LMFDB - Embedded newform 546.2.j.e.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$-0.114009 - 0.197470i$ of defining polynomial
Character	$\chi$	$=$	546.529
Dual form			546.2.j.e.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.59452 - 0.518144i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.59452 - 0.518144i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.114009 - 0.197470i) q^{10} +(-1.70561 - 2.95420i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.62906 + 3.21655i) q^{13} +(2.59452 + 0.518144i) q^{14} +(-0.114009 + 0.197470i) q^{15} +1.00000 q^{16} -5.41122 q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.17107 + 5.49246i) q^{19} +(0.114009 + 0.197470i) q^{20} +(-0.848534 - 2.50599i) q^{21} +(1.70561 + 2.95420i) q^{22} -1.91925 q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.47400 - 4.28510i) q^{25} +(1.62906 - 3.21655i) q^{26} -1.00000 q^{27} +(-2.59452 - 0.518144i) q^{28} +(0.851453 - 1.47476i) q^{29} +(0.114009 - 0.197470i) q^{30} +(-1.78052 + 3.08395i) q^{31} -1.00000 q^{32} +(1.70561 - 2.95420i) q^{33} +5.41122 q^{34} +(-0.193482 - 0.571413i) q^{35} +(-0.500000 + 0.866025i) q^{36} -4.18320 q^{37} +(3.17107 - 5.49246i) q^{38} +(-3.60014 + 0.197470i) q^{39} +(-0.114009 - 0.197470i) q^{40} +(1.59160 - 2.75673i) q^{41} +(0.848534 + 2.50599i) q^{42} +(5.17961 + 8.97135i) q^{43} +(-1.70561 - 2.95420i) q^{44} -0.228019 q^{45} +1.91925 q^{46} +(-5.57211 - 9.65117i) q^{47} +(0.500000 + 0.866025i) q^{48} +(6.46305 + 2.68867i) q^{49} +(-2.47400 + 4.28510i) q^{50} +(-2.70561 - 4.68625i) q^{51} +(-1.62906 + 3.21655i) q^{52} +(-3.31400 + 5.74001i) q^{53} +1.00000 q^{54} +(0.388911 - 0.673613i) q^{55} +(2.59452 + 0.518144i) q^{56} -6.34214 q^{57} +(-0.851453 + 1.47476i) q^{58} -14.7704 q^{59} +(-0.114009 + 0.197470i) q^{60} +(3.35999 - 5.81968i) q^{61} +(1.78052 - 3.08395i) q^{62} +(1.74599 - 1.98785i) q^{63} +1.00000 q^{64} +(-0.820899 + 0.0450268i) q^{65} +(-1.70561 + 2.95420i) q^{66} +(-5.58065 - 9.66597i) q^{67} -5.41122 q^{68} +(-0.959623 - 1.66212i) q^{69} +(0.193482 + 0.571413i) q^{70} +(-0.0390952 - 0.0677149i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.31721 + 10.9417i) q^{73} +4.18320 q^{74} +4.94801 q^{75} +(-3.17107 + 5.49246i) q^{76} +(2.89453 + 8.54848i) q^{77} +(3.60014 - 0.197470i) q^{78} +(0.811077 + 1.40483i) q^{79} +(0.114009 + 0.197470i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.59160 + 2.75673i) q^{82} -1.70291 q^{83} +(-0.848534 - 2.50599i) q^{84} +(-0.616929 - 1.06855i) q^{85} +(-5.17961 - 8.97135i) q^{86} +1.70291 q^{87} +(1.70561 + 2.95420i) q^{88} +17.5457 q^{89} +0.228019 q^{90} +(5.89325 - 7.50131i) q^{91} -1.91925 q^{92} -3.56104 q^{93} +(5.57211 + 9.65117i) q^{94} -1.44613 q^{95} +(-0.500000 - 0.866025i) q^{96} +(6.82663 + 11.8241i) q^{97} +(-6.46305 - 2.68867i) q^{98} +3.41122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9} + 2 q^{10} + 6 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} + 10 q^{16} - 8 q^{17} + 5 q^{18} + 3 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} - 12 q^{23} - 5 q^{24} - q^{25} + 4 q^{26} - 10 q^{27} - 2 q^{28} - 2 q^{30} - 10 q^{31} - 10 q^{32} - 6 q^{33} + 8 q^{34} + 16 q^{35} - 5 q^{36} - 2 q^{37} - 3 q^{38} - 2 q^{39} + 2 q^{40} - 4 q^{41} + 4 q^{42} + 3 q^{43} + 6 q^{44} + 4 q^{45} + 12 q^{46} - 15 q^{47} + 5 q^{48} + 4 q^{49} + q^{50} - 4 q^{51} - 4 q^{52} - 17 q^{53} + 10 q^{54} + 3 q^{55} + 2 q^{56} + 6 q^{57} - 4 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 10 q^{64} - 4 q^{65} + 6 q^{66} - q^{67} - 8 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} + 5 q^{72} + 12 q^{73} + 2 q^{74} - 2 q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} - 2 q^{80} - 5 q^{81} + 4 q^{82} - 4 q^{84} + q^{85} - 3 q^{86} - 6 q^{88} - 14 q^{89} - 4 q^{90} + 26 q^{91} - 12 q^{92} - 20 q^{93} + 15 q^{94} - 48 q^{95} - 5 q^{96} - 6 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9 + 2 * q^10 + 6 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 + 10 * q^16 - 8 * q^17 + 5 * q^18 + 3 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 - 12 * q^23 - 5 * q^24 - q^25 + 4 * q^26 - 10 * q^27 - 2 * q^28 - 2 * q^30 - 10 * q^31 - 10 * q^32 - 6 * q^33 + 8 * q^34 + 16 * q^35 - 5 * q^36 - 2 * q^37 - 3 * q^38 - 2 * q^39 + 2 * q^40 - 4 * q^41 + 4 * q^42 + 3 * q^43 + 6 * q^44 + 4 * q^45 + 12 * q^46 - 15 * q^47 + 5 * q^48 + 4 * q^49 + q^50 - 4 * q^51 - 4 * q^52 - 17 * q^53 + 10 * q^54 + 3 * q^55 + 2 * q^56 + 6 * q^57 - 4 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 10 * q^64 - 4 * q^65 + 6 * q^66 - q^67 - 8 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 + 5 * q^72 + 12 * q^73 + 2 * q^74 - 2 * q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 - 2 * q^80 - 5 * q^81 + 4 * q^82 - 4 * q^84 + q^85 - 3 * q^86 - 6 * q^88 - 14 * q^89 - 4 * q^90 + 26 * q^91 - 12 * q^92 - 20 * q^93 + 15 * q^94 - 48 * q^95 - 5 * q^96 - 6 * q^97 - 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.114009	+	0.197470i	0.0509865	+	0.0883113i	0.890392	−	0.455194i	$-0.150430\pi$
$5$	0.114009	+	0.197470i	0.0509865	+	0.0883113i	−0.839406	+	0.543505i	$0.817097\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.59452	−	0.518144i	−0.980636	−	0.195840i
$7$	−2.59452	−	0.518144i	−0.980636	−	0.195840i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.114009	−	0.197470i	−0.0360529	−	0.0624455i
$11$	−1.70561	−	2.95420i	−0.514260	−	0.890725i	−0.999863	−	0.0165453i	$-0.994733\pi$
$11$	−1.70561	−	2.95420i	−0.514260	−	0.890725i	0.485603	−	0.874180i	$-0.338600\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−1.62906	+	3.21655i	−0.451819	+	0.892110i
$13$	−1.62906	+	3.21655i	−0.451819	+	0.892110i
$14$	2.59452	+	0.518144i	0.693414	+	0.138480i
$15$	−0.114009	+	0.197470i	−0.0294371	+	0.0509865i
$16$	1.00000			0.250000
$17$	−5.41122			−1.31241			−0.656206	−	0.754581i	$-0.727840\pi$
$17$	−5.41122			−1.31241			−0.656206	+	0.754581i	$0.727840\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−3.17107	+	5.49246i	−0.727494	+	1.26006i	0.230446	+	0.973085i	$0.425982\pi$
$19$	−3.17107	+	5.49246i	−0.727494	+	1.26006i	−0.957939	+	0.286971i	$0.907352\pi$
$20$	0.114009	+	0.197470i	0.0254933	+	0.0441556i
$21$	−0.848534	−	2.50599i	−0.185165	−	0.546852i
$22$	1.70561	+	2.95420i	0.363637	+	0.629838i
$23$	−1.91925			−0.400190			−0.200095	−	0.979776i	$-0.564125\pi$
$23$	−1.91925			−0.400190			−0.200095	+	0.979776i	$0.564125\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.47400	−	4.28510i	0.494801	−	0.857020i
$26$	1.62906	−	3.21655i	0.319484	−	0.630817i
$27$	−1.00000			−0.192450
$28$	−2.59452	−	0.518144i	−0.490318	−	0.0979200i
$29$	0.851453	−	1.47476i	0.158111	−	0.273856i	−0.776077	−	0.630639i	$-0.782793\pi$
$29$	0.851453	−	1.47476i	0.158111	−	0.273856i	0.934187	+	0.356783i	$0.116126\pi$
$30$	0.114009	−	0.197470i	0.0208152	−	0.0360529i
$31$	−1.78052	+	3.08395i	−0.319791	+	0.553895i	−0.980444	−	0.196797i	$-0.936946\pi$
$31$	−1.78052	+	3.08395i	−0.319791	+	0.553895i	0.660653	+	0.750691i	$0.270279\pi$
$32$	−1.00000			−0.176777
$33$	1.70561	−	2.95420i	0.296908	−	0.514260i
$34$	5.41122			0.928016
$35$	−0.193482	−	0.571413i	−0.0327043	−	0.0965864i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−4.18320			−0.687713			−0.343857	−	0.939022i	$-0.611733\pi$
$37$	−4.18320			−0.687713			−0.343857	+	0.939022i	$0.611733\pi$
$38$	3.17107	−	5.49246i	0.514416	−	0.890994i
$39$	−3.60014	+	0.197470i	−0.576484	+	0.0316205i
$40$	−0.114009	−	0.197470i	−0.0180265	−	0.0312227i
$41$	1.59160	−	2.75673i	0.248566	−	0.430529i	−0.714562	−	0.699572i	$-0.753374\pi$
$41$	1.59160	−	2.75673i	0.248566	−	0.430529i	0.963128	+	0.269043i	$0.0867074\pi$
$42$	0.848534	+	2.50599i	0.130932	+	0.386683i
$43$	5.17961	+	8.97135i	0.789883	+	1.36812i	0.926038	+	0.377431i	$0.123192\pi$
$43$	5.17961	+	8.97135i	0.789883	+	1.36812i	−0.136154	+	0.990688i	$0.543474\pi$
$44$	−1.70561	−	2.95420i	−0.257130	−	0.445362i
$45$	−0.228019			−0.0339910
$46$	1.91925			0.282977
$47$	−5.57211	−	9.65117i	−0.812775	−	1.40777i	−0.910914	−	0.412596i	$-0.864622\pi$
$47$	−5.57211	−	9.65117i	−0.812775	−	1.40777i	0.0981388	−	0.995173i	$-0.468711\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	6.46305	+	2.68867i	0.923293	+	0.384095i
$50$	−2.47400	+	4.28510i	−0.349877	+	0.606005i
$51$	−2.70561	−	4.68625i	−0.378861	−	0.656206i
$52$	−1.62906	+	3.21655i	−0.225909	+	0.446055i
$53$	−3.31400	+	5.74001i	−0.455212	+	0.788451i	−0.998700	−	0.0509659i	$-0.983770\pi$
$53$	−3.31400	+	5.74001i	−0.455212	+	0.788451i	0.543488	+	0.839417i	$0.317103\pi$
$54$	1.00000			0.136083
$55$	0.388911	−	0.673613i	0.0524407	−	0.0908299i
$56$	2.59452	+	0.518144i	0.346707	+	0.0692399i
$57$	−6.34214			−0.840037
$58$	−0.851453	+	1.47476i	−0.111801	+	0.193646i
$59$	−14.7704			−1.92295			−0.961474	−	0.274897i	$-0.911356\pi$
$59$	−14.7704			−1.92295			−0.961474	+	0.274897i	$0.911356\pi$
$60$	−0.114009	+	0.197470i	−0.0147185	+	0.0254933i
$61$	3.35999	−	5.81968i	0.430203	−	0.745134i	−0.566687	−	0.823933i	$-0.691775\pi$
$61$	3.35999	−	5.81968i	0.430203	−	0.745134i	0.996891	+	0.0787991i	$0.0251086\pi$
$62$	1.78052	−	3.08395i	0.226127	−	0.391663i
$63$	1.74599	−	1.98785i	0.219973	−	0.250445i
$64$	1.00000			0.125000
$65$	−0.820899	+	0.0450268i	−0.101820	+	0.00558489i
$66$	−1.70561	+	2.95420i	−0.209946	+	0.363637i
$67$	−5.58065	−	9.66597i	−0.681785	−	1.18089i	−0.974436	−	0.224667i	$-0.927871\pi$
$67$	−5.58065	−	9.66597i	−0.681785	−	1.18089i	0.292651	−	0.956219i	$-0.405463\pi$
$68$	−5.41122			−0.656206
$69$	−0.959623	−	1.66212i	−0.115525	−	0.200095i
$70$	0.193482	+	0.571413i	0.0231255	+	0.0682969i
$71$	−0.0390952	−	0.0677149i	−0.00463975	−	0.00803628i	0.863696	−	0.504013i	$-0.168144\pi$
$71$	−0.0390952	−	0.0677149i	−0.00463975	−	0.00803628i	−0.868336	+	0.495976i	$0.834810\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−6.31721	+	10.9417i	−0.739373	+	1.28063i	0.213404	+	0.976964i	$0.431545\pi$
$73$	−6.31721	+	10.9417i	−0.739373	+	1.28063i	−0.952778	+	0.303668i	$0.901789\pi$
$74$	4.18320			0.486287
$75$	4.94801			0.571347
$76$	−3.17107	+	5.49246i	−0.363747	+	0.630028i
$77$	2.89453	+	8.54848i	0.329862	+	0.974189i
$78$	3.60014	−	0.197470i	0.407636	−	0.0223591i
$79$	0.811077	+	1.40483i	0.0912532	+	0.158055i	0.908039	−	0.418886i	$-0.137579\pi$
$79$	0.811077	+	1.40483i	0.0912532	+	0.158055i	−0.816785	+	0.576941i	$0.804246\pi$
$80$	0.114009	+	0.197470i	0.0127466	+	0.0220778i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.59160	+	2.75673i	−0.175763	+	0.304430i
$83$	−1.70291			−0.186918			−0.0934592	−	0.995623i	$-0.529792\pi$
$83$	−1.70291			−0.186918			−0.0934592	+	0.995623i	$0.529792\pi$
$84$	−0.848534	−	2.50599i	−0.0925826	−	0.273426i
$85$	−0.616929	−	1.06855i	−0.0669154	−	0.115901i
$86$	−5.17961	−	8.97135i	−0.558532	−	0.967406i
$87$	1.70291			0.182571
$88$	1.70561	+	2.95420i	0.181818	+	0.314919i
$89$	17.5457			1.85984			0.929920	−	0.367762i	$-0.119876\pi$
$89$	17.5457			1.85984			0.929920	+	0.367762i	$0.119876\pi$
$90$	0.228019			0.0240353
$91$	5.89325	−	7.50131i	0.617780	−	0.786351i
$92$	−1.91925			−0.200095
$93$	−3.56104			−0.369263
$94$	5.57211	+	9.65117i	0.574719	+	0.995443i
$95$	−1.44613			−0.148369
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	6.82663	+	11.8241i	0.693140	+	1.20055i	0.970804	+	0.239875i	$0.0771064\pi$
$97$	6.82663	+	11.8241i	0.693140	+	1.20055i	−0.277664	+	0.960678i	$0.589560\pi$
$98$	−6.46305	−	2.68867i	−0.652867	−	0.271596i
$99$	3.41122			0.342840
$100$	2.47400	−	4.28510i	0.247400	−	0.428510i
$101$	8.25823	+	14.3037i	0.821724	+	1.42327i	0.904397	+	0.426691i	$0.140321\pi$
$101$	8.25823	+	14.3037i	0.821724	+	1.42327i	−0.0826732	+	0.996577i	$0.526346\pi$
$102$	2.70561	+	4.68625i	0.267895	+	0.464008i
$103$	−3.17961	−	5.50725i	−0.313296	−	0.542645i	0.665777	−	0.746150i	$-0.268100\pi$
$103$	−3.17961	−	5.50725i	−0.313296	−	0.542645i	−0.979074	+	0.203505i	$0.934767\pi$
$104$	1.62906	−	3.21655i	0.159742	−	0.315408i
$105$	0.398117	−	0.453266i	0.0388523	−	0.0442343i
$106$	3.31400	−	5.74001i	0.321884	−	0.557519i
$107$	6.54724			0.632945			0.316473	−	0.948602i	$-0.397501\pi$
$107$	6.54724			0.632945			0.316473	+	0.948602i	$0.397501\pi$
$108$	−1.00000			−0.0962250
$109$	0.797093	−	1.38061i	0.0763477	−	0.132238i	−0.825324	−	0.564660i	$-0.809007\pi$
$109$	0.797093	−	1.38061i	0.0763477	−	0.132238i	0.901672	+	0.432422i	$0.142341\pi$
$110$	−0.388911	+	0.673613i	−0.0370812	+	0.0642265i
$111$	−2.09160	−	3.62276i	−0.198526	−	0.343857i
$112$	−2.59452	−	0.518144i	−0.245159	−	0.0489600i
$113$	−4.12255	−	7.14047i	−0.387817	−	0.671719i	0.604339	−	0.796728i	$-0.293437\pi$
$113$	−4.12255	−	7.14047i	−0.387817	−	0.671719i	−0.992156	+	0.125009i	$0.960104\pi$
$114$	6.34214			0.593996
$115$	−0.218812	−	0.378993i	−0.0204043	−	0.0353413i
$116$	0.851453	−	1.47476i	0.0790555	−	0.136928i
$117$	−1.97108	−	3.01908i	−0.182227	−	0.279114i
$118$	14.7704			1.35973
$119$	14.0395	+	2.80379i	1.28700	+	0.257023i
$120$	0.114009	−	0.197470i	0.0104076	−	0.0180265i
$121$	−0.318198	+	0.551135i	−0.0289271	+	0.0501032i
$122$	−3.35999	+	5.81968i	−0.304200	+	0.526889i
$123$	3.18320			0.287019
$124$	−1.78052	+	3.08395i	−0.159896	+	0.276947i
$125$	2.26833			0.202886
$126$	−1.74599	+	1.98785i	−0.155545	+	0.177091i
$127$	−6.40560	+	11.0948i	−0.568405	+	0.984506i	0.428319	+	0.903627i	$0.359106\pi$
$127$	−6.40560	+	11.0948i	−0.568405	+	0.984506i	−0.996724	+	0.0808783i	$0.974227\pi$
$128$	−1.00000			−0.0883883
$129$	−5.17961	+	8.97135i	−0.456039	+	0.789883i
$130$	0.820899	−	0.0450268i	0.0719976	−	0.00394912i
$131$	−1.75964	−	3.04778i	−0.153740	−	0.266286i	0.778859	−	0.627199i	$-0.215799\pi$
$131$	−1.75964	−	3.04778i	−0.153740	−	0.266286i	−0.932600	+	0.360913i	$0.882465\pi$
$132$	1.70561	−	2.95420i	0.148454	−	0.257130i
$133$	11.0733	−	12.6072i	0.960176	−	1.09318i
$134$	5.58065	+	9.66597i	0.482095	+	0.835012i
$135$	−0.114009	−	0.197470i	−0.00981236	−	0.0169955i
$136$	5.41122			0.464008
$137$	17.6955			1.51183			0.755915	−	0.654669i	$-0.227192\pi$
$137$	17.6955			1.51183			0.755915	+	0.654669i	$0.227192\pi$
$138$	0.959623	+	1.66212i	0.0816885	+	0.141489i
$139$	3.98321	+	6.89912i	0.337851	+	0.585176i	0.984028	−	0.178012i	$-0.0569665\pi$
$139$	3.98321	+	6.89912i	0.337851	+	0.585176i	−0.646177	+	0.763188i	$0.723633\pi$
$140$	−0.193482	−	0.571413i	−0.0163522	−	0.0482932i
$141$	5.57211	−	9.65117i	0.469256	−	0.812775i
$142$	0.0390952	+	0.0677149i	0.00328080	+	0.00568251i
$143$	12.2809	−	0.673613i	1.02698	−	0.0563303i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.388295			0.0322461
$146$	6.31721	−	10.9417i	0.522816	−	0.905544i
$147$	0.903072	+	6.94150i	0.0744842	+	0.572525i
$148$	−4.18320			−0.343857
$149$	−1.34679	+	2.33271i	−0.110333	+	0.191103i	−0.915905	−	0.401396i	$-0.868525\pi$
$149$	−1.34679	+	2.33271i	−0.110333	+	0.191103i	0.805571	+	0.592499i	$0.201859\pi$
$150$	−4.94801			−0.404003
$151$	6.56432	−	11.3697i	0.534197	−	0.925256i	−0.465005	−	0.885308i	$-0.653947\pi$
$151$	6.56432	−	11.3697i	0.534197	−	0.925256i	0.999202	−	0.0399480i	$-0.0127192\pi$
$152$	3.17107	−	5.49246i	0.257208	−	0.445497i
$153$	2.70561	−	4.68625i	0.218735	−	0.378861i
$154$	−2.89453	−	8.54848i	−0.233248	−	0.688856i
$155$	−0.811985			−0.0652202
$156$	−3.60014	+	0.197470i	−0.288242	+	0.0158103i
$157$	−1.59071	+	2.75520i	−0.126953	+	0.219889i	−0.922495	−	0.386010i	$-0.873853\pi$
$157$	−1.59071	+	2.75520i	−0.126953	+	0.219889i	0.795542	+	0.605899i	$0.207186\pi$
$158$	−0.811077	−	1.40483i	−0.0645258	−	0.111762i
$159$	−6.62799			−0.525634
$160$	−0.114009	−	0.197470i	−0.00901323	−	0.0156114i
$161$	4.97952	+	0.994446i	0.392441	+	0.0783733i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	8.14702	−	14.1111i	0.638124	−	1.10526i	−0.347720	−	0.937598i	$-0.613044\pi$
$163$	8.14702	−	14.1111i	0.638124	−	1.10526i	0.985844	−	0.167665i	$-0.0536226\pi$
$164$	1.59160	−	2.75673i	0.124283	−	0.215264i
$165$	0.777821			0.0605533
$166$	1.70291			0.132171
$167$	0.826739	−	1.43195i	0.0639750	−	0.110808i	−0.832264	−	0.554380i	$-0.812956\pi$
$167$	0.826739	−	1.43195i	0.0639750	−	0.110808i	0.896239	+	0.443572i	$0.146289\pi$
$168$	0.848534	+	2.50599i	0.0654658	+	0.193341i
$169$	−7.69235	−	10.4799i	−0.591720	−	0.806144i
$170$	0.616929	+	1.06855i	0.0473163	+	0.0819543i
$171$	−3.17107	−	5.49246i	−0.242498	−	0.420019i
$172$	5.17961	+	8.97135i	0.394942	+	0.684059i
$173$	−7.02100	+	12.1607i	−0.533797	+	0.924563i	0.465424	+	0.885088i	$0.345902\pi$
$173$	−7.02100	+	12.1607i	−0.533797	+	0.924563i	−0.999221	+	0.0394751i	$0.987431\pi$
$174$	−1.70291			−0.129097
$175$	−8.63915	+	9.83588i	−0.653058	+	0.743523i
$176$	−1.70561	−	2.95420i	−0.128565	−	0.222681i
$177$	−7.38522	−	12.7916i	−0.555107	−	0.961474i
$178$	−17.5457			−1.31511
$179$	4.66663	+	8.08283i	0.348800	+	0.604139i	0.986037	−	0.166529i	$-0.0532559\pi$
$179$	4.66663	+	8.08283i	0.348800	+	0.604139i	−0.637237	+	0.770668i	$0.719923\pi$
$180$	−0.228019			−0.0169955
$181$	1.13838			0.0846148			0.0423074	−	0.999105i	$-0.486529\pi$
$181$	1.13838			0.0846148			0.0423074	+	0.999105i	$0.486529\pi$
$182$	−5.89325	+	7.50131i	−0.436837	+	0.556034i
$183$	6.71999			0.496756
$184$	1.91925			0.141489
$185$	−0.476924	−	0.826056i	−0.0350641	−	0.0607328i
$186$	3.56104			0.261108
$187$	9.22941	+	15.9858i	0.674922	+	1.16900i
$188$	−5.57211	−	9.65117i	−0.406388	−	0.703884i
$189$	2.59452	+	0.518144i	0.188723	+	0.0376894i
$190$	1.44613			0.104913
$191$	−9.04253	+	15.6621i	−0.654294	+	1.13327i	0.327776	+	0.944755i	$0.393701\pi$
$191$	−9.04253	+	15.6621i	−0.654294	+	1.13327i	−0.982070	+	0.188515i	$0.939632\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	2.91296	+	5.04539i	0.209679	+	0.363175i	0.951614	−	0.307297i	$-0.0994246\pi$
$193$	2.91296	+	5.04539i	0.209679	+	0.363175i	−0.741934	+	0.670473i	$0.766091\pi$
$194$	−6.82663	−	11.8241i	−0.490124	−	0.848919i
$195$	−0.449444	−	0.688406i	−0.0321854	−	0.0492978i
$196$	6.46305	+	2.68867i	0.461647	+	0.192048i
$197$	−10.3527	+	17.9315i	−0.737602	+	1.27756i	0.215970	+	0.976400i	$0.430709\pi$
$197$	−10.3527	+	17.9315i	−0.737602	+	1.27756i	−0.953572	+	0.301165i	$0.902625\pi$
$198$	−3.41122			−0.242425
$199$	−16.3984			−1.16245			−0.581227	−	0.813741i	$-0.697427\pi$
$199$	−16.3984			−1.16245			−0.581227	+	0.813741i	$0.697427\pi$
$200$	−2.47400	+	4.28510i	−0.174938	+	0.303002i
$201$	5.58065	−	9.66597i	0.393629	−	0.681785i
$202$	−8.25823	−	14.3037i	−0.581047	−	1.00640i
$203$	−2.97325	+	3.38512i	−0.208681	+	0.237589i
$204$	−2.70561	−	4.68625i	−0.189430	−	0.328103i
$205$	0.725829			0.0506941
$206$	3.17961	+	5.50725i	0.221534	+	0.383708i
$207$	0.959623	−	1.66212i	0.0666984	−	0.115525i
$208$	−1.62906	+	3.21655i	−0.112955	+	0.223027i
$209$	21.6344			1.49648
$210$	−0.398117	+	0.453266i	−0.0274727	+	0.0312783i
$211$	3.74446	−	6.48560i	0.257779	−	0.446487i	−0.707867	−	0.706345i	$-0.750343\pi$
$211$	3.74446	−	6.48560i	0.257779	−	0.446487i	0.965647	+	0.259858i	$0.0836759\pi$
$212$	−3.31400	+	5.74001i	−0.227606	+	0.394226i
$213$	0.0390952	−	0.0677149i	0.00267876	−	0.00463975i
$214$	−6.54724			−0.447560
$215$	−1.18105	+	2.04564i	−0.0805468	+	0.139511i
$216$	1.00000			0.0680414
$217$	6.21753	−	7.07881i	0.422073	−	0.480541i
$218$	−0.797093	+	1.38061i	−0.0539860	+	0.0935064i
$219$	−12.6344			−0.853755
$220$	0.388911	−	0.673613i	0.0262203	−	0.0454150i
$221$	8.81517	−	17.4054i	0.592973	−	1.17082i
$222$	2.09160	+	3.62276i	0.140379	+	0.243143i
$223$	−8.41325	+	14.5722i	−0.563393	+	0.975825i	0.433804	+	0.901007i	$0.357171\pi$
$223$	−8.41325	+	14.5722i	−0.563393	+	0.975825i	−0.997197	+	0.0748181i	$0.976162\pi$
$224$	2.59452	+	0.518144i	0.173354	+	0.0346199i
$225$	2.47400	+	4.28510i	0.164934	+	0.285673i
$226$	4.12255	+	7.14047i	0.274228	+	0.474977i
$227$	−4.23214			−0.280897			−0.140449	−	0.990088i	$-0.544854\pi$
$227$	−4.23214			−0.280897			−0.140449	+	0.990088i	$0.544854\pi$
$228$	−6.34214			−0.420019
$229$	−6.86498	−	11.8905i	−0.453650	−	0.785745i	0.544959	−	0.838463i	$-0.316545\pi$
$229$	−6.86498	−	11.8905i	−0.453650	−	0.785745i	−0.998609	+	0.0527171i	$0.983212\pi$
$230$	0.218812	+	0.378993i	0.0144280	+	0.0249901i
$231$	−5.95593	+	6.78098i	−0.391872	+	0.446155i
$232$	−0.851453	+	1.47476i	−0.0559007	+	0.0968228i
$233$	−3.85349	−	6.67444i	−0.252450	−	0.437257i	0.711749	−	0.702433i	$-0.247903\pi$
$233$	−3.85349	−	6.67444i	−0.252450	−	0.437257i	−0.964200	+	0.265176i	$0.914570\pi$
$234$	1.97108	+	3.01908i	0.128854	+	0.197363i
$235$	1.27054	−	2.20065i	0.0828812	−	0.143554i
$236$	−14.7704			−0.961474
$237$	−0.811077	+	1.40483i	−0.0526851	+	0.0912532i
$238$	−14.0395	−	2.80379i	−0.910046	−	0.181743i
$239$	−25.2189			−1.63128			−0.815638	−	0.578562i	$-0.803614\pi$
$239$	−25.2189			−1.63128			−0.815638	+	0.578562i	$0.803614\pi$
$240$	−0.114009	+	0.197470i	−0.00735927	+	0.0127466i
$241$	27.8367			1.79312			0.896560	−	0.442923i	$-0.146059\pi$
$241$	27.8367			1.79312			0.896560	+	0.442923i	$0.146059\pi$
$242$	0.318198	−	0.551135i	0.0204545	−	0.0354283i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.35999	−	5.81968i	0.215102	−	0.372567i
$245$	0.205917	+	1.58279i	0.0131556	+	0.101121i
$246$	−3.18320			−0.202953
$247$	−12.5009	−	19.1474i	−0.795413	−	1.21832i
$248$	1.78052	−	3.08395i	0.113063	−	0.195831i
$249$	−0.851453	−	1.47476i	−0.0539587	−	0.0934592i
$250$	−2.26833			−0.143462
$251$	2.12395	+	3.67878i	0.134062	+	0.232203i	0.925239	−	0.379385i	$-0.123864\pi$
$251$	2.12395	+	3.67878i	0.134062	+	0.232203i	−0.791177	+	0.611588i	$0.790531\pi$
$252$	1.74599	−	1.98785i	0.109987	−	0.125223i
$253$	3.27348	+	5.66984i	0.205802	+	0.356460i
$254$	6.40560	−	11.0948i	0.401923	−	0.696151i
$255$	0.616929	−	1.06855i	0.0386336	−	0.0669154i
$256$	1.00000			0.0625000
$257$	14.7167			0.918003			0.459002	−	0.888435i	$-0.348207\pi$
$257$	14.7167			0.918003			0.459002	+	0.888435i	$0.348207\pi$
$258$	5.17961	−	8.97135i	0.322469	−	0.558532i
$259$	10.8534	+	2.16750i	0.674396	+	0.134682i
$260$	−0.820899	+	0.0450268i	−0.0509100	+	0.00279245i
$261$	0.851453	+	1.47476i	0.0527036	+	0.0912854i
$262$	1.75964	+	3.04778i	0.108711	+	0.188292i
$263$	−11.7053	−	20.2741i	−0.721777	−	1.25015i	−0.960287	−	0.279015i	$-0.909992\pi$
$263$	−11.7053	−	20.2741i	−0.721777	−	1.25015i	0.238510	−	0.971140i	$-0.423341\pi$
$264$	−1.70561	+	2.95420i	−0.104973	+	0.181818i
$265$	−1.51131			−0.0928388
$266$	−11.0733	+	12.6072i	−0.678947	+	0.772998i
$267$	8.77285	+	15.1950i	0.536890	+	0.929920i
$268$	−5.58065	−	9.66597i	−0.340892	−	0.590443i
$269$	−9.35772			−0.570550			−0.285275	−	0.958446i	$-0.592085\pi$
$269$	−9.35772			−0.570550			−0.285275	+	0.958446i	$0.592085\pi$
$270$	0.114009	+	0.197470i	0.00693839	+	0.0120176i
$271$	−15.1475			−0.920145			−0.460072	−	0.887881i	$-0.652177\pi$
$271$	−15.1475			−0.920145			−0.460072	+	0.887881i	$0.652177\pi$
$272$	−5.41122			−0.328103
$273$	9.44295	+	1.35305i	0.571513	+	0.0818903i
$274$	−17.6955			−1.06903
$275$	−16.8787			−1.01783
$276$	−0.959623	−	1.66212i	−0.0577625	−	0.100048i
$277$	−32.8782			−1.97546			−0.987731	−	0.156165i	$-0.950087\pi$
$277$	−32.8782			−1.97546			−0.987731	+	0.156165i	$0.950087\pi$
$278$	−3.98321	−	6.89912i	−0.238897	−	0.413782i
$279$	−1.78052	−	3.08395i	−0.106597	−	0.184632i
$280$	0.193482	+	0.571413i	0.0115627	+	0.0341484i
$281$	−16.8072			−1.00263			−0.501316	−	0.865264i	$-0.667150\pi$
$281$	−16.8072			−1.00263			−0.501316	+	0.865264i	$0.667150\pi$
$282$	−5.57211	+	9.65117i	−0.331814	+	0.574719i
$283$	6.07998	+	10.5308i	0.361417	+	0.625993i	0.988194	−	0.153205i	$-0.0489596\pi$
$283$	6.07998	+	10.5308i	0.361417	+	0.625993i	−0.626777	+	0.779199i	$0.715626\pi$
$284$	−0.0390952	−	0.0677149i	−0.00231988	−	0.00401814i
$285$	−0.723063	−	1.25238i	−0.0428306	−	0.0741847i
$286$	−12.2809	+	0.673613i	−0.726182	+	0.0398316i
$287$	−5.55782	+	6.32771i	−0.328067	+	0.373513i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	12.2813			0.722427
$290$	−0.388295			−0.0228014
$291$	−6.82663	+	11.8241i	−0.400184	+	0.693140i
$292$	−6.31721	+	10.9417i	−0.369687	+	0.640316i
$293$	13.8954	+	24.0675i	0.811778	+	1.40604i	0.911619	+	0.411037i	$0.134833\pi$
$293$	13.8954	+	24.0675i	0.811778	+	1.40604i	−0.0998407	+	0.995003i	$0.531833\pi$
$294$	−0.903072	−	6.94150i	−0.0526683	−	0.404837i
$295$	−1.68397	−	2.91672i	−0.0980444	−	0.169818i
$296$	4.18320			0.243143
$297$	1.70561	+	2.95420i	0.0989694	+	0.171420i
$298$	1.34679	−	2.33271i	0.0780175	−	0.135130i
$299$	3.12656	−	6.17335i	0.180814	−	0.357014i
$300$	4.94801			0.285673
$301$	−8.79015	−	25.9601i	−0.506656	−	1.49632i
$302$	−6.56432	+	11.3697i	−0.377734	+	0.654255i
$303$	−8.25823	+	14.3037i	−0.474423	+	0.821724i
$304$	−3.17107	+	5.49246i	−0.181873	+	0.315014i
$305$	1.53228			0.0877383
$306$	−2.70561	+	4.68625i	−0.154669	+	0.267895i
$307$	−14.6849			−0.838110			−0.419055	−	0.907961i	$-0.637639\pi$
$307$	−14.6849			−0.838110			−0.419055	+	0.907961i	$0.637639\pi$
$308$	2.89453	+	8.54848i	0.164931	+	0.487095i
$309$	3.17961	−	5.50725i	0.180882	−	0.313296i
$310$	0.811985			0.0461176
$311$	3.86348	−	6.69174i	0.219078	−	0.379453i	−0.735449	−	0.677580i	$-0.763029\pi$
$311$	3.86348	−	6.69174i	0.219078	−	0.379453i	0.954526	+	0.298127i	$0.0963619\pi$
$312$	3.60014	−	0.197470i	0.203818	−	0.0111795i
$313$	−10.0982	−	17.4906i	−0.570784	−	0.988626i	−0.996486	−	0.0837628i	$-0.973306\pi$
$313$	−10.0982	−	17.4906i	−0.570784	−	0.988626i	0.425702	−	0.904863i	$-0.360027\pi$
$314$	1.59071	−	2.75520i	0.0897692	−	0.155485i
$315$	0.591599	+	0.118146i	0.0333328	+	0.00665680i
$316$	0.811077	+	1.40483i	0.0456266	+	0.0790276i
$317$	7.36088	+	12.7494i	0.413428	+	0.716079i	0.995262	−	0.0972291i	$-0.0309980\pi$
$317$	7.36088	+	12.7494i	0.413428	+	0.716079i	−0.581834	+	0.813308i	$0.697665\pi$
$318$	6.62799			0.371679
$319$	−5.80898			−0.325241
$320$	0.114009	+	0.197470i	0.00637332	+	0.0110389i
$321$	3.27362	+	5.67008i	0.182716	+	0.316473i
$322$	−4.97952	−	0.994446i	−0.277498	−	0.0554183i
$323$	17.1594	−	29.7209i	0.954772	−	1.65371i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	9.75294	+	14.9384i	0.540996	+	0.828634i
$326$	−8.14702	+	14.1111i	−0.451222	+	0.781539i
$327$	1.59419			0.0881587
$328$	−1.59160	+	2.75673i	−0.0878813	+	0.152215i
$329$	9.45624	+	27.9273i	0.521339	+	1.53968i
$330$	−0.777821			−0.0428176
$331$	−2.05436	+	3.55826i	−0.112918	+	0.195579i	−0.916946	−	0.399012i	$-0.869353\pi$
$331$	−2.05436	+	3.55826i	−0.112918	+	0.195579i	0.804028	+	0.594592i	$0.202686\pi$
$332$	−1.70291			−0.0934592
$333$	2.09160	−	3.62276i	0.114619	−	0.198526i
$334$	−0.826739	+	1.43195i	−0.0452371	+	0.0783530i
$335$	1.27249	−	2.20402i	0.0695237	−	0.120419i
$336$	−0.848534	−	2.50599i	−0.0462913	−	0.136713i
$337$	−7.44592			−0.405605			−0.202802	−	0.979220i	$-0.565005\pi$
$337$	−7.44592			−0.405605			−0.202802	+	0.979220i	$0.565005\pi$
$338$	7.69235	+	10.4799i	0.418409	+	0.570030i
$339$	4.12255	−	7.14047i	0.223906	−	0.387817i
$340$	−0.616929	−	1.06855i	−0.0334577	−	0.0579504i
$341$	12.1475			0.657824
$342$	3.17107	+	5.49246i	0.171472	+	0.296998i
$343$	−15.3754	−	10.3246i	−0.830193	−	0.557475i
$344$	−5.17961	−	8.97135i	−0.279266	−	0.483703i
$345$	0.218812	−	0.378993i	0.0117804	−	0.0204043i
$346$	7.02100	−	12.1607i	0.377451	−	0.653765i
$347$	−10.5281			−0.565180			−0.282590	−	0.959241i	$-0.591194\pi$
$347$	−10.5281			−0.565180			−0.282590	+	0.959241i	$0.591194\pi$
$348$	1.70291			0.0912854
$349$	−4.74127	+	8.21212i	−0.253794	+	0.439585i	−0.964567	−	0.263837i	$-0.915012\pi$
$349$	−4.74127	+	8.21212i	−0.253794	+	0.439585i	0.710773	+	0.703422i	$0.248345\pi$
$350$	8.63915	−	9.83588i	0.461782	−	0.525750i
$351$	1.62906	−	3.21655i	0.0869526	−	0.171687i
$352$	1.70561	+	2.95420i	0.0909092	+	0.157459i
$353$	−2.72112	−	4.71311i	−0.144830	−	0.250854i	0.784479	−	0.620155i	$-0.212930\pi$
$353$	−2.72112	−	4.71311i	−0.144830	−	0.250854i	−0.929310	+	0.369301i	$0.879597\pi$
$354$	7.38522	+	12.7916i	0.392520	+	0.679865i
$355$	0.00891445	−	0.0154403i	0.000473130	−	0.000819485i
$356$	17.5457			0.929920
$357$	4.59160	+	13.5605i	0.243013	+	0.717696i
$358$	−4.66663	−	8.08283i	−0.246639	−	0.427191i
$359$	−5.29579	−	9.17257i	−0.279501	−	0.484110i	0.691760	−	0.722128i	$-0.256836\pi$
$359$	−5.29579	−	9.17257i	−0.279501	−	0.484110i	−0.971261	+	0.238018i	$0.923502\pi$
$360$	0.228019			0.0120176
$361$	−10.6114	−	18.3795i	−0.558494	−	0.967340i
$362$	−1.13838			−0.0598317
$363$	−0.636396			−0.0334021
$364$	5.89325	−	7.50131i	0.308890	−	0.393175i
$365$	−2.88088			−0.150792
$366$	−6.71999			−0.351259
$367$	3.59896	+	6.23359i	0.187864	+	0.325391i	0.944538	−	0.328402i	$-0.106510\pi$
$367$	3.59896	+	6.23359i	0.187864	+	0.325391i	−0.756674	+	0.653793i	$0.773177\pi$
$368$	−1.91925			−0.100048
$369$	1.59160	+	2.75673i	0.0828553	+	0.143510i
$370$	0.476924	+	0.826056i	0.0247941	+	0.0429446i
$371$	11.5724	−	13.1754i	0.600808	−	0.684035i
$372$	−3.56104			−0.184632
$373$	14.2762	−	24.7271i	0.739192	−	1.28032i	−0.213667	−	0.976907i	$-0.568541\pi$
$373$	14.2762	−	24.7271i	0.739192	−	1.28032i	0.952859	−	0.303412i	$-0.0981259\pi$
$374$	−9.22941	−	15.9858i	−0.477242	−	0.826607i
$375$	1.13417	+	1.96443i	0.0585681	+	0.101443i
$376$	5.57211	+	9.65117i	0.287360	+	0.497721i
$377$	3.35657	+	5.14121i	0.172872	+	0.264786i
$378$	−2.59452	−	0.518144i	−0.133448	−	0.0266504i
$379$	15.5638	−	26.9572i	0.799457	−	1.38470i	−0.120513	−	0.992712i	$-0.538454\pi$
$379$	15.5638	−	26.9572i	0.799457	−	1.38470i	0.919970	−	0.391989i	$-0.128213\pi$
$380$	−1.44613			−0.0741847
$381$	−12.8112			−0.656337
$382$	9.04253	−	15.6621i	0.462656	−	0.801343i
$383$	−10.9760	+	19.0111i	−0.560849	+	0.971420i	0.436573	+	0.899669i	$0.356192\pi$
$383$	−10.9760	+	19.0111i	−0.560849	+	0.971420i	−0.997423	+	0.0717509i	$0.977141\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−1.35806	+	1.54619i	−0.0692133	+	0.0788011i
$386$	−2.91296	−	5.04539i	−0.148266	−	0.256804i
$387$	−10.3592			−0.526589
$388$	6.82663	+	11.8241i	0.346570	+	0.600277i
$389$	1.87365	−	3.24525i	0.0949976	−	0.164541i	−0.814610	−	0.580009i	$-0.803049\pi$
$389$	1.87365	−	3.24525i	0.0949976	−	0.164541i	0.909608	+	0.415468i	$0.136382\pi$
$390$	0.449444	+	0.688406i	0.0227585	+	0.0348588i
$391$	10.3855			0.525215
$392$	−6.46305	−	2.68867i	−0.326434	−	0.135798i
$393$	1.75964	−	3.04778i	0.0887619	−	0.153740i
$394$	10.3527	−	17.9315i	0.521564	−	0.903375i
$395$	−0.184941	+	0.320327i	−0.00930537	+	0.0161174i
$396$	3.41122			0.171420
$397$	1.95502	−	3.38620i	0.0981198	−	0.169949i	−0.812787	−	0.582562i	$-0.802050\pi$
$397$	1.95502	−	3.38620i	0.0981198	−	0.169949i	0.910906	+	0.412613i	$0.135384\pi$
$398$	16.3984			0.821979
$399$	16.4548	+	3.28614i	0.823771	+	0.164513i
$400$	2.47400	−	4.28510i	0.123700	−	0.214255i
$401$	−26.2260			−1.30967			−0.654833	−	0.755774i	$-0.727261\pi$
$401$	−26.2260			−1.30967			−0.654833	+	0.755774i	$0.727261\pi$
$402$	−5.58065	+	9.66597i	−0.278337	+	0.482095i
$403$	−7.01912	−	10.7511i	−0.349647	−	0.535549i
$404$	8.25823	+	14.3037i	0.410862	+	0.711634i
$405$	0.114009	−	0.197470i	0.00566517	−	0.00981236i
$406$	2.97325	−	3.38512i	0.147560	−	0.168001i
$407$	7.13490	+	12.3580i	0.353664	+	0.612563i
$408$	2.70561	+	4.68625i	0.133948	+	0.232004i
$409$	4.03519			0.199527			0.0997635	−	0.995011i	$-0.468191\pi$
$409$	4.03519			0.199527			0.0997635	+	0.995011i	$0.468191\pi$
$410$	−0.725829			−0.0358461
$411$	8.84776	+	15.3248i	0.436428	+	0.755915i
$412$	−3.17961	−	5.50725i	−0.156648	−	0.271323i
$413$	38.3222	+	7.65321i	1.88571	+	0.376590i
$414$	−0.959623	+	1.66212i	−0.0471629	+	0.0816885i
$415$	−0.194147	−	0.336273i	−0.00953032	−	0.0165070i
$416$	1.62906	−	3.21655i	0.0798710	−	0.157704i
$417$	−3.98321	+	6.89912i	−0.195059	+	0.337851i
$418$	−21.6344			−1.05817
$419$	1.74139	−	3.01617i	0.0850723	−	0.147350i	−0.820350	−	0.571862i	$-0.806221\pi$
$419$	1.74139	−	3.01617i	0.0850723	−	0.147350i	0.905422	+	0.424513i	$0.139555\pi$
$420$	0.398117	−	0.453266i	0.0194261	−	0.0221171i
$421$	18.6028			0.906647			0.453323	−	0.891346i	$-0.350238\pi$
$421$	18.6028			0.906647			0.453323	+	0.891346i	$0.350238\pi$
$422$	−3.74446	+	6.48560i	−0.182277	+	0.315714i
$423$	11.1442			0.541850
$424$	3.31400	−	5.74001i	0.160942	−	0.278760i
$425$	−13.3874	+	23.1876i	−0.649383	+	1.12476i
$426$	−0.0390952	+	0.0677149i	−0.00189417	+	0.00328080i
$427$	−11.7330	+	13.3583i	−0.567800	+	0.646454i
$428$	6.54724			0.316473
$429$	6.72379	+	10.2987i	0.324628	+	0.497227i
$430$	1.18105	−	2.04564i	0.0569552	−	0.0986493i
$431$	9.52662	+	16.5006i	0.458881	+	0.794806i	0.998902	−	0.0468461i	$-0.0149170\pi$
$431$	9.52662	+	16.5006i	0.458881	+	0.794806i	−0.540021	+	0.841652i	$0.681584\pi$
$432$	−1.00000			−0.0481125
$433$	−16.7336	−	28.9834i	−0.804164	−	1.39285i	−0.916854	−	0.399223i	$-0.869280\pi$
$433$	−16.7336	−	28.9834i	−0.804164	−	1.39285i	0.112689	−	0.993630i	$-0.464053\pi$
$434$	−6.21753	+	7.07881i	−0.298451	+	0.339794i
$435$	0.194147	+	0.336273i	0.00930865	+	0.0161231i
$436$	0.797093	−	1.38061i	0.0381738	−	0.0661190i
$437$	6.08607	−	10.5414i	0.291136	−	0.504262i
$438$	12.6344			0.603696
$439$	38.0459			1.81583			0.907915	−	0.419154i	$-0.137673\pi$
$439$	38.0459			1.81583			0.907915	+	0.419154i	$0.137673\pi$
$440$	−0.388911	+	0.673613i	−0.0185406	+	0.0321132i
$441$	−5.55998	+	4.25284i	−0.264761	+	0.202516i
$442$	−8.81517	+	17.4054i	−0.419295	+	0.827892i
$443$	4.35467	+	7.54250i	0.206896	+	0.358355i	0.950735	−	0.310004i	$-0.100330\pi$
$443$	4.35467	+	7.54250i	0.206896	+	0.358355i	−0.743839	+	0.668359i	$0.766997\pi$
$444$	−2.09160	−	3.62276i	−0.0992629	−	0.171928i
$445$	2.00037	+	3.46475i	0.0948268	+	0.164245i
$446$	8.41325	−	14.5722i	0.398379	−	0.690013i
$447$	−2.69358			−0.127402
$448$	−2.59452	−	0.518144i	−0.122579	−	0.0244800i
$449$	−11.4930	−	19.9065i	−0.542389	−	0.939445i	−0.998766	−	0.0496589i	$-0.984187\pi$
$449$	−11.4930	−	19.9065i	−0.542389	−	0.939445i	0.456377	−	0.889786i	$-0.349147\pi$
$450$	−2.47400	−	4.28510i	−0.116626	−	0.202002i
$451$	−10.8586			−0.511310
$452$	−4.12255	−	7.14047i	−0.193908	−	0.335859i
$453$	13.1286			0.616837
$454$	4.23214			0.198624
$455$	2.15317	+	0.308521i	0.100942	+	0.0144637i
$456$	6.34214			0.296998
$457$	11.5899			0.542150			0.271075	−	0.962558i	$-0.412621\pi$
$457$	11.5899			0.542150			0.271075	+	0.962558i	$0.412621\pi$
$458$	6.86498	+	11.8905i	0.320779	+	0.555606i
$459$	5.41122			0.252574
$460$	−0.218812	−	0.378993i	−0.0102022	−	0.0176707i
$461$	−17.4236	−	30.1785i	−0.811496	−	1.40555i	−0.911817	−	0.410597i	$-0.865320\pi$
$461$	−17.4236	−	30.1785i	−0.811496	−	1.40555i	0.100321	−	0.994955i	$-0.468013\pi$
$462$	5.95593	−	6.78098i	0.277095	−	0.315480i
$463$	−39.5334			−1.83727			−0.918635	−	0.395106i	$-0.870708\pi$
$463$	−39.5334			−1.83727			−0.918635	+	0.395106i	$0.870708\pi$
$464$	0.851453	−	1.47476i	0.0395277	−	0.0684640i
$465$	−0.405992	−	0.703199i	−0.0188274	−	0.0326101i
$466$	3.85349	+	6.67444i	0.178509	+	0.309187i
$467$	−0.425191	−	0.736452i	−0.0196755	−	0.0340789i	0.856020	−	0.516943i	$-0.172930\pi$
$467$	−0.425191	−	0.736452i	−0.0196755	−	0.0340789i	−0.875695	+	0.482864i	$0.839597\pi$
$468$	−1.97108	−	3.01908i	−0.0911134	−	0.139557i
$469$	9.47074	+	27.9701i	0.437318	+	1.29154i
$470$	−1.27054	+	2.20065i	−0.0586059	+	0.101508i
$471$	−3.18143			−0.146592
$472$	14.7704			0.679865
$473$	17.6688	−	30.6032i	0.812411	−	1.40714i
$474$	0.811077	−	1.40483i	0.0372540	−	0.0645258i
$475$	15.6905	+	27.1767i	0.719929	+	1.24695i
$476$	14.0395	+	2.80379i	0.643499	+	0.128511i
$477$	−3.31400	−	5.74001i	−0.151737	−	0.262817i
$478$	25.2189			1.15349
$479$	−5.78732	−	10.0239i	−0.264429	−	0.458005i	0.702985	−	0.711205i	$-0.251850\pi$
$479$	−5.78732	−	10.0239i	−0.264429	−	0.458005i	−0.967414	+	0.253200i	$0.918517\pi$
$480$	0.114009	−	0.197470i	0.00520379	−	0.00901323i
$481$	6.81466	−	13.4555i	0.310722	−	0.613516i
$482$	−27.8367			−1.26793
$483$	1.62854	+	4.80961i	0.0741014	+	0.218845i
$484$	−0.318198	+	0.551135i	−0.0144635	+	0.0250516i
$485$	−1.55660	+	2.69611i	−0.0706816	+	0.122424i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−13.9320			−0.631321			−0.315661	−	0.948872i	$-0.602226\pi$
$487$	−13.9320			−0.631321			−0.315661	+	0.948872i	$0.602226\pi$
$488$	−3.35999	+	5.81968i	−0.152100	+	0.263445i
$489$	16.2940			0.736842
$490$	−0.205917	−	1.58279i	−0.00930240	−	0.0715033i
$491$	4.76716	−	8.25697i	0.215139	−	0.372632i	−0.738177	−	0.674608i	$-0.764313\pi$
$491$	4.76716	−	8.25697i	0.215139	−	0.372632i	0.953316	+	0.301976i	$0.0976462\pi$
$492$	3.18320			0.143510
$493$	−4.60740	+	7.98025i	−0.207507	+	0.359412i
$494$	12.5009	+	19.1474i	0.562442	+	0.861483i
$495$	0.388911	+	0.673613i	0.0174802	+	0.0302766i
$496$	−1.78052	+	3.08395i	−0.0799478	+	0.138474i
$497$	0.0663472	+	0.195945i	0.00297608	+	0.00878932i
$498$	0.851453	+	1.47476i	0.0381545	+	0.0660856i
$499$	21.9135	+	37.9553i	0.980982	+	1.69911i	0.658585	+	0.752506i	$0.271155\pi$
$499$	21.9135	+	37.9553i	0.980982	+	1.69911i	0.322397	+	0.946605i	$0.395511\pi$
$500$	2.26833			0.101443
$501$	1.65348			0.0738719
$502$	−2.12395	−	3.67878i	−0.0947963	−	0.164192i
$503$	−7.35181	−	12.7337i	−0.327801	−	0.567768i	0.654274	−	0.756257i	$-0.272974\pi$
$503$	−7.35181	−	12.7337i	−0.327801	−	0.567768i	−0.982075	+	0.188489i	$0.939641\pi$
$504$	−1.74599	+	1.98785i	−0.0777724	+	0.0885457i
$505$	−1.88303	+	3.26150i	−0.0837937	+	0.145135i
$506$	−3.27348	−	5.66984i	−0.145524	−	0.252055i
$507$	5.22966	−	11.9017i	0.232257	−	0.528573i
$508$	−6.40560	+	11.0948i	−0.284202	+	0.492253i
$509$	−14.4795			−0.641792			−0.320896	−	0.947114i	$-0.603984\pi$
$509$	−14.4795			−0.641792			−0.320896	+	0.947114i	$0.603984\pi$
$510$	−0.616929	+	1.06855i	−0.0273181	+	0.0473163i
$511$	22.0595	−	25.1153i	0.975855	−	1.11104i
$512$	−1.00000			−0.0441942
$513$	3.17107	−	5.49246i	0.140006	−	0.242498i
$514$	−14.7167			−0.649126
$515$	0.725011	−	1.25576i	0.0319478	−	0.0553352i
$516$	−5.17961	+	8.97135i	−0.228020	+	0.394942i
$517$	−19.0077	+	32.9222i	−0.835956	+	1.44792i
$518$	−10.8534	−	2.16750i	−0.476870	−	0.0952344i
$519$	−14.0420			−0.616375
$520$	0.820899	−	0.0450268i	0.0359988	−	0.00197456i
$521$	7.18959	−	12.4527i	0.314982	−	0.545564i	−0.664452	−	0.747331i	$-0.731335\pi$
$521$	7.18959	−	12.4527i	0.314982	−	0.545564i	0.979434	+	0.201767i	$0.0646683\pi$
$522$	−0.851453	−	1.47476i	−0.0372671	−	0.0645485i
$523$	−1.02354			−0.0447563			−0.0223781	−	0.999750i	$-0.507124\pi$
$523$	−1.02354			−0.0447563			−0.0223781	+	0.999750i	$0.507124\pi$
$524$	−1.75964	−	3.04778i	−0.0768701	−	0.133143i
$525$	−12.8377	−	2.56378i	−0.560283	−	0.111893i
$526$	11.7053	+	20.2741i	0.510374	+	0.883993i
$527$	9.63479	−	16.6879i	0.419698	−	0.726938i
$528$	1.70561	−	2.95420i	0.0742271	−	0.128565i
$529$	−19.3165			−0.839848
$530$	1.51131			0.0656470
$531$	7.38522	−	12.7916i	0.320491	−	0.555107i
$532$	11.0733	−	12.6072i	0.480088	−	0.546592i
$533$	6.27435	+	9.61032i	0.271772	+	0.416269i
$534$	−8.77285	−	15.1950i	−0.379638	−	0.657553i
$535$	0.746446	+	1.29288i	0.0322717	+	0.0558962i
$536$	5.58065	+	9.66597i	0.241047	+	0.417506i
$537$	−4.66663	+	8.08283i	−0.201380	+	0.348800i
$538$	9.35772			0.403440
$539$	−3.08058	−	23.6790i	−0.132690	−	1.01993i
$540$	−0.114009	−	0.197470i	−0.00490618	−	0.00849776i
$541$	0.804352	+	1.39318i	0.0345818	+	0.0598974i	0.882798	−	0.469752i	$-0.155657\pi$
$541$	0.804352	+	1.39318i	0.0345818	+	0.0598974i	−0.848217	+	0.529650i	$0.822323\pi$
$542$	15.1475			0.650641
$543$	0.569188	+	0.985863i	0.0244262	+	0.0423074i
$544$	5.41122			0.232004
$545$	0.363504			0.0155708
$546$	−9.44295	−	1.35305i	−0.404121	−	0.0579052i
$547$	26.9289			1.15140			0.575699	−	0.817661i	$-0.304730\pi$
$547$	26.9289			1.15140			0.575699	+	0.817661i	$0.304730\pi$
$548$	17.6955			0.755915
$549$	3.35999	+	5.81968i	0.143401	+	0.248378i
$550$	16.8787			0.719711
$551$	5.40004	+	9.35314i	0.230049	+	0.398457i
$552$	0.959623	+	1.66212i	0.0408443	+	0.0707444i
$553$	−1.37645	−	4.06510i	−0.0585327	−	0.172866i
$554$	32.8782			1.39686
$555$	0.476924	−	0.826056i	0.0202443	−	0.0350641i
$556$	3.98321	+	6.89912i	0.168926	+	0.292588i
$557$	18.1841	+	31.4957i	0.770484	+	1.33452i	0.937298	+	0.348528i	$0.113319\pi$
$557$	18.1841	+	31.4957i	0.770484	+	1.33452i	−0.166815	+	0.985988i	$0.553348\pi$
$558$	1.78052	+	3.08395i	0.0753755	+	0.130554i
$559$	−37.2947	+	2.04564i	−1.57740	+	0.0865212i
$560$	−0.193482	−	0.571413i	−0.00817609	−	0.0241466i
$561$	−9.22941	+	15.9858i	−0.389666	+	0.674922i
$562$	16.8072			0.708968
$563$	−3.73021			−0.157210			−0.0786048	−	0.996906i	$-0.525047\pi$
$563$	−3.73021			−0.157210			−0.0786048	+	0.996906i	$0.525047\pi$
$564$	5.57211	−	9.65117i	0.234628	−	0.406388i
$565$	0.940019	−	1.62816i	0.0395469	−	0.0684972i
$566$	−6.07998	−	10.5308i	−0.255561	−	0.442644i
$567$	0.848534	+	2.50599i	0.0356351	+	0.105242i
$568$	0.0390952	+	0.0677149i	0.00164040	+	0.00284126i
$569$	−15.3919			−0.645263			−0.322632	−	0.946525i	$-0.604567\pi$
$569$	−15.3919			−0.645263			−0.322632	+	0.946525i	$0.604567\pi$
$570$	0.723063	+	1.25238i	0.0302858	+	0.0524565i
$571$	−10.1994	+	17.6659i	−0.426832	+	0.739296i	−0.996590	−	0.0825176i	$-0.973704\pi$
$571$	−10.1994	+	17.6659i	−0.426832	+	0.739296i	0.569757	+	0.821813i	$0.307037\pi$
$572$	12.2809	−	0.673613i	0.513488	−	0.0281652i
$573$	−18.0851			−0.755514
$574$	5.55782	−	6.32771i	0.231979	−	0.264114i
$575$	−4.74822	+	8.22416i	−0.198015	+	0.342971i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−5.90380	+	10.2257i	−0.245779	+	0.425701i	−0.962350	−	0.271813i	$-0.912377\pi$
$577$	−5.90380	+	10.2257i	−0.245779	+	0.425701i	0.716572	+	0.697513i	$0.245710\pi$
$578$	−12.2813			−0.510833
$579$	−2.91296	+	5.04539i	−0.121058	+	0.209679i
$580$	0.388295			0.0161231
$581$	4.41822	+	0.882351i	0.183299	+	0.0366061i
$582$	6.82663	−	11.8241i	0.282973	−	0.490124i
$583$	22.6095			0.936391
$584$	6.31721	−	10.9417i	0.261408	−	0.452772i
$585$	0.371455	−	0.733433i	0.0153578	−	0.0303237i
$586$	−13.8954	−	24.0675i	−0.574014	−	0.994221i
$587$	−21.9241	+	37.9736i	−0.904903	+	1.56734i	−0.0838564	+	0.996478i	$0.526724\pi$
$587$	−21.9241	+	37.9736i	−0.904903	+	1.56734i	−0.821047	+	0.570861i	$0.806610\pi$
$588$	0.903072	+	6.94150i	0.0372421	+	0.286263i
$589$	−11.2923	−	19.5589i	−0.465292	−	0.805910i
$590$	1.68397	+	2.91672i	0.0693279	+	0.120079i
$591$	−20.7055			−0.851710
$592$	−4.18320			−0.171928
$593$	−5.18125	−	8.97419i	−0.212768	−	0.368526i	0.739812	−	0.672814i	$-0.234915\pi$
$593$	−5.18125	−	8.97419i	−0.212768	−	0.368526i	−0.952580	+	0.304288i	$0.901581\pi$
$594$	−1.70561	−	2.95420i	−0.0699819	−	0.121212i
$595$	1.04697	+	3.09204i	0.0429216	+	0.126761i
$596$	−1.34679	+	2.33271i	−0.0551667	+	0.0955515i
$597$	−8.19922	−	14.2015i	−0.335572	−	0.581227i
$598$	−3.12656	+	6.17335i	−0.127855	+	0.252447i
$599$	−19.7135	+	34.1448i	−0.805471	+	1.39512i	0.110501	+	0.993876i	$0.464754\pi$
$599$	−19.7135	+	34.1448i	−0.805471	+	1.39512i	−0.915973	+	0.401241i	$0.868579\pi$
$600$	−4.94801			−0.202002
$601$	−1.03443	+	1.79169i	−0.0421954	+	0.0730845i	−0.886352	−	0.463012i	$-0.846769\pi$
$601$	−1.03443	+	1.79169i	−0.0421954	+	0.0730845i	0.844156	+	0.536097i	$0.180102\pi$
$602$	8.79015	+	25.9601i	0.358260	+	1.05806i
$603$	11.1613			0.454523
$604$	6.56432	−	11.3697i	0.267098	−	0.462628i
$605$	−0.145110			−0.00589957
$606$	8.25823	−	14.3037i	0.335467	−	0.581047i
$607$	−2.88978	+	5.00524i	−0.117292	+	0.203157i	−0.918694	−	0.394970i	$-0.870755\pi$
$607$	−2.88978	+	5.00524i	−0.117292	+	0.203157i	0.801401	+	0.598127i	$0.204088\pi$
$608$	3.17107	−	5.49246i	0.128604	−	0.222749i
$609$	−4.41822	−	0.882351i	−0.179035	−	0.0357547i
$610$	−1.53228			−0.0620403
$611$	40.1207	−	2.20065i	1.62311	−	0.0890287i
$612$	2.70561	−	4.68625i	0.109368	−	0.189430i
$613$	−7.45451	−	12.9116i	−0.301085	−	0.521494i	0.675297	−	0.737546i	$-0.264015\pi$
$613$	−7.45451	−	12.9116i	−0.301085	−	0.521494i	−0.976382	+	0.216051i	$0.930682\pi$
$614$	14.6849			0.592633
$615$	0.362914	+	0.628586i	0.0146341	+	0.0253470i
$616$	−2.89453	−	8.54848i	−0.116624	−	0.344428i
$617$	−1.29988	−	2.25147i	−0.0523314	−	0.0906406i	0.838673	−	0.544635i	$-0.183332\pi$
$617$	−1.29988	−	2.25147i	−0.0523314	−	0.0906406i	−0.891004	+	0.453995i	$0.849999\pi$
$618$	−3.17961	+	5.50725i	−0.127903	+	0.221534i
$619$	24.4693	−	42.3821i	0.983505	−	1.70348i	0.335106	−	0.942180i	$-0.391228\pi$
$619$	24.4693	−	42.3821i	0.983505	−	1.70348i	0.648399	−	0.761300i	$-0.275439\pi$
$620$	−0.811985			−0.0326101
$621$	1.91925			0.0770167
$622$	−3.86348	+	6.69174i	−0.154911	+	0.268314i
$623$	−45.5226	−	9.09119i	−1.82383	−	0.364231i
$624$	−3.60014	+	0.197470i	−0.144121	+	0.00790513i
$625$	−12.1114	−	20.9776i	−0.484456	−	0.839103i
$626$	10.0982	+	17.4906i	0.403605	+	0.699064i
$627$	10.8172	+	18.7360i	0.431998	+	0.748242i
$628$	−1.59071	+	2.75520i	−0.0634764	+	0.109944i
$629$	22.6362			0.902564
$630$	−0.591599	−	0.118146i	−0.0235699	−	0.00470707i
$631$	14.0099	+	24.2659i	0.557726	+	0.966010i	0.997686	+	0.0679924i	$0.0216594\pi$
$631$	14.0099	+	24.2659i	0.557726	+	0.966010i	−0.439960	+	0.898017i	$0.645007\pi$
$632$	−0.811077	−	1.40483i	−0.0322629	−	0.0558810i
$633$	7.48892			0.297658
$634$	−7.36088	−	12.7494i	−0.292338	−	0.506344i
$635$	−2.92119			−0.115924
$636$	−6.62799			−0.262817
$637$	−19.1769	+	16.4087i	−0.759817	+	0.650138i
$638$	5.80898			0.229980
$639$	0.0781905			0.00309317
$640$	−0.114009	−	0.197470i	−0.00450662	−	0.00780569i
$641$	−35.9312			−1.41920			−0.709598	−	0.704607i	$-0.751123\pi$
$641$	−35.9312			−1.41920			−0.709598	+	0.704607i	$0.751123\pi$
$642$	−3.27362	−	5.67008i	−0.129199	−	0.223780i
$643$	10.6007	+	18.3609i	0.418050	+	0.724084i	0.995743	−	0.0921702i	$-0.0293804\pi$
$643$	10.6007	+	18.3609i	0.418050	+	0.724084i	−0.577693	+	0.816254i	$0.696047\pi$
$644$	4.97952	+	0.994446i	0.196221	+	0.0391866i
$645$	−2.36210			−0.0930075
$646$	−17.1594	+	29.7209i	−0.675126	+	1.16935i
$647$	−2.06144	−	3.57052i	−0.0810436	−	0.140372i	0.822655	−	0.568541i	$-0.192492\pi$
$647$	−2.06144	−	3.57052i	−0.0810436	−	0.140372i	−0.903698	+	0.428169i	$0.859159\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	25.1926	+	43.6348i	0.988895	+	1.71282i
$650$	−9.75294	−	14.9384i	−0.382542	−	0.585933i
$651$	9.23920	+	1.84513i	0.362113	+	0.0723165i
$652$	8.14702	−	14.1111i	0.319062	−	0.552632i
$653$	−47.4371			−1.85636			−0.928179	−	0.372134i	$-0.878626\pi$
$653$	−47.4371			−1.85636			−0.928179	+	0.372134i	$0.878626\pi$
$654$	−1.59419			−0.0623376
$655$	0.401230	−	0.694951i	0.0156773	−	0.0271540i
$656$	1.59160	−	2.75673i	0.0621415	−	0.107632i
$657$	−6.31721	−	10.9417i	−0.246458	−	0.426877i
$658$	−9.45624	−	27.9273i	−0.368643	−	1.08872i
$659$	−12.4744	−	21.6062i	−0.485932	−	0.841659i	0.513937	−	0.857828i	$-0.328186\pi$
$659$	−12.4744	−	21.6062i	−0.485932	−	0.841659i	−0.999869	+	0.0161688i	$0.994853\pi$
$660$	0.777821			0.0302766
$661$	4.30765	+	7.46106i	0.167548	+	0.290202i	0.937557	−	0.347831i	$-0.113082\pi$
$661$	4.30765	+	7.46106i	0.167548	+	0.290202i	−0.770009	+	0.638033i	$0.779748\pi$
$662$	2.05436	−	3.55826i	0.0798450	−	0.138296i
$663$	19.4811	−	1.06855i	0.756585	−	0.0414992i
$664$	1.70291			0.0660856
$665$	3.75200	+	0.749302i	0.145496	+	0.0290567i
$666$	−2.09160	+	3.62276i	−0.0810478	+	0.140379i
$667$	−1.63415	+	2.83043i	−0.0632745	+	0.109595i
$668$	0.826739	−	1.43195i	0.0319875	−	0.0554040i
$669$	−16.8265			−0.650550
$670$	−1.27249	+	2.20402i	−0.0491607	+	0.0851488i
$671$	−22.9233			−0.884946
$672$	0.848534	+	2.50599i	0.0327329	+	0.0966707i
$673$	3.15527	−	5.46509i	0.121627	−	0.210664i	−0.798783	−	0.601620i	$-0.794522\pi$
$673$	3.15527	−	5.46509i	0.121627	−	0.210664i	0.920409	+	0.390956i	$0.127856\pi$
$674$	7.44592			0.286806
$675$	−2.47400	+	4.28510i	−0.0952244	+	0.164934i
$676$	−7.69235	−	10.4799i	−0.295860	−	0.403072i
$677$	−3.67011	−	6.35682i	−0.141054	−	0.244313i	0.786840	−	0.617157i	$-0.211716\pi$
$677$	−3.67011	−	6.35682i	−0.141054	−	0.244313i	−0.927894	+	0.372845i	$0.878382\pi$
$678$	−4.12255	+	7.14047i	−0.158326	+	0.274228i
$679$	−11.5853	−	34.2150i	−0.444601	−	1.31305i
$680$	0.616929	+	1.06855i	0.0236582	+	0.0409771i
$681$	−2.11607	−	3.66514i	−0.0810880	−	0.140449i
$682$	−12.1475			−0.465152
$683$	19.9112			0.761880			0.380940	−	0.924600i	$-0.375600\pi$
$683$	19.9112			0.761880			0.380940	+	0.924600i	$0.375600\pi$
$684$	−3.17107	−	5.49246i	−0.121249	−	0.210009i
$685$	2.01746	+	3.49434i	0.0770830	+	0.133512i
$686$	15.3754	+	10.3246i	0.587035	+	0.394195i
$687$	6.86498	−	11.8905i	0.261915	−	0.453650i
$688$	5.17961	+	8.97135i	0.197471	+	0.342030i
$689$	−13.0643	−	20.0104i	−0.497711	−	0.762336i
$690$	−0.218812	+	0.378993i	−0.00833003	+	0.0144280i
$691$	−19.0691			−0.725422			−0.362711	−	0.931902i	$-0.618149\pi$
$691$	−19.0691			−0.725422			−0.362711	+	0.931902i	$0.618149\pi$
$692$	−7.02100	+	12.1607i	−0.266898	+	0.462282i
$693$	−8.85046	−	1.76750i	−0.336201	−	0.0671418i
$694$	10.5281			0.399642
$695$	−0.908246	+	1.57313i	−0.0344518	+	0.0596722i
$696$	−1.70291			−0.0645485
$697$	−8.61248	+	14.9173i	−0.326221	+	0.565032i
$698$	4.74127	−	8.21212i	0.179460	−	0.310833i
$699$	3.85349	−	6.67444i	0.145752	−	0.252450i
$700$	−8.63915	+	9.83588i	−0.326529	+	0.371761i
$701$	21.2816			0.803796			0.401898	−	0.915685i	$-0.368351\pi$
$701$	21.2816			0.803796			0.401898	+	0.915685i	$0.368351\pi$
$702$	−1.62906	+	3.21655i	−0.0614847	+	0.121401i
$703$	13.2652	−	22.9760i	0.500307	−	0.866557i
$704$	−1.70561	−	2.95420i	−0.0642825	−	0.111341i
$705$	2.54109			0.0957030
$706$	2.72112	+	4.71311i	0.102411	+	0.177380i
$707$	−14.0148	−	41.3901i	−0.527079	−	1.55663i
$708$	−7.38522	−	12.7916i	−0.277554	−	0.480737i
$709$	13.4109	−	23.2283i	0.503655	−	0.872357i	−0.496336	−	0.868131i	$-0.665321\pi$
$709$	13.4109	−	23.2283i	0.503655	−	0.872357i	0.999991	−	0.00422606i	$-0.00134520\pi$
$710$	−0.00891445	+	0.0154403i	−0.000334553	+	0.000579463i
$711$	−1.62215			−0.0608355
$712$	−17.5457			−0.657553
$713$	3.41726	−	5.91887i	0.127977	−	0.221663i
$714$	−4.59160	−	13.5605i	−0.171836	−	0.507487i
$715$	1.53315	+	2.34830i	0.0573366	+	0.0878215i
$716$	4.66663	+	8.08283i	0.174400	+	0.302070i
$717$	−12.6095	−	21.8402i	−0.470909	−	0.815638i
$718$	5.29579	+	9.17257i	0.197637	+	0.342317i
$719$	21.5853	−	37.3869i	0.804997	−	1.39430i	−0.111297	−	0.993787i	$-0.535500\pi$
$719$	21.5853	−	37.3869i	0.804997	−	1.39430i	0.916293	−	0.400508i	$-0.131166\pi$
$720$	−0.228019			−0.00849776
$721$	5.39601	+	15.9362i	0.200958	+	0.593494i
$722$	10.6114	+	18.3795i	0.394915	+	0.684012i
$723$	13.9183	+	24.1073i	0.517629	+	0.896560i
$724$	1.13838			0.0423074
$725$	−4.21300	−	7.29713i	−0.156467	−	0.271008i
$726$	0.636396			0.0236189
$727$	−16.1609			−0.599373			−0.299687	−	0.954038i	$-0.596882\pi$
$727$	−16.1609			−0.599373			−0.299687	+	0.954038i	$0.596882\pi$
$728$	−5.89325	+	7.50131i	−0.218418	+	0.278017i
$729$	1.00000			0.0370370
$730$	2.88088			0.106626
$731$	−28.0280	−	48.5459i	−1.03665	−	1.79554i
$732$	6.71999			0.248378
$733$	6.79983	+	11.7777i	0.251158	+	0.435018i	0.963845	−	0.266464i	$-0.0858554\pi$
$733$	6.79983	+	11.7777i	0.251158	+	0.435018i	−0.712687	+	0.701482i	$0.752522\pi$
$734$	−3.59896	−	6.23359i	−0.132840	−	0.230086i
$735$	−1.26778	+	0.969726i	−0.0467628	+	0.0357689i
$736$	1.91925			0.0707444
$737$	−19.0368	+	32.9727i	−0.701230	+	1.21457i
$738$	−1.59160	−	2.75673i	−0.0585876	−	0.101477i
$739$	−0.191803	−	0.332212i	−0.00705557	−	0.0122206i	0.862476	−	0.506098i	$-0.168913\pi$
$739$	−0.191803	−	0.332212i	−0.00705557	−	0.0122206i	−0.869532	+	0.493877i	$0.835579\pi$
$740$	−0.476924	−	0.826056i	−0.0175321	−	0.0303664i
$741$	10.3317	−	20.3998i	0.379545	−	0.749405i
$742$	−11.5724	+	13.1754i	−0.424835	+	0.483685i
$743$	10.4715	−	18.1372i	0.384162	−	0.665388i	−0.607491	−	0.794327i	$-0.707824\pi$
$743$	10.4715	−	18.1372i	0.384162	−	0.665388i	0.991653	+	0.128939i	$0.0411572\pi$
$744$	3.56104			0.130554
$745$	−0.614187			−0.0225021
$746$	−14.2762	+	24.7271i	−0.522688	+	0.905322i
$747$	0.851453	−	1.47476i	0.0311531	−	0.0539587i
$748$	9.22941	+	15.9858i	0.337461	+	0.584499i
$749$	−16.9869	−	3.39241i	−0.620689	−	0.123956i
$750$	−1.13417	−	1.96443i	−0.0414139	−	0.0717309i
$751$	15.8139			0.577057			0.288529	−	0.957471i	$-0.406834\pi$
$751$	15.8139			0.577057			0.288529	+	0.957471i	$0.406834\pi$
$752$	−5.57211	−	9.65117i	−0.203194	−	0.351942i
$753$	−2.12395	+	3.67878i	−0.0774009	+	0.134062i
$754$	−3.35657	−	5.14121i	−0.122239	−	0.187232i
$755$	2.99358			0.108947
$756$	2.59452	+	0.518144i	0.0943617	+	0.0188447i
$757$	−4.41633	+	7.64930i	−0.160514	+	0.278019i	−0.935053	−	0.354507i	$-0.884649\pi$
$757$	−4.41633	+	7.64930i	−0.160514	+	0.278019i	0.774539	+	0.632526i	$0.217982\pi$
$758$	−15.5638	+	26.9572i	−0.565302	+	0.979131i
$759$	−3.27348	+	5.66984i	−0.118820	+	0.205802i
$760$	1.44613			0.0524565
$761$	−19.3703	+	33.5503i	−0.702172	+	1.21620i	0.265530	+	0.964103i	$0.414453\pi$
$761$	−19.3703	+	33.5503i	−0.702172	+	1.21620i	−0.967702	+	0.252096i	$0.918880\pi$
$762$	12.8112			0.464100
$763$	−2.78343	+	3.16900i	−0.100767	+	0.114725i
$764$	−9.04253	+	15.6621i	−0.327147	+	0.566635i
$765$	1.23386			0.0446102
$766$	10.9760	−	19.0111i	0.396580	−	0.686897i
$767$	24.0619	−	47.5098i	0.868824	−	1.71548i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−9.17950	+	15.8994i	−0.331021	+	0.573345i	−0.982712	−	0.185139i	$-0.940726\pi$
$769$	−9.17950	+	15.8994i	−0.331021	+	0.573345i	0.651691	+	0.758484i	$0.274060\pi$
$770$	1.35806	−	1.54619i	0.0489412	−	0.0557208i
$771$	7.35836	+	12.7450i	0.265005	+	0.459002i
$772$	2.91296	+	5.04539i	0.104840	+	0.181588i
$773$	12.8481			0.462116			0.231058	−	0.972940i	$-0.425781\pi$
$773$	12.8481			0.462116			0.231058	+	0.972940i	$0.425781\pi$
$774$	10.3592			0.372355
$775$	8.81004	+	15.2594i	0.316466	+	0.548135i
$776$	−6.82663	−	11.8241i	−0.245062	−	0.424460i
$777$	3.54958	+	10.4831i	0.127341	+	0.376078i
$778$	−1.87365	+	3.24525i	−0.0671734	+	0.116348i
$779$	10.0941	+	17.4836i	0.361660	+	0.626414i
$780$	−0.449444	−	0.688406i	−0.0160927	−	0.0246489i
$781$	−0.133362	+	0.230990i	−0.00477208	+	0.00826548i
$782$	−10.3855			−0.371383
$783$	−0.851453	+	1.47476i	−0.0304285	+	0.0527036i
$784$	6.46305	+	2.68867i	0.230823	+	0.0960238i
$785$	−0.725425			−0.0258915
$786$	−1.75964	+	3.04778i	−0.0627641	+	0.108711i
$787$	−3.39457			−0.121003			−0.0605017	−	0.998168i	$-0.519270\pi$
$787$	−3.39457			−0.121003			−0.0605017	+	0.998168i	$0.519270\pi$
$788$	−10.3527	+	17.9315i	−0.368801	+	0.638782i
$789$	11.7053	−	20.2741i	0.416718	−	0.721777i
$790$	0.184941	−	0.320327i	0.00657989	−	0.0113967i
$791$	6.99624	+	20.6621i	0.248758	+	0.734661i
$792$	−3.41122			−0.121212
$793$	13.2457	+	20.2882i	0.470367	+	0.720454i
$794$	−1.95502	+	3.38620i	−0.0693812	+	0.120172i
$795$	−0.755653	−	1.30883i	−0.0268003	−	0.0464194i
$796$	−16.3984			−0.581227
$797$	1.71983	+	2.97884i	0.0609197	+	0.105516i	0.894877	−	0.446313i	$-0.147263\pi$
$797$	1.71983	+	2.97884i	0.0609197	+	0.105516i	−0.833957	+	0.551829i	$0.813930\pi$
$798$	−16.4548	−	3.28614i	−0.582494	−	0.116328i
$799$	30.1519	+	52.2246i	1.06670	+	1.84757i
$800$	−2.47400	+	4.28510i	−0.0874692	+	0.151501i
$801$	−8.77285	+	15.1950i	−0.309973	+	0.536890i
$802$	26.2260			0.926074
$803$	43.0987			1.52092
$804$	5.58065	−	9.66597i	0.196814	−	0.340892i
$805$	0.371339	+	1.09668i	0.0130880	+	0.0386530i
$806$	7.01912	+	10.7511i	0.247238	+	0.378690i
$807$	−4.67886	−	8.10402i	−0.164704	−	0.285275i
$808$	−8.25823	−	14.3037i	−0.290523	−	0.503201i
$809$	13.9913	+	24.2336i	0.491908	+	0.852009i	0.999957	−	0.00931928i	$-0.00296646\pi$
$809$	13.9913	+	24.2336i	0.491908	+	0.852009i	−0.508049	+	0.861328i	$0.669633\pi$
$810$	−0.114009	+	0.197470i	−0.00400588	+	0.00693839i
$811$	26.2105			0.920377			0.460188	−	0.887821i	$-0.347782\pi$
$811$	26.2105			0.920377			0.460188	+	0.887821i	$0.347782\pi$
$812$	−2.97325	+	3.38512i	−0.104341	+	0.118794i
$813$	−7.57375	−	13.1181i	−0.265623	−	0.460072i
$814$	−7.13490	−	12.3580i	−0.250078	−	0.433148i
$815$	3.71535			0.130143
$816$	−2.70561	−	4.68625i	−0.0947152	−	0.164052i
$817$	−65.6997			−2.29854
$818$	−4.03519			−0.141087
$819$	3.54970	+	8.85436i	0.124036	+	0.309396i
$820$	0.725829			0.0253470
$821$	−15.5463			−0.542571			−0.271285	−	0.962499i	$-0.587449\pi$
$821$	−15.5463			−0.542571			−0.271285	+	0.962499i	$0.587449\pi$
$822$	−8.84776	−	15.3248i	−0.308601	−	0.534513i
$823$	−47.8212			−1.66694			−0.833471	−	0.552563i	$-0.813650\pi$
$823$	−47.8212			−1.66694			−0.833471	+	0.552563i	$0.813650\pi$
$824$	3.17961	+	5.50725i	0.110767	+	0.191854i
$825$	−8.43936	−	14.6174i	−0.293821	−	0.508913i
$826$	−38.3222	−	7.65321i	−1.33340	−	0.266289i
$827$	28.2671			0.982944			0.491472	−	0.870893i	$-0.336459\pi$
$827$	28.2671			0.982944			0.491472	+	0.870893i	$0.336459\pi$
$828$	0.959623	−	1.66212i	0.0333492	−	0.0577625i
$829$	−19.8413	−	34.3661i	−0.689116	−	1.19358i	−0.972124	−	0.234466i	$-0.924666\pi$
$829$	−19.8413	−	34.3661i	−0.689116	−	1.19358i	0.283009	−	0.959117i	$-0.408667\pi$
$830$	0.194147	+	0.336273i	0.00673895	+	0.0116722i
$831$	−16.4391	−	28.4734i	−0.570267	−	0.987731i
$832$	−1.62906	+	3.21655i	−0.0564773	+	0.111514i
$833$	−34.9730	−	14.5490i	−1.21174	−	0.504092i
$834$	3.98321	−	6.89912i	0.137927	−	0.238897i
$835$	0.377024			0.0130474
$836$	21.6344			0.748242
$837$	1.78052	−	3.08395i	0.0615439	−	0.106597i
$838$	−1.74139	+	3.01617i	−0.0601552	+	0.104192i
$839$	2.60142	+	4.50579i	0.0898110	+	0.155557i	0.907431	−	0.420201i	$-0.138040\pi$
$839$	2.60142	+	4.50579i	0.0898110	+	0.155557i	−0.817620	+	0.575758i	$0.804707\pi$
$840$	−0.398117	+	0.453266i	−0.0137363	+	0.0156392i
$841$	13.0501	+	22.6034i	0.450002	+	0.779426i
$842$	−18.6028			−0.641096
$843$	−8.40358	−	14.5554i	−0.289435	−	0.501316i
$844$	3.74446	−	6.48560i	0.128890	−	0.223243i
$845$	1.19246	−	2.71381i	0.0410219	−	0.0933580i
$846$	−11.1442			−0.383146
$847$	1.11114	−	1.26506i	0.0381792	−	0.0434679i
$848$	−3.31400	+	5.74001i	−0.113803	+	0.197113i
$849$	−6.07998	+	10.5308i	−0.208664	+	0.361417i
$850$	13.3874	−	23.1876i	0.459183	−	0.795328i
$851$	8.02859			0.275216
$852$	0.0390952	−	0.0677149i	0.00133938	−	0.00231988i
$853$	21.5926			0.739318			0.369659	−	0.929167i	$-0.379474\pi$
$853$	21.5926			0.739318			0.369659	+	0.929167i	$0.379474\pi$
$854$	11.7330	−	13.3583i	0.401495	−	0.457112i
$855$	0.723063	−	1.25238i	0.0247282	−	0.0428306i
$856$	−6.54724			−0.223780
$857$	−6.31723	+	10.9418i	−0.215792	+	0.373763i	−0.953517	−	0.301338i	$-0.902567\pi$
$857$	−6.31723	+	10.9418i	−0.215792	+	0.373763i	0.737725	+	0.675101i	$0.235900\pi$
$858$	−6.72379	−	10.2987i	−0.229547	−	0.351593i
$859$	4.17670	+	7.23426i	0.142507	+	0.246830i	0.928440	−	0.371482i	$-0.121150\pi$
$859$	4.17670	+	7.23426i	0.142507	+	0.246830i	−0.785933	+	0.618312i	$0.787817\pi$
$860$	−1.18105	+	2.04564i	−0.0402734	+	0.0697556i
$861$	−8.25887	−	1.64935i	−0.281461	−	0.0562098i
$862$	−9.52662	−	16.5006i	−0.324478	−	0.562012i
$863$	−6.28858	−	10.8921i	−0.214066	−	0.370772i	0.738918	−	0.673796i	$-0.235337\pi$
$863$	−6.28858	−	10.8921i	−0.214066	−	0.370772i	−0.952983	+	0.303023i	$0.902004\pi$
$864$	1.00000			0.0340207
$865$	−3.20184			−0.108866
$866$	16.7336	+	28.9834i	0.568630	+	0.984896i
$867$	6.14063	+	10.6359i	0.208547	+	0.361214i
$868$	6.21753	−	7.07881i	0.211037	−	0.240271i
$869$	2.76676	−	4.79216i	0.0938558	−	0.162563i
$870$	−0.194147	−	0.336273i	−0.00658221	−	0.0114007i
$871$	40.1822	−	2.20402i	1.36152	−	0.0746804i
$872$	−0.797093	+	1.38061i	−0.0269930	+	0.0467532i
$873$	−13.6533			−0.462093
$874$	−6.08607	+	10.5414i	−0.205864	+	0.356567i
$875$	−5.88523	−	1.17532i	−0.198957	−	0.0397331i
$876$	−12.6344			−0.426877
$877$	−3.24950	+	5.62831i	−0.109728	+	0.190054i	−0.915660	−	0.401954i	$-0.868331\pi$
$877$	−3.24950	+	5.62831i	−0.109728	+	0.190054i	0.805932	+	0.592008i	$0.201665\pi$
$878$	−38.0459			−1.28399
$879$	−13.8954	+	24.0675i	−0.468680	+	0.811778i
$880$	0.388911	−	0.673613i	0.0131102	−	0.0227075i
$881$	6.17234	−	10.6908i	0.207951	−	0.360182i	−0.743118	−	0.669161i	$-0.766654\pi$
$881$	6.17234	−	10.6908i	0.207951	−	0.360182i	0.951069	+	0.308979i	$0.0999871\pi$
$882$	5.55998	−	4.25284i	0.187214	−	0.143200i
$883$	42.2001			1.42015			0.710073	−	0.704128i	$-0.248662\pi$
$883$	42.2001			1.42015			0.710073	+	0.704128i	$0.248662\pi$
$884$	8.81517	−	17.4054i	0.296486	−	0.585408i
$885$	1.68397	−	2.91672i	0.0566060	−	0.0980444i
$886$	−4.35467	−	7.54250i	−0.146298	−	0.253395i
$887$	−34.3380			−1.15296			−0.576478	−	0.817112i	$-0.695574\pi$
$887$	−34.3380			−1.15296			−0.576478	+	0.817112i	$0.695574\pi$
$888$	2.09160	+	3.62276i	0.0701895	+	0.121572i
$889$	22.3681	−	25.4667i	0.750204	−	0.854125i
$890$	−2.00037	−	3.46475i	−0.0670527	−	0.116139i
$891$	−1.70561	+	2.95420i	−0.0571400	+	0.0989694i
$892$	−8.41325	+	14.5722i	−0.281696	+	0.487913i
$893$	70.6782			2.36516
$894$	2.69358			0.0900868
$895$	−1.06408	+	1.84304i	−0.0355682	+	0.0616059i
$896$	2.59452	+	0.518144i	0.0866768	+	0.0173100i
$897$	6.90955	−	0.378993i	0.230703	−	0.0126542i
$898$	11.4930	+	19.9065i	0.383527	+	0.664288i
$899$	3.03206	+	5.25169i	0.101125	+	0.175154i
$900$	2.47400	+	4.28510i	0.0824668	+	0.142837i
$901$	17.9328	−	31.0604i	0.597427	−	1.03477i
$902$	10.8586			0.361551
$903$	18.0870	−	20.5926i	0.601899	−	0.685277i
$904$	4.12255	+	7.14047i	0.137114	+	0.237488i
$905$	0.129786	+	0.224795i	0.00431422	+	0.00747244i
$906$	−13.1286			−0.436170
$907$	9.36040	+	16.2127i	0.310807	+	0.538334i	0.978537	−	0.206070i	$-0.0660674\pi$
$907$	9.36040	+	16.2127i	0.310807	+	0.538334i	−0.667730	+	0.744403i	$0.732734\pi$
$908$	−4.23214			−0.140449
$909$	−16.5165			−0.547816
$910$	−2.15317	−	0.308521i	−0.0713768	−	0.0102274i
$911$	−30.3513			−1.00558			−0.502791	−	0.864408i	$-0.667694\pi$
$911$	−30.3513			−1.00558			−0.502791	+	0.864408i	$0.667694\pi$
$912$	−6.34214			−0.210009
$913$	2.90449	+	5.03073i	0.0961247	+	0.166493i
$914$	−11.5899			−0.383358
$915$	0.766142	+	1.32700i	0.0253279	+	0.0438691i
$916$	−6.86498	−	11.8905i	−0.226825	−	0.392873i
$917$	2.98622	+	8.81926i	0.0986137	+	0.291238i
$918$	−5.41122			−0.178597
$919$	−20.3758	+	35.2919i	−0.672135	+	1.16417i	0.305162	+	0.952300i	$0.401289\pi$
$919$	−20.3758	+	35.2919i	−0.672135	+	1.16417i	−0.977297	+	0.211872i	$0.932044\pi$
$920$	0.218812	+	0.378993i	0.00721402	+	0.0124950i
$921$	−7.34243	−	12.7175i	−0.241941	−	0.419055i
$922$	17.4236	+	30.1785i	0.573814	+	0.993876i
$923$	0.281497	−	0.0154403i	0.00926557	−	0.000508223i
$924$	−5.95593	+	6.78098i	−0.195936	+	0.223078i
$925$	−10.3492	+	17.9254i	−0.340281	+	0.589384i
$926$	39.5334			1.29915
$927$	6.35922			0.208864
$928$	−0.851453	+	1.47476i	−0.0279503	+	0.0484114i
$929$	−2.60978	+	4.52027i	−0.0856242	+	0.148305i	−0.905657	−	0.424011i	$-0.860622\pi$
$929$	−2.60978	+	4.52027i	−0.0856242	+	0.148305i	0.820033	+	0.572316i	$0.193955\pi$
$930$	0.405992	+	0.703199i	0.0133130	+	0.0230588i
$931$	−35.2622	+	26.9721i	−1.15567	+	0.883974i
$932$	−3.85349	−	6.67444i	−0.126225	−	0.218629i
$933$	7.72695			0.252969
$934$	0.425191	+	0.736452i	0.0139127	+	0.0240974i
$935$	−2.10448	+	3.64506i	−0.0688238	+	0.119206i
$936$	1.97108	+	3.01908i	0.0644269	+	0.0986816i
$937$	−31.2199			−1.01991			−0.509956	−	0.860201i	$-0.670338\pi$
$937$	−31.2199			−1.01991			−0.509956	+	0.860201i	$0.670338\pi$
$938$	−9.47074	−	27.9701i	−0.309231	−	0.913257i
$939$	10.0982	−	17.4906i	0.329542	−	0.570784i
$940$	1.27054	−	2.20065i	0.0414406	−	0.0717772i
$941$	−25.3480	+	43.9041i	−0.826322	+	1.43123i	0.0745820	+	0.997215i	$0.476238\pi$
$941$	−25.3480	+	43.9041i	−0.826322	+	1.43123i	−0.900904	+	0.434018i	$0.857096\pi$
$942$	3.18143			0.103657
$943$	−3.05467	+	5.29084i	−0.0994737	+	0.172294i
$944$	−14.7704			−0.480737
$945$	0.193482	+	0.571413i	0.00629395	+	0.0185881i
$946$	−17.6688	+	30.6032i	−0.574461	+	0.994996i
$947$	48.3407			1.57086			0.785431	−	0.618949i	$-0.212441\pi$
$947$	48.3407			1.57086			0.785431	+	0.618949i	$0.212441\pi$
$948$	−0.811077	+	1.40483i	−0.0263425	+	0.0456266i
$949$	−24.9035	−	38.1443i	−0.808402	−	1.23822i
$950$	−15.6905	−	27.1767i	−0.509066	−	0.881729i
$951$	−7.36088	+	12.7494i	−0.238693	+	0.413428i
$952$	−14.0395	−	2.80379i	−0.455023	−	0.0908713i
$953$	0.444682	+	0.770211i	0.0144046	+	0.0249496i	0.873138	−	0.487473i	$-0.162081\pi$
$953$	0.444682	+	0.770211i	0.0144046	+	0.0249496i	−0.858733	+	0.512423i	$0.828748\pi$
$954$	3.31400	+	5.74001i	0.107295	+	0.185840i
$955$	−4.12373			−0.133441
$956$	−25.2189			−0.815638
$957$	−2.90449	−	5.03073i	−0.0938889	−	0.162620i
$958$	5.78732	+	10.0239i	0.186980	+	0.323859i
$959$	−45.9114	−	9.16883i	−1.48256	−	0.296077i
$960$	−0.114009	+	0.197470i	−0.00367964	+	0.00637332i
$961$	9.15948	+	15.8647i	0.295467	+	0.511764i
$962$	−6.81466	+	13.4555i	−0.219714	+	0.433821i
$963$	−3.27362	+	5.67008i	−0.105491	+	0.182716i
$964$	27.8367			0.896560
$965$	−0.664209	+	1.15044i	−0.0213817	+	0.0370341i
$966$	−1.62854	−	4.80961i	−0.0523976	−	0.154747i
$967$	4.75544			0.152925			0.0764623	−	0.997072i	$-0.475638\pi$
$967$	4.75544			0.152925			0.0764623	+	0.997072i	$0.475638\pi$
$968$	0.318198	−	0.551135i	0.0102273	−	0.0177142i
$969$	34.3187			1.10248
$970$	1.55660	−	2.69611i	0.0499794	−	0.0865669i
$971$	−0.775940	+	1.34397i	−0.0249011	+	0.0431300i	−0.878207	−	0.478280i	$-0.841260\pi$
$971$	−0.775940	+	1.34397i	−0.0249011	+	0.0431300i	0.853306	+	0.521410i	$0.174594\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−6.75978	−	19.9638i	−0.216708	−	0.640009i
$974$	13.9320			0.446412
$975$	−8.06058	+	15.9155i	−0.258145	+	0.509704i
$976$	3.35999	−	5.81968i	0.107551	−	0.186283i
$977$	15.7709	+	27.3161i	0.504557	+	0.873919i	0.999986	+	0.00527014i	$0.00167755\pi$
$977$	15.7709	+	27.3161i	0.504557	+	0.873919i	−0.495429	+	0.868648i	$0.664989\pi$
$978$	−16.2940			−0.521026
$979$	−29.9261	−	51.8335i	−0.956442	−	1.65661i
$980$	0.205917	+	1.58279i	0.00657779	+	0.0505604i
$981$	0.797093	+	1.38061i	0.0254492	+	0.0440793i
$982$	−4.76716	+	8.25697i	−0.152126	+	0.263490i
$983$	−15.7150	+	27.2192i	−0.501230	+	0.868157i	0.498769	+	0.866735i	$0.333786\pi$
$983$	−15.7150	+	27.2192i	−0.501230	+	0.868157i	−0.999999	+	0.00142135i	$0.999548\pi$
$984$	−3.18320			−0.101477
$985$	−4.72124			−0.150431
$986$	4.60740	−	7.98025i	0.146729	−	0.254143i
$987$	−19.4576	+	22.1530i	−0.619343	+	0.705138i
$988$	−12.5009	−	19.1474i	−0.397706	−	0.609160i
$989$	−9.94095	−	17.2182i	−0.316104	−	0.547508i
$990$	−0.388911	−	0.673613i	−0.0123604	−	0.0214088i
$991$	−0.302804	−	0.524472i	−0.00961888	−	0.0166604i	0.861176	−	0.508307i	$-0.169729\pi$
$991$	−0.302804	−	0.524472i	−0.00961888	−	0.0166604i	−0.870795	+	0.491647i	$0.836395\pi$
$992$	1.78052	−	3.08395i	0.0565316	−	0.0979157i
$993$	−4.10872			−0.130386
$994$	−0.0663472	−	0.195945i	−0.00210441	−	0.00621499i
$995$	−1.86957	−	3.23820i	−0.0592695	−	0.102658i
$996$	−0.851453	−	1.47476i	−0.0269793	−	0.0467296i
$997$	0.368340			0.0116654			0.00583272	−	0.999983i	$-0.498143\pi$
$997$	0.368340			0.0116654			0.00583272	+	0.999983i	$0.498143\pi$
$998$	−21.9135	−	37.9553i	−0.693659	−	1.20145i
$999$	4.18320			0.132351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.e.529.3	yes	10
3.2	odd	2		1638.2.m.k.1621.3		10
7.2	even	3		546.2.k.e.373.3	yes	10
13.3	even	3		546.2.k.e.445.3	yes	10
21.2	odd	6		1638.2.p.j.919.3		10
39.29	odd	6		1638.2.p.j.991.3		10
91.16	even	3	inner	546.2.j.e.289.3	✓	10
273.107	odd	6		1638.2.m.k.289.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.3	✓	10	91.16	even	3	inner
546.2.j.e.529.3	yes	10	1.1	even	1	trivial
546.2.k.e.373.3	yes	10	7.2	even	3
546.2.k.e.445.3	yes	10	13.3	even	3
1638.2.m.k.289.3		10	273.107	odd	6
1638.2.m.k.1621.3		10	3.2	odd	2
1638.2.p.j.919.3		10	21.2	odd	6
1638.2.p.j.991.3		10	39.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.59452 - 0.518144i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.59452 - 0.518144i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.114009 - 0.197470i) q^{10} +(-1.70561 - 2.95420i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.62906 + 3.21655i) q^{13} +(2.59452 + 0.518144i) q^{14} +(-0.114009 + 0.197470i) q^{15} +1.00000 q^{16} -5.41122 q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.17107 + 5.49246i) q^{19} +(0.114009 + 0.197470i) q^{20} +(-0.848534 - 2.50599i) q^{21} +(1.70561 + 2.95420i) q^{22} -1.91925 q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.47400 - 4.28510i) q^{25} +(1.62906 - 3.21655i) q^{26} -1.00000 q^{27} +(-2.59452 - 0.518144i) q^{28} +(0.851453 - 1.47476i) q^{29} +(0.114009 - 0.197470i) q^{30} +(-1.78052 + 3.08395i) q^{31} -1.00000 q^{32} +(1.70561 - 2.95420i) q^{33} +5.41122 q^{34} +(-0.193482 - 0.571413i) q^{35} +(-0.500000 + 0.866025i) q^{36} -4.18320 q^{37} +(3.17107 - 5.49246i) q^{38} +(-3.60014 + 0.197470i) q^{39} +(-0.114009 - 0.197470i) q^{40} +(1.59160 - 2.75673i) q^{41} +(0.848534 + 2.50599i) q^{42} +(5.17961 + 8.97135i) q^{43} +(-1.70561 - 2.95420i) q^{44} -0.228019 q^{45} +1.91925 q^{46} +(-5.57211 - 9.65117i) q^{47} +(0.500000 + 0.866025i) q^{48} +(6.46305 + 2.68867i) q^{49} +(-2.47400 + 4.28510i) q^{50} +(-2.70561 - 4.68625i) q^{51} +(-1.62906 + 3.21655i) q^{52} +(-3.31400 + 5.74001i) q^{53} +1.00000 q^{54} +(0.388911 - 0.673613i) q^{55} +(2.59452 + 0.518144i) q^{56} -6.34214 q^{57} +(-0.851453 + 1.47476i) q^{58} -14.7704 q^{59} +(-0.114009 + 0.197470i) q^{60} +(3.35999 - 5.81968i) q^{61} +(1.78052 - 3.08395i) q^{62} +(1.74599 - 1.98785i) q^{63} +1.00000 q^{64} +(-0.820899 + 0.0450268i) q^{65} +(-1.70561 + 2.95420i) q^{66} +(-5.58065 - 9.66597i) q^{67} -5.41122 q^{68} +(-0.959623 - 1.66212i) q^{69} +(0.193482 + 0.571413i) q^{70} +(-0.0390952 - 0.0677149i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.31721 + 10.9417i) q^{73} +4.18320 q^{74} +4.94801 q^{75} +(-3.17107 + 5.49246i) q^{76} +(2.89453 + 8.54848i) q^{77} +(3.60014 - 0.197470i) q^{78} +(0.811077 + 1.40483i) q^{79} +(0.114009 + 0.197470i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.59160 + 2.75673i) q^{82} -1.70291 q^{83} +(-0.848534 - 2.50599i) q^{84} +(-0.616929 - 1.06855i) q^{85} +(-5.17961 - 8.97135i) q^{86} +1.70291 q^{87} +(1.70561 + 2.95420i) q^{88} +17.5457 q^{89} +0.228019 q^{90} +(5.89325 - 7.50131i) q^{91} -1.91925 q^{92} -3.56104 q^{93} +(5.57211 + 9.65117i) q^{94} -1.44613 q^{95} +(-0.500000 - 0.866025i) q^{96} +(6.82663 + 11.8241i) q^{97} +(-6.46305 - 2.68867i) q^{98} +3.41122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q - 10 q^{2} + 5 q^{3} + 10 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 10 q^{8} - 5 q^{9} + 2 q^{10} + 6 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} + 10 q^{16} - 8 q^{17} + 5 q^{18} + 3 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} - 12 q^{23} - 5 q^{24} - q^{25} + 4 q^{26} - 10 q^{27} - 2 q^{28} - 2 q^{30} - 10 q^{31} - 10 q^{32} - 6 q^{33} + 8 q^{34} + 16 q^{35} - 5 q^{36} - 2 q^{37} - 3 q^{38} - 2 q^{39} + 2 q^{40} - 4 q^{41} + 4 q^{42} + 3 q^{43} + 6 q^{44} + 4 q^{45} + 12 q^{46} - 15 q^{47} + 5 q^{48} + 4 q^{49} + q^{50} - 4 q^{51} - 4 q^{52} - 17 q^{53} + 10 q^{54} + 3 q^{55} + 2 q^{56} + 6 q^{57} - 4 q^{59} + 2 q^{60} + 11 q^{61} + 10 q^{62} - 2 q^{63} + 10 q^{64} - 4 q^{65} + 6 q^{66} - q^{67} - 8 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} + 5 q^{72} + 12 q^{73} + 2 q^{74} - 2 q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} - 2 q^{80} - 5 q^{81} + 4 q^{82} - 4 q^{84} + q^{85} - 3 q^{86} - 6 q^{88} - 14 q^{89} - 4 q^{90} + 26 q^{91} - 12 q^{92} - 20 q^{93} + 15 q^{94} - 48 q^{95} - 5 q^{96} - 6 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 5 * q^3 + 10 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 10 * q^8 - 5 * q^9 + 2 * q^10 + 6 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 + 10 * q^16 - 8 * q^17 + 5 * q^18 + 3 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 - 12 * q^23 - 5 * q^24 - q^25 + 4 * q^26 - 10 * q^27 - 2 * q^28 - 2 * q^30 - 10 * q^31 - 10 * q^32 - 6 * q^33 + 8 * q^34 + 16 * q^35 - 5 * q^36 - 2 * q^37 - 3 * q^38 - 2 * q^39 + 2 * q^40 - 4 * q^41 + 4 * q^42 + 3 * q^43 + 6 * q^44 + 4 * q^45 + 12 * q^46 - 15 * q^47 + 5 * q^48 + 4 * q^49 + q^50 - 4 * q^51 - 4 * q^52 - 17 * q^53 + 10 * q^54 + 3 * q^55 + 2 * q^56 + 6 * q^57 - 4 * q^59 + 2 * q^60 + 11 * q^61 + 10 * q^62 - 2 * q^63 + 10 * q^64 - 4 * q^65 + 6 * q^66 - q^67 - 8 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 + 5 * q^72 + 12 * q^73 + 2 * q^74 - 2 * q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 - 2 * q^80 - 5 * q^81 + 4 * q^82 - 4 * q^84 + q^85 - 3 * q^86 - 6 * q^88 - 14 * q^89 - 4 * q^90 + 26 * q^91 - 12 * q^92 - 20 * q^93 + 15 * q^94 - 48 * q^95 - 5 * q^96 - 6 * q^97 - 4 * q^98 - 12 * q^99

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