LMFDB - Embedded newform 546.2.j.c.289.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 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			289.2
Root			$-0.571299 + 1.29368i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.c.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.369922 + 2.61976i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.369922 + 2.61976i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.441221 + 0.764218i) q^{10} +(-0.775934 + 1.34396i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.13422 + 2.90605i) q^{13} +(0.369922 + 2.61976i) q^{14} +(-0.441221 - 0.764218i) q^{15} +1.00000 q^{16} -7.17592 q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.37080 - 4.10635i) q^{19} +(-0.441221 + 0.764218i) q^{20} +(-2.45374 - 0.989520i) q^{21} +(-0.775934 + 1.34396i) q^{22} +5.29348 q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.11065 + 3.65575i) q^{25} +(2.13422 + 2.90605i) q^{26} +1.00000 q^{27} +(0.369922 + 2.61976i) q^{28} +(3.87494 + 6.71160i) q^{29} +(-0.441221 - 0.764218i) q^{30} +(3.24911 + 5.62762i) q^{31} +1.00000 q^{32} +(-0.775934 - 1.34396i) q^{33} -7.17592 q^{34} +(-2.16529 - 0.873194i) q^{35} +(-0.500000 - 0.866025i) q^{36} +0.330574 q^{37} +(-2.37080 - 4.10635i) q^{38} +(-3.58382 + 0.395262i) q^{39} +(-0.441221 + 0.764218i) q^{40} +(-3.02918 - 5.24669i) q^{41} +(-2.45374 - 0.989520i) q^{42} +(3.35975 - 5.81927i) q^{43} +(-0.775934 + 1.34396i) q^{44} +0.882443 q^{45} +5.29348 q^{46} +(0.976430 - 1.69123i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-6.72632 + 1.93822i) q^{49} +(2.11065 + 3.65575i) q^{50} +(3.58796 - 6.21453i) q^{51} +(2.13422 + 2.90605i) q^{52} +(-6.74308 - 11.6794i) q^{53} +1.00000 q^{54} +(-0.684718 - 1.18597i) q^{55} +(0.369922 + 2.61976i) q^{56} +4.74161 q^{57} +(3.87494 + 6.71160i) q^{58} +5.27138 q^{59} +(-0.441221 - 0.764218i) q^{60} +(7.17592 + 12.4291i) q^{61} +(3.24911 + 5.62762i) q^{62} +(2.08382 - 1.63024i) q^{63} +1.00000 q^{64} +(-3.16252 + 0.348796i) q^{65} +(-0.775934 - 1.34396i) q^{66} +(3.75236 - 6.49929i) q^{67} -7.17592 q^{68} +(-2.64674 + 4.58428i) q^{69} +(-2.16529 - 0.873194i) q^{70} +(5.00985 - 8.67732i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.93284 - 3.34778i) q^{73} +0.330574 q^{74} -4.22129 q^{75} +(-2.37080 - 4.10635i) q^{76} +(-3.80789 - 1.53560i) q^{77} +(-3.58382 + 0.395262i) q^{78} +(6.67928 - 11.5689i) q^{79} +(-0.441221 + 0.764218i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.02918 - 5.24669i) q^{82} -10.5519 q^{83} +(-2.45374 - 0.989520i) q^{84} +(3.16617 - 5.48396i) q^{85} +(3.35975 - 5.81927i) q^{86} -7.74989 q^{87} +(-0.775934 + 1.34396i) q^{88} +14.8167 q^{89} +0.882443 q^{90} +(-6.82366 + 6.66615i) q^{91} +5.29348 q^{92} -6.49821 q^{93} +(0.976430 - 1.69123i) q^{94} +4.18420 q^{95} +(-0.500000 + 0.866025i) q^{96} +(5.79259 - 10.0331i) q^{97} +(-6.72632 + 1.93822i) q^{98} +1.55187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 2 q^{25} + 3 q^{26} + 8 q^{27} + 3 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} + 4 q^{34} - 22 q^{35} - 4 q^{36} + 12 q^{37} - 4 q^{38} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 3 q^{42} + 4 q^{44} - 4 q^{45} - 8 q^{46} + 7 q^{47} - 4 q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - q^{53} + 8 q^{54} - 25 q^{55} + 3 q^{56} + 8 q^{57} + 2 q^{58} - 32 q^{59} + 2 q^{60} - 4 q^{61} + 14 q^{62} + 8 q^{64} + 10 q^{65} + 4 q^{66} + 19 q^{67} + 4 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} - 4 q^{72} - 7 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} + 2 q^{80} - 4 q^{81} + 12 q^{82} - 64 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{87} + 4 q^{88} + 22 q^{89} - 4 q^{90} - 38 q^{91} - 8 q^{92} - 28 q^{93} + 7 q^{94} - 56 q^{95} - 4 q^{96} + 11 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 + 8 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 2 * q^25 + 3 * q^26 + 8 * q^27 + 3 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 + 4 * q^34 - 22 * q^35 - 4 * q^36 + 12 * q^37 - 4 * q^38 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 3 * q^42 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 7 * q^47 - 4 * q^48 + 5 * q^49 + 2 * q^50 - 2 * q^51 + 3 * q^52 - q^53 + 8 * q^54 - 25 * q^55 + 3 * q^56 + 8 * q^57 + 2 * q^58 - 32 * q^59 + 2 * q^60 - 4 * q^61 + 14 * q^62 + 8 * q^64 + 10 * q^65 + 4 * q^66 + 19 * q^67 + 4 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 - 4 * q^72 - 7 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 + 2 * q^80 - 4 * q^81 + 12 * q^82 - 64 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^87 + 4 * q^88 + 22 * q^89 - 4 * q^90 - 38 * q^91 - 8 * q^92 - 28 * q^93 + 7 * q^94 - 56 * q^95 - 4 * q^96 + 11 * q^97 + 5 * q^98 - 8 * 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
$5$	−0.441221	+	0.764218i	−0.197320	+	0.341769i	−0.947659	−	0.319285i	$-0.896557\pi$
$5$	−0.441221	+	0.764218i	−0.197320	+	0.341769i	0.750338	+	0.661054i	$0.229891\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.369922	+	2.61976i	0.139817	+	0.990177i
$7$	0.369922	+	2.61976i	0.139817	+	0.990177i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.441221	+	0.764218i	−0.139526	+	0.241667i
$11$	−0.775934	+	1.34396i	−0.233953	+	0.405219i	−0.958968	−	0.283515i	$-0.908500\pi$
$11$	−0.775934	+	1.34396i	−0.233953	+	0.405219i	0.725015	+	0.688733i	$0.241833\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.13422	+	2.90605i	0.591925	+	0.805993i
$13$	2.13422	+	2.90605i	0.591925	+	0.805993i
$14$	0.369922	+	2.61976i	0.0988658	+	0.700161i
$15$	−0.441221	−	0.764218i	−0.113923	−	0.197320i
$16$	1.00000			0.250000
$17$	−7.17592			−1.74042			−0.870208	−	0.492685i	$-0.836016\pi$
$17$	−7.17592			−1.74042			−0.870208	+	0.492685i	$0.836016\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−2.37080	−	4.10635i	−0.543900	−	0.942062i	−0.998675	−	0.0514558i	$-0.983614\pi$
$19$	−2.37080	−	4.10635i	−0.543900	−	0.942062i	0.454776	−	0.890606i	$-0.349719\pi$
$20$	−0.441221	+	0.764218i	−0.0986601	+	0.170884i
$21$	−2.45374	−	0.989520i	−0.535450	−	0.215931i
$22$	−0.775934	+	1.34396i	−0.165430	+	0.286533i
$23$	5.29348			1.10377			0.551883	−	0.833922i	$-0.313909\pi$
$23$	5.29348			1.10377			0.551883	+	0.833922i	$0.313909\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.11065	+	3.65575i	0.422129	+	0.731150i
$26$	2.13422	+	2.90605i	0.418554	+	0.569923i
$27$	1.00000			0.192450
$28$	0.369922	+	2.61976i	0.0699087	+	0.495089i
$29$	3.87494	+	6.71160i	0.719559	+	1.24631i	0.961175	+	0.275940i	$0.0889893\pi$
$29$	3.87494	+	6.71160i	0.719559	+	1.24631i	−0.241616	+	0.970372i	$0.577677\pi$
$30$	−0.441221	−	0.764218i	−0.0805556	−	0.139526i
$31$	3.24911	+	5.62762i	0.583557	+	1.01075i	0.995054	+	0.0993390i	$0.0316728\pi$
$31$	3.24911	+	5.62762i	0.583557	+	1.01075i	−0.411497	+	0.911411i	$0.634994\pi$
$32$	1.00000			0.176777
$33$	−0.775934	−	1.34396i	−0.135073	−	0.233953i
$34$	−7.17592			−1.23066
$35$	−2.16529	−	0.873194i	−0.366000	−	0.147597i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	0.330574			0.0543460			0.0271730	−	0.999631i	$-0.491349\pi$
$37$	0.330574			0.0543460			0.0271730	+	0.999631i	$0.491349\pi$
$38$	−2.37080	−	4.10635i	−0.384595	−	0.666138i
$39$	−3.58382	+	0.395262i	−0.573871	+	0.0632926i
$40$	−0.441221	+	0.764218i	−0.0697632	+	0.120833i
$41$	−3.02918	−	5.24669i	−0.473079	−	0.819396i	0.526447	−	0.850208i	$-0.323524\pi$
$41$	−3.02918	−	5.24669i	−0.473079	−	0.819396i	−0.999525	+	0.0308121i	$0.990191\pi$
$42$	−2.45374	−	0.989520i	−0.378621	−	0.152686i
$43$	3.35975	−	5.81927i	0.512358	−	0.887430i	−0.487540	−	0.873101i	$-0.662106\pi$
$43$	3.35975	−	5.81927i	0.512358	−	0.887430i	0.999897	−	0.0143288i	$-0.00456116\pi$
$44$	−0.775934	+	1.34396i	−0.116977	+	0.202609i
$45$	0.882443			0.131547
$46$	5.29348			0.780480
$47$	0.976430	−	1.69123i	0.142427	−	0.246691i	−0.785983	−	0.618248i	$-0.787843\pi$
$47$	0.976430	−	1.69123i	0.142427	−	0.246691i	0.928410	+	0.371557i	$0.121176\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.72632	+	1.93822i	−0.960902	+	0.276888i
$50$	2.11065	+	3.65575i	0.298491	+	0.517001i
$51$	3.58796	−	6.21453i	0.502415	−	0.870208i
$52$	2.13422	+	2.90605i	0.295963	+	0.402996i
$53$	−6.74308	−	11.6794i	−0.926233	−	1.60428i	−0.789566	−	0.613666i	$-0.789694\pi$
$53$	−6.74308	−	11.6794i	−0.926233	−	1.60428i	−0.136667	−	0.990617i	$-0.543639\pi$
$54$	1.00000			0.136083
$55$	−0.684718	−	1.18597i	−0.0923273	−	0.159916i
$56$	0.369922	+	2.61976i	0.0494329	+	0.350081i
$57$	4.74161			0.628041
$58$	3.87494	+	6.71160i	0.508805	+	0.881276i
$59$	5.27138			0.686275			0.343137	−	0.939285i	$-0.388510\pi$
$59$	5.27138			0.686275			0.343137	+	0.939285i	$0.388510\pi$
$60$	−0.441221	−	0.764218i	−0.0569614	−	0.0986601i
$61$	7.17592	+	12.4291i	0.918782	+	1.59138i	0.801267	+	0.598306i	$0.204159\pi$
$61$	7.17592	+	12.4291i	0.918782	+	1.59138i	0.117515	+	0.993071i	$0.462507\pi$
$62$	3.24911	+	5.62762i	0.412637	+	0.714708i
$63$	2.08382	−	1.63024i	0.262537	−	0.205391i
$64$	1.00000			0.125000
$65$	−3.16252	+	0.348796i	−0.392262	+	0.0432628i
$66$	−0.775934	−	1.34396i	−0.0955109	−	0.165430i
$67$	3.75236	−	6.49929i	0.458424	−	0.794014i	−0.540454	−	0.841374i	$-0.681747\pi$
$67$	3.75236	−	6.49929i	0.458424	−	0.794014i	0.998878	+	0.0473596i	$0.0150807\pi$
$68$	−7.17592			−0.870208
$69$	−2.64674	+	4.58428i	−0.318630	+	0.551883i
$70$	−2.16529	−	0.873194i	−0.258801	−	0.104367i
$71$	5.00985	−	8.67732i	0.594560	−	1.02981i	−0.399049	−	0.916930i	$-0.630660\pi$
$71$	5.00985	−	8.67732i	0.594560	−	1.02981i	0.993609	−	0.112879i	$-0.0360072\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−1.93284	−	3.34778i	−0.226222	−	0.391828i	0.730464	−	0.682952i	$-0.239304\pi$
$73$	−1.93284	−	3.34778i	−0.226222	−	0.391828i	−0.956685	+	0.291124i	$0.905971\pi$
$74$	0.330574			0.0384284
$75$	−4.22129			−0.487433
$76$	−2.37080	−	4.10635i	−0.271950	−	0.471031i
$77$	−3.80789	−	1.53560i	−0.433949	−	0.174998i
$78$	−3.58382	+	0.395262i	−0.405788	+	0.0447546i
$79$	6.67928	−	11.5689i	0.751478	−	1.30160i	−0.195629	−	0.980678i	$-0.562675\pi$
$79$	6.67928	−	11.5689i	0.751478	−	1.30160i	0.947106	−	0.320920i	$-0.103992\pi$
$80$	−0.441221	+	0.764218i	−0.0493300	+	0.0854422i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.02918	−	5.24669i	−0.334517	−	0.579401i
$83$	−10.5519			−1.15822			−0.579109	−	0.815250i	$-0.696599\pi$
$83$	−10.5519			−1.15822			−0.579109	+	0.815250i	$0.696599\pi$
$84$	−2.45374	−	0.989520i	−0.267725	−	0.107965i
$85$	3.16617	−	5.48396i	0.343419	−	0.594820i
$86$	3.35975	−	5.81927i	0.362292	−	0.627508i
$87$	−7.74989			−0.830875
$88$	−0.775934	+	1.34396i	−0.0827149	+	0.143266i
$89$	14.8167			1.57057			0.785285	−	0.619134i	$-0.212516\pi$
$89$	14.8167			1.57057			0.785285	+	0.619134i	$0.212516\pi$
$90$	0.882443			0.0930176
$91$	−6.82366	+	6.66615i	−0.715314	+	0.698803i
$92$	5.29348			0.551883
$93$	−6.49821			−0.673833
$94$	0.976430	−	1.69123i	0.100711	−	0.174437i
$95$	4.18420			0.429290
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	5.79259	−	10.0331i	0.588149	−	1.01870i	−0.406326	−	0.913728i	$-0.633190\pi$
$97$	5.79259	−	10.0331i	0.588149	−	1.01870i	0.994475	−	0.104975i	$-0.0334764\pi$
$98$	−6.72632	+	1.93822i	−0.679460	+	0.195789i
$99$	1.55187			0.155969
$100$	2.11065	+	3.65575i	0.211065	+	0.365575i
$101$	−3.91439	+	6.77993i	−0.389497	+	0.674628i	−0.992382	−	0.123200i	$-0.960684\pi$
$101$	−3.91439	+	6.77993i	−0.389497	+	0.674628i	0.602885	+	0.797828i	$0.294018\pi$
$102$	3.58796	−	6.21453i	0.355261	−	0.615330i
$103$	0.430172	−	0.745081i	0.0423862	−	0.0734150i	−0.844054	−	0.536258i	$-0.819837\pi$
$103$	0.430172	−	0.745081i	0.0423862	−	0.0734150i	0.886440	+	0.462843i	$0.153171\pi$
$104$	2.13422	+	2.90605i	0.209277	+	0.284961i
$105$	1.83885	−	1.43860i	0.179454	−	0.140393i
$106$	−6.74308	−	11.6794i	−0.654946	−	1.13440i
$107$	−8.14260			−0.787175			−0.393587	−	0.919287i	$-0.628766\pi$
$107$	−8.14260			−0.787175			−0.393587	+	0.919287i	$0.628766\pi$
$108$	1.00000			0.0962250
$109$	4.73806	+	8.20656i	0.453824	+	0.786046i	0.998620	−	0.0525229i	$-0.0167263\pi$
$109$	4.73806	+	8.20656i	0.453824	+	0.786046i	−0.544796	+	0.838569i	$0.683393\pi$
$110$	−0.684718	−	1.18597i	−0.0652853	−	0.113077i
$111$	−0.165287	+	0.286285i	−0.0156883	+	0.0271730i
$112$	0.369922	+	2.61976i	0.0349543	+	0.247544i
$113$	5.71537	−	9.89931i	0.537657	−	0.931249i	−0.461373	−	0.887206i	$-0.652643\pi$
$113$	5.71537	−	9.89931i	0.537657	−	0.931249i	0.999030	−	0.0440426i	$-0.0140237\pi$
$114$	4.74161			0.444092
$115$	−2.33559	+	4.04537i	−0.217795	+	0.377233i
$116$	3.87494	+	6.71160i	0.359779	+	0.623156i
$117$	1.44960	−	3.30131i	0.134016	−	0.305206i
$118$	5.27138			0.485270
$119$	−2.65453	−	18.7992i	−0.243340	−	1.72332i
$120$	−0.441221	−	0.764218i	−0.0402778	−	0.0697632i
$121$	4.29585	+	7.44063i	0.390532	+	0.676421i
$122$	7.17592	+	12.4291i	0.649677	+	1.12527i
$123$	6.05836			0.546264
$124$	3.24911	+	5.62762i	0.291778	+	0.505375i
$125$	−8.13726			−0.727819
$126$	2.08382	−	1.63024i	0.185641	−	0.145234i
$127$	3.02592	+	5.24105i	0.268507	+	0.465068i	0.968477	−	0.249105i	$-0.0801363\pi$
$127$	3.02592	+	5.24105i	0.268507	+	0.465068i	−0.699969	+	0.714173i	$0.746803\pi$
$128$	1.00000			0.0883883
$129$	3.35975	+	5.81927i	0.295810	+	0.512358i
$130$	−3.16252	+	0.348796i	−0.277371	+	0.0305914i
$131$	−2.66045	+	4.60804i	−0.232445	+	0.402606i	−0.958527	−	0.285002i	$-0.908006\pi$
$131$	−2.66045	+	4.60804i	−0.232445	+	0.402606i	0.726082	+	0.687608i	$0.241339\pi$
$132$	−0.775934	−	1.34396i	−0.0675364	−	0.116977i
$133$	9.88066	−	7.72997i	0.856762	−	0.670274i
$134$	3.75236	−	6.49929i	0.324155	−	0.561453i
$135$	−0.441221	+	0.764218i	−0.0379743	+	0.0657734i
$136$	−7.17592			−0.615330
$137$	−8.01122			−0.684445			−0.342222	−	0.939619i	$-0.611180\pi$
$137$	−8.01122			−0.684445			−0.342222	+	0.939619i	$0.611180\pi$
$138$	−2.64674	+	4.58428i	−0.225305	+	0.390240i
$139$	8.87582	−	15.3734i	0.752838	−	1.30395i	−0.193605	−	0.981080i	$-0.562018\pi$
$139$	8.87582	−	15.3734i	0.752838	−	1.30395i	0.946442	−	0.322873i	$-0.104649\pi$
$140$	−2.16529	−	0.873194i	−0.183000	−	0.0737984i
$141$	0.976430	+	1.69123i	0.0822303	+	0.142427i
$142$	5.00985	−	8.67732i	0.420418	−	0.728185i
$143$	−5.56162	+	0.613395i	−0.465086	+	0.0512947i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−6.83883			−0.567934
$146$	−1.93284	−	3.34778i	−0.159963	−	0.277064i
$147$	1.68461	−	6.79427i	0.138945	−	0.560382i
$148$	0.330574			0.0271730
$149$	−8.66161	−	15.0024i	−0.709587	−	1.22904i	−0.965010	−	0.262211i	$-0.915548\pi$
$149$	−8.66161	−	15.0024i	−0.709587	−	1.22904i	0.255424	−	0.966829i	$-0.417785\pi$
$150$	−4.22129			−0.344667
$151$	−1.40927	−	2.44093i	−0.114685	−	0.198640i	0.802969	−	0.596021i	$-0.203252\pi$
$151$	−1.40927	−	2.44093i	−0.114685	−	0.198640i	−0.917654	+	0.397381i	$0.869919\pi$
$152$	−2.37080	−	4.10635i	−0.192298	−	0.333069i
$153$	3.58796	+	6.21453i	0.290069	+	0.502415i
$154$	−3.80789	−	1.53560i	−0.306848	−	0.123743i
$155$	−5.73430			−0.460590
$156$	−3.58382	+	0.395262i	−0.286935	+	0.0316463i
$157$	6.39822	+	11.0820i	0.510634	+	0.884443i	0.999924	+	0.0123225i	$0.00392247\pi$
$157$	6.39822	+	11.0820i	0.510634	+	0.884443i	−0.489290	+	0.872121i	$0.662744\pi$
$158$	6.67928	−	11.5689i	0.531375	−	0.920368i
$159$	13.4862			1.06952
$160$	−0.441221	+	0.764218i	−0.0348816	+	0.0604167i
$161$	1.95817	+	13.8677i	0.154326	+	1.09292i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	5.34387	+	9.25586i	0.418564	+	0.724975i	0.995795	−	0.0916061i	$-0.0292001\pi$
$163$	5.34387	+	9.25586i	0.418564	+	0.724975i	−0.577231	+	0.816581i	$0.695867\pi$
$164$	−3.02918	−	5.24669i	−0.236539	−	0.409698i
$165$	1.36944			0.106610
$166$	−10.5519			−0.818984
$167$	−9.90412	−	17.1544i	−0.766404	−	1.32745i	−0.939501	−	0.342546i	$-0.888711\pi$
$167$	−9.90412	−	17.1544i	−0.766404	−	1.32745i	0.173097	−	0.984905i	$-0.444623\pi$
$168$	−2.45374	−	0.989520i	−0.189310	−	0.0763431i
$169$	−3.89023	+	12.4043i	−0.299249	+	0.954175i
$170$	3.16617	−	5.48396i	0.242834	−	0.420601i
$171$	−2.37080	+	4.10635i	−0.181300	+	0.314021i
$172$	3.35975	−	5.81927i	0.256179	−	0.443715i
$173$	0.869332	+	1.50573i	0.0660941	+	0.114478i	0.897179	−	0.441668i	$-0.145613\pi$
$173$	0.869332	+	1.50573i	0.0660941	+	0.114478i	−0.831085	+	0.556146i	$0.812280\pi$
$174$	−7.74989			−0.587517
$175$	−8.79642	+	6.88174i	−0.664947	+	0.520210i
$176$	−0.775934	+	1.34396i	−0.0584883	+	0.101305i
$177$	−2.63569	+	4.56515i	−0.198111	+	0.343137i
$178$	14.8167			1.11056
$179$	−4.89644	+	8.48088i	−0.365977	+	0.633890i	−0.988932	−	0.148367i	$-0.952598\pi$
$179$	−4.89644	+	8.48088i	−0.365977	+	0.633890i	0.622956	+	0.782257i	$0.285932\pi$
$180$	0.882443			0.0657734
$181$	−11.5901			−0.861486			−0.430743	−	0.902475i	$-0.641748\pi$
$181$	−11.5901			−0.861486			−0.430743	+	0.902475i	$0.641748\pi$
$182$	−6.82366	+	6.66615i	−0.505804	+	0.494128i
$183$	−14.3518			−1.06092
$184$	5.29348			0.390240
$185$	−0.145856	+	0.252631i	−0.0107236	+	0.0185738i
$186$	−6.49821			−0.476472
$187$	5.56804	−	9.64413i	0.407176	−	0.705249i
$188$	0.976430	−	1.69123i	0.0712135	−	0.123345i
$189$	0.369922	+	2.61976i	0.0269079	+	0.190560i
$190$	4.18420			0.303554
$191$	0.631864	+	1.09442i	0.0457200	+	0.0791894i	0.887980	−	0.459882i	$-0.152108\pi$
$191$	0.631864	+	1.09442i	0.0457200	+	0.0791894i	−0.842260	+	0.539072i	$0.818775\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−9.49130	+	16.4394i	−0.683199	+	1.18334i	0.290800	+	0.956784i	$0.406079\pi$
$193$	−9.49130	+	16.4394i	−0.683199	+	1.18334i	−0.973999	+	0.226552i	$0.927255\pi$
$194$	5.79259	−	10.0331i	0.415884	−	0.720332i
$195$	1.27919	−	2.91322i	0.0916048	−	0.208620i
$196$	−6.72632	+	1.93822i	−0.480451	+	0.138444i
$197$	12.1786	+	21.0939i	0.867688	+	1.50288i	0.864353	+	0.502886i	$0.167728\pi$
$197$	12.1786	+	21.0939i	0.867688	+	1.50288i	0.00333546	+	0.999994i	$0.498938\pi$
$198$	1.55187			0.110287
$199$	21.5059			1.52451			0.762255	−	0.647277i	$-0.224092\pi$
$199$	21.5059			1.52451			0.762255	+	0.647277i	$0.224092\pi$
$200$	2.11065	+	3.65575i	0.149245	+	0.258500i
$201$	3.75236	+	6.49929i	0.264671	+	0.458424i
$202$	−3.91439	+	6.77993i	−0.275416	+	0.477034i
$203$	−16.1494	+	12.6342i	−1.13346	+	0.886747i
$204$	3.58796	−	6.21453i	0.251207	−	0.435104i
$205$	5.34616			0.373392
$206$	0.430172	−	0.745081i	0.0299715	−	0.0519122i
$207$	−2.64674	−	4.58428i	−0.183961	−	0.318630i
$208$	2.13422	+	2.90605i	0.147981	+	0.201498i
$209$	7.35835			0.508988
$210$	1.83885	−	1.43860i	0.126893	−	0.0992726i
$211$	3.56775	+	6.17953i	0.245614	+	0.425416i	0.962304	−	0.271976i	$-0.0876771\pi$
$211$	3.56775	+	6.17953i	0.245614	+	0.425416i	−0.716690	+	0.697392i	$0.754344\pi$
$212$	−6.74308	−	11.6794i	−0.463117	−	0.802141i
$213$	5.00985	+	8.67732i	0.343270	+	0.594560i
$214$	−8.14260			−0.556617
$215$	2.96479	+	5.13517i	0.202197	+	0.350216i
$216$	1.00000			0.0680414
$217$	−13.5411	+	10.5937i	−0.919231	+	0.719145i
$218$	4.73806	+	8.20656i	0.320902	+	0.555818i
$219$	3.86568			0.261218
$220$	−0.684718	−	1.18597i	−0.0461637	−	0.0799578i
$221$	−15.3150	−	20.8536i	−1.03020	−	1.40276i
$222$	−0.165287	+	0.286285i	−0.0110933	+	0.0192142i
$223$	−12.1673	−	21.0744i	−0.814784	−	1.41125i	−0.909483	−	0.415742i	$-0.863522\pi$
$223$	−12.1673	−	21.0744i	−0.814784	−	1.41125i	0.0946981	−	0.995506i	$-0.469811\pi$
$224$	0.369922	+	2.61976i	0.0247164	+	0.175040i
$225$	2.11065	−	3.65575i	0.140710	−	0.243717i
$226$	5.71537	−	9.89931i	0.380181	−	0.658492i
$227$	9.56035			0.634543			0.317271	−	0.948335i	$-0.397233\pi$
$227$	9.56035			0.634543			0.317271	+	0.948335i	$0.397233\pi$
$228$	4.74161			0.314021
$229$	−5.40570	+	9.36295i	−0.357219	+	0.618721i	−0.987495	−	0.157650i	$-0.949608\pi$
$229$	−5.40570	+	9.36295i	−0.357219	+	0.618721i	0.630276	+	0.776371i	$0.282942\pi$
$230$	−2.33559	+	4.04537i	−0.154005	+	0.266744i
$231$	3.23382	−	2.52992i	0.212769	−	0.166457i
$232$	3.87494	+	6.71160i	0.254402	+	0.440638i
$233$	−5.15806	+	8.93403i	−0.337916	+	0.585288i	−0.984041	−	0.177944i	$-0.943055\pi$
$233$	−5.15806	+	8.93403i	−0.337916	+	0.585288i	0.646125	+	0.763232i	$0.276389\pi$
$234$	1.44960	−	3.30131i	0.0947635	−	0.215813i
$235$	0.861644	+	1.49241i	0.0562074	+	0.0973541i
$236$	5.27138			0.343137
$237$	6.67928	+	11.5689i	0.433866	+	0.751478i
$238$	−2.65453	−	18.7992i	−0.172068	−	1.21857i
$239$	11.0866			0.717130			0.358565	−	0.933505i	$-0.383266\pi$
$239$	11.0866			0.717130			0.358565	+	0.933505i	$0.383266\pi$
$240$	−0.441221	−	0.764218i	−0.0284807	−	0.0493300i
$241$	−18.6739			−1.20289			−0.601447	−	0.798913i	$-0.705409\pi$
$241$	−18.6739			−1.20289			−0.601447	+	0.798913i	$0.705409\pi$
$242$	4.29585	+	7.44063i	0.276148	+	0.478302i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.17592	+	12.4291i	0.459391	+	0.795689i
$245$	1.48658	−	5.99555i	0.0949738	−	0.383042i
$246$	6.05836			0.386267
$247$	6.87345	−	15.6535i	0.437347	−	0.996009i
$248$	3.24911	+	5.62762i	0.206319	+	0.357354i
$249$	5.27593	−	9.13819i	0.334349	−	0.579109i
$250$	−8.13726			−0.514646
$251$	0.00354883	−	0.00614676i	0.000224000	−	0.000387980i	−0.865913	−	0.500194i	$-0.833262\pi$
$251$	0.00354883	−	0.00614676i	0.000224000	−	0.000387980i	0.866137	+	0.499806i	$0.166595\pi$
$252$	2.08382	−	1.63024i	0.131268	−	0.102696i
$253$	−4.10739	+	7.11421i	−0.258229	+	0.447266i
$254$	3.02592	+	5.24105i	0.189863	+	0.328853i
$255$	3.16617	+	5.48396i	0.198273	+	0.343419i
$256$	1.00000			0.0625000
$257$	12.6759			0.790701			0.395350	−	0.918530i	$-0.370623\pi$
$257$	12.6759			0.790701			0.395350	+	0.918530i	$0.370623\pi$
$258$	3.35975	+	5.81927i	0.209169	+	0.362292i
$259$	0.122287	+	0.866025i	0.00759852	+	0.0538122i
$260$	−3.16252	+	0.348796i	−0.196131	+	0.0216314i
$261$	3.87494	−	6.71160i	0.239853	−	0.415437i
$262$	−2.66045	+	4.60804i	−0.164363	+	0.284686i
$263$	2.59901	−	4.50161i	0.160262	−	0.277581i	−0.774701	−	0.632328i	$-0.782100\pi$
$263$	2.59901	−	4.50161i	0.160262	−	0.277581i	0.934963	+	0.354747i	$0.115433\pi$
$264$	−0.775934	−	1.34396i	−0.0477555	−	0.0827149i
$265$	11.9008			0.731058
$266$	9.88066	−	7.72997i	0.605822	−	0.473955i
$267$	−7.40837	+	12.8317i	−0.453385	+	0.785285i
$268$	3.75236	−	6.49929i	0.229212	−	0.397007i
$269$	−0.685009			−0.0417657			−0.0208829	−	0.999782i	$-0.506648\pi$
$269$	−0.685009			−0.0417657			−0.0208829	+	0.999782i	$0.506648\pi$
$270$	−0.441221	+	0.764218i	−0.0268519	+	0.0465088i
$271$	−5.05126			−0.306842			−0.153421	−	0.988161i	$-0.549029\pi$
$271$	−5.05126			−0.306842			−0.153421	+	0.988161i	$0.549029\pi$
$272$	−7.17592			−0.435104
$273$	−2.36123	−	9.24254i	−0.142908	−	0.559384i
$274$	−8.01122			−0.483976
$275$	−6.55090			−0.395034
$276$	−2.64674	+	4.58428i	−0.159315	+	0.275942i
$277$	−12.4497			−0.748029			−0.374015	−	0.927423i	$-0.622019\pi$
$277$	−12.4497			−0.748029			−0.374015	+	0.927423i	$0.622019\pi$
$278$	8.87582	−	15.3734i	0.532337	−	0.922034i
$279$	3.24911	−	5.62762i	0.194519	−	0.336917i
$280$	−2.16529	−	0.873194i	−0.129401	−	0.0521834i
$281$	−23.5917			−1.40736			−0.703680	−	0.710517i	$-0.748461\pi$
$281$	−23.5917			−1.40736			−0.703680	+	0.710517i	$0.748461\pi$
$282$	0.976430	+	1.69123i	0.0581456	+	0.100711i
$283$	−10.5148	+	18.2121i	−0.625038	+	1.08260i	0.363495	+	0.931596i	$0.381583\pi$
$283$	−10.5148	+	18.2121i	−0.625038	+	1.08260i	−0.988533	+	0.151002i	$0.951750\pi$
$284$	5.00985	−	8.67732i	0.297280	−	0.514904i
$285$	−2.09210	+	3.62362i	−0.123925	+	0.214645i
$286$	−5.56162	+	0.613395i	−0.328865	+	0.0362708i
$287$	12.6245	−	9.87660i	0.745203	−	0.582997i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	34.4938			2.02905
$290$	−6.83883			−0.401590
$291$	5.79259	+	10.0331i	0.339568	+	0.588149i
$292$	−1.93284	−	3.34778i	−0.113111	−	0.195914i
$293$	−6.41251	+	11.1068i	−0.374623	+	0.648865i	−0.990270	−	0.139156i	$-0.955561\pi$
$293$	−6.41251	+	11.1068i	−0.374623	+	0.648865i	0.615648	+	0.788021i	$0.288894\pi$
$294$	1.68461	−	6.79427i	0.0982487	−	0.396250i
$295$	−2.32584	+	4.02848i	−0.135416	+	0.234547i
$296$	0.330574			0.0192142
$297$	−0.775934	+	1.34396i	−0.0450243	+	0.0779843i
$298$	−8.66161	−	15.0024i	−0.501754	−	0.869063i
$299$	11.2974	+	15.3831i	0.653347	+	0.889627i
$300$	−4.22129			−0.243717
$301$	16.4879	+	6.64909i	0.950349	+	0.383247i
$302$	−1.40927	−	2.44093i	−0.0810944	−	0.140460i
$303$	−3.91439	−	6.77993i	−0.224876	−	0.389497i
$304$	−2.37080	−	4.10635i	−0.135975	−	0.235515i
$305$	−12.6647			−0.725177
$306$	3.58796	+	6.21453i	0.205110	+	0.355261i
$307$	−20.4988			−1.16993			−0.584963	−	0.811060i	$-0.698891\pi$
$307$	−20.4988			−1.16993			−0.584963	+	0.811060i	$0.698891\pi$
$308$	−3.80789	−	1.53560i	−0.216974	−	0.0874992i
$309$	0.430172	+	0.745081i	0.0244717	+	0.0423862i
$310$	−5.73430			−0.325686
$311$	7.06023	+	12.2287i	0.400349	+	0.693425i	0.993768	−	0.111469i	$-0.0355556\pi$
$311$	7.06023	+	12.2287i	0.400349	+	0.693425i	−0.593419	+	0.804894i	$0.702222\pi$
$312$	−3.58382	+	0.395262i	−0.202894	+	0.0223773i
$313$	14.5296	−	25.1661i	0.821264	−	1.42247i	−0.0834772	−	0.996510i	$-0.526603\pi$
$313$	14.5296	−	25.1661i	0.821264	−	1.42247i	0.904741	−	0.425961i	$-0.140064\pi$
$314$	6.39822	+	11.0820i	0.361072	+	0.625396i
$315$	0.326435	+	2.31179i	0.0183925	+	0.130255i
$316$	6.67928	−	11.5689i	0.375739	−	0.650799i
$317$	−6.08027	+	10.5313i	−0.341502	+	0.591499i	−0.984712	−	0.174191i	$-0.944269\pi$
$317$	−6.08027	+	10.5313i	−0.341502	+	0.591499i	0.643210	+	0.765690i	$0.277602\pi$
$318$	13.4862			0.756266
$319$	−12.0268			−0.673372
$320$	−0.441221	+	0.764218i	−0.0246650	+	0.0427211i
$321$	4.07130	−	7.05170i	0.227238	−	0.393587i
$322$	1.95817	+	13.8677i	0.109125	+	0.772814i
$323$	17.0127	+	29.4669i	0.946612	+	1.63958i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−6.11920	+	13.9358i	−0.339432	+	0.773019i
$326$	5.34387	+	9.25586i	0.295970	+	0.512635i
$327$	−9.47612			−0.524030
$328$	−3.02918	−	5.24669i	−0.167259	−	0.289700i
$329$	4.79182	+	1.93239i	0.264181	+	0.106536i
$330$	1.36944			0.0753849
$331$	−4.96685	−	8.60284i	−0.273003	−	0.472855i	0.696626	−	0.717434i	$-0.254684\pi$
$331$	−4.96685	−	8.60284i	−0.273003	−	0.472855i	−0.969629	+	0.244579i	$0.921350\pi$
$332$	−10.5519			−0.579109
$333$	−0.165287	−	0.286285i	−0.00905767	−	0.0156883i
$334$	−9.90412	−	17.1544i	−0.541930	−	0.938649i
$335$	3.31125	+	5.73525i	0.180913	+	0.313350i
$336$	−2.45374	−	0.989520i	−0.133863	−	0.0539827i
$337$	−3.38360			−0.184316			−0.0921582	−	0.995744i	$-0.529377\pi$
$337$	−3.38360			−0.184316			−0.0921582	+	0.995744i	$0.529377\pi$
$338$	−3.89023	+	12.4043i	−0.211601	+	0.674704i
$339$	5.71537	+	9.89931i	0.310416	+	0.537657i
$340$	3.16617	−	5.48396i	0.171710	−	0.297410i
$341$	−10.0844			−0.546100
$342$	−2.37080	+	4.10635i	−0.128198	+	0.222046i
$343$	−7.56588	−	16.9044i	−0.408519	−	0.912750i
$344$	3.35975	−	5.81927i	0.181146	−	0.313754i
$345$	−2.33559	−	4.04537i	−0.125744	−	0.217795i
$346$	0.869332	+	1.50573i	0.0467356	+	0.0809484i
$347$	22.2544			1.19468			0.597340	−	0.801988i	$-0.296224\pi$
$347$	22.2544			1.19468			0.597340	+	0.801988i	$0.296224\pi$
$348$	−7.74989			−0.415437
$349$	−5.16027	−	8.93784i	−0.276223	−	0.478432i	0.694220	−	0.719763i	$-0.255749\pi$
$349$	−5.16027	−	8.93784i	−0.276223	−	0.478432i	−0.970443	+	0.241331i	$0.922416\pi$
$350$	−8.79642	+	6.88174i	−0.470188	+	0.367844i
$351$	2.13422	+	2.90605i	0.113916	+	0.155113i
$352$	−0.775934	+	1.34396i	−0.0413574	+	0.0716332i
$353$	0.485103	−	0.840224i	0.0258195	−	0.0447206i	−0.852827	−	0.522194i	$-0.825114\pi$
$353$	0.485103	−	0.840224i	0.0258195	−	0.0447206i	0.878646	+	0.477473i	$0.158447\pi$
$354$	−2.63569	+	4.56515i	−0.140085	+	0.242635i
$355$	4.42091	+	7.65724i	0.234637	+	0.406404i
$356$	14.8167			0.785285
$357$	17.6079	+	7.10071i	0.931906	+	0.375810i
$358$	−4.89644	+	8.48088i	−0.258785	+	0.448228i
$359$	−1.03017	+	1.78430i	−0.0543701	+	0.0941717i	−0.891929	−	0.452175i	$-0.850648\pi$
$359$	−1.03017	+	1.78430i	−0.0543701	+	0.0941717i	0.837559	+	0.546346i	$0.183982\pi$
$360$	0.882443			0.0465088
$361$	−1.74142	+	3.01623i	−0.0916537	+	0.158749i
$362$	−11.5901			−0.609162
$363$	−8.59170			−0.450947
$364$	−6.82366	+	6.66615i	−0.357657	+	0.349401i
$365$	3.41124			0.178552
$366$	−14.3518			−0.750183
$367$	4.63538	−	8.02871i	0.241965	−	0.419095i	−0.719309	−	0.694690i	$-0.755542\pi$
$367$	4.63538	−	8.02871i	0.241965	−	0.419095i	0.961274	+	0.275595i	$0.0888749\pi$
$368$	5.29348			0.275942
$369$	−3.02918	+	5.24669i	−0.157693	+	0.273132i
$370$	−0.145856	+	0.252631i	−0.00758271	+	0.0131336i
$371$	28.1027	−	21.9857i	1.45902	−	1.14144i
$372$	−6.49821			−0.336917
$373$	3.76618	+	6.52322i	0.195006	+	0.337760i	0.946902	−	0.321521i	$-0.104194\pi$
$373$	3.76618	+	6.52322i	0.195006	+	0.337760i	−0.751897	+	0.659281i	$0.770861\pi$
$374$	5.56804	−	9.64413i	0.287917	−	0.498686i
$375$	4.06863	−	7.04708i	0.210103	−	0.363910i
$376$	0.976430	−	1.69123i	0.0503555	−	0.0872184i
$377$	−11.2343	+	25.5848i	−0.578594	+	1.31768i
$378$	0.369922	+	2.61976i	0.0190267	+	0.134746i
$379$	−8.94169	−	15.4875i	−0.459304	−	0.795537i	0.539621	−	0.841908i	$-0.318568\pi$
$379$	−8.94169	−	15.4875i	−0.459304	−	0.795537i	−0.998924	+	0.0463711i	$0.985234\pi$
$380$	4.18420			0.214645
$381$	−6.05185			−0.310045
$382$	0.631864	+	1.09442i	0.0323290	+	0.0559954i
$383$	9.09536	+	15.7536i	0.464751	+	0.804972i	0.999190	−	0.0402346i	$-0.0128105\pi$
$383$	9.09536	+	15.7536i	0.464751	+	0.804972i	−0.534439	+	0.845207i	$0.679477\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	2.85366	−	2.23251i	0.145436	−	0.113779i
$386$	−9.49130	+	16.4394i	−0.483095	+	0.836745i
$387$	−6.71951			−0.341572
$388$	5.79259	−	10.0331i	0.294074	−	0.509352i
$389$	8.54918	+	14.8076i	0.433461	+	0.750776i	0.997169	−	0.0751984i	$-0.0239590\pi$
$389$	8.54918	+	14.8076i	0.433461	+	0.750776i	−0.563708	+	0.825974i	$0.690626\pi$
$390$	1.27919	−	2.91322i	0.0647744	−	0.147516i
$391$	−37.9856			−1.92101
$392$	−6.72632	+	1.93822i	−0.339730	+	0.0978947i
$393$	−2.66045	−	4.60804i	−0.134202	−	0.232445i
$394$	12.1786	+	21.0939i	0.613548	+	1.06270i
$395$	5.89408	+	10.2088i	0.296563	+	0.513663i
$396$	1.55187			0.0779843
$397$	−13.8385	−	23.9691i	−0.694536	−	1.20297i	−0.970337	−	0.241757i	$-0.922276\pi$
$397$	−13.8385	−	23.9691i	−0.694536	−	1.20297i	0.275800	−	0.961215i	$-0.411057\pi$
$398$	21.5059			1.07799
$399$	1.75402	+	12.4219i	0.0878111	+	0.621872i
$400$	2.11065	+	3.65575i	0.105532	+	0.182787i
$401$	−0.784039			−0.0391531			−0.0195765	−	0.999808i	$-0.506232\pi$
$401$	−0.784039			−0.0391531			−0.0195765	+	0.999808i	$0.506232\pi$
$402$	3.75236	+	6.49929i	0.187151	+	0.324155i
$403$	−9.41983	+	21.4526i	−0.469235	+	1.06863i
$404$	−3.91439	+	6.77993i	−0.194748	+	0.337314i
$405$	−0.441221	−	0.764218i	−0.0219245	−	0.0379743i
$406$	−16.1494	+	12.6342i	−0.801480	+	0.627025i
$407$	−0.256504	+	0.444277i	−0.0127144	+	0.0220220i
$408$	3.58796	−	6.21453i	0.177630	−	0.307665i
$409$	25.9739			1.28433			0.642164	−	0.766567i	$-0.278037\pi$
$409$	25.9739			1.28433			0.642164	+	0.766567i	$0.278037\pi$
$410$	5.34616			0.264028
$411$	4.00561	−	6.93792i	0.197582	−	0.342222i
$412$	0.430172	−	0.745081i	0.0211931	−	0.0367075i
$413$	1.95000	+	13.8098i	0.0959531	+	0.679534i
$414$	−2.64674	−	4.58428i	−0.130080	−	0.225305i
$415$	4.65571	−	8.06393i	0.228540	−	0.395843i
$416$	2.13422	+	2.90605i	0.104639	+	0.142481i
$417$	8.87582	+	15.3734i	0.434651	+	0.752838i
$418$	7.35835			0.359909
$419$	0.207579	+	0.359537i	0.0101409	+	0.0175645i	0.871051	−	0.491192i	$-0.163439\pi$
$419$	0.207579	+	0.359537i	0.0101409	+	0.0175645i	−0.860910	+	0.508757i	$0.830105\pi$
$420$	1.83885	−	1.43860i	0.0897268	−	0.0701963i
$421$	−8.45284			−0.411966			−0.205983	−	0.978556i	$-0.566039\pi$
$421$	−8.45284			−0.411966			−0.205983	+	0.978556i	$0.566039\pi$
$422$	3.56775	+	6.17953i	0.173675	+	0.300815i
$423$	−1.95286			−0.0949513
$424$	−6.74308	−	11.6794i	−0.327473	−	0.567200i
$425$	−15.1458	−	26.2334i	−0.734681	−	1.27250i
$426$	5.00985	+	8.67732i	0.242728	+	0.420418i
$427$	−29.9067	+	23.3970i	−1.44728	+	1.13226i
$428$	−8.14260			−0.393587
$429$	2.24959	−	5.12320i	0.108611	−	0.247350i
$430$	2.96479	+	5.13517i	0.142975	+	0.247640i
$431$	12.3935	−	21.4662i	0.596973	−	1.03399i	−0.396292	−	0.918125i	$-0.629703\pi$
$431$	12.3935	−	21.4662i	0.596973	−	1.03399i	0.993265	−	0.115864i	$-0.0369636\pi$
$432$	1.00000			0.0481125
$433$	18.5723	−	32.1682i	0.892529	−	1.54591i	0.0556964	−	0.998448i	$-0.482262\pi$
$433$	18.5723	−	32.1682i	0.892529	−	1.54591i	0.836833	−	0.547458i	$-0.184405\pi$
$434$	−13.5411	+	10.5937i	−0.649994	+	0.508512i
$435$	3.41942	−	5.92260i	0.163948	−	0.283967i
$436$	4.73806	+	8.20656i	0.226912	+	0.393023i
$437$	−12.5498	−	21.7369i	−0.600338	−	1.03982i
$438$	3.86568			0.184709
$439$	−8.75366			−0.417790			−0.208895	−	0.977938i	$-0.566987\pi$
$439$	−8.75366			−0.417790			−0.208895	+	0.977938i	$0.566987\pi$
$440$	−0.684718	−	1.18597i	−0.0326426	−	0.0565387i
$441$	5.04170	+	4.85605i	0.240081	+	0.231241i
$442$	−15.3150	−	20.8536i	−0.728459	−	0.991903i
$443$	1.48601	−	2.57384i	0.0706023	−	0.122287i	−0.828563	−	0.559896i	$-0.810841\pi$
$443$	1.48601	−	2.57384i	0.0706023	−	0.122287i	0.899165	+	0.437609i	$0.144175\pi$
$444$	−0.165287	+	0.286285i	−0.00784417	+	0.0135865i
$445$	−6.53746	+	11.3232i	−0.309905	+	0.536772i
$446$	−12.1673	−	21.0744i	−0.576140	−	0.997903i
$447$	17.3232			0.819360
$448$	0.369922	+	2.61976i	0.0174772	+	0.123772i
$449$	2.95700	−	5.12167i	0.139549	−	0.241707i	−0.787777	−	0.615961i	$-0.788768\pi$
$449$	2.95700	−	5.12167i	0.139549	−	0.241707i	0.927326	+	0.374254i	$0.122101\pi$
$450$	2.11065	−	3.65575i	0.0994969	−	0.172334i
$451$	9.40178			0.442713
$452$	5.71537	−	9.89931i	0.268828	−	0.465624i
$453$	2.81854			0.132427
$454$	9.56035			0.448690
$455$	−2.08365	−	8.15602i	−0.0976829	−	0.382360i
$456$	4.74161			0.222046
$457$	−14.1933			−0.663935			−0.331968	−	0.943291i	$-0.607712\pi$
$457$	−14.1933			−0.663935			−0.331968	+	0.943291i	$0.607712\pi$
$458$	−5.40570	+	9.36295i	−0.252592	+	0.437502i
$459$	−7.17592			−0.334943
$460$	−2.33559	+	4.04537i	−0.108898	+	0.188616i
$461$	15.1395	−	26.2224i	0.705117	−	1.22130i	−0.261532	−	0.965195i	$-0.584228\pi$
$461$	15.1395	−	26.2224i	0.705117	−	1.22130i	0.966649	−	0.256104i	$-0.0824391\pi$
$462$	3.23382	−	2.52992i	0.150451	−	0.117703i
$463$	−32.8167			−1.52512			−0.762561	−	0.646916i	$-0.776059\pi$
$463$	−32.8167			−1.52512			−0.762561	+	0.646916i	$0.776059\pi$
$464$	3.87494	+	6.71160i	0.179890	+	0.311578i
$465$	2.86715	−	4.96605i	0.132961	−	0.230295i
$466$	−5.15806	+	8.93403i	−0.238943	+	0.413861i
$467$	−10.4247	+	18.0562i	−0.482399	+	0.835540i	−0.999796	−	0.0202058i	$-0.993568\pi$
$467$	−10.4247	+	18.0562i	−0.482399	+	0.835540i	0.517397	+	0.855746i	$0.326901\pi$
$468$	1.44960	−	3.30131i	0.0670079	−	0.152603i
$469$	18.4147	+	7.42608i	0.850310	+	0.342904i
$470$	0.861644	+	1.49241i	0.0397447	+	0.0688398i
$471$	−12.7964			−0.589629
$472$	5.27138			0.242635
$473$	5.21390	+	9.03074i	0.239735	+	0.415234i
$474$	6.67928	+	11.5689i	0.306789	+	0.531375i
$475$	10.0079	−	17.3341i	0.459192	−	0.795344i
$476$	−2.65453	−	18.7992i	−0.121670	−	0.861660i
$477$	−6.74308	+	11.6794i	−0.308744	+	0.534761i
$478$	11.0866			0.507087
$479$	12.0950	−	20.9492i	0.552637	−	0.957195i	−0.445447	−	0.895308i	$-0.646955\pi$
$479$	12.0950	−	20.9492i	0.552637	−	0.957195i	0.998083	−	0.0618862i	$-0.0197116\pi$
$480$	−0.441221	−	0.764218i	−0.0201389	−	0.0348816i
$481$	0.705517	+	0.960664i	0.0321688	+	0.0438025i
$482$	−18.6739			−0.850574
$483$	−12.9888	−	5.23800i	−0.591012	−	0.238337i
$484$	4.29585	+	7.44063i	0.195266	+	0.338211i
$485$	5.11163	+	8.85361i	0.232107	+	0.402022i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−40.3065			−1.82646			−0.913230	−	0.407444i	$-0.866420\pi$
$487$	−40.3065			−1.82646			−0.913230	+	0.407444i	$0.866420\pi$
$488$	7.17592	+	12.4291i	0.324839	+	0.562637i
$489$	−10.6877			−0.483317
$490$	1.48658	−	5.99555i	0.0671566	−	0.270851i
$491$	−3.58602	−	6.21117i	−0.161835	−	0.280306i	0.773692	−	0.633562i	$-0.218408\pi$
$491$	−3.58602	−	6.21117i	−0.161835	−	0.280306i	−0.935527	+	0.353256i	$0.885075\pi$
$492$	6.05836			0.273132
$493$	−27.8063	−	48.1619i	−1.25233	−	2.16910i
$494$	6.87345	−	15.6535i	0.309251	−	0.704285i
$495$	−0.684718	+	1.18597i	−0.0307758	+	0.0533052i
$496$	3.24911	+	5.62762i	0.145889	+	0.252688i
$497$	24.5858	+	9.91470i	1.10282	+	0.444735i
$498$	5.27593	−	9.13819i	0.236420	−	0.409492i
$499$	8.24802	−	14.2860i	0.369232	−	0.639528i	−0.620214	−	0.784433i	$-0.712954\pi$
$499$	8.24802	−	14.2860i	0.369232	−	0.639528i	0.989446	+	0.144904i	$0.0462875\pi$
$500$	−8.13726			−0.363910
$501$	19.8082			0.884967
$502$	0.00354883	−	0.00614676i	0.000158392	−	0.000274343i
$503$	0.187093	−	0.324055i	0.00834208	−	0.0144489i	−0.861824	−	0.507207i	$-0.830678\pi$
$503$	0.187093	−	0.324055i	0.00834208	−	0.0144489i	0.870166	+	0.492758i	$0.164011\pi$
$504$	2.08382	−	1.63024i	0.0928207	−	0.0726168i
$505$	−3.45423	−	5.98290i	−0.153711	−	0.266236i
$506$	−4.10739	+	7.11421i	−0.182596	+	0.316265i
$507$	−8.79730	−	9.57118i	−0.390702	−	0.425071i
$508$	3.02592	+	5.24105i	0.134254	+	0.232534i
$509$	5.26899			0.233544			0.116772	−	0.993159i	$-0.462745\pi$
$509$	5.26899			0.233544			0.116772	+	0.993159i	$0.462745\pi$
$510$	3.16617	+	5.48396i	0.140200	+	0.242834i
$511$	8.05538	−	6.30200i	0.356349	−	0.278784i
$512$	1.00000			0.0441942
$513$	−2.37080	−	4.10635i	−0.104674	−	0.181300i
$514$	12.6759			0.559110
$515$	0.379603	+	0.657491i	0.0167273	+	0.0289725i
$516$	3.35975	+	5.81927i	0.147905	+	0.256179i
$517$	1.51529	+	2.62456i	0.0666424	+	0.115428i
$518$	0.122287	+	0.866025i	0.00537296	+	0.0380510i
$519$	−1.73866			−0.0763189
$520$	−3.16252	+	0.348796i	−0.138686	+	0.0152957i
$521$	3.43343	+	5.94687i	0.150421	+	0.260537i	0.931382	−	0.364042i	$-0.118604\pi$
$521$	3.43343	+	5.94687i	0.150421	+	0.260537i	−0.780961	+	0.624580i	$0.785270\pi$
$522$	3.87494	−	6.71160i	0.169602	−	0.293759i
$523$	−2.18445			−0.0955193			−0.0477596	−	0.998859i	$-0.515208\pi$
$523$	−2.18445			−0.0955193			−0.0477596	+	0.998859i	$0.515208\pi$
$524$	−2.66045	+	4.60804i	−0.116222	+	0.201303i
$525$	−1.56155	−	11.0588i	−0.0681516	−	0.482645i
$526$	2.59901	−	4.50161i	0.113322	−	0.196280i
$527$	−23.3153	−	40.3833i	−1.01563	−	1.75913i
$528$	−0.775934	−	1.34396i	−0.0337682	−	0.0584883i
$529$	5.02089			0.218299
$530$	11.9008			0.516936
$531$	−2.63569	−	4.56515i	−0.114379	−	0.198111i
$532$	9.88066	−	7.72997i	0.428381	−	0.335137i
$533$	8.78222	−	20.0005i	0.380400	−	0.866319i
$534$	−7.40837	+	12.8317i	−0.320591	+	0.555281i
$535$	3.59269	−	6.22272i	0.155325	−	0.269032i
$536$	3.75236	−	6.49929i	0.162077	−	0.280726i
$537$	−4.89644	−	8.48088i	−0.211297	−	0.365977i
$538$	−0.685009			−0.0295328
$539$	2.61430	−	10.5438i	0.112606	−	0.454154i
$540$	−0.441221	+	0.764218i	−0.0189871	+	0.0328867i
$541$	−18.7629	+	32.4982i	−0.806679	+	1.39721i	0.108473	+	0.994099i	$0.465404\pi$
$541$	−18.7629	+	32.4982i	−0.806679	+	1.39721i	−0.915152	+	0.403109i	$0.867929\pi$
$542$	−5.05126			−0.216970
$543$	5.79505	−	10.0373i	0.248689	−	0.430743i
$544$	−7.17592			−0.307665
$545$	−8.36213			−0.358194
$546$	−2.36123	−	9.24254i	−0.101051	−	0.395544i
$547$	26.8987			1.15011			0.575054	−	0.818116i	$-0.304981\pi$
$547$	26.8987			1.15011			0.575054	+	0.818116i	$0.304981\pi$
$548$	−8.01122			−0.342222
$549$	7.17592	−	12.4291i	0.306261	−	0.530459i
$550$	−6.55090			−0.279331
$551$	18.3735	−	31.8238i	0.782736	−	1.35574i
$552$	−2.64674	+	4.58428i	−0.112653	+	0.195120i
$553$	32.7785	+	13.2186i	1.39388	+	0.562110i
$554$	−12.4497			−0.528937
$555$	−0.145856	−	0.252631i	−0.00619125	−	0.0107236i
$556$	8.87582	−	15.3734i	0.376419	−	0.651976i
$557$	−1.58336	+	2.74245i	−0.0670889	+	0.116201i	−0.897619	−	0.440773i	$-0.854704\pi$
$557$	−1.58336	+	2.74245i	−0.0670889	+	0.116201i	0.830530	+	0.556974i	$0.188038\pi$
$558$	3.24911	−	5.62762i	0.137546	−	0.238236i
$559$	24.0815	−	2.65597i	1.01854	−	0.112335i
$560$	−2.16529	−	0.873194i	−0.0915001	−	0.0368992i
$561$	5.56804	+	9.64413i	0.235083	+	0.407176i
$562$	−23.5917			−0.995154
$563$	30.8984			1.30221			0.651106	−	0.758987i	$-0.274306\pi$
$563$	30.8984			1.30221			0.651106	+	0.758987i	$0.274306\pi$
$564$	0.976430	+	1.69123i	0.0411151	+	0.0712135i
$565$	5.04349	+	8.73558i	0.212181	+	0.367508i
$566$	−10.5148	+	18.2121i	−0.441969	+	0.765512i
$567$	−2.45374	−	0.989520i	−0.103047	−	0.0415559i
$568$	5.00985	−	8.67732i	0.210209	−	0.364092i
$569$	11.7828			0.493962			0.246981	−	0.969020i	$-0.420561\pi$
$569$	11.7828			0.493962			0.246981	+	0.969020i	$0.420561\pi$
$570$	−2.09210	+	3.62362i	−0.0876284	+	0.151777i
$571$	−11.9777	−	20.7459i	−0.501250	−	0.868190i	−0.999999	−	0.00144398i	$-0.999540\pi$
$571$	−11.9777	−	20.7459i	−0.501250	−	0.868190i	0.498749	−	0.866746i	$-0.333793\pi$
$572$	−5.56162	+	0.613395i	−0.232543	+	0.0256473i
$573$	−1.26373			−0.0527930
$574$	12.6245	−	9.87660i	0.526938	−	0.412241i
$575$	11.1727	+	19.3516i	0.465932	+	0.807018i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−13.2068	−	22.8748i	−0.549805	−	0.952291i	−0.998287	−	0.0584990i	$-0.981369\pi$
$577$	−13.2068	−	22.8748i	−0.549805	−	0.952291i	0.448482	−	0.893792i	$-0.351965\pi$
$578$	34.4938			1.43475
$579$	−9.49130	−	16.4394i	−0.394445	−	0.683199i
$580$	−6.83883			−0.283967
$581$	−3.90337	−	27.6434i	−0.161939	−	1.14684i
$582$	5.79259	+	10.0331i	0.240111	+	0.415884i
$583$	20.9287			0.866780
$584$	−1.93284	−	3.34778i	−0.0799815	−	0.138532i
$585$	1.88332	+	2.56442i	0.0778659	+	0.106026i
$586$	−6.41251	+	11.1068i	−0.264898	+	0.458817i
$587$	15.3403	+	26.5702i	0.633162	+	1.09667i	0.986901	+	0.161325i	$0.0515767\pi$
$587$	15.3403	+	26.5702i	0.633162	+	1.09667i	−0.353739	+	0.935344i	$0.615090\pi$
$588$	1.68461	−	6.79427i	0.0694723	−	0.280191i
$589$	15.4060	−	26.6840i	0.634793	−	1.09949i
$590$	−2.32584	+	4.02848i	−0.0957535	+	0.165850i
$591$	−24.3572			−1.00192
$592$	0.330574			0.0135865
$593$	6.14941	−	10.6511i	0.252526	−	0.437388i	−0.711695	−	0.702489i	$-0.752072\pi$
$593$	6.14941	−	10.6511i	0.252526	−	0.437388i	0.964221	+	0.265101i	$0.0854054\pi$
$594$	−0.775934	+	1.34396i	−0.0318370	+	0.0551433i
$595$	15.5379	+	6.26597i	0.636993	+	0.256880i
$596$	−8.66161	−	15.0024i	−0.354793	−	0.614520i
$597$	−10.7529	+	18.6246i	−0.440088	+	0.762255i
$598$	11.2974	+	15.3831i	0.461986	+	0.629062i
$599$	−3.22732	−	5.58989i	−0.131865	−	0.228397i	0.792531	−	0.609832i	$-0.208763\pi$
$599$	−3.22732	−	5.58989i	−0.131865	−	0.228397i	−0.924395	+	0.381436i	$0.875430\pi$
$600$	−4.22129			−0.172334
$601$	−1.05552	−	1.82822i	−0.0430556	−	0.0745745i	0.843695	−	0.536824i	$-0.180376\pi$
$601$	−1.05552	−	1.82822i	−0.0430556	−	0.0745745i	−0.886750	+	0.462249i	$0.847043\pi$
$602$	16.4879	+	6.64909i	0.671998	+	0.270997i
$603$	−7.50473			−0.305616
$604$	−1.40927	−	2.44093i	−0.0573424	−	0.0993199i
$605$	−7.58169			−0.308239
$606$	−3.91439	−	6.77993i	−0.159011	−	0.275416i
$607$	−12.5828	−	21.7941i	−0.510722	−	0.884596i	−0.999923	−	0.0124247i	$-0.996045\pi$
$607$	−12.5828	−	21.7941i	−0.510722	−	0.884596i	0.489201	−	0.872171i	$-0.337288\pi$
$608$	−2.37080	−	4.10635i	−0.0961488	−	0.166535i
$609$	−2.86685	−	20.3029i	−0.116171	−	0.822713i
$610$	−12.6647			−0.512778
$611$	6.99870	−	0.771892i	0.283137	−	0.0312274i
$612$	3.58796	+	6.21453i	0.145035	+	0.251207i
$613$	12.7273	−	22.0444i	0.514052	−	0.890364i	−0.485815	−	0.874061i	$-0.661477\pi$
$613$	12.7273	−	22.0444i	0.514052	−	0.890364i	0.999867	−	0.0163023i	$-0.00518940\pi$
$614$	−20.4988			−0.827263
$615$	−2.67308	+	4.62991i	−0.107789	+	0.186696i
$616$	−3.80789	−	1.53560i	−0.153424	−	0.0618713i
$617$	16.4252	−	28.4493i	0.661254	−	1.14532i	−0.319033	−	0.947744i	$-0.603358\pi$
$617$	16.4252	−	28.4493i	0.661254	−	1.14532i	0.980287	−	0.197581i	$-0.0633086\pi$
$618$	0.430172	+	0.745081i	0.0173041	+	0.0299715i
$619$	0.180058	+	0.311869i	0.00723713	+	0.0125351i	0.869621	−	0.493719i	$-0.164363\pi$
$619$	0.180058	+	0.311869i	0.00723713	+	0.0125351i	−0.862384	+	0.506254i	$0.831030\pi$
$620$	−5.73430			−0.230295
$621$	5.29348			0.212420
$622$	7.06023	+	12.2287i	0.283089	+	0.490325i
$623$	5.48103	+	38.8163i	0.219593	+	1.55514i
$624$	−3.58382	+	0.395262i	−0.143468	+	0.0158231i
$625$	−6.96290	+	12.0601i	−0.278516	+	0.482404i
$626$	14.5296	−	25.1661i	0.580721	−	1.00584i
$627$	−3.67918	+	6.37252i	−0.146932	+	0.254494i
$628$	6.39822	+	11.0820i	0.255317	+	0.442222i
$629$	−2.37217			−0.0945847
$630$	0.326435	+	2.31179i	0.0130055	+	0.0921039i
$631$	−7.36478	+	12.7562i	−0.293187	+	0.507815i	−0.974562	−	0.224120i	$-0.928049\pi$
$631$	−7.36478	+	12.7562i	−0.293187	+	0.507815i	0.681374	+	0.731935i	$0.261383\pi$
$632$	6.67928	−	11.5689i	0.265687	−	0.460184i
$633$	−7.13550			−0.283611
$634$	−6.08027	+	10.5313i	−0.241478	+	0.418253i
$635$	−5.34041			−0.211928
$636$	13.4862			0.534761
$637$	−19.9880	−	15.4104i	−0.791952	−	0.610583i
$638$	−12.0268			−0.476146
$639$	−10.0197			−0.396373
$640$	−0.441221	+	0.764218i	−0.0174408	+	0.0302084i
$641$	−48.3368			−1.90919			−0.954595	−	0.297906i	$-0.903712\pi$
$641$	−48.3368			−1.90919			−0.954595	+	0.297906i	$0.903712\pi$
$642$	4.07130	−	7.05170i	0.160681	−	0.278308i
$643$	−0.0861739	+	0.149258i	−0.00339837	+	0.00588614i	−0.867720	−	0.497054i	$-0.834415\pi$
$643$	−0.0861739	+	0.149258i	−0.00339837	+	0.00588614i	0.864321	+	0.502940i	$0.167748\pi$
$644$	1.95817	+	13.8677i	0.0771628	+	0.546462i
$645$	−5.92958			−0.233477
$646$	17.0127	+	29.4669i	0.669355	+	1.15936i
$647$	−13.9682	+	24.1937i	−0.549147	+	0.951151i	0.449186	+	0.893438i	$0.351714\pi$
$647$	−13.9682	+	24.1937i	−0.549147	+	0.951151i	−0.998333	+	0.0577129i	$0.981619\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−4.09024	+	7.08451i	−0.160556	+	0.278091i
$650$	−6.11920	+	13.9358i	−0.240015	+	0.546607i
$651$	−2.40383	−	17.0238i	−0.0942136	−	0.667215i
$652$	5.34387	+	9.25586i	0.209282	+	0.362487i
$653$	−41.8489			−1.63767			−0.818836	−	0.574027i	$-0.805380\pi$
$653$	−41.8489			−1.63767			−0.818836	+	0.574027i	$0.805380\pi$
$654$	−9.47612			−0.370545
$655$	−2.34770	−	4.06633i	−0.0917322	−	0.158885i
$656$	−3.02918	−	5.24669i	−0.118270	−	0.204849i
$657$	−1.93284	+	3.34778i	−0.0754073	+	0.130609i
$658$	4.79182	+	1.93239i	0.186804	+	0.0753326i
$659$	3.26341	−	5.65240i	0.127125	−	0.220186i	−0.795437	−	0.606036i	$-0.792759\pi$
$659$	3.26341	−	5.65240i	0.127125	−	0.220186i	0.922561	+	0.385850i	$0.126092\pi$
$660$	1.36944			0.0533052
$661$	−0.526326	+	0.911623i	−0.0204717	+	0.0354580i	−0.876080	−	0.482166i	$-0.839850\pi$
$661$	−0.526326	+	0.911623i	−0.0204717	+	0.0354580i	0.855608	+	0.517624i	$0.173183\pi$
$662$	−4.96685	−	8.60284i	−0.193042	−	0.334359i
$663$	25.7172	−	2.83637i	0.998773	−	0.110155i
$664$	−10.5519			−0.409492
$665$	1.54783	+	10.9616i	0.0600221	+	0.425073i
$666$	−0.165287	−	0.286285i	−0.00640474	−	0.0110933i
$667$	20.5119	+	35.5277i	0.794225	+	1.37564i
$668$	−9.90412	−	17.1544i	−0.383202	−	0.663725i
$669$	24.3347			0.940832
$670$	3.31125	+	5.73525i	0.127925	+	0.221572i
$671$	−22.2722			−0.859808
$672$	−2.45374	−	0.989520i	−0.0946552	−	0.0381716i
$673$	−13.1957	−	22.8556i	−0.508655	−	0.881017i	−0.999950	−	0.0100234i	$-0.996809\pi$
$673$	−13.1957	−	22.8556i	−0.508655	−	0.881017i	0.491294	−	0.870994i	$-0.336524\pi$
$674$	−3.38360			−0.130331
$675$	2.11065	+	3.65575i	0.0812389	+	0.140710i
$676$	−3.89023	+	12.4043i	−0.149624	+	0.477088i
$677$	−10.3481	+	17.9235i	−0.397711	+	0.688856i	−0.993443	−	0.114327i	$-0.963529\pi$
$677$	−10.3481	+	17.9235i	−0.397711	+	0.688856i	0.595732	+	0.803183i	$0.296862\pi$
$678$	5.71537	+	9.89931i	0.219497	+	0.380181i
$679$	28.4271	+	11.4638i	1.09093	+	0.439939i
$680$	3.16617	−	5.48396i	0.121417	−	0.210300i
$681$	−4.78018	+	8.27951i	−0.183177	+	0.317271i
$682$	−10.0844			−0.386151
$683$	−36.9788			−1.41495			−0.707477	−	0.706736i	$-0.750167\pi$
$683$	−36.9788			−1.41495			−0.707477	+	0.706736i	$0.750167\pi$
$684$	−2.37080	+	4.10635i	−0.0906499	+	0.157010i
$685$	3.53472	−	6.12232i	0.135055	−	0.233922i
$686$	−7.56588	−	16.9044i	−0.288866	−	0.645412i
$687$	−5.40570	−	9.36295i	−0.206240	−	0.357219i
$688$	3.35975	−	5.81927i	0.128089	−	0.221857i
$689$	19.5496	−	44.5220i	0.744780	−	1.69615i
$690$	−2.33559	−	4.04537i	−0.0889146	−	0.154005i
$691$	3.51208			0.133606			0.0668029	−	0.997766i	$-0.478720\pi$
$691$	3.51208			0.133606			0.0668029	+	0.997766i	$0.478720\pi$
$692$	0.869332	+	1.50573i	0.0330470	+	0.0572391i
$693$	0.574070	+	4.06553i	0.0218071	+	0.154437i
$694$	22.2544			0.844766
$695$	7.83241	+	13.5661i	0.297100	+	0.514593i
$696$	−7.74989			−0.293759
$697$	21.7372	+	37.6499i	0.823353	+	1.42609i
$698$	−5.16027	−	8.93784i	−0.195319	−	0.338302i
$699$	−5.15806	−	8.93403i	−0.195096	−	0.337916i
$700$	−8.79642	+	6.88174i	−0.332473	+	0.260105i
$701$	−9.53390			−0.360090			−0.180045	−	0.983658i	$-0.557624\pi$
$701$	−9.53390			−0.360090			−0.180045	+	0.983658i	$0.557624\pi$
$702$	2.13422	+	2.90605i	0.0805508	+	0.109682i
$703$	−0.783726	−	1.35745i	−0.0295588	−	0.0511973i
$704$	−0.775934	+	1.34396i	−0.0292441	+	0.0506523i
$705$	−1.72329			−0.0649028
$706$	0.485103	−	0.840224i	0.0182571	−	0.0316222i
$707$	−19.2098	−	7.74674i	−0.722460	−	0.291346i
$708$	−2.63569	+	4.56515i	−0.0990553	+	0.171569i
$709$	−9.56380	−	16.5650i	−0.359176	−	0.622111i	0.628647	−	0.777690i	$-0.283609\pi$
$709$	−9.56380	−	16.5650i	−0.359176	−	0.622111i	−0.987823	+	0.155579i	$0.950276\pi$
$710$	4.42091	+	7.65724i	0.165914	+	0.287371i
$711$	−13.3586			−0.500985
$712$	14.8167			0.555281
$713$	17.1991	+	29.7897i	0.644110	+	1.11563i
$714$	17.6079	+	7.10071i	0.658957	+	0.265738i
$715$	1.98514	−	4.52093i	0.0742399	−	0.169073i
$716$	−4.89644	+	8.48088i	−0.182988	+	0.316945i
$717$	−5.54328	+	9.60124i	−0.207017	+	0.358565i
$718$	−1.03017	+	1.78430i	−0.0384455	+	0.0665895i
$719$	13.8837	+	24.0473i	0.517775	+	0.896812i	0.999787	+	0.0206477i	$0.00657283\pi$
$719$	13.8837	+	24.0473i	0.517775	+	0.896812i	−0.482012	+	0.876165i	$0.660094\pi$
$720$	0.882443			0.0328867
$721$	2.11106	+	0.851328i	0.0786202	+	0.0317051i
$722$	−1.74142	+	3.01623i	−0.0648089	+	0.112252i
$723$	9.33696	−	16.1721i	0.347245	−	0.601447i
$724$	−11.5901			−0.430743
$725$	−16.3573	+	28.3316i	−0.607494	+	1.05221i
$726$	−8.59170			−0.318868
$727$	27.4082			1.01651			0.508257	−	0.861205i	$-0.330290\pi$
$727$	27.4082			1.01651			0.508257	+	0.861205i	$0.330290\pi$
$728$	−6.82366	+	6.66615i	−0.252902	+	0.247064i
$729$	1.00000			0.0370370
$730$	3.41124			0.126256
$731$	−24.1093	+	41.7586i	−0.891716	+	1.54450i
$732$	−14.3518			−0.530459
$733$	9.70789	−	16.8146i	0.358569	−	0.621060i	−0.629153	−	0.777282i	$-0.716598\pi$
$733$	9.70789	−	16.8146i	0.358569	−	0.621060i	0.987722	+	0.156222i	$0.0499314\pi$
$734$	4.63538	−	8.02871i	0.171095	−	0.296345i
$735$	4.44901	+	4.28519i	0.164104	+	0.158062i
$736$	5.29348			0.195120
$737$	5.82318	+	10.0860i	0.214500	+	0.371524i
$738$	−3.02918	+	5.24669i	−0.111506	+	0.193134i
$739$	−7.58084	+	13.1304i	−0.278866	+	0.483010i	−0.971103	−	0.238660i	$-0.923292\pi$
$739$	−7.58084	+	13.1304i	−0.278866	+	0.483010i	0.692237	+	0.721670i	$0.256625\pi$
$740$	−0.145856	+	0.252631i	−0.00536178	+	0.00928688i
$741$	10.1196	+	13.7793i	0.371754	+	0.506197i
$742$	28.1027	−	21.9857i	1.03168	−	0.807121i
$743$	−5.85184	−	10.1357i	−0.214683	−	0.371842i	0.738491	−	0.674263i	$-0.235539\pi$
$743$	−5.85184	−	10.1357i	−0.214683	−	0.371842i	−0.953174	+	0.302421i	$0.902205\pi$
$744$	−6.49821			−0.238236
$745$	15.2868			0.560063
$746$	3.76618	+	6.52322i	0.137890	+	0.238832i
$747$	5.27593	+	9.13819i	0.193036	+	0.334349i
$748$	5.56804	−	9.64413i	0.203588	−	0.352624i
$749$	−3.01213	−	21.3317i	−0.110061	−	0.779443i
$750$	4.06863	−	7.04708i	0.148565	−	0.257323i
$751$	36.7832			1.34224			0.671119	−	0.741350i	$-0.265814\pi$
$751$	36.7832			1.34224			0.671119	+	0.741350i	$0.265814\pi$
$752$	0.976430	−	1.69123i	0.0356067	−	0.0616727i
$753$	0.00354883	+	0.00614676i	0.000129327	+	0.000224000i
$754$	−11.2343	+	25.5848i	−0.409128	+	0.931743i
$755$	2.48720			0.0905185
$756$	0.369922	+	2.61976i	0.0134539	+	0.0952799i
$757$	0.469542	+	0.813271i	0.0170658	+	0.0295589i	0.874432	−	0.485148i	$-0.161234\pi$
$757$	0.469542	+	0.813271i	0.0170658	+	0.0295589i	−0.857366	+	0.514707i	$0.827901\pi$
$758$	−8.94169	−	15.4875i	−0.324777	−	0.562530i
$759$	−4.10739	−	7.11421i	−0.149089	−	0.258229i
$760$	4.18420			0.151777
$761$	2.83559	+	4.91139i	0.102790	+	0.178038i	0.912833	−	0.408333i	$-0.133890\pi$
$761$	2.83559	+	4.91139i	0.102790	+	0.178038i	−0.810043	+	0.586370i	$0.800556\pi$
$762$	−6.05185			−0.219235
$763$	−19.7465	+	15.4484i	−0.714872	+	0.559269i
$764$	0.631864	+	1.09442i	0.0228600	+	0.0395947i
$765$	−6.33234			−0.228946
$766$	9.09536	+	15.7536i	0.328629	+	0.569201i
$767$	11.2503	+	15.3189i	0.406224	+	0.553133i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	0.775934	+	1.34396i	0.0279809	+	0.0484644i	0.879677	−	0.475572i	$-0.157759\pi$
$769$	0.775934	+	1.34396i	0.0279809	+	0.0484644i	−0.851696	+	0.524036i	$0.824426\pi$
$770$	2.85366	−	2.23251i	0.102839	−	0.0804542i
$771$	−6.33795	+	10.9776i	−0.228256	+	0.395350i
$772$	−9.49130	+	16.4394i	−0.341600	+	0.591668i
$773$	−29.3595			−1.05599			−0.527994	−	0.849248i	$-0.677056\pi$
$773$	−29.3595			−1.05599			−0.527994	+	0.849248i	$0.677056\pi$
$774$	−6.71951			−0.241528
$775$	−13.7154	+	23.7558i	−0.492673	+	0.853335i
$776$	5.79259	−	10.0331i	0.207942	−	0.360166i
$777$	−0.811143	−	0.327109i	−0.0290996	−	0.0117350i
$778$	8.54918	+	14.8076i	0.306503	+	0.530879i
$779$	−14.3632	+	24.8778i	−0.514615	+	0.891338i
$780$	1.27919	−	2.91322i	0.0458024	−	0.104310i
$781$	7.77464	+	13.4661i	0.278198	+	0.481854i
$782$	−37.9856			−1.35836
$783$	3.87494	+	6.71160i	0.138479	+	0.239853i
$784$	−6.72632	+	1.93822i	−0.240226	+	0.0692220i
$785$	−11.2921			−0.403033
$786$	−2.66045	−	4.60804i	−0.0948953	−	0.164363i
$787$	−18.3264			−0.653265			−0.326632	−	0.945151i	$-0.605914\pi$
$787$	−18.3264			−0.653265			−0.326632	+	0.945151i	$0.605914\pi$
$788$	12.1786	+	21.0939i	0.433844	+	0.751440i
$789$	2.59901	+	4.50161i	0.0925271	+	0.160262i
$790$	5.89408	+	10.2088i	0.209702	+	0.363215i
$791$	28.0481	+	11.3109i	0.997275	+	0.402171i
$792$	1.55187			0.0551433
$793$	−20.8045	+	47.3799i	−0.738788	+	1.68251i
$794$	−13.8385	−	23.9691i	−0.491111	−	0.850630i
$795$	−5.95038	+	10.3064i	−0.211038	+	0.365529i
$796$	21.5059			0.762255
$797$	6.67504	−	11.5615i	0.236442	−	0.409529i	−0.723249	−	0.690588i	$-0.757352\pi$
$797$	6.67504	−	11.5615i	0.236442	−	0.409529i	0.959691	+	0.281058i	$0.0906854\pi$
$798$	1.75402	+	12.4219i	0.0620918	+	0.439730i
$799$	−7.00678	+	12.1361i	−0.247882	+	0.429345i
$800$	2.11065	+	3.65575i	0.0746227	+	0.129250i
$801$	−7.40837	−	12.8317i	−0.261762	−	0.453385i
$802$	−0.784039			−0.0276854
$803$	5.99903			0.211701
$804$	3.75236	+	6.49929i	0.132336	+	0.229212i
$805$	−11.4619	−	4.62223i	−0.403979	−	0.162912i
$806$	−9.41983	+	21.4526i	−0.331799	+	0.755636i
$807$	0.342505	−	0.593235i	0.0120567	−	0.0208829i
$808$	−3.91439	+	6.77993i	−0.137708	+	0.238517i
$809$	16.1928	−	28.0467i	0.569307	−	0.986069i	−0.427327	−	0.904097i	$-0.640545\pi$
$809$	16.1928	−	28.0467i	0.569307	−	0.986069i	0.996635	−	0.0819722i	$-0.0261219\pi$
$810$	−0.441221	−	0.764218i	−0.0155029	−	0.0268519i
$811$	−11.1640			−0.392022			−0.196011	−	0.980602i	$-0.562799\pi$
$811$	−11.1640			−0.392022			−0.196011	+	0.980602i	$0.562799\pi$
$812$	−16.1494	+	12.6342i	−0.566732	+	0.443373i
$813$	2.52563	−	4.37452i	0.0885778	−	0.153421i
$814$	−0.256504	+	0.444277i	−0.00899045	+	0.0155719i
$815$	−9.43132			−0.330365
$816$	3.58796	−	6.21453i	0.125604	−	0.217552i
$817$	−31.8613			−1.11468
$818$	25.9739			0.908157
$819$	9.18489	+	2.57639i	0.320946	+	0.0900263i
$820$	5.34616			0.186696
$821$	−31.7025			−1.10643			−0.553213	−	0.833040i	$-0.686598\pi$
$821$	−31.7025			−1.10643			−0.553213	+	0.833040i	$0.686598\pi$
$822$	4.00561	−	6.93792i	0.139712	−	0.241988i
$823$	52.5002			1.83004			0.915022	−	0.403405i	$-0.132173\pi$
$823$	52.5002			1.83004			0.915022	+	0.403405i	$0.132173\pi$
$824$	0.430172	−	0.745081i	0.0149858	−	0.0259561i
$825$	3.27545	−	5.67324i	0.114036	−	0.197517i
$826$	1.95000	+	13.8098i	0.0678491	+	0.480503i
$827$	33.4939			1.16470			0.582348	−	0.812939i	$-0.302134\pi$
$827$	33.4939			1.16470			0.582348	+	0.812939i	$0.302134\pi$
$828$	−2.64674	−	4.58428i	−0.0919805	−	0.159315i
$829$	19.0624	−	33.0170i	0.662064	−	1.14673i	−0.318008	−	0.948088i	$-0.603014\pi$
$829$	19.0624	−	33.0170i	0.662064	−	1.14673i	0.980072	−	0.198641i	$-0.0636528\pi$
$830$	4.65571	−	8.06393i	0.161602	−	0.279903i
$831$	6.22484	−	10.7817i	0.215937	−	0.374015i
$832$	2.13422	+	2.90605i	0.0739907	+	0.100749i
$833$	48.2675	−	13.9085i	1.67237	−	0.481900i
$834$	8.87582	+	15.3734i	0.307345	+	0.532337i
$835$	17.4796			0.604908
$836$	7.35835			0.254494
$837$	3.24911	+	5.62762i	0.112306	+	0.194519i
$838$	0.207579	+	0.359537i	0.00717069	+	0.0124200i
$839$	12.6246	−	21.8665i	0.435851	−	0.754916i	−0.561514	−	0.827467i	$-0.689781\pi$
$839$	12.6246	−	21.8665i	0.435851	−	0.754916i	0.997365	+	0.0725514i	$0.0231141\pi$
$840$	1.83885	−	1.43860i	0.0634464	−	0.0496363i
$841$	−15.5304	+	26.8994i	−0.535530	+	0.927565i
$842$	−8.45284			−0.291304
$843$	11.7958	−	20.4310i	0.406270	−	0.703680i
$844$	3.56775	+	6.17953i	0.122807	+	0.212708i
$845$	−7.76311	−	8.44602i	−0.267059	−	0.290552i
$846$	−1.95286			−0.0671407
$847$	−17.9036	+	14.0066i	−0.615174	+	0.481271i
$848$	−6.74308	−	11.6794i	−0.231558	−	0.401071i
$849$	−10.5148	−	18.2121i	−0.360866	−	0.625038i
$850$	−15.1458	−	26.2334i	−0.519498	−	0.899797i
$851$	1.74989			0.0599853
$852$	5.00985	+	8.67732i	0.171635	+	0.297280i
$853$	30.1001			1.03061			0.515304	−	0.857007i	$-0.327679\pi$
$853$	30.1001			1.03061			0.515304	+	0.857007i	$0.327679\pi$
$854$	−29.9067	+	23.3970i	−1.02338	+	0.800628i
$855$	−2.09210	−	3.62362i	−0.0715483	−	0.123925i
$856$	−8.14260			−0.278308
$857$	−11.8157	−	20.4655i	−0.403618	−	0.699087i	0.590541	−	0.807007i	$-0.298914\pi$
$857$	−11.8157	−	20.4655i	−0.403618	−	0.699087i	−0.994160	+	0.107920i	$0.965581\pi$
$858$	2.24959	−	5.12320i	0.0767999	−	0.174903i
$859$	−17.7282	+	30.7061i	−0.604878	+	1.04768i	0.387193	+	0.921999i	$0.373445\pi$
$859$	−17.7282	+	30.7061i	−0.604878	+	1.04768i	−0.992071	+	0.125680i	$0.959889\pi$
$860$	2.96479	+	5.13517i	0.101099	+	0.175108i
$861$	2.24112	+	15.8715i	0.0763772	+	0.540898i
$862$	12.3935	−	21.4662i	0.422124	−	0.731140i
$863$	0.0283138	−	0.0490410i	0.000963813	−	0.00166937i	−0.865543	−	0.500834i	$-0.833027\pi$
$863$	0.0283138	−	0.0490410i	0.000963813	−	0.00166937i	0.866507	+	0.499165i	$0.166360\pi$
$864$	1.00000			0.0340207
$865$	−1.53427			−0.0521668
$866$	18.5723	−	32.1682i	0.631114	−	1.09312i
$867$	−17.2469	+	29.8725i	−0.585736	+	1.01452i
$868$	−13.5411	+	10.5937i	−0.459615	+	0.359573i
$869$	10.3654	+	17.9533i	0.351621	+	0.609025i
$870$	3.41942	−	5.92260i	0.115929	−	0.200795i
$871$	26.8956	−	2.96633i	0.911323	−	0.100510i
$872$	4.73806	+	8.20656i	0.160451	+	0.277909i
$873$	−11.5852			−0.392099
$874$	−12.5498	−	21.7369i	−0.424503	−	0.735261i
$875$	−3.01015	−	21.3177i	−0.101762	−	0.720670i
$876$	3.86568			0.130609
$877$	−17.0082	−	29.4590i	−0.574324	−	0.994759i	−0.996115	−	0.0880657i	$-0.971931\pi$
$877$	−17.0082	−	29.4590i	−0.574324	−	0.994759i	0.421790	−	0.906693i	$-0.361402\pi$
$878$	−8.75366			−0.295422
$879$	−6.41251	−	11.1068i	−0.216288	−	0.374623i
$880$	−0.684718	−	1.18597i	−0.0230818	−	0.0399789i
$881$	19.0164	+	32.9374i	0.640680	+	1.10969i	0.985281	+	0.170941i	$0.0546807\pi$
$881$	19.0164	+	32.9374i	0.640680	+	1.10969i	−0.344601	+	0.938749i	$0.611986\pi$
$882$	5.04170	+	4.85605i	0.169763	+	0.163512i
$883$	22.6536			0.762356			0.381178	−	0.924502i	$-0.375519\pi$
$883$	22.6536			0.762356			0.381178	+	0.924502i	$0.375519\pi$
$884$	−15.3150	−	20.8536i	−0.515098	−	0.701381i
$885$	−2.32584	−	4.02848i	−0.0781824	−	0.135416i
$886$	1.48601	−	2.57384i	0.0499234	−	0.0864698i
$887$	21.3076			0.715441			0.357720	−	0.933829i	$-0.383554\pi$
$887$	21.3076			0.715441			0.357720	+	0.933829i	$0.383554\pi$
$888$	−0.165287	+	0.286285i	−0.00554667	+	0.00960711i
$889$	−12.6110	+	9.86598i	−0.422958	+	0.330894i
$890$	−6.53746	+	11.3232i	−0.219136	+	0.379555i
$891$	−0.775934	−	1.34396i	−0.0259948	−	0.0450243i
$892$	−12.1673	−	21.0744i	−0.407392	−	0.705624i
$893$	−9.25970			−0.309864
$894$	17.3232			0.579375
$895$	−4.32082	−	7.48389i	−0.144429	−	0.250159i
$896$	0.369922	+	2.61976i	0.0123582	+	0.0875201i
$897$	−18.9709	+	2.09231i	−0.633419	+	0.0698602i
$898$	2.95700	−	5.12167i	0.0986764	−	0.170912i
$899$	−25.1802	+	43.6134i	−0.839807	+	1.45459i
$900$	2.11065	−	3.65575i	0.0703549	−	0.121858i
$901$	48.3878	+	83.8101i	1.61203	+	2.79212i
$902$	9.40178			0.313045
$903$	−14.0022	+	10.9544i	−0.465966	+	0.364541i
$904$	5.71537	−	9.89931i	0.190090	−	0.329246i
$905$	5.11380	−	8.85736i	0.169989	−	0.294429i
$906$	2.81854			0.0936397
$907$	−26.7022	+	46.2496i	−0.886632	+	1.53569i	−0.0428006	+	0.999084i	$0.513628\pi$
$907$	−26.7022	+	46.2496i	−0.886632	+	1.53569i	−0.843832	+	0.536608i	$0.819705\pi$
$908$	9.56035			0.317271
$909$	7.82879			0.259665
$910$	−2.08365	−	8.15602i	−0.0690722	−	0.270369i
$911$	5.96942			0.197776			0.0988878	−	0.995099i	$-0.468472\pi$
$911$	5.96942			0.197776			0.0988878	+	0.995099i	$0.468472\pi$
$912$	4.74161			0.157010
$913$	8.18756	−	14.1813i	0.270969	−	0.469331i
$914$	−14.1933			−0.469473
$915$	6.33234	−	10.9679i	0.209341	−	0.362589i
$916$	−5.40570	+	9.36295i	−0.178609	+	0.309360i
$917$	−13.0561	−	5.26514i	−0.431152	−	0.173870i
$918$	−7.17592			−0.236841
$919$	13.4203	+	23.2446i	0.442695	+	0.766770i	0.997888	−	0.0649513i	$-0.0206892\pi$
$919$	13.4203	+	23.2446i	0.442695	+	0.766770i	−0.555194	+	0.831721i	$0.687356\pi$
$920$	−2.33559	+	4.04537i	−0.0770023	+	0.133372i
$921$	10.2494	−	17.7525i	0.337729	−	0.584963i
$922$	15.1395	−	26.2224i	0.498593	−	0.863589i
$923$	35.9088	−	3.96041i	1.18195	−	0.130358i
$924$	3.23382	−	2.52992i	0.106385	−	0.0832284i
$925$	0.697725	+	1.20850i	0.0229411	+	0.0397351i
$926$	−32.8167			−1.07842
$927$	−0.860345			−0.0282574
$928$	3.87494	+	6.71160i	0.127201	+	0.220319i
$929$	4.10661	+	7.11286i	0.134734	+	0.233365i	0.925496	−	0.378758i	$-0.123649\pi$
$929$	4.10661	+	7.11286i	0.134734	+	0.233365i	−0.790762	+	0.612124i	$0.790315\pi$
$930$	2.86715	−	4.96605i	0.0940176	−	0.162843i
$931$	23.9058	+	23.0255i	0.783480	+	0.754630i
$932$	−5.15806	+	8.93403i	−0.168958	+	0.292644i
$933$	−14.1205			−0.462283
$934$	−10.4247	+	18.0562i	−0.341108	+	0.590816i
$935$	4.91348	+	8.51039i	0.160688	+	0.278320i
$936$	1.44960	−	3.30131i	0.0473818	−	0.107907i
$937$	−22.5249			−0.735855			−0.367927	−	0.929854i	$-0.619933\pi$
$937$	−22.5249			−0.735855			−0.367927	+	0.929854i	$0.619933\pi$
$938$	18.4147	+	7.42608i	0.601260	+	0.242470i
$939$	14.5296	+	25.1661i	0.474157	+	0.821264i
$940$	0.861644	+	1.49241i	0.0281037	+	0.0486771i
$941$	−7.98410	−	13.8289i	−0.260274	−	0.450808i	0.706040	−	0.708172i	$-0.250480\pi$
$941$	−7.98410	−	13.8289i	−0.260274	−	0.450808i	−0.966315	+	0.257363i	$0.917146\pi$
$942$	−12.7964			−0.416931
$943$	−16.0349	−	27.7733i	−0.522168	−	0.904422i
$944$	5.27138			0.171569
$945$	−2.16529	−	0.873194i	−0.0704368	−	0.0284050i
$946$	5.21390	+	9.03074i	0.169518	+	0.293615i
$947$	−1.35007			−0.0438715			−0.0219358	−	0.999759i	$-0.506983\pi$
$947$	−1.35007			−0.0438715			−0.0219358	+	0.999759i	$0.506983\pi$
$948$	6.67928	+	11.5689i	0.216933	+	0.375739i
$949$	5.60370	−	12.7618i	0.181904	−	0.414266i
$950$	10.0079	−	17.3341i	0.324698	−	0.562393i
$951$	−6.08027	−	10.5313i	−0.197166	−	0.341502i
$952$	−2.65453	−	18.7992i	−0.0860338	−	0.609286i
$953$	−21.1684	+	36.6647i	−0.685711	+	1.18769i	0.287502	+	0.957780i	$0.407175\pi$
$953$	−21.1684	+	36.6647i	−0.685711	+	1.18769i	−0.973213	+	0.229906i	$0.926158\pi$
$954$	−6.74308	+	11.6794i	−0.218315	+	0.378133i
$955$	−1.11517			−0.0360860
$956$	11.0866			0.358565
$957$	6.01340	−	10.4155i	0.194386	−	0.336686i
$958$	12.0950	−	20.9492i	0.390773	−	0.676839i
$959$	−2.96353	−	20.9875i	−0.0956973	−	0.677722i
$960$	−0.441221	−	0.764218i	−0.0142404	−	0.0246650i
$961$	−5.61340	+	9.72269i	−0.181077	+	0.313635i
$962$	0.705517	+	0.960664i	0.0227468	+	0.0309730i
$963$	4.07130	+	7.05170i	0.131196	+	0.227238i
$964$	−18.6739			−0.601447
$965$	−8.37553	−	14.5068i	−0.269618	−	0.466992i
$966$	−12.9888	−	5.23800i	−0.417909	−	0.168530i
$967$	−24.2814			−0.780838			−0.390419	−	0.920637i	$-0.627670\pi$
$967$	−24.2814			−0.780838			−0.390419	+	0.920637i	$0.627670\pi$
$968$	4.29585	+	7.44063i	0.138074	+	0.239151i
$969$	−34.0254			−1.09305
$970$	5.11163	+	8.85361i	0.164125	+	0.284272i
$971$	12.3692	+	21.4241i	0.396946	+	0.687531i	0.993347	−	0.115155i	$-0.0367366\pi$
$971$	12.3692	+	21.4241i	0.396946	+	0.687531i	−0.596401	+	0.802686i	$0.703403\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	43.5580	+	17.5656i	1.39640	+	0.563127i
$974$	−40.3065			−1.29150
$975$	−9.00916	−	12.2673i	−0.288524	−	0.392868i
$976$	7.17592	+	12.4291i	0.229696	+	0.397844i
$977$	2.83780	−	4.91521i	0.0907892	−	0.157251i	−0.817054	−	0.576561i	$-0.804394\pi$
$977$	2.83780	−	4.91521i	0.0907892	−	0.157251i	0.907843	+	0.419309i	$0.137728\pi$
$978$	−10.6877			−0.341756
$979$	−11.4968	+	19.9131i	−0.367440	+	0.636424i
$980$	1.48658	−	5.99555i	0.0474869	−	0.191521i
$981$	4.73806	−	8.20656i	0.151275	−	0.262015i
$982$	−3.58602	−	6.21117i	−0.114435	−	0.198207i
$983$	−14.6863	−	25.4374i	−0.468419	−	0.811326i	0.530929	−	0.847416i	$-0.321843\pi$
$983$	−14.6863	−	25.4374i	−0.468419	−	0.811326i	−0.999349	+	0.0360900i	$0.988510\pi$
$984$	6.05836			0.193134
$985$	−21.4938			−0.684850
$986$	−27.8063	−	48.1619i	−0.885532	−	1.53379i
$987$	−4.06941	+	3.18364i	−0.129531	+	0.101336i
$988$	6.87345	−	15.6535i	0.218674	−	0.498005i
$989$	17.7848	−	30.8041i	0.565523	−	0.979515i
$990$	−0.684718	+	1.18597i	−0.0217618	+	0.0376925i
$991$	−2.80304	+	4.85500i	−0.0890414	+	0.154224i	−0.907106	−	0.420902i	$-0.861714\pi$
$991$	−2.80304	+	4.85500i	−0.0890414	+	0.154224i	0.818065	+	0.575126i	$0.195047\pi$
$992$	3.24911	+	5.62762i	0.103159	+	0.178677i
$993$	9.93371			0.315237
$994$	24.5858	+	9.91470i	0.779814	+	0.314475i
$995$	−9.48885	+	16.4352i	−0.300817	+	0.521030i
$996$	5.27593	−	9.13819i	0.167174	−	0.289555i
$997$	52.0689			1.64904			0.824520	−	0.565833i	$-0.191445\pi$
$997$	52.0689			1.64904			0.824520	+	0.565833i	$0.191445\pi$
$998$	8.24802	−	14.2860i	0.261086	−	0.452215i
$999$	0.330574			0.0104589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.c.289.2	✓	8
3.2	odd	2		1638.2.m.h.289.3		8
7.4	even	3		546.2.k.c.445.2	yes	8
13.9	even	3		546.2.k.c.373.2	yes	8
21.11	odd	6		1638.2.p.h.991.3		8
39.35	odd	6		1638.2.p.h.919.3		8
91.74	even	3	inner	546.2.j.c.529.2	yes	8
273.74	odd	6		1638.2.m.h.1621.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.2	✓	8	1.1	even	1	trivial
546.2.j.c.529.2	yes	8	91.74	even	3	inner
546.2.k.c.373.2	yes	8	13.9	even	3
546.2.k.c.445.2	yes	8	7.4	even	3
1638.2.m.h.289.3		8	3.2	odd	2
1638.2.m.h.1621.3		8	273.74	odd	6
1638.2.p.h.919.3		8	39.35	odd	6
1638.2.p.h.991.3		8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.369922 + 2.61976i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.441221 + 0.764218i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.369922 + 2.61976i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.441221 + 0.764218i) q^{10} +(-0.775934 + 1.34396i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.13422 + 2.90605i) q^{13} +(0.369922 + 2.61976i) q^{14} +(-0.441221 - 0.764218i) q^{15} +1.00000 q^{16} -7.17592 q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.37080 - 4.10635i) q^{19} +(-0.441221 + 0.764218i) q^{20} +(-2.45374 - 0.989520i) q^{21} +(-0.775934 + 1.34396i) q^{22} +5.29348 q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.11065 + 3.65575i) q^{25} +(2.13422 + 2.90605i) q^{26} +1.00000 q^{27} +(0.369922 + 2.61976i) q^{28} +(3.87494 + 6.71160i) q^{29} +(-0.441221 - 0.764218i) q^{30} +(3.24911 + 5.62762i) q^{31} +1.00000 q^{32} +(-0.775934 - 1.34396i) q^{33} -7.17592 q^{34} +(-2.16529 - 0.873194i) q^{35} +(-0.500000 - 0.866025i) q^{36} +0.330574 q^{37} +(-2.37080 - 4.10635i) q^{38} +(-3.58382 + 0.395262i) q^{39} +(-0.441221 + 0.764218i) q^{40} +(-3.02918 - 5.24669i) q^{41} +(-2.45374 - 0.989520i) q^{42} +(3.35975 - 5.81927i) q^{43} +(-0.775934 + 1.34396i) q^{44} +0.882443 q^{45} +5.29348 q^{46} +(0.976430 - 1.69123i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-6.72632 + 1.93822i) q^{49} +(2.11065 + 3.65575i) q^{50} +(3.58796 - 6.21453i) q^{51} +(2.13422 + 2.90605i) q^{52} +(-6.74308 - 11.6794i) q^{53} +1.00000 q^{54} +(-0.684718 - 1.18597i) q^{55} +(0.369922 + 2.61976i) q^{56} +4.74161 q^{57} +(3.87494 + 6.71160i) q^{58} +5.27138 q^{59} +(-0.441221 - 0.764218i) q^{60} +(7.17592 + 12.4291i) q^{61} +(3.24911 + 5.62762i) q^{62} +(2.08382 - 1.63024i) q^{63} +1.00000 q^{64} +(-3.16252 + 0.348796i) q^{65} +(-0.775934 - 1.34396i) q^{66} +(3.75236 - 6.49929i) q^{67} -7.17592 q^{68} +(-2.64674 + 4.58428i) q^{69} +(-2.16529 - 0.873194i) q^{70} +(5.00985 - 8.67732i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.93284 - 3.34778i) q^{73} +0.330574 q^{74} -4.22129 q^{75} +(-2.37080 - 4.10635i) q^{76} +(-3.80789 - 1.53560i) q^{77} +(-3.58382 + 0.395262i) q^{78} +(6.67928 - 11.5689i) q^{79} +(-0.441221 + 0.764218i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.02918 - 5.24669i) q^{82} -10.5519 q^{83} +(-2.45374 - 0.989520i) q^{84} +(3.16617 - 5.48396i) q^{85} +(3.35975 - 5.81927i) q^{86} -7.74989 q^{87} +(-0.775934 + 1.34396i) q^{88} +14.8167 q^{89} +0.882443 q^{90} +(-6.82366 + 6.66615i) q^{91} +5.29348 q^{92} -6.49821 q^{93} +(0.976430 - 1.69123i) q^{94} +4.18420 q^{95} +(-0.500000 + 0.866025i) q^{96} +(5.79259 - 10.0331i) q^{97} +(-6.72632 + 1.93822i) q^{98} +1.55187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 2 q^{25} + 3 q^{26} + 8 q^{27} + 3 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} + 4 q^{34} - 22 q^{35} - 4 q^{36} + 12 q^{37} - 4 q^{38} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 3 q^{42} + 4 q^{44} - 4 q^{45} - 8 q^{46} + 7 q^{47} - 4 q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - q^{53} + 8 q^{54} - 25 q^{55} + 3 q^{56} + 8 q^{57} + 2 q^{58} - 32 q^{59} + 2 q^{60} - 4 q^{61} + 14 q^{62} + 8 q^{64} + 10 q^{65} + 4 q^{66} + 19 q^{67} + 4 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} - 4 q^{72} - 7 q^{73} + 12 q^{74} - 4 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} + 2 q^{80} - 4 q^{81} + 12 q^{82} - 64 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{87} + 4 q^{88} + 22 q^{89} - 4 q^{90} - 38 q^{91} - 8 q^{92} - 28 q^{93} + 7 q^{94} - 56 q^{95} - 4 q^{96} + 11 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 + 2 * q^15 + 8 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^20 - 3 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 2 * q^25 + 3 * q^26 + 8 * q^27 + 3 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 + 4 * q^34 - 22 * q^35 - 4 * q^36 + 12 * q^37 - 4 * q^38 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 3 * q^42 + 4 * q^44 - 4 * q^45 - 8 * q^46 + 7 * q^47 - 4 * q^48 + 5 * q^49 + 2 * q^50 - 2 * q^51 + 3 * q^52 - q^53 + 8 * q^54 - 25 * q^55 + 3 * q^56 + 8 * q^57 + 2 * q^58 - 32 * q^59 + 2 * q^60 - 4 * q^61 + 14 * q^62 + 8 * q^64 + 10 * q^65 + 4 * q^66 + 19 * q^67 + 4 * q^68 + 4 * q^69 - 22 * q^70 + 20 * q^71 - 4 * q^72 - 7 * q^73 + 12 * q^74 - 4 * q^75 - 4 * q^76 - 24 * q^77 - 12 * q^78 + 24 * q^79 + 2 * q^80 - 4 * q^81 + 12 * q^82 - 64 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^87 + 4 * q^88 + 22 * q^89 - 4 * q^90 - 38 * q^91 - 8 * q^92 - 28 * q^93 + 7 * q^94 - 56 * q^95 - 4 * q^96 + 11 * q^97 + 5 * q^98 - 8 * q^99

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