LMFDB - Embedded newform 546.2.by.b.115.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			115.7
Character	$\chi$	$=$	546.115
Dual form			546.2.by.b.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.66136 - 0.445159i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.48285 - 0.914026i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.66136 - 0.445159i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.48285 - 0.914026i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.71996 q^{10} +(3.98221 - 3.98221i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.62078 - 3.22072i) q^{13} +(2.16168 - 1.52549i) q^{14} +(0.445159 - 1.66136i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.82932 + 6.63258i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-0.256740 + 0.256740i) q^{19} +(-1.66136 + 0.445159i) q^{20} +(0.914026 + 2.48285i) q^{21} +(2.81585 - 4.87719i) q^{22} +(5.49685 + 3.17361i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-1.76819 - 1.02087i) q^{25} +(-2.39914 - 2.69149i) q^{26} -1.00000i q^{27} +(1.69320 - 2.03300i) q^{28} +(3.90529 + 6.76416i) q^{29} -1.71996i q^{30} +(0.0384066 + 0.143335i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.98221 + 3.98221i) q^{33} +(5.41548 + 5.41548i) q^{34} +(-4.53179 + 0.413258i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.81158 - 6.76092i) q^{37} +(-0.181543 + 0.314441i) q^{38} +(3.22072 - 1.62078i) q^{39} +(-1.48953 + 0.859981i) q^{40} +(-8.72661 - 2.33829i) q^{41} +(1.52549 + 2.16168i) q^{42} +(-6.41578 - 3.70415i) q^{43} +(1.45759 - 5.43980i) q^{44} +(1.66136 + 0.445159i) q^{45} +(6.13094 + 1.64278i) q^{46} +(0.195741 - 0.730514i) q^{47} +(0.866025 + 0.500000i) q^{48} +(5.32911 - 4.53878i) q^{49} +(-1.97216 - 0.528439i) q^{50} +(-6.63258 + 3.82932i) q^{51} +(-3.01400 - 1.97884i) q^{52} +(0.431525 - 0.747424i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(-8.38858 + 4.84315i) q^{55} +(1.10933 - 2.40196i) q^{56} +(-0.256740 - 0.256740i) q^{57} +(5.52291 + 5.52291i) q^{58} +(0.335934 - 1.25372i) q^{59} +(-0.445159 - 1.66136i) q^{60} +7.79066i q^{61} +(0.0741959 + 0.128511i) q^{62} +(-2.48285 + 0.914026i) q^{63} -1.00000i q^{64} +(1.25896 + 6.07227i) q^{65} +(4.87719 + 2.81585i) q^{66} +(-2.36041 - 2.36041i) q^{67} +(6.63258 + 3.82932i) q^{68} +(-3.17361 + 5.49685i) q^{69} +(-4.27041 + 1.57209i) q^{70} +(-14.4500 + 3.87187i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-8.44718 + 2.26342i) q^{73} +(-3.49971 - 6.06168i) q^{74} +(1.02087 - 1.76819i) q^{75} +(-0.0939735 + 0.350714i) q^{76} +(6.24739 - 13.5271i) q^{77} +(2.69149 - 2.39914i) q^{78} +(6.10060 + 10.5665i) q^{79} +(-1.21620 + 1.21620i) q^{80} +1.00000 q^{81} -9.03445 q^{82} +(1.17131 - 1.17131i) q^{83} +(2.03300 + 1.69320i) q^{84} +(-3.40931 - 12.7237i) q^{85} +(-7.15588 - 1.91741i) q^{86} +(-6.76416 + 3.90529i) q^{87} -5.63169i q^{88} +(4.04389 - 1.08356i) q^{89} +1.71996 q^{90} +(-6.96799 - 6.51515i) q^{91} +6.34721 q^{92} +(-0.143335 + 0.0384066i) q^{93} -0.756284i q^{94} +(0.540827 - 0.312247i) q^{95} +(0.965926 + 0.258819i) q^{96} +(0.740288 + 2.76279i) q^{97} +(3.97280 - 5.76340i) q^{98} +(-3.98221 + 3.98221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.66136	−	0.445159i	−0.742981	−	0.199081i	−0.132578	−	0.991173i	$-0.542326\pi$
$5$	−1.66136	−	0.445159i	−0.742981	−	0.199081i	−0.610403	+	0.792091i	$0.708992\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	2.48285	−	0.914026i	0.938430	−	0.345469i
$7$	2.48285	−	0.914026i	0.938430	−	0.345469i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−1.71996			−0.543900
$11$	3.98221	−	3.98221i	1.20068	−	1.20068i	0.226721	−	0.973960i	$-0.427200\pi$
$11$	3.98221	−	3.98221i	1.20068	−	1.20068i	0.973960	−	0.226721i	$-0.0728004\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−1.62078	−	3.22072i	−0.449524	−	0.893268i
$13$	−1.62078	−	3.22072i	−0.449524	−	0.893268i
$14$	2.16168	−	1.52549i	0.577734	−	0.407705i
$15$	0.445159	−	1.66136i	0.114940	−	0.428960i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.82932	+	6.63258i	0.928747	+	1.60864i	0.785421	+	0.618962i	$0.212446\pi$
$17$	3.82932	+	6.63258i	0.928747	+	1.60864i	0.143326	+	0.989676i	$0.454220\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−0.256740	+	0.256740i	−0.0589003	+	0.0589003i	−0.735943	−	0.677043i	$-0.763261\pi$
$19$	−0.256740	+	0.256740i	−0.0589003	+	0.0589003i	0.677043	+	0.735943i	$0.263261\pi$
$20$	−1.66136	+	0.445159i	−0.371490	+	0.0995406i
$21$	0.914026	+	2.48285i	0.199457	+	0.541803i
$22$	2.81585	−	4.87719i	0.600340	−	1.03982i
$23$	5.49685	+	3.17361i	1.14617	+	0.661743i	0.947952	−	0.318415i	$-0.103150\pi$
$23$	5.49685	+	3.17361i	1.14617	+	0.661743i	0.198221	+	0.980157i	$0.436484\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−1.76819	−	1.02087i	−0.353638	−	0.204173i
$26$	−2.39914	−	2.69149i	−0.470510	−	0.527845i
$27$		−	1.00000i		−	0.192450i
$28$	1.69320	−	2.03300i	0.319985	−	0.384200i
$29$	3.90529	+	6.76416i	0.725194	+	1.25607i	0.958894	+	0.283763i	$0.0915831\pi$
$29$	3.90529	+	6.76416i	0.725194	+	1.25607i	−0.233701	+	0.972309i	$0.575084\pi$
$30$		−	1.71996i		−	0.314021i
$31$	0.0384066	+	0.143335i	0.00689803	+	0.0257438i	0.969289	−	0.245924i	$-0.0790914\pi$
$31$	0.0384066	+	0.143335i	0.00689803	+	0.0257438i	−0.962391	+	0.271668i	$0.912425\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	3.98221	+	3.98221i	0.693213	+	0.693213i
$34$	5.41548	+	5.41548i	0.928747	+	0.928747i
$35$	−4.53179	+	0.413258i	−0.766012	+	0.0698534i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−1.81158	−	6.76092i	−0.297823	−	1.11149i	−0.938950	−	0.344054i	$-0.888200\pi$
$37$	−1.81158	−	6.76092i	−0.297823	−	1.11149i	0.641127	−	0.767435i	$-0.278467\pi$
$38$	−0.181543	+	0.314441i	−0.0294501	+	0.0510091i
$39$	3.22072	−	1.62078i	0.515729	−	0.259533i
$40$	−1.48953	+	0.859981i	−0.235516	+	0.135975i
$41$	−8.72661	−	2.33829i	−1.36287	−	0.365179i	−0.497999	−	0.867178i	$-0.665932\pi$
$41$	−8.72661	−	2.33829i	−1.36287	−	0.365179i	−0.864869	+	0.501998i	$0.832598\pi$
$42$	1.52549	+	2.16168i	0.235388	+	0.333555i
$43$	−6.41578	−	3.70415i	−0.978398	−	0.564878i	−0.0766118	−	0.997061i	$-0.524410\pi$
$43$	−6.41578	−	3.70415i	−0.978398	−	0.564878i	−0.901786	+	0.432183i	$0.857744\pi$
$44$	1.45759	−	5.43980i	0.219740	−	0.820080i
$45$	1.66136	+	0.445159i	0.247660	+	0.0663604i
$46$	6.13094	+	1.64278i	0.903957	+	0.242215i
$47$	0.195741	−	0.730514i	0.0285517	−	0.106556i	−0.950179	−	0.311703i	$-0.899101\pi$
$47$	0.195741	−	0.730514i	0.0285517	−	0.106556i	0.978731	+	0.205147i	$0.0657672\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	5.32911	−	4.53878i	0.761302	−	0.648398i
$50$	−1.97216	−	0.528439i	−0.278906	−	0.0747325i
$51$	−6.63258	+	3.82932i	−0.928747	+	0.536212i
$52$	−3.01400	−	1.97884i	−0.417967	−	0.274416i
$53$	0.431525	−	0.747424i	0.0592745	−	0.102667i	−0.834865	−	0.550454i	$-0.814455\pi$
$53$	0.431525	−	0.747424i	0.0592745	−	0.102667i	0.894140	+	0.447788i	$0.147788\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	−8.38858	+	4.84315i	−1.13112	+	0.653050i
$56$	1.10933	−	2.40196i	0.148240	−	0.320975i
$57$	−0.256740	−	0.256740i	−0.0340061	−	0.0340061i
$58$	5.52291	+	5.52291i	0.725194	+	0.725194i
$59$	0.335934	−	1.25372i	0.0437349	−	0.163221i	−0.940605	−	0.339504i	$-0.889741\pi$
$59$	0.335934	−	1.25372i	0.0437349	−	0.163221i	0.984340	+	0.176283i	$0.0564074\pi$
$60$	−0.445159	−	1.66136i	−0.0574698	−	0.214480i
$61$			7.79066i			0.997491i	0.866748	+	0.498746i	$0.166206\pi$
$61$			7.79066i			0.997491i	−0.866748	+	0.498746i	$0.833794\pi$
$62$	0.0741959	+	0.128511i	0.00942289	+	0.0163209i
$63$	−2.48285	+	0.914026i	−0.312810	+	0.115156i
$64$		−	1.00000i		−	0.125000i
$65$	1.25896	+	6.07227i	0.156155	+	0.753173i
$66$	4.87719	+	2.81585i	0.600340	+	0.346607i
$67$	−2.36041	−	2.36041i	−0.288370	−	0.288370i	0.548065	−	0.836436i	$-0.315365\pi$
$67$	−2.36041	−	2.36041i	−0.288370	−	0.288370i	−0.836436	+	0.548065i	$0.815365\pi$
$68$	6.63258	+	3.82932i	0.804319	+	0.464374i
$69$	−3.17361	+	5.49685i	−0.382057	+	0.661743i
$70$	−4.27041	+	1.57209i	−0.510412	+	0.187901i
$71$	−14.4500	+	3.87187i	−1.71490	+	0.459507i	−0.976618	−	0.214982i	$-0.931031\pi$
$71$	−14.4500	+	3.87187i	−1.71490	+	0.459507i	−0.738285	+	0.674489i	$0.764364\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−8.44718	+	2.26342i	−0.988668	+	0.264913i	−0.716691	−	0.697391i	$-0.754344\pi$
$73$	−8.44718	+	2.26342i	−0.988668	+	0.264913i	−0.271977	+	0.962304i	$0.587677\pi$
$74$	−3.49971	−	6.06168i	−0.406833	−	0.704656i
$75$	1.02087	−	1.76819i	0.117879	−	0.204173i
$76$	−0.0939735	+	0.350714i	−0.0107795	+	0.0402296i
$77$	6.24739	−	13.5271i	0.711956	−	1.54155i
$78$	2.69149	−	2.39914i	0.304751	−	0.271649i
$79$	6.10060	+	10.5665i	0.686371	+	1.18883i	0.973004	+	0.230789i	$0.0741307\pi$
$79$	6.10060	+	10.5665i	0.686371	+	1.18883i	−0.286633	+	0.958041i	$0.592536\pi$
$80$	−1.21620	+	1.21620i	−0.135975	+	0.135975i
$81$	1.00000			0.111111
$82$	−9.03445			−0.997688
$83$	1.17131	−	1.17131i	0.128568	−	0.128568i	−0.639895	−	0.768463i	$-0.721022\pi$
$83$	1.17131	−	1.17131i	0.128568	−	0.128568i	0.768463	+	0.639895i	$0.221022\pi$
$84$	2.03300	+	1.69320i	0.221818	+	0.184743i
$85$	−3.40931	−	12.7237i	−0.369792	−	1.38008i
$86$	−7.15588	−	1.91741i	−0.771638	−	0.206760i
$87$	−6.76416	+	3.90529i	−0.725194	+	0.418691i
$88$		−	5.63169i		−	0.600340i
$89$	4.04389	−	1.08356i	0.428651	−	0.114857i	−0.0380417	−	0.999276i	$-0.512112\pi$
$89$	4.04389	−	1.08356i	0.428651	−	0.114857i	0.466693	+	0.884419i	$0.345445\pi$
$90$	1.71996			0.181300
$91$	−6.96799	−	6.51515i	−0.730444	−	0.682973i
$92$	6.34721			0.661743
$93$	−0.143335	+	0.0384066i	−0.0148632	+	0.00398258i
$94$		−	0.756284i		−	0.0780048i
$95$	0.540827	−	0.312247i	0.0554877	−	0.0320358i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	0.740288	+	2.76279i	0.0751648	+	0.280519i	0.993271	−	0.115816i	$-0.0369484\pi$
$97$	0.740288	+	2.76279i	0.0751648	+	0.280519i	−0.918106	+	0.396335i	$0.870282\pi$
$98$	3.97280	−	5.76340i	0.401314	−	0.582192i
$99$	−3.98221	+	3.98221i	−0.400227	+	0.400227i
$100$	−2.04173			−0.204173
$101$	−7.04385			−0.700889			−0.350445	−	0.936583i	$-0.613969\pi$
$101$	−7.04385			−0.700889			−0.350445	+	0.936583i	$0.613969\pi$
$102$	−5.41548	+	5.41548i	−0.536212	+	0.536212i
$103$	3.37530	+	5.84620i	0.332579	+	0.576043i	0.983017	−	0.183516i	$-0.0587480\pi$
$103$	3.37530	+	5.84620i	0.332579	+	0.576043i	−0.650438	+	0.759559i	$0.725415\pi$
$104$	−3.42346	−	1.13133i	−0.335698	−	0.110936i
$105$	−0.413258	−	4.53179i	−0.0403299	−	0.442257i
$106$	0.223374	−	0.833643i	0.0216960	−	0.0809705i
$107$	−8.58995	+	14.8782i	−0.830422	+	1.43833i	0.0672817	+	0.997734i	$0.478567\pi$
$107$	−8.58995	+	14.8782i	−0.830422	+	1.43833i	−0.897704	+	0.440599i	$0.854766\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	5.36017	−	1.43625i	0.513411	−	0.137568i	0.00719395	−	0.999974i	$-0.497710\pi$
$109$	5.36017	−	1.43625i	0.513411	−	0.137568i	0.506217	+	0.862406i	$0.331043\pi$
$110$	−6.84924	+	6.84924i	−0.653050	+	0.653050i
$111$	6.76092	−	1.81158i	0.641719	−	0.171948i
$112$	0.449857	−	2.60723i	0.0425075	−	0.246360i
$113$	6.03531	−	10.4535i	0.567754	−	0.983379i	−0.429033	−	0.903289i	$-0.641146\pi$
$113$	6.03531	−	10.4535i	0.567754	−	0.983379i	0.996788	−	0.0800906i	$-0.0255209\pi$
$114$	−0.314441	−	0.181543i	−0.0294501	−	0.0170030i
$115$	−7.71946	−	7.71946i	−0.719843	−	0.719843i
$116$	6.76416	+	3.90529i	0.628036	+	0.362597i
$117$	1.62078	+	3.22072i	0.149841	+	0.297756i
$118$		−	1.29795i		−	0.119486i
$119$	15.5700	+	12.9676i	1.42730	+	1.18874i
$120$	−0.859981	−	1.48953i	−0.0785052	−	0.135975i
$121$		−	20.7159i		−	1.88327i
$122$	2.01637	+	7.52520i	0.182554	+	0.681299i
$123$	2.33829	−	8.72661i	0.210836	−	0.786852i
$124$	0.104929	+	0.104929i	0.00942289	+	0.00942289i
$125$	8.56413	+	8.56413i	0.765999	+	0.765999i
$126$	−2.16168	+	1.52549i	−0.192578	+	0.135902i
$127$	3.08064	−	1.77861i	0.273363	−	0.157826i	−0.357052	−	0.934084i	$-0.616218\pi$
$127$	3.08064	−	1.77861i	0.273363	−	0.157826i	0.630415	+	0.776258i	$0.282885\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	3.70415	−	6.41578i	0.326133	−	0.564878i
$130$	2.78768	+	5.53952i	0.244496	+	0.485848i
$131$	−15.3929	+	8.88709i	−1.34488	+	0.776469i	−0.987520	−	0.157497i	$-0.949658\pi$
$131$	−15.3929	+	8.88709i	−1.34488	+	0.776469i	−0.357364	+	0.933965i	$0.616324\pi$
$132$	5.43980	+	1.45759i	0.473473	+	0.126867i
$133$	−0.402781	+	0.872116i	−0.0349256	+	0.0756220i
$134$	−2.89090	−	1.66906i	−0.249736	−	0.144185i
$135$	−0.445159	+	1.66136i	−0.0383132	+	0.142987i
$136$	7.39768	+	1.98220i	0.634346	+	0.169973i
$137$	−7.45580	−	1.99778i	−0.636992	−	0.170682i	−0.0741515	−	0.997247i	$-0.523625\pi$
$137$	−7.45580	−	1.99778i	−0.636992	−	0.170682i	−0.562841	+	0.826565i	$0.690292\pi$
$138$	−1.64278	+	6.13094i	−0.139843	+	0.521900i
$139$	−5.78099	−	3.33766i	−0.490337	−	0.283096i	0.234377	−	0.972146i	$-0.424695\pi$
$139$	−5.78099	−	3.33766i	−0.490337	−	0.283096i	−0.724714	+	0.689049i	$0.758028\pi$
$140$	−3.71801	+	2.62379i	−0.314230	+	0.221750i
$141$	0.730514	+	0.195741i	0.0615204	+	0.0164843i
$142$	−12.9555	+	7.47989i	−1.08720	+	0.627698i
$143$	−19.2799	−	6.37130i	−1.61226	−	0.532795i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.47695	−	12.9761i	−0.288745	−	1.07761i
$146$	−7.57354	+	4.37258i	−0.626790	+	0.361878i
$147$	4.53878	+	5.32911i	0.374353	+	0.439538i
$148$	−4.94934	−	4.94934i	−0.406833	−	0.406833i
$149$	14.3630	+	14.3630i	1.17667	+	1.17667i	0.980589	+	0.196076i	$0.0628201\pi$
$149$	14.3630	+	14.3630i	1.17667	+	1.17667i	0.196076	+	0.980589i	$0.437180\pi$
$150$	0.528439	−	1.97216i	0.0431468	−	0.161026i
$151$	3.82389	+	14.2709i	0.311184	+	1.16135i	0.927490	+	0.373847i	$0.121962\pi$
$151$	3.82389	+	14.2709i	0.311184	+	1.16135i	−0.616307	+	0.787506i	$0.711372\pi$
$152$			0.363086i			0.0294501i
$153$	−3.82932	−	6.63258i	−0.309582	−	0.536212i
$154$	2.53345	−	14.6831i	0.204151	−	1.18320i
$155$		−	0.255228i		−	0.0205004i
$156$	1.97884	−	3.01400i	0.158434	−	0.241313i
$157$	−8.08225	−	4.66629i	−0.645033	−	0.372410i	0.141517	−	0.989936i	$-0.454802\pi$
$157$	−8.08225	−	4.66629i	−0.645033	−	0.372410i	−0.786551	+	0.617526i	$0.788135\pi$
$158$	8.62755	+	8.62755i	0.686371	+	0.686371i
$159$	0.747424	+	0.431525i	0.0592745	+	0.0342222i
$160$	−0.859981	+	1.48953i	−0.0679875	+	0.117758i
$161$	16.5486	+	2.85534i	1.30421	+	0.225032i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	6.07415	−	6.07415i	0.475764	−	0.475764i	−0.428010	−	0.903774i	$-0.640785\pi$
$163$	6.07415	−	6.07415i	0.475764	−	0.475764i	0.903774	+	0.428010i	$0.140785\pi$
$164$	−8.72661	+	2.33829i	−0.681434	+	0.182590i
$165$	−4.84315	−	8.38858i	−0.377039	−	0.653050i
$166$	0.828241	−	1.43456i	0.0642840	−	0.111343i
$167$	−4.01471	+	14.9831i	−0.310668	+	1.15943i	0.617288	+	0.786738i	$0.288232\pi$
$167$	−4.01471	+	14.9831i	−0.310668	+	1.15943i	−0.927956	+	0.372691i	$0.878435\pi$
$168$	2.40196	+	1.10933i	0.185315	+	0.0855865i
$169$	−7.74613	+	10.4402i	−0.595856	+	0.803091i
$170$	−6.58629	−	11.4078i	−0.505145	−	0.874937i
$171$	0.256740	−	0.256740i	0.0196334	−	0.0196334i
$172$	−7.40831			−0.564878
$173$	4.55205			0.346086			0.173043	−	0.984914i	$-0.444640\pi$
$173$	4.55205			0.346086			0.173043	+	0.984914i	$0.444640\pi$
$174$	−5.52291	+	5.52291i	−0.418691	+	0.418691i
$175$	−5.32325	−	0.918486i	−0.402400	−	0.0694310i
$176$	−1.45759	−	5.43980i	−0.109870	−	0.410040i
$177$	1.25372	+	0.335934i	0.0942357	+	0.0252504i
$178$	3.62565	−	2.09327i	0.271754	−	0.156897i
$179$			1.67598i			0.125268i	0.998037	+	0.0626342i	$0.0199502\pi$
$179$			1.67598i			0.125268i	−0.998037	+	0.0626342i	$0.980050\pi$
$180$	1.66136	−	0.445159i	0.123830	−	0.0331802i
$181$	1.85011			0.137518			0.0687588	−	0.997633i	$-0.478096\pi$
$181$	1.85011			0.137518			0.0687588	+	0.997633i	$0.478096\pi$
$182$	−8.41680	−	4.48970i	−0.623895	−	0.332799i
$183$	−7.79066			−0.575902
$184$	6.13094	−	1.64278i	0.451979	−	0.121107i
$185$			12.0387i			0.885106i
$186$	−0.128511	+	0.0741959i	−0.00942289	+	0.00544031i
$187$	41.6615	+	11.1632i	3.04659	+	0.816331i
$188$	−0.195741	−	0.730514i	−0.0142759	−	0.0532782i
$189$	−0.914026	−	2.48285i	−0.0664856	−	0.180601i
$190$	0.441584	−	0.441584i	0.0320358	−	0.0320358i
$191$	−4.51532			−0.326717			−0.163359	−	0.986567i	$-0.552233\pi$
$191$	−4.51532			−0.326717			−0.163359	+	0.986567i	$0.552233\pi$
$192$	1.00000			0.0721688
$193$	−16.7057	+	16.7057i	−1.20250	+	1.20250i	−0.229100	+	0.973403i	$0.573578\pi$
$193$	−16.7057	+	16.7057i	−1.20250	+	1.20250i	−0.973403	+	0.229100i	$0.926422\pi$
$194$	1.43013	+	2.47705i	0.102677	+	0.177842i
$195$	−6.07227	+	1.25896i	−0.434845	+	0.0901560i
$196$	2.34576	−	6.59526i	0.167554	−	0.471090i
$197$	4.81988	−	17.9880i	0.343402	−	1.28159i	−0.551066	−	0.834462i	$-0.685779\pi$
$197$	4.81988	−	17.9880i	0.343402	−	1.28159i	0.894468	−	0.447132i	$-0.147555\pi$
$198$	−2.81585	+	4.87719i	−0.200113	+	0.346607i
$199$	6.51955	+	11.2922i	0.462159	+	0.800483i	0.999068	−	0.0431572i	$-0.0137416\pi$
$199$	6.51955	+	11.2922i	0.462159	+	0.800483i	−0.536909	+	0.843640i	$0.680408\pi$
$200$	−1.97216	+	0.528439i	−0.139453	+	0.0373663i
$201$	2.36041	−	2.36041i	0.166491	−	0.166491i
$202$	−6.80384	+	1.82308i	−0.478716	+	0.128272i
$203$	15.8789	+	13.2249i	1.11448	+	0.928204i
$204$	−3.82932	+	6.63258i	−0.268106	+	0.464374i
$205$	13.4571	+	7.76946i	0.939884	+	0.542642i
$206$	4.77340	+	4.77340i	0.332579	+	0.332579i
$207$	−5.49685	−	3.17361i	−0.382057	−	0.220581i
$208$	−3.59962	−	0.206724i	−0.249589	−	0.0143338i
$209$			2.04479i			0.141441i
$210$	−1.57209	−	4.27041i	−0.108485	−	0.294686i
$211$	−8.05119	−	13.9451i	−0.554267	−	0.960018i	−0.997960	−	0.0638394i	$-0.979665\pi$
$211$	−8.05119	−	13.9451i	−0.554267	−	0.960018i	0.443694	−	0.896179i	$-0.353668\pi$
$212$		−	0.863050i		−	0.0592745i
$213$	−3.87187	−	14.4500i	−0.265296	−	0.990100i
$214$	−4.44649	+	16.5945i	−0.303956	+	1.13438i
$215$	9.00996	+	9.00996i	0.614474	+	0.614474i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	0.226370	+	0.320776i	0.0153670	+	0.0217757i
$218$	4.80580	−	2.77463i	0.325490	−	0.187922i
$219$	−2.26342	−	8.44718i	−0.152947	−	0.570808i
$220$	−4.84315	+	8.38858i	−0.326525	+	0.565558i
$221$	15.1552	−	23.0832i	1.01945	−	1.55274i
$222$	6.06168	−	3.49971i	0.406833	−	0.234885i
$223$	−13.2808	−	3.55858i	−0.889348	−	0.238300i	−0.214912	−	0.976633i	$-0.568946\pi$
$223$	−13.2808	−	3.55858i	−0.889348	−	0.238300i	−0.674436	+	0.738333i	$0.735613\pi$
$224$	−0.240272	−	2.63482i	−0.0160538	−	0.176046i
$225$	1.76819	+	1.02087i	0.117879	+	0.0680577i
$226$	3.12411	−	11.6593i	0.207812	−	0.775567i
$227$	27.0911	+	7.25905i	1.79810	+	0.481800i	0.993679	−	0.112258i	$-0.0358083\pi$
$227$	27.0911	+	7.25905i	1.79810	+	0.481800i	0.804422	+	0.594058i	$0.202475\pi$
$228$	−0.350714	−	0.0939735i	−0.0232266	−	0.00622355i
$229$	3.78049	−	14.1090i	0.249822	−	0.932347i	−0.721077	−	0.692855i	$-0.756352\pi$
$229$	3.78049	−	14.1090i	0.249822	−	0.932347i	0.970898	−	0.239492i	$-0.0769809\pi$
$230$	−9.45437	−	5.45848i	−0.623403	−	0.359922i
$231$	13.5271	+	6.24739i	0.890016	+	0.411048i
$232$	7.54443	+	2.02153i	0.495316	+	0.132720i
$233$	0.538452	−	0.310875i	0.0352751	−	0.0203661i	−0.482259	−	0.876029i	$-0.660183\pi$
$233$	0.538452	−	0.310875i	0.0352751	−	0.0203661i	0.517534	+	0.855663i	$0.326850\pi$
$234$	2.39914	+	2.69149i	0.156837	+	0.175948i
$235$	−0.650390	+	1.12651i	−0.0424268	+	0.0734853i
$236$	−0.335934	−	1.25372i	−0.0218675	−	0.0816105i
$237$	−10.5665	+	6.10060i	−0.686371	+	0.396276i
$238$	18.3957	+	8.49595i	1.19242	+	0.550711i
$239$	−11.6685	−	11.6685i	−0.754774	−	0.754774i	0.220592	−	0.975366i	$-0.429201\pi$
$239$	−11.6685	−	11.6685i	−0.754774	−	0.754774i	−0.975366	+	0.220592i	$0.929201\pi$
$240$	−1.21620	−	1.21620i	−0.0785052	−	0.0785052i
$241$	2.39343	−	8.93241i	0.154175	−	0.575387i	−0.845000	−	0.534766i	$-0.820400\pi$
$241$	2.39343	−	8.93241i	0.154175	−	0.575387i	0.999175	−	0.0406210i	$-0.0129336\pi$
$242$	−5.36168	−	20.0101i	−0.344662	−	1.28630i
$243$			1.00000i			0.0641500i
$244$	3.89533	+	6.74691i	0.249373	+	0.431926i
$245$	−10.8740	+	5.16823i	−0.694716	+	0.330186i
$246$		−	9.03445i		−	0.576016i
$247$	1.24301	+	0.410770i	0.0790908	+	0.0261367i
$248$	0.128511	+	0.0741959i	0.00816046	+	0.00471144i
$249$	1.17131	+	1.17131i	0.0742288	+	0.0742288i
$250$	10.4889	+	6.05575i	0.663375	+	0.383000i
$251$	12.1225	−	20.9967i	0.765163	−	1.32530i	−0.174998	−	0.984569i	$-0.555992\pi$
$251$	12.1225	−	20.9967i	0.765163	−	1.32530i	0.940160	−	0.340732i	$-0.110675\pi$
$252$	−1.69320	+	2.03300i	−0.106662	+	0.128067i
$253$	34.5275	−	9.25163i	2.17073	−	0.581645i
$254$	2.51533	−	2.51533i	0.157826	−	0.157826i
$255$	12.7237	−	3.40931i	0.796791	−	0.213500i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.06358	+	8.77038i	−0.315858	+	0.547081i	−0.979619	−	0.200863i	$-0.935625\pi$
$257$	−5.06358	+	8.77038i	−0.315858	+	0.547081i	0.663762	+	0.747944i	$0.268959\pi$
$258$	1.91741	−	7.15588i	0.119373	−	0.445505i
$259$	−10.6776	−	15.1305i	−0.663471	−	0.940166i
$260$	4.12643	+	4.62926i	0.255910	+	0.287095i
$261$	−3.90529	−	6.76416i	−0.241731	−	0.418691i
$262$	−12.5682	+	12.5682i	−0.776469	+	0.776469i
$263$	−5.35437			−0.330165			−0.165082	−	0.986280i	$-0.552789\pi$
$263$	−5.35437			−0.330165			−0.165082	+	0.986280i	$0.552789\pi$
$264$	5.63169			0.346607
$265$	−1.04964	+	1.04964i	−0.0644788	+	0.0644788i
$266$	−0.163337	+	0.946647i	−0.0100148	+	0.0580426i
$267$	1.08356	+	4.04389i	0.0663126	+	0.247482i
$268$	−3.22438	−	0.863971i	−0.196961	−	0.0527754i
$269$	14.0802	−	8.12919i	0.858483	−	0.495645i	−0.00502094	−	0.999987i	$-0.501598\pi$
$269$	14.0802	−	8.12919i	0.858483	−	0.495645i	0.863504	+	0.504342i	$0.168265\pi$
$270$			1.71996i			0.104674i
$271$	18.3126	−	4.90684i	1.11241	−	0.298069i	0.344601	−	0.938749i	$-0.388014\pi$
$271$	18.3126	−	4.90684i	1.11241	−	0.298069i	0.767808	+	0.640680i	$0.221348\pi$
$272$	7.65864			0.464374
$273$	6.51515	−	6.96799i	0.394315	−	0.421722i
$274$	−7.71881			−0.466311
$275$	−11.1066	+	2.97600i	−0.669753	+	0.179460i
$276$			6.34721i			0.382057i
$277$	3.95951	−	2.28602i	0.237904	−	0.137354i	−0.376309	−	0.926494i	$-0.622807\pi$
$277$	3.95951	−	2.28602i	0.237904	−	0.137354i	0.614213	+	0.789140i	$0.289474\pi$
$278$	−6.44786	−	1.72770i	−0.386717	−	0.103620i
$279$	−0.0384066	−	0.143335i	−0.00229934	−	0.00858127i
$280$	−2.91224	+	3.49668i	−0.174040	+	0.208966i
$281$	−0.329312	+	0.329312i	−0.0196451	+	0.0196451i	−0.716861	−	0.697216i	$-0.754422\pi$
$281$	−0.329312	+	0.329312i	−0.0196451	+	0.0196451i	0.697216	+	0.716861i	$0.254422\pi$
$282$	0.756284			0.0450361
$283$	−20.9641			−1.24618			−0.623092	−	0.782148i	$-0.714124\pi$
$283$	−20.9641			−1.24618			−0.623092	+	0.782148i	$0.714124\pi$
$284$	−10.5782	+	10.5782i	−0.627698	+	0.627698i
$285$	0.312247	+	0.540827i	0.0184959	+	0.0320358i
$286$	−20.2719	−	1.16421i	−1.19871	−	0.0688410i
$287$	−23.8041	+	2.17072i	−1.40511	+	0.128134i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	−20.8274	+	36.0741i	−1.22514	+	2.12201i
$290$	−6.71695	−	11.6341i	−0.394433	−	0.683177i
$291$	−2.76279	+	0.740288i	−0.161958	+	0.0433964i
$292$	−6.18377	+	6.18377i	−0.361878	+	0.361878i
$293$	−13.5614	+	3.63378i	−0.792268	+	0.212288i	−0.632186	−	0.774816i	$-0.717842\pi$
$293$	−13.5614	+	3.63378i	−0.792268	+	0.212288i	−0.160081	+	0.987104i	$0.551176\pi$
$294$	5.76340	+	3.97280i	0.336129	+	0.231699i
$295$	−1.11621	+	1.93334i	−0.0649884	+	0.112563i
$296$	−6.06168	−	3.49971i	−0.352328	−	0.203417i
$297$	−3.98221	−	3.98221i	−0.231071	−	0.231071i
$298$	17.5910	+	10.1562i	1.01902	+	0.588333i
$299$	1.31212	−	22.8476i	0.0758820	−	1.32131i
$300$		−	2.04173i		−	0.117879i
$301$	−19.3151	−	3.33268i	−1.11331	−	0.192092i
$302$	7.38719	+	12.7950i	0.425085	+	0.736269i
$303$		−	7.04385i		−	0.404659i
$304$	0.0939735	+	0.350714i	0.00538975	+	0.0201148i
$305$	3.46808	−	12.9431i	0.198582	−	0.741117i
$306$	−5.41548	−	5.41548i	−0.309582	−	0.309582i
$307$	−8.18103	−	8.18103i	−0.466916	−	0.466916i	0.433998	−	0.900914i	$-0.357102\pi$
$307$	−8.18103	−	8.18103i	−0.466916	−	0.466916i	−0.900914	+	0.433998i	$0.857102\pi$
$308$	−1.35314	−	14.8385i	−0.0771021	−	0.845501i
$309$	−5.84620	+	3.37530i	−0.332579	+	0.192014i
$310$	−0.0660579	−	0.246532i	−0.00375184	−	0.0140021i
$311$	0.769431	−	1.33269i	0.0436304	−	0.0755701i	−0.843386	−	0.537309i	$-0.819441\pi$
$311$	0.769431	−	1.33269i	0.0436304	−	0.0755701i	0.887016	+	0.461739i	$0.152774\pi$
$312$	1.13133	−	3.42346i	0.0640490	−	0.193815i
$313$	13.7899	−	7.96159i	0.779450	−	0.450016i	−0.0567851	−	0.998386i	$-0.518085\pi$
$313$	13.7899	−	7.96159i	0.779450	−	0.450016i	0.836235	+	0.548371i	$0.184752\pi$
$314$	−9.01457	−	2.41545i	−0.508722	−	0.136312i
$315$	4.53179	−	0.413258i	0.255337	−	0.0232845i
$316$	10.5665	+	6.10060i	0.594415	+	0.343186i
$317$	−0.678566	+	2.53244i	−0.0381121	+	0.142236i	−0.982360	−	0.186998i	$-0.940124\pi$
$317$	−0.678566	+	2.53244i	−0.0381121	+	0.142236i	0.944248	+	0.329235i	$0.106791\pi$
$318$	0.833643	+	0.223374i	0.0467484	+	0.0125262i
$319$	42.4879	+	11.3846i	2.37887	+	0.637415i
$320$	−0.445159	+	1.66136i	−0.0248851	+	0.0928726i
$321$	−14.8782	−	8.58995i	−0.830422	−	0.479444i
$322$	16.7238	−	1.52506i	0.931979	−	0.0849880i
$323$	−2.68599	−	0.719710i	−0.149453	−	0.0400457i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−0.422075	+	7.34945i	−0.0234125	+	0.407674i
$326$	4.29507	−	7.43928i	0.237882	−	0.412024i
$327$	1.43625	+	5.36017i	0.0794250	+	0.296418i
$328$	−7.82407	+	4.51723i	−0.432012	+	0.249422i
$329$	−0.181714	−	1.99267i	−0.0100182	−	0.109860i
$330$	−6.84924	−	6.84924i	−0.377039	−	0.377039i
$331$	5.26324	+	5.26324i	0.289294	+	0.289294i	0.836801	−	0.547507i	$-0.184423\pi$
$331$	5.26324	+	5.26324i	0.289294	+	0.289294i	−0.547507	+	0.836801i	$0.684423\pi$
$332$	0.428729	−	1.60004i	0.0235296	−	0.0878136i
$333$	1.81158	+	6.76092i	0.0992742	+	0.370496i
$334$			15.5117i			0.848761i
$335$	2.87073	+	4.97224i	0.156845	+	0.271663i
$336$	2.60723	+	0.449857i	0.142236	+	0.0245417i
$337$		−	18.7350i		−	1.02056i	−0.860008	−	0.510280i	$-0.829542\pi$
$337$		−	18.7350i		−	1.02056i	0.860008	−	0.510280i	$-0.170458\pi$
$338$	−4.78007	+	12.0893i	−0.260002	+	0.657571i
$339$	10.4535	+	6.03531i	0.567754	+	0.327793i
$340$	−9.31442	−	9.31442i	−0.505145	−	0.505145i
$341$	0.723735	+	0.417848i	0.0391924	+	0.0226278i
$342$	0.181543	−	0.314441i	0.00981671	−	0.0170030i
$343$	9.08284	−	16.1401i	0.490427	−	0.871482i
$344$	−7.15588	+	1.91741i	−0.385819	+	0.103380i
$345$	7.71946	−	7.71946i	0.415602	−	0.415602i
$346$	4.39694	−	1.17816i	0.236381	−	0.0633381i
$347$	7.38080	+	12.7839i	0.396222	+	0.686277i	0.993256	−	0.115939i	$-0.0369877\pi$
$347$	7.38080	+	12.7839i	0.396222	+	0.686277i	−0.597034	+	0.802216i	$0.703654\pi$
$348$	−3.90529	+	6.76416i	−0.209345	+	0.362597i
$349$	5.94235	−	22.1772i	0.318087	−	1.18712i	−0.602994	−	0.797746i	$-0.706026\pi$
$349$	5.94235	−	22.1772i	0.318087	−	1.18712i	0.921081	−	0.389371i	$-0.127308\pi$
$350$	−5.37959	+	0.490570i	−0.287551	+	0.0262221i
$351$	−3.22072	+	1.62078i	−0.171910	+	0.0865109i
$352$	−2.81585	−	4.87719i	−0.150085	−	0.259955i
$353$	12.9635	−	12.9635i	0.689978	−	0.689978i	−0.272249	−	0.962227i	$-0.587767\pi$
$353$	12.9635	−	12.9635i	0.689978	−	0.689978i	0.962227	+	0.272249i	$0.0877674\pi$
$354$	1.29795			0.0689853
$355$	25.7302			1.36562
$356$	2.96033	−	2.96033i	0.156897	−	0.156897i
$357$	−12.9676	+	15.5700i	−0.686319	+	0.824051i
$358$	0.433775	+	1.61887i	0.0229257	+	0.0855600i
$359$	−10.7643	−	2.88428i	−0.568116	−	0.152226i	−0.0366838	−	0.999327i	$-0.511679\pi$
$359$	−10.7643	−	2.88428i	−0.568116	−	0.152226i	−0.531433	+	0.847101i	$0.678346\pi$
$360$	1.48953	−	0.859981i	0.0785052	−	0.0453250i
$361$			18.8682i			0.993062i
$362$	1.78707	−	0.478843i	0.0939262	−	0.0251675i
$363$	20.7159			1.08730
$364$	−9.29203	−	2.15829i	−0.487035	−	0.113125i
$365$	15.0414			0.787300
$366$	−7.52520	+	2.01637i	−0.393348	+	0.105397i
$367$			17.0369i			0.889321i	0.895699	+	0.444661i	$0.146676\pi$
$367$			17.0369i			0.889321i	−0.895699	+	0.444661i	$0.853324\pi$
$368$	5.49685	−	3.17361i	0.286543	−	0.165436i
$369$	8.72661	+	2.33829i	0.454289	+	0.121726i
$370$	3.11586	+	11.6285i	0.161986	+	0.604539i
$371$	0.388249	−	2.25017i	0.0201569	−	0.116823i
$372$	−0.104929	+	0.104929i	−0.00544031	+	0.00544031i
$373$	28.5726			1.47943			0.739717	−	0.672918i	$-0.234959\pi$
$373$	28.5726			1.47943			0.739717	+	0.672918i	$0.234959\pi$
$374$	43.1311			2.23026
$375$	−8.56413	+	8.56413i	−0.442250	+	0.442250i
$376$	−0.378142	−	0.654961i	−0.0195012	−	0.0337771i
$377$	15.4559	−	23.5411i	0.796017	−	1.21243i
$378$	−1.52549	−	2.16168i	−0.0784628	−	0.111185i
$379$	−5.26352	+	19.6437i	−0.270369	+	1.00903i	0.688513	+	0.725224i	$0.258264\pi$
$379$	−5.26352	+	19.6437i	−0.270369	+	1.00903i	−0.958882	+	0.283806i	$0.908403\pi$
$380$	0.312247	−	0.540827i	0.0160179	−	0.0277439i
$381$	1.77861	+	3.08064i	0.0911209	+	0.157826i
$382$	−4.36147	+	1.16865i	−0.223152	+	0.0597934i
$383$	6.01701	−	6.01701i	0.307455	−	0.307455i	−0.536467	−	0.843922i	$-0.680241\pi$
$383$	6.01701	−	6.01701i	0.307455	−	0.307455i	0.843922	+	0.536467i	$0.180241\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	−16.4008	+	19.6922i	−0.835864	+	1.00361i
$386$	−11.8127	+	20.4602i	−0.601251	+	1.04140i
$387$	6.41578	+	3.70415i	0.326133	+	0.188293i
$388$	2.02250	+	2.02250i	0.102677	+	0.102677i
$389$	16.6395	+	9.60684i	0.843658	+	0.487086i	0.858506	−	0.512804i	$-0.171393\pi$
$389$	16.6395	+	9.60684i	0.843658	+	0.487086i	−0.0148482	+	0.999890i	$0.504727\pi$
$390$	−5.53952	+	2.78768i	−0.280505	+	0.141160i
$391$			48.6111i			2.45837i
$392$	0.558848	−	6.97766i	0.0282261	−	0.352425i
$393$	−8.88709	−	15.3929i	−0.448294	−	0.776469i
$394$		−	18.6226i		−	0.938192i
$395$	−5.43147	−	20.2705i	−0.273287	−	1.01992i
$396$	−1.45759	+	5.43980i	−0.0732466	+	0.273360i
$397$	−21.8088	−	21.8088i	−1.09455	−	1.09455i	−0.995036	−	0.0995182i	$-0.968270\pi$
$397$	−21.8088	−	21.8088i	−1.09455	−	1.09455i	−0.0995182	−	0.995036i	$-0.531730\pi$
$398$	9.22004	+	9.22004i	0.462159	+	0.462159i
$399$	−0.872116	−	0.402781i	−0.0436604	−	0.0201643i
$400$	−1.76819	+	1.02087i	−0.0884095	+	0.0510433i
$401$	7.41193	+	27.6617i	0.370134	+	1.38136i	0.860326	+	0.509744i	$0.170260\pi$
$401$	7.41193	+	27.6617i	0.370134	+	1.38136i	−0.490192	+	0.871614i	$0.663073\pi$
$402$	1.66906	−	2.89090i	0.0832453	−	0.144185i
$403$	0.399395	−	0.356013i	0.0198953	−	0.0177343i
$404$	−6.10015	+	3.52192i	−0.303494	+	0.175222i
$405$	−1.66136	−	0.445159i	−0.0825534	−	0.0221201i
$406$	18.7607	+	8.66449i	0.931076	+	0.430011i
$407$	−34.1375	−	19.7093i	−1.69213	−	0.976953i
$408$	−1.98220	+	7.39768i	−0.0981337	+	0.366240i
$409$	5.27949	+	1.41464i	0.261054	+	0.0699492i	0.386972	−	0.922091i	$-0.373521\pi$
$409$	5.27949	+	1.41464i	0.261054	+	0.0699492i	−0.125918	+	0.992041i	$0.540188\pi$
$410$	15.0094	+	4.02177i	0.741263	+	0.198621i
$411$	1.99778	−	7.45580i	0.0985430	−	0.367768i
$412$	5.84620	+	3.37530i	0.288022	+	0.166289i
$413$	−0.311861	−	3.41987i	−0.0153457	−	0.168281i
$414$	−6.13094	−	1.64278i	−0.301319	−	0.0807382i
$415$	−2.46738	+	1.42454i	−0.121119	+	0.0699281i
$416$	−3.53047	+	0.731970i	−0.173096	+	0.0358878i
$417$	3.33766	−	5.78099i	0.163446	−	0.283096i
$418$	0.529230	+	1.97511i	0.0258855	+	0.0966059i
$419$	12.2654	−	7.08143i	0.599204	−	0.345950i	−0.169525	−	0.985526i	$-0.554223\pi$
$419$	12.2654	−	7.08143i	0.599204	−	0.345950i	0.768728	+	0.639576i	$0.220890\pi$
$420$	−2.62379	−	3.71801i	−0.128028	−	0.181421i
$421$	13.1845	+	13.1845i	0.642573	+	0.642573i	0.951187	−	0.308614i	$-0.0998653\pi$
$421$	13.1845	+	13.1845i	0.642573	+	0.642573i	−0.308614	+	0.951187i	$0.599865\pi$
$422$	−11.3861	−	11.3861i	−0.554267	−	0.554267i
$423$	−0.195741	+	0.730514i	−0.00951724	+	0.0355188i
$424$	−0.223374	−	0.833643i	−0.0108480	−	0.0404853i
$425$		−	15.6369i		−	0.758500i
$426$	−7.47989	−	12.9555i	−0.362402	−	0.627698i
$427$	7.12086	+	19.3431i	0.344603	+	0.936076i
$428$			17.1799i			0.830422i
$429$	6.37130	−	19.2799i	0.307609	−	0.930841i
$430$	11.0349	+	6.37100i	0.532150	+	0.307237i
$431$	−10.1553	−	10.1553i	−0.489162	−	0.489162i	0.418880	−	0.908042i	$-0.362423\pi$
$431$	−10.1553	−	10.1553i	−0.489162	−	0.489162i	−0.908042	+	0.418880i	$0.862423\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	11.0126	−	19.0743i	0.529230	−	0.916653i	−0.470189	−	0.882566i	$-0.655814\pi$
$433$	11.0126	−	19.0743i	0.529230	−	0.916653i	0.999419	−	0.0340875i	$-0.0108525\pi$
$434$	0.301680	+	0.251257i	0.0144811	+	0.0120607i
$435$	12.9761	−	3.47695i	0.622158	−	0.166707i
$436$	3.92392	−	3.92392i	0.187922	−	0.187922i
$437$	−2.22606	+	0.596470i	−0.106487	+	0.0285330i
$438$	−4.37258	−	7.57354i	−0.208930	−	0.361878i
$439$	−6.61018	+	11.4492i	−0.315487	+	0.546439i	−0.979541	−	0.201245i	$-0.935501\pi$
$439$	−6.61018	+	11.4492i	−0.315487	+	0.546439i	0.664054	+	0.747685i	$0.268834\pi$
$440$	−2.50700	+	9.35624i	−0.119516	+	0.446041i
$441$	−5.32911	+	4.53878i	−0.253767	+	0.216133i
$442$	8.66446	−	26.2191i	0.412126	−	1.24711i
$443$	−17.8431	−	30.9052i	−0.847752	−	1.46835i	−0.883210	−	0.468978i	$-0.844622\pi$
$443$	−17.8431	−	30.9052i	−0.847752	−	1.46835i	0.0354579	−	0.999371i	$-0.488711\pi$
$444$	4.94934	−	4.94934i	0.234885	−	0.234885i
$445$	−7.20069			−0.341346
$446$	−13.7493			−0.651048
$447$	−14.3630	+	14.3630i	−0.679348	+	0.679348i
$448$	−0.914026	−	2.48285i	−0.0431837	−	0.117304i
$449$	−1.32333	−	4.93874i	−0.0624519	−	0.233074i	0.927644	−	0.373465i	$-0.121831\pi$
$449$	−1.32333	−	4.93874i	−0.0624519	−	0.233074i	−0.990096	+	0.140392i	$0.955164\pi$
$450$	1.97216	+	0.528439i	0.0929685	+	0.0249108i
$451$	−44.0627	+	25.4396i	−2.07483	+	1.19790i
$452$		−	12.0706i		−	0.567754i
$453$	−14.2709	+	3.82389i	−0.670508	+	0.179662i
$454$	28.0468			1.31630
$455$	8.67603	+	13.9258i	0.406739	+	0.652853i
$456$	−0.363086			−0.0170030
$457$	−19.9569	+	5.34744i	−0.933546	+	0.250143i	−0.693366	−	0.720586i	$-0.743873\pi$
$457$	−19.9569	+	5.34744i	−0.933546	+	0.250143i	−0.240180	+	0.970728i	$0.577206\pi$
$458$		−	14.6067i		−	0.682526i
$459$	6.63258	−	3.82932i	0.309582	−	0.178737i
$460$	−10.5450	−	2.82552i	−0.491662	−	0.131741i
$461$	−1.92392	−	7.18018i	−0.0896060	−	0.334414i	0.906541	−	0.422119i	$-0.138713\pi$
$461$	−1.92392	−	7.18018i	−0.0896060	−	0.334414i	−0.996147	+	0.0877047i	$0.972047\pi$
$462$	14.6831	+	2.53345i	0.683119	+	0.117867i
$463$	2.57262	−	2.57262i	0.119560	−	0.119560i	−0.644795	−	0.764355i	$-0.723057\pi$
$463$	2.57262	−	2.57262i	0.119560	−	0.119560i	0.764355	+	0.644795i	$0.223057\pi$
$464$	7.81057			0.362597
$465$	0.255228			0.0118359
$466$	0.439644	−	0.439644i	0.0203661	−	0.0203661i
$467$	−4.99519	−	8.65193i	−0.231150	−	0.400363i	0.726997	−	0.686641i	$-0.240915\pi$
$467$	−4.99519	−	8.65193i	−0.231150	−	0.400363i	−0.958147	+	0.286277i	$0.907582\pi$
$468$	3.01400	+	1.97884i	0.139322	+	0.0914718i
$469$	−8.01804	−	3.70308i	−0.370238	−	0.170992i
$470$	−0.336667	+	1.25646i	−0.0155293	+	0.0579560i
$471$	4.66629	−	8.08225i	0.215011	−	0.372410i
$472$	−0.648975	−	1.12406i	−0.0298715	−	0.0517390i
$473$	−40.2997	+	10.7983i	−1.85298	+	0.496505i
$474$	−8.62755	+	8.62755i	−0.396276	+	0.396276i
$475$	0.716063	−	0.191869i	0.0328552	−	0.00880353i
$476$	19.9678	+	3.44529i	0.915224	+	0.157915i
$477$	−0.431525	+	0.747424i	−0.0197582	+	0.0342222i
$478$	−14.2910	−	8.25089i	−0.653653	−	0.377387i
$479$	17.6146	+	17.6146i	0.804833	+	0.804833i	0.983847	−	0.179014i	$-0.0572907\pi$
$479$	17.6146	+	17.6146i	0.804833	+	0.804833i	−0.179014	+	0.983847i	$0.557291\pi$
$480$	−1.48953	−	0.859981i	−0.0679875	−	0.0392526i
$481$	−18.8389	+	16.7926i	−0.858980	+	0.765676i
$482$		−	9.24751i		−	0.421213i
$483$	−2.85534	+	16.5486i	−0.129922	+	0.752988i
$484$	−10.3580	−	17.9405i	−0.470817	−	0.815479i
$485$		−	4.91952i		−	0.223384i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	−8.18459	+	30.5453i	−0.370879	+	1.38414i	0.488395	+	0.872623i	$0.337583\pi$
$487$	−8.18459	+	30.5453i	−0.370879	+	1.38414i	−0.859274	+	0.511516i	$0.829084\pi$
$488$	5.50883	+	5.50883i	0.249373	+	0.249373i
$489$	6.07415	+	6.07415i	0.274682	+	0.274682i
$490$	−9.16587	+	7.80653i	−0.414072	+	0.352663i
$491$	−6.01809	+	3.47455i	−0.271593	+	0.156804i	−0.629611	−	0.776910i	$-0.716786\pi$
$491$	−6.01809	+	3.47455i	−0.271593	+	0.156804i	0.358019	+	0.933714i	$0.383452\pi$
$492$	−2.33829	−	8.72661i	−0.105418	−	0.393426i
$493$	−29.9092	+	51.8043i	−1.34704	+	2.33315i
$494$	1.30697	+	0.0750586i	0.0588034	+	0.00337705i
$495$	8.38858	−	4.84315i	0.377039	−	0.217683i
$496$	0.143335	+	0.0384066i	0.00643595	+	0.00172451i
$497$	−32.3383	+	22.8210i	−1.45057	+	1.02366i
$498$	1.43456	+	0.828241i	0.0642840	+	0.0371144i
$499$	7.18554	−	26.8168i	0.321669	−	1.20049i	−0.595949	−	0.803022i	$-0.703224\pi$
$499$	7.18554	−	26.8168i	0.321669	−	1.20049i	0.917618	−	0.397463i	$-0.130109\pi$
$500$	11.6988	+	3.13469i	0.523187	+	0.140188i
$501$	−14.9831	−	4.01471i	−0.669396	−	0.179364i
$502$	6.27505	−	23.4188i	0.280069	−	1.04523i
$503$	−25.2684	−	14.5887i	−1.12666	−	0.650478i	−0.183568	−	0.983007i	$-0.558765\pi$
$503$	−25.2684	−	14.5887i	−1.12666	−	0.650478i	−0.943093	+	0.332529i	$0.892098\pi$
$504$	−1.10933	+	2.40196i	−0.0494134	+	0.106992i
$505$	11.7023	+	3.13563i	0.520747	+	0.139534i
$506$	30.9565	−	17.8728i	1.37619	−	0.794542i
$507$	−10.4402	−	7.74613i	−0.463665	−	0.344018i
$508$	1.77861	−	3.08064i	0.0789130	−	0.136681i
$509$	7.52241	+	28.0740i	0.333425	+	1.24436i	0.905567	+	0.424204i	$0.139446\pi$
$509$	7.52241	+	28.0740i	0.333425	+	1.24436i	−0.572142	+	0.820155i	$0.693887\pi$
$510$	11.4078	−	6.58629i	0.505145	−	0.291646i
$511$	−18.9043	+	13.3407i	−0.836276	+	0.590156i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.256740	+	0.256740i	0.0113354	+	0.0113354i
$514$	−2.62110	+	9.78209i	−0.115612	+	0.431469i
$515$	−3.00509	−	11.2152i	−0.132420	−	0.494199i
$516$		−	7.40831i		−	0.326133i
$517$	−2.12958	−	3.68854i	−0.0936588	−	0.162222i
$518$	−14.2298	−	11.8514i	−0.625222	−	0.520722i
$519$			4.55205i			0.199813i
$520$	5.18397	+	3.40353i	0.227332	+	0.149255i
$521$	−19.8371	−	11.4529i	−0.869077	−	0.501762i	−0.00203587	−	0.999998i	$-0.500648\pi$
$521$	−19.8371	−	11.4529i	−0.869077	−	0.501762i	−0.867042	+	0.498236i	$0.833981\pi$
$522$	−5.52291	−	5.52291i	−0.241731	−	0.241731i
$523$	−30.7302	−	17.7421i	−1.34374	−	0.775807i	−0.356384	−	0.934340i	$-0.615991\pi$
$523$	−30.7302	−	17.7421i	−1.34374	−	0.775807i	−0.987354	+	0.158532i	$0.949324\pi$
$524$	−8.88709	+	15.3929i	−0.388234	+	0.672442i
$525$	0.918486	−	5.32325i	0.0400860	−	0.232326i
$526$	−5.17192	+	1.38581i	−0.225507	+	0.0604243i
$527$	−0.803613	+	0.803613i	−0.0350059	+	0.0350059i
$528$	5.43980	−	1.45759i	0.236737	−	0.0634334i
$529$	8.64356	+	14.9711i	0.375807	+	0.650917i
$530$	−0.742207	+	1.28554i	−0.0322394	+	0.0558403i
$531$	−0.335934	+	1.25372i	−0.0145783	+	0.0544070i
$532$	0.0872392	+	0.956665i	0.00378230	+	0.0414767i
$533$	6.61295	+	31.8959i	0.286439	+	1.38156i
$534$	2.09327	+	3.62565i	0.0905847	+	0.156897i
$535$	20.8941	−	20.8941i	0.903333	−	0.903333i
$536$	−3.33813			−0.144185
$537$	−1.67598			−0.0723238
$538$	11.4964	−	11.4964i	0.495645	−	0.495645i
$539$	3.14726	−	39.2960i	0.135562	−	1.69260i
$540$	0.445159	+	1.66136i	0.0191566	+	0.0714934i
$541$	17.3492	+	4.64871i	0.745901	+	0.199864i	0.611699	−	0.791090i	$-0.290486\pi$
$541$	17.3492	+	4.64871i	0.745901	+	0.199864i	0.134202	+	0.990954i	$0.457153\pi$
$542$	16.4186	−	9.47928i	0.705239	−	0.407170i
$543$			1.85011i			0.0793958i
$544$	7.39768	−	1.98220i	0.317173	−	0.0849863i
$545$	−9.54451			−0.408842
$546$	4.48970	−	8.41680i	0.192141	−	0.360206i
$547$	13.7457			0.587723			0.293862	−	0.955848i	$-0.405060\pi$
$547$	13.7457			0.587723			0.293862	+	0.955848i	$0.405060\pi$
$548$	−7.45580	+	1.99778i	−0.318496	+	0.0853408i
$549$		−	7.79066i		−	0.332497i
$550$	−9.95790	+	5.74920i	−0.424606	+	0.245147i
$551$	−2.73928	−	0.733987i	−0.116697	−	0.0312689i
$552$	1.64278	+	6.13094i	0.0699214	+	0.260950i
$553$	24.8050	+	20.6591i	1.05482	+	0.878513i
$554$	3.23292	−	3.23292i	0.137354	−	0.137354i
$555$	−12.0387			−0.511016
$556$	−6.67532			−0.283096
$557$	−3.17599	+	3.17599i	−0.134571	+	0.134571i	−0.771184	−	0.636613i	$-0.780335\pi$
$557$	−3.17599	+	3.17599i	−0.134571	+	0.134571i	0.636613	+	0.771184i	$0.280335\pi$
$558$	−0.0741959	−	0.128511i	−0.00314096	−	0.00544031i
$559$	−1.53148	+	26.6671i	−0.0647746	+	1.12790i
$560$	−1.90800	+	4.13127i	−0.0806278	+	0.174578i
$561$	−11.1632	+	41.6615i	−0.471309	+	1.75895i
$562$	−0.232859	+	0.403323i	−0.00982255	+	0.0170132i
$563$	3.02684	+	5.24264i	0.127566	+	0.220951i	0.922733	−	0.385440i	$-0.125950\pi$
$563$	3.02684	+	5.24264i	0.127566	+	0.220951i	−0.795167	+	0.606390i	$0.792617\pi$
$564$	0.730514	−	0.195741i	0.0307602	−	0.00824217i
$565$	−14.6803	+	14.6803i	−0.617603	+	0.617603i
$566$	−20.2497	+	5.42590i	−0.851160	+	0.228068i
$567$	2.48285	−	0.914026i	0.104270	−	0.0383855i
$568$	−7.47989	+	12.9555i	−0.313849	+	0.543602i
$569$	19.9649	+	11.5267i	0.836973	+	0.483226i	0.856234	−	0.516588i	$-0.172798\pi$
$569$	19.9649	+	11.5267i	0.836973	+	0.483226i	−0.0192614	+	0.999814i	$0.506131\pi$
$570$	0.441584	+	0.441584i	0.0184959	+	0.0184959i
$571$	−23.8718	−	13.7824i	−0.999005	−	0.576776i	−0.0910513	−	0.995846i	$-0.529023\pi$
$571$	−23.8718	−	13.7824i	−0.999005	−	0.576776i	−0.907954	+	0.419070i	$0.862356\pi$
$572$	−19.8825	+	4.12223i	−0.831330	+	0.172359i
$573$		−	4.51532i		−	0.188630i
$574$	−22.4312	+	8.25772i	−0.936261	+	0.344671i
$575$	−6.47965	−	11.2231i	−0.270220	−	0.468035i
$576$			1.00000i			0.0416667i
$577$	−11.7744	−	43.9428i	−0.490176	−	1.82936i	−0.555524	−	0.831501i	$-0.687482\pi$
$577$	−11.7744	−	43.9428i	−0.490176	−	1.82936i	0.0653474	−	0.997863i	$-0.479184\pi$
$578$	−10.7811	+	40.2355i	−0.448433	+	1.67358i
$579$	−16.7057	−	16.7057i	−0.694265	−	0.694265i
$580$	−9.49919	−	9.49919i	−0.394433	−	0.394433i
$581$	1.83758	−	3.97880i	0.0762358	−	0.165068i
$582$	−2.47705	+	1.43013i	−0.102677	+	0.0592806i
$583$	−1.25797	−	4.69482i	−0.0520999	−	0.194439i
$584$	−4.37258	+	7.57354i	−0.180939	+	0.313395i
$585$	−1.25896	−	6.07227i	−0.0520516	−	0.251058i
$586$	−12.1589	+	7.01992i	−0.502278	+	0.289990i
$587$	−42.4335	−	11.3700i	−1.75142	−	0.469291i	−0.766489	−	0.642257i	$-0.777998\pi$
$587$	−42.4335	−	11.3700i	−1.75142	−	0.469291i	−0.984928	+	0.172966i	$0.944665\pi$
$588$	6.59526	+	2.34576i	0.271984	+	0.0967373i
$589$	−0.0466605	−	0.0269395i	−0.00192261	−	0.00111002i
$590$	−0.577794	+	2.15636i	−0.0237874	+	0.0887759i
$591$	17.9880	+	4.81988i	0.739929	+	0.198263i
$592$	−6.76092	−	1.81158i	−0.277872	−	0.0744557i
$593$	−3.48718	+	13.0143i	−0.143201	+	0.534434i	0.856628	+	0.515935i	$0.172555\pi$
$593$	−3.48718	+	13.0143i	−0.143201	+	0.534434i	−0.999829	+	0.0184992i	$0.994111\pi$
$594$	−4.87719	−	2.81585i	−0.200113	−	0.115536i
$595$	−20.0946	−	28.4750i	−0.823800	−	1.16736i
$596$	19.6203	+	5.25723i	0.803677	+	0.215345i
$597$	−11.2922	+	6.51955i	−0.462159	+	0.266828i
$598$	−4.64597	−	22.4086i	−0.189988	−	0.916358i
$599$	−7.08320	+	12.2685i	−0.289412	+	0.501276i	−0.973669	−	0.227965i	$-0.926793\pi$
$599$	−7.08320	+	12.2685i	−0.289412	+	0.501276i	0.684258	+	0.729240i	$0.260126\pi$
$600$	−0.528439	−	1.97216i	−0.0215734	−	0.0805131i
$601$	32.7519	−	18.9093i	1.33598	−	0.771327i	0.349769	−	0.936836i	$-0.386260\pi$
$601$	32.7519	−	18.9093i	1.33598	−	0.771327i	0.986208	+	0.165509i	$0.0529266\pi$
$602$	−19.5195	+	1.78001i	−0.795557	+	0.0725477i
$603$	2.36041	+	2.36041i	0.0961234	+	0.0961234i
$604$	10.4471	+	10.4471i	0.425085	+	0.425085i
$605$	−9.22189	+	34.4165i	−0.374923	+	1.39923i
$606$	−1.82308	−	6.80384i	−0.0740576	−	0.276387i
$607$		−	41.0746i		−	1.66717i	−0.552394	−	0.833583i	$-0.686286\pi$
$607$		−	41.0746i		−	1.66717i	0.552394	−	0.833583i	$-0.313714\pi$
$608$	0.181543	+	0.314441i	0.00736254	+	0.0127523i
$609$	−13.2249	+	15.8789i	−0.535899	+	0.643444i
$610$		−	13.3996i		−	0.542535i
$611$	−2.67004	+	0.553577i	−0.108018	+	0.0223953i
$612$	−6.63258	−	3.82932i	−0.268106	−	0.154791i
$613$	16.7901	+	16.7901i	0.678145	+	0.678145i	0.959580	−	0.281435i	$-0.0908104\pi$
$613$	16.7901	+	16.7901i	0.678145	+	0.678145i	−0.281435	+	0.959580i	$0.590810\pi$
$614$	−10.0197	−	5.78486i	−0.404361	−	0.233458i
$615$	−7.76946	+	13.4571i	−0.313295	+	0.542642i
$616$	−5.14751	−	13.9827i	−0.207399	−	0.563377i
$617$	−22.7619	+	6.09903i	−0.916358	+	0.245538i	−0.686028	−	0.727575i	$-0.740647\pi$
$617$	−22.7619	+	6.09903i	−0.916358	+	0.245538i	−0.230330	+	0.973113i	$0.573981\pi$
$618$	−4.77340	+	4.77340i	−0.192014	+	0.192014i
$619$	11.2303	−	3.00915i	0.451384	−	0.120948i	−0.0259629	−	0.999663i	$-0.508265\pi$
$619$	11.2303	−	3.00915i	0.451384	−	0.120948i	0.477347	+	0.878715i	$0.341599\pi$
$620$	−0.127614	−	0.221034i	−0.00512511	−	0.00887695i
$621$	3.17361	−	5.49685i	0.127352	−	0.220581i
$622$	0.398287	−	1.48643i	0.0159698	−	0.0596002i
$623$	9.04998	−	6.38653i	0.362580	−	0.255871i
$624$	0.206724	−	3.59962i	0.00827559	−	0.144100i
$625$	−5.31134	−	9.19952i	−0.212454	−	0.367981i
$626$	11.2594	−	11.2594i	0.450016	−	0.450016i
$627$	−2.04479			−0.0816609
$628$	−9.33257			−0.372410
$629$	37.9052	−	37.9052i	1.51138	−	1.51138i
$630$	4.27041	−	1.57209i	0.170137	−	0.0626336i
$631$	−2.59285	−	9.67665i	−0.103220	−	0.385222i	0.894917	−	0.446232i	$-0.147234\pi$
$631$	−2.59285	−	9.67665i	−0.103220	−	0.385222i	−0.998137	+	0.0610104i	$0.980568\pi$
$632$	11.7855	+	3.15790i	0.468800	+	0.125615i
$633$	13.9451	−	8.05119i	0.554267	−	0.320006i
$634$			2.62178i			0.104124i
$635$	−5.90980	+	1.58353i	−0.234523	+	0.0628403i
$636$	0.863050			0.0342222
$637$	−23.2555	−	9.80723i	−0.921416	−	0.388577i
$638$	43.9867			1.74145
$639$	14.4500	−	3.87187i	0.571634	−	0.153169i
$640$			1.71996i			0.0679875i
$641$	24.3035	−	14.0316i	0.959931	−	0.554216i	0.0637792	−	0.997964i	$-0.479685\pi$
$641$	24.3035	−	14.0316i	0.959931	−	0.554216i	0.896152	+	0.443748i	$0.146351\pi$
$642$	−16.5945	−	4.44649i	−0.654933	−	0.175489i
$643$	3.74858	+	13.9899i	0.147830	+	0.551708i	0.999613	+	0.0278139i	$0.00885459\pi$
$643$	3.74858	+	13.9899i	0.147830	+	0.551708i	−0.851783	+	0.523894i	$0.824479\pi$
$644$	15.7592	−	5.80152i	0.620999	−	0.228612i
$645$	−9.00996	+	9.00996i	−0.354767	+	0.354767i
$646$	−2.78074			−0.109407
$647$	3.35527			0.131909			0.0659545	−	0.997823i	$-0.478991\pi$
$647$	3.35527			0.131909			0.0659545	+	0.997823i	$0.478991\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−3.65483	−	6.33035i	−0.143465	−	0.248488i
$650$	1.49449	+	7.20827i	0.0586185	+	0.282732i
$651$	−0.320776	+	0.226370i	−0.0125722	+	0.00887215i
$652$	2.22329	−	8.29744i	0.0870708	−	0.324953i
$653$	−19.4159	+	33.6292i	−0.759801	+	1.31601i	0.183151	+	0.983085i	$0.441370\pi$
$653$	−19.4159	+	33.6292i	−0.759801	+	1.31601i	−0.942952	+	0.332929i	$0.891963\pi$
$654$	2.77463	+	4.80580i	0.108497	+	0.187922i
$655$	29.5292	−	7.91234i	1.15380	−	0.309161i
$656$	−6.38832	+	6.38832i	−0.249422	+	0.249422i
$657$	8.44718	−	2.26342i	0.329556	−	0.0883043i
$658$	−0.691263	−	1.87774i	−0.0269483	−	0.0732020i
$659$	−18.4258	+	31.9145i	−0.717769	+	1.24321i	0.244113	+	0.969747i	$0.421503\pi$
$659$	−18.4258	+	31.9145i	−0.717769	+	1.24321i	−0.961882	+	0.273465i	$0.911830\pi$
$660$	−8.38858	−	4.84315i	−0.326525	−	0.188519i
$661$	−14.7779	−	14.7779i	−0.574793	−	0.574793i	0.358671	−	0.933464i	$-0.383230\pi$
$661$	−14.7779	−	14.7779i	−0.574793	−	0.574793i	−0.933464	+	0.358671i	$0.883230\pi$
$662$	6.44612	+	3.72167i	0.250536	+	0.144647i
$663$	23.0832	+	15.1552i	0.896476	+	0.588580i
$664$		−	1.65648i		−	0.0642840i
$665$	1.05739	−	1.26959i	0.0410039	−	0.0492327i
$666$	3.49971	+	6.06168i	0.135611	+	0.234885i
$667$			49.5754i			1.91957i
$668$	4.01471	+	14.9831i	0.155334	+	0.579714i
$669$	3.55858	−	13.2808i	0.137583	−	0.513465i
$670$	4.05982	+	4.05982i	0.156845	+	0.156845i
$671$	31.0240	+	31.0240i	1.19767	+	1.19767i
$672$	2.63482	−	0.240272i	0.101640	−	0.00926868i
$673$	24.0567	−	13.8891i	0.927316	−	0.535386i	0.0413542	−	0.999145i	$-0.486833\pi$
$673$	24.0567	−	13.8891i	0.927316	−	0.535386i	0.885962	+	0.463758i	$0.153499\pi$
$674$	−4.84898	−	18.0966i	−0.186776	−	0.697056i
$675$	−1.02087	+	1.76819i	−0.0392931	+	0.0680577i
$676$	−1.48826	+	12.9145i	−0.0572407	+	0.496713i
$677$	11.4753	−	6.62524i	0.441030	−	0.254629i	−0.263004	−	0.964795i	$-0.584713\pi$
$677$	11.4753	−	6.62524i	0.441030	−	0.254629i	0.704034	+	0.710166i	$0.251380\pi$
$678$	11.6593	+	3.12411i	0.447774	+	0.119981i
$679$	4.36329	+	6.18296i	0.167448	+	0.237280i
$680$	−11.4078	−	6.58629i	−0.437469	−	0.252573i
$681$	−7.25905	+	27.0911i	−0.278167	+	1.03813i
$682$	0.807221	+	0.216294i	0.0309101	+	0.00828233i
$683$	9.74982	+	2.61246i	0.373067	+	0.0999629i	0.440480	−	0.897762i	$-0.354808\pi$
$683$	9.74982	+	2.61246i	0.373067	+	0.0999629i	−0.0674139	+	0.997725i	$0.521475\pi$
$684$	0.0939735	−	0.350714i	0.00359317	−	0.0134099i
$685$	11.4974	+	6.63803i	0.439294	+	0.253626i
$686$	4.59599	−	17.9409i	0.175476	−	0.684988i
$687$	14.1090	+	3.78049i	0.538291	+	0.144235i
$688$	−6.41578	+	3.70415i	−0.244599	+	0.141220i
$689$	−3.10665	−	0.178413i	−0.118354	−	0.00679701i
$690$	5.45848	−	9.45437i	0.207801	−	0.359922i
$691$	1.66274	+	6.20544i	0.0632537	+	0.236066i	0.990314	−	0.138846i	$-0.0443394\pi$
$691$	1.66274	+	6.20544i	0.0632537	+	0.236066i	−0.927060	+	0.374912i	$0.877673\pi$
$692$	3.94219	−	2.27602i	0.149859	−	0.0865214i
$693$	−6.24739	+	13.5271i	−0.237319	+	0.513851i
$694$	10.4380	+	10.4380i	0.396222	+	0.396222i
$695$	8.11850	+	8.11850i	0.307952	+	0.307952i
$696$	−2.02153	+	7.54443i	−0.0766257	+	0.285971i
$697$	−17.9081	−	66.8340i	−0.678318	−	2.53152i
$698$		−	22.9595i		−	0.869030i
$699$	0.310875	+	0.538452i	0.0117584	+	0.0203661i
$700$	−5.06932	+	1.86619i	−0.191602	+	0.0705355i
$701$		−	6.99459i		−	0.264182i	−0.991238	−	0.132091i	$-0.957831\pi$
$701$		−	6.99459i		−	0.264182i	0.991238	−	0.132091i	$-0.0421691\pi$
$702$	−2.69149	+	2.39914i	−0.101584	+	0.0905497i
$703$	2.20091	+	1.27070i	0.0830089	+	0.0479252i
$704$	−3.98221	−	3.98221i	−0.150085	−	0.150085i
$705$	−1.12651	−	0.650390i	−0.0424268	−	0.0244951i
$706$	9.16659	−	15.8770i	0.344989	−	0.597539i
$707$	−17.4888	+	6.43826i	−0.657735	+	0.242136i
$708$	1.25372	−	0.335934i	0.0471178	−	0.0126252i
$709$	10.6966	−	10.6966i	0.401721	−	0.401721i	−0.477118	−	0.878839i	$-0.658319\pi$
$709$	10.6966	−	10.6966i	0.401721	−	0.401721i	0.878839	+	0.477118i	$0.158319\pi$
$710$	24.8535	−	6.65948i	0.932735	−	0.249926i
$711$	−6.10060	−	10.5665i	−0.228790	−	0.396276i
$712$	2.09327	−	3.62565i	0.0784486	−	0.135877i
$713$	−0.243775	+	0.909781i	−0.00912945	+	0.0340716i
$714$	−8.49595	+	18.3957i	−0.317953	+	0.688443i
$715$	29.1945	+	19.1676i	1.09181	+	0.716828i
$716$	0.837989	+	1.45144i	0.0313171	+	0.0542428i
$717$	11.6685	−	11.6685i	0.435769	−	0.435769i
$718$	−11.1440			−0.415890
$719$	5.59107			0.208512			0.104256	−	0.994551i	$-0.466754\pi$
$719$	5.59107			0.208512			0.104256	+	0.994551i	$0.466754\pi$
$720$	1.21620	−	1.21620i	0.0453250	−	0.0453250i
$721$	13.7240	+	11.4301i	0.511107	+	0.425680i
$722$	4.88344	+	18.2253i	0.181743	+	0.678274i
$723$	8.93241	+	2.39343i	0.332200	+	0.0890127i
$724$	1.60224	−	0.925054i	0.0595468	−	0.0343794i
$725$		−	15.9471i		−	0.592260i
$726$	20.0101	−	5.36168i	0.742643	−	0.198991i
$727$	−21.2421			−0.787826			−0.393913	−	0.919148i	$-0.628879\pi$
$727$	−21.2421			−0.787826			−0.393913	+	0.919148i	$0.628879\pi$
$728$	−9.53402	+	0.320206i	−0.353354	+	0.0118676i
$729$	−1.00000			−0.0370370
$730$	14.5288	−	3.89299i	0.537736	−	0.144086i
$731$		−	56.7376i		−	2.09852i
$732$	−6.74691	+	3.89533i	−0.249373	+	0.143975i
$733$	−20.4271	−	5.47343i	−0.754492	−	0.202166i	−0.138983	−	0.990295i	$-0.544383\pi$
$733$	−20.4271	−	5.47343i	−0.754492	−	0.202166i	−0.615510	+	0.788129i	$0.711050\pi$
$734$	4.40949	+	16.4564i	0.162757	+	0.607418i
$735$	−5.16823	−	10.8740i	−0.190633	−	0.401095i
$736$	4.48816	−	4.48816i	0.165436	−	0.165436i
$737$	−18.7993			−0.692481
$738$	9.03445			0.332563
$739$	20.4324	−	20.4324i	0.751619	−	0.751619i	−0.223162	−	0.974781i	$-0.571638\pi$
$739$	20.4324	−	20.4324i	0.751619	−	0.751619i	0.974781	+	0.223162i	$0.0716380\pi$
$740$	6.01937	+	10.4259i	0.221277	+	0.383262i
$741$	−0.410770	+	1.24301i	−0.0150900	+	0.0456631i
$742$	−0.207367	−	2.27398i	−0.00761267	−	0.0834805i
$743$	−4.32089	+	16.1258i	−0.158518	+	0.591597i	0.840260	+	0.542183i	$0.182402\pi$
$743$	−4.32089	+	16.1258i	−0.158518	+	0.591597i	−0.998778	+	0.0494140i	$0.984265\pi$
$744$	−0.0741959	+	0.128511i	−0.00272015	+	0.00471144i
$745$	−17.4683	−	30.2559i	−0.639988	−	1.10849i
$746$	27.5990	−	7.39514i	1.01047	−	0.270755i
$747$	−1.17131	+	1.17131i	−0.0428560	+	0.0428560i
$748$	41.6615	−	11.1632i	1.52329	−	0.408165i
$749$	−7.72849	+	44.7919i	−0.282393	+	1.63666i
$750$	−6.05575	+	10.4889i	−0.221125	+	0.383000i
$751$	−1.67292	−	0.965861i	−0.0610457	−	0.0352448i	0.469167	−	0.883110i	$-0.344554\pi$
$751$	−1.67292	−	0.965861i	−0.0610457	−	0.0352448i	−0.530212	+	0.847865i	$0.677888\pi$
$752$	−0.534774	−	0.534774i	−0.0195012	−	0.0195012i
$753$	20.9967	+	12.1225i	0.765163	+	0.441767i
$754$	8.83634	−	26.7392i	0.321801	−	0.973784i
$755$		−	25.4114i		−	0.924814i
$756$	−2.03300	−	1.69320i	−0.0739393	−	0.0615811i
$757$	−4.58127	−	7.93499i	−0.166509	−	0.288402i	0.770681	−	0.637221i	$-0.219916\pi$
$757$	−4.58127	−	7.93499i	−0.166509	−	0.288402i	−0.937190	+	0.348819i	$0.886583\pi$
$758$			20.3367i			0.738662i
$759$	9.25163	+	34.5275i	0.335813	+	1.25327i
$760$	0.161631	−	0.603215i	0.00586297	−	0.0218809i
$761$	−1.03438	−	1.03438i	−0.0374961	−	0.0374961i	0.688110	−	0.725606i	$-0.258441\pi$
$761$	−1.03438	−	1.03438i	−0.0374961	−	0.0374961i	−0.725606	+	0.688110i	$0.758441\pi$
$762$	2.51533	+	2.51533i	0.0911209	+	0.0911209i
$763$	11.9957	−	8.46534i	0.434275	−	0.306466i
$764$	−3.91038	+	2.25766i	−0.141473	+	0.0816793i
$765$	3.40931	+	12.7237i	0.123264	+	0.460028i
$766$	4.25467	−	7.36930i	0.153727	−	0.266264i
$767$	−4.58238	+	0.950061i	−0.165460	+	0.0343047i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−6.35786	−	1.70358i	−0.229270	−	0.0614328i	0.142355	−	0.989816i	$-0.454533\pi$
$769$	−6.35786	−	1.70358i	−0.229270	−	0.0614328i	−0.371625	+	0.928383i	$0.621199\pi$
$770$	−10.7453	+	23.2661i	−0.387233	+	0.838450i
$771$	−8.77038	−	5.06358i	−0.315858	−	0.182360i
$772$	−6.11471	+	22.8204i	−0.220073	+	0.821325i
$773$	−20.9673	−	5.61817i	−0.754141	−	0.202071i	−0.138787	−	0.990322i	$-0.544320\pi$
$773$	−20.9673	−	5.61817i	−0.754141	−	0.202071i	−0.615354	+	0.788251i	$0.710987\pi$
$774$	7.15588	+	1.91741i	0.257213	+	0.0689199i
$775$	0.0784160	−	0.292652i	0.00281679	−	0.0105124i
$776$	2.47705	+	1.43013i	0.0889209	+	0.0513385i
$777$	15.1305	−	10.6776i	0.542805	−	0.383055i
$778$	18.5590	+	4.97286i	0.665372	+	0.178286i
$779$	2.84081	−	1.64014i	0.101782	−	0.0587641i
$780$	−4.62926	+	4.12643i	−0.165754	+	0.147750i
$781$	−42.1244	+	72.9616i	−1.50733	+	2.61077i
$782$	12.5815	+	46.9547i	0.449912	+	1.67910i
$783$	6.76416	−	3.90529i	0.241731	−	0.139564i
$784$	−1.26614	−	6.88454i	−0.0452195	−	0.245876i
$785$	11.3502	+	11.3502i	0.405108	+	0.405108i
$786$	−12.5682	−	12.5682i	−0.448294	−	0.448294i
$787$	0.230874	−	0.861634i	0.00822977	−	0.0307139i	−0.961689	−	0.274143i	$-0.911606\pi$
$787$	0.230874	−	0.861634i	0.00822977	−	0.0307139i	0.969919	+	0.243429i	$0.0782724\pi$
$788$	−4.81988	−	17.9880i	−0.171701	−	0.640797i
$789$		−	5.35437i		−	0.190621i
$790$	−10.4928	−	18.1741i	−0.373317	−	0.646604i
$791$	5.43005	−	31.4708i	0.193070	−	1.11897i
$792$			5.63169i			0.200113i
$793$	25.0916	−	12.6270i	0.891027	−	0.448396i
$794$	−26.7103	−	15.4212i	−0.947912	−	0.547277i
$795$	−1.04964	−	1.04964i	−0.0372269	−	0.0372269i
$796$	11.2922	+	6.51955i	0.400241	+	0.231079i
$797$	19.6735	−	34.0755i	0.696872	−	1.20702i	−0.272673	−	0.962107i	$-0.587908\pi$
$797$	19.6735	−	34.0755i	0.696872	−	1.20702i	0.969546	−	0.244911i	$-0.0787588\pi$
$798$	−0.946647	−	0.163337i	−0.0335109	−	0.00578205i
$799$	5.59475	−	1.49911i	0.197928	−	0.0530347i
$800$	−1.44372	+	1.44372i	−0.0510433	+	0.0510433i
$801$	−4.04389	+	1.08356i	−0.142884	+	0.0382856i
$802$	14.3187	+	24.8008i	0.505612	+	0.875746i
$803$	−24.6250	+	42.6518i	−0.868999	+	1.50515i
$804$	0.863971	−	3.22438i	0.0304699	−	0.113715i
$805$	−26.2221	−	12.1105i	−0.924207	−	0.426839i
$806$	0.293643	−	0.447253i	0.0103431	−	0.0157538i
$807$	8.12919	+	14.0802i	0.286161	+	0.495645i
$808$	−4.98075	+	4.98075i	−0.175222	+	0.175222i
$809$	−7.24225			−0.254624			−0.127312	−	0.991863i	$-0.540635\pi$
$809$	−7.24225			−0.254624			−0.127312	+	0.991863i	$0.540635\pi$
$810$	−1.71996			−0.0604333
$811$	30.3347	−	30.3347i	1.06520	−	1.06520i	0.0674741	−	0.997721i	$-0.478506\pi$
$811$	30.3347	−	30.3347i	1.06520	−	1.06520i	0.997721	−	0.0674741i	$-0.0214940\pi$
$812$	20.3639	+	3.51364i	0.714634	+	0.123305i
$813$	4.90684	+	18.3126i	0.172090	+	0.642249i
$814$	−38.0754	−	10.2023i	−1.33454	−	0.357590i
$815$	−12.7953	+	7.38736i	−0.448199	+	0.258768i
$816$			7.65864i			0.268106i
$817$	2.59820	−	0.696185i	0.0908994	−	0.0243564i
$818$	5.46573			0.191105
$819$	6.96799	+	6.51515i	0.243481	+	0.227658i
$820$	15.5389			0.542642
$821$	4.87932	−	1.30741i	0.170290	−	0.0456289i	−0.172667	−	0.984980i	$-0.555238\pi$
$821$	4.87932	−	1.30741i	0.170290	−	0.0456289i	0.342956	+	0.939351i	$0.388572\pi$
$822$		−	7.71881i		−	0.269225i
$823$	0.147828	−	0.0853485i	0.00515296	−	0.00297506i	−0.497421	−	0.867509i	$-0.665720\pi$
$823$	0.147828	−	0.0853485i	0.00515296	−	0.00297506i	0.502574	+	0.864534i	$0.332386\pi$
$824$	6.52059	+	1.74719i	0.227155	+	0.0608661i
$825$	−2.97600	−	11.1066i	−0.103611	−	0.386682i
$826$	−1.18636	−	3.22262i	−0.0412788	−	0.112129i
$827$	−6.15597	+	6.15597i	−0.214064	+	0.214064i	−0.805991	−	0.591927i	$-0.798367\pi$
$827$	−6.15597	+	6.15597i	−0.214064	+	0.214064i	0.591927	+	0.805991i	$0.298367\pi$
$828$	−6.34721			−0.220581
$829$	−8.78736			−0.305198			−0.152599	−	0.988288i	$-0.548764\pi$
$829$	−8.78736			−0.305198			−0.152599	+	0.988288i	$0.548764\pi$
$830$	−2.01461	+	2.01461i	−0.0699281	+	0.0699281i
$831$	2.28602	+	3.95951i	0.0793013	+	0.137354i
$832$	−3.22072	+	1.62078i	−0.111659	+	0.0561905i
$833$	50.5107	+	17.9653i	1.75009	+	0.622461i
$834$	1.72770	−	6.44786i	0.0598253	−	0.223271i
$835$	13.3397	−	23.1051i	0.461641	−	0.799585i
$836$	1.02239	+	1.77084i	0.0353602	+	0.0612457i
$837$	0.143335	−	0.0384066i	0.00495440	−	0.00132753i
$838$	10.0147	−	10.0147i	0.345950	−	0.345950i
$839$	25.4509	−	6.81955i	0.878663	−	0.235437i	0.208833	−	0.977951i	$-0.433034\pi$
$839$	25.4509	−	6.81955i	0.878663	−	0.235437i	0.669830	+	0.742515i	$0.266367\pi$
$840$	−3.49668	−	2.91224i	−0.120647	−	0.100482i
$841$	−16.0025	+	27.7172i	−0.551811	+	0.955765i
$842$	16.1476	+	9.32284i	0.556484	+	0.321286i
$843$	−0.329312	−	0.329312i	−0.0113421	−	0.0113421i
$844$	−13.9451	−	8.05119i	−0.480009	−	0.277133i
$845$	17.5166	−	13.8966i	0.602590	−	0.478057i
$846$			0.756284i			0.0260016i
$847$	−18.9349	−	51.4346i	−0.650611	−	1.76731i
$848$	−0.431525	−	0.747424i	−0.0148186	−	0.0256666i
$849$		−	20.9641i		−	0.719485i
$850$	−4.04712	−	15.1041i	−0.138815	−	0.518065i
$851$	11.4985	−	42.9130i	0.394164	−	1.47104i
$852$	−10.5782	−	10.5782i	−0.362402	−	0.362402i
$853$	31.4788	+	31.4788i	1.07781	+	1.07781i	0.996705	+	0.0811070i	$0.0258456\pi$
$853$	31.4788	+	31.4788i	1.07781	+	1.07781i	0.0811070	+	0.996705i	$0.474154\pi$
$854$	11.8846	+	16.8409i	0.406682	+	0.576285i
$855$	−0.540827	+	0.312247i	−0.0184959	+	0.0106786i
$856$	4.44649	+	16.5945i	0.151978	+	0.567189i
$857$	12.9532	−	22.4355i	0.442471	−	0.766383i	−0.555401	−	0.831583i	$-0.687435\pi$
$857$	12.9532	−	22.4355i	0.442471	−	0.766383i	0.997872	+	0.0651999i	$0.0207685\pi$
$858$	1.16421	−	20.2719i	0.0397454	−	0.692073i
$859$	20.7081	−	11.9558i	0.706552	−	0.407928i	−0.103231	−	0.994657i	$-0.532918\pi$
$859$	20.7081	−	11.9558i	0.706552	−	0.407928i	0.809783	+	0.586730i	$0.199585\pi$
$860$	12.3078	+	3.29787i	0.419694	+	0.112457i
$861$	−2.17072	−	23.8041i	−0.0739781	−	0.811243i
$862$	−12.4376	−	7.18086i	−0.423627	−	0.244581i
$863$	−10.2488	+	38.2491i	−0.348874	+	1.30201i	0.539148	+	0.842211i	$0.318746\pi$
$863$	−10.2488	+	38.2491i	−0.348874	+	1.30201i	−0.888021	+	0.459803i	$0.847920\pi$
$864$	−0.965926	−	0.258819i	−0.0328615	−	0.00880520i
$865$	−7.56257	−	2.02638i	−0.257135	−	0.0688991i
$866$	5.70052	−	21.2746i	0.193712	−	0.722942i
$867$	−36.0741	−	20.8274i	−1.22514	−	0.707336i
$868$	0.356431	+	0.164615i	0.0120980	+	0.00558740i
$869$	66.3720	+	17.7843i	2.25152	+	0.603292i
$870$	11.6341	−	6.71695i	0.394433	−	0.227726i
$871$	−3.77653	+	11.4280i	−0.127963	+	0.387221i
$872$	2.77463	−	4.80580i	0.0939608	−	0.162745i
$873$	−0.740288	−	2.76279i	−0.0250549	−	0.0935063i
$874$	−1.99583	+	1.15229i	−0.0675099	+	0.0389768i
$875$	29.0913	+	13.4356i	0.983466	+	0.454207i
$876$	−6.18377	−	6.18377i	−0.208930	−	0.208930i
$877$	6.86482	+	6.86482i	0.231808	+	0.231808i	0.813447	−	0.581639i	$-0.197588\pi$
$877$	6.86482	+	6.86482i	0.231808	+	0.231808i	−0.581639	+	0.813447i	$0.697588\pi$
$878$	−3.42168	+	12.7699i	−0.115476	+	0.430963i
$879$	−3.63378	−	13.5614i	−0.122564	−	0.457416i
$880$			9.68629i			0.326525i
$881$	10.0018	+	17.3236i	0.336969	+	0.583648i	0.983861	−	0.178934i	$-0.0572649\pi$
$881$	10.0018	+	17.3236i	0.336969	+	0.583648i	−0.646892	+	0.762582i	$0.723932\pi$
$882$	−3.97280	+	5.76340i	−0.133771	+	0.194064i
$883$		−	39.4548i		−	1.32776i	−0.747839	−	0.663880i	$-0.768908\pi$
$883$		−	39.4548i		−	1.32776i	0.747839	−	0.663880i	$-0.231092\pi$
$884$	1.58323	−	27.5682i	0.0532497	−	0.927219i
$885$	−1.93334	−	1.11621i	−0.0649884	−	0.0375211i
$886$	−25.2340	−	25.2340i	−0.847752	−	0.847752i
$887$	−2.54698	−	1.47050i	−0.0855193	−	0.0493746i	0.456630	−	0.889656i	$-0.349056\pi$
$887$	−2.54698	−	1.47050i	−0.0855193	−	0.0493746i	−0.542150	+	0.840282i	$0.682389\pi$
$888$	3.49971	−	6.06168i	0.117443	−	0.203417i
$889$	6.02308	−	7.23181i	0.202008	−	0.242547i
$890$	−6.95533	+	1.86368i	−0.233143	+	0.0624706i
$891$	3.98221	−	3.98221i	0.133409	−	0.133409i
$892$	−13.2808	+	3.55858i	−0.444674	+	0.119150i
$893$	0.137298	+	0.237807i	0.00459450	+	0.00795791i
$894$	−10.1562	+	17.5910i	−0.339674	+	0.588333i
$895$	0.746077	−	2.78440i	0.0249386	−	0.0930721i
$896$	−1.52549	−	2.16168i	−0.0509631	−	0.0722168i
$897$	22.8476	+	1.31212i	0.762858	+	0.0438105i
$898$	−2.55648	−	4.42796i	−0.0853109	−	0.147763i
$899$	−0.819555	+	0.819555i	−0.0273337	+	0.0273337i
$900$	2.04173			0.0680577
$901$	6.60980			0.220204
$902$	−35.9771	+	35.9771i	−1.19790	+	1.19790i
$903$	3.33268	−	19.3151i	0.110905	−	0.642768i
$904$	−3.12411	−	11.6593i	−0.103906	−	0.387783i
$905$	−3.07369	−	0.823593i	−0.102173	−	0.0273771i
$906$	−12.7950	+	7.38719i	−0.425085	+	0.245423i
$907$			23.6994i			0.786926i	0.919341	+	0.393463i	$0.128723\pi$
$907$			23.6994i			0.786926i	−0.919341	+	0.393463i	$0.871277\pi$
$908$	27.0911	−	7.25905i	0.899051	−	0.240900i
$909$	7.04385			0.233630
$910$	11.9847	+	11.2058i	0.397288	+	0.371469i
$911$	28.7034			0.950985			0.475493	−	0.879720i	$-0.342270\pi$
$911$	28.7034			0.950985			0.475493	+	0.879720i	$0.342270\pi$
$912$	−0.350714	+	0.0939735i	−0.0116133	+	0.00311177i
$913$		−	9.32880i		−	0.308738i
$914$	−17.8929	+	10.3305i	−0.591844	+	0.341701i
$915$	12.9431	+	3.46808i	0.427884	+	0.114651i
$916$	−3.78049	−	14.1090i	−0.124911	−	0.466174i
$917$	−30.0952	+	36.1348i	−0.993833	+	1.19328i
$918$	5.41548	−	5.41548i	0.178737	−	0.178737i
$919$	5.08008			0.167576			0.0837882	−	0.996484i	$-0.473298\pi$
$919$	5.08008			0.167576			0.0837882	+	0.996484i	$0.473298\pi$
$920$	−10.9170			−0.359922
$921$	8.18103	−	8.18103i	0.269574	−	0.269574i
$922$	−3.71673	−	6.43757i	−0.122404	−	0.212010i
$923$	35.8906	+	40.2641i	1.18135	+	1.32531i
$924$	14.8385	−	1.35314i	0.488150	−	0.0445149i
$925$	−3.69877	+	13.8040i	−0.121615	+	0.453872i
$926$	1.81912	−	3.15080i	0.0597799	−	0.103542i
$927$	−3.37530	−	5.84620i	−0.110860	−	0.192014i
$928$	7.54443	−	2.02153i	0.247658	−	0.0663598i
$929$	16.4989	−	16.4989i	0.541312	−	0.541312i	−0.382601	−	0.923914i	$-0.624972\pi$
$929$	16.4989	−	16.4989i	0.541312	−	0.541312i	0.923914	+	0.382601i	$0.124972\pi$
$930$	0.246532	−	0.0660579i	0.00808409	−	0.00216613i
$931$	−0.202910	+	2.53349i	−0.00665010	+	0.0830317i
$932$	0.310875	−	0.538452i	0.0101831	−	0.0176376i
$933$	1.33269	+	0.769431i	0.0436304	+	0.0251900i
$934$	−7.06427	−	7.06427i	−0.231150	−	0.231150i
$935$	−64.2451	−	37.0919i	−2.10104	−	1.21304i
$936$	3.42346	+	1.13133i	0.111899	+	0.0369787i
$937$			24.6163i			0.804180i	0.915600	+	0.402090i	$0.131716\pi$
$937$			24.6163i			0.804180i	−0.915600	+	0.402090i	$0.868284\pi$
$938$	−8.70325	−	1.50168i	−0.284171	−	0.0490316i
$939$	7.96159	+	13.7899i	0.259817	+	0.450016i
$940$			1.30078i			0.0424268i
$941$	1.05349	+	3.93169i	0.0343429	+	0.128169i	0.980969	−	0.194164i	$-0.0621994\pi$
$941$	1.05349	+	3.93169i	0.0343429	+	0.128169i	−0.946626	+	0.322334i	$0.895533\pi$
$942$	2.41545	−	9.01457i	0.0786995	−	0.293711i
$943$	−40.5480	−	40.5480i	−1.32043	−	1.32043i
$944$	−0.917790	−	0.917790i	−0.0298715	−	0.0298715i
$945$	0.413258	+	4.53179i	0.0134433	+	0.147419i
$946$	−36.1317	+	20.8607i	−1.17474	+	0.678238i
$947$	−4.91693	−	18.3502i	−0.159779	−	0.596303i	−0.998649	−	0.0519705i	$-0.983450\pi$
$947$	−4.91693	−	18.3502i	−0.159779	−	0.596303i	0.838870	−	0.544332i	$-0.183217\pi$
$948$	−6.10060	+	10.5665i	−0.198138	+	0.343186i
$949$	20.9809	+	23.5375i	0.681068	+	0.764061i
$950$	0.642005	−	0.370662i	0.0208294	−	0.0120258i
$951$	−2.53244	−	0.678566i	−0.0821201	−	0.0220040i
$952$	20.1791	−	1.84016i	0.654010	−	0.0596398i
$953$	−15.4454	−	8.91740i	−0.500325	−	0.288863i	0.228523	−	0.973539i	$-0.426611\pi$
$953$	−15.4454	−	8.91740i	−0.500325	−	0.288863i	−0.728848	+	0.684676i	$0.759944\pi$
$954$	−0.223374	+	0.833643i	−0.00723200	+	0.0269902i
$955$	7.50156	+	2.01004i	0.242745	+	0.0650433i
$956$	−15.9395	−	4.27097i	−0.515520	−	0.138133i
$957$	−11.3846	+	42.4879i	−0.368012	+	1.37344i
$958$	21.5734	+	12.4554i	0.697006	+	0.402416i
$959$	−20.3377	+	1.85461i	−0.656738	+	0.0598886i
$960$	−1.66136	−	0.445159i	−0.0536200	−	0.0143674i
$961$	26.8277	−	15.4890i	0.865410	−	0.499645i
$962$	−13.8507	+	21.0963i	−0.446565	+	0.680171i
$963$	8.58995	−	14.8782i	0.276807	−	0.479444i
$964$	−2.39343	−	8.93241i	−0.0770873	−	0.287694i
$965$	35.1908	−	20.3174i	1.13283	−	0.654041i
$966$	1.52506	+	16.7238i	0.0490679	+	0.538078i
$967$	19.2108	+	19.2108i	0.617778	+	0.617778i	0.944961	−	0.327183i	$-0.106099\pi$
$967$	19.2108	+	19.2108i	0.617778	+	0.617778i	−0.327183	+	0.944961i	$0.606099\pi$
$968$	−14.6484	−	14.6484i	−0.470817	−	0.470817i
$969$	0.719710	−	2.68599i	0.0231204	−	0.0862865i
$970$	−1.27327	−	4.75190i	−0.0408821	−	0.152574i
$971$		−	57.3048i		−	1.83900i	−0.393091	−	0.919500i	$-0.628594\pi$
$971$		−	57.3048i		−	1.83900i	0.393091	−	0.919500i	$-0.371406\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−17.4041	−	3.00293i	−0.557949	−	0.0962697i
$974$			31.6228i			1.01326i
$975$	−7.34945	−	0.422075i	−0.235371	−	0.0135172i
$976$	6.74691	+	3.89533i	0.215963	+	0.124686i
$977$	26.7071	+	26.7071i	0.854437	+	0.854437i	0.990676	−	0.136239i	$-0.0435014\pi$
$977$	26.7071	+	26.7071i	0.854437	+	0.854437i	−0.136239	+	0.990676i	$0.543501\pi$
$978$	7.43928	+	4.29507i	0.237882	+	0.137341i
$979$	11.7887	−	20.4185i	0.376767	−	0.652580i
$980$	−6.83307	+	9.91284i	−0.218275	+	0.316654i
$981$	−5.36017	+	1.43625i	−0.171137	+	0.0458560i
$982$	−4.91375	+	4.91375i	−0.156804	+	0.156804i
$983$	2.40262	−	0.643779i	0.0766316	−	0.0205334i	−0.220300	−	0.975432i	$-0.570703\pi$
$983$	2.40262	−	0.643779i	0.0766316	−	0.0205334i	0.296931	+	0.954899i	$0.404037\pi$
$984$	−4.51723	−	7.82407i	−0.144004	−	0.249422i
$985$	−16.0151	+	27.7389i	−0.510282	+	0.883835i
$986$	−15.4821	+	57.7801i	−0.493052	+	1.84009i
$987$	1.99267	−	0.181714i	0.0634274	−	0.00578401i
$988$	1.28186	−	0.265768i	0.0407815	−	0.00845520i
$989$	−23.5111	−	40.7223i	−0.747608	−	1.29490i
$990$	6.84924	−	6.84924i	0.217683	−	0.217683i
$991$	17.6812			0.561662			0.280831	−	0.959757i	$-0.409390\pi$
$991$	17.6812			0.561662			0.280831	+	0.959757i	$0.409390\pi$
$992$	0.148392			0.00471144
$993$	−5.26324	+	5.26324i	−0.167024	+	0.167024i
$994$	−25.3299	+	30.4132i	−0.803415	+	0.964647i
$995$	−5.80448	−	21.6626i	−0.184014	−	0.686751i
$996$	1.60004	+	0.428729i	0.0506992	+	0.0135848i
$997$	16.2579	−	9.38651i	0.514893	−	0.297274i	−0.219949	−	0.975511i	$-0.570589\pi$
$997$	16.2579	−	9.38651i	0.514893	−	0.297274i	0.734843	+	0.678237i	$0.237256\pi$
$998$		−	27.7628i		−	0.878816i
$999$	−6.76092	+	1.81158i	−0.213906	+	0.0573160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.115.7	yes	40
7.5	odd	6		546.2.cg.b.271.2	yes	40
13.6	odd	12		546.2.cg.b.409.2	yes	40
91.19	even	12	inner	546.2.by.b.19.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.7	✓	40	91.19	even	12	inner
546.2.by.b.115.7	yes	40	1.1	even	1	trivial
546.2.cg.b.271.2	yes	40	7.5	odd	6
546.2.cg.b.409.2	yes	40	13.6	odd	12

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.66136 - 0.445159i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.48285 - 0.914026i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.66136 - 0.445159i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.48285 - 0.914026i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.71996 q^{10} +(3.98221 - 3.98221i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.62078 - 3.22072i) q^{13} +(2.16168 - 1.52549i) q^{14} +(0.445159 - 1.66136i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.82932 + 6.63258i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-0.256740 + 0.256740i) q^{19} +(-1.66136 + 0.445159i) q^{20} +(0.914026 + 2.48285i) q^{21} +(2.81585 - 4.87719i) q^{22} +(5.49685 + 3.17361i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-1.76819 - 1.02087i) q^{25} +(-2.39914 - 2.69149i) q^{26} -1.00000i q^{27} +(1.69320 - 2.03300i) q^{28} +(3.90529 + 6.76416i) q^{29} -1.71996i q^{30} +(0.0384066 + 0.143335i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.98221 + 3.98221i) q^{33} +(5.41548 + 5.41548i) q^{34} +(-4.53179 + 0.413258i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.81158 - 6.76092i) q^{37} +(-0.181543 + 0.314441i) q^{38} +(3.22072 - 1.62078i) q^{39} +(-1.48953 + 0.859981i) q^{40} +(-8.72661 - 2.33829i) q^{41} +(1.52549 + 2.16168i) q^{42} +(-6.41578 - 3.70415i) q^{43} +(1.45759 - 5.43980i) q^{44} +(1.66136 + 0.445159i) q^{45} +(6.13094 + 1.64278i) q^{46} +(0.195741 - 0.730514i) q^{47} +(0.866025 + 0.500000i) q^{48} +(5.32911 - 4.53878i) q^{49} +(-1.97216 - 0.528439i) q^{50} +(-6.63258 + 3.82932i) q^{51} +(-3.01400 - 1.97884i) q^{52} +(0.431525 - 0.747424i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(-8.38858 + 4.84315i) q^{55} +(1.10933 - 2.40196i) q^{56} +(-0.256740 - 0.256740i) q^{57} +(5.52291 + 5.52291i) q^{58} +(0.335934 - 1.25372i) q^{59} +(-0.445159 - 1.66136i) q^{60} +7.79066i q^{61} +(0.0741959 + 0.128511i) q^{62} +(-2.48285 + 0.914026i) q^{63} -1.00000i q^{64} +(1.25896 + 6.07227i) q^{65} +(4.87719 + 2.81585i) q^{66} +(-2.36041 - 2.36041i) q^{67} +(6.63258 + 3.82932i) q^{68} +(-3.17361 + 5.49685i) q^{69} +(-4.27041 + 1.57209i) q^{70} +(-14.4500 + 3.87187i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-8.44718 + 2.26342i) q^{73} +(-3.49971 - 6.06168i) q^{74} +(1.02087 - 1.76819i) q^{75} +(-0.0939735 + 0.350714i) q^{76} +(6.24739 - 13.5271i) q^{77} +(2.69149 - 2.39914i) q^{78} +(6.10060 + 10.5665i) q^{79} +(-1.21620 + 1.21620i) q^{80} +1.00000 q^{81} -9.03445 q^{82} +(1.17131 - 1.17131i) q^{83} +(2.03300 + 1.69320i) q^{84} +(-3.40931 - 12.7237i) q^{85} +(-7.15588 - 1.91741i) q^{86} +(-6.76416 + 3.90529i) q^{87} -5.63169i q^{88} +(4.04389 - 1.08356i) q^{89} +1.71996 q^{90} +(-6.96799 - 6.51515i) q^{91} +6.34721 q^{92} +(-0.143335 + 0.0384066i) q^{93} -0.756284i q^{94} +(0.540827 - 0.312247i) q^{95} +(0.965926 + 0.258819i) q^{96} +(0.740288 + 2.76279i) q^{97} +(3.97280 - 5.76340i) q^{98} +(-3.98221 + 3.98221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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