LMFDB - Embedded newform 12.12.b.a.11.8

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			11.8
Root			$-12.1023 + 19.1190i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.12.b.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-24.2046 + 38.2379i) q^{2} +(-183.786 + 378.642i) q^{3} +(-876.277 - 1851.07i) q^{4} -9922.43i q^{5} +(-10030.0 - 16192.5i) q^{6} +35930.2i q^{7} +(91990.8 + 11297.3i) q^{8} +(-109593. - 139178. i) q^{9} +O(q^{10})$	\(q+(-24.2046 + 38.2379i) q^{2} +(-183.786 + 378.642i) q^{3} +(-876.277 - 1851.07i) q^{4} -9922.43i q^{5} +(-10030.0 - 16192.5i) q^{6} +35930.2i q^{7} +(91990.8 + 11297.3i) q^{8} +(-109593. - 139178. i) q^{9} +(379413. + 240168. i) q^{10} -123230. q^{11} +(861938. + 8404.29i) q^{12} +2.19224e6 q^{13} +(-1.37390e6 - 869675. i) q^{14} +(3.75705e6 + 1.82360e6i) q^{15} +(-2.65858e6 + 3.24409e6i) q^{16} -3.57618e6i q^{17} +(7.97452e6 - 821847. i) q^{18} -1.28849e7i q^{19} +(-1.83671e7 + 8.69479e6i) q^{20} +(-1.36047e7 - 6.60346e6i) q^{21} +(2.98274e6 - 4.71207e6i) q^{22} +2.29651e7 q^{23} +(-2.11842e7 + 3.27553e7i) q^{24} -4.96265e7 q^{25} +(-5.30622e7 + 8.38267e7i) q^{26} +(7.28402e7 - 1.59174e7i) q^{27} +(6.65091e7 - 3.14848e7i) q^{28} -8.68394e7i q^{29} +(-1.60669e8 + 9.95222e7i) q^{30} -1.57029e8i q^{31} +(-5.96974e7 - 1.80181e8i) q^{32} +(2.26480e7 - 4.66602e7i) q^{33} +(1.36746e8 + 8.65599e7i) q^{34} +3.56515e8 q^{35} +(-1.61594e8 + 3.24822e8i) q^{36} +4.22727e8 q^{37} +(4.92693e8 + 3.11874e8i) q^{38} +(-4.02902e8 + 8.30074e8i) q^{39} +(1.12096e8 - 9.12772e8i) q^{40} -1.60981e8i q^{41} +(5.81798e8 - 3.60381e8i) q^{42} -7.07367e8i q^{43} +(1.07984e8 + 2.28107e8i) q^{44} +(-1.38098e9 + 1.08742e9i) q^{45} +(-5.55861e8 + 8.78137e8i) q^{46} -3.00646e9 q^{47} +(-7.39740e8 - 1.60287e9i) q^{48} +6.86348e8 q^{49} +(1.20119e9 - 1.89761e9i) q^{50} +(1.35409e9 + 6.57251e8i) q^{51} +(-1.92101e9 - 4.05798e9i) q^{52} +1.95845e9i q^{53} +(-1.15442e9 + 3.17053e9i) q^{54} +1.22274e9i q^{55} +(-4.05913e8 + 3.30525e9i) q^{56} +(4.87878e9 + 2.36807e9i) q^{57} +(3.32056e9 + 2.10191e9i) q^{58} -3.47121e9 q^{59} +(8.33910e7 - 8.55252e9i) q^{60} -3.58923e9 q^{61} +(6.00445e9 + 3.80082e9i) q^{62} +(5.00069e9 - 3.93768e9i) q^{63} +(8.33468e9 + 2.07849e9i) q^{64} -2.17523e10i q^{65} +(1.23600e9 + 1.99540e9i) q^{66} +7.20969e9i q^{67} +(-6.61974e9 + 3.13372e9i) q^{68} +(-4.22066e9 + 8.69555e9i) q^{69} +(-8.62929e9 + 1.36324e10i) q^{70} +1.78852e10 q^{71} +(-8.50918e9 - 1.40412e10i) q^{72} +2.02363e9 q^{73} +(-1.02319e10 + 1.61642e10i) q^{74} +(9.12064e9 - 1.87907e10i) q^{75} +(-2.38509e10 + 1.12908e10i) q^{76} -4.42769e9i q^{77} +(-2.19882e10 - 3.54977e10i) q^{78} -2.09965e10i q^{79} +(3.21893e10 + 2.63796e10i) q^{80} +(-7.35999e9 + 3.05058e10i) q^{81} +(6.15560e9 + 3.89649e9i) q^{82} -3.45636e10 q^{83} +(-3.01968e8 + 3.09696e10i) q^{84} -3.54844e10 q^{85} +(2.70482e10 + 1.71215e10i) q^{86} +(3.28810e10 + 1.59598e10i) q^{87} +(-1.13361e10 - 1.39217e9i) q^{88} -6.54648e10i q^{89} +(-8.15471e9 - 7.91266e10i) q^{90} +7.87676e10i q^{91} +(-2.01238e10 - 4.25099e10i) q^{92} +(5.94577e10 + 2.88597e10i) q^{93} +(7.27701e10 - 1.14961e11i) q^{94} -1.27850e11 q^{95} +(7.91954e10 + 1.05107e10i) q^{96} +9.06908e10 q^{97} +(-1.66128e10 + 2.62445e10i) q^{98} +(1.35051e10 + 1.71510e10i) 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 $

$2$	−24.2046	+	38.2379i	−0.534851	+	0.844947i
$2$	−24.2046	+	38.2379i	−0.534851	+	0.844947i
$3$	−183.786	+	378.642i	−0.436662	+	0.899626i
$3$	−183.786	+	378.642i	−0.436662	+	0.899626i
$4$	−876.277	−	1851.07i	−0.427869	−	0.903841i
$5$		−	9922.43i		−	1.41998i	−0.704210	−	0.709991i	$-0.748699\pi$
$5$		−	9922.43i		−	1.41998i	0.704210	−	0.709991i	$-0.251301\pi$
$6$	−10030.0	−	16192.5i	−0.526587	−	0.850121i
$7$			35930.2i			0.808017i	0.914755	+	0.404008i	$0.132383\pi$
$7$			35930.2i			0.808017i	−0.914755	+	0.404008i	$0.867617\pi$
$8$	91990.8	+	11297.3i	0.992543	+	0.121893i
$9$	−109593.	−	139178.i	−0.618653	−	0.785664i
$10$	379413.	+	240168.i	1.19981	+	0.759479i
$11$	−123230.			−0.230705			−0.115353	−	0.993325i	$-0.536800\pi$
$11$	−123230.			−0.230705			−0.115353	+	0.993325i	$0.536800\pi$
$12$	861938.	+	8404.29i	0.999952	+	0.00974999i
$13$	2.19224e6			1.63757			0.818784	−	0.574101i	$-0.194648\pi$
$13$	2.19224e6			1.63757			0.818784	+	0.574101i	$0.194648\pi$
$14$	−1.37390e6	−	869675.i	−0.682731	−	0.432168i
$15$	3.75705e6	+	1.82360e6i	1.27745	+	0.620052i
$16$	−2.65858e6	+	3.24409e6i	−0.633855	+	0.773452i
$17$		−	3.57618e6i		−	0.610872i	−0.952213	−	0.305436i	$-0.901198\pi$
$17$		−	3.57618e6i		−	0.610872i	0.952213	−	0.305436i	$-0.0988022\pi$
$18$	7.97452e6	−	821847.i	0.994731	−	0.102516i
$19$		−	1.28849e7i		−	1.19382i	−0.802310	−	0.596908i	$-0.796396\pi$
$19$		−	1.28849e7i		−	1.19382i	0.802310	−	0.596908i	$-0.203604\pi$
$20$	−1.83671e7	+	8.69479e6i	−1.28344	+	0.607567i
$21$	−1.36047e7	−	6.60346e6i	−0.726913	−	0.352830i
$22$	2.98274e6	−	4.71207e6i	0.123393	−	0.194934i
$23$	2.29651e7			0.743987			0.371993	−	0.928235i	$-0.378674\pi$
$23$	2.29651e7			0.743987			0.371993	+	0.928235i	$0.378674\pi$
$24$	−2.11842e7	+	3.27553e7i	−0.543064	+	0.839692i
$25$	−4.96265e7			−1.01635
$26$	−5.30622e7	+	8.38267e7i	−0.875855	+	1.38366i
$27$	7.28402e7	−	1.59174e7i	0.976946	−	0.213487i
$28$	6.65091e7	−	3.14848e7i	0.730318	−	0.345726i
$29$		−	8.68394e7i		−	0.786190i	−0.919498	−	0.393095i	$-0.871404\pi$
$29$		−	8.68394e7i		−	0.786190i	0.919498	−	0.393095i	$-0.128596\pi$
$30$	−1.60669e8	+	9.95222e7i	−1.20716	+	0.747744i
$31$		−	1.57029e8i		−	0.985122i	−0.870278	−	0.492561i	$-0.836061\pi$
$31$		−	1.57029e8i		−	0.985122i	0.870278	−	0.492561i	$-0.163939\pi$
$32$	−5.96974e7	−	1.80181e8i	−0.314507	−	0.949255i
$33$	2.26480e7	−	4.66602e7i	0.100740	−	0.207549i
$34$	1.36746e8	+	8.65599e7i	0.516154	+	0.326725i
$35$	3.56515e8			1.14737
$36$	−1.61594e8	+	3.24822e8i	−0.445412	+	0.895326i
$37$	4.22727e8			1.00219			0.501096	−	0.865392i	$-0.332930\pi$
$37$	4.22727e8			1.00219			0.501096	+	0.865392i	$0.332930\pi$
$38$	4.92693e8	+	3.11874e8i	1.00871	+	0.638513i
$39$	−4.02902e8	+	8.30074e8i	−0.715063	+	1.47320i
$40$	1.12096e8	−	9.12772e8i	0.173086	−	1.40939i
$41$		−	1.60981e8i		−	0.217002i	−0.994096	−	0.108501i	$-0.965395\pi$
$41$		−	1.60981e8i		−	0.217002i	0.994096	−	0.108501i	$-0.0346051\pi$
$42$	5.81798e8	−	3.60381e8i	0.686912	−	0.425491i
$43$		−	7.07367e8i		−	0.733784i	−0.930264	−	0.366892i	$-0.880422\pi$
$43$		−	7.07367e8i		−	0.733784i	0.930264	−	0.366892i	$-0.119578\pi$
$44$	1.07984e8	+	2.28107e8i	0.0987118	+	0.208521i
$45$	−1.38098e9	+	1.08742e9i	−1.11563	+	0.878477i
$46$	−5.55861e8	+	8.78137e8i	−0.397922	+	0.628629i
$47$	−3.00646e9			−1.91213			−0.956065	−	0.293155i	$-0.905295\pi$
$47$	−3.00646e9			−1.91213			−0.956065	+	0.293155i	$0.905295\pi$
$48$	−7.39740e8	−	1.60287e9i	−0.419037	−	0.907969i
$49$	6.86348e8			0.347109
$50$	1.20119e9	−	1.89761e9i	0.543596	−	0.858762i
$51$	1.35409e9	+	6.57251e8i	0.549556	+	0.266744i
$52$	−1.92101e9	−	4.05798e9i	−0.700666	−	1.48010i
$53$			1.95845e9i			0.643274i	0.946863	+	0.321637i	$0.104233\pi$
$53$			1.95845e9i			0.643274i	−0.946863	+	0.321637i	$0.895767\pi$
$54$	−1.15442e9	+	3.17053e9i	−0.342135	+	0.939651i
$55$			1.22274e9i			0.327598i
$56$	−4.05913e8	+	3.30525e9i	−0.0984915	+	0.801992i
$57$	4.87878e9	+	2.36807e9i	1.07399	+	0.521294i
$58$	3.32056e9	+	2.10191e9i	0.664289	+	0.420494i
$59$	−3.47121e9			−0.632112			−0.316056	−	0.948740i	$-0.602359\pi$
$59$	−3.47121e9			−0.632112			−0.316056	+	0.948740i	$0.602359\pi$
$60$	8.33910e7	−	8.55252e9i	0.0138448	−	1.41992i
$61$	−3.58923e9			−0.544111			−0.272055	−	0.962282i	$-0.587703\pi$
$61$	−3.58923e9			−0.544111			−0.272055	+	0.962282i	$0.587703\pi$
$62$	6.00445e9	+	3.80082e9i	0.832375	+	0.526893i
$63$	5.00069e9	−	3.93768e9i	0.634830	−	0.499882i
$64$	8.33468e9	+	2.07849e9i	0.970284	+	0.241968i
$65$		−	2.17523e10i		−	2.32532i
$66$	1.23600e9	+	1.99540e9i	0.121487	+	0.196128i
$67$			7.20969e9i			0.652387i	0.945303	+	0.326193i	$0.105766\pi$
$67$			7.20969e9i			0.652387i	−0.945303	+	0.326193i	$0.894234\pi$
$68$	−6.61974e9	+	3.13372e9i	−0.552131	+	0.261373i
$69$	−4.22066e9	+	8.69555e9i	−0.324870	+	0.669310i
$70$	−8.62929e9	+	1.36324e10i	−0.613671	+	0.969466i
$71$	1.78852e10			1.17645			0.588223	−	0.808699i	$-0.299828\pi$
$71$	1.78852e10			1.17645			0.588223	+	0.808699i	$0.299828\pi$
$72$	−8.50918e9	−	1.40412e10i	−0.518273	−	0.855215i
$73$	2.02363e9			0.114250			0.0571248	−	0.998367i	$-0.481807\pi$
$73$	2.02363e9			0.114250			0.0571248	+	0.998367i	$0.481807\pi$
$74$	−1.02319e10	+	1.61642e10i	−0.536023	+	0.846798i
$75$	9.12064e9	−	1.87907e10i	0.443801	−	0.914335i
$76$	−2.38509e10	+	1.12908e10i	−1.07902	+	0.510797i
$77$		−	4.42769e9i		−	0.186414i
$78$	−2.19882e10	−	3.54977e10i	−0.862323	−	1.39213i
$79$		−	2.09965e10i		−	0.767713i	−0.923393	−	0.383856i	$-0.874596\pi$
$79$		−	2.09965e10i		−	0.767713i	0.923393	−	0.383856i	$-0.125404\pi$
$80$	3.21893e10	+	2.63796e10i	1.09829	+	0.900064i
$81$	−7.35999e9	+	3.05058e10i	−0.234536	+	0.972107i
$82$	6.15560e9	+	3.89649e9i	0.183355	+	0.116064i
$83$	−3.45636e10			−0.963140			−0.481570	−	0.876408i	$-0.659933\pi$
$83$	−3.45636e10			−0.963140			−0.481570	+	0.876408i	$0.659933\pi$
$84$	−3.01968e8	+	3.09696e10i	−0.00787816	+	0.807978i
$85$	−3.54844e10			−0.867428
$86$	2.70482e10	+	1.71215e10i	0.620008	+	0.392465i
$87$	3.28810e10	+	1.59598e10i	0.707277	+	0.343299i
$88$	−1.13361e10	−	1.39217e9i	−0.228985	−	0.0281214i
$89$		−	6.54648e10i		−	1.24269i	−0.783537	−	0.621345i	$-0.786587\pi$
$89$		−	6.54648e10i		−	1.24269i	0.783537	−	0.621345i	$-0.213413\pi$
$90$	−8.15471e9	−	7.91266e10i	−0.145571	−	1.41250i
$91$			7.87676e10i			1.32318i
$92$	−2.01238e10	−	4.25099e10i	−0.318329	−	0.672445i
$93$	5.94577e10	+	2.88597e10i	0.886241	+	0.430165i
$94$	7.27701e10	−	1.14961e11i	1.02270	−	1.61565i
$95$	−1.27850e11			−1.69520
$96$	7.91954e10	+	1.05107e10i	0.991308	+	0.131564i
$97$	9.06908e10			1.07231			0.536153	−	0.844121i	$-0.319877\pi$
$97$	9.06908e10			1.07231			0.536153	+	0.844121i	$0.319877\pi$
$98$	−1.66128e10	+	2.62445e10i	−0.185651	+	0.293289i
$99$	1.35051e10	+	1.71510e10i	0.142727	+	0.181257i
$100$	4.34865e10	+	9.18619e10i	0.434865	+	0.918619i
$101$			6.84917e10i			0.648441i	0.945982	+	0.324220i	$0.105102\pi$
$101$			6.84917e10i			0.648441i	−0.945982	+	0.324220i	$0.894898\pi$
$102$	−5.79071e10	+	3.58692e10i	−0.519315	+	0.321677i
$103$		−	8.02550e10i		−	0.682130i	−0.940040	−	0.341065i	$-0.889212\pi$
$103$		−	8.02550e10i		−	0.682130i	0.940040	−	0.341065i	$-0.110788\pi$
$104$	2.01666e11	+	2.47663e10i	1.62536	+	0.199608i
$105$	−6.55223e10	+	1.34991e11i	−0.501012	+	1.03220i
$106$	−7.48871e10	−	4.74035e10i	−0.543532	−	0.344055i
$107$	4.64493e10			0.320161			0.160080	−	0.987104i	$-0.448825\pi$
$107$	4.64493e10			0.320161			0.160080	+	0.987104i	$0.448825\pi$
$108$	−9.32924e10	−	1.20884e11i	−0.610964	−	0.791659i
$109$	4.98490e10			0.310321			0.155160	−	0.987889i	$-0.450411\pi$
$109$	4.98490e10			0.310321			0.155160	+	0.987889i	$0.450411\pi$
$110$	−4.67552e10	−	2.95960e10i	−0.276803	−	0.175216i
$111$	−7.76913e10	+	1.60062e11i	−0.437619	+	0.901598i
$112$	−1.16561e11	−	9.55234e10i	−0.624962	−	0.512166i
$113$		−	6.42067e10i		−	0.327830i	−0.986474	−	0.163915i	$-0.947588\pi$
$113$		−	6.42067e10i		−	0.327830i	0.986474	−	0.163915i	$-0.0524123\pi$
$114$	−2.08639e11	+	1.29236e11i	−1.01489	+	0.628648i
$115$		−	2.27870e11i		−	1.05645i
$116$	−1.60745e11	+	7.60953e10i	−0.710591	+	0.336387i
$117$	−2.40253e11	−	3.05112e11i	−1.01309	−	1.28658i
$118$	8.40191e10	−	1.32732e11i	0.338086	−	0.534101i
$119$	1.28493e11			0.493595
$120$	3.25012e11	+	2.10199e11i	1.19235	+	0.771141i
$121$	−2.70126e11			−0.946775
$122$	8.68758e10	−	1.37245e11i	0.291018	−	0.459745i
$123$	6.09543e10	+	2.95861e10i	0.195221	+	0.0947566i
$124$	−2.90671e11	+	1.37601e11i	−0.890393	+	0.421504i
$125$			7.92163e9i			0.0232172i
$126$	2.95291e10	+	2.86526e11i	0.0828347	+	0.803760i
$127$		−	6.41120e10i		−	0.172194i	−0.996287	−	0.0860971i	$-0.972560\pi$
$127$		−	6.41120e10i		−	0.172194i	0.996287	−	0.0860971i	$-0.0274395\pi$
$128$	−2.81214e11	+	2.68392e11i	−0.723407	+	0.690422i
$129$	2.67839e11	+	1.30004e11i	0.660131	+	0.320415i
$130$	8.31764e11	+	5.26506e11i	1.96477	+	1.24370i
$131$	7.25395e11			1.64279			0.821396	−	0.570359i	$-0.193196\pi$
$131$	7.25395e11			1.64279			0.821396	+	0.570359i	$0.193196\pi$
$132$	−1.06217e11	−	1.03566e9i	−0.230694	−	0.00224938i
$133$	4.62958e11			0.964623
$134$	−2.75683e11	−	1.74507e11i	−0.551232	−	0.348929i
$135$	−1.57939e11	−	7.22752e11i	−0.303148	−	1.38725i
$136$	4.04011e10	−	3.28976e11i	0.0744610	−	0.606317i
$137$			1.02042e11i			0.180640i	0.995913	+	0.0903201i	$0.0287890\pi$
$137$			1.02042e11i			0.180640i	−0.995913	+	0.0903201i	$0.971211\pi$
$138$	−2.30341e11	−	3.71861e11i	−0.391774	−	0.632479i
$139$			9.74720e11i			1.59330i	0.604438	+	0.796652i	$0.293398\pi$
$139$			9.74720e11i			1.59330i	−0.604438	+	0.796652i	$0.706602\pi$
$140$	−3.12406e11	−	6.59932e11i	−0.490924	−	1.03704i
$141$	5.52545e11	−	1.13837e12i	0.834954	−	1.72020i
$142$	−4.32903e11	+	6.83891e11i	−0.629223	+	0.994033i
$143$	−2.70150e11			−0.377796
$144$	7.42867e11	+	1.44880e10i	0.999810	+	0.0194991i
$145$	−8.61658e11			−1.11638
$146$	−4.89810e10	+	7.73793e10i	−0.0611065	+	0.0965348i
$147$	−1.26141e11	+	2.59880e11i	−0.151569	+	0.312268i
$148$	−3.70426e11	−	7.82496e11i	−0.428807	−	0.905821i
$149$			1.38737e12i			1.54763i	0.633410	+	0.773816i	$0.281655\pi$
$149$			1.38737e12i			1.54763i	−0.633410	+	0.773816i	$0.718345\pi$
$150$	4.97755e11	+	8.03575e11i	0.535197	+	0.864021i
$151$		−	4.11387e11i		−	0.426459i	−0.977002	−	0.213230i	$-0.931602\pi$
$151$		−	4.11387e11i		−	0.426459i	0.977002	−	0.213230i	$-0.0683982\pi$
$152$	1.45565e11	−	1.18530e12i	0.145518	−	1.18491i
$153$	−4.97726e11	+	3.91923e11i	−0.479940	+	0.377918i
$154$	1.69306e11	+	1.07170e11i	0.157510	+	0.0997036i
$155$	−1.55811e12			−1.39886
$156$	1.88958e12	+	1.84242e10i	1.63749	+	0.0159663i
$157$	−3.34728e11			−0.280055			−0.140028	−	0.990148i	$-0.544719\pi$
$157$	−3.34728e11			−0.280055			−0.140028	+	0.990148i	$0.544719\pi$
$158$	8.02864e11	+	5.08212e11i	0.648676	+	0.410612i
$159$	−7.41552e11	−	3.59936e11i	−0.578706	−	0.280893i
$160$	−1.78783e12	+	5.92343e11i	−1.34793	+	0.446595i
$161$			8.25140e11i			0.601154i
$162$	−9.88331e11	−	1.01981e12i	−0.695937	−	0.718103i
$163$			1.01905e12i			0.693688i	0.937923	+	0.346844i	$0.112747\pi$
$163$			1.01905e12i			0.693688i	−0.937923	+	0.346844i	$0.887253\pi$
$164$	−2.97987e11	+	1.41064e11i	−0.196136	+	0.0928487i
$165$	−4.62982e11	−	2.24723e11i	−0.294715	−	0.143049i
$166$	8.36598e11	−	1.32164e12i	0.515136	−	0.813802i
$167$	1.49614e12			0.891315			0.445657	−	0.895204i	$-0.352970\pi$
$167$	1.49614e12			0.891315			0.445657	+	0.895204i	$0.352970\pi$
$168$	−1.17690e12	−	7.61153e11i	−0.678485	−	0.438804i
$169$	3.01375e12			1.68163
$170$	8.58885e11	−	1.35685e12i	0.463944	−	0.732930i
$171$	−1.79330e12	+	1.41209e12i	−0.937938	+	0.738558i
$172$	−1.30938e12	+	6.19849e11i	−0.663224	+	0.313964i
$173$			3.61514e11i			0.177366i	0.996060	+	0.0886831i	$0.0282659\pi$
$173$			3.61514e11i			0.177366i	−0.996060	+	0.0886831i	$0.971734\pi$
$174$	−1.40614e12	+	8.71001e11i	−0.668357	+	0.413998i
$175$		−	1.78309e12i		−	0.821228i
$176$	3.27618e11	−	3.99770e11i	0.146234	−	0.178439i
$177$	6.37958e11	−	1.31434e12i	0.276019	−	0.568665i
$178$	2.50324e12	+	1.58455e12i	1.05001	+	0.664654i
$179$	3.93205e12			1.59929			0.799646	−	0.600472i	$-0.205021\pi$
$179$	3.93205e12			1.59929			0.799646	+	0.600472i	$0.205021\pi$
$180$	3.22302e12	+	1.60341e12i	1.27135	+	0.632477i
$181$	−2.04787e12			−0.783555			−0.391777	−	0.920060i	$-0.628140\pi$
$181$	−2.04787e12			−0.783555			−0.391777	+	0.920060i	$0.628140\pi$
$182$	−3.01191e12	−	1.90654e12i	−1.11802	−	0.707705i
$183$	6.59650e11	−	1.35903e12i	0.237592	−	0.489496i
$184$	2.11258e12	+	2.59443e11i	0.738439	+	0.0906867i
$185$		−	4.19448e12i		−	1.42309i
$186$	−2.54268e12	+	1.57500e12i	−0.837473	+	0.518752i
$187$			4.40694e11i			0.140932i
$188$	2.63449e12	+	5.56516e12i	0.818142	+	1.72826i
$189$	5.71916e11	+	2.61716e12i	0.172501	+	0.789389i
$190$	3.09455e12	−	4.88871e12i	0.906678	−	1.43235i
$191$	−5.71460e12			−1.62668			−0.813341	−	0.581788i	$-0.802353\pi$
$191$	−5.71460e12			−1.62668			−0.813341	+	0.581788i	$0.802353\pi$
$192$	−2.31880e12	+	2.77386e12i	−0.641366	+	0.767235i
$193$	−1.09721e12			−0.294934			−0.147467	−	0.989067i	$-0.547112\pi$
$193$	−1.09721e12			−0.294934			−0.147467	+	0.989067i	$0.547112\pi$
$194$	−2.19513e12	+	3.46783e12i	−0.573523	+	0.906041i
$195$	8.23635e12	+	3.99777e12i	2.09192	+	1.01538i
$196$	−6.01431e11	−	1.27047e12i	−0.148517	−	0.313731i
$197$		−	1.58459e12i		−	0.380497i	−0.981736	−	0.190249i	$-0.939071\pi$
$197$		−	1.58459e12i		−	0.380497i	0.981736	−	0.190249i	$-0.0609294\pi$
$198$	−9.82703e11	+	1.01276e11i	−0.229490	+	0.0236510i
$199$		−	5.79444e12i		−	1.31619i	−0.752934	−	0.658097i	$-0.771362\pi$
$199$		−	5.79444e12i		−	1.31619i	0.752934	−	0.658097i	$-0.228638\pi$
$200$	−4.56518e12	−	5.60644e11i	−1.00877	−	0.123886i
$201$	−2.72989e12	−	1.32504e12i	−0.586904	−	0.284872i
$202$	−2.61898e12	−	1.65781e12i	−0.547898	−	0.346819i
$203$	3.12016e12			0.635255
$204$	3.00553e10	−	3.08245e12i	0.00595600	−	0.610843i
$205$	−1.59733e12			−0.308140
$206$	3.06878e12	+	1.94254e12i	0.576363	+	0.364838i
$207$	−2.51680e12	−	3.19624e12i	−0.460270	−	0.584524i
$208$	−5.82825e12	+	7.11182e12i	−1.03798	+	1.26658i
$209$			1.58781e12i			0.275420i
$210$	−3.57585e12	−	5.77285e12i	−0.604190	−	0.975403i
$211$			1.54812e12i			0.254831i	0.991849	+	0.127416i	$0.0406682\pi$
$211$			1.54812e12i			0.254831i	−0.991849	+	0.127416i	$0.959332\pi$
$212$	3.62522e12	−	1.71615e12i	0.581417	−	0.275237i
$213$	−3.28704e12	+	6.77207e12i	−0.513708	+	1.05836i
$214$	−1.12429e12	+	1.77612e12i	−0.171238	+	0.270519i
$215$	−7.01880e12			−1.04196
$216$	6.88045e12	−	6.41361e11i	0.995684	−	0.0928126i
$217$	5.64207e12			0.795995
$218$	−1.20657e12	+	1.90612e12i	−0.165975	+	0.262204i
$219$	−3.71914e11	+	7.66230e11i	−0.0498884	+	0.102782i
$220$	2.26338e12	−	1.07146e12i	0.296096	−	0.140169i
$221$		−	7.83984e12i		−	1.00035i
$222$	−4.23997e12	−	6.84499e12i	−0.527741	−	0.851984i
$223$			1.39758e12i			0.169707i	0.996393	+	0.0848537i	$0.0270423\pi$
$223$			1.39758e12i			0.169707i	−0.996393	+	0.0848537i	$0.972958\pi$
$224$	6.47392e12	−	2.14494e12i	0.767014	−	0.254127i
$225$	5.43869e12	+	6.90692e12i	0.628769	+	0.798510i
$226$	2.45513e12	+	1.55410e12i	0.276999	+	0.175340i
$227$	−5.07949e12			−0.559343			−0.279671	−	0.960096i	$-0.590226\pi$
$227$	−5.07949e12			−0.559343			−0.279671	+	0.960096i	$0.590226\pi$
$228$	1.08289e11	−	1.11060e13i	0.0116397	−	1.19376i
$229$	9.30433e12			0.976315			0.488158	−	0.872755i	$-0.337669\pi$
$229$	9.30433e12			0.976315			0.488158	+	0.872755i	$0.337669\pi$
$230$	8.71326e12	+	5.51549e12i	0.892642	+	0.565042i
$231$	1.67651e12	+	8.13746e11i	0.167703	+	0.0813998i
$232$	9.81048e11	−	7.98842e12i	0.0958310	−	0.780328i
$233$			1.46589e12i			0.139844i	0.997552	+	0.0699219i	$0.0222750\pi$
$233$			1.46589e12i			0.139844i	−0.997552	+	0.0699219i	$0.977725\pi$
$234$	1.74821e13	−	1.80168e12i	1.62894	−	0.167877i
$235$			2.98314e13i			2.71519i
$236$	3.04174e12	+	6.42543e12i	0.270462	+	0.571329i
$237$	7.95017e12	+	3.85887e12i	0.690654	+	0.335231i
$238$	−3.11011e12	+	4.91330e12i	−0.264000	+	0.417061i
$239$	−2.98136e12			−0.247301			−0.123651	−	0.992326i	$-0.539460\pi$
$239$	−2.98136e12			−0.247301			−0.123651	+	0.992326i	$0.539460\pi$
$240$	−1.59044e13	+	7.34001e12i	−1.28930	+	0.595025i
$241$	−2.45812e13			−1.94764			−0.973820	−	0.227321i	$-0.927003\pi$
$241$	−2.45812e13			−1.94764			−0.973820	+	0.227321i	$0.927003\pi$
$242$	6.53829e12	−	1.03291e13i	0.506383	−	0.799974i
$243$	−1.01981e13	−	8.39333e12i	−0.772120	−	0.635477i
$244$	3.14516e12	+	6.64390e12i	0.232808	+	0.491789i
$245$		−	6.81024e12i		−	0.492889i
$246$	−2.60669e12	+	1.61465e12i	−0.184478	+	0.114271i
$247$		−	2.82469e13i		−	1.95496i
$248$	1.77400e12	−	1.44452e13i	0.120079	−	0.977776i
$249$	6.35230e12	−	1.30872e13i	0.420566	−	0.866466i
$250$	−3.02907e11	−	1.91740e11i	−0.0196173	−	0.0124177i
$251$	3.92621e12			0.248753			0.124376	−	0.992235i	$-0.460307\pi$
$251$	3.92621e12			0.248753			0.124376	+	0.992235i	$0.460307\pi$
$252$	−1.16709e13	−	5.80611e12i	−0.723438	−	0.359900i
$253$	−2.83000e12			−0.171642
$254$	2.45151e12	+	1.55180e12i	0.145495	+	0.0920982i
$255$	6.52153e12	−	1.34359e13i	0.378772	−	0.780360i
$256$	−3.45606e12	−	1.72494e13i	−0.196455	−	0.980513i
$257$			2.57517e13i			1.43276i	0.697709	+	0.716382i	$0.254203\pi$
$257$			2.57517e13i			1.43276i	−0.697709	+	0.716382i	$0.745797\pi$
$258$	−1.14540e13	+	7.09491e12i	−0.623805	+	0.386401i
$259$			1.51887e13i			0.809788i
$260$	−4.02650e13	+	1.90611e13i	−2.10172	+	0.994933i
$261$	−1.20861e13	+	9.51695e12i	−0.617682	+	0.486379i
$262$	−1.75579e13	+	2.77376e13i	−0.878648	+	1.38807i
$263$	1.56000e13			0.764482			0.382241	−	0.924063i	$-0.375152\pi$
$263$	1.56000e13			0.764482			0.382241	+	0.924063i	$0.375152\pi$
$264$	2.61054e12	−	4.03645e12i	0.125288	−	0.193721i
$265$	1.94326e13			0.913437
$266$	−1.12057e13	+	1.77026e13i	−0.515929	+	0.815055i
$267$	2.47877e13	+	1.20315e13i	1.11796	+	0.542635i
$268$	1.33456e13	−	6.31768e12i	0.589653	−	0.279136i
$269$		−	2.37956e13i		−	1.03005i	−0.857174	−	0.515027i	$-0.827782\pi$
$269$		−	2.37956e13i		−	1.03005i	0.857174	−	0.515027i	$-0.172218\pi$
$270$	3.14594e13	+	1.14546e13i	1.33429	+	0.485825i
$271$		−	1.80240e13i		−	0.749066i	−0.927214	−	0.374533i	$-0.877803\pi$
$271$		−	1.80240e13i		−	0.749066i	0.927214	−	0.374533i	$-0.122197\pi$
$272$	1.16015e13	+	9.50757e12i	0.472480	+	0.387205i
$273$	−2.98247e13	−	1.44764e13i	−1.19037	−	0.577783i
$274$	−3.90186e12	−	2.46988e12i	−0.152631	−	0.0966156i
$275$	6.11549e12			0.234478
$276$	1.97945e13	+	1.93005e11i	0.743951	+	0.00725387i
$277$	−1.10330e13			−0.406494			−0.203247	−	0.979128i	$-0.565149\pi$
$277$	−1.10330e13			−0.406494			−0.203247	+	0.979128i	$0.565149\pi$
$278$	−3.72713e13	−	2.35927e13i	−1.34626	−	0.852180i
$279$	−2.18550e13	+	1.72092e13i	−0.773975	+	0.609449i
$280$	3.27961e13	+	4.02764e12i	1.13881	+	0.139856i
$281$		−	2.11358e12i		−	0.0719672i	−0.999352	−	0.0359836i	$-0.988544\pi$
$281$		−	2.11358e12i		−	0.0719672i	0.999352	−	0.0359836i	$-0.0114564\pi$
$282$	3.01549e13	+	4.86820e13i	1.00690	+	1.62554i
$283$		−	4.58299e13i		−	1.50080i	−0.660983	−	0.750401i	$-0.729861\pi$
$283$		−	4.58299e13i		−	1.50080i	0.660983	−	0.750401i	$-0.270139\pi$
$284$	−1.56723e13	−	3.31066e13i	−0.503365	−	1.06332i
$285$	2.34970e13	−	4.84093e13i	0.740228	−	1.52504i
$286$	6.53888e12	−	1.03300e13i	0.202064	−	0.319218i
$287$	5.78409e12			0.175342
$288$	−1.85348e13	+	2.80550e13i	−0.551225	+	0.834357i
$289$	2.14828e13			0.626835
$290$	2.08561e13	−	3.29480e13i	0.597095	−	0.943279i
$291$	−1.66677e13	+	3.43393e13i	−0.468235	+	0.964674i
$292$	−1.77326e12	−	3.74587e12i	−0.0488839	−	0.103263i
$293$			4.19740e13i			1.13555i	0.823182	+	0.567777i	$0.192197\pi$
$293$			4.19740e13i			1.13555i	−0.823182	+	0.567777i	$0.807803\pi$
$294$	−6.88409e12	−	1.11137e13i	−0.182783	−	0.295085i
$295$			3.44428e13i			0.897588i
$296$	3.88870e13	+	4.77566e12i	0.994719	+	0.122160i
$297$	−8.97612e12	+	1.96151e12i	−0.225387	+	0.0492527i
$298$	−5.30501e13	−	3.35807e13i	−1.30767	−	0.827752i
$299$	5.03450e13			1.21833
$300$	−4.27750e13	−	4.17075e11i	−1.01630	−	0.00990941i
$301$	2.54158e13			0.592910
$302$	1.57306e13	+	9.95745e12i	0.360335	+	0.228092i
$303$	−2.59338e13	−	1.25878e13i	−0.583354	−	0.283149i
$304$	4.17999e13	+	3.42557e13i	0.923359	+	0.756707i
$305$			3.56139e13i			0.772628i
$306$	−2.93907e12	−	2.85183e13i	−0.0626242	−	0.607654i
$307$			1.15277e13i			0.241257i	0.992698	+	0.120629i	$0.0384910\pi$
$307$			1.15277e13i			0.241257i	−0.992698	+	0.120629i	$0.961509\pi$
$308$	−8.19594e12	+	3.87988e12i	−0.168488	+	0.0797608i
$309$	3.03879e13	+	1.47497e13i	0.613662	+	0.297860i
$310$	3.77133e13	−	5.95788e13i	0.748179	−	1.18196i
$311$	−6.15161e13			−1.19897			−0.599483	−	0.800388i	$-0.704627\pi$
$311$	−6.15161e13			−1.19897			−0.599483	+	0.800388i	$0.704627\pi$
$312$	−4.64409e13	+	7.18075e13i	−0.889304	+	1.37505i
$313$	−1.91720e13			−0.360724			−0.180362	−	0.983600i	$-0.557727\pi$
$313$	−1.91720e13			−0.360724			−0.180362	+	0.983600i	$0.557727\pi$
$314$	8.10195e12	−	1.27993e13i	0.149788	−	0.236632i
$315$	−3.90714e13	−	4.96190e13i	−0.709824	−	0.901447i
$316$	−3.88660e13	+	1.83988e13i	−0.693890	+	0.328481i
$317$			7.79588e13i			1.36785i	0.729551	+	0.683926i	$0.239729\pi$
$317$			7.79588e13i			1.36785i	−0.729551	+	0.683926i	$0.760271\pi$
$318$	3.17122e13	−	1.96433e13i	0.546860	−	0.338740i
$319$			1.07012e13i			0.181378i
$320$	2.06237e13	−	8.27003e13i	0.343590	−	1.37779i
$321$	−8.53672e12	+	1.75877e13i	−0.139802	+	0.288025i
$322$	−3.15517e13	−	1.99722e13i	−0.507943	−	0.321527i
$323$	−4.60788e13			−0.729269
$324$	6.29175e13	−	1.31077e13i	0.978981	−	0.203952i
$325$	−1.08793e14			−1.66434
$326$	−3.89664e13	−	2.46657e13i	−0.586130	−	0.371020i
$327$	−9.16154e12	+	1.88749e13i	−0.135505	+	0.279173i
$328$	1.81865e12	−	1.48088e13i	0.0264511	−	0.215384i
$329$		−	1.08023e14i		−	1.54503i
$330$	1.97992e13	−	1.22642e13i	0.278498	−	0.172509i
$331$			9.28905e12i			0.128504i	0.997934	+	0.0642521i	$0.0204662\pi$
$331$			9.28905e12i			0.128504i	−0.997934	+	0.0642521i	$0.979534\pi$
$332$	3.02873e13	+	6.39795e13i	0.412098	+	0.870525i
$333$	−4.63278e13	−	5.88343e13i	−0.620009	−	0.787386i
$334$	−3.62134e13	+	5.72092e13i	−0.476720	+	0.753113i
$335$	7.15376e13			0.926378
$336$	5.75914e13	−	2.65790e13i	0.733654	−	0.338589i
$337$	7.51907e13			0.942323			0.471162	−	0.882047i	$-0.343835\pi$
$337$	7.51907e13			0.942323			0.471162	+	0.882047i	$0.343835\pi$
$338$	−7.29467e13	+	1.15240e14i	−0.899422	+	1.42089i
$339$	2.43113e13	+	1.18003e13i	0.294924	+	0.143151i
$340$	3.10941e13	+	6.56839e13i	0.371146	+	0.784016i
$341$			1.93507e13i			0.227273i
$342$	−1.05894e13	−	1.02751e14i	−0.122385	−	1.18753i
$343$			9.57063e13i			1.08849i
$344$	7.99131e12	−	6.50712e13i	0.0894431	−	0.728312i
$345$	8.62810e13	+	4.18792e13i	0.950408	+	0.461310i
$346$	−1.38235e13	−	8.75028e12i	−0.149865	−	0.0948645i
$347$	−3.60645e13			−0.384829			−0.192415	−	0.981314i	$-0.561632\pi$
$347$	−3.60645e13			−0.384829			−0.192415	+	0.981314i	$0.561632\pi$
$348$	7.29824e11	−	7.48502e13i	0.00766535	−	0.786153i
$349$	1.05239e14			1.08802			0.544012	−	0.839078i	$-0.316905\pi$
$349$	1.05239e14			1.08802			0.544012	+	0.839078i	$0.316905\pi$
$350$	6.81816e13	+	4.31589e13i	0.693894	+	0.439234i
$351$	1.59683e14	−	3.48948e13i	1.59982	−	0.349600i
$352$	7.35653e12	+	2.22037e13i	0.0725585	+	0.218998i
$353$		−	8.86496e13i		−	0.860827i	−0.902632	−	0.430414i	$-0.858368\pi$
$353$		−	8.86496e13i		−	0.860827i	0.902632	−	0.430414i	$-0.141632\pi$
$354$	3.48163e13	+	5.62073e13i	0.332862	+	0.537372i
$355$		−	1.77464e14i		−	1.67053i
$356$	−1.21180e14	+	5.73653e13i	−1.12319	+	0.531709i
$357$	−2.36152e13	+	4.86528e13i	−0.215534	+	0.444051i
$358$	−9.51737e13	+	1.50354e14i	−0.855382	+	1.35132i
$359$	4.27669e13			0.378520			0.189260	−	0.981927i	$-0.439391\pi$
$359$	4.27669e13			0.378520			0.189260	+	0.981927i	$0.439391\pi$
$360$	−1.39323e14	+	8.44317e13i	−1.21439	+	0.735939i
$361$	−4.95312e13			−0.425196
$362$	4.95677e13	−	7.83061e13i	0.419085	−	0.662062i
$363$	4.96453e13	−	1.02281e14i	0.413420	−	0.851743i
$364$	1.45804e14	−	6.90222e13i	1.19595	−	0.566150i
$365$		−	2.00793e13i		−	0.162232i
$366$	3.60001e13	+	5.81185e13i	0.286522	+	0.462560i
$367$			8.99606e13i			0.705325i	0.935751	+	0.352662i	$0.114724\pi$
$367$			8.99606e13i			0.705325i	−0.935751	+	0.352662i	$0.885276\pi$
$368$	−6.10546e13	+	7.45009e13i	−0.471580	+	0.575438i
$369$	−2.24051e13	+	1.76424e13i	−0.170491	+	0.134249i
$370$	1.60388e14	+	1.01526e14i	1.20244	+	0.761143i
$371$	−7.03676e13			−0.519776
$372$	1.31972e12	−	1.35349e14i	0.00960493	−	0.985075i
$373$	−1.72940e14			−1.24021			−0.620107	−	0.784517i	$-0.712911\pi$
$373$	−1.72940e14			−1.24021			−0.620107	+	0.784517i	$0.712911\pi$
$374$	−1.68512e13	−	1.06668e13i	−0.119080	−	0.0753773i
$375$	−2.99946e12	−	1.45588e12i	−0.0208868	−	0.0101381i
$376$	−2.76567e14	−	3.39648e13i	−1.89787	−	0.233075i
$377$		−	1.90373e14i		−	1.28744i
$378$	−1.13918e14	−	4.14785e13i	−0.759254	−	0.276451i
$379$			8.68904e13i			0.570764i	0.958414	+	0.285382i	$0.0921204\pi$
$379$			8.68904e13i			0.570764i	−0.958414	+	0.285382i	$0.907880\pi$
$380$	1.12032e14	+	2.36658e14i	0.725323	+	1.53219i
$381$	2.42755e13	+	1.17829e13i	0.154910	+	0.0751906i
$382$	1.38320e14	−	2.18515e14i	0.870032	−	1.37446i
$383$	1.09905e14			0.681436			0.340718	−	0.940166i	$-0.389330\pi$
$383$	1.09905e14			0.681436			0.340718	+	0.940166i	$0.389330\pi$
$384$	−4.99412e13	−	1.55806e14i	−0.305237	−	0.952276i
$385$	−4.39334e13			−0.264704
$386$	2.65575e13	−	4.19550e13i	0.157745	−	0.249203i
$387$	−9.84499e13	+	7.75222e13i	−0.576508	+	0.453958i
$388$	−7.94702e13	−	1.67875e14i	−0.458807	−	0.969193i
$389$		−	7.44772e13i		−	0.423936i	−0.977277	−	0.211968i	$-0.932013\pi$
$389$		−	7.44772e13i		−	0.423936i	0.977277	−	0.211968i	$-0.0679873\pi$
$390$	−3.52224e14	+	2.18177e14i	−1.97680	+	1.22448i
$391$		−	8.21273e13i		−	0.454481i
$392$	6.31377e13	+	7.75386e12i	0.344521	+	0.0423101i
$393$	−1.33317e14	+	2.74665e14i	−0.717344	+	1.47790i
$394$	6.05913e13	+	3.83543e13i	0.321500	+	0.203509i
$395$	−2.08337e14			−1.09014
$396$	1.99133e13	−	4.00279e13i	0.102759	−	0.206557i
$397$	4.18580e12			0.0213025			0.0106513	−	0.999943i	$-0.496610\pi$
$397$	4.18580e12			0.0213025			0.0106513	+	0.999943i	$0.496610\pi$
$398$	2.21567e14	+	1.40252e14i	1.11211	+	0.703967i
$399$	−8.50851e13	+	1.75295e14i	−0.421214	+	0.867800i
$400$	1.31936e14	−	1.60993e14i	0.644219	−	0.786098i
$401$			2.94330e14i			1.41756i	0.705430	+	0.708779i	$0.250754\pi$
$401$			2.94330e14i			1.41756i	−0.705430	+	0.708779i	$0.749246\pi$
$402$	1.16743e14	−	7.23134e13i	0.554608	−	0.343538i
$403$		−	3.44245e14i		−	1.61320i
$404$	1.26783e14	−	6.00177e13i	0.586087	−	0.277448i
$405$	3.02691e14	+	7.30290e13i	1.38038	+	0.333037i
$406$	−7.55221e13	+	1.19308e14i	−0.339767	+	0.536757i
$407$	−5.20928e13			−0.231211
$408$	1.17139e14	+	7.57586e13i	0.512944	+	0.331742i
$409$	3.62272e14			1.56515			0.782575	−	0.622556i	$-0.213906\pi$
$409$	3.62272e14			1.56515			0.782575	+	0.622556i	$0.213906\pi$
$410$	3.86626e13	−	6.10785e13i	0.164809	−	0.260362i
$411$	−3.86373e13	−	1.87538e13i	−0.162509	−	0.0788787i
$412$	−1.48557e14	+	7.03255e13i	−0.616537	+	0.291863i
$413$		−	1.24721e14i		−	0.510757i
$414$	1.83136e14	−	1.88738e13i	0.740067	−	0.0762706i
$415$			3.42955e14i			1.36764i
$416$	−1.30871e14	−	3.94999e14i	−0.515027	−	1.55447i
$417$	−3.69070e14	−	1.79140e14i	−1.43338	−	0.695735i
$418$	−6.07147e13	−	3.84324e13i	−0.232715	−	0.147308i
$419$	−7.19258e13			−0.272087			−0.136043	−	0.990703i	$-0.543439\pi$
$419$	−7.19258e13			−0.272087			−0.136043	+	0.990703i	$0.543439\pi$
$420$	3.07294e14	+	2.99625e12i	1.14732	+	0.0111868i
$421$	3.14862e14			1.16030			0.580149	−	0.814511i	$-0.302994\pi$
$421$	3.14862e14			1.16030			0.580149	+	0.814511i	$0.302994\pi$
$422$	−5.91971e13	−	3.74717e13i	−0.215319	−	0.136297i
$423$	3.29486e14	+	4.18433e14i	1.18295	+	1.50229i
$424$	−2.21252e13	+	1.80160e14i	−0.0784105	+	0.638477i
$425$			1.77473e14i			0.620860i
$426$	−1.79389e14	−	2.89605e14i	−0.619501	−	1.00012i
$427$		−	1.28962e14i		−	0.439651i
$428$	−4.07024e13	−	8.59807e13i	−0.136987	−	0.289374i
$429$	4.96498e13	−	1.02290e14i	0.164969	−	0.339875i
$430$	1.69887e14	−	2.68384e14i	0.557293	−	0.880401i
$431$	−4.00082e14			−1.29576			−0.647879	−	0.761743i	$-0.724344\pi$
$431$	−4.00082e14			−1.29576			−0.647879	+	0.761743i	$0.724344\pi$
$432$	−1.42014e14	+	2.78618e14i	−0.454120	+	0.890940i
$433$	−8.13328e12			−0.0256793			−0.0128396	−	0.999918i	$-0.504087\pi$
$433$	−8.13328e12			−0.0256793			−0.0128396	+	0.999918i	$0.504087\pi$
$434$	−1.36564e14	+	2.15741e14i	−0.425738	+	0.672573i
$435$	1.58360e14	−	3.26260e14i	0.487479	−	1.00432i
$436$	−4.36815e13	−	9.22738e13i	−0.132777	−	0.280480i
$437$		−	2.95904e14i		−	0.888183i
$438$	−2.02970e13	−	3.27675e13i	−0.0601624	−	0.0971260i
$439$			1.12437e14i			0.329119i	0.986367	+	0.164560i	$0.0526203\pi$
$439$			1.12437e14i			0.329119i	−0.986367	+	0.164560i	$0.947380\pi$
$440$	−1.38137e13	+	1.12481e14i	−0.0399318	+	0.325155i
$441$	−7.52186e13	−	9.55246e13i	−0.214740	−	0.272711i
$442$	2.99779e14	+	1.89760e14i	0.845238	+	0.535035i
$443$	2.79525e14			0.778395			0.389198	−	0.921154i	$-0.372752\pi$
$443$	2.79525e14			0.778395			0.389198	+	0.921154i	$0.372752\pi$
$444$	3.64365e14	+	3.55272e12i	1.00214	+	0.00977136i
$445$	−6.49570e14			−1.76460
$446$	−5.34407e13	−	3.38279e13i	−0.143394	−	0.0907681i
$447$	−5.25317e14	−	2.54979e14i	−1.39229	−	0.675792i
$448$	−7.46805e13	+	2.99467e14i	−0.195514	+	0.784006i
$449$			1.43557e14i			0.371252i	0.982620	+	0.185626i	$0.0594313\pi$
$449$			1.43557e14i			0.371252i	−0.982620	+	0.185626i	$0.940569\pi$
$450$	−3.95747e14	+	4.07854e13i	−1.01100	+	0.104192i
$451$			1.98378e13i			0.0500636i
$452$	−1.18851e14	+	5.62628e13i	−0.296306	+	0.140268i
$453$	1.55768e14	+	7.56071e13i	0.383654	+	0.186218i
$454$	1.22947e14	−	1.94229e14i	0.299165	−	0.472615i
$455$	7.81566e14			1.87890
$456$	4.22050e14	+	2.72957e14i	1.00244	+	0.648318i
$457$	−4.26535e14			−1.00096			−0.500479	−	0.865749i	$-0.666843\pi$
$457$	−4.26535e14			−1.00096			−0.500479	+	0.865749i	$0.666843\pi$
$458$	−2.25208e14	+	3.55778e14i	−0.522183	+	0.824934i
$459$	−5.69236e13	−	2.60490e14i	−0.130413	−	0.596789i
$460$	−4.21801e14	+	1.99677e14i	−0.954861	+	0.452022i
$461$			6.15303e14i			1.37637i	0.725537	+	0.688183i	$0.241591\pi$
$461$			6.15303e14i			1.37637i	−0.725537	+	0.688183i	$0.758409\pi$
$462$	−7.16952e13	+	4.44098e13i	−0.158474	+	0.0981631i
$463$		−	3.73259e14i		−	0.815296i	−0.913139	−	0.407648i	$-0.866349\pi$
$463$		−	3.73259e14i		−	0.815296i	0.913139	−	0.407648i	$-0.133651\pi$
$464$	2.81715e14	+	2.30870e14i	0.608080	+	0.498331i
$465$	2.86358e14	−	5.89965e14i	0.610827	−	1.25845i
$466$	−5.60525e13	−	3.54812e13i	−0.118161	−	0.0747955i
$467$	5.89060e14			1.22720			0.613602	−	0.789616i	$-0.289720\pi$
$467$	5.89060e14			1.22720			0.613602	+	0.789616i	$0.289720\pi$
$468$	−3.54253e14	+	7.12087e14i	−0.729393	+	1.46616i
$469$	−2.59045e14			−0.527139
$470$	−1.14069e15	−	7.22057e14i	−2.29419	−	1.45222i
$471$	6.15182e13	−	1.26742e14i	0.122289	−	0.251945i
$472$	−3.19319e14	−	3.92151e13i	−0.627399	−	0.0770500i
$473$			8.71691e13i			0.169288i
$474$	−3.39986e14	+	2.10596e14i	−0.652649	+	0.404268i
$475$			6.39434e14i			1.21334i
$476$	−1.12595e14	−	2.37849e14i	−0.211194	−	0.446131i
$477$	2.72574e14	−	2.14632e14i	0.505397	−	0.397963i
$478$	7.21626e13	−	1.14001e14i	0.132269	−	0.208956i
$479$	3.04280e13			0.0551352			0.0275676	−	0.999620i	$-0.491224\pi$
$479$	3.04280e13			0.0551352			0.0275676	+	0.999620i	$0.491224\pi$
$480$	1.04291e14	−	7.85811e14i	0.186819	−	1.40764i
$481$	9.26719e14			1.64116
$482$	5.94977e14	−	9.39932e14i	1.04170	−	1.64565i
$483$	−3.12433e14	−	1.51649e14i	−0.540813	−	0.262501i
$484$	2.36705e14	+	5.00021e14i	0.405096	+	0.855734i
$485$		−	8.99873e14i		−	1.52265i
$486$	5.67784e14	−	1.86797e14i	0.949913	−	0.312515i
$487$			9.98276e13i			0.165136i	0.996585	+	0.0825680i	$0.0263122\pi$
$487$			9.98276e13i			0.165136i	−0.996585	+	0.0825680i	$0.973688\pi$
$488$	−3.30176e14	−	4.05485e13i	−0.540054	−	0.0663233i
$489$	−3.85856e14	−	1.87287e14i	−0.624060	−	0.302907i
$490$	2.60409e14	+	1.64839e14i	0.416465	+	0.263622i
$491$	−5.10773e14			−0.807755			−0.403877	−	0.914813i	$-0.632338\pi$
$491$	−5.10773e14			−0.807755			−0.403877	+	0.914813i	$0.632338\pi$
$492$	1.35294e12	−	1.38756e14i	0.00211577	−	0.216992i
$493$	−3.10553e14			−0.480262
$494$	1.08010e15	+	6.83703e14i	1.65183	+	1.04561i
$495$	1.70179e14	−	1.34004e14i	0.257382	−	0.202669i
$496$	5.09416e14	+	4.17474e14i	0.761944	+	0.624425i
$497$			6.42617e14i			0.950587i
$498$	3.46674e14	+	5.59670e14i	0.507177	+	0.818786i
$499$			7.81664e13i			0.113101i	0.998400	+	0.0565506i	$0.0180102\pi$
$499$			7.81664e13i			0.113101i	−0.998400	+	0.0565506i	$0.981990\pi$
$500$	1.46635e13	−	6.94154e12i	0.0209846	−	0.00993393i
$501$	−2.74969e14	+	5.66501e14i	−0.389203	+	0.801850i
$502$	−9.50323e13	+	1.50130e14i	−0.133046	+	0.210183i
$503$	1.89227e14			0.262035			0.131018	−	0.991380i	$-0.458176\pi$
$503$	1.89227e14			0.262035			0.131018	+	0.991380i	$0.458176\pi$
$504$	5.04503e14	−	3.05736e14i	0.691028	−	0.418774i
$505$	6.79604e14			0.920775
$506$	6.84989e13	−	1.08213e14i	0.0918027	−	0.145028i
$507$	−5.53885e14	+	1.14113e15i	−0.734304	+	1.51284i
$508$	−1.18675e14	+	5.61798e13i	−0.155636	+	0.0736766i
$509$			1.38838e15i			1.80119i	0.434661	+	0.900594i	$0.356868\pi$
$509$			1.38838e15i			1.80119i	−0.434661	+	0.900594i	$0.643132\pi$
$510$	3.55909e14	+	5.74579e14i	0.456776	+	0.737419i
$511$			7.27093e13i			0.0923156i
$512$	7.43232e14	+	2.85361e14i	0.933555	+	0.358434i
$513$	−2.05095e14	−	9.38541e14i	−0.254864	−	1.16629i
$514$	−9.84693e14	−	6.23310e14i	−1.21061	−	0.766315i
$515$	−7.96324e14			−0.968613
$516$	5.94492e12	−	6.09707e14i	0.00715439	−	0.733749i
$517$	3.70487e14			0.441139
$518$	−5.80783e14	−	3.67635e14i	−0.684227	−	0.433115i
$519$	−1.36884e14	−	6.64410e13i	−0.159563	−	0.0774490i
$520$	2.45742e14	−	2.00102e15i	0.283440	−	2.30798i
$521$		−	4.13539e14i		−	0.471964i	−0.971757	−	0.235982i	$-0.924169\pi$
$521$		−	4.13539e14i		−	0.471964i	0.971757	−	0.235982i	$-0.0758306\pi$
$522$	−7.13686e13	−	6.92502e14i	−0.0805971	−	0.782048i
$523$		−	5.61979e14i		−	0.628002i	−0.949423	−	0.314001i	$-0.898330\pi$
$523$		−	5.61979e14i		−	0.628002i	0.949423	−	0.314001i	$-0.101670\pi$
$524$	−6.35647e14	−	1.34275e15i	−0.702900	−	1.48482i
$525$	6.75152e14	+	3.27706e14i	0.738798	+	0.358599i
$526$	−3.77591e14	+	5.96511e14i	−0.408884	+	0.645947i
$527$	−5.61563e14			−0.601783
$528$	9.11584e13	+	1.97522e14i	0.0966740	+	0.209473i
$529$	−4.25414e14			−0.446484
$530$	−4.70358e14	+	7.43062e14i	−0.488553	+	0.771806i
$531$	3.80418e14	+	4.83116e14i	0.391058	+	0.496628i
$532$	−4.05679e14	−	8.56966e14i	−0.412733	−	0.871866i
$533$		−	3.52910e14i		−	0.355356i
$534$	−1.06004e15	+	6.56614e14i	−1.05644	+	0.654384i
$535$		−	4.60890e14i		−	0.454623i
$536$	−8.14498e13	+	6.63225e14i	−0.0795213	+	0.647522i
$537$	−7.22655e14	+	1.48884e15i	−0.698349	+	1.43876i
$538$	9.09896e14	+	5.75964e14i	0.870340	+	0.550925i
$539$	−8.45789e13			−0.0800799
$540$	−1.19946e15	+	9.25687e14i	−1.12414	+	0.867558i
$541$	−1.22124e15			−1.13296			−0.566482	−	0.824074i	$-0.691696\pi$
$541$	−1.22124e15			−1.13296			−0.566482	+	0.824074i	$0.691696\pi$
$542$	6.89200e14	+	4.36263e14i	0.632921	+	0.400638i
$543$	3.76369e14	−	7.75408e14i	0.342148	−	0.704906i
$544$	−6.44358e14	+	2.13489e14i	−0.579873	+	0.192124i
$545$		−	4.94623e14i		−	0.440650i
$546$	1.27544e15	−	7.90041e14i	1.12487	−	0.696771i
$547$			5.72737e13i			0.0500063i	0.999687	+	0.0250032i	$0.00795959\pi$
$547$			5.72737e13i			0.0500063i	−0.999687	+	0.0250032i	$0.992040\pi$
$548$	1.88886e14	−	8.94168e13i	0.163270	−	0.0772905i
$549$	3.93353e14	+	4.99542e14i	0.336616	+	0.427488i
$550$	−1.48023e14	+	2.33844e14i	−0.125410	+	0.198121i
$551$	−1.11892e15			−0.938567
$552$	−4.86498e14	+	7.52229e14i	−0.404032	+	0.624719i
$553$	7.54410e14			0.620325
$554$	2.67049e14	−	4.21878e14i	0.217414	−	0.343466i
$555$	1.58821e15	+	7.70886e14i	1.28025	+	0.621411i
$556$	1.80427e15	−	8.54125e14i	1.44009	−	0.681726i
$557$		−	6.20262e14i		−	0.490198i	−0.969498	−	0.245099i	$-0.921180\pi$
$557$		−	6.20262e14i		−	0.490198i	0.969498	−	0.245099i	$-0.0788205\pi$
$558$	−1.29054e14	−	1.25223e15i	−0.100991	−	0.979931i
$559$		−	1.55072e15i		−	1.20162i
$560$	−9.47824e14	+	1.15657e15i	−0.727266	+	0.887435i
$561$	−1.66865e14	−	8.09932e13i	−0.126786	−	0.0615394i
$562$	8.08190e13	+	5.11584e13i	0.0608084	+	0.0384917i
$563$	2.57816e15			1.92094			0.960470	−	0.278385i	$-0.0897991\pi$
$563$	2.57816e15			1.92094			0.960470	+	0.278385i	$0.0897991\pi$
$564$	−2.59138e15	−	2.52672e13i	−1.91204	−	0.0186433i
$565$	−6.37086e14			−0.465513
$566$	1.75244e15	+	1.10929e15i	1.26810	+	0.802704i
$567$	−1.09608e15	−	2.64446e14i	−0.785479	−	0.189509i
$568$	1.64527e15	+	2.02053e14i	1.16767	+	0.143400i
$569$		−	9.77476e14i		−	0.687051i	−0.939143	−	0.343525i	$-0.888379\pi$
$569$		−	9.77476e14i		−	0.687051i	0.939143	−	0.343525i	$-0.111621\pi$
$570$	1.28234e15	+	2.07020e15i	0.892669	+	1.44112i
$571$			2.50757e15i			1.72884i	0.502772	+	0.864419i	$0.332314\pi$
$571$			2.50757e15i			1.72884i	−0.502772	+	0.864419i	$0.667686\pi$
$572$	2.36727e14	+	5.00066e14i	0.161647	+	0.341467i
$573$	1.05026e15	−	2.16379e15i	0.710309	−	1.46340i
$574$	−1.40002e14	+	2.21172e14i	−0.0937816	+	0.148154i
$575$	−1.13968e15			−0.756151
$576$	−6.24139e14	−	1.38779e15i	−0.410164	−	0.912012i
$577$	2.65897e15			1.73080			0.865400	−	0.501082i	$-0.167065\pi$
$577$	2.65897e15			1.73080			0.865400	+	0.501082i	$0.167065\pi$
$578$	−5.19983e14	+	8.21459e14i	−0.335263	+	0.529642i
$579$	2.01651e14	−	4.15450e14i	0.128786	−	0.265330i
$580$	7.55050e14	+	1.59498e15i	0.477663	+	1.00903i
$581$		−	1.24188e15i		−	0.778233i
$582$	−9.09631e14	−	1.46851e15i	−0.564662	−	0.911590i
$583$		−	2.41341e14i		−	0.148407i
$584$	1.86155e14	+	2.28614e13i	0.113398	+	0.0139262i
$585$	−3.02745e15	+	2.38390e15i	−1.82692	+	1.43857i
$586$	−1.60500e15	−	1.01596e15i	−0.959483	−	0.607352i
$587$	3.27810e15			1.94139			0.970694	−	0.240319i	$-0.0772520\pi$
$587$	3.27810e15			1.94139			0.970694	+	0.240319i	$0.0772520\pi$
$588$	5.91590e14	+	5.76827e12i	0.347093	+	0.00338431i
$589$	−2.02331e15			−1.17605
$590$	−1.31702e15	−	8.33673e14i	−0.758414	−	0.480076i
$591$	5.99991e14	+	2.91224e14i	0.342305	+	0.166149i
$592$	−1.12386e15	+	1.37137e15i	−0.635245	+	0.775147i
$593$		−	3.07599e15i		−	1.72260i	−0.508099	−	0.861299i	$-0.669652\pi$
$593$		−	3.07599e15i		−	1.72260i	0.508099	−	0.861299i	$-0.330348\pi$
$594$	1.42259e14	−	3.90706e14i	0.0789324	−	0.216783i
$595$		−	1.27496e15i		−	0.700896i
$596$	2.56811e15	−	1.21572e15i	1.39881	−	0.662185i
$597$	2.19402e15	+	1.06494e15i	1.18408	+	0.574731i
$598$	−1.21858e15	+	1.92509e15i	−0.651624	+	1.02942i
$599$	−5.89069e14			−0.312118			−0.156059	−	0.987748i	$-0.549879\pi$
$599$	−5.89069e14			−0.312118			−0.156059	+	0.987748i	$0.549879\pi$
$600$	1.05130e15	−	1.62553e15i	0.551943	−	0.853421i
$601$	8.49603e14			0.441984			0.220992	−	0.975276i	$-0.429071\pi$
$601$	8.49603e14			0.441984			0.220992	+	0.975276i	$0.429071\pi$
$602$	−6.15179e14	+	9.71848e14i	−0.317118	+	0.500977i
$603$	1.00343e15	−	7.90128e14i	0.512557	−	0.403601i
$604$	−7.61505e14	+	3.60489e14i	−0.385451	+	0.182469i
$605$			2.68031e15i			1.34440i
$606$	1.10905e15	−	6.86974e14i	0.551253	−	0.341461i
$607$		−	1.57614e15i		−	0.776350i	−0.921586	−	0.388175i	$-0.873106\pi$
$607$		−	1.57614e15i		−	0.776350i	0.921586	−	0.388175i	$-0.126894\pi$
$608$	−2.32161e15	+	7.69197e14i	−1.13324	+	0.375464i
$609$	−5.73440e14	+	1.18142e15i	−0.277391	+	0.571492i
$610$	−1.36180e15	−	8.62019e14i	−0.652829	−	0.413241i
$611$	−6.59088e15			−3.13124
$612$	1.16162e15	+	5.77890e14i	0.546929	+	0.272090i
$613$	−1.22136e15			−0.569915			−0.284958	−	0.958540i	$-0.591980\pi$
$613$	−1.22136e15			−0.569915			−0.284958	+	0.958540i	$0.591980\pi$
$614$	−4.40794e14	−	2.79022e14i	−0.203850	−	0.129037i
$615$	2.93566e14	−	6.04815e14i	0.134553	−	0.277210i
$616$	5.00208e13	−	4.07307e14i	0.0227225	−	0.185024i
$617$			2.02010e15i			0.909502i	0.890619	+	0.454751i	$0.150272\pi$
$617$			2.02010e15i			0.909502i	−0.890619	+	0.454751i	$0.849728\pi$
$618$	−1.29952e15	+	8.04959e14i	−0.579893	+	0.359201i
$619$			1.99191e15i			0.880988i	0.897755	+	0.440494i	$0.145197\pi$
$619$			1.99191e15i			0.880988i	−0.897755	+	0.440494i	$0.854803\pi$
$620$	1.36533e15	+	2.88416e15i	0.598528	+	1.26434i
$621$	1.67278e15	−	3.65545e14i	0.726835	−	0.158832i
$622$	1.48897e15	−	2.35225e15i	0.641268	−	1.01306i
$623$	2.35216e15			1.00411
$624$	−1.62169e15	−	3.51387e15i	−0.686201	−	1.48686i
$625$	−2.34457e15			−0.983382
$626$	4.64051e14	−	7.33099e14i	0.192933	−	0.304792i
$627$	−6.01213e14	−	2.91818e14i	−0.247775	−	0.120265i
$628$	2.93314e14	+	6.19603e14i	0.119827	+	0.253125i
$629$		−	1.51175e15i		−	0.612211i
$630$	2.84303e15	−	2.93000e14i	1.14132	−	0.117624i
$631$			3.96648e15i			1.57850i	0.614074	+	0.789248i	$0.289530\pi$
$631$			3.96648e15i			1.57850i	−0.614074	+	0.789248i	$0.710470\pi$
$632$	2.37204e14	−	1.93149e15i	0.0935787	−	0.761988i
$633$	−5.86185e14	−	2.84523e14i	−0.229253	−	0.111275i
$634$	−2.98098e15	−	1.88696e15i	−1.15576	−	0.731597i
$635$	−6.36146e14			−0.244513
$636$	−1.64594e13	+	1.68807e15i	−0.00627191	+	0.643243i
$637$	1.50464e15			0.568415
$638$	−4.09193e14	−	2.59019e14i	−0.153255	−	0.0970104i
$639$	−1.96008e15	−	2.48922e15i	−0.727812	−	0.924291i
$640$	2.66310e15	+	2.79033e15i	0.980387	+	1.02723i
$641$			4.55042e15i			1.66086i	0.557125	+	0.830429i	$0.311904\pi$
$641$			4.55042e15i			1.66086i	−0.557125	+	0.830429i	$0.688096\pi$
$642$	−4.65888e14	−	7.52128e14i	−0.168593	−	0.272176i
$643$			5.31175e15i			1.90580i	0.303283	+	0.952901i	$0.401917\pi$
$643$			5.31175e15i			1.90580i	−0.303283	+	0.952901i	$0.598083\pi$
$644$	1.52739e15	−	7.23051e14i	0.543347	−	0.257215i
$645$	1.28996e15	−	2.65761e15i	0.454984	−	0.937374i
$646$	1.11532e15	−	1.76196e15i	0.390050	−	0.616193i
$647$	−2.94525e15			−1.02129			−0.510644	−	0.859792i	$-0.670593\pi$
$647$	−2.94525e15			−1.02129			−0.510644	+	0.859792i	$0.670593\pi$
$648$	−1.02168e15	+	2.72310e15i	−0.351280	+	0.936270i
$649$	4.27758e14			0.145832
$650$	2.63329e15	−	4.16002e15i	0.890175	−	1.40628i
$651$	−1.03693e15	+	2.13633e15i	−0.347580	+	0.716098i
$652$	1.88633e15	−	8.92971e14i	0.626984	−	0.296808i
$653$		−	1.82749e14i		−	0.0602327i	−0.999546	−	0.0301163i	$-0.990412\pi$
$653$		−	1.82749e14i		−	0.0602327i	0.999546	−	0.0301163i	$-0.00958778\pi$
$654$	−4.99987e14	−	8.07178e14i	−0.163411	−	0.263810i
$655$		−	7.19768e15i		−	2.33274i
$656$	5.22238e14	+	4.27982e14i	0.167841	+	0.137548i
$657$	−2.21774e14	−	2.81644e14i	−0.0706809	−	0.0897618i
$658$	4.13056e15	+	2.61465e15i	1.30547	+	0.826362i
$659$	2.15944e15			0.676816			0.338408	−	0.940999i	$-0.390112\pi$
$659$	2.15944e15			0.676816			0.338408	+	0.940999i	$0.390112\pi$
$660$	−1.02763e13	+	1.05393e15i	−0.00319408	+	0.327582i
$661$	−1.12302e15			−0.346163			−0.173081	−	0.984908i	$-0.555372\pi$
$661$	−1.12302e15			−0.346163			−0.173081	+	0.984908i	$0.555372\pi$
$662$	−3.55194e14	−	2.24838e14i	−0.108579	−	0.0687306i
$663$	2.96849e15	+	1.44085e15i	0.899936	+	0.436812i
$664$	−3.17953e15	−	3.90474e14i	−0.955958	−	0.117400i
$665$		−	4.59367e15i		−	1.36975i
$666$	3.37105e15	−	3.47417e14i	0.996911	−	0.102741i
$667$		−	1.99427e15i		−	0.584915i
$668$	−1.31103e15	−	2.76945e15i	−0.381366	−	0.805607i
$669$	−5.29184e14	−	2.56856e14i	−0.152673	−	0.0741047i
$670$	−1.73154e15	+	2.73545e15i	−0.495474	+	0.782740i
$671$	4.42302e14			0.125529
$672$	−3.77650e14	+	2.84551e15i	−0.106306	+	0.800993i
$673$	5.65941e15			1.58011			0.790057	−	0.613033i	$-0.210051\pi$
$673$	5.65941e15			1.58011			0.790057	+	0.613033i	$0.210051\pi$
$674$	−1.81996e15	+	2.87514e15i	−0.504002	+	0.796213i
$675$	−3.61480e15	+	7.89926e14i	−0.992919	+	0.216978i
$676$	−2.64088e15	−	5.57866e15i	−0.719519	−	1.51993i
$677$			4.61425e15i			1.24699i	0.781827	+	0.623495i	$0.214288\pi$
$677$			4.61425e15i			1.24699i	−0.781827	+	0.623495i	$0.785712\pi$
$678$	−1.03966e15	+	6.43994e14i	−0.278695	+	0.172631i
$679$			3.25854e15i			0.866441i
$680$	−3.26424e15	−	4.00877e14i	−0.860959	−	0.105733i
$681$	9.33538e14	−	1.92331e15i	0.244243	−	0.503199i
$682$	−7.39931e14	−	4.68376e14i	−0.192034	−	0.121557i
$683$	6.66436e15			1.71571			0.857857	−	0.513889i	$-0.171796\pi$
$683$	6.66436e15			1.71571			0.857857	+	0.513889i	$0.171796\pi$
$684$	4.18530e15	+	2.08213e15i	1.06885	+	0.531740i
$685$	1.01250e15			0.256506
$686$	−3.65961e15	−	2.31653e15i	−0.919713	−	0.582178i
$687$	−1.71000e15	+	3.52301e15i	−0.426319	+	0.878319i
$688$	2.29476e15	+	1.88059e15i	0.567546	+	0.465113i
$689$			4.29340e15i			1.05340i
$690$	−3.68977e15	+	2.28554e15i	−0.898109	+	0.556312i
$691$		−	7.98056e15i		−	1.92710i	−0.267530	−	0.963550i	$-0.586207\pi$
$691$		−	7.98056e15i		−	1.92710i	0.267530	−	0.963550i	$-0.413793\pi$
$692$	6.69185e14	−	3.16786e14i	0.160311	−	0.0758896i
$693$	−6.16237e14	+	4.85242e14i	−0.146459	+	0.115326i
$694$	8.72927e14	−	1.37903e15i	0.205826	−	0.325160i
$695$	9.67159e15			2.26246
$696$	2.84445e15	+	1.83962e15i	0.660157	+	0.426951i
$697$	−5.75699e14			−0.132561
$698$	−2.54727e15	+	4.02413e15i	−0.581930	+	0.919322i
$699$	−5.55047e14	−	2.69409e14i	−0.125807	−	0.0610644i
$700$	−3.30061e15	+	1.56248e15i	−0.742259	+	0.351378i
$701$		−	2.44386e15i		−	0.545291i	−0.962115	−	0.272645i	$-0.912101\pi$
$701$		−	2.44386e15i		−	0.545291i	0.962115	−	0.272645i	$-0.0878986\pi$
$702$	−2.53076e15	+	6.95057e15i	−0.560269	+	1.53874i
$703$		−	5.44681e15i		−	1.19643i
$704$	−1.02709e15	−	2.56133e14i	−0.223850	−	0.0558233i
$705$	−1.12954e16	−	5.48259e15i	−2.44266	−	1.18562i
$706$	3.38978e15	+	2.14573e15i	0.727353	+	0.460414i
$707$	−2.46092e15			−0.523951
$708$	−2.99197e15	−	2.91730e13i	−0.632082	−	0.00616309i
$709$	−8.14483e15			−1.70737			−0.853685	−	0.520790i	$-0.825638\pi$
$709$	−8.14483e15			−1.70737			−0.853685	+	0.520790i	$0.825638\pi$
$710$	6.78586e15	+	4.29545e15i	1.41151	+	0.893485i
$711$	−2.92226e15	+	2.30107e15i	−0.603164	+	0.474948i
$712$	7.39573e14	−	6.02216e15i	0.151475	−	1.23342i
$713$		−	3.60618e15i		−	0.732918i
$714$	−1.28879e15	−	2.08061e15i	−0.259921	−	0.419615i
$715$			2.68055e15i			0.536464i
$716$	−3.44557e15	−	7.27849e15i	−0.684288	−	1.44550i
$717$	5.47932e14	−	1.12887e15i	0.107987	−	0.222479i
$718$	−1.03516e15	+	1.63532e15i	−0.202451	+	0.319829i
$719$	−5.83772e15			−1.13301			−0.566505	−	0.824058i	$-0.691705\pi$
$719$	−5.83772e15			−1.13301			−0.566505	+	0.824058i	$0.691705\pi$
$720$	1.43756e14	−	7.37105e15i	0.0276883	−	1.41971i
$721$	2.88358e15			0.551172
$722$	1.19888e15	−	1.89397e15i	0.227417	−	0.359268i
$723$	4.51767e15	−	9.30746e15i	0.850459	−	1.75215i
$724$	1.79450e15	+	3.79073e15i	0.335259	+	0.708209i
$725$			4.30953e15i			0.799045i
$726$	2.70937e15	+	4.37400e15i	0.498559	+	0.804874i
$727$			8.02705e15i			1.46594i	0.680260	+	0.732971i	$0.261867\pi$
$727$			8.02705e15i			1.46594i	−0.680260	+	0.732971i	$0.738133\pi$
$728$	−8.89859e14	+	7.24589e15i	−0.161287	+	1.31332i
$729$	5.05233e15	−	2.31886e15i	0.908846	−	0.417131i
$730$	7.67790e14	+	4.86011e14i	0.137078	+	0.0867701i
$731$	−2.52967e15			−0.448248
$732$	−3.09370e15	−	3.01650e13i	−0.544085	−	0.00530508i
$733$	−6.99989e15			−1.22185			−0.610927	−	0.791687i	$-0.709203\pi$
$733$	−6.99989e15			−1.22185			−0.610927	+	0.791687i	$0.709203\pi$
$734$	−3.43991e15	−	2.17746e15i	−0.595962	−	0.377244i
$735$	2.57864e15	+	1.25162e15i	0.443415	+	0.215226i
$736$	−1.37096e15	−	4.13786e15i	−0.233989	−	0.706233i
$737$		−	8.88452e14i		−	0.150509i
$738$	−1.32302e14	−	1.28375e15i	−0.0222462	−	0.215859i
$739$		−	5.01776e15i		−	0.837462i	−0.908110	−	0.418731i	$-0.862475\pi$
$739$		−	5.01776e15i		−	0.837462i	0.908110	−	0.418731i	$-0.137525\pi$
$740$	−7.76426e15	+	3.67553e15i	−1.28625	+	0.608899i
$741$	1.06954e16	+	5.19137e15i	1.75873	+	0.853654i
$742$	1.70322e15	−	2.69071e15i	0.278002	−	0.439183i
$743$	2.18883e15			0.354628			0.177314	−	0.984154i	$-0.443259\pi$
$743$	2.18883e15			0.354628			0.177314	+	0.984154i	$0.443259\pi$
$744$	5.14353e15	+	3.32653e15i	0.827198	+	0.534984i
$745$	1.37661e16			2.19761
$746$	4.18594e15	−	6.61287e15i	0.663330	−	1.04792i
$747$	3.78792e15	+	4.81049e15i	0.595850	+	0.756705i
$748$	8.15753e14	−	3.86170e14i	0.127380	−	0.0603003i
$749$			1.66893e15i			0.258695i
$750$	1.28271e14	−	7.94542e13i	0.0197374	−	0.0122259i
$751$			8.21847e15i			1.25537i	0.778468	+	0.627684i	$0.215997\pi$
$751$			8.21847e15i			1.25537i	−0.778468	+	0.627684i	$0.784003\pi$
$752$	7.99293e15	−	9.75323e15i	1.21201	−	1.47894i
$753$	−7.21582e14	+	1.48663e15i	−0.108621	+	0.223785i
$754$	7.27946e15	+	4.60789e15i	1.08782	+	0.688589i
$755$	−4.08196e15			−0.605565
$756$	4.34338e15	−	3.35201e15i	0.639673	−	0.493669i
$757$	−3.75028e15			−0.548324			−0.274162	−	0.961684i	$-0.588400\pi$
$757$	−3.75028e15			−0.548324			−0.274162	+	0.961684i	$0.588400\pi$
$758$	−3.32251e15	−	2.10315e15i	−0.482265	−	0.305273i
$759$	5.20113e14	−	1.07156e15i	0.0749494	−	0.154413i
$760$	−1.17610e16	−	1.44435e15i	−1.68256	−	0.206633i
$761$			7.86959e15i			1.11773i	0.829259	+	0.558865i	$0.188763\pi$
$761$			7.86959e15i			1.11773i	−0.829259	+	0.558865i	$0.811237\pi$
$762$	−1.03813e15	+	6.43045e14i	−0.146386	+	0.0906752i
$763$			1.79108e15i			0.250744i
$764$	5.00757e15	+	1.05781e16i	0.696007	+	1.47026i
$765$	3.88883e15	+	4.93865e15i	0.536637	+	0.681507i
$766$	−2.66021e15	+	4.20255e15i	−0.364467	+	0.575777i
$767$	−7.60971e15			−1.03513
$768$	7.16651e15	+	1.86158e15i	0.967879	+	0.251417i
$769$	1.50855e15			0.202285			0.101143	−	0.994872i	$-0.467750\pi$
$769$	1.50855e15			0.202285			0.101143	+	0.994872i	$0.467750\pi$
$770$	1.06339e15	−	1.67992e15i	0.141577	−	0.223661i
$771$	−9.75069e15	−	4.73280e15i	−1.28895	−	0.625633i
$772$	9.61459e14	+	2.03101e15i	0.126193	+	0.266573i
$773$		−	1.29755e16i		−	1.69098i	−0.533995	−	0.845488i	$-0.679310\pi$
$773$		−	1.29755e16i		−	1.69098i	0.533995	−	0.845488i	$-0.320690\pi$
$774$	−5.81347e14	−	5.64091e15i	−0.0752246	−	0.729918i
$775$			7.79279e15i			1.00123i
$776$	8.34272e15	+	1.02456e15i	1.06431	+	0.130706i
$777$	−5.75107e15	−	2.79146e15i	−0.728506	−	0.353603i
$778$	2.84785e15	+	1.80269e15i	0.358203	+	0.226743i
$779$	−2.07424e15			−0.259061
$780$	1.82813e14	−	1.87492e16i	0.0226718	−	2.32521i
$781$	−2.20399e15			−0.271412
$782$	3.14038e15	+	1.98786e15i	0.384012	+	0.243079i
$783$	−1.38226e15	−	6.32540e15i	−0.167842	−	0.768065i
$784$	−1.82471e15	+	2.22657e15i	−0.220017	+	0.268472i
$785$			3.32131e15i			0.397674i
$786$	−7.27573e15	−	1.17459e16i	−0.865073	−	1.39657i
$787$		−	1.16489e16i		−	1.37539i	−0.726002	−	0.687693i	$-0.758624\pi$
$787$		−	1.16489e16i		−	1.37539i	0.726002	−	0.687693i	$-0.241376\pi$
$788$	−2.93317e15	+	1.38854e15i	−0.343909	+	0.162803i
$789$	−2.86705e15	+	5.90681e15i	−0.333820	+	0.687748i
$790$	5.04270e15	−	7.96636e15i	0.583061	−	0.921109i
$791$	2.30696e15			0.264892
$792$	1.04859e15	+	1.73030e15i	0.119568	+	0.197303i
$793$	−7.86846e15			−0.891019
$794$	−1.01316e14	+	1.60056e14i	−0.0113937	+	0.0179995i
$795$	−3.57144e15	+	7.35800e15i	−0.398863	+	0.821752i
$796$	−1.07259e16	+	5.07753e15i	−1.18963	+	0.563159i
$797$		−	1.19308e16i		−	1.31416i	−0.753820	−	0.657081i	$-0.771791\pi$
$797$		−	1.19308e16i		−	1.31416i	0.753820	−	0.657081i	$-0.228209\pi$
$798$	−4.64348e15	−	7.49643e15i	−0.507958	−	0.820047i
$799$			1.07516e16i			1.16807i
$800$	2.96257e15	+	8.94172e15i	0.319649	+	0.964776i
$801$	−9.11126e15	+	7.17446e15i	−0.976337	+	0.768794i
$802$	−1.12546e16	−	7.12414e15i	−1.19776	−	0.758182i
$803$	−2.49372e14			−0.0263580
$804$	−6.05923e13	+	6.21431e15i	−0.00636077	+	0.652356i
$805$	8.18740e15			0.853628
$806$	1.31632e16	+	8.33230e15i	1.36307	+	0.862824i
$807$	9.01003e15	+	4.37330e15i	0.926663	+	0.449785i
$808$	−7.73769e14	+	6.30061e15i	−0.0790404	+	0.643606i
$809$		−	5.71958e15i		−	0.580293i	−0.956982	−	0.290147i	$-0.906296\pi$
$809$		−	5.71958e15i		−	0.580293i	0.956982	−	0.290147i	$-0.0937040\pi$
$810$	−1.01190e16	+	9.80665e15i	−1.01969	+	0.988218i
$811$		−	8.13086e14i		−	0.0813808i	−0.999172	−	0.0406904i	$-0.987044\pi$
$811$		−	8.13086e14i		−	0.0813808i	0.999172	−	0.0406904i	$-0.0129557\pi$
$812$	−2.73412e15	−	5.77561e15i	−0.271806	−	0.574169i
$813$	6.82464e15	+	3.31255e15i	0.673879	+	0.327088i
$814$	1.26088e15	−	1.99192e15i	0.123663	−	0.195361i
$815$	1.01115e16			0.985025
$816$	−5.73215e15	+	2.64544e15i	−0.554653	+	0.255978i
$817$	−9.11437e15			−0.876003
$818$	−8.76863e15	+	1.38525e16i	−0.837122	+	1.32247i
$819$	1.09627e16	−	8.63234e15i	1.03958	−	0.818592i
$820$	1.39970e15	+	2.95676e15i	0.131844	+	0.278509i
$821$			1.45022e16i			1.35689i	0.734650	+	0.678446i	$0.237346\pi$
$821$			1.45022e16i			1.35689i	−0.734650	+	0.678446i	$0.762654\pi$
$822$	1.65231e15	−	1.02348e15i	0.153566	−	0.0951228i
$823$		−	7.51647e15i		−	0.693929i	−0.937878	−	0.346964i	$-0.887212\pi$
$823$		−	7.51647e15i		−	0.693929i	0.937878	−	0.346964i	$-0.112788\pi$
$824$	9.06662e14	−	7.38272e15i	0.0831468	−	0.677043i
$825$	−1.12394e15	+	2.31558e15i	−0.102387	+	0.210942i
$826$	4.76907e15	+	3.01882e15i	0.431563	+	0.273179i
$827$	−1.76173e16			−1.58365			−0.791825	−	0.610748i	$-0.790869\pi$
$827$	−1.76173e16			−1.58365			−0.791825	+	0.610748i	$0.790869\pi$
$828$	−3.71103e15	+	7.45956e15i	−0.331381	+	0.666110i
$829$	9.66932e15			0.857721			0.428861	−	0.903371i	$-0.358915\pi$
$829$	9.66932e15			0.857721			0.428861	+	0.903371i	$0.358915\pi$
$830$	−1.31139e16	−	8.30108e15i	−1.15558	−	0.731484i
$831$	2.02770e15	−	4.17755e15i	0.177500	−	0.365692i
$832$	1.82716e16	+	4.55655e15i	1.58891	+	0.396239i
$833$		−	2.45450e15i		−	0.212039i
$834$	1.57831e16	−	9.77647e15i	1.35450	−	0.839013i
$835$		−	1.48453e16i		−	1.26565i
$836$	2.93915e15	−	1.39136e15i	0.248936	−	0.117844i
$837$	−2.49949e15	−	1.14380e16i	−0.210311	−	0.962411i
$838$	1.74093e15	−	2.75029e15i	0.145526	−	0.229899i
$839$	1.24439e16			1.03339			0.516697	−	0.856169i	$-0.327162\pi$
$839$	1.24439e16			1.03339			0.516697	+	0.856169i	$0.327162\pi$
$840$	−7.55249e15	+	1.16778e16i	−0.623095	+	0.963437i
$841$	4.65943e15			0.381905
$842$	−7.62111e15	+	1.20397e16i	−0.620586	+	0.980389i
$843$	8.00291e14	+	3.88446e14i	0.0647435	+	0.0314253i
$844$	2.86568e15	−	1.35659e15i	0.230327	−	0.109034i
$845$		−	2.99038e16i		−	2.38789i
$846$	−2.39751e16	+	2.47085e15i	−1.90206	+	0.196024i
$847$		−	9.70568e15i		−	0.765010i
$848$	−6.35340e15	−	5.20671e15i	−0.497541	−	0.407742i
$849$	1.73531e16	+	8.42288e15i	1.35016	+	0.655342i
$850$	−6.78621e15	−	4.29566e15i	−0.524594	−	0.332067i
$851$	9.70797e15			0.745617
$852$	1.54159e16	+	1.50312e14i	1.17639	+	0.0114703i
$853$	−1.89452e16			−1.43642			−0.718208	−	0.695828i	$-0.755037\pi$
$853$	−1.89452e16			−1.43642			−0.718208	+	0.695828i	$0.755037\pi$
$854$	4.93123e15	+	3.12147e15i	0.371481	+	0.235147i
$855$	1.40114e16	+	1.77939e16i	1.04874	+	1.33186i
$856$	4.27291e15	+	5.24750e14i	0.317774	+	0.0390253i
$857$			4.67340e14i			0.0345333i	0.999851	+	0.0172667i	$0.00549642\pi$
$857$			4.67340e14i			0.0345333i	−0.999851	+	0.0172667i	$0.994504\pi$
$858$	2.70962e15	+	4.37440e15i	0.198943	+	0.321172i
$859$			1.46383e16i			1.06789i	0.845518	+	0.533947i	$0.179292\pi$
$859$			1.46383e16i			1.06789i	−0.845518	+	0.533947i	$0.820708\pi$
$860$	6.15041e15	+	1.29923e16i	0.445823	+	0.941766i
$861$	−1.06303e15	+	2.19010e15i	−0.0765649	+	0.157742i
$862$	9.68381e15	−	1.52983e16i	0.693037	−	1.09485i
$863$	−7.65162e15			−0.544119			−0.272059	−	0.962280i	$-0.587705\pi$
$863$	−7.65162e15			−0.544119			−0.272059	+	0.962280i	$0.587705\pi$
$864$	−7.21638e15	−	1.21742e16i	−0.509910	−	0.860228i
$865$	3.58709e15			0.251857
$866$	1.96863e14	−	3.11000e14i	0.0137346	−	0.0216976i
$867$	−3.94824e15	+	8.13430e15i	−0.273715	+	0.563917i
$868$	−4.94402e15	−	1.04438e16i	−0.340582	−	0.719452i
$869$			2.58741e15i			0.177116i
$870$	8.64245e15	+	1.39524e16i	0.587869	+	0.949055i
$871$			1.58054e16i			1.06833i
$872$	4.58565e15	+	5.63158e14i	0.308007	+	0.0378259i
$873$	−9.93904e15	−	1.26222e16i	−0.663385	−	0.842472i
$874$	1.13147e16	+	7.16223e15i	0.750467	+	0.475045i
$875$	−2.84626e14			−0.0187599
$876$	1.74424e15	+	1.70072e13i	0.114244	+	0.00111393i
$877$	1.37172e16			0.892829			0.446415	−	0.894826i	$-0.352701\pi$
$877$	1.37172e16			0.892829			0.446415	+	0.894826i	$0.352701\pi$
$878$	−4.29935e15	−	2.72149e15i	−0.278088	−	0.176030i
$879$	−1.58931e16	−	7.71422e15i	−1.02157	−	0.495853i
$880$	−3.96669e15	−	3.25077e15i	−0.253381	−	0.207650i
$881$		−	7.33510e15i		−	0.465627i	−0.972521	−	0.232814i	$-0.925207\pi$
$881$		−	7.33510e15i		−	0.465627i	0.972521	−	0.232814i	$-0.0747932\pi$
$882$	5.47330e15	−	5.64073e14i	0.345280	−	0.0355843i
$883$		−	4.88843e15i		−	0.306468i	−0.988190	−	0.153234i	$-0.951031\pi$
$883$		−	4.88843e15i		−	0.306468i	0.988190	−	0.153234i	$-0.0489689\pi$
$884$	−1.45121e16	+	6.86987e15i	−0.904152	+	0.428017i
$885$	−1.30415e16	−	6.33009e15i	−0.807494	−	0.391942i
$886$	−6.76578e15	+	1.06885e16i	−0.416325	+	0.657702i
$887$	−1.71961e15			−0.105160			−0.0525799	−	0.998617i	$-0.516744\pi$
$887$	−1.71961e15			−0.105160			−0.0525799	+	0.998617i	$0.516744\pi$
$888$	−8.95515e15	+	1.38466e16i	−0.544254	+	0.841532i
$889$	2.30355e15			0.139136
$890$	1.57226e16	−	2.48382e16i	0.943796	−	1.49099i
$891$	9.06974e14	−	3.75924e15i	0.0541087	−	0.224270i
$892$	2.58702e15	−	1.22467e15i	0.153388	−	0.0726126i
$893$			3.87381e16i			2.28273i
$894$	2.24649e16	−	1.39154e16i	1.31568	−	0.814963i
$895$		−	3.90155e16i		−	2.27097i
$896$	−9.64337e15	−	1.01041e16i	−0.557872	−	0.584525i
$897$	−9.25269e15	+	1.90627e16i	−0.531998	+	1.09604i
$898$	−5.48932e15	−	3.47473e15i	−0.313688	−	0.198565i
$899$	−1.36363e16			−0.774493
$900$	8.01935e15	−	1.61197e16i	0.452695	−	0.909965i
$901$	7.00378e15			0.392958
$902$	−7.58556e14	−	4.80166e14i	−0.0423011	−	0.0267766i
$903$	−4.67107e15	+	9.62350e15i	−0.258901	+	0.533397i
$904$	7.25360e14	−	5.90642e15i	0.0399601	−	0.325385i
$905$			2.03198e16i			1.11263i
$906$	−6.66137e15	+	4.12622e15i	−0.362542	+	0.224568i
$907$			7.39111e15i			0.399825i	0.979814	+	0.199912i	$0.0640658\pi$
$907$			7.39111e15i			0.399825i	−0.979814	+	0.199912i	$0.935934\pi$
$908$	4.45104e15	+	9.40247e15i	0.239326	+	0.505557i
$909$	9.53254e15	−	7.50618e15i	0.509457	−	0.401160i
$910$	−1.89175e16	+	2.98855e16i	−1.00493	+	1.58757i
$911$	−2.30501e16			−1.21708			−0.608542	−	0.793521i	$-0.708245\pi$
$911$	−2.30501e16			−1.21708			−0.608542	+	0.793521i	$0.708245\pi$
$912$	−2.06529e16	+	9.53149e15i	−1.08395	+	0.500253i
$913$	4.25928e15			0.222202
$914$	1.03241e16	−	1.63098e16i	0.535363	−	0.845756i
$915$	−1.34849e16	−	6.54533e15i	−0.695076	−	0.337377i
$916$	−8.15317e15	−	1.72229e16i	−0.417736	−	0.882434i
$917$			2.60636e16i			1.32740i
$918$	1.13384e16	+	4.12840e15i	0.574006	+	0.209001i
$919$			3.49695e16i			1.75976i	0.475193	+	0.879882i	$0.342378\pi$
$919$			3.49695e16i			1.75976i	−0.475193	+	0.879882i	$0.657622\pi$
$920$	2.57430e15	−	2.09619e16i	0.128774	−	1.04857i
$921$	−4.36486e15	−	2.11862e15i	−0.217041	−	0.105348i
$922$	−2.35279e16	−	1.48931e16i	−1.16296	−	0.736150i
$923$	3.92085e16			1.92651
$924$	3.72116e13	−	3.81640e15i	0.00181753	−	0.186405i
$925$	−2.09785e16			−1.01858
$926$	1.42727e16	+	9.03458e15i	0.688881	+	0.436062i
$927$	−1.11697e16	+	8.79535e15i	−0.535925	+	0.422002i
$928$	−1.56468e16	+	5.18409e15i	−0.746295	+	0.247263i
$929$		−	3.62189e16i		−	1.71731i	−0.512553	−	0.858655i	$-0.671300\pi$
$929$		−	3.62189e16i		−	1.71731i	0.512553	−	0.858655i	$-0.328700\pi$
$930$	1.56279e16	+	2.52296e16i	0.736619	+	1.18920i
$931$		−	8.84355e15i		−	0.414384i
$932$	2.71345e15	−	1.28452e15i	0.126396	−	0.0598349i
$933$	1.13058e16	−	2.32926e16i	0.523542	−	1.07862i
$934$	−1.42580e16	+	2.25244e16i	−0.656371	+	1.03692i
$935$	4.37275e15			0.200120
$936$	−1.86542e16	−	3.07817e16i	−0.848708	−	1.40047i
$937$	3.40159e15			0.153856			0.0769280	−	0.997037i	$-0.475489\pi$
$937$	3.40159e15			0.153856			0.0769280	+	0.997037i	$0.475489\pi$
$938$	6.27009e15	−	9.90536e15i	0.281941	−	0.445405i
$939$	3.52355e15	−	7.25934e15i	0.157514	−	0.324516i
$940$	5.52199e16	−	2.61406e16i	2.45410	−	1.16175i
$941$			3.25411e15i			0.143777i	0.997413	+	0.0718885i	$0.0229026\pi$
$941$			3.25411e15i			0.143777i	−0.997413	+	0.0718885i	$0.977097\pi$
$942$	3.35733e15	+	5.42007e15i	0.147474	+	0.238081i
$943$		−	3.69695e15i		−	0.161447i
$944$	9.22849e15	−	1.12609e16i	0.400668	−	0.488908i
$945$	2.59686e16	−	5.67480e15i	1.12092	−	0.244949i
$946$	−3.33316e15	−	2.10989e15i	−0.143039	−	0.0905438i
$947$	8.77434e15			0.374360			0.187180	−	0.982326i	$-0.440065\pi$
$947$	8.77434e15			0.374360			0.187180	+	0.982326i	$0.440065\pi$
$948$	1.76461e14	−	1.80977e16i	0.00748520	−	0.767676i
$949$	4.43627e15			0.187092
$950$	−2.44506e16	−	1.54772e16i	−1.02520	−	0.648953i
$951$	−2.95185e16	−	1.43277e16i	−1.23056	−	0.597288i
$952$	1.18202e16	+	1.45162e15i	0.489914	+	0.0601657i
$953$			1.40933e16i			0.580769i	0.956910	+	0.290384i	$0.0937831\pi$
$953$			1.40933e16i			0.580769i	−0.956910	+	0.290384i	$0.906217\pi$
$954$	1.60955e15	+	1.56177e16i	0.0659459	+	0.639884i
$955$			5.67027e16i			2.30986i
$956$	2.61250e15	+	5.51869e15i	0.105813	+	0.223521i
$957$	−4.05194e15	−	1.96674e15i	−0.163173	−	0.0792010i
$958$	−7.36498e14	+	1.16350e15i	−0.0294891	+	0.0465863i
$959$	−3.66638e15			−0.145960
$960$	2.75235e16	+	2.30081e16i	1.08946	+	0.910729i
$961$	7.50442e14			0.0295351
$962$	−2.24309e16	+	3.54358e16i	−0.877774	+	1.38669i
$963$	−5.09050e15	−	6.46472e15i	−0.198069	−	0.251539i
$964$	2.15399e16	+	4.55013e16i	0.833335	+	1.76036i
$965$			1.08870e16i			0.418801i
$966$	1.33610e16	−	8.27618e15i	0.511054	−	0.316560i
$967$		−	2.19092e16i		−	0.833261i	−0.909076	−	0.416630i	$-0.863211\pi$
$967$		−	2.19092e16i		−	0.833261i	0.909076	−	0.416630i	$-0.136789\pi$
$968$	−2.48491e16	−	3.05168e15i	−0.939715	−	0.115405i
$969$	8.46863e15	−	1.74474e16i	0.318444	−	0.656069i
$970$	3.44093e16	+	2.17810e16i	1.28656	+	0.814393i
$971$	4.32133e16			1.60661			0.803307	−	0.595565i	$-0.203072\pi$
$971$	4.32133e16			1.60661			0.803307	+	0.595565i	$0.203072\pi$
$972$	−6.60024e15	+	2.62322e16i	−0.244003	+	0.969774i
$973$	−3.50219e16			−1.28742
$974$	−3.81720e15	−	2.41629e15i	−0.139531	−	0.0883231i
$975$	1.99946e16	−	4.11937e16i	0.726755	−	1.49729i
$976$	9.54227e15	−	1.16438e16i	0.344888	−	0.420843i
$977$		−	1.00387e16i		−	0.360793i	−0.983594	−	0.180396i	$-0.942262\pi$
$977$		−	1.00387e16i		−	0.360793i	0.983594	−	0.180396i	$-0.0577381\pi$
$978$	1.65009e16	−	1.02211e16i	0.589719	−	0.365287i
$979$			8.06725e15i			0.286695i
$980$	−1.26062e16	+	5.96765e15i	−0.445493	+	0.210892i
$981$	−5.46308e15	−	6.93789e15i	−0.191981	−	0.243808i
$982$	1.23630e16	−	1.95309e16i	0.432028	−	0.682510i
$983$	5.16680e15			0.179547			0.0897734	−	0.995962i	$-0.471386\pi$
$983$	5.16680e15			0.179547			0.0897734	+	0.995962i	$0.471386\pi$
$984$	5.27300e15	+	3.41027e15i	0.182215	+	0.117846i
$985$	−1.57230e16			−0.540300
$986$	7.51681e15	−	1.18749e16i	0.256868	−	0.405795i
$987$	4.09020e16	+	1.98530e16i	1.38995	+	0.674657i
$988$	−5.22868e16	+	2.47521e16i	−1.76697	+	0.836466i
$989$		−	1.62447e16i		−	0.545926i
$990$	1.00491e15	+	9.75080e15i	0.0335840	+	0.325872i
$991$		−	2.85879e16i		−	0.950117i	−0.879954	−	0.475059i	$-0.842427\pi$
$991$		−	2.85879e16i		−	0.950117i	0.879954	−	0.475059i	$-0.157573\pi$
$992$	−2.82935e16	+	9.37421e15i	−0.935132	+	0.309828i
$993$	−3.51722e15	−	1.70719e15i	−0.115606	−	0.0561128i
$994$	−2.45723e16	−	1.55543e16i	−0.803196	−	0.508422i
$995$	−5.74949e16			−1.86897
$996$	−2.97917e16	−	2.90483e14i	−0.963095	−	0.00939061i
$997$	5.53793e16			1.78043			0.890213	−	0.455544i	$-0.150555\pi$
$997$	5.53793e16			1.78043			0.890213	+	0.455544i	$0.150555\pi$
$998$	−2.98892e15	−	1.89198e15i	−0.0955644	−	0.0604922i
$999$	3.07915e16	−	6.72873e15i	0.979087	−	0.213955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.12.b.a.11.8	yes	20
3.2	odd	2	inner	12.12.b.a.11.13	yes	20
4.3	odd	2	inner	12.12.b.a.11.14	yes	20
8.3	odd	2		192.12.c.d.191.8		20
8.5	even	2		192.12.c.d.191.13		20
12.11	even	2	inner	12.12.b.a.11.7	✓	20
24.5	odd	2		192.12.c.d.191.7		20
24.11	even	2		192.12.c.d.191.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.12.b.a.11.7	✓	20	12.11	even	2	inner
12.12.b.a.11.8	yes	20	1.1	even	1	trivial
12.12.b.a.11.13	yes	20	3.2	odd	2	inner
12.12.b.a.11.14	yes	20	4.3	odd	2	inner
192.12.c.d.191.7		20	24.5	odd	2
192.12.c.d.191.8		20	8.3	odd	2
192.12.c.d.191.13		20	8.5	even	2
192.12.c.d.191.14		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-24.2046 + 38.2379i) q^{2} +(-183.786 + 378.642i) q^{3} +(-876.277 - 1851.07i) q^{4} -9922.43i q^{5} +(-10030.0 - 16192.5i) q^{6} +35930.2i q^{7} +(91990.8 + 11297.3i) q^{8} +(-109593. - 139178. i) q^{9} +O(q^{10})\)	\(q+(-24.2046 + 38.2379i) q^{2} +(-183.786 + 378.642i) q^{3} +(-876.277 - 1851.07i) q^{4} -9922.43i q^{5} +(-10030.0 - 16192.5i) q^{6} +35930.2i q^{7} +(91990.8 + 11297.3i) q^{8} +(-109593. - 139178. i) q^{9} +(379413. + 240168. i) q^{10} -123230. q^{11} +(861938. + 8404.29i) q^{12} +2.19224e6 q^{13} +(-1.37390e6 - 869675. i) q^{14} +(3.75705e6 + 1.82360e6i) q^{15} +(-2.65858e6 + 3.24409e6i) q^{16} -3.57618e6i q^{17} +(7.97452e6 - 821847. i) q^{18} -1.28849e7i q^{19} +(-1.83671e7 + 8.69479e6i) q^{20} +(-1.36047e7 - 6.60346e6i) q^{21} +(2.98274e6 - 4.71207e6i) q^{22} +2.29651e7 q^{23} +(-2.11842e7 + 3.27553e7i) q^{24} -4.96265e7 q^{25} +(-5.30622e7 + 8.38267e7i) q^{26} +(7.28402e7 - 1.59174e7i) q^{27} +(6.65091e7 - 3.14848e7i) q^{28} -8.68394e7i q^{29} +(-1.60669e8 + 9.95222e7i) q^{30} -1.57029e8i q^{31} +(-5.96974e7 - 1.80181e8i) q^{32} +(2.26480e7 - 4.66602e7i) q^{33} +(1.36746e8 + 8.65599e7i) q^{34} +3.56515e8 q^{35} +(-1.61594e8 + 3.24822e8i) q^{36} +4.22727e8 q^{37} +(4.92693e8 + 3.11874e8i) q^{38} +(-4.02902e8 + 8.30074e8i) q^{39} +(1.12096e8 - 9.12772e8i) q^{40} -1.60981e8i q^{41} +(5.81798e8 - 3.60381e8i) q^{42} -7.07367e8i q^{43} +(1.07984e8 + 2.28107e8i) q^{44} +(-1.38098e9 + 1.08742e9i) q^{45} +(-5.55861e8 + 8.78137e8i) q^{46} -3.00646e9 q^{47} +(-7.39740e8 - 1.60287e9i) q^{48} +6.86348e8 q^{49} +(1.20119e9 - 1.89761e9i) q^{50} +(1.35409e9 + 6.57251e8i) q^{51} +(-1.92101e9 - 4.05798e9i) q^{52} +1.95845e9i q^{53} +(-1.15442e9 + 3.17053e9i) q^{54} +1.22274e9i q^{55} +(-4.05913e8 + 3.30525e9i) q^{56} +(4.87878e9 + 2.36807e9i) q^{57} +(3.32056e9 + 2.10191e9i) q^{58} -3.47121e9 q^{59} +(8.33910e7 - 8.55252e9i) q^{60} -3.58923e9 q^{61} +(6.00445e9 + 3.80082e9i) q^{62} +(5.00069e9 - 3.93768e9i) q^{63} +(8.33468e9 + 2.07849e9i) q^{64} -2.17523e10i q^{65} +(1.23600e9 + 1.99540e9i) q^{66} +7.20969e9i q^{67} +(-6.61974e9 + 3.13372e9i) q^{68} +(-4.22066e9 + 8.69555e9i) q^{69} +(-8.62929e9 + 1.36324e10i) q^{70} +1.78852e10 q^{71} +(-8.50918e9 - 1.40412e10i) q^{72} +2.02363e9 q^{73} +(-1.02319e10 + 1.61642e10i) q^{74} +(9.12064e9 - 1.87907e10i) q^{75} +(-2.38509e10 + 1.12908e10i) q^{76} -4.42769e9i q^{77} +(-2.19882e10 - 3.54977e10i) q^{78} -2.09965e10i q^{79} +(3.21893e10 + 2.63796e10i) q^{80} +(-7.35999e9 + 3.05058e10i) q^{81} +(6.15560e9 + 3.89649e9i) q^{82} -3.45636e10 q^{83} +(-3.01968e8 + 3.09696e10i) q^{84} -3.54844e10 q^{85} +(2.70482e10 + 1.71215e10i) q^{86} +(3.28810e10 + 1.59598e10i) q^{87} +(-1.13361e10 - 1.39217e9i) q^{88} -6.54648e10i q^{89} +(-8.15471e9 - 7.91266e10i) q^{90} +7.87676e10i q^{91} +(-2.01238e10 - 4.25099e10i) q^{92} +(5.94577e10 + 2.88597e10i) q^{93} +(7.27701e10 - 1.14961e11i) q^{94} -1.27850e11 q^{95} +(7.91954e10 + 1.05107e10i) q^{96} +9.06908e10 q^{97} +(-1.66128e10 + 2.62445e10i) q^{98} +(1.35051e10 + 1.71510e10i) 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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