LMFDB - Embedded newform 546.2.j.e.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
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			289.1
Root			$2.07085 - 3.58682i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.e.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-2.07085 + 3.58682i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.321703 - 2.62612i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-2.07085 + 3.58682i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.321703 - 2.62612i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.07085 - 3.58682i) q^{10} +(-0.261547 + 0.453013i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.28981 + 1.47551i) q^{13} +(-0.321703 + 2.62612i) q^{14} +(2.07085 + 3.58682i) q^{15} +1.00000 q^{16} -2.52309 q^{17} +(0.500000 + 0.866025i) q^{18} +(2.84997 + 4.93629i) q^{19} +(-2.07085 + 3.58682i) q^{20} +(-2.11344 - 1.59166i) q^{21} +(0.261547 - 0.453013i) q^{22} -7.39337 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-6.07684 - 10.5254i) q^{25} +(3.28981 - 1.47551i) q^{26} -1.00000 q^{27} +(0.321703 - 2.62612i) q^{28} +(-1.54066 - 2.66851i) q^{29} +(-2.07085 - 3.58682i) q^{30} +(-2.17638 - 3.76959i) q^{31} -1.00000 q^{32} +(0.261547 + 0.453013i) q^{33} +2.52309 q^{34} +(8.75321 + 6.59219i) q^{35} +(-0.500000 - 0.866025i) q^{36} -5.66479 q^{37} +(-2.84997 - 4.93629i) q^{38} +(-0.367074 + 3.58682i) q^{39} +(2.07085 - 3.58682i) q^{40} +(2.33240 + 4.03983i) q^{41} +(2.11344 + 1.59166i) q^{42} +(-4.81529 + 8.34033i) q^{43} +(-0.261547 + 0.453013i) q^{44} +4.14170 q^{45} +7.39337 q^{46} +(-5.58154 + 9.66752i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-6.79301 - 1.68966i) q^{49} +(6.07684 + 10.5254i) q^{50} +(-1.26155 + 2.18506i) q^{51} +(-3.28981 + 1.47551i) q^{52} +(-0.00192073 - 0.00332680i) q^{53} +1.00000 q^{54} +(-1.08325 - 1.87624i) q^{55} +(-0.321703 + 2.62612i) q^{56} +5.69993 q^{57} +(1.54066 + 2.66851i) q^{58} +8.10749 q^{59} +(2.07085 + 3.58682i) q^{60} +(-3.00599 - 5.20652i) q^{61} +(2.17638 + 3.76959i) q^{62} +(-2.43514 + 1.03446i) q^{63} +1.00000 q^{64} +(1.52031 - 14.8555i) q^{65} +(-0.261547 - 0.453013i) q^{66} +(-1.61622 + 2.79938i) q^{67} -2.52309 q^{68} +(-3.69669 + 6.40285i) q^{69} +(-8.75321 - 6.59219i) q^{70} +(3.98568 - 6.90340i) q^{71} +(0.500000 + 0.866025i) q^{72} +(5.99080 + 10.3764i) q^{73} +5.66479 q^{74} -12.1537 q^{75} +(2.84997 + 4.93629i) q^{76} +(1.10553 + 0.832590i) q^{77} +(0.367074 - 3.58682i) q^{78} +(1.15602 - 2.00229i) q^{79} +(-2.07085 + 3.58682i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.33240 - 4.03983i) q^{82} +3.08133 q^{83} +(-2.11344 - 1.59166i) q^{84} +(5.22495 - 9.04988i) q^{85} +(4.81529 - 8.34033i) q^{86} -3.08133 q^{87} +(0.261547 - 0.453013i) q^{88} -10.8520 q^{89} -4.14170 q^{90} +(2.81653 + 9.11412i) q^{91} -7.39337 q^{92} -4.35275 q^{93} +(5.58154 - 9.66752i) q^{94} -23.6074 q^{95} +(-0.500000 + 0.866025i) q^{96} +(-1.31892 + 2.28443i) q^{97} +(6.79301 + 1.68966i) q^{98} +0.523095 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	−2.07085	+	3.58682i	−0.926112	+	1.60407i	−0.136350	+	0.990661i	$0.543537\pi$
$5$	−2.07085	+	3.58682i	−0.926112	+	1.60407i	−0.789763	+	0.613413i	$0.789796\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.321703	−	2.62612i	0.121592	−	0.992580i
$7$	0.321703	−	2.62612i	0.121592	−	0.992580i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.07085	−	3.58682i	0.654860	−	1.13425i
$11$	−0.261547	+	0.453013i	−0.0788595	+	0.136589i	−0.902758	−	0.430149i	$-0.858461\pi$
$11$	−0.261547	+	0.453013i	−0.0788595	+	0.136589i	0.823899	+	0.566737i	$0.191795\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.28981	+	1.47551i	−0.912430	+	0.409234i
$13$	−3.28981	+	1.47551i	−0.912430	+	0.409234i
$14$	−0.321703	+	2.62612i	−0.0859787	+	0.701860i
$15$	2.07085	+	3.58682i	0.534691	+	0.926112i
$16$	1.00000			0.250000
$17$	−2.52309			−0.611940			−0.305970	−	0.952041i	$-0.598981\pi$
$17$	−2.52309			−0.611940			−0.305970	+	0.952041i	$0.598981\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.84997	+	4.93629i	0.653827	+	1.13246i	0.982186	+	0.187909i	$0.0601711\pi$
$19$	2.84997	+	4.93629i	0.653827	+	1.13246i	−0.328359	+	0.944553i	$0.606496\pi$
$20$	−2.07085	+	3.58682i	−0.463056	+	0.802037i
$21$	−2.11344	−	1.59166i	−0.461189	−	0.347329i
$22$	0.261547	−	0.453013i	0.0557621	−	0.0965827i
$23$	−7.39337			−1.54162			−0.770812	−	0.637062i	$-0.780149\pi$
$23$	−7.39337			−1.54162			−0.770812	+	0.637062i	$0.780149\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−6.07684	−	10.5254i	−1.21537	−	2.10508i
$26$	3.28981	−	1.47551i	0.645185	−	0.289372i
$27$	−1.00000			−0.192450
$28$	0.321703	−	2.62612i	0.0607961	−	0.496290i
$29$	−1.54066	−	2.66851i	−0.286094	−	0.495530i	0.686780	−	0.726866i	$-0.259024\pi$
$29$	−1.54066	−	2.66851i	−0.286094	−	0.495530i	−0.972874	+	0.231336i	$0.925690\pi$
$30$	−2.07085	−	3.58682i	−0.378084	−	0.654860i
$31$	−2.17638	−	3.76959i	−0.390889	−	0.677039i	0.601678	−	0.798739i	$-0.294499\pi$
$31$	−2.17638	−	3.76959i	−0.390889	−	0.677039i	−0.992567	+	0.121699i	$0.961166\pi$
$32$	−1.00000			−0.176777
$33$	0.261547	+	0.453013i	0.0455295	+	0.0788595i
$34$	2.52309			0.432707
$35$	8.75321	+	6.59219i	1.47956	+	1.11428i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.66479			−0.931286			−0.465643	−	0.884973i	$-0.654177\pi$
$37$	−5.66479			−0.931286			−0.465643	+	0.884973i	$0.654177\pi$
$38$	−2.84997	−	4.93629i	−0.462326	−	0.800772i
$39$	−0.367074	+	3.58682i	−0.0587788	+	0.574350i
$40$	2.07085	−	3.58682i	0.327430	−	0.567126i
$41$	2.33240	+	4.03983i	0.364259	+	0.630915i	0.988657	−	0.150191i	$-0.0479889\pi$
$41$	2.33240	+	4.03983i	0.364259	+	0.630915i	−0.624398	+	0.781107i	$0.714656\pi$
$42$	2.11344	+	1.59166i	0.326110	+	0.245599i
$43$	−4.81529	+	8.34033i	−0.734325	+	1.27189i	0.220694	+	0.975343i	$0.429168\pi$
$43$	−4.81529	+	8.34033i	−0.734325	+	1.27189i	−0.955019	+	0.296545i	$0.904166\pi$
$44$	−0.261547	+	0.453013i	−0.0394297	+	0.0682943i
$45$	4.14170			0.617408
$46$	7.39337			1.09009
$47$	−5.58154	+	9.66752i	−0.814152	+	1.41015i	0.0957835	+	0.995402i	$0.469464\pi$
$47$	−5.58154	+	9.66752i	−0.814152	+	1.41015i	−0.909935	+	0.414750i	$0.863869\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−6.79301	−	1.68966i	−0.970431	−	0.241380i
$50$	6.07684	+	10.5254i	0.859395	+	1.48852i
$51$	−1.26155	+	2.18506i	−0.176652	+	0.305970i
$52$	−3.28981	+	1.47551i	−0.456215	+	0.204617i
$53$	−0.00192073	−	0.00332680i	−0.000263832	−	0.000456971i	0.865893	−	0.500228i	$-0.166751\pi$
$53$	−0.00192073	−	0.00332680i	−0.000263832	−	0.000456971i	−0.866157	+	0.499771i	$0.833417\pi$
$54$	1.00000			0.136083
$55$	−1.08325	−	1.87624i	−0.146065	−	0.252993i
$56$	−0.321703	+	2.62612i	−0.0429894	+	0.350930i
$57$	5.69993			0.754975
$58$	1.54066	+	2.66851i	0.202299	+	0.350392i
$59$	8.10749			1.05550			0.527752	−	0.849398i	$-0.323035\pi$
$59$	8.10749			1.05550			0.527752	+	0.849398i	$0.323035\pi$
$60$	2.07085	+	3.58682i	0.267346	+	0.463056i
$61$	−3.00599	−	5.20652i	−0.384877	−	0.666627i	0.606875	−	0.794797i	$-0.292423\pi$
$61$	−3.00599	−	5.20652i	−0.384877	−	0.666627i	−0.991752	+	0.128170i	$0.959090\pi$
$62$	2.17638	+	3.76959i	0.276400	+	0.478739i
$63$	−2.43514	+	1.03446i	−0.306799	+	0.130329i
$64$	1.00000			0.125000
$65$	1.52031	−	14.8555i	0.188571	−	1.84260i
$66$	−0.261547	−	0.453013i	−0.0321942	−	0.0557621i
$67$	−1.61622	+	2.79938i	−0.197453	+	0.341998i	−0.947702	−	0.319157i	$-0.896600\pi$
$67$	−1.61622	+	2.79938i	−0.197453	+	0.341998i	0.750249	+	0.661155i	$0.229934\pi$
$68$	−2.52309			−0.305970
$69$	−3.69669	+	6.40285i	−0.445029	+	0.770812i
$70$	−8.75321	−	6.59219i	−1.04621	−	0.787917i
$71$	3.98568	−	6.90340i	0.473013	−	0.819283i	−0.526510	−	0.850169i	$-0.676500\pi$
$71$	3.98568	−	6.90340i	0.473013	−	0.819283i	0.999523	+	0.0308864i	$0.00983301\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	5.99080	+	10.3764i	0.701170	+	1.21446i	0.968056	+	0.250734i	$0.0806721\pi$
$73$	5.99080	+	10.3764i	0.701170	+	1.21446i	−0.266886	+	0.963728i	$0.585995\pi$
$74$	5.66479			0.658519
$75$	−12.1537			−1.40339
$76$	2.84997	+	4.93629i	0.326914	+	0.566231i
$77$	1.10553	+	0.832590i	0.125986	+	0.0948825i
$78$	0.367074	−	3.58682i	0.0415629	−	0.406127i
$79$	1.15602	−	2.00229i	0.130063	−	0.225275i	−0.793638	−	0.608390i	$-0.791816\pi$
$79$	1.15602	−	2.00229i	0.130063	−	0.225275i	0.923700	+	0.383115i	$0.125149\pi$
$80$	−2.07085	+	3.58682i	−0.231528	+	0.401018i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.33240	−	4.03983i	−0.257570	−	0.446125i
$83$	3.08133			0.338220			0.169110	−	0.985597i	$-0.445911\pi$
$83$	3.08133			0.338220			0.169110	+	0.985597i	$0.445911\pi$
$84$	−2.11344	−	1.59166i	−0.230595	−	0.173665i
$85$	5.22495	−	9.04988i	0.566725	−	0.981597i
$86$	4.81529	−	8.34033i	0.519246	−	0.899361i
$87$	−3.08133			−0.330353
$88$	0.261547	−	0.453013i	0.0278810	−	0.0482914i
$89$	−10.8520			−1.15031			−0.575153	−	0.818046i	$-0.695058\pi$
$89$	−10.8520			−1.15031			−0.575153	+	0.818046i	$0.695058\pi$
$90$	−4.14170			−0.436573
$91$	2.81653	+	9.11412i	0.295253	+	0.955419i
$92$	−7.39337			−0.770812
$93$	−4.35275			−0.451359
$94$	5.58154	−	9.66752i	0.575692	−	0.997128i
$95$	−23.6074			−2.42207
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−1.31892	+	2.28443i	−0.133916	+	0.231949i	−0.925183	−	0.379522i	$-0.876089\pi$
$97$	−1.31892	+	2.28443i	−0.133916	+	0.231949i	0.791267	+	0.611471i	$0.209422\pi$
$98$	6.79301	+	1.68966i	0.686198	+	0.170682i
$99$	0.523095			0.0525730
$100$	−6.07684	−	10.5254i	−0.607684	−	1.05254i
$101$	6.09224	−	10.5521i	0.606200	−	1.04997i	−0.385660	−	0.922641i	$-0.626026\pi$
$101$	6.09224	−	10.5521i	0.606200	−	1.04997i	0.991861	−	0.127329i	$-0.0406404\pi$
$102$	1.26155	−	2.18506i	0.124912	−	0.216354i
$103$	6.81529	−	11.8044i	0.671531	−	1.16313i	−0.305940	−	0.952051i	$-0.598971\pi$
$103$	6.81529	−	11.8044i	0.671531	−	1.16313i	0.977470	−	0.211074i	$-0.0676961\pi$
$104$	3.28981	−	1.47551i	0.322593	−	0.144686i
$105$	10.0856	−	4.28441i	0.984255	−	0.418116i
$106$	0.00192073	+	0.00332680i	0.000186558	+	0.000323127i
$107$	5.39721			0.521768			0.260884	−	0.965370i	$-0.415986\pi$
$107$	5.39721			0.521768			0.260884	+	0.965370i	$0.415986\pi$
$108$	−1.00000			−0.0962250
$109$	5.58133	+	9.66715i	0.534594	+	0.925945i	0.999183	+	0.0404180i	$0.0128689\pi$
$109$	5.58133	+	9.66715i	0.534594	+	0.925945i	−0.464588	+	0.885527i	$0.653798\pi$
$110$	1.08325	+	1.87624i	0.103284	+	0.178893i
$111$	−2.83240	+	4.90586i	−0.268839	+	0.465643i
$112$	0.321703	−	2.62612i	0.0303981	−	0.248145i
$113$	2.03617	−	3.52676i	0.191547	−	0.331769i	−0.754216	−	0.656626i	$-0.771983\pi$
$113$	2.03617	−	3.52676i	0.191547	−	0.331769i	0.945763	+	0.324857i	$0.105316\pi$
$114$	−5.69993			−0.533848
$115$	15.3106	−	26.5187i	1.42772	−	2.47288i
$116$	−1.54066	−	2.66851i	−0.143047	−	0.247765i
$117$	2.92274	+	2.11130i	0.270207	+	0.195190i
$118$	−8.10749			−0.746355
$119$	−0.811687	+	6.62595i	−0.0744072	+	0.607400i
$120$	−2.07085	−	3.58682i	−0.189042	−	0.327430i
$121$	5.36319	+	9.28931i	0.487562	+	0.844483i
$122$	3.00599	+	5.20652i	0.272149	+	0.471377i
$123$	4.66479			0.420610
$124$	−2.17638	−	3.76959i	−0.195444	−	0.338520i
$125$	29.6284			2.65004
$126$	2.43514	−	1.03446i	0.216939	−	0.0921568i
$127$	−3.83432	−	6.64123i	−0.340241	−	0.589314i	0.644237	−	0.764826i	$-0.277175\pi$
$127$	−3.83432	−	6.64123i	−0.340241	−	0.589314i	−0.984477	+	0.175512i	$0.943842\pi$
$128$	−1.00000			−0.0883883
$129$	4.81529	+	8.34033i	0.423963	+	0.734325i
$130$	−1.52031	+	14.8555i	−0.133340	+	1.30292i
$131$	−5.62392	+	9.74091i	−0.491364	+	0.851067i	−0.999951	−	0.00994375i	$-0.996835\pi$
$131$	−5.62392	+	9.74091i	−0.491364	+	0.851067i	0.508587	+	0.861011i	$0.330168\pi$
$132$	0.261547	+	0.453013i	0.0227648	+	0.0394297i
$133$	13.8801	−	5.89634i	1.20356	−	0.511277i
$134$	1.61622	−	2.79938i	0.139620	−	0.241829i
$135$	2.07085	−	3.58682i	0.178230	−	0.308704i
$136$	2.52309			0.216354
$137$	−7.02232			−0.599957			−0.299978	−	0.953946i	$-0.596979\pi$
$137$	−7.02232			−0.599957			−0.299978	+	0.953946i	$0.596979\pi$
$138$	3.69669	−	6.40285i	0.314683	−	0.545047i
$139$	6.59202	−	11.4177i	0.559128	−	0.968438i	−0.438441	−	0.898760i	$-0.644469\pi$
$139$	6.59202	−	11.4177i	0.559128	−	0.968438i	0.997569	−	0.0696786i	$-0.0221974\pi$
$140$	8.75321	+	6.59219i	0.739782	+	0.557142i
$141$	5.58154	+	9.66752i	0.470051	+	0.814152i
$142$	−3.98568	+	6.90340i	−0.334471	+	0.579320i
$143$	0.192014	−	1.87624i	0.0160570	−	0.156899i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	12.7619			1.05982
$146$	−5.99080	−	10.3764i	−0.495802	−	0.858755i
$147$	−4.85980	+	5.03809i	−0.400829	+	0.415535i
$148$	−5.66479			−0.465643
$149$	−9.06612	−	15.7030i	−0.742726	−	1.28644i	−0.951250	−	0.308421i	$-0.900199\pi$
$149$	−9.06612	−	15.7030i	−0.742726	−	1.28644i	0.208524	−	0.978017i	$-0.433134\pi$
$150$	12.1537			0.992343
$151$	−2.53343	−	4.38804i	−0.206168	−	0.357093i	0.744336	−	0.667805i	$-0.232766\pi$
$151$	−2.53343	−	4.38804i	−0.206168	−	0.357093i	−0.950504	+	0.310712i	$0.899433\pi$
$152$	−2.84997	−	4.93629i	−0.231163	−	0.400386i
$153$	1.26155	+	2.18506i	0.101990	+	0.176652i
$154$	−1.10553	−	0.832590i	−0.0890859	−	0.0670920i
$155$	18.0278			1.44803
$156$	−0.367074	+	3.58682i	−0.0293894	+	0.287175i
$157$	5.80481	+	10.0542i	0.463274	+	0.802415i	0.999122	−	0.0419001i	$-0.0133411\pi$
$157$	5.80481	+	10.0542i	0.463274	+	0.802415i	−0.535847	+	0.844315i	$0.680008\pi$
$158$	−1.15602	+	2.00229i	−0.0919681	+	0.159293i
$159$	−0.00384145			−0.000304647
$160$	2.07085	−	3.58682i	0.163715	−	0.283563i
$161$	−2.37847	+	19.4159i	−0.187450	+	1.53019i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	9.99637	+	17.3142i	0.782976	+	1.35615i	0.930201	+	0.367052i	$0.119633\pi$
$163$	9.99637	+	17.3142i	0.782976	+	1.35615i	−0.147224	+	0.989103i	$0.547034\pi$
$164$	2.33240	+	4.03983i	0.182130	+	0.315458i
$165$	−2.16650			−0.168662
$166$	−3.08133			−0.239158
$167$	−8.82851	−	15.2914i	−0.683171	−	1.18329i	−0.974008	−	0.226514i	$-0.927267\pi$
$167$	−8.82851	−	15.2914i	−0.683171	−	1.18329i	0.290837	−	0.956772i	$-0.406066\pi$
$168$	2.11344	+	1.59166i	0.163055	+	0.122799i
$169$	8.64572	−	9.70832i	0.665055	−	0.746794i
$170$	−5.22495	+	9.04988i	−0.400735	+	0.694094i
$171$	2.84997	−	4.93629i	0.217942	−	0.377487i
$172$	−4.81529	+	8.34033i	−0.367162	+	0.635944i
$173$	1.93492	+	3.35139i	0.147110	+	0.254801i	0.930158	−	0.367160i	$-0.119670\pi$
$173$	1.93492	+	3.35139i	0.147110	+	0.254801i	−0.783048	+	0.621961i	$0.786336\pi$
$174$	3.08133			0.233595
$175$	−29.5959	+	12.5725i	−2.23724	+	0.950388i
$176$	−0.261547	+	0.453013i	−0.0197149	+	0.0341472i
$177$	4.05374	−	7.02129i	0.304698	−	0.527752i
$178$	10.8520			0.813390
$179$	1.75984	−	3.04813i	0.131537	−	0.227828i	−0.792732	−	0.609570i	$-0.791342\pi$
$179$	1.75984	−	3.04813i	0.131537	−	0.227828i	0.924269	+	0.381742i	$0.124676\pi$
$180$	4.14170			0.308704
$181$	8.47129			0.629666			0.314833	−	0.949147i	$-0.398052\pi$
$181$	8.47129			0.629666			0.314833	+	0.949147i	$0.398052\pi$
$182$	−2.81653	−	9.11412i	−0.208775	−	0.675583i
$183$	−6.01198			−0.444418
$184$	7.39337			0.545047
$185$	11.7309	−	20.3186i	0.862476	−	1.49385i
$186$	4.35275			0.319159
$187$	0.659909	−	1.14300i	0.0482573	−	0.0835841i
$188$	−5.58154	+	9.66752i	−0.407076	+	0.705076i
$189$	−0.321703	+	2.62612i	−0.0234004	+	0.191022i
$190$	23.6074			1.71266
$191$	10.9754	+	19.0099i	0.794151	+	1.37551i	0.923377	+	0.383894i	$0.125417\pi$
$191$	10.9754	+	19.0099i	0.794151	+	1.37551i	−0.129227	+	0.991615i	$0.541249\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−6.42959	+	11.1364i	−0.462812	+	0.801614i	−0.999100	−	0.0424212i	$-0.986493\pi$
$193$	−6.42959	+	11.1364i	−0.462812	+	0.801614i	0.536288	+	0.844035i	$0.319826\pi$
$194$	1.31892	−	2.28443i	0.0946928	−	0.164013i
$195$	−12.1051	−	8.74439i	−0.866864	−	0.626198i
$196$	−6.79301	−	1.68966i	−0.485215	−	0.120690i
$197$	−5.27054	−	9.12883i	−0.375510	−	0.650403i	0.614893	−	0.788610i	$-0.289199\pi$
$197$	−5.27054	−	9.12883i	−0.375510	−	0.650403i	−0.990403	+	0.138208i	$0.955866\pi$
$198$	−0.523095			−0.0371747
$199$	13.1036			0.928893			0.464446	−	0.885601i	$-0.346253\pi$
$199$	13.1036			0.928893			0.464446	+	0.885601i	$0.346253\pi$
$200$	6.07684	+	10.5254i	0.429697	+	0.744258i
$201$	1.61622	+	2.79938i	0.113999	+	0.197453i
$202$	−6.09224	+	10.5521i	−0.428648	+	0.742441i
$203$	−7.50346	+	3.18750i	−0.526640	+	0.223719i
$204$	−1.26155	+	2.18506i	−0.0883260	+	0.152985i
$205$	−19.3202			−1.34938
$206$	−6.81529	+	11.8044i	−0.474844	+	0.822454i
$207$	3.69669	+	6.40285i	0.256937	+	0.445029i
$208$	−3.28981	+	1.47551i	−0.228107	+	0.102308i
$209$	−2.98160			−0.206242
$210$	−10.0856	+	4.28441i	−0.695973	+	0.295652i
$211$	−0.979430	−	1.69642i	−0.0674267	−	0.116787i	0.830341	−	0.557255i	$-0.188146\pi$
$211$	−0.979430	−	1.69642i	−0.0674267	−	0.116787i	−0.897768	+	0.440469i	$0.854812\pi$
$212$	−0.00192073	−	0.00332680i	−0.000131916	−	0.000228485i
$213$	−3.98568	−	6.90340i	−0.273094	−	0.473013i
$214$	−5.39721			−0.368946
$215$	−19.9435	−	34.5431i	−1.36013	−	2.35582i
$216$	1.00000			0.0680414
$217$	−10.5996	+	4.50274i	−0.719545	+	0.305666i
$218$	−5.58133	−	9.66715i	−0.378015	−	0.654742i
$219$	11.9816			0.809642
$220$	−1.08325	−	1.87624i	−0.0730327	−	0.126496i
$221$	8.30051	−	3.72286i	0.558352	−	0.250427i
$222$	2.83240	−	4.90586i	0.190098	−	0.329259i
$223$	6.26821	+	10.8569i	0.419751	+	0.727029i	0.995914	−	0.0903050i	$-0.0287842\pi$
$223$	6.26821	+	10.8569i	0.419751	+	0.727029i	−0.576164	+	0.817334i	$0.695451\pi$
$224$	−0.321703	+	2.62612i	−0.0214947	+	0.175465i
$225$	−6.07684	+	10.5254i	−0.405123	+	0.701693i
$226$	−2.03617	+	3.52676i	−0.135444	+	0.234596i
$227$	−21.7299			−1.44226			−0.721132	−	0.692798i	$-0.756378\pi$
$227$	−21.7299			−1.44226			−0.721132	+	0.692798i	$0.756378\pi$
$228$	5.69993			0.377487
$229$	−7.77570	+	13.4679i	−0.513833	+	0.889985i	0.486038	+	0.873938i	$0.338442\pi$
$229$	−7.77570	+	13.4679i	−0.513833	+	0.889985i	−0.999871	+	0.0160474i	$0.994892\pi$
$230$	−15.3106	+	26.5187i	−1.00955	+	1.74859i
$231$	1.27381	−	0.541119i	0.0838104	−	0.0356030i
$232$	1.54066	+	2.66851i	0.101150	+	0.175196i
$233$	10.3320	−	17.8955i	0.676870	−	1.17237i	−0.299048	−	0.954238i	$-0.596669\pi$
$233$	10.3320	−	17.8955i	0.676870	−	1.17237i	0.975919	−	0.218135i	$-0.0699974\pi$
$234$	−2.92274	−	2.11130i	−0.191065	−	0.138020i
$235$	−23.1171	−	40.0400i	−1.50799	−	2.61192i
$236$	8.10749			0.527752
$237$	−1.15602	−	2.00229i	−0.0750916	−	0.130063i
$238$	0.811687	−	6.62595i	0.0526139	−	0.429497i
$239$	−30.0971			−1.94682			−0.973410	−	0.229071i	$-0.926431\pi$
$239$	−30.0971			−1.94682			−0.973410	+	0.229071i	$0.926431\pi$
$240$	2.07085	+	3.58682i	0.133673	+	0.231528i
$241$	2.05219			0.132193			0.0660965	−	0.997813i	$-0.478945\pi$
$241$	2.05219			0.132193			0.0660965	+	0.997813i	$0.478945\pi$
$242$	−5.36319	−	9.28931i	−0.344759	−	0.597140i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−3.00599	−	5.20652i	−0.192439	−	0.333314i
$245$	20.1278	−	20.8663i	1.28592	−	1.33310i
$246$	−4.66479			−0.297416
$247$	−16.6594	−	12.0343i	−1.06001	−	0.765724i
$248$	2.17638	+	3.76959i	0.138200	+	0.239369i
$249$	1.54066	−	2.66851i	0.0976357	−	0.169110i
$250$	−29.6284			−1.87386
$251$	−8.23457	+	14.2627i	−0.519761	+	0.900253i	0.479975	+	0.877282i	$0.340646\pi$
$251$	−8.23457	+	14.2627i	−0.519761	+	0.900253i	−0.999736	+	0.0229705i	$0.992688\pi$
$252$	−2.43514	+	1.03446i	−0.153399	+	0.0651647i
$253$	1.93372	−	3.34929i	0.121572	−	0.210568i
$254$	3.83432	+	6.64123i	0.240586	+	0.416708i
$255$	−5.22495	−	9.04988i	−0.327199	−	0.566725i
$256$	1.00000			0.0625000
$257$	11.8742			0.740693			0.370346	−	0.928894i	$-0.379239\pi$
$257$	11.8742			0.740693			0.370346	+	0.928894i	$0.379239\pi$
$258$	−4.81529	−	8.34033i	−0.299787	−	0.519246i
$259$	−1.82238	+	14.8764i	−0.113237	+	0.924376i
$260$	1.52031	−	14.8555i	0.0942856	−	0.921300i
$261$	−1.54066	+	2.66851i	−0.0953648	+	0.165177i
$262$	5.62392	−	9.74091i	0.347447	−	0.601795i
$263$	−12.5158	+	21.6781i	−0.771760	+	1.33673i	0.164838	+	0.986321i	$0.447290\pi$
$263$	−12.5158	+	21.6781i	−0.771760	+	1.33673i	−0.936598	+	0.350406i	$0.886043\pi$
$264$	−0.261547	−	0.453013i	−0.0160971	−	0.0278810i
$265$	0.0159101			0.000977353
$266$	−13.8801	+	5.89634i	−0.851045	+	0.361528i
$267$	−5.42599	+	9.39808i	−0.332065	+	0.575153i
$268$	−1.61622	+	2.79938i	−0.0987264	+	0.170999i
$269$	−15.5300			−0.946882			−0.473441	−	0.880826i	$-0.656988\pi$
$269$	−15.5300			−0.946882			−0.473441	+	0.880826i	$0.656988\pi$
$270$	−2.07085	+	3.58682i	−0.126028	+	0.218287i
$271$	−5.27690			−0.320549			−0.160274	−	0.987072i	$-0.551238\pi$
$271$	−5.27690			−0.320549			−0.160274	+	0.987072i	$0.551238\pi$
$272$	−2.52309			−0.152985
$273$	9.30132	+	2.11787i	0.562942	+	0.128179i
$274$	7.02232			0.424234
$275$	6.35752			0.383373
$276$	−3.69669	+	6.40285i	−0.222514	+	0.385406i
$277$	−11.1319			−0.668850			−0.334425	−	0.942422i	$-0.608542\pi$
$277$	−11.1319			−0.668850			−0.334425	+	0.942422i	$0.608542\pi$
$278$	−6.59202	+	11.4177i	−0.395363	+	0.684789i
$279$	−2.17638	+	3.76959i	−0.130296	+	0.225680i
$280$	−8.75321	−	6.59219i	−0.523105	−	0.393959i
$281$	19.3908			1.15676			0.578379	−	0.815768i	$-0.303686\pi$
$281$	19.3908			1.15676			0.578379	+	0.815768i	$0.303686\pi$
$282$	−5.58154	−	9.66752i	−0.332376	−	0.575692i
$283$	−13.0180	+	22.5478i	−0.773838	+	1.34033i	0.161608	+	0.986855i	$0.448332\pi$
$283$	−13.0180	+	22.5478i	−0.773838	+	1.34033i	−0.935445	+	0.353471i	$0.885001\pi$
$284$	3.98568	−	6.90340i	0.236507	−	0.409641i
$285$	−11.8037	+	20.4446i	−0.699191	+	1.21103i
$286$	−0.192014	+	1.87624i	−0.0113540	+	0.110945i
$287$	11.3594	−	4.82553i	0.670525	−	0.284842i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−10.6340			−0.625529
$290$	−12.7619			−0.749407
$291$	1.31892	+	2.28443i	0.0773163	+	0.133916i
$292$	5.99080	+	10.3764i	0.350585	+	0.607231i
$293$	−6.46216	+	11.1928i	−0.377523	+	0.653890i	−0.990701	−	0.136055i	$-0.956558\pi$
$293$	−6.46216	+	11.1928i	−0.377523	+	0.653890i	0.613178	+	0.789945i	$0.289891\pi$
$294$	4.85980	−	5.03809i	0.283429	−	0.293828i
$295$	−16.7894	+	29.0801i	−0.977516	+	1.69311i
$296$	5.66479			0.329259
$297$	0.261547	−	0.453013i	0.0151765	−	0.0262865i
$298$	9.06612	+	15.7030i	0.525186	+	0.909649i
$299$	24.3228	−	10.9090i	1.40662	−	0.630885i
$300$	−12.1537			−0.701693
$301$	20.3536	+	15.3286i	1.17316	+	0.883528i
$302$	2.53343	+	4.38804i	0.145783	+	0.252503i
$303$	−6.09224	−	10.5521i	−0.349990	−	0.606200i
$304$	2.84997	+	4.93629i	0.163457	+	0.283116i
$305$	24.8998			1.42576
$306$	−1.26155	−	2.18506i	−0.0721179	−	0.124912i
$307$	20.0771			1.14586			0.572931	−	0.819604i	$-0.305806\pi$
$307$	20.0771			1.14586			0.572931	+	0.819604i	$0.305806\pi$
$308$	1.10553	+	0.832590i	0.0629932	+	0.0474412i
$309$	−6.81529	−	11.8044i	−0.387708	−	0.671531i
$310$	−18.0278			−1.02391
$311$	10.4837	+	18.1583i	0.594475	+	1.02966i	0.993621	+	0.112774i	$0.0359736\pi$
$311$	10.4837	+	18.1583i	0.594475	+	1.02966i	−0.399145	+	0.916888i	$0.630693\pi$
$312$	0.367074	−	3.58682i	0.0207815	−	0.203064i
$313$	9.55610	−	16.5517i	0.540143	−	0.935555i	−0.458752	−	0.888564i	$-0.651703\pi$
$313$	9.55610	−	16.5517i	0.540143	−	0.935555i	0.998895	−	0.0469909i	$-0.0149632\pi$
$314$	−5.80481	−	10.0542i	−0.327584	−	0.567393i
$315$	1.33240	−	10.8766i	0.0750721	−	0.612827i
$316$	1.15602	−	2.00229i	0.0650313	−	0.112637i
$317$	9.13122	−	15.8157i	0.512860	−	0.888300i	−0.487028	−	0.873386i	$-0.661919\pi$
$317$	9.13122	−	15.8157i	0.512860	−	0.888300i	0.999889	−	0.0149141i	$-0.00474749\pi$
$318$	0.00384145			0.000215418
$319$	1.61183			0.0902450
$320$	−2.07085	+	3.58682i	−0.115764	+	0.200509i
$321$	2.69861	−	4.67412i	0.150622	−	0.260884i
$322$	2.37847	−	19.4159i	0.132547	−	1.08200i
$323$	−7.19074	−	12.4547i	−0.400103	−	0.692999i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	35.5220	+	25.6601i	1.97041	+	1.42337i
$326$	−9.99637	−	17.3142i	−0.553648	−	0.958946i
$327$	11.1627			0.617296
$328$	−2.33240	−	4.03983i	−0.128785	−	0.223062i
$329$	23.5925	+	17.7679i	1.30069	+	0.979575i
$330$	2.16650			0.119262
$331$	5.12199	+	8.87155i	0.281530	+	0.487625i	0.971762	−	0.235964i	$-0.0758247\pi$
$331$	5.12199	+	8.87155i	0.281530	+	0.487625i	−0.690232	+	0.723589i	$0.742491\pi$
$332$	3.08133			0.169110
$333$	2.83240	+	4.90586i	0.155214	+	0.268839i
$334$	8.82851	+	15.2914i	0.483075	+	0.836710i
$335$	−6.69390	−	11.5942i	−0.365727	−	0.633457i
$336$	−2.11344	−	1.59166i	−0.115297	−	0.0868323i
$337$	−32.6266			−1.77728			−0.888642	−	0.458601i	$-0.848351\pi$
$337$	−32.6266			−1.77728			−0.888642	+	0.458601i	$0.848351\pi$
$338$	−8.64572	+	9.70832i	−0.470265	+	0.528063i
$339$	−2.03617	−	3.52676i	−0.110590	−	0.191547i
$340$	5.22495	−	9.04988i	0.283363	−	0.490799i
$341$	2.27690			0.123301
$342$	−2.84997	+	4.93629i	−0.154109	+	0.266924i
$343$	−6.62259	+	17.2957i	−0.357586	+	0.933880i
$344$	4.81529	−	8.34033i	0.259623	−	0.449680i
$345$	−15.3106	−	26.5187i	−0.824293	−	1.42772i
$346$	−1.93492	−	3.35139i	−0.104022	−	0.180172i
$347$	8.43192			0.452649			0.226325	−	0.974052i	$-0.427329\pi$
$347$	8.43192			0.452649			0.226325	+	0.974052i	$0.427329\pi$
$348$	−3.08133			−0.165177
$349$	18.3077	+	31.7099i	0.979990	+	1.69739i	0.662373	+	0.749174i	$0.269549\pi$
$349$	18.3077	+	31.7099i	0.979990	+	1.69739i	0.317617	+	0.948219i	$0.397117\pi$
$350$	29.5959	−	12.5725i	1.58197	−	0.672026i
$351$	3.28981	−	1.47551i	0.175597	−	0.0787571i
$352$	0.261547	−	0.453013i	0.0139405	−	0.0241457i
$353$	2.61947	−	4.53705i	0.139420	−	0.241483i	−0.787857	−	0.615858i	$-0.788809\pi$
$353$	2.61947	−	4.53705i	0.139420	−	0.241483i	0.927277	+	0.374375i	$0.122143\pi$
$354$	−4.05374	+	7.02129i	−0.215454	+	0.373177i
$355$	16.5075	+	28.5918i	0.876126	+	1.51750i
$356$	−10.8520			−0.575153
$357$	5.33240	+	4.01592i	0.282220	+	0.212545i
$358$	−1.75984	+	3.04813i	−0.0930105	+	0.161099i
$359$	−2.54006	+	4.39951i	−0.134059	+	0.232197i	−0.925238	−	0.379388i	$-0.876135\pi$
$359$	−2.54006	+	4.39951i	−0.134059	+	0.232197i	0.791178	+	0.611585i	$0.209468\pi$
$360$	−4.14170			−0.218287
$361$	−6.74463	+	11.6820i	−0.354980	+	0.614844i
$362$	−8.47129			−0.445241
$363$	10.7264			0.562989
$364$	2.81653	+	9.11412i	0.147626	+	0.477710i
$365$	−49.6242			−2.59745
$366$	6.01198			0.314251
$367$	−2.43151	+	4.21150i	−0.126924	+	0.219839i	−0.922483	−	0.386037i	$-0.873844\pi$
$367$	−2.43151	+	4.21150i	−0.126924	+	0.219839i	0.795559	+	0.605876i	$0.207177\pi$
$368$	−7.39337			−0.385406
$369$	2.33240	−	4.03983i	0.121420	−	0.210305i
$370$	−11.7309	+	20.3186i	−0.609862	+	1.05631i
$371$	−0.00935447	+	0.00397382i	−0.000485660	+	0.000206310i
$372$	−4.35275			−0.225680
$373$	−14.4061	−	24.9521i	−0.745919	−	1.29197i	−0.949764	−	0.312967i	$-0.898677\pi$
$373$	−14.4061	−	24.9521i	−0.745919	−	1.29197i	0.203845	−	0.979003i	$-0.434656\pi$
$374$	−0.659909	+	1.14300i	−0.0341231	+	0.0591029i
$375$	14.8142	−	25.6589i	0.765001	−	1.32502i
$376$	5.58154	−	9.66752i	0.287846	−	0.498564i
$377$	9.00592	+	6.50562i	0.463828	+	0.335057i
$378$	0.321703	−	2.62612i	0.0165466	−	0.135073i
$379$	−14.1550	−	24.5172i	−0.727094	−	1.25936i	−0.958106	−	0.286413i	$-0.907537\pi$
$379$	−14.1550	−	24.5172i	−0.727094	−	1.25936i	0.231013	−	0.972951i	$-0.425796\pi$
$380$	−23.6074			−1.21103
$381$	−7.66864			−0.392876
$382$	−10.9754	−	19.0099i	−0.561549	−	0.972632i
$383$	9.36815	+	16.2261i	0.478690	+	0.829115i	0.999701	−	0.0244344i	$-0.00777849\pi$
$383$	9.36815	+	16.2261i	0.478690	+	0.829115i	−0.521012	+	0.853550i	$0.674445\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−5.27573	+	2.24115i	−0.268876	+	0.114220i
$386$	6.42959	−	11.1364i	0.327258	−	0.566827i
$387$	9.63058			0.489550
$388$	−1.31892	+	2.28443i	−0.0669579	+	0.115974i
$389$	3.55307	+	6.15409i	0.180148	+	0.312025i	0.941931	−	0.335807i	$-0.109009\pi$
$389$	3.55307	+	6.15409i	0.180148	+	0.312025i	−0.761783	+	0.647832i	$0.775676\pi$
$390$	12.1051	+	8.74439i	0.612966	+	0.442789i
$391$	18.6542			0.943382
$392$	6.79301	+	1.68966i	0.343099	+	0.0853408i
$393$	5.62392	+	9.74091i	0.283689	+	0.491364i
$394$	5.27054	+	9.12883i	0.265526	+	0.459904i
$395$	4.78789	+	8.29287i	0.240905	+	0.417260i
$396$	0.523095			0.0262865
$397$	−19.6633	−	34.0578i	−0.986872	−	1.70931i	−0.633302	−	0.773905i	$-0.718301\pi$
$397$	−19.6633	−	34.0578i	−0.986872	−	1.70931i	−0.353571	−	0.935408i	$-0.615033\pi$
$398$	−13.1036			−0.656826
$399$	1.83369	−	14.9687i	0.0917991	−	0.749373i
$400$	−6.07684	−	10.5254i	−0.303842	−	0.526270i
$401$	−8.60307			−0.429617			−0.214808	−	0.976656i	$-0.568913\pi$
$401$	−8.60307			−0.429617			−0.214808	+	0.976656i	$0.568913\pi$
$402$	−1.61622	−	2.79938i	−0.0806098	−	0.139620i
$403$	12.7220	+	9.18998i	0.633726	+	0.457786i
$404$	6.09224	−	10.5521i	0.303100	−	0.524985i
$405$	−2.07085	−	3.58682i	−0.102901	−	0.178230i
$406$	7.50346	−	3.18750i	0.372391	−	0.158193i
$407$	1.48161	−	2.56623i	0.0734408	−	0.127203i
$408$	1.26155	−	2.18506i	0.0624559	−	0.108177i
$409$	−36.5325			−1.80642			−0.903208	−	0.429204i	$-0.858794\pi$
$409$	−36.5325			−1.80642			−0.903208	+	0.429204i	$0.858794\pi$
$410$	19.3202			0.954155
$411$	−3.51116	+	6.08150i	−0.173193	+	0.299978i
$412$	6.81529	−	11.8044i	0.335765	−	0.581563i
$413$	2.60820	−	21.2912i	0.128341	−	1.04767i
$414$	−3.69669	−	6.40285i	−0.181682	−	0.314683i
$415$	−6.38097	+	11.0522i	−0.313230	+	0.542529i
$416$	3.28981	−	1.47551i	0.161296	−	0.0723430i
$417$	−6.59202	−	11.4177i	−0.322813	−	0.559128i
$418$	2.98160			0.145835
$419$	6.77818	+	11.7402i	0.331136	+	0.573544i	0.982735	−	0.185019i	$-0.0592348\pi$
$419$	6.77818	+	11.7402i	0.331136	+	0.573544i	−0.651599	+	0.758564i	$0.725901\pi$
$420$	10.0856	−	4.28441i	0.492127	−	0.209058i
$421$	4.50209			0.219418			0.109709	−	0.993964i	$-0.465008\pi$
$421$	4.50209			0.219418			0.109709	+	0.993964i	$0.465008\pi$
$422$	0.979430	+	1.69642i	0.0476779	+	0.0825806i
$423$	11.1631			0.542768
$424$	0.00192073	+	0.00332680i	9.32788e−5	+	0.000161564i
$425$	15.3324	+	26.5566i	0.743732	+	1.28818i
$426$	3.98568	+	6.90340i	0.193107	+	0.334471i
$427$	−14.6400	+	6.21913i	−0.708479	+	0.300965i
$428$	5.39721			0.260884
$429$	−1.52887	−	1.10441i	−0.0738145	−	0.0533215i
$430$	19.9435	+	34.5431i	0.961760	+	1.66582i
$431$	0.253853	−	0.439686i	0.0122277	−	0.0211789i	−0.859847	−	0.510552i	$-0.829441\pi$
$431$	0.253853	−	0.439686i	0.0122277	−	0.0211789i	0.872074	+	0.489373i	$0.162774\pi$
$432$	−1.00000			−0.0481125
$433$	−6.41093	+	11.1041i	−0.308090	+	0.533627i	−0.977944	−	0.208865i	$-0.933023\pi$
$433$	−6.41093	+	11.1041i	−0.308090	+	0.533627i	0.669855	+	0.742492i	$0.266356\pi$
$434$	10.5996	−	4.50274i	0.508795	−	0.216138i
$435$	6.38097	−	11.0522i	0.305944	−	0.529911i
$436$	5.58133	+	9.66715i	0.267297	+	0.462972i
$437$	−21.0709	−	36.4958i	−1.00796	−	1.74583i
$438$	−11.9816			−0.572503
$439$	−0.433280			−0.0206793			−0.0103397	−	0.999947i	$-0.503291\pi$
$439$	−0.433280			−0.0206793			−0.0103397	+	0.999947i	$0.503291\pi$
$440$	1.08325	+	1.87624i	0.0516419	+	0.0894464i
$441$	1.93322	+	6.72775i	0.0920580	+	0.320369i
$442$	−8.30051	+	3.72286i	−0.394815	+	0.177078i
$443$	−7.03339	+	12.1822i	−0.334166	+	0.578793i	−0.983324	−	0.181861i	$-0.941788\pi$
$443$	−7.03339	+	12.1822i	−0.334166	+	0.578793i	0.649158	+	0.760654i	$0.275121\pi$
$444$	−2.83240	+	4.90586i	−0.134420	+	0.232822i
$445$	22.4728	−	38.9240i	1.06531	−	1.84518i
$446$	−6.26821	−	10.8569i	−0.296809	−	0.514087i
$447$	−18.1322			−0.857626
$448$	0.321703	−	2.62612i	0.0151990	−	0.124073i
$449$	15.2892	−	26.4817i	0.721542	−	1.24975i	−0.238840	−	0.971059i	$-0.576767\pi$
$449$	15.2892	−	26.4817i	0.721542	−	1.24975i	0.960382	−	0.278688i	$-0.0898997\pi$
$450$	6.07684	−	10.5254i	0.286465	−	0.496172i
$451$	−2.44013			−0.114901
$452$	2.03617	−	3.52676i	0.0957735	−	0.165885i
$453$	−5.06687			−0.238062
$454$	21.7299			1.01983
$455$	−38.5233	−	8.77158i	−1.80600	−	0.411218i
$456$	−5.69993			−0.266924
$457$	2.31026			0.108069			0.0540346	−	0.998539i	$-0.482792\pi$
$457$	2.31026			0.108069			0.0540346	+	0.998539i	$0.482792\pi$
$458$	7.77570	−	13.4679i	0.363335	−	0.629314i
$459$	2.52309			0.117768
$460$	15.3106	−	26.5187i	0.713859	−	1.23644i
$461$	−15.0409	+	26.0516i	−0.700524	+	1.21334i	0.267759	+	0.963486i	$0.413717\pi$
$461$	−15.0409	+	26.0516i	−0.700524	+	1.21334i	−0.968283	+	0.249857i	$0.919617\pi$
$462$	−1.27381	+	0.541119i	−0.0592629	+	0.0251751i
$463$	29.4727			1.36971			0.684856	−	0.728679i	$-0.259865\pi$
$463$	29.4727			1.36971			0.684856	+	0.728679i	$0.259865\pi$
$464$	−1.54066	−	2.66851i	−0.0715236	−	0.123882i
$465$	9.01390	−	15.6125i	0.418009	−	0.724014i
$466$	−10.3320	+	17.8955i	−0.478619	+	0.828993i
$467$	2.92442	−	5.06525i	0.135326	−	0.234392i	−0.790396	−	0.612596i	$-0.790125\pi$
$467$	2.92442	−	5.06525i	0.135326	−	0.234392i	0.925722	+	0.378205i	$0.123458\pi$
$468$	2.92274	+	2.11130i	0.135104	+	0.0975951i
$469$	6.83156	+	5.14496i	0.315452	+	0.237572i
$470$	23.1171	+	40.0400i	1.06631	+	1.84691i
$471$	11.6096			0.534943
$472$	−8.10749			−0.373177
$473$	−2.51885	−	4.36278i	−0.115817	−	0.200601i
$474$	1.15602	+	2.00229i	0.0530978	+	0.0919681i
$475$	34.6376	−	59.9940i	1.58928	−	2.75272i
$476$	−0.811687	+	6.62595i	−0.0372036	+	0.303700i
$477$	−0.00192073	+	0.00332680i	−8.79441e−5	+	0.000152324i
$478$	30.0971			1.37661
$479$	−8.66374	+	15.0060i	−0.395856	+	0.685643i	−0.993210	−	0.116335i	$-0.962885\pi$
$479$	−8.66374	+	15.0060i	−0.395856	+	0.685643i	0.597354	+	0.801978i	$0.296219\pi$
$480$	−2.07085	−	3.58682i	−0.0945209	−	0.163715i
$481$	18.6361	−	8.35848i	0.849733	−	0.381114i
$482$	−2.05219			−0.0934746
$483$	15.6254	+	11.7678i	0.710981	+	0.535451i
$484$	5.36319	+	9.28931i	0.243781	+	0.422241i
$485$	−5.46256	−	9.46143i	−0.248042	−	0.429622i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−38.0645			−1.72487			−0.862434	−	0.506169i	$-0.831061\pi$
$487$	−38.0645			−1.72487			−0.862434	+	0.506169i	$0.831061\pi$
$488$	3.00599	+	5.20652i	0.136075	+	0.235688i
$489$	19.9927			0.904103
$490$	−20.1278	+	20.8663i	−0.909282	+	0.942642i
$491$	−8.22130	−	14.2397i	−0.371022	−	0.642629i	0.618701	−	0.785627i	$-0.287659\pi$
$491$	−8.22130	−	14.2397i	−0.371022	−	0.642629i	−0.989723	+	0.142997i	$0.954326\pi$
$492$	4.66479			0.210305
$493$	3.88724	+	6.73290i	0.175073	+	0.303235i
$494$	16.6594	+	12.0343i	0.749542	+	0.541448i
$495$	−1.08325	+	1.87624i	−0.0486885	+	0.0843309i
$496$	−2.17638	−	3.76959i	−0.0977222	−	0.169260i
$497$	−16.8469	−	12.6877i	−0.755689	−	0.569122i
$498$	−1.54066	+	2.66851i	−0.0690388	+	0.119579i
$499$	−3.74298	+	6.48304i	−0.167559	+	0.290221i	−0.937561	−	0.347821i	$-0.886922\pi$
$499$	−3.74298	+	6.48304i	−0.167559	+	0.290221i	0.770002	+	0.638041i	$0.220255\pi$
$500$	29.6284			1.32502
$501$	−17.6570			−0.788857
$502$	8.23457	−	14.2627i	0.367527	−	0.636575i
$503$	1.27275	−	2.20447i	0.0567492	−	0.0982925i	−0.836255	−	0.548340i	$-0.815260\pi$
$503$	1.27275	−	2.20447i	0.0567492	−	0.0982925i	0.893004	+	0.450048i	$0.148593\pi$
$504$	2.43514	−	1.03446i	0.108470	−	0.0460784i
$505$	25.2322	+	43.7035i	1.12282	+	1.94478i
$506$	−1.93372	+	3.34929i	−0.0859642	+	0.148894i
$507$	−4.08479	−	12.3416i	−0.181412	−	0.548109i
$508$	−3.83432	−	6.64123i	−0.170120	−	0.294657i
$509$	−34.4426			−1.52664			−0.763320	−	0.646021i	$-0.776432\pi$
$509$	−34.4426			−1.52664			−0.763320	+	0.646021i	$0.776432\pi$
$510$	5.22495	+	9.04988i	0.231365	+	0.400735i
$511$	29.1769	−	12.3945i	1.29071	−	0.548298i
$512$	−1.00000			−0.0441942
$513$	−2.84997	−	4.93629i	−0.125829	−	0.217942i
$514$	−11.8742			−0.523749
$515$	28.2269	+	48.8904i	1.24383	+	2.15437i
$516$	4.81529	+	8.34033i	0.211981	+	0.367162i
$517$	−2.91968	−	5.05703i	−0.128407	−	0.222408i
$518$	1.82238	−	14.8764i	0.0800708	−	0.653633i
$519$	3.86985			0.169867
$520$	−1.52031	+	14.8555i	−0.0666700	+	0.651458i
$521$	21.9782	+	38.0673i	0.962881	+	1.66776i	0.715204	+	0.698916i	$0.246334\pi$
$521$	21.9782	+	38.0673i	0.962881	+	1.66776i	0.247677	+	0.968843i	$0.420333\pi$
$522$	1.54066	−	2.66851i	0.0674331	−	0.116797i
$523$	−28.4937			−1.24594			−0.622971	−	0.782245i	$-0.714075\pi$
$523$	−28.4937			−1.24594			−0.622971	+	0.782245i	$0.714075\pi$
$524$	−5.62392	+	9.74091i	−0.245682	+	0.425533i
$525$	−3.90987	+	31.9170i	−0.170641	+	1.39297i
$526$	12.5158	−	21.6781i	0.545717	−	0.945209i
$527$	5.49120	+	9.51104i	0.239201	+	0.414308i
$528$	0.261547	+	0.453013i	0.0113824	+	0.0197149i
$529$	31.6619			1.37661
$530$	−0.0159101			−0.000691093
$531$	−4.05374	−	7.02129i	−0.175917	−	0.304698i
$532$	13.8801	−	5.89634i	0.601780	−	0.255639i
$533$	−13.6340	−	9.84880i	−0.590553	−	0.426599i
$534$	5.42599	−	9.39808i	0.234805	−	0.406695i
$535$	−11.1768	+	19.3588i	−0.483216	+	0.836955i
$536$	1.61622	−	2.79938i	0.0698101	−	0.120915i
$537$	−1.75984	−	3.04813i	−0.0759427	−	0.131537i
$538$	15.5300			0.669547
$539$	2.54213	−	2.63540i	0.109497	−	0.113515i
$540$	2.07085	−	3.58682i	0.0891152	−	0.154352i
$541$	0.327013	−	0.566403i	0.0140594	−	0.0243516i	−0.858910	−	0.512126i	$-0.828858\pi$
$541$	0.327013	−	0.566403i	0.0140594	−	0.0243516i	0.872969	+	0.487775i	$0.162191\pi$
$542$	5.27690			0.226662
$543$	4.23564	−	7.33635i	0.181769	−	0.314833i
$544$	2.52309			0.108177
$545$	−46.2324			−1.98038
$546$	−9.30132	−	2.11787i	−0.398060	−	0.0906364i
$547$	4.52174			0.193336			0.0966678	−	0.995317i	$-0.469182\pi$
$547$	4.52174			0.193336			0.0966678	+	0.995317i	$0.469182\pi$
$548$	−7.02232			−0.299978
$549$	−3.00599	+	5.20652i	−0.128292	+	0.222209i
$550$	−6.35752			−0.271086
$551$	8.78169	−	15.2103i	0.374113	−	0.647982i
$552$	3.69669	−	6.40285i	0.157341	−	0.272523i
$553$	−4.88635	−	3.67999i	−0.207789	−	0.156489i
$554$	11.1319			0.472948
$555$	−11.7309	−	20.3186i	−0.497951	−	0.862476i
$556$	6.59202	−	11.4177i	0.279564	−	0.484219i
$557$	1.09711	−	1.90025i	0.0464859	−	0.0805160i	−0.841846	−	0.539717i	$-0.818531\pi$
$557$	1.09711	−	1.90025i	0.0464859	−	0.0805160i	0.888332	+	0.459201i	$0.151864\pi$
$558$	2.17638	−	3.76959i	0.0921334	−	0.159580i
$559$	3.53513	−	34.5431i	0.149520	−	1.46102i
$560$	8.75321	+	6.59219i	0.369891	+	0.278571i
$561$	−0.659909	−	1.14300i	−0.0278614	−	0.0482573i
$562$	−19.3908			−0.817951
$563$	−15.0368			−0.633725			−0.316862	−	0.948472i	$-0.602629\pi$
$563$	−15.0368			−0.633725			−0.316862	+	0.948472i	$0.602629\pi$
$564$	5.58154	+	9.66752i	0.235025	+	0.407076i
$565$	8.43322	+	14.6068i	0.354788	+	0.614511i
$566$	13.0180	−	22.5478i	0.547186	−	0.947754i
$567$	2.11344	+	1.59166i	0.0887559	+	0.0668436i
$568$	−3.98568	+	6.90340i	−0.167235	+	0.289660i
$569$	−18.1733			−0.761863			−0.380932	−	0.924603i	$-0.624397\pi$
$569$	−18.1733			−0.761863			−0.380932	+	0.924603i	$0.624397\pi$
$570$	11.8037	−	20.4446i	0.494403	−	0.856331i
$571$	−18.3240	−	31.7382i	−0.766837	−	1.32820i	−0.939270	−	0.343180i	$-0.888496\pi$
$571$	−18.3240	−	31.7382i	−0.766837	−	1.32820i	0.172433	−	0.985021i	$-0.444837\pi$
$572$	0.192014	−	1.87624i	0.00802852	−	0.0784497i
$573$	21.9508			0.917006
$574$	−11.3594	+	4.82553i	−0.474133	+	0.201414i
$575$	44.9283	+	77.8181i	1.87364	+	3.24524i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−14.3809	−	24.9085i	−0.598686	−	1.03695i	−0.993015	−	0.117985i	$-0.962357\pi$
$577$	−14.3809	−	24.9085i	−0.598686	−	1.03695i	0.394330	−	0.918969i	$-0.370977\pi$
$578$	10.6340			0.442316
$579$	6.42959	+	11.1364i	0.267205	+	0.462812i
$580$	12.7619			0.529911
$581$	0.991273	−	8.09194i	0.0411249	−	0.335710i
$582$	−1.31892	−	2.28443i	−0.0546709	−	0.0946928i
$583$	0.00200944			8.32227e−5
$584$	−5.99080	−	10.3764i	−0.247901	−	0.429377i
$585$	−13.6254	+	6.11113i	−0.563341	+	0.252664i
$586$	6.46216	−	11.1928i	0.266949	−	0.462370i
$587$	−7.20528	−	12.4799i	−0.297394	−	0.515101i	0.678145	−	0.734928i	$-0.262784\pi$
$587$	−7.20528	−	12.4799i	−0.297394	−	0.515101i	−0.975539	+	0.219827i	$0.929451\pi$
$588$	−4.85980	+	5.03809i	−0.200415	+	0.207767i
$589$	12.4052	−	21.4864i	0.511147	−	0.885333i
$590$	16.7894	−	29.0801i	0.691208	−	1.19721i
$591$	−10.5411			−0.433602
$592$	−5.66479			−0.232822
$593$	9.75838	−	16.9020i	0.400729	−	0.694083i	−0.593085	−	0.805140i	$-0.702090\pi$
$593$	9.75838	−	16.9020i	0.400729	−	0.694083i	0.993814	+	0.111057i	$0.0354236\pi$
$594$	−0.261547	+	0.453013i	−0.0107314	+	0.0185874i
$595$	−22.0852	−	16.6327i	−0.905404	−	0.681875i
$596$	−9.06612	−	15.7030i	−0.371363	−	0.643219i
$597$	6.55182	−	11.3481i	0.268148	−	0.464446i
$598$	−24.3228	+	10.9090i	−0.994633	+	0.446103i
$599$	0.837961	+	1.45139i	0.0342382	+	0.0593022i	0.882637	−	0.470056i	$-0.155766\pi$
$599$	0.837961	+	1.45139i	0.0342382	+	0.0593022i	−0.848399	+	0.529358i	$0.822433\pi$
$600$	12.1537			0.496172
$601$	−7.12111	−	12.3341i	−0.290476	−	0.503119i	0.683446	−	0.730001i	$-0.260480\pi$
$601$	−7.12111	−	12.3341i	−0.290476	−	0.503119i	−0.973922	+	0.226882i	$0.927147\pi$
$602$	−20.3536	−	15.3286i	−0.829551	−	0.624749i
$603$	3.23244			0.131635
$604$	−2.53343	−	4.38804i	−0.103084	−	0.178547i
$605$	−44.4254			−1.80615
$606$	6.09224	+	10.5521i	0.247480	+	0.428648i
$607$	17.1509	+	29.7063i	0.696135	+	1.20574i	0.969797	+	0.243915i	$0.0784319\pi$
$607$	17.1509	+	29.7063i	0.696135	+	1.20574i	−0.273662	+	0.961826i	$0.588235\pi$
$608$	−2.84997	−	4.93629i	−0.115581	−	0.200193i
$609$	−0.991273	+	8.09194i	−0.0401684	+	0.327902i
$610$	−24.8998			−1.00816
$611$	4.09768	−	40.0400i	0.165774	−	1.61984i
$612$	1.26155	+	2.18506i	0.0509950	+	0.0883260i
$613$	1.82769	−	3.16565i	0.0738197	−	0.127860i	−0.826753	−	0.562566i	$-0.809814\pi$
$613$	1.82769	−	3.16565i	0.0738197	−	0.127860i	0.900572	+	0.434706i	$0.143148\pi$
$614$	−20.0771			−0.810246
$615$	−9.66009	+	16.7318i	−0.389532	+	0.674690i
$616$	−1.10553	−	0.832590i	−0.0445429	−	0.0335460i
$617$	2.31545	−	4.01048i	0.0932167	−	0.161456i	−0.815646	−	0.578551i	$-0.803618\pi$
$617$	2.31545	−	4.01048i	0.0932167	−	0.161456i	0.908863	+	0.417095i	$0.136952\pi$
$618$	6.81529	+	11.8044i	0.274151	+	0.474844i
$619$	−0.674947	−	1.16904i	−0.0271284	−	0.0469878i	0.852142	−	0.523310i	$-0.175303\pi$
$619$	−0.674947	−	1.16904i	−0.0271284	−	0.0469878i	−0.879271	+	0.476322i	$0.841970\pi$
$620$	18.0278			0.724014
$621$	7.39337			0.296686
$622$	−10.4837	−	18.1583i	−0.420358	−	0.728081i
$623$	−3.49111	+	28.4986i	−0.139868	+	1.14177i
$624$	−0.367074	+	3.58682i	−0.0146947	+	0.143588i
$625$	−30.9717	+	53.6446i	−1.23887	+	2.14578i
$626$	−9.55610	+	16.5517i	−0.381939	+	0.661537i
$627$	−1.49080	+	2.58215i	−0.0595369	+	0.103121i
$628$	5.80481	+	10.0542i	0.231637	+	0.401207i
$629$	14.2928			0.569892
$630$	−1.33240	+	10.8766i	−0.0530840	+	0.433334i
$631$	−20.8686	+	36.1455i	−0.830766	+	1.43893i	0.0666652	+	0.997775i	$0.478764\pi$
$631$	−20.8686	+	36.1455i	−0.830766	+	1.43893i	−0.897431	+	0.441154i	$0.854569\pi$
$632$	−1.15602	+	2.00229i	−0.0459840	+	0.0796467i
$633$	−1.95886			−0.0778577
$634$	−9.13122	+	15.8157i	−0.362647	+	0.628123i
$635$	31.7612			1.26040
$636$	−0.00384145			−0.000152324
$637$	24.8409	−	4.46452i	0.984231	−	0.176891i
$638$	−1.61183			−0.0638128
$639$	−7.97136			−0.315342
$640$	2.07085	−	3.58682i	0.0818575	−	0.141781i
$641$	−15.8022			−0.624149			−0.312075	−	0.950058i	$-0.601024\pi$
$641$	−15.8022			−0.624149			−0.312075	+	0.950058i	$0.601024\pi$
$642$	−2.69861	+	4.67412i	−0.106505	+	0.184473i
$643$	17.7586	−	30.7588i	0.700330	−	1.21301i	−0.268021	−	0.963413i	$-0.586370\pi$
$643$	17.7586	−	30.7588i	0.700330	−	1.21301i	0.968351	−	0.249594i	$-0.0802971\pi$
$644$	−2.37847	+	19.4159i	−0.0937248	+	0.765093i
$645$	−39.8870			−1.57055
$646$	7.19074	+	12.4547i	0.282916	+	0.490024i
$647$	3.99546	−	6.92034i	0.157078	−	0.272067i	−0.776736	−	0.629827i	$-0.783126\pi$
$647$	3.99546	−	6.92034i	0.157078	−	0.272067i	0.933814	+	0.357760i	$0.116459\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−2.12049	+	3.67280i	−0.0832366	+	0.144170i
$650$	−35.5220	−	25.6601i	−1.39329	−	1.00647i
$651$	−1.40029	+	11.4309i	−0.0548818	+	0.448010i
$652$	9.99637	+	17.3142i	0.391488	+	0.678077i
$653$	43.4971			1.70217			0.851086	−	0.525026i	$-0.175944\pi$
$653$	43.4971			1.70217			0.851086	+	0.525026i	$0.175944\pi$
$654$	−11.1627			−0.436495
$655$	−23.2926	−	40.3439i	−0.910116	−	1.57637i
$656$	2.33240	+	4.03983i	0.0910648	+	0.157729i
$657$	5.99080	−	10.3764i	0.233723	−	0.404821i
$658$	−23.5925	−	17.7679i	−0.919730	−	0.692664i
$659$	2.30892	−	3.99917i	0.0899429	−	0.155786i	−0.817544	−	0.575866i	$-0.804665\pi$
$659$	2.30892	−	3.99917i	0.0899429	−	0.155786i	0.907487	+	0.420081i	$0.137998\pi$
$660$	−2.16650			−0.0843309
$661$	−12.9276	+	22.3912i	−0.502824	+	0.870918i	0.497170	+	0.867653i	$0.334372\pi$
$661$	−12.9276	+	22.3912i	−0.502824	+	0.870918i	−0.999995	+	0.00326450i	$0.998961\pi$
$662$	−5.12199	−	8.87155i	−0.199072	−	0.344803i
$663$	0.926162	−	9.04988i	0.0359691	−	0.351468i
$664$	−3.08133			−0.119579
$665$	−7.59458	+	61.9959i	−0.294505	+	2.40410i
$666$	−2.83240	−	4.90586i	−0.109753	−	0.190098i
$667$	11.3907	+	19.7293i	0.441050	+	0.763921i
$668$	−8.82851	−	15.2914i	−0.341585	−	0.591643i
$669$	12.5364			0.484686
$670$	6.69390	+	11.5942i	0.258608	+	0.447922i
$671$	3.14483			0.121405
$672$	2.11344	+	1.59166i	0.0815275	+	0.0613997i
$673$	6.36967	+	11.0326i	0.245533	+	0.425275i	0.962281	−	0.272056i	$-0.0877038\pi$
$673$	6.36967	+	11.0326i	0.245533	+	0.425275i	−0.716748	+	0.697332i	$0.754370\pi$
$674$	32.6266			1.25673
$675$	6.07684	+	10.5254i	0.233898	+	0.405123i
$676$	8.64572	−	9.70832i	0.332528	−	0.373397i
$677$	12.1455	−	21.0367i	0.466791	−	0.808505i	−0.532490	−	0.846436i	$-0.678744\pi$
$677$	12.1455	−	21.0367i	0.466791	−	0.808505i	0.999280	+	0.0379314i	$0.0120768\pi$
$678$	2.03617	+	3.52676i	0.0781988	+	0.135444i
$679$	5.57489	+	4.19855i	0.213945	+	0.161125i
$680$	−5.22495	+	9.04988i	−0.200368	+	0.347047i
$681$	−10.8649	+	18.8186i	−0.416346	+	0.721132i
$682$	−2.27690			−0.0871871
$683$	9.96097			0.381146			0.190573	−	0.981673i	$-0.438965\pi$
$683$	9.96097			0.381146			0.190573	+	0.981673i	$0.438965\pi$
$684$	2.84997	−	4.93629i	0.108971	−	0.188744i
$685$	14.5422	−	25.1878i	0.555627	−	0.962375i
$686$	6.62259	−	17.2957i	0.252852	−	0.660353i
$687$	7.77570	+	13.4679i	0.296662	+	0.513833i
$688$	−4.81529	+	8.34033i	−0.183581	+	0.317972i
$689$	0.0112276	+	0.00811048i	0.000427736	+	0.000308985i
$690$	15.3106	+	26.5187i	0.582863	+	1.00955i
$691$	−28.2230			−1.07365			−0.536827	−	0.843692i	$-0.680377\pi$
$691$	−28.2230			−1.07365			−0.536827	+	0.843692i	$0.680377\pi$
$692$	1.93492	+	3.35139i	0.0735548	+	0.127401i
$693$	0.168281	−	1.37371i	0.00639247	−	0.0521829i
$694$	−8.43192			−0.320071
$695$	27.3022	+	47.2888i	1.03563	+	1.79377i
$696$	3.08133			0.116797
$697$	−5.88486	−	10.1929i	−0.222905	−	0.386083i
$698$	−18.3077	−	31.7099i	−0.692958	−	1.20024i
$699$	−10.3320	−	17.8955i	−0.390791	−	0.676870i
$700$	−29.5959	+	12.5725i	−1.11862	+	0.475194i
$701$	−1.33647			−0.0504778			−0.0252389	−	0.999681i	$-0.508035\pi$
$701$	−1.33647			−0.0504778			−0.0252389	+	0.999681i	$0.508035\pi$
$702$	−3.28981	+	1.47551i	−0.124166	+	0.0556897i
$703$	−16.1445	−	27.9631i	−0.608901	−	1.05465i
$704$	−0.261547	+	0.453013i	−0.00985743	+	0.0170736i
$705$	−46.2342			−1.74128
$706$	−2.61947	+	4.53705i	−0.0985850	+	0.170754i
$707$	−25.7511	−	19.3936i	−0.968470	−	0.729371i
$708$	4.05374	−	7.02129i	0.152349	−	0.263876i
$709$	16.7552	+	29.0208i	0.629254	+	1.08990i	0.987702	+	0.156350i	$0.0499728\pi$
$709$	16.7552	+	29.0208i	0.629254	+	1.08990i	−0.358448	+	0.933550i	$0.616694\pi$
$710$	−16.5075	−	28.5918i	−0.619515	−	1.07303i
$711$	−2.31204			−0.0867083
$712$	10.8520			0.406695
$713$	16.0908	+	27.8700i	0.602604	+	1.04374i
$714$	−5.33240	−	4.01592i	−0.199560	−	0.150292i
$715$	6.33211	+	4.57414i	0.236808	+	0.171063i
$716$	1.75984	−	3.04813i	0.0657683	−	0.113914i
$717$	−15.0486	+	26.0649i	−0.561998	+	0.973410i
$718$	2.54006	−	4.39951i	0.0947942	−	0.164188i
$719$	3.53164	+	6.11698i	0.131708	+	0.228125i	0.924335	−	0.381582i	$-0.124621\pi$
$719$	3.53164	+	6.11698i	0.131708	+	0.228125i	−0.792627	+	0.609707i	$0.791287\pi$
$720$	4.14170			0.154352
$721$	−28.8074	−	21.6953i	−1.07284	−	0.807975i
$722$	6.74463	−	11.6820i	0.251009	−	0.434760i
$723$	1.02609	−	1.77725i	0.0381609	−	0.0660965i
$724$	8.47129			0.314833
$725$	−18.7247	+	32.4322i	−0.695419	+	1.20450i
$726$	−10.7264			−0.398093
$727$	−22.2264			−0.824331			−0.412166	−	0.911109i	$-0.635228\pi$
$727$	−22.2264			−0.824331			−0.412166	+	0.911109i	$0.635228\pi$
$728$	−2.81653	−	9.11412i	−0.104388	−	0.337792i
$729$	1.00000			0.0370370
$730$	49.6242			1.83667
$731$	12.1494	−	21.0434i	0.449363	−	0.778320i
$732$	−6.01198			−0.222209
$733$	7.77847	−	13.4727i	0.287304	−	0.497626i	−0.685861	−	0.727732i	$-0.740574\pi$
$733$	7.77847	−	13.4727i	0.287304	−	0.497626i	0.973165	+	0.230107i	$0.0739076\pi$
$734$	2.43151	−	4.21150i	0.0897487	−	0.155449i
$735$	−8.00681	−	27.8643i	−0.295336	−	1.02779i
$736$	7.39337			0.272523
$737$	−0.845436	−	1.46434i	−0.0311420	−	0.0539396i
$738$	−2.33240	+	4.03983i	−0.0858567	+	0.148708i
$739$	3.19399	−	5.53216i	0.117493	−	0.203504i	−0.801281	−	0.598289i	$-0.795848\pi$
$739$	3.19399	−	5.53216i	0.117493	−	0.203504i	0.918774	+	0.394785i	$0.129181\pi$
$740$	11.7309	−	20.3186i	0.431238	−	0.746926i
$741$	−18.7517	+	8.41033i	−0.688861	+	0.308961i
$742$	0.00935447	−	0.00397382i	0.000343413	−	0.000145884i
$743$	−5.24875	−	9.09109i	−0.192558	−	0.333520i	0.753539	−	0.657403i	$-0.228345\pi$
$743$	−5.24875	−	9.09109i	−0.192558	−	0.333520i	−0.946097	+	0.323883i	$0.895012\pi$
$744$	4.35275			0.159580
$745$	75.0983			2.75139
$746$	14.4061	+	24.9521i	0.527445	+	0.913561i
$747$	−1.54066	−	2.66851i	−0.0563700	−	0.0976357i
$748$	0.659909	−	1.14300i	0.0241286	−	0.0417920i
$749$	1.73630	−	14.1737i	0.0634430	−	0.517897i
$750$	−14.8142	+	25.6589i	−0.540938	+	0.936932i
$751$	16.5633			0.604404			0.302202	−	0.953244i	$-0.402278\pi$
$751$	16.5633			0.604404			0.302202	+	0.953244i	$0.402278\pi$
$752$	−5.58154	+	9.66752i	−0.203538	+	0.352538i
$753$	8.23457	+	14.2627i	0.300084	+	0.519761i
$754$	−9.00592	−	6.50562i	−0.327976	−	0.236921i
$755$	20.9854			0.763739
$756$	−0.321703	+	2.62612i	−0.0117002	+	0.0955111i
$757$	−13.5475	−	23.4649i	−0.492391	−	0.852847i	0.507570	−	0.861610i	$-0.330544\pi$
$757$	−13.5475	−	23.4649i	−0.492391	−	0.852847i	−0.999962	+	0.00876370i	$0.997210\pi$
$758$	14.1550	+	24.5172i	0.514133	+	0.890504i
$759$	−1.93372	−	3.34929i	−0.0701894	−	0.121572i
$760$	23.6074			0.856331
$761$	1.40179	+	2.42797i	0.0508148	+	0.0880139i	0.890314	−	0.455347i	$-0.150485\pi$
$761$	1.40179	+	2.42797i	0.0508148	+	0.0880139i	−0.839499	+	0.543361i	$0.817151\pi$
$762$	7.66864			0.277805
$763$	27.1826	−	11.5473i	0.984077	−	0.418040i
$764$	10.9754	+	19.0099i	0.397075	+	0.687755i
$765$	−10.4499			−0.377817
$766$	−9.36815	−	16.2261i	−0.338485	−	0.586273i
$767$	−26.6721	+	11.9627i	−0.963074	+	0.431948i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−4.67209	−	8.09231i	−0.168480	−	0.291816i	0.769406	−	0.638761i	$-0.220553\pi$
$769$	−4.67209	−	8.09231i	−0.168480	−	0.291816i	−0.937886	+	0.346945i	$0.887219\pi$
$770$	5.27573	−	2.24115i	0.190124	−	0.0807655i
$771$	5.93711	−	10.2834i	0.213820	−	0.370346i
$772$	−6.42959	+	11.1364i	−0.231406	+	0.400807i
$773$	50.5572			1.81841			0.909207	−	0.416344i	$-0.136689\pi$
$773$	50.5572			1.81841			0.909207	+	0.416344i	$0.136689\pi$
$774$	−9.63058			−0.346164
$775$	−26.4510	+	45.8144i	−0.950147	+	1.64570i
$776$	1.31892	−	2.28443i	0.0473464	−	0.0820063i
$777$	11.9722	+	9.01644i	0.429499	+	0.323463i
$778$	−3.55307	−	6.15409i	−0.127384	−	0.220635i
$779$	−13.2945	+	23.0268i	−0.476325	+	0.825020i
$780$	−12.1051	−	8.74439i	−0.433432	−	0.313099i
$781$	2.08489	+	3.61113i	0.0746031	+	0.129216i
$782$	−18.6542			−0.667072
$783$	1.54066	+	2.66851i	0.0550589	+	0.0953648i
$784$	−6.79301	−	1.68966i	−0.242608	−	0.0603450i
$785$	−48.0836			−1.71618
$786$	−5.62392	−	9.74091i	−0.200598	−	0.347447i
$787$	5.54021			0.197487			0.0987436	−	0.995113i	$-0.468518\pi$
$787$	5.54021			0.197487			0.0987436	+	0.995113i	$0.468518\pi$
$788$	−5.27054	−	9.12883i	−0.187755	−	0.325201i
$789$	12.5158	+	21.6781i	0.445576	+	0.771760i
$790$	−4.78789	−	8.29287i	−0.170346	−	0.295047i
$791$	−8.60664	−	6.48180i	−0.306017	−	0.230466i
$792$	−0.523095			−0.0185874
$793$	17.5714	+	12.6931i	0.623980	+	0.450745i
$794$	19.6633	+	34.0578i	0.697824	+	1.20867i
$795$	0.00795507	−	0.0137786i	0.000282137	−	0.000488676i
$796$	13.1036			0.464446
$797$	−4.90846	+	8.50171i	−0.173867	+	0.301146i	−0.939768	−	0.341812i	$-0.888960\pi$
$797$	−4.90846	+	8.50171i	−0.173867	+	0.301146i	0.765902	+	0.642958i	$0.222293\pi$
$798$	−1.83369	+	14.9687i	−0.0649118	+	0.529887i
$799$	14.0828	−	24.3921i	0.498212	−	0.862929i
$800$	6.07684	+	10.5254i	0.214849	+	0.372129i
$801$	5.42599	+	9.39808i	0.191718	+	0.332065i
$802$	8.60307			0.303785
$803$	−6.26751			−0.221176
$804$	1.61622	+	2.79938i	0.0569997	+	0.0987264i
$805$	−64.7158	−	48.7385i	−2.28093	−	1.71781i
$806$	−12.7220	−	9.18998i	−0.448112	−	0.323703i
$807$	−7.76501	+	13.4494i	−0.273341	+	0.473441i
$808$	−6.09224	+	10.5521i	−0.214324	+	0.371220i
$809$	20.3684	−	35.2791i	0.716114	−	1.24035i	−0.246414	−	0.969165i	$-0.579252\pi$
$809$	20.3684	−	35.2791i	0.716114	−	1.24035i	0.962528	−	0.271181i	$-0.0874143\pi$
$810$	2.07085	+	3.58682i	0.0727622	+	0.126028i
$811$	−23.9184			−0.839887			−0.419944	−	0.907550i	$-0.637950\pi$
$811$	−23.9184			−0.839887			−0.419944	+	0.907550i	$0.637950\pi$
$812$	−7.50346	+	3.18750i	−0.263320	+	0.111859i
$813$	−2.63845	+	4.56993i	−0.0925345	+	0.160274i
$814$	−1.48161	+	2.56623i	−0.0519305	+	0.0899462i
$815$	−82.8039			−2.90050
$816$	−1.26155	+	2.18506i	−0.0441630	+	0.0764925i
$817$	−54.8937			−1.92049
$818$	36.5325			1.27733
$819$	6.48479	−	6.99625i	0.226597	−	0.244469i
$820$	−19.3202			−0.674690
$821$	−21.9250			−0.765187			−0.382594	−	0.923917i	$-0.624969\pi$
$821$	−21.9250			−0.765187			−0.382594	+	0.923917i	$0.624969\pi$
$822$	3.51116	−	6.08150i	0.122466	−	0.212117i
$823$	−2.58998			−0.0902809			−0.0451404	−	0.998981i	$-0.514374\pi$
$823$	−2.58998			−0.0902809			−0.0451404	+	0.998981i	$0.514374\pi$
$824$	−6.81529	+	11.8044i	−0.237422	+	0.411227i
$825$	3.17876	−	5.50578i	0.110670	−	0.191686i
$826$	−2.60820	+	21.2912i	−0.0907510	+	0.740817i
$827$	8.21658			0.285718			0.142859	−	0.989743i	$-0.454370\pi$
$827$	8.21658			0.285718			0.142859	+	0.989743i	$0.454370\pi$
$828$	3.69669	+	6.40285i	0.128469	+	0.222514i
$829$	4.31494	−	7.47369i	0.149864	−	0.259572i	−0.781313	−	0.624139i	$-0.785450\pi$
$829$	4.31494	−	7.47369i	0.149864	−	0.259572i	0.931177	+	0.364567i	$0.118783\pi$
$830$	6.38097	−	11.0522i	0.221487	−	0.383626i
$831$	−5.56594	+	9.64049i	−0.193080	+	0.334425i
$832$	−3.28981	+	1.47551i	−0.114054	+	0.0511542i
$833$	17.1394	+	4.26318i	0.593846	+	0.147710i
$834$	6.59202	+	11.4177i	0.228263	+	0.395363i
$835$	73.1301			2.53077
$836$	−2.98160			−0.103121
$837$	2.17638	+	3.76959i	0.0752266	+	0.130296i
$838$	−6.77818	−	11.7402i	−0.234148	−	0.405557i
$839$	0.656067	−	1.13634i	0.0226499	−	0.0392309i	−0.854478	−	0.519487i	$-0.826123\pi$
$839$	0.656067	−	1.13634i	0.0226499	−	0.0392309i	0.877128	+	0.480256i	$0.159456\pi$
$840$	−10.0856	+	4.28441i	−0.347987	+	0.147826i
$841$	9.75270	−	16.8922i	0.336300	−	0.582489i
$842$	−4.50209			−0.155152
$843$	9.69540	−	16.7929i	0.333927	−	0.578379i
$844$	−0.979430	−	1.69642i	−0.0337134	−	0.0583933i
$845$	16.9180	+	51.1151i	0.581996	+	1.75841i
$846$	−11.1631			−0.383795
$847$	26.1202	−	11.0960i	0.897501	−	0.381262i
$848$	−0.00192073	−	0.00332680i	−6.59580e−5	−	0.000114243i
$849$	13.0180	+	22.5478i	0.446775	+	0.773838i
$850$	−15.3324	−	26.5566i	−0.525898	−	0.910882i
$851$	41.8819			1.43569
$852$	−3.98568	−	6.90340i	−0.136547	−	0.236507i
$853$	3.91347			0.133995			0.0669974	−	0.997753i	$-0.478658\pi$
$853$	3.91347			0.133995			0.0669974	+	0.997753i	$0.478658\pi$
$854$	14.6400	−	6.21913i	0.500970	−	0.212814i
$855$	11.8037	+	20.4446i	0.403678	+	0.699191i
$856$	−5.39721			−0.184473
$857$	−20.7141	−	35.8779i	−0.707580	−	1.22556i	−0.965752	−	0.259466i	$-0.916454\pi$
$857$	−20.7141	−	35.8779i	−0.707580	−	1.22556i	0.258172	−	0.966099i	$-0.416880\pi$
$858$	1.52887	+	1.10441i	0.0521947	+	0.0377040i
$859$	−6.13898	+	10.6330i	−0.209459	+	0.362794i	−0.951544	−	0.307511i	$-0.900504\pi$
$859$	−6.13898	+	10.6330i	−0.209459	+	0.362794i	0.742085	+	0.670306i	$0.233837\pi$
$860$	−19.9435	−	34.5431i	−0.680067	−	1.17791i
$861$	1.50068	−	12.2503i	0.0511430	−	0.417489i
$862$	−0.253853	+	0.439686i	−0.00864626	+	0.0149758i
$863$	18.8040	−	32.5694i	0.640095	−	1.10868i	−0.345316	−	0.938486i	$-0.612228\pi$
$863$	18.8040	−	32.5694i	0.640095	−	1.10868i	0.985411	−	0.170191i	$-0.0544383\pi$
$864$	1.00000			0.0340207
$865$	−16.0277			−0.544960
$866$	6.41093	−	11.1041i	0.217852	−	0.377331i
$867$	−5.31700	+	9.20931i	−0.180575	+	0.312765i
$868$	−10.5996	+	4.50274i	−0.359772	+	0.152833i
$869$	0.604708	+	1.04739i	0.0205133	+	0.0355301i
$870$	−6.38097	+	11.0522i	−0.216335	+	0.374703i
$871$	1.18654	−	11.5942i	0.0402045	−	0.392854i
$872$	−5.58133	−	9.66715i	−0.189008	−	0.327371i
$873$	2.63784			0.0892772
$874$	21.0709	+	36.4958i	0.712733	+	1.23449i
$875$	9.53154	−	77.8077i	0.322225	−	2.63038i
$876$	11.9816			0.404821
$877$	11.5660	+	20.0329i	0.390557	+	0.676465i	0.992523	−	0.122057i	$-0.0389491\pi$
$877$	11.5660	+	20.0329i	0.390557	+	0.676465i	−0.601966	+	0.798522i	$0.705616\pi$
$878$	0.433280			0.0146225
$879$	6.46216	+	11.1928i	0.217963	+	0.377523i
$880$	−1.08325	−	1.87624i	−0.0365164	−	0.0632482i
$881$	−25.2659	−	43.7618i	−0.851229	−	1.47437i	−0.880100	−	0.474788i	$-0.842525\pi$
$881$	−25.2659	−	43.7618i	−0.851229	−	1.47437i	0.0288713	−	0.999583i	$-0.490809\pi$
$882$	−1.93322	−	6.72775i	−0.0650948	−	0.226535i
$883$	30.7977			1.03643			0.518213	−	0.855251i	$-0.326597\pi$
$883$	30.7977			1.03643			0.518213	+	0.855251i	$0.326597\pi$
$884$	8.30051	−	3.72286i	0.279176	−	0.125213i
$885$	16.7894	+	29.0801i	0.564369	+	0.977516i
$886$	7.03339	−	12.1822i	0.236291	−	0.409269i
$887$	20.0317			0.672597			0.336299	−	0.941755i	$-0.390825\pi$
$887$	20.0317			0.672597			0.336299	+	0.941755i	$0.390825\pi$
$888$	2.83240	−	4.90586i	0.0950490	−	0.164630i
$889$	−18.6742	+	7.93287i	−0.626312	+	0.266060i
$890$	−22.4728	+	38.9240i	−0.753290	+	1.30474i
$891$	−0.261547	−	0.453013i	−0.00876216	−	0.0151765i
$892$	6.26821	+	10.8569i	0.209875	+	0.363515i
$893$	−63.6289			−2.12926
$894$	18.1322			0.606433
$895$	7.28873	+	12.6245i	0.243635	+	0.421989i
$896$	−0.321703	+	2.62612i	−0.0107473	+	0.0877325i
$897$	2.71391	−	26.5187i	0.0906149	−	0.885433i
$898$	−15.2892	+	26.4817i	−0.510207	+	0.883705i
$899$	−6.70613	+	11.6154i	−0.223662	+	0.387394i
$900$	−6.07684	+	10.5254i	−0.202561	+	0.350846i
$901$	0.00484618	+	0.00839382i	0.000161450	+	0.000279639i
$902$	2.44013			0.0812474
$903$	23.4518	−	9.96242i	0.780427	−	0.331529i
$904$	−2.03617	+	3.52676i	−0.0677221	+	0.117298i
$905$	−17.5428	+	30.3850i	−0.583141	+	1.01003i
$906$	5.06687			0.168335
$907$	−7.83200	+	13.5654i	−0.260057	+	0.450432i	−0.966257	−	0.257580i	$-0.917075\pi$
$907$	−7.83200	+	13.5654i	−0.260057	+	0.450432i	0.706200	+	0.708013i	$0.250408\pi$
$908$	−21.7299			−0.721132
$909$	−12.1845			−0.404134
$910$	38.5233	+	8.77158i	1.27703	+	0.290775i
$911$	6.84991			0.226948			0.113474	−	0.993541i	$-0.463802\pi$
$911$	6.84991			0.226948			0.113474	+	0.993541i	$0.463802\pi$
$912$	5.69993			0.188744
$913$	−0.805913	+	1.39588i	−0.0266718	+	0.0461970i
$914$	−2.31026			−0.0764165
$915$	12.4499	−	21.5639i	0.411581	−	0.712879i
$916$	−7.77570	+	13.4679i	−0.256917	+	0.444992i
$917$	23.7716	+	17.9028i	0.785006	+	0.591201i
$918$	−2.52309			−0.0832745
$919$	−4.77437	−	8.26945i	−0.157492	−	0.272784i	0.776472	−	0.630152i	$-0.217008\pi$
$919$	−4.77437	−	8.26945i	−0.157492	−	0.272784i	−0.933964	+	0.357368i	$0.883674\pi$
$920$	−15.3106	+	26.5187i	−0.504774	+	0.874295i
$921$	10.0386	−	17.3873i	0.330782	−	0.572931i
$922$	15.0409	−	26.0516i	0.495345	−	0.857963i
$923$	−2.92608	+	28.5918i	−0.0963130	+	0.941111i
$924$	1.27381	−	0.541119i	0.0419052	−	0.0178015i
$925$	34.4240	+	59.6242i	1.13186	+	1.96043i
$926$	−29.4727			−0.968532
$927$	−13.6306			−0.447687
$928$	1.54066	+	2.66851i	0.0505748	+	0.0875981i
$929$	19.9328	+	34.5247i	0.653975	+	1.13272i	0.982150	+	0.188101i	$0.0602334\pi$
$929$	19.9328	+	34.5247i	0.653975	+	1.13272i	−0.328174	+	0.944617i	$0.606433\pi$
$930$	−9.01390	+	15.6125i	−0.295577	+	0.511955i
$931$	−11.0192	−	38.3478i	−0.361140	−	1.25680i
$932$	10.3320	−	17.8955i	0.338435	−	0.586187i
$933$	20.9674			0.686441
$934$	−2.92442	+	5.06525i	−0.0956900	+	0.165740i
$935$	2.73314	+	4.73394i	0.0893833	+	0.154816i
$936$	−2.92274	−	2.11130i	−0.0955327	−	0.0690101i
$937$	−11.4259			−0.373268			−0.186634	−	0.982430i	$-0.559758\pi$
$937$	−11.4259			−0.373268			−0.186634	+	0.982430i	$0.559758\pi$
$938$	−6.83156	−	5.14496i	−0.223058	−	0.167989i
$939$	−9.55610	−	16.5517i	−0.311852	−	0.540143i
$940$	−23.1171	−	40.0400i	−0.753996	−	1.30596i
$941$	19.0547	+	33.0037i	0.621165	+	1.07589i	0.989269	+	0.146104i	$0.0466735\pi$
$941$	19.0547	+	33.0037i	0.621165	+	1.07589i	−0.368105	+	0.929784i	$0.619993\pi$
$942$	−11.6096			−0.378262
$943$	−17.2443	−	29.8680i	−0.561551	−	0.972635i
$944$	8.10749			0.263876
$945$	−8.75321	−	6.59219i	−0.284742	−	0.214444i
$946$	2.51885	+	4.36278i	0.0818950	+	0.141846i
$947$	−8.09255			−0.262973			−0.131486	−	0.991318i	$-0.541975\pi$
$947$	−8.09255			−0.262973			−0.131486	+	0.991318i	$0.541975\pi$
$948$	−1.15602	−	2.00229i	−0.0375458	−	0.0650313i
$949$	−35.0191	−	25.2968i	−1.13677	−	0.821169i
$950$	−34.6376	+	59.9940i	−1.12379	+	1.94646i
$951$	−9.13122	−	15.8157i	−0.296100	−	0.512860i
$952$	0.811687	−	6.62595i	0.0263069	−	0.214748i
$953$	−2.17357	+	3.76473i	−0.0704088	+	0.121952i	−0.899081	−	0.437783i	$-0.855764\pi$
$953$	−2.17357	+	3.76473i	−0.0704088	+	0.121952i	0.828672	+	0.559735i	$0.189097\pi$
$954$	0.00192073	−	0.00332680i	6.21858e−5	−	0.000107709i
$955$	−90.9134			−2.94189
$956$	−30.0971			−0.973410
$957$	0.805913	−	1.39588i	0.0260515	−	0.0451225i
$958$	8.66374	−	15.0060i	0.279913	−	0.484823i
$959$	−2.25910	+	18.4414i	−0.0729501	+	0.595505i
$960$	2.07085	+	3.58682i	0.0668364	+	0.115764i
$961$	6.02677	−	10.4387i	0.194412	−	0.336731i
$962$	−18.6361	+	8.35848i	−0.600852	+	0.269488i
$963$	−2.69861	−	4.67412i	−0.0869614	−	0.150622i
$964$	2.05219			0.0660965
$965$	−26.6294	−	46.1235i	−0.857232	−	1.48477i
$966$	−15.6254	−	11.7678i	−0.502739	−	0.378621i
$967$	−6.10945			−0.196467			−0.0982333	−	0.995163i	$-0.531319\pi$
$967$	−6.10945			−0.196467			−0.0982333	+	0.995163i	$0.531319\pi$
$968$	−5.36319	−	9.28931i	−0.172379	−	0.298570i
$969$	−14.3815			−0.462000
$970$	5.46256	+	9.46143i	0.175392	+	0.303788i
$971$	−3.52129	−	6.09906i	−0.113004	−	0.195728i	0.803976	−	0.594661i	$-0.202714\pi$
$971$	−3.52129	−	6.09906i	−0.113004	−	0.195728i	−0.916980	+	0.398933i	$0.869381\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−27.8636	−	20.9846i	−0.893267	−	0.672734i
$974$	38.0645			1.21967
$975$	39.9833	−	17.9329i	1.28049	−	0.574313i
$976$	−3.00599	−	5.20652i	−0.0962193	−	0.166657i
$977$	−15.4653	+	26.7867i	−0.494779	+	0.856982i	−0.999982	−	0.00601874i	$-0.998084\pi$
$977$	−15.4653	+	26.7867i	−0.494779	+	0.856982i	0.505203	+	0.863000i	$0.331417\pi$
$978$	−19.9927			−0.639298
$979$	2.83830	−	4.91609i	0.0907126	−	0.157119i
$980$	20.1278	−	20.8663i	0.642960	−	0.666548i
$981$	5.58133	−	9.66715i	0.178198	−	0.308648i
$982$	8.22130	+	14.2397i	0.262352	+	0.454407i
$983$	14.5237	+	25.1559i	0.463235	+	0.802347i	0.999120	−	0.0419441i	$-0.0133551\pi$
$983$	14.5237	+	25.1559i	0.463235	+	0.802347i	−0.535885	+	0.844291i	$0.680022\pi$
$984$	−4.66479			−0.148708
$985$	43.6579			1.39106
$986$	−3.88724	−	6.73290i	−0.123795	−	0.214419i
$987$	27.1837	−	11.5477i	0.865266	−	0.367568i
$988$	−16.6594	−	12.0343i	−0.530007	−	0.382862i
$989$	35.6012	−	61.6631i	1.13205	−	1.96077i
$990$	1.08325	−	1.87624i	0.0344280	−	0.0596310i
$991$	6.96955	−	12.0716i	0.221395	−	0.383468i	−0.733837	−	0.679326i	$-0.762272\pi$
$991$	6.96955	−	12.0716i	0.221395	−	0.383468i	0.955232	+	0.295858i	$0.0956056\pi$
$992$	2.17638	+	3.76959i	0.0691000	+	0.119685i
$993$	10.2440			0.325083
$994$	16.8469	+	12.6877i	0.534353	+	0.402430i
$995$	−27.1357	+	47.0004i	−0.860259	+	1.49001i
$996$	1.54066	−	2.66851i	0.0488178	−	0.0845550i
$997$	−36.8250			−1.16626			−0.583129	−	0.812379i	$-0.698172\pi$
$997$	−36.8250			−1.16626			−0.583129	+	0.812379i	$0.698172\pi$
$998$	3.74298	−	6.48304i	0.118482	−	0.205217i
$999$	5.66479			0.179226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.e.289.1	✓	10
3.2	odd	2		1638.2.m.k.289.5		10
7.4	even	3		546.2.k.e.445.1	yes	10
13.9	even	3		546.2.k.e.373.1	yes	10
21.11	odd	6		1638.2.p.j.991.5		10
39.35	odd	6		1638.2.p.j.919.5		10
91.74	even	3	inner	546.2.j.e.529.1	yes	10
273.74	odd	6		1638.2.m.k.1621.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.1	✓	10	1.1	even	1	trivial
546.2.j.e.529.1	yes	10	91.74	even	3	inner
546.2.k.e.373.1	yes	10	13.9	even	3
546.2.k.e.445.1	yes	10	7.4	even	3
1638.2.m.k.289.5		10	3.2	odd	2
1638.2.m.k.1621.5		10	273.74	odd	6
1638.2.p.j.919.5		10	39.35	odd	6
1638.2.p.j.991.5		10	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-2.07085 + 3.58682i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.321703 - 2.62612i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-2.07085 + 3.58682i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.321703 - 2.62612i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.07085 - 3.58682i) q^{10} +(-0.261547 + 0.453013i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.28981 + 1.47551i) q^{13} +(-0.321703 + 2.62612i) q^{14} +(2.07085 + 3.58682i) q^{15} +1.00000 q^{16} -2.52309 q^{17} +(0.500000 + 0.866025i) q^{18} +(2.84997 + 4.93629i) q^{19} +(-2.07085 + 3.58682i) q^{20} +(-2.11344 - 1.59166i) q^{21} +(0.261547 - 0.453013i) q^{22} -7.39337 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-6.07684 - 10.5254i) q^{25} +(3.28981 - 1.47551i) q^{26} -1.00000 q^{27} +(0.321703 - 2.62612i) q^{28} +(-1.54066 - 2.66851i) q^{29} +(-2.07085 - 3.58682i) q^{30} +(-2.17638 - 3.76959i) q^{31} -1.00000 q^{32} +(0.261547 + 0.453013i) q^{33} +2.52309 q^{34} +(8.75321 + 6.59219i) q^{35} +(-0.500000 - 0.866025i) q^{36} -5.66479 q^{37} +(-2.84997 - 4.93629i) q^{38} +(-0.367074 + 3.58682i) q^{39} +(2.07085 - 3.58682i) q^{40} +(2.33240 + 4.03983i) q^{41} +(2.11344 + 1.59166i) q^{42} +(-4.81529 + 8.34033i) q^{43} +(-0.261547 + 0.453013i) q^{44} +4.14170 q^{45} +7.39337 q^{46} +(-5.58154 + 9.66752i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-6.79301 - 1.68966i) q^{49} +(6.07684 + 10.5254i) q^{50} +(-1.26155 + 2.18506i) q^{51} +(-3.28981 + 1.47551i) q^{52} +(-0.00192073 - 0.00332680i) q^{53} +1.00000 q^{54} +(-1.08325 - 1.87624i) q^{55} +(-0.321703 + 2.62612i) q^{56} +5.69993 q^{57} +(1.54066 + 2.66851i) q^{58} +8.10749 q^{59} +(2.07085 + 3.58682i) q^{60} +(-3.00599 - 5.20652i) q^{61} +(2.17638 + 3.76959i) q^{62} +(-2.43514 + 1.03446i) q^{63} +1.00000 q^{64} +(1.52031 - 14.8555i) q^{65} +(-0.261547 - 0.453013i) q^{66} +(-1.61622 + 2.79938i) q^{67} -2.52309 q^{68} +(-3.69669 + 6.40285i) q^{69} +(-8.75321 - 6.59219i) q^{70} +(3.98568 - 6.90340i) q^{71} +(0.500000 + 0.866025i) q^{72} +(5.99080 + 10.3764i) q^{73} +5.66479 q^{74} -12.1537 q^{75} +(2.84997 + 4.93629i) q^{76} +(1.10553 + 0.832590i) q^{77} +(0.367074 - 3.58682i) q^{78} +(1.15602 - 2.00229i) q^{79} +(-2.07085 + 3.58682i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.33240 - 4.03983i) q^{82} +3.08133 q^{83} +(-2.11344 - 1.59166i) q^{84} +(5.22495 - 9.04988i) q^{85} +(4.81529 - 8.34033i) q^{86} -3.08133 q^{87} +(0.261547 - 0.453013i) q^{88} -10.8520 q^{89} -4.14170 q^{90} +(2.81653 + 9.11412i) q^{91} -7.39337 q^{92} -4.35275 q^{93} +(5.58154 - 9.66752i) q^{94} -23.6074 q^{95} +(-0.500000 + 0.866025i) q^{96} +(-1.31892 + 2.28443i) q^{97} +(6.79301 + 1.68966i) q^{98} +0.523095 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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