LMFDB - Embedded newform 546.2.bk.b.415.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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, 4, 3]))

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.3
Root			$-2.23871 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.415
Dual form			546.2.bk.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95878 + 1.13090i) q^{5} +1.00000i q^{6} +(2.41839 - 1.07303i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95878 + 1.13090i) q^{5} +1.00000i q^{6} +(2.41839 - 1.07303i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.13090 - 1.95878i) q^{10} +(1.09275 - 0.630901i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.26180 + 3.37755i) q^{13} +(-2.63090 - 0.279927i) q^{14} -2.26180i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.188776 - 0.326969i) q^{17} +(0.866025 - 0.500000i) q^{18} +(6.71612 + 3.87755i) q^{19} +2.26180i q^{20} +(-2.13846 - 1.55787i) q^{21} -1.26180 q^{22} +(-2.24665 + 3.89131i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.0578747 + 0.100242i) q^{25} +(2.78153 - 2.29414i) q^{26} +1.00000 q^{27} +(2.13846 + 1.55787i) q^{28} -2.40786 q^{29} +(-1.13090 + 1.95878i) q^{30} +(3.46410 - 2.00000i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09275 - 0.630901i) q^{33} +0.377552i q^{34} +(5.95058 + 0.633140i) q^{35} -1.00000 q^{36} +(2.92505 + 1.68878i) q^{37} +(-3.87755 - 6.71612i) q^{38} +(3.55595 - 0.596023i) q^{39} +(1.13090 - 1.95878i) q^{40} -9.90116i q^{41} +(1.07303 + 2.41839i) q^{42} +8.75510 q^{43} +(1.09275 + 0.630901i) q^{44} +(-1.95878 + 1.13090i) q^{45} +(3.89131 - 2.24665i) q^{46} +(-2.85105 - 1.64605i) q^{47} +1.00000 q^{48} +(4.69723 - 5.18999i) q^{49} -0.115749i q^{50} +(-0.188776 + 0.326969i) q^{51} +(-3.55595 + 0.596023i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(-0.866025 - 0.500000i) q^{54} +2.85395 q^{55} +(-1.07303 - 2.41839i) q^{56} -7.75510i q^{57} +(2.08526 + 1.20393i) q^{58} +(-4.04404 + 2.33483i) q^{59} +(1.95878 - 1.13090i) q^{60} +(4.45058 - 7.70863i) q^{61} -4.00000 q^{62} +(-0.279927 + 2.63090i) q^{63} -1.00000 q^{64} +(-6.29127 + 5.18890i) q^{65} +(0.630901 + 1.09275i) q^{66} +(1.11900 - 0.646053i) q^{67} +(0.188776 - 0.326969i) q^{68} +4.49330 q^{69} +(-4.83678 - 3.52360i) q^{70} +4.11575i q^{71} +(0.866025 + 0.500000i) q^{72} +(-8.26232 + 4.77026i) q^{73} +(-1.68878 - 2.92505i) q^{74} +(0.0578747 - 0.100242i) q^{75} +7.75510i q^{76} +(1.96573 - 2.69832i) q^{77} +(-3.37755 - 1.26180i) q^{78} +(3.14605 - 5.44912i) q^{79} +(-1.95878 + 1.13090i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.95058 + 8.57465i) q^{82} -6.39446i q^{83} +(0.279927 - 2.63090i) q^{84} -0.853947i q^{85} +(-7.58214 - 4.37755i) q^{86} +(1.20393 + 2.08526i) q^{87} +(-0.630901 - 1.09275i) q^{88} +(9.85325 + 5.68878i) q^{89} +2.26180 q^{90} +(0.572671 + 9.52219i) q^{91} -4.49330 q^{92} +(-3.46410 - 2.00000i) q^{93} +(1.64605 + 2.85105i) q^{94} +(8.77026 + 15.1905i) q^{95} +(-0.866025 - 0.500000i) q^{96} +8.03030i q^{97} +(-6.66292 + 2.14605i) q^{98} +1.26180i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43} + 12 q^{48} - 18 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{53} + 48 q^{55} - 6 q^{56} + 6 q^{61} - 48 q^{62} - 12 q^{64} - 12 q^{65} - 6 q^{66} - 18 q^{68} - 6 q^{75} - 24 q^{77} + 24 q^{79} - 6 q^{81} - 12 q^{82} - 6 q^{87} + 6 q^{88} - 24 q^{91} + 6 q^{94} + 24 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 + 6 * q^12 + 12 * q^13 - 18 * q^14 - 6 * q^16 + 18 * q^17 + 12 * q^22 - 6 * q^25 + 12 * q^27 + 12 * q^29 + 24 * q^35 - 12 * q^36 - 6 * q^38 - 6 * q^39 + 6 * q^42 + 24 * q^43 + 12 * q^48 - 18 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^53 + 48 * q^55 - 6 * q^56 + 6 * q^61 - 48 * q^62 - 12 * q^64 - 12 * q^65 - 6 * q^66 - 18 * q^68 - 6 * q^75 - 24 * q^77 + 24 * q^79 - 6 * q^81 - 12 * q^82 - 6 * q^87 + 6 * q^88 - 24 * q^91 + 6 * q^94 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.95878	+	1.13090i	0.875992	+	0.505754i	0.869335	−	0.494223i	$-0.164548\pi$
$5$	1.95878	+	1.13090i	0.875992	+	0.505754i	0.00665735	+	0.999978i	$0.497881\pi$
$6$			1.00000i			0.408248i
$7$	2.41839	−	1.07303i	0.914066	−	0.405566i
$7$	2.41839	−	1.07303i	0.914066	−	0.405566i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.13090	−	1.95878i	−0.357622	−	0.619420i
$11$	1.09275	−	0.630901i	0.329477	−	0.190224i	−0.326132	−	0.945324i	$-0.605745\pi$
$11$	1.09275	−	0.630901i	0.329477	−	0.190224i	0.655609	+	0.755101i	$0.272412\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.26180	+	3.37755i	−0.349961	+	0.936764i
$13$	−1.26180	+	3.37755i	−0.349961	+	0.936764i
$14$	−2.63090	−	0.279927i	−0.703138	−	0.0748137i
$15$		−	2.26180i		−	0.583995i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.188776	−	0.326969i	−0.0457849	−	0.0793017i	0.842225	−	0.539127i	$-0.181246\pi$
$17$	−0.188776	−	0.326969i	−0.0457849	−	0.0793017i	−0.888010	+	0.459825i	$0.847912\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	6.71612	+	3.87755i	1.54078	+	0.889571i	0.998790	+	0.0491885i	$0.0156635\pi$
$19$	6.71612	+	3.87755i	1.54078	+	0.889571i	0.541993	+	0.840383i	$0.317670\pi$
$20$			2.26180i			0.505754i
$21$	−2.13846	−	1.55787i	−0.466651	−	0.339956i
$22$	−1.26180			−0.269017
$23$	−2.24665	+	3.89131i	−0.468459	+	0.811395i	−0.999350	−	0.0360452i	$-0.988524\pi$
$23$	−2.24665	+	3.89131i	−0.468459	+	0.811395i	0.530891	+	0.847440i	$0.321857\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.0578747	+	0.100242i	0.0115749	+	0.0200484i
$26$	2.78153	−	2.29414i	0.545503	−	0.449919i
$27$	1.00000			0.192450
$28$	2.13846	+	1.55787i	0.404132	+	0.294411i
$29$	−2.40786			−0.447127			−0.223564	−	0.974689i	$-0.571769\pi$
$29$	−2.40786			−0.447127			−0.223564	+	0.974689i	$0.571769\pi$
$30$	−1.13090	+	1.95878i	−0.206473	+	0.357622i
$31$	3.46410	−	2.00000i	0.622171	−	0.359211i	−0.155543	−	0.987829i	$-0.549713\pi$
$31$	3.46410	−	2.00000i	0.622171	−	0.359211i	0.777714	+	0.628619i	$0.216379\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.09275	−	0.630901i	−0.190224	−	0.109826i
$34$			0.377552i			0.0647496i
$35$	5.95058	+	0.633140i	1.00583	+	0.107020i
$36$	−1.00000			−0.166667
$37$	2.92505	+	1.68878i	0.480875	+	0.277633i	0.720781	−	0.693163i	$-0.243783\pi$
$37$	2.92505	+	1.68878i	0.480875	+	0.277633i	−0.239906	+	0.970796i	$0.577117\pi$
$38$	−3.87755	−	6.71612i	−0.629022	−	1.08950i
$39$	3.55595	−	0.596023i	0.569407	−	0.0954401i
$40$	1.13090	−	1.95878i	0.178811	−	0.309710i
$41$		−	9.90116i		−	1.54630i	−0.634223	−	0.773150i	$-0.718680\pi$
$41$		−	9.90116i		−	1.54630i	0.634223	−	0.773150i	$-0.281320\pi$
$42$	1.07303	+	2.41839i	0.165572	+	0.373166i
$43$	8.75510			1.33514			0.667570	−	0.744547i	$-0.267334\pi$
$43$	8.75510			1.33514			0.667570	+	0.744547i	$0.267334\pi$
$44$	1.09275	+	0.630901i	0.164739	+	0.0951119i
$45$	−1.95878	+	1.13090i	−0.291997	+	0.168585i
$46$	3.89131	−	2.24665i	0.573743	−	0.331251i
$47$	−2.85105	−	1.64605i	−0.415868	−	0.240101i	0.277440	−	0.960743i	$-0.410514\pi$
$47$	−2.85105	−	1.64605i	−0.415868	−	0.240101i	−0.693308	+	0.720642i	$0.743847\pi$
$48$	1.00000			0.144338
$49$	4.69723	−	5.18999i	0.671033	−	0.741428i
$50$		−	0.115749i		−	0.0163694i
$51$	−0.188776	+	0.326969i	−0.0264339	+	0.0457849i
$52$	−3.55595	+	0.596023i	−0.493121	+	0.0826535i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	2.85395			0.384826
$56$	−1.07303	−	2.41839i	−0.143389	−	0.323171i
$57$		−	7.75510i		−	1.02719i
$58$	2.08526	+	1.20393i	0.273809	+	0.158083i
$59$	−4.04404	+	2.33483i	−0.526489	+	0.303969i	−0.739586	−	0.673062i	$-0.764979\pi$
$59$	−4.04404	+	2.33483i	−0.526489	+	0.303969i	0.213096	+	0.977031i	$0.431645\pi$
$60$	1.95878	−	1.13090i	0.252877	−	0.145999i
$61$	4.45058	−	7.70863i	0.569838	−	0.986989i	−0.426743	−	0.904373i	$-0.640339\pi$
$61$	4.45058	−	7.70863i	0.569838	−	0.986989i	0.996581	−	0.0826158i	$-0.0263274\pi$
$62$	−4.00000			−0.508001
$63$	−0.279927	+	2.63090i	−0.0352675	+	0.331462i
$64$	−1.00000			−0.125000
$65$	−6.29127	+	5.18890i	−0.780336	+	0.643604i
$66$	0.630901	+	1.09275i	0.0776586	+	0.134509i
$67$	1.11900	−	0.646053i	0.136707	−	0.0789279i	−0.430087	−	0.902788i	$-0.641517\pi$
$67$	1.11900	−	0.646053i	0.136707	−	0.0789279i	0.566794	+	0.823860i	$0.308184\pi$
$68$	0.188776	−	0.326969i	0.0228924	−	0.0396509i
$69$	4.49330			0.540930
$70$	−4.83678	−	3.52360i	−0.578106	−	0.421151i
$71$			4.11575i			0.488450i	0.969719	+	0.244225i	$0.0785335\pi$
$71$			4.11575i			0.488450i	−0.969719	+	0.244225i	$0.921467\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−8.26232	+	4.77026i	−0.967032	+	0.558316i	−0.898330	−	0.439321i	$-0.855219\pi$
$73$	−8.26232	+	4.77026i	−0.967032	+	0.558316i	−0.0687018	+	0.997637i	$0.521886\pi$
$74$	−1.68878	−	2.92505i	−0.196316	−	0.340030i
$75$	0.0578747	−	0.100242i	0.00668279	−	0.0115749i
$76$			7.75510i			0.889571i
$77$	1.96573	−	2.69832i	0.224016	−	0.307502i
$78$	−3.37755	−	1.26180i	−0.382432	−	0.142871i
$79$	3.14605	−	5.44912i	0.353959	−	0.613074i	−0.632981	−	0.774168i	$-0.718169\pi$
$79$	3.14605	−	5.44912i	0.353959	−	0.613074i	0.986939	+	0.161093i	$0.0515020\pi$
$80$	−1.95878	+	1.13090i	−0.218998	+	0.126439i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.95058	+	8.57465i	−0.546700	+	0.946912i
$83$		−	6.39446i		−	0.701883i	−0.936397	−	0.350941i	$-0.885862\pi$
$83$		−	6.39446i		−	0.701883i	0.936397	−	0.350941i	$-0.114138\pi$
$84$	0.279927	−	2.63090i	0.0305426	−	0.287055i
$85$		−	0.853947i		−	0.0926236i
$86$	−7.58214	−	4.37755i	−0.817603	−	0.472044i
$87$	1.20393	+	2.08526i	0.129075	+	0.223564i
$88$	−0.630901	−	1.09275i	−0.0672543	−	0.116488i
$89$	9.85325	+	5.68878i	1.04444	+	0.603009i	0.921088	−	0.389354i	$-0.127302\pi$
$89$	9.85325	+	5.68878i	1.04444	+	0.603009i	0.123354	+	0.992363i	$0.460635\pi$
$90$	2.26180			0.238415
$91$	0.572671	+	9.52219i	0.0600322	+	0.998196i
$92$	−4.49330			−0.468459
$93$	−3.46410	−	2.00000i	−0.359211	−	0.207390i
$94$	1.64605	+	2.85105i	0.169777	+	0.294063i
$95$	8.77026	+	15.1905i	0.899809	+	1.55852i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$			8.03030i			0.815354i	0.913126	+	0.407677i	$0.133661\pi$
$97$			8.03030i			0.815354i	−0.913126	+	0.407677i	$0.866339\pi$
$98$	−6.66292	+	2.14605i	−0.673056	+	0.216784i
$99$			1.26180i			0.126816i
$100$	−0.0578747	+	0.100242i	−0.00578747	+	0.0100242i
$101$	−5.81968	−	10.0800i	−0.579079	−	1.00300i	−0.995585	−	0.0938620i	$-0.970079\pi$
$101$	−5.81968	−	10.0800i	−0.579079	−	1.00300i	0.416506	−	0.909133i	$-0.363255\pi$
$102$	0.326969	−	0.188776i	0.0323748	−	0.0186916i
$103$	−6.23150	+	10.7933i	−0.614008	+	1.06349i	0.376550	+	0.926396i	$0.377110\pi$
$103$	−6.23150	+	10.7933i	−0.614008	+	1.06349i	−0.990558	+	0.137096i	$0.956223\pi$
$104$	3.37755	+	1.26180i	0.331196	+	0.123730i
$105$	−2.42697	−	5.46992i	−0.236848	−	0.533810i
$106$			3.00000i			0.291386i
$107$	−8.90116	+	15.4173i	−0.860507	+	1.49044i	0.0109328	+	0.999940i	$0.496520\pi$
$107$	−8.90116	+	15.4173i	−0.860507	+	1.49044i	−0.871440	+	0.490502i	$0.836813\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−2.83944	+	1.63935i	−0.271969	+	0.157022i	−0.629782	−	0.776772i	$-0.716856\pi$
$109$	−2.83944	+	1.63935i	−0.271969	+	0.157022i	0.357813	+	0.933793i	$0.383523\pi$
$110$	−2.47159	−	1.42697i	−0.235657	−	0.136057i
$111$		−	3.37755i		−	0.320583i
$112$	−0.279927	+	2.63090i	−0.0264506	+	0.248597i
$113$	1.32241			0.124402			0.0622009	−	0.998064i	$-0.480188\pi$
$113$	1.32241			0.124402			0.0622009	+	0.998064i	$0.480188\pi$
$114$	−3.87755	+	6.71612i	−0.363166	+	0.629022i
$115$	−8.80138	+	5.08148i	−0.820733	+	0.473850i
$116$	−1.20393	−	2.08526i	−0.111782	−	0.193612i
$117$	−2.29414	−	2.78153i	−0.212094	−	0.257152i
$118$	4.66966			0.429877
$119$	−0.807380	−	0.588178i	−0.0740124	−	0.0539182i
$120$	−2.26180			−0.206473
$121$	−4.70393	+	8.14744i	−0.427630	+	0.740677i
$122$	−7.70863	+	4.45058i	−0.697906	+	0.402936i
$123$	−8.57465	+	4.95058i	−0.773150	+	0.446379i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$		−	11.0472i		−	0.988092i
$126$	1.55787	−	2.13846i	0.138787	−	0.190509i
$127$	−16.3642			−1.45208			−0.726042	−	0.687650i	$-0.758642\pi$
$127$	−16.3642			−1.45208			−0.726042	+	0.687650i	$0.758642\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.37755	−	7.58214i	−0.385422	−	0.667570i
$130$	8.04285	−	1.34809i	0.705404	−	0.118235i
$131$	5.71908	−	9.90574i	0.499678	−	0.865468i	−0.500322	−	0.865840i	$-0.666785\pi$
$131$	5.71908	−	9.90574i	0.499678	−	0.865468i	1.00000		0.000371455i	$0.000118238\pi$
$132$		−	1.26180i		−	0.109826i
$133$	20.4029	+	2.17086i	1.76916	+	0.188238i
$134$	−1.29211			−0.111621
$135$	1.95878	+	1.13090i	0.168585	+	0.0973325i
$136$	−0.326969	+	0.188776i	−0.0280374	+	0.0161874i
$137$	−9.65276	+	5.57303i	−0.824691	+	0.476136i	−0.852032	−	0.523490i	$-0.824630\pi$
$137$	−9.65276	+	5.57303i	−0.824691	+	0.476136i	0.0273402	+	0.999626i	$0.491296\pi$
$138$	−3.89131	−	2.24665i	−0.331251	−	0.191248i
$139$	−2.49330			−0.211479			−0.105740	−	0.994394i	$-0.533721\pi$
$139$	−2.49330			−0.211479			−0.105740	+	0.994394i	$0.533721\pi$
$140$	2.42697	+	5.46992i	0.205117	+	0.462293i
$141$			3.29211i			0.277245i
$142$	2.05787	−	3.56434i	0.172693	−	0.299113i
$143$	0.752063	+	4.48690i	0.0628907	+	0.375214i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.71645	−	2.72305i	−0.391680	−	0.226137i
$146$	9.54051			0.789578
$147$	−6.84328	−	1.47292i	−0.564424	−	0.121485i
$148$			3.37755i			0.277633i
$149$	0.0262436	+	0.0151517i	0.00214996	+	0.00124128i	0.501075	−	0.865404i	$-0.332938\pi$
$149$	0.0262436	+	0.0151517i	0.00214996	+	0.00124128i	−0.498925	+	0.866645i	$0.666272\pi$
$150$	−0.100242	+	0.0578747i	−0.00818472	+	0.00472545i
$151$	3.73171	−	2.15451i	0.303683	−	0.175331i	−0.340413	−	0.940276i	$-0.610567\pi$
$151$	3.73171	−	2.15451i	0.303683	−	0.175331i	0.644096	+	0.764945i	$0.277234\pi$
$152$	3.87755	−	6.71612i	0.314511	−	0.544749i
$153$	0.377552			0.0305232
$154$	−3.05153	+	1.35395i	−0.245899	+	0.109104i
$155$	9.04721			0.726689
$156$	2.29414	+	2.78153i	0.183679	+	0.222701i
$157$	−11.3557	−	19.6687i	−0.906284	−	1.56973i	−0.819185	−	0.573530i	$-0.805574\pi$
$157$	−11.3557	−	19.6687i	−0.906284	−	1.56973i	−0.0870987	−	0.996200i	$-0.527760\pi$
$158$	−5.44912	+	3.14605i	−0.433509	+	0.250287i
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$	2.26180			0.178811
$161$	−1.25780	+	11.8214i	−0.0991283	+	0.931659i
$162$			1.00000i			0.0785674i
$163$	10.7455	+	6.20393i	0.841654	+	0.485929i	0.857826	−	0.513940i	$-0.171815\pi$
$163$	10.7455	+	6.20393i	0.841654	+	0.485929i	−0.0161722	+	0.999869i	$0.505148\pi$
$164$	8.57465	−	4.95058i	0.669568	−	0.386575i
$165$	−1.42697	−	2.47159i	−0.111090	−	0.192413i
$166$	−3.19723	+	5.53776i	−0.248153	+	0.429814i
$167$		−	24.6732i		−	1.90927i	−0.297784	−	0.954633i	$-0.596247\pi$
$167$		−	24.6732i		−	1.90927i	0.297784	−	0.954633i	$-0.403753\pi$
$168$	−1.55787	+	2.13846i	−0.120193	+	0.164986i
$169$	−9.81571	−	8.52360i	−0.755055	−	0.655662i
$170$	−0.426974	+	0.739540i	−0.0327474	+	0.0567201i
$171$	−6.71612	+	3.87755i	−0.513594	+	0.296524i
$172$	4.37755	+	7.58214i	0.333785	+	0.578133i
$173$	−11.9893	+	20.7661i	−0.911532	+	1.57882i	−0.0996316	+	0.995024i	$0.531766\pi$
$173$	−11.9893	+	20.7661i	−0.911532	+	1.57882i	−0.811901	+	0.583796i	$0.801567\pi$
$174$		−	2.40786i		−	0.182539i
$175$	0.247526	+	0.180323i	0.0187112	+	0.0136311i
$176$			1.26180i			0.0951119i
$177$	4.04404	+	2.33483i	0.303969	+	0.175496i
$178$	−5.68878	−	9.85325i	−0.426392	−	0.738532i
$179$	2.85395	+	4.94318i	0.213314	+	0.369471i	0.952750	−	0.303756i	$-0.0982409\pi$
$179$	2.85395	+	4.94318i	0.213314	+	0.369471i	−0.739436	+	0.673227i	$0.764908\pi$
$180$	−1.95878	−	1.13090i	−0.145999	−	0.0842924i
$181$	−16.6697			−1.23905			−0.619523	−	0.784979i	$-0.712674\pi$
$181$	−16.6697			−1.23905			−0.619523	+	0.784979i	$0.712674\pi$
$182$	4.26515	−	8.53279i	0.316154	−	0.632493i
$183$	−8.90116			−0.657992
$184$	3.89131	+	2.24665i	0.286871	+	0.165625i
$185$	3.81968	+	6.61587i	0.280828	+	0.486409i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−0.412571	−	0.238198i	−0.0301702	−	0.0174187i
$188$		−	3.29211i		−	0.240101i
$189$	2.41839	−	1.07303i	0.175912	−	0.0780512i
$190$		−	17.5405i		−	1.27252i
$191$	−3.63935	+	6.30355i	−0.263334	+	0.456109i	−0.967126	−	0.254298i	$-0.918156\pi$
$191$	−3.63935	+	6.30355i	−0.263334	+	0.456109i	0.703791	+	0.710407i	$0.251489\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−14.9900	+	8.65451i	−1.07901	+	0.622965i	−0.930628	−	0.365966i	$-0.880739\pi$
$193$	−14.9900	+	8.65451i	−1.07901	+	0.622965i	−0.148379	+	0.988931i	$0.547405\pi$
$194$	4.01515	−	6.95445i	0.288271	−	0.499300i
$195$	7.63935	+	2.85395i	0.547065	+	0.204375i
$196$	6.84328	+	1.47292i	0.488806	+	0.105209i
$197$		−	3.21459i		−	0.229030i	−0.993422	−	0.114515i	$-0.963469\pi$
$197$		−	3.21459i		−	0.229030i	0.993422	−	0.114515i	$-0.0365314\pi$
$198$	0.630901	−	1.09275i	0.0448362	−	0.0776586i
$199$	−5.85173	−	10.1355i	−0.414818	−	0.718487i	0.580591	−	0.814195i	$-0.302822\pi$
$199$	−5.85173	−	10.1355i	−0.414818	−	0.718487i	−0.995409	+	0.0957088i	$0.969488\pi$
$200$	0.100242	−	0.0578747i	0.00708817	−	0.00409236i
$201$	−1.11900	−	0.646053i	−0.0789279	−	0.0455691i
$202$			11.6394i			0.818942i
$203$	−5.82313	+	2.58369i	−0.408704	+	0.181340i
$204$	−0.377552			−0.0264339
$205$	11.1972	−	19.3942i	0.782048	−	1.35455i
$206$	10.7933	−	6.23150i	0.752003	−	0.434169i
$207$	−2.24665	−	3.89131i	−0.156153	−	0.270465i
$208$	−2.29414	−	2.78153i	−0.159070	−	0.192864i
$209$	9.78541			0.676871
$210$	−0.633140	+	5.95058i	−0.0436908	+	0.410629i
$211$	−8.06411			−0.555157			−0.277578	−	0.960703i	$-0.589532\pi$
$211$	−8.06411			−0.555157			−0.277578	+	0.960703i	$0.589532\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	3.56434	−	2.05787i	0.244225	−	0.141003i
$214$	15.4173	−	8.90116i	1.05390	−	0.608471i
$215$	17.1493	+	9.90116i	1.16957	+	0.675253i
$216$		−	1.00000i		−	0.0680414i
$217$	6.23150	−	8.55385i	0.423022	−	0.580673i
$218$	3.27871			0.222062
$219$	8.26232	+	4.77026i	0.558316	+	0.322344i
$220$	1.42697	+	2.47159i	0.0962065	+	0.166635i
$221$	1.34255	−	0.225029i	0.0903099	−	0.0151371i
$222$	−1.68878	+	2.92505i	−0.113343	+	0.196316i
$223$		−	23.7854i		−	1.59279i	−0.604778	−	0.796394i	$-0.706738\pi$
$223$		−	23.7854i		−	1.59279i	0.604778	−	0.796394i	$-0.293262\pi$
$224$	1.55787	−	2.13846i	0.104090	−	0.142882i
$225$	−0.115749			−0.00771663
$226$	−1.14524	−	0.661205i	−0.0761802	−	0.0439827i
$227$	8.86074	−	5.11575i	0.588108	−	0.339544i	−0.176241	−	0.984347i	$-0.556394\pi$
$227$	8.86074	−	5.11575i	0.588108	−	0.339544i	0.764349	+	0.644803i	$0.223061\pi$
$228$	6.71612	−	3.87755i	0.444786	−	0.256797i
$229$	0.906910	+	0.523604i	0.0599303	+	0.0346008i	0.529666	−	0.848206i	$-0.322317\pi$
$229$	0.906910	+	0.523604i	0.0599303	+	0.0346008i	−0.469735	+	0.882807i	$0.655651\pi$
$230$	10.1630			0.670126
$231$	−3.31968	−	0.353213i	−0.218419	−	0.0232397i
$232$			2.40786i			0.158083i
$233$	1.87580	−	3.24898i	0.122888	−	0.212848i	−0.798018	−	0.602634i	$-0.794118\pi$
$233$	1.87580	−	3.24898i	0.122888	−	0.212848i	0.920905	+	0.389787i	$0.127451\pi$
$234$	0.596023	+	3.55595i	0.0389632	+	0.232460i
$235$	−3.72305	−	6.44850i	−0.242865	−	0.420654i
$236$	−4.04404	−	2.33483i	−0.263245	−	0.151984i
$237$	−6.29211			−0.408716
$238$	0.405123	+	0.913067i	0.0262602	+	0.0591854i
$239$			29.1968i			1.88858i	0.329112	+	0.944291i	$0.393251\pi$
$239$			29.1968i			1.88858i	−0.329112	+	0.944291i	$0.606749\pi$
$240$	1.95878	+	1.13090i	0.126439	+	0.0729994i
$241$	1.47908	−	0.853947i	0.0952759	−	0.0550076i	−0.451605	−	0.892218i	$-0.649148\pi$
$241$	1.47908	−	0.853947i	0.0952759	−	0.0550076i	0.546881	+	0.837210i	$0.315815\pi$
$242$	8.14744	−	4.70393i	0.523737	−	0.302380i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	8.90116			0.569838
$245$	15.0702	−	4.85395i	0.962800	−	0.310107i
$246$	9.90116			0.631275
$247$	−21.5710	+	17.7913i	−1.37253	+	1.13204i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	−5.53776	+	3.19723i	−0.350941	+	0.202616i
$250$	−5.52360	+	9.56716i	−0.349343	+	0.605081i
$251$	19.4496			1.22765			0.613824	−	0.789443i	$-0.289630\pi$
$251$	19.4496			1.22765			0.613824	+	0.789443i	$0.289630\pi$
$252$	−2.41839	+	1.07303i	−0.152344	+	0.0675943i
$253$			5.66966i			0.356448i
$254$	14.1718	+	8.18208i	0.889216	+	0.513389i
$255$	−0.739540	+	0.426974i	−0.0463118	+	0.0267381i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.14605	+	10.6453i	−0.383380	+	0.664034i	−0.991543	−	0.129778i	$-0.958573\pi$
$257$	−6.14605	+	10.6453i	−0.383380	+	0.664034i	0.608163	+	0.793812i	$0.291907\pi$
$258$			8.75510i			0.545069i
$259$	8.88600	+	0.945469i	0.552149	+	0.0587486i
$260$	−7.63935	−	2.85395i	−0.473773	−	0.176994i
$261$	1.20393	−	2.08526i	0.0745212	−	0.129075i
$262$	−9.90574	+	5.71908i	−0.611978	+	0.353326i
$263$	−1.65451	−	2.86569i	−0.102021	−	0.176706i	0.810496	−	0.585744i	$-0.199198\pi$
$263$	−1.65451	−	2.86569i	−0.102021	−	0.176706i	−0.912517	+	0.409038i	$0.865864\pi$
$264$	−0.630901	+	1.09275i	−0.0388293	+	0.0672543i
$265$		−	6.78541i		−	0.416824i
$266$	−16.5840	−	12.0815i	−1.01683	−	0.740763i
$267$		−	11.3776i		−	0.696295i
$268$	1.11900	+	0.646053i	0.0683536	+	0.0394640i
$269$	−16.0062	−	27.7236i	−0.975918	−	1.69034i	−0.676873	−	0.736100i	$-0.736665\pi$
$269$	−16.0062	−	27.7236i	−0.975918	−	1.69034i	−0.299045	−	0.954239i	$-0.596668\pi$
$270$	−1.13090	−	1.95878i	−0.0688245	−	0.119207i
$271$	19.3202	+	11.1545i	1.17362	+	0.677588i	0.954529	−	0.298117i	$-0.0963586\pi$
$271$	19.3202	+	11.1545i	1.17362	+	0.677588i	0.219088	+	0.975705i	$0.429692\pi$
$272$	0.377552			0.0228924
$273$	7.96012	−	5.25704i	0.481768	−	0.318171i
$274$	11.1461			0.673358
$275$	0.126485	+	0.0730264i	0.00762736	+	0.00440366i
$276$	2.24665	+	3.89131i	0.135232	+	0.234230i
$277$	5.20568	+	9.01650i	0.312779	+	0.541749i	0.978963	−	0.204038i	$-0.0654067\pi$
$277$	5.20568	+	9.01650i	0.312779	+	0.541749i	−0.666184	+	0.745788i	$0.732073\pi$
$278$	2.15926	+	1.24665i	0.129504	+	0.0747691i
$279$			4.00000i			0.239474i
$280$	0.633140	−	5.95058i	0.0378374	−	0.355615i
$281$			29.5102i			1.76043i	0.474574	+	0.880216i	$0.342602\pi$
$281$			29.5102i			1.76043i	−0.474574	+	0.880216i	$0.657398\pi$
$282$	1.64605	−	2.85105i	0.0980210	−	0.169777i
$283$	−1.60730	−	2.78392i	−0.0955439	−	0.165487i	0.814292	−	0.580456i	$-0.197126\pi$
$283$	−1.60730	−	2.78392i	−0.0955439	−	0.165487i	−0.909835	+	0.414969i	$0.863792\pi$
$284$	−3.56434	+	2.05787i	−0.211505	+	0.122112i
$285$	8.77026	−	15.1905i	0.519505	−	0.899809i
$286$	1.59214	−	4.26180i	0.0941455	−	0.252006i
$287$	−10.6242	−	23.9449i	−0.627127	−	1.41342i
$288$			1.00000i			0.0589256i
$289$	8.42873	−	14.5990i	0.495807	−	0.858764i
$290$	2.72305	+	4.71645i	0.159903	+	0.276960i
$291$	6.95445	−	4.01515i	0.407677	−	0.235372i
$292$	−8.26232	−	4.77026i	−0.483516	−	0.279158i
$293$			24.7248i			1.44444i	0.691664	+	0.722219i	$0.256878\pi$
$293$			24.7248i			1.44444i	−0.691664	+	0.722219i	$0.743122\pi$
$294$	5.18999	+	4.69723i	0.302687	+	0.273948i
$295$	−10.5618			−0.614934
$296$	1.68878	−	2.92505i	0.0981581	−	0.170015i
$297$	1.09275	−	0.630901i	0.0634079	−	0.0366086i
$298$	−0.0151517	−	0.0262436i	−0.000877716	−	0.00152025i
$299$	−10.3083	−	12.4982i	−0.596143	−	0.722792i
$300$	0.115749			0.00668279
$301$	21.1733	−	9.39446i	1.22041	−	0.541488i
$302$	−4.30901			−0.247956
$303$	−5.81968	+	10.0800i	−0.334332	+	0.579079i
$304$	−6.71612	+	3.87755i	−0.385196	+	0.222393i
$305$	17.4354	−	10.0663i	0.998348	−	0.576396i
$306$	−0.326969	−	0.188776i	−0.0186916	−	0.0107916i
$307$		−	6.93939i		−	0.396052i	−0.980197	−	0.198026i	$-0.936547\pi$
$307$		−	6.93939i		−	0.396052i	0.980197	−	0.198026i	$-0.0634531\pi$
$308$	3.31968	+	0.353213i	0.189156	+	0.0201262i
$309$	12.4630			0.708995
$310$	−7.83511	−	4.52360i	−0.445005	−	0.256923i
$311$	5.53876	+	9.59341i	0.314074	+	0.543992i	0.979240	−	0.202703i	$-0.0649726\pi$
$311$	5.53876	+	9.59341i	0.314074	+	0.543992i	−0.665166	+	0.746695i	$0.731639\pi$
$312$	−0.596023	−	3.55595i	−0.0337432	−	0.201316i
$313$	10.7039	−	18.5397i	0.605022	−	1.04793i	−0.387026	−	0.922069i	$-0.626498\pi$
$313$	10.7039	−	18.5397i	0.605022	−	1.04793i	0.992048	−	0.125860i	$-0.0401689\pi$
$314$			22.7114i			1.28168i
$315$	−3.52360	+	4.83678i	−0.198533	+	0.272522i
$316$	6.29211			0.353959
$317$	−18.3754	−	10.6091i	−1.03207	−	0.595864i	−0.114490	−	0.993424i	$-0.536523\pi$
$317$	−18.3754	−	10.6091i	−1.03207	−	0.595864i	−0.917576	+	0.397561i	$0.869857\pi$
$318$	2.59808	−	1.50000i	0.145693	−	0.0841158i
$319$	−2.63119	+	1.51912i	−0.147318	+	0.0850543i
$320$	−1.95878	−	1.13090i	−0.109499	−	0.0632193i
$321$	17.8023			0.993628
$322$	7.00000	−	9.60876i	0.390095	−	0.535475i
$323$		−	2.92795i		−	0.162916i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−0.411599	+	0.0689893i	−0.0228314	+	0.00382684i
$326$	−6.20393	−	10.7455i	−0.343604	−	0.595139i
$327$	2.83944	+	1.63935i	0.157022	+	0.0906565i
$328$	−9.90116			−0.546700
$329$	−8.66120	−	0.921550i	−0.477508	−	0.0508067i
$330$			2.85395i			0.157105i
$331$	−18.2205	−	10.5196i	−1.00149	−	0.578212i	−0.0928025	−	0.995685i	$-0.529583\pi$
$331$	−18.2205	−	10.5196i	−1.00149	−	0.578212i	−0.908689	+	0.417473i	$0.862916\pi$
$332$	5.53776	−	3.19723i	0.303924	−	0.175471i
$333$	−2.92505	+	1.68878i	−0.160292	+	0.0925443i
$334$	−12.3366	+	21.3676i	−0.675028	+	1.16918i
$335$	2.92249			0.159673
$336$	2.41839	−	1.07303i	0.131934	−	0.0585384i
$337$	−25.5574			−1.39220			−0.696101	−	0.717944i	$-0.745083\pi$
$337$	−25.5574			−1.39220			−0.696101	+	0.717944i	$0.745083\pi$
$338$	4.23885	+	12.2895i	0.230563	+	0.668461i
$339$	−0.661205	−	1.14524i	−0.0359117	−	0.0622009i
$340$	0.739540	−	0.426974i	0.0401072	−	0.0231559i
$341$	2.52360	−	4.37101i	0.136661	−	0.236704i
$342$	7.75510			0.419348
$343$	5.79073	−	17.5917i	0.312670	−	0.949862i
$344$		−	8.75510i		−	0.472044i
$345$	8.80138	+	5.08148i	0.473850	+	0.273578i
$346$	20.7661	−	11.9893i	1.11639	−	0.644551i
$347$	−9.16517	−	15.8745i	−0.492012	−	0.852190i	0.507946	−	0.861389i	$-0.330405\pi$
$347$	−9.16517	−	15.8745i	−0.492012	−	0.852190i	−0.999958	+	0.00919912i	$0.997072\pi$
$348$	−1.20393	+	2.08526i	−0.0645373	+	0.111782i
$349$			4.19326i			0.224460i	0.993682	+	0.112230i	$0.0357994\pi$
$349$			4.19326i			0.224460i	−0.993682	+	0.112230i	$0.964201\pi$
$350$	−0.124202	−	0.279927i	−0.00663888	−	0.0149627i
$351$	−1.26180	+	3.37755i	−0.0673500	+	0.180280i
$352$	0.630901	−	1.09275i	0.0336271	−	0.0582439i
$353$	18.9338	−	10.9315i	1.00775	−	0.581823i	0.0972156	−	0.995263i	$-0.469006\pi$
$353$	18.9338	−	10.9315i	1.00775	−	0.581823i	0.910531	+	0.413440i	$0.135673\pi$
$354$	−2.33483	−	4.04404i	−0.124095	−	0.214938i
$355$	−4.65451	+	8.06184i	−0.247036	+	0.427878i
$356$			11.3776i			0.603009i
$357$	−0.105687	+	0.993301i	−0.00559355	+	0.0525711i
$358$		−	5.70789i		−	0.301672i
$359$	22.4341	+	12.9523i	1.18403	+	0.683598i	0.956943	−	0.290277i	$-0.0937475\pi$
$359$	22.4341	+	12.9523i	1.18403	+	0.683598i	0.227084	+	0.973875i	$0.427081\pi$
$360$	1.13090	+	1.95878i	0.0596037	+	0.103237i
$361$	20.5708	+	35.6297i	1.08267	+	1.87525i
$362$	14.4363	+	8.33483i	0.758758	+	0.438069i
$363$	9.40786			0.493784
$364$	−7.96012	+	5.25704i	−0.417224	+	0.275544i
$365$	−21.5787			−1.12948
$366$	7.70863	+	4.45058i	0.402936	+	0.232635i
$367$	8.93146	+	15.4697i	0.466218	+	0.807514i	0.999256	−	0.0385779i	$-0.0122828\pi$
$367$	8.93146	+	15.4697i	0.466218	+	0.807514i	−0.533037	+	0.846092i	$0.678949\pi$
$368$	−2.24665	−	3.89131i	−0.117115	−	0.202849i
$369$	8.57465	+	4.95058i	0.446379	+	0.257717i
$370$		−	7.63935i		−	0.397151i
$371$	−6.41539	−	4.67362i	−0.333070	−	0.242642i
$372$		−	4.00000i		−	0.207390i
$373$	7.56236	−	13.0984i	0.391564	−	0.678209i	−0.601092	−	0.799180i	$-0.705267\pi$
$373$	7.56236	−	13.0984i	0.391564	−	0.678209i	0.992656	+	0.120971i	$0.0386008\pi$
$374$	0.238198	+	0.412571i	0.0123169	+	0.0213335i
$375$	−9.56716	+	5.52360i	−0.494046	+	0.285238i
$376$	−1.64605	+	2.85105i	−0.0848887	+	0.147032i
$377$	3.03824	−	8.13265i	0.156477	−	0.418853i
$378$	−2.63090	−	0.279927i	−0.135319	−	0.0143979i
$379$			12.5236i			0.643294i	0.946860	+	0.321647i	$0.104236\pi$
$379$			12.5236i			0.643294i	−0.946860	+	0.321647i	$0.895764\pi$
$380$	−8.77026	+	15.1905i	−0.449905	+	0.779258i
$381$	8.18208	+	14.1718i	0.419180	+	0.726042i
$382$	6.30355	−	3.63935i	0.322517	−	0.186206i
$383$	−1.36723	−	0.789373i	−0.0698624	−	0.0403351i	0.464662	−	0.885488i	$-0.346176\pi$
$383$	−1.36723	−	0.789373i	−0.0698624	−	0.0403351i	−0.534524	+	0.845153i	$0.679509\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	6.90196	−	3.06236i	0.351756	−	0.156072i
$386$	17.3090			0.881005
$387$	−4.37755	+	7.58214i	−0.222523	+	0.385422i
$388$	−6.95445	+	4.01515i	−0.353059	+	0.203838i
$389$	−2.40512	−	4.16580i	−0.121945	−	0.211214i	0.798590	−	0.601876i	$-0.205580\pi$
$389$	−2.40512	−	4.16580i	−0.121945	−	0.211214i	−0.920534	+	0.390661i	$0.872246\pi$
$390$	−5.18890	−	6.29127i	−0.262750	−	0.318571i
$391$	1.69645			0.0857933
$392$	−5.18999	−	4.69723i	−0.262134	−	0.237246i
$393$	−11.4382			−0.576979
$394$	−1.60730	+	2.78392i	−0.0809744	+	0.140252i
$395$	12.3248	−	7.11575i	0.620130	−	0.358032i
$396$	−1.09275	+	0.630901i	−0.0549129	+	0.0317040i
$397$	−23.3380	−	13.4742i	−1.17130	−	0.676250i	−0.217313	−	0.976102i	$-0.569729\pi$
$397$	−23.3380	−	13.4742i	−1.17130	−	0.676250i	−0.953986	+	0.299852i	$0.903063\pi$
$398$			11.7035i			0.586642i
$399$	−8.32143	−	18.7549i	−0.416593	−	0.938918i
$400$	−0.115749			−0.00578747
$401$	−17.8364	−	10.2978i	−0.890705	−	0.514249i	−0.0165321	−	0.999863i	$-0.505263\pi$
$401$	−17.8364	−	10.2978i	−0.890705	−	0.514249i	−0.874173	+	0.485614i	$0.838596\pi$
$402$	0.646053	+	1.11900i	0.0322222	+	0.0558105i
$403$	2.38409	+	14.2238i	0.118760	+	0.708537i
$404$	5.81968	−	10.0800i	0.289540	−	0.501498i
$405$		−	2.26180i		−	0.112390i
$406$	6.33483	+	0.674024i	0.314392	+	0.0334513i
$407$	4.26180			0.211250
$408$	0.326969	+	0.188776i	0.0161874	+	0.00934580i
$409$	−4.59774	+	2.65451i	−0.227344	+	0.131257i	−0.609346	−	0.792904i	$-0.708568\pi$
$409$	−4.59774	+	2.65451i	−0.227344	+	0.131257i	0.382002	+	0.924161i	$0.375235\pi$
$410$	−19.3942	+	11.1972i	−0.957810	+	0.552992i
$411$	9.65276	+	5.57303i	0.476136	+	0.274897i
$412$	−12.4630			−0.614008
$413$	−7.27474	+	9.98589i	−0.357967	+	0.491374i
$414$			4.49330i			0.220834i
$415$	7.23150	−	12.5253i	0.354980	−	0.614844i
$416$	0.596023	+	3.55595i	0.0292224	+	0.174345i
$417$	1.24665	+	2.15926i	0.0610487	+	0.105740i
$418$	−8.47441	−	4.89270i	−0.414497	−	0.239310i
$419$	−20.5842			−1.00560			−0.502802	−	0.864401i	$-0.667698\pi$
$419$	−20.5842			−1.00560			−0.502802	+	0.864401i	$0.667698\pi$
$420$	3.52360	−	4.83678i	0.171934	−	0.236011i
$421$		−	12.8878i		−	0.628111i	−0.949405	−	0.314055i	$-0.898312\pi$
$421$		−	12.8878i		−	0.628111i	0.949405	−	0.314055i	$-0.101688\pi$
$422$	6.98373	+	4.03206i	0.339963	+	0.196277i
$423$	2.85105	−	1.64605i	0.138623	−	0.0800338i
$424$	−2.59808	+	1.50000i	−0.126174	+	0.0728464i
$425$	0.0218507	−	0.0378465i	0.00105991	−	0.00183582i
$426$	−4.11575			−0.199409
$427$	2.49168	−	23.4181i	0.120581	−	1.13328i
$428$	−17.8023			−0.860507
$429$	3.50974	−	2.89476i	0.169452	−	0.139760i
$430$	−9.90116	−	17.1493i	−0.477476	−	0.827013i
$431$	23.0588	−	13.3130i	1.11070	−	0.641264i	0.171690	−	0.985151i	$-0.445077\pi$
$431$	23.0588	−	13.3130i	1.11070	−	0.641264i	0.939011	+	0.343887i	$0.111744\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−28.0810			−1.34949			−0.674744	−	0.738052i	$-0.735746\pi$
$433$	−28.0810			−1.34949			−0.674744	+	0.738052i	$0.735746\pi$
$434$	−9.67356	+	4.29211i	−0.464346	+	0.206028i
$435$			5.44609i			0.261120i
$436$	−2.83944	−	1.63935i	−0.135985	−	0.0785108i
$437$	−30.1775	+	17.4230i	−1.44359	+	0.833455i
$438$	−4.77026	−	8.26232i	−0.227932	−	0.394789i
$439$	−13.8820	+	24.0444i	−0.662554	+	1.14758i	0.317389	+	0.948295i	$0.397194\pi$
$439$	−13.8820	+	24.0444i	−0.662554	+	1.14758i	−0.979942	+	0.199281i	$0.936139\pi$
$440$		−	2.85395i		−	0.136057i
$441$	2.14605	+	6.66292i	0.102193	+	0.317282i
$442$	−1.27520	−	0.476396i	−0.0606551	−	0.0226598i
$443$	−2.28092	+	3.95067i	−0.108370	+	0.187702i	−0.915110	−	0.403204i	$-0.867896\pi$
$443$	−2.28092	+	3.95067i	−0.108370	+	0.187702i	0.806740	+	0.590906i	$0.201230\pi$
$444$	2.92505	−	1.68878i	0.138817	−	0.0801458i
$445$	12.8669	+	22.2861i	0.609949	+	1.05646i
$446$	−11.8927	+	20.5988i	−0.563136	+	0.975380i
$447$		−	0.0303035i		−	0.00143330i
$448$	−2.41839	+	1.07303i	−0.114258	+	0.0506957i
$449$		−	2.78190i		−	0.131286i	−0.997843	−	0.0656430i	$-0.979090\pi$
$449$		−	2.78190i		−	0.131286i	0.997843	−	0.0656430i	$-0.0209098\pi$
$450$	0.100242	+	0.0578747i	0.00472545	+	0.00272824i
$451$	−6.24665	−	10.8195i	−0.294143	−	0.509471i
$452$	0.661205	+	1.14524i	0.0311004	+	0.0538676i
$453$	−3.73171	−	2.15451i	−0.175331	−	0.101228i
$454$	−10.2315			−0.480188
$455$	−9.64692	+	19.2995i	−0.452254	+	0.904774i
$456$	−7.75510			−0.363166
$457$	−25.8126	−	14.9029i	−1.20746	−	0.697129i	−0.245258	−	0.969458i	$-0.578873\pi$
$457$	−25.8126	−	14.9029i	−1.20746	−	0.697129i	−0.962204	+	0.272329i	$0.912206\pi$
$458$	−0.523604	−	0.906910i	−0.0244664	−	0.0423771i
$459$	−0.188776	−	0.326969i	−0.00881130	−	0.0152616i
$460$	−8.80138	−	5.08148i	−0.410366	−	0.236925i
$461$			18.6180i			0.867128i	0.901123	+	0.433564i	$0.142744\pi$
$461$			18.6180i			0.867128i	−0.901123	+	0.433564i	$0.857256\pi$
$462$	2.69832	+	1.96573i	0.125537	+	0.0914540i
$463$			42.0338i			1.95348i	0.214434	+	0.976738i	$0.431209\pi$
$463$			42.0338i			1.95348i	−0.214434	+	0.976738i	$0.568791\pi$
$464$	1.20393	−	2.08526i	0.0558909	−	0.0968059i
$465$	−4.52360	−	7.83511i	−0.209777	−	0.363345i
$466$	−3.24898	+	1.87580i	−0.150506	+	0.0868947i
$467$	19.4608	−	33.7071i	0.900538	−	1.55978i	0.0737402	−	0.997277i	$-0.476506\pi$
$467$	19.4608	−	33.7071i	0.900538	−	1.55978i	0.826798	−	0.562500i	$-0.190160\pi$
$468$	1.26180	−	3.37755i	0.0583268	−	0.156127i
$469$	2.01294	−	2.76312i	0.0929489	−	0.127589i
$470$			7.44609i			0.343463i
$471$	−11.3557	+	19.6687i	−0.523243	+	0.906284i
$472$	2.33483	+	4.04404i	0.107469	+	0.186142i
$473$	9.56716	−	5.52360i	0.439899	−	0.253976i
$474$	5.44912	+	3.14605i	0.250287	+	0.144503i
$475$			0.897649i			0.0411869i
$476$	0.105687	−	0.993301i	0.00484416	−	0.0455279i
$477$	3.00000			0.137361
$478$	14.5984	−	25.2851i	0.667715	−	1.15652i
$479$	−1.98029	+	1.14332i	−0.0904817	+	0.0522397i	−0.544558	−	0.838723i	$-0.683303\pi$
$479$	−1.98029	+	1.14332i	−0.0904817	+	0.0522397i	0.454076	+	0.890963i	$0.349969\pi$
$480$	−1.13090	−	1.95878i	−0.0516183	−	0.0894056i
$481$	−9.39476	+	7.74859i	−0.428364	+	0.353305i
$482$	−1.70789			−0.0777925
$483$	10.8666	−	4.82143i	0.494446	−	0.219383i
$484$	−9.40786			−0.427630
$485$	−9.08148	+	15.7296i	−0.412369	+	0.714244i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−26.7087	+	15.4203i	−1.21029	+	0.698759i	−0.962822	−	0.270138i	$-0.912931\pi$
$487$	−26.7087	+	15.4203i	−1.21029	+	0.698759i	−0.247465	+	0.968897i	$0.579598\pi$
$488$	−7.70863	−	4.45058i	−0.348953	−	0.201468i
$489$		−	12.4079i		−	0.561103i
$490$	−15.4781	−	3.33146i	−0.699232	−	0.150500i
$491$	41.1754			1.85822			0.929111	−	0.369802i	$-0.120574\pi$
$491$	41.1754			1.85822			0.929111	+	0.369802i	$0.120574\pi$
$492$	−8.57465	−	4.95058i	−0.386575	−	0.223189i
$493$	0.454545	+	0.787295i	0.0204717	+	0.0354580i
$494$	27.5767	−	4.62222i	1.24074	−	0.207964i
$495$	−1.42697	+	2.47159i	−0.0641377	+	0.111090i
$496$			4.00000i			0.179605i
$497$	4.41631	+	9.95349i	0.198098	+	0.446475i
$498$	6.39446			0.286542
$499$	13.3961	+	7.73423i	0.599691	+	0.346232i	0.768920	−	0.639345i	$-0.220794\pi$
$499$	13.3961	+	7.73423i	0.599691	+	0.346232i	−0.169229	+	0.985577i	$0.554128\pi$
$500$	9.56716	−	5.52360i	0.427857	−	0.247023i
$501$	−21.3676	+	12.3366i	−0.954633	+	0.551158i
$502$	−16.8438	−	9.72480i	−0.751778	−	0.434039i
$503$	−0.986602			−0.0439904			−0.0219952	−	0.999758i	$-0.507002\pi$
$503$	−0.986602			−0.0439904			−0.0219952	+	0.999758i	$0.507002\pi$
$504$	2.63090	+	0.279927i	0.117190	+	0.0124690i
$505$		−	26.3259i		−	1.17149i
$506$	2.83483	−	4.91007i	0.126024	−	0.218279i
$507$	−2.47380	+	12.7625i	−0.109865	+	0.566801i
$508$	−8.18208	−	14.1718i	−0.363021	−	0.628771i
$509$	−14.8588	−	8.57875i	−0.658606	−	0.380246i	0.133140	−	0.991097i	$-0.457494\pi$
$509$	−14.8588	−	8.57875i	−0.658606	−	0.380246i	−0.791746	+	0.610851i	$0.790827\pi$
$510$	0.853947			0.0378134
$511$	−14.8629	+	20.4020i	−0.657497	+	0.902533i
$512$			1.00000i			0.0441942i
$513$	6.71612	+	3.87755i	0.296524	+	0.171198i
$514$	10.6453	−	6.14605i	0.469543	−	0.271091i
$515$	−24.4122	+	14.0944i	−1.07573	+	0.621074i
$516$	4.37755	−	7.58214i	0.192711	−	0.333785i
$517$	−4.15399			−0.182692
$518$	−7.22277	−	5.26180i	−0.317350	−	0.231190i
$519$	23.9787			1.05255
$520$	5.18890	+	6.29127i	0.227548	+	0.275890i
$521$	16.2787	+	28.1955i	0.713183	+	1.23527i	0.963656	+	0.267146i	$0.0860805\pi$
$521$	16.2787	+	28.1955i	0.713183	+	1.23527i	−0.250473	+	0.968124i	$0.580586\pi$
$522$	−2.08526	+	1.20393i	−0.0912695	+	0.0526945i
$523$	17.4248	−	30.1806i	0.761932	−	1.31970i	−0.179922	−	0.983681i	$-0.557585\pi$
$523$	17.4248	−	30.1806i	0.761932	−	1.31970i	0.941854	−	0.336023i	$-0.109082\pi$
$524$	11.4382			0.499678
$525$	0.0324014	−	0.304525i	0.00141411	−	0.0132906i
$526$			3.30901i			0.144280i
$527$	−1.30788	−	0.755103i	−0.0569720	−	0.0328928i
$528$	1.09275	−	0.630901i	0.0475560	−	0.0274564i
$529$	1.40512	+	2.43374i	0.0610923	+	0.105815i
$530$	−3.39270	+	5.87633i	−0.147370	+	0.255252i
$531$		−	4.66966i		−	0.202646i
$532$	8.32143	+	18.7549i	0.360780	+	0.813127i
$533$	33.4417	+	12.4933i	1.44852	+	0.541145i
$534$	−5.68878	+	9.85325i	−0.246177	+	0.426392i
$535$	−34.8708	+	20.1327i	−1.50760	+	0.870411i
$536$	−0.646053	−	1.11900i	−0.0279052	−	0.0483333i
$537$	2.85395	−	4.94318i	0.123157	−	0.213314i
$538$			32.0125i			1.38016i
$539$	1.85854	−	8.63487i	0.0800528	−	0.371930i
$540$			2.26180i			0.0973325i
$541$	−23.3905	−	13.5045i	−1.00563	−	0.580603i	−0.0957238	−	0.995408i	$-0.530517\pi$
$541$	−23.3905	−	13.5045i	−1.00563	−	0.580603i	−0.909910	+	0.414805i	$0.863850\pi$
$542$	−11.1545	−	19.3202i	−0.479127	−	0.829872i
$543$	8.33483	+	14.4363i	0.357682	+	0.619523i
$544$	−0.326969	−	0.188776i	−0.0140187	−	0.00809370i
$545$	−7.41579			−0.317657
$546$	−9.52219	+	0.572671i	−0.407512	+	0.0245081i
$547$	33.1719			1.41833			0.709165	−	0.705043i	$-0.249072\pi$
$547$	33.1719			1.41833			0.709165	+	0.705043i	$0.249072\pi$
$548$	−9.65276	−	5.57303i	−0.412346	−	0.238068i
$549$	4.45058	+	7.70863i	0.189946	+	0.328996i
$550$	−0.0730264	−	0.126485i	−0.00311386	−	0.00539336i
$551$	−16.1714	−	9.33658i	−0.688926	−	0.397752i
$552$		−	4.49330i		−	0.191248i
$553$	1.76133	−	16.5539i	0.0748995	−	0.703944i
$554$		−	10.4114i		−	0.442336i
$555$	3.81968	−	6.61587i	0.162136	−	0.280828i
$556$	−1.24665	−	2.15926i	−0.0528698	−	0.0915731i
$557$	−16.4136	+	9.47640i	−0.695466	+	0.401528i	−0.805657	−	0.592383i	$-0.798187\pi$
$557$	−16.4136	+	9.47640i	−0.695466	+	0.401528i	0.110190	+	0.993911i	$0.464854\pi$
$558$	2.00000	−	3.46410i	0.0846668	−	0.146647i
$559$	−11.0472	+	29.5708i	−0.467247	+	1.25071i
$560$	−3.52360	+	4.83678i	−0.148899	+	0.204391i
$561$			0.476396i			0.0201134i
$562$	14.7551	−	25.5566i	0.622406	−	1.07804i
$563$	15.7720	+	27.3179i	0.664711	+	1.15131i	0.979364	+	0.202106i	$0.0647786\pi$
$563$	15.7720	+	27.3179i	0.664711	+	1.15131i	−0.314653	+	0.949207i	$0.601888\pi$
$564$	−2.85105	+	1.64605i	−0.120051	+	0.0693113i
$565$	2.59031	+	1.49551i	0.108975	+	0.0629167i
$566$			3.21459i			0.135119i
$567$	−2.13846	−	1.55787i	−0.0898070	−	0.0654246i
$568$	4.11575			0.172693
$569$	−1.53206	+	2.65360i	−0.0642272	+	0.111245i	−0.896351	−	0.443345i	$-0.853792\pi$
$569$	−1.53206	+	2.65360i	−0.0642272	+	0.111245i	0.832124	+	0.554590i	$0.187125\pi$
$570$	−15.1905	+	8.77026i	−0.636261	+	0.367346i
$571$	2.05514	+	3.55961i	0.0860050	+	0.148965i	0.905819	−	0.423665i	$-0.139257\pi$
$571$	2.05514	+	3.55961i	0.0860050	+	0.148965i	−0.819814	+	0.572630i	$0.805923\pi$
$572$	−3.50974	+	2.89476i	−0.146750	+	0.121036i
$573$	7.27871			0.304072
$574$	−2.77160	+	26.0490i	−0.115685	+	1.08726i
$575$	−0.520097			−0.0216895
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	16.4954	−	9.52360i	0.686711	−	0.396473i	−0.115668	−	0.993288i	$-0.536901\pi$
$577$	16.4954	−	9.52360i	0.686711	−	0.396473i	0.802379	+	0.596815i	$0.203567\pi$
$578$	−14.5990	+	8.42873i	−0.607238	+	0.350589i
$579$	14.9900	+	8.65451i	0.622965	+	0.359669i
$580$		−	5.44609i		−	0.226137i
$581$	−6.86142	−	15.4643i	−0.284660	−	0.641567i
$582$	−8.03030			−0.332867
$583$	−3.27826	−	1.89270i	−0.135772	−	0.0783878i
$584$	4.77026	+	8.26232i	0.197395	+	0.341897i
$585$	−1.34809	−	8.04285i	−0.0557365	−	0.332531i
$586$	12.3624	−	21.4123i	0.510686	−	0.884534i
$587$		−	36.2216i		−	1.49503i	−0.664247	−	0.747513i	$-0.731248\pi$
$587$		−	36.2216i		−	1.49503i	0.664247	−	0.747513i	$-0.268752\pi$
$588$	−2.14605	−	6.66292i	−0.0885017	−	0.274774i
$589$	31.0204			1.27817
$590$	9.14682	+	5.28092i	0.376569	+	0.217412i
$591$	−2.78392	+	1.60730i	−0.114515	+	0.0661153i
$592$	−2.92505	+	1.68878i	−0.120219	+	0.0694083i
$593$	4.35164	+	2.51242i	0.178700	+	0.103173i	0.586682	−	0.809817i	$-0.300434\pi$
$593$	4.35164	+	2.51242i	0.178700	+	0.103173i	−0.407982	+	0.912990i	$0.633767\pi$
$594$	−1.26180			−0.0517724
$595$	−0.916308	−	2.06518i	−0.0375650	−	0.0846640i
$596$			0.0303035i			0.00124128i
$597$	−5.85173	+	10.1355i	−0.239496	+	0.414818i
$598$	2.67811	+	15.9779i	0.109516	+	0.653387i
$599$	−15.4096	−	26.6902i	−0.629620	−	1.09053i	−0.987628	−	0.156815i	$-0.949877\pi$
$599$	−15.4096	−	26.6902i	−0.629620	−	1.09053i	0.358008	−	0.933718i	$-0.383456\pi$
$600$	−0.100242	−	0.0578747i	−0.00409236	−	0.00236272i
$601$	9.12121			0.372062			0.186031	−	0.982544i	$-0.440438\pi$
$601$	9.12121			0.372062			0.186031	+	0.982544i	$0.440438\pi$
$602$	−23.0338	−	2.45079i	−0.938788	−	0.0998868i
$603$			1.29211i			0.0526186i
$604$	3.73171	+	2.15451i	0.151841	+	0.0876656i
$605$	−18.4279	+	10.6394i	−0.749201	+	0.432551i
$606$	10.0800	−	5.81968i	0.409471	−	0.236408i
$607$	−11.1821	+	19.3679i	−0.453866	+	0.786120i	−0.998622	−	0.0524749i	$-0.983289\pi$
$607$	−11.1821	+	19.3679i	−0.453866	+	0.786120i	0.544756	+	0.838595i	$0.316622\pi$
$608$	7.75510			0.314511
$609$	5.14911	+	3.75114i	0.208652	+	0.152004i
$610$	−20.1327			−0.815147
$611$	9.15709	−	7.55257i	0.370456	−	0.305544i
$612$	0.188776	+	0.326969i	0.00763081	+	0.0132170i
$613$	29.9508	−	17.2921i	1.20970	−	0.698422i	0.247008	−	0.969014i	$-0.420553\pi$
$613$	29.9508	−	17.2921i	1.20970	−	0.698422i	0.962694	+	0.270592i	$0.0872194\pi$
$614$	−3.46970	+	6.00969i	−0.140026	+	0.242531i
$615$	−22.3945			−0.903032
$616$	−2.69832	−	1.96573i	−0.108718	−	0.0792015i
$617$		−	1.21810i		−	0.0490389i	−0.999699	−	0.0245194i	$-0.992194\pi$
$617$		−	1.21810i		−	0.0490389i	0.999699	−	0.0245194i	$-0.00780556\pi$
$618$	−10.7933	−	6.23150i	−0.434169	−	0.250668i
$619$	6.93507	−	4.00397i	0.278744	−	0.160933i	−0.354111	−	0.935204i	$-0.615216\pi$
$619$	6.93507	−	4.00397i	0.278744	−	0.160933i	0.632855	+	0.774271i	$0.281883\pi$
$620$	4.52360	+	7.83511i	0.181672	+	0.314666i
$621$	−2.24665	+	3.89131i	−0.0901550	+	0.156153i
$622$		−	11.0775i		−	0.444168i
$623$	29.9332	+	3.18489i	1.19925	+	0.127600i
$624$	−1.26180	+	3.37755i	−0.0505125	+	0.135210i
$625$	12.7827	−	22.1402i	0.511307	−	0.885610i
$626$	−18.5397	+	10.7039i	−0.740997	+	0.427815i
$627$	−4.89270	−	8.47441i	−0.195396	−	0.338435i
$628$	11.3557	−	19.6687i	0.453142	−	0.784865i
$629$		−	1.27520i		−	0.0508456i
$630$	5.46992	−	2.42697i	0.217927	−	0.0966929i
$631$		−	36.8843i		−	1.46834i	−0.678966	−	0.734169i	$-0.737572\pi$
$631$		−	36.8843i		−	1.46834i	0.678966	−	0.734169i	$-0.262428\pi$
$632$	−5.44912	−	3.14605i	−0.216754	−	0.125143i
$633$	4.03206	+	6.98373i	0.160260	+	0.277578i
$634$	10.6091	+	18.3754i	0.421339	+	0.729781i
$635$	−32.0537	−	18.5062i	−1.27201	−	0.734398i
$636$	−3.00000			−0.118958
$637$	11.6025	+	22.4139i	0.459708	+	0.888070i
$638$	3.03824			0.120285
$639$	−3.56434	−	2.05787i	−0.141003	−	0.0814083i
$640$	1.13090	+	1.95878i	0.0447028	+	0.0774275i
$641$	−21.5748	−	37.3686i	−0.852153	−	1.47597i	−0.879262	−	0.476339i	$-0.841963\pi$
$641$	−21.5748	−	37.3686i	−0.852153	−	1.47597i	0.0271091	−	0.999632i	$-0.491370\pi$
$642$	−15.4173	−	8.90116i	−0.608471	−	0.351301i
$643$			5.10235i			0.201217i	0.994926	+	0.100609i	$0.0320790\pi$
$643$			5.10235i			0.201217i	−0.994926	+	0.100609i	$0.967921\pi$
$644$	−10.8666	+	4.82143i	−0.428202	+	0.189991i
$645$		−	19.8023i		−	0.779715i
$646$	−1.46398	+	2.53568i	−0.0575994	+	0.0997650i
$647$	−18.4079	−	31.8833i	−0.723687	−	1.25346i	−0.959512	−	0.281668i	$-0.909112\pi$
$647$	−18.4079	−	31.8833i	−0.723687	−	1.25346i	0.235825	−	0.971796i	$-0.424221\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−2.94609	+	5.10278i	−0.115644	+	0.200302i
$650$	0.390950	+	0.146053i	0.0153343	+	0.00572866i
$651$	−10.5236	−	1.11971i	−0.412453	−	0.0438849i
$652$			12.4079i			0.485929i
$653$	−14.8669	+	25.7502i	−0.581786	+	1.00768i	0.413482	+	0.910513i	$0.364313\pi$
$653$	−14.8669	+	25.7502i	−0.581786	+	1.00768i	−0.995268	+	0.0971708i	$0.969021\pi$
$654$	−1.63935	−	2.83944i	−0.0641038	−	0.111031i
$655$	22.4048	−	12.9354i	0.875429	−	0.505429i
$656$	8.57465	+	4.95058i	0.334784	+	0.193288i
$657$		−	9.54051i		−	0.372211i
$658$	7.04005	+	5.12869i	0.274450	+	0.199937i
$659$	16.9216			0.659171			0.329585	−	0.944126i	$-0.393091\pi$
$659$	16.9216			0.659171			0.329585	+	0.944126i	$0.393091\pi$
$660$	1.42697	−	2.47159i	0.0555449	−	0.0962065i
$661$	35.9451	−	20.7529i	1.39810	−	0.807194i	0.403907	−	0.914800i	$-0.367652\pi$
$661$	35.9451	−	20.7529i	1.39810	−	0.807194i	0.994194	+	0.107606i	$0.0343185\pi$
$662$	10.5196	+	18.2205i	0.408857	+	0.708162i
$663$	−0.866158	−	1.05017i	−0.0336388	−	0.0407853i
$664$	−6.39446			−0.248153
$665$	37.5097	+	27.3259i	1.45457	+	1.05965i
$666$	3.37755			0.130877
$667$	5.40961	−	9.36972i	0.209461	−	0.362797i
$668$	21.3676	−	12.3366i	0.826737	−	0.477317i
$669$	−20.5988	+	11.8927i	−0.796394	+	0.459798i
$670$	−2.53095	−	1.46124i	−0.0977791	−	0.0564528i
$671$		−	11.2315i		−	0.433587i
$672$	−2.63090	−	0.279927i	−0.101489	−	0.0107984i
$673$	15.6394			0.602853			0.301426	−	0.953489i	$-0.402537\pi$
$673$	15.6394			0.602853			0.301426	+	0.953489i	$0.402537\pi$
$674$	22.1334	+	12.7787i	0.852546	+	0.492217i
$675$	0.0578747	+	0.100242i	0.00222760	+	0.00385831i
$676$	2.47380	−	12.7625i	0.0951463	−	0.490864i
$677$	−6.61178	+	11.4519i	−0.254111	+	0.440134i	−0.964654	−	0.263521i	$-0.915116\pi$
$677$	−6.61178	+	11.4519i	−0.254111	+	0.440134i	0.710542	+	0.703654i	$0.248450\pi$
$678$			1.32241i			0.0507868i
$679$	8.61673	+	19.4204i	0.330680	+	0.745287i
$680$	−0.853947			−0.0327474
$681$	−8.86074	−	5.11575i	−0.339544	−	0.196036i
$682$	−4.37101	+	2.52360i	−0.167375	+	0.0966338i
$683$	22.4935	−	12.9866i	0.860688	−	0.496919i	−0.00355454	−	0.999994i	$-0.501131\pi$
$683$	22.4935	−	12.9866i	0.860688	−	0.496919i	0.864243	+	0.503075i	$0.167798\pi$
$684$	−6.71612	−	3.87755i	−0.256797	−	0.148262i
$685$	−25.2102			−0.963231
$686$	−13.8108	+	12.3395i	−0.527297	+	0.471124i
$687$		−	1.04721i		−	0.0399535i
$688$	−4.37755	+	7.58214i	−0.166893	+	0.289066i
$689$	10.6678	−	1.78807i	0.406412	−	0.0681200i
$690$	−5.08148	−	8.80138i	−0.193449	−	0.335063i
$691$	14.6467	+	8.45630i	0.557188	+	0.321693i	0.752016	−	0.659145i	$-0.229082\pi$
$691$	14.6467	+	8.45630i	0.557188	+	0.321693i	−0.194828	+	0.980837i	$0.562415\pi$
$692$	−23.9787			−0.911532
$693$	1.35395	+	3.05153i	0.0514322	+	0.115918i
$694$			18.3303i			0.695810i
$695$	−4.88382	−	2.81968i	−0.185254	−	0.106956i
$696$	2.08526	−	1.20393i	0.0790417	−	0.0456348i
$697$	−3.23737	+	1.86910i	−0.122624	+	0.0707972i
$698$	2.09663	−	3.63147i	0.0793587	−	0.137453i
$699$	−3.75160			−0.141898
$700$	−0.0324014	+	0.304525i	−0.00122466	+	0.0115100i
$701$	−33.0731			−1.24915			−0.624577	−	0.780964i	$-0.714728\pi$
$701$	−33.0731			−1.24915			−0.624577	+	0.780964i	$0.714728\pi$
$702$	2.78153	−	2.29414i	0.104982	−	0.0865869i
$703$	13.0966	+	22.6840i	0.493949	+	0.855544i
$704$	−1.09275	+	0.630901i	−0.0411847	+	0.0237780i
$705$	−3.72305	+	6.44850i	−0.140218	+	0.242865i
$706$	−21.8629			−0.822822
$707$	−24.8903	−	18.1327i	−0.936097	−	0.681949i
$708$			4.66966i			0.175496i
$709$	10.4254	+	6.01912i	0.391535	+	0.226053i	0.682825	−	0.730582i	$-0.260751\pi$
$709$	10.4254	+	6.01912i	0.391535	+	0.226053i	−0.291290	+	0.956635i	$0.594084\pi$
$710$	8.06184	−	4.65451i	0.302555	−	0.174680i
$711$	3.14605	+	5.44912i	0.117986	+	0.204358i
$712$	5.68878	−	9.85325i	0.213196	−	0.369266i
$713$			17.9732i			0.673102i
$714$	0.588178	−	0.807380i	0.0220120	−	0.0302155i
$715$	−3.60112	+	9.63935i	−0.134674	+	0.360491i
$716$	−2.85395	+	4.94318i	−0.106657	+	0.184735i
$717$	25.2851	−	14.5984i	0.944291	−	0.545187i
$718$	−12.9523	−	22.4341i	−0.483377	−	0.837233i
$719$	3.59214	−	6.22178i	0.133964	−	0.232033i	−0.791237	−	0.611510i	$-0.790563\pi$
$719$	3.59214	−	6.22178i	0.133964	−	0.232033i	0.925201	+	0.379476i	$0.123896\pi$
$720$		−	2.26180i		−	0.0842924i
$721$	−3.48873	+	32.7889i	−0.129927	+	1.22112i
$722$		−	41.1416i		−	1.53113i
$723$	−1.47908	−	0.853947i	−0.0550076	−	0.0317586i
$724$	−8.33483	−	14.4363i	−0.309761	−	0.536523i
$725$	−0.139354	−	0.241368i	−0.00517547	−	0.00896418i
$726$	−8.14744	−	4.70393i	−0.302380	−	0.174579i
$727$	−41.8967			−1.55386			−0.776932	−	0.629585i	$-0.783225\pi$
$727$	−41.8967			−1.55386			−0.776932	+	0.629585i	$0.783225\pi$
$728$	9.52219	−	0.572671i	0.352916	−	0.0212246i
$729$	1.00000			0.0370370
$730$	18.6877	+	10.7894i	0.691664	+	0.399333i
$731$	−1.65275	−	2.86265i	−0.0611292	−	0.105879i
$732$	−4.45058	−	7.70863i	−0.164498	−	0.284919i
$733$	19.5022	+	11.2596i	0.720329	+	0.415882i	0.814874	−	0.579638i	$-0.196806\pi$
$733$	19.5022	+	11.2596i	0.720329	+	0.415882i	−0.0945445	+	0.995521i	$0.530139\pi$
$734$		−	17.8629i		−	0.659332i
$735$	−11.7387	−	10.6242i	−0.432990	−	0.391880i
$736$			4.49330i			0.165625i
$737$	0.815191	−	1.41195i	0.0300279	−	0.0520099i
$738$	−4.95058	−	8.57465i	−0.182233	−	0.315637i
$739$	−10.3992	+	6.00397i	−0.382540	+	0.220859i	−0.678923	−	0.734210i	$-0.737553\pi$
$739$	−10.3992	+	6.00397i	−0.382540	+	0.220859i	0.296383	+	0.955069i	$0.404220\pi$
$740$	−3.81968	+	6.61587i	−0.140414	+	0.243204i
$741$	26.1933	+	9.78541i	0.962234	+	0.359476i
$742$	3.21908	+	7.25517i	0.118176	+	0.266346i
$743$			9.52360i			0.349387i	0.984623	+	0.174694i	$0.0558935\pi$
$743$			9.52360i			0.349387i	−0.984623	+	0.174694i	$0.944107\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	0.0342702	+	0.0593577i	0.00125556	+	0.00217470i
$746$	−13.0984	+	7.56236i	−0.479566	+	0.276878i
$747$	5.53776	+	3.19723i	0.202616	+	0.116980i
$748$		−	0.476396i		−	0.0174187i
$749$	−4.98335	+	46.8361i	−0.182088	+	1.71135i
$750$	11.0472			0.403387
$751$	19.7248	−	34.1644i	0.719768	−	1.24668i	−0.241323	−	0.970445i	$-0.577581\pi$
$751$	19.7248	−	34.1644i	0.719768	−	1.24668i	0.961091	−	0.276230i	$-0.0890852\pi$
$752$	2.85105	−	1.64605i	0.103967	−	0.0600254i
$753$	−9.72480	−	16.8438i	−0.354391	−	0.613824i
$754$	−6.69752	+	5.52397i	−0.243909	+	0.201171i
$755$	9.74613			0.354698
$756$	2.13846	+	1.55787i	0.0777752	+	0.0566594i
$757$	19.4854			0.708208			0.354104	−	0.935206i	$-0.384786\pi$
$757$	19.4854			0.708208			0.354104	+	0.935206i	$0.384786\pi$
$758$	6.26180	−	10.8458i	0.227439	−	0.393936i
$759$	4.91007	−	2.83483i	0.178224	−	0.102898i
$760$	15.1905	−	8.77026i	0.551018	−	0.318131i
$761$	−5.73138	−	3.30901i	−0.207762	−	0.119952i	0.392509	−	0.919748i	$-0.371607\pi$
$761$	−5.73138	−	3.30901i	−0.207762	−	0.119952i	−0.600271	+	0.799797i	$0.704941\pi$
$762$		−	16.3642i		−	0.592811i
$763$	−5.10782	+	7.01140i	−0.184915	+	0.253830i
$764$	−7.27871			−0.263334
$765$	0.739540	+	0.426974i	0.0267381	+	0.0154373i
$766$	0.789373	+	1.36723i	0.0285212	+	0.0494002i
$767$	−2.78322	−	16.6051i	−0.100496	−	0.599574i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$			14.3900i			0.518918i	0.965754	+	0.259459i	$0.0835442\pi$
$769$			14.3900i			0.518918i	−0.965754	+	0.259459i	$0.916456\pi$
$770$	−7.50845	−	0.798898i	−0.270586	−	0.0287903i
$771$	12.2921			0.442689
$772$	−14.9900	−	8.65451i	−0.539503	−	0.311482i
$773$	47.8358	−	27.6180i	1.72053	−	0.993351i	0.802706	−	0.596375i	$-0.203393\pi$
$773$	47.8358	−	27.6180i	1.72053	−	0.993351i	0.917829	−	0.396976i	$-0.129940\pi$
$774$	7.58214	−	4.37755i	0.272534	−	0.157348i
$775$	0.400968	+	0.231499i	0.0144032	+	0.00831568i
$776$	8.03030			0.288271
$777$	−3.62420	−	8.16824i	−0.130018	−	0.293034i
$778$			4.81025i			0.172456i
$779$	38.3922	−	66.4973i	1.37554	−	2.38251i
$780$	1.34809	+	8.04285i	0.0482692	+	0.287980i
$781$	2.59663	+	4.49750i	0.0929148	+	0.160933i
$782$	−1.46917	−	0.848227i	−0.0525375	−	0.0303325i
$783$	−2.40786			−0.0860497
$784$	2.14605	+	6.66292i	0.0766447	+	0.237961i
$785$		−	51.3687i		−	1.83343i
$786$	9.90574	+	5.71908i	0.353326	+	0.203993i
$787$	−0.642336	+	0.370853i	−0.0228968	+	0.0132195i	−0.511405	−	0.859340i	$-0.670875\pi$
$787$	−0.642336	+	0.370853i	−0.0228968	+	0.0132195i	0.488508	+	0.872559i	$0.337541\pi$
$788$	2.78392	−	1.60730i	0.0991730	−	0.0572576i
$789$	−1.65451	+	2.86569i	−0.0589020	+	0.102021i
$790$	−14.2315			−0.506334
$791$	3.19810	−	1.41898i	0.113711	−	0.0504531i
$792$	1.26180			0.0448362
$793$	20.4205	+	24.7588i	0.725155	+	0.879211i
$794$	13.4742	+	23.3380i	0.478181	+	0.828234i
$795$	−5.87633	+	3.39270i	−0.208412	+	0.120327i
$796$	5.85173	−	10.1355i	0.207409	−	0.359243i
$797$	21.4685			0.760452			0.380226	−	0.924894i	$-0.375846\pi$
$797$	21.4685			0.760452			0.380226	+	0.924894i	$0.375846\pi$
$798$	−2.17086	+	20.4029i	−0.0768478	+	0.722255i
$799$			1.24294i			0.0439721i
$800$	0.100242	+	0.0578747i	0.00354409	+	0.00204618i
$801$	−9.85325	+	5.68878i	−0.348147	+	0.201003i
$802$	10.2978	+	17.8364i	0.363629	+	0.629824i
$803$	−6.01912	+	10.4254i	−0.212410	+	0.367905i
$804$		−	1.29211i		−	0.0455691i
$805$	−15.8326	+	21.7331i	−0.558026	+	0.765992i
$806$	5.04721	−	13.5102i	0.177780	−	0.475877i
$807$	−16.0062	+	27.7236i	−0.563446	+	0.975918i
$808$	−10.0800	+	5.81968i	−0.354612	+	0.204736i
$809$	6.63487	+	11.4919i	0.233270	+	0.404035i	0.958768	−	0.284189i	$-0.0917242\pi$
$809$	6.63487	+	11.4919i	0.233270	+	0.404035i	−0.725499	+	0.688223i	$0.758391\pi$
$810$	−1.13090	+	1.95878i	−0.0397358	+	0.0688245i
$811$		−	14.8236i		−	0.520529i	−0.965537	−	0.260264i	$-0.916190\pi$
$811$		−	14.8236i		−	0.520529i	0.965537	−	0.260264i	$-0.0838097\pi$
$812$	−5.14911	−	3.75114i	−0.180698	−	0.131639i
$813$		−	22.3090i		−	0.782411i
$814$	−3.69083	−	2.13090i	−0.129363	−	0.0746880i
$815$	14.0321	+	24.3042i	0.491522	+	0.851340i
$816$	−0.188776	−	0.326969i	−0.00660848	−	0.0114462i
$817$	58.8003	+	33.9484i	2.05716	+	1.18770i
$818$	5.30901			0.185625
$819$	−8.53279	−	4.26515i	−0.298160	−	0.149036i
$820$	22.3945			0.782048
$821$	28.2743	+	16.3242i	0.986779	+	0.569717i	0.904310	−	0.426876i	$-0.140386\pi$
$821$	28.2743	+	16.3242i	0.986779	+	0.569717i	0.0824692	+	0.996594i	$0.473719\pi$
$822$	−5.57303	−	9.65276i	−0.194382	−	0.336679i
$823$	5.67187	+	9.82397i	0.197709	+	0.342442i	0.947785	−	0.318909i	$-0.103317\pi$
$823$	5.67187	+	9.82397i	0.197709	+	0.342442i	−0.750076	+	0.661351i	$0.769983\pi$
$824$	10.7933	+	6.23150i	0.376001	+	0.217085i
$825$		−	0.146053i		−	0.00508491i
$826$	11.2931	−	5.01067i	0.392936	−	0.174343i
$827$			14.7988i			0.514605i	0.966331	+	0.257302i	$0.0828337\pi$
$827$			14.7988i			0.514605i	−0.966331	+	0.257302i	$0.917166\pi$
$828$	2.24665	−	3.89131i	0.0780765	−	0.135232i
$829$	−6.23598	−	10.8010i	−0.216585	−	0.375136i	0.737177	−	0.675700i	$-0.236158\pi$
$829$	−6.23598	−	10.8010i	−0.216585	−	0.375136i	−0.953762	+	0.300564i	$0.902825\pi$
$830$	−12.5253	+	7.23150i	−0.434760	+	0.251009i
$831$	5.20568	−	9.01650i	0.180583	−	0.312779i
$832$	1.26180	−	3.37755i	0.0437451	−	0.117096i
$833$	−2.58369	−	0.556104i	−0.0895196	−	0.0192679i
$834$		−	2.49330i		−	0.0863360i
$835$	27.9029	−	48.3293i	0.965620	−	1.67250i
$836$	4.89270	+	8.47441i	0.169218	+	0.293094i
$837$	3.46410	−	2.00000i	0.119737	−	0.0691301i
$838$	17.8264	+	10.2921i	0.615804	+	0.355535i
$839$		−	10.0890i		−	0.348309i	−0.984718	−	0.174155i	$-0.944281\pi$
$839$		−	10.0890i		−	0.348309i	0.984718	−	0.174155i	$-0.0557193\pi$
$840$	−5.46992	+	2.42697i	−0.188730	+	0.0837385i
$841$	−23.2022			−0.800077
$842$	−6.44388	+	11.1611i	−0.222071	+	0.384638i
$843$	25.5566	−	14.7551i	0.880216	−	0.508193i
$844$	−4.03206	−	6.98373i	−0.138789	−	0.240390i
$845$	−9.58745	−	27.7964i	−0.329818	−	0.956227i
$846$	−3.29211			−0.113185
$847$	−2.63352	+	24.7511i	−0.0904887	+	0.850459i
$848$	3.00000			0.103020
$849$	−1.60730	+	2.78392i	−0.0551623	+	0.0955439i
$850$	−0.0378465	+	0.0218507i	−0.00129812	+	0.000749472i
$851$	−13.1431	+	7.58818i	−0.450540	+	0.260119i
$852$	3.56434	+	2.05787i	0.122112	+	0.0705016i
$853$			1.48784i			0.0509426i	0.999676	+	0.0254713i	$0.00810864\pi$
$853$			1.48784i			0.0509426i	−0.999676	+	0.0254713i	$0.991891\pi$
$854$	−13.8669	+	19.0348i	−0.474515	+	0.651357i
$855$	−17.5405			−0.599873
$856$	15.4173	+	8.90116i	0.526951	+	0.304235i
$857$	22.2832	+	38.5956i	0.761179	+	1.31840i	0.942243	+	0.334930i	$0.108713\pi$
$857$	22.2832	+	38.5956i	0.761179	+	1.31840i	−0.181064	+	0.983471i	$0.557954\pi$
$858$	−4.48690	+	0.752063i	−0.153180	+	0.0256750i
$859$	9.06411	−	15.6995i	0.309264	−	0.535660i	−0.668938	−	0.743318i	$-0.733251\pi$
$859$	9.06411	−	15.6995i	0.309264	−	0.535660i	0.978201	+	0.207658i	$0.0665841\pi$
$860$			19.8023i			0.675253i
$861$	−15.4248	+	21.1733i	−0.525674	+	0.721583i
$862$	−26.6260			−0.906884
$863$	19.8838	+	11.4799i	0.676852	+	0.390780i	0.798668	−	0.601772i	$-0.205539\pi$
$863$	19.8838	+	11.4799i	0.676852	+	0.390780i	−0.121816	+	0.992553i	$0.538872\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−46.9689	+	27.1175i	−1.59699	+	0.922023i
$866$	24.3189	+	14.0405i	0.826389	+	0.477116i
$867$	−16.8575			−0.572509
$868$	10.5236	+	1.11971i	0.357194	+	0.0380054i
$869$		−	7.93939i		−	0.269325i
$870$	2.72305	−	4.71645i	0.0923199	−	0.159903i
$871$	0.770125	+	4.59466i	0.0260947	+	0.155684i
$872$	1.63935	+	2.83944i	0.0555155	+	0.0961557i
$873$	−6.95445	−	4.01515i	−0.235372	−	0.135892i
$874$	34.8460			1.17868
$875$	−11.8539	−	26.7165i	−0.400737	−	0.903182i
$876$			9.54051i			0.322344i
$877$	−26.6309	−	15.3753i	−0.899261	−	0.519188i	−0.0223003	−	0.999751i	$-0.507099\pi$
$877$	−26.6309	−	15.3753i	−0.899261	−	0.519188i	−0.876960	+	0.480563i	$0.840432\pi$
$878$	24.0444	−	13.8820i	0.811459	−	0.468496i
$879$	21.4123	−	12.3624i	0.722219	−	0.416973i
$880$	−1.42697	+	2.47159i	−0.0481033	+	0.0833173i
$881$	−28.7551			−0.968784			−0.484392	−	0.874851i	$-0.660959\pi$
$881$	−28.7551			−0.968784			−0.484392	+	0.874851i	$0.660959\pi$
$882$	1.47292	−	6.84328i	0.0495959	−	0.230425i
$883$	−31.3696			−1.05567			−0.527836	−	0.849346i	$-0.676996\pi$
$883$	−31.3696			−1.05567			−0.527836	+	0.849346i	$0.676996\pi$
$884$	0.866158	+	1.05017i	0.0291320	+	0.0353211i
$885$	5.28092	+	9.14682i	0.177516	+	0.307467i
$886$	3.95067	−	2.28092i	0.132725	−	0.0766290i
$887$	−4.40786	+	7.63463i	−0.148001	+	0.256346i	−0.930489	−	0.366321i	$-0.880617\pi$
$887$	−4.40786	+	7.63463i	−0.148001	+	0.256346i	0.782487	+	0.622666i	$0.213951\pi$
$888$	−3.37755			−0.113343
$889$	−39.5749	+	17.5592i	−1.32730	+	0.588916i
$890$		−	25.7338i		−	0.862598i
$891$	−1.09275	−	0.630901i	−0.0366086	−	0.0211360i
$892$	20.5988	−	11.8927i	0.689698	−	0.398197i
$893$	−12.7653	−	22.1102i	−0.427175	−	0.739888i
$894$	−0.0151517	+	0.0262436i	−0.000506750	+	0.000877716i
$895$			12.9101i			0.431538i
$896$	2.63090	+	0.279927i	0.0878922	+	0.00935171i
$897$	−5.66966	+	15.1764i	−0.189304	+	0.506724i
$898$	−1.39095	+	2.40920i	−0.0464166	+	0.0803959i
$899$	−8.34105	+	4.81571i	−0.278190	+	0.160613i
$900$	−0.0578747	−	0.100242i	−0.00192916	−	0.00334140i
$901$	−0.566327	+	0.980908i	−0.0188671	+	0.0326788i
$902$			12.4933i			0.415981i
$903$	−18.7225	−	13.6394i	−0.623045	−	0.453889i
$904$		−	1.32241i		−	0.0439827i
$905$	−32.6522	−	18.8517i	−1.08539	−	0.626653i
$906$	2.15451	+	3.73171i	0.0715787	+	0.123978i
$907$	2.01515	+	3.49035i	0.0669120	+	0.115895i	0.897541	−	0.440932i	$-0.145352\pi$
$907$	2.01515	+	3.49035i	0.0669120	+	0.115895i	−0.830629	+	0.556827i	$0.812019\pi$
$908$	8.86074	+	5.11575i	0.294054	+	0.169772i
$909$	11.6394			0.386053
$910$	18.0042	−	11.8904i	0.596834	−	0.394163i
$911$	−14.1212			−0.467857			−0.233928	−	0.972254i	$-0.575158\pi$
$911$	−14.1212			−0.467857			−0.233928	+	0.972254i	$0.575158\pi$
$912$	6.71612	+	3.87755i	0.222393	+	0.128399i
$913$	−4.03427	−	6.98756i	−0.133515	−	0.231255i
$914$	14.9029	+	25.8126i	0.492944	+	0.853805i
$915$	−17.4354	−	10.0663i	−0.576396	−	0.332783i
$916$			1.04721i			0.0346008i
$917$	3.20185	−	30.0927i	0.105734	−	0.993747i
$918$			0.377552i			0.0124611i
$919$	5.06411	−	8.77130i	0.167050	−	0.289339i	−0.770332	−	0.637644i	$-0.779909\pi$
$919$	5.06411	−	8.77130i	0.167050	−	0.289339i	0.937381	+	0.348305i	$0.113243\pi$
$920$	5.08148	+	8.80138i	0.167531	+	0.290173i
$921$	−6.00969	+	3.46970i	−0.198026	+	0.114330i
$922$	9.30901	−	16.1237i	0.306576	−	0.531005i
$923$	−13.9012	−	5.19326i	−0.457562	−	0.170938i
$924$	−1.35395	−	3.05153i	−0.0445416	−	0.100388i
$925$			0.390950i			0.0128543i
$926$	21.0169	−	36.4023i	0.690658	−	1.19626i
$927$	−6.23150	−	10.7933i	−0.204669	−	0.354498i
$928$	−2.08526	+	1.20393i	−0.0684521	+	0.0395209i
$929$	30.3811	+	17.5405i	0.996770	+	0.575485i	0.907291	−	0.420503i	$-0.138146\pi$
$929$	30.3811	+	17.5405i	0.996770	+	0.575485i	0.0894790	+	0.995989i	$0.471480\pi$
$930$			9.04721i			0.296670i
$931$	51.6716	−	16.6429i	1.69347	−	0.545448i
$932$	3.75160			0.122888
$933$	5.53876	−	9.59341i	0.181331	−	0.314074i
$934$	−33.7071	+	19.4608i	−1.10293	+	0.636776i
$935$	−0.538756	−	0.933153i	−0.0176192	−	0.0305174i
$936$	−2.78153	+	2.29414i	−0.0909171	+	0.0749865i
$937$	22.6055			0.738491			0.369245	−	0.929332i	$-0.379616\pi$
$937$	22.6055			0.738491			0.369245	+	0.929332i	$0.379616\pi$
$938$	−3.12482	+	1.38646i	−0.102029	+	0.0452696i
$939$	−21.4079			−0.698619
$940$	3.72305	−	6.44850i	0.121432	−	0.210327i
$941$	−23.8013	+	13.7417i	−0.775901	+	0.447967i	−0.834976	−	0.550287i	$-0.814518\pi$
$941$	−23.8013	+	13.7417i	−0.775901	+	0.447967i	0.0590745	+	0.998254i	$0.481185\pi$
$942$	19.6687	−	11.3557i	0.640839	−	0.369989i
$943$	38.5285	+	22.2444i	1.25466	+	0.724379i
$944$		−	4.66966i		−	0.151984i
$945$	5.95058	+	0.633140i	0.193572	+	0.0205961i
$946$	−11.0472			−0.359176
$947$	−24.5757	−	14.1888i	−0.798602	−	0.461073i	0.0443799	−	0.999015i	$-0.485869\pi$
$947$	−24.5757	−	14.1888i	−0.798602	−	0.461073i	−0.842982	+	0.537941i	$0.819202\pi$
$948$	−3.14605	−	5.44912i	−0.102179	−	0.176979i
$949$	−5.68636	−	33.9255i	−0.184587	−	1.10127i
$950$	0.448824	−	0.777386i	0.0145618	−	0.0252217i
$951$			21.2181i			0.688044i
$952$	−0.588178	+	0.807380i	−0.0190630	+	0.0261674i
$953$	9.58864			0.310606			0.155303	−	0.987867i	$-0.450365\pi$
$953$	9.58864			0.310606			0.155303	+	0.987867i	$0.450365\pi$
$954$	−2.59808	−	1.50000i	−0.0841158	−	0.0485643i
$955$	−14.2574	+	8.23150i	−0.461358	+	0.266365i
$956$	−25.2851	+	14.5984i	−0.817780	+	0.472146i
$957$	2.63119	+	1.51912i	0.0850543	+	0.0491061i
$958$	2.28664			0.0738780
$959$	−17.3642	+	23.8354i	−0.560718	+	0.769686i
$960$			2.26180i			0.0729994i
$961$	−7.50000	+	12.9904i	−0.241935	+	0.419045i
$962$	12.0104	−	2.01310i	0.387231	−	0.0649049i
$963$	−8.90116	−	15.4173i	−0.286836	−	0.496814i
$964$	1.47908	+	0.853947i	0.0476380	+	0.0275038i
$965$	−39.1496			−1.26027
$966$	−11.8214	−	1.25780i	−0.380348	−	0.0404690i
$967$			31.2271i			1.00419i	0.864811	+	0.502097i	$0.167438\pi$
$967$			31.2271i			1.00419i	−0.864811	+	0.502097i	$0.832562\pi$
$968$	8.14744	+	4.70393i	0.261869	+	0.151190i
$969$	−2.53568	+	1.46398i	−0.0814578	+	0.0470297i
$970$	15.7296	−	9.08148i	0.505046	−	0.291589i
$971$	18.3833	−	31.8408i	0.589947	−	1.02182i	−0.404291	−	0.914630i	$-0.632482\pi$
$971$	18.3833	−	31.8408i	0.589947	−	1.02182i	0.994239	−	0.107188i	$-0.0341848\pi$
$972$	−1.00000			−0.0320750
$973$	−6.02978	+	2.67538i	−0.193306	+	0.0857687i
$974$	30.8405			0.988195
$975$	0.265546	+	0.321960i	0.00850427	+	0.0103110i
$976$	4.45058	+	7.70863i	0.142460	+	0.246747i
$977$	14.4811	−	8.36065i	0.463290	−	0.267481i	−0.250136	−	0.968211i	$-0.580475\pi$
$977$	14.4811	−	8.36065i	0.463290	−	0.267481i	0.713427	+	0.700730i	$0.247142\pi$
$978$	−6.20393	+	10.7455i	−0.198380	+	0.343604i
$979$	14.3562			0.458827
$980$	11.7387	+	10.6242i	0.374980	+	0.339378i
$981$		−	3.27871i		−	0.104681i
$982$	−35.6590	−	20.5877i	−1.13792	−	0.656981i
$983$	−39.2534	+	22.6630i	−1.25199	+	0.722836i	−0.971504	−	0.237022i	$-0.923829\pi$
$983$	−39.2534	+	22.6630i	−1.25199	+	0.722836i	−0.280485	+	0.959859i	$0.590495\pi$
$984$	4.95058	+	8.57465i	0.157819	+	0.273350i
$985$	3.63539	−	6.29668i	0.115833	−	0.200629i
$986$		−	0.909090i		−	0.0289513i
$987$	3.53252	+	7.96160i	0.112441	+	0.253420i
$988$	−26.1933	−	9.78541i	−0.833319	−	0.311315i
$989$	−19.6697	+	34.0688i	−0.625459	+	1.08333i
$990$	2.47159	−	1.42697i	0.0785523	−	0.0453522i
$991$	−25.7417	−	44.5859i	−0.817712	−	1.41632i	−0.907364	−	0.420346i	$-0.861909\pi$
$991$	−25.7417	−	44.5859i	−0.817712	−	1.41632i	0.0896517	−	0.995973i	$-0.471425\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$			21.0393i			0.667661i
$994$	1.15211	−	10.8281i	0.0365427	−	0.343447i
$995$		−	26.4709i		−	0.839185i
$996$	−5.53776	−	3.19723i	−0.175471	−	0.101308i
$997$	26.7333	+	46.3034i	0.846651	+	1.46644i	0.884180	+	0.467146i	$0.154718\pi$
$997$	26.7333	+	46.3034i	0.846651	+	1.46644i	−0.0375294	+	0.999296i	$0.511949\pi$
$998$	−7.73423	−	13.3961i	−0.244823	−	0.424046i
$999$	2.92505	+	1.68878i	0.0925443	+	0.0534305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.b.415.3	yes	12
3.2	odd	2		1638.2.dm.c.415.4		12
7.2	even	3		3822.2.c.k.883.4		6
7.4	even	3	inner	546.2.bk.b.25.4	yes	12
7.5	odd	6		3822.2.c.j.883.6		6
13.12	even	2	inner	546.2.bk.b.415.4	yes	12
21.11	odd	6		1638.2.dm.c.1117.3		12
39.38	odd	2		1638.2.dm.c.415.3		12
91.12	odd	6		3822.2.c.j.883.1		6
91.25	even	6	inner	546.2.bk.b.25.3	✓	12
91.51	even	6		3822.2.c.k.883.3		6
273.116	odd	6		1638.2.dm.c.1117.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.b.25.3	✓	12	91.25	even	6	inner
546.2.bk.b.25.4	yes	12	7.4	even	3	inner
546.2.bk.b.415.3	yes	12	1.1	even	1	trivial
546.2.bk.b.415.4	yes	12	13.12	even	2	inner
1638.2.dm.c.415.3		12	39.38	odd	2
1638.2.dm.c.415.4		12	3.2	odd	2
1638.2.dm.c.1117.3		12	21.11	odd	6
1638.2.dm.c.1117.4		12	273.116	odd	6
3822.2.c.j.883.1		6	91.12	odd	6
3822.2.c.j.883.6		6	7.5	odd	6
3822.2.c.k.883.3		6	91.51	even	6
3822.2.c.k.883.4		6	7.2	even	3

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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95878 + 1.13090i) q^{5} +1.00000i q^{6} +(2.41839 - 1.07303i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95878 + 1.13090i) q^{5} +1.00000i q^{6} +(2.41839 - 1.07303i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.13090 - 1.95878i) q^{10} +(1.09275 - 0.630901i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.26180 + 3.37755i) q^{13} +(-2.63090 - 0.279927i) q^{14} -2.26180i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.188776 - 0.326969i) q^{17} +(0.866025 - 0.500000i) q^{18} +(6.71612 + 3.87755i) q^{19} +2.26180i q^{20} +(-2.13846 - 1.55787i) q^{21} -1.26180 q^{22} +(-2.24665 + 3.89131i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.0578747 + 0.100242i) q^{25} +(2.78153 - 2.29414i) q^{26} +1.00000 q^{27} +(2.13846 + 1.55787i) q^{28} -2.40786 q^{29} +(-1.13090 + 1.95878i) q^{30} +(3.46410 - 2.00000i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09275 - 0.630901i) q^{33} +0.377552i q^{34} +(5.95058 + 0.633140i) q^{35} -1.00000 q^{36} +(2.92505 + 1.68878i) q^{37} +(-3.87755 - 6.71612i) q^{38} +(3.55595 - 0.596023i) q^{39} +(1.13090 - 1.95878i) q^{40} -9.90116i q^{41} +(1.07303 + 2.41839i) q^{42} +8.75510 q^{43} +(1.09275 + 0.630901i) q^{44} +(-1.95878 + 1.13090i) q^{45} +(3.89131 - 2.24665i) q^{46} +(-2.85105 - 1.64605i) q^{47} +1.00000 q^{48} +(4.69723 - 5.18999i) q^{49} -0.115749i q^{50} +(-0.188776 + 0.326969i) q^{51} +(-3.55595 + 0.596023i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(-0.866025 - 0.500000i) q^{54} +2.85395 q^{55} +(-1.07303 - 2.41839i) q^{56} -7.75510i q^{57} +(2.08526 + 1.20393i) q^{58} +(-4.04404 + 2.33483i) q^{59} +(1.95878 - 1.13090i) q^{60} +(4.45058 - 7.70863i) q^{61} -4.00000 q^{62} +(-0.279927 + 2.63090i) q^{63} -1.00000 q^{64} +(-6.29127 + 5.18890i) q^{65} +(0.630901 + 1.09275i) q^{66} +(1.11900 - 0.646053i) q^{67} +(0.188776 - 0.326969i) q^{68} +4.49330 q^{69} +(-4.83678 - 3.52360i) q^{70} +4.11575i q^{71} +(0.866025 + 0.500000i) q^{72} +(-8.26232 + 4.77026i) q^{73} +(-1.68878 - 2.92505i) q^{74} +(0.0578747 - 0.100242i) q^{75} +7.75510i q^{76} +(1.96573 - 2.69832i) q^{77} +(-3.37755 - 1.26180i) q^{78} +(3.14605 - 5.44912i) q^{79} +(-1.95878 + 1.13090i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.95058 + 8.57465i) q^{82} -6.39446i q^{83} +(0.279927 - 2.63090i) q^{84} -0.853947i q^{85} +(-7.58214 - 4.37755i) q^{86} +(1.20393 + 2.08526i) q^{87} +(-0.630901 - 1.09275i) q^{88} +(9.85325 + 5.68878i) q^{89} +2.26180 q^{90} +(0.572671 + 9.52219i) q^{91} -4.49330 q^{92} +(-3.46410 - 2.00000i) q^{93} +(1.64605 + 2.85105i) q^{94} +(8.77026 + 15.1905i) q^{95} +(-0.866025 - 0.500000i) q^{96} +8.03030i q^{97} +(-6.66292 + 2.14605i) q^{98} +1.26180i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43} + 12 q^{48} - 18 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{53} + 48 q^{55} - 6 q^{56} + 6 q^{61} - 48 q^{62} - 12 q^{64} - 12 q^{65} - 6 q^{66} - 18 q^{68} - 6 q^{75} - 24 q^{77} + 24 q^{79} - 6 q^{81} - 12 q^{82} - 6 q^{87} + 6 q^{88} - 24 q^{91} + 6 q^{94} + 24 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 + 6 * q^12 + 12 * q^13 - 18 * q^14 - 6 * q^16 + 18 * q^17 + 12 * q^22 - 6 * q^25 + 12 * q^27 + 12 * q^29 + 24 * q^35 - 12 * q^36 - 6 * q^38 - 6 * q^39 + 6 * q^42 + 24 * q^43 + 12 * q^48 - 18 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^53 + 48 * q^55 - 6 * q^56 + 6 * q^61 - 48 * q^62 - 12 * q^64 - 12 * q^65 - 6 * q^66 - 18 * q^68 - 6 * q^75 - 24 * q^77 + 24 * q^79 - 6 * q^81 - 12 * q^82 - 6 * q^87 + 6 * q^88 - 24 * q^91 + 6 * q^94 + 24 * q^95

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