	1.02373
$676$	−1.76135e27	−2.29801
$677$	1.04099e27	1.33923	0.669615	−	0.742708i	$-0.266459\pi$
$677$	1.04099e27	1.33923	0.669615	+	0.742708i	$0.266459\pi$
$678$	−1.01329e27	−1.28544
$679$	−1.75366e27	−2.19373
$680$	−1.13703e27	−1.40261
$681$	−7.07365e26	−0.860490
$682$	2.34159e26	0.280905
$683$	1.44567e26	0.171030	0.0855148	−	0.996337i	$-0.472747\pi$
$683$	1.44567e26	0.171030	0.0855148	+	0.996337i	$0.472747\pi$
$684$	−2.50632e27	−2.92418
$685$	−2.04096e26	−0.234841
$686$	1.40582e27	1.59533
$687$	−1.59641e27	−1.78672
$688$	−1.01184e27	−1.11692
$689$	8.63851e25	0.0940495
$690$	3.24043e27	3.47966
$691$	−6.53138e26	−0.691773	−0.345887	−	0.938276i	$-0.612422\pi$
$691$	−6.53138e26	−0.691773	−0.345887	+	0.938276i	$0.612422\pi$
$692$	4.33803e27	4.53194
$693$	−1.10260e27	−1.13619
$694$	2.87939e26	0.292675
$695$	8.42188e26	0.844410
$696$	−5.01230e27	−4.95735
$697$	−1.29365e27	−1.26214
$698$	3.08021e27	2.96451
$699$	1.39293e26	0.132250
$700$	2.46731e27	2.31096
$701$	3.41306e26	0.315372	0.157686	−	0.987489i	$-0.449597\pi$
$701$	3.41306e26	0.315372	0.157686	+	0.987489i	$0.449597\pi$
$702$	−4.13159e26	−0.376629
$703$	−1.84645e26	−0.166059
$704$	1.99935e26	0.177398
$705$	1.76648e26	0.154637
$706$	−7.53014e26	−0.650367
$707$	3.15133e27	2.68541
$708$	−4.46958e27	−3.75795
$709$	1.57710e27	1.30834	0.654168	−	0.756350i	$-0.273019\pi$
$709$	1.57710e27	1.30834	0.654168	+	0.756350i	$0.273019\pi$
$710$	1.78904e27	1.46442
$711$	3.33521e27	2.69378
$712$	−2.36339e27	−1.88354
$713$	9.67808e26	0.761095
$714$	6.03474e27	4.68302
$715$	3.65349e25	0.0279770
$716$	−5.72102e25	−0.0432314
$717$	−3.58705e27	−2.67489
$718$	−2.30506e26	−0.169629
$719$	−1.89429e26	−0.137569	−0.0687846	−	0.997632i	$-0.521912\pi$
$719$	−1.89429e26	−0.137569	−0.0687846	+	0.997632i	$0.521912\pi$
$720$	−3.56380e27	−2.55420
$721$	−3.50681e27	−2.48043
$722$	1.54686e27	1.07981
$723$	3.92396e26	0.270341
$724$	2.61763e27	1.77989
$725$	1.09293e27	0.733469
$726$	−4.11662e27	−2.72674
$727$	8.93095e25	0.0583876	0.0291938	−	0.999574i	$-0.490706\pi$
$727$	8.93095e25	0.0583876	0.0291938	+	0.999574i	$0.490706\pi$
$728$	−7.53166e26	−0.486007
$729$	−1.75083e27	−1.11515
$730$	−3.44090e27	−2.16324
$731$	7.94751e26	0.493192
$732$	1.04268e28	6.38701
$733$	−2.78862e26	−0.168617	−0.0843084	−	0.996440i	$-0.526868\pi$
$733$	−2.78862e26	−0.168617	−0.0843084	+	0.996440i	$0.526868\pi$
$734$	−1.96686e27	−1.17398
$735$	2.78412e27	1.64043
$736$	4.40612e27	2.56281
$737$	1.11435e27	0.639854
$738$	−8.52960e27	−4.83497
$739$	−1.85137e27	−1.03603	−0.518014	−	0.855372i	$-0.673328\pi$
$739$	−1.85137e27	−1.03603	−0.518014	+	0.855372i	$0.673328\pi$
$740$	−6.76432e26	−0.373700
$741$	−2.51962e26	−0.137424
$742$	−4.07361e27	−2.19352
$743$	1.53671e27	0.816953	0.408476	−	0.912769i	$-0.366060\pi$
$743$	1.53671e27	0.816953	0.408476	+	0.912769i	$0.366060\pi$
$744$	−3.38178e27	−1.77502
$745$	−1.07337e26	−0.0556241
$746$	3.00282e27	1.53642
$747$	1.20155e27	0.607010
$748$	−1.58812e27	−0.792170
$749$	−3.98372e27	−1.96206
$750$	6.44963e27	3.13656
$751$	7.02555e26	0.337366	0.168683	−	0.985670i	$-0.446049\pi$
$751$	7.02555e26	0.337366	0.168683	+	0.985670i	$0.446049\pi$
$752$	6.50708e26	0.308544
$753$	1.39698e27	0.654092
$754$	−5.83632e26	−0.269843
$755$	9.50582e26	0.434004
$756$	1.36401e28	6.14980
$757$	7.72841e25	0.0344096	0.0172048	−	0.999852i	$-0.494523\pi$
$757$	7.72841e25	0.0344096	0.0172048	+	0.999852i	$0.494523\pi$
$758$	−1.40975e27	−0.619845
$759$	2.58723e27	1.12341
$760$	−2.23866e27	−0.959973
$761$	8.14043e26	0.344741	0.172371	−	0.985032i	$-0.444857\pi$
$761$	8.14043e26	0.344741	0.172371	+	0.985032i	$0.444857\pi$
$762$	−3.83096e27	−1.60227
$763$	9.62961e26	0.397764
$764$	1.24028e27	0.505978
$765$	2.79920e27	1.12785
$766$	1.46853e27	0.584400
$767$	−2.97501e26	−0.116932
$768$	6.48601e27	2.51794
$769$	−2.37838e27	−0.911972	−0.455986	−	0.889987i	$-0.650713\pi$
$769$	−2.37838e27	−0.911972	−0.455986	+	0.889987i	$0.650713\pi$
$770$	−1.72285e27	−0.652509
$771$	2.75088e26	0.102909
$772$	−8.82504e27	−3.26101
$773$	2.34964e27	0.857622	0.428811	−	0.903394i	$-0.358933\pi$
$773$	2.34964e27	0.857622	0.428811	+	0.903394i	$0.358933\pi$
$774$	5.24013e27	1.88931
$775$	7.37396e26	0.262624
$776$	−9.52014e27	−3.34932
$777$	2.05226e27	0.713234
$778$	−5.28299e27	−1.81374
$779$	−2.54703e27	−0.863831
$780$	−9.23043e26	−0.309260
$781$	1.42841e27	0.472790
$782$	−9.37563e27	−3.06575
$783$	6.04208e27	1.95186
$784$	1.02557e28	3.27313
$785$	−2.09826e27	−0.661604
$786$	−3.80527e27	−1.18542
$787$	2.38408e27	0.733773	0.366886	−	0.930266i	$-0.380424\pi$
$787$	2.38408e27	0.733773	0.366886	+	0.930266i	$0.380424\pi$
$788$	3.95439e27	1.20249
$789$	−9.41670e27	−2.82922
$790$	5.21140e27	1.54703
$791$	2.22668e27	0.653103
$792$	−5.98569e27	−1.73470
$793$	6.94024e26	0.198737
$794$	−9.27165e27	−2.62339
$795$	−2.85385e27	−0.797890
$796$	1.07783e28	2.97766
$797$	−4.01027e27	−1.09476	−0.547381	−	0.836884i	$-0.684375\pi$
$797$	−4.01027e27	−1.09476	−0.547381	+	0.836884i	$0.684375\pi$
$798$	1.18816e28	3.20514
$799$	−5.11100e26	−0.136242
$800$	3.35713e27	0.884327
$801$	5.81831e27	1.51456
$802$	−4.53315e27	−1.16612
$803$	−2.74729e27	−0.698404
$804$	−2.81537e28	−7.07299
$805$	−7.12076e27	−1.76793
$806$	−3.93774e26	−0.0966193
$807$	2.56545e27	0.622106
$808$	1.71077e28	4.10000
$809$	−7.49296e27	−1.77477	−0.887386	−	0.461027i	$-0.847481\pi$
$809$	−7.49296e27	−1.77477	−0.887386	+	0.461027i	$0.847481\pi$
$810$	4.23012e27	0.990250
$811$	2.22585e27	0.514988	0.257494	−	0.966280i	$-0.417103\pi$
$811$	2.22585e27	0.514988	0.257494	+	0.966280i	$0.417103\pi$
$812$	1.92682e28	4.40614
$813$	1.20583e27	0.272537
$814$	−7.71428e26	−0.172331
$815$	−1.09909e27	−0.242681
$816$	1.55736e28	3.39884
$817$	1.56476e27	0.337550
$818$	−1.05108e28	−2.24119
$819$	1.85418e27	0.390801
$820$	−9.33086e27	−1.94397
$821$	5.23686e27	1.07848	0.539238	−	0.842153i	$-0.318712\pi$
$821$	5.23686e27	1.07848	0.539238	+	0.842153i	$0.318712\pi$
$822$	5.88056e27	1.19712
$823$	5.49200e27	1.10518	0.552589	−	0.833454i	$-0.313640\pi$
$823$	5.49200e27	1.10518	0.552589	+	0.833454i	$0.313640\pi$
$824$	−1.90375e28	−3.78705
$825$	1.97127e27	0.387645
$826$	1.40291e28	2.72721
$827$	−6.15200e27	−1.18226	−0.591131	−	0.806576i	$-0.701318\pi$
$827$	−6.15200e27	−1.18226	−0.591131	+	0.806576i	$0.701318\pi$
$828$	−4.32785e28	−8.22212
$829$	−2.25398e27	−0.423334	−0.211667	−	0.977342i	$-0.567889\pi$
$829$	−2.25398e27	−0.423334	−0.211667	+	0.977342i	$0.567889\pi$
$830$	1.87747e27	0.348603
$831$	1.60668e28	2.94930
$832$	−3.36220e26	−0.0610172
$833$	−8.05536e27	−1.44530
$834$	−2.42658e28	−4.30444
$835$	1.71188e27	0.300229
$836$	−3.12680e27	−0.542176
$837$	4.07656e27	0.698880
$838$	−6.14238e27	−1.04116
$839$	1.59602e27	0.267485	0.133742	−	0.991016i	$-0.457301\pi$
$839$	1.59602e27	0.267485	0.133742	+	0.991016i	$0.457301\pi$
$840$	2.48818e28	4.12315
$841$	2.43184e27	0.398449
$842$	1.55988e28	2.52713
$843$	−7.43088e27	−1.19036
$844$	7.41998e27	1.17530
$845$	3.87311e27	0.606625
$846$	−3.36989e27	−0.521913
$847$	9.04616e27	1.38539
$848$	−1.05126e28	−1.59202
$849$	−9.85574e27	−1.47593
$850$	−7.14351e27	−1.05787
$851$	−3.18840e27	−0.466920
$852$	−3.60883e28	−5.22626
$853$	5.16929e27	0.740312	0.370156	−	0.928970i	$-0.379304\pi$
$853$	5.16929e27	0.740312	0.370156	+	0.928970i	$0.379304\pi$
$854$	−3.27276e28	−4.63516
$855$	5.51124e27	0.771918
$856$	−2.16265e28	−2.99561
$857$	−6.83211e27	−0.935916	−0.467958	−	0.883751i	$-0.655010\pi$
$857$	−6.83211e27	−0.935916	−0.467958	+	0.883751i	$0.655010\pi$
$858$	−1.05267e27	−0.142614
$859$	−3.84485e27	−0.515162	−0.257581	−	0.966257i	$-0.582925\pi$
$859$	−3.84485e27	−0.515162	−0.257581	+	0.966257i	$0.582925\pi$
$860$	5.73237e27	0.759625
$861$	2.83093e28	3.71021
$862$	−1.12045e28	−1.45236
$863$	−3.97127e27	−0.509128	−0.254564	−	0.967056i	$-0.581932\pi$
$863$	−3.97127e27	−0.509128	−0.254564	+	0.967056i	$0.581932\pi$
$864$	1.85593e28	2.35332
$865$	−9.53905e27	−1.19633
$866$	1.12601e28	1.39676
$867$	1.78898e27	0.219494
$868$	1.30001e28	1.57765
$869$	4.16090e27	0.499458
$870$	1.92810e28	2.28927
$871$	−1.87395e27	−0.220082
$872$	5.22765e27	0.607295
$873$	2.34372e28	2.69321
$874$	−1.84594e28	−2.09825
$875$	−1.41729e28	−1.59361
$876$	6.94094e28	7.72021
$877$	1.36071e28	1.49716	0.748581	−	0.663044i	$-0.230736\pi$
$877$	1.36071e28	1.49716	0.748581	+	0.663044i	$0.230736\pi$
$878$	7.93518e27	0.863692
$879$	−1.75393e27	−0.188851
$880$	−4.44608e27	−0.473578
$881$	3.37587e27	0.355725	0.177863	−	0.984055i	$-0.443082\pi$
$881$	3.37587e27	0.355725	0.177863	+	0.984055i	$0.443082\pi$
$882$	−5.31124e28	−5.53661
$883$	−7.60060e27	−0.783829	−0.391915	−	0.920002i	$-0.628187\pi$
$883$	−7.60060e27	−0.783829	−0.391915	+	0.920002i	$0.628187\pi$
$884$	2.67066e27	0.272472
$885$	9.82834e27	0.992017
$886$	2.32531e28	2.32199
$887$	−5.06677e26	−0.0500560	−0.0250280	−	0.999687i	$-0.507967\pi$
$887$	−5.06677e26	−0.0500560	−0.0250280	+	0.999687i	$0.507967\pi$
$888$	1.11411e28	1.08895
$889$	8.41843e27	0.814075
$890$	9.09134e27	0.869807
$891$	3.37742e27	0.319703
$892$	−3.85711e28	−3.61240
$893$	−1.00629e27	−0.0932466
$894$	3.09266e27	0.283548
$895$	1.25802e26	0.0114122
$896$	−9.49796e27	−0.852519
$897$	−4.35082e27	−0.386405
$898$	−1.38673e28	−1.21862
$899$	5.75859e27	0.500725
$900$	−3.29749e28	−2.83713
$901$	8.25710e27	0.702979
$902$	−1.06412e28	−0.896459
$903$	−1.73917e28	−1.44980
$904$	1.20880e28	0.997138
$905$	−5.75602e27	−0.469851
$906$	−2.73889e28	−2.21236
$907$	9.96747e26	0.0796739	0.0398369	−	0.999206i	$-0.487316\pi$
$907$	9.96747e26	0.0796739	0.0398369	+	0.999206i	$0.487316\pi$
$908$	1.47620e28	1.16769
$909$	−4.21166e28	−3.29683
$910$	2.89723e27	0.224435
$911$	1.76029e28	1.34946	0.674729	−	0.738066i	$-0.264261\pi$
$911$	1.76029e28	1.34946	0.674729	+	0.738066i	$0.264261\pi$
$912$	3.06623e28	2.32623
$913$	1.49901e27	0.112547
$914$	2.53968e28	1.88708
$915$	−2.29280e28	−1.68603
$916$	3.33154e28	2.42459
$917$	8.36196e27	0.602282
$918$	−3.94917e28	−2.81514
$919$	−7.68415e27	−0.542123	−0.271062	−	0.962562i	$-0.587375\pi$
$919$	−7.68415e27	−0.542123	−0.271062	+	0.962562i	$0.587375\pi$
$920$	−3.86566e28	−2.69923
$921$	2.71865e28	1.87883
$922$	−4.48860e25	−0.00307020
$923$	−2.40209e27	−0.162619
$924$	3.47532e28	2.32868
$925$	−2.42932e27	−0.161116
$926$	5.96432e27	0.391522
$927$	4.68674e28	3.04518
$928$	2.62170e28	1.68608
$929$	−1.66489e28	−1.05983	−0.529914	−	0.848052i	$-0.677776\pi$
$929$	−1.66489e28	−1.05983	−0.529914	+	0.848052i	$0.677776\pi$
$930$	1.30088e28	0.819691
$931$	−1.58599e28	−0.989189
$932$	−2.90689e27	−0.179464
$933$	−5.21774e28	−3.18865
$934$	3.58385e28	2.16797
$935$	3.49218e27	0.209116
$936$	1.00658e28	0.596663
$937$	1.50489e27	0.0883035	0.0441517	−	0.999025i	$-0.485941\pi$
$937$	1.50489e27	0.0883035	0.0441517	+	0.999025i	$0.485941\pi$
$938$	8.83685e28	5.13299
$939$	2.17638e28	1.25144
$940$	−3.68646e27	−0.209843
$941$	−2.86653e28	−1.61531	−0.807654	−	0.589657i	$-0.799263\pi$
$941$	−2.86653e28	−1.61531	−0.807654	+	0.589657i	$0.799263\pi$
$942$	6.04567e28	3.37257
$943$	−4.39815e28	−2.42890
$944$	3.62041e28	1.97936
$945$	−2.99938e28	−1.62341
$946$	6.53740e27	0.350299
$947$	−1.33710e28	−0.709317	−0.354659	−	0.934996i	$-0.615403\pi$
$947$	−1.33710e28	−0.709317	−0.354659	+	0.934996i	$0.615403\pi$
$948$	−1.05124e29	−5.52105
$949$	4.61998e27	0.240221
$950$	−1.40646e28	−0.724025
$951$	−2.06898e28	−1.05449
$952$	−7.19912e28	−3.63269
$953$	−1.17054e27	−0.0584794	−0.0292397	−	0.999572i	$-0.509309\pi$
$953$	−1.17054e27	−0.0584794	−0.0292397	+	0.999572i	$0.509309\pi$
$954$	5.44425e28	2.69295
$955$	−2.72729e27	−0.133567
$956$	7.48580e28	3.62985
$957$	1.53944e28	0.739093
$958$	−9.17442e26	−0.0436120
$959$	−1.29224e28	−0.608226
$960$	1.11075e28	0.517653
$961$	−1.77854e28	−0.820712
$962$	1.29727e27	0.0592744
$963$	5.32412e28	2.40879
$964$	−8.18890e27	−0.366854
$965$	1.94057e28	0.860836
$966$	2.05169e29	9.01214
$967$	−6.76607e27	−0.294297	−0.147148	−	0.989114i	$-0.547009\pi$
$967$	−6.76607e27	−0.294297	−0.147148	+	0.989114i	$0.547009\pi$
$968$	4.91091e28	2.11517
$969$	−2.40837e28	−1.02718
$970$	3.66215e28	1.54670
$971$	1.02807e28	0.429972	0.214986	−	0.976617i	$-0.431029\pi$
$971$	1.02807e28	0.429972	0.214986	+	0.976617i	$0.431029\pi$
$972$	7.70506e27	0.319115
$973$	5.33233e28	2.18698
$974$	−2.74624e28	−1.11540
$975$	−3.31499e27	−0.133333
$976$	−8.44585e28	−3.36411
$977$	−4.10318e28	−1.61854	−0.809268	−	0.587440i	$-0.800136\pi$
$977$	−4.10318e28	−1.61854	−0.809268	+	0.587440i	$0.800136\pi$
$978$	3.16678e28	1.23708
$979$	7.25872e27	0.280818
$980$	−5.81016e28	−2.22608
$981$	−1.28697e28	−0.488329
$982$	−8.27425e27	−0.310935
$983$	−3.47207e28	−1.29220	−0.646101	−	0.763252i	$-0.723601\pi$
$983$	−3.47207e28	−1.29220	−0.646101	+	0.763252i	$0.723601\pi$
$984$	1.53683e29	5.66465
$985$	−8.69546e27	−0.317430
$986$	−5.57863e28	−2.01696
$987$	1.11845e28	0.400501
$988$	5.25818e27	0.186485
$989$	2.70199e28	0.949114
$990$	2.30254e28	0.801075
$991$	−4.12923e28	−1.42288	−0.711442	−	0.702745i	$-0.751957\pi$
$991$	−4.12923e28	−1.42288	−0.711442	+	0.702745i	$0.751957\pi$
$992$	1.76885e28	0.603713
$993$	7.54836e28	2.55173
$994$	1.13274e29	3.79278
$995$	−2.37008e28	−0.786038
$996$	−3.78720e28	−1.24410
$997$	−3.41785e28	−1.11211	−0.556057	−	0.831144i	$-0.687686\pi$
$997$	−3.41785e28	−1.11211	−0.556057	+	0.831144i	$0.687686\pi$
$998$	−7.52031e28	−2.42379
$999$	−1.34301e28	−0.428752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.a.1.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1322.20 q^{2} -58648.5 q^{3} +1.22393e6 q^{4} -2.69135e6 q^{5} +7.75453e7 q^{6} -1.70403e8 q^{7} -9.25073e8 q^{8} +2.27739e9 q^{9} +O(q^{10})\)	\(q-1322.20 q^{2} -58648.5 q^{3} +1.22393e6 q^{4} -2.69135e6 q^{5} +7.75453e7 q^{6} -1.70403e8 q^{7} -9.25073e8 q^{8} +2.27739e9 q^{9} +3.55852e9 q^{10} +2.84119e9 q^{11} -7.17819e10 q^{12} -4.77789e9 q^{13} +2.25308e11 q^{14} +1.57844e11 q^{15} +5.81441e11 q^{16} -4.56694e11 q^{17} -3.01117e12 q^{18} -8.99169e11 q^{19} -3.29404e12 q^{20} +9.99391e12 q^{21} -3.75664e12 q^{22} -1.55266e13 q^{23} +5.42542e13 q^{24} -1.18301e13 q^{25} +6.31735e12 q^{26} -6.54007e13 q^{27} -2.08562e14 q^{28} -9.23856e13 q^{29} -2.08702e14 q^{30} -6.23321e13 q^{31} -2.83778e14 q^{32} -1.66632e14 q^{33} +6.03842e14 q^{34} +4.58616e14 q^{35} +2.78737e15 q^{36} +2.05351e14 q^{37} +1.18888e15 q^{38} +2.80216e14 q^{39} +2.48970e15 q^{40} +2.83265e15 q^{41} -1.32140e16 q^{42} -1.74023e15 q^{43} +3.47743e15 q^{44} -6.12926e15 q^{45} +2.05294e16 q^{46} +1.11913e15 q^{47} -3.41007e16 q^{48} +1.76384e16 q^{49} +1.56418e16 q^{50} +2.67844e16 q^{51} -5.84782e15 q^{52} -1.80802e16 q^{53} +8.64730e16 q^{54} -7.64666e15 q^{55} +1.57636e17 q^{56} +5.27350e16 q^{57} +1.22153e17 q^{58} +6.22662e16 q^{59} +1.93190e17 q^{60} -1.45257e17 q^{61} +8.24157e16 q^{62} -3.88075e17 q^{63} +7.03700e16 q^{64} +1.28590e16 q^{65} +2.20321e17 q^{66} +3.92212e17 q^{67} -5.58962e17 q^{68} +9.10614e17 q^{69} -6.06383e17 q^{70} +5.02750e17 q^{71} -2.10675e18 q^{72} -9.66948e17 q^{73} -2.71515e17 q^{74} +6.93818e17 q^{75} -1.10052e18 q^{76} -4.84149e17 q^{77} -3.70503e17 q^{78} +1.46449e18 q^{79} -1.56486e18 q^{80} +1.18873e18 q^{81} -3.74534e18 q^{82} +5.27599e17 q^{83} +1.22319e19 q^{84} +1.22912e18 q^{85} +2.30093e18 q^{86} +5.41828e18 q^{87} -2.62831e18 q^{88} +2.55481e18 q^{89} +8.10413e18 q^{90} +8.14169e17 q^{91} -1.90036e19 q^{92} +3.65569e18 q^{93} -1.47972e18 q^{94} +2.41998e18 q^{95} +1.66432e19 q^{96} +1.02912e19 q^{97} -2.33216e19 q^{98} +6.47051e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 1481 q^{2} - 74552 q^{3} + 8752837 q^{4} + 28914 q^{5} - 43599872 q^{6} - 203565056 q^{7} - 994215087 q^{8} + 10020983718 q^{9}+O(q^{10}) \) 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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