LMFDB - Embedded newform 462.2.n.c.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.1
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	462.263
Dual form			462.2.n.c.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.13746 + 0.656712i) q^{5} -1.73205i q^{6} +(1.13746 - 2.38876i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.13746 + 0.656712i) q^{5} -1.73205i q^{6} +(1.13746 - 2.38876i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.13746 - 0.656712i) q^{10} +(-0.637459 + 3.25479i) q^{11} +(1.50000 - 0.866025i) q^{12} +2.62685i q^{13} +(2.63746 - 0.209313i) q^{14} +2.27492 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.63746 + 2.83616i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-5.63746 + 3.25479i) q^{19} -1.31342i q^{20} +(-3.77492 + 2.59808i) q^{21} +(-3.13746 + 1.07534i) q^{22} +(-4.91238 + 2.83616i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-1.63746 + 2.83616i) q^{25} +(-2.27492 + 1.31342i) q^{26} -5.19615i q^{27} +(1.50000 + 2.17945i) q^{28} +1.00000 q^{29} +(1.13746 + 1.97014i) q^{30} +(5.13746 - 8.89834i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.77492 - 4.33013i) q^{33} -3.27492 q^{34} +(0.274917 + 3.46410i) q^{35} -3.00000 q^{36} +(3.63746 + 6.30026i) q^{37} +(-5.63746 - 3.25479i) q^{38} +(2.27492 - 3.94027i) q^{39} +(1.13746 - 0.656712i) q^{40} -6.54983 q^{41} +(-4.13746 - 1.97014i) q^{42} +9.97368i q^{43} +(-2.50000 - 2.17945i) q^{44} +(-3.41238 - 1.97014i) q^{45} +(-4.91238 - 2.83616i) q^{46} +(1.91238 - 1.10411i) q^{47} +1.73205i q^{48} +(-4.41238 - 5.43424i) q^{49} -3.27492 q^{50} +(4.91238 - 2.83616i) q^{51} +(-2.27492 - 1.31342i) q^{52} +(11.6873 + 6.74766i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-1.41238 - 4.12081i) q^{55} +(-1.13746 + 2.38876i) q^{56} +11.2749 q^{57} +(0.500000 + 0.866025i) q^{58} +(1.50000 + 0.866025i) q^{59} +(-1.13746 + 1.97014i) q^{60} +(-6.00000 + 3.46410i) q^{61} +10.2749 q^{62} +(7.91238 - 0.627940i) q^{63} +1.00000 q^{64} +(-1.72508 - 2.98793i) q^{65} +(5.63746 + 1.10411i) q^{66} +(4.27492 - 7.40437i) q^{67} +(-1.63746 - 2.83616i) q^{68} +9.82475 q^{69} +(-2.86254 + 1.97014i) q^{70} -9.97368i q^{71} +(-1.50000 - 2.59808i) q^{72} +(-4.54983 - 2.62685i) q^{73} +(-3.63746 + 6.30026i) q^{74} +(4.91238 - 2.83616i) q^{75} -6.50958i q^{76} +(7.04983 + 5.22492i) q^{77} +4.54983 q^{78} +(-1.86254 + 1.07534i) q^{79} +(1.13746 + 0.656712i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.27492 - 5.67232i) q^{82} +10.2749 q^{83} +(-0.362541 - 4.56821i) q^{84} -4.30136i q^{85} +(-8.63746 + 4.98684i) q^{86} +(-1.50000 - 0.866025i) q^{87} +(0.637459 - 3.25479i) q^{88} +(2.27492 - 1.31342i) q^{89} -3.94027i q^{90} +(6.27492 + 2.98793i) q^{91} -5.67232i q^{92} +(-15.4124 + 8.89834i) q^{93} +(1.91238 + 1.10411i) q^{94} +(4.27492 - 7.40437i) q^{95} +(-1.50000 + 0.866025i) q^{96} -13.5498 q^{97} +(2.50000 - 6.53835i) q^{98} +(-9.41238 + 3.22602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^7 - 4 * q^8 + 6 * q^9	$ 4 q + 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{7} - 4 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} + 6 q^{12} + 3 q^{14} - 6 q^{15} - 2 q^{16} + q^{17} - 6 q^{18} - 15 q^{19} - 5 q^{22} + 3 q^{23} + 6 q^{24} + q^{25} + 6 q^{26} + 6 q^{28} + 4 q^{29} - 3 q^{30} + 13 q^{31} + 2 q^{32} + 2 q^{34} - 14 q^{35} - 12 q^{36} + 7 q^{37} - 15 q^{38} - 6 q^{39} - 3 q^{40} + 4 q^{41} - 9 q^{42} - 10 q^{44} + 9 q^{45} + 3 q^{46} - 15 q^{47} + 5 q^{49} + 2 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{53} + 18 q^{54} + 17 q^{55} + 3 q^{56} + 30 q^{57} + 2 q^{58} + 6 q^{59} + 3 q^{60} - 24 q^{61} + 26 q^{62} + 9 q^{63} + 4 q^{64} - 22 q^{65} + 15 q^{66} + 2 q^{67} + q^{68} - 6 q^{69} - 19 q^{70} - 6 q^{72} + 12 q^{73} - 7 q^{74} - 3 q^{75} - 2 q^{77} - 12 q^{78} - 15 q^{79} - 3 q^{80} - 18 q^{81} + 2 q^{82} + 26 q^{83} - 9 q^{84} - 27 q^{86} - 6 q^{87} - 5 q^{88} - 6 q^{89} + 10 q^{91} - 39 q^{93} - 15 q^{94} + 2 q^{95} - 6 q^{96} - 24 q^{97} + 10 q^{98} - 15 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^7 - 4 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 + 6 * q^12 + 3 * q^14 - 6 * q^15 - 2 * q^16 + q^17 - 6 * q^18 - 15 * q^19 - 5 * q^22 + 3 * q^23 + 6 * q^24 + q^25 + 6 * q^26 + 6 * q^28 + 4 * q^29 - 3 * q^30 + 13 * q^31 + 2 * q^32 + 2 * q^34 - 14 * q^35 - 12 * q^36 + 7 * q^37 - 15 * q^38 - 6 * q^39 - 3 * q^40 + 4 * q^41 - 9 * q^42 - 10 * q^44 + 9 * q^45 + 3 * q^46 - 15 * q^47 + 5 * q^49 + 2 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^53 + 18 * q^54 + 17 * q^55 + 3 * q^56 + 30 * q^57 + 2 * q^58 + 6 * q^59 + 3 * q^60 - 24 * q^61 + 26 * q^62 + 9 * q^63 + 4 * q^64 - 22 * q^65 + 15 * q^66 + 2 * q^67 + q^68 - 6 * q^69 - 19 * q^70 - 6 * q^72 + 12 * q^73 - 7 * q^74 - 3 * q^75 - 2 * q^77 - 12 * q^78 - 15 * q^79 - 3 * q^80 - 18 * q^81 + 2 * q^82 + 26 * q^83 - 9 * q^84 - 27 * q^86 - 6 * q^87 - 5 * q^88 - 6 * q^89 + 10 * q^91 - 39 * q^93 - 15 * q^94 + 2 * q^95 - 6 * q^96 - 24 * q^97 + 10 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.13746	+	0.656712i	−0.508687	+	0.293691i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	−1.13746	+	0.656712i	−0.508687	+	0.293691i	0.223607	+	0.974679i	$0.428217\pi$
$6$		−	1.73205i		−	0.707107i
$7$	1.13746	−	2.38876i	0.429919	−	0.902867i
$7$	1.13746	−	2.38876i	0.429919	−	0.902867i
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.13746	−	0.656712i	−0.359696	−	0.207671i
$11$	−0.637459	+	3.25479i	−0.192201	+	0.981356i
$11$	−0.637459	+	3.25479i	−0.192201	+	0.981356i
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$			2.62685i			0.728557i	0.931290	+	0.364278i	$0.118684\pi$
$13$			2.62685i			0.728557i	−0.931290	+	0.364278i	$0.881316\pi$
$14$	2.63746	−	0.209313i	0.704890	−	0.0559414i
$15$	2.27492			0.587381
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.63746	+	2.83616i	−0.397142	+	0.687870i	−0.993372	−	0.114943i	$-0.963331\pi$
$17$	−1.63746	+	2.83616i	−0.397142	+	0.687870i	0.596230	+	0.802814i	$0.296665\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	−5.63746	+	3.25479i	−1.29332	+	0.746700i	−0.979242	−	0.202697i	$-0.935029\pi$
$19$	−5.63746	+	3.25479i	−1.29332	+	0.746700i	−0.314080	+	0.949396i	$0.601696\pi$
$20$		−	1.31342i		−	0.293691i
$21$	−3.77492	+	2.59808i	−0.823754	+	0.566947i
$22$	−3.13746	+	1.07534i	−0.668908	+	0.229263i
$23$	−4.91238	+	2.83616i	−1.02430	+	0.591381i	−0.915347	−	0.402666i	$-0.868084\pi$
$23$	−4.91238	+	2.83616i	−1.02430	+	0.591381i	−0.108954	+	0.994047i	$0.534750\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−1.63746	+	2.83616i	−0.327492	+	0.567232i
$26$	−2.27492	+	1.31342i	−0.446148	+	0.257584i
$27$		−	5.19615i		−	1.00000i
$28$	1.50000	+	2.17945i	0.283473	+	0.411877i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	1.13746	+	1.97014i	0.207671	+	0.359696i
$31$	5.13746	−	8.89834i	0.922715	−	1.59819i	0.127519	−	0.991836i	$-0.459299\pi$
$31$	5.13746	−	8.89834i	0.922715	−	1.59819i	0.795196	−	0.606353i	$-0.207368\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.77492	−	4.33013i	0.657129	−	0.753778i
$34$	−3.27492			−0.561644
$35$	0.274917	+	3.46410i	0.0464695	+	0.585540i
$36$	−3.00000			−0.500000
$37$	3.63746	+	6.30026i	0.597995	+	1.03576i	0.993117	+	0.117128i	$0.0373689\pi$
$37$	3.63746	+	6.30026i	0.597995	+	1.03576i	−0.395122	+	0.918629i	$0.629298\pi$
$38$	−5.63746	−	3.25479i	−0.914517	−	0.527996i
$39$	2.27492	−	3.94027i	0.364278	−	0.630949i
$40$	1.13746	−	0.656712i	0.179848	−	0.103835i
$41$	−6.54983			−1.02291			−0.511456	−	0.859309i	$-0.670894\pi$
$41$	−6.54983			−1.02291			−0.511456	+	0.859309i	$0.670894\pi$
$42$	−4.13746	−	1.97014i	−0.638424	−	0.303999i
$43$			9.97368i			1.52097i	0.649355	+	0.760486i	$0.275039\pi$
$43$			9.97368i			1.52097i	−0.649355	+	0.760486i	$0.724961\pi$
$44$	−2.50000	−	2.17945i	−0.376889	−	0.328564i
$45$	−3.41238	−	1.97014i	−0.508687	−	0.293691i
$46$	−4.91238	−	2.83616i	−0.724290	−	0.418169i
$47$	1.91238	−	1.10411i	0.278949	−	0.161051i	−0.353999	−	0.935246i	$-0.615178\pi$
$47$	1.91238	−	1.10411i	0.278949	−	0.161051i	0.632947	+	0.774195i	$0.281845\pi$
$48$			1.73205i			0.250000i
$49$	−4.41238	−	5.43424i	−0.630339	−	0.776320i
$50$	−3.27492			−0.463143
$51$	4.91238	−	2.83616i	0.687870	−	0.397142i
$52$	−2.27492	−	1.31342i	−0.315474	−	0.182139i
$53$	11.6873	+	6.74766i	1.60537	+	0.926863i	0.990387	+	0.138325i	$0.0441718\pi$
$53$	11.6873	+	6.74766i	1.60537	+	0.926863i	0.614986	+	0.788538i	$0.289162\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	−1.41238	−	4.12081i	−0.190445	−	0.555650i
$56$	−1.13746	+	2.38876i	−0.151999	+	0.319212i
$57$	11.2749			1.49340
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	1.50000	+	0.866025i	0.195283	+	0.112747i	0.594454	−	0.804130i	$-0.297368\pi$
$59$	1.50000	+	0.866025i	0.195283	+	0.112747i	−0.399170	+	0.916877i	$0.630702\pi$
$60$	−1.13746	+	1.97014i	−0.146845	+	0.254343i
$61$	−6.00000	+	3.46410i	−0.768221	+	0.443533i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−6.00000	+	3.46410i	−0.768221	+	0.443533i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	10.2749			1.30492
$63$	7.91238	−	0.627940i	0.996866	−	0.0791130i
$64$	1.00000			0.125000
$65$	−1.72508	−	2.98793i	−0.213970	−	0.370607i
$66$	5.63746	+	1.10411i	0.693923	+	0.135907i
$67$	4.27492	−	7.40437i	0.522264	−	0.904588i	−0.477400	−	0.878686i	$-0.658421\pi$
$67$	4.27492	−	7.40437i	0.522264	−	0.904588i	0.999664	−	0.0259023i	$-0.00824587\pi$
$68$	−1.63746	−	2.83616i	−0.198571	−	0.343935i
$69$	9.82475			1.18276
$70$	−2.86254	+	1.97014i	−0.342139	+	0.235476i
$71$		−	9.97368i		−	1.18366i	−0.806064	−	0.591829i	$-0.798406\pi$
$71$		−	9.97368i		−	1.18366i	0.806064	−	0.591829i	$-0.201594\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−4.54983	−	2.62685i	−0.532518	−	0.307449i	0.209523	−	0.977804i	$-0.432809\pi$
$73$	−4.54983	−	2.62685i	−0.532518	−	0.307449i	−0.742041	+	0.670354i	$0.766142\pi$
$74$	−3.63746	+	6.30026i	−0.422846	+	0.732391i
$75$	4.91238	−	2.83616i	0.567232	−	0.327492i
$76$		−	6.50958i		−	0.746700i
$77$	7.04983	+	5.22492i	0.803403	+	0.595435i
$78$	4.54983			0.515167
$79$	−1.86254	+	1.07534i	−0.209552	+	0.120985i	−0.601103	−	0.799171i	$-0.705272\pi$
$79$	−1.86254	+	1.07534i	−0.209552	+	0.120985i	0.391551	+	0.920156i	$0.371939\pi$
$80$	1.13746	+	0.656712i	0.127172	+	0.0734226i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.27492	−	5.67232i	−0.361654	−	0.626403i
$83$	10.2749			1.12782			0.563909	−	0.825837i	$-0.309297\pi$
$83$	10.2749			1.12782			0.563909	+	0.825837i	$0.309297\pi$
$84$	−0.362541	−	4.56821i	−0.0395565	−	0.498433i
$85$		−	4.30136i		−	0.466547i
$86$	−8.63746	+	4.98684i	−0.931401	+	0.537745i
$87$	−1.50000	−	0.866025i	−0.160817	−	0.0928477i
$88$	0.637459	−	3.25479i	0.0679533	−	0.346962i
$89$	2.27492	−	1.31342i	0.241141	−	0.139223i	−0.374560	−	0.927203i	$-0.622206\pi$
$89$	2.27492	−	1.31342i	0.241141	−	0.139223i	0.615701	+	0.787980i	$0.288873\pi$
$90$		−	3.94027i		−	0.415341i
$91$	6.27492	+	2.98793i	0.657790	+	0.313220i
$92$		−	5.67232i		−	0.591381i
$93$	−15.4124	+	8.89834i	−1.59819	+	0.922715i
$94$	1.91238	+	1.10411i	0.197247	+	0.113880i
$95$	4.27492	−	7.40437i	0.438597	−	0.759673i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	−13.5498			−1.37578			−0.687889	−	0.725816i	$-0.741462\pi$
$97$	−13.5498			−1.37578			−0.687889	+	0.725816i	$0.741462\pi$
$98$	2.50000	−	6.53835i	0.252538	−	0.660473i
$99$	−9.41238	+	3.22602i	−0.945979	+	0.324227i
$100$	−1.63746	−	2.83616i	−0.163746	−	0.283616i
$101$	4.91238	−	8.50848i	0.488800	−	0.846626i	−0.511117	−	0.859511i	$-0.670768\pi$
$101$	4.91238	−	8.50848i	0.488800	−	0.846626i	0.999917	+	0.0128851i	$0.00410157\pi$
$102$	4.91238	+	2.83616i	0.486398	+	0.280822i
$103$	6.54983	+	11.3446i	0.645374	+	1.11782i	0.984215	+	0.176977i	$0.0566319\pi$
$103$	6.54983	+	11.3446i	0.645374	+	1.11782i	−0.338841	+	0.940844i	$0.610035\pi$
$104$		−	2.62685i		−	0.257584i
$105$	2.58762	−	5.43424i	0.252526	−	0.530327i
$106$			13.4953i			1.31078i
$107$	−7.13746	−	12.3624i	−0.690004	−	1.19512i	−0.971836	−	0.235658i	$-0.924275\pi$
$107$	−7.13746	−	12.3624i	−0.690004	−	1.19512i	0.281832	−	0.959464i	$-0.409058\pi$
$108$	4.50000	+	2.59808i	0.433013	+	0.250000i
$109$	−3.72508	−	2.15068i	−0.356798	−	0.205998i	0.310877	−	0.950450i	$-0.399377\pi$
$109$	−3.72508	−	2.15068i	−0.356798	−	0.205998i	−0.667675	+	0.744453i	$0.732711\pi$
$110$	2.86254	−	3.28356i	0.272933	−	0.313075i
$111$		−	12.6005i		−	1.19599i
$112$	−2.63746	+	0.209313i	−0.249216	+	0.0197783i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	5.63746	+	9.76436i	0.527996	+	0.914517i
$115$	3.72508	−	6.45203i	0.347366	−	0.601655i
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$	−6.82475	+	3.94027i	−0.630949	+	0.364278i
$118$			1.73205i			0.159448i
$119$	4.91238	+	7.13752i	0.450317	+	0.654295i
$120$	−2.27492			−0.207671
$121$	−10.1873	−	4.14959i	−0.926118	−	0.377235i
$122$	−6.00000	−	3.46410i	−0.543214	−	0.313625i
$123$	9.82475	+	5.67232i	0.885868	+	0.511456i
$124$	5.13746	+	8.89834i	0.461357	+	0.799094i
$125$		−	10.8685i		−	0.972106i
$126$	4.50000	+	6.53835i	0.400892	+	0.582482i
$127$		−	3.52165i		−	0.312496i	−0.987718	−	0.156248i	$-0.950060\pi$
$127$		−	3.52165i		−	0.312496i	0.987718	−	0.156248i	$-0.0499398\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.63746	−	14.9605i	0.760486	−	1.31720i
$130$	1.72508	−	2.98793i	0.151300	−	0.262059i
$131$	5.13746	+	8.89834i	0.448862	+	0.777452i	0.998312	−	0.0580748i	$-0.0184962\pi$
$131$	5.13746	+	8.89834i	0.448862	+	0.777452i	−0.549450	+	0.835526i	$0.685163\pi$
$132$	1.86254	+	5.43424i	0.162113	+	0.472990i
$133$	1.36254	+	17.1687i	0.118147	+	1.48872i
$134$	8.54983			0.738593
$135$	3.41238	+	5.91041i	0.293691	+	0.508687i
$136$	1.63746	−	2.83616i	0.140411	−	0.243199i
$137$	3.72508	+	2.15068i	0.318255	+	0.183745i	0.650615	−	0.759408i	$-0.274511\pi$
$137$	3.72508	+	2.15068i	0.318255	+	0.183745i	−0.332359	+	0.943153i	$0.607845\pi$
$138$	4.91238	+	8.50848i	0.418169	+	0.724290i
$139$			0.418627i			0.0355075i	0.999842	+	0.0177537i	$0.00565148\pi$
$139$			0.418627i			0.0355075i	−0.999842	+	0.0177537i	$0.994349\pi$
$140$	−3.13746	−	1.49397i	−0.265164	−	0.126263i
$141$	−3.82475			−0.322102
$142$	8.63746	−	4.98684i	0.724839	−	0.418486i
$143$	−8.54983	−	1.67451i	−0.714973	−	0.140029i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−1.13746	+	0.656712i	−0.0944608	+	0.0545370i
$146$		−	5.25370i		−	0.434799i
$147$	1.91238	+	11.9726i	0.157730	+	0.987482i
$148$	−7.27492			−0.597995
$149$	−3.63746	−	6.30026i	−0.297992	−	0.516138i	0.677684	−	0.735353i	$-0.262984\pi$
$149$	−3.63746	−	6.30026i	−0.297992	−	0.516138i	−0.975677	+	0.219215i	$0.929650\pi$
$150$	4.91238	+	2.83616i	0.401094	+	0.231572i
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	0.862159	−	0.506637i	$-0.169112\pi$
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	−0.00768132	+	0.999970i	$0.502445\pi$
$152$	5.63746	−	3.25479i	0.457258	−	0.263998i
$153$	−9.82475			−0.794284
$154$	−1.00000	+	8.71780i	−0.0805823	+	0.702500i
$155$			13.4953i			1.08397i
$156$	2.27492	+	3.94027i	0.182139	+	0.315474i
$157$	−8.63746	+	14.9605i	−0.689344	+	1.19398i	0.282706	+	0.959207i	$0.408768\pi$
$157$	−8.63746	+	14.9605i	−0.689344	+	1.19398i	−0.972050	+	0.234773i	$0.924565\pi$
$158$	−1.86254	−	1.07534i	−0.148176	−	0.0855494i
$159$	−11.6873	−	20.2430i	−0.926863	−	1.60537i
$160$			1.31342i			0.103835i
$161$	1.18729	+	14.9605i	0.0935718	+	1.17905i
$162$	−9.00000			−0.707107
$163$	−8.27492	−	14.3326i	−0.648142	−	1.12261i	−0.983566	−	0.180547i	$-0.942213\pi$
$163$	−8.27492	−	14.3326i	−0.648142	−	1.12261i	0.335425	−	0.942067i	$-0.391120\pi$
$164$	3.27492	−	5.67232i	0.255728	−	0.442934i
$165$	−1.45017	+	7.40437i	−0.112895	+	0.576430i
$166$	5.13746	+	8.89834i	0.398744	+	0.690645i
$167$	7.45017			0.576511			0.288256	−	0.957554i	$-0.406925\pi$
$167$	7.45017			0.576511			0.288256	+	0.957554i	$0.406925\pi$
$168$	3.77492	−	2.59808i	0.291241	−	0.200446i
$169$	6.09967			0.469205
$170$	3.72508	−	2.15068i	0.285701	−	0.164949i
$171$	−16.9124	−	9.76436i	−1.29332	−	0.746700i
$172$	−8.63746	−	4.98684i	−0.658600	−	0.380243i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		−	1.73205i		−	0.131306i
$175$	4.91238	+	7.13752i	0.371341	+	0.539546i
$176$	3.13746	−	1.07534i	0.236495	−	0.0810567i
$177$	−1.50000	−	2.59808i	−0.112747	−	0.195283i
$178$	2.27492	+	1.31342i	0.170512	+	0.0984453i
$179$	12.3625	+	7.13752i	0.924020	+	0.533483i	0.884915	−	0.465752i	$-0.154216\pi$
$179$	12.3625	+	7.13752i	0.924020	+	0.533483i	0.0391045	+	0.999235i	$0.487549\pi$
$180$	3.41238	−	1.97014i	0.254343	−	0.146845i
$181$	−6.54983			−0.486845			−0.243423	−	0.969920i	$-0.578270\pi$
$181$	−6.54983			−0.486845			−0.243423	+	0.969920i	$0.578270\pi$
$182$	0.549834	+	6.92820i	0.0407564	+	0.513553i
$183$	12.0000			0.887066
$184$	4.91238	−	2.83616i	0.362145	−	0.209085i
$185$	−8.27492	−	4.77753i	−0.608384	−	0.351251i
$186$	−15.4124	−	8.89834i	−1.13009	−	0.652458i
$187$	−8.18729	−	7.13752i	−0.598714	−	0.521947i
$188$			2.20822i			0.161051i
$189$	−12.4124	−	5.91041i	−0.902867	−	0.429919i
$190$	8.54983			0.620270
$191$	−9.82475	+	5.67232i	−0.710894	+	0.410435i	−0.811392	−	0.584502i	$-0.801290\pi$
$191$	−9.82475	+	5.67232i	−0.710894	+	0.410435i	0.100498	+	0.994937i	$0.467956\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	19.1375	+	11.0490i	1.37754	+	0.795326i	0.991863	−	0.127307i	$-0.0406332\pi$
$193$	19.1375	+	11.0490i	1.37754	+	0.795326i	0.385681	+	0.922632i	$0.373967\pi$
$194$	−6.77492	−	11.7345i	−0.486411	−	0.842488i
$195$			5.97586i			0.427940i
$196$	6.91238	−	1.10411i	0.493741	−	0.0788650i
$197$	−12.7251			−0.906625			−0.453312	−	0.891352i	$-0.649758\pi$
$197$	−12.7251			−0.906625			−0.453312	+	0.891352i	$0.649758\pi$
$198$	−7.50000	−	6.53835i	−0.533002	−	0.464660i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	1.63746	−	2.83616i	0.115786	−	0.200547i
$201$	−12.8248	+	7.40437i	−0.904588	+	0.522264i
$202$	9.82475			0.691267
$203$	1.13746	−	2.38876i	0.0798339	−	0.167658i
$204$			5.67232i			0.397142i
$205$	7.45017	−	4.30136i	0.520342	−	0.300420i
$206$	−6.54983	+	11.3446i	−0.456349	+	0.790419i
$207$	−14.7371	−	8.50848i	−1.02430	−	0.591381i
$208$	2.27492	−	1.31342i	0.157737	−	0.0910696i
$209$	−7.00000	−	20.4235i	−0.484200	−	1.41272i
$210$	6.00000	−	0.476171i	0.414039	−	0.0328589i
$211$		−	19.9474i		−	1.37323i	−0.727020	−	0.686616i	$-0.759095\pi$
$211$		−	19.9474i		−	1.37323i	0.727020	−	0.686616i	$-0.240905\pi$
$212$	−11.6873	+	6.74766i	−0.802687	+	0.463431i
$213$	−8.63746	+	14.9605i	−0.591829	+	1.02508i
$214$	7.13746	−	12.3624i	0.487907	−	0.845079i
$215$	−6.54983	−	11.3446i	−0.446695	−	0.773698i
$216$			5.19615i			0.353553i
$217$	−15.4124	−	22.3937i	−1.04626	−	1.52018i
$218$		−	4.30136i		−	0.291325i
$219$	4.54983	+	7.88054i	0.307449	+	0.532518i
$220$	4.27492	+	0.837253i	0.288215	+	0.0564476i
$221$	−7.45017	−	4.30136i	−0.501152	−	0.289340i
$222$	10.9124	−	6.30026i	0.732391	−	0.422846i
$223$	2.82475			0.189159			0.0945797	−	0.995517i	$-0.469849\pi$
$223$	2.82475			0.189159			0.0945797	+	0.995517i	$0.469849\pi$
$224$	−1.50000	−	2.17945i	−0.100223	−	0.145621i
$225$	−9.82475			−0.654983
$226$		0			0
$227$	−11.6873	+	20.2430i	−0.775713	+	1.34357i	0.158680	+	0.987330i	$0.449276\pi$
$227$	−11.6873	+	20.2430i	−0.775713	+	1.34357i	−0.934393	+	0.356244i	$0.884057\pi$
$228$	−5.63746	+	9.76436i	−0.373350	+	0.646661i
$229$	3.27492	+	5.67232i	0.216413	+	0.374838i	0.953709	−	0.300732i	$-0.0972310\pi$
$229$	3.27492	+	5.67232i	0.216413	+	0.374838i	−0.737296	+	0.675570i	$0.763898\pi$
$230$	7.45017			0.491249
$231$	−6.04983	−	13.9427i	−0.398050	−	0.917364i
$232$	−1.00000			−0.0656532
$233$	8.91238	+	15.4367i	0.583869	+	1.01129i	0.995015	+	0.0997216i	$0.0317952\pi$
$233$	8.91238	+	15.4367i	0.583869	+	1.01129i	−0.411146	+	0.911569i	$0.634871\pi$
$234$	−6.82475	−	3.94027i	−0.446148	−	0.257584i
$235$	−1.45017	+	2.51176i	−0.0945984	+	0.163849i
$236$	−1.50000	+	0.866025i	−0.0976417	+	0.0563735i
$237$	3.72508			0.241970
$238$	−3.72508	+	7.82300i	−0.241461	+	0.507090i
$239$	−12.5498			−0.811781			−0.405891	−	0.913922i	$-0.633039\pi$
$239$	−12.5498			−0.811781			−0.405891	+	0.913922i	$0.633039\pi$
$240$	−1.13746	−	1.97014i	−0.0734226	−	0.127172i
$241$	3.41238	+	1.97014i	0.219810	+	0.126908i	0.605862	−	0.795569i	$-0.292828\pi$
$241$	3.41238	+	1.97014i	0.219810	+	0.126908i	−0.386052	+	0.922477i	$0.626161\pi$
$242$	−1.50000	−	10.8972i	−0.0964237	−	0.700502i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		−	6.92820i		−	0.443533i
$245$	8.58762	+	3.28356i	0.548643	+	0.209779i
$246$			11.3446i			0.723308i
$247$	−8.54983	−	14.8087i	−0.544013	−	0.942258i
$248$	−5.13746	+	8.89834i	−0.326229	+	0.565045i
$249$	−15.4124	−	8.89834i	−0.976720	−	0.563909i
$250$	9.41238	−	5.43424i	0.595291	−	0.343691i
$251$			0.894797i			0.0564791i	0.999601	+	0.0282396i	$0.00899012\pi$
$251$			0.894797i			0.0564791i	−0.999601	+	0.0282396i	$0.991010\pi$
$252$	−3.41238	+	7.16629i	−0.214959	+	0.451434i
$253$	−6.09967	−	17.7967i	−0.383483	−	1.11887i
$254$	3.04983	−	1.76082i	0.191364	−	0.110484i
$255$	−3.72508	+	6.45203i	−0.233274	+	0.404042i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.2749	−	8.24163i	0.890445	−	0.514099i	0.0163569	−	0.999866i	$-0.494793\pi$
$257$	14.2749	−	8.24163i	0.890445	−	0.514099i	0.874088	+	0.485768i	$0.161460\pi$
$258$	17.2749			1.07549
$259$	19.1873	−	1.52274i	1.19224	−	0.0946183i
$260$	3.45017			0.213970
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$	−5.13746	+	8.89834i	−0.317393	+	0.549741i
$263$	−14.5498	+	25.2011i	−0.897181	+	1.55396i	−0.0660996	+	0.997813i	$0.521056\pi$
$263$	−14.5498	+	25.2011i	−0.897181	+	1.55396i	−0.831082	+	0.556150i	$0.812278\pi$
$264$	−3.77492	+	4.33013i	−0.232330	+	0.266501i
$265$	−17.7251			−1.08884
$266$	−14.1873	+	9.76436i	−0.869879	+	0.598692i
$267$	−4.54983			−0.278445
$268$	4.27492	+	7.40437i	0.261132	+	0.452294i
$269$	2.58762	+	1.49397i	0.157770	+	0.0910887i	0.576807	−	0.816881i	$-0.304299\pi$
$269$	2.58762	+	1.49397i	0.157770	+	0.0910887i	−0.419036	+	0.907969i	$0.637632\pi$
$270$	−3.41238	+	5.91041i	−0.207671	+	0.359696i
$271$	7.23713	−	4.17836i	0.439624	−	0.253817i	−0.263814	−	0.964574i	$-0.584981\pi$
$271$	7.23713	−	4.17836i	0.439624	−	0.253817i	0.703438	+	0.710756i	$0.251647\pi$
$272$	3.27492			0.198571
$273$	−6.82475	−	9.91613i	−0.413053	−	0.600152i
$274$			4.30136i			0.259854i
$275$	−8.18729	−	7.13752i	−0.493712	−	0.430408i
$276$	−4.91238	+	8.50848i	−0.295690	+	0.512151i
$277$	7.45017	+	4.30136i	0.447637	+	0.258443i	0.706832	−	0.707382i	$-0.250124\pi$
$277$	7.45017	+	4.30136i	0.447637	+	0.258443i	−0.259195	+	0.965825i	$0.583457\pi$
$278$	−0.362541	+	0.209313i	−0.0217438	+	0.0125538i
$279$	30.8248			1.84543
$280$	−0.274917	−	3.46410i	−0.0164294	−	0.207020i
$281$	11.2749			0.672605			0.336303	−	0.941754i	$-0.390824\pi$
$281$	11.2749			0.672605			0.336303	+	0.941754i	$0.390824\pi$
$282$	−1.91238	−	3.31233i	−0.113880	−	0.197247i
$283$	5.27492	+	3.04547i	0.313561	+	0.181035i	0.648519	−	0.761198i	$-0.275389\pi$
$283$	5.27492	+	3.04547i	0.313561	+	0.181035i	−0.334958	+	0.942233i	$0.608722\pi$
$284$	8.63746	+	4.98684i	0.512539	+	0.295914i
$285$	−12.8248	+	7.40437i	−0.759673	+	0.438597i
$286$	−2.82475	−	8.24163i	−0.167031	−	0.487338i
$287$	−7.45017	+	15.6460i	−0.439769	+	0.923554i
$288$	3.00000			0.176777
$289$	3.13746	+	5.43424i	0.184556	+	0.319661i
$290$	−1.13746	−	0.656712i	−0.0667939	−	0.0385635i
$291$	20.3248	+	11.7345i	1.19146	+	0.687889i
$292$	4.54983	−	2.62685i	0.266259	−	0.153725i
$293$	6.09967			0.356346			0.178173	−	0.983999i	$-0.442981\pi$
$293$	6.09967			0.356346			0.178173	+	0.983999i	$0.442981\pi$
$294$	−9.41238	+	7.64246i	−0.548941	+	0.445717i
$295$	−2.27492			−0.132451
$296$	−3.63746	−	6.30026i	−0.211423	−	0.366195i
$297$	16.9124	+	3.31233i	0.981356	+	0.192201i
$298$	3.63746	−	6.30026i	0.210712	−	0.364964i
$299$	−7.45017	−	12.9041i	−0.430854	−	0.746261i
$300$			5.67232i			0.327492i
$301$	23.8248	+	11.3446i	1.37324	+	0.653895i
$302$			12.1244i			0.697678i
$303$	−14.7371	+	8.50848i	−0.846626	+	0.488800i
$304$	5.63746	+	3.25479i	0.323330	+	0.186675i
$305$	4.54983	−	7.88054i	0.260523	−	0.451239i
$306$	−4.91238	−	8.50848i	−0.280822	−	0.486398i
$307$			1.78959i			0.102138i	0.998695	+	0.0510688i	$0.0162628\pi$
$307$			1.78959i			0.102138i	−0.998695	+	0.0510688i	$0.983737\pi$
$308$	−8.04983	+	3.49287i	−0.458682	+	0.199025i
$309$		−	22.6893i		−	1.29075i
$310$	−11.6873	+	6.74766i	−0.663794	+	0.383241i
$311$	−15.3625	−	8.86957i	−0.871130	−	0.502947i	−0.00340628	−	0.999994i	$-0.501084\pi$
$311$	−15.3625	−	8.86957i	−0.871130	−	0.502947i	−0.867724	+	0.497047i	$0.834418\pi$
$312$	−2.27492	+	3.94027i	−0.128792	+	0.223074i
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$	−17.2749			−0.974880
$315$	−8.58762	+	5.91041i	−0.483858	+	0.333014i
$316$		−	2.15068i		−	0.120985i
$317$	−11.6873	+	6.74766i	−0.656424	+	0.378986i	−0.790913	−	0.611929i	$-0.790394\pi$
$317$	−11.6873	+	6.74766i	−0.656424	+	0.378986i	0.134489	+	0.990915i	$0.457061\pi$
$318$	11.6873	−	20.2430i	0.655391	−	1.13517i
$319$	−0.637459	+	3.25479i	−0.0356908	+	0.182233i
$320$	−1.13746	+	0.656712i	−0.0635859	+	0.0367113i
$321$			24.7249i			1.38001i
$322$	−12.3625	+	8.50848i	−0.688937	+	0.474159i
$323$		−	21.3183i		−	1.18618i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−7.45017	−	4.30136i	−0.413261	−	0.238596i
$326$	8.27492	−	14.3326i	0.458305	−	0.793808i
$327$	3.72508	+	6.45203i	0.205998	+	0.356798i
$328$	6.54983			0.361654
$329$	−0.462210	−	5.82409i	−0.0254825	−	0.321093i
$330$	−7.13746	+	2.44631i	−0.392904	+	0.134665i
$331$	2.54983	+	4.41644i	0.140152	+	0.242750i	0.927554	−	0.373690i	$-0.121908\pi$
$331$	2.54983	+	4.41644i	0.140152	+	0.242750i	−0.787402	+	0.616440i	$0.788574\pi$
$332$	−5.13746	+	8.89834i	−0.281955	+	0.488360i
$333$	−10.9124	+	18.9008i	−0.597995	+	1.03576i
$334$	3.72508	+	6.45203i	0.203827	+	0.353040i
$335$			11.2296i			0.613536i
$336$	4.13746	+	1.97014i	0.225717	+	0.107480i
$337$		−	9.19397i		−	0.500827i	−0.968139	−	0.250414i	$-0.919433\pi$
$337$		−	9.19397i		−	0.500827i	0.968139	−	0.250414i	$-0.0805666\pi$
$338$	3.04983	+	5.28247i	0.165889	+	0.287328i
$339$		0			0
$340$	3.72508	+	2.15068i	0.202021	+	0.116637i
$341$	25.6873	+	22.3937i	1.39104	+	1.21268i
$342$		−	19.5287i		−	1.05599i
$343$	−18.0000	+	4.35890i	−0.971909	+	0.235358i
$344$		−	9.97368i		−	0.537745i
$345$	−11.1752	+	6.45203i	−0.601655	+	0.347366i
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	1.50000	−	0.866025i	0.0804084	−	0.0464238i
$349$			25.3161i			1.35514i	0.735457	+	0.677571i	$0.236967\pi$
$349$			25.3161i			1.35514i	−0.735457	+	0.677571i	$0.763033\pi$
$350$	−3.72508	+	7.82300i	−0.199114	+	0.418157i
$351$	13.6495			0.728557
$352$	2.50000	+	2.17945i	0.133250	+	0.116165i
$353$	31.6495	+	18.2728i	1.68453	+	0.972566i	0.958581	+	0.284820i	$0.0919340\pi$
$353$	31.6495	+	18.2728i	1.68453	+	0.972566i	0.725952	+	0.687745i	$0.241399\pi$
$354$	1.50000	−	2.59808i	0.0797241	−	0.138086i
$355$	6.54983	+	11.3446i	0.347629	+	0.602111i
$356$			2.62685i			0.139223i
$357$	−1.18729	−	14.9605i	−0.0628382	−	0.791795i
$358$			14.2750i			0.754459i
$359$	−12.8248	−	22.2131i	−0.676865	−	1.17236i	−0.975920	−	0.218128i	$-0.930005\pi$
$359$	−12.8248	−	22.2131i	−0.676865	−	1.17236i	0.299056	−	0.954236i	$-0.403328\pi$
$360$	3.41238	+	1.97014i	0.179848	+	0.103835i
$361$	11.6873	−	20.2430i	0.615121	−	1.06542i
$362$	−3.27492	−	5.67232i	−0.172126	−	0.298131i
$363$	11.6873	+	15.0468i	0.613424	+	0.789754i
$364$	−5.72508	+	3.94027i	−0.300076	+	0.206526i
$365$	6.90033			0.361180
$366$	6.00000	+	10.3923i	0.313625	+	0.543214i
$367$	−8.86254	+	15.3504i	−0.462621	+	0.801283i	−0.999091	−	0.0426367i	$-0.986424\pi$
$367$	−8.86254	+	15.3504i	−0.462621	+	0.801283i	0.536470	+	0.843920i	$0.319758\pi$
$368$	4.91238	+	2.83616i	0.256075	+	0.147845i
$369$	−9.82475	−	17.0170i	−0.511456	−	0.885868i
$370$		−	9.55505i		−	0.496743i
$371$	29.4124	−	20.2430i	1.52701	−	1.05096i
$372$		−	17.7967i		−	0.922715i
$373$	7.45017	−	4.30136i	0.385755	−	0.222716i	−0.294564	−	0.955632i	$-0.595174\pi$
$373$	7.45017	−	4.30136i	0.385755	−	0.222716i	0.680319	+	0.732916i	$0.261841\pi$
$374$	2.08762	−	10.6592i	0.107948	−	0.551172i
$375$	−9.41238	+	16.3027i	−0.486053	+	0.841868i
$376$	−1.91238	+	1.10411i	−0.0986233	+	0.0569402i
$377$			2.62685i			0.135290i
$378$	−1.08762	−	13.7046i	−0.0559414	−	0.704890i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	4.27492	+	7.40437i	0.219299	+	0.379836i
$381$	−3.04983	+	5.28247i	−0.156248	+	0.270629i
$382$	−9.82475	−	5.67232i	−0.502678	−	0.290221i
$383$	−26.0120	+	15.0181i	−1.32915	+	0.767387i	−0.985169	−	0.171588i	$-0.945110\pi$
$383$	−26.0120	+	15.0181i	−1.32915	+	0.767387i	−0.343985	+	0.938975i	$0.611777\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	−11.4502	−	1.31342i	−0.583554	−	0.0669383i
$386$			22.0980i			1.12476i
$387$	−25.9124	+	14.9605i	−1.31720	+	0.760486i
$388$	6.77492	−	11.7345i	0.343944	−	0.595729i
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$	−5.17525	+	2.98793i	−0.262059	+	0.151300i
$391$		−	18.5764i		−	0.939448i
$392$	4.41238	+	5.43424i	0.222859	+	0.274470i
$393$		−	17.7967i		−	0.897724i
$394$	−6.36254	−	11.0202i	−0.320540	−	0.555192i
$395$	1.41238	−	2.44631i	0.0710643	−	0.123087i
$396$	1.91238	−	9.76436i	0.0961005	−	0.490678i
$397$	5.36254	+	9.28819i	0.269138	+	0.466161i	0.968640	−	0.248470i	$-0.0799278\pi$
$397$	5.36254	+	9.28819i	0.269138	+	0.466161i	−0.699501	+	0.714631i	$0.746594\pi$
$398$		0			0
$399$	12.8248	−	26.9331i	0.642041	−	1.34834i
$400$	3.27492			0.163746
$401$	19.6495	−	11.3446i	0.981249	−	0.566525i	0.0786023	−	0.996906i	$-0.474954\pi$
$401$	19.6495	−	11.3446i	0.981249	−	0.566525i	0.902647	+	0.430381i	$0.141621\pi$
$402$	−12.8248	−	7.40437i	−0.639640	−	0.369297i
$403$	23.3746	+	13.4953i	1.16437	+	0.672250i
$404$	4.91238	+	8.50848i	0.244400	+	0.423313i
$405$		−	11.8208i		−	0.587381i
$406$	2.63746	−	0.209313i	0.130895	−	0.0103880i
$407$	−22.8248	+	7.82300i	−1.13138	+	0.387772i
$408$	−4.91238	+	2.83616i	−0.243199	+	0.140411i
$409$	12.3127	+	7.10874i	0.608824	+	0.351505i	0.772505	−	0.635009i	$-0.219003\pi$
$409$	12.3127	+	7.10874i	0.608824	+	0.351505i	−0.163681	+	0.986513i	$0.552337\pi$
$410$	7.45017	+	4.30136i	0.367937	+	0.212429i
$411$	−3.72508	−	6.45203i	−0.183745	−	0.318255i
$412$	−13.0997			−0.645374
$413$	3.77492	−	2.59808i	0.185752	−	0.127843i
$414$		−	17.0170i		−	0.836338i
$415$	−11.6873	+	6.74766i	−0.573707	+	0.331230i
$416$	2.27492	+	1.31342i	0.111537	+	0.0643959i
$417$	0.362541	−	0.627940i	0.0177537	−	0.0307504i
$418$	14.1873	−	16.2739i	0.693923	−	0.795984i
$419$			27.2942i			1.33341i	0.745322	+	0.666704i	$0.232296\pi$
$419$			27.2942i			1.33341i	−0.745322	+	0.666704i	$0.767704\pi$
$420$	3.41238	+	4.95807i	0.166507	+	0.241929i
$421$	22.3746			1.09047			0.545235	−	0.838283i	$-0.316440\pi$
$421$	22.3746			1.09047			0.545235	+	0.838283i	$0.316440\pi$
$422$	17.2749	−	9.97368i	0.840930	−	0.485511i
$423$	5.73713	+	3.31233i	0.278949	+	0.161051i
$424$	−11.6873	−	6.74766i	−0.567585	−	0.327695i
$425$	−5.36254	−	9.28819i	−0.260121	−	0.450544i
$426$	−17.2749			−0.836972
$427$	1.45017	+	18.2728i	0.0701784	+	0.884285i
$428$	14.2749			0.690004
$429$	11.3746	+	9.91613i	0.549170	+	0.478755i
$430$	6.54983	−	11.3446i	0.315861	−	0.547087i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	−4.50000	+	2.59808i	−0.216506	+	0.125000i
$433$	−3.27492			−0.157382			−0.0786912	−	0.996899i	$-0.525074\pi$
$433$	−3.27492			−0.157382			−0.0786912	+	0.996899i	$0.525074\pi$
$434$	11.6873	−	24.5443i	0.561008	−	1.17817i
$435$	2.27492			0.109074
$436$	3.72508	−	2.15068i	0.178399	−	0.102999i
$437$	18.4622	−	31.9775i	0.883167	−	1.52969i
$438$	−4.54983	+	7.88054i	−0.217399	+	0.376547i
$439$	2.32475	−	1.34220i	0.110954	−	0.0640595i	−0.443496	−	0.896276i	$-0.646262\pi$
$439$	2.32475	−	1.34220i	0.110954	−	0.0640595i	0.554450	+	0.832217i	$0.312929\pi$
$440$	1.41238	+	4.12081i	0.0673324	+	0.196452i
$441$	7.50000	−	19.6150i	0.357143	−	0.934050i
$442$		−	8.60271i		−	0.409189i
$443$	3.04983	−	1.76082i	0.144902	−	0.0836592i	−0.425796	−	0.904819i	$-0.640006\pi$
$443$	3.04983	−	1.76082i	0.144902	−	0.0836592i	0.570698	+	0.821160i	$0.306673\pi$
$444$	10.9124	+	6.30026i	0.517878	+	0.298997i
$445$	−1.72508	+	2.98793i	−0.0817768	+	0.141642i
$446$	1.41238	+	2.44631i	0.0668779	+	0.115836i
$447$			12.6005i			0.595984i
$448$	1.13746	−	2.38876i	0.0537399	−	0.112858i
$449$			4.30136i			0.202993i	0.994836	+	0.101497i	$0.0323631\pi$
$449$			4.30136i			0.202993i	−0.994836	+	0.101497i	$0.967637\pi$
$450$	−4.91238	−	8.50848i	−0.231572	−	0.401094i
$451$	4.17525	−	21.3183i	0.196605	−	1.00384i
$452$		0			0
$453$	−10.5000	−	18.1865i	−0.493333	−	0.854478i
$454$	−23.3746			−1.09702
$455$	−9.09967	+	0.722166i	−0.426599	+	0.0338557i
$456$	−11.2749			−0.527996
$457$	31.3368	−	18.0923i	1.46587	−	0.846322i	0.466601	−	0.884468i	$-0.345478\pi$
$457$	31.3368	−	18.0923i	1.46587	−	0.846322i	0.999272	+	0.0381453i	$0.0121450\pi$
$458$	−3.27492	+	5.67232i	−0.153027	+	0.265050i
$459$	14.7371	+	8.50848i	0.687870	+	0.397142i
$460$	3.72508	+	6.45203i	0.173683	+	0.300828i
$461$	−9.82475			−0.457584			−0.228792	−	0.973475i	$-0.573478\pi$
$461$	−9.82475			−0.457584			−0.228792	+	0.973475i	$0.573478\pi$
$462$	9.04983	−	12.2107i	0.421036	−	0.568092i
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$	11.6873	−	20.2430i	0.541985	−	0.938746i
$466$	−8.91238	+	15.4367i	−0.412858	+	0.715091i
$467$	−1.81271	+	1.04657i	−0.0838821	+	0.0484293i	−0.541354	−	0.840795i	$-0.682088\pi$
$467$	−1.81271	+	1.04657i	−0.0838821	+	0.0484293i	0.457472	+	0.889224i	$0.348755\pi$
$468$		−	7.88054i		−	0.364278i
$469$	−12.8248	−	18.6339i	−0.592192	−	0.860435i
$470$	−2.90033			−0.133782
$471$	25.9124	−	14.9605i	1.19398	−	0.689344i
$472$	−1.50000	−	0.866025i	−0.0690431	−	0.0398621i
$473$	−32.4622	−	6.35781i	−1.49261	−	0.292332i
$474$	1.86254	+	3.22602i	0.0855494	+	0.148176i
$475$		−	21.3183i		−	0.978152i
$476$	−8.63746	+	0.685484i	−0.395897	+	0.0314191i
$477$			40.4860i			1.85373i
$478$	−6.27492	−	10.8685i	−0.287008	−	0.497112i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$	1.13746	−	1.97014i	0.0519176	−	0.0899240i
$481$	−16.5498	+	9.55505i	−0.754607	+	0.435673i
$482$			3.94027i			0.179474i
$483$	11.1752	−	23.4690i	0.508491	−	1.06788i
$484$	8.68729	−	6.74766i	0.394877	−	0.306712i
$485$	15.4124	−	8.89834i	0.699840	−	0.404053i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	9.68729	−	16.7789i	0.438973	−	0.760324i	−0.558637	−	0.829412i	$-0.688676\pi$
$487$	9.68729	−	16.7789i	0.438973	−	0.760324i	0.997611	+	0.0690882i	$0.0220090\pi$
$488$	6.00000	−	3.46410i	0.271607	−	0.156813i
$489$			28.6652i			1.29628i
$490$	1.45017	+	9.07888i	0.0655118	+	0.410142i
$491$	−15.3746			−0.693845			−0.346923	−	0.937894i	$-0.612773\pi$
$491$	−15.3746			−0.693845			−0.346923	+	0.937894i	$0.612773\pi$
$492$	−9.82475	+	5.67232i	−0.442934	+	0.255728i
$493$	−1.63746	+	2.83616i	−0.0737474	+	0.127734i
$494$	8.54983	−	14.8087i	0.384675	−	0.666277i
$495$	8.58762	−	9.85068i	0.385985	−	0.442755i
$496$	−10.2749			−0.461357
$497$	−23.8248	−	11.3446i	−1.06869	−	0.508877i
$498$		−	17.7967i		−	0.797488i
$499$	−1.72508	−	2.98793i	−0.0772253	−	0.133758i	0.824827	−	0.565386i	$-0.191273\pi$
$499$	−1.72508	−	2.98793i	−0.0772253	−	0.133758i	−0.902052	+	0.431628i	$0.857939\pi$
$500$	9.41238	+	5.43424i	0.420934	+	0.243026i
$501$	−11.1752	−	6.45203i	−0.499273	−	0.288256i
$502$	−0.774917	+	0.447399i	−0.0345862	+	0.0199684i
$503$	33.6495			1.50036			0.750179	−	0.661235i	$-0.229967\pi$
$503$	33.6495			1.50036			0.750179	+	0.661235i	$0.229967\pi$
$504$	−7.91238	+	0.627940i	−0.352445	+	0.0279707i
$505$			12.9041i			0.574223i
$506$	12.3625	−	14.1808i	0.549582	−	0.630414i
$507$	−9.14950	−	5.28247i	−0.406344	−	0.234603i
$508$	3.04983	+	1.76082i	0.135315	+	0.0781239i
$509$	−20.5876	+	11.8863i	−0.912530	+	0.526850i	−0.881244	−	0.472661i	$-0.843294\pi$
$509$	−20.5876	+	11.8863i	−0.912530	+	0.526850i	−0.0312860	+	0.999510i	$0.509960\pi$
$510$	−7.45017			−0.329899
$511$	−11.4502	+	7.88054i	−0.506526	+	0.348615i
$512$	−1.00000			−0.0441942
$513$	16.9124	+	29.2931i	0.746700	+	1.29332i
$514$	14.2749	+	8.24163i	0.629640	+	0.363523i
$515$	−14.9003	−	8.60271i	−0.656587	−	0.379081i
$516$	8.63746	+	14.9605i	0.380243	+	0.658600i
$517$	2.37459	+	6.92820i	0.104434	+	0.304702i
$518$	10.9124	+	15.8553i	0.479462	+	0.696643i
$519$		−	24.2487i		−	1.06440i
$520$	1.72508	+	2.98793i	0.0756499	+	0.131029i
$521$	−15.0997	−	8.71780i	−0.661529	−	0.381934i	0.131331	−	0.991339i	$-0.458075\pi$
$521$	−15.0997	−	8.71780i	−0.661529	−	0.381934i	−0.792859	+	0.609405i	$0.791408\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−24.0997	+	13.9140i	−1.05380	+	0.608415i	−0.923712	−	0.383087i	$-0.874861\pi$
$523$	−24.0997	+	13.9140i	−1.05380	+	0.608415i	−0.130093	+	0.991502i	$0.541528\pi$
$524$	−10.2749			−0.448862
$525$	−1.18729	−	14.9605i	−0.0518177	−	0.652930i
$526$	−29.0997			−1.26881
$527$	16.8248	+	29.1413i	0.732898	+	1.26942i
$528$	−5.63746	−	1.10411i	−0.245339	−	0.0480503i
$529$	4.58762	−	7.94600i	0.199462	−	0.345478i
$530$	−8.86254	−	15.3504i	−0.384964	−	0.666778i
$531$			5.19615i			0.225494i
$532$	−15.5498	−	7.40437i	−0.674171	−	0.321020i
$533$		−	17.2054i		−	0.745249i
$534$	−2.27492	−	3.94027i	−0.0984453	−	0.170512i
$535$	16.2371	+	9.37451i	0.701992	+	0.405295i
$536$	−4.27492	+	7.40437i	−0.184648	+	0.319820i
$537$	−12.3625	−	21.4125i	−0.533483	−	0.924020i
$538$			2.98793i			0.128819i
$539$	20.5000	−	10.8972i	0.882998	−	0.469378i
$540$	−6.82475			−0.293691
$541$	−7.45017	+	4.30136i	−0.320308	+	0.184930i	−0.651530	−	0.758623i	$-0.725872\pi$
$541$	−7.45017	+	4.30136i	−0.320308	+	0.184930i	0.331222	+	0.943553i	$0.392539\pi$
$542$	7.23713	+	4.17836i	0.310861	+	0.179476i
$543$	9.82475	+	5.67232i	0.421620	+	0.243423i
$544$	1.63746	+	2.83616i	0.0702055	+	0.121599i
$545$	5.64950			0.241998
$546$	5.17525	−	10.8685i	0.221480	−	0.465128i
$547$		−	17.0170i		−	0.727593i	−0.931478	−	0.363797i	$-0.881480\pi$
$547$		−	17.0170i		−	0.727593i	0.931478	−	0.363797i	$-0.118520\pi$
$548$	−3.72508	+	2.15068i	−0.159128	+	0.0918724i
$549$	−18.0000	−	10.3923i	−0.768221	−	0.443533i
$550$	2.08762	−	10.6592i	0.0890166	−	0.454508i
$551$	−5.63746	+	3.25479i	−0.240164	+	0.138659i
$552$	−9.82475			−0.418169
$553$	0.450166	+	5.67232i	0.0191430	+	0.241212i
$554$			8.60271i			0.365494i
$555$	8.27492	+	14.3326i	0.351251	+	0.608384i
$556$	−0.362541	−	0.209313i	−0.0153752	−	0.00887686i
$557$	−7.32475	+	12.6868i	−0.310360	+	0.537559i	−0.978440	−	0.206530i	$-0.933783\pi$
$557$	−7.32475	+	12.6868i	−0.310360	+	0.537559i	0.668081	+	0.744089i	$0.267116\pi$
$558$	15.4124	+	26.6950i	0.652458	+	1.13009i
$559$	−26.1993			−1.10811
$560$	2.86254	−	1.97014i	0.120964	−	0.0832534i
$561$	6.09967	+	17.7967i	0.257528	+	0.751376i
$562$	5.63746	+	9.76436i	0.237802	+	0.411885i
$563$	−19.1375	+	33.1471i	−0.806548	+	1.39698i	0.108694	+	0.994075i	$0.465333\pi$
$563$	−19.1375	+	33.1471i	−0.806548	+	1.39698i	−0.915241	+	0.402906i	$0.868000\pi$
$564$	1.91238	−	3.31233i	0.0805255	−	0.139474i
$565$		0			0
$566$			6.09095i			0.256022i
$567$	13.5000	+	19.6150i	0.566947	+	0.823754i
$568$			9.97368i			0.418486i
$569$	−4.18729	−	7.25260i	−0.175540	−	0.304045i	0.764808	−	0.644259i	$-0.222834\pi$
$569$	−4.18729	−	7.25260i	−0.175540	−	0.304045i	−0.940348	+	0.340214i	$0.889501\pi$
$570$	−12.8248	−	7.40437i	−0.537170	−	0.310135i
$571$	18.4622	+	10.6592i	0.772619	+	0.446072i	0.833808	−	0.552054i	$-0.186156\pi$
$571$	18.4622	+	10.6592i	0.772619	+	0.446072i	−0.0611888	+	0.998126i	$0.519489\pi$
$572$	5.72508	−	6.56712i	0.239378	−	0.274585i
$573$	19.6495			0.820870
$574$	−17.2749	+	1.37097i	−0.721041	+	0.0572231i
$575$		−	18.5764i		−	0.774689i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	18.6873	−	32.3673i	0.777962	−	1.34747i	−0.155152	−	0.987891i	$-0.549587\pi$
$577$	18.6873	−	32.3673i	0.777962	−	1.34747i	0.933114	−	0.359579i	$-0.117080\pi$
$578$	−3.13746	+	5.43424i	−0.130501	+	0.226034i
$579$	−19.1375	−	33.1471i	−0.795326	−	1.37754i
$580$		−	1.31342i		−	0.0545370i
$581$	11.6873	−	24.5443i	0.484871	−	1.01827i
$582$			23.4690i			0.972821i
$583$	−29.4124	+	33.7383i	−1.21814	+	1.39730i
$584$	4.54983	+	2.62685i	0.188273	+	0.108700i
$585$	5.17525	−	8.96379i	0.213970	−	0.370607i
$586$	3.04983	+	5.28247i	0.125987	+	0.218217i
$587$		−	13.3802i		−	0.552261i	−0.961120	−	0.276131i	$-0.910948\pi$
$587$		−	13.3802i		−	0.552261i	0.961120	−	0.276131i	$-0.0890523\pi$
$588$	−11.3248	−	4.33013i	−0.467025	−	0.178571i
$589$			66.8854i			2.75596i
$590$	−1.13746	−	1.97014i	−0.0468284	−	0.0811092i
$591$	19.0876	+	11.0202i	0.785160	+	0.453312i
$592$	3.63746	−	6.30026i	0.149499	−	0.258939i
$593$	4.91238	+	8.50848i	0.201727	+	0.349402i	0.949085	−	0.315020i	$-0.102011\pi$
$593$	4.91238	+	8.50848i	0.201727	+	0.349402i	−0.747358	+	0.664422i	$0.768678\pi$
$594$	5.58762	+	16.3027i	0.229263	+	0.668908i
$595$	−10.2749	−	4.89261i	−0.421231	−	0.200578i
$596$	7.27492			0.297992
$597$		0			0
$598$	7.45017	−	12.9041i	0.304660	−	0.527686i
$599$	−6.09967	−	3.52165i	−0.249226	−	0.143891i	0.370184	−	0.928958i	$-0.379295\pi$
$599$	−6.09967	−	3.52165i	−0.249226	−	0.143891i	−0.619410	+	0.785068i	$0.712628\pi$
$600$	−4.91238	+	2.83616i	−0.200547	+	0.115786i
$601$			20.4235i			0.833093i	0.909114	+	0.416547i	$0.136760\pi$
$601$			20.4235i			0.833093i	−0.909114	+	0.416547i	$0.863240\pi$
$602$	2.08762	+	26.3052i	0.0850852	+	1.07212i
$603$	25.6495			1.04453
$604$	−10.5000	+	6.06218i	−0.427239	+	0.246667i
$605$	14.3127	−	1.97014i	0.581894	−	0.0800974i
$606$	−14.7371	−	8.50848i	−0.598655	−	0.345634i
$607$	22.1375	−	12.7811i	0.898532	−	0.518768i	0.0218082	−	0.999762i	$-0.493058\pi$
$607$	22.1375	−	12.7811i	0.898532	−	0.518768i	0.876724	+	0.480995i	$0.159724\pi$
$608$			6.50958i			0.263998i
$609$	−3.77492	+	2.59808i	−0.152967	+	0.105279i
$610$	9.09967			0.368435
$611$	2.90033	+	5.02352i	0.117335	+	0.203230i
$612$	4.91238	−	8.50848i	0.198571	−	0.343935i
$613$	−30.8248	−	17.7967i	−1.24500	−	0.718801i	−0.274892	−	0.961475i	$-0.588642\pi$
$613$	−30.8248	−	17.7967i	−1.24500	−	0.718801i	−0.970108	+	0.242674i	$0.921975\pi$
$614$	−1.54983	+	0.894797i	−0.0625462	+	0.0361111i
$615$	−14.9003			−0.600839
$616$	−7.04983	−	5.22492i	−0.284046	−	0.210518i
$617$			31.2920i			1.25977i	0.776689	+	0.629884i	$0.216898\pi$
$617$			31.2920i			1.25977i	−0.776689	+	0.629884i	$0.783102\pi$
$618$	19.6495	−	11.3446i	0.790419	−	0.456349i
$619$	−6.54983	+	11.3446i	−0.263260	+	0.455980i	−0.967106	−	0.254373i	$-0.918131\pi$
$619$	−6.54983	+	11.3446i	−0.263260	+	0.455980i	0.703846	+	0.710352i	$0.251464\pi$
$620$	−11.6873	−	6.74766i	−0.469373	−	0.270993i
$621$	14.7371	+	25.5255i	0.591381	+	1.02430i
$622$		−	17.7391i		−	0.711275i
$623$	−0.549834	−	6.92820i	−0.0220287	−	0.277573i
$624$	−4.54983			−0.182139
$625$	−1.04983	−	1.81837i	−0.0419934	−	0.0727347i
$626$	3.50000	−	6.06218i	0.139888	−	0.242293i
$627$	−7.18729	+	36.6975i	−0.287033	+	1.46556i
$628$	−8.63746	−	14.9605i	−0.344672	−	0.596990i
$629$	−23.8248			−0.949955
$630$	−9.41238	−	4.48190i	−0.374998	−	0.178563i
$631$	−27.9244			−1.11165			−0.555827	−	0.831298i	$-0.687598\pi$
$631$	−27.9244			−1.11165			−0.555827	+	0.831298i	$0.687598\pi$
$632$	1.86254	−	1.07534i	0.0740879	−	0.0427747i
$633$	−17.2749	+	29.9210i	−0.686616	+	1.18925i
$634$	−11.6873	−	6.74766i	−0.464162	−	0.267984i
$635$	2.31271	+	4.00573i	0.0917770	+	0.158962i
$636$	23.3746			0.926863
$637$	14.2749	−	11.5906i	0.565593	−	0.459238i
$638$	−3.13746	+	1.07534i	−0.124213	+	0.0425731i
$639$	25.9124	−	14.9605i	1.02508	−	0.591829i
$640$	−1.13746	−	0.656712i	−0.0449620	−	0.0259588i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	−21.4124	+	12.3624i	−0.845079	+	0.487907i
$643$	−33.6495			−1.32701			−0.663503	−	0.748173i	$-0.730931\pi$
$643$	−33.6495			−1.32701			−0.663503	+	0.748173i	$0.730931\pi$
$644$	−13.5498	−	6.45203i	−0.533938	−	0.254246i
$645$			22.6893i			0.893390i
$646$	18.4622	−	10.6592i	0.726386	−	0.419379i
$647$	21.8248	+	12.6005i	0.858020	+	0.495378i	0.863349	−	0.504608i	$-0.168363\pi$
$647$	21.8248	+	12.6005i	0.858020	+	0.495378i	−0.00532906	+	0.999986i	$0.501696\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−3.77492	+	4.33013i	−0.148178	+	0.169972i
$650$		−	8.60271i		−	0.337426i
$651$	3.72508	+	46.9380i	0.145998	+	1.83965i
$652$	16.5498			0.648142
$653$	19.1375	−	11.0490i	0.748907	−	0.432381i	−0.0763921	−	0.997078i	$-0.524340\pi$
$653$	19.1375	−	11.0490i	0.748907	−	0.432381i	0.825299	+	0.564696i	$0.191007\pi$
$654$	−3.72508	+	6.45203i	−0.145662	+	0.252294i
$655$	−11.6873	−	6.74766i	−0.456660	−	0.263653i
$656$	3.27492	+	5.67232i	0.127864	+	0.221467i
$657$		−	15.7611i		−	0.614899i
$658$	4.81271	−	3.31233i	0.187619	−	0.129128i
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$	−5.68729	−	4.95807i	−0.221378	−	0.192993i
$661$	5.36254	−	9.28819i	0.208579	−	0.361269i	−0.742688	−	0.669637i	$-0.766450\pi$
$661$	5.36254	−	9.28819i	0.208579	−	0.361269i	0.951267	+	0.308368i	$0.0997829\pi$
$662$	−2.54983	+	4.41644i	−0.0991021	+	0.171650i
$663$	7.45017	+	12.9041i	0.289340	+	0.501152i
$664$	−10.2749			−0.398744
$665$	−12.8248	−	18.6339i	−0.497323	−	0.722593i
$666$	−21.8248			−0.845692
$667$	−4.91238	+	2.83616i	−0.190208	+	0.109817i
$668$	−3.72508	+	6.45203i	−0.144128	+	0.249637i
$669$	−4.23713	−	2.44631i	−0.163817	−	0.0945797i
$670$	−9.72508	+	5.61478i	−0.375713	+	0.216918i
$671$	−7.45017	−	21.7370i	−0.287610	−	0.839146i
$672$	0.362541	+	4.56821i	0.0139853	+	0.176223i
$673$		−	22.0980i		−	0.851817i	−0.904766	−	0.425908i	$-0.859955\pi$
$673$		−	22.0980i		−	0.851817i	0.904766	−	0.425908i	$-0.140045\pi$
$674$	7.96221	−	4.59698i	0.306693	−	0.177069i
$675$	14.7371	+	8.50848i	0.567232	+	0.327492i
$676$	−3.04983	+	5.28247i	−0.117301	+	0.203172i
$677$	16.5997	+	28.7515i	0.637977	+	1.10501i	0.985876	+	0.167477i	$0.0535619\pi$
$677$	16.5997	+	28.7515i	0.637977	+	1.10501i	−0.347899	+	0.937532i	$0.613105\pi$
$678$		0			0
$679$	−15.4124	+	32.3673i	−0.591473	+	1.24214i
$680$			4.30136i			0.164949i
$681$	35.0619	−	20.2430i	1.34357	−	0.775713i
$682$	−6.54983	+	33.4427i	−0.250806	+	1.28059i
$683$	−41.3248	−	23.8589i	−1.58125	−	0.912934i	−0.994678	−	0.103035i	$-0.967145\pi$
$683$	−41.3248	−	23.8589i	−1.58125	−	0.912934i	−0.586570	−	0.809899i	$-0.699522\pi$
$684$	16.9124	−	9.76436i	0.646661	−	0.373350i
$685$	−5.64950			−0.215856
$686$	−12.7749	−	13.4090i	−0.487749	−	0.511958i
$687$		−	11.3446i		−	0.432825i
$688$	8.63746	−	4.98684i	0.329300	−	0.190121i
$689$	−17.7251	+	30.7007i	−0.675272	+	1.16961i
$690$	−11.1752	−	6.45203i	−0.425434	−	0.245625i
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−14.0000			−0.532200
$693$	−3.00000	+	26.1534i	−0.113961	+	0.993485i
$694$	4.00000			0.151838
$695$	−0.274917	−	0.476171i	−0.0104282	−	0.0180622i
$696$	1.50000	+	0.866025i	0.0568574	+	0.0328266i
$697$	10.7251	−	18.5764i	0.406241	−	0.703631i
$698$	−21.9244	+	12.6581i	−0.829852	+	0.479115i
$699$		−	30.8734i		−	1.16774i
$700$	−8.63746	+	0.685484i	−0.326465	+	0.0259089i
$701$	−9.90033			−0.373930			−0.186965	−	0.982367i	$-0.559865\pi$
$701$	−9.90033			−0.373930			−0.186965	+	0.982367i	$0.559865\pi$
$702$	6.82475	+	11.8208i	0.257584	+	0.446148i
$703$	−41.0120	−	23.6783i	−1.54680	−	0.893045i
$704$	−0.637459	+	3.25479i	−0.0240251	+	0.122669i
$705$	4.35050	−	2.51176i	0.163849	−	0.0945984i
$706$			36.5457i			1.37542i
$707$	−14.7371	−	21.4125i	−0.554247	−	0.805302i
$708$	3.00000			0.112747
$709$	17.6375	+	30.5490i	0.662389	+	1.14729i	0.979986	+	0.199065i	$0.0637906\pi$
$709$	17.6375	+	30.5490i	0.662389	+	1.14729i	−0.317598	+	0.948226i	$0.602876\pi$
$710$	−6.54983	+	11.3446i	−0.245811	+	0.425757i
$711$	−5.58762	−	3.22602i	−0.209552	−	0.120985i
$712$	−2.27492	+	1.31342i	−0.0852561	+	0.0492226i
$713$			58.2826i			2.18270i
$714$	12.3625	−	8.50848i	0.462656	−	0.318422i
$715$	10.8248	−	3.71010i	0.404823	−	0.138750i
$716$	−12.3625	+	7.13752i	−0.462010	+	0.266742i
$717$	18.8248	+	10.8685i	0.703023	+	0.405891i
$718$	12.8248	−	22.2131i	0.478615	−	0.828986i
$719$	13.0876	−	7.55614i	0.488086	−	0.281797i	−0.235694	−	0.971827i	$-0.575736\pi$
$719$	13.0876	−	7.55614i	0.488086	−	0.281797i	0.723780	+	0.690031i	$0.242403\pi$
$720$			3.94027i			0.146845i
$721$	34.5498	−	2.74194i	1.28670	−	0.102115i
$722$	23.3746			0.869912
$723$	−3.41238	−	5.91041i	−0.126908	−	0.219810i
$724$	3.27492	−	5.67232i	0.121711	−	0.210810i
$725$	−1.63746	+	2.83616i	−0.0608137	+	0.105332i
$726$	−7.18729	+	17.6449i	−0.266745	+	0.654864i
$727$	10.2749			0.381076			0.190538	−	0.981680i	$-0.438977\pi$
$727$	10.2749			0.381076			0.190538	+	0.981680i	$0.438977\pi$
$728$	−6.27492	−	2.98793i	−0.232564	−	0.110740i
$729$	−27.0000			−1.00000
$730$	3.45017	+	5.97586i	0.127696	+	0.221177i
$731$	−28.2870	−	16.3315i	−1.04623	−	0.604042i
$732$	−6.00000	+	10.3923i	−0.221766	+	0.384111i
$733$	−33.0997	+	19.1101i	−1.22256	+	0.705848i	−0.965464	−	0.260537i	$-0.916100\pi$
$733$	−33.0997	+	19.1101i	−1.22256	+	0.705848i	−0.257100	+	0.966385i	$0.582767\pi$
$734$	−17.7251			−0.654245
$735$	−10.0378	−	12.3624i	−0.370249	−	0.455996i
$736$			5.67232i			0.209085i
$737$	21.3746	+	18.6339i	0.787343	+	0.686390i
$738$	9.82475	−	17.0170i	0.361654	−	0.626403i
$739$	−6.09967	−	3.52165i	−0.224380	−	0.129546i	0.383597	−	0.923501i	$-0.374685\pi$
$739$	−6.09967	−	3.52165i	−0.224380	−	0.129546i	−0.607977	+	0.793955i	$0.708019\pi$
$740$	8.27492	−	4.77753i	0.304192	−	0.175625i
$741$			29.6175i			1.08803i
$742$	32.2371	+	15.3504i	1.18346	+	0.563530i
$743$	2.35050			0.0862314			0.0431157	−	0.999070i	$-0.486272\pi$
$743$	2.35050			0.0862314			0.0431157	+	0.999070i	$0.486272\pi$
$744$	15.4124	−	8.89834i	0.565045	−	0.326229i
$745$	8.27492	+	4.77753i	0.303170	+	0.175035i
$746$	7.45017	+	4.30136i	0.272770	+	0.157484i
$747$	15.4124	+	26.6950i	0.563909	+	0.976720i
$748$	10.2749	−	3.52165i	0.375688	−	0.128764i
$749$	−37.6495	+	2.98793i	−1.37568	+	0.109177i
$750$	−18.8248			−0.687383
$751$	−17.1375	−	29.6829i	−0.625355	−	1.08315i	−0.988472	−	0.151403i	$-0.951621\pi$
$751$	−17.1375	−	29.6829i	−0.625355	−	1.08315i	0.363117	−	0.931743i	$-0.381712\pi$
$752$	−1.91238	−	1.10411i	−0.0697372	−	0.0402628i
$753$	0.774917	−	1.34220i	0.0282396	−	0.0489123i
$754$	−2.27492	+	1.31342i	−0.0828476	+	0.0478321i
$755$	−15.9244			−0.579549
$756$	11.3248	−	7.79423i	0.411877	−	0.283473i
$757$	35.4743			1.28933			0.644667	−	0.764464i	$-0.276996\pi$
$757$	35.4743			1.28933			0.644667	+	0.764464i	$0.276996\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$	−6.26287	+	31.9775i	−0.227328	+	1.16071i
$760$	−4.27492	+	7.40437i	−0.155068	+	0.268585i
$761$	−20.0997	−	34.8136i	−0.728612	−	1.26199i	−0.957470	−	0.288534i	$-0.906832\pi$
$761$	−20.0997	−	34.8136i	−0.728612	−	1.26199i	0.228857	−	0.973460i	$-0.426501\pi$
$762$	−6.09967			−0.220968
$763$	−9.37459	+	6.45203i	−0.339383	+	0.233579i
$764$		−	11.3446i		−	0.410435i
$765$	11.1752	−	6.45203i	0.404042	−	0.233274i
$766$	−26.0120	−	15.0181i	−0.939853	−	0.542625i
$767$	−2.27492	+	3.94027i	−0.0821425	+	0.142275i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$		−	37.8591i		−	1.36523i	−0.730776	−	0.682617i	$-0.760842\pi$
$769$		−	37.8591i		−	1.36523i	0.730776	−	0.682617i	$-0.239158\pi$
$770$	−4.58762	−	10.5728i	−0.165326	−	0.381019i
$771$	−28.5498			−1.02820
$772$	−19.1375	+	11.0490i	−0.688772	+	0.397663i
$773$	12.0000	+	6.92820i	0.431610	+	0.249190i	0.700032	−	0.714111i	$-0.253169\pi$
$773$	12.0000	+	6.92820i	0.431610	+	0.249190i	−0.268422	+	0.963301i	$0.586502\pi$
$774$	−25.9124	−	14.9605i	−0.931401	−	0.537745i
$775$	16.8248	+	29.1413i	0.604363	+	1.04679i
$776$	13.5498			0.486411
$777$	−30.0997	−	14.3326i	−1.07982	−	0.514178i
$778$		0			0
$779$	36.9244	−	21.3183i	1.32295	−	0.763808i
$780$	−5.17525	−	2.98793i	−0.185304	−	0.106985i
$781$	32.4622	+	6.35781i	1.16159	+	0.227500i
$782$	16.0876	−	9.28819i	0.575292	−	0.332145i
$783$		−	5.19615i		−	0.185695i
$784$	−2.50000	+	6.53835i	−0.0892857	+	0.233512i
$785$		−	22.6893i		−	0.809816i
$786$	15.4124	−	8.89834i	0.549741	−	0.317393i
$787$	−47.7371	−	27.5610i	−1.70164	−	0.982445i	−0.944098	−	0.329664i	$-0.893065\pi$
$787$	−47.7371	−	27.5610i	−1.70164	−	0.982445i	−0.757546	−	0.652781i	$-0.773602\pi$
$788$	6.36254	−	11.0202i	0.226656	−	0.392580i
$789$	43.6495	−	25.2011i	1.55396	−	0.897181i
$790$	2.82475			0.100500
$791$		0			0
$792$	9.41238	−	3.22602i	0.334454	−	0.114631i
$793$	−9.09967	−	15.7611i	−0.323139	−	0.559693i
$794$	−5.36254	+	9.28819i	−0.190309	+	0.329626i
$795$	26.5876	+	15.3504i	0.942966	+	0.544422i
$796$		0			0
$797$		−	24.7249i		−	0.875800i	−0.899024	−	0.437900i	$-0.855722\pi$
$797$		−	24.7249i		−	0.875800i	0.899024	−	0.437900i	$-0.144278\pi$
$798$	29.7371	−	2.35999i	1.05268	−	0.0835428i
$799$			7.23174i			0.255841i
$800$	1.63746	+	2.83616i	0.0578929	+	0.100273i
$801$	6.82475	+	3.94027i	0.241141	+	0.139223i
$802$	19.6495	+	11.3446i	0.693848	+	0.400593i
$803$	11.4502	−	13.1342i	0.404068	−	0.463497i
$804$		−	14.8087i		−	0.522264i
$805$	−11.1752	−	16.2373i	−0.393876	−	0.572288i
$806$			26.9906i			0.950705i
$807$	−2.58762	−	4.48190i	−0.0910887	−	0.157770i
$808$	−4.91238	+	8.50848i	−0.172817	+	0.299327i
$809$	15.8248	−	27.4093i	0.556369	−	0.963659i	−0.441427	−	0.897297i	$-0.645528\pi$
$809$	15.8248	−	27.4093i	0.556369	−	0.963659i	0.997796	−	0.0663616i	$-0.0211391\pi$
$810$	10.2371	−	5.91041i	0.359696	−	0.207671i
$811$		−	17.3205i		−	0.608205i	−0.952639	−	0.304103i	$-0.901643\pi$
$811$		−	17.3205i		−	0.608205i	0.952639	−	0.304103i	$-0.0983566\pi$
$812$	1.50000	+	2.17945i	0.0526397	+	0.0764837i
$813$	−14.4743			−0.507634
$814$	−18.1873	−	15.8553i	−0.637464	−	0.555728i
$815$	18.8248	+	10.8685i	0.659402	+	0.380706i
$816$	−4.91238	−	2.83616i	−0.171968	−	0.0992855i
$817$	−32.4622	−	56.2262i	−1.13571	−	1.96711i
$818$			14.2175i			0.497103i
$819$	1.64950	+	20.7846i	0.0576383	+	0.726273i
$820$			8.60271i			0.300420i
$821$	12.9622	+	22.4512i	0.452384	+	0.783553i	0.998534	−	0.0541353i	$-0.0172402\pi$
$821$	12.9622	+	22.4512i	0.452384	+	0.783553i	−0.546149	+	0.837688i	$0.683907\pi$
$822$	3.72508	−	6.45203i	0.129927	−	0.225040i
$823$	−13.4502	+	23.2964i	−0.468843	+	0.812060i	−0.999366	−	0.0356105i	$-0.988662\pi$
$823$	−13.4502	+	23.2964i	−0.468843	+	0.812060i	0.530522	+	0.847671i	$0.321996\pi$
$824$	−6.54983	−	11.3446i	−0.228174	−	0.395209i
$825$	6.09967	+	17.7967i	0.212363	+	0.619601i
$826$	4.13746	+	1.97014i	0.143961	+	0.0685498i
$827$	44.4743			1.54652			0.773261	−	0.634088i	$-0.218624\pi$
$827$	44.4743			1.54652			0.773261	+	0.634088i	$0.218624\pi$
$828$	14.7371	−	8.50848i	0.512151	−	0.295690i
$829$	8.18729	−	14.1808i	0.284356	−	0.492520i	−0.688096	−	0.725619i	$-0.741553\pi$
$829$	8.18729	−	14.1808i	0.284356	−	0.492520i	0.972453	+	0.233099i	$0.0748868\pi$
$830$	−11.6873	−	6.74766i	−0.405672	−	0.234215i
$831$	−7.45017	−	12.9041i	−0.258443	−	0.447637i
$832$			2.62685i			0.0910696i
$833$	22.6375	−	3.61587i	0.784341	−	0.125283i
$834$	0.725083			0.0251076
$835$	−8.47425	+	4.89261i	−0.293264	+	0.169316i
$836$	21.1873	+	4.14959i	0.732778	+	0.143516i
$837$	−46.2371	−	26.6950i	−1.59819	−	0.922715i
$838$	−23.6375	+	13.6471i	−0.816542	+	0.471431i
$839$			57.2152i			1.97529i	0.156712	+	0.987644i	$0.449911\pi$
$839$			57.2152i			1.97529i	−0.156712	+	0.987644i	$0.550089\pi$
$840$	−2.58762	+	5.43424i	−0.0892815	+	0.187499i
$841$	−28.0000			−0.965517
$842$	11.1873	+	19.3770i	0.385540	+	0.667774i
$843$	−16.9124	−	9.76436i	−0.582493	−	0.336303i
$844$	17.2749	+	9.97368i	0.594627	+	0.343308i
$845$	−6.93812	+	4.00573i	−0.238679	+	0.137801i
$846$			6.62466i			0.227761i
$847$	−21.5000	+	19.6150i	−0.738749	+	0.673981i
$848$		−	13.4953i		−	0.463431i
$849$	−5.27492	−	9.13642i	−0.181035	−	0.313561i
$850$	5.36254	−	9.28819i	0.183934	−	0.318582i
$851$	−35.7371	−	20.6328i	−1.22505	−	0.707285i
$852$	−8.63746	−	14.9605i	−0.295914	−	0.512539i
$853$			13.1342i			0.449708i	0.974392	+	0.224854i	$0.0721905\pi$
$853$			13.1342i			0.449708i	−0.974392	+	0.224854i	$0.927810\pi$
$854$	−15.0997	+	10.3923i	−0.516700	+	0.355617i
$855$	25.6495			0.877195
$856$	7.13746	+	12.3624i	0.243953	+	0.422540i
$857$	8.63746	−	14.9605i	0.295050	−	0.511042i	−0.679947	−	0.733262i	$-0.737997\pi$
$857$	8.63746	−	14.9605i	0.295050	−	0.511042i	0.974997	+	0.222220i	$0.0713304\pi$
$858$	−2.90033	+	14.8087i	−0.0990157	+	0.505562i
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	0.521999	−	0.852946i	$-0.325187\pi$
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	−0.999672	+	0.0255910i	$0.991853\pi$
$860$	13.0997			0.446695
$861$	24.7251	−	17.0170i	0.842629	−	0.579937i
$862$	12.0000			0.408722
$863$	−33.1993	+	19.1676i	−1.13012	+	0.652474i	−0.943965	−	0.330046i	$-0.892936\pi$
$863$	−33.1993	+	19.1676i	−1.13012	+	0.652474i	−0.186154	+	0.982521i	$0.559602\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	−15.9244	−	9.19397i	−0.541447	−	0.312604i
$866$	−1.63746	−	2.83616i	−0.0556431	−	0.0963767i
$867$		−	10.8685i		−	0.369113i
$868$	27.0997	−	2.15068i	0.919823	−	0.0729988i
$869$	−2.31271	−	6.74766i	−0.0784532	−	0.228899i
$870$	1.13746	+	1.97014i	0.0385635	+	0.0667939i
$871$	19.4502	+	11.2296i	0.659044	+	0.380499i
$872$	3.72508	+	2.15068i	0.126147	+	0.0728311i
$873$	−20.3248	−	35.2035i	−0.687889	−	1.19146i
$874$	36.9244			1.24899
$875$	−25.9622	−	12.3624i	−0.877683	−	0.417927i
$876$	−9.09967			−0.307449
$877$	19.6495	−	11.3446i	0.663517	−	0.383081i	−0.130099	−	0.991501i	$-0.541530\pi$
$877$	19.6495	−	11.3446i	0.663517	−	0.383081i	0.793616	+	0.608420i	$0.208196\pi$
$878$	2.32475	+	1.34220i	0.0784566	+	0.0452969i
$879$	−9.14950	−	5.28247i	−0.308605	−	0.178173i
$880$	−2.86254	+	3.28356i	−0.0964963	+	0.110689i
$881$			11.4597i			0.386088i	0.981190	+	0.193044i	$0.0618361\pi$
$881$			11.4597i			0.386088i	−0.981190	+	0.193044i	$0.938164\pi$
$882$	20.7371	−	3.31233i	0.698255	−	0.111532i
$883$	−34.1993			−1.15090			−0.575450	−	0.817837i	$-0.695173\pi$
$883$	−34.1993			−1.15090			−0.575450	+	0.817837i	$0.695173\pi$
$884$	7.45017	−	4.30136i	0.250576	−	0.144670i
$885$	3.41238	+	1.97014i	0.114706	+	0.0662254i
$886$	3.04983	+	1.76082i	0.102461	+	0.0591560i
$887$	−3.72508	−	6.45203i	−0.125076	−	0.216638i	0.796687	−	0.604393i	$-0.206584\pi$
$887$	−3.72508	−	6.45203i	−0.125076	−	0.216638i	−0.921763	+	0.387755i	$0.873251\pi$
$888$			12.6005i			0.422846i
$889$	−8.41238	−	4.00573i	−0.282142	−	0.134348i
$890$	−3.45017			−0.115650
$891$	−22.5000	−	19.6150i	−0.753778	−	0.657129i
$892$	−1.41238	+	2.44631i	−0.0472898	+	0.0819084i
$893$	−7.18729	+	12.4488i	−0.240514	+	0.416582i
$894$	−10.9124	+	6.30026i	−0.364964	+	0.210712i
$895$	−18.7492			−0.626716
$896$	2.63746	−	0.209313i	0.0881113	−	0.00699267i
$897$			25.8081i			0.861708i
$898$	−3.72508	+	2.15068i	−0.124308	+	0.0717690i
$899$	5.13746	−	8.89834i	0.171344	−	0.296776i
$900$	4.91238	−	8.50848i	0.163746	−	0.283616i
$901$	−38.2749	+	22.0980i	−1.27512	+	0.736192i
$902$	20.5498	−	7.04329i	0.684235	−	0.234516i
$903$	−25.9124	−	37.6498i	−0.862310	−	1.25291i
$904$		0			0
$905$	7.45017	−	4.30136i	0.247652	−	0.142982i
$906$	10.5000	−	18.1865i	0.348839	−	0.604207i
$907$	−5.72508	+	9.91613i	−0.190098	+	0.329260i	−0.945283	−	0.326253i	$-0.894214\pi$
$907$	−5.72508	+	9.91613i	−0.190098	+	0.329260i	0.755184	+	0.655512i	$0.227547\pi$
$908$	−11.6873	−	20.2430i	−0.387856	−	0.671787i
$909$	29.4743			0.977599
$910$	−5.17525	−	7.51946i	−0.171558	−	0.249268i
$911$			52.6103i			1.74306i	0.490344	+	0.871529i	$0.336871\pi$
$911$			52.6103i			1.74306i	−0.490344	+	0.871529i	$0.663129\pi$
$912$	−5.63746	−	9.76436i	−0.186675	−	0.323330i
$913$	−6.54983	+	33.4427i	−0.216768	+	1.10679i
$914$	31.3368	+	18.0923i	1.03653	+	0.598440i
$915$	−13.6495	+	7.88054i	−0.451239	+	0.260523i
$916$	−6.54983			−0.216413
$917$	27.0997	−	2.15068i	0.894910	−	0.0710216i
$918$			17.0170i			0.561644i
$919$	19.8127	−	11.4389i	0.653561	−	0.377334i	−0.136258	−	0.990673i	$-0.543508\pi$
$919$	19.8127	−	11.4389i	0.653561	−	0.377334i	0.789819	+	0.613340i	$0.210174\pi$
$920$	−3.72508	+	6.45203i	−0.122812	+	0.212717i
$921$	1.54983	−	2.68439i	0.0510688	−	0.0884537i
$922$	−4.91238	−	8.50848i	−0.161780	−	0.280212i
$923$	26.1993			0.862362
$924$	15.0997	+	1.73205i	0.496743	+	0.0569803i
$925$	−23.8248			−0.783353
$926$	10.0000	+	17.3205i	0.328620	+	0.569187i
$927$	−19.6495	+	34.0339i	−0.645374	+	1.11782i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	−16.5498	+	9.55505i	−0.542982	+	0.313491i	−0.746287	−	0.665625i	$-0.768165\pi$
$929$	−16.5498	+	9.55505i	−0.542982	+	0.313491i	0.203304	+	0.979116i	$0.434832\pi$
$930$	23.3746			0.766483
$931$	42.5619	+	16.2739i	1.39491	+	0.533357i
$932$	−17.8248			−0.583869
$933$	15.3625	+	26.6087i	0.502947	+	0.871130i
$934$	−1.81271	−	1.04657i	−0.0593136	−	0.0342447i
$935$	14.0000	+	2.74194i	0.457849	+	0.0896709i
$936$	6.82475	−	3.94027i	0.223074	−	0.128792i
$937$			12.5430i			0.409761i	0.978787	+	0.204881i	$0.0656806\pi$
$937$			12.5430i			0.409761i	−0.978787	+	0.204881i	$0.934319\pi$
$938$	9.72508	−	20.4235i	0.317535	−	0.666852i
$939$			12.1244i			0.395663i
$940$	−1.45017	−	2.51176i	−0.0472992	−	0.0819246i
$941$	16.5997	−	28.7515i	0.541134	−	0.937271i	−0.457706	−	0.889104i	$-0.651329\pi$
$941$	16.5997	−	28.7515i	0.541134	−	0.937271i	0.998839	−	0.0481673i	$-0.0153381\pi$
$942$	25.9124	+	14.9605i	0.844271	+	0.487440i
$943$	32.1752	−	18.5764i	1.04777	−	0.604930i
$944$		−	1.73205i		−	0.0563735i
$945$	18.0000	−	1.42851i	0.585540	−	0.0464695i
$946$	−10.7251	−	31.2920i	−0.348703	−	1.01739i
$947$	14.7371	−	8.50848i	0.478892	−	0.276489i	−0.241062	−	0.970510i	$-0.577496\pi$
$947$	14.7371	−	8.50848i	0.478892	−	0.276489i	0.719955	+	0.694021i	$0.244163\pi$
$948$	−1.86254	+	3.22602i	−0.0604925	+	0.104776i
$949$	6.90033	−	11.9517i	0.223994	−	0.387969i
$950$	18.4622	−	10.6592i	0.598993	−	0.345829i
$951$	23.3746			0.757973
$952$	−4.91238	−	7.13752i	−0.159211	−	0.231328i
$953$	27.6495			0.895655			0.447828	−	0.894120i	$-0.352198\pi$
$953$	27.6495			0.895655			0.447828	+	0.894120i	$0.352198\pi$
$954$	−35.0619	+	20.2430i	−1.13517	+	0.655391i
$955$	7.45017	−	12.9041i	0.241082	−	0.417566i
$956$	6.27492	−	10.8685i	0.202945	−	0.351512i
$957$	3.77492	−	4.33013i	0.122026	−	0.139973i
$958$	28.0000			0.904639
$959$	9.37459	−	6.45203i	0.302721	−	0.208347i
$960$	2.27492			0.0734226
$961$	−37.2870	−	64.5829i	−1.20281	−	2.08332i
$962$	−16.5498	−	9.55505i	−0.533588	−	0.308067i
$963$	21.4124	−	37.0873i	0.690004	−	1.19512i
$964$	−3.41238	+	1.97014i	−0.109905	+	0.0634538i
$965$	−29.0241			−0.934318
$966$	25.9124	−	2.05645i	0.833717	−	0.0661653i
$967$			27.7704i			0.893034i	0.894775	+	0.446517i	$0.147336\pi$
$967$			27.7704i			0.893034i	−0.894775	+	0.446517i	$0.852664\pi$
$968$	10.1873	+	4.14959i	0.327432	+	0.133373i
$969$	−18.4622	+	31.9775i	−0.593092	+	1.02726i
$970$	15.4124	+	8.89834i	0.494862	+	0.285708i
$971$	−49.2371	+	28.4271i	−1.58009	+	0.912268i	−0.585250	+	0.810853i	$0.699004\pi$
$971$	−49.2371	+	28.4271i	−1.58009	+	0.912268i	−0.994844	+	0.101415i	$0.967663\pi$
$972$			15.5885i			0.500000i
$973$	1.00000	+	0.476171i	0.0320585	+	0.0152653i
$974$	19.3746			0.620802
$975$	7.45017	+	12.9041i	0.238596	+	0.413261i
$976$	6.00000	+	3.46410i	0.192055	+	0.110883i
$977$	27.0997	+	15.6460i	0.866995	+	0.500560i	0.866349	−	0.499440i	$-0.166461\pi$
$977$	27.0997	+	15.6460i	0.866995	+	0.500560i	0.000646664		1.00000i	$0.499794\pi$
$978$	−24.8248	+	14.3326i	−0.793808	+	0.458305i
$979$	2.82475	+	8.24163i	0.0902795	+	0.263404i
$980$	−7.13746	+	5.79532i	−0.227998	+	0.185125i
$981$		−	12.9041i		−	0.411995i
$982$	−7.68729	−	13.3148i	−0.245311	−	0.424892i
$983$	19.1873	+	11.0778i	0.611980	+	0.353327i	0.773740	−	0.633504i	$-0.218384\pi$
$983$	19.1873	+	11.0778i	0.611980	+	0.353327i	−0.161760	+	0.986830i	$0.551717\pi$
$984$	−9.82475	−	5.67232i	−0.313202	−	0.180827i
$985$	14.4743	−	8.35671i	0.461188	−	0.266267i
$986$	−3.27492			−0.104295
$987$	−4.35050	+	9.13642i	−0.138478	+	0.290816i
$988$	17.0997			0.544013
$989$	−28.2870	−	48.9945i	−0.899473	−	1.55793i
$990$	12.8248	+	2.51176i	0.407597	+	0.0798290i
$991$	−7.41238	+	12.8386i	−0.235462	+	0.407832i	−0.959407	−	0.282026i	$-0.908994\pi$
$991$	−7.41238	+	12.8386i	−0.235462	+	0.407832i	0.723945	+	0.689858i	$0.242327\pi$
$992$	−5.13746	−	8.89834i	−0.163114	−	0.282523i
$993$		−	8.83289i		−	0.280303i
$994$	−2.08762	−	26.3052i	−0.0662154	−	0.834349i
$995$		0			0
$996$	15.4124	−	8.89834i	0.488360	−	0.281955i
$997$	5.37459	+	3.10302i	0.170215	+	0.0982736i	0.582687	−	0.812697i	$-0.302001\pi$
$997$	5.37459	+	3.10302i	0.170215	+	0.0982736i	−0.412472	+	0.910970i	$0.635335\pi$
$998$	1.72508	−	2.98793i	0.0546065	−	0.0945813i
$999$	32.7371	−	18.9008i	1.03576	−	0.597995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.c.263.1	yes	4
3.2	odd	2		462.2.n.b.263.2	yes	4
7.2	even	3		462.2.n.d.65.2	yes	4
11.10	odd	2		462.2.n.a.263.1	yes	4
21.2	odd	6		462.2.n.a.65.1	✓	4
33.32	even	2		462.2.n.d.263.2	yes	4
77.65	odd	6		462.2.n.b.65.2	yes	4
231.65	even	6	inner	462.2.n.c.65.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.a.65.1	✓	4	21.2	odd	6
462.2.n.a.263.1	yes	4	11.10	odd	2
462.2.n.b.65.2	yes	4	77.65	odd	6
462.2.n.b.263.2	yes	4	3.2	odd	2
462.2.n.c.65.1	yes	4	231.65	even	6	inner
462.2.n.c.263.1	yes	4	1.1	even	1	trivial
462.2.n.d.65.2	yes	4	7.2	even	3
462.2.n.d.263.2	yes	4	33.32	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.13746 + 0.656712i) q^{5} -1.73205i q^{6} +(1.13746 - 2.38876i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.13746 + 0.656712i) q^{5} -1.73205i q^{6} +(1.13746 - 2.38876i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.13746 - 0.656712i) q^{10} +(-0.637459 + 3.25479i) q^{11} +(1.50000 - 0.866025i) q^{12} +2.62685i q^{13} +(2.63746 - 0.209313i) q^{14} +2.27492 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.63746 + 2.83616i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-5.63746 + 3.25479i) q^{19} -1.31342i q^{20} +(-3.77492 + 2.59808i) q^{21} +(-3.13746 + 1.07534i) q^{22} +(-4.91238 + 2.83616i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-1.63746 + 2.83616i) q^{25} +(-2.27492 + 1.31342i) q^{26} -5.19615i q^{27} +(1.50000 + 2.17945i) q^{28} +1.00000 q^{29} +(1.13746 + 1.97014i) q^{30} +(5.13746 - 8.89834i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.77492 - 4.33013i) q^{33} -3.27492 q^{34} +(0.274917 + 3.46410i) q^{35} -3.00000 q^{36} +(3.63746 + 6.30026i) q^{37} +(-5.63746 - 3.25479i) q^{38} +(2.27492 - 3.94027i) q^{39} +(1.13746 - 0.656712i) q^{40} -6.54983 q^{41} +(-4.13746 - 1.97014i) q^{42} +9.97368i q^{43} +(-2.50000 - 2.17945i) q^{44} +(-3.41238 - 1.97014i) q^{45} +(-4.91238 - 2.83616i) q^{46} +(1.91238 - 1.10411i) q^{47} +1.73205i q^{48} +(-4.41238 - 5.43424i) q^{49} -3.27492 q^{50} +(4.91238 - 2.83616i) q^{51} +(-2.27492 - 1.31342i) q^{52} +(11.6873 + 6.74766i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-1.41238 - 4.12081i) q^{55} +(-1.13746 + 2.38876i) q^{56} +11.2749 q^{57} +(0.500000 + 0.866025i) q^{58} +(1.50000 + 0.866025i) q^{59} +(-1.13746 + 1.97014i) q^{60} +(-6.00000 + 3.46410i) q^{61} +10.2749 q^{62} +(7.91238 - 0.627940i) q^{63} +1.00000 q^{64} +(-1.72508 - 2.98793i) q^{65} +(5.63746 + 1.10411i) q^{66} +(4.27492 - 7.40437i) q^{67} +(-1.63746 - 2.83616i) q^{68} +9.82475 q^{69} +(-2.86254 + 1.97014i) q^{70} -9.97368i q^{71} +(-1.50000 - 2.59808i) q^{72} +(-4.54983 - 2.62685i) q^{73} +(-3.63746 + 6.30026i) q^{74} +(4.91238 - 2.83616i) q^{75} -6.50958i q^{76} +(7.04983 + 5.22492i) q^{77} +4.54983 q^{78} +(-1.86254 + 1.07534i) q^{79} +(1.13746 + 0.656712i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.27492 - 5.67232i) q^{82} +10.2749 q^{83} +(-0.362541 - 4.56821i) q^{84} -4.30136i q^{85} +(-8.63746 + 4.98684i) q^{86} +(-1.50000 - 0.866025i) q^{87} +(0.637459 - 3.25479i) q^{88} +(2.27492 - 1.31342i) q^{89} -3.94027i q^{90} +(6.27492 + 2.98793i) q^{91} -5.67232i q^{92} +(-15.4124 + 8.89834i) q^{93} +(1.91238 + 1.10411i) q^{94} +(4.27492 - 7.40437i) q^{95} +(-1.50000 + 0.866025i) q^{96} -13.5498 q^{97} +(2.50000 - 6.53835i) q^{98} +(-9.41238 + 3.22602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^7 - 4 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{7} - 4 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} + 6 q^{12} + 3 q^{14} - 6 q^{15} - 2 q^{16} + q^{17} - 6 q^{18} - 15 q^{19} - 5 q^{22} + 3 q^{23} + 6 q^{24} + q^{25} + 6 q^{26} + 6 q^{28} + 4 q^{29} - 3 q^{30} + 13 q^{31} + 2 q^{32} + 2 q^{34} - 14 q^{35} - 12 q^{36} + 7 q^{37} - 15 q^{38} - 6 q^{39} - 3 q^{40} + 4 q^{41} - 9 q^{42} - 10 q^{44} + 9 q^{45} + 3 q^{46} - 15 q^{47} + 5 q^{49} + 2 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{53} + 18 q^{54} + 17 q^{55} + 3 q^{56} + 30 q^{57} + 2 q^{58} + 6 q^{59} + 3 q^{60} - 24 q^{61} + 26 q^{62} + 9 q^{63} + 4 q^{64} - 22 q^{65} + 15 q^{66} + 2 q^{67} + q^{68} - 6 q^{69} - 19 q^{70} - 6 q^{72} + 12 q^{73} - 7 q^{74} - 3 q^{75} - 2 q^{77} - 12 q^{78} - 15 q^{79} - 3 q^{80} - 18 q^{81} + 2 q^{82} + 26 q^{83} - 9 q^{84} - 27 q^{86} - 6 q^{87} - 5 q^{88} - 6 q^{89} + 10 q^{91} - 39 q^{93} - 15 q^{94} + 2 q^{95} - 6 q^{96} - 24 q^{97} + 10 q^{98} - 15 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 - 3 * q^7 - 4 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 + 6 * q^12 + 3 * q^14 - 6 * q^15 - 2 * q^16 + q^17 - 6 * q^18 - 15 * q^19 - 5 * q^22 + 3 * q^23 + 6 * q^24 + q^25 + 6 * q^26 + 6 * q^28 + 4 * q^29 - 3 * q^30 + 13 * q^31 + 2 * q^32 + 2 * q^34 - 14 * q^35 - 12 * q^36 + 7 * q^37 - 15 * q^38 - 6 * q^39 - 3 * q^40 + 4 * q^41 - 9 * q^42 - 10 * q^44 + 9 * q^45 + 3 * q^46 - 15 * q^47 + 5 * q^49 + 2 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^53 + 18 * q^54 + 17 * q^55 + 3 * q^56 + 30 * q^57 + 2 * q^58 + 6 * q^59 + 3 * q^60 - 24 * q^61 + 26 * q^62 + 9 * q^63 + 4 * q^64 - 22 * q^65 + 15 * q^66 + 2 * q^67 + q^68 - 6 * q^69 - 19 * q^70 - 6 * q^72 + 12 * q^73 - 7 * q^74 - 3 * q^75 - 2 * q^77 - 12 * q^78 - 15 * q^79 - 3 * q^80 - 18 * q^81 + 2 * q^82 + 26 * q^83 - 9 * q^84 - 27 * q^86 - 6 * q^87 - 5 * q^88 - 6 * q^89 + 10 * q^91 - 39 * q^93 - 15 * q^94 + 2 * q^95 - 6 * q^96 - 24 * q^97 + 10 * q^98 - 15 * q^99

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