LMFDB - Embedded newform 722.2.e.n.389.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.186694177220038656.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 343x^{6} + 117649 $ x^12 + 343*x^6 + 117649
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			389.2
Root			$0.459430 + 2.60556i$ of defining polynomial
Character	$\chi$	$=$	722.389
Dual form			722.2.e.n.245.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(2.02676 - 1.70066i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.54650 + 0.562880i) q^{5} +(2.02676 + 1.70066i) q^{6} +(-1.82288 + 3.15731i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.694593 - 3.93923i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(2.02676 - 1.70066i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.54650 + 0.562880i) q^{5} +(2.02676 + 1.70066i) q^{6} +(-1.82288 + 3.15731i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.694593 - 3.93923i) q^{9} +(-0.285782 + 1.62075i) q^{10} +(2.32288 + 4.02334i) q^{11} +(-1.32288 + 2.29129i) q^{12} +(1.53209 + 1.28558i) q^{13} +(-3.42589 - 1.24692i) q^{14} +(4.09166 - 1.48924i) q^{15} +(0.766044 - 0.642788i) q^{16} +4.00000 q^{18} -1.64575 q^{20} +(1.67497 + 9.49921i) q^{21} +(-3.55885 + 2.98623i) q^{22} +(1.54650 - 0.562880i) q^{23} +(-2.48619 - 0.904900i) q^{24} +(-1.75539 - 1.47295i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-1.32288 - 2.29129i) q^{27} +(0.633078 - 3.59036i) q^{28} +(0.285782 - 1.62075i) q^{29} +(2.17712 + 3.77089i) q^{30} +(2.82288 - 4.88936i) q^{31} +(0.766044 + 0.642788i) q^{32} +(11.5502 + 4.20394i) q^{33} +(-4.59627 + 3.85673i) q^{35} +(0.694593 + 3.93923i) q^{36} +0.354249 q^{37} +5.29150 q^{39} +(-0.285782 - 1.62075i) q^{40} +(-0.223304 + 0.187374i) q^{41} +(-9.06404 + 3.29904i) q^{42} +(-10.6105 - 3.86192i) q^{43} +(-3.55885 - 2.98623i) q^{44} +(3.29150 - 5.70105i) q^{45} +(0.822876 + 1.42526i) q^{46} +(0.756107 - 4.28810i) q^{47} +(0.459430 - 2.60556i) q^{48} +(-3.14575 - 5.44860i) q^{49} +(1.14575 - 1.98450i) q^{50} +(-1.87939 - 0.684040i) q^{52} +(11.8242 - 4.30364i) q^{53} +(2.02676 - 1.70066i) q^{54} +(1.32767 + 7.52960i) q^{55} +3.64575 q^{56} +1.64575 q^{58} +(-1.37829 - 7.81667i) q^{59} +(-3.33555 + 2.79886i) q^{60} +(-0.880731 + 0.320560i) q^{61} +(5.30527 + 1.93096i) q^{62} +(11.1712 + 9.37378i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.64575 + 2.85052i) q^{65} +(-2.13440 + 12.1048i) q^{66} +(0.112134 - 0.635941i) q^{67} +(2.17712 - 3.77089i) q^{69} +(-4.59627 - 3.85673i) q^{70} +(2.54515 + 0.926361i) q^{71} +(-3.75877 + 1.36808i) q^{72} +(1.30878 - 1.09820i) q^{73} +(0.0615146 + 0.348867i) q^{74} -6.06275 q^{75} -16.9373 q^{77} +(0.918860 + 5.21111i) q^{78} +(-3.06418 + 2.57115i) q^{79} +(1.54650 - 0.562880i) q^{80} +(4.69846 + 1.71010i) q^{81} +(-0.223304 - 0.187374i) q^{82} +(-3.96863 + 6.87386i) q^{83} +(-4.82288 - 8.35347i) q^{84} +(1.96075 - 11.1200i) q^{86} +(-2.17712 - 3.77089i) q^{87} +(2.32288 - 4.02334i) q^{88} +(6.18600 + 2.25152i) q^{90} +(-6.85177 + 2.49384i) q^{91} +(-1.26072 + 1.05787i) q^{92} +(-2.59383 - 14.7103i) q^{93} +4.35425 q^{94} +2.64575 q^{96} +(-0.643974 - 3.65216i) q^{97} +(4.81957 - 4.04410i) q^{98} +(17.4623 - 6.35576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8	$ 12 q - 6 q^{7} - 6 q^{8} + 12 q^{11} + 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} + 18 q^{31} + 36 q^{37} - 24 q^{45} - 6 q^{46} - 6 q^{49} - 18 q^{50} + 12 q^{56} - 12 q^{58} - 6 q^{64} - 12 q^{65} + 42 q^{69} - 168 q^{75} - 108 q^{77} - 42 q^{84} - 42 q^{87} + 12 q^{88} + 84 q^{94}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 12 * q^11 + 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 + 18 * q^31 + 36 * q^37 - 24 * q^45 - 6 * q^46 - 6 * q^49 - 18 * q^50 + 12 * q^56 - 12 * q^58 - 6 * q^64 - 12 * q^65 + 42 * q^69 - 168 * q^75 - 108 * q^77 - 42 * q^84 - 42 * q^87 + 12 * q^88 + 84 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	2.02676	−	1.70066i	1.17015	−	0.981874i	0.170158	−	0.985417i	$-0.445572\pi$
$3$	2.02676	−	1.70066i	1.17015	−	0.981874i	0.999994	+	0.00354242i	$0.00112759\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	1.54650	+	0.562880i	0.691616	+	0.251728i	0.663827	−	0.747886i	$-0.268931\pi$
$5$	1.54650	+	0.562880i	0.691616	+	0.251728i	0.0277890	+	0.999614i	$0.491153\pi$
$6$	2.02676	+	1.70066i	0.827423	+	0.694290i
$7$	−1.82288	+	3.15731i	−0.688982	+	1.19335i	0.283185	+	0.959065i	$0.408609\pi$
$7$	−1.82288	+	3.15731i	−0.688982	+	1.19335i	−0.972167	+	0.234287i	$0.924724\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.694593	−	3.93923i	0.231531	−	1.31308i
$10$	−0.285782	+	1.62075i	−0.0903721	+	0.512526i
$11$	2.32288	+	4.02334i	0.700373	+	1.21308i	0.968335	+	0.249653i	$0.0803165\pi$
$11$	2.32288	+	4.02334i	0.700373	+	1.21308i	−0.267962	+	0.963429i	$0.586350\pi$
$12$	−1.32288	+	2.29129i	−0.381881	+	0.661438i
$13$	1.53209	+	1.28558i	0.424925	+	0.356554i	0.830033	−	0.557714i	$-0.188322\pi$
$13$	1.53209	+	1.28558i	0.424925	+	0.356554i	−0.405108	+	0.914269i	$0.632766\pi$
$14$	−3.42589	−	1.24692i	−0.915606	−	0.333253i
$15$	4.09166	−	1.48924i	1.05646	−	0.384520i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$17$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$18$	4.00000			0.942809
$19$		0			0
$19$		0			0
$20$	−1.64575			−0.368001
$21$	1.67497	+	9.49921i	0.365508	+	2.07290i
$22$	−3.55885	+	2.98623i	−0.758750	+	0.636667i
$23$	1.54650	−	0.562880i	0.322468	−	0.117369i	−0.175714	−	0.984441i	$-0.556223\pi$
$23$	1.54650	−	0.562880i	0.322468	−	0.117369i	0.498182	+	0.867073i	$0.334001\pi$
$24$	−2.48619	−	0.904900i	−0.507492	−	0.184712i
$25$	−1.75539	−	1.47295i	−0.351079	−	0.294590i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	−1.32288	−	2.29129i	−0.254588	−	0.440959i
$28$	0.633078	−	3.59036i	0.119641	−	0.678515i
$29$	0.285782	−	1.62075i	0.0530683	−	0.300965i	−0.946708	−	0.322092i	$-0.895614\pi$
$29$	0.285782	−	1.62075i	0.0530683	−	0.300965i	0.999777	+	0.0211262i	$0.00672518\pi$
$30$	2.17712	+	3.77089i	0.397487	+	0.688467i
$31$	2.82288	−	4.88936i	0.507003	−	0.878156i	−0.492964	−	0.870050i	$-0.664086\pi$
$31$	2.82288	−	4.88936i	0.507003	−	0.878156i	0.999967	−	0.00810584i	$-0.00258020\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	11.5502	+	4.20394i	2.01064	+	0.731812i
$34$		0			0
$35$	−4.59627	+	3.85673i	−0.776911	+	0.651906i
$36$	0.694593	+	3.93923i	0.115765	+	0.656539i
$37$	0.354249			0.0582381			0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249			0.0582381			0.0291191	+	0.999576i	$0.490730\pi$
$38$		0			0
$39$	5.29150			0.847319
$40$	−0.285782	−	1.62075i	−0.0451861	−	0.256263i
$41$	−0.223304	+	0.187374i	−0.0348742	+	0.0292629i	−0.660058	−	0.751214i	$-0.729468\pi$
$41$	−0.223304	+	0.187374i	−0.0348742	+	0.0292629i	0.625184	+	0.780477i	$0.285024\pi$
$42$	−9.06404	+	3.29904i	−1.39861	+	0.509053i
$43$	−10.6105	−	3.86192i	−1.61809	−	0.588937i	−0.635075	−	0.772450i	$-0.719031\pi$
$43$	−10.6105	−	3.86192i	−1.61809	−	0.588937i	−0.983017	+	0.183513i	$0.941253\pi$
$44$	−3.55885	−	2.98623i	−0.536517	−	0.450191i
$45$	3.29150	−	5.70105i	0.490668	−	0.849862i
$46$	0.822876	+	1.42526i	0.121326	+	0.210143i
$47$	0.756107	−	4.28810i	0.110290	−	0.625483i	−0.878685	−	0.477401i	$-0.841579\pi$
$47$	0.756107	−	4.28810i	0.110290	−	0.625483i	0.988975	−	0.148082i	$-0.0473100\pi$
$48$	0.459430	−	2.60556i	0.0663130	−	0.376080i
$49$	−3.14575	−	5.44860i	−0.449393	−	0.778372i
$50$	1.14575	−	1.98450i	0.162034	−	0.280651i
$51$		0			0
$52$	−1.87939	−	0.684040i	−0.260624	−	0.0948593i
$53$	11.8242	−	4.30364i	1.62417	−	0.591151i	0.640002	−	0.768373i	$-0.278933\pi$
$53$	11.8242	−	4.30364i	1.62417	−	0.591151i	0.984171	+	0.177223i	$0.0567112\pi$
$54$	2.02676	−	1.70066i	0.275808	−	0.231430i
$55$	1.32767	+	7.52960i	0.179023	+	1.01529i
$56$	3.64575			0.487184
$57$		0			0
$58$	1.64575			0.216098
$59$	−1.37829	−	7.81667i	−0.179438	−	1.01764i	−0.932896	−	0.360147i	$-0.882727\pi$
$59$	−1.37829	−	7.81667i	−0.179438	−	1.01764i	0.753458	−	0.657497i	$-0.228385\pi$
$60$	−3.33555	+	2.79886i	−0.430617	+	0.361331i
$61$	−0.880731	+	0.320560i	−0.112766	+	0.0410435i	−0.397787	−	0.917478i	$-0.630222\pi$
$61$	−0.880731	+	0.320560i	−0.112766	+	0.0410435i	0.285021	+	0.958521i	$0.407999\pi$
$62$	5.30527	+	1.93096i	0.673770	+	0.245232i
$63$	11.1712	+	9.37378i	1.40744	+	1.18098i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.64575	+	2.85052i	0.204130	+	0.353564i
$66$	−2.13440	+	12.1048i	−0.262726	+	1.48999i
$67$	0.112134	−	0.635941i	0.0136993	−	0.0776925i	−0.977192	−	0.212359i	$-0.931885\pi$
$67$	0.112134	−	0.635941i	0.0136993	−	0.0776925i	0.990891	+	0.134667i	$0.0429964\pi$
$68$		0			0
$69$	2.17712	−	3.77089i	0.262095	−	0.453962i
$70$	−4.59627	−	3.85673i	−0.549359	−	0.460967i
$71$	2.54515	+	0.926361i	0.302054	+	0.109939i	0.488601	−	0.872507i	$-0.337507\pi$
$71$	2.54515	+	0.926361i	0.302054	+	0.109939i	−0.186547	+	0.982446i	$0.559730\pi$
$72$	−3.75877	+	1.36808i	−0.442975	+	0.161230i
$73$	1.30878	−	1.09820i	0.153182	−	0.128535i	−0.562976	−	0.826473i	$-0.690344\pi$
$73$	1.30878	−	1.09820i	0.153182	−	0.128535i	0.716158	+	0.697939i	$0.245899\pi$
$74$	0.0615146	+	0.348867i	0.00715093	+	0.0405549i
$75$	−6.06275			−0.700066
$76$		0			0
$77$	−16.9373			−1.93018
$78$	0.918860	+	5.21111i	0.104040	+	0.590042i
$79$	−3.06418	+	2.57115i	−0.344747	+	0.289277i	−0.798677	−	0.601760i	$-0.794466\pi$
$79$	−3.06418	+	2.57115i	−0.344747	+	0.289277i	0.453930	+	0.891038i	$0.350022\pi$
$80$	1.54650	−	0.562880i	0.172904	−	0.0629319i
$81$	4.69846	+	1.71010i	0.522051	+	0.190011i
$82$	−0.223304	−	0.187374i	−0.0246598	−	0.0206920i
$83$	−3.96863	+	6.87386i	−0.435613	+	0.754505i	−0.997345	−	0.0728147i	$-0.976802\pi$
$83$	−3.96863	+	6.87386i	−0.435613	+	0.754505i	0.561732	+	0.827319i	$0.310135\pi$
$84$	−4.82288	−	8.35347i	−0.526219	−	0.911438i
$85$		0			0
$86$	1.96075	−	11.1200i	0.211433	−	1.19910i
$87$	−2.17712	−	3.77089i	−0.233412	−	0.404282i
$88$	2.32288	−	4.02334i	0.247619	−	0.428889i
$89$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$89$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$90$	6.18600	+	2.25152i	0.652062	+	0.237331i
$91$	−6.85177	+	2.49384i	−0.718261	+	0.261426i
$92$	−1.26072	+	1.05787i	−0.131439	+	0.110290i
$93$	−2.59383	−	14.7103i	−0.268967	−	1.52539i
$94$	4.35425			0.449106
$95$		0			0
$96$	2.64575			0.270031
$97$	−0.643974	−	3.65216i	−0.0653856	−	0.370820i	−0.999889	−	0.0148673i	$-0.995267\pi$
$97$	−0.643974	−	3.65216i	−0.0653856	−	0.370820i	0.934504	−	0.355953i	$-0.115844\pi$
$98$	4.81957	−	4.04410i	0.486850	−	0.408516i
$99$	17.4623	−	6.35576i	1.75503	−	0.638778i
$100$	2.15331	+	0.783740i	0.215331	+	0.0783740i
$101$	−10.4533	−	8.77132i	−1.04014	−	0.872779i	−0.0481152	−	0.998842i	$-0.515321\pi$
$101$	−10.4533	−	8.77132i	−1.04014	−	0.872779i	−0.992022	+	0.126063i	$0.959766\pi$
$102$		0			0
$103$	6.64575	+	11.5108i	0.654825	+	1.13419i	0.981938	+	0.189205i	$0.0605912\pi$
$103$	6.64575	+	11.5108i	0.654825	+	1.13419i	−0.327112	+	0.944985i	$0.606076\pi$
$104$	0.347296	−	1.96962i	0.0340552	−	0.193137i
$105$	−2.75658	+	15.6333i	−0.269015	+	1.52566i
$106$	6.29150	+	10.8972i	0.611085	+	1.05843i
$107$	−7.64575	+	13.2428i	−0.739143	+	1.28023i	0.213739	+	0.976891i	$0.431436\pi$
$107$	−7.64575	+	13.2428i	−0.739143	+	1.28023i	−0.952882	+	0.303342i	$0.901898\pi$
$108$	2.02676	+	1.70066i	0.195025	+	0.163646i
$109$	−13.7035	−	4.98768i	−1.31256	−	0.477733i	−0.411494	−	0.911412i	$-0.634993\pi$
$109$	−13.7035	−	4.98768i	−1.31256	−	0.477733i	−0.901067	+	0.433679i	$0.857215\pi$
$110$	−7.18466	+	2.61500i	−0.685030	+	0.249331i
$111$	0.717978	−	0.602455i	0.0681475	−	0.0571825i
$112$	0.633078	+	3.59036i	0.0598203	+	0.339258i
$113$	−15.5830			−1.46593			−0.732963	−	0.680269i	$-0.761863\pi$
$113$	−15.5830			−1.46593			−0.732963	+	0.680269i	$0.761863\pi$
$114$		0			0
$115$	2.70850			0.252569
$116$	0.285782	+	1.62075i	0.0265342	+	0.150483i
$117$	6.12836	−	5.14230i	0.566567	−	0.475406i
$118$	7.45858	−	2.71470i	0.686618	−	0.249908i
$119$		0			0
$120$	−3.33555	−	2.79886i	−0.304492	−	0.255500i
$121$	−5.29150	+	9.16515i	−0.481046	+	0.833196i
$122$	−0.468627	−	0.811686i	−0.0424275	−	0.0734866i
$123$	−0.133925	+	0.759527i	−0.0120756	+	0.0684842i
$124$	−0.980374	+	5.55998i	−0.0880402	+	0.499301i
$125$	−6.00000	−	10.3923i	−0.536656	−	0.929516i
$126$	−7.29150	+	12.6293i	−0.649579	+	1.12510i
$127$	−10.1819	−	8.54361i	−0.903496	−	0.758123i	0.0673746	−	0.997728i	$-0.478538\pi$
$127$	−10.1819	−	8.54361i	−0.903496	−	0.758123i	−0.970871	+	0.239605i	$0.922982\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−28.0729	+	10.2177i	−2.47168	+	0.899617i
$130$	−2.52144	+	2.11574i	−0.221145	+	0.185562i
$131$	0.336401	+	1.90782i	0.0293915	+	0.166687i	0.995970	−	0.0896816i	$-0.0285849\pi$
$131$	0.336401	+	1.90782i	0.0293915	+	0.166687i	−0.966579	+	0.256369i	$0.917474\pi$
$132$	−12.2915			−1.06984
$133$		0			0
$134$	0.645751			0.0557844
$135$	−0.756107	−	4.28810i	−0.0650754	−	0.369061i
$136$		0			0
$137$	−14.6432	+	5.32970i	−1.25106	+	0.455347i	−0.880758	−	0.473566i	$-0.842967\pi$
$137$	−14.6432	+	5.32970i	−1.25106	+	0.455347i	−0.370298	+	0.928913i	$0.620744\pi$
$138$	4.09166	+	1.48924i	0.348305	+	0.126773i
$139$	14.2835	+	11.9853i	1.21151	+	1.01658i	0.999225	+	0.0393682i	$0.0125345\pi$
$139$	14.2835	+	11.9853i	1.21151	+	1.01658i	0.212284	+	0.977208i	$0.431910\pi$
$140$	3.00000	−	5.19615i	0.253546	−	0.439155i
$141$	−5.76013	−	9.97684i	−0.485090	−	0.840201i
$142$	−0.470326	+	2.66735i	−0.0394689	+	0.223839i
$143$	−1.61345	+	9.15034i	−0.134924	+	0.765190i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	1.35425	−	2.34563i	0.112464	−	0.194794i
$146$	1.30878	+	1.09820i	0.108316	+	0.0908878i
$147$	−15.6419	−	5.69318i	−1.29012	−	0.469566i
$148$	−0.332885	+	0.121160i	−0.0273630	+	0.00995931i
$149$	8.37842	−	7.03033i	0.686387	−	0.575947i	−0.231478	−	0.972840i	$-0.574356\pi$
$149$	8.37842	−	7.03033i	0.686387	−	0.575947i	0.917865	+	0.396893i	$0.129912\pi$
$150$	−1.05278	−	5.97064i	−0.0859595	−	0.487501i
$151$	12.9373			1.05282			0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373			1.05282			0.526409	+	0.850231i	$0.323538\pi$
$152$		0			0
$153$		0			0
$154$	−2.94112	−	16.6799i	−0.237002	−	1.34411i
$155$	7.11770	−	5.97246i	0.571708	−	0.479720i
$156$	−4.97239	+	1.80980i	−0.398109	+	0.144900i
$157$	9.94477	+	3.61960i	0.793679	+	0.288876i	0.706865	−	0.707349i	$-0.250109\pi$
$157$	9.94477	+	3.61960i	0.793679	+	0.288876i	0.0868146	+	0.996224i	$0.472331\pi$
$158$	−3.06418	−	2.57115i	−0.243773	−	0.204550i
$159$	16.6458	−	28.8313i	1.32009	−	2.28647i
$160$	0.822876	+	1.42526i	0.0650540	+	0.112677i
$161$	−1.04189	+	5.90885i	−0.0821124	+	0.465682i
$162$	−0.868241	+	4.92404i	−0.0682154	+	0.386869i
$163$	−1.96863	−	3.40976i	−0.154195	−	0.267073i	0.778571	−	0.627557i	$-0.215945\pi$
$163$	−1.96863	−	3.40976i	−0.154195	−	0.267073i	−0.932766	+	0.360484i	$0.882612\pi$
$164$	0.145751	−	0.252449i	0.0113813	−	0.0197129i
$165$	15.4961	+	13.0028i	1.20637	+	1.01227i
$166$	−7.45858	−	2.71470i	−0.578898	−	0.210702i
$167$	11.2763	−	4.10424i	0.872587	−	0.317596i	0.133373	−	0.991066i	$-0.457419\pi$
$167$	11.2763	−	4.10424i	0.872587	−	0.317596i	0.739214	+	0.673470i	$0.235197\pi$
$168$	7.38907	−	6.20017i	0.570079	−	0.478353i
$169$	−1.56283	−	8.86327i	−0.120218	−	0.681790i
$170$		0			0
$171$		0			0
$172$	11.2915			0.860969
$173$	−1.04189	−	5.90885i	−0.0792134	−	0.449241i	−0.998456	−	0.0555496i	$-0.982309\pi$
$173$	−1.04189	−	5.90885i	−0.0792134	−	0.449241i	0.919243	−	0.393692i	$-0.128802\pi$
$174$	3.33555	−	2.79886i	0.252867	−	0.212181i
$175$	7.85043	−	2.85732i	0.593436	−	0.215993i
$176$	4.36558	+	1.58894i	0.329068	+	0.119771i
$177$	−16.0869	−	13.4985i	−1.20917	−	1.01461i
$178$		0			0
$179$	−2.03137	−	3.51844i	−0.151832	−	0.262981i	0.780069	−	0.625693i	$-0.215184\pi$
$179$	−2.03137	−	3.51844i	−0.151832	−	0.262981i	−0.931901	+	0.362713i	$0.881851\pi$
$180$	−1.14313	+	6.48299i	−0.0852036	+	0.483214i
$181$	3.85998	−	21.8911i	0.286910	−	1.62715i	−0.411471	−	0.911423i	$-0.634985\pi$
$181$	3.85998	−	21.8911i	0.286910	−	1.62715i	0.698381	−	0.715726i	$-0.253904\pi$
$182$	−3.64575	−	6.31463i	−0.270241	−	0.468071i
$183$	−1.23987	+	2.14752i	−0.0916539	+	0.158749i
$184$	−1.26072	−	1.05787i	−0.0929414	−	0.0779871i
$185$	0.547846	+	0.199400i	0.0402784	+	0.0146601i
$186$	14.0364	−	5.10884i	1.02920	−	0.374598i
$187$		0			0
$188$	0.756107	+	4.28810i	0.0551448	+	0.312742i
$189$	9.64575			0.701625
$190$		0			0
$191$	6.58301			0.476330			0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301			0.476330			0.238165	+	0.971225i	$0.423454\pi$
$192$	0.459430	+	2.60556i	0.0331565	+	0.188040i
$193$	11.1712	−	9.37378i	0.804123	−	0.674739i	−0.145075	−	0.989421i	$-0.546342\pi$
$193$	11.1712	−	9.37378i	0.804123	−	0.674739i	0.949197	+	0.314682i	$0.101898\pi$
$194$	3.48485	−	1.26838i	0.250197	−	0.0910644i
$195$	8.18331	+	2.97848i	0.586019	+	0.213293i
$196$	4.81957	+	4.04410i	0.344255	+	0.288864i
$197$	3.82288	−	6.62141i	0.272369	−	0.471756i	−0.697099	−	0.716975i	$-0.745526\pi$
$197$	3.82288	−	6.62141i	0.272369	−	0.471756i	0.969468	+	0.245218i	$0.0788597\pi$
$198$	9.29150	+	16.0934i	0.660318	+	1.14370i
$199$	−3.45117	+	19.5726i	−0.244647	+	1.38746i	0.576664	+	0.816982i	$0.304354\pi$
$199$	−3.45117	+	19.5726i	−0.244647	+	1.38746i	−0.821311	+	0.570481i	$0.806757\pi$
$200$	−0.397915	+	2.25669i	−0.0281369	+	0.159572i
$201$	−0.854249	−	1.47960i	−0.0602541	−	0.104363i
$202$	6.82288	−	11.8176i	0.480056	−	0.831481i
$203$	4.59627	+	3.85673i	0.322595	+	0.270689i
$204$		0			0
$205$	−0.450809	+	0.164081i	−0.0314859	+	0.0114599i
$206$	−10.1819	+	8.54361i	−0.709405	+	0.595262i
$207$	−1.14313	−	6.48299i	−0.0794528	−	0.450599i
$208$	2.00000			0.138675
$209$		0			0
$210$	−15.8745			−1.09545
$211$	−2.30805	−	13.0896i	−0.158892	−	0.901123i	−0.955140	−	0.296153i	$-0.904296\pi$
$211$	−2.30805	−	13.0896i	−0.158892	−	0.901123i	0.796248	−	0.604970i	$-0.206815\pi$
$212$	−9.63914	+	8.08820i	−0.662019	+	0.555500i
$213$	6.73385	−	2.45092i	0.461396	−	0.167934i
$214$	−14.3693	−	5.23000i	−0.982266	−	0.357516i
$215$	−14.2354	−	11.9449i	−0.970847	−	0.814637i
$216$	−1.32288	+	2.29129i	−0.0900103	+	0.155902i
$217$	10.2915	+	17.8254i	0.698633	+	1.21007i
$218$	2.53231	−	14.3615i	0.171510	−	0.972681i
$219$	0.784935	−	4.45159i	0.0530410	−	0.300810i
$220$	−3.82288	−	6.62141i	−0.257738	−	0.446416i
$221$		0			0
$222$	0.717978	+	0.602455i	0.0481875	+	0.0404341i
$223$	17.6773	+	6.43400i	1.18376	+	0.430853i	0.857528	−	0.514438i	$-0.171999\pi$
$223$	17.6773	+	6.43400i	1.18376	+	0.430853i	0.326230	+	0.945290i	$0.394222\pi$
$224$	−3.42589	+	1.24692i	−0.228902	+	0.0833134i
$225$	−7.02157	+	5.89180i	−0.468105	+	0.392787i
$226$	−2.70596	−	15.3463i	−0.179998	−	1.02082i
$227$	−7.35425			−0.488119			−0.244059	−	0.969760i	$-0.578479\pi$
$227$	−7.35425			−0.488119			−0.244059	+	0.969760i	$0.578479\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	0.470326	+	2.66735i	0.0310124	+	0.175880i
$231$	−34.3278	+	28.8044i	−2.25860	+	1.89519i
$232$	−1.54650	+	0.562880i	−0.101533	+	0.0369549i
$233$	−17.7362	−	6.45546i	−1.16194	−	0.422911i	−0.312150	−	0.950033i	$-0.601049\pi$
$233$	−17.7362	−	6.45546i	−1.16194	−	0.422911i	−0.849790	+	0.527122i	$0.823271\pi$
$234$	6.12836	+	5.14230i	0.400623	+	0.336163i
$235$	3.58301	−	6.20595i	0.233729	−	0.404831i
$236$	3.96863	+	6.87386i	0.258336	+	0.447450i
$237$	−1.83772	+	10.4222i	−0.119373	+	0.676996i
$238$		0			0
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$	2.17712	−	3.77089i	0.140533	−	0.243410i
$241$	−5.80892	−	4.87426i	−0.374185	−	0.313979i	0.436229	−	0.899836i	$-0.356314\pi$
$241$	−5.80892	−	4.87426i	−0.374185	−	0.313979i	−0.810415	+	0.585857i	$0.800758\pi$
$242$	−9.94477	−	3.61960i	−0.639274	−	0.232677i
$243$	19.8895	−	7.23920i	1.27591	−	0.464395i
$244$	0.717978	−	0.602455i	0.0459638	−	0.0385682i
$245$	−1.79800	−	10.1969i	−0.114870	−	0.651459i
$246$	−0.771243			−0.0491727
$247$		0			0
$248$	−5.64575			−0.358506
$249$	3.64661	+	20.6810i	0.231095	+	1.31060i
$250$	9.19253	−	7.71345i	0.581387	−	0.487841i
$251$	−27.4660	+	9.99682i	−1.73364	+	0.630994i	−0.998879	−	0.0473308i	$-0.984928\pi$
$251$	−27.4660	+	9.99682i	−1.73364	+	0.630994i	−0.734762	+	0.678325i	$0.762706\pi$
$252$	−13.7035	−	4.98768i	−0.863242	−	0.314194i
$253$	5.85699	+	4.91459i	0.368226	+	0.308978i
$254$	6.64575	−	11.5108i	0.416992	−	0.722251i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.13440	−	12.1048i	0.133140	−	0.755075i	−0.842997	−	0.537918i	$-0.819211\pi$
$257$	2.13440	−	12.1048i	0.133140	−	0.755075i	0.976137	−	0.217156i	$-0.0696781\pi$
$258$	−14.9373	−	25.8721i	−0.929953	−	1.61073i
$259$	−0.645751	+	1.11847i	−0.0401250	+	0.0694986i
$260$	−2.52144	−	2.11574i	−0.156373	−	0.131212i
$261$	−6.18600	−	2.25152i	−0.382904	−	0.139366i
$262$	−1.82042	+	0.662580i	−0.112466	+	0.0409343i
$263$	−8.37842	+	7.03033i	−0.516636	+	0.433509i	−0.863457	−	0.504422i	$-0.831705\pi$
$263$	−8.37842	+	7.03033i	−0.516636	+	0.433509i	0.346821	+	0.937931i	$0.387261\pi$
$264$	−2.13440	−	12.1048i	−0.131363	−	0.744997i
$265$	20.7085			1.27211
$266$		0			0
$267$		0			0
$268$	0.112134	+	0.635941i	0.00684965	+	0.0388463i
$269$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$269$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$270$	4.09166	−	1.48924i	0.249010	−	0.0906323i
$271$	−11.6092	−	4.22540i	−0.705208	−	0.256675i	−0.0355754	−	0.999367i	$-0.511326\pi$
$271$	−11.6092	−	4.22540i	−0.705208	−	0.256675i	−0.669633	+	0.742692i	$0.733549\pi$
$272$		0			0
$273$	−9.64575	+	16.7069i	−0.583787	+	1.01115i
$274$	−7.79150	−	13.4953i	−0.470702	−	0.815280i
$275$	1.84862	−	10.4840i	0.111476	−	0.632210i
$276$	−0.756107	+	4.28810i	−0.0455123	+	0.258113i
$277$	13.7601	+	23.8332i	0.826766	+	1.43200i	0.900562	+	0.434727i	$0.143155\pi$
$277$	13.7601	+	23.8332i	0.826766	+	1.43200i	−0.0737960	+	0.997273i	$0.523511\pi$
$278$	−9.32288	+	16.1477i	−0.559149	+	0.968474i
$279$	−17.2996	−	14.5161i	−1.03570	−	0.869055i
$280$	5.63816	+	2.05212i	0.336944	+	0.122638i
$281$	−23.9222	+	8.70698i	−1.42708	+	0.519415i	−0.936093	−	0.351752i	$-0.885586\pi$
$281$	−23.9222	+	8.70698i	−1.42708	+	0.519415i	−0.490988	+	0.871167i	$0.663364\pi$
$282$	8.82503	−	7.40508i	0.525523	−	0.440966i
$283$	5.32158	+	30.1802i	0.316335	+	1.79403i	0.564634	+	0.825342i	$0.309017\pi$
$283$	5.32158	+	30.1802i	0.316335	+	1.79403i	−0.248299	+	0.968684i	$0.579871\pi$
$284$	−2.70850			−0.160720
$285$		0			0
$286$	−9.29150			−0.549418
$287$	−0.184544	−	1.04660i	−0.0108933	−	0.0617789i
$288$	3.06418	−	2.57115i	0.180558	−	0.151506i
$289$	15.9748	−	5.81434i	0.939693	−	0.342020i
$290$	2.54515	+	0.926361i	0.149457	+	0.0543978i
$291$	−7.51625	−	6.30688i	−0.440610	−	0.369716i
$292$	−0.854249	+	1.47960i	−0.0499911	+	0.0865872i
$293$	−14.4686	−	25.0604i	−0.845266	−	1.46404i	−0.885390	−	0.464849i	$-0.846109\pi$
$293$	−14.4686	−	25.0604i	−0.845266	−	1.46404i	0.0401236	−	0.999195i	$-0.487225\pi$
$294$	2.89050	−	16.3929i	0.168578	−	0.956051i
$295$	2.26832	−	12.8643i	0.132067	−	0.748988i
$296$	−0.177124	−	0.306788i	−0.0102951	−	0.0178317i
$297$	6.14575	−	10.6448i	0.356613	−	0.617671i
$298$	8.37842	+	7.03033i	0.485349	+	0.407256i
$299$	3.09300	+	1.12576i	0.178873	+	0.0651044i
$300$	5.69712	−	2.07358i	0.328923	−	0.119718i
$301$	31.5350	−	26.4610i	1.81765	−	1.52519i
$302$	2.24653	+	12.7407i	0.129273	+	0.733145i
$303$	−36.1033			−2.07408
$304$		0			0
$305$	−1.54249			−0.0883225
$306$		0			0
$307$	0.494674	−	0.415081i	0.0282325	−	0.0236899i	−0.628562	−	0.777759i	$-0.716356\pi$
$307$	0.494674	−	0.415081i	0.0282325	−	0.0236899i	0.656795	+	0.754069i	$0.271912\pi$
$308$	15.9158	−	5.79288i	0.906888	−	0.330080i
$309$	33.0452	+	12.0275i	1.87988	+	0.684220i
$310$	7.11770	+	5.97246i	0.404258	+	0.339213i
$311$	−6.82288	+	11.8176i	−0.386890	+	0.670113i	−0.992029	−	0.126007i	$-0.959784\pi$
$311$	−6.82288	+	11.8176i	−0.386890	+	0.670113i	0.605140	+	0.796119i	$0.293117\pi$
$312$	−2.64575	−	4.58258i	−0.149786	−	0.259437i
$313$	1.54104	−	8.73968i	0.0871049	−	0.493996i	−0.909778	−	0.415096i	$-0.863748\pi$
$313$	1.54104	−	8.73968i	0.0871049	−	0.493996i	0.996883	−	0.0789003i	$-0.0251409\pi$
$314$	−1.83772	+	10.4222i	−0.103709	+	0.588160i
$315$	12.0000	+	20.7846i	0.676123	+	1.17108i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−4.59627	−	3.85673i	−0.258152	−	0.216615i	0.504521	−	0.863399i	$-0.331669\pi$
$317$	−4.59627	−	3.85673i	−0.258152	−	0.216615i	−0.762673	+	0.646784i	$0.776114\pi$
$318$	31.2838	+	11.3864i	1.75431	+	0.638516i
$319$	7.18466	−	2.61500i	0.402264	−	0.146412i
$320$	−1.26072	+	1.05787i	−0.0704763	+	0.0591366i
$321$	7.02537	+	39.8429i	0.392118	+	2.22381i
$322$	−6.00000			−0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	−0.795831	−	4.51338i	−0.0441447	−	0.250357i
$326$	3.01611	−	2.53082i	0.167047	−	0.140169i
$327$	−36.2562	+	13.1962i	−2.00497	+	0.729750i
$328$	0.273923	+	0.0996998i	0.0151249	+	0.00550500i
$329$	12.1606	+	10.2039i	0.670434	+	0.562561i
$330$	−10.1144	+	17.5186i	−0.556778	+	0.964368i
$331$	−9.90588	−	17.1575i	−0.544476	−	0.943061i	−0.998640	−	0.0521424i	$-0.983395\pi$
$331$	−9.90588	−	17.1575i	−0.544476	−	0.943061i	0.454163	−	0.890919i	$-0.349938\pi$
$332$	1.37829	−	7.81667i	0.0756435	−	0.428995i
$333$	0.246059	−	1.39547i	0.0134839	−	0.0764711i
$334$	6.00000	+	10.3923i	0.328305	+	0.568642i
$335$	0.531373	−	0.920365i	0.0290320	−	0.0502849i
$336$	7.38907	+	6.20017i	0.403107	+	0.338247i
$337$	9.12300	+	3.32050i	0.496962	+	0.180879i	0.578327	−	0.815805i	$-0.303706\pi$
$337$	9.12300	+	3.32050i	0.496962	+	0.180879i	−0.0813653	+	0.996684i	$0.525928\pi$
$338$	8.45723	−	3.07818i	0.460013	−	0.167431i
$339$	−31.5831	+	26.5013i	−1.71536	+	1.43935i
$340$		0			0
$341$	26.2288			1.42037
$342$		0			0
$343$	−2.58301			−0.139469
$344$	1.96075	+	11.1200i	0.105716	+	0.599548i
$345$	5.48948	−	4.60622i	0.295544	−	0.247991i
$346$	5.63816	−	2.05212i	0.303109	−	0.110323i
$347$	21.8279	+	7.94470i	1.17178	+	0.426494i	0.853293	−	0.521432i	$-0.174602\pi$
$347$	21.8279	+	7.94470i	1.17178	+	0.426494i	0.318490	+	0.947926i	$0.396824\pi$
$348$	3.33555	+	2.79886i	0.178804	+	0.150034i
$349$	−10.5830	+	18.3303i	−0.566495	+	0.981199i	0.430414	+	0.902632i	$0.358368\pi$
$349$	−10.5830	+	18.3303i	−0.566495	+	0.981199i	−0.996909	+	0.0785668i	$0.974966\pi$
$350$	4.17712	+	7.23499i	0.223277	+	0.386727i
$351$	0.918860	−	5.21111i	0.0490451	−	0.278149i
$352$	−0.806726	+	4.57517i	−0.0429987	+	0.243857i
$353$	−6.43725	−	11.1497i	−0.342620	−	0.593436i	0.642298	−	0.766455i	$-0.277981\pi$
$353$	−6.43725	−	11.1497i	−0.342620	−	0.593436i	−0.984918	+	0.173019i	$0.944648\pi$
$354$	10.5000	−	18.1865i	0.558069	−	0.966603i
$355$	3.41465	+	2.86523i	0.181231	+	0.152071i
$356$		0			0
$357$		0			0
$358$	3.11224	−	2.61148i	0.164487	−	0.138021i
$359$	−0.857345	−	4.86225i	−0.0452489	−	0.256620i	0.953789	−	0.300478i	$-0.0971461\pi$
$359$	−0.857345	−	4.86225i	−0.0452489	−	0.256620i	−0.999038	+	0.0438582i	$0.986035\pi$
$360$	−6.58301			−0.346955
$361$		0			0
$362$	22.2288			1.16832
$363$	4.86215	+	27.5746i	0.255197	+	1.44729i
$364$	5.58562	−	4.68689i	0.292766	−	0.245660i
$365$	2.64219	−	0.961679i	0.138299	−	0.0503366i
$366$	−2.33019	−	0.848121i	−0.121801	−	0.0443320i
$367$	12.4319	+	10.4316i	0.648942	+	0.544527i	0.906750	−	0.421669i	$-0.138556\pi$
$367$	12.4319	+	10.4316i	0.648942	+	0.544527i	−0.257807	+	0.966196i	$0.583000\pi$
$368$	0.822876	−	1.42526i	0.0428954	−	0.0742969i
$369$	0.583005	+	1.00979i	0.0303500	+	0.0525678i
$370$	−0.101238	+	0.574148i	−0.00526310	+	0.0298485i
$371$	−7.96602	+	45.1776i	−0.413575	+	2.34550i
$372$	7.46863	+	12.9360i	0.387230	+	0.670703i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	−29.8343	−	10.8588i	−1.54064	−	0.560746i
$376$	−4.09166	+	1.48924i	−0.211011	+	0.0768017i
$377$	2.52144	−	2.11574i	0.129861	−	0.108966i
$378$	1.67497	+	9.49921i	0.0861510	+	0.488587i
$379$	10.7085			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$380$		0			0
$381$	−35.1660			−1.80161
$382$	1.14313	+	6.48299i	0.0584875	+	0.331699i
$383$	4.22876	−	3.54835i	0.216080	−	0.181312i	−0.528323	−	0.849044i	$-0.677179\pi$
$383$	4.22876	−	3.54835i	0.216080	−	0.181312i	0.744402	+	0.667731i	$0.232734\pi$
$384$	−2.48619	+	0.904900i	−0.126873	+	0.0461780i
$385$	−26.1935	−	9.53364i	−1.33494	−	0.485879i
$386$	11.1712	+	9.37378i	0.568601	+	0.477113i
$387$	−22.5830	+	39.1149i	−1.14796	+	1.98832i
$388$	1.85425	+	3.21165i	0.0941352	+	0.163047i
$389$	2.08378	−	11.8177i	0.105652	−	0.599181i	−0.885306	−	0.465008i	$-0.846051\pi$
$389$	2.08378	−	11.8177i	0.105652	−	0.599181i	0.990958	−	0.134172i	$-0.0428376\pi$
$390$	−1.51221	+	8.57620i	−0.0765740	+	0.434273i
$391$		0			0
$392$	−3.14575	+	5.44860i	−0.158884	+	0.275196i
$393$	3.92635	+	3.29460i	0.198058	+	0.166191i
$394$	7.18466	+	2.61500i	0.361958	+	0.131742i
$395$	−6.18600	+	2.25152i	−0.311252	+	0.113286i
$396$	−14.2354	+	11.9449i	−0.715356	+	0.600255i
$397$	3.65751	+	20.7428i	0.183565	+	1.04105i	0.927785	+	0.373115i	$0.121710\pi$
$397$	3.65751	+	20.7428i	0.183565	+	1.04105i	−0.744220	+	0.667934i	$0.767179\pi$
$398$	−19.8745			−0.996219
$399$		0			0
$400$	−2.29150			−0.114575
$401$	4.78974	+	27.1640i	0.239188	+	1.35650i	0.833612	+	0.552351i	$0.186269\pi$
$401$	4.78974	+	27.1640i	0.239188	+	1.35650i	−0.594423	+	0.804152i	$0.702620\pi$
$402$	1.30878	−	1.09820i	0.0652763	−	0.0547733i
$403$	10.6105	−	3.86192i	0.528549	−	0.192376i
$404$	12.8228	+	4.66712i	0.637959	+	0.232198i
$405$	6.30359	+	5.28934i	0.313228	+	0.262830i
$406$	−3.00000	+	5.19615i	−0.148888	+	0.257881i
$407$	0.822876	+	1.42526i	0.0407884	+	0.0706476i
$408$		0			0
$409$	−1.31678	+	7.46780i	−0.0651103	+	0.369259i	0.934791	+	0.355199i	$0.115587\pi$
$409$	−1.31678	+	7.46780i	−0.0651103	+	0.369259i	−0.999901	+	0.0140603i	$0.995524\pi$
$410$	−0.239870	−	0.415468i	−0.0118464	−	0.0205185i
$411$	−20.6144	+	35.7052i	−1.01683	+	1.76121i
$412$	−10.1819	−	8.54361i	−0.501625	−	0.420914i
$413$	27.1921	+	9.89712i	1.33804	+	0.487006i
$414$	6.18600	−	2.25152i	0.304025	−	0.110656i
$415$	−10.0066	+	8.39657i	−0.491207	+	0.412171i
$416$	0.347296	+	1.96962i	0.0170276	+	0.0965683i
$417$	49.3320			2.41580
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$	−2.75658	−	15.6333i	−0.134507	−	0.762829i
$421$	−19.0069	+	15.9487i	−0.926340	+	0.777292i	−0.975157	−	0.221516i	$-0.928899\pi$
$421$	−19.0069	+	15.9487i	−0.926340	+	0.777292i	0.0488165	+	0.998808i	$0.484455\pi$
$422$	12.4899	−	4.54596i	0.608000	−	0.221294i
$423$	−16.3666	−	5.95696i	−0.795772	−	0.289637i
$424$	−9.63914	−	8.08820i	−0.468118	−	0.392798i
$425$		0			0
$426$	3.58301	+	6.20595i	0.173597	+	0.300679i
$427$	0.593355	−	3.36508i	0.0287145	−	0.162848i
$428$	2.65534	−	15.0592i	0.128351	−	0.727913i
$429$	12.2915	+	21.2895i	0.593439	+	1.02787i
$430$	9.29150	−	16.0934i	0.448076	−	0.776090i
$431$	21.3531	+	17.9174i	1.02854	+	0.863050i	0.990677	−	0.136233i	$-0.0434994\pi$
$431$	21.3531	+	17.9174i	1.02854	+	0.863050i	0.0378663	+	0.999283i	$0.487944\pi$
$432$	−2.48619	−	0.904900i	−0.119617	−	0.0435370i
$433$	−16.7965	+	6.11344i	−0.807190	+	0.293793i	−0.712463	−	0.701710i	$-0.752420\pi$
$433$	−16.7965	+	6.11344i	−0.807190	+	0.293793i	−0.0947276	+	0.995503i	$0.530198\pi$
$434$	−15.7675	+	13.2305i	−0.756864	+	0.635084i
$435$	−1.24436	−	7.05714i	−0.0596627	−	0.338364i
$436$	14.5830			0.698399
$437$		0			0
$438$	4.52026			0.215986
$439$	1.87744	+	10.6475i	0.0896055	+	0.508178i	0.996267	+	0.0863200i	$0.0275107\pi$
$439$	1.87744	+	10.6475i	0.0896055	+	0.508178i	−0.906662	+	0.421858i	$0.861378\pi$
$440$	5.85699	−	4.91459i	0.279221	−	0.234294i
$441$	−23.6483	+	8.60728i	−1.12611	+	0.409871i
$442$		0			0
$443$	8.15512	+	6.84296i	0.387461	+	0.325119i	0.815623	−	0.578583i	$-0.196394\pi$
$443$	8.15512	+	6.84296i	0.387461	+	0.325119i	−0.428162	+	0.903702i	$0.640839\pi$
$444$	−0.468627	+	0.811686i	−0.0222401	+	0.0385209i
$445$		0			0
$446$	−3.26663	+	18.5260i	−0.154679	+	0.877230i
$447$	5.02490	−	28.4976i	0.237670	−	1.34789i
$448$	−1.82288	−	3.15731i	−0.0861228	−	0.149169i
$449$	12.1458	−	21.0371i	0.573193	−	0.992800i	−0.423042	−	0.906110i	$-0.639038\pi$
$449$	12.1458	−	21.0371i	0.573193	−	0.992800i	0.996235	−	0.0866900i	$-0.0276290\pi$
$450$	−7.02157	−	5.89180i	−0.331000	−	0.277742i
$451$	−1.27258	−	0.463180i	−0.0599233	−	0.0218103i
$452$	14.6432	−	5.32970i	0.688760	−	0.250688i
$453$	26.2207	−	22.0018i	1.23196	−	1.03374i
$454$	−1.27705	−	7.24252i	−0.0599350	−	0.339908i
$455$	−12.0000			−0.562569
$456$		0			0
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$	3.47296	+	19.6962i	0.162281	+	0.920341i
$459$		0			0
$460$	−2.54515	+	0.926361i	−0.118668	+	0.0431918i
$461$	−18.0102	−	6.55516i	−0.838817	−	0.305304i	−0.113344	−	0.993556i	$-0.536156\pi$
$461$	−18.0102	−	6.55516i	−0.838817	−	0.305304i	−0.725472	+	0.688251i	$0.758379\pi$
$462$	−34.3278	−	28.8044i	−1.59707	−	1.34010i
$463$	19.2288	−	33.3052i	0.893636	−	1.54782i	0.0581525	−	0.998308i	$-0.481479\pi$
$463$	19.2288	−	33.3052i	0.893636	−	1.54782i	0.835484	−	0.549515i	$-0.185188\pi$
$464$	−0.822876	−	1.42526i	−0.0382010	−	0.0661661i
$465$	4.26879	−	24.2095i	0.197961	−	1.12269i
$466$	3.27752	−	18.5878i	0.151828	−	0.861061i
$467$	9.67712	+	16.7613i	0.447804	+	0.775619i	0.998243	−	0.0592563i	$-0.0188729\pi$
$467$	9.67712	+	16.7613i	0.447804	+	0.775619i	−0.550439	+	0.834875i	$0.685540\pi$
$468$	−4.00000	+	6.92820i	−0.184900	+	0.320256i
$469$	1.80346	+	1.51328i	0.0832760	+	0.0698769i
$470$	6.73385	+	2.45092i	0.310609	+	0.113053i
$471$	26.3114	−	9.57656i	1.21237	−	0.441265i
$472$	−6.08029	+	5.10197i	−0.279868	+	0.234837i
$473$	−9.10915	−	51.6606i	−0.418839	−	2.37536i
$474$	−10.5830			−0.486094
$475$		0			0
$476$		0			0
$477$	−8.74006	−	49.5674i	−0.400180	−	2.26953i
$478$	−9.19253	+	7.71345i	−0.420457	+	0.352805i
$479$	−6.18600	+	2.25152i	−0.282646	+	0.102875i	−0.479453	−	0.877568i	$-0.659165\pi$
$479$	−6.18600	+	2.25152i	−0.282646	+	0.102875i	0.196807	+	0.980442i	$0.436943\pi$
$480$	4.09166	+	1.48924i	0.186758	+	0.0679742i
$481$	0.542740	+	0.455413i	0.0247468	+	0.0207651i
$482$	3.79150	−	6.56708i	0.172698	−	0.299122i
$483$	7.93725	+	13.7477i	0.361158	+	0.625543i
$484$	1.83772	−	10.4222i	0.0835327	−	0.473738i
$485$	1.05982	−	6.01054i	0.0481240	−	0.272925i
$486$	10.5830	+	18.3303i	0.480055	+	0.831479i
$487$	−2.11438	+	3.66221i	−0.0958116	+	0.165951i	−0.909947	−	0.414724i	$-0.863878\pi$
$487$	−2.11438	+	3.66221i	−0.0958116	+	0.165951i	0.814135	+	0.580675i	$0.197211\pi$
$488$	0.717978	+	0.602455i	0.0325013	+	0.0272719i
$489$	−9.78877	−	3.56282i	−0.442664	−	0.161116i
$490$	9.72981	−	3.54136i	0.439548	−	0.159982i
$491$	30.0990	−	25.2561i	1.35835	−	1.13979i	0.381863	−	0.924219i	$-0.375283\pi$
$491$	30.0990	−	25.2561i	1.35835	−	1.13979i	0.976488	−	0.215572i	$-0.0691617\pi$
$492$	−0.133925	−	0.759527i	−0.00603781	−	0.0342421i
$493$		0			0
$494$		0			0
$495$	30.5830			1.37460
$496$	−0.980374	−	5.55998i	−0.0440201	−	0.249650i
$497$	−7.56431	+	6.34721i	−0.339306	+	0.284711i
$498$	−19.7335	+	7.18242i	−0.884281	+	0.321852i
$499$	4.48350	+	1.63186i	0.200709	+	0.0730521i	0.440419	−	0.897792i	$-0.354830\pi$
$499$	4.48350	+	1.63186i	0.200709	+	0.0730521i	−0.239710	+	0.970845i	$0.577052\pi$
$500$	9.19253	+	7.71345i	0.411103	+	0.344956i
$501$	15.8745	−	27.4955i	0.709221	−	1.22841i
$502$	−14.6144	−	25.3128i	−0.652272	−	1.12977i
$503$	−7.10868	+	40.3153i	−0.316960	+	1.79757i	0.244050	+	0.969763i	$0.421524\pi$
$503$	−7.10868	+	40.3153i	−0.316960	+	1.79757i	−0.561010	+	0.827809i	$0.689587\pi$
$504$	2.53231	−	14.3615i	0.112798	−	0.639710i
$505$	−11.2288	−	19.4488i	−0.499673	−	0.865459i
$506$	−3.82288	+	6.62141i	−0.169948	+	0.294358i
$507$	−18.2409	−	15.3059i	−0.810105	−	0.679759i
$508$	12.4899	+	4.54596i	0.554151	+	0.201694i
$509$	29.8343	−	10.8588i	1.32238	−	0.481308i	0.418162	−	0.908373i	$-0.362675\pi$
$509$	29.8343	−	10.8588i	1.32238	−	0.481308i	0.904221	+	0.427065i	$0.140452\pi$
$510$		0			0
$511$	1.08161	+	6.13413i	0.0478477	+	0.271358i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.2915			0.542155
$515$	3.79847	+	21.5422i	0.167381	+	0.949262i
$516$	22.8852	−	19.2030i	1.00746	−	0.845363i
$517$	19.0088	−	6.91864i	0.836007	−	0.304282i
$518$	−1.21362	−	0.441720i	−0.0533232	−	0.0194081i
$519$	−12.1606	−	10.2039i	−0.533790	−	0.447903i
$520$	1.64575	−	2.85052i	0.0721710	−	0.125004i
$521$	5.85425	+	10.1399i	0.256479	+	0.444235i	0.965296	−	0.261157i	$-0.0841041\pi$
$521$	5.85425	+	10.1399i	0.256479	+	0.444235i	−0.708817	+	0.705392i	$0.750771\pi$
$522$	1.14313	−	6.48299i	0.0500333	−	0.283753i
$523$	−0.325505	+	1.84603i	−0.0142333	+	0.0807213i	−0.991097	−	0.133142i	$-0.957493\pi$
$523$	−0.325505	+	1.84603i	−0.0142333	+	0.0807213i	0.976864	+	0.213863i	$0.0686046\pi$
$524$	−0.968627	−	1.67771i	−0.0423147	−	0.0732912i
$525$	11.0516	−	19.1420i	0.482333	−	0.835425i
$526$	−8.37842	−	7.03033i	−0.365317	−	0.306537i
$527$		0			0
$528$	11.5502	−	4.20394i	0.502659	−	0.182953i
$529$	−15.5442	+	13.0431i	−0.675834	+	0.567092i
$530$	3.59599	+	20.3939i	0.156200	+	0.885854i
$531$	−31.7490			−1.37779
$532$		0			0
$533$	−0.583005			−0.0252528
$534$		0			0
$535$	−19.2783	+	16.1764i	−0.833473	+	0.699367i
$536$	−0.606808	+	0.220860i	−0.0262101	+	0.00953970i
$537$	−10.1008	−	3.67638i	−0.435880	−	0.158648i
$538$		0			0
$539$	14.6144	−	25.3128i	0.629486	−	1.09030i
$540$	2.17712	+	3.77089i	0.0936885	+	0.162273i
$541$	1.38919	−	7.87846i	0.0597257	−	0.338722i	−0.940273	−	0.340422i	$-0.889430\pi$
$541$	1.38919	−	7.87846i	0.0597257	−	0.338722i	0.999999	+	0.00170033i	$0.000541231\pi$
$542$	2.14529	−	12.1666i	0.0921482	−	0.522598i
$543$	−29.4059	−	50.9325i	−1.26193	−	2.18572i
$544$		0			0
$545$	−18.3851	−	15.4269i	−0.787530	−	0.660816i
$546$	−18.1281	−	6.59808i	−0.775810	−	0.282372i
$547$	−10.6105	+	3.86192i	−0.453674	+	0.165124i	−0.558743	−	0.829341i	$-0.688716\pi$
$547$	−10.6105	+	3.86192i	−0.453674	+	0.165124i	0.105069	+	0.994465i	$0.466494\pi$
$548$	11.9373	−	10.0166i	0.509935	−	0.427886i
$549$	0.651010	+	3.69206i	0.0277844	+	0.157573i
$550$	10.6458			0.453936
$551$		0			0
$552$	−4.35425			−0.185329
$553$	−2.53231	−	14.3615i	−0.107685	−	0.610711i
$554$	−21.0817	+	17.6897i	−0.895677	+	0.751563i
$555$	1.44946	−	0.527562i	0.0615263	−	0.0223937i
$556$	−17.5213	−	6.37722i	−0.743068	−	0.270454i
$557$	−4.14966	−	3.48198i	−0.175827	−	0.147536i	0.550627	−	0.834751i	$-0.314389\pi$
$557$	−4.14966	−	3.48198i	−0.175827	−	0.147536i	−0.726454	+	0.687215i	$0.758833\pi$
$558$	11.2915	−	19.5575i	0.478007	−	0.827933i
$559$	−11.2915	−	19.5575i	−0.477580	−	0.827192i
$560$	−1.04189	+	5.90885i	−0.0440278	+	0.249694i
$561$		0			0
$562$	−12.7288	−	22.0469i	−0.536930	−	0.929990i
$563$	−5.03137	+	8.71459i	−0.212047	+	0.367276i	−0.952355	−	0.304992i	$-0.901346\pi$
$563$	−5.03137	+	8.71459i	−0.212047	+	0.367276i	0.740308	+	0.672268i	$0.234680\pi$
$564$	8.82503	+	7.40508i	0.371601	+	0.311810i
$565$	−24.0991	−	8.77136i	−1.01386	−	0.369014i
$566$	−28.7976	+	10.4815i	−1.21045	+	0.440569i
$567$	−13.9640	+	11.7172i	−0.586434	+	0.492077i
$568$	−0.470326	−	2.66735i	−0.0197344	−	0.111919i
$569$	6.58301			0.275974			0.137987	−	0.990434i	$-0.455937\pi$
$569$	6.58301			0.275974			0.137987	+	0.990434i	$0.455937\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	−1.61345	−	9.15034i	−0.0674618	−	0.382595i
$573$	13.3422	−	11.1954i	0.557378	−	0.467696i
$574$	0.998655	−	0.363481i	0.0416830	−	0.0151714i
$575$	−3.54381	−	1.28984i	−0.147787	−	0.0537901i
$576$	3.06418	+	2.57115i	0.127674	+	0.107131i
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	6.69987	−	37.9968i	0.278437	−	1.57909i
$580$	−0.470326	+	2.66735i	−0.0195292	+	0.110756i
$581$	−14.4686	−	25.0604i	−0.600260	−	1.03968i
$582$	4.90588	−	8.49723i	0.203355	−	0.352222i
$583$	44.7811	+	37.5758i	1.85464	+	1.55623i
$584$	−1.60546	−	0.584341i	−0.0664345	−	0.0241802i
$585$	12.3720	−	4.50304i	0.511519	−	0.186178i
$586$	22.1672	−	18.6005i	0.915720	−	0.768380i
$587$	−2.45287	−	13.9109i	−0.101241	−	0.574164i	−0.992655	−	0.120976i	$-0.961398\pi$
$587$	−2.45287	−	13.9109i	−0.101241	−	0.574164i	0.891415	−	0.453188i	$-0.149713\pi$
$588$	16.6458			0.686459
$589$		0			0
$590$	13.0627			0.537785
$591$	−3.51269	−	19.9214i	−0.144493	−	0.819458i
$592$	0.271370	−	0.227707i	0.0111532	−	0.00935869i
$593$	−27.9169	+	10.1609i	−1.14641	+	0.417258i	−0.844224	−	0.535991i	$-0.819938\pi$
$593$	−27.9169	+	10.1609i	−1.14641	+	0.417258i	−0.302184	+	0.953250i	$0.597716\pi$
$594$	11.5502	+	4.20394i	0.473912	+	0.172490i
$595$		0			0
$596$	−5.46863	+	9.47194i	−0.224004	+	0.387986i
$597$	26.2915	+	45.5382i	1.07604	+	1.86376i
$598$	−0.571563	+	3.24150i	−0.0233730	+	0.132555i
$599$	−2.94112	+	16.6799i	−0.120171	+	0.681524i	0.863888	+	0.503683i	$0.168022\pi$
$599$	−2.94112	+	16.6799i	−0.120171	+	0.681524i	−0.984059	+	0.177840i	$0.943089\pi$
$600$	3.03137	+	5.25049i	0.123755	+	0.214350i
$601$	−5.20850	+	9.02138i	−0.212459	+	0.367990i	−0.952484	−	0.304590i	$-0.901481\pi$
$601$	−5.20850	+	9.02138i	−0.212459	+	0.367990i	0.740025	+	0.672580i	$0.234814\pi$
$602$	31.5350	+	26.4610i	1.28527	+	1.07847i
$603$	−2.42723	−	0.883440i	−0.0988445	−	0.0359765i
$604$	−12.1570	+	4.42480i	−0.494663	+	0.180043i
$605$	−13.3422	+	11.1954i	−0.542437	+	0.455159i
$606$	−6.26927	−	35.5548i	−0.254672	−	1.44431i
$607$	6.93725			0.281574			0.140787	−	0.990040i	$-0.455037\pi$
$607$	6.93725			0.281574			0.140787	+	0.990040i	$0.455037\pi$
$608$		0			0
$609$	15.8745			0.643268
$610$	−0.267850	−	1.51905i	−0.0108449	−	0.0615047i
$611$	6.67110	−	5.59771i	0.269884	−	0.226459i
$612$		0			0
$613$	−6.96970	−	2.53676i	−0.281503	−	0.102459i	0.197410	−	0.980321i	$-0.436747\pi$
$613$	−6.96970	−	2.53676i	−0.281503	−	0.102459i	−0.478913	+	0.877862i	$0.658969\pi$
$614$	0.494674	+	0.415081i	0.0199634	+	0.0167513i
$615$	−0.634637	+	1.09922i	−0.0255911	+	0.0443250i
$616$	8.46863	+	14.6681i	0.341211	+	0.590994i
$617$	−5.36130	+	30.4055i	−0.215838	+	1.22408i	0.663609	+	0.748080i	$0.269024\pi$
$617$	−5.36130	+	30.4055i	−0.215838	+	1.22408i	−0.879447	+	0.475998i	$0.842087\pi$
$618$	−6.10651	+	34.6318i	−0.245640	+	1.39309i
$619$	4.22876	+	7.32442i	0.169968	+	0.294393i	0.938408	−	0.345528i	$-0.112300\pi$
$619$	4.22876	+	7.32442i	0.169968	+	0.294393i	−0.768440	+	0.639921i	$0.778967\pi$
$620$	−4.64575	+	8.04668i	−0.186578	+	0.323162i
$621$	−3.33555	−	2.79886i	−0.133851	−	0.112314i
$622$	−12.8228	−	4.66712i	−0.514148	−	0.187135i
$623$		0			0
$624$	4.05353	−	3.40131i	0.162271	−	0.136161i
$625$	−1.43980	−	8.16554i	−0.0575922	−	0.326621i
$626$	8.87451			0.354697
$627$		0			0
$628$	−10.5830			−0.422308
$629$		0			0
$630$	−18.3851	+	15.4269i	−0.732479	+	0.614623i
$631$	23.3154	−	8.48612i	0.928173	−	0.337827i	0.166688	−	0.986010i	$-0.446693\pi$
$631$	23.3154	−	8.48612i	0.928173	−	0.337827i	0.761485	+	0.648183i	$0.224471\pi$
$632$	3.75877	+	1.36808i	0.149516	+	0.0544193i
$633$	−26.9387	−	22.6043i	−1.07072	−	0.898439i
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$	−10.9373	−	18.9439i	−0.434032	−	0.751765i
$636$	−5.78101	+	32.7857i	−0.229232	+	1.30004i
$637$	2.18502	−	12.3918i	0.0865735	−	0.490983i
$638$	3.82288	+	6.62141i	0.151349	+	0.262144i
$639$	5.41699	−	9.38251i	0.214293	−	0.371166i
$640$	−1.26072	−	1.05787i	−0.0498343	−	0.0418159i
$641$	−12.0981	−	4.40334i	−0.477845	−	0.173922i	0.0918576	−	0.995772i	$-0.470720\pi$
$641$	−12.0981	−	4.40334i	−0.477845	−	0.173922i	−0.569703	+	0.821851i	$0.692942\pi$
$642$	−38.0176	+	13.8373i	−1.50044	+	0.546114i
$643$	−4.99481	+	4.19114i	−0.196976	+	0.165282i	−0.735941	−	0.677046i	$-0.763260\pi$
$643$	−4.99481	+	4.19114i	−0.196976	+	0.165282i	0.538965	+	0.842328i	$0.318816\pi$
$644$	−1.04189	−	5.90885i	−0.0410562	−	0.232841i
$645$	−49.1660			−1.93591
$646$		0			0
$647$	−22.4575			−0.882896			−0.441448	−	0.897287i	$-0.645535\pi$
$647$	−22.4575			−0.882896			−0.441448	+	0.897287i	$0.645535\pi$
$648$	−0.868241	−	4.92404i	−0.0341077	−	0.193435i
$649$	28.2475	−	23.7025i	1.10881	−	0.930404i
$650$	4.30662	−	1.56748i	0.168919	−	0.0614816i
$651$	51.1733	+	18.6256i	2.00564	+	0.729994i
$652$	3.01611	+	2.53082i	0.118120	+	0.0991145i
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	−0.999396	−	0.0347583i	$-0.988934\pi$
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	0.529799	+	0.848123i	$0.322267\pi$
$654$	−19.2915	−	33.4139i	−0.754357	−	1.30659i
$655$	−0.553632	+	3.13980i	−0.0216322	+	0.122682i
$656$	−0.0506189	+	0.287074i	−0.00197634	+	0.0112084i
$657$	−3.41699	−	5.91841i	−0.133310	−	0.230899i
$658$	−7.93725	+	13.7477i	−0.309426	+	0.535942i
$659$	−14.2354	−	11.9449i	−0.554533	−	0.465308i	0.321940	−	0.946760i	$-0.395665\pi$
$659$	−14.2354	−	11.9449i	−0.554533	−	0.465308i	−0.876472	+	0.481452i	$0.840110\pi$
$660$	−19.0088	−	6.91864i	−0.739917	−	0.269308i
$661$	−15.2500	+	5.55056i	−0.593158	+	0.215892i	−0.621118	−	0.783717i	$-0.713321\pi$
$661$	−15.2500	+	5.55056i	−0.593158	+	0.215892i	0.0279599	+	0.999609i	$0.491099\pi$
$662$	15.1767	−	12.7348i	0.589859	−	0.494950i
$663$		0			0
$664$	7.93725			0.308025
$665$		0			0
$666$	1.41699			0.0549074
$667$	−0.470326	−	2.66735i	−0.0182111	−	0.103280i
$668$	−9.19253	+	7.71345i	−0.355670	+	0.298442i
$669$	46.7697	−	17.0228i	1.80822	−	0.658138i
$670$	0.998655	+	0.363481i	0.0385814	+	0.0140425i
$671$	−3.33555	−	2.79886i	−0.128767	−	0.108049i
$672$	−4.82288	+	8.35347i	−0.186046	+	0.322242i
$673$	6.93725	+	12.0157i	0.267411	+	0.463170i	0.968193	−	0.250206i	$-0.0804984\pi$
$673$	6.93725	+	12.0157i	0.267411	+	0.463170i	−0.700781	+	0.713376i	$0.747165\pi$
$674$	−1.68586	+	9.56100i	−0.0649370	+	0.368276i
$675$	−1.05278	+	5.97064i	−0.0405217	+	0.229810i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	5.70850	−	9.88741i	0.219395	−	0.380004i	−0.735228	−	0.677820i	$-0.762925\pi$
$677$	5.70850	−	9.88741i	0.219395	−	0.380004i	0.954623	+	0.297816i	$0.0962582\pi$
$678$	−31.5831	−	26.5013i	−1.21294	−	1.01778i
$679$	12.7049	+	4.62420i	0.487569	+	0.177461i
$680$		0			0
$681$	−14.9053	+	12.5070i	−0.571173	+	0.479271i
$682$	4.55458	+	25.8303i	0.174404	+	0.989093i
$683$	−5.41699			−0.207276			−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699			−0.207276			−0.103638	+	0.994615i	$0.533048\pi$
$684$		0			0
$685$	−25.6458			−0.979874
$686$	−0.448534	−	2.54376i	−0.0171251	−	0.0971213i
$687$	40.5353	−	34.0131i	1.54652	−	1.29768i
$688$	−10.6105	+	3.86192i	−0.404523	+	0.147234i
$689$	23.6483	+	8.60728i	0.900929	+	0.327911i
$690$	5.48948	+	4.60622i	0.208981	+	0.175356i
$691$	−1.29150	+	2.23695i	−0.0491311	+	0.0850975i	−0.889545	−	0.456847i	$-0.848979\pi$
$691$	−1.29150	+	2.23695i	−0.0491311	+	0.0850975i	0.840414	+	0.541945i	$0.182312\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	−11.7645	+	66.7198i	−0.446896	+	2.53447i
$694$	−4.03363	+	22.8759i	−0.153115	+	0.868356i
$695$	15.3431	+	26.5751i	0.581998	+	1.00805i
$696$	−2.17712	+	3.77089i	−0.0825237	+	0.142935i
$697$		0			0
$698$	−19.8895	−	7.23920i	−0.752830	−	0.274008i
$699$	−46.9257	+	17.0795i	−1.77489	+	0.646008i
$700$	−6.39973	+	5.37001i	−0.241887	+	0.202967i
$701$	1.79800	+	10.1969i	0.0679094	+	0.385133i	0.999752	+	0.0222705i	$0.00708951\pi$
$701$	1.79800	+	10.1969i	0.0679094	+	0.385133i	−0.931843	+	0.362863i	$0.881799\pi$
$702$	5.29150			0.199715
$703$		0			0
$704$	−4.64575			−0.175093
$705$	−3.29228	−	18.6714i	−0.123994	−	0.703207i
$706$	9.86245	−	8.27557i	0.371178	−	0.311455i
$707$	46.7488	−	17.0152i	1.75817	−	0.639921i
$708$	19.7335	+	7.18242i	0.741632	+	0.269932i
$709$	2.79281	+	2.34344i	0.104886	+	0.0880099i	0.693723	−	0.720242i	$-0.255969\pi$
$709$	2.79281	+	2.34344i	0.104886	+	0.0880099i	−0.588837	+	0.808252i	$0.700414\pi$
$710$	−2.22876	+	3.86032i	−0.0836437	+	0.144875i
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$	1.61345	−	9.15034i	0.0604243	−	0.342683i
$714$		0			0
$715$	−7.64575	+	13.2428i	−0.285935	+	0.495254i
$716$	3.11224	+	2.61148i	0.116310	+	0.0975957i
$717$	29.8343	+	10.8588i	1.11418	+	0.405529i
$718$	4.63950	−	1.68864i	0.173145	−	0.0630195i
$719$	2.07483	−	1.74099i	0.0773781	−	0.0649279i	−0.603278	−	0.797531i	$-0.706139\pi$
$719$	2.07483	−	1.74099i	0.0773781	−	0.0649279i	0.680656	+	0.732603i	$0.261695\pi$
$720$	−1.14313	−	6.48299i	−0.0426018	−	0.241607i
$721$	−48.4575			−1.80465
$722$		0			0
$723$	−20.0627			−0.746142
$724$	3.85998	+	21.8911i	0.143455	+	0.813575i
$725$	−2.88894	+	2.42411i	−0.107293	+	0.0900291i
$726$	−26.3114	+	9.57656i	−0.976507	+	0.355420i
$727$	−1.33154	−	0.484641i	−0.0493841	−	0.0179743i	0.317210	−	0.948355i	$-0.397254\pi$
$727$	−1.33154	−	0.484641i	−0.0493841	−	0.0179743i	−0.366594	+	0.930381i	$0.619476\pi$
$728$	5.58562	+	4.68689i	0.207017	+	0.173708i
$729$	20.5000	−	35.5070i	0.759259	−	1.31508i
$730$	1.40588	+	2.43506i	0.0520340	+	0.0901255i
$731$		0			0
$732$	0.430602	−	2.44207i	0.0159155	−	0.0902614i
$733$	8.05163	+	13.9458i	0.297394	+	0.515101i	0.975539	−	0.219827i	$-0.0705492\pi$
$733$	8.05163	+	13.9458i	0.297394	+	0.515101i	−0.678145	+	0.734928i	$0.737216\pi$
$734$	−8.11438	+	14.0545i	−0.299507	+	0.518762i
$735$	−20.9856	−	17.6090i	−0.774066	−	0.649518i
$736$	1.54650	+	0.562880i	0.0570048	+	0.0207480i
$737$	2.81908	−	1.02606i	0.103842	−	0.0377954i
$738$	−0.893216	+	0.749497i	−0.0328797	+	0.0275894i
$739$	−5.87135	−	33.2981i	−0.215981	−	1.22489i	−0.879196	−	0.476461i	$-0.841919\pi$
$739$	−5.87135	−	33.2981i	−0.215981	−	1.22489i	0.663215	−	0.748429i	$-0.269192\pi$
$740$	−0.583005			−0.0214317
$741$		0			0
$742$	−45.8745			−1.68411
$743$	−8.25181	−	46.7983i	−0.302729	−	1.71686i	−0.634004	−	0.773330i	$-0.718590\pi$
$743$	−8.25181	−	46.7983i	−0.302729	−	1.71686i	0.331275	−	0.943534i	$-0.392521\pi$
$744$	−11.4426	+	9.60148i	−0.419506	+	0.352007i
$745$	16.9145	−	6.15636i	0.619698	−	0.225552i
$746$	3.75877	+	1.36808i	0.137618	+	0.0500890i
$747$	24.3212	+	20.4079i	0.889865	+	0.746685i
$748$		0			0
$749$	−27.8745	−	48.2801i	−1.01851	−	1.76412i
$750$	5.51316	−	31.2667i	0.201312	−	1.14170i
$751$	−1.36739	+	7.75488i	−0.0498969	+	0.282979i	−0.999539	−	0.0303569i	$-0.990336\pi$
$751$	−1.36739	+	7.75488i	−0.0498969	+	0.282979i	0.949642	+	0.313336i	$0.101447\pi$
$752$	−2.17712	−	3.77089i	−0.0793916	−	0.137510i
$753$	−38.6660	+	66.9715i	−1.40907	+	2.44058i
$754$	2.52144	+	2.11574i	0.0918253	+	0.0770506i
$755$	20.0075	+	7.28212i	0.728146	+	0.265024i
$756$	−9.06404	+	3.29904i	−0.329656	+	0.119985i
$757$	−3.51079	+	2.94590i	−0.127602	+	0.107071i	−0.704355	−	0.709848i	$-0.748764\pi$
$757$	−3.51079	+	2.94590i	−0.127602	+	0.107071i	0.576754	+	0.816918i	$0.304319\pi$
$758$	1.85951	+	10.5458i	0.0675405	+	0.383041i
$759$	20.2288			0.734257
$760$		0			0
$761$	42.8745			1.55420			0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745			1.55420			0.777100	+	0.629377i	$0.216690\pi$
$762$	−6.10651	−	34.6318i	−0.221216	−	1.25458i
$763$	40.7275	−	34.1745i	1.47444	−	1.23720i
$764$	−6.18600	+	2.25152i	−0.223802	+	0.0814571i
$765$		0			0
$766$	4.22876	+	3.54835i	0.152791	+	0.128207i
$767$	7.93725	−	13.7477i	0.286598	−	0.496402i
$768$	−1.32288	−	2.29129i	−0.0477352	−	0.0826797i
$769$	6.12831	−	34.7553i	0.220992	−	1.25331i	−0.649208	−	0.760611i	$-0.724899\pi$
$769$	6.12831	−	34.7553i	0.220992	−	1.25331i	0.870200	−	0.492699i	$-0.163989\pi$
$770$	4.84036	−	27.4510i	0.174434	−	0.989267i
$771$	−16.2601	−	28.1634i	−0.585594	−	1.01428i
$772$	−7.29150	+	12.6293i	−0.262427	+	0.454537i
$773$	−3.78216	−	3.17361i	−0.136035	−	0.114147i	0.572231	−	0.820092i	$-0.306078\pi$
$773$	−3.78216	−	3.17361i	−0.136035	−	0.114147i	−0.708266	+	0.705945i	$0.750522\pi$
$774$	−42.4422	−	15.4477i	−1.52555	−	0.555256i
$775$	−12.1570	+	4.42480i	−0.436694	+	0.158944i
$776$	−2.84087	+	2.38378i	−0.101981	+	0.0855726i
$777$	0.593355	+	3.36508i	0.0212865	+	0.120722i
$778$	12.0000			0.430221
$779$		0			0
$780$	−8.70850			−0.311814
$781$	2.18502	+	12.3918i	0.0781860	+	0.443415i
$782$		0			0
$783$	−4.09166	+	1.48924i	−0.146224	+	0.0532211i
$784$	−5.91208	−	2.15182i	−0.211146	−	0.0768507i
$785$	13.3422	+	11.1954i	0.476203	+	0.399582i
$786$	−2.56275	+	4.43881i	−0.0914101	+	0.158327i
$787$	21.2601	+	36.8236i	0.757842	+	1.31262i	0.943949	+	0.330091i	$0.107079\pi$
$787$	21.2601	+	36.8236i	0.757842	+	1.31262i	−0.186107	+	0.982529i	$0.559587\pi$
$788$	−1.32767	+	7.52960i	−0.0472963	+	0.268231i
$789$	−5.02490	+	28.4976i	−0.178891	+	1.01454i
$790$	−3.29150	−	5.70105i	−0.117106	−	0.202834i
$791$	28.4059	−	49.2004i	1.01000	−	1.74937i
$792$	−14.2354	−	11.9449i	−0.505833	−	0.424444i
$793$	−1.76146	−	0.641119i	−0.0625513	−	0.0227668i
$794$	−19.7925	+	7.20388i	−0.702410	+	0.255656i
$795$	41.9712	−	35.2180i	1.48857	−	1.24905i
$796$	−3.45117	−	19.5726i	−0.122324	−	0.693731i
$797$	−44.8118			−1.58731			−0.793657	−	0.608365i	$-0.791826\pi$
$797$	−44.8118			−1.58731			−0.793657	+	0.608365i	$0.791826\pi$
$798$		0			0
$799$		0			0
$800$	−0.397915	−	2.25669i	−0.0140684	−	0.0797860i
$801$		0			0
$802$	−25.9195	+	9.43394i	−0.915251	+	0.333124i
$803$	7.45858	+	2.71470i	0.263208	+	0.0957997i
$804$	1.30878	+	1.09820i	0.0461573	+	0.0387306i
$805$	−4.93725	+	8.55157i	−0.174015	+	0.301403i
$806$	5.64575	+	9.77873i	0.198863	+	0.344441i
$807$		0			0
$808$	−2.36956	+	13.4384i	−0.0833608	+	0.472763i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$	−4.11438	+	7.12631i	−0.144565	+	0.250393i
$811$	−23.9707	−	20.1138i	−0.841724	−	0.706291i	0.116226	−	0.993223i	$-0.462920\pi$
$811$	−23.9707	−	20.1138i	−0.841724	−	0.706291i	−0.957951	+	0.286932i	$0.907365\pi$
$812$	−5.63816	−	2.05212i	−0.197860	−	0.0720153i
$813$	−30.7150	+	11.1794i	−1.07722	+	0.392077i
$814$	−1.26072	+	1.05787i	−0.0441882	+	0.0370783i
$815$	−1.12520	−	6.38130i	−0.0394139	−	0.223527i
$816$		0			0
$817$		0			0
$818$	−7.58301			−0.265134
$819$	5.06462	+	28.7229i	0.176972	+	1.00366i
$820$	0.367503	−	0.308371i	0.0128338	−	0.0107688i
$821$	5.63816	−	2.05212i	0.196773	−	0.0716195i	−0.241754	−	0.970338i	$-0.577723\pi$
$821$	5.63816	−	2.05212i	0.196773	−	0.0716195i	0.438527	+	0.898718i	$0.355500\pi$
$822$	−38.7424	−	14.1011i	−1.35129	−	0.491831i
$823$	−24.4173	−	20.4885i	−0.851133	−	0.714186i	0.108906	−	0.994052i	$-0.465265\pi$
$823$	−24.4173	−	20.4885i	−0.851133	−	0.714186i	−0.960039	+	0.279867i	$0.909710\pi$
$824$	6.64575	−	11.5108i	0.231516	−	0.400997i
$825$	−14.0830	−	24.3925i	−0.490307	−	0.849237i
$826$	−5.02490	+	28.4976i	−0.174839	+	0.991559i
$827$	−9.14184	+	51.8459i	−0.317893	+	1.80286i	0.237627	+	0.971357i	$0.423631\pi$
$827$	−9.14184	+	51.8459i	−0.317893	+	1.80286i	−0.555519	+	0.831504i	$0.687481\pi$
$828$	3.29150	+	5.70105i	0.114388	+	0.198125i
$829$	8.58301	−	14.8662i	0.298100	−	0.516325i	−0.677601	−	0.735430i	$-0.736980\pi$
$829$	8.58301	−	14.8662i	0.298100	−	0.516325i	0.975701	+	0.219105i	$0.0703137\pi$
$830$	−10.0066	−	8.39657i	−0.347336	−	0.291449i
$831$	68.4207	+	24.9031i	2.37349	+	0.863879i
$832$	−1.87939	+	0.684040i	−0.0651560	+	0.0237148i
$833$		0			0
$834$	8.56642	+	48.5826i	0.296631	+	1.68228i
$835$	19.7490			0.683443
$836$		0			0
$837$	−14.9373			−0.516307
$838$	−5.51316	−	31.2667i	−0.190449	−	1.08009i
$839$	−31.8064	+	26.6887i	−1.09808	+	0.921397i	−0.997294	−	0.0735119i	$-0.976579\pi$
$839$	−31.8064	+	26.6887i	−1.09808	+	0.921397i	−0.100783	+	0.994908i	$0.532135\pi$
$840$	14.9172	−	5.42940i	0.514691	−	0.187332i
$841$	24.7059	+	8.99222i	0.851929	+	0.310077i
$842$	−19.0069	−	15.9487i	−0.655021	−	0.549628i
$843$	−33.6771	+	58.3305i	−1.15990	+	2.00901i
$844$	6.64575	+	11.5108i	0.228756	+	0.396217i
$845$	2.57204	−	14.5867i	0.0884807	−	0.501799i
$846$	3.02443	−	17.1524i	0.103982	−	0.589711i
$847$	−19.2915	−	33.4139i	−0.662864	−	1.14811i
$848$	6.29150	−	10.8972i	0.216051	−	0.374211i
$849$	62.1117	+	52.1179i	2.13167	+	1.78868i
$850$		0			0
$851$	0.547846	−	0.199400i	0.0187799	−	0.00683533i
$852$	−5.48948	+	4.60622i	−0.188067	+	0.157807i
$853$	1.49042	+	8.45261i	0.0510311	+	0.289412i	0.999634	−	0.0270574i	$-0.00861369\pi$
$853$	1.49042	+	8.45261i	0.0510311	+	0.289412i	−0.948603	+	0.316469i	$0.897503\pi$
$854$	3.41699			0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	3.64661	+	20.6810i	0.124566	+	0.706448i	0.981565	+	0.191130i	$0.0612152\pi$
$857$	3.64661	+	20.6810i	0.124566	+	0.706448i	−0.856999	+	0.515318i	$0.827674\pi$
$858$	−18.8317	+	15.8017i	−0.642903	+	0.539459i
$859$	−12.4310	+	4.52450i	−0.424139	+	0.154374i	−0.545266	−	0.838263i	$-0.683571\pi$
$859$	−12.4310	+	4.52450i	−0.424139	+	0.154374i	0.121127	+	0.992637i	$0.461349\pi$
$860$	17.4623	+	6.35576i	0.595460	+	0.216730i
$861$	−2.15393	−	1.80737i	−0.0734059	−	0.0615949i
$862$	−13.9373	+	24.1400i	−0.474705	+	0.822213i
$863$	15.5314	+	26.9011i	0.528694	+	0.915725i	0.999440	+	0.0334563i	$0.0106515\pi$
$863$	15.5314	+	26.9011i	0.528694	+	0.915725i	−0.470746	+	0.882269i	$0.656015\pi$
$864$	0.459430	−	2.60556i	0.0156301	−	0.0886428i
$865$	1.71469	−	9.72449i	0.0583012	−	0.330643i
$866$	−8.93725	−	15.4798i	−0.303700	−	0.526024i
$867$	22.4889	−	38.9519i	0.763763	−	1.32288i
$868$	−15.7675	−	13.2305i	−0.535184	−	0.449072i
$869$	−17.4623	−	6.35576i	−0.592368	−	0.215604i
$870$	6.73385	−	2.45092i	0.228299	−	0.0830940i
$871$	0.989348	−	0.830162i	0.0335228	−	0.0281290i
$872$	2.53231	+	14.3615i	0.0857549	+	0.486340i
$873$	−14.8340			−0.502054
$874$		0			0
$875$	43.7490			1.47899
$876$	0.784935	+	4.45159i	0.0265205	+	0.150405i
$877$	−31.9025	+	26.7694i	−1.07727	+	0.903937i	−0.995691	−	0.0927293i	$-0.970441\pi$
$877$	−31.9025	+	26.7694i	−1.07727	+	0.903937i	−0.0815794	+	0.996667i	$0.525996\pi$
$878$	−10.1597	+	3.69784i	−0.342874	+	0.124796i
$879$	−71.9436	−	26.1853i	−2.42660	−	0.883209i
$880$	5.85699	+	4.91459i	0.197439	+	0.165671i
$881$	18.4373	−	31.9343i	0.621167	−	1.07589i	−0.368102	−	0.929785i	$-0.619992\pi$
$881$	18.4373	−	31.9343i	0.621167	−	1.07589i	0.989269	−	0.146107i	$-0.0466744\pi$
$882$	−12.5830	−	21.7944i	−0.423692	−	0.733856i
$883$	−4.93070	+	27.9634i	−0.165931	+	0.941043i	0.782168	+	0.623068i	$0.214114\pi$
$883$	−4.93070	+	27.9634i	−0.165931	+	0.941043i	−0.948099	+	0.317975i	$0.896997\pi$
$884$		0			0
$885$	−17.2804	−	29.9305i	−0.580874	−	1.00610i
$886$	−5.32288	+	9.21949i	−0.178826	+	0.309735i
$887$	−13.3422	−	11.1954i	−0.447987	−	0.375906i	0.390701	−	0.920518i	$-0.372233\pi$
$887$	−13.3422	−	11.1954i	−0.447987	−	0.375906i	−0.838688	+	0.544612i	$0.816677\pi$
$888$	−0.880731	−	0.320560i	−0.0295554	−	0.0107573i
$889$	45.5352	−	16.5734i	1.52720	−	0.555856i
$890$		0			0
$891$	4.03363	+	22.8759i	0.135132	+	0.766370i
$892$	−18.8118			−0.629864
$893$		0			0
$894$	28.9373			0.967807
$895$	−1.16106	−	6.58469i	−0.0388099	−	0.220102i
$896$	2.79281	−	2.34344i	0.0933012	−	0.0782890i
$897$	8.18331	−	2.97848i	0.273233	−	0.0994486i
$898$	22.8265	+	8.30818i	0.761732	+	0.277248i
$899$	−7.11770	−	5.97246i	−0.237389	−	0.199193i
$900$	4.58301	−	7.93800i	0.152767	−	0.264600i
$901$		0			0
$902$	0.235163	−	1.33367i	0.00783007	−	0.0444065i
$903$	18.9129	−	107.260i	0.629382	−	3.56940i
$904$	7.79150	+	13.4953i	0.259142	+	0.448846i
$905$	18.2915	−	31.6818i	0.608030	−	1.05314i
$906$	26.2207	+	22.0018i	0.871126	+	0.730962i
$907$	−37.5287	−	13.6593i	−1.24612	−	0.453551i	−0.367032	−	0.930208i	$-0.619626\pi$
$907$	−37.5287	−	13.6593i	−1.24612	−	0.453551i	−0.879089	+	0.476657i	$0.841848\pi$
$908$	6.91073	−	2.51530i	0.229341	−	0.0834732i
$909$	−41.8130	+	35.0853i	−1.38685	+	1.16371i
$910$	−2.08378	−	11.8177i	−0.0690766	−	0.391753i
$911$	16.9373			0.561156			0.280578	−	0.959831i	$-0.409474\pi$
$911$	16.9373			0.561156			0.280578	+	0.959831i	$0.409474\pi$
$912$		0			0
$913$	−36.8745			−1.22037
$914$	5.70860	+	32.3751i	0.188824	+	1.07087i
$915$	−3.12626	+	2.62324i	−0.103351	+	0.0867216i
$916$	−18.7939	+	6.84040i	−0.620966	+	0.226013i
$917$	−6.63681	−	2.41560i	−0.219167	−	0.0797702i
$918$		0			0
$919$	9.93725	−	17.2118i	0.327800	−	0.567766i	−0.654275	−	0.756257i	$-0.727026\pi$
$919$	9.93725	−	17.2118i	0.327800	−	0.567766i	0.982075	+	0.188491i	$0.0603595\pi$
$920$	−1.35425	−	2.34563i	−0.0446483	−	0.0773330i
$921$	0.296677	−	1.68254i	0.00977585	−	0.0554416i
$922$	3.32814	−	18.8748i	0.109607	−	0.621610i
$923$	2.70850	+	4.69126i	0.0891513	+	0.154415i
$924$	22.4059	−	38.8081i	0.737099	−	1.27669i
$925$	−0.621846	−	0.521790i	−0.0204462	−	0.0171564i
$926$	36.1382	+	13.1532i	1.18758	+	0.432242i
$927$	49.9597	−	18.1838i	1.64089	−	0.597236i
$928$	1.26072	−	1.05787i	0.0413851	−	0.0347262i
$929$	−1.66407	−	9.43742i	−0.0545964	−	0.309632i	0.945265	−	0.326305i	$-0.105804\pi$
$929$	−1.66407	−	9.43742i	−0.0545964	−	0.309632i	−0.999861	+	0.0166732i	$0.994692\pi$
$930$	24.5830			0.806108
$931$		0			0
$932$	18.8745			0.618255
$933$	6.26927	+	35.5548i	0.205247	+	1.16401i
$934$	−14.8262	+	12.4407i	−0.485129	+	0.407071i
$935$		0			0
$936$	−7.51754	−	2.73616i	−0.245719	−	0.0894342i
$937$	5.45844	+	4.58018i	0.178320	+	0.149628i	0.727579	−	0.686024i	$-0.240646\pi$
$937$	5.45844	+	4.58018i	0.178320	+	0.149628i	−0.549259	+	0.835652i	$0.685090\pi$
$938$	−1.17712	+	2.03884i	−0.0384345	+	0.0665705i
$939$	−11.7399	−	20.3341i	−0.383116	−	0.663577i
$940$	−1.24436	+	7.05714i	−0.0405867	+	0.230179i
$941$	2.92319	−	16.5782i	0.0952933	−	0.540435i	−0.899364	−	0.437201i	$-0.855970\pi$
$941$	2.92319	−	16.5782i	0.0952933	−	0.540435i	0.994657	−	0.103234i	$-0.0329191\pi$
$942$	14.0000	+	24.2487i	0.456145	+	0.790066i
$943$	−0.239870	+	0.415468i	−0.00781126	+	0.0135295i
$944$	−6.08029	−	5.10197i	−0.197897	−	0.166055i
$945$	14.9172	+	5.42940i	0.485255	+	0.176618i
$946$	49.2939	−	17.9415i	1.60268	−	0.583329i
$947$	−5.93609	+	4.98097i	−0.192897	+	0.161860i	−0.734121	−	0.679019i	$-0.762406\pi$
$947$	−5.93609	+	4.98097i	−0.192897	+	0.161860i	0.541224	+	0.840878i	$0.317961\pi$
$948$	−1.83772	−	10.4222i	−0.0596864	−	0.338498i
$949$	3.41699			0.110920
$950$		0			0
$951$	−15.8745			−0.514766
$952$		0			0
$953$	−10.3091	+	8.65032i	−0.333943	+	0.280211i	−0.794304	−	0.607520i	$-0.792164\pi$
$953$	−10.3091	+	8.65032i	−0.333943	+	0.280211i	0.460361	+	0.887732i	$0.347720\pi$
$954$	47.2966	−	17.2146i	1.53128	−	0.557342i
$955$	10.1806	+	3.70544i	0.329437	+	0.119905i
$956$	−9.19253	−	7.71345i	−0.297308	−	0.249471i
$957$	10.1144	−	17.5186i	0.326951	−	0.566296i
$958$	−3.29150	−	5.70105i	−0.106344	−	0.184193i
$959$	9.86526	−	55.9487i	0.318566	−	1.80668i
$960$	−0.756107	+	4.28810i	−0.0244033	+	0.138398i
$961$	−0.437254	−	0.757346i	−0.0141050	−	0.0244305i
$962$	−0.354249	+	0.613577i	−0.0114214	+	0.0197825i
$963$	46.8559	+	39.3168i	1.50991	+	1.26696i
$964$	7.12569	+	2.59354i	0.229503	+	0.0835323i
$965$	22.5526	−	8.20848i	0.725995	−	0.264240i
$966$	−12.1606	+	10.2039i	−0.391260	+	0.328306i
$967$	−2.30805	−	13.0896i	−0.0742217	−	0.420932i	−0.999166	−	0.0408299i	$-0.987000\pi$
$967$	−2.30805	−	13.0896i	−0.0742217	−	0.420932i	0.924944	−	0.380102i	$-0.124111\pi$
$968$	10.5830			0.340151
$969$		0			0
$970$	6.10326			0.195964
$971$	−9.44555	−	53.5684i	−0.303122	−	1.71909i	−0.632214	−	0.774794i	$-0.717854\pi$
$971$	−9.44555	−	53.5684i	−0.303122	−	1.71909i	0.329092	−	0.944298i	$-0.393257\pi$
$972$	−16.2141	+	13.6052i	−0.520068	+	0.436389i
$973$	−63.8782	+	23.2498i	−2.04784	+	0.745353i
$974$	−3.97373	−	1.44632i	−0.127327	−	0.0463431i
$975$	−9.28867	−	7.79412i	−0.297475	−	0.249611i
$976$	−0.468627	+	0.811686i	−0.0150004	+	0.0259814i
$977$	3.72876	+	6.45840i	0.119293	+	0.206622i	0.919488	−	0.393118i	$-0.128604\pi$
$977$	3.72876	+	6.45840i	0.119293	+	0.206622i	−0.800194	+	0.599741i	$0.795270\pi$
$978$	1.80889	−	10.2587i	0.0578420	−	0.328038i
$979$		0			0
$980$	5.17712	+	8.96704i	0.165377	+	0.286442i
$981$	−29.1660	+	50.5170i	−0.931199	+	1.61288i
$982$	30.0990	+	25.2561i	0.960499	+	0.805954i
$983$	−29.8343	−	10.8588i	−0.951567	−	0.346342i	−0.180843	−	0.983512i	$-0.557883\pi$
$983$	−29.8343	−	10.8588i	−0.951567	−	0.346342i	−0.770723	+	0.637170i	$0.780105\pi$
$984$	0.724732	−	0.263781i	0.0231036	−	0.00840902i
$985$	9.63914	−	8.08820i	0.307129	−	0.257711i
$986$		0			0
$987$	42.0000			1.33687
$988$		0			0
$989$	−18.5830			−0.590905
$990$	5.31068	+	30.1184i	0.168785	+	0.957225i
$991$	−2.17096	+	1.82165i	−0.0689629	+	0.0578667i	−0.676618	−	0.736335i	$-0.736555\pi$
$991$	−2.17096	+	1.82165i	−0.0689629	+	0.0578667i	0.607655	+	0.794201i	$0.292110\pi$
$992$	5.30527	−	1.93096i	0.168443	−	0.0613081i
$993$	−49.2559	−	17.9277i	−1.56309	−	0.568917i
$994$	−7.56431	−	6.34721i	−0.239925	−	0.201321i
$995$	−16.3542	+	28.3264i	−0.518465	+	0.898007i
$996$	−10.5000	−	18.1865i	−0.332705	−	0.576262i
$997$	2.81809	−	15.9822i	0.0892499	−	0.506162i	−0.907108	−	0.420897i	$-0.861715\pi$
$997$	2.81809	−	15.9822i	0.0892499	−	0.506162i	0.996358	−	0.0852645i	$-0.0271735\pi$
$998$	−0.828518	+	4.69876i	−0.0262263	+	0.148737i
$999$	−0.468627	−	0.811686i	−0.0148267	−	0.0256806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.n.389.2		12
19.2	odd	18		722.2.e.o.245.1		12
19.3	odd	18		722.2.e.o.423.1		12
19.4	even	9		38.2.c.b.11.1	yes	4
19.5	even	9	inner	722.2.e.n.415.1		12
19.6	even	9		722.2.a.j.1.2		2
19.7	even	3	inner	722.2.e.n.99.2		12
19.8	odd	6		722.2.e.o.595.2		12
19.9	even	9		38.2.c.b.7.1	✓	4
19.10	odd	18		722.2.c.j.653.2		4
19.11	even	3	inner	722.2.e.n.595.1		12
19.12	odd	6		722.2.e.o.99.1		12
19.13	odd	18		722.2.a.g.1.1		2
19.14	odd	18		722.2.e.o.415.2		12
19.15	odd	18		722.2.c.j.429.2		4
19.16	even	9	inner	722.2.e.n.423.2		12
19.17	even	9	inner	722.2.e.n.245.2		12
19.18	odd	2		722.2.e.o.389.1		12
57.23	odd	18		342.2.g.f.163.1		4
57.32	even	18		6498.2.a.bg.1.2		2
57.44	odd	18		6498.2.a.ba.1.2		2
57.47	odd	18		342.2.g.f.235.1		4
76.23	odd	18		304.2.i.e.49.2		4
76.47	odd	18		304.2.i.e.273.2		4
76.51	even	18		5776.2.a.z.1.2		2
76.63	odd	18		5776.2.a.ba.1.1		2
95.4	even	18		950.2.e.k.201.2		4
95.9	even	18		950.2.e.k.501.2		4
95.23	odd	36		950.2.j.g.49.3		8
95.28	odd	36		950.2.j.g.349.2		8
95.42	odd	36		950.2.j.g.49.2		8
95.47	odd	36		950.2.j.g.349.3		8
152.61	even	18		1216.2.i.l.961.2		4
152.85	even	18		1216.2.i.l.577.2		4
152.99	odd	18		1216.2.i.k.961.1		4
152.123	odd	18		1216.2.i.k.577.1		4
228.23	even	18		2736.2.s.v.1873.1		4
228.47	even	18		2736.2.s.v.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	19.9	even	9
38.2.c.b.11.1	yes	4	19.4	even	9
304.2.i.e.49.2		4	76.23	odd	18
304.2.i.e.273.2		4	76.47	odd	18
342.2.g.f.163.1		4	57.23	odd	18
342.2.g.f.235.1		4	57.47	odd	18
722.2.a.g.1.1		2	19.13	odd	18
722.2.a.j.1.2		2	19.6	even	9
722.2.c.j.429.2		4	19.15	odd	18
722.2.c.j.653.2		4	19.10	odd	18
722.2.e.n.99.2		12	19.7	even	3	inner
722.2.e.n.245.2		12	19.17	even	9	inner
722.2.e.n.389.2		12	1.1	even	1	trivial
722.2.e.n.415.1		12	19.5	even	9	inner
722.2.e.n.423.2		12	19.16	even	9	inner
722.2.e.n.595.1		12	19.11	even	3	inner
722.2.e.o.99.1		12	19.12	odd	6
722.2.e.o.245.1		12	19.2	odd	18
722.2.e.o.389.1		12	19.18	odd	2
722.2.e.o.415.2		12	19.14	odd	18
722.2.e.o.423.1		12	19.3	odd	18
722.2.e.o.595.2		12	19.8	odd	6
950.2.e.k.201.2		4	95.4	even	18
950.2.e.k.501.2		4	95.9	even	18
950.2.j.g.49.2		8	95.42	odd	36
950.2.j.g.49.3		8	95.23	odd	36
950.2.j.g.349.2		8	95.28	odd	36
950.2.j.g.349.3		8	95.47	odd	36
1216.2.i.k.577.1		4	152.123	odd	18
1216.2.i.k.961.1		4	152.99	odd	18
1216.2.i.l.577.2		4	152.85	even	18
1216.2.i.l.961.2		4	152.61	even	18
2736.2.s.v.577.1		4	228.47	even	18
2736.2.s.v.1873.1		4	228.23	even	18
5776.2.a.z.1.2		2	76.51	even	18
5776.2.a.ba.1.1		2	76.63	odd	18
6498.2.a.ba.1.2		2	57.44	odd	18
6498.2.a.bg.1.2		2	57.32	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(2.02676 - 1.70066i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.54650 + 0.562880i) q^{5} +(2.02676 + 1.70066i) q^{6} +(-1.82288 + 3.15731i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.694593 - 3.93923i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(2.02676 - 1.70066i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.54650 + 0.562880i) q^{5} +(2.02676 + 1.70066i) q^{6} +(-1.82288 + 3.15731i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.694593 - 3.93923i) q^{9} +(-0.285782 + 1.62075i) q^{10} +(2.32288 + 4.02334i) q^{11} +(-1.32288 + 2.29129i) q^{12} +(1.53209 + 1.28558i) q^{13} +(-3.42589 - 1.24692i) q^{14} +(4.09166 - 1.48924i) q^{15} +(0.766044 - 0.642788i) q^{16} +4.00000 q^{18} -1.64575 q^{20} +(1.67497 + 9.49921i) q^{21} +(-3.55885 + 2.98623i) q^{22} +(1.54650 - 0.562880i) q^{23} +(-2.48619 - 0.904900i) q^{24} +(-1.75539 - 1.47295i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-1.32288 - 2.29129i) q^{27} +(0.633078 - 3.59036i) q^{28} +(0.285782 - 1.62075i) q^{29} +(2.17712 + 3.77089i) q^{30} +(2.82288 - 4.88936i) q^{31} +(0.766044 + 0.642788i) q^{32} +(11.5502 + 4.20394i) q^{33} +(-4.59627 + 3.85673i) q^{35} +(0.694593 + 3.93923i) q^{36} +0.354249 q^{37} +5.29150 q^{39} +(-0.285782 - 1.62075i) q^{40} +(-0.223304 + 0.187374i) q^{41} +(-9.06404 + 3.29904i) q^{42} +(-10.6105 - 3.86192i) q^{43} +(-3.55885 - 2.98623i) q^{44} +(3.29150 - 5.70105i) q^{45} +(0.822876 + 1.42526i) q^{46} +(0.756107 - 4.28810i) q^{47} +(0.459430 - 2.60556i) q^{48} +(-3.14575 - 5.44860i) q^{49} +(1.14575 - 1.98450i) q^{50} +(-1.87939 - 0.684040i) q^{52} +(11.8242 - 4.30364i) q^{53} +(2.02676 - 1.70066i) q^{54} +(1.32767 + 7.52960i) q^{55} +3.64575 q^{56} +1.64575 q^{58} +(-1.37829 - 7.81667i) q^{59} +(-3.33555 + 2.79886i) q^{60} +(-0.880731 + 0.320560i) q^{61} +(5.30527 + 1.93096i) q^{62} +(11.1712 + 9.37378i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.64575 + 2.85052i) q^{65} +(-2.13440 + 12.1048i) q^{66} +(0.112134 - 0.635941i) q^{67} +(2.17712 - 3.77089i) q^{69} +(-4.59627 - 3.85673i) q^{70} +(2.54515 + 0.926361i) q^{71} +(-3.75877 + 1.36808i) q^{72} +(1.30878 - 1.09820i) q^{73} +(0.0615146 + 0.348867i) q^{74} -6.06275 q^{75} -16.9373 q^{77} +(0.918860 + 5.21111i) q^{78} +(-3.06418 + 2.57115i) q^{79} +(1.54650 - 0.562880i) q^{80} +(4.69846 + 1.71010i) q^{81} +(-0.223304 - 0.187374i) q^{82} +(-3.96863 + 6.87386i) q^{83} +(-4.82288 - 8.35347i) q^{84} +(1.96075 - 11.1200i) q^{86} +(-2.17712 - 3.77089i) q^{87} +(2.32288 - 4.02334i) q^{88} +(6.18600 + 2.25152i) q^{90} +(-6.85177 + 2.49384i) q^{91} +(-1.26072 + 1.05787i) q^{92} +(-2.59383 - 14.7103i) q^{93} +4.35425 q^{94} +2.64575 q^{96} +(-0.643974 - 3.65216i) q^{97} +(4.81957 - 4.04410i) q^{98} +(17.4623 - 6.35576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8	\( 12 q - 6 q^{7} - 6 q^{8} + 12 q^{11} + 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} + 18 q^{31} + 36 q^{37} - 24 q^{45} - 6 q^{46} - 6 q^{49} - 18 q^{50} + 12 q^{56} - 12 q^{58} - 6 q^{64} - 12 q^{65} + 42 q^{69} - 168 q^{75} - 108 q^{77} - 42 q^{84} - 42 q^{87} + 12 q^{88} + 84 q^{94}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 12 * q^11 + 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 + 18 * q^31 + 36 * q^37 - 24 * q^45 - 6 * q^46 - 6 * q^49 - 18 * q^50 + 12 * q^56 - 12 * q^58 - 6 * q^64 - 12 * q^65 + 42 * q^69 - 168 * q^75 - 108 * q^77 - 42 * q^84 - 42 * q^87 + 12 * q^88 + 84 * q^94

Introduction

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