LMFDB - Embedded newform 20.11.d.d.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	20.19
Dual form			20.11.d.d.19.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.302723 + 31.9986i) q^{2} +375.794 q^{3} +(-1023.82 + 19.3734i) q^{4} +(2240.90 - 2178.07i) q^{5} +(113.762 + 12024.9i) q^{6} +19635.7 q^{7} +(-929.854 - 32754.8i) q^{8} +82172.5 q^{9} +O(q^{10})$	\(q+(0.302723 + 31.9986i) q^{2} +375.794 q^{3} +(-1023.82 + 19.3734i) q^{4} +(2240.90 - 2178.07i) q^{5} +(113.762 + 12024.9i) q^{6} +19635.7 q^{7} +(-929.854 - 32754.8i) q^{8} +82172.5 q^{9} +(70373.6 + 71046.1i) q^{10} -163868. i q^{11} +(-384745. + 7280.42i) q^{12} -86535.9i q^{13} +(5944.18 + 628314. i) q^{14} +(842116. - 818508. i) q^{15} +(1.04783e6 - 39669.6i) q^{16} +2.09541e6i q^{17} +(24875.5 + 2.62940e6i) q^{18} +3.13936e6i q^{19} +(-2.25207e6 + 2.27336e6i) q^{20} +7.37899e6 q^{21} +(5.24354e6 - 49606.6i) q^{22} -1.05386e7 q^{23} +(-349434. - 1.23091e7i) q^{24} +(277605. - 9.76168e6i) q^{25} +(2.76902e6 - 26196.4i) q^{26} +8.68968e6 q^{27} +(-2.01034e7 + 380410. i) q^{28} +1.13219e7 q^{29} +(2.64460e7 + 2.66987e7i) q^{30} +1.21645e7i q^{31} +(1.58657e6 + 3.35169e7i) q^{32} -6.15807e7i q^{33} +(-6.70503e7 + 634330. i) q^{34} +(4.40016e7 - 4.27680e7i) q^{35} +(-8.41296e7 + 1.59196e6i) q^{36} -4.87589e7i q^{37} +(-1.00455e8 + 950356. i) q^{38} -3.25197e7i q^{39} +(-7.34261e7 - 7.13748e7i) q^{40} +4.55341e7 q^{41} +(2.23379e6 + 2.36117e8i) q^{42} -7.47838e7 q^{43} +(3.17468e6 + 1.67771e8i) q^{44} +(1.84140e8 - 1.78978e8i) q^{45} +(-3.19029e6 - 3.37222e8i) q^{46} -9.62539e6 q^{47} +(3.93767e8 - 1.49076e7i) q^{48} +1.03086e8 q^{49} +(3.12444e8 + 5.92788e6i) q^{50} +7.87445e8i q^{51} +(1.67649e6 + 8.85969e7i) q^{52} -1.27224e8i q^{53} +(2.63056e6 + 2.78057e8i) q^{54} +(-3.56917e8 - 3.67211e8i) q^{55} +(-1.82583e7 - 6.43164e8i) q^{56} +1.17975e9i q^{57} +(3.42739e6 + 3.62283e8i) q^{58} -1.18280e9i q^{59} +(-8.46315e8 + 8.54317e8i) q^{60} +2.97404e8 q^{61} +(-3.89246e8 + 3.68246e6i) q^{62} +1.61351e9 q^{63} +(-1.07201e9 + 6.09144e7i) q^{64} +(-1.88482e8 - 1.93918e8i) q^{65} +(1.97049e9 - 1.86419e7i) q^{66} -7.15670e8 q^{67} +(-4.05953e7 - 2.14532e9i) q^{68} -3.96036e9 q^{69} +(1.38184e9 + 1.39504e9i) q^{70} +2.56419e9i q^{71} +(-7.64084e7 - 2.69154e9i) q^{72} +2.10771e9i q^{73} +(1.56022e9 - 1.47604e7i) q^{74} +(1.04322e8 - 3.66838e9i) q^{75} +(-6.08201e7 - 3.21413e9i) q^{76} -3.21766e9i q^{77} +(1.04058e9 - 9.84446e6i) q^{78} +3.44771e9i q^{79} +(2.26166e9 - 2.37114e9i) q^{80} -1.58667e9 q^{81} +(1.37842e7 + 1.45702e9i) q^{82} -7.09842e9 q^{83} +(-7.55473e9 + 1.42956e8i) q^{84} +(4.56397e9 + 4.69561e9i) q^{85} +(-2.26388e7 - 2.39297e9i) q^{86} +4.25469e9 q^{87} +(-5.36747e9 + 1.52373e8i) q^{88} -3.39502e9 q^{89} +(5.78278e9 + 5.83804e9i) q^{90} -1.69919e9i q^{91} +(1.07896e10 - 2.04169e8i) q^{92} +4.57134e9i q^{93} +(-2.91383e6 - 3.07999e8i) q^{94} +(6.83776e9 + 7.03498e9i) q^{95} +(5.96225e8 + 1.25955e10i) q^{96} -5.71771e9i q^{97} +(3.12064e7 + 3.29859e9i) q^{98} -1.34654e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0.302723	+	31.9986i	0.00946009	+	0.999955i
$2$	0.302723	+	31.9986i	0.00946009	+	0.999955i
$3$	375.794			1.54648			0.773240	−	0.634114i	$-0.218635\pi$
$3$	375.794			1.54648			0.773240	+	0.634114i	$0.218635\pi$
$4$	−1023.82	+	19.3734i	−0.999821	+	0.0189193i
$5$	2240.90	−	2178.07i	0.717087	−	0.696984i
$5$	2240.90	−	2178.07i	0.717087	−	0.696984i
$6$	113.762	+	12024.9i	0.0146298	+	1.54641i
$7$	19635.7			1.16831			0.584153	−	0.811644i	$-0.301427\pi$
$7$	19635.7			1.16831			0.584153	+	0.811644i	$0.301427\pi$
$8$	−929.854	−	32754.8i	−0.0283769	−	0.999597i
$9$	82172.5			1.39160
$10$	70373.6	+	71046.1i	0.703736	+	0.710461i
$11$		−	163868.i		−	1.01749i	−0.860917	−	0.508746i	$-0.830109\pi$
$11$		−	163868.i		−	1.01749i	0.860917	−	0.508746i	$-0.169891\pi$
$12$	−384745.	+	7280.42i	−1.54620	+	0.0292584i
$13$		−	86535.9i		−	0.233066i	−0.993187	−	0.116533i	$-0.962822\pi$
$13$		−	86535.9i		−	0.233066i	0.993187	−	0.116533i	$-0.0371781\pi$
$14$	5944.18	+	628314.i	0.0110523	+	1.16825i
$15$	842116.	−	818508.i	1.10896	−	1.07787i
$16$	1.04783e6	−	39669.6i	0.999284	−	0.0378319i
$17$			2.09541e6i			1.47579i	0.674914	+	0.737896i	$0.264181\pi$
$17$			2.09541e6i			1.47579i	−0.674914	+	0.737896i	$0.735819\pi$
$18$	24875.5	+	2.62940e6i	0.0131646	+	1.39154i
$19$			3.13936e6i			1.26787i	0.773388	+	0.633933i	$0.218560\pi$
$19$			3.13936e6i			1.26787i	−0.773388	+	0.633933i	$0.781440\pi$
$20$	−2.25207e6	+	2.27336e6i	−0.703772	+	0.710426i
$21$	7.37899e6			1.80676
$22$	5.24354e6	−	49606.6i	1.01745	−	0.00962557i
$23$	−1.05386e7			−1.63737			−0.818683	−	0.574246i	$-0.805295\pi$
$23$	−1.05386e7			−1.63737			−0.818683	+	0.574246i	$0.805295\pi$
$24$	−349434.	−	1.23091e7i	−0.0438843	−	1.54586i
$25$	277605.	−	9.76168e6i	0.0284268	−	0.999596i
$26$	2.76902e6	−	26196.4i	0.233056	−	0.00220483i
$27$	8.68968e6			0.605598
$28$	−2.01034e7	+	380410.i	−1.16810	+	0.0221036i
$29$	1.13219e7			0.551986			0.275993	−	0.961160i	$-0.410993\pi$
$29$	1.13219e7			0.551986			0.275993	+	0.961160i	$0.410993\pi$
$30$	2.64460e7	+	2.66987e7i	1.08831	+	1.09871i
$31$			1.21645e7i			0.424898i	0.977172	+	0.212449i	$0.0681439\pi$
$31$			1.21645e7i			0.424898i	−0.977172	+	0.212449i	$0.931856\pi$
$32$	1.58657e6	+	3.35169e7i	0.0472835	+	0.998882i
$33$		−	6.15807e7i		−	1.57353i
$34$	−6.70503e7	+	634330.i	−1.47573	+	0.0139611i
$35$	4.40016e7	−	4.27680e7i	0.837776	−	0.814290i
$36$	−8.41296e7	+	1.59196e6i	−1.39135	+	0.0263281i
$37$		−	4.87589e7i		−	0.703146i	−0.936160	−	0.351573i	$-0.885647\pi$
$37$		−	4.87589e7i		−	0.703146i	0.936160	−	0.351573i	$-0.114353\pi$
$38$	−1.00455e8	+	950356.i	−1.26781	+	0.0119941i
$39$		−	3.25197e7i		−	0.360432i
$40$	−7.34261e7	−	7.13748e7i	−0.717052	−	0.697020i
$41$	4.55341e7			0.393022			0.196511	−	0.980502i	$-0.437039\pi$
$41$	4.55341e7			0.393022			0.196511	+	0.980502i	$0.437039\pi$
$42$	2.23379e6	+	2.36117e8i	0.0170921	+	1.80668i
$43$	−7.47838e7			−0.508704			−0.254352	−	0.967112i	$-0.581862\pi$
$43$	−7.47838e7			−0.508704			−0.254352	+	0.967112i	$0.581862\pi$
$44$	3.17468e6	+	1.67771e8i	0.0192503	+	1.01731i
$45$	1.84140e8	−	1.78978e8i	0.997897	−	0.969922i
$46$	−3.19029e6	−	3.37222e8i	−0.0154896	−	1.63729i
$47$	−9.62539e6			−0.0419690			−0.0209845	−	0.999780i	$-0.506680\pi$
$47$	−9.62539e6			−0.0419690			−0.0209845	+	0.999780i	$0.506680\pi$
$48$	3.93767e8	−	1.49076e7i	1.54537	−	0.0585062i
$49$	1.03086e8			0.364937
$50$	3.12444e8	+	5.92788e6i	0.999820	+	0.0189692i
$51$			7.87445e8i			2.28228i
$52$	1.67649e6	+	8.85969e7i	0.00440946	+	0.233025i
$53$		−	1.27224e8i		−	0.304222i	−0.988363	−	0.152111i	$-0.951393\pi$
$53$		−	1.27224e8i		−	0.304222i	0.988363	−	0.152111i	$-0.0486071\pi$
$54$	2.63056e6	+	2.78057e8i	0.00572902	+	0.605571i
$55$	−3.56917e8	−	3.67211e8i	−0.709175	−	0.729630i
$56$	−1.82583e7	−	6.43164e8i	−0.0331529	−	1.16783i
$57$			1.17975e9i			1.96073i
$58$	3.42739e6	+	3.62283e8i	0.00522184	+	0.551961i
$59$		−	1.18280e9i		−	1.65444i	−0.561881	−	0.827218i	$-0.689922\pi$
$59$		−	1.18280e9i		−	1.65444i	0.561881	−	0.827218i	$-0.310078\pi$
$60$	−8.46315e8	+	8.54317e8i	−1.08837	+	1.09866i
$61$	2.97404e8			0.352126			0.176063	−	0.984379i	$-0.443664\pi$
$61$	2.97404e8			0.352126			0.176063	+	0.984379i	$0.443664\pi$
$62$	−3.89246e8	+	3.68246e6i	−0.424879	+	0.00401957i
$63$	1.61351e9			1.62581
$64$	−1.07201e9	+	6.09144e7i	−0.998390	+	0.0567309i
$65$	−1.88482e8	−	1.93918e8i	−0.162443	−	0.167129i
$66$	1.97049e9	−	1.86419e7i	1.57346	−	0.0148857i
$67$	−7.15670e8			−0.530077			−0.265039	−	0.964238i	$-0.585385\pi$
$67$	−7.15670e8			−0.530077			−0.265039	+	0.964238i	$0.585385\pi$
$68$	−4.05953e7	−	2.14532e9i	−0.0279210	−	1.47553i
$69$	−3.96036e9			−2.53215
$70$	1.38184e9	+	1.39504e9i	0.822179	+	0.830035i
$71$			2.56419e9i			1.42121i	0.703589	+	0.710607i	$0.251579\pi$
$71$			2.56419e9i			1.42121i	−0.703589	+	0.710607i	$0.748421\pi$
$72$	−7.64084e7	−	2.69154e9i	−0.0394892	−	1.39104i
$73$			2.10771e9i			1.01671i	0.861148	+	0.508355i	$0.169746\pi$
$73$			2.10771e9i			1.01671i	−0.861148	+	0.508355i	$0.830254\pi$
$74$	1.56022e9	−	1.47604e7i	0.703115	−	0.00665183i
$75$	1.04322e8	−	3.66838e9i	0.0439614	−	1.54585i
$76$	−6.08201e7	−	3.21413e9i	−0.0239872	−	1.26764i
$77$		−	3.21766e9i		−	1.18874i
$78$	1.04058e9	−	9.84446e6i	0.360416	−	0.00340972i
$79$			3.44771e9i			1.12046i	0.828338	+	0.560229i	$0.189287\pi$
$79$			3.44771e9i			1.12046i	−0.828338	+	0.560229i	$0.810713\pi$
$80$	2.26166e9	−	2.37114e9i	0.690205	−	0.723614i
$81$	−1.58667e9			−0.455053
$82$	1.37842e7	+	1.45702e9i	0.00371803	+	0.393005i
$83$	−7.09842e9			−1.80207			−0.901034	−	0.433748i	$-0.857191\pi$
$83$	−7.09842e9			−1.80207			−0.901034	+	0.433748i	$0.857191\pi$
$84$	−7.55473e9	+	1.42956e8i	−1.80644	+	0.0341827i
$85$	4.56397e9	+	4.69561e9i	1.02860	+	1.05827i
$86$	−2.26388e7	−	2.39297e9i	−0.00481238	−	0.508681i
$87$	4.25469e9			0.853634
$88$	−5.36747e9	+	1.52373e8i	−1.01708	+	0.0288733i
$89$	−3.39502e9			−0.607984			−0.303992	−	0.952675i	$-0.598320\pi$
$89$	−3.39502e9			−0.607984			−0.303992	+	0.952675i	$0.598320\pi$
$90$	5.78278e9	+	5.83804e9i	0.979318	+	0.988676i
$91$		−	1.69919e9i		−	0.272292i
$92$	1.07896e10	−	2.04169e8i	1.63707	−	0.0309779i
$93$			4.57134e9i			0.657096i
$94$	−2.91383e6	−	3.07999e8i	−0.000397031	−	0.0419671i
$95$	6.83776e9	+	7.03498e9i	0.883682	+	0.909170i
$96$	5.96225e8	+	1.25955e10i	0.0731230	+	1.54475i
$97$		−	5.71771e9i		−	0.665830i	−0.942957	−	0.332915i	$-0.891968\pi$
$97$		−	5.71771e9i		−	0.665830i	0.942957	−	0.332915i	$-0.108032\pi$
$98$	3.12064e7	+	3.29859e9i	0.00345233	+	0.364920i
$99$		−	1.34654e10i		−	1.41594i
$100$	−9.50998e7	+	9.99955e9i	−0.00950998	+	0.999955i
$101$	1.71412e10			1.63093			0.815465	−	0.578807i	$-0.196481\pi$
$101$	1.71412e10			1.63093			0.815465	+	0.578807i	$0.196481\pi$
$102$	−2.51971e10	+	2.38378e8i	−2.28218	+	0.0215906i
$103$	7.45366e9			0.642960			0.321480	−	0.946916i	$-0.395820\pi$
$103$	7.45366e9			0.642960			0.321480	+	0.946916i	$0.395820\pi$
$104$	−2.83447e9	+	8.04657e7i	−0.232972	+	0.00661370i
$105$	1.65355e10	−	1.60720e10i	1.29560	−	1.25928i
$106$	4.07099e9	−	3.85137e7i	0.304208	−	0.00287797i
$107$	−7.26790e9			−0.518191			−0.259096	−	0.965852i	$-0.583424\pi$
$107$	−7.26790e9			−0.518191			−0.259096	+	0.965852i	$0.583424\pi$
$108$	−8.89664e9	+	1.68349e8i	−0.605490	+	0.0114575i
$109$	−9.09372e9			−0.591029			−0.295515	−	0.955338i	$-0.595491\pi$
$109$	−9.09372e9			−0.591029			−0.295515	+	0.955338i	$0.595491\pi$
$110$	1.16422e10	−	1.15320e10i	0.722888	−	0.716046i
$111$		−	1.83233e10i		−	1.08740i
$112$	2.05748e10	−	7.78941e8i	1.16747	−	0.0441992i
$113$		−	7.57770e9i		−	0.411287i	−0.978627	−	0.205644i	$-0.934071\pi$
$113$		−	7.57770e9i		−	0.411287i	0.978627	−	0.205644i	$-0.0659288\pi$
$114$	−3.77504e10	+	3.57139e8i	−1.96064	+	0.0185487i
$115$	−2.36160e10	+	2.29540e10i	−1.17413	+	1.14122i
$116$	−1.15915e10	+	2.19343e8i	−0.551887	+	0.0104432i
$117$		−	7.11087e9i		−	0.324335i
$118$	3.78478e10	−	3.58060e8i	1.65436	−	0.0156511i
$119$			4.11449e10i			1.72418i
$120$	−2.75931e10	−	2.68223e10i	−1.10891	−	1.07793i
$121$	−9.15322e8			−0.0352896
$122$	9.00312e7	+	9.51652e9i	0.00333115	+	0.352110i
$123$	1.71115e10			0.607801
$124$	−2.35667e8	−	1.24542e10i	−0.00803879	−	0.424822i
$125$	−2.06396e10	−	2.24796e10i	−0.676318	−	0.736610i
$126$	4.88448e8	+	5.16302e10i	0.0153803	+	1.62574i
$127$	−6.24479e9			−0.189016			−0.0945081	−	0.995524i	$-0.530128\pi$
$127$	−6.24479e9			−0.189016			−0.0945081	+	0.995524i	$0.530128\pi$
$128$	−2.27370e9	−	3.42844e10i	−0.0661732	−	0.997808i
$129$	−2.81033e10			−0.786700
$130$	6.14804e9	−	6.08984e9i	0.165585	−	0.164017i
$131$		−	5.72133e10i		−	1.48300i	−0.670953	−	0.741499i	$-0.734115\pi$
$131$		−	5.72133e10i		−	1.48300i	0.670953	−	0.741499i	$-0.265885\pi$
$132$	1.19303e9	+	6.30474e10i	0.0297701	+	1.57325i
$133$			6.16435e10i			1.48125i
$134$	−2.16650e8	−	2.29004e10i	−0.00501458	−	0.530053i
$135$	1.94727e10	−	1.89268e10i	0.434267	−	0.422092i
$136$	6.86349e10	−	1.94843e9i	1.47520	−	0.0418784i
$137$			1.24420e10i			0.257803i	0.991657	+	0.128902i	$0.0411451\pi$
$137$			1.24420e10i			0.257803i	−0.991657	+	0.128902i	$0.958855\pi$
$138$	−1.19889e9	−	1.26726e11i	−0.0239544	−	2.53204i
$139$		−	3.88376e9i		−	0.0748477i	−0.999299	−	0.0374239i	$-0.988085\pi$
$139$		−	3.88376e9i		−	0.0748477i	0.999299	−	0.0374239i	$-0.0119152\pi$
$140$	−4.42210e10	+	4.46391e10i	−0.822220	+	0.829994i
$141$	−3.61717e9			−0.0649042
$142$	−8.20506e10	+	7.76241e8i	−1.42115	+	0.0134448i
$143$	−1.41805e10			−0.237143
$144$	8.61024e10	−	3.25975e9i	1.39060	−	0.0526468i
$145$	2.53711e10	−	2.46599e10i	0.395822	−	0.384725i
$146$	−6.74438e10	+	6.38053e8i	−1.01666	+	0.00961817i
$147$	3.87390e10			0.564367
$148$	9.44626e8	+	4.99202e10i	0.0133031	+	0.703020i
$149$	5.05127e10			0.687811			0.343905	−	0.939004i	$-0.388250\pi$
$149$	5.05127e10			0.687811			0.343905	+	0.939004i	$0.388250\pi$
$150$	1.17415e11	+	2.22766e9i	1.54620	+	0.0293355i
$151$			5.51200e10i			0.702141i	0.936349	+	0.351070i	$0.114182\pi$
$151$			5.51200e10i			0.702141i	−0.936349	+	0.351070i	$0.885818\pi$
$152$	1.02829e11	−	2.91915e9i	1.26735	−	0.0359781i
$153$			1.72185e11i			2.05371i
$154$	1.02961e11	−	9.74061e8i	1.18869	−	0.0112456i
$155$	2.64951e10	+	2.72593e10i	0.296147	+	0.304689i
$156$	6.30017e8	+	3.32942e10i	0.00681914	+	0.360368i
$157$			8.96109e10i			0.939426i	0.882819	+	0.469713i	$0.155643\pi$
$157$			8.96109e10i			0.939426i	−0.882819	+	0.469713i	$0.844357\pi$
$158$	−1.10322e11	+	1.04370e9i	−1.12041	+	0.0105996i
$159$		−	4.78101e10i		−	0.470473i
$160$	7.65577e10	+	7.16522e10i	0.730111	+	0.683329i
$161$	−2.06934e11			−1.91294
$162$	−4.80322e8	−	5.07712e10i	−0.00430484	−	0.455032i
$163$	−1.16440e11			−1.01197			−0.505983	−	0.862543i	$-0.668870\pi$
$163$	−1.16440e11			−1.01197			−0.505983	+	0.862543i	$0.668870\pi$
$164$	−4.66185e10	+	8.82150e8i	−0.392952	+	0.00743572i
$165$	−1.34127e11	−	1.37996e11i	−1.09673	−	1.12836i
$166$	−2.14885e9	−	2.27139e11i	−0.0170477	−	1.80199i
$167$	−9.33076e10			−0.718348			−0.359174	−	0.933271i	$-0.616942\pi$
$167$	−9.33076e10			−0.718348			−0.359174	+	0.933271i	$0.616942\pi$
$168$	−6.86138e9	−	2.41697e11i	−0.0512702	−	1.80603i
$169$	1.30370e11			0.945680
$170$	−1.48871e11	+	1.47462e11i	−1.04849	+	1.03857i
$171$			2.57969e11i			1.76436i
$172$	7.65649e10	−	1.44882e9i	0.508613	−	0.00962434i
$173$			9.17264e10i			0.591921i	0.955200	+	0.295961i	$0.0956397\pi$
$173$			9.17264e10i			0.591921i	−0.955200	+	0.295961i	$0.904360\pi$
$174$	1.28799e9	+	1.36144e11i	0.00807546	+	0.853596i
$175$	5.45097e9	−	1.91677e11i	0.0332111	−	1.16783i
$176$	−6.50058e9	−	1.71705e11i	−0.0384936	−	1.01676i
$177$		−	4.44488e11i		−	2.55855i
$178$	−1.02775e9	−	1.08636e11i	−0.00575159	−	0.607957i
$179$		−	1.07881e11i		−	0.587059i	−0.955950	−	0.293529i	$-0.905170\pi$
$179$		−	1.07881e11i		−	0.587059i	0.955950	−	0.293529i	$-0.0948298\pi$
$180$	−1.85058e11	+	1.86808e11i	−0.979368	+	0.988628i
$181$	3.43268e11			1.76702			0.883508	−	0.468417i	$-0.155175\pi$
$181$	3.43268e11			1.76702			0.883508	+	0.468417i	$0.155175\pi$
$182$	5.43717e10	−	5.14385e8i	0.272280	−	0.00257591i
$183$	1.11763e11			0.544556
$184$	9.79940e9	+	3.45191e11i	0.0464633	+	1.63671i
$185$	−1.06201e11	−	1.09264e11i	−0.490082	−	0.504217i
$186$	−1.46276e11	+	1.38385e9i	−0.657066	+	0.00621619i
$187$	3.43372e11			1.50161
$188$	9.85463e9	−	1.86476e8i	0.0419615	−	0.000794026i
$189$	1.70628e11			0.707524
$190$	−2.23039e11	+	2.20928e11i	−0.900769	+	0.892243i
$191$			2.33817e10i			0.0919832i	0.998942	+	0.0459916i	$0.0146447\pi$
$191$			2.33817e10i			0.0919832i	−0.998942	+	0.0459916i	$0.985355\pi$
$192$	−4.02856e11	+	2.28913e10i	−1.54399	+	0.0877332i
$193$			2.97973e11i			1.11273i	0.830937	+	0.556366i	$0.187805\pi$
$193$			2.97973e11i			1.11273i	−0.830937	+	0.556366i	$0.812195\pi$
$194$	1.82958e11	−	1.73088e9i	0.665800	−	0.00629881i
$195$	−7.08303e10	−	7.28733e10i	−0.251215	−	0.258461i
$196$	−1.05541e11	+	1.99712e9i	−0.364871	+	0.00690436i
$197$		−	4.56567e11i		−	1.53877i	−0.638785	−	0.769385i	$-0.720563\pi$
$197$		−	4.56567e11i		−	1.53877i	0.638785	−	0.769385i	$-0.279437\pi$
$198$	4.30875e11	−	4.07630e9i	1.41588	−	0.0133949i
$199$		−	1.61572e11i		−	0.517728i	−0.965914	−	0.258864i	$-0.916652\pi$
$199$		−	1.61572e11i		−	0.517728i	0.965914	−	0.258864i	$-0.0833481\pi$
$200$	−3.20000e11	−	1.59651e7i	−1.00000	−	4.98910e-5i
$201$	−2.68945e11			−0.819753
$202$	5.18904e9	+	5.48495e11i	0.0154287	+	1.63086i
$203$	2.22313e11			0.644888
$204$	−1.52555e10	−	8.06200e11i	−0.0431793	−	2.28187i
$205$	1.02037e11	−	9.91766e10i	0.281831	−	0.273930i
$206$	2.25640e9	+	2.38507e11i	0.00608246	+	0.642931i
$207$	−8.65987e11			−2.27855
$208$	−3.43285e9	−	9.06745e10i	−0.00881734	−	0.232899i
$209$	5.14441e11			1.29004
$210$	5.19286e11	+	5.24248e11i	1.27148	+	1.28363i
$211$			1.81757e11i			0.434588i	0.976106	+	0.217294i	$0.0697231\pi$
$211$			1.81757e11i			0.434588i	−0.976106	+	0.217294i	$0.930277\pi$
$212$	2.46476e9	+	1.30254e11i	0.00575567	+	0.304167i
$213$			9.63610e11i			2.19788i
$214$	−2.20016e9	−	2.32562e11i	−0.00490214	−	0.518168i
$215$	−1.67583e11	+	1.62885e11i	−0.364785	+	0.354558i
$216$	−8.08013e9	−	2.84629e11i	−0.0171850	−	0.605355i
$217$			2.38858e11i			0.496410i
$218$	−2.75288e9	−	2.90986e11i	−0.00559119	−	0.591003i
$219$			7.92067e11i			1.57232i
$220$	3.72532e11	+	3.69042e11i	0.722853	+	0.716082i
$221$	1.81329e11			0.343957
$222$	5.86321e11	−	5.54689e9i	1.08735	−	0.0102869i
$223$	1.11110e11			0.201479			0.100740	−	0.994913i	$-0.467879\pi$
$223$	1.11110e11			0.201479			0.100740	+	0.994913i	$0.467879\pi$
$224$	3.11535e10	+	6.58128e11i	0.0552416	+	1.16700i
$225$	2.28115e10	−	8.02141e11i	0.0395586	−	1.39104i
$226$	2.42476e11	−	2.29394e9i	0.411269	−	0.00389082i
$227$	9.00145e11			1.49343			0.746713	−	0.665147i	$-0.231631\pi$
$227$	9.00145e11			1.49343			0.746713	+	0.665147i	$0.231631\pi$
$228$	−2.28559e10	−	1.20785e12i	−0.0370957	−	1.96038i
$229$	−5.43837e11			−0.863558			−0.431779	−	0.901979i	$-0.642114\pi$
$229$	−5.43837e11			−0.863558			−0.431779	+	0.901979i	$0.642114\pi$
$230$	−7.41643e11	−	7.48730e11i	−1.15227	−	1.16328i
$231$		−	1.20918e12i		−	1.83836i
$232$	−1.05277e10	−	3.70845e11i	−0.0156636	−	0.551763i
$233$		−	6.34760e11i		−	0.924336i	−0.886792	−	0.462168i	$-0.847072\pi$
$233$		−	6.34760e11i		−	0.924336i	0.886792	−	0.462168i	$-0.152928\pi$
$234$	2.27538e11	−	2.15262e9i	0.324320	−	0.00306823i
$235$	−2.15695e10	+	2.09648e10i	−0.0300954	+	0.0292517i
$236$	2.29148e10	+	1.21097e12i	0.0313008	+	1.65414i
$237$			1.29563e12i			1.73277i
$238$	−1.31658e12	+	1.24555e10i	−1.72410	+	0.0163109i
$239$		−	9.24284e10i		−	0.118527i	−0.998242	−	0.0592633i	$-0.981125\pi$
$239$		−	9.24284e10i		−	0.118527i	0.998242	−	0.0592633i	$-0.0188752\pi$
$240$	8.49921e11	−	8.91060e11i	1.06739	−	1.11905i
$241$	−9.05993e11			−1.11440			−0.557198	−	0.830379i	$-0.688124\pi$
$241$	−9.05993e11			−1.11440			−0.557198	+	0.830379i	$0.688124\pi$
$242$	−2.77089e8	−	2.92890e10i	−0.000333843	−	0.0352880i
$243$	−1.10938e12			−1.30933
$244$	−3.04488e11	+	5.76174e9i	−0.352063	+	0.00666199i
$245$	2.31004e11	−	2.24528e11i	0.261691	−	0.254355i
$246$	5.18003e9	+	5.47542e11i	0.00574985	+	0.607774i
$247$	2.71667e11			0.295497
$248$	3.98445e11	−	1.13112e10i	0.424727	−	0.0120573i
$249$	−2.66755e12			−2.78686
$250$	7.13065e11	−	6.67242e11i	0.730179	−	0.683256i
$251$		−	1.13681e12i		−	1.14109i	−0.821266	−	0.570546i	$-0.806732\pi$
$251$		−	1.13681e12i		−	1.14109i	0.821266	−	0.570546i	$-0.193268\pi$
$252$	−1.65194e12	+	3.12593e10i	−1.62552	+	0.0307593i
$253$			1.72695e12i			1.66601i
$254$	−1.89044e9	−	1.99824e11i	−0.00178811	−	0.189008i
$255$	1.71511e12	+	1.76458e12i	1.59071	+	1.63659i
$256$	1.09636e12	−	8.31337e10i	0.997137	−	0.0756096i
$257$		−	6.98643e11i		−	0.623146i	−0.950222	−	0.311573i	$-0.899144\pi$
$257$		−	6.98643e11i		−	0.623146i	0.950222	−	0.311573i	$-0.100856\pi$
$258$	−8.50752e9	−	8.99266e11i	−0.00744225	−	0.786665i
$259$		−	9.57416e11i		−	0.821489i
$260$	1.96727e11	+	1.94885e11i	0.165576	+	0.164025i
$261$	9.30345e11			0.768142
$262$	1.83075e12	−	1.73198e10i	1.48293	−	0.0140293i
$263$	4.94717e10			0.0393168			0.0196584	−	0.999807i	$-0.493742\pi$
$263$	4.94717e10			0.0393168			0.0196584	+	0.999807i	$0.493742\pi$
$264$	−2.01706e12	+	5.72611e10i	−1.57290	+	0.0446519i
$265$	−2.77104e11	−	2.85096e11i	−0.212038	−	0.218153i
$266$	−1.97251e12	+	1.86609e10i	−1.48119	+	0.0140128i
$267$	−1.27583e12			−0.940235
$268$	7.32715e11	−	1.38650e10i	0.529982	−	0.0100287i
$269$	1.80389e12			1.28070			0.640351	−	0.768083i	$-0.278789\pi$
$269$	1.80389e12			1.28070			0.640351	+	0.768083i	$0.278789\pi$
$270$	6.11524e11	+	6.17368e11i	0.426182	+	0.430254i
$271$			2.03271e12i			1.39069i	0.718677	+	0.695344i	$0.244748\pi$
$271$			2.03271e12i			1.39069i	−0.718677	+	0.695344i	$0.755252\pi$
$272$	8.31243e10	+	2.19563e12i	0.0558320	+	1.47474i
$273$		−	6.38547e11i		−	0.421095i
$274$	−3.98127e11	+	3.76649e9i	−0.257792	+	0.00243884i
$275$	−1.59963e12	−	4.54906e10i	−1.01708	−	0.0289240i
$276$	4.05469e12	−	7.67257e10i	2.53170	−	0.0479066i
$277$		−	9.87952e11i		−	0.605811i	−0.953021	−	0.302905i	$-0.902043\pi$
$277$		−	9.87952e11i		−	0.605811i	0.953021	−	0.302905i	$-0.0979566\pi$
$278$	1.24275e11	−	1.17570e9i	0.0748444	−	0.000708066i
$279$			9.99584e11i			0.591287i
$280$	−1.44177e12	−	1.40149e12i	−0.837735	−	0.814332i
$281$	2.84398e12			1.62328			0.811642	−	0.584155i	$-0.198574\pi$
$281$	2.84398e12			1.62328			0.811642	+	0.584155i	$0.198574\pi$
$282$	−1.09500e9	−	1.15744e11i	−0.000614000	−	0.0649013i
$283$	−9.25646e10			−0.0509932			−0.0254966	−	0.999675i	$-0.508117\pi$
$283$	−9.25646e10			−0.0509932			−0.0254966	+	0.999675i	$0.508117\pi$
$284$	−4.96772e10	−	2.62527e12i	−0.0268884	−	1.42096i
$285$	2.56959e12	+	2.64371e12i	1.36660	+	1.40601i
$286$	−4.29275e9	−	4.53755e11i	−0.00224339	−	0.237132i
$287$	8.94093e11			0.459170
$288$	1.30373e11	+	2.75417e12i	0.0657997	+	1.39004i
$289$	−2.37477e12			−1.17796
$290$	7.96761e11	+	8.04374e11i	0.388452	+	0.392164i
$291$		−	2.14868e12i		−	1.02969i
$292$	−4.08336e10	−	2.15791e12i	−0.0192355	−	1.01653i
$293$		−	2.24927e12i		−	1.04161i	−0.853677	−	0.520803i	$-0.825633\pi$
$293$		−	2.24927e12i		−	1.04161i	0.853677	−	0.520803i	$-0.174367\pi$
$294$	1.17272e10	+	1.23959e12i	0.00533896	+	0.564342i
$295$	−2.57622e12	−	2.65052e12i	−1.15312	−	1.18637i
$296$	−1.59709e12	+	4.53387e10i	−0.702863	+	0.0199531i
$297$		−	1.42396e12i		−	0.616192i
$298$	1.52913e10	+	1.61633e12i	0.00650675	+	0.687780i
$299$			9.11971e11i			0.381615i
$300$	−3.57380e10	+	3.75777e12i	−0.0147070	+	1.54641i
$301$	−1.46843e12			−0.594321
$302$	−1.76376e12	+	1.66861e10i	−0.702110	+	0.00664232i
$303$	6.44158e12			2.52220
$304$	1.24537e11	+	3.28950e12i	0.0479658	+	1.26696i
$305$	6.66453e11	−	6.47769e11i	0.252505	−	0.245426i
$306$	−5.50969e12	+	5.21245e10i	−2.05362	+	0.0194283i
$307$	2.31537e11			0.0849040			0.0424520	−	0.999099i	$-0.486483\pi$
$307$	2.31537e11			0.0849040			0.0424520	+	0.999099i	$0.486483\pi$
$308$	6.23371e10	+	3.29430e12i	0.0224902	+	1.18853i
$309$	2.80105e12			0.994324
$310$	−8.64238e11	+	8.56058e11i	−0.301873	+	0.299016i
$311$			3.78881e12i			1.30227i	0.758962	+	0.651135i	$0.225707\pi$
$311$			3.78881e12i			1.30227i	−0.758962	+	0.651135i	$0.774293\pi$
$312$	−1.06518e12	+	3.02386e10i	−0.360287	+	0.0102279i
$313$		−	2.24116e12i		−	0.746022i	−0.927827	−	0.373011i	$-0.878325\pi$
$313$		−	2.24116e12i		−	0.746022i	0.927827	−	0.373011i	$-0.121675\pi$
$314$	−2.86742e12	+	2.71273e10i	−0.939384	+	0.00888705i
$315$	3.61572e12	−	3.51436e12i	1.16585	−	1.13316i
$316$	−6.67939e10	−	3.52983e12i	−0.0211983	−	1.12026i
$317$			1.42968e12i			0.446623i	0.974747	+	0.223312i	$0.0716868\pi$
$317$			1.42968e12i			0.446623i	−0.974747	+	0.223312i	$0.928313\pi$
$318$	1.52986e12	−	1.44732e10i	0.470452	−	0.00445071i
$319$		−	1.85529e12i		−	0.561641i
$320$	−2.26959e12	+	2.47143e12i	−0.676391	+	0.736542i
$321$	−2.73124e12			−0.801372
$322$	−6.26436e10	−	6.62158e12i	−0.0180966	−	1.91286i
$323$	−6.57826e12			−1.87111
$324$	1.62446e12	−	3.07392e10i	0.454971	−	0.00860929i
$325$	−8.44735e11	−	2.40228e10i	−0.232972	−	0.00662532i
$326$	−3.52492e10	−	3.72593e12i	−0.00957329	−	1.01192i
$327$	−3.41737e12			−0.914015
$328$	−4.23400e10	−	1.49146e12i	−0.0111527	−	0.392864i
$329$	−1.89001e11			−0.0490326
$330$	4.37507e12	−	4.33366e12i	1.11793	−	1.10735i
$331$			6.11524e12i			1.53912i	0.638572	+	0.769562i	$0.279526\pi$
$331$			6.11524e12i			1.53912i	−0.638572	+	0.769562i	$0.720474\pi$
$332$	7.26748e12	−	1.37521e11i	1.80175	−	0.0340939i
$333$		−	4.00664e12i		−	0.978497i
$334$	−2.82464e10	−	2.98571e12i	−0.00679564	−	0.718316i
$335$	−1.60374e12	+	1.55878e12i	−0.380111	+	0.369455i
$336$	7.73189e12	−	2.92722e11i	1.80547	−	0.0683531i
$337$		−	9.97821e11i		−	0.229564i	−0.993391	−	0.114782i	$-0.963383\pi$
$337$		−	9.97821e11i		−	0.229564i	0.993391	−	0.114782i	$-0.0366169\pi$
$338$	3.94660e10	+	4.17165e12i	0.00894622	+	0.945638i
$339$		−	2.84766e12i		−	0.636047i
$340$	−4.76364e12	−	4.71902e12i	−1.04844	−	1.03862i
$341$	1.99337e12			0.432330
$342$	−8.25464e12	+	7.80931e10i	−1.76428	+	0.0166910i
$343$	−3.52244e12			−0.741948
$344$	6.95380e10	+	2.44953e12i	0.0144354	+	0.508499i
$345$	−8.87476e12	+	8.62597e12i	−1.81577	+	1.76487i
$346$	−2.93511e12	+	2.77677e10i	−0.591895	+	0.00559963i
$347$	5.29192e12			1.05188			0.525940	−	0.850522i	$-0.323714\pi$
$347$	5.29192e12			1.05188			0.525940	+	0.850522i	$0.323714\pi$
$348$	−4.35603e12	+	8.24279e10i	−0.853482	+	0.0161502i
$349$	3.21483e11			0.0620912			0.0310456	−	0.999518i	$-0.490116\pi$
$349$	3.21483e11			0.0620912			0.0310456	+	0.999518i	$0.490116\pi$
$350$	6.13505e12	+	1.16398e11i	1.16809	+	0.0221618i
$351$		−	7.51969e11i		−	0.141145i
$352$	5.49235e12	−	2.59988e11i	1.01635	−	0.0481106i
$353$		−	6.41611e12i		−	1.17057i	−0.810827	−	0.585286i	$-0.800982\pi$
$353$		−	6.41611e12i		−	1.17057i	0.810827	−	0.585286i	$-0.199018\pi$
$354$	1.42230e13	−	1.34557e11i	2.55844	−	0.0242041i
$355$	5.58501e12	+	5.74609e12i	0.990563	+	1.01913i
$356$	3.47588e12	−	6.57731e10i	0.607876	−	0.0115027i
$357$			1.54620e13i			2.66640i
$358$	3.45205e12	−	3.26582e10i	0.587032	−	0.00555363i
$359$		−	4.19883e12i		−	0.704136i	−0.935975	−	0.352068i	$-0.885479\pi$
$359$		−	4.19883e12i		−	0.704136i	0.935975	−	0.352068i	$-0.114521\pi$
$360$	−6.03361e12	−	5.86505e12i	−0.997848	−	0.969971i
$361$	−3.72452e12			−0.607483
$362$	1.03915e11	+	1.09841e13i	0.0167161	+	1.76694i
$363$	−3.43973e11			−0.0545747
$364$	3.29191e10	+	1.73966e12i	0.00515159	+	0.272244i
$365$	4.59076e12	+	4.72317e12i	0.708631	+	0.729069i
$366$	3.38332e10	+	3.57625e12i	0.00515155	+	0.544532i
$367$	2.48261e12			0.372888			0.186444	−	0.982466i	$-0.440304\pi$
$367$	2.48261e12			0.372888			0.186444	+	0.982466i	$0.440304\pi$
$368$	−1.10427e13	+	4.18064e11i	−1.63619	+	0.0619446i
$369$	3.74165e12			0.546929
$370$	3.46413e12	−	3.43134e12i	0.499558	−	0.494830i
$371$		−	2.49814e12i		−	0.355424i
$372$	−8.85624e10	−	4.68021e12i	−0.0124318	−	0.656978i
$373$			8.44089e12i			1.16908i	0.811365	+	0.584539i	$0.198725\pi$
$373$			8.44089e12i			1.16908i	−0.811365	+	0.584539i	$0.801275\pi$
$374$	1.03946e11	+	1.09874e13i	0.0142053	+	1.50154i
$375$	−7.75624e12	−	8.44769e12i	−1.04591	−	1.13915i
$376$	8.95020e9	+	3.15278e11i	0.00119095	+	0.0419521i
$377$		−	9.79747e11i		−	0.128649i
$378$	5.16530e10	+	5.45985e12i	0.00669324	+	0.707492i
$379$			5.11317e12i			0.653874i	0.945046	+	0.326937i	$0.106016\pi$
$379$			5.11317e12i			0.653874i	−0.945046	+	0.326937i	$0.893984\pi$
$380$	−7.13691e12	−	7.07006e12i	−0.900725	−	0.892288i
$381$	−2.34676e12			−0.292310
$382$	−7.48180e11	+	7.07816e9i	−0.0919791	+	0.000870169i
$383$	8.87564e12			1.07698			0.538488	−	0.842633i	$-0.318996\pi$
$383$	8.87564e12			1.07698			0.538488	+	0.842633i	$0.318996\pi$
$384$	−8.54442e11	−	1.28839e13i	−0.102336	−	1.54309i
$385$	−7.00831e12	−	7.21045e12i	−0.828533	−	0.852430i
$386$	−9.53472e12	+	9.02033e10i	−1.11268	+	0.0105266i
$387$	−6.14517e12			−0.707911
$388$	1.10771e11	+	5.85388e12i	0.0125971	+	0.665710i
$389$	1.08604e13			1.21927			0.609635	−	0.792683i	$-0.291316\pi$
$389$	1.08604e13			1.21927			0.609635	+	0.792683i	$0.291316\pi$
$390$	2.31040e12	−	2.28853e12i	0.256073	−	0.253649i
$391$		−	2.20828e13i		−	2.41641i
$392$	−9.58545e10	−	3.37655e12i	−0.0103558	−	0.364790i
$393$		−	2.15005e13i		−	2.29343i
$394$	1.46095e13	−	1.38213e11i	1.53870	−	0.0145569i
$395$	7.50938e12	+	7.72597e12i	0.780941	+	0.803466i
$396$	2.60871e11	+	1.37861e13i	0.0267886	+	1.41569i
$397$			4.51332e12i			0.457660i	0.973466	+	0.228830i	$0.0734900\pi$
$397$			4.51332e12i			0.457660i	−0.973466	+	0.228830i	$0.926510\pi$
$398$	5.17008e12	−	4.89116e10i	0.517705	−	0.00489775i
$399$			2.31653e13i			2.29073i
$400$	−9.63605e10	−	1.02395e13i	−0.00941020	−	0.999956i
$401$	−4.32327e12			−0.416956			−0.208478	−	0.978027i	$-0.566851\pi$
$401$	−4.32327e12			−0.416956			−0.208478	+	0.978027i	$0.566851\pi$
$402$	−8.14158e10	−	8.60585e12i	−0.00775494	−	0.819717i
$403$	1.05266e12			0.0990294
$404$	−1.75495e13	+	3.32084e11i	−1.63064	+	0.0308561i
$405$	−3.55556e12	+	3.45589e12i	−0.326312	+	0.317164i
$406$	6.72991e10	+	7.11369e12i	0.00610070	+	0.644859i
$407$	−7.99003e12			−0.715446
$408$	2.57926e13	−	7.32209e11i	2.28136	−	0.0647641i
$409$	6.11557e11			0.0534343			0.0267172	−	0.999643i	$-0.491495\pi$
$409$	6.11557e11			0.0534343			0.0267172	+	0.999643i	$0.491495\pi$
$410$	3.20440e12	+	3.23502e12i	0.276584	+	0.279227i
$411$			4.67564e12i			0.398687i
$412$	−7.63119e12	+	1.44403e11i	−0.642845	+	0.0121644i
$413$		−	2.32250e13i		−	1.93289i
$414$	−2.62154e11	−	2.77103e13i	−0.0215553	−	2.27845i
$415$	−1.59068e13	+	1.54609e13i	−1.29224	+	1.25601i
$416$	2.90041e12	−	1.37295e11i	0.232806	−	0.0110202i
$417$		−	1.45950e12i		−	0.115750i
$418$	1.55733e11	+	1.64614e13i	0.0122039	+	1.28999i
$419$		−	1.05743e13i		−	0.818808i	−0.912353	−	0.409404i	$-0.865737\pi$
$419$		−	1.05743e13i		−	0.818808i	0.912353	−	0.409404i	$-0.134263\pi$
$420$	−1.66180e13	+	1.67751e13i	−1.27155	+	1.28357i
$421$	6.20493e12			0.469166			0.234583	−	0.972096i	$-0.424628\pi$
$421$	6.20493e12			0.469166			0.234583	+	0.972096i	$0.424628\pi$
$422$	−5.81595e12	+	5.50219e10i	−0.434569	+	0.00411124i
$423$	−7.90942e11			−0.0584040
$424$	−4.16720e12	+	1.18300e11i	−0.304099	+	0.00863287i
$425$	2.04548e13	+	5.81698e11i	1.47520	+	0.0419520i
$426$	−3.08341e13	+	2.91707e11i	−2.19778	+	0.0207921i
$427$	5.83975e12			0.411391
$428$	7.44100e12	−	1.40804e11i	0.518098	−	0.00980383i
$429$	−5.32894e12			−0.366737
$430$	−5.26281e12	−	5.31310e12i	−0.357993	−	0.361414i
$431$		−	3.75598e12i		−	0.252544i	−0.991996	−	0.126272i	$-0.959699\pi$
$431$		−	3.75598e12i		−	0.252544i	0.991996	−	0.126272i	$-0.0403011\pi$
$432$	9.10526e12	−	3.44716e11i	0.605165	−	0.0229109i
$433$			2.25078e13i			1.47874i	0.673297	+	0.739372i	$0.264878\pi$
$433$			2.25078e13i			1.47874i	−0.673297	+	0.739372i	$0.735122\pi$
$434$	−7.64311e12	+	7.23078e10i	−0.496388	+	0.00469609i
$435$	9.53432e12	−	9.26704e12i	0.612130	−	0.594970i
$436$	9.31030e12	−	1.76176e11i	0.590924	−	0.0111819i
$437$		−	3.30846e13i		−	2.07596i
$438$	−2.53450e13	+	2.39777e11i	−1.57225	+	0.0148743i
$439$		−	1.93911e13i		−	1.18927i	−0.803997	−	0.594633i	$-0.797297\pi$
$439$		−	1.93911e13i		−	1.18927i	0.803997	−	0.594633i	$-0.202703\pi$
$440$	−1.16961e13	+	1.20322e13i	−0.709212	+	0.729595i
$441$	8.47080e12			0.507845
$442$	5.48923e10	+	5.80225e12i	0.00325387	+	0.343942i
$443$	−3.53441e12			−0.207157			−0.103578	−	0.994621i	$-0.533029\pi$
$443$	−3.53441e12			−0.207157			−0.103578	+	0.994621i	$0.533029\pi$
$444$	3.54985e11	+	1.87597e13i	0.0205729	+	1.08721i
$445$	−7.60789e12	+	7.39461e12i	−0.435978	+	0.423755i
$446$	3.36357e10	+	3.55537e12i	0.00190601	+	0.201470i
$447$	1.89824e13			1.06369
$448$	−2.10497e13	+	1.19610e12i	−1.16642	+	0.0662790i
$449$	−3.48899e12			−0.191192			−0.0955958	−	0.995420i	$-0.530476\pi$
$449$	−3.48899e12			−0.191192			−0.0955958	+	0.995420i	$0.530476\pi$
$450$	2.56743e13	+	4.87109e11i	1.39135	+	0.0263975i
$451$		−	7.46158e12i		−	0.399897i
$452$	1.46806e11	+	7.75818e12i	0.00778128	+	0.411214i
$453$			2.07138e13i			1.08585i
$454$	2.72495e11	+	2.88034e13i	0.0141279	+	1.49336i
$455$	−3.70097e12	−	3.80771e12i	−0.189783	−	0.195257i
$456$	3.86426e13	−	1.09700e12i	1.95994	−	0.0556394i
$457$			3.56649e12i			0.178921i	0.995990	+	0.0894603i	$0.0285142\pi$
$457$			3.56649e12i			0.178921i	−0.995990	+	0.0894603i	$0.971486\pi$
$458$	−1.64632e11	−	1.74020e13i	−0.00816934	−	0.863519i
$459$			1.82085e13i			0.893738i
$460$	2.37338e13	−	2.39582e13i	1.15233	−	1.16323i
$461$	2.11360e13			1.01512			0.507562	−	0.861615i	$-0.330547\pi$
$461$	2.11360e13			1.01512			0.507562	+	0.861615i	$0.330547\pi$
$462$	3.86920e13	−	3.66047e11i	1.83828	−	0.0173911i
$463$	2.00573e13			0.942686			0.471343	−	0.881950i	$-0.343769\pi$
$463$	2.00573e13			0.942686			0.471343	+	0.881950i	$0.343769\pi$
$464$	1.18633e13	−	4.49134e11i	0.551591	−	0.0208827i
$465$	9.95672e12	+	1.02439e13i	0.457985	+	0.471195i
$466$	2.03114e13	−	1.92156e11i	0.924295	−	0.00874431i
$467$	−1.63231e13			−0.734884			−0.367442	−	0.930046i	$-0.619766\pi$
$467$	−1.63231e13			−0.734884			−0.367442	+	0.930046i	$0.619766\pi$
$468$	1.37762e11	+	7.28022e12i	0.00613620	+	0.324277i
$469$	−1.40527e13			−0.619292
$470$	−6.77374e11	−	6.83846e11i	−0.0295351	−	0.0298174i
$471$			3.36753e13i			1.45280i
$472$	−3.87423e13	+	1.09983e12i	−1.65377	+	0.0469478i
$473$			1.22547e13i			0.517602i
$474$	−4.14584e13	+	3.92217e11i	−1.73269	+	0.0163921i
$475$	3.06454e13	+	8.71502e11i	1.26735	+	0.0360413i
$476$	−7.97117e11	−	4.21249e13i	−0.0326203	−	1.72387i
$477$		−	1.04543e13i		−	0.423354i
$478$	2.95758e12	−	2.79802e10i	0.118521	−	0.00112127i
$479$		−	1.92868e13i		−	0.764863i	−0.923984	−	0.382431i	$-0.875087\pi$
$479$		−	1.92868e13i		−	0.764863i	0.923984	−	0.382431i	$-0.124913\pi$
$480$	2.87699e13	+	2.69265e13i	1.12910	+	1.05675i
$481$	−4.21940e12			−0.163880
$482$	−2.74265e11	−	2.89905e13i	−0.0105423	−	1.11435i
$483$	−7.77645e13			−2.95833
$484$	9.37122e11	−	1.77329e10i	0.0352833	−	0.000667656i
$485$	−1.24536e13	−	1.28128e13i	−0.464073	−	0.477458i
$486$	−3.35834e11	−	3.54985e13i	−0.0123864	−	1.30927i
$487$	−1.78624e13			−0.652071			−0.326035	−	0.945358i	$-0.605713\pi$
$487$	−1.78624e13			−0.652071			−0.326035	+	0.945358i	$0.605713\pi$
$488$	−2.76543e11	−	9.74143e12i	−0.00999225	−	0.351984i
$489$	−4.37577e13			−1.56498
$490$	7.25451e12	+	7.32383e12i	0.256819	+	0.259273i
$491$			3.49899e13i			1.22613i	0.790034	+	0.613063i	$0.210063\pi$
$491$			3.49899e13i			1.22613i	−0.790034	+	0.613063i	$0.789937\pi$
$492$	−1.75190e13	+	3.31507e11i	−0.607692	+	0.0114992i
$493$			2.37240e13i			0.814616i
$494$	8.22399e10	+	8.69296e12i	0.00279543	+	0.295483i
$495$	−2.93287e13	−	3.01747e13i	−0.986887	−	1.01535i
$496$	4.82560e11	+	1.27462e13i	0.0160747	+	0.424594i
$497$			5.03498e13i			1.66041i
$498$	−8.07528e11	−	8.53577e13i	−0.0263640	−	2.78674i
$499$		−	2.40650e13i		−	0.777828i	−0.921274	−	0.388914i	$-0.872850\pi$
$499$		−	2.40650e13i		−	0.777828i	0.921274	−	0.388914i	$-0.127150\pi$
$500$	2.15667e13	+	2.26151e13i	0.690133	+	0.723683i
$501$	−3.50645e13			−1.11091
$502$	3.63764e13	−	3.44139e11i	1.14104	−	0.0107948i
$503$	5.61224e13			1.74299			0.871497	−	0.490401i	$-0.163150\pi$
$503$	5.61224e13			1.74299			0.871497	+	0.490401i	$0.163150\pi$
$504$	−1.50033e12	−	5.28503e13i	−0.0461355	−	1.62516i
$505$	3.84117e13	−	3.73349e13i	1.16952	−	1.13673i
$506$	−5.52598e13	+	5.22787e11i	−1.66593	+	0.0157606i
$507$	4.89923e13			1.46247
$508$	6.39352e12	−	1.20983e11i	0.188982	−	0.00357606i
$509$	−5.17336e13			−1.51420			−0.757100	−	0.653298i	$-0.773385\pi$
$509$	−5.17336e13			−1.51420			−0.757100	+	0.653298i	$0.773385\pi$
$510$	−5.59449e13	+	5.54154e13i	−1.62147	+	1.60613i
$511$			4.13864e13i			1.18783i
$512$	2.99205e12	+	3.50569e13i	0.0850393	+	0.996378i
$513$			2.72800e13i			0.767817i
$514$	2.23556e13	−	2.11495e11i	0.623118	−	0.00589502i
$515$	1.67029e13	−	1.62346e13i	0.461058	−	0.448133i
$516$	2.87727e13	−	5.44457e11i	0.786559	−	0.0148838i
$517$			1.57729e12i			0.0427031i
$518$	3.06359e13	−	2.89832e11i	0.821452	−	0.00777136i
$519$			3.44703e13i			0.915394i
$520$	−6.17648e12	+	6.35399e12i	−0.162452	+	0.167121i
$521$	−4.68852e13			−1.22137			−0.610684	−	0.791874i	$-0.709106\pi$
$521$	−4.68852e13			−1.22137			−0.610684	+	0.791874i	$0.709106\pi$
$522$	2.81637e11	+	2.97697e13i	0.00726670	+	0.768108i
$523$	−2.65731e13			−0.679100			−0.339550	−	0.940588i	$-0.610275\pi$
$523$	−2.65731e13			−0.679100			−0.339550	+	0.940588i	$0.610275\pi$
$524$	1.10842e12	+	5.85760e13i	0.0280574	+	1.48273i
$525$	2.04844e12	−	7.20313e13i	0.0513603	−	1.80603i
$526$	1.49762e10	+	1.58302e12i	0.000371941	+	0.0393151i
$527$	−2.54896e13			−0.627061
$528$	−2.44288e12	−	6.45258e13i	−0.0595296	−	1.57240i
$529$	6.96365e13			1.68097
$530$	9.03878e12	−	8.95323e12i	0.216138	−	0.214092i
$531$		−	9.71933e13i		−	2.30231i
$532$	−1.19425e12	−	6.31117e13i	−0.0280243	−	1.48099i
$533$		−	3.94033e12i		−	0.0916002i
$534$	−3.86223e11	−	4.08247e13i	−0.00889471	−	0.940193i
$535$	−1.62866e13	+	1.58300e13i	−0.371588	+	0.361171i
$536$	6.65469e11	+	2.34416e13i	0.0150419	+	0.529864i
$537$		−	4.05412e13i		−	0.907874i
$538$	5.46078e11	+	5.77218e13i	0.0121156	+	1.28064i
$539$		−	1.68924e13i		−	0.371320i
$540$	−1.95698e13	+	1.97548e13i	−0.426203	+	0.430233i
$541$	6.66188e13			1.43751			0.718755	−	0.695264i	$-0.244712\pi$
$541$	6.66188e13			1.43751			0.718755	+	0.695264i	$0.244712\pi$
$542$	−6.50440e13	+	6.15349e11i	−1.39063	+	0.0131560i
$543$	1.28998e14			2.73265
$544$	−7.02318e13	+	3.32453e12i	−1.47414	+	0.0697807i
$545$	−2.03781e13	+	1.98068e13i	−0.423819	+	0.411938i
$546$	2.04326e13	−	1.93303e11i	0.421076	−	0.00398359i
$547$	−2.28605e13			−0.466819			−0.233410	−	0.972378i	$-0.574988\pi$
$547$	−2.28605e13			−0.466819			−0.233410	+	0.972378i	$0.574988\pi$
$548$	−2.41044e11	−	1.27384e13i	−0.00487746	−	0.257757i
$549$	2.44385e13			0.490018
$550$	9.71390e11	−	5.11996e13i	0.0193010	−	1.01731i
$551$			3.55434e13i			0.699844i
$552$	3.68256e12	+	1.29721e14i	0.0718546	+	2.53113i
$553$			6.76983e13i			1.30904i
$554$	3.16130e13	−	2.99076e11i	0.605784	−	0.00573103i
$555$	−3.99096e13	−	4.10607e13i	−0.757901	−	0.779761i
$556$	7.52417e10	+	3.97626e12i	0.00141607	+	0.0748343i
$557$		−	1.22463e12i		−	0.0228417i	−0.999935	−	0.0114208i	$-0.996365\pi$
$557$		−	1.22463e12i		−	0.0228417i	0.999935	−	0.0114208i	$-0.00363545\pi$
$558$	−3.19853e13	+	3.02597e11i	−0.591261	+	0.00559363i
$559$			6.47148e12i			0.118562i
$560$	4.44094e13	−	4.65590e13i	0.806370	−	0.845402i
$561$	1.29037e14			2.32220
$562$	8.60937e11	+	9.10032e13i	0.0153564	+	1.62321i
$563$	−7.79602e13			−1.37826			−0.689130	−	0.724638i	$-0.742007\pi$
$563$	−7.79602e13			−1.37826			−0.689130	+	0.724638i	$0.742007\pi$
$564$	3.70332e12	−	7.00768e10i	0.0648926	−	0.00122794i
$565$	−1.65048e13	−	1.69808e13i	−0.286661	−	0.294929i
$566$	−2.80214e10	−	2.96193e12i	−0.000482401	−	0.0509910i
$567$	−3.11554e13			−0.531640
$568$	8.39897e13	−	2.38433e12i	1.42064	−	0.0403296i
$569$	7.32445e13			1.22804			0.614021	−	0.789290i	$-0.289551\pi$
$569$	7.32445e13			1.22804			0.614021	+	0.789290i	$0.289551\pi$
$570$	−8.38170e13	+	8.30236e13i	−1.39302	+	1.37984i
$571$			2.41704e13i			0.398202i	0.979979	+	0.199101i	$0.0638021\pi$
$571$			2.41704e13i			0.398202i	−0.979979	+	0.199101i	$0.936198\pi$
$572$	1.45182e13	−	2.74724e11i	0.237101	−	0.00448659i
$573$			8.78670e12i			0.142250i
$574$	2.70663e11	+	2.86097e13i	0.00434379	+	0.459149i
$575$	−2.92558e12	+	1.02875e14i	−0.0465450	+	1.63670i
$576$	−8.80899e13	+	5.00548e12i	−1.38936	+	0.0789466i
$577$		−	8.99224e13i		−	1.40601i	−0.711184	−	0.703006i	$-0.751841\pi$
$577$		−	8.99224e13i		−	1.40601i	0.711184	−	0.703006i	$-0.248159\pi$
$578$	−7.18897e11	−	7.59892e13i	−0.0111436	−	1.17791i
$579$			1.11977e14i			1.72082i
$580$	−2.54976e13	+	2.57387e13i	−0.388472	+	0.392145i
$581$	−1.39382e14			−2.10537
$582$	6.87547e13	−	6.50455e11i	1.02965	−	0.00974098i
$583$	−2.08480e13			−0.309543
$584$	6.90377e13	−	1.95987e12i	1.01630	−	0.0288511i
$585$	−1.54880e13	−	1.59347e13i	−0.226056	−	0.232576i
$586$	7.19734e13	−	6.80906e11i	1.04156	−	0.00985369i
$587$	6.12391e13			0.878695			0.439347	−	0.898317i	$-0.355210\pi$
$587$	6.12391e13			0.878695			0.439347	+	0.898317i	$0.355210\pi$
$588$	−3.96616e13	+	7.50506e11i	−0.564266	+	0.0106774i
$589$	−3.81886e13			−0.538713
$590$	8.40331e13	−	8.32377e13i	1.17541	−	1.16429i
$591$		−	1.71576e14i		−	2.37968i
$592$	−1.93425e12	−	5.10909e13i	−0.0266014	−	0.702643i
$593$			6.82796e13i			0.931145i	0.885010	+	0.465573i	$0.154152\pi$
$593$			6.82796e13i			0.931145i	−0.885010	+	0.465573i	$0.845848\pi$
$594$	4.55647e13	−	4.31065e11i	0.616164	−	0.00582923i
$595$	8.96168e13	+	9.22015e13i	1.20172	+	1.23638i
$596$	−5.17157e13	+	9.78602e11i	−0.687688	+	0.0130129i
$597$		−	6.07180e13i		−	0.800655i
$598$	−2.91818e13	+	2.76074e11i	−0.381598	+	0.00361011i
$599$		−	1.28055e14i		−	1.66059i	−0.557320	−	0.830297i	$-0.688171\pi$
$599$		−	1.28055e14i		−	1.66059i	0.557320	−	0.830297i	$-0.311829\pi$
$600$	−1.20254e14	−	5.99960e9i	−1.54648	−	7.71554e-5i
$601$	2.79462e13			0.356410			0.178205	−	0.983993i	$-0.442971\pi$
$601$	2.79462e13			0.356410			0.178205	+	0.983993i	$0.442971\pi$
$602$	−4.44528e11	−	4.69877e13i	−0.00562233	−	0.594295i
$603$	−5.88084e13			−0.737654
$604$	−1.06786e12	−	5.64328e13i	−0.0132840	−	0.702015i
$605$	−2.05114e12	+	1.99364e12i	−0.0253057	+	0.0245963i
$606$	1.95001e12	+	2.06121e14i	0.0238602	+	2.52209i
$607$	−3.52260e13			−0.427484			−0.213742	−	0.976890i	$-0.568565\pi$
$607$	−3.52260e13			−0.427484			−0.213742	+	0.976890i	$0.568565\pi$
$608$	−1.05222e14	+	4.98082e12i	−1.26645	+	0.0599492i
$609$	8.35439e13			0.997305
$610$	2.09294e13	+	2.11294e13i	0.247804	+	0.250172i
$611$			8.32941e11i			0.00978156i
$612$	−3.33582e12	−	1.76286e14i	−0.0388548	−	2.05334i
$613$		−	1.16497e14i		−	1.34590i	−0.739688	−	0.672950i	$-0.765027\pi$
$613$		−	1.16497e14i		−	1.34590i	0.739688	−	0.672950i	$-0.234973\pi$
$614$	7.00915e10	+	7.40885e12i	0.000803200	+	0.0849002i
$615$	3.83450e13	−	3.72700e13i	0.435846	−	0.423627i
$616$	−1.05394e14	+	2.99196e12i	−1.18826	+	0.0337328i
$617$			6.43868e13i			0.720064i	0.932940	+	0.360032i	$0.117234\pi$
$617$			6.43868e13i			0.720064i	−0.932940	+	0.360032i	$0.882766\pi$
$618$	8.47941e11	+	8.96295e13i	0.00940639	+	0.994279i
$619$		−	9.70473e13i		−	1.06790i	−0.845516	−	0.533950i	$-0.820707\pi$
$619$		−	9.70473e13i		−	1.06790i	0.845516	−	0.533950i	$-0.179293\pi$
$620$	−2.76543e13	−	2.73952e13i	−0.301859	−	0.299031i
$621$	−9.15774e13			−0.991586
$622$	−1.21237e14	+	1.14696e12i	−1.30221	+	0.0123196i
$623$	−6.66636e13			−0.710311
$624$	−1.29004e12	−	3.40750e13i	−0.0136358	−	0.360174i
$625$	−9.52133e13	−	5.41978e12i	−0.998384	−	0.0568305i
$626$	7.17140e13	−	6.78451e11i	0.745989	−	0.00705744i
$627$	1.93324e14			1.99502
$628$	−1.73607e12	−	9.17451e13i	−0.0177733	−	0.939257i
$629$	1.02170e14			1.03770
$630$	1.13549e14	+	1.14634e14i	1.14414	+	1.15508i
$631$		−	3.20145e13i		−	0.320037i	−0.987114	−	0.160019i	$-0.948845\pi$
$631$		−	3.20145e13i		−	0.320037i	0.987114	−	0.160019i	$-0.0511554\pi$
$632$	1.12929e14	−	3.20587e12i	1.12001	−	0.0317951i
$633$			6.83031e13i			0.672082i
$634$	−4.57476e13	+	4.32796e11i	−0.446603	+	0.00422510i
$635$	−1.39939e13	+	1.36016e13i	−0.135541	+	0.131741i
$636$	9.26245e11	+	4.89488e13i	0.00890103	+	0.470388i
$637$		−	8.92060e12i		−	0.0850544i
$638$	5.93667e13	−	5.61639e11i	0.561616	−	0.00531317i
$639$			2.10706e14i			1.97776i
$640$	−7.97692e13	−	7.18756e13i	−0.742908	−	0.669393i
$641$	−1.25436e14			−1.15913			−0.579566	−	0.814926i	$-0.696778\pi$
$641$	−1.25436e14			−1.15913			−0.579566	+	0.814926i	$0.696778\pi$
$642$	−8.26808e11	−	8.73957e13i	−0.00758105	−	0.801336i
$643$	6.91453e13			0.629083			0.314542	−	0.949244i	$-0.398149\pi$
$643$	6.91453e13			0.629083			0.314542	+	0.949244i	$0.398149\pi$
$644$	2.11862e14	−	4.00901e12i	1.91260	−	0.0361916i
$645$	−6.29766e13	+	6.12111e13i	−0.564132	+	0.548317i
$646$	−1.99139e12	−	2.10495e14i	−0.0177008	−	1.87102i
$647$	−1.38085e14			−1.21794			−0.608971	−	0.793193i	$-0.708417\pi$
$647$	−1.38085e14			−1.21794			−0.608971	+	0.793193i	$0.708417\pi$
$648$	1.47537e12	+	5.19711e13i	0.0129130	+	0.454869i
$649$	−1.93823e14			−1.68338
$650$	5.12974e11	−	2.70376e13i	0.00442108	−	0.233024i
$651$			8.97615e13i			0.767688i
$652$	1.19214e14	−	2.25585e12i	1.01179	−	0.0191457i
$653$			1.70786e14i			1.43842i	0.694792	+	0.719211i	$0.255497\pi$
$653$			1.70786e14i			1.43842i	−0.694792	+	0.719211i	$0.744503\pi$
$654$	−1.03452e12	−	1.09351e14i	−0.00864666	−	0.913974i
$655$	−1.24615e14	−	1.28209e14i	−1.03363	−	1.06344i
$656$	4.77118e13	−	1.80632e12i	0.392741	−	0.0148688i
$657$			1.73196e14i			1.41485i
$658$	−5.72150e10	−	6.04777e12i	−0.000463853	−	0.0490304i
$659$			1.58743e14i			1.27722i	0.769530	+	0.638611i	$0.220491\pi$
$659$			1.58743e14i			1.27722i	−0.769530	+	0.638611i	$0.779509\pi$
$660$	1.39995e14	+	1.38684e14i	1.11788	+	1.10741i
$661$	−4.27414e13			−0.338720			−0.169360	−	0.985554i	$-0.554170\pi$
$661$	−4.27414e13			−0.338720			−0.169360	+	0.985554i	$0.554170\pi$
$662$	−1.95679e14	+	1.85122e12i	−1.53906	+	0.0145603i
$663$	6.81423e13			0.531923
$664$	6.60049e12	+	2.32507e14i	0.0511371	+	1.80134i
$665$	1.34264e14	+	1.38137e14i	1.03241	+	1.06219i
$666$	1.28207e14	−	1.21290e12i	0.978453	−	0.00925667i
$667$	−1.19317e14			−0.903802
$668$	9.55299e13	−	1.80769e12i	0.718219	−	0.0135907i
$669$	4.17547e13			0.311584
$670$	−5.03643e13	−	5.08456e13i	−0.373035	−	0.376599i
$671$		−	4.87351e13i		−	0.358286i
$672$	1.17073e13	+	2.47321e14i	0.0854300	+	1.80474i
$673$		−	1.88489e14i		−	1.36525i	−0.730770	−	0.682623i	$-0.760839\pi$
$673$		−	1.88489e14i		−	1.36525i	0.730770	−	0.682623i	$-0.239161\pi$
$674$	3.19289e13	−	3.02063e11i	0.229553	−	0.00217169i
$675$	2.41230e12	−	8.48258e13i	0.0172152	−	0.605354i
$676$	−1.33475e14	+	2.52571e12i	−0.945511	+	0.0178916i
$677$		−	4.14436e13i		−	0.291417i	−0.989328	−	0.145708i	$-0.953454\pi$
$677$		−	4.14436e13i		−	0.291417i	0.989328	−	0.145708i	$-0.0465461\pi$
$678$	9.11210e13	−	8.62052e11i	0.636019	−	0.00601707i
$679$		−	1.12271e14i		−	0.777892i
$680$	1.49560e14	−	1.53858e14i	1.02866	−	1.05822i
$681$	3.38270e14			2.30955
$682$	6.03438e11	+	6.37849e13i	0.00408988	+	0.432311i
$683$	1.25711e14			0.845801			0.422901	−	0.906176i	$-0.361012\pi$
$683$	1.25711e14			0.845801			0.422901	+	0.906176i	$0.361012\pi$
$684$	−4.99774e12	−	2.64113e14i	−0.0333805	−	1.76404i
$685$	2.70997e13	+	2.78813e13i	0.179685	+	0.184867i
$686$	−1.06632e12	−	1.12713e14i	−0.00701889	−	0.741915i
$687$	−2.04371e14			−1.33547
$688$	−7.83603e13	+	2.96664e12i	−0.508340	+	0.0192452i
$689$	−1.10095e13			−0.0709038
$690$	−2.78705e14	−	2.81368e14i	−1.78197	−	1.79900i
$691$			2.51924e14i			1.59911i	0.600592	+	0.799556i	$0.294932\pi$
$691$			2.51924e14i			1.59911i	−0.600592	+	0.799556i	$0.705068\pi$
$692$	−1.77705e12	−	9.39110e13i	−0.0111988	−	0.591815i
$693$		−	2.64403e14i		−	1.65425i
$694$	1.60199e12	+	1.69334e14i	0.00995087	+	1.05183i
$695$	−8.45912e12	−	8.70311e12i	−0.0521677	−	0.0536723i
$696$	−3.95624e12	−	1.39362e14i	−0.0242235	−	0.853291i
$697$			9.54128e13i			0.580019i
$698$	9.73202e10	+	1.02870e13i	0.000587389	+	0.0620885i
$699$		−	2.38539e14i		−	1.42947i
$700$	−1.86735e12	+	1.96348e14i	−0.0111106	+	1.16825i
$701$	−9.22547e13			−0.545002			−0.272501	−	0.962155i	$-0.587851\pi$
$701$	−9.22547e13			−0.545002			−0.272501	+	0.962155i	$0.587851\pi$
$702$	2.40619e13	−	2.27638e11i	0.141138	−	0.00133524i
$703$	1.53072e14			0.891495
$704$	9.98192e12	+	1.75669e14i	0.0577232	+	1.01585i
$705$	−8.10570e12	+	7.87846e12i	−0.0465420	+	0.0452372i
$706$	2.05306e14	−	1.94230e12i	1.17052	−	0.0110737i
$707$	3.36580e14			1.90542
$708$	8.61125e12	+	4.55075e14i	0.0484061	+	2.55809i
$709$	5.98699e13			0.334177			0.167089	−	0.985942i	$-0.446563\pi$
$709$	5.98699e13			0.334177			0.167089	+	0.985942i	$0.446563\pi$
$710$	−1.82176e14	+	1.80452e14i	−1.00972	+	1.00016i
$711$			2.83307e14i			1.55923i
$712$	3.15687e12	+	1.11203e14i	0.0172527	+	0.607740i
$713$		−	1.28197e14i		−	0.695713i
$714$	−4.94763e14	+	4.68071e12i	−2.66628	+	0.0252244i
$715$	−3.17770e13	+	3.08861e13i	−0.170052	+	0.165285i
$716$	2.09003e12	+	1.10451e14i	0.0111068	+	0.586954i
$717$		−	3.47341e13i		−	0.183299i
$718$	1.34357e14	−	1.27108e12i	0.704104	−	0.00666119i
$719$		−	2.79087e14i		−	1.45243i	−0.687469	−	0.726214i	$-0.741278\pi$
$719$		−	2.79087e14i		−	1.45243i	0.687469	−	0.726214i	$-0.258722\pi$
$720$	1.85847e14	−	1.94842e14i	0.960488	−	1.00698i
$721$	1.46358e14			0.751173
$722$	−1.12750e12	−	1.19179e14i	−0.00574684	−	0.607456i
$723$	−3.40467e14			−1.72339
$724$	−3.51443e14	+	6.65027e12i	−1.76670	+	0.0334308i
$725$	3.14301e12	−	1.10520e14i	0.0156912	−	0.551763i
$726$	−1.04128e11	−	1.10066e13i	−0.000516281	−	0.0545722i
$727$	3.87651e14			1.90883			0.954417	−	0.298476i	$-0.0964781\pi$
$727$	3.87651e14			1.90883			0.954417	+	0.298476i	$0.0964781\pi$
$728$	−5.56567e13	+	1.58000e12i	−0.272183	+	0.00772681i
$729$	−3.23207e14			−1.56980
$730$	−1.49745e14	+	1.48327e14i	−0.722333	+	0.715496i
$731$		−	1.56703e14i		−	0.750741i
$732$	−1.14425e14	+	2.16523e12i	−0.544458	+	0.0103026i
$733$		−	2.86598e14i		−	1.35442i	−0.735790	−	0.677210i	$-0.763189\pi$
$733$		−	2.86598e14i		−	1.35442i	0.735790	−	0.677210i	$-0.236811\pi$
$734$	7.51543e11	+	7.94400e13i	0.00352755	+	0.372871i
$735$	8.68100e13	−	8.43764e13i	0.404700	−	0.393355i
$736$	−1.67203e13	−	3.53223e14i	−0.0774204	−	1.63553i
$737$			1.17276e14i			0.539349i
$738$	1.13268e12	+	1.19727e14i	0.00517400	+	0.546905i
$739$		−	1.44810e14i		−	0.657017i	−0.944501	−	0.328508i	$-0.893454\pi$
$739$		−	1.44810e14i		−	0.657017i	0.944501	−	0.328508i	$-0.106546\pi$
$740$	1.10847e14	+	1.09809e14i	0.499533	+	0.494855i
$741$	1.02091e14			0.456979
$742$	7.99368e13	−	7.56243e11i	0.355408	−	0.00336234i
$743$	−4.64148e13			−0.204980			−0.102490	−	0.994734i	$-0.532681\pi$
$743$	−4.64148e13			−0.204980			−0.102490	+	0.994734i	$0.532681\pi$
$744$	1.49733e14	−	4.25068e12i	0.656831	−	0.0186463i
$745$	1.13194e14	−	1.10020e14i	0.493220	−	0.479393i
$746$	−2.70096e14	+	2.55525e12i	−1.16903	+	0.0110596i
$747$	−5.83295e14			−2.50776
$748$	−3.51550e14	+	6.65227e12i	−1.50134	+	0.0284094i
$749$	−1.42710e14			−0.605405
$750$	2.67966e14	−	2.50746e14i	1.12921	−	1.05664i
$751$			1.55194e14i			0.649642i	0.945775	+	0.324821i	$0.105304\pi$
$751$			1.55194e14i			0.649642i	−0.945775	+	0.324821i	$0.894696\pi$
$752$	−1.00857e13	+	3.81835e11i	−0.0419390	+	0.00158777i
$753$		−	4.27208e14i		−	1.76467i
$754$	3.13505e13	−	2.96592e11i	0.128643	−	0.00121703i
$755$	1.20055e14	+	1.23518e14i	0.489381	+	0.503496i
$756$	−1.74692e14	+	3.30564e12i	−0.707397	+	0.0133859i
$757$			2.71076e14i			1.09046i	0.838285	+	0.545232i	$0.183558\pi$
$757$			2.71076e14i			1.09046i	−0.838285	+	0.545232i	$0.816442\pi$
$758$	−1.63614e14	+	1.54787e12i	−0.653845	+	0.00618571i
$759$			6.48977e14i			2.57644i
$760$	2.24071e14	−	2.30511e14i	0.883727	−	0.909125i
$761$	−3.23023e14			−1.26564			−0.632819	−	0.774300i	$-0.718102\pi$
$761$	−3.23023e14			−1.26564			−0.632819	+	0.774300i	$0.718102\pi$
$762$	−7.10417e11	−	7.50928e13i	−0.00276528	−	0.292297i
$763$	−1.78562e14			−0.690503
$764$	−4.52982e11	−	2.39385e13i	−0.00174026	−	0.0919667i
$765$	3.75033e14	+	3.85850e14i	1.43140	+	1.47269i
$766$	2.68686e12	+	2.84008e14i	0.0101883	+	1.07693i
$767$	−1.02354e14			−0.385593
$768$	4.12008e14	−	3.12412e13i	1.54205	−	0.116929i
$769$	1.81547e14			0.675085			0.337542	−	0.941310i	$-0.390404\pi$
$769$	1.81547e14			0.675085			0.337542	+	0.941310i	$0.390404\pi$
$770$	2.28603e14	−	2.26439e14i	0.844554	−	0.836560i
$771$		−	2.62546e14i		−	0.963683i
$772$	−5.77276e12	−	3.05070e14i	−0.0210522	−	1.11253i
$773$			7.48801e13i			0.271312i	0.990756	+	0.135656i	$0.0433142\pi$
$773$			7.48801e13i			0.271312i	−0.990756	+	0.135656i	$0.956686\pi$
$774$	−1.86028e12	−	1.96637e14i	−0.00669691	−	0.707880i
$775$	1.18746e14	+	3.37692e12i	0.424726	+	0.0120785i
$776$	−1.87282e14	+	5.31663e12i	−0.665561	+	0.0188942i
$777$		−	3.59792e14i		−	1.27042i
$778$	3.28771e12	+	3.47519e14i	0.0115344	+	1.21921i
$779$			1.42948e14i			0.498299i
$780$	7.39291e13	+	7.32366e13i	0.256060	+	0.253662i
$781$	4.20190e14			1.44607
$782$	7.06619e14	−	6.68498e12i	2.41630	−	0.0228595i
$783$	9.83833e13			0.334282
$784$	1.08016e14	−	4.08937e12i	0.364675	−	0.0138062i
$785$	1.95179e14	+	2.00809e14i	0.654765	+	0.673650i
$786$	6.87984e14	−	6.50868e12i	2.29332	−	0.0216960i
$787$	1.15967e14			0.384116			0.192058	−	0.981384i	$-0.438484\pi$
$787$	1.15967e14			0.384116			0.192058	+	0.981384i	$0.438484\pi$
$788$	8.84526e12	+	4.67441e14i	0.0291125	+	1.53849i
$789$	1.85912e13			0.0608026
$790$	−2.44947e14	+	2.42628e14i	−0.796042	+	0.788507i
$791$		−	1.48794e14i		−	0.480509i
$792$	−4.41058e14	+	1.25209e13i	−1.41537	+	0.0401800i
$793$		−	2.57362e13i		−	0.0820687i
$794$	−1.44420e14	+	1.36628e12i	−0.457640	+	0.00432951i
$795$	−1.04134e14	−	1.07138e14i	−0.327912	−	0.337370i
$796$	3.13021e12	+	1.65420e14i	0.00979507	+	0.517635i
$797$			1.98139e14i			0.616140i	0.951364	+	0.308070i	$0.0996830\pi$
$797$			1.98139e14i			0.616140i	−0.951364	+	0.308070i	$0.900317\pi$
$798$	−7.41257e14	+	7.01267e12i	−2.29063	+	0.0216705i
$799$		−	2.01692e13i		−	0.0619376i
$800$	3.27622e14	−	6.18314e12i	0.999822	−	0.0188695i
$801$	−2.78977e14			−0.846070
$802$	−1.30875e12	−	1.38338e14i	−0.00394444	−	0.416938i
$803$	3.45387e14			1.03449
$804$	2.75350e14	−	5.21038e12i	0.819607	−	0.0155092i
$805$	−4.63717e14	+	4.50717e14i	−1.37175	+	1.33329i
$806$	3.18665e11	+	3.36837e13i	0.000936827	+	0.0990249i
$807$	6.77891e14			1.98058
$808$	−1.59388e13	−	5.61458e14i	−0.0462807	−	1.63027i
$809$	−3.55439e14			−1.02570			−0.512852	−	0.858477i	$-0.671411\pi$
$809$	−3.55439e14			−1.02570			−0.512852	+	0.858477i	$0.671411\pi$
$810$	−1.11660e14	−	1.12727e14i	−0.320237	−	0.323297i
$811$		−	6.30302e14i		−	1.79657i	−0.439413	−	0.898285i	$-0.644813\pi$
$811$		−	6.30302e14i		−	1.79657i	0.439413	−	0.898285i	$-0.355187\pi$
$812$	−2.27607e14	+	4.30695e12i	−0.644772	+	0.0122008i
$813$			7.63883e14i			2.15067i
$814$	−2.41877e12	−	2.55670e14i	−0.00676818	−	0.715413i
$815$	−2.60931e14	+	2.53616e14i	−0.725668	+	0.705324i
$816$	3.12377e13	+	8.25105e14i	0.0863431	+	2.28065i
$817$		−	2.34773e14i		−	0.644968i
$818$	1.85132e11	+	1.95689e13i	0.000505494	+	0.0534319i
$819$		−	1.39627e14i		−	0.378922i
$820$	−1.02546e14	+	1.03515e14i	−0.276598	+	0.279213i
$821$	−4.02625e13			−0.107941			−0.0539703	−	0.998543i	$-0.517188\pi$
$821$	−4.02625e13			−0.107941			−0.0539703	+	0.998543i	$0.517188\pi$
$822$	−1.49614e14	+	1.41542e12i	−0.398669	+	0.00377162i
$823$	−5.78856e14			−1.53310			−0.766551	−	0.642183i	$-0.778029\pi$
$823$	−5.78856e14			−1.53310			−0.766551	+	0.642183i	$0.778029\pi$
$824$	−6.93082e12	−	2.44143e14i	−0.0182452	−	0.642701i
$825$	−6.01131e14	−	1.70951e13i	−1.57289	−	0.0447304i
$826$	7.43168e14	−	7.03075e12i	1.93280	−	0.0182853i
$827$	−4.26504e14			−1.10254			−0.551271	−	0.834326i	$-0.685857\pi$
$827$	−4.26504e14			−1.10254			−0.551271	+	0.834326i	$0.685857\pi$
$828$	8.86612e14	−	1.67771e13i	2.27815	−	0.0431087i
$829$	8.67325e13			0.221518			0.110759	−	0.993847i	$-0.464672\pi$
$829$	8.67325e13			0.221518			0.110759	+	0.993847i	$0.464672\pi$
$830$	−4.99542e14	−	5.04315e14i	−1.26818	−	1.28030i
$831$		−	3.71267e14i		−	0.936874i
$832$	5.27128e12	+	9.27675e13i	0.0132221	+	0.232691i
$833$			2.16007e14i			0.538571i
$834$	4.67018e13	−	4.41823e11i	0.115745	−	0.00109501i
$835$	−2.09093e14	+	2.03231e14i	−0.515118	+	0.500677i
$836$	−5.26693e14	+	9.96647e12i	−1.28981	+	0.0244068i
$837$			1.05705e14i			0.257318i
$838$	3.38363e14	−	3.20109e12i	0.818771	−	0.00774600i
$839$		−	6.16766e13i		−	0.148358i	−0.997245	−	0.0741790i	$-0.976366\pi$
$839$		−	6.16766e13i		−	0.148358i	0.997245	−	0.0741790i	$-0.0236336\pi$
$840$	−5.41810e14	−	5.26674e14i	−1.29554	−	1.25935i
$841$	−2.92523e14			−0.695312
$842$	1.87837e12	+	1.98549e14i	0.00443835	+	0.469145i
$843$	1.06875e15			2.51037
$844$	−3.52124e12	−	1.86085e14i	−0.00822212	−	0.434510i
$845$	2.92146e14	−	2.83956e14i	0.678135	−	0.659124i
$846$	−2.39436e11	−	2.53090e13i	−0.000552507	−	0.0584014i
$847$	−1.79730e13			−0.0412290
$848$	−5.04693e12	−	1.33309e14i	−0.0115093	−	0.304004i
$849$	−3.47853e13			−0.0788600
$850$	−1.24214e13	+	6.54699e14i	−0.0279946	+	1.47553i
$851$			5.13853e14i			1.15131i
$852$	−1.86684e13	−	9.86560e14i	−0.0415824	−	2.19748i
$853$		−	5.00937e14i		−	1.10927i	−0.832093	−	0.554636i	$-0.812857\pi$
$853$		−	5.00937e14i		−	1.10927i	0.832093	−	0.554636i	$-0.187143\pi$
$854$	1.76782e12	+	1.86864e14i	0.00389179	+	0.411372i
$855$	5.61876e14	+	5.78082e14i	1.22973	+	1.26520i
$856$	6.75808e12	+	2.38059e14i	0.0147047	+	0.517982i
$857$		−	5.92500e14i		−	1.28169i	−0.767668	−	0.640847i	$-0.778583\pi$
$857$		−	5.92500e14i		−	1.28169i	0.767668	−	0.640847i	$-0.221417\pi$
$858$	−1.61319e12	−	1.70518e14i	−0.00346936	−	0.366720i
$859$			6.13470e14i			1.31168i	0.754901	+	0.655839i	$0.227685\pi$
$859$			6.13470e14i			1.31168i	−0.754901	+	0.655839i	$0.772315\pi$
$860$	1.68418e14	−	1.70011e14i	0.358011	−	0.361396i
$861$	3.35995e14			0.710097
$862$	1.20186e14	−	1.13702e12i	0.252532	−	0.00238909i
$863$	−6.03721e14			−1.26119			−0.630597	−	0.776110i	$-0.717190\pi$
$863$	−6.03721e14			−1.26119			−0.630597	+	0.776110i	$0.717190\pi$
$864$	1.37868e13	+	2.91251e14i	0.0286348	+	0.604921i
$865$	1.99787e14	+	2.05549e14i	0.412560	+	0.424459i
$866$	−7.20217e14	+	6.81362e12i	−1.47868	+	0.0139891i
$867$	−8.92425e14			−1.82170
$868$	−4.62749e12	−	2.44547e14i	−0.00939176	−	0.496322i
$869$	5.64970e14			1.14006
$870$	2.99418e14	+	3.02279e14i	0.600734	+	0.606474i
$871$			6.19312e13i			0.123543i
$872$	8.45583e12	+	2.97863e14i	0.0167716	+	0.590791i
$873$		−	4.69838e14i		−	0.926567i
$874$	1.05866e15	−	1.00155e13i	2.07587	−	0.0196388i
$875$	−4.05273e14	−	4.41402e14i	−0.790146	−	0.860585i
$876$	−1.53450e13	−	8.10931e14i	−0.0297473	−	1.57204i
$877$			9.12906e14i			1.75966i	0.475292	+	0.879828i	$0.342343\pi$
$877$			9.12906e14i			1.75966i	−0.475292	+	0.879828i	$0.657657\pi$
$878$	6.20486e14	−	5.87012e12i	1.18921	−	0.0112506i
$879$		−	8.45263e14i		−	1.61082i
$880$	−3.88554e14	−	3.70615e14i	−0.736271	−	0.702278i
$881$	−5.56277e14			−1.04812			−0.524060	−	0.851681i	$-0.675583\pi$
$881$	−5.56277e14			−1.04812			−0.524060	+	0.851681i	$0.675583\pi$
$882$	2.56430e12	+	2.71053e14i	0.00480426	+	0.507822i
$883$	4.22428e14			0.786954			0.393477	−	0.919334i	$-0.371272\pi$
$883$	4.22428e14			0.786954			0.393477	+	0.919334i	$0.371272\pi$
$884$	−1.85647e14	+	3.51295e12i	−0.343896	+	0.00650745i
$885$	−9.68129e14	−	9.96052e14i	−1.78327	−	1.83470i
$886$	−1.06995e12	−	1.13096e14i	−0.00195972	−	0.207147i
$887$	4.26239e14			0.776310			0.388155	−	0.921594i	$-0.373112\pi$
$887$	4.26239e14			0.776310			0.388155	+	0.921594i	$0.373112\pi$
$888$	−6.00177e14	+	1.70380e13i	−1.08696	+	0.0308571i
$889$	−1.22621e14			−0.220829
$890$	−2.38920e14	−	2.41203e14i	−0.427861	−	0.431949i
$891$			2.60005e14i			0.463012i
$892$	−1.13757e14	+	2.15259e12i	−0.201443	+	0.00381186i
$893$		−	3.02176e13i		−	0.0532111i
$894$	5.74640e12	+	6.07409e14i	0.0100626	+	1.06364i
$895$	−2.34974e14	−	2.41751e14i	−0.409170	−	0.420972i
$896$	−4.46456e13	−	6.73199e14i	−0.0773105	−	1.16574i
$897$			3.42714e14i			0.590159i
$898$	−1.05620e12	−	1.11643e14i	−0.00180869	−	0.191183i
$899$			1.37724e14i			0.234538i
$900$	−7.81459e12	+	8.21688e14i	−0.0132341	+	1.39154i
$901$	2.66587e14			0.448968
$902$	2.38760e14	−	2.25879e12i	0.399879	−	0.00378306i
$903$	−5.51828e14			−0.919105
$904$	−2.48206e14	+	7.04616e12i	−0.411122	+	0.0116711i
$905$	7.69228e14	−	7.47663e14i	1.26710	−	1.23158i
$906$	−6.62811e14	+	6.27054e12i	−1.08580	+	0.0102722i
$907$	3.83030e14			0.624017			0.312008	−	0.950079i	$-0.398998\pi$
$907$	3.83030e14			0.624017			0.312008	+	0.950079i	$0.398998\pi$
$908$	−9.21584e14	+	1.74389e13i	−1.49316	+	0.0282546i
$909$	1.40854e15			2.26960
$910$	1.20721e14	−	1.19578e14i	0.193453	−	0.191622i
$911$			1.36122e14i			0.216939i	0.994100	+	0.108470i	$0.0345950\pi$
$911$			1.36122e14i			0.216939i	−0.994100	+	0.108470i	$0.965405\pi$
$912$	4.68004e13	+	1.23618e15i	0.0741781	+	1.95932i
$913$			1.16320e15i			1.83359i
$914$	−1.14123e14	+	1.07966e12i	−0.178913	+	0.00169261i
$915$	2.50449e14	−	2.43428e14i	0.390494	−	0.379547i
$916$	5.56789e14	−	1.05360e13i	0.863403	−	0.0163379i
$917$		−	1.12342e15i		−	1.73260i
$918$	−5.82645e14	+	5.51212e12i	−0.893698	+	0.00845484i
$919$			1.45106e14i			0.221365i	0.993856	+	0.110682i	$0.0353036\pi$
$919$			1.45106e14i			0.221365i	−0.993856	+	0.110682i	$0.964696\pi$
$920$	7.73812e14	+	7.52194e14i	1.17408	+	1.14128i
$921$	8.70103e13			0.131302
$922$	6.39836e12	+	6.76323e14i	0.00960316	+	1.01508i
$923$	2.21895e14			0.331237
$924$	2.34259e13	+	1.23798e15i	0.0347806	+	1.83803i
$925$	−4.75969e14	−	1.35357e13i	−0.702862	−	0.0199882i
$926$	6.07180e12	+	6.41804e14i	0.00891789	+	0.942643i
$927$	6.12486e14			0.894742
$928$	1.79629e13	+	3.79474e14i	0.0260998	+	0.551368i
$929$	8.80611e14			1.27264			0.636320	−	0.771425i	$-0.280456\pi$
$929$	8.80611e14			1.27264			0.636320	+	0.771425i	$0.280456\pi$
$930$	−3.24776e14	+	3.21702e14i	−0.466841	+	0.462422i
$931$			3.23623e14i			0.462691i
$932$	1.22975e13	+	6.49878e14i	0.0174878	+	0.924171i
$933$			1.42382e15i			2.01394i
$934$	−4.94139e12	−	5.22317e14i	−0.00695207	−	0.734851i
$935$	7.69460e14	−	7.47889e14i	1.07678	−	1.04660i
$936$	−2.32915e14	+	6.61207e12i	−0.324204	+	0.00920361i
$937$			4.17114e14i			0.577506i	0.957404	+	0.288753i	$0.0932406\pi$
$937$			4.17114e14i			0.577506i	−0.957404	+	0.288753i	$0.906759\pi$
$938$	−4.25407e12	−	4.49666e14i	−0.00585856	−	0.619264i
$939$		−	8.42216e14i		−	1.15371i
$940$	2.16770e13	−	2.18820e13i	0.0295366	−	0.0298159i
$941$	−1.11785e14			−0.151507			−0.0757537	−	0.997127i	$-0.524136\pi$
$941$	−1.11785e14			−0.151507			−0.0757537	+	0.997127i	$0.524136\pi$
$942$	−1.07756e15	+	1.01943e13i	−1.45274	+	0.0137436i
$943$	−4.79867e14			−0.643521
$944$	−4.69211e13	−	1.23936e15i	−0.0625905	−	1.65325i
$945$	3.82359e14	−	3.71640e14i	0.507356	−	0.493133i
$946$	−3.92132e14	+	3.70977e12i	−0.517579	+	0.00489656i
$947$	5.17902e14			0.679982			0.339991	−	0.940429i	$-0.389576\pi$
$947$	5.17902e14			0.679982			0.339991	+	0.940429i	$0.389576\pi$
$948$	−2.51008e13	−	1.32649e15i	−0.0327828	−	1.73246i
$949$	1.82393e14			0.236961
$950$	−1.86098e13	+	9.80874e14i	−0.0240504	+	1.26764i
$951$			5.37264e14i			0.690694i
$952$	1.34769e15	−	3.82588e13i	1.72348	−	0.0489267i
$953$		−	1.16104e15i		−	1.47701i	−0.674249	−	0.738504i	$-0.735532\pi$
$953$		−	1.16104e15i		−	1.47701i	0.674249	−	0.738504i	$-0.264468\pi$
$954$	3.34523e14	−	3.16476e12i	0.423335	−	0.00400497i
$955$	5.09270e13	+	5.23959e13i	0.0641108	+	0.0659599i
$956$	1.79065e12	+	9.46298e13i	0.00224245	+	0.118505i
$957$		−	6.97208e14i		−	0.868566i
$958$	6.17151e14	−	5.83857e12i	0.764828	−	0.00723567i
$959$			2.44308e14i			0.301193i
$960$	−8.52900e14	+	9.28748e14i	−1.04603	+	1.13905i
$961$	6.71654e14			0.819462
$962$	−1.27731e12	−	1.35015e14i	−0.00155032	−	0.163872i
$963$	−5.97221e14			−0.721114
$964$	9.27571e14	−	1.75522e13i	1.11420	−	0.0210836i
$965$	6.49008e14	+	6.67727e14i	0.775557	+	0.797926i
$966$	−2.35411e13	−	2.48835e15i	−0.0279860	−	2.95819i
$967$	−1.64367e15			−1.94394			−0.971972	−	0.235098i	$-0.924459\pi$
$967$	−1.64367e15			−1.94394			−0.971972	+	0.235098i	$0.924459\pi$
$968$	8.51116e11	+	2.99812e13i	0.00100141	+	0.0352754i
$969$	−2.47207e15			−2.89363
$970$	4.06221e14	−	4.02376e14i	0.473046	−	0.468569i
$971$			1.09038e15i			1.26323i	0.775284	+	0.631613i	$0.217607\pi$
$971$			1.09038e15i			1.26323i	−0.775284	+	0.631613i	$0.782393\pi$
$972$	1.13580e15	−	2.14924e13i	1.30909	−	0.0247716i
$973$		−	7.62604e13i		−	0.0874450i
$974$	−5.40735e12	−	5.71571e14i	−0.00616865	−	0.652042i
$975$	−3.17447e14	−	9.02763e12i	−0.360286	−	0.0102459i
$976$	3.11628e14	−	1.17979e13i	0.351874	−	0.0133216i
$977$		−	8.20193e14i		−	0.921389i	−0.887559	−	0.460695i	$-0.847600\pi$
$977$		−	8.20193e14i		−	0.921389i	0.887559	−	0.460695i	$-0.152400\pi$
$978$	−1.32465e13	−	1.40018e15i	−0.0148049	−	1.56491i
$979$			5.56336e14i			0.618619i
$980$	−2.32156e14	+	2.34351e14i	−0.256832	+	0.259260i
$981$	−7.47254e14			−0.822475
$982$	−1.11963e15	+	1.05922e13i	−1.22607	+	0.0115993i
$983$	−1.04826e15			−1.14209			−0.571047	−	0.820917i	$-0.693463\pi$
$983$	−1.04826e15			−1.14209			−0.571047	+	0.820917i	$0.693463\pi$
$984$	−1.59111e13	−	5.60482e14i	−0.0172475	−	0.607556i
$985$	−9.94438e14	−	1.02312e15i	−1.07250	−	1.10343i
$986$	−7.59134e14	+	7.18180e12i	−0.814580	+	0.00770635i
$987$	−7.10256e13			−0.0758279
$988$	−2.78138e14	+	5.26312e12i	−0.295444	+	0.00559060i
$989$	7.88119e14			0.832934
$990$	9.56668e14	−	9.47613e14i	1.00597	−	0.996448i
$991$		−	3.12148e13i		−	0.0326582i	−0.999867	−	0.0163291i	$-0.994802\pi$
$991$		−	3.12148e13i		−	0.0326582i	0.999867	−	0.0163291i	$-0.00519794\pi$
$992$	−4.07715e14	+	1.92998e13i	−0.424423	+	0.0200907i
$993$			2.29807e15i			2.38022i
$994$	−1.61112e15	+	1.52420e13i	−1.66034	+	0.0157076i
$995$	−3.51917e14	−	3.62067e14i	−0.360848	−	0.371256i
$996$	2.73108e15	−	5.16795e13i	2.78636	−	0.0527256i
$997$			4.10229e14i			0.416438i	0.978082	+	0.208219i	$0.0667667\pi$
$997$			4.10229e14i			0.416438i	−0.978082	+	0.208219i	$0.933233\pi$
$998$	7.70046e14	−	7.28503e12i	0.777793	−	0.00735832i
$999$		−	4.23699e14i		−	0.425824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.d.d.19.14	yes	24
4.3	odd	2	inner	20.11.d.d.19.12	yes	24
5.2	odd	4		100.11.b.h.51.2		24
5.3	odd	4		100.11.b.h.51.23		24
5.4	even	2	inner	20.11.d.d.19.11	✓	24
20.3	even	4		100.11.b.h.51.24		24
20.7	even	4		100.11.b.h.51.1		24
20.19	odd	2	inner	20.11.d.d.19.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.11	✓	24	5.4	even	2	inner
20.11.d.d.19.12	yes	24	4.3	odd	2	inner
20.11.d.d.19.13	yes	24	20.19	odd	2	inner
20.11.d.d.19.14	yes	24	1.1	even	1	trivial
100.11.b.h.51.1		24	20.7	even	4
100.11.b.h.51.2		24	5.2	odd	4
100.11.b.h.51.23		24	5.3	odd	4
100.11.b.h.51.24		24	20.3	even	4

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.302723 + 31.9986i) q^{2} +375.794 q^{3} +(-1023.82 + 19.3734i) q^{4} +(2240.90 - 2178.07i) q^{5} +(113.762 + 12024.9i) q^{6} +19635.7 q^{7} +(-929.854 - 32754.8i) q^{8} +82172.5 q^{9} +O(q^{10})\)	\(q+(0.302723 + 31.9986i) q^{2} +375.794 q^{3} +(-1023.82 + 19.3734i) q^{4} +(2240.90 - 2178.07i) q^{5} +(113.762 + 12024.9i) q^{6} +19635.7 q^{7} +(-929.854 - 32754.8i) q^{8} +82172.5 q^{9} +(70373.6 + 71046.1i) q^{10} -163868. i q^{11} +(-384745. + 7280.42i) q^{12} -86535.9i q^{13} +(5944.18 + 628314. i) q^{14} +(842116. - 818508. i) q^{15} +(1.04783e6 - 39669.6i) q^{16} +2.09541e6i q^{17} +(24875.5 + 2.62940e6i) q^{18} +3.13936e6i q^{19} +(-2.25207e6 + 2.27336e6i) q^{20} +7.37899e6 q^{21} +(5.24354e6 - 49606.6i) q^{22} -1.05386e7 q^{23} +(-349434. - 1.23091e7i) q^{24} +(277605. - 9.76168e6i) q^{25} +(2.76902e6 - 26196.4i) q^{26} +8.68968e6 q^{27} +(-2.01034e7 + 380410. i) q^{28} +1.13219e7 q^{29} +(2.64460e7 + 2.66987e7i) q^{30} +1.21645e7i q^{31} +(1.58657e6 + 3.35169e7i) q^{32} -6.15807e7i q^{33} +(-6.70503e7 + 634330. i) q^{34} +(4.40016e7 - 4.27680e7i) q^{35} +(-8.41296e7 + 1.59196e6i) q^{36} -4.87589e7i q^{37} +(-1.00455e8 + 950356. i) q^{38} -3.25197e7i q^{39} +(-7.34261e7 - 7.13748e7i) q^{40} +4.55341e7 q^{41} +(2.23379e6 + 2.36117e8i) q^{42} -7.47838e7 q^{43} +(3.17468e6 + 1.67771e8i) q^{44} +(1.84140e8 - 1.78978e8i) q^{45} +(-3.19029e6 - 3.37222e8i) q^{46} -9.62539e6 q^{47} +(3.93767e8 - 1.49076e7i) q^{48} +1.03086e8 q^{49} +(3.12444e8 + 5.92788e6i) q^{50} +7.87445e8i q^{51} +(1.67649e6 + 8.85969e7i) q^{52} -1.27224e8i q^{53} +(2.63056e6 + 2.78057e8i) q^{54} +(-3.56917e8 - 3.67211e8i) q^{55} +(-1.82583e7 - 6.43164e8i) q^{56} +1.17975e9i q^{57} +(3.42739e6 + 3.62283e8i) q^{58} -1.18280e9i q^{59} +(-8.46315e8 + 8.54317e8i) q^{60} +2.97404e8 q^{61} +(-3.89246e8 + 3.68246e6i) q^{62} +1.61351e9 q^{63} +(-1.07201e9 + 6.09144e7i) q^{64} +(-1.88482e8 - 1.93918e8i) q^{65} +(1.97049e9 - 1.86419e7i) q^{66} -7.15670e8 q^{67} +(-4.05953e7 - 2.14532e9i) q^{68} -3.96036e9 q^{69} +(1.38184e9 + 1.39504e9i) q^{70} +2.56419e9i q^{71} +(-7.64084e7 - 2.69154e9i) q^{72} +2.10771e9i q^{73} +(1.56022e9 - 1.47604e7i) q^{74} +(1.04322e8 - 3.66838e9i) q^{75} +(-6.08201e7 - 3.21413e9i) q^{76} -3.21766e9i q^{77} +(1.04058e9 - 9.84446e6i) q^{78} +3.44771e9i q^{79} +(2.26166e9 - 2.37114e9i) q^{80} -1.58667e9 q^{81} +(1.37842e7 + 1.45702e9i) q^{82} -7.09842e9 q^{83} +(-7.55473e9 + 1.42956e8i) q^{84} +(4.56397e9 + 4.69561e9i) q^{85} +(-2.26388e7 - 2.39297e9i) q^{86} +4.25469e9 q^{87} +(-5.36747e9 + 1.52373e8i) q^{88} -3.39502e9 q^{89} +(5.78278e9 + 5.83804e9i) q^{90} -1.69919e9i q^{91} +(1.07896e10 - 2.04169e8i) q^{92} +4.57134e9i q^{93} +(-2.91383e6 - 3.07999e8i) q^{94} +(6.83776e9 + 7.03498e9i) q^{95} +(5.96225e8 + 1.25955e10i) q^{96} -5.71771e9i q^{97} +(3.12064e7 + 3.29859e9i) q^{98} -1.34654e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

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