LMFDB - Embedded newform 20.11.d.d.19.4

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			19.4
Character	$\chi$	$=$	20.19
Dual form			20.11.d.d.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-28.1904 + 15.1426i) q^{2} -349.582 q^{3} +(565.401 - 853.755i) q^{4} +(1690.09 + 2628.54i) q^{5} +(9854.87 - 5293.59i) q^{6} +15402.9 q^{7} +(-3010.79 + 32629.4i) q^{8} +63158.6 q^{9} +O(q^{10})$	\(q+(-28.1904 + 15.1426i) q^{2} -349.582 q^{3} +(565.401 - 853.755i) q^{4} +(1690.09 + 2628.54i) q^{5} +(9854.87 - 5293.59i) q^{6} +15402.9 q^{7} +(-3010.79 + 32629.4i) q^{8} +63158.6 q^{9} +(-87447.4 - 48507.3i) q^{10} +136872. i q^{11} +(-197654. + 298457. i) q^{12} -467497. i q^{13} +(-434214. + 233240. i) q^{14} +(-590824. - 918891. i) q^{15} +(-409220. - 965428. i) q^{16} +1.19215e6i q^{17} +(-1.78047e6 + 956388. i) q^{18} +1.42028e6i q^{19} +(3.19971e6 + 43258.3i) q^{20} -5.38457e6 q^{21} +(-2.07260e6 - 3.85847e6i) q^{22} -1.04315e7 q^{23} +(1.05252e6 - 1.14066e7i) q^{24} +(-4.05283e6 + 8.88493e6i) q^{25} +(7.07913e6 + 1.31789e7i) q^{26} -1.43664e6 q^{27} +(8.70880e6 - 1.31503e7i) q^{28} +8.98269e6 q^{29} +(3.05700e7 + 1.69573e7i) q^{30} +2.79449e7i q^{31} +(2.61552e7 + 2.10192e7i) q^{32} -4.78478e7i q^{33} +(-1.80524e7 - 3.36073e7i) q^{34} +(2.60322e7 + 4.04871e7i) q^{35} +(3.57099e7 - 5.39220e7i) q^{36} -1.06972e8i q^{37} +(-2.15067e7 - 4.00382e7i) q^{38} +1.63428e8i q^{39} +(-9.08562e7 + 4.72326e7i) q^{40} -1.66613e8 q^{41} +(1.51793e8 - 8.15366e7i) q^{42} -7.53526e7 q^{43} +(1.16855e8 + 7.73873e7i) q^{44} +(1.06744e8 + 1.66015e8i) q^{45} +(2.94070e8 - 1.57961e8i) q^{46} -2.17109e8 q^{47} +(1.43056e8 + 3.37496e8i) q^{48} -4.52265e7 q^{49} +(-2.02903e7 - 3.11841e8i) q^{50} -4.16755e8i q^{51} +(-3.99128e8 - 2.64323e8i) q^{52} +5.32584e8i q^{53} +(4.04996e7 - 2.17546e7i) q^{54} +(-3.59773e8 + 2.31325e8i) q^{55} +(-4.63748e7 + 5.02587e8i) q^{56} -4.96503e8i q^{57} +(-2.53226e8 + 1.36022e8i) q^{58} -2.43551e6i q^{59} +(-1.11856e9 - 1.51223e7i) q^{60} -1.38721e9 q^{61} +(-4.23159e8 - 7.87777e8i) q^{62} +9.72824e8 q^{63} +(-1.05561e9 - 1.96480e8i) q^{64} +(1.22883e9 - 7.90110e8i) q^{65} +(7.24543e8 + 1.34885e9i) q^{66} +1.26950e9 q^{67} +(1.01781e9 + 6.74045e8i) q^{68} +3.64668e9 q^{69} +(-1.34694e9 - 7.47152e8i) q^{70} -2.18640e9i q^{71} +(-1.90157e8 + 2.06083e9i) q^{72} +5.11042e8i q^{73} +(1.61983e9 + 3.01558e9i) q^{74} +(1.41680e9 - 3.10601e9i) q^{75} +(1.21257e9 + 8.03026e8i) q^{76} +2.10822e9i q^{77} +(-2.47474e9 - 4.60712e9i) q^{78} +4.53243e9i q^{79} +(1.84605e9 - 2.70731e9i) q^{80} -3.22723e9 q^{81} +(4.69690e9 - 2.52297e9i) q^{82} +8.51402e8 q^{83} +(-3.04444e9 + 4.59711e9i) q^{84} +(-3.13362e9 + 2.01484e9i) q^{85} +(2.12422e9 - 1.14104e9i) q^{86} -3.14019e9 q^{87} +(-4.46604e9 - 4.12091e8i) q^{88} +2.46239e9 q^{89} +(-5.52305e9 - 3.06365e9i) q^{90} -7.20080e9i q^{91} +(-5.89801e9 + 8.90599e9i) q^{92} -9.76902e9i q^{93} +(6.12041e9 - 3.28761e9i) q^{94} +(-3.73326e9 + 2.40039e9i) q^{95} +(-9.14339e9 - 7.34792e9i) q^{96} +8.02939e9i q^{97} +(1.27495e9 - 6.84848e8i) q^{98} +8.64462e9i 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 $

$2$	−28.1904	+	15.1426i	−0.880951	+	0.473208i
$2$	−28.1904	+	15.1426i	−0.880951	+	0.473208i
$3$	−349.582			−1.43861			−0.719305	−	0.694695i	$-0.755539\pi$
$3$	−349.582			−1.43861			−0.719305	+	0.694695i	$0.755539\pi$
$4$	565.401	−	853.755i	0.552149	−	0.833745i
$5$	1690.09	+	2628.54i	0.540828	+	0.841133i
$5$	1690.09	+	2628.54i	0.540828	+	0.841133i
$6$	9854.87	−	5293.59i	1.26734	−	0.680761i
$7$	15402.9			0.916456			0.458228	−	0.888835i	$-0.348484\pi$
$7$	15402.9			0.916456			0.458228	+	0.888835i	$0.348484\pi$
$8$	−3010.79	+	32629.4i	−0.0918820	+	0.995770i
$9$	63158.6			1.06960
$10$	−87447.4	−	48507.3i	−0.874474	−	0.485073i
$11$			136872.i			0.849865i	0.905225	+	0.424932i	$0.139702\pi$
$11$			136872.i			0.849865i	−0.905225	+	0.424932i	$0.860298\pi$
$12$	−197654.	+	298457.i	−0.794327	+	1.19943i
$13$		−	467497.i		−	1.25910i	−0.776958	−	0.629552i	$-0.783238\pi$
$13$		−	467497.i		−	1.25910i	0.776958	−	0.629552i	$-0.216762\pi$
$14$	−434214.	+	233240.i	−0.807353	+	0.433674i
$15$	−590824.	−	918891.i	−0.778040	−	1.21006i
$16$	−409220.	−	965428.i	−0.390262	−	0.920704i
$17$			1.19215e6i			0.839629i	0.907610	+	0.419815i	$0.137905\pi$
$17$			1.19215e6i			0.839629i	−0.907610	+	0.419815i	$0.862095\pi$
$18$	−1.78047e6	+	956388.i	−0.942262	+	0.506141i
$19$			1.42028e6i			0.573595i	0.957991	+	0.286797i	$0.0925906\pi$
$19$			1.42028e6i			0.573595i	−0.957991	+	0.286797i	$0.907409\pi$
$20$	3.19971e6	+	43258.3i	0.999909	+	0.0135182i
$21$	−5.38457e6			−1.31842
$22$	−2.07260e6	−	3.85847e6i	−0.402162	−	0.748689i
$23$	−1.04315e7			−1.62073			−0.810363	−	0.585928i	$-0.800730\pi$
$23$	−1.04315e7			−1.62073			−0.810363	+	0.585928i	$0.800730\pi$
$24$	1.05252e6	−	1.14066e7i	0.132182	−	1.43252i
$25$	−4.05283e6	+	8.88493e6i	−0.415010	+	0.909817i
$26$	7.07913e6	+	1.31789e7i	0.595818	+	1.10921i
$27$	−1.43664e6			−0.100122
$28$	8.70880e6	−	1.31503e7i	0.506021	−	0.764091i
$29$	8.98269e6			0.437942			0.218971	−	0.975731i	$-0.429730\pi$
$29$	8.98269e6			0.437942			0.218971	+	0.975731i	$0.429730\pi$
$30$	3.05700e7	+	1.69573e7i	1.25803	+	0.697831i
$31$			2.79449e7i			0.976098i	0.872816	+	0.488049i	$0.162291\pi$
$31$			2.79449e7i			0.976098i	−0.872816	+	0.488049i	$0.837709\pi$
$32$	2.61552e7	+	2.10192e7i	0.779486	+	0.626420i
$33$		−	4.78478e7i		−	1.22262i
$34$	−1.80524e7	−	3.36073e7i	−0.397319	−	0.739672i
$35$	2.60322e7	+	4.04871e7i	0.495645	+	0.770862i
$36$	3.57099e7	−	5.39220e7i	0.590577	−	0.891771i
$37$		−	1.06972e8i		−	1.54262i	−0.636458	−	0.771311i	$-0.719601\pi$
$37$		−	1.06972e8i		−	1.54262i	0.636458	−	0.771311i	$-0.280399\pi$
$38$	−2.15067e7	−	4.00382e7i	−0.271429	−	0.505309i
$39$			1.63428e8i			1.81136i
$40$	−9.08562e7	+	4.72326e7i	−0.887267	+	0.461255i
$41$	−1.66613e8			−1.43811			−0.719053	−	0.694956i	$-0.755424\pi$
$41$	−1.66613e8			−1.43811			−0.719053	+	0.694956i	$0.755424\pi$
$42$	1.51793e8	−	8.15366e7i	1.16147	−	0.623887i
$43$	−7.53526e7			−0.512574			−0.256287	−	0.966601i	$-0.582499\pi$
$43$	−7.53526e7			−0.512574			−0.256287	+	0.966601i	$0.582499\pi$
$44$	1.16855e8	+	7.73873e7i	0.708571	+	0.469252i
$45$	1.06744e8	+	1.66015e8i	0.578468	+	0.899673i
$46$	2.94070e8	−	1.57961e8i	1.42778	−	0.766940i
$47$	−2.17109e8			−0.946650			−0.473325	−	0.880888i	$-0.656946\pi$
$47$	−2.17109e8			−0.946650			−0.473325	+	0.880888i	$0.656946\pi$
$48$	1.43056e8	+	3.37496e8i	0.561435	+	1.32453i
$49$	−4.52265e7			−0.160108
$50$	−2.02903e7	−	3.11841e8i	−0.0649288	−	0.997890i
$51$		−	4.16755e8i		−	1.20790i
$52$	−3.99128e8	−	2.64323e8i	−1.04977	−	0.695214i
$53$			5.32584e8i			1.27353i	0.771058	+	0.636765i	$0.219728\pi$
$53$			5.32584e8i			1.27353i	−0.771058	+	0.636765i	$0.780272\pi$
$54$	4.04996e7	−	2.17546e7i	0.0882026	−	0.0473785i
$55$	−3.59773e8	+	2.31325e8i	−0.714850	+	0.459631i
$56$	−4.63748e7	+	5.02587e8i	−0.0842058	+	0.912580i
$57$		−	4.96503e8i		−	0.825178i
$58$	−2.53226e8	+	1.36022e8i	−0.385805	+	0.207237i
$59$		−	2.43551e6i		−	0.00340667i	−0.999999	−	0.00170333i	$-0.999458\pi$
$59$		−	2.43551e6i		−	0.00340667i	0.999999	−	0.00170333i	$-0.000542188\pi$
$60$	−1.11856e9	−	1.51223e7i	−1.43848	−	0.0194474i
$61$	−1.38721e9			−1.64245			−0.821227	−	0.570602i	$-0.806710\pi$
$61$	−1.38721e9			−1.64245			−0.821227	+	0.570602i	$0.806710\pi$
$62$	−4.23159e8	−	7.87777e8i	−0.461897	−	0.859894i
$63$	9.72824e8			0.980238
$64$	−1.05561e9	−	1.96480e8i	−0.983115	−	0.182987i
$65$	1.22883e9	−	7.90110e8i	1.05907	−	0.680959i
$66$	7.24543e8	+	1.34885e9i	0.578555	+	1.07707i
$67$	1.26950e9			0.940281			0.470141	−	0.882591i	$-0.344203\pi$
$67$	1.26950e9			0.940281			0.470141	+	0.882591i	$0.344203\pi$
$68$	1.01781e9	+	6.74045e8i	0.700037	+	0.463601i
$69$	3.64668e9			2.33159
$70$	−1.34694e9	−	7.47152e8i	−0.801417	−	0.444548i
$71$		−	2.18640e9i		−	1.21182i	−0.795534	−	0.605909i	$-0.792810\pi$
$71$		−	2.18640e9i		−	1.21182i	0.795534	−	0.605909i	$-0.207190\pi$
$72$	−1.90157e8	+	2.06083e9i	−0.0982766	+	1.06507i
$73$			5.11042e8i			0.246514i	0.992375	+	0.123257i	$0.0393340\pi$
$73$			5.11042e8i			0.246514i	−0.992375	+	0.123257i	$0.960666\pi$
$74$	1.61983e9	+	3.01558e9i	0.729981	+	1.35898i
$75$	1.41680e9	−	3.10601e9i	0.597037	−	1.30887i
$76$	1.21257e9	+	8.03026e8i	0.478232	+	0.316710i
$77$			2.10822e9i			0.778864i
$78$	−2.47474e9	−	4.60712e9i	−0.857149	−	1.59572i
$79$			4.53243e9i			1.47297i	0.676451	+	0.736487i	$0.263517\pi$
$79$			4.53243e9i			1.47297i	−0.676451	+	0.736487i	$0.736483\pi$
$80$	1.84605e9	−	2.70731e9i	0.563370	−	0.826205i
$81$	−3.22723e9			−0.925560
$82$	4.69690e9	−	2.52297e9i	1.26690	−	0.680522i
$83$	8.51402e8			0.216145			0.108072	−	0.994143i	$-0.465532\pi$
$83$	8.51402e8			0.216145			0.108072	+	0.994143i	$0.465532\pi$
$84$	−3.04444e9	+	4.59711e9i	−0.727966	+	1.09923i
$85$	−3.13362e9	+	2.01484e9i	−0.706240	+	0.454095i
$86$	2.12422e9	−	1.14104e9i	0.451552	−	0.242554i
$87$	−3.14019e9			−0.630027
$88$	−4.46604e9	−	4.12091e8i	−0.846270	−	0.0780873i
$89$	2.46239e9			0.440967			0.220484	−	0.975391i	$-0.429236\pi$
$89$	2.46239e9			0.440967			0.220484	+	0.975391i	$0.429236\pi$
$90$	−5.52305e9	−	3.06365e9i	−0.935334	−	0.518832i
$91$		−	7.20080e9i		−	1.15391i
$92$	−5.89801e9	+	8.90599e9i	−0.894883	+	1.35127i
$93$		−	9.76902e9i		−	1.40422i
$94$	6.12041e9	−	3.28761e9i	0.833952	−	0.447962i
$95$	−3.73326e9	+	2.40039e9i	−0.482469	+	0.310216i
$96$	−9.14339e9	−	7.34792e9i	−1.12138	−	0.901173i
$97$			8.02939e9i			0.935026i	0.883986	+	0.467513i	$0.154850\pi$
$97$			8.02939e9i			0.935026i	−0.883986	+	0.467513i	$0.845150\pi$
$98$	1.27495e9	−	6.84848e8i	0.141047	−	0.0757642i
$99$			8.64462e9i			0.909012i
$100$	5.29408e9	+	8.48367e9i	0.529408	+	0.848367i
$101$	8.05325e9			0.766239			0.383120	−	0.923699i	$-0.374850\pi$
$101$	8.05325e9			0.766239			0.383120	+	0.923699i	$0.374850\pi$
$102$	6.31078e9	+	1.17485e10i	0.571587	+	1.06410i
$103$	−8.03199e9			−0.692846			−0.346423	−	0.938078i	$-0.612604\pi$
$103$	−8.03199e9			−0.692846			−0.346423	+	0.938078i	$0.612604\pi$
$104$	1.52541e10	+	1.40753e9i	1.25378	+	0.115689i
$105$	−9.10040e9	−	1.41536e10i	−0.713040	−	1.10897i
$106$	−8.06473e9	−	1.50138e10i	−0.602644	−	1.12192i
$107$	2.10995e9			0.150436			0.0752182	−	0.997167i	$-0.476035\pi$
$107$	2.10995e9			0.150436			0.0752182	+	0.997167i	$0.476035\pi$
$108$	−8.12279e8	+	1.22654e9i	−0.0552823	+	0.0834763i
$109$	−1.22312e10			−0.794945			−0.397473	−	0.917614i	$-0.630113\pi$
$109$	−1.22312e10			−0.794945			−0.397473	+	0.917614i	$0.630113\pi$
$110$	6.63927e9	−	1.19691e10i	0.412247	−	0.743184i
$111$			3.73953e10i			2.21923i
$112$	−6.30316e9	−	1.48704e10i	−0.357658	−	0.843785i
$113$			2.90497e10i			1.57670i	0.615225	+	0.788352i	$0.289065\pi$
$113$			2.90497e10i			1.57670i	−0.615225	+	0.788352i	$0.710935\pi$
$114$	7.51837e9	+	1.39966e10i	0.390481	+	0.726942i
$115$	−1.76302e10	−	2.74198e10i	−0.876534	−	1.36325i
$116$	5.07882e9	−	7.66902e9i	0.241809	−	0.365132i
$117$		−	2.95264e10i		−	1.34673i
$118$	3.68800e7	+	6.86580e7i	0.00161206	+	0.00300111i
$119$			1.83626e10i			0.769484i
$120$	3.17617e10	−	1.65117e10i	1.27643	−	0.663566i
$121$	7.20359e9			0.277730
$122$	3.91061e10	−	2.10060e10i	1.44692	−	0.777221i
$123$	5.82451e10			2.06887
$124$	2.38581e10	+	1.58000e10i	0.813817	+	0.538952i
$125$	−3.02040e10	+	4.36328e9i	−0.989726	+	0.142976i
$126$	−2.74243e10	+	1.47311e10i	−0.863542	+	0.463856i
$127$	−3.67613e10			−1.11268			−0.556342	−	0.830953i	$-0.687796\pi$
$127$	−3.67613e10			−1.11268			−0.556342	+	0.830953i	$0.687796\pi$
$128$	3.27334e10	−	1.04459e10i	0.952667	−	0.304015i
$129$	2.63419e10			0.737393
$130$	−2.26770e10	+	4.08814e10i	−0.610758	+	1.10105i
$131$		−	2.28988e10i		−	0.593548i	−0.954948	−	0.296774i	$-0.904089\pi$
$131$		−	2.28988e10i		−	0.593548i	0.954948	−	0.296774i	$-0.0959108\pi$
$132$	−4.08503e10	−	2.70532e10i	−1.01936	−	0.675071i
$133$			2.18764e10i			0.525674i
$134$	−3.57877e10	+	1.92235e10i	−0.828342	+	0.444948i
$135$	−2.42805e9	−	3.77627e9i	−0.0541488	−	0.0842160i
$136$	−3.88992e10	−	3.58932e9i	−0.836078	−	0.0771468i
$137$		−	4.70399e10i		−	0.974683i	−0.873211	−	0.487342i	$-0.837967\pi$
$137$		−	4.70399e10i		−	0.974683i	0.873211	−	0.487342i	$-0.162033\pi$
$138$	−1.02802e11	+	5.52204e10i	−2.05402	+	1.10333i
$139$		−	2.73069e10i		−	0.526257i	−0.964761	−	0.263129i	$-0.915246\pi$
$139$		−	2.73069e10i		−	0.526257i	0.964761	−	0.263129i	$-0.0847543\pi$
$140$	4.92847e10	+	6.66302e8i	0.916373	+	0.0123888i
$141$	7.58975e10			1.36186
$142$	3.31078e10	+	6.16355e10i	0.573441	+	1.06755i
$143$	6.39870e10			1.07007
$144$	−2.58457e10	−	6.09751e10i	−0.417423	−	0.984781i
$145$	1.51815e10	+	2.36114e10i	0.236851	+	0.368367i
$146$	−7.73852e9	−	1.44065e10i	−0.116652	−	0.217167i
$147$	1.58104e10			0.230332
$148$	−9.13275e10	−	6.04818e10i	−1.28615	−	0.851758i
$149$	−1.48875e10			−0.202717			−0.101358	−	0.994850i	$-0.532319\pi$
$149$	−1.48875e10			−0.202717			−0.101358	+	0.994850i	$0.532319\pi$
$150$	7.09311e9	+	1.09014e11i	0.0934072	+	1.43557i
$151$		−	7.59340e10i		−	0.967278i	−0.875268	−	0.483639i	$-0.839315\pi$
$151$		−	7.59340e10i		−	0.967278i	0.875268	−	0.483639i	$-0.160685\pi$
$152$	−4.63428e10	−	4.27615e9i	−0.571168	−	0.0527030i
$153$			7.52947e10i			0.898064i
$154$	−3.19240e10	−	5.94315e10i	−0.368564	−	0.686141i
$155$	−7.34542e10	+	4.72293e10i	−0.821028	+	0.527901i
$156$	1.39528e11	+	9.24026e10i	1.51021	+	1.00014i
$157$			8.81276e10i			0.923876i	0.886912	+	0.461938i	$0.152846\pi$
$157$			8.81276e10i			0.923876i	−0.886912	+	0.461938i	$0.847154\pi$
$158$	−6.86329e10	−	1.27771e11i	−0.697023	−	1.29762i
$159$		−	1.86182e11i		−	1.83211i
$160$	−1.10451e10	+	1.04274e11i	−0.105335	+	0.994437i
$161$	−1.60676e11			−1.48532
$162$	9.09769e10	−	4.88688e10i	0.815373	−	0.437982i
$163$	2.21477e9			0.0192482			0.00962412	−	0.999954i	$-0.496937\pi$
$163$	2.21477e9			0.0192482			0.00962412	+	0.999954i	$0.496937\pi$
$164$	−9.42034e10	+	1.42247e11i	−0.794049	+	1.19901i
$165$	1.25770e11	−	8.08671e10i	1.02839	−	0.661229i
$166$	−2.40014e10	+	1.28925e10i	−0.190413	+	0.102281i
$167$	−8.78029e9			−0.0675968			−0.0337984	−	0.999429i	$-0.510760\pi$
$167$	−8.78029e9			−0.0675968			−0.0337984	+	0.999429i	$0.510760\pi$
$168$	1.62118e10	−	1.75695e11i	0.121139	−	1.31285i
$169$	−8.06947e10			−0.585344
$170$	5.78282e10	−	1.04251e11i	0.407282	−	0.734234i
$171$			8.97027e10i			0.613515i
$172$	−4.26044e10	+	6.43327e10i	−0.283017	+	0.427356i
$173$		−	8.45977e10i		−	0.545919i	−0.962026	−	0.272959i	$-0.911998\pi$
$173$		−	8.45977e10i		−	0.545919i	0.962026	−	0.272959i	$-0.0880025\pi$
$174$	8.85232e10	−	4.75507e10i	0.555023	−	0.298134i
$175$	−6.24253e10	+	1.36854e11i	−0.380338	+	0.833807i
$176$	1.32140e11	−	5.60105e10i	0.782474	−	0.331670i
$177$			8.51410e8i			0.00490086i
$178$	−6.94157e10	+	3.72870e10i	−0.388470	+	0.208669i
$179$			2.11430e11i			1.15054i	0.817964	+	0.575270i	$0.195103\pi$
$179$			2.11430e11i			1.15054i	−0.817964	+	0.575270i	$0.804897\pi$
$180$	2.02089e11	+	2.73213e9i	1.06950	+	0.0144590i
$181$	3.16259e9			0.0162798			0.00813992	−	0.999967i	$-0.497409\pi$
$181$	3.16259e9			0.0162798			0.00813992	+	0.999967i	$0.497409\pi$
$182$	1.09039e11	+	2.02994e11i	0.546041	+	1.01654i
$183$	4.84944e11			2.36285
$184$	3.14072e10	−	3.40375e11i	0.148915	−	1.61387i
$185$	2.81179e11	−	1.80791e11i	1.29755	−	0.834294i
$186$	1.47929e11	+	2.75393e11i	0.664489	+	1.23705i
$187$	−1.63172e11			−0.713571
$188$	−1.22754e11	+	1.85358e11i	−0.522692	+	0.789265i
$189$	−2.21284e10			−0.0917575
$190$	6.88938e10	−	1.24199e11i	0.278235	−	0.501593i
$191$			1.03963e11i			0.408988i	0.978868	+	0.204494i	$0.0655549\pi$
$191$			1.03963e11i			0.408988i	−0.978868	+	0.204494i	$0.934445\pi$
$192$	3.69023e11	+	6.86860e10i	1.41432	+	0.263246i
$193$			2.01647e11i			0.753016i	0.926413	+	0.376508i	$0.122875\pi$
$193$			2.01647e11i			0.753016i	−0.926413	+	0.376508i	$0.877125\pi$
$194$	−1.21586e11	−	2.26352e11i	−0.442461	−	0.823712i
$195$	−4.29578e11	+	2.76208e11i	−1.52359	+	0.979634i
$196$	−2.55711e10	+	3.86123e10i	−0.0884034	+	0.133489i
$197$		−	2.57466e11i		−	0.867740i	−0.900976	−	0.433870i	$-0.857148\pi$
$197$		−	2.57466e11i		−	0.867740i	0.900976	−	0.433870i	$-0.142852\pi$
$198$	−1.30902e11	−	2.43696e11i	−0.430152	−	0.800795i
$199$		−	2.73905e11i		−	0.877675i	−0.898566	−	0.438838i	$-0.855390\pi$
$199$		−	2.73905e11i		−	0.877675i	0.898566	−	0.438838i	$-0.144610\pi$
$200$	−2.77708e11	−	1.58992e11i	−0.867836	−	0.496850i
$201$	−4.43793e11			−1.35270
$202$	−2.27025e11	+	1.21948e11i	−0.675019	+	0.362590i
$203$	1.38359e11			0.401355
$204$	−3.55807e11	−	2.35634e11i	−1.00708	−	0.666940i
$205$	−2.81591e11	−	4.37950e11i	−0.777768	−	1.20964i
$206$	2.26425e11	−	1.21625e11i	0.610364	−	0.327860i
$207$	−6.58842e11			−1.73352
$208$	−4.51334e11	+	1.91309e11i	−1.15926	+	0.491381i
$209$	−1.94396e11			−0.487478
$210$	4.70867e11	+	2.61191e11i	1.15293	+	0.639531i
$211$			1.24487e11i			0.297655i	0.988863	+	0.148827i	$0.0475498\pi$
$211$			1.24487e11i			0.297655i	−0.988863	+	0.148827i	$0.952450\pi$
$212$	4.54697e11	+	3.01124e11i	1.06180	+	0.703179i
$213$			7.64325e11i			1.74333i
$214$	−5.94803e10	+	3.19502e10i	−0.132527	+	0.0711876i
$215$	−1.27353e11	−	1.98067e11i	−0.277214	−	0.431143i
$216$	4.32543e9	−	4.68767e10i	0.00919941	−	0.0996985i
$217$			4.30431e11i			0.894551i
$218$	3.44803e11	−	1.85213e11i	0.700308	−	0.376174i
$219$		−	1.78651e11i		−	0.354638i
$220$	−5.92083e9	+	4.37949e11i	−0.0114886	+	0.849787i
$221$	5.57328e11			1.05718
$222$	−5.66264e11	−	1.05419e12i	−1.05016	−	1.95503i
$223$	3.90019e11			0.707231			0.353615	−	0.935391i	$-0.384952\pi$
$223$	3.90019e11			0.707231			0.353615	+	0.935391i	$0.384952\pi$
$224$	4.02866e11	+	3.23756e11i	0.714365	+	0.574086i
$225$	−2.55971e11	+	5.61160e11i	−0.443893	+	0.973137i
$226$	−4.39890e11	−	8.18925e11i	−0.746108	−	1.38900i
$227$	5.52903e11			0.917318			0.458659	−	0.888612i	$-0.348330\pi$
$227$	5.52903e11			0.917318			0.458659	+	0.888612i	$0.348330\pi$
$228$	−4.23892e11	−	2.80723e11i	−0.687989	−	0.455622i
$229$	4.80260e11			0.762605			0.381302	−	0.924450i	$-0.375476\pi$
$229$	4.80260e11			0.762605			0.381302	+	0.924450i	$0.375476\pi$
$230$	9.12211e11	+	5.06006e11i	1.41728	+	0.786171i
$231$		−	7.36995e11i		−	1.12048i
$232$	−2.70450e10	+	2.93100e11i	−0.0402390	+	0.436089i
$233$			2.30713e10i			0.0335964i	0.999859	+	0.0167982i	$0.00534729\pi$
$233$			2.30713e10i			0.0335964i	−0.999859	+	0.0167982i	$0.994653\pi$
$234$	4.47108e11	+	8.32363e11i	0.637284	+	1.18641i
$235$	−3.66934e11	−	5.70681e11i	−0.511975	−	0.796258i
$236$	−2.07933e9	−	1.37704e9i	−0.00284029	−	0.00188099i
$237$		−	1.58445e12i		−	2.11903i
$238$	−2.78058e11	−	5.17650e11i	−0.364125	−	0.677877i
$239$			1.06169e12i			1.36147i	0.732530	+	0.680734i	$0.238339\pi$
$239$			1.06169e12i			1.36147i	−0.732530	+	0.680734i	$0.761661\pi$
$240$	−6.45346e11	+	9.46426e11i	−0.810469	+	1.18859i
$241$	1.28269e12			1.57775			0.788874	−	0.614555i	$-0.210665\pi$
$241$	1.28269e12			1.57775			0.788874	+	0.614555i	$0.210665\pi$
$242$	−2.03072e11	+	1.09081e11i	−0.244666	+	0.131424i
$243$	1.21301e12			1.43164
$244$	−7.84330e11	+	1.18434e12i	−0.906880	+	1.36939i
$245$	−7.64367e10	−	1.18880e11i	−0.0865908	−	0.134672i
$246$	−1.64195e12	+	8.81984e11i	−1.82257	+	0.979005i
$247$	6.63975e11			0.722215
$248$	−9.11823e11	−	8.41360e10i	−0.971969	−	0.0896858i
$249$	−2.97635e11			−0.310948
$250$	7.85393e11	−	5.80372e11i	0.804243	−	0.594301i
$251$			5.70243e11i			0.572389i	0.958172	+	0.286195i	$0.0923904\pi$
$251$			5.70243e11i			0.572389i	−0.958172	+	0.286195i	$0.907610\pi$
$252$	5.50036e11	−	8.30554e11i	0.541238	−	0.817269i
$253$		−	1.42778e12i		−	1.37740i
$254$	1.03632e12	−	5.56663e11i	0.980221	−	0.526531i
$255$	1.09546e12	−	7.04353e11i	1.01600	−	0.653265i
$256$	−7.64590e11	+	7.90144e11i	−0.695391	+	0.718632i
$257$			1.31540e12i			1.17326i	0.809856	+	0.586629i	$0.199545\pi$
$257$			1.31540e12i			1.17326i	−0.809856	+	0.586629i	$0.800455\pi$
$258$	−7.42590e11	+	3.98886e11i	−0.649607	+	0.348940i
$259$		−	1.64767e12i		−	1.41375i
$260$	2.02231e10	−	1.49585e12i	0.0170208	−	1.25899i
$261$	5.67334e11			0.468421
$262$	3.46748e11	+	6.45527e11i	0.280871	+	0.522887i
$263$	−1.33251e12			−1.05899			−0.529494	−	0.848314i	$-0.677618\pi$
$263$	−1.33251e12			−1.05899			−0.529494	+	0.848314i	$0.677618\pi$
$264$	1.56125e12	+	1.44060e11i	1.21745	+	0.112337i
$265$	−1.39992e12	+	9.00114e11i	−1.07121	+	0.688761i
$266$	−3.31266e11	−	6.16704e11i	−0.248753	−	0.463093i
$267$	−8.60806e11			−0.634379
$268$	7.17775e11	−	1.08384e12i	0.519176	−	0.783955i
$269$	2.85417e11			0.202637			0.101318	−	0.994854i	$-0.467694\pi$
$269$	2.85417e11			0.202637			0.101318	+	0.994854i	$0.467694\pi$
$270$	1.25631e11	+	6.96876e10i	0.0875541	+	0.0485665i
$271$			1.32070e12i			0.903561i	0.892129	+	0.451781i	$0.149211\pi$
$271$			1.32070e12i			0.903561i	−0.892129	+	0.451781i	$0.850789\pi$
$272$	1.15094e12	−	4.87853e11i	0.773050	−	0.327676i
$273$			2.51727e12i			1.66003i
$274$	7.12308e11	+	1.32607e12i	0.461227	+	0.858648i
$275$	−1.21609e12	−	5.54717e11i	−0.773221	−	0.352702i
$276$	2.06184e12	−	3.11337e12i	1.28739	−	1.94395i
$277$		−	1.71012e11i		−	0.104864i	−0.998624	−	0.0524321i	$-0.983303\pi$
$277$		−	1.71012e11i		−	0.104864i	0.998624	−	0.0524321i	$-0.0166973\pi$
$278$	4.13498e11	+	7.69793e11i	0.249029	+	0.463607i
$279$			1.76496e12i			1.04403i
$280$	−1.39945e12	+	7.27517e11i	−0.813142	+	0.422720i
$281$	−2.82707e12			−1.61363			−0.806817	−	0.590802i	$-0.798811\pi$
$281$	−2.82707e12			−1.61363			−0.806817	+	0.590802i	$0.798811\pi$
$282$	−2.13958e12	+	1.14929e12i	−1.19973	+	0.644442i
$283$	5.80867e11			0.319996			0.159998	−	0.987117i	$-0.448851\pi$
$283$	5.80867e11			0.319996			0.159998	+	0.987117i	$0.448851\pi$
$284$	−1.86665e12	−	1.23619e12i	−1.01035	−	0.669105i
$285$	1.30508e12	−	8.39134e11i	0.694085	−	0.446280i
$286$	−1.80382e12	+	9.68932e11i	−0.942678	+	0.506365i
$287$	−2.56633e12			−1.31796
$288$	1.65193e12	+	1.32754e12i	0.833735	+	0.670016i
$289$	5.94764e11			0.295023
$290$	−7.85513e11	−	4.35726e11i	−0.382969	−	0.212434i
$291$		−	2.80693e12i		−	1.34514i
$292$	4.36305e11	+	2.88944e11i	0.205530	+	0.136113i
$293$		−	1.45592e12i		−	0.674215i	−0.941466	−	0.337108i	$-0.890551\pi$
$293$		−	1.45592e12i		−	0.674215i	0.941466	−	0.337108i	$-0.109449\pi$
$294$	−4.45701e11	+	2.39411e11i	−0.202912	+	0.108995i
$295$	6.40183e9	−	4.11622e9i	0.00286546	−	0.00184242i
$296$	3.49042e12	+	3.22069e11i	1.53610	+	0.141739i
$297$		−	1.96635e11i		−	0.0850902i
$298$	4.19684e11	−	2.25436e11i	0.178584	−	0.0959271i
$299$			4.87671e12i			2.04066i
$300$	−1.85072e12	−	2.96574e12i	−0.761611	−	1.22047i
$301$	−1.16065e12			−0.469751
$302$	1.14984e12	+	2.14061e12i	0.457723	+	0.852125i
$303$	−2.81527e12			−1.10232
$304$	1.37117e12	−	5.81205e11i	0.528111	−	0.223852i
$305$	−2.34451e12	−	3.64634e12i	−0.888285	−	1.38152i
$306$	−1.14016e12	−	2.12259e12i	−0.424971	−	0.791151i
$307$	3.77121e12			1.38289			0.691446	−	0.722428i	$-0.256974\pi$
$307$	3.77121e12			1.38289			0.691446	+	0.722428i	$0.256974\pi$
$308$	1.79990e12	+	1.19199e12i	0.649374	+	0.430049i
$309$	2.80784e12			0.996735
$310$	1.35553e12	−	2.44370e12i	0.473479	−	0.853572i
$311$			4.61244e11i			0.158536i	0.996853	+	0.0792682i	$0.0252584\pi$
$311$			4.61244e11i			0.158536i	−0.996853	+	0.0792682i	$0.974742\pi$
$312$	−5.33257e12	−	4.92048e11i	−1.80370	−	0.166431i
$313$		−	1.26212e12i		−	0.420124i	−0.977688	−	0.210062i	$-0.932633\pi$
$313$		−	1.26212e12i		−	0.420124i	0.977688	−	0.210062i	$-0.0673666\pi$
$314$	−1.33449e12	−	2.48436e12i	−0.437185	−	0.813890i
$315$	1.64416e12	+	2.55711e12i	0.530141	+	0.824511i
$316$	3.86958e12	+	2.56264e12i	1.22809	+	0.813302i
$317$			1.74363e12i			0.544700i	0.962198	+	0.272350i	$0.0878009\pi$
$317$			1.74363e12i			0.544700i	−0.962198	+	0.272350i	$0.912199\pi$
$318$	2.81929e12	+	5.24855e12i	0.866969	+	1.61400i
$319$			1.22948e12i			0.372191i
$320$	−1.26762e12	−	3.10679e12i	−0.377780	−	0.925895i
$321$	−7.37600e11			−0.216419
$322$	4.52952e12	−	2.43306e12i	1.30850	−	0.702867i
$323$	−1.69319e12			−0.481607
$324$	−1.82468e12	+	2.75526e12i	−0.511047	+	0.771681i
$325$	4.15368e12	+	1.89469e12i	1.14555	+	0.522541i
$326$	−6.24354e10	+	3.35375e10i	−0.0169568	+	0.00910841i
$327$	4.27581e12			1.14362
$328$	5.01638e11	−	5.43649e12i	0.132136	−	1.43202i
$329$	−3.34411e12			−0.867563
$330$	−2.32097e12	+	4.18417e12i	−0.593062	+	1.06915i
$331$		−	2.14680e12i		−	0.540320i	−0.962815	−	0.270160i	$-0.912923\pi$
$331$		−	2.14680e12i		−	0.540320i	0.962815	−	0.270160i	$-0.0870767\pi$
$332$	4.81384e11	−	7.26889e11i	0.119344	−	0.180210i
$333$		−	6.75618e12i		−	1.64998i
$334$	2.47520e11	−	1.32957e11i	0.0595495	−	0.0319873i
$335$	2.14556e12	+	3.33693e12i	0.508531	+	0.790902i
$336$	2.20347e12	+	5.19841e12i	0.514531	+	1.21388i
$337$			5.43849e12i			1.25121i	0.780141	+	0.625603i	$0.215147\pi$
$337$			5.43849e12i			1.25121i	−0.780141	+	0.625603i	$0.784853\pi$
$338$	2.27482e12	−	1.22193e12i	0.515660	−	0.276989i
$339$		−	1.01553e13i		−	2.26826i
$340$	−5.15705e10	+	3.81454e12i	−0.0113503	+	0.839553i
$341$	−3.82486e12			−0.829551
$342$	−1.35834e12	−	2.52876e12i	−0.290320	−	0.540476i
$343$	−5.04755e12			−1.06319
$344$	2.26871e11	−	2.45871e12i	0.0470963	−	0.510405i
$345$	6.16321e12	+	9.58545e12i	1.26099	+	1.96118i
$346$	1.28103e12	+	2.38485e12i	0.258333	+	0.480928i
$347$	−5.05927e12			−1.00564			−0.502818	−	0.864393i	$-0.667703\pi$
$347$	−5.05927e12			−1.00564			−0.502818	+	0.864393i	$0.667703\pi$
$348$	−1.77546e12	+	2.68095e12i	−0.347869	+	0.525282i
$349$	2.62528e12			0.507047			0.253524	−	0.967329i	$-0.418410\pi$
$349$	2.62528e12			0.507047			0.253524	+	0.967329i	$0.418410\pi$
$350$	−3.12528e11	−	4.80324e12i	−0.0595044	−	0.914523i
$351$			6.71625e11i			0.126064i
$352$	−2.87693e12	+	3.57990e12i	−0.532372	+	0.662458i
$353$			4.49441e12i			0.819972i	0.912092	+	0.409986i	$0.134466\pi$
$353$			4.49441e12i			0.819972i	−0.912092	+	0.409986i	$0.865534\pi$
$354$	−1.28926e10	−	2.40016e10i	−0.00231912	−	0.00431742i
$355$	5.74704e12	−	3.69520e12i	1.01930	−	0.655385i
$356$	1.39224e12	−	2.10228e12i	0.243480	−	0.367654i
$357$		−	6.41923e12i		−	1.10699i
$358$	−3.20161e12	−	5.96031e12i	−0.544444	−	1.01357i
$359$		−	1.08461e13i		−	1.81887i	−0.415849	−	0.909434i	$-0.636515\pi$
$359$		−	1.08461e13i		−	1.81887i	0.415849	−	0.909434i	$-0.363485\pi$
$360$	−5.73835e12	+	2.98314e12i	−0.949018	+	0.493357i
$361$	4.11388e12			0.670989
$362$	−8.91548e10	+	4.78900e10i	−0.0143417	+	0.00770374i
$363$	−2.51825e12			−0.399544
$364$	−6.14772e12	−	4.07134e12i	−0.962071	−	0.637133i
$365$	−1.34329e12	+	8.63706e11i	−0.207351	+	0.133322i
$366$	−1.36708e13	+	7.34333e12i	−2.08155	+	1.11812i
$367$	8.70804e12			1.30795			0.653974	−	0.756517i	$-0.273101\pi$
$367$	8.70804e12			1.30795			0.653974	+	0.756517i	$0.273101\pi$
$368$	4.26879e12	+	1.00709e13i	0.632508	+	1.49221i
$369$	−1.05231e13			−1.53819
$370$	−5.18890e12	+	9.35438e12i	−0.748285	+	1.34898i
$371$			8.20333e12i			1.16713i
$372$	−8.34035e12	−	5.52341e12i	−1.17076	−	0.775341i
$373$		−	8.15755e12i		−	1.12984i	−0.825147	−	0.564918i	$-0.808908\pi$
$373$		−	8.15755e12i		−	1.12984i	0.825147	−	0.564918i	$-0.191092\pi$
$374$	4.59989e12	−	2.47085e12i	0.628621	−	0.337667i
$375$	1.05588e13	−	1.52532e12i	1.42383	−	0.205687i
$376$	6.53670e11	−	7.08415e12i	0.0869800	−	0.942645i
$377$		−	4.19938e12i		−	0.551415i
$378$	6.23810e11	−	3.35083e11i	0.0808339	−	0.0434203i
$379$			8.76598e12i			1.12100i	0.828156	+	0.560498i	$0.189390\pi$
$379$			8.76598e12i			1.12100i	−0.828156	+	0.560498i	$0.810610\pi$
$380$	−6.14387e10	+	4.54447e12i	−0.00775397	+	0.573542i
$381$	1.28511e13			1.60072
$382$	−1.57427e12	−	2.93075e12i	−0.193536	−	0.360299i
$383$	−1.43805e13			−1.74494			−0.872469	−	0.488669i	$-0.837482\pi$
$383$	−1.43805e13			−1.74494			−0.872469	+	0.488669i	$0.837482\pi$
$384$	−1.14430e13	+	3.65169e12i	−1.37052	+	0.437359i
$385$	−5.54153e12	+	3.56307e12i	−0.655128	+	0.421232i
$386$	−3.05346e12	−	5.68450e12i	−0.356333	−	0.663370i
$387$	−4.75917e12			−0.548247
$388$	6.85513e12	+	4.53982e12i	0.779574	+	0.516274i
$389$	2.07436e12			0.232882			0.116441	−	0.993198i	$-0.462851\pi$
$389$	2.07436e12			0.232882			0.116441	+	0.993198i	$0.462851\pi$
$390$	7.92748e12	−	1.42914e13i	0.878642	−	1.58399i
$391$		−	1.24360e13i		−	1.36081i
$392$	1.36167e11	−	1.47571e12i	0.0147110	−	0.159430i
$393$			8.00500e12i			0.853884i
$394$	3.89872e12	+	7.25809e12i	0.410621	+	0.764436i
$395$	−1.19137e13	+	7.66020e12i	−1.23897	+	0.796626i
$396$	7.38039e12	+	4.88767e12i	0.757885	+	0.501911i
$397$			3.27569e12i			0.332162i	0.986112	+	0.166081i	$0.0531114\pi$
$397$			3.27569e12i			0.332162i	−0.986112	+	0.166081i	$0.946889\pi$
$398$	4.14764e12	+	7.72149e12i	0.415322	+	0.773189i
$399$		−	7.64758e12i		−	0.756240i
$400$	1.02363e13	+	2.76828e11i	0.999635	+	0.0270339i
$401$	3.07496e12			0.296564			0.148282	−	0.988945i	$-0.452626\pi$
$401$	3.07496e12			0.296564			0.148282	+	0.988945i	$0.452626\pi$
$402$	1.25107e13	−	6.72021e12i	1.19166	−	0.640107i
$403$	1.30641e13			1.22901
$404$	4.55332e12	−	6.87551e12i	0.423079	−	0.638848i
$405$	−5.45430e12	−	8.48290e12i	−0.500569	−	0.778519i
$406$	−3.90041e12	+	2.09513e12i	−0.353574	+	0.189924i
$407$	1.46414e13			1.31102
$408$	1.35985e13	+	1.25476e12i	1.20279	+	0.110984i
$409$	2.37374e12			0.207404			0.103702	−	0.994608i	$-0.466931\pi$
$409$	2.37374e12			0.207404			0.103702	+	0.994608i	$0.466931\pi$
$410$	1.45699e13	+	8.08197e12i	1.25759	+	0.697586i
$411$			1.64443e13i			1.40219i
$412$	−4.54129e12	+	6.85735e12i	−0.382555	+	0.577657i
$413$		−	3.75138e10i		−	0.00312206i
$414$	1.85730e13	−	9.97661e12i	1.52715	−	0.820316i
$415$	1.43894e12	+	2.23795e12i	0.116897	+	0.181806i
$416$	9.82639e12	−	1.22275e13i	0.788728	−	0.981454i
$417$			9.54599e12i			0.757078i
$418$	5.48009e12	−	2.94366e12i	0.429444	−	0.230678i
$419$			1.15767e13i			0.896425i	0.893927	+	0.448213i	$0.147939\pi$
$419$			1.15767e13i			0.896425i	−0.893927	+	0.448213i	$0.852061\pi$
$420$	−1.72291e13	−	2.32927e11i	−1.31830	−	0.0178227i
$421$	−1.46083e12			−0.110456			−0.0552280	−	0.998474i	$-0.517589\pi$
$421$	−1.46083e12			−0.110456			−0.0552280	+	0.998474i	$0.517589\pi$
$422$	−1.88507e12	−	3.50935e12i	−0.140852	−	0.262219i
$423$	−1.37123e13			−1.01253
$424$	−1.73779e13	−	1.60350e12i	−1.26814	−	0.117014i
$425$	−1.05922e13	−	4.83160e12i	−0.763909	−	0.348454i
$426$	−1.15739e13	−	2.15467e13i	−0.824958	−	1.53579i
$427$	−2.13670e13			−1.50524
$428$	1.19297e12	−	1.80138e12i	0.0830633	−	0.125426i
$429$	−2.23687e13			−1.53941
$430$	6.58939e12	+	3.65515e12i	0.448232	+	0.248636i
$431$			2.67029e13i			1.79545i	0.440559	+	0.897724i	$0.354780\pi$
$431$			2.67029e13i			1.79545i	−0.440559	+	0.897724i	$0.645220\pi$
$432$	5.87902e11	+	1.38697e12i	0.0390739	+	0.0921827i
$433$		−	2.61290e13i		−	1.71666i	−0.513100	−	0.858329i	$-0.671503\pi$
$433$		−	2.61290e13i		−	1.71666i	0.513100	−	0.858329i	$-0.328497\pi$
$434$	−6.51787e12	−	1.21340e13i	−0.423308	−	0.788056i
$435$	−5.30719e12	−	8.25411e12i	−0.340736	−	0.529937i
$436$	−6.91554e12	+	1.04425e13i	−0.438928	+	0.662782i
$437$		−	1.48157e13i		−	0.929639i
$438$	2.70525e12	+	5.03625e12i	0.167817	+	0.312419i
$439$			2.23622e12i			0.137149i	0.997646	+	0.0685743i	$0.0218450\pi$
$439$			2.23622e12i			0.137149i	−0.997646	+	0.0685743i	$0.978155\pi$
$440$	−6.46479e12	−	1.24356e13i	−0.392005	−	0.754057i
$441$	−2.85644e12			−0.171251
$442$	−1.57113e13	+	8.43941e12i	−0.931325	+	0.500266i
$443$	1.37467e13			0.805711			0.402855	−	0.915264i	$-0.368018\pi$
$443$	1.37467e13			0.805711			0.402855	+	0.915264i	$0.368018\pi$
$444$	3.19265e13	+	2.11434e13i	1.85027	+	1.22535i
$445$	4.16165e12	+	6.47248e12i	0.238487	+	0.370912i
$446$	−1.09948e13	+	5.90591e12i	−0.623036	+	0.334667i
$447$	5.20439e12			0.291630
$448$	−1.62595e13	−	3.02636e12i	−0.900982	−	0.167699i
$449$	2.15001e13			1.17817			0.589086	−	0.808070i	$-0.299488\pi$
$449$	2.15001e13			1.17817			0.589086	+	0.808070i	$0.299488\pi$
$450$	−1.28150e12	−	1.96954e13i	−0.0694476	−	1.06734i
$451$		−	2.28046e13i		−	1.22220i
$452$	2.48014e13	+	1.64247e13i	1.31457	+	0.870576i
$453$			2.65452e13i			1.39154i
$454$	−1.55866e13	+	8.37241e12i	−0.808112	+	0.434082i
$455$	1.89276e13	−	1.21700e13i	0.970596	−	0.624069i
$456$	1.62006e13	+	1.49487e12i	0.821688	+	0.0758190i
$457$			1.60551e13i			0.805440i	0.915323	+	0.402720i	$0.131935\pi$
$457$			1.60551e13i			0.805440i	−0.915323	+	0.402720i	$0.868065\pi$
$458$	−1.35387e13	+	7.27241e12i	−0.671817	+	0.360870i
$459$		−	1.71270e12i		−	0.0840654i
$460$	−3.33779e13	−	4.51251e11i	−1.62058	−	0.0219093i
$461$	3.13459e12			0.150548			0.0752741	−	0.997163i	$-0.476017\pi$
$461$	3.13459e12			0.150548			0.0752741	+	0.997163i	$0.476017\pi$
$462$	1.11600e13	+	2.07762e13i	0.530220	+	0.987089i
$463$	−3.34837e13			−1.57372			−0.786862	−	0.617129i	$-0.788296\pi$
$463$	−3.34837e13			−1.57372			−0.786862	+	0.617129i	$0.788296\pi$
$464$	−3.67589e12	−	8.67214e12i	−0.170912	−	0.403215i
$465$	2.56783e13	−	1.65105e13i	1.18114	−	0.759443i
$466$	−3.49361e11	−	6.50391e11i	−0.0158981	−	0.0295968i
$467$	−7.93968e12			−0.357452			−0.178726	−	0.983899i	$-0.557198\pi$
$467$	−7.93968e12			−0.357452			−0.178726	+	0.983899i	$0.557198\pi$
$468$	−2.52083e13	−	1.66943e13i	−1.12283	−	0.743598i
$469$	1.95539e13			0.861727
$470$	1.89856e13	+	1.05314e13i	0.827820	+	0.459194i
$471$		−	3.08078e13i		−	1.32910i
$472$	7.94691e10	+	7.33280e9i	0.00339226	+	0.000313011i
$473$		−	1.03136e13i		−	0.435618i
$474$	2.39928e13	+	4.46665e13i	1.00274	+	1.86677i
$475$	−1.26191e13	−	5.75614e12i	−0.521866	−	0.238047i
$476$	1.56772e13	+	1.03822e13i	0.641553	+	0.424870i
$477$			3.36373e13i			1.36216i
$478$	−1.60768e13	−	2.99295e13i	−0.644257	−	1.19939i
$479$			3.20867e13i			1.27247i	0.771496	+	0.636234i	$0.219509\pi$
$479$			3.20867e13i			1.27247i	−0.771496	+	0.636234i	$0.780491\pi$
$480$	3.86118e12	−	3.64524e13i	0.151535	−	1.43061i
$481$	−5.00089e13			−1.94232
$482$	−3.61597e13	+	1.94234e13i	−1.38992	+	0.746602i
$483$	5.61694e13			2.13680
$484$	4.07292e12	−	6.15010e12i	0.153348	−	0.231556i
$485$	−2.11056e13	+	1.35704e13i	−0.786482	+	0.505688i
$486$	−3.41954e13	+	1.83682e13i	−1.26121	+	0.677463i
$487$	7.95230e12			0.290301			0.145150	−	0.989410i	$-0.453633\pi$
$487$	7.95230e12			0.290301			0.145150	+	0.989410i	$0.453633\pi$
$488$	4.17660e12	−	4.52638e13i	0.150912	−	1.63551i
$489$	−7.74244e11			−0.0276907
$490$	3.95493e12	+	2.19381e12i	0.140010	+	0.0776640i
$491$		−	3.68359e13i		−	1.29082i	−0.763838	−	0.645408i	$-0.776687\pi$
$491$		−	3.68359e13i		−	1.29082i	0.763838	−	0.645408i	$-0.223313\pi$
$492$	3.29318e13	−	4.97270e13i	1.14233	−	1.72491i
$493$			1.07087e13i			0.367709i
$494$	−1.87177e13	+	1.00543e13i	−0.636236	+	0.341758i
$495$	−2.27227e13	+	1.46102e13i	−0.764600	+	0.491619i
$496$	2.69787e13	−	1.14356e13i	0.898697	−	0.380934i
$497$		−	3.36768e13i		−	1.11058i
$498$	8.39046e12	−	4.50698e12i	0.273930	−	0.147143i
$499$		−	1.72566e13i		−	0.557767i	−0.960325	−	0.278883i	$-0.910036\pi$
$499$		−	1.72566e13i		−	0.557767i	0.960325	−	0.278883i	$-0.0899643\pi$
$500$	−1.33522e13	+	2.82539e13i	−0.427271	+	0.904124i
$501$	3.06943e12			0.0972454
$502$	−8.63498e12	−	1.60754e13i	−0.270859	−	0.504247i
$503$	2.01556e13			0.625974			0.312987	−	0.949757i	$-0.398670\pi$
$503$	2.01556e13			0.625974			0.312987	+	0.949757i	$0.398670\pi$
$504$	−2.92897e12	+	3.17427e13i	−0.0900662	+	0.976092i
$505$	1.36107e13	+	2.11683e13i	0.414404	+	0.644509i
$506$	2.16204e13	+	4.02498e13i	0.651795	+	1.21342i
$507$	2.82094e13			0.842082
$508$	−2.07849e13	+	3.13851e13i	−0.614368	+	0.927696i
$509$	3.17187e13			0.928381			0.464191	−	0.885735i	$-0.346345\pi$
$509$	3.17187e13			0.928381			0.464191	+	0.885735i	$0.346345\pi$
$510$	−2.02157e13	+	3.64442e13i	−0.585919	+	1.05628i
$511$			7.87152e12i			0.225920i
$512$	9.58926e12	−	3.38524e13i	0.272543	−	0.962144i
$513$		−	2.04043e12i		−	0.0574295i
$514$	−1.99187e13	−	3.70818e13i	−0.555195	−	1.03358i
$515$	−1.35748e13	−	2.11124e13i	−0.374711	−	0.582776i
$516$	1.48937e13	−	2.24896e13i	0.407151	−	0.614798i
$517$		−	2.97161e13i		−	0.804524i
$518$	2.49501e13	+	4.64485e13i	0.668996	+	1.24544i
$519$			2.95738e13i			0.785364i
$520$	2.20811e13	+	4.24750e13i	0.580769	+	1.11716i
$521$	1.65183e13			0.430307			0.215153	−	0.976580i	$-0.430975\pi$
$521$	1.65183e13			0.430307			0.215153	+	0.976580i	$0.430975\pi$
$522$	−1.59934e13	+	8.59094e12i	−0.412656	+	0.221660i
$523$	6.83907e13			1.74779			0.873894	−	0.486116i	$-0.161587\pi$
$523$	6.83907e13			1.74779			0.873894	+	0.486116i	$0.161587\pi$
$524$	−1.95500e13	−	1.29470e13i	−0.494868	−	0.327727i
$525$	2.18228e13	−	4.78415e13i	0.547158	−	1.19952i
$526$	3.75640e13	−	2.01777e13i	0.932916	−	0.501121i
$527$	−3.33145e13			−0.819560
$528$	−4.61936e13	+	1.95803e13i	−1.12567	+	0.477144i
$529$	6.73907e13			1.62675
$530$	2.58342e13	−	4.65731e13i	0.617755	−	1.11367i
$531$		−	1.53823e11i		−	0.00364376i
$532$	1.86771e13	+	1.23689e13i	0.438278	+	0.290251i
$533$			7.78912e13i			1.81072i
$534$	2.42665e13	−	1.30349e13i	0.558857	−	0.300193i
$535$	3.56600e12	+	5.54608e12i	0.0813602	+	0.126537i
$536$	−3.82219e12	+	4.14229e13i	−0.0863949	+	0.936304i
$537$		−	7.39122e13i		−	1.65518i
$538$	−8.04602e12	+	4.32196e12i	−0.178513	+	0.0958892i
$539$		−	6.19022e12i		−	0.136070i
$540$	−4.59683e12	−	6.21466e10i	−0.100113	−	0.00135347i
$541$	−5.70039e13			−1.23004			−0.615019	−	0.788512i	$-0.710852\pi$
$541$	−5.70039e13			−1.23004			−0.615019	+	0.788512i	$0.710852\pi$
$542$	−1.99989e13	−	3.72311e13i	−0.427572	−	0.795993i
$543$	−1.10558e12			−0.0234203
$544$	−2.50581e13	+	3.11810e13i	−0.525960	+	0.654479i
$545$	−2.06718e13	−	3.21503e13i	−0.429929	−	0.668655i
$546$	−3.81181e13	−	7.09629e13i	−0.785540	−	1.46241i
$547$	−6.42238e13			−1.31147			−0.655736	−	0.754990i	$-0.727642\pi$
$547$	−6.42238e13			−1.31147			−0.655736	+	0.754990i	$0.727642\pi$
$548$	−4.01605e13	−	2.65964e13i	−0.812637	−	0.538171i
$549$	−8.76142e13			−1.75676
$550$	4.26821e13	−	2.77716e12i	0.848072	−	0.0551807i
$551$			1.27579e13i			0.251201i
$552$	−1.09794e13	+	1.18989e14i	−0.214231	+	2.32173i
$553$			6.98124e13i			1.34992i
$554$	2.58957e12	+	4.82090e12i	0.0496225	+	0.0923802i
$555$	−9.82952e13	+	6.32014e13i	−1.86667	+	1.20022i
$556$	−2.33134e13	−	1.54393e13i	−0.438764	−	0.290573i
$557$			3.80459e13i			0.709631i	0.934936	+	0.354815i	$0.115456\pi$
$557$			3.80459e13i			0.709631i	−0.934936	+	0.354815i	$0.884544\pi$
$558$	−2.67261e13	−	4.97549e13i	−0.494043	−	0.919740i
$559$			3.52271e13i			0.645384i
$560$	2.84345e13	−	4.17004e13i	0.516304	−	0.757181i
$561$	5.70420e13			1.02655
$562$	7.96963e13	−	4.28093e13i	1.42153	−	0.763583i
$563$	3.66327e13			0.647630			0.323815	−	0.946120i	$-0.395034\pi$
$563$	3.66327e13			0.647630			0.323815	+	0.946120i	$0.395034\pi$
$564$	4.29125e13	−	6.47979e13i	0.751949	−	1.13544i
$565$	−7.63584e13	+	4.90966e13i	−1.32622	+	0.852726i
$566$	−1.63749e13	+	8.79586e12i	−0.281901	+	0.151424i
$567$	−4.97086e13			−0.848235
$568$	7.13408e13	+	6.58278e12i	1.20669	+	0.111344i
$569$	−9.20861e13			−1.54395			−0.771974	−	0.635654i	$-0.780731\pi$
$569$	−9.20861e13			−1.54395			−0.771974	+	0.635654i	$0.780731\pi$
$570$	−2.40840e13	+	4.34179e13i	−0.400272	+	0.721597i
$571$			5.96944e13i			0.983452i	0.870750	+	0.491726i	$0.163634\pi$
$571$			5.96944e13i			0.983452i	−0.870750	+	0.491726i	$0.836366\pi$
$572$	3.61783e13	−	5.46292e13i	0.590838	−	0.892165i
$573$		−	3.63435e13i		−	0.588374i
$574$	7.23459e13	−	3.88610e13i	1.16106	−	0.623669i
$575$	4.22773e13	−	9.26836e13i	0.672617	−	1.47456i
$576$	−6.66710e13	−	1.24094e13i	−1.05154	−	0.195722i
$577$		−	2.08153e13i		−	0.325464i	−0.986670	−	0.162732i	$-0.947969\pi$
$577$		−	2.08153e13i		−	0.325464i	0.986670	−	0.162732i	$-0.0520307\pi$
$578$	−1.67667e13	+	9.00630e12i	−0.259901	+	0.139607i
$579$		−	7.04920e13i		−	1.08330i
$580$	2.87420e13	+	3.88576e11i	0.437902	+	0.00592019i
$581$	1.31141e13			0.198087
$582$	4.25043e13	+	7.91286e13i	0.636529	+	1.18500i
$583$	−7.28957e13			−1.08233
$584$	−1.66750e13	−	1.53864e12i	−0.245472	−	0.0226502i
$585$	7.76115e13	−	4.99023e13i	1.13278	−	0.728351i
$586$	2.20464e13	+	4.10429e13i	0.319044	+	0.593951i
$587$	−1.00421e13			−0.144090			−0.0720450	−	0.997401i	$-0.522953\pi$
$587$	−1.00421e13			−0.144090			−0.0720450	+	0.997401i	$0.522953\pi$
$588$	8.93919e12	−	1.34982e13i	0.127178	−	0.192039i
$589$	−3.96894e13			−0.559884
$590$	−1.18140e11	+	2.12979e11i	−0.00165248	+	0.00297904i
$591$			9.00056e13i			1.24834i
$592$	−1.03273e14	+	4.37749e13i	−1.42030	+	0.602028i
$593$		−	4.65383e13i		−	0.634655i	−0.948316	−	0.317327i	$-0.897215\pi$
$593$		−	4.65383e13i		−	0.634655i	0.948316	−	0.317327i	$-0.102785\pi$
$594$	2.97758e12	+	5.54324e12i	0.0402653	+	0.0749603i
$595$	−4.82668e13	+	3.10344e13i	−0.647238	+	0.416158i
$596$	−8.41739e12	+	1.27103e13i	−0.111930	+	0.169014i
$597$			9.57521e13i			1.26263i
$598$	−7.38463e13	−	1.37477e14i	−0.965657	−	1.79772i
$599$		−	1.30743e14i		−	1.69545i	−0.530439	−	0.847723i	$-0.677973\pi$
$599$		−	1.30743e14i		−	1.69545i	0.530439	−	0.847723i	$-0.322027\pi$
$600$	9.70816e13	+	5.55808e13i	1.24848	+	0.714773i
$601$	1.39835e14			1.78338			0.891689	−	0.452649i	$-0.149521\pi$
$601$	1.39835e14			1.78338			0.891689	+	0.452649i	$0.149521\pi$
$602$	3.27192e13	−	1.75753e13i	0.413828	−	0.222290i
$603$	8.01797e13			1.00572
$604$	−6.48290e13	−	4.29331e13i	−0.806464	−	0.534082i
$605$	1.21747e13	+	1.89349e13i	0.150204	+	0.233608i
$606$	7.93638e13	−	4.26307e13i	0.971089	−	0.521626i
$607$	1.00912e14			1.22461			0.612306	−	0.790621i	$-0.290242\pi$
$607$	1.00912e14			1.22461			0.612306	+	0.790621i	$0.290242\pi$
$608$	−2.98530e13	+	3.71476e13i	−0.359311	+	0.447109i
$609$	−4.83679e13			−0.577393
$610$	1.21308e14	+	6.72898e13i	1.43628	+	0.796710i
$611$			1.01498e14i			1.19193i
$612$	6.42833e13	+	4.25717e13i	0.748757	+	0.495866i
$613$		−	1.16357e14i		−	1.34429i	−0.740421	−	0.672143i	$-0.765374\pi$
$613$		−	1.16357e14i		−	1.34429i	0.740421	−	0.672143i	$-0.234626\pi$
$614$	−1.06312e14	+	5.71060e13i	−1.21826	+	0.654395i
$615$	9.84393e13	+	1.53100e14i	1.11890	+	1.74020i
$616$	−6.87898e13	−	6.34740e12i	−0.775569	−	0.0715636i
$617$			1.32589e13i			0.148280i	0.997248	+	0.0741399i	$0.0236211\pi$
$617$			1.32589e13i			0.148280i	−0.997248	+	0.0741399i	$0.976379\pi$
$618$	−7.91542e13	+	4.25181e13i	−0.878075	+	0.471662i
$619$			3.69464e13i			0.406555i	0.979121	+	0.203277i	$0.0651593\pi$
$619$			3.69464e13i			0.406555i	−0.979121	+	0.203277i	$0.934841\pi$
$620$	−1.20885e12	+	8.94154e13i	−0.0131951	+	0.976009i
$621$	1.49864e13			0.162270
$622$	−6.98446e12	−	1.30027e13i	−0.0750207	−	0.139663i
$623$	3.79279e13			0.404127
$624$	1.57778e14	−	6.68781e13i	1.66773	−	0.706905i
$625$	−6.25166e13	−	7.20182e13i	−0.655534	−	0.755166i
$626$	1.91118e13	+	3.55796e13i	0.198806	+	0.370109i
$627$	6.79572e13			0.701290
$628$	7.52394e13	+	4.98274e13i	0.770278	+	0.510118i
$629$	1.27527e14			1.29523
$630$	−8.50709e13	−	4.71891e13i	−0.857193	−	0.475487i
$631$		−	1.27591e14i		−	1.27548i	−0.770252	−	0.637739i	$-0.779870\pi$
$631$		−	1.27591e14i		−	1.27548i	0.770252	−	0.637739i	$-0.220130\pi$
$632$	−1.47890e14	−	1.36462e13i	−1.46674	−	0.135340i
$633$		−	4.35185e13i		−	0.428209i
$634$	−2.64031e13	−	4.91536e13i	−0.257756	−	0.479854i
$635$	−6.21298e13	−	9.66286e13i	−0.601771	−	0.935916i
$636$	−1.58954e14	−	1.05267e14i	−1.52751	−	1.01160i
$637$			2.11432e13i			0.201592i
$638$	−1.86175e13	−	3.46594e13i	−0.176124	−	0.327882i
$639$		−	1.38090e14i		−	1.29616i
$640$	8.27798e13	+	6.83866e13i	0.770947	+	0.636900i
$641$	7.50958e13			0.693946			0.346973	−	0.937875i	$-0.387210\pi$
$641$	7.50958e13			0.693946			0.346973	+	0.937875i	$0.387210\pi$
$642$	2.07933e13	−	1.11692e13i	0.190655	−	0.102411i
$643$	−2.60160e13			−0.236693			−0.118346	−	0.992972i	$-0.537759\pi$
$643$	−2.60160e13			−0.236693			−0.118346	+	0.992972i	$0.537759\pi$
$644$	−9.08463e13	+	1.37178e14i	−0.820121	+	1.23838i
$645$	4.45202e13	+	6.92408e13i	0.398803	+	0.620246i
$646$	4.77317e13	−	2.56393e13i	0.424272	−	0.227900i
$647$	5.04262e13			0.444769			0.222385	−	0.974959i	$-0.428616\pi$
$647$	5.04262e13			0.444769			0.222385	+	0.974959i	$0.428616\pi$
$648$	9.71650e12	−	1.05302e14i	0.0850423	−	0.921645i
$649$	3.33352e11			0.00289521
$650$	−1.45784e14	+	9.48563e12i	−1.25645	+	0.0817522i
$651$		−	1.50471e14i		−	1.28691i
$652$	1.25223e12	−	1.89087e12i	0.0106279	−	0.0160481i
$653$			1.99170e14i			1.67749i	0.544528	+	0.838743i	$0.316709\pi$
$653$			1.99170e14i			1.67749i	−0.544528	+	0.838743i	$0.683291\pi$
$654$	−1.20537e14	+	6.47471e13i	−1.00747	+	0.541167i
$655$	6.01904e13	−	3.87010e13i	0.499253	−	0.321007i
$656$	6.81815e13	+	1.60853e14i	0.561238	+	1.32407i
$657$			3.22767e13i			0.263671i
$658$	9.42719e13	−	5.06387e13i	0.764281	−	0.410537i
$659$			8.85224e13i			0.712239i	0.934440	+	0.356120i	$0.115900\pi$
$659$			8.85224e13i			0.712239i	−0.934440	+	0.356120i	$0.884100\pi$
$660$	2.06981e12	−	1.53099e14i	0.0165277	−	1.22251i
$661$	−1.36514e14			−1.08185			−0.540927	−	0.841069i	$-0.681927\pi$
$661$	−1.36514e14			−1.08185			−0.540927	+	0.841069i	$0.681927\pi$
$662$	3.25082e13	+	6.05192e13i	0.255684	+	0.475996i
$663$	−1.94832e14			−1.52087
$664$	−2.56339e12	+	2.77807e13i	−0.0198598	+	0.215230i
$665$	−5.75029e13	+	3.69730e13i	−0.442162	+	0.284299i
$666$	1.02306e14	+	1.90459e14i	0.780785	+	1.45356i
$667$	−9.37034e13			−0.709784
$668$	−4.96438e12	+	7.49621e12i	−0.0373235	+	0.0563585i
$669$	−1.36344e14			−1.01743
$670$	−1.11014e14	−	6.15799e13i	−0.822251	−	0.456105i
$671$		−	1.89870e14i		−	1.39586i
$672$	−1.40835e14	−	1.13179e14i	−1.02769	−	0.825886i
$673$			1.47469e13i			0.106813i	0.998573	+	0.0534066i	$0.0170080\pi$
$673$			1.47469e13i			0.106813i	−0.998573	+	0.0534066i	$0.982992\pi$
$674$	−8.23532e13	−	1.53313e14i	−0.592081	−	1.10225i
$675$	5.82247e12	−	1.27645e13i	0.0415516	−	0.0910927i
$676$	−4.56248e13	+	6.88935e13i	−0.323197	+	0.488028i
$677$			5.61839e13i			0.395065i	0.980296	+	0.197532i	$0.0632927\pi$
$677$			5.61839e13i			0.395065i	−0.980296	+	0.197532i	$0.936707\pi$
$678$	1.53778e14	+	2.86281e14i	1.07336	+	1.99823i
$679$			1.23676e14i			0.856911i
$680$	−5.63085e13	−	1.08315e14i	−0.387284	−	0.744976i
$681$	−1.93285e14			−1.31966
$682$	1.07824e14	−	5.79184e13i	0.730794	−	0.392550i
$683$	4.45893e13			0.300004			0.150002	−	0.988686i	$-0.452072\pi$
$683$	4.45893e13			0.300004			0.150002	+	0.988686i	$0.452072\pi$
$684$	7.65841e13	+	5.07180e13i	0.511515	+	0.338752i
$685$	1.23646e14	−	7.95015e13i	0.819838	−	0.527136i
$686$	1.42293e14	−	7.64332e13i	0.936617	−	0.503109i
$687$	−1.67890e14			−1.09709
$688$	3.08358e13	+	7.27475e13i	0.200038	+	0.471928i
$689$	2.48981e14			1.60351
$690$	−3.18893e14	−	1.76891e14i	−2.03891	−	1.13099i
$691$			1.51251e14i			0.960079i	0.877247	+	0.480039i	$0.159378\pi$
$691$			1.51251e14i			0.960079i	−0.877247	+	0.480039i	$0.840622\pi$
$692$	−7.22257e13	−	4.78316e13i	−0.455157	−	0.301429i
$693$			1.33152e14i			0.833070i
$694$	1.42623e14	−	7.66107e13i	0.885915	−	0.475874i
$695$	7.17772e13	−	4.61510e13i	0.442652	−	0.284615i
$696$	9.45444e12	−	1.02462e14i	0.0578881	−	0.627362i
$697$		−	1.98629e14i		−	1.20748i
$698$	−7.40077e13	+	3.97537e13i	−0.446684	+	0.239938i
$699$		−	8.06533e12i		−	0.0483322i
$700$	8.15441e13	+	1.30673e14i	0.485179	+	0.777492i
$701$	−4.00119e13			−0.236374			−0.118187	−	0.992991i	$-0.537708\pi$
$701$	−4.00119e13			−0.236374			−0.118187	+	0.992991i	$0.537708\pi$
$702$	−1.01702e13	−	1.89334e13i	−0.0596545	−	0.111056i
$703$	1.51929e14			0.884840
$704$	2.68926e13	−	1.44483e14i	0.155514	−	0.835515i
$705$	1.28273e14	+	1.99500e14i	0.736532	+	1.14550i
$706$	−6.80572e13	−	1.26699e14i	−0.388017	−	0.722355i
$707$	1.24043e14			0.702225
$708$	7.26896e11	+	4.81388e11i	0.00408607	+	0.00270601i
$709$	1.72605e14			0.963437			0.481719	−	0.876326i	$-0.340013\pi$
$709$	1.72605e14			0.963437			0.481719	+	0.876326i	$0.340013\pi$
$710$	−1.06056e14	+	1.91195e14i	−0.587820	+	1.05970i
$711$			2.86262e14i			1.57549i
$712$	−7.41373e12	+	8.03462e13i	−0.0405169	+	0.439102i
$713$		−	2.91508e14i		−	1.58199i
$714$	9.72042e13	+	1.80961e14i	0.523834	+	0.975201i
$715$	1.08144e14	+	1.68192e14i	0.578723	+	0.900070i
$716$	1.80510e14	+	1.19543e14i	0.959257	+	0.635270i
$717$		−	3.71147e14i		−	1.95862i
$718$	1.64239e14	+	3.05756e14i	0.860702	+	1.60233i
$719$		−	7.47546e13i		−	0.389040i	−0.980899	−	0.194520i	$-0.937685\pi$
$719$		−	7.47546e13i		−	0.389040i	0.980899	−	0.194520i	$-0.0623148\pi$
$720$	1.16594e14	−	1.70990e14i	0.602578	−	0.883706i
$721$	−1.23716e14			−0.634963
$722$	−1.15972e14	+	6.22950e13i	−0.591109	+	0.317517i
$723$	−4.48406e14			−2.26976
$724$	1.78813e12	−	2.70008e12i	0.00898890	−	0.0135732i
$725$	−3.64053e13	+	7.98106e13i	−0.181750	+	0.398447i
$726$	7.09905e13	−	3.81329e13i	0.351979	−	0.189067i
$727$	2.18551e14			1.07617			0.538085	−	0.842890i	$-0.319148\pi$
$727$	2.18551e14			1.07617			0.538085	+	0.842890i	$0.319148\pi$
$728$	2.34958e14	+	2.16801e13i	1.14903	+	0.106024i
$729$	−2.33483e14			−1.13401
$730$	2.47893e13	−	4.46893e13i	0.119577	−	0.215570i
$731$		−	8.98319e13i		−	0.430372i
$732$	2.74188e14	−	4.14023e14i	1.30465	−	1.97001i
$733$		−	2.14755e14i		−	1.01490i	−0.861681	−	0.507450i	$-0.830588\pi$
$733$		−	2.14755e14i		−	1.01490i	0.861681	−	0.507450i	$-0.169412\pi$
$734$	−2.45483e14	+	1.31863e14i	−1.15224	+	0.618930i
$735$	2.67209e13	+	4.15582e13i	0.124570	+	0.193740i
$736$	−2.72839e14	−	2.19262e14i	−1.26333	−	1.01525i
$737$			1.73758e14i			0.799112i
$738$	2.96650e14	−	1.59347e14i	1.35507	−	0.727884i
$739$			4.07171e14i			1.84737i	0.383150	+	0.923686i	$0.374839\pi$
$739$			4.07171e14i			1.84737i	−0.383150	+	0.923686i	$0.625161\pi$
$740$	4.62740e12	−	3.42278e14i	0.0208535	−	1.54248i
$741$	−2.32114e14			−1.03899
$742$	−1.24220e14	−	2.31256e14i	−0.552297	−	1.02819i
$743$	−2.99073e14			−1.32079			−0.660393	−	0.750920i	$-0.729610\pi$
$743$	−2.99073e14			−1.32079			−0.660393	+	0.750920i	$0.729610\pi$
$744$	3.18757e14	+	2.94124e13i	1.39828	+	0.129023i
$745$	−2.51611e13	−	3.91323e13i	−0.109635	−	0.170512i
$746$	1.23527e14	+	2.29965e14i	0.534647	+	0.995331i
$747$	5.37734e13			0.231187
$748$	−9.22576e13	+	1.39309e14i	−0.393998	+	0.594937i
$749$	3.24993e13			0.137868
$750$	−2.74559e14	+	2.02888e14i	−1.15699	+	0.854966i
$751$		−	1.79799e14i		−	0.752639i	−0.926490	−	0.376319i	$-0.877190\pi$
$751$		−	1.79799e14i		−	0.752639i	0.926490	−	0.376319i	$-0.122810\pi$
$752$	8.88454e13	+	2.09603e14i	0.369442	+	0.871584i
$753$		−	1.99347e14i		−	0.823444i
$754$	6.35897e13	+	1.18382e14i	0.260934	+	0.485769i
$755$	1.99596e14	−	1.28335e14i	0.813610	−	0.523131i
$756$	−1.25114e13	+	1.88923e13i	−0.0506638	+	0.0765024i
$757$			3.58885e14i			1.44370i	0.692051	+	0.721849i	$0.256707\pi$
$757$			3.58885e14i			1.44370i	−0.692051	+	0.721849i	$0.743293\pi$
$758$	−1.32740e14	−	2.47117e14i	−0.530464	−	0.987543i
$759$			4.99127e14i			1.98154i
$760$	−6.70833e13	−	1.29041e14i	−0.264574	−	0.508932i
$761$	1.92531e14			0.754358			0.377179	−	0.926140i	$-0.376894\pi$
$761$	1.92531e14			0.754358			0.377179	+	0.926140i	$0.376894\pi$
$762$	−3.62278e14	+	1.94599e14i	−1.41015	+	0.757472i
$763$	−1.88396e14			−0.728532
$764$	8.87587e13	+	5.87806e13i	0.340992	+	0.225823i
$765$	−1.97915e14	+	1.27255e14i	−0.755392	+	0.485698i
$766$	4.05392e14	−	2.17759e14i	1.53721	−	0.825718i
$767$	−1.13859e12			−0.00428935
$768$	2.67287e14	−	2.76220e14i	1.00040	−	1.03383i
$769$	−4.06464e13			−0.151144			−0.0755719	−	0.997140i	$-0.524078\pi$
$769$	−4.06464e13			−0.151144			−0.0755719	+	0.997140i	$0.524078\pi$
$770$	1.02264e14	−	1.84358e14i	0.377806	−	0.681096i
$771$		−	4.59842e14i		−	1.68786i
$772$	1.72157e14	+	1.14011e14i	0.627823	+	0.415777i
$773$		−	2.57422e14i		−	0.932713i	−0.884597	−	0.466357i	$-0.845566\pi$
$773$		−	2.57422e14i		−	0.932713i	0.884597	−	0.466357i	$-0.154434\pi$
$774$	1.34163e14	−	7.20664e13i	0.482979	−	0.259434i
$775$	−2.48288e14	−	1.13256e14i	−0.888070	−	0.405090i
$776$	−2.61994e14	−	2.41748e13i	−0.931071	−	0.0859120i
$777$			5.75996e14i			2.03383i
$778$	−5.84772e13	+	3.14113e13i	−0.205158	+	0.110202i
$779$		−	2.36637e14i		−	0.824889i
$780$	−7.06963e12	+	5.22923e14i	−0.0244863	+	1.81119i
$781$	2.99256e14			1.02988
$782$	1.88314e14	+	3.50576e14i	0.643945	+	1.19881i
$783$	−1.29049e13			−0.0438476
$784$	1.85076e13	+	4.36629e13i	0.0624840	+	0.147412i
$785$	−2.31647e14	+	1.48943e14i	−0.777103	+	0.499658i
$786$	−1.21217e14	−	2.25664e14i	−0.404064	−	0.752230i
$787$	5.23175e13			0.173290			0.0866449	−	0.996239i	$-0.472385\pi$
$787$	5.23175e13			0.173290			0.0866449	+	0.996239i	$0.472385\pi$
$788$	−2.19813e14	−	1.45572e14i	−0.723474	−	0.479122i
$789$	4.65821e14			1.52347
$790$	2.19856e14	−	3.96349e14i	0.714500	−	1.28808i
$791$			4.47450e14i			1.44498i
$792$	−2.82069e14	−	2.60271e13i	−0.905167	−	0.0835219i
$793$			6.48516e14i			2.06802i
$794$	−4.96026e13	−	9.23432e13i	−0.157182	−	0.292619i
$795$	4.89387e14	−	3.14664e14i	1.54105	−	0.990857i
$796$	−2.33847e14	−	1.54866e14i	−0.731758	−	0.484608i
$797$		−	4.27188e14i		−	1.32839i	−0.747557	−	0.664197i	$-0.768773\pi$
$797$		−	4.27188e14i		−	1.32839i	0.747557	−	0.664197i	$-0.231227\pi$
$798$	1.15805e14	+	2.15589e14i	0.357858	+	0.666210i
$799$		−	2.58828e14i		−	0.794835i
$800$	−2.92756e14	+	1.47200e14i	−0.893422	+	0.449219i
$801$	1.55521e14			0.471657
$802$	−8.66845e13	+	4.65630e13i	−0.261258	+	0.140336i
$803$	−6.99471e13			−0.209504
$804$	−2.50921e14	+	3.78891e14i	−0.746891	+	1.12781i
$805$	−2.71556e14	−	4.22343e14i	−0.803305	−	1.24936i
$806$	−3.68283e14	+	1.97825e14i	−1.08270	+	0.581576i
$807$	−9.97765e13			−0.291515
$808$	−2.42466e13	+	2.62773e14i	−0.0704036	+	0.762998i
$809$	−3.68589e14			−1.06365			−0.531826	−	0.846853i	$-0.678494\pi$
$809$	−3.68589e14			−1.06365			−0.531826	+	0.846853i	$0.678494\pi$
$810$	2.82213e14	+	1.56544e14i	0.809378	+	0.448964i
$811$		−	1.16475e14i		−	0.331993i	−0.986126	−	0.165996i	$-0.946916\pi$
$811$		−	1.16475e14i		−	0.331993i	0.986126	−	0.165996i	$-0.0530840\pi$
$812$	7.82285e13	−	1.18125e14i	0.221608	−	0.334628i
$813$		−	4.61693e14i		−	1.29987i
$814$	−4.12747e14	+	2.21709e14i	−1.15495	+	0.620385i
$815$	3.74316e12	+	5.82162e12i	0.0104100	+	0.0161903i
$816$	−4.02347e14	+	1.70545e14i	−1.11212	+	0.471397i
$817$		−	1.07022e14i		−	0.294009i
$818$	−6.69168e13	+	3.59447e13i	−0.182713	+	0.0981451i
$819$		−	4.54792e14i		−	1.23422i
$820$	−5.33114e14	−	7.20741e12i	−1.43797	−	0.0194406i
$821$	2.90981e14			0.780096			0.390048	−	0.920794i	$-0.372458\pi$
$821$	2.90981e14			0.780096			0.390048	+	0.920794i	$0.372458\pi$
$822$	−2.49010e14	−	4.63572e14i	−0.663526	−	1.23526i
$823$	−1.39385e14			−0.369163			−0.184581	−	0.982817i	$-0.559093\pi$
$823$	−1.39385e14			−0.369163			−0.184581	+	0.982817i	$0.559093\pi$
$824$	2.41826e13	−	2.62079e14i	0.0636601	−	0.689915i
$825$	4.25125e14	+	1.93919e14i	1.11236	+	0.507401i
$826$	5.68059e11	+	1.05753e12i	0.00147738	+	0.00275038i
$827$	1.26818e14			0.327834			0.163917	−	0.986474i	$-0.447587\pi$
$827$	1.26818e14			0.327834			0.163917	+	0.986474i	$0.447587\pi$
$828$	−3.72510e14	+	5.62490e14i	−0.957163	+	1.44532i
$829$	2.21372e14			0.565392			0.282696	−	0.959210i	$-0.408771\pi$
$829$	2.21372e14			0.565392			0.282696	+	0.959210i	$0.408771\pi$
$830$	−7.44529e13	−	4.12992e13i	−0.189013	−	0.104846i
$831$			5.97826e13i			0.150859i
$832$	−9.18539e13	+	4.93495e14i	−0.230399	+	1.23785i
$833$		−	5.39169e13i		−	0.134431i
$834$	−1.44552e14	−	2.69106e14i	−0.358255	−	0.666949i
$835$	−1.48395e13	−	2.30793e13i	−0.0365583	−	0.0568579i
$836$	−1.09911e14	+	1.65966e14i	−0.269161	+	0.406432i
$837$		−	4.01467e13i		−	0.0977289i
$838$	−1.75302e14	−	3.26352e14i	−0.424195	−	0.789707i
$839$		−	1.89623e14i		−	0.456123i	−0.973647	−	0.228062i	$-0.926761\pi$
$839$		−	1.89623e14i		−	0.456123i	0.973647	−	0.228062i	$-0.0732388\pi$
$840$	4.89222e14	−	2.54327e14i	1.16979	−	0.608130i
$841$	−3.40018e14			−0.808207
$842$	4.11815e13	−	2.21208e13i	0.0973064	−	0.0522687i
$843$	9.88292e14			2.32139
$844$	1.06282e14	+	7.03852e13i	0.248168	+	0.164350i
$845$	−1.36381e14	−	2.12109e14i	−0.316571	−	0.492352i
$846$	3.86556e14	−	2.07641e14i	0.891992	−	0.479138i
$847$	1.10956e14			0.254527
$848$	5.14172e14	−	2.17944e14i	1.17254	−	0.497011i
$849$	−2.03061e14			−0.460349
$850$	3.71762e14	−	2.41891e13i	0.837858	−	0.0545161i
$851$			1.11588e15i			2.50017i
$852$	6.52547e14	+	4.32150e14i	1.45350	+	0.962580i
$853$			4.26940e14i			0.945414i	0.881220	+	0.472707i	$0.156723\pi$
$853$			4.26940e14i			0.945414i	−0.881220	+	0.472707i	$0.843277\pi$
$854$	6.02346e14	−	3.23553e14i	1.32604	−	0.712289i
$855$	−2.35787e14	+	1.51605e14i	−0.516047	+	0.331806i
$856$	−6.35260e12	+	6.88463e13i	−0.0138224	+	0.149800i
$857$			5.83755e14i			1.26278i	0.775467	+	0.631388i	$0.217515\pi$
$857$			5.83755e14i			1.26278i	−0.775467	+	0.631388i	$0.782485\pi$
$858$	6.30584e14	−	3.38721e14i	1.35615	−	0.728461i
$859$		−	5.32334e14i		−	1.13820i	−0.822268	−	0.569100i	$-0.807292\pi$
$859$		−	5.32334e14i		−	1.13820i	0.822268	−	0.569100i	$-0.192708\pi$
$860$	−2.41106e14	−	3.25962e12i	−0.512527	−	0.00692907i
$861$	8.97142e14			1.89603
$862$	−4.04353e14	−	7.52768e14i	−0.849619	−	1.58170i
$863$	5.81000e14			1.21373			0.606865	−	0.794805i	$-0.292427\pi$
$863$	5.81000e14			1.21373			0.606865	+	0.794805i	$0.292427\pi$
$864$	−3.75757e13	−	3.01970e13i	−0.0780437	−	0.0627184i
$865$	2.22369e14	−	1.42978e14i	0.459191	−	0.295248i
$866$	3.95662e14	+	7.36588e14i	0.812335	+	1.51229i
$867$	−2.07919e14			−0.424422
$868$	3.67483e14	+	2.43366e14i	0.745828	+	0.493926i
$869$	−6.20360e14			−1.25183
$870$	2.74601e14	+	1.52322e14i	0.550942	+	0.305609i
$871$		−	5.93486e14i		−	1.18391i
$872$	3.68256e13	−	3.99097e14i	0.0730411	−	0.791582i
$873$			5.07125e14i			1.00010i
$874$	2.24349e14	+	4.17661e14i	0.439912	+	0.818967i
$875$	−4.65229e14	+	6.72071e13i	−0.907041	+	0.131031i
$876$	−1.52524e14	−	1.01009e14i	−0.295678	−	0.195813i
$877$			2.07860e14i			0.400658i	0.979729	+	0.200329i	$0.0642011\pi$
$877$			2.07860e14i			0.400658i	−0.979729	+	0.200329i	$0.935799\pi$
$878$	−3.38622e13	−	6.30400e13i	−0.0648998	−	0.120821i
$879$			5.08962e14i			0.969932i
$880$	3.70554e14	+	2.52672e14i	0.702163	+	0.478788i
$881$	1.10923e14			0.208999			0.104499	−	0.994525i	$-0.466676\pi$
$881$	1.10923e14			0.208999			0.104499	+	0.994525i	$0.466676\pi$
$882$	8.05243e13	−	4.32540e13i	0.150863	−	0.0810371i
$883$	−9.33232e14			−1.73855			−0.869273	−	0.494333i	$-0.835412\pi$
$883$	−9.33232e14			−1.73855			−0.869273	+	0.494333i	$0.835412\pi$
$884$	3.15114e14	−	4.75821e14i	0.583722	−	0.881420i
$885$	−2.23797e12	+	1.43896e12i	−0.00412228	+	0.00265052i
$886$	−3.87525e14	+	2.08161e14i	−0.709792	+	0.381268i
$887$	8.01103e13			0.145905			0.0729525	−	0.997335i	$-0.476758\pi$
$887$	8.01103e13			0.145905			0.0729525	+	0.997335i	$0.476758\pi$
$888$	−1.22019e15	−	1.12589e14i	−2.20984	−	0.203907i
$889$	−5.66230e14			−1.01973
$890$	−2.15329e14	−	1.19444e14i	−0.385614	−	0.213901i
$891$		−	4.41716e14i		−	0.786601i
$892$	2.20517e14	−	3.32981e14i	0.390497	−	0.589650i
$893$		−	3.08355e14i		−	0.542993i
$894$	−1.46714e14	+	7.88083e13i	−0.256912	+	0.138002i
$895$	−5.55753e14	+	3.57335e14i	−0.967757	+	0.622244i
$896$	5.04189e14	−	1.60897e14i	0.873078	−	0.278617i
$897$		−	1.70481e15i		−	2.93572i
$898$	−6.06097e14	+	3.25568e14i	−1.03791	+	0.557520i
$899$			2.51020e14i			0.427474i
$900$	3.34367e14	+	5.35817e14i	0.566253	+	0.907411i
$901$	−6.34922e14			−1.06929
$902$	3.45322e14	+	6.42873e14i	0.578352	+	1.07669i
$903$	4.05742e14			0.675788
$904$	−9.47875e14	−	8.74626e13i	−1.57003	−	0.144871i
$905$	5.34505e12	+	8.31300e12i	0.00880459	+	0.0136935i
$906$	−4.01964e14	−	7.48319e14i	−0.658485	−	1.22587i
$907$	−7.86921e13			−0.128202			−0.0641010	−	0.997943i	$-0.520418\pi$
$907$	−7.86921e13			−0.128202			−0.0641010	+	0.997943i	$0.520418\pi$
$908$	3.12612e14	−	4.72044e14i	0.506496	−	0.764809i
$909$	5.08632e14			0.819567
$910$	−3.49291e14	+	6.29691e14i	−0.559733	+	1.00907i
$911$			4.29113e14i			0.683879i	0.939722	+	0.341940i	$0.111084\pi$
$911$			4.29113e14i			0.683879i	−0.939722	+	0.341940i	$0.888916\pi$
$912$	−4.79338e14	+	2.03179e14i	−0.759745	+	0.322036i
$913$			1.16533e14i			0.183694i
$914$	−2.43117e14	−	4.52601e14i	−0.381140	−	0.709553i
$915$	8.19598e14	+	1.27469e15i	1.27789	+	1.98747i
$916$	2.71540e14	−	4.10025e14i	0.421072	−	0.635818i
$917$		−	3.52707e14i		−	0.543961i
$918$	2.59348e13	+	4.82817e13i	0.0397804	+	0.0740575i
$919$		−	4.06265e14i		−	0.619772i	−0.950774	−	0.309886i	$-0.899709\pi$
$919$		−	4.06265e14i		−	0.619772i	0.950774	−	0.309886i	$-0.100291\pi$
$920$	9.47771e14	−	4.92709e14i	1.43802	−	0.747569i
$921$	−1.31835e15			−1.98944
$922$	−8.83654e13	+	4.74659e13i	−0.132626	+	0.0712406i
$923$	−1.02213e15			−1.52581
$924$	−6.29213e14	−	4.16698e14i	−0.934196	−	0.618673i
$925$	9.50435e14	+	4.33538e14i	1.40350	+	0.640204i
$926$	9.43920e14	−	5.07032e14i	1.38637	−	0.744698i
$927$	−5.07289e14			−0.741066
$928$	2.34944e14	+	1.88809e14i	0.341370	+	0.274336i
$929$	−1.91958e14			−0.277414			−0.138707	−	0.990333i	$-0.544295\pi$
$929$	−1.91958e14			−0.277414			−0.138707	+	0.990333i	$0.544295\pi$
$930$	−4.73869e14	+	8.54275e14i	−0.681151	+	1.22796i
$931$		−	6.42341e13i		−	0.0918369i
$932$	1.96973e13	+	1.30446e13i	0.0280109	+	0.0185503i
$933$		−	1.61243e14i		−	0.228072i
$934$	2.23823e14	−	1.20228e14i	0.314898	−	0.169149i
$935$	−2.75775e14	−	4.28904e14i	−0.385919	−	0.600209i
$936$	9.63430e14	+	8.88979e13i	1.34104	+	0.123741i
$937$			6.65525e14i			0.921439i	0.887546	+	0.460719i	$0.152409\pi$
$937$			6.65525e14i			0.921439i	−0.887546	+	0.460719i	$0.847591\pi$
$938$	−5.51233e14	+	2.96098e14i	−0.759139	+	0.407776i
$939$			4.41213e14i			0.604395i
$940$	−6.94686e14	−	9.39177e12i	−0.946563	−	0.0127970i
$941$	−1.61715e13			−0.0219181			−0.0109590	−	0.999940i	$-0.503488\pi$
$941$	−1.61715e13			−0.0219181			−0.0109590	+	0.999940i	$0.503488\pi$
$942$	4.66512e14	+	8.68486e14i	0.628939	+	1.17087i
$943$	1.73804e15			2.33077
$944$	−2.35131e12	+	9.96658e11i	−0.00313653	+	0.00132949i
$945$	−3.73990e13	−	5.81655e13i	−0.0496250	−	0.0771803i
$946$	1.56176e14	+	2.90746e14i	0.206138	+	0.383758i
$947$	−1.27120e15			−1.66902			−0.834512	−	0.550990i	$-0.814250\pi$
$947$	−1.27120e15			−1.66902			−0.834512	+	0.550990i	$0.814250\pi$
$948$	−1.35274e15	−	8.95852e14i	−1.76674	−	1.17002i
$949$	2.38910e14			0.310387
$950$	4.42900e14	−	2.88178e13i	0.572384	−	0.0372428i
$951$		−	6.09541e14i		−	0.783611i
$952$	−5.99160e14	−	5.52859e13i	−0.766229	−	0.0707017i
$953$			6.45347e14i			0.820973i	0.911867	+	0.410487i	$0.134641\pi$
$953$			6.45347e14i			0.820973i	−0.911867	+	0.410487i	$0.865359\pi$
$954$	−5.09357e14	−	9.48250e14i	−0.644586	−	1.20000i
$955$	−2.73270e14	+	1.75706e14i	−0.344014	+	0.221192i
$956$	9.06422e14	+	6.00280e14i	1.13512	+	0.751734i
$957$		−	4.29802e14i		−	0.535438i
$958$	−4.85877e14	−	9.04537e14i	−0.602142	−	1.12098i
$959$		−	7.24550e14i		−	0.893255i
$960$	4.43137e14	+	1.08608e15i	0.543478	+	1.33200i
$961$	3.87136e13			0.0472331
$962$	1.40977e15	−	7.57266e14i	1.71109	−	0.919122i
$963$	1.33261e14			0.160906
$964$	7.25236e14	−	1.09511e15i	0.871152	−	1.31544i
$965$	−5.30036e14	+	3.40800e14i	−0.633387	+	0.407252i
$966$	−1.58344e15	+	8.50553e14i	−1.88242	+	1.01115i
$967$	9.14805e13			0.108192			0.0540961	−	0.998536i	$-0.482772\pi$
$967$	9.14805e13			0.108192			0.0540961	+	0.998536i	$0.482772\pi$
$968$	−2.16885e13	+	2.35049e14i	−0.0255183	+	0.276555i
$969$	5.91908e14			0.692844
$970$	3.89484e14	−	7.02149e14i	0.453556	−	0.817656i
$971$			1.39347e15i			1.61436i	0.590304	+	0.807181i	$0.299008\pi$
$971$			1.39347e15i			1.61436i	−0.590304	+	0.807181i	$0.700992\pi$
$972$	6.85839e14	−	1.03562e15i	0.790480	−	1.19362i
$973$		−	4.20605e14i		−	0.482292i
$974$	−2.24179e14	+	1.20419e14i	−0.255741	+	0.137372i
$975$	−1.45205e15	−	6.62348e14i	−1.64801	−	0.751732i
$976$	5.67674e14	+	1.33925e15i	0.640988	+	1.51221i
$977$			5.42012e14i			0.608886i	0.952531	+	0.304443i	$0.0984703\pi$
$977$			5.42012e14i			0.608886i	−0.952531	+	0.304443i	$0.901530\pi$
$978$	2.18263e13	−	1.17241e13i	0.0243941	−	0.0131034i
$979$			3.37031e14i			0.374762i
$980$	−1.44711e14	−	1.95642e12i	−0.160093	−	0.00216437i
$981$	−7.72506e14			−0.850270
$982$	5.57793e14	+	1.03842e15i	0.610824	+	1.13715i
$983$	1.58099e15			1.72251			0.861253	−	0.508177i	$-0.169680\pi$
$983$	1.58099e15			1.72251			0.861253	+	0.508177i	$0.169680\pi$
$984$	−1.75364e14	+	1.90050e15i	−0.190092	+	2.06012i
$985$	6.76761e14	−	4.35141e14i	0.729885	−	0.469298i
$986$	−1.62159e14	−	3.01884e14i	−0.174003	−	0.323933i
$987$	1.16904e15			1.24808
$988$	3.75412e14	−	5.66872e14i	0.398771	−	0.602144i
$989$	7.86045e14			0.830741
$990$	4.19327e14	−	7.55949e14i	0.440938	−	0.794907i
$991$		−	1.33300e15i		−	1.39464i	−0.716761	−	0.697319i	$-0.754376\pi$
$991$		−	1.33300e15i		−	1.39464i	0.716761	−	0.697319i	$-0.245624\pi$
$992$	−5.87377e14	+	7.30903e14i	−0.611447	+	0.760854i
$993$			7.50482e14i			0.777310i
$994$	5.09956e14	+	9.49364e14i	0.525534	+	0.978365i
$995$	7.19969e14	−	4.62923e14i	0.738242	−	0.474671i
$996$	−1.68283e14	+	2.54107e14i	−0.171690	+	0.259251i
$997$		−	1.75181e14i		−	0.177833i	−0.996039	−	0.0889163i	$-0.971660\pi$
$997$		−	1.75181e14i		−	0.177833i	0.996039	−	0.0889163i	$-0.0283403\pi$
$998$	2.61311e14	+	4.86471e14i	0.263940	+	0.491365i
$999$			1.53680e14i			0.154451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.d.d.19.4	yes	24
4.3	odd	2	inner	20.11.d.d.19.22	yes	24
5.2	odd	4		100.11.b.h.51.9		24
5.3	odd	4		100.11.b.h.51.16		24
5.4	even	2	inner	20.11.d.d.19.21	yes	24
20.3	even	4		100.11.b.h.51.15		24
20.7	even	4		100.11.b.h.51.10		24
20.19	odd	2	inner	20.11.d.d.19.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.3	✓	24	20.19	odd	2	inner
20.11.d.d.19.4	yes	24	1.1	even	1	trivial
20.11.d.d.19.21	yes	24	5.4	even	2	inner
20.11.d.d.19.22	yes	24	4.3	odd	2	inner
100.11.b.h.51.9		24	5.2	odd	4
100.11.b.h.51.10		24	20.7	even	4
100.11.b.h.51.15		24	20.3	even	4
100.11.b.h.51.16		24	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-28.1904 + 15.1426i) q^{2} -349.582 q^{3} +(565.401 - 853.755i) q^{4} +(1690.09 + 2628.54i) q^{5} +(9854.87 - 5293.59i) q^{6} +15402.9 q^{7} +(-3010.79 + 32629.4i) q^{8} +63158.6 q^{9} +O(q^{10})\)	\(q+(-28.1904 + 15.1426i) q^{2} -349.582 q^{3} +(565.401 - 853.755i) q^{4} +(1690.09 + 2628.54i) q^{5} +(9854.87 - 5293.59i) q^{6} +15402.9 q^{7} +(-3010.79 + 32629.4i) q^{8} +63158.6 q^{9} +(-87447.4 - 48507.3i) q^{10} +136872. i q^{11} +(-197654. + 298457. i) q^{12} -467497. i q^{13} +(-434214. + 233240. i) q^{14} +(-590824. - 918891. i) q^{15} +(-409220. - 965428. i) q^{16} +1.19215e6i q^{17} +(-1.78047e6 + 956388. i) q^{18} +1.42028e6i q^{19} +(3.19971e6 + 43258.3i) q^{20} -5.38457e6 q^{21} +(-2.07260e6 - 3.85847e6i) q^{22} -1.04315e7 q^{23} +(1.05252e6 - 1.14066e7i) q^{24} +(-4.05283e6 + 8.88493e6i) q^{25} +(7.07913e6 + 1.31789e7i) q^{26} -1.43664e6 q^{27} +(8.70880e6 - 1.31503e7i) q^{28} +8.98269e6 q^{29} +(3.05700e7 + 1.69573e7i) q^{30} +2.79449e7i q^{31} +(2.61552e7 + 2.10192e7i) q^{32} -4.78478e7i q^{33} +(-1.80524e7 - 3.36073e7i) q^{34} +(2.60322e7 + 4.04871e7i) q^{35} +(3.57099e7 - 5.39220e7i) q^{36} -1.06972e8i q^{37} +(-2.15067e7 - 4.00382e7i) q^{38} +1.63428e8i q^{39} +(-9.08562e7 + 4.72326e7i) q^{40} -1.66613e8 q^{41} +(1.51793e8 - 8.15366e7i) q^{42} -7.53526e7 q^{43} +(1.16855e8 + 7.73873e7i) q^{44} +(1.06744e8 + 1.66015e8i) q^{45} +(2.94070e8 - 1.57961e8i) q^{46} -2.17109e8 q^{47} +(1.43056e8 + 3.37496e8i) q^{48} -4.52265e7 q^{49} +(-2.02903e7 - 3.11841e8i) q^{50} -4.16755e8i q^{51} +(-3.99128e8 - 2.64323e8i) q^{52} +5.32584e8i q^{53} +(4.04996e7 - 2.17546e7i) q^{54} +(-3.59773e8 + 2.31325e8i) q^{55} +(-4.63748e7 + 5.02587e8i) q^{56} -4.96503e8i q^{57} +(-2.53226e8 + 1.36022e8i) q^{58} -2.43551e6i q^{59} +(-1.11856e9 - 1.51223e7i) q^{60} -1.38721e9 q^{61} +(-4.23159e8 - 7.87777e8i) q^{62} +9.72824e8 q^{63} +(-1.05561e9 - 1.96480e8i) q^{64} +(1.22883e9 - 7.90110e8i) q^{65} +(7.24543e8 + 1.34885e9i) q^{66} +1.26950e9 q^{67} +(1.01781e9 + 6.74045e8i) q^{68} +3.64668e9 q^{69} +(-1.34694e9 - 7.47152e8i) q^{70} -2.18640e9i q^{71} +(-1.90157e8 + 2.06083e9i) q^{72} +5.11042e8i q^{73} +(1.61983e9 + 3.01558e9i) q^{74} +(1.41680e9 - 3.10601e9i) q^{75} +(1.21257e9 + 8.03026e8i) q^{76} +2.10822e9i q^{77} +(-2.47474e9 - 4.60712e9i) q^{78} +4.53243e9i q^{79} +(1.84605e9 - 2.70731e9i) q^{80} -3.22723e9 q^{81} +(4.69690e9 - 2.52297e9i) q^{82} +8.51402e8 q^{83} +(-3.04444e9 + 4.59711e9i) q^{84} +(-3.13362e9 + 2.01484e9i) q^{85} +(2.12422e9 - 1.14104e9i) q^{86} -3.14019e9 q^{87} +(-4.46604e9 - 4.12091e8i) q^{88} +2.46239e9 q^{89} +(-5.52305e9 - 3.06365e9i) q^{90} -7.20080e9i q^{91} +(-5.89801e9 + 8.90599e9i) q^{92} -9.76902e9i q^{93} +(6.12041e9 - 3.28761e9i) q^{94} +(-3.73326e9 + 2.40039e9i) q^{95} +(-9.14339e9 - 7.34792e9i) q^{96} +8.02939e9i q^{97} +(1.27495e9 - 6.84848e8i) q^{98} +8.64462e9i 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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