LMFDB - Embedded newform 110.2.k.a.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$110 = 2 \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	110.k (of order $20$ , degree $8$ , 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	110.73
Dual form			110.2.k.a.107.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(0.346247 - 0.176422i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(2.14909 + 0.617590i) q^{5} +(0.228415 + 0.314386i) q^{6} +(-0.00697389 + 0.0136870i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-1.67459 + 2.30488i) q^{9} +(-0.273795 + 2.21924i) q^{10} +(2.43343 - 2.25353i) q^{11} +(-0.274783 + 0.274783i) q^{12} +(-2.31203 + 0.366190i) q^{13} +(-0.0146095 - 0.00474691i) q^{14} +(0.853072 - 0.165307i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-3.88580 - 0.615451i) q^{17} +(-2.53847 - 1.29341i) q^{18} +(1.78456 - 5.49230i) q^{19} +(-2.23475 + 0.0767418i) q^{20} +0.00596944i q^{21} +(2.60646 + 2.05094i) q^{22} +(-4.75841 - 4.75841i) q^{23} +(-0.314386 - 0.228415i) q^{24} +(4.23716 + 2.65451i) q^{25} +(-0.723362 - 2.22628i) q^{26} +(-0.355564 + 2.24494i) q^{27} +(0.00240304 - 0.0151722i) q^{28} +(-1.28099 - 3.94247i) q^{29} +(0.296722 + 0.816709i) q^{30} +(4.70277 + 3.41676i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.444997 - 1.20959i) q^{33} -3.93424i q^{34} +(-0.0234405 + 0.0251076i) q^{35} +(0.880386 - 2.70955i) q^{36} +(-1.00521 - 0.512178i) q^{37} +(5.70385 + 0.903401i) q^{38} +(-0.735929 + 0.534684i) q^{39} +(-0.425389 - 2.19523i) q^{40} +(-4.46390 - 1.45041i) q^{41} +(-0.00589594 + 0.000933826i) q^{42} +(-5.68946 + 5.68946i) q^{43} +(-1.61795 + 2.89521i) q^{44} +(-5.02232 + 3.91918i) q^{45} +(3.95544 - 5.44420i) q^{46} +(-0.703097 - 1.37991i) q^{47} +(0.176422 - 0.346247i) q^{48} +(4.11436 + 5.66293i) q^{49} +(-1.95899 + 4.60026i) q^{50} +(-1.45403 + 0.472442i) q^{51} +(2.08571 - 1.06272i) q^{52} +(2.19559 + 13.8624i) q^{53} -2.27293 q^{54} +(6.62142 - 3.34018i) q^{55} +0.0153613 q^{56} +(-0.351063 - 2.21653i) q^{57} +(3.69354 - 1.88195i) q^{58} +(1.86696 - 0.606613i) q^{59} +(-0.760237 + 0.420830i) q^{60} +(4.84534 + 6.66904i) q^{61} +(-2.63902 + 5.17937i) q^{62} +(-0.0198685 - 0.0389942i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-5.19491 - 0.640913i) q^{65} +(1.26431 + 0.250297i) q^{66} +(3.67640 - 3.67640i) q^{67} +(3.88580 - 0.615451i) q^{68} +(-2.48707 - 0.808098i) q^{69} +(-0.0284654 - 0.0192242i) q^{70} +(-5.20051 + 3.77839i) q^{71} +(2.81391 + 0.445680i) q^{72} +(4.10721 + 2.09273i) q^{73} +(0.348623 - 1.07295i) q^{74} +(1.93542 + 0.171589i) q^{75} +5.77495i q^{76} +(0.0138737 + 0.0490224i) q^{77} +(-0.643226 - 0.643226i) q^{78} +(3.84472 + 2.79336i) q^{79} +(2.10166 - 0.763562i) q^{80} +(-2.36821 - 7.28861i) q^{81} +(0.734244 - 4.63584i) q^{82} +(2.08413 - 13.1587i) q^{83} +(-0.00184466 - 0.00567727i) q^{84} +(-7.97084 - 3.72249i) q^{85} +(-6.50944 - 4.72938i) q^{86} +(-1.13908 - 1.13908i) q^{87} +(-3.11267 - 1.14512i) q^{88} -9.48232i q^{89} +(-4.65659 - 4.34739i) q^{90} +(0.0111118 - 0.0341986i) q^{91} +(5.99594 + 3.05509i) q^{92} +(2.23111 + 0.353373i) q^{93} +(1.25293 - 0.910306i) q^{94} +(7.22716 - 10.7013i) q^{95} +(0.369582 + 0.120085i) q^{96} +(4.39615 - 0.696283i) q^{97} +(-4.94958 + 4.94958i) q^{98} +(1.11911 + 9.38252i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36}+ \cdots + 72 q^{97}+O(q^{100})$ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$ .

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

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

)

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

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	0.346247	−	0.176422i	0.199906	−	0.101857i	−0.351172	−	0.936311i	$-0.614217\pi$
$3$	0.346247	−	0.176422i	0.199906	−	0.101857i	0.551078	+	0.834454i	$0.314217\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	2.14909	+	0.617590i	0.961102	+	0.276195i
$5$	2.14909	+	0.617590i	0.961102	+	0.276195i
$6$	0.228415	+	0.314386i	0.0932498	+	0.128347i
$7$	−0.00697389	+	0.0136870i	−0.00263588	+	0.00517321i	−0.892321	−	0.451402i	$-0.850924\pi$
$7$	−0.00697389	+	0.0136870i	−0.00263588	+	0.00517321i	0.889685	+	0.456575i	$0.150924\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−1.67459	+	2.30488i	−0.558198	+	0.768293i
$10$	−0.273795	+	2.21924i	−0.0865816	+	0.701786i
$11$	2.43343	−	2.25353i	0.733708	−	0.679465i
$11$	2.43343	−	2.25353i	0.733708	−	0.679465i
$12$	−0.274783	+	0.274783i	−0.0793230	+	0.0793230i
$13$	−2.31203	+	0.366190i	−0.641242	+	0.101563i	−0.468584	−	0.883419i	$-0.655236\pi$
$13$	−2.31203	+	0.366190i	−0.641242	+	0.101563i	−0.172658	+	0.984982i	$0.555236\pi$
$14$	−0.0146095	−	0.00474691i	−0.00390455	−	0.00126866i
$15$	0.853072	−	0.165307i	0.220262	−	0.0426821i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−3.88580	−	0.615451i	−0.942446	−	0.149269i	−0.333740	−	0.942665i	$-0.608311\pi$
$17$	−3.88580	−	0.615451i	−0.942446	−	0.149269i	−0.608705	+	0.793396i	$0.708311\pi$
$18$	−2.53847	−	1.29341i	−0.598322	−	0.304861i
$19$	1.78456	−	5.49230i	0.409406	−	1.26002i	−0.507755	−	0.861502i	$-0.669524\pi$
$19$	1.78456	−	5.49230i	0.409406	−	1.26002i	0.917160	−	0.398519i	$-0.130476\pi$
$20$	−2.23475	+	0.0767418i	−0.499705	+	0.0171600i
$21$			0.00596944i			0.00130264i
$22$	2.60646	+	2.05094i	0.555699	+	0.437263i
$23$	−4.75841	−	4.75841i	−0.992196	−	0.992196i	0.00777340	−	0.999970i	$-0.497526\pi$
$23$	−4.75841	−	4.75841i	−0.992196	−	0.992196i	−0.999970	+	0.00777340i	$0.997526\pi$
$24$	−0.314386	−	0.228415i	−0.0641737	−	0.0466249i
$25$	4.23716	+	2.65451i	0.847433	+	0.530902i
$26$	−0.723362	−	2.22628i	−0.141863	−	0.436609i
$27$	−0.355564	+	2.24494i	−0.0684284	+	0.432040i
$28$	0.00240304	−	0.0151722i	0.000454132	−	0.00286728i
$29$	−1.28099	−	3.94247i	−0.237873	−	0.732099i	−0.996727	−	0.0808379i	$-0.974240\pi$
$29$	−1.28099	−	3.94247i	−0.237873	−	0.732099i	0.758854	−	0.651261i	$-0.225760\pi$
$30$	0.296722	+	0.816709i	0.0541737	+	0.149110i
$31$	4.70277	+	3.41676i	0.844642	+	0.613668i	0.923663	−	0.383205i	$-0.125180\pi$
$31$	4.70277	+	3.41676i	0.844642	+	0.613668i	−0.0790218	+	0.996873i	$0.525180\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.444997	−	1.20959i	0.0774640	−	0.210562i
$34$		−	3.93424i		−	0.674716i
$35$	−0.0234405	+	0.0251076i	−0.00396217	+	0.00424397i
$36$	0.880386	−	2.70955i	0.146731	−	0.451592i
$37$	−1.00521	−	0.512178i	−0.165255	−	0.0842015i	0.369407	−	0.929268i	$-0.379561\pi$
$37$	−1.00521	−	0.512178i	−0.165255	−	0.0842015i	−0.534662	+	0.845066i	$0.679561\pi$
$38$	5.70385	+	0.903401i	0.925287	+	0.146551i
$39$	−0.735929	+	0.534684i	−0.117843	+	0.0856180i
$40$	−0.425389	−	2.19523i	−0.0672599	−	0.347097i
$41$	−4.46390	−	1.45041i	−0.697144	−	0.226516i	−0.0610584	−	0.998134i	$-0.519448\pi$
$41$	−4.46390	−	1.45041i	−0.697144	−	0.226516i	−0.636086	+	0.771618i	$0.719448\pi$
$42$	−0.00589594		0.000933826i	−0.000909764		0.000144092i
$43$	−5.68946	+	5.68946i	−0.867634	+	0.867634i	−0.992210	−	0.124576i	$-0.960243\pi$
$43$	−5.68946	+	5.68946i	−0.867634	+	0.867634i	0.124576	+	0.992210i	$0.460243\pi$
$44$	−1.61795	+	2.89521i	−0.243915	+	0.436469i
$45$	−5.02232	+	3.91918i	−0.748683	+	0.584237i
$46$	3.95544	−	5.44420i	0.583198	−	0.802704i
$47$	−0.703097	−	1.37991i	−0.102557	−	0.201280i	0.834026	−	0.551725i	$-0.186030\pi$
$47$	−0.703097	−	1.37991i	−0.102557	−	0.201280i	−0.936583	+	0.350445i	$0.886030\pi$
$48$	0.176422	−	0.346247i	0.0254643	−	0.0499764i
$49$	4.11436	+	5.66293i	0.587765	+	0.808990i
$50$	−1.95899	+	4.60026i	−0.277043	+	0.650574i
$51$	−1.45403	+	0.472442i	−0.203604	+	0.0661551i
$52$	2.08571	−	1.06272i	0.289236	−	0.147373i
$53$	2.19559	+	13.8624i	0.301587	+	1.90415i	0.413635	+	0.910443i	$0.364259\pi$
$53$	2.19559	+	13.8624i	0.301587	+	1.90415i	−0.112048	+	0.993703i	$0.535741\pi$
$54$	−2.27293			−0.309306
$55$	6.62142	−	3.34018i	0.892832	−	0.450389i
$56$	0.0153613			0.00205274
$57$	−0.351063	−	2.21653i	−0.0464995	−	0.293586i
$58$	3.69354	−	1.88195i	0.484986	−	0.247113i
$59$	1.86696	−	0.606613i	0.243058	−	0.0789743i	−0.184955	−	0.982747i	$-0.559214\pi$
$59$	1.86696	−	0.606613i	0.243058	−	0.0789743i	0.428013	+	0.903773i	$0.359214\pi$
$60$	−0.760237	+	0.420830i	−0.0981461	+	0.0543289i
$61$	4.84534	+	6.66904i	0.620382	+	0.853883i	0.997381	−	0.0723312i	$-0.0230439\pi$
$61$	4.84534	+	6.66904i	0.620382	+	0.853883i	−0.376999	+	0.926214i	$0.623044\pi$
$62$	−2.63902	+	5.17937i	−0.335156	+	0.657780i
$63$	−0.0198685	−	0.0389942i	−0.00250320	−	0.00491281i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−5.19491	−	0.640913i	−0.644350	−	0.0794955i
$66$	1.26431	+	0.250297i	0.155626	+	0.0308094i
$67$	3.67640	−	3.67640i	0.449143	−	0.449143i	−0.445926	−	0.895070i	$-0.647126\pi$
$67$	3.67640	−	3.67640i	0.449143	−	0.449143i	0.895070	+	0.445926i	$0.147126\pi$
$68$	3.88580	−	0.615451i	0.471223	−	0.0746344i
$69$	−2.48707	−	0.808098i	−0.299408	−	0.0972835i
$70$	−0.0284654	−	0.0192242i	−0.00340227	−	0.00229773i
$71$	−5.20051	+	3.77839i	−0.617187	+	0.448413i	−0.851938	−	0.523643i	$-0.824573\pi$
$71$	−5.20051	+	3.77839i	−0.617187	+	0.448413i	0.234751	+	0.972056i	$0.424573\pi$
$72$	2.81391	+	0.445680i	0.331623	+	0.0525239i
$73$	4.10721	+	2.09273i	0.480713	+	0.244935i	0.677517	−	0.735508i	$-0.263056\pi$
$73$	4.10721	+	2.09273i	0.480713	+	0.244935i	−0.196804	+	0.980443i	$0.563056\pi$
$74$	0.348623	−	1.07295i	0.0405266	−	0.124728i
$75$	1.93542	+	0.171589i	0.223483	+	0.0198134i
$76$			5.77495i			0.662432i
$77$	0.0138737	+	0.0490224i	0.00158105	+	0.00558662i
$78$	−0.643226	−	0.643226i	−0.0728310	−	0.0728310i
$79$	3.84472	+	2.79336i	0.432565	+	0.314277i	0.782674	−	0.622432i	$-0.213855\pi$
$79$	3.84472	+	2.79336i	0.432565	+	0.314277i	−0.350109	+	0.936709i	$0.613855\pi$
$80$	2.10166	−	0.763562i	0.234973	−	0.0853688i
$81$	−2.36821	−	7.28861i	−0.263135	−	0.809846i
$82$	0.734244	−	4.63584i	0.0810837	−	0.511943i
$83$	2.08413	−	13.1587i	0.228763	−	1.44436i	−0.559405	−	0.828895i	$-0.688970\pi$
$83$	2.08413	−	13.1587i	0.228763	−	1.44436i	0.788168	−	0.615460i	$-0.211030\pi$
$84$	−0.00184466	−	0.00567727i	−0.000201269	−	0.000619441i
$85$	−7.97084	−	3.72249i	−0.864559	−	0.403761i
$86$	−6.50944	−	4.72938i	−0.701931	−	0.509983i
$87$	−1.13908	−	1.13908i	−0.122122	−	0.122122i
$88$	−3.11267	−	1.14512i	−0.331811	−	0.122070i
$89$		−	9.48232i		−	1.00512i	−0.864541	−	0.502562i	$-0.832391\pi$
$89$		−	9.48232i		−	1.00512i	0.864541	−	0.502562i	$-0.167609\pi$
$90$	−4.65659	−	4.34739i	−0.490848	−	0.458255i
$91$	0.0111118	−	0.0341986i	0.00116483	−	0.00358499i
$92$	5.99594	+	3.05509i	0.625120	+	0.318515i
$93$	2.23111	+	0.353373i	0.231355	+	0.0366431i
$94$	1.25293	−	0.910306i	0.129230	−	0.0938909i
$95$	7.22716	−	10.7013i	0.741491	−	1.09793i
$96$	0.369582	+	0.120085i	0.0377204	+	0.0122561i
$97$	4.39615	−	0.696283i	0.446362	−	0.0706968i	0.0707925	−	0.997491i	$-0.477447\pi$
$97$	4.39615	−	0.696283i	0.446362	−	0.0706968i	0.375569	+	0.926794i	$0.377447\pi$
$98$	−4.94958	+	4.94958i	−0.499983	+	0.499983i
$99$	1.11911	+	9.38252i	0.112475	+	0.942979i
$100$	−4.85007	−	1.21523i	−0.485007	−	0.121523i
$101$	−10.2067	+	14.0483i	−1.01561	+	1.39786i	−0.100365	+	0.994951i	$0.532001\pi$
$101$	−10.2067	+	14.0483i	−1.01561	+	1.39786i	−0.915240	+	0.402910i	$0.867999\pi$
$102$	−0.694085	−	1.36222i	−0.0687246	−	0.134880i
$103$	−0.155063	+	0.304328i	−0.0152788	+	0.0299864i	−0.898520	−	0.438933i	$-0.855357\pi$
$103$	−0.155063	+	0.304328i	−0.0152788	+	0.0299864i	0.883241	+	0.468919i	$0.155357\pi$
$104$	1.37592	+	1.89379i	0.134920	+	0.185701i
$105$	−0.00368667	+	0.0128289i	−0.000359782	+	0.00125197i
$106$	−13.3483	+	4.33711i	−1.29650	+	0.421257i
$107$	−2.04336	+	1.04115i	−0.197539	+	0.100651i	−0.549962	−	0.835190i	$-0.685358\pi$
$107$	−2.04336	+	1.04115i	−0.197539	+	0.100651i	0.352423	+	0.935841i	$0.385358\pi$
$108$	−0.355564	−	2.24494i	−0.0342142	−	0.216020i
$109$	−2.42843			−0.232602			−0.116301	−	0.993214i	$-0.537104\pi$
$109$	−2.42843			−0.232602			−0.116301	+	0.993214i	$0.537104\pi$
$110$	4.33487	+	6.01738i	0.413314	+	0.573735i
$111$	−0.438409			−0.0416119
$112$	0.00240304	+	0.0151722i	0.000227066	+	0.00143364i
$113$	9.70357	−	4.94421i	0.912835	−	0.465113i	0.0665137	−	0.997786i	$-0.478812\pi$
$113$	9.70357	−	4.94421i	0.912835	−	0.465113i	0.846321	+	0.532673i	$0.178812\pi$
$114$	2.13432	−	0.693483i	0.199897	−	0.0649506i
$115$	−7.28749	−	13.1650i	−0.679562	−	1.22764i
$116$	2.43658	+	3.35367i	0.226231	+	0.311380i
$117$	3.02769	−	5.94217i	0.279910	−	0.549354i
$118$	0.891202	+	1.74908i	0.0820418	+	0.161016i
$119$	0.0355229	−	0.0488930i	0.00325638	−	0.00448202i
$120$	−0.534576	−	0.685044i	−0.0487999	−	0.0625357i
$121$	0.843188	−	10.9676i	0.0766535	−	0.997058i
$122$	−5.82895	+	5.82895i	−0.527728	+	0.527728i
$123$	−1.80150	+	0.285329i	−0.162435	+	0.0257272i
$124$	−5.52843	−	1.79630i	−0.496468	−	0.161312i
$125$	7.46664	+	8.32161i	0.667837	+	0.744308i
$126$	0.0354060	−	0.0257240i	0.00315422	−	0.00229167i
$127$	−17.3079	−	2.74131i	−1.53583	−	0.243252i	−0.669535	−	0.742781i	$-0.733506\pi$
$127$	−17.3079	−	2.74131i	−1.53583	−	0.243252i	−0.866297	+	0.499529i	$0.833506\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	−0.966214	+	2.97370i	−0.0850704	+	0.261820i
$130$	−0.179641	−	5.23122i	−0.0157556	−	0.458808i
$131$		−	3.65271i		−	0.319138i	−0.987187	−	0.159569i	$-0.948989\pi$
$131$		−	3.65271i		−	0.319138i	0.987187	−	0.159569i	$-0.0510105\pi$
$132$	−0.0494337	+	1.28790i	−0.00430265	+	0.112097i
$133$	0.0627280	+	0.0627280i	0.00543921	+	0.00543921i
$134$	4.20625	+	3.05602i	0.363364	+	0.264000i
$135$	−2.15060	+	4.60499i	−0.185094	+	0.396335i
$136$	1.21575	+	3.74168i	0.104249	+	0.320847i
$137$	2.63360	−	16.6279i	0.225004	−	1.42062i	−0.573784	−	0.819006i	$-0.694525\pi$
$137$	2.63360	−	16.6279i	0.225004	−	1.42062i	0.798788	−	0.601612i	$-0.205475\pi$
$138$	0.409085	−	2.58286i	0.0348237	−	0.219868i
$139$	6.84479	+	21.0661i	0.580567	+	1.78680i	0.616386	+	0.787444i	$0.288596\pi$
$139$	6.84479	+	21.0661i	0.580567	+	1.78680i	−0.0358190	+	0.999358i	$0.511404\pi$
$140$	0.0145345	−	0.0311223i	0.00122839	−	0.00263031i
$141$	−0.486890	−	0.353747i	−0.0410036	−	0.0297908i
$142$	−4.54541	−	4.54541i	−0.381443	−	0.381443i
$143$	−4.80095	+	6.10133i	−0.401476	+	0.510219i
$144$			2.84899i			0.237416i
$145$	−0.318123	−	9.26385i	−0.0264186	−	0.769321i
$146$	−1.42445	+	4.38402i	−0.117889	+	0.362824i
$147$	2.42365	+	1.23491i	0.199899	+	0.101854i
$148$	1.11428	+	0.176484i	0.0915932	+	0.0145069i
$149$	11.4310	−	8.30508i	0.936461	−	0.680379i	−0.0111054	−	0.999938i	$-0.503535\pi$
$149$	11.4310	−	8.30508i	0.936461	−	0.680379i	0.947566	+	0.319560i	$0.103535\pi$
$150$	0.133290	+	1.93843i	0.0108831	+	0.158272i
$151$	3.14883	+	1.02312i	0.256248	+	0.0832600i	0.434324	−	0.900757i	$-0.356987\pi$
$151$	3.14883	+	1.02312i	0.256248	+	0.0832600i	−0.178076	+	0.984017i	$0.556987\pi$
$152$	−5.70385	+	0.903401i	−0.462643	+	0.0732755i
$153$	7.92568	−	7.92568i	0.640753	−	0.640753i
$154$	−0.0462485	+	0.0213716i	−0.00372681	+	0.00172218i
$155$	7.99650	+	10.2473i	0.642295	+	0.823083i
$156$	0.534684	−	0.735929i	0.0428090	−	0.0589215i
$157$	5.84266	+	11.4669i	0.466295	+	0.915155i	0.997683	+	0.0680269i	$0.0216704\pi$
$157$	5.84266	+	11.4669i	0.466295	+	0.915155i	−0.531389	+	0.847128i	$0.678330\pi$
$158$	−2.15752	+	4.23437i	−0.171643	+	0.336868i
$159$	3.20584	+	4.41246i	0.254240	+	0.349931i
$160$	1.08293	+	1.95634i	0.0856134	+	0.154662i
$161$	0.0983131	−	0.0319439i	0.00774816	−	0.00251753i
$162$	6.82841	−	3.47925i	0.536490	−	0.273355i
$163$	−0.263165	−	1.66156i	−0.0206127	−	0.130143i	0.975236	−	0.221166i	$-0.0709864\pi$
$163$	−0.263165	−	1.66156i	−0.0206127	−	0.130143i	−0.995849	+	0.0910229i	$0.970986\pi$
$164$	4.69362			0.366510
$165$	1.70337	−	2.32469i	0.132607	−	0.180977i
$166$	13.3227			1.03404
$167$	2.54594	+	16.0744i	0.197011	+	1.24388i	0.865787	+	0.500413i	$0.166818\pi$
$167$	2.54594	+	16.0744i	0.197011	+	1.24388i	−0.668776	+	0.743464i	$0.733182\pi$
$168$	0.00531881	−	0.00271007i	0.000410355	−	0.000209086i
$169$	−7.15235	+	2.32394i	−0.550181	+	0.178764i
$170$	2.42975	−	8.45503i	0.186353	−	0.648471i
$171$	9.67069	+	13.3106i	0.739536	+	1.01788i
$172$	3.65286	−	7.16914i	0.278528	−	0.546642i
$173$	6.86850	+	13.4802i	0.522202	+	1.02488i	0.990003	+	0.141046i	$0.0450464\pi$
$173$	6.86850	+	13.4802i	0.522202	+	1.02488i	−0.467801	+	0.883834i	$0.654954\pi$
$174$	0.946861	−	1.30324i	0.0717813	−	0.0987985i
$175$	−0.0658819	+	0.0394819i	−0.00498021	+	0.00298455i
$176$	0.644096	−	3.25348i	0.0485505	−	0.245240i
$177$	0.539411	−	0.539411i	0.0405446	−	0.0405446i
$178$	9.36557	−	1.48336i	0.701979	−	0.111183i
$179$	−22.4795	−	7.30404i	−1.68020	−	0.545930i	−0.695249	−	0.718769i	$-0.744706\pi$
$179$	−22.4795	−	7.30404i	−1.68020	−	0.545930i	−0.984950	+	0.172839i	$0.944706\pi$
$180$	3.56542	−	5.27934i	0.265751	−	0.393499i
$181$	−15.4698	+	11.2395i	−1.14986	+	0.835423i	−0.988462	−	0.151466i	$-0.951601\pi$
$181$	−15.4698	+	11.2395i	−1.14986	+	0.835423i	−0.161399	+	0.986889i	$0.551601\pi$
$182$	0.0355158	+	0.00562515i	0.00263261	+	0.000416964i
$183$	2.85425	+	1.45431i	0.210992	+	0.107506i
$184$	−2.07950	+	6.40004i	−0.153303	+	0.471817i
$185$	−1.84396	−	1.72152i	−0.135571	−	0.126569i
$186$			2.25892i			0.165632i
$187$	−10.8428	+	7.25912i	−0.792902	+	0.530840i
$188$	1.09510	+	1.09510i	0.0798683	+	0.0798683i
$189$	−0.0282470	−	0.0205226i	−0.00205466	−	0.00149280i
$190$	11.7001	+	5.46413i	0.848818	+	0.396410i
$191$	−3.70271	−	11.3958i	−0.267919	−	0.824569i	−0.991007	−	0.133813i	$-0.957278\pi$
$191$	−3.70271	−	11.3958i	−0.267919	−	0.824569i	0.723088	−	0.690756i	$-0.242722\pi$
$192$	−0.0607907	+	0.383818i	−0.00438719	+	0.0276997i
$193$	2.50920	−	15.8424i	0.180616	−	1.14036i	−0.716179	−	0.697917i	$-0.754110\pi$
$193$	2.50920	−	15.8424i	0.180616	−	1.14036i	0.896795	−	0.442447i	$-0.145890\pi$
$194$	1.37542	+	4.23311i	0.0987494	+	0.303919i
$195$	−1.91179	+	0.694581i	−0.136906	+	0.0497400i
$196$	−5.66293	−	4.11436i	−0.404495	−	0.293883i
$197$	5.90309	+	5.90309i	0.420578	+	0.420578i	0.885403	−	0.464825i	$-0.153883\pi$
$197$	5.90309	+	5.90309i	0.420578	+	0.420578i	−0.464825	+	0.885403i	$0.653883\pi$
$198$	−9.09194	+	2.57308i	−0.646136	+	0.182861i
$199$			8.46646i			0.600171i	0.953912	+	0.300086i	$0.0970153\pi$
$199$			8.46646i			0.600171i	−0.953912	+	0.300086i	$0.902985\pi$
$200$	0.441555	−	4.98046i	0.0312226	−	0.352172i
$201$	0.624345	−	1.92154i	0.0440379	−	0.135535i
$202$	−15.4720	−	7.88340i	−1.08861	−	0.554674i
$203$	0.0628942	+	0.00996146i	0.00441431	+	0.000699158i
$204$	1.23687	−	0.898637i	0.0865981	−	0.0629172i
$205$	−8.69756	−	5.87392i	−0.607464	−	0.410252i
$206$	−0.324839	−	0.105546i	−0.0226326	−	0.00735377i
$207$	18.9360	−	2.99916i	1.31614	−	0.208456i
$208$	−1.65523	+	1.65523i	−0.114770	+	0.114770i
$209$	−8.03448	−	17.3867i	−0.555757	−	1.20266i
$210$	−0.0132476	−	0.00163440i	−0.000914173	−	0.000112784i
$211$	4.11272	−	5.66067i	0.283131	−	0.389697i	−0.643637	−	0.765331i	$-0.722575\pi$
$211$	4.11272	−	5.66067i	0.283131	−	0.389697i	0.926768	+	0.375635i	$0.122575\pi$
$212$	−6.37184	−	12.5054i	−0.437620	−	0.858877i
$213$	−1.13407	+	2.22574i	−0.0777053	+	0.152505i
$214$	−1.34798	−	1.85533i	−0.0921460	−	0.126828i
$215$	−15.7409	+	8.71340i	−1.07352	+	0.594249i
$216$	2.16168	−	0.702374i	0.147084	−	0.0477905i
$217$	−0.0795619	+	0.0405388i	−0.00540101	+	0.00275195i
$218$	−0.379891	−	2.39853i	−0.0257294	−	0.162449i
$219$	1.79131			0.121046
$220$	−5.26518	+	5.22283i	−0.354978	+	0.352123i
$221$	9.20946			0.619496
$222$	−0.0685822	−	0.433011i	−0.00460294	−	0.0290618i
$223$	−16.6612	+	8.48928i	−1.11571	+	0.568484i	−0.911854	−	0.410516i	$-0.865349\pi$
$223$	−16.6612	+	8.48928i	−1.11571	+	0.568484i	−0.203860	+	0.979000i	$0.565349\pi$
$224$	−0.0146095	+	0.00474691i	−0.000976137	+	0.000317166i
$225$	−13.2139	+	5.32093i	−0.880924	+	0.354729i
$226$	6.40132	+	8.81066i	0.425809	+	0.586076i
$227$	−4.59950	+	9.02703i	−0.305280	+	0.599145i	−0.991776	−	0.127989i	$-0.959148\pi$
$227$	−4.59950	+	9.02703i	−0.305280	+	0.599145i	0.686496	+	0.727134i	$0.259148\pi$
$228$	1.01883	+	1.99956i	0.0674734	+	0.132424i
$229$	6.38012	−	8.78149i	0.421610	−	0.580297i	−0.544392	−	0.838831i	$-0.683239\pi$
$229$	6.38012	−	8.78149i	0.421610	−	0.580297i	0.966002	+	0.258534i	$0.0832395\pi$
$230$	11.8629	−	9.25723i	0.782215	−	0.610404i
$231$	0.0134523	+	0.0145262i	0.000885098	+	0.000955755i
$232$	−2.93121	+	2.93121i	−0.192444	+	0.192444i
$233$	−4.69333	+	0.743350i	−0.307470	+	0.0486985i	−0.308263	−	0.951301i	$-0.599748\pi$
$233$	−4.69333	+	0.743350i	−0.307470	+	0.0486985i	0.000792791		1.00000i	$0.499748\pi$
$234$	6.34265	+	2.06085i	0.414632	+	0.134722i
$235$	−0.658802	−	3.39977i	−0.0429755	−	0.221776i
$236$	−1.58813	+	1.15385i	−0.103379	+	0.0751091i
$237$	1.82403	+	0.288898i	0.118484	+	0.0187660i
$238$	0.0538481	+	0.0274370i	0.00349045	+	0.00177847i
$239$	4.17166	−	12.8391i	0.269842	−	0.830490i	−0.720696	−	0.693252i	$-0.756177\pi$
$239$	4.17166	−	12.8391i	0.269842	−	0.830490i	0.990538	−	0.137238i	$-0.0438225\pi$
$240$	0.592984	−	0.635159i	0.0382770	−	0.0409993i
$241$		−	21.5441i		−	1.38778i	−0.720081	−	0.693890i	$-0.755895\pi$
$241$		−	21.5441i		−	1.38778i	0.720081	−	0.693890i	$-0.244105\pi$
$242$	10.9645	−	0.882909i	0.704825	−	0.0567555i
$243$	−6.92746	−	6.92746i	−0.444397	−	0.444397i
$244$	−6.66904	−	4.84534i	−0.426941	−	0.310191i
$245$	5.34475	+	14.7111i	0.341464	+	0.939859i
$246$	−0.563632	−	1.73468i	−0.0359359	−	0.110599i
$247$	−2.11473	+	13.3519i	−0.134557	+	0.849558i
$248$	0.909344	−	5.74137i	0.0577434	−	0.364577i
$249$	−1.59985	−	4.92385i	−0.101387	−	0.312036i
$250$	−7.05112	+	8.67650i	−0.445952	+	0.548750i
$251$	−15.8467	−	11.5133i	−1.00023	−	0.726713i	−0.0380961	−	0.999274i	$-0.512129\pi$
$251$	−15.8467	−	11.5133i	−1.00023	−	0.726713i	−0.962138	+	0.272561i	$0.912129\pi$
$252$	0.0309460	+	0.0309460i	0.00194941	+	0.00194941i
$253$	−22.3025	−	0.856041i	−1.40215	−	0.0538188i
$254$		−	17.5237i		−	1.09953i
$255$	−3.41661	+	0.117327i	−0.213956	+	0.00734730i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.5999	+	8.96760i	1.09785	+	0.559384i	0.906529	−	0.422143i	$-0.138722\pi$
$257$	17.5999	+	8.96760i	1.09785	+	0.559384i	0.191323	+	0.981527i	$0.438722\pi$
$258$	−3.08824	−	0.489129i	−0.192265	−	0.0304518i
$259$	0.0140204	−	0.0101864i	0.000871185	−	0.000632953i
$260$	5.13871	−	0.995772i	0.318689	−	0.0617551i
$261$	11.2321	+	3.64952i	0.695247	+	0.225899i
$262$	3.60774	−	0.571409i	0.222887	−	0.0353018i
$263$	20.0880	−	20.0880i	1.23868	−	1.23868i	0.278140	−	0.960541i	$-0.410282\pi$
$263$	20.0880	−	20.0880i	1.23868	−	1.23868i	0.960541	−	0.278140i	$-0.0897178\pi$
$264$	−1.27978	+	0.152647i	−0.0787647	+	0.00939475i
$265$	−3.84276	+	31.1475i	−0.236059	+	1.91337i
$266$	−0.0521429	+	0.0717686i	−0.00319709	+	0.00440041i
$267$	−1.67289	−	3.28322i	−0.102379	−	0.200930i
$268$	−2.36039	+	4.63253i	−0.144184	+	0.282977i
$269$	−5.50591	−	7.57823i	−0.335701	−	0.462053i	0.607479	−	0.794336i	$-0.292181\pi$
$269$	−5.50591	−	7.57823i	−0.335701	−	0.462053i	−0.943180	+	0.332283i	$0.892181\pi$
$270$	−4.88473	−	1.40374i	−0.297275	−	0.0854288i
$271$	5.85356	−	1.90194i	0.355578	−	0.115534i	−0.125780	−	0.992058i	$-0.540143\pi$
$271$	5.85356	−	1.90194i	0.355578	−	0.115534i	0.481359	+	0.876524i	$0.340143\pi$
$272$	−3.50543	+	1.78611i	−0.212548	+	0.108299i
$273$	−0.00218595	−	0.0138015i	−0.000132299	−	0.000835306i
$274$	16.8352			1.01705
$275$	16.2929	−	3.08901i	0.982498	−	0.186274i
$276$	2.61506			0.157408
$277$	−4.66256	−	29.4382i	−0.280146	−	1.76877i	−0.579834	−	0.814734i	$-0.696883\pi$
$277$	−4.66256	−	29.4382i	−0.280146	−	1.76877i	0.299688	−	0.954037i	$-0.403117\pi$
$278$	−19.7360	+	10.0560i	−1.18368	+	0.603117i
$279$	−15.7504	+	5.11763i	−0.942954	+	0.306384i
$280$	0.0330128	+	0.00948700i	0.00197289	+	0.000566957i
$281$	3.35941	+	4.62383i	0.200406	+	0.275835i	0.897377	−	0.441264i	$-0.145470\pi$
$281$	3.35941	+	4.62383i	0.200406	+	0.275835i	−0.696972	+	0.717099i	$0.745470\pi$
$282$	0.273225	−	0.536234i	0.0162703	−	0.0319323i
$283$	−1.97387	−	3.87395i	−0.117335	−	0.230282i	0.824868	−	0.565325i	$-0.191249\pi$
$283$	−1.97387	−	3.87395i	−0.117335	−	0.230282i	−0.942203	+	0.335043i	$0.891249\pi$
$284$	3.77839	−	5.20051i	0.224206	−	0.308594i
$285$	0.614439	−	4.98033i	0.0363962	−	0.295009i
$286$	−6.77725	−	3.78738i	−0.400747	−	0.223953i
$287$	0.0509826	−	0.0509826i	0.00300941	−	0.00300941i
$288$	−2.81391	+	0.445680i	−0.165811	+	0.0262619i
$289$	−1.44728	−	0.470250i	−0.0851341	−	0.0276618i
$290$	9.10003	−	1.76339i	0.534372	−	0.103550i
$291$	1.39932	−	1.01666i	0.0820293	−	0.0595978i
$292$	−4.55288	−	0.721105i	−0.266437	−	0.0421995i
$293$	12.1120	+	6.17139i	0.707593	+	0.360537i	0.770463	−	0.637485i	$-0.220025\pi$
$293$	12.1120	+	6.17139i	0.707593	+	0.360537i	−0.0628696	+	0.998022i	$0.520025\pi$
$294$	−0.840564	+	2.58699i	−0.0490227	+	0.150876i
$295$	4.38691	−	0.150647i	0.255416	−	0.00877103i
$296$			1.12817i			0.0655735i
$297$	4.19381	+	6.26420i	0.243350	+	0.363486i
$298$	9.99102	+	9.99102i	0.578765	+	0.578765i
$299$	12.7441	+	9.25910i	0.737008	+	0.535468i
$300$	−1.89372	+	0.434886i	−0.109334	+	0.0251082i
$301$	−0.0381941	−	0.117549i	−0.00220147	−	0.00677544i
$302$	−0.517934	+	3.27011i	−0.0298038	+	0.188174i
$303$	−1.05561	+	6.66487i	−0.0606433	+	0.382887i
$304$	−1.78456	−	5.49230i	−0.102351	−	0.315005i
$305$	6.29433	+	17.3248i	0.360412	+	0.992014i
$306$	9.06795	+	6.58825i	0.518380	+	0.376625i
$307$	16.8816	+	16.8816i	0.963484	+	0.963484i	0.999356	−	0.0358726i	$-0.0114211\pi$
$307$	16.8816	+	16.8816i	0.963484	+	0.963484i	−0.0358726	+	0.999356i	$0.511421\pi$
$308$	−0.0283434	−	0.0423358i	−0.00161501	−	0.00241231i
$309$			0.132729i			0.00755070i
$310$	−8.87021	+	9.50108i	−0.503794	+	0.539625i
$311$	8.96103	−	27.5792i	0.508133	−	1.56387i	−0.287305	−	0.957839i	$-0.592759\pi$
$311$	8.96103	−	27.5792i	0.508133	−	1.56387i	0.795439	−	0.606034i	$-0.207241\pi$
$312$	0.810512	+	0.412976i	0.0458862	+	0.0233802i
$313$	17.0901	+	2.70681i	0.965990	+	0.152998i	0.619449	−	0.785037i	$-0.287356\pi$
$313$	17.0901	+	2.70681i	0.965990	+	0.152998i	0.346541	+	0.938035i	$0.387356\pi$
$314$	−10.4117	+	7.56454i	−0.587566	+	0.426891i
$315$	−0.0186168	−	0.0960726i	−0.00104894	−	0.00541308i
$316$	−4.51974	−	1.46855i	−0.254255	−	0.0826126i
$317$	−20.4927	+	3.24572i	−1.15098	+	0.182298i	−0.702628	−	0.711558i	$-0.747990\pi$
$317$	−20.4927	+	3.24572i	−1.15098	+	0.182298i	−0.448355	+	0.893855i	$0.647990\pi$
$318$	−3.85663	+	3.85663i	−0.216269	+	0.216269i
$319$	−12.0017	−	6.70700i	−0.671965	−	0.375520i
$320$	−1.76284	+	1.37564i	−0.0985460	+	0.0769006i
$321$	−0.523827	+	0.720986i	−0.0292372	+	0.0402415i
$322$	0.0469301	+	0.0921056i	0.00261531	+	0.00513284i
$323$	−10.3147	+	20.2437i	−0.573924	+	1.12639i
$324$	4.50461	+	6.20006i	0.250256	+	0.344448i
$325$	−10.7685	−	4.58571i	−0.597329	−	0.254369i
$326$	1.59994	−	0.519851i	0.0886122	−	0.0287919i
$327$	−0.840837	+	0.428428i	−0.0464984	+	0.0236921i
$328$	0.734244	+	4.63584i	0.0405419	+	0.255971i
$329$	0.0237901			0.00131159
$330$	2.56253	+	1.31873i	0.141063	+	0.0725940i
$331$	27.7235			1.52382			0.761912	−	0.647681i	$-0.224261\pi$
$331$	27.7235			1.52382			0.761912	+	0.647681i	$0.224261\pi$
$332$	2.08413	+	13.1587i	0.114382	+	0.722178i
$333$	2.86382	−	1.45919i	0.156936	−	0.0799631i
$334$	−15.4782	+	5.02919i	−0.846932	+	0.275185i
$335$	10.1714	−	5.63039i	0.555723	−	0.307621i
$336$	0.00350875	+	0.00482938i	0.000191418	+	0.000263464i
$337$	3.19123	−	6.26314i	0.173837	−	0.341175i	−0.787606	−	0.616180i	$-0.788680\pi$
$337$	3.19123	−	6.26314i	0.173837	−	0.341175i	0.961443	+	0.275005i	$0.0886795\pi$
$338$	−3.41420	−	6.70075i	−0.185708	−	0.364473i
$339$	2.48756	−	3.42384i	0.135106	−	0.185957i
$340$	8.73103	+	1.07718i	0.473507	+	0.0584180i
$341$	19.1436	−	2.28338i	1.03669	−	0.123652i
$342$	−11.6339	+	11.6339i	−0.629087	+	0.629087i
$343$	−0.212407	+	0.0336420i	−0.0114689	+	0.00181650i
$344$	7.65230	+	2.48638i	0.412585	+	0.134057i
$345$	−4.84586	−	3.27266i	−0.260892	−	0.176194i
$346$	−12.2398	+	8.89270i	−0.658013	+	0.478075i
$347$	−21.4415	−	3.39601i	−1.15104	−	0.182307i	−0.448388	−	0.893839i	$-0.648002\pi$
$347$	−21.4415	−	3.39601i	−1.15104	−	0.182307i	−0.702654	+	0.711532i	$0.748002\pi$
$348$	1.43532	+	0.731331i	0.0769411	+	0.0392035i
$349$	−3.67193	+	11.3010i	−0.196554	+	0.604930i	0.803401	+	0.595438i	$0.203021\pi$
$349$	−3.67193	+	11.3010i	−0.196554	+	0.604930i	−0.999955	+	0.00949216i	$0.996979\pi$
$350$	−0.0493021	−	0.0588945i	−0.00263531	−	0.00314804i
$351$		−	5.32058i		−	0.283992i
$352$	3.31418	+	0.127209i	0.176647	+	0.00678026i
$353$	0.766521	+	0.766521i	0.0407978	+	0.0407978i	0.727211	−	0.686414i	$-0.240816\pi$
$353$	0.766521	+	0.766521i	0.0407978	+	0.0407978i	−0.686414	+	0.727211i	$0.740816\pi$
$354$	0.617152	+	0.448387i	0.0328013	+	0.0238315i
$355$	−13.5099	+	4.90832i	−0.717029	+	0.260506i
$356$	2.93020	+	9.01822i	0.155300	+	0.477965i
$357$	0.00367389	−	0.0231961i	0.000194443	−	0.00122767i
$358$	3.69755	−	23.3454i	0.195421	−	1.23384i
$359$	2.56417	+	7.89171i	0.135332	+	0.416508i	0.995641	−	0.0932633i	$-0.0297298\pi$
$359$	2.56417	+	7.89171i	0.135332	+	0.416508i	−0.860310	+	0.509772i	$0.829730\pi$
$360$	5.77210	+	2.69565i	0.304216	+	0.142073i
$361$	−11.6094	−	8.43474i	−0.611022	−	0.443934i
$362$	−13.5211	−	13.5211i	−0.710653	−	0.710653i
$363$	−1.64298	−	3.94627i	−0.0862339	−	0.207125i
$364$			0.0359585i			0.00188474i
$365$	7.53431	+	7.03403i	0.394364	+	0.368178i
$366$	−0.989903	+	3.04661i	−0.0517431	+	0.159249i
$367$	13.4231	+	6.83943i	0.700683	+	0.357016i	0.767765	−	0.640732i	$-0.221369\pi$
$367$	13.4231	+	6.83943i	0.700683	+	0.357016i	−0.0670822	+	0.997747i	$0.521369\pi$
$368$	−6.64655	−	1.05271i	−0.346476	−	0.0548763i
$369$	10.8182	−	7.85991i	0.563175	−	0.409171i
$370$	1.41187	−	2.09056i	0.0733995	−	0.108683i
$371$	−0.205047	−	0.0666237i	−0.0106455	−	0.00345893i
$372$	−2.23111	+	0.353373i	−0.115678	+	0.0183215i
$373$	−5.33739	+	5.33739i	−0.276360	+	0.276360i	−0.831654	−	0.555294i	$-0.812606\pi$
$373$	−5.33739	+	5.33739i	−0.276360	+	0.276360i	0.555294	+	0.831654i	$0.312606\pi$
$374$	−8.86593	−	9.57371i	−0.458447	−	0.495045i
$375$	4.05341	+	1.56406i	0.209317	+	0.0807675i
$376$	−0.910306	+	1.25293i	−0.0469454	+	0.0646149i
$377$	4.40537	+	8.64603i	0.226888	+	0.445293i
$378$	0.0158512	−	0.0311096i	0.000815296	−	0.00160011i
$379$	5.86042	+	8.06617i	0.301029	+	0.414331i	0.932557	−	0.361022i	$-0.117572\pi$
$379$	5.86042	+	8.06617i	0.301029	+	0.414331i	−0.631528	+	0.775353i	$0.717572\pi$
$380$	−3.56655	+	12.4109i	−0.182960	+	0.636665i
$381$	−6.47645	+	2.10433i	−0.331799	+	0.107808i
$382$	10.6762	−	5.43982i	0.546244	−	0.278325i
$383$	−3.72711	−	23.5321i	−0.190447	−	1.20243i	−0.878848	−	0.477103i	$-0.841687\pi$
$383$	−3.72711	−	23.5321i	−0.190447	−	1.20243i	0.688401	−	0.725330i	$-0.258313\pi$
$384$	−0.388602			−0.0198308
$385$	−0.000459977		0.113922i	−2.34426e−5		0.00580598i
$386$	16.0399			0.816410
$387$	−3.58599	−	22.6411i	−0.182286	−	1.15091i
$388$	−3.96583	+	2.02069i	−0.201334	+	0.102585i
$389$	−4.97947	+	1.61793i	−0.252469	+	0.0820322i	−0.432517	−	0.901626i	$-0.642375\pi$
$389$	−4.97947	+	1.61793i	−0.252469	+	0.0820322i	0.180048	+	0.983658i	$0.442375\pi$
$390$	−0.985100	−	1.77960i	−0.0498825	−	0.0901135i
$391$	15.5617	+	21.4188i	0.786987	+	1.08319i
$392$	3.17783	−	6.23684i	0.160504	−	0.315008i
$393$	−0.644416	−	1.26474i	−0.0325065	−	0.0637976i
$394$	−4.90697	+	6.75386i	−0.247209	+	0.340255i
$395$	6.53750	+	8.37763i	0.328938	+	0.421524i
$396$	−3.96370	−	8.57748i	−0.199183	−	0.431035i
$397$	1.68624	−	1.68624i	0.0846300	−	0.0846300i	−0.663525	−	0.748155i	$-0.730940\pi$
$397$	1.68624	−	1.68624i	0.0846300	−	0.0846300i	0.748155	+	0.663525i	$0.230940\pi$
$398$	−8.36222	+	1.32445i	−0.419160	+	0.0663885i
$399$	0.0327860	+	0.0106528i	0.00164135	+	0.000533307i
$400$	4.98822	−	0.342998i	0.249411	−	0.0171499i
$401$	−12.7078	+	9.23274i	−0.634596	+	0.461061i	−0.857989	−	0.513667i	$-0.828287\pi$
$401$	−12.7078	+	9.23274i	−0.634596	+	0.461061i	0.223393	+	0.974728i	$0.428287\pi$
$402$	1.99555	+	0.316064i	0.0995289	+	0.0157638i
$403$	−12.1241	−	6.17755i	−0.603945	−	0.307725i
$404$	5.36598	−	16.5148i	0.266968	−	0.821642i
$405$	−0.588127	−	17.1265i	−0.0292242	−	0.851021i
$406$			0.0636782i			0.00316030i
$407$	−3.60031	+	1.01891i	−0.178461	+	0.0505056i
$408$	1.08106	+	1.08106i	0.0535206	+	0.0535206i
$409$	1.39836	+	1.01597i	0.0691444	+	0.0502363i	0.621820	−	0.783160i	$-0.286393\pi$
$409$	1.39836	+	1.01597i	0.0691444	+	0.0502363i	−0.552676	+	0.833396i	$0.686393\pi$
$410$	4.44100	−	9.50936i	0.219326	−	0.469634i
$411$	−2.02165	−	6.22199i	−0.0997205	−	0.306908i
$412$	0.0534311	−	0.337350i	0.00263236	−	0.0166201i
$413$	−0.00471727	+	0.0297837i	−0.000232122	+	0.00146556i
$414$	5.92447	+	18.2336i	0.291172	+	0.896135i
$415$	12.6057	−	26.9921i	0.618788	−	1.32499i
$416$	−1.89379	−	1.37592i	−0.0928506	−	0.0674599i
$417$	6.08650	+	6.08650i	0.298057	+	0.298057i
$418$	15.9158	−	10.6554i	0.778466	−	0.521175i
$419$		−	16.7994i		−	0.820703i	−0.911927	−	0.410351i	$-0.865406\pi$
$419$		−	16.7994i		−	0.820703i	0.911927	−	0.410351i	$-0.134594\pi$
$420$	−0.000458106	−	0.0133402i	−2.23533e−5	−	0.000650935i
$421$	3.47207	−	10.6859i	0.169219	−	0.520801i	−0.830104	−	0.557609i	$-0.811719\pi$
$421$	3.47207	−	10.6859i	0.169219	−	0.520801i	0.999322	+	0.0368077i	$0.0117189\pi$
$422$	6.23435	+	3.17656i	0.303483	+	0.154632i
$423$	4.35792	+	0.690227i	0.211889	+	0.0335600i
$424$	11.3547	−	8.24968i	0.551433	−	0.400640i
$425$	−14.8311	−	12.9227i	−0.719412	−	0.626842i
$426$	−2.37575	−	0.771926i	−0.115105	−	0.0374000i
$427$	−0.125070	+	0.0198092i	−0.00605257	+	0.000958633i
$428$	1.62162	−	1.62162i	0.0783840	−	0.0783840i
$429$	−0.585907	+	2.95956i	−0.0282879	+	0.142889i
$430$	−11.0685	−	14.1840i	−0.533772	−	0.684015i
$431$	−22.5280	+	31.0071i	−1.08513	+	1.49356i	−0.231392	+	0.972861i	$0.574328\pi$
$431$	−22.5280	+	31.0071i	−1.08513	+	1.49356i	−0.853741	+	0.520697i	$0.825672\pi$
$432$	1.03189	+	2.02519i	0.0496467	+	0.0974372i
$433$	8.91179	−	17.4904i	0.428273	−	0.840533i	−0.571528	−	0.820583i	$-0.693649\pi$
$433$	8.91179	−	17.4904i	0.428273	−	0.840533i	0.999801	−	0.0199507i	$-0.00635091\pi$
$434$	−0.0524859	−	0.0722407i	−0.00251940	−	0.00346766i
$435$	−1.74449	−	3.15145i	−0.0836420	−	0.151101i
$436$	2.30958	−	0.750427i	0.110609	−	0.0359389i
$437$	−34.6263	+	17.6430i	−1.65640	+	0.843977i
$438$	0.280223	+	1.76926i	0.0133896	+	0.0845384i
$439$	1.05214			0.0502158			0.0251079	−	0.999685i	$-0.492007\pi$
$439$	1.05214			0.0502158			0.0251079	+	0.999685i	$0.492007\pi$
$440$	−5.98218	−	4.38332i	−0.285189	−	0.208967i
$441$	−19.9422			−0.949631
$442$	1.44068	+	9.09608i	0.0685260	+	0.432656i
$443$	−0.280755	+	0.143052i	−0.0133391	+	0.00679659i	−0.460647	−	0.887583i	$-0.652383\pi$
$443$	−0.280755	+	0.143052i	−0.0133391	+	0.00679659i	0.447308	+	0.894380i	$0.352383\pi$
$444$	0.416951	−	0.135476i	0.0197876	−	0.00642939i
$445$	5.85619	−	20.3783i	0.277610	−	0.966026i
$446$	−10.9911	−	15.1280i	−0.520446	−	0.716332i
$447$	2.49274	−	4.89228i	0.117903	−	0.231397i
$448$	−0.00697389	−	0.0136870i	−0.000329485	−	0.000646652i
$449$	−19.7505	+	27.1842i	−0.932084	+	1.28290i	0.0269576	+	0.999637i	$0.491418\pi$
$449$	−19.7505	+	27.1842i	−0.932084	+	1.28290i	−0.959041	+	0.283266i	$0.908582\pi$
$450$	−7.32252	−	12.2188i	−0.345187	−	0.576000i
$451$	−14.1311	+	6.53007i	−0.665410	+	0.307489i
$452$	−7.70080	+	7.70080i	−0.362215	+	0.362215i
$453$	1.27077	−	0.201270i	0.0597060	−	0.00945651i
$454$	−9.63541	−	3.13074i	−0.452212	−	0.146933i
$455$	0.0450010	−	0.0666333i	0.00210968	−	0.00312382i
$456$	−1.81556	+	1.31908i	−0.0850214	+	0.0617717i
$457$	29.5629	+	4.68231i	1.38290	+	0.219029i	0.803154	−	0.595771i	$-0.203153\pi$
$457$	29.5629	+	4.68231i	1.38290	+	0.219029i	0.579742	+	0.814800i	$0.303153\pi$
$458$	9.67144	+	4.92785i	0.451917	+	0.230263i
$459$	2.76331	−	8.50458i	0.128980	−	0.396960i
$460$	10.9990	+	10.2687i	0.512832	+	0.478780i
$461$			27.6150i			1.28616i	0.765800	+	0.643079i	$0.222343\pi$
$461$			27.6150i			1.28616i	−0.765800	+	0.643079i	$0.777657\pi$
$462$	−0.0122430	+	0.0155591i	−0.000569595	+	0.000723875i
$463$	−26.6620	−	26.6620i	−1.23909	−	1.23909i	−0.960373	−	0.278717i	$-0.910091\pi$
$463$	−26.6620	−	26.6620i	−1.23909	−	1.23909i	−0.278717	−	0.960373i	$-0.589909\pi$
$464$	−3.35367	−	2.43658i	−0.155690	−	0.113115i
$465$	4.57661	+	2.13734i	0.212235	+	0.0991168i
$466$	−1.46840	−	4.51926i	−0.0680221	−	0.209351i
$467$	4.66728	−	29.4680i	0.215976	−	1.36362i	−0.606620	−	0.794992i	$-0.707475\pi$
$467$	4.66728	−	29.4680i	0.215976	−	1.36362i	0.822596	−	0.568626i	$-0.192525\pi$
$468$	−1.04327	+	6.58695i	−0.0482252	+	0.304482i
$469$	0.0246802	+	0.0759577i	0.00113962	+	0.00350740i
$470$	3.25485	−	1.18253i	0.150135	−	0.0545461i
$471$	4.04600	+	2.93959i	0.186430	+	0.135449i
$472$	−1.38808	−	1.38808i	−0.0638916	−	0.0638916i
$473$	−1.02354	+	26.6663i	−0.0470623	+	1.22612i
$474$			1.84677i			0.0848249i
$475$	22.1408	−	18.5347i	1.01589	−	0.850429i
$476$	−0.0186755	+	0.0574772i	−0.000855989	+	0.00263446i
$477$	−35.6279	−	18.1533i	−1.63129	−	0.831183i
$478$	13.3336	+	2.11183i	0.609864	+	0.0965929i
$479$	−5.27658	+	3.83366i	−0.241093	+	0.175165i	−0.701770	−	0.712403i	$-0.747607\pi$
$479$	−5.27658	+	3.83366i	−0.241093	+	0.175165i	0.460677	+	0.887568i	$0.347607\pi$
$480$	0.720102	+	0.486323i	0.0328680	+	0.0221975i
$481$	2.51162	+	0.816075i	0.114520	+	0.0372098i
$482$	21.2789	−	3.37025i	0.969227	−	0.153510i
$483$	0.0284050	−	0.0284050i	0.00129247	−	0.00129247i
$484$	2.58727	+	10.6914i	0.117603	+	0.485973i
$485$	9.87774	+	1.21865i	0.448525	+	0.0553360i
$486$	5.75848	−	7.92587i	0.261210	−	0.359525i
$487$	3.88945	+	7.63347i	0.176248	+	0.345906i	0.962183	−	0.272403i	$-0.0878183\pi$
$487$	3.88945	+	7.63347i	0.176248	+	0.345906i	−0.785936	+	0.618308i	$0.787818\pi$
$488$	3.74242	−	7.34491i	0.169411	−	0.332488i
$489$	−0.384255	−	0.528882i	−0.0173766	−	0.0239169i
$490$	−13.6939	+	7.58028i	−0.618627	+	0.342442i
$491$	−24.6223	+	8.00027i	−1.11119	+	0.361047i	−0.806399	−	0.591372i	$-0.798586\pi$
$491$	−24.6223	+	8.00027i	−1.11119	+	0.361047i	−0.304790	+	0.952419i	$0.598586\pi$
$492$	1.62515	−	0.828057i	0.0732675	−	0.0373317i
$493$	2.55126	+	16.1081i	0.114903	+	0.725470i
$494$	−13.5183			−0.608217
$495$	−3.38948	+	20.8550i	−0.152346	+	0.937363i
$496$	5.81294			0.261009
$497$	−0.0154472	−	0.0975297i	−0.000692901	−	0.00437480i
$498$	4.61295	−	2.35042i	0.206711	−	0.105325i
$499$	15.9071	−	5.16853i	0.712099	−	0.231375i	0.0695049	−	0.997582i	$-0.477858\pi$
$499$	15.9071	−	5.16853i	0.712099	−	0.231375i	0.642594	+	0.766207i	$0.277858\pi$
$500$	−9.67272	−	5.60700i	−0.432577	−	0.250753i
$501$	3.71740	+	5.11656i	0.166081	+	0.228591i
$502$	8.89258	−	17.4527i	0.396895	−	0.778951i
$503$	6.24553	+	12.2575i	0.278475	+	0.546537i	0.987304	−	0.158843i	$-0.0507764\pi$
$503$	6.24553	+	12.2575i	0.278475	+	0.546537i	−0.708829	+	0.705380i	$0.750776\pi$
$504$	−0.0257240	+	0.0354060i	−0.00114584	+	0.00157711i
$505$	−30.6112	+	23.8875i	−1.36218	+	1.06298i
$506$	−2.64338	−	22.1618i	−0.117512	−	0.985213i
$507$	−2.06649	+	2.06649i	−0.0917758	+	0.0917758i
$508$	17.3079	−	2.74131i	0.767916	−	0.121626i
$509$	32.6519	+	10.6092i	1.44727	+	0.470246i	0.924155	−	0.382017i	$-0.124771\pi$
$509$	32.6519	+	10.6092i	1.44727	+	0.470246i	0.523113	+	0.852263i	$0.324771\pi$
$510$	−0.650357	−	3.35619i	−0.0287983	−	0.148614i
$511$	−0.0572865	+	0.0416211i	−0.00253421	+	0.00184121i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	11.6954	+	5.95910i	0.516364	+	0.263101i
$514$	−6.10397	+	18.7861i	−0.269234	+	0.828618i
$515$	−0.521194	+	0.558263i	−0.0229666	+	0.0246000i
$516$		−	3.12673i		−	0.137647i
$517$	−4.82060	−	1.77346i	−0.212010	−	0.0779965i
$518$	0.0122543	+	0.0122543i	0.000538422	+	0.000538422i
$519$	4.75639	+	3.45572i	0.208782	+	0.151689i
$520$	1.78738	+	4.91967i	0.0783819	+	0.215742i
$521$	1.49330	+	4.59591i	0.0654227	+	0.201351i	0.978424	−	0.206606i	$-0.0662417\pi$
$521$	1.49330	+	4.59591i	0.0654227	+	0.201351i	−0.913002	+	0.407956i	$0.866242\pi$
$522$	−1.84750	+	11.6647i	−0.0808631	+	0.510549i
$523$	−2.62342	+	16.5636i	−0.114714	+	0.724276i	0.861547	+	0.507678i	$0.169496\pi$
$523$	−2.62342	+	16.5636i	−0.114714	+	0.724276i	−0.976261	+	0.216598i	$0.930504\pi$
$524$	1.12875	+	3.47393i	0.0493096	+	0.151759i
$525$	−0.0158459	+	0.0252935i	−0.000691574	+	0.00110390i
$526$	22.9832	+	16.6982i	1.00211	+	0.728078i
$527$	−16.1712	−	16.1712i	−0.704427	−	0.704427i
$528$	−0.350968	−	1.24014i	−0.0152739	−	0.0539702i
$529$			22.2849i			0.968907i
$530$	−31.3651	+	1.07709i	−1.36241	+	0.0467856i
$531$	−1.72823	+	5.31896i	−0.0749990	+	0.230823i
$532$	−0.0790419	−	0.0402739i	−0.00342690	−	0.00174609i
$533$	10.8518	+	1.71876i	0.470044	+	0.0744476i
$534$	2.98110	−	2.16590i	0.129005	−	0.0937276i
$535$	−5.03437	+	0.975553i	−0.217655	+	0.0421768i
$536$	−4.94474	−	1.60664i	−0.213580	−	0.0693964i
$537$	−9.07206	+	1.43687i	−0.391488	+	0.0620057i
$538$	6.62361	−	6.62361i	0.285564	−	0.285564i
$539$	22.7736	+	4.50852i	0.980928	+	0.194196i
$540$	0.622316	−	5.04418i	0.0267802	−	0.217067i
$541$	6.42200	−	8.83913i	0.276103	−	0.380024i	−0.648335	−	0.761355i	$-0.724534\pi$
$541$	6.42200	−	8.83913i	0.276103	−	0.380024i	0.924438	+	0.381331i	$0.124534\pi$
$542$	2.79422	+	5.48397i	0.120022	+	0.235556i
$543$	−3.37349	+	6.62084i	−0.144770	+	0.284127i
$544$	−2.31249	−	3.18287i	−0.0991471	−	0.136464i
$545$	−5.21892	−	1.49978i	−0.223554	−	0.0642433i
$546$	0.0132896	−	0.00431807i	0.000568744	−	0.000184796i
$547$	31.3306	−	15.9637i	1.33960	−	0.682559i	0.370407	−	0.928870i	$-0.379218\pi$
$547$	31.3306	−	15.9637i	1.33960	−	0.682559i	0.969191	+	0.246310i	$0.0792182\pi$
$548$	2.63360	+	16.6279i	0.112502	+	0.710309i
$549$	−23.4853			−1.00233
$550$	5.59975	+	15.6091i	0.238774	+	0.665573i
$551$	−23.9392			−1.01985
$552$	0.409085	+	2.58286i	0.0174118	+	0.109934i
$553$	−0.0650454	+	0.0331423i	−0.00276601	+	0.00140935i
$554$	28.3464	−	9.21031i	1.20432	−	0.391308i
$555$	−0.942179	−	0.270757i	−0.0399933	−	0.0114930i
$556$	−13.0196	−	17.9199i	−0.552152	−	0.759972i
$557$	−1.38133	+	2.71100i	−0.0585286	+	0.114869i	−0.918418	−	0.395612i	$-0.870533\pi$
$557$	−1.38133	+	2.71100i	−0.0585286	+	0.114869i	0.859889	+	0.510481i	$0.170533\pi$
$558$	−7.51853	−	14.7560i	−0.318285	−	0.624669i
$559$	11.0708	−	15.2376i	0.468244	−	0.644483i
$560$	−0.00420585	+	0.0340905i	−0.000177730	+	0.00144059i
$561$	−2.47361	+	4.42635i	−0.104436	+	0.186881i
$562$	−4.04138	+	4.04138i	−0.170475	+	0.170475i
$563$	36.3351	−	5.75492i	1.53134	−	0.242541i	0.666852	−	0.745190i	$-0.267641\pi$
$563$	36.3351	−	5.75492i	1.53134	−	0.242541i	0.864490	+	0.502649i	$0.167641\pi$
$564$	0.572374	+	0.185976i	0.0241013	+	0.00783099i
$565$	23.9073	−	4.63273i	1.00579	−	0.194900i
$566$	3.51747	−	2.55559i	0.147850	−	0.107419i
$567$	0.116275	+	0.0184162i	0.00488310	+	0.000773407i
$568$	5.72756	+	2.91834i	0.240323	+	0.122451i
$569$	−5.11991	+	15.7575i	−0.214638	+	0.660587i	0.784541	+	0.620077i	$0.212898\pi$
$569$	−5.11991	+	15.7575i	−0.214638	+	0.660587i	−0.999179	+	0.0405107i	$0.987102\pi$
$570$	5.01513	−	0.172221i	0.210061	−	0.00721353i
$571$			10.4437i			0.437057i	0.975831	+	0.218529i	$0.0701257\pi$
$571$			10.4437i			0.437057i	−0.975831	+	0.218529i	$0.929874\pi$
$572$	2.68056	−	7.28629i	0.112080	−	0.304655i
$573$	−3.29251	−	3.29251i	−0.137547	−	0.137547i
$574$	0.0583303	+	0.0423795i	0.00243466	+	0.00176888i
$575$	−7.53091	−	32.7934i	−0.314061	−	1.36758i
$576$	−0.880386	−	2.70955i	−0.0366827	−	0.112898i
$577$	−0.310767	+	1.96210i	−0.0129374	+	0.0816834i	−0.993312	−	0.115459i	$-0.963166\pi$
$577$	−0.310767	+	1.96210i	−0.0129374	+	0.0816834i	0.980375	+	0.197142i	$0.0631661\pi$
$578$	0.238056	−	1.50302i	0.00990181	−	0.0625176i
$579$	−1.92615	−	5.92807i	−0.0800480	−	0.246362i
$580$	3.16524	+	8.71214i	0.131429	+	0.361752i
$581$	0.165569	+	0.120293i	0.00686896	+	0.00499059i
$582$	1.22305	+	1.22305i	0.0506969	+	0.0506969i
$583$	36.5822	+	28.7854i	1.51508	+	1.19217i
$584$		−	4.60963i		−	0.190748i
$585$	10.1766	−	10.9004i	0.420750	−	0.450675i
$586$	−4.20067	+	12.9283i	−0.173528	+	0.534065i
$587$	12.4878	+	6.36284i	0.515426	+	0.262623i	0.692299	−	0.721611i	$-0.256598\pi$
$587$	12.4878	+	6.36284i	0.515426	+	0.262623i	−0.176873	+	0.984234i	$0.556598\pi$
$588$	−2.68663	−	0.425521i	−0.110795	−	0.0175482i
$589$	27.1582	−	19.7316i	1.11904	−	0.813027i
$590$	0.835057	+	4.30933i	0.0343787	+	0.177412i
$591$	3.08536	+	1.00249i	0.126915	+	0.0412371i
$592$	−1.11428	+	0.176484i	−0.0457966	+	0.00725347i
$593$	−24.8101	+	24.8101i	−1.01883	+	1.01883i	−0.0190108	+	0.999819i	$0.506052\pi$
$593$	−24.8101	+	24.8101i	−1.01883	+	1.01883i	−0.999819	+	0.0190108i	$0.993948\pi$
$594$	−5.53102	+	5.12212i	−0.226940	+	0.210163i
$595$	0.106538	−	0.0831369i	0.00436762	−	0.00340828i
$596$	−8.30508	+	11.4310i	−0.340189	+	0.468230i
$597$	1.49367	+	2.93148i	0.0611317	+	0.119978i
$598$	−7.15150	+	14.0356i	−0.292446	+	0.573958i
$599$	6.95362	+	9.57083i	0.284117	+	0.391054i	0.927092	−	0.374833i	$-0.122300\pi$
$599$	6.95362	+	9.57083i	0.284117	+	0.391054i	−0.642975	+	0.765887i	$0.722300\pi$
$600$	−0.725775	−	1.80237i	−0.0296296	−	0.0735815i
$601$	−18.9484	+	6.15671i	−0.772922	+	0.251138i	−0.668815	−	0.743429i	$-0.733198\pi$
$601$	−18.9484	+	6.15671i	−0.772922	+	0.251138i	−0.104107	+	0.994566i	$0.533198\pi$
$602$	0.110127	−	0.0561127i	0.00448846	−	0.00228698i
$603$	2.31718	+	14.6301i	0.0943630	+	0.595784i
$604$	−3.31087			−0.134717
$605$	8.58559	−	23.0497i	0.349054	−	0.937103i
$606$	−6.74795			−0.274117
$607$	−3.67280	−	23.1891i	−0.149074	−	0.941218i	−0.942901	−	0.333074i	$-0.891914\pi$
$607$	−3.67280	−	23.1891i	−0.149074	−	0.941218i	0.793827	−	0.608144i	$-0.208086\pi$
$608$	5.14552	−	2.62177i	0.208678	−	0.106327i
$609$	0.0235343	−	0.00764677i	0.000953660	−	0.000309863i
$610$	−16.1268	+	8.92703i	−0.652957	+	0.361445i
$611$	2.13089	+	2.93292i	0.0862065	+	0.118653i
$612$	−5.08860	+	9.98694i	−0.205694	+	0.403698i
$613$	−11.3849	−	22.3442i	−0.459833	−	0.902473i	−0.998212	−	0.0597703i	$-0.980963\pi$
$613$	−11.3849	−	22.3442i	−0.459833	−	0.902473i	0.538379	−	0.842703i	$-0.319037\pi$
$614$	−14.0329	+	19.3146i	−0.566322	+	0.779475i
$615$	−4.04779	−	0.499389i	−0.163223	−	0.0201373i
$616$	0.0373807	−	0.0346172i	0.00150611	−	0.00139477i
$617$	25.6695	−	25.6695i	1.03341	−	1.03341i	0.0339923	−	0.999422i	$-0.489178\pi$
$617$	25.6695	−	25.6695i	1.03341	−	1.03341i	0.999422	−	0.0339923i	$-0.0108222\pi$
$618$	−0.131095	+	0.0207634i	−0.00527342	+	0.000835227i
$619$	−15.3896	−	5.00040i	−0.618562	−	0.200983i	−0.0170601	−	0.999854i	$-0.505431\pi$
$619$	−15.3896	−	5.00040i	−0.618562	−	0.200983i	−0.601502	+	0.798872i	$0.705431\pi$
$620$	−10.7717	−	7.27471i	−0.432603	−	0.292159i
$621$	12.3743	−	8.99044i	0.496563	−	0.360774i
$622$	28.6415	+	4.53636i	1.14842	+	0.181892i
$623$	0.129785	+	0.0661287i	0.00519972	+	0.00264939i
$624$	−0.281100	+	0.865137i	−0.0112530	+	0.0346332i
$625$	10.9071	+	22.4952i	0.436285	+	0.899808i
$626$			17.3031i			0.691573i
$627$	−5.84930	−	4.60264i	−0.233599	−	0.183812i
$628$	−9.10015	−	9.10015i	−0.363136	−	0.363136i
$629$	3.59081	+	2.60888i	0.143175	+	0.104023i
$630$	0.0919775	−	0.0334167i	0.00366447	−	0.00133135i
$631$	−4.71355	−	14.5068i	−0.187644	−	0.577508i	0.812340	−	0.583184i	$-0.198193\pi$
$631$	−4.71355	−	14.5068i	−0.187644	−	0.577508i	−0.999984	+	0.00567610i	$0.998193\pi$
$632$	0.743430	−	4.69383i	0.0295720	−	0.186711i
$633$	0.425351	−	2.68556i	0.0169062	−	0.106741i
$634$	−6.41152	−	19.7326i	−0.254634	−	0.783683i
$635$	−35.5033	−	16.5805i	−1.40891	−	0.657978i
$636$	−4.41246	−	3.20584i	−0.174965	−	0.127120i
$637$	−11.5862	−	11.5862i	−0.459063	−	0.459063i
$638$	4.74694	−	12.9031i	0.187933	−	0.510840i
$639$		−	18.3138i		−	0.724484i
$640$	−1.63447	−	1.52594i	−0.0646082	−	0.0603182i
$641$	3.02959	−	9.32412i	0.119662	−	0.368280i	−0.873229	−	0.487310i	$-0.837978\pi$
$641$	3.02959	−	9.32412i	0.119662	−	0.368280i	0.992891	+	0.119029i	$0.0379782\pi$
$642$	−0.794055	−	0.404591i	−0.0313388	−	0.0159679i
$643$	4.86380	+	0.770351i	0.191810	+	0.0303797i	0.251600	−	0.967831i	$-0.419043\pi$
$643$	4.86380	+	0.770351i	0.191810	+	0.0303797i	−0.0597904	+	0.998211i	$0.519043\pi$
$644$	−0.0836301	+	0.0607608i	−0.00329549	+	0.00239431i
$645$	−3.91301	+	5.79402i	−0.154075	+	0.228139i
$646$	−21.6080	−	7.02088i	−0.850157	−	0.276233i
$647$	−8.21829	+	1.30165i	−0.323094	+	0.0511731i	−0.315875	−	0.948801i	$-0.602298\pi$
$647$	−8.21829	+	1.30165i	−0.323094	+	0.0511731i	−0.00721944	+	0.999974i	$0.502298\pi$
$648$	−5.41905	+	5.41905i	−0.212881	+	0.212881i
$649$	3.17611	−	5.68342i	0.124673	−	0.223094i
$650$	2.84468	−	11.3533i	0.111578	−	0.445313i
$651$	−0.0203961	+	0.0280729i	−0.000799387	+	0.00110026i
$652$	0.763736	+	1.49892i	0.0299102	+	0.0587021i
$653$	10.2557	−	20.1279i	0.401335	−	0.787665i	−0.598575	−	0.801067i	$-0.704266\pi$
$653$	10.2557	−	20.1279i	0.401335	−	0.787665i	0.999910	+	0.0134022i	$0.00426617\pi$
$654$	−0.554689	−	0.763464i	−0.0216901	−	0.0298538i
$655$	2.25588	−	7.84999i	0.0881444	−	0.306725i
$656$	−4.46390	+	1.45041i	−0.174286	+	0.0566290i
$657$	−11.7014	+	5.96216i	−0.456515	+	0.232606i
$658$	0.00372160	+	0.0234972i	0.000145083	+	0.000916018i
$659$	−25.7362			−1.00254			−0.501270	−	0.865291i	$-0.667134\pi$
$659$	−25.7362			−1.00254			−0.501270	+	0.865291i	$0.667134\pi$
$660$	−0.901631	+	2.73728i	−0.0350959	+	0.106548i
$661$	−14.3297			−0.557360			−0.278680	−	0.960384i	$-0.589897\pi$
$661$	−14.3297			−0.557360			−0.278680	+	0.960384i	$0.589897\pi$
$662$	4.33692	+	27.3822i	0.168559	+	1.06424i
$663$	3.18875	−	1.62475i	0.123841	−	0.0631000i
$664$	−12.6707	+	4.11695i	−0.491717	+	0.159769i
$665$	0.0960679	+	0.173548i	0.00372535	+	0.00672991i
$666$	1.88922	+	2.60029i	0.0732059	+	0.100759i
$667$	−12.6644	+	24.8553i	−0.490369	+	0.962403i
$668$	−7.38860	−	14.5009i	−0.285874	−	0.561058i
$669$	−4.27118	+	5.87878i	−0.165133	+	0.227287i
$670$	7.15223	+	9.16539i	0.276315	+	0.354090i
$671$	26.8197	+	5.30953i	1.03536	+	0.204972i
$672$	−0.00422103	+	0.00422103i	−0.000162830	+	0.000162830i
$673$	−36.8427	+	5.83531i	−1.42018	+	0.224935i	−0.818824	−	0.574045i	$-0.805373\pi$
$673$	−36.8427	+	5.83531i	−1.42018	+	0.224935i	−0.601358	+	0.798980i	$0.705373\pi$
$674$	6.68524	+	2.17217i	0.257506	+	0.0836688i
$675$	−7.46582	+	8.56835i	−0.287359	+	0.329796i
$676$	6.08415	−	4.42039i	0.234006	−	0.170015i
$677$	−10.9011	−	1.72656i	−0.418963	−	0.0663572i	−0.0566060	−	0.998397i	$-0.518028\pi$
$677$	−10.9011	−	1.72656i	−0.418963	−	0.0663572i	−0.362357	+	0.932039i	$0.618028\pi$
$678$	3.77083	+	1.92133i	0.144818	+	0.0737883i
$679$	−0.0211283	+	0.0650261i	−0.000810828	+	0.00249547i
$680$	0.301921	+	8.79204i	0.0115781	+	0.337160i
$681$			3.93703i			0.150867i
$682$	5.24999	+	18.5507i	0.201033	+	0.710345i
$683$	−4.64732	−	4.64732i	−0.177825	−	0.177825i	0.612582	−	0.790407i	$-0.290131\pi$
$683$	−4.64732	−	4.64732i	−0.177825	−	0.177825i	−0.790407	+	0.612582i	$0.790131\pi$
$684$	−13.3106	−	9.67069i	−0.508942	−	0.369768i
$685$	15.9291	−	34.1084i	0.608619	−	1.30321i
$686$	−0.0664556	−	0.204529i	−0.00253729	−	0.00780896i
$687$	0.659854	−	4.16615i	0.0251750	−	0.158949i
$688$	−1.25869	+	7.94705i	−0.0479871	+	0.302978i
$689$	−10.1525	−	31.2463i	−0.386780	−	1.19039i
$690$	2.47431	−	5.29816i	0.0941954	−	0.201697i
$691$	−1.72951	−	1.25656i	−0.0657935	−	0.0478018i	0.554402	−	0.832249i	$-0.312947\pi$
$691$	−1.72951	−	1.25656i	−0.0657935	−	0.0478018i	−0.620196	+	0.784447i	$0.712947\pi$
$692$	−10.6979	−	10.6979i	−0.406674	−	0.406674i
$693$	−0.136223	−	0.0501154i	−0.00517470	−	0.00190373i
$694$		−	21.7088i		−	0.824055i
$695$	1.69985	+	49.5002i	0.0644789	+	1.87765i
$696$	−0.497794	+	1.53205i	−0.0188688	+	0.0580723i
$697$	16.4532	+	8.38331i	0.623209	+	0.317541i
$698$	−11.7363	−	1.85885i	−0.444226	−	0.0703585i
$699$	−1.49391	+	1.08539i	−0.0565048	+	0.0410531i
$700$	0.0504568	−	0.0579082i	0.00190709	−	0.00218872i
$701$	16.0121	+	5.20265i	0.604769	+	0.196501i	0.595366	−	0.803454i	$-0.297007\pi$
$701$	16.0121	+	5.20265i	0.604769	+	0.196501i	0.00940286	+	0.999956i	$0.497007\pi$
$702$	5.25508	−	0.832323i	0.198340	−	0.0314140i
$703$	−4.60688	+	4.60688i	−0.173752	+	0.173752i
$704$	0.392810	+	3.29328i	0.0148046	+	0.124120i
$705$	−0.827900	−	1.06093i	−0.0311805	−	0.0399570i
$706$	−0.637174	+	0.876995i	−0.0239804	+	0.0330061i
$707$	−0.121099	−	0.237671i	−0.00455441	−	0.00893854i
$708$	−0.346323	+	0.679697i	−0.0130156	+	0.0255446i
$709$	10.9910	+	15.1277i	0.412774	+	0.568134i	0.963892	−	0.266293i	$-0.0857988\pi$
$709$	10.9910	+	15.1277i	0.412774	+	0.568134i	−0.551118	+	0.834427i	$0.685799\pi$
$710$	−6.96130	−	12.5757i	−0.261253	−	0.471958i
$711$	−12.8767	+	4.18389i	−0.482914	+	0.156908i
$712$	−8.44881	+	4.30488i	−0.316632	+	0.161332i
$713$	−6.11934	−	38.6360i	−0.229171	−	1.44693i
$714$	0.0234852			0.000878911
$715$	−14.0858	+	10.1473i	−0.526779	+	0.379487i
$716$	23.6364			0.883333
$717$	−0.820662	−	5.18146i	−0.0306482	−	0.193505i
$718$	−7.39342	+	3.76714i	−0.275920	+	0.140588i
$719$	16.7305	−	5.43605i	0.623941	−	0.202731i	0.0200516	−	0.999799i	$-0.493617\pi$
$719$	16.7305	−	5.43605i	0.623941	−	0.202731i	0.603889	+	0.797068i	$0.293617\pi$
$720$	−1.75951	+	6.12273i	−0.0655730	+	0.228181i
$721$	−0.00308396	−	0.00424470i	−0.000114853	−	0.000158081i
$722$	6.51478	−	12.7860i	0.242455	−	0.475845i
$723$	−3.80085	−	7.45959i	−0.141355	−	0.277425i
$724$	11.2395	−	15.4698i	0.417712	−	0.574931i
$725$	5.03759	−	20.1053i	0.187091	−	0.746692i
$726$	3.64066	−	2.24008i	0.135118	−	0.0831372i
$727$	−3.51865	+	3.51865i	−0.130500	+	0.130500i	−0.769340	−	0.638840i	$-0.779415\pi$
$727$	−3.51865	+	3.51865i	−0.130500	+	0.130500i	0.638840	+	0.769340i	$0.279415\pi$
$728$	−0.0355158	+	0.00562515i	−0.00131630	+	0.000208482i
$729$	18.2451	+	5.92818i	0.675743	+	0.219562i
$730$	−5.76881	+	8.54192i	−0.213513	+	0.316151i
$731$	25.6097	−	18.6065i	0.947209	−	0.688187i
$732$	−3.16396	−	0.501121i	−0.116943	−	0.0185220i
$733$	−8.32881	−	4.24374i	−0.307631	−	0.156746i	0.293359	−	0.956002i	$-0.405227\pi$
$733$	−8.32881	−	4.24374i	−0.307631	−	0.156746i	−0.600990	+	0.799256i	$0.705227\pi$
$734$	−4.65539	+	14.3278i	−0.171833	+	0.528849i
$735$	4.44596	+	4.15075i	0.163992	+	0.153103i
$736$		−	6.72940i		−	0.248049i
$737$	0.661386	−	17.2311i	0.0243625	−	0.634717i
$738$	9.45549	+	9.45549i	0.348061	+	0.348061i
$739$	−22.0128	−	15.9932i	−0.809754	−	0.588321i	0.104005	−	0.994577i	$-0.466834\pi$
$739$	−22.0128	−	15.9932i	−0.809754	−	0.588321i	−0.913759	+	0.406256i	$0.866834\pi$
$740$	2.28569	+	1.06745i	0.0840236	+	0.0392402i
$741$	1.62334	+	4.99612i	0.0596348	+	0.183537i
$742$	0.0337271	−	0.212945i	0.00123816	−	0.00781744i
$743$	−3.73190	+	23.5623i	−0.136910	+	0.864417i	0.819646	+	0.572870i	$0.194170\pi$
$743$	−3.73190	+	23.5623i	−0.136910	+	0.864417i	−0.956557	+	0.291547i	$0.905830\pi$
$744$	−0.698044	−	2.14836i	−0.0255915	−	0.0787627i
$745$	29.6953	−	10.7887i	1.08795	−	0.395267i
$746$	−6.10663	−	4.43673i	−0.223580	−	0.162440i
$747$	26.8392	+	26.8392i	0.981993	+	0.981993i
$748$	8.06890	−	10.2544i	0.295028	−	0.374939i
$749$		−	0.0352284i		−	0.00128722i
$750$	−0.910706	+	4.24818i	−0.0332543	+	0.155122i
$751$	5.95219	−	18.3190i	0.217199	−	0.668469i	−0.781792	−	0.623540i	$-0.785694\pi$
$751$	5.95219	−	18.3190i	0.217199	−	0.668469i	0.998990	−	0.0449289i	$-0.0143061\pi$
$752$	−1.37991	−	0.703097i	−0.0503200	−	0.0256393i
$753$	−7.51806	−	1.19074i	−0.273973	−	0.0433931i
$754$	−7.85043	+	5.70367i	−0.285896	+	0.207715i
$755$	6.13524	+	4.14345i	0.223284	+	0.150796i
$756$	0.0332063	+	0.0107894i	0.00120770	+	0.000392406i
$757$	−10.6845	+	1.69226i	−0.388336	+	0.0615063i	−0.347550	−	0.937662i	$-0.612986\pi$
$757$	−10.6845	+	1.69226i	−0.388336	+	0.0615063i	−0.0407860	+	0.999168i	$0.512986\pi$
$758$	−7.05009	+	7.05009i	−0.256071	+	0.256071i
$759$	−7.87319	+	3.63824i	−0.285779	+	0.132060i
$760$	−12.8160	−	1.58115i	−0.464886	−	0.0573544i
$761$	13.9786	−	19.2399i	0.506723	−	0.697444i	−0.476640	−	0.879099i	$-0.658145\pi$
$761$	13.9786	−	19.2399i	0.506723	−	0.697444i	0.983362	+	0.181655i	$0.0581453\pi$
$762$	−3.09156	−	6.06752i	−0.111995	−	0.219803i
$763$	0.0169356	−	0.0332380i	0.000613111	−	0.00120330i
$764$	7.04298	+	9.69383i	0.254806	+	0.350710i
$765$	21.9278	−	12.1382i	0.792802	−	0.438856i
$766$	22.6593	−	7.36246i	0.818714	−	0.266016i
$767$	−4.09434	+	2.08617i	−0.147838	+	0.0753273i
$768$	−0.0607907	−	0.383818i	−0.00219360	−	0.0138498i
$769$	5.84739			0.210862			0.105431	−	0.994427i	$-0.466378\pi$
$769$	5.84739			0.210862			0.105431	+	0.994427i	$0.466378\pi$
$770$	−0.112591	+	0.0173670i	−0.00405750	+	0.000625862i
$771$	7.67600			0.276444
$772$	2.50920	+	15.8424i	0.0903080	+	0.570182i
$773$	−8.04258	+	4.09790i	−0.289272	+	0.147391i	−0.592605	−	0.805493i	$-0.701900\pi$
$773$	−8.04258	+	4.09790i	−0.289272	+	0.147391i	0.303333	+	0.952885i	$0.401900\pi$
$774$	21.8013	−	7.08368i	0.783633	−	0.254618i
$775$	10.8566	+	26.9609i	0.389979	+	0.968465i
$776$	−2.61620	−	3.60090i	−0.0939163	−	0.129265i
$777$	0.00305741	−	0.00600051i	0.000109684	−	0.000215267i
$778$	−2.37697	−	4.66507i	−0.0852185	−	0.167251i
$779$	−15.9322	+	21.9288i	−0.570829	+	0.785679i
$780$	1.60359	−	1.25136i	0.0574176	−	0.0448060i
$781$	−4.14037	+	20.9140i	−0.148154	+	0.748361i
$782$	−18.7207	+	18.7207i	−0.669451	+	0.669451i
$783$	9.30611	−	1.47394i	0.332573	−	0.0526744i
$784$	6.65717	+	2.16305i	0.237756	+	0.0772516i
$785$	5.47457	+	28.2517i	0.195396	+	1.00835i
$786$	1.14836	−	0.834331i	0.0409606	−	0.0297596i
$787$	−46.5577	−	7.37402i	−1.65960	−	0.262855i	−0.744957	−	0.667112i	$-0.767530\pi$
$787$	−46.5577	−	7.37402i	−1.65960	−	0.262855i	−0.914646	+	0.404257i	$0.867530\pi$
$788$	−7.43833	−	3.79002i	−0.264979	−	0.135014i
$789$	3.41145	−	10.4994i	0.121451	−	0.373788i
$790$	−7.25180	+	7.76757i	−0.258007	+	0.276358i
$791$			0.167293i			0.00594827i
$792$	7.85182	−	5.25671i	0.279002	−	0.186789i
$793$	−13.6447	−	13.6447i	−0.484537	−	0.484537i
$794$	1.92927	+	1.40169i	0.0684671	+	0.0497443i
$795$	4.16454	+	11.4627i	0.147701	+	0.406539i
$796$	−2.61628	−	8.05208i	−0.0927316	−	0.285398i
$797$	0.195418	−	1.23382i	0.00692208	−	0.0437043i	−0.983986	−	0.178248i	$-0.942957\pi$
$797$	0.195418	−	1.23382i	0.00692208	−	0.0437043i	0.990908	+	0.134544i	$0.0429570\pi$
$798$	−0.00539280	+	0.0340488i	−0.000190903	+	0.00120531i
$799$	1.88283	+	5.79476i	0.0666098	+	0.205004i
$800$	1.11910	+	4.87315i	0.0395663	+	0.172292i
$801$	21.8556	+	15.8790i	0.772230	+	0.561058i
$802$	−11.1070	−	11.1070i	−0.392202	−	0.392202i
$803$	14.7107	−	4.16322i	0.519128	−	0.146917i
$804$			2.02042i			0.0712548i
$805$	0.231012	−	0.00793300i	0.00814209	−	0.000279601i
$806$	4.20486	−	12.9412i	0.148110	−	0.455835i
$807$	−3.24337	−	1.65258i	−0.114172	−	0.0581735i
$808$	17.1509	+	2.71643i	0.603366	+	0.0955638i
$809$	−16.9646	+	12.3255i	−0.596442	+	0.433341i	−0.844614	−	0.535375i	$-0.820170\pi$
$809$	−16.9646	+	12.3255i	−0.596442	+	0.433341i	0.248172	+	0.968716i	$0.420170\pi$
$810$	16.8236	−	3.26005i	0.591121	−	0.114547i
$811$	2.18611	+	0.710312i	0.0767649	+	0.0249424i	0.347148	−	0.937810i	$-0.387150\pi$
$811$	2.18611	+	0.710312i	0.0767649	+	0.0249424i	−0.270383	+	0.962753i	$0.587150\pi$
$812$	−0.0628942	+	0.00996146i	−0.00220715	+	0.000349579i
$813$	1.69123	−	1.69123i	0.0593142	−	0.0593142i
$814$	−1.56958	−	3.39659i	−0.0550138	−	0.119050i
$815$	0.460598	−	3.73337i	0.0161340	−	0.130774i
$816$	−0.898637	+	1.23687i	−0.0314586	+	0.0432990i
$817$	21.0951	+	41.4014i	0.738023	+	1.44845i
$818$	−0.784707	+	1.54007i	−0.0274366	+	0.0538474i
$819$	0.0602159	+	0.0828801i	0.00210411	+	0.00289607i
$820$	10.0870	+	2.89874i	0.352254	+	0.101228i
$821$	28.7277	−	9.33418i	1.00260	−	0.325765i	0.238697	−	0.971094i	$-0.423280\pi$
$821$	28.7277	−	9.33418i	1.00260	−	0.325765i	0.763905	+	0.645329i	$0.223280\pi$
$822$	5.82913	−	2.97009i	0.203314	−	0.103594i
$823$	0.511401	+	3.22886i	0.0178263	+	0.112551i	0.994997	−	0.0999048i	$-0.0318538\pi$
$823$	0.511401	+	3.22886i	0.0178263	+	0.112551i	−0.977171	+	0.212456i	$0.931854\pi$
$824$	0.341556			0.0118987
$825$	5.09639	−	3.94398i	0.177434	−	0.137312i
$826$	−0.0301549			−0.00104922
$827$	−1.84276	−	11.6347i	−0.0640791	−	0.404579i	−0.998790	−	0.0491714i	$-0.984342\pi$
$827$	−1.84276	−	11.6347i	−0.0640791	−	0.404579i	0.934711	−	0.355408i	$-0.115658\pi$
$828$	−17.0824	+	8.70390i	−0.593653	+	0.302482i
$829$	−19.4970	+	6.33497i	−0.677160	+	0.220023i	−0.627351	−	0.778736i	$-0.715861\pi$
$829$	−19.4970	+	6.33497i	−0.677160	+	0.220023i	−0.0498083	+	0.998759i	$0.515861\pi$
$830$	28.6317	+	8.22798i	0.993821	+	0.285597i
$831$	−6.80794	−	9.37032i	−0.236165	−	0.325053i
$832$	1.06272	−	2.08571i	0.0368433	−	0.0723091i
$833$	−12.5023	−	24.5372i	−0.433180	−	0.850164i
$834$	−5.05943	+	6.96370i	−0.175194	+	0.241133i
$835$	−4.45596	+	36.1177i	−0.154205	+	1.24990i
$836$	13.0140	+	14.0529i	0.450100	+	0.486031i
$837$	−9.34257	+	9.34257i	−0.322927	+	0.322927i
$838$	16.5925	−	2.62800i	0.573180	−	0.0907828i
$839$	−15.2019	−	4.93940i	−0.524828	−	0.170527i	0.0346074	−	0.999401i	$-0.488982\pi$
$839$	−15.2019	−	4.93940i	−0.524828	−	0.170527i	−0.559435	+	0.828874i	$0.688982\pi$
$840$	0.0131043	−	0.00253933i	0.000452141	−	8.76153e-5i
$841$	9.55933	−	6.94526i	0.329632	−	0.239492i
$842$	11.0975	+	1.75768i	0.382446	+	0.0605736i
$843$	1.97893	+	1.00832i	0.0681580	+	0.0347282i
$844$	−2.16218	+	6.65452i	−0.0744254	+	0.229058i
$845$	−16.8063	+	0.577131i	−0.578153	+	0.0198539i
$846$			4.41224i			0.151696i
$847$	0.144234	+	0.0880279i	0.00495594	+	0.00302467i
$848$	9.92438	+	9.92438i	0.340804	+	0.340804i
$849$	−1.36690	−	0.993108i	−0.0469117	−	0.0340834i
$850$	10.4435	−	16.6700i	0.358209	−	0.571777i
$851$	2.34603	+	7.22033i	0.0804208	+	0.247510i
$852$	0.390774	−	2.46725i	0.0133877	−	0.0845266i
$853$	−6.04382	+	38.1592i	−0.206936	+	1.30655i	0.637317	+	0.770601i	$0.280044\pi$
$853$	−6.04382	+	38.1592i	−0.206936	+	1.30655i	−0.844254	+	0.535944i	$0.819956\pi$
$854$	−0.0391306	−	0.120432i	−0.00133902	−	0.00412108i
$855$	12.5627	+	34.5781i	0.429635	+	1.18255i
$856$	1.85533	+	1.34798i	0.0634140	+	0.0460730i
$857$	26.7350	+	26.7350i	0.913251	+	0.913251i	0.996527	−	0.0832758i	$-0.0265382\pi$
$857$	26.7350	+	26.7350i	0.913251	+	0.913251i	−0.0832758	+	0.996527i	$0.526538\pi$
$858$	−3.01478	−	0.115717i	−0.102923	−	0.00395051i
$859$			35.7867i			1.22103i	0.792005	+	0.610514i	$0.209037\pi$
$859$			35.7867i			1.22103i	−0.792005	+	0.610514i	$0.790963\pi$
$860$	12.2779	−	13.1511i	0.418673	−	0.448450i
$861$	0.00865813	−	0.0266470i	0.000295068	−	0.000908127i
$862$	−34.1495	−	17.4000i	−1.16314	−	0.592647i
$863$	−38.2576	−	6.05941i	−1.30230	−	0.206265i	−0.533528	−	0.845782i	$-0.679134\pi$
$863$	−38.2576	−	6.05941i	−1.30230	−	0.206265i	−0.768776	+	0.639518i	$0.779134\pi$
$864$	−1.83884	+	1.33599i	−0.0625585	+	0.0454514i
$865$	6.43578	+	33.2120i	0.218823	+	1.12924i
$866$	18.6691	+	6.06597i	0.634403	+	0.206130i
$867$	−0.584078	+	0.0925089i	−0.0198363	+	0.00314177i
$868$	0.0631407	−	0.0631407i	0.00214313	−	0.00214313i
$869$	15.6508	−	1.86677i	0.530917	−	0.0633257i
$870$	2.83976	−	2.21601i	0.0962768	−	0.0751298i
$871$	−7.15368	+	9.84619i	−0.242393	+	0.333626i
$872$	1.10249	+	2.16375i	0.0373349	+	0.0732738i
$873$	−5.75692	+	11.2986i	−0.194842	+	0.382400i
$874$	−22.8425	−	31.4400i	−0.772659	−	1.06347i
$875$	−0.165970	+	0.0441622i	−0.00561080	+	0.00149295i
$876$	−1.70364	+	0.553546i	−0.0575606	+	0.0187026i
$877$	−9.96725	+	5.07857i	−0.336570	+	0.171491i	−0.614105	−	0.789225i	$-0.710483\pi$
$877$	−9.96725	+	5.07857i	−0.336570	+	0.171491i	0.277534	+	0.960716i	$0.410483\pi$
$878$	0.164590	+	1.03918i	0.00555466	+	0.0350707i
$879$	5.28252			0.178175
$880$	3.39354	−	6.59423i	0.114396	−	0.222292i
$881$	−2.54074			−0.0855998			−0.0427999	−	0.999084i	$-0.513628\pi$
$881$	−2.54074			−0.0855998			−0.0427999	+	0.999084i	$0.513628\pi$
$882$	−3.11965	−	19.6967i	−0.105044	−	0.663223i
$883$	13.9170	−	7.09109i	0.468346	−	0.238634i	−0.203858	−	0.979001i	$-0.565348\pi$
$883$	13.9170	−	7.09109i	0.468346	−	0.238634i	0.672203	+	0.740366i	$0.265348\pi$
$884$	−8.75872	+	2.84588i	−0.294588	+	0.0957173i
$885$	1.49238	−	0.826107i	0.0501657	−	0.0277693i
$886$	−0.185210	−	0.254920i	−0.00622226	−	0.00856421i
$887$	−1.38930	+	2.72665i	−0.0466480	+	0.0915519i	−0.913154	−	0.407615i	$-0.866361\pi$
$887$	−1.38930	+	2.72665i	−0.0466480	+	0.0915519i	0.866506	+	0.499167i	$0.166361\pi$
$888$	0.199033	+	0.390625i	0.00667912	+	0.0131085i
$889$	0.158224	−	0.217777i	0.00530667	−	0.00730400i
$890$	21.0436	+	2.59621i	0.705382	+	0.0870252i
$891$	−22.1880	−	12.3995i	−0.743326	−	0.415399i
$892$	13.2224	−	13.2224i	0.442718	−	0.442718i
$893$	−8.83358	+	1.39910i	−0.295604	+	0.0468191i
$894$	5.22199	+	1.69673i	0.174650	+	0.0567471i
$895$	−43.7996	−	29.5802i	−1.46406	−	0.988756i
$896$	0.0124276	−	0.00902916i	0.000415176	−	0.000301643i
$897$	6.04610	+	0.957607i	0.201873	+	0.0319736i
$898$	−29.9392	−	15.2548i	−0.999084	−	0.509059i
$899$	7.44630	−	22.9173i	0.248348	−	0.764336i
$900$	10.9229	−	9.14381i	0.364096	−	0.304794i
$901$		−	55.2178i		−	1.83957i
$902$	−8.66027	−	12.9356i	−0.288356	−	0.430710i
$903$	−0.0339629	−	0.0339629i	−0.00113021	−	0.00113021i
$904$	−8.81066	−	6.40132i	−0.293038	−	0.212905i
$905$	−40.1874	+	14.6006i	−1.33587	+	0.485341i
$906$	0.397585	+	1.22364i	0.0132089	+	0.0406527i
$907$	−8.26589	+	52.1888i	−0.274464	+	1.73290i	0.336892	+	0.941543i	$0.390624\pi$
$907$	−8.26589	+	52.1888i	−0.274464	+	1.73290i	−0.611356	+	0.791356i	$0.709376\pi$
$908$	1.58488	−	10.0065i	0.0525961	−	0.332079i
$909$	−15.2876	−	47.0505i	−0.507058	−	1.56057i
$910$	0.0728526	+	0.0340232i	0.00241504	+	0.00112786i
$911$	9.97151	+	7.24473i	0.330371	+	0.240029i	0.740588	−	0.671959i	$-0.234547\pi$
$911$	9.97151	+	7.24473i	0.330371	+	0.240029i	−0.410217	+	0.911988i	$0.634547\pi$
$912$	−1.58686	−	1.58686i	−0.0525461	−	0.0525461i
$913$	−24.5820	−	36.7175i	−0.813544	−	1.21517i
$914$			29.9314i			0.990044i
$915$	5.23586	+	4.88820i	0.173092	+	0.161599i
$916$	−3.35423	+	10.3233i	−0.110827	+	0.341090i
$917$	0.0499947	+	0.0254736i	0.00165097	+	0.000841212i
$918$	8.83215	+	1.39888i	0.291504	+	0.0461698i
$919$	0.0894366	−	0.0649795i	0.00295024	−	0.00214348i	−0.586309	−	0.810087i	$-0.699420\pi$
$919$	0.0894366	−	0.0649795i	0.00295024	−	0.00214348i	0.589259	+	0.807944i	$0.299420\pi$
$920$	−8.42163	+	12.4700i	−0.277653	+	0.411123i
$921$	8.82348	+	2.86692i	0.290744	+	0.0944683i
$922$	−27.2750	+	4.31993i	−0.898254	+	0.142269i
$923$	10.6401	−	10.6401i	0.350224	−	0.350224i
$924$	−0.0172828	−	0.00965827i	−0.000568561	−	0.000317734i
$925$	−2.89964	−	4.83851i	−0.0953396	−	0.159089i
$926$	22.1629	−	30.5047i	0.728319	−	1.00245i
$927$	−0.441773	−	0.867028i	−0.0145097	−	0.0284769i
$928$	1.88195	−	3.69354i	0.0617782	−	0.121247i
$929$	−6.25774	−	8.61305i	−0.205310	−	0.282585i	0.693928	−	0.720044i	$-0.255878\pi$
$929$	−6.25774	−	8.61305i	−0.205310	−	0.282585i	−0.899238	+	0.437459i	$0.855878\pi$
$930$	−1.39509	+	4.85462i	−0.0457467	+	0.159189i
$931$	38.4448	−	12.4915i	1.25998	−	0.409392i
$932$	4.23391	−	2.15729i	0.138686	−	0.0706643i
$933$	−1.76284	−	11.1301i	−0.0577128	−	0.364384i
$934$	29.8354			0.976243
$935$	−27.7852	+	8.90411i	−0.908675	+	0.291195i
$936$	−6.66905			−0.217985
$937$	4.09535	+	25.8570i	0.133789	+	0.844712i	0.959724	+	0.280946i	$0.0906482\pi$
$937$	4.09535	+	25.8570i	0.133789	+	0.844712i	−0.825934	+	0.563766i	$0.809352\pi$
$938$	−0.0711617	+	0.0362587i	−0.00232351	+	0.00118389i
$939$	6.39494	−	2.07784i	0.208691	−	0.0678078i
$940$	1.67714	+	3.02979i	0.0547024	+	0.0988208i
$941$	−19.4803	−	26.8123i	−0.635038	−	0.874055i	0.363300	−	0.931672i	$-0.381650\pi$
$941$	−19.4803	−	26.8123i	−0.635038	−	0.874055i	−0.998339	+	0.0576167i	$0.981650\pi$
$942$	−2.27047	+	4.45604i	−0.0739758	+	0.145186i
$943$	14.3394	+	28.1427i	0.466956	+	0.916452i
$944$	1.15385	−	1.58813i	0.0375545	−	0.0516894i
$945$	−0.0480307	−	0.0615500i	−0.00156244	−	0.00200222i
$946$	−26.4981	+	3.16059i	−0.861528	+	0.102760i
$947$	31.2894	−	31.2894i	1.01677	−	1.01677i	0.0169134	−	0.999857i	$-0.494616\pi$
$947$	31.2894	−	31.2894i	1.01677	−	1.01677i	0.999857	−	0.0169134i	$-0.00538397\pi$
$948$	−1.82403	+	0.288898i	−0.0592418	+	0.00938298i
$949$	−10.2623	−	3.33443i	−0.333129	−	0.108240i
$950$	21.7701	+	18.9688i	0.706314	+	0.615429i
$951$	−6.52291	+	4.73917i	−0.211520	+	0.153678i
$952$	−0.0596910	−	0.00945413i	−0.00193460	−	0.000306410i
$953$	−17.3932	−	8.86229i	−0.563421	−	0.287078i	0.148991	−	0.988839i	$-0.452397\pi$
$953$	−17.3932	−	8.86229i	−0.563421	−	0.287078i	−0.712412	+	0.701761i	$0.752397\pi$
$954$	12.3564	−	38.0290i	0.400053	−	1.23124i
$955$	−0.919538	−	26.7773i	−0.0297556	−	0.866493i
$956$			13.4998i			0.436614i
$957$	−5.33880	−	0.204920i	−0.172579	−	0.00662414i
$958$	−4.61190	−	4.61190i	−0.149004	−	0.149004i
$959$	0.209220	+	0.152007i	0.00675608	+	0.00490858i
$960$	−0.367687	+	0.787314i	−0.0118670	+	0.0254105i
$961$	0.862234	+	2.65368i	0.0278140	+	0.0856027i
$962$	−0.413124	+	2.60836i	−0.0133196	+	0.0840969i
$963$	1.02209	−	6.45320i	0.0329363	−	0.207951i
$964$	6.65750	+	20.4897i	0.214424	+	0.659929i
$965$	15.1766	−	32.4972i	0.488553	−	1.04612i
$966$	0.0324988	+	0.0236118i	0.00104563	+	0.000759697i
$967$	−25.7251	−	25.7251i	−0.827262	−	0.827262i	0.159875	−	0.987137i	$-0.448891\pi$
$967$	−25.7251	−	25.7251i	−0.827262	−	0.827262i	−0.987137	+	0.159875i	$0.948891\pi$
$968$	−10.1550	+	4.22792i	−0.326395	+	0.135890i
$969$			8.82905i			0.283630i
$970$	0.341574	+	9.94677i	0.0109673	+	0.319372i
$971$	−12.5009	+	38.4738i	−0.401173	+	1.23468i	0.522876	+	0.852409i	$0.324859\pi$
$971$	−12.5009	+	38.4738i	−0.401173	+	1.23468i	−0.924049	+	0.382274i	$0.875141\pi$
$972$	8.72912	+	4.44771i	0.279986	+	0.142660i
$973$	−0.336067	−	0.0532278i	−0.0107738	−	0.00170640i
$974$	−6.93105	+	5.03570i	−0.222085	+	0.161354i
$975$	−4.53758	+	0.312011i	−0.145319	+	0.00999235i
$976$	7.83992	+	2.54735i	0.250950	+	0.0815385i
$977$	37.1310	−	5.88097i	1.18792	−	0.188149i	0.468975	−	0.883211i	$-0.344623\pi$
$977$	37.1310	−	5.88097i	1.18792	−	0.188149i	0.718949	+	0.695063i	$0.244623\pi$
$978$	0.462260	−	0.462260i	0.0147814	−	0.0147814i
$979$	−21.3687	−	23.0746i	−0.682947	−	0.737467i
$980$	−9.62915	−	12.3395i	−0.307592	−	0.394171i
$981$	4.06664	−	5.59725i	0.129838	−	0.178706i
$982$	−11.7536	−	23.0676i	−0.375071	−	0.736118i
$983$	6.95538	−	13.6507i	0.221842	−	0.435390i	−0.753082	−	0.657927i	$-0.771434\pi$
$983$	6.95538	−	13.6507i	0.221842	−	0.435390i	0.974924	+	0.222537i	$0.0714337\pi$
$984$	1.07209	+	1.47561i	0.0341770	+	0.0470407i
$985$	9.04058	+	16.3320i	0.288057	+	0.520379i
$986$	−15.5106	+	5.03971i	−0.493959	+	0.160497i
$987$	0.00823726	−	0.00419710i	0.000262195	−	0.000133595i
$988$	−2.11473	−	13.3519i	−0.0672784	−	0.424779i
$989$	54.1455			1.72173
$990$	−21.1285	−	0.0853098i	−0.671508	−	0.00271132i
$991$	−42.6744			−1.35560			−0.677798	−	0.735248i	$-0.737066\pi$
$991$	−42.6744			−1.35560			−0.677798	+	0.735248i	$0.737066\pi$
$992$	0.909344	+	5.74137i	0.0288717	+	0.182289i
$993$	9.59919	−	4.89103i	0.304621	−	0.155212i
$994$	0.0939125	−	0.0305140i	0.00297872	−	0.000967846i
$995$	−5.22880	+	18.1952i	−0.165764	+	0.576826i
$996$	3.04310	+	4.18847i	0.0964244	+	0.132717i
$997$	7.94283	−	15.5887i	0.251552	−	0.493698i	−0.730354	−	0.683069i	$-0.760645\pi$
$997$	7.94283	−	15.5887i	0.251552	−	0.493698i	0.981906	+	0.189371i	$0.0606448\pi$
$998$	7.59331	+	14.9027i	0.240362	+	0.471737i
$999$	1.50723	−	2.07452i	0.0476865	−	0.0656349i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.73.5	yes	48
3.2	odd	2		990.2.bh.c.73.1		48
4.3	odd	2		880.2.cm.c.513.4		48
5.2	odd	4	inner	110.2.k.a.7.2	✓	48
5.3	odd	4		550.2.bh.b.7.5		48
5.4	even	2		550.2.bh.b.293.2		48
11.8	odd	10	inner	110.2.k.a.63.2	yes	48
15.2	even	4		990.2.bh.c.667.5		48
20.7	even	4		880.2.cm.c.337.3		48
33.8	even	10		990.2.bh.c.613.5		48
44.19	even	10		880.2.cm.c.833.3		48
55.8	even	20		550.2.bh.b.107.2		48
55.19	odd	10		550.2.bh.b.393.5		48
55.52	even	20	inner	110.2.k.a.107.5	yes	48
165.107	odd	20		990.2.bh.c.217.1		48
220.107	odd	20		880.2.cm.c.657.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.2	✓	48	5.2	odd	4	inner
110.2.k.a.63.2	yes	48	11.8	odd	10	inner
110.2.k.a.73.5	yes	48	1.1	even	1	trivial
110.2.k.a.107.5	yes	48	55.52	even	20	inner
550.2.bh.b.7.5		48	5.3	odd	4
550.2.bh.b.107.2		48	55.8	even	20
550.2.bh.b.293.2		48	5.4	even	2
550.2.bh.b.393.5		48	55.19	odd	10
880.2.cm.c.337.3		48	20.7	even	4
880.2.cm.c.513.4		48	4.3	odd	2
880.2.cm.c.657.4		48	220.107	odd	20
880.2.cm.c.833.3		48	44.19	even	10
990.2.bh.c.73.1		48	3.2	odd	2
990.2.bh.c.217.1		48	165.107	odd	20
990.2.bh.c.613.5		48	33.8	even	10
990.2.bh.c.667.5		48	15.2	even	4

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	110.2.k.a.73.5

Level	$110$
Weight	$2$
Character	110.73
Analytic conductor	$0.878$
Analytic rank	$0$
Dimension	$48$
Inner twists	$4$