LMFDB - Embedded newform 722.2.e.o.245.1

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			245.1
Root			$-0.459430 + 2.60556i$ of defining polynomial
Character	$\chi$	$=$	722.245
Dual form			722.2.e.o.389.1

$q$-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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	$-0.554428\pi$
$3$	−2.02676	−	1.70066i	−1.17015	−	0.981874i	−0.999994	+	0.00354242i	$0.998872\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	1.54650	−	0.562880i	0.691616	−	0.251728i	0.0277890	−	0.999614i	$-0.491153\pi$
$5$	1.54650	−	0.562880i	0.691616	−	0.251728i	0.663827	+	0.747886i	$0.268931\pi$
$6$	2.02676	−	1.70066i	0.827423	−	0.694290i
$7$	−1.82288	−	3.15731i	−0.688982	−	1.19335i	−0.972167	−	0.234287i	$-0.924724\pi$
$7$	−1.82288	−	3.15731i	−0.688982	−	1.19335i	0.283185	−	0.959065i	$-0.408609\pi$
$8$	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	−0.267962	−	0.963429i	$-0.586350\pi$
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	0.968335	−	0.249653i	$-0.0803165\pi$
$12$	1.32288	+	2.29129i	0.381881	+	0.661438i
$13$	−1.53209	+	1.28558i	−0.424925	+	0.356554i	−0.830033	−	0.557714i	$-0.811678\pi$
$13$	−1.53209	+	1.28558i	−0.424925	+	0.356554i	0.405108	+	0.914269i	$0.367234\pi$
$14$	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	$-0.944444\pi$
$17$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$18$	−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	0.498182	−	0.867073i	$-0.334001\pi$
$23$	1.54650	+	0.562880i	0.322468	+	0.117369i	−0.175714	+	0.984441i	$0.556223\pi$
$24$	−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	$-0.104386\pi$
$29$	−0.285782	−	1.62075i	−0.0530683	−	0.300965i	−0.999777	+	0.0211262i	$0.993275\pi$
$30$	2.17712	−	3.77089i	0.397487	−	0.688467i
$31$	−2.82288	−	4.88936i	−0.507003	−	0.878156i	−0.999967	−	0.00810584i	$-0.997420\pi$
$31$	−2.82288	−	4.88936i	−0.507003	−	0.878156i	0.492964	−	0.870050i	$-0.335914\pi$
$32$	−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	$-0.509270\pi$
$37$	−0.354249			−0.0582381			−0.0291191	+	0.999576i	$0.509270\pi$
$38$		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	$-0.270532\pi$
$41$	0.223304	+	0.187374i	0.0348742	+	0.0292629i	−0.625184	+	0.780477i	$0.714976\pi$
$42$	−9.06404	−	3.29904i	−1.39861	−	0.509053i
$43$	−10.6105	+	3.86192i	−1.61809	+	0.588937i	−0.983017	−	0.183513i	$-0.941253\pi$
$43$	−10.6105	+	3.86192i	−1.61809	+	0.588937i	−0.635075	+	0.772450i	$0.719031\pi$
$44$	−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	0.988975	+	0.148082i	$0.0473100\pi$
$47$	0.756107	+	4.28810i	0.110290	+	0.625483i	−0.878685	+	0.477401i	$0.841579\pi$
$48$	−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	$-0.721067\pi$
$53$	−11.8242	−	4.30364i	−1.62417	−	0.591151i	−0.984171	+	0.177223i	$0.943289\pi$
$54$	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	−0.753458	−	0.657497i	$-0.771615\pi$
$59$	1.37829	−	7.81667i	0.179438	−	1.01764i	0.932896	−	0.360147i	$-0.117273\pi$
$60$	3.33555	+	2.79886i	0.430617	+	0.361331i
$61$	−0.880731	−	0.320560i	−0.112766	−	0.0410435i	0.285021	−	0.958521i	$-0.407999\pi$
$61$	−0.880731	−	0.320560i	−0.112766	−	0.0410435i	−0.397787	+	0.917478i	$0.630222\pi$
$62$	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	$-0.0681147\pi$
$67$	−0.112134	−	0.635941i	−0.0136993	−	0.0776925i	−0.990891	+	0.134667i	$0.957004\pi$
$68$		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	$-0.662493\pi$
$71$	−2.54515	+	0.926361i	−0.302054	+	0.109939i	0.186547	+	0.982446i	$0.440270\pi$
$72$	3.75877	+	1.36808i	0.442975	+	0.161230i
$73$	1.30878	+	1.09820i	0.153182	+	0.128535i	0.716158	−	0.697939i	$-0.245899\pi$
$73$	1.30878	+	1.09820i	0.153182	+	0.128535i	−0.562976	+	0.826473i	$0.690344\pi$
$74$	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	$-0.205534\pi$
$79$	3.06418	+	2.57115i	0.344747	+	0.289277i	−0.453930	+	0.891038i	$0.649978\pi$
$80$	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	0.561732	−	0.827319i	$-0.310135\pi$
$83$	−3.96863	−	6.87386i	−0.435613	−	0.754505i	−0.997345	+	0.0728147i	$0.976802\pi$
$84$	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	$-0.722222\pi$
$89$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$90$	−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	−0.934504	−	0.355953i	$-0.884156\pi$
$97$	0.643974	−	3.65216i	0.0653856	−	0.370820i	0.999889	−	0.0148673i	$-0.00473259\pi$
$98$	−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	−0.992022	−	0.126063i	$-0.959766\pi$
$101$	−10.4533	+	8.77132i	−1.04014	+	0.872779i	−0.0481152	+	0.998842i	$0.515321\pi$
$102$		0			0
$103$	−6.64575	+	11.5108i	−0.654825	+	1.13419i	0.327112	+	0.944985i	$0.393924\pi$
$103$	−6.64575	+	11.5108i	−0.654825	+	1.13419i	−0.981938	+	0.189205i	$0.939409\pi$
$104$	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	0.952882	+	0.303342i	$0.0981024\pi$
$107$	7.64575	+	13.2428i	0.739143	+	1.28023i	−0.213739	+	0.976891i	$0.568564\pi$
$108$	−2.02676	+	1.70066i	−0.195025	+	0.163646i
$109$	13.7035	−	4.98768i	1.31256	−	0.477733i	0.411494	−	0.911412i	$-0.365007\pi$
$109$	13.7035	−	4.98768i	1.31256	−	0.477733i	0.901067	+	0.433679i	$0.142785\pi$
$110$	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	$-0.238137\pi$
$113$	15.5830			1.46593			0.732963	+	0.680269i	$0.238137\pi$
$114$		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	$-0.521462\pi$
$127$	10.1819	−	8.54361i	0.903496	−	0.758123i	0.970871	+	0.239605i	$0.0770178\pi$
$128$	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	−0.966579	−	0.256369i	$-0.917474\pi$
$131$	0.336401	−	1.90782i	0.0293915	−	0.166687i	0.995970	+	0.0896816i	$0.0285849\pi$
$132$	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	−0.370298	−	0.928913i	$-0.620744\pi$
$137$	−14.6432	−	5.32970i	−1.25106	−	0.455347i	−0.880758	+	0.473566i	$0.842967\pi$
$138$	4.09166	−	1.48924i	0.348305	−	0.126773i
$139$	14.2835	−	11.9853i	1.21151	−	1.01658i	0.212284	−	0.977208i	$-0.431910\pi$
$139$	14.2835	−	11.9853i	1.21151	−	1.01658i	0.999225	−	0.0393682i	$-0.0125345\pi$
$140$	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	0.917865	−	0.396893i	$-0.129912\pi$
$149$	8.37842	+	7.03033i	0.686387	+	0.575947i	−0.231478	+	0.972840i	$0.574356\pi$
$150$	−1.05278	+	5.97064i	−0.0859595	+	0.487501i
$151$	−12.9373			−1.05282			−0.526409	−	0.850231i	$-0.676462\pi$
$151$	−12.9373			−1.05282			−0.526409	+	0.850231i	$0.676462\pi$
$152$		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	0.0868146	−	0.996224i	$-0.472331\pi$
$157$	9.94477	−	3.61960i	0.793679	−	0.288876i	0.706865	+	0.707349i	$0.250109\pi$
$158$	−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	−0.932766	−	0.360484i	$-0.882612\pi$
$163$	−1.96863	+	3.40976i	−0.154195	+	0.267073i	0.778571	+	0.627557i	$0.215945\pi$
$164$	−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	$-0.542581\pi$
$167$	−11.2763	−	4.10424i	−0.872587	−	0.317596i	−0.739214	+	0.673470i	$0.764803\pi$
$168$	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	−0.919243	−	0.393692i	$-0.871198\pi$
$173$	1.04189	−	5.90885i	0.0792134	−	0.449241i	0.998456	−	0.0555496i	$-0.0176911\pi$
$174$	−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	$-0.784816\pi$
$179$	2.03137	−	3.51844i	0.151832	−	0.262981i	0.931901	+	0.362713i	$0.118149\pi$
$180$	−1.14313	−	6.48299i	−0.0852036	−	0.483214i
$181$	−3.85998	−	21.8911i	−0.286910	−	1.62715i	−0.698381	−	0.715726i	$-0.746096\pi$
$181$	−3.85998	−	21.8911i	−0.286910	−	1.62715i	0.411471	−	0.911423i	$-0.365015\pi$
$182$	−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	$-0.453658\pi$
$193$	−11.1712	−	9.37378i	−0.804123	−	0.674739i	−0.949197	+	0.314682i	$0.898102\pi$
$194$	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	0.969468	−	0.245218i	$-0.0788597\pi$
$197$	3.82288	+	6.62141i	0.272369	+	0.471756i	−0.697099	+	0.716975i	$0.745526\pi$
$198$	−9.29150	+	16.0934i	−0.660318	+	1.14370i
$199$	−3.45117	−	19.5726i	−0.244647	−	1.38746i	−0.821311	−	0.570481i	$-0.806757\pi$
$199$	−3.45117	−	19.5726i	−0.244647	−	1.38746i	0.576664	−	0.816982i	$-0.304354\pi$
$200$	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	−0.796248	−	0.604970i	$-0.793185\pi$
$211$	2.30805	−	13.0896i	0.158892	−	0.901123i	0.955140	−	0.296153i	$-0.0957039\pi$
$212$	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	$-0.828001\pi$
$223$	−17.6773	+	6.43400i	−1.18376	+	0.430853i	−0.326230	+	0.945290i	$0.605778\pi$
$224$	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	$-0.421521\pi$
$227$	7.35425			0.488119			0.244059	+	0.969760i	$0.421521\pi$
$228$		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	−0.849790	−	0.527122i	$-0.823271\pi$
$233$	−17.7362	+	6.45546i	−1.16194	+	0.422911i	−0.312150	+	0.950033i	$0.601049\pi$
$234$	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	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$	−2.17712	−	3.77089i	−0.140533	−	0.243410i
$241$	5.80892	−	4.87426i	0.374185	−	0.313979i	−0.436229	−	0.899836i	$-0.643686\pi$
$241$	5.80892	−	4.87426i	0.374185	−	0.313979i	0.810415	+	0.585857i	$0.199242\pi$
$242$	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	−0.734762	−	0.678325i	$-0.762706\pi$
$251$	−27.4660	−	9.99682i	−1.73364	−	0.630994i	−0.998879	+	0.0473308i	$0.984928\pi$
$252$	−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	−0.976137	−	0.217156i	$-0.930322\pi$
$257$	−2.13440	−	12.1048i	−0.133140	−	0.755075i	0.842997	−	0.537918i	$-0.180789\pi$
$258$	−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	0.346821	−	0.937931i	$-0.387261\pi$
$263$	−8.37842	−	7.03033i	−0.516636	−	0.433509i	−0.863457	+	0.504422i	$0.831705\pi$
$264$	−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	$-0.277778\pi$
$269$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$270$	4.09166	+	1.48924i	0.249010	+	0.0906323i
$271$	−11.6092	+	4.22540i	−0.705208	+	0.256675i	−0.669633	−	0.742692i	$-0.733549\pi$
$271$	−11.6092	+	4.22540i	−0.705208	+	0.256675i	−0.0355754	+	0.999367i	$0.511326\pi$
$272$		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	−0.0737960	−	0.997273i	$-0.523511\pi$
$277$	13.7601	−	23.8332i	0.826766	−	1.43200i	0.900562	−	0.434727i	$-0.143155\pi$
$278$	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	$-0.114414\pi$
$281$	23.9222	+	8.70698i	1.42708	+	0.519415i	0.490988	+	0.871167i	$0.336636\pi$
$282$	8.82503	+	7.40508i	0.525523	+	0.440966i
$283$	5.32158	−	30.1802i	0.316335	−	1.79403i	−0.248299	−	0.968684i	$-0.579871\pi$
$283$	5.32158	−	30.1802i	0.316335	−	1.79403i	0.564634	−	0.825342i	$-0.309017\pi$
$284$	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	−0.0401236	−	0.999195i	$-0.512775\pi$
$293$	14.4686	−	25.0604i	0.845266	−	1.46404i	0.885390	−	0.464849i	$-0.153891\pi$
$294$	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	$-0.283644\pi$
$307$	−0.494674	−	0.415081i	−0.0282325	−	0.0236899i	−0.656795	+	0.754069i	$0.728088\pi$
$308$	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	0.605140	−	0.796119i	$-0.293117\pi$
$311$	−6.82288	−	11.8176i	−0.386890	−	0.670113i	−0.992029	+	0.126007i	$0.959784\pi$
$312$	2.64575	−	4.58258i	0.149786	−	0.259437i
$313$	1.54104	+	8.73968i	0.0871049	+	0.493996i	0.996883	+	0.0789003i	$0.0251409\pi$
$313$	1.54104	+	8.73968i	0.0871049	+	0.493996i	−0.909778	+	0.415096i	$0.863748\pi$
$314$	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	$-0.668331\pi$
$317$	4.59627	−	3.85673i	0.258152	−	0.216615i	0.762673	+	0.646784i	$0.223886\pi$
$318$	−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	−0.454163	−	0.890919i	$-0.650062\pi$
$331$	9.90588	−	17.1575i	0.544476	−	0.943061i	0.998640	−	0.0521424i	$-0.0166050\pi$
$332$	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	$-0.696294\pi$
$337$	−9.12300	+	3.32050i	−0.496962	+	0.180879i	0.0813653	+	0.996684i	$0.474072\pi$
$338$	−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	0.318490	−	0.947926i	$-0.396824\pi$
$347$	21.8279	−	7.94470i	1.17178	−	0.426494i	0.853293	+	0.521432i	$0.174602\pi$
$348$	3.33555	−	2.79886i	0.178804	−	0.150034i
$349$	−10.5830	−	18.3303i	−0.566495	−	0.981199i	−0.996909	−	0.0785668i	$-0.974966\pi$
$349$	−10.5830	−	18.3303i	−0.566495	−	0.981199i	0.430414	−	0.902632i	$-0.358368\pi$
$350$	−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	−0.984918	−	0.173019i	$-0.944648\pi$
$353$	−6.43725	+	11.1497i	−0.342620	+	0.593436i	0.642298	+	0.766455i	$0.277981\pi$
$354$	−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	−0.999038	−	0.0438582i	$-0.986035\pi$
$359$	−0.857345	+	4.86225i	−0.0452489	+	0.256620i	0.953789	+	0.300478i	$0.0971461\pi$
$360$	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	−0.257807	−	0.966196i	$-0.583000\pi$
$367$	12.4319	−	10.4316i	0.648942	−	0.544527i	0.906750	+	0.421669i	$0.138556\pi$
$368$	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	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		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	$-0.588688\pi$
$379$	−10.7085			−0.550059			−0.275029	+	0.961436i	$0.588688\pi$
$380$		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	$-0.322821\pi$
$383$	−4.22876	−	3.54835i	−0.216080	−	0.181312i	−0.744402	+	0.667731i	$0.767266\pi$
$384$	−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	0.990958	+	0.134172i	$0.0428376\pi$
$389$	2.08378	+	11.8177i	0.105652	+	0.599181i	−0.885306	+	0.465008i	$0.846051\pi$
$390$	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	−0.744220	−	0.667934i	$-0.767179\pi$
$397$	3.65751	−	20.7428i	0.183565	−	1.04105i	0.927785	−	0.373115i	$-0.121710\pi$
$398$	19.8745			0.996219
$399$		0			0
$400$	−2.29150			−0.114575
$401$	−4.78974	+	27.1640i	−0.239188	+	1.35650i	0.594423	+	0.804152i	$0.297380\pi$
$401$	−4.78974	+	27.1640i	−0.239188	+	1.35650i	−0.833612	+	0.552351i	$0.813731\pi$
$402$	−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	0.999901	+	0.0140603i	$0.00447569\pi$
$409$	1.31678	+	7.46780i	0.0651103	+	0.369259i	−0.934791	+	0.355199i	$0.884413\pi$
$410$	−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	$-0.0711005\pi$
$421$	19.0069	+	15.9487i	0.926340	+	0.777292i	−0.0488165	+	0.998808i	$0.515545\pi$
$422$	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	$-0.956501\pi$
$431$	−21.3531	+	17.9174i	−1.02854	+	0.863050i	−0.0378663	+	0.999283i	$0.512056\pi$
$432$	2.48619	−	0.904900i	0.119617	−	0.0435370i
$433$	16.7965	+	6.11344i	0.807190	+	0.293793i	0.712463	−	0.701710i	$-0.247580\pi$
$433$	16.7965	+	6.11344i	0.807190	+	0.293793i	0.0947276	+	0.995503i	$0.469802\pi$
$434$	−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	0.906662	+	0.421858i	$0.138622\pi$
$439$	−1.87744	+	10.6475i	−0.0896055	+	0.508178i	−0.996267	+	0.0863200i	$0.972489\pi$
$440$	−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	−0.428162	−	0.903702i	$-0.640839\pi$
$443$	8.15512	−	6.84296i	0.387461	−	0.325119i	0.815623	+	0.578583i	$0.196394\pi$
$444$	−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	−0.996235	−	0.0866900i	$-0.972371\pi$
$449$	−12.1458	−	21.0371i	−0.573193	−	0.992800i	0.423042	−	0.906110i	$-0.360962\pi$
$450$	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	−0.725472	−	0.688251i	$-0.758379\pi$
$461$	−18.0102	+	6.55516i	−0.838817	+	0.305304i	−0.113344	+	0.993556i	$0.536156\pi$
$462$	−34.3278	+	28.8044i	−1.59707	+	1.34010i
$463$	19.2288	+	33.3052i	0.893636	+	1.54782i	0.835484	+	0.549515i	$0.185188\pi$
$463$	19.2288	+	33.3052i	0.893636	+	1.54782i	0.0581525	+	0.998308i	$0.481479\pi$
$464$	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	−0.550439	−	0.834875i	$-0.685540\pi$
$467$	9.67712	−	16.7613i	0.447804	−	0.775619i	0.998243	+	0.0592563i	$0.0188729\pi$
$468$	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	0.196807	−	0.980442i	$-0.436943\pi$
$479$	−6.18600	−	2.25152i	−0.282646	−	0.102875i	−0.479453	+	0.877568i	$0.659165\pi$
$480$	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	$-0.136122\pi$
$487$	2.11438	+	3.66221i	0.0958116	+	0.165951i	−0.814135	+	0.580675i	$0.802789\pi$
$488$	−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	0.976488	+	0.215572i	$0.0691617\pi$
$491$	30.0990	+	25.2561i	1.35835	+	1.13979i	0.381863	+	0.924219i	$0.375283\pi$
$492$	−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	−0.239710	−	0.970845i	$-0.577052\pi$
$499$	4.48350	−	1.63186i	0.200709	−	0.0730521i	0.440419	+	0.897792i	$0.354830\pi$
$500$	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	−0.561010	−	0.827809i	$-0.689587\pi$
$503$	−7.10868	−	40.3153i	−0.316960	−	1.79757i	0.244050	−	0.969763i	$-0.421524\pi$
$504$	−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	$-0.637325\pi$
$509$	−29.8343	−	10.8588i	−1.32238	−	0.481308i	−0.904221	+	0.427065i	$0.859548\pi$
$510$		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	$-0.915896\pi$
$521$	−5.85425	+	10.1399i	−0.256479	+	0.444235i	0.708817	+	0.705392i	$0.249229\pi$
$522$	1.14313	+	6.48299i	0.0500333	+	0.283753i
$523$	0.325505	+	1.84603i	0.0142333	+	0.0807213i	0.991097	−	0.133142i	$-0.0425065\pi$
$523$	0.325505	+	1.84603i	0.0142333	+	0.0807213i	−0.976864	+	0.213863i	$0.931395\pi$
$524$	−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	0.999999	−	0.00170033i	$-0.000541231\pi$
$541$	1.38919	+	7.87846i	0.0597257	+	0.338722i	−0.940273	+	0.340422i	$0.889430\pi$
$542$	−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	$-0.311284\pi$
$547$	10.6105	+	3.86192i	0.453674	+	0.165124i	−0.105069	+	0.994465i	$0.533506\pi$
$548$	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	−0.726454	−	0.687215i	$-0.758833\pi$
$557$	−4.14966	+	3.48198i	−0.175827	+	0.147536i	0.550627	+	0.834751i	$0.314389\pi$
$558$	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	$-0.0986536\pi$
$563$	5.03137	+	8.71459i	0.212047	+	0.367276i	−0.740308	+	0.672268i	$0.765320\pi$
$564$	−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	$-0.544063\pi$
$569$	−6.58301			−0.275974			−0.137987	+	0.990434i	$0.544063\pi$
$570$		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	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−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	0.891415	+	0.453188i	$0.149713\pi$
$587$	−2.45287	+	13.9109i	−0.101241	+	0.574164i	−0.992655	+	0.120976i	$0.961398\pi$
$588$	−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	−0.302184	−	0.953250i	$-0.597716\pi$
$593$	−27.9169	−	10.1609i	−1.14641	−	0.417258i	−0.844224	+	0.535991i	$0.819938\pi$
$594$	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	0.984059	+	0.177840i	$0.0569111\pi$
$599$	2.94112	+	16.6799i	0.120171	+	0.681524i	−0.863888	+	0.503683i	$0.831978\pi$
$600$	3.03137	−	5.25049i	0.123755	−	0.214350i
$601$	5.20850	+	9.02138i	0.212459	+	0.367990i	0.952484	−	0.304590i	$-0.0985195\pi$
$601$	5.20850	+	9.02138i	0.212459	+	0.367990i	−0.740025	+	0.672580i	$0.765186\pi$
$602$	−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	$-0.544963\pi$
$607$	−6.93725			−0.281574			−0.140787	+	0.990040i	$0.544963\pi$
$608$		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	−0.478913	−	0.877862i	$-0.658969\pi$
$613$	−6.96970	+	2.53676i	−0.281503	+	0.102459i	0.197410	+	0.980321i	$0.436747\pi$
$614$	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	−0.879447	−	0.475998i	$-0.842087\pi$
$617$	−5.36130	−	30.4055i	−0.215838	−	1.22408i	0.663609	−	0.748080i	$-0.269024\pi$
$618$	6.10651	+	34.6318i	0.245640	+	1.39309i
$619$	4.22876	−	7.32442i	0.169968	−	0.294393i	−0.768440	−	0.639921i	$-0.778967\pi$
$619$	4.22876	−	7.32442i	0.169968	−	0.294393i	0.938408	+	0.345528i	$0.112300\pi$
$620$	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	0.761485	−	0.648183i	$-0.224471\pi$
$631$	23.3154	+	8.48612i	0.928173	+	0.337827i	0.166688	+	0.986010i	$0.446693\pi$
$632$	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	$-0.529280\pi$
$641$	12.0981	−	4.40334i	0.477845	−	0.173922i	0.569703	+	0.821851i	$0.307058\pi$
$642$	38.0176	+	13.8373i	1.50044	+	0.546114i
$643$	−4.99481	−	4.19114i	−0.196976	−	0.165282i	0.538965	−	0.842328i	$-0.318816\pi$
$643$	−4.99481	−	4.19114i	−0.196976	−	0.165282i	−0.735941	+	0.677046i	$0.763260\pi$
$644$	−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	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	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	$-0.604335\pi$
$659$	14.2354	−	11.9449i	0.554533	−	0.465308i	0.876472	+	0.481452i	$0.159890\pi$
$660$	19.0088	−	6.91864i	0.739917	−	0.269308i
$661$	15.2500	+	5.55056i	0.593158	+	0.215892i	0.621118	−	0.783717i	$-0.286679\pi$
$661$	15.2500	+	5.55056i	0.593158	+	0.215892i	−0.0279599	+	0.999609i	$0.508901\pi$
$662$	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	$-0.919502\pi$
$673$	−6.93725	+	12.0157i	−0.267411	+	0.463170i	0.700781	+	0.713376i	$0.252835\pi$
$674$	−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	$-0.237075\pi$
$677$	−5.70850	−	9.88741i	−0.219395	−	0.380004i	−0.954623	+	0.297816i	$0.903742\pi$
$678$	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	$-0.466952\pi$
$683$	5.41699			0.207276			0.103638	+	0.994615i	$0.466952\pi$
$684$		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	0.840414	−	0.541945i	$-0.182312\pi$
$691$	−1.29150	−	2.23695i	−0.0491311	−	0.0850975i	−0.889545	+	0.456847i	$0.848979\pi$
$692$	−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	−0.931843	−	0.362863i	$-0.881799\pi$
$701$	1.79800	−	10.1969i	0.0679094	−	0.385133i	0.999752	−	0.0222705i	$-0.00708951\pi$
$702$	−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	−0.588837	−	0.808252i	$-0.700414\pi$
$709$	2.79281	−	2.34344i	0.104886	−	0.0880099i	0.693723	+	0.720242i	$0.255969\pi$
$710$	−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	0.680656	−	0.732603i	$-0.261695\pi$
$719$	2.07483	+	1.74099i	0.0773781	+	0.0649279i	−0.603278	+	0.797531i	$0.706139\pi$
$720$	−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	−0.366594	−	0.930381i	$-0.619476\pi$
$727$	−1.33154	+	0.484641i	−0.0493841	+	0.0179743i	0.317210	+	0.948355i	$0.397254\pi$
$728$	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	−0.678145	−	0.734928i	$-0.737216\pi$
$733$	8.05163	−	13.9458i	0.297394	−	0.515101i	0.975539	+	0.219827i	$0.0705492\pi$
$734$	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	0.663215	+	0.748429i	$0.269192\pi$
$739$	−5.87135	+	33.2981i	−0.215981	+	1.22489i	−0.879196	+	0.476461i	$0.841919\pi$
$740$	0.583005			0.0214317
$741$		0			0
$742$	−45.8745			−1.68411
$743$	8.25181	−	46.7983i	0.302729	−	1.71686i	−0.331275	−	0.943534i	$-0.607479\pi$
$743$	8.25181	−	46.7983i	0.302729	−	1.71686i	0.634004	−	0.773330i	$-0.281410\pi$
$744$	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	$-0.00966439\pi$
$751$	1.36739	+	7.75488i	0.0498969	+	0.282979i	−0.949642	+	0.313336i	$0.898553\pi$
$752$	−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	0.576754	−	0.816918i	$-0.304319\pi$
$757$	−3.51079	−	2.94590i	−0.127602	−	0.107071i	−0.704355	+	0.709848i	$0.748764\pi$
$758$	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	0.870200	+	0.492699i	$0.163989\pi$
$769$	6.12831	+	34.7553i	0.220992	+	1.25331i	−0.649208	+	0.760611i	$0.724899\pi$
$770$	−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	$-0.693922\pi$
$773$	3.78216	−	3.17361i	0.136035	−	0.114147i	0.708266	+	0.705945i	$0.249478\pi$
$774$	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	0.186107	+	0.982529i	$0.440413\pi$
$787$	−21.2601	+	36.8236i	−0.757842	+	1.31262i	−0.943949	+	0.330091i	$0.892921\pi$
$788$	−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	$-0.208174\pi$
$797$	44.8118			1.58731			0.793657	+	0.608365i	$0.208174\pi$
$798$		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	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	4.11438	+	7.12631i	0.144565	+	0.250393i
$811$	23.9707	−	20.1138i	0.841724	−	0.706291i	−0.116226	−	0.993223i	$-0.537080\pi$
$811$	23.9707	−	20.1138i	0.841724	−	0.706291i	0.957951	+	0.286932i	$0.0926354\pi$
$812$	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	0.438527	−	0.898718i	$-0.355500\pi$
$821$	5.63816	+	2.05212i	0.196773	+	0.0716195i	−0.241754	+	0.970338i	$0.577723\pi$
$822$	−38.7424	+	14.1011i	−1.35129	+	0.491831i
$823$	−24.4173	+	20.4885i	−0.851133	+	0.714186i	−0.960039	−	0.279867i	$-0.909710\pi$
$823$	−24.4173	+	20.4885i	−0.851133	+	0.714186i	0.108906	+	0.994052i	$0.465265\pi$
$824$	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	0.555519	+	0.831504i	$0.312519\pi$
$827$	9.14184	+	51.8459i	0.317893	+	1.80286i	−0.237627	+	0.971357i	$0.576369\pi$
$828$	3.29150	−	5.70105i	0.114388	−	0.198125i
$829$	−8.58301	−	14.8662i	−0.298100	−	0.516325i	0.677601	−	0.735430i	$-0.263020\pi$
$829$	−8.58301	−	14.8662i	−0.298100	−	0.516325i	−0.975701	+	0.219105i	$0.929686\pi$
$830$	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	$-0.0234207\pi$
$839$	31.8064	+	26.6887i	1.09808	+	0.921397i	0.100783	+	0.994908i	$0.467865\pi$
$840$	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	−0.948603	−	0.316469i	$-0.897503\pi$
$853$	1.49042	−	8.45261i	0.0510311	−	0.289412i	0.999634	+	0.0270574i	$0.00861369\pi$
$854$	−3.41699			−0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	−3.64661	+	20.6810i	−0.124566	+	0.706448i	0.856999	+	0.515318i	$0.172326\pi$
$857$	−3.64661	+	20.6810i	−0.124566	+	0.706448i	−0.981565	+	0.191130i	$0.938785\pi$
$858$	18.8317	+	15.8017i	0.642903	+	0.539459i
$859$	−12.4310	−	4.52450i	−0.424139	−	0.154374i	0.121127	−	0.992637i	$-0.461349\pi$
$859$	−12.4310	−	4.52450i	−0.424139	−	0.154374i	−0.545266	+	0.838263i	$0.683571\pi$
$860$	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	0.470746	+	0.882269i	$0.343985\pi$
$863$	−15.5314	+	26.9011i	−0.528694	+	0.915725i	−0.999440	+	0.0334563i	$0.989349\pi$
$864$	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	$-0.0295591\pi$
$877$	31.9025	+	26.7694i	1.07727	+	0.903937i	0.0815794	+	0.996667i	$0.474004\pi$
$878$	−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	0.989269	+	0.146107i	$0.0466744\pi$
$881$	18.4373	+	31.9343i	0.621167	+	1.07589i	−0.368102	+	0.929785i	$0.619992\pi$
$882$	12.5830	−	21.7944i	0.423692	−	0.733856i
$883$	−4.93070	−	27.9634i	−0.165931	−	0.941043i	−0.948099	−	0.317975i	$-0.896997\pi$
$883$	−4.93070	−	27.9634i	−0.165931	−	0.941043i	0.782168	−	0.623068i	$-0.214114\pi$
$884$		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	$-0.627767\pi$
$887$	13.3422	−	11.1954i	0.447987	−	0.375906i	0.838688	+	0.544612i	$0.183323\pi$
$888$	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	$-0.380374\pi$
$907$	37.5287	−	13.6593i	1.24612	−	0.453551i	0.879089	+	0.476657i	$0.158152\pi$
$908$	−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	$-0.590526\pi$
$911$	−16.9373			−0.561156			−0.280578	+	0.959831i	$0.590526\pi$
$912$		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	0.982075	−	0.188491i	$-0.0603595\pi$
$919$	9.93725	+	17.2118i	0.327800	+	0.567766i	−0.654275	+	0.756257i	$0.727026\pi$
$920$	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	−0.999861	−	0.0166732i	$-0.994692\pi$
$929$	−1.66407	+	9.43742i	−0.0545964	+	0.309632i	0.945265	+	0.326305i	$0.105804\pi$
$930$	−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	−0.549259	−	0.835652i	$-0.685090\pi$
$937$	5.45844	−	4.58018i	0.178320	−	0.149628i	0.727579	+	0.686024i	$0.240646\pi$
$938$	−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	−0.994657	−	0.103234i	$-0.967081\pi$
$941$	−2.92319	−	16.5782i	−0.0952933	−	0.540435i	0.899364	−	0.437201i	$-0.144030\pi$
$942$	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	0.541224	−	0.840878i	$-0.317961\pi$
$947$	−5.93609	−	4.98097i	−0.192897	−	0.161860i	−0.734121	+	0.679019i	$0.762406\pi$
$948$	−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	$-0.207836\pi$
$953$	10.3091	+	8.65032i	0.333943	+	0.280211i	−0.460361	+	0.887732i	$0.652280\pi$
$954$	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	0.924944	+	0.380102i	$0.124111\pi$
$967$	−2.30805	+	13.0896i	−0.0742217	+	0.420932i	−0.999166	+	0.0408299i	$0.987000\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$	6.10326			0.195964
$971$	9.44555	−	53.5684i	0.303122	−	1.71909i	−0.329092	−	0.944298i	$-0.606743\pi$
$971$	9.44555	−	53.5684i	0.303122	−	1.71909i	0.632214	−	0.774794i	$-0.282146\pi$
$972$	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	$-0.871396\pi$
$977$	−3.72876	+	6.45840i	−0.119293	+	0.206622i	0.800194	+	0.599741i	$0.204730\pi$
$978$	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	$-0.442117\pi$
$983$	29.8343	−	10.8588i	0.951567	−	0.346342i	0.770723	+	0.637170i	$0.219895\pi$
$984$	−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	$-0.263445\pi$
$991$	2.17096	+	1.82165i	0.0689629	+	0.0578667i	−0.607655	+	0.794201i	$0.707890\pi$
$992$	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	0.996358	+	0.0852645i	$0.0271735\pi$
$997$	2.81809	+	15.9822i	0.0892499	+	0.506162i	−0.907108	+	0.420897i	$0.861715\pi$
$998$	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.o.245.1		12
19.2	odd	18		38.2.c.b.11.1	yes	4
19.3	odd	18		722.2.a.j.1.2		2
19.4	even	9	inner	722.2.e.o.595.2		12
19.5	even	9		722.2.c.j.653.2		4
19.6	even	9	inner	722.2.e.o.99.1		12
19.7	even	3	inner	722.2.e.o.415.2		12
19.8	odd	6		722.2.e.n.423.2		12
19.9	even	9	inner	722.2.e.o.389.1		12
19.10	odd	18		722.2.e.n.389.2		12
19.11	even	3	inner	722.2.e.o.423.1		12
19.12	odd	6		722.2.e.n.415.1		12
19.13	odd	18		722.2.e.n.99.2		12
19.14	odd	18		38.2.c.b.7.1	✓	4
19.15	odd	18		722.2.e.n.595.1		12
19.16	even	9		722.2.a.g.1.1		2
19.17	even	9		722.2.c.j.429.2		4
19.18	odd	2		722.2.e.n.245.2		12
57.2	even	18		342.2.g.f.163.1		4
57.14	even	18		342.2.g.f.235.1		4
57.35	odd	18		6498.2.a.bg.1.2		2
57.41	even	18		6498.2.a.ba.1.2		2
76.3	even	18		5776.2.a.ba.1.1		2
76.35	odd	18		5776.2.a.z.1.2		2
76.59	even	18		304.2.i.e.49.2		4
76.71	even	18		304.2.i.e.273.2		4
95.2	even	36		950.2.j.g.49.2		8
95.14	odd	18		950.2.e.k.501.2		4
95.33	even	36		950.2.j.g.349.2		8
95.52	even	36		950.2.j.g.349.3		8
95.59	odd	18		950.2.e.k.201.2		4
95.78	even	36		950.2.j.g.49.3		8
152.21	odd	18		1216.2.i.l.961.2		4
152.59	even	18		1216.2.i.k.961.1		4
152.109	odd	18		1216.2.i.l.577.2		4
152.147	even	18		1216.2.i.k.577.1		4
228.59	odd	18		2736.2.s.v.1873.1		4
228.71	odd	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	19.14	odd	18
38.2.c.b.11.1	yes	4	19.2	odd	18
304.2.i.e.49.2		4	76.59	even	18
304.2.i.e.273.2		4	76.71	even	18
342.2.g.f.163.1		4	57.2	even	18
342.2.g.f.235.1		4	57.14	even	18
722.2.a.g.1.1		2	19.16	even	9
722.2.a.j.1.2		2	19.3	odd	18
722.2.c.j.429.2		4	19.17	even	9
722.2.c.j.653.2		4	19.5	even	9
722.2.e.n.99.2		12	19.13	odd	18
722.2.e.n.245.2		12	19.18	odd	2
722.2.e.n.389.2		12	19.10	odd	18
722.2.e.n.415.1		12	19.12	odd	6
722.2.e.n.423.2		12	19.8	odd	6
722.2.e.n.595.1		12	19.15	odd	18
722.2.e.o.99.1		12	19.6	even	9	inner
722.2.e.o.245.1		12	1.1	even	1	trivial
722.2.e.o.389.1		12	19.9	even	9	inner
722.2.e.o.415.2		12	19.7	even	3	inner
722.2.e.o.423.1		12	19.11	even	3	inner
722.2.e.o.595.2		12	19.4	even	9	inner
950.2.e.k.201.2		4	95.59	odd	18
950.2.e.k.501.2		4	95.14	odd	18
950.2.j.g.49.2		8	95.2	even	36
950.2.j.g.49.3		8	95.78	even	36
950.2.j.g.349.2		8	95.33	even	36
950.2.j.g.349.3		8	95.52	even	36
1216.2.i.k.577.1		4	152.147	even	18
1216.2.i.k.961.1		4	152.59	even	18
1216.2.i.l.577.2		4	152.109	odd	18
1216.2.i.l.961.2		4	152.21	odd	18
2736.2.s.v.577.1		4	228.71	odd	18
2736.2.s.v.1873.1		4	228.59	odd	18
5776.2.a.z.1.2		2	76.35	odd	18
5776.2.a.ba.1.1		2	76.3	even	18
6498.2.a.ba.1.2		2	57.41	even	18
6498.2.a.bg.1.2		2	57.35	odd	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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