LMFDB - Embedded newform 12.12.b.a.11.19

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			11.19
Root			$22.4409 - 2.89952i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.12.b.a.11.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(44.8817 - 5.79904i) q^{2} +(353.249 + 228.828i) q^{3} +(1980.74 - 520.542i) q^{4} -12652.7i q^{5} +(17181.4 + 8221.72i) q^{6} +32182.6i q^{7} +(85880.5 - 34849.2i) q^{8} +(72422.0 + 161667. i) q^{9} +O(q^{10})$	\(q+(44.8817 - 5.79904i) q^{2} +(353.249 + 228.828i) q^{3} +(1980.74 - 520.542i) q^{4} -12652.7i q^{5} +(17181.4 + 8221.72i) q^{6} +32182.6i q^{7} +(85880.5 - 34849.2i) q^{8} +(72422.0 + 161667. i) q^{9} +(-73373.6 - 567877. i) q^{10} +250656. q^{11} +(818809. + 269370. i) q^{12} -976876. q^{13} +(186628. + 1.44441e6i) q^{14} +(2.89530e6 - 4.46956e6i) q^{15} +(3.65238e6 - 2.06212e6i) q^{16} +2.81662e6i q^{17} +(4.18794e6 + 6.83590e6i) q^{18} +6.17831e6i q^{19} +(-6.58627e6 - 2.50618e7i) q^{20} +(-7.36430e6 + 1.13685e7i) q^{21} +(1.12499e7 - 1.45356e6i) q^{22} -3.69826e7 q^{23} +(3.83117e7 + 7.34148e6i) q^{24} -1.11263e8 q^{25} +(-4.38439e7 + 5.66494e6i) q^{26} +(-1.14110e7 + 7.36807e7i) q^{27} +(1.67524e7 + 6.37455e7i) q^{28} +9.70893e7i q^{29} +(1.04027e8 - 2.17392e8i) q^{30} -2.18413e8i q^{31} +(1.51967e8 - 1.13732e8i) q^{32} +(8.85438e7 + 5.73572e7i) q^{33} +(1.63337e7 + 1.26415e8i) q^{34} +4.07198e8 q^{35} +(2.27604e8 + 2.82521e8i) q^{36} -4.00660e8 q^{37} +(3.58283e7 + 2.77293e8i) q^{38} +(-3.45080e8 - 2.23537e8i) q^{39} +(-4.40938e8 - 1.08662e9i) q^{40} -3.38841e7i q^{41} +(-2.64596e8 + 5.52942e8i) q^{42} +9.95581e8i q^{43} +(4.96485e8 - 1.30477e8i) q^{44} +(2.04552e9 - 9.16336e8i) q^{45} +(-1.65984e9 + 2.14464e8i) q^{46} -4.43757e8 q^{47} +(1.76207e9 + 1.07328e8i) q^{48} +9.41607e8 q^{49} +(-4.99370e9 + 6.45221e8i) q^{50} +(-6.44524e8 + 9.94968e8i) q^{51} +(-1.93494e9 + 5.08505e8i) q^{52} -3.45255e9i q^{53} +(-8.48666e7 + 3.37309e9i) q^{54} -3.17148e9i q^{55} +(1.12154e9 + 2.76386e9i) q^{56} +(-1.41377e9 + 2.18248e9i) q^{57} +(5.63025e8 + 4.35754e9i) q^{58} +5.47057e9 q^{59} +(3.40826e9 - 1.03602e10i) q^{60} +2.88673e9 q^{61} +(-1.26658e9 - 9.80275e9i) q^{62} +(-5.20285e9 + 2.33073e9i) q^{63} +(6.16100e9 - 5.98574e9i) q^{64} +1.23601e10i q^{65} +(4.30662e9 + 2.06082e9i) q^{66} +1.87169e9i q^{67} +(1.46617e9 + 5.57901e9i) q^{68} +(-1.30641e10 - 8.46268e9i) q^{69} +(1.82757e10 - 2.36135e9i) q^{70} +2.17623e10 q^{71} +(1.18536e10 + 1.13602e10i) q^{72} -1.38840e10 q^{73} +(-1.79823e10 + 2.32344e9i) q^{74} +(-3.93036e10 - 2.54602e10i) q^{75} +(3.21607e9 + 1.22376e10i) q^{76} +8.06676e9i q^{77} +(-1.67841e10 - 8.03160e9i) q^{78} +2.31856e10i q^{79} +(-2.60914e10 - 4.62125e10i) q^{80} +(-2.08912e10 + 2.34165e10i) q^{81} +(-1.96495e8 - 1.52078e9i) q^{82} +1.51750e10 q^{83} +(-8.66902e9 + 2.63514e10i) q^{84} +3.56380e10 q^{85} +(5.77341e9 + 4.46834e10i) q^{86} +(-2.22168e10 + 3.42967e10i) q^{87} +(2.15265e10 - 8.73516e9i) q^{88} -3.51186e10i q^{89} +(8.64928e10 - 5.29888e10i) q^{90} -3.14384e10i q^{91} +(-7.32530e10 + 1.92510e10i) q^{92} +(4.99791e10 - 7.71540e10i) q^{93} +(-1.99166e10 + 2.57336e9i) q^{94} +7.81725e10 q^{95} +(7.97071e10 - 5.40124e9i) q^{96} +3.62332e10 q^{97} +(4.22609e10 - 5.46041e9i) q^{98} +(1.81530e10 + 4.05227e10i) 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 $

$2$	44.8817	−	5.79904i	0.991756	−	0.128142i
$2$	44.8817	−	5.79904i	0.991756	−	0.128142i
$3$	353.249	+	228.828i	0.839293	+	0.543680i
$3$	353.249	+	228.828i	0.839293	+	0.543680i
$4$	1980.74	−	520.542i	0.967159	−	0.254171i
$5$		−	12652.7i		−	1.81071i	−0.424654	−	0.905356i	$-0.639604\pi$
$5$		−	12652.7i		−	1.81071i	0.424654	−	0.905356i	$-0.360396\pi$
$6$	17181.4	+	8221.72i	0.902042	+	0.431649i
$7$			32182.6i			0.723739i	0.932229	+	0.361870i	$0.117861\pi$
$7$			32182.6i			0.723739i	−0.932229	+	0.361870i	$0.882139\pi$
$8$	85880.5	−	34849.2i	0.926616	−	0.376009i
$9$	72422.0	+	161667.i	0.408825	+	0.912613i
$10$	−73373.6	−	567877.i	−0.232028	−	1.79578i
$11$	250656.			0.469265			0.234632	−	0.972084i	$-0.424611\pi$
$11$	250656.			0.469265			0.234632	+	0.972084i	$0.424611\pi$
$12$	818809.	+	269370.i	0.949917	+	0.312501i
$13$	−976876.			−0.729711			−0.364856	−	0.931064i	$-0.618882\pi$
$13$	−976876.			−0.729711			−0.364856	+	0.931064i	$0.618882\pi$
$14$	186628.	+	1.44441e6i	0.0927412	+	0.717772i
$15$	2.89530e6	−	4.46956e6i	0.984447	−	1.51972i
$16$	3.65238e6	−	2.06212e6i	0.870794	−	0.491647i
$17$			2.81662e6i			0.481127i	0.970633	+	0.240563i	$0.0773322\pi$
$17$			2.81662e6i			0.481127i	−0.970633	+	0.240563i	$0.922668\pi$
$18$	4.18794e6	+	6.83590e6i	0.522398	+	0.852702i
$19$			6.17831e6i			0.572434i	0.958165	+	0.286217i	$0.0923977\pi$
$19$			6.17831e6i			0.572434i	−0.958165	+	0.286217i	$0.907602\pi$
$20$	−6.58627e6	−	2.50618e7i	−0.460230	−	1.75125i
$21$	−7.36430e6	+	1.13685e7i	−0.393482	+	0.607429i
$22$	1.12499e7	−	1.45356e6i	0.465396	−	0.0601324i
$23$	−3.69826e7			−1.19810			−0.599052	−	0.800710i	$-0.704456\pi$
$23$	−3.69826e7			−1.19810			−0.599052	+	0.800710i	$0.704456\pi$
$24$	3.83117e7	+	7.34148e6i	0.982131	+	0.188201i
$25$	−1.11263e8			−2.27867
$26$	−4.38439e7	+	5.66494e6i	−0.723696	+	0.0935065i
$27$	−1.14110e7	+	7.36807e7i	−0.153046	+	0.988219i
$28$	1.67524e7	+	6.37455e7i	0.183953	+	0.699971i
$29$			9.70893e7i			0.878987i	0.898246	+	0.439494i	$0.144842\pi$
$29$			9.70893e7i			0.878987i	−0.898246	+	0.439494i	$0.855158\pi$
$30$	1.04027e8	−	2.17392e8i	0.781592	−	1.63334i
$31$		−	2.18413e8i		−	1.37022i	−0.728442	−	0.685108i	$-0.759755\pi$
$31$		−	2.18413e8i		−	1.37022i	0.728442	−	0.685108i	$-0.240245\pi$
$32$	1.51967e8	−	1.13732e8i	0.800615	−	0.599179i
$33$	8.85438e7	+	5.73572e7i	0.393851	+	0.255130i
$34$	1.63337e7	+	1.26415e8i	0.0616525	+	0.477160i
$35$	4.07198e8			1.31048
$36$	2.27604e8	+	2.82521e8i	0.627358	+	0.778731i
$37$	−4.00660e8			−0.949876			−0.474938	−	0.880019i	$-0.657530\pi$
$37$	−4.00660e8			−0.949876			−0.474938	+	0.880019i	$0.657530\pi$
$38$	3.58283e7	+	2.77293e8i	0.0733527	+	0.567714i
$39$	−3.45080e8	−	2.23537e8i	−0.612441	−	0.396729i
$40$	−4.40938e8	−	1.08662e9i	−0.680843	−	1.67783i
$41$		−	3.38841e7i		−	0.0456756i	−0.999739	−	0.0228378i	$-0.992730\pi$
$41$		−	3.38841e7i		−	0.0456756i	0.999739	−	0.0228378i	$-0.00727013\pi$
$42$	−2.64596e8	+	5.52942e8i	−0.312401	+	0.652843i
$43$			9.95581e8i			1.03276i	0.856359	+	0.516381i	$0.172721\pi$
$43$			9.95581e8i			1.03276i	−0.856359	+	0.516381i	$0.827279\pi$
$44$	4.96485e8	−	1.30477e8i	0.453854	−	0.119273i
$45$	2.04552e9	−	9.16336e8i	1.65248	−	0.740263i
$46$	−1.65984e9	+	2.14464e8i	−1.18823	+	0.153527i
$47$	−4.43757e8			−0.282233			−0.141116	−	0.989993i	$-0.545069\pi$
$47$	−4.43757e8			−0.282233			−0.141116	+	0.989993i	$0.545069\pi$
$48$	1.76207e9	+	1.07328e8i	0.998150	+	0.0607974i
$49$	9.41607e8			0.476202
$50$	−4.99370e9	+	6.45221e8i	−2.25989	+	0.291993i
$51$	−6.44524e8	+	9.94968e8i	−0.261579	+	0.403806i
$52$	−1.93494e9	+	5.08505e8i	−0.705747	+	0.185471i
$53$		−	3.45255e9i		−	1.13403i	−0.823709	−	0.567013i	$-0.808099\pi$
$53$		−	3.45255e9i		−	1.13403i	0.823709	−	0.567013i	$-0.191901\pi$
$54$	−8.48666e7	+	3.37309e9i	−0.0251519	+	0.999684i
$55$		−	3.17148e9i		−	0.849703i
$56$	1.12154e9	+	2.76386e9i	0.272132	+	0.670628i
$57$	−1.41377e9	+	2.18248e9i	−0.311221	+	0.480439i
$58$	5.63025e8	+	4.35754e9i	0.112635	+	0.871741i
$59$	5.47057e9			0.996200			0.498100	−	0.867120i	$-0.334031\pi$
$59$	5.47057e9			0.996200			0.498100	+	0.867120i	$0.334031\pi$
$60$	3.40826e9	−	1.03602e10i	0.565850	−	1.72003i
$61$	2.88673e9			0.437615			0.218808	−	0.975768i	$-0.429783\pi$
$61$	2.88673e9			0.437615			0.218808	+	0.975768i	$0.429783\pi$
$62$	−1.26658e9	−	9.80275e9i	−0.175582	−	1.35892i
$63$	−5.20285e9	+	2.33073e9i	−0.660494	+	0.295882i
$64$	6.16100e9	−	5.98574e9i	0.717235	−	0.696832i
$65$			1.23601e10i			1.32130i
$66$	4.30662e9	+	2.06082e9i	0.423296	+	0.202558i
$67$			1.87169e9i			0.169364i	0.996408	+	0.0846822i	$0.0269875\pi$
$67$			1.87169e9i			0.169364i	−0.996408	+	0.0846822i	$0.973013\pi$
$68$	1.46617e9	+	5.57901e9i	0.122288	+	0.465326i
$69$	−1.30641e10	−	8.46268e9i	−1.00556	−	0.651385i
$70$	1.82757e10	−	2.36135e9i	1.29968	−	0.167928i
$71$	2.17623e10			1.43147			0.715737	−	0.698370i	$-0.246091\pi$
$71$	2.17623e10			1.43147			0.715737	+	0.698370i	$0.246091\pi$
$72$	1.18536e10	+	1.13602e10i	0.721974	+	0.691920i
$73$	−1.38840e10			−0.783859			−0.391929	−	0.919995i	$-0.628192\pi$
$73$	−1.38840e10			−0.783859			−0.391929	+	0.919995i	$0.628192\pi$
$74$	−1.79823e10	+	2.32344e9i	−0.942045	+	0.121719i
$75$	−3.93036e10	−	2.54602e10i	−1.91248	−	1.23887i
$76$	3.21607e9	+	1.22376e10i	0.145496	+	0.553634i
$77$			8.06676e9i			0.339625i
$78$	−1.67841e10	−	8.03160e9i	−0.658230	−	0.314979i
$79$			2.31856e10i			0.847752i	0.905720	+	0.423876i	$0.139331\pi$
$79$			2.31856e10i			0.847752i	−0.905720	+	0.423876i	$0.860669\pi$
$80$	−2.60914e10	−	4.62125e10i	−0.890231	−	1.57676i
$81$	−2.08912e10	+	2.34165e10i	−0.665725	+	0.746197i
$82$	−1.96495e8	−	1.52078e9i	−0.00585295	−	0.0452990i
$83$	1.51750e10			0.422863			0.211432	−	0.977393i	$-0.432187\pi$
$83$	1.51750e10			0.422863			0.211432	+	0.977393i	$0.432187\pi$
$84$	−8.66902e9	+	2.63514e10i	−0.226169	+	0.687492i
$85$	3.56380e10			0.871182
$86$	5.77341e9	+	4.46834e10i	0.132340	+	1.02425i
$87$	−2.22168e10	+	3.42967e10i	−0.477888	+	0.737728i
$88$	2.15265e10	−	8.73516e9i	0.434828	−	0.176448i
$89$		−	3.51186e10i		−	0.666642i	−0.942813	−	0.333321i	$-0.891831\pi$
$89$		−	3.51186e10i		−	0.666642i	0.942813	−	0.333321i	$-0.108169\pi$
$90$	8.64928e10	−	5.29888e10i	1.54400	−	0.945912i
$91$		−	3.14384e10i		−	0.528121i
$92$	−7.32530e10	+	1.92510e10i	−1.15876	+	0.304523i
$93$	4.99791e10	−	7.71540e10i	0.744959	−	1.15001i
$94$	−1.99166e10	+	2.57336e9i	−0.279906	+	0.0361658i
$95$	7.81725e10			1.03651
$96$	7.97071e10	−	5.40124e9i	0.997712	−	0.0676086i
$97$	3.62332e10			0.428413			0.214206	−	0.976788i	$-0.431283\pi$
$97$	3.62332e10			0.428413			0.214206	+	0.976788i	$0.431283\pi$
$98$	4.22609e10	−	5.46041e9i	0.472276	−	0.0610214i
$99$	1.81530e10	+	4.05227e10i	0.191847	+	0.428257i
$100$	−2.20384e11	+	5.79172e10i	−2.20384	+	0.579172i
$101$			3.76323e10i			0.356281i	0.984005	+	0.178141i	$0.0570082\pi$
$101$			3.76323e10i			0.356281i	−0.984005	+	0.178141i	$0.942992\pi$
$102$	−2.31575e10	+	4.83935e10i	−0.207678	+	0.433997i
$103$		−	1.32326e11i		−	1.12471i	−0.826897	−	0.562353i	$-0.809896\pi$
$103$		−	1.32326e11i		−	1.12471i	0.826897	−	0.562353i	$-0.190104\pi$
$104$	−8.38947e10	+	3.40434e10i	−0.676162	+	0.274378i
$105$	1.43842e11	+	9.31785e10i	1.09988	+	0.712483i
$106$	−2.00215e10	−	1.54957e11i	−0.145316	−	1.12468i
$107$	2.01786e9			0.0139085			0.00695426	−	0.999976i	$-0.497786\pi$
$107$	2.01786e9			0.0139085			0.00695426	+	0.999976i	$0.497786\pi$
$108$	1.57517e10	+	1.51882e11i	0.103157	+	0.994665i
$109$	−1.27441e11			−0.793346			−0.396673	−	0.917960i	$-0.629835\pi$
$109$	−1.27441e11			−0.793346			−0.396673	+	0.917960i	$0.629835\pi$
$110$	−1.83915e10	−	1.42342e11i	−0.108882	−	0.842698i
$111$	−1.41533e11	−	9.16825e10i	−0.797224	−	0.516428i
$112$	6.63643e10	+	1.17543e11i	0.355824	+	0.630228i
$113$		−	2.20977e11i		−	1.12828i	−0.825681	−	0.564138i	$-0.809209\pi$
$113$		−	2.20977e11i		−	1.12828i	0.825681	−	0.564138i	$-0.190791\pi$
$114$	−5.07964e10	+	1.06152e11i	−0.247090	+	0.516359i
$115$			4.67931e11i			2.16942i
$116$	5.05390e10	+	1.92309e11i	0.223413	+	0.850121i
$117$	−7.07474e10	−	1.57928e11i	−0.298324	−	0.665944i
$118$	2.45529e11	−	3.17240e10i	0.987987	−	0.127655i
$119$	−9.06463e10			−0.348210
$120$	9.28897e10	−	4.84747e11i	0.340778	−	1.77835i
$121$	−2.22483e11			−0.779791
$122$	1.29562e11	−	1.67403e10i	0.434007	−	0.0560768i
$123$	7.75364e9	−	1.19695e10i	0.0248329	−	0.0383352i
$124$	−1.13693e11	−	4.32620e11i	−0.348269	−	1.32522i
$125$			7.89977e11i			2.31531i
$126$	−2.19997e11	+	1.34779e11i	−0.617134	+	0.378080i
$127$		−	4.64618e11i		−	1.24789i	−0.781469	−	0.623944i	$-0.785529\pi$
$127$		−	4.64618e11i		−	1.24789i	0.781469	−	0.623944i	$-0.214471\pi$
$128$	2.41805e11	−	3.04378e11i	0.622028	−	0.782995i
$129$	−2.27817e11	+	3.51688e11i	−0.561492	+	0.866789i
$130$	7.16770e10	+	5.54745e11i	0.169313	+	1.31040i
$131$	−2.19572e11			−0.497262			−0.248631	−	0.968598i	$-0.579981\pi$
$131$	−2.19572e11			−0.497262			−0.248631	+	0.968598i	$0.579981\pi$
$132$	2.05239e11	+	6.75191e10i	0.445763	+	0.146646i
$133$	−1.98834e11			−0.414292
$134$	1.08540e10	+	8.40046e10i	0.0217027	+	0.167968i
$135$	9.32262e11	+	1.44380e11i	1.78938	+	0.277122i
$136$	9.81571e10	+	2.41893e11i	0.180908	+	0.445820i
$137$		−	8.45778e11i		−	1.49725i	−0.662995	−	0.748624i	$-0.730715\pi$
$137$		−	8.45778e11i		−	1.49725i	0.662995	−	0.748624i	$-0.269285\pi$
$138$	−6.35413e11	−	3.04061e11i	−1.08074	−	0.517161i
$139$		−	7.50806e11i		−	1.22729i	−0.789583	−	0.613644i	$-0.789703\pi$
$139$		−	7.50806e11i		−	1.22729i	0.789583	−	0.613644i	$-0.210297\pi$
$140$	8.06554e11	−	2.11963e11i	1.26745	−	0.333086i
$141$	−1.56757e11	−	1.01544e11i	−0.236876	−	0.153444i
$142$	9.76729e11	−	1.26200e11i	1.41967	−	0.183432i
$143$	−2.44860e11			−0.342428
$144$	5.97888e11	+	4.41125e11i	0.804686	+	0.593701i
$145$	1.22844e12			1.59159
$146$	−6.23136e11	+	8.05136e10i	−0.777396	+	0.100445i
$147$	3.32621e11	+	2.15466e11i	0.399673	+	0.258901i
$148$	−7.93605e11	+	2.08560e11i	−0.918681	+	0.241431i
$149$			1.36627e11i			0.152410i	0.997092	+	0.0762049i	$0.0242803\pi$
$149$			1.36627e11i			0.152410i	−0.997092	+	0.0762049i	$0.975720\pi$
$150$	−1.91166e12	−	9.14777e11i	−2.05546	−	0.983588i
$151$			1.88094e12i			1.94985i	0.222535	+	0.974925i	$0.428567\pi$
$151$			1.88094e12i			1.94985i	−0.222535	+	0.974925i	$0.571433\pi$
$152$	2.15309e11	+	5.30597e11i	0.215240	+	0.530426i
$153$	−4.55354e11	+	2.03986e11i	−0.439083	+	0.196697i
$154$	4.67794e10	+	3.62050e11i	0.0435202	+	0.336825i
$155$	−2.76352e12			−2.48106
$156$	−7.99875e11	−	2.63141e11i	−0.693165	−	0.228036i
$157$	1.05160e12			0.879836			0.439918	−	0.898038i	$-0.355007\pi$
$157$	1.05160e12			0.879836			0.439918	+	0.898038i	$0.355007\pi$
$158$	1.34454e11	+	1.04061e12i	0.108632	+	0.840763i
$159$	7.90042e11	−	1.21961e12i	0.616547	−	0.951780i
$160$	−1.43902e12	−	1.92279e12i	−1.08494	−	1.44968i
$161$		−	1.19020e12i		−	0.867115i
$162$	−8.01839e11	+	1.17212e12i	−0.564618	+	0.825353i
$163$			8.25786e11i			0.562128i	0.959689	+	0.281064i	$0.0906874\pi$
$163$			8.25786e11i			0.562128i	−0.959689	+	0.281064i	$0.909313\pi$
$164$	−1.76381e10	−	6.71156e10i	−0.0116094	−	0.0441756i
$165$	7.25725e11	−	1.12032e12i	0.461966	−	0.713150i
$166$	6.81081e11	−	8.80005e10i	0.419377	−	0.0541864i
$167$	2.62256e12			1.56237			0.781186	−	0.624298i	$-0.214615\pi$
$167$	2.62256e12			1.56237			0.781186	+	0.624298i	$0.214615\pi$
$168$	−2.36268e11	+	1.23297e12i	−0.136208	+	0.710806i
$169$	−8.37873e11			−0.467521
$170$	1.59949e12	−	2.06666e11i	0.864000	−	0.111635i
$171$	−9.98827e11	+	4.47446e11i	−0.522410	+	0.234025i
$172$	5.18241e11	+	1.97199e12i	0.262498	+	0.998845i
$173$			2.60982e10i			0.0128043i	0.999980	+	0.00640216i	$0.00203788\pi$
$173$			2.60982e10i			0.0128043i	−0.999980	+	0.00640216i	$0.997962\pi$
$174$	−7.98241e11	+	1.66813e12i	−0.379414	+	0.792883i
$175$		−	3.58075e12i		−	1.64917i
$176$	9.15489e11	−	5.16882e11i	0.408633	−	0.230713i
$177$	1.93247e12	+	1.25182e12i	0.836103	+	0.541614i
$178$	−2.03654e11	−	1.57618e12i	−0.0854246	−	0.661146i
$179$	7.07847e11			0.287904			0.143952	−	0.989585i	$-0.454019\pi$
$179$	7.07847e11			0.287904			0.143952	+	0.989585i	$0.454019\pi$
$180$	3.57467e12	−	2.87981e12i	1.41006	−	1.13596i
$181$	−1.26031e12			−0.482221			−0.241110	−	0.970498i	$-0.577512\pi$
$181$	−1.26031e12			−0.482221			−0.241110	+	0.970498i	$0.577512\pi$
$182$	−1.82313e11	−	1.41101e12i	−0.0676743	−	0.523767i
$183$	1.01973e12	+	6.60567e11i	0.367287	+	0.237923i
$184$	−3.17609e12	+	1.28882e12i	−1.11018	+	0.450498i
$185$			5.06945e12i			1.71995i
$186$	1.79573e12	−	3.75264e12i	0.591452	−	1.23599i
$187$			7.06003e11i			0.225776i
$188$	−8.78968e11	+	2.30994e11i	−0.272964	+	0.0717353i
$189$	−2.37124e12	−	3.67234e11i	−0.715213	−	0.110765i
$190$	3.50852e12	−	4.53325e11i	1.02797	−	0.132820i
$191$	−1.33364e11			−0.0379626			−0.0189813	−	0.999820i	$-0.506042\pi$
$191$	−1.33364e11			−0.0379626			−0.0189813	+	0.999820i	$0.506042\pi$
$192$	3.54607e12	−	7.04641e11i	0.980823	−	0.194900i
$193$	−6.05081e12			−1.62648			−0.813240	−	0.581929i	$-0.802298\pi$
$193$	−6.05081e12			−1.62648			−0.813240	+	0.581929i	$0.802298\pi$
$194$	1.62621e12	−	2.10118e11i	0.424881	−	0.0548976i
$195$	−2.82835e12	+	4.36620e12i	−0.718362	+	1.10895i
$196$	1.86508e12	−	4.90146e11i	0.460563	−	0.121037i
$197$		−	4.22106e12i		−	1.01358i	−0.862070	−	0.506790i	$-0.830832\pi$
$197$		−	4.22106e12i		−	1.01358i	0.862070	−	0.506790i	$-0.169168\pi$
$198$	1.04973e12	+	1.71346e12i	0.245143	+	0.400143i
$199$		−	2.61366e12i		−	0.593687i	−0.954926	−	0.296844i	$-0.904066\pi$
$199$		−	2.61366e12i		−	0.593687i	0.954926	−	0.296844i	$-0.0959340\pi$
$200$	−9.55536e12	+	3.87744e12i	−2.11146	+	0.856802i
$201$	−4.28295e11	+	6.61171e11i	−0.0920800	+	0.142146i
$202$	2.18231e11	+	1.68900e12i	0.0456545	+	0.353344i
$203$	−3.12459e12			−0.636157
$204$	−7.58713e11	+	2.30628e12i	−0.150353	+	0.457031i
$205$	−4.28726e11			−0.0827053
$206$	−7.67360e11	−	5.93900e12i	−0.144122	−	1.11543i
$207$	−2.67836e12	−	5.97886e12i	−0.489814	−	1.09341i
$208$	−3.56792e12	+	2.01443e12i	−0.635429	+	0.358761i
$209$			1.54863e12i			0.268623i
$210$	6.99623e12	+	3.34787e12i	1.18211	+	0.565669i
$211$			9.02008e12i			1.48476i	0.669978	+	0.742381i	$0.266303\pi$
$211$			9.02008e12i			1.48476i	−0.669978	+	0.742381i	$0.733697\pi$
$212$	−1.79720e12	−	6.83862e12i	−0.288236	−	1.09678i
$213$	7.68749e12	+	4.97983e12i	1.20143	+	0.778263i
$214$	9.05652e10	−	1.17017e10i	0.0137939	−	0.00178226i
$215$	1.25968e13			1.87003
$216$	1.58774e12	+	6.72540e12i	0.229764	+	0.973246i
$217$	7.02910e12			0.991679
$218$	−5.71976e12	+	7.39034e11i	−0.786806	+	0.101661i
$219$	−4.90449e12	−	3.17705e12i	−0.657887	−	0.426168i
$220$	−1.65089e12	−	6.28188e12i	−0.215970	−	0.821798i
$221$		−	2.75149e12i		−	0.351084i
$222$	−6.88390e12	−	3.29412e12i	−0.856828	−	0.410013i
$223$		−	6.09863e12i		−	0.740552i	−0.928922	−	0.370276i	$-0.879263\pi$
$223$		−	6.09863e12i		−	0.740552i	0.928922	−	0.370276i	$-0.120737\pi$
$224$	3.66018e12	+	4.89069e12i	0.433649	+	0.579436i
$225$	−8.05792e12	−	1.79876e13i	−0.931578	−	2.07955i
$226$	−1.28145e12	−	9.91782e12i	−0.144579	−	1.11897i
$227$	−8.24431e10			−0.00907846			−0.00453923	−	0.999990i	$-0.501445\pi$
$227$	−8.24431e10			−0.00907846			−0.00453923	+	0.999990i	$0.501445\pi$
$228$	−1.66425e12	+	5.05886e12i	−0.178886	+	0.543765i
$229$	6.00729e12			0.630352			0.315176	−	0.949033i	$-0.397936\pi$
$229$	6.00729e12			0.630352			0.315176	+	0.949033i	$0.397936\pi$
$230$	2.71355e12	+	2.10016e13i	0.277993	+	2.15154i
$231$	−1.84590e12	+	2.84957e12i	−0.184647	+	0.285045i
$232$	3.38349e12	+	8.33808e12i	0.330507	+	0.814484i
$233$			6.70487e12i			0.639636i	0.947479	+	0.319818i	$0.103622\pi$
$233$			6.70487e12i			0.639636i	−0.947479	+	0.319818i	$0.896378\pi$
$234$	−4.09110e12	−	6.67783e12i	−0.381200	−	0.622226i
$235$			5.61474e12i			0.511042i
$236$	1.08358e13	−	2.84766e12i	0.963484	−	0.253205i
$237$	−5.30552e12	+	8.19027e12i	−0.460906	+	0.711512i
$238$	−4.06836e12	+	5.25661e11i	−0.345340	+	0.0446203i
$239$	2.15848e13			1.79044			0.895222	−	0.445621i	$-0.147017\pi$
$239$	2.15848e13			1.79044			0.895222	+	0.445621i	$0.147017\pi$
$240$	1.35799e12	−	2.22950e13i	0.110087	−	1.80736i
$241$	2.16323e13			1.71399			0.856996	−	0.515323i	$-0.172328\pi$
$241$	2.16323e13			1.71399			0.856996	+	0.515323i	$0.172328\pi$
$242$	−9.98544e12	+	1.29019e12i	−0.773362	+	0.0999238i
$243$	−1.27381e13	+	3.49134e12i	−0.964430	+	0.264337i
$244$	5.71787e12	−	1.50266e12i	0.423244	−	0.111229i
$245$		−	1.19139e13i		−	0.862264i
$246$	2.78585e11	−	5.82175e11i	0.0197158	−	0.0412013i
$247$		−	6.03545e12i		−	0.417711i
$248$	−7.61152e12	−	1.87574e13i	−0.515213	−	1.26966i
$249$	5.36055e12	+	3.47248e12i	0.354906	+	0.229902i
$250$	4.58110e12	+	3.54555e13i	0.296688	+	2.29622i
$251$	−2.04494e13			−1.29561			−0.647805	−	0.761806i	$-0.724313\pi$
$251$	−2.04494e13			−1.29561			−0.647805	+	0.761806i	$0.724313\pi$
$252$	−9.09227e12	+	7.32488e12i	−0.563598	+	0.454043i
$253$	−9.26991e12			−0.562228
$254$	−2.69434e12	−	2.08529e13i	−0.159907	−	1.23760i
$255$	1.25891e13	+	8.15498e12i	0.731177	+	0.473644i
$256$	9.08752e12	−	1.50633e13i	0.516566	−	0.856247i
$257$		−	4.06690e12i		−	0.226273i	−0.993579	−	0.113136i	$-0.963910\pi$
$257$		−	4.06690e12i		−	0.226273i	0.993579	−	0.113136i	$-0.0360897\pi$
$258$	−8.18539e12	+	1.71055e13i	−0.445791	+	0.931594i
$259$		−	1.28943e13i		−	0.687462i
$260$	6.43397e12	+	2.44823e13i	0.335835	+	1.27790i
$261$	−1.56961e13	+	7.03141e12i	−0.802175	+	0.359352i
$262$	−9.85478e12	+	1.27331e12i	−0.493162	+	0.0637200i
$263$	−1.53194e13			−0.750731			−0.375366	−	0.926877i	$-0.622483\pi$
$263$	−1.53194e13			−0.750731			−0.375366	+	0.926877i	$0.622483\pi$
$264$	9.60304e12	+	1.84018e12i	0.460879	+	0.0883161i
$265$	−4.36842e13			−2.05339
$266$	−8.92403e12	+	1.15305e12i	−0.410877	+	0.0530882i
$267$	8.03614e12	−	1.24056e13i	0.362440	−	0.559507i
$268$	9.74292e11	+	3.70733e12i	0.0430475	+	0.163802i
$269$			3.13857e13i			1.35861i	0.733856	+	0.679305i	$0.237719\pi$
$269$			3.13857e13i			1.35861i	−0.733856	+	0.679305i	$0.762281\pi$
$270$	4.26788e13	+	1.07379e12i	1.81014	+	0.0455429i
$271$			2.22952e13i			0.926574i	0.886208	+	0.463287i	$0.153330\pi$
$271$			2.22952e13i			0.926574i	−0.886208	+	0.463287i	$0.846670\pi$
$272$	5.80821e12	+	1.02874e13i	0.236545	+	0.418963i
$273$	7.19401e12	−	1.11056e13i	0.287129	−	0.443248i
$274$	−4.90470e12	−	3.79600e13i	−0.191860	−	1.48490i
$275$	−2.78888e13			−1.06930
$276$	−3.02817e13	−	9.96200e12i	−1.13810	−	0.374409i
$277$	−1.14392e13			−0.421462			−0.210731	−	0.977544i	$-0.567584\pi$
$277$	−1.14392e13			−0.421462			−0.210731	+	0.977544i	$0.567584\pi$
$278$	−4.35395e12	−	3.36975e13i	−0.157267	−	1.21717i
$279$	3.53101e13	−	1.58179e13i	1.25048	−	0.560178i
$280$	3.49704e13	−	1.41905e13i	1.21431	−	0.492753i
$281$			4.92302e12i			0.167628i	0.996481	+	0.0838140i	$0.0267102\pi$
$281$			4.92302e12i			0.167628i	−0.996481	+	0.0838140i	$0.973290\pi$
$282$	−7.62437e12	−	3.64845e12i	−0.254585	−	0.121825i
$283$			2.98543e13i			0.977647i	0.872383	+	0.488823i	$0.162574\pi$
$283$			2.98543e13i			0.977647i	−0.872383	+	0.488823i	$0.837426\pi$
$284$	4.31055e13	−	1.13282e13i	1.38446	−	0.363839i
$285$	2.76143e13	+	1.78881e13i	0.869937	+	0.563530i
$286$	−1.09897e13	+	1.41995e12i	−0.339605	+	0.0438793i
$287$	1.09048e12			0.0330572
$288$	2.93924e13	+	1.63313e13i	0.874130	+	0.485692i
$289$	2.63385e13			0.768517
$290$	5.51348e13	−	7.12380e12i	1.57847	−	0.203949i
$291$	1.27993e13	+	8.29120e12i	0.359564	+	0.232919i
$292$	−2.75006e13	+	7.22718e12i	−0.758116	+	0.199234i
$293$		−	3.39982e13i		−	0.919780i	−0.887976	−	0.459890i	$-0.847889\pi$
$293$		−	3.39982e13i		−	0.919780i	0.887976	−	0.459890i	$-0.152111\pi$
$294$	1.61781e13	+	7.74163e12i	0.429554	+	0.205552i
$295$		−	6.92176e13i		−	1.80383i
$296$	−3.44089e13	+	1.39627e13i	−0.880170	+	0.357162i
$297$	−2.86022e12	+	1.84685e13i	−0.0718190	+	0.463736i
$298$	7.92307e11	+	6.13207e12i	0.0195301	+	0.151153i
$299$	3.61274e13			0.874270
$300$	−9.11035e13	−	2.99710e13i	−2.16455	−	0.712089i
$301$	−3.20404e13			−0.747450
$302$	1.09076e13	+	8.44197e13i	0.249857	+	1.93377i
$303$	−8.61134e12	+	1.32935e13i	−0.193703	+	0.299024i
$304$	1.27404e13	+	2.25655e13i	0.281435	+	0.498472i
$305$		−	3.65250e13i		−	0.792395i
$306$	−1.92542e13	+	1.17958e13i	−0.410258	+	0.251340i
$307$		−	1.60204e13i		−	0.335283i	−0.985848	−	0.167642i	$-0.946385\pi$
$307$		−	1.60204e13i		−	0.335283i	0.985848	−	0.167642i	$-0.0536152\pi$
$308$	4.19908e12	+	1.59782e13i	0.0863228	+	0.328472i
$309$	3.02798e13	−	4.67438e13i	0.611480	−	0.943957i
$310$	−1.24032e14	+	1.60257e13i	−2.46061	+	0.317928i
$311$	−7.98608e13			−1.55651			−0.778254	−	0.627949i	$-0.783895\pi$
$311$	−7.98608e13			−1.55651			−0.778254	+	0.627949i	$0.783895\pi$
$312$	−3.74258e13	−	7.17172e12i	−0.716672	−	0.137332i
$313$	3.64491e13			0.685792			0.342896	−	0.939373i	$-0.388592\pi$
$313$	3.64491e13			0.685792			0.342896	+	0.939373i	$0.388592\pi$
$314$	4.71976e13	−	6.09826e12i	0.872583	−	0.112744i
$315$	2.94901e13	+	6.58303e13i	0.535757	+	1.19596i
$316$	1.20691e13	+	4.59247e13i	0.215474	+	0.819911i
$317$			4.22845e13i			0.741916i	0.928650	+	0.370958i	$0.120971\pi$
$317$			4.22845e13i			0.741916i	−0.928650	+	0.370958i	$0.879029\pi$
$318$	2.83859e13	−	5.93197e13i	0.489501	−	1.02294i
$319$			2.43360e13i			0.412478i
$320$	−7.57359e13	−	7.79534e13i	−1.26176	−	1.29870i
$321$	7.12807e11	+	4.61744e11i	0.0116733	+	0.00756178i
$322$	−6.90200e12	−	5.34181e13i	−0.111114	−	0.859966i
$323$	−1.74020e13			−0.275413
$324$	−2.91908e13	+	5.72567e13i	−0.454201	+	0.890899i
$325$	1.08691e14			1.66277
$326$	4.78876e12	+	3.70627e13i	0.0720321	+	0.557494i
$327$	−4.50183e13	−	2.91621e13i	−0.665850	−	0.431326i
$328$	−1.18083e12	−	2.90998e12i	−0.0171744	−	0.0423237i
$329$		−	1.42813e13i		−	0.204263i
$330$	2.60750e13	−	5.44904e13i	0.366774	−	0.766467i
$331$			6.76842e13i			0.936339i	0.883639	+	0.468170i	$0.155086\pi$
$331$			6.76842e13i			0.936339i	−0.883639	+	0.468170i	$0.844914\pi$
$332$	3.00578e13	−	7.89923e12i	0.408976	−	0.107479i
$333$	−2.90166e13	−	6.47734e13i	−0.388333	−	0.866869i
$334$	1.17705e14	−	1.52083e13i	1.54949	−	0.200205i
$335$	2.36820e13			0.306670
$336$	−3.45408e12	+	5.67079e13i	−0.0440014	+	0.722400i
$337$	−6.58730e13			−0.825549			−0.412774	−	0.910833i	$-0.635440\pi$
$337$	−6.58730e13			−0.825549			−0.412774	+	0.910833i	$0.635440\pi$
$338$	−3.76052e13	+	4.85886e12i	−0.463667	+	0.0599090i
$339$	5.05658e13	−	7.80597e13i	0.613420	−	0.946953i
$340$	7.05896e13	−	1.85510e13i	0.842572	−	0.221429i
$341$		−	5.47465e13i		−	0.642994i
$342$	−4.22343e13	+	2.58744e13i	−0.488115	+	0.299038i
$343$			9.39389e13i			1.06838i
$344$	3.46952e13	+	8.55010e13i	0.388328	+	0.956973i
$345$	−1.07076e14	+	1.65296e14i	−1.17947	+	1.82078i
$346$	1.51344e11	+	1.17133e12i	0.00164077	+	0.0126988i
$347$	4.33886e13			0.462981			0.231491	−	0.972837i	$-0.425640\pi$
$347$	4.33886e13			0.462981			0.231491	+	0.972837i	$0.425640\pi$
$348$	−2.61529e13	+	7.94976e13i	−0.274685	+	0.834965i
$349$	−2.49854e13			−0.258314			−0.129157	−	0.991624i	$-0.541227\pi$
$349$	−2.49854e13			−0.258314			−0.129157	+	0.991624i	$0.541227\pi$
$350$	−2.07649e13	−	1.60710e14i	−0.211327	−	1.63557i
$351$	1.11471e13	−	7.19770e13i	0.111679	−	0.721115i
$352$	3.80913e13	−	2.85075e13i	0.375700	−	0.281174i
$353$			6.48993e13i			0.630201i	0.949058	+	0.315100i	$0.102038\pi$
$353$			6.48993e13i			0.630201i	−0.949058	+	0.315100i	$0.897962\pi$
$354$	9.39920e13	+	4.49775e13i	0.898613	+	0.430009i
$355$		−	2.75352e14i		−	2.59199i
$356$	−1.82807e13	−	6.95609e13i	−0.169441	−	0.644749i
$357$	−3.20207e13	−	2.07425e13i	−0.292250	−	0.189315i
$358$	3.17694e13	−	4.10483e12i	0.285530	−	0.0368925i
$359$	6.55782e13			0.580417			0.290208	−	0.956963i	$-0.406275\pi$
$359$	6.55782e13			0.580417			0.290208	+	0.956963i	$0.406275\pi$
$360$	1.43737e14	−	1.49980e14i	1.25287	−	1.30729i
$361$	7.83187e13			0.672320
$362$	−5.65650e13	+	7.30859e12i	−0.478245	+	0.0617926i
$363$	−7.85919e13	−	5.09105e13i	−0.654473	−	0.423956i
$364$	−1.63650e13	−	6.22714e13i	−0.134233	−	0.510777i
$365$			1.75670e14i			1.41934i
$366$	4.95981e13	+	2.37339e13i	0.394747	+	0.188896i
$367$			2.18845e14i			1.71583i	0.513792	+	0.857915i	$0.328240\pi$
$367$			2.18845e14i			1.71583i	−0.513792	+	0.857915i	$0.671760\pi$
$368$	−1.35074e14	+	7.62625e13i	−1.04330	+	0.589045i
$369$	5.47792e12	−	2.45395e12i	0.0416841	−	0.0186733i
$370$	2.93979e13	+	2.27526e14i	0.220398	+	1.70577i
$371$	1.11112e14			0.820739
$372$	5.88338e13	−	1.78838e14i	0.428194	−	1.30159i
$373$	−2.63525e14			−1.88983			−0.944917	−	0.327309i	$-0.893858\pi$
$373$	−2.63525e14			−1.88983			−0.944917	+	0.327309i	$0.893858\pi$
$374$	4.09414e12	+	3.16866e13i	0.0289313	+	0.223915i
$375$	−1.80769e14	+	2.79058e14i	−1.25879	+	1.94322i
$376$	−3.81101e13	+	1.54646e13i	−0.261521	+	0.106122i
$377$		−	9.48443e13i		−	0.641407i
$378$	−1.08555e14	−	2.73123e12i	−0.723510	−	0.0182034i
$379$		−	1.02574e14i		−	0.673783i	−0.941543	−	0.336892i	$-0.890624\pi$
$379$		−	1.02574e14i		−	0.673783i	0.941543	−	0.336892i	$-0.109376\pi$
$380$	1.54840e14	−	4.06921e13i	1.00247	−	0.263451i
$381$	1.06318e14	−	1.64126e14i	0.678452	−	1.04734i
$382$	−5.98562e12	+	7.73384e11i	−0.0376496	+	0.00486459i
$383$	−1.03017e14			−0.638728			−0.319364	−	0.947632i	$-0.603469\pi$
$383$	−1.03017e14			−0.638728			−0.319364	+	0.947632i	$0.603469\pi$
$384$	1.55068e14	−	5.21893e13i	0.947762	−	0.318977i
$385$	1.02066e14			0.614963
$386$	−2.71571e14	+	3.50889e13i	−1.61307	+	0.208420i
$387$	−1.60952e14	+	7.21020e13i	−0.942512	+	0.422218i
$388$	7.17687e13	−	1.88609e13i	0.414344	−	0.108890i
$389$		−	4.81981e13i		−	0.274351i	−0.990547	−	0.137176i	$-0.956198\pi$
$389$		−	4.81981e13i		−	0.274351i	0.990547	−	0.137176i	$-0.0438025\pi$
$390$	−1.01622e14	+	2.12365e14i	−0.570337	+	1.19186i
$391$		−	1.04166e14i		−	0.576440i
$392$	8.08657e13	−	3.28143e13i	0.441256	−	0.179056i
$393$	−7.75635e13	−	5.02443e13i	−0.417348	−	0.270351i
$394$	−2.44781e13	−	1.89449e14i	−0.129882	−	1.00522i
$395$	2.93361e14			1.53503
$396$	5.70502e13	+	7.08156e13i	0.294397	+	0.365431i
$397$	9.32139e13			0.474387			0.237194	−	0.971462i	$-0.423772\pi$
$397$	9.32139e13			0.474387			0.237194	+	0.971462i	$0.423772\pi$
$398$	−1.51567e13	−	1.17306e14i	−0.0760761	−	0.588793i
$399$	−7.02379e13	−	4.54989e13i	−0.347713	−	0.225242i
$400$	−4.06376e14	+	2.29438e14i	−1.98426	+	1.12030i
$401$		−	8.43049e13i		−	0.406031i	−0.979176	−	0.203015i	$-0.934926\pi$
$401$		−	8.43049e13i		−	0.406031i	0.979176	−	0.203015i	$-0.0650741\pi$
$402$	−1.53885e13	+	3.21582e13i	−0.0731060	+	0.152774i
$403$			2.13362e14i			0.999862i
$404$	1.95892e13	+	7.45398e13i	0.0905563	+	0.344581i
$405$	2.96282e14	+	2.64330e14i	1.35115	+	1.20544i
$406$	−1.40237e14	+	1.81196e13i	−0.630913	+	0.0815183i
$407$	−1.00428e14			−0.445743
$408$	−2.06782e13	+	1.07910e14i	−0.0905485	+	0.472529i
$409$	6.60335e12			0.0285290			0.0142645	−	0.999898i	$-0.495459\pi$
$409$	6.60335e12			0.0285290			0.0142645	+	0.999898i	$0.495459\pi$
$410$	−1.92420e13	+	2.48620e12i	−0.0820235	+	0.0105980i
$411$	1.93538e14	−	2.98770e14i	0.814023	−	1.25663i
$412$	−6.88810e13	−	2.62103e14i	−0.285867	−	1.08777i
$413$			1.76057e14i			0.720988i
$414$	−1.54881e14	−	2.52810e14i	−0.625887	−	1.02163i
$415$		−	1.92005e14i		−	0.765683i
$416$	−1.48453e14	+	1.11102e14i	−0.584218	+	0.437228i
$417$	1.71806e14	−	2.65221e14i	0.667252	−	1.03005i
$418$	8.98056e12	+	6.95052e13i	0.0344218	+	0.266408i
$419$	3.34130e14			1.26398			0.631988	−	0.774979i	$-0.282239\pi$
$419$	3.34130e14			1.26398			0.631988	+	0.774979i	$0.282239\pi$
$420$	3.33417e14	+	1.09687e14i	1.24485	+	0.409527i
$421$	4.84680e13			0.178609			0.0893045	−	0.996004i	$-0.471536\pi$
$421$	4.84680e13			0.178609			0.0893045	+	0.996004i	$0.471536\pi$
$422$	5.23077e13	+	4.04837e14i	0.190260	+	1.47252i
$423$	−3.21378e13	−	7.17407e13i	−0.115384	−	0.257569i
$424$	−1.20319e14	−	2.96507e14i	−0.426404	−	1.05081i
$425$		−	3.13387e14i		−	1.09633i
$426$	3.73906e14	+	1.78923e14i	1.29125	+	0.617894i
$427$			9.29026e13i			0.316719i
$428$	3.99687e12	−	1.05038e12i	0.0134517	−	0.00353514i
$429$	−8.64963e13	−	5.60309e13i	−0.287397	−	0.186171i
$430$	5.65367e14	−	7.30494e13i	1.85462	−	0.239629i
$431$	−2.57169e14			−0.832903			−0.416451	−	0.909158i	$-0.636726\pi$
$431$	−2.57169e14			−0.832903			−0.416451	+	0.909158i	$0.636726\pi$
$432$	1.10261e14	+	2.92641e14i	0.352584	+	0.935780i
$433$	−1.79717e12			−0.00567421			−0.00283710	−	0.999996i	$-0.500903\pi$
$433$	−1.79717e12			−0.00567421			−0.00283710	+	0.999996i	$0.500903\pi$
$434$	3.15478e14	−	4.07620e13i	0.983503	−	0.127075i
$435$	4.33946e14	+	2.81103e14i	1.33581	+	0.865316i
$436$	−2.52427e14	+	6.63382e13i	−0.767292	+	0.201645i
$437$		−	2.28490e14i		−	0.685835i
$438$	−2.38546e14	−	1.14150e14i	−0.707073	−	0.338352i
$439$			1.80614e14i			0.528684i	0.964429	+	0.264342i	$0.0851548\pi$
$439$			1.80614e14i			0.528684i	−0.964429	+	0.264342i	$0.914845\pi$
$440$	−1.10524e14	−	2.72368e14i	−0.319496	−	0.787348i
$441$	6.81931e13	+	1.52226e14i	0.194683	+	0.434588i
$442$	−1.59560e13	−	1.23492e14i	−0.0449885	−	0.348189i
$443$	−6.36828e14			−1.77338			−0.886690	−	0.462364i	$-0.847001\pi$
$443$	−6.36828e14			−1.77338			−0.886690	+	0.462364i	$0.847001\pi$
$444$	−3.28064e14	−	1.07926e14i	−0.902304	−	0.296838i
$445$	−4.44346e14			−1.20710
$446$	−3.53662e13	−	2.73717e14i	−0.0948957	−	0.734447i
$447$	−3.12642e13	+	4.82634e13i	−0.0828622	+	0.127916i
$448$	1.92637e14	+	1.98277e14i	0.504324	+	0.519091i
$449$			7.24372e14i			1.87330i	0.350271	+	0.936648i	$0.386090\pi$
$449$			7.24372e14i			1.87330i	−0.350271	+	0.936648i	$0.613910\pi$
$450$	−4.65964e14	−	7.60586e14i	−1.19038	−	1.94303i
$451$		−	8.49323e12i		−	0.0214339i
$452$	−1.15028e14	−	4.37698e14i	−0.286775	−	1.09122i
$453$	−4.30412e14	+	6.64438e14i	−1.06009	+	1.63649i
$454$	−3.70019e12	+	4.78090e11i	−0.00900361	+	0.00116333i
$455$	−3.97782e14			−0.956274
$456$	−4.53580e13	+	2.36701e14i	−0.107733	+	0.562204i
$457$	3.12175e14			0.732587			0.366293	−	0.930499i	$-0.380627\pi$
$457$	3.12175e14			0.732587			0.366293	+	0.930499i	$0.380627\pi$
$458$	2.69617e14	−	3.48365e13i	0.625155	−	0.0807744i
$459$	−2.07531e14	−	3.21404e13i	−0.475459	−	0.0736345i
$460$	2.43578e14	+	9.26851e14i	0.551403	+	2.09818i
$461$		−	1.89009e14i		−	0.422793i	−0.977400	−	0.211397i	$-0.932199\pi$
$461$		−	1.89009e14i		−	0.422793i	0.977400	−	0.211397i	$-0.0678011\pi$
$462$	−6.63226e13	+	1.38598e14i	−0.146599	+	0.306356i
$463$		−	2.09620e14i		−	0.457865i	−0.973442	−	0.228933i	$-0.926476\pi$
$463$		−	2.09620e14i		−	0.457865i	0.973442	−	0.228933i	$-0.0735235\pi$
$464$	2.00210e14	+	3.54607e14i	0.432152	+	0.765417i
$465$	−9.76209e14	−	6.32372e14i	−2.08234	−	1.34890i
$466$	3.88818e13	+	3.00926e14i	0.0819641	+	0.634363i
$467$	5.21389e14			1.08622			0.543112	−	0.839660i	$-0.317246\pi$
$467$	5.21389e14			1.08622			0.543112	+	0.839660i	$0.317246\pi$
$468$	−2.22341e14	−	2.75988e14i	−0.457790	−	0.568249i
$469$	−6.02358e13			−0.122576
$470$	3.25601e13	+	2.51999e14i	0.0654858	+	0.506828i
$471$	3.71476e14	+	2.40636e14i	0.738440	+	0.478349i
$472$	4.69815e14	−	1.90645e14i	0.923094	−	0.374580i
$473$			2.49548e14i			0.484639i
$474$	−1.90625e14	+	3.98361e14i	−0.365931	+	0.764708i
$475$		−	6.87420e14i		−	1.30439i
$476$	−1.79547e14	+	4.71852e13i	−0.336775	+	0.0885049i
$477$	5.58163e14	−	2.50041e14i	1.03493	−	0.463618i
$478$	9.68766e14	−	1.25171e14i	1.77568	−	0.229431i
$479$	−2.13955e14			−0.387684			−0.193842	−	0.981033i	$-0.562095\pi$
$479$	−2.13955e14			−0.387684			−0.193842	+	0.981033i	$0.562095\pi$
$480$	−6.83404e13	−	1.00851e15i	−0.122420	−	1.80657i
$481$	3.91396e14			0.693135
$482$	9.70895e14	−	1.25446e14i	1.69986	−	0.219634i
$483$	2.72351e14	−	4.20435e14i	0.471433	−	0.727763i
$484$	−4.40682e14	+	1.15812e14i	−0.754182	+	0.198200i
$485$		−	4.58449e14i		−	0.775732i
$486$	−5.51463e14	+	2.30566e14i	−0.922607	+	0.385741i
$487$			7.29519e14i			1.20678i	0.797447	+	0.603389i	$0.206183\pi$
$487$			7.29519e14i			1.20678i	−0.797447	+	0.603389i	$0.793817\pi$
$488$	2.47914e14	−	1.00600e14i	0.405501	−	0.164547i
$489$	−1.88963e14	+	2.91708e14i	−0.305618	+	0.471790i
$490$	−6.90891e13	−	5.34716e14i	−0.110492	−	0.855155i
$491$	−5.09156e14			−0.805198			−0.402599	−	0.915376i	$-0.631893\pi$
$491$	−5.09156e14			−0.805198			−0.402599	+	0.915376i	$0.631893\pi$
$492$	9.12734e12	−	2.77446e13i	0.0142737	−	0.0433880i
$493$	−2.73464e14			−0.422904
$494$	−3.49998e13	−	2.70881e14i	−0.0535263	−	0.414268i
$495$	5.12723e14	−	2.29685e14i	0.775450	−	0.347379i
$496$	−4.50393e14	−	7.97726e14i	−0.673663	−	1.19318i
$497$			7.00367e14i			1.03601i
$498$	2.60728e14	+	1.24765e14i	0.381440	+	0.182528i
$499$			6.58172e14i			0.952328i	0.879356	+	0.476164i	$0.157973\pi$
$499$			6.58172e14i			0.952328i	−0.879356	+	0.476164i	$0.842027\pi$
$500$	4.11216e14	+	1.56474e15i	0.588484	+	2.23927i
$501$	9.26415e14	+	6.00116e14i	1.31129	+	0.849430i
$502$	−9.17803e14	+	1.18587e14i	−1.28493	+	0.166022i
$503$	1.05696e15			1.46364			0.731821	−	0.681497i	$-0.238671\pi$
$503$	1.05696e15			1.46364			0.731821	+	0.681497i	$0.238671\pi$
$504$	−3.65600e14	+	3.81480e14i	−0.500770	+	0.522521i
$505$	4.76151e14			0.645122
$506$	−4.16050e14	+	5.37565e13i	−0.557593	+	0.0720449i
$507$	−2.95977e14	−	1.91729e14i	−0.392387	−	0.254182i
$508$	−2.41853e14	−	9.20289e14i	−0.317177	−	1.20691i
$509$		−	7.65100e14i		−	0.992592i	−0.868153	−	0.496296i	$-0.834693\pi$
$509$		−	7.65100e14i		−	0.992592i	0.868153	−	0.496296i	$-0.165307\pi$
$510$	6.12310e14	+	2.93005e14i	0.785842	+	0.376045i
$511$		−	4.46822e14i		−	0.567309i
$512$	3.20512e14	−	7.28764e14i	0.402586	−	0.915382i
$513$	−4.55223e14	−	7.05005e13i	−0.565690	−	0.0876086i
$514$	−2.35841e13	−	1.82530e14i	−0.0289950	−	0.224407i
$515$	−1.67428e15			−2.03652
$516$	−2.68179e14	+	8.15191e14i	−0.322739	+	0.981038i
$517$	−1.11230e14			−0.132442
$518$	−7.47745e13	−	5.78718e14i	−0.0880927	−	0.681795i
$519$	−5.97200e12	+	9.21914e12i	−0.00696145	+	0.0107466i
$520$	4.30742e14	+	1.06150e15i	0.496819	+	1.22433i
$521$		−	1.30770e15i		−	1.49246i	−0.665689	−	0.746229i	$-0.731862\pi$
$521$		−	1.30770e15i		−	1.49246i	0.665689	−	0.746229i	$-0.268138\pi$
$522$	−6.63693e14	+	4.06604e14i	−0.749514	+	0.459181i
$523$			4.40719e14i			0.492496i	0.969207	+	0.246248i	$0.0791977\pi$
$523$			4.40719e14i			0.492496i	−0.969207	+	0.246248i	$0.920802\pi$
$524$	−4.34916e14	+	1.14296e14i	−0.480931	+	0.126389i
$525$	8.19377e14	−	1.26489e15i	0.896618	−	1.38413i
$526$	−6.87560e14	+	8.88376e13i	−0.744542	+	0.0962000i
$527$	6.15187e14			0.659248
$528$	4.41673e14	+	2.69023e13i	0.468397	+	0.0285301i
$529$	4.14904e14			0.435454
$530$	−1.96062e15	+	2.53326e14i	−2.03647	+	0.263126i
$531$	3.96190e14	+	8.84408e14i	0.407271	+	0.909145i
$532$	−3.93839e14	+	1.03501e14i	−0.400687	+	0.105301i
$533$			3.31005e13i			0.0333300i
$534$	2.88736e14	−	6.03387e14i	0.287755	−	0.601338i
$535$		−	2.55315e13i		−	0.0251843i
$536$	6.52269e13	+	1.60742e14i	0.0636825	+	0.156936i
$537$	2.50046e14	+	1.61975e14i	0.241636	+	0.156527i
$538$	1.82007e14	+	1.40865e15i	0.174095	+	1.34741i
$539$	2.36019e14			0.223465
$540$	1.92173e15	−	1.99302e14i	1.80105	−	0.186787i
$541$	−5.98536e13			−0.0555271			−0.0277636	−	0.999615i	$-0.508839\pi$
$541$	−5.98536e13			−0.0555271			−0.0277636	+	0.999615i	$0.508839\pi$
$542$	1.29291e14	+	1.00065e15i	0.118733	+	0.918935i
$543$	−4.45203e14	−	2.88395e14i	−0.404724	−	0.262174i
$544$	3.20339e14	+	4.28033e14i	0.288281	+	0.385197i
$545$			1.61247e15i			1.43652i
$546$	2.58478e14	−	5.40156e14i	0.227963	−	0.476387i
$547$		−	1.72876e15i		−	1.50940i	−0.656070	−	0.754700i	$-0.727783\pi$
$547$		−	1.72876e15i		−	1.50940i	0.656070	−	0.754700i	$-0.272217\pi$
$548$	−4.40263e14	−	1.67527e15i	−0.380556	−	1.44808i
$549$	2.09063e14	+	4.66688e14i	0.178908	+	0.399373i
$550$	−1.25170e15	+	1.61728e14i	−1.06049	+	0.137022i
$551$	−5.99848e14			−0.503162
$552$	−1.41687e15	−	2.71507e14i	−1.17669	−	0.225484i
$553$	−7.46172e14			−0.613551
$554$	−5.13413e14	+	6.63365e13i	−0.417987	+	0.0540069i
$555$	−1.16003e15	+	1.79077e15i	−0.935103	+	1.44354i
$556$	−3.90826e14	−	1.48715e15i	−0.311941	−	1.18698i
$557$			1.36737e15i			1.08064i	0.841459	+	0.540320i	$0.181697\pi$
$557$			1.36737e15i			1.08064i	−0.841459	+	0.540320i	$0.818303\pi$
$558$	1.49305e15	−	9.14700e14i	1.16839	−	0.715798i
$559$		−	9.72559e14i		−	0.753618i
$560$	1.48724e15	−	8.39690e14i	1.14116	−	0.644295i
$561$	−1.61554e14	+	2.49395e14i	−0.122750	+	0.189492i
$562$	2.85487e13	+	2.20954e14i	0.0214802	+	0.166246i
$563$	1.40936e15			1.05009			0.525045	−	0.851074i	$-0.324048\pi$
$563$	1.40936e15			1.05009			0.525045	+	0.851074i	$0.324048\pi$
$564$	−3.63352e14	−	1.19535e14i	−0.268098	−	0.0881980i
$565$	−2.79596e15			−2.04298
$566$	1.73126e14	+	1.33991e15i	0.125277	+	0.969587i
$567$	−7.53603e14	−	6.72332e14i	−0.540052	−	0.481811i
$568$	1.86896e15	−	7.58398e14i	1.32643	−	0.538247i
$569$		−	2.06059e15i		−	1.44835i	−0.689614	−	0.724177i	$-0.742220\pi$
$569$		−	2.06059e15i		−	1.44835i	0.689614	−	0.724177i	$-0.257780\pi$
$570$	1.34311e15	+	6.42713e14i	0.934977	+	0.447409i
$571$			2.46008e15i			1.69610i	0.529919	+	0.848048i	$0.322222\pi$
$571$			2.46008e15i			1.69610i	−0.529919	+	0.848048i	$0.677778\pi$
$572$	−4.85004e14	+	1.27460e14i	−0.331182	+	0.0870352i
$573$	−4.71107e13	−	3.05175e13i	−0.0318617	−	0.0206395i
$574$	4.89425e13	−	6.32372e12i	0.0327847	−	0.00423601i
$575$	4.11481e15			2.73009
$576$	1.41389e15	+	5.62529e14i	0.929161	+	0.369676i
$577$	−1.96715e14			−0.128047			−0.0640236	−	0.997948i	$-0.520393\pi$
$577$	−1.96715e14			−0.128047			−0.0640236	+	0.997948i	$0.520393\pi$
$578$	1.18212e15	−	1.52738e14i	0.762181	−	0.0984791i
$579$	−2.13744e15	−	1.38460e15i	−1.36509	−	0.884284i
$580$	2.43323e15	−	6.39457e14i	1.53932	−	0.404536i
$581$			4.88372e14i			0.306043i
$582$	6.22538e14	+	2.97900e14i	0.386446	+	0.184924i
$583$		−	8.65402e14i		−	0.532159i
$584$	−1.19236e15	+	4.83845e14i	−0.726336	+	0.294738i
$585$	−1.99822e15	+	8.95147e14i	−1.20583	+	0.540178i
$586$	−1.97157e14	−	1.52590e15i	−0.117862	−	0.912197i
$587$	4.98562e13			0.0295264			0.0147632	−	0.999891i	$-0.495301\pi$
$587$	4.98562e13			0.0295264			0.0147632	+	0.999891i	$0.495301\pi$
$588$	7.70996e14	+	2.53640e14i	0.452352	+	0.148814i
$589$	1.34942e15			0.784357
$590$	−4.01395e14	−	3.10661e15i	−0.231146	−	1.78896i
$591$	9.65900e14	−	1.49108e15i	0.551062	−	0.850690i
$592$	−1.46336e15	+	8.26209e14i	−0.827147	+	0.467004i
$593$			1.64271e15i			0.919943i	0.887934	+	0.459972i	$0.152140\pi$
$593$			1.64271e15i			0.919943i	−0.887934	+	0.459972i	$0.847860\pi$
$594$	−2.12723e13	+	8.45485e14i	−0.0118029	+	0.469116i
$595$			1.14692e15i			0.630508i
$596$	7.11202e13	+	2.70624e14i	0.0387381	+	0.147405i
$597$	5.98081e14	−	9.23273e14i	0.322776	−	0.498277i
$598$	1.62146e15	−	2.09504e14i	0.867063	−	0.112031i
$599$	−2.46882e15			−1.30810			−0.654052	−	0.756450i	$-0.726932\pi$
$599$	−2.46882e15			−1.30810			−0.654052	+	0.756450i	$0.726932\pi$
$600$	−4.26269e15	−	8.16838e14i	−2.23796	−	0.428849i
$601$	3.68424e15			1.91663			0.958316	−	0.285710i	$-0.0922294\pi$
$601$	3.68424e15			1.91663			0.958316	+	0.285710i	$0.0922294\pi$
$602$	−1.43803e15	+	1.85803e14i	−0.741288	+	0.0957796i
$603$	−3.02590e14	+	1.35551e14i	−0.154564	+	0.0692403i
$604$	9.79106e14	+	3.72565e15i	0.495595	+	1.88582i
$605$			2.81502e15i			1.41198i
$606$	−3.09402e14	+	6.46575e14i	−0.153788	+	0.321380i
$607$		−	6.32003e14i		−	0.311302i	−0.987812	−	0.155651i	$-0.950253\pi$
$607$		−	6.32003e14i		−	0.311302i	0.987812	−	0.155651i	$-0.0497475\pi$
$608$	7.02670e14	+	9.38898e14i	0.342990	+	0.458299i
$609$	−1.10376e15	−	7.14995e14i	−0.533922	−	0.345866i
$610$	−2.11810e14	−	1.63931e15i	−0.101539	−	0.785862i
$611$	4.33496e14			0.205948
$612$	−7.95756e14	+	6.41074e14i	−0.374668	+	0.301839i
$613$	−3.30656e15			−1.54292			−0.771461	−	0.636276i	$-0.780474\pi$
$613$	−3.30656e15			−1.54292			−0.771461	+	0.636276i	$0.780474\pi$
$614$	−9.29028e13	−	7.19023e14i	−0.0429638	−	0.332519i
$615$	−1.51447e14	−	9.81047e13i	−0.0694140	−	0.0449652i
$616$	2.81120e14	+	6.92777e14i	0.127702	+	0.314702i
$617$		−	4.14251e15i		−	1.86507i	−0.361079	−	0.932535i	$-0.617592\pi$
$617$		−	4.14251e15i		−	1.86507i	0.361079	−	0.932535i	$-0.382408\pi$
$618$	1.08794e15	−	2.27354e15i	0.485478	−	1.01453i
$619$			2.84268e15i			1.25727i	0.777699	+	0.628637i	$0.216387\pi$
$619$			2.84268e15i			1.25727i	−0.777699	+	0.628637i	$0.783613\pi$
$620$	−5.47382e15	+	1.43853e15i	−2.39959	+	0.630614i
$621$	4.22007e14	−	2.72491e15i	0.183365	−	1.18399i
$622$	−3.58429e15	+	4.63116e14i	−1.54368	+	0.199454i
$623$	1.13021e15			0.482475
$624$	−1.72132e15	−	1.04846e14i	−0.728361	−	0.0443646i
$625$	4.56258e15			1.91368
$626$	1.63590e15	−	2.11370e14i	0.680139	−	0.0878787i
$627$	−3.54371e14	+	5.47051e14i	−0.146045	+	0.225453i
$628$	2.08295e15	−	5.47401e14i	0.850942	−	0.223629i
$629$		−	1.12851e15i		−	0.457011i
$630$	1.70532e15	+	2.78356e15i	0.684593	+	1.11745i
$631$		−	1.14814e15i		−	0.456913i	−0.973554	−	0.228456i	$-0.926632\pi$
$631$		−	1.14814e15i		−	0.456913i	0.973554	−	0.228456i	$-0.0733679\pi$
$632$	8.07999e14	+	1.99119e15i	0.318762	+	0.785541i
$633$	−2.06405e15	+	3.18633e15i	−0.807235	+	1.24615i
$634$	2.45209e14	+	1.89780e15i	0.0950705	+	0.735800i
$635$	−5.87869e15			−2.25957
$636$	9.30013e14	−	2.82698e15i	0.354385	−	1.07723i
$637$	−9.19833e14			−0.347490
$638$	1.41125e14	+	1.09224e15i	0.0528556	+	0.409077i
$639$	1.57607e15	+	3.51823e15i	0.585222	+	1.30638i
$640$	−3.85122e15	−	3.05949e15i	−1.41778	−	1.12631i
$641$		−	4.44505e15i		−	1.62240i	−0.584769	−	0.811200i	$-0.698815\pi$
$641$		−	4.44505e15i		−	1.62240i	0.584769	−	0.811200i	$-0.301185\pi$
$642$	3.46697e13	+	1.65903e13i	0.0125461	+	0.00600360i
$643$		−	4.05182e15i		−	1.45375i	−0.686769	−	0.726876i	$-0.740972\pi$
$643$		−	4.05182e15i		−	1.45375i	0.686769	−	0.726876i	$-0.259028\pi$
$644$	−6.19547e14	−	2.35747e15i	−0.220395	−	0.838638i
$645$	4.44981e15	+	2.88251e15i	1.56950	+	1.01670i
$646$	−7.81031e14	+	1.00915e14i	−0.273143	+	0.0352919i
$647$	2.99331e15			1.03795			0.518977	−	0.854788i	$-0.326313\pi$
$647$	2.99331e15			1.03795			0.518977	+	0.854788i	$0.326313\pi$
$648$	−9.78098e14	+	2.73906e15i	−0.336295	+	0.941757i
$649$	1.37123e15			0.467481
$650$	4.87822e15	−	6.30301e14i	1.64907	−	0.213071i
$651$	2.48302e15	+	1.60846e15i	0.832309	+	0.539156i
$652$	4.29856e14	+	1.63567e15i	0.142877	+	0.543668i
$653$			2.36368e15i			0.779051i	0.921016	+	0.389526i	$0.127361\pi$
$653$			2.36368e15i			0.779051i	−0.921016	+	0.389526i	$0.872639\pi$
$654$	−2.18961e15	−	1.04778e15i	−0.715631	−	0.342447i
$655$			2.77819e15i			0.900397i
$656$	−6.98729e13	−	1.23757e14i	−0.0224563	−	0.0397740i
$657$	−1.00550e15	−	2.24457e15i	−0.320461	−	0.715359i
$658$	−8.28175e13	−	6.40968e14i	−0.0261746	−	0.202579i
$659$	2.02258e14			0.0633921			0.0316961	−	0.999498i	$-0.489909\pi$
$659$	2.02258e14			0.0633921			0.0316961	+	0.999498i	$0.489909\pi$
$660$	8.54301e14	−	2.59684e15i	0.265533	−	0.807148i
$661$	4.41176e15			1.35989			0.679945	−	0.733264i	$-0.262004\pi$
$661$	4.41176e15			1.35989			0.679945	+	0.733264i	$0.262004\pi$
$662$	3.92503e14	+	3.03779e15i	0.119984	+	0.928620i
$663$	6.29620e14	−	9.71961e14i	0.190877	−	0.294662i
$664$	1.30324e15	−	5.28838e14i	0.391832	−	0.159000i
$665$			2.51580e15i			0.750164i
$666$	−1.67794e15	−	2.73888e15i	−0.496213	−	0.809961i
$667$		−	3.59062e15i		−	1.05312i
$668$	5.19461e15	−	1.36515e15i	1.51106	−	0.397109i
$669$	1.39554e15	−	2.15433e15i	0.402623	−	0.621540i
$670$	1.06289e15	−	1.37333e14i	0.304142	−	0.0392972i
$671$	7.23576e14			0.205357
$672$	1.73826e14	+	2.56518e15i	0.0489310	+	0.722083i
$673$	−4.53547e15			−1.26631			−0.633154	−	0.774026i	$-0.718240\pi$
$673$	−4.53547e15			−1.26631			−0.633154	+	0.774026i	$0.718240\pi$
$674$	−2.95649e15	+	3.82000e14i	−0.818743	+	0.105787i
$675$	1.26962e15	−	8.19797e15i	0.348742	−	2.25183i
$676$	−1.65961e15	+	4.36148e14i	−0.452168	+	0.118830i
$677$			9.60756e14i			0.259642i	0.991537	+	0.129821i	$0.0414403\pi$
$677$			9.60756e14i			0.259642i	−0.991537	+	0.129821i	$0.958560\pi$
$678$	1.81681e15	−	3.79669e15i	0.487019	−	1.01775i
$679$			1.16608e15i			0.310059i
$680$	3.06061e15	−	1.24196e15i	0.807251	−	0.327572i
$681$	−2.91229e13	−	1.88653e13i	−0.00761948	−	0.00493577i
$682$	−3.17477e14	−	2.45712e15i	−0.0823944	−	0.637693i
$683$	5.80399e14			0.149421			0.0747107	−	0.997205i	$-0.476197\pi$
$683$	5.80399e14			0.149421			0.0747107	+	0.997205i	$0.476197\pi$
$684$	−1.74550e15	+	1.40621e15i	−0.445772	+	0.359121i
$685$	−1.07014e16			−2.71108
$686$	5.44755e14	+	4.21614e15i	0.136905	+	1.05958i
$687$	2.12206e15	+	1.37464e15i	0.529050	+	0.342710i
$688$	2.05301e15	+	3.63624e15i	0.507754	+	0.899323i
$689$			3.37272e15i			0.827512i
$690$	−3.84720e15	+	8.03971e15i	−0.936429	+	1.95691i
$691$			4.87443e15i			1.17705i	0.808480	+	0.588524i	$0.200291\pi$
$691$			4.87443e15i			1.17705i	−0.808480	+	0.588524i	$0.799709\pi$
$692$	1.35852e13	+	5.16937e13i	0.00325448	+	0.0123838i
$693$	−1.30413e15	+	5.84211e14i	−0.309946	+	0.138847i
$694$	1.94736e15	−	2.51612e14i	0.459164	−	0.0593273i
$695$	−9.49975e15			−2.22226
$696$	−7.12779e14	+	3.71965e15i	−0.165426	+	0.863280i
$697$	9.54386e13			0.0219758
$698$	−1.12139e15	+	1.44891e14i	−0.256184	+	0.0331008i
$699$	−1.53427e15	+	2.36849e15i	−0.347757	+	0.536842i
$700$	−1.86393e15	−	7.09254e15i	−0.419170	−	1.59501i
$701$		−	4.68302e15i		−	1.04490i	−0.852669	−	0.522452i	$-0.825017\pi$
$701$		−	4.68302e15i		−	1.04490i	0.852669	−	0.522452i	$-0.174983\pi$
$702$	8.29042e13	−	3.29509e15i	0.0183536	−	0.729481i
$703$		−	2.47540e15i		−	0.543741i
$704$	1.54429e15	−	1.50036e15i	0.336573	−	0.326999i
$705$	−1.28481e15	+	1.98340e15i	−0.277843	+	0.428913i
$706$	3.76353e14	+	2.91279e15i	0.0807550	+	0.625005i
$707$	−1.21110e15			−0.257855
$708$	4.47935e15	+	1.47361e15i	0.946307	+	0.311314i
$709$	−2.81997e15			−0.591139			−0.295570	−	0.955321i	$-0.595509\pi$
$709$	−2.81997e15			−0.591139			−0.295570	+	0.955321i	$0.595509\pi$
$710$	−1.59678e15	−	1.23583e16i	−0.332142	−	2.57062i
$711$	−3.74833e15	+	1.67915e15i	−0.773670	+	0.346582i
$712$	−1.22386e15	−	3.01601e15i	−0.250663	−	0.617721i
$713$			8.07748e15i			1.64166i
$714$	−1.55743e15	−	7.45268e14i	−0.314100	−	0.150305i
$715$			3.09814e15i			0.620038i
$716$	1.40206e15	−	3.68464e14i	0.278449	−	0.0731767i
$717$	7.62482e15	+	4.93923e15i	1.50271	+	0.973428i
$718$	2.94326e15	−	3.80290e14i	0.575632	−	0.0743756i
$719$	1.60198e15			0.310920			0.155460	−	0.987842i	$-0.450314\pi$
$719$	1.60198e15			0.310920			0.155460	+	0.987842i	$0.450314\pi$
$720$	5.58143e15	−	7.56492e15i	1.07502	−	1.45705i
$721$	4.25858e15			0.813993
$722$	3.51508e15	−	4.54173e14i	0.666777	−	0.0861523i
$723$	7.64157e15	+	4.95008e15i	1.43854	+	0.931863i
$724$	−2.49635e15	+	6.56045e14i	−0.466384	+	0.122566i
$725$		−	1.08025e16i		−	2.00293i
$726$	−3.82257e15	−	1.82920e15i	−0.703403	−	0.336596i
$727$			1.05087e15i			0.191916i	0.995385	+	0.0959578i	$0.0305914\pi$
$727$			1.05087e15i			0.191916i	−0.995385	+	0.0959578i	$0.969409\pi$
$728$	−1.09560e15	−	2.69995e15i	−0.198578	−	0.489365i
$729$	−5.29864e15	−	1.68154e15i	−0.953154	−	0.302486i
$730$	1.01872e15	+	7.88438e15i	0.181877	+	1.40764i
$731$	−2.80418e15			−0.496889
$732$	2.36368e15	+	7.77598e14i	0.415698	+	0.136755i
$733$	−2.62345e15			−0.457933			−0.228966	−	0.973434i	$-0.573535\pi$
$733$	−2.62345e15			−0.457933			−0.228966	+	0.973434i	$0.573535\pi$
$734$	1.26909e15	+	9.82216e15i	0.219869	+	1.70168i
$735$	2.72624e15	−	4.20857e15i	0.468795	−	0.723692i
$736$	−5.62013e15	+	4.20610e15i	−0.959220	+	0.717879i
$737$			4.69149e14i			0.0794767i
$738$	2.31628e14	−	1.41904e14i	0.0389477	−	0.0238608i
$739$		−	6.95539e15i		−	1.16085i	−0.814313	−	0.580427i	$-0.802886\pi$
$739$		−	6.95539e15i		−	1.16085i	0.814313	−	0.580427i	$-0.197114\pi$
$740$	2.63886e15	+	1.00413e16i	0.437161	+	1.66347i
$741$	1.38108e15	−	2.13201e15i	0.227101	−	0.350582i
$742$	4.98691e15	−	6.44343e14i	0.813973	−	0.105171i
$743$	−8.86508e15			−1.43630			−0.718148	−	0.695890i	$-0.755010\pi$
$743$	−8.86508e15			−1.43630			−0.718148	+	0.695890i	$0.755010\pi$
$744$	1.60347e15	−	8.36776e15i	0.257876	−	1.34573i
$745$	1.72871e15			0.275970
$746$	−1.18275e16	+	1.52819e15i	−1.87425	+	0.242167i
$747$	1.09901e15	+	2.45329e15i	0.172877	+	0.385910i
$748$	3.67504e14	+	1.39841e15i	0.0573856	+	0.218361i
$749$			6.49401e13i			0.0100661i
$750$	−6.49497e15	+	1.35729e16i	−0.999402	+	2.08851i
$751$		−	1.04973e16i		−	1.60346i	−0.597685	−	0.801731i	$-0.703913\pi$
$751$		−	1.04973e16i		−	1.60346i	0.597685	−	0.801731i	$-0.296087\pi$
$752$	−1.62077e15	+	9.15079e14i	−0.245767	+	0.138759i
$753$	−7.22370e15	−	4.67939e15i	−1.08740	−	0.704397i
$754$	−5.50005e14	−	4.25678e15i	−0.0821910	−	0.636119i
$755$	2.37990e16			3.53061
$756$	−4.88797e15	+	5.06932e14i	−0.719878	+	0.0746585i
$757$	8.84480e15			1.29318			0.646592	−	0.762836i	$-0.276194\pi$
$757$	8.84480e15			1.29318			0.646592	+	0.762836i	$0.276194\pi$
$758$	−5.94828e14	−	4.60368e15i	−0.0863398	−	0.668228i
$759$	−3.27458e15	−	2.12122e15i	−0.471874	−	0.305672i
$760$	6.71350e15	−	2.72425e15i	0.960448	−	0.389738i
$761$			5.31012e15i			0.754204i	0.926172	+	0.377102i	$0.123079\pi$
$761$			5.31012e15i			0.754204i	−0.926172	+	0.377102i	$0.876921\pi$
$762$	3.81996e15	−	7.98279e15i	0.538650	−	1.12565i
$763$		−	4.10138e15i		−	0.574175i
$764$	−2.64160e14	+	6.94216e13i	−0.0367159	+	0.00964898i
$765$	2.58097e15	+	5.76147e15i	0.356161	+	0.795052i
$766$	−4.62359e15	+	5.97400e14i	−0.633462	+	0.0818478i
$767$	−5.34407e15			−0.726938
$768$	6.65706e15	−	3.24159e15i	0.899074	−	0.437796i
$769$	1.36475e16			1.83003			0.915016	−	0.403418i	$-0.132178\pi$
$769$	1.36475e16			1.83003			0.915016	+	0.403418i	$0.132178\pi$
$770$	4.58092e15	−	5.91887e14i	0.609893	−	0.0788025i
$771$	9.30624e14	−	1.43663e15i	0.123020	−	0.189909i
$772$	−1.19851e16	+	3.14970e15i	−1.57306	+	0.413404i
$773$			8.86752e14i			0.115562i	0.998329	+	0.0577810i	$0.0184025\pi$
$773$			8.86752e14i			0.115562i	−0.998329	+	0.0577810i	$0.981597\pi$
$774$	−6.80570e15	+	4.16943e15i	−0.880638	+	0.539513i
$775$			2.43014e16i			3.12228i
$776$	3.11173e15	−	1.26270e15i	0.396974	−	0.161087i
$777$	2.95058e15	−	4.55489e15i	0.373759	−	0.576982i
$778$	−2.79502e14	−	2.16321e15i	−0.0351559	−	0.272089i
$779$	2.09346e14			0.0261462
$780$	−3.32945e15	+	1.01206e16i	−0.412907	+	1.25512i
$781$	5.45484e15			0.671740
$782$	−6.04063e14	−	4.67516e15i	−0.0738661	−	0.571688i
$783$	−7.15361e15	−	1.10788e15i	−0.868632	−	0.134525i
$784$	3.43910e15	−	1.94170e15i	0.414674	−	0.234123i
$785$		−	1.33056e16i		−	1.59313i
$786$	−3.77255e15	−	1.80526e15i	−0.448551	−	0.214643i
$787$			7.23856e15i			0.854656i	0.904097	+	0.427328i	$0.140545\pi$
$787$			7.23856e15i			0.854656i	−0.904097	+	0.427328i	$0.859455\pi$
$788$	−2.19724e15	−	8.36084e15i	−0.257622	−	0.980292i
$789$	−5.41155e15	−	3.50551e15i	−0.630083	−	0.408157i
$790$	1.31665e16	−	1.70121e15i	1.52238	−	0.196702i
$791$	7.11161e15			0.816577
$792$	2.97117e15	+	2.84749e15i	0.338797	+	0.324694i
$793$	−2.81998e15			−0.319333
$794$	4.18360e15	−	5.40551e14i	0.470476	−	0.0607888i
$795$	−1.54314e16	−	9.99619e15i	−1.72340	−	1.11639i
$796$	−1.36052e15	−	5.17699e15i	−0.150898	−	0.574190i
$797$		−	2.85996e15i		−	0.315021i	−0.987517	−	0.157510i	$-0.949653\pi$
$797$		−	2.85996e15i		−	0.315021i	0.987517	−	0.157510i	$-0.0503467\pi$
$798$	−3.41625e15	−	1.63476e15i	−0.373709	−	0.178829i
$799$		−	1.24990e15i		−	0.135790i
$800$	−1.69083e16	+	1.26542e16i	−1.82434	+	1.36533i
$801$	5.67751e15	−	2.54336e15i	0.608386	−	0.272539i
$802$	−4.88887e14	−	3.78375e15i	−0.0520295	−	0.402683i
$803$	−3.48010e15			−0.367837
$804$	−5.04176e14	+	1.53255e15i	−0.0529266	+	0.160882i
$805$	−1.50592e16			−1.57009
$806$	1.23730e15	+	9.57608e15i	0.128124	+	0.991619i
$807$	−7.18195e15	+	1.10870e16i	−0.738649	+	1.14027i
$808$	1.31146e15	+	3.23188e15i	0.133965	+	0.330136i
$809$			1.13678e16i			1.15334i	0.816976	+	0.576671i	$0.195649\pi$
$809$			1.13678e16i			1.15334i	−0.816976	+	0.576671i	$0.804351\pi$
$810$	1.48305e16	+	1.01454e16i	1.49448	+	1.02236i
$811$		−	6.60126e15i		−	0.660712i	−0.943856	−	0.330356i	$-0.892831\pi$
$811$		−	6.60126e15i		−	0.660712i	0.943856	−	0.330356i	$-0.107169\pi$
$812$	−6.18900e15	+	1.62648e15i	−0.615265	+	0.161693i
$813$	−5.10178e15	+	7.87574e15i	−0.503760	+	0.777667i
$814$	−4.50738e15	+	5.82385e14i	−0.442069	+	0.0571184i
$815$	1.04484e16			1.01785
$816$	−3.02302e14	+	4.96308e15i	−0.0292513	+	0.480237i
$817$	−6.15101e15			−0.591187
$818$	2.96370e14	−	3.82931e13i	0.0282938	−	0.00365575i
$819$	5.08254e15	−	2.27683e15i	0.481970	−	0.215909i
$820$	−8.49195e14	+	2.23170e14i	−0.0799892	+	0.0210213i
$821$			9.38148e15i			0.877777i	0.898542	+	0.438888i	$0.144628\pi$
$821$			9.38148e15i			0.877777i	−0.898542	+	0.438888i	$0.855372\pi$
$822$	6.95375e15	−	1.45317e16i	0.646285	−	1.35058i
$823$			1.16112e16i			1.07196i	0.844231	+	0.535980i	$0.180058\pi$
$823$			1.16112e16i			1.07196i	−0.844231	+	0.535980i	$0.819942\pi$
$824$	−4.61144e15	−	1.13642e16i	−0.422899	−	1.04217i
$825$	−9.85168e15	−	6.38176e15i	−0.897457	−	0.581358i
$826$	1.02096e15	+	7.90175e15i	0.0923888	+	0.715045i
$827$	5.37765e15			0.483406			0.241703	−	0.970350i	$-0.422294\pi$
$827$	5.37765e15			0.483406			0.241703	+	0.970350i	$0.422294\pi$
$828$	−8.41738e15	−	1.04484e16i	−0.751640	−	0.933001i
$829$	−3.61395e15			−0.320577			−0.160288	−	0.987070i	$-0.551242\pi$
$829$	−3.61395e15			−0.320577			−0.160288	+	0.987070i	$0.551242\pi$
$830$	−1.11345e15	−	8.61754e15i	−0.0981160	−	0.759370i
$831$	−4.04089e15	−	2.61762e15i	−0.353730	−	0.229140i
$832$	−6.01853e15	+	5.84733e15i	−0.523374	+	0.508486i
$833$			2.65215e15i			0.229114i
$834$	6.17292e15	−	1.28999e16i	0.529758	−	1.10706i
$835$		−	3.31825e16i		−	2.82900i
$836$	8.06126e14	+	3.06744e15i	0.0682761	+	0.259801i
$837$	1.60928e16	+	2.49230e15i	1.35407	+	0.209706i
$838$	1.49963e16	−	1.93763e15i	1.25355	−	0.161968i
$839$	−7.73967e15			−0.642734			−0.321367	−	0.946955i	$-0.604142\pi$
$839$	−7.73967e15			−0.642734			−0.321367	+	0.946955i	$0.604142\pi$
$840$	1.56004e16	+	2.98943e15i	1.28706	+	0.246634i
$841$	2.77417e15			0.227382
$842$	2.17533e15	−	2.81067e14i	0.177136	−	0.0228873i
$843$	−1.12653e15	+	1.73905e15i	−0.0911360	+	0.140689i
$844$	4.69533e15	+	1.78664e16i	0.377383	+	1.43600i
$845$			1.06014e16i			0.846546i
$846$	−1.85843e15	−	3.03348e15i	−0.147438	−	0.240660i
$847$		−	7.16009e15i		−	0.564365i
$848$	−7.11957e15	−	1.26100e16i	−0.557541	−	0.987504i
$849$	−6.83152e15	+	1.05460e16i	−0.531527	+	0.820532i
$850$	−1.81734e15	−	1.40654e16i	−0.140486	−	1.08729i
$851$	1.48175e16			1.13805
$852$	1.78192e16	+	5.86210e15i	1.35978	+	0.447337i
$853$	−7.55971e15			−0.573173			−0.286586	−	0.958054i	$-0.592521\pi$
$853$	−7.55971e15			−0.573173			−0.286586	+	0.958054i	$0.592521\pi$
$854$	5.38745e14	+	4.16963e15i	0.0405850	+	0.314108i
$855$	5.66141e15	+	1.26379e16i	0.423751	+	0.945934i
$856$	1.73295e14	−	7.03209e13i	0.0128879	−	0.00522972i
$857$		−	1.99276e16i		−	1.47251i	−0.676702	−	0.736257i	$-0.736591\pi$
$857$		−	1.99276e16i		−	1.47251i	0.676702	−	0.736257i	$-0.263409\pi$
$858$	−4.20703e15	−	2.01317e15i	−0.308884	−	0.147809i
$859$			1.15303e16i			0.841160i	0.907255	+	0.420580i	$0.138173\pi$
$859$			1.15303e16i			0.841160i	−0.907255	+	0.420580i	$0.861827\pi$
$860$	2.49510e16	−	6.55717e15i	1.80862	−	0.475308i
$861$	3.85209e14	+	2.49532e14i	0.0277447	+	0.0179725i
$862$	−1.15422e16	+	1.49133e15i	−0.826036	+	0.106730i
$863$	6.91894e15			0.492017			0.246009	−	0.969268i	$-0.420881\pi$
$863$	6.91894e15			0.492017			0.246009	+	0.969268i	$0.420881\pi$
$864$	6.64575e15	+	1.24948e16i	0.469590	+	0.882885i
$865$	3.30213e14			0.0231849
$866$	−8.06600e13	+	1.04218e13i	−0.00562743	+	0.000727103i
$867$	9.30405e15	+	6.02701e15i	0.645011	+	0.417827i
$868$	1.39228e16	−	3.65894e15i	0.959111	−	0.252056i
$869$			5.81160e15i			0.397820i
$870$	2.11064e16	+	1.00999e16i	1.43568	+	0.687009i
$871$		−	1.82841e15i		−	0.123587i
$872$	−1.09447e16	+	4.44121e15i	−0.735127	+	0.298305i
$873$	2.62408e15	+	5.85771e15i	0.175146	+	0.390975i
$874$	−1.32502e15	−	1.02550e16i	−0.0878841	−	0.680181i
$875$	−2.54235e16			−1.67568
$876$	−1.13683e16	−	3.73992e15i	−0.744601	−	0.244957i
$877$	−2.46990e16			−1.60761			−0.803806	−	0.594891i	$-0.797195\pi$
$877$	−2.46990e16			−1.60761			−0.803806	+	0.594891i	$0.797195\pi$
$878$	1.04739e15	+	8.10627e15i	0.0677465	+	0.524326i
$879$	7.77976e15	−	1.20098e16i	0.500066	−	0.771965i
$880$	−6.53997e15	−	1.15834e16i	−0.417754	−	0.739917i
$881$		−	9.03879e15i		−	0.573776i	−0.957964	−	0.286888i	$-0.907379\pi$
$881$		−	9.03879e15i		−	0.573776i	0.957964	−	0.286888i	$-0.0926208\pi$
$882$	3.94339e15	+	6.43673e15i	0.248767	+	0.406058i
$883$			1.32723e16i			0.832074i	0.909348	+	0.416037i	$0.136581\pi$
$883$			1.32723e16i			0.832074i	−0.909348	+	0.416037i	$0.863419\pi$
$884$	−1.43227e15	−	5.45000e15i	−0.0892352	−	0.339554i
$885$	1.58390e16	−	2.44510e16i	0.980706	−	1.51394i
$886$	−2.85820e16	+	3.69299e15i	−1.75876	+	0.227244i
$887$	−2.48889e16			−1.52204			−0.761020	−	0.648729i	$-0.775301\pi$
$887$	−2.48889e16			−1.52204			−0.761020	+	0.648729i	$0.775301\pi$
$888$	−1.53500e16	−	2.94144e15i	−0.932902	−	0.178768i
$889$	1.49526e16			0.903145
$890$	−1.99430e16	+	2.57678e15i	−1.19714	+	0.154679i
$891$	−5.23649e15	+	5.86947e15i	−0.312401	+	0.350164i
$892$	−3.17459e15	−	1.20798e16i	−0.188227	−	0.716232i
$893$		−	2.74167e15i		−	0.161559i
$894$	−1.12331e15	+	2.34745e15i	−0.0657876	+	0.137480i
$895$		−	8.95619e15i		−	0.521311i
$896$	9.79569e15	+	7.78191e15i	0.566684	+	0.450186i
$897$	1.27620e16	+	8.26699e15i	0.733769	+	0.475323i
$898$	4.20066e15	+	3.25111e16i	0.240048	+	1.85785i
$899$	2.12056e16			1.20440
$900$	−2.53240e16	−	3.14343e16i	−1.42954	−	1.77447i
$901$	9.72454e15			0.545610
$902$	−4.92526e13	−	3.81191e14i	−0.00274658	−	0.0212572i
$903$	−1.13182e16	−	7.33175e15i	−0.627329	−	0.406373i
$904$	−7.70087e15	−	1.89776e16i	−0.424242	−	1.04548i
$905$			1.59464e16i			0.873162i
$906$	−1.54645e16	+	3.23171e16i	−0.841651	+	1.75885i
$907$			2.71352e16i			1.46789i	0.679211	+	0.733943i	$0.262322\pi$
$907$			2.71352e16i			1.46789i	−0.679211	+	0.733943i	$0.737678\pi$
$908$	−1.63299e14	+	4.29151e13i	−0.00878031	+	0.00230748i
$909$	−6.08388e15	+	2.72541e15i	−0.325147	+	0.145656i
$910$	−1.78531e16	+	2.30675e15i	−0.948390	+	0.122539i
$911$	−2.87458e15			−0.151783			−0.0758916	−	0.997116i	$-0.524180\pi$
$911$	−2.87458e15			−0.151783			−0.0758916	+	0.997116i	$0.524180\pi$
$912$	−6.63104e14	+	1.08866e16i	−0.0348025	+	0.571375i
$913$	3.80371e15			0.198435
$914$	1.40110e16	−	1.81031e15i	0.726547	−	0.0938750i
$915$	8.35797e15	−	1.29024e16i	0.430809	−	0.665051i
$916$	1.18989e16	−	3.12704e15i	0.609651	−	0.160217i
$917$		−	7.06640e15i		−	0.359888i
$918$	−9.50073e15	−	2.39037e14i	−0.480975	−	0.0121013i
$919$		−	9.25693e15i		−	0.465834i	−0.972497	−	0.232917i	$-0.925173\pi$
$919$		−	9.25693e15i		−	0.465834i	0.972497	−	0.232917i	$-0.0748271\pi$
$920$	1.63070e16	+	4.01862e16i	0.815721	+	2.01022i
$921$	3.66592e15	−	5.65918e15i	0.182287	−	0.281401i
$922$	−1.09607e15	−	8.48306e15i	−0.0541775	−	0.419308i
$923$	−2.12591e16			−1.04456
$924$	−2.17294e15	+	6.60513e15i	−0.106133	+	0.322616i
$925$	4.45788e16			2.16446
$926$	−1.21559e15	−	9.40812e15i	−0.0586716	−	0.454090i
$927$	2.13926e16	−	9.58328e15i	1.02642	−	0.459807i
$928$	1.10421e16	+	1.47543e16i	0.526671	+	0.703730i
$929$		−	2.88037e16i		−	1.36572i	−0.730550	−	0.682859i	$-0.760736\pi$
$929$		−	2.88037e16i		−	1.36572i	0.730550	−	0.682859i	$-0.239264\pi$
$930$	−4.74811e16	−	2.27209e16i	−2.23802	−	1.07095i
$931$			5.81754e15i			0.272594i
$932$	3.49016e15	+	1.32806e16i	0.162577	+	0.618630i
$933$	−2.82107e16	−	1.82744e16i	−1.30637	−	0.846242i
$934$	2.34009e16	−	3.02356e15i	1.07727	−	0.139191i
$935$	8.93286e15			0.408815
$936$	−1.15795e16	−	1.10975e16i	−0.526833	−	0.504902i
$937$	−1.10897e16			−0.501594			−0.250797	−	0.968040i	$-0.580693\pi$
$937$	−1.10897e16			−0.501594			−0.250797	+	0.968040i	$0.580693\pi$
$938$	−2.70349e15	+	3.49310e14i	−0.121565	+	0.0157071i
$939$	1.28756e16	+	8.34059e15i	0.575581	+	0.372852i
$940$	2.92271e15	+	1.11213e16i	0.129892	+	0.494259i
$941$		−	2.37996e16i		−	1.05154i	−0.850626	−	0.525771i	$-0.823777\pi$
$941$		−	2.37996e16i		−	1.05154i	0.850626	−	0.525771i	$-0.176223\pi$
$942$	1.80679e16	+	8.64595e15i	0.793649	+	0.379781i
$943$			1.25312e15i			0.0547241i
$944$	1.99806e16	−	1.12810e16i	0.867485	−	0.489779i
$945$	−4.64652e15	+	3.00026e16i	−0.200564	+	1.29504i
$946$	1.44714e15	+	1.12002e16i	0.0621025	+	0.480643i
$947$	−1.42613e16			−0.608461			−0.304231	−	0.952598i	$-0.598399\pi$
$947$	−1.42613e16			−0.608461			−0.304231	+	0.952598i	$0.598399\pi$
$948$	−6.24549e15	+	1.89846e16i	−0.264924	+	0.805294i
$949$	1.35629e16			0.571990
$950$	−3.98637e15	−	3.08526e16i	−0.167147	−	1.29364i
$951$	−9.67589e15	+	1.49369e16i	−0.403365	+	0.622685i
$952$	−7.78475e15	+	3.15895e15i	−0.322657	+	0.130930i
$953$			2.70315e15i			0.111393i	0.998448	+	0.0556966i	$0.0177380\pi$
$953$			2.70315e15i			0.111393i	−0.998448	+	0.0556966i	$0.982262\pi$
$954$	2.36013e16	−	1.44591e16i	0.966986	−	0.592413i
$955$			1.68742e15i			0.0687393i
$956$	4.27540e16	−	1.12358e16i	1.73164	−	0.455078i
$957$	−5.56877e15	+	8.59666e15i	−0.224256	+	0.346190i
$958$	−9.60269e15	+	1.24073e15i	−0.384488	+	0.0496785i
$959$	2.72194e16			1.08362
$960$	−8.91564e15	−	4.48675e16i	−0.352907	−	1.77599i
$961$	−2.22957e16			−0.877491
$962$	1.75665e16	−	2.26972e15i	0.687421	−	0.0888196i
$963$	1.46138e14	+	3.26221e14i	0.00568614	+	0.0126931i
$964$	4.28480e16	−	1.12605e16i	1.65770	−	0.435647i
$965$			7.65593e16i			2.94508i
$966$	9.78547e15	−	2.04492e16i	0.374289	−	0.782174i
$967$		−	5.03785e16i		−	1.91602i	−0.286738	−	0.958009i	$-0.592571\pi$
$967$		−	5.03785e16i		−	1.91602i	0.286738	−	0.958009i	$-0.407429\pi$
$968$	−1.91070e16	+	7.75337e15i	−0.722566	+	0.293208i
$969$	−6.14722e15	−	3.98207e15i	−0.231152	−	0.149737i
$970$	−2.65856e15	−	2.05760e16i	−0.0994037	−	0.769337i
$971$	−2.86569e16			−1.06543			−0.532713	−	0.846296i	$-0.678827\pi$
$971$	−2.86569e16			−1.06543			−0.532713	+	0.846296i	$0.678827\pi$
$972$	−2.34136e16	+	1.35462e16i	−0.865571	+	0.500786i
$973$	2.41629e16			0.888236
$974$	4.23050e15	+	3.27421e16i	0.154639	+	1.19683i
$975$	3.83948e16	+	2.48715e16i	1.39555	+	0.904017i
$976$	1.05434e16	−	5.95278e15i	0.381073	−	0.215152i
$977$			2.46762e16i			0.886866i	0.896307	+	0.443433i	$0.146240\pi$
$977$			2.46762e16i			0.886866i	−0.896307	+	0.443433i	$0.853760\pi$
$978$	−6.78938e15	+	1.41881e16i	−0.242642	+	0.507063i
$979$		−	8.80269e15i		−	0.312831i
$980$	−6.20168e15	−	2.35984e16i	−0.219162	−	0.833947i
$981$	−9.22952e15	−	2.06029e16i	−0.324339	−	0.724018i
$982$	−2.28518e16	+	2.95261e15i	−0.798560	+	0.103180i
$983$	−1.93957e16			−0.674001			−0.337000	−	0.941505i	$-0.609412\pi$
$983$	−1.93957e16			−0.674001			−0.337000	+	0.941505i	$0.609412\pi$
$984$	2.48759e14	−	1.29815e15i	0.00859619	−	0.0448594i
$985$	−5.34080e16			−1.83530
$986$	−1.22735e16	+	1.58583e15i	−0.419418	+	0.0541917i
$987$	3.26796e15	−	5.04483e15i	0.111053	−	0.171436i
$988$	−3.14170e15	−	1.19547e16i	−0.106170	−	0.403993i
$989$		−	3.68192e16i		−	1.23736i
$990$	2.16799e16	−	1.32820e16i	0.724543	−	0.443883i
$991$			2.05308e16i			0.682341i	0.940001	+	0.341170i	$0.110823\pi$
$991$			2.05308e16i			0.682341i	−0.940001	+	0.341170i	$0.889177\pi$
$992$	−2.48405e16	−	3.31915e16i	−0.821005	−	1.09702i
$993$	−1.54881e16	+	2.39093e16i	−0.509069	+	0.785863i
$994$	4.06145e15	+	3.14337e16i	0.132757	+	1.02747i
$995$	−3.30700e16			−1.07500
$996$	1.24254e16	+	4.08769e15i	0.401685	+	0.132145i
$997$	−3.27724e16			−1.05362			−0.526812	−	0.849982i	$-0.676613\pi$
$997$	−3.27724e16			−1.05362			−0.526812	+	0.849982i	$0.676613\pi$
$998$	3.81677e15	+	2.95399e16i	0.122033	+	0.944477i
$999$	4.57192e15	−	2.95209e16i	0.145375	−	0.938686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.12.b.a.11.19	yes	20
3.2	odd	2	inner	12.12.b.a.11.2	yes	20
4.3	odd	2	inner	12.12.b.a.11.1	✓	20
8.3	odd	2		192.12.c.d.191.16		20
8.5	even	2		192.12.c.d.191.5		20
12.11	even	2	inner	12.12.b.a.11.20	yes	20
24.5	odd	2		192.12.c.d.191.15		20
24.11	even	2		192.12.c.d.191.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.12.b.a.11.1	✓	20	4.3	odd	2	inner
12.12.b.a.11.2	yes	20	3.2	odd	2	inner
12.12.b.a.11.19	yes	20	1.1	even	1	trivial
12.12.b.a.11.20	yes	20	12.11	even	2	inner
192.12.c.d.191.5		20	8.5	even	2
192.12.c.d.191.6		20	24.11	even	2
192.12.c.d.191.15		20	24.5	odd	2
192.12.c.d.191.16		20	8.3	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)

\(f(q)\)	\(=\)	\(q+(44.8817 - 5.79904i) q^{2} +(353.249 + 228.828i) q^{3} +(1980.74 - 520.542i) q^{4} -12652.7i q^{5} +(17181.4 + 8221.72i) q^{6} +32182.6i q^{7} +(85880.5 - 34849.2i) q^{8} +(72422.0 + 161667. i) q^{9} +O(q^{10})\)	\(q+(44.8817 - 5.79904i) q^{2} +(353.249 + 228.828i) q^{3} +(1980.74 - 520.542i) q^{4} -12652.7i q^{5} +(17181.4 + 8221.72i) q^{6} +32182.6i q^{7} +(85880.5 - 34849.2i) q^{8} +(72422.0 + 161667. i) q^{9} +(-73373.6 - 567877. i) q^{10} +250656. q^{11} +(818809. + 269370. i) q^{12} -976876. q^{13} +(186628. + 1.44441e6i) q^{14} +(2.89530e6 - 4.46956e6i) q^{15} +(3.65238e6 - 2.06212e6i) q^{16} +2.81662e6i q^{17} +(4.18794e6 + 6.83590e6i) q^{18} +6.17831e6i q^{19} +(-6.58627e6 - 2.50618e7i) q^{20} +(-7.36430e6 + 1.13685e7i) q^{21} +(1.12499e7 - 1.45356e6i) q^{22} -3.69826e7 q^{23} +(3.83117e7 + 7.34148e6i) q^{24} -1.11263e8 q^{25} +(-4.38439e7 + 5.66494e6i) q^{26} +(-1.14110e7 + 7.36807e7i) q^{27} +(1.67524e7 + 6.37455e7i) q^{28} +9.70893e7i q^{29} +(1.04027e8 - 2.17392e8i) q^{30} -2.18413e8i q^{31} +(1.51967e8 - 1.13732e8i) q^{32} +(8.85438e7 + 5.73572e7i) q^{33} +(1.63337e7 + 1.26415e8i) q^{34} +4.07198e8 q^{35} +(2.27604e8 + 2.82521e8i) q^{36} -4.00660e8 q^{37} +(3.58283e7 + 2.77293e8i) q^{38} +(-3.45080e8 - 2.23537e8i) q^{39} +(-4.40938e8 - 1.08662e9i) q^{40} -3.38841e7i q^{41} +(-2.64596e8 + 5.52942e8i) q^{42} +9.95581e8i q^{43} +(4.96485e8 - 1.30477e8i) q^{44} +(2.04552e9 - 9.16336e8i) q^{45} +(-1.65984e9 + 2.14464e8i) q^{46} -4.43757e8 q^{47} +(1.76207e9 + 1.07328e8i) q^{48} +9.41607e8 q^{49} +(-4.99370e9 + 6.45221e8i) q^{50} +(-6.44524e8 + 9.94968e8i) q^{51} +(-1.93494e9 + 5.08505e8i) q^{52} -3.45255e9i q^{53} +(-8.48666e7 + 3.37309e9i) q^{54} -3.17148e9i q^{55} +(1.12154e9 + 2.76386e9i) q^{56} +(-1.41377e9 + 2.18248e9i) q^{57} +(5.63025e8 + 4.35754e9i) q^{58} +5.47057e9 q^{59} +(3.40826e9 - 1.03602e10i) q^{60} +2.88673e9 q^{61} +(-1.26658e9 - 9.80275e9i) q^{62} +(-5.20285e9 + 2.33073e9i) q^{63} +(6.16100e9 - 5.98574e9i) q^{64} +1.23601e10i q^{65} +(4.30662e9 + 2.06082e9i) q^{66} +1.87169e9i q^{67} +(1.46617e9 + 5.57901e9i) q^{68} +(-1.30641e10 - 8.46268e9i) q^{69} +(1.82757e10 - 2.36135e9i) q^{70} +2.17623e10 q^{71} +(1.18536e10 + 1.13602e10i) q^{72} -1.38840e10 q^{73} +(-1.79823e10 + 2.32344e9i) q^{74} +(-3.93036e10 - 2.54602e10i) q^{75} +(3.21607e9 + 1.22376e10i) q^{76} +8.06676e9i q^{77} +(-1.67841e10 - 8.03160e9i) q^{78} +2.31856e10i q^{79} +(-2.60914e10 - 4.62125e10i) q^{80} +(-2.08912e10 + 2.34165e10i) q^{81} +(-1.96495e8 - 1.52078e9i) q^{82} +1.51750e10 q^{83} +(-8.66902e9 + 2.63514e10i) q^{84} +3.56380e10 q^{85} +(5.77341e9 + 4.46834e10i) q^{86} +(-2.22168e10 + 3.42967e10i) q^{87} +(2.15265e10 - 8.73516e9i) q^{88} -3.51186e10i q^{89} +(8.64928e10 - 5.29888e10i) q^{90} -3.14384e10i q^{91} +(-7.32530e10 + 1.92510e10i) q^{92} +(4.99791e10 - 7.71540e10i) q^{93} +(-1.99166e10 + 2.57336e9i) q^{94} +7.81725e10 q^{95} +(7.97071e10 - 5.40124e9i) q^{96} +3.62332e10 q^{97} +(4.22609e10 - 5.46041e9i) q^{98} +(1.81530e10 + 4.05227e10i) 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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