LMFDB - Embedded newform 12.12.b.a.11.10

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			11.10
Root			$-0.544378 + 22.6209i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.12.b.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08876 + 45.2417i) q^{2} +(-399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} +4150.68i q^{5} +(6436.35 - 17926.8i) q^{6} -39165.5i q^{7} +(6684.15 - 92440.6i) q^{8} +(141953. + 105973. i) q^{9} +O(q^{10})$	\(q+(-1.08876 + 45.2417i) q^{2} +(-399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} +4150.68i q^{5} +(6436.35 - 17926.8i) q^{6} -39165.5i q^{7} +(6684.15 - 92440.6i) q^{8} +(141953. + 105973. i) q^{9} +(-187784. - 4519.08i) q^{10} +715661. q^{11} +(804032. + 310710. i) q^{12} -605992. q^{13} +(1.77192e6 + 42641.7i) q^{14} +(550602. - 1.65794e6i) q^{15} +(4.17489e6 + 403048. i) q^{16} -5.31852e6i q^{17} +(-4.94897e6 + 6.30683e6i) q^{18} -1.51325e7i q^{19} +(408902. - 8.49076e6i) q^{20} +(-5.19544e6 + 1.56442e7i) q^{21} +(-779180. + 3.23777e7i) q^{22} -4.01248e7 q^{23} +(-1.49324e7 + 3.60375e7i) q^{24} +3.16000e7 q^{25} +(659777. - 2.74161e7i) q^{26} +(-4.26437e7 - 6.11603e7i) q^{27} +(-3.85837e6 + 8.01182e7i) q^{28} -1.84980e6i q^{29} +(7.44085e7 + 2.67153e7i) q^{30} -2.41637e8i q^{31} +(-2.27800e7 + 1.88441e8i) q^{32} +(-2.85862e8 - 9.49348e7i) q^{33} +(2.40619e8 + 5.79057e6i) q^{34} +1.62564e8 q^{35} +(-2.79944e8 - 2.30767e8i) q^{36} +4.80485e8 q^{37} +(6.84620e8 + 1.64756e7i) q^{38} +(2.42056e8 + 8.03868e7i) q^{39} +(3.83691e8 + 2.77438e7i) q^{40} +1.82276e8i q^{41} +(-7.02113e8 - 2.52083e8i) q^{42} +1.12750e9i q^{43} +(-1.46398e9 - 7.05029e7i) q^{44} +(-4.39862e8 + 5.89203e8i) q^{45} +(4.36861e7 - 1.81531e9i) q^{46} -4.80730e8 q^{47} +(-1.61414e9 - 7.14806e8i) q^{48} +4.43388e8 q^{49} +(-3.44046e7 + 1.42964e9i) q^{50} +(-7.05519e8 + 2.12442e9i) q^{51} +(1.23963e9 + 5.96989e7i) q^{52} -4.89614e9i q^{53} +(2.81342e9 - 1.86269e9i) q^{54} +2.97048e9i q^{55} +(-3.62048e9 - 2.61788e8i) q^{56} +(-2.00737e9 + 6.04448e9i) q^{57} +(8.36882e7 + 2.01398e6i) q^{58} +3.77738e9 q^{59} +(-1.28966e9 + 3.33728e9i) q^{60} +1.72291e9 q^{61} +(1.09321e10 + 2.63084e8i) q^{62} +(4.15050e9 - 5.55967e9i) q^{63} +(-8.50058e9 - 1.23577e9i) q^{64} -2.51528e9i q^{65} +(4.60625e9 - 1.28295e10i) q^{66} -1.69232e10i q^{67} +(-5.23951e8 + 1.08797e10i) q^{68} +(1.60273e10 + 5.32268e9i) q^{69} +(-1.76992e8 + 7.35466e9i) q^{70} -1.32561e10 q^{71} +(1.07451e10 - 1.24139e10i) q^{72} -3.00051e10 q^{73} +(-5.23131e8 + 2.17380e10i) q^{74} +(-1.26222e10 - 4.19184e9i) q^{75} +(-1.49077e9 + 3.09555e10i) q^{76} -2.80292e10i q^{77} +(-3.90038e9 + 1.08635e10i) q^{78} +3.23010e9i q^{79} +(-1.67292e9 + 1.73287e10i) q^{80} +(8.92037e9 + 3.00865e10i) q^{81} +(-8.24646e9 - 1.98454e8i) q^{82} -3.04488e9 q^{83} +(1.21691e10 - 3.14904e10i) q^{84} +2.20755e10 q^{85} +(-5.10099e10 - 1.22757e9i) q^{86} +(-2.45382e8 + 7.38880e8i) q^{87} +(4.78359e9 - 6.61561e10i) q^{88} -3.87715e10i q^{89} +(-2.61777e10 - 2.05416e10i) q^{90} +2.37340e10i q^{91} +(8.20804e10 + 3.95287e9i) q^{92} +(-3.20540e10 + 9.65190e10i) q^{93} +(5.23397e8 - 2.17490e10i) q^{94} +6.28102e10 q^{95} +(3.40965e10 - 7.22484e10i) q^{96} +3.29498e10 q^{97} +(-4.82741e8 + 2.00596e10i) q^{98} +(1.01590e11 + 7.58410e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9}+O(q^{10}) $ 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9	$ 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9} + 202000 q^{10} + 1064760 q^{12} + 1543864 q^{13} + 3482912 q^{16} + 2557392 q^{18} - 12211752 q^{21} - 5920464 q^{22} + 12133152 q^{24} - 141128700 q^{25} - 3604848 q^{28} + 73456080 q^{30} + 229769760 q^{33} + 222167104 q^{34} + 298087896 q^{36} - 44517800 q^{37} - 439643840 q^{40} + 281776944 q^{42} + 1020227520 q^{45} - 2392795680 q^{46} + 689090592 q^{48} - 1018138084 q^{49} - 3959246384 q^{52} - 4249352520 q^{54} + 1438636392 q^{57} + 9671853040 q^{58} + 5688375360 q^{60} + 6873199864 q^{61} - 1452752512 q^{64} - 10961242896 q^{66} - 13308470976 q^{69} + 35188514400 q^{70} + 30438127680 q^{72} - 12426469112 q^{73} - 60088673808 q^{76} - 81037845456 q^{78} - 42462874764 q^{81} + 88180337440 q^{82} + 125502443664 q^{84} + 17135502080 q^{85} - 166086469440 q^{88} - 257976145200 q^{90} + 114387515256 q^{93} + 391966360512 q^{94} + 446868262272 q^{96} + 75764383528 q^{97}+O(q^{100}) $ 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9 + 202000 * q^10 + 1064760 * q^12 + 1543864 * q^13 + 3482912 * q^16 + 2557392 * q^18 - 12211752 * q^21 - 5920464 * q^22 + 12133152 * q^24 - 141128700 * q^25 - 3604848 * q^28 + 73456080 * q^30 + 229769760 * q^33 + 222167104 * q^34 + 298087896 * q^36 - 44517800 * q^37 - 439643840 * q^40 + 281776944 * q^42 + 1020227520 * q^45 - 2392795680 * q^46 + 689090592 * q^48 - 1018138084 * q^49 - 3959246384 * q^52 - 4249352520 * q^54 + 1438636392 * q^57 + 9671853040 * q^58 + 5688375360 * q^60 + 6873199864 * q^61 - 1452752512 * q^64 - 10961242896 * q^66 - 13308470976 * q^69 + 35188514400 * q^70 + 30438127680 * q^72 - 12426469112 * q^73 - 60088673808 * q^76 - 81037845456 * q^78 - 42462874764 * q^81 + 88180337440 * q^82 + 125502443664 * q^84 + 17135502080 * q^85 - 166086469440 * q^88 - 257976145200 * q^90 + 114387515256 * q^93 + 391966360512 * q^94 + 446868262272 * q^96 + 75764383528 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.08876	+	45.2417i	−0.0240583	+	0.999711i
$2$	−1.08876	+	45.2417i	−0.0240583	+	0.999711i
$3$	−399.437	−	132.653i	−0.949034	−	0.315175i
$3$	−399.437	−	132.653i	−0.949034	−	0.315175i
$4$	−2045.63	−	98.5144i	−0.998842	−	0.0481027i
$5$			4150.68i			0.593997i	0.954878	+	0.296999i	$0.0959857\pi$
$5$			4150.68i			0.593997i	−0.954878	+	0.296999i	$0.904014\pi$
$6$	6436.35	−	17926.8i	0.337915	−	0.941176i
$7$		−	39165.5i		−	0.880775i	−0.897808	−	0.440387i	$-0.854841\pi$
$7$		−	39165.5i		−	0.880775i	0.897808	−	0.440387i	$-0.145159\pi$
$8$	6684.15	−	92440.6i	0.0721193	−	0.997396i
$9$	141953.	+	105973.i	0.801330	+	0.598223i
$10$	−187784.	−	4519.08i	−0.593825	−	0.0142906i
$11$	715661.			1.33982			0.669912	−	0.742441i	$-0.266332\pi$
$11$	715661.			1.33982			0.669912	+	0.742441i	$0.266332\pi$
$12$	804032.	+	310710.i	0.932774	+	0.360461i
$13$	−605992.			−0.452667			−0.226333	−	0.974050i	$-0.572674\pi$
$13$	−605992.			−0.452667			−0.226333	+	0.974050i	$0.572674\pi$
$14$	1.77192e6	+	42641.7i	0.880520	+	0.0211900i
$15$	550602.	−	1.65794e6i	0.187213	−	0.563723i
$16$	4.17489e6	+	403048.i	0.995372	+	0.0960941i
$17$		−	5.31852e6i		−	0.908493i	−0.890876	−	0.454247i	$-0.849908\pi$
$17$		−	5.31852e6i		−	0.908493i	0.890876	−	0.454247i	$-0.150092\pi$
$18$	−4.94897e6	+	6.30683e6i	−0.617328	+	0.786706i
$19$		−	1.51325e7i		−	1.40206i	−0.713133	−	0.701028i	$-0.752725\pi$
$19$		−	1.51325e7i		−	1.40206i	0.713133	−	0.701028i	$-0.247275\pi$
$20$	408902.	−	8.49076e6i	0.0285729	−	0.593310i
$21$	−5.19544e6	+	1.56442e7i	−0.277598	+	0.835885i
$22$	−779180.	+	3.23777e7i	−0.0322339	+	1.33944i
$23$	−4.01248e7			−1.29990			−0.649949	−	0.759978i	$-0.725210\pi$
$23$	−4.01248e7			−1.29990			−0.649949	+	0.759978i	$0.725210\pi$
$24$	−1.49324e7	+	3.60375e7i	−0.382797	+	0.923832i
$25$	3.16000e7			0.647167
$26$	659777.	−	2.74161e7i	0.0108904	−	0.452535i
$27$	−4.26437e7	−	6.11603e7i	−0.571945	−	0.820292i
$28$	−3.85837e6	+	8.01182e7i	−0.0423677	+	0.879755i
$29$		−	1.84980e6i		−	0.0167470i	−0.999965	−	0.00837348i	$-0.997335\pi$
$29$		−	1.84980e6i		−	0.0167470i	0.999965	−	0.00837348i	$-0.00266539\pi$
$30$	7.44085e7	+	2.67153e7i	0.559056	+	0.200721i
$31$		−	2.41637e8i		−	1.51592i	−0.652304	−	0.757958i	$-0.726197\pi$
$31$		−	2.41637e8i		−	1.51592i	0.652304	−	0.757958i	$-0.273803\pi$
$32$	−2.27800e7	+	1.88441e8i	−0.120013	+	0.992772i
$33$	−2.85862e8	−	9.49348e7i	−1.27154	−	0.422278i
$34$	2.40619e8	+	5.79057e6i	0.908231	+	0.0218568i
$35$	1.62564e8			0.523178
$36$	−2.79944e8	−	2.30767e8i	−0.771626	−	0.636076i
$37$	4.80485e8			1.13912			0.569561	−	0.821949i	$-0.307113\pi$
$37$	4.80485e8			1.13912			0.569561	+	0.821949i	$0.307113\pi$
$38$	6.84620e8	+	1.64756e7i	1.40165	+	0.0337311i
$39$	2.42056e8	+	8.03868e7i	0.429596	+	0.142669i
$40$	3.83691e8	+	2.77438e7i	0.592451	+	0.0428387i
$41$			1.82276e8i			0.245707i	0.992425	+	0.122853i	$0.0392045\pi$
$41$			1.82276e8i			0.245707i	−0.992425	+	0.122853i	$0.960795\pi$
$42$	−7.02113e8	−	2.52083e8i	−0.828964	−	0.297627i
$43$			1.12750e9i			1.16960i	0.811176	+	0.584802i	$0.198828\pi$
$43$			1.12750e9i			1.16960i	−0.811176	+	0.584802i	$0.801172\pi$
$44$	−1.46398e9	−	7.05029e7i	−1.33827	−	0.0644492i
$45$	−4.39862e8	+	5.89203e8i	−0.355343	+	0.475988i
$46$	4.36861e7	−	1.81531e9i	0.0312734	−	1.29952i
$47$	−4.80730e8			−0.305747			−0.152874	−	0.988246i	$-0.548853\pi$
$47$	−4.80730e8			−0.305747			−0.152874	+	0.988246i	$0.548853\pi$
$48$	−1.61414e9	−	7.14806e8i	−0.914355	−	0.404913i
$49$	4.43388e8			0.224236
$50$	−3.44046e7	+	1.42964e9i	−0.0155698	+	0.646980i
$51$	−7.05519e8	+	2.12442e9i	−0.286334	+	0.862191i
$52$	1.23963e9	+	5.96989e7i	0.452143	+	0.0217745i
$53$		−	4.89614e9i		−	1.60819i	−0.594503	−	0.804093i	$-0.702651\pi$
$53$		−	4.89614e9i		−	1.60819i	0.594503	−	0.804093i	$-0.297349\pi$
$54$	2.81342e9	−	1.86269e9i	0.833815	−	0.552044i
$55$			2.97048e9i			0.795851i
$56$	−3.62048e9	−	2.61788e8i	−0.878481	−	0.0635208i
$57$	−2.00737e9	+	6.04448e9i	−0.441893	+	1.33060i
$58$	8.36882e7	+	2.01398e6i	0.0167421	+	0.000402904i
$59$	3.77738e9			0.687867			0.343934	−	0.938994i	$-0.388241\pi$
$59$	3.77738e9			0.687867			0.343934	+	0.938994i	$0.388241\pi$
$60$	−1.28966e9	+	3.33728e9i	−0.214113	+	0.554065i
$61$	1.72291e9			0.261186			0.130593	−	0.991436i	$-0.458312\pi$
$61$	1.72291e9			0.261186			0.130593	+	0.991436i	$0.458312\pi$
$62$	1.09321e10	+	2.63084e8i	1.51548	+	0.0364704i
$63$	4.15050e9	−	5.55967e9i	0.526899	−	0.705791i
$64$	−8.50058e9	−	1.23577e9i	−0.989598	−	0.143863i
$65$		−	2.51528e9i		−	0.268883i
$66$	4.60625e9	−	1.28295e10i	0.452747	−	1.26101i
$67$		−	1.69232e10i		−	1.53134i	−0.643233	−	0.765671i	$-0.722407\pi$
$67$		−	1.69232e10i		−	1.53134i	0.643233	−	0.765671i	$-0.277593\pi$
$68$	−5.23951e8	+	1.08797e10i	−0.0437010	+	0.907442i
$69$	1.60273e10	+	5.32268e9i	1.23365	+	0.409695i
$70$	−1.76992e8	+	7.35466e9i	−0.0125868	+	0.523026i
$71$	−1.32561e10			−0.871957			−0.435978	−	0.899957i	$-0.643598\pi$
$71$	−1.32561e10			−0.871957			−0.435978	+	0.899957i	$0.643598\pi$
$72$	1.07451e10	−	1.24139e10i	0.654456	−	0.756100i
$73$	−3.00051e10			−1.69402			−0.847011	−	0.531576i	$-0.821600\pi$
$73$	−3.00051e10			−1.69402			−0.847011	+	0.531576i	$0.821600\pi$
$74$	−5.23131e8	+	2.17380e10i	−0.0274054	+	1.13879i
$75$	−1.26222e10	−	4.19184e9i	−0.614183	−	0.203971i
$76$	−1.49077e9	+	3.09555e10i	−0.0674428	+	1.40043i
$77$		−	2.80292e10i		−	1.18008i
$78$	−3.90038e9	+	1.08635e10i	−0.152963	+	0.426039i
$79$			3.23010e9i			0.118105i	0.998255	+	0.0590524i	$0.0188079\pi$
$79$			3.23010e9i			0.118105i	−0.998255	+	0.0590524i	$0.981192\pi$
$80$	−1.67292e9	+	1.73287e10i	−0.0570796	+	0.591248i
$81$	8.92037e9	+	3.00865e10i	0.284260	+	0.958747i
$82$	−8.24646e9	−	1.98454e8i	−0.245636	−	0.00591130i
$83$	−3.04488e9			−0.0848477			−0.0424238	−	0.999100i	$-0.513508\pi$
$83$	−3.04488e9			−0.0848477			−0.0424238	+	0.999100i	$0.513508\pi$
$84$	1.21691e10	−	3.14904e10i	0.317485	−	0.821564i
$85$	2.20755e10			0.539643
$86$	−5.10099e10	−	1.22757e9i	−1.16927	−	0.0281387i
$87$	−2.45382e8	+	7.38880e8i	−0.00527822	+	0.0158934i
$88$	4.78359e9	−	6.61561e10i	0.0966271	−	1.33633i
$89$		−	3.87715e10i		−	0.735983i	−0.929829	−	0.367991i	$-0.880046\pi$
$89$		−	3.87715e10i		−	0.735983i	0.929829	−	0.367991i	$-0.119954\pi$
$90$	−2.61777e10	−	2.05416e10i	−0.467301	−	0.366691i
$91$			2.37340e10i			0.398697i
$92$	8.20804e10	+	3.95287e9i	1.29839	+	0.0625287i
$93$	−3.20540e10	+	9.65190e10i	−0.477778	+	1.43865i
$94$	5.23397e8	−	2.17490e10i	0.00735577	−	0.305659i
$95$	6.28102e10			0.832818
$96$	3.40965e10	−	7.22484e10i	0.426793	−	0.904349i
$97$	3.29498e10			0.389591			0.194795	−	0.980844i	$-0.437596\pi$
$97$	3.29498e10			0.389591			0.194795	+	0.980844i	$0.437596\pi$
$98$	−4.82741e8	+	2.00596e10i	−0.00539474	+	0.224171i
$99$	1.01590e11	+	7.58410e10i	1.07364	+	0.801512i
$100$	−6.46418e10	−	3.11305e9i	−0.646418	−	0.0311305i
$101$		−	1.33079e11i		−	1.25992i	−0.776628	−	0.629959i	$-0.783072\pi$
$101$		−	1.33079e11i		−	1.25992i	0.776628	−	0.629959i	$-0.216928\pi$
$102$	−9.53441e10	−	3.42319e10i	−0.855053	−	0.306994i
$103$			1.22881e11i			1.04443i	0.852814	+	0.522215i	$0.174894\pi$
$103$			1.22881e11i			1.04443i	−0.852814	+	0.522215i	$0.825106\pi$
$104$	−4.05054e9	+	5.60182e10i	−0.0326460	+	0.451488i
$105$	−6.49340e10	−	2.15646e10i	−0.496513	−	0.164892i
$106$	2.21510e11	+	5.33070e9i	1.60772	+	0.0386903i
$107$	−2.53485e10			−0.174719			−0.0873597	−	0.996177i	$-0.527843\pi$
$107$	−2.53485e10			−0.174719			−0.0873597	+	0.996177i	$0.527843\pi$
$108$	8.12080e10	+	1.29312e11i	0.531824	+	0.846855i
$109$	3.69555e10			0.230056			0.115028	−	0.993362i	$-0.463304\pi$
$109$	3.69555e10			0.230056			0.115028	+	0.993362i	$0.463304\pi$
$110$	−1.34390e11	−	3.23413e9i	−0.795621	−	0.0191469i
$111$	−1.91924e11	−	6.37379e10i	−1.08106	−	0.359022i
$112$	1.57856e10	−	1.63512e11i	0.0846373	−	0.876699i
$113$			1.78738e11i			0.912610i	0.889823	+	0.456305i	$0.150827\pi$
$113$			1.78738e11i			0.912610i	−0.889823	+	0.456305i	$0.849173\pi$
$114$	−2.71277e11	−	9.73981e10i	−1.31958	−	0.473777i
$115$		−	1.66545e11i		−	0.772136i
$116$	−1.82232e8	+	3.78401e9i	−0.000805575	+	0.0167276i
$117$	−8.60225e10	−	6.42190e10i	−0.362735	−	0.270795i
$118$	−4.11264e9	+	1.70895e11i	−0.0165489	+	0.687668i
$119$	−2.08303e11			−0.800178
$120$	−1.49580e11	−	6.19798e10i	−0.548754	−	0.227381i
$121$	2.26859e11			0.795126
$122$	−1.87583e9	+	7.79476e10i	−0.00628369	+	0.261110i
$123$	2.41795e10	−	7.28077e10i	0.0774405	−	0.233184i
$124$	−2.38048e10	+	4.94301e11i	−0.0729197	+	1.51416i
$125$			3.33831e11i			0.978413i
$126$	2.47010e11	+	1.93829e11i	0.692911	+	0.543727i
$127$		−	3.47864e11i		−	0.934305i	−0.884177	−	0.467153i	$-0.845280\pi$
$127$		−	3.47864e11i		−	0.934305i	0.884177	−	0.467153i	$-0.154720\pi$
$128$	6.51636e10	−	3.83235e11i	0.167629	−	0.985850i
$129$	1.49566e11	−	4.50364e11i	0.368629	−	1.10999i
$130$	1.13796e11	+	2.73853e9i	0.268805	+	0.00646887i
$131$	3.41263e11			0.772853			0.386426	−	0.922320i	$-0.373709\pi$
$131$	3.41263e11			0.772853			0.386426	+	0.922320i	$0.373709\pi$
$132$	5.75414e11	+	2.22363e11i	1.24975	+	0.482954i
$133$	−5.92672e11			−1.23490
$134$	7.65637e11	+	1.84253e10i	1.53090	+	0.0368415i
$135$	2.53857e11	−	1.77000e11i	0.487251	−	0.339734i
$136$	−4.91647e11	−	3.55498e10i	−0.906128	−	0.0655199i
$137$		−	2.07058e11i		−	0.366546i	−0.983062	−	0.183273i	$-0.941331\pi$
$137$		−	2.07058e11i		−	0.366546i	0.983062	−	0.183273i	$-0.0586692\pi$
$138$	−2.58257e11	+	7.19309e11i	−0.439256	+	1.22343i
$139$		−	8.74875e10i		−	0.143009i	−0.997440	−	0.0715047i	$-0.977220\pi$
$139$		−	8.74875e10i		−	0.143009i	0.997440	−	0.0715047i	$-0.0227801\pi$
$140$	−3.32545e11	−	1.60149e10i	−0.522572	−	0.0251663i
$141$	1.92021e11	+	6.37704e10i	0.290165	+	0.0963638i
$142$	1.44327e10	−	5.99729e11i	0.0209778	−	0.871705i
$143$	−4.33685e11			−0.606493
$144$	5.49927e11	+	4.99641e11i	0.740136	+	0.672457i
$145$	7.67794e9			0.00994765
$146$	3.26682e10	−	1.35748e12i	0.0407553	−	1.69353i
$147$	−1.77106e11	−	5.88168e10i	−0.212807	−	0.0706735i
$148$	−9.82894e11	−	4.73347e10i	−1.13780	−	0.0547949i
$149$			8.29939e11i			0.925810i	0.886408	+	0.462905i	$0.153193\pi$
$149$			8.29939e11i			0.925810i	−0.886408	+	0.462905i	$0.846807\pi$
$150$	2.03389e11	−	5.66486e11i	0.218688	−	0.609099i
$151$			1.14841e12i			1.19049i	0.803545	+	0.595244i	$0.202945\pi$
$151$			1.14841e12i			1.19049i	−0.803545	+	0.595244i	$0.797055\pi$
$152$	−1.39886e12	−	1.01148e11i	−1.39841	−	0.101115i
$153$	5.63621e11	−	7.54981e11i	0.543481	−	0.728003i
$154$	1.26809e12	+	3.05170e10i	1.17974	+	0.0283908i
$155$	1.00296e12			0.900450
$156$	−4.87237e11	−	1.88288e11i	−0.422236	−	0.163169i
$157$	−6.21510e10			−0.0519996			−0.0259998	−	0.999662i	$-0.508277\pi$
$157$	−6.21510e10			−0.0519996			−0.0259998	+	0.999662i	$0.508277\pi$
$158$	−1.46136e11	−	3.51679e9i	−0.118071	−	0.00284140i
$159$	−6.49489e11	+	1.95570e12i	−0.506859	+	1.52622i
$160$	−7.82157e11	−	9.45526e10i	−0.589704	−	0.0712876i
$161$			1.57151e12i			1.14492i
$162$	−1.37088e12	+	3.70816e11i	−0.965309	+	0.261111i
$163$			1.15508e12i			0.786284i	0.919478	+	0.393142i	$0.128612\pi$
$163$			1.15508e12i			0.786284i	−0.919478	+	0.393142i	$0.871388\pi$
$164$	1.79568e10	−	3.72868e11i	0.0118192	−	0.245422i
$165$	3.94044e11	−	1.18652e12i	0.250832	−	0.755290i
$166$	3.31513e9	−	1.37755e11i	0.00204129	−	0.0848231i
$167$	−1.73332e12			−1.03261			−0.516307	−	0.856404i	$-0.672694\pi$
$167$	−1.73332e12			−1.03261			−0.516307	+	0.856404i	$0.672694\pi$
$168$	1.41143e12	+	5.84837e11i	0.813688	+	0.337158i
$169$	−1.42493e12			−0.795093
$170$	−2.40348e10	+	9.98734e11i	−0.0129829	+	0.539486i
$171$	1.60364e12	−	2.14811e12i	0.838742	−	1.12351i
$172$	1.11075e11	−	2.30644e12i	0.0562612	−	1.16825i
$173$		−	1.42423e12i		−	0.698756i	−0.936982	−	0.349378i	$-0.886393\pi$
$173$		−	1.42423e12i		−	0.698756i	0.936982	−	0.349378i	$-0.113607\pi$
$174$	−3.31610e10	−	1.19060e10i	−0.0157618	−	0.00565906i
$175$		−	1.23763e12i		−	0.570008i
$176$	2.98781e12	+	2.88446e11i	1.33362	+	0.128749i
$177$	−1.50883e12	−	5.01082e11i	−0.652809	−	0.216798i
$178$	1.75409e12	+	4.22127e10i	0.735770	+	0.0177065i
$179$	3.46465e12			1.40918			0.704591	−	0.709613i	$-0.251130\pi$
$179$	3.46465e12			1.40918			0.704591	+	0.709613i	$0.251130\pi$
$180$	9.57839e11	−	1.16196e12i	0.377828	−	0.458344i
$181$	3.07059e12			1.17487			0.587435	−	0.809271i	$-0.300138\pi$
$181$	3.07059e12			1.17487			0.587435	+	0.809271i	$0.300138\pi$
$182$	−1.07377e12	−	2.58405e10i	−0.398582	−	0.00959199i
$183$	−6.88196e11	−	2.28550e11i	−0.247874	−	0.0823191i
$184$	−2.68200e11	+	3.70916e12i	−0.0937478	+	1.29651i
$185$			1.99434e12i			0.676635i
$186$	−4.33179e12	−	1.55526e12i	−1.42674	−	0.512251i
$187$		−	3.80626e12i		−	1.21722i
$188$	9.83395e11	+	4.73588e10i	0.305393	+	0.0147073i
$189$	−2.39537e12	+	1.67016e12i	−0.722493	+	0.503754i
$190$	−6.83849e10	+	2.84164e12i	−0.0200362	+	0.832577i
$191$	−3.96739e12			−1.12933			−0.564666	−	0.825320i	$-0.690995\pi$
$191$	−3.96739e12			−1.12933			−0.564666	+	0.825320i	$0.690995\pi$
$192$	3.23152e12	+	1.62124e12i	0.893820	+	0.448427i
$193$	3.42054e12			0.919452			0.459726	−	0.888061i	$-0.347948\pi$
$193$	3.42054e12			0.919452			0.459726	+	0.888061i	$0.347948\pi$
$194$	−3.58743e10	+	1.49071e12i	−0.00937291	+	0.389478i
$195$	−3.33660e11	+	1.00470e12i	−0.0847450	+	0.255179i
$196$	−9.07007e11	−	4.36801e10i	−0.223976	−	0.0107864i
$197$		−	3.92037e12i		−	0.941375i	−0.882300	−	0.470687i	$-0.844006\pi$
$197$		−	3.92037e12i		−	0.941375i	0.882300	−	0.470687i	$-0.155994\pi$
$198$	−3.54178e12	+	4.51355e12i	−0.827110	+	1.05405i
$199$		−	4.18407e11i		−	0.0950402i	−0.998870	−	0.0475201i	$-0.984868\pi$
$199$		−	4.18407e11i		−	0.0950402i	0.998870	−	0.0475201i	$-0.0151318\pi$
$200$	2.11219e11	−	2.92112e12i	0.0466732	−	0.645482i
$201$	−2.24492e12	+	6.75977e12i	−0.482640	+	1.45329i
$202$	6.02073e12	+	1.44891e11i	1.25955	+	0.0303115i
$203$	−7.24485e10			−0.0147503
$204$	1.65252e12	−	4.27626e12i	0.327476	−	0.847419i
$205$	−7.56568e11			−0.145949
$206$	−5.55934e12	−	1.33787e11i	−1.04413	−	0.0251272i
$207$	−5.69584e12	−	4.25216e12i	−1.04165	−	0.777629i
$208$	−2.52995e12	−	2.44244e11i	−0.450572	−	0.0434986i
$209$		−	1.08297e13i		−	1.87851i
$210$	1.04632e12	−	2.91425e12i	0.176790	−	0.492403i
$211$			1.11017e12i			0.182742i	0.995817	+	0.0913708i	$0.0291249\pi$
$211$			1.11017e12i			0.182742i	−0.995817	+	0.0913708i	$0.970875\pi$
$212$	−4.82340e11	+	1.00157e13i	−0.0773582	+	1.60632i
$213$	5.29498e12	+	1.75847e12i	0.827517	+	0.274819i
$214$	2.75983e10	−	1.14681e12i	0.00420346	−	0.174669i
$215$	−4.67988e12			−0.694742
$216$	−5.93872e12	+	3.53320e12i	−0.859404	+	0.511296i
$217$	−9.46386e12			−1.33518
$218$	−4.02356e10	+	1.67193e12i	−0.00553477	+	0.229990i
$219$	1.19851e13	+	3.98027e12i	1.60768	+	0.533912i
$220$	2.92635e11	−	6.07650e12i	0.0382826	−	0.794930i
$221$			3.22298e12i			0.411245i
$222$	3.09257e12	−	8.61356e12i	0.384927	−	1.07211i
$223$			9.67899e12i			1.17531i	0.809111	+	0.587656i	$0.199949\pi$
$223$			9.67899e12i			1.17531i	−0.809111	+	0.587656i	$0.800051\pi$
$224$	7.38038e12	+	8.92192e11i	0.874409	+	0.105705i
$225$	4.48572e12	+	3.34875e12i	0.518595	+	0.387150i
$226$	−8.08641e12	−	1.94602e11i	−0.912346	−	0.0219559i
$227$	1.46078e13			1.60858			0.804288	−	0.594240i	$-0.202547\pi$
$227$	1.46078e13			1.60858			0.804288	+	0.594240i	$0.202547\pi$
$228$	4.70181e12	−	1.21670e13i	0.505386	−	1.30780i
$229$	1.96967e12			0.206680			0.103340	−	0.994646i	$-0.467047\pi$
$229$	1.96967e12			0.206680			0.103340	+	0.994646i	$0.467047\pi$
$230$	7.53479e12	+	1.81327e11i	0.771913	+	0.0185763i
$231$	−3.71817e12	+	1.11959e13i	−0.371932	+	1.11994i
$232$	−1.70997e11	−	1.23644e10i	−0.0167034	−	0.00120778i
$233$			3.00912e11i			0.0287066i	0.999897	+	0.0143533i	$0.00456895\pi$
$233$			3.00912e11i			0.0287066i	−0.999897	+	0.0143533i	$0.995431\pi$
$234$	2.99904e12	−	3.82189e12i	0.279444	−	0.356115i
$235$		−	1.99536e12i		−	0.181613i
$236$	−7.72712e12	−	3.72126e11i	−0.687071	−	0.0330883i
$237$	4.28484e11	−	1.29022e12i	0.0372236	−	0.112085i
$238$	2.26791e11	−	9.42398e12i	0.0192509	−	0.799946i
$239$	−1.14714e12			−0.0951538			−0.0475769	−	0.998868i	$-0.515150\pi$
$239$	−1.14714e12			−0.0951538			−0.0475769	+	0.998868i	$0.515150\pi$
$240$	2.96693e12	−	6.69979e12i	0.240517	−	0.543125i
$241$	8.43435e12			0.668279			0.334139	−	0.942524i	$-0.391554\pi$
$241$	8.43435e12			0.668279			0.334139	+	0.942524i	$0.391554\pi$
$242$	−2.46994e11	+	1.02635e13i	−0.0191294	+	0.794896i
$243$	4.27947e11	−	1.32010e13i	0.0324008	−	0.999475i
$244$	−3.52444e12	−	1.69732e11i	−0.260883	−	0.0125638i
$245$			1.84036e12i			0.133196i
$246$	3.26762e12	+	1.17319e12i	0.231254	+	0.0830282i
$247$			9.17017e12i			0.634664i
$248$	−2.23371e13	−	1.61514e12i	−1.51197	−	0.109327i
$249$	1.21624e12	+	4.03913e11i	0.0805233	+	0.0267418i
$250$	−1.51031e13	−	3.63461e11i	−0.978130	−	0.0235390i
$251$	2.10245e11			0.0133205			0.00666025	−	0.999978i	$-0.497880\pi$
$251$	2.10245e11			0.0133205			0.00666025	+	0.999978i	$0.497880\pi$
$252$	−9.03810e12	+	1.09641e13i	−0.560240	+	0.679629i
$253$	−2.87157e13			−1.74163
$254$	1.57380e13	+	3.78739e11i	0.934035	+	0.0224778i
$255$	−8.81777e12	−	2.92839e12i	−0.512139	−	0.170082i
$256$	1.72673e13	+	3.36536e12i	0.981532	+	0.191299i
$257$		−	1.33118e13i		−	0.740634i	−0.928905	−	0.370317i	$-0.879249\pi$
$257$		−	1.33118e13i		−	0.740634i	0.928905	−	0.370317i	$-0.120751\pi$
$258$	2.02124e13	+	7.25697e12i	1.10080	+	0.395227i
$259$		−	1.88184e13i		−	1.00331i
$260$	−2.47791e11	+	5.14533e12i	−0.0129340	+	0.268571i
$261$	1.96030e11	−	2.62585e11i	0.0100184	−	0.0134198i
$262$	−3.71552e11	+	1.54393e13i	−0.0185935	+	0.772629i
$263$	−3.56786e13			−1.74844			−0.874221	−	0.485528i	$-0.838627\pi$
$263$	−3.56786e13			−1.74844			−0.874221	+	0.485528i	$0.838627\pi$
$264$	−1.06866e13	+	2.57906e13i	−0.512881	+	1.23777i
$265$	2.03223e13			0.955258
$266$	6.45275e11	−	2.68135e13i	0.0297095	−	1.23454i
$267$	−5.14317e12	+	1.54868e13i	−0.231963	+	0.698473i
$268$	−1.66718e12	+	3.46187e13i	−0.0736617	+	1.52957i
$269$			1.14048e13i			0.493683i	0.969056	+	0.246842i	$0.0793928\pi$
$269$			1.14048e13i			0.493683i	−0.969056	+	0.246842i	$0.920607\pi$
$270$	7.73142e12	+	1.16776e13i	0.327913	+	0.495284i
$271$		−	1.26428e13i		−	0.525425i	−0.964874	−	0.262713i	$-0.915383\pi$
$271$		−	1.26428e13i		−	0.525425i	0.964874	−	0.262713i	$-0.0846171\pi$
$272$	2.14362e12	−	2.22043e13i	0.0873009	−	0.904289i
$273$	3.14839e12	−	9.48024e12i	0.125659	−	0.378377i
$274$	9.36765e12	+	2.25435e11i	0.366440	+	0.00881848i
$275$	2.26149e13			0.867090
$276$	−3.22616e13	−	1.24672e13i	−1.21251	−	0.468563i
$277$	1.07355e13			0.395533			0.197767	−	0.980249i	$-0.436631\pi$
$277$	1.07355e13			0.395533			0.197767	+	0.980249i	$0.436631\pi$
$278$	3.95809e12	+	9.52526e10i	0.142968	+	0.00344057i
$279$	2.56071e13	−	3.43012e13i	0.906855	−	1.21475i
$280$	1.08660e12	−	1.50275e13i	0.0377312	−	0.521815i
$281$			3.54105e13i			1.20572i	0.797845	+	0.602862i	$0.205973\pi$
$281$			3.54105e13i			1.20572i	−0.797845	+	0.602862i	$0.794027\pi$
$282$	−3.09415e12	+	8.61795e12i	−0.103317	+	0.287762i
$283$		−	2.18613e13i		−	0.715897i	−0.933741	−	0.357948i	$-0.883476\pi$
$283$		−	2.18613e13i		−	0.715897i	0.933741	−	0.357948i	$-0.116524\pi$
$284$	2.71171e13	+	1.30592e12i	0.870948	+	0.0419435i
$285$	−2.50887e13	−	8.33197e12i	−0.790372	−	0.262483i
$286$	4.72177e11	−	1.96206e13i	0.0145912	−	0.606318i
$287$	7.13892e12			0.216412
$288$	−2.32034e13	+	2.43357e13i	−0.690069	+	0.723744i
$289$	5.98523e12			0.174640
$290$	−8.35940e9	+	3.47363e11i	−0.000239324	+	0.00994477i
$291$	−1.31614e13	−	4.37090e12i	−0.369735	−	0.122789i
$292$	6.13793e13	+	2.95593e12i	1.69206	+	0.0814871i
$293$			9.02580e12i			0.244182i	0.992519	+	0.122091i	$0.0389600\pi$
$293$			9.02580e12i			0.244182i	−0.992519	+	0.122091i	$0.961040\pi$
$294$	2.85380e12	−	7.94853e12i	0.0757728	−	0.211046i
$295$			1.56787e13i			0.408591i
$296$	3.21163e12	−	4.44163e13i	0.0821527	−	1.13616i
$297$	−3.05184e13	−	4.37700e13i	−0.766305	−	1.09905i
$298$	−3.75479e13	−	9.03601e11i	−0.925542	−	0.0222734i
$299$	2.43153e13			0.588421
$300$	2.54074e13	+	9.81842e12i	0.603661	+	0.233278i
$301$	4.41590e13			1.03016
$302$	−5.19562e13	−	1.25034e12i	−1.19014	−	0.0286411i
$303$	−1.76534e13	+	5.31568e13i	−0.397094	+	1.19570i
$304$	6.09912e12	−	6.31765e13i	0.134729	−	1.39557i
$305$			7.15127e12i			0.155144i
$306$	3.35430e13	+	2.63212e13i	0.714717	+	0.560838i
$307$			7.44927e13i			1.55902i	0.626388	+	0.779511i	$0.284532\pi$
$307$			7.44927e13i			1.55902i	−0.626388	+	0.779511i	$0.715468\pi$
$308$	−2.76128e12	+	5.73374e13i	−0.0567652	+	1.17872i
$309$	1.63005e13	−	4.90832e13i	0.329178	−	0.991199i
$310$	−1.09198e12	+	4.53757e13i	−0.0216633	+	0.900189i
$311$	3.90535e12			0.0761163			0.0380582	−	0.999276i	$-0.487883\pi$
$311$	3.90535e12			0.0761163			0.0380582	+	0.999276i	$0.487883\pi$
$312$	9.04894e12	−	2.18384e13i	0.173280	−	0.418188i
$313$	−5.14001e13			−0.967096			−0.483548	−	0.875318i	$-0.660652\pi$
$313$	−5.14001e13			−0.967096			−0.483548	+	0.875318i	$0.660652\pi$
$314$	6.76672e10	−	2.81182e12i	0.00125102	−	0.0519845i
$315$	2.30764e13	+	1.72274e13i	0.419238	+	0.312977i
$316$	3.18212e11	−	6.60760e12i	0.00568116	−	0.117968i
$317$			6.93372e13i			1.21658i	0.793715	+	0.608290i	$0.208144\pi$
$317$			6.93372e13i			1.21658i	−0.793715	+	0.608290i	$0.791856\pi$
$318$	−8.77721e13	−	3.15133e13i	−1.51359	−	0.543431i
$319$		−	1.32383e12i		−	0.0224380i
$320$	5.12930e12	−	3.52832e13i	0.0854542	−	0.587818i
$321$	1.01251e13	+	3.36256e12i	0.165815	+	0.0550671i
$322$	−7.10978e13	−	1.71099e12i	−1.14459	−	0.0275448i
$323$	−8.04825e13			−1.27376
$324$	−1.52838e13	−	6.24246e13i	−0.237812	−	0.971311i
$325$	−1.91493e13			−0.292951
$326$	−5.22577e13	−	1.25760e12i	−0.786057	−	0.0189167i
$327$	−1.47614e13	−	4.90227e12i	−0.218331	−	0.0725078i
$328$	1.68497e13	+	1.21836e12i	0.245067	+	0.0177202i
$329$			1.88280e13i			0.269294i
$330$	5.32512e13	+	1.91191e13i	0.749037	+	0.268930i
$331$			3.38041e13i			0.467645i	0.972279	+	0.233822i	$0.0751234\pi$
$331$			3.38041e13i			0.467645i	−0.972279	+	0.233822i	$0.924877\pi$
$332$	6.22869e12	+	2.99964e11i	0.0847495	+	0.00408141i
$333$	6.82064e13	+	5.09186e13i	0.912812	+	0.681448i
$334$	1.88716e12	−	7.84184e13i	0.0248430	−	1.03231i
$335$	7.02430e13			0.909613
$336$	−2.79957e13	+	6.32187e13i	−0.356637	+	0.805341i
$337$	6.23777e13			0.781744			0.390872	−	0.920445i	$-0.372173\pi$
$337$	6.23777e13			0.781744			0.390872	+	0.920445i	$0.372173\pi$
$338$	1.55141e12	−	6.44665e13i	0.0191286	−	0.794863i
$339$	2.37102e13	−	7.13946e13i	0.287631	−	0.866098i
$340$	−4.51583e13	−	2.17475e12i	−0.539018	−	0.0259583i
$341$		−	1.72930e14i		−	2.03106i
$342$	9.54380e13	+	7.48902e13i	1.10301	+	0.865529i
$343$		−	9.48086e13i		−	1.07828i
$344$	1.04226e14	+	7.53636e12i	1.16656	+	0.0843510i
$345$	−2.20928e13	+	6.65244e13i	−0.243358	+	0.732783i
$346$	6.44345e13	+	1.55064e12i	0.698554	+	0.0168109i
$347$	−4.89995e13			−0.522853			−0.261427	−	0.965223i	$-0.584193\pi$
$347$	−4.89995e13			−0.522853			−0.261427	+	0.965223i	$0.584193\pi$
$348$	5.74751e11	−	1.48730e12i	0.00603662	−	0.0156211i
$349$	−1.52960e14			−1.58139			−0.790695	−	0.612210i	$-0.790281\pi$
$349$	−1.52960e14			−1.58139			−0.790695	+	0.612210i	$0.790281\pi$
$350$	5.59925e13	+	1.34748e12i	0.569843	+	0.0137135i
$351$	2.58417e13	+	3.70626e13i	0.258900	+	0.371319i
$352$	−1.63028e13	+	1.34860e14i	−0.160797	+	1.33014i
$353$			1.76488e13i			0.171378i	0.996322	+	0.0856888i	$0.0273091\pi$
$353$			1.76488e13i			0.171378i	−0.996322	+	0.0856888i	$0.972691\pi$
$354$	2.43126e13	−	6.77163e13i	0.232441	−	0.647404i
$355$		−	5.50219e13i		−	0.517940i
$356$	−3.81955e12	+	7.93121e13i	−0.0354028	+	0.735131i
$357$	8.32039e13	+	2.76320e13i	0.759396	+	0.252196i
$358$	−3.77215e12	+	1.56747e14i	−0.0339026	+	1.40878i
$359$	1.67111e14			1.47906			0.739528	−	0.673125i	$-0.235049\pi$
$359$	1.67111e14			1.47906			0.739528	+	0.673125i	$0.235049\pi$
$360$	5.15261e13	+	4.45994e13i	0.449121	+	0.388745i
$361$	−1.12502e14			−0.965763
$362$	−3.34312e12	+	1.38919e14i	−0.0282654	+	1.17453i
$363$	−9.06159e13	−	3.00936e13i	−0.754602	−	0.250604i
$364$	2.33814e12	−	4.85510e13i	0.0191784	−	0.398236i
$365$		−	1.24542e14i		−	1.00624i
$366$	1.10893e13	−	3.08863e13i	0.0882587	−	0.245822i
$367$		−	9.73718e13i		−	0.763431i	−0.924280	−	0.381716i	$-0.875333\pi$
$367$		−	9.73718e13i		−	0.763431i	0.924280	−	0.381716i	$-0.124667\pi$
$368$	−1.67517e14	−	1.61722e13i	−1.29388	−	0.124913i
$369$	−1.93163e13	+	2.58746e13i	−0.146987	+	0.196892i
$370$	−9.02274e13	−	2.17135e12i	−0.676439	−	0.0162787i
$371$	−1.91760e14			−1.41645
$372$	7.50791e13	−	1.94284e14i	0.546428	−	1.41401i
$373$	2.07348e14			1.48697			0.743484	−	0.668753i	$-0.233172\pi$
$373$	2.07348e14			1.48697			0.743484	+	0.668753i	$0.233172\pi$
$374$	1.72202e14	+	4.14408e12i	1.21687	+	0.0292843i
$375$	4.42838e13	−	1.33345e14i	0.308371	−	0.928547i
$376$	−3.21327e12	+	4.44389e13i	−0.0220503	+	0.304951i
$377$			1.12096e12i			0.00758079i
$378$	−7.29531e13	−	1.10189e14i	−0.486227	−	0.734403i
$379$			8.28818e12i			0.0544432i	0.999629	+	0.0272216i	$0.00866598\pi$
$379$			8.28818e12i			0.0544432i	−0.999629	+	0.0272216i	$0.991334\pi$
$380$	−1.28486e14	−	6.18771e12i	−0.831854	−	0.0400608i
$381$	−4.61453e13	+	1.38950e14i	−0.294469	+	0.886687i
$382$	4.31952e12	−	1.79492e14i	0.0271698	−	1.12900i
$383$	−1.15533e14			−0.716328			−0.358164	−	0.933659i	$-0.616597\pi$
$383$	−1.15533e14			−0.716328			−0.358164	+	0.933659i	$0.616597\pi$
$384$	−7.68662e13	+	1.44434e14i	−0.469801	+	0.882772i
$385$	1.16340e14			0.700966
$386$	−3.72413e12	+	1.54751e14i	−0.0221205	+	0.919186i
$387$	−1.19485e14	+	1.60052e14i	−0.699683	+	0.937239i
$388$	−6.74032e13	−	3.24603e12i	−0.389140	−	0.0187404i
$389$			1.31210e14i			0.746866i	0.927657	+	0.373433i	$0.121819\pi$
$389$			1.31210e14i			0.746866i	−0.927657	+	0.373433i	$0.878181\pi$
$390$	−4.50909e13	−	1.61892e13i	−0.253066	−	0.0908596i
$391$			2.13404e14i			1.18095i
$392$	2.96367e12	−	4.09870e13i	0.0161717	−	0.223652i
$393$	−1.36313e14	−	4.52696e13i	−0.733463	−	0.243583i
$394$	1.77364e14	+	4.26832e12i	0.941102	+	0.0226479i
$395$	−1.34071e13			−0.0701539
$396$	−2.00345e14	−	1.65151e14i	−1.03384	−	0.852230i
$397$	−1.37733e14			−0.700953			−0.350477	−	0.936571i	$-0.613980\pi$
$397$	−1.37733e14			−0.700953			−0.350477	+	0.936571i	$0.613980\pi$
$398$	1.89295e13	+	4.55543e11i	0.0950127	+	0.00228651i
$399$	2.36735e14	+	7.86199e13i	1.17196	+	0.389208i
$400$	1.31926e14	+	1.27363e13i	0.644172	+	0.0621890i
$401$		−	2.01390e14i		−	0.969939i	−0.874531	−	0.484969i	$-0.838831\pi$
$401$		−	2.01390e14i		−	0.969939i	0.874531	−	0.484969i	$-0.161169\pi$
$402$	−3.03380e14	−	1.08924e14i	−1.44126	−	0.517464i
$403$			1.46430e14i			0.686204i
$404$	−1.31102e13	+	2.72231e14i	−0.0606055	+	1.25846i
$405$	−1.24880e14	+	3.70256e13i	−0.569493	+	0.168849i
$406$	7.88787e10	−	3.27769e12i	0.000354868	−	0.0147460i
$407$	3.43864e14			1.52622
$408$	1.91666e14	+	7.94185e13i	0.839296	+	0.347769i
$409$	4.27309e14			1.84614			0.923069	−	0.384636i	$-0.125673\pi$
$409$	4.27309e14			1.84614			0.923069	+	0.384636i	$0.125673\pi$
$410$	8.23718e11	−	3.42285e13i	0.00351129	−	0.145907i
$411$	−2.74669e13	+	8.27066e13i	−0.115526	+	0.347864i
$412$	1.21055e13	−	2.51368e14i	0.0502399	−	1.04322i
$413$		−	1.47943e14i		−	0.605856i
$414$	1.98576e14	−	2.53060e14i	0.802464	−	1.02264i
$415$		−	1.26383e13i		−	0.0503993i
$416$	1.38045e13	−	1.14193e14i	0.0543260	−	0.449395i
$417$	−1.16055e13	+	3.49458e13i	−0.0450729	+	0.135721i
$418$	4.89956e14	+	1.17909e13i	1.87796	+	0.0451938i
$419$	1.04709e14			0.396102			0.198051	−	0.980192i	$-0.436539\pi$
$419$	1.04709e14			0.396102			0.198051	+	0.980192i	$0.436539\pi$
$420$	1.30706e14	+	5.05101e13i	0.488007	+	0.188585i
$421$	−3.55392e14			−1.30965			−0.654826	−	0.755780i	$-0.727258\pi$
$421$	−3.55392e14			−1.30965			−0.654826	+	0.755780i	$0.727258\pi$
$422$	−5.02262e13	−	1.20871e12i	−0.182689	−	0.00439646i
$423$	−6.82411e13	−	5.09445e13i	−0.245005	−	0.182905i
$424$	−4.52602e14	−	3.27265e13i	−1.60400	−	0.115981i
$425$		−	1.68065e14i		−	0.587947i
$426$	−8.53210e13	+	2.37640e14i	−0.294648	+	0.820665i
$427$		−	6.74789e13i		−	0.230046i
$428$	5.18536e13	+	2.49719e12i	0.174517	+	0.00840448i
$429$	1.73230e14	+	5.75297e13i	0.575582	+	0.191151i
$430$	5.09525e12	−	2.11726e14i	0.0167143	−	0.694541i
$431$	−1.42826e13			−0.0462576			−0.0231288	−	0.999732i	$-0.507363\pi$
$431$	−1.42826e13			−0.0462576			−0.0231288	+	0.999732i	$0.507363\pi$
$432$	−1.53382e14	−	2.72525e14i	−0.490473	−	0.871457i
$433$	−9.80964e13			−0.309720			−0.154860	−	0.987936i	$-0.549493\pi$
$433$	−9.80964e13			−0.309720			−0.154860	+	0.987936i	$0.549493\pi$
$434$	1.03038e13	−	4.28161e14i	0.0321222	−	1.33479i
$435$	−3.06685e12	−	1.01850e12i	−0.00944066	−	0.00313525i
$436$	−7.55973e13	−	3.64065e12i	−0.229790	−	0.0110663i
$437$			6.07188e14i			1.82253i
$438$	−1.93123e14	+	5.37895e14i	−0.572436	+	1.59437i
$439$		−	7.16595e13i		−	0.209758i	−0.994485	−	0.104879i	$-0.966554\pi$
$439$		−	7.16595e13i		−	0.209758i	0.994485	−	0.104879i	$-0.0334455\pi$
$440$	2.74593e14	+	1.98551e13i	0.793779	+	0.0573962i
$441$	6.29403e13	+	4.69873e13i	0.179687	+	0.134143i
$442$	−1.45813e14	−	3.50904e12i	−0.411126	−	0.00989386i
$443$	−3.04787e14			−0.848743			−0.424372	−	0.905488i	$-0.639505\pi$
$443$	−3.04787e14			−0.848743			−0.424372	+	0.905488i	$0.639505\pi$
$444$	3.86325e14	+	1.49291e14i	1.06254	+	0.410609i
$445$	1.60928e14			0.437172
$446$	−4.37894e14	−	1.05381e13i	−1.17497	−	0.0282761i
$447$	1.10094e14	−	3.31508e14i	0.291792	−	0.878624i
$448$	−4.83997e13	+	3.32930e14i	−0.126711	+	0.871613i
$449$		−	4.09389e13i		−	0.105872i	−0.998598	−	0.0529360i	$-0.983142\pi$
$449$		−	4.09389e13i		−	0.105872i	0.998598	−	0.0529360i	$-0.0168579\pi$
$450$	−1.56387e14	+	1.99296e14i	−0.399514	+	0.509130i
$451$			1.30448e14i			0.329204i
$452$	1.76083e13	−	3.65631e14i	0.0438990	−	0.911553i
$453$	1.52341e14	−	4.58719e14i	0.375211	−	1.12981i
$454$	−1.59043e13	+	6.60881e14i	−0.0386997	+	1.60811i
$455$	−9.85123e13			−0.236825
$456$	5.45337e14	+	2.25965e14i	1.29527	+	0.536704i
$457$	2.14695e14			0.503828			0.251914	−	0.967750i	$-0.418940\pi$
$457$	2.14695e14			0.503828			0.251914	+	0.967750i	$0.418940\pi$
$458$	−2.14449e12	+	8.91115e13i	−0.00497238	+	0.206621i
$459$	−3.25282e14	+	2.26801e14i	−0.745230	+	0.519608i
$460$	−1.64071e13	+	3.40690e14i	−0.0371419	+	0.771242i
$461$		−	6.63309e13i		−	0.148375i	−0.997244	−	0.0741875i	$-0.976364\pi$
$461$		−	6.63309e13i		−	0.148375i	0.997244	−	0.0741875i	$-0.0236363\pi$
$462$	−5.02475e14	−	1.80406e14i	−1.11067	−	0.398768i
$463$		−	5.59646e14i		−	1.22241i	−0.791471	−	0.611206i	$-0.790684\pi$
$463$		−	5.59646e14i		−	1.22241i	0.791471	−	0.611206i	$-0.209316\pi$
$464$	7.45559e11	−	7.72272e12i	0.00160928	−	0.0166695i
$465$	−4.00620e14	−	1.33046e14i	−0.854557	−	0.283799i
$466$	−1.36138e13	−	3.27620e11i	−0.0286983	−	0.000690633i
$467$	−5.02983e14			−1.04788			−0.523939	−	0.851756i	$-0.675538\pi$
$467$	−5.02983e14			−1.04788			−0.523939	+	0.851756i	$0.675538\pi$
$468$	1.69644e14	+	1.39843e14i	0.349289	+	0.287930i
$469$	−6.62808e14			−1.34877
$470$	9.02734e13	+	2.17246e12i	0.181561	+	0.00436931i
$471$	2.48254e13	+	8.24453e12i	0.0493493	+	0.0163889i
$472$	2.52486e13	−	3.49183e14i	0.0496085	−	0.686076i
$473$			8.06905e14i			1.56706i
$474$	5.79055e13	+	2.07901e13i	0.111157	+	0.0399094i
$475$		−	4.78186e14i		−	0.907365i
$476$	4.26110e14	+	2.05208e13i	0.799252	+	0.0384908i
$477$	5.18860e14	−	6.95023e14i	0.962053	−	1.28869i
$478$	1.24895e12	−	5.18984e13i	0.00228924	−	0.0951263i
$479$	1.01548e14			0.184004			0.0920018	−	0.995759i	$-0.470673\pi$
$479$	1.01548e14			0.184004			0.0920018	+	0.995759i	$0.470673\pi$
$480$	2.99880e14	+	1.41524e14i	0.537181	+	0.253514i
$481$	−2.91170e14			−0.515642
$482$	−9.18294e12	+	3.81584e14i	−0.0160777	+	0.668085i
$483$	2.08466e14	−	6.27719e14i	0.360849	−	1.08657i
$484$	−4.64069e14	−	2.23489e13i	−0.794206	−	0.0382477i
$485$			1.36764e14i			0.231416i
$486$	5.96770e14	+	3.37337e13i	0.998406	+	0.0564371i
$487$			3.32633e14i			0.550246i	0.961409	+	0.275123i	$0.0887185\pi$
$487$			3.32633e14i			0.550246i	−0.961409	+	0.275123i	$0.911281\pi$
$488$	1.15162e13	−	1.59267e14i	0.0188365	−	0.260506i
$489$	1.53225e14	−	4.61381e14i	0.247817	−	0.746210i
$490$	−8.32612e13	−	2.00370e12i	−0.133157	−	0.00320446i
$491$	1.14114e15			1.80464			0.902322	−	0.431062i	$-0.141861\pi$
$491$	1.14114e15			1.80464			0.902322	+	0.431062i	$0.141861\pi$
$492$	−5.66348e13	+	1.46555e14i	−0.0885677	+	0.229189i
$493$	−9.83821e12			−0.0152145
$494$	−4.14874e14	−	9.98407e12i	−0.634480	−	0.0152690i
$495$	−3.14792e14	+	4.21669e14i	−0.476096	+	0.637740i
$496$	9.73915e13	−	1.00881e15i	0.145671	−	1.50890i
$497$			5.19182e14i			0.767998i
$498$	−1.95979e13	+	5.45849e13i	−0.0286713	+	0.0798566i
$499$			4.71083e14i			0.681623i	0.940132	+	0.340811i	$0.110702\pi$
$499$			4.71083e14i			0.681623i	−0.940132	+	0.340811i	$0.889298\pi$
$500$	3.28872e13	−	6.82895e14i	0.0470643	−	0.977280i
$501$	6.92352e14	+	2.29930e14i	0.979985	+	0.325454i
$502$	−2.28906e11	+	9.51185e12i	−0.000320469	+	0.0133166i
$503$	4.42390e14			0.612606			0.306303	−	0.951934i	$-0.400908\pi$
$503$	4.42390e14			0.612606			0.306303	+	0.951934i	$0.400908\pi$
$504$	−4.86197e14	−	4.20836e14i	−0.665954	−	0.576428i
$505$	5.52369e14			0.748388
$506$	3.12644e13	−	1.29915e15i	0.0419008	−	1.74113i
$507$	5.69172e14	+	1.89022e14i	0.754570	+	0.250593i
$508$	−3.42696e13	+	7.11600e14i	−0.0449426	+	0.933224i
$509$		−	1.97515e13i		−	0.0256243i	−0.999918	−	0.0128122i	$-0.995922\pi$
$509$		−	1.97515e13i		−	0.0256243i	0.999918	−	0.0128122i	$-0.00407835\pi$
$510$	1.42086e14	−	3.95743e14i	0.182354	−	0.507899i
$511$			1.17516e15i			1.49205i
$512$	−1.71055e14	+	7.77538e14i	−0.214857	+	0.976645i
$513$	−9.25507e14	+	6.45305e14i	−1.15010	+	0.801899i
$514$	6.02248e14	+	1.44933e13i	0.740420	+	0.0178184i
$515$	−5.10039e14			−0.620388
$516$	−3.50324e14	+	9.06544e14i	−0.421596	+	1.09098i
$517$	−3.44039e14			−0.409647
$518$	8.51379e14	+	2.04887e13i	1.00302	+	0.0241380i
$519$	−1.88928e14	+	5.68890e14i	−0.220230	+	0.663143i
$520$	−2.32514e14	−	1.68125e13i	−0.268183	−	0.0193916i
$521$		−	1.34420e15i		−	1.53411i	−0.641583	−	0.767054i	$-0.721722\pi$
$521$		−	1.34420e15i		−	1.53411i	0.641583	−	0.767054i	$-0.278278\pi$
$522$	1.16664e13	+	9.15461e12i	0.0131749	+	0.0103384i
$523$		−	4.37710e14i		−	0.489133i	−0.969633	−	0.244566i	$-0.921354\pi$
$523$		−	4.37710e14i		−	0.489133i	0.969633	−	0.244566i	$-0.0786456\pi$
$524$	−6.98097e14	−	3.36193e13i	−0.771958	−	0.0371763i
$525$	−1.64176e14	+	4.94355e14i	−0.179652	+	0.540957i
$526$	3.88453e13	−	1.61416e15i	0.0420646	−	1.74794i
$527$	−1.28515e15			−1.37720
$528$	−1.15518e15	−	5.11558e14i	−1.22507	−	0.542511i
$529$	6.57188e14			0.689737
$530$	−2.21260e13	+	9.19417e14i	−0.0229819	+	0.954982i
$531$	5.36211e14	+	4.00301e14i	0.551209	+	0.411498i
$532$	1.21239e15	+	5.83867e13i	1.23347	+	0.0594019i
$533$		−	1.10458e14i		−	0.111223i
$534$	−6.95049e14	−	2.49547e14i	−0.692690	−	0.248700i
$535$		−	1.05213e14i		−	0.103783i
$536$	−1.56439e15	−	1.13118e14i	−1.52735	−	0.110439i
$537$	−1.38391e15	−	4.59597e14i	−1.33736	−	0.444139i
$538$	−5.15971e14	−	1.24170e13i	−0.493540	−	0.0118772i
$539$	3.17315e14			0.300437
$540$	−5.36734e14	+	3.37069e14i	−0.503029	+	0.315902i
$541$	9.84565e14			0.913397			0.456698	−	0.889622i	$-0.349032\pi$
$541$	9.84565e14			0.913397			0.456698	+	0.889622i	$0.349032\pi$
$542$	5.71981e14	+	1.37649e13i	0.525273	+	0.0126409i
$543$	−1.22651e15	−	4.07324e14i	−1.11499	−	0.370289i
$544$	1.00223e15	+	1.21156e14i	0.901927	+	0.109031i
$545$			1.53391e14i			0.136653i
$546$	4.25475e14	+	1.52760e14i	0.375244	+	0.134726i
$547$			3.02327e14i			0.263965i	0.991252	+	0.131983i	$0.0421343\pi$
$547$			3.02327e14i			0.263965i	−0.991252	+	0.131983i	$0.957866\pi$
$548$	−2.03982e13	+	4.23563e14i	−0.0176319	+	0.366122i
$549$	2.44573e14	+	1.82583e14i	0.209296	+	0.156247i
$550$	−2.46221e13	+	1.02314e15i	−0.0208607	+	0.866839i
$551$	−2.79921e13			−0.0234802
$552$	5.99161e14	−	1.44600e15i	0.497598	−	1.20089i
$553$	1.26509e14			0.104024
$554$	−1.16883e13	+	4.85692e14i	−0.00951587	+	0.395419i
$555$	2.64556e14	−	7.96614e14i	0.213258	−	0.642150i
$556$	−8.61878e12	+	1.78967e14i	−0.00687915	+	0.142844i
$557$		−	1.52188e15i		−	1.20275i	−0.798966	−	0.601376i	$-0.794619\pi$
$557$		−	1.52188e15i		−	1.20275i	0.798966	−	0.601376i	$-0.205381\pi$
$558$	1.52397e15	+	1.19586e15i	1.19258	+	0.935817i
$559$		−	6.83254e14i		−	0.529441i
$560$	6.78686e14	+	6.55209e13i	0.520757	+	0.0502743i
$561$	−5.04913e14	+	1.52036e15i	−0.383637	+	1.15518i
$562$	−1.60203e15	−	3.85534e13i	−1.20538	−	0.0290077i
$563$	1.33301e15			0.993203			0.496602	−	0.867979i	$-0.334581\pi$
$563$	1.33301e15			0.993203			0.496602	+	0.867979i	$0.334581\pi$
$564$	−3.86522e14	−	1.49367e14i	−0.285193	−	0.110210i
$565$	−7.41884e14			−0.542088
$566$	9.89043e14	+	2.38016e13i	0.715690	+	0.0172233i
$567$	1.17835e15	−	3.49371e14i	0.844440	−	0.250369i
$568$	−8.86058e13	+	1.22540e15i	−0.0628849	+	0.869686i
$569$			1.19810e15i			0.842123i	0.907032	+	0.421061i	$0.138342\pi$
$569$			1.19810e15i			0.842123i	−0.907032	+	0.421061i	$0.861658\pi$
$570$	4.04268e14	−	1.12599e15i	0.281422	−	0.783829i
$571$		−	3.71418e13i		−	0.0256073i	−0.999918	−	0.0128037i	$-0.995924\pi$
$571$		−	3.71418e13i		−	0.0256073i	0.999918	−	0.0128037i	$-0.00407564\pi$
$572$	8.87158e14	+	4.27242e13i	0.605791	+	0.0291740i
$573$	1.58472e15	+	5.26288e14i	1.07177	+	0.355937i
$574$	−7.77254e12	+	3.22977e14i	−0.00520652	+	0.216350i
$575$	−1.26794e15			−0.841252
$576$	−1.07573e15	−	1.07626e15i	−0.706932	−	0.707281i
$577$	1.38947e15			0.904443			0.452222	−	0.891906i	$-0.350632\pi$
$577$	1.38947e15			0.904443			0.452222	+	0.891906i	$0.350632\pi$
$578$	−6.51645e12	+	2.70782e14i	−0.00420154	+	0.174589i
$579$	−1.36629e15	−	4.53745e14i	−0.872591	−	0.289788i
$580$	−1.57062e13	−	7.56387e11i	−0.00993614	−	0.000478509i
$581$			1.19254e14i			0.0747317i
$582$	2.12077e14	−	5.90685e14i	0.131649	−	0.366674i
$583$		−	3.50397e15i		−	2.15469i
$584$	−2.00558e14	+	2.77369e15i	−0.122172	+	1.68961i
$585$	2.66553e14	−	3.57052e14i	0.160852	−	0.215464i
$586$	−4.08343e14	−	9.82690e12i	−0.244112	−	0.00587462i
$587$	2.30295e15			1.36388			0.681938	−	0.731410i	$-0.261137\pi$
$587$	2.30295e15			1.36388			0.681938	+	0.731410i	$0.261137\pi$
$588$	3.56498e14	+	1.37765e14i	0.209162	+	0.0808283i
$589$	−3.65658e15			−2.12540
$590$	−7.09332e14	−	1.70703e13i	−0.408473	−	0.00983002i
$591$	−5.20050e14	+	1.56594e15i	−0.296697	+	0.893396i
$592$	2.00597e15	+	1.93658e14i	1.13385	+	0.109463i
$593$		−	3.12601e15i		−	1.75061i	−0.483569	−	0.875306i	$-0.660660\pi$
$593$		−	3.12601e15i		−	1.75061i	0.483569	−	0.875306i	$-0.339340\pi$
$594$	2.01346e15	−	1.33305e15i	1.11716	−	0.739642i
$595$		−	8.64598e14i		−	0.475304i
$596$	8.17609e13	−	1.69775e15i	0.0445340	−	0.924738i
$597$	−5.55031e13	+	1.67127e14i	−0.0299542	+	0.0901963i
$598$	−2.64734e13	+	1.10007e15i	−0.0141564	+	0.588250i
$599$	−3.23992e15			−1.71667			−0.858336	−	0.513088i	$-0.828502\pi$
$599$	−3.23992e15			−1.71667			−0.858336	+	0.513088i	$0.828502\pi$
$600$	−4.71865e14	+	1.13878e15i	−0.247734	+	0.597874i
$601$	1.76981e15			0.920695			0.460348	−	0.887739i	$-0.347725\pi$
$601$	1.76981e15			0.920695			0.460348	+	0.887739i	$0.347725\pi$
$602$	−4.80784e13	+	1.99783e15i	−0.0247839	+	1.02986i
$603$	1.79341e15	−	2.40231e15i	0.916083	−	1.22711i
$604$	1.13135e14	−	2.34923e15i	0.0572657	−	1.18911i
$605$			9.41619e14i			0.472303i
$606$	−2.38568e15	−	8.56544e14i	−1.18581	−	0.425746i
$607$			3.71788e15i			1.83129i	0.401986	+	0.915646i	$0.368320\pi$
$607$			3.71788e15i			1.83129i	−0.401986	+	0.915646i	$0.631680\pi$
$608$	2.85158e15	+	3.44718e14i	1.39192	+	0.168265i
$609$	2.89386e13	+	9.61053e12i	0.0139985	+	0.00464892i
$610$	−3.23536e14	−	7.78599e12i	−0.155099	−	0.00373250i
$611$	2.91318e14			0.138402
$612$	−1.22734e15	+	1.48889e15i	−0.577871	+	0.701017i
$613$	−2.22778e15			−1.03954			−0.519769	−	0.854307i	$-0.673982\pi$
$613$	−2.22778e15			−1.03954			−0.519769	+	0.854307i	$0.673982\pi$
$614$	−3.37018e15	−	8.11043e13i	−1.55857	−	0.0375075i
$615$	3.02201e14	+	1.00361e14i	0.138511	+	0.0459995i
$616$	−2.59104e15	−	1.87352e14i	−1.17701	−	0.0851067i
$617$		−	4.65663e14i		−	0.209654i	−0.994490	−	0.104827i	$-0.966571\pi$
$617$		−	4.65663e14i		−	0.209654i	0.994490	−	0.104827i	$-0.0334289\pi$
$618$	2.20286e15	+	7.90904e14i	0.982993	+	0.352929i
$619$			2.22056e15i			0.982118i	0.871126	+	0.491059i	$0.163390\pi$
$619$			2.22056e15i			0.982118i	−0.871126	+	0.491059i	$0.836610\pi$
$620$	−2.05168e15	−	9.88060e13i	−0.899407	−	0.0433141i
$621$	1.71107e15	+	2.45404e15i	0.743470	+	1.06630i
$622$	−4.25197e12	+	1.76685e14i	−0.00183123	+	0.0760943i
$623$	−1.51851e15			−0.648235
$624$	9.78157e14	+	4.33166e14i	0.413898	+	0.183290i
$625$	1.57339e14			0.0659926
$626$	5.59621e13	−	2.32543e15i	0.0232667	−	0.966817i
$627$	−1.43660e15	+	4.32580e15i	−0.592058	+	1.78277i
$628$	1.27138e14	+	6.12276e12i	0.0519394	+	0.00250132i
$629$		−	2.55547e15i		−	1.03488i
$630$	−8.04523e14	+	1.02526e15i	−0.322972	+	0.411587i
$631$			3.80227e15i			1.51315i	0.653909	+	0.756574i	$0.273128\pi$
$631$			3.80227e15i			1.51315i	−0.653909	+	0.756574i	$0.726872\pi$
$632$	2.98593e14	+	2.15905e13i	0.117797	+	0.00851763i
$633$	1.47268e14	−	4.43445e14i	0.0575955	−	0.173428i
$634$	−3.13694e15	−	7.54913e13i	−1.21623	−	0.0292689i
$635$	1.44387e15			0.554975
$636$	1.52128e15	−	3.93665e15i	0.579688	−	1.50007i
$637$	−2.68689e14			−0.101504
$638$	5.98924e13	+	1.44133e12i	0.0224315	+	0.000539820i
$639$	−1.88175e15	−	1.40479e15i	−0.698725	−	0.521624i
$640$	1.59069e15	+	2.70473e14i	0.585592	+	0.0995714i
$641$			4.11701e15i			1.50267i	0.659922	+	0.751334i	$0.270589\pi$
$641$			4.11701e15i			1.50267i	−0.659922	+	0.751334i	$0.729411\pi$
$642$	−1.63152e14	+	4.54417e14i	−0.0590404	+	0.164442i
$643$		−	5.21378e15i		−	1.87065i	−0.353791	−	0.935325i	$-0.615108\pi$
$643$		−	5.21378e15i		−	1.87065i	0.353791	−	0.935325i	$-0.384892\pi$
$644$	1.54816e14	−	3.21472e15i	0.0550737	−	1.14359i
$645$	1.86932e15	+	6.20802e14i	0.659333	+	0.218965i
$646$	8.76257e13	−	3.64117e15i	0.0306445	−	1.27339i
$647$	4.70489e15			1.63146			0.815730	−	0.578434i	$-0.196336\pi$
$647$	4.70489e15			1.63146			0.815730	+	0.578434i	$0.196336\pi$
$648$	2.84084e15	−	6.23501e14i	0.976751	−	0.214375i
$649$	2.70332e15			0.921620
$650$	2.08489e13	−	8.66348e14i	0.00704791	−	0.292866i
$651$	3.78022e15	+	1.25541e15i	1.26713	+	0.420815i
$652$	1.13792e14	−	2.36286e15i	0.0378224	−	0.785374i
$653$			1.14113e15i			0.376107i	0.982159	+	0.188053i	$0.0602178\pi$
$653$			1.14113e15i			0.376107i	−0.982159	+	0.188053i	$0.939782\pi$
$654$	2.37859e14	−	6.62495e14i	0.0777395	−	0.216523i
$655$			1.41647e15i			0.459072i
$656$	−7.34658e13	+	7.60981e14i	−0.0236110	+	0.244570i
$657$	−4.25932e15	−	3.17974e15i	−1.35747	−	1.01340i
$658$	−8.51813e14	−	2.04991e13i	−0.269217	−	0.00647878i
$659$	−1.18429e15			−0.371185			−0.185592	−	0.982627i	$-0.559420\pi$
$659$	−1.18429e15			−0.371185			−0.185592	+	0.982627i	$0.559420\pi$
$660$	−9.22957e14	+	2.38836e15i	−0.286873	+	0.742350i
$661$	−1.96964e15			−0.607125			−0.303562	−	0.952812i	$-0.598176\pi$
$661$	−1.96964e15			−0.607125			−0.303562	+	0.952812i	$0.598176\pi$
$662$	−1.52936e15	−	3.68044e13i	−0.467509	−	0.0112507i
$663$	4.27539e14	−	1.28738e15i	0.129614	−	0.390285i
$664$	−2.03524e13	+	2.81470e14i	−0.00611915	+	0.0846267i
$665$		−	2.45999e15i		−	0.733525i
$666$	−2.37790e15	+	3.03034e15i	−0.703212	+	0.896154i
$667$			7.42229e13i			0.0217694i
$668$	3.54573e15	+	1.70757e14i	1.03142	+	0.0496715i
$669$	1.28395e15	−	3.86615e15i	0.370428	−	1.11541i
$670$	−7.64775e13	+	3.17791e15i	−0.0218838	+	0.909350i
$671$	1.23302e15			0.349943
$672$	−2.82965e15	−	1.33541e15i	−0.796528	−	0.375909i
$673$	1.93443e15			0.540096			0.270048	−	0.962847i	$-0.412960\pi$
$673$	1.93443e15			0.540096			0.270048	+	0.962847i	$0.412960\pi$
$674$	−6.79141e13	+	2.82207e15i	−0.0188075	+	0.781518i
$675$	−1.34754e15	−	1.93266e15i	−0.370144	−	0.530866i
$676$	2.91489e15	+	1.40377e14i	0.794173	+	0.0382461i
$677$			7.06371e15i			1.90895i	0.298287	+	0.954476i	$0.403585\pi$
$677$			7.06371e15i			1.90895i	−0.298287	+	0.954476i	$0.596415\pi$
$678$	3.20420e15	+	1.15042e15i	0.858927	+	0.308385i
$679$		−	1.29050e15i		−	0.343142i
$680$	1.47556e14	−	2.04067e15i	0.0389186	−	0.538237i
$681$	−5.83489e15	−	1.93777e15i	−1.52659	−	0.506982i
$682$	7.82367e15	+	1.88279e14i	2.03047	+	0.0488639i
$683$	−3.79254e15			−0.976375			−0.488188	−	0.872739i	$-0.662342\pi$
$683$	−3.79254e15			−0.976375			−0.488188	+	0.872739i	$0.662342\pi$
$684$	−3.49207e15	+	4.23625e15i	−0.891815	+	1.08186i
$685$	8.59431e14			0.217727
$686$	4.28930e15	+	1.03223e14i	1.07796	+	0.0259415i
$687$	−7.86761e14	−	2.61284e14i	−0.196147	−	0.0651404i
$688$	−4.54435e14	+	4.70718e15i	−0.112392	+	1.16419i
$689$			2.96702e15i			0.727972i
$690$	−2.98562e15	−	1.07194e15i	−0.726717	−	0.260917i
$691$			1.46454e15i			0.353649i	0.984242	+	0.176824i	$0.0565825\pi$
$691$			1.46454e15i			0.353649i	−0.984242	+	0.176824i	$0.943418\pi$
$692$	−1.40307e14	+	2.91344e15i	−0.0336121	+	0.697948i
$693$	2.97035e15	−	3.97884e15i	0.705952	−	0.945635i
$694$	5.33485e13	−	2.21682e15i	0.0125790	−	0.522702i
$695$	3.63133e14			0.0849472
$696$	6.66623e13	+	2.76221e13i	0.0154714	+	0.00641070i
$697$	9.69437e14			0.223223
$698$	1.66537e14	−	6.92019e15i	0.0380456	−	1.58093i
$699$	3.99169e13	−	1.20195e14i	0.00904759	−	0.0272435i
$700$	−1.21924e14	+	2.53173e15i	−0.0274190	+	0.569349i
$701$		−	4.25945e15i		−	0.950396i	−0.879879	−	0.475198i	$-0.842376\pi$
$701$		−	4.25945e15i		−	0.950396i	0.879879	−	0.475198i	$-0.157624\pi$
$702$	−1.70491e15	+	1.12877e15i	−0.377440	+	0.249892i
$703$		−	7.27093e15i		−	1.59711i
$704$	−6.08353e15	−	8.84395e14i	−1.32589	−	0.192751i
$705$	−2.64691e14	+	7.97019e14i	−0.0572398	+	0.172357i
$706$	−7.98462e14	−	1.92152e13i	−0.171328	−	0.00412306i
$707$	−5.21211e15			−1.10970
$708$	3.03713e15	+	1.17367e15i	0.641625	+	0.247949i
$709$	6.74458e14			0.141384			0.0706920	−	0.997498i	$-0.477479\pi$
$709$	6.74458e14			0.141384			0.0706920	+	0.997498i	$0.477479\pi$
$710$	2.48929e15	+	5.99054e13i	0.517790	+	0.0124608i
$711$	−3.42305e14	+	4.58524e14i	−0.0706530	+	0.0946409i
$712$	−3.58406e15	−	2.59155e14i	−0.734066	−	0.0530786i
$713$			9.69565e15i			1.97054i
$714$	−1.34071e15	+	3.73420e15i	−0.270393	+	0.753109i
$715$		−	1.80009e15i		−	0.360255i
$716$	−7.08738e15	−	3.41318e14i	−1.40755	−	0.0677856i
$717$	4.58209e14	+	1.52171e14i	0.0903042	+	0.0299901i
$718$	−1.81943e14	+	7.56038e15i	−0.0355836	+	1.47863i
$719$	−3.92005e15			−0.760822			−0.380411	−	0.924818i	$-0.624217\pi$
$719$	−3.92005e15			−0.760822			−0.380411	+	0.924818i	$0.624217\pi$
$720$	−2.07385e15	+	2.28257e15i	−0.399438	+	0.439639i
$721$	4.81269e15			0.919907
$722$	1.22487e14	−	5.08979e15i	0.0232346	−	0.965484i
$723$	−3.36899e15	−	1.11884e15i	−0.634219	−	0.210624i
$724$	−6.28129e15	−	3.02497e14i	−1.17351	−	0.0565145i
$725$		−	5.84537e13i		−	0.0108381i
$726$	1.46014e15	−	4.06685e15i	0.268685	−	0.748354i
$727$		−	3.73420e15i		−	0.681959i	−0.940071	−	0.340979i	$-0.889241\pi$
$727$		−	3.73420e15i		−	0.681959i	0.940071	−	0.340979i	$-0.110759\pi$
$728$	2.19398e15	+	1.58642e14i	0.397659	+	0.0287538i
$729$	−1.92209e15	+	5.21620e15i	−0.345758	+	0.938324i
$730$	5.63447e15	+	1.35595e14i	1.00595	+	0.0242086i
$731$	5.99662e15			1.06258
$732$	1.38528e15	+	5.35326e14i	0.243627	+	0.0941472i
$733$	−6.93709e15			−1.21089			−0.605446	−	0.795886i	$-0.707005\pi$
$733$	−6.93709e15			−1.21089			−0.605446	+	0.795886i	$0.707005\pi$
$734$	4.40527e15	+	1.06014e14i	0.763210	+	0.0183669i
$735$	2.44130e14	−	7.35109e14i	0.0419798	−	0.126407i
$736$	9.14043e14	−	7.56114e15i	0.156005	−	1.29050i
$737$		−	1.21113e16i		−	2.05173i
$738$	−1.14958e15	−	9.02076e14i	−0.193299	−	0.151682i
$739$			8.85830e15i			1.47845i	0.673459	+	0.739224i	$0.264808\pi$
$739$			8.85830e15i			1.47845i	−0.673459	+	0.739224i	$0.735192\pi$
$740$	1.96471e14	−	4.07968e15i	0.0325480	−	0.675852i
$741$	1.21645e15	−	3.66291e15i	0.200030	−	0.602318i
$742$	2.08780e14	−	8.67555e15i	0.0340774	−	1.41604i
$743$	1.14543e16			1.85580			0.927901	−	0.372827i	$-0.121611\pi$
$743$	1.14543e16			1.85580			0.927901	+	0.372827i	$0.121611\pi$
$744$	8.70802e15	+	3.60824e15i	1.40045	+	0.580288i
$745$	−3.44481e15			−0.549928
$746$	−2.25752e14	+	9.38079e15i	−0.0357740	+	1.48654i
$747$	−4.32230e14	−	3.22676e14i	−0.0679910	−	0.0507578i
$748$	−3.74971e14	+	7.78619e15i	−0.0585516	+	1.21581i
$749$			9.92786e14i			0.153888i
$750$	5.98453e15	+	2.14866e15i	0.920859	+	0.330621i
$751$			1.05302e16i			1.60849i	0.594297	+	0.804246i	$0.297430\pi$
$751$			1.05302e16i			1.60849i	−0.594297	+	0.804246i	$0.702570\pi$
$752$	−2.00700e15	−	1.93757e14i	−0.304332	−	0.0293805i
$753$	−8.39797e13	−	2.78897e13i	−0.0126416	−	0.00419828i
$754$	−5.07144e13	−	1.22046e12i	−0.00757860	−	0.000182381i
$755$	−4.76670e15			−0.707147
$756$	5.06458e15	−	3.18055e15i	0.745888	−	0.468417i
$757$	6.90026e15			1.00888			0.504438	−	0.863448i	$-0.331700\pi$
$757$	6.90026e15			1.00888			0.504438	+	0.863448i	$0.331700\pi$
$758$	−3.74972e14	−	9.02381e12i	−0.0544275	−	0.00130981i
$759$	1.14701e16	+	3.80924e15i	1.65287	+	0.548919i
$760$	4.19833e14	−	5.80621e15i	0.0600622	−	0.830649i
$761$			9.67264e14i			0.137382i	0.997638	+	0.0686909i	$0.0218822\pi$
$761$			9.67264e14i			0.137382i	−0.997638	+	0.0686909i	$0.978118\pi$
$762$	−6.23609e15	−	2.23897e15i	−0.879346	−	0.315716i
$763$		−	1.44738e15i		−	0.202628i
$764$	8.11581e15	+	3.90845e14i	1.12802	+	0.0543239i
$765$	3.13369e15	+	2.33941e15i	0.432432	+	0.322826i
$766$	1.25787e14	−	5.22690e15i	0.0172337	−	0.716120i
$767$	−2.28906e15			−0.311374
$768$	−6.45077e15	−	3.63481e15i	−0.871214	−	0.490903i
$769$	−2.91878e15			−0.391387			−0.195693	−	0.980665i	$-0.562696\pi$
$769$	−2.91878e15			−0.391387			−0.195693	+	0.980665i	$0.562696\pi$
$770$	−1.26666e14	+	5.26344e15i	−0.0168641	+	0.700763i
$771$	−1.76585e15	+	5.31722e15i	−0.233429	+	0.702887i
$772$	−6.99715e15	−	3.36972e14i	−0.918388	−	0.0442282i
$773$		−	7.62729e15i		−	0.993992i	−0.867753	−	0.496996i	$-0.834436\pi$
$773$		−	7.62729e15i		−	0.993992i	0.867753	−	0.496996i	$-0.165564\pi$
$774$	−7.11093e15	−	5.57995e15i	−0.920134	−	0.722029i
$775$		−	7.63573e15i		−	0.981051i
$776$	2.20242e14	−	3.04590e15i	0.0280970	−	0.388576i
$777$	−2.49633e15	+	7.51679e15i	−0.316218	+	0.952175i
$778$	−5.93615e15	−	1.42855e14i	−0.746650	−	0.0179684i
$779$	2.75828e15			0.344495
$780$	7.81522e14	−	2.02237e15i	0.0969217	−	0.250807i
$781$	−9.48688e15			−1.16827
$782$	−9.65479e15	−	2.32345e14i	−1.18061	−	0.0284117i
$783$	−1.13134e14	+	7.88824e13i	−0.0137374	+	0.00957834i
$784$	1.85110e15	+	1.78706e14i	0.223198	+	0.0215478i
$785$		−	2.57969e14i		−	0.0308876i
$786$	2.19649e15	−	6.11775e15i	0.261159	−	0.727391i
$787$			7.61628e15i			0.899253i	0.893217	+	0.449626i	$0.148443\pi$
$787$			7.61628e15i			0.899253i	−0.893217	+	0.449626i	$0.851557\pi$
$788$	−3.86213e14	+	8.01962e15i	−0.0452827	+	0.940285i
$789$	1.42514e16	+	4.73288e15i	1.65933	+	0.551064i
$790$	1.45971e13	−	6.06562e14i	0.00168779	−	0.0701336i
$791$	7.00036e15			0.803804
$792$	7.68983e15	−	8.88414e15i	0.876855	−	1.01304i
$793$	−1.04407e15			−0.118230
$794$	1.49957e14	−	6.23126e15i	0.0168638	−	0.700750i
$795$	−8.11749e15	−	2.69582e15i	−0.906572	−	0.301073i
$796$	−4.12191e13	+	8.55906e14i	−0.00457169	+	0.0949302i
$797$			1.30065e16i			1.43265i	0.697768	+	0.716324i	$0.254177\pi$
$797$			1.30065e16i			1.43265i	−0.697768	+	0.716324i	$0.745823\pi$
$798$	−3.81465e15	+	1.06247e16i	−0.417290	+	1.16226i
$799$			2.55677e15i			0.277769i
$800$	−7.19848e14	+	5.95472e15i	−0.0776687	+	0.642490i
$801$	4.10875e15	−	5.50374e15i	0.440282	−	0.589765i
$802$	9.11124e15	+	2.19265e14i	0.969658	+	0.0233351i
$803$	−2.14735e16			−2.26969
$804$	5.25822e15	−	1.36068e16i	0.551989	−	1.42840i
$805$	−6.52283e15			−0.680078
$806$	−6.62476e15	−	1.59427e14i	−0.686005	−	0.0165089i
$807$	1.51288e15	−	4.55548e15i	0.155596	−	0.468522i
$808$	−1.23019e16	−	8.89521e14i	−1.25664	−	0.0908644i
$809$		−	1.23491e16i		−	1.25291i	−0.779457	−	0.626455i	$-0.784505\pi$
$809$		−	1.23491e16i		−	1.25291i	0.779457	−	0.626455i	$-0.215495\pi$
$810$	−1.53914e15	−	5.69008e15i	−0.155100	−	0.573391i
$811$			1.90880e15i			0.191050i	0.995427	+	0.0955248i	$0.0304529\pi$
$811$			1.90880e15i			0.191050i	−0.995427	+	0.0955248i	$0.969547\pi$
$812$	1.48203e14	+	7.13722e12i	0.0147332	+	0.000709530i
$813$	−1.67710e15	+	5.04999e15i	−0.165601	+	0.498646i
$814$	−3.74384e14	+	1.55570e16i	−0.0367183	+	1.52578i
$815$	−4.79436e15			−0.467051
$816$	−3.80171e15	+	8.58485e15i	−0.367860	+	0.830686i
$817$	1.70618e16			1.63985
$818$	−4.65235e14	+	1.93322e16i	−0.0444150	+	1.84560i
$819$	−2.51517e15	+	3.36912e15i	−0.238510	+	0.319488i
$820$	1.54766e15	+	7.45329e13i	0.145780	+	0.00702056i
$821$		−	8.84373e15i		−	0.827462i	−0.910399	−	0.413731i	$-0.864225\pi$
$821$		−	8.84373e15i		−	0.827462i	0.910399	−	0.413731i	$-0.135775\pi$
$822$	−3.71188e15	−	1.33270e15i	−0.344984	−	0.123862i
$823$		−	9.57635e15i		−	0.884099i	−0.896991	−	0.442050i	$-0.854252\pi$
$823$		−	9.57635e15i		−	0.884099i	0.896991	−	0.442050i	$-0.145748\pi$
$824$	1.13592e16	+	8.21354e14i	1.04171	+	0.0753235i
$825$	−9.03322e15	−	2.99993e15i	−0.822897	−	0.273285i
$826$	6.69320e15	+	1.61074e14i	0.605681	+	0.0145759i
$827$	1.16797e16			1.04991			0.524953	−	0.851131i	$-0.324083\pi$
$827$	1.16797e16			1.04991			0.524953	+	0.851131i	$0.324083\pi$
$828$	1.12327e16	+	9.25946e15i	1.00304	+	0.826835i
$829$	−1.35174e16			−1.19907			−0.599533	−	0.800350i	$-0.704647\pi$
$829$	−1.35174e16			−1.19907			−0.599533	+	0.800350i	$0.704647\pi$
$830$	5.71779e14	+	1.37600e13i	0.0503847	+	0.00121252i
$831$	−4.28815e15	−	1.42410e15i	−0.375374	−	0.124662i
$832$	5.15128e15	+	7.48869e14i	0.447958	+	0.0651220i
$833$		−	2.35817e15i		−	0.203717i
$834$	−1.56837e15	−	5.63101e14i	−0.134597	−	0.0483251i
$835$		−	7.19446e15i		−	0.613370i
$836$	−1.06688e15	+	2.21536e16i	−0.0903614	+	1.87633i
$837$	−1.47786e16	+	1.03043e16i	−1.24349	+	0.867020i
$838$	−1.14003e14	+	4.73722e15i	−0.00952956	+	0.395988i
$839$	2.24086e16			1.86091			0.930454	−	0.366410i	$-0.119413\pi$
$839$	2.24086e16			1.86091			0.930454	+	0.366410i	$0.119413\pi$
$840$	−2.42747e15	+	5.85839e15i	−0.200271	+	0.483329i
$841$	1.21971e16			0.999720
$842$	3.86935e14	−	1.60785e16i	0.0315080	−	1.30927i
$843$	4.69733e15	−	1.41443e16i	0.380013	−	1.14427i
$844$	1.09368e14	−	2.27100e15i	0.00879037	−	0.182530i
$845$		−	5.91445e15i		−	0.472283i
$846$	2.37912e15	−	3.03188e15i	0.188746	−	0.240533i
$847$		−	8.88505e15i		−	0.700327i
$848$	1.97338e15	−	2.04409e16i	0.154537	−	1.60074i
$849$	−2.89997e15	+	8.73221e15i	−0.225632	+	0.679410i
$850$	7.60355e15	+	1.82982e14i	0.587777	+	0.0141450i
$851$	−1.92793e16			−1.48074
$852$	−1.06583e16	−	4.11880e15i	−0.813339	−	0.314306i
$853$	8.03055e15			0.608872			0.304436	−	0.952533i	$-0.401532\pi$
$853$	8.03055e15			0.608872			0.304436	+	0.952533i	$0.401532\pi$
$854$	3.05286e15	+	7.34680e13i	0.229979	+	0.00553452i
$855$	8.91610e15	+	6.65620e15i	0.667362	+	0.498210i
$856$	−1.69433e14	+	2.34323e15i	−0.0126006	+	0.174264i
$857$		−	5.77487e15i		−	0.426725i	−0.976973	−	0.213362i	$-0.931559\pi$
$857$		−	5.77487e15i		−	0.426725i	0.976973	−	0.213362i	$-0.0684415\pi$
$858$	−2.79135e15	+	7.77458e15i	−0.204943	+	0.570817i
$859$		−	2.20254e16i		−	1.60680i	−0.595440	−	0.803400i	$-0.703022\pi$
$859$		−	2.20254e16i		−	1.60680i	0.595440	−	0.803400i	$-0.296978\pi$
$860$	9.57330e15	+	4.61036e14i	0.693937	+	0.0334190i
$861$	−2.85155e15	−	9.47001e14i	−0.205383	−	0.0682077i
$862$	1.55503e13	−	6.46170e14i	0.00111288	−	0.0462442i
$863$	−1.60087e16			−1.13841			−0.569203	−	0.822197i	$-0.692748\pi$
$863$	−1.60087e16			−1.13841			−0.569203	+	0.822197i	$0.692748\pi$
$864$	1.24965e16	−	6.64257e15i	0.883004	−	0.469365i
$865$	5.91152e15			0.415059
$866$	1.06803e14	−	4.43805e15i	0.00745135	−	0.309631i
$867$	−2.39072e15	−	7.93960e14i	−0.165739	−	0.0550420i
$868$	1.93595e16	+	9.32326e14i	1.33363	+	0.0642258i
$869$			2.31166e15i			0.158240i
$870$	4.94179e13	−	1.37641e14i	0.00336147	−	0.00936250i
$871$			1.02553e16i			0.693187i
$872$	2.47017e14	−	3.41619e15i	0.0165915	−	0.229457i
$873$	4.67734e15	+	3.49180e15i	0.312191	+	0.233062i
$874$	−2.74702e16	−	6.61079e14i	−1.82200	−	0.0438471i
$875$	1.30747e16			0.861761
$876$	−2.41250e16	−	9.32287e15i	−1.58014	−	0.610628i
$877$	1.83813e16			1.19641			0.598203	−	0.801344i	$-0.295882\pi$
$877$	1.83813e16			1.19641			0.598203	+	0.801344i	$0.295882\pi$
$878$	3.24200e15	+	7.80196e13i	0.209697	+	0.00504643i
$879$	1.19730e15	−	3.60524e15i	0.0769600	−	0.231737i
$880$	−1.19725e15	+	1.24014e16i	−0.0764766	+	0.792168i
$881$			1.06343e16i			0.675059i	0.941315	+	0.337529i	$0.109591\pi$
$881$			1.06343e16i			0.675059i	−0.941315	+	0.337529i	$0.890409\pi$
$882$	−2.19431e15	+	2.79637e15i	−0.138427	+	0.176408i
$883$			2.50986e16i			1.57350i	0.617273	+	0.786749i	$0.288237\pi$
$883$			2.50986e16i			1.57350i	−0.617273	+	0.786749i	$0.711763\pi$
$884$	3.17510e14	−	6.59302e15i	0.0197820	−	0.410769i
$885$	2.07983e15	−	6.26266e15i	0.128778	−	0.387767i
$886$	3.31839e14	−	1.37891e16i	0.0204194	−	0.848498i
$887$	8.10030e15			0.495360			0.247680	−	0.968842i	$-0.420332\pi$
$887$	8.10030e15			0.495360			0.247680	+	0.968842i	$0.420332\pi$
$888$	−7.17481e15	+	1.73155e16i	−0.436053	+	1.05236i
$889$	−1.36243e16			−0.822912
$890$	−1.75212e14	+	7.28067e15i	−0.0105176	+	0.437045i
$891$	6.38396e15	+	2.15317e16i	0.380858	+	1.28455i
$892$	9.53520e14	−	1.97996e16i	0.0565357	−	1.17395i
$893$			7.27464e15i			0.428675i
$894$	1.48782e16	+	5.34178e15i	0.871350	+	0.312845i
$895$			1.43807e16i			0.837051i
$896$	−1.50096e16	−	2.55217e15i	−0.868312	−	0.147644i
$897$	−9.71243e15	−	3.22550e15i	−0.558431	−	0.185455i
$898$	1.85215e15	+	4.45724e13i	0.105841	+	0.00254710i
$899$	−4.46981e14			−0.0253870
$900$	−8.84621e15	−	7.29221e15i	−0.499371	−	0.411648i
$901$	−2.60402e16			−1.46103
$902$	−5.90167e15	−	1.42025e14i	−0.329108	−	0.00792009i
$903$	−1.76388e16	−	5.85784e15i	−0.977654	−	0.324679i
$904$	1.65226e16	+	1.19471e15i	0.910233	+	0.0658168i
$905$			1.27450e16i			0.697870i
$906$	2.05874e16	+	7.39159e15i	1.12046	+	0.402284i
$907$			1.27721e16i			0.690913i	0.938435	+	0.345457i	$0.112276\pi$
$907$			1.27721e16i			0.690913i	−0.938435	+	0.345457i	$0.887724\pi$
$908$	−2.98821e16	−	1.43908e15i	−1.60671	−	0.0773769i
$909$	1.41028e16	−	1.88910e16i	0.753711	−	1.00961i
$910$	1.07256e14	−	4.45687e15i	0.00569762	−	0.236757i
$911$	−1.59406e16			−0.841692			−0.420846	−	0.907132i	$-0.638267\pi$
$911$	−1.59406e16			−0.841692			−0.420846	+	0.907132i	$0.638267\pi$
$912$	−1.08168e16	+	2.44260e16i	−0.567710	+	1.28198i
$913$	−2.17910e15			−0.113681
$914$	−2.33750e14	+	9.71316e15i	−0.0121213	+	0.503682i
$915$	9.48639e14	−	2.85648e15i	0.0488973	−	0.147237i
$916$	−4.02922e15	−	1.94041e14i	−0.206441	−	0.00994189i
$917$		−	1.33657e16i		−	0.680709i
$918$	−9.90673e15	−	1.49633e16i	−0.501529	−	0.757515i
$919$			1.53167e15i			0.0770778i	0.999257	+	0.0385389i	$0.0122703\pi$
$919$			1.53167e15i			0.0770778i	−0.999257	+	0.0385389i	$0.987730\pi$
$920$	−1.53955e16	−	1.11321e15i	−0.770126	−	0.0556859i
$921$	9.88170e15	−	2.97551e16i	0.491364	−	1.47956i
$922$	3.00093e15	+	7.22182e13i	0.148332	+	0.00356966i
$923$	8.03309e15			0.394706
$924$	8.70896e15	−	2.25364e16i	0.425373	−	1.10075i
$925$	1.51833e16			0.737202
$926$	2.53194e16	+	6.09318e14i	1.22206	+	0.0294092i
$927$	−1.30221e16	+	1.74433e16i	−0.624801	+	0.836933i
$928$	3.48578e14	+	4.21385e13i	0.0166259	+	0.00200986i
$929$			2.52232e16i			1.19595i	0.801514	+	0.597976i	$0.204028\pi$
$929$			2.52232e16i			1.19595i	−0.801514	+	0.597976i	$0.795972\pi$
$930$	6.45541e15	−	1.79799e16i	0.304276	−	0.847482i
$931$		−	6.70956e15i		−	0.314392i
$932$	2.96442e13	−	6.15554e14i	0.00138087	−	0.0286734i
$933$	−1.55994e15	−	5.18058e14i	−0.0722370	−	0.0239899i
$934$	5.47626e14	−	2.27558e16i	0.0252102	−	1.04757i
$935$	1.57986e16			0.723026
$936$	−6.51143e15	+	7.52272e15i	−0.296250	+	0.342261i
$937$	−1.24623e16			−0.563679			−0.281840	−	0.959462i	$-0.590945\pi$
$937$	−1.24623e16			−0.563679			−0.281840	+	0.959462i	$0.590945\pi$
$938$	7.21636e14	−	2.99866e16i	0.0324491	−	1.34838i
$939$	2.05311e16	+	6.81839e15i	0.917807	+	0.304804i
$940$	−1.96571e14	+	4.08176e15i	−0.00873609	+	0.181403i
$941$			2.79391e16i			1.23444i	0.786791	+	0.617220i	$0.211741\pi$
$941$			2.79391e16i			1.23444i	−0.786791	+	0.617220i	$0.788259\pi$
$942$	−4.00026e14	+	1.11417e15i	−0.0175715	+	0.0489408i
$943$		−	7.31377e15i		−	0.319394i
$944$	1.57702e16	+	1.52246e15i	0.684684	+	0.0661000i
$945$	−6.93232e15	−	9.94244e15i	−0.299229	−	0.429159i
$946$	−3.65058e16	−	8.78523e14i	−1.56661	−	0.0377009i
$947$	1.21950e15			0.0520303			0.0260152	−	0.999662i	$-0.491718\pi$
$947$	1.21950e15			0.0520303			0.0260152	+	0.999662i	$0.491718\pi$
$948$	−1.00362e15	+	2.59711e15i	−0.0425722	+	0.110165i
$949$	1.81828e16			0.766827
$950$	2.16340e16	+	5.20628e14i	0.907102	+	0.0218297i
$951$	9.19781e15	−	2.76959e16i	0.383435	−	1.15457i
$952$	−1.39233e15	+	1.92556e16i	−0.0577083	+	0.798094i
$953$		−	3.83011e14i		−	0.0157834i	−0.999969	−	0.00789170i	$-0.997488\pi$
$953$		−	3.83011e14i		−	0.0157834i	0.999969	−	0.00789170i	$-0.00251203\pi$
$954$	3.08791e16	+	2.42308e16i	1.26517	+	0.992779i
$955$		−	1.64674e16i		−	0.670820i
$956$	2.34661e15	+	1.13009e14i	0.0950437	+	0.00457716i
$957$	−1.75610e14	+	5.28787e14i	−0.00707188	+	0.0212944i
$958$	−1.10561e14	+	4.59421e15i	−0.00442682	+	0.183950i
$959$	−8.10953e15			−0.322844
$960$	−6.72927e15	+	1.34130e16i	−0.266364	+	0.530926i
$961$	−3.29802e16			−1.29800
$962$	3.17013e14	−	1.31730e16i	0.0124055	−	0.515493i
$963$	−3.59830e15	−	2.68626e15i	−0.140008	−	0.104521i
$964$	−1.72535e16	−	8.30905e14i	−0.667505	−	0.0321460i
$965$			1.41976e16i			0.546152i
$966$	2.81721e16	+	1.01148e16i	1.07757	+	0.386885i
$967$			1.86204e16i			0.708180i	0.935211	+	0.354090i	$0.115209\pi$
$967$			1.86204e16i			0.708180i	−0.935211	+	0.354090i	$0.884791\pi$
$968$	1.51636e15	−	2.09710e16i	0.0573439	−	0.793056i
$969$	3.21477e16	+	1.06763e16i	1.20884	+	0.401457i
$970$	−6.18746e15	−	1.48903e14i	−0.231349	−	0.00556748i
$971$	2.43169e16			0.904070			0.452035	−	0.892000i	$-0.350698\pi$
$971$	2.43169e16			0.904070			0.452035	+	0.892000i	$0.350698\pi$
$972$	−2.17591e15	+	2.69622e16i	−0.0804407	+	0.996759i
$973$	−3.42650e15			−0.125959
$974$	−1.50489e16	−	3.62157e14i	−0.550086	−	0.0132380i
$975$	7.64895e15	+	2.54022e15i	0.278020	+	0.0923307i
$976$	7.19298e15	+	6.94417e14i	0.259977	+	0.0250984i
$977$		−	4.43473e15i		−	0.159385i	−0.996820	−	0.0796924i	$-0.974606\pi$
$977$		−	4.43473e15i		−	0.159385i	0.996820	−	0.0796924i	$-0.0253938\pi$
$978$	2.07069e16	+	7.43449e15i	0.740032	+	0.265698i
$979$		−	2.77473e16i		−	0.986087i
$980$	1.81302e14	−	3.76470e15i	0.00640707	−	0.133041i
$981$	5.24596e15	+	3.91630e15i	0.184351	+	0.137625i
$982$	−1.24243e15	+	5.16273e16i	−0.0434167	+	1.80412i
$983$	−2.74166e16			−0.952728			−0.476364	−	0.879248i	$-0.658045\pi$
$983$	−2.74166e16			−0.952728			−0.476364	+	0.879248i	$0.658045\pi$
$984$	−6.56876e15	−	2.72182e15i	−0.226992	−	0.0940560i
$985$	1.62722e16			0.559174
$986$	1.07114e13	−	4.45098e14i	0.000366036	−	0.0152101i
$987$	2.49760e15	−	7.52062e15i	0.0848748	−	0.255570i
$988$	9.03393e14	−	1.87588e16i	0.0305291	−	0.633929i
$989$		−	4.52406e16i		−	1.52037i
$990$	−1.87343e16	−	1.47008e16i	−0.626101	−	0.491301i
$991$		−	1.32543e16i		−	0.440505i	−0.975443	−	0.220253i	$-0.929312\pi$
$991$		−	1.32543e16i		−	0.440505i	0.975443	−	0.220253i	$-0.0706882\pi$
$992$	4.55343e16	+	5.50451e15i	1.50496	+	0.181930i
$993$	4.48423e15	−	1.35026e16i	0.147390	−	0.443810i
$994$	−2.34887e16	−	5.65263e14i	−0.767775	−	0.0184767i
$995$	1.73668e15			0.0564536
$996$	−2.44818e15	−	9.46072e14i	−0.0791437	−	0.0305843i
$997$	−1.06442e16			−0.342208			−0.171104	−	0.985253i	$-0.554733\pi$
$997$	−1.06442e16			−0.342208			−0.171104	+	0.985253i	$0.554733\pi$
$998$	−2.13126e16	−	5.12894e14i	−0.681425	−	0.0163987i
$999$	−2.04896e16	−	2.93866e16i	−0.651515	−	0.934413i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.08876 + 45.2417i) q^{2} +(-399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} +4150.68i q^{5} +(6436.35 - 17926.8i) q^{6} -39165.5i q^{7} +(6684.15 - 92440.6i) q^{8} +(141953. + 105973. i) q^{9} +O(q^{10})\)	\(q+(-1.08876 + 45.2417i) q^{2} +(-399.437 - 132.653i) q^{3} +(-2045.63 - 98.5144i) q^{4} +4150.68i q^{5} +(6436.35 - 17926.8i) q^{6} -39165.5i q^{7} +(6684.15 - 92440.6i) q^{8} +(141953. + 105973. i) q^{9} +(-187784. - 4519.08i) q^{10} +715661. q^{11} +(804032. + 310710. i) q^{12} -605992. q^{13} +(1.77192e6 + 42641.7i) q^{14} +(550602. - 1.65794e6i) q^{15} +(4.17489e6 + 403048. i) q^{16} -5.31852e6i q^{17} +(-4.94897e6 + 6.30683e6i) q^{18} -1.51325e7i q^{19} +(408902. - 8.49076e6i) q^{20} +(-5.19544e6 + 1.56442e7i) q^{21} +(-779180. + 3.23777e7i) q^{22} -4.01248e7 q^{23} +(-1.49324e7 + 3.60375e7i) q^{24} +3.16000e7 q^{25} +(659777. - 2.74161e7i) q^{26} +(-4.26437e7 - 6.11603e7i) q^{27} +(-3.85837e6 + 8.01182e7i) q^{28} -1.84980e6i q^{29} +(7.44085e7 + 2.67153e7i) q^{30} -2.41637e8i q^{31} +(-2.27800e7 + 1.88441e8i) q^{32} +(-2.85862e8 - 9.49348e7i) q^{33} +(2.40619e8 + 5.79057e6i) q^{34} +1.62564e8 q^{35} +(-2.79944e8 - 2.30767e8i) q^{36} +4.80485e8 q^{37} +(6.84620e8 + 1.64756e7i) q^{38} +(2.42056e8 + 8.03868e7i) q^{39} +(3.83691e8 + 2.77438e7i) q^{40} +1.82276e8i q^{41} +(-7.02113e8 - 2.52083e8i) q^{42} +1.12750e9i q^{43} +(-1.46398e9 - 7.05029e7i) q^{44} +(-4.39862e8 + 5.89203e8i) q^{45} +(4.36861e7 - 1.81531e9i) q^{46} -4.80730e8 q^{47} +(-1.61414e9 - 7.14806e8i) q^{48} +4.43388e8 q^{49} +(-3.44046e7 + 1.42964e9i) q^{50} +(-7.05519e8 + 2.12442e9i) q^{51} +(1.23963e9 + 5.96989e7i) q^{52} -4.89614e9i q^{53} +(2.81342e9 - 1.86269e9i) q^{54} +2.97048e9i q^{55} +(-3.62048e9 - 2.61788e8i) q^{56} +(-2.00737e9 + 6.04448e9i) q^{57} +(8.36882e7 + 2.01398e6i) q^{58} +3.77738e9 q^{59} +(-1.28966e9 + 3.33728e9i) q^{60} +1.72291e9 q^{61} +(1.09321e10 + 2.63084e8i) q^{62} +(4.15050e9 - 5.55967e9i) q^{63} +(-8.50058e9 - 1.23577e9i) q^{64} -2.51528e9i q^{65} +(4.60625e9 - 1.28295e10i) q^{66} -1.69232e10i q^{67} +(-5.23951e8 + 1.08797e10i) q^{68} +(1.60273e10 + 5.32268e9i) q^{69} +(-1.76992e8 + 7.35466e9i) q^{70} -1.32561e10 q^{71} +(1.07451e10 - 1.24139e10i) q^{72} -3.00051e10 q^{73} +(-5.23131e8 + 2.17380e10i) q^{74} +(-1.26222e10 - 4.19184e9i) q^{75} +(-1.49077e9 + 3.09555e10i) q^{76} -2.80292e10i q^{77} +(-3.90038e9 + 1.08635e10i) q^{78} +3.23010e9i q^{79} +(-1.67292e9 + 1.73287e10i) q^{80} +(8.92037e9 + 3.00865e10i) q^{81} +(-8.24646e9 - 1.98454e8i) q^{82} -3.04488e9 q^{83} +(1.21691e10 - 3.14904e10i) q^{84} +2.20755e10 q^{85} +(-5.10099e10 - 1.22757e9i) q^{86} +(-2.45382e8 + 7.38880e8i) q^{87} +(4.78359e9 - 6.61561e10i) q^{88} -3.87715e10i q^{89} +(-2.61777e10 - 2.05416e10i) q^{90} +2.37340e10i q^{91} +(8.20804e10 + 3.95287e9i) q^{92} +(-3.20540e10 + 9.65190e10i) q^{93} +(5.23397e8 - 2.17490e10i) q^{94} +6.28102e10 q^{95} +(3.40965e10 - 7.22484e10i) q^{96} +3.29498e10 q^{97} +(-4.82741e8 + 2.00596e10i) q^{98} +(1.01590e11 + 7.58410e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9}+O(q^{10}) \) 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9	\( 20 q + 1976 q^{4} + 13128 q^{6} + 103620 q^{9} + 202000 q^{10} + 1064760 q^{12} + 1543864 q^{13} + 3482912 q^{16} + 2557392 q^{18} - 12211752 q^{21} - 5920464 q^{22} + 12133152 q^{24} - 141128700 q^{25} - 3604848 q^{28} + 73456080 q^{30} + 229769760 q^{33} + 222167104 q^{34} + 298087896 q^{36} - 44517800 q^{37} - 439643840 q^{40} + 281776944 q^{42} + 1020227520 q^{45} - 2392795680 q^{46} + 689090592 q^{48} - 1018138084 q^{49} - 3959246384 q^{52} - 4249352520 q^{54} + 1438636392 q^{57} + 9671853040 q^{58} + 5688375360 q^{60} + 6873199864 q^{61} - 1452752512 q^{64} - 10961242896 q^{66} - 13308470976 q^{69} + 35188514400 q^{70} + 30438127680 q^{72} - 12426469112 q^{73} - 60088673808 q^{76} - 81037845456 q^{78} - 42462874764 q^{81} + 88180337440 q^{82} + 125502443664 q^{84} + 17135502080 q^{85} - 166086469440 q^{88} - 257976145200 q^{90} + 114387515256 q^{93} + 391966360512 q^{94} + 446868262272 q^{96} + 75764383528 q^{97}+O(q^{100}) \) 20 * q + 1976 * q^4 + 13128 * q^6 + 103620 * q^9 + 202000 * q^10 + 1064760 * q^12 + 1543864 * q^13 + 3482912 * q^16 + 2557392 * q^18 - 12211752 * q^21 - 5920464 * q^22 + 12133152 * q^24 - 141128700 * q^25 - 3604848 * q^28 + 73456080 * q^30 + 229769760 * q^33 + 222167104 * q^34 + 298087896 * q^36 - 44517800 * q^37 - 439643840 * q^40 + 281776944 * q^42 + 1020227520 * q^45 - 2392795680 * q^46 + 689090592 * q^48 - 1018138084 * q^49 - 3959246384 * q^52 - 4249352520 * q^54 + 1438636392 * q^57 + 9671853040 * q^58 + 5688375360 * q^60 + 6873199864 * q^61 - 1452752512 * q^64 - 10961242896 * q^66 - 13308470976 * q^69 + 35188514400 * q^70 + 30438127680 * q^72 - 12426469112 * q^73 - 60088673808 * q^76 - 81037845456 * q^78 - 42462874764 * q^81 + 88180337440 * q^82 + 125502443664 * q^84 + 17135502080 * q^85 - 166086469440 * q^88 - 257976145200 * q^90 + 114387515256 * q^93 + 391966360512 * q^94 + 446868262272 * q^96 + 75764383528 * q^97

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