LMFDB - Embedded newform 546.2.k.e.445.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
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			445.3
Root			$-0.114009 + 0.197470i$ of defining polynomial
Character	$\chi$	$=$	546.445
Dual form			546.2.k.e.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.848534 + 2.50599i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.848534 + 2.50599i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.228019 q^{10} +3.41122 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} +(-0.500000 + 0.866025i) q^{16} +(2.70561 + 4.68625i) q^{17} +(0.500000 - 0.866025i) q^{18} +6.34214 q^{19} +(0.114009 - 0.197470i) q^{20} +(-0.848534 - 2.50599i) q^{21} +(1.70561 - 2.95420i) q^{22} +(0.959623 - 1.66212i) q^{23} +1.00000 q^{24} +(2.47400 - 4.28510i) q^{25} +(-3.60014 - 0.197470i) q^{26} -1.00000 q^{27} +(1.74599 - 1.98785i) q^{28} +(0.851453 + 1.47476i) q^{29} -0.228019 q^{30} +(-1.78052 + 3.08395i) q^{31} +(0.500000 + 0.866025i) q^{32} -3.41122 q^{33} +5.41122 q^{34} +(-0.398117 + 0.453266i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.09160 - 3.62276i) q^{37} +(3.17107 - 5.49246i) q^{38} +(1.62906 + 3.21655i) q^{39} +(-0.114009 - 0.197470i) q^{40} +(1.59160 + 2.75673i) q^{41} +(-2.59452 - 0.518144i) q^{42} +(5.17961 - 8.97135i) q^{43} +(-1.70561 - 2.95420i) q^{44} +(0.114009 + 0.197470i) q^{45} +(-0.959623 - 1.66212i) q^{46} +(-5.57211 - 9.65117i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-5.55998 + 4.25284i) q^{49} +(-2.47400 - 4.28510i) q^{50} +(-2.70561 - 4.68625i) q^{51} +(-1.97108 + 3.01908i) q^{52} +(-3.31400 + 5.74001i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.388911 + 0.673613i) q^{55} +(-0.848534 - 2.50599i) q^{56} -6.34214 q^{57} +1.70291 q^{58} +(7.38522 + 12.7916i) q^{59} +(-0.114009 + 0.197470i) q^{60} -6.71999 q^{61} +(1.78052 + 3.08395i) q^{62} +(0.848534 + 2.50599i) q^{63} +1.00000 q^{64} +(0.449444 - 0.688406i) q^{65} +(-1.70561 + 2.95420i) q^{66} +11.1613 q^{67} +(2.70561 - 4.68625i) q^{68} +(-0.959623 + 1.66212i) q^{69} +(0.193482 + 0.571413i) q^{70} +(-0.0390952 + 0.0677149i) q^{71} -1.00000 q^{72} +(-6.31721 + 10.9417i) q^{73} +(-2.09160 - 3.62276i) q^{74} +(-2.47400 + 4.28510i) 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} -0.228019 q^{80} +1.00000 q^{81} +3.18320 q^{82} -1.70291 q^{83} +(-1.74599 + 1.98785i) q^{84} +(-0.616929 + 1.06855i) q^{85} +(-5.17961 - 8.97135i) q^{86} +(-0.851453 - 1.47476i) q^{87} -3.41122 q^{88} +(-8.77285 + 15.1950i) q^{89} +0.228019 q^{90} +(6.67833 - 6.81175i) q^{91} -1.91925 q^{92} +(1.78052 - 3.08395i) q^{93} -11.1442 q^{94} +(0.723063 + 1.25238i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(6.82663 - 11.8241i) q^{97} +(0.903072 + 6.94150i) q^{98} +3.41122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.114009	+	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
$7$	0.848534	+	2.50599i	0.320716	+	0.947176i
$7$	0.848534	+	2.50599i	0.320716	+	0.947176i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	0.228019			0.0721058
$11$	3.41122			1.02852			0.514260	−	0.857634i	$-0.328067\pi$
$11$	3.41122			1.02852			0.514260	+	0.857634i	$0.328067\pi$
$12$	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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.70561	+	4.68625i	0.656206	+	1.13658i	0.981590	+	0.191001i	$0.0611733\pi$
$17$	2.70561	+	4.68625i	0.656206	+	1.13658i	−0.325384	+	0.945582i	$0.605493\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	6.34214			1.45499			0.727494	−	0.686115i	$-0.240685\pi$
$19$	6.34214			1.45499			0.727494	+	0.686115i	$0.240685\pi$
$20$	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
$23$	0.959623	−	1.66212i	0.200095	−	0.346575i	−0.748464	−	0.663176i	$-0.769208\pi$
$23$	0.959623	−	1.66212i	0.200095	−	0.346575i	0.948559	+	0.316601i	$0.102542\pi$
$24$	1.00000			0.204124
$25$	2.47400	−	4.28510i	0.494801	−	0.857020i
$26$	−3.60014	−	0.197470i	−0.706045	−	0.0387270i
$27$	−1.00000			−0.192450
$28$	1.74599	−	1.98785i	0.329960	−	0.375668i
$29$	0.851453	+	1.47476i	0.158111	+	0.273856i	0.934187	−	0.356783i	$-0.116126\pi$
$29$	0.851453	+	1.47476i	0.158111	+	0.273856i	−0.776077	+	0.630639i	$0.782793\pi$
$30$	−0.228019			−0.0416303
$31$	−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	$0.270279\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.41122			−0.593817
$34$	5.41122			0.928016
$35$	−0.398117	+	0.453266i	−0.0672941	+	0.0766160i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.09160	−	3.62276i	0.343857	−	0.595577i	−0.641289	−	0.767300i	$-0.721600\pi$
$37$	2.09160	−	3.62276i	0.343857	−	0.595577i	0.985145	+	0.171722i	$0.0549332\pi$
$38$	3.17107	−	5.49246i	0.514416	−	0.890994i
$39$	1.62906	+	3.21655i	0.260858	+	0.515060i
$40$	−0.114009	−	0.197470i	−0.0180265	−	0.0312227i
$41$	1.59160	+	2.75673i	0.248566	+	0.430529i	0.963128	−	0.269043i	$-0.0867074\pi$
$41$	1.59160	+	2.75673i	0.248566	+	0.430529i	−0.714562	+	0.699572i	$0.753374\pi$
$42$	−2.59452	−	0.518144i	−0.400343	−	0.0799513i
$43$	5.17961	−	8.97135i	0.789883	−	1.36812i	−0.136154	−	0.990688i	$-0.543474\pi$
$43$	5.17961	−	8.97135i	0.789883	−	1.36812i	0.926038	−	0.377431i	$-0.123192\pi$
$44$	−1.70561	−	2.95420i	−0.257130	−	0.445362i
$45$	0.114009	+	0.197470i	0.0169955	+	0.0294371i
$46$	−0.959623	−	1.66212i	−0.141489	−	0.245066i
$47$	−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
$49$	−5.55998	+	4.25284i	−0.794283	+	0.607548i
$50$	−2.47400	−	4.28510i	−0.349877	−	0.606005i
$51$	−2.70561	−	4.68625i	−0.378861	−	0.656206i
$52$	−1.97108	+	3.01908i	−0.273340	+	0.418671i
$53$	−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	$0.317103\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.388911	+	0.673613i	0.0524407	+	0.0908299i
$56$	−0.848534	−	2.50599i	−0.113390	−	0.334877i
$57$	−6.34214			−0.840037
$58$	1.70291			0.223603
$59$	7.38522	+	12.7916i	0.961474	+	1.66532i	0.718804	+	0.695212i	$0.244690\pi$
$59$	7.38522	+	12.7916i	0.961474	+	1.66532i	0.242669	+	0.970109i	$0.421977\pi$
$60$	−0.114009	+	0.197470i	−0.0147185	+	0.0254933i
$61$	−6.71999			−0.860406			−0.430203	−	0.902732i	$-0.641558\pi$
$61$	−6.71999			−0.860406			−0.430203	+	0.902732i	$0.641558\pi$
$62$	1.78052	+	3.08395i	0.226127	+	0.391663i
$63$	0.848534	+	2.50599i	0.106905	+	0.315725i
$64$	1.00000			0.125000
$65$	0.449444	−	0.688406i	0.0557467	−	0.0853863i
$66$	−1.70561	+	2.95420i	−0.209946	+	0.363637i
$67$	11.1613			1.36357			0.681785	−	0.731553i	$-0.261204\pi$
$67$	11.1613			1.36357			0.681785	+	0.731553i	$0.261204\pi$
$68$	2.70561	−	4.68625i	0.328103	−	0.568291i
$69$	−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	−0.868336	−	0.495976i	$-0.834810\pi$
$71$	−0.0390952	+	0.0677149i	−0.00463975	+	0.00803628i	0.863696	+	0.504013i	$0.168144\pi$
$72$	−1.00000			−0.117851
$73$	−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	$0.901789\pi$
$74$	−2.09160	−	3.62276i	−0.243143	−	0.421137i
$75$	−2.47400	+	4.28510i	−0.285673	+	0.494801i
$76$	−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	$0.804246\pi$
$80$	−0.228019			−0.0254933
$81$	1.00000			0.111111
$82$	3.18320			0.351525
$83$	−1.70291			−0.186918			−0.0934592	−	0.995623i	$-0.529792\pi$
$83$	−1.70291			−0.186918			−0.0934592	+	0.995623i	$0.529792\pi$
$84$	−1.74599	+	1.98785i	−0.190503	+	0.216892i
$85$	−0.616929	+	1.06855i	−0.0669154	+	0.115901i
$86$	−5.17961	−	8.97135i	−0.558532	−	0.967406i
$87$	−0.851453	−	1.47476i	−0.0912854	−	0.158111i
$88$	−3.41122			−0.363637
$89$	−8.77285	+	15.1950i	−0.929920	+	1.61067i	−0.146469	+	0.989215i	$0.546791\pi$
$89$	−8.77285	+	15.1950i	−0.929920	+	1.61067i	−0.783451	+	0.621454i	$0.786542\pi$
$90$	0.228019			0.0240353
$91$	6.67833	−	6.81175i	0.700079	−	0.714065i
$92$	−1.91925			−0.200095
$93$	1.78052	−	3.08395i	0.184632	−	0.319791i
$94$	−11.1442			−1.14944
$95$	0.723063	+	1.25238i	0.0741847	+	0.128492i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	6.82663	−	11.8241i	0.693140	−	1.20055i	−0.277664	−	0.960678i	$-0.589560\pi$
$97$	6.82663	−	11.8241i	0.693140	−	1.20055i	0.970804	−	0.239875i	$-0.0771064\pi$
$98$	0.903072	+	6.94150i	0.0912241	+	0.701198i
$99$	3.41122			0.342840
$100$	−4.94801			−0.494801
$101$	−16.5165			−1.64345			−0.821724	−	0.569885i	$-0.806988\pi$
$101$	−16.5165			−1.64345			−0.821724	+	0.569885i	$0.806988\pi$
$102$	−5.41122			−0.535790
$103$	−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
$107$	−3.27362	+	5.67008i	−0.316473	+	0.548147i	−0.979749	−	0.200227i	$-0.935832\pi$
$107$	−3.27362	+	5.67008i	−0.316473	+	0.548147i	0.663277	+	0.748374i	$0.269165\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	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	$0.142341\pi$
$110$	0.777821			0.0741623
$111$	−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	−0.992156	−	0.125009i	$-0.960104\pi$
$113$	−4.12255	+	7.14047i	−0.387817	+	0.671719i	0.604339	+	0.796728i	$0.293437\pi$
$114$	−3.17107	+	5.49246i	−0.296998	+	0.514416i
$115$	0.437624			0.0408086
$116$	0.851453	−	1.47476i	0.0790555	−	0.136928i
$117$	−1.62906	−	3.21655i	−0.150606	−	0.297370i
$118$	14.7704			1.35973
$119$	−9.44790	+	10.7567i	−0.866088	+	0.986062i
$120$	0.114009	+	0.197470i	0.0104076	+	0.0180265i
$121$	0.636396			0.0578542
$122$	−3.35999	+	5.81968i	−0.304200	+	0.526889i
$123$	−1.59160	−	2.75673i	−0.143510	−	0.248566i
$124$	3.56104			0.319791
$125$	2.26833			0.202886
$126$	2.59452	+	0.518144i	0.231138	+	0.0461599i
$127$	−6.40560	−	11.0948i	−0.568405	−	0.984506i	−0.996724	−	0.0808783i	$-0.974227\pi$
$127$	−6.40560	−	11.0948i	−0.568405	−	0.984506i	0.428319	−	0.903627i	$-0.359106\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.17961	+	8.97135i	−0.456039	+	0.789883i
$130$	−0.371455	−	0.733433i	−0.0325788	−	0.0643263i
$131$	−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
$133$	5.38152	+	15.8934i	0.466637	+	1.37813i
$134$	5.58065	−	9.66597i	0.482095	−	0.835012i
$135$	−0.114009	−	0.197470i	−0.00981236	−	0.0169955i
$136$	−2.70561	−	4.68625i	−0.232004	−	0.401843i
$137$	−8.84776	−	15.3248i	−0.755915	−	1.30928i	−0.944918	−	0.327307i	$-0.893859\pi$
$137$	−8.84776	−	15.3248i	−0.755915	−	1.30928i	0.189003	−	0.981977i	$-0.439475\pi$
$138$	0.959623	+	1.66212i	0.0816885	+	0.141489i
$139$	3.98321	−	6.89912i	0.337851	−	0.585176i	−0.646177	−	0.763188i	$-0.723633\pi$
$139$	3.98321	−	6.89912i	0.337851	−	0.585176i	0.984028	+	0.178012i	$0.0569665\pi$
$140$	0.591599	+	0.118146i	0.0499992	+	0.00998520i
$141$	5.57211	+	9.65117i	0.469256	+	0.812775i
$142$	0.0390952	+	0.0677149i	0.00328080	+	0.00568251i
$143$	−5.55706	−	10.9723i	−0.464705	−	0.917553i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.194147	+	0.336273i	−0.0161231	+	0.0279260i
$146$	6.31721	+	10.9417i	0.522816	+	0.905544i
$147$	5.55998	−	4.25284i	0.458580	−	0.350768i
$148$	−4.18320			−0.343857
$149$	2.69358			0.220667			0.110333	−	0.993895i	$-0.464808\pi$
$149$	2.69358			0.220667			0.110333	+	0.993895i	$0.464808\pi$
$150$	2.47400	+	4.28510i	0.202002	+	0.349877i
$151$	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	$-0.0127192\pi$
$152$	−6.34214			−0.514416
$153$	2.70561	+	4.68625i	0.218735	+	0.378861i
$154$	8.85046	+	1.76750i	0.713191	+	0.142429i
$155$	−0.811985			−0.0652202
$156$	1.97108	−	3.01908i	0.157813	−	0.241720i
$157$	−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	$0.207186\pi$
$158$	1.62215			0.129052
$159$	3.31400	−	5.74001i	0.262817	−	0.455212i
$160$	−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
$163$	−16.2940			−1.27625			−0.638124	−	0.769934i	$-0.720289\pi$
$163$	−16.2940			−1.27625			−0.638124	+	0.769934i	$0.720289\pi$
$164$	1.59160	−	2.75673i	0.124283	−	0.215264i
$165$	−0.388911	−	0.673613i	−0.0302766	−	0.0524407i
$166$	−0.851453	+	1.47476i	−0.0660856	+	0.114464i
$167$	0.826739	+	1.43195i	0.0639750	+	0.110808i	0.896239	−	0.443572i	$-0.146289\pi$
$167$	0.826739	+	1.43195i	0.0639750	+	0.110808i	−0.832264	+	0.554380i	$0.812956\pi$
$168$	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
$171$	6.34214			0.484996
$172$	−10.3592			−0.789883
$173$	14.0420			1.06759			0.533797	−	0.845613i	$-0.320765\pi$
$173$	14.0420			1.06759			0.533797	+	0.845613i	$0.320765\pi$
$174$	−1.70291			−0.129097
$175$	12.8377	+	2.56378i	0.970439	+	0.193804i
$176$	−1.70561	+	2.95420i	−0.128565	+	0.222681i
$177$	−7.38522	−	12.7916i	−0.555107	−	0.961474i
$178$	8.77285	+	15.1950i	0.657553	+	1.13891i
$179$	−9.33325			−0.697600			−0.348800	−	0.937197i	$-0.613411\pi$
$179$	−9.33325			−0.697600			−0.348800	+	0.937197i	$0.613411\pi$
$180$	0.114009	−	0.197470i	0.00849776	−	0.0147185i
$181$	1.13838			0.0846148			0.0423074	−	0.999105i	$-0.486529\pi$
$181$	1.13838			0.0846148			0.0423074	+	0.999105i	$0.486529\pi$
$182$	−2.55998	−	9.18948i	−0.189758	−	0.681169i
$183$	6.71999			0.496756
$184$	−0.959623	+	1.66212i	−0.0707444	+	0.122533i
$185$	0.953847			0.0701282
$186$	−1.78052	−	3.08395i	−0.130554	−	0.226127i
$187$	9.22941	+	15.9858i	0.674922	+	1.16900i
$188$	−5.57211	+	9.65117i	−0.406388	+	0.703884i
$189$	−0.848534	−	2.50599i	−0.0617217	−	0.182284i
$190$	1.44613			0.104913
$191$	18.0851			1.30859			0.654294	−	0.756240i	$-0.272966\pi$
$191$	18.0851			1.30859			0.654294	+	0.756240i	$0.272966\pi$
$192$	−1.00000			−0.0721688
$193$	−5.82592			−0.419359			−0.209679	−	0.977770i	$-0.567242\pi$
$193$	−5.82592			−0.419359			−0.209679	+	0.977770i	$0.567242\pi$
$194$	−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	−0.953572	−	0.301165i	$-0.902625\pi$
$197$	−10.3527	−	17.9315i	−0.737602	−	1.27756i	0.215970	−	0.976400i	$-0.430709\pi$
$198$	1.70561	−	2.95420i	0.121212	−	0.209946i
$199$	8.19922	+	14.2015i	0.581227	+	1.00671i	0.995334	+	0.0964867i	$0.0307605\pi$
$199$	8.19922	+	14.2015i	0.581227	+	1.00671i	−0.414107	+	0.910228i	$0.635906\pi$
$200$	−2.47400	+	4.28510i	−0.174938	+	0.303002i
$201$	−11.1613			−0.787257
$202$	−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
$205$	−0.362914	+	0.628586i	−0.0253470	+	0.0439023i
$206$	−6.35922			−0.443068
$207$	0.959623	−	1.66212i	0.0666984	−	0.115525i
$208$	3.60014	+	0.197470i	0.249625	+	0.0136921i
$209$	21.6344			1.49648
$210$	−0.193482	−	0.571413i	−0.0133515	−	0.0394312i
$211$	3.74446	+	6.48560i	0.257779	+	0.446487i	0.965647	−	0.259858i	$-0.0836759\pi$
$211$	3.74446	+	6.48560i	0.257779	+	0.446487i	−0.707867	+	0.706345i	$0.750343\pi$
$212$	6.62799			0.455212
$213$	0.0390952	−	0.0677149i	0.00267876	−	0.00463975i
$214$	3.27362	+	5.67008i	0.223780	+	0.387598i
$215$	2.36210			0.161094
$216$	1.00000			0.0680414
$217$	−9.23920	−	1.84513i	−0.627198	−	0.125256i
$218$	−0.797093	−	1.38061i	−0.0539860	−	0.0935064i
$219$	6.31721	−	10.9417i	0.426877	−	0.739373i
$220$	0.388911	−	0.673613i	0.0262203	−	0.0454150i
$221$	10.6660	−	16.3369i	0.717470	−	1.09894i
$222$	2.09160	+	3.62276i	0.140379	+	0.243143i
$223$	−8.41325	−	14.5722i	−0.563393	−	0.975825i	−0.997197	−	0.0748181i	$-0.976162\pi$
$223$	−8.41325	−	14.5722i	−0.563393	−	0.975825i	0.433804	−	0.901007i	$-0.357171\pi$
$224$	−1.74599	+	1.98785i	−0.116659	+	0.132819i
$225$	2.47400	−	4.28510i	0.164934	−	0.285673i
$226$	4.12255	+	7.14047i	0.274228	+	0.474977i
$227$	2.11607	+	3.66514i	0.140449	+	0.243264i	0.927666	−	0.373412i	$-0.121812\pi$
$227$	2.11607	+	3.66514i	0.140449	+	0.243264i	−0.787217	+	0.616676i	$0.788479\pi$
$228$	3.17107	+	5.49246i	0.210009	+	0.363747i
$229$	−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
$231$	−2.89453	−	8.54848i	−0.190446	−	0.562448i
$232$	−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	$0.914570\pi$
$234$	−3.60014	−	0.197470i	−0.235348	−	0.0129090i
$235$	1.27054	−	2.20065i	0.0828812	−	0.143554i
$236$	7.38522	−	12.7916i	0.480737	−	0.832661i
$237$	−0.811077	−	1.40483i	−0.0526851	−	0.0912532i
$238$	4.59160	+	13.5605i	0.297629	+	0.878994i
$239$	−25.2189			−1.63128			−0.815638	−	0.578562i	$-0.803614\pi$
$239$	−25.2189			−1.63128			−0.815638	+	0.578562i	$0.803614\pi$
$240$	0.228019			0.0147185
$241$	−13.9183	−	24.1073i	−0.896560	−	1.55289i	−0.831863	−	0.554982i	$-0.812725\pi$
$241$	−13.9183	−	24.1073i	−0.896560	−	1.55289i	−0.0646969	−	0.997905i	$-0.520608\pi$
$242$	0.318198	−	0.551135i	0.0204545	−	0.0354283i
$243$	−1.00000			−0.0641500
$244$	3.35999	+	5.81968i	0.215102	+	0.372567i
$245$	−1.47370	−	0.613066i	−0.0941511	−	0.0391674i
$246$	−3.18320			−0.202953
$247$	−10.3317	−	20.3998i	−0.657391	−	1.29801i
$248$	1.78052	−	3.08395i	0.113063	−	0.195831i
$249$	1.70291			0.107917
$250$	1.13417	−	1.96443i	0.0717309	−	0.124242i
$251$	2.12395	−	3.67878i	0.134062	−	0.232203i	−0.791177	−	0.611588i	$-0.790531\pi$
$251$	2.12395	−	3.67878i	0.134062	−	0.232203i	0.925239	+	0.379385i	$0.123864\pi$
$252$	1.74599	−	1.98785i	0.109987	−	0.125223i
$253$	3.27348	−	5.66984i	0.205802	−	0.356460i
$254$	−12.8112			−0.803846
$255$	0.616929	−	1.06855i	0.0386336	−	0.0669154i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.35836	+	12.7450i	−0.459002	+	0.795014i	−0.998908	−	0.0467106i	$-0.985126\pi$
$257$	−7.35836	+	12.7450i	−0.459002	+	0.795014i	0.539907	+	0.841725i	$0.318459\pi$
$258$	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
$262$	−3.51927			−0.217421
$263$	23.4105			1.44355			0.721777	−	0.692125i	$-0.243325\pi$
$263$	23.4105			1.44355			0.721777	+	0.692125i	$0.243325\pi$
$264$	3.41122			0.209946
$265$	−1.51131			−0.0928388
$266$	16.4548	+	3.28614i	1.00891	+	0.201486i
$267$	8.77285	−	15.1950i	0.536890	−	0.929920i
$268$	−5.58065	−	9.66597i	−0.340892	−	0.590443i
$269$	4.67886	+	8.10402i	0.285275	+	0.494111i	0.972676	−	0.232167i	$-0.0745817\pi$
$269$	4.67886	+	8.10402i	0.285275	+	0.494111i	−0.687401	+	0.726278i	$0.741248\pi$
$270$	−0.228019			−0.0138768
$271$	7.57375	−	13.1181i	0.460072	−	0.796869i	−0.538892	−	0.842375i	$-0.681157\pi$
$271$	7.57375	−	13.1181i	0.460072	−	0.796869i	0.998964	+	0.0455064i	$0.0144901\pi$
$272$	−5.41122			−0.328103
$273$	−6.67833	+	6.81175i	−0.404191	+	0.412266i
$274$	−17.6955			−1.06903
$275$	8.43936	−	14.6174i	0.508913	−	0.881463i
$276$	1.91925			0.115525
$277$	16.4391	+	28.4734i	0.987731	+	1.71080i	0.629109	+	0.777317i	$0.283420\pi$
$277$	16.4391	+	28.4734i	0.987731	+	1.71080i	0.358622	+	0.933483i	$0.383247\pi$
$278$	−3.98321	−	6.89912i	−0.238897	−	0.413782i
$279$	−1.78052	+	3.08395i	−0.106597	+	0.184632i
$280$	0.398117	−	0.453266i	0.0237921	−	0.0270878i
$281$	−16.8072			−1.00263			−0.501316	−	0.865264i	$-0.667150\pi$
$281$	−16.8072			−1.00263			−0.501316	+	0.865264i	$0.667150\pi$
$282$	11.1442			0.663628
$283$	−12.1600			−0.722835			−0.361417	−	0.932404i	$-0.617707\pi$
$283$	−12.1600			−0.722835			−0.361417	+	0.932404i	$0.617707\pi$
$284$	0.0781905			0.00463975
$285$	−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
$289$	−6.14063	+	10.6359i	−0.361214	+	0.625640i
$290$	0.194147	+	0.336273i	0.0114007	+	0.0197466i
$291$	−6.82663	+	11.8241i	−0.400184	+	0.693140i
$292$	12.6344			0.739373
$293$	13.8954	−	24.0675i	0.811778	−	1.40604i	−0.0998407	−	0.995003i	$-0.531833\pi$
$293$	13.8954	−	24.0675i	0.811778	−	1.40604i	0.911619	−	0.411037i	$-0.134833\pi$
$294$	−0.903072	−	6.94150i	−0.0526683	−	0.404837i
$295$	−1.68397	+	2.91672i	−0.0980444	+	0.169818i
$296$	−2.09160	+	3.62276i	−0.121572	+	0.210568i
$297$	−3.41122			−0.197939
$298$	1.34679	−	2.33271i	0.0780175	−	0.135130i
$299$	−6.90955	−	0.378993i	−0.399590	−	0.0219178i
$300$	4.94801			0.285673
$301$	26.8772	+	5.36757i	1.54918	+	0.309381i
$302$	−6.56432	−	11.3697i	−0.377734	−	0.654255i
$303$	16.5165			0.948845
$304$	−3.17107	+	5.49246i	−0.181873	+	0.315014i
$305$	−0.766142	−	1.32700i	−0.0438691	−	0.0759836i
$306$	5.41122			0.309339
$307$	−14.6849			−0.838110			−0.419055	−	0.907961i	$-0.637639\pi$
$307$	−14.6849			−0.838110			−0.419055	+	0.907961i	$0.637639\pi$
$308$	5.95593	−	6.78098i	0.339371	−	0.386382i
$309$	3.17961	+	5.50725i	0.180882	+	0.313296i
$310$	−0.405992	+	0.703199i	−0.0230588	+	0.0399390i
$311$	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	$0.0963619\pi$
$312$	−1.62906	−	3.21655i	−0.0922271	−	0.182101i
$313$	−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
$315$	−0.398117	+	0.453266i	−0.0224314	+	0.0255387i
$316$	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	$0.697665\pi$
$318$	−3.31400	−	5.74001i	−0.185840	−	0.321884i
$319$	2.90449	+	5.03073i	0.162620	+	0.281667i
$320$	0.114009	+	0.197470i	0.00637332	+	0.0110389i
$321$	3.27362	−	5.67008i	0.182716	−	0.316473i
$322$	3.35098	−	3.81517i	0.186743	−	0.212611i
$323$	17.1594	+	29.7209i	0.954772	+	1.65371i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−17.8135	−	0.977083i	−0.988116	−	0.0541988i
$326$	−8.14702	+	14.1111i	−0.451222	+	0.781539i
$327$	−0.797093	+	1.38061i	−0.0440793	+	0.0763477i
$328$	−1.59160	−	2.75673i	−0.0878813	−	0.152215i
$329$	19.4576	−	22.1530i	1.07273	−	1.22133i
$330$	−0.777821			−0.0428176
$331$	4.10872			0.225836			0.112918	−	0.993604i	$-0.463980\pi$
$331$	4.10872			0.225836			0.112918	+	0.993604i	$0.463980\pi$
$332$	0.851453	+	1.47476i	0.0467296	+	0.0809380i
$333$	2.09160	−	3.62276i	0.114619	−	0.198526i
$334$	1.65348			0.0904743
$335$	1.27249	+	2.20402i	0.0695237	+	0.120419i
$336$	2.59452	+	0.518144i	0.141543	+	0.0282671i
$337$	−7.44592			−0.405605			−0.202802	−	0.979220i	$-0.565005\pi$
$337$	−7.44592			−0.405605			−0.202802	+	0.979220i	$0.565005\pi$
$338$	5.22966	+	11.9017i	0.284456	+	0.647368i
$339$	4.12255	−	7.14047i	0.223906	−	0.387817i
$340$	1.23386			0.0669154
$341$	−6.07375	+	10.5200i	−0.328912	+	0.569692i
$342$	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
$345$	−0.437624			−0.0235609
$346$	7.02100	−	12.1607i	0.377451	−	0.653765i
$347$	5.26407	+	9.11763i	0.282590	+	0.489460i	0.972022	−	0.234890i	$-0.0754731\pi$
$347$	5.26407	+	9.11763i	0.282590	+	0.489460i	−0.689432	+	0.724350i	$0.742140\pi$
$348$	−0.851453	+	1.47476i	−0.0456427	+	0.0790555i
$349$	−4.74127	−	8.21212i	−0.253794	−	0.439585i	0.710773	−	0.703422i	$-0.248345\pi$
$349$	−4.74127	−	8.21212i	−0.253794	−	0.439585i	−0.964567	+	0.263837i	$0.915012\pi$
$350$	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
$353$	5.44223			0.289661			0.144830	−	0.989456i	$-0.453736\pi$
$353$	5.44223			0.289661			0.144830	+	0.989456i	$0.453736\pi$
$354$	−14.7704			−0.785040
$355$	−0.0178289			−0.000946259
$356$	17.5457			0.929920
$357$	9.44790	−	10.7567i	0.500036	−	0.569303i
$358$	−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	$0.923502\pi$
$360$	−0.114009	−	0.197470i	−0.00600882	−	0.0104076i
$361$	21.2228			1.11699
$362$	0.569188	−	0.985863i	0.0299159	−	0.0518158i
$363$	−0.636396			−0.0334021
$364$	−9.23831	−	2.37773i	−0.484219	−	0.124627i
$365$	−2.88088			−0.150792
$366$	3.35999	−	5.81968i	0.175630	−	0.304200i
$367$	−7.19793			−0.375729			−0.187864	−	0.982195i	$-0.560157\pi$
$367$	−7.19793			−0.375729			−0.187864	+	0.982195i	$0.560157\pi$
$368$	0.959623	+	1.66212i	0.0500238	+	0.0866438i
$369$	1.59160	+	2.75673i	0.0828553	+	0.143510i
$370$	0.476924	−	0.826056i	0.0247941	−	0.0429446i
$371$	−17.1965	−	3.43425i	−0.892795	−	0.178298i
$372$	−3.56104			−0.184632
$373$	−28.5523			−1.47838			−0.739192	−	0.673494i	$-0.764793\pi$
$373$	−28.5523			−1.47838			−0.739192	+	0.673494i	$0.764793\pi$
$374$	18.4588			0.954483
$375$	−2.26833			−0.117136
$376$	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	0.919970	+	0.391989i	$0.128213\pi$
$379$	15.5638	+	26.9572i	0.799457	+	1.38470i	−0.120513	+	0.992712i	$0.538454\pi$
$380$	0.723063	−	1.25238i	0.0370924	−	0.0642459i
$381$	6.40560	+	11.0948i	0.328169	+	0.568405i
$382$	9.04253	−	15.6621i	0.462656	−	0.801343i
$383$	21.9521			1.12170			0.560849	−	0.827918i	$-0.310475\pi$
$383$	21.9521			1.12170			0.560849	+	0.827918i	$0.310475\pi$
$384$	−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
$387$	5.17961	−	8.97135i	0.263294	−	0.456039i
$388$	−13.6533			−0.693140
$389$	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	$0.136382\pi$
$390$	0.371455	+	0.733433i	0.0188094	+	0.0371388i
$391$	10.3855			0.525215
$392$	5.55998	−	4.25284i	0.280821	−	0.214801i
$393$	1.75964	+	3.04778i	0.0887619	+	0.153740i
$394$	−20.7055			−1.04313
$395$	−0.184941	+	0.320327i	−0.00930537	+	0.0161174i
$396$	−1.70561	−	2.95420i	−0.0857100	−	0.148454i
$397$	−3.91005			−0.196240			−0.0981198	−	0.995175i	$-0.531283\pi$
$397$	−3.91005			−0.196240			−0.0981198	+	0.995175i	$0.531283\pi$
$398$	16.3984			0.821979
$399$	−5.38152	−	15.8934i	−0.269413	−	0.795663i
$400$	2.47400	+	4.28510i	0.123700	+	0.214255i
$401$	13.1130	−	22.7124i	0.654833	−	1.13420i	−0.327103	−	0.944989i	$-0.606072\pi$
$401$	13.1130	−	22.7124i	0.654833	−	1.13420i	0.981936	−	0.189215i	$-0.0605944\pi$
$402$	−5.58065	+	9.66597i	−0.278337	+	0.482095i
$403$	12.8203	+	0.703199i	0.638623	+	0.0350289i
$404$	8.25823	+	14.3037i	0.410862	+	0.711634i
$405$	0.114009	+	0.197470i	0.00566517	+	0.00981236i
$406$	1.44497	+	4.26747i	0.0717128	+	0.211791i
$407$	7.13490	−	12.3580i	0.353664	−	0.612563i
$408$	2.70561	+	4.68625i	0.133948	+	0.232004i
$409$	−2.01759	−	3.49457i	−0.0997635	−	0.172796i	0.811823	−	0.583903i	$-0.198475\pi$
$409$	−2.01759	−	3.49457i	−0.0997635	−	0.172796i	−0.911587	+	0.411108i	$0.865142\pi$
$410$	0.362914	+	0.628586i	0.0179231	+	0.0310436i
$411$	8.84776	+	15.3248i	0.436428	+	0.755915i
$412$	−3.17961	+	5.50725i	−0.156648	+	0.271323i
$413$	−25.7890	+	29.3614i	−1.26899	+	1.44478i
$414$	−0.959623	−	1.66212i	−0.0471629	−	0.0816885i
$415$	−0.194147	−	0.336273i	−0.00953032	−	0.0165070i
$416$	1.97108	−	3.01908i	0.0966403	−	0.148022i
$417$	−3.98321	+	6.89912i	−0.195059	+	0.337851i
$418$	10.8172	−	18.7360i	0.529087	−	0.916406i
$419$	1.74139	+	3.01617i	0.0850723	+	0.147350i	0.905422	−	0.424513i	$-0.139555\pi$
$419$	1.74139	+	3.01617i	0.0850723	+	0.147350i	−0.820350	+	0.571862i	$0.806221\pi$
$420$	−0.591599	−	0.118146i	−0.0288671	−	0.00576496i
$421$	18.6028			0.906647			0.453323	−	0.891346i	$-0.350238\pi$
$421$	18.6028			0.906647			0.453323	+	0.891346i	$0.350238\pi$
$422$	7.48892			0.364555
$423$	−5.57211	−	9.65117i	−0.270925	−	0.469256i
$424$	3.31400	−	5.74001i	0.160942	−	0.278760i
$425$	26.7747			1.29877
$426$	−0.0390952	−	0.0677149i	−0.00189417	−	0.00328080i
$427$	−5.70214	−	16.8402i	−0.275946	−	0.814956i
$428$	6.54724			0.316473
$429$	5.55706	+	10.9723i	0.268297	+	0.529750i
$430$	1.18105	−	2.04564i	0.0569552	−	0.0986493i
$431$	−19.0532			−0.917762			−0.458881	−	0.888498i	$-0.651750\pi$
$431$	−19.0532			−0.917762			−0.458881	+	0.888498i	$0.651750\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−16.7336	+	28.9834i	−0.804164	+	1.39285i	0.112689	+	0.993630i	$0.464053\pi$
$433$	−16.7336	+	28.9834i	−0.804164	+	1.39285i	−0.916854	+	0.399223i	$0.869280\pi$
$434$	−6.21753	+	7.07881i	−0.298451	+	0.339794i
$435$	0.194147	−	0.336273i	0.00930865	−	0.0161231i
$436$	−1.59419			−0.0763477
$437$	6.08607	−	10.5414i	0.291136	−	0.504262i
$438$	−6.31721	−	10.9417i	−0.301848	−	0.522816i
$439$	−19.0229	+	32.9487i	−0.907915	+	1.57255i	−0.0909591	+	0.995855i	$0.528993\pi$
$439$	−19.0229	+	32.9487i	−0.907915	+	1.57255i	−0.816956	+	0.576700i	$0.804340\pi$
$440$	−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	$0.766997\pi$
$444$	4.18320			0.198526
$445$	−4.00075			−0.189654
$446$	−16.8265			−0.796758
$447$	−2.69358			−0.127402
$448$	0.848534	+	2.50599i	0.0400894	+	0.118397i
$449$	−11.4930	+	19.9065i	−0.542389	+	0.939445i	0.456377	+	0.889786i	$0.349147\pi$
$449$	−11.4930	+	19.9065i	−0.542389	+	0.939445i	−0.998766	+	0.0496589i	$0.984187\pi$
$450$	−2.47400	−	4.28510i	−0.116626	−	0.202002i
$451$	5.42929	+	9.40380i	0.255655	+	0.442808i
$452$	8.24510			0.387817
$453$	−6.56432	+	11.3697i	−0.308419	+	0.534197i
$454$	4.23214			0.198624
$455$	2.10651	+	0.542167i	0.0987546	+	0.0254172i
$456$	6.34214			0.296998
$457$	−5.79493	+	10.0371i	−0.271075	+	0.469516i	−0.969137	−	0.246521i	$-0.920713\pi$
$457$	−5.79493	+	10.0371i	−0.271075	+	0.469516i	0.698062	+	0.716037i	$0.254046\pi$
$458$	−13.7300			−0.641558
$459$	−2.70561	−	4.68625i	−0.126287	−	0.218735i
$460$	−0.218812	−	0.378993i	−0.0102022	−	0.0176707i
$461$	−17.4236	+	30.1785i	−0.811496	+	1.40555i	0.100321	+	0.994955i	$0.468013\pi$
$461$	−17.4236	+	30.1785i	−0.811496	+	1.40555i	−0.911817	+	0.410597i	$0.865320\pi$
$462$	−8.85046	−	1.76750i	−0.411761	−	0.0822316i
$463$	−39.5334			−1.83727			−0.918635	−	0.395106i	$-0.870708\pi$
$463$	−39.5334			−1.83727			−0.918635	+	0.395106i	$0.870708\pi$
$464$	−1.70291			−0.0790555
$465$	0.811985			0.0376549
$466$	−7.70698			−0.357019
$467$	−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
$471$	1.59071	−	2.75520i	0.0732962	−	0.126953i
$472$	−7.38522	−	12.7916i	−0.339932	−	0.588780i
$473$	17.6688	−	30.6032i	0.812411	−	1.40714i
$474$	−1.62215			−0.0745080
$475$	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
$478$	−12.6095	+	21.8402i	−0.576743	+	0.998949i
$479$	11.5746			0.528859			0.264429	−	0.964405i	$-0.414816\pi$
$479$	11.5746			0.528859			0.264429	+	0.964405i	$0.414816\pi$
$480$	0.114009	−	0.197470i	0.00520379	−	0.00901323i
$481$	−15.0601	−	0.826056i	−0.686681	−	0.0376649i
$482$	−27.8367			−1.26793
$483$	−4.97952	−	0.994446i	−0.226576	−	0.0452488i
$484$	−0.318198	−	0.551135i	−0.0144635	−	0.0250516i
$485$	3.11320			0.141363
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	6.96602	+	12.0655i	0.315661	+	0.546740i	0.979578	−	0.201066i	$-0.0644405\pi$
$487$	6.96602	+	12.0655i	0.315661	+	0.546740i	−0.663917	+	0.747806i	$0.731107\pi$
$488$	6.71999			0.304200
$489$	16.2940			0.736842
$490$	−1.26778	+	0.969726i	−0.0572724	+	0.0438078i
$491$	4.76716	+	8.25697i	0.215139	+	0.372632i	0.953316	−	0.301976i	$-0.0976462\pi$
$491$	4.76716	+	8.25697i	0.215139	+	0.372632i	−0.738177	+	0.674608i	$0.764313\pi$
$492$	−1.59160	+	2.75673i	−0.0717548	+	0.124283i
$493$	−4.60740	+	7.98025i	−0.207507	+	0.359412i
$494$	−22.8326	−	1.25238i	−1.02729	−	0.0563474i
$495$	0.388911	+	0.673613i	0.0174802	+	0.0302766i
$496$	−1.78052	−	3.08395i	−0.0799478	−	0.138474i
$497$	−0.202867	−	0.0405139i	−0.00909981	−	0.00181730i
$498$	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	$0.395511\pi$
$500$	−1.13417	−	1.96443i	−0.0507214	−	0.0878521i
$501$	−0.826739	−	1.43195i	−0.0369360	−	0.0639750i
$502$	−2.12395	−	3.67878i	−0.0947963	−	0.164192i
$503$	−7.35181	+	12.7337i	−0.327801	+	0.567768i	−0.982075	−	0.188489i	$-0.939641\pi$
$503$	−7.35181	+	12.7337i	−0.327801	+	0.567768i	0.654274	+	0.756257i	$0.272974\pi$
$504$	−0.848534	−	2.50599i	−0.0377967	−	0.111626i
$505$	−1.88303	−	3.26150i	−0.0837937	−	0.145135i
$506$	−3.27348	−	5.66984i	−0.145524	−	0.252055i
$507$	7.69235	−	10.4799i	0.341629	−	0.465427i
$508$	−6.40560	+	11.0948i	−0.284202	+	0.492253i
$509$	7.23975	−	12.5396i	0.320896	−	0.555809i	−0.659777	−	0.751461i	$-0.729349\pi$
$509$	7.23975	−	12.5396i	0.320896	−	0.555809i	0.980673	+	0.195653i	$0.0626826\pi$
$510$	−0.616929	−	1.06855i	−0.0273181	−	0.0473163i
$511$	−32.7802	−	6.54645i	−1.45011	−	0.289598i
$512$	−1.00000			−0.0441942
$513$	−6.34214			−0.280012
$514$	7.35836	+	12.7450i	0.324563	+	0.562160i
$515$	0.725011	−	1.25576i	0.0319478	−	0.0553352i
$516$	10.3592			0.456039
$517$	−19.0077	−	32.9222i	−0.835956	−	1.44792i
$518$	7.30380	−	8.31556i	0.320911	−	0.365365i
$519$	−14.0420			−0.616375
$520$	−0.449444	+	0.688406i	−0.0197094	+	0.0301886i
$521$	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	$0.0646683\pi$
$522$	1.70291			0.0745342
$523$	0.511770	−	0.886412i	0.0223781	−	0.0387601i	−0.854619	−	0.519255i	$-0.826210\pi$
$523$	0.511770	−	0.886412i	0.0223781	−	0.0387601i	0.876998	+	0.480495i	$0.159543\pi$
$524$	−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
$527$	−19.2696			−0.839396
$528$	1.70561	−	2.95420i	0.0742271	−	0.128565i
$529$	9.65825	+	16.7286i	0.419924	+	0.727329i
$530$	−0.755653	+	1.30883i	−0.0328235	+	0.0568519i
$531$	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
$535$	−1.49289			−0.0645434
$536$	−11.1613			−0.482095
$537$	9.33325			0.402760
$538$	9.35772			0.403440
$539$	−18.9663	+	14.5073i	−0.816936	+	0.624875i
$540$	−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	$0.822323\pi$
$542$	−7.57375	−	13.1181i	−0.325320	−	0.563471i
$543$	−1.13838			−0.0488524
$544$	−2.70561	+	4.68625i	−0.116002	+	0.200921i
$545$	0.363504			0.0155708
$546$	2.55998	+	9.18948i	0.109557	+	0.393273i
$547$	26.9289			1.15140			0.575699	−	0.817661i	$-0.304730\pi$
$547$	26.9289			1.15140			0.575699	+	0.817661i	$0.304730\pi$
$548$	−8.84776	+	15.3248i	−0.377958	+	0.654642i
$549$	−6.71999			−0.286802
$550$	−8.43936	−	14.6174i	−0.359856	−	0.623288i
$551$	5.40004	+	9.35314i	0.230049	+	0.398457i
$552$	0.959623	−	1.66212i	0.0408443	−	0.0707444i
$553$	−2.83226	+	3.22459i	−0.120440	+	0.137124i
$554$	32.8782			1.39686
$555$	−0.953847			−0.0404886
$556$	−7.96642			−0.337851
$557$	−36.3681			−1.54097			−0.770484	−	0.637460i	$-0.779985\pi$
$557$	−36.3681			−1.54097			−0.770484	+	0.637460i	$0.779985\pi$
$558$	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
$562$	−8.40358	+	14.5554i	−0.354484	+	0.613984i
$563$	1.86510	+	3.23046i	0.0786048	+	0.136147i	0.902648	−	0.430379i	$-0.141620\pi$
$563$	1.86510	+	3.23046i	0.0786048	+	0.136147i	−0.824043	+	0.566527i	$0.808287\pi$
$564$	5.57211	−	9.65117i	0.234628	−	0.406388i
$565$	−1.88004			−0.0790938
$566$	−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
$569$	7.69596	−	13.3298i	0.322632	−	0.558814i	−0.658399	−	0.752669i	$-0.728766\pi$
$569$	7.69596	−	13.3298i	0.322632	−	0.558814i	0.981030	+	0.193855i	$0.0620992\pi$
$570$	−1.44613			−0.0605716
$571$	−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	$0.307037\pi$
$572$	−6.72379	+	10.2987i	−0.281136	+	0.430611i
$573$	−18.0851			−0.755514
$574$	2.70105	+	7.97706i	0.112740	+	0.332956i
$575$	−4.74822	−	8.22416i	−0.198015	−	0.342971i
$576$	1.00000			0.0416667
$577$	−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	$0.245710\pi$
$578$	6.14063	+	10.6359i	0.255417	+	0.442394i
$579$	5.82592			0.242117
$580$	0.388295			0.0161231
$581$	−1.44497	−	4.26747i	−0.0599476	−	0.177044i
$582$	6.82663	+	11.8241i	0.282973	+	0.490124i
$583$	−11.3048	+	19.5804i	−0.468195	+	0.810938i
$584$	6.31721	−	10.9417i	0.261408	−	0.452772i
$585$	0.449444	−	0.688406i	0.0185822	−	0.0284621i
$586$	−13.8954	−	24.0675i	−0.574014	−	0.994221i
$587$	−21.9241	−	37.9736i	−0.904903	−	1.56734i	−0.821047	−	0.570861i	$-0.806610\pi$
$587$	−21.9241	−	37.9736i	−0.904903	−	1.56734i	−0.0838564	−	0.996478i	$-0.526724\pi$
$588$	−6.46305	−	2.68867i	−0.266532	−	0.110879i
$589$	−11.2923	+	19.5589i	−0.465292	+	0.805910i
$590$	1.68397	+	2.91672i	0.0693279	+	0.120079i
$591$	10.3527	+	17.9315i	0.425855	+	0.737602i
$592$	2.09160	+	3.62276i	0.0859642	+	0.148894i
$593$	−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
$595$	−3.20127	−	0.639316i	−0.131239	−	0.0262094i
$596$	−1.34679	−	2.33271i	−0.0551667	−	0.0955515i
$597$	−8.19922	−	14.2015i	−0.335572	−	0.581227i
$598$	−3.78300	+	5.79435i	−0.154698	+	0.236949i
$599$	−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	$0.868579\pi$
$600$	2.47400	−	4.28510i	0.101001	−	0.174938i
$601$	−1.03443	−	1.79169i	−0.0421954	−	0.0730845i	0.844156	−	0.536097i	$-0.180102\pi$
$601$	−1.03443	−	1.79169i	−0.0421954	−	0.0730845i	−0.886352	+	0.463012i	$0.846769\pi$
$602$	18.0870	−	20.5926i	0.737173	−	0.839290i
$603$	11.1613			0.454523
$604$	−13.1286			−0.534197
$605$	0.0725551	+	0.125669i	0.00294978	+	0.00510918i
$606$	8.25823	−	14.3037i	0.335467	−	0.581047i
$607$	5.77956			0.234585			0.117292	−	0.993097i	$-0.462579\pi$
$607$	5.77956			0.234585			0.117292	+	0.993097i	$0.462579\pi$
$608$	3.17107	+	5.49246i	0.128604	+	0.222749i
$609$	2.97325	−	3.38512i	0.120482	−	0.137172i
$610$	−1.53228			−0.0620403
$611$	−21.9662	+	33.6453i	−0.888657	+	1.36114i
$612$	2.70561	−	4.68625i	0.109368	−	0.189430i
$613$	14.9090			0.602170			0.301085	−	0.953597i	$-0.402651\pi$
$613$	14.9090			0.602170			0.301085	+	0.953597i	$0.402651\pi$
$614$	−7.34243	+	12.7175i	−0.296317	+	0.513235i
$615$	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	−0.891004	−	0.453995i	$-0.849999\pi$
$617$	−1.29988	+	2.25147i	−0.0523314	+	0.0906406i	0.838673	+	0.544635i	$0.183332\pi$
$618$	6.35922			0.255805
$619$	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	$-0.275439\pi$
$620$	0.405992	+	0.703199i	0.0163050	+	0.0282412i
$621$	−0.959623	+	1.66212i	−0.0385083	+	0.0666984i
$622$	−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
$626$	−20.1964			−0.807210
$627$	−21.6344			−0.863995
$628$	3.18143			0.126953
$629$	22.6362			0.902564
$630$	0.193482	+	0.571413i	0.00770849	+	0.0227656i
$631$	14.0099	−	24.2659i	0.557726	−	0.966010i	−0.439960	−	0.898017i	$-0.645007\pi$
$631$	14.0099	−	24.2659i	0.557726	−	0.966010i	0.997686	−	0.0679924i	$-0.0216594\pi$
$632$	−0.811077	−	1.40483i	−0.0322629	−	0.0558810i
$633$	−3.74446	−	6.48560i	−0.148829	−	0.257779i
$634$	14.7218			0.584676
$635$	1.46060	−	2.52983i	0.0579620	−	0.100393i
$636$	−6.62799			−0.262817
$637$	22.7370	+	10.9558i	0.900871	+	0.434086i
$638$	5.80898			0.229980
$639$	−0.0390952	+	0.0677149i	−0.00154658	+	0.00267876i
$640$	0.228019			0.00901323
$641$	17.9656	+	31.1173i	0.709598	+	1.22906i	0.965006	+	0.262226i	$0.0844566\pi$
$641$	17.9656	+	31.1173i	0.709598	+	1.22906i	−0.255409	+	0.966833i	$0.582210\pi$
$642$	−3.27362	−	5.67008i	−0.129199	−	0.223780i
$643$	10.6007	−	18.3609i	0.418050	−	0.724084i	−0.577693	−	0.816254i	$-0.696047\pi$
$643$	10.6007	−	18.3609i	0.418050	−	0.724084i	0.995743	+	0.0921702i	$0.0293804\pi$
$644$	−1.62854	−	4.80961i	−0.0641737	−	0.189525i
$645$	−2.36210			−0.0930075
$646$	34.3187			1.35025
$647$	4.12288			0.162087			0.0810436	−	0.996711i	$-0.474175\pi$
$647$	4.12288			0.162087			0.0810436	+	0.996711i	$0.474175\pi$
$648$	−1.00000			−0.0392837
$649$	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
$653$	23.7186	−	41.0818i	0.928179	−	1.60765i	0.141812	−	0.989894i	$-0.454707\pi$
$653$	23.7186	−	41.0818i	0.928179	−	1.60765i	0.786367	−	0.617760i	$-0.211960\pi$
$654$	0.797093	+	1.38061i	0.0311688	+	0.0539860i
$655$	0.401230	−	0.694951i	0.0156773	−	0.0271540i
$656$	−3.18320			−0.124283
$657$	−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	−0.999869	−	0.0161688i	$-0.994853\pi$
$659$	−12.4744	+	21.6062i	−0.485932	+	0.841659i	0.513937	+	0.857828i	$0.328186\pi$
$660$	−0.388911	+	0.673613i	−0.0151383	+	0.0262203i
$661$	−8.61529			−0.335096			−0.167548	−	0.985864i	$-0.553585\pi$
$661$	−8.61529			−0.335096			−0.167548	+	0.985864i	$0.553585\pi$
$662$	2.05436	−	3.55826i	0.0798450	−	0.138296i
$663$	−10.6660	+	16.3369i	−0.414232	+	0.634472i
$664$	1.70291			0.0660856
$665$	−2.52492	+	2.87468i	−0.0979120	+	0.111475i
$666$	−2.09160	−	3.62276i	−0.0810478	−	0.140379i
$667$	3.26830			0.126549
$668$	0.826739	−	1.43195i	0.0319875	−	0.0554040i
$669$	8.41325	+	14.5722i	0.325275	+	0.563393i
$670$	2.54498			0.0983213
$671$	−22.9233			−0.884946
$672$	1.74599	−	1.98785i	0.0673528	−	0.0766829i
$673$	3.15527	+	5.46509i	0.121627	+	0.210664i	0.920409	−	0.390956i	$-0.127856\pi$
$673$	3.15527	+	5.46509i	0.121627	+	0.210664i	−0.798783	+	0.601620i	$0.794522\pi$
$674$	−3.72296	+	6.44835i	−0.143403	+	0.248381i
$675$	−2.47400	+	4.28510i	−0.0952244	+	0.164934i
$676$	12.9220	+	1.42184i	0.497000	+	0.0546861i
$677$	−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
$679$	35.4237	+	7.07436i	1.35944	+	0.271489i
$680$	0.616929	−	1.06855i	0.0236582	−	0.0409771i
$681$	−2.11607	−	3.66514i	−0.0810880	−	0.140449i
$682$	6.07375	+	10.5200i	0.232576	+	0.402833i
$683$	−9.95558	−	17.2436i	−0.380940	−	0.659807i	0.610257	−	0.792204i	$-0.291066\pi$
$683$	−9.95558	−	17.2436i	−0.380940	−	0.659807i	−0.991197	+	0.132396i	$0.957733\pi$
$684$	−3.17107	−	5.49246i	−0.121249	−	0.210009i
$685$	2.01746	−	3.49434i	0.0770830	−	0.133512i
$686$	−16.6291	+	8.15319i	−0.634900	+	0.311290i
$687$	6.86498	+	11.8905i	0.261915	+	0.453650i
$688$	5.17961	+	8.97135i	0.197471	+	0.342030i
$689$	23.8617	+	1.30883i	0.909058	+	0.0498624i
$690$	−0.218812	+	0.378993i	−0.00833003	+	0.0144280i
$691$	9.53454	−	16.5143i	0.362711	−	0.628234i	−0.625695	−	0.780068i	$-0.715185\pi$
$691$	9.53454	−	16.5143i	0.362711	−	0.628234i	0.988406	+	0.151834i	$0.0485179\pi$
$692$	−7.02100	−	12.1607i	−0.266898	−	0.462282i
$693$	2.89453	+	8.54848i	0.109954	+	0.324730i
$694$	10.5281			0.399642
$695$	1.81649			0.0689035
$696$	0.851453	+	1.47476i	0.0322743	+	0.0559007i
$697$	−8.61248	+	14.9173i	−0.326221	+	0.565032i
$698$	−9.48254			−0.358920
$699$	3.85349	+	6.67444i	0.145752	+	0.252450i
$700$	−4.19855	−	12.3997i	−0.158690	−	0.468663i
$701$	21.2816			0.803796			0.401898	−	0.915685i	$-0.368351\pi$
$701$	21.2816			0.803796			0.401898	+	0.915685i	$0.368351\pi$
$702$	3.60014	+	0.197470i	0.135879	+	0.00745302i
$703$	13.2652	−	22.9760i	0.500307	−	0.866557i
$704$	3.41122			0.128565
$705$	−1.27054	+	2.20065i	−0.0478515	+	0.0828812i
$706$	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
$709$	−26.8217			−1.00731			−0.503655	−	0.863905i	$-0.668012\pi$
$709$	−26.8217			−1.00731			−0.503655	+	0.863905i	$0.668012\pi$
$710$	−0.00891445	+	0.0154403i	−0.000334553	+	0.000579463i
$711$	0.811077	+	1.40483i	0.0304177	+	0.0526851i
$712$	8.77285	−	15.1950i	0.328776	−	0.569457i
$713$	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
$717$	25.2189			0.941818
$718$	−10.5916			−0.395274
$719$	−43.1706			−1.60999			−0.804997	−	0.593279i	$-0.797833\pi$
$719$	−43.1706			−1.60999			−0.804997	+	0.593279i	$0.797833\pi$
$720$	−0.228019			−0.00849776
$721$	11.1031	−	12.6412i	0.413501	−	0.470782i
$722$	10.6114	−	18.3795i	0.394915	−	0.684012i
$723$	13.9183	+	24.1073i	0.517629	+	0.896560i
$724$	−0.569188	−	0.985863i	−0.0211537	−	0.0366393i
$725$	8.42600			0.312934
$726$	−0.318198	+	0.551135i	−0.0118094	+	0.0204545i
$727$	−16.1609			−0.599373			−0.299687	−	0.954038i	$-0.596882\pi$
$727$	−16.1609			−0.599373			−0.299687	+	0.954038i	$0.596882\pi$
$728$	−6.67833	+	6.81175i	−0.247515	+	0.252460i
$729$	1.00000			0.0370370
$730$	−1.44044	+	2.49492i	−0.0533131	+	0.0923411i
$731$	56.0560			2.07331
$732$	−3.35999	−	5.81968i	−0.124189	−	0.215102i
$733$	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
$735$	1.47370	+	0.613066i	0.0543581	+	0.0226133i
$736$	1.91925			0.0707444
$737$	38.0736			1.40246
$738$	3.18320			0.117175
$739$	0.383605			0.0141111			0.00705557	−	0.999975i	$-0.497754\pi$
$739$	0.383605			0.0141111			0.00705557	+	0.999975i	$0.497754\pi$
$740$	−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	0.991653	−	0.128939i	$-0.0411572\pi$
$743$	10.4715	+	18.1372i	0.384162	+	0.665388i	−0.607491	+	0.794327i	$0.707824\pi$
$744$	−1.78052	+	3.08395i	−0.0652771	+	0.113063i
$745$	0.307093	+	0.531901i	0.0112510	+	0.0194874i
$746$	−14.2762	+	24.7271i	−0.522688	+	0.905322i
$747$	−1.70291			−0.0623061
$748$	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
$751$	−7.90695	+	13.6952i	−0.288529	+	0.499746i	−0.973459	−	0.228862i	$-0.926499\pi$
$751$	−7.90695	+	13.6952i	−0.288529	+	0.499746i	0.684930	+	0.728609i	$0.259833\pi$
$752$	11.1442			0.406388
$753$	−2.12395	+	3.67878i	−0.0774009	+	0.134062i
$754$	−2.77413	−	5.47748i	−0.101028	−	0.199478i
$755$	2.99358			0.108947
$756$	−1.74599	+	1.98785i	−0.0635009	+	0.0722973i
$757$	−4.41633	−	7.64930i	−0.160514	−	0.278019i	0.774539	−	0.632526i	$-0.217982\pi$
$757$	−4.41633	−	7.64930i	−0.160514	−	0.278019i	−0.935053	+	0.354507i	$0.884649\pi$
$758$	31.1275			1.13060
$759$	−3.27348	+	5.66984i	−0.118820	+	0.205802i
$760$	−0.723063	−	1.25238i	−0.0262283	−	0.0454287i
$761$	38.7406			1.40434			0.702172	−	0.712007i	$-0.252214\pi$
$761$	38.7406			1.40434			0.702172	+	0.712007i	$0.252214\pi$
$762$	12.8112			0.464100
$763$	4.13615	+	0.826018i	0.149739	+	0.0299038i
$764$	−9.04253	−	15.6621i	−0.327147	−	0.566635i
$765$	−0.616929	+	1.06855i	−0.0223051	+	0.0386336i
$766$	10.9760	−	19.0111i	0.396580	−	0.686897i
$767$	29.1138	−	44.5931i	1.05124	−	1.61016i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−9.17950	−	15.8994i	−0.331021	−	0.573345i	0.651691	−	0.758484i	$-0.274060\pi$
$769$	−9.17950	−	15.8994i	−0.331021	−	0.573345i	−0.982712	+	0.185139i	$0.940726\pi$
$770$	0.660007	+	1.94921i	0.0237850	+	0.0702447i
$771$	7.35836	−	12.7450i	0.265005	−	0.459002i
$772$	2.91296	+	5.04539i	0.104840	+	0.181588i
$773$	−6.42407	−	11.1268i	−0.231058	−	0.400204i	0.727062	−	0.686572i	$-0.240885\pi$
$773$	−6.42407	−	11.1268i	−0.231058	−	0.400204i	−0.958120	+	0.286368i	$0.907552\pi$
$774$	−5.17961	−	8.97135i	−0.186177	−	0.322469i
$775$	8.81004	+	15.2594i	0.316466	+	0.548135i
$776$	−6.82663	+	11.8241i	−0.245062	+	0.424460i
$777$	−10.8534	−	2.16750i	−0.389363	−	0.0777586i
$778$	−1.87365	−	3.24525i	−0.0671734	−	0.116348i
$779$	10.0941	+	17.4836i	0.361660	+	0.626414i
$780$	0.820899	+	0.0450268i	0.0293929	+	0.00161222i
$781$	−0.133362	+	0.230990i	−0.00477208	+	0.00826548i
$782$	5.19273	−	8.99407i	0.185692	−	0.321627i
$783$	−0.851453	−	1.47476i	−0.0304285	−	0.0527036i
$784$	−0.903072	−	6.94150i	−0.0322526	−	0.247911i
$785$	−0.725425			−0.0258915
$786$	3.51927			0.125528
$787$	1.69729	+	2.93979i	0.0605017	+	0.104792i	0.894690	−	0.446688i	$-0.147397\pi$
$787$	1.69729	+	2.93979i	0.0605017	+	0.104792i	−0.834188	+	0.551480i	$0.814063\pi$
$788$	−10.3527	+	17.9315i	−0.368801	+	0.638782i
$789$	−23.4105			−0.833437
$790$	0.184941	+	0.320327i	0.00657989	+	0.0113967i
$791$	−21.3921	−	4.27215i	−0.760614	−	0.151900i
$792$	−3.41122			−0.121212
$793$	10.9472	+	21.6152i	0.388748	+	0.767577i
$794$	−1.95502	+	3.38620i	−0.0693812	+	0.120172i
$795$	1.51131			0.0536005
$796$	8.19922	−	14.2015i	0.290614	−	0.503357i
$797$	1.71983	−	2.97884i	0.0609197	−	0.105516i	−0.833957	−	0.551829i	$-0.813930\pi$
$797$	1.71983	−	2.97884i	0.0609197	−	0.105516i	0.894877	+	0.446313i	$0.147263\pi$
$798$	−16.4548	−	3.28614i	−0.582494	−	0.116328i
$799$	30.1519	−	52.2246i	1.06670	−	1.84757i
$800$	4.94801			0.174938
$801$	−8.77285	+	15.1950i	−0.309973	+	0.536890i
$802$	−13.1130	−	22.7124i	−0.463037	−	0.802003i
$803$	−21.5494	+	37.3246i	−0.760461	+	1.31716i
$804$	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
$808$	16.5165			0.581047
$809$	−27.9826			−0.983815			−0.491908	−	0.870647i	$-0.663700\pi$
$809$	−27.9826			−0.983815			−0.491908	+	0.870647i	$0.663700\pi$
$810$	0.228019			0.00801176
$811$	26.2105			0.920377			0.460188	−	0.887821i	$-0.347782\pi$
$811$	26.2105			0.920377			0.460188	+	0.887821i	$0.347782\pi$
$812$	4.41822	+	0.882351i	0.155049	+	0.0309644i
$813$	−7.57375	+	13.1181i	−0.265623	+	0.460072i
$814$	−7.13490	−	12.3580i	−0.250078	−	0.433148i
$815$	−1.85767	−	3.21758i	−0.0650715	−	0.112707i
$816$	5.41122			0.189430
$817$	32.8498	−	56.8976i	1.14927	−	1.99059i
$818$	−4.03519			−0.141087
$819$	6.67833	−	6.81175i	0.233360	−	0.238022i
$820$	0.725829			0.0253470
$821$	7.77317	−	13.4635i	0.271285	−	0.469880i	−0.697906	−	0.716190i	$-0.745885\pi$
$821$	7.77317	−	13.4635i	0.271285	−	0.469880i	0.969191	+	0.246309i	$0.0792179\pi$
$822$	17.6955			0.617202
$823$	23.9106	+	41.4144i	0.833471	+	1.44361i	0.895269	+	0.445526i	$0.146983\pi$
$823$	23.9106	+	41.4144i	0.833471	+	1.44361i	−0.0617981	+	0.998089i	$0.519683\pi$
$824$	3.17961	+	5.50725i	0.110767	+	0.191854i
$825$	−8.43936	+	14.6174i	−0.293821	+	0.508913i
$826$	12.5332	+	37.0146i	0.436086	+	1.28790i
$827$	28.2671			0.982944			0.491472	−	0.870893i	$-0.336459\pi$
$827$	28.2671			0.982944			0.491472	+	0.870893i	$0.336459\pi$
$828$	−1.91925			−0.0666984
$829$	39.6825			1.37823			0.689116	−	0.724651i	$-0.257999\pi$
$829$	39.6825			1.37823			0.689116	+	0.724651i	$0.257999\pi$
$830$	−0.388295			−0.0134779
$831$	−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
$835$	−0.188512	+	0.326512i	−0.00652372	+	0.0112994i
$836$	−10.8172	−	18.7360i	−0.374121	−	0.647997i
$837$	1.78052	−	3.08395i	0.0615439	−	0.106597i
$838$	3.48277			0.120310
$839$	2.60142	−	4.50579i	0.0898110	−	0.155557i	−0.817620	−	0.575758i	$-0.804707\pi$
$839$	2.60142	−	4.50579i	0.0898110	−	0.155557i	0.907431	+	0.420201i	$0.138040\pi$
$840$	−0.398117	+	0.453266i	−0.0137363	+	0.0156392i
$841$	13.0501	−	22.6034i	0.450002	−	0.779426i
$842$	9.30142	−	16.1105i	0.320548	−	0.555205i
$843$	16.8072			0.578870
$844$	3.74446	−	6.48560i	0.128890	−	0.223243i
$845$	−2.94646	−	0.324206i	−0.101361	−	0.0111530i
$846$	−11.1442			−0.383146
$847$	0.540003	+	1.59480i	0.0185547	+	0.0547981i
$848$	−3.31400	−	5.74001i	−0.113803	−	0.197113i
$849$	12.1600			0.417329
$850$	13.3874	−	23.1876i	0.459183	−	0.795328i
$851$	−4.01429	−	6.95296i	−0.137608	−	0.238344i
$852$	−0.0781905			−0.00267876
$853$	21.5926			0.739318			0.369659	−	0.929167i	$-0.379474\pi$
$853$	21.5926			0.739318			0.369659	+	0.929167i	$0.379474\pi$
$854$	−17.4351	−	3.48192i	−0.596618	−	0.119149i
$855$	0.723063	+	1.25238i	0.0247282	+	0.0428306i
$856$	3.27362	−	5.67008i	0.111890	−	0.193799i
$857$	−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	$0.235900\pi$
$858$	12.2809	+	0.673613i	0.419261	+	0.0229968i
$859$	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
$861$	5.55782	−	6.32771i	0.189410	−	0.215648i
$862$	−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	$0.902004\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	1.60092	+	2.77287i	0.0544329	+	0.0942805i
$866$	16.7336	+	28.9834i	0.568630	+	0.984896i
$867$	6.14063	−	10.6359i	0.208547	−	0.361214i
$868$	3.02167	+	8.92395i	0.102562	+	0.302898i
$869$	2.76676	+	4.79216i	0.0938558	+	0.162563i
$870$	−0.194147	−	0.336273i	−0.00658221	−	0.0114007i
$871$	−18.1824	−	35.9008i	−0.616086	−	1.21645i
$872$	−0.797093	+	1.38061i	−0.0269930	+	0.0467532i
$873$	6.82663	−	11.8241i	0.231047	−	0.400184i
$874$	−6.08607	−	10.5414i	−0.205864	−	0.356567i
$875$	1.92476	+	5.68442i	0.0650686	+	0.192168i
$876$	−12.6344			−0.426877
$877$	6.49901			0.219456			0.109728	−	0.993962i	$-0.465002\pi$
$877$	6.49901			0.219456			0.109728	+	0.993962i	$0.465002\pi$
$878$	19.0229	+	32.9487i	0.641993	+	1.11196i
$879$	−13.8954	+	24.0675i	−0.468680	+	0.811778i
$880$	−0.777821			−0.0262203
$881$	6.17234	+	10.6908i	0.207951	+	0.360182i	0.951069	−	0.308979i	$-0.0999871\pi$
$881$	6.17234	+	10.6908i	0.207951	+	0.360182i	−0.743118	+	0.669161i	$0.766654\pi$
$882$	0.903072	+	6.94150i	0.0304080	+	0.233733i
$883$	42.2001			1.42015			0.710073	−	0.704128i	$-0.248662\pi$
$883$	42.2001			1.42015			0.710073	+	0.704128i	$0.248662\pi$
$884$	−19.4811	−	1.06855i	−0.655221	−	0.0359393i
$885$	1.68397	−	2.91672i	0.0566060	−	0.0980444i
$886$	8.70933			0.292596
$887$	17.1690	−	29.7376i	0.576478	−	0.998490i	−0.419401	−	0.907801i	$-0.637760\pi$
$887$	17.1690	−	29.7376i	0.576478	−	0.998490i	0.995879	−	0.0906888i	$-0.0289068\pi$
$888$	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
$891$	3.41122			0.114280
$892$	−8.41325	+	14.5722i	−0.281696	+	0.487913i
$893$	−35.3391	−	61.2091i	−1.18258	−	2.04828i
$894$	−1.34679	+	2.33271i	−0.0450434	+	0.0780175i
$895$	−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
$899$	−6.06413			−0.202250
$900$	−4.94801			−0.164934
$901$	−35.8655			−1.19485
$902$	10.8586			0.361551
$903$	−26.8772	−	5.36757i	−0.894417	−	0.178621i
$904$	4.12255	−	7.14047i	0.137114	−	0.237488i
$905$	0.129786	+	0.224795i	0.00431422	+	0.00747244i
$906$	6.56432	+	11.3697i	0.218085	+	0.377734i
$907$	−18.7208			−0.621614			−0.310807	−	0.950473i	$-0.600599\pi$
$907$	−18.7208			−0.621614			−0.310807	+	0.950473i	$0.600599\pi$
$908$	2.11607	−	3.66514i	0.0702243	−	0.121632i
$909$	−16.5165			−0.547816
$910$	1.52278	−	1.55321i	0.0504798	−	0.0514883i
$911$	−30.3513			−1.00558			−0.502791	−	0.864408i	$-0.667694\pi$
$911$	−30.3513			−1.00558			−0.502791	+	0.864408i	$0.667694\pi$
$912$	3.17107	−	5.49246i	0.105005	−	0.181873i
$913$	−5.80898			−0.192249
$914$	5.79493	+	10.0371i	0.191679	+	0.331998i
$915$	0.766142	+	1.32700i	0.0253279	+	0.0438691i
$916$	−6.86498	+	11.8905i	−0.226825	+	0.392873i
$917$	6.14460	−	6.99577i	0.202912	−	0.231021i
$918$	−5.41122			−0.178597
$919$	40.7516			1.34427			0.672135	−	0.740428i	$-0.265377\pi$
$919$	40.7516			1.34427			0.672135	+	0.740428i	$0.265377\pi$
$920$	−0.437624			−0.0144280
$921$	14.6849			0.483883
$922$	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
$926$	−19.7667	+	34.2369i	−0.649573	+	1.12509i
$927$	−3.17961	−	5.50725i	−0.104432	−	0.180882i
$928$	−0.851453	+	1.47476i	−0.0279503	+	0.0484114i
$929$	5.21956			0.171248			0.0856242	−	0.996328i	$-0.472712\pi$
$929$	5.21956			0.171248			0.0856242	+	0.996328i	$0.472712\pi$
$930$	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
$933$	−3.86348	+	6.69174i	−0.126484	+	0.219078i
$934$	−0.850382			−0.0278253
$935$	−2.10448	+	3.64506i	−0.0688238	+	0.119206i
$936$	1.62906	+	3.21655i	0.0532474	+	0.105136i
$937$	−31.2199			−1.01991			−0.509956	−	0.860201i	$-0.670338\pi$
$937$	−31.2199			−1.01991			−0.509956	+	0.860201i	$0.670338\pi$
$938$	28.9582	+	5.78316i	0.945519	+	0.188827i
$939$	10.0982	+	17.4906i	0.329542	+	0.570784i
$940$	−2.54109			−0.0828812
$941$	−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	$0.857096\pi$
$942$	−1.59071	−	2.75520i	−0.0518283	−	0.0897692i
$943$	6.10934			0.198947
$944$	−14.7704			−0.480737
$945$	0.398117	−	0.453266i	0.0129508	−	0.0147448i
$946$	−17.6688	−	30.6032i	−0.574461	−	0.994996i
$947$	−24.1704	+	41.8643i	−0.785431	+	1.36041i	0.143310	+	0.989678i	$0.454225\pi$
$947$	−24.1704	+	41.8643i	−0.785431	+	1.36041i	−0.928741	+	0.370729i	$0.879108\pi$
$948$	−0.811077	+	1.40483i	−0.0263425	+	0.0456266i
$949$	45.4857	+	2.49492i	1.47653	+	0.0809885i
$950$	−15.6905	−	27.1767i	−0.509066	−	0.881729i
$951$	−7.36088	−	12.7494i	−0.238693	−	0.413428i
$952$	9.44790	−	10.7567i	0.306208	−	0.348626i
$953$	0.444682	−	0.770211i	0.0144046	−	0.0249496i	−0.858733	−	0.512423i	$-0.828748\pi$
$953$	0.444682	−	0.770211i	0.0144046	−	0.0249496i	0.873138	+	0.487473i	$0.162081\pi$
$954$	3.31400	+	5.74001i	0.107295	+	0.185840i
$955$	2.06187	+	3.57125i	0.0667204	+	0.115563i
$956$	12.6095	+	21.8402i	0.407819	+	0.706363i
$957$	−2.90449	−	5.03073i	−0.0938889	−	0.162620i
$958$	5.78732	−	10.0239i	0.186980	−	0.323859i
$959$	30.8961	−	35.1760i	0.997688	−	1.13589i
$960$	−0.114009	−	0.197470i	−0.00367964	−	0.00637332i
$961$	9.15948	+	15.8647i	0.295467	+	0.511764i
$962$	−8.24543	+	12.6294i	−0.265843	+	0.407188i
$963$	−3.27362	+	5.67008i	−0.105491	+	0.182716i
$964$	−13.9183	+	24.1073i	−0.448280	+	0.776443i
$965$	−0.664209	−	1.15044i	−0.0213817	−	0.0370341i
$966$	−3.35098	+	3.81517i	−0.107816	+	0.122751i
$967$	4.75544			0.152925			0.0764623	−	0.997072i	$-0.475638\pi$
$967$	4.75544			0.152925			0.0764623	+	0.997072i	$0.475638\pi$
$968$	−0.636396			−0.0204545
$969$	−17.1594	−	29.7209i	−0.551238	−	0.954772i
$970$	1.55660	−	2.69611i	0.0499794	−	0.0865669i
$971$	1.55188			0.0498022			0.0249011	−	0.999690i	$-0.492073\pi$
$971$	1.55188			0.0498022			0.0249011	+	0.999690i	$0.492073\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	20.6690	+	4.12775i	0.662619	+	0.132330i
$974$	13.9320			0.446412
$975$	17.8135	+	0.977083i	0.570489	+	0.0312917i
$976$	3.35999	−	5.81968i	0.107551	−	0.186283i
$977$	−31.5419			−1.00911			−0.504557	−	0.863378i	$-0.668344\pi$
$977$	−31.5419			−1.00911			−0.504557	+	0.863378i	$0.668344\pi$
$978$	8.14702	−	14.1111i	0.260513	−	0.451222i
$979$	−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
$982$	9.53433			0.304253
$983$	−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	$0.999548\pi$
$984$	1.59160	+	2.75673i	0.0507383	+	0.0878813i
$985$	2.36062	−	4.08871i	0.0752156	−	0.130277i
$986$	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
$990$	0.777821			0.0247208
$991$	0.605608			0.0192378			0.00961888	−	0.999954i	$-0.496938\pi$
$991$	0.605608			0.0192378			0.00961888	+	0.999954i	$0.496938\pi$
$992$	−3.56104			−0.113063
$993$	−4.10872			−0.130386
$994$	−0.136519	+	0.155431i	−0.00433013	+	0.00492996i
$995$	−1.86957	+	3.23820i	−0.0592695	+	0.102658i
$996$	−0.851453	−	1.47476i	−0.0269793	−	0.0467296i
$997$	−0.184170	−	0.318992i	−0.00583272	−	0.0101026i	0.863094	−	0.505043i	$-0.168523\pi$
$997$	−0.184170	−	0.318992i	−0.00583272	−	0.0101026i	−0.868927	+	0.494940i	$0.835190\pi$
$998$	43.8270			1.38732
$999$	−2.09160	+	3.62276i	−0.0661753	+	0.114619i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.3	✓	10	7.2	even	3
546.2.j.e.529.3	yes	10	13.9	even	3
546.2.k.e.373.3	yes	10	91.9	even	3	inner
546.2.k.e.445.3	yes	10	1.1	even	1	trivial
1638.2.m.k.289.3		10	21.2	odd	6
1638.2.m.k.1621.3		10	39.35	odd	6
1638.2.p.j.919.3		10	273.191	odd	6
1638.2.p.j.991.3		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.848534 + 2.50599i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.114009 + 0.197470i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.848534 + 2.50599i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.228019 q^{10} +3.41122 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} +(-0.500000 + 0.866025i) q^{16} +(2.70561 + 4.68625i) q^{17} +(0.500000 - 0.866025i) q^{18} +6.34214 q^{19} +(0.114009 - 0.197470i) q^{20} +(-0.848534 - 2.50599i) q^{21} +(1.70561 - 2.95420i) q^{22} +(0.959623 - 1.66212i) q^{23} +1.00000 q^{24} +(2.47400 - 4.28510i) q^{25} +(-3.60014 - 0.197470i) q^{26} -1.00000 q^{27} +(1.74599 - 1.98785i) q^{28} +(0.851453 + 1.47476i) q^{29} -0.228019 q^{30} +(-1.78052 + 3.08395i) q^{31} +(0.500000 + 0.866025i) q^{32} -3.41122 q^{33} +5.41122 q^{34} +(-0.398117 + 0.453266i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.09160 - 3.62276i) q^{37} +(3.17107 - 5.49246i) q^{38} +(1.62906 + 3.21655i) q^{39} +(-0.114009 - 0.197470i) q^{40} +(1.59160 + 2.75673i) q^{41} +(-2.59452 - 0.518144i) q^{42} +(5.17961 - 8.97135i) q^{43} +(-1.70561 - 2.95420i) q^{44} +(0.114009 + 0.197470i) q^{45} +(-0.959623 - 1.66212i) q^{46} +(-5.57211 - 9.65117i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-5.55998 + 4.25284i) q^{49} +(-2.47400 - 4.28510i) q^{50} +(-2.70561 - 4.68625i) q^{51} +(-1.97108 + 3.01908i) q^{52} +(-3.31400 + 5.74001i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.388911 + 0.673613i) q^{55} +(-0.848534 - 2.50599i) q^{56} -6.34214 q^{57} +1.70291 q^{58} +(7.38522 + 12.7916i) q^{59} +(-0.114009 + 0.197470i) q^{60} -6.71999 q^{61} +(1.78052 + 3.08395i) q^{62} +(0.848534 + 2.50599i) q^{63} +1.00000 q^{64} +(0.449444 - 0.688406i) q^{65} +(-1.70561 + 2.95420i) q^{66} +11.1613 q^{67} +(2.70561 - 4.68625i) q^{68} +(-0.959623 + 1.66212i) q^{69} +(0.193482 + 0.571413i) q^{70} +(-0.0390952 + 0.0677149i) q^{71} -1.00000 q^{72} +(-6.31721 + 10.9417i) q^{73} +(-2.09160 - 3.62276i) q^{74} +(-2.47400 + 4.28510i) 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} -0.228019 q^{80} +1.00000 q^{81} +3.18320 q^{82} -1.70291 q^{83} +(-1.74599 + 1.98785i) q^{84} +(-0.616929 + 1.06855i) q^{85} +(-5.17961 - 8.97135i) q^{86} +(-0.851453 - 1.47476i) q^{87} -3.41122 q^{88} +(-8.77285 + 15.1950i) q^{89} +0.228019 q^{90} +(6.67833 - 6.81175i) q^{91} -1.91925 q^{92} +(1.78052 - 3.08395i) q^{93} -11.1442 q^{94} +(0.723063 + 1.25238i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(6.82663 - 11.8241i) q^{97} +(0.903072 + 6.94150i) q^{98} +3.41122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

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