LMFDB - Embedded newform 12.12.b.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,12,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	12.b (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:	$9.22011816672$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 247 x^{18} - 23916 x^{16} + 14713536 x^{14} - 45723119616 x^{12} + 40864324780032 x^{10} + \cdots + 12\!\cdots\!24 $ x^20 - 247x^18 - 23916x^16 + 14713536x^14 - 45723119616x^12 + 40864324780032x^10 - 11986041468616704x^8 + 1011106494856298496x^6 - 430832354752771129344x^4 - 1166424521268802367782912*x^2 + 1237940039285380274899124224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{104}\cdot 3^{42}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.15
Root			$16.0196 - 15.9804i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.12.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0392 - 31.9607i) q^{2} +(-70.6484 - 414.917i) q^{3} +(5.02409 - 2047.99i) q^{4} -1842.04i q^{5} +(-15524.6 - 11035.6i) q^{6} +16302.4i q^{7} +(-65294.4 - 65776.7i) q^{8} +(-167165. + 58626.4i) q^{9} +O(q^{10})$	\(q+(32.0392 - 31.9607i) q^{2} +(-70.6484 - 414.917i) q^{3} +(5.02409 - 2047.99i) q^{4} -1842.04i q^{5} +(-15524.6 - 11035.6i) q^{6} +16302.4i q^{7} +(-65294.4 - 65776.7i) q^{8} +(-167165. + 58626.4i) q^{9} +(-58872.8 - 59017.4i) q^{10} +485828. q^{11} +(-850102. + 142603. i) q^{12} -1.36551e6 q^{13} +(521035. + 522315. i) q^{14} +(-764291. + 130137. i) q^{15} +(-4.19425e6 - 20578.6i) q^{16} -8.90746e6i q^{17} +(-3.48208e6 + 7.22105e6i) q^{18} -107974. i q^{19} +(-3.77248e6 - 9254.56i) q^{20} +(6.76412e6 - 1.15174e6i) q^{21} +(1.55655e7 - 1.55274e7i) q^{22} +5.58155e7 q^{23} +(-2.26789e7 + 3.17388e7i) q^{24} +4.54350e7 q^{25} +(-4.37498e7 + 4.36426e7i) q^{26} +(3.61350e7 + 6.52175e7i) q^{27} +(3.33871e7 + 81904.5i) q^{28} -1.27942e8i q^{29} +(-2.03280e7 + 2.85968e7i) q^{30} -1.30377e8i q^{31} +(-1.35038e8 + 1.33392e8i) q^{32} +(-3.43230e7 - 2.01578e8i) q^{33} +(-2.84689e8 - 2.85388e8i) q^{34} +3.00295e7 q^{35} +(1.19227e8 + 3.42647e8i) q^{36} -3.44489e8 q^{37} +(-3.45092e6 - 3.45939e6i) q^{38} +(9.64708e7 + 5.66571e8i) q^{39} +(-1.21163e8 + 1.20275e8i) q^{40} +9.40493e8i q^{41} +(1.79907e8 - 2.53087e8i) q^{42} -9.39748e8i q^{43} +(2.44084e6 - 9.94972e8i) q^{44} +(1.07992e8 + 3.07923e8i) q^{45} +(1.78829e9 - 1.78391e9i) q^{46} -9.85584e8 q^{47} +(2.87779e8 + 1.74172e9i) q^{48} +1.71156e9 q^{49} +(1.45570e9 - 1.45214e9i) q^{50} +(-3.69585e9 + 6.29298e8i) q^{51} +(-6.86043e6 + 2.79655e9i) q^{52} +1.84952e9i q^{53} +(3.24214e9 + 9.34618e8i) q^{54} -8.94912e8i q^{55} +(1.07232e9 - 1.06445e9i) q^{56} +(-4.48001e7 + 7.62817e6i) q^{57} +(-4.08912e9 - 4.09916e9i) q^{58} +5.76202e9 q^{59} +(2.62680e8 + 1.56592e9i) q^{60} -7.38482e9 q^{61} +(-4.16694e9 - 4.17717e9i) q^{62} +(-9.55749e8 - 2.72518e9i) q^{63} +(-6.32172e7 + 8.58970e9i) q^{64} +2.51531e9i q^{65} +(-7.54226e9 - 5.36142e9i) q^{66} +1.05400e10i q^{67} +(-1.82424e10 - 4.47519e7i) q^{68} +(-3.94328e9 - 2.31588e10i) q^{69} +(9.62123e8 - 9.59766e8i) q^{70} +1.58034e10 q^{71} +(1.47712e10 + 7.16756e9i) q^{72} +1.99415e10 q^{73} +(-1.10371e10 + 1.10101e10i) q^{74} +(-3.20991e9 - 1.88517e10i) q^{75} +(-2.21129e8 - 542469. i) q^{76} +7.92014e9i q^{77} +(2.11989e10 + 1.50692e10i) q^{78} +1.66155e10i q^{79} +(-3.79066e7 + 7.72597e9i) q^{80} +(2.45069e10 - 1.96005e10i) q^{81} +(3.00588e10 + 3.01327e10i) q^{82} +3.12525e10 q^{83} +(-2.32476e9 - 1.38587e10i) q^{84} -1.64079e10 q^{85} +(-3.00350e10 - 3.01088e10i) q^{86} +(-5.30852e10 + 9.03889e9i) q^{87} +(-3.17218e10 - 3.19562e10i) q^{88} +5.55310e10i q^{89} +(1.33014e10 + 6.41412e9i) q^{90} -2.22610e10i q^{91} +(2.80422e8 - 1.14310e11i) q^{92} +(-5.40955e10 + 9.21092e9i) q^{93} +(-3.15774e10 + 3.15000e10i) q^{94} -1.98891e8 q^{95} +(6.48868e10 + 4.66057e10i) q^{96} -4.52802e10 q^{97} +(5.48371e10 - 5.47027e10i) q^{98} +(-8.12132e10 + 2.84823e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9}+O(q^{10}) $ 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9	$ 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9} + 202000 q^{10} + 1064760 q^{12} + 1543864 q^{13} + 3482912 q^{16} + 2557392 q^{18} - 12211752 q^{21} - 5920464 q^{22} + 12133152 q^{24} - 141128700 q^{25} - 3604848 q^{28} + 73456080 q^{30} + 229769760 q^{33} + 222167104 q^{34} + 298087896 q^{36} - 44517800 q^{37} - 439643840 q^{40} + 281776944 q^{42} + 1020227520 q^{45} - 2392795680 q^{46} + 689090592 q^{48} - 1018138084 q^{49} - 3959246384 q^{52} - 4249352520 q^{54} + 1438636392 q^{57} + 9671853040 q^{58} + 5688375360 q^{60} + 6873199864 q^{61} - 1452752512 q^{64} - 10961242896 q^{66} - 13308470976 q^{69} + 35188514400 q^{70} + 30438127680 q^{72} - 12426469112 q^{73} - 60088673808 q^{76} - 81037845456 q^{78} - 42462874764 q^{81} + 88180337440 q^{82} + 125502443664 q^{84} + 17135502080 q^{85} - 166086469440 q^{88} - 257976145200 q^{90} + 114387515256 q^{93} + 391966360512 q^{94} + 446868262272 q^{96} + 75764383528 q^{97}+O(q^{100}) $ 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9 + 202000 * q^10 + 1064760 * q^12 + 1543864 * q^13 + 3482912 * q^16 + 2557392 * q^18 - 12211752 * q^21 - 5920464 * q^22 + 12133152 * q^24 - 141128700 * q^25 - 3604848 * q^28 + 73456080 * q^30 + 229769760 * q^33 + 222167104 * q^34 + 298087896 * q^36 - 44517800 * q^37 - 439643840 * q^40 + 281776944 * q^42 + 1020227520 * q^45 - 2392795680 * q^46 + 689090592 * q^48 - 1018138084 * q^49 - 3959246384 * q^52 - 4249352520 * q^54 + 1438636392 * q^57 + 9671853040 * q^58 + 5688375360 * q^60 + 6873199864 * q^61 - 1452752512 * q^64 - 10961242896 * q^66 - 13308470976 * q^69 + 35188514400 * q^70 + 30438127680 * q^72 - 12426469112 * q^73 - 60088673808 * q^76 - 81037845456 * q^78 - 42462874764 * q^81 + 88180337440 * q^82 + 125502443664 * q^84 + 17135502080 * q^85 - 166086469440 * q^88 - 257976145200 * q^90 + 114387515256 * q^93 + 391966360512 * q^94 + 446868262272 * q^96 + 75764383528 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	32.0392	−	31.9607i	0.707974	−	0.706239i
$2$	32.0392	−	31.9607i	0.707974	−	0.706239i
$3$	−70.6484	−	414.917i	−0.167855	−	0.985812i
$3$	−70.6484	−	414.917i	−0.167855	−	0.985812i
$4$	5.02409	−	2047.99i	0.00245317	−	0.999997i
$5$		−	1842.04i		−	0.263611i	−0.991276	−	0.131805i	$-0.957923\pi$
$5$		−	1842.04i		−	0.263611i	0.991276	−	0.131805i	$-0.0420774\pi$
$6$	−15524.6	−	11035.6i	−0.815056	−	0.579383i
$7$			16302.4i			0.366616i	0.983056	+	0.183308i	$0.0586805\pi$
$7$			16302.4i			0.366616i	−0.983056	+	0.183308i	$0.941319\pi$
$8$	−65294.4	−	65776.7i	−0.704500	−	0.709704i
$9$	−167165.	+	58626.4i	−0.943649	+	0.330948i
$10$	−58872.8	−	59017.4i	−0.186172	−	0.186629i
$11$	485828.			0.909542			0.454771	−	0.890608i	$-0.349721\pi$
$11$	485828.			0.909542			0.454771	+	0.890608i	$0.349721\pi$
$12$	−850102.	+	142603.i	−0.986220	+	0.165437i
$13$	−1.36551e6			−1.02001			−0.510006	−	0.860171i	$-0.670357\pi$
$13$	−1.36551e6			−1.02001			−0.510006	+	0.860171i	$0.670357\pi$
$14$	521035.	+	522315.i	0.258918	+	0.259554i
$15$	−764291.	+	130137.i	−0.259871	+	0.0442485i
$16$	−4.19425e6	−	20578.6i	−0.999988	−	0.00490632i
$17$		−	8.90746e6i		−	1.52154i	−0.649019	−	0.760772i	$-0.724820\pi$
$17$		−	8.90746e6i		−	1.52154i	0.649019	−	0.760772i	$-0.275180\pi$
$18$	−3.48208e6	+	7.22105e6i	−0.434350	+	0.900744i
$19$		−	107974.i		−	0.0100040i	−0.999987	−	0.00500199i	$-0.998408\pi$
$19$		−	107974.i		−	0.0100040i	0.999987	−	0.00500199i	$-0.00159219\pi$
$20$	−3.77248e6	−	9254.56i	−0.263610	−	0.000646682i
$21$	6.76412e6	−	1.15174e6i	0.361414	−	0.0615385i
$22$	1.55655e7	−	1.55274e7i	0.643931	−	0.642354i
$23$	5.58155e7			1.80822			0.904112	−	0.427296i	$-0.140534\pi$
$23$	5.58155e7			1.80822			0.904112	+	0.427296i	$0.140534\pi$
$24$	−2.26789e7	+	3.17388e7i	−0.581380	+	0.813632i
$25$	4.54350e7			0.930509
$26$	−4.37498e7	+	4.36426e7i	−0.722141	+	0.720372i
$27$	3.61350e7	+	6.52175e7i	0.484649	+	0.874709i
$28$	3.33871e7	+	81904.5i	0.366615	+	0.000899371i
$29$		−	1.27942e8i		−	1.15831i	−0.815218	−	0.579154i	$-0.803383\pi$
$29$		−	1.27942e8i		−	1.15831i	0.815218	−	0.579154i	$-0.196617\pi$
$30$	−2.03280e7	+	2.85968e7i	−0.152731	+	0.214857i
$31$		−	1.30377e8i		−	0.817921i	−0.912552	−	0.408960i	$-0.865891\pi$
$31$		−	1.30377e8i		−	0.817921i	0.912552	−	0.408960i	$-0.134109\pi$
$32$	−1.35038e8	+	1.33392e8i	−0.711430	+	0.702757i
$33$	−3.43230e7	−	2.01578e8i	−0.152672	−	0.896637i
$34$	−2.84689e8	−	2.85388e8i	−1.07457	−	1.07721i
$35$	3.00295e7			0.0966439
$36$	1.19227e8	+	3.42647e8i	0.328632	+	0.944458i
$37$	−3.44489e8			−0.816705			−0.408353	−	0.912824i	$-0.633897\pi$
$37$	−3.44489e8			−0.816705			−0.408353	+	0.912824i	$0.633897\pi$
$38$	−3.45092e6	−	3.45939e6i	−0.00706520	−	0.00708255i
$39$	9.64708e7	+	5.66571e8i	0.171215	+	1.00554i
$40$	−1.21163e8	+	1.20275e8i	−0.187086	+	0.185714i
$41$			9.40493e8i			1.26778i	0.773423	+	0.633891i	$0.218543\pi$
$41$			9.40493e8i			1.26778i	−0.773423	+	0.633891i	$0.781457\pi$
$42$	1.79907e8	−	2.53087e8i	0.212411	−	0.298812i
$43$		−	9.39748e8i		−	0.974844i	−0.873167	−	0.487422i	$-0.837937\pi$
$43$		−	9.39748e8i		−	0.974844i	0.873167	−	0.487422i	$-0.162063\pi$
$44$	2.44084e6	−	9.94972e8i	0.00223126	−	0.909539i
$45$	1.07992e8	+	3.07923e8i	0.0872414	+	0.248756i
$46$	1.78829e9	−	1.78391e9i	1.28017	−	1.27704i
$47$	−9.85584e8			−0.626838			−0.313419	−	0.949615i	$-0.601474\pi$
$47$	−9.85584e8			−0.626838			−0.313419	+	0.949615i	$0.601474\pi$
$48$	2.87779e8	+	1.74172e9i	0.163017	+	0.986623i
$49$	1.71156e9			0.865593
$50$	1.45570e9	−	1.45214e9i	0.658776	−	0.657162i
$51$	−3.69585e9	+	6.29298e8i	−1.49996	+	0.255400i
$52$	−6.86043e6	+	2.79655e9i	−0.00250226	+	1.02001i
$53$			1.84952e9i			0.607495i	0.952753	+	0.303748i	$0.0982379\pi$
$53$			1.84952e9i			0.607495i	−0.952753	+	0.303748i	$0.901762\pi$
$54$	3.24214e9	+	9.34618e8i	0.960872	+	0.276993i
$55$		−	8.94912e8i		−	0.239765i
$56$	1.07232e9	−	1.06445e9i	0.260189	−	0.258281i
$57$	−4.48001e7	+	7.62817e6i	−0.00986204	+	0.00167922i
$58$	−4.08912e9	−	4.09916e9i	−0.818042	−	0.820051i
$59$	5.76202e9			1.04927			0.524637	−	0.851326i	$-0.324201\pi$
$59$	5.76202e9			1.04927			0.524637	+	0.851326i	$0.324201\pi$
$60$	2.62680e8	+	1.56592e9i	0.0436109	+	0.259978i
$61$	−7.38482e9			−1.11950			−0.559752	−	0.828660i	$-0.689104\pi$
$61$	−7.38482e9			−1.11950			−0.559752	+	0.828660i	$0.689104\pi$
$62$	−4.16694e9	−	4.17717e9i	−0.577647	−	0.579066i
$63$	−9.55749e8	−	2.72518e9i	−0.121331	−	0.345957i
$64$	−6.32172e7	+	8.58970e9i	−0.00735945	+	0.999973i
$65$			2.51531e9i			0.268886i
$66$	−7.54226e9	−	5.36142e9i	−0.741327	−	0.526973i
$67$			1.05400e10i			0.953735i	0.878975	+	0.476868i	$0.158228\pi$
$67$			1.05400e10i			0.953735i	−0.878975	+	0.476868i	$0.841772\pi$
$68$	−1.82424e10	−	4.47519e7i	−1.52154	−	0.00373261i
$69$	−3.94328e9	−	2.31588e10i	−0.303520	−	1.78257i
$70$	9.62123e8	−	9.59766e8i	0.0684213	−	0.0682537i
$71$	1.58034e10			1.03951			0.519755	−	0.854315i	$-0.326023\pi$
$71$	1.58034e10			1.03951			0.519755	+	0.854315i	$0.326023\pi$
$72$	1.47712e10	+	7.16756e9i	0.899676	+	0.436559i
$73$	1.99415e10			1.12585			0.562927	−	0.826506i	$-0.309675\pi$
$73$	1.99415e10			1.12585			0.562927	+	0.826506i	$0.309675\pi$
$74$	−1.10371e10	+	1.10101e10i	−0.578206	+	0.576789i
$75$	−3.20991e9	−	1.88517e10i	−0.156191	−	0.917307i
$76$	−2.21129e8	−	542469.i	−0.0100040	−	2.45415e-5i
$77$			7.92014e9i			0.333452i
$78$	2.11989e10	+	1.50692e10i	0.831366	+	0.590977i
$79$			1.66155e10i			0.607525i	0.952748	+	0.303762i	$0.0982429\pi$
$79$			1.66155e10i			0.607525i	−0.952748	+	0.303762i	$0.901757\pi$
$80$	−3.79066e7	+	7.72597e9i	−0.00129336	+	0.263608i
$81$	2.45069e10	−	1.96005e10i	0.780947	−	0.624597i
$82$	3.00588e10	+	3.01327e10i	0.895357	+	0.897556i
$83$	3.12525e10			0.870873			0.435436	−	0.900219i	$-0.356594\pi$
$83$	3.12525e10			0.870873			0.435436	+	0.900219i	$0.356594\pi$
$84$	−2.32476e9	−	1.38587e10i	−0.0606517	−	0.361564i
$85$	−1.64079e10			−0.401096
$86$	−3.00350e10	−	3.01088e10i	−0.688473	−	0.690164i
$87$	−5.30852e10	+	9.03889e9i	−1.14187	+	0.194428i
$88$	−3.17218e10	−	3.19562e10i	−0.640772	−	0.645505i
$89$			5.55310e10i			1.05412i	0.849828	+	0.527061i	$0.176706\pi$
$89$			5.55310e10i			1.05412i	−0.849828	+	0.527061i	$0.823294\pi$
$90$	1.33014e10	+	6.41412e9i	0.237446	+	0.114499i
$91$		−	2.22610e10i		−	0.373952i
$92$	2.80422e8	−	1.14310e11i	0.00443588	−	1.80822i
$93$	−5.40955e10	+	9.21092e9i	−0.806316	+	0.137292i
$94$	−3.15774e10	+	3.15000e10i	−0.443785	+	0.442698i
$95$	−1.98891e8			−0.00263716
$96$	6.48868e10	+	4.66057e10i	0.812203	+	0.583374i
$97$	−4.52802e10			−0.535382			−0.267691	−	0.963505i	$-0.586261\pi$
$97$	−4.52802e10			−0.535382			−0.267691	+	0.963505i	$0.586261\pi$
$98$	5.48371e10	−	5.47027e10i	0.612817	−	0.611315i
$99$	−8.12132e10	+	2.84823e10i	−0.858288	+	0.301011i
$100$	2.28270e8	−	9.30507e10i	0.00228270	−	0.930507i
$101$			7.04743e10i			0.667211i	0.942713	+	0.333606i	$0.108265\pi$
$101$			7.04743e10i			0.667211i	−0.942713	+	0.333606i	$0.891735\pi$
$102$	−9.82994e10	+	1.38284e11i	−0.881556	+	1.24014i
$103$		−	8.56630e10i		−	0.728096i	−0.931380	−	0.364048i	$-0.881394\pi$
$103$		−	8.56630e10i		−	0.728096i	0.931380	−	0.364048i	$-0.118606\pi$
$104$	8.91599e10	+	8.98185e10i	0.718598	+	0.723906i
$105$	−2.12154e9	−	1.24598e10i	−0.0162222	−	0.0952727i
$106$	5.91121e10	+	5.92573e10i	0.429037	+	0.430090i
$107$	−6.87116e10			−0.473608			−0.236804	−	0.971557i	$-0.576100\pi$
$107$	−6.87116e10			−0.473608			−0.236804	+	0.971557i	$0.576100\pi$
$108$	1.33747e11	−	7.36766e10i	0.875895	−	0.482502i
$109$	1.08394e11			0.674777			0.337388	−	0.941366i	$-0.390456\pi$
$109$	1.08394e11			0.674777			0.337388	+	0.941366i	$0.390456\pi$
$110$	−2.86021e10	−	2.86723e10i	−0.169331	−	0.169747i
$111$	2.43376e10	+	1.42934e11i	0.137088	+	0.805117i
$112$	3.35480e8	−	6.83762e10i	0.00179874	−	0.366611i
$113$		−	2.57009e10i		−	0.131225i	−0.997845	−	0.0656125i	$-0.979100\pi$
$113$		−	2.57009e10i		−	0.131225i	0.997845	−	0.0656125i	$-0.0209001\pi$
$114$	−1.19156e9	+	1.67624e9i	−0.00579613	+	0.00815380i
$115$		−	1.02814e11i		−	0.476667i
$116$	−2.62024e11	−	6.42792e8i	−1.15830	−	0.00284152i
$117$	2.28264e11	−	8.00547e10i	0.962533	−	0.337571i
$118$	1.84611e11	−	1.84158e11i	0.742858	−	0.741038i
$119$	1.45213e11			0.557822
$120$	5.84639e10	+	4.17754e10i	0.214482	+	0.153258i
$121$	−4.92830e10			−0.172734
$122$	−2.36604e11	+	2.36024e11i	−0.792579	+	0.790637i
$123$	3.90226e11	−	6.64443e10i	1.24979	−	0.212804i
$124$	−2.67011e11	−	6.55025e8i	−0.817918	−	0.00200650i
$125$		−	1.73636e11i		−	0.508903i
$126$	−1.17720e11	−	5.67662e10i	−0.330227	−	0.159240i
$127$			2.98675e11i			0.802191i	0.916036	+	0.401096i	$0.131370\pi$
$127$			2.98675e11i			0.802191i	−0.916036	+	0.401096i	$0.868630\pi$
$128$	2.72508e11	+	2.77228e11i	0.701010	+	0.713152i
$129$	−3.89917e11	+	6.63917e10i	−0.961012	+	0.163633i
$130$	8.03912e10	+	8.05886e10i	0.189898	+	0.190364i
$131$	−2.12063e10			−0.0480255			−0.0240127	−	0.999712i	$-0.507644\pi$
$131$	−2.12063e10			−0.0480255			−0.0240127	+	0.999712i	$0.507644\pi$
$132$	−4.13003e11	+	6.92805e10i	−0.897009	+	0.150471i
$133$	1.76022e9			0.00366762
$134$	3.36865e11	+	3.37692e11i	0.673565	+	0.675219i
$135$	1.20133e11	−	6.65619e10i	0.230583	−	0.127759i
$136$	−5.85903e11	+	5.81607e11i	−1.07985	+	1.07193i
$137$		−	1.01885e12i		−	1.80363i	−0.432117	−	0.901817i	$-0.642233\pi$
$137$		−	1.01885e12i		−	1.80363i	0.432117	−	0.901817i	$-0.357767\pi$
$138$	−8.66512e11	−	6.15960e11i	−1.47380	−	1.04765i
$139$		−	2.22475e11i		−	0.363663i	−0.983330	−	0.181832i	$-0.941797\pi$
$139$		−	2.22475e11i		−	0.363663i	0.983330	−	0.181832i	$-0.0582026\pi$
$140$	1.50871e8	−	6.15003e10i	0.000237084	−	0.0966436i
$141$	6.96300e10	+	4.08935e11i	0.105218	+	0.617944i
$142$	5.06327e11	−	5.05087e11i	0.735945	−	0.734142i
$143$	−6.63401e11			−0.927743
$144$	7.02337e11	−	2.42454e11i	0.945261	−	0.326314i
$145$	−2.35674e11			−0.305342
$146$	6.38911e11	−	6.37345e11i	0.797075	−	0.795122i
$147$	−1.20919e11	−	7.10155e11i	−0.145294	−	0.853311i
$148$	−1.73074e9	+	7.05510e11i	−0.00200352	+	0.816703i
$149$			4.83320e11i			0.539150i	0.962979	+	0.269575i	$0.0868833\pi$
$149$			4.83320e11i			0.539150i	−0.962979	+	0.269575i	$0.913117\pi$
$150$	−7.05359e11	−	5.01404e11i	−0.758417	−	0.539121i
$151$			1.38396e12i			1.43466i	0.696733	+	0.717331i	$0.254636\pi$
$151$			1.38396e12i			1.43466i	−0.696733	+	0.717331i	$0.745364\pi$
$152$	−7.10215e9	+	7.05007e9i	−0.00709987	+	0.00704781i
$153$	5.22212e11	+	1.48901e12i	0.503552	+	1.43580i
$154$	2.53133e11	+	2.53755e11i	0.235497	+	0.236075i
$155$	−2.40159e11			−0.215613
$156$	1.16082e12	−	1.94725e11i	1.00596	−	0.168747i
$157$	5.51215e11			0.461183			0.230592	−	0.973051i	$-0.425934\pi$
$157$	5.51215e11			0.461183			0.230592	+	0.973051i	$0.425934\pi$
$158$	5.31043e11	+	5.32347e11i	0.429058	+	0.430112i
$159$	7.67398e11	−	1.30666e11i	0.598876	−	0.101971i
$160$	2.45713e11	+	2.48746e11i	0.185254	+	0.187541i
$161$			9.09925e11i			0.662923i
$162$	1.58737e11	−	1.41125e12i	0.111775	−	0.993734i
$163$		−	1.35112e12i		−	0.919735i	−0.887988	−	0.459867i	$-0.847897\pi$
$163$		−	1.35112e12i		−	0.919735i	0.887988	−	0.459867i	$-0.152103\pi$
$164$	1.92612e12	+	4.72512e9i	1.26778	+	0.00311008i
$165$	−3.71314e11	+	6.32241e10i	−0.236363	+	0.0402459i
$166$	1.00130e12	−	9.98852e11i	0.616555	−	0.615044i
$167$	−2.76988e12			−1.65014			−0.825070	−	0.565030i	$-0.808865\pi$
$167$	−2.76988e12			−1.65014			−0.825070	+	0.565030i	$0.808865\pi$
$168$	−5.17417e11	−	3.69720e11i	−0.298290	−	0.213143i
$169$	7.24460e10			0.0404239
$170$	−5.25695e11	+	5.24407e11i	−0.283965	+	0.283269i
$171$	6.33011e9	+	1.80494e10i	0.00331080	+	0.00944025i
$172$	−1.92460e12	−	4.72138e9i	−0.974841	−	0.00239146i
$173$		−	1.53462e12i		−	0.752915i	−0.926434	−	0.376458i	$-0.877142\pi$
$173$		−	1.53462e12i		−	0.752915i	0.926434	−	0.376458i	$-0.122858\pi$
$174$	−1.41192e12	+	1.98624e12i	−0.671103	+	0.944085i
$175$			7.40698e11i			0.341139i
$176$	−2.03769e12	−	9.99766e9i	−0.909531	−	0.00446251i
$177$	−4.07077e11	−	2.39076e12i	−0.176126	−	1.03439i
$178$	1.77481e12	+	1.77917e12i	0.744462	+	0.746290i
$179$	1.08982e12			0.443263			0.221632	−	0.975130i	$-0.428862\pi$
$179$	1.08982e12			0.443263			0.221632	+	0.975130i	$0.428862\pi$
$180$	6.31167e11	−	2.19620e11i	0.248969	−	0.0866309i
$181$	−2.29429e12			−0.877841			−0.438921	−	0.898526i	$-0.644639\pi$
$181$	−2.29429e12			−0.877841			−0.438921	+	0.898526i	$0.644639\pi$
$182$	−7.11477e11	−	7.13224e11i	−0.264100	−	0.264748i
$183$	5.21726e11	+	3.06408e12i	0.187915	+	1.10362i
$184$	−3.64444e12	−	3.67136e12i	−1.27389	−	1.28330i
$185$			6.34560e11i			0.215292i
$186$	−1.43879e12	+	2.02404e12i	−0.473889	+	0.666651i
$187$		−	4.32749e12i		−	1.38391i
$188$	−4.95166e9	+	2.01847e12i	−0.00153774	+	0.626836i
$189$	−1.06320e12	+	5.89085e11i	−0.320682	+	0.177680i
$190$	−6.37232e9	+	6.35671e9i	−0.00186704	+	0.00186246i
$191$	6.77238e12			1.92778			0.963891	−	0.266299i	$-0.0858008\pi$
$191$	6.77238e12			1.92778			0.963891	+	0.266299i	$0.0858008\pi$
$192$	3.56848e12	−	5.80619e11i	0.987020	−	0.160596i
$193$	2.41050e12			0.647950			0.323975	−	0.946066i	$-0.394981\pi$
$193$	2.41050e12			0.647950			0.323975	+	0.946066i	$0.394981\pi$
$194$	−1.45074e12	+	1.44719e12i	−0.379037	+	0.378108i
$195$	1.04364e12	−	1.77703e11i	0.265071	−	0.0451340i
$196$	8.59903e9	−	3.50526e12i	0.00212345	−	0.865590i
$197$		−	1.77642e12i		−	0.426562i	−0.976991	−	0.213281i	$-0.931585\pi$
$197$		−	1.77642e12i		−	0.426562i	0.976991	−	0.213281i	$-0.0684150\pi$
$198$	−1.69169e12	+	3.50819e12i	−0.395060	+	0.819264i
$199$			4.72841e12i			1.07405i	0.843567	+	0.537024i	$0.180451\pi$
$199$			4.72841e12i			1.07405i	−0.843567	+	0.537024i	$0.819549\pi$
$200$	−2.96665e12	−	2.98857e12i	−0.655544	−	0.660386i
$201$	4.37321e12	−	7.44632e11i	0.940203	−	0.160090i
$202$	2.25241e12	+	2.25794e12i	0.471211	+	0.472368i
$203$	2.08576e12			0.424654
$204$	1.27023e12	+	7.57224e12i	0.251719	+	1.50058i
$205$	1.73242e12			0.334201
$206$	−2.73785e12	−	2.74458e12i	−0.514210	−	0.515473i
$207$	−9.33038e12	+	3.27226e12i	−1.70633	+	0.598427i
$208$	5.72728e12	+	2.81002e10i	1.02000	+	0.00500451i
$209$		−	5.24566e10i		−	0.00909904i
$210$	−4.66195e11	−	3.31395e11i	−0.0787702	−	0.0559938i
$211$		−	8.68943e12i		−	1.43033i	−0.698953	−	0.715167i	$-0.746350\pi$
$211$		−	8.68943e12i		−	1.43033i	0.698953	−	0.715167i	$-0.253650\pi$
$212$	3.78781e12	+	9.29218e9i	0.607493	+	0.00149029i
$213$	−1.11648e12	−	6.55708e12i	−0.174487	−	1.02476i
$214$	−2.20147e12	+	2.19607e12i	−0.335302	+	0.334481i
$215$	−1.73105e12			−0.256979
$216$	1.93038e12	−	6.63518e12i	0.279349	−	0.960190i
$217$	2.12545e12			0.299863
$218$	3.47287e12	−	3.46436e12i	0.477724	−	0.476554i
$219$	−1.40884e12	−	8.27406e12i	−0.188981	−	1.10988i
$220$	−1.83278e12	−	4.49612e9i	−0.239764	−	0.000588184i
$221$			1.21632e13i			1.55199i
$222$	5.34803e12	+	3.80165e12i	0.665660	+	0.473185i
$223$			1.25001e13i			1.51788i	0.651160	+	0.758941i	$0.274283\pi$
$223$			1.25001e13i			1.51788i	−0.651160	+	0.758941i	$0.725717\pi$
$224$	−2.17461e12	−	2.20144e12i	−0.257642	−	0.260822i
$225$	−7.59513e12	+	2.66369e12i	−0.878074	+	0.307950i
$226$	−8.21419e11	−	8.23437e11i	−0.0926762	−	0.0929039i
$227$	−7.81442e11			−0.0860507			−0.0430253	−	0.999074i	$-0.513700\pi$
$227$	−7.81442e11			−0.0860507			−0.0430253	+	0.999074i	$0.513700\pi$
$228$	1.53974e10	+	9.17886e10i	0.00165502	+	0.00986613i
$229$	−1.14635e13			−1.20288			−0.601439	−	0.798919i	$-0.705406\pi$
$229$	−1.14635e13			−1.20288			−0.601439	+	0.798919i	$0.705406\pi$
$230$	−3.28602e12	−	3.29409e12i	−0.336641	−	0.337468i
$231$	3.28620e12	−	5.59545e11i	0.328721	−	0.0559718i
$232$	−8.41560e12	+	8.35389e12i	−0.822055	+	0.816028i
$233$			1.35109e13i			1.28892i	0.764638	+	0.644460i	$0.222918\pi$
$233$			1.35109e13i			1.28892i	−0.764638	+	0.644460i	$0.777082\pi$
$234$	4.75480e12	−	9.86038e12i	0.443043	−	0.918769i
$235$			1.81548e12i			0.165241i
$236$	2.89489e10	−	1.18006e13i	0.00257405	−	1.04927i
$237$	6.89404e12	−	1.17386e12i	0.598905	−	0.101976i
$238$	4.65250e12	−	4.64110e12i	0.394924	−	0.393956i
$239$	−6.11384e12			−0.507137			−0.253569	−	0.967317i	$-0.581604\pi$
$239$	−6.11384e12			−0.507137			−0.253569	+	0.967317i	$0.581604\pi$
$240$	3.20831e12	−	5.30099e11i	0.260085	−	0.0429730i
$241$	−6.42898e12			−0.509387			−0.254694	−	0.967022i	$-0.581975\pi$
$241$	−6.42898e12			−0.509387			−0.254694	+	0.967022i	$0.581975\pi$
$242$	−1.57899e12	+	1.57512e12i	−0.122291	+	0.121991i
$243$	−9.86396e12	−	8.78360e12i	−0.746821	−	0.665025i
$244$	−3.71020e10	+	1.51241e13i	−0.00274633	+	1.11950i
$245$		−	3.15276e12i		−	0.228180i
$246$	1.03789e13	−	1.46007e13i	0.734530	−	1.03331i
$247$			1.47439e11i			0.0102042i
$248$	−8.57576e12	+	8.51288e12i	−0.580482	+	0.576225i
$249$	−2.20794e12	−	1.29672e13i	−0.146181	−	0.858517i
$250$	−5.54954e12	−	5.56317e12i	−0.359407	−	0.360290i
$251$	6.62584e12			0.419793			0.209897	−	0.977724i	$-0.432687\pi$
$251$	6.62584e12			0.419793			0.209897	+	0.977724i	$0.432687\pi$
$252$	−5.58595e12	+	1.94368e12i	−0.346253	+	0.120482i
$253$	2.71167e13			1.64465
$254$	9.54586e12	+	9.56930e12i	0.566539	+	0.567930i
$255$	1.15919e12	+	6.80789e12i	0.0673261	+	0.395405i
$256$	1.75913e13	+	1.72624e11i	0.999952	+	0.00981253i
$257$		−	2.03446e13i		−	1.13193i	−0.824431	−	0.565963i	$-0.808505\pi$
$257$		−	2.03446e13i		−	1.13193i	0.824431	−	0.565963i	$-0.191495\pi$
$258$	−1.03707e13	+	1.45892e13i	−0.564807	+	0.794552i
$259$		−	5.61598e12i		−	0.299417i
$260$	5.15134e12	+	1.26372e10i	0.268885	+	0.000659623i
$261$	7.50077e12	+	2.13874e13i	0.383339	+	1.09304i
$262$	−6.79432e11	+	6.77767e11i	−0.0340008	+	0.0339175i
$263$	2.41081e12			0.118142			0.0590712	−	0.998254i	$-0.481186\pi$
$263$	2.41081e12			0.118142			0.0590712	+	0.998254i	$0.481186\pi$
$264$	−1.10180e13	+	1.54196e13i	−0.528790	+	0.740032i
$265$	3.40689e12			0.160142
$266$	5.63962e10	−	5.62581e10i	0.00259658	−	0.00259021i
$267$	2.30407e13	−	3.92318e12i	1.03917	−	0.176940i
$268$	2.15858e13	+	5.29538e10i	0.953732	+	0.00233967i
$269$		−	1.94916e13i		−	0.843745i	−0.906655	−	0.421872i	$-0.861373\pi$
$269$		−	1.94916e13i		−	0.843745i	0.906655	−	0.421872i	$-0.138627\pi$
$270$	1.72160e12	−	5.97213e12i	0.0730183	−	0.253296i
$271$			2.17704e13i			0.904766i	0.891824	+	0.452383i	$0.149426\pi$
$271$			2.17704e13i			0.904766i	−0.891824	+	0.452383i	$0.850574\pi$
$272$	−1.83303e11	+	3.73601e13i	−0.00746519	+	1.52153i
$273$	−9.23645e12	+	1.57270e12i	−0.368647	+	0.0627700i
$274$	−3.25633e13	−	3.26433e13i	−1.27380	−	1.27693i
$275$	2.20736e13			0.846337
$276$	−4.74489e13	+	7.95946e12i	−1.78331	+	0.299146i
$277$	−1.17163e13			−0.431669			−0.215835	−	0.976430i	$-0.569247\pi$
$277$	−1.17163e13			−0.431669			−0.215835	+	0.976430i	$0.569247\pi$
$278$	−7.11046e12	−	7.12792e12i	−0.256833	−	0.257464i
$279$	7.64353e12	+	2.17944e13i	0.270689	+	0.771830i
$280$	−1.96076e12	−	1.97524e12i	−0.0680856	−	0.0685886i
$281$		−	9.99836e12i		−	0.340443i	−0.985406	−	0.170221i	$-0.945552\pi$
$281$		−	9.99836e12i		−	0.340443i	0.985406	−	0.170221i	$-0.0544483\pi$
$282$	1.53008e13	+	1.08765e13i	0.510908	+	0.363179i
$283$		−	4.71859e13i		−	1.54521i	−0.634889	−	0.772603i	$-0.718954\pi$
$283$		−	4.71859e13i		−	1.54521i	0.634889	−	0.772603i	$-0.281046\pi$
$284$	7.93975e10	−	3.23652e13i	0.00255009	−	1.03951i
$285$	1.40514e10	+	8.25233e10i	0.000442661	+	0.00259974i
$286$	−2.12548e13	+	2.12028e13i	−0.656818	+	0.655208i
$287$	−1.53323e13			−0.464789
$288$	1.47533e13	−	3.02152e13i	0.438765	−	0.898602i
$289$	−4.50709e13			−1.31510
$290$	−7.55080e12	+	7.53230e12i	−0.216174	+	0.215645i
$291$	3.19898e12	+	1.87875e13i	0.0898669	+	0.527786i
$292$	1.00188e11	−	4.08401e13i	0.00276191	−	1.12585i
$293$		−	2.18955e13i		−	0.592357i	−0.955133	−	0.296178i	$-0.904288\pi$
$293$		−	2.18955e13i		−	0.592357i	0.955133	−	0.296178i	$-0.0957123\pi$
$294$	−2.65712e13	−	1.88881e13i	−0.705506	−	0.501509i
$295$		−	1.06138e13i		−	0.276600i
$296$	2.24932e13	+	2.26593e13i	0.575369	+	0.579619i
$297$	1.75554e13	+	3.16845e13i	0.440808	+	0.795584i
$298$	1.54472e13	+	1.54852e13i	0.380769	+	0.381704i
$299$	−7.62165e13			−1.84441
$300$	−3.86244e13	+	6.47917e12i	−0.917687	+	0.153940i
$301$	1.53201e13			0.357393
$302$	4.42323e13	+	4.43409e13i	1.01321	+	1.01570i
$303$	2.92410e13	−	4.97890e12i	0.657745	−	0.111995i
$304$	−2.22195e9	+	4.52869e11i	−4.90828e−5	+	0.0100039i
$305$			1.36031e13i			0.295113i
$306$	6.43212e13	+	3.10165e13i	1.37052	+	0.660884i
$307$			2.68610e13i			0.562162i	0.959684	+	0.281081i	$0.0906929\pi$
$307$			2.68610e13i			0.562162i	−0.959684	+	0.281081i	$0.909307\pi$
$308$	1.62204e13	+	3.97915e10i	0.333451	+	0.000818015i
$309$	−3.55430e13	+	6.05196e12i	−0.717766	+	0.122215i
$310$	−7.69450e12	+	7.67565e12i	−0.152648	+	0.152274i
$311$	−3.44085e13			−0.670630			−0.335315	−	0.942106i	$-0.608843\pi$
$311$	−3.44085e13			−0.670630			−0.335315	+	0.942106i	$0.608843\pi$
$312$	3.09682e13	−	4.33395e13i	0.593015	−	0.829914i
$313$	9.40692e13			1.76992			0.884960	−	0.465668i	$-0.154186\pi$
$313$	9.40692e13			1.76992			0.884960	+	0.465668i	$0.154186\pi$
$314$	1.76605e13	−	1.76172e13i	0.326505	−	0.325705i
$315$	−5.01988e12	+	1.76052e12i	−0.0911979	+	0.0319841i
$316$	3.40284e13	+	8.34777e10i	0.607523	+	0.00149036i
$317$			7.46947e13i			1.31058i	0.755377	+	0.655291i	$0.227454\pi$
$317$			7.46947e13i			1.31058i	−0.755377	+	0.655291i	$0.772546\pi$
$318$	2.04107e13	−	2.87130e13i	0.351972	−	0.495142i
$319$		−	6.21577e13i		−	1.05353i
$320$	1.58225e13	+	1.16448e11i	0.263604	+	0.00194003i
$321$	4.85436e12	+	2.85096e13i	0.0794977	+	0.466888i
$322$	2.90819e13	+	2.91533e13i	0.468182	+	0.469332i
$323$	−9.61771e11			−0.0152215
$324$	−4.00186e13	−	5.02886e13i	−0.622679	−	0.782477i
$325$	−6.20418e13			−0.949130
$326$	−4.31828e13	−	4.32889e13i	−0.649553	−	0.651148i
$327$	−7.65788e12	−	4.49745e13i	−0.113265	−	0.665203i
$328$	6.18625e13	−	6.14089e13i	0.899750	−	0.893152i
$329$		−	1.60673e13i		−	0.229809i
$330$	−9.87593e12	+	1.38931e13i	−0.138916	+	0.195422i
$331$			9.71996e13i			1.34465i	0.740254	+	0.672327i	$0.234705\pi$
$331$			9.71996e13i			1.34465i	−0.740254	+	0.672327i	$0.765295\pi$
$332$	1.57015e11	−	6.40049e13i	0.00213640	−	0.870870i
$333$	5.75863e13	−	2.01961e13i	0.770683	−	0.270287i
$334$	−8.87449e13	+	8.85275e13i	−1.16826	+	1.16539i
$335$	1.94150e13			0.251415
$336$	−2.83941e13	+	4.69148e12i	−0.361712	+	0.0597645i
$337$	−3.36820e12			−0.0422117			−0.0211059	−	0.999777i	$-0.506719\pi$
$337$	−3.36820e12			−0.0422117			−0.0211059	+	0.999777i	$0.506719\pi$
$338$	2.32111e12	−	2.31543e12i	0.0286190	−	0.0285489i
$339$	−1.06637e13	+	1.81573e12i	−0.129363	+	0.0220268i
$340$	−8.24346e10	+	3.36032e13i	−0.000983955	+	0.401094i
$341$		−	6.33407e13i		−	0.743933i
$342$	7.79683e11	+	3.75973e11i	0.00901103	+	0.00434523i
$343$			6.01376e13i			0.683956i
$344$	−6.18136e13	+	6.13603e13i	−0.691851	+	0.686777i
$345$	−4.26593e13	+	7.26366e12i	−0.469904	+	0.0800112i
$346$	−4.90474e13	−	4.91679e13i	−0.531738	−	0.533044i
$347$	8.18457e13			0.873340			0.436670	−	0.899622i	$-0.356158\pi$
$347$	8.18457e13			0.873340			0.436670	+	0.899622i	$0.356158\pi$
$348$	1.82449e13	+	1.08764e14i	0.191626	+	1.14235i
$349$	−1.19377e14			−1.23419			−0.617095	−	0.786889i	$-0.711690\pi$
$349$	−1.19377e14			−1.23419			−0.617095	+	0.786889i	$0.711690\pi$
$350$	2.36733e13	+	2.37314e13i	0.240926	+	0.241518i
$351$	−4.93425e13	−	8.90549e13i	−0.494347	−	0.892213i
$352$	−6.56054e13	+	6.48056e13i	−0.647075	+	0.639187i
$353$		−	4.57746e13i		−	0.444491i	−0.974991	−	0.222246i	$-0.928661\pi$
$353$		−	4.57746e13i		−	0.444491i	0.974991	−	0.222246i	$-0.0713387\pi$
$354$	−8.94528e13	−	6.35875e13i	−0.855216	−	0.607931i
$355$		−	2.91104e13i		−	0.274026i
$356$	1.13727e14	+	2.78993e11i	1.05412	+	0.00258594i
$357$	−1.02590e13	−	6.02511e13i	−0.0936335	−	0.549908i
$358$	3.49169e13	−	3.48313e13i	0.313819	−	0.313050i
$359$	1.78716e14			1.58177			0.790886	−	0.611964i	$-0.209620\pi$
$359$	1.78716e14			1.58177			0.790886	+	0.611964i	$0.209620\pi$
$360$	1.32029e13	−	2.72090e13i	0.115082	−	0.237164i
$361$	1.16479e14			0.999900
$362$	−7.35073e13	+	7.33272e13i	−0.621489	+	0.619966i
$363$	3.48177e12	+	2.04483e13i	0.0289943	+	0.170283i
$364$	−4.55903e13	−	1.11841e11i	−0.373951	−	0.000917369i
$365$		−	3.67330e13i		−	0.296787i
$366$	1.14646e14	+	8.14961e13i	0.912458	+	0.648621i
$367$		−	2.55478e12i		−	0.0200304i	−0.999950	−	0.0100152i	$-0.996812\pi$
$367$		−	2.55478e12i		−	0.0200304i	0.999950	−	0.0100152i	$-0.00318799\pi$
$368$	−2.34105e14	−	1.14861e12i	−1.80820	−	0.00887173i
$369$	−5.51377e13	−	1.57217e14i	−0.419569	−	1.19634i
$370$	2.02810e13	+	2.03308e13i	0.152048	+	0.152421i
$371$	−3.01516e13			−0.222717
$372$	1.85921e13	+	1.10834e14i	0.135314	+	0.806650i
$373$	7.10115e13			0.509249			0.254625	−	0.967040i	$-0.418048\pi$
$373$	7.10115e13			0.509249			0.254625	+	0.967040i	$0.418048\pi$
$374$	−1.38310e14	−	1.38649e14i	−0.977370	−	0.979770i
$375$	−7.20445e13	+	1.22671e13i	−0.501683	+	0.0854222i
$376$	6.43531e13	+	6.48285e13i	0.441608	+	0.444870i
$377$			1.74705e14i			1.18149i
$378$	−1.52365e13	+	5.28545e13i	−0.101550	+	0.352271i
$379$			1.80425e14i			1.18517i	0.805507	+	0.592587i	$0.201893\pi$
$379$			1.80425e14i			1.18517i	−0.805507	+	0.592587i	$0.798107\pi$
$380$	−9.99248e8	+	4.07328e11i	−6.46939e−6	+	0.00263715i
$381$	1.23925e14	−	2.11009e13i	0.790809	−	0.134652i
$382$	2.16982e14	−	2.16450e14i	1.36482	−	1.36147i
$383$	3.90572e12			0.0242163			0.0121082	−	0.999927i	$-0.496146\pi$
$383$	3.90572e12			0.0242163			0.0121082	+	0.999927i	$0.496146\pi$
$384$	9.57742e13	−	1.32654e14i	0.585365	−	0.810770i
$385$	1.45892e13			0.0879016
$386$	7.72305e13	−	7.70413e13i	0.458732	−	0.457608i
$387$	5.50941e13	+	1.57093e14i	0.322622	+	0.919910i
$388$	−2.27492e11	+	9.27336e13i	−0.00131338	+	0.535381i
$389$			1.85772e14i			1.05744i	0.848795	+	0.528722i	$0.177328\pi$
$389$			1.85772e14i			1.05744i	−0.848795	+	0.528722i	$0.822672\pi$
$390$	2.77581e13	−	3.90491e13i	0.155788	−	0.219157i
$391$		−	4.97175e14i		−	2.75129i
$392$	−1.11755e14	−	1.12581e14i	−0.609810	−	0.614315i
$393$	1.49819e12	+	8.79883e12i	0.00806134	+	0.0473441i
$394$	−5.67758e13	−	5.69153e13i	−0.301255	−	0.301995i
$395$	3.06063e13			0.160150
$396$	5.79236e13	+	1.66467e14i	0.298904	+	0.859024i
$397$	2.02762e13			0.103190			0.0515951	−	0.998668i	$-0.483569\pi$
$397$	2.02762e13			0.103190			0.0515951	+	0.998668i	$0.483569\pi$
$398$	1.51123e14	+	1.51495e14i	0.758534	+	0.760397i
$399$	−1.24357e11	−	7.30347e11i	−0.000615630	−	0.00361558i
$400$	−1.90566e14	−	9.34990e11i	−0.930498	−	0.00456538i
$401$			1.37435e14i			0.661915i	0.943646	+	0.330957i	$0.107372\pi$
$401$			1.37435e14i			0.661915i	−0.943646	+	0.330957i	$0.892628\pi$
$402$	1.16315e14	−	1.63628e14i	0.552577	−	0.777347i
$403$			1.78030e14i			0.834289i
$404$	1.44331e14	+	3.54069e11i	0.667209	+	0.00163678i
$405$	−3.61049e13	−	4.51427e13i	−0.164651	−	0.205866i
$406$	6.68260e13	−	6.66622e13i	0.300644	−	0.299907i
$407$	−1.67362e14			−0.742827
$408$	2.82712e14	+	2.02011e14i	1.23798	+	0.884596i
$409$	−2.48502e14			−1.07362			−0.536812	−	0.843702i	$-0.680372\pi$
$409$	−2.48502e14			−1.07362			−0.536812	+	0.843702i	$0.680372\pi$
$410$	5.55055e13	−	5.53695e13i	0.236605	−	0.236026i
$411$	−4.22739e14	+	7.19804e13i	−1.77804	+	0.302750i
$412$	−1.75437e14	−	4.30379e11i	−0.728094	−	0.00178614i
$413$			9.39345e13i			0.384680i
$414$	−1.94354e14	+	4.03047e14i	−0.785403	+	1.62875i
$415$		−	5.75682e13i		−	0.229571i
$416$	1.84396e14	−	1.82148e14i	0.725667	−	0.716820i
$417$	−9.23085e13	+	1.57175e13i	−0.358504	+	0.0610429i
$418$	−1.67655e12	−	1.68067e12i	−0.00642610	−	0.00644188i
$419$	−1.45011e14			−0.548558			−0.274279	−	0.961650i	$-0.588439\pi$
$419$	−1.45011e14			−0.548558			−0.274279	+	0.961650i	$0.588439\pi$
$420$	−2.55282e13	+	4.28230e12i	−0.0953122	+	0.0159884i
$421$	−6.30248e13			−0.232252			−0.116126	−	0.993234i	$-0.537048\pi$
$421$	−6.30248e13			−0.232252			−0.116126	+	0.993234i	$0.537048\pi$
$422$	−2.77720e14	−	2.78403e14i	−1.01016	−	1.01264i
$423$	1.64755e14	−	5.77812e13i	0.591515	−	0.207451i
$424$	1.21656e14	−	1.20764e14i	0.431142	−	0.427980i
$425$		−	4.04711e14i		−	1.41581i
$426$	−2.45340e14	−	1.74400e14i	−0.847258	−	0.602274i
$427$		−	1.20390e14i		−	0.410428i
$428$	−3.45213e11	+	1.40721e14i	−0.00116184	+	0.473607i
$429$	4.68682e13	+	2.75256e14i	0.155727	+	0.914580i
$430$	−5.54615e13	+	5.53256e13i	−0.181935	+	0.181489i
$431$	1.07798e14			0.349128			0.174564	−	0.984646i	$-0.444148\pi$
$431$	1.07798e14			0.349128			0.174564	+	0.984646i	$0.444148\pi$
$432$	−1.50217e14	−	2.74282e14i	−0.480351	−	0.877076i
$433$	1.20967e14			0.381930			0.190965	−	0.981597i	$-0.438838\pi$
$433$	1.20967e14			0.381930			0.190965	+	0.981597i	$0.438838\pi$
$434$	6.80978e13	−	6.79309e13i	0.212295	−	0.211775i
$435$	1.66500e13	+	9.77849e13i	0.0512534	+	0.301010i
$436$	5.44582e11	−	2.21991e14i	0.00165534	−	0.674775i
$437$		−	6.02661e12i		−	0.0180894i
$438$	−3.09583e14	−	2.20067e14i	−0.917634	−	0.652300i
$439$		−	3.29980e13i		−	0.0965901i	−0.998833	−	0.0482950i	$-0.984621\pi$
$439$		−	3.29980e13i		−	0.0965901i	0.998833	−	0.0482950i	$-0.0153788\pi$
$440$	−5.88644e13	+	5.84328e13i	−0.170162	+	0.168914i
$441$	−2.86112e14	+	1.00343e14i	−0.816816	+	0.286466i
$442$	3.88744e14	+	3.89699e14i	1.09608	+	1.09877i
$443$	3.24790e14			0.904445			0.452222	−	0.891905i	$-0.350631\pi$
$443$	3.24790e14			0.904445			0.452222	+	0.891905i	$0.350631\pi$
$444$	2.92850e14	−	4.91251e13i	0.805451	−	0.135113i
$445$	1.02290e14			0.277878
$446$	3.99513e14	+	4.00494e14i	1.07199	+	1.07462i
$447$	2.00537e14	−	3.41458e13i	0.531501	−	0.0904993i
$448$	−1.40032e14	−	1.03059e12i	−0.366606	−	0.00269809i
$449$			9.66778e13i			0.250018i	0.992156	+	0.125009i	$0.0398960\pi$
$449$			9.66778e13i			0.250018i	−0.992156	+	0.125009i	$0.960104\pi$
$450$	−1.58209e14	+	3.28088e14i	−0.404167	+	0.838151i
$451$			4.56918e14i			1.15310i
$452$	−5.26353e13	−	1.29124e11i	−0.131225	−	0.000321917i
$453$	5.74227e14	−	9.77744e13i	1.41431	−	0.240816i
$454$	−2.50368e13	+	2.49754e13i	−0.0609216	+	0.0607723i
$455$	−4.10055e13			−0.0985779
$456$	3.42695e12	+	2.44872e12i	0.00813956	+	0.00581612i
$457$	2.56726e14			0.602463			0.301231	−	0.953551i	$-0.402602\pi$
$457$	2.56726e14			0.602463			0.301231	+	0.953551i	$0.402602\pi$
$458$	−3.67281e14	+	3.66381e14i	−0.851606	+	0.849519i
$459$	5.80922e14	−	3.21871e14i	1.33091	−	0.737415i
$460$	−2.10563e14	−	5.16548e11i	−0.476666	−	0.00116935i
$461$		−	6.32926e14i		−	1.41579i	−0.706319	−	0.707894i	$-0.749646\pi$
$461$		−	6.32926e14i		−	1.41579i	0.706319	−	0.707894i	$-0.250354\pi$
$462$	8.74038e13	−	1.22957e14i	0.193196	−	0.271782i
$463$			1.88075e14i			0.410804i	0.978678	+	0.205402i	$0.0658502\pi$
$463$			1.88075e14i			0.410804i	−0.978678	+	0.205402i	$0.934150\pi$
$464$	−2.63287e12	+	5.36621e14i	−0.00568303	+	1.15829i
$465$	1.69668e13	+	9.96459e13i	0.0361918	+	0.212553i
$466$	4.31817e14	+	4.32878e14i	0.910286	+	0.912521i
$467$	−3.69467e14			−0.769720			−0.384860	−	0.922975i	$-0.625750\pi$
$467$	−3.69467e14			−0.769720			−0.384860	+	0.922975i	$0.625750\pi$
$468$	−1.62805e14	−	4.67886e14i	−0.335208	−	0.963358i
$469$	−1.71826e14			−0.349654
$470$	5.80241e13	+	5.81666e13i	0.116700	+	0.116986i
$471$	−3.89425e13	−	2.28708e14i	−0.0774121	−	0.454640i
$472$	−3.76228e14	−	3.79007e14i	−0.739213	−	0.744673i
$473$		−	4.56556e14i		−	0.886661i
$474$	1.83362e14	−	2.57948e14i	0.351989	−	0.495167i
$475$		−	4.90578e12i		−	0.00930880i
$476$	7.29561e11	−	2.97394e14i	0.00136843	−	0.557821i
$477$	−1.08431e14	−	3.09175e14i	−0.201049	−	0.573262i
$478$	−1.95883e14	+	1.95403e14i	−0.359040	+	0.358160i
$479$	−2.87674e14			−0.521260			−0.260630	−	0.965439i	$-0.583930\pi$
$479$	−2.87674e14			−0.521260			−0.260630	+	0.965439i	$0.583930\pi$
$480$	8.58494e13	−	1.19524e14i	0.153784	−	0.214106i
$481$	4.70401e14			0.833049
$482$	−2.05979e14	+	2.05475e14i	−0.360633	+	0.359749i
$483$	3.77543e14	−	6.42848e13i	0.653517	−	0.111275i
$484$	−2.47602e11	+	1.00931e14i	−0.000423746	+	0.172733i
$485$			8.34078e13i			0.141133i
$486$	−5.96764e14	+	3.38396e13i	−0.998396	+	0.0566143i
$487$			2.50643e13i			0.0414616i	0.999785	+	0.0207308i	$0.00659929\pi$
$487$			2.50643e13i			0.0414616i	−0.999785	+	0.0207308i	$0.993401\pi$
$488$	4.82187e14	+	4.85749e14i	0.788691	+	0.794517i
$489$	−5.60603e14	+	9.54546e13i	−0.906685	+	0.154383i
$490$	−1.00764e14	−	1.01012e14i	−0.161149	−	0.161545i
$491$	−5.60964e14			−0.887129			−0.443565	−	0.896242i	$-0.646286\pi$
$491$	−5.60964e14			−0.887129			−0.443565	+	0.896242i	$0.646286\pi$
$492$	−1.34117e14	−	7.99515e14i	−0.209737	−	1.25031i
$493$	−1.13964e15			−1.76242
$494$	4.71225e12	+	4.72382e12i	0.00720659	+	0.00722429i
$495$	5.24655e13	+	1.49598e14i	0.0793497	+	0.226254i
$496$	−2.68297e12	+	5.46834e14i	−0.00401298	+	0.817911i
$497$			2.57632e14i			0.381101i
$498$	−4.85181e14	−	3.44891e14i	−0.709810	−	0.504569i
$499$			4.82841e13i			0.0698636i	0.999390	+	0.0349318i	$0.0111214\pi$
$499$			4.82841e13i			0.0698636i	−0.999390	+	0.0349318i	$0.988879\pi$
$500$	−3.55606e14	−	8.72364e11i	−0.508902	−	0.00124843i
$501$	1.95688e14	+	1.14927e15i	0.276985	+	1.62673i
$502$	2.12287e14	−	2.11767e14i	0.297202	−	0.296474i
$503$	5.99429e14			0.830068			0.415034	−	0.909806i	$-0.363770\pi$
$503$	5.99429e14			0.830068			0.415034	+	0.909806i	$0.363770\pi$
$504$	−1.16848e14	+	2.40805e14i	−0.160049	+	0.329835i
$505$	1.29816e14			0.175884
$506$	8.68799e14	−	8.66671e14i	1.16437	−	1.16152i
$507$	−5.11820e12	−	3.00591e13i	−0.00678537	−	0.0398503i
$508$	6.11684e14	+	1.50057e12i	0.802189	+	0.00196791i
$509$			2.04513e14i			0.265322i	0.991161	+	0.132661i	$0.0423522\pi$
$509$			2.04513e14i			0.265322i	−0.991161	+	0.132661i	$0.957648\pi$
$510$	2.54725e14	+	1.81071e14i	0.326915	+	0.232388i
$511$			3.25094e14i			0.412756i
$512$	5.69130e14	−	5.56701e14i	0.714869	−	0.699258i
$513$	7.04177e12	−	3.90163e12i	0.00875057	−	0.00484842i
$514$	−6.50229e14	−	6.51827e14i	−0.799410	−	0.801373i
$515$	−1.57794e14			−0.191934
$516$	1.34011e14	+	7.98882e14i	0.161275	+	0.961411i
$517$	−4.78824e14			−0.570136
$518$	−1.79491e14	−	1.79932e14i	−0.211460	−	0.211979i
$519$	−6.36737e14	+	1.08418e14i	−0.742232	+	0.126381i
$520$	1.65449e14	−	1.64236e14i	0.190830	−	0.189430i
$521$			1.15393e15i			1.31695i	0.752601	+	0.658477i	$0.228799\pi$
$521$			1.15393e15i			1.31695i	−0.752601	+	0.658477i	$0.771201\pi$
$522$	9.23875e14	+	4.45504e14i	1.04334	+	0.503111i
$523$		−	1.32762e15i		−	1.48359i	−0.670628	−	0.741794i	$-0.733975\pi$
$523$		−	1.32762e15i		−	1.48359i	0.670628	−	0.741794i	$-0.266025\pi$
$524$	−1.06542e11	+	4.34303e13i	−0.000117815	+	0.0480253i
$525$	3.07328e14	−	5.23291e13i	0.336299	−	0.0572621i
$526$	7.72404e13	−	7.70511e13i	0.0836417	−	0.0834367i
$527$	−1.16133e15			−1.24450
$528$	1.39811e14	+	8.46176e14i	0.148271	+	0.897375i
$529$	2.16256e15			2.26967
$530$	1.09154e14	−	1.08887e14i	0.113376	−	0.113099i
$531$	−9.63206e14	+	3.37806e14i	−0.990146	+	0.347255i
$532$	8.84353e9	−	3.60493e12i	8.99729e−6	−	0.00366761i
$533$		−	1.28425e15i		−	1.29315i
$534$	6.12820e14	−	8.62094e14i	0.610739	−	0.859168i
$535$			1.26569e14i			0.124848i
$536$	6.93284e14	−	6.88201e14i	0.676870	−	0.671906i
$537$	−7.69938e13	−	4.52183e14i	−0.0744042	−	0.436974i
$538$	−6.22967e14	−	6.24497e14i	−0.595885	−	0.597349i
$539$	8.31523e14			0.787293
$540$	−1.35715e14	−	2.46366e14i	−0.127193	−	0.230895i
$541$	−9.52340e14			−0.883501			−0.441750	−	0.897138i	$-0.645642\pi$
$541$	−9.52340e14			−0.883501			−0.441750	+	0.897138i	$0.645642\pi$
$542$	6.95799e14	+	6.97508e14i	0.638981	+	0.640550i
$543$	1.62088e14	+	9.51939e14i	0.147350	+	0.865386i
$544$	1.18818e15	+	1.20285e15i	1.06928	+	1.08247i
$545$		−	1.99666e14i		−	0.177878i
$546$	−2.45664e14	+	3.45592e14i	−0.216662	+	0.304792i
$547$		−	1.34526e15i		−	1.17456i	−0.809382	−	0.587282i	$-0.800198\pi$
$547$		−	1.34526e15i		−	1.17456i	0.809382	−	0.587282i	$-0.199802\pi$
$548$	−2.08661e15	−	5.11881e12i	−1.80363	−	0.00442462i
$549$	1.23448e15	−	4.32945e14i	1.05642	−	0.370497i
$550$	7.07221e14	−	7.05488e14i	0.599184	−	0.597716i
$551$	−1.38144e13			−0.0115877
$552$	−1.26584e15	+	1.77152e15i	−1.05127	+	1.47123i
$553$	−2.70872e14			−0.222728
$554$	−3.75381e14	+	3.74461e14i	−0.305611	+	0.304862i
$555$	2.63290e14	−	4.48307e13i	0.212238	−	0.0361380i
$556$	−4.55627e14	−	1.11773e12i	−0.363662	−	0.000892128i
$557$			1.99341e15i			1.57541i	0.616053	+	0.787705i	$0.288731\pi$
$557$			1.99341e15i			1.57541i	−0.616053	+	0.787705i	$0.711269\pi$
$558$	9.41457e14	+	4.53983e14i	0.736737	+	0.355264i
$559$			1.28323e15i			0.994352i
$560$	−1.25951e14	−	6.17966e11i	−0.0966427	−	0.000474166i
$561$	−1.79555e15	+	3.05730e14i	−1.36427	+	0.232297i
$562$	−3.19555e14	−	3.20340e14i	−0.240434	−	0.241024i
$563$	2.09224e15			1.55889			0.779444	−	0.626472i	$-0.215502\pi$
$563$	2.09224e15			1.55889			0.779444	+	0.626472i	$0.215502\pi$
$564$	8.37847e14	−	1.40547e14i	0.618201	−	0.103702i
$565$	−4.73420e13			−0.0345923
$566$	−1.50809e15	−	1.51180e15i	−1.09129	−	1.09397i
$567$	3.19535e14	+	3.99521e14i	0.228987	+	0.286308i
$568$	−1.03187e15	−	1.03949e15i	−0.732335	−	0.737744i
$569$		−	8.04249e14i		−	0.565292i	−0.959224	−	0.282646i	$-0.908788\pi$
$569$		−	8.04249e14i		−	0.565292i	0.959224	−	0.282646i	$-0.0912122\pi$
$570$	3.08770e12	+	2.19489e12i	0.00214943	+	0.00152792i
$571$		−	3.99575e14i		−	0.275486i	−0.990468	−	0.137743i	$-0.956015\pi$
$571$		−	3.99575e14i		−	0.275486i	0.990468	−	0.137743i	$-0.0439848\pi$
$572$	−3.33299e12	+	1.35864e15i	−0.00227591	+	0.927740i
$573$	−4.78458e14	−	2.80997e15i	−0.323589	−	1.90043i
$574$	−4.91234e14	+	4.90030e14i	−0.329058	+	0.328252i
$575$	2.53598e15			1.68257
$576$	−4.93016e14	−	1.43960e15i	−0.323994	−	0.946059i
$577$	−2.75977e14			−0.179641			−0.0898205	−	0.995958i	$-0.528629\pi$
$577$	−2.75977e14			−0.179641			−0.0898205	+	0.995958i	$0.528629\pi$
$578$	−1.44404e15	+	1.44050e15i	−0.931055	+	0.928773i
$579$	−1.70298e14	−	1.00016e15i	−0.108762	−	0.638757i
$580$	−1.18405e12	+	4.82658e14i	−0.000749056	+	0.305341i
$581$			5.09489e14i			0.319276i
$582$	7.02955e14	+	4.99696e14i	0.436367	+	0.310191i
$583$			8.98550e14i			0.552542i
$584$	−1.30207e15	−	1.31169e15i	−0.793165	−	0.799023i
$585$	−1.47464e14	−	4.20471e14i	−0.0889872	−	0.253734i
$586$	−6.99797e14	−	7.01515e14i	−0.418345	−	0.419373i
$587$	−1.45165e15			−0.859712			−0.429856	−	0.902898i	$-0.641436\pi$
$587$	−1.45165e15			−0.859712			−0.429856	+	0.902898i	$0.641436\pi$
$588$	−1.45500e15	+	2.44073e14i	−0.853665	+	0.143201i
$589$	−1.40773e13			−0.00818246
$590$	−3.39226e14	−	3.40059e14i	−0.195345	−	0.195825i
$591$	−7.37068e14	+	1.25502e14i	−0.420510	+	0.0716008i
$592$	1.44487e15	+	7.08910e12i	0.816695	+	0.00400702i
$593$		−	6.13996e14i		−	0.343846i	−0.985110	−	0.171923i	$-0.945002\pi$
$593$		−	6.13996e14i		−	0.343846i	0.985110	−	0.171923i	$-0.0549981\pi$
$594$	1.57512e15	+	4.54064e14i	0.873953	+	0.251937i
$595$		−	2.67487e14i		−	0.147048i
$596$	9.89836e14	+	2.42824e12i	0.539149	+	0.00132263i
$597$	1.96190e15	−	3.34055e14i	1.05881	−	0.180285i
$598$	−2.44192e15	+	2.43593e15i	−1.30579	+	1.30259i
$599$	−1.34920e15			−0.714872			−0.357436	−	0.933938i	$-0.616349\pi$
$599$	−1.34920e15			−0.714872			−0.357436	+	0.933938i	$0.616349\pi$
$600$	−1.03042e15	+	1.44205e15i	−0.540980	+	0.757092i
$601$	−6.98822e14			−0.363544			−0.181772	−	0.983341i	$-0.558183\pi$
$601$	−6.98822e14			−0.363544			−0.181772	+	0.983341i	$0.558183\pi$
$602$	4.90845e14	−	4.89642e14i	0.253025	−	0.252405i
$603$	−6.17920e14	−	1.76191e15i	−0.315637	−	0.899991i
$604$	2.83434e15	+	6.95313e12i	1.43466	+	0.00351947i
$605$			9.07811e13i			0.0455345i
$606$	7.77729e14	−	1.09408e15i	0.386571	−	0.543814i
$607$			3.22822e15i			1.59010i	0.606541	+	0.795052i	$0.292557\pi$
$607$			3.22822e15i			1.59010i	−0.606541	+	0.795052i	$0.707443\pi$
$608$	1.44028e13	+	1.45806e13i	0.00703037	+	0.00711713i
$609$	−1.47355e14	−	8.65415e14i	−0.0712805	−	0.418629i
$610$	4.34765e14	+	4.35833e14i	0.208421	+	0.208932i
$611$	1.34582e15			0.639382
$612$	3.05211e15	−	1.06201e15i	1.43704	−	0.500028i
$613$	1.30407e15			0.608510			0.304255	−	0.952591i	$-0.401593\pi$
$613$	1.30407e15			0.608510			0.304255	+	0.952591i	$0.401593\pi$
$614$	8.58498e14	+	8.60606e14i	0.397021	+	0.397996i
$615$	−1.22393e14	−	7.18811e14i	−0.0560974	−	0.329459i
$616$	5.20961e14	−	5.17141e14i	0.236652	−	0.234917i
$617$			3.21229e14i			0.144626i	0.997382	+	0.0723131i	$0.0230381\pi$
$617$			3.21229e14i			0.144626i	−0.997382	+	0.0723131i	$0.976962\pi$
$618$	−9.45346e14	+	1.32988e15i	−0.421846	+	0.593439i
$619$		−	1.82215e15i		−	0.805906i	−0.915221	−	0.402953i	$-0.867984\pi$
$619$		−	1.82215e15i		−	0.805906i	0.915221	−	0.402953i	$-0.132016\pi$
$620$	−1.20658e12	+	4.91844e14i	−0.000528934	+	0.215612i
$621$	2.01689e15	+	3.64015e15i	0.876353	+	1.58167i
$622$	−1.10242e15	+	1.09972e15i	−0.474788	+	0.473625i
$623$	−9.05287e14			−0.386458
$624$	−3.92964e14	−	2.37833e15i	−0.166279	−	1.00637i
$625$	1.89866e15			0.796357
$626$	3.01390e15	−	3.00652e15i	1.25306	−	1.24999i
$627$	−2.17651e13	+	3.70598e12i	−0.00896994	+	0.00152732i
$628$	2.76936e12	−	1.12889e15i	0.00113136	−	0.461182i
$629$			3.06852e15i			1.24265i
$630$	−1.04565e14	+	2.16845e14i	−0.0419773	+	0.0870514i
$631$		−	2.15030e15i		−	0.855731i	−0.903843	−	0.427865i	$-0.859266\pi$
$631$		−	2.15030e15i		−	0.855731i	0.903843	−	0.427865i	$-0.140734\pi$
$632$	1.09291e15	−	1.08490e15i	0.431163	−	0.428001i
$633$	−3.60539e15	+	6.13894e14i	−1.41004	+	0.240090i
$634$	2.38730e15	+	2.39316e15i	0.925583	+	0.927857i
$635$	5.50169e14			0.211466
$636$	−2.63748e14	−	1.57228e15i	−0.100502	−	0.599124i
$637$	−2.33715e15			−0.882915
$638$	−1.98661e15	−	1.99149e15i	−0.744043	−	0.745871i
$639$	−2.64176e15	+	9.26494e14i	−0.980932	+	0.344023i
$640$	5.10664e14	−	5.01969e14i	0.187995	−	0.184794i
$641$			1.81435e15i			0.662219i	0.943592	+	0.331109i	$0.107423\pi$
$641$			1.81435e15i			0.662219i	−0.943592	+	0.331109i	$0.892577\pi$
$642$	1.06672e15	+	7.58276e14i	0.386017	+	0.274400i
$643$			5.04028e15i			1.80840i	0.427111	+	0.904199i	$0.359532\pi$
$643$			5.04028e15i			1.80840i	−0.427111	+	0.904199i	$0.640468\pi$
$644$	1.86352e15	+	4.57155e12i	0.662921	+	0.00162626i
$645$	1.22296e14	+	7.18242e14i	0.0431354	+	0.253333i
$646$	−3.08144e13	+	3.07389e13i	−0.0107764	+	0.0107500i
$647$	3.96904e14			0.137630			0.0688149	−	0.997629i	$-0.478078\pi$
$647$	3.96904e14			0.137630			0.0688149	+	0.997629i	$0.478078\pi$
$648$	−2.88942e15	−	3.32183e14i	−0.993456	−	0.114213i
$649$	2.79935e15			0.954358
$650$	−1.98777e15	+	1.98290e15i	−0.671959	+	0.670313i
$651$	−1.50160e14	−	8.81885e14i	−0.0503336	−	0.295608i
$652$	−2.76709e15	−	6.78816e12i	−0.919732	−	0.00225627i
$653$		−	5.63137e15i		−	1.85606i	−0.372507	−	0.928030i	$-0.621502\pi$
$653$		−	5.63137e15i		−	1.85606i	0.372507	−	0.928030i	$-0.378498\pi$
$654$	−1.68277e15	−	1.19620e15i	−0.549981	−	0.390954i
$655$			3.90627e13i			0.0126600i
$656$	1.93540e13	−	3.94467e15i	0.00622015	−	1.26777i
$657$	−3.33351e15	+	1.16910e15i	−1.06241	+	0.372599i
$658$	−5.13524e14	−	5.14785e14i	−0.162300	−	0.162699i
$659$	−5.78078e15			−1.81183			−0.905914	−	0.423463i	$-0.860815\pi$
$659$	−5.78078e15			−1.81183			−0.905914	+	0.423463i	$0.860815\pi$
$660$	1.27617e14	+	7.60767e14i	0.0396659	+	0.236461i
$661$	−5.65482e15			−1.74306			−0.871528	−	0.490347i	$-0.836870\pi$
$661$	−5.65482e15			−1.74306			−0.871528	+	0.490347i	$0.836870\pi$
$662$	3.10657e15	+	3.11420e15i	0.949647	+	0.951979i
$663$	5.04671e15	−	8.59310e14i	1.52997	−	0.260511i
$664$	−2.04061e15	−	2.05568e15i	−0.613530	−	0.618062i
$665$		−	3.24240e12i		−	0.000966824i
$666$	1.19954e15	−	2.48757e15i	0.354736	−	0.735642i
$667$		−	7.14115e15i		−	2.09448i
$668$	−1.39161e13	+	5.67270e15i	−0.00404807	+	1.65014i
$669$	5.18651e15	−	8.83114e14i	1.49634	−	0.254785i
$670$	6.22042e14	−	6.20517e14i	0.177995	−	0.177559i
$671$	−3.58775e15			−1.01824
$672$	−7.59783e14	+	1.05781e15i	−0.213874	+	0.297767i
$673$	2.96214e13			0.00827032			0.00413516	−	0.999991i	$-0.498684\pi$
$673$	2.96214e13			0.00827032			0.00413516	+	0.999991i	$0.498684\pi$
$674$	−1.07914e14	+	1.07650e14i	−0.0298848	+	0.0298116i
$675$	1.64179e15	+	2.96316e15i	0.450970	+	0.813925i
$676$	3.63975e11	−	1.48369e14i	9.91666e−5	−	0.0404237i
$677$		−	1.99030e15i		−	0.537874i	−0.963158	−	0.268937i	$-0.913328\pi$
$677$		−	1.99030e15i		−	0.537874i	0.963158	−	0.268937i	$-0.0866723\pi$
$678$	−2.83626e14	+	3.98995e14i	−0.0760295	+	0.106956i
$679$		−	7.38175e14i		−	0.196280i
$680$	1.07134e15	+	1.07926e15i	0.282572	+	0.284659i
$681$	5.52076e13	+	3.24233e14i	0.0144441	+	0.0848298i
$682$	−2.02441e15	−	2.02939e15i	−0.525394	−	0.526685i
$683$	5.07970e15			1.30775			0.653874	−	0.756603i	$-0.273143\pi$
$683$	5.07970e15			1.30775			0.653874	+	0.756603i	$0.273143\pi$
$684$	3.69968e13	−	1.28733e13i	0.00944834	−	0.00328763i
$685$	−1.87677e15			−0.475458
$686$	1.92204e15	+	1.92676e15i	0.483036	+	0.484223i
$687$	8.09877e14	+	4.75639e15i	0.201910	+	1.18581i
$688$	−1.93387e13	+	3.94154e15i	−0.00478290	+	0.974832i
$689$		−	2.52554e15i		−	0.619652i
$690$	−1.13462e15	+	1.59615e15i	−0.276173	+	0.388510i
$691$			2.69916e15i			0.651777i	0.945408	+	0.325889i	$0.105663\pi$
$691$			2.69916e15i			0.651777i	−0.945408	+	0.325889i	$0.894337\pi$
$692$	−3.14288e15	−	7.71005e12i	−0.752913	−	0.00184703i
$693$	−4.64329e14	−	1.32397e15i	−0.110355	−	0.314662i
$694$	2.62227e15	−	2.61585e15i	0.618302	−	0.616787i
$695$	−4.09807e14			−0.0958656
$696$	4.06072e15	+	2.90158e15i	0.942436	+	0.673417i
$697$	8.37740e15			1.92899
$698$	−3.82476e15	+	3.81538e15i	−0.873774	+	0.871633i
$699$	5.60589e15	−	9.54522e14i	1.27063	−	0.216352i
$700$	1.51695e15	+	3.72133e12i	0.341138	+	0.000836873i
$701$			4.18730e15i			0.934298i	0.884179	+	0.467149i	$0.154719\pi$
$701$			4.18730e15i			0.934298i	−0.884179	+	0.467149i	$0.845281\pi$
$702$	−4.42716e15	−	1.27623e15i	−0.980101	−	0.282536i
$703$			3.71957e13i			0.00817030i
$704$	−3.07127e13	+	4.17312e15i	−0.00669373	+	0.909517i
$705$	7.53274e14	−	1.28261e14i	0.162897	−	0.0277367i
$706$	−1.46299e15	−	1.46658e15i	−0.313917	−	0.314688i
$707$	−1.14890e15			−0.244610
$708$	−4.89830e15	+	8.21681e14i	−1.03481	+	0.173588i
$709$	−3.09885e14			−0.0649601			−0.0324801	−	0.999472i	$-0.510341\pi$
$709$	−3.09885e14			−0.0649601			−0.0324801	+	0.999472i	$0.510341\pi$
$710$	−9.30388e14	−	9.32674e14i	−0.193528	−	0.194003i
$711$	−9.74106e14	−	2.77752e15i	−0.201059	−	0.573290i
$712$	3.65265e15	−	3.62586e15i	0.748114	−	0.742629i
$713$		−	7.27705e15i		−	1.47898i
$714$	−2.25436e15	−	1.60251e15i	−0.454656	−	0.323193i
$715$			1.22201e15i			0.244563i
$716$	5.47534e12	−	2.23194e15i	0.00108740	−	0.443262i
$717$	4.31933e14	+	2.53673e15i	0.0851258	+	0.499942i
$718$	5.72592e15	−	5.71189e15i	1.11985	−	1.11711i
$719$	6.87880e15			1.33507			0.667534	−	0.744579i	$-0.267350\pi$
$719$	6.87880e15			1.33507			0.667534	+	0.744579i	$0.267350\pi$
$720$	−4.46609e14	−	1.29373e15i	−0.0860199	−	0.249181i
$721$	1.39651e15			0.266932
$722$	3.73188e15	−	3.72274e15i	0.707903	−	0.706168i
$723$	4.54197e14	+	2.66749e15i	0.0855035	+	0.502160i
$724$	−1.15267e13	+	4.69869e15i	−0.00215349	+	0.877839i
$725$		−	5.81304e15i		−	1.07782i
$726$	7.65097e14	+	5.43869e14i	0.140788	+	0.100079i
$727$		−	9.49131e15i		−	1.73335i	−0.498871	−	0.866676i	$-0.666252\pi$
$727$		−	9.49131e15i		−	1.73335i	0.498871	−	0.866676i	$-0.333748\pi$
$728$	−1.46425e15	+	1.45352e15i	−0.265396	+	0.263450i
$729$	−2.94759e15	+	4.71327e15i	−0.530231	+	0.847853i
$730$	−1.17401e15	−	1.17690e15i	−0.209603	−	0.210118i
$731$	−8.37077e15			−1.48327
$732$	6.27785e15	−	1.05310e15i	1.10408	−	0.185207i
$733$	−1.98406e15			−0.346324			−0.173162	−	0.984893i	$-0.555398\pi$
$733$	−1.98406e15			−0.346324			−0.173162	+	0.984893i	$0.555398\pi$
$734$	−8.16525e13	−	8.18530e13i	−0.0141462	−	0.0141810i
$735$	−1.30813e15	+	2.22737e14i	−0.224942	+	0.0383012i
$736$	−7.53724e15	+	7.44535e15i	−1.28642	+	1.27074i
$737$			5.12061e15i			0.867462i
$738$	−6.79134e15	−	3.27487e15i	−1.14195	−	0.550661i
$739$			8.24660e15i			1.37636i	0.725542	+	0.688178i	$0.241589\pi$
$739$			8.24660e15i			1.37636i	−0.725542	+	0.688178i	$0.758411\pi$
$740$	1.29958e15	+	3.18809e12i	0.215292	+	0.000528148i
$741$	6.11747e13	−	1.04163e13i	0.0100594	−	0.00171283i
$742$	−9.66034e14	+	9.63667e14i	−0.157678	+	0.157292i
$743$	2.64416e15			0.428399			0.214199	−	0.976790i	$-0.431286\pi$
$743$	2.64416e15			0.428399			0.214199	+	0.976790i	$0.431286\pi$
$744$	4.13800e15	+	2.95680e15i	0.665486	+	0.475523i
$745$	8.90292e14			0.142126
$746$	2.27515e15	−	2.26958e15i	0.360535	−	0.359652i
$747$	−5.22431e15	+	1.83222e15i	−0.821798	+	0.288213i
$748$	−8.86267e15	−	2.17417e13i	−1.38390	−	0.00339496i
$749$		−	1.12016e15i		−	0.173632i
$750$	−1.91618e15	+	2.69562e15i	−0.294850	+	0.414784i
$751$			2.39438e15i			0.365742i	0.983137	+	0.182871i	$0.0585390\pi$
$751$			2.39438e15i			0.365742i	−0.983137	+	0.182871i	$0.941461\pi$
$752$	4.13379e15	+	2.02820e13i	0.626831	+	0.00307547i
$753$	−4.68105e14	−	2.74917e15i	−0.0704646	−	0.413837i
$754$	5.58371e15	+	5.59743e15i	0.834412	+	0.836462i
$755$	2.54930e15			0.378192
$756$	1.20110e15	+	2.18039e15i	0.176893	+	0.321117i
$757$	−1.10647e16			−1.61775			−0.808875	−	0.587981i	$-0.799923\pi$
$757$	−1.10647e16			−1.61775			−0.808875	+	0.587981i	$0.799923\pi$
$758$	5.76652e15	+	5.78069e15i	0.837015	+	0.839071i
$759$	−1.91575e15	−	1.12512e16i	−0.276064	−	1.62132i
$760$	1.29865e13	+	1.30824e13i	0.00185788	+	0.00187160i
$761$			7.90096e15i			1.12218i	0.827753	+	0.561092i	$0.189619\pi$
$761$			7.90096e15i			1.12218i	−0.827753	+	0.561092i	$0.810381\pi$
$762$	3.29606e15	−	4.63679e15i	0.464775	−	0.653830i
$763$			1.76708e15i			0.247384i
$764$	3.40250e13	−	1.38698e16i	0.00472917	−	1.92778i
$765$	2.74281e15	−	9.61934e14i	0.378493	−	0.132742i
$766$	1.25136e14	−	1.24830e14i	0.0171445	−	0.0171025i
$767$	−7.86807e15			−1.07027
$768$	−1.17118e15	−	7.31113e15i	−0.158174	−	0.987411i
$769$	−4.46095e15			−0.598181			−0.299091	−	0.954225i	$-0.596683\pi$
$769$	−4.46095e15			−0.598181			−0.299091	+	0.954225i	$0.596683\pi$
$770$	4.67426e14	−	4.66281e14i	0.0622320	−	0.0620796i
$771$	−8.44133e15	+	1.43732e15i	−1.11587	+	0.190000i
$772$	1.21106e13	−	4.93669e15i	0.00158953	−	0.647948i
$773$			7.87880e15i			1.02677i	0.858159	+	0.513385i	$0.171609\pi$
$773$			7.87880e15i			1.02677i	−0.858159	+	0.513385i	$0.828391\pi$
$774$	6.78597e15	+	3.27228e15i	0.878085	+	0.423424i
$775$		−	5.92368e15i		−	0.761083i
$776$	2.95655e15	+	2.97838e15i	0.377177	+	0.379963i
$777$	−2.33016e15	+	3.96760e14i	−0.295169	+	0.0502588i
$778$	5.93740e15	+	5.95199e15i	0.746808	+	0.748642i
$779$	1.01548e14			0.0126829
$780$	−3.58691e14	−	2.13827e15i	−0.0444836	−	0.265181i
$781$	7.67771e15			0.945477
$782$	−1.58901e16	−	1.59291e16i	−1.94307	−	1.94784i
$783$	8.34405e15	−	4.62318e15i	1.01318	−	0.561372i
$784$	−7.17872e15	−	3.52215e13i	−0.865582	−	0.00424688i
$785$		−	1.01536e15i		−	0.121573i
$786$	3.29218e14	+	2.34024e14i	0.0391435	+	0.0278251i
$787$			9.38324e15i			1.10788i	0.832557	+	0.553939i	$0.186876\pi$
$787$			9.38324e15i			1.10788i	−0.832557	+	0.553939i	$0.813124\pi$
$788$	−3.63811e15	−	8.92492e12i	−0.426561	−	0.00104643i
$789$	−1.70320e14	−	1.00028e15i	−0.0198308	−	0.116466i
$790$	9.80603e14	−	9.78200e14i	0.113382	−	0.113104i
$791$	4.18985e14			0.0481092
$792$	7.17624e15	+	3.48220e15i	0.818293	+	0.397068i
$793$	1.00840e16			1.14191
$794$	6.49633e14	−	6.48041e14i	0.0730559	−	0.0728769i
$795$	−2.40691e14	−	1.41358e15i	−0.0268808	−	0.157870i
$796$	9.68376e15	+	2.37560e13i	1.07404	+	0.00263482i
$797$			5.92155e15i			0.652251i	0.945327	+	0.326125i	$0.105743\pi$
$797$			5.92155e15i			0.652251i	−0.945327	+	0.326125i	$0.894257\pi$
$798$	−2.73267e13	−	1.94252e13i	−0.00298931	−	0.00212495i
$799$			8.77905e15i			0.953762i
$800$	−6.13547e15	+	6.06067e15i	−0.661992	+	0.653922i
$801$	−3.25558e15	−	9.28282e15i	−0.348859	−	0.994721i
$802$	4.39251e15	+	4.40330e15i	0.467470	+	0.468618i
$803$	9.68814e15			1.02401
$804$	−1.50303e15	−	8.96004e15i	−0.157783	−	0.940593i
$805$	1.67611e15			0.174754
$806$	5.68998e15	+	5.70396e15i	0.589207	+	0.590654i
$807$	−8.08741e15	+	1.37705e15i	−0.831773	+	0.141627i
$808$	4.63557e15	−	4.60158e15i	0.473523	−	0.470050i
$809$			1.37849e16i			1.39858i	0.714837	+	0.699291i	$0.246501\pi$
$809$			1.37849e16i			1.39858i	−0.714837	+	0.699291i	$0.753499\pi$
$810$	−2.59957e15	−	2.92399e14i	−0.261959	−	0.0294651i
$811$		−	3.77518e15i		−	0.377853i	−0.981991	−	0.188926i	$-0.939499\pi$
$811$		−	3.77518e15i		−	0.377853i	0.981991	−	0.188926i	$-0.0605008\pi$
$812$	1.04790e13	−	4.27161e15i	0.00104175	−	0.424653i
$813$	9.03292e15	−	1.53805e15i	0.891928	−	0.151870i
$814$	−5.36215e15	+	5.34901e15i	−0.525902	+	0.524614i
$815$	−2.48882e15			−0.242452
$816$	1.55143e16	−	2.56338e15i	1.50119	−	0.248037i
$817$	−1.01468e14			−0.00975232
$818$	−7.96182e15	+	7.94232e15i	−0.760098	+	0.758235i
$819$	1.30508e15	+	3.72125e15i	0.123759	+	0.352880i
$820$	8.70385e12	−	3.54799e15i	0.000819851	−	0.334200i
$821$		−	8.31426e15i		−	0.777922i	−0.921254	−	0.388961i	$-0.872834\pi$
$821$		−	8.31426e15i		−	0.777922i	0.921254	−	0.388961i	$-0.127166\pi$
$822$	−1.12437e16	+	1.58172e16i	−1.04499	+	1.47006i
$823$		−	1.53630e16i		−	1.41833i	−0.705042	−	0.709166i	$-0.749072\pi$
$823$		−	1.53630e16i		−	1.41833i	0.705042	−	0.709166i	$-0.250928\pi$
$824$	−5.63463e15	+	5.59332e15i	−0.516733	+	0.512944i
$825$	−1.55946e15	−	9.15870e15i	−0.142062	−	0.834329i
$826$	3.00221e15	+	3.00959e15i	0.271676	+	0.272343i
$827$	1.57568e16			1.41640			0.708201	−	0.706011i	$-0.249507\pi$
$827$	1.57568e16			1.41640			0.708201	+	0.706011i	$0.249507\pi$
$828$	6.65470e15	+	1.91250e16i	0.594240	+	1.70779i
$829$	−4.80421e15			−0.426159			−0.213079	−	0.977035i	$-0.568349\pi$
$829$	−4.80421e15			−0.426159			−0.213079	+	0.977035i	$0.568349\pi$
$830$	−1.83992e15	−	1.84444e15i	−0.162132	−	0.162531i
$831$	8.27737e14	+	4.86128e15i	0.0724581	+	0.425545i
$832$	8.63234e13	−	1.17293e16i	0.00750672	−	1.01998i
$833$		−	1.52456e16i		−	1.31704i
$834$	−2.45515e15	+	3.45382e15i	−0.210700	+	0.296406i
$835$			5.10223e15i			0.434995i
$836$	−1.07431e14	−	2.63547e11i	−0.00909901	−	2.23215e-5i
$837$	8.50285e15	−	4.71117e15i	0.715442	−	0.396404i
$838$	−4.64603e15	+	4.63464e15i	−0.388365	+	0.387413i
$839$	1.39625e16			1.15950			0.579752	−	0.814793i	$-0.303150\pi$
$839$	1.39625e16			1.15950			0.579752	+	0.814793i	$0.303150\pi$
$840$	−6.81037e14	+	9.53100e14i	−0.0561868	+	0.0786326i
$841$	−4.16863e15			−0.341676
$842$	−2.01927e15	+	2.01432e15i	−0.164429	+	0.164026i
$843$	−4.14848e15	+	7.06368e14i	−0.335612	+	0.0571452i
$844$	−1.77959e16	−	4.36565e13i	−1.43033	−	0.00350885i
$845$		−	1.33448e14i		−	0.0106562i
$846$	3.43189e15	−	7.11695e15i	0.272267	−	0.564621i
$847$		−	8.03429e14i		−	0.0633270i
$848$	3.80606e13	−	7.75737e15i	0.00298057	−	0.607488i
$849$	−1.95782e16	+	3.33361e15i	−1.52328	+	0.259371i
$850$	−1.29348e16	−	1.29666e16i	−0.999901	−	1.00236i
$851$	−1.92278e16			−1.47679
$852$	−1.34345e16	+	2.25361e15i	−1.02519	+	0.171973i
$853$	−3.75114e15			−0.284409			−0.142205	−	0.989837i	$-0.545419\pi$
$853$	−3.75114e15			−0.284409			−0.142205	+	0.989837i	$0.545419\pi$
$854$	−3.84775e15	−	3.85720e15i	−0.289860	−	0.290572i
$855$	3.32476e13	−	1.16603e13i	0.00248855	−	0.000872761i
$856$	4.48648e15	+	4.51962e15i	0.333657	+	0.336122i
$857$		−	1.49867e16i		−	1.10742i	−0.832709	−	0.553710i	$-0.813211\pi$
$857$		−	1.49867e16i		−	1.10742i	0.832709	−	0.553710i	$-0.186789\pi$
$858$	1.02990e16	+	7.32105e15i	0.756162	+	0.537518i
$859$		−	5.52120e15i		−	0.402783i	−0.979511	−	0.201392i	$-0.935454\pi$
$859$		−	5.52120e15i		−	0.402783i	0.979511	−	0.201392i	$-0.0645464\pi$
$860$	−8.69695e12	+	3.54518e15i	−0.000630414	+	0.256979i
$861$	1.08320e15	+	6.36161e15i	0.0780173	+	0.458194i
$862$	3.45375e15	−	3.44529e15i	0.247173	−	0.246568i
$863$	1.49995e16			1.06664			0.533320	−	0.845913i	$-0.320944\pi$
$863$	1.49995e16			1.06664			0.533320	+	0.845913i	$0.320944\pi$
$864$	−1.35791e16	−	3.98675e15i	−0.959501	−	0.281704i
$865$	−2.82682e15			−0.198477
$866$	3.87569e15	−	3.86619e15i	0.270396	−	0.269734i
$867$	3.18419e15	+	1.87007e16i	0.220746	+	1.29644i
$868$	1.06785e13	−	4.35291e15i	0.000735614	−	0.299862i
$869$			8.07227e15i			0.552569i
$870$	3.65873e15	+	2.60081e15i	0.248871	+	0.176910i
$871$		−	1.43924e16i		−	0.972821i
$872$	−7.07753e15	−	7.12981e15i	−0.475380	−	0.478892i
$873$	7.56925e15	−	2.65462e15i	0.505213	−	0.177184i
$874$	−1.92615e14	−	1.93088e14i	−0.0127755	−	0.0128068i
$875$	2.83068e15			0.186572
$876$	−1.69523e16	+	2.84372e15i	−1.11034	+	0.186258i
$877$	5.40949e15			0.352094			0.176047	−	0.984382i	$-0.443669\pi$
$877$	5.40949e15			0.352094			0.176047	+	0.984382i	$0.443669\pi$
$878$	−1.05464e15	−	1.05723e15i	−0.0682157	−	0.0683832i
$879$	−9.08481e15	+	1.54688e15i	−0.583952	+	0.0994303i
$880$	−1.84161e13	+	3.75349e15i	−0.00117636	+	0.239762i
$881$			1.56262e16i			0.991939i	0.868340	+	0.495970i	$0.165187\pi$
$881$			1.56262e16i			0.991939i	−0.868340	+	0.495970i	$0.834813\pi$
$882$	−5.95979e15	+	1.23593e16i	−0.375971	+	0.779678i
$883$			1.67545e16i			1.05038i	0.850985	+	0.525191i	$0.176006\pi$
$883$			1.67545e16i			1.05038i	−0.850985	+	0.525191i	$0.823994\pi$
$884$	2.49101e16	+	6.11090e13i	1.55199	+	0.00380730i
$885$	−4.40386e15	+	7.49851e14i	−0.272675	+	0.0464288i
$886$	1.04060e16	−	1.03805e16i	0.640323	−	0.638754i
$887$	1.40157e14			0.00857104			0.00428552	−	0.999991i	$-0.498636\pi$
$887$	1.40157e14			0.00857104			0.00428552	+	0.999991i	$0.498636\pi$
$888$	7.81262e15	−	1.09336e16i	0.474816	−	0.664497i
$889$	−4.86910e15			−0.294096
$890$	3.27730e15	−	3.26927e15i	0.196730	−	0.196248i
$891$	1.19062e16	−	9.52248e15i	0.710304	−	0.568097i
$892$	2.56002e16	+	6.28018e13i	1.51788	+	0.00372362i
$893$			1.06417e14i			0.00627088i
$894$	5.33374e15	−	7.50332e15i	0.312374	−	0.439438i
$895$		−	2.00748e15i		−	0.116849i
$896$	−4.51947e15	+	4.44252e15i	−0.261453	+	0.257001i
$897$	5.38457e15	+	3.16235e16i	0.309594	+	1.81824i
$898$	3.08989e15	+	3.09748e15i	0.176573	+	0.177006i
$899$	−1.66807e16			−0.947404
$900$	5.41707e15	+	1.55682e16i	0.305795	+	0.878827i
$901$	1.64746e16			0.924331
$902$	1.46034e16	+	1.46393e16i	0.814364	+	0.816364i
$903$	−1.08234e15	−	6.35657e15i	−0.0599904	−	0.352322i
$904$	−1.69052e15	+	1.67812e15i	−0.0931309	+	0.0924481i
$905$			4.22616e15i			0.231408i
$906$	1.52728e16	−	2.14853e16i	0.831218	−	1.16933i
$907$		−	2.50422e16i		−	1.35467i	−0.735676	−	0.677334i	$-0.763135\pi$
$907$		−	2.50422e16i		−	1.35467i	0.735676	−	0.677334i	$-0.236865\pi$
$908$	−3.92603e12	+	1.60039e15i	−0.000211097	+	0.0860504i
$909$	−4.13166e15	−	1.17808e16i	−0.220812	−	0.629613i
$910$	−1.31378e15	+	1.31057e15i	−0.0697905	+	0.0696195i
$911$	−3.70211e16			−1.95478			−0.977390	−	0.211445i	$-0.932183\pi$
$911$	−3.70211e16			−1.95478			−0.977390	+	0.211445i	$0.932183\pi$
$912$	1.88060e14	−	3.10725e13i	0.00987016	−	0.00163082i
$913$	1.51833e16			0.792095
$914$	8.22529e15	−	8.20514e15i	0.426528	−	0.425483i
$915$	5.64415e15	−	9.61038e14i	0.290926	−	0.0495364i
$916$	−5.75936e13	+	2.34771e16i	−0.00295086	+	1.20287i
$917$		−	3.45712e14i		−	0.0176069i
$918$	8.32507e15	−	2.88792e16i	0.421457	−	1.46201i
$919$			1.66848e16i			0.839625i	0.907611	+	0.419813i	$0.137904\pi$
$919$			1.66848e16i			0.839625i	−0.907611	+	0.419813i	$0.862096\pi$
$920$	−6.76278e15	+	6.71319e15i	−0.338293	+	0.335812i
$921$	1.11451e16	−	1.89769e15i	0.554186	−	0.0943619i
$922$	−2.02288e16	−	2.02785e16i	−0.999884	−	1.00234i
$923$	−2.15796e16			−1.06031
$924$	−1.12944e15	−	6.73292e15i	−0.0551652	−	0.328858i
$925$	−1.56518e16			−0.759952
$926$	6.01100e15	+	6.02576e15i	0.290126	+	0.290838i
$927$	5.02212e15	+	1.43198e16i	0.240962	+	0.687067i
$928$	1.70664e16	+	1.72771e16i	0.814009	+	0.824055i
$929$		−	1.97824e16i		−	0.937977i	−0.883204	−	0.468989i	$-0.844619\pi$
$929$		−	1.97824e16i		−	0.937977i	0.883204	−	0.468989i	$-0.155381\pi$
$930$	3.72836e15	+	2.65031e15i	0.175736	+	0.124922i
$931$		−	1.84803e14i		−	0.00865937i
$932$	2.76702e16	+	6.78799e13i	1.28892	+	0.00316194i
$933$	2.43090e15	+	1.42766e16i	0.112569	+	0.661115i
$934$	−1.18374e16	+	1.18084e16i	−0.544941	+	0.543606i
$935$	−7.97139e15			−0.364813
$936$	−2.01701e16	−	9.78735e15i	−0.917680	−	0.445295i
$937$	−7.46411e15			−0.337606			−0.168803	−	0.985650i	$-0.553990\pi$
$937$	−7.46411e15			−0.337606			−0.168803	+	0.985650i	$0.553990\pi$
$938$	−5.50518e15	+	5.49169e15i	−0.247546	+	0.246940i
$939$	−6.64584e15	−	3.90309e16i	−0.297091	−	1.74481i
$940$	3.71810e15	+	9.12115e12i	0.165241	+	0.000405365i
$941$		−	1.75071e14i		−	0.00773518i	−0.999993	−	0.00386759i	$-0.998769\pi$
$941$		−	1.75071e14i		−	0.00773518i	0.999993	−	0.00386759i	$-0.00123110\pi$
$942$	−8.55738e15	−	6.08301e15i	−0.375890	−	0.267201i
$943$			5.24941e16i			2.29243i
$944$	−2.41674e16	−	1.18574e14i	−1.04926	−	0.00514807i
$945$	1.08512e15	+	1.95845e15i	0.0468383	+	0.0845353i
$946$	−1.45919e16	−	1.46277e16i	−0.626195	−	0.627733i
$947$	8.61225e15			0.367444			0.183722	−	0.982978i	$-0.441185\pi$
$947$	8.61225e15			0.367444			0.183722	+	0.982978i	$0.441185\pi$
$948$	−2.36942e15	−	1.41249e16i	−0.100507	−	0.599153i
$949$	−2.72303e16			−1.14838
$950$	−1.56792e14	−	1.57178e14i	−0.00657424	−	0.00659038i
$951$	3.09921e16	−	5.27706e15i	1.29199	−	0.219988i
$952$	−9.48157e15	−	9.55161e15i	−0.392986	−	0.395889i
$953$			9.31560e15i			0.383884i	0.981406	+	0.191942i	$0.0614785\pi$
$953$			9.31560e15i			0.383884i	−0.981406	+	0.191942i	$0.938521\pi$
$954$	−1.33555e16	−	6.44020e15i	−0.547198	−	0.263866i
$955$		−	1.24750e16i		−	0.508184i
$956$	−3.07165e13	+	1.25211e16i	−0.00124409	+	0.507136i
$957$	−2.57903e16	+	4.39135e15i	−1.03858	+	0.176841i
$958$	−9.21684e15	+	9.19426e15i	−0.369039	+	0.368134i
$959$	1.66097e16			0.661241
$960$	−1.06952e15	−	6.57326e15i	−0.0423348	−	0.260189i
$961$	8.41035e15			0.331006
$962$	1.50713e16	−	1.50344e16i	0.589777	−	0.588331i
$963$	1.14861e16	−	4.02831e15i	0.446920	−	0.156740i
$964$	−3.22998e13	+	1.31665e16i	−0.00124961	+	0.509386i
$965$		−	4.44023e15i		−	0.170807i
$966$	1.00416e16	−	1.41262e16i	0.384086	−	0.540319i
$967$		−	4.03279e16i		−	1.53377i	−0.641785	−	0.766885i	$-0.721806\pi$
$967$		−	4.03279e16i		−	1.53377i	0.641785	−	0.766885i	$-0.278194\pi$
$968$	3.21790e15	+	3.24167e15i	0.121691	+	0.122590i
$969$	6.79476e13	+	3.99055e14i	0.00255501	+	0.0150055i
$970$	2.66577e15	+	2.67232e15i	0.0996733	+	0.0999181i
$971$	3.67060e16			1.36468			0.682341	−	0.731034i	$-0.260962\pi$
$971$	3.67060e16			1.36468			0.682341	+	0.731034i	$0.260962\pi$
$972$	−1.80383e16	+	2.01572e16i	−0.666855	+	0.745188i
$973$	3.62687e15			0.133325
$974$	8.01073e14	+	8.03041e14i	0.0292818	+	0.0293537i
$975$	4.38315e15	+	2.57422e16i	0.159317	+	0.935664i
$976$	3.09738e16	+	1.51969e14i	1.11949	+	0.00549265i
$977$		−	1.96544e16i		−	0.706383i	−0.935551	−	0.353192i	$-0.885096\pi$
$977$		−	1.96544e16i		−	0.706383i	0.935551	−	0.353192i	$-0.114904\pi$
$978$	−1.49105e16	+	2.09756e16i	−0.532878	+	0.749635i
$979$			2.69785e16i			0.958767i
$980$	−6.45682e15	−	1.58397e13i	−0.228179	−	0.000559763i
$981$	−1.81197e16	+	6.35476e15i	−0.636753	+	0.223316i
$982$	−1.79729e16	+	1.79288e16i	−0.628064	+	0.626525i
$983$	−2.22734e16			−0.774003			−0.387002	−	0.922079i	$-0.626489\pi$
$983$	−2.22734e16			−0.774003			−0.387002	+	0.922079i	$0.626489\pi$
$984$	−2.98501e16	−	2.13294e16i	−1.03151	−	0.737063i
$985$	−3.27224e15			−0.112446
$986$	−3.65131e16	+	3.64236e16i	−1.24774	+	1.24469i
$987$	−6.66661e15	+	1.13513e15i	−0.226548	+	0.0385747i
$988$	3.01953e14	+	7.40745e11i	0.0102041	+	2.50326e-5i
$989$		−	5.24526e16i		−	1.76274i
$990$	6.46220e15	+	3.11616e15i	0.215967	+	0.104142i
$991$			5.30529e16i			1.76321i	0.471988	+	0.881605i	$0.343537\pi$
$991$			5.30529e16i			1.76321i	−0.471988	+	0.881605i	$0.656463\pi$
$992$	1.73912e16	+	1.76059e16i	0.574799	+	0.581893i
$993$	4.03297e16	−	6.86700e15i	1.32558	−	0.225707i
$994$	8.23411e15	+	8.25433e15i	0.269148	+	0.269809i
$995$	8.70990e15			0.283130
$996$	−2.65678e16	+	4.45669e15i	−0.858873	+	0.144074i
$997$	4.29174e16			1.37978			0.689891	−	0.723913i	$-0.257658\pi$
$997$	4.29174e16			1.37978			0.689891	+	0.723913i	$0.257658\pi$
$998$	1.54319e15	+	1.54698e15i	0.0493404	+	0.0494616i
$999$	−1.24481e16	−	2.24667e16i	−0.395815	−	0.714379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.12.b.a.11.15	yes	20
3.2	odd	2	inner	12.12.b.a.11.6	yes	20
4.3	odd	2	inner	12.12.b.a.11.5	✓	20
8.3	odd	2		192.12.c.d.191.9		20
8.5	even	2		192.12.c.d.191.12		20
12.11	even	2	inner	12.12.b.a.11.16	yes	20
24.5	odd	2		192.12.c.d.191.10		20
24.11	even	2		192.12.c.d.191.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.12.b.a.11.5	✓	20	4.3	odd	2	inner
12.12.b.a.11.6	yes	20	3.2	odd	2	inner
12.12.b.a.11.15	yes	20	1.1	even	1	trivial
12.12.b.a.11.16	yes	20	12.11	even	2	inner
192.12.c.d.191.9		20	8.3	odd	2
192.12.c.d.191.10		20	24.5	odd	2
192.12.c.d.191.11		20	24.11	even	2
192.12.c.d.191.12		20	8.5	even	2

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(32.0392 - 31.9607i) q^{2} +(-70.6484 - 414.917i) q^{3} +(5.02409 - 2047.99i) q^{4} -1842.04i q^{5} +(-15524.6 - 11035.6i) q^{6} +16302.4i q^{7} +(-65294.4 - 65776.7i) q^{8} +(-167165. + 58626.4i) q^{9} +O(q^{10})\)	\(q+(32.0392 - 31.9607i) q^{2} +(-70.6484 - 414.917i) q^{3} +(5.02409 - 2047.99i) q^{4} -1842.04i q^{5} +(-15524.6 - 11035.6i) q^{6} +16302.4i q^{7} +(-65294.4 - 65776.7i) q^{8} +(-167165. + 58626.4i) q^{9} +(-58872.8 - 59017.4i) q^{10} +485828. q^{11} +(-850102. + 142603. i) q^{12} -1.36551e6 q^{13} +(521035. + 522315. i) q^{14} +(-764291. + 130137. i) q^{15} +(-4.19425e6 - 20578.6i) q^{16} -8.90746e6i q^{17} +(-3.48208e6 + 7.22105e6i) q^{18} -107974. i q^{19} +(-3.77248e6 - 9254.56i) q^{20} +(6.76412e6 - 1.15174e6i) q^{21} +(1.55655e7 - 1.55274e7i) q^{22} +5.58155e7 q^{23} +(-2.26789e7 + 3.17388e7i) q^{24} +4.54350e7 q^{25} +(-4.37498e7 + 4.36426e7i) q^{26} +(3.61350e7 + 6.52175e7i) q^{27} +(3.33871e7 + 81904.5i) q^{28} -1.27942e8i q^{29} +(-2.03280e7 + 2.85968e7i) q^{30} -1.30377e8i q^{31} +(-1.35038e8 + 1.33392e8i) q^{32} +(-3.43230e7 - 2.01578e8i) q^{33} +(-2.84689e8 - 2.85388e8i) q^{34} +3.00295e7 q^{35} +(1.19227e8 + 3.42647e8i) q^{36} -3.44489e8 q^{37} +(-3.45092e6 - 3.45939e6i) q^{38} +(9.64708e7 + 5.66571e8i) q^{39} +(-1.21163e8 + 1.20275e8i) q^{40} +9.40493e8i q^{41} +(1.79907e8 - 2.53087e8i) q^{42} -9.39748e8i q^{43} +(2.44084e6 - 9.94972e8i) q^{44} +(1.07992e8 + 3.07923e8i) q^{45} +(1.78829e9 - 1.78391e9i) q^{46} -9.85584e8 q^{47} +(2.87779e8 + 1.74172e9i) q^{48} +1.71156e9 q^{49} +(1.45570e9 - 1.45214e9i) q^{50} +(-3.69585e9 + 6.29298e8i) q^{51} +(-6.86043e6 + 2.79655e9i) q^{52} +1.84952e9i q^{53} +(3.24214e9 + 9.34618e8i) q^{54} -8.94912e8i q^{55} +(1.07232e9 - 1.06445e9i) q^{56} +(-4.48001e7 + 7.62817e6i) q^{57} +(-4.08912e9 - 4.09916e9i) q^{58} +5.76202e9 q^{59} +(2.62680e8 + 1.56592e9i) q^{60} -7.38482e9 q^{61} +(-4.16694e9 - 4.17717e9i) q^{62} +(-9.55749e8 - 2.72518e9i) q^{63} +(-6.32172e7 + 8.58970e9i) q^{64} +2.51531e9i q^{65} +(-7.54226e9 - 5.36142e9i) q^{66} +1.05400e10i q^{67} +(-1.82424e10 - 4.47519e7i) q^{68} +(-3.94328e9 - 2.31588e10i) q^{69} +(9.62123e8 - 9.59766e8i) q^{70} +1.58034e10 q^{71} +(1.47712e10 + 7.16756e9i) q^{72} +1.99415e10 q^{73} +(-1.10371e10 + 1.10101e10i) q^{74} +(-3.20991e9 - 1.88517e10i) q^{75} +(-2.21129e8 - 542469. i) q^{76} +7.92014e9i q^{77} +(2.11989e10 + 1.50692e10i) q^{78} +1.66155e10i q^{79} +(-3.79066e7 + 7.72597e9i) q^{80} +(2.45069e10 - 1.96005e10i) q^{81} +(3.00588e10 + 3.01327e10i) q^{82} +3.12525e10 q^{83} +(-2.32476e9 - 1.38587e10i) q^{84} -1.64079e10 q^{85} +(-3.00350e10 - 3.01088e10i) q^{86} +(-5.30852e10 + 9.03889e9i) q^{87} +(-3.17218e10 - 3.19562e10i) q^{88} +5.55310e10i q^{89} +(1.33014e10 + 6.41412e9i) q^{90} -2.22610e10i q^{91} +(2.80422e8 - 1.14310e11i) q^{92} +(-5.40955e10 + 9.21092e9i) q^{93} +(-3.15774e10 + 3.15000e10i) q^{94} -1.98891e8 q^{95} +(6.48868e10 + 4.66057e10i) q^{96} -4.52802e10 q^{97} +(5.48371e10 - 5.47027e10i) q^{98} +(-8.12132e10 + 2.84823e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9}+O(q^{10}) \) 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9	\( 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9} + 202000 q^{10} + 1064760 q^{12} + 1543864 q^{13} + 3482912 q^{16} + 2557392 q^{18} - 12211752 q^{21} - 5920464 q^{22} + 12133152 q^{24} - 141128700 q^{25} - 3604848 q^{28} + 73456080 q^{30} + 229769760 q^{33} + 222167104 q^{34} + 298087896 q^{36} - 44517800 q^{37} - 439643840 q^{40} + 281776944 q^{42} + 1020227520 q^{45} - 2392795680 q^{46} + 689090592 q^{48} - 1018138084 q^{49} - 3959246384 q^{52} - 4249352520 q^{54} + 1438636392 q^{57} + 9671853040 q^{58} + 5688375360 q^{60} + 6873199864 q^{61} - 1452752512 q^{64} - 10961242896 q^{66} - 13308470976 q^{69} + 35188514400 q^{70} + 30438127680 q^{72} - 12426469112 q^{73} - 60088673808 q^{76} - 81037845456 q^{78} - 42462874764 q^{81} + 88180337440 q^{82} + 125502443664 q^{84} + 17135502080 q^{85} - 166086469440 q^{88} - 257976145200 q^{90} + 114387515256 q^{93} + 391966360512 q^{94} + 446868262272 q^{96} + 75764383528 q^{97}+O(q^{100}) \) 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9 + 202000 * q^10 + 1064760 * q^12 + 1543864 * q^13 + 3482912 * q^16 + 2557392 * q^18 - 12211752 * q^21 - 5920464 * q^22 + 12133152 * q^24 - 141128700 * q^25 - 3604848 * q^28 + 73456080 * q^30 + 229769760 * q^33 + 222167104 * q^34 + 298087896 * q^36 - 44517800 * q^37 - 439643840 * q^40 + 281776944 * q^42 + 1020227520 * q^45 - 2392795680 * q^46 + 689090592 * q^48 - 1018138084 * q^49 - 3959246384 * q^52 - 4249352520 * q^54 + 1438636392 * q^57 + 9671853040 * q^58 + 5688375360 * q^60 + 6873199864 * q^61 - 1452752512 * q^64 - 10961242896 * q^66 - 13308470976 * q^69 + 35188514400 * q^70 + 30438127680 * q^72 - 12426469112 * q^73 - 60088673808 * q^76 - 81037845456 * q^78 - 42462874764 * q^81 + 88180337440 * q^82 + 125502443664 * q^84 + 17135502080 * q^85 - 166086469440 * q^88 - 257976145200 * q^90 + 114387515256 * q^93 + 391966360512 * q^94 + 446868262272 * q^96 + 75764383528 * q^97

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