LMFDB - Embedded newform 546.2.cg.b.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.1
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-4.23240 + 1.13407i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.34853 + 2.27629i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-4.23240 + 1.13407i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.34853 + 2.27629i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.19085 - 3.79467i) q^{10} +(3.11756 - 0.835348i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.90215 + 2.13951i) q^{13} +(-2.56313 - 0.656024i) q^{14} +(4.23240 + 1.13407i) q^{15} -1.00000 q^{16} -6.34145 q^{17} +(-0.965926 - 0.258819i) q^{18} +(1.39923 - 5.22199i) q^{19} +(1.13407 + 4.23240i) q^{20} +(-0.0297166 - 2.64558i) q^{21} +(-1.61377 + 2.79513i) q^{22} -1.98551i q^{23} +(-0.258819 - 0.965926i) q^{24} +(12.2970 - 7.09968i) q^{25} +(0.539271 - 3.56499i) q^{26} -1.00000i q^{27} +(2.27629 - 1.34853i) q^{28} +(-1.73874 - 3.01158i) q^{29} +(-3.79467 + 2.19085i) q^{30} +(2.21076 - 8.25065i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.11756 - 0.835348i) q^{33} +(4.48408 - 4.48408i) q^{34} +(-8.28898 - 8.10484i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.127237 + 0.127237i) q^{37} +(2.70310 + 4.68191i) q^{38} +(3.58309 - 0.401793i) q^{39} +(-3.79467 - 2.19085i) q^{40} +(-0.00297886 + 0.0111173i) q^{41} +(1.89172 + 1.84970i) q^{42} +(-2.69459 - 1.55572i) q^{43} +(-0.835348 - 3.11756i) q^{44} +(-3.09834 - 3.09834i) q^{45} +(1.40397 + 1.40397i) q^{46} +(0.994423 + 3.71124i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.36295 + 6.13927i) q^{49} +(-3.67507 + 13.7155i) q^{50} +(5.49185 + 3.17072i) q^{51} +(2.13951 + 2.90215i) q^{52} +(-6.19883 - 10.7367i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-12.2474 + 7.07106i) q^{55} +(-0.656024 + 2.56313i) q^{56} +(-3.82276 + 3.82276i) q^{57} +(3.35899 + 0.900038i) q^{58} +(4.55586 - 4.55586i) q^{59} +(1.13407 - 4.23240i) q^{60} +(4.94487 - 2.85492i) q^{61} +(4.27085 + 7.39733i) q^{62} +(-1.29706 + 2.30600i) q^{63} +1.00000i q^{64} +(9.85674 - 12.3465i) q^{65} +(2.79513 - 1.61377i) q^{66} +(-1.37471 - 5.13050i) q^{67} +6.34145i q^{68} +(-0.992755 + 1.71950i) q^{69} +(11.5922 - 0.130210i) q^{70} +(1.61017 + 6.00925i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(3.47471 + 0.931045i) q^{73} -0.179940 q^{74} -14.1994 q^{75} +(-5.22199 - 1.39923i) q^{76} +(6.10560 + 5.96997i) q^{77} +(-2.24952 + 2.81774i) q^{78} +(-7.63746 + 13.2285i) q^{79} +(4.23240 - 1.13407i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.00575472 - 0.00996747i) q^{82} +(-1.17696 - 1.17696i) q^{83} +(-2.64558 + 0.0297166i) q^{84} +(26.8396 - 7.19164i) q^{85} +(3.00543 - 0.805301i) q^{86} +3.47748i q^{87} +(2.79513 + 1.61377i) q^{88} +(12.6058 - 12.6058i) q^{89} +4.38171 q^{90} +(-8.78377 - 3.72094i) q^{91} -1.98551 q^{92} +(-6.03990 + 6.03990i) q^{93} +(-3.32740 - 1.92108i) q^{94} +23.6884i q^{95} +(-0.965926 + 0.258819i) q^{96} +(2.25048 - 0.603015i) q^{97} +(-1.96315 - 6.71908i) q^{98} +(2.28221 + 2.28221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	−4.23240	+	1.13407i	−1.89279	+	0.507171i	−0.894610	+	0.446848i	$0.852547\pi$
$5$	−4.23240	+	1.13407i	−1.89279	+	0.507171i	−0.998179	+	0.0603236i	$0.980787\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	1.34853	+	2.27629i	0.509696	+	0.860355i
$7$	1.34853	+	2.27629i	0.509696	+	0.860355i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.19085	−	3.79467i	0.692809	−	1.19998i
$11$	3.11756	−	0.835348i	0.939980	−	0.251867i	0.243875	−	0.969807i	$-0.421581\pi$
$11$	3.11756	−	0.835348i	0.939980	−	0.251867i	0.696105	+	0.717940i	$0.254915\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.90215	+	2.13951i	−0.804913	+	0.593393i
$13$	−2.90215	+	2.13951i	−0.804913	+	0.593393i
$14$	−2.56313	−	0.656024i	−0.685025	−	0.175330i
$15$	4.23240	+	1.13407i	1.09280	+	0.292815i
$16$	−1.00000			−0.250000
$17$	−6.34145			−1.53803			−0.769013	−	0.639233i	$-0.779252\pi$
$17$	−6.34145			−1.53803			−0.769013	+	0.639233i	$0.779252\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	1.39923	−	5.22199i	0.321005	−	1.19801i	−0.597262	−	0.802046i	$-0.703745\pi$
$19$	1.39923	−	5.22199i	0.321005	−	1.19801i	0.918267	−	0.395961i	$-0.129589\pi$
$20$	1.13407	+	4.23240i	0.253586	+	0.946394i
$21$	−0.0297166	−	2.64558i	−0.00648470	−	0.577314i
$22$	−1.61377	+	2.79513i	−0.344056	+	0.595923i
$23$		−	1.98551i		−	0.414008i	−0.978340	−	0.207004i	$-0.933629\pi$
$23$		−	1.98551i		−	0.414008i	0.978340	−	0.207004i	$-0.0663713\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	12.2970	−	7.09968i	2.45940	−	1.41994i
$26$	0.539271	−	3.56499i	0.105760	−	0.699153i
$27$		−	1.00000i		−	0.192450i
$28$	2.27629	−	1.34853i	0.430177	−	0.254848i
$29$	−1.73874	−	3.01158i	−0.322876	−	0.559237i	0.658204	−	0.752839i	$-0.271316\pi$
$29$	−1.73874	−	3.01158i	−0.322876	−	0.559237i	−0.981080	+	0.193602i	$0.937983\pi$
$30$	−3.79467	+	2.19085i	−0.692809	+	0.399993i
$31$	2.21076	−	8.25065i	0.397063	−	1.48186i	−0.421174	−	0.906980i	$-0.638382\pi$
$31$	2.21076	−	8.25065i	0.397063	−	1.48186i	0.818237	−	0.574881i	$-0.194952\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.11756	−	0.835348i	−0.542698	−	0.145415i
$34$	4.48408	−	4.48408i	0.769013	−	0.769013i
$35$	−8.28898	−	8.10484i	−1.40109	−	1.36997i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	0.127237	+	0.127237i	0.0209176	+	0.0209176i	0.717488	−	0.696571i	$-0.245292\pi$
$37$	0.127237	+	0.127237i	0.0209176	+	0.0209176i	−0.696571	+	0.717488i	$0.745292\pi$
$38$	2.70310	+	4.68191i	0.438501	+	0.759506i
$39$	3.58309	−	0.401793i	0.573754	−	0.0643384i
$40$	−3.79467	−	2.19085i	−0.599990	−	0.346404i
$41$	−0.00297886	+	0.0111173i	−0.000465220	+	0.00173623i	−0.966158	−	0.257951i	$-0.916953\pi$
$41$	−0.00297886	+	0.0111173i	−0.000465220	+	0.00173623i	0.965693	+	0.259687i	$0.0836194\pi$
$42$	1.89172	+	1.84970i	0.291899	+	0.285415i
$43$	−2.69459	−	1.55572i	−0.410921	−	0.237245i	0.280264	−	0.959923i	$-0.409578\pi$
$43$	−2.69459	−	1.55572i	−0.410921	−	0.237245i	−0.691185	+	0.722677i	$0.742911\pi$
$44$	−0.835348	−	3.11756i	−0.125933	−	0.469990i
$45$	−3.09834	−	3.09834i	−0.461873	−	0.461873i
$46$	1.40397	+	1.40397i	0.207004	+	0.207004i
$47$	0.994423	+	3.71124i	0.145051	+	0.541339i	0.999753	+	0.0222199i	$0.00707338\pi$
$47$	0.994423	+	3.71124i	0.145051	+	0.541339i	−0.854702	+	0.519120i	$0.826260\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−3.36295	+	6.13927i	−0.480421	+	0.877038i
$50$	−3.67507	+	13.7155i	−0.519733	+	1.93967i
$51$	5.49185	+	3.17072i	0.769013	+	0.443990i
$52$	2.13951	+	2.90215i	0.296697	+	0.402456i
$53$	−6.19883	−	10.7367i	−0.851475	−	1.47480i	−0.879877	−	0.475202i	$-0.842375\pi$
$53$	−6.19883	−	10.7367i	−0.851475	−	1.47480i	0.0284016	−	0.999597i	$-0.490958\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−12.2474	+	7.07106i	−1.65144	+	0.953461i
$56$	−0.656024	+	2.56313i	−0.0876648	+	0.342513i
$57$	−3.82276	+	3.82276i	−0.506337	+	0.506337i
$58$	3.35899	+	0.900038i	0.441057	+	0.118181i
$59$	4.55586	−	4.55586i	0.593122	−	0.593122i	−0.345351	−	0.938473i	$-0.612240\pi$
$59$	4.55586	−	4.55586i	0.593122	−	0.593122i	0.938473	+	0.345351i	$0.112240\pi$
$60$	1.13407	−	4.23240i	0.146408	−	0.546401i
$61$	4.94487	−	2.85492i	0.633126	−	0.365535i	−0.148836	−	0.988862i	$-0.547553\pi$
$61$	4.94487	−	2.85492i	0.633126	−	0.365535i	0.781962	+	0.623326i	$0.214219\pi$
$62$	4.27085	+	7.39733i	0.542399	+	0.939462i
$63$	−1.29706	+	2.30600i	−0.163414	+	0.290529i
$64$			1.00000i			0.125000i
$65$	9.85674	−	12.3465i	1.22258	−	1.53140i
$66$	2.79513	−	1.61377i	0.344056	−	0.198641i
$67$	−1.37471	−	5.13050i	−0.167948	−	0.626790i	−0.997646	−	0.0685772i	$-0.978154\pi$
$67$	−1.37471	−	5.13050i	−0.167948	−	0.626790i	0.829698	−	0.558213i	$-0.188513\pi$
$68$			6.34145i			0.769013i
$69$	−0.992755	+	1.71950i	−0.119514	+	0.207004i
$70$	11.5922	−	0.130210i	1.38553	−	0.0155630i
$71$	1.61017	+	6.00925i	0.191092	+	0.713167i	0.993244	+	0.116046i	$0.0370220\pi$
$71$	1.61017	+	6.00925i	0.191092	+	0.713167i	−0.802151	+	0.597121i	$0.796311\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	3.47471	+	0.931045i	0.406684	+	0.108971i	0.456361	−	0.889795i	$-0.349153\pi$
$73$	3.47471	+	0.931045i	0.406684	+	0.108971i	−0.0496772	+	0.998765i	$0.515819\pi$
$74$	−0.179940			−0.0209176
$75$	−14.1994			−1.63960
$76$	−5.22199	−	1.39923i	−0.599004	−	0.160503i
$77$	6.10560	+	5.96997i	0.695798	+	0.680341i
$78$	−2.24952	+	2.81774i	−0.254708	+	0.319046i
$79$	−7.63746	+	13.2285i	−0.859282	+	1.48832i	0.0133334	+	0.999911i	$0.495756\pi$
$79$	−7.63746	+	13.2285i	−0.859282	+	1.48832i	−0.872615	+	0.488408i	$0.837578\pi$
$80$	4.23240	−	1.13407i	0.473197	−	0.126793i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.00575472	−	0.00996747i	−0.000635503	−	0.00110072i
$83$	−1.17696	−	1.17696i	−0.129188	−	0.129188i	0.639556	−	0.768744i	$-0.279118\pi$
$83$	−1.17696	−	1.17696i	−0.129188	−	0.129188i	−0.768744	+	0.639556i	$0.779118\pi$
$84$	−2.64558	+	0.0297166i	−0.288657	+	0.00324235i
$85$	26.8396	−	7.19164i	2.91116	−	0.780043i
$86$	3.00543	−	0.805301i	0.324083	−	0.0868379i
$87$			3.47748i			0.372825i
$88$	2.79513	+	1.61377i	0.297962	+	0.172028i
$89$	12.6058	−	12.6058i	1.33621	−	1.33621i	0.436516	−	0.899696i	$-0.356212\pi$
$89$	12.6058	−	12.6058i	1.33621	−	1.33621i	0.899696	−	0.436516i	$-0.143788\pi$
$90$	4.38171			0.461873
$91$	−8.78377	−	3.72094i	−0.920789	−	0.390061i
$92$	−1.98551			−0.207004
$93$	−6.03990	+	6.03990i	−0.626308	+	0.626308i
$94$	−3.32740	−	1.92108i	−0.343195	−	0.198144i
$95$			23.6884i			2.43038i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	2.25048	−	0.603015i	0.228502	−	0.0612269i	−0.142751	−	0.989759i	$-0.545595\pi$
$97$	2.25048	−	0.603015i	0.228502	−	0.0612269i	0.371253	+	0.928532i	$0.378928\pi$
$98$	−1.96315	−	6.71908i	−0.198309	−	0.678729i
$99$	2.28221	+	2.28221i	0.229371	+	0.229371i
$100$	−7.09968	−	12.2970i	−0.709968	−	1.22970i
$101$	−4.16096	+	7.20699i	−0.414031	+	0.717122i	−0.995326	−	0.0965702i	$-0.969213\pi$
$101$	−4.16096	+	7.20699i	−0.414031	+	0.717122i	0.581295	+	0.813693i	$0.302546\pi$
$102$	−6.12537	+	1.64129i	−0.606502	+	0.162512i
$103$	1.19202	−	2.06463i	0.117453	−	0.203434i	−0.801305	−	0.598256i	$-0.795860\pi$
$103$	1.19202	−	2.06463i	0.117453	−	0.203434i	0.918758	+	0.394822i	$0.129194\pi$
$104$	−3.56499	−	0.539271i	−0.349576	−	0.0528798i
$105$	3.12605	+	11.1635i	0.305071	+	1.08944i
$106$	11.9752	+	3.20875i	1.16314	+	0.311662i
$107$	−4.26472			−0.412286			−0.206143	−	0.978522i	$-0.566091\pi$
$107$	−4.26472			−0.412286			−0.206143	+	0.978522i	$0.566091\pi$
$108$	−1.00000			−0.0962250
$109$	−18.0839	−	4.84556i	−1.73212	−	0.464120i	−0.751451	−	0.659789i	$-0.770646\pi$
$109$	−18.0839	−	4.84556i	−1.73212	−	0.464120i	−0.980670	+	0.195668i	$0.937312\pi$
$110$	3.66025	−	13.6602i	0.348991	−	1.30245i
$111$	−0.0465718	−	0.173808i	−0.00442040	−	0.0164972i
$112$	−1.34853	−	2.27629i	−0.127424	−	0.215089i
$113$	3.88176	−	6.72341i	0.365166	−	0.632486i	−0.623637	−	0.781714i	$-0.714346\pi$
$113$	3.88176	−	6.72341i	0.365166	−	0.632486i	0.988803	+	0.149228i	$0.0476790\pi$
$114$		−	5.40620i		−	0.506337i
$115$	2.25171	+	8.40349i	0.209973	+	0.783629i
$116$	−3.01158	+	1.73874i	−0.279619	+	0.161438i
$117$	−3.30395	−	1.44358i	−0.305450	−	0.133459i
$118$			6.44295i			0.593122i
$119$	−8.55162	−	14.4349i	−0.783925	−	1.32325i
$120$	2.19085	+	3.79467i	0.199997	+	0.346404i
$121$	−0.504905	+	0.291507i	−0.0459005	+	0.0265007i
$122$	−1.47782	+	5.51529i	−0.133795	+	0.499331i
$123$	0.00813841	−	0.00813841i	0.000733816	−	0.000733816i
$124$	−8.25065	−	2.21076i	−0.740930	−	0.198532i
$125$	−28.5027	+	28.5027i	−2.54936	+	2.54936i
$126$	−0.713432	−	2.54775i	−0.0635575	−	0.226971i
$127$	−0.607656	+	0.350830i	−0.0539207	+	0.0311311i	−0.526718	−	0.850040i	$-0.676578\pi$
$127$	−0.607656	+	0.350830i	−0.0539207	+	0.0311311i	0.472797	+	0.881171i	$0.343244\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.55572	+	2.69459i	0.136974	+	0.237245i
$130$	1.76054	+	15.7001i	0.154410	+	1.37699i
$131$	6.17726	+	3.56644i	0.539710	+	0.311602i	0.744961	−	0.667108i	$-0.232468\pi$
$131$	6.17726	+	3.56644i	0.539710	+	0.311602i	−0.205252	+	0.978709i	$0.565801\pi$
$132$	−0.835348	+	3.11756i	−0.0727077	+	0.271349i
$133$	13.7736	−	3.85696i	1.19433	−	0.334441i
$134$	4.59988	+	2.65574i	0.397369	+	0.229421i
$135$	1.13407	+	4.23240i	0.0976052	+	0.364267i
$136$	−4.48408	−	4.48408i	−0.384507	−	0.384507i
$137$	−0.639858	−	0.639858i	−0.0546668	−	0.0546668i	0.679245	−	0.733912i	$-0.262307\pi$
$137$	−0.639858	−	0.639858i	−0.0546668	−	0.0546668i	−0.733912	+	0.679245i	$0.762307\pi$
$138$	−0.513888	−	1.91786i	−0.0437451	−	0.163259i
$139$	−17.7912	−	10.2718i	−1.50903	−	0.871239i	−0.999945	−	0.0105224i	$-0.996651\pi$
$139$	−17.7912	−	10.2718i	−1.50903	−	0.871239i	−0.509085	−	0.860716i	$-0.670016\pi$
$140$	−8.10484	+	8.28898i	−0.684984	+	0.700547i
$141$	0.994423	−	3.71124i	0.0837455	−	0.312542i
$142$	−5.38775	−	3.11062i	−0.452130	−	0.261037i
$143$	−7.26040	+	9.09436i	−0.607145	+	0.760508i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	10.7744	+	10.7744i	0.894765	+	0.894765i
$146$	−3.11534	+	1.79864i	−0.257827	+	0.148857i
$147$	5.98203	−	3.63529i	0.493390	−	0.299833i
$148$	0.127237	−	0.127237i	0.0104588	−	0.0104588i
$149$	6.98514	+	1.87166i	0.572245	+	0.153332i	0.533326	−	0.845910i	$-0.320942\pi$
$149$	6.98514	+	1.87166i	0.572245	+	0.153332i	0.0389188	+	0.999242i	$0.487609\pi$
$150$	10.0405	−	10.0405i	0.819801	−	0.819801i
$151$	0.876878	−	3.27255i	0.0713593	−	0.266317i	−0.921024	−	0.389506i	$-0.872646\pi$
$151$	0.876878	−	3.27255i	0.0713593	−	0.266317i	0.992383	+	0.123190i	$0.0393123\pi$
$152$	4.68191	−	2.70310i	0.379753	−	0.219251i
$153$	−3.17072	−	5.49185i	−0.256338	−	0.443990i
$154$	−8.53872	+	0.0959114i	−0.688069	+	0.00772876i
$155$			37.4272i			3.00623i
$156$	−0.401793	−	3.58309i	−0.0321692	−	0.286877i
$157$	−1.58306	+	0.913980i	−0.126342	+	0.0729436i	−0.561839	−	0.827247i	$-0.689906\pi$
$157$	−1.58306	+	0.913980i	−0.126342	+	0.0729436i	0.435497	+	0.900190i	$0.356573\pi$
$158$	−3.95344	−	14.7544i	−0.314519	−	1.17380i
$159$			12.3977i			0.983199i
$160$	−2.19085	+	3.79467i	−0.173202	+	0.299995i
$161$	4.51959	−	2.67752i	0.356193	−	0.211018i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	2.96661	−	11.0716i	0.232363	−	0.867191i	−0.746957	−	0.664873i	$-0.768486\pi$
$163$	2.96661	−	11.0716i	0.232363	−	0.867191i	0.979320	−	0.202318i	$-0.0648475\pi$
$164$	0.0111173	+	0.00297886i	0.000868113	+	0.000232610i
$165$	14.1421			1.10096
$166$	1.66448			0.129188
$167$	9.75066	+	2.61268i	0.754529	+	0.202175i	0.615526	−	0.788117i	$-0.288944\pi$
$167$	9.75066	+	2.61268i	0.754529	+	0.202175i	0.139003	+	0.990292i	$0.455610\pi$
$168$	1.84970	−	1.89172i	0.142707	−	0.145950i
$169$	3.84499	−	12.4184i	0.295769	−	0.955260i
$170$	−13.8932	+	24.0637i	−1.06556	+	1.84560i
$171$	5.22199	−	1.39923i	0.399336	−	0.107002i
$172$	−1.55572	+	2.69459i	−0.118623	+	0.205461i
$173$	−5.46401	−	9.46394i	−0.415421	−	0.719530i	0.580052	−	0.814580i	$-0.303032\pi$
$173$	−5.46401	−	9.46394i	−0.415421	−	0.719530i	−0.995473	+	0.0950498i	$0.969699\pi$
$174$	−2.45895	−	2.45895i	−0.186412	−	0.186412i
$175$	32.7438	+	18.4174i	2.47520	+	1.39222i
$176$	−3.11756	+	0.835348i	−0.234995	+	0.0629667i
$177$	−6.22342	+	1.66756i	−0.467781	+	0.125341i
$178$			17.8273i			1.33621i
$179$	−8.69473	−	5.01990i	−0.649875	−	0.375205i	0.138534	−	0.990358i	$-0.455761\pi$
$179$	−8.69473	−	5.01990i	−0.649875	−	0.375205i	−0.788408	+	0.615152i	$0.789094\pi$
$180$	−3.09834	+	3.09834i	−0.230936	+	0.230936i
$181$	0.280875			0.0208773			0.0104386	−	0.999946i	$-0.496677\pi$
$181$	0.280875			0.0208773			0.0104386	+	0.999946i	$0.496677\pi$
$182$	8.84217	−	3.57996i	0.655425	−	0.265364i
$183$	−5.70985			−0.422084
$184$	1.40397	−	1.40397i	0.103502	−	0.103502i
$185$	−0.682812	−	0.394222i	−0.0502013	−	0.0289838i
$186$		−	8.54170i		−	0.626308i
$187$	−19.7698	+	5.29731i	−1.44571	+	0.387378i
$188$	3.71124	−	0.994423i	0.270670	−	0.0725257i
$189$	2.27629	−	1.34853i	0.165575	−	0.0980909i
$190$	−16.7502	−	16.7502i	−1.21519	−	1.21519i
$191$	−1.99049	−	3.44763i	−0.144027	−	0.249461i	0.784983	−	0.619518i	$-0.212672\pi$
$191$	−1.99049	−	3.44763i	−0.144027	−	0.249461i	−0.929009	+	0.370056i	$0.879338\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−23.6743	+	6.34351i	−1.70411	+	0.456616i	−0.973970	−	0.226679i	$-0.927213\pi$
$193$	−23.6743	+	6.34351i	−1.70411	+	0.456616i	−0.730143	+	0.683294i	$0.760547\pi$
$194$	−1.16494	+	2.01773i	−0.0836375	+	0.144864i
$195$	−14.7094	+	5.76403i	−1.05337	+	0.412771i
$196$	6.13927	+	3.36295i	0.438519	+	0.240210i
$197$	3.65004	+	0.978025i	0.260054	+	0.0696814i	0.386491	−	0.922293i	$-0.373687\pi$
$197$	3.65004	+	0.978025i	0.260054	+	0.0696814i	−0.126436	+	0.991975i	$0.540354\pi$
$198$	−3.22754			−0.229371
$199$	−3.57417			−0.253366			−0.126683	−	0.991943i	$-0.540433\pi$
$199$	−3.57417			−0.253366			−0.126683	+	0.991943i	$0.540433\pi$
$200$	13.7155	+	3.67507i	0.969835	+	0.259866i
$201$	−1.37471	+	5.13050i	−0.0969647	+	0.361877i
$202$	−2.15387	−	8.03835i	−0.151546	−	0.565577i
$203$	4.51049	−	8.01907i	0.316574	−	0.562828i
$204$	3.17072	−	5.49185i	0.221995	−	0.384507i
$205$		−	0.0504310i		−	0.00352226i
$206$	0.617033	+	2.30280i	0.0429907	+	0.160443i
$207$	1.71950	−	0.992755i	0.119514	−	0.0690013i
$208$	2.90215	−	2.13951i	0.201228	−	0.148348i
$209$		−	17.4487i		−	1.20695i
$210$	−10.1042	−	5.68332i	−0.697258	−	0.392187i
$211$	−7.71910	−	13.3699i	−0.531405	−	0.920420i	−0.999328	−	0.0366508i	$-0.988331\pi$
$211$	−7.71910	−	13.3699i	−0.531405	−	0.920420i	0.467924	−	0.883769i	$-0.345002\pi$
$212$	−10.7367	+	6.19883i	−0.737399	+	0.425738i
$213$	1.61017	−	6.00925i	0.110327	−	0.411747i
$214$	3.01561	−	3.01561i	0.206143	−	0.206143i
$215$	13.1689	+	3.52860i	0.898111	+	0.240648i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	21.7621	−	6.09392i	1.47731	−	0.413682i
$218$	16.2136	−	9.36090i	1.09812	−	0.634000i
$219$	−2.54366	−	2.54366i	−0.171885	−	0.171885i
$220$	7.07106	+	12.2474i	0.476731	+	0.825722i
$221$	18.4039	−	13.5676i	1.23798	−	0.912655i
$222$	0.155832	+	0.0899699i	0.0104588	+	0.00603838i
$223$	−5.78209	+	21.5790i	−0.387197	+	1.44504i	0.447477	+	0.894295i	$0.352323\pi$
$223$	−5.78209	+	21.5790i	−0.387197	+	1.44504i	−0.834674	+	0.550744i	$0.814344\pi$
$224$	2.56313	+	0.656024i	0.171256	+	0.0438324i
$225$	12.2970	+	7.09968i	0.819801	+	0.473312i
$226$	2.00935	+	7.49899i	0.133660	+	0.498826i
$227$	−16.3453	−	16.3453i	−1.08488	−	1.08488i	−0.996047	−	0.0888311i	$-0.971687\pi$
$227$	−16.3453	−	16.3453i	−1.08488	−	1.08488i	−0.0888311	−	0.996047i	$-0.528313\pi$
$228$	3.82276	+	3.82276i	0.253169	+	0.253169i
$229$	3.69250	+	13.7806i	0.244007	+	0.910646i	0.973880	+	0.227064i	$0.0729125\pi$
$229$	3.69250	+	13.7806i	0.244007	+	0.910646i	−0.729873	+	0.683583i	$0.760421\pi$
$230$	−7.53436	−	4.34996i	−0.496801	−	0.286828i
$231$	−2.30263	−	8.22294i	−0.151502	−	0.541030i
$232$	0.900038	−	3.35899i	0.0590904	−	0.220528i
$233$	−1.76570	−	1.01943i	−0.115675	−	0.0667851i	0.441046	−	0.897484i	$-0.354608\pi$
$233$	−1.76570	−	1.01943i	−0.115675	−	0.0667851i	−0.556721	+	0.830699i	$0.687941\pi$
$234$	3.35701	−	1.31548i	0.219455	−	0.0859953i
$235$	−8.41760	−	14.5797i	−0.549104	−	0.951075i
$236$	−4.55586	−	4.55586i	−0.296561	−	0.296561i
$237$	13.2285	−	7.63746i	0.859282	−	0.496107i
$238$	16.2540	+	4.16014i	1.05359	+	0.269662i
$239$	7.26823	−	7.26823i	0.470143	−	0.470143i	−0.431818	−	0.901961i	$-0.642128\pi$
$239$	7.26823	−	7.26823i	0.470143	−	0.470143i	0.901961	+	0.431818i	$0.142128\pi$
$240$	−4.23240	−	1.13407i	−0.273201	−	0.0732039i
$241$	7.76419	−	7.76419i	0.500136	−	0.500136i	−0.411344	−	0.911480i	$-0.634941\pi$
$241$	7.76419	−	7.76419i	0.500136	−	0.500136i	0.911480	+	0.411344i	$0.134941\pi$
$242$	0.150895	−	0.563149i	0.00969991	−	0.0362006i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−2.85492	−	4.94487i	−0.182768	−	0.316563i
$245$	7.27100	−	29.7977i	0.464527	−	1.90370i
$246$			0.0115094i			0.000733816i
$247$	7.11173	+	18.1487i	0.452508	+	1.15477i
$248$	7.39733	−	4.27085i	0.469731	−	0.271199i
$249$	0.430798	+	1.60776i	0.0273007	+	0.101888i
$250$		−	40.3089i		−	2.54936i
$251$	6.53973	−	11.3271i	0.412784	−	0.714963i	−0.582409	−	0.812896i	$-0.697890\pi$
$251$	6.53973	−	11.3271i	0.412784	−	0.714963i	0.995193	+	0.0979333i	$0.0312232\pi$
$252$	2.30600	+	1.29706i	0.145264	+	0.0817069i
$253$	−1.65859	−	6.18995i	−0.104275	−	0.389159i
$254$	0.181603	−	0.677752i	0.0113948	−	0.0425259i
$255$	−26.8396	−	7.19164i	−1.68076	−	0.450358i
$256$	1.00000			0.0625000
$257$	0.0646125			0.00403042			0.00201521	−	0.999998i	$-0.499359\pi$
$257$	0.0646125			0.00403042			0.00201521	+	0.999998i	$0.499359\pi$
$258$	−3.00543	−	0.805301i	−0.187110	−	0.0501359i
$259$	−0.118045	+	0.461209i	−0.00733494	+	0.0286581i
$260$	−12.3465	−	9.85674i	−0.765698	−	0.611289i
$261$	1.73874	−	3.01158i	0.107625	−	0.186412i
$262$	−6.88984	+	1.84613i	−0.425656	+	0.114054i
$263$	1.99949	−	3.46323i	0.123294	−	0.213552i	−0.797771	−	0.602961i	$-0.793987\pi$
$263$	1.99949	−	3.46323i	0.123294	−	0.213552i	0.921065	+	0.389409i	$0.127321\pi$
$264$	−1.61377	−	2.79513i	−0.0993205	−	0.172028i
$265$	38.4121	+	38.4121i	2.35964	+	2.35964i
$266$	−7.01215	+	12.4667i	−0.429943	+	0.764383i
$267$	−17.2198	+	4.61404i	−1.05384	+	0.282375i
$268$	−5.13050	+	1.37471i	−0.313395	+	0.0839739i
$269$			4.29672i			0.261976i	0.991384	+	0.130988i	$0.0418149\pi$
$269$			4.29672i			0.261976i	−0.991384	+	0.130988i	$0.958185\pi$
$270$	−3.79467	−	2.19085i	−0.230936	−	0.133331i
$271$	−5.39082	+	5.39082i	−0.327469	+	0.327469i	−0.851623	−	0.524154i	$-0.824381\pi$
$271$	−5.39082	+	5.39082i	−0.327469	+	0.327469i	0.524154	+	0.851623i	$0.324381\pi$
$272$	6.34145			0.384507
$273$	5.74650	+	7.61431i	0.347794	+	0.460839i
$274$	0.904896			0.0546668
$275$	32.4060	−	32.4060i	1.95415	−	1.95415i
$276$	1.71950	+	0.992755i	0.103502	+	0.0597569i
$277$		−	1.27884i		−	0.0768382i	−0.999262	−	0.0384191i	$-0.987768\pi$
$277$		−	1.27884i		−	0.0768382i	0.999262	−	0.0384191i	$-0.0122322\pi$
$278$	19.8435	−	5.31705i	1.19013	−	0.318895i
$279$	8.25065	−	2.21076i	0.493954	−	0.132354i
$280$	−0.130210	−	11.5922i	−0.00778151	−	0.692765i
$281$	7.17377	+	7.17377i	0.427951	+	0.427951i	0.887930	−	0.459979i	$-0.152143\pi$
$281$	7.17377	+	7.17377i	0.427951	+	0.427951i	−0.459979	+	0.887930i	$0.652143\pi$
$282$	1.92108	+	3.32740i	0.114398	+	0.198144i
$283$	−2.16909	+	3.75698i	−0.128939	+	0.223329i	−0.923266	−	0.384162i	$-0.874491\pi$
$283$	−2.16909	+	3.75698i	−0.128939	+	0.223329i	0.794327	+	0.607491i	$0.207824\pi$
$284$	6.00925	−	1.61017i	0.356583	−	0.0955462i
$285$	11.8442	−	20.5148i	0.701590	−	1.21519i
$286$	−1.29680	−	11.5646i	−0.0766815	−	0.683827i
$287$	−0.0293232	+	0.00821120i	−0.00173089	+	0.000484692i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	23.2140			1.36553
$290$	−15.2373			−0.894765
$291$	−2.25048	−	0.603015i	−0.131926	−	0.0353494i
$292$	0.931045	−	3.47471i	0.0544853	−	0.203342i
$293$	−4.70535	−	17.5606i	−0.274890	−	1.02590i	−0.955915	−	0.293643i	$-0.905132\pi$
$293$	−4.70535	−	17.5606i	−0.274890	−	1.02590i	0.681026	−	0.732260i	$-0.261534\pi$
$294$	−1.65940	+	6.80047i	−0.0967781	+	0.396611i
$295$	−14.1156	+	24.4489i	−0.821840	+	1.42347i
$296$			0.179940i			0.0104588i
$297$	−0.835348	−	3.11756i	−0.0484718	−	0.180899i
$298$	−6.26270	+	3.61577i	−0.362789	+	0.209456i
$299$	4.24802	+	5.76226i	0.245669	+	0.333240i
$300$			14.1994i			0.819801i
$301$	−0.0924616	−	8.23159i	−0.00532940	−	0.474461i
$302$	1.69400	+	2.93409i	0.0974786	+	0.168838i
$303$	7.20699	−	4.16096i	0.414031	−	0.239041i
$304$	−1.39923	+	5.22199i	−0.0802513	+	0.299502i
$305$	−17.6910	+	17.6910i	−1.01298	+	1.01298i
$306$	6.12537	+	1.64129i	0.350164	+	0.0938262i
$307$	−7.72652	+	7.72652i	−0.440976	+	0.440976i	−0.892340	−	0.451364i	$-0.850938\pi$
$307$	−7.72652	+	7.72652i	−0.440976	+	0.440976i	0.451364	+	0.892340i	$0.350938\pi$
$308$	5.96997	−	6.10560i	0.340170	−	0.347899i
$309$	−2.06463	+	1.19202i	−0.117453	+	0.0678114i
$310$	−26.4651	−	26.4651i	−1.50311	−	1.50311i
$311$	−5.76925	−	9.99263i	−0.327144	−	0.566630i	0.654800	−	0.755802i	$-0.272753\pi$
$311$	−5.76925	−	9.99263i	−0.327144	−	0.566630i	−0.981944	+	0.189172i	$0.939420\pi$
$312$	2.81774	+	2.24952i	0.159523	+	0.127354i
$313$	−15.6924	−	9.06000i	−0.886986	−	0.512101i	−0.0140304	−	0.999902i	$-0.504466\pi$
$313$	−15.6924	−	9.06000i	−0.886986	−	0.512101i	−0.872955	+	0.487800i	$0.837799\pi$
$314$	0.473111	−	1.76567i	0.0266992	−	0.0996428i
$315$	2.87450	−	11.2309i	0.161960	−	0.632789i
$316$	13.2285	+	7.63746i	0.744160	+	0.429641i
$317$	6.42219	+	23.9680i	0.360706	+	1.34617i	0.873149	+	0.487453i	$0.162074\pi$
$317$	6.42219	+	23.9680i	0.360706	+	1.34617i	−0.512443	+	0.858721i	$0.671259\pi$
$318$	−8.76647	−	8.76647i	−0.491599	−	0.491599i
$319$	−7.93634	−	7.93634i	−0.444350	−	0.444350i
$320$	−1.13407	−	4.23240i	−0.0633964	−	0.236599i
$321$	3.69335	+	2.13236i	0.206143	+	0.119017i
$322$	−1.30254	+	5.08912i	−0.0725878	+	0.283606i
$323$	−8.87314	+	33.1150i	−0.493714	+	1.84257i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	−20.4980	+	46.9139i	−1.13702	+	2.60232i
$326$	5.73106	+	9.92648i	0.317414	+	0.549777i
$327$	13.2383	+	13.2383i	0.732081	+	0.732081i
$328$	−0.00996747	+	0.00575472i	−0.000550362	+	0.000317751i
$329$	−7.10682	+	7.26829i	−0.391812	+	0.400714i
$330$	−9.99999	+	9.99999i	−0.550481	+	0.550481i
$331$	−12.4551	−	3.33732i	−0.684592	−	0.183436i	−0.100273	−	0.994960i	$-0.531972\pi$
$331$	−12.4551	−	3.33732i	−0.684592	−	0.183436i	−0.584319	+	0.811524i	$0.698638\pi$
$332$	−1.17696	+	1.17696i	−0.0645942	+	0.0645942i
$333$	−0.0465718	+	0.173808i	−0.00255212	+	0.00952464i
$334$	−8.74221	+	5.04731i	−0.478352	+	0.276177i
$335$	11.6367	+	20.1553i	0.635780	+	1.10120i
$336$	0.0297166	+	2.64558i	0.00162117	+	0.144328i
$337$			10.2939i			0.560743i	0.959892	+	0.280372i	$0.0904577\pi$
$337$			10.2939i			0.560743i	−0.959892	+	0.280372i	$0.909542\pi$
$338$	6.06230	+	11.4999i	0.329745	+	0.625514i
$339$	−6.72341	+	3.88176i	−0.365166	+	0.210829i
$340$	−7.19164	−	26.8396i	−0.390022	−	1.45558i
$341$		−	27.5687i		−	1.49293i
$342$	−2.70310	+	4.68191i	−0.146167	+	0.253169i
$343$	−18.5097	+	0.623944i	−0.999432	+	0.0336898i
$344$	−0.805301	−	3.00543i	−0.0434189	−	0.162042i
$345$	2.25171	−	8.40349i	0.121228	−	0.452428i
$346$	10.5557	+	2.82838i	0.567475	+	0.152055i
$347$	27.2227			1.46139			0.730694	−	0.682705i	$-0.239197\pi$
$347$	27.2227			1.46139			0.730694	+	0.682705i	$0.239197\pi$
$348$	3.47748			0.186412
$349$	−20.4872	−	5.48954i	−1.09666	−	0.293848i	−0.335254	−	0.942128i	$-0.608822\pi$
$349$	−20.4872	−	5.48954i	−1.09666	−	0.293848i	−0.761402	+	0.648280i	$0.775489\pi$
$350$	−36.1764	+	10.1303i	−1.93371	+	0.541486i
$351$	2.13951	+	2.90215i	0.114199	+	0.154906i
$352$	1.61377	−	2.79513i	0.0860141	−	0.148981i
$353$	3.44843	−	0.924004i	0.183541	−	0.0491797i	−0.165878	−	0.986146i	$-0.553046\pi$
$353$	3.44843	−	0.924004i	0.183541	−	0.0491797i	0.349419	+	0.936967i	$0.386379\pi$
$354$	3.22148	−	5.57976i	0.171220	−	0.296561i
$355$	−13.6298	−	23.6075i	−0.723395	−	1.25296i
$356$	−12.6058	−	12.6058i	−0.668106	−	0.668106i
$357$	0.188446	+	16.7768i	0.00997364	+	0.887924i
$358$	9.69771	−	2.59849i	0.512540	−	0.137335i
$359$	−17.5556	+	4.70401i	−0.926549	+	0.248268i	−0.690383	−	0.723444i	$-0.742558\pi$
$359$	−17.5556	+	4.70401i	−0.926549	+	0.248268i	−0.236167	+	0.971713i	$0.575891\pi$
$360$		−	4.38171i		−	0.230936i
$361$	−8.85688	−	5.11352i	−0.466152	−	0.269133i
$362$	−0.198609	+	0.198609i	−0.0104386	+	0.0104386i
$363$	0.583014			0.0306003
$364$	−3.72094	+	8.78377i	−0.195030	+	0.460395i
$365$	−15.7622			−0.825033
$366$	4.03747	−	4.03747i	0.211042	−	0.211042i
$367$	0.307242	+	0.177386i	0.0160379	+	0.00925948i	0.507998	−	0.861359i	$-0.330386\pi$
$367$	0.307242	+	0.177386i	0.0160379	+	0.00925948i	−0.491960	+	0.870618i	$0.663719\pi$
$368$			1.98551i			0.103502i
$369$	−0.0111173	+	0.00297886i	−0.000578742	+	0.000155073i
$370$	0.761578	−	0.204064i	0.0395925	−	0.0106088i
$371$	16.0805	−	28.5890i	0.834857	−	1.48427i
$372$	6.03990	+	6.03990i	0.313154	+	0.313154i
$373$	−10.6004	−	18.3604i	−0.548867	−	0.950666i	−0.998353	−	0.0573783i	$-0.981726\pi$
$373$	−10.6004	−	18.3604i	−0.548867	−	0.950666i	0.449485	−	0.893288i	$-0.351607\pi$
$374$	10.2336	−	17.7252i	0.529168	−	0.916546i
$375$	38.9354	−	10.4327i	2.01062	−	0.538743i
$376$	−1.92108	+	3.32740i	−0.0990720	+	0.171598i
$377$	11.4894	+	5.02003i	0.591734	+	0.258545i
$378$	−0.656024	+	2.56313i	−0.0337422	+	0.131833i
$379$	10.3631	+	2.77679i	0.532317	+	0.142634i	0.514958	−	0.857215i	$-0.327807\pi$
$379$	10.3631	+	2.77679i	0.532317	+	0.142634i	0.0173592	+	0.999849i	$0.494474\pi$
$380$	23.6884			1.21519
$381$	0.701660			0.0359471
$382$	3.84533	+	1.03035i	0.196744	+	0.0527174i
$383$	3.79762	−	14.1729i	0.194049	−	0.724202i	−0.798462	−	0.602046i	$-0.794352\pi$
$383$	3.79762	−	14.1729i	0.194049	−	0.724202i	0.992511	−	0.122156i	$-0.0389809\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−32.6117	−	18.3431i	−1.66205	−	0.934853i
$386$	12.2547	−	21.2258i	0.623748	−	1.08036i
$387$		−	3.11145i		−	0.158164i
$388$	−0.603015	−	2.25048i	−0.0306135	−	0.114251i
$389$	−6.90619	+	3.98729i	−0.350158	+	0.202164i	−0.664755	−	0.747062i	$-0.731464\pi$
$389$	−6.90619	+	3.98729i	−0.350158	+	0.202164i	0.314597	+	0.949225i	$0.398131\pi$
$390$	6.32536	−	14.4769i	0.320297	−	0.733068i
$391$			12.5910i			0.636755i
$392$	−6.71908	+	1.96315i	−0.339365	+	0.0991543i
$393$	−3.56644	−	6.17726i	−0.179903	−	0.311602i
$394$	−3.27253	+	1.88940i	−0.164868	+	0.0951865i
$395$	17.3228	−	64.6497i	0.871606	−	3.25288i
$396$	2.28221	−	2.28221i	0.114685	−	0.114685i
$397$	20.7747	+	5.56656i	1.04265	+	0.279378i	0.739212	−	0.673473i	$-0.235198\pi$
$397$	20.7747	+	5.56656i	1.04265	+	0.279378i	0.303440	+	0.952851i	$0.401865\pi$
$398$	2.52732	−	2.52732i	0.126683	−	0.126683i
$399$	−13.8568	−	3.54660i	−0.693708	−	0.177552i
$400$	−12.2970	+	7.09968i	−0.614850	+	0.354984i
$401$	15.3971	+	15.3971i	0.768896	+	0.768896i	0.977912	−	0.209016i	$-0.0670261\pi$
$401$	15.3971	+	15.3971i	0.768896	+	0.768896i	−0.209016	+	0.977912i	$0.567026\pi$
$402$	−2.65574	−	4.59988i	−0.132456	−	0.229421i
$403$	11.2364	+	28.6746i	0.559725	+	1.42838i
$404$	7.20699	+	4.16096i	0.358561	+	0.207015i
$405$	1.13407	−	4.23240i	0.0563524	−	0.210310i
$406$	2.48094	+	8.85974i	0.123127	+	0.439701i
$407$	0.502955	+	0.290381i	0.0249305	+	0.0143936i
$408$	1.64129	+	6.12537i	0.0812558	+	0.303251i
$409$	−22.8606	−	22.8606i	−1.13038	−	1.13038i	−0.990113	−	0.140269i	$-0.955203\pi$
$409$	−22.8606	−	22.8606i	−1.13038	−	1.13038i	−0.140269	−	0.990113i	$-0.544797\pi$
$410$	0.0356601	+	0.0356601i	0.00176113	+	0.00176113i
$411$	0.234204	+	0.874063i	0.0115525	+	0.0431143i
$412$	−2.06463	−	1.19202i	−0.101717	−	0.0587264i
$413$	16.5141	+	4.22673i	0.812607	+	0.207984i
$414$	−0.513888	+	1.91786i	−0.0252562	+	0.0942575i
$415$	6.31614	+	3.64662i	0.310047	+	0.179006i
$416$	−0.539271	+	3.56499i	−0.0264399	+	0.174788i
$417$	10.2718	+	17.7912i	0.503010	+	0.871239i
$418$	12.3381	+	12.3381i	0.603477	+	0.603477i
$419$	−4.47379	+	2.58295i	−0.218559	+	0.126185i	−0.605283	−	0.796010i	$-0.706940\pi$
$419$	−4.47379	+	2.58295i	−0.218559	+	0.126185i	0.386724	+	0.922196i	$0.373607\pi$
$420$	11.1635	−	3.12605i	0.544722	−	0.152536i
$421$	10.2156	−	10.2156i	0.497877	−	0.497877i	−0.412899	−	0.910777i	$-0.635484\pi$
$421$	10.2156	−	10.2156i	0.497877	−	0.497877i	0.910777	+	0.412899i	$0.135484\pi$
$422$	14.9122	+	3.99570i	0.725912	+	0.194508i
$423$	−2.71681	+	2.71681i	−0.132096	+	0.132096i
$424$	3.20875	−	11.9752i	0.155831	−	0.581568i
$425$	−77.9808	+	45.0223i	−3.78263	+	2.18390i
$426$	3.11062	+	5.38775i	0.150710	+	0.261037i
$427$	13.1669	+	7.40600i	0.637192	+	0.358401i
$428$			4.26472i			0.206143i
$429$	10.8349	−	4.24574i	0.523113	−	0.204986i
$430$	−11.8069	+	6.81672i	−0.569380	+	0.328732i
$431$	−1.11609	−	4.16529i	−0.0537600	−	0.200635i	0.933822	−	0.357737i	$-0.116452\pi$
$431$	−1.11609	−	4.16529i	−0.0537600	−	0.200635i	−0.987582	+	0.157102i	$0.949785\pi$
$432$			1.00000i			0.0481125i
$433$	19.0775	−	33.0433i	0.916808	−	1.58796i	0.112575	−	0.993643i	$-0.464090\pi$
$433$	19.0775	−	33.0433i	0.916808	−	1.58796i	0.804233	−	0.594314i	$-0.202576\pi$
$434$	−11.0791	+	19.6972i	−0.531813	+	0.945495i
$435$	−3.94370	−	14.7181i	−0.189086	−	0.705679i
$436$	−4.84556	+	18.0839i	−0.232060	+	0.866061i
$437$	−10.3683	−	2.77818i	−0.495984	−	0.132899i
$438$	3.59728			0.171885
$439$	19.7623			0.943205			0.471602	−	0.881811i	$-0.343676\pi$
$439$	19.7623			0.943205			0.471602	+	0.881811i	$0.343676\pi$
$440$	−13.6602	−	3.66025i	−0.651226	−	0.174496i
$441$	−6.99823	+	0.157236i	−0.333249	+	0.00748741i
$442$	−3.41976	+	22.6072i	−0.162661	+	1.07532i
$443$	−13.7162	+	23.7572i	−0.651677	+	1.12874i	0.331039	+	0.943617i	$0.392601\pi$
$443$	−13.7162	+	23.7572i	−0.651677	+	1.12874i	−0.982716	+	0.185120i	$0.940733\pi$
$444$	−0.173808	+	0.0465718i	−0.00824858	+	0.00221020i
$445$	−39.0570	+	67.6487i	−1.85148	+	3.20686i
$446$	−11.1701	−	19.3472i	−0.528921	−	0.916118i
$447$	−5.11347	−	5.11347i	−0.241859	−	0.241859i
$448$	−2.27629	+	1.34853i	−0.107544	+	0.0637119i
$449$	−21.2137	+	5.68419i	−1.00114	+	0.268253i	−0.721921	−	0.691975i	$-0.756741\pi$
$449$	−21.2137	+	5.68419i	−1.00114	+	0.268253i	−0.279214	+	0.960229i	$0.590074\pi$
$450$	−13.7155	+	3.67507i	−0.646556	+	0.173244i
$451$			0.0371472i			0.00174919i
$452$	−6.72341	−	3.88176i	−0.316243	−	0.182583i
$453$	−2.39568	+	2.39568i	−0.112559	+	0.112559i
$454$	23.1158			1.08488
$455$	41.3963	+	5.78712i	1.94069	+	0.271305i
$456$	−5.40620			−0.253169
$457$	−6.28612	+	6.28612i	−0.294052	+	0.294052i	−0.838679	−	0.544626i	$-0.816671\pi$
$457$	−6.28612	+	6.28612i	−0.294052	+	0.294052i	0.544626	+	0.838679i	$0.316671\pi$
$458$	−12.3553	−	7.13335i	−0.577327	−	0.333320i
$459$			6.34145i			0.295993i
$460$	8.40349	−	2.25171i	0.391815	−	0.104986i
$461$	−12.8354	+	3.43922i	−0.597802	+	0.160181i	−0.545017	−	0.838425i	$-0.683477\pi$
$461$	−12.8354	+	3.43922i	−0.597802	+	0.160181i	−0.0527857	+	0.998606i	$0.516810\pi$
$462$	7.44270	+	4.18630i	0.346266	+	0.194764i
$463$	16.8995	+	16.8995i	0.785385	+	0.785385i	0.980734	−	0.195349i	$-0.0625838\pi$
$463$	16.8995	+	16.8995i	0.785385	+	0.785385i	−0.195349	+	0.980734i	$0.562584\pi$
$464$	1.73874	+	3.01158i	0.0807189	+	0.139809i
$465$	18.7136	−	32.4129i	0.867824	−	1.50311i
$466$	1.96939	−	0.527696i	0.0912301	−	0.0244450i
$467$	−5.72210	+	9.91096i	−0.264787	+	0.458625i	−0.967508	−	0.252841i	$-0.918635\pi$
$467$	−5.72210	+	9.91096i	−0.264787	+	0.458625i	0.702721	+	0.711466i	$0.251968\pi$
$468$	−1.44358	+	3.30395i	−0.0667297	+	0.152725i
$469$	9.82463	−	10.0479i	0.453659	−	0.463967i
$470$	16.2616	+	4.35727i	0.750089	+	0.200986i
$471$	1.82796			0.0842280
$472$	6.44295			0.296561
$473$	−9.70012	−	2.59914i	−0.446012	−	0.119509i
$474$	−3.95344	+	14.7544i	−0.181588	+	0.677694i
$475$	−19.8682	−	74.1490i	−0.911614	−	3.40219i
$476$	−14.4349	+	8.55162i	−0.661624	+	0.391963i
$477$	6.19883	−	10.7367i	0.283825	−	0.491599i
$478$			10.2788i			0.470143i
$479$	−8.55605	−	31.9316i	−0.390936	−	1.45899i	−0.828594	−	0.559850i	$-0.810859\pi$
$479$	−8.55605	−	31.9316i	−0.390936	−	1.45899i	0.437658	−	0.899142i	$-0.355808\pi$
$480$	3.79467	−	2.19085i	0.173202	−	0.0999983i
$481$	−0.641484	−	0.0970362i	−0.0292492	−	0.00442447i
$482$			10.9802i			0.500136i
$483$	−5.25284	+	0.0590026i	−0.239012	+	0.00268471i
$484$	0.291507	+	0.504905i	0.0132503	+	0.0229502i
$485$	−8.84110	+	5.10441i	−0.401454	+	0.231779i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	26.5915	−	26.5915i	1.20498	−	1.20498i	0.232343	−	0.972634i	$-0.425361\pi$
$487$	26.5915	−	26.5915i	1.20498	−	1.20498i	0.972634	−	0.232343i	$-0.0746391\pi$
$488$	5.51529	+	1.47782i	0.249665	+	0.0668976i
$489$	−8.10494	+	8.10494i	−0.366518	+	0.366518i
$490$	15.9288	+	26.2115i	0.719588	+	1.18412i
$491$	−14.7584	+	8.52076i	−0.666036	+	0.384536i	−0.794573	−	0.607168i	$-0.792305\pi$
$491$	−14.7584	+	8.52076i	−0.666036	+	0.384536i	0.128537	+	0.991705i	$0.458972\pi$
$492$	−0.00813841	−	0.00813841i	−0.000366908	−	0.000366908i
$493$	11.0261	+	19.0978i	0.496592	+	0.860122i
$494$	−17.8618	−	7.80431i	−0.803641	−	0.351133i
$495$	−12.2474	−	7.07106i	−0.550481	−	0.317820i
$496$	−2.21076	+	8.25065i	−0.0992658	+	0.370465i
$497$	−11.5074	+	11.7689i	−0.516177	+	0.527905i
$498$	−1.44148	−	0.832238i	−0.0645942	−	0.0372935i
$499$	0.171927	+	0.641641i	0.00769651	+	0.0287238i	0.969667	−	0.244429i	$-0.0786004\pi$
$499$	0.171927	+	0.641641i	0.00769651	+	0.0287238i	−0.961971	+	0.273152i	$0.911934\pi$
$500$	28.5027	+	28.5027i	1.27468	+	1.27468i
$501$	−7.13798	−	7.13798i	−0.318901	−	0.318901i
$502$	3.38521	+	12.6338i	0.151089	+	0.563873i
$503$	−28.3846	−	16.3878i	−1.26561	−	0.730698i	−0.291452	−	0.956585i	$-0.594138\pi$
$503$	−28.3846	−	16.3878i	−1.26561	−	0.730698i	−0.974153	+	0.225888i	$0.927472\pi$
$504$	−2.54775	+	0.713432i	−0.113486	+	0.0317788i
$505$	9.43763	−	35.2217i	0.419969	−	1.56735i
$506$	5.54976	+	3.20415i	0.246717	+	0.142442i
$507$	−9.53905	+	8.83213i	−0.423644	+	0.392249i
$508$	0.350830	+	0.607656i	0.0155656	+	0.0269604i
$509$	21.7594	+	21.7594i	0.964469	+	0.964469i	0.999390	−	0.0349214i	$-0.0111181\pi$
$509$	21.7594	+	21.7594i	0.964469	+	0.964469i	−0.0349214	+	0.999390i	$0.511118\pi$
$510$	24.0637	−	13.8932i	1.06556	−	0.615201i
$511$	2.56641	+	9.16496i	0.113532	+	0.405434i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−5.22199	−	1.39923i	−0.230557	−	0.0617775i
$514$	−0.0456880	+	0.0456880i	−0.00201521	+	0.00201521i
$515$	−2.70366	+	10.0902i	−0.119137	+	0.444627i
$516$	2.69459	−	1.55572i	0.118623	−	0.0684869i
$517$	6.20034	+	10.7393i	0.272691	+	0.472314i
$518$	−0.242654	−	0.409594i	−0.0106616	−	0.0179965i
$519$			10.9280i			0.479687i
$520$	15.7001	−	1.76054i	0.688494	−	0.0772048i
$521$	−25.3802	+	14.6533i	−1.11193	+	0.641972i	−0.939328	−	0.343020i	$-0.888550\pi$
$521$	−25.3802	+	14.6533i	−1.11193	+	0.641972i	−0.172600	+	0.984992i	$0.555217\pi$
$522$	0.900038	+	3.35899i	0.0393936	+	0.147019i
$523$			35.2285i			1.54043i	0.637782	+	0.770217i	$0.279852\pi$
$523$			35.2285i			1.54043i	−0.637782	+	0.770217i	$0.720148\pi$
$524$	3.56644	−	6.17726i	0.155801	−	0.269855i
$525$	−19.1482	−	32.3218i	−0.835697	−	1.41064i
$526$	1.03501	+	3.86273i	0.0451288	+	0.168423i
$527$	−14.0194	+	52.3211i	−0.610694	+	2.27914i
$528$	3.11756	+	0.835348i	0.135674	+	0.0363538i
$529$	19.0577			0.828598
$530$	−54.3230			−2.35964
$531$	6.22342	+	1.66756i	0.270073	+	0.0723659i
$532$	−3.85696	−	13.7736i	−0.167220	−	0.597163i
$533$	−0.0151404	−	0.0386373i	−0.000655803	−	0.00167357i
$534$	8.91365	−	15.4389i	0.385731	−	0.668106i
$535$	18.0500	−	4.83648i	0.780370	−	0.209099i
$536$	2.65574	−	4.59988i	0.114710	−	0.198684i
$537$	5.01990	+	8.69473i	0.216625	+	0.375205i
$538$	−3.03824	−	3.03824i	−0.130988	−	0.130988i
$539$	−5.35577	+	21.9488i	−0.230689	+	0.945400i
$540$	4.23240	−	1.13407i	0.182134	−	0.0488026i
$541$	−3.56804	+	0.956053i	−0.153402	+	0.0411039i	−0.334703	−	0.942324i	$-0.608636\pi$
$541$	−3.56804	+	0.956053i	−0.153402	+	0.0411039i	0.181301	+	0.983428i	$0.441969\pi$
$542$		−	7.62377i		−	0.327469i
$543$	−0.243245	−	0.140438i	−0.0104386	−	0.00602676i
$544$	−4.48408	+	4.48408i	−0.192253	+	0.192253i
$545$	82.0335			3.51393
$546$	−9.44752	−	1.32075i	−0.404317	−	0.0565227i
$547$	−21.9784			−0.939729			−0.469864	−	0.882739i	$-0.655697\pi$
$547$	−21.9784			−0.939729			−0.469864	+	0.882739i	$0.655697\pi$
$548$	−0.639858	+	0.639858i	−0.0273334	+	0.0273334i
$549$	4.94487	+	2.85492i	0.211042	+	0.121845i
$550$			45.8289i			1.95415i
$551$	−18.1594	+	4.86579i	−0.773615	+	0.207290i
$552$	−1.91786	+	0.513888i	−0.0816294	+	0.0218725i
$553$	−40.4111	+	0.453919i	−1.71845	+	0.0193026i
$554$	0.904278	+	0.904278i	0.0384191	+	0.0384191i
$555$	0.394222	+	0.682812i	0.0167338	+	0.0289838i
$556$	−10.2718	+	17.7912i	−0.435619	+	0.754515i
$557$	7.93096	−	2.12509i	0.336046	−	0.0900431i	−0.0868504	−	0.996221i	$-0.527680\pi$
$557$	7.93096	−	2.12509i	0.336046	−	0.0900431i	0.422896	+	0.906178i	$0.361014\pi$
$558$	−4.27085	+	7.39733i	−0.180800	+	0.313154i
$559$	11.1486	−	1.25016i	0.471536	−	0.0528760i
$560$	8.28898	+	8.10484i	0.350273	+	0.342492i
$561$	19.7698	+	5.29731i	0.834683	+	0.223653i
$562$	−10.1452			−0.427951
$563$	9.64925			0.406667			0.203334	−	0.979110i	$-0.434822\pi$
$563$	9.64925			0.406667			0.203334	+	0.979110i	$0.434822\pi$
$564$	−3.71124	−	0.994423i	−0.156271	−	0.0418727i
$565$	−8.80438	+	32.8584i	−0.370403	+	1.38236i
$566$	−1.12281	−	4.19037i	−0.0471950	−	0.176134i
$567$	−2.64558	+	0.0297166i	−0.111104	+	0.00124798i
$568$	−3.11062	+	5.38775i	−0.130519	+	0.226065i
$569$		−	24.3106i		−	1.01915i	−0.860425	−	0.509577i	$-0.829802\pi$
$569$		−	24.3106i		−	1.01915i	0.860425	−	0.509577i	$-0.170198\pi$
$570$	6.13101	+	22.8812i	0.256800	+	0.958390i
$571$	−17.5708	+	10.1445i	−0.735315	+	0.424534i	−0.820363	−	0.571843i	$-0.806229\pi$
$571$	−17.5708	+	10.1445i	−0.735315	+	0.424534i	0.0850485	+	0.996377i	$0.472895\pi$
$572$	9.09436	+	7.26040i	0.380254	+	0.303573i
$573$			3.98098i			0.166308i
$574$	0.0149284	−	0.0265408i	0.000623100	−	0.00110779i
$575$	−14.0965	−	24.4158i	−0.587864	−	1.01821i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−8.41915	+	31.4207i	−0.350494	+	1.30806i	0.535568	+	0.844492i	$0.320098\pi$
$577$	−8.41915	+	31.4207i	−0.350494	+	1.30806i	−0.886061	+	0.463568i	$0.846569\pi$
$578$	−16.4147	+	16.4147i	−0.682763	+	0.682763i
$579$	23.6743	+	6.34351i	0.983870	+	0.263627i
$580$	10.7744	−	10.7744i	0.447382	−	0.447382i
$581$	1.09194	−	4.26627i	0.0453011	−	0.176995i
$582$	2.01773	−	1.16494i	0.0836375	−	0.0482882i
$583$	−28.2941	−	28.2941i	−1.17182	−	1.17182i
$584$	1.79864	+	3.11534i	0.0744283	+	0.128914i
$585$	15.6208	+	2.36293i	0.645839	+	0.0976950i
$586$	15.7444	+	9.09005i	0.650396	+	0.375506i
$587$	−9.53490	+	35.5847i	−0.393548	+	1.46874i	0.430692	+	0.902499i	$0.358269\pi$
$587$	−9.53490	+	35.5847i	−0.393548	+	1.46874i	−0.824240	+	0.566241i	$0.808397\pi$
$588$	−3.63529	−	5.98203i	−0.149917	−	0.246695i
$589$	−39.9915	−	23.0891i	−1.64782	−	0.951370i
$590$	−7.30676	−	27.2692i	−0.300814	−	1.12265i
$591$	−2.67201	−	2.67201i	−0.109912	−	0.109912i
$592$	−0.127237	−	0.127237i	−0.00522939	−	0.00522939i
$593$	−8.70551	−	32.4894i	−0.357493	−	1.33418i	−0.877319	−	0.479908i	$-0.840670\pi$
$593$	−8.70551	−	32.4894i	−0.357493	−	1.33418i	0.519826	−	0.854272i	$-0.325997\pi$
$594$	2.79513	+	1.61377i	0.114685	+	0.0662137i
$595$	52.5641	+	51.3964i	2.15492	+	2.10705i
$596$	1.87166	−	6.98514i	0.0766662	−	0.286122i
$597$	3.09532	+	1.78708i	0.126683	+	0.0731405i
$598$	−7.07834	−	1.07073i	−0.289455	−	0.0437853i
$599$	−4.56535	−	7.90742i	−0.186535	−	0.323088i	0.757558	−	0.652768i	$-0.226393\pi$
$599$	−4.56535	−	7.90742i	−0.186535	−	0.323088i	−0.944093	+	0.329680i	$0.893059\pi$
$600$	−10.0405	−	10.0405i	−0.409900	−	0.409900i
$601$	−39.0133	+	22.5243i	−1.59139	+	0.918787i	−0.598316	+	0.801260i	$0.704163\pi$
$601$	−39.0133	+	22.5243i	−1.59139	+	0.918787i	−0.993070	+	0.117527i	$0.962503\pi$
$602$	5.88599	+	5.75523i	0.239895	+	0.234566i
$603$	3.75578	−	3.75578i	0.152947	−	0.152947i
$604$	−3.27255	−	0.876878i	−0.133158	−	0.0356797i
$605$	1.80637	−	1.80637i	0.0734396	−	0.0734396i
$606$	−2.15387	+	8.03835i	−0.0874950	+	0.326536i
$607$	16.8519	−	9.72944i	0.683997	−	0.394906i	−0.117362	−	0.993089i	$-0.537444\pi$
$607$	16.8519	−	9.72944i	0.683997	−	0.394906i	0.801359	+	0.598183i	$0.204111\pi$
$608$	−2.70310	−	4.68191i	−0.109625	−	0.189877i
$609$	−7.91573	+	4.68948i	−0.320762	+	0.190027i
$610$		−	25.0189i		−	1.01298i
$611$	−10.8262	−	8.64300i	−0.437981	−	0.349658i
$612$	−5.49185	+	3.17072i	−0.221995	+	0.128169i
$613$	−3.76048	−	14.0343i	−0.151884	−	0.566840i	−0.999352	−	0.0359930i	$-0.988541\pi$
$613$	−3.76048	−	14.0343i	−0.151884	−	0.566840i	0.847468	−	0.530847i	$-0.178126\pi$
$614$		−	10.9270i		−	0.440976i
$615$	−0.0252155	+	0.0436746i	−0.00101679	+	0.00176113i
$616$	0.0959114	+	8.53872i	0.00386438	+	0.344035i
$617$	4.14330	+	15.4630i	0.166803	+	0.622518i	0.997803	+	0.0662456i	$0.0211021\pi$
$617$	4.14330	+	15.4630i	0.166803	+	0.622518i	−0.831000	+	0.556272i	$0.812231\pi$
$618$	0.617033	−	2.30280i	0.0248207	−	0.0926321i
$619$	41.5376	+	11.1300i	1.66954	+	0.447351i	0.964986	−	0.262301i	$-0.0844812\pi$
$619$	41.5376	+	11.1300i	1.66954	+	0.447351i	0.704552	+	0.709652i	$0.251148\pi$
$620$	37.4272			1.50311
$621$	−1.98551			−0.0796758
$622$	11.1453	+	2.98638i	0.446887	+	0.119743i
$623$	45.6937	+	11.6951i	1.83068	+	0.468555i
$624$	−3.58309	+	0.401793i	−0.143439	+	0.0160846i
$625$	52.8126	−	91.4740i	2.11250	−	3.65896i
$626$	17.5026	−	4.68980i	0.699544	−	0.187442i
$627$	−8.72436	+	15.1110i	−0.348417	+	0.603477i
$628$	0.913980	+	1.58306i	0.0364718	+	0.0631710i
$629$	−0.806864	−	0.806864i	−0.0321718	−	0.0321718i
$630$	5.90885	+	9.97402i	0.235414	+	0.397374i
$631$	−4.52314	+	1.21197i	−0.180063	+	0.0482478i	−0.347724	−	0.937597i	$-0.613045\pi$
$631$	−4.52314	+	1.21197i	−0.180063	+	0.0482478i	0.167661	+	0.985845i	$0.446379\pi$
$632$	−14.7544	+	3.95344i	−0.586900	+	0.157259i
$633$			15.4382i			0.613613i
$634$	−21.4891	−	12.4067i	−0.853440	−	0.492734i
$635$	2.17398	−	2.17398i	0.0862717	−	0.0862717i
$636$	12.3977			0.491599
$637$	−3.37523	−	25.0122i	−0.133732	−	0.991018i
$638$	11.2237			0.444350
$639$	−4.39908	+	4.39908i	−0.174025	+	0.174025i
$640$	3.79467	+	2.19085i	0.149998	+	0.0866011i
$641$			7.18039i			0.283608i	0.989895	+	0.141804i	$0.0452903\pi$
$641$			7.18039i			0.283608i	−0.989895	+	0.141804i	$0.954710\pi$
$642$	−4.11940	+	1.10379i	−0.162580	+	0.0435631i
$643$	29.2307	−	7.83235i	1.15275	−	0.308878i	0.368682	−	0.929556i	$-0.379809\pi$
$643$	29.2307	−	7.83235i	1.15275	−	0.308878i	0.784066	+	0.620678i	$0.213142\pi$
$644$	−2.67752	−	4.51959i	−0.105509	−	0.178097i
$645$	−9.64030	−	9.64030i	−0.379586	−	0.379586i
$646$	−17.1416	−	29.6901i	−0.674427	−	1.16814i
$647$	9.25822	−	16.0357i	0.363978	−	0.630428i	−0.624634	−	0.780918i	$-0.714752\pi$
$647$	9.25822	−	16.0357i	0.363978	−	0.630428i	0.988612	+	0.150490i	$0.0480850\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	10.3974	−	18.0089i	0.408135	−	0.706910i
$650$	−18.6789	−	47.6674i	−0.732647	−	1.86967i
$651$	−21.8935	−	5.60356i	−0.858074	−	0.219621i
$652$	−11.0716	−	2.96661i	−0.433595	−	0.116182i
$653$	−9.36427			−0.366452			−0.183226	−	0.983071i	$-0.558654\pi$
$653$	−9.36427			−0.366452			−0.183226	+	0.983071i	$0.558654\pi$
$654$	−18.7218			−0.732081
$655$	−30.1893	−	8.08919i	−1.17959	−	0.316071i
$656$	0.00297886	−	0.0111173i	0.000116305	−	0.000434057i
$657$	0.931045	+	3.47471i	0.0363235	+	0.135561i
$658$	−0.114176	−	10.1647i	−0.00445104	−	0.396263i
$659$	16.2208	−	28.0953i	0.631874	−	1.09444i	−0.355294	−	0.934754i	$-0.615619\pi$
$659$	16.2208	−	28.0953i	0.631874	−	1.09444i	0.987168	−	0.159683i	$-0.0510473\pi$
$660$		−	14.1421i		−	0.550481i
$661$	1.08268	+	4.04063i	0.0421115	+	0.157162i	0.983780	−	0.179380i	$-0.0574092\pi$
$661$	1.08268	+	4.04063i	0.0421115	+	0.157162i	−0.941668	+	0.336542i	$0.890742\pi$
$662$	11.1669	−	6.44721i	0.434014	−	0.250578i
$663$	−22.7220	+	2.54795i	−0.882449	+	0.0989542i
$664$		−	1.66448i		−	0.0645942i
$665$	−53.9216	+	31.9445i	−2.09099	+	1.23875i
$666$	−0.0899699	−	0.155832i	−0.00348626	−	0.00603838i
$667$	−5.97953	+	3.45229i	−0.231528	+	0.133673i
$668$	2.61268	−	9.75066i	0.101088	−	0.377264i
$669$	15.7970	−	15.7970i	0.610745	−	0.610745i
$670$	−22.4803	−	6.02359i	−0.868491	−	0.232711i
$671$	13.0311	−	13.0311i	0.503059	−	0.503059i
$672$	−1.89172	−	1.84970i	−0.0729748	−	0.0713536i
$673$	24.5261	−	14.1601i	0.945412	−	0.545834i	0.0537590	−	0.998554i	$-0.482880\pi$
$673$	24.5261	−	14.1601i	0.945412	−	0.545834i	0.891653	+	0.452720i	$0.149546\pi$
$674$	−7.27887	−	7.27887i	−0.280372	−	0.280372i
$675$	−7.09968	−	12.2970i	−0.273267	−	0.473312i
$676$	−12.4184	−	3.84499i	−0.477630	−	0.147884i
$677$	23.0893	+	13.3306i	0.887395	+	0.512337i	0.873089	−	0.487560i	$-0.162113\pi$
$677$	23.0893	+	13.3306i	0.887395	+	0.512337i	0.0143051	+	0.999898i	$0.495446\pi$
$678$	2.00935	−	7.49899i	0.0771686	−	0.287997i
$679$	4.40747	+	4.30956i	0.169143	+	0.165386i
$680$	24.0637	+	13.8932i	0.922801	+	0.532779i
$681$	5.98281	+	22.3281i	0.229262	+	0.855616i
$682$	19.4940	+	19.4940i	0.746463	+	0.746463i
$683$	19.4046	+	19.4046i	0.742496	+	0.742496i	0.973058	−	0.230562i	$-0.0740565\pi$
$683$	19.4046	+	19.4046i	0.742496	+	0.742496i	−0.230562	+	0.973058i	$0.574056\pi$
$684$	−1.39923	−	5.22199i	−0.0535008	−	0.199668i
$685$	3.43378	+	1.98250i	0.131198	+	0.0757473i
$686$	12.6472	−	13.5296i	0.482871	−	0.516561i
$687$	3.69250	−	13.7806i	0.140877	−	0.525762i
$688$	2.69459	+	1.55572i	0.102730	+	0.0593114i
$689$	40.9612	+	17.8971i	1.56050	+	0.681824i
$690$	4.34996	+	7.53436i	0.165600	+	0.286828i
$691$	12.9729	+	12.9729i	0.493511	+	0.493511i	0.909410	−	0.415900i	$-0.136533\pi$
$691$	12.9729	+	12.9729i	0.493511	+	0.493511i	−0.415900	+	0.909410i	$0.636533\pi$
$692$	−9.46394	+	5.46401i	−0.359765	+	0.207710i
$693$	−2.11734	+	8.27259i	−0.0804311	+	0.314250i
$694$	−19.2493	+	19.2493i	−0.730694	+	0.730694i
$695$	86.9484	+	23.2978i	3.29814	+	0.883734i
$696$	−2.45895	+	2.45895i	−0.0932062	+	0.0932062i
$697$	0.0188903	−	0.0704996i	0.000715522	−	0.00267036i
$698$	18.3684	−	10.6050i	0.695252	−	0.401404i
$699$	1.01943	+	1.76570i	0.0385584	+	0.0667851i
$700$	18.4174	−	32.7438i	0.696112	−	1.23760i
$701$		−	41.7640i		−	1.57740i	−0.614775	−	0.788702i	$-0.710753\pi$
$701$		−	41.7640i		−	1.57740i	0.614775	−	0.788702i	$-0.289247\pi$
$702$	−3.56499	−	0.539271i	−0.134552	−	0.0203535i
$703$	0.842462	−	0.486396i	0.0317740	−	0.0183448i
$704$	0.835348	+	3.11756i	0.0314833	+	0.117497i
$705$			16.8352i			0.634050i
$706$	−1.78504	+	3.09178i	−0.0671808	+	0.116361i
$707$	−22.0163	+	0.247299i	−0.828009	+	0.00930064i
$708$	1.66756	+	6.22342i	0.0626707	+	0.233890i
$709$	2.22709	−	8.31161i	0.0836401	−	0.312149i	−0.911413	−	0.411493i	$-0.865008\pi$
$709$	2.22709	−	8.31161i	0.0836401	−	0.312149i	0.995053	+	0.0993436i	$0.0316743\pi$
$710$	26.3308	+	7.05531i	0.988176	+	0.264781i
$711$	−15.2749			−0.572854
$712$	17.8273			0.668106
$713$	−16.3818	−	4.38948i	−0.613502	−	0.164387i
$714$	−11.9963	−	11.7298i	−0.448949	−	0.438975i
$715$	20.4153	−	46.7248i	0.763490	−	1.74741i
$716$	−5.01990	+	8.69473i	−0.187603	+	0.324937i
$717$	−9.92859	+	2.66036i	−0.370790	+	0.0993529i
$718$	9.08745	−	15.7399i	0.339141	−	0.587409i
$719$	−8.55226	−	14.8130i	−0.318946	−	0.552430i	0.661323	−	0.750101i	$-0.269995\pi$
$719$	−8.55226	−	14.8130i	−0.318946	−	0.552430i	−0.980268	+	0.197672i	$0.936662\pi$
$720$	3.09834	+	3.09834i	0.115468	+	0.115468i
$721$	6.30716	−	0.0708453i	0.234891	−	0.00263842i
$722$	9.87857	−	2.64696i	0.367642	−	0.0985095i
$723$	−10.6061	+	2.84189i	−0.394444	+	0.105691i
$724$		−	0.280875i		−	0.0104386i
$725$	−42.7626	−	24.6890i	−1.58816	−	0.916926i
$726$	−0.412253	+	0.412253i	−0.0153002	+	0.0153002i
$727$	−45.6775			−1.69409			−0.847043	−	0.531525i	$-0.821619\pi$
$727$	−45.6775			−1.69409			−0.847043	+	0.531525i	$0.821619\pi$
$728$	−3.57996	−	8.84217i	−0.132682	−	0.327712i
$729$	−1.00000			−0.0370370
$730$	11.1456	−	11.1456i	0.412517	−	0.412517i
$731$	17.0876	+	9.86553i	0.632008	+	0.364890i
$732$			5.70985i			0.211042i
$733$	33.2325	−	8.90463i	1.22747	−	0.328900i	0.413877	−	0.910333i	$-0.364174\pi$
$733$	33.2325	−	8.90463i	1.22747	−	0.328900i	0.813594	+	0.581433i	$0.197508\pi$
$734$	−0.342684	+	0.0918218i	−0.0126487	+	0.00338920i
$735$	−21.1957	+	22.1700i	−0.781815	+	0.817754i
$736$	−1.40397	−	1.40397i	−0.0517510	−	0.0517510i
$737$	−8.57149	−	14.8463i	−0.315735	−	0.546869i
$738$	0.00575472	−	0.00996747i	0.000211834	−	0.000366908i
$739$	−2.12943	+	0.570579i	−0.0783323	+	0.0209891i	−0.297772	−	0.954637i	$-0.596244\pi$
$739$	−2.12943	+	0.570579i	−0.0783323	+	0.0209891i	0.219440	+	0.975626i	$0.429577\pi$
$740$	−0.394222	+	0.682812i	−0.0144919	+	0.0251007i
$741$	2.91541	−	19.2731i	0.107100	−	0.708015i
$742$	8.84489	+	31.5861i	0.324706	+	1.15956i
$743$	−22.1382	−	5.93191i	−0.812172	−	0.217621i	−0.171251	−	0.985227i	$-0.554781\pi$
$743$	−22.1382	−	5.93191i	−0.812172	−	0.217621i	−0.640921	+	0.767607i	$0.721447\pi$
$744$	−8.54170			−0.313154
$745$	−31.6865			−1.16090
$746$	20.4784	+	5.48717i	0.749767	+	0.200899i
$747$	0.430798	−	1.60776i	0.0157621	−	0.0588249i
$748$	5.29731	+	19.7698i	0.193689	+	0.722857i
$749$	−5.75109	−	9.70771i	−0.210140	−	0.354712i
$750$	−20.1545	+	34.9086i	−0.735937	+	1.27468i
$751$			37.7097i			1.37605i	0.725689	+	0.688023i	$0.241521\pi$
$751$			37.7097i			1.37605i	−0.725689	+	0.688023i	$0.758479\pi$
$752$	−0.994423	−	3.71124i	−0.0362629	−	0.135335i
$753$	−11.3271	+	6.53973i	−0.412784	+	0.238321i
$754$	−11.6739	+	4.57454i	−0.425140	+	0.166595i
$755$			14.8452i			0.540273i
$756$	−1.34853	−	2.27629i	−0.0490455	−	0.0827877i
$757$	−14.6011	−	25.2898i	−0.530685	−	0.919173i	−0.999359	−	0.0358019i	$-0.988601\pi$
$757$	−14.6011	−	25.2898i	−0.530685	−	0.919173i	0.468674	−	0.883371i	$-0.344732\pi$
$758$	−9.29131	+	5.36434i	−0.337476	+	0.194842i
$759$	−1.65859	+	6.18995i	−0.0602031	+	0.224681i
$760$	−16.7502	+	16.7502i	−0.607595	+	0.607595i
$761$	−29.1354	−	7.80681i	−1.05616	−	0.282997i	−0.311364	−	0.950291i	$-0.600786\pi$
$761$	−29.1354	−	7.80681i	−1.05616	−	0.282997i	−0.744794	+	0.667294i	$0.767452\pi$
$762$	−0.496149	+	0.496149i	−0.0179736	+	0.0179736i
$763$	−13.3567	−	47.6984i	−0.483546	−	1.72680i
$764$	−3.44763	+	1.99049i	−0.124731	+	0.0720133i
$765$	19.6479	+	19.6479i	0.710372	+	0.710372i
$766$	7.33644	+	12.7071i	0.265076	+	0.459126i
$767$	−3.47450	+	22.9691i	−0.125457	+	0.829366i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	5.78494	−	21.5897i	0.208610	−	0.778544i	−0.779709	−	0.626143i	$-0.784633\pi$
$769$	5.78494	−	21.5897i	0.208610	−	0.778544i	0.988319	−	0.152401i	$-0.0487006\pi$
$770$	36.0305	−	10.0894i	1.29845	−	0.363598i
$771$	−0.0559561	−	0.0323063i	−0.00201521	−	0.00116348i
$772$	6.34351	+	23.6743i	0.228308	+	0.852056i
$773$	−0.327420	−	0.327420i	−0.0117765	−	0.0117765i	0.701194	−	0.712971i	$-0.252651\pi$
$773$	−0.327420	−	0.327420i	−0.0117765	−	0.0117765i	−0.712971	+	0.701194i	$0.752651\pi$
$774$	2.20012	+	2.20012i	0.0790818	+	0.0790818i
$775$	−31.3913	−	117.154i	−1.12761	−	4.20830i
$776$	2.01773	+	1.16494i	0.0724322	+	0.0418188i
$777$	0.332834	−	0.340396i	0.0119404	−	0.0122116i
$778$	2.06397	−	7.70285i	0.0739970	−	0.276161i
$779$	0.0538862	+	0.0311112i	0.00193067	+	0.00111467i
$780$	5.76403	+	14.7094i	0.206385	+	0.526683i
$781$	10.0396	+	17.3891i	0.359246	+	0.622232i
$782$	−8.90319	−	8.90319i	−0.318377	−	0.318377i
$783$	−3.01158	+	1.73874i	−0.107625	+	0.0621375i
$784$	3.36295	−	6.13927i	0.120105	−	0.219260i
$785$	5.66363	−	5.66363i	0.202144	−	0.202144i
$786$	6.88984	+	1.84613i	0.245752	+	0.0658491i
$787$	−15.4333	+	15.4333i	−0.550139	+	0.550139i	−0.926481	−	0.376342i	$-0.877182\pi$
$787$	−15.4333	+	15.4333i	−0.550139	+	0.550139i	0.376342	+	0.926481i	$0.377182\pi$
$788$	0.978025	−	3.65004i	0.0348407	−	0.130027i
$789$	−3.46323	+	1.99949i	−0.123294	+	0.0711839i
$790$	33.4651	+	57.9633i	1.19064	+	2.06224i
$791$	20.5391	−	0.230706i	0.730285	−	0.00820295i
$792$			3.22754i			0.114685i
$793$	−8.24264	+	18.8650i	−0.292705	+	0.669917i
$794$	−18.6261	+	10.7538i	−0.661015	+	0.381637i
$795$	−14.0598	−	52.4719i	−0.498650	−	1.86099i
$796$			3.57417i			0.126683i
$797$	8.23632	−	14.2657i	0.291745	−	0.505318i	−0.682477	−	0.730907i	$-0.739097\pi$
$797$	8.23632	−	14.2657i	0.291745	−	0.505318i	0.974223	+	0.225589i	$0.0724307\pi$
$798$	12.3061	−	7.29042i	0.435630	−	0.258078i
$799$	−6.30608	−	23.5346i	−0.223093	−	0.832595i
$800$	3.67507	−	13.7155i	0.129933	−	0.484917i
$801$	17.2198	+	4.61404i	0.608433	+	0.163029i
$802$	−21.7748			−0.768896
$803$	11.6104			0.409721
$804$	5.13050	+	1.37471i	0.180939	+	0.0484824i
$805$	−16.0922	+	16.4579i	−0.567177	+	0.580063i
$806$	−28.2213	−	12.3307i	−0.994054	−	0.434329i
$807$	2.14836	−	3.72107i	0.0756259	−	0.130988i
$808$	−8.03835	+	2.15387i	−0.282788	+	0.0757729i
$809$	−8.54142	+	14.7942i	−0.300300	+	0.520135i	−0.976204	−	0.216855i	$-0.930420\pi$
$809$	−8.54142	+	14.7942i	−0.300300	+	0.520135i	0.675904	+	0.736990i	$0.263754\pi$
$810$	2.19085	+	3.79467i	0.0769788	+	0.133331i
$811$	−18.8226	−	18.8226i	−0.660952	−	0.660952i	0.294653	−	0.955604i	$-0.404796\pi$
$811$	−18.8226	−	18.8226i	−0.660952	−	0.660952i	−0.955604	+	0.294653i	$0.904796\pi$
$812$	−8.01907	−	4.51049i	−0.281414	−	0.158287i
$813$	7.36399	−	1.97318i	0.258267	−	0.0692023i
$814$	−0.560973	+	0.150312i	−0.0196621	+	0.00526844i
$815$			50.2236i			1.75926i
$816$	−5.49185	−	3.17072i	−0.192253	−	0.110998i
$817$	−11.8943	+	11.8943i	−0.416130	+	0.416130i
$818$	32.3297			1.13038
$819$	−1.16945	−	9.46744i	−0.0408641	−	0.330819i
$820$	−0.0504310			−0.00176113
$821$	−2.70052	+	2.70052i	−0.0942489	+	0.0942489i	−0.752659	−	0.658410i	$-0.771229\pi$
$821$	−2.70052	+	2.70052i	−0.0942489	+	0.0942489i	0.658410	+	0.752659i	$0.271229\pi$
$822$	−0.783663	−	0.452448i	−0.0273334	−	0.0157809i
$823$			18.2336i			0.635582i	0.948161	+	0.317791i	$0.102941\pi$
$823$			18.2336i			0.635582i	−0.948161	+	0.317791i	$0.897059\pi$
$824$	2.30280	−	0.617033i	0.0802217	−	0.0214954i
$825$	−44.2674	+	11.8614i	−1.54119	+	0.412961i
$826$	−14.6660	+	8.68850i	−0.510295	+	0.302312i
$827$	0.844609	+	0.844609i	0.0293699	+	0.0293699i	0.721639	−	0.692269i	$-0.243389\pi$
$827$	0.844609	+	0.844609i	0.0293699	+	0.0293699i	−0.692269	+	0.721639i	$0.743389\pi$
$828$	−0.992755	−	1.71950i	−0.0345006	−	0.0597569i
$829$	11.0192	−	19.0858i	0.382713	−	0.662878i	−0.608736	−	0.793373i	$-0.708323\pi$
$829$	11.0192	−	19.0858i	0.382713	−	0.662878i	0.991449	+	0.130495i	$0.0416565\pi$
$830$	−7.04473	+	1.88763i	−0.244526	+	0.0655206i
$831$	−0.639421	+	1.10751i	−0.0221813	+	0.0384191i
$832$	−2.13951	−	2.90215i	−0.0741742	−	0.100614i
$833$	21.3260	−	38.9318i	0.738900	−	1.34891i
$834$	−19.8435	−	5.31705i	−0.687124	−	0.184114i
$835$	−44.2317			−1.53070
$836$	−17.4487			−0.603477
$837$	−8.25065	−	2.21076i	−0.285184	−	0.0764149i
$838$	1.33703	−	4.98987i	0.0461870	−	0.172372i
$839$	12.2092	+	45.5653i	0.421508	+	1.57309i	0.771433	+	0.636311i	$0.219540\pi$
$839$	12.2092	+	45.5653i	0.421508	+	1.57309i	−0.349925	+	0.936778i	$0.613793\pi$
$840$	−5.68332	+	10.1042i	−0.196093	+	0.348629i
$841$	8.45357	−	14.6420i	0.291502	−	0.504897i
$842$			14.4470i			0.497877i
$843$	−2.62578	−	9.79955i	−0.0904367	−	0.337514i
$844$	−13.3699	+	7.71910i	−0.460210	+	0.265702i
$845$	−2.19027	+	56.9201i	−0.0753476	+	1.95811i
$846$		−	3.84215i		−	0.132096i
$847$	−1.34443	−	0.756203i	−0.0461952	−	0.0259834i
$848$	6.19883	+	10.7367i	0.212869	+	0.368700i
$849$	3.75698	−	2.16909i	0.128939	−	0.0744431i
$850$	23.3052	−	86.9763i	0.799363	−	2.98326i
$851$	0.252630	−	0.252630i	0.00866003	−	0.00866003i
$852$	−6.00925	−	1.61017i	−0.205873	−	0.0551636i
$853$	17.7773	−	17.7773i	0.608682	−	0.608682i	−0.333919	−	0.942602i	$-0.608371\pi$
$853$	17.7773	−	17.7773i	0.608682	−	0.608682i	0.942602	+	0.333919i	$0.108371\pi$
$854$	−14.5472	+	4.07359i	−0.497796	+	0.139395i
$855$	−20.5148	+	11.8442i	−0.701590	+	0.405063i
$856$	−3.01561	−	3.01561i	−0.103071	−	0.103071i
$857$	−6.86537	−	11.8912i	−0.234517	−	0.406195i	0.724616	−	0.689153i	$-0.242017\pi$
$857$	−6.86537	−	11.8912i	−0.234517	−	0.406195i	−0.959132	+	0.282959i	$0.908684\pi$
$858$	−4.65922	+	10.6636i	−0.159063	+	0.364050i
$859$	27.2083	+	15.7087i	0.928334	+	0.535974i	0.886284	−	0.463141i	$-0.153278\pi$
$859$	27.2083	+	15.7087i	0.928334	+	0.535974i	0.0420501	+	0.999116i	$0.486611\pi$
$860$	3.52860	−	13.1689i	0.120324	−	0.449056i
$861$	0.0295002	+	0.00755047i	0.00100536	+	0.000257319i
$862$	3.73450	+	2.15611i	0.127198	+	0.0734375i
$863$	−14.9670	−	55.8578i	−0.509484	−	1.90142i	−0.425513	−	0.904952i	$-0.639906\pi$
$863$	−14.9670	−	55.8578i	−0.509484	−	1.90142i	−0.0839709	−	0.996468i	$-0.526760\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	33.8587	+	33.8587i	1.15123	+	1.15123i
$866$	9.87526	+	36.8550i	0.335575	+	1.25238i
$867$	−20.1039	−	11.6070i	−0.682763	−	0.394194i
$868$	−6.09392	−	21.7621i	−0.206841	−	0.738654i
$869$	−12.7599	+	47.6205i	−0.432849	+	1.61541i
$870$	13.1959	+	7.61865i	0.447382	+	0.258296i
$871$	14.9664	+	11.9483i	0.507116	+	0.404852i
$872$	−9.36090	−	16.2136i	−0.317000	−	0.549060i
$873$	1.64747	+	1.64747i	0.0557584	+	0.0557584i
$874$	9.29598	−	5.36704i	0.314441	−	0.181543i
$875$	−103.317	−	26.4436i	−3.49275	−	0.893957i
$876$	−2.54366	+	2.54366i	−0.0859424	+	0.0859424i
$877$	34.9338	+	9.36047i	1.17963	+	0.316081i	0.794779	−	0.606899i	$-0.207587\pi$
$877$	34.9338	+	9.36047i	1.17963	+	0.316081i	0.384850	+	0.922979i	$0.374253\pi$
$878$	−13.9741	+	13.9741i	−0.471602	+	0.471602i
$879$	−4.70535	+	17.5606i	−0.158708	+	0.592305i
$880$	12.2474	−	7.07106i	0.412861	−	0.238365i
$881$	8.96533	+	15.5284i	0.302050	+	0.523165i	0.976600	−	0.215063i	$-0.0689958\pi$
$881$	8.96533	+	15.5284i	0.302050	+	0.523165i	−0.674550	+	0.738229i	$0.735663\pi$
$882$	4.83732	−	5.05968i	0.162881	−	0.170368i
$883$		−	15.9776i		−	0.537689i	−0.963184	−	0.268844i	$-0.913358\pi$
$883$		−	15.9776i		−	0.537689i	0.963184	−	0.268844i	$-0.0866417\pi$
$884$	−13.5676	−	18.4039i	−0.456327	−	0.618989i
$885$	24.4489	−	14.1156i	0.821840	−	0.474490i
$886$	−7.10003	−	26.4977i	−0.238530	−	0.890207i
$887$			30.5008i			1.02412i	0.858951	+	0.512058i	$0.171117\pi$
$887$			30.5008i			1.02412i	−0.858951	+	0.512058i	$0.828883\pi$
$888$	0.0899699	−	0.155832i	0.00301919	−	0.00522939i
$889$	−1.61803	−	0.910093i	−0.0542670	−	0.0305235i
$890$	−20.2174	−	75.4523i	−0.677689	−	2.52917i
$891$	−0.835348	+	3.11756i	−0.0279852	+	0.104442i
$892$	21.5790	+	5.78209i	0.722520	+	0.193599i
$893$	20.7715			0.695091
$894$	7.23154			0.241859
$895$	42.4925	+	11.3858i	1.42037	+	0.380587i
$896$	0.656024	−	2.56313i	0.0219162	−	0.0856281i
$897$	−0.797765	−	7.11427i	−0.0266366	−	0.237539i
$898$	10.9810	−	19.0197i	0.366441	−	0.634694i
$899$	−28.6915	+	7.68785i	−0.956914	+	0.256404i
$900$	7.09968	−	12.2970i	0.236656	−	0.409900i
$901$	39.3096	+	68.0862i	1.30959	+	2.26828i
$902$	−0.0262670	−	0.0262670i	−0.000874596	−	0.000874596i
$903$	−4.03572	+	7.17500i	−0.134300	+	0.238769i
$904$	7.49899	−	2.00935i	0.249413	−	0.0668300i
$905$	−1.18878	+	0.318532i	−0.0395163	+	0.0105884i
$906$		−	3.38800i		−	0.112559i
$907$	6.96043	+	4.01860i	0.231117	+	0.133436i	0.611087	−	0.791563i	$-0.290732\pi$
$907$	6.96043	+	4.01860i	0.231117	+	0.133436i	−0.379970	+	0.924999i	$0.624066\pi$
$908$	−16.3453	+	16.3453i	−0.542439	+	0.542439i
$909$	−8.32192			−0.276021
$910$	−33.3637	+	25.1795i	−1.10600	+	0.834691i
$911$	−35.0854			−1.16243			−0.581216	−	0.813750i	$-0.697423\pi$
$911$	−35.0854			−1.16243			−0.581216	+	0.813750i	$0.697423\pi$
$912$	3.82276	−	3.82276i	0.126584	−	0.126584i
$913$	−4.65242	−	2.68608i	−0.153973	−	0.0888962i
$914$		−	8.88992i		−	0.294052i
$915$	24.1664	−	6.47536i	0.798916	−	0.214069i
$916$	13.7806	−	3.69250i	0.455323	−	0.122003i
$917$	0.211965	+	18.8706i	0.00699971	+	0.623164i
$918$	−4.48408	−	4.48408i	−0.147997	−	0.147997i
$919$	−1.66409	−	2.88228i	−0.0548932	−	0.0950777i	0.837273	−	0.546785i	$-0.184148\pi$
$919$	−1.66409	−	2.88228i	−0.0548932	−	0.0950777i	−0.892166	+	0.451707i	$0.850815\pi$
$920$	−4.34996	+	7.53436i	−0.143414	+	0.248400i
$921$	10.5546	−	2.82810i	0.347787	−	0.0931892i
$922$	6.64407	−	11.5079i	0.218811	−	0.378992i
$923$	−17.5298	−	13.9948i	−0.577001	−	0.460644i
$924$	−8.22294	+	2.30263i	−0.270515	+	0.0757508i
$925$	2.46797	+	0.661290i	0.0811463	+	0.0217431i
$926$	−23.8995			−0.785385
$927$	2.38403			0.0783019
$928$	−3.35899	−	0.900038i	−0.110264	−	0.0295452i
$929$	7.21753	−	26.9362i	0.236799	−	0.883747i	−0.740530	−	0.672023i	$-0.765426\pi$
$929$	7.21753	−	26.9362i	0.236799	−	0.883747i	0.977329	−	0.211724i	$-0.0679078\pi$
$930$	9.68688	+	36.1519i	0.317645	+	1.18547i
$931$	27.3537	+	26.1515i	0.896480	+	0.857082i
$932$	−1.01943	+	1.76570i	−0.0333925	+	0.0578376i
$933$			11.5385i			0.377753i
$934$	−2.96197	−	11.0542i	−0.0969188	−	0.361706i
$935$	77.6665	−	44.8407i	2.53996	−	1.46645i
$936$	−1.31548	−	3.35701i	−0.0429977	−	0.109727i
$937$		−	18.5913i		−	0.607351i	−0.952776	−	0.303676i	$-0.901786\pi$
$937$		−	18.5913i		−	0.607351i	0.952776	−	0.303676i	$-0.0982139\pi$
$938$	0.157839	+	14.0520i	0.00515363	+	0.458813i
$939$	9.06000	+	15.6924i	0.295662	+	0.512101i
$940$	−14.5797	+	8.41760i	−0.475538	+	0.274552i
$941$	−7.25100	+	27.0611i	−0.236376	+	0.882167i	0.741148	+	0.671342i	$0.234282\pi$
$941$	−7.25100	+	27.0611i	−0.236376	+	0.882167i	−0.977524	+	0.210825i	$0.932385\pi$
$942$	−1.29256	+	1.29256i	−0.0421140	+	0.0421140i
$943$	0.0220735	+	0.00591457i	0.000718811	+	0.000192605i
$944$	−4.55586	+	4.55586i	−0.148280	+	0.148280i
$945$	−8.10484	+	8.28898i	−0.263650	+	0.269641i
$946$	8.69689	−	5.02115i	0.282760	−	0.163252i
$947$	21.4302	+	21.4302i	0.696386	+	0.696386i	0.963629	−	0.267243i	$-0.0861126\pi$
$947$	21.4302	+	21.4302i	0.696386	+	0.696386i	−0.267243	+	0.963629i	$0.586113\pi$
$948$	−7.63746	−	13.2285i	−0.248053	−	0.429641i
$949$	−12.0761	+	4.73214i	−0.392007	+	0.153612i
$950$	66.4801	+	38.3823i	2.15690	+	1.24529i
$951$	6.42219	−	23.9680i	0.208254	−	0.777214i
$952$	4.16014	−	16.2540i	0.134831	−	0.526794i
$953$	−23.0230	−	13.2923i	−0.745789	−	0.430581i	0.0783816	−	0.996923i	$-0.475025\pi$
$953$	−23.0230	−	13.2923i	−0.745789	−	0.430581i	−0.824170	+	0.566342i	$0.808358\pi$
$954$	3.20875	+	11.9752i	0.103887	+	0.387712i
$955$	12.3344	+	12.3344i	0.399132	+	0.399132i
$956$	−7.26823	−	7.26823i	−0.235071	−	0.235071i
$957$	2.90490	+	10.8412i	0.0939022	+	0.350448i
$958$	28.6291	+	16.5290i	0.924964	+	0.534028i
$959$	0.593633	−	2.31937i	0.0191694	−	0.0748963i
$960$	−1.13407	+	4.23240i	−0.0366019	+	0.136600i
$961$	−36.3390	−	20.9803i	−1.17223	−	0.676785i
$962$	0.522213	−	0.384983i	0.0168368	−	0.0124123i
$963$	−2.13236	−	3.69335i	−0.0687143	−	0.119017i
$964$	−7.76419	−	7.76419i	−0.250068	−	0.250068i
$965$	93.0052	−	53.6966i	2.99394	−	1.72855i
$966$	3.67260	−	3.75604i	0.118164	−	0.120849i
$967$	24.4165	−	24.4165i	0.785182	−	0.785182i	−0.195518	−	0.980700i	$-0.562639\pi$
$967$	24.4165	−	24.4165i	0.785182	−	0.785182i	0.980700	+	0.195518i	$0.0626387\pi$
$968$	−0.563149	−	0.150895i	−0.0181003	−	0.00484996i
$969$	24.2419	−	24.2419i	0.778761	−	0.778761i
$970$	2.64224	−	9.86096i	0.0848371	−	0.316616i
$971$	24.4163	−	14.0967i	0.783555	−	0.452386i	−0.0541334	−	0.998534i	$-0.517240\pi$
$971$	24.4163	−	14.0967i	0.783555	−	0.452386i	0.837689	+	0.546148i	$0.183906\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−0.610483	−	54.3496i	−0.0195712	−	1.74237i
$974$			37.6061i			1.20498i
$975$	41.2087	−	30.3797i	1.31974	−	0.972928i
$976$	−4.94487	+	2.85492i	−0.158281	+	0.0913839i
$977$	−4.07217	−	15.1975i	−0.130280	−	0.486213i	0.869692	−	0.493594i	$-0.164317\pi$
$977$	−4.07217	−	15.1975i	−0.130280	−	0.486213i	−0.999973	+	0.00738133i	$0.997650\pi$
$978$		−	11.4621i		−	0.366518i
$979$	28.7691	−	49.8296i	0.919465	−	1.59256i
$980$	−29.7977	−	7.27100i	−0.951852	−	0.232264i
$981$	−4.84556	−	18.0839i	−0.154707	−	0.577374i
$982$	4.41067	−	16.4608i	0.140750	−	0.525286i
$983$	46.2105	+	12.3821i	1.47388	+	0.394926i	0.904261	−	0.426979i	$-0.140422\pi$
$983$	46.2105	+	12.3821i	1.47388	+	0.394926i	0.569624	+	0.821906i	$0.307089\pi$
$984$	0.0115094			0.000366908
$985$	−16.5576			−0.527569
$986$	−21.3008	−	5.70754i	−0.678357	−	0.181765i
$987$	9.78884	−	2.74111i	0.311582	−	0.0872506i
$988$	18.1487	−	7.11173i	0.577387	−	0.226254i
$989$	−3.08890	+	5.35014i	−0.0982214	+	0.170125i
$990$	13.6602	−	3.66025i	0.434151	−	0.116330i
$991$	4.43151	−	7.67560i	0.140771	−	0.243823i	−0.787016	−	0.616933i	$-0.788375\pi$
$991$	4.43151	−	7.67560i	0.140771	−	0.243823i	0.927787	+	0.373109i	$0.121708\pi$
$992$	−4.27085	−	7.39733i	−0.135600	−	0.234866i
$993$	9.11773	+	9.11773i	0.289343	+	0.289343i
$994$	−0.184874	−	16.4588i	−0.00586385	−	0.522041i
$995$	15.1273	−	4.05335i	0.479568	−	0.128500i
$996$	1.60776	−	0.430798i	0.0509438	−	0.0136504i
$997$			20.9767i			0.664338i	0.943220	+	0.332169i	$0.107780\pi$
$997$			20.9767i			0.664338i	−0.943220	+	0.332169i	$0.892220\pi$
$998$	−0.575279	−	0.332138i	−0.0182101	−	0.0105136i
$999$	0.127237	−	0.127237i	0.00402559	−	0.00402559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.145.1	yes	40
7.3	odd	6		546.2.by.b.535.1	yes	40
13.7	odd	12		546.2.by.b.397.1	✓	40
91.59	even	12	inner	546.2.cg.b.241.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.1	✓	40	13.7	odd	12
546.2.by.b.535.1	yes	40	7.3	odd	6
546.2.cg.b.145.1	yes	40	1.1	even	1	trivial
546.2.cg.b.241.1	yes	40	91.59	even	12	inner

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.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-4.23240 + 1.13407i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.34853 + 2.27629i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-4.23240 + 1.13407i) q^{5} +(0.965926 - 0.258819i) q^{6} +(1.34853 + 2.27629i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.19085 - 3.79467i) q^{10} +(3.11756 - 0.835348i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.90215 + 2.13951i) q^{13} +(-2.56313 - 0.656024i) q^{14} +(4.23240 + 1.13407i) q^{15} -1.00000 q^{16} -6.34145 q^{17} +(-0.965926 - 0.258819i) q^{18} +(1.39923 - 5.22199i) q^{19} +(1.13407 + 4.23240i) q^{20} +(-0.0297166 - 2.64558i) q^{21} +(-1.61377 + 2.79513i) q^{22} -1.98551i q^{23} +(-0.258819 - 0.965926i) q^{24} +(12.2970 - 7.09968i) q^{25} +(0.539271 - 3.56499i) q^{26} -1.00000i q^{27} +(2.27629 - 1.34853i) q^{28} +(-1.73874 - 3.01158i) q^{29} +(-3.79467 + 2.19085i) q^{30} +(2.21076 - 8.25065i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.11756 - 0.835348i) q^{33} +(4.48408 - 4.48408i) q^{34} +(-8.28898 - 8.10484i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.127237 + 0.127237i) q^{37} +(2.70310 + 4.68191i) q^{38} +(3.58309 - 0.401793i) q^{39} +(-3.79467 - 2.19085i) q^{40} +(-0.00297886 + 0.0111173i) q^{41} +(1.89172 + 1.84970i) q^{42} +(-2.69459 - 1.55572i) q^{43} +(-0.835348 - 3.11756i) q^{44} +(-3.09834 - 3.09834i) q^{45} +(1.40397 + 1.40397i) q^{46} +(0.994423 + 3.71124i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.36295 + 6.13927i) q^{49} +(-3.67507 + 13.7155i) q^{50} +(5.49185 + 3.17072i) q^{51} +(2.13951 + 2.90215i) q^{52} +(-6.19883 - 10.7367i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-12.2474 + 7.07106i) q^{55} +(-0.656024 + 2.56313i) q^{56} +(-3.82276 + 3.82276i) q^{57} +(3.35899 + 0.900038i) q^{58} +(4.55586 - 4.55586i) q^{59} +(1.13407 - 4.23240i) q^{60} +(4.94487 - 2.85492i) q^{61} +(4.27085 + 7.39733i) q^{62} +(-1.29706 + 2.30600i) q^{63} +1.00000i q^{64} +(9.85674 - 12.3465i) q^{65} +(2.79513 - 1.61377i) q^{66} +(-1.37471 - 5.13050i) q^{67} +6.34145i q^{68} +(-0.992755 + 1.71950i) q^{69} +(11.5922 - 0.130210i) q^{70} +(1.61017 + 6.00925i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(3.47471 + 0.931045i) q^{73} -0.179940 q^{74} -14.1994 q^{75} +(-5.22199 - 1.39923i) q^{76} +(6.10560 + 5.96997i) q^{77} +(-2.24952 + 2.81774i) q^{78} +(-7.63746 + 13.2285i) q^{79} +(4.23240 - 1.13407i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.00575472 - 0.00996747i) q^{82} +(-1.17696 - 1.17696i) q^{83} +(-2.64558 + 0.0297166i) q^{84} +(26.8396 - 7.19164i) q^{85} +(3.00543 - 0.805301i) q^{86} +3.47748i q^{87} +(2.79513 + 1.61377i) q^{88} +(12.6058 - 12.6058i) q^{89} +4.38171 q^{90} +(-8.78377 - 3.72094i) q^{91} -1.98551 q^{92} +(-6.03990 + 6.03990i) q^{93} +(-3.32740 - 1.92108i) q^{94} +23.6884i q^{95} +(-0.965926 + 0.258819i) q^{96} +(2.25048 - 0.603015i) q^{97} +(-1.96315 - 6.71908i) q^{98} +(2.28221 + 2.28221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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