LMFDB - Embedded newform 546.2.bd.b.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.4
Root			$1.77962i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.b.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.542536 + 2.58953i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.542536 + 2.58953i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.77962 q^{10} -0.0292310i q^{11} +(0.500000 - 0.866025i) q^{12} +(0.100748 + 3.60414i) q^{13} +(-0.824914 - 2.51386i) q^{14} +(1.54119 + 0.889808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.05630 + 5.29367i) q^{17} +(-0.866025 + 0.500000i) q^{18} -6.65918i q^{19} +(1.54119 - 0.889808i) q^{20} +(-0.542536 + 2.58953i) q^{21} +(0.0146155 + 0.0253148i) q^{22} +(2.40138 + 4.15932i) q^{23} +1.00000i q^{24} +(-0.916484 - 1.58740i) q^{25} +(-1.88932 - 3.07091i) q^{26} +1.00000 q^{27} +(1.97133 + 1.76461i) q^{28} +(-2.29119 + 3.96846i) q^{29} -1.77962 q^{30} +(3.81631 - 2.20335i) q^{31} +(0.866025 + 0.500000i) q^{32} -0.0292310i q^{33} -6.11260i q^{34} +(-3.14033 + 3.50821i) q^{35} +(0.500000 - 0.866025i) q^{36} +(9.49435 - 5.48157i) q^{37} +(3.32959 + 5.76702i) q^{38} +(0.100748 + 3.60414i) q^{39} +(-0.889808 + 1.54119i) q^{40} +(-6.40202 - 3.69621i) q^{41} +(-0.824914 - 2.51386i) q^{42} +(4.27767 + 7.40915i) q^{43} +(-0.0253148 - 0.0146155i) q^{44} +(1.54119 + 0.889808i) q^{45} +(-4.15932 - 2.40138i) q^{46} +(4.84344 + 2.79636i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-6.41131 - 2.80982i) q^{49} +(1.58740 + 0.916484i) q^{50} +(-3.05630 + 5.29367i) q^{51} +(3.17165 + 1.71482i) q^{52} +(0.0633613 + 0.109745i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.0260100 - 0.0450507i) q^{55} +(-2.58953 - 0.542536i) q^{56} -6.65918i q^{57} -4.58238i q^{58} +(11.0448 + 6.37671i) q^{59} +(1.54119 - 0.889808i) q^{60} -6.42985 q^{61} +(-2.20335 + 3.81631i) q^{62} +(-0.542536 + 2.58953i) q^{63} -1.00000 q^{64} +(-3.05172 + 5.64432i) q^{65} +(0.0146155 + 0.0253148i) q^{66} -5.69640i q^{67} +(3.05630 + 5.29367i) q^{68} +(2.40138 + 4.15932i) q^{69} +(0.965505 - 4.60836i) q^{70} +(-7.24189 + 4.18111i) q^{71} +1.00000i q^{72} +(-5.21521 + 3.01100i) q^{73} +(-5.48157 + 9.49435i) q^{74} +(-0.916484 - 1.58740i) q^{75} +(-5.76702 - 3.32959i) q^{76} +(0.0756946 + 0.0158589i) q^{77} +(-1.88932 - 3.07091i) q^{78} +(0.798515 - 1.38307i) q^{79} -1.77962i q^{80} +1.00000 q^{81} +7.39241 q^{82} -8.39736i q^{83} +(1.97133 + 1.76461i) q^{84} +(-9.42070 + 5.43904i) q^{85} +(-7.40915 - 4.27767i) q^{86} +(-2.29119 + 3.96846i) q^{87} +0.0292310 q^{88} +(11.6920 - 6.75038i) q^{89} -1.77962 q^{90} +(-9.38769 - 1.69449i) q^{91} +4.80277 q^{92} +(3.81631 - 2.20335i) q^{93} -5.59272 q^{94} +(5.92539 - 10.2631i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-9.75571 + 5.63246i) q^{97} +(6.95727 - 0.772276i) q^{98} -0.0292310i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.54119	+	0.889808i	0.689242	+	0.397934i	0.803328	−	0.595537i	$-0.203061\pi$
$5$	1.54119	+	0.889808i	0.689242	+	0.397934i	−0.114086	+	0.993471i	$0.536394\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.542536	+	2.58953i	−0.205059	+	0.978750i
$7$	−0.542536	+	2.58953i	−0.205059	+	0.978750i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−1.77962			−0.562764
$11$		−	0.0292310i		−	0.00881349i	−0.999990	−	0.00440675i	$-0.998597\pi$
$11$		−	0.0292310i		−	0.00881349i	0.999990	−	0.00440675i	$-0.00140272\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.100748	+	3.60414i	0.0279425	+	0.999610i
$13$	0.100748	+	3.60414i	0.0279425	+	0.999610i
$14$	−0.824914	−	2.51386i	−0.220468	−	0.671859i
$15$	1.54119	+	0.889808i	0.397934	+	0.229747i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.05630	+	5.29367i	−0.741262	+	1.28390i	0.210659	+	0.977560i	$0.432439\pi$
$17$	−3.05630	+	5.29367i	−0.741262	+	1.28390i	−0.951921	+	0.306344i	$0.900894\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$		−	6.65918i		−	1.52772i	−0.645382	−	0.763860i	$-0.723302\pi$
$19$		−	6.65918i		−	1.52772i	0.645382	−	0.763860i	$-0.276698\pi$
$20$	1.54119	−	0.889808i	0.344621	−	0.198967i
$21$	−0.542536	+	2.58953i	−0.118391	+	0.565081i
$22$	0.0146155	+	0.0253148i	0.00311604	+	0.00539714i
$23$	2.40138	+	4.15932i	0.500723	+	0.867278i	1.00000		0.000834974i	$0.000265781\pi$
$23$	2.40138	+	4.15932i	0.500723	+	0.867278i	−0.499277	+	0.866443i	$0.666401\pi$
$24$			1.00000i			0.204124i
$25$	−0.916484	−	1.58740i	−0.183297	−	0.317479i
$26$	−1.88932	−	3.07091i	−0.370527	−	0.602254i
$27$	1.00000			0.192450
$28$	1.97133	+	1.76461i	0.372546	+	0.333481i
$29$	−2.29119	+	3.96846i	−0.425463	+	0.736924i	−0.996464	−	0.0840257i	$-0.973222\pi$
$29$	−2.29119	+	3.96846i	−0.425463	+	0.736924i	0.571000	+	0.820950i	$0.306556\pi$
$30$	−1.77962			−0.324912
$31$	3.81631	−	2.20335i	0.685430	−	0.395733i	−0.116468	−	0.993194i	$-0.537157\pi$
$31$	3.81631	−	2.20335i	0.685430	−	0.395733i	0.801898	+	0.597461i	$0.203824\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		−	0.0292310i		−	0.00508847i
$34$		−	6.11260i		−	1.04830i
$35$	−3.14033	+	3.50821i	−0.530813	+	0.592995i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	9.49435	−	5.48157i	1.56086	−	0.901164i	0.563692	−	0.825985i	$-0.309381\pi$
$37$	9.49435	−	5.48157i	1.56086	−	0.901164i	0.997170	−	0.0751786i	$-0.0239527\pi$
$38$	3.32959	+	5.76702i	0.540131	+	0.935534i
$39$	0.100748	+	3.60414i	0.0161326	+	0.577125i
$40$	−0.889808	+	1.54119i	−0.140691	+	0.243684i
$41$	−6.40202	−	3.69621i	−0.999827	−	0.577251i	−0.0916301	−	0.995793i	$-0.529208\pi$
$41$	−6.40202	−	3.69621i	−0.999827	−	0.577251i	−0.908197	+	0.418543i	$0.862541\pi$
$42$	−0.824914	−	2.51386i	−0.127287	−	0.387898i
$43$	4.27767	+	7.40915i	0.652339	+	1.12988i	0.982554	+	0.185979i	$0.0595455\pi$
$43$	4.27767	+	7.40915i	0.652339	+	1.12988i	−0.330215	+	0.943906i	$0.607121\pi$
$44$	−0.0253148	−	0.0146155i	−0.00381635	−	0.00220337i
$45$	1.54119	+	0.889808i	0.229747	+	0.132645i
$46$	−4.15932	−	2.40138i	−0.613258	−	0.354065i
$47$	4.84344	+	2.79636i	0.706488	+	0.407891i	0.809759	−	0.586762i	$-0.199598\pi$
$47$	4.84344	+	2.79636i	0.706488	+	0.407891i	−0.103271	+	0.994653i	$0.532931\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−6.41131	−	2.80982i	−0.915901	−	0.401403i
$50$	1.58740	+	0.916484i	0.224492	+	0.129610i
$51$	−3.05630	+	5.29367i	−0.427968	+	0.741262i
$52$	3.17165	+	1.71482i	0.439829	+	0.237803i
$53$	0.0633613	+	0.109745i	0.00870334	+	0.0150746i	0.870344	−	0.492444i	$-0.163896\pi$
$53$	0.0633613	+	0.109745i	0.00870334	+	0.0150746i	−0.861641	+	0.507518i	$0.830563\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	0.0260100	−	0.0450507i	0.00350719	−	0.00607463i
$56$	−2.58953	−	0.542536i	−0.346040	−	0.0724994i
$57$		−	6.65918i		−	0.882030i
$58$		−	4.58238i		−	0.601696i
$59$	11.0448	+	6.37671i	1.43791	+	0.830177i	0.997704	−	0.0677203i	$-0.0215725\pi$
$59$	11.0448	+	6.37671i	1.43791	+	0.830177i	0.440205	+	0.897897i	$0.354906\pi$
$60$	1.54119	−	0.889808i	0.198967	−	0.114874i
$61$	−6.42985			−0.823257			−0.411629	−	0.911352i	$-0.635040\pi$
$61$	−6.42985			−0.823257			−0.411629	+	0.911352i	$0.635040\pi$
$62$	−2.20335	+	3.81631i	−0.279825	+	0.484672i
$63$	−0.542536	+	2.58953i	−0.0683531	+	0.326250i
$64$	−1.00000			−0.125000
$65$	−3.05172	+	5.64432i	−0.378520	+	0.700092i
$66$	0.0146155	+	0.0253148i	0.00179905	+	0.00311604i
$67$		−	5.69640i		−	0.695926i	−0.937508	−	0.347963i	$-0.886873\pi$
$67$		−	5.69640i		−	0.695926i	0.937508	−	0.347963i	$-0.113127\pi$
$68$	3.05630	+	5.29367i	0.370631	+	0.641952i
$69$	2.40138	+	4.15932i	0.289093	+	0.500723i
$70$	0.965505	−	4.60836i	0.115400	−	0.550805i
$71$	−7.24189	+	4.18111i	−0.859455	+	0.496206i	−0.863830	−	0.503784i	$-0.831941\pi$
$71$	−7.24189	+	4.18111i	−0.859455	+	0.496206i	0.00437501	+	0.999990i	$0.498607\pi$
$72$			1.00000i			0.117851i
$73$	−5.21521	+	3.01100i	−0.610394	+	0.352411i	−0.773120	−	0.634260i	$-0.781305\pi$
$73$	−5.21521	+	3.01100i	−0.610394	+	0.352411i	0.162726	+	0.986671i	$0.447971\pi$
$74$	−5.48157	+	9.49435i	−0.637219	+	1.10370i
$75$	−0.916484	−	1.58740i	−0.105826	−	0.183297i
$76$	−5.76702	−	3.32959i	−0.661522	−	0.381930i
$77$	0.0756946	+	0.0158589i	0.00862620	+	0.00180729i
$78$	−1.88932	−	3.07091i	−0.213924	−	0.347712i
$79$	0.798515	−	1.38307i	0.0898400	−	0.155607i	−0.817603	−	0.575782i	$-0.804698\pi$
$79$	0.798515	−	1.38307i	0.0898400	−	0.155607i	0.907443	+	0.420174i	$0.138031\pi$
$80$		−	1.77962i		−	0.198967i
$81$	1.00000			0.111111
$82$	7.39241			0.816356
$83$		−	8.39736i		−	0.921730i	−0.887470	−	0.460865i	$-0.847539\pi$
$83$		−	8.39736i		−	0.921730i	0.887470	−	0.460865i	$-0.152461\pi$
$84$	1.97133	+	1.76461i	0.215090	+	0.192535i
$85$	−9.42070	+	5.43904i	−1.02182	+	0.589947i
$86$	−7.40915	−	4.27767i	−0.798949	−	0.461273i
$87$	−2.29119	+	3.96846i	−0.245641	+	0.425463i
$88$	0.0292310			0.00311604
$89$	11.6920	−	6.75038i	1.23935	−	0.715539i	0.270388	−	0.962751i	$-0.412848\pi$
$89$	11.6920	−	6.75038i	1.23935	−	0.715539i	0.968961	+	0.247213i	$0.0795147\pi$
$90$	−1.77962			−0.187588
$91$	−9.38769	−	1.69449i	−0.984097	−	0.177631i
$92$	4.80277			0.500723
$93$	3.81631	−	2.20335i	0.395733	−	0.228477i
$94$	−5.59272			−0.576845
$95$	5.92539	−	10.2631i	0.607932	−	1.05297i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−9.75571	+	5.63246i	−0.990543	+	0.571890i	−0.905436	−	0.424482i	$-0.860456\pi$
$97$	−9.75571	+	5.63246i	−0.990543	+	0.571890i	−0.0851062	+	0.996372i	$0.527123\pi$
$98$	6.95727	−	0.772276i	0.702790	−	0.0780117i
$99$		−	0.0292310i		−	0.00293783i
$100$	−1.83297			−0.183297
$101$	0.642014			0.0638828			0.0319414	−	0.999490i	$-0.489831\pi$
$101$	0.642014			0.0638828			0.0319414	+	0.999490i	$0.489831\pi$
$102$		−	6.11260i		−	0.605238i
$103$	9.07044	−	15.7105i	0.893737	−	1.54800i	0.0583760	−	0.998295i	$-0.481408\pi$
$103$	9.07044	−	15.7105i	0.893737	−	1.54800i	0.835361	−	0.549702i	$-0.185259\pi$
$104$	−3.60414	+	0.100748i	−0.353415	+	0.00987915i
$105$	−3.14033	+	3.50821i	−0.306465	+	0.342366i
$106$	−0.109745	−	0.0633613i	−0.0106594	−	0.00615419i
$107$	−0.276497	−	0.478908i	−0.0267300	−	0.0462978i	0.852351	−	0.522970i	$-0.175176\pi$
$107$	−0.276497	−	0.478908i	−0.0267300	−	0.0462978i	−0.879081	+	0.476672i	$0.841843\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	17.1187	−	9.88349i	1.63968	−	0.946667i	0.658731	−	0.752379i	$-0.271094\pi$
$109$	17.1187	−	9.88349i	1.63968	−	0.946667i	0.980945	−	0.194288i	$-0.0622396\pi$
$110$			0.0520200i			0.00495991i
$111$	9.49435	−	5.48157i	0.901164	−	0.520287i
$112$	2.51386	−	0.824914i	0.237538	−	0.0779471i
$113$	−1.00335	−	1.73785i	−0.0943873	−	0.163484i	0.814965	−	0.579510i	$-0.196756\pi$
$113$	−1.00335	−	1.73785i	−0.0943873	−	0.163484i	−0.909353	+	0.416026i	$0.863423\pi$
$114$	3.32959	+	5.76702i	0.311845	+	0.540131i
$115$			8.54708i			0.797019i
$116$	2.29119	+	3.96846i	0.212732	+	0.368462i
$117$	0.100748	+	3.60414i	0.00931415	+	0.333203i
$118$	−12.7534			−1.17405
$119$	−12.0500	−	10.7864i	−1.10462	−	0.988786i
$120$	−0.889808	+	1.54119i	−0.0812280	+	0.140691i
$121$	10.9991			0.999922
$122$	5.56841	−	3.21492i	0.504140	−	0.291065i
$123$	−6.40202	−	3.69621i	−0.577251	−	0.333276i
$124$		−	4.40670i		−	0.395733i
$125$		−	12.1601i		−	1.08763i
$126$	−0.824914	−	2.51386i	−0.0734892	−	0.223953i
$127$	5.01216	−	8.68131i	0.444757	−	0.770342i	−0.553278	−	0.832997i	$-0.686623\pi$
$127$	5.01216	−	8.68131i	0.444757	−	0.770342i	0.998035	+	0.0626548i	$0.0199567\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.27767	+	7.40915i	0.376628	+	0.652339i
$130$	−0.179293	−	6.41399i	−0.0157250	−	0.562544i
$131$	0.434167	−	0.751999i	0.0379333	−	0.0657025i	−0.846435	−	0.532491i	$-0.821256\pi$
$131$	0.434167	−	0.751999i	0.0379333	−	0.0657025i	0.884369	+	0.466789i	$0.154589\pi$
$132$	−0.0253148	−	0.0146155i	−0.00220337	−	0.00127212i
$133$	17.2441	+	3.61284i	1.49526	+	0.313273i
$134$	2.84820	+	4.93323i	0.246047	+	0.426166i
$135$	1.54119	+	0.889808i	0.132645	+	0.0765825i
$136$	−5.29367	−	3.05630i	−0.453928	−	0.262076i
$137$	−17.0004	−	9.81520i	−1.45244	−	0.838569i	−0.453825	−	0.891091i	$-0.649941\pi$
$137$	−17.0004	−	9.81520i	−1.45244	−	0.838569i	−0.998620	+	0.0525218i	$0.983274\pi$
$138$	−4.15932	−	2.40138i	−0.354065	−	0.204419i
$139$	−1.50591	−	2.60832i	−0.127730	−	0.221235i	0.795067	−	0.606522i	$-0.207436\pi$
$139$	−1.50591	−	2.60832i	−0.127730	−	0.221235i	−0.922797	+	0.385287i	$0.874102\pi$
$140$	1.46803	+	4.47371i	0.124071	+	0.378098i
$141$	4.84344	+	2.79636i	0.407891	+	0.235496i
$142$	4.18111	−	7.24189i	0.350871	−	0.607726i
$143$	0.105353	−	0.00294497i	0.00881005	−	0.000246271i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−7.06233	+	4.07744i	−0.586495	+	0.338613i
$146$	3.01100	−	5.21521i	0.249192	−	0.431614i
$147$	−6.41131	−	2.80982i	−0.528796	−	0.231750i
$148$		−	10.9631i		−	0.901164i
$149$		−	14.7964i		−	1.21217i	−0.795401	−	0.606084i	$-0.792739\pi$
$149$		−	14.7964i		−	1.21217i	0.795401	−	0.606084i	$-0.207261\pi$
$150$	1.58740	+	0.916484i	0.129610	+	0.0748306i
$151$	0.606515	−	0.350172i	0.0493575	−	0.0284966i	−0.475118	−	0.879922i	$-0.657595\pi$
$151$	0.606515	−	0.350172i	0.0493575	−	0.0284966i	0.524476	+	0.851425i	$0.324261\pi$
$152$	6.65918			0.540131
$153$	−3.05630	+	5.29367i	−0.247087	+	0.427968i
$154$	−0.0734829	+	0.0241131i	−0.00592142	+	0.00194309i
$155$	7.84222			0.629903
$156$	3.17165	+	1.71482i	0.253936	+	0.137296i
$157$	−4.48136	−	7.76194i	−0.357651	−	0.619470i	0.629917	−	0.776663i	$-0.283089\pi$
$157$	−4.48136	−	7.76194i	−0.357651	−	0.619470i	−0.987568	+	0.157193i	$0.949756\pi$
$158$			1.59703i			0.127053i
$159$	0.0633613	+	0.109745i	0.00502488	+	0.00870334i
$160$	0.889808	+	1.54119i	0.0703455	+	0.121842i
$161$	−12.0735	+	3.96187i	−0.951525	+	0.312239i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$		−	6.70067i		−	0.524837i	−0.964954	−	0.262418i	$-0.915480\pi$
$163$		−	6.70067i		−	0.524837i	0.964954	−	0.262418i	$-0.0845200\pi$
$164$	−6.40202	+	3.69621i	−0.499914	+	0.288625i
$165$	0.0260100	−	0.0450507i	0.00202488	−	0.00350719i
$166$	4.19868	+	7.27232i	0.325881	+	0.564442i
$167$	4.07956	+	2.35534i	0.315686	+	0.182261i	0.649468	−	0.760389i	$-0.274992\pi$
$167$	4.07956	+	2.35534i	0.315686	+	0.182261i	−0.333782	+	0.942650i	$0.608325\pi$
$168$	−2.58953	−	0.542536i	−0.199786	−	0.0418576i
$169$	−12.9797	+	0.726220i	−0.998438	+	0.0558631i
$170$	5.43904	−	9.42070i	0.417155	−	0.722534i
$171$		−	6.65918i		−	0.509240i
$172$	8.55535			0.652339
$173$	−22.5042			−1.71096			−0.855482	−	0.517832i	$-0.826739\pi$
$173$	−22.5042			−1.71096			−0.855482	+	0.517832i	$0.826739\pi$
$174$		−	4.58238i		−	0.347389i
$175$	4.60783	−	1.51204i	0.348320	−	0.114300i
$176$	−0.0253148	+	0.0146155i	−0.00190818	+	0.00110169i
$177$	11.0448	+	6.37671i	0.830177	+	0.479303i
$178$	−6.75038	+	11.6920i	−0.505962	+	0.876352i
$179$	16.1669			1.20837			0.604184	−	0.796845i	$-0.293499\pi$
$179$	16.1669			1.20837			0.604184	+	0.796845i	$0.293499\pi$
$180$	1.54119	−	0.889808i	0.114874	−	0.0663224i
$181$	−13.5438			−1.00671			−0.503353	−	0.864081i	$-0.667900\pi$
$181$	−13.5438			−1.00671			−0.503353	+	0.864081i	$0.667900\pi$
$182$	8.97722	−	3.22638i	0.665436	−	0.239155i
$183$	−6.42985			−0.475308
$184$	−4.15932	+	2.40138i	−0.306629	+	0.177032i
$185$	19.5102			1.43442
$186$	−2.20335	+	3.81631i	−0.161557	+	0.279825i
$187$	0.154739	+	0.0893389i	0.0113157	+	0.00653311i
$188$	4.84344	−	2.79636i	0.353244	−	0.203946i
$189$	−0.542536	+	2.58953i	−0.0394637	+	0.188360i
$190$			11.8508i			0.859746i
$191$	1.73677			0.125668			0.0628340	−	0.998024i	$-0.479986\pi$
$191$	1.73677			0.125668			0.0628340	+	0.998024i	$0.479986\pi$
$192$	−1.00000			−0.0721688
$193$			13.8289i			0.995423i	0.867343	+	0.497711i	$0.165826\pi$
$193$			13.8289i			0.995423i	−0.867343	+	0.497711i	$0.834174\pi$
$194$	5.63246	−	9.75571i	0.404387	−	0.700419i
$195$	−3.05172	+	5.64432i	−0.218538	+	0.404198i
$196$	−5.63903	+	4.14745i	−0.402788	+	0.296246i
$197$	−3.25356	−	1.87845i	−0.231807	−	0.133834i	0.379598	−	0.925151i	$-0.376062\pi$
$197$	−3.25356	−	1.87845i	−0.231807	−	0.133834i	−0.611405	+	0.791318i	$0.709395\pi$
$198$	0.0146155	+	0.0253148i	0.00103868	+	0.00179905i
$199$	−8.48076	+	14.6891i	−0.601185	+	1.04128i	0.391457	+	0.920197i	$0.371971\pi$
$199$	−8.48076	+	14.6891i	−0.601185	+	1.04128i	−0.992642	+	0.121087i	$0.961362\pi$
$200$	1.58740	−	0.916484i	0.112246	−	0.0648052i
$201$		−	5.69640i		−	0.401793i
$202$	−0.556000	+	0.321007i	−0.0391201	+	0.0225860i
$203$	−9.03338	−	8.08613i	−0.634019	−	0.567535i
$204$	3.05630	+	5.29367i	0.213984	+	0.370631i
$205$	−6.57783	−	11.3931i	−0.459415	−	0.795731i
$206$			18.1409i			1.26393i
$207$	2.40138	+	4.15932i	0.166908	+	0.289093i
$208$	3.07091	−	1.88932i	0.212929	−	0.131001i
$209$	−0.194655			−0.0134645
$210$	0.965505	−	4.60836i	0.0666262	−	0.318007i
$211$	8.09895	−	14.0278i	0.557555	−	0.965713i	−0.440145	−	0.897927i	$-0.645073\pi$
$211$	8.09895	−	14.0278i	0.557555	−	0.965713i	0.997700	−	0.0677867i	$-0.0215937\pi$
$212$	0.126723			0.00870334
$213$	−7.24189	+	4.18111i	−0.496206	+	0.286485i
$214$	0.478908	+	0.276497i	0.0327375	+	0.0189010i
$215$			15.2252i			1.03835i
$216$			1.00000i			0.0680414i
$217$	3.63515	+	11.0778i	0.246770	+	0.752013i
$218$	−9.88349	+	17.1187i	−0.669395	+	1.15943i
$219$	−5.21521	+	3.01100i	−0.352411	+	0.203465i
$220$	−0.0260100	−	0.0450507i	−0.00175359	−	0.00303731i
$221$	−19.3871	−	10.4820i	−1.30411	−	0.705097i
$222$	−5.48157	+	9.49435i	−0.367899	+	0.637219i
$223$	8.12362	+	4.69017i	0.543998	+	0.314077i	0.746698	−	0.665164i	$-0.231638\pi$
$223$	8.12362	+	4.69017i	0.543998	+	0.314077i	−0.202700	+	0.979241i	$0.564972\pi$
$224$	−1.76461	+	1.97133i	−0.117903	+	0.131715i
$225$	−0.916484	−	1.58740i	−0.0610989	−	0.105826i
$226$	1.73785	+	1.00335i	0.115600	+	0.0667419i
$227$	−2.63975	−	1.52406i	−0.175206	−	0.101155i	0.409832	−	0.912161i	$-0.365587\pi$
$227$	−2.63975	−	1.52406i	−0.175206	−	0.101155i	−0.585038	+	0.811006i	$0.698921\pi$
$228$	−5.76702	−	3.32959i	−0.381930	−	0.220507i
$229$	6.40547	+	3.69820i	0.423285	+	0.244384i	0.696482	−	0.717574i	$-0.254748\pi$
$229$	6.40547	+	3.69820i	0.423285	+	0.244384i	−0.273197	+	0.961958i	$0.588081\pi$
$230$	−4.27354	−	7.40199i	−0.281789	−	0.488072i
$231$	0.0756946	+	0.0158589i	0.00498034	+	0.00104344i
$232$	−3.96846	−	2.29119i	−0.260542	−	0.150424i
$233$	6.38845	−	11.0651i	0.418522	−	0.724901i	−0.577269	−	0.816554i	$-0.695882\pi$
$233$	6.38845	−	11.0651i	0.418522	−	0.724901i	0.995791	+	0.0916531i	$0.0292151\pi$
$234$	−1.88932	−	3.07091i	−0.123509	−	0.200751i
$235$	4.97645	+	8.61946i	0.324628	+	0.562272i
$236$	11.0448	−	6.37671i	0.718955	−	0.415089i
$237$	0.798515	−	1.38307i	0.0518691	−	0.0898400i
$238$	15.8288	+	3.31631i	1.02603	+	0.214964i
$239$		−	23.2357i		−	1.50299i	−0.659739	−	0.751495i	$-0.729333\pi$
$239$		−	23.2357i		−	1.50299i	0.659739	−	0.751495i	$-0.270667\pi$
$240$		−	1.77962i		−	0.114874i
$241$	7.40524	+	4.27542i	0.477013	+	0.275404i	0.719171	−	0.694833i	$-0.244522\pi$
$241$	7.40524	+	4.27542i	0.477013	+	0.275404i	−0.242158	+	0.970237i	$0.577855\pi$
$242$	−9.52554	+	5.49957i	−0.612325	+	0.353526i
$243$	1.00000			0.0641500
$244$	−3.21492	+	5.56841i	−0.205814	+	0.356481i
$245$	−7.38086	−	10.0353i	−0.471546	−	0.641133i
$246$	7.39241			0.471323
$247$	24.0006	−	0.670898i	1.52712	−	0.0426882i
$248$	2.20335	+	3.81631i	0.139913	+	0.242336i
$249$		−	8.39736i		−	0.532161i
$250$	6.08003	+	10.5309i	0.384535	+	0.666034i
$251$	10.8191	+	18.7393i	0.682898	+	1.18281i	0.974092	+	0.226150i	$0.0726141\pi$
$251$	10.8191	+	18.7393i	0.682898	+	1.18281i	−0.291194	+	0.956664i	$0.594053\pi$
$252$	1.97133	+	1.76461i	0.124182	+	0.111160i
$253$	0.121581	−	0.0701949i	0.00764374	−	0.00441312i
$254$			10.0243i			0.628981i
$255$	−9.42070	+	5.43904i	−0.589947	+	0.340606i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.692232	−	1.19898i	−0.0431802	−	0.0747904i	0.843628	−	0.536929i	$-0.180416\pi$
$257$	−0.692232	−	1.19898i	−0.0431802	−	0.0747904i	−0.886808	+	0.462138i	$0.847082\pi$
$258$	−7.40915	−	4.27767i	−0.461273	−	0.266316i
$259$	9.04364	+	27.5598i	0.561945	+	1.71248i
$260$	3.36227	+	5.46503i	0.208519	+	0.338927i
$261$	−2.29119	+	3.96846i	−0.141821	+	0.245641i
$262$			0.868334i			0.0536458i
$263$	−2.19087			−0.135095			−0.0675474	−	0.997716i	$-0.521517\pi$
$263$	−2.19087			−0.135095			−0.0675474	+	0.997716i	$0.521517\pi$
$264$	0.0292310			0.00179905
$265$			0.225518i			0.0138534i
$266$	−16.7403	+	5.49325i	−1.02641	+	0.336813i
$267$	11.6920	−	6.75038i	0.715539	−	0.413116i
$268$	−4.93323	−	2.84820i	−0.301345	−	0.173981i
$269$	−15.5623	+	26.9547i	−0.948850	+	1.64346i	−0.200998	+	0.979592i	$0.564419\pi$
$269$	−15.5623	+	26.9547i	−0.948850	+	1.64346i	−0.747852	+	0.663866i	$0.768915\pi$
$270$	−1.77962			−0.108304
$271$	−21.5712	+	12.4541i	−1.31035	+	0.756533i	−0.982155	−	0.188075i	$-0.939775\pi$
$271$	−21.5712	+	12.4541i	−1.31035	+	0.756533i	−0.328200	+	0.944608i	$0.606442\pi$
$272$	6.11260			0.370631
$273$	−9.38769	−	1.69449i	−0.568169	−	0.102555i
$274$	19.6304			1.18592
$275$	−0.0464013	+	0.0267898i	−0.00279810	+	0.00161548i
$276$	4.80277			0.289093
$277$	3.01675	−	5.22517i	0.181259	−	0.313950i	−0.761050	−	0.648693i	$-0.775316\pi$
$277$	3.01675	−	5.22517i	0.181259	−	0.313950i	0.942310	+	0.334743i	$0.108649\pi$
$278$	2.60832	+	1.50591i	0.156437	+	0.0903187i
$279$	3.81631	−	2.20335i	0.228477	−	0.131911i
$280$	−3.50821	−	3.14033i	−0.209656	−	0.187671i
$281$			8.67723i			0.517640i	0.965926	+	0.258820i	$0.0833336\pi$
$281$			8.67723i			0.517640i	−0.965926	+	0.258820i	$0.916666\pi$
$282$	−5.59272			−0.333042
$283$	−22.7509			−1.35240			−0.676199	−	0.736719i	$-0.736374\pi$
$283$	−22.7509			−1.35240			−0.676199	+	0.736719i	$0.736374\pi$
$284$			8.36222i			0.496206i
$285$	5.92539	−	10.2631i	0.350990	−	0.607932i
$286$	−0.0897658	+	0.0552268i	−0.00530796	+	0.00326563i
$287$	13.0448	−	14.5729i	0.770008	−	0.860210i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−10.1820	−	17.6357i	−0.598939	−	1.03739i
$290$	4.07744	−	7.06233i	0.239435	−	0.414714i
$291$	−9.75571	+	5.63246i	−0.571890	+	0.330181i
$292$			6.02201i			0.352411i
$293$	−17.0486	+	9.84301i	−0.995989	+	0.575035i	−0.907059	−	0.421003i	$-0.861678\pi$
$293$	−17.0486	+	9.84301i	−0.995989	+	0.575035i	−0.0889301	+	0.996038i	$0.528345\pi$
$294$	6.95727	−	0.772276i	0.405756	−	0.0450401i
$295$	11.3481	+	19.6555i	0.660712	+	1.14439i
$296$	5.48157	+	9.49435i	0.318610	+	0.551848i
$297$		−	0.0292310i		−	0.00169616i
$298$	7.39820	+	12.8141i	0.428566	+	0.742298i
$299$	−14.7488	+	9.07397i	−0.852947	+	0.524761i
$300$	−1.83297			−0.105826
$301$	−21.5070	+	7.05743i	−1.23964	+	0.406783i
$302$	−0.350172	+	0.606515i	−0.0201501	+	0.0349010i
$303$	0.642014			0.0368827
$304$	−5.76702	+	3.32959i	−0.330761	+	0.190965i
$305$	−9.90963	−	5.72133i	−0.567424	−	0.327602i
$306$		−	6.11260i		−	0.349434i
$307$			5.38807i			0.307514i	0.988109	+	0.153757i	$0.0491372\pi$
$307$			5.38807i			0.307514i	−0.988109	+	0.153757i	$0.950863\pi$
$308$	0.0515815	−	0.0576240i	0.00293913	−	0.00328343i
$309$	9.07044	−	15.7105i	0.515999	−	0.893737i
$310$	−6.79157	+	3.92111i	−0.385735	+	0.222704i
$311$	1.17445	+	2.03422i	0.0665972	+	0.115350i	0.897401	−	0.441215i	$-0.145452\pi$
$311$	1.17445	+	2.03422i	0.0665972	+	0.115350i	−0.830804	+	0.556565i	$0.812119\pi$
$312$	−3.60414	+	0.100748i	−0.204044	+	0.00570373i
$313$	−12.6664	+	21.9389i	−0.715948	+	1.24006i	0.246645	+	0.969106i	$0.420672\pi$
$313$	−12.6664	+	21.9389i	−0.715948	+	1.24006i	−0.962593	+	0.270953i	$0.912661\pi$
$314$	7.76194	+	4.48136i	0.438031	+	0.252898i
$315$	−3.14033	+	3.50821i	−0.176938	+	0.197665i
$316$	−0.798515	−	1.38307i	−0.0449200	−	0.0778037i
$317$	24.2674	+	14.0108i	1.36299	+	0.786923i	0.990021	−	0.140921i	$-0.0450062\pi$
$317$	24.2674	+	14.0108i	1.36299	+	0.786923i	0.372970	+	0.927844i	$0.378340\pi$
$318$	−0.109745	−	0.0633613i	−0.00615419	−	0.00355313i
$319$	0.116002	+	0.0669739i	0.00649487	+	0.00374982i
$320$	−1.54119	−	0.889808i	−0.0861553	−	0.0497418i
$321$	−0.276497	−	0.478908i	−0.0154326	−	0.0267300i
$322$	8.47503	−	9.46783i	0.472295	−	0.527622i
$323$	35.2515	+	20.3525i	1.96144	+	1.13244i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	5.62887	−	3.46307i	0.312234	−	0.192096i
$326$	3.35033	+	5.80295i	0.185558	+	0.321395i
$327$	17.1187	−	9.88349i	0.946667	−	0.546558i
$328$	3.69621	−	6.40202i	0.204089	−	0.353492i
$329$	−9.86900	+	11.0251i	−0.544095	+	0.607833i
$330$			0.0520200i			0.00286361i
$331$			10.8406i			0.595852i	0.954589	+	0.297926i	$0.0962948\pi$
$331$			10.8406i			0.595852i	−0.954589	+	0.297926i	$0.903705\pi$
$332$	−7.27232	−	4.19868i	−0.399121	−	0.230432i
$333$	9.49435	−	5.48157i	0.520287	−	0.300388i
$334$	−4.71067			−0.257757
$335$	5.06870	−	8.77925i	0.276933	−	0.479661i
$336$	2.51386	−	0.824914i	0.137143	−	0.0450028i
$337$	12.1641			0.662620			0.331310	−	0.943522i	$-0.392509\pi$
$337$	12.1641			0.662620			0.331310	+	0.943522i	$0.392509\pi$
$338$	10.8776	−	7.11877i	0.591666	−	0.387210i
$339$	−1.00335	−	1.73785i	−0.0544945	−	0.0943873i
$340$			10.8781i			0.589947i
$341$	−0.0644062	−	0.111555i	−0.00348779	−	0.00604103i
$342$	3.32959	+	5.76702i	0.180044	+	0.311845i
$343$	10.7545	−	15.0778i	0.580687	−	0.814127i
$344$	−7.40915	+	4.27767i	−0.399474	+	0.230637i
$345$			8.54708i			0.460159i
$346$	19.4892	−	11.2521i	1.04775	−	0.604917i
$347$	10.2304	−	17.7196i	0.549196	−	0.951236i	−0.449133	−	0.893465i	$-0.648267\pi$
$347$	10.2304	−	17.7196i	0.549196	−	0.951236i	0.998330	−	0.0577713i	$-0.0183994\pi$
$348$	2.29119	+	3.96846i	0.122821	+	0.212732i
$349$	29.4511	+	17.0036i	1.57648	+	0.910181i	0.995345	+	0.0963745i	$0.0307246\pi$
$349$	29.4511	+	17.0036i	1.57648	+	0.910181i	0.581135	+	0.813807i	$0.302609\pi$
$350$	−3.23448	+	3.61338i	−0.172890	+	0.193143i
$351$	0.100748	+	3.60414i	0.00537753	+	0.192375i
$352$	0.0146155	−	0.0253148i	0.000779010	−	0.00134928i
$353$		−	7.95855i		−	0.423591i	−0.977314	−	0.211796i	$-0.932069\pi$
$353$		−	7.95855i		−	0.423591i	0.977314	−	0.211796i	$-0.0679311\pi$
$354$	−12.7534			−0.677837
$355$	−14.8815			−0.789830
$356$		−	13.5008i		−	0.715539i
$357$	−12.0500	−	10.7864i	−0.637751	−	0.570876i
$358$	−14.0009	+	8.08343i	−0.739971	+	0.427222i
$359$	10.5261	+	6.07723i	0.555545	+	0.320744i	0.751355	−	0.659898i	$-0.229400\pi$
$359$	10.5261	+	6.07723i	0.555545	+	0.320744i	−0.195811	+	0.980642i	$0.562734\pi$
$360$	−0.889808	+	1.54119i	−0.0468970	+	0.0812280i
$361$	−25.3446			−1.33393
$362$	11.7293	−	6.77192i	0.616478	−	0.355924i
$363$	10.9991			0.577305
$364$	−6.16131	+	7.28273i	−0.322941	+	0.381719i
$365$	−10.7169			−0.560946
$366$	5.56841	−	3.21492i	0.291065	−	0.168047i
$367$	−0.937821			−0.0489539			−0.0244769	−	0.999700i	$-0.507792\pi$
$367$	−0.937821			−0.0489539			−0.0244769	+	0.999700i	$0.507792\pi$
$368$	2.40138	−	4.15932i	0.125181	−	0.216819i
$369$	−6.40202	−	3.69621i	−0.333276	−	0.192417i
$370$	−16.8963	+	9.75508i	−0.878397	+	0.507142i
$371$	−0.318563	+	0.104535i	−0.0165390	+	0.00542720i
$372$		−	4.40670i		−	0.228477i
$373$	−11.0636			−0.572853			−0.286427	−	0.958102i	$-0.592467\pi$
$373$	−11.0636			−0.572853			−0.286427	+	0.958102i	$0.592467\pi$
$374$	−0.178678			−0.00923921
$375$		−	12.1601i		−	0.627943i
$376$	−2.79636	+	4.84344i	−0.144211	+	0.249781i
$377$	−14.5337	−	7.85797i	−0.748525	−	0.404706i
$378$	−0.824914	−	2.51386i	−0.0424290	−	0.129299i
$379$	−9.27986	−	5.35773i	−0.476675	−	0.275208i	0.242355	−	0.970188i	$-0.422080\pi$
$379$	−9.27986	−	5.35773i	−0.476675	−	0.275208i	−0.719030	+	0.694979i	$0.755413\pi$
$380$	−5.92539	−	10.2631i	−0.303966	−	0.526485i
$381$	5.01216	−	8.68131i	0.256781	−	0.444757i
$382$	−1.50408	+	0.868384i	−0.0769557	+	0.0444304i
$383$		−	13.5876i		−	0.694294i	−0.937811	−	0.347147i	$-0.887150\pi$
$383$		−	13.5876i		−	0.694294i	0.937811	−	0.347147i	$-0.112850\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	0.102549	+	0.0917952i	0.00522636	+	0.00467832i
$386$	−6.91443	−	11.9761i	−0.351935	−	0.609570i
$387$	4.27767	+	7.40915i	0.217446	+	0.376628i
$388$			11.2649i			0.571890i
$389$	6.60006	+	11.4316i	0.334637	+	0.579608i	0.983415	−	0.181370i	$-0.0580531\pi$
$389$	6.60006	+	11.4316i	0.334637	+	0.579608i	−0.648778	+	0.760977i	$0.724720\pi$
$390$	−0.179293	−	6.41399i	−0.00907883	−	0.324785i
$391$	−29.3574			−1.48467
$392$	2.80982	−	6.41131i	0.141918	−	0.323820i
$393$	0.434167	−	0.751999i	0.0219008	−	0.0379333i
$394$	3.75689			0.189270
$395$	2.46133	−	1.42105i	0.123843	−	0.0715008i
$396$	−0.0253148	−	0.0146155i	−0.00127212	−	0.000734458i
$397$		−	20.2374i		−	1.01569i	−0.861450	−	0.507843i	$-0.830443\pi$
$397$		−	20.2374i		−	1.01569i	0.861450	−	0.507843i	$-0.169557\pi$
$398$		−	16.9615i		−	0.850204i
$399$	17.2441	+	3.61284i	0.863286	+	0.180868i
$400$	−0.916484	+	1.58740i	−0.0458242	+	0.0793699i
$401$	−1.99871	+	1.15395i	−0.0998107	+	0.0576257i	−0.549074	−	0.835773i	$-0.685020\pi$
$401$	−1.99871	+	1.15395i	−0.0998107	+	0.0576257i	0.449264	+	0.893399i	$0.351686\pi$
$402$	2.84820	+	4.93323i	0.142055	+	0.246047i
$403$	8.32567	+	13.5325i	0.414731	+	0.674104i
$404$	0.321007	−	0.556000i	0.0159707	−	0.0276621i
$405$	1.54119	+	0.889808i	0.0765825	+	0.0442149i
$406$	11.8662	+	2.48611i	0.588910	+	0.123383i
$407$	−0.160232	−	0.277530i	−0.00794240	−	0.0137566i
$408$	−5.29367	−	3.05630i	−0.262076	−	0.151309i
$409$	−0.126397	−	0.0729754i	−0.00624993	−	0.00360840i	0.496872	−	0.867824i	$-0.334482\pi$
$409$	−0.126397	−	0.0729754i	−0.00624993	−	0.00360840i	−0.503122	+	0.864216i	$0.667815\pi$
$410$	11.3931	+	6.57783i	0.562667	+	0.324856i
$411$	−17.0004	−	9.81520i	−0.838569	−	0.484148i
$412$	−9.07044	−	15.7105i	−0.446868	−	0.773999i
$413$	−22.5049	+	25.1412i	−1.10739	+	1.23712i
$414$	−4.15932	−	2.40138i	−0.204419	−	0.118022i
$415$	7.47203	−	12.9419i	0.366788	−	0.635295i
$416$	−1.71482	+	3.17165i	−0.0840760	+	0.155503i
$417$	−1.50591	−	2.60832i	−0.0737449	−	0.127730i
$418$	0.168576	−	0.0973273i	0.00824532	−	0.00476044i
$419$	12.7971	−	22.1652i	0.625178	−	1.08284i	−0.363328	−	0.931661i	$-0.618360\pi$
$419$	12.7971	−	22.1652i	0.625178	−	1.08284i	0.988506	−	0.151179i	$-0.0483071\pi$
$420$	1.46803	+	4.47371i	0.0716325	+	0.218295i
$421$		−	15.2002i		−	0.740810i	−0.928870	−	0.370405i	$-0.879219\pi$
$421$		−	15.2002i		−	0.740810i	0.928870	−	0.370405i	$-0.120781\pi$
$422$			16.1979i			0.788502i
$423$	4.84344	+	2.79636i	0.235496	+	0.135964i
$424$	−0.109745	+	0.0633613i	−0.00532969	+	0.00307710i
$425$	11.2042			0.543484
$426$	4.18111	−	7.24189i	0.202575	−	0.350871i
$427$	3.48842	−	16.6503i	0.168817	−	0.805763i
$428$	−0.552995			−0.0267300
$429$	0.105353	−	0.00294497i	0.00508648	−	0.000142184i
$430$	−7.61261	−	13.1854i	−0.367113	−	0.635858i
$431$		−	37.1441i		−	1.78917i	−0.446899	−	0.894584i	$-0.647472\pi$
$431$		−	37.1441i		−	1.78917i	0.446899	−	0.894584i	$-0.352528\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	3.09784	+	5.36562i	0.148873	+	0.257855i	0.930811	−	0.365501i	$-0.119102\pi$
$433$	3.09784	+	5.36562i	0.148873	+	0.257855i	−0.781938	+	0.623356i	$0.785769\pi$
$434$	−8.68705	−	7.77612i	−0.416992	−	0.373266i
$435$	−7.06233	+	4.07744i	−0.338613	+	0.195498i
$436$		−	19.7670i		−	0.946667i
$437$	27.6976	−	15.9912i	1.32496	−	0.764964i
$438$	3.01100	−	5.21521i	0.143871	−	0.249192i
$439$	−10.9736	−	19.0068i	−0.523740	−	0.907144i	−0.999618	−	0.0276326i	$-0.991203\pi$
$439$	−10.9736	−	19.0068i	−0.523740	−	0.907144i	0.475879	−	0.879511i	$-0.342130\pi$
$440$	0.0450507	+	0.0260100i	0.00214771	+	0.00123998i
$441$	−6.41131	−	2.80982i	−0.305300	−	0.133801i
$442$	22.0307	−	0.615832i	1.04789	−	0.0292921i
$443$	−3.54473	+	6.13966i	−0.168415	+	0.291704i	−0.937863	−	0.347006i	$-0.887198\pi$
$443$	−3.54473	+	6.13966i	−0.168415	+	0.291704i	0.769447	+	0.638710i	$0.220532\pi$
$444$		−	10.9631i		−	0.520287i
$445$	24.0262			1.13895
$446$	−9.38035			−0.444172
$447$		−	14.7964i		−	0.699846i
$448$	0.542536	−	2.58953i	0.0256324	−	0.122344i
$449$	−7.50529	+	4.33318i	−0.354196	+	0.204495i	−0.666532	−	0.745476i	$-0.732222\pi$
$449$	−7.50529	+	4.33318i	−0.354196	+	0.204495i	0.312336	+	0.949972i	$0.398889\pi$
$450$	1.58740	+	0.916484i	0.0748306	+	0.0432035i
$451$	−0.108044	+	0.187138i	−0.00508759	+	0.00881197i
$452$	−2.00670			−0.0943873
$453$	0.606515	−	0.350172i	0.0284966	−	0.0164525i
$454$	3.04812			0.143055
$455$	−12.9605	−	10.9648i	−0.607596	−	0.514036i
$456$	6.65918			0.311845
$457$	10.1115	−	5.83786i	0.472995	−	0.273084i	−0.244498	−	0.969650i	$-0.578623\pi$
$457$	10.1115	−	5.83786i	0.472995	−	0.273084i	0.717493	+	0.696566i	$0.245290\pi$
$458$	−7.39639			−0.345611
$459$	−3.05630	+	5.29367i	−0.142656	+	0.247087i
$460$	7.40199	+	4.27354i	0.345119	+	0.199255i
$461$	−8.18825	+	4.72749i	−0.381365	+	0.220181i	−0.678412	−	0.734682i	$-0.737332\pi$
$461$	−8.18825	+	4.72749i	−0.381365	+	0.220181i	0.297047	+	0.954863i	$0.403998\pi$
$462$	−0.0734829	+	0.0241131i	−0.00341873	+	0.00112184i
$463$			9.04408i			0.420314i	0.977668	+	0.210157i	$0.0673975\pi$
$463$			9.04408i			0.420314i	−0.977668	+	0.210157i	$0.932602\pi$
$464$	4.58238			0.212732
$465$	7.84222			0.363674
$466$			12.7769i			0.591879i
$467$	−9.79237	+	16.9609i	−0.453137	+	0.784856i	−0.998579	−	0.0532924i	$-0.983028\pi$
$467$	−9.79237	+	16.9609i	−0.453137	+	0.784856i	0.545442	+	0.838149i	$0.316362\pi$
$468$	3.17165	+	1.71482i	0.146610	+	0.0792676i
$469$	14.7510	+	3.09050i	0.681137	+	0.142706i
$470$	−8.61946	−	4.97645i	−0.397586	−	0.229546i
$471$	−4.48136	−	7.76194i	−0.206490	−	0.357651i
$472$	−6.37671	+	11.0448i	−0.293512	+	0.508378i
$473$	0.216577	−	0.125041i	0.00995822	−	0.00574938i
$474$			1.59703i			0.0733540i
$475$	−10.5708	+	6.10303i	−0.485020	+	0.280026i
$476$	−15.3663	+	5.04237i	−0.704311	+	0.231117i
$477$	0.0633613	+	0.109745i	0.00290111	+	0.00502488i
$478$	11.6178	+	20.1227i	0.531387	+	0.920390i
$479$		−	35.3310i		−	1.61431i	−0.590338	−	0.807156i	$-0.701005\pi$
$479$		−	35.3310i		−	1.61431i	0.590338	−	0.807156i	$-0.298995\pi$
$480$	0.889808	+	1.54119i	0.0406140	+	0.0703455i
$481$	20.7129	+	33.6667i	0.944426	+	1.53507i
$482$	−8.55083			−0.389480
$483$	−12.0735	+	3.96187i	−0.549363	+	0.180271i
$484$	5.49957	−	9.52554i	0.249981	−	0.432979i
$485$	−20.0472			−0.910298
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	30.5044	+	17.6117i	1.38228	+	0.798062i	0.992430	−	0.122814i	$-0.0391919\pi$
$487$	30.5044	+	17.6117i	1.38228	+	0.798062i	0.389855	+	0.920876i	$0.372525\pi$
$488$		−	6.42985i		−	0.291065i
$489$		−	6.70067i		−	0.303015i
$490$	11.4097	+	5.00041i	0.515436	+	0.225895i
$491$	−1.60083	+	2.77271i	−0.0722442	+	0.125131i	−0.899885	−	0.436128i	$-0.856349\pi$
$491$	−1.60083	+	2.77271i	−0.0722442	+	0.125131i	0.827640	+	0.561259i	$0.189683\pi$
$492$	−6.40202	+	3.69621i	−0.288625	+	0.166638i
$493$	−14.0051	−	24.2576i	−0.630760	−	1.09251i
$494$	−20.4497	+	12.5813i	−0.920076	+	0.566061i
$495$	0.0260100	−	0.0450507i	0.00116906	−	0.00202488i
$496$	−3.81631	−	2.20335i	−0.171357	−	0.0989332i
$497$	−6.89811	−	21.0215i	−0.309423	−	0.942943i
$498$	4.19868	+	7.27232i	0.188147	+	0.325881i
$499$	−9.15044	−	5.28301i	−0.409630	−	0.236500i	0.281001	−	0.959708i	$-0.409334\pi$
$499$	−9.15044	−	5.28301i	−0.409630	−	0.236500i	−0.690631	+	0.723207i	$0.742667\pi$
$500$	−10.5309	−	6.08003i	−0.470957	−	0.271907i
$501$	4.07956	+	2.35534i	0.182261	+	0.105229i
$502$	−18.7393	−	10.8191i	−0.836376	−	0.482882i
$503$	16.8302	+	29.1508i	0.750422	+	1.29977i	0.947618	+	0.319406i	$0.103483\pi$
$503$	16.8302	+	29.1508i	0.750422	+	1.29977i	−0.197196	+	0.980364i	$0.563183\pi$
$504$	−2.58953	−	0.542536i	−0.115347	−	0.0241665i
$505$	0.989467	+	0.571269i	0.0440307	+	0.0254211i
$506$	−0.0701949	+	0.121581i	−0.00312054	+	0.00540494i
$507$	−12.9797	+	0.726220i	−0.576449	+	0.0322526i
$508$	−5.01216	−	8.68131i	−0.222379	−	0.385171i
$509$	−35.0037	+	20.2094i	−1.55151	+	0.895766i	−0.553494	+	0.832853i	$0.686706\pi$
$509$	−35.0037	+	20.2094i	−1.55151	+	0.895766i	−0.998019	+	0.0629133i	$0.979961\pi$
$510$	5.43904	−	9.42070i	0.240845	−	0.417155i
$511$	−4.96764	−	15.1385i	−0.219755	−	0.669688i
$512$		−	1.00000i		−	0.0441942i
$513$		−	6.65918i		−	0.294010i
$514$	1.19898	+	0.692232i	0.0528848	+	0.0305330i
$515$	27.9586	−	16.1419i	1.23200	−	0.711297i
$516$	8.55535			0.376628
$517$	0.0817406	−	0.141579i	0.00359495	−	0.00622663i
$518$	−21.6119	−	19.3457i	−0.949574	−	0.850001i
$519$	−22.5042			−0.987826
$520$	−5.64432	−	3.05172i	−0.247520	−	0.133827i
$521$	6.99447	+	12.1148i	0.306433	+	0.530758i	0.977579	−	0.210567i	$-0.0675310\pi$
$521$	6.99447	+	12.1148i	0.306433	+	0.530758i	−0.671146	+	0.741325i	$0.734198\pi$
$522$		−	4.58238i		−	0.200565i
$523$	18.3508	+	31.7844i	0.802422	+	1.38984i	0.918017	+	0.396540i	$0.129789\pi$
$523$	18.3508	+	31.7844i	0.802422	+	1.38984i	−0.115595	+	0.993296i	$0.536877\pi$
$524$	−0.434167	−	0.751999i	−0.0189667	−	0.0328512i
$525$	4.60783	−	1.51204i	0.201102	−	0.0659909i
$526$	1.89735	−	1.09543i	0.0827283	−	0.0477632i
$527$			26.9364i			1.17337i
$528$	−0.0253148	+	0.0146155i	−0.00110169	+	0.000636059i
$529$	−0.0332790	+	0.0576410i	−0.00144691	+	0.00250613i
$530$	−0.112759	−	0.195304i	−0.00489793	−	0.00848346i
$531$	11.0448	+	6.37671i	0.479303	+	0.276726i
$532$	11.7509	−	13.1274i	0.509465	−	0.569146i
$533$	12.6767	−	23.4462i	0.549088	−	1.01557i
$534$	−6.75038	+	11.6920i	−0.292117	+	0.505962i
$535$		−	0.984119i		−	0.0425472i
$536$	5.69640			0.246047
$537$	16.1669			0.697651
$538$		−	31.1246i		−	1.34188i
$539$	−0.0821341	+	0.187409i	−0.00353776	+	0.00807229i
$540$	1.54119	−	0.889808i	0.0663224	−	0.0382912i
$541$	8.41504	+	4.85843i	0.361791	+	0.208880i	0.669866	−	0.742482i	$-0.266352\pi$
$541$	8.41504	+	4.85843i	0.361791	+	0.208880i	−0.308075	+	0.951362i	$0.599685\pi$
$542$	12.4541	−	21.5712i	0.534950	−	0.926560i
$543$	−13.5438			−0.581221
$544$	−5.29367	+	3.05630i	−0.226964	+	0.131038i
$545$	35.1776			1.50684
$546$	8.97722	−	3.22638i	0.384190	−	0.138076i
$547$	−8.41788			−0.359922			−0.179961	−	0.983674i	$-0.557597\pi$
$547$	−8.41788			−0.359922			−0.179961	+	0.983674i	$0.557597\pi$
$548$	−17.0004	+	9.81520i	−0.726222	+	0.419285i
$549$	−6.42985			−0.274419
$550$	0.0267898	−	0.0464013i	0.00114232	−	0.00197856i
$551$	26.4267	+	15.2574i	1.12581	+	0.649989i
$552$	−4.15932	+	2.40138i	−0.177032	+	0.102210i
$553$	3.14827	+	2.81814i	0.133878	+	0.119840i
$554$			6.03351i			0.256339i
$555$	19.5102			0.828160
$556$	−3.01183			−0.127730
$557$			20.0160i			0.848105i	0.905638	+	0.424053i	$0.139393\pi$
$557$			20.0160i			0.848105i	−0.905638	+	0.424053i	$0.860607\pi$
$558$	−2.20335	+	3.81631i	−0.0932752	+	0.161557i
$559$	−26.2727	+	16.1638i	−1.11122	+	0.683656i
$560$	4.60836	+	0.965505i	0.194739	+	0.0408000i
$561$	0.154739	+	0.0893389i	0.00653311	+	0.00377189i
$562$	−4.33861	−	7.51470i	−0.183013	−	0.316988i
$563$	−5.67320	+	9.82626i	−0.239097	+	0.414128i	−0.960455	−	0.278434i	$-0.910185\pi$
$563$	−5.67320	+	9.82626i	−0.239097	+	0.414128i	0.721359	+	0.692562i	$0.243518\pi$
$564$	4.84344	−	2.79636i	0.203946	−	0.117748i
$565$		−	3.57116i		−	0.150240i
$566$	19.7028	−	11.3754i	0.828172	−	0.478145i
$567$	−0.542536	+	2.58953i	−0.0227844	+	0.108750i
$568$	−4.18111	−	7.24189i	−0.175435	−	0.303863i
$569$	−5.64013	−	9.76899i	−0.236446	−	0.409537i	0.723246	−	0.690591i	$-0.242649\pi$
$569$	−5.64013	−	9.76899i	−0.236446	−	0.409537i	−0.959692	+	0.281054i	$0.909316\pi$
$570$			11.8508i			0.496374i
$571$	6.97786	+	12.0860i	0.292014	+	0.505784i	0.974286	−	0.225315i	$-0.0723412\pi$
$571$	6.97786	+	12.0860i	0.292014	+	0.505784i	−0.682272	+	0.731099i	$0.739008\pi$
$572$	0.0501260	−	0.0927107i	0.00209587	−	0.00387643i
$573$	1.73677			0.0725545
$574$	−4.01065	+	19.1429i	−0.167401	+	0.799008i
$575$	4.40166	−	7.62390i	0.183562	−	0.317938i
$576$	−1.00000			−0.0416667
$577$	35.8798	−	20.7152i	1.49370	−	0.862385i	0.493722	−	0.869620i	$-0.335636\pi$
$577$	35.8798	−	20.7152i	1.49370	−	0.862385i	0.999974	+	0.00723460i	$0.00230286\pi$
$578$	17.6357	+	10.1820i	0.733547	+	0.423513i
$579$			13.8289i			0.574708i
$580$			8.15488i			0.338613i
$581$	21.7452	+	4.55587i	0.902142	+	0.189009i
$582$	5.63246	−	9.75571i	0.233473	−	0.404387i
$583$	0.00320796	−	0.00185212i	0.000132860	−	7.67068e-5i
$584$	−3.01100	−	5.21521i	−0.124596	−	0.215807i
$585$	−3.05172	+	5.64432i	−0.126173	+	0.233364i
$586$	9.84301	−	17.0486i	0.406611	−	0.704271i
$587$	7.56169	+	4.36574i	0.312104	+	0.180194i	0.647868	−	0.761753i	$-0.275661\pi$
$587$	7.56169	+	4.36574i	0.312104	+	0.180194i	−0.335763	+	0.941946i	$0.608994\pi$
$588$	−5.63903	+	4.14745i	−0.232550	+	0.171038i
$589$	−14.6725	−	25.4135i	−0.604569	−	1.04714i
$590$	−19.6555	−	11.3481i	−0.809203	−	0.467194i
$591$	−3.25356	−	1.87845i	−0.133834	−	0.0772690i
$592$	−9.49435	−	5.48157i	−0.390215	−	0.225291i
$593$	−34.7875	−	20.0846i	−1.42855	−	0.824774i	−0.431544	−	0.902092i	$-0.642031\pi$
$593$	−34.7875	−	20.0846i	−1.42855	−	0.824774i	−0.997006	+	0.0773179i	$0.975364\pi$
$594$	0.0146155	+	0.0253148i	0.000599682	+	0.00103868i
$595$	−8.97348	−	27.3460i	−0.367877	−	1.12108i
$596$	−12.8141	−	7.39820i	−0.524884	−	0.303042i
$597$	−8.48076	+	14.6891i	−0.347094	+	0.601185i
$598$	8.23589	−	15.2327i	0.336790	−	0.622912i
$599$	−16.9134	−	29.2948i	−0.691062	−	1.19695i	−0.971490	−	0.237080i	$-0.923810\pi$
$599$	−16.9134	−	29.2948i	−0.691062	−	1.19695i	0.280428	−	0.959875i	$-0.409524\pi$
$600$	1.58740	−	0.916484i	0.0648052	−	0.0374153i
$601$	−14.8249	+	25.6775i	−0.604720	+	1.04741i	0.387376	+	0.921922i	$0.373382\pi$
$601$	−14.8249	+	25.6775i	−0.604720	+	1.04741i	−0.992096	+	0.125484i	$0.959952\pi$
$602$	15.0969	−	16.8654i	0.615303	−	0.687382i
$603$		−	5.69640i		−	0.231975i
$604$		−	0.700344i		−	0.0284966i
$605$	16.9518	+	9.78713i	0.689189	+	0.397903i
$606$	−0.556000	+	0.321007i	−0.0225860	+	0.0130400i
$607$	28.1015			1.14060			0.570302	−	0.821435i	$-0.306826\pi$
$607$	28.1015			1.14060			0.570302	+	0.821435i	$0.306826\pi$
$608$	3.32959	−	5.76702i	0.135033	−	0.233883i
$609$	−9.03338	−	8.08613i	−0.366051	−	0.327667i
$610$	11.4427			0.463300
$611$	−9.59052	+	17.7382i	−0.387991	+	0.717610i
$612$	3.05630	+	5.29367i	0.123544	+	0.213984i
$613$			46.4236i			1.87503i	0.347944	+	0.937515i	$0.386880\pi$
$613$			46.4236i			1.87503i	−0.347944	+	0.937515i	$0.613120\pi$
$614$	−2.69404	−	4.66621i	−0.108722	−	0.188313i
$615$	−6.57783	−	11.3931i	−0.265244	−	0.459415i
$616$	−0.0158589	+	0.0756946i	−0.000638973	+	0.00304982i
$617$	−22.1378	+	12.7812i	−0.891233	+	0.514553i	−0.874346	−	0.485304i	$-0.838709\pi$
$617$	−22.1378	+	12.7812i	−0.891233	+	0.514553i	−0.0168872	+	0.999857i	$0.505376\pi$
$618$			18.1409i			0.729733i
$619$	−9.23893	+	5.33410i	−0.371344	+	0.214395i	−0.674045	−	0.738690i	$-0.735445\pi$
$619$	−9.23893	+	5.33410i	−0.371344	+	0.214395i	0.302702	+	0.953085i	$0.402111\pi$
$620$	3.92111	−	6.79157i	0.157476	−	0.272756i
$621$	2.40138	+	4.15932i	0.0963642	+	0.166908i
$622$	−2.03422	−	1.17445i	−0.0815646	−	0.0470914i
$623$	11.1370	+	33.9391i	0.446193	+	1.35974i
$624$	3.07091	−	1.88932i	0.122935	−	0.0756334i
$625$	6.23769	−	10.8040i	0.249508	−	0.432160i
$626$		−	25.3328i		−	1.01250i
$627$	−0.194655			−0.00777376
$628$	−8.96271			−0.357651
$629$			67.0133i			2.67199i
$630$	0.965505	−	4.60836i	0.0384667	−	0.183602i
$631$	−2.30419	+	1.33033i	−0.0917284	+	0.0529594i	−0.545163	−	0.838330i	$-0.683532\pi$
$631$	−2.30419	+	1.33033i	−0.0917284	+	0.0529594i	0.453434	+	0.891290i	$0.350199\pi$
$632$	1.38307	+	0.798515i	0.0550155	+	0.0317632i
$633$	8.09895	−	14.0278i	0.321904	−	0.557555i
$634$	−28.0215			−1.11288
$635$	15.4494	−	8.91971i	0.613091	−	0.353968i
$636$	0.126723			0.00502488
$637$	9.48108	−	23.3904i	0.375654	−	0.926760i
$638$	−0.133948			−0.00530304
$639$	−7.24189	+	4.18111i	−0.286485	+	0.165402i
$640$	1.77962			0.0703455
$641$	−10.4953	+	18.1784i	−0.414539	+	0.718003i	−0.995380	−	0.0960140i	$-0.969391\pi$
$641$	−10.4953	+	18.1784i	−0.414539	+	0.718003i	0.580841	+	0.814017i	$0.302724\pi$
$642$	0.478908	+	0.276497i	0.0189010	+	0.0109125i
$643$	−2.73391	+	1.57843i	−0.107815	+	0.0622471i	−0.552938	−	0.833222i	$-0.686493\pi$
$643$	−2.73391	+	1.57843i	−0.107815	+	0.0622471i	0.445123	+	0.895470i	$0.353160\pi$
$644$	−2.60567	+	12.4369i	−0.102678	+	0.490082i
$645$			15.2252i			0.599493i
$646$	−40.7049			−1.60151
$647$	17.3446			0.681887			0.340944	−	0.940084i	$-0.389253\pi$
$647$	17.3446			0.681887			0.340944	+	0.940084i	$0.389253\pi$
$648$			1.00000i			0.0392837i
$649$	0.186398	−	0.322851i	0.00731676	−	0.0126730i
$650$	−3.14321	+	5.81354i	−0.123287	+	0.228026i
$651$	3.63515	+	11.0778i	0.142473	+	0.434175i
$652$	−5.80295	−	3.35033i	−0.227261	−	0.131209i
$653$	−17.2170	−	29.8208i	−0.673755	−	1.16698i	−0.976831	−	0.214012i	$-0.931347\pi$
$653$	−17.2170	−	29.8208i	−0.673755	−	1.16698i	0.303076	−	0.952966i	$-0.401986\pi$
$654$	−9.88349	+	17.1187i	−0.386475	+	0.669395i
$655$	1.33827	−	0.772650i	0.0522905	−	0.0301899i
$656$			7.39241i			0.288625i
$657$	−5.21521	+	3.01100i	−0.203465	+	0.117470i
$658$	3.03425	−	14.4825i	0.118288	−	0.564587i
$659$	4.87150	+	8.43769i	0.189767	+	0.328686i	0.945172	−	0.326572i	$-0.105893\pi$
$659$	4.87150	+	8.43769i	0.189767	+	0.328686i	−0.755406	+	0.655257i	$0.772560\pi$
$660$	−0.0260100	−	0.0450507i	−0.00101244	−	0.00175359i
$661$			12.1749i			0.473547i	0.971565	+	0.236774i	$0.0760900\pi$
$661$			12.1749i			0.473547i	−0.971565	+	0.236774i	$0.923910\pi$
$662$	−5.42029	−	9.38821i	−0.210665	−	0.364883i
$663$	−19.3871	−	10.4820i	−0.752931	−	0.407088i
$664$	8.39736			0.325881
$665$	23.3618	+	20.9120i	0.905931	+	0.810934i
$666$	−5.48157	+	9.49435i	−0.212406	+	0.367899i
$667$	−22.0081			−0.852157
$668$	4.07956	−	2.35534i	0.157843	−	0.0911307i
$669$	8.12362	+	4.69017i	0.314077	+	0.181333i
$670$			10.1374i			0.391642i
$671$			0.187951i			0.00725577i
$672$	−1.76461	+	1.97133i	−0.0680715	+	0.0760457i
$673$	−10.4665	+	18.1284i	−0.403452	+	0.698800i	−0.994140	−	0.108100i	$-0.965523\pi$
$673$	−10.4665	+	18.1284i	−0.403452	+	0.698800i	0.590688	+	0.806900i	$0.298857\pi$
$674$	−10.5344	+	6.08204i	−0.405770	+	0.234272i
$675$	−0.916484	−	1.58740i	−0.0352755	−	0.0610989i
$676$	−5.86092	+	11.6039i	−0.225420	+	0.446302i
$677$	−1.32267	+	2.29094i	−0.0508345	+	0.0880480i	−0.890323	−	0.455330i	$-0.849521\pi$
$677$	−1.32267	+	2.29094i	−0.0508345	+	0.0880480i	0.839488	+	0.543378i	$0.182855\pi$
$678$	1.73785	+	1.00335i	0.0667419	+	0.0385334i
$679$	−9.29260	−	28.3185i	−0.356617	−	1.08676i
$680$	−5.43904	−	9.42070i	−0.208578	−	0.361267i
$681$	−2.63975	−	1.52406i	−0.101155	−	0.0584020i
$682$	0.111555	+	0.0644062i	0.00427165	+	0.00246624i
$683$	−26.4802	−	15.2884i	−1.01324	−	0.584993i	−0.101100	−	0.994876i	$-0.532236\pi$
$683$	−26.4802	−	15.2884i	−1.01324	−	0.584993i	−0.912138	+	0.409883i	$0.865570\pi$
$684$	−5.76702	−	3.32959i	−0.220507	−	0.127310i
$685$	−17.4673	−	30.2542i	−0.667391	−	1.15595i
$686$	−1.77474	+	18.4350i	−0.0677598	+	0.703853i
$687$	6.40547	+	3.69820i	0.244384	+	0.141095i
$688$	4.27767	−	7.40915i	0.163085	−	0.282471i
$689$	−0.389153	+	0.239420i	−0.0148256	+	0.00912117i
$690$	−4.27354	−	7.40199i	−0.162691	−	0.281789i
$691$	−10.6654	+	6.15765i	−0.405730	+	0.234248i	−0.688953	−	0.724806i	$-0.741929\pi$
$691$	−10.6654	+	6.15765i	−0.405730	+	0.234248i	0.283224	+	0.959054i	$0.408596\pi$
$692$	−11.2521	+	19.4892i	−0.427741	+	0.740869i
$693$	0.0756946	+	0.0158589i	0.00287540	+	0.000602429i
$694$			20.4608i			0.776681i
$695$		−	5.35989i		−	0.203312i
$696$	−3.96846	−	2.29119i	−0.150424	−	0.0868474i
$697$	39.1330	−	22.5934i	1.48227	−	0.855788i
$698$	−34.0072			−1.28719
$699$	6.38845	−	11.0651i	0.241634	−	0.418522i
$700$	0.994451	−	4.74652i	0.0375867	−	0.179402i
$701$	41.1257			1.55330			0.776648	−	0.629935i	$-0.216918\pi$
$701$	41.1257			1.55330			0.776648	+	0.629935i	$0.216918\pi$
$702$	−1.88932	−	3.07091i	−0.0713079	−	0.115904i
$703$	−36.5027	−	63.2246i	−1.37673	−	2.38456i
$704$			0.0292310i			0.00110169i
$705$	4.97645	+	8.61946i	0.187424	+	0.324628i
$706$	3.97928	+	6.89231i	0.149762	+	0.259395i
$707$	−0.348316	+	1.66251i	−0.0130998	+	0.0625253i
$708$	11.0448	−	6.37671i	0.415089	−	0.239652i
$709$		−	31.0777i		−	1.16715i	−0.812060	−	0.583574i	$-0.801654\pi$
$709$		−	31.0777i		−	1.16715i	0.812060	−	0.583574i	$-0.198346\pi$
$710$	12.8878	−	7.44077i	0.483670	−	0.279247i
$711$	0.798515	−	1.38307i	0.0299467	−	0.0518691i
$712$	6.75038	+	11.6920i	0.252981	+	0.438176i
$713$	18.3288	+	10.5822i	0.686421	+	0.396305i
$714$	15.8288	+	3.31631i	0.592376	+	0.124110i
$715$	0.164989	+	0.0892050i	0.00617026	+	0.00333608i
$716$	8.08343	−	14.0009i	0.302092	−	0.523238i
$717$		−	23.2357i		−	0.867752i
$718$	−12.1545			−0.453600
$719$	18.2378			0.680156			0.340078	−	0.940397i	$-0.389546\pi$
$719$	18.2378			0.680156			0.340078	+	0.940397i	$0.389546\pi$
$720$		−	1.77962i		−	0.0663224i
$721$	35.7616	+	32.0116i	1.33183	+	1.19218i
$722$	21.9491	−	12.6723i	0.816861	−	0.471615i
$723$	7.40524	+	4.27542i	0.275404	+	0.159004i
$724$	−6.77192	+	11.7293i	−0.251676	+	0.435916i
$725$	8.39936			0.311944
$726$	−9.52554	+	5.49957i	−0.353526	+	0.204108i
$727$	−8.65849			−0.321126			−0.160563	−	0.987026i	$-0.551331\pi$
$727$	−8.65849			−0.321126			−0.160563	+	0.987026i	$0.551331\pi$
$728$	1.69449	−	9.38769i	0.0628019	−	0.347931i
$729$	1.00000			0.0370370
$730$	9.28107	−	5.35843i	0.343508	−	0.198324i
$731$	−52.2954			−1.93422
$732$	−3.21492	+	5.56841i	−0.118827	+	0.205814i
$733$	−10.5215	−	6.07458i	−0.388620	−	0.224370i	0.292942	−	0.956130i	$-0.405366\pi$
$733$	−10.5215	−	6.07458i	−0.388620	−	0.224370i	−0.681562	+	0.731760i	$0.738699\pi$
$734$	0.812177	−	0.468911i	0.0299780	−	0.0173078i
$735$	−7.38086	−	10.0353i	−0.272247	−	0.370158i
$736$			4.80277i			0.177032i
$737$	−0.166512			−0.00613354
$738$	7.39241			0.272119
$739$			10.3150i			0.379445i	0.981838	+	0.189722i	$0.0607588\pi$
$739$			10.3150i			0.379445i	−0.981838	+	0.189722i	$0.939241\pi$
$740$	9.75508	−	16.8963i	0.358604	−	0.621120i
$741$	24.0006	−	0.670898i	0.881685	−	0.0246461i
$742$	0.223616	−	0.249812i	0.00820922	−	0.00917088i
$743$	−13.3027	−	7.68032i	−0.488029	−	0.281764i	0.235727	−	0.971819i	$-0.424253\pi$
$743$	−13.3027	−	7.68032i	−0.488029	−	0.281764i	−0.723756	+	0.690055i	$0.757586\pi$
$744$	2.20335	+	3.81631i	0.0807787	+	0.139913i
$745$	13.1660	−	22.8041i	0.482363	−	0.835478i
$746$	9.58139	−	5.53182i	0.350800	−	0.202534i
$747$		−	8.39736i		−	0.307243i
$748$	0.154739	−	0.0893389i	0.00565783	−	0.00326655i
$749$	1.39015	−	0.456173i	0.0507951	−	0.0166682i
$750$	6.08003	+	10.5309i	0.222011	+	0.384535i
$751$	−10.1391	−	17.5615i	−0.369983	−	0.640829i	0.619580	−	0.784934i	$-0.287303\pi$
$751$	−10.1391	−	17.5615i	−0.369983	−	0.640829i	−0.989562	+	0.144105i	$0.953970\pi$
$752$		−	5.59272i		−	0.203946i
$753$	10.8191	+	18.7393i	0.394271	+	0.682898i
$754$	16.5156	−	0.461666i	0.601461	−	0.0168129i
$755$	1.24634			0.0453591
$756$	1.97133	+	1.76461i	0.0716965	+	0.0641784i
$757$	−2.14762	+	3.71978i	−0.0780564	+	0.135198i	−0.902411	−	0.430876i	$-0.858205\pi$
$757$	−2.14762	+	3.71978i	−0.0780564	+	0.135198i	0.824355	+	0.566073i	$0.191538\pi$
$758$	10.7155			0.389203
$759$	0.121581	−	0.0701949i	0.00441312	−	0.00254791i
$760$	10.2631	+	5.92539i	0.372281	+	0.214936i
$761$			10.0214i			0.363274i	0.983366	+	0.181637i	$0.0581396\pi$
$761$			10.0214i			0.363274i	−0.983366	+	0.181637i	$0.941860\pi$
$762$			10.0243i			0.363143i
$763$	16.3061	+	49.6915i	0.590319	+	1.79895i
$764$	0.868384	−	1.50408i	0.0314170	−	0.0544159i
$765$	−9.42070	+	5.43904i	−0.340606	+	0.196649i
$766$	6.79380	+	11.7672i	0.245470	+	0.425167i
$767$	−21.8698	+	40.4494i	−0.789674	+	1.46054i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	29.2300	+	16.8760i	1.05406	+	0.608563i	0.923784	−	0.382914i	$-0.125080\pi$
$769$	29.2300	+	16.8760i	1.05406	+	0.608563i	0.130278	+	0.991477i	$0.458413\pi$
$770$	−0.134707	−	0.0282227i	−0.00485451	−	0.00101708i
$771$	−0.692232	−	1.19898i	−0.0249301	−	0.0431802i
$772$	11.9761	+	6.91443i	0.431031	+	0.248856i
$773$	27.8052	+	16.0534i	1.00008	+	0.577399i	0.908273	−	0.418377i	$-0.137401\pi$
$773$	27.8052	+	16.0534i	1.00008	+	0.577399i	0.0918111	+	0.995776i	$0.470734\pi$
$774$	−7.40915	−	4.27767i	−0.266316	−	0.153758i
$775$	−6.99518	−	4.03867i	−0.251274	−	0.145073i
$776$	−5.63246	−	9.75571i	−0.202194	−	0.350210i
$777$	9.04364	+	27.5598i	0.324439	+	0.988704i
$778$	−11.4316	−	6.60006i	−0.409844	−	0.236624i
$779$	−24.6137	+	42.6322i	−0.881877	+	1.52746i
$780$	3.36227	+	5.46503i	0.120388	+	0.195680i
$781$	0.122218	+	0.211688i	0.00437331	+	0.00757479i
$782$	25.4243	−	14.6787i	0.909169	−	0.524909i
$783$	−2.29119	+	3.96846i	−0.0818805	+	0.141821i
$784$	0.772276	+	6.95727i	0.0275813	+	0.248474i
$785$		−	15.9502i		−	0.569286i
$786$			0.868334i			0.0309724i
$787$	−25.4607	−	14.6998i	−0.907577	−	0.523990i	−0.0279263	−	0.999610i	$-0.508890\pi$
$787$	−25.4607	−	14.6998i	−0.907577	−	0.523990i	−0.879651	+	0.475620i	$0.842224\pi$
$788$	−3.25356	+	1.87845i	−0.115903	+	0.0669169i
$789$	−2.19087			−0.0779970
$790$	−1.42105	+	2.46133i	−0.0505587	+	0.0875702i
$791$	5.04458	−	1.65536i	0.179364	−	0.0588577i
$792$	0.0292310			0.00103868
$793$	−0.647794	−	23.1741i	−0.0230038	−	0.822936i
$794$	10.1187	+	17.5261i	0.359099	+	0.621978i
$795$			0.225518i			0.00799828i
$796$	8.48076	+	14.6891i	0.300593	+	0.520642i
$797$	−1.39371	−	2.41398i	−0.0493678	−	0.0855075i	0.840286	−	0.542144i	$-0.182387\pi$
$797$	−1.39371	−	2.41398i	−0.0493678	−	0.0855075i	−0.889653	+	0.456637i	$0.849054\pi$
$798$	−16.7403	+	5.49325i	−0.592599	+	0.194459i
$799$	−29.6060	+	17.0930i	−1.04739	+	0.604709i
$800$		−	1.83297i		−	0.0648052i
$801$	11.6920	−	6.75038i	0.413116	−	0.238513i
$802$	1.15395	−	1.99871i	0.0407475	−	0.0705768i
$803$	0.0880147	+	0.152446i	0.00310597	+	0.00537970i
$804$	−4.93323	−	2.84820i	−0.173981	−	0.100448i
$805$	−22.1329	−	4.63710i	−0.780082	−	0.163436i
$806$	−13.9765	−	7.55670i	−0.492302	−	0.266173i
$807$	−15.5623	+	26.9547i	−0.547819	+	0.948850i
$808$			0.642014i			0.0225860i
$809$	−12.6560			−0.444961			−0.222481	−	0.974937i	$-0.571415\pi$
$809$	−12.6560			−0.444961			−0.222481	+	0.974937i	$0.571415\pi$
$810$	−1.77962			−0.0625293
$811$			7.23316i			0.253990i	0.991903	+	0.126995i	$0.0405333\pi$
$811$			7.23316i			0.253990i	−0.991903	+	0.126995i	$0.959467\pi$
$812$	−11.5195	+	3.78007i	−0.404255	+	0.132654i
$813$	−21.5712	+	12.4541i	−0.756533	+	0.436785i
$814$	0.277530	+	0.160232i	0.00972741	+	0.00561612i
$815$	5.96230	−	10.3270i	0.208850	−	0.361740i
$816$	6.11260			0.213984
$817$	49.3388	−	28.4858i	1.72615	−	0.996591i
$818$	0.145951			0.00510305
$819$	−9.38769	−	1.69449i	−0.328032	−	0.0592102i
$820$	−13.1557			−0.459415
$821$	20.0517	−	11.5769i	0.699811	−	0.404036i	−0.107466	−	0.994209i	$-0.534274\pi$
$821$	20.0517	−	11.5769i	0.699811	−	0.404036i	0.807277	+	0.590173i	$0.200940\pi$
$822$	19.6304			0.684689
$823$	19.7449	−	34.1992i	0.688264	−	1.19211i	−0.284135	−	0.958784i	$-0.591706\pi$
$823$	19.7449	−	34.1992i	0.688264	−	1.19211i	0.972399	−	0.233324i	$-0.0749602\pi$
$824$	15.7105	+	9.07044i	0.547300	+	0.315984i
$825$	−0.0464013	+	0.0267898i	−0.00161548	+	0.000932701i
$826$	6.91919	−	33.0253i	0.240749	−	1.14910i
$827$			42.9388i			1.49313i	0.665314	+	0.746564i	$0.268298\pi$
$827$			42.9388i			1.49313i	−0.665314	+	0.746564i	$0.731702\pi$
$828$	4.80277			0.166908
$829$	−20.2675			−0.703920			−0.351960	−	0.936015i	$-0.614485\pi$
$829$	−20.2675			−0.703920			−0.351960	+	0.936015i	$0.614485\pi$
$830$			14.9441i			0.518716i
$831$	3.01675	−	5.22517i	0.104650	−	0.181259i
$832$	−0.100748	−	3.60414i	−0.00349281	−	0.124951i
$833$	34.4692	−	25.3517i	1.19429	−	0.878384i
$834$	2.60832	+	1.50591i	0.0903187	+	0.0521455i
$835$	4.19159	+	7.26005i	0.145056	+	0.251244i
$836$	−0.0973273	+	0.168576i	−0.00336614	+	0.00583032i
$837$	3.81631	−	2.20335i	0.131911	−	0.0761588i
$838$			25.5942i			0.884136i
$839$	38.1707	−	22.0379i	1.31780	−	0.760832i	0.334426	−	0.942422i	$-0.391458\pi$
$839$	38.1707	−	22.0379i	1.31780	−	0.760832i	0.983374	+	0.181590i	$0.0581243\pi$
$840$	−3.50821	−	3.14033i	−0.121045	−	0.108352i
$841$	4.00089	+	6.92975i	0.137962	+	0.238957i
$842$	7.60008	+	13.1637i	0.261916	+	0.453652i
$843$			8.67723i			0.298860i
$844$	−8.09895	−	14.0278i	−0.278777	−	0.482857i
$845$	−20.6504	−	10.4302i	−0.710396	−	0.358810i
$846$	−5.59272			−0.192282
$847$	−5.96743	+	28.4826i	−0.205043	+	0.978674i
$848$	0.0633613	−	0.109745i	0.00217584	−	0.00376866i
$849$	−22.7509			−0.780808
$850$	−9.70313	+	5.60210i	−0.332815	+	0.192151i
$851$	45.5991	+	26.3267i	1.56312	+	0.902467i
$852$			8.36222i			0.286485i
$853$			21.7050i			0.743165i	0.928400	+	0.371583i	$0.121185\pi$
$853$			21.7050i			0.743165i	−0.928400	+	0.371583i	$0.878815\pi$
$854$	5.30407	+	16.1638i	0.181502	+	0.553113i
$855$	5.92539	−	10.2631i	0.202644	−	0.350990i
$856$	0.478908	−	0.276497i	0.0163687	−	0.00945049i
$857$	−14.1784	−	24.5577i	−0.484325	−	0.838876i	0.515513	−	0.856882i	$-0.327601\pi$
$857$	−14.1784	−	24.5577i	−0.484325	−	0.838876i	−0.999838	+	0.0180062i	$0.994268\pi$
$858$	−0.0897658	+	0.0552268i	−0.00306455	+	0.00188541i
$859$	−1.23295	+	2.13552i	−0.0420675	+	0.0728631i	−0.886293	−	0.463126i	$-0.846728\pi$
$859$	−1.23295	+	2.13552i	−0.0420675	+	0.0728631i	0.844225	+	0.535989i	$0.180061\pi$
$860$	13.1854	+	7.61261i	0.449620	+	0.259588i
$861$	13.0448	−	14.5729i	0.444564	−	0.496642i
$862$	18.5721	+	32.1677i	0.632567	+	1.09564i
$863$	12.6037	+	7.27673i	0.429034	+	0.247703i	0.698935	−	0.715185i	$-0.253658\pi$
$863$	12.6037	+	7.27673i	0.429034	+	0.247703i	−0.269901	+	0.962888i	$0.586991\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−34.6833	−	20.0244i	−1.17927	−	0.680851i
$866$	−5.36562	−	3.09784i	−0.182331	−	0.105269i
$867$	−10.1820	−	17.6357i	−0.345797	−	0.598939i
$868$	11.4113	+	2.39079i	0.387323	+	0.0811487i
$869$	−0.0404285	−	0.0233414i	−0.00137144	−	0.000791804i
$870$	4.07744	−	7.06233i	0.138238	−	0.239435i
$871$	20.5306	−	0.573901i	0.695654	−	0.0194459i
$872$	9.88349	+	17.1187i	0.334697	+	0.579713i
$873$	−9.75571	+	5.63246i	−0.330181	+	0.190630i
$874$	−15.9912	+	27.6976i	−0.540912	+	0.936886i
$875$	31.4888	+	6.59727i	1.06452	+	0.223028i
$876$			6.02201i			0.203465i
$877$		−	37.2140i		−	1.25663i	−0.777960	−	0.628314i	$-0.783745\pi$
$877$		−	37.2140i		−	1.25663i	0.777960	−	0.628314i	$-0.216255\pi$
$878$	19.0068	+	10.9736i	0.641447	+	0.370340i
$879$	−17.0486	+	9.84301i	−0.575035	+	0.331996i
$880$	−0.0520200			−0.00175359
$881$	16.2543	−	28.1532i	0.547620	−	0.948506i	−0.450817	−	0.892617i	$-0.648867\pi$
$881$	16.2543	−	28.1532i	0.547620	−	0.948506i	0.998437	−	0.0558898i	$-0.0177995\pi$
$882$	6.95727	−	0.772276i	0.234263	−	0.0260039i
$883$	−47.0222			−1.58242			−0.791211	−	0.611543i	$-0.790549\pi$
$883$	−47.0222			−1.58242			−0.791211	+	0.611543i	$0.790549\pi$
$884$	−18.7712	+	11.5487i	−0.631345	+	0.388424i
$885$	11.3481	+	19.6555i	0.381462	+	0.660712i
$886$		−	7.08947i		−	0.238175i
$887$	8.73522	+	15.1299i	0.293300	+	0.508011i	0.974588	−	0.224005i	$-0.0719132\pi$
$887$	8.73522	+	15.1299i	0.293300	+	0.508011i	−0.681288	+	0.732016i	$0.738580\pi$
$888$	5.48157	+	9.49435i	0.183949	+	0.318610i
$889$	19.7612	+	17.6890i	0.662770	+	0.593271i
$890$	−20.8073	+	12.0131i	−0.697461	+	0.402679i
$891$		−	0.0292310i		−	0.000979277i
$892$	8.12362	−	4.69017i	0.271999	−	0.157039i
$893$	18.6215	−	32.2533i	0.623144	−	1.07932i
$894$	7.39820	+	12.8141i	0.247433	+	0.428566i
$895$	24.9162	+	14.3854i	0.832858	+	0.480851i
$896$	0.824914	+	2.51386i	0.0275584	+	0.0839823i
$897$	−14.7488	+	9.07397i	−0.492449	+	0.302971i
$898$	4.33318	−	7.50529i	0.144600	−	0.250455i
$899$			20.1932i			0.673480i
$900$	−1.83297			−0.0610989
$901$	−0.774605			−0.0258058
$902$		−	0.216088i		−	0.00719494i
$903$	−21.5070	+	7.05743i	−0.715708	+	0.234856i
$904$	1.73785	−	1.00335i	0.0578002	−	0.0333709i
$905$	−20.8736	−	12.0514i	−0.693864	−	0.400602i
$906$	−0.350172	+	0.606515i	−0.0116337	+	0.0201501i
$907$	−15.5692			−0.516968			−0.258484	−	0.966016i	$-0.583223\pi$
$907$	−15.5692			−0.516968			−0.258484	+	0.966016i	$0.583223\pi$
$908$	−2.63975	+	1.52406i	−0.0876030	+	0.0505776i
$909$	0.642014			0.0212943
$910$	16.7065	+	3.01554i	0.553814	+	0.0999641i
$911$	−11.8389			−0.392241			−0.196120	−	0.980580i	$-0.562834\pi$
$911$	−11.8389			−0.392241			−0.196120	+	0.980580i	$0.562834\pi$
$912$	−5.76702	+	3.32959i	−0.190965	+	0.110254i
$913$	−0.245463			−0.00812365
$914$	−5.83786	+	10.1115i	−0.193099	+	0.334458i
$915$	−9.90963	−	5.72133i	−0.327602	−	0.189141i
$916$	6.40547	−	3.69820i	0.211643	−	0.122192i
$917$	1.71177	+	1.53227i	0.0565277	+	0.0506001i
$918$		−	6.11260i		−	0.201746i
$919$	1.78699			0.0589472			0.0294736	−	0.999566i	$-0.490617\pi$
$919$	1.78699			0.0589472			0.0294736	+	0.999566i	$0.490617\pi$
$920$	−8.54708			−0.281789
$921$			5.38807i			0.177543i
$922$	4.72749	−	8.18825i	0.155692	−	0.269666i
$923$	−15.7989	−	25.6796i	−0.520028	−	0.845254i
$924$	0.0515815	−	0.0576240i	0.00169691	−	0.00189569i
$925$	−17.4028	−	10.0475i	−0.572202	−	0.330361i
$926$	−4.52204	−	7.83240i	−0.148603	−	0.257389i
$927$	9.07044	−	15.7105i	0.297912	−	0.515999i
$928$	−3.96846	+	2.29119i	−0.130271	+	0.0752120i
$929$		−	32.6431i		−	1.07098i	−0.844540	−	0.535492i	$-0.820126\pi$
$929$		−	32.6431i		−	1.07098i	0.844540	−	0.535492i	$-0.179874\pi$
$930$	−6.79157	+	3.92111i	−0.222704	+	0.128578i
$931$	−18.7111	+	42.6940i	−0.613232	+	1.39924i
$932$	−6.38845	−	11.0651i	−0.209261	−	0.362450i
$933$	1.17445	+	2.03422i	0.0384499	+	0.0665972i
$934$		−	19.5847i		−	0.640832i
$935$	0.158989	+	0.275377i	0.00519949	+	0.00900578i
$936$	−3.60414	+	0.100748i	−0.117805	+	0.00329305i
$937$	16.5322			0.540083			0.270041	−	0.962849i	$-0.412963\pi$
$937$	16.5322			0.540083			0.270041	+	0.962849i	$0.412963\pi$
$938$	−14.3200	+	4.69904i	−0.467564	+	0.153429i
$939$	−12.6664	+	21.9389i	−0.413353	+	0.715948i
$940$	9.95290			0.324628
$941$	−20.6335	+	11.9128i	−0.672634	+	0.388345i	−0.797074	−	0.603882i	$-0.793620\pi$
$941$	−20.6335	+	11.9128i	−0.672634	+	0.388345i	0.124440	+	0.992227i	$0.460287\pi$
$942$	7.76194	+	4.48136i	0.252898	+	0.146010i
$943$		−	35.5040i		−	1.15617i
$944$		−	12.7534i		−	0.415089i
$945$	−3.14033	+	3.50821i	−0.102155	+	0.114122i
$946$	−0.125041	+	0.216577i	−0.00406543	+	0.00704153i
$947$	−33.1165	+	19.1198i	−1.07614	+	0.621311i	−0.929853	−	0.367931i	$-0.880066\pi$
$947$	−33.1165	+	19.1198i	−1.07614	+	0.621311i	−0.146289	+	0.989242i	$0.546733\pi$
$948$	−0.798515	−	1.38307i	−0.0259346	−	0.0449200i
$949$	−11.3775	−	18.4930i	−0.369330	−	0.600309i
$950$	6.10303	−	10.5708i	0.198008	−	0.342961i
$951$	24.2674	+	14.0108i	0.786923	+	0.454330i
$952$	10.7864	−	12.0500i	0.349589	−	0.390541i
$953$	16.8722	+	29.2234i	0.546543	+	0.946640i	0.998508	+	0.0546042i	$0.0173897\pi$
$953$	16.8722	+	29.2234i	0.546543	+	0.946640i	−0.451965	+	0.892035i	$0.649277\pi$
$954$	−0.109745	−	0.0633613i	−0.00355313	−	0.00205140i
$955$	2.67669	+	1.54539i	0.0866157	+	0.0500076i
$956$	−20.1227	−	11.6178i	−0.650814	−	0.375748i
$957$	0.116002	+	0.0669739i	0.00374982	+	0.00216496i
$958$	17.6655	+	30.5975i	0.570746	+	0.988561i
$959$	34.6401	−	38.6980i	1.11859	−	1.24962i
$960$	−1.54119	−	0.889808i	−0.0497418	−	0.0287184i
$961$	−5.79052	+	10.0295i	−0.186791	+	0.323531i
$962$	−34.7713	−	18.7998i	−1.12107	−	0.606130i
$963$	−0.276497	−	0.478908i	−0.00891001	−	0.0154326i
$964$	7.40524	−	4.27542i	0.238507	−	0.137702i
$965$	−12.3050	+	21.3129i	−0.396113	+	0.686087i
$966$	8.47503	−	9.46783i	0.272680	−	0.304622i
$967$		−	19.3580i		−	0.622511i	−0.950326	−	0.311256i	$-0.899250\pi$
$967$		−	19.3580i		−	0.622511i	0.950326	−	0.311256i	$-0.100750\pi$
$968$			10.9991i			0.353526i
$969$	35.2515	+	20.3525i	1.13244	+	0.653815i
$970$	17.3614	−	10.0236i	0.557442	−	0.321839i
$971$	−52.9890			−1.70050			−0.850249	−	0.526381i	$-0.823549\pi$
$971$	−52.9890			−1.70050			−0.850249	+	0.526381i	$0.823549\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	7.57132	−	2.48450i	0.242726	−	0.0796493i
$974$	−35.2234			−1.12863
$975$	5.62887	−	3.46307i	0.180268	−	0.110907i
$976$	3.21492	+	5.56841i	0.102907	+	0.178240i
$977$		−	5.65239i		−	0.180836i	−0.995904	−	0.0904180i	$-0.971180\pi$
$977$		−	5.65239i		−	0.180836i	0.995904	−	0.0904180i	$-0.0288203\pi$
$978$	3.35033	+	5.80295i	0.107132	+	0.185558i
$979$	−0.197321	−	0.341769i	−0.00630639	−	0.0109230i
$980$	−12.3813	+	1.37435i	−0.395505	+	0.0439021i
$981$	17.1187	−	9.88349i	0.546558	−	0.315556i
$982$		−	3.20165i		−	0.102169i
$983$	−17.5700	+	10.1441i	−0.560397	+	0.323546i	−0.753305	−	0.657671i	$-0.771542\pi$
$983$	−17.5700	+	10.1441i	−0.560397	+	0.323546i	0.192908	+	0.981217i	$0.438208\pi$
$984$	3.69621	−	6.40202i	0.117831	−	0.204089i
$985$	−3.34291	−	5.79009i	−0.106514	−	0.184488i
$986$	24.2576	+	14.0051i	0.772520	+	0.446014i
$987$	−9.86900	+	11.0251i	−0.314134	+	0.350933i
$988$	11.4193	−	21.1206i	0.363296	−	0.671936i
$989$	−20.5447	+	35.5844i	−0.653282	+	1.13152i
$990$			0.0520200i			0.00165330i
$991$	−39.2094			−1.24553			−0.622764	−	0.782410i	$-0.713990\pi$
$991$	−39.2094			−1.24553			−0.622764	+	0.782410i	$0.713990\pi$
$992$	4.40670			0.139913
$993$			10.8406i			0.344015i
$994$	16.4847	+	14.7561i	0.522862	+	0.468035i
$995$	−26.1410	+	15.0925i	−0.828724	+	0.478464i
$996$	−7.27232	−	4.19868i	−0.230432	−	0.133040i
$997$	−0.320864	+	0.555752i	−0.0101619	+	0.0176008i	−0.871062	−	0.491174i	$-0.836568\pi$
$997$	−0.320864	+	0.555752i	−0.0101619	+	0.0176008i	0.860900	+	0.508775i	$0.169901\pi$
$998$	10.5660			0.334462
$999$	9.49435	−	5.48157i	0.300388	−	0.173429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.b.121.4	✓	20
3.2	odd	2		1638.2.cr.b.667.7		20
7.4	even	3		546.2.bm.b.277.2	yes	20
13.10	even	6		546.2.bm.b.205.7	yes	20
21.11	odd	6		1638.2.dt.b.1369.9		20
39.23	odd	6		1638.2.dt.b.1297.4		20
91.88	even	6	inner	546.2.bd.b.361.4	yes	20
273.179	odd	6		1638.2.cr.b.361.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.4	✓	20	1.1	even	1	trivial
546.2.bd.b.361.4	yes	20	91.88	even	6	inner
546.2.bm.b.205.7	yes	20	13.10	even	6
546.2.bm.b.277.2	yes	20	7.4	even	3
1638.2.cr.b.361.7		20	273.179	odd	6
1638.2.cr.b.667.7		20	3.2	odd	2
1638.2.dt.b.1297.4		20	39.23	odd	6
1638.2.dt.b.1369.9		20	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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.542536 + 2.58953i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.54119 + 0.889808i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.542536 + 2.58953i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.77962 q^{10} -0.0292310i q^{11} +(0.500000 - 0.866025i) q^{12} +(0.100748 + 3.60414i) q^{13} +(-0.824914 - 2.51386i) q^{14} +(1.54119 + 0.889808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.05630 + 5.29367i) q^{17} +(-0.866025 + 0.500000i) q^{18} -6.65918i q^{19} +(1.54119 - 0.889808i) q^{20} +(-0.542536 + 2.58953i) q^{21} +(0.0146155 + 0.0253148i) q^{22} +(2.40138 + 4.15932i) q^{23} +1.00000i q^{24} +(-0.916484 - 1.58740i) q^{25} +(-1.88932 - 3.07091i) q^{26} +1.00000 q^{27} +(1.97133 + 1.76461i) q^{28} +(-2.29119 + 3.96846i) q^{29} -1.77962 q^{30} +(3.81631 - 2.20335i) q^{31} +(0.866025 + 0.500000i) q^{32} -0.0292310i q^{33} -6.11260i q^{34} +(-3.14033 + 3.50821i) q^{35} +(0.500000 - 0.866025i) q^{36} +(9.49435 - 5.48157i) q^{37} +(3.32959 + 5.76702i) q^{38} +(0.100748 + 3.60414i) q^{39} +(-0.889808 + 1.54119i) q^{40} +(-6.40202 - 3.69621i) q^{41} +(-0.824914 - 2.51386i) q^{42} +(4.27767 + 7.40915i) q^{43} +(-0.0253148 - 0.0146155i) q^{44} +(1.54119 + 0.889808i) q^{45} +(-4.15932 - 2.40138i) q^{46} +(4.84344 + 2.79636i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-6.41131 - 2.80982i) q^{49} +(1.58740 + 0.916484i) q^{50} +(-3.05630 + 5.29367i) q^{51} +(3.17165 + 1.71482i) q^{52} +(0.0633613 + 0.109745i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.0260100 - 0.0450507i) q^{55} +(-2.58953 - 0.542536i) q^{56} -6.65918i q^{57} -4.58238i q^{58} +(11.0448 + 6.37671i) q^{59} +(1.54119 - 0.889808i) q^{60} -6.42985 q^{61} +(-2.20335 + 3.81631i) q^{62} +(-0.542536 + 2.58953i) q^{63} -1.00000 q^{64} +(-3.05172 + 5.64432i) q^{65} +(0.0146155 + 0.0253148i) q^{66} -5.69640i q^{67} +(3.05630 + 5.29367i) q^{68} +(2.40138 + 4.15932i) q^{69} +(0.965505 - 4.60836i) q^{70} +(-7.24189 + 4.18111i) q^{71} +1.00000i q^{72} +(-5.21521 + 3.01100i) q^{73} +(-5.48157 + 9.49435i) q^{74} +(-0.916484 - 1.58740i) q^{75} +(-5.76702 - 3.32959i) q^{76} +(0.0756946 + 0.0158589i) q^{77} +(-1.88932 - 3.07091i) q^{78} +(0.798515 - 1.38307i) q^{79} -1.77962i q^{80} +1.00000 q^{81} +7.39241 q^{82} -8.39736i q^{83} +(1.97133 + 1.76461i) q^{84} +(-9.42070 + 5.43904i) q^{85} +(-7.40915 - 4.27767i) q^{86} +(-2.29119 + 3.96846i) q^{87} +0.0292310 q^{88} +(11.6920 - 6.75038i) q^{89} -1.77962 q^{90} +(-9.38769 - 1.69449i) q^{91} +4.80277 q^{92} +(3.81631 - 2.20335i) q^{93} -5.59272 q^{94} +(5.92539 - 10.2631i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-9.75571 + 5.63246i) q^{97} +(6.95727 - 0.772276i) q^{98} -0.0292310i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

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