LMFDB - Embedded newform 750.2.l.b.257.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			257.5
Character	$\chi$	$=$	750.257
Dual form			750.2.l.b.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(1.43185 + 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(-3.13589 - 3.13589i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(1.43185 + 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(-3.13589 - 3.13589i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +(-3.57685 - 1.16219i) q^{11} +(-1.63007 + 0.585546i) q^{12} +(-3.49677 - 1.78169i) q^{13} +(-1.37043 + 4.21776i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-0.0644499 + 0.406920i) q^{17} +(1.98715 - 2.24749i) q^{18} +(-2.93913 - 4.04536i) q^{19} +(-1.43394 - 7.54629i) q^{21} +(0.588338 + 3.71462i) q^{22} +(-4.48117 + 2.28327i) q^{23} +(1.26176 + 1.18657i) q^{24} +3.92451i q^{26} +(-1.14438 + 5.06857i) q^{27} +(4.38021 - 0.693758i) q^{28} +(1.49299 + 1.08472i) q^{29} +(2.69808 - 1.96027i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.98886 - 5.15001i) q^{33} +(0.391828 - 0.127313i) q^{34} +(-2.90468 - 0.750223i) q^{36} +(2.39714 - 4.70465i) q^{37} +(-2.27011 + 4.45534i) q^{38} +(-3.27044 - 5.95899i) q^{39} +(3.24600 - 1.05469i) q^{41} +(-6.07280 + 4.70360i) q^{42} +(-3.71639 + 3.71639i) q^{43} +(3.04265 - 2.21062i) q^{44} +(4.06882 + 2.95617i) q^{46} +(-5.10512 + 0.808572i) q^{47} +(0.484416 - 1.66293i) q^{48} +12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(3.49677 - 1.78169i) q^{52} +(-1.29952 - 8.20487i) q^{53} +(5.03567 - 1.28143i) q^{54} +(-2.60672 - 3.58784i) q^{56} +(-0.265855 - 8.65677i) q^{57} +(0.288689 - 1.82271i) q^{58} +(-1.73564 - 5.34175i) q^{59} +(4.43829 - 13.6596i) q^{61} +(-2.97152 - 1.51406i) q^{62} +(5.30128 - 12.2026i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.77779 + 5.89216i) q^{66} +(6.11731 + 0.968887i) q^{67} +(-0.291323 - 0.291323i) q^{68} +(-8.64159 - 1.09796i) q^{69} +(-0.992045 + 1.36543i) q^{71} +(0.650243 + 2.92868i) q^{72} +(1.62628 + 3.19175i) q^{73} -5.28015 q^{74} +5.00034 q^{76} +(7.57211 + 14.8611i) q^{77} +(-3.82475 + 5.61931i) q^{78} +(-6.24842 + 8.60021i) q^{79} +(-6.57831 + 6.14214i) q^{81} +(-2.41339 - 2.41339i) q^{82} +(-7.00394 - 1.10932i) q^{83} +(6.94793 + 3.27552i) q^{84} +(4.99854 + 1.62412i) q^{86} +(1.08059 + 3.00819i) q^{87} +(-3.35101 - 1.70742i) q^{88} +(0.324819 - 0.999689i) q^{89} +(5.37828 + 16.5526i) q^{91} +(0.786761 - 4.96742i) q^{92} +(5.77369 - 0.177314i) q^{93} +(3.03812 + 4.18162i) q^{94} +(-1.70160 + 0.323338i) q^{96} +(1.20630 + 7.61627i) q^{97} +(11.2869 - 5.75096i) q^{98} +(-0.692350 - 11.2615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$-1$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	1.43185	+	0.974581i	0.826679	+	0.562674i
$3$	1.43185	+	0.974581i	0.826679	+	0.562674i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	0.218312	−	1.71824i	0.0891255	−	0.701467i
$7$	−3.13589	−	3.13589i	−1.18525	−	1.18525i	−0.978364	−	0.206890i	$-0.933666\pi$
$7$	−3.13589	−	3.13589i	−1.18525	−	1.18525i	−0.206890	−	0.978364i	$-0.566334\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	1.10038	+	2.79091i	0.366795	+	0.930302i
$10$		0			0
$11$	−3.57685	−	1.16219i	−1.07846	−	0.350413i	−0.284684	−	0.958622i	$-0.591889\pi$
$11$	−3.57685	−	1.16219i	−1.07846	−	0.350413i	−0.793778	+	0.608208i	$0.791889\pi$
$12$	−1.63007	+	0.585546i	−0.470561	+	0.169033i
$13$	−3.49677	−	1.78169i	−0.969828	−	0.494152i	−0.104046	−	0.994573i	$-0.533179\pi$
$13$	−3.49677	−	1.78169i	−0.969828	−	0.494152i	−0.865783	+	0.500420i	$0.833179\pi$
$14$	−1.37043	+	4.21776i	−0.366264	+	1.12724i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.0644499	+	0.406920i	−0.0156314	+	0.0986927i	−0.994271	−	0.106893i	$-0.965910\pi$
$17$	−0.0644499	+	0.406920i	−0.0156314	+	0.0986927i	0.978639	+	0.205585i	$0.0659098\pi$
$18$	1.98715	−	2.24749i	0.468376	−	0.529739i
$19$	−2.93913	−	4.04536i	−0.674282	−	0.928070i	0.325565	−	0.945520i	$-0.394445\pi$
$19$	−2.93913	−	4.04536i	−0.674282	−	0.928070i	−0.999848	+	0.0174495i	$0.994445\pi$
$20$		0			0
$21$	−1.43394	−	7.54629i	−0.312912	−	1.64674i
$22$	0.588338	+	3.71462i	0.125434	+	0.791960i
$23$	−4.48117	+	2.28327i	−0.934389	+	0.476095i	−0.853770	−	0.520650i	$-0.825690\pi$
$23$	−4.48117	+	2.28327i	−0.934389	+	0.476095i	−0.0806186	+	0.996745i	$0.525690\pi$
$24$	1.26176	+	1.18657i	0.257556	+	0.242208i
$25$		0			0
$26$			3.92451i			0.769660i
$27$	−1.14438	+	5.06857i	−0.220236	+	0.975447i
$28$	4.38021	−	0.693758i	0.827783	−	0.131108i
$29$	1.49299	+	1.08472i	0.277241	+	0.201427i	0.717713	−	0.696339i	$-0.245189\pi$
$29$	1.49299	+	1.08472i	0.277241	+	0.201427i	−0.440472	+	0.897766i	$0.645189\pi$
$30$		0			0
$31$	2.69808	−	1.96027i	0.484590	−	0.352075i	−0.318510	−	0.947920i	$-0.603182\pi$
$31$	2.69808	−	1.96027i	0.484590	−	0.352075i	0.803100	+	0.595844i	$0.203182\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.98886	−	5.15001i	−0.694372	−	0.896502i
$34$	0.391828	−	0.127313i	0.0671980	−	0.0218340i
$35$		0			0
$36$	−2.90468	−	0.750223i	−0.484113	−	0.125037i
$37$	2.39714	−	4.70465i	0.394087	−	0.773440i	−0.605664	−	0.795720i	$-0.707093\pi$
$37$	2.39714	−	4.70465i	0.394087	−	0.773440i	0.999752	+	0.0222802i	$0.00709259\pi$
$38$	−2.27011	+	4.45534i	−0.368260	+	0.722751i
$39$	−3.27044	−	5.95899i	−0.523689	−	0.954203i
$40$		0			0
$41$	3.24600	−	1.05469i	0.506941	−	0.164715i	−0.0443698	−	0.999015i	$-0.514128\pi$
$41$	3.24600	−	1.05469i	0.506941	−	0.164715i	0.551310	+	0.834300i	$0.314128\pi$
$42$	−6.07280	+	4.70360i	−0.937053	+	0.725781i
$43$	−3.71639	+	3.71639i	−0.566745	+	0.566745i	−0.931215	−	0.364470i	$-0.881250\pi$
$43$	−3.71639	+	3.71639i	−0.566745	+	0.566745i	0.364470	+	0.931215i	$0.381250\pi$
$44$	3.04265	−	2.21062i	0.458697	−	0.333263i
$45$		0			0
$46$	4.06882	+	2.95617i	0.599914	+	0.435863i
$47$	−5.10512	+	0.808572i	−0.744659	+	0.117942i	−0.517223	−	0.855851i	$-0.673034\pi$
$47$	−5.10512	+	0.808572i	−0.744659	+	0.117942i	−0.227436	+	0.973793i	$0.573034\pi$
$48$	0.484416	−	1.66293i	0.0699194	−	0.240023i
$49$			12.6676i			1.80965i
$50$		0			0
$51$	−0.488859	+	0.519837i	−0.0684540	+	0.0727917i
$52$	3.49677	−	1.78169i	0.484914	−	0.247076i
$53$	−1.29952	−	8.20487i	−0.178503	−	1.12703i	−0.900412	−	0.435037i	$-0.856735\pi$
$53$	−1.29952	−	8.20487i	−0.178503	−	1.12703i	0.721909	−	0.691988i	$-0.243265\pi$
$54$	5.03567	−	1.28143i	0.685267	−	0.174381i
$55$		0			0
$56$	−2.60672	−	3.58784i	−0.348337	−	0.479445i
$57$	−0.265855	−	8.65677i	−0.0352134	−	1.14662i
$58$	0.288689	−	1.82271i	0.0379068	−	0.239334i
$59$	−1.73564	−	5.34175i	−0.225961	−	0.695437i	−0.998193	−	0.0600956i	$-0.980859\pi$
$59$	−1.73564	−	5.34175i	−0.225961	−	0.695437i	0.772231	−	0.635341i	$-0.219141\pi$
$60$		0			0
$61$	4.43829	−	13.6596i	0.568264	−	1.74894i	−0.0897825	−	0.995961i	$-0.528617\pi$
$61$	4.43829	−	13.6596i	0.568264	−	1.74894i	0.658047	−	0.752977i	$-0.271383\pi$
$62$	−2.97152	−	1.51406i	−0.377383	−	0.192286i
$63$	5.30128	−	12.2026i	0.667899	−	1.53739i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$		0			0
$66$	−2.77779	+	5.89216i	−0.341922	+	0.725275i
$67$	6.11731	+	0.968887i	0.747349	+	0.118368i	0.518481	−	0.855089i	$-0.326498\pi$
$67$	6.11731	+	0.968887i	0.747349	+	0.118368i	0.228868	+	0.973458i	$0.426498\pi$
$68$	−0.291323	−	0.291323i	−0.0353281	−	0.0353281i
$69$	−8.64159	−	1.09796i	−1.04033	−	0.132179i
$70$		0			0
$71$	−0.992045	+	1.36543i	−0.117734	+	0.162047i	−0.863817	−	0.503806i	$-0.831932\pi$
$71$	−0.992045	+	1.36543i	−0.117734	+	0.162047i	0.746082	+	0.665854i	$0.231932\pi$
$72$	0.650243	+	2.92868i	0.0766319	+	0.345149i
$73$	1.62628	+	3.19175i	0.190342	+	0.373567i	0.966380	−	0.257120i	$-0.0827735\pi$
$73$	1.62628	+	3.19175i	0.190342	+	0.373567i	−0.776038	+	0.630686i	$0.782773\pi$
$74$	−5.28015			−0.613805
$75$		0			0
$76$	5.00034			0.573579
$77$	7.57211	+	14.8611i	0.862922	+	1.69358i
$78$	−3.82475	+	5.61931i	−0.433068	+	0.636262i
$79$	−6.24842	+	8.60021i	−0.703002	+	0.967599i	0.296918	+	0.954903i	$0.404041\pi$
$79$	−6.24842	+	8.60021i	−0.703002	+	0.967599i	−0.999919	+	0.0126959i	$0.995959\pi$
$80$		0			0
$81$	−6.57831	+	6.14214i	−0.730923	+	0.682460i
$82$	−2.41339	−	2.41339i	−0.266514	−	0.266514i
$83$	−7.00394	−	1.10932i	−0.768782	−	0.121763i	−0.240290	−	0.970701i	$-0.577243\pi$
$83$	−7.00394	−	1.10932i	−0.768782	−	0.121763i	−0.528493	+	0.848938i	$0.677243\pi$
$84$	6.94793	+	3.27552i	0.758081	+	0.357388i
$85$		0			0
$86$	4.99854	+	1.62412i	0.539006	+	0.175134i
$87$	1.08059	+	3.00819i	0.115851	+	0.322512i
$88$	−3.35101	−	1.70742i	−0.357219	−	0.182012i
$89$	0.324819	−	0.999689i	0.0344307	−	0.105967i	−0.932364	−	0.361521i	$-0.882258\pi$
$89$	0.324819	−	0.999689i	0.0344307	−	0.105967i	0.966795	+	0.255554i	$0.0822577\pi$
$90$		0			0
$91$	5.37828	+	16.5526i	0.563797	+	1.73519i
$92$	0.786761	−	4.96742i	0.0820255	−	0.517889i
$93$	5.77369	−	0.177314i	0.598704	−	0.0183866i
$94$	3.03812	+	4.18162i	0.313358	+	0.431301i
$95$		0			0
$96$	−1.70160	+	0.323338i	−0.173669	+	0.0330005i
$97$	1.20630	+	7.61627i	0.122481	+	0.773315i	0.970099	+	0.242709i	$0.0780359\pi$
$97$	1.20630	+	7.61627i	0.122481	+	0.773315i	−0.847618	+	0.530607i	$0.821964\pi$
$98$	11.2869	−	5.75096i	1.14015	−	0.580935i
$99$	−0.692350	−	11.2615i	−0.0695838	−	1.13182i
$100$		0			0
$101$			11.0847i			1.10297i	0.834184	+	0.551487i	$0.185939\pi$
$101$			11.0847i			1.10297i	−0.834184	+	0.551487i	$0.814061\pi$
$102$	0.685116	+	0.199576i	0.0678366	+	0.0197609i
$103$	−2.42213	+	0.383628i	−0.238660	+	0.0378000i	−0.274618	−	0.961553i	$-0.588552\pi$
$103$	−2.42213	+	0.383628i	−0.238660	+	0.0378000i	0.0359588	+	0.999353i	$0.488552\pi$
$104$	−3.17500	−	2.30677i	−0.311334	−	0.226197i
$105$		0			0
$106$	−6.72062	+	4.88282i	−0.652764	+	0.474261i
$107$	4.30681	−	4.30681i	0.416355	−	0.416355i	−0.467590	−	0.883945i	$-0.654878\pi$
$107$	4.30681	−	4.30681i	0.416355	−	0.416355i	0.883945	+	0.467590i	$0.154878\pi$
$108$	−3.42791	−	3.90505i	−0.329851	−	0.375764i
$109$	4.46242	−	1.44993i	0.427422	−	0.138878i	−0.0874029	−	0.996173i	$-0.527857\pi$
$109$	4.46242	−	1.44993i	0.427422	−	0.138878i	0.514825	+	0.857295i	$0.327857\pi$
$110$		0			0
$111$	8.01741	−	4.40015i	0.760979	−	0.417643i
$112$	−2.01336	+	3.95145i	−0.190245	+	0.373377i
$113$	−7.76223	+	15.2342i	−0.730209	+	1.43312i	0.164459	+	0.986384i	$0.447412\pi$
$113$	−7.76223	+	15.2342i	−0.730209	+	1.43312i	−0.894668	+	0.446732i	$0.852588\pi$
$114$	−7.59254	+	4.16697i	−0.711107	+	0.390272i
$115$		0			0
$116$	−1.75511	+	0.570270i	−0.162958	+	0.0529483i
$117$	1.12475	−	11.7197i	0.103983	−	1.08349i
$118$	−3.97157	+	3.97157i	−0.365613	+	0.365613i
$119$	1.47816	−	1.07395i	0.135503	−	0.0984487i
$120$		0			0
$121$	2.54399	+	1.84832i	0.231272	+	0.168029i
$122$	−14.1858	+	2.24681i	−1.28432	+	0.203416i
$123$	5.67567	+	1.65334i	0.511758	+	0.149076i
$124$			3.33501i			0.299493i
$125$		0			0
$126$	−13.2794	+	0.816407i	−1.18302	+	0.0727313i
$127$	17.4755	−	8.90421i	1.55070	−	0.790121i	0.551666	−	0.834065i	$-0.313992\pi$
$127$	17.4755	−	8.90421i	1.55070	−	0.790121i	0.999034	+	0.0439442i	$0.0139924\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	−8.94324	+	1.69939i	−0.787409	+	0.149623i
$130$		0			0
$131$	−12.0644	−	16.6052i	−1.05407	−	1.45080i	−0.885228	−	0.465158i	$-0.845998\pi$
$131$	−12.0644	−	16.6052i	−1.05407	−	1.45080i	−0.168841	−	0.985643i	$-0.554002\pi$
$132$	6.51104	−	0.199959i	0.566713	−	0.0174042i
$133$	−3.46903	+	21.9026i	−0.300803	+	1.89919i
$134$	−1.91392	−	5.89043i	−0.165337	−	0.508856i
$135$		0			0
$136$	−0.127313	+	0.391828i	−0.0109170	+	0.0335990i
$137$	−6.44062	−	3.28166i	−0.550259	−	0.280371i	0.156675	−	0.987650i	$-0.449922\pi$
$137$	−6.44062	−	3.28166i	−0.550259	−	0.280371i	−0.706935	+	0.707279i	$0.749922\pi$
$138$	2.94491	+	8.19818i	0.250687	+	0.697875i
$139$	9.21867	+	2.99533i	0.781918	+	0.254060i	0.672659	−	0.739953i	$-0.265152\pi$
$139$	9.21867	+	2.99533i	0.781918	+	0.254060i	0.109259	+	0.994013i	$0.465152\pi$
$140$		0			0
$141$	−8.09779	−	3.81760i	−0.681957	−	0.321500i
$142$	1.66699	+	0.264025i	0.139891	+	0.0221565i
$143$	10.4367	+	10.4367i	0.872765	+	0.872765i
$144$	2.31427	−	1.90897i	0.192856	−	0.159080i
$145$		0			0
$146$	2.10556	−	2.89805i	0.174257	−	0.239845i
$147$	−12.3456	+	18.1381i	−1.01825	+	1.49600i
$148$	2.39714	+	4.70465i	0.197044	+	0.386720i
$149$	4.14920			0.339915			0.169958	−	0.985451i	$-0.445637\pi$
$149$	4.14920			0.339915			0.169958	+	0.985451i	$0.445637\pi$
$150$		0			0
$151$	−9.50070			−0.773156			−0.386578	−	0.922257i	$-0.626343\pi$
$151$	−9.50070			−0.773156			−0.386578	+	0.922257i	$0.626343\pi$
$152$	−2.27011	−	4.45534i	−0.184130	−	0.361376i
$153$	−1.20660	+	0.267895i	−0.0975475	+	0.0216581i
$154$	9.80367	−	13.4936i	0.790002	−	1.08734i
$155$		0			0
$156$	6.74324	+	0.856768i	0.539892	+	0.0685963i
$157$	−2.98265	−	2.98265i	−0.238041	−	0.238041i	0.577997	−	0.816039i	$-0.303834\pi$
$157$	−2.98265	−	2.98265i	−0.238041	−	0.238041i	−0.816039	+	0.577997i	$0.803834\pi$
$158$	10.4996	+	1.66297i	0.835300	+	0.132299i
$159$	6.13559	−	13.0146i	0.486584	−	1.03213i
$160$		0			0
$161$	21.2125	+	6.89237i	1.67178	+	0.543195i
$162$	8.45917	+	3.07284i	0.664616	+	0.241425i
$163$	9.28593	+	4.73142i	0.727330	+	0.370593i	0.778119	−	0.628116i	$-0.216174\pi$
$163$	9.28593	+	4.73142i	0.727330	+	0.370593i	−0.0507896	+	0.998709i	$0.516174\pi$
$164$	−1.05469	+	3.24600i	−0.0823575	+	0.253470i
$165$		0			0
$166$	2.19132	+	6.74418i	0.170079	+	0.523450i
$167$	2.18995	−	13.8268i	0.169464	−	1.06995i	−0.745527	−	0.666476i	$-0.767802\pi$
$167$	2.18995	−	13.8268i	0.169464	−	1.06995i	0.914990	−	0.403476i	$-0.132198\pi$
$168$	−0.235788	−	7.67770i	−0.0181914	−	0.592348i
$169$	1.41174	+	1.94309i	0.108595	+	0.149469i
$170$		0			0
$171$	8.05606	−	12.6543i	0.616062	−	0.967697i
$172$	−0.822184	−	5.19107i	−0.0626910	−	0.395815i
$173$	6.24576	−	3.18237i	0.474856	−	0.241951i	−0.200147	−	0.979766i	$-0.564142\pi$
$173$	6.24576	−	3.18237i	0.474856	−	0.241951i	0.675003	+	0.737815i	$0.264142\pi$
$174$	2.18974	−	2.32850i	0.166004	−	0.176523i
$175$		0			0
$176$			3.76092i			0.283490i
$177$	2.72079	−	9.34011i	0.204507	−	0.702045i
$178$	−1.03819	+	0.164434i	−0.0778159	+	0.0123248i
$179$	2.28996	+	1.66375i	0.171159	+	0.124355i	0.670067	−	0.742301i	$-0.266265\pi$
$179$	2.28996	+	1.66375i	0.171159	+	0.124355i	−0.498908	+	0.866655i	$0.666265\pi$
$180$		0			0
$181$	−0.283169	+	0.205734i	−0.0210478	+	0.0152921i	−0.598259	−	0.801302i	$-0.704141\pi$
$181$	−0.283169	+	0.205734i	−0.0210478	+	0.0152921i	0.577212	+	0.816595i	$0.304141\pi$
$182$	12.3068	−	12.3068i	0.912243	−	0.912243i
$183$	19.6674	−	15.2331i	1.45386	−	1.12606i
$184$	−4.78318	+	1.55415i	−0.352621	+	0.114573i
$185$		0			0
$186$	−2.77919	−	5.06390i	−0.203780	−	0.371303i
$187$	0.703446	−	1.38059i	0.0514411	−	0.100959i
$188$	2.34657	−	4.60540i	0.171141	−	0.335883i
$189$	19.4831	−	12.3058i	1.41719	−	0.895117i
$190$		0			0
$191$	−1.07980	+	0.350849i	−0.0781318	+	0.0253866i	−0.347822	−	0.937561i	$-0.613079\pi$
$191$	−1.07980	+	0.350849i	−0.0781318	+	0.0253866i	0.269690	+	0.962947i	$0.413079\pi$
$192$	1.06061	+	1.36935i	0.0765428	+	0.0988241i
$193$	−4.16176	+	4.16176i	−0.299570	+	0.299570i	−0.840845	−	0.541275i	$-0.817942\pi$
$193$	−4.16176	+	4.16176i	−0.299570	+	0.299570i	0.541275	+	0.840845i	$0.317942\pi$
$194$	6.23850	−	4.53254i	0.447898	−	0.325417i
$195$		0			0
$196$	−10.2483	−	7.44581i	−0.732020	−	0.531844i
$197$	18.9787	−	3.00593i	1.35218	−	0.214164i	0.562048	−	0.827105i	$-0.310014\pi$
$197$	18.9787	−	3.00593i	1.35218	−	0.214164i	0.790129	+	0.612941i	$0.210014\pi$
$198$	−9.71976	+	5.72951i	−0.690753	+	0.407178i
$199$		−	12.7124i		−	0.901157i	−0.892737	−	0.450579i	$-0.851218\pi$
$199$		−	12.7124i		−	0.901157i	0.892737	−	0.450579i	$-0.148782\pi$
$200$		0			0
$201$	7.81481	+	7.34912i	0.551214	+	0.518367i
$202$	9.87658	−	5.03237i	0.694914	−	0.354076i
$203$	−1.28028	−	8.08340i	−0.0898583	−	0.567343i
$204$	−0.133213	−	0.701048i	−0.00932676	−	0.0490832i
$205$		0			0
$206$	1.44144	+	1.98397i	0.100430	+	0.138230i
$207$	−11.3034	−	9.99405i	−0.785641	−	0.694634i
$208$	−0.613929	+	3.87619i	−0.0425683	+	0.268766i
$209$	5.81135	+	17.8855i	0.401979	+	1.23716i
$210$		0			0
$211$	−5.38805	+	16.5827i	−0.370929	+	1.14160i	0.575255	+	0.817974i	$0.304903\pi$
$211$	−5.38805	+	16.5827i	−0.370929	+	1.14160i	−0.946184	+	0.323628i	$0.895097\pi$
$212$	7.40172	+	3.77136i	0.508352	+	0.259018i
$213$	−2.75118	+	0.988266i	−0.188508	+	0.0677149i
$214$	−5.79265	−	1.88215i	−0.395977	−	0.128661i
$215$		0			0
$216$	−1.92319	+	4.82715i	−0.130856	+	0.328446i
$217$	−14.6081	−	2.31369i	−0.991661	−	0.157064i
$218$	−3.31779	−	3.31779i	−0.224709	−	0.224709i
$219$	−0.782035	+	6.15505i	−0.0528450	+	0.415920i
$220$		0			0
$221$	0.950373	−	1.30808i	0.0639290	−	0.0879907i
$222$	−7.56039	−	5.14594i	−0.507420	−	0.345373i
$223$	−10.2765	−	20.1688i	−0.688167	−	1.35060i	−0.925341	−	0.379136i	$-0.876221\pi$
$223$	−10.2765	−	20.1688i	−0.688167	−	1.35060i	0.237174	−	0.971467i	$-0.423779\pi$
$224$	4.43481			0.296313
$225$		0			0
$226$	17.0978			1.13733
$227$	8.76566	+	17.2036i	0.581797	+	1.14184i	0.974962	+	0.222373i	$0.0713804\pi$
$227$	8.76566	+	17.2036i	0.581797	+	1.14184i	−0.393164	+	0.919468i	$0.628620\pi$
$228$	7.15974	+	4.87324i	0.474165	+	0.322738i
$229$	9.58051	−	13.1864i	0.633098	−	0.871384i	−0.365126	−	0.930958i	$-0.618974\pi$
$229$	9.58051	−	13.1864i	0.633098	−	0.871384i	0.998224	+	0.0595738i	$0.0189742\pi$
$230$		0			0
$231$	−3.64122	+	28.6585i	−0.239575	+	1.88559i
$232$	1.30492	+	1.30492i	0.0856721	+	0.0856721i
$233$	−0.601093	−	0.0952038i	−0.0393789	−	0.00623701i	0.136714	−	0.990611i	$-0.456346\pi$
$233$	−0.601093	−	0.0952038i	−0.0393789	−	0.00623701i	−0.176093	+	0.984374i	$0.556346\pi$
$234$	−10.9529	+	4.31847i	−0.716016	+	0.282307i
$235$		0			0
$236$	5.34175	+	1.73564i	0.347718	+	0.112981i
$237$	−17.3284	+	6.22461i	−1.12560	+	0.404332i
$238$	−1.62797	−	0.829491i	−0.105525	−	0.0537679i
$239$	2.47857	−	7.62825i	0.160325	−	0.493430i	−0.838336	−	0.545154i	$-0.816471\pi$
$239$	2.47857	−	7.62825i	0.160325	−	0.493430i	0.998661	+	0.0517231i	$0.0164713\pi$
$240$		0			0
$241$	−2.23962	−	6.89284i	−0.144267	−	0.444007i	0.852649	−	0.522484i	$-0.174994\pi$
$241$	−2.23962	−	6.89284i	−0.144267	−	0.444007i	−0.996916	+	0.0784767i	$0.974994\pi$
$242$	0.491916	−	3.10583i	0.0316215	−	0.199650i
$243$	−15.4052	+	2.38352i	−0.988241	+	0.152903i
$244$	8.44212	+	11.6196i	0.540452	+	0.743868i
$245$		0			0
$246$	−1.10357	−	5.80766i	−0.0703609	−	0.370283i
$247$	3.06986	+	19.3823i	0.195330	+	1.23327i
$248$	2.97152	−	1.51406i	0.188692	−	0.0961432i
$249$	−8.94747	−	8.41428i	−0.567023	−	0.533233i
$250$		0			0
$251$			14.5520i			0.918511i	0.888304	+	0.459256i	$0.151884\pi$
$251$			14.5520i			0.918511i	−0.888304	+	0.459256i	$0.848116\pi$
$252$	6.75613	+	11.4614i	0.425596	+	0.721998i
$253$	18.6821	−	2.95895i	1.17453	−	0.186028i
$254$	−15.8674	−	11.5284i	−0.995611	−	0.723353i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.03830	−	1.03830i	0.0647675	−	0.0647675i	−0.673981	−	0.738749i	$-0.735417\pi$
$257$	1.03830	−	1.03830i	0.0647675	−	0.0647675i	0.738749	+	0.673981i	$0.235417\pi$
$258$	5.57431	+	7.19698i	0.347042	+	0.448064i
$259$	−22.2704	+	7.23610i	−1.38382	+	0.449629i
$260$		0			0
$261$	−1.38449	+	5.36039i	−0.0856976	+	0.331800i
$262$	−9.31821	+	18.2880i	−0.575681	+	1.12984i
$263$	10.1330	−	19.8871i	0.624825	−	1.22629i	−0.334075	−	0.942546i	$-0.608424\pi$
$263$	10.1330	−	19.8871i	0.624825	−	1.22629i	0.958901	−	0.283743i	$-0.0915761\pi$
$264$	−3.13412	−	5.71060i	−0.192891	−	0.351463i
$265$		0			0
$266$	21.0902	−	6.85264i	1.29313	−	0.420162i
$267$	1.43937	−	1.11484i	0.0880880	−	0.0682272i
$268$	−4.37951	+	4.37951i	−0.267521	+	0.267521i
$269$	−20.2239	+	14.6936i	−1.23308	+	0.895882i	−0.997117	−	0.0758813i	$-0.975823\pi$
$269$	−20.2239	+	14.6936i	−1.23308	+	0.895882i	−0.235959	+	0.971763i	$0.575823\pi$
$270$		0			0
$271$	−13.1402	−	9.54690i	−0.798209	−	0.579933i	0.112179	−	0.993688i	$-0.464217\pi$
$271$	−13.1402	−	9.54690i	−0.798209	−	0.579933i	−0.910388	+	0.413755i	$0.864217\pi$
$272$	0.406920	−	0.0644499i	0.0246732	−	0.00390785i
$273$	−8.43100	+	28.9425i	−0.510268	+	1.75168i
$274$			7.22848i			0.436688i
$275$		0			0
$276$	5.96767	−	6.34583i	0.359212	−	0.381974i
$277$	6.13564	−	3.12626i	0.368655	−	0.187839i	−0.259842	−	0.965651i	$-0.583670\pi$
$277$	6.13564	−	3.12626i	0.368655	−	0.187839i	0.628497	+	0.777812i	$0.283670\pi$
$278$	−1.51633	−	9.57375i	−0.0909436	−	0.574195i
$279$	8.43986	+	5.37304i	0.505281	+	0.321676i
$280$		0			0
$281$	−14.3948	−	19.8128i	−0.858723	−	1.18193i	−0.981873	−	0.189542i	$-0.939300\pi$
$281$	−14.3948	−	19.8128i	−0.858723	−	1.18193i	0.123150	−	0.992388i	$-0.460700\pi$
$282$	0.274810	+	8.94834i	0.0163647	+	0.532866i
$283$	1.14551	−	7.23244i	0.0680933	−	0.429924i	−0.929966	−	0.367646i	$-0.880164\pi$
$283$	1.14551	−	7.23244i	0.0680933	−	0.429924i	0.998059	−	0.0622774i	$-0.0198363\pi$
$284$	−0.521549	−	1.60516i	−0.0309482	−	0.0952489i
$285$		0			0
$286$	4.56103	−	14.0374i	0.269699	−	0.830049i
$287$	−13.4865	−	6.87171i	−0.796083	−	0.405624i
$288$	−2.75156	−	1.19538i	−0.162137	−	0.0704384i
$289$	16.0065	+	5.20084i	0.941561	+	0.305932i
$290$		0			0
$291$	−5.69543	+	12.0810i	−0.333872	+	0.708200i
$292$	−3.53809	−	0.560378i	−0.207051	−	0.0327936i
$293$	1.14628	+	1.14628i	0.0669662	+	0.0669662i	0.739797	−	0.672830i	$-0.234922\pi$
$293$	1.14628	+	1.14628i	0.0669662	+	0.0669662i	−0.672830	+	0.739797i	$0.734922\pi$
$294$	21.7659	+	2.76548i	1.26941	+	0.161286i
$295$		0			0
$296$	3.10360	−	4.27173i	0.180393	−	0.248290i
$297$	9.98391	−	16.7995i	0.579325	−	0.974808i
$298$	−1.88370	−	3.69696i	−0.109120	−	0.214159i
$299$	19.7377			1.14146
$300$		0			0
$301$	23.3084			1.34347
$302$	4.31323	+	8.46519i	0.248198	+	0.487117i
$303$	−10.8030	+	15.8717i	−0.620615	+	0.911804i
$304$	−2.93913	+	4.04536i	−0.168571	+	0.232018i
$305$		0			0
$306$	0.786480	+	0.953463i	0.0449600	+	0.0545058i
$307$	8.29257	+	8.29257i	0.473282	+	0.473282i	0.902975	−	0.429693i	$-0.141378\pi$
$307$	8.29257	+	8.29257i	0.473282	+	0.473282i	−0.429693	+	0.902975i	$0.641378\pi$
$308$	−16.4737	−	2.60917i	−0.938673	−	0.148671i
$309$	−3.84200	−	1.81126i	−0.218564	−	0.103039i
$310$		0			0
$311$	−31.4637	−	10.2232i	−1.78414	−	0.579703i	−0.784937	−	0.619575i	$-0.787305\pi$
$311$	−31.4637	−	10.2232i	−1.78414	−	0.579703i	−0.999205	+	0.0398725i	$0.987305\pi$
$312$	−2.29798	−	6.39724i	−0.130098	−	0.362172i
$313$	−3.90255	−	1.98845i	−0.220585	−	0.112394i	0.340206	−	0.940351i	$-0.389503\pi$
$313$	−3.90255	−	1.98845i	−0.220585	−	0.112394i	−0.560791	+	0.827957i	$0.689503\pi$
$314$	−1.30346	+	4.01165i	−0.0735587	+	0.226391i
$315$		0			0
$316$	−3.28499	−	10.1102i	−0.184795	−	0.568740i
$317$	−4.38047	+	27.6572i	−0.246032	+	1.55338i	0.487131	+	0.873329i	$0.338043\pi$
$317$	−4.38047	+	27.6572i	−0.246032	+	1.55338i	−0.733163	+	0.680053i	$0.761957\pi$
$318$	−14.3816	+	0.441669i	−0.806481	+	0.0247676i
$319$	−4.07954	−	5.61501i	−0.228411	−	0.314380i
$320$		0			0
$321$	10.3640	−	1.96937i	0.578464	−	0.109919i
$322$	−3.48914	−	22.0296i	−0.194442	−	1.22766i
$323$	1.83557	−	0.935268i	0.102134	−	0.0520397i
$324$	−1.10246	−	8.93222i	−0.0612479	−	0.496235i
$325$		0			0
$326$		−	10.4218i		−	0.577212i
$327$	7.80259	+	2.27291i	0.431484	+	0.125692i
$328$	3.37103	−	0.533919i	0.186134	−	0.0294807i
$329$	18.5447	+	13.4735i	1.02240	+	0.742818i
$330$		0			0
$331$	7.75360	−	5.63332i	0.426176	−	0.309635i	−0.353942	−	0.935267i	$-0.615159\pi$
$331$	7.75360	−	5.63332i	0.426176	−	0.309635i	0.780118	+	0.625632i	$0.215159\pi$
$332$	5.01427	−	5.01427i	0.275194	−	0.275194i
$333$	15.7680	+	1.51327i	0.864082	+	0.0829264i
$334$	−13.3140	+	4.32598i	−0.728510	+	0.236707i
$335$		0			0
$336$	−6.73384	+	3.69569i	−0.367361	+	0.201617i
$337$	7.11185	−	13.9578i	0.387407	−	0.760329i	−0.612130	−	0.790757i	$-0.709687\pi$
$337$	7.11185	−	13.9578i	0.387407	−	0.760329i	0.999537	+	0.0304279i	$0.00968701\pi$
$338$	1.09039	−	2.14002i	0.0593095	−	0.116401i
$339$	−25.9613	+	14.2482i	−1.41003	+	0.773856i
$340$		0			0
$341$	−11.9289	+	3.87592i	−0.645983	+	0.209893i
$342$	−14.9324	−	1.43307i	−0.807453	−	0.0774917i
$343$	17.7729	−	17.7729i	0.959645	−	0.959645i
$344$	−4.25201	+	3.08927i	−0.229253	+	0.166562i
$345$		0			0
$346$	−5.67103	−	4.12024i	−0.304876	−	0.221506i
$347$	−36.4678	+	5.77593i	−1.95769	+	0.310068i	−0.957963	+	0.286891i	$0.907378\pi$
$347$	−36.4678	+	5.77593i	−1.95769	+	0.310068i	−0.999731	+	0.0231773i	$0.992622\pi$
$348$	−3.06883	−	0.893957i	−0.164507	−	0.0479211i
$349$		−	15.0145i		−	0.803705i	−0.915704	−	0.401853i	$-0.868366\pi$
$349$		−	15.0145i		−	0.803705i	0.915704	−	0.401853i	$-0.131634\pi$
$350$		0			0
$351$	13.0322	−	15.6847i	0.695610	−	0.837186i
$352$	3.35101	−	1.70742i	0.178609	−	0.0910060i
$353$	4.70953	+	29.7348i	0.250663	+	1.58263i	0.716392	+	0.697698i	$0.245792\pi$
$353$	4.70953	+	29.7348i	0.250663	+	1.58263i	−0.465729	+	0.884927i	$0.654208\pi$
$354$	−9.55731	+	1.81607i	−0.507965	+	0.0965233i
$355$		0			0
$356$	0.617842	+	0.850386i	0.0327456	+	0.0450704i
$357$	3.16316	−	0.0971428i	0.167412	−	0.00514134i
$358$	0.442795	−	2.79569i	0.0234024	−	0.147757i
$359$	−1.07807	−	3.31797i	−0.0568986	−	0.175116i	0.918568	−	0.395263i	$-0.129346\pi$
$359$	−1.07807	−	3.31797i	−0.0568986	−	0.175116i	−0.975467	+	0.220147i	$0.929346\pi$
$360$		0			0
$361$	−1.85517	+	5.70961i	−0.0976403	+	0.300506i
$362$	0.311866	+	0.158904i	0.0163913	+	0.00835180i
$363$	1.84128	+	5.12584i	0.0966420	+	0.269037i
$364$	−16.5526	−	5.37828i	−0.867594	−	0.281898i
$365$		0			0
$366$	−22.5016	−	10.6081i	−1.17618	−	0.554494i
$367$	−15.4679	−	2.44988i	−0.807418	−	0.127882i	−0.260939	−	0.965355i	$-0.584032\pi$
$367$	−15.4679	−	2.44988i	−0.807418	−	0.127882i	−0.546479	+	0.837473i	$0.684032\pi$
$368$	3.55628	+	3.55628i	0.185384	+	0.185384i
$369$	6.51539	+	7.89873i	0.339178	+	0.411191i
$370$		0			0
$371$	−21.6544	+	29.8047i	−1.12424	+	1.54738i
$372$	−3.25024	+	4.77524i	−0.168517	+	0.247585i
$373$	−2.89590	−	5.68352i	−0.149944	−	0.294282i	0.803801	−	0.594898i	$-0.202808\pi$
$373$	−2.89590	−	5.68352i	−0.149944	−	0.294282i	−0.953745	+	0.300616i	$0.902808\pi$
$374$	−1.54947			−0.0801213
$375$		0			0
$376$	−5.16876			−0.266558
$377$	−3.28799	−	6.45305i	−0.169340	−	0.332349i
$378$	−19.8097	−	11.7728i	−1.01890	−	0.605530i
$379$	−15.8374	+	21.7983i	−0.813510	+	1.11970i	0.177262	+	0.984164i	$0.443276\pi$
$379$	−15.8374	+	21.7983i	−0.813510	+	1.11970i	−0.990772	+	0.135537i	$0.956724\pi$
$380$		0			0
$381$	33.7002	+	4.28180i	1.72651	+	0.219363i
$382$	0.802829	+	0.802829i	0.0410763	+	0.0410763i
$383$	−29.5784	−	4.68475i	−1.51138	−	0.239380i	−0.654964	−	0.755660i	$-0.727316\pi$
$383$	−29.5784	−	4.68475i	−1.51138	−	0.239380i	−0.856420	+	0.516280i	$0.827316\pi$
$384$	0.738592	−	1.56668i	0.0376911	−	0.0799492i
$385$		0			0
$386$	5.59756	+	1.81876i	0.284908	+	0.0925723i
$387$	−14.4616	−	6.28264i	−0.735123	−	0.319365i
$388$	−6.87074	−	3.50082i	−0.348809	−	0.177727i
$389$	−3.57268	+	10.9956i	−0.181142	+	0.557497i	−0.999861	−	0.0166975i	$-0.994685\pi$
$389$	−3.57268	+	10.9956i	−0.181142	+	0.557497i	0.818719	+	0.574195i	$0.194685\pi$
$390$		0			0
$391$	−0.640299	−	1.97064i	−0.0323813	−	0.0996594i
$392$	−1.98165	+	12.5116i	−0.100088	+	0.631932i
$393$	−1.09127	−	35.5338i	−0.0550472	−	1.79244i
$394$	−11.2945	−	15.5455i	−0.569007	−	0.783170i
$395$		0			0
$396$	9.51771	+	6.05923i	0.478283	+	0.304488i
$397$	2.09608	+	13.2341i	0.105199	+	0.664203i	0.982781	+	0.184775i	$0.0591557\pi$
$397$	2.09608	+	13.2341i	0.105199	+	0.664203i	−0.877581	+	0.479427i	$0.840844\pi$
$398$	−11.3268	+	5.77130i	−0.567762	+	0.289289i
$399$	−26.3130	+	27.9803i	−1.31730	+	1.40077i
$400$		0			0
$401$		−	22.2904i		−	1.11313i	−0.830804	−	0.556565i	$-0.812119\pi$
$401$		−	22.2904i		−	1.11313i	0.830804	−	0.556565i	$-0.187881\pi$
$402$	3.00026	−	10.2995i	0.149639	−	0.513691i
$403$	−12.9272	+	2.04746i	−0.643948	+	0.101991i
$404$	−8.96775	−	6.51545i	−0.446162	−	0.324156i
$405$		0			0
$406$	−6.62112	+	4.81053i	−0.328601	+	0.238742i
$407$	−14.0419	+	14.0419i	−0.696032	+	0.696032i
$408$	−0.564161	+	0.436963i	−0.0279301	+	0.0216329i
$409$	13.3939	−	4.35194i	0.662285	−	0.215190i	0.0414620	−	0.999140i	$-0.486798\pi$
$409$	13.3939	−	4.35194i	0.662285	−	0.215190i	0.620823	+	0.783951i	$0.286798\pi$
$410$		0			0
$411$	−6.02376	−	10.9757i	−0.297130	−	0.541394i
$412$	1.11333	−	2.18504i	0.0548499	−	0.107649i
$413$	−11.3084	+	22.1939i	−0.556448	+	1.09209i
$414$	−3.77313	+	14.6086i	−0.185439	+	0.717974i
$415$		0			0
$416$	3.73243	−	1.21274i	0.182998	−	0.0594595i
$417$	10.2806	+	13.2732i	0.503441	+	0.649992i
$418$	13.2978	−	13.2978i	0.650416	−	0.650416i
$419$	4.58918	−	3.33423i	0.224196	−	0.162888i	−0.470017	−	0.882657i	$-0.655752\pi$
$419$	4.58918	−	3.33423i	0.224196	−	0.162888i	0.694213	+	0.719769i	$0.255752\pi$
$420$		0			0
$421$	5.16685	+	3.75393i	0.251817	+	0.182956i	0.706532	−	0.707682i	$-0.250259\pi$
$421$	5.16685	+	3.75393i	0.251817	+	0.182956i	−0.454715	+	0.890637i	$0.650259\pi$
$422$	17.2214	−	2.72761i	0.838327	−	0.132778i
$423$	−7.87425	−	13.3582i	−0.382859	−	0.649497i
$424$		−	8.30714i		−	0.403431i
$425$		0			0
$426$	2.12956	+	2.00266i	0.103178	+	0.0970292i
$427$	−56.7531	+	28.9171i	−2.74647	+	1.39940i
$428$	0.952804	+	6.01577i	0.0460555	+	0.290783i
$429$	4.77240	+	25.1153i	0.230413	+	1.21258i
$430$		0			0
$431$	−11.7415	−	16.1608i	−0.565568	−	0.778437i	0.426453	−	0.904510i	$-0.359763\pi$
$431$	−11.7415	−	16.1608i	−0.565568	−	0.778437i	−0.992021	+	0.126072i	$0.959763\pi$
$432$	5.17413	−	0.477906i	0.248940	−	0.0229932i
$433$	3.62919	−	22.9138i	0.174408	−	1.10117i	−0.732787	−	0.680458i	$-0.761781\pi$
$433$	3.62919	−	22.9138i	0.174408	−	1.10117i	0.907195	−	0.420710i	$-0.138219\pi$
$434$	4.57041	+	14.0663i	0.219387	+	0.675203i
$435$		0			0
$436$	−1.44993	+	4.46242i	−0.0694390	+	0.213711i
$437$	22.4074	+	11.4171i	1.07189	+	0.546156i
$438$	5.83923	−	2.09754i	0.279009	−	0.100224i
$439$	10.7777	+	3.50189i	0.514393	+	0.167136i	0.554699	−	0.832051i	$-0.312833\pi$
$439$	10.7777	+	3.50189i	0.514393	+	0.167136i	−0.0403065	+	0.999187i	$0.512833\pi$
$440$		0			0
$441$	−35.3540	+	13.9392i	−1.68352	+	0.663772i
$442$	−1.59696	−	0.252934i	−0.0759598	−	0.0120309i
$443$	−5.43418	−	5.43418i	−0.258186	−	0.258186i	0.566130	−	0.824316i	$-0.308440\pi$
$443$	−5.43418	−	5.43418i	−0.258186	−	0.258186i	−0.824316	+	0.566130i	$0.808440\pi$
$444$	−1.15272	+	9.07256i	−0.0547057	+	0.430565i
$445$		0			0
$446$	−13.3051	+	18.3129i	−0.630015	+	0.867141i
$447$	5.94102	+	4.04373i	0.281001	+	0.191262i
$448$	−2.01336	−	3.95145i	−0.0951225	−	0.186688i
$449$	−26.9459			−1.27165			−0.635827	−	0.771831i	$-0.719341\pi$
$449$	−26.9459			−1.27165			−0.635827	+	0.771831i	$0.719341\pi$
$450$		0			0
$451$	−12.8362			−0.604434
$452$	−7.76223	−	15.2342i	−0.365104	−	0.716558i
$453$	−13.6036	−	9.25920i	−0.639152	−	0.435035i
$454$	11.3490	−	15.6205i	0.532634	−	0.733108i
$455$		0			0
$456$	1.09163	−	8.59178i	0.0511205	−	0.402347i
$457$	−24.1951	−	24.1951i	−1.13180	−	1.13180i	−0.989878	−	0.141919i	$-0.954673\pi$
$457$	−24.1951	−	24.1951i	−1.13180	−	1.13180i	−0.141919	−	0.989878i	$-0.545327\pi$
$458$	−16.0987	−	2.54978i	−0.752241	−	0.119143i
$459$	−1.98875	−	0.792339i	−0.0928269	−	0.0369832i
$460$		0			0
$461$	35.3066	+	11.4718i	1.64439	+	0.534295i	0.977513	−	0.210873i	$-0.0676307\pi$
$461$	35.3066	+	11.4718i	1.64439	+	0.534295i	0.666877	+	0.745168i	$0.267631\pi$
$462$	27.1880	−	9.76632i	1.26490	−	0.454370i
$463$	−6.25735	−	3.18828i	−0.290804	−	0.148172i	0.302503	−	0.953149i	$-0.402178\pi$
$463$	−6.25735	−	3.18828i	−0.290804	−	0.148172i	−0.593307	+	0.804977i	$0.702178\pi$
$464$	0.570270	−	1.75511i	0.0264741	−	0.0814790i
$465$		0			0
$466$	0.188063	+	0.578799i	0.00871187	+	0.0268124i
$467$	4.48899	−	28.3424i	0.207726	−	1.31153i	−0.634718	−	0.772744i	$-0.718884\pi$
$467$	4.48899	−	28.3424i	0.207726	−	1.31153i	0.842444	−	0.538785i	$-0.181116\pi$
$468$	8.82032	+	7.79860i	0.407719	+	0.360490i
$469$	−16.1449	−	22.2215i	−0.745502	−	1.02609i
$470$		0			0
$471$	−1.36387	−	7.17753i	−0.0628438	−	0.330723i
$472$	−0.878638	−	5.54750i	−0.0404426	−	0.255344i
$473$	17.6121	−	8.97383i	0.809807	−	0.412617i
$474$	13.4131	+	12.6138i	0.616084	+	0.579371i
$475$		0			0
$476$			1.82711i			0.0837455i
$477$	21.4690	−	12.6554i	0.983000	−	0.579449i
$478$	−7.92207	+	1.25473i	−0.362347	+	0.0573901i
$479$	10.3928	+	7.55082i	0.474860	+	0.345006i	0.799332	−	0.600889i	$-0.205187\pi$
$479$	10.3928	+	7.55082i	0.474860	+	0.345006i	−0.324473	+	0.945895i	$0.605187\pi$
$480$		0			0
$481$	−16.7645	+	12.1801i	−0.764394	+	0.555365i
$482$	−5.12480	+	5.12480i	−0.233428	+	0.233428i
$483$	23.6560	+	30.5421i	1.07638	+	1.38972i
$484$	−2.99064	+	0.971718i	−0.135938	+	0.0441690i
$485$		0			0
$486$	9.11753	+	12.6440i	0.413580	+	0.573543i
$487$	−9.39682	+	18.4423i	−0.425810	+	0.835700i	0.574047	+	0.818822i	$0.305373\pi$
$487$	−9.39682	+	18.4423i	−0.425810	+	0.835700i	−0.999858	+	0.0168777i	$0.994627\pi$
$488$	6.52048	−	12.7972i	0.295168	−	0.579301i
$489$	8.68490	+	15.8246i	0.392745	+	0.715611i
$490$		0			0
$491$	26.5707	−	8.63333i	1.19912	−	0.389617i	0.359681	−	0.933075i	$-0.382886\pi$
$491$	26.5707	−	8.63333i	1.19912	−	0.389617i	0.839436	+	0.543459i	$0.182886\pi$
$492$	−4.67365	+	3.61991i	−0.210704	+	0.163198i
$493$	−0.537617	+	0.537617i	−0.0242131	+	0.0242131i
$494$	15.8761	−	11.5346i	0.714298	−	0.518968i
$495$		0			0
$496$	−2.69808	−	1.96027i	−0.121148	−	0.0880188i
$497$	7.39279	−	1.17090i	0.331612	−	0.0525221i
$498$	−3.43511	+	11.7923i	−0.153931	+	0.528424i
$499$		−	0.405848i		−	0.0181683i	−0.999959	−	0.00908413i	$-0.997108\pi$
$499$		−	0.405848i		−	0.0181683i	0.999959	−	0.00908413i	$-0.00289161\pi$
$500$		0			0
$501$	16.6110	−	17.6636i	0.742126	−	0.789153i
$502$	12.9659	−	6.60645i	0.578696	−	0.294860i
$503$	−0.948431	−	5.98816i	−0.0422885	−	0.266999i	0.957480	−	0.288498i	$-0.0931560\pi$
$503$	−0.948431	−	5.98816i	−0.0422885	−	0.266999i	−0.999769	+	0.0214995i	$0.993156\pi$
$504$	7.14493	−	11.2231i	0.318260	−	0.499917i
$505$		0			0
$506$	−11.1179	−	15.3025i	−0.494252	−	0.680280i
$507$	0.127697	+	4.15807i	0.00567123	+	0.184666i
$508$	−3.06818	+	19.3717i	−0.136129	+	0.859482i
$509$	−1.17675	−	3.62167i	−0.0521586	−	0.160528i	0.921584	−	0.388178i	$-0.126896\pi$
$509$	−1.17675	−	3.62167i	−0.0521586	−	0.160528i	−0.973743	+	0.227651i	$0.926896\pi$
$510$		0			0
$511$	4.90915	−	15.1088i	0.217168	−	0.668375i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	23.8677	−	10.2678i	1.05378	−	0.453332i
$514$	−1.39651	−	0.453755i	−0.0615976	−	0.0200143i
$515$		0			0
$516$	3.88187	−	8.23411i	0.170890	−	0.362487i
$517$	19.2000	+	3.04098i	0.844414	+	0.133742i
$518$	16.5580	+	16.5580i	0.727515	+	0.727515i
$519$	12.0445	+	1.53032i	0.528693	+	0.0671735i
$520$		0			0
$521$	1.70955	−	2.35299i	0.0748966	−	0.103086i	−0.769925	−	0.638134i	$-0.779706\pi$
$521$	1.70955	−	2.35299i	0.0748966	−	0.103086i	0.844822	+	0.535048i	$0.179706\pi$
$522$	5.40469	−	1.19998i	0.236557	−	0.0525217i
$523$	−4.02250	−	7.89460i	−0.175892	−	0.345207i	0.786183	−	0.617994i	$-0.212054\pi$
$523$	−4.02250	−	7.89460i	−0.175892	−	0.345207i	−0.962074	+	0.272787i	$0.912054\pi$
$524$	20.5251			0.896645
$525$		0			0
$526$	−22.3198			−0.973188
$527$	0.623784	+	1.22424i	0.0271724	+	0.0533289i
$528$	−3.66532	+	5.38508i	−0.159513	+	0.234355i
$529$	1.34851	−	1.85606i	0.0586307	−	0.0806982i
$530$		0			0
$531$	12.9985	−	10.7220i	0.564085	−	0.465295i
$532$	−15.6805	−	15.6805i	−0.679837	−	0.679837i
$533$	−13.2296	−	2.09537i	−0.573040	−	0.0907606i
$534$	−1.64679	−	0.776360i	−0.0712636	−	0.0335964i
$535$		0			0
$536$	5.89043	+	1.91392i	0.254428	+	0.0826686i
$537$	1.65741	+	4.61399i	0.0715227	+	0.199108i
$538$	22.2735	+	11.3489i	0.960280	+	0.489287i
$539$	14.7221	−	45.3100i	0.634127	−	1.95164i
$540$		0			0
$541$	−11.3923	−	35.0618i	−0.489792	−	1.50742i	−0.824919	−	0.565251i	$-0.808779\pi$
$541$	−11.3923	−	35.0618i	−0.489792	−	1.50742i	0.335128	−	0.942173i	$-0.391221\pi$
$542$	−2.54083	+	16.0422i	−0.109138	+	0.689071i
$543$	−0.605959	+	0.0186094i	−0.0260042	+	0.000798607i
$544$	−0.242163	−	0.333309i	−0.0103827	−	0.0142905i
$545$		0			0
$546$	29.6155	−	5.62752i	1.26743	−	0.240836i
$547$	−4.14971	−	26.2003i	−0.177429	−	1.12024i	−0.902221	−	0.431274i	$-0.858064\pi$
$547$	−4.14971	−	26.2003i	−0.177429	−	1.12024i	0.724792	−	0.688968i	$-0.241936\pi$
$548$	6.44062	−	3.28166i	0.275130	−	0.140186i
$549$	43.0066	−	2.64402i	1.83548	−	0.112844i
$550$		0			0
$551$		−	9.22780i		−	0.393118i
$552$	−8.36344	−	2.43629i	−0.355972	−	0.103695i
$553$	46.5636	−	7.37495i	1.98009	−	0.313615i
$554$	−5.57104	−	4.04760i	−0.236691	−	0.171966i
$555$		0			0
$556$	−7.84187	+	5.69745i	−0.332569	+	0.241626i
$557$	−20.9449	+	20.9449i	−0.887465	+	0.887465i	−0.994279	−	0.106814i	$-0.965935\pi$
$557$	−20.9449	+	20.9449i	−0.887465	+	0.887465i	0.106814	+	0.994279i	$0.465935\pi$
$558$	0.955798	−	9.95928i	0.0404622	−	0.421610i
$559$	19.6168	−	6.37389i	0.829703	−	0.269587i
$560$		0			0
$561$	2.35273	−	1.29123i	0.0993322	−	0.0545159i
$562$	−11.1182	+	21.8207i	−0.468993	+	0.920450i
$563$	−6.85128	+	13.4464i	−0.288747	+	0.566698i	−0.989126	−	0.147073i	$-0.953015\pi$
$563$	−6.85128	+	13.4464i	−0.288747	+	0.566698i	0.700378	+	0.713772i	$0.253015\pi$
$564$	7.84827	−	4.30732i	0.330472	−	0.181371i
$565$		0			0
$566$	−6.96420	+	2.26281i	−0.292727	+	0.0951128i
$567$	39.8899	+	1.36778i	1.67522	+	0.0574413i
$568$	−1.19343	+	1.19343i	−0.0500753	+	0.0500753i
$569$	−7.06373	+	5.13210i	−0.296127	+	0.215149i	−0.725921	−	0.687778i	$-0.758586\pi$
$569$	−7.06373	+	5.13210i	−0.296127	+	0.215149i	0.429794	+	0.902927i	$0.358586\pi$
$570$		0			0
$571$	19.6305	+	14.2624i	0.821513	+	0.596864i	0.917145	−	0.398553i	$-0.130487\pi$
$571$	19.6305	+	14.2624i	0.821513	+	0.596864i	−0.0956328	+	0.995417i	$0.530487\pi$
$572$	−14.5781	+	2.30894i	−0.609540	+	0.0965416i
$573$	−1.88805	−	0.549992i	−0.0788743	−	0.0229762i
$574$			15.1362i			0.631775i
$575$		0			0
$576$	0.184091	+	2.99435i	0.00767044	+	0.124764i
$577$	−32.6160	+	16.6187i	−1.35782	+	0.691845i	−0.972927	−	0.231114i	$-0.925763\pi$
$577$	−32.6160	+	16.6187i	−1.35782	+	0.691845i	−0.384896	+	0.922960i	$0.625763\pi$
$578$	−2.63283	−	16.6231i	−0.109511	−	0.691428i
$579$	−10.0150	+	1.90304i	−0.416209	+	0.0790877i
$580$		0			0
$581$	18.4849	+	25.4423i	0.766882	+	1.05552i
$582$	13.3499	−	0.409985i	0.553372	−	0.0169944i
$583$	−4.88741	+	30.8579i	−0.202416	+	1.27800i
$584$	1.10696	+	3.40687i	0.0458062	+	0.140977i
$585$		0			0
$586$	0.500941	−	1.54174i	0.0206937	−	0.0636887i
$587$	10.1304	+	5.16169i	0.418126	+	0.213046i	0.650379	−	0.759609i	$-0.274610\pi$
$587$	10.1304	+	5.16169i	0.418126	+	0.213046i	−0.232254	+	0.972655i	$0.574610\pi$
$588$	−7.41745	−	20.6491i	−0.305890	−	0.851553i
$589$	−15.8600	−	5.15324i	−0.653501	−	0.212335i
$590$		0			0
$591$	30.1042	+	14.1922i	1.23832	+	0.583791i
$592$	−5.21515	−	0.825998i	−0.214341	−	0.0339483i
$593$	16.4362	+	16.4362i	0.674952	+	0.674952i	0.958854	−	0.283901i	$-0.0916288\pi$
$593$	16.4362	+	16.4362i	0.674952	+	0.674952i	−0.283901	+	0.958854i	$0.591629\pi$
$594$	−19.5011	−	1.26890i	−0.800140	−	0.0520636i
$595$		0			0
$596$	−2.43884	+	3.35677i	−0.0998986	+	0.137499i
$597$	12.3893	−	18.2022i	0.507058	−	0.744968i
$598$	−8.96072	−	17.5864i	−0.366431	−	0.719162i
$599$	−16.9386			−0.692094			−0.346047	−	0.938217i	$-0.612476\pi$
$599$	−16.9386			−0.692094			−0.346047	+	0.938217i	$0.612476\pi$
$600$		0			0
$601$	−26.0220			−1.06146			−0.530730	−	0.847541i	$-0.678082\pi$
$601$	−26.0220			−1.06146			−0.530730	+	0.847541i	$0.678082\pi$
$602$	−10.5818	−	20.7679i	−0.431281	−	0.846437i
$603$	4.02732	+	18.1390i	0.164005	+	0.738677i
$604$	5.58437	−	7.68623i	0.227225	−	0.312748i
$605$		0			0
$606$	19.0462	+	2.41993i	0.773700	+	0.0983030i
$607$	29.4219	+	29.4219i	1.19420	+	1.19420i	0.975877	+	0.218322i	$0.0700583\pi$
$607$	29.4219	+	29.4219i	1.19420	+	1.19420i	0.218322	+	0.975877i	$0.429942\pi$
$608$	4.93878	+	0.782226i	0.200294	+	0.0317235i
$609$	6.04475	−	12.8219i	0.244946	−	0.519571i
$610$		0			0
$611$	19.2921	+	6.26837i	0.780473	+	0.253591i
$612$	0.492487	−	1.13362i	0.0199076	−	0.0458239i
$613$	−5.01575	−	2.55565i	−0.202584	−	0.103222i	0.349755	−	0.936841i	$-0.386265\pi$
$613$	−5.01575	−	2.55565i	−0.202584	−	0.103222i	−0.552339	+	0.833619i	$0.686265\pi$
$614$	3.62398	−	11.1535i	0.146252	−	0.450118i
$615$		0			0
$616$	5.15409	+	15.8627i	0.207664	+	0.639125i
$617$	5.57460	−	35.1967i	0.224425	−	1.41696i	−0.575960	−	0.817478i	$-0.695372\pi$
$617$	5.57460	−	35.1967i	0.224425	−	1.41696i	0.800385	−	0.599486i	$-0.204628\pi$
$618$	0.130384	+	4.24555i	0.00524480	+	0.170781i
$619$	−20.2991	−	27.9393i	−0.815889	−	1.12297i	−0.990388	−	0.138317i	$-0.955831\pi$
$619$	−20.2991	−	27.9393i	−0.815889	−	1.12297i	0.174499	−	0.984657i	$-0.444169\pi$
$620$		0			0
$621$	−6.44476	−	25.3261i	−0.258619	−	1.01630i
$622$	5.17530	+	32.6756i	0.207511	+	1.31017i
$623$	−4.15351	+	2.11632i	−0.166407	+	0.0847885i
$624$	−4.65672	+	4.95180i	−0.186418	+	0.198231i
$625$		0			0
$626$			4.37993i			0.175057i
$627$	−9.10988	+	31.2729i	−0.363814	+	1.24892i
$628$	4.16617	−	0.659856i	0.166248	−	0.0263311i
$629$	1.75992	+	1.27866i	0.0701727	+	0.0509835i
$630$		0			0
$631$	−6.95722	+	5.05472i	−0.276963	+	0.201225i	−0.717591	−	0.696464i	$-0.754755\pi$
$631$	−6.95722	+	5.05472i	−0.276963	+	0.201225i	0.440629	+	0.897689i	$0.354755\pi$
$632$	−7.51686	+	7.51686i	−0.299005	+	0.299005i
$633$	−23.8761	+	18.4929i	−0.948989	+	0.735026i
$634$	26.6314	−	8.65307i	1.05767	−	0.343657i
$635$		0			0
$636$	6.92265	+	12.6136i	0.274501	+	0.500162i
$637$	22.5697	−	44.2955i	0.894244	−	1.75505i
$638$	−3.15094	+	6.18406i	−0.124747	+	0.244829i
$639$	−4.90243	−	1.26620i	−0.193937	−	0.0500902i
$640$		0			0
$641$	12.9664	−	4.21305i	0.512144	−	0.166406i	−0.0415332	−	0.999137i	$-0.513224\pi$
$641$	12.9664	−	4.21305i	0.512144	−	0.166406i	0.553677	+	0.832732i	$0.313224\pi$
$642$	−6.45990	−	8.34036i	−0.254952	−	0.329168i
$643$	11.4059	−	11.4059i	0.449806	−	0.449806i	−0.445484	−	0.895290i	$-0.646968\pi$
$643$	11.4059	−	11.4059i	0.449806	−	0.449806i	0.895290	+	0.445484i	$0.146968\pi$
$644$	−18.0445	+	13.1101i	−0.711051	+	0.516609i
$645$		0			0
$646$	−1.66666	−	1.21090i	−0.0655739	−	0.0476422i
$647$	30.9551	−	4.90280i	1.21697	−	0.192749i	0.485263	−	0.874368i	$-0.338724\pi$
$647$	30.9551	−	4.90280i	1.21697	−	0.192749i	0.731707	+	0.681619i	$0.238724\pi$
$648$	−7.45816	+	5.03744i	−0.292984	+	0.197889i
$649$			21.1238i			0.829181i
$650$		0			0
$651$	−18.6617	−	17.5496i	−0.731409	−	0.687823i
$652$	−9.28593	+	4.73142i	−0.363665	+	0.185297i
$653$	−5.98789	−	37.8061i	−0.234324	−	1.47947i	−0.771626	−	0.636076i	$-0.780556\pi$
$653$	−5.98789	−	37.8061i	−0.234324	−	1.47947i	0.537302	−	0.843390i	$-0.319444\pi$
$654$	−1.51712	−	7.98404i	−0.0593242	−	0.312201i
$655$		0			0
$656$	−2.00614	−	2.76122i	−0.0783266	−	0.107807i
$657$	−7.11835	+	8.05095i	−0.277713	+	0.314098i
$658$	3.58587	−	22.6403i	0.139792	−	0.882610i
$659$	−6.33270	−	19.4901i	−0.246687	−	0.759225i	−0.995354	−	0.0962789i	$-0.969306\pi$
$659$	−6.33270	−	19.4901i	−0.246687	−	0.759225i	0.748667	−	0.662946i	$-0.230694\pi$
$660$		0			0
$661$	−13.4948	+	41.5327i	−0.524887	+	1.61544i	0.239652	+	0.970859i	$0.422967\pi$
$661$	−13.4948	+	41.5327i	−0.524887	+	1.61544i	−0.764539	+	0.644577i	$0.777033\pi$
$662$	−8.53939	−	4.35103i	−0.331893	−	0.169108i
$663$	2.63562	−	0.946752i	0.102359	−	0.0367688i
$664$	−6.74418	−	2.19132i	−0.261725	−	0.0850395i
$665$		0			0
$666$	−5.81020	−	14.7364i	−0.225141	−	0.571024i
$667$	−9.16704	−	1.45192i	−0.354949	−	0.0562184i
$668$	9.89891	+	9.89891i	0.383000	+	0.383000i
$669$	4.94171	−	38.8940i	0.191057	−	1.50373i
$670$		0			0
$671$	−31.7502	+	43.7004i	−1.22570	+	1.68703i
$672$	6.34998	+	4.32208i	0.244956	+	0.166728i
$673$	16.8283	+	33.0273i	0.648681	+	1.27311i	0.947792	+	0.318890i	$0.103310\pi$
$673$	16.8283	+	33.0273i	0.648681	+	1.27311i	−0.299110	+	0.954219i	$0.596690\pi$
$674$	−15.6652			−0.603401
$675$		0			0
$676$	−2.40180			−0.0923767
$677$	−18.9516	−	37.1946i	−0.728369	−	1.42951i	−0.896182	−	0.443686i	$-0.853670\pi$
$677$	−18.9516	−	37.1946i	−0.728369	−	1.42951i	0.167813	−	0.985819i	$-0.446330\pi$
$678$	24.4814	+	16.6632i	0.940204	+	0.639945i
$679$	20.1010	−	27.6666i	0.771404	−	1.06175i
$680$		0			0
$681$	−4.21517	+	33.1758i	−0.161526	+	1.27130i
$682$	8.86905	+	8.86905i	0.339614	+	0.339614i
$683$	50.2616	+	7.96066i	1.92321	+	0.304606i	0.997318	−	0.0731865i	$-0.0233168\pi$
$683$	50.2616	+	7.96066i	1.92321	+	0.304606i	0.925890	+	0.377793i	$0.123317\pi$
$684$	5.50230	+	13.9555i	0.210386	+	0.533601i
$685$		0			0
$686$	−23.9045	−	7.76703i	−0.912677	−	0.296547i
$687$	26.5691	−	9.54401i	1.01367	−	0.364127i
$688$	4.68293	+	2.38607i	0.178535	+	0.0909681i
$689$	−10.0744	+	31.0059i	−0.383805	+	1.18123i
$690$		0			0
$691$	−9.91187	−	30.5056i	−0.377065	−	1.16049i	−0.942075	−	0.335403i	$-0.891128\pi$
$691$	−9.91187	−	30.5056i	−0.377065	−	1.16049i	0.565010	−	0.825084i	$-0.308872\pi$
$692$	−1.09657	+	6.92347i	−0.0416854	+	0.263191i
$693$	−33.1437	+	37.4860i	−1.25902	+	1.42397i
$694$	21.7024	+	29.8708i	0.823813	+	1.13388i
$695$		0			0
$696$	0.596698	+	3.14020i	0.0226178	+	0.119029i
$697$	0.219971	+	1.38884i	0.00833198	+	0.0526061i
$698$	−13.3780	+	6.81642i	−0.506364	+	0.258005i
$699$	−0.767891	−	0.722131i	−0.0290443	−	0.0273135i
$700$		0			0
$701$			32.1785i			1.21536i	0.794180	+	0.607682i	$0.207900\pi$
$701$			32.1785i			1.21536i	−0.794180	+	0.607682i	$0.792100\pi$
$702$	−19.8917	−	4.49113i	−0.750762	−	0.169507i
$703$	−26.0775	+	4.13027i	−0.983533	+	0.155776i
$704$	−3.04265	−	2.21062i	−0.114674	−	0.0833157i
$705$		0			0
$706$	24.3558	−	17.6956i	0.916644	−	0.665981i
$707$	34.7605	−	34.7605i	1.30730	−	1.30730i
$708$	5.95706	+	7.69114i	0.223880	+	0.289051i
$709$	−2.62130	+	0.851713i	−0.0984451	+	0.0319867i	−0.357825	−	0.933789i	$-0.616482\pi$
$709$	−2.62130	+	0.851713i	−0.0984451	+	0.0319867i	0.259380	+	0.965775i	$0.416482\pi$
$710$		0			0
$711$	−30.8780	−	7.97521i	−1.15802	−	0.299094i
$712$	0.477205	−	0.936569i	0.0178840	−	0.0350994i
$713$	−7.61474	+	14.9448i	−0.285174	+	0.559686i
$714$	−1.52260	−	2.77429i	−0.0569818	−	0.103825i
$715$		0			0
$716$	−2.69201	+	0.874686i	−0.100605	+	0.0326886i
$717$	10.9833	−	8.50694i	0.410178	−	0.317697i
$718$	−2.46690	+	2.46690i	−0.0920639	+	0.0920639i
$719$	6.94235	−	5.04392i	0.258906	−	0.188106i	−0.450759	−	0.892646i	$-0.648846\pi$
$719$	6.94235	−	5.04392i	0.258906	−	0.188106i	0.709665	+	0.704540i	$0.248846\pi$
$720$		0			0
$721$	8.79854	+	6.39251i	0.327675	+	0.238070i
$722$	5.92953	−	0.939145i	0.220674	−	0.0349514i
$723$	3.51083	−	12.0522i	0.130569	−	0.448226i
$724$		−	0.350016i		−	0.0130082i
$725$		0			0
$726$	3.73123	−	3.96767i	0.138479	−	0.147254i
$727$	30.4942	−	15.5376i	1.13097	−	0.576257i	0.214644	−	0.976692i	$-0.431141\pi$
$727$	30.4942	−	15.5376i	1.13097	−	0.576257i	0.916325	+	0.400435i	$0.131141\pi$
$728$	2.72266	+	17.1902i	0.100909	+	0.637111i
$729$	−24.3808	−	11.6007i	−0.902992	−	0.429656i
$730$		0			0
$731$	−1.27276	−	1.75180i	−0.0470746	−	0.0647926i
$732$	0.763622	+	24.8650i	0.0282243	+	0.919038i
$733$	6.22770	−	39.3201i	0.230025	−	1.45232i	−0.554478	−	0.832198i	$-0.687082\pi$
$733$	6.22770	−	39.3201i	0.230025	−	1.45232i	0.784504	−	0.620124i	$-0.212918\pi$
$734$	4.83943	+	14.8942i	0.178627	+	0.549756i
$735$		0			0
$736$	1.55415	−	4.78318i	0.0572867	−	0.176310i
$737$	−20.7547	−	10.5750i	−0.764509	−	0.389537i
$738$	4.07989	−	9.39121i	0.150183	−	0.345695i
$739$	19.6010	+	6.36874i	0.721033	+	0.234278i	0.646471	−	0.762939i	$-0.276244\pi$
$739$	19.6010	+	6.36874i	0.721033	+	0.234278i	0.0745620	+	0.997216i	$0.476244\pi$
$740$		0			0
$741$	−14.4941	+	30.7444i	−0.532452	+	1.12942i
$742$	36.3871	+	5.76314i	1.33581	+	0.211572i
$743$	−25.7253	−	25.7253i	−0.943771	−	0.943771i	0.0547306	−	0.998501i	$-0.482570\pi$
$743$	−25.7253	−	25.7253i	−0.943771	−	0.943771i	−0.998501	+	0.0547306i	$0.982570\pi$
$744$	5.73035	+	0.728073i	0.210085	+	0.0266925i
$745$		0			0
$746$	−3.74935	+	5.16053i	−0.137273	+	0.188940i
$747$	−4.61103	−	20.7680i	−0.168709	−	0.759862i
$748$	0.703446	+	1.38059i	0.0257205	+	0.0504794i
$749$	−27.0114			−0.986973
$750$		0			0
$751$	−13.8571			−0.505654			−0.252827	−	0.967511i	$-0.581360\pi$
$751$	−13.8571			−0.505654			−0.252827	+	0.967511i	$0.581360\pi$
$752$	2.34657	+	4.60540i	0.0855705	+	0.167942i
$753$	−14.1821	+	20.8362i	−0.516823	+	0.759314i
$754$	−4.25699	+	5.85925i	−0.155031	+	0.213381i
$755$		0			0
$756$	−1.49626	+	22.9953i	−0.0544186	+	0.836332i
$757$	28.7075	+	28.7075i	1.04339	+	1.04339i	0.999015	+	0.0443764i	$0.0141301\pi$
$757$	28.7075	+	28.7075i	1.04339	+	1.04339i	0.0443764	+	0.999015i	$0.485870\pi$
$758$	26.6124	+	4.21499i	0.966606	+	0.153095i
$759$	29.6336	+	13.9704i	1.07563	+	0.507094i
$760$		0			0
$761$	−36.3818	−	11.8212i	−1.31884	−	0.428517i	−0.436744	−	0.899586i	$-0.643868\pi$
$761$	−36.3818	−	11.8212i	−1.31884	−	0.428517i	−0.882096	+	0.471069i	$0.843868\pi$
$762$	−11.4844	−	31.9710i	−0.416037	−	1.15819i
$763$	−18.5405	−	9.44684i	−0.671210	−	0.341998i
$764$	0.350849	−	1.07980i	0.0126933	−	0.0390659i
$765$		0			0
$766$	9.25415	+	28.4814i	0.334366	+	1.02907i
$767$	−3.44822	+	21.7712i	−0.124508	+	0.786114i
$768$	−1.73123	+	0.0531674i	−0.0624705	+	0.00191851i
$769$	23.2438	+	31.9924i	0.838194	+	1.15368i	0.986342	+	0.164710i	$0.0526688\pi$
$769$	23.2438	+	31.9924i	0.838194	+	1.15368i	−0.148148	+	0.988965i	$0.547331\pi$
$770$		0			0
$771$	2.49860	−	0.474783i	0.0899850	−	0.0170989i
$772$	−0.920714	−	5.81316i	−0.0331372	−	0.209220i
$773$	32.0052	−	16.3075i	1.15115	−	0.586539i	0.229019	−	0.973422i	$-0.426448\pi$
$773$	32.0052	−	16.3075i	1.15115	−	0.586539i	0.922129	+	0.386883i	$0.126448\pi$
$774$	0.967539	+	15.7376i	0.0347775	+	0.565677i
$775$		0			0
$776$			7.71121i			0.276816i
$777$	−38.9400	−	11.3433i	−1.39697	−	0.406939i
$778$	11.4191	−	1.80860i	0.409394	−	0.0648416i
$779$	−13.8070	−	10.0314i	−0.494688	−	0.359412i
$780$		0			0
$781$	5.13529	−	3.73101i	0.183755	−	0.133506i
$782$	−1.46516	+	1.46516i	−0.0523940	+	0.0523940i
$783$	−7.20652	+	6.32598i	−0.257540	+	0.226072i
$784$	12.0476	−	3.91450i	0.430271	−	0.139803i
$785$		0			0
$786$	−31.1654	+	17.1043i	−1.11163	+	0.610092i
$787$	13.0206	−	25.5543i	0.464133	−	0.910913i	−0.533735	−	0.845652i	$-0.679212\pi$
$787$	13.0206	−	25.5543i	0.464133	−	0.910913i	0.997868	−	0.0652610i	$-0.0207880\pi$
$788$	−8.72355	+	17.1209i	−0.310764	+	0.609908i
$789$	33.8904	−	18.5999i	1.20653	−	0.662173i
$790$		0			0
$791$	72.1143	−	23.4314i	2.56409	−	0.833123i
$792$	1.07786	−	11.2312i	0.0383001	−	0.399082i
$793$	−39.8569	+	39.8569i	−1.41536	+	1.41536i
$794$	10.8401	−	7.87580i	0.384701	−	0.279502i
$795$		0			0
$796$	10.2845	+	7.47216i	0.364526	+	0.264844i
$797$	9.56827	−	1.51547i	0.338926	−	0.0536805i	0.0153481	−	0.999882i	$-0.495114\pi$
$797$	9.56827	−	1.51547i	0.338926	−	0.0536805i	0.323578	+	0.946202i	$0.395114\pi$
$798$	36.8765	+	10.7422i	1.30541	+	0.380270i
$799$		−	2.12949i		−	0.0753360i
$800$		0			0
$801$	3.14746	−	0.193504i	0.111210	−	0.00683713i
$802$	−19.8609	+	10.1196i	−0.701313	+	0.357337i
$803$	−2.10754	−	13.3065i	−0.0743734	−	0.469575i
$804$	−10.5390	+	2.00261i	−0.371682	+	0.0706267i
$805$		0			0
$806$	7.69311	+	10.5887i	0.270978	+	0.372970i
$807$	−43.2777	+	1.32909i	−1.52345	+	0.0467861i
$808$	−1.73404	+	10.9483i	−0.0610032	+	0.385159i
$809$	−17.2607	−	53.1231i	−0.606855	−	1.86771i	−0.483496	−	0.875346i	$-0.660633\pi$
$809$	−17.2607	−	53.1231i	−0.606855	−	1.86771i	−0.123359	−	0.992362i	$-0.539367\pi$
$810$		0			0
$811$	−6.13462	+	18.8804i	−0.215416	+	0.662981i	0.783708	+	0.621129i	$0.213326\pi$
$811$	−6.13462	+	18.8804i	−0.215416	+	0.662981i	−0.999124	+	0.0418519i	$0.986674\pi$
$812$	7.29214	+	3.71553i	0.255904	+	0.130390i
$813$	−9.51053	−	26.4759i	−0.333549	−	0.928550i
$814$	18.8863	+	6.13654i	0.661965	+	0.215086i
$815$		0			0
$816$	0.645460	+	0.304294i	0.0225956	+	0.0106524i
$817$	25.9571	+	4.11120i	0.908125	+	0.143833i
$818$	−9.95831	−	9.95831i	−0.348184	−	0.348184i
$819$	−40.2787	+	33.2245i	−1.40745	+	1.16096i
$820$		0			0
$821$	22.0314	−	30.3236i	0.768899	−	1.05830i	−0.227522	−	0.973773i	$-0.573062\pi$
$821$	22.0314	−	30.3236i	0.768899	−	1.05830i	0.996421	−	0.0845263i	$-0.0269377\pi$
$822$	−7.04474	+	10.3501i	−0.245713	+	0.361001i
$823$	17.9173	+	35.1647i	0.624559	+	1.22577i	0.959015	+	0.283355i	$0.0914474\pi$
$823$	17.9173	+	35.1647i	0.624559	+	1.22577i	−0.334456	+	0.942411i	$0.608553\pi$
$824$	−2.45232			−0.0854307
$825$		0			0
$826$	24.9088			0.866688
$827$	−11.4419	−	22.4561i	−0.397875	−	0.780874i	0.601969	−	0.798519i	$-0.294383\pi$
$827$	−11.4419	−	22.4561i	−0.397875	−	0.780874i	−0.999844	+	0.0176456i	$0.994383\pi$
$828$	14.7293	−	3.27029i	0.511880	−	0.113650i
$829$	−22.7111	+	31.2592i	−0.788791	+	1.08568i	0.205467	+	0.978664i	$0.434129\pi$
$829$	−22.7111	+	31.2592i	−0.788791	+	1.08568i	−0.994258	+	0.107013i	$0.965871\pi$
$830$		0			0
$831$	11.8321	+	1.50334i	0.410451	+	0.0521502i
$832$	−2.77505	−	2.77505i	−0.0962075	−	0.0962075i
$833$	−5.15469	−	0.816423i	−0.178600	−	0.0282874i
$834$	7.15923	−	15.1860i	0.247904	−	0.525847i
$835$		0			0
$836$	−17.8855	−	5.81135i	−0.618582	−	0.200990i
$837$	6.84815	+	15.9187i	0.236707	+	0.550231i
$838$	−5.05427	−	2.57528i	−0.174597	−	0.0889615i
$839$	−1.11037	+	3.41736i	−0.0383342	+	0.117980i	−0.968392	−	0.249432i	$-0.919756\pi$
$839$	−1.11037	+	3.41736i	−0.0383342	+	0.117980i	0.930058	+	0.367412i	$0.119756\pi$
$840$		0			0
$841$	−7.90910	−	24.3417i	−0.272727	−	0.839369i
$842$	0.999080	−	6.30794i	0.0344306	−	0.217386i
$843$	−1.30207	−	42.3978i	−0.0448455	−	1.46026i
$844$	−10.2487	−	14.1061i	−0.352774	−	0.485552i
$845$		0			0
$846$	−8.32739	+	13.0805i	−0.286302	+	0.449717i
$847$	−2.18155	−	13.7738i	−0.0749591	−	0.473273i
$848$	−7.40172	+	3.77136i	−0.254176	+	0.129509i
$849$	8.68879	−	9.23937i	0.298198	−	0.317095i
$850$		0			0
$851$			26.5557i			0.910317i
$852$	0.817581	−	2.80664i	0.0280099	−	0.0961540i
$853$	−44.8288	+	7.10018i	−1.53491	+	0.243106i	−0.865926	−	0.500172i	$-0.833270\pi$
$853$	−44.8288	+	7.10018i	−1.53491	+	0.243106i	−0.668983	+	0.743278i	$0.733270\pi$
$854$	51.5307	+	37.4393i	1.76334	+	1.28114i
$855$		0			0
$856$	4.92752	−	3.58005i	0.168419	−	0.122364i
$857$	−5.49063	+	5.49063i	−0.187556	+	0.187556i	−0.794639	−	0.607082i	$-0.792340\pi$
$857$	−5.49063	+	5.49063i	−0.187556	+	0.187556i	0.607082	+	0.794639i	$0.292340\pi$
$858$	20.2113	−	15.6543i	0.690002	−	0.534431i
$859$	10.7387	−	3.48922i	0.366400	−	0.119051i	−0.120030	−	0.992770i	$-0.538299\pi$
$859$	10.7387	−	3.48922i	0.366400	−	0.119051i	0.486430	+	0.873720i	$0.338299\pi$
$860$		0			0
$861$	−12.6136	−	22.9829i	−0.429870	−	0.783256i
$862$	−9.06883	+	17.7986i	−0.308886	+	0.606222i
$863$	−5.28199	+	10.3665i	−0.179801	+	0.352880i	−0.963263	−	0.268560i	$-0.913452\pi$
$863$	−5.28199	+	10.3665i	−0.179801	+	0.352880i	0.783462	+	0.621440i	$0.213452\pi$
$864$	−2.77482	−	4.39322i	−0.0944014	−	0.149460i
$865$		0			0
$866$	−22.0640	+	7.16903i	−0.749765	+	0.243613i
$867$	17.8503	+	23.0465i	0.606228	+	0.782699i
$868$	10.4582	−	10.4582i	0.354975	−	0.354975i
$869$	32.3447	−	23.4998i	1.09722	−	0.797177i
$870$		0			0
$871$	−19.6646	−	14.2871i	−0.666308	−	0.484101i
$872$	4.63430	−	0.734001i	0.156937	−	0.0248564i
$873$	−19.9289	+	11.7475i	−0.674491	+	0.397592i
$874$		−	25.1484i		−	0.850658i
$875$		0			0
$876$	−4.51987	−	4.25053i	−0.152712	−	0.143612i
$877$	−22.0344	+	11.2271i	−0.744049	+	0.379112i	−0.784548	−	0.620068i	$-0.787105\pi$
$877$	−22.0344	+	11.2271i	−0.744049	+	0.379112i	0.0404992	+	0.999180i	$0.487105\pi$
$878$	−1.77277	−	11.1928i	−0.0598282	−	0.377740i
$879$	0.524156	+	2.75844i	0.0176794	+	0.0930397i
$880$		0			0
$881$	−7.08613	−	9.75322i	−0.238738	−	0.328594i	0.672790	−	0.739834i	$-0.265096\pi$
$881$	−7.08613	−	9.75322i	−0.238738	−	0.328594i	−0.911527	+	0.411240i	$0.865096\pi$
$882$	28.4703	+	25.1724i	0.958645	+	0.847598i
$883$	−1.11758	+	7.05614i	−0.0376097	+	0.237458i	−0.999331	−	0.0365710i	$-0.988356\pi$
$883$	−1.11758	+	7.05614i	−0.0376097	+	0.237458i	0.961721	+	0.274029i	$0.0883565\pi$
$884$	0.499640	+	1.53774i	0.0168047	+	0.0517196i
$885$		0			0
$886$	−2.37482	+	7.30895i	−0.0797837	+	0.245549i
$887$	3.17069	+	1.61555i	0.106461	+	0.0542448i	0.506410	−	0.862293i	$-0.330972\pi$
$887$	3.17069	+	1.61555i	0.106461	+	0.0542448i	−0.399949	+	0.916537i	$0.630972\pi$
$888$	8.60703	−	3.09177i	0.288833	−	0.103753i
$889$	−82.7238	−	26.8786i	−2.77447	−	0.901479i
$890$		0			0
$891$	30.6680	−	14.3243i	1.02742	−	0.479881i
$892$	22.3573	+	3.54105i	0.748578	+	0.118563i
$893$	18.2756	+	18.2756i	0.611569	+	0.611569i
$894$	0.905819	−	7.12930i	0.0302951	−	0.238440i
$895$		0			0
$896$	−2.60672	+	3.58784i	−0.0870843	+	0.119861i
$897$	28.2614	+	19.2360i	0.943620	+	0.642270i
$898$	12.2332	+	24.0090i	0.408226	+	0.801189i
$899$	6.15455			0.205266
$900$		0			0
$901$	3.42248			0.114019
$902$	5.82752	+	11.4372i	0.194035	+	0.380816i
$903$	33.3741	+	22.7159i	1.11062	+	0.755938i
$904$	−10.0498	+	13.8324i	−0.334252	+	0.460058i
$905$		0			0
$906$	−2.07412	+	16.3245i	−0.0689079	+	0.542344i
$907$	−1.89862	−	1.89862i	−0.0630427	−	0.0630427i	0.674883	−	0.737925i	$-0.264194\pi$
$907$	−1.89862	−	1.89862i	−0.0630427	−	0.0630427i	−0.737925	+	0.674883i	$0.764194\pi$
$908$	−19.0703	−	3.02044i	−0.632871	−	0.100237i
$909$	−30.9365	+	12.1975i	−1.02610	+	0.404565i
$910$		0			0
$911$	−2.38886	−	0.776187i	−0.0791464	−	0.0257162i	0.269176	−	0.963091i	$-0.413249\pi$
$911$	−2.38886	−	0.776187i	−0.0791464	−	0.0257162i	−0.348323	+	0.937375i	$0.613249\pi$
$912$	−8.15092	+	2.92793i	−0.269904	+	0.0969535i
$913$	23.7628	+	12.1078i	0.786435	+	0.400708i
$914$	−10.5736	+	32.5423i	−0.349744	+	1.07640i
$915$		0			0
$916$	5.03677	+	15.5016i	0.166420	+	0.512187i
$917$	−14.2395	+	89.9045i	−0.470229	+	2.96891i
$918$	0.196894	+	2.13170i	0.00649846	+	0.0703567i
$919$	−5.62589	−	7.74338i	−0.185581	−	0.255430i	0.706082	−	0.708130i	$-0.250461\pi$
$919$	−5.62589	−	7.74338i	−0.185581	−	0.255430i	−0.891663	+	0.452700i	$0.850461\pi$
$920$		0			0
$921$	3.79193	+	19.9555i	0.124948	+	0.657555i
$922$	−5.80740	−	36.6665i	−0.191256	−	1.20755i
$923$	5.90173	−	3.00708i	0.194258	−	0.0989793i
$924$	−21.0449	−	19.7908i	−0.692328	−	0.651071i
$925$		0			0
$926$			7.02279i			0.230783i
$927$	−3.73594	−	6.33780i	−0.122704	−	0.208161i
$928$	−1.82271	+	0.288689i	−0.0598335	+	0.00947670i
$929$	−28.0139	−	20.3533i	−0.919106	−	0.667770i	0.0241953	−	0.999707i	$-0.492298\pi$
$929$	−28.0139	−	20.3533i	−0.919106	−	0.667770i	−0.943301	+	0.331938i	$0.892298\pi$
$930$		0			0
$931$	51.2449	−	37.2316i	1.67949	−	1.22022i
$932$	0.430335	−	0.430335i	0.0140961	−	0.0140961i
$933$	−35.0879	−	45.3019i	−1.14873	−	1.48312i
$934$	−27.2912	+	8.86745i	−0.892995	+	0.290152i
$935$		0			0
$936$	2.94426	−	11.3995i	0.0962362	−	0.372603i
$937$	−6.94494	+	13.6302i	−0.226881	+	0.445280i	−0.976183	−	0.216949i	$-0.930389\pi$
$937$	−6.94494	+	13.6302i	−0.226881	+	0.445280i	0.749302	+	0.662229i	$0.230389\pi$
$938$	−12.4699	+	24.4736i	−0.407157	+	0.799090i
$939$	−3.64996	−	6.65050i	−0.119112	−	0.217031i
$940$		0			0
$941$	27.0255	−	8.78112i	0.881006	−	0.286256i	0.166631	−	0.986019i	$-0.446711\pi$
$941$	27.0255	−	8.78112i	0.881006	−	0.286256i	0.714375	+	0.699763i	$0.246711\pi$
$942$	−5.77604	+	4.47375i	−0.188194	+	0.145763i
$943$	−12.1378	+	12.1378i	−0.395260	+	0.395260i
$944$	−4.54397	+	3.30138i	−0.147893	+	0.107451i
$945$		0			0
$946$	−15.9915	−	11.6185i	−0.519928	−	0.377750i
$947$	37.1437	−	5.88298i	1.20701	−	0.191171i	0.479669	−	0.877450i	$-0.340757\pi$
$947$	37.1437	−	5.88298i	1.20701	−	0.191171i	0.727339	+	0.686279i	$0.240757\pi$
$948$	5.14955	−	17.6777i	0.167250	−	0.574145i
$949$		−	14.0583i		−	0.456353i
$950$		0			0
$951$	−33.2263	+	35.3318i	−1.07744	+	1.14571i
$952$	1.62797	−	0.829491i	0.0527627	−	0.0268840i
$953$	−4.16742	−	26.3120i	−0.134996	−	0.852331i	−0.958515	−	0.285042i	$-0.907992\pi$
$953$	−4.16742	−	26.3120i	−0.134996	−	0.852331i	0.823519	−	0.567289i	$-0.192008\pi$
$954$	−21.0227	−	13.3836i	−0.680636	−	0.433311i
$955$		0			0
$956$	4.71452	+	6.48898i	0.152478	+	0.209868i
$957$	−0.369010	−	12.0157i	−0.0119284	−	0.388412i
$958$	2.00959	−	12.6881i	0.0649269	−	0.409933i
$959$	9.90614	+	30.4880i	0.319886	+	0.984508i
$960$		0			0
$961$	−6.14254	+	18.9048i	−0.198146	+	0.609832i
$962$	18.4635	+	9.40760i	0.595286	+	0.303313i
$963$	16.7591	+	7.28076i	0.540053	+	0.234619i
$964$	6.89284	+	2.23962i	0.222003	+	0.0721333i
$965$		0			0
$966$	16.4737	−	34.9435i	0.530032	−	1.12429i
$967$	−41.4802	−	6.56982i	−1.33391	−	0.211271i	−0.551576	−	0.834125i	$-0.685973\pi$
$967$	−41.4802	−	6.56982i	−1.33391	−	0.211271i	−0.782339	+	0.622853i	$0.785973\pi$
$968$	2.22353	+	2.22353i	0.0714670	+	0.0714670i
$969$	3.53975	+	0.449746i	0.113713	+	0.0144479i
$970$		0			0
$971$	8.52779	−	11.7375i	0.273670	−	0.376674i	−0.649955	−	0.759973i	$-0.725212\pi$
$971$	8.52779	−	11.7375i	0.273670	−	0.376674i	0.923624	+	0.383299i	$0.125212\pi$
$972$	7.12661	−	13.8640i	0.228586	−	0.444689i
$973$	−19.5157	−	38.3017i	−0.625645	−	1.22790i
$974$	20.6983			0.663215
$975$		0			0
$976$	−14.3626			−0.459736
$977$	−0.545186	−	1.06999i	−0.0174420	−	0.0342319i	0.882121	−	0.471023i	$-0.156115\pi$
$977$	−0.545186	−	1.06999i	−0.0174420	−	0.0342319i	−0.899563	+	0.436791i	$0.856115\pi$
$978$	10.1569	−	14.9225i	0.324783	−	0.477169i
$979$	−2.32366	+	3.19824i	−0.0742644	+	0.102216i
$980$		0			0
$981$	8.95699	+	10.8587i	0.285975	+	0.346692i
$982$	−19.7552	−	19.7552i	−0.630413	−	0.630413i
$983$	−17.7113	−	2.80520i	−0.564903	−	0.0894719i	−0.132550	−	0.991176i	$-0.542317\pi$
$983$	−17.7113	−	2.80520i	−0.564903	−	0.0894719i	−0.432353	+	0.901704i	$0.642317\pi$
$984$	5.34715	+	2.52085i	0.170461	+	0.0803618i
$985$		0			0
$986$	0.723093	+	0.234947i	0.0230280	+	0.00748224i
$987$	13.4222	+	37.3653i	0.427233	+	1.18935i
$988$	−17.4850	−	8.90907i	−0.556273	−	0.283435i
$989$	8.16826	−	25.1393i	0.259736	−	0.799384i
$990$		0			0
$991$	14.9087	+	45.8841i	0.473589	+	1.45756i	0.847851	+	0.530234i	$0.177896\pi$
$991$	14.9087	+	45.8841i	0.473589	+	1.45756i	−0.374262	+	0.927323i	$0.622104\pi$
$992$	−0.521711	+	3.29395i	−0.0165643	+	0.104583i
$993$	16.5921	−	0.509555i	0.526535	−	0.0161702i
$994$	−4.39954	−	6.05544i	−0.139545	−	0.192067i
$995$		0			0
$996$	12.0665	−	2.29287i	0.382341	−	0.0726523i
$997$	−3.38611	−	21.3791i	−0.107239	−	0.677082i	−0.981476	−	0.191583i	$-0.938638\pi$
$997$	−3.38611	−	21.3791i	−0.107239	−	0.677082i	0.874237	−	0.485499i	$-0.161362\pi$
$998$	−0.361613	+	0.184251i	−0.0114467	+	0.00583237i
$999$	21.1026	+	17.5340i	0.667657	+	0.554750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.257.5		80
3.2	odd	2	inner	750.2.l.b.257.9		80
5.2	odd	4		750.2.l.c.743.9		80
5.3	odd	4		750.2.l.a.743.2		80
5.4	even	2		150.2.l.a.47.6	yes	80
15.2	even	4		750.2.l.c.743.2		80
15.8	even	4		750.2.l.a.743.9		80
15.14	odd	2		150.2.l.a.47.2	✓	80
25.6	even	5		750.2.l.a.107.9		80
25.8	odd	20	inner	750.2.l.b.143.9		80
25.17	odd	20		150.2.l.a.83.2	yes	80
25.19	even	10		750.2.l.c.107.2		80
75.8	even	20	inner	750.2.l.b.143.5		80
75.17	even	20		150.2.l.a.83.6	yes	80
75.44	odd	10		750.2.l.c.107.9		80
75.56	odd	10		750.2.l.a.107.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.2	✓	80	15.14	odd	2
150.2.l.a.47.6	yes	80	5.4	even	2
150.2.l.a.83.2	yes	80	25.17	odd	20
150.2.l.a.83.6	yes	80	75.17	even	20
750.2.l.a.107.2		80	75.56	odd	10
750.2.l.a.107.9		80	25.6	even	5
750.2.l.a.743.2		80	5.3	odd	4
750.2.l.a.743.9		80	15.8	even	4
750.2.l.b.143.5		80	75.8	even	20	inner
750.2.l.b.143.9		80	25.8	odd	20	inner
750.2.l.b.257.5		80	1.1	even	1	trivial
750.2.l.b.257.9		80	3.2	odd	2	inner
750.2.l.c.107.2		80	25.19	even	10
750.2.l.c.107.9		80	75.44	odd	10
750.2.l.c.743.2		80	15.2	even	4
750.2.l.c.743.9		80	5.2	odd	4

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.43185 + 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(-3.13589 - 3.13589i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.43185 + 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(-3.13589 - 3.13589i) q^{7} +(0.987688 + 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +(-3.57685 - 1.16219i) q^{11} +(-1.63007 + 0.585546i) q^{12} +(-3.49677 - 1.78169i) q^{13} +(-1.37043 + 4.21776i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-0.0644499 + 0.406920i) q^{17} +(1.98715 - 2.24749i) q^{18} +(-2.93913 - 4.04536i) q^{19} +(-1.43394 - 7.54629i) q^{21} +(0.588338 + 3.71462i) q^{22} +(-4.48117 + 2.28327i) q^{23} +(1.26176 + 1.18657i) q^{24} +3.92451i q^{26} +(-1.14438 + 5.06857i) q^{27} +(4.38021 - 0.693758i) q^{28} +(1.49299 + 1.08472i) q^{29} +(2.69808 - 1.96027i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.98886 - 5.15001i) q^{33} +(0.391828 - 0.127313i) q^{34} +(-2.90468 - 0.750223i) q^{36} +(2.39714 - 4.70465i) q^{37} +(-2.27011 + 4.45534i) q^{38} +(-3.27044 - 5.95899i) q^{39} +(3.24600 - 1.05469i) q^{41} +(-6.07280 + 4.70360i) q^{42} +(-3.71639 + 3.71639i) q^{43} +(3.04265 - 2.21062i) q^{44} +(4.06882 + 2.95617i) q^{46} +(-5.10512 + 0.808572i) q^{47} +(0.484416 - 1.66293i) q^{48} +12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(3.49677 - 1.78169i) q^{52} +(-1.29952 - 8.20487i) q^{53} +(5.03567 - 1.28143i) q^{54} +(-2.60672 - 3.58784i) q^{56} +(-0.265855 - 8.65677i) q^{57} +(0.288689 - 1.82271i) q^{58} +(-1.73564 - 5.34175i) q^{59} +(4.43829 - 13.6596i) q^{61} +(-2.97152 - 1.51406i) q^{62} +(5.30128 - 12.2026i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.77779 + 5.89216i) q^{66} +(6.11731 + 0.968887i) q^{67} +(-0.291323 - 0.291323i) q^{68} +(-8.64159 - 1.09796i) q^{69} +(-0.992045 + 1.36543i) q^{71} +(0.650243 + 2.92868i) q^{72} +(1.62628 + 3.19175i) q^{73} -5.28015 q^{74} +5.00034 q^{76} +(7.57211 + 14.8611i) q^{77} +(-3.82475 + 5.61931i) q^{78} +(-6.24842 + 8.60021i) q^{79} +(-6.57831 + 6.14214i) q^{81} +(-2.41339 - 2.41339i) q^{82} +(-7.00394 - 1.10932i) q^{83} +(6.94793 + 3.27552i) q^{84} +(4.99854 + 1.62412i) q^{86} +(1.08059 + 3.00819i) q^{87} +(-3.35101 - 1.70742i) q^{88} +(0.324819 - 0.999689i) q^{89} +(5.37828 + 16.5526i) q^{91} +(0.786761 - 4.96742i) q^{92} +(5.77369 - 0.177314i) q^{93} +(3.03812 + 4.18162i) q^{94} +(-1.70160 + 0.323338i) q^{96} +(1.20630 + 7.61627i) q^{97} +(11.2869 - 5.75096i) q^{98} +(-0.692350 - 11.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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