LMFDB - Embedded newform 546.2.k.d.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (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:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.4
Root			$-0.186817 + 0.323577i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.d.445.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.30278 q^{10} +2.11879 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.0315412 - 3.60541i) q^{13} +(2.36323 + 1.18960i) q^{14} +(0.651388 - 1.12824i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.243381 - 0.421549i) q^{17} +(0.500000 + 0.866025i) q^{18} -6.27630 q^{19} +(0.651388 + 1.12824i) q^{20} +(2.21184 - 1.45181i) q^{21} +(1.05939 + 1.83493i) q^{22} +(2.39477 + 4.14786i) q^{23} -1.00000 q^{24} +(1.65139 + 2.86029i) q^{25} +(3.13815 - 1.77539i) q^{26} +1.00000 q^{27} +(0.151388 + 2.64142i) q^{28} +(1.74338 - 3.01962i) q^{29} +1.30278 q^{30} +(2.24338 + 3.88565i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.11879 q^{33} +0.486762 q^{34} +(-0.197224 - 3.44117i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.578756 + 1.00243i) q^{37} +(-3.13815 - 5.43544i) q^{38} +(0.0315412 - 3.60541i) q^{39} +(-0.651388 + 1.12824i) q^{40} +(-6.31845 + 10.9439i) q^{41} +(2.36323 + 1.18960i) q^{42} +(-4.01356 - 6.95169i) q^{43} +(-1.05939 + 1.83493i) q^{44} +(0.651388 - 1.12824i) q^{45} +(-2.39477 + 4.14786i) q^{46} +(-3.98570 + 6.90344i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(2.78447 - 6.42236i) q^{49} +(-1.65139 + 2.86029i) q^{50} +(0.243381 - 0.421549i) q^{51} +(3.10661 + 1.83002i) q^{52} +(4.29060 + 7.43153i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.38015 - 2.39050i) q^{55} +(-2.21184 + 1.45181i) q^{56} -6.27630 q^{57} +3.48676 q^{58} +(4.57507 - 7.92425i) q^{59} +(0.651388 + 1.12824i) q^{60} -10.1846 q^{61} +(-2.24338 + 3.88565i) q^{62} +(2.21184 - 1.45181i) q^{63} +1.00000 q^{64} +(-4.04721 - 2.38411i) q^{65} +(1.05939 + 1.83493i) q^{66} -3.35848 q^{67} +(0.243381 + 0.421549i) q^{68} +(2.39477 + 4.14786i) q^{69} +(2.88153 - 1.89139i) q^{70} +(1.46740 + 2.54161i) q^{71} -1.00000 q^{72} +(-8.09337 - 14.0181i) q^{73} +(-0.578756 + 1.00243i) q^{74} +(1.65139 + 2.86029i) q^{75} +(3.13815 - 5.43544i) q^{76} +(4.68642 - 3.07609i) q^{77} +(3.13815 - 1.77539i) q^{78} +(-7.16738 + 12.4143i) q^{79} -1.30278 q^{80} +1.00000 q^{81} -12.6369 q^{82} +3.48676 q^{83} +(0.151388 + 2.64142i) q^{84} +(-0.317071 - 0.549183i) q^{85} +(4.01356 - 6.95169i) q^{86} +(1.74338 - 3.01962i) q^{87} -2.11879 q^{88} +(-4.69860 - 8.13822i) q^{89} +1.30278 q^{90} +(-5.16463 - 8.02039i) q^{91} -4.78954 q^{92} +(2.24338 + 3.88565i) q^{93} -7.97141 q^{94} +(-4.08831 + 7.08115i) q^{95} +(0.500000 - 0.866025i) q^{96} +(0.698602 + 1.21001i) q^{97} +(6.95416 - 0.799757i) q^{98} +2.11879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} + 4 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 6 q^{28} + 6 q^{29} - 4 q^{30} + 10 q^{31} + 4 q^{32} + 4 q^{33} - 12 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{37} - 2 q^{38} + 7 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} - 2 q^{45} - 4 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} - 5 q^{52} + 3 q^{53} + 4 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} + 12 q^{58} - 2 q^{60} + 8 q^{61} - 10 q^{62} + 3 q^{63} + 8 q^{64} - 9 q^{65} + 2 q^{66} + 14 q^{67} - 6 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} - 8 q^{72} - 19 q^{73} + 12 q^{74} + 6 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} - 12 q^{82} + 12 q^{83} - 6 q^{84} - 3 q^{85} + 4 q^{86} + 6 q^{87} - 4 q^{88} - 7 q^{89} - 4 q^{90} - 50 q^{91} - 8 q^{92} + 10 q^{93} - 34 q^{94} - 12 q^{95} + 4 q^{96} - 25 q^{97} + 34 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 + 4 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 4 * q^33 - 12 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^37 - 2 * q^38 + 7 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 - 2 * q^45 - 4 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 - 5 * q^52 + 3 * q^53 + 4 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 + 12 * q^58 - 2 * q^60 + 8 * q^61 - 10 * q^62 + 3 * q^63 + 8 * q^64 - 9 * q^65 + 2 * q^66 + 14 * q^67 - 6 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 - 8 * q^72 - 19 * q^73 + 12 * q^74 + 6 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 - 12 * q^82 + 12 * q^83 - 6 * q^84 - 3 * q^85 + 4 * q^86 + 6 * q^87 - 4 * q^88 - 7 * q^89 - 4 * q^90 - 50 * q^91 - 8 * q^92 + 10 * q^93 - 34 * q^94 - 12 * q^95 + 4 * q^96 - 25 * q^97 + 34 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.651388	−	1.12824i	0.291309	−	0.504563i	−0.682810	−	0.730596i	$-0.739242\pi$
$5$	0.651388	−	1.12824i	0.291309	−	0.504563i	0.974120	+	0.226033i	$0.0725757\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	2.21184	−	1.45181i	0.835997	−	0.548734i
$7$	2.21184	−	1.45181i	0.835997	−	0.548734i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	1.30278			0.411974
$11$	2.11879			0.638839			0.319419	−	0.947613i	$-0.396512\pi$
$11$	2.11879			0.638839			0.319419	+	0.947613i	$0.396512\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.0315412	−	3.60541i	0.00874794	−	0.999962i
$13$	0.0315412	−	3.60541i	0.00874794	−	0.999962i
$14$	2.36323	+	1.18960i	0.631599	+	0.317935i
$15$	0.651388	−	1.12824i	0.168188	−	0.291309i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.243381	−	0.421549i	0.0590286	−	0.102241i	−0.835001	−	0.550248i	$-0.814533\pi$
$17$	0.243381	−	0.421549i	0.0590286	−	0.102241i	0.894030	+	0.448008i	$0.147866\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−6.27630			−1.43988			−0.719941	−	0.694035i	$-0.755831\pi$
$19$	−6.27630			−1.43988			−0.719941	+	0.694035i	$0.755831\pi$
$20$	0.651388	+	1.12824i	0.145655	+	0.252281i
$21$	2.21184	−	1.45181i	0.482663	−	0.316812i
$22$	1.05939	+	1.83493i	0.225864	+	0.391207i
$23$	2.39477	+	4.14786i	0.499344	+	0.864889i	1.00000		0.000757495i	$-0.000241118\pi$
$23$	2.39477	+	4.14786i	0.499344	+	0.864889i	−0.500656	+	0.865646i	$0.666908\pi$
$24$	−1.00000			−0.204124
$25$	1.65139	+	2.86029i	0.330278	+	0.572058i
$26$	3.13815	−	1.77539i	0.615442	−	0.348183i
$27$	1.00000			0.192450
$28$	0.151388	+	2.64142i	0.0286096	+	0.499181i
$29$	1.74338	−	3.01962i	0.323738	−	0.560730i	−0.657518	−	0.753439i	$-0.728394\pi$
$29$	1.74338	−	3.01962i	0.323738	−	0.560730i	0.981256	+	0.192708i	$0.0617271\pi$
$30$	1.30278			0.237853
$31$	2.24338	+	3.88565i	0.402923	+	0.697883i	0.994077	−	0.108675i	$-0.0346609\pi$
$31$	2.24338	+	3.88565i	0.402923	+	0.697883i	−0.591154	+	0.806559i	$0.701328\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.11879			0.368834
$34$	0.486762			0.0834790
$35$	−0.197224	−	3.44117i	−0.0333370	−	0.581664i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	0.578756	+	1.00243i	0.0951468	+	0.164799i	0.909670	−	0.415332i	$-0.136335\pi$
$37$	0.578756	+	1.00243i	0.0951468	+	0.164799i	−0.814523	+	0.580131i	$0.803001\pi$
$38$	−3.13815	−	5.43544i	−0.509075	−	0.881744i
$39$	0.0315412	−	3.60541i	0.00505063	−	0.577328i
$40$	−0.651388	+	1.12824i	−0.102993	+	0.178390i
$41$	−6.31845	+	10.9439i	−0.986776	+	1.70915i	−0.353014	+	0.935618i	$0.614843\pi$
$41$	−6.31845	+	10.9439i	−0.986776	+	1.70915i	−0.633762	+	0.773528i	$0.718490\pi$
$42$	2.36323	+	1.18960i	0.364654	+	0.183560i
$43$	−4.01356	−	6.95169i	−0.612062	−	1.06012i	−0.990892	−	0.134656i	$-0.957007\pi$
$43$	−4.01356	−	6.95169i	−0.612062	−	1.06012i	0.378831	−	0.925466i	$-0.376326\pi$
$44$	−1.05939	+	1.83493i	−0.159710	+	0.276625i
$45$	0.651388	−	1.12824i	0.0971032	−	0.168188i
$46$	−2.39477	+	4.14786i	−0.353089	+	0.611569i
$47$	−3.98570	+	6.90344i	−0.581375	+	1.00697i	0.413942	+	0.910303i	$0.364152\pi$
$47$	−3.98570	+	6.90344i	−0.581375	+	1.00697i	−0.995317	+	0.0966674i	$0.969182\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	2.78447	−	6.42236i	0.397782	−	0.917480i
$50$	−1.65139	+	2.86029i	−0.233542	+	0.404506i
$51$	0.243381	−	0.421549i	0.0340802	−	0.0590286i
$52$	3.10661	+	1.83002i	0.430809	+	0.253778i
$53$	4.29060	+	7.43153i	0.589359	+	1.02080i	0.994317	+	0.106464i	$0.0339528\pi$
$53$	4.29060	+	7.43153i	0.589359	+	1.02080i	−0.404958	+	0.914335i	$0.632714\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	1.38015	−	2.39050i	0.186100	−	0.322334i
$56$	−2.21184	+	1.45181i	−0.295570	+	0.194007i
$57$	−6.27630			−0.831316
$58$	3.48676			0.457834
$59$	4.57507	−	7.92425i	0.595623	−	1.03165i	−0.397836	−	0.917457i	$-0.630239\pi$
$59$	4.57507	−	7.92425i	0.595623	−	1.03165i	0.993459	−	0.114193i	$-0.0364281\pi$
$60$	0.651388	+	1.12824i	0.0840938	+	0.145655i
$61$	−10.1846			−1.30401			−0.652004	−	0.758216i	$-0.726071\pi$
$61$	−10.1846			−1.30401			−0.652004	+	0.758216i	$0.726071\pi$
$62$	−2.24338	+	3.88565i	−0.284910	+	0.493478i
$63$	2.21184	−	1.45181i	0.278666	−	0.182911i
$64$	1.00000			0.125000
$65$	−4.04721	−	2.38411i	−0.501995	−	0.295712i
$66$	1.05939	+	1.83493i	0.130402	+	0.225864i
$67$	−3.35848			−0.410304			−0.205152	−	0.978730i	$-0.565769\pi$
$67$	−3.35848			−0.410304			−0.205152	+	0.978730i	$0.565769\pi$
$68$	0.243381	+	0.421549i	0.0295143	+	0.0511203i
$69$	2.39477	+	4.14786i	0.288296	+	0.499344i
$70$	2.88153	−	1.89139i	0.344409	−	0.226064i
$71$	1.46740	+	2.54161i	0.174148	+	0.301634i	0.939866	−	0.341543i	$-0.110949\pi$
$71$	1.46740	+	2.54161i	0.174148	+	0.301634i	−0.765718	+	0.643177i	$0.777616\pi$
$72$	−1.00000			−0.117851
$73$	−8.09337	−	14.0181i	−0.947257	−	1.64070i	−0.751167	−	0.660112i	$-0.770509\pi$
$73$	−8.09337	−	14.0181i	−0.947257	−	1.64070i	−0.196090	−	0.980586i	$-0.562825\pi$
$74$	−0.578756	+	1.00243i	−0.0672790	+	0.116531i
$75$	1.65139	+	2.86029i	0.190686	+	0.330278i
$76$	3.13815	−	5.43544i	0.359971	−	0.623487i
$77$	4.68642	−	3.07609i	0.534067	−	0.350553i
$78$	3.13815	−	1.77539i	0.355326	−	0.201023i
$79$	−7.16738	+	12.4143i	−0.806393	+	1.39671i	0.108953	+	0.994047i	$0.465250\pi$
$79$	−7.16738	+	12.4143i	−0.806393	+	1.39671i	−0.915346	+	0.402667i	$0.868083\pi$
$80$	−1.30278			−0.145655
$81$	1.00000			0.111111
$82$	−12.6369			−1.39551
$83$	3.48676			0.382722			0.191361	−	0.981520i	$-0.438710\pi$
$83$	3.48676			0.382722			0.191361	+	0.981520i	$0.438710\pi$
$84$	0.151388	+	2.64142i	0.0165178	+	0.288202i
$85$	−0.317071	−	0.549183i	−0.0343912	−	0.0595673i
$86$	4.01356	−	6.95169i	0.432793	−	0.749620i
$87$	1.74338	−	3.01962i	0.186910	−	0.323738i
$88$	−2.11879			−0.225864
$89$	−4.69860	−	8.13822i	−0.498051	−	0.862649i	0.501947	−	0.864899i	$-0.332617\pi$
$89$	−4.69860	−	8.13822i	−0.498051	−	0.862649i	−0.999997	+	0.00224923i	$0.999284\pi$
$90$	1.30278			0.137325
$91$	−5.16463	−	8.02039i	−0.541400	−	0.840765i
$92$	−4.78954			−0.499344
$93$	2.24338	+	3.88565i	0.232628	+	0.402923i
$94$	−7.97141			−0.822188
$95$	−4.08831	+	7.08115i	−0.419451	+	0.726511i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	0.698602	+	1.21001i	0.0709323	+	0.122858i	0.899310	−	0.437311i	$-0.144069\pi$
$97$	0.698602	+	1.21001i	0.0709323	+	0.122858i	−0.828378	+	0.560170i	$0.810736\pi$
$98$	6.95416	−	0.799757i	0.702477	−	0.0807876i
$99$	2.11879			0.212946
$100$	−3.30278			−0.330278
$101$	−6.03449			−0.600454			−0.300227	−	0.953868i	$-0.597062\pi$
$101$	−6.03449			−0.600454			−0.300227	+	0.953868i	$0.597062\pi$
$102$	0.486762			0.0481966
$103$	5.64770	−	9.78210i	0.556484	−	0.963859i	−0.441302	−	0.897359i	$-0.645483\pi$
$103$	5.64770	−	9.78210i	0.556484	−	0.963859i	0.997786	−	0.0665006i	$-0.0211834\pi$
$104$	−0.0315412	+	3.60541i	−0.00309287	+	0.353540i
$105$	−0.197224	−	3.44117i	−0.0192471	−	0.335824i
$106$	−4.29060	+	7.43153i	−0.416739	+	0.721814i
$107$	7.01462	+	12.1497i	0.678128	+	1.17455i	0.975544	+	0.219805i	$0.0705420\pi$
$107$	7.01462	+	12.1497i	0.678128	+	1.17455i	−0.297415	+	0.954748i	$0.596125\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	2.76031			0.263185
$111$	0.578756	+	1.00243i	0.0549331	+	0.0951468i
$112$	−2.36323	−	1.18960i	−0.223304	−	0.112407i
$113$	3.56552	+	6.17566i	0.335416	+	0.580957i	0.983565	−	0.180557i	$-0.0577899\pi$
$113$	3.56552	+	6.17566i	0.335416	+	0.580957i	−0.648149	+	0.761514i	$0.724457\pi$
$114$	−3.13815	−	5.43544i	−0.293915	−	0.509075i
$115$	6.23969			0.581854
$116$	1.74338	+	3.01962i	0.161869	+	0.280365i
$117$	0.0315412	−	3.60541i	0.00291598	−	0.333321i
$118$	9.15014			0.842338
$119$	−0.0736899	−	1.28574i	−0.00675514	−	0.117864i
$120$	−0.651388	+	1.12824i	−0.0594633	+	0.102993i
$121$	−6.51073			−0.591885
$122$	−5.09231	−	8.82015i	−0.461036	−	0.798538i
$123$	−6.31845	+	10.9439i	−0.569715	+	0.986776i
$124$	−4.48676			−0.402923
$125$	10.8167			0.967471
$126$	2.36323	+	1.18960i	0.210533	+	0.105978i
$127$	2.59305	−	4.49130i	0.230096	−	0.398538i	−0.727740	−	0.685853i	$-0.759429\pi$
$127$	2.59305	−	4.49130i	0.230096	−	0.398538i	0.957836	+	0.287315i	$0.0927626\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.01356	−	6.95169i	−0.353374	−	0.612062i
$130$	0.0410911	−	4.69704i	0.00360392	−	0.411958i
$131$	4.03186	−	6.98339i	0.352265	−	0.610142i	−0.634381	−	0.773021i	$-0.718745\pi$
$131$	4.03186	−	6.98339i	0.352265	−	0.610142i	0.986646	+	0.162879i	$0.0520781\pi$
$132$	−1.05939	+	1.83493i	−0.0922085	+	0.159710i
$133$	−13.8822	+	9.11202i	−1.20374	+	0.790112i
$134$	−1.67924	−	2.90853i	−0.145064	−	0.251259i
$135$	0.651388	−	1.12824i	0.0560625	−	0.0971032i
$136$	−0.243381	+	0.421549i	−0.0208698	+	0.0361475i
$137$	3.39583	−	5.88174i	0.290125	−	0.502511i	−0.683714	−	0.729750i	$-0.739636\pi$
$137$	3.39583	−	5.88174i	0.290125	−	0.502511i	0.973839	+	0.227239i	$0.0729698\pi$
$138$	−2.39477	+	4.14786i	−0.203856	+	0.353089i
$139$	6.45522	+	11.1808i	0.547525	+	0.948341i	0.998443	+	0.0557755i	$0.0177631\pi$
$139$	6.45522	+	11.1808i	0.547525	+	0.948341i	−0.450919	+	0.892565i	$0.648904\pi$
$140$	3.07876	+	1.54979i	0.260202	+	0.130981i
$141$	−3.98570	+	6.90344i	−0.335657	+	0.581375i
$142$	−1.46740	+	2.54161i	−0.123142	+	0.213287i
$143$	0.0668291	−	7.63911i	0.00558853	−	0.638814i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.27123	−	3.93389i	−0.188616	−	0.326692i
$146$	8.09337	−	14.0181i	0.669812	−	1.16015i
$147$	2.78447	−	6.42236i	0.229659	−	0.529707i
$148$	−1.15751			−0.0951468
$149$	−23.3640			−1.91405			−0.957026	−	0.290001i	$-0.906345\pi$
$149$	−23.3640			−1.91405			−0.957026	+	0.290001i	$0.906345\pi$
$150$	−1.65139	+	2.86029i	−0.134835	+	0.233542i
$151$	−2.93692	−	5.08689i	−0.239003	−	0.413965i	0.721425	−	0.692492i	$-0.243487\pi$
$151$	−2.93692	−	5.08689i	−0.239003	−	0.413965i	−0.960428	+	0.278527i	$0.910154\pi$
$152$	6.27630			0.509075
$153$	0.243381	−	0.421549i	0.0196762	−	0.0340802i
$154$	5.00718	+	2.52052i	0.403490	+	0.203109i
$155$	5.84524			0.469501
$156$	3.10661	+	1.83002i	0.248728	+	0.146519i
$157$	−3.12248	−	5.40829i	−0.249201	−	0.431628i	0.714104	−	0.700040i	$-0.246835\pi$
$157$	−3.12248	−	5.40829i	−0.249201	−	0.431628i	−0.963304	+	0.268412i	$0.913501\pi$
$158$	−14.3348			−1.14041
$159$	4.29060	+	7.43153i	0.340266	+	0.589359i
$160$	−0.651388	−	1.12824i	−0.0514967	−	0.0891950i
$161$	11.3188	+	5.69765i	0.892044	+	0.449037i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−2.60767			−0.204248			−0.102124	−	0.994772i	$-0.532564\pi$
$163$	−2.60767			−0.204248			−0.102124	+	0.994772i	$0.532564\pi$
$164$	−6.31845	−	10.9439i	−0.493388	−	0.854573i
$165$	1.38015	−	2.39050i	0.107445	−	0.186100i
$166$	1.74338	+	3.01962i	0.135313	+	0.234368i
$167$	−3.45416	+	5.98279i	−0.267291	+	0.462962i	−0.968161	−	0.250327i	$-0.919462\pi$
$167$	−3.45416	+	5.98279i	−0.267291	+	0.462962i	0.700870	+	0.713289i	$0.252795\pi$
$168$	−2.21184	+	1.45181i	−0.170647	+	0.112010i
$169$	−12.9980	−	0.227438i	−0.999847	−	0.0174952i
$170$	0.317071	−	0.549183i	0.0243182	−	0.0421204i
$171$	−6.27630			−0.479961
$172$	8.02712			0.612062
$173$	−7.72710			−0.587480			−0.293740	−	0.955885i	$-0.594900\pi$
$173$	−7.72710			−0.587480			−0.293740	+	0.955885i	$0.594900\pi$
$174$	3.48676			0.264331
$175$	7.80521	+	3.92899i	0.590019	+	0.297004i
$176$	−1.05939	−	1.83493i	−0.0798549	−	0.138313i
$177$	4.57507	−	7.92425i	0.343883	−	0.595623i
$178$	4.69860	−	8.13822i	0.352175	−	0.609985i
$179$	19.1508			1.43140			0.715698	−	0.698410i	$-0.246109\pi$
$179$	19.1508			1.43140			0.715698	+	0.698410i	$0.246109\pi$
$180$	0.651388	+	1.12824i	0.0485516	+	0.0840938i
$181$	13.0972			0.973506			0.486753	−	0.873540i	$-0.338181\pi$
$181$	13.0972			0.973506			0.486753	+	0.873540i	$0.338181\pi$
$182$	4.36355	−	8.48289i	0.323448	−	0.628794i
$183$	−10.1846			−0.752869
$184$	−2.39477	−	4.14786i	−0.176545	−	0.305784i
$185$	1.50798			0.110869
$186$	−2.24338	+	3.88565i	−0.164493	+	0.284910i
$187$	0.515673	−	0.893172i	0.0377098	−	0.0653152i
$188$	−3.98570	−	6.90344i	−0.290687	−	0.503485i
$189$	2.21184	−	1.45181i	0.160888	−	0.105604i
$190$	−8.17661			−0.593194
$191$	−11.4889			−0.831306			−0.415653	−	0.909523i	$-0.636447\pi$
$191$	−11.4889			−0.831306			−0.415653	+	0.909523i	$0.636447\pi$
$192$	1.00000			0.0721688
$193$	−0.276300			−0.0198885			−0.00994426	−	0.999951i	$-0.503165\pi$
$193$	−0.276300			−0.0198885			−0.00994426	+	0.999951i	$0.503165\pi$
$194$	−0.698602	+	1.21001i	−0.0501567	+	0.0868740i
$195$	−4.04721	−	2.38411i	−0.289827	−	0.170730i
$196$	4.16969	+	5.62260i	0.297835	+	0.401615i
$197$	−6.63552	+	11.4931i	−0.472761	+	0.818846i	−0.999514	−	0.0311721i	$-0.990076\pi$
$197$	−6.63552	+	11.4931i	−0.472761	+	0.818846i	0.526753	+	0.850019i	$0.323409\pi$
$198$	1.05939	+	1.83493i	0.0752879	+	0.130402i
$199$	−9.51093	+	16.4734i	−0.674212	+	1.16777i	0.302487	+	0.953154i	$0.402183\pi$
$199$	−9.51093	+	16.4734i	−0.674212	+	1.16777i	−0.976699	+	0.214616i	$0.931150\pi$
$200$	−1.65139	−	2.86029i	−0.116771	−	0.202253i
$201$	−3.35848			−0.236889
$202$	−3.01725	−	5.22602i	−0.212293	−	0.367702i
$203$	−0.527853	−	9.20999i	−0.0370480	−	0.646415i
$204$	0.243381	+	0.421549i	0.0170401	+	0.0295143i
$205$	8.23152	+	14.2574i	0.574914	+	0.995781i
$206$	11.2954			0.786988
$207$	2.39477	+	4.14786i	0.166448	+	0.288296i
$208$	−3.13815	+	1.77539i	−0.217592	+	0.123101i
$209$	−13.2982			−0.919853
$210$	2.88153	−	1.89139i	0.198845	−	0.130518i
$211$	−1.98750	+	3.44245i	−0.136825	+	0.236988i	−0.926293	−	0.376804i	$-0.877023\pi$
$211$	−1.98750	+	3.44245i	−0.136825	+	0.236988i	0.789468	+	0.613792i	$0.210357\pi$
$212$	−8.58119			−0.589359
$213$	1.46740	+	2.54161i	0.100545	+	0.174148i
$214$	−7.01462	+	12.1497i	−0.479509	+	0.830534i
$215$	−10.4575			−0.713198
$216$	−1.00000			−0.0680414
$217$	10.6032	+	5.33746i	0.719795	+	0.362331i
$218$	5.50000	−	9.52628i	0.372507	−	0.645201i
$219$	−8.09337	−	14.0181i	−0.546899	−	0.947257i
$220$	1.38015	+	2.39050i	0.0930499	+	0.161167i
$221$	−1.51218	−	0.890786i	−0.101720	−	0.0599207i
$222$	−0.578756	+	1.00243i	−0.0388435	+	0.0672790i
$223$	9.58013	−	16.5933i	0.641533	−	1.11117i	−0.343557	−	0.939132i	$-0.611632\pi$
$223$	9.58013	−	16.5933i	0.641533	−	1.11117i	0.985091	−	0.172036i	$-0.0550347\pi$
$224$	−0.151388	−	2.64142i	−0.0101150	−	0.176487i
$225$	1.65139	+	2.86029i	0.110093	+	0.190686i
$226$	−3.56552	+	6.17566i	−0.237175	+	0.410799i
$227$	0.591256	−	1.02409i	0.0392430	−	0.0679709i	−0.845737	−	0.533600i	$-0.820839\pi$
$227$	0.591256	−	1.02409i	0.0392430	−	0.0679709i	0.884980	+	0.465629i	$0.154172\pi$
$228$	3.13815	−	5.43544i	0.207829	−	0.359971i
$229$	7.51599	−	13.0181i	0.496671	−	0.860259i	−0.503322	−	0.864099i	$-0.667889\pi$
$229$	7.51599	−	13.0181i	0.496671	−	0.860259i	0.999993	+	0.00383994i	$0.00122229\pi$
$230$	3.11985	+	5.40373i	0.205717	+	0.356312i
$231$	4.68642	−	3.07609i	0.308344	−	0.202392i
$232$	−1.74338	+	3.01962i	−0.114459	+	0.198248i
$233$	−2.59706	+	4.49824i	−0.170139	+	0.294689i	−0.938468	−	0.345365i	$-0.887755\pi$
$233$	−2.59706	+	4.49824i	−0.170139	+	0.294689i	0.768329	+	0.640055i	$0.221088\pi$
$234$	3.13815	−	1.77539i	0.205147	−	0.116061i
$235$	5.19248	+	8.99364i	0.338720	+	0.586680i
$236$	4.57507	+	7.92425i	0.297812	+	0.515825i
$237$	−7.16738	+	12.4143i	−0.465571	+	0.806393i
$238$	1.07664	−	0.706688i	0.0697882	−	0.0458078i
$239$	25.3978			1.64285			0.821425	−	0.570317i	$-0.193179\pi$
$239$	25.3978			1.64285			0.821425	+	0.570317i	$0.193179\pi$
$240$	−1.30278			−0.0840938
$241$	5.92875	−	10.2689i	0.381904	−	0.661477i	−0.609430	−	0.792840i	$-0.708602\pi$
$241$	5.92875	−	10.2689i	0.381904	−	0.661477i	0.991334	+	0.131362i	$0.0419351\pi$
$242$	−3.25537	−	5.63846i	−0.209263	−	0.362454i
$243$	1.00000			0.0641500
$244$	5.09231	−	8.82015i	0.326002	−	0.564652i
$245$	−5.43217	−	7.32499i	−0.347049	−	0.467977i
$246$	−12.6369			−0.805699
$247$	−0.197962	+	22.6287i	−0.0125960	+	1.43983i
$248$	−2.24338	−	3.88565i	−0.142455	−	0.246739i
$249$	3.48676			0.220965
$250$	5.40833	+	9.36750i	0.342053	+	0.592453i
$251$	10.7397	+	18.6017i	0.677883	+	1.17413i	0.975617	+	0.219480i	$0.0704359\pi$
$251$	10.7397	+	18.6017i	0.677883	+	1.17413i	−0.297734	+	0.954649i	$0.596231\pi$
$252$	0.151388	+	2.64142i	0.00953654	+	0.166394i
$253$	5.07401	+	8.78844i	0.319000	+	0.552525i
$254$	5.18610			0.325405
$255$	−0.317071	−	0.549183i	−0.0198558	−	0.0343912i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.42294	+	5.92871i	0.213517	+	0.369823i	0.952813	−	0.303558i	$-0.0981747\pi$
$257$	3.42294	+	5.92871i	0.213517	+	0.369823i	−0.739296	+	0.673381i	$0.764841\pi$
$258$	4.01356	−	6.95169i	0.249873	−	0.432793i
$259$	2.73546	+	1.37698i	0.169973	+	0.0855613i
$260$	4.08831	−	2.31294i	0.253546	−	0.143442i
$261$	1.74338	−	3.01962i	0.107913	−	0.186910i
$262$	8.06372			0.498178
$263$	15.4000			0.949602			0.474801	−	0.880093i	$-0.342520\pi$
$263$	15.4000			0.949602			0.474801	+	0.880093i	$0.342520\pi$
$264$	−2.11879			−0.130402
$265$	11.1794			0.686743
$266$	−14.8323	−	7.46630i	−0.909428	−	0.457788i
$267$	−4.69860	−	8.13822i	−0.287550	−	0.498051i
$268$	1.67924	−	2.90853i	0.102576	−	0.177667i
$269$	5.86566	−	10.1596i	0.357636	−	0.619443i	−0.629930	−	0.776652i	$-0.716916\pi$
$269$	5.86566	−	10.1596i	0.357636	−	0.619443i	0.987565	+	0.157209i	$0.0502496\pi$
$270$	1.30278			0.0792844
$271$	13.0428	+	22.5908i	0.792293	+	1.37229i	0.924544	+	0.381075i	$0.124446\pi$
$271$	13.0428	+	22.5908i	0.792293	+	1.37229i	−0.132251	+	0.991216i	$0.542220\pi$
$272$	−0.486762			−0.0295143
$273$	−5.16463	−	8.02039i	−0.312577	−	0.485416i
$274$	6.79165			0.410299
$275$	3.49894	+	6.06035i	0.210994	+	0.365453i
$276$	−4.78954			−0.288296
$277$	−11.7153	+	20.2916i	−0.703906	+	1.21920i	0.263179	+	0.964747i	$0.415229\pi$
$277$	−11.7153	+	20.2916i	−0.703906	+	1.21920i	−0.967085	+	0.254454i	$0.918104\pi$
$278$	−6.45522	+	11.1808i	−0.387158	+	0.670578i
$279$	2.24338	+	3.88565i	0.134308	+	0.232628i
$280$	0.197224	+	3.44117i	0.0117864	+	0.205649i
$281$	6.15751			0.367326			0.183663	−	0.982989i	$-0.441204\pi$
$281$	6.15751			0.367326			0.183663	+	0.982989i	$0.441204\pi$
$282$	−7.97141			−0.474691
$283$	21.9323			1.30374			0.651870	−	0.758331i	$-0.273985\pi$
$283$	21.9323			1.30374			0.651870	+	0.758331i	$0.273985\pi$
$284$	−2.93480			−0.174148
$285$	−4.08831	+	7.08115i	−0.242170	+	0.419451i
$286$	6.64908	−	3.76168i	0.393168	−	0.222433i
$287$	1.91307	+	33.3793i	0.112925	+	1.97032i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	8.38153	+	14.5172i	0.493031	+	0.853955i
$290$	2.27123	−	3.93389i	0.133371	−	0.231006i
$291$	0.698602	+	1.21001i	0.0409528	+	0.0709323i
$292$	16.1867			0.947257
$293$	−8.74075	−	15.1394i	−0.510640	−	0.884455i	−0.999924	−	0.0123300i	$-0.996075\pi$
$293$	−8.74075	−	15.1394i	−0.510640	−	0.884455i	0.489284	−	0.872125i	$-0.337258\pi$
$294$	6.95416	−	0.799757i	0.405575	−	0.0466428i
$295$	−5.96029	−	10.3235i	−0.347021	−	0.601059i
$296$	−0.578756	−	1.00243i	−0.0336395	−	0.0582653i
$297$	2.11879			0.122945
$298$	−11.6820	−	20.2338i	−0.676720	−	1.17211i
$299$	15.0303	−	8.50330i	0.869224	−	0.491759i
$300$	−3.30278			−0.190686
$301$	−18.9699	−	9.54908i	−1.09341	−	0.550400i
$302$	2.93692	−	5.08689i	0.169001	−	0.292718i
$303$	−6.03449			−0.346672
$304$	3.13815	+	5.43544i	0.179985	+	0.311744i
$305$	−6.63414	+	11.4907i	−0.379870	+	0.657954i
$306$	0.486762			0.0278263
$307$	−12.0673			−0.688718			−0.344359	−	0.938838i	$-0.611904\pi$
$307$	−12.0673			−0.688718			−0.344359	+	0.938838i	$0.611904\pi$
$308$	0.320759	+	5.59660i	0.0182769	+	0.318896i
$309$	5.64770	−	9.78210i	0.321286	−	0.556484i
$310$	2.92262	+	5.06213i	0.165994	+	0.287510i
$311$	0.755881	+	1.30923i	0.0428621	+	0.0742393i	0.886661	−	0.462421i	$-0.153019\pi$
$311$	0.755881	+	1.30923i	0.0428621	+	0.0742393i	−0.843798	+	0.536660i	$0.819686\pi$
$312$	−0.0315412	+	3.60541i	−0.00178567	+	0.204116i
$313$	−0.862908	+	1.49460i	−0.0487744	+	0.0844798i	−0.889382	−	0.457165i	$-0.848865\pi$
$313$	−0.862908	+	1.49460i	−0.0487744	+	0.0844798i	0.840607	+	0.541645i	$0.182198\pi$
$314$	3.12248	−	5.40829i	0.176212	−	0.305207i
$315$	−0.197224	−	3.44117i	−0.0111123	−	0.193888i
$316$	−7.16738	−	12.4143i	−0.403197	−	0.698357i
$317$	−10.6520	+	18.4499i	−0.598278	+	1.03625i	0.394798	+	0.918768i	$0.370815\pi$
$317$	−10.6520	+	18.4499i	−0.598278	+	1.03625i	−0.993075	+	0.117479i	$0.962519\pi$
$318$	−4.29060	+	7.43153i	−0.240605	+	0.416739i
$319$	3.69386	−	6.39795i	0.206816	−	0.358216i
$320$	0.651388	−	1.12824i	0.0364137	−	0.0630704i
$321$	7.01462	+	12.1497i	0.391518	+	0.678128i
$322$	0.725078	+	12.6512i	0.0404070	+	0.705022i
$323$	−1.52753	+	2.64576i	−0.0849942	+	0.147214i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	10.3646	−	5.86372i	0.574925	−	0.325261i
$326$	−1.30383	−	2.25831i	−0.0722126	−	0.125076i
$327$	−5.50000	−	9.52628i	−0.304151	−	0.526804i
$328$	6.31845	−	10.9439i	0.348878	−	0.604274i
$329$	1.20677	+	21.0558i	0.0665316	+	1.16084i
$330$	2.76031			0.151950
$331$	16.4338			0.903284			0.451642	−	0.892199i	$-0.350838\pi$
$331$	16.4338			0.903284			0.451642	+	0.892199i	$0.350838\pi$
$332$	−1.74338	+	3.01962i	−0.0956805	+	0.165723i
$333$	0.578756	+	1.00243i	0.0317156	+	0.0549331i
$334$	−6.90833			−0.378007
$335$	−2.18767	+	3.78916i	−0.119525	+	0.207024i
$336$	−2.36323	−	1.18960i	−0.128925	−	0.0648981i
$337$	−12.9178			−0.703678			−0.351839	−	0.936060i	$-0.614444\pi$
$337$	−12.9178			−0.703678			−0.351839	+	0.936060i	$0.614444\pi$
$338$	−6.30204	−	11.3703i	−0.342786	−	0.618464i
$339$	3.56552	+	6.17566i	0.193652	+	0.335416i
$340$	0.634142			0.0343912
$341$	4.75325	+	8.23287i	0.257403	+	0.445835i
$342$	−3.13815	−	5.43544i	−0.169692	−	0.293915i
$343$	−3.16527	−	18.2478i	−0.170908	−	0.985287i
$344$	4.01356	+	6.95169i	0.216397	+	0.374810i
$345$	6.23969			0.335934
$346$	−3.86355	−	6.69186i	−0.207706	−	0.359757i
$347$	8.01936	−	13.8899i	0.430502	−	0.745651i	−0.566415	−	0.824120i	$-0.691670\pi$
$347$	8.01936	−	13.8899i	0.430502	−	0.745651i	0.996917	+	0.0784693i	$0.0250033\pi$
$348$	1.74338	+	3.01962i	0.0934550	+	0.161869i
$349$	−3.81951	+	6.61558i	−0.204453	+	0.354124i	−0.949958	−	0.312376i	$-0.898875\pi$
$349$	−3.81951	+	6.61558i	−0.204453	+	0.354124i	0.745505	+	0.666500i	$0.232208\pi$
$350$	0.500000	+	8.72401i	0.0267261	+	0.466318i
$351$	0.0315412	−	3.60541i	0.00168354	−	0.192443i
$352$	1.05939	−	1.83493i	0.0564659	−	0.0978018i
$353$	−32.3911			−1.72400			−0.862002	−	0.506904i	$-0.830790\pi$
$353$	−32.3911			−1.72400			−0.862002	+	0.506904i	$0.830790\pi$
$354$	9.15014			0.486324
$355$	3.82339			0.202924
$356$	9.39720			0.498051
$357$	−0.0736899	−	1.28574i	−0.00390008	−	0.0680487i
$358$	9.57539	+	16.5851i	0.506075	+	0.876548i
$359$	1.57507	−	2.72810i	0.0831289	−	0.143983i	−0.821463	−	0.570261i	$-0.806842\pi$
$359$	1.57507	−	2.72810i	0.0831289	−	0.143983i	0.904592	+	0.426278i	$0.140175\pi$
$360$	−0.651388	+	1.12824i	−0.0343312	+	0.0594633i
$361$	20.3919			1.07326
$362$	6.54859	+	11.3425i	0.344186	+	0.596148i
$363$	−6.51073			−0.341725
$364$	9.52817	−	0.462502i	0.499412	−	0.0242417i
$365$	−21.0877			−1.10378
$366$	−5.09231	−	8.82015i	−0.266179	−	0.461036i
$367$	−4.46926			−0.233293			−0.116647	−	0.993173i	$-0.537214\pi$
$367$	−4.46926			−0.233293			−0.116647	+	0.993173i	$0.537214\pi$
$368$	2.39477	−	4.14786i	0.124836	−	0.216222i
$369$	−6.31845	+	10.9439i	−0.328925	+	0.569715i
$370$	0.753989	+	1.30595i	0.0391980	+	0.0678929i
$371$	20.2793	+	10.2082i	1.05285	+	0.529984i
$372$	−4.48676			−0.232628
$373$	4.95231			0.256421			0.128210	−	0.991747i	$-0.459077\pi$
$373$	4.95231			0.256421			0.128210	+	0.991747i	$0.459077\pi$
$374$	1.03135			0.0533297
$375$	10.8167			0.558570
$376$	3.98570	−	6.90344i	0.205547	−	0.356018i
$377$	−10.8320	−	6.38085i	−0.557877	−	0.328631i
$378$	2.36323	+	1.18960i	0.121551	+	0.0611866i
$379$	6.55920	−	11.3609i	0.336923	−	0.583569i	−0.646929	−	0.762550i	$-0.723947\pi$
$379$	6.55920	−	11.3609i	0.336923	−	0.583569i	0.983852	+	0.178982i	$0.0572803\pi$
$380$	−4.08831	−	7.08115i	−0.209726	−	0.363255i
$381$	2.59305	−	4.49130i	0.132846	−	0.230096i
$382$	−5.74444	−	9.94966i	−0.293911	−	0.509069i
$383$	−12.1800			−0.622369			−0.311185	−	0.950349i	$-0.600726\pi$
$383$	−12.1800			−0.622369			−0.311185	+	0.950349i	$0.600726\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−0.417877	−	7.29112i	−0.0212970	−	0.371590i
$386$	−0.138150	−	0.239283i	−0.00703165	−	0.0121792i
$387$	−4.01356	−	6.95169i	−0.204021	−	0.353374i
$388$	−1.39720			−0.0709323
$389$	3.34598	+	5.79541i	0.169648	+	0.293839i	0.938296	−	0.345833i	$-0.112404\pi$
$389$	3.34598	+	5.79541i	0.169648	+	0.293839i	−0.768648	+	0.639672i	$0.779070\pi$
$390$	0.0410911	−	4.69704i	0.00208073	−	0.237844i
$391$	2.33137			0.117902
$392$	−2.78447	+	6.42236i	−0.140637	+	0.324378i
$393$	4.03186	−	6.98339i	0.203381	−	0.352265i
$394$	−13.2710			−0.668585
$395$	9.33749	+	16.1730i	0.469820	+	0.813752i
$396$	−1.05939	+	1.83493i	−0.0532366	+	0.0922085i
$397$	24.5825			1.23376			0.616879	−	0.787058i	$-0.288397\pi$
$397$	24.5825			1.23376			0.616879	+	0.787058i	$0.288397\pi$
$398$	−19.0219			−0.953479
$399$	−13.8822	+	9.11202i	−0.694978	+	0.456172i
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	−17.3273	−	30.0117i	−0.865282	−	1.49871i	−0.866767	−	0.498714i	$-0.833806\pi$
$401$	−17.3273	−	30.0117i	−0.865282	−	1.49871i	0.00148462	−	0.999999i	$-0.499527\pi$
$402$	−1.67924	−	2.90853i	−0.0837529	−	0.145064i
$403$	14.0801	−	7.96576i	0.701381	−	0.396803i
$404$	3.01725	−	5.22602i	0.150114	−	0.260004i
$405$	0.651388	−	1.12824i	0.0323677	−	0.0560625i
$406$	7.71216	−	5.06213i	0.382748	−	0.251229i
$407$	1.22626	+	2.12395i	0.0607835	+	0.105280i
$408$	−0.243381	+	0.421549i	−0.0120492	+	0.0208698i
$409$	11.9545	−	20.7058i	0.591111	−	1.02383i	−0.402972	−	0.915212i	$-0.632023\pi$
$409$	11.9545	−	20.7058i	0.591111	−	1.02383i	0.994083	−	0.108622i	$-0.0346439\pi$
$410$	−8.23152	+	14.2574i	−0.406526	+	0.704123i
$411$	3.39583	−	5.88174i	0.167504	−	0.290125i
$412$	5.64770	+	9.78210i	0.278242	+	0.481930i
$413$	−1.38522	−	24.1693i	−0.0681622	−	1.18929i
$414$	−2.39477	+	4.14786i	−0.117696	+	0.203856i
$415$	2.27123	−	3.93389i	0.111491	−	0.193107i
$416$	−3.10661	−	1.83002i	−0.152314	−	0.0897242i
$417$	6.45522	+	11.1808i	0.316114	+	0.547525i
$418$	−6.64908	−	11.5165i	−0.325217	−	0.563292i
$419$	−6.09738	+	10.5610i	−0.297876	+	0.515937i	−0.975650	−	0.219334i	$-0.929612\pi$
$419$	−6.09738	+	10.5610i	−0.297876	+	0.515937i	0.677773	+	0.735271i	$0.262945\pi$
$420$	3.07876	+	1.54979i	0.150228	+	0.0756218i
$421$	14.0504			0.684777			0.342388	−	0.939558i	$-0.388764\pi$
$421$	14.0504			0.684777			0.342388	+	0.939558i	$0.388764\pi$
$422$	−3.97500			−0.193500
$423$	−3.98570	+	6.90344i	−0.193792	+	0.335657i
$424$	−4.29060	−	7.43153i	−0.208370	−	0.360907i
$425$	1.60767			0.0779833
$426$	−1.46740	+	2.54161i	−0.0710958	+	0.123142i
$427$	−22.5268	+	14.7862i	−1.09015	+	0.715554i
$428$	−14.0292			−0.678128
$429$	0.0668291	−	7.63911i	0.00322654	−	0.368820i
$430$	−5.22877	−	9.05649i	−0.252153	−	0.436743i
$431$	17.3034			0.833476			0.416738	−	0.909027i	$-0.363173\pi$
$431$	17.3034			0.833476			0.416738	+	0.909027i	$0.363173\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	10.1803	+	17.6328i	0.489234	+	0.847378i	0.999923	−	0.0123873i	$-0.00394309\pi$
$433$	10.1803	+	17.6328i	0.489234	+	0.847378i	−0.510689	+	0.859765i	$0.670610\pi$
$434$	0.679241	+	11.8514i	0.0326046	+	0.568886i
$435$	−2.27123	−	3.93389i	−0.108897	−	0.188616i
$436$	11.0000			0.526804
$437$	−15.0303	−	26.0332i	−0.718996	−	1.24534i
$438$	8.09337	−	14.0181i	0.386716	−	0.669812i
$439$	−2.02199	−	3.50219i	−0.0965044	−	0.167150i	0.813731	−	0.581242i	$-0.197433\pi$
$439$	−2.02199	−	3.50219i	−0.0965044	−	0.167150i	−0.910235	+	0.414091i	$0.864100\pi$
$440$	−1.38015	+	2.39050i	−0.0657962	+	0.113962i
$441$	2.78447	−	6.42236i	0.132594	−	0.305827i
$442$	0.0153530	−	1.75498i	0.000730270	−	0.0834758i
$443$	10.1092	−	17.5097i	0.480304	−	0.831912i	−0.519440	−	0.854507i	$-0.673860\pi$
$443$	10.1092	−	17.5097i	0.480304	−	0.831912i	0.999745	+	0.0225951i	$0.00719285\pi$
$444$	−1.15751			−0.0549331
$445$	−12.2424			−0.580348
$446$	19.1603			0.907265
$447$	−23.3640			−1.10508
$448$	2.21184	−	1.45181i	0.104500	−	0.0685918i
$449$	−19.8059	−	34.3047i	−0.934696	−	1.61894i	−0.775175	−	0.631746i	$-0.782338\pi$
$449$	−19.8059	−	34.3047i	−0.934696	−	1.61894i	−0.159521	−	0.987195i	$-0.550995\pi$
$450$	−1.65139	+	2.86029i	−0.0778472	+	0.134835i
$451$	−13.3875	+	23.1878i	−0.630391	+	1.09187i
$452$	−7.13104			−0.335416
$453$	−2.93692	−	5.08689i	−0.137988	−	0.239003i
$454$	1.18251			0.0554980
$455$	−12.4131	+	0.602537i	−0.581934	+	0.0282474i
$456$	6.27630			0.293915
$457$	3.32371	+	5.75683i	0.155477	+	0.269293i	0.933232	−	0.359273i	$-0.116975\pi$
$457$	3.32371	+	5.75683i	0.155477	+	0.269293i	−0.777756	+	0.628566i	$0.783642\pi$
$458$	15.0320			0.702399
$459$	0.243381	−	0.421549i	0.0113601	−	0.0196762i
$460$	−3.11985	+	5.40373i	−0.145464	+	0.251950i
$461$	−10.2371	−	17.7311i	−0.476788	−	0.825820i	0.522859	−	0.852419i	$-0.324866\pi$
$461$	−10.2371	−	17.7311i	−0.476788	−	0.825820i	−0.999646	+	0.0265991i	$0.991532\pi$
$462$	5.00718	+	2.52052i	0.232955	+	0.117265i
$463$	17.2668			0.802457			0.401228	−	0.915978i	$-0.368583\pi$
$463$	17.2668			0.802457			0.401228	+	0.915978i	$0.368583\pi$
$464$	−3.48676			−0.161869
$465$	5.84524			0.271067
$466$	−5.19412			−0.240613
$467$	4.37922	−	7.58503i	0.202646	−	0.350994i	−0.746734	−	0.665123i	$-0.768379\pi$
$467$	4.37922	−	7.58503i	0.202646	−	0.350994i	0.949380	+	0.314129i	$0.101713\pi$
$468$	3.10661	+	1.83002i	0.143603	+	0.0845928i
$469$	−7.42843	+	4.87589i	−0.343013	+	0.225148i
$470$	−5.19248	+	8.99364i	−0.239511	+	0.414846i
$471$	−3.12248	−	5.40829i	−0.143876	−	0.249201i
$472$	−4.57507	+	7.92425i	−0.210585	+	0.364743i
$473$	−8.50388	−	14.7292i	−0.391009	−	0.677247i
$474$	−14.3348			−0.658417
$475$	−10.3646	−	17.9520i	−0.475561	−	0.823695i
$476$	1.15033	+	0.579054i	0.0527253	+	0.0265409i
$477$	4.29060	+	7.43153i	0.196453	+	0.340266i
$478$	12.6989	+	21.9952i	0.580835	+	1.00604i
$479$	−27.0253			−1.23482			−0.617408	−	0.786643i	$-0.711817\pi$
$479$	−27.0253			−1.23482			−0.617408	+	0.786643i	$0.711817\pi$
$480$	−0.651388	−	1.12824i	−0.0297317	−	0.0514967i
$481$	3.63244	−	2.05504i	0.165625	−	0.0937015i
$482$	11.8575			0.540094
$483$	11.3188	+	5.69765i	0.515022	+	0.259252i
$484$	3.25537	−	5.63846i	0.147971	−	0.256294i
$485$	1.82024			0.0826530
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−10.9717	+	19.0036i	−0.497177	+	0.861135i	−0.999995	−	0.00325721i	$-0.998963\pi$
$487$	−10.9717	+	19.0036i	−0.497177	+	0.861135i	0.502818	+	0.864392i	$0.332297\pi$
$488$	10.1846			0.461036
$489$	−2.60767			−0.117923
$490$	3.62754	−	8.36689i	0.163876	−	0.377978i
$491$	−7.09020	+	12.2806i	−0.319976	+	0.554215i	−0.980483	−	0.196605i	$-0.937008\pi$
$491$	−7.09020	+	12.2806i	−0.319976	+	0.554215i	0.660507	+	0.750820i	$0.270342\pi$
$492$	−6.31845	−	10.9439i	−0.284858	−	0.493388i
$493$	−0.848612	−	1.46984i	−0.0382196	−	0.0661982i
$494$	−19.6960	+	11.1429i	−0.886164	+	0.501342i
$495$	1.38015	−	2.39050i	0.0620333	−	0.107445i
$496$	2.24338	−	3.88565i	0.100731	−	0.174471i
$497$	6.93561	+	3.49125i	0.311104	+	0.156604i
$498$	1.74338	+	3.01962i	0.0781228	+	0.135313i
$499$	14.7488	−	25.5456i	0.660245	−	1.14358i	−0.320306	−	0.947314i	$-0.603786\pi$
$499$	14.7488	−	25.5456i	0.660245	−	1.14358i	0.980551	−	0.196264i	$-0.0628811\pi$
$500$	−5.40833	+	9.36750i	−0.241868	+	0.418927i
$501$	−3.45416	+	5.98279i	−0.154321	+	0.267291i
$502$	−10.7397	+	18.6017i	−0.479336	+	0.830234i
$503$	−7.49400	−	12.9800i	−0.334141	−	0.578749i	0.649178	−	0.760636i	$-0.275113\pi$
$503$	−7.49400	−	12.9800i	−0.334141	−	0.578749i	−0.983319	+	0.181887i	$0.941780\pi$
$504$	−2.21184	+	1.45181i	−0.0985232	+	0.0646689i
$505$	−3.93079	+	6.80834i	−0.174918	+	0.302967i
$506$	−5.07401	+	8.78844i	−0.225567	+	0.390694i
$507$	−12.9980	−	0.227438i	−0.577262	−	0.0101009i
$508$	2.59305	+	4.49130i	0.115048	+	0.199269i
$509$	−20.9837	−	36.3449i	−0.930087	−	1.61096i	−0.783169	−	0.621809i	$-0.786398\pi$
$509$	−20.9837	−	36.3449i	−0.930087	−	1.61096i	−0.146918	−	0.989149i	$-0.546935\pi$
$510$	0.317071	−	0.549183i	0.0140401	−	0.0243182i
$511$	−38.2530	−	19.2558i	−1.69221	−	0.851826i
$512$	−1.00000			−0.0441942
$513$	−6.27630			−0.277105
$514$	−3.42294	+	5.92871i	−0.150980	+	0.261504i
$515$	−7.35769	−	12.7439i	−0.324218	−	0.561563i
$516$	8.02712			0.353374
$517$	−8.44487	+	14.6269i	−0.371405	+	0.643292i
$518$	0.175233	+	3.05747i	0.00769930	+	0.134337i
$519$	−7.72710			−0.339182
$520$	4.04721	+	2.38411i	0.177482	+	0.104550i
$521$	−8.68748	−	15.0472i	−0.380605	−	0.659228i	0.610544	−	0.791983i	$-0.290951\pi$
$521$	−8.68748	−	15.0472i	−0.380605	−	0.659228i	−0.991149	+	0.132755i	$0.957618\pi$
$522$	3.48676			0.152611
$523$	−16.5017	−	28.5818i	−0.721569	−	1.24979i	−0.960371	−	0.278726i	$-0.910088\pi$
$523$	−16.5017	−	28.5818i	−0.721569	−	1.24979i	0.238802	−	0.971068i	$-0.423245\pi$
$524$	4.03186	+	6.98339i	0.176133	+	0.305071i
$525$	7.80521	+	3.92899i	0.340647	+	0.171475i
$526$	7.69998	+	13.3368i	0.335735	+	0.581510i
$527$	2.18399			0.0951360
$528$	−1.05939	−	1.83493i	−0.0461042	−	0.0798549i
$529$	0.0301633	−	0.0522443i	0.00131145	−	0.00227149i
$530$	5.58968	+	9.68162i	0.242800	+	0.420543i
$531$	4.57507	−	7.92425i	0.198541	−	0.343883i
$532$	−0.950155	−	16.5783i	−0.0411945	−	0.718761i
$533$	39.2579	+	23.1258i	1.70045	+	1.00169i
$534$	4.69860	−	8.13822i	0.203328	−	0.352175i
$535$	18.2769			0.790181
$536$	3.35848			0.145064
$537$	19.1508			0.826417
$538$	11.7313			0.505773
$539$	5.89971	−	13.6076i	0.254118	−	0.586122i
$540$	0.651388	+	1.12824i	0.0280313	+	0.0485516i
$541$	−8.93967	+	15.4840i	−0.384347	+	0.665708i	−0.991678	−	0.128741i	$-0.958907\pi$
$541$	−8.93967	+	15.4840i	−0.384347	+	0.665708i	0.607332	+	0.794448i	$0.292240\pi$
$542$	−13.0428	+	22.5908i	−0.560236	+	0.970357i
$543$	13.0972			0.562054
$544$	−0.243381	−	0.421549i	−0.0104349	−	0.0180737i
$545$	−14.3305			−0.613853
$546$	4.36355	−	8.48289i	0.186743	−	0.363034i
$547$	11.4550			0.489782			0.244891	−	0.969551i	$-0.421248\pi$
$547$	11.4550			0.489782			0.244891	+	0.969551i	$0.421248\pi$
$548$	3.39583	+	5.88174i	0.145063	+	0.251256i
$549$	−10.1846			−0.434669
$550$	−3.49894	+	6.06035i	−0.149195	+	0.258414i
$551$	−10.9420	+	18.9521i	−0.466144	+	0.807385i
$552$	−2.39477	−	4.14786i	−0.101928	−	0.176545i
$553$	2.17011	+	37.8641i	0.0922824	+	1.61014i
$554$	−23.4307			−0.995474
$555$	1.50798			0.0640101
$556$	−12.9104			−0.547525
$557$	40.6243			1.72131			0.860654	−	0.509190i	$-0.170055\pi$
$557$	40.6243			1.72131			0.860654	+	0.509190i	$0.170055\pi$
$558$	−2.24338	+	3.88565i	−0.0949699	+	0.164493i
$559$	−25.1903	+	14.2513i	−1.06544	+	0.602765i
$560$	−2.88153	+	1.89139i	−0.121767	+	0.0799257i
$561$	0.515673	−	0.893172i	0.0217717	−	0.0377098i
$562$	3.07876	+	5.33256i	0.129869	+	0.224941i
$563$	−16.5928	+	28.7395i	−0.699301	+	1.21123i	0.269408	+	0.963026i	$0.413172\pi$
$563$	−16.5928	+	28.7395i	−0.699301	+	1.21123i	−0.968709	+	0.248199i	$0.920161\pi$
$564$	−3.98570	−	6.90344i	−0.167828	−	0.290687i
$565$	9.29014			0.390839
$566$	10.9661	+	18.9939i	0.460942	+	0.798374i
$567$	2.21184	−	1.45181i	0.0928885	−	0.0609705i
$568$	−1.46740	−	2.54161i	−0.0615708	−	0.106644i
$569$	−0.0339767	−	0.0588494i	−0.00142438	−	0.00246710i	0.865312	−	0.501233i	$-0.167120\pi$
$569$	−0.0339767	−	0.0588494i	−0.00142438	−	0.00246710i	−0.866737	+	0.498766i	$0.833787\pi$
$570$	−8.17661			−0.342481
$571$	−10.2822	−	17.8092i	−0.430295	−	0.745293i	0.566603	−	0.823991i	$-0.308257\pi$
$571$	−10.2822	−	17.8092i	−0.430295	−	0.745293i	−0.996899	+	0.0786977i	$0.974924\pi$
$572$	6.58225	+	3.87743i	0.275218	+	0.162124i
$573$	−11.4889			−0.479955
$574$	−27.9508	+	18.3464i	−1.16664	+	0.765765i
$575$	−7.90938	+	13.6995i	−0.329844	+	0.571307i
$576$	1.00000			0.0416667
$577$	22.7814	+	39.4586i	0.948403	+	1.64268i	0.748790	+	0.662808i	$0.230635\pi$
$577$	22.7814	+	39.4586i	0.948403	+	1.64268i	0.199613	+	0.979875i	$0.436031\pi$
$578$	−8.38153	+	14.5172i	−0.348626	+	0.603837i
$579$	−0.276300			−0.0114826
$580$	4.54247			0.188616
$581$	7.71216	−	5.06213i	0.319954	−	0.210013i
$582$	−0.698602	+	1.21001i	−0.0289580	+	0.0501567i
$583$	9.09087	+	15.7458i	0.376505	+	0.652126i
$584$	8.09337	+	14.0181i	0.334906	+	0.580074i
$585$	−4.04721	−	2.38411i	−0.167332	−	0.0985707i
$586$	8.74075	−	15.1394i	0.361077	−	0.625404i
$587$	2.71527	−	4.70298i	0.112071	−	0.194113i	−0.804534	−	0.593906i	$-0.797585\pi$
$587$	2.71527	−	4.70298i	0.112071	−	0.194113i	0.916605	+	0.399794i	$0.130918\pi$
$588$	4.16969	+	5.62260i	0.171955	+	0.231872i
$589$	−14.0801	−	24.3875i	−0.580162	−	1.00487i
$590$	5.96029	−	10.3235i	0.245381	−	0.425013i
$591$	−6.63552	+	11.4931i	−0.272949	+	0.472761i
$592$	0.578756	−	1.00243i	0.0237867	−	0.0411998i
$593$	−2.77524	+	4.80686i	−0.113966	+	0.197394i	−0.917366	−	0.398045i	$-0.869689\pi$
$593$	−2.77524	+	4.80686i	−0.113966	+	0.197394i	0.803400	+	0.595439i	$0.203022\pi$
$594$	1.05939	+	1.83493i	0.0434675	+	0.0752879i
$595$	−1.49862	−	0.754377i	−0.0614375	−	0.0309264i
$596$	11.6820	−	20.2338i	0.478513	−	0.828809i
$597$	−9.51093	+	16.4734i	−0.389256	+	0.674212i
$598$	14.8792	+	8.76496i	0.608457	+	0.358426i
$599$	−7.94019	−	13.7528i	−0.324427	−	0.561925i	0.656969	−	0.753918i	$-0.271838\pi$
$599$	−7.94019	−	13.7528i	−0.324427	−	0.561925i	−0.981396	+	0.191993i	$0.938505\pi$
$600$	−1.65139	−	2.86029i	−0.0674176	−	0.116771i
$601$	19.1239	−	33.1235i	0.780078	−	1.35114i	−0.151817	−	0.988409i	$-0.548513\pi$
$601$	19.1239	−	33.1235i	0.780078	−	1.35114i	0.931896	−	0.362727i	$-0.118154\pi$
$602$	−1.21521	−	21.2030i	−0.0495282	−	0.864168i
$603$	−3.35848			−0.136768
$604$	5.87384			0.239003
$605$	−4.24101	+	7.34565i	−0.172422	+	0.298643i
$606$	−3.01725	−	5.22602i	−0.122567	−	0.212293i
$607$	−19.3219			−0.784251			−0.392125	−	0.919912i	$-0.628260\pi$
$607$	−19.3219			−0.784251			−0.392125	+	0.919912i	$0.628260\pi$
$608$	−3.13815	+	5.43544i	−0.127269	+	0.220436i
$609$	−0.527853	−	9.20999i	−0.0213897	−	0.373208i
$610$	−13.2683			−0.537217
$611$	24.7641	+	14.5879i	1.00185	+	0.590161i
$612$	0.243381	+	0.421549i	0.00983810	+	0.0170401i
$613$	−30.5251			−1.23290			−0.616448	−	0.787395i	$-0.711429\pi$
$613$	−30.5251			−1.23290			−0.616448	+	0.787395i	$0.711429\pi$
$614$	−6.03366	−	10.4506i	−0.243499	−	0.421752i
$615$	8.23152	+	14.2574i	0.331927	+	0.574914i
$616$	−4.68642	+	3.07609i	−0.188821	+	0.123939i
$617$	−12.5446	−	21.7279i	−0.505026	−	0.874731i	−0.999983	−	0.00581322i	$-0.998150\pi$
$617$	−12.5446	−	21.7279i	−0.505026	−	0.874731i	0.494957	−	0.868917i	$-0.335184\pi$
$618$	11.2954			0.454368
$619$	9.35717	+	16.2071i	0.376096	+	0.651418i	0.990490	−	0.137581i	$-0.0439328\pi$
$619$	9.35717	+	16.2071i	0.376096	+	0.651418i	−0.614394	+	0.788999i	$0.710599\pi$
$620$	−2.92262	+	5.06213i	−0.117375	+	0.203300i
$621$	2.39477	+	4.14786i	0.0960988	+	0.166448i
$622$	−0.755881	+	1.30923i	−0.0303081	+	0.0524951i
$623$	−22.2077	−	11.1789i	−0.889734	−	0.447875i
$624$	−3.13815	+	1.77539i	−0.125627	+	0.0710725i
$625$	−1.21110	+	2.09769i	−0.0484441	+	0.0839076i
$626$	−1.72582			−0.0689774
$627$	−13.2982			−0.531077
$628$	6.24495			0.249201
$629$	0.563433			0.0224655
$630$	2.88153	−	1.89139i	0.114803	−	0.0753547i
$631$	−14.4362	−	25.0042i	−0.574695	−	0.995401i	−0.996075	−	0.0885169i	$-0.971787\pi$
$631$	−14.4362	−	25.0042i	−0.574695	−	0.995401i	0.421379	−	0.906884i	$-0.361546\pi$
$632$	7.16738	−	12.4143i	0.285103	−	0.493813i
$633$	−1.98750	+	3.44245i	−0.0789960	+	0.136825i
$634$	−21.3041			−0.846092
$635$	−3.37816	−	5.85115i	−0.134058	−	0.232196i
$636$	−8.58119			−0.340266
$637$	−23.0674	−	10.2417i	−0.913965	−	0.405793i
$638$	7.38771			0.292482
$639$	1.46740	+	2.54161i	0.0580495	+	0.100545i
$640$	1.30278			0.0514967
$641$	−1.09911	+	1.90371i	−0.0434121	+	0.0751920i	−0.886915	−	0.461933i	$-0.847156\pi$
$641$	−1.09911	+	1.90371i	−0.0434121	+	0.0751920i	0.843503	+	0.537125i	$0.180490\pi$
$642$	−7.01462	+	12.1497i	−0.276845	+	0.479509i
$643$	8.74713	+	15.1505i	0.344953	+	0.597476i	0.985345	−	0.170572i	$-0.0545615\pi$
$643$	8.74713	+	15.1505i	0.344953	+	0.597476i	−0.640392	+	0.768048i	$0.721228\pi$
$644$	−10.5937	+	6.95352i	−0.417450	+	0.274007i
$645$	−10.4575			−0.411765
$646$	−3.05507			−0.120200
$647$	32.1735			1.26487			0.632436	−	0.774612i	$-0.282055\pi$
$647$	32.1735			1.26487			0.632436	+	0.774612i	$0.282055\pi$
$648$	−1.00000			−0.0392837
$649$	9.69360	−	16.7898i	0.380507	−	0.659058i
$650$	10.2604	+	6.04415i	0.402447	+	0.237071i
$651$	10.6032	+	5.33746i	0.415574	+	0.209192i
$652$	1.30383	−	2.25831i	0.0510621	−	0.0884421i
$653$	−23.7831	−	41.1935i	−0.930703	−	1.61203i	−0.782122	−	0.623125i	$-0.785863\pi$
$653$	−23.7831	−	41.1935i	−0.930703	−	1.61203i	−0.148581	−	0.988900i	$-0.547471\pi$
$654$	5.50000	−	9.52628i	0.215067	−	0.372507i
$655$	−5.25261	−	9.09779i	−0.205236	−	0.355480i
$656$	12.6369			0.493388
$657$	−8.09337	−	14.0181i	−0.315752	−	0.546899i
$658$	−17.6315	+	11.5730i	−0.687347	+	0.451163i
$659$	−3.69892	−	6.40672i	−0.144090	−	0.249570i	0.784943	−	0.619568i	$-0.212692\pi$
$659$	−3.69892	−	6.40672i	−0.144090	−	0.249570i	−0.929033	+	0.369997i	$0.879359\pi$
$660$	1.38015	+	2.39050i	0.0537224	+	0.0930499i
$661$	12.2297			0.475680			0.237840	−	0.971304i	$-0.423561\pi$
$661$	12.2297			0.475680			0.237840	+	0.971304i	$0.423561\pi$
$662$	8.21691	+	14.2321i	0.319359	+	0.553146i
$663$	−1.51218	−	0.890786i	−0.0587282	−	0.0345953i
$664$	−3.48676			−0.135313
$665$	1.23784	+	21.5978i	0.0480013	+	0.837528i
$666$	−0.578756	+	1.00243i	−0.0224263	+	0.0388435i
$667$	16.7000			0.646626
$668$	−3.45416	−	5.98279i	−0.133646	−	0.231481i
$669$	9.58013	−	16.5933i	0.370389	−	0.641533i
$670$	−4.37535			−0.169034
$671$	−21.5791			−0.833051
$672$	−0.151388	−	2.64142i	−0.00583991	−	0.101895i
$673$	24.4511	−	42.3506i	0.942521	−	1.63249i	0.181882	−	0.983320i	$-0.441781\pi$
$673$	24.4511	−	42.3506i	0.942521	−	1.63249i	0.760640	−	0.649174i	$-0.224885\pi$
$674$	−6.45891	−	11.1872i	−0.248788	−	0.430913i
$675$	1.65139	+	2.86029i	0.0635619	+	0.110093i
$676$	6.69597	−	11.1429i	0.257537	−	0.428573i
$677$	−9.74027	+	16.8707i	−0.374349	+	0.648392i	−0.990229	−	0.139448i	$-0.955467\pi$
$677$	−9.74027	+	16.8707i	−0.374349	+	0.648392i	0.615880	+	0.787840i	$0.288801\pi$
$678$	−3.56552	+	6.17566i	−0.136933	+	0.237175i
$679$	3.30191	+	1.66212i	0.126716	+	0.0637862i
$680$	0.317071	+	0.549183i	0.0121591	+	0.0210602i
$681$	0.591256	−	1.02409i	0.0226570	−	0.0392430i
$682$	−4.75325	+	8.23287i	−0.182011	+	0.315253i
$683$	9.08013	−	15.7273i	0.347442	−	0.601787i	−0.638353	−	0.769744i	$-0.720384\pi$
$683$	9.08013	−	15.7273i	0.347442	−	0.601787i	0.985794	+	0.167958i	$0.0537171\pi$
$684$	3.13815	−	5.43544i	0.119990	−	0.207829i
$685$	−4.42400	−	7.66259i	−0.169032	−	0.292773i
$686$	14.2204	−	11.8651i	0.542937	−	0.453011i
$687$	7.51599	−	13.0181i	0.286753	−	0.496671i
$688$	−4.01356	+	6.95169i	−0.153015	+	0.265031i
$689$	26.9291	−	15.2350i	1.02592	−	0.580406i
$690$	3.11985	+	5.40373i	0.118771	+	0.205717i
$691$	−18.5024	−	32.0472i	−0.703866	−	1.21913i	−0.967099	−	0.254399i	$-0.918122\pi$
$691$	−18.5024	−	32.0472i	−0.703866	−	1.21913i	0.263233	−	0.964732i	$-0.415211\pi$
$692$	3.86355	−	6.69186i	0.146870	−	0.254386i
$693$	4.68642	−	3.07609i	0.178022	−	0.116851i
$694$	16.0387			0.608822
$695$	16.8194			0.637997
$696$	−1.74338	+	3.01962i	−0.0660827	+	0.114459i
$697$	3.07558	+	5.32707i	0.116496	+	0.201777i
$698$	−7.63901			−0.289141
$699$	−2.59706	+	4.49824i	−0.0982298	+	0.170139i
$700$	−7.30521	+	4.79502i	−0.276111	+	0.181235i
$701$	36.3972			1.37470			0.687352	−	0.726325i	$-0.258773\pi$
$701$	36.3972			1.37470			0.687352	+	0.726325i	$0.258773\pi$
$702$	3.13815	−	1.77539i	0.118442	−	0.0670078i
$703$	−3.63244	−	6.29158i	−0.137000	−	0.237291i
$704$	2.11879			0.0798549
$705$	5.19248	+	8.99364i	0.195560	+	0.338720i
$706$	−16.1956	−	28.0515i	−0.609528	−	1.05573i
$707$	−13.3473	+	8.76096i	−0.501978	+	0.329490i
$708$	4.57507	+	7.92425i	0.171942	+	0.297812i
$709$	−0.331366			−0.0124447			−0.00622236	−	0.999981i	$-0.501981\pi$
$709$	−0.331366			−0.0124447			−0.00622236	+	0.999981i	$0.501981\pi$
$710$	1.91169	+	3.31115i	0.0717446	+	0.124265i
$711$	−7.16738	+	12.4143i	−0.268798	+	0.465571i
$712$	4.69860	+	8.13822i	0.176088	+	0.304993i
$713$	−10.7448	+	18.6105i	−0.402394	+	0.696968i
$714$	1.07664	−	0.706688i	0.0402922	−	0.0264471i
$715$	−8.57519	−	5.05142i	−0.320694	−	0.188912i
$716$	−9.57539	+	16.5851i	−0.357849	+	0.619813i
$717$	25.3978			0.948500
$718$	3.15014			0.117562
$719$	47.5862			1.77467			0.887333	−	0.461130i	$-0.152556\pi$
$719$	47.5862			1.77467			0.887333	+	0.461130i	$0.152556\pi$
$720$	−1.30278			−0.0485516
$721$	−1.70999	−	29.8359i	−0.0636832	−	1.11115i
$722$	10.1960	+	17.6599i	0.379455	+	0.657235i
$723$	5.92875	−	10.2689i	0.220492	−	0.381904i
$724$	−6.54859	+	11.3425i	−0.243377	+	0.421540i
$725$	11.5160			0.427693
$726$	−3.25537	−	5.63846i	−0.120818	−	0.209263i
$727$	−32.9021			−1.22027			−0.610136	−	0.792297i	$-0.708885\pi$
$727$	−32.9021			−1.22027			−0.610136	+	0.792297i	$0.708885\pi$
$728$	5.16463	+	8.02039i	0.191414	+	0.297255i
$729$	1.00000			0.0370370
$730$	−10.5438	−	18.2625i	−0.390245	−	0.675925i
$731$	−3.90730			−0.144517
$732$	5.09231	−	8.82015i	0.188217	−	0.326002i
$733$	−10.5040	+	18.1935i	−0.387974	+	0.671991i	−0.992177	−	0.124839i	$-0.960158\pi$
$733$	−10.5040	+	18.1935i	−0.387974	+	0.671991i	0.604203	+	0.796831i	$0.293492\pi$
$734$	−2.23463	−	3.87049i	−0.0824816	−	0.142862i
$735$	−5.43217	−	7.32499i	−0.200369	−	0.270186i
$736$	4.78954			0.176545
$737$	−7.11592			−0.262118
$738$	−12.6369			−0.465171
$739$	6.52170			0.239905			0.119952	−	0.992780i	$-0.461726\pi$
$739$	6.52170			0.239905			0.119952	+	0.992780i	$0.461726\pi$
$740$	−0.753989	+	1.30595i	−0.0277172	+	0.0480076i
$741$	−0.197962	+	22.6287i	−0.00727231	+	0.831284i
$742$	1.29909	+	22.6665i	0.0476910	+	0.832113i
$743$	−8.64802	+	14.9788i	−0.317265	+	0.549519i	−0.979916	−	0.199409i	$-0.936098\pi$
$743$	−8.64802	+	14.9788i	−0.317265	+	0.549519i	0.662651	+	0.748928i	$0.269431\pi$
$744$	−2.24338	−	3.88565i	−0.0822463	−	0.142455i
$745$	−15.2190	+	26.3601i	−0.557582	+	0.965760i
$746$	2.47615	+	4.28883i	0.0906585	+	0.157025i
$747$	3.48676			0.127574
$748$	0.515673	+	0.893172i	0.0188549	+	0.0326576i
$749$	33.1543	+	16.6892i	1.21143	+	0.609810i
$750$	5.40833	+	9.36750i	0.197484	+	0.342053i
$751$	4.81213	+	8.33486i	0.175597	+	0.304143i	0.940368	−	0.340159i	$-0.110481\pi$
$751$	4.81213	+	8.33486i	0.175597	+	0.304143i	−0.764771	+	0.644303i	$0.777148\pi$
$752$	7.97141			0.290687
$753$	10.7397	+	18.6017i	0.391376	+	0.677883i
$754$	0.109977	−	12.5712i	0.00400511	−	0.457817i
$755$	−7.65229			−0.278495
$756$	0.151388	+	2.64142i	0.00550592	+	0.0960674i
$757$	−19.5740	+	33.9032i	−0.711429	+	1.23223i	0.252891	+	0.967495i	$0.418619\pi$
$757$	−19.5740	+	33.9032i	−0.711429	+	1.23223i	−0.964321	+	0.264737i	$0.914715\pi$
$758$	13.1184			0.476482
$759$	5.07401	+	8.78844i	0.184175	+	0.319000i
$760$	4.08831	−	7.08115i	0.148298	−	0.256860i
$761$	−10.3776			−0.376187			−0.188094	−	0.982151i	$-0.560231\pi$
$761$	−10.3776			−0.376187			−0.188094	+	0.982151i	$0.560231\pi$
$762$	5.18610			0.187873
$763$	−25.9955	−	13.0856i	−0.941100	−	0.473732i
$764$	5.74444	−	9.94966i	0.207827	−	0.359966i
$765$	−0.317071	−	0.549183i	−0.0114637	−	0.0198558i
$766$	−6.09000	−	10.5482i	−0.220041	−	0.381122i
$767$	−28.4259	−	16.7450i	−1.02640	−	0.604625i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	17.5102	−	30.3285i	0.631434	−	1.09368i	−0.355825	−	0.934553i	$-0.615800\pi$
$769$	17.5102	−	30.3285i	0.631434	−	1.09368i	0.987259	−	0.159123i	$-0.0508665\pi$
$770$	6.10536	−	4.00745i	0.220022	−	0.144419i
$771$	3.42294	+	5.92871i	0.123274	+	0.213517i
$772$	0.138150	−	0.239283i	0.00497213	−	0.00861198i
$773$	−10.0617	+	17.4274i	−0.361894	+	0.626819i	−0.988273	−	0.152700i	$-0.951203\pi$
$773$	−10.0617	+	17.4274i	−0.361894	+	0.626819i	0.626378	+	0.779519i	$0.284537\pi$
$774$	4.01356	−	6.95169i	0.144264	−	0.249873i
$775$	−7.40938	+	12.8334i	−0.266153	+	0.460990i
$776$	−0.698602	−	1.21001i	−0.0250784	−	0.0434370i
$777$	2.73546	+	1.37698i	0.0981342	+	0.0493988i
$778$	−3.34598	+	5.79541i	−0.119959	+	0.207776i
$779$	39.6565	−	68.6870i	1.42084	−	2.46097i
$780$	4.08831	−	2.31294i	0.146385	−	0.0828164i
$781$	3.10911	+	5.38514i	0.111253	+	0.192696i
$782$	1.16568	+	2.01902i	0.0416847	+	0.0722001i
$783$	1.74338	−	3.01962i	0.0623034	−	0.107913i
$784$	−6.95416	+	0.799757i	−0.248363	+	0.0285627i
$785$	−8.13577			−0.290378
$786$	8.06372			0.287623
$787$	−0.951533	+	1.64810i	−0.0339185	+	0.0587486i	−0.882486	−	0.470338i	$-0.844132\pi$
$787$	−0.951533	+	1.64810i	−0.0339185	+	0.0587486i	0.848568	+	0.529087i	$0.177465\pi$
$788$	−6.63552	−	11.4931i	−0.236381	−	0.409423i
$789$	15.4000			0.548253
$790$	−9.33749	+	16.1730i	−0.332213	+	0.575410i
$791$	16.8523	+	8.48310i	0.599197	+	0.301624i
$792$	−2.11879			−0.0752879
$793$	−0.321235	+	36.7198i	−0.0114074	+	1.30396i
$794$	12.2912	+	21.2890i	0.436200	+	0.755520i
$795$	11.1794			0.396491
$796$	−9.51093	−	16.4734i	−0.337106	−	0.583885i
$797$	10.9112	+	18.8987i	0.386494	+	0.669427i	0.991975	−	0.126433i	$-0.0403527\pi$
$797$	10.9112	+	18.8987i	0.386494	+	0.669427i	−0.605481	+	0.795859i	$0.707019\pi$
$798$	−14.8323	−	7.46630i	−0.525059	−	0.264304i
$799$	1.94009	+	3.36034i	0.0686355	+	0.118880i
$800$	3.30278			0.116771
$801$	−4.69860	−	8.13822i	−0.166017	−	0.287550i
$802$	17.3273	−	30.0117i	0.611847	−	1.05975i
$803$	−17.1481	−	29.7015i	−0.605145	−	1.04814i
$804$	1.67924	−	2.90853i	0.0592223	−	0.102576i
$805$	13.8012	−	9.05887i	0.486428	−	0.319283i
$806$	13.9386	+	8.21087i	0.490967	+	0.289216i
$807$	5.86566	−	10.1596i	0.206481	−	0.357636i
$808$	6.03449			0.212293
$809$	45.9037			1.61389			0.806944	−	0.590628i	$-0.201120\pi$
$809$	45.9037			1.61389			0.806944	+	0.590628i	$0.201120\pi$
$810$	1.30278			0.0457749
$811$	3.66652			0.128749			0.0643744	−	0.997926i	$-0.479495\pi$
$811$	3.66652			0.128749			0.0643744	+	0.997926i	$0.479495\pi$
$812$	8.24001	+	4.14786i	0.289168	+	0.145561i
$813$	13.0428	+	22.5908i	0.457431	+	0.792293i
$814$	−1.22626	+	2.12395i	−0.0429804	+	0.0744443i
$815$	−1.69860	+	2.94207i	−0.0594994	+	0.103056i
$816$	−0.486762			−0.0170401
$817$	25.1903	+	43.6309i	0.881297	+	1.52645i
$818$	23.9090			0.835957
$819$	−5.16463	−	8.02039i	−0.180467	−	0.280255i
$820$	−16.4630			−0.574914
$821$	10.1742	+	17.6222i	0.355081	+	0.615019i	0.987132	−	0.159908i	$-0.0511199\pi$
$821$	10.1742	+	17.6222i	0.355081	+	0.615019i	−0.632051	+	0.774927i	$0.717787\pi$
$822$	6.79165			0.236886
$823$	−13.8672	+	24.0188i	−0.483381	+	0.837241i	−0.999818	−	0.0190843i	$-0.993925\pi$
$823$	−13.8672	+	24.0188i	−0.483381	+	0.837241i	0.516436	+	0.856326i	$0.327258\pi$
$824$	−5.64770	+	9.78210i	−0.196747	+	0.340776i
$825$	3.49894	+	6.06035i	0.121818	+	0.210994i
$826$	20.2386	−	13.2843i	0.704192	−	0.462220i
$827$	36.6640			1.27493			0.637466	−	0.770478i	$-0.279983\pi$
$827$	36.6640			1.27493			0.637466	+	0.770478i	$0.279983\pi$
$828$	−4.78954			−0.166448
$829$	14.4624			0.502300			0.251150	−	0.967948i	$-0.419191\pi$
$829$	14.4624			0.502300			0.251150	+	0.967948i	$0.419191\pi$
$830$	4.54247			0.157671
$831$	−11.7153	+	20.2916i	−0.406400	+	0.703906i
$832$	0.0315412	−	3.60541i	0.00109349	−	0.124995i
$833$	−2.02965	−	2.73687i	−0.0703232	−	0.0948270i
$834$	−6.45522	+	11.1808i	−0.223526	+	0.387158i
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	6.64908	−	11.5165i	0.229963	−	0.398308i
$837$	2.24338	+	3.88565i	0.0775426	+	0.134308i
$838$	−12.1948			−0.421261
$839$	−2.51779	−	4.36094i	−0.0869237	−	0.150556i	0.819286	−	0.573386i	$-0.194370\pi$
$839$	−2.51779	−	4.36094i	−0.0869237	−	0.150556i	−0.906209	+	0.422829i	$0.861037\pi$
$840$	0.197224	+	3.44117i	0.00680489	+	0.118732i
$841$	8.42124	+	14.5860i	0.290388	+	0.502966i
$842$	7.02522	+	12.1680i	0.242105	+	0.419338i
$843$	6.15751			0.212076
$844$	−1.98750	−	3.44245i	−0.0684126	−	0.118494i
$845$	−8.72335	+	14.5167i	−0.300092	+	0.499389i
$846$	−7.97141			−0.274063
$847$	−14.4007	+	9.45237i	−0.494814	+	0.324787i
$848$	4.29060	−	7.43153i	0.147340	−	0.255200i
$849$	21.9323			0.752715
$850$	0.803833	+	1.39228i	0.0275713	+	0.0477548i
$851$	−2.77197	+	4.80120i	−0.0950220	+	0.164583i
$852$	−2.93480			−0.100545
$853$	21.9833			0.752693			0.376346	−	0.926479i	$-0.377180\pi$
$853$	21.9833			0.752693			0.376346	+	0.926479i	$0.377180\pi$
$854$	−24.0686	−	12.1157i	−0.823610	−	0.414589i
$855$	−4.08831	+	7.08115i	−0.139817	+	0.242170i
$856$	−7.01462	−	12.1497i	−0.239755	−	0.415267i
$857$	21.6450	+	37.4902i	0.739378	+	1.28064i	0.952776	+	0.303675i	$0.0982137\pi$
$857$	21.6450	+	37.4902i	0.739378	+	1.28064i	−0.213397	+	0.976965i	$0.568453\pi$
$858$	6.64908	−	3.76168i	0.226996	−	0.128422i
$859$	22.6834	−	39.2888i	0.773947	−	1.34052i	−0.161438	−	0.986883i	$-0.551613\pi$
$859$	22.6834	−	39.2888i	0.773947	−	1.34052i	0.935385	−	0.353632i	$-0.115054\pi$
$860$	5.22877	−	9.05649i	0.178299	−	0.308824i
$861$	1.91307	+	33.3793i	0.0651973	+	1.13756i
$862$	8.65171	+	14.9852i	0.294678	+	0.510398i
$863$	−6.76755	+	11.7217i	−0.230370	+	0.399012i	−0.957917	−	0.287045i	$-0.907327\pi$
$863$	−6.76755	+	11.7217i	−0.230370	+	0.399012i	0.727547	+	0.686058i	$0.240660\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−5.03334	+	8.71799i	−0.171139	+	0.296421i
$866$	−10.1803	+	17.6328i	−0.345941	+	0.599187i
$867$	8.38153	+	14.5172i	0.284652	+	0.493031i
$868$	−9.92400	+	6.51394i	−0.336843	+	0.221098i
$869$	−15.1862	+	26.3032i	−0.515155	+	0.892275i
$870$	2.27123	−	3.93389i	0.0770021	−	0.133371i
$871$	−0.105930	+	12.1087i	−0.00358932	+	0.410288i
$872$	5.50000	+	9.52628i	0.186254	+	0.322601i
$873$	0.698602	+	1.21001i	0.0236441	+	0.0409528i
$874$	15.0303	−	26.0332i	0.508407	−	0.880587i
$875$	23.9247	−	15.7038i	0.808803	−	0.530884i
$876$	16.1867			0.546899
$877$	19.4218			0.655828			0.327914	−	0.944708i	$-0.393654\pi$
$877$	19.4218			0.655828			0.327914	+	0.944708i	$0.393654\pi$
$878$	2.02199	−	3.50219i	0.0682389	−	0.118193i
$879$	−8.74075	−	15.1394i	−0.294818	−	0.510640i
$880$	−2.76031			−0.0930499
$881$	−2.77059	+	4.79881i	−0.0933437	+	0.161676i	−0.908916	−	0.416979i	$-0.863089\pi$
$881$	−2.77059	+	4.79881i	−0.0933437	+	0.161676i	0.815572	+	0.578655i	$0.196422\pi$
$882$	6.95416	−	0.799757i	0.234159	−	0.0269292i
$883$	51.6940			1.73964			0.869821	−	0.493367i	$-0.164234\pi$
$883$	51.6940			1.73964			0.869821	+	0.493367i	$0.164234\pi$
$884$	1.52753	−	0.864193i	0.0513765	−	0.0290660i
$885$	−5.96029	−	10.3235i	−0.200353	−	0.347021i
$886$	20.2185			0.679253
$887$	1.77418	+	3.07298i	0.0595713	+	0.103181i	0.894273	−	0.447522i	$-0.147693\pi$
$887$	1.77418	+	3.07298i	0.0595713	+	0.103181i	−0.834702	+	0.550702i	$0.814360\pi$
$888$	−0.578756	−	1.00243i	−0.0194218	−	0.0336395i
$889$	−0.785113	−	13.6987i	−0.0263318	−	0.459438i
$890$	−6.12122	−	10.6023i	−0.205184	−	0.355389i
$891$	2.11879			0.0709821
$892$	9.58013	+	16.5933i	0.320767	+	0.555584i
$893$	25.0155	−	43.3281i	0.837111	−	1.44992i
$894$	−11.6820	−	20.2338i	−0.390704	−	0.676720i
$895$	12.4746	−	21.6066i	0.416979	−	0.722229i
$896$	2.36323	+	1.18960i	0.0789499	+	0.0397418i
$897$	15.0303	−	8.50330i	0.501847	−	0.283917i
$898$	19.8059	−	34.3047i	0.660930	−	1.14476i
$899$	15.6443			0.521766
$900$	−3.30278			−0.110093
$901$	4.17700			0.139156
$902$	−26.7749			−0.891507
$903$	−18.9699	−	9.54908i	−0.631279	−	0.317773i
$904$	−3.56552	−	6.17566i	−0.118587	−	0.205399i
$905$	8.53135	−	14.7767i	0.283592	−	0.491195i
$906$	2.93692	−	5.08689i	0.0975726	−	0.169001i
$907$	−43.6906			−1.45072			−0.725362	−	0.688368i	$-0.758327\pi$
$907$	−43.6906			−1.45072			−0.725362	+	0.688368i	$0.758327\pi$
$908$	0.591256	+	1.02409i	0.0196215	+	0.0339855i
$909$	−6.03449			−0.200151
$910$	−6.72835	−	10.4488i	−0.223043	−	0.346373i
$911$	−5.97013			−0.197799			−0.0988996	−	0.995097i	$-0.531532\pi$
$911$	−5.97013			−0.197799			−0.0988996	+	0.995097i	$0.531532\pi$
$912$	3.13815	+	5.43544i	0.103915	+	0.179985i
$913$	7.38771			0.244498
$914$	−3.32371	+	5.75683i	−0.109939	+	0.190419i
$915$	−6.63414	+	11.4907i	−0.219318	+	0.379870i
$916$	7.51599	+	13.0181i	0.248335	+	0.430130i
$917$	−1.22075	−	21.2997i	−0.0403127	−	0.703376i
$918$	0.486762			0.0160655
$919$	−57.6579			−1.90196			−0.950980	−	0.309254i	$-0.899921\pi$
$919$	−57.6579			−1.90196			−0.950980	+	0.309254i	$0.899921\pi$
$920$	−6.23969			−0.205717
$921$	−12.0673			−0.397631
$922$	10.2371	−	17.7311i	0.337140	−	0.583943i
$923$	9.20985	−	5.21042i	0.303146	−	0.171503i
$924$	0.320759	+	5.59660i	0.0105522	+	0.184115i
$925$	−1.91150	+	3.31081i	−0.0628497	+	0.108859i
$926$	8.63340	+	14.9535i	0.283711	+	0.491402i
$927$	5.64770	−	9.78210i	0.185495	−	0.321286i
$928$	−1.74338	−	3.01962i	−0.0572293	−	0.0991240i
$929$	4.11918			0.135146			0.0675729	−	0.997714i	$-0.478474\pi$
$929$	4.11918			0.135146			0.0675729	+	0.997714i	$0.478474\pi$
$930$	2.92262	+	5.06213i	0.0958366	+	0.165994i
$931$	−17.4762	+	40.3087i	−0.572759	+	1.32106i
$932$	−2.59706	−	4.49824i	−0.0850695	−	0.147345i
$933$	0.755881	+	1.30923i	0.0247464	+	0.0428621i
$934$	8.75844			0.286585
$935$	−0.671807	−	1.16360i	−0.0219704	−	0.0380539i
$936$	−0.0315412	+	3.60541i	−0.00103096	+	0.117847i
$937$	22.6483			0.739888			0.369944	−	0.929054i	$-0.379377\pi$
$937$	22.6483			0.739888			0.369944	+	0.929054i	$0.379377\pi$
$938$	−7.93686	−	3.99526i	−0.259148	−	0.130450i
$939$	−0.862908	+	1.49460i	−0.0281599	+	0.0487744i
$940$	−10.3850			−0.338720
$941$	10.0011	+	17.3223i	0.326025	+	0.564692i	0.981719	−	0.190334i	$-0.0609572\pi$
$941$	10.0011	+	17.3223i	0.326025	+	0.564692i	−0.655694	+	0.755027i	$0.727624\pi$
$942$	3.12248	−	5.40829i	0.101736	−	0.176212i
$943$	−60.5249			−1.97096
$944$	−9.15014			−0.297812
$945$	−0.197224	−	3.44117i	−0.00641571	−	0.111941i
$946$	8.50388	−	14.7292i	0.276485	−	0.478886i
$947$	−3.76592	−	6.52276i	−0.122376	−	0.211961i	0.798328	−	0.602222i	$-0.205718\pi$
$947$	−3.76592	−	6.52276i	−0.122376	−	0.211961i	−0.920704	+	0.390261i	$0.872385\pi$
$948$	−7.16738	−	12.4143i	−0.232786	−	0.403197i
$949$	−50.7964	+	28.7378i	−1.64892	+	0.932868i
$950$	10.3646	−	17.9520i	0.336272	−	0.582441i
$951$	−10.6520	+	18.4499i	−0.345416	+	0.598278i
$952$	0.0736899	+	1.28574i	0.00238830	+	0.0416711i
$953$	−2.65075	−	4.59123i	−0.0858661	−	0.148724i	0.819894	−	0.572516i	$-0.194032\pi$
$953$	−2.65075	−	4.59123i	−0.0858661	−	0.148724i	−0.905760	+	0.423791i	$0.860699\pi$
$954$	−4.29060	+	7.43153i	−0.138913	+	0.240605i
$955$	−7.48371	+	12.9622i	−0.242167	+	0.419446i
$956$	−12.6989	+	21.9952i	−0.410713	+	0.711375i
$957$	3.69386	−	6.39795i	0.119405	−	0.206816i
$958$	−13.5126	−	23.4046i	−0.436573	−	0.756167i
$959$	−1.02817	−	17.9396i	−0.0332015	−	0.579299i
$960$	0.651388	−	1.12824i	0.0210235	−	0.0364137i
$961$	5.43448	−	9.41280i	0.175306	−	0.303639i
$962$	3.59593	+	2.11827i	0.115938	+	0.0682958i
$963$	7.01462	+	12.1497i	0.226043	+	0.391518i
$964$	5.92875	+	10.2689i	0.190952	+	0.330739i
$965$	−0.179979	+	0.311732i	−0.00579372	+	0.0100350i
$966$	0.725078	+	12.6512i	0.0233290	+	0.407045i
$967$	−7.46926			−0.240195			−0.120098	−	0.992762i	$-0.538321\pi$
$967$	−7.46926			−0.240195			−0.120098	+	0.992762i	$0.538321\pi$
$968$	6.51073			0.209263
$969$	−1.52753	+	2.64576i	−0.0490714	+	0.0849942i
$970$	0.910122	+	1.57638i	0.0292223	+	0.0506144i
$971$	−3.28791			−0.105514			−0.0527570	−	0.998607i	$-0.516801\pi$
$971$	−3.28791			−0.105514			−0.0527570	+	0.998607i	$0.516801\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	30.5103	+	15.3583i	0.978116	+	0.492364i
$974$	−21.9435			−0.703114
$975$	10.3646	−	5.86372i	0.331933	−	0.187789i
$976$	5.09231	+	8.82015i	0.163001	+	0.282326i
$977$	−0.832998			−0.0266500			−0.0133250	−	0.999911i	$-0.504242\pi$
$977$	−0.832998			−0.0266500			−0.0133250	+	0.999911i	$0.504242\pi$
$978$	−1.30383	−	2.25831i	−0.0416920	−	0.0722126i
$979$	−9.95535	−	17.2432i	−0.318174	−	0.551094i
$980$	9.05971	−	1.04190i	0.289402	−	0.0332824i
$981$	−5.50000	−	9.52628i	−0.175601	−	0.304151i
$982$	−14.1804			−0.452515
$983$	20.9860	+	36.3487i	0.669348	+	1.15934i	0.978087	+	0.208198i	$0.0667598\pi$
$983$	20.9860	+	36.3487i	0.669348	+	1.15934i	−0.308739	+	0.951147i	$0.599907\pi$
$984$	6.31845	−	10.9439i	0.201425	−	0.348878i
$985$	8.64459	+	14.9729i	0.275440	+	0.477075i
$986$	0.848612	−	1.46984i	0.0270253	−	0.0468092i
$987$	1.20677	+	21.0558i	0.0384120	+	0.670214i
$988$	−19.4980	−	11.4858i	−0.620314	−	0.365411i
$989$	19.2231	−	33.2954i	0.611259	−	1.05873i
$990$	2.76031			0.0877283
$991$	−51.9215			−1.64934			−0.824670	−	0.565614i	$-0.808639\pi$
$991$	−51.9215			−1.64934			−0.824670	+	0.565614i	$0.808639\pi$
$992$	4.48676			0.142455
$993$	16.4338			0.521511
$994$	0.444293	+	7.75204i	0.0140921	+	0.245880i
$995$	12.3906	+	21.4612i	0.392809	+	0.680364i
$996$	−1.74338	+	3.01962i	−0.0552411	+	0.0956805i
$997$	24.2587	−	42.0173i	0.768281	−	1.33070i	−0.170214	−	0.985407i	$-0.554446\pi$
$997$	24.2587	−	42.0173i	0.768281	−	1.33070i	0.938494	−	0.345294i	$-0.112221\pi$
$998$	29.4975			0.933728
$999$	0.578756	+	1.00243i	0.0183110	+	0.0317156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.d.373.4	yes	8
3.2	odd	2		1638.2.p.g.919.2		8
7.4	even	3		546.2.j.b.529.3	yes	8
13.3	even	3		546.2.j.b.289.3	✓	8
21.11	odd	6		1638.2.m.i.1621.1		8
39.29	odd	6		1638.2.m.i.289.1		8
91.81	even	3	inner	546.2.k.d.445.4	yes	8
273.263	odd	6		1638.2.p.g.991.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.3	✓	8	13.3	even	3
546.2.j.b.529.3	yes	8	7.4	even	3
546.2.k.d.373.4	yes	8	1.1	even	1	trivial
546.2.k.d.445.4	yes	8	91.81	even	3	inner
1638.2.m.i.289.1		8	39.29	odd	6
1638.2.m.i.1621.1		8	21.11	odd	6
1638.2.p.g.919.2		8	3.2	odd	2
1638.2.p.g.991.2		8	273.263	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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.30278 q^{10} +2.11879 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.0315412 - 3.60541i) q^{13} +(2.36323 + 1.18960i) q^{14} +(0.651388 - 1.12824i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.243381 - 0.421549i) q^{17} +(0.500000 + 0.866025i) q^{18} -6.27630 q^{19} +(0.651388 + 1.12824i) q^{20} +(2.21184 - 1.45181i) q^{21} +(1.05939 + 1.83493i) q^{22} +(2.39477 + 4.14786i) q^{23} -1.00000 q^{24} +(1.65139 + 2.86029i) q^{25} +(3.13815 - 1.77539i) q^{26} +1.00000 q^{27} +(0.151388 + 2.64142i) q^{28} +(1.74338 - 3.01962i) q^{29} +1.30278 q^{30} +(2.24338 + 3.88565i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.11879 q^{33} +0.486762 q^{34} +(-0.197224 - 3.44117i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.578756 + 1.00243i) q^{37} +(-3.13815 - 5.43544i) q^{38} +(0.0315412 - 3.60541i) q^{39} +(-0.651388 + 1.12824i) q^{40} +(-6.31845 + 10.9439i) q^{41} +(2.36323 + 1.18960i) q^{42} +(-4.01356 - 6.95169i) q^{43} +(-1.05939 + 1.83493i) q^{44} +(0.651388 - 1.12824i) q^{45} +(-2.39477 + 4.14786i) q^{46} +(-3.98570 + 6.90344i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(2.78447 - 6.42236i) q^{49} +(-1.65139 + 2.86029i) q^{50} +(0.243381 - 0.421549i) q^{51} +(3.10661 + 1.83002i) q^{52} +(4.29060 + 7.43153i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.38015 - 2.39050i) q^{55} +(-2.21184 + 1.45181i) q^{56} -6.27630 q^{57} +3.48676 q^{58} +(4.57507 - 7.92425i) q^{59} +(0.651388 + 1.12824i) q^{60} -10.1846 q^{61} +(-2.24338 + 3.88565i) q^{62} +(2.21184 - 1.45181i) q^{63} +1.00000 q^{64} +(-4.04721 - 2.38411i) q^{65} +(1.05939 + 1.83493i) q^{66} -3.35848 q^{67} +(0.243381 + 0.421549i) q^{68} +(2.39477 + 4.14786i) q^{69} +(2.88153 - 1.89139i) q^{70} +(1.46740 + 2.54161i) q^{71} -1.00000 q^{72} +(-8.09337 - 14.0181i) q^{73} +(-0.578756 + 1.00243i) q^{74} +(1.65139 + 2.86029i) q^{75} +(3.13815 - 5.43544i) q^{76} +(4.68642 - 3.07609i) q^{77} +(3.13815 - 1.77539i) q^{78} +(-7.16738 + 12.4143i) q^{79} -1.30278 q^{80} +1.00000 q^{81} -12.6369 q^{82} +3.48676 q^{83} +(0.151388 + 2.64142i) q^{84} +(-0.317071 - 0.549183i) q^{85} +(4.01356 - 6.95169i) q^{86} +(1.74338 - 3.01962i) q^{87} -2.11879 q^{88} +(-4.69860 - 8.13822i) q^{89} +1.30278 q^{90} +(-5.16463 - 8.02039i) q^{91} -4.78954 q^{92} +(2.24338 + 3.88565i) q^{93} -7.97141 q^{94} +(-4.08831 + 7.08115i) q^{95} +(0.500000 - 0.866025i) q^{96} +(0.698602 + 1.21001i) q^{97} +(6.95416 - 0.799757i) q^{98} +2.11879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q + 4 q^{2} + 8 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} + 4 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 6 q^{28} + 6 q^{29} - 4 q^{30} + 10 q^{31} + 4 q^{32} + 4 q^{33} - 12 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{37} - 2 q^{38} + 7 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} - 2 q^{45} - 4 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} - 5 q^{52} + 3 q^{53} + 4 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} + 12 q^{58} - 2 q^{60} + 8 q^{61} - 10 q^{62} + 3 q^{63} + 8 q^{64} - 9 q^{65} + 2 q^{66} + 14 q^{67} - 6 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} - 8 q^{72} - 19 q^{73} + 12 q^{74} + 6 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} - 12 q^{82} + 12 q^{83} - 6 q^{84} - 3 q^{85} + 4 q^{86} + 6 q^{87} - 4 q^{88} - 7 q^{89} - 4 q^{90} - 50 q^{91} - 8 q^{92} + 10 q^{93} - 34 q^{94} - 12 q^{95} + 4 q^{96} - 25 q^{97} + 34 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^3 - 4 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 + 4 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 4 * q^33 - 12 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^37 - 2 * q^38 + 7 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 - 2 * q^45 - 4 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 - 5 * q^52 + 3 * q^53 + 4 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 + 12 * q^58 - 2 * q^60 + 8 * q^61 - 10 * q^62 + 3 * q^63 + 8 * q^64 - 9 * q^65 + 2 * q^66 + 14 * q^67 - 6 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 - 8 * q^72 - 19 * q^73 + 12 * q^74 + 6 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 - 12 * q^82 + 12 * q^83 - 6 * q^84 - 3 * q^85 + 4 * q^86 + 6 * q^87 - 4 * q^88 - 7 * q^89 - 4 * q^90 - 50 * q^91 - 8 * q^92 + 10 * q^93 - 34 * q^94 - 12 * q^95 + 4 * q^96 - 25 * q^97 + 34 * q^98 + 4 * q^99

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