LMFDB - Embedded newform 546.2.ch.a.137.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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			137.14
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.922039 + 1.46623i) q^{3} -1.00000i q^{4} +(-3.25307 - 0.871657i) q^{5} +(-1.68876 - 0.384805i) q^{6} +(2.64559 - 0.0294574i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.29969 + 2.70385i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.922039 + 1.46623i) q^{3} -1.00000i q^{4} +(-3.25307 - 0.871657i) q^{5} +(-1.68876 - 0.384805i) q^{6} +(2.64559 - 0.0294574i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.29969 + 2.70385i) q^{9} +(2.91662 - 1.68391i) q^{10} +(-1.06937 + 3.99094i) q^{11} +(1.46623 - 0.922039i) q^{12} +(-3.57579 - 0.462333i) q^{13} +(-1.84988 + 1.89154i) q^{14} +(-1.72140 - 5.57346i) q^{15} -1.00000 q^{16} +4.16951 q^{17} +(-0.992892 - 2.83093i) q^{18} +(-5.38596 + 1.44316i) q^{19} +(-0.871657 + 3.25307i) q^{20} +(2.48253 + 3.85189i) q^{21} +(-2.06586 - 3.57818i) q^{22} -5.03964 q^{23} +(-0.384805 + 1.68876i) q^{24} +(5.49254 + 3.17112i) q^{25} +(2.85538 - 2.20154i) q^{26} +(-5.16284 + 0.587405i) q^{27} +(-0.0294574 - 2.64559i) q^{28} +(-3.13983 - 1.81278i) q^{29} +(5.15825 + 2.72382i) q^{30} +(-8.35267 + 2.23809i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.83765 + 2.11185i) q^{33} +(-2.94829 + 2.94829i) q^{34} +(-8.63195 - 2.21022i) q^{35} +(2.70385 + 1.29969i) q^{36} +(-0.169703 + 0.169703i) q^{37} +(2.78798 - 4.82892i) q^{38} +(-2.61913 - 5.66923i) q^{39} +(-1.68391 - 2.91662i) q^{40} +(2.85709 + 10.6628i) q^{41} +(-4.47911 - 0.968288i) q^{42} +(6.26650 - 3.61796i) q^{43} +(3.99094 + 1.06937i) q^{44} +(6.58481 - 7.66293i) q^{45} +(3.56356 - 3.56356i) q^{46} +(1.50531 - 5.61788i) q^{47} +(-0.922039 - 1.46623i) q^{48} +(6.99826 - 0.155864i) q^{49} +(-6.12614 + 1.64149i) q^{50} +(3.84445 + 6.11348i) q^{51} +(-0.462333 + 3.57579i) q^{52} +(3.10829 + 1.79457i) q^{53} +(3.23532 - 4.06604i) q^{54} +(6.95746 - 12.0507i) q^{55} +(1.89154 + 1.84988i) q^{56} +(-7.08208 - 6.56643i) q^{57} +(3.50202 - 0.938365i) q^{58} +(-8.02122 - 8.02122i) q^{59} +(-5.57346 + 1.72140i) q^{60} +(0.578368 - 1.00176i) q^{61} +(4.32366 - 7.48880i) q^{62} +(-3.35879 + 7.19156i) q^{63} +1.00000i q^{64} +(11.2293 + 4.62086i) q^{65} +(3.34164 - 6.32825i) q^{66} +(-3.44895 + 12.8717i) q^{67} -4.16951i q^{68} +(-4.64674 - 7.38929i) q^{69} +(7.66657 - 4.54085i) q^{70} +(3.17072 + 0.849592i) q^{71} +(-2.83093 + 0.992892i) q^{72} +(-0.263856 - 0.984725i) q^{73} -0.239996i q^{74} +(0.414729 + 10.9773i) q^{75} +(1.44316 + 5.38596i) q^{76} +(-2.71154 + 10.5899i) q^{77} +(5.86075 + 2.15675i) q^{78} +(5.85567 + 10.1423i) q^{79} +(3.25307 + 0.871657i) q^{80} +(-5.62162 - 7.02833i) q^{81} +(-9.56002 - 5.51948i) q^{82} +(-3.09157 + 3.09157i) q^{83} +(3.85189 - 2.48253i) q^{84} +(-13.5637 - 3.63438i) q^{85} +(-1.87280 + 6.98937i) q^{86} +(-0.237081 - 6.27518i) q^{87} +(-3.57818 + 2.06586i) q^{88} +(9.26652 + 9.26652i) q^{89} +(0.762346 + 10.0747i) q^{90} +(-9.47367 - 1.11781i) q^{91} +5.03964i q^{92} +(-10.9831 - 10.1834i) q^{93} +(2.90803 + 5.03685i) q^{94} +18.7789 q^{95} +(1.68876 + 0.384805i) q^{96} +(2.87528 - 10.7307i) q^{97} +(-4.83831 + 5.05873i) q^{98} +(-9.40105 - 8.07839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.922039	+	1.46623i	0.532339	+	0.846531i
$3$	0.922039	+	1.46623i	0.532339	+	0.846531i
$4$		−	1.00000i		−	0.500000i
$5$	−3.25307	−	0.871657i	−1.45482	−	0.389817i	−0.557120	−	0.830432i	$-0.688094\pi$
$5$	−3.25307	−	0.871657i	−1.45482	−	0.389817i	−0.897696	+	0.440615i	$0.854760\pi$
$6$	−1.68876	−	0.384805i	−0.689435	−	0.157096i
$7$	2.64559	−	0.0294574i	0.999938	−	0.0111338i
$7$	2.64559	−	0.0294574i	0.999938	−	0.0111338i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.29969	+	2.70385i	−0.433230	+	0.901284i
$10$	2.91662	−	1.68391i	0.922317	−	0.532500i
$11$	−1.06937	+	3.99094i	−0.322427	+	1.20331i	0.594447	+	0.804135i	$0.297371\pi$
$11$	−1.06937	+	3.99094i	−0.322427	+	1.20331i	−0.916874	+	0.399178i	$0.869296\pi$
$12$	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
$15$	−1.72140	−	5.57346i	−0.444464	−	1.43906i
$16$	−1.00000			−0.250000
$17$	4.16951			1.01126			0.505628	−	0.862752i	$-0.331261\pi$
$17$	4.16951			1.01126			0.505628	+	0.862752i	$0.331261\pi$
$18$	−0.992892	−	2.83093i	−0.234027	−	0.667257i
$19$	−5.38596	+	1.44316i	−1.23562	+	0.331085i	−0.816767	−	0.576967i	$-0.804236\pi$
$19$	−5.38596	+	1.44316i	−1.23562	+	0.331085i	−0.418857	+	0.908052i	$0.637569\pi$
$20$	−0.871657	+	3.25307i	−0.194908	+	0.727408i
$21$	2.48253	+	3.85189i	0.541731	+	0.840552i
$22$	−2.06586	−	3.57818i	−0.440443	−	0.762869i
$23$	−5.03964			−1.05084			−0.525418	−	0.850844i	$-0.676091\pi$
$23$	−5.03964			−1.05084			−0.525418	+	0.850844i	$0.676091\pi$
$24$	−0.384805	+	1.68876i	−0.0785479	+	0.344718i
$25$	5.49254	+	3.17112i	1.09851	+	0.634224i
$26$	2.85538	−	2.20154i	0.559986	−	0.431758i
$27$	−5.16284	+	0.587405i	−0.993590	+	0.113046i
$28$	−0.0294574	−	2.64559i	−0.00556692	−	0.499969i
$29$	−3.13983	−	1.81278i	−0.583052	−	0.336625i	0.179294	−	0.983796i	$-0.442619\pi$
$29$	−3.13983	−	1.81278i	−0.583052	−	0.336625i	−0.762345	+	0.647171i	$0.775952\pi$
$30$	5.15825	+	2.72382i	0.941763	+	0.497299i
$31$	−8.35267	+	2.23809i	−1.50018	+	0.401973i	−0.913162	−	0.407598i	$-0.866367\pi$
$31$	−8.35267	+	2.23809i	−1.50018	+	0.401973i	−0.587022	+	0.809571i	$0.699700\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−6.83765	+	2.11185i	−1.19028	+	0.367626i
$34$	−2.94829	+	2.94829i	−0.505628	+	0.505628i
$35$	−8.63195	−	2.21022i	−1.45907	−	0.373595i
$36$	2.70385	+	1.29969i	0.450642	+	0.216615i
$37$	−0.169703	+	0.169703i	−0.0278990	+	0.0278990i	−0.720919	−	0.693020i	$-0.756280\pi$
$37$	−0.169703	+	0.169703i	−0.0278990	+	0.0278990i	0.693020	+	0.720919i	$0.256280\pi$
$38$	2.78798	−	4.82892i	0.452270	−	0.783355i
$39$	−2.61913	−	5.66923i	−0.419396	−	0.907804i
$40$	−1.68391	−	2.91662i	−0.266250	−	0.461158i
$41$	2.85709	+	10.6628i	0.446203	+	1.66525i	0.712741	+	0.701428i	$0.247454\pi$
$41$	2.85709	+	10.6628i	0.446203	+	1.66525i	−0.266538	+	0.963825i	$0.585880\pi$
$42$	−4.47911	−	0.968288i	−0.691142	−	0.149410i
$43$	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	$0.147300\pi$
$44$	3.99094	+	1.06937i	0.601656	+	0.161213i
$45$	6.58481	−	7.66293i	0.981605	−	1.14232i
$46$	3.56356	−	3.56356i	0.525418	−	0.525418i
$47$	1.50531	−	5.61788i	0.219571	−	0.819452i	−0.764936	−	0.644107i	$-0.777229\pi$
$47$	1.50531	−	5.61788i	0.219571	−	0.819452i	0.984507	−	0.175345i	$-0.0561041\pi$
$48$	−0.922039	−	1.46623i	−0.133085	−	0.211633i
$49$	6.99826	−	0.155864i	0.999752	−	0.0222663i
$50$	−6.12614	+	1.64149i	−0.866367	+	0.232142i
$51$	3.84445	+	6.11348i	0.538331	+	0.856059i
$52$	−0.462333	+	3.57579i	−0.0641140	+	0.495872i
$53$	3.10829	+	1.79457i	0.426957	+	0.246504i	0.698049	−	0.716050i	$-0.254052\pi$
$53$	3.10829	+	1.79457i	0.426957	+	0.246504i	−0.271092	+	0.962553i	$0.587385\pi$
$54$	3.23532	−	4.06604i	0.440272	−	0.553318i
$55$	6.95746	−	12.0507i	0.938143	−	1.62491i
$56$	1.89154	+	1.84988i	0.252768	+	0.247201i
$57$	−7.08208	−	6.56643i	−0.938045	−	0.869745i
$58$	3.50202	−	0.938365i	0.459838	−	0.123213i
$59$	−8.02122	−	8.02122i	−1.04427	−	1.04427i	−0.998973	−	0.0453009i	$-0.985575\pi$
$59$	−8.02122	−	8.02122i	−1.04427	−	1.04427i	−0.0453009	−	0.998973i	$-0.514425\pi$
$60$	−5.57346	+	1.72140i	−0.719531	+	0.222232i
$61$	0.578368	−	1.00176i	0.0740524	−	0.128263i	−0.826621	−	0.562758i	$-0.809740\pi$
$61$	0.578368	−	1.00176i	0.0740524	−	0.128263i	0.900674	+	0.434496i	$0.143073\pi$
$62$	4.32366	−	7.48880i	0.549105	−	0.951079i
$63$	−3.35879	+	7.19156i	−0.423168	+	0.906051i
$64$			1.00000i			0.125000i
$65$	11.2293	+	4.62086i	1.39282	+	0.573147i
$66$	3.34164	−	6.32825i	0.411328	−	0.778954i
$67$	−3.44895	+	12.8717i	−0.421356	+	1.57252i	0.350397	+	0.936601i	$0.386047\pi$
$67$	−3.44895	+	12.8717i	−0.421356	+	1.57252i	−0.771753	+	0.635922i	$0.780620\pi$
$68$		−	4.16951i		−	0.505628i
$69$	−4.64674	−	7.38929i	−0.559402	−	0.889566i
$70$	7.66657	−	4.54085i	0.916331	−	0.542736i
$71$	3.17072	+	0.849592i	0.376295	+	0.100828i	0.442009	−	0.897010i	$-0.354266\pi$
$71$	3.17072	+	0.849592i	0.376295	+	0.100828i	−0.0657139	+	0.997839i	$0.520932\pi$
$72$	−2.83093	+	0.992892i	−0.333628	+	0.117013i
$73$	−0.263856	−	0.984725i	−0.0308820	−	0.115253i	0.948764	−	0.315985i	$-0.102335\pi$
$73$	−0.263856	−	0.984725i	−0.0308820	−	0.115253i	−0.979646	+	0.200731i	$0.935668\pi$
$74$		−	0.239996i		−	0.0278990i
$75$	0.414729	+	10.9773i	0.0478888	+	1.26754i
$76$	1.44316	+	5.38596i	0.165542	+	0.617812i
$77$	−2.71154	+	10.5899i	−0.309009	+	1.20683i
$78$	5.86075	+	2.15675i	0.663600	+	0.244204i
$79$	5.85567	+	10.1423i	0.658815	+	1.14110i	0.980923	+	0.194397i	$0.0622752\pi$
$79$	5.85567	+	10.1423i	0.658815	+	1.14110i	−0.322108	+	0.946703i	$0.604392\pi$
$80$	3.25307	+	0.871657i	0.363704	+	0.0974542i
$81$	−5.62162	−	7.02833i	−0.624624	−	0.780926i
$82$	−9.56002	−	5.51948i	−1.05573	−	0.609525i
$83$	−3.09157	+	3.09157i	−0.339344	+	0.339344i	−0.856120	−	0.516777i	$-0.827132\pi$
$83$	−3.09157	+	3.09157i	−0.339344	+	0.339344i	0.516777	+	0.856120i	$0.327132\pi$
$84$	3.85189	−	2.48253i	0.420276	−	0.270866i
$85$	−13.5637	−	3.63438i	−1.47119	−	0.394204i
$86$	−1.87280	+	6.98937i	−0.201949	+	0.753683i
$87$	−0.237081	−	6.27518i	−0.0254178	−	0.672770i
$88$	−3.57818	+	2.06586i	−0.381435	+	0.220221i
$89$	9.26652	+	9.26652i	0.982249	+	0.982249i	0.999845	−	0.0175962i	$-0.00560134\pi$
$89$	9.26652	+	9.26652i	0.982249	+	0.982249i	−0.0175962	+	0.999845i	$0.505601\pi$
$90$	0.762346	+	10.0747i	0.0803583	+	1.06196i
$91$	−9.47367	−	1.11781i	−0.993111	−	0.117178i
$92$			5.03964i			0.525418i
$93$	−10.9831	−	10.1834i	−1.13889	−	1.05597i
$94$	2.90803	+	5.03685i	0.299940	+	0.519512i
$95$	18.7789			1.92667
$96$	1.68876	+	0.384805i	0.172359	+	0.0392740i
$97$	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	$-0.107399\pi$
$98$	−4.83831	+	5.05873i	−0.488743	+	0.511009i
$99$	−9.40105	−	8.07839i	−0.944841	−	0.811908i
$100$	3.17112	−	5.49254i	0.317112	−	0.549254i
$101$	−2.01049	−	3.48226i	−0.200051	−	0.346498i	0.748494	−	0.663142i	$-0.230777\pi$
$101$	−2.01049	−	3.48226i	−0.200051	−	0.346498i	−0.948545	+	0.316644i	$0.897444\pi$
$102$	−7.04132	−	1.60445i	−0.697195	−	0.158864i
$103$	−9.32328	+	5.38280i	−0.918650	+	0.530383i	−0.883204	−	0.468989i	$-0.844619\pi$
$103$	−9.32328	+	5.38280i	−0.918650	+	0.530383i	−0.0354461	+	0.999372i	$0.511285\pi$
$104$	−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
$107$			19.0616i			1.84275i	0.388671	+	0.921377i	$0.372934\pi$
$107$			19.0616i			1.84275i	−0.388671	+	0.921377i	$0.627066\pi$
$108$	0.587405	+	5.16284i	0.0565231	+	0.496795i
$109$	−1.00062	+	0.268115i	−0.0958419	+	0.0256808i	−0.306421	−	0.951896i	$-0.599132\pi$
$109$	−1.00062	+	0.268115i	−0.0958419	+	0.0256808i	0.210579	+	0.977577i	$0.432465\pi$
$110$	3.60144	+	13.4408i	0.343384	+	1.28153i
$111$	−0.405297	−	0.0923516i	−0.0384691	−	0.00876563i
$112$	−2.64559	+	0.0294574i	−0.249985	+	0.00278346i
$113$	2.68484	−	1.55009i	0.252569	−	0.145821i	−0.368371	−	0.929679i	$-0.620084\pi$
$113$	2.68484	−	1.55009i	0.252569	−	0.145821i	0.620940	+	0.783858i	$0.286751\pi$
$114$	9.65096	−	0.364621i	0.903895	−	0.0341498i
$115$	16.3943	+	4.39283i	1.52877	+	0.409634i
$116$	−1.81278	+	3.13983i	−0.168312	+	0.291526i
$117$	5.89749	−	9.06750i	0.545223	−	0.838291i
$118$	11.3437			1.04427
$119$	11.0308	−	0.122823i	1.01119	−	0.0112591i
$120$	2.72382	−	5.15825i	0.248650	−	0.470882i
$121$	−5.25774	−	3.03556i	−0.477976	−	0.275960i
$122$	0.299385	+	1.11732i	0.0271051	+	0.101158i
$123$	−12.9998	+	14.0207i	−1.17216	+	1.26420i
$124$	2.23809	+	8.35267i	0.200987	+	0.750092i
$125$	−3.19643	−	3.19643i	−0.285898	−	0.285898i
$126$	−2.71017	−	7.46022i	−0.241442	−	0.664610i
$127$	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	$0.326788\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	11.0827	+	5.85225i	0.975780	+	0.515262i
$130$	−11.2077	+	4.67286i	−0.982984	+	0.409837i
$131$	15.8588	−	9.15610i	1.38559	−	0.799972i	0.392778	−	0.919633i	$-0.371514\pi$
$131$	15.8588	−	9.15610i	1.38559	−	0.799972i	0.992815	+	0.119661i	$0.0381808\pi$
$132$	2.11185	+	6.83765i	0.183813	+	0.595141i
$133$	−14.2065	+	3.97667i	−1.23186	+	0.344821i
$134$	−6.66286	−	11.5404i	−0.575584	−	0.996940i
$135$	17.3071	+	2.58936i	1.48956	+	0.222857i
$136$	2.94829	+	2.94829i	0.252814	+	0.252814i
$137$	0.384843	+	0.384843i	0.0328793	+	0.0328793i	0.723355	−	0.690476i	$-0.242599\pi$
$137$	0.384843	+	0.384843i	0.0328793	+	0.0328793i	−0.690476	+	0.723355i	$0.742599\pi$
$138$	8.51076	+	1.93928i	0.724484	+	0.165082i
$139$	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	$0.802658\pi$
$140$	−2.21022	+	8.63195i	−0.186798	+	0.729533i
$141$	9.62508	−	2.97277i	0.810578	−	0.250352i
$142$	−2.84279	+	1.64129i	−0.238562	+	0.137734i
$143$	5.66897	−	13.7763i	0.474063	−	1.15203i
$144$	1.29969	−	2.70385i	0.108307	−	0.225321i
$145$	8.63396	+	8.63396i	0.717011	+	0.717011i
$146$	0.882880	+	0.509731i	0.0730677	+	0.0421857i
$147$	6.68120	+	10.1174i	0.551056	+	0.834468i
$148$	0.169703	+	0.169703i	0.0139495	+	0.0139495i
$149$	−0.766087	−	2.85908i	−0.0627603	−	0.234225i	0.927420	−	0.374022i	$-0.122022\pi$
$149$	−0.766087	−	2.85908i	−0.0627603	−	0.234225i	−0.990180	+	0.139797i	$0.955355\pi$
$150$	−8.05535	−	7.46883i	−0.657717	−	0.609828i
$151$	−2.63519	−	9.83467i	−0.214449	−	0.800334i	−0.986360	−	0.164604i	$-0.947365\pi$
$151$	−2.63519	−	9.83467i	−0.214449	−	0.800334i	0.771911	−	0.635731i	$-0.219301\pi$
$152$	−4.82892	−	2.78798i	−0.391677	−	0.226135i
$153$	−5.41907	+	11.2737i	−0.438106	+	0.911428i
$154$	−5.57082	−	9.40552i	−0.448909	−	0.757918i
$155$	29.1227			2.33919
$156$	−5.66923	+	2.61913i	−0.453902	+	0.209698i
$157$	3.49202	−	6.04836i	0.278694	−	0.482712i	−0.692367	−	0.721546i	$-0.743432\pi$
$157$	3.49202	−	6.04836i	0.278694	−	0.482712i	0.971060	+	0.238834i	$0.0767652\pi$
$158$	−11.3123	−	3.03112i	−0.899957	−	0.241143i
$159$	0.234700	+	6.21216i	0.0186129	+	0.492656i
$160$	−2.91662	+	1.68391i	−0.230579	+	0.133125i
$161$	−13.3328	+	0.148454i	−1.05077	+	0.0116998i
$162$	8.94486	+	0.994697i	0.702775	+	0.0781508i
$163$	0.286706	+	1.07000i	0.0224566	+	0.0838091i	0.976245	−	0.216671i	$-0.0695198\pi$
$163$	0.286706	+	1.07000i	0.0224566	+	0.0838091i	−0.953788	+	0.300480i	$0.902853\pi$
$164$	10.6628	−	2.85709i	0.832626	−	0.223102i
$165$	24.0841	−	0.909917i	1.87495	−	0.0708370i
$166$		−	4.37214i		−	0.339344i
$167$	−12.8984	+	3.45613i	−0.998111	+	0.267443i	−0.720654	−	0.693295i	$-0.756158\pi$
$167$	−12.8984	+	3.45613i	−0.998111	+	0.267443i	−0.277457	+	0.960738i	$0.589492\pi$
$168$	−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
$171$	3.09798	−	16.4385i	0.236908	−	1.25708i
$172$	−3.61796	−	6.26650i	−0.275867	−	0.477816i
$173$	−1.59132	+	2.75625i	−0.120986	+	0.209554i	−0.920157	−	0.391550i	$-0.871939\pi$
$173$	−1.59132	+	2.75625i	−0.120986	+	0.209554i	0.799171	+	0.601104i	$0.205272\pi$
$174$	4.60486	+	4.26958i	0.349094	+	0.323676i
$175$	14.6244	+	8.22768i	1.10550	+	0.621954i
$176$	1.06937	−	3.99094i	0.0806066	−	0.300828i
$177$	4.36512	−	19.1569i	0.328102	−	1.43992i
$178$	−13.1048			−0.982249
$179$	3.27575	+	5.67377i	0.244841	+	0.424077i	0.962087	−	0.272743i	$-0.0879308\pi$
$179$	3.27575	+	5.67377i	0.244841	+	0.424077i	−0.717246	+	0.696820i	$0.754597\pi$
$180$	−7.66293	−	6.58481i	−0.571161	−	0.490803i
$181$		−	5.01185i		−	0.372528i	−0.982500	−	0.186264i	$-0.940362\pi$
$181$		−	5.01185i		−	0.372528i	0.982500	−	0.186264i	$-0.0596380\pi$
$182$	7.48931	−	5.90849i	0.555145	−	0.437966i
$183$	2.00210	−	0.0756408i	0.147999	−	0.00559153i
$184$	−3.56356	−	3.56356i	−0.262709	−	0.262709i
$185$	0.699978	−	0.404132i	0.0514634	−	0.0297124i
$186$	14.9669	−	0.565462i	1.09743	−	0.0414617i
$187$	−4.45874	+	16.6403i	−0.326056	+	1.21686i
$188$	−5.61788	−	1.50531i	−0.409726	−	0.109786i
$189$	−13.6415	+	1.70612i	−0.992270	+	0.124102i
$190$	−13.2787	+	13.2787i	−0.963335	+	0.963335i
$191$	−6.54592	−	3.77929i	−0.473646	−	0.273460i	0.244119	−	0.969745i	$-0.421501\pi$
$191$	−6.54592	−	3.77929i	−0.473646	−	0.273460i	−0.717765	+	0.696286i	$0.754835\pi$
$192$	−1.46623	+	0.922039i	−0.105816	+	0.0665424i
$193$	11.9582	+	3.20420i	0.860772	+	0.230643i	0.662093	−	0.749421i	$-0.269668\pi$
$193$	11.9582	+	3.20420i	0.860772	+	0.230643i	0.198679	+	0.980065i	$0.436335\pi$
$194$	5.55462	+	9.62088i	0.398798	+	0.690739i
$195$	3.57857	+	20.7254i	0.256267	+	1.48418i
$196$	−0.155864	−	6.99826i	−0.0111331	−	0.499876i
$197$	3.26334	+	12.1789i	0.232503	+	0.867714i	0.979259	+	0.202615i	$0.0649439\pi$
$197$	3.26334	+	12.1789i	0.232503	+	0.867714i	−0.746755	+	0.665099i	$0.768389\pi$
$198$	12.3598	−	0.935262i	0.878375	−	0.0664662i
$199$			0.595154i			0.0421893i	0.999777	+	0.0210947i	$0.00671514\pi$
$199$			0.595154i			0.0421893i	−0.999777	+	0.0210947i	$0.993285\pi$
$200$	1.64149	+	6.12614i	0.116071	+	0.433183i
$201$	−22.0529	+	6.81120i	−1.55549	+	0.480425i
$202$	3.88396	+	1.04070i	0.273274	+	0.0732237i
$203$	−8.36009	−	4.70338i	−0.586763	−	0.330113i
$204$	6.11348	−	3.84445i	0.428029	−	0.269165i
$205$		−	37.1773i		−	2.59657i
$206$	2.78634	−	10.3988i	0.194134	−	0.724517i
$207$	6.54996	−	13.6264i	0.455254	−	0.947102i
$208$	3.57579	+	0.462333i	0.247936	+	0.0320570i
$209$		−	23.0383i		−	1.59359i
$210$	13.7268	+	7.05416i	0.947242	+	0.486783i
$211$	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	$0.146015\pi$
$212$	1.79457	−	3.10829i	0.123252	−	0.213479i
$213$	1.67783	+	5.43238i	0.114963	+	0.372221i
$214$	−13.4786	−	13.4786i	−0.921377	−	0.921377i
$215$	−23.5390	+	6.30725i	−1.60534	+	0.430151i
$216$	−4.06604	−	3.23532i	−0.276659	−	0.220136i
$217$	−22.0318	+	6.16711i	−1.49562	+	0.418651i
$218$	0.517959	−	0.897131i	0.0350806	−	0.0607614i
$219$	1.20055	−	1.29483i	0.0811258	−	0.0874965i
$220$	−12.0507	−	6.95746i	−0.812456	−	0.469072i
$221$	−14.9093	−	1.92770i	−1.00291	−	0.129671i
$222$	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	$0.489575\pi$
$224$	1.84988	−	1.89154i	0.123601	−	0.126384i
$225$	−15.7128	+	10.7295i	−1.04752	+	0.715303i
$226$	−0.802388	+	2.99455i	−0.0533741	+	0.199195i
$227$	0.601011	−	0.601011i	0.0398905	−	0.0398905i	−0.686880	−	0.726771i	$-0.741020\pi$
$227$	0.601011	−	0.601011i	0.0398905	−	0.0398905i	0.726771	+	0.686880i	$0.241020\pi$
$228$	−6.56643	+	7.08208i	−0.434873	+	0.469022i
$229$	6.49414	+	1.74010i	0.429145	+	0.114989i	0.466925	−	0.884297i	$-0.345362\pi$
$229$	6.49414	+	1.74010i	0.429145	+	0.114989i	−0.0377798	+	0.999286i	$0.512029\pi$
$230$	−14.6987	+	8.48631i	−0.969204	+	0.559570i
$231$	−18.0274	+	5.78851i	−1.18611	+	0.380856i
$232$	−0.938365	−	3.50202i	−0.0616067	−	0.229919i
$233$	−1.40499	−	2.43351i	−0.0920437	−	0.159424i	0.816327	−	0.577590i	$-0.196007\pi$
$233$	−1.40499	−	2.43351i	−0.0920437	−	0.159424i	−0.908371	+	0.418165i	$0.862673\pi$
$234$	2.24154	+	10.5818i	0.146534	+	0.691757i
$235$	−9.79373	+	16.9632i	−0.638872	+	1.10656i
$236$	−8.02122	+	8.02122i	−0.522137	+	0.522137i
$237$	−9.47187	+	17.9374i	−0.615264	+	1.16516i
$238$	−7.71311	+	7.88681i	−0.499967	+	0.511226i
$239$	4.28240	−	4.28240i	0.277005	−	0.277005i	−0.554907	−	0.831912i	$-0.687246\pi$
$239$	4.28240	−	4.28240i	0.277005	−	0.277005i	0.831912	+	0.554907i	$0.187246\pi$
$240$	1.72140	+	5.57346i	0.111116	+	0.359766i
$241$	−2.86631	+	2.86631i	−0.184636	+	0.184636i	−0.793372	−	0.608737i	$-0.791677\pi$
$241$	−2.86631	+	2.86631i	−0.184636	+	0.184636i	0.608737	+	0.793372i	$0.291677\pi$
$242$	5.86425	−	1.57132i	0.376968	−	0.101008i
$243$	5.12184	−	14.7230i	0.328566	−	0.944481i
$244$	−1.00176	−	0.578368i	−0.0641313	−	0.0370262i
$245$	−22.9017	−	5.59305i	−1.46314	−	0.357327i
$246$	−0.721855	−	19.1064i	−0.0460238	−	1.21818i
$247$	19.9263	−	2.67034i	1.26788	−	0.169910i
$248$	−7.48880	−	4.32366i	−0.475539	−	0.274553i
$249$	−7.38351	−	1.68242i	−0.467911	−	0.106619i
$250$	4.52044			0.285898
$251$	−13.2520	−	22.9531i	−0.836457	−	1.44879i	−0.892839	−	0.450377i	$-0.851290\pi$
$251$	−13.2520	−	22.9531i	−0.836457	−	1.44879i	0.0563815	−	0.998409i	$-0.482044\pi$
$252$	7.19156	+	3.35879i	0.453026	+	0.211584i
$253$	5.38923	−	20.1129i	0.338818	−	1.26448i
$254$	−19.0740	+	5.11085i	−1.19681	+	0.320683i
$255$	−7.17740	−	23.2386i	−0.449466	−	1.45526i
$256$	1.00000			0.0625000
$257$	−0.593611			−0.0370284			−0.0185142	−	0.999829i	$-0.505894\pi$
$257$	−0.593611			−0.0370284			−0.0185142	+	0.999829i	$0.505894\pi$
$258$	−11.9748	+	3.69851i	−0.745521	+	0.230259i
$259$	−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
$262$	−4.73955	+	17.6882i	−0.292810	+	1.09278i
$263$	−10.1757	+	5.87492i	−0.627458	+	0.362263i	−0.779767	−	0.626070i	$-0.784663\pi$
$263$	−10.1757	+	5.87492i	−0.627458	+	0.362263i	0.152309	+	0.988333i	$0.451329\pi$
$264$	−6.32825	−	3.34164i	−0.389477	−	0.205664i
$265$	−8.54724	−	8.54724i	−0.525053	−	0.525053i
$266$	7.23360	−	12.8575i	0.443520	−	0.788342i
$267$	−5.04280	+	22.1310i	−0.308615	+	1.35439i
$268$	12.8717	+	3.44895i	0.786262	+	0.210678i
$269$		−	1.18655i		−	0.0723450i	−0.999346	−	0.0361725i	$-0.988483\pi$
$269$		−	1.18655i		−	0.0723450i	0.999346	−	0.0361725i	$-0.0115166\pi$
$270$	−14.0689	+	10.4070i	−0.856207	+	0.633351i
$271$	14.5017	−	14.5017i	0.880913	−	0.880913i	−0.112714	−	0.993627i	$-0.535954\pi$
$271$	14.5017	−	14.5017i	0.880913	−	0.880913i	0.993627	+	0.112714i	$0.0359545\pi$
$272$	−4.16951			−0.252814
$273$	−7.09613	−	14.9213i	−0.429477	−	0.903078i
$274$	−0.544250			−0.0328793
$275$	−18.5293	+	18.5293i	−1.11736	+	1.11736i
$276$	−7.38929	+	4.64674i	−0.444783	+	0.279701i
$277$			12.1661i			0.730987i	0.930814	+	0.365494i	$0.119100\pi$
$277$			12.1661i			0.730987i	−0.930814	+	0.365494i	$0.880900\pi$
$278$	−2.19156	−	0.587226i	−0.131441	−	0.0352195i
$279$	4.80441	−	25.4932i	0.287633	−	1.52624i
$280$	−4.54085	−	7.66657i	−0.271368	−	0.458165i
$281$	−0.703268	−	0.703268i	−0.0419535	−	0.0419535i	0.685819	−	0.727772i	$-0.259444\pi$
$281$	−0.703268	−	0.703268i	−0.0419535	−	0.0419535i	−0.727772	+	0.685819i	$0.759444\pi$
$282$	−4.70389	+	8.90802i	−0.280113	+	0.530465i
$283$	−1.18657	+	0.685065i	−0.0705341	+	0.0407229i	−0.534852	−	0.844946i	$-0.679633\pi$
$283$	−1.18657	+	0.685065i	−0.0705341	+	0.0407229i	0.464318	+	0.885668i	$0.346299\pi$
$284$	0.849592	−	3.17072i	0.0504140	−	0.188148i
$285$	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
$288$	0.992892	+	2.83093i	0.0585067	+	0.166814i
$289$	0.384824			0.0226367
$290$	−12.2103			−0.717011
$291$	18.3848	−	5.67828i	1.07774	−	0.332867i
$292$	−0.984725	+	0.263856i	−0.0576267	+	0.0154410i
$293$	−3.42884	+	12.7966i	−0.200315	+	0.747585i	0.790512	+	0.612447i	$0.209815\pi$
$293$	−3.42884	+	12.7966i	−0.200315	+	0.747585i	−0.990827	+	0.135139i	$0.956852\pi$
$294$	−11.8784	−	2.42975i	−0.692762	−	0.141706i
$295$	19.1018	+	33.0853i	1.11215	+	1.92630i
$296$	−0.239996			−0.0139495
$297$	3.17668	−	21.2327i	0.184330	−	1.23205i
$298$	2.56338	+	1.47997i	0.148493	+	0.0857322i
$299$	18.0207	+	2.32999i	1.04216	+	0.134747i
$300$	10.9773	−	0.414729i	0.633772	−	0.0239444i
$301$	16.4720	−	9.75623i	0.949429	−	0.562340i
$302$	8.81753	+	5.09080i	0.507392	+	0.292943i
$303$	3.25207	−	6.15863i	0.186827	−	0.353804i
$304$	5.38596	−	1.44316i	0.308906	−	0.0827712i
$305$	−2.75466	+	2.75466i	−0.157732	+	0.157732i
$306$	−4.13987	−	11.8036i	−0.236661	−	0.674767i
$307$	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	$0.236761\pi$
$308$	10.5899	+	2.71154i	0.603414	+	0.154505i
$309$	−16.4889	−	8.70697i	−0.938019	−	0.495322i
$310$	−20.5928	+	20.5928i	−1.16959	+	1.16959i
$311$	−8.14577	+	14.1089i	−0.461904	+	0.800041i	−0.999056	−	0.0434444i	$-0.986167\pi$
$311$	−8.14577	+	14.1089i	−0.461904	+	0.800041i	0.537152	+	0.843486i	$0.319500\pi$
$312$	2.15675	−	5.86075i	0.122102	−	0.331800i
$313$	−1.78684	−	3.09490i	−0.100998	−	0.174934i	0.811098	−	0.584910i	$-0.198870\pi$
$313$	−1.78684	−	3.09490i	−0.100998	−	0.174934i	−0.912096	+	0.409976i	$0.865537\pi$
$314$	1.80760	+	6.74607i	0.102009	+	0.380703i
$315$	17.1950	−	20.4669i	0.968826	−	1.15318i
$316$	10.1423	−	5.85567i	0.570550	−	0.329407i
$317$	19.2547	+	5.15929i	1.08145	+	0.289775i	0.755191	−	0.655504i	$-0.227544\pi$
$317$	19.2547	+	5.15929i	1.08145	+	0.289775i	0.326263	+	0.945279i	$0.394211\pi$
$318$	−4.55862	−	4.22670i	−0.255635	−	0.237022i
$319$	10.5923	−	10.5923i	0.593056	−	0.593056i
$320$	0.871657	−	3.25307i	0.0487271	−	0.181852i
$321$	−27.9488	+	17.5755i	−1.55995	+	0.980970i
$322$	9.32274	−	9.53268i	0.519536	−	0.531236i
$323$	−22.4568	+	6.01729i	−1.24953	+	0.334811i
$324$	−7.02833	+	5.62162i	−0.390463	+	0.312312i
$325$	−18.1740	−	13.8786i	−1.00811	−	0.769848i
$326$	−0.959338	−	0.553874i	−0.0531328	−	0.0306763i
$327$	−1.31573	−	1.21993i	−0.0727600	−	0.0674623i
$328$	−5.51948	+	9.56002i	−0.304762	+	0.527864i
$329$	3.81693	−	14.9069i	0.210434	−	0.821846i
$330$	−16.3867	+	17.6735i	−0.902056	+	0.972893i
$331$	−16.2817	+	4.36268i	−0.894925	+	0.239795i	−0.676836	−	0.736134i	$-0.736649\pi$
$331$	−16.2817	+	4.36268i	−0.894925	+	0.239795i	−0.218090	+	0.975929i	$0.569983\pi$
$332$	3.09157	+	3.09157i	0.169672	+	0.169672i
$333$	−0.238290	−	0.679412i	−0.0130582	−	0.0372316i
$334$	6.67672	−	11.5644i	0.365334	−	0.632777i
$335$	22.4393	−	38.8661i	1.22599	−	2.12348i
$336$	−2.48253	−	3.85189i	−0.135433	−	0.210138i
$337$			3.74321i			0.203906i	0.994789	+	0.101953i	$0.0325091\pi$
$337$			3.74321i			0.203906i	−0.994789	+	0.101953i	$0.967491\pi$
$338$	−11.2281	+	6.55212i	−0.610727	+	0.356388i
$339$	4.74833	+	2.50736i	0.257894	+	0.136181i
$340$	−3.63438	+	13.5637i	−0.197102	+	0.735595i
$341$		−	35.7283i		−	1.93480i
$342$	9.43318	+	13.8144i	0.510088	+	0.746996i
$343$	18.5099	−	0.618502i	0.999442	−	0.0333960i
$344$	6.98937	+	1.87280i	0.376841	+	0.100974i
$345$	8.67524	+	28.0882i	0.467059	+	1.51222i
$346$	−0.823728	−	3.07420i	−0.0442839	−	0.165270i
$347$		−	5.56202i		−	0.298585i	−0.988793	−	0.149292i	$-0.952300\pi$
$347$		−	5.56202i		−	0.298585i	0.988793	−	0.149292i	$-0.0476996\pi$
$348$	−6.27518	+	0.237081i	−0.336385	+	0.0127089i
$349$	−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
$351$	18.7328	+	0.286515i	0.999883	+	0.0152930i
$352$	2.06586	+	3.57818i	0.110111	+	0.190717i
$353$	−34.8648	−	9.34199i	−1.85567	−	0.497224i	−0.855865	−	0.517200i	$-0.826974\pi$
$353$	−34.8648	−	9.34199i	−1.85567	−	0.497224i	−0.999800	+	0.0199756i	$0.993641\pi$
$354$	10.4594	+	16.6326i	0.555908	+	0.884011i
$355$	−9.57402	−	5.52757i	−0.508136	−	0.293373i
$356$	9.26652	−	9.26652i	0.491124	−	0.491124i
$357$	10.3509	+	16.0605i	0.547829	+	0.850012i
$358$	−6.32827	−	1.69565i	−0.334459	−	0.0896181i
$359$	3.13200	−	11.6888i	0.165301	−	0.616910i	−0.832701	−	0.553723i	$-0.813207\pi$
$359$	3.13200	−	11.6888i	0.165301	−	0.616910i	0.998002	−	0.0631875i	$-0.0201266\pi$
$360$	10.0747	−	0.762346i	0.530982	−	0.0401791i
$361$	10.4714	−	6.04566i	0.551126	−	0.318193i
$362$	3.54391	+	3.54391i	0.186264	+	0.186264i
$363$	−0.397000	−	10.5080i	−0.0208371	−	0.551526i
$364$	−1.11781	+	9.47367i	−0.0585891	+	0.496555i
$365$			3.43337i			0.179711i
$366$	−1.36221	+	1.46918i	−0.0712039	+	0.0767954i
$367$	11.5300	+	19.9706i	0.601861	+	1.04245i	0.992539	+	0.121927i	$0.0389074\pi$
$367$	11.5300	+	19.9706i	0.601861	+	1.04245i	−0.390678	+	0.920528i	$0.627759\pi$
$368$	5.03964			0.262709
$369$	−32.5440	−	6.13319i	−1.69417	−	0.319281i
$370$	−0.209194	+	0.780724i	−0.0108755	+	0.0405879i
$371$	8.27613	+	4.65614i	0.429675	+	0.241735i
$372$	−10.1834	+	10.9831i	−0.527983	+	0.569445i
$373$	−7.55573	+	13.0869i	−0.391221	+	0.677614i	−0.992611	−	0.121341i	$-0.961280\pi$
$373$	−7.55573	+	13.0869i	−0.391221	+	0.677614i	0.601390	+	0.798956i	$0.294614\pi$
$374$	−8.61363	−	14.9192i	−0.445400	−	0.771456i
$375$	1.73949	−	7.63396i	0.0898267	−	0.394216i
$376$	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	$0.575012\pi$
$380$		−	18.7789i		−	0.963335i
$381$	1.29127	+	34.1781i	0.0661540	+	1.75100i
$382$	7.30102	−	1.95630i	0.373553	−	0.100093i
$383$	−3.97924	−	14.8507i	−0.203330	−	0.758837i	−0.989952	−	0.141403i	$-0.954839\pi$
$383$	−3.97924	−	14.8507i	−0.203330	−	0.758837i	0.786622	−	0.617435i	$-0.211828\pi$
$384$	0.384805	−	1.68876i	0.0196370	−	0.0861794i
$385$	18.0516	−	32.0860i	0.919993	−	1.63526i
$386$	−10.7215	+	6.19003i	−0.545708	+	0.315064i
$387$	1.63793	+	21.6459i	0.0832609	+	1.10032i
$388$	−10.7307	−	2.87528i	−0.544768	−	0.145970i
$389$	−0.274003	+	0.474587i	−0.0138925	+	0.0240625i	−0.872888	−	0.487920i	$-0.837756\pi$
$389$	−0.274003	+	0.474587i	−0.0138925	+	0.0240625i	0.858996	+	0.511983i	$0.171089\pi$
$390$	−17.1855	−	12.1246i	−0.870221	−	0.613954i
$391$	−21.0128			−1.06266
$392$	5.05873	+	4.83831i	0.255505	+	0.244371i
$393$	28.0475	+	14.8105i	1.41481	+	0.747091i
$394$	−10.9193	−	6.30428i	−0.550108	−	0.317605i
$395$	−10.2083	−	38.0978i	−0.513634	−	1.91691i
$396$	−8.07839	+	9.40105i	−0.405954	+	0.472420i
$397$	−7.23468	−	27.0002i	−0.363098	−	1.35510i	−0.869981	−	0.493085i	$-0.835869\pi$
$397$	−7.23468	−	27.0002i	−0.363098	−	1.35510i	0.506883	−	0.862015i	$-0.330798\pi$
$398$	−0.420837	−	0.420837i	−0.0210947	−	0.0210947i
$399$	−18.9297	−	17.1635i	−0.947670	−	0.859247i
$400$	−5.49254	−	3.17112i	−0.274627	−	0.158556i
$401$	−12.6163	−	12.6163i	−0.630026	−	0.630026i	0.318049	−	0.948074i	$-0.396972\pi$
$401$	−12.6163	−	12.6163i	−0.630026	−	0.630026i	−0.948074	+	0.318049i	$0.896972\pi$
$402$	10.7775	−	20.4100i	0.537535	−	1.01796i
$403$	30.9021	−	4.14122i	1.53934	−	0.206289i
$404$	−3.48226	+	2.01049i	−0.173249	+	0.100025i
$405$	12.1612	+	27.7638i	0.604295	+	1.37959i
$406$	9.23727	−	2.58569i	0.458438	−	0.128325i
$407$	−0.495798	−	0.858748i	−0.0245758	−	0.0425666i
$408$	−1.60445	+	7.04132i	−0.0794320	+	0.348597i
$409$	18.1944	+	18.1944i	0.899656	+	0.899656i	0.995405	−	0.0957492i	$-0.0305247\pi$
$409$	18.1944	+	18.1944i	0.899656	+	0.899656i	−0.0957492	+	0.995405i	$0.530525\pi$
$410$	26.2883	+	26.2883i	1.29829	+	1.29829i
$411$	−0.209430	+	0.919109i	−0.0103304	+	0.0453363i
$412$	5.38280	+	9.32328i	0.265192	+	0.459325i
$413$	−21.4571	−	20.9846i	−1.05584	−	1.03258i
$414$	5.00381	+	14.2669i	0.245924	+	0.701178i
$415$	12.7519	−	7.36230i	0.625965	−	0.361401i
$416$	−2.85538	+	2.20154i	−0.139997	+	0.107940i
$417$	−1.83501	+	3.47506i	−0.0898608	+	0.170174i
$418$	16.2905	+	16.2905i	0.796796	+	0.796796i
$419$	−33.6399	−	19.4220i	−1.64342	−	0.948827i	−0.979607	−	0.200924i	$-0.935605\pi$
$419$	−33.6399	−	19.4220i	−1.64342	−	0.948827i	−0.663809	−	0.747902i	$-0.731061\pi$
$420$	−14.6944	+	4.71830i	−0.717012	+	0.230229i
$421$	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	$0.688922\pi$
$422$	0.487501	+	1.81938i	0.0237312	+	0.0885659i
$423$	13.2335	+	11.3716i	0.643434	+	0.552907i
$424$	0.928940	+	3.46685i	0.0451133	+	0.168365i
$425$	22.9012	+	13.2220i	1.11087	+	0.641363i
$426$	−5.02768	−	2.65487i	−0.243592	−	0.128629i
$427$	1.50061	−	2.66729i	0.0726198	−	0.129079i
$428$	19.0616			0.921377
$429$	25.4263	−	4.39027i	1.22760	−	0.211964i
$430$	12.1847	−	21.1045i	0.587597	−	1.01775i
$431$	−5.15794	−	1.38207i	−0.248449	−	0.0665718i	0.132445	−	0.991190i	$-0.457717\pi$
$431$	−5.15794	−	1.38207i	−0.248449	−	0.0665718i	−0.380894	+	0.924619i	$0.624384\pi$
$432$	5.16284	−	0.587405i	0.248397	−	0.0282616i
$433$	−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	$0.455292\pi$
$434$	11.2180	−	19.9396i	0.538482	−	0.957133i
$435$	−4.69857	+	20.6202i	−0.225279	+	0.988665i
$436$	0.268115	+	1.00062i	0.0128404	+	0.0479210i
$437$	27.1433	−	7.27302i	1.29844	−	0.347916i
$438$	0.0666642	+	1.76450i	0.00318534	+	0.0843112i
$439$			36.3180i			1.73337i	0.498860	+	0.866683i	$0.333752\pi$
$439$			36.3180i			1.73337i	−0.498860	+	0.866683i	$0.666248\pi$
$440$	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	−0.344476	−	0.938795i	$-0.611943\pi$
$443$	6.23652	−	3.60066i	0.296306	−	0.171072i	0.640782	+	0.767723i	$0.278610\pi$
$444$	−0.0923516	+	0.405297i	−0.00438281	+	0.0192345i
$445$	−22.0674	−	38.2218i	−1.04609	−	1.81189i
$446$	3.39061	−	5.87271i	0.160550	−	0.278081i
$447$	3.48572	−	3.75944i	0.164869	−	0.177816i
$448$	0.0294574	+	2.64559i	0.00139173	+	0.124992i
$449$	1.65994	−	6.19497i	0.0783373	−	0.292359i	−0.915632	−	0.402017i	$-0.868309\pi$
$449$	1.65994	−	6.19497i	0.0783373	−	0.292359i	0.993969	+	0.109659i	$0.0349758\pi$
$450$	3.52372	−	18.6976i	0.166110	−	0.881413i
$451$	−45.6099			−2.14769
$452$	−1.55009	−	2.68484i	−0.0729103	−	0.126284i
$453$	11.9902	−	12.9318i	0.563348	−	0.607587i
$454$			0.849958i			0.0398905i
$455$	29.8442	+	11.8941i	1.39912	+	0.557604i
$456$	−0.364621	−	9.65096i	−0.0170749	−	0.451948i
$457$	−15.7898	−	15.7898i	−0.738617	−	0.738617i	0.233694	−	0.972310i	$-0.424919\pi$
$457$	−15.7898	−	15.7898i	−0.738617	−	0.738617i	−0.972310	+	0.233694i	$0.924919\pi$
$458$	−5.82249	+	3.36161i	−0.272067	+	0.157078i
$459$	−21.5265	+	2.44919i	−1.00477	+	0.114319i
$460$	4.39283	−	16.3943i	0.204817	−	0.764387i
$461$	36.7770	+	9.85437i	1.71288	+	0.458964i	0.976127	−	0.217202i	$-0.0696929\pi$
$461$	36.7770	+	9.85437i	1.71288	+	0.458964i	0.736750	+	0.676166i	$0.236360\pi$
$462$	8.65419	−	16.8404i	0.402629	−	0.783485i
$463$	−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	$0.312322\pi$
$464$	3.13983	+	1.81278i	0.145763	+	0.0841562i
$465$	26.8522	+	42.7007i	1.24524	+	1.98020i
$466$	2.71422	+	0.727274i	0.125734	+	0.0336903i
$467$	15.1184	+	26.1858i	0.699595	+	1.21173i	0.968607	+	0.248598i	$0.0799698\pi$
$467$	15.1184	+	26.1858i	0.699595	+	1.21173i	−0.269011	+	0.963137i	$0.586697\pi$
$468$	−9.06750	−	5.89749i	−0.419145	−	0.272612i
$469$	−8.74534	+	34.1547i	−0.403822	+	1.57712i
$470$	−5.06961	−	18.9200i	−0.233844	−	0.872716i
$471$	12.0881	−	0.456697i	0.556990	−	0.0210435i
$472$		−	11.3437i		−	0.522137i
$473$	7.73787	+	28.8781i	0.355788	+	1.32782i
$474$	−5.98604	−	19.3813i	−0.274948	−	0.890212i
$475$	−34.1591	−	9.15290i	−1.56733	−	0.419964i
$476$	−0.122823	−	11.0308i	−0.00562957	−	0.505596i
$477$	−8.89208	+	6.07197i	−0.407140	+	0.278017i
$478$			6.05623i			0.277005i
$479$	−9.67121	+	36.0934i	−0.441889	+	1.64915i	0.282133	+	0.959375i	$0.408958\pi$
$479$	−9.67121	+	36.0934i	−0.441889	+	1.64915i	−0.724022	+	0.689777i	$0.757709\pi$
$480$	−5.15825	−	2.72382i	−0.235441	−	0.124325i
$481$	0.685280	−	0.528362i	0.0312461	−	0.0240912i
$482$		−	4.05358i		−	0.184636i
$483$	−12.5110	−	19.4121i	−0.569271	−	0.883283i
$484$	−3.03556	+	5.25774i	−0.137980	+	0.238988i
$485$	−18.7070	+	32.4014i	−0.849440	+	1.47127i
$486$	6.78905	+	14.0324i	0.307958	+	0.636523i
$487$	3.04113	+	3.04113i	0.137807	+	0.137807i	0.772645	−	0.634838i	$-0.218933\pi$
$487$	3.04113	+	3.04113i	0.137807	+	0.137807i	−0.634838	+	0.772645i	$0.718933\pi$
$488$	1.11732	−	0.299385i	0.0505788	−	0.0135525i
$489$	−1.30452	+	1.40696i	−0.0589925	+	0.0636251i
$490$	20.1488	−	12.2391i	0.910231	−	0.552904i
$491$	−1.41156	+	2.44489i	−0.0637028	+	0.110336i	−0.896118	−	0.443816i	$-0.853624\pi$
$491$	−1.41156	+	2.44489i	−0.0637028	+	0.110336i	0.832415	+	0.554153i	$0.186958\pi$
$492$	14.0207	+	12.9998i	0.632102	+	0.586078i
$493$	−13.0916	−	7.55841i	−0.589614	−	0.340414i
$494$	−12.2018	+	15.9782i	−0.548984	+	0.718894i
$495$	23.5407	+	34.4740i	1.05807	+	1.54949i
$496$	8.35267	−	2.23809i	0.375046	−	0.100493i
$497$	8.41345	+	2.15427i	0.377395	+	0.0966322i
$498$	6.41058	−	4.03128i	0.287265	−	0.180646i
$499$	1.59339	−	5.94661i	0.0713298	−	0.266207i	−0.921046	−	0.389453i	$-0.872664\pi$
$499$	1.59339	−	5.94661i	0.0713298	−	0.266207i	0.992376	+	0.123247i	$0.0393306\pi$
$500$	−3.19643	+	3.19643i	−0.142949	+	0.142949i
$501$	−16.9604	−	15.7255i	−0.757733	−	0.702562i
$502$	25.6008	+	6.85973i	1.14262	+	0.306165i
$503$	3.76379	−	2.17302i	0.167819	−	0.0968903i	−0.413738	−	0.910396i	$-0.635777\pi$
$503$	3.76379	−	2.17302i	0.167819	−	0.0968903i	0.581557	+	0.813506i	$0.302444\pi$
$504$	−7.46022	+	2.71017i	−0.332305	+	0.120721i
$505$	3.50491	+	13.0805i	0.155966	+	0.582074i
$506$	10.4112	+	18.0327i	0.462834	+	0.801651i
$507$	6.74436	+	21.4829i	0.299528	+	0.954088i
$508$	9.87340	−	17.1012i	0.438061	−	0.758745i
$509$	5.58261	−	5.58261i	0.247445	−	0.247445i	−0.572476	−	0.819921i	$-0.694017\pi$
$509$	5.58261	−	5.58261i	0.247445	−	0.247445i	0.819921	+	0.572476i	$0.194017\pi$
$510$	21.5074	+	11.3570i	0.952363	+	0.502896i
$511$	−0.727062	−	2.59740i	−0.0321633	−	0.114902i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	26.9592	−	10.6146i	1.19028	−	0.468645i
$514$	0.419746	−	0.419746i	0.0185142	−	0.0185142i
$515$	35.0212	−	9.38391i	1.54322	−	0.413505i
$516$	5.85225	−	11.0827i	0.257631	−	0.487890i
$517$	20.8109	+	12.0152i	0.915261	+	0.528426i
$518$	−0.00706965	−	0.634930i	−0.000310623	−	0.0278972i
$519$	−5.50857	+	0.208118i	−0.241799	+	0.00913536i
$520$	4.67286	+	11.2077i	0.204919	+	0.491492i
$521$	−14.4992	−	8.37113i	−0.635222	−	0.366746i	0.147549	−	0.989055i	$-0.452861\pi$
$521$	−14.4992	−	8.37113i	−0.635222	−	0.366746i	−0.782772	+	0.622309i	$0.786195\pi$
$522$	−2.01435	+	10.6885i	−0.0881655	+	0.467824i
$523$	−33.9473			−1.48441			−0.742205	−	0.670173i	$-0.766220\pi$
$523$	−33.9473			−1.48441			−0.742205	+	0.670173i	$0.766220\pi$
$524$	−9.15610	−	15.8588i	−0.399986	−	0.692796i
$525$	1.42056	+	29.0291i	0.0619984	+	1.26693i
$526$	3.04108	−	11.3495i	0.132598	−	0.494861i
$527$	−34.8266	+	9.33175i	−1.51707	+	0.406497i
$528$	6.83765	−	2.11185i	0.297570	−	0.0919066i
$529$	2.39793			0.104258
$530$	12.0876			0.525053
$531$	32.1133	−	11.2631i	1.39360	−	0.488777i
$532$	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
$535$	16.6152	−	62.0087i	0.718336	−	2.68087i
$536$	−11.5404	+	6.66286i	−0.498470	+	0.287792i
$537$	−5.29871	+	10.0345i	−0.228656	+	0.433019i
$538$	0.839015	+	0.839015i	0.0361725	+	0.0361725i
$539$	−6.86168	+	28.0963i	−0.295553	+	1.21019i
$540$	2.58936	−	17.3071i	0.111428	−	0.744779i
$541$	−1.33319	−	0.357228i	−0.0573184	−	0.0153584i	0.230046	−	0.973180i	$-0.426112\pi$
$541$	−1.33319	−	0.357228i	−0.0573184	−	0.0153584i	−0.287364	+	0.957821i	$0.592779\pi$
$542$			20.5084i			0.880913i
$543$	7.34855	−	4.62112i	0.315356	−	0.198311i
$544$	2.94829	−	2.94829i	0.126407	−	0.126407i
$545$	3.48879			0.149443
$546$	15.5687	+	5.53323i	0.666277	+	0.236800i
$547$	0.425089			0.0181755			0.00908776	−	0.999959i	$-0.497107\pi$
$547$	0.425089			0.0181755			0.00908776	+	0.999959i	$0.497107\pi$
$548$	0.384843	−	0.384843i	0.0164397	−	0.0164397i
$549$	1.95692	+	2.86580i	0.0835192	+	0.122309i
$550$		−	26.2044i		−	1.11736i
$551$	19.5271	+	5.23228i	0.831884	+	0.222903i
$552$	1.93928	−	8.51076i	0.0825411	−	0.362242i
$553$	15.7905	+	26.6599i	0.671479	+	1.13369i
$554$	−8.60270	−	8.60270i	−0.365494	−	0.365494i
$555$	1.23796	+	0.653706i	0.0525484	+	0.0277483i
$556$	1.96490	−	1.13443i	0.0833302	−	0.0481107i
$557$	3.85194	−	14.3756i	0.163212	−	0.609115i	−0.835050	−	0.550174i	$-0.814561\pi$
$557$	3.85194	−	14.3756i	0.163212	−	0.609115i	0.998262	−	0.0589402i	$-0.0187721\pi$
$558$	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
$561$	−28.5096	+	8.80539i	−1.20368	+	0.371764i
$562$	0.994571			0.0419535
$563$	−0.598308			−0.0252157			−0.0126078	−	0.999921i	$-0.504013\pi$
$563$	−0.598308			−0.0252157			−0.0126078	+	0.999921i	$0.504013\pi$
$564$	−2.97277	−	9.62508i	−0.125176	−	0.405289i
$565$	−10.0851	+	2.70230i	−0.424285	+	0.113687i
$566$	0.354616	−	1.32344i	0.0149056	−	0.0556285i
$567$	−15.0795	−	18.4285i	−0.633280	−	0.773923i
$568$	1.64129	+	2.84279i	0.0688669	+	0.119281i
$569$	19.1905			0.804507			0.402253	−	0.915528i	$-0.368227\pi$
$569$	19.1905			0.804507			0.402253	+	0.915528i	$0.368227\pi$
$570$	−31.7131	−	7.22619i	−1.32831	−	0.302672i
$571$	13.4751	+	7.77984i	0.563915	+	0.325576i	0.754715	−	0.656053i	$-0.227775\pi$
$571$	13.4751	+	7.77984i	0.563915	+	0.325576i	−0.190801	+	0.981629i	$0.561108\pi$
$572$	−13.7763	−	5.66897i	−0.576017	−	0.237032i
$573$	−0.494267	−	13.0825i	−0.0206483	−	0.546529i
$574$	−25.4545	−	14.3207i	−1.06245	−	0.597733i
$575$	−27.6804	−	15.9813i	−1.15435	−	0.666466i
$576$	−2.70385	−	1.29969i	−0.112660	−	0.0541537i
$577$	−31.2646	+	8.37734i	−1.30156	+	0.348753i	−0.842041	−	0.539413i	$-0.818646\pi$
$577$	−31.2646	+	8.37734i	−1.30156	+	0.348753i	−0.459523	+	0.888166i	$0.651980\pi$
$578$	−0.272112	+	0.272112i	−0.0113184	+	0.0113184i
$579$	6.32784	+	20.4880i	0.262976	+	0.851451i
$580$	8.63396	−	8.63396i	0.358506	−	0.358506i
$581$	−8.08795	+	8.27009i	−0.335545	+	0.343101i
$582$	−8.98489	+	17.0152i	−0.372436	+	0.705302i
$583$	−10.4859	+	10.4859i	−0.434283	+	0.434283i
$584$	0.509731	−	0.882880i	0.0210928	−	0.0365339i
$585$	−27.0887	+	24.3566i	−1.11998	+	1.00702i
$586$	−6.62401	−	11.4731i	−0.273635	−	0.473950i
$587$	1.24748	+	4.65565i	0.0514890	+	0.192159i	0.986880	−	0.161456i	$-0.0516189\pi$
$587$	1.24748	+	4.65565i	0.0514890	+	0.192159i	−0.935391	+	0.353615i	$0.884952\pi$
$588$	10.1174	−	6.68120i	0.417234	−	0.275528i
$589$	41.7572	−	24.1086i	1.72058	−	0.993376i
$590$	−36.9019	−	9.88784i	−1.51923	−	0.407076i
$591$	−14.8483	+	16.0143i	−0.610776	+	0.658739i
$592$	0.169703	−	0.169703i	0.00697474	−	0.00697474i
$593$	2.55091	−	9.52012i	0.104753	−	0.390944i	−0.893564	−	0.448936i	$-0.851803\pi$
$593$	2.55091	−	9.52012i	0.104753	−	0.390944i	0.998317	+	0.0579918i	$0.0184697\pi$
$594$	12.7676	+	17.2601i	0.523859	+	0.708189i
$595$	−35.9910	−	9.21553i	−1.47549	−	0.377800i
$596$	−2.85908	+	0.766087i	−0.117112	+	0.0313802i
$597$	−0.872635	+	0.548755i	−0.0357146	+	0.0224590i
$598$	−14.3901	+	11.0950i	−0.588454	+	0.453708i
$599$	−22.9575	−	13.2545i	−0.938018	−	0.541565i	−0.0486798	−	0.998814i	$-0.515501\pi$
$599$	−22.9575	−	13.2545i	−0.938018	−	0.541565i	−0.889339	+	0.457249i	$0.848835\pi$
$600$	−7.46883	+	8.05535i	−0.304914	+	0.328858i
$601$	−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	$0.242835\pi$
$602$	−4.74876	+	18.5461i	−0.193545	+	0.755885i
$603$	−30.3205	−	26.0546i	−1.23475	−	1.06103i
$604$	−9.83467	+	2.63519i	−0.400167	+	0.107224i
$605$	14.4578	+	14.4578i	0.587794	+	0.587794i
$606$	2.05525	+	6.65437i	0.0834886	+	0.270315i
$607$	15.3348	−	26.5607i	0.622421	−	1.07806i	−0.366613	−	0.930374i	$-0.619483\pi$
$607$	15.3348	−	26.5607i	0.622421	−	1.07806i	0.989034	−	0.147691i	$-0.0471840\pi$
$608$	−2.78798	+	4.82892i	−0.113067	+	0.195839i
$609$	−0.812069	−	16.5946i	−0.0329067	−	0.672445i
$610$		−	3.89568i		−	0.157732i
$611$	−7.97998	+	19.3924i	−0.322836	+	0.784532i
$612$	11.2737	+	5.41907i	0.455714	+	0.219053i
$613$	2.15866	−	8.05623i	0.0871874	−	0.325388i	−0.908532	−	0.417815i	$-0.862796\pi$
$613$	2.15866	−	8.05623i	0.0871874	−	0.325388i	0.995719	+	0.0924274i	$0.0294626\pi$
$614$			1.45705i			0.0588019i
$615$	54.5106	−	34.2789i	2.19808	−	1.38226i
$616$	−9.40552	+	5.57082i	−0.378959	+	0.224455i
$617$	36.2213	+	9.70547i	1.45821	+	0.390727i	0.898873	−	0.438210i	$-0.144387\pi$
$617$	36.2213	+	9.70547i	1.45821	+	0.390727i	0.559342	+	0.828937i	$0.311054\pi$
$618$	17.8162	−	5.50264i	0.716671	−	0.221349i
$619$	9.16130	+	34.1905i	0.368224	+	1.37423i	0.862997	+	0.505208i	$0.168584\pi$
$619$	9.16130	+	34.1905i	0.368224	+	1.37423i	−0.494774	+	0.869022i	$0.664749\pi$
$620$		−	29.1227i		−	1.16959i
$621$	26.0189	−	2.96031i	1.04410	−	0.118793i
$622$	−4.21656	−	15.7364i	−0.169069	−	0.630973i
$623$	24.7884	+	24.2424i	0.993124	+	0.971252i
$624$	2.61913	+	5.66923i	0.104849	+	0.226951i
$625$	−8.24358	−	14.2783i	−0.329743	−	0.571132i
$626$	3.45191	+	0.924937i	0.137966	+	0.0369679i
$627$	33.7796	−	21.2422i	1.34903	−	0.848332i
$628$	−6.04836	−	3.49202i	−0.241356	−	0.139347i
$629$	−0.707578	+	0.707578i	−0.0282130	+	0.0282130i
$630$	2.31363	+	26.6310i	0.0921770	+	1.06100i
$631$	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	$0.364375\pi$
$632$	−3.03112	+	11.3123i	−0.120571	+	0.449979i
$633$	3.26009	−	0.123169i	0.129577	−	0.00489552i
$634$	−17.2633	+	9.96699i	−0.685614	+	0.395840i
$635$	−47.0253	−	47.0253i	−1.86614	−	1.86614i
$636$	6.21216	−	0.234700i	0.246328	−	0.00930646i
$637$	−25.0964	−	2.67819i	−0.994354	−	0.106114i
$638$			14.9798i			0.593056i
$639$	−6.41812	+	7.46895i	−0.253897	+	0.295467i
$640$	1.68391	+	2.91662i	0.0665625	+	0.115290i
$641$	30.6521			1.21069			0.605343	−	0.795964i	$-0.293036\pi$
$641$	30.6521			1.21069			0.605343	+	0.795964i	$0.293036\pi$
$642$	7.33499	−	32.1905i	0.289489	−	1.27046i
$643$	−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	$0.726993\pi$
$644$	0.148454	+	13.3328i	0.00584992	+	0.525386i
$645$	−30.9517	−	28.6981i	−1.21872	−	1.12999i
$646$	11.6245	−	20.1342i	0.457360	−	0.792171i
$647$	10.5067	+	18.1981i	0.413059	+	0.715440i	0.995223	−	0.0976321i	$-0.0311268\pi$
$647$	10.5067	+	18.1981i	0.413059	+	0.715440i	−0.582163	+	0.813072i	$0.697794\pi$
$648$	0.994697	−	8.94486i	0.0390754	−	0.351387i
$649$	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
$653$		−	14.1365i		−	0.553203i	−0.960985	−	0.276601i	$-0.910792\pi$
$653$		−	14.1365i		−	0.553203i	0.960985	−	0.276601i	$-0.0892081\pi$
$654$	1.79298	−	0.0677402i	0.0701112	−	0.00264885i
$655$	−59.5709	+	15.9620i	−2.32763	+	0.623686i
$656$	−2.85709	−	10.6628i	−0.111551	−	0.416313i
$657$	3.00548	+	0.566409i	0.117255	+	0.0220977i
$658$	7.84181	+	13.2398i	0.305706	+	0.516140i
$659$	13.2278	−	7.63705i	0.515280	−	0.297497i	−0.219721	−	0.975563i	$-0.570515\pi$
$659$	13.2278	−	7.63705i	0.515280	−	0.297497i	0.735001	+	0.678066i	$0.237181\pi$
$660$	−0.909917	−	24.0841i	−0.0354185	−	0.937474i
$661$	36.7927	+	9.85858i	1.43107	+	0.383454i	0.889397	−	0.457135i	$-0.151124\pi$
$661$	36.7927	+	9.85858i	1.43107	+	0.383454i	0.541673	+	0.840589i	$0.317791\pi$
$662$	8.42805	−	14.5978i	0.327565	−	0.567360i
$663$	−10.9205	−	23.6379i	−0.424116	−	0.918021i
$664$	−4.37214			−0.169672
$665$	49.6811	−	0.553175i	1.92655	−	0.0214512i
$666$	0.648913	+	0.311920i	0.0251449	+	0.0120867i
$667$	15.8236	+	9.13576i	0.612692	+	0.353738i
$668$	3.45613	+	12.8984i	0.133722	+	0.499056i
$669$	−8.61290	−	7.98579i	−0.332994	−	0.308748i
$670$	11.6155	+	43.3495i	0.448744	+	1.67474i
$671$	3.37948	+	3.37948i	0.130463	+	0.130463i
$672$	4.47911	+	0.968288i	0.172785	+	0.0373525i
$673$	−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	$-0.670177\pi$
$674$	−2.64685	−	2.64685i	−0.101953	−	0.101953i
$675$	−30.2199	−	13.1457i	−1.16316	−	0.505976i
$676$	3.30641	−	12.5725i	0.127169	−	0.483558i
$677$	5.26711	−	3.04097i	0.202431	−	0.116874i	−0.395358	−	0.918527i	$-0.629379\pi$
$677$	5.26711	−	3.04097i	0.202431	−	0.116874i	0.597789	+	0.801653i	$0.296046\pi$
$678$	−5.13055	+	1.58460i	−0.197038	+	0.0608564i
$679$	7.29071	−	28.4737i	0.279792	−	1.09272i
$680$	−7.02109	−	12.1609i	−0.269247	−	0.466349i
$681$	1.43538	+	0.327068i	0.0550038	+	0.0125333i
$682$	25.2637	+	25.2637i	0.967398	+	0.967398i
$683$	36.0759	+	36.0759i	1.38041	+	1.38041i	0.843889	+	0.536518i	$0.180261\pi$
$683$	36.0759	+	36.0759i	1.38041	+	1.38041i	0.536518	+	0.843889i	$0.319739\pi$
$684$	−16.4385	−	3.09798i	−0.628542	−	0.118454i
$685$	−0.916468	−	1.58737i	−0.0350165	−	0.0606503i
$686$	−12.6511	+	13.5258i	−0.483023	+	0.516419i
$687$	3.43645	+	11.1264i	0.131109	+	0.424498i
$688$	−6.26650	+	3.61796i	−0.238908	+	0.137934i
$689$	−10.2849	−	7.85408i	−0.391824	−	0.299217i
$690$	−25.9957	−	13.7271i	−0.989639	−	0.522580i
$691$	28.8015	+	28.8015i	1.09566	+	1.09566i	0.994912	+	0.100751i	$0.0321245\pi$
$691$	28.8015	+	28.8015i	1.09566	+	1.09566i	0.100751	+	0.994912i	$0.467876\pi$
$692$	2.75625	+	1.59132i	0.104777	+	0.0604930i
$693$	−25.1093	−	21.0951i	−0.953822	−	0.801338i
$694$	3.93294	+	3.93294i	0.149292	+	0.149292i
$695$	−1.97768	−	7.38078i	−0.0750175	−	0.279969i
$696$	4.26958	−	4.60486i	0.161838	−	0.174547i
$697$	11.9127	+	44.4587i	0.451225	+	1.68399i
$698$	6.03496	+	3.48428i	0.228426	+	0.131882i
$699$	2.27264	−	4.30383i	0.0859592	−	0.162786i
$700$	8.22768	−	14.6244i	0.310977	−	0.552751i
$701$	−52.1993			−1.97154			−0.985771	−	0.168094i	$-0.946239\pi$
$701$	−52.1993			−1.97154			−0.985771	+	0.168094i	$0.946239\pi$
$702$	−13.4487	+	13.0435i	−0.507588	+	0.492295i
$703$	0.669104	−	1.15892i	0.0252357	−	0.0437096i
$704$	−3.99094	−	1.06937i	−0.150414	−	0.0403033i
$705$	−33.9023	+	1.28085i	−1.27683	+	0.0482398i
$706$	31.2589	−	18.0473i	1.17644	−	0.679221i
$707$	−5.42149	−	9.15341i	−0.203896	−	0.344249i
$708$	−19.1569	−	4.36512i	−0.719959	−	0.164051i
$709$	−2.93842	−	10.9663i	−0.110355	−	0.411849i	0.888543	−	0.458794i	$-0.151718\pi$
$709$	−2.93842	−	10.9663i	−0.110355	−	0.411849i	−0.998897	+	0.0469445i	$0.985052\pi$
$710$	10.6784	−	2.86128i	0.400755	−	0.107382i
$711$	−35.0339	+	2.65100i	−1.31387	+	0.0994202i
$712$			13.1048i			0.491124i
$713$	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
$717$	10.2275	+	2.33047i	0.381955	+	0.0870328i
$718$	6.05056	+	10.4799i	0.225805	+	0.391105i
$719$	−17.2500	+	29.8779i	−0.643316	+	1.11426i	0.341372	+	0.939928i	$0.389108\pi$
$719$	−17.2500	+	29.8779i	−0.643316	+	1.11426i	−0.984688	+	0.174328i	$0.944225\pi$
$720$	−6.58481	+	7.66293i	−0.245401	+	0.285580i
$721$	−24.5070	+	14.5153i	−0.912688	+	0.540578i
$722$	−3.12946	+	11.6793i	−0.116467	+	0.434659i
$723$	−6.84554	−	1.55984i	−0.254589	−	0.0580110i
$724$	−5.01185			−0.186264
$725$	−11.4971	−	19.9136i	−0.426992	−	0.739571i
$726$	7.71099	+	7.14955i	0.286182	+	0.265345i
$727$			0.934609i			0.0346627i	0.999850	+	0.0173314i	$0.00551702\pi$
$727$			0.934609i			0.0346627i	−0.999850	+	0.0173314i	$0.994483\pi$
$728$	−5.90849	−	7.48931i	−0.218983	−	0.277572i
$729$	26.3099	−	6.06536i	0.974441	−	0.224643i
$730$	−2.42776	−	2.42776i	−0.0898554	−	0.0898554i
$731$	26.1282	−	15.0851i	0.966387	−	0.557944i
$732$	−0.0756408	−	2.00210i	−0.00279576	−	0.0739996i
$733$	−6.48894	+	24.2171i	−0.239675	+	0.894478i	0.736311	+	0.676643i	$0.236566\pi$
$733$	−6.48894	+	24.2171i	−0.239675	+	0.894478i	−0.975986	+	0.217835i	$0.930101\pi$
$734$	−22.2743	−	5.96837i	−0.822158	−	0.220297i
$735$	−12.9155	−	38.7363i	−0.476396	−	1.42881i
$736$	−3.56356	+	3.56356i	−0.131355	+	0.131355i
$737$	−47.6818	−	27.5291i	−1.75638	−	1.01405i
$738$	27.3489	−	18.6753i	1.00673	−	0.687446i
$739$	−11.0187	−	2.95245i	−0.405329	−	0.108607i	0.0503937	−	0.998729i	$-0.483952\pi$
$739$	−11.0187	−	2.95245i	−0.405329	−	0.108607i	−0.455722	+	0.890122i	$0.650619\pi$
$740$	−0.404132	−	0.699978i	−0.0148562	−	0.0257317i
$741$	22.2881	+	26.7544i	0.818775	+	0.982849i
$742$	−9.14450	+	2.55972i	−0.335705	+	0.0939702i
$743$	−4.63127	−	17.2841i	−0.169905	−	0.634094i	−0.997364	−	0.0725670i	$-0.976881\pi$
$743$	−4.63127	−	17.2841i	−0.169905	−	0.634094i	0.827459	−	0.561527i	$-0.189786\pi$
$744$	−0.565462	−	14.9669i	−0.0207308	−	0.548714i
$745$			9.96854i			0.365219i
$746$	−3.91113	−	14.5965i	−0.143197	−	0.534417i
$747$	−4.34106	−	12.3772i	−0.158831	−	0.452859i
$748$	16.6403	+	4.45874i	0.608428	+	0.163028i
$749$	0.561504	+	50.4291i	0.0205169	+	1.84264i
$750$	4.16802	+	6.62803i	0.152195	+	0.242021i
$751$		−	2.54650i		−	0.0929230i	−0.998920	−	0.0464615i	$-0.985206\pi$
$751$		−	2.54650i		−	0.0929230i	0.998920	−	0.0464615i	$-0.0147945\pi$
$752$	−1.50531	+	5.61788i	−0.0548929	+	0.204863i
$753$	21.4358	−	40.5941i	0.781164	−	1.47933i
$754$	−12.9563	+	1.73629i	−0.471842	+	0.0632320i
$755$			34.2899i			1.24794i
$756$	1.70612	+	13.6415i	0.0620508	+	0.496135i
$757$	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	$-0.0329684\pi$
$758$	9.28991	−	16.0906i	0.337425	−	0.584437i
$759$	34.4593	−	10.6430i	1.25079	−	0.386315i
$760$	13.2787	+	13.2787i	0.481667	+	0.481667i
$761$	−42.0919	+	11.2785i	−1.52583	+	0.408845i	−0.921657	−	0.388006i	$-0.873164\pi$
$761$	−42.0919	+	11.2785i	−1.52583	+	0.408845i	−0.604175	+	0.796852i	$0.706497\pi$
$762$	−25.0806	−	23.2545i	−0.908575	−	0.842421i
$763$	−2.63933	+	0.738798i	−0.0955501	+	0.0267463i
$764$	−3.77929	+	6.54592i	−0.136730	+	0.236823i
$765$	27.4554	−	31.9507i	0.992653	−	1.15518i
$766$	13.3148	+	7.68731i	0.481084	+	0.277754i
$767$	24.9737	+	32.3907i	0.901748	+	1.16956i
$768$	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	$0.213231\pi$
$770$	9.92386	+	35.4526i	0.357631	+	1.27762i
$771$	−0.547332	−	0.870372i	−0.0197117	−	0.0313457i
$772$	3.20420	−	11.9582i	0.115322	−	0.430386i
$773$	−1.52176	+	1.52176i	−0.0547341	+	0.0547341i	−0.733944	−	0.679210i	$-0.762323\pi$
$773$	−1.52176	+	1.52176i	−0.0547341	+	0.0547341i	0.679210	+	0.733944i	$0.262323\pi$
$774$	−16.4642	−	14.1478i	−0.591792	−	0.508531i
$775$	−52.9747	−	14.1945i	−1.90291	−	0.509882i
$776$	9.62088	−	5.55462i	0.345369	−	0.199399i
$777$	−1.07497	−	0.232385i	−0.0385643	−	0.00833678i
$778$	−0.141834	−	0.529333i	−0.00508501	−	0.0189775i
$779$	−30.7764	−	53.3063i	−1.10268	−	1.90990i
$780$	20.7254	−	3.57857i	0.742088	−	0.128133i
$781$	−6.78134	+	11.7456i	−0.242655	+	0.420291i
$782$	14.8583	−	14.8583i	0.531332	−	0.531332i
$783$	17.2753	+	7.51475i	0.617368	+	0.268555i
$784$	−6.99826	+	0.155864i	−0.249938	+	0.00556657i
$785$	−16.6319	+	16.6319i	−0.593617	+	0.593617i
$786$	−30.3051	+	9.35994i	−1.08095	+	0.333858i
$787$	22.4630	−	22.4630i	0.800720	−	0.800720i	−0.182488	−	0.983208i	$-0.558415\pi$
$787$	22.4630	−	22.4630i	0.800720	−	0.800720i	0.983208	+	0.182488i	$0.0584152\pi$
$788$	12.1789	−	3.26334i	0.433857	−	0.116252i
$789$	−17.9964	−	9.50301i	−0.640688	−	0.338316i
$790$	34.1576	+	19.7209i	1.21527	+	0.701637i
$791$	7.05733	−	4.18000i	0.250930	−	0.148624i
$792$	−0.935262	−	12.3598i	−0.0332331	−	0.439187i
$793$	−2.53127	+	3.31469i	−0.0898880	+	0.117708i
$794$	24.2077	+	13.9763i	0.859099	+	0.496001i
$795$	4.65138	−	20.4132i	0.164967	−	0.723980i
$796$	0.595154			0.0210947
$797$	10.9107	+	18.8980i	0.386478	+	0.669400i	0.991973	−	0.126449i	$-0.0403581\pi$
$797$	10.9107	+	18.8980i	0.386478	+	0.669400i	−0.605495	+	0.795849i	$0.707025\pi$
$798$	25.5217	−	1.24893i	0.903459	−	0.0442115i
$799$	6.27639	−	23.4238i	0.222043	−	0.828675i
$800$	6.12614	−	1.64149i	0.216592	−	0.0580356i
$801$	−37.0989	+	13.0117i	−1.31082	+	0.459745i
$802$	17.8421			0.630026
$803$	4.21213			0.148643
$804$	6.81120	+	22.0529i	0.240212	+	0.777747i
$805$	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
$808$	1.04070	−	3.88396i	0.0366118	−	0.136637i
$809$	−32.1839	+	18.5814i	−1.13153	+	0.653287i	−0.944319	−	0.329033i	$-0.893277\pi$
$809$	−32.1839	+	18.5814i	−1.13153	+	0.653287i	−0.187209	+	0.982320i	$0.559944\pi$
$810$	−28.2312	−	11.0327i	−0.991944	−	0.387649i
$811$	−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	$-0.615235\pi$
$812$	−4.70338	+	8.36009i	−0.165056	+	0.293382i
$813$	34.6339	+	7.89175i	1.21467	+	0.276776i
$814$	0.957809	+	0.256644i	0.0335712	+	0.00899537i
$815$		−	3.73070i		−	0.130681i
$816$	−3.84445	−	6.11348i	−0.134583	−	0.214015i
$817$	−28.5298	+	28.5298i	−0.998131	+	0.998131i
$818$	−25.7308			−0.899656
$819$	15.3352	−	24.1626i	0.535856	−	0.844309i
$820$	−37.1773			−1.29829
$821$	−25.3635	+	25.3635i	−0.885191	+	0.885191i	−0.994056	−	0.108866i	$-0.965278\pi$
$821$	−25.3635	+	25.3635i	−0.885191	+	0.885191i	0.108866	+	0.994056i	$0.465278\pi$
$822$	−0.501819	−	0.797998i	−0.0175030	−	0.0278334i
$823$		−	13.7471i		−	0.479195i	−0.970872	−	0.239597i	$-0.922985\pi$
$823$		−	13.7471i		−	0.479195i	0.970872	−	0.239597i	$-0.0770155\pi$
$824$	−10.3988	−	2.78634i	−0.362258	−	0.0970668i
$825$	−44.2530	−	10.0836i	−1.54069	−	0.351065i
$826$	30.0108	−	0.334156i	1.04421	−	0.0116268i
$827$	16.8232	+	16.8232i	0.584999	+	0.584999i	0.936273	−	0.351274i	$-0.114251\pi$
$827$	16.8232	+	16.8232i	0.584999	+	0.584999i	−0.351274	+	0.936273i	$0.614251\pi$
$828$	−13.6264	−	6.54996i	−0.473551	−	0.227627i
$829$	10.4498	−	6.03317i	0.362935	−	0.209541i	−0.307432	−	0.951570i	$-0.599470\pi$
$829$	10.4498	−	6.03317i	0.362935	−	0.209541i	0.670368	+	0.742029i	$0.266136\pi$
$830$	−3.81101	+	14.2229i	−0.132282	+	0.493683i
$831$	−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
$834$	−1.15969	−	3.75478i	−0.0401568	−	0.130018i
$835$	44.9721			1.55632
$836$	−23.0383			−0.796796
$837$	41.8089	−	16.4613i	1.44513	−	0.568986i
$838$	37.5204	−	10.0536i	1.29612	−	0.347295i
$839$	−5.43784	+	20.2943i	−0.187735	+	0.700637i	0.806293	+	0.591516i	$0.201470\pi$
$839$	−5.43784	+	20.2943i	−0.187735	+	0.700637i	−0.994028	+	0.109121i	$0.965196\pi$
$840$	7.05416	−	13.7268i	0.243391	−	0.473621i
$841$	−7.92765	−	13.7311i	−0.273367	−	0.473486i
$842$	−7.82596			−0.269700
$843$	0.382716	−	1.67960i	0.0131814	−	0.0578484i
$844$	−1.63121	−	0.941779i	−0.0561485	−	0.0324174i
$845$	−38.0171	−	21.7149i	−1.30783	−	0.747014i
$846$	−17.3984	+	1.31653i	−0.598170	+	0.0452633i
$847$	−13.9992	−	7.87595i	−0.481019	−	0.270621i
$848$	−3.10829	−	1.79457i	−0.106739	−	0.0616259i
$849$	−2.09853	−	1.10813i	−0.0720212	−	0.0380309i
$850$	−25.5430	+	6.84422i	−0.876117	+	0.234755i
$851$	0.855241	−	0.855241i	0.0293173	−	0.0293173i
$852$	5.43238	−	1.67783i	0.186110	−	0.0574814i
$853$	−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	$0.271128\pi$
$854$	0.824963	+	2.94715i	0.0282297	+	0.100849i
$855$	−24.4067	+	50.7752i	−0.834691	+	1.73648i
$856$	−13.4786	+	13.4786i	−0.460688	+	0.460688i
$857$	−21.6487	+	37.4967i	−0.739507	+	1.28086i	0.213210	+	0.977006i	$0.431608\pi$
$857$	−21.6487	+	37.4967i	−0.739507	+	1.28086i	−0.952718	+	0.303857i	$0.901725\pi$
$858$	−14.8748	+	21.0835i	−0.507816	+	0.719780i
$859$	−0.127045	−	0.220049i	−0.00433473	−	0.00750798i	0.863850	−	0.503749i	$-0.168046\pi$
$859$	−0.127045	−	0.220049i	−0.00433473	−	0.00750798i	−0.868185	+	0.496241i	$0.834713\pi$
$860$	6.30725	+	23.5390i	0.215075	+	0.802672i
$861$	−33.9792	+	37.4759i	−1.15801	+	1.27718i
$862$	4.62448	−	2.66995i	0.157511	−	0.0909387i
$863$	−8.40521	−	2.25217i	−0.286117	−	0.0766647i	0.112906	−	0.993606i	$-0.463984\pi$
$863$	−8.40521	−	2.25217i	−0.286117	−	0.0766647i	−0.399023	+	0.916941i	$0.630651\pi$
$864$	−3.23532	+	4.06604i	−0.110068	+	0.138329i
$865$	7.57918	−	7.57918i	0.257700	−	0.257700i
$866$	4.02673	−	15.0280i	0.136834	−	0.510671i
$867$	0.354823	+	0.564243i	0.0120504	+	0.0191627i
$868$	6.16711	+	22.0318i	0.209325	+	0.747808i
$869$	−46.7392	+	12.5237i	−1.58552	+	0.424839i
$870$	−11.2583	−	17.9031i	−0.381693	−	0.606972i
$871$	18.2837	−	44.4317i	0.619520	−	1.50551i
$872$	−0.897131	−	0.517959i	−0.0303807	−	0.0175403i
$873$	25.2772	+	21.7209i	0.855504	+	0.735141i
$874$	−14.0504	+	24.3360i	−0.475262	+	0.823178i
$875$	−8.55060	−	8.36228i	−0.289063	−	0.282697i
$876$	−1.29483	−	1.20055i	−0.0437483	−	0.0405629i
$877$	−33.9732	+	9.10309i	−1.14719	+	0.307389i	−0.781840	−	0.623480i	$-0.785718\pi$
$877$	−33.9732	+	9.10309i	−1.14719	+	0.307389i	−0.365353	+	0.930869i	$0.619052\pi$
$878$	−25.6807	−	25.6807i	−0.866683	−	0.866683i
$879$	−21.9243	+	6.77148i	−0.739490	+	0.228396i
$880$	−6.95746	+	12.0507i	−0.234536	+	0.406228i
$881$	26.4851	−	45.8735i	0.892304	−	1.54552i	0.0551982	−	0.998475i	$-0.482421\pi$
$881$	26.4851	−	45.8735i	0.892304	−	1.54552i	0.837106	−	0.547041i	$-0.184246\pi$
$882$	−7.38976	−	19.6568i	−0.248826	−	0.661880i
$883$			49.7396i			1.67387i	0.547301	+	0.836936i	$0.315655\pi$
$883$			49.7396i			1.67387i	−0.547301	+	0.836936i	$0.684345\pi$
$884$	−1.92770	+	14.9093i	−0.0648356	+	0.501453i
$885$	−30.8983	+	58.5137i	−1.03863	+	1.96692i
$886$	−1.86384	+	6.95594i	−0.0626169	+	0.233689i
$887$			44.9799i			1.51028i	0.655565	+	0.755139i	$0.272431\pi$
$887$			44.9799i			1.51028i	−0.655565	+	0.755139i	$0.727569\pi$
$888$	−0.221286	−	0.351891i	−0.00742586	−	0.0118087i
$889$	45.5337	+	25.6172i	1.52715	+	0.859173i
$890$	42.6309	+	11.4229i	1.42899	+	0.382897i
$891$	34.0612	−	14.9196i	1.14109	−	0.499827i
$892$	1.75511	+	6.55015i	0.0587654	+	0.219315i
$893$			32.4301i			1.08523i
$894$	0.193555	+	5.12310i	0.00647344	+	0.171342i
$895$	−5.71067	−	21.3125i	−0.190887	−	0.712398i
$896$	−1.89154	−	1.84988i	−0.0631920	−	0.0618003i
$897$	13.1994	+	28.5709i	0.440716	+	0.953953i
$898$	3.20675	+	5.55426i	0.107011	+	0.185348i
$899$	30.2831	+	8.11434i	1.01000	+	0.270628i
$900$	10.7295	+	15.7128i	0.357651	+	0.523761i
$901$	12.9601	+	7.48250i	0.431762	+	0.249278i
$902$	32.2511	−	32.2511i	1.07384	−	1.07384i
$903$	29.4927	+	15.1562i	0.981457	+	0.504366i
$904$	2.99455	+	0.802388i	0.0995974	+	0.0266870i
$905$	−4.36862	+	16.3039i	−0.145218	+	0.541960i
$906$	0.665791	+	17.6225i	0.0221194	+	0.585468i
$907$	−41.4806	+	23.9488i	−1.37734	+	0.795207i	−0.991839	−	0.127500i	$-0.959305\pi$
$907$	−41.4806	+	23.9488i	−1.37734	+	0.795207i	−0.385501	+	0.922708i	$0.625971\pi$
$908$	−0.601011	−	0.601011i	−0.0199452	−	0.0199452i
$909$	12.0285	−	0.910193i	0.398961	−	0.0301892i
$910$	−29.5134	+	12.6926i	−0.978360	+	0.420756i
$911$			11.8282i			0.391886i	0.980615	+	0.195943i	$0.0627767\pi$
$911$			11.8282i			0.391886i	−0.980615	+	0.195943i	$0.937223\pi$
$912$	7.08208	+	6.56643i	0.234511	+	0.217436i
$913$	−9.03223	−	15.6443i	−0.298923	−	0.517750i
$914$	22.3302			0.738617
$915$	−6.57889	−	1.49908i	−0.217492	−	0.0495580i
$916$	1.74010	−	6.49414i	0.0574945	−	0.214572i
$917$	41.6862	−	24.6904i	1.37660	−	0.815350i
$918$	13.4897	−	16.9534i	0.445227	−	0.559546i
$919$	0.220406	−	0.381755i	0.00727053	−	0.0125929i	−0.862367	−	0.506283i	$-0.831019\pi$
$919$	0.220406	−	0.381755i	0.00727053	−	0.0125929i	0.869638	+	0.493690i	$0.164352\pi$
$920$	8.48631	+	14.6987i	0.279785	+	0.484602i
$921$	2.46062	+	0.560681i	0.0810802	+	0.0184751i
$922$	−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
$926$		−	8.37202i		−	0.275122i
$927$	−2.43692	−	32.2047i	−0.0800388	−	1.05774i
$928$	−3.50202	+	0.938365i	−0.114960	+	0.0308033i
$929$	−3.90916	−	14.5892i	−0.128255	−	0.478655i	0.871679	−	0.490076i	$-0.163031\pi$
$929$	−3.90916	−	14.5892i	−0.128255	−	0.478655i	−0.999935	+	0.0114211i	$0.996364\pi$
$930$	−49.1813	−	11.2065i	−1.61272	−	0.367477i
$931$	−37.4675	+	10.9391i	−1.22795	+	0.358515i
$932$	−2.43351	+	1.40499i	−0.0797122	+	0.0460218i
$933$	−28.1976	+	1.06533i	−0.923149	+	0.0348773i
$934$	−29.2065	−	7.82585i	−0.955665	−	0.256070i
$935$	29.0092	−	50.2454i	0.948702	−	1.64320i
$936$	10.5818	−	2.24154i	0.345879	−	0.0732670i
$937$	50.3863			1.64605			0.823024	−	0.568007i	$-0.192285\pi$
$937$	50.3863			1.64605			0.823024	+	0.568007i	$0.192285\pi$
$938$	−17.9671	−	30.3349i	−0.586648	−	0.990470i
$939$	2.89031	−	5.47355i	0.0943218	−	0.178622i
$940$	16.9632	+	9.79373i	0.553280	+	0.319436i
$941$	−0.866823	−	3.23503i	−0.0282576	−	0.105459i	0.950357	−	0.311163i	$-0.100718\pi$
$941$	−0.866823	−	3.23503i	−0.0282576	−	0.105459i	−0.978614	+	0.205704i	$0.934052\pi$
$942$	−8.22464	+	8.87051i	−0.267973	+	0.289017i
$943$	−14.3987	−	53.7367i	−0.468887	−	1.74991i
$944$	8.02122	+	8.02122i	0.261069	+	0.261069i
$945$	45.8637	+	6.34055i	1.49195	+	0.206258i
$946$	−25.8914	−	14.9484i	−0.841802	−	0.486015i
$947$	8.69958	+	8.69958i	0.282698	+	0.282698i	0.834184	−	0.551486i	$-0.185939\pi$
$947$	8.69958	+	8.69958i	0.282698	+	0.282698i	−0.551486	+	0.834184i	$0.685939\pi$
$948$	17.9374	+	9.47187i	0.582580	+	0.307632i
$949$	0.488223	+	3.64316i	0.0158484	+	0.118262i
$950$	30.6262	−	17.6820i	0.993645	−	0.573681i
$951$	10.1889	+	32.9890i	0.330397	+	1.06974i
$952$	7.88681	+	7.71311i	0.255613	+	0.249983i
$953$	−12.5519	−	21.7405i	−0.406596	−	0.704245i	0.587910	−	0.808927i	$-0.299951\pi$
$953$	−12.5519	−	21.7405i	−0.406596	−	0.704245i	−0.994506	+	0.104681i	$0.966618\pi$
$954$	1.99411	−	10.5812i	0.0645618	−	0.342578i
$955$	18.0001	+	18.0001i	0.582469	+	0.582469i
$956$	−4.28240	−	4.28240i	−0.138503	−	0.138503i
$957$	25.2974	+	5.76430i	0.817748	+	0.186333i
$958$	−18.6833	−	32.3605i	−0.603631	−	1.04552i
$959$	1.02947	+	1.00680i	0.0332434	+	0.0325112i
$960$	5.57346	−	1.72140i	0.179883	−	0.0555580i
$961$	37.9113	−	21.8881i	1.22294	−	0.706067i
$962$	−0.110958	+	0.858175i	−0.00357743	+	0.0276687i
$963$	−51.5397	−	24.7741i	−1.66084	−	0.798335i
$964$	2.86631	+	2.86631i	0.0923178	+	0.0923178i
$965$	−36.1080	−	20.8470i	−1.16236	−	0.671087i
$966$	22.5731	+	4.87982i	0.726277	+	0.157006i
$967$	−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	$0.870723\pi$
$968$	−1.57132	−	5.86425i	−0.0505041	−	0.188484i
$969$	−29.5288	−	27.3788i	−0.948603	−	0.879534i
$970$	−9.68344	−	36.1391i	−0.310917	−	1.16036i
$971$	31.9444	+	18.4431i	1.02515	+	0.591868i	0.915590	−	0.402113i	$-0.131724\pi$
$971$	31.9444	+	18.4431i	1.02515	+	0.591868i	0.109555	+	0.993981i	$0.465057\pi$
$972$	−14.7230	−	5.12184i	−0.472241	−	0.164283i
$973$	3.05913	+	5.16489i	0.0980711	+	0.165579i
$974$	−4.30081			−0.137807
$975$	3.59216	−	39.4441i	0.115041	−	1.26322i
$976$	−0.578368	+	1.00176i	−0.0185131	+	0.0320656i
$977$	−11.9793	−	3.20985i	−0.383252	−	0.102692i	0.0620485	−	0.998073i	$-0.480237\pi$
$977$	−11.9793	−	3.20985i	−0.383252	−	0.102692i	−0.445301	+	0.895381i	$0.646903\pi$
$978$	−0.0724374	−	1.91731i	−0.00231629	−	0.0613088i
$979$	−46.8914	+	27.0728i	−1.49866	+	0.865249i
$980$	−5.59305	+	22.9017i	−0.178663	+	0.731568i
$981$	0.575551	−	3.05399i	0.0183759	−	0.0975064i
$982$	−0.730677	−	2.72692i	−0.0233168	−	0.0870196i
$983$	−32.4673	+	8.69958i	−1.03554	+	0.277473i	−0.736266	−	0.676692i	$-0.763413\pi$
$983$	−32.4673	+	8.69958i	−1.03554	+	0.277473i	−0.299279	+	0.954166i	$0.596746\pi$
$984$	−19.1064	+	0.721855i	−0.609090	+	0.0230119i
$985$		−	42.4634i		−	1.35300i
$986$	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
$990$	−41.0226	−	7.73106i	−1.30378	−	0.245709i
$991$	4.11808	+	7.13273i	0.130815	+	0.226579i	0.923991	−	0.382414i	$-0.124907\pi$
$991$	4.11808	+	7.13273i	0.130815	+	0.226579i	−0.793176	+	0.608993i	$0.791574\pi$
$992$	−4.32366	+	7.48880i	−0.137276	+	0.237770i
$993$	−21.4091	−	19.8503i	−0.679397	−	0.629930i
$994$	−7.47251	+	4.42591i	−0.237013	+	0.140381i
$995$	0.518770	−	1.93608i	0.0164461	−	0.0613778i
$996$	−1.68242	+	7.38351i	−0.0533095	+	0.233956i
$997$	−22.8890			−0.724902			−0.362451	−	0.932003i	$-0.618060\pi$
$997$	−22.8890			−0.724902			−0.362451	+	0.932003i	$0.618060\pi$
$998$	3.07819	+	5.33158i	0.0974384	+	0.168768i
$999$	0.776465	−	0.975834i	0.0245663	−	0.0308740i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.1	✓	152	13.2	odd	12
546.2.bw.a.431.20	yes	152	39.2	even	12
546.2.bw.a.527.1	yes	152	21.2	odd	6
546.2.bw.a.527.20	yes	152	7.2	even	3
546.2.ch.a.137.14	yes	152	1.1	even	1	trivial
546.2.ch.a.137.32	yes	152	3.2	odd	2	inner
546.2.ch.a.275.14	yes	152	273.2	even	12	inner
546.2.ch.a.275.32	yes	152	91.2	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.922039 + 1.46623i) q^{3} -1.00000i q^{4} +(-3.25307 - 0.871657i) q^{5} +(-1.68876 - 0.384805i) q^{6} +(2.64559 - 0.0294574i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.29969 + 2.70385i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.922039 + 1.46623i) q^{3} -1.00000i q^{4} +(-3.25307 - 0.871657i) q^{5} +(-1.68876 - 0.384805i) q^{6} +(2.64559 - 0.0294574i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.29969 + 2.70385i) q^{9} +(2.91662 - 1.68391i) q^{10} +(-1.06937 + 3.99094i) q^{11} +(1.46623 - 0.922039i) q^{12} +(-3.57579 - 0.462333i) q^{13} +(-1.84988 + 1.89154i) q^{14} +(-1.72140 - 5.57346i) q^{15} -1.00000 q^{16} +4.16951 q^{17} +(-0.992892 - 2.83093i) q^{18} +(-5.38596 + 1.44316i) q^{19} +(-0.871657 + 3.25307i) q^{20} +(2.48253 + 3.85189i) q^{21} +(-2.06586 - 3.57818i) q^{22} -5.03964 q^{23} +(-0.384805 + 1.68876i) q^{24} +(5.49254 + 3.17112i) q^{25} +(2.85538 - 2.20154i) q^{26} +(-5.16284 + 0.587405i) q^{27} +(-0.0294574 - 2.64559i) q^{28} +(-3.13983 - 1.81278i) q^{29} +(5.15825 + 2.72382i) q^{30} +(-8.35267 + 2.23809i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.83765 + 2.11185i) q^{33} +(-2.94829 + 2.94829i) q^{34} +(-8.63195 - 2.21022i) q^{35} +(2.70385 + 1.29969i) q^{36} +(-0.169703 + 0.169703i) q^{37} +(2.78798 - 4.82892i) q^{38} +(-2.61913 - 5.66923i) q^{39} +(-1.68391 - 2.91662i) q^{40} +(2.85709 + 10.6628i) q^{41} +(-4.47911 - 0.968288i) q^{42} +(6.26650 - 3.61796i) q^{43} +(3.99094 + 1.06937i) q^{44} +(6.58481 - 7.66293i) q^{45} +(3.56356 - 3.56356i) q^{46} +(1.50531 - 5.61788i) q^{47} +(-0.922039 - 1.46623i) q^{48} +(6.99826 - 0.155864i) q^{49} +(-6.12614 + 1.64149i) q^{50} +(3.84445 + 6.11348i) q^{51} +(-0.462333 + 3.57579i) q^{52} +(3.10829 + 1.79457i) q^{53} +(3.23532 - 4.06604i) q^{54} +(6.95746 - 12.0507i) q^{55} +(1.89154 + 1.84988i) q^{56} +(-7.08208 - 6.56643i) q^{57} +(3.50202 - 0.938365i) q^{58} +(-8.02122 - 8.02122i) q^{59} +(-5.57346 + 1.72140i) q^{60} +(0.578368 - 1.00176i) q^{61} +(4.32366 - 7.48880i) q^{62} +(-3.35879 + 7.19156i) q^{63} +1.00000i q^{64} +(11.2293 + 4.62086i) q^{65} +(3.34164 - 6.32825i) q^{66} +(-3.44895 + 12.8717i) q^{67} -4.16951i q^{68} +(-4.64674 - 7.38929i) q^{69} +(7.66657 - 4.54085i) q^{70} +(3.17072 + 0.849592i) q^{71} +(-2.83093 + 0.992892i) q^{72} +(-0.263856 - 0.984725i) q^{73} -0.239996i q^{74} +(0.414729 + 10.9773i) q^{75} +(1.44316 + 5.38596i) q^{76} +(-2.71154 + 10.5899i) q^{77} +(5.86075 + 2.15675i) q^{78} +(5.85567 + 10.1423i) q^{79} +(3.25307 + 0.871657i) q^{80} +(-5.62162 - 7.02833i) q^{81} +(-9.56002 - 5.51948i) q^{82} +(-3.09157 + 3.09157i) q^{83} +(3.85189 - 2.48253i) q^{84} +(-13.5637 - 3.63438i) q^{85} +(-1.87280 + 6.98937i) q^{86} +(-0.237081 - 6.27518i) q^{87} +(-3.57818 + 2.06586i) q^{88} +(9.26652 + 9.26652i) q^{89} +(0.762346 + 10.0747i) q^{90} +(-9.47367 - 1.11781i) q^{91} +5.03964i q^{92} +(-10.9831 - 10.1834i) q^{93} +(2.90803 + 5.03685i) q^{94} +18.7789 q^{95} +(1.68876 + 0.384805i) q^{96} +(2.87528 - 10.7307i) q^{97} +(-4.83831 + 5.05873i) q^{98} +(-9.40105 - 8.07839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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