LMFDB - Embedded newform 750.2.l.c.743.9

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			743.9
Character	$\chi$	$=$	750.743
Dual form			750.2.l.c.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(0.974581 - 1.43185i) q^{3} +(0.587785 - 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(3.13589 - 3.13589i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.10038 - 2.79091i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(0.974581 - 1.43185i) q^{3} +(0.587785 - 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(3.13589 - 3.13589i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.10038 - 2.79091i) q^{9} +(-3.57685 - 1.16219i) q^{11} +(-0.585546 - 1.63007i) q^{12} +(-1.78169 + 3.49677i) q^{13} +(1.37043 - 4.21776i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-0.406920 - 0.0644499i) q^{17} +(-2.24749 - 1.98715i) q^{18} +(2.93913 + 4.04536i) q^{19} +(-1.43394 - 7.54629i) q^{21} +(-3.71462 + 0.588338i) q^{22} +(2.28327 + 4.48117i) q^{23} +(-1.26176 - 1.18657i) q^{24} +3.92451i q^{26} +(-5.06857 - 1.14438i) q^{27} +(-0.693758 - 4.38021i) q^{28} +(-1.49299 - 1.08472i) q^{29} +(2.69808 - 1.96027i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-5.15001 + 3.98886i) q^{33} +(-0.391828 + 0.127313i) q^{34} +(-2.90468 - 0.750223i) q^{36} +(4.70465 + 2.39714i) q^{37} +(4.45534 + 2.27011i) q^{38} +(3.27044 + 5.95899i) q^{39} +(3.24600 - 1.05469i) q^{41} +(-4.70360 - 6.07280i) q^{42} +(3.71639 + 3.71639i) q^{43} +(-3.04265 + 2.21062i) q^{44} +(4.06882 + 2.95617i) q^{46} +(-0.808572 - 5.10512i) q^{47} +(-1.66293 - 0.484416i) q^{48} -12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(1.78169 + 3.49677i) q^{52} +(-8.20487 + 1.29952i) q^{53} +(-5.03567 + 1.28143i) q^{54} +(-2.60672 - 3.58784i) q^{56} +(8.65677 - 0.265855i) q^{57} +(-1.82271 - 0.288689i) q^{58} +(1.73564 + 5.34175i) q^{59} +(4.43829 - 13.6596i) q^{61} +(1.51406 - 2.97152i) q^{62} +(-12.2026 - 5.30128i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-2.77779 + 5.89216i) q^{66} +(-0.968887 + 6.11731i) q^{67} +(-0.291323 + 0.291323i) q^{68} +(8.64159 + 1.09796i) q^{69} +(-0.992045 + 1.36543i) q^{71} +(-2.92868 + 0.650243i) q^{72} +(3.19175 - 1.62628i) q^{73} +5.28015 q^{74} +5.00034 q^{76} +(-14.8611 + 7.57211i) q^{77} +(5.61931 + 3.82475i) q^{78} +(6.24842 - 8.60021i) q^{79} +(-6.57831 + 6.14214i) q^{81} +(2.41339 - 2.41339i) q^{82} +(-1.10932 + 7.00394i) q^{83} +(-6.94793 - 3.27552i) q^{84} +(4.99854 + 1.62412i) q^{86} +(-3.00819 + 1.08059i) q^{87} +(-1.70742 + 3.35101i) q^{88} +(-0.324819 + 0.999689i) q^{89} +(5.37828 + 16.5526i) q^{91} +(4.96742 + 0.786761i) q^{92} +(-0.177314 - 5.77369i) q^{93} +(-3.03812 - 4.18162i) q^{94} +(-1.70160 + 0.323338i) q^{96} +(-7.61627 + 1.20630i) q^{97} +(-5.75096 - 11.2869i) 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} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$	0.974581	−	1.43185i	0.562674	−	0.826679i
$3$	0.974581	−	1.43185i	0.562674	−	0.826679i
$4$	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	0.206890	−	0.978364i	$-0.433666\pi$
$7$	3.13589	−	3.13589i	1.18525	−	1.18525i	0.978364	−	0.206890i	$-0.0663341\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−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	$0.791889\pi$
$12$	−0.585546	−	1.63007i	−0.169033	−	0.470561i
$13$	−1.78169	+	3.49677i	−0.494152	+	0.969828i	0.500420	+	0.865783i	$0.333179\pi$
$13$	−1.78169	+	3.49677i	−0.494152	+	0.969828i	−0.994573	+	0.104046i	$0.966821\pi$
$14$	1.37043	−	4.21776i	0.366264	−	1.12724i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.406920	−	0.0644499i	−0.0986927	−	0.0156314i	0.106893	−	0.994271i	$-0.465910\pi$
$17$	−0.406920	−	0.0644499i	−0.0986927	−	0.0156314i	−0.205585	+	0.978639i	$0.565910\pi$
$18$	−2.24749	−	1.98715i	−0.529739	−	0.468376i
$19$	2.93913	+	4.04536i	0.674282	+	0.928070i	0.999848	−	0.0174495i	$-0.00555464\pi$
$19$	2.93913	+	4.04536i	0.674282	+	0.928070i	−0.325565	+	0.945520i	$0.605555\pi$
$20$		0			0
$21$	−1.43394	−	7.54629i	−0.312912	−	1.64674i
$22$	−3.71462	+	0.588338i	−0.791960	+	0.125434i
$23$	2.28327	+	4.48117i	0.476095	+	0.934389i	0.996745	+	0.0806186i	$0.0256896\pi$
$23$	2.28327	+	4.48117i	0.476095	+	0.934389i	−0.520650	+	0.853770i	$0.674310\pi$
$24$	−1.26176	−	1.18657i	−0.257556	−	0.242208i
$25$		0			0
$26$			3.92451i			0.769660i
$27$	−5.06857	−	1.14438i	−0.975447	−	0.220236i
$28$	−0.693758	−	4.38021i	−0.131108	−	0.827783i
$29$	−1.49299	−	1.08472i	−0.277241	−	0.201427i	0.440472	−	0.897766i	$-0.354811\pi$
$29$	−1.49299	−	1.08472i	−0.277241	−	0.201427i	−0.717713	+	0.696339i	$0.754811\pi$
$30$		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
$33$	−5.15001	+	3.98886i	−0.896502	+	0.694372i
$34$	−0.391828	+	0.127313i	−0.0671980	+	0.0218340i
$35$		0			0
$36$	−2.90468	−	0.750223i	−0.484113	−	0.125037i
$37$	4.70465	+	2.39714i	0.773440	+	0.394087i	0.795720	−	0.605664i	$-0.207093\pi$
$37$	4.70465	+	2.39714i	0.773440	+	0.394087i	−0.0222802	+	0.999752i	$0.507093\pi$
$38$	4.45534	+	2.27011i	0.722751	+	0.368260i
$39$	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	$0.314128\pi$
$42$	−4.70360	−	6.07280i	−0.725781	−	0.937053i
$43$	3.71639	+	3.71639i	0.566745	+	0.566745i	0.931215	−	0.364470i	$-0.118750\pi$
$43$	3.71639	+	3.71639i	0.566745	+	0.566745i	−0.364470	+	0.931215i	$0.618750\pi$
$44$	−3.04265	+	2.21062i	−0.458697	+	0.333263i
$45$		0			0
$46$	4.06882	+	2.95617i	0.599914	+	0.435863i
$47$	−0.808572	−	5.10512i	−0.117942	−	0.744659i	−0.973793	−	0.227436i	$-0.926966\pi$
$47$	−0.808572	−	5.10512i	−0.117942	−	0.744659i	0.855851	−	0.517223i	$-0.173034\pi$
$48$	−1.66293	−	0.484416i	−0.240023	−	0.0699194i
$49$		−	12.6676i		−	1.80965i
$50$		0			0
$51$	−0.488859	+	0.519837i	−0.0684540	+	0.0727917i
$52$	1.78169	+	3.49677i	0.247076	+	0.484914i
$53$	−8.20487	+	1.29952i	−1.12703	+	0.178503i	−0.691988	−	0.721909i	$-0.743265\pi$
$53$	−8.20487	+	1.29952i	−1.12703	+	0.178503i	−0.435037	+	0.900412i	$0.643265\pi$
$54$	−5.03567	+	1.28143i	−0.685267	+	0.174381i
$55$		0			0
$56$	−2.60672	−	3.58784i	−0.348337	−	0.479445i
$57$	8.65677	−	0.265855i	1.14662	−	0.0352134i
$58$	−1.82271	−	0.288689i	−0.239334	−	0.0379068i
$59$	1.73564	+	5.34175i	0.225961	+	0.695437i	0.998193	+	0.0600956i	$0.0191406\pi$
$59$	1.73564	+	5.34175i	0.225961	+	0.695437i	−0.772231	+	0.635341i	$0.780859\pi$
$60$		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	$-0.271383\pi$
$62$	1.51406	−	2.97152i	0.192286	−	0.377383i
$63$	−12.2026	−	5.30128i	−1.53739	−	0.667899i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$		0			0
$66$	−2.77779	+	5.89216i	−0.341922	+	0.725275i
$67$	−0.968887	+	6.11731i	−0.118368	+	0.747349i	0.855089	+	0.518481i	$0.173502\pi$
$67$	−0.968887	+	6.11731i	−0.118368	+	0.747349i	−0.973458	+	0.228868i	$0.926498\pi$
$68$	−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	$0.231932\pi$
$72$	−2.92868	+	0.650243i	−0.345149	+	0.0766319i
$73$	3.19175	−	1.62628i	0.373567	−	0.190342i	−0.257120	−	0.966380i	$-0.582773\pi$
$73$	3.19175	−	1.62628i	0.373567	−	0.190342i	0.630686	+	0.776038i	$0.282773\pi$
$74$	5.28015			0.613805
$75$		0			0
$76$	5.00034			0.573579
$77$	−14.8611	+	7.57211i	−1.69358	+	0.862922i
$78$	5.61931	+	3.82475i	0.636262	+	0.433068i
$79$	6.24842	−	8.60021i	0.703002	−	0.967599i	−0.296918	−	0.954903i	$-0.595959\pi$
$79$	6.24842	−	8.60021i	0.703002	−	0.967599i	0.999919	−	0.0126959i	$-0.00404134\pi$
$80$		0			0
$81$	−6.57831	+	6.14214i	−0.730923	+	0.682460i
$82$	2.41339	−	2.41339i	0.266514	−	0.266514i
$83$	−1.10932	+	7.00394i	−0.121763	+	0.768782i	0.848938	+	0.528493i	$0.177243\pi$
$83$	−1.10932	+	7.00394i	−0.121763	+	0.768782i	−0.970701	+	0.240290i	$0.922757\pi$
$84$	−6.94793	−	3.27552i	−0.758081	−	0.357388i
$85$		0			0
$86$	4.99854	+	1.62412i	0.539006	+	0.175134i
$87$	−3.00819	+	1.08059i	−0.322512	+	0.115851i
$88$	−1.70742	+	3.35101i	−0.182012	+	0.357219i
$89$	−0.324819	+	0.999689i	−0.0344307	+	0.105967i	−0.966795	−	0.255554i	$-0.917742\pi$
$89$	−0.324819	+	0.999689i	−0.0344307	+	0.105967i	0.932364	+	0.361521i	$0.117742\pi$
$90$		0			0
$91$	5.37828	+	16.5526i	0.563797	+	1.73519i
$92$	4.96742	+	0.786761i	0.517889	+	0.0820255i
$93$	−0.177314	−	5.77369i	−0.0183866	−	0.598704i
$94$	−3.03812	−	4.18162i	−0.313358	−	0.431301i
$95$		0			0
$96$	−1.70160	+	0.323338i	−0.173669	+	0.0330005i
$97$	−7.61627	+	1.20630i	−0.773315	+	0.122481i	−0.530607	−	0.847618i	$-0.678036\pi$
$97$	−7.61627	+	1.20630i	−0.773315	+	0.122481i	−0.242709	+	0.970099i	$0.578036\pi$
$98$	−5.75096	−	11.2869i	−0.580935	−	1.14015i
$99$	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	$0.814061\pi$
$102$	−0.199576	+	0.685116i	−0.0197609	+	0.0678366i
$103$	0.383628	+	2.42213i	0.0378000	+	0.238660i	0.999353	−	0.0359588i	$-0.0114485\pi$
$103$	0.383628	+	2.42213i	0.0378000	+	0.238660i	−0.961553	+	0.274618i	$0.911448\pi$
$104$	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	0.883945	−	0.467590i	$-0.154878\pi$
$107$	4.30681	+	4.30681i	0.416355	+	0.416355i	−0.467590	+	0.883945i	$0.654878\pi$
$108$	−3.90505	+	3.42791i	−0.375764	+	0.329851i
$109$	−4.46242	+	1.44993i	−0.427422	+	0.138878i	−0.514825	−	0.857295i	$-0.672143\pi$
$109$	−4.46242	+	1.44993i	−0.427422	+	0.138878i	0.0874029	+	0.996173i	$0.472143\pi$
$110$		0			0
$111$	8.01741	−	4.40015i	0.760979	−	0.417643i
$112$	−3.95145	−	2.01336i	−0.373377	−	0.190245i
$113$	15.2342	+	7.76223i	1.43312	+	0.730209i	0.986384	−	0.164459i	$-0.0525879\pi$
$113$	15.2342	+	7.76223i	1.43312	+	0.730209i	0.446732	+	0.894668i	$0.352588\pi$
$114$	7.59254	−	4.16697i	0.711107	−	0.390272i
$115$		0			0
$116$	−1.75511	+	0.570270i	−0.162958	+	0.0529483i
$117$	11.7197	+	1.12475i	1.08349	+	0.103983i
$118$	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
$122$	−2.24681	−	14.1858i	−0.203416	−	1.28432i
$123$	1.65334	−	5.67567i	0.149076	−	0.511758i
$124$		−	3.33501i		−	0.299493i
$125$		0			0
$126$	−13.2794	+	0.816407i	−1.18302	+	0.0727313i
$127$	8.90421	+	17.4755i	0.790121	+	1.55070i	0.834065	+	0.551666i	$0.186008\pi$
$127$	8.90421	+	17.4755i	0.790121	+	1.55070i	−0.0439442	+	0.999034i	$0.513992\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	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	$-0.554002\pi$
$132$	0.199959	+	6.51104i	0.0174042	+	0.566713i
$133$	21.9026	+	3.46903i	1.89919	+	0.300803i
$134$	1.91392	+	5.89043i	0.165337	+	0.508856i
$135$		0			0
$136$	−0.127313	+	0.391828i	−0.0109170	+	0.0335990i
$137$	3.28166	−	6.44062i	0.280371	−	0.550259i	−0.707279	−	0.706935i	$-0.750078\pi$
$137$	3.28166	−	6.44062i	0.280371	−	0.550259i	0.987650	+	0.156675i	$0.0500775\pi$
$138$	8.19818	−	2.94491i	0.697875	−	0.250687i
$139$	−9.21867	−	2.99533i	−0.781918	−	0.254060i	−0.109259	−	0.994013i	$-0.534848\pi$
$139$	−9.21867	−	2.99533i	−0.781918	−	0.254060i	−0.672659	+	0.739953i	$0.734848\pi$
$140$		0			0
$141$	−8.09779	−	3.81760i	−0.681957	−	0.321500i
$142$	−0.264025	+	1.66699i	−0.0221565	+	0.139891i
$143$	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
$147$	−18.1381	−	12.3456i	−1.49600	−	1.01825i
$148$	4.70465	−	2.39714i	0.386720	−	0.197044i
$149$	−4.14920			−0.339915			−0.169958	−	0.985451i	$-0.554363\pi$
$149$	−4.14920			−0.339915			−0.169958	+	0.985451i	$0.554363\pi$
$150$		0			0
$151$	−9.50070			−0.773156			−0.386578	−	0.922257i	$-0.626343\pi$
$151$	−9.50070			−0.773156			−0.386578	+	0.922257i	$0.626343\pi$
$152$	4.45534	−	2.27011i	0.361376	−	0.184130i
$153$	0.267895	+	1.20660i	0.0216581	+	0.0975475i
$154$	−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	$-0.696166\pi$
$157$	2.98265	−	2.98265i	0.238041	−	0.238041i	0.816039	+	0.577997i	$0.196166\pi$
$158$	1.66297	−	10.4996i	0.132299	−	0.835300i
$159$	−6.13559	+	13.0146i	−0.486584	+	1.03213i
$160$		0			0
$161$	21.2125	+	6.89237i	1.67178	+	0.543195i
$162$	−3.07284	+	8.45917i	−0.241425	+	0.664616i
$163$	4.73142	−	9.28593i	0.370593	−	0.727330i	−0.628116	−	0.778119i	$-0.716174\pi$
$163$	4.73142	−	9.28593i	0.370593	−	0.727330i	0.998709	+	0.0507896i	$0.0161738\pi$
$164$	1.05469	−	3.24600i	0.0823575	−	0.253470i
$165$		0			0
$166$	2.19132	+	6.74418i	0.170079	+	0.523450i
$167$	13.8268	+	2.18995i	1.06995	+	0.169464i	0.666476	−	0.745527i	$-0.267802\pi$
$167$	13.8268	+	2.18995i	1.06995	+	0.169464i	0.403476	+	0.914990i	$0.367802\pi$
$168$	−7.67770	+	0.235788i	−0.592348	+	0.0181914i
$169$	−1.41174	−	1.94309i	−0.108595	−	0.149469i
$170$		0			0
$171$	8.05606	−	12.6543i	0.616062	−	0.967697i
$172$	5.19107	−	0.822184i	0.395815	−	0.0626910i
$173$	−3.18237	−	6.24576i	−0.241951	−	0.474856i	0.737815	−	0.675003i	$-0.235858\pi$
$173$	−3.18237	−	6.24576i	−0.241951	−	0.474856i	−0.979766	+	0.200147i	$0.935858\pi$
$174$	−2.18974	+	2.32850i	−0.166004	+	0.176523i
$175$		0			0
$176$			3.76092i			0.283490i
$177$	9.34011	+	2.72079i	0.702045	+	0.204507i
$178$	0.164434	+	1.03819i	0.0123248	+	0.0778159i
$179$	−2.28996	−	1.66375i	−0.171159	−	0.124355i	0.498908	−	0.866655i	$-0.333735\pi$
$179$	−2.28996	−	1.66375i	−0.171159	−	0.124355i	−0.670067	+	0.742301i	$0.733735\pi$
$180$		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
$183$	−15.2331	−	19.6674i	−1.12606	−	1.45386i
$184$	4.78318	−	1.55415i	0.352621	−	0.114573i
$185$		0			0
$186$	−2.77919	−	5.06390i	−0.203780	−	0.371303i
$187$	1.38059	+	0.703446i	0.100959	+	0.0514411i
$188$	−4.60540	−	2.34657i	−0.335883	−	0.171141i
$189$	−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	$0.413079\pi$
$192$	−1.36935	+	1.06061i	−0.0988241	+	0.0765428i
$193$	4.16176	+	4.16176i	0.299570	+	0.299570i	0.840845	−	0.541275i	$-0.182058\pi$
$193$	4.16176	+	4.16176i	0.299570	+	0.299570i	−0.541275	+	0.840845i	$0.682058\pi$
$194$	−6.23850	+	4.53254i	−0.447898	+	0.325417i
$195$		0			0
$196$	−10.2483	−	7.44581i	−0.732020	−	0.531844i
$197$	3.00593	+	18.9787i	0.214164	+	1.35218i	0.827105	+	0.562048i	$0.189986\pi$
$197$	3.00593	+	18.9787i	0.214164	+	1.35218i	−0.612941	+	0.790129i	$0.710014\pi$
$198$	5.72951	+	9.71976i	0.407178	+	0.690753i
$199$			12.7124i			0.901157i	0.892737	+	0.450579i	$0.148782\pi$
$199$			12.7124i			0.901157i	−0.892737	+	0.450579i	$0.851218\pi$
$200$		0			0
$201$	7.81481	+	7.34912i	0.551214	+	0.518367i
$202$	5.03237	+	9.87658i	0.354076	+	0.694914i
$203$	−8.08340	+	1.28028i	−0.567343	+	0.0898583i
$204$	0.133213	+	0.701048i	0.00932676	+	0.0490832i
$205$		0			0
$206$	1.44144	+	1.98397i	0.100430	+	0.138230i
$207$	9.99405	−	11.3034i	0.694634	−	0.785641i
$208$	3.87619	+	0.613929i	0.268766	+	0.0425683i
$209$	−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	$0.895097\pi$
$212$	−3.77136	+	7.40172i	−0.259018	+	0.508352i
$213$	0.988266	+	2.75118i	0.0677149	+	0.188508i
$214$	5.79265	+	1.88215i	0.395977	+	0.128661i
$215$		0			0
$216$	−1.92319	+	4.82715i	−0.130856	+	0.328446i
$217$	2.31369	−	14.6081i	0.157064	−	0.991661i
$218$	−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
$222$	5.14594	−	7.56039i	0.345373	−	0.507420i
$223$	−20.1688	+	10.2765i	−1.35060	+	0.688167i	−0.971467	−	0.237174i	$-0.923779\pi$
$223$	−20.1688	+	10.2765i	−1.35060	+	0.688167i	−0.379136	+	0.925341i	$0.623779\pi$
$224$	−4.43481			−0.296313
$225$		0			0
$226$	17.0978			1.13733
$227$	−17.2036	+	8.76566i	−1.14184	+	0.581797i	−0.919468	−	0.393164i	$-0.871380\pi$
$227$	−17.2036	+	8.76566i	−1.14184	+	0.581797i	−0.222373	+	0.974962i	$0.571380\pi$
$228$	4.87324	−	7.15974i	0.322738	−	0.474165i
$229$	−9.58051	+	13.1864i	−0.633098	+	0.871384i	−0.998224	−	0.0595738i	$-0.981026\pi$
$229$	−9.58051	+	13.1864i	−0.633098	+	0.871384i	0.365126	+	0.930958i	$0.381026\pi$
$230$		0			0
$231$	−3.64122	+	28.6585i	−0.239575	+	1.88559i
$232$	−1.30492	+	1.30492i	−0.0856721	+	0.0856721i
$233$	−0.0952038	+	0.601093i	−0.00623701	+	0.0393789i	−0.990611	−	0.136714i	$-0.956346\pi$
$233$	−0.0952038	+	0.601093i	−0.00623701	+	0.0393789i	0.984374	+	0.176093i	$0.0563459\pi$
$234$	10.9529	−	4.31847i	0.716016	−	0.282307i
$235$		0			0
$236$	5.34175	+	1.73564i	0.347718	+	0.112981i
$237$	−6.22461	−	17.3284i	−0.404332	−	1.12560i
$238$	−0.829491	+	1.62797i	−0.0537679	+	0.105525i
$239$	−2.47857	+	7.62825i	−0.160325	+	0.493430i	−0.998661	−	0.0517231i	$-0.983529\pi$
$239$	−2.47857	+	7.62825i	−0.160325	+	0.493430i	0.838336	+	0.545154i	$0.183529\pi$
$240$		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	$0.974994\pi$
$242$	3.10583	+	0.491916i	0.199650	+	0.0316215i
$243$	2.38352	+	15.4052i	0.152903	+	0.988241i
$244$	−8.44212	−	11.6196i	−0.540452	−	0.743868i
$245$		0			0
$246$	−1.10357	−	5.80766i	−0.0703609	−	0.370283i
$247$	−19.3823	+	3.06986i	−1.23327	+	0.195330i
$248$	−1.51406	−	2.97152i	−0.0961432	−	0.188692i
$249$	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	$0.848116\pi$
$252$	−11.4614	+	6.75613i	−0.721998	+	0.425596i
$253$	−2.95895	−	18.6821i	−0.186028	−	1.17453i
$254$	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	0.738749	−	0.673981i	$-0.235417\pi$
$257$	1.03830	+	1.03830i	0.0647675	+	0.0647675i	−0.673981	+	0.738749i	$0.735417\pi$
$258$	7.19698	−	5.57431i	0.448064	−	0.347042i
$259$	22.2704	−	7.23610i	1.38382	−	0.449629i
$260$		0			0
$261$	−1.38449	+	5.36039i	−0.0856976	+	0.331800i
$262$	−18.2880	−	9.31821i	−1.12984	−	0.575681i
$263$	−19.8871	−	10.1330i	−1.22629	−	0.624825i	−0.283743	−	0.958901i	$-0.591576\pi$
$263$	−19.8871	−	10.1330i	−1.22629	−	0.624825i	−0.942546	+	0.334075i	$0.891576\pi$
$264$	3.13412	+	5.71060i	0.192891	+	0.351463i
$265$		0			0
$266$	21.0902	−	6.85264i	1.29313	−	0.420162i
$267$	1.11484	+	1.43937i	0.0682272	+	0.0880880i
$268$	4.37951	+	4.37951i	0.267521	+	0.267521i
$269$	20.2239	−	14.6936i	1.23308	−	0.895882i	0.235959	−	0.971763i	$-0.424177\pi$
$269$	20.2239	−	14.6936i	1.23308	−	0.895882i	0.997117	+	0.0758813i	$0.0241770\pi$
$270$		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	$0.864217\pi$
$272$	0.0644499	+	0.406920i	0.00390785	+	0.0246732i
$273$	28.9425	+	8.43100i	1.75168	+	0.510268i
$274$		−	7.22848i		−	0.436688i
$275$		0			0
$276$	5.96767	−	6.34583i	0.359212	−	0.381974i
$277$	3.12626	+	6.13564i	0.187839	+	0.368655i	0.965651	−	0.259842i	$-0.0836705\pi$
$277$	3.12626	+	6.13564i	0.187839	+	0.368655i	−0.777812	+	0.628497i	$0.783670\pi$
$278$	−9.57375	+	1.51633i	−0.574195	+	0.0909436i
$279$	−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	$-0.460700\pi$
$282$	−8.94834	+	0.274810i	−0.532866	+	0.0163647i
$283$	−7.23244	−	1.14551i	−0.429924	−	0.0680933i	−0.0622774	−	0.998059i	$-0.519836\pi$
$283$	−7.23244	−	1.14551i	−0.429924	−	0.0680933i	−0.367646	+	0.929966i	$0.619836\pi$
$284$	0.521549	+	1.60516i	0.0309482	+	0.0952489i
$285$		0			0
$286$	4.56103	−	14.0374i	0.269699	−	0.830049i
$287$	6.87171	−	13.4865i	0.405624	−	0.796083i
$288$	−1.19538	+	2.75156i	−0.0704384	+	0.162137i
$289$	−16.0065	−	5.20084i	−0.941561	−	0.305932i
$290$		0			0
$291$	−5.69543	+	12.0810i	−0.333872	+	0.708200i
$292$	0.560378	−	3.53809i	0.0327936	−	0.207051i
$293$	1.14628	−	1.14628i	0.0669662	−	0.0669662i	−0.672830	−	0.739797i	$-0.734922\pi$
$293$	1.14628	−	1.14628i	0.0669662	−	0.0669662i	0.739797	+	0.672830i	$0.234922\pi$
$294$	−21.7659	−	2.76548i	−1.26941	−	0.161286i
$295$		0			0
$296$	3.10360	−	4.27173i	0.180393	−	0.248290i
$297$	16.7995	+	9.98391i	0.974808	+	0.579325i
$298$	−3.69696	+	1.88370i	−0.214159	+	0.109120i
$299$	−19.7377			−1.14146
$300$		0			0
$301$	23.3084			1.34347
$302$	−8.46519	+	4.31323i	−0.487117	+	0.248198i
$303$	15.8717	+	10.8030i	0.911804	+	0.620615i
$304$	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	$-0.858622\pi$
$307$	−8.29257	+	8.29257i	−0.473282	+	0.473282i	0.429693	+	0.902975i	$0.358622\pi$
$308$	−2.60917	+	16.4737i	−0.148671	+	0.938673i
$309$	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	$0.987305\pi$
$312$	6.39724	−	2.29798i	0.362172	−	0.130098i
$313$	−1.98845	+	3.90255i	−0.112394	+	0.220585i	−0.940351	−	0.340206i	$-0.889503\pi$
$313$	−1.98845	+	3.90255i	−0.112394	+	0.220585i	0.827957	+	0.560791i	$0.189503\pi$
$314$	1.30346	−	4.01165i	0.0735587	−	0.226391i
$315$		0			0
$316$	−3.28499	−	10.1102i	−0.184795	−	0.568740i
$317$	−27.6572	−	4.38047i	−1.55338	−	0.246032i	−0.680053	−	0.733163i	$-0.738043\pi$
$317$	−27.6572	−	4.38047i	−1.55338	−	0.246032i	−0.873329	+	0.487131i	$0.838043\pi$
$318$	0.441669	+	14.3816i	0.0247676	+	0.806481i
$319$	4.07954	+	5.61501i	0.228411	+	0.314380i
$320$		0			0
$321$	10.3640	−	1.96937i	0.578464	−	0.109919i
$322$	22.0296	−	3.48914i	1.22766	−	0.194442i
$323$	−0.935268	−	1.83557i	−0.0520397	−	0.102134i
$324$	1.10246	+	8.93222i	0.0612479	+	0.496235i
$325$		0			0
$326$		−	10.4218i		−	0.577212i
$327$	−2.27291	+	7.80259i	−0.125692	+	0.431484i
$328$	−0.533919	−	3.37103i	−0.0294807	−	0.186134i
$329$	−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
$333$	1.51327	−	15.7680i	0.0829264	−	0.864082i
$334$	13.3140	−	4.32598i	0.728510	−	0.236707i
$335$		0			0
$336$	−6.73384	+	3.69569i	−0.367361	+	0.201617i
$337$	13.9578	+	7.11185i	0.760329	+	0.387407i	0.790757	−	0.612130i	$-0.209687\pi$
$337$	13.9578	+	7.11185i	0.760329	+	0.387407i	−0.0304279	+	0.999537i	$0.509687\pi$
$338$	−2.14002	−	1.09039i	−0.116401	−	0.0593095i
$339$	25.9613	−	14.2482i	1.41003	−	0.773856i
$340$		0			0
$341$	−11.9289	+	3.87592i	−0.645983	+	0.209893i
$342$	1.43307	−	14.9324i	0.0774917	−	0.807453i
$343$	−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
$347$	−5.77593	−	36.4678i	−0.310068	−	1.95769i	−0.286891	−	0.957963i	$-0.592622\pi$
$347$	−5.77593	−	36.4678i	−0.310068	−	1.95769i	−0.0231773	−	0.999731i	$-0.507378\pi$
$348$	−0.893957	+	3.06883i	−0.0479211	+	0.164507i
$349$			15.0145i			0.803705i	0.915704	+	0.401853i	$0.131634\pi$
$349$			15.0145i			0.803705i	−0.915704	+	0.401853i	$0.868366\pi$
$350$		0			0
$351$	13.0322	−	15.6847i	0.695610	−	0.837186i
$352$	1.70742	+	3.35101i	0.0910060	+	0.178609i
$353$	29.7348	−	4.70953i	1.58263	−	0.250663i	0.697698	−	0.716392i	$-0.254208\pi$
$353$	29.7348	−	4.70953i	1.58263	−	0.250663i	0.884927	+	0.465729i	$0.154208\pi$
$354$	9.55731	−	1.81607i	0.507965	−	0.0965233i
$355$		0			0
$356$	0.617842	+	0.850386i	0.0327456	+	0.0450704i
$357$	0.0971428	+	3.16316i	0.00514134	+	0.167412i
$358$	−2.79569	−	0.442795i	−0.147757	−	0.0234024i
$359$	1.07807	+	3.31797i	0.0568986	+	0.175116i	0.975467	−	0.220147i	$-0.0706536\pi$
$359$	1.07807	+	3.31797i	0.0568986	+	0.175116i	−0.918568	+	0.395263i	$0.870654\pi$
$360$		0			0
$361$	−1.85517	+	5.70961i	−0.0976403	+	0.300506i
$362$	−0.158904	+	0.311866i	−0.00835180	+	0.0163913i
$363$	5.12584	−	1.84128i	0.269037	−	0.0966420i
$364$	16.5526	+	5.37828i	0.867594	+	0.281898i
$365$		0			0
$366$	−22.5016	−	10.6081i	−1.17618	−	0.554494i
$367$	2.44988	−	15.4679i	0.127882	−	0.807418i	−0.837473	−	0.546479i	$-0.815968\pi$
$367$	2.44988	−	15.4679i	0.127882	−	0.807418i	0.965355	−	0.260939i	$-0.0840322\pi$
$368$	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
$372$	−4.77524	−	3.25024i	−0.247585	−	0.168517i
$373$	−5.68352	+	2.89590i	−0.294282	+	0.149944i	−0.594898	−	0.803801i	$-0.702808\pi$
$373$	−5.68352	+	2.89590i	−0.294282	+	0.149944i	0.300616	+	0.953745i	$0.402808\pi$
$374$	1.54947			0.0801213
$375$		0			0
$376$	−5.16876			−0.266558
$377$	6.45305	−	3.28799i	0.332349	−	0.169340i
$378$	−11.7728	+	19.8097i	−0.605530	+	1.01890i
$379$	15.8374	−	21.7983i	0.813510	−	1.11970i	−0.177262	−	0.984164i	$-0.556724\pi$
$379$	15.8374	−	21.7983i	0.813510	−	1.11970i	0.990772	−	0.135537i	$-0.0432760\pi$
$380$		0			0
$381$	33.7002	+	4.28180i	1.72651	+	0.219363i
$382$	−0.802829	+	0.802829i	−0.0410763	+	0.0410763i
$383$	−4.68475	+	29.5784i	−0.239380	+	1.51138i	0.516280	+	0.856420i	$0.327316\pi$
$383$	−4.68475	+	29.5784i	−0.239380	+	1.51138i	−0.755660	+	0.654964i	$0.772684\pi$
$384$	−0.738592	+	1.56668i	−0.0376911	+	0.0799492i
$385$		0			0
$386$	5.59756	+	1.81876i	0.284908	+	0.0925723i
$387$	6.28264	−	14.4616i	0.319365	−	0.735123i
$388$	−3.50082	+	6.87074i	−0.177727	+	0.348809i
$389$	3.57268	−	10.9956i	0.181142	−	0.557497i	−0.818719	−	0.574195i	$-0.805315\pi$
$389$	3.57268	−	10.9956i	0.181142	−	0.557497i	0.999861	+	0.0166975i	$0.00531522\pi$
$390$		0			0
$391$	−0.640299	−	1.97064i	−0.0323813	−	0.0996594i
$392$	−12.5116	−	1.98165i	−0.631932	−	0.100088i
$393$	−35.5338	+	1.09127i	−1.79244	+	0.0550472i
$394$	11.2945	+	15.5455i	0.569007	+	0.783170i
$395$		0			0
$396$	9.51771	+	6.05923i	0.478283	+	0.304488i
$397$	−13.2341	+	2.09608i	−0.664203	+	0.105199i	−0.479427	−	0.877581i	$-0.659156\pi$
$397$	−13.2341	+	2.09608i	−0.664203	+	0.105199i	−0.184775	+	0.982781i	$0.559156\pi$
$398$	5.77130	+	11.3268i	0.289289	+	0.567762i
$399$	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	$-0.187881\pi$
$402$	10.2995	+	3.00026i	0.513691	+	0.149639i
$403$	2.04746	+	12.9272i	0.101991	+	0.643948i
$404$	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
$408$	0.436963	+	0.564161i	0.0216329	+	0.0279301i
$409$	−13.3939	+	4.35194i	−0.662285	+	0.215190i	−0.620823	−	0.783951i	$-0.713202\pi$
$409$	−13.3939	+	4.35194i	−0.662285	+	0.215190i	−0.0414620	+	0.999140i	$0.513202\pi$
$410$		0			0
$411$	−6.02376	−	10.9757i	−0.297130	−	0.541394i
$412$	2.18504	+	1.11333i	0.107649	+	0.0548499i
$413$	22.1939	+	11.3084i	1.09209	+	0.556448i
$414$	3.77313	−	14.6086i	0.185439	−	0.717974i
$415$		0			0
$416$	3.73243	−	1.21274i	0.182998	−	0.0594595i
$417$	−13.2732	+	10.2806i	−0.649992	+	0.503441i
$418$	−13.2978	−	13.2978i	−0.650416	−	0.650416i
$419$	−4.58918	+	3.33423i	−0.224196	+	0.162888i	−0.694213	−	0.719769i	$-0.744248\pi$
$419$	−4.58918	+	3.33423i	−0.224196	+	0.162888i	0.470017	+	0.882657i	$0.344248\pi$
$420$		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	$0.650259\pi$
$422$	2.72761	+	17.2214i	0.132778	+	0.838327i
$423$	−13.3582	+	7.87425i	−0.649497	+	0.382859i
$424$			8.30714i			0.403431i
$425$		0			0
$426$	2.12956	+	2.00266i	0.103178	+	0.0970292i
$427$	−28.9171	−	56.7531i	−1.39940	−	2.74647i
$428$	6.01577	−	0.952804i	0.290783	−	0.0460555i
$429$	−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	$0.959763\pi$
$432$	0.477906	+	5.17413i	0.0229932	+	0.248940i
$433$	−22.9138	−	3.62919i	−1.10117	−	0.174408i	−0.420710	−	0.907195i	$-0.638219\pi$
$433$	−22.9138	−	3.62919i	−1.10117	−	0.174408i	−0.680458	+	0.732787i	$0.738219\pi$
$434$	−4.57041	−	14.0663i	−0.219387	−	0.675203i
$435$		0			0
$436$	−1.44993	+	4.46242i	−0.0694390	+	0.213711i
$437$	−11.4171	+	22.4074i	−0.546156	+	1.07189i
$438$	−2.09754	−	5.83923i	−0.100224	−	0.279009i
$439$	−10.7777	−	3.50189i	−0.514393	−	0.167136i	0.0403065	−	0.999187i	$-0.487167\pi$
$439$	−10.7777	−	3.50189i	−0.514393	−	0.167136i	−0.554699	+	0.832051i	$0.687167\pi$
$440$		0			0
$441$	−35.3540	+	13.9392i	−1.68352	+	0.663772i
$442$	0.252934	−	1.59696i	0.0120309	−	0.0759598i
$443$	−5.43418	+	5.43418i	−0.258186	+	0.258186i	−0.824316	−	0.566130i	$-0.808440\pi$
$443$	−5.43418	+	5.43418i	−0.258186	+	0.258186i	0.566130	+	0.824316i	$0.308440\pi$
$444$	1.15272	−	9.07256i	0.0547057	−	0.430565i
$445$		0			0
$446$	−13.3051	+	18.3129i	−0.630015	+	0.867141i
$447$	−4.04373	+	5.94102i	−0.191262	+	0.281001i
$448$	−3.95145	+	2.01336i	−0.186688	+	0.0951225i
$449$	26.9459			1.27165			0.635827	−	0.771831i	$-0.280659\pi$
$449$	26.9459			1.27165			0.635827	+	0.771831i	$0.280659\pi$
$450$		0			0
$451$	−12.8362			−0.604434
$452$	15.2342	−	7.76223i	0.716558	−	0.365104i
$453$	−9.25920	+	13.6036i	−0.435035	+	0.639152i
$454$	−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	0.141919	−	0.989878i	$-0.454673\pi$
$457$	24.1951	−	24.1951i	1.13180	−	1.13180i	0.989878	−	0.141919i	$-0.0453271\pi$
$458$	−2.54978	+	16.0987i	−0.119143	+	0.752241i
$459$	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	$0.267631\pi$
$462$	9.76632	+	27.1880i	0.454370	+	1.26490i
$463$	−3.18828	+	6.25735i	−0.148172	+	0.290804i	−0.953149	−	0.302503i	$-0.902178\pi$
$463$	−3.18828	+	6.25735i	−0.148172	+	0.290804i	0.804977	+	0.593307i	$0.202178\pi$
$464$	−0.570270	+	1.75511i	−0.0264741	+	0.0814790i
$465$		0			0
$466$	0.188063	+	0.578799i	0.00871187	+	0.0268124i
$467$	28.3424	+	4.48899i	1.31153	+	0.207726i	0.772744	−	0.634718i	$-0.218884\pi$
$467$	28.3424	+	4.48899i	1.31153	+	0.207726i	0.538785	+	0.842444i	$0.318884\pi$
$468$	7.79860	−	8.82032i	0.360490	−	0.407719i
$469$	16.1449	+	22.2215i	0.745502	+	1.02609i
$470$		0			0
$471$	−1.36387	−	7.17753i	−0.0628438	−	0.330723i
$472$	5.54750	−	0.878638i	0.255344	−	0.0404426i
$473$	−8.97383	−	17.6121i	−0.412617	−	0.809807i
$474$	−13.4131	−	12.6138i	−0.616084	−	0.579371i
$475$		0			0
$476$			1.82711i			0.0837455i
$477$	12.6554	+	21.4690i	0.579449	+	0.983000i
$478$	1.25473	+	7.92207i	0.0573901	+	0.362347i
$479$	−10.3928	−	7.55082i	−0.474860	−	0.345006i	0.324473	−	0.945895i	$-0.394813\pi$
$479$	−10.3928	−	7.55082i	−0.474860	−	0.345006i	−0.799332	+	0.600889i	$0.794813\pi$
$480$		0			0
$481$	−16.7645	+	12.1801i	−0.764394	+	0.555365i
$482$	−5.12480	−	5.12480i	−0.233428	−	0.233428i
$483$	30.5421	−	23.6560i	1.38972	−	1.07638i
$484$	2.99064	−	0.971718i	0.135938	−	0.0441690i
$485$		0			0
$486$	9.11753	+	12.6440i	0.413580	+	0.573543i
$487$	−18.4423	−	9.39682i	−0.835700	−	0.425810i	−0.0168777	−	0.999858i	$-0.505373\pi$
$487$	−18.4423	−	9.39682i	−0.835700	−	0.425810i	−0.818822	+	0.574047i	$0.805373\pi$
$488$	−12.7972	−	6.52048i	−0.579301	−	0.295168i
$489$	−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	$0.182886\pi$
$492$	−3.61991	−	4.67365i	−0.163198	−	0.210704i
$493$	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
$497$	1.17090	+	7.39279i	0.0525221	+	0.331612i
$498$	11.7923	+	3.43511i	0.528424	+	0.153931i
$499$			0.405848i			0.0181683i	0.999959	+	0.00908413i	$0.00289161\pi$
$499$			0.405848i			0.0181683i	−0.999959	+	0.00908413i	$0.997108\pi$
$500$		0			0
$501$	16.6110	−	17.6636i	0.742126	−	0.789153i
$502$	6.60645	+	12.9659i	0.294860	+	0.578696i
$503$	−5.98816	+	0.948431i	−0.266999	+	0.0422885i	−0.288498	−	0.957480i	$-0.593156\pi$
$503$	−5.98816	+	0.948431i	−0.266999	+	0.0422885i	0.0214995	+	0.999769i	$0.493156\pi$
$504$	−7.14493	+	11.2231i	−0.318260	+	0.499917i
$505$		0			0
$506$	−11.1179	−	15.3025i	−0.494252	−	0.680280i
$507$	−4.15807	+	0.127697i	−0.184666	+	0.00567123i
$508$	19.3717	+	3.06818i	0.859482	+	0.136129i
$509$	1.17675	+	3.62167i	0.0521586	+	0.160528i	0.973743	−	0.227651i	$-0.0731044\pi$
$509$	1.17675	+	3.62167i	0.0521586	+	0.160528i	−0.921584	+	0.388178i	$0.873104\pi$
$510$		0			0
$511$	4.90915	−	15.1088i	0.217168	−	0.668375i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	−10.2678	−	23.8677i	−0.453332	−	1.05378i
$514$	1.39651	+	0.453755i	0.0615976	+	0.0200143i
$515$		0			0
$516$	3.88187	−	8.23411i	0.170890	−	0.362487i
$517$	−3.04098	+	19.2000i	−0.133742	+	0.844414i
$518$	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	$0.179706\pi$
$522$	1.19998	+	5.40469i	0.0525217	+	0.236557i
$523$	−7.89460	+	4.02250i	−0.345207	+	0.175892i	−0.617994	−	0.786183i	$-0.712054\pi$
$523$	−7.89460	+	4.02250i	−0.345207	+	0.175892i	0.272787	+	0.962074i	$0.412054\pi$
$524$	−20.5251			−0.896645
$525$		0			0
$526$	−22.3198			−0.973188
$527$	−1.22424	+	0.623784i	−0.0533289	+	0.0271724i
$528$	5.38508	+	3.66532i	0.234355	+	0.159513i
$529$	−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
$533$	−2.09537	+	13.2296i	−0.0907606	+	0.573040i
$534$	1.64679	+	0.776360i	0.0712636	+	0.0335964i
$535$		0			0
$536$	5.89043	+	1.91392i	0.254428	+	0.0826686i
$537$	−4.61399	+	1.65741i	−0.199108	+	0.0715227i
$538$	11.3489	−	22.2735i	0.489287	−	0.960280i
$539$	−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	$-0.391221\pi$
$542$	−16.0422	−	2.54083i	−0.689071	−	0.109138i
$543$	0.0186094	+	0.605959i	0.000798607	+	0.0260042i
$544$	0.242163	+	0.333309i	0.0103827	+	0.0142905i
$545$		0			0
$546$	29.6155	−	5.62752i	1.26743	−	0.240836i
$547$	26.2003	−	4.14971i	1.12024	−	0.177429i	0.431274	−	0.902221i	$-0.358064\pi$
$547$	26.2003	−	4.14971i	1.12024	−	0.177429i	0.688968	+	0.724792i	$0.258064\pi$
$548$	−3.28166	−	6.44062i	−0.140186	−	0.275130i
$549$	−43.0066	+	2.64402i	−1.83548	+	0.112844i
$550$		0			0
$551$		−	9.22780i		−	0.393118i
$552$	2.43629	−	8.36344i	0.103695	−	0.355972i
$553$	−7.37495	−	46.5636i	−0.313615	−	1.98009i
$554$	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	0.106814	−	0.994279i	$-0.465935\pi$
$557$	−20.9449	−	20.9449i	−0.887465	−	0.887465i	−0.994279	+	0.106814i	$0.965935\pi$
$558$	−9.95928	−	0.955798i	−0.421610	−	0.0404622i
$559$	−19.6168	+	6.37389i	−0.829703	+	0.269587i
$560$		0			0
$561$	2.35273	−	1.29123i	0.0993322	−	0.0545159i
$562$	−21.8207	−	11.1182i	−0.920450	−	0.468993i
$563$	13.4464	+	6.85128i	0.566698	+	0.288747i	0.713772	−	0.700378i	$-0.246985\pi$
$563$	13.4464	+	6.85128i	0.566698	+	0.288747i	−0.147073	+	0.989126i	$0.546985\pi$
$564$	−7.84827	+	4.30732i	−0.330472	+	0.181371i
$565$		0			0
$566$	−6.96420	+	2.26281i	−0.292727	+	0.0951128i
$567$	−1.36778	+	39.8899i	−0.0574413	+	1.67522i
$568$	1.19343	+	1.19343i	0.0500753	+	0.0500753i
$569$	7.06373	−	5.13210i	0.296127	−	0.215149i	−0.429794	−	0.902927i	$-0.641414\pi$
$569$	7.06373	−	5.13210i	0.296127	−	0.215149i	0.725921	+	0.687778i	$0.241414\pi$
$570$		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	$0.530487\pi$
$572$	−2.30894	−	14.5781i	−0.0965416	−	0.609540i
$573$	−0.549992	+	1.88805i	−0.0229762	+	0.0788743i
$574$		−	15.1362i		−	0.631775i
$575$		0			0
$576$	0.184091	+	2.99435i	0.00767044	+	0.124764i
$577$	−16.6187	−	32.6160i	−0.691845	−	1.35782i	−0.922960	−	0.384896i	$-0.874237\pi$
$577$	−16.6187	−	32.6160i	−0.691845	−	1.35782i	0.231114	−	0.972927i	$-0.425763\pi$
$578$	−16.6231	+	2.63283i	−0.691428	+	0.109511i
$579$	10.0150	−	1.90304i	0.416209	−	0.0790877i
$580$		0			0
$581$	18.4849	+	25.4423i	0.766882	+	1.05552i
$582$	0.409985	+	13.3499i	0.0169944	+	0.553372i
$583$	30.8579	+	4.88741i	1.27800	+	0.202416i
$584$	−1.10696	−	3.40687i	−0.0458062	−	0.140977i
$585$		0			0
$586$	0.500941	−	1.54174i	0.0206937	−	0.0636887i
$587$	−5.16169	+	10.1304i	−0.213046	+	0.418126i	−0.972655	−	0.232254i	$-0.925390\pi$
$587$	−5.16169	+	10.1304i	−0.213046	+	0.418126i	0.759609	+	0.650379i	$0.225390\pi$
$588$	−20.6491	+	7.41745i	−0.851553	+	0.305890i
$589$	15.8600	+	5.15324i	0.653501	+	0.212335i
$590$		0			0
$591$	30.1042	+	14.1922i	1.23832	+	0.583791i
$592$	0.825998	−	5.21515i	0.0339483	−	0.214341i
$593$	16.4362	−	16.4362i	0.674952	−	0.674952i	−0.283901	−	0.958854i	$-0.591629\pi$
$593$	16.4362	−	16.4362i	0.674952	−	0.674952i	0.958854	+	0.283901i	$0.0916288\pi$
$594$	19.5011	+	1.26890i	0.800140	+	0.0520636i
$595$		0			0
$596$	−2.43884	+	3.35677i	−0.0998986	+	0.137499i
$597$	18.2022	+	12.3893i	0.744968	+	0.507058i
$598$	−17.5864	+	8.96072i	−0.719162	+	0.366431i
$599$	16.9386			0.692094			0.346047	−	0.938217i	$-0.387524\pi$
$599$	16.9386			0.692094			0.346047	+	0.938217i	$0.387524\pi$
$600$		0			0
$601$	−26.0220			−1.06146			−0.530730	−	0.847541i	$-0.678082\pi$
$601$	−26.0220			−1.06146			−0.530730	+	0.847541i	$0.678082\pi$
$602$	20.7679	−	10.5818i	0.846437	−	0.431281i
$603$	18.1390	−	4.02732i	0.738677	−	0.164005i
$604$	−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	−0.218322	+	0.975877i	$0.570058\pi$
$607$	−29.4219	+	29.4219i	−1.19420	+	1.19420i	−0.975877	+	0.218322i	$0.929942\pi$
$608$	0.782226	−	4.93878i	0.0317235	−	0.200294i
$609$	−6.04475	+	12.8219i	−0.244946	+	0.519571i
$610$		0			0
$611$	19.2921	+	6.26837i	0.780473	+	0.253591i
$612$	1.13362	+	0.492487i	0.0458239	+	0.0199076i
$613$	−2.55565	+	5.01575i	−0.103222	+	0.202584i	−0.936841	−	0.349755i	$-0.886265\pi$
$613$	−2.55565	+	5.01575i	−0.103222	+	0.202584i	0.833619	+	0.552339i	$0.186265\pi$
$614$	−3.62398	+	11.1535i	−0.146252	+	0.450118i
$615$		0			0
$616$	5.15409	+	15.8627i	0.207664	+	0.639125i
$617$	35.1967	+	5.57460i	1.41696	+	0.224425i	0.817478	−	0.575960i	$-0.195372\pi$
$617$	35.1967	+	5.57460i	1.41696	+	0.224425i	0.599486	+	0.800385i	$0.295372\pi$
$618$	4.24555	−	0.130384i	0.170781	−	0.00524480i
$619$	20.2991	+	27.9393i	0.815889	+	1.12297i	0.990388	+	0.138317i	$0.0441694\pi$
$619$	20.2991	+	27.9393i	0.815889	+	1.12297i	−0.174499	+	0.984657i	$0.555831\pi$
$620$		0			0
$621$	−6.44476	−	25.3261i	−0.258619	−	1.01630i
$622$	−32.6756	+	5.17530i	−1.31017	+	0.207511i
$623$	2.11632	+	4.15351i	0.0847885	+	0.166407i
$624$	4.65672	−	4.95180i	0.186418	−	0.198231i
$625$		0			0
$626$			4.37993i			0.175057i
$627$	−31.2729	−	9.10988i	−1.24892	−	0.363814i
$628$	−0.659856	−	4.16617i	−0.0263311	−	0.166248i
$629$	−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
$633$	18.4929	+	23.8761i	0.735026	+	0.948989i
$634$	−26.6314	+	8.65307i	−1.05767	+	0.343657i
$635$		0			0
$636$	6.92265	+	12.6136i	0.274501	+	0.500162i
$637$	44.2955	+	22.5697i	1.75505	+	0.894244i
$638$	6.18406	+	3.15094i	0.244829	+	0.124747i
$639$	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	$0.313224\pi$
$642$	8.34036	−	6.45990i	0.329168	−	0.254952i
$643$	−11.4059	−	11.4059i	−0.449806	−	0.449806i	0.445484	−	0.895290i	$-0.353032\pi$
$643$	−11.4059	−	11.4059i	−0.449806	−	0.449806i	−0.895290	+	0.445484i	$0.853032\pi$
$644$	18.0445	−	13.1101i	0.711051	−	0.516609i
$645$		0			0
$646$	−1.66666	−	1.21090i	−0.0655739	−	0.0476422i
$647$	4.90280	+	30.9551i	0.192749	+	1.21697i	0.874368	+	0.485263i	$0.161276\pi$
$647$	4.90280	+	30.9551i	0.192749	+	1.21697i	−0.681619	+	0.731707i	$0.738724\pi$
$648$	5.03744	+	7.45816i	0.197889	+	0.292984i
$649$		−	21.1238i		−	0.829181i
$650$		0			0
$651$	−18.6617	−	17.5496i	−0.731409	−	0.687823i
$652$	−4.73142	−	9.28593i	−0.185297	−	0.363665i
$653$	−37.8061	+	5.98789i	−1.47947	+	0.234324i	−0.843390	−	0.537302i	$-0.819444\pi$
$653$	−37.8061	+	5.98789i	−1.47947	+	0.234324i	−0.636076	+	0.771626i	$0.719444\pi$
$654$	1.51712	+	7.98404i	0.0593242	+	0.312201i
$655$		0			0
$656$	−2.00614	−	2.76122i	−0.0783266	−	0.107807i
$657$	−8.05095	−	7.11835i	−0.314098	−	0.277713i
$658$	−22.6403	−	3.58587i	−0.882610	−	0.139792i
$659$	6.33270	+	19.4901i	0.246687	+	0.759225i	0.995354	+	0.0962789i	$0.0306941\pi$
$659$	6.33270	+	19.4901i	0.246687	+	0.759225i	−0.748667	+	0.662946i	$0.769306\pi$
$660$		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	$0.777033\pi$
$662$	4.35103	−	8.53939i	0.169108	−	0.331893i
$663$	−0.946752	−	2.63562i	−0.0367688	−	0.102359i
$664$	6.74418	+	2.19132i	0.261725	+	0.0850395i
$665$		0			0
$666$	−5.81020	−	14.7364i	−0.225141	−	0.571024i
$667$	1.45192	−	9.16704i	0.0562184	−	0.354949i
$668$	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
$672$	−4.32208	+	6.34998i	−0.166728	+	0.244956i
$673$	33.0273	−	16.8283i	1.27311	−	0.648681i	0.318890	−	0.947792i	$-0.396690\pi$
$673$	33.0273	−	16.8283i	1.27311	−	0.648681i	0.954219	+	0.299110i	$0.0966898\pi$
$674$	15.6652			0.603401
$675$		0			0
$676$	−2.40180			−0.0923767
$677$	37.1946	−	18.9516i	1.42951	−	0.728369i	0.443686	−	0.896182i	$-0.353670\pi$
$677$	37.1946	−	18.9516i	1.42951	−	0.728369i	0.985819	+	0.167813i	$0.0536704\pi$
$678$	16.6632	−	24.4814i	0.639945	−	0.940204i
$679$	−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
$683$	7.96066	−	50.2616i	0.304606	−	1.92321i	−0.0731865	−	0.997318i	$-0.523317\pi$
$683$	7.96066	−	50.2616i	0.304606	−	1.92321i	0.377793	−	0.925890i	$-0.376683\pi$
$684$	−5.50230	−	13.9555i	−0.210386	−	0.533601i
$685$		0			0
$686$	−23.9045	−	7.76703i	−0.912677	−	0.296547i
$687$	9.54401	+	26.5691i	0.364127	+	1.01367i
$688$	2.38607	−	4.68293i	0.0909681	−	0.178535i
$689$	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	$-0.308872\pi$
$692$	−6.92347	−	1.09657i	−0.263191	−	0.0416854i
$693$	37.4860	+	33.1437i	1.42397	+	1.25902i
$694$	−21.7024	−	29.8708i	−0.823813	−	1.13388i
$695$		0			0
$696$	0.596698	+	3.14020i	0.0226178	+	0.119029i
$697$	−1.38884	+	0.219971i	−0.0526061	+	0.00833198i
$698$	6.81642	+	13.3780i	0.258005	+	0.506364i
$699$	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	$0.792100\pi$
$702$	4.49113	−	19.8917i	0.169507	−	0.750762i
$703$	4.13027	+	26.0775i	0.155776	+	0.983533i
$704$	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
$708$	7.69114	−	5.95706i	0.289051	−	0.223880i
$709$	2.62130	−	0.851713i	0.0984451	−	0.0319867i	−0.259380	−	0.965775i	$-0.583518\pi$
$709$	2.62130	−	0.851713i	0.0984451	−	0.0319867i	0.357825	+	0.933789i	$0.383518\pi$
$710$		0			0
$711$	−30.8780	−	7.97521i	−1.15802	−	0.299094i
$712$	0.936569	+	0.477205i	0.0350994	+	0.0178840i
$713$	14.9448	+	7.61474i	0.559686	+	0.285174i
$714$	1.52260	+	2.77429i	0.0569818	+	0.103825i
$715$		0			0
$716$	−2.69201	+	0.874686i	−0.100605	+	0.0326886i
$717$	8.50694	+	10.9833i	0.317697	+	0.410178i
$718$	2.46690	+	2.46690i	0.0920639	+	0.0920639i
$719$	−6.94235	+	5.04392i	−0.258906	+	0.188106i	−0.709665	−	0.704540i	$-0.751154\pi$
$719$	−6.94235	+	5.04392i	−0.258906	+	0.188106i	0.450759	+	0.892646i	$0.351154\pi$
$720$		0			0
$721$	8.79854	+	6.39251i	0.327675	+	0.238070i
$722$	0.939145	+	5.92953i	0.0349514	+	0.220674i
$723$	−12.0522	−	3.51083i	−0.448226	−	0.130569i
$724$			0.350016i			0.0130082i
$725$		0			0
$726$	3.73123	−	3.96767i	0.138479	−	0.147254i
$727$	15.5376	+	30.4942i	0.576257	+	1.13097i	0.976692	+	0.214644i	$0.0688590\pi$
$727$	15.5376	+	30.4942i	0.576257	+	1.13097i	−0.400435	+	0.916325i	$0.631141\pi$
$728$	17.1902	−	2.72266i	0.637111	−	0.100909i
$729$	24.3808	+	11.6007i	0.902992	+	0.429656i
$730$		0			0
$731$	−1.27276	−	1.75180i	−0.0470746	−	0.0647926i
$732$	−24.8650	+	0.763622i	−0.919038	+	0.0282243i
$733$	−39.3201	−	6.22770i	−1.45232	−	0.230025i	−0.620124	−	0.784504i	$-0.712918\pi$
$733$	−39.3201	−	6.22770i	−1.45232	−	0.230025i	−0.832198	+	0.554478i	$0.812918\pi$
$734$	−4.83943	−	14.8942i	−0.178627	−	0.549756i
$735$		0			0
$736$	1.55415	−	4.78318i	0.0572867	−	0.176310i
$737$	10.5750	−	20.7547i	0.389537	−	0.764509i
$738$	−9.39121	−	4.07989i	−0.345695	−	0.150183i
$739$	−19.6010	−	6.36874i	−0.721033	−	0.234278i	−0.0745620	−	0.997216i	$-0.523756\pi$
$739$	−19.6010	−	6.36874i	−0.721033	−	0.234278i	−0.646471	+	0.762939i	$0.723756\pi$
$740$		0			0
$741$	−14.4941	+	30.7444i	−0.532452	+	1.12942i
$742$	−5.76314	+	36.3871i	−0.211572	+	1.33581i
$743$	−25.7253	+	25.7253i	−0.943771	+	0.943771i	−0.998501	−	0.0547306i	$-0.982570\pi$
$743$	−25.7253	+	25.7253i	−0.943771	+	0.943771i	0.0547306	+	0.998501i	$0.482570\pi$
$744$	−5.73035	−	0.728073i	−0.210085	−	0.0266925i
$745$		0			0
$746$	−3.74935	+	5.16053i	−0.137273	+	0.188940i
$747$	20.7680	−	4.61103i	0.759862	−	0.168709i
$748$	1.38059	−	0.703446i	0.0504794	−	0.0257205i
$749$	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	$0.581360\pi$
$752$	−4.60540	+	2.34657i	−0.167942	+	0.0855705i
$753$	20.8362	+	14.1821i	0.759314	+	0.516823i
$754$	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	−0.0443764	+	0.999015i	$0.514130\pi$
$757$	−28.7075	+	28.7075i	−1.04339	+	1.04339i	−0.999015	+	0.0443764i	$0.985870\pi$
$758$	4.21499	−	26.6124i	0.153095	−	0.966606i
$759$	−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	$0.843868\pi$
$762$	31.9710	−	11.4844i	1.15819	−	0.416037i
$763$	−9.44684	+	18.5405i	−0.341998	+	0.671210i
$764$	−0.350849	+	1.07980i	−0.0126933	+	0.0390659i
$765$		0			0
$766$	9.25415	+	28.4814i	0.334366	+	1.02907i
$767$	−21.7712	−	3.44822i	−0.786114	−	0.124508i
$768$	0.0531674	+	1.73123i	0.00191851	+	0.0624705i
$769$	−23.2438	−	31.9924i	−0.838194	−	1.15368i	−0.986342	−	0.164710i	$-0.947331\pi$
$769$	−23.2438	−	31.9924i	−0.838194	−	1.15368i	0.148148	−	0.988965i	$-0.452669\pi$
$770$		0			0
$771$	2.49860	−	0.474783i	0.0899850	−	0.0170989i
$772$	5.81316	−	0.920714i	0.209220	−	0.0331372i
$773$	−16.3075	−	32.0052i	−0.586539	−	1.15115i	−0.973422	−	0.229019i	$-0.926448\pi$
$773$	−16.3075	−	32.0052i	−0.586539	−	1.15115i	0.386883	−	0.922129i	$-0.373552\pi$
$774$	−0.967539	−	15.7376i	−0.0347775	−	0.565677i
$775$		0			0
$776$			7.71121i			0.276816i
$777$	11.3433	−	38.9400i	0.406939	−	1.39697i
$778$	−1.80860	−	11.4191i	−0.0648416	−	0.409394i
$779$	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
$783$	6.32598	+	7.20652i	0.226072	+	0.257540i
$784$	−12.0476	+	3.91450i	−0.430271	+	0.139803i
$785$		0			0
$786$	−31.1654	+	17.1043i	−1.11163	+	0.610092i
$787$	25.5543	+	13.0206i	0.910913	+	0.464133i	0.845652	−	0.533735i	$-0.179212\pi$
$787$	25.5543	+	13.0206i	0.910913	+	0.464133i	0.0652610	+	0.997868i	$0.479212\pi$
$788$	17.1209	+	8.72355i	0.609908	+	0.310764i
$789$	−33.8904	+	18.5999i	−1.20653	+	0.662173i
$790$		0			0
$791$	72.1143	−	23.4314i	2.56409	−	0.833123i
$792$	11.2312	+	1.07786i	0.399082	+	0.0383001i
$793$	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
$797$	1.51547	+	9.56827i	0.0536805	+	0.338926i	0.999882	+	0.0153481i	$0.00488564\pi$
$797$	1.51547	+	9.56827i	0.0536805	+	0.338926i	−0.946202	+	0.323578i	$0.895114\pi$
$798$	10.7422	−	36.8765i	0.380270	−	1.30541i
$799$			2.12949i			0.0753360i
$800$		0			0
$801$	3.14746	−	0.193504i	0.111210	−	0.00683713i
$802$	−10.1196	−	19.8609i	−0.357337	−	0.701313i
$803$	−13.3065	+	2.10754i	−0.469575	+	0.0743734i
$804$	10.5390	−	2.00261i	0.371682	−	0.0706267i
$805$		0			0
$806$	7.69311	+	10.5887i	0.270978	+	0.372970i
$807$	−1.32909	−	43.2777i	−0.0467861	−	1.52345i
$808$	10.9483	+	1.73404i	0.385159	+	0.0610032i
$809$	17.2607	+	53.1231i	0.606855	+	1.86771i	0.483496	+	0.875346i	$0.339367\pi$
$809$	17.2607	+	53.1231i	0.606855	+	1.86771i	0.123359	+	0.992362i	$0.460633\pi$
$810$		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	$0.986674\pi$
$812$	−3.71553	+	7.29214i	−0.130390	+	0.255904i
$813$	−26.4759	+	9.51053i	−0.928550	+	0.333549i
$814$	−18.8863	−	6.13654i	−0.661965	−	0.215086i
$815$		0			0
$816$	0.645460	+	0.304294i	0.0225956	+	0.0106524i
$817$	−4.11120	+	25.9571i	−0.143833	+	0.908125i
$818$	−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	$-0.0269377\pi$
$822$	−10.3501	−	7.04474i	−0.361001	−	0.245713i
$823$	35.1647	−	17.9173i	1.22577	−	0.624559i	0.283355	−	0.959015i	$-0.408553\pi$
$823$	35.1647	−	17.9173i	1.22577	−	0.624559i	0.942411	+	0.334456i	$0.108553\pi$
$824$	2.45232			0.0854307
$825$		0			0
$826$	24.9088			0.866688
$827$	22.4561	−	11.4419i	0.780874	−	0.397875i	−0.0176456	−	0.999844i	$-0.505617\pi$
$827$	22.4561	−	11.4419i	0.780874	−	0.397875i	0.798519	+	0.601969i	$0.205617\pi$
$828$	−3.27029	−	14.7293i	−0.113650	−	0.511880i
$829$	22.7111	−	31.2592i	0.788791	−	1.08568i	−0.205467	−	0.978664i	$-0.565871\pi$
$829$	22.7111	−	31.2592i	0.788791	−	1.08568i	0.994258	−	0.107013i	$-0.0341287\pi$
$830$		0			0
$831$	11.8321	+	1.50334i	0.410451	+	0.0521502i
$832$	2.77505	−	2.77505i	0.0962075	−	0.0962075i
$833$	−0.816423	+	5.15469i	−0.0282874	+	0.178600i
$834$	−7.15923	+	15.1860i	−0.247904	+	0.525847i
$835$		0			0
$836$	−17.8855	−	5.81135i	−0.618582	−	0.200990i
$837$	−15.9187	+	6.84815i	−0.550231	+	0.236707i
$838$	−2.57528	+	5.05427i	−0.0889615	+	0.174597i
$839$	1.11037	−	3.41736i	0.0383342	−	0.117980i	−0.930058	−	0.367412i	$-0.880244\pi$
$839$	1.11037	−	3.41736i	0.0383342	−	0.117980i	0.968392	+	0.249432i	$0.0802438\pi$
$840$		0			0
$841$	−7.90910	−	24.3417i	−0.272727	−	0.839369i
$842$	6.30794	+	0.999080i	0.217386	+	0.0344306i
$843$	−42.3978	+	1.30207i	−1.46026	+	0.0448455i
$844$	10.2487	+	14.1061i	0.352774	+	0.485552i
$845$		0			0
$846$	−8.32739	+	13.0805i	−0.286302	+	0.449717i
$847$	13.7738	−	2.18155i	0.473273	−	0.0749591i
$848$	3.77136	+	7.40172i	0.129509	+	0.254176i
$849$	−8.68879	+	9.23937i	−0.298198	+	0.317095i
$850$		0			0
$851$			26.5557i			0.910317i
$852$	2.80664	+	0.817581i	0.0961540	+	0.0280099i
$853$	7.10018	+	44.8288i	0.243106	+	1.53491i	0.743278	+	0.668983i	$0.233270\pi$
$853$	7.10018	+	44.8288i	0.243106	+	1.53491i	−0.500172	+	0.865926i	$0.666730\pi$
$854$	−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	0.607082	−	0.794639i	$-0.292340\pi$
$857$	−5.49063	−	5.49063i	−0.187556	−	0.187556i	−0.794639	+	0.607082i	$0.792340\pi$
$858$	−15.6543	−	20.2113i	−0.534431	−	0.690002i
$859$	−10.7387	+	3.48922i	−0.366400	+	0.119051i	−0.486430	−	0.873720i	$-0.661701\pi$
$859$	−10.7387	+	3.48922i	−0.366400	+	0.119051i	0.120030	+	0.992770i	$0.461701\pi$
$860$		0			0
$861$	−12.6136	−	22.9829i	−0.429870	−	0.783256i
$862$	−17.7986	−	9.06883i	−0.606222	−	0.308886i
$863$	10.3665	+	5.28199i	0.352880	+	0.179801i	0.621440	−	0.783462i	$-0.286548\pi$
$863$	10.3665	+	5.28199i	0.352880	+	0.179801i	−0.268560	+	0.963263i	$0.586548\pi$
$864$	2.77482	+	4.39322i	0.0944014	+	0.149460i
$865$		0			0
$866$	−22.0640	+	7.16903i	−0.749765	+	0.243613i
$867$	−23.0465	+	17.8503i	−0.782699	+	0.606228i
$868$	−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
$872$	0.734001	+	4.63430i	0.0248564	+	0.156937i
$873$	11.7475	+	19.9289i	0.397592	+	0.674491i
$874$			25.1484i			0.850658i
$875$		0			0
$876$	−4.51987	−	4.25053i	−0.152712	−	0.143612i
$877$	−11.2271	−	22.0344i	−0.379112	−	0.744049i	0.620068	−	0.784548i	$-0.287105\pi$
$877$	−11.2271	−	22.0344i	−0.379112	−	0.744049i	−0.999180	+	0.0404992i	$0.987105\pi$
$878$	−11.1928	+	1.77277i	−0.377740	+	0.0598282i
$879$	−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	$0.865096\pi$
$882$	−25.1724	+	28.4703i	−0.847598	+	0.958645i
$883$	7.05614	+	1.11758i	0.237458	+	0.0376097i	0.274029	−	0.961721i	$-0.411644\pi$
$883$	7.05614	+	1.11758i	0.237458	+	0.0376097i	−0.0365710	+	0.999331i	$0.511644\pi$
$884$	−0.499640	−	1.53774i	−0.0168047	−	0.0517196i
$885$		0			0
$886$	−2.37482	+	7.30895i	−0.0797837	+	0.245549i
$887$	−1.61555	+	3.17069i	−0.0542448	+	0.106461i	−0.916537	−	0.399949i	$-0.869028\pi$
$887$	−1.61555	+	3.17069i	−0.0542448	+	0.106461i	0.862293	+	0.506410i	$0.169028\pi$
$888$	−3.09177	−	8.60703i	−0.103753	−	0.288833i
$889$	82.7238	+	26.8786i	2.77447	+	0.901479i
$890$		0			0
$891$	30.6680	−	14.3243i	1.02742	−	0.479881i
$892$	−3.54105	+	22.3573i	−0.118563	+	0.748578i
$893$	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
$897$	−19.2360	+	28.2614i	−0.642270	+	0.943620i
$898$	24.0090	−	12.2332i	0.801189	−	0.408226i
$899$	−6.15455			−0.205266
$900$		0			0
$901$	3.42248			0.114019
$902$	−11.4372	+	5.82752i	−0.380816	+	0.194035i
$903$	22.7159	−	33.3741i	0.755938	−	1.11062i
$904$	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	$-0.735806\pi$
$907$	1.89862	−	1.89862i	0.0630427	−	0.0630427i	0.737925	+	0.674883i	$0.235806\pi$
$908$	−3.02044	+	19.0703i	−0.100237	+	0.632871i
$909$	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	$0.613249\pi$
$912$	−2.92793	−	8.15092i	−0.0969535	−	0.269904i
$913$	12.1078	−	23.7628i	0.400708	−	0.786435i
$914$	10.5736	−	32.5423i	0.349744	−	1.07640i
$915$		0			0
$916$	5.03677	+	15.5016i	0.166420	+	0.512187i
$917$	−89.9045	−	14.2395i	−2.96891	−	0.470229i
$918$	2.13170	−	0.196894i	0.0703567	−	0.00649846i
$919$	5.62589	+	7.74338i	0.185581	+	0.255430i	0.891663	−	0.452700i	$-0.149539\pi$
$919$	5.62589	+	7.74338i	0.185581	+	0.255430i	−0.706082	+	0.708130i	$0.749539\pi$
$920$		0			0
$921$	3.79193	+	19.9555i	0.124948	+	0.657555i
$922$	36.6665	−	5.80740i	1.20755	−	0.191256i
$923$	−3.00708	−	5.90173i	−0.0989793	−	0.194258i
$924$	21.0449	+	19.7908i	0.692328	+	0.651071i
$925$		0			0
$926$			7.02279i			0.230783i
$927$	6.33780	−	3.73594i	0.208161	−	0.122704i
$928$	0.288689	+	1.82271i	0.00947670	+	0.0598335i
$929$	28.0139	+	20.3533i	0.919106	+	0.667770i	0.943301	−	0.331938i	$-0.107702\pi$
$929$	28.0139	+	20.3533i	0.919106	+	0.667770i	−0.0241953	+	0.999707i	$0.507702\pi$
$930$		0			0
$931$	51.2449	−	37.2316i	1.67949	−	1.22022i
$932$	0.430335	+	0.430335i	0.0140961	+	0.0140961i
$933$	−45.3019	+	35.0879i	−1.48312	+	1.14873i
$934$	27.2912	−	8.86745i	0.892995	−	0.290152i
$935$		0			0
$936$	2.94426	−	11.3995i	0.0962362	−	0.372603i
$937$	−13.6302	−	6.94494i	−0.445280	−	0.226881i	0.216949	−	0.976183i	$-0.430389\pi$
$937$	−13.6302	−	6.94494i	−0.445280	−	0.226881i	−0.662229	+	0.749302i	$0.730389\pi$
$938$	24.4736	+	12.4699i	0.799090	+	0.407157i
$939$	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	$0.246711\pi$
$942$	−4.47375	−	5.77604i	−0.145763	−	0.188194i
$943$	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
$947$	5.88298	+	37.1437i	0.191171	+	1.20701i	0.877450	+	0.479669i	$0.159243\pi$
$947$	5.88298	+	37.1437i	0.191171	+	1.20701i	−0.686279	+	0.727339i	$0.740757\pi$
$948$	−17.6777	−	5.14955i	−0.574145	−	0.167250i
$949$			14.0583i			0.456353i
$950$		0			0
$951$	−33.2263	+	35.3318i	−1.07744	+	1.14571i
$952$	0.829491	+	1.62797i	0.0268840	+	0.0527627i
$953$	−26.3120	+	4.16742i	−0.852331	+	0.134996i	−0.567289	−	0.823519i	$-0.692008\pi$
$953$	−26.3120	+	4.16742i	−0.852331	+	0.134996i	−0.285042	+	0.958515i	$0.592008\pi$
$954$	21.0227	+	13.3836i	0.680636	+	0.433311i
$955$		0			0
$956$	4.71452	+	6.48898i	0.152478	+	0.209868i
$957$	12.0157	−	0.369010i	0.388412	−	0.0119284i
$958$	−12.6881	−	2.00959i	−0.409933	−	0.0649269i
$959$	−9.90614	−	30.4880i	−0.319886	−	0.984508i
$960$		0			0
$961$	−6.14254	+	18.9048i	−0.198146	+	0.609832i
$962$	−9.40760	+	18.4635i	−0.303313	+	0.595286i
$963$	7.28076	−	16.7591i	0.234619	−	0.540053i
$964$	−6.89284	−	2.23962i	−0.222003	−	0.0721333i
$965$		0			0
$966$	16.4737	−	34.9435i	0.530032	−	1.12429i
$967$	6.56982	−	41.4802i	0.211271	−	1.33391i	−0.622853	−	0.782339i	$-0.714027\pi$
$967$	6.56982	−	41.4802i	0.211271	−	1.33391i	0.834125	−	0.551576i	$-0.185973\pi$
$968$	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	$0.125212\pi$
$972$	13.8640	+	7.12661i	0.444689	+	0.228586i
$973$	−38.3017	+	19.5157i	−1.22790	+	0.625645i
$974$	−20.6983			−0.663215
$975$		0			0
$976$	−14.3626			−0.459736
$977$	1.06999	−	0.545186i	0.0342319	−	0.0174420i	−0.436791	−	0.899563i	$-0.643885\pi$
$977$	1.06999	−	0.545186i	0.0342319	−	0.0174420i	0.471023	+	0.882121i	$0.343885\pi$
$978$	−14.9225	−	10.1569i	−0.477169	−	0.324783i
$979$	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
$983$	−2.80520	+	17.7113i	−0.0894719	+	0.564903i	0.901704	+	0.432353i	$0.142317\pi$
$983$	−2.80520	+	17.7113i	−0.0894719	+	0.564903i	−0.991176	+	0.132550i	$0.957683\pi$
$984$	−5.34715	−	2.52085i	−0.170461	−	0.0803618i
$985$		0			0
$986$	0.723093	+	0.234947i	0.0230280	+	0.00748224i
$987$	−37.3653	+	13.4222i	−1.18935	+	0.427233i
$988$	−8.90907	+	17.4850i	−0.283435	+	0.556273i
$989$	−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	$0.622104\pi$
$992$	−3.29395	−	0.521711i	−0.104583	−	0.0165643i
$993$	−0.509555	−	16.5921i	−0.0161702	−	0.526535i
$994$	4.39954	+	6.05544i	0.139545	+	0.192067i
$995$		0			0
$996$	12.0665	−	2.29287i	0.382341	−	0.0726523i
$997$	21.3791	−	3.38611i	0.677082	−	0.107239i	0.191583	−	0.981476i	$-0.438638\pi$
$997$	21.3791	−	3.38611i	0.677082	−	0.107239i	0.485499	+	0.874237i	$0.338638\pi$
$998$	0.184251	+	0.361613i	0.00583237	+	0.0114467i
$999$	−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.c.743.9		80
3.2	odd	2	inner	750.2.l.c.743.2		80
5.2	odd	4		150.2.l.a.47.6	yes	80
5.3	odd	4		750.2.l.b.257.5		80
5.4	even	2		750.2.l.a.743.2		80
15.2	even	4		150.2.l.a.47.2	✓	80
15.8	even	4		750.2.l.b.257.9		80
15.14	odd	2		750.2.l.a.743.9		80
25.6	even	5		150.2.l.a.83.2	yes	80
25.8	odd	20		750.2.l.a.107.9		80
25.17	odd	20	inner	750.2.l.c.107.2		80
25.19	even	10		750.2.l.b.143.9		80
75.8	even	20		750.2.l.a.107.2		80
75.17	even	20	inner	750.2.l.c.107.9		80
75.44	odd	10		750.2.l.b.143.5		80
75.56	odd	10		150.2.l.a.83.6	yes	80

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

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)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.974581 - 1.43185i) q^{3} +(0.587785 - 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(3.13589 - 3.13589i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.10038 - 2.79091i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.974581 - 1.43185i) q^{3} +(0.587785 - 0.809017i) q^{4} +(0.218312 - 1.71824i) q^{6} +(3.13589 - 3.13589i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.10038 - 2.79091i) q^{9} +(-3.57685 - 1.16219i) q^{11} +(-0.585546 - 1.63007i) q^{12} +(-1.78169 + 3.49677i) q^{13} +(1.37043 - 4.21776i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-0.406920 - 0.0644499i) q^{17} +(-2.24749 - 1.98715i) q^{18} +(2.93913 + 4.04536i) q^{19} +(-1.43394 - 7.54629i) q^{21} +(-3.71462 + 0.588338i) q^{22} +(2.28327 + 4.48117i) q^{23} +(-1.26176 - 1.18657i) q^{24} +3.92451i q^{26} +(-5.06857 - 1.14438i) q^{27} +(-0.693758 - 4.38021i) q^{28} +(-1.49299 - 1.08472i) q^{29} +(2.69808 - 1.96027i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-5.15001 + 3.98886i) q^{33} +(-0.391828 + 0.127313i) q^{34} +(-2.90468 - 0.750223i) q^{36} +(4.70465 + 2.39714i) q^{37} +(4.45534 + 2.27011i) q^{38} +(3.27044 + 5.95899i) q^{39} +(3.24600 - 1.05469i) q^{41} +(-4.70360 - 6.07280i) q^{42} +(3.71639 + 3.71639i) q^{43} +(-3.04265 + 2.21062i) q^{44} +(4.06882 + 2.95617i) q^{46} +(-0.808572 - 5.10512i) q^{47} +(-1.66293 - 0.484416i) q^{48} -12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(1.78169 + 3.49677i) q^{52} +(-8.20487 + 1.29952i) q^{53} +(-5.03567 + 1.28143i) q^{54} +(-2.60672 - 3.58784i) q^{56} +(8.65677 - 0.265855i) q^{57} +(-1.82271 - 0.288689i) q^{58} +(1.73564 + 5.34175i) q^{59} +(4.43829 - 13.6596i) q^{61} +(1.51406 - 2.97152i) q^{62} +(-12.2026 - 5.30128i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-2.77779 + 5.89216i) q^{66} +(-0.968887 + 6.11731i) q^{67} +(-0.291323 + 0.291323i) q^{68} +(8.64159 + 1.09796i) q^{69} +(-0.992045 + 1.36543i) q^{71} +(-2.92868 + 0.650243i) q^{72} +(3.19175 - 1.62628i) q^{73} +5.28015 q^{74} +5.00034 q^{76} +(-14.8611 + 7.57211i) q^{77} +(5.61931 + 3.82475i) q^{78} +(6.24842 - 8.60021i) q^{79} +(-6.57831 + 6.14214i) q^{81} +(2.41339 - 2.41339i) q^{82} +(-1.10932 + 7.00394i) q^{83} +(-6.94793 - 3.27552i) q^{84} +(4.99854 + 1.62412i) q^{86} +(-3.00819 + 1.08059i) q^{87} +(-1.70742 + 3.35101i) q^{88} +(-0.324819 + 0.999689i) q^{89} +(5.37828 + 16.5526i) q^{91} +(4.96742 + 0.786761i) q^{92} +(-0.177314 - 5.77369i) q^{93} +(-3.03812 - 4.18162i) q^{94} +(-1.70160 + 0.323338i) q^{96} +(-7.61627 + 1.20630i) q^{97} +(-5.75096 - 11.2869i) 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	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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