LMFDB - Embedded newform 12.12.b.a.11.11

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			11.11
Root			$0.544378 - 22.6209i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.12.b.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08876 - 45.2417i) q^{2} +(399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} -4150.68i q^{5} +(-5566.58 - 18215.7i) q^{6} -39165.5i q^{7} +(-6684.15 + 92440.6i) q^{8} +(141953. - 105973. i) q^{9} +O(q^{10})$	\(q+(1.08876 - 45.2417i) q^{2} +(399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} -4150.68i q^{5} +(-5566.58 - 18215.7i) q^{6} -39165.5i q^{7} +(-6684.15 + 92440.6i) q^{8} +(141953. - 105973. i) q^{9} +(-187784. - 4519.08i) q^{10} -715661. q^{11} +(-830169. + 232009. i) q^{12} -605992. q^{13} +(-1.77192e6 - 42641.7i) q^{14} +(-550602. - 1.65794e6i) q^{15} +(4.17489e6 + 403048. i) q^{16} +5.31852e6i q^{17} +(-4.63986e6 - 6.53759e6i) q^{18} -1.51325e7i q^{19} +(-408902. + 8.49076e6i) q^{20} +(-5.19544e6 - 1.56442e7i) q^{21} +(-779180. + 3.23777e7i) q^{22} +4.01248e7 q^{23} +(9.59264e6 + 3.78109e7i) q^{24} +3.16000e7 q^{25} +(-659777. + 2.74161e7i) q^{26} +(4.26437e7 - 6.11603e7i) q^{27} +(-3.85837e6 + 8.01182e7i) q^{28} +1.84980e6i q^{29} +(-7.56074e7 + 2.31051e7i) q^{30} -2.41637e8i q^{31} +(2.27800e7 - 1.88441e8i) q^{32} +(-2.85862e8 + 9.49348e7i) q^{33} +(2.40619e8 + 5.79057e6i) q^{34} -1.62564e8 q^{35} +(-3.00824e8 + 2.02798e8i) q^{36} +4.80485e8 q^{37} +(-6.84620e8 - 1.64756e7i) q^{38} +(-2.42056e8 + 8.03868e7i) q^{39} +(3.83691e8 + 2.77438e7i) q^{40} -1.82276e8i q^{41} +(-7.13426e8 + 2.18018e8i) q^{42} +1.12750e9i q^{43} +(1.46398e9 + 7.05029e7i) q^{44} +(-4.39862e8 - 5.89203e8i) q^{45} +(4.36861e7 - 1.81531e9i) q^{46} +4.80730e8 q^{47} +(1.72107e9 - 3.92821e8i) q^{48} +4.43388e8 q^{49} +(3.44046e7 - 1.42964e9i) q^{50} +(7.05519e8 + 2.12442e9i) q^{51} +(1.23963e9 + 5.96989e7i) q^{52} +4.89614e9i q^{53} +(-2.72057e9 - 1.99586e9i) q^{54} +2.97048e9i q^{55} +(3.62048e9 + 2.61788e8i) q^{56} +(-2.00737e9 - 6.04448e9i) q^{57} +(8.36882e7 + 2.01398e6i) q^{58} -3.77738e9 q^{59} +(9.62996e8 + 3.44577e9i) q^{60} +1.72291e9 q^{61} +(-1.09321e10 - 2.63084e8i) q^{62} +(-4.15050e9 - 5.55967e9i) q^{63} +(-8.50058e9 - 1.23577e9i) q^{64} +2.51528e9i q^{65} +(3.98378e9 + 1.30362e10i) q^{66} -1.69232e10i q^{67} +(5.23951e8 - 1.08797e10i) q^{68} +(1.60273e10 - 5.32268e9i) q^{69} +(-1.76992e8 + 7.35466e9i) q^{70} +1.32561e10 q^{71} +(8.84740e9 + 1.38306e10i) q^{72} -3.00051e10 q^{73} +(5.23131e8 - 2.17380e10i) q^{74} +(1.26222e10 - 4.19184e9i) q^{75} +(-1.49077e9 + 3.09555e10i) q^{76} +2.80292e10i q^{77} +(3.37330e9 + 1.10385e10i) q^{78} +3.23010e9i q^{79} +(1.67292e9 - 1.73287e10i) q^{80} +(8.92037e9 - 3.00865e10i) q^{81} +(-8.24646e9 - 1.98454e8i) q^{82} +3.04488e9 q^{83} +(9.08676e9 + 3.25140e10i) q^{84} +2.20755e10 q^{85} +(5.10099e10 + 1.22757e9i) q^{86} +(2.45382e8 + 7.38880e8i) q^{87} +(4.78359e9 - 6.61561e10i) q^{88} +3.87715e10i q^{89} +(-2.71355e10 + 1.92586e10i) q^{90} +2.37340e10i q^{91} +(-8.20804e10 - 3.95287e9i) q^{92} +(-3.20540e10 - 9.65190e10i) q^{93} +(5.23397e8 - 2.17490e10i) q^{94} -6.28102e10 q^{95} +(-1.58981e10 - 7.82920e10i) q^{96} +3.29498e10 q^{97} +(4.82741e8 - 2.00596e10i) q^{98} +(-1.01590e11 + 7.58410e10i) 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 $

$2$	1.08876	−	45.2417i	0.0240583	−	0.999711i
$2$	1.08876	−	45.2417i	0.0240583	−	0.999711i
$3$	399.437	−	132.653i	0.949034	−	0.315175i
$3$	399.437	−	132.653i	0.949034	−	0.315175i
$4$	−2045.63	−	98.5144i	−0.998842	−	0.0481027i
$5$		−	4150.68i		−	0.593997i	−0.954878	−	0.296999i	$-0.904014\pi$
$5$		−	4150.68i		−	0.593997i	0.954878	−	0.296999i	$-0.0959857\pi$
$6$	−5566.58	−	18215.7i	−0.292251	−	0.956342i
$7$		−	39165.5i		−	0.880775i	−0.897808	−	0.440387i	$-0.854841\pi$
$7$		−	39165.5i		−	0.880775i	0.897808	−	0.440387i	$-0.145159\pi$
$8$	−6684.15	+	92440.6i	−0.0721193	+	0.997396i
$9$	141953.	−	105973.i	0.801330	−	0.598223i
$10$	−187784.	−	4519.08i	−0.593825	−	0.0142906i
$11$	−715661.			−1.33982			−0.669912	−	0.742441i	$-0.733668\pi$
$11$	−715661.			−1.33982			−0.669912	+	0.742441i	$0.733668\pi$
$12$	−830169.	+	232009.i	−0.963096	+	0.269159i
$13$	−605992.			−0.452667			−0.226333	−	0.974050i	$-0.572674\pi$
$13$	−605992.			−0.452667			−0.226333	+	0.974050i	$0.572674\pi$
$14$	−1.77192e6	−	42641.7i	−0.880520	−	0.0211900i
$15$	−550602.	−	1.65794e6i	−0.187213	−	0.563723i
$16$	4.17489e6	+	403048.i	0.995372	+	0.0960941i
$17$			5.31852e6i			0.908493i	0.890876	+	0.454247i	$0.150092\pi$
$17$			5.31852e6i			0.908493i	−0.890876	+	0.454247i	$0.849908\pi$
$18$	−4.63986e6	−	6.53759e6i	−0.578771	−	0.815490i
$19$		−	1.51325e7i		−	1.40206i	−0.713133	−	0.701028i	$-0.752725\pi$
$19$		−	1.51325e7i		−	1.40206i	0.713133	−	0.701028i	$-0.247275\pi$
$20$	−408902.	+	8.49076e6i	−0.0285729	+	0.593310i
$21$	−5.19544e6	−	1.56442e7i	−0.277598	−	0.835885i
$22$	−779180.	+	3.23777e7i	−0.0322339	+	1.33944i
$23$	4.01248e7			1.29990			0.649949	−	0.759978i	$-0.274790\pi$
$23$	4.01248e7			1.29990			0.649949	+	0.759978i	$0.274790\pi$
$24$	9.59264e6	+	3.78109e7i	0.245910	+	0.969293i
$25$	3.16000e7			0.647167
$26$	−659777.	+	2.74161e7i	−0.0108904	+	0.452535i
$27$	4.26437e7	−	6.11603e7i	0.571945	−	0.820292i
$28$	−3.85837e6	+	8.01182e7i	−0.0423677	+	0.879755i
$29$			1.84980e6i			0.0167470i	0.999965	+	0.00837348i	$0.00266539\pi$
$29$			1.84980e6i			0.0167470i	−0.999965	+	0.00837348i	$0.997335\pi$
$30$	−7.56074e7	+	2.31051e7i	−0.568064	+	0.173596i
$31$		−	2.41637e8i		−	1.51592i	−0.652304	−	0.757958i	$-0.726197\pi$
$31$		−	2.41637e8i		−	1.51592i	0.652304	−	0.757958i	$-0.273803\pi$
$32$	2.27800e7	−	1.88441e8i	0.120013	−	0.992772i
$33$	−2.85862e8	+	9.49348e7i	−1.27154	+	0.422278i
$34$	2.40619e8	+	5.79057e6i	0.908231	+	0.0218568i
$35$	−1.62564e8			−0.523178
$36$	−3.00824e8	+	2.02798e8i	−0.829179	+	0.558984i
$37$	4.80485e8			1.13912			0.569561	−	0.821949i	$-0.307113\pi$
$37$	4.80485e8			1.13912			0.569561	+	0.821949i	$0.307113\pi$
$38$	−6.84620e8	−	1.64756e7i	−1.40165	−	0.0337311i
$39$	−2.42056e8	+	8.03868e7i	−0.429596	+	0.142669i
$40$	3.83691e8	+	2.77438e7i	0.592451	+	0.0428387i
$41$		−	1.82276e8i		−	0.245707i	−0.992425	−	0.122853i	$-0.960795\pi$
$41$		−	1.82276e8i		−	0.245707i	0.992425	−	0.122853i	$-0.0392045\pi$
$42$	−7.13426e8	+	2.18018e8i	−0.842321	+	0.257407i
$43$			1.12750e9i			1.16960i	0.811176	+	0.584802i	$0.198828\pi$
$43$			1.12750e9i			1.16960i	−0.811176	+	0.584802i	$0.801172\pi$
$44$	1.46398e9	+	7.05029e7i	1.33827	+	0.0644492i
$45$	−4.39862e8	−	5.89203e8i	−0.355343	−	0.475988i
$46$	4.36861e7	−	1.81531e9i	0.0312734	−	1.29952i
$47$	4.80730e8			0.305747			0.152874	−	0.988246i	$-0.451147\pi$
$47$	4.80730e8			0.305747			0.152874	+	0.988246i	$0.451147\pi$
$48$	1.72107e9	−	3.92821e8i	0.974928	−	0.222519i
$49$	4.43388e8			0.224236
$50$	3.44046e7	−	1.42964e9i	0.0155698	−	0.646980i
$51$	7.05519e8	+	2.12442e9i	0.286334	+	0.862191i
$52$	1.23963e9	+	5.96989e7i	0.452143	+	0.0217745i
$53$			4.89614e9i			1.60819i	0.594503	+	0.804093i	$0.297349\pi$
$53$			4.89614e9i			1.60819i	−0.594503	+	0.804093i	$0.702651\pi$
$54$	−2.72057e9	−	1.99586e9i	−0.806295	−	0.591514i
$55$			2.97048e9i			0.795851i
$56$	3.62048e9	+	2.61788e8i	0.878481	+	0.0635208i
$57$	−2.00737e9	−	6.04448e9i	−0.441893	−	1.33060i
$58$	8.36882e7	+	2.01398e6i	0.0167421	+	0.000402904i
$59$	−3.77738e9			−0.687867			−0.343934	−	0.938994i	$-0.611759\pi$
$59$	−3.77738e9			−0.687867			−0.343934	+	0.938994i	$0.611759\pi$
$60$	9.62996e8	+	3.44577e9i	0.159879	+	0.572076i
$61$	1.72291e9			0.261186			0.130593	−	0.991436i	$-0.458312\pi$
$61$	1.72291e9			0.261186			0.130593	+	0.991436i	$0.458312\pi$
$62$	−1.09321e10	−	2.63084e8i	−1.51548	−	0.0364704i
$63$	−4.15050e9	−	5.55967e9i	−0.526899	−	0.705791i
$64$	−8.50058e9	−	1.23577e9i	−0.989598	−	0.143863i
$65$			2.51528e9i			0.268883i
$66$	3.98378e9	+	1.30362e10i	0.391565	+	1.28133i
$67$		−	1.69232e10i		−	1.53134i	−0.643233	−	0.765671i	$-0.722407\pi$
$67$		−	1.69232e10i		−	1.53134i	0.643233	−	0.765671i	$-0.277593\pi$
$68$	5.23951e8	−	1.08797e10i	0.0437010	−	0.907442i
$69$	1.60273e10	−	5.32268e9i	1.23365	−	0.409695i
$70$	−1.76992e8	+	7.35466e9i	−0.0125868	+	0.523026i
$71$	1.32561e10			0.871957			0.435978	−	0.899957i	$-0.356402\pi$
$71$	1.32561e10			0.871957			0.435978	+	0.899957i	$0.356402\pi$
$72$	8.84740e9	+	1.38306e10i	0.538873	+	0.842387i
$73$	−3.00051e10			−1.69402			−0.847011	−	0.531576i	$-0.821600\pi$
$73$	−3.00051e10			−1.69402			−0.847011	+	0.531576i	$0.821600\pi$
$74$	5.23131e8	−	2.17380e10i	0.0274054	−	1.13879i
$75$	1.26222e10	−	4.19184e9i	0.614183	−	0.203971i
$76$	−1.49077e9	+	3.09555e10i	−0.0674428	+	1.40043i
$77$			2.80292e10i			1.18008i
$78$	3.37330e9	+	1.10385e10i	0.132292	+	0.432904i
$79$			3.23010e9i			0.118105i	0.998255	+	0.0590524i	$0.0188079\pi$
$79$			3.23010e9i			0.118105i	−0.998255	+	0.0590524i	$0.981192\pi$
$80$	1.67292e9	−	1.73287e10i	0.0570796	−	0.591248i
$81$	8.92037e9	−	3.00865e10i	0.284260	−	0.958747i
$82$	−8.24646e9	−	1.98454e8i	−0.245636	−	0.00591130i
$83$	3.04488e9			0.0848477			0.0424238	−	0.999100i	$-0.486492\pi$
$83$	3.04488e9			0.0848477			0.0424238	+	0.999100i	$0.486492\pi$
$84$	9.08676e9	+	3.25140e10i	0.237068	+	0.848270i
$85$	2.20755e10			0.539643
$86$	5.10099e10	+	1.22757e9i	1.16927	+	0.0281387i
$87$	2.45382e8	+	7.38880e8i	0.00527822	+	0.0158934i
$88$	4.78359e9	−	6.61561e10i	0.0966271	−	1.33633i
$89$			3.87715e10i			0.735983i	0.929829	+	0.367991i	$0.119954\pi$
$89$			3.87715e10i			0.735983i	−0.929829	+	0.367991i	$0.880046\pi$
$90$	−2.71355e10	+	1.92586e10i	−0.484399	+	0.343788i
$91$			2.37340e10i			0.398697i
$92$	−8.20804e10	−	3.95287e9i	−1.29839	−	0.0625287i
$93$	−3.20540e10	−	9.65190e10i	−0.477778	−	1.43865i
$94$	5.23397e8	−	2.17490e10i	0.00735577	−	0.305659i
$95$	−6.28102e10			−0.832818
$96$	−1.58981e10	−	7.82920e10i	−0.199000	−	0.980000i
$97$	3.29498e10			0.389591			0.194795	−	0.980844i	$-0.437596\pi$
$97$	3.29498e10			0.389591			0.194795	+	0.980844i	$0.437596\pi$
$98$	4.82741e8	−	2.00596e10i	0.00539474	−	0.224171i
$99$	−1.01590e11	+	7.58410e10i	−1.07364	+	0.801512i
$100$	−6.46418e10	−	3.11305e9i	−0.646418	−	0.0311305i
$101$			1.33079e11i			1.25992i	0.776628	+	0.629959i	$0.216928\pi$
$101$			1.33079e11i			1.25992i	−0.776628	+	0.629959i	$0.783072\pi$
$102$	9.68804e10	−	2.96059e10i	0.868830	−	0.265508i
$103$			1.22881e11i			1.04443i	0.852814	+	0.522215i	$0.174894\pi$
$103$			1.22881e11i			1.04443i	−0.852814	+	0.522215i	$0.825106\pi$
$104$	4.05054e9	−	5.60182e10i	0.0326460	−	0.451488i
$105$	−6.49340e10	+	2.15646e10i	−0.496513	+	0.164892i
$106$	2.21510e11	+	5.33070e9i	1.60772	+	0.0386903i
$107$	2.53485e10			0.174719			0.0873597	−	0.996177i	$-0.472157\pi$
$107$	2.53485e10			0.174719			0.0873597	+	0.996177i	$0.472157\pi$
$108$	−9.32583e10	+	1.20910e11i	−0.610741	+	0.791830i
$109$	3.69555e10			0.230056			0.115028	−	0.993362i	$-0.463304\pi$
$109$	3.69555e10			0.230056			0.115028	+	0.993362i	$0.463304\pi$
$110$	1.34390e11	+	3.23413e9i	0.795621	+	0.0191469i
$111$	1.91924e11	−	6.37379e10i	1.08106	−	0.359022i
$112$	1.57856e10	−	1.63512e11i	0.0846373	−	0.876699i
$113$		−	1.78738e11i		−	0.912610i	−0.889823	−	0.456305i	$-0.849173\pi$
$113$		−	1.78738e11i		−	0.912610i	0.889823	−	0.456305i	$-0.150827\pi$
$114$	−2.75648e11	+	8.42361e10i	−1.34085	+	0.409753i
$115$		−	1.66545e11i		−	0.772136i
$116$	1.82232e8	−	3.78401e9i	0.000805575	−	0.0167276i
$117$	−8.60225e10	+	6.42190e10i	−0.362735	+	0.270795i
$118$	−4.11264e9	+	1.70895e11i	−0.0165489	+	0.687668i
$119$	2.08303e11			0.800178
$120$	1.56941e11	−	3.98160e10i	0.575757	−	0.146070i
$121$	2.26859e11			0.795126
$122$	1.87583e9	−	7.79476e10i	0.00628369	−	0.261110i
$123$	−2.41795e10	−	7.28077e10i	−0.0774405	−	0.233184i
$124$	−2.38048e10	+	4.94301e11i	−0.0729197	+	1.51416i
$125$		−	3.33831e11i		−	0.978413i
$126$	−2.56048e11	+	1.81723e11i	−0.718263	+	0.509767i
$127$		−	3.47864e11i		−	0.934305i	−0.884177	−	0.467153i	$-0.845280\pi$
$127$		−	3.47864e11i		−	0.934305i	0.884177	−	0.467153i	$-0.154720\pi$
$128$	−6.51636e10	+	3.83235e11i	−0.167629	+	0.985850i
$129$	1.49566e11	+	4.50364e11i	0.368629	+	1.10999i
$130$	1.13796e11	+	2.73853e9i	0.268805	+	0.00646887i
$131$	−3.41263e11			−0.772853			−0.386426	−	0.922320i	$-0.626291\pi$
$131$	−3.41263e11			−0.772853			−0.386426	+	0.922320i	$0.626291\pi$
$132$	5.94119e11	−	1.66040e11i	1.29038	−	0.360625i
$133$	−5.92672e11			−1.23490
$134$	−7.65637e11	−	1.84253e10i	−1.53090	−	0.0368415i
$135$	−2.53857e11	−	1.77000e11i	−0.487251	−	0.339734i
$136$	−4.91647e11	−	3.55498e10i	−0.906128	−	0.0655199i
$137$			2.07058e11i			0.366546i	0.983062	+	0.183273i	$0.0586692\pi$
$137$			2.07058e11i			0.366546i	−0.983062	+	0.183273i	$0.941331\pi$
$138$	−2.23358e11	−	7.30899e11i	−0.379897	−	1.24315i
$139$		−	8.74875e10i		−	0.143009i	−0.997440	−	0.0715047i	$-0.977220\pi$
$139$		−	8.74875e10i		−	0.143009i	0.997440	−	0.0715047i	$-0.0227801\pi$
$140$	3.32545e11	+	1.60149e10i	0.522572	+	0.0251663i
$141$	1.92021e11	−	6.37704e10i	0.290165	−	0.0963638i
$142$	1.44327e10	−	5.99729e11i	0.0209778	−	0.871705i
$143$	4.33685e11			0.606493
$144$	6.35352e11	−	3.85213e11i	0.855107	−	0.518451i
$145$	7.67794e9			0.00994765
$146$	−3.26682e10	+	1.35748e12i	−0.0407553	+	1.69353i
$147$	1.77106e11	−	5.88168e10i	0.212807	−	0.0706735i
$148$	−9.82894e11	−	4.73347e10i	−1.13780	−	0.0547949i
$149$		−	8.29939e11i		−	0.925810i	−0.886408	−	0.462905i	$-0.846807\pi$
$149$		−	8.29939e11i		−	0.925810i	0.886408	−	0.462905i	$-0.153193\pi$
$150$	−1.75904e11	−	5.75614e11i	−0.189135	−	0.618913i
$151$			1.14841e12i			1.19049i	0.803545	+	0.595244i	$0.202945\pi$
$151$			1.14841e12i			1.19049i	−0.803545	+	0.595244i	$0.797055\pi$
$152$	1.39886e12	+	1.01148e11i	1.39841	+	0.101115i
$153$	5.63621e11	+	7.54981e11i	0.543481	+	0.728003i
$154$	1.26809e12	+	3.05170e10i	1.17974	+	0.0283908i
$155$	−1.00296e12			−0.900450
$156$	5.03076e11	−	1.40596e11i	0.435961	−	0.121839i
$157$	−6.21510e10			−0.0519996			−0.0259998	−	0.999662i	$-0.508277\pi$
$157$	−6.21510e10			−0.0519996			−0.0259998	+	0.999662i	$0.508277\pi$
$158$	1.46136e11	+	3.51679e9i	0.118071	+	0.00284140i
$159$	6.49489e11	+	1.95570e12i	0.506859	+	1.52622i
$160$	−7.82157e11	−	9.45526e10i	−0.589704	−	0.0712876i
$161$		−	1.57151e12i		−	1.14492i
$162$	−1.35145e12	−	4.36330e11i	−0.951631	−	0.307243i
$163$			1.15508e12i			0.786284i	0.919478	+	0.393142i	$0.128612\pi$
$163$			1.15508e12i			0.786284i	−0.919478	+	0.393142i	$0.871388\pi$
$164$	−1.79568e10	+	3.72868e11i	−0.0118192	+	0.245422i
$165$	3.94044e11	+	1.18652e12i	0.250832	+	0.755290i
$166$	3.31513e9	−	1.37755e11i	0.00204129	−	0.0848231i
$167$	1.73332e12			1.03261			0.516307	−	0.856404i	$-0.327306\pi$
$167$	1.73332e12			1.03261			0.516307	+	0.856404i	$0.327306\pi$
$168$	1.48088e12	−	3.75701e11i	0.853728	−	0.216591i
$169$	−1.42493e12			−0.795093
$170$	2.40348e10	−	9.98734e11i	0.0129829	−	0.539486i
$171$	−1.60364e12	−	2.14811e12i	−0.838742	−	1.12351i
$172$	1.11075e11	−	2.30644e12i	0.0562612	−	1.16825i
$173$			1.42423e12i			0.698756i	0.936982	+	0.349378i	$0.113607\pi$
$173$			1.42423e12i			0.698756i	−0.936982	+	0.349378i	$0.886393\pi$
$174$	3.36954e10	−	1.02971e10i	0.0160158	−	0.00489432i
$175$		−	1.23763e12i		−	0.570008i
$176$	−2.98781e12	−	2.88446e11i	−1.33362	−	0.128749i
$177$	−1.50883e12	+	5.01082e11i	−0.652809	+	0.216798i
$178$	1.75409e12	+	4.22127e10i	0.735770	+	0.0177065i
$179$	−3.46465e12			−1.40918			−0.704591	−	0.709613i	$-0.748870\pi$
$179$	−3.46465e12			−1.40918			−0.704591	+	0.709613i	$0.748870\pi$
$180$	8.41749e11	+	1.24862e12i	0.332035	+	0.492530i
$181$	3.07059e12			1.17487			0.587435	−	0.809271i	$-0.300138\pi$
$181$	3.07059e12			1.17487			0.587435	+	0.809271i	$0.300138\pi$
$182$	1.07377e12	+	2.58405e10i	0.398582	+	0.00959199i
$183$	6.88196e11	−	2.28550e11i	0.247874	−	0.0823191i
$184$	−2.68200e11	+	3.70916e12i	−0.0937478	+	1.29651i
$185$		−	1.99434e12i		−	0.676635i
$186$	−4.40159e12	+	1.34509e12i	−1.44973	+	0.443028i
$187$		−	3.80626e12i		−	1.21722i
$188$	−9.83395e11	−	4.73588e10i	−0.305393	−	0.0147073i
$189$	−2.39537e12	−	1.67016e12i	−0.722493	−	0.503754i
$190$	−6.83849e10	+	2.84164e12i	−0.0200362	+	0.832577i
$191$	3.96739e12			1.12933			0.564666	−	0.825320i	$-0.309005\pi$
$191$	3.96739e12			1.12933			0.564666	+	0.825320i	$0.309005\pi$
$192$	−3.55938e12	+	6.34016e11i	−0.984503	+	0.175365i
$193$	3.42054e12			0.919452			0.459726	−	0.888061i	$-0.347948\pi$
$193$	3.42054e12			0.919452			0.459726	+	0.888061i	$0.347948\pi$
$194$	3.58743e10	−	1.49071e12i	0.00937291	−	0.389478i
$195$	3.33660e11	+	1.00470e12i	0.0847450	+	0.255179i
$196$	−9.07007e11	−	4.36801e10i	−0.223976	−	0.0107864i
$197$			3.92037e12i			0.941375i	0.882300	+	0.470687i	$0.155994\pi$
$197$			3.92037e12i			0.941375i	−0.882300	+	0.470687i	$0.844006\pi$
$198$	3.32057e12	+	4.67870e12i	0.775450	+	1.09261i
$199$		−	4.18407e11i		−	0.0950402i	−0.998870	−	0.0475201i	$-0.984868\pi$
$199$		−	4.18407e11i		−	0.0950402i	0.998870	−	0.0475201i	$-0.0151318\pi$
$200$	−2.11219e11	+	2.92112e12i	−0.0466732	+	0.645482i
$201$	−2.24492e12	−	6.75977e12i	−0.482640	−	1.45329i
$202$	6.02073e12	+	1.44891e11i	1.25955	+	0.0303115i
$203$	7.24485e10			0.0147503
$204$	−1.23395e12	−	4.41527e12i	−0.244529	−	0.874966i
$205$	−7.56568e11			−0.145949
$206$	5.55934e12	+	1.33787e11i	1.04413	+	0.0251272i
$207$	5.69584e12	−	4.25216e12i	1.04165	−	0.777629i
$208$	−2.52995e12	−	2.44244e11i	−0.450572	−	0.0434986i
$209$			1.08297e13i			1.87851i
$210$	9.04923e11	+	2.96120e12i	0.152899	+	0.500337i
$211$			1.11017e12i			0.182742i	0.995817	+	0.0913708i	$0.0291249\pi$
$211$			1.11017e12i			0.182742i	−0.995817	+	0.0913708i	$0.970875\pi$
$212$	4.82340e11	−	1.00157e13i	0.0773582	−	1.60632i
$213$	5.29498e12	−	1.75847e12i	0.827517	−	0.274819i
$214$	2.75983e10	−	1.14681e12i	0.00420346	−	0.174669i
$215$	4.67988e12			0.694742
$216$	5.36865e12	+	4.35081e12i	0.776908	+	0.629614i
$217$	−9.46386e12			−1.33518
$218$	4.02356e10	−	1.67193e12i	0.00553477	−	0.229990i
$219$	−1.19851e13	+	3.98027e12i	−1.60768	+	0.533912i
$220$	2.92635e11	−	6.07650e12i	0.0382826	−	0.794930i
$221$		−	3.22298e12i		−	0.411245i
$222$	−2.67465e12	−	8.75235e12i	−0.332910	−	1.08939i
$223$			9.67899e12i			1.17531i	0.809111	+	0.587656i	$0.199949\pi$
$223$			9.67899e12i			1.17531i	−0.809111	+	0.587656i	$0.800051\pi$
$224$	−7.38038e12	−	8.92192e11i	−0.874409	−	0.105705i
$225$	4.48572e12	−	3.34875e12i	0.518595	−	0.387150i
$226$	−8.08641e12	−	1.94602e11i	−0.912346	−	0.0219559i
$227$	−1.46078e13			−1.60858			−0.804288	−	0.594240i	$-0.797453\pi$
$227$	−1.46078e13			−1.60858			−0.804288	+	0.594240i	$0.797453\pi$
$228$	3.51088e12	+	1.25625e13i	0.377376	+	1.35032i
$229$	1.96967e12			0.206680			0.103340	−	0.994646i	$-0.467047\pi$
$229$	1.96967e12			0.206680			0.103340	+	0.994646i	$0.467047\pi$
$230$	−7.53479e12	−	1.81327e11i	−0.771913	−	0.0185763i
$231$	3.71817e12	+	1.11959e13i	0.371932	+	1.11994i
$232$	−1.70997e11	−	1.23644e10i	−0.0167034	−	0.00120778i
$233$		−	3.00912e11i		−	0.0287066i	−0.999897	−	0.0143533i	$-0.995431\pi$
$233$		−	3.00912e11i		−	0.0287066i	0.999897	−	0.0143533i	$-0.00456895\pi$
$234$	2.81172e12	+	3.96173e12i	0.261990	+	0.369145i
$235$		−	1.99536e12i		−	0.181613i
$236$	7.72712e12	+	3.72126e11i	0.687071	+	0.0330883i
$237$	4.28484e11	+	1.29022e12i	0.0372236	+	0.112085i
$238$	2.26791e11	−	9.42398e12i	0.0192509	−	0.799946i
$239$	1.14714e12			0.0951538			0.0475769	−	0.998868i	$-0.484850\pi$
$239$	1.14714e12			0.0951538			0.0475769	+	0.998868i	$0.484850\pi$
$240$	−1.63048e12	−	7.14363e12i	−0.132176	−	0.579105i
$241$	8.43435e12			0.668279			0.334139	−	0.942524i	$-0.391554\pi$
$241$	8.43435e12			0.668279			0.334139	+	0.942524i	$0.391554\pi$
$242$	2.46994e11	−	1.02635e13i	0.0191294	−	0.794896i
$243$	−4.27947e11	−	1.32010e13i	−0.0324008	−	0.999475i
$244$	−3.52444e12	−	1.69732e11i	−0.260883	−	0.0125638i
$245$		−	1.84036e12i		−	0.133196i
$246$	−3.32027e12	+	1.01465e12i	−0.234980	+	0.0718081i
$247$			9.17017e12i			0.634664i
$248$	2.23371e13	+	1.61514e12i	1.51197	+	0.109327i
$249$	1.21624e12	−	4.03913e11i	0.0805233	−	0.0267418i
$250$	−1.51031e13	−	3.63461e11i	−0.978130	−	0.0235390i
$251$	−2.10245e11			−0.0133205			−0.00666025	−	0.999978i	$-0.502120\pi$
$251$	−2.10245e11			−0.0133205			−0.00666025	+	0.999978i	$0.502120\pi$
$252$	7.94268e12	+	1.17819e13i	0.492339	+	0.730319i
$253$	−2.87157e13			−1.74163
$254$	−1.57380e13	−	3.78739e11i	−0.934035	−	0.0224778i
$255$	8.81777e12	−	2.92839e12i	0.512139	−	0.170082i
$256$	1.72673e13	+	3.36536e12i	0.981532	+	0.191299i
$257$			1.33118e13i			0.740634i	0.928905	+	0.370317i	$0.120751\pi$
$257$			1.33118e13i			0.740634i	−0.928905	+	0.370317i	$0.879249\pi$
$258$	2.05381e13	−	6.27630e12i	1.11854	−	0.341818i
$259$		−	1.88184e13i		−	1.00331i
$260$	2.47791e11	−	5.14533e12i	0.0129340	−	0.268571i
$261$	1.96030e11	+	2.62585e11i	0.0100184	+	0.0134198i
$262$	−3.71552e11	+	1.54393e13i	−0.0185935	+	0.772629i
$263$	3.56786e13			1.74844			0.874221	−	0.485528i	$-0.161373\pi$
$263$	3.56786e13			1.74844			0.874221	+	0.485528i	$0.161373\pi$
$264$	−6.86508e12	−	2.70598e13i	−0.329476	−	1.29868i
$265$	2.03223e13			0.955258
$266$	−6.45275e11	+	2.68135e13i	−0.0297095	+	1.23454i
$267$	5.14317e12	+	1.54868e13i	0.231963	+	0.698473i
$268$	−1.66718e12	+	3.46187e13i	−0.0736617	+	1.52957i
$269$		−	1.14048e13i		−	0.493683i	−0.969056	−	0.246842i	$-0.920607\pi$
$269$		−	1.14048e13i		−	0.493683i	0.969056	−	0.246842i	$-0.0793928\pi$
$270$	−8.28419e12	+	1.12922e13i	−0.351358	+	0.478937i
$271$		−	1.26428e13i		−	0.525425i	−0.964874	−	0.262713i	$-0.915383\pi$
$271$		−	1.26428e13i		−	0.525425i	0.964874	−	0.262713i	$-0.0846171\pi$
$272$	−2.14362e12	+	2.22043e13i	−0.0873009	+	0.904289i
$273$	3.14839e12	+	9.48024e12i	0.125659	+	0.378377i
$274$	9.36765e12	+	2.25435e11i	0.366440	+	0.00881848i
$275$	−2.26149e13			−0.867090
$276$	−3.33103e13	+	9.30931e12i	−1.25193	+	0.349879i
$277$	1.07355e13			0.395533			0.197767	−	0.980249i	$-0.436631\pi$
$277$	1.07355e13			0.395533			0.197767	+	0.980249i	$0.436631\pi$
$278$	−3.95809e12	−	9.52526e10i	−0.142968	−	0.00344057i
$279$	−2.56071e13	−	3.43012e13i	−0.906855	−	1.21475i
$280$	1.08660e12	−	1.50275e13i	0.0377312	−	0.521815i
$281$		−	3.54105e13i		−	1.20572i	−0.797845	−	0.602862i	$-0.794027\pi$
$281$		−	3.54105e13i		−	1.20572i	0.797845	−	0.602862i	$-0.205973\pi$
$282$	−2.67602e12	−	8.75681e12i	−0.0893550	−	0.292399i
$283$		−	2.18613e13i		−	0.715897i	−0.933741	−	0.357948i	$-0.883476\pi$
$283$		−	2.18613e13i		−	0.715897i	0.933741	−	0.357948i	$-0.116524\pi$
$284$	−2.71171e13	−	1.30592e12i	−0.870948	−	0.0419435i
$285$	−2.50887e13	+	8.33197e12i	−0.790372	+	0.262483i
$286$	4.72177e11	−	1.96206e13i	0.0145912	−	0.606318i
$287$	−7.13892e12			−0.216412
$288$	−1.67360e13	−	2.91638e13i	−0.497728	−	0.867333i
$289$	5.98523e12			0.174640
$290$	8.35940e9	−	3.47363e11i	0.000239324	−	0.00994477i
$291$	1.31614e13	−	4.37090e12i	0.369735	−	0.122789i
$292$	6.13793e13	+	2.95593e12i	1.69206	+	0.0814871i
$293$		−	9.02580e12i		−	0.244182i	−0.992519	−	0.122091i	$-0.961040\pi$
$293$		−	9.02580e12i		−	0.244182i	0.992519	−	0.122091i	$-0.0389600\pi$
$294$	−2.46815e12	−	8.07660e12i	−0.0655332	−	0.214446i
$295$			1.56787e13i			0.408591i
$296$	−3.21163e12	+	4.44163e13i	−0.0821527	+	1.13616i
$297$	−3.05184e13	+	4.37700e13i	−0.766305	+	1.09905i
$298$	−3.75479e13	−	9.03601e11i	−0.925542	−	0.0222734i
$299$	−2.43153e13			−0.588421
$300$	−2.62333e13	+	7.33148e12i	−0.623284	+	0.174191i
$301$	4.41590e13			1.03016
$302$	5.19562e13	+	1.25034e12i	1.19014	+	0.0286411i
$303$	1.76534e13	+	5.31568e13i	0.397094	+	1.19570i
$304$	6.09912e12	−	6.31765e13i	0.134729	−	1.39557i
$305$		−	7.15127e12i		−	0.155144i
$306$	3.47703e13	−	2.46772e13i	0.740868	−	0.525809i
$307$			7.44927e13i			1.55902i	0.626388	+	0.779511i	$0.284532\pi$
$307$			7.44927e13i			1.55902i	−0.626388	+	0.779511i	$0.715468\pi$
$308$	2.76128e12	−	5.73374e13i	0.0567652	−	1.17872i
$309$	1.63005e13	+	4.90832e13i	0.329178	+	0.991199i
$310$	−1.09198e12	+	4.53757e13i	−0.0216633	+	0.900189i
$311$	−3.90535e12			−0.0761163			−0.0380582	−	0.999276i	$-0.512117\pi$
$311$	−3.90535e12			−0.0761163			−0.0380582	+	0.999276i	$0.512117\pi$
$312$	−5.81306e12	−	2.29131e13i	−0.111315	−	0.438766i
$313$	−5.14001e13			−0.967096			−0.483548	−	0.875318i	$-0.660652\pi$
$313$	−5.14001e13			−0.967096			−0.483548	+	0.875318i	$0.660652\pi$
$314$	−6.76672e10	+	2.81182e12i	−0.00125102	+	0.0519845i
$315$	−2.30764e13	+	1.72274e13i	−0.419238	+	0.312977i
$316$	3.18212e11	−	6.60760e12i	0.00568116	−	0.117968i
$317$		−	6.93372e13i		−	1.21658i	−0.793715	−	0.608290i	$-0.791856\pi$
$317$		−	6.93372e13i		−	1.21658i	0.793715	−	0.608290i	$-0.208144\pi$
$318$	8.91864e13	−	2.72547e13i	1.53798	−	0.469994i
$319$		−	1.32383e12i		−	0.0224380i
$320$	−5.12930e12	+	3.52832e13i	−0.0854542	+	0.587818i
$321$	1.01251e13	−	3.36256e12i	0.165815	−	0.0550671i
$322$	−7.10978e13	−	1.71099e12i	−1.14459	−	0.0275448i
$323$	8.04825e13			1.27376
$324$	−2.12117e13	+	6.06671e13i	−0.330049	+	0.943964i
$325$	−1.91493e13			−0.292951
$326$	5.22577e13	+	1.25760e12i	0.786057	+	0.0189167i
$327$	1.47614e13	−	4.90227e12i	0.218331	−	0.0725078i
$328$	1.68497e13	+	1.21836e12i	0.245067	+	0.0177202i
$329$		−	1.88280e13i		−	0.269294i
$330$	5.41093e13	−	1.65354e13i	0.761106	−	0.232588i
$331$			3.38041e13i			0.467645i	0.972279	+	0.233822i	$0.0751234\pi$
$331$			3.38041e13i			0.467645i	−0.972279	+	0.233822i	$0.924877\pi$
$332$	−6.22869e12	−	2.99964e11i	−0.0847495	−	0.00408141i
$333$	6.82064e13	−	5.09186e13i	0.912812	−	0.681448i
$334$	1.88716e12	−	7.84184e13i	0.0248430	−	1.03231i
$335$	−7.02430e13			−0.909613
$336$	−1.53850e13	−	6.74068e13i	−0.195989	−	0.858692i
$337$	6.23777e13			0.781744			0.390872	−	0.920445i	$-0.372173\pi$
$337$	6.23777e13			0.781744			0.390872	+	0.920445i	$0.372173\pi$
$338$	−1.55141e12	+	6.44665e13i	−0.0191286	+	0.794863i
$339$	−2.37102e13	−	7.13946e13i	−0.287631	−	0.866098i
$340$	−4.51583e13	−	2.17475e12i	−0.539018	−	0.0259583i
$341$			1.72930e14i			2.03106i
$342$	−9.89300e13	+	7.02127e13i	−1.14336	+	0.811469i
$343$		−	9.48086e13i		−	1.07828i
$344$	−1.04226e14	−	7.53636e12i	−1.16656	−	0.0843510i
$345$	−2.20928e13	−	6.65244e13i	−0.243358	−	0.732783i
$346$	6.44345e13	+	1.55064e12i	0.698554	+	0.0168109i
$347$	4.89995e13			0.522853			0.261427	−	0.965223i	$-0.415807\pi$
$347$	4.89995e13			0.522853			0.261427	+	0.965223i	$0.415807\pi$
$348$	−4.29171e11	−	1.53565e12i	−0.00450759	−	0.0161289i
$349$	−1.52960e14			−1.58139			−0.790695	−	0.612210i	$-0.790281\pi$
$349$	−1.52960e14			−1.58139			−0.790695	+	0.612210i	$0.790281\pi$
$350$	−5.59925e13	−	1.34748e12i	−0.569843	−	0.0137135i
$351$	−2.58417e13	+	3.70626e13i	−0.258900	+	0.371319i
$352$	−1.63028e13	+	1.34860e14i	−0.160797	+	1.33014i
$353$		−	1.76488e13i		−	0.171378i	−0.996322	−	0.0856888i	$-0.972691\pi$
$353$		−	1.76488e13i		−	0.171378i	0.996322	−	0.0856888i	$-0.0273091\pi$
$354$	2.10271e13	+	6.88075e13i	0.201030	+	0.657836i
$355$		−	5.50219e13i		−	0.517940i
$356$	3.81955e12	−	7.93121e13i	0.0354028	−	0.735131i
$357$	8.32039e13	−	2.76320e13i	0.759396	−	0.252196i
$358$	−3.77215e12	+	1.56747e14i	−0.0339026	+	1.40878i
$359$	−1.67111e14			−1.47906			−0.739528	−	0.673125i	$-0.764951\pi$
$359$	−1.67111e14			−1.47906			−0.739528	+	0.673125i	$0.764951\pi$
$360$	5.74063e13	−	3.67227e13i	0.500375	−	0.320089i
$361$	−1.12502e14			−0.965763
$362$	3.34312e12	−	1.38919e14i	0.0282654	−	1.17453i
$363$	9.06159e13	−	3.00936e13i	0.754602	−	0.250604i
$364$	2.33814e12	−	4.85510e13i	0.0191784	−	0.398236i
$365$			1.24542e14i			1.00624i
$366$	−9.59073e12	−	3.13840e13i	−0.0763318	−	0.249783i
$367$		−	9.73718e13i		−	0.763431i	−0.924280	−	0.381716i	$-0.875333\pi$
$367$		−	9.73718e13i		−	0.763431i	0.924280	−	0.381716i	$-0.124667\pi$
$368$	1.67517e14	+	1.61722e13i	1.29388	+	0.124913i
$369$	−1.93163e13	−	2.58746e13i	−0.146987	−	0.196892i
$370$	−9.02274e13	−	2.17135e12i	−0.676439	−	0.0162787i
$371$	1.91760e14			1.41645
$372$	5.60621e13	+	2.00600e14i	0.408022	+	1.45997i
$373$	2.07348e14			1.48697			0.743484	−	0.668753i	$-0.233172\pi$
$373$	2.07348e14			1.48697			0.743484	+	0.668753i	$0.233172\pi$
$374$	−1.72202e14	−	4.14408e12i	−1.21687	−	0.0292843i
$375$	−4.42838e13	−	1.33345e14i	−0.308371	−	0.928547i
$376$	−3.21327e12	+	4.44389e13i	−0.0220503	+	0.304951i
$377$		−	1.12096e12i		−	0.00758079i
$378$	−7.81690e13	+	1.06552e14i	−0.520991	+	0.710164i
$379$			8.28818e12i			0.0544432i	0.999629	+	0.0272216i	$0.00866598\pi$
$379$			8.28818e12i			0.0544432i	−0.999629	+	0.0272216i	$0.991334\pi$
$380$	1.28486e14	+	6.18771e12i	0.831854	+	0.0400608i
$381$	−4.61453e13	−	1.38950e14i	−0.294469	−	0.886687i
$382$	4.31952e12	−	1.79492e14i	0.0271698	−	1.12900i
$383$	1.15533e14			0.716328			0.358164	−	0.933659i	$-0.383403\pi$
$383$	1.15533e14			0.716328			0.358164	+	0.933659i	$0.383403\pi$
$384$	2.48087e13	+	1.61723e14i	0.151629	+	0.988437i
$385$	1.16340e14			0.700966
$386$	3.72413e12	−	1.54751e14i	0.0221205	−	0.919186i
$387$	1.19485e14	+	1.60052e14i	0.699683	+	0.937239i
$388$	−6.74032e13	−	3.24603e12i	−0.389140	−	0.0187404i
$389$		−	1.31210e14i		−	0.746866i	−0.927657	−	0.373433i	$-0.878181\pi$
$389$		−	1.31210e14i		−	0.746866i	0.927657	−	0.373433i	$-0.121819\pi$
$390$	4.58175e13	−	1.40015e13i	0.257144	−	0.0785813i
$391$			2.13404e14i			1.18095i
$392$	−2.96367e12	+	4.09870e13i	−0.0161717	+	0.223652i
$393$	−1.36313e14	+	4.52696e13i	−0.733463	+	0.243583i
$394$	1.77364e14	+	4.26832e12i	0.941102	+	0.0226479i
$395$	1.34071e13			0.0701539
$396$	2.15288e14	−	1.45134e14i	1.11095	−	0.748940i
$397$	−1.37733e14			−0.700953			−0.350477	−	0.936571i	$-0.613980\pi$
$397$	−1.37733e14			−0.700953			−0.350477	+	0.936571i	$0.613980\pi$
$398$	−1.89295e13	−	4.55543e11i	−0.0950127	−	0.00228651i
$399$	−2.36735e14	+	7.86199e13i	−1.17196	+	0.389208i
$400$	1.31926e14	+	1.27363e13i	0.644172	+	0.0621890i
$401$			2.01390e14i			0.969939i	0.874531	+	0.484969i	$0.161169\pi$
$401$			2.01390e14i			0.969939i	−0.874531	+	0.484969i	$0.838831\pi$
$402$	−3.08268e14	+	9.42045e13i	−1.46449	+	0.447536i
$403$			1.46430e14i			0.686204i
$404$	1.31102e13	−	2.72231e14i	0.0606055	−	1.25846i
$405$	−1.24880e14	−	3.70256e13i	−0.569493	−	0.168849i
$406$	7.88787e10	−	3.27769e12i	0.000354868	−	0.0147460i
$407$	−3.43864e14			−1.52622
$408$	−2.01098e14	+	5.10187e13i	−0.880596	+	0.223408i
$409$	4.27309e14			1.84614			0.923069	−	0.384636i	$-0.125673\pi$
$409$	4.27309e14			1.84614			0.923069	+	0.384636i	$0.125673\pi$
$410$	−8.23718e11	+	3.42285e13i	−0.00351129	+	0.145907i
$411$	2.74669e13	+	8.27066e13i	0.115526	+	0.347864i
$412$	1.21055e13	−	2.51368e14i	0.0502399	−	1.04322i
$413$			1.47943e14i			0.605856i
$414$	−1.86174e14	−	2.62319e14i	−0.752343	−	1.06005i
$415$		−	1.26383e13i		−	0.0503993i
$416$	−1.38045e13	+	1.14193e14i	−0.0543260	+	0.449395i
$417$	−1.16055e13	−	3.49458e13i	−0.0450729	−	0.135721i
$418$	4.89956e14	+	1.17909e13i	1.87796	+	0.0451938i
$419$	−1.04709e14			−0.396102			−0.198051	−	0.980192i	$-0.563461\pi$
$419$	−1.04709e14			−0.396102			−0.198051	+	0.980192i	$0.563461\pi$
$420$	1.34955e14	−	3.77163e13i	0.503870	−	0.140818i
$421$	−3.55392e14			−1.30965			−0.654826	−	0.755780i	$-0.727258\pi$
$421$	−3.55392e14			−1.30965			−0.654826	+	0.755780i	$0.727258\pi$
$422$	5.02262e13	+	1.20871e12i	0.182689	+	0.00439646i
$423$	6.82411e13	−	5.09445e13i	0.245005	−	0.182905i
$424$	−4.52602e14	−	3.27265e13i	−1.60400	−	0.115981i
$425$			1.68065e14i			0.587947i
$426$	−7.37911e13	−	2.41469e14i	−0.254830	−	0.833889i
$427$		−	6.74789e13i		−	0.230046i
$428$	−5.18536e13	−	2.49719e12i	−0.174517	−	0.00840448i
$429$	1.73230e14	−	5.75297e13i	0.575582	−	0.191151i
$430$	5.09525e12	−	2.11726e14i	0.0167143	−	0.694541i
$431$	1.42826e13			0.0462576			0.0231288	−	0.999732i	$-0.492637\pi$
$431$	1.42826e13			0.0462576			0.0231288	+	0.999732i	$0.492637\pi$
$432$	2.02683e14	−	2.38150e14i	0.648123	−	0.761536i
$433$	−9.80964e13			−0.309720			−0.154860	−	0.987936i	$-0.549493\pi$
$433$	−9.80964e13			−0.309720			−0.154860	+	0.987936i	$0.549493\pi$
$434$	−1.03038e13	+	4.28161e14i	−0.0321222	+	1.33479i
$435$	3.06685e12	−	1.01850e12i	0.00944066	−	0.00313525i
$436$	−7.55973e13	−	3.64065e12i	−0.229790	−	0.0110663i
$437$		−	6.07188e14i		−	1.82253i
$438$	1.67025e14	+	5.46562e14i	0.495080	+	1.62006i
$439$		−	7.16595e13i		−	0.209758i	−0.994485	−	0.104879i	$-0.966554\pi$
$439$		−	7.16595e13i		−	0.209758i	0.994485	−	0.104879i	$-0.0334455\pi$
$440$	−2.74593e14	−	1.98551e13i	−0.793779	−	0.0573962i
$441$	6.29403e13	−	4.69873e13i	0.179687	−	0.134143i
$442$	−1.45813e14	−	3.50904e12i	−0.411126	−	0.00989386i
$443$	3.04787e14			0.848743			0.424372	−	0.905488i	$-0.360495\pi$
$443$	3.04787e14			0.848743			0.424372	+	0.905488i	$0.360495\pi$
$444$	−3.98883e14	+	1.11477e14i	−1.09708	+	0.306604i
$445$	1.60928e14			0.437172
$446$	4.37894e14	+	1.05381e13i	1.17497	+	0.0282761i
$447$	−1.10094e14	−	3.31508e14i	−0.291792	−	0.878624i
$448$	−4.83997e13	+	3.32930e14i	−0.126711	+	0.871613i
$449$			4.09389e13i			0.105872i	0.998598	+	0.0529360i	$0.0168579\pi$
$449$			4.09389e13i			0.105872i	−0.998598	+	0.0529360i	$0.983142\pi$
$450$	−1.46620e14	−	2.06588e14i	−0.374561	−	0.527759i
$451$			1.30448e14i			0.329204i
$452$	−1.76083e13	+	3.65631e14i	−0.0438990	+	0.911553i
$453$	1.52341e14	+	4.58719e14i	0.375211	+	1.12981i
$454$	−1.59043e13	+	6.60881e14i	−0.0386997	+	1.60811i
$455$	9.85123e13			0.236825
$456$	5.72173e14	−	1.45161e14i	1.35900	−	0.344780i
$457$	2.14695e14			0.503828			0.251914	−	0.967750i	$-0.418940\pi$
$457$	2.14695e14			0.503828			0.251914	+	0.967750i	$0.418940\pi$
$458$	2.14449e12	−	8.91115e13i	0.00497238	−	0.206621i
$459$	3.25282e14	+	2.26801e14i	0.745230	+	0.519608i
$460$	−1.64071e13	+	3.40690e14i	−0.0371419	+	0.771242i
$461$			6.63309e13i			0.148375i	0.997244	+	0.0741875i	$0.0236363\pi$
$461$			6.63309e13i			0.148375i	−0.997244	+	0.0741875i	$0.976364\pi$
$462$	5.10571e14	−	1.56027e14i	1.12856	−	0.344880i
$463$		−	5.59646e14i		−	1.22241i	−0.791471	−	0.611206i	$-0.790684\pi$
$463$		−	5.59646e14i		−	1.22241i	0.791471	−	0.611206i	$-0.209316\pi$
$464$	−7.45559e11	+	7.72272e12i	−0.00160928	+	0.0166695i
$465$	−4.00620e14	+	1.33046e14i	−0.854557	+	0.283799i
$466$	−1.36138e13	−	3.27620e11i	−0.0286983	−	0.000690633i
$467$	5.02983e14			1.04788			0.523939	−	0.851756i	$-0.324462\pi$
$467$	5.02983e14			1.04788			0.523939	+	0.851756i	$0.324462\pi$
$468$	1.82297e14	−	1.22894e14i	0.375341	−	0.253033i
$469$	−6.62808e14			−1.34877
$470$	−9.02734e13	−	2.17246e12i	−0.181561	−	0.00436931i
$471$	−2.48254e13	+	8.24453e12i	−0.0493493	+	0.0163889i
$472$	2.52486e13	−	3.49183e14i	0.0496085	−	0.686076i
$473$		−	8.06905e14i		−	1.56706i
$474$	5.88385e13	−	1.79806e13i	0.112949	−	0.0345163i
$475$		−	4.78186e14i		−	0.907365i
$476$	−4.26110e14	−	2.05208e13i	−0.799252	−	0.0384908i
$477$	5.18860e14	+	6.95023e14i	0.962053	+	1.28869i
$478$	1.24895e12	−	5.18984e13i	0.00228924	−	0.0951263i
$479$	−1.01548e14			−0.184004			−0.0920018	−	0.995759i	$-0.529327\pi$
$479$	−1.01548e14			−0.184004			−0.0920018	+	0.995759i	$0.529327\pi$
$480$	−3.24965e14	+	6.59879e13i	−0.582117	+	0.118205i
$481$	−2.91170e14			−0.515642
$482$	9.18294e12	−	3.81584e14i	0.0160777	−	0.668085i
$483$	−2.08466e14	−	6.27719e14i	−0.360849	−	1.08657i
$484$	−4.64069e14	−	2.23489e13i	−0.794206	−	0.0382477i
$485$		−	1.36764e14i		−	0.231416i
$486$	−5.97702e14	+	4.98840e12i	−0.999965	+	0.00834569i
$487$			3.32633e14i			0.550246i	0.961409	+	0.275123i	$0.0887185\pi$
$487$			3.32633e14i			0.550246i	−0.961409	+	0.275123i	$0.911281\pi$
$488$	−1.15162e13	+	1.59267e14i	−0.0188365	+	0.260506i
$489$	1.53225e14	+	4.61381e14i	0.247817	+	0.746210i
$490$	−8.32612e13	−	2.00370e12i	−0.133157	−	0.00320446i
$491$	−1.14114e15			−1.80464			−0.902322	−	0.431062i	$-0.858139\pi$
$491$	−1.14114e15			−1.80464			−0.902322	+	0.431062i	$0.858139\pi$
$492$	4.22896e13	+	1.51319e14i	0.0661341	+	0.236639i
$493$	−9.83821e12			−0.0152145
$494$	4.14874e14	+	9.98407e12i	0.634480	+	0.0152690i
$495$	3.14792e14	+	4.21669e14i	0.476096	+	0.637740i
$496$	9.73915e13	−	1.00881e15i	0.145671	−	1.50890i
$497$		−	5.19182e14i		−	0.767998i
$498$	−1.69495e13	−	5.54644e13i	−0.0247968	−	0.0811434i
$499$			4.71083e14i			0.681623i	0.940132	+	0.340811i	$0.110702\pi$
$499$			4.71083e14i			0.681623i	−0.940132	+	0.340811i	$0.889298\pi$
$500$	−3.28872e13	+	6.82895e14i	−0.0470643	+	0.977280i
$501$	6.92352e14	−	2.29930e14i	0.979985	−	0.325454i
$502$	−2.28906e11	+	9.51185e12i	−0.000320469	+	0.0133166i
$503$	−4.42390e14			−0.612606			−0.306303	−	0.951934i	$-0.599092\pi$
$503$	−4.42390e14			−0.612606			−0.306303	+	0.951934i	$0.599092\pi$
$504$	5.41682e14	−	3.46513e14i	0.741953	−	0.474626i
$505$	5.52369e14			0.748388
$506$	−3.12644e13	+	1.29915e15i	−0.0419008	+	1.74113i
$507$	−5.69172e14	+	1.89022e14i	−0.754570	+	0.250593i
$508$	−3.42696e13	+	7.11600e14i	−0.0449426	+	0.933224i
$509$			1.97515e13i			0.0256243i	0.999918	+	0.0128122i	$0.00407835\pi$
$509$			1.97515e13i			0.0256243i	−0.999918	+	0.0128122i	$0.995922\pi$
$510$	−1.22885e14	−	4.02120e14i	−0.157711	−	0.516083i
$511$			1.17516e15i			1.49205i
$512$	1.71055e14	−	7.77538e14i	0.214857	−	0.976645i
$513$	−9.25507e14	−	6.45305e14i	−1.15010	−	0.801899i
$514$	6.02248e14	+	1.44933e13i	0.740420	+	0.0178184i
$515$	5.10039e14			0.620388
$516$	−2.61590e14	−	9.36013e14i	−0.314809	−	1.12644i
$517$	−3.44039e14			−0.409647
$518$	−8.51379e14	−	2.04887e13i	−1.00302	−	0.0241380i
$519$	1.88928e14	+	5.68890e14i	0.220230	+	0.663143i
$520$	−2.32514e14	−	1.68125e13i	−0.268183	−	0.0193916i
$521$			1.34420e15i			1.53411i	0.641583	+	0.767054i	$0.278278\pi$
$521$			1.34420e15i			1.53411i	−0.641583	+	0.767054i	$0.721722\pi$
$522$	1.20932e13	−	8.58283e12i	0.0136570	−	0.00969265i
$523$		−	4.37710e14i		−	0.489133i	−0.969633	−	0.244566i	$-0.921354\pi$
$523$		−	4.37710e14i		−	0.489133i	0.969633	−	0.244566i	$-0.0786456\pi$
$524$	6.98097e14	+	3.36193e13i	0.771958	+	0.0371763i
$525$	−1.64176e14	−	4.94355e14i	−0.179652	−	0.540957i
$526$	3.88453e13	−	1.61416e15i	0.0420646	−	1.74794i
$527$	1.28515e15			1.37720
$528$	−1.23171e15	+	2.81127e14i	−1.30623	+	0.298137i
$529$	6.57188e14			0.689737
$530$	2.21260e13	−	9.19417e14i	0.0229819	−	0.954982i
$531$	−5.36211e14	+	4.00301e14i	−0.551209	+	0.411498i
$532$	1.21239e15	+	5.83867e13i	1.23347	+	0.0594019i
$533$			1.10458e14i			0.111223i
$534$	7.06249e14	−	2.15825e14i	0.703851	−	0.215092i
$535$		−	1.05213e14i		−	0.103783i
$536$	1.56439e15	+	1.13118e14i	1.52735	+	0.110439i
$537$	−1.38391e15	+	4.59597e14i	−1.33736	+	0.444139i
$538$	−5.15971e14	−	1.24170e13i	−0.493540	−	0.0118772i
$539$	−3.17315e14			−0.300437
$540$	5.01860e14	+	3.87086e14i	0.470345	+	0.362778i
$541$	9.84565e14			0.913397			0.456698	−	0.889622i	$-0.349032\pi$
$541$	9.84565e14			0.913397			0.456698	+	0.889622i	$0.349032\pi$
$542$	−5.71981e14	−	1.37649e13i	−0.525273	−	0.0126409i
$543$	1.22651e15	−	4.07324e14i	1.11499	−	0.370289i
$544$	1.00223e15	+	1.21156e14i	0.901927	+	0.109031i
$545$		−	1.53391e14i		−	0.136653i
$546$	4.32330e14	−	1.32117e14i	0.381291	−	0.116520i
$547$			3.02327e14i			0.263965i	0.991252	+	0.131983i	$0.0421343\pi$
$547$			3.02327e14i			0.263965i	−0.991252	+	0.131983i	$0.957866\pi$
$548$	2.03982e13	−	4.23563e14i	0.0176319	−	0.366122i
$549$	2.44573e14	−	1.82583e14i	0.209296	−	0.156247i
$550$	−2.46221e13	+	1.02314e15i	−0.0208607	+	0.866839i
$551$	2.79921e13			0.0234802
$552$	3.84903e14	+	1.51715e15i	0.319658	+	1.25998i
$553$	1.26509e14			0.104024
$554$	1.16883e13	−	4.85692e14i	0.00951587	−	0.395419i
$555$	−2.64556e14	−	7.96614e14i	−0.213258	−	0.642150i
$556$	−8.61878e12	+	1.78967e14i	−0.00687915	+	0.142844i
$557$			1.52188e15i			1.20275i	0.798966	+	0.601376i	$0.205381\pi$
$557$			1.52188e15i			1.20275i	−0.798966	+	0.601376i	$0.794619\pi$
$558$	−1.57973e15	+	1.12117e15i	−1.23621	+	0.877367i
$559$		−	6.83254e14i		−	0.529441i
$560$	−6.78686e14	−	6.55209e13i	−0.520757	−	0.0502743i
$561$	−5.04913e14	−	1.52036e15i	−0.383637	−	1.15518i
$562$	−1.60203e15	−	3.85534e13i	−1.20538	−	0.0290077i
$563$	−1.33301e15			−0.993203			−0.496602	−	0.867979i	$-0.665419\pi$
$563$	−1.33301e15			−0.993203			−0.496602	+	0.867979i	$0.665419\pi$
$564$	−3.99087e14	+	1.11534e14i	−0.294464	+	0.0822945i
$565$	−7.41884e14			−0.542088
$566$	−9.89043e14	−	2.38016e13i	−0.715690	−	0.0172233i
$567$	−1.17835e15	−	3.49371e14i	−0.844440	−	0.250369i
$568$	−8.86058e13	+	1.22540e15i	−0.0628849	+	0.869686i
$569$		−	1.19810e15i		−	0.842123i	−0.907032	−	0.421061i	$-0.861658\pi$
$569$		−	1.19810e15i		−	0.842123i	0.907032	−	0.421061i	$-0.138342\pi$
$570$	3.49637e14	+	1.14413e15i	0.243392	+	0.796458i
$571$		−	3.71418e13i		−	0.0256073i	−0.999918	−	0.0128037i	$-0.995924\pi$
$571$		−	3.71418e13i		−	0.0256073i	0.999918	−	0.0128037i	$-0.00407564\pi$
$572$	−8.87158e14	−	4.27242e13i	−0.605791	−	0.0291740i
$573$	1.58472e15	−	5.26288e14i	1.07177	−	0.355937i
$574$	−7.77254e12	+	3.22977e14i	−0.00520652	+	0.216350i
$575$	1.26794e15			0.841252
$576$	−1.33764e15	+	7.25413e14i	−0.879056	+	0.476718i
$577$	1.38947e15			0.904443			0.452222	−	0.891906i	$-0.350632\pi$
$577$	1.38947e15			0.904443			0.452222	+	0.891906i	$0.350632\pi$
$578$	6.51645e12	−	2.70782e14i	0.00420154	−	0.174589i
$579$	1.36629e15	−	4.53745e14i	0.872591	−	0.289788i
$580$	−1.57062e13	−	7.56387e11i	−0.00993614	−	0.000478509i
$581$		−	1.19254e14i		−	0.0747317i
$582$	−1.83418e14	−	6.00203e14i	−0.113858	−	0.372582i
$583$		−	3.50397e15i		−	2.15469i
$584$	2.00558e14	−	2.77369e15i	0.122172	−	1.68961i
$585$	2.66553e14	+	3.57052e14i	0.160852	+	0.215464i
$586$	−4.08343e14	−	9.82690e12i	−0.244112	−	0.00587462i
$587$	−2.30295e15			−1.36388			−0.681938	−	0.731410i	$-0.738863\pi$
$587$	−2.30295e15			−1.36388			−0.681938	+	0.731410i	$0.738863\pi$
$588$	−3.68087e14	+	1.02870e14i	−0.215961	+	0.0603550i
$589$	−3.65658e15			−2.12540
$590$	7.09332e14	+	1.70703e13i	0.408473	+	0.00983002i
$591$	5.20050e14	+	1.56594e15i	0.296697	+	0.893396i
$592$	2.00597e15	+	1.93658e14i	1.13385	+	0.109463i
$593$			3.12601e15i			1.75061i	0.483569	+	0.875306i	$0.339340\pi$
$593$			3.12601e15i			1.75061i	−0.483569	+	0.875306i	$0.660660\pi$
$594$	1.94700e15	+	1.42836e15i	1.08029	+	0.792524i
$595$		−	8.64598e14i		−	0.475304i
$596$	−8.17609e13	+	1.69775e15i	−0.0445340	+	0.924738i
$597$	−5.55031e13	−	1.67127e14i	−0.0299542	−	0.0901963i
$598$	−2.64734e13	+	1.10007e15i	−0.0141564	+	0.588250i
$599$	3.23992e15			1.71667			0.858336	−	0.513088i	$-0.171498\pi$
$599$	3.23992e15			1.71667			0.858336	+	0.513088i	$0.171498\pi$
$600$	3.03127e14	+	1.19482e15i	0.159145	+	0.627294i
$601$	1.76981e15			0.920695			0.460348	−	0.887739i	$-0.347725\pi$
$601$	1.76981e15			0.920695			0.460348	+	0.887739i	$0.347725\pi$
$602$	4.80784e13	−	1.99783e15i	0.0247839	−	1.02986i
$603$	−1.79341e15	−	2.40231e15i	−0.916083	−	1.22711i
$604$	1.13135e14	−	2.34923e15i	0.0572657	−	1.18911i
$605$		−	9.41619e14i		−	0.472303i
$606$	2.42412e15	−	7.40795e14i	1.20491	−	0.368213i
$607$			3.71788e15i			1.83129i	0.401986	+	0.915646i	$0.368320\pi$
$607$			3.71788e15i			1.83129i	−0.401986	+	0.915646i	$0.631680\pi$
$608$	−2.85158e15	−	3.44718e14i	−1.39192	−	0.168265i
$609$	2.89386e13	−	9.61053e12i	0.0139985	−	0.00464892i
$610$	−3.23536e14	−	7.78599e12i	−0.155099	−	0.00373250i
$611$	−2.91318e14			−0.138402
$612$	−1.07858e15	−	1.59994e15i	−0.507833	−	0.753303i
$613$	−2.22778e15			−1.03954			−0.519769	−	0.854307i	$-0.673982\pi$
$613$	−2.22778e15			−1.03954			−0.519769	+	0.854307i	$0.673982\pi$
$614$	3.37018e15	+	8.11043e13i	1.55857	+	0.0375075i
$615$	−3.02201e14	+	1.00361e14i	−0.138511	+	0.0459995i
$616$	−2.59104e15	−	1.87352e14i	−1.17701	−	0.0851067i
$617$			4.65663e14i			0.209654i	0.994490	+	0.104827i	$0.0334289\pi$
$617$			4.65663e14i			0.209654i	−0.994490	+	0.104827i	$0.966571\pi$
$618$	2.23835e15	−	6.84025e14i	0.998832	−	0.305236i
$619$			2.22056e15i			0.982118i	0.871126	+	0.491059i	$0.163390\pi$
$619$			2.22056e15i			0.982118i	−0.871126	+	0.491059i	$0.836610\pi$
$620$	2.05168e15	+	9.88060e13i	0.899407	+	0.0433141i
$621$	1.71107e15	−	2.45404e15i	0.743470	−	1.06630i
$622$	−4.25197e12	+	1.76685e14i	−0.00183123	+	0.0760943i
$623$	1.51851e15			0.648235
$624$	−1.04296e15	+	2.38046e14i	−0.441317	+	0.100727i
$625$	1.57339e14			0.0659926
$626$	−5.59621e13	+	2.32543e15i	−0.0232667	+	0.966817i
$627$	1.43660e15	+	4.32580e15i	0.592058	+	1.78277i
$628$	1.27138e14	+	6.12276e12i	0.0519394	+	0.00250132i
$629$			2.55547e15i			1.03488i
$630$	7.54274e14	+	1.06277e15i	0.302800	+	0.426646i
$631$			3.80227e15i			1.51315i	0.653909	+	0.756574i	$0.273128\pi$
$631$			3.80227e15i			1.51315i	−0.653909	+	0.756574i	$0.726872\pi$
$632$	−2.98593e14	−	2.15905e13i	−0.117797	−	0.00851763i
$633$	1.47268e14	+	4.43445e14i	0.0575955	+	0.173428i
$634$	−3.13694e15	−	7.54913e13i	−1.21623	−	0.0292689i
$635$	−1.44387e15			−0.554975
$636$	−1.13595e15	−	4.06462e15i	−0.432857	−	1.54884i
$637$	−2.68689e14			−0.101504
$638$	−5.98924e13	−	1.44133e12i	−0.0224315	−	0.000539820i
$639$	1.88175e15	−	1.40479e15i	0.698725	−	0.521624i
$640$	1.59069e15	+	2.70473e14i	0.585592	+	0.0995714i
$641$		−	4.11701e15i		−	1.50267i	−0.659922	−	0.751334i	$-0.729411\pi$
$641$		−	4.11701e15i		−	1.50267i	0.659922	−	0.751334i	$-0.270589\pi$
$642$	−1.41104e14	−	4.61739e14i	−0.0510619	−	0.167091i
$643$		−	5.21378e15i		−	1.87065i	−0.353791	−	0.935325i	$-0.615108\pi$
$643$		−	5.21378e15i		−	1.87065i	0.353791	−	0.935325i	$-0.384892\pi$
$644$	−1.54816e14	+	3.21472e15i	−0.0550737	+	1.14359i
$645$	1.86932e15	−	6.20802e14i	0.659333	−	0.218965i
$646$	8.76257e13	−	3.64117e15i	0.0306445	−	1.27339i
$647$	−4.70489e15			−1.63146			−0.815730	−	0.578434i	$-0.803664\pi$
$647$	−4.70489e15			−1.63146			−0.815730	+	0.578434i	$0.803664\pi$
$648$	2.72159e15	+	1.02571e15i	0.935750	+	0.352664i
$649$	2.70332e15			0.921620
$650$	−2.08489e13	+	8.66348e14i	−0.00704791	+	0.292866i
$651$	−3.78022e15	+	1.25541e15i	−1.26713	+	0.420815i
$652$	1.13792e14	−	2.36286e15i	0.0378224	−	0.785374i
$653$		−	1.14113e15i		−	0.376107i	−0.982159	−	0.188053i	$-0.939782\pi$
$653$		−	1.14113e15i		−	0.376107i	0.982159	−	0.188053i	$-0.0602178\pi$
$654$	−2.05716e14	−	6.73170e14i	−0.0672342	−	0.220012i
$655$			1.41647e15i			0.459072i
$656$	7.34658e13	−	7.60981e14i	0.0236110	−	0.244570i
$657$	−4.25932e15	+	3.17974e15i	−1.35747	+	1.01340i
$658$	−8.51813e14	−	2.04991e13i	−0.269217	−	0.00647878i
$659$	1.18429e15			0.371185			0.185592	−	0.982627i	$-0.440580\pi$
$659$	1.18429e15			0.371185			0.185592	+	0.982627i	$0.440580\pi$
$660$	−6.89179e14	−	2.46600e15i	−0.214210	−	0.766481i
$661$	−1.96964e15			−0.607125			−0.303562	−	0.952812i	$-0.598176\pi$
$661$	−1.96964e15			−0.607125			−0.303562	+	0.952812i	$0.598176\pi$
$662$	1.52936e15	+	3.68044e13i	0.467509	+	0.0112507i
$663$	−4.27539e14	−	1.28738e15i	−0.129614	−	0.390285i
$664$	−2.03524e13	+	2.81470e14i	−0.00611915	+	0.0846267i
$665$			2.45999e15i			0.733525i
$666$	−2.22938e15	−	3.14121e15i	−0.659290	−	0.928943i
$667$			7.42229e13i			0.0217694i
$668$	−3.54573e15	−	1.70757e14i	−1.03142	−	0.0496715i
$669$	1.28395e15	+	3.86615e15i	0.370428	+	1.11541i
$670$	−7.64775e13	+	3.17791e15i	−0.0218838	+	0.909350i
$671$	−1.23302e15			−0.349943
$672$	−3.06635e15	+	6.22657e14i	−0.863159	+	0.175274i
$673$	1.93443e15			0.540096			0.270048	−	0.962847i	$-0.412960\pi$
$673$	1.93443e15			0.540096			0.270048	+	0.962847i	$0.412960\pi$
$674$	6.79141e13	−	2.82207e15i	0.0188075	−	0.781518i
$675$	1.34754e15	−	1.93266e15i	0.370144	−	0.530866i
$676$	2.91489e15	+	1.40377e14i	0.794173	+	0.0382461i
$677$		−	7.06371e15i		−	1.90895i	−0.298287	−	0.954476i	$-0.596415\pi$
$677$		−	7.06371e15i		−	1.90895i	0.298287	−	0.954476i	$-0.403585\pi$
$678$	−3.25583e15	+	9.94958e14i	−0.872767	+	0.266711i
$679$		−	1.29050e15i		−	0.343142i
$680$	−1.47556e14	+	2.04067e15i	−0.0389186	+	0.538237i
$681$	−5.83489e15	+	1.93777e15i	−1.52659	+	0.506982i
$682$	7.82367e15	+	1.88279e14i	2.03047	+	0.0488639i
$683$	3.79254e15			0.976375			0.488188	−	0.872739i	$-0.337658\pi$
$683$	3.79254e15			0.976375			0.488188	+	0.872739i	$0.337658\pi$
$684$	3.06883e15	+	4.55221e15i	0.783727	+	1.16256i
$685$	8.59431e14			0.217727
$686$	−4.28930e15	−	1.03223e14i	−1.07796	−	0.0259415i
$687$	7.86761e14	−	2.61284e14i	0.196147	−	0.0651404i
$688$	−4.54435e14	+	4.70718e15i	−0.112392	+	1.16419i
$689$		−	2.96702e15i		−	0.727972i
$690$	−3.03373e15	+	9.27086e14i	−0.738426	+	0.225658i
$691$			1.46454e15i			0.353649i	0.984242	+	0.176824i	$0.0565825\pi$
$691$			1.46454e15i			0.353649i	−0.984242	+	0.176824i	$0.943418\pi$
$692$	1.40307e14	−	2.91344e15i	0.0336121	−	0.697948i
$693$	2.97035e15	+	3.97884e15i	0.705952	+	0.945635i
$694$	5.33485e13	−	2.21682e15i	0.0125790	−	0.522702i
$695$	−3.63133e14			−0.0849472
$696$	−6.99426e13	+	1.77445e13i	−0.0162327	+	0.00411825i
$697$	9.69437e14			0.223223
$698$	−1.66537e14	+	6.92019e15i	−0.0380456	+	1.58093i
$699$	−3.99169e13	−	1.20195e14i	−0.00904759	−	0.0272435i
$700$	−1.21924e14	+	2.53173e15i	−0.0274190	+	0.569349i
$701$			4.25945e15i			0.950396i	0.879879	+	0.475198i	$0.157624\pi$
$701$			4.25945e15i			0.950396i	−0.879879	+	0.475198i	$0.842376\pi$
$702$	1.64864e15	+	1.20948e15i	0.364983	+	0.267759i
$703$		−	7.27093e15i		−	1.59711i
$704$	6.08353e15	+	8.84395e14i	1.32589	+	0.192751i
$705$	−2.64691e14	−	7.97019e14i	−0.0572398	−	0.172357i
$706$	−7.98462e14	−	1.92152e13i	−0.171328	−	0.00412306i
$707$	5.21211e15			1.10970
$708$	3.13586e15	−	8.76386e14i	0.662482	−	0.185145i
$709$	6.74458e14			0.141384			0.0706920	−	0.997498i	$-0.477479\pi$
$709$	6.74458e14			0.141384			0.0706920	+	0.997498i	$0.477479\pi$
$710$	−2.48929e15	−	5.99054e13i	−0.517790	−	0.0124608i
$711$	3.42305e14	+	4.58524e14i	0.0706530	+	0.0946409i
$712$	−3.58406e15	−	2.59155e14i	−0.734066	−	0.0530786i
$713$		−	9.69565e15i		−	1.97054i
$714$	−1.15953e15	−	3.79437e15i	−0.233853	−	0.765244i
$715$		−	1.80009e15i		−	0.360255i
$716$	7.08738e15	+	3.41318e14i	1.40755	+	0.0677856i
$717$	4.58209e14	−	1.52171e14i	0.0903042	−	0.0299901i
$718$	−1.81943e14	+	7.56038e15i	−0.0355836	+	1.47863i
$719$	3.92005e15			0.760822			0.380411	−	0.924818i	$-0.375783\pi$
$719$	3.92005e15			0.760822			0.380411	+	0.924818i	$0.375783\pi$
$720$	−1.59890e15	−	2.63714e15i	−0.307959	−	0.507931i
$721$	4.81269e15			0.919907
$722$	−1.22487e14	+	5.08979e15i	−0.0232346	+	0.965484i
$723$	3.36899e15	−	1.11884e15i	0.634219	−	0.210624i
$724$	−6.28129e15	−	3.02497e14i	−1.17351	−	0.0565145i
$725$			5.84537e13i			0.0108381i
$726$	−1.26283e15	−	4.13238e15i	−0.232377	−	0.760412i
$727$		−	3.73420e15i		−	0.681959i	−0.940071	−	0.340979i	$-0.889241\pi$
$727$		−	3.73420e15i		−	0.681959i	0.940071	−	0.340979i	$-0.110759\pi$
$728$	−2.19398e15	−	1.58642e14i	−0.397659	−	0.0287538i
$729$	−1.92209e15	−	5.21620e15i	−0.345758	−	0.938324i
$730$	5.63447e15	+	1.35595e14i	1.00595	+	0.0242086i
$731$	−5.99662e15			−1.06258
$732$	−1.43031e15	+	3.99732e14i	−0.251547	+	0.0703004i
$733$	−6.93709e15			−1.21089			−0.605446	−	0.795886i	$-0.707005\pi$
$733$	−6.93709e15			−1.21089			−0.605446	+	0.795886i	$0.707005\pi$
$734$	−4.40527e15	−	1.06014e14i	−0.763210	−	0.0183669i
$735$	−2.44130e14	−	7.35109e14i	−0.0419798	−	0.126407i
$736$	9.14043e14	−	7.56114e15i	0.156005	−	1.29050i
$737$			1.21113e16i			2.05173i
$738$	−1.19164e15	+	8.45734e14i	−0.200372	+	0.142208i
$739$			8.85830e15i			1.47845i	0.673459	+	0.739224i	$0.264808\pi$
$739$			8.85830e15i			1.47845i	−0.673459	+	0.739224i	$0.735192\pi$
$740$	−1.96471e14	+	4.07968e15i	−0.0325480	+	0.675852i
$741$	1.21645e15	+	3.66291e15i	0.200030	+	0.602318i
$742$	2.08780e14	−	8.67555e15i	0.0340774	−	1.41604i
$743$	−1.14543e16			−1.85580			−0.927901	−	0.372827i	$-0.878389\pi$
$743$	−1.14543e16			−1.85580			−0.927901	+	0.372827i	$0.878389\pi$
$744$	9.13652e15	−	2.31794e15i	1.46937	−	0.372779i
$745$	−3.44481e15			−0.549928
$746$	2.25752e14	−	9.38079e15i	0.0357740	−	1.48654i
$747$	4.32230e14	−	3.22676e14i	0.0679910	−	0.0507578i
$748$	−3.74971e14	+	7.78619e15i	−0.0585516	+	1.21581i
$749$		−	9.92786e14i		−	0.153888i
$750$	−6.08096e15	+	1.85830e15i	−0.935697	+	0.285942i
$751$			1.05302e16i			1.60849i	0.594297	+	0.804246i	$0.297430\pi$
$751$			1.05302e16i			1.60849i	−0.594297	+	0.804246i	$0.702570\pi$
$752$	2.00700e15	+	1.93757e14i	0.304332	+	0.0293805i
$753$	−8.39797e13	+	2.78897e13i	−0.0126416	+	0.00419828i
$754$	−5.07144e13	−	1.22046e12i	−0.00757860	−	0.000182381i
$755$	4.76670e15			0.707147
$756$	4.73551e15	+	3.65251e15i	0.697424	+	0.537925i
$757$	6.90026e15			1.00888			0.504438	−	0.863448i	$-0.331700\pi$
$757$	6.90026e15			1.00888			0.504438	+	0.863448i	$0.331700\pi$
$758$	3.74972e14	+	9.02381e12i	0.0544275	+	0.00130981i
$759$	−1.14701e16	+	3.80924e15i	−1.65287	+	0.548919i
$760$	4.19833e14	−	5.80621e15i	0.0600622	−	0.830649i
$761$		−	9.67264e14i		−	0.137382i	−0.997638	−	0.0686909i	$-0.978118\pi$
$761$		−	9.67264e14i		−	0.137382i	0.997638	−	0.0686909i	$-0.0218822\pi$
$762$	−6.33657e15	+	1.93641e15i	−0.893515	+	0.273052i
$763$		−	1.44738e15i		−	0.202628i
$764$	−8.11581e15	−	3.90845e14i	−1.12802	−	0.0543239i
$765$	3.13369e15	−	2.33941e15i	0.432432	−	0.322826i
$766$	1.25787e14	−	5.22690e15i	0.0172337	−	0.716120i
$767$	2.28906e15			0.311374
$768$	7.34363e15	−	9.46311e14i	0.991799	−	0.127805i
$769$	−2.91878e15			−0.391387			−0.195693	−	0.980665i	$-0.562696\pi$
$769$	−2.91878e15			−0.391387			−0.195693	+	0.980665i	$0.562696\pi$
$770$	1.26666e14	−	5.26344e15i	0.0168641	−	0.700763i
$771$	1.76585e15	+	5.31722e15i	0.233429	+	0.702887i
$772$	−6.99715e15	−	3.36972e14i	−0.918388	−	0.0442282i
$773$			7.62729e15i			0.993992i	0.867753	+	0.496996i	$0.165564\pi$
$773$			7.62729e15i			0.993992i	−0.867753	+	0.496996i	$0.834436\pi$
$774$	7.37111e15	−	5.23143e15i	0.953801	−	0.676933i
$775$		−	7.63573e15i		−	0.981051i
$776$	−2.20242e14	+	3.04590e15i	−0.0280970	+	0.388576i
$777$	−2.49633e15	−	7.51679e15i	−0.316218	−	0.952175i
$778$	−5.93615e15	−	1.42855e14i	−0.746650	−	0.0179684i
$779$	−2.75828e15			−0.344495
$780$	−5.83568e14	−	2.08811e15i	−0.0723721	−	0.258960i
$781$	−9.48688e15			−1.16827
$782$	9.65479e15	+	2.32345e14i	1.18061	+	0.0284117i
$783$	1.13134e14	+	7.88824e13i	0.0137374	+	0.00957834i
$784$	1.85110e15	+	1.78706e14i	0.223198	+	0.0215478i
$785$			2.57969e14i			0.0308876i
$786$	1.89966e15	+	6.21633e15i	0.225867	+	0.739111i
$787$			7.61628e15i			0.899253i	0.893217	+	0.449626i	$0.148443\pi$
$787$			7.61628e15i			0.899253i	−0.893217	+	0.449626i	$0.851557\pi$
$788$	3.86213e14	−	8.01962e15i	0.0452827	−	0.940285i
$789$	1.42514e16	−	4.73288e15i	1.65933	−	0.551064i
$790$	1.45971e13	−	6.06562e14i	0.00168779	−	0.0701336i
$791$	−7.00036e15			−0.803804
$792$	−6.33174e15	−	9.89800e15i	−0.721995	−	1.12865i
$793$	−1.04407e15			−0.118230
$794$	−1.49957e14	+	6.23126e15i	−0.0168638	+	0.700750i
$795$	8.11749e15	−	2.69582e15i	0.906572	−	0.301073i
$796$	−4.12191e13	+	8.55906e14i	−0.00457169	+	0.0949302i
$797$		−	1.30065e16i		−	1.43265i	−0.697768	−	0.716324i	$-0.745823\pi$
$797$		−	1.30065e16i		−	1.43265i	0.697768	−	0.716324i	$-0.254177\pi$
$798$	3.29915e15	+	1.07959e16i	0.360900	+	1.18098i
$799$			2.55677e15i			0.277769i
$800$	7.19848e14	−	5.95472e15i	0.0776687	−	0.642490i
$801$	4.10875e15	+	5.50374e15i	0.440282	+	0.589765i
$802$	9.11124e15	+	2.19265e14i	0.969658	+	0.0233351i
$803$	2.14735e16			2.26969
$804$	3.92635e15	+	1.40491e16i	0.412174	+	1.47483i
$805$	−6.52283e15			−0.680078
$806$	6.62476e15	+	1.59427e14i	0.686005	+	0.0165089i
$807$	−1.51288e15	−	4.55548e15i	−0.155596	−	0.468522i
$808$	−1.23019e16	−	8.89521e14i	−1.25664	−	0.0908644i
$809$			1.23491e16i			1.25291i	0.779457	+	0.626455i	$0.215495\pi$
$809$			1.23491e16i			1.25291i	−0.779457	+	0.626455i	$0.784505\pi$
$810$	−1.81107e15	+	5.60946e15i	−0.182502	+	0.565266i
$811$			1.90880e15i			0.191050i	0.995427	+	0.0955248i	$0.0304529\pi$
$811$			1.90880e15i			0.191050i	−0.995427	+	0.0955248i	$0.969547\pi$
$812$	−1.48203e14	−	7.13722e12i	−0.0147332	−	0.000709530i
$813$	−1.67710e15	−	5.04999e15i	−0.165601	−	0.498646i
$814$	−3.74384e14	+	1.55570e16i	−0.0367183	+	1.52578i
$815$	4.79436e15			0.467051
$816$	2.08923e15	+	9.15357e15i	0.202157	+	0.885716i
$817$	1.70618e16			1.63985
$818$	4.65235e14	−	1.93322e16i	0.0444150	−	1.84560i
$819$	2.51517e15	+	3.36912e15i	0.238510	+	0.319488i
$820$	1.54766e15	+	7.45329e13i	0.145780	+	0.00702056i
$821$			8.84373e15i			0.827462i	0.910399	+	0.413731i	$0.135775\pi$
$821$			8.84373e15i			0.827462i	−0.910399	+	0.413731i	$0.864225\pi$
$822$	3.77169e15	−	1.15260e15i	0.350543	−	0.107123i
$823$		−	9.57635e15i		−	0.884099i	−0.896991	−	0.442050i	$-0.854252\pi$
$823$		−	9.57635e15i		−	0.884099i	0.896991	−	0.442050i	$-0.145748\pi$
$824$	−1.13592e16	−	8.21354e14i	−1.04171	−	0.0753235i
$825$	−9.03322e15	+	2.99993e15i	−0.822897	+	0.273285i
$826$	6.69320e15	+	1.61074e14i	0.605681	+	0.0145759i
$827$	−1.16797e16			−1.04991			−0.524953	−	0.851131i	$-0.675917\pi$
$827$	−1.16797e16			−1.04991			−0.524953	+	0.851131i	$0.675917\pi$
$828$	−1.20705e16	+	8.13721e15i	−1.07785	+	0.726622i
$829$	−1.35174e16			−1.19907			−0.599533	−	0.800350i	$-0.704647\pi$
$829$	−1.35174e16			−1.19907			−0.599533	+	0.800350i	$0.704647\pi$
$830$	−5.71779e14	−	1.37600e13i	−0.0503847	−	0.00121252i
$831$	4.28815e15	−	1.42410e15i	0.375374	−	0.124662i
$832$	5.15128e15	+	7.48869e14i	0.447958	+	0.0651220i
$833$			2.35817e15i			0.203717i
$834$	−1.59364e15	+	4.87006e14i	−0.136766	+	0.0417947i
$835$		−	7.19446e15i		−	0.613370i
$836$	1.06688e15	−	2.21536e16i	0.0903614	−	1.87633i
$837$	−1.47786e16	−	1.03043e16i	−1.24349	−	0.867020i
$838$	−1.14003e14	+	4.73722e15i	−0.00952956	+	0.395988i
$839$	−2.24086e16			−1.86091			−0.930454	−	0.366410i	$-0.880587\pi$
$839$	−2.24086e16			−1.86091			−0.930454	+	0.366410i	$0.880587\pi$
$840$	−1.55942e15	−	6.14668e15i	−0.128655	−	0.507112i
$841$	1.21971e16			0.999720
$842$	−3.86935e14	+	1.60785e16i	−0.0315080	+	1.30927i
$843$	−4.69733e15	−	1.41443e16i	−0.380013	−	1.14427i
$844$	1.09368e14	−	2.27100e15i	0.00879037	−	0.182530i
$845$			5.91445e15i			0.472283i
$846$	−2.23052e15	−	3.14281e15i	−0.176958	−	0.249334i
$847$		−	8.88505e15i		−	0.700327i
$848$	−1.97338e15	+	2.04409e16i	−0.154537	+	1.60074i
$849$	−2.89997e15	−	8.73221e15i	−0.225632	−	0.679410i
$850$	7.60355e15	+	1.82982e14i	0.587777	+	0.0141450i
$851$	1.92793e16			1.48074
$852$	−1.10048e16	+	3.07554e15i	−0.839778	+	0.234695i
$853$	8.03055e15			0.608872			0.304436	−	0.952533i	$-0.401532\pi$
$853$	8.03055e15			0.608872			0.304436	+	0.952533i	$0.401532\pi$
$854$	−3.05286e15	−	7.34680e13i	−0.229979	−	0.00553452i
$855$	−8.91610e15	+	6.65620e15i	−0.667362	+	0.498210i
$856$	−1.69433e14	+	2.34323e15i	−0.0126006	+	0.174264i
$857$			5.77487e15i			0.426725i	0.976973	+	0.213362i	$0.0684415\pi$
$857$			5.77487e15i			0.426725i	−0.976973	+	0.213362i	$0.931559\pi$
$858$	−2.41414e15	−	7.89985e15i	−0.177248	−	0.580015i
$859$		−	2.20254e16i		−	1.60680i	−0.595440	−	0.803400i	$-0.703022\pi$
$859$		−	2.20254e16i		−	1.60680i	0.595440	−	0.803400i	$-0.296978\pi$
$860$	−9.57330e15	−	4.61036e14i	−0.693937	−	0.0334190i
$861$	−2.85155e15	+	9.47001e14i	−0.205383	+	0.0682077i
$862$	1.55503e13	−	6.46170e14i	0.00111288	−	0.0462442i
$863$	1.60087e16			1.13841			0.569203	−	0.822197i	$-0.307252\pi$
$863$	1.60087e16			1.13841			0.569203	+	0.822197i	$0.307252\pi$
$864$	−1.05537e16	−	9.42904e15i	−0.745722	−	0.666257i
$865$	5.91152e15			0.415059
$866$	−1.06803e14	+	4.43805e15i	−0.00745135	+	0.309631i
$867$	2.39072e15	−	7.93960e14i	0.165739	−	0.0550420i
$868$	1.93595e16	+	9.32326e14i	1.33363	+	0.0642258i
$869$		−	2.31166e15i		−	0.158240i
$870$	−4.27398e13	−	1.39859e14i	−0.00290721	−	0.00951335i
$871$			1.02553e16i			0.693187i
$872$	−2.47017e14	+	3.41619e15i	−0.0165915	+	0.229457i
$873$	4.67734e15	−	3.49180e15i	0.312191	−	0.233062i
$874$	−2.74702e16	−	6.61079e14i	−1.82200	−	0.0438471i
$875$	−1.30747e16			−0.861761
$876$	2.49093e16	−	6.96145e15i	1.63151	−	0.455960i
$877$	1.83813e16			1.19641			0.598203	−	0.801344i	$-0.295882\pi$
$877$	1.83813e16			1.19641			0.598203	+	0.801344i	$0.295882\pi$
$878$	−3.24200e15	−	7.80196e13i	−0.209697	−	0.00504643i
$879$	−1.19730e15	−	3.60524e15i	−0.0769600	−	0.231737i
$880$	−1.19725e15	+	1.24014e16i	−0.0764766	+	0.792168i
$881$		−	1.06343e16i		−	0.675059i	−0.941315	−	0.337529i	$-0.890409\pi$
$881$		−	1.06343e16i		−	0.675059i	0.941315	−	0.337529i	$-0.109591\pi$
$882$	−2.05726e15	−	2.89869e15i	−0.129781	−	0.182862i
$883$			2.50986e16i			1.57350i	0.617273	+	0.786749i	$0.288237\pi$
$883$			2.50986e16i			1.57350i	−0.617273	+	0.786749i	$0.711763\pi$
$884$	−3.17510e14	+	6.59302e15i	−0.0197820	+	0.410769i
$885$	2.07983e15	+	6.26266e15i	0.128778	+	0.387767i
$886$	3.31839e14	−	1.37891e16i	0.0204194	−	0.848498i
$887$	−8.10030e15			−0.495360			−0.247680	−	0.968842i	$-0.579668\pi$
$887$	−8.10030e15			−0.495360			−0.247680	+	0.968842i	$0.579668\pi$
$888$	4.60912e15	+	1.81676e16i	0.280122	+	1.10414i
$889$	−1.36243e16			−0.822912
$890$	1.75212e14	−	7.28067e15i	0.0105176	−	0.437045i
$891$	−6.38396e15	+	2.15317e16i	−0.380858	+	1.28455i
$892$	9.53520e14	−	1.97996e16i	0.0565357	−	1.17395i
$893$		−	7.27464e15i		−	0.428675i
$894$	−1.51179e16	+	4.61992e15i	−0.885390	+	0.270569i
$895$			1.43807e16i			0.837051i
$896$	1.50096e16	+	2.55217e15i	0.868312	+	0.147644i
$897$	−9.71243e15	+	3.22550e15i	−0.558431	+	0.185455i
$898$	1.85215e15	+	4.45724e13i	0.105841	+	0.00254710i
$899$	4.46981e14			0.0253870
$900$	−9.50601e15	+	6.40840e15i	−0.536617	+	0.361756i
$901$	−2.60402e16			−1.46103
$902$	5.90167e15	+	1.42025e14i	0.329108	+	0.00792009i
$903$	1.76388e16	−	5.85784e15i	0.977654	−	0.324679i
$904$	1.65226e16	+	1.19471e15i	0.910233	+	0.0658168i
$905$		−	1.27450e16i		−	0.697870i
$906$	2.09191e16	−	6.39273e15i	1.13851	−	0.347921i
$907$			1.27721e16i			0.690913i	0.938435	+	0.345457i	$0.112276\pi$
$907$			1.27721e16i			0.690913i	−0.938435	+	0.345457i	$0.887724\pi$
$908$	2.98821e16	+	1.43908e15i	1.60671	+	0.0773769i
$909$	1.41028e16	+	1.88910e16i	0.753711	+	1.00961i
$910$	1.07256e14	−	4.45687e15i	0.00569762	−	0.236757i
$911$	1.59406e16			0.841692			0.420846	−	0.907132i	$-0.361733\pi$
$911$	1.59406e16			0.841692			0.420846	+	0.907132i	$0.361733\pi$
$912$	−5.94436e15	−	2.60441e16i	−0.311985	−	1.36690i
$913$	−2.17910e15			−0.113681
$914$	2.33750e14	−	9.71316e15i	0.0121213	−	0.503682i
$915$	−9.48639e14	−	2.85648e15i	−0.0488973	−	0.147237i
$916$	−4.02922e15	−	1.94041e14i	−0.206441	−	0.00994189i
$917$			1.33657e16i			0.680709i
$918$	1.06150e16	−	1.44694e16i	0.537387	−	0.732513i
$919$			1.53167e15i			0.0770778i	0.999257	+	0.0385389i	$0.0122703\pi$
$919$			1.53167e15i			0.0770778i	−0.999257	+	0.0385389i	$0.987730\pi$
$920$	1.53955e16	+	1.11321e15i	0.770126	+	0.0556859i
$921$	9.88170e15	+	2.97551e16i	0.491364	+	1.47956i
$922$	3.00093e15	+	7.22182e13i	0.148332	+	0.00356966i
$923$	−8.03309e15			−0.394706
$924$	−6.50304e15	−	2.32690e16i	−0.317629	−	1.13653i
$925$	1.51833e16			0.737202
$926$	−2.53194e16	−	6.09318e14i	−1.22206	−	0.0294092i
$927$	1.30221e16	+	1.74433e16i	0.624801	+	0.836933i
$928$	3.48578e14	+	4.21385e13i	0.0166259	+	0.00200986i
$929$		−	2.52232e16i		−	1.19595i	−0.801514	−	0.597976i	$-0.795972\pi$
$929$		−	2.52232e16i		−	1.19595i	0.801514	−	0.597976i	$-0.204028\pi$
$930$	5.58305e15	+	1.82696e16i	0.263157	+	0.861137i
$931$		−	6.70956e15i		−	0.314392i
$932$	−2.96442e13	+	6.15554e14i	−0.00138087	+	0.0286734i
$933$	−1.55994e15	+	5.18058e14i	−0.0722370	+	0.0239899i
$934$	5.47626e14	−	2.27558e16i	0.0252102	−	1.04757i
$935$	−1.57986e16			−0.723026
$936$	−5.36145e15	−	8.38122e15i	−0.243930	−	0.381320i
$937$	−1.24623e16			−0.563679			−0.281840	−	0.959462i	$-0.590945\pi$
$937$	−1.24623e16			−0.563679			−0.281840	+	0.959462i	$0.590945\pi$
$938$	−7.21636e14	+	2.99866e16i	−0.0324491	+	1.34838i
$939$	−2.05311e16	+	6.81839e15i	−0.917807	+	0.304804i
$940$	−1.96571e14	+	4.08176e15i	−0.00873609	+	0.181403i
$941$		−	2.79391e16i		−	1.23444i	−0.786791	−	0.617220i	$-0.788259\pi$
$941$		−	2.79391e16i		−	1.23444i	0.786791	−	0.617220i	$-0.211741\pi$
$942$	3.45968e14	+	1.13212e15i	0.0151969	+	0.0497293i
$943$		−	7.31377e15i		−	0.319394i
$944$	−1.57702e16	−	1.52246e15i	−0.684684	−	0.0661000i
$945$	−6.93232e15	+	9.94244e15i	−0.299229	+	0.429159i
$946$	−3.65058e16	−	8.78523e14i	−1.56661	−	0.0377009i
$947$	−1.21950e15			−0.0520303			−0.0260152	−	0.999662i	$-0.508282\pi$
$947$	−1.21950e15			−0.0520303			−0.0260152	+	0.999662i	$0.508282\pi$
$948$	−7.49414e14	−	2.68153e15i	−0.0317889	−	0.113746i
$949$	1.81828e16			0.766827
$950$	−2.16340e16	−	5.20628e14i	−0.907102	−	0.0218297i
$951$	−9.19781e15	−	2.76959e16i	−0.383435	−	1.15457i
$952$	−1.39233e15	+	1.92556e16i	−0.0577083	+	0.798094i
$953$			3.83011e14i			0.0157834i	0.999969	+	0.00789170i	$0.00251203\pi$
$953$			3.83011e14i			0.0157834i	−0.999969	+	0.00789170i	$0.997488\pi$
$954$	3.20089e16	−	2.27174e16i	1.31146	−	0.930771i
$955$		−	1.64674e16i		−	0.670820i
$956$	−2.34661e15	−	1.13009e14i	−0.0950437	−	0.00457716i
$957$	−1.75610e14	−	5.28787e14i	−0.00707188	−	0.0212944i
$958$	−1.10561e14	+	4.59421e15i	−0.00442682	+	0.183950i
$959$	8.10953e15			0.322844
$960$	2.63160e15	+	1.47738e16i	0.104166	+	0.584792i
$961$	−3.29802e16			−1.29800
$962$	−3.17013e14	+	1.31730e16i	−0.0124055	+	0.515493i
$963$	3.59830e15	−	2.68626e15i	0.140008	−	0.104521i
$964$	−1.72535e16	−	8.30905e14i	−0.667505	−	0.0321460i
$965$		−	1.41976e16i		−	0.546152i
$966$	−2.86261e16	+	8.74792e15i	−1.09493	+	0.334604i
$967$			1.86204e16i			0.708180i	0.935211	+	0.354090i	$0.115209\pi$
$967$			1.86204e16i			0.708180i	−0.935211	+	0.354090i	$0.884791\pi$
$968$	−1.51636e15	+	2.09710e16i	−0.0573439	+	0.793056i
$969$	3.21477e16	−	1.06763e16i	1.20884	−	0.401457i
$970$	−6.18746e15	−	1.48903e14i	−0.231349	−	0.00556748i
$971$	−2.43169e16			−0.904070			−0.452035	−	0.892000i	$-0.649302\pi$
$971$	−2.43169e16			−0.904070			−0.452035	+	0.892000i	$0.649302\pi$
$972$	−4.25067e14	+	2.70465e16i	−0.0157142	+	0.999877i
$973$	−3.42650e15			−0.125959
$974$	1.50489e16	+	3.62157e14i	0.550086	+	0.0132380i
$975$	−7.64895e15	+	2.54022e15i	−0.278020	+	0.0923307i
$976$	7.19298e15	+	6.94417e14i	0.259977	+	0.0250984i
$977$			4.43473e15i			0.159385i	0.996820	+	0.0796924i	$0.0253938\pi$
$977$			4.43473e15i			0.159385i	−0.996820	+	0.0796924i	$0.974606\pi$
$978$	2.10405e16	−	6.42983e15i	0.751956	−	0.229792i
$979$		−	2.77473e16i		−	0.986087i
$980$	−1.81302e14	+	3.76470e15i	−0.00640707	+	0.133041i
$981$	5.24596e15	−	3.91630e15i	0.184351	−	0.137625i
$982$	−1.24243e15	+	5.16273e16i	−0.0434167	+	1.80412i
$983$	2.74166e16			0.952728			0.476364	−	0.879248i	$-0.341955\pi$
$983$	2.74166e16			0.952728			0.476364	+	0.879248i	$0.341955\pi$
$984$	6.89200e15	−	1.74850e15i	0.238162	−	0.0604218i
$985$	1.62722e16			0.559174
$986$	−1.07114e13	+	4.45098e14i	−0.000366036	+	0.0152101i
$987$	−2.49760e15	−	7.52062e15i	−0.0848748	−	0.255570i
$988$	9.03393e14	−	1.87588e16i	0.0305291	−	0.633929i
$989$			4.52406e16i			1.52037i
$990$	1.94198e16	−	1.37826e16i	0.649009	−	0.460615i
$991$		−	1.32543e16i		−	0.440505i	−0.975443	−	0.220253i	$-0.929312\pi$
$991$		−	1.32543e16i		−	0.440505i	0.975443	−	0.220253i	$-0.0706882\pi$
$992$	−4.55343e16	−	5.50451e15i	−1.50496	−	0.181930i
$993$	4.48423e15	+	1.35026e16i	0.147390	+	0.443810i
$994$	−2.34887e16	−	5.65263e14i	−0.767775	−	0.0184767i
$995$	−1.73668e15			−0.0564536
$996$	−2.52776e15	+	7.06439e14i	−0.0817165	+	0.0228375i
$997$	−1.06442e16			−0.342208			−0.171104	−	0.985253i	$-0.554733\pi$
$997$	−1.06442e16			−0.342208			−0.171104	+	0.985253i	$0.554733\pi$
$998$	2.13126e16	+	5.12894e14i	0.681425	+	0.0163987i
$999$	2.04896e16	−	2.93866e16i	0.651515	−	0.934413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.12.b.a.11.11	yes	20
3.2	odd	2	inner	12.12.b.a.11.10	yes	20
4.3	odd	2	inner	12.12.b.a.11.9	✓	20
8.3	odd	2		192.12.c.d.191.19		20
8.5	even	2		192.12.c.d.191.2		20
12.11	even	2	inner	12.12.b.a.11.12	yes	20
24.5	odd	2		192.12.c.d.191.20		20
24.11	even	2		192.12.c.d.191.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.12.b.a.11.9	✓	20	4.3	odd	2	inner
12.12.b.a.11.10	yes	20	3.2	odd	2	inner
12.12.b.a.11.11	yes	20	1.1	even	1	trivial
12.12.b.a.11.12	yes	20	12.11	even	2	inner
192.12.c.d.191.1		20	24.11	even	2
192.12.c.d.191.2		20	8.5	even	2
192.12.c.d.191.19		20	8.3	odd	2
192.12.c.d.191.20		20	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(1.08876 - 45.2417i) q^{2} +(399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} -4150.68i q^{5} +(-5566.58 - 18215.7i) q^{6} -39165.5i q^{7} +(-6684.15 + 92440.6i) q^{8} +(141953. - 105973. i) q^{9} +O(q^{10})\)	\(q+(1.08876 - 45.2417i) q^{2} +(399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} -4150.68i q^{5} +(-5566.58 - 18215.7i) q^{6} -39165.5i q^{7} +(-6684.15 + 92440.6i) q^{8} +(141953. - 105973. i) q^{9} +(-187784. - 4519.08i) q^{10} -715661. q^{11} +(-830169. + 232009. i) q^{12} -605992. q^{13} +(-1.77192e6 - 42641.7i) q^{14} +(-550602. - 1.65794e6i) q^{15} +(4.17489e6 + 403048. i) q^{16} +5.31852e6i q^{17} +(-4.63986e6 - 6.53759e6i) q^{18} -1.51325e7i q^{19} +(-408902. + 8.49076e6i) q^{20} +(-5.19544e6 - 1.56442e7i) q^{21} +(-779180. + 3.23777e7i) q^{22} +4.01248e7 q^{23} +(9.59264e6 + 3.78109e7i) q^{24} +3.16000e7 q^{25} +(-659777. + 2.74161e7i) q^{26} +(4.26437e7 - 6.11603e7i) q^{27} +(-3.85837e6 + 8.01182e7i) q^{28} +1.84980e6i q^{29} +(-7.56074e7 + 2.31051e7i) q^{30} -2.41637e8i q^{31} +(2.27800e7 - 1.88441e8i) q^{32} +(-2.85862e8 + 9.49348e7i) q^{33} +(2.40619e8 + 5.79057e6i) q^{34} -1.62564e8 q^{35} +(-3.00824e8 + 2.02798e8i) q^{36} +4.80485e8 q^{37} +(-6.84620e8 - 1.64756e7i) q^{38} +(-2.42056e8 + 8.03868e7i) q^{39} +(3.83691e8 + 2.77438e7i) q^{40} -1.82276e8i q^{41} +(-7.13426e8 + 2.18018e8i) q^{42} +1.12750e9i q^{43} +(1.46398e9 + 7.05029e7i) q^{44} +(-4.39862e8 - 5.89203e8i) q^{45} +(4.36861e7 - 1.81531e9i) q^{46} +4.80730e8 q^{47} +(1.72107e9 - 3.92821e8i) q^{48} +4.43388e8 q^{49} +(3.44046e7 - 1.42964e9i) q^{50} +(7.05519e8 + 2.12442e9i) q^{51} +(1.23963e9 + 5.96989e7i) q^{52} +4.89614e9i q^{53} +(-2.72057e9 - 1.99586e9i) q^{54} +2.97048e9i q^{55} +(3.62048e9 + 2.61788e8i) q^{56} +(-2.00737e9 - 6.04448e9i) q^{57} +(8.36882e7 + 2.01398e6i) q^{58} -3.77738e9 q^{59} +(9.62996e8 + 3.44577e9i) q^{60} +1.72291e9 q^{61} +(-1.09321e10 - 2.63084e8i) q^{62} +(-4.15050e9 - 5.55967e9i) q^{63} +(-8.50058e9 - 1.23577e9i) q^{64} +2.51528e9i q^{65} +(3.98378e9 + 1.30362e10i) q^{66} -1.69232e10i q^{67} +(5.23951e8 - 1.08797e10i) q^{68} +(1.60273e10 - 5.32268e9i) q^{69} +(-1.76992e8 + 7.35466e9i) q^{70} +1.32561e10 q^{71} +(8.84740e9 + 1.38306e10i) q^{72} -3.00051e10 q^{73} +(5.23131e8 - 2.17380e10i) q^{74} +(1.26222e10 - 4.19184e9i) q^{75} +(-1.49077e9 + 3.09555e10i) q^{76} +2.80292e10i q^{77} +(3.37330e9 + 1.10385e10i) q^{78} +3.23010e9i q^{79} +(1.67292e9 - 1.73287e10i) q^{80} +(8.92037e9 - 3.00865e10i) q^{81} +(-8.24646e9 - 1.98454e8i) q^{82} +3.04488e9 q^{83} +(9.08676e9 + 3.25140e10i) q^{84} +2.20755e10 q^{85} +(5.10099e10 + 1.22757e9i) q^{86} +(2.45382e8 + 7.38880e8i) q^{87} +(4.78359e9 - 6.61561e10i) q^{88} +3.87715e10i q^{89} +(-2.71355e10 + 1.92586e10i) q^{90} +2.37340e10i q^{91} +(-8.20804e10 - 3.95287e9i) q^{92} +(-3.20540e10 - 9.65190e10i) q^{93} +(5.23397e8 - 2.17490e10i) q^{94} -6.28102e10 q^{95} +(-1.58981e10 - 7.82920e10i) q^{96} +3.29498e10 q^{97} +(4.82741e8 - 2.00596e10i) q^{98} +(-1.01590e11 + 7.58410e10i) 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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