LMFDB - Embedded newform 546.2.bw.a.527.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.1
Character	$\chi$	$=$	546.527
Dual form			546.2.bw.a.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-1.73082 - 0.0653915i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.871657 - 3.25307i) q^{5} +(1.65492 + 0.511132i) q^{6} +(2.27642 + 1.34830i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99145 + 0.226361i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.73082 - 0.0653915i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.871657 - 3.25307i) q^{5} +(1.65492 + 0.511132i) q^{6} +(2.27642 + 1.34830i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99145 + 0.226361i) q^{9} +3.36782i q^{10} +(2.92157 + 2.92157i) q^{11} +(-1.46623 - 0.922039i) q^{12} +(-3.57579 - 0.462333i) q^{13} +(-1.84988 - 1.89154i) q^{14} +(1.29595 + 5.68746i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.08476 - 3.61090i) q^{17} +(-2.83093 - 0.992892i) q^{18} +(3.94280 + 3.94280i) q^{19} +(0.871657 - 3.25307i) q^{20} +(-3.85189 - 2.48253i) q^{21} +(-2.06586 - 3.57818i) q^{22} +(-2.51982 - 4.36445i) q^{23} +(1.17763 + 1.27011i) q^{24} +(-5.49254 + 3.17112i) q^{25} +(3.33428 + 1.37206i) q^{26} +(-5.16284 - 0.587405i) q^{27} +(1.29728 + 2.30587i) q^{28} +(3.13983 + 1.81278i) q^{29} +(0.220227 - 5.82908i) q^{30} +(2.23809 - 8.35267i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-4.86565 - 5.24774i) q^{33} +(-2.94829 + 2.94829i) q^{34} +(2.40187 - 8.58060i) q^{35} +(2.47749 + 1.69176i) q^{36} +(0.231818 + 0.0621155i) q^{37} +(-2.78798 - 4.82892i) q^{38} +(6.15880 + 1.03404i) q^{39} +(-1.68391 + 2.91662i) q^{40} +(-2.85709 - 10.6628i) q^{41} +(3.07812 + 3.39488i) q^{42} +(6.26650 - 3.61796i) q^{43} +(1.06937 + 3.99094i) q^{44} +(-1.87115 - 9.92870i) q^{45} +(1.30435 + 4.86791i) q^{46} +(5.61788 - 1.50531i) q^{47} +(-0.808777 - 1.53163i) q^{48} +(3.36415 + 6.13861i) q^{49} +(6.12614 - 1.64149i) q^{50} +(-3.84445 + 6.11348i) q^{51} +(-2.86556 - 2.18829i) q^{52} +(3.10829 - 1.79457i) q^{53} +(4.83489 + 1.90363i) q^{54} +(6.95746 - 12.0507i) q^{55} +(-0.656275 - 2.56307i) q^{56} +(-6.56643 - 7.08208i) q^{57} +(-2.56366 - 2.56366i) q^{58} +(-10.9572 + 2.93597i) q^{59} +(-1.72140 + 5.57346i) q^{60} -1.15674 q^{61} +(-4.32366 + 7.48880i) q^{62} +(6.50458 + 4.54868i) q^{63} +1.00000i q^{64} +(1.61286 + 12.0353i) q^{65} +(3.34164 + 6.32825i) q^{66} +(-9.42271 - 9.42271i) q^{67} +(3.61090 - 2.08476i) q^{68} +(4.07594 + 7.71884i) q^{69} +(-4.54085 + 7.66657i) q^{70} +(-3.17072 - 0.849592i) q^{71} +(-1.95521 - 2.27533i) q^{72} +(0.984725 + 0.263856i) q^{73} +(-0.207843 - 0.119998i) q^{74} +(9.71395 - 5.12946i) q^{75} +(1.44316 + 5.38596i) q^{76} +(2.71154 + 10.5899i) q^{77} +(-5.68131 - 2.59282i) q^{78} +(5.85567 - 10.1423i) q^{79} +(2.38141 - 2.38141i) q^{80} +(8.89752 + 1.35430i) q^{81} +11.0390i q^{82} +(3.09157 - 3.09157i) q^{83} +(-2.09457 - 4.07588i) q^{84} +(-13.5637 - 3.63438i) q^{85} +(-6.98937 + 1.87280i) q^{86} +(-5.31593 - 3.34291i) q^{87} -4.13172i q^{88} +(-3.39178 + 12.6583i) q^{89} +(-0.762346 + 10.0747i) q^{90} +(-7.51662 - 5.87371i) q^{91} -5.03964i q^{92} +(-4.41992 + 14.3106i) q^{93} -5.81606 q^{94} +(9.38943 - 16.2630i) q^{95} +(0.384805 + 1.68876i) q^{96} +(2.87528 - 10.7307i) q^{97} +(-1.66073 - 6.80015i) q^{98} +(8.07839 + 9.40105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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
$3$	−1.73082	−	0.0653915i	−0.999287	−	0.0377538i
$3$	−1.73082	−	0.0653915i	−0.999287	−	0.0377538i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.871657	−	3.25307i	−0.389817	−	1.45482i	−0.830432	−	0.557120i	$-0.811906\pi$
$5$	−0.871657	−	3.25307i	−0.389817	−	1.45482i	0.440615	−	0.897696i	$-0.354760\pi$
$6$	1.65492	+	0.511132i	0.675616	+	0.208669i
$7$	2.27642	+	1.34830i	0.860405	+	0.509611i
$7$	2.27642	+	1.34830i	0.860405	+	0.509611i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.99145	+	0.226361i	0.997149	+	0.0754538i
$10$			3.36782i			1.06500i
$11$	2.92157	+	2.92157i	0.880886	+	0.880886i	0.993625	−	0.112739i	$-0.0359623\pi$
$11$	2.92157	+	2.92157i	0.880886	+	0.880886i	−0.112739	+	0.993625i	$0.535962\pi$
$12$	−1.46623	−	0.922039i	−0.423266	−	0.266170i
$13$	−3.57579	−	0.462333i	−0.991745	−	0.128228i
$13$	−3.57579	−	0.462333i	−0.991745	−	0.128228i
$14$	−1.84988	−	1.89154i	−0.494402	−	0.505536i
$15$	1.29595	+	5.68746i	0.334614	+	1.46850i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.08476	−	3.61090i	0.505628	−	0.875773i	−0.494351	−	0.869262i	$-0.664594\pi$
$17$	2.08476	−	3.61090i	0.505628	−	0.875773i	0.999979	−	0.00651033i	$-0.00207232\pi$
$18$	−2.83093	−	0.992892i	−0.667257	−	0.234027i
$19$	3.94280	+	3.94280i	0.904540	+	0.904540i	0.995825	−	0.0912848i	$-0.0290974\pi$
$19$	3.94280	+	3.94280i	0.904540	+	0.904540i	−0.0912848	+	0.995825i	$0.529097\pi$
$20$	0.871657	−	3.25307i	0.194908	−	0.727408i
$21$	−3.85189	−	2.48253i	−0.840552	−	0.541731i
$22$	−2.06586	−	3.57818i	−0.440443	−	0.762869i
$23$	−2.51982	−	4.36445i	−0.525418	−	0.910051i	−0.999562	−	0.0296037i	$-0.990575\pi$
$23$	−2.51982	−	4.36445i	−0.525418	−	0.910051i	0.474143	−	0.880448i	$-0.342758\pi$
$24$	1.17763	+	1.27011i	0.240383	+	0.259260i
$25$	−5.49254	+	3.17112i	−1.09851	+	0.634224i
$26$	3.33428	+	1.37206i	0.653907	+	0.269083i
$27$	−5.16284	−	0.587405i	−0.993590	−	0.113046i
$28$	1.29728	+	2.30587i	0.245163	+	0.435769i
$29$	3.13983	+	1.81278i	0.583052	+	0.336625i	0.762345	−	0.647171i	$-0.224048\pi$
$29$	3.13983	+	1.81278i	0.583052	+	0.336625i	−0.179294	+	0.983796i	$0.557381\pi$
$30$	0.220227	−	5.82908i	0.0402078	−	1.06424i
$31$	2.23809	−	8.35267i	0.401973	−	1.50018i	−0.407598	−	0.913162i	$-0.633633\pi$
$31$	2.23809	−	8.35267i	0.401973	−	1.50018i	0.809571	−	0.587022i	$-0.199700\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−4.86565	−	5.24774i	−0.847001	−	0.913515i
$34$	−2.94829	+	2.94829i	−0.505628	+	0.505628i
$35$	2.40187	−	8.58060i	0.405990	−	1.45039i
$36$	2.47749	+	1.69176i	0.412915	+	0.281960i
$37$	0.231818	+	0.0621155i	0.0381107	+	0.0102117i	0.277824	−	0.960632i	$-0.410387\pi$
$37$	0.231818	+	0.0621155i	0.0381107	+	0.0102117i	−0.239713	+	0.970844i	$0.577053\pi$
$38$	−2.78798	−	4.82892i	−0.452270	−	0.783355i
$39$	6.15880	+	1.03404i	0.986197	+	0.165579i
$40$	−1.68391	+	2.91662i	−0.266250	+	0.461158i
$41$	−2.85709	−	10.6628i	−0.446203	−	1.66525i	−0.712741	−	0.701428i	$-0.752546\pi$
$41$	−2.85709	−	10.6628i	−0.446203	−	1.66525i	0.266538	−	0.963825i	$-0.414120\pi$
$42$	3.07812	+	3.39488i	0.474964	+	0.523841i
$43$	6.26650	−	3.61796i	0.955632	−	0.551734i	0.0608058	−	0.998150i	$-0.480633\pi$
$43$	6.26650	−	3.61796i	0.955632	−	0.551734i	0.894826	+	0.446415i	$0.147300\pi$
$44$	1.06937	+	3.99094i	0.161213	+	0.601656i
$45$	−1.87115	−	9.92870i	−0.278934	−	1.48008i
$46$	1.30435	+	4.86791i	0.192316	+	0.717735i
$47$	5.61788	−	1.50531i	0.819452	−	0.219571i	0.175345	−	0.984507i	$-0.443896\pi$
$47$	5.61788	−	1.50531i	0.819452	−	0.219571i	0.644107	+	0.764936i	$0.277229\pi$
$48$	−0.808777	−	1.53163i	−0.116737	−	0.221071i
$49$	3.36415	+	6.13861i	0.480593	+	0.876944i
$50$	6.12614	−	1.64149i	0.866367	−	0.232142i
$51$	−3.84445	+	6.11348i	−0.538331	+	0.856059i
$52$	−2.86556	−	2.18829i	−0.397381	−	0.303461i
$53$	3.10829	−	1.79457i	0.426957	−	0.246504i	−0.271092	−	0.962553i	$-0.587385\pi$
$53$	3.10829	−	1.79457i	0.426957	−	0.246504i	0.698049	+	0.716050i	$0.254052\pi$
$54$	4.83489	+	1.90363i	0.657946	+	0.259052i
$55$	6.95746	−	12.0507i	0.938143	−	1.62491i
$56$	−0.656275	−	2.56307i	−0.0876984	−	0.342504i
$57$	−6.56643	−	7.08208i	−0.869745	−	0.938045i
$58$	−2.56366	−	2.56366i	−0.336625	−	0.336625i
$59$	−10.9572	+	2.93597i	−1.42651	+	0.382231i	−0.887787	−	0.460255i	$-0.847758\pi$
$59$	−10.9572	+	2.93597i	−1.42651	+	0.382231i	−0.538718	+	0.842486i	$0.681091\pi$
$60$	−1.72140	+	5.57346i	−0.222232	+	0.719531i
$61$	−1.15674			−0.148105			−0.0740524	−	0.997254i	$-0.523593\pi$
$61$	−1.15674			−0.148105			−0.0740524	+	0.997254i	$0.523593\pi$
$62$	−4.32366	+	7.48880i	−0.549105	+	0.951079i
$63$	6.50458	+	4.54868i	0.819500	+	0.573079i
$64$			1.00000i			0.125000i
$65$	1.61286	+	12.0353i	0.200051	+	1.49279i
$66$	3.34164	+	6.32825i	0.411328	+	0.778954i
$67$	−9.42271	−	9.42271i	−1.15117	−	1.15117i	−0.986319	−	0.164848i	$-0.947287\pi$
$67$	−9.42271	−	9.42271i	−1.15117	−	1.15117i	−0.164848	−	0.986319i	$-0.552713\pi$
$68$	3.61090	−	2.08476i	0.437886	−	0.252814i
$69$	4.07594	+	7.71884i	0.490686	+	0.929239i
$70$	−4.54085	+	7.66657i	−0.542736	+	0.916331i
$71$	−3.17072	−	0.849592i	−0.376295	−	0.100828i	0.0657139	−	0.997839i	$-0.479068\pi$
$71$	−3.17072	−	0.849592i	−0.376295	−	0.100828i	−0.442009	+	0.897010i	$0.645734\pi$
$72$	−1.95521	−	2.27533i	−0.230424	−	0.268151i
$73$	0.984725	+	0.263856i	0.115253	+	0.0308820i	0.315985	−	0.948764i	$-0.397665\pi$
$73$	0.984725	+	0.263856i	0.115253	+	0.0308820i	−0.200731	+	0.979646i	$0.564332\pi$
$74$	−0.207843	−	0.119998i	−0.0241612	−	0.0139495i
$75$	9.71395	−	5.12946i	1.12167	−	0.592299i
$76$	1.44316	+	5.38596i	0.165542	+	0.617812i
$77$	2.71154	+	10.5899i	0.309009	+	1.20683i
$78$	−5.68131	−	2.59282i	−0.643282	−	0.293579i
$79$	5.85567	−	10.1423i	0.658815	−	1.14110i	−0.322108	−	0.946703i	$-0.604392\pi$
$79$	5.85567	−	10.1423i	0.658815	−	1.14110i	0.980923	−	0.194397i	$-0.0622752\pi$
$80$	2.38141	−	2.38141i	0.266250	−	0.266250i
$81$	8.89752	+	1.35430i	0.988613	+	0.150477i
$82$			11.0390i			1.21905i
$83$	3.09157	−	3.09157i	0.339344	−	0.339344i	−0.516777	−	0.856120i	$-0.672868\pi$
$83$	3.09157	−	3.09157i	0.339344	−	0.339344i	0.856120	+	0.516777i	$0.172868\pi$
$84$	−2.09457	−	4.07588i	−0.228537	−	0.444715i
$85$	−13.5637	−	3.63438i	−1.47119	−	0.394204i
$86$	−6.98937	+	1.87280i	−0.753683	+	0.201949i
$87$	−5.31593	−	3.34291i	−0.569927	−	0.358397i
$88$		−	4.13172i		−	0.440443i
$89$	−3.39178	+	12.6583i	−0.359528	+	1.34178i	0.515161	+	0.857093i	$0.327732\pi$
$89$	−3.39178	+	12.6583i	−0.359528	+	1.34178i	−0.874689	+	0.484684i	$0.838935\pi$
$90$	−0.762346	+	10.0747i	−0.0803583	+	1.06196i
$91$	−7.51662	−	5.87371i	−0.787955	−	0.615732i
$92$		−	5.03964i		−	0.525418i
$93$	−4.41992	+	14.3106i	−0.458324	+	1.48394i
$94$	−5.81606			−0.599880
$95$	9.38943	−	16.2630i	0.963335	−	1.66854i
$96$	0.384805	+	1.68876i	0.0392740	+	0.172359i
$97$	2.87528	−	10.7307i	0.291941	−	1.08954i	−0.651676	−	0.758497i	$-0.725934\pi$
$97$	2.87528	−	10.7307i	0.291941	−	1.08954i	0.943617	−	0.331040i	$-0.107399\pi$
$98$	−1.66073	−	6.80015i	−0.167759	−	0.686918i
$99$	8.07839	+	9.40105i	0.811908	+	0.944841i
$100$	−6.34224			−0.634224
$101$	−4.02097			−0.400102			−0.200051	−	0.979786i	$-0.564111\pi$
$101$	−4.02097			−0.400102			−0.200051	+	0.979786i	$0.564111\pi$
$102$	5.29574	−	4.91015i	0.524356	−	0.486178i
$103$	9.32328	+	5.38280i	0.918650	+	0.530383i	0.883204	−	0.468989i	$-0.155381\pi$
$103$	9.32328	+	5.38280i	0.918650	+	0.530383i	0.0354461	+	0.999372i	$0.488715\pi$
$104$	2.20154	+	2.85538i	0.215879	+	0.279993i
$105$	−4.71830	+	14.6944i	−0.460459	+	1.43402i
$106$	−3.46685	+	0.928940i	−0.336730	+	0.0902266i
$107$	−16.5078	+	9.53079i	−1.59587	+	0.921377i	−0.603600	+	0.797287i	$0.706268\pi$
$107$	−16.5078	+	9.53079i	−1.59587	+	0.921377i	−0.992271	+	0.124089i	$0.960399\pi$
$108$	−4.17745	−	3.09013i	−0.401975	−	0.297348i
$109$	0.268115	−	1.00062i	0.0256808	−	0.0958419i	−0.951896	−	0.306421i	$-0.900868\pi$
$109$	0.268115	−	1.00062i	0.0256808	−	0.0958419i	0.977577	+	0.210579i	$0.0675350\pi$
$110$	−9.83933	+	9.83933i	−0.938143	+	0.938143i
$111$	−0.397173	−	0.122670i	−0.0376980	−	0.0116433i
$112$	−0.0294574	+	2.64559i	−0.00278346	+	0.249985i
$113$	−2.68484	+	1.55009i	−0.252569	+	0.145821i	−0.620940	−	0.783858i	$-0.713249\pi$
$113$	−2.68484	+	1.55009i	−0.252569	+	0.145821i	0.368371	+	0.929679i	$0.379916\pi$
$114$	4.50971	+	8.54029i	0.422373	+	0.799871i
$115$	−12.0014	+	12.0014i	−1.11914	+	1.11914i
$116$	1.81278	+	3.13983i	0.168312	+	0.291526i
$117$	−10.5921	−	2.19246i	−0.979242	−	0.202693i
$118$	11.3437			1.04427
$119$	9.61437	−	5.40904i	0.881348	−	0.495845i
$120$	3.10526	−	4.93802i	0.283471	−	0.450778i
$121$			6.07112i			0.551920i
$122$	1.11732	+	0.299385i	0.101158	+	0.0271051i
$123$	4.24784	+	18.6422i	0.383015	+	1.68091i
$124$	6.11458	−	6.11458i	0.549105	−	0.549105i
$125$	3.19643	+	3.19643i	0.285898	+	0.285898i
$126$	−5.10566	−	6.07719i	−0.454848	−	0.541399i
$127$	17.1012	+	9.87340i	1.51749	+	0.876123i	0.999789	+	0.0205611i	$0.00654525\pi$
$127$	17.1012	+	9.87340i	1.51749	+	0.876123i	0.517701	+	0.855562i	$0.326788\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−11.0827	+	5.85225i	−0.975780	+	0.515262i
$130$	1.55706	−	12.0426i	0.136563	−	1.05621i
$131$	15.8588	+	9.15610i	1.38559	+	0.799972i	0.992815	−	0.119661i	$-0.0381808\pi$
$131$	15.8588	+	9.15610i	1.38559	+	0.799972i	0.392778	+	0.919633i	$0.371514\pi$
$132$	−1.58991	−	6.97750i	−0.138384	−	0.607314i
$133$	3.65936	+	14.2915i	0.317307	+	1.23923i
$134$	6.66286	+	11.5404i	0.575584	+	0.996940i
$135$	2.58936	+	17.3071i	0.222857	+	1.48956i
$136$	−4.02744	+	1.07915i	−0.345350	+	0.0925363i
$137$	0.525705	−	0.140862i	0.0449140	−	0.0120347i	−0.236292	−	0.971682i	$-0.575932\pi$
$137$	0.525705	−	0.140862i	0.0449140	−	0.0120347i	0.281206	+	0.959647i	$0.409266\pi$
$138$	−1.93928	−	8.51076i	−0.165082	−	0.724484i
$139$	1.13443	+	1.96490i	0.0962214	+	0.166660i	0.910118	−	0.414350i	$-0.135991\pi$
$139$	1.13443	+	1.96490i	0.0962214	+	0.166660i	−0.813896	+	0.581010i	$0.802658\pi$
$140$	6.37038	−	6.23008i	0.538396	−	0.526538i
$141$	−9.82195	+	2.23805i	−0.827157	+	0.188477i
$142$	2.84279	+	1.64129i	0.238562	+	0.137734i
$143$	−9.09617	−	11.7976i	−0.760660	−	0.986568i
$144$	1.29969	+	2.70385i	0.108307	+	0.225321i
$145$	3.16025	−	11.7942i	0.262444	−	0.979455i
$146$	−0.882880	−	0.509731i	−0.0730677	−	0.0421857i
$147$	−5.42131	−	10.8448i	−0.447142	−	0.894463i
$148$	0.169703	+	0.169703i	0.0139495	+	0.0139495i
$149$	2.09299	−	2.09299i	0.171464	−	0.171464i	−0.616158	−	0.787623i	$-0.711312\pi$
$149$	2.09299	−	2.09299i	0.171464	−	0.171464i	0.787623	+	0.616158i	$0.211312\pi$
$150$	−10.7106	+	2.44053i	−0.874513	+	0.199268i
$151$	9.83467	+	2.63519i	0.800334	+	0.214449i	0.635731	−	0.771911i	$-0.280699\pi$
$151$	9.83467	+	2.63519i	0.800334	+	0.214449i	0.164604	+	0.986360i	$0.447365\pi$
$152$		−	5.57596i		−	0.452270i
$153$	7.05381	−	10.3299i	0.570267	−	0.835124i
$154$	0.121710	−	10.9308i	0.00980764	−	0.880831i
$155$	−29.1227			−2.33919
$156$	4.81665	+	3.97490i	0.385641	+	0.318247i
$157$	3.49202	+	6.04836i	0.278694	+	0.482712i	0.971060	−	0.238834i	$-0.0767652\pi$
$157$	3.49202	+	6.04836i	0.278694	+	0.482712i	−0.692367	+	0.721546i	$0.743432\pi$
$158$	−8.28117	+	8.28117i	−0.658815	+	0.658815i
$159$	−5.49724	+	2.90282i	−0.435959	+	0.230209i
$160$	−2.91662	+	1.68391i	−0.230579	+	0.133125i
$161$	0.148454	−	13.3328i	0.0116998	−	1.05077i
$162$	−8.24383	−	3.61100i	−0.647696	−	0.283707i
$163$	0.783296	−	0.783296i	0.0613525	−	0.0613525i	−0.675765	−	0.737117i	$-0.736186\pi$
$163$	0.783296	−	0.783296i	0.0613525	−	0.0613525i	0.737117	+	0.675765i	$0.236186\pi$
$164$	2.85709	−	10.6628i	0.223102	−	0.832626i
$165$	−12.8301	+	20.4025i	−0.998821	+	1.58833i
$166$	−3.78638	+	2.18607i	−0.293880	+	0.169672i
$167$	12.8984	−	3.45613i	0.998111	−	0.267443i	0.277457	−	0.960738i	$-0.410508\pi$
$167$	12.8984	−	3.45613i	0.998111	−	0.267443i	0.720654	+	0.693295i	$0.243842\pi$
$168$	0.968288	+	4.47911i	0.0747050	+	0.345571i
$169$	12.5725	+	3.30641i	0.967115	+	0.254339i
$170$	12.1609	+	7.02109i	0.932697	+	0.538493i
$171$	10.9022	+	12.6872i	0.833710	+	0.970212i
$172$	7.23593			0.551734
$173$	−3.18264			−0.241972			−0.120986	−	0.992654i	$-0.538606\pi$
$173$	−3.18264			−0.241972			−0.120986	+	0.992654i	$0.538606\pi$
$174$	4.26958	+	4.60486i	0.323676	+	0.349094i
$175$	−16.7790	−	0.186826i	−1.26837	−	0.0141227i
$176$	−1.06937	+	3.99094i	−0.0806066	+	0.300828i
$177$	19.1569	−	4.36512i	1.43992	−	0.328102i
$178$	6.55242	−	11.3491i	0.491124	−	0.850653i
$179$	6.55150			0.489682			0.244841	−	0.969563i	$-0.421264\pi$
$179$	6.55150			0.489682			0.244841	+	0.969563i	$0.421264\pi$
$180$	3.34389	−	9.53408i	0.249239	−	0.710628i
$181$		−	5.01185i		−	0.372528i	−0.982500	−	0.186264i	$-0.940362\pi$
$181$		−	5.01185i		−	0.372528i	0.982500	−	0.186264i	$-0.0596380\pi$
$182$	5.74027	+	7.61901i	0.425497	+	0.564759i
$183$	2.00210	+	0.0756408i	0.147999	+	0.00559153i
$184$	−1.30435	+	4.86791i	−0.0961582	+	0.358867i
$185$		−	0.808265i		−	0.0594248i
$186$	7.97317	−	12.6790i	0.584621	−	0.929670i
$187$	16.6403	−	4.45874i	1.21686	−	0.326056i
$188$	5.61788	+	1.50531i	0.409726	+	0.109786i
$189$	−10.9608	−	8.29827i	−0.797280	−	0.603610i
$190$	−13.2787	+	13.2787i	−0.963335	+	0.963335i
$191$		−	7.55857i		−	0.546919i	−0.961884	−	0.273460i	$-0.911832\pi$
$191$		−	7.55857i		−	0.546919i	0.961884	−	0.273460i	$-0.0881680\pi$
$192$	0.0653915	−	1.73082i	0.00471923	−	0.124911i
$193$	−8.75403	+	8.75403i	−0.630129	+	0.630129i	−0.948100	−	0.317971i	$-0.896998\pi$
$193$	−8.75403	+	8.75403i	−0.630129	+	0.630129i	0.317971	+	0.948100i	$0.396998\pi$
$194$	−5.55462	+	9.62088i	−0.398798	+	0.690739i
$195$	−2.00456	−	20.9363i	−0.143549	−	1.49928i
$196$	−0.155864	+	6.99826i	−0.0111331	+	0.499876i
$197$	−3.26334	−	12.1789i	−0.232503	−	0.867714i	−0.979259	−	0.202615i	$-0.935056\pi$
$197$	−3.26334	−	12.1789i	−0.232503	−	0.867714i	0.746755	−	0.665099i	$-0.231611\pi$
$198$	−5.36995	−	11.1716i	−0.381626	−	0.793928i
$199$	−0.515418	−	0.297577i	−0.0365370	−	0.0210947i	0.481620	−	0.876380i	$-0.340048\pi$
$199$	−0.515418	−	0.297577i	−0.0365370	−	0.0210947i	−0.518157	+	0.855285i	$0.673382\pi$
$200$	6.12614	+	1.64149i	0.433183	+	0.116071i
$201$	15.6928	+	16.9251i	1.10689	+	1.19381i
$202$	3.88396	+	1.04070i	0.273274	+	0.0732237i
$203$	4.70338	+	8.36009i	0.330113	+	0.586763i
$204$	−6.38613	+	3.37221i	−0.447119	+	0.236102i
$205$	−32.1965	+	18.5886i	−2.24870	+	1.29829i
$206$	−7.61243	−	7.61243i	−0.530383	−	0.530383i
$207$	−6.54996	−	13.6264i	−0.455254	−	0.947102i
$208$	−1.38750	−	3.32789i	−0.0962059	−	0.230748i
$209$			23.0383i			1.59359i
$210$	8.36071	−	12.9725i	0.576944	−	0.895187i
$211$	0.941779	−	1.63121i	0.0648347	−	0.112297i	−0.831786	−	0.555097i	$-0.812681\pi$
$211$	0.941779	−	1.63121i	0.0648347	−	0.112297i	0.896621	+	0.442799i	$0.146015\pi$
$212$	3.58915			0.246504
$213$	5.43238	+	1.67783i	0.372221	+	0.114963i
$214$	18.4121	−	4.93350i	1.25862	−	0.337247i
$215$	−17.2317	−	17.2317i	−1.17519	−	1.17519i
$216$	3.23532	+	4.06604i	0.220136	+	0.276659i
$217$	16.3568	−	15.9965i	1.11037	−	1.08592i
$218$	−0.517959	+	0.897131i	−0.0350806	+	0.0607614i
$219$	−1.68712	−	0.521079i	−0.114005	−	0.0352113i
$220$	12.0507	−	6.95746i	0.812456	−	0.469072i
$221$	−9.12408	+	11.9480i	−0.613752	+	0.803707i
$222$	0.351891	+	0.221286i	0.0236173	+	0.0148517i
$223$	−6.55015	+	1.75511i	−0.438631	+	0.117531i	−0.471375	−	0.881933i	$-0.656242\pi$
$223$	−6.55015	+	1.75511i	−0.438631	+	0.117531i	0.0327440	+	0.999464i	$0.489575\pi$
$224$	0.713182	−	2.54782i	0.0476515	−	0.170233i
$225$	−17.1485	+	8.24294i	−1.14323	+	0.549530i
$226$	2.99455	−	0.802388i	0.199195	−	0.0533741i
$227$	−0.219985	−	0.820996i	−0.0146009	−	0.0544914i	0.958241	−	0.285962i	$-0.0923130\pi$
$227$	−0.219985	−	0.820996i	−0.0146009	−	0.0544914i	−0.972842	+	0.231470i	$0.925646\pi$
$228$	−2.14566	−	9.41648i	−0.142100	−	0.623622i
$229$	−1.74010	−	6.49414i	−0.114989	−	0.429145i	0.884297	−	0.466925i	$-0.154638\pi$
$229$	−1.74010	−	6.49414i	−0.114989	−	0.429145i	−0.999286	+	0.0377798i	$0.987971\pi$
$230$	14.6987	−	8.48631i	0.969204	−	0.559570i
$231$	−4.00070	−	18.5064i	−0.263226	−	1.21763i
$232$	−0.938365	−	3.50202i	−0.0616067	−	0.229919i
$233$	1.40499	−	2.43351i	0.0920437	−	0.159424i	−0.816327	−	0.577590i	$-0.803993\pi$
$233$	1.40499	−	2.43351i	0.0920437	−	0.159424i	0.908371	+	0.418165i	$0.137327\pi$
$234$	9.66376	+	4.85920i	0.631739	+	0.317656i
$235$	−9.79373	−	16.9632i	−0.638872	−	1.10656i
$236$	−10.9572	−	2.93597i	−0.713253	−	0.191115i
$237$	−10.7983	+	17.1716i	−0.701426	+	1.11541i
$238$	−10.6867	+	2.73635i	−0.692718	+	0.177371i
$239$	−4.28240	+	4.28240i	−0.277005	+	0.277005i	−0.831912	−	0.554907i	$-0.812754\pi$
$239$	−4.28240	+	4.28240i	−0.277005	+	0.277005i	0.554907	+	0.831912i	$0.312754\pi$
$240$	−4.27751	+	3.96606i	−0.276112	+	0.256008i
$241$	−1.04914	−	3.91546i	−0.0675813	−	0.252217i	0.923868	−	0.382712i	$-0.125010\pi$
$241$	−1.04914	−	3.91546i	−0.0675813	−	0.252217i	−0.991449	+	0.130495i	$0.958343\pi$
$242$	1.57132	−	5.86425i	0.101008	−	0.376968i
$243$	−15.3114	−	2.92586i	−0.982228	−	0.187694i
$244$	−1.00176	−	0.578368i	−0.0641313	−	0.0370262i
$245$	17.0369	−	16.2946i	1.08845	−	1.04102i
$246$	0.721855	−	19.1064i	0.0460238	−	1.21818i
$247$	−12.2757	−	15.9215i	−0.781085	−	1.01306i
$248$	−7.48880	+	4.32366i	−0.475539	+	0.274553i
$249$	−5.55310	+	5.14878i	−0.351913	+	0.326290i
$250$	−2.26022	−	3.91482i	−0.142949	−	0.247595i
$251$	13.2520	+	22.9531i	0.836457	+	1.44879i	0.892839	+	0.450377i	$0.148710\pi$
$251$	13.2520	+	22.9531i	0.836457	+	1.44879i	−0.0563815	+	0.998409i	$0.517956\pi$
$252$	3.35879	+	7.19156i	0.211584	+	0.453026i
$253$	5.38923	−	20.1129i	0.338818	−	1.26448i
$254$	−13.9631	−	13.9631i	−0.876123	−	0.876123i
$255$	23.2386	+	7.17740i	1.45526	+	0.449466i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.296805	−	0.514082i	−0.0185142	−	0.0320675i	0.856620	−	0.515948i	$-0.172560\pi$
$257$	−0.296805	−	0.514082i	−0.0185142	−	0.0320675i	−0.875134	+	0.483881i	$0.839227\pi$
$258$	12.2198	−	2.78442i	0.760770	−	0.173350i
$259$	0.443965	+	0.453963i	0.0275866	+	0.0282079i
$260$	−4.62086	+	11.2293i	−0.286574	+	0.696411i
$261$	8.98229	+	6.13358i	0.555990	+	0.379659i
$262$	−12.9487	−	12.9487i	−0.799972	−	0.799972i
$263$			11.7498i			0.724527i	0.932076	+	0.362263i	$0.117996\pi$
$263$			11.7498i			0.724527i	−0.932076	+	0.362263i	$0.882004\pi$
$264$	−0.270180	+	7.15125i	−0.0166284	+	0.440129i
$265$	−8.54724	−	8.54724i	−0.525053	−	0.525053i
$266$	0.164253	−	14.7517i	0.0100710	−	0.904484i
$267$	6.69829	−	21.6874i	0.409929	−	1.32725i
$268$	−3.44895	−	12.8717i	−0.210678	−	0.786262i
$269$	−1.02758	−	0.593273i	−0.0626526	−	0.0361725i	0.468346	−	0.883545i	$-0.344850\pi$
$269$	−1.02758	−	0.593273i	−0.0626526	−	0.0361725i	−0.530999	+	0.847372i	$0.678183\pi$
$270$	1.97828	−	17.3876i	0.120394	−	1.05817i
$271$	−19.8096	−	5.30798i	−1.20335	−	0.322437i	−0.399200	−	0.916864i	$-0.630712\pi$
$271$	−19.8096	−	5.30798i	−1.20335	−	0.322437i	−0.804150	+	0.594427i	$0.797379\pi$
$272$	4.16951			0.252814
$273$	12.6258	+	10.6578i	0.764147	+	0.645042i
$274$	−0.544250			−0.0328793
$275$	−25.3115	−	6.78219i	−1.52634	−	0.408982i
$276$	−0.329550	+	8.72268i	−0.0198366	+	0.525044i
$277$	−10.5361	−	6.08303i	−0.633053	−	0.365494i	0.148880	−	0.988855i	$-0.452433\pi$
$277$	−10.5361	−	6.08303i	−0.633053	−	0.365494i	−0.781934	+	0.623362i	$0.785766\pi$
$278$	−0.587226	−	2.19156i	−0.0352195	−	0.131441i
$279$	8.58586	−	24.4800i	0.514022	−	1.46558i
$280$	−7.76578	+	4.36902i	−0.464094	+	0.261099i
$281$	0.703268	+	0.703268i	0.0419535	+	0.0419535i	0.727772	−	0.685819i	$-0.240556\pi$
$281$	0.703268	+	0.703268i	0.0419535	+	0.0419535i	−0.685819	+	0.727772i	$0.740556\pi$
$282$	10.0665	+	0.380321i	0.599453	+	0.0226478i
$283$		−	1.37013i		−	0.0814457i	−0.999170	−	0.0407229i	$-0.987034\pi$
$283$		−	1.37013i		−	0.0814457i	0.999170	−	0.0407229i	$-0.0129661\pi$
$284$	−2.32113	−	2.32113i	−0.137734	−	0.137734i
$285$	−17.3148	+	27.5342i	−1.02564	+	1.63099i
$286$	5.73277	+	13.7499i	0.338986	+	0.813049i
$287$	7.87279	−	28.1253i	0.464716	−	1.66018i
$288$	−0.555595	−	2.94810i	−0.0327388	−	0.173719i
$289$	−0.192412	−	0.333268i	−0.0113184	−	0.0196040i
$290$	−6.10513	+	10.5744i	−0.358506	+	0.620950i
$291$	−5.67828	+	18.3848i	−0.332867	+	1.07774i
$292$	0.720869	+	0.720869i	0.0421857	+	0.0421857i
$293$	3.42884	−	12.7966i	0.200315	−	0.747585i	−0.790512	−	0.612447i	$-0.790185\pi$
$293$	3.42884	−	12.7966i	0.200315	−	0.747585i	0.990827	−	0.135139i	$-0.0431480\pi$
$294$	2.42975	+	11.8784i	0.141706	+	0.692762i
$295$	19.1018	+	33.0853i	1.11215	+	1.92630i
$296$	−0.119998	−	0.207843i	−0.00697474	−	0.0120806i
$297$	−13.3675	−	16.7997i	−0.775658	−	0.974820i
$298$	−2.56338	+	1.47997i	−0.148493	+	0.0857322i
$299$	6.99250	+	16.7713i	0.404387	+	0.969912i
$300$	10.9773	+	0.414729i	0.633772	+	0.0239444i
$301$	19.1433	+	0.213151i	1.10340	+	0.0122858i
$302$	−8.81753	−	5.09080i	−0.507392	−	0.292943i
$303$	6.95956	+	0.262938i	0.399816	+	0.0151054i
$304$	−1.44316	+	5.38596i	−0.0827712	+	0.308906i
$305$	1.00828	+	3.76294i	0.0577338	+	0.215465i
$306$	−9.48703	+	8.15228i	−0.542338	+	0.466035i
$307$	1.03029	−	1.03029i	0.0588019	−	0.0588019i	−0.677094	−	0.735896i	$-0.736761\pi$
$307$	1.03029	−	1.03029i	0.0588019	−	0.0588019i	0.735896	+	0.677094i	$0.236761\pi$
$308$	−2.94667	+	10.5269i	−0.167902	+	0.599824i
$309$	−15.7849	−	9.92630i	−0.897971	−	0.564687i
$310$	28.1303	+	7.53750i	1.59770	+	0.428101i
$311$	8.14577	+	14.1089i	0.461904	+	0.800041i	0.999056	−	0.0434444i	$-0.0138331\pi$
$311$	8.14577	+	14.1089i	0.461904	+	0.800041i	−0.537152	+	0.843486i	$0.680500\pi$
$312$	−3.62375	−	5.08610i	−0.205154	−	0.287944i
$313$	−1.78684	+	3.09490i	−0.100998	+	0.174934i	−0.912096	−	0.409976i	$-0.865537\pi$
$313$	−1.78684	+	3.09490i	−0.100998	+	0.174934i	0.811098	+	0.584910i	$0.198870\pi$
$314$	−1.80760	−	6.74607i	−0.102009	−	0.380703i
$315$	9.12739	−	25.1247i	0.514270	−	1.41562i
$316$	10.1423	−	5.85567i	0.570550	−	0.329407i
$317$	5.15929	+	19.2547i	0.289775	+	1.08145i	0.945279	+	0.326263i	$0.105789\pi$
$317$	5.15929	+	19.2547i	0.289775	+	1.08145i	−0.655504	+	0.755191i	$0.727544\pi$
$318$	6.06123	−	1.38112i	0.339897	−	0.0774495i
$319$	3.87706	+	14.4694i	0.217074	+	0.810130i
$320$	3.25307	−	0.871657i	0.181852	−	0.0487271i
$321$	29.1952	−	15.4166i	1.62952	−	0.860469i
$322$	−3.59418	+	12.8401i	−0.200296	+	0.715549i
$323$	22.4568	−	6.01729i	1.24953	−	0.334811i
$324$	7.02833	+	5.62162i	0.390463	+	0.312312i
$325$	21.1063	−	8.79987i	1.17077	−	0.488129i
$326$	−0.959338	+	0.553874i	−0.0531328	+	0.0306763i
$327$	−0.529490	+	1.71436i	−0.0292809	+	0.0948041i
$328$	−5.51948	+	9.56002i	−0.304762	+	0.527864i
$329$	14.8182	+	4.14791i	0.816956	+	0.228681i
$330$	17.6735	−	16.3867i	0.972893	−	0.902056i
$331$	11.9191	+	11.9191i	0.655131	+	0.655131i	0.954224	−	0.299093i	$-0.0966841\pi$
$331$	11.9191	+	11.9191i	0.655131	+	0.655131i	−0.299093	+	0.954224i	$0.596684\pi$
$332$	4.22316	−	1.13159i	0.231776	−	0.0621042i
$333$	0.679412	+	0.238290i	0.0372316	+	0.0130582i
$334$	−13.3534			−0.730668
$335$	−22.4393	+	38.8661i	−1.22599	+	2.12348i
$336$	0.223984	−	4.57710i	0.0122193	−	0.249701i
$337$			3.74321i			0.203906i	0.994789	+	0.101953i	$0.0325091\pi$
$337$			3.74321i			0.203906i	−0.994789	+	0.101953i	$0.967491\pi$
$338$	−11.2883	−	6.44774i	−0.614005	−	0.350711i
$339$	4.74833	−	2.50736i	0.257894	−	0.136181i
$340$	−9.92932	−	9.92932i	−0.538493	−	0.538493i
$341$	30.9416	−	17.8642i	1.67558	−	0.967398i
$342$	−7.24701	−	15.0766i	−0.391874	−	0.815247i
$343$	−0.618502	+	18.5099i	−0.0333960	+	0.999442i
$344$	−6.98937	−	1.87280i	−0.376841	−	0.100974i
$345$	21.5571	−	19.9875i	1.16059	−	1.07609i
$346$	3.07420	+	0.823728i	0.165270	+	0.0442839i
$347$	−4.81685	−	2.78101i	−0.258582	−	0.149292i	0.365105	−	0.930966i	$-0.381033\pi$
$347$	−4.81685	−	2.78101i	−0.258582	−	0.149292i	−0.623688	+	0.781674i	$0.714366\pi$
$348$	−2.93227	−	5.55301i	−0.157186	−	0.297672i
$349$	−1.80360	−	6.73112i	−0.0965444	−	0.360309i	0.900705	−	0.434432i	$-0.143051\pi$
$349$	−1.80360	−	6.73112i	−0.0965444	−	0.360309i	−0.997249	+	0.0741233i	$0.976384\pi$
$350$	16.1589	+	4.52317i	0.863728	+	0.241774i
$351$	18.1896	+	4.48739i	0.970892	+	0.239519i
$352$	2.06586	−	3.57818i	0.110111	−	0.190717i
$353$	−25.5228	+	25.5228i	−1.35844	+	1.35844i	−0.482601	+	0.875840i	$0.660308\pi$
$353$	−25.5228	+	25.5228i	−1.35844	+	1.35844i	−0.875840	+	0.482601i	$0.839692\pi$
$354$	−19.6339	−	0.741784i	−1.04353	−	0.0394253i
$355$			11.0551i			0.586745i
$356$	−9.26652	+	9.26652i	−0.491124	+	0.491124i
$357$	−16.9944	+	8.73335i	−0.899440	+	0.462218i
$358$	−6.32827	−	1.69565i	−0.334459	−	0.0896181i
$359$	11.6888	−	3.13200i	0.616910	−	0.165301i	0.0631875	−	0.998002i	$-0.479873\pi$
$359$	11.6888	−	3.13200i	0.616910	−	0.165301i	0.553723	+	0.832701i	$0.313207\pi$
$360$	−5.69755	+	8.34375i	−0.300287	+	0.439754i
$361$			12.0913i			0.636385i
$362$	−1.29716	+	4.84108i	−0.0681773	+	0.254441i
$363$	0.397000	−	10.5080i	0.0208371	−	0.551526i
$364$	−3.57273	−	8.84509i	−0.187262	−	0.463609i
$365$		−	3.43337i		−	0.179711i
$366$	−1.91430	−	0.591244i	−0.100062	−	0.0309048i
$367$	−23.0600			−1.20372			−0.601861	−	0.798601i	$-0.705574\pi$
$367$	−23.0600			−1.20372			−0.601861	+	0.798601i	$0.705574\pi$
$368$	2.51982	−	4.36445i	0.131355	−	0.227513i
$369$	−6.13319	−	32.5440i	−0.319281	−	1.69417i
$370$	−0.209194	+	0.780724i	−0.0108755	+	0.0405879i
$371$	9.49541	+	0.105727i	0.492977	+	0.00548907i
$372$	−10.9831	+	10.1834i	−0.569445	+	0.527983i
$373$	15.1115			0.782441			0.391221	−	0.920297i	$-0.372053\pi$
$373$	15.1115			0.782441			0.391221	+	0.920297i	$0.372053\pi$
$374$	−17.2273			−0.890800
$375$	−5.32342	−	5.74146i	−0.274900	−	0.296488i
$376$	−5.03685	−	2.90803i	−0.259756	−	0.149970i
$377$	−10.3892	−	7.93376i	−0.535074	−	0.408610i
$378$	8.43956	+	10.8524i	0.434084	+	0.558186i
$379$	−17.9467	+	4.80881i	−0.921862	+	0.247012i	−0.688381	−	0.725349i	$-0.741678\pi$
$379$	−17.9467	+	4.80881i	−0.921862	+	0.247012i	−0.233481	+	0.972361i	$0.575012\pi$
$380$	16.2630	−	9.38943i	0.834272	−	0.481667i
$381$	−28.9535	−	18.2073i	−1.48333	−	0.932789i
$382$	−1.95630	+	7.30102i	−0.100093	+	0.373553i
$383$	10.8715	−	10.8715i	0.555508	−	0.555508i	−0.372518	−	0.928025i	$-0.621505\pi$
$383$	10.8715	−	10.8715i	0.555508	−	0.555508i	0.928025	+	0.372518i	$0.121505\pi$
$384$	−0.511132	+	1.65492i	−0.0260836	+	0.0844520i
$385$	32.0860	−	18.0516i	1.63526	−	0.919993i
$386$	10.7215	−	6.19003i	0.545708	−	0.315064i
$387$	19.5649	−	9.40445i	0.994538	−	0.478055i
$388$	7.85541	−	7.85541i	0.398798	−	0.398798i
$389$	0.274003	+	0.474587i	0.0138925	+	0.0240625i	0.872888	−	0.487920i	$-0.162244\pi$
$389$	0.274003	+	0.474587i	0.0138925	+	0.0240625i	−0.858996	+	0.511983i	$0.828911\pi$
$390$	−3.48246	+	20.7417i	−0.176341	+	1.05030i
$391$	−21.0128			−1.06266
$392$	1.96184	−	6.71946i	0.0990877	−	0.339384i
$393$	−26.8500	−	16.8846i	−1.35440	−	0.851713i
$394$			12.6086i			0.635211i
$395$	−38.0978	−	10.2083i	−1.91691	−	0.513634i
$396$	2.29556	+	12.1807i	0.115356	+	0.612105i
$397$	−19.7655	+	19.7655i	−0.992002	+	0.992002i	−0.999968	−	0.00796600i	$-0.997464\pi$
$397$	−19.7655	+	19.7655i	−0.992002	+	0.992002i	0.00796600	+	0.999968i	$0.497464\pi$
$398$	0.420837	+	0.420837i	0.0210947	+	0.0210947i
$399$	−5.39913	−	24.9753i	−0.270295	−	1.25033i
$400$	−5.49254	−	3.17112i	−0.274627	−	0.158556i
$401$	4.61787	−	17.2341i	0.230605	−	0.860631i	−0.749475	−	0.662032i	$-0.769694\pi$
$401$	4.61787	−	17.2341i	0.230605	−	0.860631i	0.980081	−	0.198599i	$-0.0636391\pi$
$402$	−10.7775	−	20.4100i	−0.537535	−	1.01796i
$403$	−11.8646	+	28.8326i	−0.591020	+	1.43626i
$404$	−3.48226	−	2.01049i	−0.173249	−	0.100025i
$405$	−3.34997	−	30.1247i	−0.166461	−	1.49691i
$406$	−2.37936	−	9.29255i	−0.118086	−	0.461182i
$407$	0.495798	+	0.858748i	0.0245758	+	0.0425666i
$408$	7.04132	−	1.60445i	0.348597	−	0.0794320i
$409$	−24.8540	+	6.65962i	−1.22895	+	0.329297i	−0.814172	−	0.580624i	$-0.802809\pi$
$409$	−24.8540	+	6.65962i	−1.22895	+	0.329297i	−0.414782	+	0.909921i	$0.636142\pi$
$410$	35.9105	−	9.62219i	1.77349	−	0.475206i
$411$	−0.919109	+	0.209430i	−0.0453363	+	0.0103304i
$412$	5.38280	+	9.32328i	0.265192	+	0.459325i
$413$	−28.9017	−	8.09014i	−1.42216	−	0.398090i
$414$	2.80000	+	14.8574i	0.137612	+	0.730200i
$415$	−12.7519	−	7.36230i	−0.625965	−	0.361401i
$416$	0.478903	+	3.57360i	0.0234801	+	0.175210i
$417$	−1.83501	−	3.47506i	−0.0898608	−	0.170174i
$418$	5.96275	−	22.2533i	0.291648	−	1.08844i
$419$	33.6399	+	19.4220i	1.64342	+	0.948827i	0.979607	+	0.200924i	$0.0643946\pi$
$419$	33.6399	+	19.4220i	1.64342	+	0.948827i	0.663809	+	0.747902i	$0.268939\pi$
$420$	−11.4334	+	10.3666i	−0.557891	+	0.505836i
$421$	5.53379	+	5.53379i	0.269700	+	0.269700i	0.828979	−	0.559279i	$-0.188922\pi$
$421$	5.53379	+	5.53379i	0.269700	+	0.269700i	−0.559279	+	0.828979i	$0.688922\pi$
$422$	−1.33188	+	1.33188i	−0.0648347	+	0.0648347i
$423$	17.1463	−	3.23137i	0.833683	−	0.157115i
$424$	−3.46685	−	0.928940i	−0.168365	−	0.0451133i
$425$			26.4441i			1.28273i
$426$	−4.81302	−	3.02666i	−0.233192	−	0.146642i
$427$	−2.63321	−	1.55963i	−0.127430	−	0.0754759i
$428$	−19.0616			−0.921377
$429$	14.9723	+	21.0144i	0.722871	+	1.01458i
$430$	12.1847	+	21.1045i	0.587597	+	1.01775i
$431$	−3.77587	+	3.77587i	−0.181877	+	0.181877i	−0.792173	−	0.610296i	$-0.791051\pi$
$431$	−3.77587	+	3.77587i	−0.181877	+	0.181877i	0.610296	+	0.792173i	$0.291051\pi$
$432$	−2.07271	−	4.76486i	−0.0997235	−	0.229249i
$433$	−13.4737	+	7.77905i	−0.647505	+	0.373837i	−0.787500	−	0.616315i	$-0.788625\pi$
$433$	−13.4737	+	7.77905i	−0.647505	+	0.373837i	0.139995	+	0.990152i	$0.455292\pi$
$434$	−19.9396	+	11.2180i	−0.957133	+	0.538482i
$435$	−6.24105	+	20.2069i	−0.299235	+	0.968849i
$436$	0.732504	−	0.732504i	0.0350806	−	0.0350806i
$437$	7.27302	−	27.1433i	0.347916	−	1.29844i
$438$	1.49477	+	0.939984i	0.0714229	+	0.0449142i
$439$	31.4523	−	18.1590i	1.50114	−	0.866683i	0.501139	−	0.865367i	$-0.332914\pi$
$439$	31.4523	−	18.1590i	1.50114	−	0.866683i	0.999999	−	0.00131587i	$-0.000418855\pi$
$440$	−13.4408	+	3.60144i	−0.640764	+	0.171692i
$441$	8.67414	+	19.1248i	0.413054	+	0.910707i
$442$	11.9055	−	9.17936i	0.566289	−	0.436618i
$443$	6.23652	+	3.60066i	0.296306	+	0.171072i	0.640782	−	0.767723i	$-0.278610\pi$
$443$	6.23652	+	3.60066i	0.296306	+	0.171072i	−0.344476	+	0.938795i	$0.611943\pi$
$444$	−0.282627	−	0.304822i	−0.0134129	−	0.0144662i
$445$	44.1348			2.09219
$446$	6.78122			0.321100
$447$	−3.75944	+	3.48572i	−0.177816	+	0.164869i
$448$	−1.34830	+	2.27642i	−0.0637014	+	0.107551i
$449$	−1.65994	+	6.19497i	−0.0783373	+	0.292359i	−0.993969	−	0.109659i	$-0.965024\pi$
$449$	−1.65994	+	6.19497i	−0.0783373	+	0.292359i	0.915632	+	0.402017i	$0.131691\pi$
$450$	18.6976	−	3.52372i	0.881413	−	0.166110i
$451$	22.8050	−	39.4993i	1.07384	−	1.85995i
$452$	−3.10019			−0.145821
$453$	−16.8497	−	5.20414i	−0.791668	−	0.244512i
$454$			0.849958i			0.0398905i
$455$	−12.5557	+	29.5719i	−0.588619	+	1.38635i
$456$	−0.364621	+	9.65096i	−0.0170749	+	0.451948i
$457$	−5.77948	+	21.5693i	−0.270352	+	1.00897i	0.688540	+	0.725199i	$0.258252\pi$
$457$	−5.77948	+	21.5693i	−0.270352	+	1.00897i	−0.958892	+	0.283771i	$0.908415\pi$
$458$			6.72323i			0.314156i
$459$	−12.8843	+	17.4179i	−0.601389	+	0.812999i
$460$	−16.3943	+	4.39283i	−0.764387	+	0.204817i
$461$	−36.7770	−	9.85437i	−1.71288	−	0.458964i	−0.736750	−	0.676166i	$-0.763640\pi$
$461$	−36.7770	−	9.85437i	−1.71288	−	0.458964i	−0.976127	+	0.217202i	$0.930307\pi$
$462$	−0.925441	+	18.9113i	−0.0430554	+	0.879833i
$463$	−5.91991	+	5.91991i	−0.275122	+	0.275122i	−0.831158	−	0.556036i	$-0.812322\pi$
$463$	−5.91991	+	5.91991i	−0.275122	+	0.275122i	0.556036	+	0.831158i	$0.312322\pi$
$464$			3.62556i			0.168312i
$465$	50.4060	+	1.90438i	2.33752	+	0.0883133i
$466$	−1.98695	+	1.98695i	−0.0920437	+	0.0920437i
$467$	−15.1184	+	26.1858i	−0.699595	+	1.21173i	0.269011	+	0.963137i	$0.413303\pi$
$467$	−15.1184	+	26.1858i	−0.699595	+	1.21173i	−0.968607	+	0.248598i	$0.920030\pi$
$468$	−8.07682	−	7.19479i	−0.373351	−	0.332579i
$469$	−8.74534	−	34.1547i	−0.403822	−	1.57712i
$470$	5.06961	+	18.9200i	0.233844	+	0.872716i
$471$	−5.64854	−	10.6969i	−0.260271	−	0.492889i
$472$	9.82395	+	5.67186i	0.452184	+	0.261069i
$473$	28.8781	+	7.73787i	1.32782	+	0.355788i
$474$	14.8747	−	13.7917i	0.683218	−	0.633472i
$475$	−34.1591	−	9.15290i	−1.56733	−	0.419964i
$476$	11.0308	+	0.122823i	0.505596	+	0.00562957i
$477$	9.70452	−	4.66478i	0.444340	−	0.213586i
$478$	5.24485	−	3.02811i	0.239894	−	0.138503i
$479$	26.4222	+	26.4222i	1.20726	+	1.20726i	0.971910	+	0.235353i	$0.0756246\pi$
$479$	26.4222	+	26.4222i	1.20726	+	1.20726i	0.235353	+	0.971910i	$0.424375\pi$
$480$	5.15825	−	2.72382i	0.235441	−	0.124325i
$481$	−0.800215	−	0.329289i	−0.0364867	−	0.0150143i
$482$			4.05358i			0.184636i
$483$	−1.12880	+	23.0669i	−0.0513622	+	1.04958i
$484$	−3.03556	+	5.25774i	−0.137980	+	0.238988i
$485$	−37.4139			−1.69888
$486$	14.0324	+	6.78905i	0.636523	+	0.307958i
$487$	−4.15427	+	1.11313i	−0.188248	+	0.0504408i	−0.351711	−	0.936109i	$-0.614400\pi$
$487$	−4.15427	+	1.11313i	−0.188248	+	0.0504408i	0.163463	+	0.986549i	$0.447733\pi$
$488$	0.817936	+	0.817936i	0.0370262	+	0.0370262i
$489$	−1.40696	+	1.30452i	−0.0636251	+	0.0589925i
$490$	−20.6738	+	11.3299i	−0.933945	+	0.511831i
$491$	1.41156	−	2.44489i	0.0637028	−	0.110336i	−0.832415	−	0.554153i	$-0.813042\pi$
$491$	1.41156	−	2.44489i	0.0637028	−	0.110336i	0.896118	+	0.443816i	$0.146376\pi$
$492$	−5.64236	+	18.2685i	−0.254377	+	0.823610i
$493$	13.0916	−	7.55841i	0.589614	−	0.340414i
$494$	7.73665	+	18.5562i	0.348088	+	0.834881i
$495$	23.5407	−	34.4740i	1.05807	−	1.54949i
$496$	8.35267	−	2.23809i	0.375046	−	0.100493i
$497$	−6.07238	−	6.20913i	−0.272383	−	0.278517i
$498$	6.69648	−	3.53609i	0.300077	−	0.158456i
$499$	−5.94661	+	1.59339i	−0.266207	+	0.0713298i	−0.389453	−	0.921046i	$-0.627336\pi$
$499$	−5.94661	+	1.59339i	−0.266207	+	0.0713298i	0.123247	+	0.992376i	$0.460669\pi$
$500$	1.16998	+	4.36641i	0.0523229	+	0.195272i
$501$	−22.5508	+	5.13847i	−1.00750	+	0.229570i
$502$	−6.85973	−	25.6008i	−0.306165	−	1.14262i
$503$	−3.76379	+	2.17302i	−0.167819	+	0.0968903i	−0.581557	−	0.813506i	$-0.697556\pi$
$503$	−3.76379	+	2.17302i	−0.167819	+	0.0968903i	0.413738	+	0.910396i	$0.364223\pi$
$504$	−1.38303	−	7.81583i	−0.0616052	−	0.348145i
$505$	3.50491	+	13.0805i	0.155966	+	0.582074i
$506$	−10.4112	+	18.0327i	−0.462834	+	0.801651i
$507$	−21.5445	−	6.54491i	−0.956823	−	0.290670i
$508$	9.87340	+	17.1012i	0.438061	+	0.758745i
$509$	7.62599	+	2.04338i	0.338016	+	0.0905712i	0.423835	−	0.905740i	$-0.360684\pi$
$509$	7.62599	+	2.04338i	0.338016	+	0.0905712i	−0.0858184	+	0.996311i	$0.527350\pi$
$510$	−20.5891	−	12.9474i	−0.911702	−	0.573322i
$511$	1.88589	+	1.92836i	0.0834267	+	0.0853055i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.0400	−	22.6721i	−0.796487	−	1.00100i
$514$	0.153638	+	0.573384i	0.00677667	+	0.0252909i
$515$	9.38391	−	35.0212i	0.413505	−	1.54322i
$516$	−12.5241	−	0.473168i	−0.551341	−	0.0208301i
$517$	20.8109	+	12.0152i	0.915261	+	0.528426i
$518$	−0.311343	−	0.553401i	−0.0136796	−	0.0243150i
$519$	5.50857	+	0.208118i	0.241799	+	0.00913536i
$520$	7.36976	−	9.65069i	0.323185	−	0.423211i
$521$	−14.4992	+	8.37113i	−0.635222	+	0.366746i	−0.782772	−	0.622309i	$-0.786195\pi$
$521$	−14.4992	+	8.37113i	−0.635222	+	0.366746i	0.147549	+	0.989055i	$0.452861\pi$
$522$	−7.08874	−	8.24937i	−0.310266	−	0.361065i
$523$	16.9736	+	29.3992i	0.742205	+	1.28554i	0.951489	+	0.307682i	$0.0995532\pi$
$523$	16.9736	+	29.3992i	0.742205	+	1.28554i	−0.209284	+	0.977855i	$0.567113\pi$
$524$	9.15610	+	15.8588i	0.399986	+	0.692796i
$525$	29.0291	+	1.42056i	1.26693	+	0.0619984i
$526$	3.04108	−	11.3495i	0.132598	−	0.494861i
$527$	−25.4948	−	25.4948i	−1.11057	−	1.11057i
$528$	2.11185	−	6.83765i	0.0919066	−	0.297570i
$529$	−1.19897	+	2.07667i	−0.0521290	+	0.0902900i
$530$	6.04381	+	10.4682i	0.262526	+	0.454709i
$531$	−33.4425	+	6.30252i	−1.45128	+	0.273506i
$532$	−3.97667	+	14.2065i	−0.172411	+	0.615931i
$533$	5.28659	+	39.4489i	0.228987	+	1.70872i
$534$	−12.0832	+	19.2148i	−0.522890	+	0.831504i
$535$	45.3935	+	45.3935i	1.96253	+	1.96253i
$536$			13.3257i			0.575584i
$537$	−11.3394	−	0.428413i	−0.489333	−	0.0184874i
$538$	0.839015	+	0.839015i	0.0361725	+	0.0361725i
$539$	−8.10576	+	27.7629i	−0.349140	+	1.19583i
$540$	−6.41110	+	16.2831i	−0.275890	+	0.700712i
$541$	0.357228	+	1.33319i	0.0153584	+	0.0573184i	0.973180	−	0.230046i	$-0.0738876\pi$
$541$	0.357228	+	1.33319i	0.0153584	+	0.0573184i	−0.957821	+	0.287364i	$0.907221\pi$
$542$	17.7608	+	10.2542i	0.762893	+	0.440457i
$543$	−0.327733	+	8.67459i	−0.0140644	+	0.372262i
$544$	−4.02744	−	1.07915i	−0.172675	−	0.0462681i
$545$	−3.48879			−0.149443
$546$	−9.43712	−	13.5625i	−0.403872	−	0.580420i
$547$	0.425089			0.0181755			0.00908776	−	0.999959i	$-0.497107\pi$
$547$	0.425089			0.0181755			0.00908776	+	0.999959i	$0.497107\pi$
$548$	0.525705	+	0.140862i	0.0224570	+	0.00601733i
$549$	−3.46032	−	0.261840i	−0.147683	−	0.0111751i
$550$	22.6937	+	13.1022i	0.967661	+	0.558679i
$551$	5.23228	+	19.5271i	0.222903	+	0.831884i
$552$	2.57592	−	8.34017i	0.109638	−	0.354981i
$553$	27.0049	−	15.1929i	1.14836	−	0.646069i
$554$	8.60270	+	8.60270i	0.365494	+	0.365494i
$555$	−0.0528537	+	1.39896i	−0.00224351	+	0.0593824i
$556$			2.26887i			0.0962214i
$557$	−10.5237	−	10.5237i	−0.445903	−	0.445903i	0.448087	−	0.893990i	$-0.352105\pi$
$557$	−10.5237	−	10.5237i	−0.445903	−	0.445903i	−0.893990	+	0.448087i	$0.852105\pi$
$558$	−14.6292	+	21.4236i	−0.619303	+	0.906935i
$559$	−24.0804	+	10.0399i	−1.01849	+	0.424641i
$560$	8.63195	−	2.21022i	0.364767	−	0.0933988i
$561$	−29.0928	+	6.62913i	−1.22830	+	0.279882i
$562$	−0.497286	−	0.861324i	−0.0209767	−	0.0363328i
$563$	−0.299154	+	0.518150i	−0.0126078	+	0.0218374i	−0.872260	−	0.489042i	$-0.837347\pi$
$563$	−0.299154	+	0.518150i	−0.0126078	+	0.0218374i	0.859653	+	0.510879i	$0.170680\pi$
$564$	−9.62508	−	2.97277i	−0.405289	−	0.125176i
$565$	7.38283	+	7.38283i	0.310598	+	0.310598i
$566$	−0.354616	+	1.32344i	−0.0149056	+	0.0556285i
$567$	18.4285	+	15.0795i	0.773923	+	0.633280i
$568$	1.64129	+	2.84279i	0.0688669	+	0.119281i
$569$	9.59524	+	16.6194i	0.402253	+	0.696723i	0.993998	−	0.109403i	$-0.0348937\pi$
$569$	9.59524	+	16.6194i	0.402253	+	0.696723i	−0.591744	+	0.806126i	$0.701560\pi$
$570$	23.8512	−	22.1146i	0.999018	−	0.926278i
$571$	−13.4751	+	7.77984i	−0.563915	+	0.325576i	−0.754715	−	0.656053i	$-0.772225\pi$
$571$	−13.4751	+	7.77984i	−0.563915	+	0.325576i	0.190801	+	0.981629i	$0.438892\pi$
$572$	−1.97869	−	14.7651i	−0.0827333	−	0.617361i
$573$	−0.494267	+	13.0825i	−0.0206483	+	0.546529i
$574$	−14.8839	+	25.1293i	−0.621241	+	1.04888i
$575$	27.6804	+	15.9813i	1.15435	+	0.666466i
$576$	−0.226361	+	2.99145i	−0.00943173	+	0.124644i
$577$	8.37734	−	31.2646i	0.348753	−	1.30156i	−0.539413	−	0.842041i	$-0.681354\pi$
$577$	8.37734	−	31.2646i	0.348753	−	1.30156i	0.888166	−	0.459523i	$-0.151980\pi$
$578$	0.0995999	+	0.371712i	0.00414281	+	0.0154612i
$579$	15.7241	−	14.5792i	0.653469	−	0.605890i
$580$	8.63396	−	8.63396i	0.358506	−	0.358506i
$581$	11.2061	−	2.86932i	0.464906	−	0.119040i
$582$	10.2431	−	16.2887i	0.424592	−	0.675190i
$583$	14.3241	+	3.83812i	0.593242	+	0.158959i
$584$	−0.509731	−	0.882880i	−0.0210928	−	0.0365339i
$585$	2.10046	+	36.3680i	0.0868435	+	1.50363i
$586$	−6.62401	+	11.4731i	−0.273635	+	0.473950i
$587$	−1.24748	−	4.65565i	−0.0514890	−	0.192159i	0.935391	−	0.353615i	$-0.115048\pi$
$587$	−1.24748	−	4.65565i	−0.0514890	−	0.192159i	−0.986880	+	0.161456i	$0.948381\pi$
$588$	0.727399	−	12.1025i	0.0299974	−	0.499099i
$589$	41.7572	−	24.1086i	1.72058	−	0.993376i
$590$	−9.88784	−	36.9019i	−0.407076	−	1.51923i
$591$	4.85184	+	21.2929i	0.199578	+	0.875873i
$592$	0.0621155	+	0.231818i	0.00255293	+	0.00952768i
$593$	9.52012	−	2.55091i	0.390944	−	0.104753i	−0.0579918	−	0.998317i	$-0.518470\pi$
$593$	9.52012	−	2.55091i	0.390944	−	0.104753i	0.448936	+	0.893564i	$0.351803\pi$
$594$	8.56387	+	19.6871i	0.351380	+	0.807770i
$595$	−25.9764	−	26.5614i	−1.06493	−	1.08891i
$596$	2.85908	−	0.766087i	0.117112	−	0.0313802i
$597$	0.872635	+	0.548755i	0.0357146	+	0.0224590i
$598$	−2.41349	−	18.0097i	−0.0986951	−	0.736470i
$599$	−22.9575	+	13.2545i	−0.938018	+	0.541565i	−0.889339	−	0.457249i	$-0.848835\pi$
$599$	−22.9575	+	13.2545i	−0.938018	+	0.541565i	−0.0486798	+	0.998814i	$0.515501\pi$
$600$	−10.4959	−	3.24172i	−0.428492	−	0.132343i
$601$	−5.81044	+	10.0640i	−0.237013	+	0.410518i	−0.959856	−	0.280494i	$-0.909502\pi$
$601$	−5.81044	+	10.0640i	−0.237013	+	0.410518i	0.722843	+	0.691012i	$0.242835\pi$
$602$	−18.4358	−	5.16053i	−0.751388	−	0.210328i
$603$	−26.0546	−	30.3205i	−1.06103	−	1.23475i
$604$	7.19948	+	7.19948i	0.292943	+	0.292943i
$605$	19.7498	−	5.29193i	0.802942	−	0.215148i
$606$	−6.65437	−	2.05525i	−0.270315	−	0.0834886i
$607$	−30.6696			−1.24484			−0.622421	−	0.782683i	$-0.713851\pi$
$607$	−30.6696			−1.24484			−0.622421	+	0.782683i	$0.713851\pi$
$608$	2.78798	−	4.82892i	0.113067	−	0.195839i
$609$	−7.59401	−	14.7773i	−0.307725	−	0.598808i
$610$		−	3.89568i		−	0.157732i
$611$	−20.7843	+	2.78532i	−0.840842	+	0.112682i
$612$	11.2737	−	5.41907i	0.455714	−	0.219053i
$613$	5.89757	+	5.89757i	0.238200	+	0.238200i	0.816105	−	0.577904i	$-0.196129\pi$
$613$	5.89757	+	5.89757i	0.238200	+	0.238200i	−0.577904	+	0.816105i	$0.696129\pi$
$614$	−1.26185	+	0.728527i	−0.0509240	+	0.0294010i
$615$	56.9417	−	30.0681i	2.29611	−	1.21246i
$616$	5.57082	−	9.40552i	0.224455	−	0.378959i
$617$	−36.2213	−	9.70547i	−1.45821	−	0.390727i	−0.559342	−	0.828937i	$-0.688946\pi$
$617$	−36.2213	−	9.70547i	−1.45821	−	0.390727i	−0.898873	+	0.438210i	$0.855613\pi$
$618$	12.6779	+	13.6735i	0.509981	+	0.550029i
$619$	−34.1905	−	9.16130i	−1.37423	−	0.368224i	−0.505208	−	0.862997i	$-0.668584\pi$
$619$	−34.1905	−	9.16130i	−1.37423	−	0.368224i	−0.869022	+	0.494774i	$0.835251\pi$
$620$	−25.2210	−	14.5613i	−1.01290	−	0.584797i
$621$	10.4457	+	24.0131i	0.419172	+	0.963614i
$622$	−4.21656	−	15.7364i	−0.169069	−	0.630973i
$623$	−24.7884	+	24.2424i	−0.993124	+	0.971252i
$624$	2.18389	+	5.85069i	0.0874257	+	0.234215i
$625$	−8.24358	+	14.2783i	−0.329743	+	0.571132i
$626$	2.52698	−	2.52698i	0.100998	−	0.100998i
$627$	1.50651	−	39.8751i	0.0601642	−	1.59246i
$628$			6.98404i			0.278694i
$629$	0.707578	−	0.707578i	0.0282130	−	0.0282130i
$630$	−15.3191	+	21.9063i	−0.610329	+	0.872767i
$631$	30.8101	+	8.25554i	1.22653	+	0.328648i	0.813228	−	0.581946i	$-0.197708\pi$
$631$	30.8101	+	8.25554i	1.22653	+	0.328648i	0.413303	+	0.910594i	$0.364375\pi$
$632$	−11.3123	+	3.03112i	−0.449979	+	0.120571i
$633$	−1.73671	+	2.76174i	−0.0690282	+	0.109769i
$634$		−	19.9340i		−	0.791679i
$635$	17.2124	−	64.2377i	0.683055	−	2.54920i
$636$	−6.21216	−	0.234700i	−0.246328	−	0.00930646i
$637$	−9.19140	−	23.5057i	−0.364177	−	0.931330i
$638$		−	14.9798i		−	0.593056i
$639$	−9.29273	−	3.25924i	−0.367615	−	0.128934i
$640$	−3.36782			−0.133125
$641$	15.3261	−	26.5455i	0.605343	−	1.04849i	−0.386654	−	0.922225i	$-0.626369\pi$
$641$	15.3261	−	26.5455i	0.605343	−	1.04849i	0.991997	−	0.126260i	$-0.0402975\pi$
$642$	−32.1905	+	7.33499i	−1.27046	+	0.289489i
$643$	−11.8117	+	44.0819i	−0.465808	+	1.73842i	0.188389	+	0.982094i	$0.439673\pi$
$643$	−11.8117	+	44.0819i	−0.465808	+	1.73842i	−0.654197	+	0.756324i	$0.726993\pi$
$644$	6.79496	−	11.4723i	0.267759	−	0.452073i
$645$	28.6981	+	30.9517i	1.12999	+	1.21872i
$646$	−23.2490			−0.914721
$647$	21.0133			0.826119			0.413059	−	0.910704i	$-0.364460\pi$
$647$	21.0133			0.826119			0.413059	+	0.910704i	$0.364460\pi$
$648$	−5.33386	−	7.24913i	−0.209534	−	0.284773i
$649$	−40.5898	−	23.4345i	−1.59329	−	0.919886i
$650$	−22.6647	+	3.03732i	−0.888982	+	0.119133i
$651$	−29.3566	+	26.6175i	−1.15058	+	1.04322i
$652$	1.07000	−	0.286706i	0.0419045	−	0.0112283i
$653$	12.2425	−	7.06823i	0.479088	−	0.276601i	−0.240949	−	0.970538i	$-0.577459\pi$
$653$	12.2425	−	7.06823i	0.479088	−	0.276601i	0.720036	+	0.693937i	$0.244125\pi$
$654$	0.955156	−	1.51890i	0.0373495	−	0.0593936i
$655$	15.9620	−	59.5709i	0.623686	−	2.32763i
$656$	7.80572	−	7.80572i	0.304762	−	0.304762i
$657$	2.88603	+	1.01222i	0.112595	+	0.0394903i
$658$	−13.2398	−	7.84181i	−0.516140	−	0.305706i
$659$	−13.2278	+	7.63705i	−0.515280	+	0.297497i	−0.735001	−	0.678066i	$-0.762819\pi$
$659$	−13.2278	+	7.63705i	−0.515280	+	0.297497i	0.219721	+	0.975563i	$0.429485\pi$
$660$	−21.3124	+	11.2541i	−0.829586	+	0.438064i
$661$	−26.9341	+	26.9341i	−1.04762	+	1.04762i	−0.0488084	+	0.998808i	$0.515542\pi$
$661$	−26.9341	+	26.9341i	−1.04762	+	1.04762i	−0.998808	+	0.0488084i	$0.984458\pi$
$662$	−8.42805	−	14.5978i	−0.327565	−	0.567360i
$663$	16.5734	−	20.0831i	0.643657	−	0.779963i
$664$	−4.37214			−0.169672
$665$	43.3017	−	24.3615i	1.67917	−	0.944698i
$666$	−0.594588	−	0.406015i	−0.0230398	−	0.0157328i
$667$		−	18.2715i		−	0.707476i
$668$	12.8984	+	3.45613i	0.499056	+	0.133722i
$669$	11.4519	−	2.60945i	0.442755	−	0.100887i
$670$	31.7340	−	31.7340i	1.22599	−	1.22599i
$671$	−3.37948	−	3.37948i	−0.130463	−	0.130463i
$672$	−1.40099	+	4.36317i	−0.0540445	+	0.168313i
$673$	−39.1587	−	22.6083i	−1.50946	−	0.871486i	−0.999939	−	0.0110269i	$-0.996490\pi$
$673$	−39.1587	−	22.6083i	−1.50946	−	0.871486i	−0.509519	−	0.860459i	$-0.670177\pi$
$674$	0.968814	−	3.61566i	0.0373173	−	0.139270i
$675$	30.2199	−	13.1457i	1.16316	−	0.505976i
$676$	9.23490	+	9.14968i	0.355188	+	0.351911i
$677$	5.26711	+	3.04097i	0.202431	+	0.116874i	0.597789	−	0.801653i	$-0.296046\pi$
$677$	5.26711	+	3.04097i	0.202431	+	0.116874i	−0.395358	+	0.918527i	$0.629379\pi$
$678$	−5.23549	+	1.19297i	−0.201068	+	0.0458157i
$679$	21.0136	−	20.5508i	0.806427	−	0.788667i
$680$	7.02109	+	12.1609i	0.269247	+	0.466349i
$681$	0.327068	+	1.43538i	0.0125333	+	0.0550038i
$682$	−34.5109	+	9.24717i	−1.32149	+	0.354092i
$683$	49.2806	−	13.2047i	1.88567	−	0.505264i	0.886583	−	0.462570i	$-0.153073\pi$
$683$	49.2806	−	13.2047i	1.88567	−	0.505264i	0.999088	−	0.0426936i	$-0.0135939\pi$
$684$	3.09798	+	16.4385i	0.118454	+	0.628542i
$685$	−0.916468	−	1.58737i	−0.0350165	−	0.0606503i
$686$	5.38815	−	17.7191i	0.205721	−	0.676520i
$687$	2.58713	+	11.3540i	0.0987052	+	0.433180i
$688$	6.26650	+	3.61796i	0.238908	+	0.137934i
$689$	−11.9443	+	4.97995i	−0.455041	+	0.189721i
$690$	−25.9957	+	13.7271i	−0.989639	+	0.522580i
$691$	10.5421	−	39.3436i	0.401040	−	1.49670i	−0.410203	−	0.911994i	$-0.634542\pi$
$691$	10.5421	−	39.3436i	0.401040	−	1.49670i	0.811243	−	0.584709i	$-0.198791\pi$
$692$	−2.75625	−	1.59132i	−0.104777	−	0.0604930i
$693$	5.71430	+	32.2928i	0.217068	+	1.22670i
$694$	3.93294	+	3.93294i	0.149292	+	0.149292i
$695$	5.40311	−	5.40311i	0.204952	−	0.204952i
$696$	1.39513	+	6.12272i	0.0528824	+	0.232081i
$697$	−44.4587	−	11.9127i	−1.68399	−	0.451225i
$698$			6.96857i			0.263764i
$699$	−2.59090	+	4.12008i	−0.0979970	+	0.155836i
$700$	−14.4376	−	8.55127i	−0.545690	−	0.323208i
$701$	52.1993			1.97154			0.985771	−	0.168094i	$-0.0537613\pi$
$701$	52.1993			1.97154			0.985771	+	0.168094i	$0.0537613\pi$
$702$	−16.4084	−	9.04231i	−0.619296	−	0.341280i
$703$	0.669104	+	1.15892i	0.0252357	+	0.0437096i
$704$	−2.92157	+	2.92157i	−0.110111	+	0.110111i
$705$	15.8419	+	30.0007i	0.596640	+	1.12989i
$706$	31.2589	−	18.0473i	1.17644	−	0.679221i
$707$	−9.15341	−	5.42149i	−0.344249	−	0.203896i
$708$	18.7729	+	5.79813i	0.705529	+	0.217907i
$709$	−8.02791	+	8.02791i	−0.301494	+	0.301494i	−0.841598	−	0.540104i	$-0.818385\pi$
$709$	−8.02791	+	8.02791i	−0.301494	+	0.301494i	0.540104	+	0.841598i	$0.318385\pi$
$710$	2.86128	−	10.6784i	0.107382	−	0.400755i
$711$	19.8128	−	29.0147i	0.743037	−	1.08814i
$712$	11.3491	−	6.55242i	0.425326	−	0.245562i
$713$	−42.0944	+	11.2792i	−1.57645	+	0.422408i
$714$	18.6757	−	4.03729i	0.698920	−	0.151092i
$715$	−30.4498	+	39.8739i	−1.13876	+	1.49120i
$716$	5.67377	+	3.27575i	0.212039	+	0.122421i
$717$	7.69208	−	7.13201i	0.287266	−	0.266350i
$718$	−12.1011			−0.451610
$719$	−34.5000			−1.28663			−0.643316	−	0.765601i	$-0.722442\pi$
$719$	−34.5000			−1.28663			−0.643316	+	0.765601i	$0.722442\pi$
$720$	7.66293	−	6.58481i	0.285580	−	0.245401i
$721$	13.9660	+	24.8241i	0.520122	+	0.924499i
$722$	3.12946	−	11.6793i	0.116467	−	0.434659i
$723$	1.55984	+	6.84554i	0.0580110	+	0.254589i
$724$	2.50593	−	4.34039i	0.0931320	−	0.161309i
$725$	−22.9942			−0.853983
$726$	−3.10314	+	10.0472i	−0.115168	+	0.372886i
$727$			0.934609i			0.0346627i	0.999850	+	0.0173314i	$0.00551702\pi$
$727$			0.934609i			0.0346627i	−0.999850	+	0.0173314i	$0.994483\pi$
$728$	1.16171	+	9.46839i	0.0430558	+	0.350922i
$729$	26.3099	+	6.06536i	0.974441	+	0.224643i
$730$	−0.888622	+	3.31638i	−0.0328894	+	0.122745i
$731$		−	30.1703i		−	1.11589i
$732$	1.69605	+	1.06656i	0.0626877	+	0.0394210i
$733$	24.2171	−	6.48894i	0.894478	−	0.239675i	0.217835	−	0.975986i	$-0.430101\pi$
$733$	24.2171	−	6.48894i	0.894478	−	0.239675i	0.676643	+	0.736311i	$0.263434\pi$
$734$	22.2743	+	5.96837i	0.822158	+	0.220297i
$735$	−30.5533	+	27.0888i	−1.12698	+	0.999187i
$736$	−3.56356	+	3.56356i	−0.131355	+	0.131355i
$737$		−	55.0582i		−	2.02809i
$738$	−2.49880	+	33.0225i	−0.0919819	+	1.21557i
$739$	8.06623	−	8.06623i	0.296721	−	0.296721i	−0.543007	−	0.839728i	$-0.682714\pi$
$739$	8.06623	−	8.06623i	0.296721	−	0.296721i	0.839728	+	0.543007i	$0.182714\pi$
$740$	0.404132	−	0.699978i	0.0148562	−	0.0257317i
$741$	20.2059	+	28.3599i	0.742282	+	1.04183i
$742$	−9.14450	−	2.55972i	−0.335705	−	0.0939702i
$743$	4.63127	+	17.2841i	0.169905	+	0.634094i	0.997364	+	0.0725670i	$0.0231191\pi$
$743$	4.63127	+	17.2841i	0.169905	+	0.634094i	−0.827459	+	0.561527i	$0.810214\pi$
$744$	13.2445	−	6.99376i	0.485566	−	0.256404i
$745$	−8.63301	−	4.98427i	−0.316289	−	0.182610i
$746$	−14.5965	−	3.91113i	−0.534417	−	0.143197i
$747$	9.94808	−	8.54846i	0.363981	−	0.312772i
$748$	16.6403	+	4.45874i	0.608428	+	0.163028i
$749$	−50.4291	−	0.561504i	−1.84264	−	0.0205169i
$750$	3.65603	+	6.92362i	0.133499	+	0.252815i
$751$	−2.20533	+	1.27325i	−0.0804737	+	0.0464615i	−0.539697	−	0.841859i	$-0.681461\pi$
$751$	−2.20533	+	1.27325i	−0.0804737	+	0.0464615i	0.459223	+	0.888321i	$0.348128\pi$
$752$	4.11257	+	4.11257i	0.149970	+	0.149970i
$753$	−21.4358	−	40.5941i	−0.781164	−	1.47933i
$754$	7.98184	+	10.3524i	0.290681	+	0.377011i
$755$		−	34.2899i		−	1.24794i
$756$	−5.34319	−	12.6669i	−0.194330	−	0.460691i
$757$	16.1466	−	27.9667i	0.586857	−	1.01647i	−0.407784	−	0.913078i	$-0.633698\pi$
$757$	16.1466	−	27.9667i	0.586857	−	1.01647i	0.994641	−	0.103388i	$-0.0329684\pi$
$758$	18.5798			0.674850
$759$	−10.6430	+	34.4593i	−0.386315	+	1.25079i
$760$	−18.1390	+	4.86032i	−0.657970	+	0.176303i
$761$	−30.8134	−	30.8134i	−1.11699	−	1.11699i	−0.992181	−	0.124805i	$-0.960169\pi$
$761$	−30.8134	−	30.8134i	−1.11699	−	1.11699i	−0.124805	−	0.992181i	$-0.539831\pi$
$762$	23.2545	+	25.0806i	0.842421	+	0.908575i
$763$	1.95948	−	1.91633i	0.0709380	−	0.0693757i
$764$	3.77929	−	6.54592i	0.136730	−	0.236823i
$765$	−39.7524	−	13.9424i	−1.43725	−	0.504088i
$766$	−13.3148	+	7.68731i	−0.481084	+	0.277754i
$767$	40.5380	−	5.43254i	1.46374	−	0.196158i
$768$	0.922039	−	1.46623i	0.0332712	−	0.0529082i
$769$	31.9548	−	8.56226i	1.15232	−	0.308763i	0.368425	−	0.929658i	$-0.379897\pi$
$769$	31.9548	−	8.56226i	1.15232	−	0.308763i	0.783894	+	0.620895i	$0.213231\pi$
$770$	−35.6648	+	9.13200i	−1.28527	+	0.329095i
$771$	0.480099	+	0.909190i	0.0172903	+	0.0327437i
$772$	−11.9582	+	3.20420i	−0.430386	+	0.115322i
$773$	0.557005	+	2.07877i	0.0200341	+	0.0747681i	0.975219	−	0.221241i	$-0.0710108\pi$
$773$	0.557005	+	2.07877i	0.0200341	+	0.0747681i	−0.955185	+	0.296009i	$0.904344\pi$
$774$	−21.3323	+	4.02025i	−0.766772	+	0.144505i
$775$	14.1945	+	52.9747i	0.509882	+	1.90291i
$776$	−9.62088	+	5.55462i	−0.345369	+	0.199399i
$777$	−0.738736	−	0.814757i	−0.0265020	−	0.0292293i
$778$	−0.141834	−	0.529333i	−0.00508501	−	0.0189775i
$779$	30.7764	−	53.3063i	1.10268	−	1.90990i
$780$	8.73216	−	19.1337i	0.312661	−	0.685095i
$781$	−6.78134	−	11.7456i	−0.242655	−	0.420291i
$782$	20.2968	+	5.43852i	0.725813	+	0.194481i
$783$	−15.1456	−	11.2035i	−0.541260	−	0.400379i
$784$	−3.63411	+	5.98274i	−0.129790	+	0.213669i
$785$	16.6319	−	16.6319i	0.593617	−	0.593617i
$786$	21.5651	+	23.2585i	0.769200	+	0.829604i
$787$	8.22203	+	30.6850i	0.293084	+	1.09380i	0.942727	+	0.333565i	$0.108252\pi$
$787$	8.22203	+	30.6850i	0.293084	+	1.09380i	−0.649643	+	0.760239i	$0.725082\pi$
$788$	3.26334	−	12.1789i	0.116252	−	0.433857i
$789$	0.768341	−	20.3368i	0.0273536	−	0.724010i
$790$	34.1576	+	19.7209i	1.21527	+	0.701637i
$791$	−8.20182	−	0.0913234i	−0.291623	−	0.00324709i
$792$	0.935262	−	12.3598i	0.0332331	−	0.439187i
$793$	4.13624	+	0.534797i	0.146882	+	0.0189912i
$794$	24.2077	−	13.9763i	0.859099	−	0.496001i
$795$	14.2348	+	15.3526i	0.504856	+	0.544501i
$796$	−0.297577	−	0.515418i	−0.0105473	−	0.0182685i
$797$	−10.9107	−	18.8980i	−0.386478	−	0.669400i	0.605495	−	0.795849i	$-0.292975\pi$
$797$	−10.9107	−	18.8980i	−0.386478	−	0.669400i	−0.991973	+	0.126449i	$0.959642\pi$
$798$	−1.24893	+	25.5217i	−0.0442115	+	0.903459i
$799$	6.27639	−	23.4238i	0.222043	−	0.828675i
$800$	4.48464	+	4.48464i	0.158556	+	0.158556i
$801$	−13.0117	+	37.0989i	−0.459745	+	1.31082i
$802$	−8.92104	+	15.4517i	−0.315013	+	0.545618i
$803$	2.10607	+	3.64782i	0.0743215	+	0.128729i
$804$	5.12780	+	22.5040i	0.180844	+	0.793655i
$805$	−43.5019	+	11.1387i	−1.53324	+	0.392587i
$806$	18.9228	−	24.7794i	0.666527	−	0.872816i
$807$	1.73976	+	1.09404i	0.0612423	+	0.0385121i
$808$	2.84326	+	2.84326i	0.100025	+	0.100025i
$809$			37.1628i			1.30657i	0.757110	+	0.653287i	$0.226611\pi$
$809$			37.1628i			1.30657i	−0.757110	+	0.653287i	$0.773389\pi$
$810$	−4.56103	+	29.9653i	−0.160258	+	1.05287i
$811$	−36.7181	−	36.7181i	−1.28935	−	1.28935i	−0.935183	−	0.354165i	$-0.884765\pi$
$811$	−36.7181	−	36.7181i	−1.28935	−	1.28935i	−0.354165	−	0.935183i	$-0.615235\pi$
$812$	−0.106800	+	9.59174i	−0.00374793	+	0.336604i
$813$	33.9397	+	10.4825i	1.19032	+	0.367638i
$814$	−0.256644	−	0.957809i	−0.00899537	−	0.0335712i
$815$	−3.23088	−	1.86535i	−0.113173	−	0.0653404i
$816$	−7.21666	−	0.272651i	−0.252634	−	0.00954469i
$817$	38.9724	+	10.4426i	1.36347	+	0.365341i
$818$	25.7308			0.899656
$819$	−21.1560	−	19.2724i	−0.739250	−	0.673431i
$820$	−37.1773			−1.29829
$821$	−34.6471	−	9.28367i	−1.20919	−	0.324002i	−0.402748	−	0.915311i	$-0.631945\pi$
$821$	−34.6471	−	9.28367i	−1.20919	−	0.324002i	−0.806445	+	0.591309i	$0.798611\pi$
$822$	0.941996	+	0.0355893i	0.0328559	+	0.00124132i
$823$	11.9054	+	6.87357i	0.414995	+	0.239597i	0.692934	−	0.721001i	$-0.256318\pi$
$823$	11.9054	+	6.87357i	0.414995	+	0.239597i	−0.277939	+	0.960599i	$0.589651\pi$
$824$	−2.78634	−	10.3988i	−0.0970668	−	0.362258i
$825$	43.3660	+	13.3939i	1.50981	+	0.466315i
$826$	25.8230	+	15.2948i	0.898499	+	0.532174i
$827$	−16.8232	−	16.8232i	−0.584999	−	0.584999i	0.351274	−	0.936273i	$-0.385749\pi$
$827$	−16.8232	−	16.8232i	−0.584999	−	0.584999i	−0.936273	+	0.351274i	$0.885749\pi$
$828$	1.14078	−	15.0758i	0.0396448	−	0.523921i
$829$			12.0663i			0.419082i	0.977800	+	0.209541i	$0.0671969\pi$
$829$			12.0663i			0.419082i	−0.977800	+	0.209541i	$0.932803\pi$
$830$	10.4119	+	10.4119i	0.361401	+	0.361401i
$831$	17.8383	+	11.2176i	0.618803	+	0.389133i
$832$	0.462333	−	3.57579i	0.0160285	−	0.123968i
$833$	29.1793	+	0.649877i	1.01100	+	0.0225169i
$834$	0.873071	+	3.83158i	0.0302320	+	0.132677i
$835$	−22.4860	−	38.9470i	−0.778161	−	1.34781i
$836$	−11.5192	+	19.9518i	−0.398398	+	0.690046i
$837$	−16.4613	+	41.8089i	−0.568986	+	1.44513i
$838$	−27.4668	−	27.4668i	−0.948827	−	0.948827i
$839$	5.43784	−	20.2943i	0.187735	−	0.700637i	−0.806293	−	0.591516i	$-0.798530\pi$
$839$	5.43784	−	20.2943i	0.187735	−	0.700637i	0.994028	−	0.109121i	$-0.0348036\pi$
$840$	13.7268	−	7.05416i	0.473621	−	0.243391i
$841$	−7.92765	−	13.7311i	−0.273367	−	0.473486i
$842$	−3.91298	−	6.77748i	−0.134850	−	0.233567i
$843$	−1.17124	−	1.26322i	−0.0403396	−	0.0435075i
$844$	1.63121	−	0.941779i	0.0561485	−	0.0324174i
$845$	−0.202942	−	43.7813i	−0.00698142	−	1.50612i
$846$	−17.3984	−	1.31653i	−0.598170	−	0.0452633i
$847$	−8.18571	+	13.8204i	−0.281264	+	0.474874i
$848$	3.10829	+	1.79457i	0.106739	+	0.0616259i
$849$	−0.0895949	+	2.37144i	−0.00307489	+	0.0813877i
$850$	6.84422	−	25.5430i	0.234755	−	0.876117i
$851$	−0.313040	−	1.16828i	−0.0107309	−	0.0400481i
$852$	3.86567	+	4.16923i	0.132436	+	0.142835i
$853$	−2.73959	+	2.73959i	−0.0938019	+	0.0938019i	−0.752451	−	0.658649i	$-0.771128\pi$
$853$	−2.73959	+	2.73959i	−0.0938019	+	0.0938019i	0.658649	+	0.752451i	$0.271128\pi$
$854$	2.13983	+	2.18802i	0.0732234	+	0.0748723i
$855$	31.7693	−	46.5244i	1.08649	−	1.59110i
$856$	18.4121	+	4.93350i	0.629312	+	0.168624i
$857$	21.6487	+	37.4967i	0.739507	+	1.28086i	0.952718	+	0.303857i	$0.0982747\pi$
$857$	21.6487	+	37.4967i	0.739507	+	1.28086i	−0.213210	+	0.977006i	$0.568392\pi$
$858$	−9.02324	−	24.1734i	−0.308048	−	0.825267i
$859$	−0.127045	+	0.220049i	−0.00433473	+	0.00750798i	−0.868185	−	0.496241i	$-0.834713\pi$
$859$	−0.127045	+	0.220049i	−0.00433473	+	0.00750798i	0.863850	+	0.503749i	$0.168046\pi$
$860$	−6.30725	−	23.5390i	−0.215075	−	0.802672i
$861$	−15.4655	+	48.1648i	−0.527063	+	1.64145i
$862$	4.62448	−	2.66995i	0.157511	−	0.0909387i
$863$	−2.25217	−	8.40521i	−0.0766647	−	0.286117i	0.916941	−	0.399023i	$-0.130651\pi$
$863$	−2.25217	−	8.40521i	−0.0766647	−	0.286117i	−0.993606	+	0.112906i	$0.963984\pi$
$864$	0.768852	+	5.13896i	0.0261569	+	0.174831i
$865$	2.77417	+	10.3534i	0.0943247	+	0.352025i
$866$	15.0280	−	4.02673i	0.510671	−	0.136834i
$867$	0.311237	+	0.589407i	0.0105702	+	0.0200173i
$868$	22.1636	−	5.67502i	0.752283	−	0.192623i
$869$	46.7392	−	12.5237i	1.58552	−	0.424839i
$870$	11.2583	−	17.9031i	0.381693	−	0.606972i
$871$	29.3372	+	38.0500i	0.994052	+	1.28928i
$872$	−0.897131	+	0.517959i	−0.0303807	+	0.0175403i
$873$	11.0303	−	31.4495i	0.373318	−	1.06440i
$874$	−14.0504	+	24.3360i	−0.475262	+	0.823178i
$875$	2.96665	+	11.5862i	0.100291	+	0.391684i
$876$	−1.20055	−	1.29483i	−0.0405629	−	0.0437483i
$877$	24.8701	+	24.8701i	0.839803	+	0.839803i	0.988833	−	0.149029i	$-0.0476149\pi$
$877$	24.8701	+	24.8701i	0.839803	+	0.839803i	−0.149029	+	0.988833i	$0.547615\pi$
$878$	−35.0805	+	9.39980i	−1.18391	+	0.317228i
$879$	−6.77148	+	21.9243i	−0.228396	+	0.739490i
$880$	13.9149			0.469072
$881$	−26.4851	+	45.8735i	−0.892304	+	1.54552i	−0.0551982	+	0.998475i	$0.517579\pi$
$881$	−26.4851	+	45.8735i	−0.892304	+	1.54552i	−0.837106	+	0.547041i	$0.815754\pi$
$882$	−3.42870	−	20.7182i	−0.115450	−	0.697618i
$883$			49.7396i			1.67387i	0.547301	+	0.836936i	$0.315655\pi$
$883$			49.7396i			1.67387i	−0.547301	+	0.836936i	$0.684345\pi$
$884$	−13.8757	+	5.78520i	−0.466689	+	0.194577i
$885$	−30.8983	−	58.5137i	−1.03863	−	1.96692i
$886$	−5.09210	−	5.09210i	−0.171072	−	0.171072i
$887$	−38.9538	+	22.4900i	−1.30794	+	0.755139i	−0.981752	−	0.190166i	$-0.939097\pi$
$887$	−38.9538	+	22.4900i	−1.30794	+	0.755139i	−0.326187	+	0.945305i	$0.605764\pi$
$888$	0.194103	+	0.367584i	0.00651368	+	0.0123353i
$889$	25.6172	+	45.5337i	0.859173	+	1.52715i
$890$	−42.6309	−	11.4229i	−1.42899	−	0.382897i
$891$	22.0380	+	29.9514i	0.738302	+	1.00341i
$892$	−6.55015	−	1.75511i	−0.219315	−	0.0587654i
$893$	28.0853	+	16.2150i	0.939838	+	0.542616i
$894$	4.53351	−	2.39393i	0.151623	−	0.0800649i
$895$	−5.71067	−	21.3125i	−0.190887	−	0.712398i
$896$	1.89154	−	1.84988i	0.0631920	−	0.0618003i
$897$	−11.0060	−	29.4854i	−0.367481	−	0.984488i
$898$	3.20675	−	5.55426i	0.107011	−	0.185348i
$899$	22.1688	−	22.1688i	0.739370	−	0.739370i
$900$	−18.9725	−	1.43564i	−0.632416	−	0.0478546i
$901$		−	14.9650i		−	0.498556i
$902$	−32.2511	+	32.2511i	−1.07384	+	1.07384i
$903$	−33.1195	−	1.62073i	−1.10215	−	0.0539346i
$904$	2.99455	+	0.802388i	0.0995974	+	0.0266870i
$905$	−16.3039	+	4.36862i	−0.541960	+	0.145218i
$906$	14.9286	+	9.38783i	0.495970	+	0.311890i
$907$		−	47.8976i		−	1.59041i	−0.606338	−	0.795207i	$-0.707362\pi$
$907$		−	47.8976i		−	1.59041i	0.606338	−	0.795207i	$-0.292638\pi$
$908$	0.219985	−	0.820996i	0.00730046	−	0.0272457i
$909$	−12.0285	−	0.910193i	−0.398961	−	0.0301892i
$910$	19.7816	−	25.3146i	0.655755	−	0.839172i
$911$		−	11.8282i		−	0.391886i	−0.980615	−	0.195943i	$-0.937223\pi$
$911$		−	11.8282i		−	0.391886i	0.980615	−	0.195943i	$-0.0627767\pi$
$912$	2.85005	−	9.22774i	0.0943745	−	0.305561i
$913$	18.0645			0.597846
$914$	11.1651	−	19.3385i	0.369308	−	0.639661i
$915$	−1.49908	−	6.57889i	−0.0495580	−	0.217492i
$916$	1.74010	−	6.49414i	0.0574945	−	0.214572i
$917$	23.7561	+	42.2256i	0.784496	+	1.39441i
$918$	16.9534	−	13.4897i	0.559546	−	0.445227i
$919$	−0.440812			−0.0145411			−0.00727053	−	0.999974i	$-0.502314\pi$
$919$	−0.440812			−0.0145411			−0.00727053	+	0.999974i	$0.502314\pi$
$920$	16.9726			0.559570
$921$	−1.85062	+	1.71587i	−0.0609800	+	0.0565400i
$922$	32.9734	+	19.0372i	1.08592	+	0.626956i
$923$	10.9450	+	4.50389i	0.360260	+	0.148247i
$924$	5.78851	−	18.0274i	0.190428	−	0.593057i
$925$	−1.47025	+	0.393952i	−0.0483415	+	0.0129531i
$926$	7.25038	−	4.18601i	0.238262	−	0.137561i
$927$	26.6717	+	18.2128i	0.876012	+	0.598187i
$928$	0.938365	−	3.50202i	0.0308033	−	0.114960i
$929$	10.6800	−	10.6800i	0.350400	−	0.350400i	−0.509858	−	0.860258i	$-0.670302\pi$
$929$	10.6800	−	10.6800i	0.350400	−	0.350400i	0.860258	+	0.509858i	$0.170302\pi$
$930$	−48.1955	−	14.8855i	−1.58039	−	0.488115i
$931$	−10.9391	+	37.4675i	−0.358515	+	1.22795i
$932$	2.43351	−	1.40499i	0.0797122	−	0.0460218i
$933$	−13.1762	−	24.9525i	−0.431370	−	0.816909i
$934$	21.3806	−	21.3806i	0.699595	−	0.699595i
$935$	−29.0092	−	50.2454i	−0.948702	−	1.64320i
$936$	5.93946	+	9.04007i	0.194137	+	0.295484i
$937$	50.3863			1.64605			0.823024	−	0.568007i	$-0.192285\pi$
$937$	50.3863			1.64605			0.823024	+	0.568007i	$0.192285\pi$
$938$	−0.392541	+	35.2544i	−0.0128169	+	1.15110i
$939$	3.29507	−	5.23986i	0.107531	−	0.170996i
$940$		−	19.5875i		−	0.638872i
$941$	−3.23503	−	0.866823i	−0.105459	−	0.0282576i	0.205704	−	0.978614i	$-0.434052\pi$
$941$	−3.23503	−	0.866823i	−0.105459	−	0.0282576i	−0.311163	+	0.950357i	$0.600718\pi$
$942$	2.68749	+	11.7944i	0.0875633	+	0.384282i
$943$	−39.3380	+	39.3380i	−1.28102	+	1.28102i
$944$	−8.02122	−	8.02122i	−0.261069	−	0.261069i
$945$	−17.4408	+	42.8894i	−0.567349	+	1.39519i
$946$	−25.8914	−	14.9484i	−0.841802	−	0.486015i
$947$	−3.18427	+	11.8838i	−0.103475	+	0.386173i	−0.998168	−	0.0605087i	$-0.980728\pi$
$947$	−3.18427	+	11.8838i	−0.103475	+	0.386173i	0.894693	+	0.446682i	$0.147394\pi$
$948$	−17.9374	+	9.47187i	−0.582580	+	0.307632i
$949$	−3.39918	−	1.39876i	−0.110342	−	0.0454058i
$950$	30.6262	+	17.6820i	0.993645	+	0.573681i
$951$	−7.67069	−	33.6638i	−0.248739	−	1.09162i
$952$	−10.6232	−	2.97362i	−0.344298	−	0.0963756i
$953$	12.5519	+	21.7405i	0.406596	+	0.704245i	0.994506	−	0.104681i	$-0.0333823\pi$
$953$	12.5519	+	21.7405i	0.406596	+	0.704245i	−0.587910	+	0.808927i	$0.700049\pi$
$954$	−10.5812	+	1.99411i	−0.342578	+	0.0645618i
$955$	−24.5886	+	6.58848i	−0.795667	+	0.213198i
$956$	−5.84987	+	1.56747i	−0.189198	+	0.0506955i
$957$	−5.76430	−	25.2974i	−0.186333	−	0.817748i
$958$	−18.6833	−	32.3605i	−0.603631	−	1.04552i
$959$	1.38665	+	0.388149i	0.0447772	+	0.0125340i
$960$	−5.68746	+	1.29595i	−0.183562	+	0.0418268i
$961$	−37.9113	−	21.8881i	−1.22294	−	0.706067i
$962$	0.687722	+	0.525180i	0.0221730	+	0.0169325i
$963$	−51.5397	+	24.7741i	−1.66084	+	0.798335i
$964$	1.04914	−	3.91546i	0.0337907	−	0.126108i
$965$	36.1080	+	20.8470i	1.16236	+	0.671087i
$966$	7.06049	−	21.9888i	0.227168	−	0.707477i
$967$	−16.2820	−	16.2820i	−0.523593	−	0.523593i	0.395062	−	0.918655i	$-0.370723\pi$
$967$	−16.2820	−	16.2820i	−0.523593	−	0.523593i	−0.918655	+	0.395062i	$0.870723\pi$
$968$	4.29293	−	4.29293i	0.137980	−	0.137980i
$969$	−39.2621	+	8.94634i	−1.26128	+	0.287398i
$970$	36.1391	+	9.68344i	1.16036	+	0.310917i
$971$			36.8862i			1.18374i	0.806035	+	0.591868i	$0.201609\pi$
$971$			36.8862i			1.18374i	−0.806035	+	0.591868i	$0.798391\pi$
$972$	−11.7971	−	10.1896i	−0.378393	−	0.326831i
$973$	−0.0668349	+	6.00249i	−0.00214263	+	0.192431i
$974$	4.30081			0.137807
$975$	−37.1065	+	13.8508i	−1.18836	+	0.443580i
$976$	−0.578368	−	1.00176i	−0.0185131	−	0.0320656i
$977$	−8.76947	+	8.76947i	−0.280560	+	0.280560i	−0.833332	−	0.552772i	$-0.813570\pi$
$977$	−8.76947	+	8.76947i	−0.280560	+	0.280560i	0.552772	+	0.833332i	$0.313570\pi$
$978$	1.69666	−	0.895922i	0.0542531	−	0.0286484i
$979$	−46.8914	+	27.0728i	−1.49866	+	0.865249i
$980$	22.9017	−	5.59305i	0.731568	−	0.178663i
$981$	1.02855	−	2.93261i	0.0328392	−	0.0936310i
$982$	−1.99625	+	1.99625i	−0.0637028	+	0.0637028i
$983$	−8.69958	+	32.4673i	−0.277473	+	1.03554i	0.676692	+	0.736266i	$0.263413\pi$
$983$	−8.69958	+	32.4673i	−0.277473	+	1.03554i	−0.954166	+	0.299279i	$0.903254\pi$
$984$	10.1783	−	16.1857i	0.324474	−	0.515982i
$985$	−36.7744	+	21.2317i	−1.17173	+	0.676499i
$986$	−14.6017	+	3.91252i	−0.465014	+	0.124600i
$987$	−25.3764	−	8.14825i	−0.807740	−	0.259362i
$988$	−2.67034	−	19.9263i	−0.0849549	−	0.633939i
$989$	−31.5809	−	18.2332i	−1.00421	−	0.579783i
$990$	−31.6611	+	27.2066i	−1.00626	+	0.864682i
$991$	−8.23616			−0.261630			−0.130815	−	0.991407i	$-0.541759\pi$
$991$	−8.23616			−0.261630			−0.130815	+	0.991407i	$0.541759\pi$
$992$	−8.64732			−0.274553
$993$	−19.8503	−	21.4091i	−0.629930	−	0.679397i
$994$	4.25843	+	7.56920i	0.135069	+	0.240080i
$995$	−0.518770	+	1.93608i	−0.0164461	+	0.0613778i
$996$	−7.38351	+	1.68242i	−0.233956	+	0.0533095i
$997$	11.4445	−	19.8225i	0.362451	−	0.627783i	−0.625913	−	0.779893i	$-0.715273\pi$
$997$	11.4445	−	19.8225i	0.362451	−	0.627783i	0.988364	+	0.152110i	$0.0486067\pi$
$998$	6.15638			0.194877
$999$	−1.16036	−	0.456864i	−0.0367120	−	0.0144545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.527.1	yes	152
3.2	odd	2	inner	546.2.bw.a.527.20	yes	152
7.4	even	3		546.2.ch.a.137.32	yes	152
13.2	odd	12		546.2.ch.a.275.14	yes	152
21.11	odd	6		546.2.ch.a.137.14	yes	152
39.2	even	12		546.2.ch.a.275.32	yes	152
91.67	odd	12	inner	546.2.bw.a.431.20	yes	152
273.158	even	12	inner	546.2.bw.a.431.1	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.1	✓	152	273.158	even	12	inner
546.2.bw.a.431.20	yes	152	91.67	odd	12	inner
546.2.bw.a.527.1	yes	152	1.1	even	1	trivial
546.2.bw.a.527.20	yes	152	3.2	odd	2	inner
546.2.ch.a.137.14	yes	152	21.11	odd	6
546.2.ch.a.137.32	yes	152	7.4	even	3
546.2.ch.a.275.14	yes	152	13.2	odd	12
546.2.ch.a.275.32	yes	152	39.2	even	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.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.73082 - 0.0653915i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.871657 - 3.25307i) q^{5} +(1.65492 + 0.511132i) q^{6} +(2.27642 + 1.34830i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99145 + 0.226361i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.73082 - 0.0653915i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.871657 - 3.25307i) q^{5} +(1.65492 + 0.511132i) q^{6} +(2.27642 + 1.34830i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99145 + 0.226361i) q^{9} +3.36782i q^{10} +(2.92157 + 2.92157i) q^{11} +(-1.46623 - 0.922039i) q^{12} +(-3.57579 - 0.462333i) q^{13} +(-1.84988 - 1.89154i) q^{14} +(1.29595 + 5.68746i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.08476 - 3.61090i) q^{17} +(-2.83093 - 0.992892i) q^{18} +(3.94280 + 3.94280i) q^{19} +(0.871657 - 3.25307i) q^{20} +(-3.85189 - 2.48253i) q^{21} +(-2.06586 - 3.57818i) q^{22} +(-2.51982 - 4.36445i) q^{23} +(1.17763 + 1.27011i) q^{24} +(-5.49254 + 3.17112i) q^{25} +(3.33428 + 1.37206i) q^{26} +(-5.16284 - 0.587405i) q^{27} +(1.29728 + 2.30587i) q^{28} +(3.13983 + 1.81278i) q^{29} +(0.220227 - 5.82908i) q^{30} +(2.23809 - 8.35267i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-4.86565 - 5.24774i) q^{33} +(-2.94829 + 2.94829i) q^{34} +(2.40187 - 8.58060i) q^{35} +(2.47749 + 1.69176i) q^{36} +(0.231818 + 0.0621155i) q^{37} +(-2.78798 - 4.82892i) q^{38} +(6.15880 + 1.03404i) q^{39} +(-1.68391 + 2.91662i) q^{40} +(-2.85709 - 10.6628i) q^{41} +(3.07812 + 3.39488i) q^{42} +(6.26650 - 3.61796i) q^{43} +(1.06937 + 3.99094i) q^{44} +(-1.87115 - 9.92870i) q^{45} +(1.30435 + 4.86791i) q^{46} +(5.61788 - 1.50531i) q^{47} +(-0.808777 - 1.53163i) q^{48} +(3.36415 + 6.13861i) q^{49} +(6.12614 - 1.64149i) q^{50} +(-3.84445 + 6.11348i) q^{51} +(-2.86556 - 2.18829i) q^{52} +(3.10829 - 1.79457i) q^{53} +(4.83489 + 1.90363i) q^{54} +(6.95746 - 12.0507i) q^{55} +(-0.656275 - 2.56307i) q^{56} +(-6.56643 - 7.08208i) q^{57} +(-2.56366 - 2.56366i) q^{58} +(-10.9572 + 2.93597i) q^{59} +(-1.72140 + 5.57346i) q^{60} -1.15674 q^{61} +(-4.32366 + 7.48880i) q^{62} +(6.50458 + 4.54868i) q^{63} +1.00000i q^{64} +(1.61286 + 12.0353i) q^{65} +(3.34164 + 6.32825i) q^{66} +(-9.42271 - 9.42271i) q^{67} +(3.61090 - 2.08476i) q^{68} +(4.07594 + 7.71884i) q^{69} +(-4.54085 + 7.66657i) q^{70} +(-3.17072 - 0.849592i) q^{71} +(-1.95521 - 2.27533i) q^{72} +(0.984725 + 0.263856i) q^{73} +(-0.207843 - 0.119998i) q^{74} +(9.71395 - 5.12946i) q^{75} +(1.44316 + 5.38596i) q^{76} +(2.71154 + 10.5899i) q^{77} +(-5.68131 - 2.59282i) q^{78} +(5.85567 - 10.1423i) q^{79} +(2.38141 - 2.38141i) q^{80} +(8.89752 + 1.35430i) q^{81} +11.0390i q^{82} +(3.09157 - 3.09157i) q^{83} +(-2.09457 - 4.07588i) q^{84} +(-13.5637 - 3.63438i) q^{85} +(-6.98937 + 1.87280i) q^{86} +(-5.31593 - 3.34291i) q^{87} -4.13172i q^{88} +(-3.39178 + 12.6583i) q^{89} +(-0.762346 + 10.0747i) q^{90} +(-7.51662 - 5.87371i) q^{91} -5.03964i q^{92} +(-4.41992 + 14.3106i) q^{93} -5.81606 q^{94} +(9.38943 - 16.2630i) q^{95} +(0.384805 + 1.68876i) q^{96} +(2.87528 - 10.7307i) q^{97} +(-1.66073 - 6.80015i) q^{98} +(8.07839 + 9.40105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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