LMFDB - Embedded newform 546.2.j.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (of order $3$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$1.19003 - 0.764088i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.c.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.924396 + 1.60110i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.61442 + 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.924396 + 1.60110i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.61442 + 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.924396 + 1.60110i) q^{10} +(-0.357690 + 0.619538i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.81454 + 2.25352i) q^{13} +(2.61442 + 0.405935i) q^{14} +(-0.924396 - 1.60110i) q^{15} +1.00000 q^{16} +4.31156 q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.43786 + 5.95456i) q^{19} +(-0.924396 + 1.60110i) q^{20} +(-1.65876 + 2.06119i) q^{21} +(-0.357690 + 0.619538i) q^{22} -7.16035 q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.790985 + 1.37003i) q^{25} +(-2.81454 + 2.25352i) q^{26} +1.00000 q^{27} +(2.61442 + 0.405935i) q^{28} +(-4.63798 - 8.03322i) q^{29} +(-0.924396 - 1.60110i) q^{30} +(1.11104 + 1.92438i) q^{31} +1.00000 q^{32} +(-0.357690 - 0.619538i) q^{33} +4.31156 q^{34} +(-3.06671 + 3.81071i) q^{35} +(-0.500000 - 0.866025i) q^{36} +2.13341 q^{37} +(3.43786 + 5.95456i) q^{38} +(-0.544337 - 3.56422i) q^{39} +(-0.924396 + 1.60110i) q^{40} +(2.23138 + 3.86487i) q^{41} +(-1.65876 + 2.06119i) q^{42} +(-0.0979721 + 0.169693i) q^{43} +(-0.357690 + 0.619538i) q^{44} +1.84879 q^{45} -7.16035 q^{46} +(4.60553 - 7.97700i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.67043 + 2.12257i) q^{49} +(0.790985 + 1.37003i) q^{50} +(-2.15578 + 3.73392i) q^{51} +(-2.81454 + 2.25352i) q^{52} +(3.80147 + 6.58434i) q^{53} +1.00000 q^{54} +(-0.661295 - 1.14540i) q^{55} +(2.61442 + 0.405935i) q^{56} -6.87573 q^{57} +(-4.63798 - 8.03322i) q^{58} -2.48056 q^{59} +(-0.924396 - 1.60110i) q^{60} +(-4.31156 - 7.46783i) q^{61} +(1.11104 + 1.92438i) q^{62} +(-0.955663 - 2.46713i) q^{63} +1.00000 q^{64} +(-1.00637 - 6.58951i) q^{65} +(-0.357690 - 0.619538i) q^{66} +(6.96322 - 12.0606i) q^{67} +4.31156 q^{68} +(3.58017 - 6.20104i) q^{69} +(-3.06671 + 3.81071i) q^{70} +(7.50874 - 13.0055i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-0.989914 - 1.71458i) q^{73} +2.13341 q^{74} -1.58197 q^{75} +(3.43786 + 5.95456i) q^{76} +(-1.18665 + 1.47454i) q^{77} +(-0.544337 - 3.56422i) q^{78} +(7.37533 - 12.7744i) q^{79} +(-0.924396 + 1.60110i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.23138 + 3.86487i) q^{82} -9.71538 q^{83} +(-1.65876 + 2.06119i) q^{84} +(-3.98558 + 6.90323i) q^{85} +(-0.0979721 + 0.169693i) q^{86} +9.27596 q^{87} +(-0.357690 + 0.619538i) q^{88} -4.46953 q^{89} +1.84879 q^{90} +(-8.27319 + 4.74914i) q^{91} -7.16035 q^{92} -2.22209 q^{93} +(4.60553 - 7.97700i) q^{94} -12.7118 q^{95} +(-0.500000 + 0.866025i) q^{96} +(1.39194 - 2.41091i) q^{97} +(6.67043 + 2.12257i) q^{98} +0.715381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 2 q^{25} + 3 q^{26} + 8 q^{27} + 3 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} + 4 q^{34} - 22 q^{35} - 4 q^{36} + 12 q^{37} - 4 q^{38} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 3 q^{42} + 4 q^{44} - 4 q^{45} - 8 q^{46} + 7 q^{47} - 4 q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - q^{53} + 8 q^{54} - 25 q^{55} + 3 q^{56} + 8 q^{57} + 2 q^{58} - 32 q^{59} + 2 q^{60} - 4 q^{61} + 14 q^{62} + 8 q^{64} + 10 q^{65} + 4 q^{66} + 19 q^{67} + 4 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} - 4 q^{72} - 7 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} + 2 q^{80} - 4 q^{81} + 12 q^{82} - 64 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{87} + 4 q^{88} + 22 q^{89} - 4 q^{90} - 38 q^{91} - 8 q^{92} - 28 q^{93} + 7 q^{94} - 56 q^{95} - 4 q^{96} + 11 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 + 8 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 2 * q^25 + 3 * q^26 + 8 * q^27 + 3 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 + 4 * q^34 - 22 * q^35 - 4 * q^36 + 12 * q^37 - 4 * q^38 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 3 * q^42 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 7 * q^47 - 4 * q^48 + 5 * q^49 + 2 * q^50 - 2 * q^51 + 3 * q^52 - q^53 + 8 * q^54 - 25 * q^55 + 3 * q^56 + 8 * q^57 + 2 * q^58 - 32 * q^59 + 2 * q^60 - 4 * q^61 + 14 * q^62 + 8 * q^64 + 10 * q^65 + 4 * q^66 + 19 * q^67 + 4 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 - 4 * q^72 - 7 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 + 2 * q^80 - 4 * q^81 + 12 * q^82 - 64 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^87 + 4 * q^88 + 22 * q^89 - 4 * q^90 - 38 * q^91 - 8 * q^92 - 28 * q^93 + 7 * q^94 - 56 * q^95 - 4 * q^96 + 11 * q^97 + 5 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.924396	+	1.60110i	−0.413402	+	0.716034i	−0.995259	−	0.0972573i	$-0.968993\pi$
$5$	−0.924396	+	1.60110i	−0.413402	+	0.716034i	0.581857	+	0.813291i	$0.302326\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.61442	+	0.405935i	0.988160	+	0.153429i
$7$	2.61442	+	0.405935i	0.988160	+	0.153429i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.924396	+	1.60110i	−0.292320	+	0.506312i
$11$	−0.357690	+	0.619538i	−0.107848	+	0.186798i	−0.914898	−	0.403685i	$-0.867729\pi$
$11$	−0.357690	+	0.619538i	−0.107848	+	0.186798i	0.807050	+	0.590483i	$0.201063\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.81454	+	2.25352i	−0.780613	+	0.625015i
$13$	−2.81454	+	2.25352i	−0.780613	+	0.625015i
$14$	2.61442	+	0.405935i	0.698734	+	0.108491i
$15$	−0.924396	−	1.60110i	−0.238678	−	0.413402i
$16$	1.00000			0.250000
$17$	4.31156			1.04571			0.522853	−	0.852423i	$-0.324868\pi$
$17$	4.31156			1.04571			0.522853	+	0.852423i	$0.324868\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.43786	+	5.95456i	0.788700	+	1.36607i	0.926763	+	0.375645i	$0.122579\pi$
$19$	3.43786	+	5.95456i	0.788700	+	1.36607i	−0.138063	+	0.990423i	$0.544088\pi$
$20$	−0.924396	+	1.60110i	−0.206701	+	0.358017i
$21$	−1.65876	+	2.06119i	−0.361972	+	0.449789i
$22$	−0.357690	+	0.619538i	−0.0762599	+	0.132086i
$23$	−7.16035			−1.49304			−0.746518	−	0.665365i	$-0.768276\pi$
$23$	−7.16035			−1.49304			−0.746518	+	0.665365i	$0.768276\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	0.790985	+	1.37003i	0.158197	+	0.274005i
$26$	−2.81454	+	2.25352i	−0.551977	+	0.441952i
$27$	1.00000			0.192450
$28$	2.61442	+	0.405935i	0.494080	+	0.0767145i
$29$	−4.63798	−	8.03322i	−0.861251	−	1.49173i	−0.870722	−	0.491776i	$-0.836348\pi$
$29$	−4.63798	−	8.03322i	−0.861251	−	1.49173i	0.00947068	−	0.999955i	$-0.496985\pi$
$30$	−0.924396	−	1.60110i	−0.168771	−	0.292320i
$31$	1.11104	+	1.92438i	0.199549	+	0.345629i	0.948382	−	0.317129i	$-0.102719\pi$
$31$	1.11104	+	1.92438i	0.199549	+	0.345629i	−0.748833	+	0.662759i	$0.769386\pi$
$32$	1.00000			0.176777
$33$	−0.357690	−	0.619538i	−0.0622659	−	0.107848i
$34$	4.31156			0.739426
$35$	−3.06671	+	3.81071i	−0.518368	+	0.644128i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.13341			0.350731			0.175365	−	0.984503i	$-0.443889\pi$
$37$	2.13341			0.350731			0.175365	+	0.984503i	$0.443889\pi$
$38$	3.43786	+	5.95456i	0.557695	+	0.965956i
$39$	−0.544337	−	3.56422i	−0.0871637	−	0.570733i
$40$	−0.924396	+	1.60110i	−0.146160	+	0.253156i
$41$	2.23138	+	3.86487i	0.348483	+	0.603591i	0.985980	−	0.166862i	$-0.0533634\pi$
$41$	2.23138	+	3.86487i	0.348483	+	0.603591i	−0.637497	+	0.770453i	$0.720030\pi$
$42$	−1.65876	+	2.06119i	−0.255953	+	0.318049i
$43$	−0.0979721	+	0.169693i	−0.0149406	+	0.0258779i	−0.873399	−	0.487005i	$-0.838089\pi$
$43$	−0.0979721	+	0.169693i	−0.0149406	+	0.0258779i	0.858458	+	0.512883i	$0.171423\pi$
$44$	−0.357690	+	0.619538i	−0.0539239	+	0.0933989i
$45$	1.84879			0.275602
$46$	−7.16035			−1.05574
$47$	4.60553	−	7.97700i	0.671785	−	1.16357i	−0.305613	−	0.952156i	$-0.598861\pi$
$47$	4.60553	−	7.97700i	0.671785	−	1.16357i	0.977398	−	0.211410i	$-0.0678054\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	6.67043	+	2.12257i	0.952919	+	0.303225i
$50$	0.790985	+	1.37003i	0.111862	+	0.193751i
$51$	−2.15578	+	3.73392i	−0.301869	+	0.522853i
$52$	−2.81454	+	2.25352i	−0.390307	+	0.312507i
$53$	3.80147	+	6.58434i	0.522172	+	0.904429i	0.999667	+	0.0257942i	$0.00821145\pi$
$53$	3.80147	+	6.58434i	0.522172	+	0.904429i	−0.477495	+	0.878634i	$0.658455\pi$
$54$	1.00000			0.136083
$55$	−0.661295	−	1.14540i	−0.0891690	−	0.154445i
$56$	2.61442	+	0.405935i	0.349367	+	0.0542453i
$57$	−6.87573			−0.910712
$58$	−4.63798	−	8.03322i	−0.608997	−	1.05481i
$59$	−2.48056			−0.322942			−0.161471	−	0.986877i	$-0.551624\pi$
$59$	−2.48056			−0.322942			−0.161471	+	0.986877i	$0.551624\pi$
$60$	−0.924396	−	1.60110i	−0.119339	−	0.206701i
$61$	−4.31156	−	7.46783i	−0.552038	−	0.956158i	−0.998127	−	0.0611697i	$-0.980517\pi$
$61$	−4.31156	−	7.46783i	−0.552038	−	0.956158i	0.446089	−	0.894989i	$-0.352816\pi$
$62$	1.11104	+	1.92438i	0.141103	+	0.244397i
$63$	−0.955663	−	2.46713i	−0.120402	−	0.310829i
$64$	1.00000			0.125000
$65$	−1.00637	−	6.58951i	−0.124824	−	0.817328i
$66$	−0.357690	−	0.619538i	−0.0440287	−	0.0762599i
$67$	6.96322	−	12.0606i	0.850692	−	1.47344i	−0.0298923	−	0.999553i	$-0.509516\pi$
$67$	6.96322	−	12.0606i	0.850692	−	1.47344i	0.880585	−	0.473889i	$-0.157150\pi$
$68$	4.31156			0.522853
$69$	3.58017	−	6.20104i	0.431002	−	0.746518i
$70$	−3.06671	+	3.81071i	−0.366541	+	0.455467i
$71$	7.50874	−	13.0055i	0.891124	−	1.54347i	0.0525935	−	0.998616i	$-0.483251\pi$
$71$	7.50874	−	13.0055i	0.891124	−	1.54347i	0.838530	−	0.544855i	$-0.183415\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−0.989914	−	1.71458i	−0.115861	−	0.200676i	0.802263	−	0.596971i	$-0.203629\pi$
$73$	−0.989914	−	1.71458i	−0.115861	−	0.200676i	−0.918123	+	0.396294i	$0.870296\pi$
$74$	2.13341			0.248004
$75$	−1.58197			−0.182670
$76$	3.43786	+	5.95456i	0.394350	+	0.683034i
$77$	−1.18665	+	1.47454i	−0.135231	+	0.168039i
$78$	−0.544337	−	3.56422i	−0.0616341	−	0.403569i
$79$	7.37533	−	12.7744i	0.829790	−	1.43724i	−0.0684137	−	0.997657i	$-0.521794\pi$
$79$	7.37533	−	12.7744i	0.829790	−	1.43724i	0.898203	−	0.439581i	$-0.144873\pi$
$80$	−0.924396	+	1.60110i	−0.103351	+	0.179008i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.23138	+	3.86487i	0.246415	+	0.426803i
$83$	−9.71538			−1.06640			−0.533201	−	0.845989i	$-0.679011\pi$
$83$	−9.71538			−1.06640			−0.533201	+	0.845989i	$0.679011\pi$
$84$	−1.65876	+	2.06119i	−0.180986	+	0.224894i
$85$	−3.98558	+	6.90323i	−0.432297	+	0.748761i
$86$	−0.0979721	+	0.169693i	−0.0105646	+	0.0182984i
$87$	9.27596			0.994487
$88$	−0.357690	+	0.619538i	−0.0381299	+	0.0660430i
$89$	−4.46953			−0.473769			−0.236885	−	0.971538i	$-0.576126\pi$
$89$	−4.46953			−0.473769			−0.236885	+	0.971538i	$0.576126\pi$
$90$	1.84879			0.194880
$91$	−8.27319	+	4.74914i	−0.867266	+	0.497846i
$92$	−7.16035			−0.746518
$93$	−2.22209			−0.230419
$94$	4.60553	−	7.97700i	0.475024	−	0.822765i
$95$	−12.7118			−1.30420
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	1.39194	−	2.41091i	0.141330	−	0.244791i	−0.786668	−	0.617377i	$-0.788195\pi$
$97$	1.39194	−	2.41091i	0.141330	−	0.244791i	0.927998	+	0.372586i	$0.121529\pi$
$98$	6.67043	+	2.12257i	0.673816	+	0.214412i
$99$	0.715381			0.0718985
$100$	0.790985	+	1.37003i	0.0790985	+	0.137003i
$101$	−2.67775	+	4.63800i	−0.266446	+	0.461498i	−0.967941	−	0.251176i	$-0.919183\pi$
$101$	−2.67775	+	4.63800i	−0.266446	+	0.461498i	0.701496	+	0.712674i	$0.252516\pi$
$102$	−2.15578	+	3.73392i	−0.213454	+	0.369713i
$103$	3.26429	−	5.65391i	0.321640	−	0.557097i	−0.659187	−	0.751979i	$-0.729099\pi$
$103$	3.26429	−	5.65391i	0.321640	−	0.557097i	0.980827	+	0.194883i	$0.0624326\pi$
$104$	−2.81454	+	2.25352i	−0.275988	+	0.220976i
$105$	−1.76682	−	4.56120i	−0.172424	−	0.445128i
$106$	3.80147	+	6.58434i	0.369231	+	0.639528i
$107$	−4.61994			−0.446627			−0.223313	−	0.974747i	$-0.571687\pi$
$107$	−4.61994			−0.446627			−0.223313	+	0.974747i	$0.571687\pi$
$108$	1.00000			0.0962250
$109$	4.95093	+	8.57527i	0.474214	+	0.821362i	0.999564	−	0.0295240i	$-0.00939913\pi$
$109$	4.95093	+	8.57527i	0.474214	+	0.821362i	−0.525351	+	0.850886i	$0.676066\pi$
$110$	−0.661295	−	1.14540i	−0.0630520	−	0.109209i
$111$	−1.06671	+	1.84759i	−0.101247	+	0.175365i
$112$	2.61442	+	0.405935i	0.247040	+	0.0383572i
$113$	1.50417	−	2.60530i	0.141501	−	0.245086i	−0.786561	−	0.617512i	$-0.788141\pi$
$113$	1.50417	−	2.60530i	0.141501	−	0.245086i	0.928062	+	0.372426i	$0.121474\pi$
$114$	−6.87573			−0.643971
$115$	6.61899	−	11.4644i	0.617224	−	1.06906i
$116$	−4.63798	−	8.03322i	−0.430626	−	0.745865i
$117$	3.35888	+	1.31070i	0.310528	+	0.121174i
$118$	−2.48056			−0.228354
$119$	11.2722	+	1.75021i	1.03332	+	0.160442i
$120$	−0.924396	−	1.60110i	−0.0843854	−	0.146160i
$121$	5.24412	+	9.08307i	0.476738	+	0.825734i
$122$	−4.31156	−	7.46783i	−0.390350	−	0.676106i
$123$	−4.46276			−0.402394
$124$	1.11104	+	1.92438i	0.0997746	+	0.172815i
$125$	−12.1687			−1.08840
$126$	−0.955663	−	2.46713i	−0.0851372	−	0.219789i
$127$	−7.58356	−	13.1351i	−0.672932	−	1.16555i	−0.977069	−	0.212924i	$-0.931701\pi$
$127$	−7.58356	−	13.1351i	−0.672932	−	1.16555i	0.304137	−	0.952628i	$-0.401632\pi$
$128$	1.00000			0.0883883
$129$	−0.0979721	−	0.169693i	−0.00862596	−	0.0149406i
$130$	−1.00637	−	6.58951i	−0.0882642	−	0.577938i
$131$	9.69444	−	16.7913i	0.847007	−	1.46706i	−0.0368595	−	0.999320i	$-0.511735\pi$
$131$	9.69444	−	16.7913i	0.847007	−	1.46706i	0.883867	−	0.467739i	$-0.154931\pi$
$132$	−0.357690	−	0.619538i	−0.0311330	−	0.0539239i
$133$	6.57088	+	16.9633i	0.569767	+	1.47090i
$134$	6.96322	−	12.0606i	0.601530	−	1.04188i
$135$	−0.924396	+	1.60110i	−0.0795593	+	0.137801i
$136$	4.31156			0.369713
$137$	−4.74829			−0.405673			−0.202837	−	0.979213i	$-0.565016\pi$
$137$	−4.74829			−0.405673			−0.202837	+	0.979213i	$0.565016\pi$
$138$	3.58017	−	6.20104i	0.304765	−	0.527868i
$139$	−7.69027	+	13.3199i	−0.652280	+	1.12978i	0.330288	+	0.943880i	$0.392854\pi$
$139$	−7.69027	+	13.3199i	−0.652280	+	1.12978i	−0.982568	+	0.185902i	$0.940479\pi$
$140$	−3.06671	+	3.81071i	−0.259184	+	0.322064i
$141$	4.60553	+	7.97700i	0.387855	+	0.671785i
$142$	7.50874	−	13.0055i	0.630120	−	1.09140i
$143$	−0.389409	−	2.54978i	−0.0325640	−	0.213223i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	17.1493			1.42417
$146$	−0.989914	−	1.71458i	−0.0819258	−	0.141900i
$147$	−5.17342	+	4.71548i	−0.426696	+	0.388926i
$148$	2.13341			0.175365
$149$	5.82384	+	10.0872i	0.477107	+	0.826374i	0.999656	−	0.0262354i	$-0.00835195\pi$
$149$	5.82384	+	10.0872i	0.477107	+	0.826374i	−0.522548	+	0.852610i	$0.675019\pi$
$150$	−1.58197			−0.129167
$151$	−4.09544	−	7.09351i	−0.333282	−	0.577262i	0.649871	−	0.760044i	$-0.274823\pi$
$151$	−4.09544	−	7.09351i	−0.333282	−	0.577262i	−0.983153	+	0.182783i	$0.941489\pi$
$152$	3.43786	+	5.95456i	0.278848	+	0.482978i
$153$	−2.15578	−	3.73392i	−0.174284	−	0.301869i
$154$	−1.18665	+	1.47454i	−0.0956227	+	0.118822i
$155$	−4.10817			−0.329976
$156$	−0.544337	−	3.56422i	−0.0435819	−	0.285366i
$157$	11.4353	+	19.8066i	0.912639	+	1.58074i	0.810322	+	0.585985i	$0.199292\pi$
$157$	11.4353	+	19.8066i	0.912639	+	1.58074i	0.102317	+	0.994752i	$0.467374\pi$
$158$	7.37533	−	12.7744i	0.586750	−	1.01628i
$159$	−7.60294			−0.602952
$160$	−0.924396	+	1.60110i	−0.0730799	+	0.126578i
$161$	−18.7202	−	2.90663i	−1.47536	−	0.229075i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−9.01923	−	15.6218i	−0.706440	−	1.22359i	−0.966169	−	0.257909i	$-0.916967\pi$
$163$	−9.01923	−	15.6218i	−0.706440	−	1.22359i	0.259729	−	0.965682i	$-0.416367\pi$
$164$	2.23138	+	3.86487i	0.174242	+	0.301795i
$165$	1.32259			0.102964
$166$	−9.71538			−0.754060
$167$	3.86936	+	6.70193i	0.299420	+	0.518611i	0.976003	−	0.217755i	$-0.0698734\pi$
$167$	3.86936	+	6.70193i	0.299420	+	0.518611i	−0.676583	+	0.736366i	$0.736540\pi$
$168$	−1.65876	+	2.06119i	−0.127976	+	0.159024i
$169$	2.84327	−	12.6853i	0.218713	−	0.975789i
$170$	−3.98558	+	6.90323i	−0.305680	+	0.529454i
$171$	3.43786	−	5.95456i	0.262900	−	0.455356i
$172$	−0.0979721	+	0.169693i	−0.00747030	+	0.0129389i
$173$	−6.01212	−	10.4133i	−0.457093	−	0.791709i	0.541713	−	0.840564i	$-0.317776\pi$
$173$	−6.01212	−	10.4133i	−0.457093	−	0.791709i	−0.998806	+	0.0488550i	$0.984443\pi$
$174$	9.27596			0.703209
$175$	1.51183	+	3.90292i	0.114284	+	0.295033i
$176$	−0.357690	+	0.619538i	−0.0269619	+	0.0466994i
$177$	1.24028	−	2.14823i	0.0932253	−	0.161471i
$178$	−4.46953			−0.335005
$179$	−5.65742	+	9.79893i	−0.422855	+	0.732407i	−0.996217	−	0.0868953i	$-0.972305\pi$
$179$	−5.65742	+	9.79893i	−0.422855	+	0.732407i	0.573362	+	0.819302i	$0.305639\pi$
$180$	1.84879			0.137801
$181$	−2.49725			−0.185619			−0.0928095	−	0.995684i	$-0.529585\pi$
$181$	−2.49725			−0.185619			−0.0928095	+	0.995684i	$0.529585\pi$
$182$	−8.27319	+	4.74914i	−0.613249	+	0.352030i
$183$	8.62311			0.637439
$184$	−7.16035			−0.527868
$185$	−1.97212	+	3.41580i	−0.144993	+	0.251135i
$186$	−2.22209			−0.162931
$187$	−1.54220	+	2.67117i	−0.112777	+	0.195336i
$188$	4.60553	−	7.97700i	0.335892	−	0.581783i
$189$	2.61442	+	0.405935i	0.190171	+	0.0295274i
$190$	−12.7118			−0.922210
$191$	2.66349	+	4.61330i	0.192723	+	0.333807i	0.946152	−	0.323723i	$-0.104935\pi$
$191$	2.66349	+	4.61330i	0.192723	+	0.333807i	−0.753428	+	0.657530i	$0.771601\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−4.86186	+	8.42099i	−0.349964	+	0.606156i	−0.986243	−	0.165303i	$-0.947140\pi$
$193$	−4.86186	+	8.42099i	−0.349964	+	0.606156i	0.636278	+	0.771460i	$0.280473\pi$
$194$	1.39194	−	2.41091i	0.0999356	−	0.173093i
$195$	6.20986	+	2.42321i	0.444698	+	0.173530i
$196$	6.67043	+	2.12257i	0.476460	+	0.151612i
$197$	−3.08593	−	5.34499i	−0.219863	−	0.380815i	0.734903	−	0.678173i	$-0.237228\pi$
$197$	−3.08593	−	5.34499i	−0.219863	−	0.380815i	−0.954766	+	0.297358i	$0.903895\pi$
$198$	0.715381			0.0508399
$199$	5.41454			0.383827			0.191913	−	0.981412i	$-0.438531\pi$
$199$	5.41454			0.383827			0.191913	+	0.981412i	$0.438531\pi$
$200$	0.790985	+	1.37003i	0.0559311	+	0.0968755i
$201$	6.96322	+	12.0606i	0.491147	+	0.850692i
$202$	−2.67775	+	4.63800i	−0.188406	+	0.326328i
$203$	−8.86469	−	22.8850i	−0.622179	−	1.60621i
$204$	−2.15578	+	3.73392i	−0.150935	+	0.261426i
$205$	−8.25072			−0.576255
$206$	3.26429	−	5.65391i	0.227434	−	0.393927i
$207$	3.58017	+	6.20104i	0.248839	+	0.431002i
$208$	−2.81454	+	2.25352i	−0.195153	+	0.156254i
$209$	−4.91877			−0.340238
$210$	−1.76682	−	4.56120i	−0.121922	−	0.314753i
$211$	13.6366	+	23.6193i	0.938785	+	1.62602i	0.767742	+	0.640759i	$0.221380\pi$
$211$	13.6366	+	23.6193i	0.938785	+	1.62602i	0.171043	+	0.985264i	$0.445286\pi$
$212$	3.80147	+	6.58434i	0.261086	+	0.452214i
$213$	7.50874	+	13.0055i	0.514490	+	0.891124i
$214$	−4.61994			−0.315813
$215$	−0.181130	−	0.313726i	−0.0123530	−	0.0213960i
$216$	1.00000			0.0680414
$217$	2.12356	+	5.48216i	0.144157	+	0.372153i
$218$	4.95093	+	8.57527i	0.335320	+	0.580791i
$219$	1.97983			0.133784
$220$	−0.661295	−	1.14540i	−0.0445845	−	0.0772226i
$221$	−12.1350	+	9.71619i	−0.816292	+	0.653582i
$222$	−1.06671	+	1.84759i	−0.0715926	+	0.124002i
$223$	−2.88502	−	4.99700i	−0.193195	−	0.334624i	0.753112	−	0.657892i	$-0.228552\pi$
$223$	−2.88502	−	4.99700i	−0.193195	−	0.334624i	−0.946307	+	0.323268i	$0.895218\pi$
$224$	2.61442	+	0.405935i	0.174684	+	0.0271227i
$225$	0.790985	−	1.37003i	0.0527324	−	0.0913351i
$226$	1.50417	−	2.60530i	0.100056	−	0.173302i
$227$	16.9846			1.12731			0.563653	−	0.826012i	$-0.309396\pi$
$227$	16.9846			1.12731			0.563653	+	0.826012i	$0.309396\pi$
$228$	−6.87573			−0.455356
$229$	0.460390	−	0.797420i	0.0304235	−	0.0526950i	−0.850413	−	0.526116i	$-0.823648\pi$
$229$	0.460390	−	0.797420i	0.0304235	−	0.0526950i	0.880836	+	0.473421i	$0.156981\pi$
$230$	6.61899	−	11.4644i	0.436444	−	0.755942i
$231$	−0.683663	−	1.76493i	−0.0449817	−	0.116124i
$232$	−4.63798	−	8.03322i	−0.304498	−	0.527407i
$233$	−2.50283	+	4.33502i	−0.163966	+	0.283997i	−0.936287	−	0.351235i	$-0.885762\pi$
$233$	−2.50283	+	4.33502i	−0.163966	+	0.283997i	0.772322	+	0.635231i	$0.219095\pi$
$234$	3.35888	+	1.31070i	0.219577	+	0.0856833i
$235$	8.51466	+	14.7478i	0.555435	+	0.962041i
$236$	−2.48056			−0.161471
$237$	7.37533	+	12.7744i	0.479079	+	0.829790i
$238$	11.2722	+	1.75021i	0.730671	+	0.113449i
$239$	13.8239			0.894195			0.447097	−	0.894485i	$-0.352458\pi$
$239$	13.8239			0.894195			0.447097	+	0.894485i	$0.352458\pi$
$240$	−0.924396	−	1.60110i	−0.0596695	−	0.103351i
$241$	10.7589			0.693041			0.346521	−	0.938042i	$-0.387363\pi$
$241$	10.7589			0.693041			0.346521	+	0.938042i	$0.387363\pi$
$242$	5.24412	+	9.08307i	0.337104	+	0.583882i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.31156	−	7.46783i	−0.276019	−	0.478079i
$245$	−9.56457	+	8.71794i	−0.611058	+	0.556969i
$246$	−4.46276			−0.284535
$247$	−23.0947	−	9.01203i	−1.46948	−	0.573422i
$248$	1.11104	+	1.92438i	0.0705513	+	0.122198i
$249$	4.85769	−	8.41377i	0.307844	−	0.533201i
$250$	−12.1687			−0.769616
$251$	−11.8267	+	20.4844i	−0.746492	+	1.29296i	0.203002	+	0.979178i	$0.434930\pi$
$251$	−11.8267	+	20.4844i	−0.746492	+	1.29296i	−0.949494	+	0.313784i	$0.898403\pi$
$252$	−0.955663	−	2.46713i	−0.0602011	−	0.155414i
$253$	2.56119	−	4.43611i	0.161021	−	0.278896i
$254$	−7.58356	−	13.1351i	−0.475835	−	0.824170i
$255$	−3.98558	−	6.90323i	−0.249587	−	0.432297i
$256$	1.00000			0.0625000
$257$	−19.1940			−1.19729			−0.598646	−	0.801014i	$-0.704294\pi$
$257$	−19.1940			−1.19729			−0.598646	+	0.801014i	$0.704294\pi$
$258$	−0.0979721	−	0.169693i	−0.00609948	−	0.0105646i
$259$	5.57764	+	0.866025i	0.346578	+	0.0538122i
$260$	−1.00637	−	6.58951i	−0.0624122	−	0.408664i
$261$	−4.63798	+	8.03322i	−0.287084	+	0.497244i
$262$	9.69444	−	16.7913i	0.598925	−	1.03737i
$263$	−5.49567	+	9.51878i	−0.338878	+	0.586953i	−0.984222	−	0.176939i	$-0.943381\pi$
$263$	−5.49567	+	9.51878i	−0.338878	+	0.586953i	0.645344	+	0.763892i	$0.276714\pi$
$264$	−0.357690	−	0.619538i	−0.0220143	−	0.0381299i
$265$	−14.0562			−0.863469
$266$	6.57088	+	16.9633i	0.402886	+	1.04009i
$267$	2.23476	−	3.87073i	0.136765	−	0.236885i
$268$	6.96322	−	12.0606i	0.425346	−	0.736721i
$269$	16.5175			1.00709			0.503546	−	0.863968i	$-0.332028\pi$
$269$	16.5175			1.00709			0.503546	+	0.863968i	$0.332028\pi$
$270$	−0.924396	+	1.60110i	−0.0562569	+	0.0974399i
$271$	−18.1906			−1.10500			−0.552499	−	0.833514i	$-0.686326\pi$
$271$	−18.1906			−1.10500			−0.552499	+	0.833514i	$0.686326\pi$
$272$	4.31156			0.261426
$273$	0.0237134	−	9.53936i	0.00143520	−	0.577348i
$274$	−4.74829			−0.286854
$275$	−1.13171			−0.0682448
$276$	3.58017	−	6.20104i	0.215501	−	0.373259i
$277$	16.4894			0.990751			0.495376	−	0.868679i	$-0.335030\pi$
$277$	16.4894			0.990751			0.495376	+	0.868679i	$0.335030\pi$
$278$	−7.69027	+	13.3199i	−0.461232	+	0.798877i
$279$	1.11104	−	1.92438i	0.0665164	−	0.115210i
$280$	−3.06671	+	3.81071i	−0.183271	+	0.227734i
$281$	15.2768			0.911335			0.455667	−	0.890150i	$-0.349401\pi$
$281$	15.2768			0.911335			0.455667	+	0.890150i	$0.349401\pi$
$282$	4.60553	+	7.97700i	0.274255	+	0.475024i
$283$	4.57838	−	7.92998i	0.272156	−	0.471388i	−0.697257	−	0.716821i	$-0.745597\pi$
$283$	4.57838	−	7.92998i	0.272156	−	0.471388i	0.969414	+	0.245432i	$0.0789299\pi$
$284$	7.50874	−	13.0055i	0.445562	−	0.771736i
$285$	6.35589	−	11.0087i	0.376491	−	0.652101i
$286$	−0.389409	−	2.54978i	−0.0230262	−	0.150772i
$287$	4.26490	+	11.0102i	0.251749	+	0.649912i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	1.58952			0.0935010
$290$	17.1493			1.00704
$291$	1.39194	+	2.41091i	0.0815971	+	0.141330i
$292$	−0.989914	−	1.71458i	−0.0579303	−	0.100338i
$293$	5.93488	−	10.2795i	0.346719	−	0.600536i	−0.638945	−	0.769252i	$-0.720629\pi$
$293$	5.93488	−	10.2795i	0.346719	−	0.600536i	0.985665	+	0.168717i	$0.0539623\pi$
$294$	−5.17342	+	4.71548i	−0.301720	+	0.275012i
$295$	2.29302	−	3.97163i	0.133505	−	0.231237i
$296$	2.13341			0.124002
$297$	−0.357690	+	0.619538i	−0.0207553	+	0.0359492i
$298$	5.82384	+	10.0872i	0.337366	+	0.584335i
$299$	20.1531	−	16.1360i	1.16548	−	0.933169i
$300$	−1.58197			−0.0913351
$301$	−0.325025	+	0.403878i	−0.0187341	+	0.0232792i
$302$	−4.09544	−	7.09351i	−0.235666	−	0.408186i
$303$	−2.67775	−	4.63800i	−0.153833	−	0.266446i
$304$	3.43786	+	5.95456i	0.197175	+	0.341517i
$305$	15.9423			0.912855
$306$	−2.15578	−	3.73392i	−0.123238	−	0.213454i
$307$	−28.0679			−1.60192			−0.800959	−	0.598719i	$-0.795677\pi$
$307$	−28.0679			−1.60192			−0.800959	+	0.598719i	$0.795677\pi$
$308$	−1.18665	+	1.47454i	−0.0676155	+	0.0840195i
$309$	3.26429	+	5.65391i	0.185699	+	0.321640i
$310$	−4.10817			−0.233328
$311$	−12.7326	−	22.0536i	−0.722001	−	1.25054i	−0.960196	−	0.279325i	$-0.909889\pi$
$311$	−12.7326	−	22.0536i	−0.722001	−	1.25054i	0.238195	−	0.971217i	$-0.423444\pi$
$312$	−0.544337	−	3.56422i	−0.0308170	−	0.201784i
$313$	−8.82204	+	15.2802i	−0.498651	+	0.863689i	−0.999999	−	0.00155673i	$-0.999504\pi$
$313$	−8.82204	+	15.2802i	−0.498651	+	0.863689i	0.501348	+	0.865246i	$0.332838\pi$
$314$	11.4353	+	19.8066i	0.645333	+	1.11775i
$315$	4.83353	+	0.750489i	0.272338	+	0.0422852i
$316$	7.37533	−	12.7744i	0.414895	−	0.718619i
$317$	−14.8710	+	25.7573i	−0.835239	+	1.44668i	0.0585974	+	0.998282i	$0.481337\pi$
$317$	−14.8710	+	25.7573i	−0.835239	+	1.44668i	−0.893836	+	0.448394i	$0.851996\pi$
$318$	−7.60294			−0.426352
$319$	6.63585			0.371536
$320$	−0.924396	+	1.60110i	−0.0516753	+	0.0895042i
$321$	2.30997	−	4.00099i	0.128930	−	0.223313i
$322$	−18.7202	−	2.90663i	−1.04324	−	0.161980i
$323$	14.8225	+	25.6734i	0.824748	+	1.42851i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−5.31365	−	2.07349i	−0.294748	−	0.115017i
$326$	−9.01923	−	15.6218i	−0.499529	−	0.865209i
$327$	−9.90187			−0.547575
$328$	2.23138	+	3.86487i	0.123207	+	0.213402i
$329$	15.2789	−	18.9857i	0.842355	−	1.04672i
$330$	1.32259			0.0728062
$331$	−12.0197	−	20.8187i	−0.660661	−	1.14430i	−0.980442	−	0.196807i	$-0.936943\pi$
$331$	−12.0197	−	20.8187i	−0.660661	−	1.14430i	0.319781	−	0.947491i	$-0.396391\pi$
$332$	−9.71538			−0.533201
$333$	−1.06671	−	1.84759i	−0.0584551	−	0.101247i
$334$	3.86936	+	6.70193i	0.211722	+	0.366713i
$335$	12.8735	+	22.2976i	0.703356	+	1.21825i
$336$	−1.65876	+	2.06119i	−0.0904929	+	0.112447i
$337$	−2.21939			−0.120898			−0.0604490	−	0.998171i	$-0.519253\pi$
$337$	−2.21939			−0.120898			−0.0604490	+	0.998171i	$0.519253\pi$
$338$	2.84327	−	12.6853i	0.154654	−	0.689987i
$339$	1.50417	+	2.60530i	0.0816954	+	0.141501i
$340$	−3.98558	+	6.90323i	−0.216149	+	0.374380i
$341$	−1.58964			−0.0860837
$342$	3.43786	−	5.95456i	0.185898	−	0.321985i
$343$	16.5777	+	8.25707i	0.895113	+	0.445840i
$344$	−0.0979721	+	0.169693i	−0.00528230	+	0.00914921i
$345$	6.61899	+	11.4644i	0.356355	+	0.617224i
$346$	−6.01212	−	10.4133i	−0.323214	−	0.559823i
$347$	−2.01895			−0.108383			−0.0541916	−	0.998531i	$-0.517258\pi$
$347$	−2.01895			−0.108383			−0.0541916	+	0.998531i	$0.517258\pi$
$348$	9.27596			0.497244
$349$	−16.8191	−	29.1316i	−0.900306	−	1.55938i	−0.827097	−	0.562060i	$-0.810009\pi$
$349$	−16.8191	−	29.1316i	−0.900306	−	1.55938i	−0.0732096	−	0.997317i	$-0.523324\pi$
$350$	1.51183	+	3.90292i	0.0808107	+	0.208620i
$351$	−2.81454	+	2.25352i	−0.150229	+	0.120284i
$352$	−0.357690	+	0.619538i	−0.0190650	+	0.0330215i
$353$	−11.6388	+	20.1590i	−0.619472	+	1.07296i	0.370110	+	0.928988i	$0.379320\pi$
$353$	−11.6388	+	20.1590i	−0.619472	+	1.07296i	−0.989582	+	0.143970i	$0.954013\pi$
$354$	1.24028	−	2.14823i	0.0659202	−	0.114177i
$355$	13.8821	+	24.0445i	0.736785	+	1.27615i
$356$	−4.46953			−0.236885
$357$	−7.15185	+	8.88694i	−0.378516	+	0.470347i
$358$	−5.65742	+	9.79893i	−0.299004	+	0.517890i
$359$	5.44896	−	9.43787i	0.287585	−	0.498112i	−0.685648	−	0.727933i	$-0.740481\pi$
$359$	5.44896	−	9.43787i	0.287585	−	0.498112i	0.973233	+	0.229822i	$0.0738143\pi$
$360$	1.84879			0.0974399
$361$	−14.1378	+	24.4874i	−0.744096	+	1.28881i
$362$	−2.49725			−0.131252
$363$	−10.4882			−0.550489
$364$	−8.27319	+	4.74914i	−0.433633	+	0.248923i
$365$	3.66029			0.191588
$366$	8.62311			0.450737
$367$	−2.44394	+	4.23302i	−0.127573	+	0.220962i	−0.922736	−	0.385434i	$-0.874052\pi$
$367$	−2.44394	+	4.23302i	−0.127573	+	0.220962i	0.795163	+	0.606396i	$0.207385\pi$
$368$	−7.16035			−0.373259
$369$	2.23138	−	3.86487i	0.116161	−	0.201197i
$370$	−1.97212	+	3.41580i	−0.102525	+	0.177579i
$371$	7.26584	+	18.7574i	0.377224	+	0.973836i
$372$	−2.22209			−0.115210
$373$	7.68366	+	13.3085i	0.397845	+	0.689088i	0.993460	−	0.114182i	$-0.0364249\pi$
$373$	7.68366	+	13.3085i	0.397845	+	0.689088i	−0.595615	+	0.803270i	$0.703092\pi$
$374$	−1.54220	+	2.67117i	−0.0797454	+	0.138123i
$375$	6.08435	−	10.5384i	0.314194	−	0.544200i
$376$	4.60553	−	7.97700i	0.237512	−	0.411383i
$377$	31.1568	+	12.1580i	1.60466	+	0.626170i
$378$	2.61442	+	0.405935i	0.134472	+	0.0208790i
$379$	8.66626	+	15.0104i	0.445156	+	0.771033i	0.998063	−	0.0622101i	$-0.0198149\pi$
$379$	8.66626	+	15.0104i	0.445156	+	0.771033i	−0.552907	+	0.833243i	$0.686482\pi$
$380$	−12.7118			−0.652101
$381$	15.1671			0.777035
$382$	2.66349	+	4.61330i	0.136276	+	0.236037i
$383$	5.99628	+	10.3859i	0.306396	+	0.530693i	0.977571	−	0.210606i	$-0.0675436\pi$
$383$	5.99628	+	10.3859i	0.306396	+	0.530693i	−0.671175	+	0.741298i	$0.734210\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−1.26395	−	3.26300i	−0.0644169	−	0.166298i
$386$	−4.86186	+	8.42099i	−0.247462	+	0.428617i
$387$	0.195944			0.00996040
$388$	1.39194	−	2.41091i	0.0706651	−	0.122396i
$389$	−8.89274	−	15.4027i	−0.450880	−	0.780947i	0.547561	−	0.836766i	$-0.315556\pi$
$389$	−8.89274	−	15.4027i	−0.450880	−	0.780947i	−0.998441	+	0.0558191i	$0.982223\pi$
$390$	6.20986	+	2.42321i	0.314449	+	0.122704i
$391$	−30.8722			−1.56128
$392$	6.67043	+	2.12257i	0.336908	+	0.107206i
$393$	9.69444	+	16.7913i	0.489020	+	0.847007i
$394$	−3.08593	−	5.34499i	−0.155467	−	0.269277i
$395$	13.6354	+	23.6173i	0.686074	+	1.18831i
$396$	0.715381			0.0359492
$397$	−7.02952	−	12.1755i	−0.352802	−	0.611070i	0.633938	−	0.773384i	$-0.281438\pi$
$397$	−7.02952	−	12.1755i	−0.352802	−	0.611070i	−0.986739	+	0.162314i	$0.948104\pi$
$398$	5.41454			0.271406
$399$	−17.9761	−	2.79110i	−0.899929	−	0.139730i
$400$	0.790985	+	1.37003i	0.0395493	+	0.0685013i
$401$	4.13072			0.206278			0.103139	−	0.994667i	$-0.467111\pi$
$401$	4.13072			0.206278			0.103139	+	0.994667i	$0.467111\pi$
$402$	6.96322	+	12.0606i	0.347294	+	0.601530i
$403$	−7.46371	−	2.91249i	−0.371794	−	0.145082i
$404$	−2.67775	+	4.63800i	−0.133223	+	0.230749i
$405$	−0.924396	−	1.60110i	−0.0459336	−	0.0795593i
$406$	−8.86469	−	22.8850i	−0.439947	−	1.13576i
$407$	−0.763101	+	1.32173i	−0.0378255	+	0.0655157i
$408$	−2.15578	+	3.73392i	−0.106727	+	0.184856i
$409$	−5.21490			−0.257860			−0.128930	−	0.991654i	$-0.541154\pi$
$409$	−5.21490			−0.257860			−0.128930	+	0.991654i	$0.541154\pi$
$410$	−8.25072			−0.407474
$411$	2.37414	−	4.11214i	0.117108	−	0.202837i
$412$	3.26429	−	5.65391i	0.160820	−	0.278548i
$413$	−6.48525	−	1.00695i	−0.319118	−	0.0495486i
$414$	3.58017	+	6.20104i	0.175956	+	0.304765i
$415$	8.98086	−	15.5553i	0.440853	−	0.763580i
$416$	−2.81454	+	2.25352i	−0.137994	+	0.110488i
$417$	−7.69027	−	13.3199i	−0.376594	−	0.652280i
$418$	−4.91877			−0.240585
$419$	3.69624	+	6.40207i	0.180573	+	0.312762i	0.942076	−	0.335400i	$-0.108871\pi$
$419$	3.69624	+	6.40207i	0.180573	+	0.312762i	−0.761503	+	0.648162i	$0.775538\pi$
$420$	−1.76682	−	4.56120i	−0.0862120	−	0.222564i
$421$	4.67144			0.227672			0.113836	−	0.993500i	$-0.463686\pi$
$421$	4.67144			0.227672			0.113836	+	0.993500i	$0.463686\pi$
$422$	13.6366	+	23.6193i	0.663821	+	1.14977i
$423$	−9.21105			−0.447857
$424$	3.80147	+	6.58434i	0.184616	+	0.319764i
$425$	3.41038	+	5.90695i	0.165428	+	0.286529i
$426$	7.50874	+	13.0055i	0.363800	+	0.630120i
$427$	−8.24079	−	21.2743i	−0.398800	−	1.02954i
$428$	−4.61994			−0.223313
$429$	2.40288	+	0.937651i	0.116012	+	0.0452702i
$430$	−0.181130	−	0.313726i	−0.00873486	−	0.0151292i
$431$	11.0089	−	19.0680i	0.530280	−	0.918472i	−0.469096	−	0.883147i	$-0.655420\pi$
$431$	11.0089	−	19.0680i	0.530280	−	0.918472i	0.999376	−	0.0353247i	$-0.0112465\pi$
$432$	1.00000			0.0481125
$433$	−12.5366	+	21.7141i	−0.602472	+	1.04351i	0.389973	+	0.920826i	$0.372484\pi$
$433$	−12.5366	+	21.7141i	−0.602472	+	1.04351i	−0.992446	+	0.122686i	$0.960849\pi$
$434$	2.12356	+	5.48216i	0.101934	+	0.263152i
$435$	−8.57466	+	14.8517i	−0.411123	+	0.712086i
$436$	4.95093	+	8.57527i	0.237107	+	0.410681i
$437$	−24.6163	−	42.6367i	−1.17756	−	2.03959i
$438$	1.97983			0.0945998
$439$	−13.9493			−0.665764			−0.332882	−	0.942969i	$-0.608021\pi$
$439$	−13.9493			−0.665764			−0.332882	+	0.942969i	$0.608021\pi$
$440$	−0.661295	−	1.14540i	−0.0315260	−	0.0546046i
$441$	−1.49702	−	6.83805i	−0.0712865	−	0.325621i
$442$	−12.1350	+	9.71619i	−0.577205	+	0.462152i
$443$	1.69137	−	2.92955i	0.0803596	−	0.139187i	−0.823045	−	0.567976i	$-0.807726\pi$
$443$	1.69137	−	2.92955i	0.0803596	−	0.139187i	0.903404	+	0.428789i	$0.141060\pi$
$444$	−1.06671	+	1.84759i	−0.0506236	+	0.0876826i
$445$	4.13161	−	7.15616i	0.195857	−	0.339235i
$446$	−2.88502	−	4.99700i	−0.136610	−	0.236615i
$447$	−11.6477			−0.550916
$448$	2.61442	+	0.405935i	0.123520	+	0.0191786i
$449$	7.51094	−	13.0093i	0.354463	−	0.613948i	−0.632563	−	0.774509i	$-0.717997\pi$
$449$	7.51094	−	13.0093i	0.354463	−	0.613948i	0.987026	+	0.160561i	$0.0513304\pi$
$450$	0.790985	−	1.37003i	0.0372874	−	0.0645837i
$451$	−3.19258			−0.150333
$452$	1.50417	−	2.60530i	0.0707503	−	0.122543i
$453$	8.19088			0.384841
$454$	16.9846			0.797126
$455$	0.0438411	−	17.6363i	0.00205530	−	0.826802i
$456$	−6.87573			−0.321985
$457$	−11.9647			−0.559686			−0.279843	−	0.960046i	$-0.590282\pi$
$457$	−11.9647			−0.559686			−0.279843	+	0.960046i	$0.590282\pi$
$458$	0.460390	−	0.797420i	0.0215126	−	0.0372610i
$459$	4.31156			0.201246
$460$	6.61899	−	11.4644i	0.308612	−	0.534532i
$461$	5.35595	−	9.27677i	0.249451	−	0.432062i	−0.713922	−	0.700225i	$-0.753083\pi$
$461$	5.35595	−	9.27677i	0.249451	−	0.432062i	0.963374	+	0.268163i	$0.0864164\pi$
$462$	−0.683663	−	1.76493i	−0.0318069	−	0.0821122i
$463$	−13.5305			−0.628814			−0.314407	−	0.949288i	$-0.601806\pi$
$463$	−13.5305			−0.628814			−0.314407	+	0.949288i	$0.601806\pi$
$464$	−4.63798	−	8.03322i	−0.215313	−	0.372933i
$465$	2.05409	−	3.55778i	0.0952560	−	0.164988i
$466$	−2.50283	+	4.33502i	−0.115941	+	0.200816i
$467$	−13.9783	+	24.2112i	−0.646840	+	1.12036i	0.337034	+	0.941493i	$0.390576\pi$
$467$	−13.9783	+	24.2112i	−0.646840	+	1.12036i	−0.983873	+	0.178867i	$0.942757\pi$
$468$	3.35888	+	1.31070i	0.155264	+	0.0605872i
$469$	23.1006	−	28.7050i	1.06669	−	1.32548i
$470$	8.51466	+	14.7478i	0.392752	+	0.680266i
$471$	−22.8707			−1.05382
$472$	−2.48056			−0.114177
$473$	−0.0700874	−	0.121395i	−0.00322262	−	0.00558174i
$474$	7.37533	+	12.7744i	0.338760	+	0.586750i
$475$	−5.43860	+	9.41993i	−0.249540	+	0.432216i
$476$	11.2722	+	1.75021i	0.516662	+	0.0802208i
$477$	3.80147	−	6.58434i	0.174057	−	0.301476i
$478$	13.8239			0.632291
$479$	5.79262	−	10.0331i	0.264672	−	0.458425i	−0.702806	−	0.711382i	$-0.748070\pi$
$479$	5.79262	−	10.0331i	0.264672	−	0.458425i	0.967478	+	0.252957i	$0.0814031\pi$
$480$	−0.924396	−	1.60110i	−0.0421927	−	0.0730799i
$481$	−6.00457	+	4.80769i	−0.273785	+	0.219212i
$482$	10.7589			0.490054
$483$	11.8773	−	14.7588i	0.540436	−	0.671551i
$484$	5.24412	+	9.08307i	0.238369	+	0.412867i
$485$	2.57341	+	4.45728i	0.116853	+	0.202394i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−8.48336			−0.384418			−0.192209	−	0.981354i	$-0.561565\pi$
$487$	−8.48336			−0.384418			−0.192209	+	0.981354i	$0.561565\pi$
$488$	−4.31156	−	7.46783i	−0.195175	−	0.338053i
$489$	18.0385			0.815727
$490$	−9.56457	+	8.71794i	−0.432083	+	0.393836i
$491$	−14.8606	−	25.7394i	−0.670650	−	1.16160i	−0.977720	−	0.209914i	$-0.932682\pi$
$491$	−14.8606	−	25.7394i	−0.670650	−	1.16160i	0.307069	−	0.951687i	$-0.400652\pi$
$492$	−4.46276			−0.201197
$493$	−19.9969	−	34.6357i	−0.900616	−	1.55991i
$494$	−23.0947	−	9.01203i	−1.03908	−	0.405471i
$495$	−0.661295	+	1.14540i	−0.0297230	+	0.0514818i
$496$	1.11104	+	1.92438i	0.0498873	+	0.0864073i
$497$	24.9104	−	30.9539i	1.11739	−	1.38847i
$498$	4.85769	−	8.41377i	0.217678	−	0.377030i
$499$	17.7944	−	30.8208i	0.796586	−	1.37973i	−0.125241	−	0.992126i	$-0.539970\pi$
$499$	17.7944	−	30.8208i	0.796586	−	1.37973i	0.921827	−	0.387601i	$-0.126696\pi$
$500$	−12.1687			−0.544200
$501$	−7.73872			−0.345741
$502$	−11.8267	+	20.4844i	−0.527850	+	0.914263i
$503$	13.5658	−	23.4966i	0.604867	−	1.04766i	−0.387205	−	0.921994i	$-0.626560\pi$
$503$	13.5658	−	23.4966i	0.604867	−	1.04766i	0.992072	−	0.125667i	$-0.0401072\pi$
$504$	−0.955663	−	2.46713i	−0.0425686	−	0.109895i
$505$	−4.95060	−	8.57469i	−0.220299	−	0.381568i
$506$	2.56119	−	4.43611i	0.113859	−	0.197209i
$507$	9.56412	+	8.80498i	0.424757	+	0.391043i
$508$	−7.58356	−	13.1351i	−0.336466	−	0.582776i
$509$	7.21670			0.319875			0.159937	−	0.987127i	$-0.448871\pi$
$509$	7.21670			0.319875			0.159937	+	0.987127i	$0.448871\pi$
$510$	−3.98558	−	6.90323i	−0.176485	−	0.305680i
$511$	−1.89205	−	4.88448i	−0.0836992	−	0.216077i
$512$	1.00000			0.0441942
$513$	3.43786	+	5.95456i	0.151785	+	0.262900i
$514$	−19.1940			−0.846613
$515$	6.03499	+	10.4529i	0.265933	+	0.460610i
$516$	−0.0979721	−	0.169693i	−0.00431298	−	0.00747030i
$517$	3.29471	+	5.70660i	0.144901	+	0.250976i
$518$	5.57764	+	0.866025i	0.245067	+	0.0380510i
$519$	12.0242			0.527806
$520$	−1.00637	−	6.58951i	−0.0441321	−	0.288969i
$521$	11.6165	+	20.1203i	0.508926	+	0.881486i	0.999947	+	0.0103382i	$0.00329081\pi$
$521$	11.6165	+	20.1203i	0.508926	+	0.881486i	−0.491020	+	0.871148i	$0.663376\pi$
$522$	−4.63798	+	8.03322i	−0.202999	+	0.351604i
$523$	−39.7226			−1.73695			−0.868475	−	0.495734i	$-0.834899\pi$
$523$	−39.7226			−1.73695			−0.868475	+	0.495734i	$0.834899\pi$
$524$	9.69444	−	16.7913i	0.423504	−	0.733530i
$525$	−4.13594	−	0.642177i	−0.180507	−	0.0280269i
$526$	−5.49567	+	9.51878i	−0.239623	+	0.415039i
$527$	4.79032	+	8.29708i	0.208670	+	0.361427i
$528$	−0.357690	−	0.619538i	−0.0155665	−	0.0269619i
$529$	28.2706			1.22916
$530$	−14.0562			−0.610564
$531$	1.24028	+	2.14823i	0.0538236	+	0.0932253i
$532$	6.57088	+	16.9633i	0.284884	+	0.735452i
$533$	−14.9899	−	5.84936i	−0.649284	−	0.253364i
$534$	2.23476	−	3.87073i	0.0967077	−	0.167503i
$535$	4.27065	−	7.39699i	0.184636	−	0.319800i
$536$	6.96322	−	12.0606i	0.300765	−	0.520940i
$537$	−5.65742	−	9.79893i	−0.244136	−	0.422855i
$538$	16.5175			0.712122
$539$	−3.70096	+	3.37336i	−0.159412	+	0.145301i
$540$	−0.924396	+	1.60110i	−0.0397797	+	0.0689004i
$541$	17.6323	−	30.5400i	0.758070	−	1.31302i	−0.185764	−	0.982594i	$-0.559476\pi$
$541$	17.6323	−	30.5400i	0.758070	−	1.31302i	0.943834	−	0.330421i	$-0.107191\pi$
$542$	−18.1906			−0.781352
$543$	1.24862	−	2.16268i	0.0535836	−	0.0928095i
$544$	4.31156			0.184856
$545$	−18.3065			−0.784164
$546$	0.0237134	−	9.53936i	0.00101484	−	0.408247i
$547$	−37.3861			−1.59851			−0.799257	−	0.600990i	$-0.794773\pi$
$547$	−37.3861			−1.59851			−0.799257	+	0.600990i	$0.794773\pi$
$548$	−4.74829			−0.202837
$549$	−4.31156	+	7.46783i	−0.184013	+	0.318719i
$550$	−1.13171			−0.0482563
$551$	31.8895	−	55.2342i	1.35854	−	2.35306i
$552$	3.58017	−	6.20104i	0.152382	−	0.263934i
$553$	24.4678	−	30.4039i	1.04048	−	1.29291i
$554$	16.4894			0.700567
$555$	−1.97212	−	3.41580i	−0.0837116	−	0.144993i
$556$	−7.69027	+	13.3199i	−0.326140	+	0.564891i
$557$	−16.6350	+	28.8127i	−0.704847	+	1.22083i	0.261899	+	0.965095i	$0.415651\pi$
$557$	−16.6350	+	28.8127i	−0.704847	+	1.22083i	−0.966747	+	0.255736i	$0.917682\pi$
$558$	1.11104	−	1.92438i	0.0470342	−	0.0814656i
$559$	−0.106660	−	0.698389i	−0.00451123	−	0.0295387i
$560$	−3.06671	+	3.81071i	−0.129592	+	0.161032i
$561$	−1.54220	−	2.67117i	−0.0651118	−	0.112777i
$562$	15.2768			0.644411
$563$	14.6410			0.617045			0.308523	−	0.951217i	$-0.400165\pi$
$563$	14.6410			0.617045			0.308523	+	0.951217i	$0.400165\pi$
$564$	4.60553	+	7.97700i	0.193928	+	0.335892i
$565$	2.78090	+	4.81666i	0.116993	+	0.202638i
$566$	4.57838	−	7.92998i	0.192444	−	0.333322i
$567$	−1.65876	+	2.06119i	−0.0696615	+	0.0865619i
$568$	7.50874	−	13.0055i	0.315060	−	0.545700i
$569$	34.8196			1.45972			0.729858	−	0.683599i	$-0.239586\pi$
$569$	34.8196			1.45972			0.729858	+	0.683599i	$0.239586\pi$
$570$	6.35589	−	11.0087i	0.266219	−	0.461105i
$571$	17.3721	+	30.0894i	0.727001	+	1.25920i	0.958145	+	0.286283i	$0.0924199\pi$
$571$	17.3721	+	30.0894i	0.727001	+	1.25920i	−0.231144	+	0.972920i	$0.574247\pi$
$572$	−0.389409	−	2.54978i	−0.0162820	−	0.106612i
$573$	−5.32698			−0.222538
$574$	4.26490	+	11.0102i	0.178013	+	0.459557i
$575$	−5.66373	−	9.80987i	−0.236194	−	0.409100i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.2007	−	19.4003i	−0.466293	−	0.807643i	0.532966	−	0.846137i	$-0.321077\pi$
$577$	−11.2007	−	19.4003i	−0.466293	−	0.807643i	−0.999259	+	0.0384934i	$0.987744\pi$
$578$	1.58952			0.0661152
$579$	−4.86186	−	8.42099i	−0.202052	−	0.349964i
$580$	17.1493			0.712086
$581$	−25.4001	−	3.94381i	−1.05378	−	0.163617i
$582$	1.39194	+	2.41091i	0.0576978	+	0.0999356i
$583$	−5.43900			−0.225260
$584$	−0.989914	−	1.71458i	−0.0409629	−	0.0709499i
$585$	−5.20350	+	4.16629i	−0.215138	+	0.172255i
$586$	5.93488	−	10.2795i	0.245168	−	0.424643i
$587$	−7.57505	−	13.1204i	−0.312656	−	0.541536i	0.666280	−	0.745701i	$-0.267885\pi$
$587$	−7.57505	−	13.1204i	−0.312656	−	0.541536i	−0.978936	+	0.204165i	$0.934552\pi$
$588$	−5.17342	+	4.71548i	−0.213348	+	0.194463i
$589$	−7.63923	+	13.2315i	−0.314769	+	0.545196i
$590$	2.29302	−	3.97163i	0.0944022	−	0.163509i
$591$	6.17186			0.253876
$592$	2.13341			0.0876826
$593$	−3.85455	+	6.67627i	−0.158287	+	0.274162i	−0.934251	−	0.356616i	$-0.883931\pi$
$593$	−3.85455	+	6.67627i	−0.158287	+	0.274162i	0.775964	+	0.630777i	$0.217264\pi$
$594$	−0.357690	+	0.619538i	−0.0146762	+	0.0254200i
$595$	−13.2223	+	16.4301i	−0.542060	+	0.673568i
$596$	5.82384	+	10.0872i	0.238554	+	0.413187i
$597$	−2.70727	+	4.68913i	−0.110801	+	0.191913i
$598$	20.1531	−	16.1360i	0.824121	−	0.659850i
$599$	−8.99448	−	15.5789i	−0.367505	−	0.636537i	0.621670	−	0.783279i	$-0.286454\pi$
$599$	−8.99448	−	15.5789i	−0.367505	−	0.636537i	−0.989175	+	0.146743i	$0.953121\pi$
$600$	−1.58197			−0.0645837
$601$	4.77657	+	8.27326i	0.194840	+	0.337473i	0.946848	−	0.321681i	$-0.104248\pi$
$601$	4.77657	+	8.27326i	0.194840	+	0.337473i	−0.752008	+	0.659154i	$0.770914\pi$
$602$	−0.325025	+	0.403878i	−0.0132470	+	0.0164609i
$603$	−13.9264			−0.567128
$604$	−4.09544	−	7.09351i	−0.166641	−	0.288631i
$605$	−19.3905			−0.788338
$606$	−2.67775	−	4.63800i	−0.108776	−	0.188406i
$607$	−10.7619	−	18.6402i	−0.436813	−	0.756582i	0.560629	−	0.828067i	$-0.310559\pi$
$607$	−10.7619	−	18.6402i	−0.436813	−	0.756582i	−0.997442	+	0.0714855i	$0.977226\pi$
$608$	3.43786	+	5.95456i	0.139424	+	0.241489i
$609$	24.2513	+	3.76543i	0.982712	+	0.152583i
$610$	15.9423			0.645486
$611$	5.01392	+	32.8303i	0.202841	+	1.32817i
$612$	−2.15578	−	3.73392i	−0.0871422	−	0.150935i
$613$	18.4945	−	32.0334i	0.746985	−	1.29382i	−0.202276	−	0.979328i	$-0.564834\pi$
$613$	18.4945	−	32.0334i	0.746985	−	1.29382i	0.949262	−	0.314488i	$-0.101833\pi$
$614$	−28.0679			−1.13273
$615$	4.12536	−	7.14533i	0.166351	−	0.288128i
$616$	−1.18665	+	1.47454i	−0.0478114	+	0.0594108i
$617$	1.88766	−	3.26953i	0.0759945	−	0.131626i	−0.825524	−	0.564367i	$-0.809120\pi$
$617$	1.88766	−	3.26953i	0.0759945	−	0.131626i	0.901518	+	0.432741i	$0.142454\pi$
$618$	3.26429	+	5.65391i	0.131309	+	0.227434i
$619$	−14.0117	−	24.2689i	−0.563177	−	0.975451i	−0.997217	−	0.0745570i	$-0.976246\pi$
$619$	−14.0117	−	24.2689i	−0.563177	−	0.975451i	0.434040	−	0.900894i	$-0.357088\pi$
$620$	−4.10817			−0.164988
$621$	−7.16035			−0.287335
$622$	−12.7326	−	22.0536i	−0.510532	−	0.884267i
$623$	−11.6852	−	1.81434i	−0.468160	−	0.0726899i
$624$	−0.544337	−	3.56422i	−0.0217909	−	0.142683i
$625$	7.29376	−	12.6332i	0.291750	−	0.505326i
$626$	−8.82204	+	15.2802i	−0.352600	+	0.610721i
$627$	2.45938	−	4.25978i	0.0982183	−	0.170119i
$628$	11.4353	+	19.8066i	0.456319	+	0.790368i
$629$	9.19832			0.366761
$630$	4.83353	+	0.750489i	0.192572	+	0.0299002i
$631$	6.85038	−	11.8652i	0.272709	−	0.472346i	−0.696845	−	0.717221i	$-0.745414\pi$
$631$	6.85038	−	11.8652i	0.272709	−	0.472346i	0.969555	+	0.244875i	$0.0787470\pi$
$632$	7.37533	−	12.7744i	0.293375	−	0.508140i
$633$	−27.2733			−1.08402
$634$	−14.8710	+	25.7573i	−0.590603	+	1.02295i
$635$	28.0408			1.11277
$636$	−7.60294			−0.301476
$637$	−23.5575	+	9.05791i	−0.933381	+	0.358887i
$638$	6.63585			0.262716
$639$	−15.0175			−0.594082
$640$	−0.924396	+	1.60110i	−0.0365399	+	0.0632890i
$641$	−6.40335			−0.252917			−0.126458	−	0.991972i	$-0.540361\pi$
$641$	−6.40335			−0.252917			−0.126458	+	0.991972i	$0.540361\pi$
$642$	2.30997	−	4.00099i	0.0911673	−	0.157906i
$643$	9.93369	−	17.2057i	0.391747	−	0.678525i	−0.600933	−	0.799299i	$-0.705204\pi$
$643$	9.93369	−	17.2057i	0.391747	−	0.678525i	0.992680	+	0.120774i	$0.0385377\pi$
$644$	−18.7202	−	2.90663i	−0.737679	−	0.114537i
$645$	0.362260			0.0142640
$646$	14.8225	+	25.6734i	0.583185	+	1.01011i
$647$	−15.2592	+	26.4297i	−0.599902	+	1.03906i	0.392933	+	0.919567i	$0.371460\pi$
$647$	−15.2592	+	26.4297i	−0.599902	+	1.03906i	−0.992835	+	0.119494i	$0.961873\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	0.887274	−	1.53680i	0.0348285	−	0.0603248i
$650$	−5.31365	−	2.07349i	−0.208418	−	0.0813291i
$651$	−5.80947	−	0.902022i	−0.227691	−	0.0353530i
$652$	−9.01923	−	15.6218i	−0.353220	−	0.611795i
$653$	3.65412			0.142997			0.0714984	−	0.997441i	$-0.477222\pi$
$653$	3.65412			0.142997			0.0714984	+	0.997441i	$0.477222\pi$
$654$	−9.90187			−0.387194
$655$	17.9230	+	31.0435i	0.700309	+	1.21297i
$656$	2.23138	+	3.86487i	0.0871208	+	0.150898i
$657$	−0.989914	+	1.71458i	−0.0386202	+	0.0668922i
$658$	15.2789	−	18.9857i	0.595635	−	0.740141i
$659$	4.12332	−	7.14181i	0.160622	−	0.278205i	−0.774470	−	0.632611i	$-0.781983\pi$
$659$	4.12332	−	7.14181i	0.160622	−	0.278205i	0.935092	+	0.354405i	$0.115317\pi$
$660$	1.32259			0.0514818
$661$	−23.0565	+	39.9351i	−0.896796	+	1.55330i	−0.0652290	+	0.997870i	$0.520778\pi$
$661$	−23.0565	+	39.9351i	−0.896796	+	1.55330i	−0.831567	+	0.555425i	$0.812556\pi$
$662$	−12.0197	−	20.8187i	−0.467158	−	0.809141i
$663$	−2.34694	−	15.3674i	−0.0911476	−	0.596819i
$664$	−9.71538			−0.377030
$665$	−33.2340	−	5.16016i	−1.28876	−	0.200102i
$666$	−1.06671	−	1.84759i	−0.0413340	−	0.0715926i
$667$	33.2095	+	57.5206i	1.28588	+	2.22721i
$668$	3.86936	+	6.70193i	0.149710	+	0.259306i
$669$	5.77004			0.223083
$670$	12.8735	+	22.2976i	0.497348	+	0.861432i
$671$	6.16881			0.238144
$672$	−1.65876	+	2.06119i	−0.0639881	+	0.0795122i
$673$	−3.98669	−	6.90515i	−0.153676	−	0.266174i	0.778900	−	0.627148i	$-0.215778\pi$
$673$	−3.98669	−	6.90515i	−0.153676	−	0.266174i	−0.932576	+	0.360974i	$0.882444\pi$
$674$	−2.21939			−0.0854879
$675$	0.790985	+	1.37003i	0.0304450	+	0.0527324i
$676$	2.84327	−	12.6853i	0.109357	−	0.487895i
$677$	−20.4979	+	35.5033i	−0.787797	+	1.36450i	0.139517	+	0.990220i	$0.455445\pi$
$677$	−20.4979	+	35.5033i	−0.787797	+	1.36450i	−0.927314	+	0.374285i	$0.877888\pi$
$678$	1.50417	+	2.60530i	0.0577674	+	0.100056i
$679$	4.61780	−	5.73811i	0.177215	−	0.220209i
$680$	−3.98558	+	6.90323i	−0.152840	+	0.264727i
$681$	−8.49229	+	14.7091i	−0.325425	+	0.563653i
$682$	−1.58964			−0.0608704
$683$	35.2665			1.34944			0.674718	−	0.738076i	$-0.264265\pi$
$683$	35.2665			1.34944			0.674718	+	0.738076i	$0.264265\pi$
$684$	3.43786	−	5.95456i	0.131450	−	0.227678i
$685$	4.38930	−	7.60248i	0.167706	−	0.290476i
$686$	16.5777	+	8.25707i	0.632940	+	0.315256i
$687$	0.460390	+	0.797420i	0.0175650	+	0.0304235i
$688$	−0.0979721	+	0.169693i	−0.00373515	+	0.00646947i
$689$	−25.5373	−	9.96519i	−0.972895	−	0.379644i
$690$	6.61899	+	11.4644i	0.251981	+	0.436444i
$691$	40.7075			1.54859			0.774293	−	0.632827i	$-0.218105\pi$
$691$	40.7075			1.54859			0.774293	+	0.632827i	$0.218105\pi$
$692$	−6.01212	−	10.4133i	−0.228547	−	0.395854i
$693$	1.87031	+	0.290398i	0.0710472	+	0.0110313i
$694$	−2.01895			−0.0766384
$695$	−14.2177	−	24.6258i	−0.539308	−	0.934109i
$696$	9.27596			0.351604
$697$	9.62073	+	16.6636i	0.364411	+	0.631179i
$698$	−16.8191	−	29.1316i	−0.636613	−	1.10265i
$699$	−2.50283	−	4.33502i	−0.0946656	−	0.163966i
$700$	1.51183	+	3.90292i	0.0571418	+	0.147517i
$701$	−33.7968			−1.27649			−0.638243	−	0.769835i	$-0.720339\pi$
$701$	−33.7968			−1.27649			−0.638243	+	0.769835i	$0.720339\pi$
$702$	−2.81454	+	2.25352i	−0.106228	+	0.0850537i
$703$	7.33438	+	12.7035i	0.276621	+	0.479122i
$704$	−0.357690	+	0.619538i	−0.0134810	+	0.0233497i
$705$	−17.0293			−0.641361
$706$	−11.6388	+	20.1590i	−0.438033	+	0.758696i
$707$	−8.88349	+	11.0387i	−0.334098	+	0.415153i
$708$	1.24028	−	2.14823i	0.0466126	−	0.0807355i
$709$	1.67680	+	2.90430i	0.0629736	+	0.109073i	0.895793	−	0.444471i	$-0.146608\pi$
$709$	1.67680	+	2.90430i	0.0629736	+	0.109073i	−0.832820	+	0.553544i	$0.813275\pi$
$710$	13.8821	+	24.0445i	0.520986	+	0.902374i
$711$	−14.7507			−0.553193
$712$	−4.46953			−0.167503
$713$	−7.95545	−	13.7792i	−0.297934	−	0.516037i
$714$	−7.15185	+	8.88694i	−0.267651	+	0.332585i
$715$	4.44242	+	1.73352i	0.166137	+	0.0648300i
$716$	−5.65742	+	9.79893i	−0.211428	+	0.366203i
$717$	−6.91196	+	11.9719i	−0.258132	+	0.447097i
$718$	5.44896	−	9.43787i	0.203353	−	0.352218i
$719$	19.5541	+	33.8687i	0.729245	+	1.26309i	0.957203	+	0.289419i	$0.0934619\pi$
$719$	19.5541	+	33.8687i	0.729245	+	1.26309i	−0.227958	+	0.973671i	$0.573205\pi$
$720$	1.84879			0.0689004
$721$	10.8294	−	13.4566i	0.403306	−	0.501151i
$722$	−14.1378	+	24.4874i	−0.526155	+	0.911328i
$723$	−5.37945	+	9.31748i	−0.200064	+	0.346521i
$724$	−2.49725			−0.0928095
$725$	7.33715	−	12.7083i	0.272495	−	0.471975i
$726$	−10.4882			−0.389255
$727$	−3.65073			−0.135398			−0.0676990	−	0.997706i	$-0.521566\pi$
$727$	−3.65073			−0.135398			−0.0676990	+	0.997706i	$0.521566\pi$
$728$	−8.27319	+	4.74914i	−0.306625	+	0.176015i
$729$	1.00000			0.0370370
$730$	3.66029			0.135473
$731$	−0.422412	+	0.731639i	−0.0156235	+	0.0270607i
$732$	8.62311			0.318719
$733$	16.3999	−	28.4054i	0.605744	−	1.04918i	−0.386190	−	0.922419i	$-0.626209\pi$
$733$	16.3999	−	28.4054i	0.605744	−	1.04918i	0.991933	−	0.126760i	$-0.0404577\pi$
$734$	−2.44394	+	4.23302i	−0.0902074	+	0.156244i
$735$	−2.76767	−	12.6421i	−0.102087	−	0.466312i
$736$	−7.16035			−0.263934
$737$	4.98135	+	8.62796i	0.183490	+	0.317815i
$738$	2.23138	−	3.86487i	0.0821383	−	0.142268i
$739$	−5.11506	+	8.85954i	−0.188160	+	0.325903i	−0.944637	−	0.328118i	$-0.893586\pi$
$739$	−5.11506	+	8.85954i	−0.188160	+	0.325903i	0.756477	+	0.654021i	$0.226919\pi$
$740$	−1.97212	+	3.41580i	−0.0724964	+	0.125567i
$741$	19.3520	−	15.4946i	0.710914	−	0.569209i
$742$	7.26584	+	18.7574i	0.266738	+	0.688606i
$743$	17.1231	+	29.6581i	0.628186	+	1.08805i	0.987915	+	0.154994i	$0.0495357\pi$
$743$	17.1231	+	29.6581i	0.628186	+	1.08805i	−0.359729	+	0.933057i	$0.617131\pi$
$744$	−2.22209			−0.0814656
$745$	−21.5341			−0.788949
$746$	7.68366	+	13.3085i	0.281319	+	0.487259i
$747$	4.85769	+	8.41377i	0.177734	+	0.307844i
$748$	−1.54220	+	2.67117i	−0.0563885	+	0.0976678i
$749$	−12.0785	−	1.87539i	−0.441338	−	0.0685254i
$750$	6.08435	−	10.5384i	0.222169	−	0.384808i
$751$	11.7925			0.430316			0.215158	−	0.976579i	$-0.430973\pi$
$751$	11.7925			0.430316			0.215158	+	0.976579i	$0.430973\pi$
$752$	4.60553	−	7.97700i	0.167946	−	0.290891i
$753$	−11.8267	−	20.4844i	−0.430988	−	0.746492i
$754$	31.1568	+	12.1580i	1.13466	+	0.442769i
$755$	15.1432			0.551118
$756$	2.61442	+	0.405935i	0.0950857	+	0.0147637i
$757$	24.1278	+	41.7906i	0.876940	+	1.51890i	0.854682	+	0.519152i	$0.173752\pi$
$757$	24.1278	+	41.7906i	0.876940	+	1.51890i	0.0222575	+	0.999752i	$0.492915\pi$
$758$	8.66626	+	15.0104i	0.314773	+	0.545203i
$759$	2.56119	+	4.43611i	0.0929652	+	0.161021i
$760$	−12.7118			−0.461105
$761$	−6.11899	−	10.5984i	−0.221813	−	0.384192i	0.733545	−	0.679641i	$-0.237864\pi$
$761$	−6.11899	−	10.5984i	−0.221813	−	0.384192i	−0.955359	+	0.295449i	$0.904531\pi$
$762$	15.1671			0.549446
$763$	9.46285	+	24.4292i	0.342578	+	0.884395i
$764$	2.66349	+	4.61330i	0.0963617	+	0.166903i
$765$	7.97117			0.288198
$766$	5.99628	+	10.3859i	0.216654	+	0.375256i
$767$	6.98165	−	5.59000i	0.252093	−	0.201843i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	0.357690	+	0.619538i	0.0128986	+	0.0223411i	0.872403	−	0.488788i	$-0.162561\pi$
$769$	0.357690	+	0.619538i	0.0128986	+	0.0223411i	−0.859504	+	0.511129i	$0.829227\pi$
$770$	−1.26395	−	3.26300i	−0.0455496	−	0.117590i
$771$	9.59702	−	16.6225i	0.345628	−	0.598646i
$772$	−4.86186	+	8.42099i	−0.174982	+	0.303078i
$773$	5.43066			0.195327			0.0976636	−	0.995219i	$-0.468863\pi$
$773$	5.43066			0.195327			0.0976636	+	0.995219i	$0.468863\pi$
$774$	0.195944			0.00704307
$775$	−1.75764	+	3.04432i	−0.0631362	+	0.109355i
$776$	1.39194	−	2.41091i	0.0499678	−	0.0865467i
$777$	−3.53882	+	4.39737i	−0.126954	+	0.157755i
$778$	−8.89274	−	15.4027i	−0.318820	−	0.552213i
$779$	−15.3424	+	26.5738i	−0.549698	+	0.952105i
$780$	6.20986	+	2.42321i	0.222349	+	0.0867650i
$781$	5.37161	+	9.30390i	0.192211	+	0.332920i
$782$	−30.8722			−1.10399
$783$	−4.63798	−	8.03322i	−0.165748	−	0.287084i
$784$	6.67043	+	2.12257i	0.238230	+	0.0758061i
$785$	−42.2831			−1.50915
$786$	9.69444	+	16.7913i	0.345789	+	0.598925i
$787$	−5.17027			−0.184300			−0.0921501	−	0.995745i	$-0.529374\pi$
$787$	−5.17027			−0.184300			−0.0921501	+	0.995745i	$0.529374\pi$
$788$	−3.08593	−	5.34499i	−0.109932	−	0.190407i
$789$	−5.49567	−	9.51878i	−0.195651	−	0.338878i
$790$	13.6354	+	23.6173i	0.485127	+	0.840265i
$791$	4.99013	−	6.20077i	0.177428	−	0.220474i
$792$	0.715381			0.0254200
$793$	28.9640	+	11.3023i	1.02854	+	0.401358i
$794$	−7.02952	−	12.1755i	−0.249468	−	0.432092i
$795$	7.02812	−	12.1731i	0.249262	−	0.431734i
$796$	5.41454			0.191913
$797$	3.24073	−	5.61311i	0.114793	−	0.198827i	−0.802904	−	0.596108i	$-0.796713\pi$
$797$	3.24073	−	5.61311i	0.114793	−	0.198827i	0.917697	+	0.397281i	$0.130046\pi$
$798$	−17.9761	−	2.79110i	−0.636346	−	0.0988038i
$799$	19.8570	−	34.3933i	0.702490	−	1.21675i
$800$	0.790985	+	1.37003i	0.0279656	+	0.0484378i
$801$	2.23476	+	3.87073i	0.0789615	+	0.136765i
$802$	4.13072			0.145861
$803$	1.41633			0.0499812
$804$	6.96322	+	12.0606i	0.245574	+	0.425346i
$805$	21.9587	−	27.2860i	0.773942	−	0.961706i
$806$	−7.46371	−	2.91249i	−0.262898	−	0.102588i
$807$	−8.25877	+	14.3046i	−0.290723	+	0.503546i
$808$	−2.67775	+	4.63800i	−0.0942028	+	0.163164i
$809$	−23.2909	+	40.3409i	−0.818863	+	1.41831i	0.0876578	+	0.996151i	$0.472062\pi$
$809$	−23.2909	+	40.3409i	−0.818863	+	1.41831i	−0.906521	+	0.422161i	$0.861272\pi$
$810$	−0.924396	−	1.60110i	−0.0324800	−	0.0562569i
$811$	44.2321			1.55320			0.776600	−	0.629994i	$-0.216943\pi$
$811$	44.2321			1.55320			0.776600	+	0.629994i	$0.216943\pi$
$812$	−8.86469	−	22.8850i	−0.311090	−	0.803105i
$813$	9.09528	−	15.7535i	0.318985	−	0.552499i
$814$	−0.763101	+	1.32173i	−0.0267467	+	0.0463266i
$815$	33.3493			1.16818
$816$	−2.15578	+	3.73392i	−0.0754673	+	0.130713i
$817$	−1.34726			−0.0471346
$818$	−5.21490			−0.182335
$819$	8.24947	+	4.79022i	0.288260	+	0.167384i
$820$	−8.25072			−0.288128
$821$	−8.26567			−0.288474			−0.144237	−	0.989543i	$-0.546073\pi$
$821$	−8.26567			−0.288474			−0.144237	+	0.989543i	$0.546073\pi$
$822$	2.37414	−	4.11214i	0.0828078	−	0.143427i
$823$	−51.2361			−1.78598			−0.892989	−	0.450078i	$-0.851396\pi$
$823$	−51.2361			−1.78598			−0.892989	+	0.450078i	$0.851396\pi$
$824$	3.26429	−	5.65391i	0.113717	−	0.196963i
$825$	0.565856	−	0.980091i	0.0197006	−	0.0341224i
$826$	−6.48525	−	1.00695i	−0.225651	−	0.0350362i
$827$	−4.84895			−0.168615			−0.0843073	−	0.996440i	$-0.526868\pi$
$827$	−4.84895			−0.168615			−0.0843073	+	0.996440i	$0.526868\pi$
$828$	3.58017	+	6.20104i	0.124420	+	0.215501i
$829$	−0.997594	+	1.72788i	−0.0346479	+	0.0600118i	−0.882829	−	0.469694i	$-0.844364\pi$
$829$	−0.997594	+	1.72788i	−0.0346479	+	0.0600118i	0.848181	+	0.529706i	$0.177698\pi$
$830$	8.98086	−	15.5553i	0.311730	−	0.539932i
$831$	−8.24469	+	14.2802i	−0.286005	+	0.495376i
$832$	−2.81454	+	2.25352i	−0.0975766	+	0.0781268i
$833$	28.7600	+	9.15159i	0.996473	+	0.317084i
$834$	−7.69027	−	13.3199i	−0.266292	−	0.461232i
$835$	−14.3073			−0.495124
$836$	−4.91877			−0.170119
$837$	1.11104	+	1.92438i	0.0384032	+	0.0665164i
$838$	3.69624	+	6.40207i	0.127684	+	0.221156i
$839$	11.0996	−	19.2251i	0.383201	−	0.663724i	−0.608317	−	0.793694i	$-0.708155\pi$
$839$	11.0996	−	19.2251i	0.383201	−	0.663724i	0.991518	+	0.129971i	$0.0414883\pi$
$840$	−1.76682	−	4.56120i	−0.0609611	−	0.157376i
$841$	−28.5217	+	49.4011i	−0.983507	+	1.70348i
$842$	4.67144			0.160989
$843$	−7.63838	+	13.2301i	−0.263080	+	0.455667i
$844$	13.6366	+	23.6193i	0.469392	+	0.813011i
$845$	17.6821	+	16.2786i	0.608281	+	0.560000i
$846$	−9.21105			−0.316682
$847$	10.0232	+	25.8758i	0.344402	+	0.889102i
$848$	3.80147	+	6.58434i	0.130543	+	0.226107i
$849$	4.57838	+	7.92998i	0.157129	+	0.272156i
$850$	3.41038	+	5.90695i	0.116975	+	0.202607i
$851$	−15.2760			−0.523653
$852$	7.50874	+	13.0055i	0.257245	+	0.445562i
$853$	−20.8901			−0.715262			−0.357631	−	0.933863i	$-0.616415\pi$
$853$	−20.8901			−0.715262			−0.357631	+	0.933863i	$0.616415\pi$
$854$	−8.24079	−	21.2743i	−0.281994	−	0.727992i
$855$	6.35589	+	11.0087i	0.217367	+	0.376491i
$856$	−4.61994			−0.157906
$857$	6.25195	+	10.8287i	0.213563	+	0.369901i	0.952827	−	0.303514i	$-0.0981599\pi$
$857$	6.25195	+	10.8287i	0.213563	+	0.369901i	−0.739264	+	0.673415i	$0.764827\pi$
$858$	2.40288	+	0.937651i	0.0820329	+	0.0320109i
$859$	4.94030	−	8.55685i	0.168561	−	0.291956i	−0.769353	−	0.638824i	$-0.779421\pi$
$859$	4.94030	−	8.55685i	0.168561	−	0.291956i	0.937914	+	0.346868i	$0.112755\pi$
$860$	−0.181130	−	0.313726i	−0.00617648	−	0.0106980i
$861$	−11.6676	−	1.81159i	−0.397629	−	0.0617389i
$862$	11.0089	−	19.0680i	0.374965	−	0.649458i
$863$	−20.2808	+	35.1274i	−0.690367	+	1.19575i	0.281350	+	0.959605i	$0.409218\pi$
$863$	−20.2808	+	35.1274i	−0.690367	+	1.19575i	−0.971718	+	0.236146i	$0.924116\pi$
$864$	1.00000			0.0340207
$865$	22.2303			0.755854
$866$	−12.5366	+	21.7141i	−0.426012	+	0.737875i
$867$	−0.794759	+	1.37656i	−0.0269914	+	0.0467505i
$868$	2.12356	+	5.48216i	0.0720784	+	0.186077i
$869$	5.27617	+	9.13860i	0.178982	+	0.310006i
$870$	−8.57466	+	14.8517i	−0.290708	+	0.503521i
$871$	7.58068	+	49.6369i	0.256861	+	1.68188i
$872$	4.95093	+	8.57527i	0.167660	+	0.290395i
$873$	−2.78388			−0.0942202
$874$	−24.6163	−	42.6367i	−0.832659	−	1.44221i
$875$	−31.8141	−	4.93969i	−1.07551	−	0.166992i
$876$	1.97983			0.0668922
$877$	15.6174	+	27.0502i	0.527363	+	0.913420i	0.999491	+	0.0318902i	$0.0101527\pi$
$877$	15.6174	+	27.0502i	0.527363	+	0.913420i	−0.472128	+	0.881530i	$0.656514\pi$
$878$	−13.9493			−0.470766
$879$	5.93488	+	10.2795i	0.200179	+	0.346719i
$880$	−0.661295	−	1.14540i	−0.0222923	−	0.0386113i
$881$	−19.0177	−	32.9396i	−0.640722	−	1.10976i	−0.985272	−	0.170994i	$-0.945302\pi$
$881$	−19.0177	−	32.9396i	−0.640722	−	1.10976i	0.344550	−	0.938768i	$-0.388031\pi$
$882$	−1.49702	−	6.83805i	−0.0504071	−	0.230249i
$883$	22.5813			0.759921			0.379961	−	0.925003i	$-0.375938\pi$
$883$	22.5813			0.759921			0.379961	+	0.925003i	$0.375938\pi$
$884$	−12.1350	+	9.71619i	−0.408146	+	0.326791i
$885$	2.29302	+	3.97163i	0.0770791	+	0.133505i
$886$	1.69137	−	2.92955i	0.0568228	−	0.0984201i
$887$	7.73646			0.259765			0.129882	−	0.991529i	$-0.458540\pi$
$887$	7.73646			0.259765			0.129882	+	0.991529i	$0.458540\pi$
$888$	−1.06671	+	1.84759i	−0.0357963	+	0.0620010i
$889$	−14.4946	−	37.4192i	−0.486135	−	1.25500i
$890$	4.13161	−	7.15616i	0.138492	−	0.239875i
$891$	−0.357690	−	0.619538i	−0.0119831	−	0.0207553i
$892$	−2.88502	−	4.99700i	−0.0965976	−	0.167312i
$893$	63.3327			2.11935
$894$	−11.6477			−0.389557
$895$	−10.4594	−	18.1162i	−0.349619	−	0.605557i
$896$	2.61442	+	0.405935i	0.0873418	+	0.0135613i
$897$	3.89765	+	25.5211i	0.130139	+	0.852124i
$898$	7.51094	−	13.0093i	0.250643	−	0.434127i
$899$	10.3060	−	17.8505i	0.343724	−	0.595347i
$900$	0.790985	−	1.37003i	0.0263662	−	0.0456676i
$901$	16.3903	+	28.3887i	0.546038	+	0.945766i
$902$	−3.19258			−0.106301
$903$	−0.187257	−	0.483419i	−0.00623151	−	0.0160872i
$904$	1.50417	−	2.60530i	0.0500280	−	0.0866510i
$905$	2.30845	−	3.99835i	0.0767353	−	0.132909i
$906$	8.19088			0.272124
$907$	20.3205	−	35.1961i	0.674731	−	1.16867i	−0.301817	−	0.953366i	$-0.597593\pi$
$907$	20.3205	−	35.1961i	0.674731	−	1.16867i	0.976548	−	0.215302i	$-0.0690735\pi$
$908$	16.9846			0.563653
$909$	5.35550			0.177631
$910$	0.0438411	−	17.6363i	0.00145332	−	0.584637i
$911$	2.41059			0.0798664			0.0399332	−	0.999202i	$-0.487285\pi$
$911$	2.41059			0.0798664			0.0399332	+	0.999202i	$0.487285\pi$
$912$	−6.87573			−0.227678
$913$	3.47510	−	6.01905i	0.115009	−	0.199201i
$914$	−11.9647			−0.395758
$915$	−7.97117	+	13.8065i	−0.263519	+	0.456428i
$916$	0.460390	−	0.797420i	0.0152117	−	0.0263475i
$917$	32.1615	−	39.9642i	1.06207	−	1.31973i
$918$	4.31156			0.142303
$919$	−6.62695	−	11.4782i	−0.218603	−	0.378631i	0.735778	−	0.677223i	$-0.236817\pi$
$919$	−6.62695	−	11.4782i	−0.218603	−	0.378631i	−0.954381	+	0.298591i	$0.903483\pi$
$920$	6.61899	−	11.4644i	0.218222	−	0.377971i
$921$	14.0339	−	24.3075i	0.462434	−	0.800959i
$922$	5.35595	−	9.27677i	0.176389	−	0.305514i
$923$	8.17458	+	53.5257i	0.269069	+	1.76182i
$924$	−0.683663	−	1.76493i	−0.0224909	−	0.0580621i
$925$	1.68750	+	2.92283i	0.0554845	+	0.0961020i
$926$	−13.5305			−0.444639
$927$	−6.52858			−0.214427
$928$	−4.63798	−	8.03322i	−0.152249	−	0.263703i
$929$	12.3258	+	21.3489i	0.404397	+	0.700436i	0.994251	−	0.107074i	$-0.0341481\pi$
$929$	12.3258	+	21.3489i	0.404397	+	0.700436i	−0.589854	+	0.807510i	$0.700815\pi$
$930$	2.05409	−	3.55778i	0.0673561	−	0.116664i
$931$	10.2931	+	47.0166i	0.337342	+	1.54091i
$932$	−2.50283	+	4.33502i	−0.0819828	+	0.141998i
$933$	25.4653			0.833695
$934$	−13.9783	+	24.2112i	−0.457385	+	0.792214i
$935$	−2.85121	−	4.93844i	−0.0932446	−	0.161504i
$936$	3.35888	+	1.31070i	0.109788	+	0.0428416i
$937$	−26.6818			−0.871656			−0.435828	−	0.900030i	$-0.643544\pi$
$937$	−26.6818			−0.871656			−0.435828	+	0.900030i	$0.643544\pi$
$938$	23.1006	−	28.7050i	0.754263	−	0.937253i
$939$	−8.82204	−	15.2802i	−0.287896	−	0.498651i
$940$	8.51466	+	14.7478i	0.277717	+	0.481021i
$941$	−20.1805	−	34.9536i	−0.657865	−	1.13946i	−0.981167	−	0.193159i	$-0.938127\pi$
$941$	−20.1805	−	34.9536i	−0.657865	−	1.13946i	0.323303	−	0.946296i	$-0.395207\pi$
$942$	−22.8707			−0.745166
$943$	−15.9775	−	27.6738i	−0.520298	−	0.901183i
$944$	−2.48056			−0.0807355
$945$	−3.06671	+	3.81071i	−0.0997599	+	0.123962i
$946$	−0.0700874	−	0.121395i	−0.00227874	−	0.00394689i
$947$	5.51853			0.179328			0.0896641	−	0.995972i	$-0.471421\pi$
$947$	5.51853			0.179328			0.0896641	+	0.995972i	$0.471421\pi$
$948$	7.37533	+	12.7744i	0.239540	+	0.414895i
$949$	6.65000	+	2.59496i	0.215868	+	0.0842361i
$950$	−5.43860	+	9.41993i	−0.176451	+	0.305623i
$951$	−14.8710	−	25.7573i	−0.482225	−	0.835239i
$952$	11.2722	+	1.75021i	0.365335	+	0.0567246i
$953$	−2.92091	+	5.05916i	−0.0946175	+	0.163882i	−0.909449	−	0.415816i	$-0.863496\pi$
$953$	−2.92091	+	5.05916i	−0.0946175	+	0.163882i	0.814831	+	0.579698i	$0.196829\pi$
$954$	3.80147	−	6.58434i	0.123077	−	0.213176i
$955$	−9.84847			−0.318689
$956$	13.8239			0.447097
$957$	−3.31792	+	5.74681i	−0.107253	+	0.185768i
$958$	5.79262	−	10.0331i	0.187151	−	0.324155i
$959$	−12.4140	−	1.92749i	−0.400870	−	0.0622420i
$960$	−0.924396	−	1.60110i	−0.0298347	−	0.0516753i
$961$	13.0312	−	22.5706i	0.420360	−	0.728085i
$962$	−6.00457	+	4.80769i	−0.193595	+	0.155006i
$963$	2.30997	+	4.00099i	0.0744378	+	0.128930i
$964$	10.7589			0.346521
$965$	−8.98857	−	15.5687i	−0.289352	−	0.501173i
$966$	11.8773	−	14.7588i	0.382146	−	0.474858i
$967$	4.98537			0.160319			0.0801594	−	0.996782i	$-0.474457\pi$
$967$	4.98537			0.160319			0.0801594	+	0.996782i	$0.474457\pi$
$968$	5.24412	+	9.08307i	0.168552	+	0.291941i
$969$	−29.6451			−0.952338
$970$	2.57341	+	4.45728i	0.0826272	+	0.143115i
$971$	1.37240	+	2.37707i	0.0440424	+	0.0762837i	0.887206	−	0.461373i	$-0.152643\pi$
$971$	1.37240	+	2.37707i	0.0440424	+	0.0762837i	−0.843164	+	0.537657i	$0.819310\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−25.5127	+	31.7022i	−0.817898	+	1.01633i
$974$	−8.48336			−0.271824
$975$	4.45252	−	3.56501i	0.142595	−	0.114172i
$976$	−4.31156	−	7.46783i	−0.138010	−	0.239040i
$977$	8.19729	−	14.1981i	0.262255	−	0.454238i	−0.704586	−	0.709618i	$-0.748867\pi$
$977$	8.19729	−	14.1981i	0.262255	−	0.454238i	0.966841	+	0.255380i	$0.0822007\pi$
$978$	18.0385			0.576806
$979$	1.59871	−	2.76904i	0.0510949	−	0.0884990i
$980$	−9.56457	+	8.71794i	−0.305529	+	0.278484i
$981$	4.95093	−	8.57527i	0.158071	−	0.273787i
$982$	−14.8606	−	25.7394i	−0.474221	−	0.821376i
$983$	15.1127	+	26.1760i	0.482021	+	0.834884i	0.999787	−	0.0206379i	$-0.00656971\pi$
$983$	15.1127	+	26.1760i	0.482021	+	0.834884i	−0.517766	+	0.855522i	$0.673236\pi$
$984$	−4.46276			−0.142268
$985$	11.4105			0.363568
$986$	−19.9969	−	34.6357i	−0.636831	−	1.10302i
$987$	8.80266	+	22.7248i	0.280192	+	0.723339i
$988$	−23.0947	−	9.01203i	−0.734741	−	0.286711i
$989$	0.701514	−	1.21506i	0.0223069	−	0.0386366i
$990$	−0.661295	+	1.14540i	−0.0210173	+	0.0364031i
$991$	−10.0272	+	17.3677i	−0.318525	+	0.551702i	−0.980181	−	0.198106i	$-0.936521\pi$
$991$	−10.0272	+	17.3677i	−0.318525	+	0.551702i	0.661655	+	0.749808i	$0.269854\pi$
$992$	1.11104	+	1.92438i	0.0352756	+	0.0610992i
$993$	24.0394			0.762866
$994$	24.9104	−	30.9539i	0.790111	−	0.981798i
$995$	−5.00518	+	8.66922i	−0.158675	+	0.274833i
$996$	4.85769	−	8.41377i	0.153922	−	0.266600i
$997$	−43.4877			−1.37727			−0.688635	−	0.725108i	$-0.741790\pi$
$997$	−43.4877			−1.37727			−0.688635	+	0.725108i	$0.741790\pi$
$998$	17.7944	−	30.8208i	0.563272	−	0.975615i
$999$	2.13341			0.0674981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.c.289.1	✓	8
3.2	odd	2		1638.2.m.h.289.4		8
7.4	even	3		546.2.k.c.445.1	yes	8
13.9	even	3		546.2.k.c.373.1	yes	8
21.11	odd	6		1638.2.p.h.991.4		8
39.35	odd	6		1638.2.p.h.919.4		8
91.74	even	3	inner	546.2.j.c.529.1	yes	8
273.74	odd	6		1638.2.m.h.1621.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.1	✓	8	1.1	even	1	trivial
546.2.j.c.529.1	yes	8	91.74	even	3	inner
546.2.k.c.373.1	yes	8	13.9	even	3
546.2.k.c.445.1	yes	8	7.4	even	3
1638.2.m.h.289.4		8	3.2	odd	2
1638.2.m.h.1621.4		8	273.74	odd	6
1638.2.p.h.919.4		8	39.35	odd	6
1638.2.p.h.991.4		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.924396 + 1.60110i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.61442 + 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.924396 + 1.60110i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.61442 + 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.924396 + 1.60110i) q^{10} +(-0.357690 + 0.619538i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.81454 + 2.25352i) q^{13} +(2.61442 + 0.405935i) q^{14} +(-0.924396 - 1.60110i) q^{15} +1.00000 q^{16} +4.31156 q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.43786 + 5.95456i) q^{19} +(-0.924396 + 1.60110i) q^{20} +(-1.65876 + 2.06119i) q^{21} +(-0.357690 + 0.619538i) q^{22} -7.16035 q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.790985 + 1.37003i) q^{25} +(-2.81454 + 2.25352i) q^{26} +1.00000 q^{27} +(2.61442 + 0.405935i) q^{28} +(-4.63798 - 8.03322i) q^{29} +(-0.924396 - 1.60110i) q^{30} +(1.11104 + 1.92438i) q^{31} +1.00000 q^{32} +(-0.357690 - 0.619538i) q^{33} +4.31156 q^{34} +(-3.06671 + 3.81071i) q^{35} +(-0.500000 - 0.866025i) q^{36} +2.13341 q^{37} +(3.43786 + 5.95456i) q^{38} +(-0.544337 - 3.56422i) q^{39} +(-0.924396 + 1.60110i) q^{40} +(2.23138 + 3.86487i) q^{41} +(-1.65876 + 2.06119i) q^{42} +(-0.0979721 + 0.169693i) q^{43} +(-0.357690 + 0.619538i) q^{44} +1.84879 q^{45} -7.16035 q^{46} +(4.60553 - 7.97700i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.67043 + 2.12257i) q^{49} +(0.790985 + 1.37003i) q^{50} +(-2.15578 + 3.73392i) q^{51} +(-2.81454 + 2.25352i) q^{52} +(3.80147 + 6.58434i) q^{53} +1.00000 q^{54} +(-0.661295 - 1.14540i) q^{55} +(2.61442 + 0.405935i) q^{56} -6.87573 q^{57} +(-4.63798 - 8.03322i) q^{58} -2.48056 q^{59} +(-0.924396 - 1.60110i) q^{60} +(-4.31156 - 7.46783i) q^{61} +(1.11104 + 1.92438i) q^{62} +(-0.955663 - 2.46713i) q^{63} +1.00000 q^{64} +(-1.00637 - 6.58951i) q^{65} +(-0.357690 - 0.619538i) q^{66} +(6.96322 - 12.0606i) q^{67} +4.31156 q^{68} +(3.58017 - 6.20104i) q^{69} +(-3.06671 + 3.81071i) q^{70} +(7.50874 - 13.0055i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-0.989914 - 1.71458i) q^{73} +2.13341 q^{74} -1.58197 q^{75} +(3.43786 + 5.95456i) q^{76} +(-1.18665 + 1.47454i) q^{77} +(-0.544337 - 3.56422i) q^{78} +(7.37533 - 12.7744i) q^{79} +(-0.924396 + 1.60110i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.23138 + 3.86487i) q^{82} -9.71538 q^{83} +(-1.65876 + 2.06119i) q^{84} +(-3.98558 + 6.90323i) q^{85} +(-0.0979721 + 0.169693i) q^{86} +9.27596 q^{87} +(-0.357690 + 0.619538i) q^{88} -4.46953 q^{89} +1.84879 q^{90} +(-8.27319 + 4.74914i) q^{91} -7.16035 q^{92} -2.22209 q^{93} +(4.60553 - 7.97700i) q^{94} -12.7118 q^{95} +(-0.500000 + 0.866025i) q^{96} +(1.39194 - 2.41091i) q^{97} +(6.67043 + 2.12257i) q^{98} +0.715381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 2 q^{25} + 3 q^{26} + 8 q^{27} + 3 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} + 4 q^{34} - 22 q^{35} - 4 q^{36} + 12 q^{37} - 4 q^{38} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 3 q^{42} + 4 q^{44} - 4 q^{45} - 8 q^{46} + 7 q^{47} - 4 q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - q^{53} + 8 q^{54} - 25 q^{55} + 3 q^{56} + 8 q^{57} + 2 q^{58} - 32 q^{59} + 2 q^{60} - 4 q^{61} + 14 q^{62} + 8 q^{64} + 10 q^{65} + 4 q^{66} + 19 q^{67} + 4 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} - 4 q^{72} - 7 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} + 2 q^{80} - 4 q^{81} + 12 q^{82} - 64 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{87} + 4 q^{88} + 22 q^{89} - 4 q^{90} - 38 q^{91} - 8 q^{92} - 28 q^{93} + 7 q^{94} - 56 q^{95} - 4 q^{96} + 11 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 + 8 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 2 * q^25 + 3 * q^26 + 8 * q^27 + 3 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 + 4 * q^34 - 22 * q^35 - 4 * q^36 + 12 * q^37 - 4 * q^38 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 3 * q^42 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 7 * q^47 - 4 * q^48 + 5 * q^49 + 2 * q^50 - 2 * q^51 + 3 * q^52 - q^53 + 8 * q^54 - 25 * q^55 + 3 * q^56 + 8 * q^57 + 2 * q^58 - 32 * q^59 + 2 * q^60 - 4 * q^61 + 14 * q^62 + 8 * q^64 + 10 * q^65 + 4 * q^66 + 19 * q^67 + 4 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 - 4 * q^72 - 7 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 + 2 * q^80 - 4 * q^81 + 12 * q^82 - 64 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^87 + 4 * q^88 + 22 * q^89 - 4 * q^90 - 38 * q^91 - 8 * q^92 - 28 * q^93 + 7 * q^94 - 56 * q^95 - 4 * q^96 + 11 * q^97 + 5 * q^98 - 8 * q^99

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