LMFDB - Embedded newform 150.2.l.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, 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("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	150.47
Dual form			150.2.l.a.83.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 + 0.891007i) q^{2} +(-1.43185 - 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.483575 + 2.18315i) q^{5} +(0.218312 - 1.71824i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +O(q^{10})$	\(q+(0.453990 + 0.891007i) q^{2} +(-1.43185 - 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.483575 + 2.18315i) q^{5} +(0.218312 - 1.71824i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +(-2.16474 + 0.560262i) q^{10} +(-3.57685 - 1.16219i) q^{11} +(1.63007 - 0.585546i) q^{12} +(3.49677 + 1.78169i) q^{13} +(-1.37043 + 4.21776i) q^{14} +(2.82006 - 2.65466i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(0.0644499 - 0.406920i) q^{17} +(-1.98715 + 2.24749i) q^{18} +(-2.93913 - 4.04536i) q^{19} +(-1.48197 - 1.67445i) q^{20} +(-1.43394 - 7.54629i) q^{21} +(-0.588338 - 3.71462i) q^{22} +(4.48117 - 2.28327i) q^{23} +(1.26176 + 1.18657i) q^{24} +(-4.53231 - 2.11143i) q^{25} +3.92451i q^{26} +(1.14438 - 5.06857i) q^{27} +(-4.38021 + 0.693758i) q^{28} +(1.49299 + 1.08472i) q^{29} +(3.64560 + 1.30750i) q^{30} +(2.69808 - 1.96027i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.98886 + 5.15001i) q^{33} +(0.391828 - 0.127313i) q^{34} +(-8.36256 + 5.32968i) q^{35} +(-2.90468 - 0.750223i) q^{36} +(-2.39714 + 4.70465i) q^{37} +(2.27011 - 4.45534i) q^{38} +(-3.27044 - 5.95899i) q^{39} +(0.819141 - 2.08063i) q^{40} +(3.24600 - 1.05469i) q^{41} +(6.07280 - 4.70360i) q^{42} +(3.71639 - 3.71639i) q^{43} +(3.04265 - 2.21062i) q^{44} +(-6.62509 + 1.05270i) q^{45} +(4.06882 + 2.95617i) q^{46} +(5.10512 - 0.808572i) q^{47} +(-0.484416 + 1.66293i) q^{48} +12.6676i q^{49} +(-0.176325 - 4.99689i) q^{50} +(-0.488859 + 0.519837i) q^{51} +(-3.49677 + 1.78169i) q^{52} +(1.29952 + 8.20487i) q^{53} +(5.03567 - 1.28143i) q^{54} +(4.26691 - 7.24681i) q^{55} +(-2.60672 - 3.58784i) q^{56} +(0.265855 + 8.65677i) q^{57} +(-0.288689 + 1.82271i) q^{58} +(-1.73564 - 5.34175i) q^{59} +(0.490075 + 3.84185i) q^{60} +(4.43829 - 13.6596i) q^{61} +(2.97152 + 1.51406i) q^{62} +(-5.30128 + 12.2026i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-5.58065 + 6.77239i) q^{65} +(-2.77779 + 5.89216i) q^{66} +(-6.11731 - 0.968887i) q^{67} +(0.291323 + 0.291323i) q^{68} +(-8.64159 - 1.09796i) q^{69} +(-8.54530 - 5.03147i) q^{70} +(-0.992045 + 1.36543i) q^{71} +(-0.650243 - 2.92868i) q^{72} +(-1.62628 - 3.19175i) q^{73} -5.28015 q^{74} +(4.43182 + 7.44036i) q^{75} +5.00034 q^{76} +(-7.57211 - 14.8611i) q^{77} +(3.82475 - 5.61931i) q^{78} +(-6.24842 + 8.60021i) q^{79} +(2.22573 - 0.214725i) q^{80} +(-6.57831 + 6.14214i) q^{81} +(2.41339 + 2.41339i) q^{82} +(7.00394 + 1.10932i) q^{83} +(6.94793 + 3.27552i) q^{84} +(0.857203 + 0.337480i) q^{85} +(4.99854 + 1.62412i) q^{86} +(-1.08059 - 3.00819i) q^{87} +(3.35101 + 1.70742i) q^{88} +(0.324819 - 0.999689i) q^{89} +(-3.94569 - 5.42509i) q^{90} +(5.37828 + 16.5526i) q^{91} +(-0.786761 + 4.96742i) q^{92} +(-5.77369 + 0.177314i) q^{93} +(3.03812 + 4.18162i) q^{94} +(10.2529 - 4.46033i) q^{95} +(-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^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	0.453990	+	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
$5$	−0.483575	+	2.18315i	−0.216261	+	0.976336i
$5$	−0.483575	+	2.18315i	−0.216261	+	0.976336i
$6$	0.218312	−	1.71824i	0.0891255	−	0.701467i
$7$	3.13589	+	3.13589i	1.18525	+	1.18525i	0.978364	+	0.206890i	$0.0663341\pi$
$7$	3.13589	+	3.13589i	1.18525	+	1.18525i	0.206890	+	0.978364i	$0.433666\pi$
$8$	−0.987688	−	0.156434i	−0.349201	−	0.0553079i
$9$	1.10038	+	2.79091i	0.366795	+	0.930302i
$10$	−2.16474	+	0.560262i	−0.684551	+	0.177171i
$11$	−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	0.865783	−	0.500420i	$-0.166821\pi$
$13$	3.49677	+	1.78169i	0.969828	+	0.494152i	0.104046	+	0.994573i	$0.466821\pi$
$14$	−1.37043	+	4.21776i	−0.366264	+	1.12724i
$15$	2.82006	−	2.65466i	0.728138	−	0.685431i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	0.0644499	−	0.406920i	0.0156314	−	0.0986927i	−0.978639	−	0.205585i	$-0.934090\pi$
$17$	0.0644499	−	0.406920i	0.0156314	−	0.0986927i	0.994271	+	0.106893i	$0.0340902\pi$
$18$	−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	$0.994445\pi$
$20$	−1.48197	−	1.67445i	−0.331378	−	0.374417i
$21$	−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	0.0806186	−	0.996745i	$-0.474310\pi$
$23$	4.48117	−	2.28327i	0.934389	−	0.476095i	0.853770	+	0.520650i	$0.174310\pi$
$24$	1.26176	+	1.18657i	0.257556	+	0.242208i
$25$	−4.53231	−	2.11143i	−0.906462	−	0.422287i
$26$			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	$0.645189\pi$
$30$	3.64560	+	1.30750i	0.665593	+	0.238717i
$31$	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
$35$	−8.36256	+	5.32968i	−1.41353	+	0.900881i
$36$	−2.90468	−	0.750223i	−0.484113	−	0.125037i
$37$	−2.39714	+	4.70465i	−0.394087	+	0.773440i	−0.999752	−	0.0222802i	$-0.992907\pi$
$37$	−2.39714	+	4.70465i	−0.394087	+	0.773440i	0.605664	+	0.795720i	$0.292907\pi$
$38$	2.27011	−	4.45534i	0.368260	−	0.722751i
$39$	−3.27044	−	5.95899i	−0.523689	−	0.954203i
$40$	0.819141	−	2.08063i	0.129518	−	0.328976i
$41$	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	−0.364470	−	0.931215i	$-0.618750\pi$
$43$	3.71639	−	3.71639i	0.566745	−	0.566745i	0.931215	+	0.364470i	$0.118750\pi$
$44$	3.04265	−	2.21062i	0.458697	−	0.333263i
$45$	−6.62509	+	1.05270i	−0.987610	+	0.156927i
$46$	4.06882	+	2.95617i	0.599914	+	0.435863i
$47$	5.10512	−	0.808572i	0.744659	−	0.117942i	0.227436	−	0.973793i	$-0.426966\pi$
$47$	5.10512	−	0.808572i	0.744659	−	0.117942i	0.517223	+	0.855851i	$0.326966\pi$
$48$	−0.484416	+	1.66293i	−0.0699194	+	0.240023i
$49$			12.6676i			1.80965i
$50$	−0.176325	−	4.99689i	−0.0249361	−	0.706667i
$51$	−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	$0.143265\pi$
$53$	1.29952	+	8.20487i	0.178503	+	1.12703i	−0.721909	+	0.691988i	$0.756735\pi$
$54$	5.03567	−	1.28143i	0.685267	−	0.174381i
$55$	4.26691	−	7.24681i	0.575350	−	0.977159i
$56$	−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	$-0.219141\pi$
$60$	0.490075	+	3.84185i	0.0632684	+	0.495981i
$61$	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
$65$	−5.58065	+	6.77239i	−0.692195	+	0.840012i
$66$	−2.77779	+	5.89216i	−0.341922	+	0.725275i
$67$	−6.11731	−	0.968887i	−0.747349	−	0.118368i	−0.228868	−	0.973458i	$-0.573502\pi$
$67$	−6.11731	−	0.968887i	−0.747349	−	0.118368i	−0.518481	+	0.855089i	$0.673502\pi$
$68$	0.291323	+	0.291323i	0.0353281	+	0.0353281i
$69$	−8.64159	−	1.09796i	−1.04033	−	0.132179i
$70$	−8.54530	−	5.03147i	−1.02136	−	0.601375i
$71$	−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	0.776038	−	0.630686i	$-0.217227\pi$
$73$	−1.62628	−	3.19175i	−0.190342	−	0.373567i	−0.966380	+	0.257120i	$0.917227\pi$
$74$	−5.28015			−0.613805
$75$	4.43182	+	7.44036i	0.511743	+	0.859139i
$76$	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	$0.995959\pi$
$80$	2.22573	−	0.214725i	0.248845	−	0.0240069i
$81$	−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	0.528493	−	0.848938i	$-0.322757\pi$
$83$	7.00394	+	1.10932i	0.768782	+	0.121763i	0.240290	+	0.970701i	$0.422757\pi$
$84$	6.94793	+	3.27552i	0.758081	+	0.357388i
$85$	0.857203	+	0.337480i	0.0929767	+	0.0366049i
$86$	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	$0.0822577\pi$
$90$	−3.94569	−	5.42509i	−0.415912	−	0.571854i
$91$	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
$95$	10.2529	−	4.46033i	1.05193	−	0.457620i
$96$	−1.70160	+	0.323338i	−0.173669	+	0.0330005i
$97$	−1.20630	−	7.61627i	−0.122481	−	0.773315i	−0.970099	−	0.242709i	$-0.921964\pi$
$97$	−1.20630	−	7.61627i	−0.122481	−	0.773315i	0.847618	−	0.530607i	$-0.178036\pi$
$98$	−11.2869	+	5.75096i	−1.14015	+	0.580935i
$99$	−0.692350	−	11.2615i	−0.0695838	−	1.13182i
$100$	4.37221	−	2.42565i	0.437221	−	0.242565i
$101$			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	−0.0359588	−	0.999353i	$-0.511448\pi$
$103$	2.42213	−	0.383628i	0.238660	−	0.0378000i	0.274618	+	0.961553i	$0.411448\pi$
$104$	−3.17500	−	2.30677i	−0.311334	−	0.226197i
$105$	17.1681	+	0.518681i	1.67544	+	0.0506181i
$106$	−6.72062	+	4.88282i	−0.652764	+	0.474261i
$107$	−4.30681	+	4.30681i	−0.416355	+	0.416355i	−0.883945	−	0.467590i	$-0.845122\pi$
$107$	−4.30681	+	4.30681i	−0.416355	+	0.416355i	0.467590	+	0.883945i	$0.345122\pi$
$108$	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	$0.327857\pi$
$110$	8.39409	+	0.511864i	0.800345	+	0.0488043i
$111$	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	$-0.552588\pi$
$113$	7.76223	−	15.2342i	0.730209	−	1.43312i	0.894668	−	0.446732i	$-0.147412\pi$
$114$	−7.59254	+	4.16697i	−0.711107	+	0.390272i
$115$	2.81775	+	10.8872i	0.262756	+	1.01524i
$116$	−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
$120$	−3.20063	+	2.18082i	−0.292176	+	0.199081i
$121$	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
$125$	6.80129	−	8.87369i	0.608326	−	0.793687i
$126$	−13.2794	+	0.816407i	−1.18302	+	0.0727313i
$127$	−17.4755	+	8.90421i	−1.55070	+	0.790121i	−0.999034	−	0.0439442i	$-0.986008\pi$
$127$	−17.4755	+	8.90421i	−1.55070	+	0.790121i	−0.551666	+	0.834065i	$0.686008\pi$
$128$	0.156434	+	0.987688i	0.0138270	+	0.0873001i
$129$	−8.94324	+	1.69939i	−0.787409	+	0.149623i
$130$	−8.56781	−	1.89779i	−0.751447	−	0.166448i
$131$	−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
$135$	10.5121	+	4.94938i	0.904735	+	0.425975i
$136$	−0.127313	+	0.391828i	−0.0109170	+	0.0335990i
$137$	6.44062	+	3.28166i	0.550259	+	0.280371i	0.706935	−	0.707279i	$-0.250078\pi$
$137$	6.44062	+	3.28166i	0.550259	+	0.280371i	−0.156675	+	0.987650i	$0.550078\pi$
$138$	−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	$0.465152\pi$
$140$	0.603581	−	9.89816i	0.0510119	−	0.836547i
$141$	−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
$145$	−3.09008	+	2.73488i	−0.256617	+	0.227119i
$146$	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	$0.445637\pi$
$150$	−4.61740	+	7.32664i	−0.377009	+	0.598217i
$151$	−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
$155$	2.97485	+	6.83827i	0.238946	+	0.549263i
$156$	6.74324	+	0.856768i	0.539892	+	0.0685963i
$157$	2.98265	+	2.98265i	0.238041	+	0.238041i	0.816039	−	0.577997i	$-0.196166\pi$
$157$	2.98265	+	2.98265i	0.238041	+	0.238041i	−0.577997	+	0.816039i	$0.696166\pi$
$158$	−10.4996	−	1.66297i	−0.835300	−	0.132299i
$159$	6.13559	−	13.0146i	0.486584	−	1.03213i
$160$	1.20178	+	1.88566i	0.0950093	+	0.149075i
$161$	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	0.0507896	−	0.998709i	$-0.483826\pi$
$163$	−9.28593	−	4.73142i	−0.727330	−	0.370593i	−0.778119	+	0.628116i	$0.783826\pi$
$164$	−1.05469	+	3.24600i	−0.0823575	+	0.253470i
$165$	−13.1722	+	6.21788i	−1.02545	+	0.484062i
$166$	2.19132	+	6.74418i	0.170079	+	0.523450i
$167$	−2.18995	+	13.8268i	−0.169464	+	1.06995i	0.745527	+	0.666476i	$0.232198\pi$
$167$	−2.18995	+	13.8268i	−0.169464	+	1.06995i	−0.914990	+	0.403476i	$0.867802\pi$
$168$	0.235788	+	7.67770i	0.0181914	+	0.592348i
$169$	1.41174	+	1.94309i	0.108595	+	0.149469i
$170$	0.0884649	+	0.916986i	0.00678495	+	0.0703296i
$171$	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	−0.675003	−	0.737815i	$-0.735858\pi$
$173$	−6.24576	+	3.18237i	−0.474856	+	0.241951i	0.200147	+	0.979766i	$0.435858\pi$
$174$	2.18974	−	2.32850i	0.166004	−	0.176523i
$175$	−7.59160	−	20.8340i	−0.573871	−	1.57491i
$176$			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	$0.666265\pi$
$180$	3.04248	−	5.97857i	0.226773	−	0.445616i
$181$	−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
$185$	−9.11178	−	7.50837i	−0.669911	−	0.552027i
$186$	−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
$190$	8.62892	+	7.11048i	0.626008	+	0.515849i
$191$	−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	−0.541275	−	0.840845i	$-0.682058\pi$
$193$	4.16176	−	4.16176i	0.299570	−	0.299570i	0.840845	+	0.541275i	$0.182058\pi$
$194$	6.23850	−	4.53254i	0.447898	−	0.325417i
$195$	14.5909	−	4.25825i	1.04488	−	0.304940i
$196$	−10.2483	−	7.44581i	−0.732020	−	0.531844i
$197$	−18.9787	+	3.00593i	−1.35218	+	0.214164i	−0.790129	−	0.612941i	$-0.789986\pi$
$197$	−18.9787	+	3.00593i	−1.35218	+	0.214164i	−0.562048	+	0.827105i	$0.689986\pi$
$198$	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	$-0.148782\pi$
$200$	4.14621	+	2.79445i	0.293181	+	0.197597i
$201$	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
$205$	0.732866	+	7.59654i	0.0511856	+	0.530566i
$206$	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
$210$	7.33202	+	15.5324i	0.505957	+	1.07184i
$211$	−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
$215$	6.31630	+	9.91061i	0.430768	+	0.675898i
$216$	−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
$220$	3.35476	+	7.71157i	0.226178	+	0.519914i
$221$	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	$0.123779\pi$
$223$	10.2765	+	20.1688i	0.688167	+	1.35060i	−0.237174	+	0.971467i	$0.576221\pi$
$224$	4.43481			0.296313
$225$	0.905529	−	14.9726i	0.0603686	−	0.998176i
$226$	17.0978			1.13733
$227$	−8.76566	−	17.2036i	−0.581797	−	1.14184i	−0.974962	−	0.222373i	$-0.928620\pi$
$227$	−8.76566	−	17.2036i	−0.581797	−	1.14184i	0.393164	−	0.919468i	$-0.371380\pi$
$228$	−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	$0.0189742\pi$
$230$	−8.42135	+	7.45332i	−0.555287	+	0.491458i
$231$	−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	0.176093	−	0.984374i	$-0.443654\pi$
$233$	0.601093	+	0.0952038i	0.0393789	+	0.00623701i	−0.136714	+	0.990611i	$0.543654\pi$
$234$	−10.9529	+	4.31847i	−0.716016	+	0.282307i
$235$	−0.703472	+	11.5363i	−0.0458894	+	0.752543i
$236$	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	$0.0164713\pi$
$240$	−3.39618	−	1.86170i	−0.219223	−	0.120173i
$241$	−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
$245$	−27.6552	−	6.12572i	−1.76683	−	0.391358i
$246$	−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
$250$	10.9942	+	2.03143i	0.695337	+	0.128479i
$251$			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
$255$	−0.898484	−	1.31863i	−0.0562652	−	0.0825761i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.03830	+	1.03830i	−0.0647675	+	0.0647675i	−0.738749	−	0.673981i	$-0.764583\pi$
$257$	−1.03830	+	1.03830i	−0.0647675	+	0.0647675i	0.673981	+	0.738749i	$0.264583\pi$
$258$	−5.57431	−	7.19698i	−0.347042	−	0.448064i
$259$	−22.2704	+	7.23610i	−1.38382	+	0.449629i
$260$	−2.19876	−	8.49555i	−0.136361	−	0.526872i
$261$	−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	$0.391576\pi$
$263$	−10.1330	+	19.8871i	−0.624825	+	1.22629i	−0.958901	+	0.283743i	$0.908424\pi$
$264$	−3.13412	−	5.71060i	−0.192891	−	0.351463i
$265$	−18.5409	−	1.13061i	−1.13896	−	0.0694527i
$266$	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	$0.575823\pi$
$270$	0.362446	+	11.6133i	0.0220577	+	0.706763i
$271$	−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
$275$	13.7575	+	12.8197i	0.829609	+	0.773056i
$276$	5.96767	−	6.34583i	0.359212	−	0.381974i
$277$	−6.13564	+	3.12626i	−0.368655	+	0.187839i	−0.628497	−	0.777812i	$-0.716330\pi$
$277$	−6.13564	+	3.12626i	−0.368655	+	0.187839i	0.259842	+	0.965651i	$0.416330\pi$
$278$	1.51633	+	9.57375i	0.0909436	+	0.574195i
$279$	8.43986	+	5.37304i	0.505281	+	0.321676i
$280$	9.09334	−	3.95588i	0.543431	−	0.236409i
$281$	−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	$0.119836\pi$
$283$	−1.14551	+	7.23244i	−0.0680933	+	0.429924i	−0.998059	+	0.0622774i	$0.980164\pi$
$284$	−0.521549	−	1.60516i	−0.0309482	−	0.0952489i
$285$	−19.0276	−	3.60579i	−1.12710	−	0.213589i
$286$	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
$290$	−3.83966	−	1.51167i	−0.225473	−	0.0887684i
$291$	−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	0.672830	−	0.739797i	$-0.265078\pi$
$293$	−1.14628	−	1.14628i	−0.0669662	−	0.0669662i	−0.739797	+	0.672830i	$0.765078\pi$
$294$	21.7659	+	2.76548i	1.26941	+	0.161286i
$295$	12.5012	−	1.20603i	0.727846	−	0.0702179i
$296$	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
$300$	−8.62434	−	0.787913i	−0.497926	−	0.0454902i
$301$	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
$305$	27.6748	+	16.2949i	1.58466	+	0.933044i
$306$	0.786480	+	0.953463i	0.0449600	+	0.0545058i
$307$	−8.29257	−	8.29257i	−0.473282	−	0.473282i	0.429693	−	0.902975i	$-0.358622\pi$
$307$	−8.29257	−	8.29257i	−0.473282	−	0.473282i	−0.902975	+	0.429693i	$0.858622\pi$
$308$	16.4737	+	2.60917i	0.938673	+	0.148671i
$309$	−3.84200	−	1.81126i	−0.218564	−	0.103039i
$310$	−4.74239	+	5.75512i	−0.269349	+	0.326869i
$311$	−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	0.560791	−	0.827957i	$-0.310497\pi$
$313$	3.90255	+	1.98845i	0.220585	+	0.112394i	−0.340206	+	0.940351i	$0.610497\pi$
$314$	−1.30346	+	4.01165i	−0.0735587	+	0.226391i
$315$	−24.0767	−	17.4744i	−1.35657	−	0.984571i
$316$	−3.28499	−	10.1102i	−0.184795	−	0.568740i
$317$	4.38047	−	27.6572i	0.246032	−	1.55338i	−0.487131	−	0.873329i	$-0.661957\pi$
$317$	4.38047	−	27.6572i	0.246032	−	1.55338i	0.733163	−	0.680053i	$-0.238043\pi$
$318$	14.3816	−	0.441669i	0.806481	−	0.0247676i
$319$	−4.07954	−	5.61501i	−0.228411	−	0.314380i
$320$	−1.13454	+	1.92687i	−0.0634226	+	0.107715i
$321$	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
$325$	−12.0865	−	15.4584i	−0.670439	−	0.857476i
$326$		−	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
$330$	−11.5202	−	8.91363i	−0.634167	−	0.490679i
$331$	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
$335$	5.07341	−	12.8865i	0.277190	−	0.704065i
$336$	−6.73384	+	3.69569i	−0.367361	+	0.201617i
$337$	−7.11185	+	13.9578i	−0.387407	+	0.760329i	−0.999537	−	0.0304279i	$-0.990313\pi$
$337$	−7.11185	+	13.9578i	−0.387407	+	0.760329i	0.612130	+	0.790757i	$0.290313\pi$
$338$	−1.09039	+	2.14002i	−0.0593095	+	0.116401i
$339$	−25.9613	+	14.2482i	−1.41003	+	0.773856i
$340$	−0.776879	+	0.495126i	−0.0421322	+	0.0268520i
$341$	−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
$345$	6.57588	−	18.3350i	0.354033	−	0.987122i
$346$	−5.67103	−	4.12024i	−0.304876	−	0.221506i
$347$	36.4678	−	5.77593i	1.95769	−	0.310068i	0.957963	−	0.286891i	$-0.0926218\pi$
$347$	36.4678	−	5.77593i	1.95769	−	0.310068i	0.999731	−	0.0231773i	$-0.00737823\pi$
$348$	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	$-0.131634\pi$
$350$	15.1167	−	16.2226i	0.808024	−	0.867135i
$351$	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	$-0.754208\pi$
$353$	−4.70953	−	29.7348i	−0.250663	−	1.58263i	0.465729	−	0.884927i	$-0.345792\pi$
$354$	−9.55731	+	1.81607i	−0.507965	+	0.0965233i
$355$	−2.50122	−	2.82607i	−0.132751	−	0.149992i
$356$	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	$0.929346\pi$
$360$	6.70820	−	0.00334326i	0.353553	−	0.000176205i
$361$	−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
$365$	7.75452	−	2.00697i	0.405890	−	0.105049i
$366$	−22.5016	−	10.6081i	−1.17618	−	0.554494i
$367$	15.4679	+	2.44988i	0.807418	+	0.127882i	0.546479	−	0.837473i	$-0.315968\pi$
$367$	15.4679	+	2.44988i	0.807418	+	0.127882i	0.260939	+	0.965355i	$0.415968\pi$
$368$	−3.55628	−	3.55628i	−0.185384	−	0.185384i
$369$	6.51539	+	7.89873i	0.339178	+	0.411191i
$370$	2.55335	−	11.5274i	0.132742	−	0.599280i
$371$	−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	0.953745	−	0.300616i	$-0.0971924\pi$
$373$	2.89590	+	5.68352i	0.149944	+	0.294282i	−0.803801	+	0.594898i	$0.797192\pi$
$374$	−1.54947			−0.0801213
$375$	−18.3866	+	6.07738i	−0.949478	+	0.313834i
$376$	−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	$0.956724\pi$
$380$	−2.41804	+	10.9165i	−0.124043	+	0.560005i
$381$	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	0.856420	−	0.516280i	$-0.172684\pi$
$383$	29.5784	+	4.68475i	1.51138	+	0.239380i	0.654964	+	0.755660i	$0.272684\pi$
$384$	0.738592	−	1.56668i	0.0376911	−	0.0799492i
$385$	36.1057	−	9.34462i	1.84012	−	0.476246i
$386$	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	$0.194685\pi$
$390$	10.4183	+	11.0674i	0.527549	+	0.560418i
$391$	−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
$395$	−15.7540	−	17.8001i	−0.792669	−	0.895620i
$396$	9.51771	+	6.05923i	0.478283	+	0.304488i
$397$	−2.09608	−	13.2341i	−0.105199	−	0.664203i	−0.982781	−	0.184775i	$-0.940844\pi$
$397$	−2.09608	−	13.2341i	−0.105199	−	0.664203i	0.877581	−	0.479427i	$-0.159156\pi$
$398$	11.3268	−	5.77130i	0.567762	−	0.289289i
$399$	−26.3130	+	27.9803i	−1.31730	+	1.40077i
$400$	−0.607532	+	4.96295i	−0.0303766	+	0.248148i
$401$		−	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
$405$	−10.2281	−	17.3316i	−0.508240	−	0.861216i
$406$	−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	$0.286798\pi$
$410$	−6.43586	+	4.10175i	−0.317844	+	0.202571i
$411$	−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
$415$	−5.80873	+	14.7542i	−0.285139	+	0.724257i
$416$	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	$0.255752\pi$
$420$	−10.5108	+	13.5844i	−0.512874	+	0.662852i
$421$	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
$425$	−1.15129	+	1.70821i	−0.0558459	+	0.0828603i
$426$	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
$430$	−5.96288	+	10.1272i	−0.287555	+	0.488376i
$431$	−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	$0.238219\pi$
$433$	−3.62919	+	22.9138i	−0.174408	+	1.10117i	−0.907195	+	0.420710i	$0.861781\pi$
$434$	4.57041	+	14.0663i	0.219387	+	0.675203i
$435$	7.08988	−	0.904401i	0.339934	−	0.0433627i
$436$	−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	$0.512833\pi$
$440$	−5.34803	+	6.49009i	−0.254957	+	0.309403i
$441$	−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	0.824316	−	0.566130i	$-0.191560\pi$
$443$	5.43418	+	5.43418i	0.258186	+	0.258186i	−0.566130	+	0.824316i	$0.691560\pi$
$444$	−1.15272	+	9.07256i	−0.0547057	+	0.430565i
$445$	2.02540	+	1.19255i	0.0960132	+	0.0565324i
$446$	−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	$0.719341\pi$
$450$	13.7518	−	5.99061i	0.648267	−	0.282400i
$451$	−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
$455$	−38.7378	+	3.73717i	−1.81605	+	0.175201i
$456$	1.09163	−	8.59178i	0.0511205	−	0.402347i
$457$	24.1951	+	24.1951i	1.13180	+	1.13180i	0.989878	+	0.141919i	$0.0453271\pi$
$457$	24.1951	+	24.1951i	1.13180	+	1.13180i	0.141919	+	0.989878i	$0.454673\pi$
$458$	16.0987	+	2.54978i	0.752241	+	0.119143i
$459$	−1.98875	−	0.792339i	−0.0928269	−	0.0369832i
$460$	−10.4642	−	4.11974i	−0.487894	−	0.192084i
$461$	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	0.593307	−	0.804977i	$-0.297822\pi$
$463$	6.25735	+	3.18828i	0.290804	+	0.148172i	−0.302503	+	0.953149i	$0.597822\pi$
$464$	0.570270	−	1.75511i	0.0264741	−	0.0814790i
$465$	2.40491	−	12.6906i	0.111525	−	0.588512i
$466$	0.188063	+	0.578799i	0.00871187	+	0.0268124i
$467$	−4.48899	+	28.3424i	−0.207726	+	1.31153i	0.634718	+	0.772744i	$0.281116\pi$
$467$	−4.48899	+	28.3424i	−0.207726	+	1.31153i	−0.842444	+	0.538785i	$0.818884\pi$
$468$	−8.82032	−	7.79860i	−0.407719	−	0.360490i
$469$	−16.1449	−	22.2215i	−0.745502	−	1.02609i
$470$	−10.5983	+	4.61056i	−0.488861	+	0.212669i
$471$	−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
$475$	4.77953	+	24.5406i	0.219300	+	1.12600i
$476$			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	$0.605187\pi$
$480$	0.116957	−	3.87122i	0.00533832	−	0.176696i
$481$	−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
$485$	17.2108	+	1.04950i	0.781503	+	0.0476554i
$486$	9.11753	+	12.6440i	0.413580	+	0.573543i
$487$	9.39682	−	18.4423i	0.425810	−	0.835700i	−0.574047	−	0.818822i	$-0.694627\pi$
$487$	9.39682	−	18.4423i	0.425810	−	0.835700i	0.999858	−	0.0168777i	$-0.00537258\pi$
$488$	−6.52048	+	12.7972i	−0.295168	+	0.579301i
$489$	8.68490	+	15.8246i	0.392745	+	0.715611i
$490$	−7.09717	−	27.4220i	−0.320617	−	1.23880i
$491$	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
$495$	24.9204	+	3.93427i	1.12009	+	0.176832i
$496$	−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	$-0.00289161\pi$
$500$	3.18127	+	10.7182i	0.142271	+	0.479332i
$501$	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	0.999769	−	0.0214995i	$-0.00684402\pi$
$503$	0.948431	+	5.98816i	0.0422885	+	0.266999i	−0.957480	+	0.288498i	$0.906844\pi$
$504$	7.14493	−	11.2231i	0.318260	−	0.499917i
$505$	−24.1997	−	5.36030i	−1.07687	−	0.238530i
$506$	−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	$0.926896\pi$
$510$	0.767009	−	1.39920i	0.0339637	−	0.0619577i
$511$	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
$515$	−0.333763	+	5.47339i	−0.0147073	+	0.241187i
$516$	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
$520$	6.57138	−	5.81601i	0.288174	−	0.255049i
$521$	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	0.962074	−	0.272787i	$-0.0879455\pi$
$523$	4.02250	+	7.89460i	0.175892	+	0.345207i	−0.786183	+	0.617994i	$0.787946\pi$
$524$	20.5251			0.896645
$525$	−9.43443	+	37.2298i	−0.411752	+	1.62484i
$526$	−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
$530$	−7.41001	−	17.0333i	−0.321870	−	0.739881i
$531$	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
$535$	−7.31976	−	11.4851i	−0.316461	−	0.496544i
$536$	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
$540$	−10.1830	+	5.59527i	−0.438205	+	0.240782i
$541$	−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
$545$	1.00750	+	10.4433i	0.0431566	+	0.447342i
$546$	29.6155	−	5.62752i	1.26743	−	0.240836i
$547$	4.14971	+	26.2003i	0.177429	+	1.12024i	0.902221	+	0.431274i	$0.141936\pi$
$547$	4.14971	+	26.2003i	0.177429	+	1.12024i	−0.724792	+	0.688968i	$0.758064\pi$
$548$	−6.44062	+	3.28166i	−0.275130	+	0.140186i
$549$	43.0066	−	2.64402i	1.83548	−	0.112844i
$550$	−5.17665	+	18.0781i	−0.220733	+	0.770851i
$551$		−	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
$555$	5.72918	+	19.6310i	0.243190	+	0.833290i
$556$	−7.84187	+	5.69745i	−0.332569	+	0.241626i
$557$	20.9449	−	20.9449i	0.887465	−	0.887465i	−0.106814	−	0.994279i	$-0.534065\pi$
$557$	20.9449	−	20.9449i	0.887465	−	0.887465i	0.994279	+	0.106814i	$0.0340648\pi$
$558$	−0.955798	+	9.95928i	−0.0404622	+	0.421610i
$559$	19.6168	−	6.37389i	0.829703	−	0.269587i
$560$	7.65300	+	6.30630i	0.323398	+	0.266490i
$561$	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	−0.700378	−	0.713772i	$-0.746985\pi$
$563$	6.85128	−	13.4464i	0.288747	−	0.566698i	0.989126	+	0.147073i	$0.0469854\pi$
$564$	7.84827	−	4.30732i	0.330472	−	0.181371i
$565$	29.5050	+	24.3130i	1.24129	+	1.02286i
$566$	−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	$0.358586\pi$
$570$	−5.42557	−	18.5907i	−0.227252	−	0.778679i
$571$	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
$575$	−25.1310	+	0.886795i	−1.04804	+	0.0369819i
$576$	0.184091	+	2.99435i	0.00767044	+	0.124764i
$577$	32.6160	−	16.6187i	1.35782	−	0.691845i	0.384896	−	0.922960i	$-0.374237\pi$
$577$	32.6160	−	16.6187i	1.35782	−	0.691845i	0.972927	+	0.231114i	$0.0742372\pi$
$578$	2.63283	+	16.6231i	0.109511	+	0.691428i
$579$	−10.0150	+	1.90304i	−0.416209	+	0.0790877i
$580$	−0.396260	−	4.10745i	−0.0164538	−	0.170552i
$581$	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
$585$	−25.0420	−	8.12283i	−1.03536	−	0.335838i
$586$	0.500941	−	1.54174i	0.0206937	−	0.0636887i
$587$	−10.1304	−	5.16169i	−0.418126	−	0.213046i	0.232254	−	0.972655i	$-0.425390\pi$
$587$	−10.1304	−	5.16169i	−0.418126	−	0.213046i	−0.650379	+	0.759609i	$0.725390\pi$
$588$	7.41745	+	20.6491i	0.305890	+	0.851553i
$589$	−15.8600	−	5.15324i	−0.653501	−	0.212335i
$590$	6.75000	+	10.5911i	0.277893	+	0.436029i
$591$	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	0.283901	−	0.958854i	$-0.408371\pi$
$593$	−16.4362	−	16.4362i	−0.674952	−	0.674952i	−0.958854	+	0.283901i	$0.908371\pi$
$594$	−19.5011	−	1.26890i	−0.800140	−	0.0520636i
$595$	1.62979	+	3.74639i	0.0668150	+	0.153587i
$596$	−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	$0.612476\pi$
$600$	−3.21333	−	8.04205i	−0.131184	−	0.328315i
$601$	−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
$605$	−5.26537	+	4.66012i	−0.214068	+	0.189461i
$606$	19.0462	+	2.41993i	0.773700	+	0.0983030i
$607$	−29.4219	−	29.4219i	−1.19420	−	1.19420i	−0.975877	−	0.218322i	$-0.929942\pi$
$607$	−29.4219	−	29.4219i	−1.19420	−	1.19420i	−0.218322	−	0.975877i	$-0.570058\pi$
$608$	−4.93878	−	0.782226i	−0.200294	−	0.0317235i
$609$	6.04475	−	12.8219i	0.244946	−	0.519571i
$610$	−1.95476	+	32.0562i	−0.0791459	+	1.29792i
$611$	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	0.552339	−	0.833619i	$-0.313735\pi$
$613$	5.01575	+	2.55565i	0.202584	+	0.103222i	−0.349755	+	0.936841i	$0.613735\pi$
$614$	3.62398	−	11.1535i	0.146252	−	0.450118i
$615$	6.35409	−	11.5913i	0.256222	−	0.467408i
$616$	5.15409	+	15.8627i	0.207664	+	0.639125i
$617$	−5.57460	+	35.1967i	−0.224425	+	1.41696i	0.575960	+	0.817478i	$0.304628\pi$
$617$	−5.57460	+	35.1967i	−0.224425	+	1.41696i	−0.800385	+	0.599486i	$0.795372\pi$
$618$	−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	$-0.444169\pi$
$620$	−7.28085	−	1.61273i	−0.292406	−	0.0647687i
$621$	−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
$625$	16.0837	+	19.1394i	0.643348	+	0.765574i
$626$			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
$630$	4.63922	−	29.3857i	0.184831	−	1.17075i
$631$	−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
$635$	−10.9885	−	42.4575i	−0.436067	−	1.68488i
$636$	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
$640$	−2.23192	−	0.136101i	−0.0882245	−	0.00537985i
$641$	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	−0.895290	−	0.445484i	$-0.853032\pi$
$643$	−11.4059	+	11.4059i	−0.449806	+	0.449806i	0.445484	+	0.895290i	$0.353032\pi$
$644$	−18.0445	+	13.1101i	−0.711051	+	0.516609i
$645$	0.614698	−	20.3462i	0.0242037	−	0.801133i
$646$	−1.66666	−	1.21090i	−0.0655739	−	0.0476422i
$647$	−30.9551	+	4.90280i	−1.21697	+	0.192749i	−0.731707	−	0.681619i	$-0.761276\pi$
$647$	−30.9551	+	4.90280i	−1.21697	+	0.192749i	−0.485263	+	0.874368i	$0.661276\pi$
$648$	7.45816	−	5.03744i	0.292984	−	0.197889i
$649$			21.1238i			0.829181i
$650$	8.28635	−	17.7871i	0.325017	−	0.697668i
$651$	−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	$0.219444\pi$
$653$	5.98789	+	37.8061i	0.234324	+	1.47947i	−0.537302	+	0.843390i	$0.680556\pi$
$654$	−1.51712	−	7.98404i	−0.0593242	−	0.312201i
$655$	42.0857	−	18.3085i	1.64442	−	0.715373i
$656$	−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	$-0.230694\pi$
$660$	2.71203	−	14.3113i	0.105566	−	0.557066i
$661$	−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
$665$	46.1391	+	18.1649i	1.78920	+	0.704406i
$666$	−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
$670$	13.7852	−	1.32991i	0.532570	−	0.0513789i
$671$	−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	$-0.896690\pi$
$673$	−16.8283	−	33.0273i	−0.648681	−	1.27311i	0.299110	−	0.954219i	$-0.403310\pi$
$674$	−15.6652			−0.603401
$675$	−15.8886	+	20.5561i	−0.611554	+	0.791203i
$676$	−2.40180			−0.0923767
$677$	18.9516	+	37.1946i	0.728369	+	1.42951i	0.896182	+	0.443686i	$0.146330\pi$
$677$	18.9516	+	37.1946i	0.728369	+	1.42951i	−0.167813	+	0.985819i	$0.553670\pi$
$678$	−24.4814	−	16.6632i	−0.940204	−	0.639945i
$679$	20.1010	−	27.6666i	0.771404	−	1.06175i
$680$	−0.793856	−	0.467421i	−0.0304430	−	0.0179248i
$681$	−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	−0.925890	−	0.377793i	$-0.876683\pi$
$683$	−50.2616	−	7.96066i	−1.92321	−	0.304606i	−0.997318	+	0.0731865i	$0.976683\pi$
$684$	5.50230	+	13.9555i	0.210386	+	0.533601i
$685$	−10.2789	+	12.4739i	−0.392736	+	0.476604i
$686$	−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
$690$	19.3220	−	2.46475i	0.735575	−	0.0938315i
$691$	−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
$695$	−10.9972	+	18.6773i	−0.417147	+	0.708471i
$696$	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
$700$	21.3173	+	6.10421i	0.805719	+	0.230717i
$701$			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
$705$	12.2503	−	15.8326i	0.461373	−	0.596291i
$706$	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	$0.416482\pi$
$710$	1.38252	−	3.51162i	0.0518851	−	0.131789i
$711$	−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
$715$	27.8320	−	17.7381i	1.04086	−	0.663366i
$716$	−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	$0.248846\pi$
$720$	3.04844	+	5.97553i	0.113609	+	0.222695i
$721$	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
$725$	−4.47637	−	8.06863i	−0.166248	−	0.299661i
$726$	3.73123	−	3.96767i	0.138479	−	0.147254i
$727$	−30.4942	+	15.5376i	−1.13097	+	0.576257i	−0.916325	−	0.400435i	$-0.868859\pi$
$727$	−30.4942	+	15.5376i	−1.13097	+	0.576257i	−0.214644	+	0.976692i	$0.568859\pi$
$728$	−2.72266	−	17.1902i	−0.100909	−	0.637111i
$729$	−24.3808	−	11.6007i	−0.902992	−	0.429656i
$730$	5.30870	+	5.99818i	0.196484	+	0.222003i
$731$	−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	$0.312918\pi$
$733$	−6.22770	+	39.3201i	−0.230025	+	1.45232i	−0.784504	+	0.620124i	$0.787082\pi$
$734$	4.83943	+	14.8942i	0.178627	+	0.549756i
$735$	33.6281	+	35.7234i	1.24039	+	1.31768i
$736$	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	$0.476244\pi$
$740$	11.4302	−	2.95827i	0.420181	−	0.108748i
$741$	−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	0.998501	−	0.0547306i	$-0.0174300\pi$
$743$	25.7253	+	25.7253i	0.943771	+	0.943771i	−0.0547306	+	0.998501i	$0.517430\pi$
$744$	5.73035	+	0.728073i	0.210085	+	0.0266925i
$745$	−2.00645	+	9.05833i	−0.0735105	+	0.331871i
$746$	−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
$750$	−13.7623	−	13.6235i	−0.502528	−	0.497459i
$751$	−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
$755$	4.59430	−	20.7415i	0.167204	−	0.754860i
$756$	−1.49626	+	22.9953i	−0.0544186	+	0.836332i
$757$	−28.7075	−	28.7075i	−1.04339	−	1.04339i	−0.999015	−	0.0443764i	$-0.985870\pi$
$757$	−28.7075	−	28.7075i	−1.04339	−	1.04339i	−0.0443764	−	0.999015i	$-0.514130\pi$
$758$	−26.6124	−	4.21499i	−0.966606	−	0.153095i
$759$	29.6336	+	13.9704i	1.07563	+	0.507094i
$760$	−10.8245	+	2.80151i	−0.392644	+	0.101621i
$761$	−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
$765$	0.00137740	+	2.76373i	4.98000e−5	+	0.0999229i
$766$	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	$0.547331\pi$
$770$	24.7178	+	27.9281i	0.890766	+	1.00646i
$771$	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	−0.922129	−	0.386883i	$-0.873552\pi$
$773$	−32.0052	+	16.3075i	−1.15115	+	0.586539i	−0.229019	+	0.973422i	$0.573552\pi$
$774$	0.967539	+	15.7376i	0.0347775	+	0.565677i
$775$	−16.3675	+	3.18774i	−0.587939	+	0.114507i
$776$			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
$780$	−5.13132	+	14.3072i	−0.183731	+	0.512281i
$781$	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
$785$	−7.95390	+	5.06924i	−0.283887	+	0.180929i
$786$	−31.1654	+	17.1043i	−1.11163	+	0.610092i
$787$	−13.0206	+	25.5543i	−0.464133	+	0.910913i	0.533735	+	0.845652i	$0.320788\pi$
$787$	−13.0206	+	25.5543i	−0.464133	+	0.910913i	−0.997868	+	0.0652610i	$0.979212\pi$
$788$	8.72355	−	17.1209i	0.310764	−	0.609908i
$789$	33.8904	−	18.5999i	1.20653	−	0.662173i
$790$	8.70783	−	22.1180i	0.309811	−	0.786922i
$791$	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
$795$	25.4459	+	19.6885i	0.902473	+	0.698278i
$796$	10.2845	+	7.47216i	0.364526	+	0.264844i
$797$	−9.56827	+	1.51547i	−0.338926	+	0.0536805i	−0.323578	−	0.946202i	$-0.604886\pi$
$797$	−9.56827	+	1.51547i	−0.338926	+	0.0536805i	−0.0153481	+	0.999882i	$0.504886\pi$
$798$	−36.8765	−	10.7422i	−1.30541	−	0.380270i
$799$		−	2.12949i		−	0.0753360i
$800$	−4.69784	+	1.71182i	−0.166094	+	0.0605219i
$801$	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
$805$	−25.3049	+	42.9772i	−0.891881	+	1.51475i
$806$	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	$-0.539367\pi$
$810$	10.7991	−	16.9817i	0.379443	−	0.596677i
$811$	−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
$815$	14.8198	−	17.9846i	0.519116	−	0.629973i
$816$	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
$820$	−6.57650	−	3.87224i	−0.229661	−	0.135224i
$821$	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	$-0.908553\pi$
$823$	−17.9173	−	35.1647i	−0.624559	−	1.22577i	0.334456	−	0.942411i	$-0.391447\pi$
$824$	−2.45232			−0.0854307
$825$	−7.20486	−	31.7637i	−0.250841	−	1.10587i
$826$	24.9088			0.866688
$827$	11.4419	+	22.4561i	0.397875	+	0.780874i	0.999844	−	0.0176456i	$-0.00561705\pi$
$827$	11.4419	+	22.4561i	0.397875	+	0.780874i	−0.601969	+	0.798519i	$0.705617\pi$
$828$	−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	$0.965871\pi$
$830$	−15.7832	+	1.52266i	−0.547844	+	0.0528525i
$831$	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
$835$	−29.1271	−	11.4673i	−1.00798	−	0.396842i
$836$	−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	$0.119756\pi$
$840$	−16.8756	−	3.19798i	−0.582264	−	0.110341i
$841$	−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
$845$	−4.92475	+	2.14241i	−0.169417	+	0.0737013i
$846$	−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
$850$	−2.04470	−	0.250299i	−0.0701326	−	0.00858518i
$851$			26.5557i			0.910317i
$852$	−0.817581	+	2.80664i	−0.0280099	+	0.0961540i
$853$	44.8288	−	7.10018i	1.53491	−	0.243106i	0.668983	−	0.743278i	$-0.266730\pi$
$853$	44.8288	−	7.10018i	1.53491	−	0.243106i	0.865926	+	0.500172i	$0.166730\pi$
$854$	51.5307	+	37.4393i	1.76334	+	1.28114i
$855$	23.7305	+	23.7069i	0.811567	+	0.810759i
$856$	4.92752	−	3.58005i	0.168419	−	0.122364i
$857$	5.49063	−	5.49063i	0.187556	−	0.187556i	−0.607082	−	0.794639i	$-0.707660\pi$
$857$	5.49063	−	5.49063i	0.187556	−	0.187556i	0.794639	+	0.607082i	$0.207660\pi$
$858$	−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	$0.338299\pi$
$860$	−11.7305	−	0.715314i	−0.400006	−	0.0243920i
$861$	−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	−0.783462	−	0.621440i	$-0.786548\pi$
$863$	5.28199	−	10.3665i	0.179801	−	0.352880i	0.963263	+	0.268560i	$0.0865479\pi$
$864$	−2.77482	−	4.39322i	−0.0944014	−	0.149460i
$865$	−3.92731	−	15.1744i	−0.133533	−	0.515944i
$866$	−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
$870$	4.02457	+	5.90654i	0.136446	+	0.200251i
$871$	−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
$875$	49.1550	−	6.49880i	1.66174	−	0.219700i
$876$	−4.51987	−	4.25053i	−0.152712	−	0.143612i
$877$	22.0344	−	11.2271i	0.744049	−	0.379112i	−0.0404992	−	0.999180i	$-0.512895\pi$
$877$	22.0344	−	11.2271i	0.744049	−	0.379112i	0.784548	+	0.620068i	$0.212895\pi$
$878$	1.77277	+	11.1928i	0.0598282	+	0.377740i
$879$	0.524156	+	2.75844i	0.0176794	+	0.0930397i
$880$	−8.21067	−	1.81869i	−0.276782	−	0.0613079i
$881$	−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	−0.961721	−	0.274029i	$-0.911644\pi$
$883$	1.11758	−	7.05614i	0.0376097	−	0.237458i	0.999331	+	0.0365710i	$0.0116435\pi$
$884$	0.499640	+	1.53774i	0.0168047	+	0.0517196i
$885$	−19.0752	−	10.4565i	−0.641205	−	0.351493i
$886$	−2.37482	+	7.30895i	−0.0797837	+	0.245549i
$887$	−3.17069	−	1.61555i	−0.106461	−	0.0542448i	0.399949	−	0.916537i	$-0.369028\pi$
$887$	−3.17069	−	1.61555i	−0.106461	−	0.0542448i	−0.506410	+	0.862293i	$0.669028\pi$
$888$	−8.60703	+	3.09177i	−0.288833	+	0.103753i
$889$	−82.7238	−	26.8786i	−2.77447	−	0.901479i
$890$	−0.143060	+	2.34605i	−0.00479539	+	0.0786399i
$891$	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
$895$	−4.73959	+	4.19478i	−0.158427	+	0.140216i
$896$	−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
$900$	11.5809	+	9.53329i	0.386029	+	0.317776i
$901$	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
$905$	−0.312216	−	0.717688i	−0.0103784	−	0.0238568i
$906$	−2.07412	+	16.3245i	−0.0689079	+	0.542344i
$907$	1.89862	+	1.89862i	0.0630427	+	0.0630427i	0.737925	−	0.674883i	$-0.235806\pi$
$907$	1.89862	+	1.89862i	0.0630427	+	0.0630427i	−0.674883	+	0.737925i	$0.735806\pi$
$908$	19.0703	+	3.02044i	0.632871	+	0.100237i
$909$	−30.9365	+	12.1975i	−1.02610	+	0.404565i
$910$	−20.9164	−	32.8190i	−0.693372	−	1.08794i
$911$	−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
$915$	−23.7455	−	50.3032i	−0.785002	−	1.66297i
$916$	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	$0.850461\pi$
$920$	−1.07992	−	11.1940i	−0.0356040	−	0.369054i
$921$	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
$925$	20.7981	−	16.2615i	0.683839	−	0.534676i
$926$			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	$0.892298\pi$
$930$	12.3992	−	3.61862i	0.406586	−	0.118659i
$931$	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
$935$	−2.67387	−	2.20335i	−0.0874449	−	0.0720572i
$936$	2.94426	−	11.3995i	0.0962362	−	0.372603i
$937$	6.94494	−	13.6302i	0.226881	−	0.445280i	−0.749302	−	0.662229i	$-0.769611\pi$
$937$	6.94494	−	13.6302i	0.226881	−	0.445280i	0.976183	+	0.216949i	$0.0696106\pi$
$938$	12.4699	−	24.4736i	0.407157	−	0.799090i
$939$	−3.64996	−	6.65050i	−0.119112	−	0.217031i
$940$	−8.91955	−	7.34997i	−0.290924	−	0.239730i
$941$	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
$945$	17.4440	+	48.4854i	0.567452	+	1.57723i
$946$	−15.9915	−	11.6185i	−0.519928	−	0.377750i
$947$	−37.1437	+	5.88298i	−1.20701	+	0.191171i	−0.727339	−	0.686279i	$-0.759243\pi$
$947$	−37.1437	+	5.88298i	−1.20701	+	0.191171i	−0.479669	+	0.877450i	$0.659243\pi$
$948$	−5.14955	+	17.6777i	−0.167250	+	0.574145i
$949$		−	14.0583i		−	0.456353i
$950$	−19.6960	+	15.3998i	−0.639022	+	0.499635i
$951$	−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	$0.0920076\pi$
$953$	4.16742	+	26.3120i	0.134996	+	0.852331i	−0.823519	+	0.567289i	$0.807992\pi$
$954$	−21.0227	−	13.3836i	−0.680636	−	0.433311i
$955$	−0.243792	−	2.52704i	−0.00788893	−	0.0817730i
$956$	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
$960$	3.50238	−	1.65329i	0.113039	−	0.0533596i
$961$	−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
$965$	7.07324	+	11.0983i	0.227696	+	0.357266i
$966$	16.4737	−	34.9435i	0.530032	−	1.12429i
$967$	41.4802	+	6.56982i	1.33391	+	0.211271i	0.782339	−	0.622853i	$-0.214027\pi$
$967$	41.4802	+	6.56982i	1.33391	+	0.211271i	0.551576	+	0.834125i	$0.314027\pi$
$968$	−2.22353	−	2.22353i	−0.0714670	−	0.0714670i
$969$	3.53975	+	0.449746i	0.113713	+	0.0144479i
$970$	6.87844	+	15.8114i	0.220853	+	0.507674i
$971$	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
$975$	2.24063	+	33.9133i	0.0717574	+	1.08610i
$976$	−14.3626			−0.459736
$977$	0.545186	+	1.06999i	0.0174420	+	0.0342319i	0.899563	−	0.436791i	$-0.143885\pi$
$977$	0.545186	+	1.06999i	0.0174420	+	0.0342319i	−0.882121	+	0.471023i	$0.843885\pi$
$978$	−10.1569	+	14.9225i	−0.324783	+	0.477169i
$979$	−2.32366	+	3.19824i	−0.0742644	+	0.102216i
$980$	21.2112	−	18.7730i	0.677566	−	0.599680i
$981$	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	0.432353	−	0.901704i	$-0.357683\pi$
$983$	17.7113	+	2.80520i	0.564903	+	0.0894719i	0.132550	+	0.991176i	$0.457683\pi$
$984$	5.34715	+	2.52085i	0.170461	+	0.0803618i
$985$	2.61521	−	42.8870i	0.0833276	−	1.36649i
$986$	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
$990$	7.80816	+	23.9904i	0.248160	+	0.762464i
$991$	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
$995$	27.7531	+	6.14739i	0.879832	+	0.194885i
$996$	12.0665	−	2.29287i	0.382341	−	0.0726523i
$997$	3.38611	+	21.3791i	0.107239	+	0.677082i	0.981476	+	0.191583i	$0.0613621\pi$
$997$	3.38611	+	21.3791i	0.107239	+	0.677082i	−0.874237	+	0.485499i	$0.838638\pi$
$998$	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	150.2.l.a.47.6	yes	80
3.2	odd	2	inner	150.2.l.a.47.2	✓	80
5.2	odd	4		750.2.l.a.743.2		80
5.3	odd	4		750.2.l.c.743.9		80
5.4	even	2		750.2.l.b.257.5		80
15.2	even	4		750.2.l.a.743.9		80
15.8	even	4		750.2.l.c.743.2		80
15.14	odd	2		750.2.l.b.257.9		80
25.6	even	5		750.2.l.c.107.2		80
25.8	odd	20	inner	150.2.l.a.83.2	yes	80
25.17	odd	20		750.2.l.b.143.9		80
25.19	even	10		750.2.l.a.107.9		80
75.8	even	20	inner	150.2.l.a.83.6	yes	80
75.17	even	20		750.2.l.b.143.5		80
75.44	odd	10		750.2.l.a.107.2		80
75.56	odd	10		750.2.l.c.107.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.2	✓	80	3.2	odd	2	inner
150.2.l.a.47.6	yes	80	1.1	even	1	trivial
150.2.l.a.83.2	yes	80	25.8	odd	20	inner
150.2.l.a.83.6	yes	80	75.8	even	20	inner
750.2.l.a.107.2		80	75.44	odd	10
750.2.l.a.107.9		80	25.19	even	10
750.2.l.a.743.2		80	5.2	odd	4
750.2.l.a.743.9		80	15.2	even	4
750.2.l.b.143.5		80	75.17	even	20
750.2.l.b.143.9		80	25.17	odd	20
750.2.l.b.257.5		80	5.4	even	2
750.2.l.b.257.9		80	15.14	odd	2
750.2.l.c.107.2		80	25.6	even	5
750.2.l.c.107.9		80	75.56	odd	10
750.2.l.c.743.2		80	15.8	even	4
750.2.l.c.743.9		80	5.3	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 + 0.891007i) q^{2} +(-1.43185 - 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.483575 + 2.18315i) q^{5} +(0.218312 - 1.71824i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +O(q^{10})\)	\(q+(0.453990 + 0.891007i) q^{2} +(-1.43185 - 0.974581i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.483575 + 2.18315i) q^{5} +(0.218312 - 1.71824i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.10038 + 2.79091i) q^{9} +(-2.16474 + 0.560262i) q^{10} +(-3.57685 - 1.16219i) q^{11} +(1.63007 - 0.585546i) q^{12} +(3.49677 + 1.78169i) q^{13} +(-1.37043 + 4.21776i) q^{14} +(2.82006 - 2.65466i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(0.0644499 - 0.406920i) q^{17} +(-1.98715 + 2.24749i) q^{18} +(-2.93913 - 4.04536i) q^{19} +(-1.48197 - 1.67445i) q^{20} +(-1.43394 - 7.54629i) q^{21} +(-0.588338 - 3.71462i) q^{22} +(4.48117 - 2.28327i) q^{23} +(1.26176 + 1.18657i) q^{24} +(-4.53231 - 2.11143i) q^{25} +3.92451i q^{26} +(1.14438 - 5.06857i) q^{27} +(-4.38021 + 0.693758i) q^{28} +(1.49299 + 1.08472i) q^{29} +(3.64560 + 1.30750i) q^{30} +(2.69808 - 1.96027i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.98886 + 5.15001i) q^{33} +(0.391828 - 0.127313i) q^{34} +(-8.36256 + 5.32968i) q^{35} +(-2.90468 - 0.750223i) q^{36} +(-2.39714 + 4.70465i) q^{37} +(2.27011 - 4.45534i) q^{38} +(-3.27044 - 5.95899i) q^{39} +(0.819141 - 2.08063i) q^{40} +(3.24600 - 1.05469i) q^{41} +(6.07280 - 4.70360i) q^{42} +(3.71639 - 3.71639i) q^{43} +(3.04265 - 2.21062i) q^{44} +(-6.62509 + 1.05270i) q^{45} +(4.06882 + 2.95617i) q^{46} +(5.10512 - 0.808572i) q^{47} +(-0.484416 + 1.66293i) q^{48} +12.6676i q^{49} +(-0.176325 - 4.99689i) q^{50} +(-0.488859 + 0.519837i) q^{51} +(-3.49677 + 1.78169i) q^{52} +(1.29952 + 8.20487i) q^{53} +(5.03567 - 1.28143i) q^{54} +(4.26691 - 7.24681i) q^{55} +(-2.60672 - 3.58784i) q^{56} +(0.265855 + 8.65677i) q^{57} +(-0.288689 + 1.82271i) q^{58} +(-1.73564 - 5.34175i) q^{59} +(0.490075 + 3.84185i) q^{60} +(4.43829 - 13.6596i) q^{61} +(2.97152 + 1.51406i) q^{62} +(-5.30128 + 12.2026i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-5.58065 + 6.77239i) q^{65} +(-2.77779 + 5.89216i) q^{66} +(-6.11731 - 0.968887i) q^{67} +(0.291323 + 0.291323i) q^{68} +(-8.64159 - 1.09796i) q^{69} +(-8.54530 - 5.03147i) q^{70} +(-0.992045 + 1.36543i) q^{71} +(-0.650243 - 2.92868i) q^{72} +(-1.62628 - 3.19175i) q^{73} -5.28015 q^{74} +(4.43182 + 7.44036i) q^{75} +5.00034 q^{76} +(-7.57211 - 14.8611i) q^{77} +(3.82475 - 5.61931i) q^{78} +(-6.24842 + 8.60021i) q^{79} +(2.22573 - 0.214725i) q^{80} +(-6.57831 + 6.14214i) q^{81} +(2.41339 + 2.41339i) q^{82} +(7.00394 + 1.10932i) q^{83} +(6.94793 + 3.27552i) q^{84} +(0.857203 + 0.337480i) q^{85} +(4.99854 + 1.62412i) q^{86} +(-1.08059 - 3.00819i) q^{87} +(3.35101 + 1.70742i) q^{88} +(0.324819 - 0.999689i) q^{89} +(-3.94569 - 5.42509i) q^{90} +(5.37828 + 16.5526i) q^{91} +(-0.786761 + 4.96742i) q^{92} +(-5.77369 + 0.177314i) q^{93} +(3.03812 + 4.18162i) q^{94} +(10.2529 - 4.46033i) q^{95} +(-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	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

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