LMFDB - Embedded newform 59.18.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,18,Mod(1,59)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("59.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	59.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:	$108.101031533$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-648.649 q^{2} -13388.7 q^{3} +289673. q^{4} +688083. q^{5} +8.68455e6 q^{6} -5.33195e6 q^{7} -1.02876e8 q^{8} +5.01164e7 q^{9} +O(q^{10})$	\(q-648.649 q^{2} -13388.7 q^{3} +289673. q^{4} +688083. q^{5} +8.68455e6 q^{6} -5.33195e6 q^{7} -1.02876e8 q^{8} +5.01164e7 q^{9} -4.46324e8 q^{10} -3.51148e8 q^{11} -3.87834e9 q^{12} -3.65152e9 q^{13} +3.45856e9 q^{14} -9.21252e9 q^{15} +2.87626e10 q^{16} -4.79864e10 q^{17} -3.25079e10 q^{18} +1.10502e11 q^{19} +1.99319e11 q^{20} +7.13877e10 q^{21} +2.27772e11 q^{22} -5.96605e11 q^{23} +1.37738e12 q^{24} -2.89482e11 q^{25} +2.36855e12 q^{26} +1.05802e12 q^{27} -1.54452e12 q^{28} +1.57478e12 q^{29} +5.97569e12 q^{30} +2.50979e12 q^{31} -5.17261e12 q^{32} +4.70141e12 q^{33} +3.11263e13 q^{34} -3.66882e12 q^{35} +1.45174e13 q^{36} -2.15437e13 q^{37} -7.16767e13 q^{38} +4.88890e13 q^{39} -7.07875e13 q^{40} -6.74806e13 q^{41} -4.63055e13 q^{42} -1.10639e14 q^{43} -1.01718e14 q^{44} +3.44842e13 q^{45} +3.86987e14 q^{46} +1.26001e14 q^{47} -3.85093e14 q^{48} -2.04201e14 q^{49} +1.87772e14 q^{50} +6.42474e14 q^{51} -1.05775e15 q^{52} -3.90578e14 q^{53} -6.86285e14 q^{54} -2.41619e14 q^{55} +5.48532e14 q^{56} -1.47947e15 q^{57} -1.02148e15 q^{58} +1.46830e14 q^{59} -2.66862e15 q^{60} +1.71259e15 q^{61} -1.62797e15 q^{62} -2.67218e14 q^{63} -4.14765e14 q^{64} -2.51255e15 q^{65} -3.04956e15 q^{66} -1.67688e15 q^{67} -1.39004e16 q^{68} +7.98775e15 q^{69} +2.37978e15 q^{70} -2.09742e15 q^{71} -5.15580e15 q^{72} +4.47847e15 q^{73} +1.39743e16 q^{74} +3.87577e15 q^{75} +3.20093e16 q^{76} +1.87230e15 q^{77} -3.17118e16 q^{78} -1.31590e16 q^{79} +1.97911e16 q^{80} -2.06376e16 q^{81} +4.37712e16 q^{82} -2.29114e16 q^{83} +2.06791e16 q^{84} -3.30186e16 q^{85} +7.17661e16 q^{86} -2.10842e16 q^{87} +3.61248e16 q^{88} -2.71787e16 q^{89} -2.23682e16 q^{90} +1.94697e16 q^{91} -1.72820e17 q^{92} -3.36027e16 q^{93} -8.17301e16 q^{94} +7.60342e16 q^{95} +6.92544e16 q^{96} +1.29543e16 q^{97} +1.32455e17 q^{98} -1.75983e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9}+O(q^{10}) $ 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9} + 246619918 q^{10} + 896501218 q^{11} + 2579890176 q^{12} + 5139901152 q^{13} - 1065727269 q^{14} + 52608606500 q^{15} + 170254553019 q^{16} + 31152575372 q^{17} + 371065029637 q^{18} + 222944612638 q^{19} + 632345964652 q^{20} + 518768862104 q^{21} - 1188197076091 q^{22} - 314739342184 q^{23} - 1830638682468 q^{24} + 8265149117122 q^{25} - 1422210694649 q^{26} + 1055641354104 q^{27} + 4733828767179 q^{28} + 7952343701542 q^{29} + 33815332595226 q^{30} + 22703202725740 q^{31} + 51508227606921 q^{32} + 39808250652964 q^{33} + 42559210973877 q^{34} + 53084789167044 q^{35} + 286899333699545 q^{36} + 70719636063816 q^{37} + 70760432282360 q^{38} + 89621954178128 q^{39} + 176727288274300 q^{40} + 77283001373080 q^{41} - 142968851337140 q^{42} + 218112956325030 q^{43} - 146577440549739 q^{44} + 156445227241670 q^{45} - 436430382603480 q^{46} - 206155334901712 q^{47} - 694457384549320 q^{48} + 17\!\cdots\!92 q^{49}+ \cdots - 33\!\cdots\!26 q^{99}+O(q^{100}) \) 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9 + 246619918 * q^10 + 896501218 * q^11 + 2579890176 * q^12 + 5139901152 * q^13 - 1065727269 * q^14 + 52608606500 * q^15 + 170254553019 * q^16 + 31152575372 * q^17 + 371065029637 * q^18 + 222944612638 * q^19 + 632345964652 * q^20 + 518768862104 * q^21 - 1188197076091 * q^22 - 314739342184 * q^23 - 1830638682468 * q^24 + 8265149117122 * q^25 - 1422210694649 * q^26 + 1055641354104 * q^27 + 4733828767179 * q^28 + 7952343701542 * q^29 + 33815332595226 * q^30 + 22703202725740 * q^31 + 51508227606921 * q^32 + 39808250652964 * q^33 + 42559210973877 * q^34 + 53084789167044 * q^35 + 286899333699545 * q^36 + 70719636063816 * q^37 + 70760432282360 * q^38 + 89621954178128 * q^39 + 176727288274300 * q^40 + 77283001373080 * q^41 - 142968851337140 * q^42 + 218112956325030 * q^43 - 146577440549739 * q^44 + 156445227241670 * q^45 - 436430382603480 * q^46 - 206155334901712 * q^47 - 694457384549320 * q^48 + 1711133899986192 * q^49 - 636149584416999 * q^50 + 158951699286348 * q^51 - 3158033385800149 * q^52 - 404876214856866 * q^53 - 1832749628980958 * q^54 - 611379564042440 * q^55 - 2900007168369351 * q^56 - 1013357232316788 * q^57 - 455786716037158 * q^58 + 6460539254590124 * q^59 + 4624863641607938 * q^60 + 4875940646057436 * q^61 - 15281797209467076 * q^62 - 16054536748044808 * q^63 + 5329292222614591 * q^64 - 7625310499015476 * q^65 - 10349172696837322 * q^66 - 4206243743451792 * q^67 - 552954195428233 * q^68 + 8020251305435444 * q^69 + 3876379104148138 * q^70 + 19535505651668622 * q^71 + 71495174696263183 * q^72 + 33833193336852456 * q^73 + 40772046703252163 * q^74 + 75968477185276688 * q^75 + 38838328992025026 * q^76 + 53055532951436968 * q^77 + 73057936571746858 * q^78 + 61045424159854942 * q^79 + 80004004628116616 * q^80 + 155795318109062036 * q^81 + 52248236930642133 * q^82 + 1235564168216730 * q^83 + 164143534194509272 * q^84 + 113286530641911588 * q^85 + 50368241096487595 * q^86 + 18062036297697056 * q^87 - 116796176360505729 * q^88 + 5837731242014800 * q^89 + 269698982682069798 * q^90 - 57230636051197354 * q^91 + 85549613709158172 * q^92 - 42635139630610976 * q^93 + 217633917061493766 * q^94 - 190986541078108154 * q^95 + 173923507159625020 * q^96 + 233342043840904176 * q^97 + 216259456237342020 * q^98 - 333859997478074426 * 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 $

$2$	−648.649	−1.79166	−0.895828	−	0.444401i	$-0.853416\pi$
$2$	−648.649	−1.79166	−0.895828	+	0.444401i	$0.853416\pi$
$3$	−13388.7	−1.17817	−0.589084	−	0.808072i	$-0.700511\pi$
$3$	−13388.7	−1.17817	−0.589084	+	0.808072i	$0.700511\pi$
$4$	289673.	2.21003
$5$	688083.	0.787763	0.393882	−	0.919161i	$-0.371132\pi$
$5$	688083.	0.787763	0.393882	+	0.919161i	$0.371132\pi$
$6$	8.68455e6	2.11087
$7$	−5.33195e6	−0.349585	−0.174792	−	0.984605i	$-0.555925\pi$
$7$	−5.33195e6	−0.349585	−0.174792	+	0.984605i	$0.555925\pi$
$8$	−1.02876e8	−2.16796
$9$	5.01164e7	0.388078
$10$	−4.46324e8	−1.41140
$11$	−3.51148e8	−0.493915	−0.246958	−	0.969026i	$-0.579431\pi$
$11$	−3.51148e8	−0.493915	−0.246958	+	0.969026i	$0.579431\pi$
$12$	−3.87834e9	−2.60379
$13$	−3.65152e9	−1.24152	−0.620762	−	0.783999i	$-0.713177\pi$
$13$	−3.65152e9	−1.24152	−0.620762	+	0.783999i	$0.713177\pi$
$14$	3.45856e9	0.626336
$15$	−9.21252e9	−0.928117
$16$	2.87626e10	1.67420
$17$	−4.79864e10	−1.66841	−0.834204	−	0.551456i	$-0.814072\pi$
$17$	−4.79864e10	−1.66841	−0.834204	+	0.551456i	$0.814072\pi$
$18$	−3.25079e10	−0.695302
$19$	1.10502e11	1.49267	0.746333	−	0.665572i	$-0.231812\pi$
$19$	1.10502e11	1.49267	0.746333	+	0.665572i	$0.231812\pi$
$20$	1.99319e11	1.74098
$21$	7.13877e10	0.411869
$22$	2.27772e11	0.884926
$23$	−5.96605e11	−1.58855	−0.794274	−	0.607560i	$-0.792148\pi$
$23$	−5.96605e11	−1.58855	−0.794274	+	0.607560i	$0.792148\pi$
$24$	1.37738e12	2.55422
$25$	−2.89482e11	−0.379429
$26$	2.36855e12	2.22438
$27$	1.05802e12	0.720947
$28$	−1.54452e12	−0.772593
$29$	1.57478e12	0.584569	0.292285	−	0.956331i	$-0.405585\pi$
$29$	1.57478e12	0.584569	0.292285	+	0.956331i	$0.405585\pi$
$30$	5.97569e12	1.66287
$31$	2.50979e12	0.528522	0.264261	−	0.964451i	$-0.414872\pi$
$31$	2.50979e12	0.528522	0.264261	+	0.964451i	$0.414872\pi$
$32$	−5.17261e12	−0.831639
$33$	4.70141e12	0.581915
$34$	3.11263e13	2.98921
$35$	−3.66882e12	−0.275390
$36$	1.45174e13	0.857664
$37$	−2.15437e13	−1.00834	−0.504169	−	0.863605i	$-0.668201\pi$
$37$	−2.15437e13	−1.00834	−0.504169	+	0.863605i	$0.668201\pi$
$38$	−7.16767e13	−2.67435
$39$	4.88890e13	1.46272
$40$	−7.07875e13	−1.70784
$41$	−6.74806e13	−1.31982	−0.659912	−	0.751342i	$-0.729407\pi$
$41$	−6.74806e13	−1.31982	−0.659912	+	0.751342i	$0.729407\pi$
$42$	−4.63055e13	−0.737928
$43$	−1.10639e14	−1.44354	−0.721769	−	0.692134i	$-0.756671\pi$
$43$	−1.10639e14	−1.44354	−0.721769	+	0.692134i	$0.756671\pi$
$44$	−1.01718e14	−1.09157
$45$	3.44842e13	0.305713
$46$	3.86987e14	2.84613
$47$	1.26001e14	0.771864	0.385932	−	0.922527i	$-0.373880\pi$
$47$	1.26001e14	0.771864	0.385932	+	0.922527i	$0.373880\pi$
$48$	−3.85093e14	−1.97249
$49$	−2.04201e14	−0.877790
$50$	1.87772e14	0.679807
$51$	6.42474e14	1.96566
$52$	−1.05775e15	−2.74381
$53$	−3.90578e14	−0.861714	−0.430857	−	0.902420i	$-0.641789\pi$
$53$	−3.90578e14	−0.861714	−0.430857	+	0.902420i	$0.641789\pi$
$54$	−6.86285e14	−1.29169
$55$	−2.41619e14	−0.389088
$56$	5.48532e14	0.757885
$57$	−1.47947e15	−1.75861
$58$	−1.02148e15	−1.04735
$59$	1.46830e14	0.130189
$59$	1.46830e14	0.130189
$60$	−2.66862e15	−2.05117
$61$	1.71259e15	1.14380	0.571901	−	0.820323i	$-0.306206\pi$
$61$	1.71259e15	1.14380	0.571901	+	0.820323i	$0.306206\pi$
$62$	−1.62797e15	−0.946929
$63$	−2.67218e14	−0.135666
$64$	−4.14765e14	−0.184193
$65$	−2.51255e15	−0.978027
$66$	−3.04956e15	−1.04259
$67$	−1.67688e15	−0.504505	−0.252252	−	0.967661i	$-0.581171\pi$
$67$	−1.67688e15	−0.504505	−0.252252	+	0.967661i	$0.581171\pi$
$68$	−1.39004e16	−3.68723
$69$	7.98775e15	1.87157
$70$	2.37978e15	0.493404
$71$	−2.09742e15	−0.385469	−0.192735	−	0.981251i	$-0.561736\pi$
$71$	−2.09742e15	−0.385469	−0.192735	+	0.981251i	$0.561736\pi$
$72$	−5.15580e15	−0.841336
$73$	4.47847e15	0.649959	0.324979	−	0.945721i	$-0.394643\pi$
$73$	4.47847e15	0.649959	0.324979	+	0.945721i	$0.394643\pi$
$74$	1.39743e16	1.80660
$75$	3.87577e15	0.447031
$76$	3.20093e16	3.29884
$77$	1.87230e15	0.172665
$78$	−3.17118e16	−2.62069
$79$	−1.31590e16	−0.975869	−0.487935	−	0.872880i	$-0.662250\pi$
$79$	−1.31590e16	−0.975869	−0.487935	+	0.872880i	$0.662250\pi$
$80$	1.97911e16	1.31888
$81$	−2.06376e16	−1.23747
$82$	4.37712e16	2.36467
$83$	−2.29114e16	−1.11658	−0.558288	−	0.829647i	$-0.688541\pi$
$83$	−2.29114e16	−1.11658	−0.558288	+	0.829647i	$0.688541\pi$
$84$	2.06791e16	0.910244
$85$	−3.30186e16	−1.31431
$86$	7.17661e16	2.58632
$87$	−2.10842e16	−0.688720
$88$	3.61248e16	1.07079
$89$	−2.71787e16	−0.731837	−0.365918	−	0.930647i	$-0.619245\pi$
$89$	−2.71787e16	−0.731837	−0.365918	+	0.930647i	$0.619245\pi$
$90$	−2.23682e16	−0.547733
$91$	1.94697e16	0.434018
$92$	−1.72820e17	−3.51074
$93$	−3.36027e16	−0.622687
$94$	−8.17301e16	−1.38291
$95$	7.60342e16	1.17587
$96$	6.92544e16	0.979810
$97$	1.29543e16	0.167824	0.0839119	−	0.996473i	$-0.473259\pi$
$97$	1.29543e16	0.167824	0.0839119	+	0.996473i	$0.473259\pi$
$98$	1.32455e17	1.57270
$99$	−1.75983e16	−0.191678
$100$	−8.38550e16	−0.838550
$101$	−7.63142e16	−0.701251	−0.350625	−	0.936516i	$-0.614031\pi$
$101$	−7.63142e16	−0.701251	−0.350625	+	0.936516i	$0.614031\pi$
$102$	−4.16740e17	−3.52179
$103$	−1.81385e17	−1.41087	−0.705433	−	0.708777i	$-0.749247\pi$
$103$	−1.81385e17	−1.41087	−0.705433	+	0.708777i	$0.749247\pi$
$104$	3.75655e17	2.69157
$105$	4.91206e16	0.324455
$106$	2.53348e17	1.54389
$107$	−2.70895e16	−0.152419	−0.0762095	−	0.997092i	$-0.524282\pi$
$107$	−2.70895e16	−0.152419	−0.0762095	+	0.997092i	$0.524282\pi$
$108$	3.06481e17	1.59331
$109$	−2.97842e16	−0.143173	−0.0715864	−	0.997434i	$-0.522806\pi$
$109$	−2.97842e16	−0.143173	−0.0715864	+	0.997434i	$0.522806\pi$
$110$	1.56726e17	0.697112
$111$	2.88442e17	1.18799
$112$	−1.53361e17	−0.585276
$113$	4.39253e17	1.55435	0.777173	−	0.629287i	$-0.216653\pi$
$113$	4.39253e17	1.55435	0.777173	+	0.629287i	$0.216653\pi$
$114$	9.59656e17	3.15083
$115$	−4.10514e17	−1.25140
$116$	4.56170e17	1.29192
$117$	−1.83001e17	−0.481808
$118$	−9.52414e16	−0.233254
$119$	2.55861e17	0.583250
$120$	9.47750e17	2.01212
$121$	−3.82142e17	−0.756048
$122$	−1.11087e18	−2.04930
$123$	9.03476e17	1.55497
$124$	7.27018e17	1.16805
$125$	−7.24153e17	−1.08666
$126$	1.73331e17	0.243067
$127$	5.59452e17	0.733553	0.366776	−	0.930309i	$-0.380461\pi$
$127$	5.59452e17	0.733553	0.366776	+	0.930309i	$0.380461\pi$
$128$	9.47021e17	1.16165
$129$	1.48132e18	1.70073
$130$	1.62976e18	1.75229
$131$	5.05707e17	0.509440	0.254720	−	0.967015i	$-0.418017\pi$
$131$	5.05707e17	0.509440	0.254720	+	0.967015i	$0.418017\pi$
$132$	1.36187e18	1.28605
$133$	−5.89189e17	−0.521814
$134$	1.08770e18	0.903899
$135$	7.28007e17	0.567935
$136$	4.93667e18	3.61704
$137$	6.16277e16	0.0424278	0.0212139	−	0.999775i	$-0.493247\pi$
$137$	6.16277e16	0.0424278	0.0212139	+	0.999775i	$0.493247\pi$
$138$	−5.18124e18	−3.35322
$139$	−1.56336e18	−0.951553	−0.475777	−	0.879566i	$-0.657833\pi$
$139$	−1.56336e18	−0.951553	−0.475777	+	0.879566i	$0.657833\pi$
$140$	−1.06276e18	−0.608620
$141$	−1.68698e18	−0.909385
$142$	1.36049e18	0.690629
$143$	1.28222e18	0.613208
$144$	1.44148e18	0.649721
$145$	1.08358e18	0.460502
$146$	−2.90496e18	−1.16450
$147$	2.73398e18	1.03418
$148$	−6.24064e18	−2.22846
$149$	−4.44407e18	−1.49864	−0.749321	−	0.662207i	$-0.769620\pi$
$149$	−4.44407e18	−1.49864	−0.749321	+	0.662207i	$0.769620\pi$
$150$	−2.51402e18	−0.800926
$151$	−2.78992e18	−0.840018	−0.420009	−	0.907520i	$-0.637973\pi$
$151$	−2.78992e18	−0.840018	−0.420009	+	0.907520i	$0.637973\pi$
$152$	−1.13680e19	−3.23604
$153$	−2.40491e18	−0.647472
$154$	−1.21447e18	−0.309357
$155$	1.72694e18	0.416350
$156$	1.41618e19	3.23266
$157$	−3.21872e18	−0.695882	−0.347941	−	0.937516i	$-0.613119\pi$
$157$	−3.21872e18	−0.695882	−0.347941	+	0.937516i	$0.613119\pi$
$158$	8.53555e18	1.74842
$159$	5.22932e18	1.01524
$160$	−3.55918e18	−0.655135
$161$	3.18107e18	0.555332
$162$	1.33865e19	2.21713
$163$	−5.33129e18	−0.837987	−0.418994	−	0.907989i	$-0.637617\pi$
$163$	−5.33129e18	−0.837987	−0.418994	+	0.907989i	$0.637617\pi$
$164$	−1.95473e19	−2.91685
$165$	3.23496e18	0.458411
$166$	1.48615e19	2.00052
$167$	−6.85090e18	−0.876309	−0.438155	−	0.898900i	$-0.644368\pi$
$167$	−6.85090e18	−0.876309	−0.438155	+	0.898900i	$0.644368\pi$
$168$	−7.34411e18	−0.892915
$169$	4.68317e18	0.541381
$170$	2.14175e19	2.35479
$171$	5.53794e18	0.579271
$172$	−3.20493e19	−3.19026
$173$	−1.50943e19	−1.43028	−0.715141	−	0.698980i	$-0.753638\pi$
$173$	−1.50943e19	−1.43028	−0.715141	+	0.698980i	$0.753638\pi$
$174$	1.36762e19	1.23395
$175$	1.54350e18	0.132643
$176$	−1.00999e19	−0.826915
$177$	−1.96586e18	−0.153384
$178$	1.76295e19	1.31120
$179$	−2.20733e19	−1.56537	−0.782684	−	0.622419i	$-0.786150\pi$
$179$	−2.20733e19	−1.56537	−0.782684	+	0.622419i	$0.786150\pi$
$180$	9.98916e18	0.675636
$181$	2.59103e19	1.67188	0.835938	−	0.548824i	$-0.184924\pi$
$181$	2.59103e19	1.67188	0.835938	+	0.548824i	$0.184924\pi$
$182$	−1.26290e19	−0.777610
$183$	−2.29294e19	−1.34759
$184$	6.13766e19	3.44390
$185$	−1.48239e19	−0.794332
$186$	2.17964e19	1.11564
$187$	1.68503e19	0.824052
$188$	3.64990e19	1.70584
$189$	−5.64132e18	−0.252032
$190$	−4.93195e19	−2.10675
$191$	−1.85724e19	−0.758723	−0.379362	−	0.925248i	$-0.623856\pi$
$191$	−1.85724e19	−0.758723	−0.379362	+	0.925248i	$0.623856\pi$
$192$	5.55315e18	0.217010
$193$	4.17806e19	1.56220	0.781102	−	0.624404i	$-0.214658\pi$
$193$	4.17806e19	1.56220	0.781102	+	0.624404i	$0.214658\pi$
$194$	−8.40278e18	−0.300682
$195$	3.36397e19	1.15228
$196$	−5.91515e19	−1.93994
$197$	−2.48476e19	−0.780407	−0.390204	−	0.920729i	$-0.627595\pi$
$197$	−2.48476e19	−0.780407	−0.390204	+	0.920729i	$0.627595\pi$
$198$	1.14151e19	0.343420
$199$	2.77834e19	0.800818	0.400409	−	0.916337i	$-0.368868\pi$
$199$	2.77834e19	0.800818	0.400409	+	0.916337i	$0.368868\pi$
$200$	2.97808e19	0.822587
$201$	2.24512e19	0.594391
$202$	4.95011e19	1.25640
$203$	−8.39663e18	−0.204356
$204$	1.86107e20	4.34417
$205$	−4.64323e19	−1.03971
$206$	1.17655e20	2.52779
$207$	−2.98997e19	−0.616480
$208$	−1.05027e20	−2.07856
$209$	−3.88024e19	−0.737251
$210$	−3.18620e19	−0.581312
$211$	−2.40191e19	−0.420878	−0.210439	−	0.977607i	$-0.567489\pi$
$211$	−2.40191e19	−0.420878	−0.210439	+	0.977607i	$0.567489\pi$
$212$	−1.13140e20	−1.90441
$213$	2.80817e19	0.454147
$214$	1.75716e19	0.273082
$215$	−7.61291e19	−1.13717
$216$	−1.08846e20	−1.56298
$217$	−1.33821e19	−0.184763
$218$	1.93195e19	0.256516
$219$	−5.99608e19	−0.765760
$220$	−6.99905e19	−0.859897
$221$	1.75223e20	2.07137
$222$	−1.87098e20	−2.12847
$223$	4.65718e18	0.0509955	0.0254977	−	0.999675i	$-0.491883\pi$
$223$	4.65718e18	0.0509955	0.0254977	+	0.999675i	$0.491883\pi$
$224$	2.75801e19	0.290728
$225$	−1.45078e19	−0.147248
$226$	−2.84921e20	−2.78485
$227$	5.05057e19	0.475467	0.237734	−	0.971330i	$-0.423595\pi$
$227$	5.05057e19	0.475467	0.237734	+	0.971330i	$0.423595\pi$
$228$	−4.28563e20	−3.88658
$229$	7.77037e19	0.678954	0.339477	−	0.940614i	$-0.389750\pi$
$229$	7.77037e19	0.678954	0.339477	+	0.940614i	$0.389750\pi$
$230$	2.66279e20	2.24208
$231$	−2.50677e19	−0.203429
$232$	−1.62007e20	−1.26732
$233$	−2.05726e20	−1.55154	−0.775771	−	0.631015i	$-0.782639\pi$
$233$	−2.05726e20	−1.55154	−0.775771	+	0.631015i	$0.782639\pi$
$234$	1.18703e20	0.863233
$235$	8.66988e19	0.608046
$236$	4.25328e19	0.287721
$237$	1.76181e20	1.14974
$238$	−1.65964e20	−1.04498
$239$	1.81709e18	0.0110406	0.00552031	−	0.999985i	$-0.498243\pi$
$239$	1.81709e18	0.0110406	0.00552031	+	0.999985i	$0.498243\pi$
$240$	−2.64976e20	−1.55386
$241$	2.85314e20	1.61502	0.807511	−	0.589852i	$-0.200814\pi$
$241$	2.85314e20	1.61502	0.807511	+	0.589852i	$0.200814\pi$
$242$	2.47876e20	1.35458
$243$	1.39676e20	0.737004
$244$	4.96092e20	2.52784
$245$	−1.40507e20	−0.691491
$246$	−5.86039e20	−2.78598
$247$	−4.03499e20	−1.85318
$248$	−2.58198e20	−1.14581
$249$	3.06753e20	1.31551
$250$	4.69721e20	1.94693
$251$	−1.20607e20	−0.483223	−0.241611	−	0.970373i	$-0.577676\pi$
$251$	−1.20607e20	−0.483223	−0.241611	+	0.970373i	$0.577676\pi$
$252$	−7.74059e19	−0.299826
$253$	2.09497e20	0.784608
$254$	−3.62888e20	−1.31427
$255$	4.42075e20	1.54848
$256$	−5.59920e20	−1.89708
$257$	4.62297e20	1.51527	0.757634	−	0.652680i	$-0.226355\pi$
$257$	4.62297e20	1.51527	0.757634	+	0.652680i	$0.226355\pi$
$258$	−9.60853e20	−3.04712
$259$	1.14870e20	0.352500
$260$	−7.27817e20	−2.16147
$261$	7.89222e19	0.226858
$262$	−3.28026e20	−0.912742
$263$	−1.99537e20	−0.537526	−0.268763	−	0.963206i	$-0.586615\pi$
$263$	−1.99537e20	−0.537526	−0.268763	+	0.963206i	$0.586615\pi$
$264$	−4.83664e20	−1.26157
$265$	−2.68750e20	−0.678826
$266$	3.82176e20	0.934910
$267$	3.63887e20	0.862226
$268$	−4.85746e20	−1.11497
$269$	−8.25431e19	−0.183563	−0.0917817	−	0.995779i	$-0.529256\pi$
$269$	−8.25431e19	−0.183563	−0.0917817	+	0.995779i	$0.529256\pi$
$270$	−4.72221e20	−1.01754
$271$	4.36494e20	0.911464	0.455732	−	0.890117i	$-0.349378\pi$
$271$	4.36494e20	0.911464	0.455732	+	0.890117i	$0.349378\pi$
$272$	−1.38021e21	−2.79325
$273$	−2.60674e20	−0.511345
$274$	−3.99747e19	−0.0760161
$275$	1.01651e20	0.187406
$276$	2.31384e21	4.13624
$277$	7.78555e20	1.34962	0.674810	−	0.737992i	$-0.264226\pi$
$277$	7.78555e20	1.34962	0.674810	+	0.737992i	$0.264226\pi$
$278$	1.01407e21	1.70486
$279$	1.25782e20	0.205107
$280$	3.77435e20	0.597034
$281$	−3.84753e20	−0.590444	−0.295222	−	0.955429i	$-0.595394\pi$
$281$	−3.84753e20	−0.590444	−0.295222	+	0.955429i	$0.595394\pi$
$282$	1.09426e21	1.62930
$283$	8.48775e20	1.22633	0.613166	−	0.789954i	$-0.289896\pi$
$283$	8.48775e20	1.22633	0.613166	+	0.789954i	$0.289896\pi$
$284$	−6.07567e20	−0.851899
$285$	−1.01800e21	−1.38537
$286$	−8.31713e20	−1.09866
$287$	3.59803e20	0.461391
$288$	−2.59233e20	−0.322741
$289$	1.47545e21	1.78358
$290$	−7.02860e20	−0.825061
$291$	−1.73441e20	−0.197724
$292$	1.29729e21	1.43643
$293$	−4.42243e20	−0.475649	−0.237824	−	0.971308i	$-0.576434\pi$
$293$	−4.42243e20	−0.475649	−0.237824	+	0.971308i	$0.576434\pi$
$294$	−1.77339e21	−1.85290
$295$	1.01031e20	0.102558
$296$	2.21634e21	2.18604
$297$	−3.71523e20	−0.356087
$298$	2.88264e21	2.68505
$299$	2.17851e21	1.97222
$300$	1.12271e21	0.987952
$301$	5.89924e20	0.504639
$302$	1.80968e21	1.50502
$303$	1.02175e21	0.826191
$304$	3.17831e21	2.49903
$305$	1.17841e21	0.901045
$306$	1.55994e21	1.16005
$307$	6.13473e19	0.0443730	0.0221865	−	0.999754i	$-0.492937\pi$
$307$	6.13473e19	0.0443730	0.0221865	+	0.999754i	$0.492937\pi$
$308$	5.42356e20	0.381595
$309$	2.42851e21	1.66224
$310$	−1.12018e21	−0.745956
$311$	2.37389e21	1.53814	0.769071	−	0.639163i	$-0.220719\pi$
$311$	2.37389e21	1.53814	0.769071	+	0.639163i	$0.220719\pi$
$312$	−5.02952e21	−3.17112
$313$	−1.67397e20	−0.102712	−0.0513559	−	0.998680i	$-0.516354\pi$
$313$	−1.67397e20	−0.102712	−0.0513559	+	0.998680i	$0.516354\pi$
$314$	2.08782e21	1.24678
$315$	−1.83868e20	−0.106873
$316$	−3.81180e21	−2.15670
$317$	−4.17566e20	−0.229997	−0.114998	−	0.993366i	$-0.536686\pi$
$317$	−4.17566e20	−0.229997	−0.114998	+	0.993366i	$0.536686\pi$
$318$	−3.39199e21	−1.81897
$319$	−5.52980e20	−0.288728
$320$	−2.85393e20	−0.145100
$321$	3.62693e20	0.179575
$322$	−2.06339e21	−0.994964
$323$	−5.30257e21	−2.49038
$324$	−5.97815e21	−2.73485
$325$	1.05705e21	0.471070
$326$	3.45813e21	1.50138
$327$	3.98771e20	0.168681
$328$	6.94216e21	2.86132
$329$	−6.71829e20	−0.269832
$330$	−2.09835e21	−0.821315
$331$	−4.20786e21	−1.60518	−0.802590	−	0.596531i	$-0.796545\pi$
$331$	−4.20786e21	−1.60518	−0.802590	+	0.596531i	$0.796545\pi$
$332$	−6.63682e21	−2.46767
$333$	−1.07970e21	−0.391314
$334$	4.44383e21	1.57004
$335$	−1.15383e21	−0.397430
$336$	2.05330e21	0.689553
$337$	4.39754e21	1.43998	0.719988	−	0.693986i	$-0.244147\pi$
$337$	4.39754e21	1.43998	0.719988	+	0.693986i	$0.244147\pi$
$338$	−3.03773e21	−0.969968
$339$	−5.88101e21	−1.83128
$340$	−9.56460e21	−2.90466
$341$	−8.81307e20	−0.261045
$342$	−3.59218e21	−1.03785
$343$	2.32916e21	0.656447
$344$	1.13822e22	3.12953
$345$	5.49623e21	1.47436
$346$	9.79091e21	2.56257
$347$	−2.97784e21	−0.760502	−0.380251	−	0.924883i	$-0.624162\pi$
$347$	−2.97784e21	−0.760502	−0.380251	+	0.924883i	$0.624162\pi$
$348$	−6.10752e21	−1.52209
$349$	1.70180e21	0.413897	0.206949	−	0.978352i	$-0.433647\pi$
$349$	1.70180e21	0.413897	0.206949	+	0.978352i	$0.433647\pi$
$350$	−1.00119e21	−0.237650
$351$	−3.86339e21	−0.895072
$352$	1.81635e21	0.410759
$353$	2.18366e21	0.482059	0.241029	−	0.970518i	$-0.422515\pi$
$353$	2.18366e21	0.482059	0.241029	+	0.970518i	$0.422515\pi$
$354$	1.27516e21	0.274812
$355$	−1.44320e21	−0.303659
$356$	−7.87295e21	−1.61738
$357$	−3.42564e21	−0.687166
$358$	1.43178e22	2.80460
$359$	−3.42309e21	−0.654809	−0.327405	−	0.944884i	$-0.606174\pi$
$359$	−3.42309e21	−0.654809	−0.327405	+	0.944884i	$0.606174\pi$
$360$	−3.54761e21	−0.662774
$361$	6.73021e21	1.22805
$362$	−1.68067e22	−2.99543
$363$	5.11638e21	0.890751
$364$	5.63985e21	0.959192
$365$	3.08156e21	0.512013
$366$	1.48731e22	2.41442
$367$	8.04611e21	1.27622	0.638108	−	0.769946i	$-0.279717\pi$
$367$	8.04611e21	1.27622	0.638108	+	0.769946i	$0.279717\pi$
$368$	−1.71599e22	−2.65955
$369$	−3.38189e21	−0.512195
$370$	9.61549e21	1.42317
$371$	2.08254e21	0.301242
$372$	−9.73381e21	−1.37616
$373$	7.57610e21	1.04694	0.523469	−	0.852045i	$-0.324638\pi$
$373$	7.57610e21	1.04694	0.523469	+	0.852045i	$0.324638\pi$
$374$	−1.09299e22	−1.47642
$375$	9.69544e21	1.28027
$376$	−1.29625e22	−1.67337
$377$	−5.75033e21	−0.725757
$378$	3.65924e21	0.451555
$379$	−1.38745e22	−1.67412	−0.837058	−	0.547114i	$-0.815726\pi$
$379$	−1.38745e22	−1.67412	−0.837058	+	0.547114i	$0.815726\pi$
$380$	2.20251e22	2.59870
$381$	−7.49032e21	−0.864248
$382$	1.20469e22	1.35937
$383$	1.31276e22	1.44875	0.724376	−	0.689405i	$-0.242128\pi$
$383$	1.31276e22	1.44875	0.724376	+	0.689405i	$0.242128\pi$
$384$	−1.26794e22	−1.36862
$385$	1.28830e21	0.136019
$386$	−2.71009e22	−2.79893
$387$	−5.54485e21	−0.560205
$388$	3.75251e21	0.370896
$389$	−2.21783e21	−0.214465	−0.107232	−	0.994234i	$-0.534199\pi$
$389$	−2.21783e21	−0.214465	−0.107232	+	0.994234i	$0.534199\pi$
$390$	−2.18203e22	−2.06449
$391$	2.86289e22	2.65034
$392$	2.10074e22	1.90301
$393$	−6.77075e21	−0.600206
$394$	1.61174e22	1.39822
$395$	−9.05446e21	−0.768754
$396$	−5.09775e21	−0.423613
$397$	1.75232e22	1.42526	0.712632	−	0.701538i	$-0.247503\pi$
$397$	1.75232e22	1.42526	0.712632	+	0.701538i	$0.247503\pi$
$398$	−1.80216e22	−1.43479
$399$	7.88845e21	0.614784
$400$	−8.32624e21	−0.635242
$401$	3.44098e21	0.257013	0.128506	−	0.991709i	$-0.458982\pi$
$401$	3.44098e21	0.257013	0.128506	+	0.991709i	$0.458982\pi$
$402$	−1.45629e22	−1.06494
$403$	−9.16454e21	−0.656172
$404$	−2.21062e22	−1.54979
$405$	−1.42004e22	−0.974836
$406$	5.44646e21	0.366136
$407$	7.56504e21	0.498034
$408$	−6.60954e22	−4.26147
$409$	−1.43413e22	−0.905607	−0.452804	−	0.891610i	$-0.649576\pi$
$409$	−1.43413e22	−0.905607	−0.452804	+	0.891610i	$0.649576\pi$
$410$	3.01182e22	1.86280
$411$	−8.25113e20	−0.0499871
$412$	−5.25425e22	−3.11806
$413$	−7.82892e20	−0.0455121
$414$	1.93944e22	1.10452
$415$	−1.57649e22	−0.879597
$416$	1.88879e22	1.03250
$417$	2.09313e22	1.12109
$418$	2.51691e22	1.32090
$419$	2.68927e21	0.138298	0.0691490	−	0.997606i	$-0.477972\pi$
$419$	2.68927e21	0.138298	0.0691490	+	0.997606i	$0.477972\pi$
$420$	1.42289e22	0.717056
$421$	−1.81754e22	−0.897608	−0.448804	−	0.893630i	$-0.648150\pi$
$421$	−1.81754e22	−0.897608	−0.448804	+	0.893630i	$0.648150\pi$
$422$	1.55800e22	0.754069
$423$	6.31470e21	0.299543
$424$	4.01813e22	1.86816
$425$	1.38912e22	0.633043
$426$	−1.82152e22	−0.813676
$427$	−9.13146e21	−0.399856
$428$	−7.84711e21	−0.336851
$429$	−1.71673e22	−0.722461
$430$	4.93810e22	2.03741
$431$	7.10690e21	0.287490	0.143745	−	0.989615i	$-0.454085\pi$
$431$	7.10690e21	0.287490	0.143745	+	0.989615i	$0.454085\pi$
$432$	3.04315e22	1.20701
$433$	4.65251e22	1.80943	0.904713	−	0.426022i	$-0.140086\pi$
$433$	4.65251e22	1.80943	0.904713	+	0.426022i	$0.140086\pi$
$434$	8.68026e21	0.331032
$435$	−1.45077e22	−0.542548
$436$	−8.62768e21	−0.316416
$437$	−6.59258e22	−2.37117
$438$	3.88935e22	1.37198
$439$	−5.56307e22	−1.92472	−0.962358	−	0.271786i	$-0.912386\pi$
$439$	−5.56307e22	−1.92472	−0.962358	+	0.271786i	$0.912386\pi$
$440$	2.48569e22	0.843527
$441$	−1.02338e22	−0.340651
$442$	−1.13658e23	−3.71118
$443$	−3.80531e22	−1.21887	−0.609436	−	0.792835i	$-0.708604\pi$
$443$	−3.80531e22	−1.21887	−0.609436	+	0.792835i	$0.708604\pi$
$444$	8.35539e22	2.62550
$445$	−1.87012e22	−0.576514
$446$	−3.02087e21	−0.0913663
$447$	5.95003e22	1.76565
$448$	2.21150e21	0.0643909
$449$	−2.17941e22	−0.622653	−0.311326	−	0.950303i	$-0.600773\pi$
$449$	−2.17941e22	−0.622653	−0.311326	+	0.950303i	$0.600773\pi$
$450$	9.41045e21	0.263818
$451$	2.36957e22	0.651882
$452$	1.27240e23	3.43515
$453$	3.73534e22	0.989681
$454$	−3.27605e22	−0.851874
$455$	1.33968e22	0.341903
$456$	1.52203e23	3.81259
$457$	−4.66391e22	−1.14673	−0.573366	−	0.819299i	$-0.694363\pi$
$457$	−4.66391e22	−1.14673	−0.573366	+	0.819299i	$0.694363\pi$
$458$	−5.04024e22	−1.21645
$459$	−5.07707e22	−1.20283
$460$	−1.18915e23	−2.76563
$461$	3.37489e22	0.770552	0.385276	−	0.922801i	$-0.374106\pi$
$461$	3.37489e22	0.770552	0.385276	+	0.922801i	$0.374106\pi$
$462$	1.62601e22	0.364474
$463$	−6.26535e22	−1.37882	−0.689409	−	0.724372i	$-0.742130\pi$
$463$	−6.26535e22	−1.37882	−0.689409	+	0.724372i	$0.742130\pi$
$464$	4.52947e22	0.978688
$465$	−2.31215e22	−0.490530
$466$	1.33444e23	2.77983
$467$	−1.63734e22	−0.334924	−0.167462	−	0.985879i	$-0.553557\pi$
$467$	−1.63734e22	−0.334924	−0.167462	+	0.985879i	$0.553557\pi$
$468$	−5.30105e22	−1.06481
$469$	8.94102e21	0.176367
$470$	−5.62371e22	−1.08941
$471$	4.30943e22	0.819865
$472$	−1.51054e22	−0.282244
$473$	3.88508e22	0.712985
$474$	−1.14280e23	−2.05993
$475$	−3.19882e22	−0.566362
$476$	7.41160e22	1.28900
$477$	−1.95744e22	−0.334412
$478$	−1.17865e21	−0.0197810
$479$	−6.39690e22	−1.05467	−0.527336	−	0.849657i	$-0.676809\pi$
$479$	−6.39690e22	−1.05467	−0.527336	+	0.849657i	$0.676809\pi$
$480$	4.76528e22	0.771858
$481$	7.86674e22	1.25188
$482$	−1.85069e23	−2.89356
$483$	−4.25902e22	−0.654274
$484$	−1.10696e23	−1.67089
$485$	8.91362e21	0.132205
$486$	−9.06009e22	−1.32046
$487$	−5.64012e22	−0.807778	−0.403889	−	0.914808i	$-0.632342\pi$
$487$	−5.64012e22	−0.807778	−0.403889	+	0.914808i	$0.632342\pi$
$488$	−1.76186e23	−2.47971
$489$	7.13789e22	0.987289
$490$	9.11397e22	1.23891
$491$	3.43090e22	0.458369	0.229184	−	0.973383i	$-0.426394\pi$
$491$	3.43090e22	0.458369	0.229184	+	0.973383i	$0.426394\pi$
$492$	2.61713e23	3.43654
$493$	−7.55678e22	−0.975300
$494$	2.61729e23	3.32026
$495$	−1.21091e22	−0.150996
$496$	7.21881e22	0.884853
$497$	1.11833e22	0.134754
$498$	−1.98975e23	−2.35694
$499$	1.16491e23	1.35655	0.678277	−	0.734807i	$-0.262727\pi$
$499$	1.16491e23	1.35655	0.678277	+	0.734807i	$0.262727\pi$
$500$	−2.09768e23	−2.40156
$501$	9.17244e22	1.03244
$502$	7.82318e22	0.865769
$503$	−1.87363e22	−0.203871	−0.101936	−	0.994791i	$-0.532504\pi$
$503$	−1.87363e22	−0.203871	−0.101936	+	0.994791i	$0.532504\pi$
$504$	2.74904e22	0.294118
$505$	−5.25105e22	−0.552420
$506$	−1.35890e23	−1.40575
$507$	−6.27015e22	−0.637837
$508$	1.62058e23	1.62117
$509$	−2.63894e22	−0.259614	−0.129807	−	0.991539i	$-0.541436\pi$
$509$	−2.63894e22	−0.259614	−0.129807	+	0.991539i	$0.541436\pi$
$510$	−2.86752e23	−2.77434
$511$	−2.38790e22	−0.227216
$512$	2.39063e23	2.23727
$513$	1.16913e23	1.07613
$514$	−2.99868e23	−2.71484
$515$	−1.24808e23	−1.11143
$516$	4.29097e23	3.75866
$517$	−4.42449e22	−0.381236
$518$	−7.45103e22	−0.631559
$519$	2.02093e23	1.68511
$520$	2.58482e23	2.12032
$521$	1.33754e23	1.07941	0.539705	−	0.841855i	$-0.318536\pi$
$521$	1.33754e23	1.07941	0.539705	+	0.841855i	$0.318536\pi$
$522$	−5.11928e22	−0.406452
$523$	−9.21959e22	−0.720191	−0.360095	−	0.932916i	$-0.617256\pi$
$523$	−9.21959e22	−0.720191	−0.360095	+	0.932916i	$0.617256\pi$
$524$	1.46490e23	1.12588
$525$	−2.06654e22	−0.156275
$526$	1.29429e23	0.963061
$527$	−1.20436e23	−0.881789
$528$	1.35225e23	0.974244
$529$	2.14887e23	1.52348
$530$	1.74324e23	1.21622
$531$	7.35862e21	0.0505234
$532$	−1.70672e23	−1.15322
$533$	2.46407e23	1.63859
$534$	−2.36035e23	−1.54481
$535$	−1.86398e22	−0.120070
$536$	1.72511e23	1.09375
$537$	2.95532e23	1.84427
$538$	5.35414e22	0.328882
$539$	7.17047e22	0.433554
$540$	2.10884e23	1.25515
$541$	4.99783e22	0.292823	0.146411	−	0.989224i	$-0.453228\pi$
$541$	4.99783e22	0.292823	0.146411	+	0.989224i	$0.453228\pi$
$542$	−2.83131e23	−1.63303
$543$	−3.46904e23	−1.96975
$544$	2.48215e23	1.38751
$545$	−2.04940e22	−0.112786
$546$	1.69086e23	0.916155
$547$	1.99798e22	0.106585	0.0532927	−	0.998579i	$-0.483028\pi$
$547$	1.99798e22	0.106585	0.0532927	+	0.998579i	$0.483028\pi$
$548$	1.78519e22	0.0937668
$549$	8.58291e22	0.443884
$550$	−6.59357e22	−0.335767
$551$	1.74015e23	0.872567
$552$	−8.21751e23	−4.05749
$553$	7.01630e22	0.341149
$554$	−5.05009e23	−2.41805
$555$	1.98472e23	0.935856
$556$	−4.52863e23	−2.10296
$557$	3.44865e23	1.57718	0.788588	−	0.614922i	$-0.210812\pi$
$557$	3.44865e23	1.57718	0.788588	+	0.614922i	$0.210812\pi$
$558$	−8.15881e22	−0.367482
$559$	4.04002e23	1.79219
$560$	−1.05525e23	−0.461059
$561$	−2.25603e23	−0.970871
$562$	2.49570e23	1.05787
$563$	9.84517e22	0.411057	0.205528	−	0.978651i	$-0.434109\pi$
$563$	9.84517e22	0.411057	0.205528	+	0.978651i	$0.434109\pi$
$564$	−4.88673e23	−2.00977
$565$	3.02242e23	1.22446
$566$	−5.50557e23	−2.19716
$567$	1.10038e23	0.432602
$568$	2.15775e23	0.835682
$569$	4.46269e22	0.170272	0.0851359	−	0.996369i	$-0.472868\pi$
$569$	4.46269e22	0.170272	0.0851359	+	0.996369i	$0.472868\pi$
$570$	6.60323e23	2.48210
$571$	3.74449e23	1.38671	0.693355	−	0.720596i	$-0.256132\pi$
$571$	3.74449e23	1.38671	0.693355	+	0.720596i	$0.256132\pi$
$572$	3.71426e23	1.35521
$573$	2.48659e23	0.893903
$574$	−2.33386e23	−0.826653
$575$	1.72706e23	0.602741
$576$	−2.07865e22	−0.0714811
$577$	−4.39483e23	−1.48918	−0.744591	−	0.667521i	$-0.767355\pi$
$577$	−4.39483e23	−1.48918	−0.744591	+	0.667521i	$0.767355\pi$
$578$	−9.57050e23	−3.19557
$579$	−5.59387e23	−1.84054
$580$	3.13883e23	1.01772
$581$	1.22162e23	0.390338
$582$	1.12502e23	0.354254
$583$	1.37151e23	0.425614
$584$	−4.60729e23	−1.40908
$585$	−1.25920e23	−0.379550
$586$	2.86860e23	0.852199
$587$	−1.73788e23	−0.508857	−0.254429	−	0.967092i	$-0.581887\pi$
$587$	−1.73788e23	−0.508857	−0.254429	+	0.967092i	$0.581887\pi$
$588$	7.91960e23	2.28558
$589$	2.77336e23	0.788907
$590$	−6.55339e22	−0.183749
$591$	3.32676e23	0.919450
$592$	−6.19654e23	−1.68816
$593$	−6.67680e23	−1.79309	−0.896547	−	0.442948i	$-0.853933\pi$
$593$	−6.67680e23	−1.79309	−0.896547	+	0.442948i	$0.853933\pi$
$594$	2.40988e23	0.637985
$595$	1.76053e23	0.459463
$596$	−1.28733e24	−3.31205
$597$	−3.71982e23	−0.943497
$598$	−1.41309e24	−3.53354
$599$	−3.94229e23	−0.971898	−0.485949	−	0.873987i	$-0.661526\pi$
$599$	−3.94229e23	−0.971898	−0.485949	+	0.873987i	$0.661526\pi$
$600$	−3.98726e23	−0.969145
$601$	6.19823e23	1.48537	0.742685	−	0.669641i	$-0.233552\pi$
$601$	6.19823e23	1.48537	0.742685	+	0.669641i	$0.233552\pi$
$602$	−3.82653e23	−0.904139
$603$	−8.40390e22	−0.195787
$604$	−8.08166e23	−1.85646
$605$	−2.62945e23	−0.595586
$606$	−6.62754e23	−1.48025
$607$	5.27455e23	1.16167	0.580834	−	0.814022i	$-0.302727\pi$
$607$	5.27455e23	1.16167	0.580834	+	0.814022i	$0.302727\pi$
$608$	−5.71582e23	−1.24136
$609$	1.12420e23	0.240766
$610$	−7.64372e23	−1.61436
$611$	−4.60094e23	−0.958288
$612$	−6.96636e23	−1.43093
$613$	−6.96452e23	−1.41084	−0.705419	−	0.708791i	$-0.749241\pi$
$613$	−6.96452e23	−1.41084	−0.705419	+	0.708791i	$0.749241\pi$
$614$	−3.97928e22	−0.0795012
$615$	6.21666e23	1.22495
$616$	−1.92616e23	−0.374331
$617$	1.71278e23	0.328305	0.164153	−	0.986435i	$-0.447511\pi$
$617$	1.71278e23	0.328305	0.164153	+	0.986435i	$0.447511\pi$
$618$	−1.57525e24	−2.97815
$619$	−5.68032e21	−0.0105926	−0.00529630	−	0.999986i	$-0.501686\pi$
$619$	−5.68032e21	−0.0105926	−0.00529630	+	0.999986i	$0.501686\pi$
$620$	5.00249e23	0.920146
$621$	−6.31222e23	−1.14526
$622$	−1.53982e24	−2.75582
$623$	1.44916e23	0.255839
$624$	1.40617e24	2.44890
$625$	−2.77420e23	−0.476604
$626$	1.08582e23	0.184024
$627$	5.19513e23	0.868605
$628$	−9.32375e23	−1.53792
$629$	1.03381e24	1.68232
$630$	1.19266e23	0.191479
$631$	1.20802e24	1.91348	0.956742	−	0.290938i	$-0.0939674\pi$
$631$	1.20802e24	1.91348	0.956742	+	0.290938i	$0.0939674\pi$
$632$	1.35375e24	2.11564
$633$	3.21584e23	0.495865
$634$	2.70854e23	0.412075
$635$	3.84949e23	0.577866
$636$	1.51479e24	2.24372
$637$	7.45643e23	1.08980
$638$	3.58690e23	0.517301
$639$	−1.05115e23	−0.149592
$640$	6.51629e23	0.915104
$641$	−4.92269e23	−0.682197	−0.341098	−	0.940028i	$-0.610799\pi$
$641$	−4.92269e23	−0.682197	−0.341098	+	0.940028i	$0.610799\pi$
$642$	−2.35260e23	−0.321737
$643$	5.36567e23	0.724154	0.362077	−	0.932148i	$-0.382068\pi$
$643$	5.36567e23	0.724154	0.362077	+	0.932148i	$0.382068\pi$
$644$	9.21469e23	1.22730
$645$	1.01927e24	1.33977
$646$	3.43951e24	4.46190
$647$	−9.65335e23	−1.23592	−0.617962	−	0.786208i	$-0.712041\pi$
$647$	−9.65335e23	−1.23592	−0.617962	+	0.786208i	$0.712041\pi$
$648$	2.12312e24	2.68279
$649$	−5.15592e22	−0.0643023
$650$	−6.85652e23	−0.843996
$651$	1.79168e23	0.217682
$652$	−1.54433e24	−1.85198
$653$	6.65392e23	0.787618	0.393809	−	0.919192i	$-0.371157\pi$
$653$	6.65392e23	0.787618	0.393809	+	0.919192i	$0.371157\pi$
$654$	−2.58662e23	−0.302219
$655$	3.47969e23	0.401318
$656$	−1.94092e24	−2.20966
$657$	2.24445e23	0.252234
$658$	4.35781e23	0.483446
$659$	−2.54971e23	−0.279232	−0.139616	−	0.990206i	$-0.544587\pi$
$659$	−2.54971e23	−0.279232	−0.139616	+	0.990206i	$0.544587\pi$
$660$	9.37080e23	1.01310
$661$	−1.23768e24	−1.32098	−0.660488	−	0.750837i	$-0.729651\pi$
$661$	−1.23768e24	−1.32098	−0.660488	+	0.750837i	$0.729651\pi$
$662$	2.72943e24	2.87593
$663$	−2.34601e24	−2.44042
$664$	2.35704e24	2.42069
$665$	−4.05411e23	−0.411066
$666$	7.00343e23	0.701100
$667$	−9.39519e23	−0.928616
$668$	−1.98452e24	−1.93667
$669$	−6.23534e22	−0.0600812
$670$	7.48430e23	0.712058
$671$	−6.01374e23	−0.564941
$672$	−3.69261e23	−0.342527
$673$	8.64611e23	0.791941	0.395970	−	0.918263i	$-0.370408\pi$
$673$	8.64611e23	0.791941	0.395970	+	0.918263i	$0.370408\pi$
$674$	−2.85246e24	−2.57994
$675$	−3.06278e23	−0.273548
$676$	1.35659e24	1.19647
$677$	1.63690e24	1.42566	0.712832	−	0.701335i	$-0.247412\pi$
$677$	1.63690e24	1.42566	0.712832	+	0.701335i	$0.247412\pi$
$678$	3.81471e24	3.28102
$679$	−6.90715e22	−0.0586686
$680$	3.39683e24	2.84937
$681$	−6.76204e23	−0.560180
$682$	5.71659e23	0.467703
$683$	−2.52665e23	−0.204159	−0.102079	−	0.994776i	$-0.532550\pi$
$683$	−2.52665e23	−0.204159	−0.102079	+	0.994776i	$0.532550\pi$
$684$	1.60419e24	1.28021
$685$	4.24049e22	0.0334231
$686$	−1.51081e24	−1.17613
$687$	−1.04035e24	−0.799921
$688$	−3.18228e24	−2.41678
$689$	1.42620e24	1.06984
$690$	−3.56512e24	−2.64154
$691$	−4.43169e23	−0.324344	−0.162172	−	0.986762i	$-0.551850\pi$
$691$	−4.43169e23	−0.324344	−0.162172	+	0.986762i	$0.551850\pi$
$692$	−4.37242e24	−3.16097
$693$	9.38331e22	0.0670075
$694$	1.93157e24	1.36256
$695$	−1.07572e24	−0.749598
$696$	2.16906e24	1.49312
$697$	3.23815e24	2.20201
$698$	−1.10387e24	−0.741561
$699$	2.75439e24	1.82797
$700$	4.47111e23	0.293144
$701$	−1.25910e24	−0.815564	−0.407782	−	0.913079i	$-0.633698\pi$
$701$	−1.25910e24	−0.815564	−0.407782	+	0.913079i	$0.633698\pi$
$702$	2.50598e24	1.60366
$703$	−2.38062e24	−1.50511
$704$	1.45644e23	0.0909756
$705$	−1.16078e24	−0.716380
$706$	−1.41643e24	−0.863684
$707$	4.06903e23	0.245147
$708$	−5.69458e23	−0.338984
$709$	2.20575e24	1.29737	0.648684	−	0.761058i	$-0.275320\pi$
$709$	2.20575e24	1.29737	0.648684	+	0.761058i	$0.275320\pi$
$710$	9.36130e23	0.544052
$711$	−6.59481e23	−0.378713
$712$	2.79605e24	1.58659
$713$	−1.49735e24	−0.839582
$714$	2.22204e24	1.23116
$715$	8.82276e23	0.483062
$716$	−6.39404e24	−3.45951
$717$	−2.43284e22	−0.0130077
$718$	2.22038e24	1.17319
$719$	2.06394e24	1.07771	0.538855	−	0.842399i	$-0.318857\pi$
$719$	2.06394e24	1.07771	0.538855	+	0.842399i	$0.318857\pi$
$720$	9.91857e23	0.511826
$721$	9.67137e23	0.493217
$722$	−4.36554e24	−2.20025
$723$	−3.81998e24	−1.90277
$724$	7.50551e24	3.69490
$725$	−4.55869e23	−0.221803
$726$	−3.31873e24	−1.59592
$727$	2.87271e24	1.36537	0.682684	−	0.730713i	$-0.260812\pi$
$727$	2.87271e24	1.36537	0.682684	+	0.730713i	$0.260812\pi$
$728$	−2.00297e24	−0.940932
$729$	7.95057e23	0.369160
$730$	−1.99885e24	−0.917352
$731$	5.30919e24	2.40841
$732$	−6.64202e24	−2.97821
$733$	−3.13941e23	−0.139144	−0.0695719	−	0.997577i	$-0.522163\pi$
$733$	−3.13941e23	−0.139144	−0.0695719	+	0.997577i	$0.522163\pi$
$734$	−5.21910e24	−2.28654
$735$	1.88120e24	0.814692
$736$	3.08600e24	1.32110
$737$	5.88832e23	0.249183
$738$	2.19366e24	0.917676
$739$	3.58547e24	1.48275	0.741375	−	0.671091i	$-0.234174\pi$
$739$	3.58547e24	1.48275	0.741375	+	0.671091i	$0.234174\pi$
$740$	−4.29408e24	−1.75550
$741$	5.40231e24	2.18336
$742$	−1.35084e24	−0.539722
$743$	−2.86593e24	−1.13204	−0.566019	−	0.824392i	$-0.691517\pi$
$743$	−2.86593e24	−1.13204	−0.566019	+	0.824392i	$0.691517\pi$
$744$	3.45693e24	1.34996
$745$	−3.05789e24	−1.18058
$746$	−4.91423e24	−1.87575
$747$	−1.14824e24	−0.433318
$748$	4.88109e24	1.82118
$749$	1.44440e23	0.0532834
$750$	−6.28894e24	−2.29381
$751$	−2.55227e24	−0.920422	−0.460211	−	0.887809i	$-0.652226\pi$
$751$	−2.55227e24	−0.920422	−0.460211	+	0.887809i	$0.652226\pi$
$752$	3.62411e24	1.29226
$753$	1.61477e24	0.569317
$754$	3.72994e24	1.30031
$755$	−1.91970e24	−0.661735
$756$	−1.63414e24	−0.556998
$757$	−3.97550e24	−1.33991	−0.669956	−	0.742401i	$-0.733687\pi$
$757$	−3.97550e24	−1.33991	−0.669956	+	0.742401i	$0.733687\pi$
$758$	8.99971e24	2.99944
$759$	−2.80488e24	−0.924399
$760$	−7.82213e24	−2.54923
$761$	5.57009e24	1.79512	0.897558	−	0.440897i	$-0.145340\pi$
$761$	5.57009e24	1.79512	0.897558	+	0.440897i	$0.145340\pi$
$762$	4.85859e24	1.54843
$763$	1.58808e23	0.0500510
$764$	−5.37991e24	−1.67680
$765$	−1.65477e24	−0.510054
$766$	−8.51517e24	−2.59567
$767$	−5.36154e23	−0.161633
$768$	7.49659e24	2.23508
$769$	−1.22029e24	−0.359822	−0.179911	−	0.983683i	$-0.557581\pi$
$769$	−1.22029e24	−0.359822	−0.179911	+	0.983683i	$0.557581\pi$
$770$	−8.35654e23	−0.243700
$771$	−6.18954e24	−1.78524
$772$	1.21027e25	3.45252
$773$	1.29918e24	0.366558	0.183279	−	0.983061i	$-0.441329\pi$
$773$	1.29918e24	0.366558	0.183279	+	0.983061i	$0.441329\pi$
$774$	3.59666e24	1.00369
$775$	−7.26538e23	−0.200537
$776$	−1.33269e24	−0.363835
$777$	−1.53796e24	−0.415304
$778$	1.43859e24	0.384247
$779$	−7.45672e24	−1.97006
$780$	9.74451e24	2.54657
$781$	7.36506e23	0.190389
$782$	−1.85701e25	−4.74850
$783$	1.66615e24	0.421443
$784$	−5.87335e24	−1.46960
$785$	−2.21474e24	−0.548190
$786$	4.39184e24	1.07536
$787$	−5.23516e24	−1.26808	−0.634038	−	0.773302i	$-0.718604\pi$
$787$	−5.23516e24	−1.26808	−0.634038	+	0.773302i	$0.718604\pi$
$788$	−7.19768e24	−1.72472
$789$	2.67153e24	0.633295
$790$	5.87317e24	1.37734
$791$	−2.34207e24	−0.543376
$792$	1.81045e24	0.415549
$793$	−6.25357e24	−1.42006
$794$	−1.13664e25	−2.55358
$795$	3.59821e24	0.799771
$796$	8.04809e24	1.76983
$797$	−1.38038e24	−0.300333	−0.150166	−	0.988661i	$-0.547981\pi$
$797$	−1.38038e24	−0.300333	−0.150166	+	0.988661i	$0.547981\pi$
$798$	−5.11684e24	−1.10148
$799$	−6.04631e24	−1.28778
$800$	1.49738e24	0.315548
$801$	−1.36210e24	−0.284010
$802$	−2.23198e24	−0.460478
$803$	−1.57261e24	−0.321025
$804$	6.50349e24	1.31362
$805$	2.18884e24	0.437470
$806$	5.94457e24	1.17563
$807$	1.10514e24	0.216268
$808$	7.85093e24	1.52028
$809$	1.07203e24	0.205422	0.102711	−	0.994711i	$-0.467248\pi$
$809$	1.07203e24	0.205422	0.102711	+	0.994711i	$0.467248\pi$
$810$	9.21104e24	1.74657
$811$	9.15638e24	1.71809	0.859046	−	0.511898i	$-0.171057\pi$
$811$	9.15638e24	1.71809	0.859046	+	0.511898i	$0.171057\pi$
$812$	−2.43228e24	−0.451634
$813$	−5.84408e24	−1.07386
$814$	−4.90706e24	−0.892305
$815$	−3.66837e24	−0.660135
$816$	1.84792e25	3.29092
$817$	−1.22258e25	−2.15472
$818$	9.30245e24	1.62254
$819$	9.75752e23	0.168433
$820$	−1.34502e25	−2.29779
$821$	1.05958e25	1.79150	0.895749	−	0.444559i	$-0.146640\pi$
$821$	1.05958e25	1.79150	0.895749	+	0.444559i	$0.146640\pi$
$822$	5.35208e23	0.0895597
$823$	1.14628e25	1.89841	0.949206	−	0.314655i	$-0.101889\pi$
$823$	1.14628e25	1.89841	0.949206	+	0.314655i	$0.101889\pi$
$824$	1.86603e25	3.05870
$825$	−1.36097e24	−0.220795
$826$	5.07822e23	0.0815419
$827$	−3.43103e24	−0.545291	−0.272645	−	0.962115i	$-0.587899\pi$
$827$	−3.43103e24	−0.545291	−0.272645	+	0.962115i	$0.587899\pi$
$828$	−8.66114e24	−1.36244
$829$	2.52550e24	0.393219	0.196609	−	0.980482i	$-0.437007\pi$
$829$	2.52550e24	0.393219	0.196609	+	0.980482i	$0.437007\pi$
$830$	1.02259e25	1.57593
$831$	−1.04238e25	−1.59008
$832$	1.51452e24	0.228680
$833$	9.79886e24	1.46451
$834$	−1.35771e25	−2.00860
$835$	−4.71398e24	−0.690324
$836$	−1.12400e25	−1.62935
$837$	2.65541e24	0.381036
$838$	−1.74439e24	−0.247782
$839$	−1.19266e25	−1.67703	−0.838515	−	0.544879i	$-0.816576\pi$
$839$	−1.19266e25	−1.67703	−0.838515	+	0.544879i	$0.816576\pi$
$840$	−5.05336e24	−0.703406
$841$	−4.77723e24	−0.658279
$842$	1.17895e25	1.60821
$843$	5.15134e24	0.695642
$844$	−6.95770e24	−0.930154
$845$	3.22241e24	0.426480
$846$	−4.09602e24	−0.536678
$847$	2.03756e24	0.264303
$848$	−1.12340e25	−1.44269
$849$	−1.13640e25	−1.44482
$850$	−9.01049e24	−1.13419
$851$	1.28531e25	1.60179
$852$	8.13452e24	1.00368
$853$	1.04592e25	1.27771	0.638855	−	0.769327i	$-0.279408\pi$
$853$	1.04592e25	1.27771	0.638855	+	0.769327i	$0.279408\pi$
$854$	5.92311e24	0.716404
$855$	3.81056e24	0.456328
$856$	2.78687e24	0.330438
$857$	3.99923e24	0.469504	0.234752	−	0.972055i	$-0.424572\pi$
$857$	3.99923e24	0.469504	0.234752	+	0.972055i	$0.424572\pi$
$858$	1.11355e25	1.29440
$859$	−4.51335e24	−0.519466	−0.259733	−	0.965680i	$-0.583635\pi$
$859$	−4.51335e24	−0.519466	−0.259733	+	0.965680i	$0.583635\pi$
$860$	−2.20526e25	−2.51317
$861$	−4.81729e24	−0.543595
$862$	−4.60988e24	−0.515084
$863$	6.82347e24	0.754941	0.377471	−	0.926022i	$-0.376794\pi$
$863$	6.82347e24	0.754941	0.377471	+	0.926022i	$0.376794\pi$
$864$	−5.47274e24	−0.599568
$865$	−1.03861e25	−1.12672
$866$	−3.01785e25	−3.24187
$867$	−1.97543e25	−2.10136
$868$	−3.87642e24	−0.408332
$869$	4.62075e24	0.481997
$870$	9.41037e24	0.972060
$871$	6.12315e24	0.626355
$872$	3.06409e24	0.310393
$873$	6.49222e23	0.0651287
$874$	4.27627e25	4.24832
$875$	3.86114e24	0.379881
$876$	−1.73690e25	−1.69235
$877$	−1.37774e25	−1.32945	−0.664725	−	0.747088i	$-0.731451\pi$
$877$	−1.37774e25	−1.32945	−0.664725	+	0.747088i	$0.731451\pi$
$878$	3.60848e25	3.44843
$879$	5.92105e24	0.560394
$880$	−6.94959e24	−0.651413
$881$	−5.09769e24	−0.473237	−0.236618	−	0.971603i	$-0.576039\pi$
$881$	−5.09769e24	−0.473237	−0.236618	+	0.971603i	$0.576039\pi$
$882$	6.63815e24	0.610329
$883$	−3.29282e24	−0.299849	−0.149924	−	0.988697i	$-0.547903\pi$
$883$	−3.29282e24	−0.299849	−0.149924	+	0.988697i	$0.547903\pi$
$884$	5.07574e25	4.57778
$885$	−1.35268e24	−0.120830
$886$	2.46831e25	2.18380
$887$	2.95971e24	0.259357	0.129678	−	0.991556i	$-0.458605\pi$
$887$	2.95971e24	0.259357	0.129678	+	0.991556i	$0.458605\pi$
$888$	−2.96739e25	−2.57552
$889$	−2.98297e24	−0.256439
$890$	1.21305e25	1.03291
$891$	7.24684e24	0.611207
$892$	1.34906e24	0.112702
$893$	1.39233e25	1.15214
$894$	−3.85948e25	−3.16344
$895$	−1.51883e25	−1.23314
$896$	−5.04947e24	−0.406095
$897$	−2.91674e25	−2.32360
$898$	1.41367e25	1.11558
$899$	3.95236e24	0.308957
$900$	−4.20251e24	−0.325423
$901$	1.87424e25	1.43769
$902$	−1.53702e25	−1.16795
$903$	−7.89830e24	−0.594549
$904$	−4.51888e25	−3.36976
$905$	1.78284e25	1.31704
$906$	−2.42292e25	−1.77317
$907$	−1.50153e25	−1.08861	−0.544304	−	0.838888i	$-0.683206\pi$
$907$	−1.50153e25	−1.08861	−0.544304	+	0.838888i	$0.683206\pi$
$908$	1.46301e25	1.05080
$909$	−3.82459e24	−0.272140
$910$	−8.68980e24	−0.612573
$911$	−1.02305e25	−0.714484	−0.357242	−	0.934012i	$-0.616283\pi$
$911$	−1.02305e25	−0.714484	−0.357242	+	0.934012i	$0.616283\pi$
$912$	−4.25534e25	−2.94427
$913$	8.04530e24	0.551494
$914$	3.02524e25	2.05455
$915$	−1.57773e25	−1.06158
$916$	2.25087e25	1.50051
$917$	−2.69641e24	−0.178093
$918$	3.29323e25	2.15506
$919$	2.65378e24	0.172061	0.0860306	−	0.996292i	$-0.472582\pi$
$919$	2.65378e24	0.172061	0.0860306	+	0.996292i	$0.472582\pi$
$920$	4.22322e25	2.71298
$921$	−8.21359e23	−0.0522788
$922$	−2.18912e25	−1.38056
$923$	7.65878e24	0.478569
$924$	−7.26143e24	−0.449583
$925$	6.23652e24	0.382593
$926$	4.06401e25	2.47037
$927$	−9.09038e24	−0.547526
$928$	−8.14571e24	−0.486151
$929$	5.90912e24	0.349453	0.174727	−	0.984617i	$-0.444096\pi$
$929$	5.90912e24	0.349453	0.174727	+	0.984617i	$0.444096\pi$
$930$	1.49977e25	0.878860
$931$	−2.25645e25	−1.31025
$932$	−5.95932e25	−3.42895
$933$	−3.17832e25	−1.81219
$934$	1.06206e25	0.600069
$935$	1.15944e25	0.649158
$936$	1.88265e25	1.04454
$937$	−2.91477e25	−1.60257	−0.801286	−	0.598281i	$-0.795850\pi$
$937$	−2.91477e25	−1.60257	−0.801286	+	0.598281i	$0.795850\pi$
$938$	−5.79958e24	−0.315989
$939$	2.24122e24	0.121012
$940$	2.51143e25	1.34380
$941$	3.71382e24	0.196929	0.0984644	−	0.995141i	$-0.468607\pi$
$941$	3.71382e24	0.196929	0.0984644	+	0.995141i	$0.468607\pi$
$942$	−2.79531e25	−1.46892
$943$	4.02593e25	2.09660
$944$	4.22323e24	0.217963
$945$	−3.88170e24	−0.198542
$946$	−2.52005e25	−1.27742
$947$	1.72785e24	0.0868023	0.0434011	−	0.999058i	$-0.486181\pi$
$947$	1.72785e24	0.0868023	0.0434011	+	0.999058i	$0.486181\pi$
$948$	5.10350e25	2.54095
$949$	−1.63532e25	−0.806939
$950$	2.07491e25	1.01472
$951$	5.59066e24	0.270974
$952$	−2.63220e25	−1.26446
$953$	−1.54800e23	−0.00737022	−0.00368511	−	0.999993i	$-0.501173\pi$
$953$	−1.54800e23	−0.00737022	−0.00368511	+	0.999993i	$0.501173\pi$
$954$	1.26969e25	0.599151
$955$	−1.27793e25	−0.597694
$956$	5.26361e23	0.0244001
$957$	7.40367e24	0.340169
$958$	4.14934e25	1.88961
$959$	−3.28596e23	−0.0148321
$960$	3.82103e24	0.170952
$961$	−1.62511e25	−0.720665
$962$	−5.10275e25	−2.24293
$963$	−1.35763e24	−0.0591504
$964$	8.26479e25	3.56925
$965$	2.87485e25	1.23065
$966$	2.76261e25	1.17223
$967$	−3.13256e25	−1.31757	−0.658785	−	0.752331i	$-0.728929\pi$
$967$	−3.13256e25	−1.31757	−0.658785	+	0.752331i	$0.728929\pi$
$968$	3.93134e25	1.63908
$969$	7.09944e25	2.93408
$970$	−5.78181e24	−0.236867
$971$	3.93612e25	1.59847	0.799235	−	0.601019i	$-0.205238\pi$
$971$	3.93612e25	1.59847	0.799235	+	0.601019i	$0.205238\pi$
$972$	4.04605e25	1.62880
$973$	8.33575e24	0.332648
$974$	3.65845e25	1.44726
$975$	−1.41525e25	−0.555000
$976$	4.92587e25	1.91496
$977$	−3.19313e25	−1.23059	−0.615294	−	0.788298i	$-0.710963\pi$
$977$	−3.19313e25	−1.23059	−0.615294	+	0.788298i	$0.710963\pi$
$978$	−4.62998e25	−1.76888
$979$	9.54376e24	0.361465
$980$	−4.07011e25	−1.52822
$981$	−1.49268e24	−0.0555622
$982$	−2.22545e25	−0.821239
$983$	−1.46710e25	−0.536729	−0.268364	−	0.963317i	$-0.586483\pi$
$983$	−1.46710e25	−0.536729	−0.268364	+	0.963317i	$0.586483\pi$
$984$	−9.29464e25	−3.37112
$985$	−1.70972e25	−0.614776
$986$	4.90170e25	1.74740
$987$	8.99489e24	0.317907
$988$	−1.16883e26	−4.09559
$989$	6.60080e25	2.29313
$990$	7.85454e24	0.270534
$991$	−1.14082e25	−0.389576	−0.194788	−	0.980845i	$-0.562402\pi$
$991$	−1.14082e25	−0.389576	−0.194788	+	0.980845i	$0.562402\pi$
$992$	−1.29822e25	−0.439539
$993$	5.63377e25	1.89117
$994$	−7.25406e24	−0.241433
$995$	1.91173e25	0.630855
$996$	8.88582e25	2.90732
$997$	3.73744e25	1.21245	0.606227	−	0.795291i	$-0.292682\pi$
$997$	3.73744e25	1.21245	0.606227	+	0.795291i	$0.292682\pi$
$998$	−7.55616e25	−2.43048
$999$	−2.27938e25	−0.726959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.18.a.b.1.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.18.a.b.1.3	✓	44	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:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	59.a (trivial)

\(f(q)\)	\(=\)	\(q-648.649 q^{2} -13388.7 q^{3} +289673. q^{4} +688083. q^{5} +8.68455e6 q^{6} -5.33195e6 q^{7} -1.02876e8 q^{8} +5.01164e7 q^{9} +O(q^{10})\)	\(q-648.649 q^{2} -13388.7 q^{3} +289673. q^{4} +688083. q^{5} +8.68455e6 q^{6} -5.33195e6 q^{7} -1.02876e8 q^{8} +5.01164e7 q^{9} -4.46324e8 q^{10} -3.51148e8 q^{11} -3.87834e9 q^{12} -3.65152e9 q^{13} +3.45856e9 q^{14} -9.21252e9 q^{15} +2.87626e10 q^{16} -4.79864e10 q^{17} -3.25079e10 q^{18} +1.10502e11 q^{19} +1.99319e11 q^{20} +7.13877e10 q^{21} +2.27772e11 q^{22} -5.96605e11 q^{23} +1.37738e12 q^{24} -2.89482e11 q^{25} +2.36855e12 q^{26} +1.05802e12 q^{27} -1.54452e12 q^{28} +1.57478e12 q^{29} +5.97569e12 q^{30} +2.50979e12 q^{31} -5.17261e12 q^{32} +4.70141e12 q^{33} +3.11263e13 q^{34} -3.66882e12 q^{35} +1.45174e13 q^{36} -2.15437e13 q^{37} -7.16767e13 q^{38} +4.88890e13 q^{39} -7.07875e13 q^{40} -6.74806e13 q^{41} -4.63055e13 q^{42} -1.10639e14 q^{43} -1.01718e14 q^{44} +3.44842e13 q^{45} +3.86987e14 q^{46} +1.26001e14 q^{47} -3.85093e14 q^{48} -2.04201e14 q^{49} +1.87772e14 q^{50} +6.42474e14 q^{51} -1.05775e15 q^{52} -3.90578e14 q^{53} -6.86285e14 q^{54} -2.41619e14 q^{55} +5.48532e14 q^{56} -1.47947e15 q^{57} -1.02148e15 q^{58} +1.46830e14 q^{59} -2.66862e15 q^{60} +1.71259e15 q^{61} -1.62797e15 q^{62} -2.67218e14 q^{63} -4.14765e14 q^{64} -2.51255e15 q^{65} -3.04956e15 q^{66} -1.67688e15 q^{67} -1.39004e16 q^{68} +7.98775e15 q^{69} +2.37978e15 q^{70} -2.09742e15 q^{71} -5.15580e15 q^{72} +4.47847e15 q^{73} +1.39743e16 q^{74} +3.87577e15 q^{75} +3.20093e16 q^{76} +1.87230e15 q^{77} -3.17118e16 q^{78} -1.31590e16 q^{79} +1.97911e16 q^{80} -2.06376e16 q^{81} +4.37712e16 q^{82} -2.29114e16 q^{83} +2.06791e16 q^{84} -3.30186e16 q^{85} +7.17661e16 q^{86} -2.10842e16 q^{87} +3.61248e16 q^{88} -2.71787e16 q^{89} -2.23682e16 q^{90} +1.94697e16 q^{91} -1.72820e17 q^{92} -3.36027e16 q^{93} -8.17301e16 q^{94} +7.60342e16 q^{95} +6.92544e16 q^{96} +1.29543e16 q^{97} +1.32455e17 q^{98} -1.75983e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9}+O(q^{10}) \) 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9} + 246619918 q^{10} + 896501218 q^{11} + 2579890176 q^{12} + 5139901152 q^{13} - 1065727269 q^{14} + 52608606500 q^{15} + 170254553019 q^{16} + 31152575372 q^{17} + 371065029637 q^{18} + 222944612638 q^{19} + 632345964652 q^{20} + 518768862104 q^{21} - 1188197076091 q^{22} - 314739342184 q^{23} - 1830638682468 q^{24} + 8265149117122 q^{25} - 1422210694649 q^{26} + 1055641354104 q^{27} + 4733828767179 q^{28} + 7952343701542 q^{29} + 33815332595226 q^{30} + 22703202725740 q^{31} + 51508227606921 q^{32} + 39808250652964 q^{33} + 42559210973877 q^{34} + 53084789167044 q^{35} + 286899333699545 q^{36} + 70719636063816 q^{37} + 70760432282360 q^{38} + 89621954178128 q^{39} + 176727288274300 q^{40} + 77283001373080 q^{41} - 142968851337140 q^{42} + 218112956325030 q^{43} - 146577440549739 q^{44} + 156445227241670 q^{45} - 436430382603480 q^{46} - 206155334901712 q^{47} - 694457384549320 q^{48} + 17\!\cdots\!92 q^{49}+ \cdots - 33\!\cdots\!26 q^{99}+O(q^{100}) \) 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9 + 246619918 * q^10 + 896501218 * q^11 + 2579890176 * q^12 + 5139901152 * q^13 - 1065727269 * q^14 + 52608606500 * q^15 + 170254553019 * q^16 + 31152575372 * q^17 + 371065029637 * q^18 + 222944612638 * q^19 + 632345964652 * q^20 + 518768862104 * q^21 - 1188197076091 * q^22 - 314739342184 * q^23 - 1830638682468 * q^24 + 8265149117122 * q^25 - 1422210694649 * q^26 + 1055641354104 * q^27 + 4733828767179 * q^28 + 7952343701542 * q^29 + 33815332595226 * q^30 + 22703202725740 * q^31 + 51508227606921 * q^32 + 39808250652964 * q^33 + 42559210973877 * q^34 + 53084789167044 * q^35 + 286899333699545 * q^36 + 70719636063816 * q^37 + 70760432282360 * q^38 + 89621954178128 * q^39 + 176727288274300 * q^40 + 77283001373080 * q^41 - 142968851337140 * q^42 + 218112956325030 * q^43 - 146577440549739 * q^44 + 156445227241670 * q^45 - 436430382603480 * q^46 - 206155334901712 * q^47 - 694457384549320 * q^48 + 1711133899986192 * q^49 - 636149584416999 * q^50 + 158951699286348 * q^51 - 3158033385800149 * q^52 - 404876214856866 * q^53 - 1832749628980958 * q^54 - 611379564042440 * q^55 - 2900007168369351 * q^56 - 1013357232316788 * q^57 - 455786716037158 * q^58 + 6460539254590124 * q^59 + 4624863641607938 * q^60 + 4875940646057436 * q^61 - 15281797209467076 * q^62 - 16054536748044808 * q^63 + 5329292222614591 * q^64 - 7625310499015476 * q^65 - 10349172696837322 * q^66 - 4206243743451792 * q^67 - 552954195428233 * q^68 + 8020251305435444 * q^69 + 3876379104148138 * q^70 + 19535505651668622 * q^71 + 71495174696263183 * q^72 + 33833193336852456 * q^73 + 40772046703252163 * q^74 + 75968477185276688 * q^75 + 38838328992025026 * q^76 + 53055532951436968 * q^77 + 73057936571746858 * q^78 + 61045424159854942 * q^79 + 80004004628116616 * q^80 + 155795318109062036 * q^81 + 52248236930642133 * q^82 + 1235564168216730 * q^83 + 164143534194509272 * q^84 + 113286530641911588 * q^85 + 50368241096487595 * q^86 + 18062036297697056 * q^87 - 116796176360505729 * q^88 + 5837731242014800 * q^89 + 269698982682069798 * q^90 - 57230636051197354 * q^91 + 85549613709158172 * q^92 - 42635139630610976 * q^93 + 217633917061493766 * q^94 - 190986541078108154 * q^95 + 173923507159625020 * q^96 + 233342043840904176 * q^97 + 216259456237342020 * q^98 - 333859997478074426 * q^99

Introduction

L-functions

Modular forms

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