LMFDB - Embedded newform 93.2.g.f.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(26,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("93.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.g (of order $6$, degree $2$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	93.26
Dual form			93.2.g.f.68.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.792287i q^{2} +(0.500000 - 1.65831i) q^{3} +1.37228 q^{4} +(-0.686141 + 0.396143i) q^{5} +(-1.31386 - 0.396143i) q^{6} +(-1.68614 + 2.92048i) q^{7} -2.67181i q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q-0.792287i q^{2} +(0.500000 - 1.65831i) q^{3} +1.37228 q^{4} +(-0.686141 + 0.396143i) q^{5} +(-1.31386 - 0.396143i) q^{6} +(-1.68614 + 2.92048i) q^{7} -2.67181i q^{8} +(-2.50000 - 1.65831i) q^{9} +(0.313859 + 0.543620i) q^{10} +(0.686141 + 1.18843i) q^{11} +(0.686141 - 2.27567i) q^{12} +(1.50000 - 0.866025i) q^{13} +(2.31386 + 1.33591i) q^{14} +(0.313859 + 1.33591i) q^{15} +0.627719 q^{16} +(-3.68614 + 6.38458i) q^{17} +(-1.31386 + 1.98072i) q^{18} +(1.87228 - 3.24289i) q^{19} +(-0.941578 + 0.543620i) q^{20} +(4.00000 + 4.25639i) q^{21} +(0.941578 - 0.543620i) q^{22} +(-4.43070 - 1.33591i) q^{24} +(-2.18614 + 3.78651i) q^{25} +(-0.686141 - 1.18843i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-2.31386 + 4.00772i) q^{28} +6.00000 q^{29} +(1.05842 - 0.248667i) q^{30} +(-2.00000 - 5.19615i) q^{31} -5.84096i q^{32} +(2.31386 - 0.543620i) q^{33} +(5.05842 + 2.92048i) q^{34} -2.67181i q^{35} +(-3.43070 - 2.27567i) q^{36} +(1.50000 + 0.866025i) q^{37} +(-2.56930 - 1.48338i) q^{38} +(-0.686141 - 2.92048i) q^{39} +(1.05842 + 1.83324i) q^{40} +(-0.686141 + 0.396143i) q^{41} +(3.37228 - 3.16915i) q^{42} +(-7.50000 - 4.33013i) q^{43} +(0.941578 + 1.63086i) q^{44} +(2.37228 + 0.147477i) q^{45} -6.63325i q^{47} +(0.313859 - 1.04095i) q^{48} +(-2.18614 - 3.78651i) q^{49} +(3.00000 + 1.73205i) q^{50} +(8.74456 + 9.30506i) q^{51} +(2.05842 - 1.18843i) q^{52} +(0.686141 + 1.18843i) q^{53} +(2.62772 + 3.16915i) q^{54} +(-0.941578 - 0.543620i) q^{55} +(7.80298 + 4.50506i) q^{56} +(-4.44158 - 4.72627i) q^{57} -4.75372i q^{58} +(-12.4307 - 7.17687i) q^{59} +(0.430703 + 1.83324i) q^{60} +(-4.11684 + 1.58457i) q^{62} +(9.05842 - 4.50506i) q^{63} -3.37228 q^{64} +(-0.686141 + 1.18843i) q^{65} +(-0.430703 - 1.83324i) q^{66} +(-3.05842 - 5.29734i) q^{67} +(-5.05842 + 8.76144i) q^{68} -2.11684 q^{70} +(12.4307 - 7.17687i) q^{71} +(-4.43070 + 6.67954i) q^{72} +(-11.6168 + 6.70699i) q^{73} +(0.686141 - 1.18843i) q^{74} +(5.18614 + 5.51856i) q^{75} +(2.56930 - 4.45015i) q^{76} -4.62772 q^{77} +(-2.31386 + 0.543620i) q^{78} +(8.05842 + 4.65253i) q^{79} +(-0.430703 + 0.248667i) q^{80} +(3.50000 + 8.29156i) q^{81} +(0.313859 + 0.543620i) q^{82} +(6.68614 + 11.5807i) q^{83} +(5.48913 + 5.84096i) q^{84} -5.84096i q^{85} +(-3.43070 + 5.94215i) q^{86} +(3.00000 - 9.94987i) q^{87} +(3.17527 - 1.83324i) q^{88} -6.00000 q^{89} +(0.116844 - 1.87953i) q^{90} +5.84096i q^{91} +(-9.61684 + 0.718549i) q^{93} -5.25544 q^{94} +2.96677i q^{95} +(-9.68614 - 2.92048i) q^{96} +0.372281 q^{97} +(-3.00000 + 1.73205i) q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 6 q^{4} + 3 q^{5} - 11 q^{6} - q^{7} - 10 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 6 * q^4 + 3 * q^5 - 11 * q^6 - q^7 - 10 * q^9	$ 4 q + 2 q^{3} - 6 q^{4} + 3 q^{5} - 11 q^{6} - q^{7} - 10 q^{9} + 7 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} + 15 q^{14} + 7 q^{15} + 14 q^{16} - 9 q^{17} - 11 q^{18} - 4 q^{19} - 21 q^{20} + 16 q^{21} + 21 q^{22} + 11 q^{24} - 3 q^{25} + 3 q^{26} - 16 q^{27} - 15 q^{28} + 24 q^{29} - 13 q^{30} - 8 q^{31} + 15 q^{33} + 3 q^{34} + 15 q^{36} + 6 q^{37} - 39 q^{38} + 3 q^{39} - 13 q^{40} + 3 q^{41} + 2 q^{42} - 30 q^{43} + 21 q^{44} - 2 q^{45} + 7 q^{48} - 3 q^{49} + 12 q^{50} + 12 q^{51} - 9 q^{52} - 3 q^{53} + 22 q^{54} - 21 q^{55} - 9 q^{56} - 35 q^{57} - 21 q^{59} - 27 q^{60} + 18 q^{62} + 19 q^{63} - 2 q^{64} + 3 q^{65} + 27 q^{66} + 5 q^{67} - 3 q^{68} + 26 q^{70} + 21 q^{71} + 11 q^{72} - 12 q^{73} - 3 q^{74} + 15 q^{75} + 39 q^{76} - 30 q^{77} - 15 q^{78} + 15 q^{79} + 27 q^{80} + 14 q^{81} + 7 q^{82} + 21 q^{83} - 24 q^{84} + 15 q^{86} + 12 q^{87} - 39 q^{88} - 24 q^{89} - 34 q^{90} - 4 q^{93} - 44 q^{94} - 33 q^{96} - 10 q^{97} - 12 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^4 + 3 * q^5 - 11 * q^6 - q^7 - 10 * q^9 + 7 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 + 15 * q^14 + 7 * q^15 + 14 * q^16 - 9 * q^17 - 11 * q^18 - 4 * q^19 - 21 * q^20 + 16 * q^21 + 21 * q^22 + 11 * q^24 - 3 * q^25 + 3 * q^26 - 16 * q^27 - 15 * q^28 + 24 * q^29 - 13 * q^30 - 8 * q^31 + 15 * q^33 + 3 * q^34 + 15 * q^36 + 6 * q^37 - 39 * q^38 + 3 * q^39 - 13 * q^40 + 3 * q^41 + 2 * q^42 - 30 * q^43 + 21 * q^44 - 2 * q^45 + 7 * q^48 - 3 * q^49 + 12 * q^50 + 12 * q^51 - 9 * q^52 - 3 * q^53 + 22 * q^54 - 21 * q^55 - 9 * q^56 - 35 * q^57 - 21 * q^59 - 27 * q^60 + 18 * q^62 + 19 * q^63 - 2 * q^64 + 3 * q^65 + 27 * q^66 + 5 * q^67 - 3 * q^68 + 26 * q^70 + 21 * q^71 + 11 * q^72 - 12 * q^73 - 3 * q^74 + 15 * q^75 + 39 * q^76 - 30 * q^77 - 15 * q^78 + 15 * q^79 + 27 * q^80 + 14 * q^81 + 7 * q^82 + 21 * q^83 - 24 * q^84 + 15 * q^86 + 12 * q^87 - 39 * q^88 - 24 * q^89 - 34 * q^90 - 4 * q^93 - 44 * q^94 - 33 * q^96 - 10 * q^97 - 12 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	0.792287i		−	0.560232i	−0.959966	−	0.280116i	$-0.909627\pi$
$2$		−	0.792287i		−	0.560232i	0.959966	−	0.280116i	$-0.0903729\pi$
$3$	0.500000	−	1.65831i	0.288675	−	0.957427i
$3$	0.500000	−	1.65831i	0.288675	−	0.957427i
$4$	1.37228			0.686141
$5$	−0.686141	+	0.396143i	−0.306851	+	0.177161i	−0.645517	−	0.763746i	$-0.723358\pi$
$5$	−0.686141	+	0.396143i	−0.306851	+	0.177161i	0.338665	+	0.940907i	$0.390025\pi$
$6$	−1.31386	−	0.396143i	−0.536381	−	0.161725i
$7$	−1.68614	+	2.92048i	−0.637301	+	1.10384i	0.348721	+	0.937226i	$0.386616\pi$
$7$	−1.68614	+	2.92048i	−0.637301	+	1.10384i	−0.986023	+	0.166612i	$0.946717\pi$
$8$		−	2.67181i		−	0.944629i
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$	0.313859	+	0.543620i	0.0992510	+	0.171908i
$11$	0.686141	+	1.18843i	0.206879	+	0.358325i	0.950730	−	0.310021i	$-0.100336\pi$
$11$	0.686141	+	1.18843i	0.206879	+	0.358325i	−0.743851	+	0.668346i	$0.767003\pi$
$12$	0.686141	−	2.27567i	0.198072	−	0.656930i
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	0.693375	+	0.720577i	$0.256123\pi$
$14$	2.31386	+	1.33591i	0.618405	+	0.357036i
$15$	0.313859	+	1.33591i	0.0810381	+	0.344930i
$16$	0.627719			0.156930
$17$	−3.68614	+	6.38458i	−0.894020	+	1.54849i	−0.0590081	+	0.998258i	$0.518794\pi$
$17$	−3.68614	+	6.38458i	−0.894020	+	1.54849i	−0.835012	+	0.550231i	$0.814540\pi$
$18$	−1.31386	+	1.98072i	−0.309680	+	0.466860i
$19$	1.87228	−	3.24289i	0.429531	−	0.743969i	−0.567301	−	0.823511i	$-0.692012\pi$
$19$	1.87228	−	3.24289i	0.429531	−	0.743969i	0.996832	+	0.0795415i	$0.0253456\pi$
$20$	−0.941578	+	0.543620i	−0.210543	+	0.121557i
$21$	4.00000	+	4.25639i	0.872872	+	0.928820i
$22$	0.941578	−	0.543620i	0.200745	−	0.115900i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−4.43070	−	1.33591i	−0.904414	−	0.272691i
$25$	−2.18614	+	3.78651i	−0.437228	+	0.757301i
$26$	−0.686141	−	1.18843i	−0.134563	−	0.233070i
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$	−2.31386	+	4.00772i	−0.437278	+	0.757388i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	1.05842	−	0.248667i	0.193241	−	0.0454001i
$31$	−2.00000	−	5.19615i	−0.359211	−	0.933257i
$31$	−2.00000	−	5.19615i	−0.359211	−	0.933257i
$32$		−	5.84096i		−	1.03255i
$33$	2.31386	−	0.543620i	0.402791	−	0.0946322i
$34$	5.05842	+	2.92048i	0.867512	+	0.500858i
$35$		−	2.67181i		−	0.451619i
$36$	−3.43070	−	2.27567i	−0.571784	−	0.379279i
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	0.618206	−	0.786016i	$-0.287860\pi$
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	−0.371607	+	0.928390i	$0.621193\pi$
$38$	−2.56930	−	1.48338i	−0.416795	−	0.240637i
$39$	−0.686141	−	2.92048i	−0.109870	−	0.467651i
$40$	1.05842	+	1.83324i	0.167351	+	0.289861i
$41$	−0.686141	+	0.396143i	−0.107157	+	0.0618672i	−0.552621	−	0.833433i	$-0.686372\pi$
$41$	−0.686141	+	0.396143i	−0.107157	+	0.0618672i	0.445464	+	0.895300i	$0.353039\pi$
$42$	3.37228	−	3.16915i	0.520354	−	0.489010i
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.196385	−	0.980527i	$-0.562920\pi$
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.947354	+	0.320189i	$0.896254\pi$
$44$	0.941578	+	1.63086i	0.141948	+	0.245862i
$45$	2.37228	+	0.147477i	0.353639	+	0.0219845i
$46$		0			0
$47$		−	6.63325i		−	0.967559i	−0.875190	−	0.483779i	$-0.839264\pi$
$47$		−	6.63325i		−	0.967559i	0.875190	−	0.483779i	$-0.160736\pi$
$48$	0.313859	−	1.04095i	0.0453017	−	0.150249i
$49$	−2.18614	−	3.78651i	−0.312306	−	0.540930i
$50$	3.00000	+	1.73205i	0.424264	+	0.244949i
$51$	8.74456	+	9.30506i	1.22448	+	1.30297i
$52$	2.05842	−	1.18843i	0.285452	−	0.164806i
$53$	0.686141	+	1.18843i	0.0942487	+	0.163243i	0.909295	−	0.416153i	$-0.136622\pi$
$53$	0.686141	+	1.18843i	0.0942487	+	0.163243i	−0.815046	+	0.579396i	$0.803288\pi$
$54$	2.62772	+	3.16915i	0.357587	+	0.431266i
$55$	−0.941578	−	0.543620i	−0.126962	−	0.0733017i
$56$	7.80298	+	4.50506i	1.04272	+	0.602013i
$57$	−4.44158	−	4.72627i	−0.588301	−	0.626010i
$58$		−	4.75372i		−	0.624194i
$59$	−12.4307	−	7.17687i	−1.61834	−	0.934349i	−0.987350	−	0.158558i	$-0.949316\pi$
$59$	−12.4307	−	7.17687i	−1.61834	−	0.934349i	−0.630990	−	0.775791i	$-0.717351\pi$
$60$	0.430703	+	1.83324i	0.0556036	+	0.236670i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−4.11684	+	1.58457i	−0.522840	+	0.201241i
$63$	9.05842	−	4.50506i	1.14125	−	0.567584i
$64$	−3.37228			−0.421535
$65$	−0.686141	+	1.18843i	−0.0851053	+	0.147407i
$66$	−0.430703	−	1.83324i	−0.0530159	−	0.225656i
$67$	−3.05842	−	5.29734i	−0.373646	−	0.647173i	0.616478	−	0.787372i	$-0.288559\pi$
$67$	−3.05842	−	5.29734i	−0.373646	−	0.647173i	−0.990123	+	0.140199i	$0.955226\pi$
$68$	−5.05842	+	8.76144i	−0.613424	+	1.06248i
$69$		0			0
$70$	−2.11684			−0.253011
$71$	12.4307	−	7.17687i	1.47525	−	0.851738i	0.475642	−	0.879639i	$-0.342216\pi$
$71$	12.4307	−	7.17687i	1.47525	−	0.851738i	0.999611	+	0.0279010i	$0.00888231\pi$
$72$	−4.43070	+	6.67954i	−0.522163	+	0.787191i
$73$	−11.6168	+	6.70699i	−1.35965	+	0.784994i	−0.989576	−	0.144009i	$-0.954000\pi$
$73$	−11.6168	+	6.70699i	−1.35965	+	0.784994i	−0.370072	+	0.929003i	$0.620667\pi$
$74$	0.686141	−	1.18843i	0.0797622	−	0.138152i
$75$	5.18614	+	5.51856i	0.598844	+	0.637228i
$76$	2.56930	−	4.45015i	0.294719	−	0.510467i
$77$	−4.62772			−0.527377
$78$	−2.31386	+	0.543620i	−0.261993	+	0.0615529i
$79$	8.05842	+	4.65253i	0.906643	+	0.523451i	0.879350	−	0.476177i	$-0.157978\pi$
$79$	8.05842	+	4.65253i	0.906643	+	0.523451i	0.0272937	+	0.999627i	$0.491311\pi$
$80$	−0.430703	+	0.248667i	−0.0481541	+	0.0278018i
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$	0.313859	+	0.543620i	0.0346600	+	0.0600328i
$83$	6.68614	+	11.5807i	0.733899	+	1.27115i	0.955205	+	0.295946i	$0.0956349\pi$
$83$	6.68614	+	11.5807i	0.733899	+	1.27115i	−0.221305	+	0.975205i	$0.571032\pi$
$84$	5.48913	+	5.84096i	0.598913	+	0.637301i
$85$		−	5.84096i		−	0.633541i
$86$	−3.43070	+	5.94215i	−0.369942	+	0.640759i
$87$	3.00000	−	9.94987i	0.321634	−	1.06674i
$88$	3.17527	−	1.83324i	0.338484	−	0.195424i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	0.116844	−	1.87953i	0.0123164	−	0.198120i
$91$			5.84096i			0.612299i
$92$		0			0
$93$	−9.61684	+	0.718549i	−0.997220	+	0.0745100i
$94$	−5.25544			−0.542057
$95$			2.96677i			0.304384i
$96$	−9.68614	−	2.92048i	−0.988588	−	0.298070i
$97$	0.372281			0.0377994			0.0188997	−	0.999821i	$-0.493984\pi$
$97$	0.372281			0.0377994			0.0188997	+	0.999821i	$0.493984\pi$
$98$	−3.00000	+	1.73205i	−0.303046	+	0.174964i
$99$	0.255437	−	4.10891i	0.0256724	−	0.412961i
$100$	−3.00000	+	5.19615i	−0.300000	+	0.519615i
$101$			11.9769i			1.19174i	0.803079	+	0.595872i	$0.203193\pi$
$101$			11.9769i			1.19174i	−0.803079	+	0.595872i	$0.796807\pi$
$102$	7.37228	−	6.92820i	0.729965	−	0.685994i
$103$	−1.12772	−	1.95327i	−0.111117	−	0.192461i	0.805104	−	0.593134i	$-0.202110\pi$
$103$	−1.12772	−	1.95327i	−0.111117	−	0.192461i	−0.916221	+	0.400673i	$0.868776\pi$
$104$	−2.31386	−	4.00772i	−0.226893	−	0.392989i
$105$	−4.43070	−	1.33591i	−0.432392	−	0.130371i
$106$	0.941578	−	0.543620i	0.0914541	−	0.0528011i
$107$	0.686141	+	0.396143i	0.0663317	+	0.0382966i	0.532799	−	0.846242i	$-0.321140\pi$
$107$	0.686141	+	0.396143i	0.0663317	+	0.0382966i	−0.466467	+	0.884538i	$0.654473\pi$
$108$	−5.48913	+	4.55134i	−0.528191	+	0.437953i
$109$	12.3723			1.18505			0.592525	−	0.805552i	$-0.298131\pi$
$109$	12.3723			1.18505			0.592525	+	0.805552i	$0.298131\pi$
$110$	−0.430703	+	0.746000i	−0.0410659	+	0.0711283i
$111$	2.18614	−	2.05446i	0.207499	−	0.195000i
$112$	−1.05842	+	1.83324i	−0.100011	+	0.173225i
$113$	12.4307	−	7.17687i	1.16938	−	0.675143i	0.215848	−	0.976427i	$-0.430749\pi$
$113$	12.4307	−	7.17687i	1.16938	−	0.675143i	0.953534	+	0.301284i	$0.0974152\pi$
$114$	−3.74456	+	3.51900i	−0.350710	+	0.329585i
$115$		0			0
$116$	8.23369			0.764479
$117$	−5.18614	−	0.322405i	−0.479459	−	0.0298064i
$118$	−5.68614	+	9.84868i	−0.523452	+	0.906645i
$119$	−12.4307	−	21.5306i	−1.13952	−	1.97371i
$120$	3.56930	−	0.838574i	0.325831	−	0.0765510i
$121$	4.55842	−	7.89542i	0.414402	−	0.717765i
$122$		0			0
$123$	0.313859	+	1.33591i	0.0282997	+	0.120455i
$124$	−2.74456	−	7.13058i	−0.246469	−	0.640345i
$125$		−	7.42554i		−	0.664160i
$126$	−3.56930	−	7.17687i	−0.317978	−	0.639366i
$127$	5.61684	+	3.24289i	0.498414	+	0.287760i	0.728058	−	0.685515i	$-0.240423\pi$
$127$	5.61684	+	3.24289i	0.498414	+	0.287760i	−0.229644	+	0.973275i	$0.573756\pi$
$128$		−	9.01011i		−	0.796389i
$129$	−10.9307	+	10.2723i	−0.962395	+	0.904424i
$130$	0.941578	+	0.543620i	0.0825819	+	0.0476787i
$131$	12.6861	+	7.32435i	1.10839	+	0.639931i	0.938413	−	0.345516i	$-0.112296\pi$
$131$	12.6861	+	7.32435i	1.10839	+	0.639931i	0.169981	+	0.985447i	$0.445630\pi$
$132$	3.17527	−	0.746000i	0.276371	−	0.0649310i
$133$	6.31386	+	10.9359i	0.547481	+	0.948265i
$134$	−4.19702	+	2.42315i	−0.362567	+	0.209328i
$135$	1.43070	−	3.86025i	0.123135	−	0.332237i
$136$	17.0584	+	9.84868i	1.46275	+	0.844518i
$137$	−5.31386	−	9.20387i	−0.453994	−	0.786340i	0.544636	−	0.838672i	$-0.316668\pi$
$137$	−5.31386	−	9.20387i	−0.453994	−	0.786340i	−0.998630	+	0.0523324i	$0.983334\pi$
$138$		0			0
$139$		−	10.3923i		−	0.881464i	−0.897639	−	0.440732i	$-0.854719\pi$
$139$		−	10.3923i		−	0.881464i	0.897639	−	0.440732i	$-0.145281\pi$
$140$		−	3.66648i		−	0.309874i
$141$	−11.0000	−	3.31662i	−0.926367	−	0.279310i
$142$	−5.68614	−	9.84868i	−0.477170	−	0.826483i
$143$	2.05842	+	1.18843i	0.172134	+	0.0993815i
$144$	−1.56930	−	1.04095i	−0.130775	−	0.0867461i
$145$	−4.11684	+	2.37686i	−0.341885	+	0.197388i
$146$	5.31386	+	9.20387i	0.439778	+	0.761718i
$147$	−7.37228	+	1.73205i	−0.608056	+	0.142857i
$148$	2.05842	+	1.18843i	0.169201	+	0.0976884i
$149$	3.68614	+	2.12819i	0.301980	+	0.174348i	0.643332	−	0.765587i	$-0.277551\pi$
$149$	3.68614	+	2.12819i	0.301980	+	0.174348i	−0.341352	+	0.939936i	$0.610885\pi$
$150$	4.37228	−	4.10891i	0.356995	−	0.335491i
$151$			13.2116i			1.07514i	0.843218	+	0.537572i	$0.180658\pi$
$151$			13.2116i			1.07514i	−0.843218	+	0.537572i	$0.819342\pi$
$152$	−8.66439	−	5.00239i	−0.702775	−	0.405747i
$153$	19.8030	−	9.84868i	1.60098	−	0.796219i
$154$			3.66648i			0.295453i
$155$	3.43070	+	2.77300i	0.275561	+	0.222733i
$156$	−0.941578	−	4.00772i	−0.0753866	−	0.320875i
$157$	12.3723			0.987416			0.493708	−	0.869628i	$-0.335641\pi$
$157$	12.3723			0.987416			0.493708	+	0.869628i	$0.335641\pi$
$158$	3.68614	−	6.38458i	0.293254	−	0.507930i
$159$	2.31386	−	0.543620i	0.183501	−	0.0431119i
$160$	2.31386	+	4.00772i	0.182927	+	0.316838i
$161$		0			0
$162$	6.56930	−	2.77300i	0.516133	−	0.217868i
$163$	6.37228			0.499116			0.249558	−	0.968360i	$-0.419715\pi$
$163$	6.37228			0.499116			0.249558	+	0.968360i	$0.419715\pi$
$164$	−0.941578	+	0.543620i	−0.0735249	+	0.0424496i
$165$	−1.37228	+	1.28962i	−0.106832	+	0.100397i
$166$	9.17527	−	5.29734i	0.712139	−	0.411153i
$167$	5.31386	−	9.20387i	0.411199	−	0.712217i	−0.583822	−	0.811881i	$-0.698444\pi$
$167$	5.31386	−	9.20387i	0.411199	−	0.712217i	0.995021	+	0.0996643i	$0.0317769\pi$
$168$	11.3723	−	10.6873i	0.877391	−	0.824540i
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$	−4.62772			−0.354930
$171$	−10.0584	+	5.00239i	−0.769187	+	0.382542i
$172$	−10.2921	−	5.94215i	−0.784766	−	0.453085i
$173$	−7.80298	+	4.50506i	−0.593250	+	0.342513i	−0.766382	−	0.642386i	$-0.777945\pi$
$173$	−7.80298	+	4.50506i	−0.593250	+	0.342513i	0.173132	+	0.984899i	$0.444611\pi$
$174$	−7.88316	−	2.37686i	−0.597621	−	0.180189i
$175$	−7.37228	−	12.7692i	−0.557292	−	0.965258i
$176$	0.430703	+	0.746000i	0.0324655	+	0.0562319i
$177$	−18.1168	+	17.0256i	−1.36175	+	1.27972i
$178$			4.75372i			0.356307i
$179$	−6.68614	+	11.5807i	−0.499746	+	0.865585i	−1.00000		0.000293712i	$-0.999907\pi$
$179$	−6.68614	+	11.5807i	−0.499746	+	0.865585i	0.500254	+	0.865879i	$0.333240\pi$
$180$	3.25544	+	0.202380i	0.242646	+	0.0150845i
$181$	−11.6168	+	6.70699i	−0.863473	+	0.498526i	−0.865174	−	0.501472i	$-0.832792\pi$
$181$	−11.6168	+	6.70699i	−0.863473	+	0.498526i	0.00170063	+	0.999999i	$0.499459\pi$
$182$	4.62772			0.343029
$183$		0			0
$184$		0			0
$185$	−1.37228			−0.100892
$186$	0.569297	+	7.61930i	0.0417429	+	0.558674i
$187$	−10.1168			−0.739817
$188$		−	9.10268i		−	0.663881i
$189$	−2.94158	−	17.2742i	−0.213968	−	1.25651i
$190$	2.35053			0.170526
$191$	−18.6861	+	10.7884i	−1.35208	+	0.780625i	−0.988541	−	0.150954i	$-0.951766\pi$
$191$	−18.6861	+	10.7884i	−1.35208	+	0.780625i	−0.363541	+	0.931578i	$0.618432\pi$
$192$	−1.68614	+	5.59230i	−0.121687	+	0.403589i
$193$	4.87228	−	8.43904i	0.350714	−	0.607455i	−0.635660	−	0.771969i	$-0.719272\pi$
$193$	4.87228	−	8.43904i	0.350714	−	0.607455i	0.986375	+	0.164514i	$0.0526054\pi$
$194$		−	0.294954i		−	0.0211764i
$195$	1.62772	+	1.73205i	0.116563	+	0.124035i
$196$	−3.00000	−	5.19615i	−0.214286	−	0.371154i
$197$	7.80298	+	13.5152i	0.555940	+	0.962916i	0.997830	+	0.0658465i	$0.0209748\pi$
$197$	7.80298	+	13.5152i	0.555940	+	0.962916i	−0.441890	+	0.897069i	$0.645692\pi$
$198$	−3.25544	−	0.202380i	−0.231354	−	0.0143825i
$199$	−14.0584	+	8.11663i	−0.996575	+	0.575373i	−0.907233	−	0.420628i	$-0.861810\pi$
$199$	−14.0584	+	8.11663i	−0.996575	+	0.575373i	−0.0893420	+	0.996001i	$0.528476\pi$
$200$	10.1168	+	5.84096i	0.715369	+	0.413018i
$201$	−10.3139	+	2.42315i	−0.727484	+	0.170916i
$202$	9.48913			0.667653
$203$	−10.1168	+	17.5229i	−0.710063	+	1.22987i
$204$	12.0000	+	12.7692i	0.840168	+	0.894020i
$205$	0.313859	−	0.543620i	0.0219209	−	0.0379681i
$206$	−1.54755	+	0.893477i	−0.107823	+	0.0622515i
$207$		0			0
$208$	0.941578	−	0.543620i	0.0652867	−	0.0376933i
$209$	5.13859			0.355444
$210$	−1.05842	+	3.51039i	−0.0730381	+	0.242240i
$211$	0.755437	−	1.30846i	0.0520065	−	0.0900778i	−0.838850	−	0.544362i	$-0.816772\pi$
$211$	0.755437	−	1.30846i	0.0520065	−	0.0900778i	0.890857	+	0.454284i	$0.150105\pi$
$212$	0.941578	+	1.63086i	0.0646678	+	0.112008i
$213$	−5.68614	−	24.2024i	−0.389608	−	1.65832i
$214$	0.313859	−	0.543620i	0.0214550	−	0.0371611i
$215$	6.86141			0.467944
$216$	8.86141	+	10.6873i	0.602942	+	0.727176i
$217$	18.5475	+	2.92048i	1.25909	+	0.198255i
$218$		−	9.80240i		−	0.663902i
$219$	5.31386	+	22.6179i	0.359077	+	1.52837i
$220$	−1.29211	−	0.746000i	−0.0871140	−	0.0502953i
$221$			12.7692i			0.858947i
$222$	−1.62772	−	1.73205i	−0.109245	−	0.116248i
$223$	−7.50000	−	4.33013i	−0.502237	−	0.289967i	0.227400	−	0.973801i	$-0.426978\pi$
$223$	−7.50000	−	4.33013i	−0.502237	−	0.289967i	−0.729637	+	0.683835i	$0.760311\pi$
$224$	17.0584	+	9.84868i	1.13976	+	0.658043i
$225$	11.7446	−	5.84096i	0.782971	−	0.389398i
$226$	−5.68614	−	9.84868i	−0.378236	−	0.655125i
$227$	−7.80298	+	4.50506i	−0.517902	+	0.299011i	−0.736076	−	0.676899i	$-0.763323\pi$
$227$	−7.80298	+	4.50506i	−0.517902	+	0.299011i	0.218174	+	0.975910i	$0.429990\pi$
$228$	−6.09509	−	6.48577i	−0.403657	−	0.429531i
$229$	14.6168	+	8.43904i	0.965908	+	0.557667i	0.897986	−	0.440023i	$-0.145030\pi$
$229$	14.6168	+	8.43904i	0.965908	+	0.557667i	0.0679219	+	0.997691i	$0.478363\pi$
$230$		0			0
$231$	−2.31386	+	7.67420i	−0.152241	+	0.504926i
$232$		−	16.0309i		−	1.05248i
$233$		−	3.16915i		−	0.207618i	−0.994597	−	0.103809i	$-0.966897\pi$
$233$		−	3.16915i		−	0.207618i	0.994597	−	0.103809i	$-0.0331030\pi$
$234$	−0.255437	+	4.10891i	−0.0166985	+	0.268608i
$235$	2.62772	+	4.55134i	0.171413	+	0.296897i
$236$	−17.0584	−	9.84868i	−1.11041	−	0.641095i
$237$	11.7446	−	11.0371i	0.762891	−	0.716938i
$238$	−17.0584	+	9.84868i	−1.10573	+	0.638395i
$239$	−6.43070	−	11.1383i	−0.415968	−	0.720477i	0.579562	−	0.814928i	$-0.303224\pi$
$239$	−6.43070	−	11.1383i	−0.415968	−	0.720477i	−0.995529	+	0.0944512i	$0.969890\pi$
$240$	0.197015	+	0.838574i	0.0127173	+	0.0541297i
$241$	6.38316	+	3.68532i	0.411175	+	0.237392i	0.691295	−	0.722573i	$-0.257041\pi$
$241$	6.38316	+	3.68532i	0.411175	+	0.237392i	−0.280119	+	0.959965i	$0.590374\pi$
$242$	−6.25544	−	3.61158i	−0.402115	−	0.232161i
$243$	15.5000	−	1.65831i	0.994325	−	0.106381i
$244$		0			0
$245$	3.00000	+	1.73205i	0.191663	+	0.110657i
$246$	1.05842	−	0.248667i	0.0674825	−	0.0158544i
$247$		−	6.48577i		−	0.412680i
$248$	−13.8832	+	5.34363i	−0.881581	+	0.339321i
$249$	22.5475	−	5.29734i	1.42889	−	0.335705i
$250$	−5.88316			−0.372083
$251$	5.31386	−	9.20387i	0.335408	−	0.580943i	−0.648155	−	0.761508i	$-0.724459\pi$
$251$	5.31386	−	9.20387i	0.335408	−	0.580943i	0.983563	+	0.180565i	$0.0577926\pi$
$252$	12.4307	−	6.18220i	0.783061	−	0.389442i
$253$		0			0
$254$	2.56930	−	4.45015i	0.161212	−	0.279227i
$255$	−9.68614	−	2.92048i	−0.606570	−	0.182888i
$256$	−13.8832			−0.867697
$257$	7.54755	−	4.35758i	0.470803	−	0.271818i	−0.245773	−	0.969327i	$-0.579042\pi$
$257$	7.54755	−	4.35758i	0.470803	−	0.271818i	0.716576	+	0.697509i	$0.245708\pi$
$258$	8.13859	+	8.66025i	0.506687	+	0.539164i
$259$	−5.05842	+	2.92048i	−0.314315	+	0.181470i
$260$	−0.941578	+	1.63086i	−0.0583942	+	0.101142i
$261$	−15.0000	−	9.94987i	−0.928477	−	0.615882i
$262$	5.80298	−	10.0511i	0.358510	−	0.620957i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$	−1.45245	−	6.18220i	−0.0893923	−	0.380488i
$265$	−0.941578	−	0.543620i	−0.0578407	−	0.0333943i
$266$	8.66439	−	5.00239i	0.531248	−	0.306716i
$267$	−3.00000	+	9.94987i	−0.183597	+	0.608922i
$268$	−4.19702	−	7.26944i	−0.256374	−	0.444052i
$269$	−6.43070	−	11.1383i	−0.392087	−	0.679114i	0.600638	−	0.799521i	$-0.294913\pi$
$269$	−6.43070	−	11.1383i	−0.392087	−	0.679114i	−0.992725	+	0.120407i	$0.961580\pi$
$270$	−3.05842	−	1.13353i	−0.186130	−	0.0689843i
$271$		−	7.57301i		−	0.460028i	−0.973187	−	0.230014i	$-0.926123\pi$
$271$		−	7.57301i		−	0.460028i	0.973187	−	0.230014i	$-0.0738772\pi$
$272$	−2.31386	+	4.00772i	−0.140298	+	0.243004i
$273$	9.68614	+	2.92048i	0.586232	+	0.176756i
$274$	−7.29211	+	4.21010i	−0.440532	+	0.254342i
$275$	−6.00000			−0.361814
$276$		0			0
$277$			17.9653i			1.07943i	0.841847	+	0.539716i	$0.181468\pi$
$277$			17.9653i			1.07943i	−0.841847	+	0.539716i	$0.818532\pi$
$278$	−8.23369			−0.493824
$279$	−3.61684	+	16.3070i	−0.216535	+	0.976275i
$280$	−7.13859			−0.426613
$281$		−	18.3152i		−	1.09259i	−0.837592	−	0.546296i	$-0.816037\pi$
$281$		−	18.3152i		−	1.09259i	0.837592	−	0.546296i	$-0.183963\pi$
$282$	−2.62772	+	8.71516i	−0.156478	+	0.518980i
$283$	−25.3505			−1.50693			−0.753466	−	0.657486i	$-0.771620\pi$
$283$	−25.3505			−1.50693			−0.753466	+	0.657486i	$0.771620\pi$
$284$	17.0584	−	9.84868i	1.01223	−	0.584412i
$285$	4.91983	+	1.48338i	0.291425	+	0.0878681i
$286$	0.941578	−	1.63086i	0.0556767	−	0.0964348i
$287$		−	2.67181i		−	0.157712i
$288$	−9.68614	+	14.6024i	−0.570761	+	0.860455i
$289$	−18.6753	−	32.3465i	−1.09855	−	1.90274i
$290$	1.88316	+	3.26172i	0.110583	+	0.191535i
$291$	0.186141	−	0.617359i	0.0109118	−	0.0361902i
$292$	−15.9416	+	9.20387i	−0.932910	+	0.538616i
$293$	−14.3139	−	8.26411i	−0.836225	−	0.482794i	0.0197545	−	0.999805i	$-0.493712\pi$
$293$	−14.3139	−	8.26411i	−0.836225	−	0.482794i	−0.855979	+	0.517010i	$0.827045\pi$
$294$	1.37228	+	5.84096i	0.0800331	+	0.340652i
$295$	11.3723			0.662120
$296$	2.31386	−	4.00772i	0.134490	−	0.232944i
$297$	−6.68614	−	2.47805i	−0.387969	−	0.143791i
$298$	1.68614	−	2.92048i	0.0976755	−	0.169179i
$299$		0			0
$300$	7.11684	+	7.57301i	0.410891	+	0.437228i
$301$	25.2921	−	14.6024i	1.45781	−	0.841669i
$302$	10.4674			0.602330
$303$	19.8614	+	5.98844i	1.14101	+	0.344027i
$304$	1.17527	−	2.03562i	0.0674061	−	0.116751i
$305$		0			0
$306$	−7.80298	−	15.6896i	−0.446067	−	0.896917i
$307$	7.87228	−	13.6352i	0.449295	−	0.778201i	−0.549045	−	0.835793i	$-0.685009\pi$
$307$	7.87228	−	13.6352i	0.449295	−	0.778201i	0.998340	+	0.0575910i	$0.0183419\pi$
$308$	−6.35053			−0.361855
$309$	−3.80298	+	0.893477i	−0.216344	+	0.0508281i
$310$	2.19702	−	2.71810i	0.124782	−	0.154378i
$311$		−	4.05401i		−	0.229882i	−0.993372	−	0.114941i	$-0.963332\pi$
$311$		−	4.05401i		−	0.229882i	0.993372	−	0.114941i	$-0.0366679\pi$
$312$	−7.80298	+	1.83324i	−0.441757	+	0.103787i
$313$	14.6168	+	8.43904i	0.826193	+	0.477003i	0.852547	−	0.522650i	$-0.175057\pi$
$313$	14.6168	+	8.43904i	0.826193	+	0.477003i	−0.0263545	+	0.999653i	$0.508390\pi$
$314$		−	9.80240i		−	0.553181i
$315$	−4.43070	+	6.67954i	−0.249642	+	0.376349i
$316$	11.0584	+	6.38458i	0.622085	+	0.359161i
$317$	−21.4307	−	12.3730i	−1.20367	−	0.694938i	−0.242299	−	0.970202i	$-0.577902\pi$
$317$	−21.4307	−	12.3730i	−1.20367	−	0.694938i	−0.961369	+	0.275263i	$0.911235\pi$
$318$	−0.430703	−	1.83324i	−0.0241526	−	0.102803i
$319$	4.11684	+	7.13058i	0.230499	+	0.399236i
$320$	2.31386	−	1.33591i	0.129349	−	0.0746795i
$321$	1.00000	−	0.939764i	0.0558146	−	0.0524525i
$322$		0			0
$323$	13.8030	+	23.9075i	0.768019	+	1.33025i
$324$	4.80298	+	11.3784i	0.266832	+	0.632131i
$325$			7.57301i			0.420075i
$326$		−	5.04868i		−	0.279620i
$327$	6.18614	−	20.5171i	0.342094	−	1.13460i
$328$	1.05842	+	1.83324i	0.0584416	+	0.101224i
$329$	19.3723	+	11.1846i	1.06803	+	0.616627i
$330$	1.02175	+	1.08724i	0.0562455	+	0.0598506i
$331$	1.50000	−	0.866025i	0.0824475	−	0.0476011i	−0.458209	−	0.888844i	$-0.651509\pi$
$331$	1.50000	−	0.866025i	0.0824475	−	0.0476011i	0.540657	+	0.841243i	$0.318176\pi$
$332$	9.17527	+	15.8920i	0.503558	+	0.872188i
$333$	−2.31386	−	4.65253i	−0.126799	−	0.254957i
$334$	−7.29211	−	4.21010i	−0.399007	−	0.230367i
$335$	4.19702	+	2.42315i	0.229307	+	0.132391i
$336$	2.51087	+	2.67181i	0.136979	+	0.145759i
$337$			30.2921i			1.65011i	0.565050	+	0.825057i	$0.308857\pi$
$337$			30.2921i			1.65011i	−0.565050	+	0.825057i	$0.691143\pi$
$338$	6.86141	+	3.96143i	0.373211	+	0.215474i
$339$	−5.68614	−	24.2024i	−0.308829	−	1.31450i
$340$		−	8.01544i		−	0.434698i
$341$	4.80298	−	5.94215i	0.260096	−	0.321786i
$342$	3.96333	+	7.96916i	0.214312	+	0.430923i
$343$	−8.86141			−0.478471
$344$	−11.5693	+	20.0386i	−0.623775	+	1.08041i
$345$		0			0
$346$	3.56930	+	6.18220i	0.191887	+	0.332357i
$347$	−0.686141	+	1.18843i	−0.0368340	+	0.0637983i	−0.883855	−	0.467762i	$-0.845061\pi$
$347$	−0.686141	+	1.18843i	−0.0368340	+	0.0637983i	0.847021	+	0.531560i	$0.178394\pi$
$348$	4.11684	−	13.6540i	0.220686	−	0.731933i
$349$	−5.11684			−0.273898			−0.136949	−	0.990578i	$-0.543730\pi$
$349$	−5.11684			−0.273898			−0.136949	+	0.990578i	$0.543730\pi$
$350$	−10.1168	+	5.84096i	−0.540768	+	0.312213i
$351$	−3.12772	+	8.43904i	−0.166945	+	0.450443i
$352$	6.94158	−	4.00772i	0.369987	−	0.213612i
$353$	−9.68614	+	16.7769i	−0.515541	+	0.892944i	0.484296	+	0.874904i	$0.339076\pi$
$353$	−9.68614	+	16.7769i	−0.515541	+	0.892944i	−0.999837	+	0.0180394i	$0.994258\pi$
$354$	13.4891	+	14.3537i	0.716939	+	0.762893i
$355$	−5.68614	+	9.84868i	−0.301789	+	0.522714i
$356$	−8.23369			−0.436385
$357$	−41.9198	+	9.84868i	−2.21863	+	0.521248i
$358$	9.17527	+	5.29734i	0.484928	+	0.279973i
$359$	−18.6861	+	10.7884i	−0.986217	+	0.569393i	−0.904141	−	0.427234i	$-0.859488\pi$
$359$	−18.6861	+	10.7884i	−0.986217	+	0.569393i	−0.0820755	+	0.996626i	$0.526155\pi$
$360$	0.394031	−	6.33830i	0.0207672	−	0.334058i
$361$	2.48913	+	4.31129i	0.131007	+	0.226910i
$362$	5.31386	+	9.20387i	0.279290	+	0.483745i
$363$	−10.8139	−	11.5070i	−0.567580	−	0.603961i
$364$			8.01544i			0.420123i
$365$	5.31386	−	9.20387i	0.278140	−	0.481753i
$366$		0			0
$367$	22.8505	−	13.1928i	1.19279	−	0.688657i	0.233850	−	0.972273i	$-0.424867\pi$
$367$	22.8505	−	13.1928i	1.19279	−	0.688657i	0.958938	+	0.283616i	$0.0915341\pi$
$368$		0			0
$369$	2.37228	+	0.147477i	0.123496	+	0.00767734i
$370$			1.08724i			0.0565229i
$371$	−4.62772			−0.240259
$372$	−13.1970	+	0.986051i	−0.684233	+	0.0511244i
$373$	−13.8614			−0.717716			−0.358858	−	0.933392i	$-0.616834\pi$
$373$	−13.8614			−0.717716			−0.358858	+	0.933392i	$0.616834\pi$
$374$			8.01544i			0.414469i
$375$	−12.3139	−	3.71277i	−0.635885	−	0.191727i
$376$	−17.7228			−0.913984
$377$	9.00000	−	5.19615i	0.463524	−	0.267615i
$378$	−13.6861	+	2.33057i	−0.703939	+	0.119872i
$379$	4.61684	−	7.99661i	0.237151	−	0.410758i	−0.722744	−	0.691115i	$-0.757120\pi$
$379$	4.61684	−	7.99661i	0.237151	−	0.410758i	0.959896	+	0.280357i	$0.0904529\pi$
$380$			4.07124i			0.208850i
$381$	8.18614	−	7.69304i	0.419389	−	0.394126i
$382$	8.54755	+	14.8048i	0.437331	+	0.757479i
$383$	0.686141	+	1.18843i	0.0350602	+	0.0607260i	0.883023	−	0.469330i	$-0.155504\pi$
$383$	0.686141	+	1.18843i	0.0350602	+	0.0607260i	−0.847963	+	0.530056i	$0.822171\pi$
$384$	−14.9416	−	4.50506i	−0.762484	−	0.229898i
$385$	3.17527	−	1.83324i	0.161827	−	0.0934306i
$386$	−6.68614	−	3.86025i	−0.340316	−	0.196481i
$387$	11.5693	+	23.2627i	0.588100	+	1.18251i
$388$	0.510875			0.0259357
$389$	8.31386	−	14.4000i	0.421529	−	0.730110i	−0.574560	−	0.818463i	$-0.694827\pi$
$389$	8.31386	−	14.4000i	0.421529	−	0.730110i	0.996089	+	0.0883522i	$0.0281601\pi$
$390$	1.37228	−	1.28962i	0.0694882	−	0.0653025i
$391$		0			0
$392$	−10.1168	+	5.84096i	−0.510978	+	0.295013i
$393$	18.4891	−	17.3754i	0.932653	−	0.876474i
$394$	10.7079	−	6.18220i	0.539456	−	0.311455i
$395$	−7.37228			−0.370940
$396$	0.350532	−	5.63858i	0.0176149	−	0.283349i
$397$	−10.6861	+	18.5089i	−0.536322	+	0.928937i	0.462776	+	0.886475i	$0.346853\pi$
$397$	−10.6861	+	18.5089i	−0.536322	+	0.928937i	−0.999098	+	0.0424618i	$0.986480\pi$
$398$	6.43070	+	11.1383i	0.322342	+	0.558313i
$399$	21.2921	−	5.00239i	1.06594	−	0.250433i
$400$	−1.37228	+	2.37686i	−0.0686141	+	0.118843i
$401$	−20.2337			−1.01042			−0.505211	−	0.862996i	$-0.668585\pi$
$401$	−20.2337			−1.01042			−0.505211	+	0.862996i	$0.668585\pi$
$402$	1.91983	+	8.17154i	0.0957523	+	0.407559i
$403$	−7.50000	−	6.06218i	−0.373602	−	0.301979i
$404$			16.4356i			0.817704i
$405$	−5.68614	−	4.30268i	−0.282547	−	0.213802i
$406$	13.8832	+	8.01544i	0.689009	+	0.397800i
$407$			2.37686i			0.117817i
$408$	24.8614	−	23.3639i	1.23082	−	1.15668i
$409$	−3.38316	−	1.95327i	−0.167286	−	0.0965828i	0.414019	−	0.910268i	$-0.364125\pi$
$409$	−3.38316	−	1.95327i	−0.167286	−	0.0965828i	−0.581306	+	0.813685i	$0.697458\pi$
$410$	−0.430703	−	0.248667i	−0.0212709	−	0.0122808i
$411$	−17.9198	+	4.21010i	−0.883920	+	0.207669i
$412$	−1.54755	−	2.68043i	−0.0762422	−	0.132055i
$413$	41.9198	−	24.2024i	2.06274	−	1.19092i
$414$		0			0
$415$	−9.17527	−	5.29734i	−0.450396	−	0.260036i
$416$	−5.05842	−	8.76144i	−0.248010	−	0.429565i
$417$	−17.2337	−	5.19615i	−0.843937	−	0.254457i
$418$		−	4.07124i		−	0.199131i
$419$			11.0920i			0.541881i	0.962596	+	0.270940i	$0.0873346\pi$
$419$			11.0920i			0.541881i	−0.962596	+	0.270940i	$0.912665\pi$
$420$	−6.08017	−	1.83324i	−0.296682	−	0.0894530i
$421$	7.31386	+	12.6680i	0.356456	+	0.617399i	0.987366	−	0.158456i	$-0.0506517\pi$
$421$	7.31386	+	12.6680i	0.356456	+	0.617399i	−0.630910	+	0.775856i	$0.717318\pi$
$422$	−1.03667	−	0.598523i	−0.0504644	−	0.0291357i
$423$	−11.0000	+	16.5831i	−0.534838	+	0.806299i
$424$	3.17527	−	1.83324i	0.154205	−	0.0890300i
$425$	−16.1168	−	27.9152i	−0.781782	−	1.35409i
$426$	−19.1753	+	4.50506i	−0.929045	+	0.218271i
$427$		0			0
$428$	0.941578	+	0.543620i	0.0455129	+	0.0262769i
$429$	3.00000	−	2.81929i	0.144841	−	0.136117i
$430$		−	5.43620i		−	0.262157i
$431$	−0.430703	−	0.248667i	−0.0207462	−	0.0119779i	0.489591	−	0.871952i	$-0.337146\pi$
$431$	−0.430703	−	0.248667i	−0.0207462	−	0.0119779i	−0.510337	+	0.859974i	$0.670479\pi$
$432$	−2.51087	+	2.08191i	−0.120805	+	0.100166i
$433$		−	38.7499i		−	1.86220i	−0.364761	−	0.931101i	$-0.618849\pi$
$433$		−	38.7499i		−	1.86220i	0.364761	−	0.931101i	$-0.381151\pi$
$434$	2.31386	−	14.6950i	0.111069	−	0.705382i
$435$	1.88316	+	8.01544i	0.0902904	+	0.384311i
$436$	16.9783			0.813111
$437$		0			0
$438$	17.9198	−	4.21010i	0.856243	−	0.201166i
$439$	5.98913	+	10.3735i	0.285845	+	0.495099i	0.972814	−	0.231589i	$-0.0743923\pi$
$439$	5.98913	+	10.3735i	0.285845	+	0.495099i	−0.686968	+	0.726687i	$0.741059\pi$
$440$	−1.45245	+	2.51572i	−0.0692430	+	0.119932i
$441$	−0.813859	+	13.0916i	−0.0387552	+	0.623408i
$442$	10.1168			0.481209
$443$	−5.56930	+	3.21543i	−0.264605	+	0.152770i	−0.626434	−	0.779475i	$-0.715486\pi$
$443$	−5.56930	+	3.21543i	−0.264605	+	0.152770i	0.361828	+	0.932245i	$0.382153\pi$
$444$	3.00000	−	2.81929i	0.142374	−	0.133798i
$445$	4.11684	−	2.37686i	0.195157	−	0.112674i
$446$	−3.43070	+	5.94215i	−0.162449	+	0.281369i
$447$	5.37228	−	5.04868i	0.254100	−	0.238794i
$448$	5.68614	−	9.84868i	0.268645	−	0.465307i
$449$	−3.76631			−0.177743			−0.0888716	−	0.996043i	$-0.528326\pi$
$449$	−3.76631			−0.177743			−0.0888716	+	0.996043i	$0.528326\pi$
$450$	−4.62772	−	9.30506i	−0.218153	−	0.438645i
$451$	−0.941578	−	0.543620i	−0.0443372	−	0.0255981i
$452$	17.0584	−	9.84868i	0.802361	−	0.463243i
$453$	21.9090	+	6.60580i	1.02937	+	0.310367i
$454$	3.56930	+	6.18220i	0.167515	+	0.290145i
$455$	−2.31386	−	4.00772i	−0.108475	−	0.187885i
$456$	−12.6277	+	11.8671i	−0.591347	+	0.555727i
$457$		−	2.81929i		−	0.131881i	−0.997824	−	0.0659404i	$-0.978995\pi$
$457$		−	2.81929i		−	0.131881i	0.997824	−	0.0659404i	$-0.0210047\pi$
$458$	6.68614	−	11.5807i	0.312423	−	0.541132i
$459$	−6.43070	−	37.7639i	−0.300160	−	1.76267i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	6.08017	+	1.83324i	0.282875	+	0.0852901i
$463$			28.3576i			1.31789i	0.752191	+	0.658945i	$0.228997\pi$
$463$			28.3576i			1.31789i	−0.752191	+	0.658945i	$0.771003\pi$
$464$	3.76631			0.174847
$465$	6.31386	−	4.30268i	0.292798	−	0.199532i
$466$	−2.51087			−0.116314
$467$			22.3692i			1.03512i	0.855646	+	0.517561i	$0.173160\pi$
$467$			22.3692i			1.03512i	−0.855646	+	0.517561i	$0.826840\pi$
$468$	−7.11684	−	0.442430i	−0.328976	−	0.0204514i
$469$	20.6277			0.952500
$470$	3.60597	−	2.08191i	0.166331	−	0.0960312i
$471$	6.18614	−	20.5171i	0.285042	−	0.945378i
$472$	−19.1753	+	33.2125i	−0.882613	+	1.52873i
$473$		−	11.8843i		−	0.546441i
$474$	−8.74456	−	9.30506i	−0.401651	−	0.427396i
$475$	8.18614	+	14.1788i	0.375606	+	0.650568i
$476$	−17.0584	−	29.5461i	−0.781871	−	1.35424i
$477$	0.255437	−	4.10891i	0.0116957	−	0.188134i
$478$	−8.82473	+	5.09496i	−0.403634	+	0.233038i
$479$	5.56930	+	3.21543i	0.254468	+	0.146917i	0.621808	−	0.783170i	$-0.286398\pi$
$479$	5.56930	+	3.21543i	0.254468	+	0.146917i	−0.367341	+	0.930086i	$0.619732\pi$
$480$	7.80298	−	1.83324i	0.356156	−	0.0836756i
$481$	3.00000			0.136788
$482$	2.91983	−	5.05729i	0.132995	−	0.230353i
$483$		0			0
$484$	6.25544	−	10.8347i	0.284338	−	0.492488i
$485$	−0.255437	+	0.147477i	−0.0115988	+	0.00669658i
$486$	−1.31386	−	12.2804i	−0.0595979	−	0.557052i
$487$	6.38316	−	3.68532i	0.289248	−	0.166998i	−0.348354	−	0.937363i	$-0.613259\pi$
$487$	6.38316	−	3.68532i	0.289248	−	0.166998i	0.637603	+	0.770365i	$0.279926\pi$
$488$		0			0
$489$	3.18614	−	10.5672i	0.144082	−	0.477867i
$490$	1.37228	−	2.37686i	0.0619934	−	0.107376i
$491$	5.56930	+	9.64630i	0.251339	+	0.435332i	0.963895	−	0.266284i	$-0.0857958\pi$
$491$	5.56930	+	9.64630i	0.251339	+	0.435332i	−0.712556	+	0.701615i	$0.752462\pi$
$492$	0.430703	+	1.83324i	0.0194176	+	0.0826489i
$493$	−22.1168	+	38.3075i	−0.996093	+	1.72528i
$494$	−5.13859			−0.231196
$495$	1.45245	+	2.92048i	0.0652829	+	0.131266i
$496$	−1.25544	−	3.26172i	−0.0563708	−	0.146456i
$497$			48.4048i			2.17125i
$498$	−4.19702	−	17.8641i	−0.188073	−	0.800511i
$499$	8.05842	+	4.65253i	0.360745	+	0.208276i	0.669407	−	0.742896i	$-0.266548\pi$
$499$	8.05842	+	4.65253i	0.360745	+	0.208276i	−0.308663	+	0.951172i	$0.599881\pi$
$500$		−	10.1899i		−	0.455707i
$501$	−12.6060	−	13.4140i	−0.563193	−	0.599292i
$502$	−7.29211	−	4.21010i	−0.325463	−	0.187906i
$503$	−30.4307	−	17.5692i	−1.35684	−	0.783371i	−0.367642	−	0.929968i	$-0.619835\pi$
$503$	−30.4307	−	17.5692i	−1.35684	−	0.783371i	−0.989196	+	0.146597i	$0.953168\pi$
$504$	−12.0367	−	24.2024i	−0.536156	−	1.07806i
$505$	−4.74456	−	8.21782i	−0.211130	−	0.365688i
$506$		0			0
$507$	11.8614	+	12.6217i	0.526784	+	0.560549i
$508$	7.70789	+	4.45015i	0.341982	+	0.197444i
$509$	−6.43070	−	11.1383i	−0.285036	−	0.493697i	0.687582	−	0.726107i	$-0.258672\pi$
$509$	−6.43070	−	11.1383i	−0.285036	−	0.493697i	−0.972618	+	0.232410i	$0.925339\pi$
$510$	−2.31386	+	7.67420i	−0.102459	+	0.339819i
$511$		−	45.2357i		−	2.00111i
$512$		−	7.02078i		−	0.310277i
$513$	3.26631	+	19.1812i	0.144211	+	0.846871i
$514$	−3.45245	−	5.97982i	−0.152281	−	0.263759i
$515$	1.54755	+	0.893477i	0.0681931	+	0.0393713i
$516$	−15.0000	+	14.0965i	−0.660338	+	0.620562i
$517$	7.88316	−	4.55134i	0.346701	−	0.200168i
$518$	2.31386	+	4.00772i	0.101665	+	0.176089i
$519$	3.56930	+	15.1923i	0.156675	+	0.666869i
$520$	3.17527	+	1.83324i	0.139245	+	0.0803929i
$521$	−9.43070	−	5.44482i	−0.413167	−	0.238542i	0.278983	−	0.960296i	$-0.410003\pi$
$521$	−9.43070	−	5.44482i	−0.413167	−	0.238542i	−0.692149	+	0.721754i	$0.743336\pi$
$522$	−7.88316	+	11.8843i	−0.345036	+	0.520162i
$523$			19.8997i			0.870155i	0.900393	+	0.435078i	$0.143279\pi$
$523$			19.8997i			0.870155i	−0.900393	+	0.435078i	$0.856721\pi$
$524$	17.4090	+	10.0511i	0.760514	+	0.439083i
$525$	−24.8614	+	5.84096i	−1.08504	+	0.254921i
$526$		−	19.0149i		−	0.829089i
$527$	40.5475	+	6.38458i	1.76628	+	0.278117i
$528$	1.45245	−	0.341241i	0.0632099	−	0.0148506i
$529$	−23.0000			−1.00000
$530$	−0.430703	+	0.746000i	−0.0187086	+	0.0324042i
$531$	19.1753	+	38.5562i	0.832136	+	1.67320i
$532$	8.66439	+	15.0072i	0.375649	+	0.650643i
$533$	−0.686141	+	1.18843i	−0.0297201	+	0.0514766i
$534$	7.88316	+	2.37686i	0.341138	+	0.102857i
$535$	−0.627719			−0.0271386
$536$	−14.1535	+	8.17154i	−0.611339	+	0.352957i
$537$	15.8614	+	16.8781i	0.684470	+	0.728343i
$538$	−8.82473	+	5.09496i	−0.380461	+	0.219659i
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$	1.96333	−	5.29734i	0.0844882	−	0.227961i
$541$	17.9891	−	31.1581i	0.773413	−	1.33959i	−0.162269	−	0.986747i	$-0.551881\pi$
$541$	17.9891	−	31.1581i	0.773413	−	1.33959i	0.935682	−	0.352844i	$-0.114785\pi$
$542$	−6.00000			−0.257722
$543$	5.31386	+	22.6179i	0.228040	+	0.970625i
$544$	37.2921	+	21.5306i	1.59889	+	0.923117i
$545$	−8.48913	+	4.90120i	−0.363634	+	0.209944i
$546$	2.31386	−	7.67420i	0.0990240	−	0.328426i
$547$	−21.3614	−	36.9990i	−0.913348	−	1.58196i	−0.809302	−	0.587392i	$-0.800155\pi$
$547$	−21.3614	−	36.9990i	−0.913348	−	1.58196i	−0.104045	−	0.994573i	$-0.533179\pi$
$548$	−7.29211	−	12.6303i	−0.311503	−	0.539540i
$549$		0			0
$550$			4.75372i			0.202699i
$551$	11.2337	−	19.4573i	0.478571	−	0.828910i
$552$		0			0
$553$	−27.1753	+	15.6896i	−1.15561	+	0.667192i
$554$	14.2337			0.604731
$555$	−0.686141	+	2.27567i	−0.0291250	+	0.0965969i
$556$		−	14.2612i		−	0.604808i
$557$	20.2337			0.857329			0.428664	−	0.903464i	$-0.358984\pi$
$557$	20.2337			0.857329			0.428664	+	0.903464i	$0.358984\pi$
$558$	12.9198	+	2.86558i	0.546940	+	0.121310i
$559$	−15.0000			−0.634432
$560$		−	1.67715i		−	0.0708724i
$561$	−5.05842	+	16.7769i	−0.213567	+	0.708321i
$562$	−14.5109			−0.612104
$563$	17.3139	−	9.99616i	0.729692	−	0.421288i	−0.0886174	−	0.996066i	$-0.528245\pi$
$563$	17.3139	−	9.99616i	0.729692	−	0.421288i	0.818310	+	0.574778i	$0.194912\pi$
$564$	−15.0951	−	4.55134i	−0.635618	−	0.191646i
$565$	−5.68614	+	9.84868i	−0.239218	+	0.414337i
$566$			20.0849i			0.844231i
$567$	−30.1168	−	3.75906i	−1.26479	−	0.157865i
$568$	−19.1753	−	33.2125i	−0.804576	−	1.39357i
$569$	13.8030	+	23.9075i	0.578651	+	1.00225i	0.995634	+	0.0933391i	$0.0297541\pi$
$569$	13.8030	+	23.9075i	0.578651	+	1.00225i	−0.416983	+	0.908914i	$0.636913\pi$
$570$	1.17527	−	3.89792i	0.0492265	−	0.163266i
$571$	6.38316	−	3.68532i	0.267127	−	0.154226i	−0.360454	−	0.932777i	$-0.617378\pi$
$571$	6.38316	−	3.68532i	0.267127	−	0.154226i	0.627581	+	0.778551i	$0.284045\pi$
$572$	2.82473	+	1.63086i	0.118108	+	0.0681897i
$573$	8.54755	+	36.3817i	0.357079	+	1.51987i
$574$	−2.11684			−0.0883554
$575$		0			0
$576$	8.43070	+	5.59230i	0.351279	+	0.233012i
$577$	16.0584	−	27.8140i	0.668521	−	1.15791i	−0.309797	−	0.950803i	$-0.600261\pi$
$577$	16.0584	−	27.8140i	0.668521	−	1.15791i	0.978318	−	0.207109i	$-0.0664056\pi$
$578$	−25.6277	+	14.7962i	−1.06597	+	0.615440i
$579$	−11.5584	−	12.2993i	−0.480352	−	0.511141i
$580$	−5.64947	+	3.26172i	−0.234581	+	0.135436i
$581$	−45.0951			−1.87086
$582$	−0.489125	−	0.147477i	−0.0202749	−	0.00611311i
$583$	−0.941578	+	1.63086i	−0.0389962	+	0.0675434i
$584$	17.9198	+	31.0381i	0.741528	+	1.28436i
$585$	3.68614	−	1.83324i	0.152403	−	0.0757952i
$586$	−6.54755	+	11.3407i	−0.270477	+	0.468479i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$	−10.1168	+	2.37686i	−0.417212	+	0.0980201i
$589$	−20.5951	−	3.24289i	−0.848606	−	0.133621i
$590$		−	9.01011i		−	0.370940i
$591$	26.3139	−	6.18220i	1.08241	−	0.254302i
$592$	0.941578	+	0.543620i	0.0386986	+	0.0223427i
$593$			36.6303i			1.50423i	0.659033	+	0.752114i	$0.270966\pi$
$593$			36.6303i			1.50423i	−0.659033	+	0.752114i	$0.729034\pi$
$594$	−1.96333	+	5.29734i	−0.0805563	+	0.217353i
$595$	17.0584	+	9.84868i	0.699327	+	0.403757i
$596$	5.05842	+	2.92048i	0.207201	+	0.119628i
$597$	6.43070	+	27.3716i	0.263191	+	1.12024i
$598$		0			0
$599$	−18.6861	+	10.7884i	−0.763495	+	0.440804i	−0.830549	−	0.556945i	$-0.811973\pi$
$599$	−18.6861	+	10.7884i	−0.763495	+	0.440804i	0.0670542	+	0.997749i	$0.478640\pi$
$600$	14.7446	−	13.8564i	0.601944	−	0.565685i
$601$	−27.1753	−	15.6896i	−1.10850	−	0.639994i	−0.170061	−	0.985434i	$-0.554397\pi$
$601$	−27.1753	−	15.6896i	−1.10850	−	0.639994i	−0.938441	+	0.345439i	$0.887730\pi$
$602$	−11.5693	−	20.0386i	−0.471529	−	0.816713i
$603$	−1.13859	+	18.3152i	−0.0463671	+	0.745852i
$604$			18.1300i			0.737700i
$605$			7.22316i			0.293663i
$606$	4.74456	−	15.7359i	0.192735	−	0.639229i
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	0.732551	−	0.680712i	$-0.238329\pi$
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	−0.955789	+	0.294052i	$0.904996\pi$
$608$	−18.9416	−	10.9359i	−0.768182	−	0.443510i
$609$	24.0000	+	25.5383i	0.972529	+	1.03487i
$610$		0			0
$611$	−5.74456	−	9.94987i	−0.232400	−	0.402529i
$612$	27.1753	−	13.5152i	1.09850	−	0.546318i
$613$	−29.6168	−	17.0993i	−1.19621	−	0.690634i	−0.236504	−	0.971630i	$-0.576002\pi$
$613$	−29.6168	−	17.0993i	−1.19621	−	0.690634i	−0.959709	+	0.280997i	$0.909335\pi$
$614$	−10.8030	−	6.23711i	−0.435973	−	0.251709i
$615$	−0.744563	−	0.792287i	−0.0300237	−	0.0319481i
$616$			12.3644i			0.498176i
$617$	25.0367	+	14.4549i	1.00794	+	0.581934i	0.910587	−	0.413317i	$-0.135630\pi$
$617$	25.0367	+	14.4549i	1.00794	+	0.581934i	0.0973511	+	0.995250i	$0.468963\pi$
$618$	0.707890	+	3.01306i	0.0284755	+	0.121203i
$619$			28.3576i			1.13979i	0.821718	+	0.569895i	$0.193016\pi$
$619$			28.3576i			1.13979i	−0.821718	+	0.569895i	$0.806984\pi$
$620$	4.70789	+	3.80534i	0.189073	+	0.152826i
$621$		0			0
$622$	−3.21194			−0.128787
$623$	10.1168	−	17.5229i	0.405323	−	0.702040i
$624$	−0.430703	−	1.83324i	−0.0172419	−	0.0733884i
$625$	−7.98913	−	13.8376i	−0.319565	−	0.553503i
$626$	6.68614	−	11.5807i	0.267232	−	0.462859i
$627$	2.56930	−	8.52139i	0.102608	−	0.340312i
$628$	16.9783			0.677506
$629$	−11.0584	+	6.38458i	−0.440928	+	0.254570i
$630$	5.29211	+	3.51039i	0.210843	+	0.139857i
$631$	−14.0584	+	8.11663i	−0.559657	+	0.323118i	−0.753008	−	0.658012i	$-0.771398\pi$
$631$	−14.0584	+	8.11663i	−0.559657	+	0.323118i	0.193351	+	0.981130i	$0.438064\pi$
$632$	12.4307	−	21.5306i	0.494467	−	0.856442i
$633$	−1.79211	−	1.90698i	−0.0712300	−	0.0757956i
$634$	−9.80298	+	16.9793i	−0.389326	+	0.674333i
$635$	−5.13859			−0.203919
$636$	3.17527	−	0.746000i	0.125907	−	0.0295808i
$637$	−6.55842	−	3.78651i	−0.259854	−	0.150027i
$638$	5.64947	−	3.26172i	0.223665	−	0.129133i
$639$	−42.9783	−	2.67181i	−1.70019	−	0.105695i
$640$	3.56930	+	6.18220i	0.141089	+	0.244373i
$641$	−11.3139	−	19.5962i	−0.446871	−	0.774003i	0.551310	−	0.834301i	$-0.314128\pi$
$641$	−11.3139	−	19.5962i	−0.446871	−	0.774003i	−0.998180	+	0.0602980i	$0.980795\pi$
$642$	−0.744563	−	0.792287i	−0.0293855	−	0.0312691i
$643$			1.93443i			0.0762865i	0.999272	+	0.0381432i	$0.0121443\pi$
$643$			1.93443i			0.0762865i	−0.999272	+	0.0381432i	$0.987856\pi$
$644$		0			0
$645$	3.43070	−	11.3784i	0.135084	−	0.448022i
$646$	18.9416	−	10.9359i	0.745246	−	0.430268i
$647$	−2.23369			−0.0878153			−0.0439077	−	0.999036i	$-0.513981\pi$
$647$	−2.23369			−0.0878153			−0.0439077	+	0.999036i	$0.513981\pi$
$648$	22.1535	−	9.35135i	0.870272	−	0.367356i
$649$		−	19.6974i		−	0.773189i
$650$	6.00000			0.235339
$651$	14.1168	−	29.2974i	0.553283	−	1.14826i
$652$	8.74456			0.342464
$653$		−	1.87953i		−	0.0735516i	−0.999324	−	0.0367758i	$-0.988291\pi$
$653$		−	1.87953i		−	0.0735516i	0.999324	−	0.0367758i	$-0.0117087\pi$
$654$	−16.2554	−	4.90120i	−0.635638	−	0.191652i
$655$	−11.6060			−0.453483
$656$	−0.430703	+	0.248667i	−0.0168161	+	0.00970880i
$657$	40.1644	+	2.49689i	1.56696	+	0.0974128i
$658$	8.86141	−	15.3484i	0.345454	−	0.598343i
$659$		−	13.5615i		−	0.528279i	−0.964484	−	0.264140i	$-0.914912\pi$
$659$		−	13.5615i		−	0.528279i	0.964484	−	0.264140i	$-0.0850880\pi$
$660$	−1.88316	+	1.76972i	−0.0733017	+	0.0688863i
$661$	5.98913	+	10.3735i	0.232950	+	0.403481i	0.958675	−	0.284504i	$-0.0918288\pi$
$661$	5.98913	+	10.3735i	0.232950	+	0.403481i	−0.725725	+	0.687985i	$0.758495\pi$
$662$	−0.686141	−	1.18843i	−0.0266676	−	0.0461897i
$663$	21.1753	+	6.38458i	0.822379	+	0.247957i
$664$	30.9416	−	17.8641i	1.20077	−	0.693263i
$665$	−8.66439	−	5.00239i	−0.335991	−	0.193984i
$666$	−3.68614	+	1.83324i	−0.142835	+	0.0710366i
$667$		0			0
$668$	7.29211	−	12.6303i	0.282140	−	0.488681i
$669$	−10.9307	+	10.2723i	−0.422605	+	0.397149i
$670$	1.91983	−	3.32524i	0.0741694	−	0.128465i
$671$		0			0
$672$	24.8614	−	23.3639i	0.959050	−	0.901280i
$673$	7.29211	−	4.21010i	0.281090	−	0.162287i	−0.352827	−	0.935689i	$-0.614779\pi$
$673$	7.29211	−	4.21010i	0.281090	−	0.162287i	0.633917	+	0.773401i	$0.281446\pi$
$674$	24.0000			0.924445
$675$	−3.81386	−	22.3966i	−0.146796	−	0.862047i
$676$	−6.86141	+	11.8843i	−0.263900	+	0.457089i
$677$	20.9198	+	36.2342i	0.804014	+	1.39259i	0.916954	+	0.398992i	$0.130640\pi$
$677$	20.9198	+	36.2342i	0.804014	+	1.39259i	−0.112940	+	0.993602i	$0.536027\pi$
$678$	−19.1753	+	4.50506i	−0.736422	+	0.173016i
$679$	−0.627719	+	1.08724i	−0.0240896	+	0.0417245i
$680$	−15.6060			−0.598462
$681$	3.56930	+	15.1923i	0.136776	+	0.582171i
$682$	−4.70789	−	3.80534i	−0.180274	−	0.145714i
$683$			11.0920i			0.424424i	0.977224	+	0.212212i	$0.0680668\pi$
$683$			11.0920i			0.424424i	−0.977224	+	0.212212i	$0.931933\pi$
$684$	−13.8030	+	6.86468i	−0.527770	+	0.262478i
$685$	7.29211	+	4.21010i	0.278617	+	0.160860i
$686$			7.02078i			0.268055i
$687$	21.3030	−	20.0198i	0.812760	−	0.763802i
$688$	−4.70789	−	2.71810i	−0.179487	−	0.103627i
$689$	2.05842	+	1.18843i	0.0784196	+	0.0452756i
$690$		0			0
$691$	14.4307	+	24.9947i	0.548970	+	0.950844i	0.998345	+	0.0575007i	$0.0183132\pi$
$691$	14.4307	+	24.9947i	0.548970	+	0.950844i	−0.449376	+	0.893343i	$0.648354\pi$
$692$	−10.7079	+	6.18220i	−0.407053	+	0.235012i
$693$	11.5693	+	7.67420i	0.439481	+	0.291519i
$694$	0.941578	+	0.543620i	0.0357418	+	0.0206355i
$695$	4.11684	+	7.13058i	0.156161	+	0.270478i
$696$	−26.5842	−	8.01544i	−1.00767	−	0.303825i
$697$		−	5.84096i		−	0.221242i
$698$			4.05401i			0.153447i
$699$	−5.25544	−	1.58457i	−0.198779	−	0.0599341i
$700$	−10.1168	−	17.5229i	−0.382381	−	0.662303i
$701$	−16.5475	−	9.55373i	−0.624992	−	0.360839i	0.153818	−	0.988099i	$-0.450843\pi$
$701$	−16.5475	−	9.55373i	−0.624992	−	0.360839i	−0.778810	+	0.627260i	$0.784176\pi$
$702$	6.68614	+	2.47805i	0.252352	+	0.0935280i
$703$	5.61684	−	3.24289i	0.211843	−	0.122308i
$704$	−2.31386	−	4.00772i	−0.0872069	−	0.151047i
$705$	8.86141	−	2.08191i	0.333740	−	0.0784092i
$706$	13.2921	+	7.67420i	0.500255	+	0.288822i
$707$	−34.9783	−	20.1947i	−1.31549	−	0.759500i
$708$	−24.8614	+	23.3639i	−0.934349	+	0.878067i
$709$		−	27.4728i		−	1.03176i	−0.856660	−	0.515881i	$-0.827465\pi$
$709$		−	27.4728i		−	1.03176i	0.856660	−	0.515881i	$-0.172535\pi$
$710$	7.80298	+	4.50506i	0.292841	+	0.169072i
$711$	−12.4307	−	24.9947i	−0.466188	−	0.937375i
$712$			16.0309i			0.600783i
$713$		0			0
$714$	7.80298	+	33.2125i	0.292019	+	1.24295i
$715$	−1.88316			−0.0704260
$716$	−9.17527	+	15.8920i	−0.342896	+	0.593913i
$717$	−21.6861	+	5.09496i	−0.809884	+	0.190275i
$718$	8.54755	+	14.8048i	0.318992	+	0.552510i
$719$	24.4307	−	42.3152i	0.911111	−	1.57809i	0.0986147	−	0.995126i	$-0.468559\pi$
$719$	24.4307	−	42.3152i	0.911111	−	1.57809i	0.812497	−	0.582966i	$-0.198108\pi$
$720$	1.48913	+	0.0925740i	0.0554964	+	0.00345003i
$721$	7.60597			0.283261
$722$	3.41578	−	1.97210i	0.127122	−	0.0733940i
$723$	9.30298	−	8.74261i	0.345982	−	0.325141i
$724$	−15.9416	+	9.20387i	−0.592464	+	0.342059i
$725$	−13.1168	+	22.7190i	−0.487147	+	0.843764i
$726$	−9.11684	+	8.56768i	−0.338358	+	0.317976i
$727$	20.9891	−	36.3542i	0.778444	−	1.34830i	−0.154395	−	0.988009i	$-0.549343\pi$
$727$	20.9891	−	36.3542i	0.778444	−	1.34830i	0.932839	−	0.360295i	$-0.117324\pi$
$728$	15.6060			0.578396
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−7.29211	−	4.21010i	−0.269893	−	0.155823i
$731$	55.2921	−	31.9229i	2.04505	−	1.18071i
$732$		0			0
$733$	11.9891	+	20.7658i	0.442828	+	0.767001i	0.997898	−	0.0648025i	$-0.0206417\pi$
$733$	11.9891	+	20.7658i	0.442828	+	0.767001i	−0.555070	+	0.831804i	$0.687308\pi$
$734$	−10.4525	−	18.1042i	−0.385807	−	0.668237i
$735$	4.37228	−	4.10891i	0.161274	−	0.151559i
$736$		0			0
$737$	4.19702	−	7.26944i	0.154599	−	0.267773i
$738$	0.116844	−	1.87953i	0.00430109	−	0.0691864i
$739$	−21.3832	+	12.3456i	−0.786592	+	0.454139i	−0.838761	−	0.544499i	$-0.816720\pi$
$739$	−21.3832	+	12.3456i	−0.786592	+	0.454139i	0.0521693	+	0.998638i	$0.483386\pi$
$740$	−1.88316			−0.0692262
$741$	−10.7554	−	3.24289i	−0.395111	−	0.119130i
$742$			3.66648i			0.134601i
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	1.91983	+	25.6944i	0.0703843	+	0.942003i
$745$	−3.37228			−0.123551
$746$			10.9822i			0.402087i
$747$	2.48913	−	40.0395i	0.0910723	−	1.46497i
$748$	−13.8832			−0.507618
$749$	−2.31386	+	1.33591i	−0.0845466	+	0.0488130i
$750$	−2.94158	+	9.75611i	−0.107411	+	0.356243i
$751$	0.755437	−	1.30846i	0.0275663	−	0.0477462i	−0.851913	−	0.523683i	$-0.824558\pi$
$751$	0.755437	−	1.30846i	0.0275663	−	0.0477462i	0.879479	+	0.475937i	$0.157891\pi$
$752$		−	4.16381i		−	0.151839i
$753$	−12.6060	−	13.4140i	−0.459387	−	0.488832i
$754$	−4.11684	−	7.13058i	−0.149927	−	0.259681i
$755$	−5.23369	−	9.06501i	−0.190473	−	0.329910i
$756$	−4.03667	−	23.7051i	−0.146812	−	0.862146i
$757$	8.82473	−	5.09496i	0.320740	−	0.185180i	−0.330982	−	0.943637i	$-0.607380\pi$
$757$	8.82473	−	5.09496i	0.320740	−	0.185180i	0.651723	+	0.758457i	$0.274047\pi$
$758$	−6.33561	−	3.65787i	−0.230120	−	0.132860i
$759$		0			0
$760$	7.92665			0.287530
$761$	15.4307	−	26.7268i	0.559363	−	0.968844i	−0.438187	−	0.898884i	$-0.644379\pi$
$761$	15.4307	−	26.7268i	0.559363	−	0.968844i	0.997550	−	0.0699606i	$-0.0222874\pi$
$762$	−6.09509	−	6.48577i	−0.220802	−	0.234955i
$763$	−20.8614	+	36.1330i	−0.755234	+	1.30810i
$764$	−25.6426	+	14.8048i	−0.927718	+	0.535618i
$765$	−9.68614	+	14.6024i	−0.350203	+	0.527951i
$766$	0.941578	−	0.543620i	0.0340206	−	0.0196418i
$767$	−24.8614			−0.897693
$768$	−6.94158	+	23.0226i	−0.250483	+	0.830757i
$769$	−10.6861	+	18.5089i	−0.385352	+	0.667449i	−0.991818	−	0.127660i	$-0.959253\pi$
$769$	−10.6861	+	18.5089i	−0.385352	+	0.667449i	0.606466	+	0.795110i	$0.292587\pi$
$770$	−1.45245	−	2.51572i	−0.0523428	−	0.0906603i
$771$	−3.45245	−	14.6950i	−0.124337	−	0.529227i
$772$	6.68614	−	11.5807i	0.240639	−	0.416800i
$773$	8.23369			0.296145			0.148073	−	0.988976i	$-0.452693\pi$
$773$	8.23369			0.296145			0.148073	+	0.988976i	$0.452693\pi$
$774$	18.4307	−	9.16620i	0.662478	−	0.329472i
$775$	24.0475	+	3.78651i	0.863813	+	0.136015i
$776$		−	0.994667i		−	0.0357065i
$777$	2.31386	+	9.84868i	0.0830092	+	0.353320i
$778$	−11.4090	−	6.58696i	−0.409031	−	0.236154i
$779$			2.96677i			0.106296i
$780$	2.23369	+	2.37686i	0.0799789	+	0.0851053i
$781$	17.0584	+	9.84868i	0.610398	+	0.352414i
$782$		0			0
$783$	−24.0000	+	19.8997i	−0.857690	+	0.711159i
$784$	−1.37228	−	2.37686i	−0.0490100	−	0.0848879i
$785$	−8.48913	+	4.90120i	−0.302990	+	0.174931i
$786$	−13.7663	−	14.6487i	−0.491028	−	0.522502i
$787$	0.733688	+	0.423595i	0.0261532	+	0.0150995i	0.513020	−	0.858377i	$-0.328527\pi$
$787$	0.733688	+	0.423595i	0.0261532	+	0.0150995i	−0.486866	+	0.873476i	$0.661860\pi$
$788$	10.7079	+	18.5466i	0.381453	+	0.660696i
$789$	12.0000	−	39.7995i	0.427211	−	1.41690i
$790$			5.84096i			0.207812i
$791$			48.4048i			1.72108i
$792$	−10.9783	−	0.682481i	−0.390095	−	0.0242509i
$793$		0			0
$794$	14.6644	+	8.46649i	0.520420	+	0.300464i
$795$	−1.37228	+	1.28962i	−0.0486698	+	0.0457381i
$796$	−19.2921	+	11.1383i	−0.683791	+	0.394787i
$797$	5.56930	+	9.64630i	0.197275	+	0.341690i	0.947644	−	0.319329i	$-0.103458\pi$
$797$	5.56930	+	9.64630i	0.197275	+	0.341690i	−0.750369	+	0.661019i	$0.770124\pi$
$798$	−3.96333	−	16.8695i	−0.140300	−	0.597172i
$799$	42.3505	+	24.4511i	1.49825	+	0.865017i
$800$	22.1168	+	12.7692i	0.781949	+	0.451458i
$801$	15.0000	+	9.94987i	0.529999	+	0.351562i
$802$			16.0309i			0.566070i
$803$	−15.9416	−	9.20387i	−0.562566	−	0.324798i
$804$	−14.1535	+	3.32524i	−0.499156	+	0.117272i
$805$		0			0
$806$	−4.80298	+	5.94215i	−0.169178	+	0.209303i
$807$	−21.6861	+	5.09496i	−0.763388	+	0.179351i
$808$	32.0000			1.12576
$809$	−16.8030	+	29.1036i	−0.590761	+	1.02323i	0.403369	+	0.915038i	$0.367839\pi$
$809$	−16.8030	+	29.1036i	−0.590761	+	1.02323i	−0.994130	+	0.108191i	$0.965494\pi$
$810$	−3.40895	+	4.50506i	−0.119778	+	0.158292i
$811$	0.500000	+	0.866025i	0.0175574	+	0.0304103i	0.874671	−	0.484718i	$-0.161078\pi$
$811$	0.500000	+	0.866025i	0.0175574	+	0.0304103i	−0.857113	+	0.515128i	$0.827744\pi$
$812$	−13.8832	+	24.0463i	−0.487203	+	0.843861i
$813$	−12.5584	−	3.78651i	−0.440443	−	0.132799i
$814$	1.88316			0.0660046
$815$	−4.37228	+	2.52434i	−0.153154	+	0.0884237i
$816$	5.48913	+	5.84096i	0.192158	+	0.204475i
$817$	−28.0842	+	16.2144i	−0.982542	+	0.567271i
$818$	−1.54755	+	2.68043i	−0.0541087	+	0.0937191i
$819$	9.68614	−	14.6024i	0.338461	−	0.510249i
$820$	0.430703	−	0.746000i	0.0150408	−	0.0260515i
$821$	15.7663			0.550248			0.275124	−	0.961409i	$-0.411281\pi$
$821$	15.7663			0.550248			0.275124	+	0.961409i	$0.411281\pi$
$822$	3.33561	+	14.1976i	0.116343	+	0.495200i
$823$	−0.175266	−	0.101190i	−0.00610939	−	0.00352726i	0.496942	−	0.867784i	$-0.334456\pi$
$823$	−0.175266	−	0.101190i	−0.00610939	−	0.00352726i	−0.503052	+	0.864256i	$0.667789\pi$
$824$	−5.21876	+	3.01306i	−0.181804	+	0.104965i
$825$	−3.00000	+	9.94987i	−0.104447	+	0.346410i
$826$	−19.1753	−	33.2125i	−0.667193	−	1.15561i
$827$	−13.5475	−	23.4650i	−0.471094	−	0.815959i	0.528359	−	0.849021i	$-0.322808\pi$
$827$	−13.5475	−	23.4650i	−0.471094	−	0.815959i	−0.999453	+	0.0330617i	$0.989474\pi$
$828$		0			0
$829$		−	36.9802i		−	1.28438i	−0.766547	−	0.642188i	$-0.778027\pi$
$829$		−	36.9802i		−	1.28438i	0.766547	−	0.642188i	$-0.221973\pi$
$830$	−4.19702	+	7.26944i	−0.145681	+	0.252326i
$831$	29.7921	+	8.98266i	1.03348	+	0.311605i
$832$	−5.05842	+	2.92048i	−0.175369	+	0.101249i
$833$	32.2337			1.11683
$834$	−4.11684	+	13.6540i	−0.142555	+	0.472800i
$835$			8.42020i			0.291393i
$836$	7.05160			0.243885
$837$	25.2337	+	14.1514i	0.872204	+	0.489143i
$838$	8.78806			0.303579
$839$			18.0202i			0.622127i	0.950389	+	0.311064i	$0.100685\pi$
$839$			18.0202i			0.622127i	−0.950389	+	0.311064i	$0.899315\pi$
$840$	−3.56930	+	11.8380i	−0.123152	+	0.408450i
$841$	7.00000			0.241379
$842$	10.0367	−	5.79468i	0.345887	−	0.199698i
$843$	−30.3723	−	9.15759i	−1.04608	−	0.315404i
$844$	1.03667	−	1.79557i	0.0356837	−	0.0618061i
$845$		−	7.92287i		−	0.272555i
$846$	13.1386	+	8.71516i	0.451714	+	0.299633i
$847$	15.3723	+	26.6256i	0.528198	+	0.914865i
$848$	0.430703	+	0.746000i	0.0147904	+	0.0256177i
$849$	−12.6753	+	42.0391i	−0.435014	+	1.44278i
$850$	−22.1168	+	12.7692i	−0.758601	+	0.437979i
$851$		0			0
$852$	−7.80298	−	33.2125i	−0.267326	−	1.13784i
$853$	47.3505			1.62125			0.810626	−	0.585565i	$-0.199127\pi$
$853$	47.3505			1.62125			0.810626	+	0.585565i	$0.199127\pi$
$854$		0			0
$855$	4.91983	−	7.41692i	0.168255	−	0.253653i
$856$	1.05842	−	1.83324i	0.0361761	−	0.0626589i
$857$	34.8981	−	20.1484i	1.19210	−	0.688257i	0.233314	−	0.972401i	$-0.425043\pi$
$857$	34.8981	−	20.1484i	1.19210	−	0.688257i	0.958781	+	0.284145i	$0.0917096\pi$
$858$	−2.23369	−	2.37686i	−0.0762568	−	0.0811447i
$859$	22.8505	−	13.1928i	0.779650	−	0.450131i	−0.0566562	−	0.998394i	$-0.518044\pi$
$859$	22.8505	−	13.1928i	0.779650	−	0.450131i	0.836306	+	0.548263i	$0.184711\pi$
$860$	9.41578			0.321075
$861$	−4.43070	−	1.33591i	−0.150998	−	0.0455276i
$862$	−0.197015	+	0.341241i	−0.00671037	+	0.0116227i
$863$	−13.5475	−	23.4650i	−0.461164	−	0.798759i	0.537855	−	0.843037i	$-0.319235\pi$
$863$	−13.5475	−	23.4650i	−0.461164	−	0.798759i	−0.999019	+	0.0442779i	$0.985901\pi$
$864$	19.3723	+	23.3639i	0.659058	+	0.794854i
$865$	3.56930	−	6.18220i	0.121360	−	0.210201i
$866$	−30.7011			−1.04326
$867$	−62.9783	+	14.7962i	−2.13885	+	0.502504i
$868$	25.4525	+	4.00772i	0.863913	+	0.136031i
$869$			12.7692i			0.433164i
$870$	6.35053	−	1.49200i	0.215303	−	0.0505835i
$871$	−9.17527	−	5.29734i	−0.310892	−	0.179494i
$872$		−	33.0564i		−	1.11943i
$873$	−0.930703	−	0.617359i	−0.0314995	−	0.0208944i
$874$		0			0
$875$	21.6861	+	12.5205i	0.733125	+	0.423270i
$876$	7.29211	+	31.0381i	0.246378	+	1.04868i
$877$	−1.12772	−	1.95327i	−0.0380804	−	0.0659571i	0.846357	−	0.532616i	$-0.178791\pi$
$877$	−1.12772	−	1.95327i	−0.0380804	−	0.0659571i	−0.884437	+	0.466659i	$0.845458\pi$
$878$	8.21876	−	4.74511i	0.277370	−	0.160140i
$879$	−20.8614	+	19.6048i	−0.703638	+	0.661253i
$880$	−0.591046	−	0.341241i	−0.0199242	−	0.0115032i
$881$	7.80298	+	13.5152i	0.262889	+	0.455338i	0.967008	−	0.254744i	$-0.0819913\pi$
$881$	7.80298	+	13.5152i	0.262889	+	0.455338i	−0.704119	+	0.710082i	$0.748658\pi$
$882$	10.3723	+	0.644810i	0.349253	+	0.0217119i
$883$		−	1.93443i		−	0.0650988i	−0.999470	−	0.0325494i	$-0.989637\pi$
$883$		−	1.93443i		−	0.0650988i	0.999470	−	0.0325494i	$-0.0103626\pi$
$884$			17.5229i			0.589358i
$885$	5.68614	−	18.8588i	0.191138	−	0.633931i
$886$	2.54755	+	4.41248i	0.0855865	+	0.148240i
$887$	0.686141	+	0.396143i	0.0230383	+	0.0133012i	0.511475	−	0.859298i	$-0.329099\pi$
$887$	0.686141	+	0.396143i	0.0230383	+	0.0133012i	−0.488437	+	0.872599i	$0.662433\pi$
$888$	−5.48913	−	5.84096i	−0.184203	−	0.196010i
$889$	−18.9416	+	10.9359i	−0.635280	+	0.366779i
$890$	−1.88316	−	3.26172i	−0.0631235	−	0.109333i
$891$	−7.45245	+	9.84868i	−0.249667	+	0.329943i
$892$	−10.2921	−	5.94215i	−0.344605	−	0.198958i
$893$	−21.5109	−	12.4193i	−0.719834	−	0.415596i
$894$	−4.00000	−	4.25639i	−0.133780	−	0.142355i
$895$		−	10.5947i		−	0.354141i
$896$	26.3139	+	15.1923i	0.879084	+	0.507540i
$897$		0			0
$898$			2.98400i			0.0995774i
$899$	−12.0000	−	31.1769i	−0.400222	−	1.03981i
$900$	16.1168	−	8.01544i	0.537228	−	0.267181i
$901$	−10.1168			−0.337041
$902$	−0.430703	+	0.746000i	−0.0143409	+	0.0248391i
$903$	−11.5693	−	49.2434i	−0.385002	−	1.63872i
$904$	−19.1753	−	33.2125i	−0.637760	−	1.10463i
$905$	5.31386	−	9.20387i	0.176639	−	0.305947i
$906$	5.23369	−	17.3582i	0.173878	−	0.576687i
$907$	9.02175			0.299562			0.149781	−	0.988719i	$-0.452143\pi$
$907$	9.02175			0.299562			0.149781	+	0.988719i	$0.452143\pi$
$908$	−10.7079	+	6.18220i	−0.355354	+	0.205164i
$909$	19.8614	−	29.9422i	0.658761	−	0.993120i
$910$	−3.17527	+	1.83324i	−0.105259	+	0.0607713i
$911$	−5.56930	+	9.64630i	−0.184519	+	0.319596i	−0.943414	−	0.331616i	$-0.892406\pi$
$911$	−5.56930	+	9.64630i	−0.184519	+	0.319596i	0.758895	+	0.651213i	$0.225739\pi$
$912$	−2.78806	−	2.96677i	−0.0923219	−	0.0982395i
$913$	−9.17527	+	15.8920i	−0.303657	+	0.525949i
$914$	−2.23369			−0.0738838
$915$		0			0
$916$	20.0584	+	11.5807i	0.662749	+	0.382638i
$917$	−42.7812	+	24.6998i	−1.41276	+	0.815658i
$918$	−29.9198	+	5.09496i	−0.987501	+	0.168159i
$919$	5.38316	+	9.32390i	0.177574	+	0.307567i	0.941049	−	0.338270i	$-0.109842\pi$
$919$	5.38316	+	9.32390i	0.177574	+	0.307567i	−0.763475	+	0.645837i	$0.776508\pi$
$920$		0			0
$921$	−18.6753	−	19.8723i	−0.615371	−	0.654814i
$922$		−	4.75372i		−	0.156555i
$923$	12.4307	−	21.5306i	0.409162	−	0.708689i
$924$	−3.17527	+	10.5312i	−0.104459	+	0.346450i
$925$	−6.55842	+	3.78651i	−0.215640	+	0.124500i
$926$	22.4674			0.738324
$927$	−0.419829	+	6.75327i	−0.0137890	+	0.221807i
$928$		−	35.0458i		−	1.15043i
$929$	8.23369			0.270139			0.135069	−	0.990836i	$-0.456874\pi$
$929$	8.23369			0.270139			0.135069	+	0.990836i	$0.456874\pi$
$930$	−3.40895	−	5.00239i	−0.111784	−	0.164035i
$931$	−16.3723			−0.536580
$932$		−	4.34896i		−	0.142455i
$933$	−6.72281	−	2.02700i	−0.220095	−	0.0663611i
$934$	17.7228			0.579908
$935$	6.94158	−	4.00772i	0.227014	−	0.131067i
$936$	−0.861407	+	13.8564i	−0.0281560	+	0.452911i
$937$	5.38316	−	9.32390i	0.175860	−	0.304599i	−0.764599	−	0.644507i	$-0.777063\pi$
$937$	5.38316	−	9.32390i	0.175860	−	0.304599i	0.940459	+	0.339908i	$0.110396\pi$
$938$		−	16.3431i		−	0.533620i
$939$	21.3030	−	20.0198i	0.695197	−	0.653321i
$940$	3.60597	+	6.24572i	0.117614	+	0.203713i
$941$	−12.4307	−	21.5306i	−0.405229	−	0.701878i	0.589119	−	0.808046i	$-0.299475\pi$
$941$	−12.4307	−	21.5306i	−0.405229	−	0.701878i	−0.994348	+	0.106169i	$0.966142\pi$
$942$	−16.2554	−	4.90120i	−0.529631	−	0.159690i
$943$		0			0
$944$	−7.80298	−	4.50506i	−0.253966	−	0.146627i
$945$	8.86141	+	10.6873i	0.288262	+	0.347657i
$946$	−9.41578			−0.306133
$947$	12.4307	−	21.5306i	0.403944	−	0.699651i	−0.590254	−	0.807217i	$-0.700973\pi$
$947$	12.4307	−	21.5306i	0.403944	−	0.699651i	0.994198	+	0.107567i	$0.0343059\pi$
$948$	16.1168	−	15.1460i	0.523451	−	0.491920i
$949$	−11.6168	+	20.1210i	−0.377099	+	0.653154i
$950$	11.2337	−	6.48577i	0.364469	−	0.210426i
$951$	−31.2337	+	29.3523i	−1.01282	+	0.951813i
$952$	−57.5258	+	33.2125i	−1.86442	+	1.07642i
$953$	−34.4674			−1.11651			−0.558254	−	0.829670i	$-0.688528\pi$
$953$	−34.4674			−1.11651			−0.558254	+	0.829670i	$0.688528\pi$
$954$	−3.25544	−	0.202380i	−0.105399	−	0.00655228i
$955$	8.54755	−	14.8048i	0.276592	−	0.479072i
$956$	−8.82473	−	15.2849i	−0.285412	−	0.494349i
$957$	13.8832	−	3.26172i	0.448779	−	0.105436i
$958$	2.54755	−	4.41248i	0.0823075	−	0.142561i
$959$	35.8397			1.15732
$960$	−1.05842	−	4.50506i	−0.0341604	−	0.145400i
$961$	−23.0000	+	20.7846i	−0.741935	+	0.670471i
$962$		−	2.37686i		−	0.0766331i
$963$	−1.05842	−	2.12819i	−0.0341072	−	0.0685801i
$964$	8.75949	+	5.05729i	0.282124	+	0.162884i
$965$			7.72049i			0.248531i
$966$		0			0
$967$	8.05842	+	4.65253i	0.259141	+	0.149615i	0.623943	−	0.781470i	$-0.285530\pi$
$967$	8.05842	+	4.65253i	0.259141	+	0.149615i	−0.364801	+	0.931085i	$0.618863\pi$
$968$	−21.0951	−	12.1793i	−0.678022	−	0.391456i
$969$	46.5475	−	10.9359i	1.49532	−	0.351313i
$970$	0.116844	+	0.202380i	0.00375163	+	0.00649802i
$971$	0.430703	−	0.248667i	0.0138219	−	0.00798009i	−0.493073	−	0.869988i	$-0.664126\pi$
$971$	0.430703	−	0.248667i	0.0138219	−	0.00798009i	0.506895	+	0.862008i	$0.330793\pi$
$972$	21.2704	−	2.27567i	0.682247	−	0.0729922i
$973$	30.3505	+	17.5229i	0.972993	+	0.561758i
$974$	−2.91983	−	5.05729i	−0.0935573	−	0.162046i
$975$	12.5584	+	3.78651i	0.402191	+	0.121265i
$976$		0			0
$977$		−	14.4463i		−	0.462179i	−0.972933	−	0.231089i	$-0.925771\pi$
$977$		−	14.4463i		−	0.462179i	0.972933	−	0.231089i	$-0.0742289\pi$
$978$	−8.37228	−	2.52434i	−0.267716	−	0.0807194i
$979$	−4.11684	−	7.13058i	−0.131575	−	0.227894i
$980$	4.11684	+	2.37686i	0.131508	+	0.0759260i
$981$	−30.9307	−	20.5171i	−0.987541	−	0.655061i
$982$	7.64264	−	4.41248i	0.243887	−	0.140808i
$983$	−0.430703	−	0.746000i	−0.0137373	−	0.0237937i	0.859075	−	0.511850i	$-0.171040\pi$
$983$	−0.430703	−	0.746000i	−0.0137373	−	0.0237937i	−0.872812	+	0.488056i	$0.837706\pi$
$984$	3.56930	−	0.838574i	0.113785	−	0.0267328i
$985$	−10.7079	−	6.18220i	−0.341182	−	0.196981i
$986$	30.3505	+	17.5229i	0.966558	+	0.558042i
$987$	28.2337	−	26.5330i	0.898688	−	0.844555i
$988$		−	8.90030i		−	0.283156i
$989$		0			0
$990$	2.31386	−	1.15076i	0.0735393	−	0.0365735i
$991$			43.5036i			1.38194i	0.722884	+	0.690969i	$0.242816\pi$
$991$			43.5036i			1.38194i	−0.722884	+	0.690969i	$0.757184\pi$
$992$	−30.3505	+	11.6819i	−0.963630	+	0.370901i
$993$	−0.686141	−	2.92048i	−0.0217740	−	0.0926787i
$994$	38.3505			1.21641
$995$	6.43070	−	11.1383i	0.203867	−	0.353108i
$996$	30.9416	−	7.26944i	0.980421	−	0.230341i
$997$	13.3139	+	23.0603i	0.421654	+	0.730326i	0.996101	−	0.0882152i	$-0.0281163\pi$
$997$	13.3139	+	23.0603i	0.421654	+	0.730326i	−0.574447	+	0.818542i	$0.694783\pi$
$998$	3.68614	−	6.38458i	0.116683	−	0.202100i
$999$	−8.87228	+	1.51084i	−0.280707	+	0.0478007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.g.f.26.1	yes	4
3.2	odd	2		93.2.g.e.26.2	✓	4
31.6	odd	6		93.2.g.e.68.1	yes	4
93.68	even	6	inner	93.2.g.f.68.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.g.e.26.2	✓	4	3.2	odd	2
93.2.g.e.68.1	yes	4	31.6	odd	6
93.2.g.f.26.1	yes	4	1.1	even	1	trivial
93.2.g.f.68.2	yes	4	93.68	even	6	inner

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.792287i q^{2} +(0.500000 - 1.65831i) q^{3} +1.37228 q^{4} +(-0.686141 + 0.396143i) q^{5} +(-1.31386 - 0.396143i) q^{6} +(-1.68614 + 2.92048i) q^{7} -2.67181i q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q-0.792287i q^{2} +(0.500000 - 1.65831i) q^{3} +1.37228 q^{4} +(-0.686141 + 0.396143i) q^{5} +(-1.31386 - 0.396143i) q^{6} +(-1.68614 + 2.92048i) q^{7} -2.67181i q^{8} +(-2.50000 - 1.65831i) q^{9} +(0.313859 + 0.543620i) q^{10} +(0.686141 + 1.18843i) q^{11} +(0.686141 - 2.27567i) q^{12} +(1.50000 - 0.866025i) q^{13} +(2.31386 + 1.33591i) q^{14} +(0.313859 + 1.33591i) q^{15} +0.627719 q^{16} +(-3.68614 + 6.38458i) q^{17} +(-1.31386 + 1.98072i) q^{18} +(1.87228 - 3.24289i) q^{19} +(-0.941578 + 0.543620i) q^{20} +(4.00000 + 4.25639i) q^{21} +(0.941578 - 0.543620i) q^{22} +(-4.43070 - 1.33591i) q^{24} +(-2.18614 + 3.78651i) q^{25} +(-0.686141 - 1.18843i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-2.31386 + 4.00772i) q^{28} +6.00000 q^{29} +(1.05842 - 0.248667i) q^{30} +(-2.00000 - 5.19615i) q^{31} -5.84096i q^{32} +(2.31386 - 0.543620i) q^{33} +(5.05842 + 2.92048i) q^{34} -2.67181i q^{35} +(-3.43070 - 2.27567i) q^{36} +(1.50000 + 0.866025i) q^{37} +(-2.56930 - 1.48338i) q^{38} +(-0.686141 - 2.92048i) q^{39} +(1.05842 + 1.83324i) q^{40} +(-0.686141 + 0.396143i) q^{41} +(3.37228 - 3.16915i) q^{42} +(-7.50000 - 4.33013i) q^{43} +(0.941578 + 1.63086i) q^{44} +(2.37228 + 0.147477i) q^{45} -6.63325i q^{47} +(0.313859 - 1.04095i) q^{48} +(-2.18614 - 3.78651i) q^{49} +(3.00000 + 1.73205i) q^{50} +(8.74456 + 9.30506i) q^{51} +(2.05842 - 1.18843i) q^{52} +(0.686141 + 1.18843i) q^{53} +(2.62772 + 3.16915i) q^{54} +(-0.941578 - 0.543620i) q^{55} +(7.80298 + 4.50506i) q^{56} +(-4.44158 - 4.72627i) q^{57} -4.75372i q^{58} +(-12.4307 - 7.17687i) q^{59} +(0.430703 + 1.83324i) q^{60} +(-4.11684 + 1.58457i) q^{62} +(9.05842 - 4.50506i) q^{63} -3.37228 q^{64} +(-0.686141 + 1.18843i) q^{65} +(-0.430703 - 1.83324i) q^{66} +(-3.05842 - 5.29734i) q^{67} +(-5.05842 + 8.76144i) q^{68} -2.11684 q^{70} +(12.4307 - 7.17687i) q^{71} +(-4.43070 + 6.67954i) q^{72} +(-11.6168 + 6.70699i) q^{73} +(0.686141 - 1.18843i) q^{74} +(5.18614 + 5.51856i) q^{75} +(2.56930 - 4.45015i) q^{76} -4.62772 q^{77} +(-2.31386 + 0.543620i) q^{78} +(8.05842 + 4.65253i) q^{79} +(-0.430703 + 0.248667i) q^{80} +(3.50000 + 8.29156i) q^{81} +(0.313859 + 0.543620i) q^{82} +(6.68614 + 11.5807i) q^{83} +(5.48913 + 5.84096i) q^{84} -5.84096i q^{85} +(-3.43070 + 5.94215i) q^{86} +(3.00000 - 9.94987i) q^{87} +(3.17527 - 1.83324i) q^{88} -6.00000 q^{89} +(0.116844 - 1.87953i) q^{90} +5.84096i q^{91} +(-9.61684 + 0.718549i) q^{93} -5.25544 q^{94} +2.96677i q^{95} +(-9.68614 - 2.92048i) q^{96} +0.372281 q^{97} +(-3.00000 + 1.73205i) q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 6 q^{4} + 3 q^{5} - 11 q^{6} - q^{7} - 10 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 6 * q^4 + 3 * q^5 - 11 * q^6 - q^7 - 10 * q^9	\( 4 q + 2 q^{3} - 6 q^{4} + 3 q^{5} - 11 q^{6} - q^{7} - 10 q^{9} + 7 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} + 15 q^{14} + 7 q^{15} + 14 q^{16} - 9 q^{17} - 11 q^{18} - 4 q^{19} - 21 q^{20} + 16 q^{21} + 21 q^{22} + 11 q^{24} - 3 q^{25} + 3 q^{26} - 16 q^{27} - 15 q^{28} + 24 q^{29} - 13 q^{30} - 8 q^{31} + 15 q^{33} + 3 q^{34} + 15 q^{36} + 6 q^{37} - 39 q^{38} + 3 q^{39} - 13 q^{40} + 3 q^{41} + 2 q^{42} - 30 q^{43} + 21 q^{44} - 2 q^{45} + 7 q^{48} - 3 q^{49} + 12 q^{50} + 12 q^{51} - 9 q^{52} - 3 q^{53} + 22 q^{54} - 21 q^{55} - 9 q^{56} - 35 q^{57} - 21 q^{59} - 27 q^{60} + 18 q^{62} + 19 q^{63} - 2 q^{64} + 3 q^{65} + 27 q^{66} + 5 q^{67} - 3 q^{68} + 26 q^{70} + 21 q^{71} + 11 q^{72} - 12 q^{73} - 3 q^{74} + 15 q^{75} + 39 q^{76} - 30 q^{77} - 15 q^{78} + 15 q^{79} + 27 q^{80} + 14 q^{81} + 7 q^{82} + 21 q^{83} - 24 q^{84} + 15 q^{86} + 12 q^{87} - 39 q^{88} - 24 q^{89} - 34 q^{90} - 4 q^{93} - 44 q^{94} - 33 q^{96} - 10 q^{97} - 12 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^4 + 3 * q^5 - 11 * q^6 - q^7 - 10 * q^9 + 7 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 + 15 * q^14 + 7 * q^15 + 14 * q^16 - 9 * q^17 - 11 * q^18 - 4 * q^19 - 21 * q^20 + 16 * q^21 + 21 * q^22 + 11 * q^24 - 3 * q^25 + 3 * q^26 - 16 * q^27 - 15 * q^28 + 24 * q^29 - 13 * q^30 - 8 * q^31 + 15 * q^33 + 3 * q^34 + 15 * q^36 + 6 * q^37 - 39 * q^38 + 3 * q^39 - 13 * q^40 + 3 * q^41 + 2 * q^42 - 30 * q^43 + 21 * q^44 - 2 * q^45 + 7 * q^48 - 3 * q^49 + 12 * q^50 + 12 * q^51 - 9 * q^52 - 3 * q^53 + 22 * q^54 - 21 * q^55 - 9 * q^56 - 35 * q^57 - 21 * q^59 - 27 * q^60 + 18 * q^62 + 19 * q^63 - 2 * q^64 + 3 * q^65 + 27 * q^66 + 5 * q^67 - 3 * q^68 + 26 * q^70 + 21 * q^71 + 11 * q^72 - 12 * q^73 - 3 * q^74 + 15 * q^75 + 39 * q^76 - 30 * q^77 - 15 * q^78 + 15 * q^79 + 27 * q^80 + 14 * q^81 + 7 * q^82 + 21 * q^83 - 24 * q^84 + 15 * q^86 + 12 * q^87 - 39 * q^88 - 24 * q^89 - 34 * q^90 - 4 * q^93 - 44 * q^94 - 33 * q^96 - 10 * q^97 - 12 * q^98 + 24 * q^99

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