LMFDB - Embedded newform 546.2.bv.a.317.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.20
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-1.71747 - 0.224294i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.30125 + 0.616617i) q^{5} +(-1.71700 + 0.227862i) q^{6} +(2.49307 - 0.885767i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.89938 + 0.770435i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.71747 - 0.224294i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.30125 + 0.616617i) q^{5} +(-1.71700 + 0.227862i) q^{6} +(2.49307 - 0.885767i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.89938 + 0.770435i) q^{9} +(-2.06324 + 1.19121i) q^{10} +(-4.42909 - 1.18677i) q^{11} +(-1.59952 + 0.664489i) q^{12} +(-1.86076 - 3.08830i) q^{13} +(2.17887 - 1.50084i) q^{14} +(4.09062 - 0.542863i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.95298 - 5.11472i) q^{17} +(2.99999 - 0.00623244i) q^{18} +(0.323512 + 1.20736i) q^{19} +(-1.68463 + 1.68463i) q^{20} +(-4.48044 + 0.962094i) q^{21} -4.58533 q^{22} +(3.26170 - 5.64943i) q^{23} +(-1.37303 + 1.05583i) q^{24} +(0.585393 - 0.337977i) q^{25} +(-2.59666 - 2.50147i) q^{26} +(-4.80679 - 1.97351i) q^{27} +(1.71618 - 2.01363i) q^{28} +2.63146i q^{29} +(3.81073 - 1.58310i) q^{30} +(-5.95364 - 1.59527i) q^{31} +(0.258819 - 0.965926i) q^{32} +(7.34063 + 3.03166i) q^{33} +(-4.17615 - 4.17615i) q^{34} +(-5.19100 + 3.57564i) q^{35} +(2.89616 - 0.782476i) q^{36} +(-1.75031 + 0.468993i) q^{37} +(0.624977 + 1.08249i) q^{38} +(2.50310 + 5.72141i) q^{39} +(-1.19121 + 2.06324i) q^{40} +(-1.95111 - 1.95111i) q^{41} +(-4.07877 + 2.08894i) q^{42} -9.07474i q^{43} +(-4.42909 + 1.18677i) q^{44} +(-7.14726 + 0.0148483i) q^{45} +(1.68838 - 6.30112i) q^{46} +(-0.736826 - 2.74987i) q^{47} +(-1.05298 + 1.37522i) q^{48} +(5.43083 - 4.41657i) q^{49} +(0.477971 - 0.477971i) q^{50} +(3.92445 + 9.44670i) q^{51} +(-3.15561 - 1.74417i) q^{52} +(-3.46376 + 1.99980i) q^{53} +(-5.15379 - 0.662177i) q^{54} +10.9242 q^{55} +(1.13654 - 2.38920i) q^{56} +(-0.284816 - 2.14617i) q^{57} +(0.681073 + 2.54180i) q^{58} +(11.8887 + 3.18558i) q^{59} +(3.27115 - 2.51544i) q^{60} +(-2.99008 + 5.17897i) q^{61} -6.16367 q^{62} +(7.91081 - 0.647427i) q^{63} -1.00000i q^{64} +(6.18636 + 5.95956i) q^{65} +(7.87515 + 1.02846i) q^{66} +(9.93115 + 2.66104i) q^{67} +(-5.11472 - 2.95298i) q^{68} +(-6.86899 + 8.97112i) q^{69} +(-4.08868 + 4.79733i) q^{70} +(8.41870 + 8.41870i) q^{71} +(2.59495 - 1.50539i) q^{72} +(-2.85119 + 10.6408i) q^{73} +(-1.56928 + 0.906026i) q^{74} +(-1.08120 + 0.449163i) q^{75} +(0.883851 + 0.883851i) q^{76} +(-12.0932 + 0.964434i) q^{77} +(3.89862 + 4.87860i) q^{78} +(3.81078 - 6.60047i) q^{79} +(-0.616617 + 2.30125i) q^{80} +(7.81286 + 4.46758i) q^{81} +(-2.38961 - 1.37964i) q^{82} +(9.74816 + 9.74816i) q^{83} +(-3.39913 + 3.07342i) q^{84} +(9.94937 + 9.94937i) q^{85} +(-2.34872 - 8.76553i) q^{86} +(0.590222 - 4.51945i) q^{87} +(-3.97101 + 2.29266i) q^{88} +(-2.47718 - 9.24498i) q^{89} +(-6.89988 + 1.86419i) q^{90} +(-7.37452 - 6.05116i) q^{91} -6.52340i q^{92} +(9.86737 + 4.07520i) q^{93} +(-1.42344 - 2.46547i) q^{94} +(-1.48896 - 2.57896i) q^{95} +(-0.661165 + 1.60089i) q^{96} +(3.90221 - 3.90221i) q^{97} +(4.10269 - 5.67168i) q^{98} +(-11.9273 - 6.85323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−1.71747	−	0.224294i	−0.991580	−	0.129496i
$3$	−1.71747	−	0.224294i	−0.991580	−	0.129496i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.30125	+	0.616617i	−1.02915	+	0.275760i	−0.733610	−	0.679571i	$-0.762166\pi$
$5$	−2.30125	+	0.616617i	−1.02915	+	0.275760i	−0.295539	+	0.955331i	$0.595499\pi$
$6$	−1.71700	+	0.227862i	−0.700961	+	0.0930241i
$7$	2.49307	−	0.885767i	0.942293	−	0.334789i
$7$	2.49307	−	0.885767i	0.942293	−	0.334789i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.89938	+	0.770435i	0.966461	+	0.256812i
$10$	−2.06324	+	1.19121i	−0.652454	+	0.376695i
$11$	−4.42909	−	1.18677i	−1.33542	−	0.357825i	−0.480687	−	0.876892i	$-0.659613\pi$
$11$	−4.42909	−	1.18677i	−1.33542	−	0.357825i	−0.854733	+	0.519067i	$0.826279\pi$
$12$	−1.59952	+	0.664489i	−0.461741	+	0.191821i
$13$	−1.86076	−	3.08830i	−0.516081	−	0.856540i
$13$	−1.86076	−	3.08830i	−0.516081	−	0.856540i
$14$	2.17887	−	1.50084i	0.582328	−	0.401116i
$15$	4.09062	−	0.542863i	1.05619	−	0.140167i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.95298	−	5.11472i	−0.716204	−	1.24050i	−0.962493	−	0.271305i	$-0.912545\pi$
$17$	−2.95298	−	5.11472i	−0.716204	−	1.24050i	0.246289	−	0.969196i	$-0.420789\pi$
$18$	2.99999	−	0.00623244i	0.707105	−	0.00146900i
$19$	0.323512	+	1.20736i	0.0742187	+	0.276988i	0.993055	−	0.117651i	$-0.0375364\pi$
$19$	0.323512	+	1.20736i	0.0742187	+	0.276988i	−0.918836	+	0.394639i	$0.870870\pi$
$20$	−1.68463	+	1.68463i	−0.376695	+	0.376695i
$21$	−4.48044	+	0.962094i	−0.977713	+	0.209946i
$22$	−4.58533			−0.977596
$23$	3.26170	−	5.64943i	0.680111	−	1.17799i	−0.294836	−	0.955548i	$-0.595265\pi$
$23$	3.26170	−	5.64943i	0.680111	−	1.17799i	0.974947	−	0.222439i	$-0.0714018\pi$
$24$	−1.37303	+	1.05583i	−0.280269	+	0.215521i
$25$	0.585393	−	0.337977i	0.117079	−	0.0675953i
$26$	−2.59666	−	2.50147i	−0.509248	−	0.490578i
$27$	−4.80679	−	1.97351i	−0.925068	−	0.379803i
$28$	1.71618	−	2.01363i	0.324328	−	0.380541i
$29$			2.63146i			0.488650i	0.969693	+	0.244325i	$0.0785664\pi$
$29$			2.63146i			0.488650i	−0.969693	+	0.244325i	$0.921434\pi$
$30$	3.81073	−	1.58310i	0.695741	−	0.289032i
$31$	−5.95364	−	1.59527i	−1.06931	−	0.286520i	−0.319098	−	0.947722i	$-0.603380\pi$
$31$	−5.95364	−	1.59527i	−1.06931	−	0.286520i	−0.750208	+	0.661202i	$0.770047\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	7.34063	+	3.03166i	1.27784	+	0.527744i
$34$	−4.17615	−	4.17615i	−0.716204	−	0.716204i
$35$	−5.19100	+	3.57564i	−0.877439	+	0.604394i
$36$	2.89616	−	0.782476i	0.482693	−	0.130413i
$37$	−1.75031	+	0.468993i	−0.287749	+	0.0771020i	−0.399806	−	0.916600i	$-0.630923\pi$
$37$	−1.75031	+	0.468993i	−0.287749	+	0.0771020i	0.112057	+	0.993702i	$0.464256\pi$
$38$	0.624977	+	1.08249i	0.101385	+	0.175603i
$39$	2.50310	+	5.72141i	0.400817	+	0.916158i
$40$	−1.19121	+	2.06324i	−0.188347	+	0.326227i
$41$	−1.95111	−	1.95111i	−0.304712	−	0.304712i	0.538142	−	0.842854i	$-0.319126\pi$
$41$	−1.95111	−	1.95111i	−0.304712	−	0.304712i	−0.842854	+	0.538142i	$0.819126\pi$
$42$	−4.07877	+	2.08894i	−0.629368	+	0.322330i
$43$		−	9.07474i		−	1.38389i	−0.721953	−	0.691943i	$-0.756755\pi$
$43$		−	9.07474i		−	1.38389i	0.721953	−	0.691943i	$-0.243245\pi$
$44$	−4.42909	+	1.18677i	−0.667710	+	0.178912i
$45$	−7.14726	+	0.0148483i	−1.06545	+	0.00221346i
$46$	1.68838	−	6.30112i	0.248938	−	0.929049i
$47$	−0.736826	−	2.74987i	−0.107477	−	0.401110i	0.891137	−	0.453734i	$-0.149908\pi$
$47$	−0.736826	−	2.74987i	−0.107477	−	0.401110i	−0.998614	+	0.0526238i	$0.983242\pi$
$48$	−1.05298	+	1.37522i	−0.151984	+	0.198496i
$49$	5.43083	−	4.41657i	0.775833	−	0.630938i
$50$	0.477971	−	0.477971i	0.0675953	−	0.0675953i
$51$	3.92445	+	9.44670i	0.549533	+	1.32280i
$52$	−3.15561	−	1.74417i	−0.437605	−	0.241872i
$53$	−3.46376	+	1.99980i	−0.475784	+	0.274694i	−0.718658	−	0.695364i	$-0.755243\pi$
$53$	−3.46376	+	1.99980i	−0.475784	+	0.274694i	0.242874	+	0.970058i	$0.421910\pi$
$54$	−5.15379	−	0.662177i	−0.701342	−	0.0901109i
$55$	10.9242			1.47302
$56$	1.13654	−	2.38920i	0.151876	−	0.319270i
$57$	−0.284816	−	2.14617i	−0.0377249	−	0.284267i
$58$	0.681073	+	2.54180i	0.0894292	+	0.333754i
$59$	11.8887	+	3.18558i	1.54778	+	0.414727i	0.928770	−	0.370656i	$-0.120867\pi$
$59$	11.8887	+	3.18558i	1.54778	+	0.414727i	0.619010	+	0.785383i	$0.287534\pi$
$60$	3.27115	−	2.51544i	0.422303	−	0.324742i
$61$	−2.99008	+	5.17897i	−0.382841	+	0.663099i	−0.991467	−	0.130358i	$-0.958387\pi$
$61$	−2.99008	+	5.17897i	−0.382841	+	0.663099i	0.608626	+	0.793457i	$0.291721\pi$
$62$	−6.16367			−0.782786
$63$	7.91081	−	0.647427i	0.996668	−	0.0815682i
$64$		−	1.00000i		−	0.125000i
$65$	6.18636	+	5.95956i	0.767323	+	0.739193i
$66$	7.87515	+	1.02846i	0.969364	+	0.126595i
$67$	9.93115	+	2.66104i	1.21328	+	0.325098i	0.808049	−	0.589115i	$-0.200524\pi$
$67$	9.93115	+	2.66104i	1.21328	+	0.325098i	0.405234	+	0.914213i	$0.367190\pi$
$68$	−5.11472	−	2.95298i	−0.620251	−	0.358102i
$69$	−6.86899	+	8.97112i	−0.826929	+	1.08000i
$70$	−4.08868	+	4.79733i	−0.488690	+	0.573391i
$71$	8.41870	+	8.41870i	0.999116	+	0.999116i	1.00000		0.000883786i	$-0.000281318\pi$
$71$	8.41870	+	8.41870i	0.999116	+	0.999116i	−0.000883786		1.00000i	$0.500281\pi$
$72$	2.59495	−	1.50539i	0.305818	−	0.177412i
$73$	−2.85119	+	10.6408i	−0.333706	+	1.24541i	0.571559	+	0.820561i	$0.306339\pi$
$73$	−2.85119	+	10.6408i	−0.333706	+	1.24541i	−0.905265	+	0.424847i	$0.860328\pi$
$74$	−1.56928	+	0.906026i	−0.182425	+	0.105323i
$75$	−1.08120	+	0.449163i	−0.124846	+	0.0518649i
$76$	0.883851	+	0.883851i	0.101385	+	0.101385i
$77$	−12.0932	+	0.964434i	−1.37815	+	0.109907i
$78$	3.89862	+	4.87860i	0.441432	+	0.552393i
$79$	3.81078	−	6.60047i	0.428747	−	0.742611i	−0.568015	−	0.823018i	$-0.692289\pi$
$79$	3.81078	−	6.60047i	0.428747	−	0.742611i	0.996762	+	0.0804068i	$0.0256219\pi$
$80$	−0.616617	+	2.30125i	−0.0689399	+	0.257287i
$81$	7.81286	+	4.46758i	0.868095	+	0.496397i
$82$	−2.38961	−	1.37964i	−0.263888	−	0.152356i
$83$	9.74816	+	9.74816i	1.07000	+	1.07000i	0.997358	+	0.0726418i	$0.0231430\pi$
$83$	9.74816	+	9.74816i	1.07000	+	1.07000i	0.0726418	+	0.997358i	$0.476857\pi$
$84$	−3.39913	+	3.07342i	−0.370876	+	0.335338i
$85$	9.94937	+	9.94937i	1.07916	+	1.07916i
$86$	−2.34872	−	8.76553i	−0.253269	−	0.945211i
$87$	0.590222	−	4.51945i	0.0632784	−	0.484536i
$88$	−3.97101	+	2.29266i	−0.423311	+	0.244399i
$89$	−2.47718	−	9.24498i	−0.262581	−	0.979966i	−0.963714	−	0.266936i	$-0.913989\pi$
$89$	−2.47718	−	9.24498i	−0.262581	−	0.979966i	0.701133	−	0.713030i	$-0.252678\pi$
$90$	−6.89988	+	1.86419i	−0.727311	+	0.196503i
$91$	−7.37452	−	6.05116i	−0.773059	−	0.634334i
$92$		−	6.52340i		−	0.680111i
$93$	9.86737	+	4.07520i	1.02320	+	0.422578i
$94$	−1.42344	−	2.46547i	−0.146816	−	0.254294i
$95$	−1.48896	−	2.57896i	−0.152764	−	0.264595i
$96$	−0.661165	+	1.60089i	−0.0674798	+	0.163391i
$97$	3.90221	−	3.90221i	0.396210	−	0.396210i	−0.480684	−	0.876894i	$-0.659612\pi$
$97$	3.90221	−	3.90221i	0.396210	−	0.396210i	0.876894	+	0.480684i	$0.159612\pi$
$98$	4.10269	−	5.67168i	0.414434	−	0.572926i
$99$	−11.9273	−	6.85323i	−1.19874	−	0.688776i
$100$	0.337977	−	0.585393i	0.0337977	−	0.0585393i
$101$	−1.78120	−	3.08513i	−0.177236	−	0.306982i	0.763697	−	0.645575i	$-0.223382\pi$
$101$	−1.78120	−	3.08513i	−0.177236	−	0.306982i	−0.940933	+	0.338593i	$0.890049\pi$
$102$	6.23571	+	8.10909i	0.617428	+	0.802919i
$103$	6.40506	+	3.69796i	0.631109	+	0.364371i	0.781181	−	0.624304i	$-0.214617\pi$
$103$	6.40506	+	3.69796i	0.631109	+	0.364371i	−0.150072	+	0.988675i	$0.547951\pi$
$104$	−3.49951	−	0.868003i	−0.343155	−	0.0851147i
$105$	9.71736	−	4.97673i	0.948317	−	0.485680i
$106$	−2.82815	+	2.82815i	−0.274694	+	0.274694i
$107$	−4.79107	−	2.76613i	−0.463170	−	0.267411i	0.250206	−	0.968193i	$-0.419502\pi$
$107$	−4.79107	−	2.76613i	−0.463170	−	0.267411i	−0.713376	+	0.700781i	$0.752835\pi$
$108$	−5.14956	+	0.694285i	−0.495517	+	0.0668076i
$109$	−16.9228	−	4.53445i	−1.62091	−	0.434321i	−0.669641	−	0.742685i	$-0.733552\pi$
$109$	−16.9228	−	4.53445i	−1.62091	−	0.434321i	−0.951269	+	0.308363i	$0.900219\pi$
$110$	10.5520	−	2.82739i	1.00609	−	0.269581i
$111$	3.11129	−	0.412897i	0.295310	−	0.0391904i
$112$	0.479440	−	2.60195i	0.0453028	−	0.245861i
$113$		−	9.52648i		−	0.896176i	−0.893989	−	0.448088i	$-0.852105\pi$
$113$		−	9.52648i		−	0.896176i	0.893989	−	0.448088i	$-0.147895\pi$
$114$	−0.830580	−	1.99932i	−0.0777910	−	0.187254i
$115$	−4.02244	+	15.0119i	−0.375094	+	1.39987i
$116$	1.31573	+	2.27891i	0.122163	+	0.211592i
$117$	−3.01572	−	10.3878i	−0.278803	−	0.960348i
$118$	12.3081			1.13305
$119$	−11.8925	−	10.1357i	−1.09018	−	0.929139i
$120$	2.50864	−	3.27637i	0.229007	−	0.299090i
$121$	8.68212	+	5.01263i	0.789284	+	0.455693i
$122$	−1.54778	+	5.77639i	−0.140129	+	0.522970i
$123$	2.91334	+	3.78858i	0.262687	+	0.341605i
$124$	−5.95364	+	1.59527i	−0.534653	+	0.143260i
$125$	7.28442	−	7.28442i	0.651538	−	0.651538i
$126$	7.47368	−	2.67283i	0.665809	−	0.238115i
$127$			9.86636i			0.875497i	0.899097	+	0.437749i	$0.144224\pi$
$127$			9.86636i			0.875497i	−0.899097	+	0.437749i	$0.855776\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−2.03541	+	15.5856i	−0.179208	+	1.37223i
$130$	7.51801	+	4.15535i	0.659373	+	0.364448i
$131$	10.0357	+	5.79409i	0.876819	+	0.506232i	0.869608	−	0.493742i	$-0.164371\pi$
$131$	10.0357	+	5.79409i	0.876819	+	0.506232i	0.00721095	+	0.999974i	$0.497705\pi$
$132$	7.87300	−	1.04482i	0.685257	−	0.0909400i
$133$	1.87598	+	2.72349i	0.162668	+	0.236156i
$134$	10.2815			0.888185
$135$	12.2785	+	1.57759i	1.05677	+	0.135777i
$136$	−5.70473	−	1.52858i	−0.489176	−	0.131074i
$137$	−10.5912	−	2.83789i	−0.904864	−	0.242458i	−0.223760	−	0.974644i	$-0.571833\pi$
$137$	−10.5912	−	2.83789i	−0.904864	−	0.242458i	−0.681104	+	0.732187i	$0.738500\pi$
$138$	−4.31304	+	10.4433i	−0.367150	+	0.888990i
$139$	−13.6682			−1.15932			−0.579661	−	0.814858i	$-0.696815\pi$
$139$	−13.6682			−1.15932			−0.579661	+	0.814858i	$0.696815\pi$
$140$	−2.70772	+	5.69210i	−0.228844	+	0.481070i
$141$	0.648694	+	4.88808i	0.0546299	+	0.411650i
$142$	10.3108	+	5.95292i	0.865260	+	0.499558i
$143$	4.57636	+	15.8866i	0.382694	+	1.32851i
$144$	2.11691	−	2.12572i	0.176409	−	0.177144i
$145$	−1.62261	−	6.05565i	−0.134750	−	0.502894i
$146$			11.0161i			0.911702i
$147$	−10.3179	+	6.36720i	−0.851005	+	0.525158i
$148$	−1.28131	+	1.28131i	−0.105323	+	0.105323i
$149$	−6.71519	+	1.79933i	−0.550130	+	0.147407i	−0.523168	−	0.852230i	$-0.675250\pi$
$149$	−6.71519	+	1.79933i	−0.550130	+	0.147407i	−0.0269619	+	0.999636i	$0.508583\pi$
$150$	−0.928105	+	0.713693i	−0.0757795	+	0.0582728i
$151$	0.402539	−	1.50230i	0.0327582	−	0.122255i	−0.947611	−	0.319428i	$-0.896509\pi$
$151$	0.402539	−	1.50230i	0.0327582	−	0.122255i	0.980369	+	0.197173i	$0.0631760\pi$
$152$	1.08249	+	0.624977i	0.0878017	+	0.0506923i
$153$	−4.62128	−	17.1046i	−0.373608	−	1.38283i
$154$	−11.4316	+	4.06153i	−0.921182	+	0.327288i
$155$	14.6845			1.17949
$156$	5.02845	+	3.70333i	0.402598	+	0.296504i
$157$	4.37974	+	7.58593i	0.349541	+	0.605423i	0.986168	−	0.165749i	$-0.0530042\pi$
$157$	4.37974	+	7.58593i	0.349541	+	0.605423i	−0.636627	+	0.771172i	$0.719671\pi$
$158$	1.97261	−	7.36187i	0.156932	−	0.585679i
$159$	6.39744	−	2.65770i	0.507350	−	0.210769i
$160$			2.38243i			0.188347i
$161$	3.12758	−	16.9735i	0.246488	−	1.33770i
$162$	8.70294	+	2.29323i	0.683767	+	0.180173i
$163$	−4.97496	+	1.33304i	−0.389669	+	0.104411i	−0.448334	−	0.893866i	$-0.647982\pi$
$163$	−4.97496	+	1.33304i	−0.389669	+	0.104411i	0.0586647	+	0.998278i	$0.481316\pi$
$164$	−2.66526	−	0.714154i	−0.208122	−	0.0557661i
$165$	−18.7620	−	2.45024i	−1.46062	−	0.190751i
$166$	11.9390	+	6.89299i	0.926647	+	0.535000i
$167$	12.1133	−	12.1133i	0.937356	−	0.937356i	−0.0607939	−	0.998150i	$-0.519363\pi$
$167$	12.1133	−	12.1133i	0.937356	−	0.937356i	0.998150	+	0.0607939i	$0.0193632\pi$
$168$	−2.48785	+	3.84846i	−0.191942	+	0.296915i
$169$	−6.07517	+	11.4931i	−0.467321	+	0.884088i
$170$	12.1854	+	7.03527i	0.934581	+	0.539580i
$171$	0.00779026	+	3.74985i	0.000595736	+	0.286758i
$172$	−4.53737	−	7.85896i	−0.345971	−	0.599240i
$173$	−2.78524	+	4.82417i	−0.211758	+	0.366775i	−0.952265	−	0.305274i	$-0.901252\pi$
$173$	−2.78524	+	4.82417i	−0.211758	+	0.366775i	0.740507	+	0.672049i	$0.234585\pi$
$174$	−0.599609	−	4.51821i	−0.0454563	−	0.342525i
$175$	1.16006	−	1.36112i	0.0876922	−	0.102891i
$176$	−3.24232	+	3.24232i	−0.244399	+	0.244399i
$177$	−19.7040	−	8.13769i	−1.48104	−	0.611666i
$178$	−4.78555	−	8.28882i	−0.358692	−	0.621273i
$179$	−9.81003	−	16.9915i	−0.733236	−	1.27000i	−0.955493	−	0.295014i	$-0.904676\pi$
$179$	−9.81003	−	16.9915i	−0.733236	−	1.27000i	0.222257	−	0.974988i	$-0.428658\pi$
$180$	−6.18229	+	3.58649i	−0.460800	+	0.267321i
$181$		−	17.7356i		−	1.31828i	−0.752021	−	0.659139i	$-0.770921\pi$
$181$		−	17.7356i		−	1.31828i	0.752021	−	0.659139i	$-0.229079\pi$
$182$	−8.68939	−	3.93630i	−0.644101	−	0.291778i
$183$	6.29698	−	8.22405i	0.465486	−	0.607940i
$184$	−1.68838	−	6.30112i	−0.124469	−	0.464524i
$185$	3.73870	−	2.15854i	0.274875	−	0.158699i
$186$	10.5859	+	1.38247i	0.776195	+	0.101368i
$187$	7.00903	+	26.1581i	0.512551	+	1.91287i
$188$	−2.01305	−	2.01305i	−0.146816	−	0.146816i
$189$	−13.7318	−	0.662412i	−0.998839	−	0.0481834i
$190$	−2.10571	−	2.10571i	−0.152764	−	0.152764i
$191$	−10.2093	−	5.89437i	−0.738722	−	0.426501i	0.0828824	−	0.996559i	$-0.473587\pi$
$191$	−10.2093	−	5.89437i	−0.738722	−	0.426501i	−0.821604	+	0.570058i	$0.806921\pi$
$192$	−0.224294	+	1.71747i	−0.0161870	+	0.123947i
$193$	−3.71322	+	13.8579i	−0.267284	+	0.997517i	0.693554	+	0.720405i	$0.256044\pi$
$193$	−3.71322	+	13.8579i	−0.267284	+	0.997517i	−0.960838	+	0.277112i	$0.910623\pi$
$194$	2.75928	−	4.77922i	0.198105	−	0.343128i
$195$	−9.28817	−	11.6229i	−0.665140	−	0.832334i
$196$	2.49496	−	6.54027i	0.178211	−	0.467162i
$197$	−7.28557	−	7.28557i	−0.519075	−	0.519075i	0.398216	−	0.917292i	$-0.369629\pi$
$197$	−7.28557	−	7.28557i	−0.519075	−	0.519075i	−0.917292	+	0.398216i	$0.869629\pi$
$198$	−13.2946	−	3.53270i	−0.944808	−	0.251058i
$199$	−4.21320	+	2.43249i	−0.298666	+	0.172435i	−0.641843	−	0.766836i	$-0.721830\pi$
$199$	−4.21320	+	2.43249i	−0.298666	+	0.172435i	0.343178	+	0.939271i	$0.388497\pi$
$200$	0.174950	−	0.652921i	0.0123708	−	0.0461685i
$201$	−16.4596	−	6.79775i	−1.16097	−	0.479476i
$202$	−2.51900	−	2.51900i	−0.177236	−	0.177236i
$203$	2.33086	+	6.56043i	0.163595	+	0.460452i
$204$	8.12202	+	6.21885i	0.568655	+	0.435407i
$205$	5.69306	+	3.28689i	0.397621	+	0.229566i
$206$	7.14391	+	1.91421i	0.497740	+	0.133369i
$207$	13.8094	−	13.8669i	0.959822	−	0.963818i
$208$	−3.60492	+	0.0673138i	−0.249956	+	0.00466737i
$209$		−	5.73145i		−	0.396453i
$210$	8.09818	−	7.32219i	0.558827	−	0.505279i
$211$	12.6419			0.870302			0.435151	−	0.900357i	$-0.356695\pi$
$211$	12.6419			0.870302			0.435151	+	0.900357i	$0.356695\pi$
$212$	−1.99980	+	3.46376i	−0.137347	+	0.237892i
$213$	−12.5706	−	16.3471i	−0.861321	−	1.12008i
$214$	−5.34374	−	1.43185i	−0.365291	−	0.0978794i
$215$	5.59564	+	20.8832i	0.381620	+	1.42422i
$216$	−4.79440	+	2.00343i	−0.326218	+	0.136316i
$217$	−16.2559	+	1.29641i	−1.10352	+	0.0880058i
$218$	−17.5198			−1.18659
$219$	7.28348	−	17.6357i	0.492172	−	1.19171i
$220$	9.46064	−	5.46210i	0.637836	−	0.368255i
$221$	−10.3010	+	18.6369i	−0.692920	+	1.25366i
$222$	2.89841	−	1.20409i	0.194528	−	0.0808131i
$223$	17.5457	−	17.5457i	1.17495	−	1.17495i	0.193930	−	0.981015i	$-0.437876\pi$
$223$	17.5457	−	17.5457i	1.17495	−	1.17495i	0.981015	−	0.193930i	$-0.0621235\pi$
$224$	−0.210330	−	2.63738i	−0.0140533	−	0.176217i
$225$	1.95767	−	0.528917i	0.130511	−	0.0352611i
$226$	−2.46564	−	9.20188i	−0.164012	−	0.612100i
$227$	−0.686338	+	2.56145i	−0.0455538	+	0.170009i	−0.984955	−	0.172810i	$-0.944715\pi$
$227$	−0.686338	+	2.56145i	−0.0455538	+	0.170009i	0.939401	+	0.342819i	$0.111382\pi$
$228$	−1.31974	−	1.71623i	−0.0874020	−	0.113660i
$229$	28.1786	−	7.55043i	1.86209	−	0.498946i	0.862123	−	0.506699i	$-0.169134\pi$
$229$	28.1786	−	7.55043i	1.86209	−	0.498946i	0.999970	+	0.00775282i	$0.00246782\pi$
$230$			15.5415i			1.02478i
$231$	20.9861	+	1.05606i	1.38078	+	0.0694837i
$232$	1.86073	+	1.86073i	0.122163	+	0.122163i
$233$	−1.67441	+	2.90016i	−0.109694	+	0.189996i	−0.915646	−	0.401985i	$-0.868320\pi$
$233$	−1.67441	+	2.90016i	−0.109694	+	0.189996i	0.805952	+	0.591981i	$0.201654\pi$
$234$	−5.60151	−	9.25328i	−0.366182	−	0.604906i
$235$	3.39124	+	5.87379i	0.221220	+	0.383164i
$236$	11.8887	−	3.18558i	0.773890	−	0.207363i
$237$	−8.02534	+	10.4814i	−0.521302	+	0.680837i
$238$	−14.1105	−	6.71235i	−0.914651	−	0.435097i
$239$	11.4031	+	11.4031i	0.737605	+	0.737605i	0.972114	−	0.234509i	$-0.0753482\pi$
$239$	11.4031	+	11.4031i	0.737605	+	0.737605i	−0.234509	+	0.972114i	$0.575348\pi$
$240$	1.57518	−	3.81401i	0.101677	−	0.246193i
$241$	0.0441972	−	0.164946i	0.00284699	−	0.0106251i	−0.964488	−	0.264128i	$-0.914916\pi$
$241$	0.0441972	−	0.164946i	0.00284699	−	0.0106251i	0.967335	+	0.253503i	$0.0815826\pi$
$242$	9.68365	+	2.59473i	0.622489	+	0.166795i
$243$	−12.4163	−	9.42529i	−0.796504	−	0.604633i
$244$			5.98016i			0.382841i
$245$	−9.77436	+	13.5124i	−0.624461	+	0.863273i
$246$	3.79463	+	2.90546i	0.241936	+	0.185245i
$247$	3.12672	−	3.24571i	0.198948	−	0.206520i
$248$	−5.33789	+	3.08183i	−0.338956	+	0.195697i
$249$	−14.5557	−	18.9286i	−0.922429	−	1.19955i
$250$	5.15086	−	8.92155i	0.325769	−	0.564249i
$251$	−1.99521			−0.125937			−0.0629683	−	0.998016i	$-0.520057\pi$
$251$	−1.99521			−0.125937			−0.0629683	+	0.998016i	$0.520057\pi$
$252$	6.52724	−	4.51609i	0.411178	−	0.284487i
$253$	−21.1509	+	21.1509i	−1.32975	+	1.32975i
$254$	2.55360	+	9.53017i	0.160227	+	0.597976i
$255$	−14.8561	−	19.3193i	−0.930327	−	1.20982i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.34151	−	4.05562i	0.146060	−	0.252983i	−0.783708	−	0.621129i	$-0.786674\pi$
$257$	2.34151	−	4.05562i	0.146060	−	0.252983i	0.929768	+	0.368147i	$0.120008\pi$
$258$	2.06779	+	15.5813i	0.128735	+	0.970050i
$259$	−3.94823	+	2.71960i	−0.245331	+	0.168988i
$260$	8.33732	+	2.06795i	0.517059	+	0.128249i
$261$	−2.02737	+	7.62962i	−0.125491	+	0.472262i
$262$	11.1933	+	2.99924i	0.691526	+	0.185294i
$263$	7.97634	−	4.60514i	0.491842	−	0.283965i	−0.233496	−	0.972358i	$-0.575017\pi$
$263$	7.97634	−	4.60514i	0.491842	−	0.283965i	0.725338	+	0.688392i	$0.241683\pi$
$264$	7.33431	−	3.04690i	0.451396	−	0.187524i
$265$	6.73786	−	6.73786i	0.413903	−	0.413903i
$266$	2.51695	+	2.14515i	0.154324	+	0.131527i
$267$	2.18089	+	16.4336i	0.133468	+	1.00572i
$268$	9.93115	−	2.66104i	0.606641	−	0.162549i
$269$	−11.1019	+	6.40967i	−0.676893	+	0.390805i	−0.798683	−	0.601751i	$-0.794470\pi$
$269$	−11.1019	+	6.40967i	−0.676893	+	0.390805i	0.121790	+	0.992556i	$0.461136\pi$
$270$	12.2684	−	1.65408i	0.746634	−	0.100664i
$271$	−7.42167	+	1.98863i	−0.450835	+	0.120801i	−0.477090	−	0.878855i	$-0.658308\pi$
$271$	−7.42167	+	1.98863i	−0.450835	+	0.120801i	0.0262553	+	0.999655i	$0.491642\pi$
$272$	−5.90597			−0.358102
$273$	11.3082	+	12.0467i	0.684406	+	0.729101i
$274$	−10.9648			−0.662406
$275$	−2.99386	+	0.802201i	−0.180536	+	0.0483746i
$276$	−1.46316	+	11.2037i	−0.0880718	+	0.674384i
$277$	25.0130	−	14.4413i	1.50288	−	0.867691i	0.502890	−	0.864350i	$-0.332270\pi$
$277$	25.0130	−	14.4413i	1.50288	−	0.867691i	0.999994	−	0.00334019i	$-0.00106322\pi$
$278$	−13.2025	+	3.53759i	−0.791832	+	0.212171i
$279$	−16.0328	−	9.21221i	−0.959861	−	0.551521i
$280$	−1.14223	+	6.19895i	−0.0682613	+	0.370458i
$281$	−13.3466	+	13.3466i	−0.796190	+	0.796190i	−0.982492	−	0.186303i	$-0.940349\pi$
$281$	−13.3466	+	13.3466i	−0.796190	+	0.796190i	0.186303	+	0.982492i	$0.440349\pi$
$282$	1.89172	+	4.55363i	0.112650	+	0.271165i
$283$	21.4097	−	12.3609i	1.27268	−	0.734780i	0.297185	−	0.954820i	$-0.403952\pi$
$283$	21.4097	−	12.3609i	1.27268	−	0.734780i	0.975491	+	0.220040i	$0.0706187\pi$
$284$	11.5002	+	3.08146i	0.682409	+	0.182851i
$285$	1.97880	+	4.76324i	0.117214	+	0.282150i
$286$	8.53218	+	14.1609i	0.504519	+	0.837349i
$287$	−6.59248	−	3.13603i	−0.389142	−	0.185114i
$288$	1.49460	−	2.60119i	0.0880701	−	0.153276i
$289$	−8.94023	+	15.4849i	−0.525896	+	0.910879i
$290$	−3.13463	−	5.42934i	−0.184072	−	0.318822i
$291$	−7.57717	+	5.82668i	−0.444181	+	0.341566i
$292$	2.85119	+	10.6408i	0.166853	+	0.622704i
$293$	11.8909	−	11.8909i	0.694677	−	0.694677i	−0.268581	−	0.963257i	$-0.586555\pi$
$293$	11.8909	−	11.8909i	0.694677	−	0.694677i	0.963257	+	0.268581i	$0.0865545\pi$
$294$	−8.31836	+	8.82071i	−0.485137	+	0.514434i
$295$	−29.3232			−1.70726
$296$	−0.906026	+	1.56928i	−0.0526617	+	0.0912127i
$297$	18.9476	+	14.4454i	1.09945	+	0.838208i
$298$	−6.02067	+	3.47604i	−0.348768	+	0.201361i
$299$	−23.5163	+	0.439114i	−1.35998	+	0.0253946i
$300$	−0.711764	+	0.929586i	−0.0410937	+	0.0536697i
$301$	−8.03811	−	22.6240i	−0.463309	−	1.30403i
$302$		−	1.55529i		−	0.0894970i
$303$	2.36718	+	5.69813i	0.135991	+	0.327349i
$304$	1.20736	+	0.323512i	0.0692470	+	0.0185547i
$305$	3.68747	−	13.7618i	0.211144	−	0.788000i
$306$	−8.89081	−	15.3257i	−0.508254	−	0.876113i
$307$	−19.6594	−	19.6594i	−1.12202	−	1.12202i	−0.991437	−	0.130583i	$-0.958315\pi$
$307$	−19.6594	−	19.6594i	−1.12202	−	1.12202i	−0.130583	−	0.991437i	$-0.541685\pi$
$308$	−9.99084	+	6.88185i	−0.569281	+	0.392130i
$309$	−10.1710	−	7.78774i	−0.578610	−	0.443029i
$310$	14.1841	−	3.80062i	0.805604	−	0.215861i
$311$	4.60208	+	7.97103i	0.260960	+	0.451996i	0.966497	−	0.256677i	$-0.0826277\pi$
$311$	4.60208	+	7.97103i	0.260960	+	0.451996i	−0.705537	+	0.708673i	$0.749294\pi$
$312$	5.81560	+	2.27569i	0.329244	+	0.128835i
$313$	−0.335748	+	0.581532i	−0.0189776	+	0.0328701i	−0.875358	−	0.483475i	$-0.839374\pi$
$313$	−0.335748	+	0.581532i	−0.0189776	+	0.0328701i	0.856381	+	0.516345i	$0.172708\pi$
$314$	6.19388	+	6.19388i	0.349541	+	0.349541i
$315$	−17.8055	+	6.36783i	−1.00323	+	0.358786i
$316$		−	7.62157i		−	0.428747i
$317$	15.8697	−	4.25228i	0.891332	−	0.238832i	0.216042	−	0.976384i	$-0.430685\pi$
$317$	15.8697	−	4.25228i	0.891332	−	0.238832i	0.675290	+	0.737552i	$0.264018\pi$
$318$	5.49159	−	4.22292i	0.307953	−	0.236809i
$319$	3.12294	−	11.6550i	0.174851	−	0.652554i
$320$	0.616617	+	2.30125i	0.0344699	+	0.128644i
$321$	7.60808	+	5.82534i	0.424641	+	0.325139i
$322$	−1.37207	−	17.2047i	−0.0764624	−	0.958778i
$323$	5.21999	−	5.21999i	0.290448	−	0.290448i
$324$	8.99992	−	0.0373946i	0.499996	−	0.00207748i
$325$	−2.13305	−	1.17897i	−0.118320	−	0.0653977i
$326$	−4.46043	+	2.57523i	−0.247040	+	0.142629i
$327$	28.0473	+	11.5834i	1.55102	+	0.640566i
$328$	−2.75928			−0.152356
$329$	−4.27271	−	6.20298i	−0.235562	−	0.341981i
$330$	−18.7568	+	2.48921i	−1.03253	+	0.137026i
$331$	−5.45650	−	20.3640i	−0.299917	−	1.11930i	−0.937234	−	0.348702i	$-0.886622\pi$
$331$	−5.45650	−	20.3640i	−0.299917	−	1.11930i	0.637317	−	0.770602i	$-0.280044\pi$
$332$	13.3162	+	3.56808i	0.730824	+	0.195824i
$333$	−5.43614	+	0.0112935i	−0.297899	+	0.000618880i
$334$	8.56541	−	14.8357i	0.468678	−	0.811774i
$335$	−24.4949			−1.33830
$336$	−1.40702	+	4.36122i	−0.0767595	+	0.237924i
$337$			14.5606i			0.793168i	0.917998	+	0.396584i	$0.129804\pi$
$337$			14.5606i			0.793168i	−0.917998	+	0.396584i	$0.870196\pi$
$338$	−2.89352	+	12.6739i	−0.157387	+	0.689369i
$339$	−2.13673	+	16.3614i	−0.116051	+	0.888630i
$340$	13.5911	+	3.64172i	0.737080	+	0.197500i
$341$	24.4760	+	14.1312i	1.32545	+	0.765248i
$342$	0.978058	+	3.62006i	0.0528873	+	0.195751i
$343$	9.62742	−	15.8213i	0.519832	−	0.854269i
$344$	−6.41681	−	6.41681i	−0.345971	−	0.345971i
$345$	10.2755	−	24.8803i	0.553214	−	1.33951i
$346$	−1.44174	+	5.38066i	−0.0775086	+	0.289266i
$347$	16.7977	−	9.69816i	0.901748	−	0.520624i	0.0239811	−	0.999712i	$-0.492366\pi$
$347$	16.7977	−	9.69816i	0.901748	−	0.520624i	0.877767	+	0.479088i	$0.159033\pi$
$348$	−1.74858	−	4.20907i	−0.0937336	−	0.225630i
$349$	10.6752	+	10.6752i	0.571429	+	0.571429i	0.932528	−	0.361099i	$-0.117598\pi$
$349$	10.6752	+	10.6752i	0.571429	+	0.571429i	−0.361099	+	0.932528i	$0.617598\pi$
$350$	0.768246	−	1.61499i	0.0410645	−	0.0863247i
$351$	2.84948	+	18.5170i	0.152094	+	0.988366i
$352$	−2.29266	+	3.97101i	−0.122199	+	0.211656i
$353$	−4.17743	+	15.5904i	−0.222342	+	0.829793i	0.761109	+	0.648623i	$0.224655\pi$
$353$	−4.17743	+	15.5904i	−0.222342	+	0.829793i	−0.983452	+	0.181170i	$0.942012\pi$
$354$	−21.1388	−	2.76064i	−1.12351	−	0.146726i
$355$	−24.5646	−	14.1824i	−1.30375	−	0.752723i
$356$	−6.76779	−	6.76779i	−0.358692	−	0.358692i
$357$	18.1515	+	20.0752i	0.960680	+	1.06249i
$358$	−13.8735	−	13.8735i	−0.733236	−	0.733236i
$359$	7.58226	+	28.2974i	0.400176	+	1.49348i	0.812782	+	0.582568i	$0.197952\pi$
$359$	7.58226	+	28.2974i	0.400176	+	1.49348i	−0.412606	+	0.910910i	$0.635381\pi$
$360$	−5.04338	+	5.06438i	−0.265809	+	0.266916i
$361$	15.1014	−	8.71881i	0.794811	−	0.458885i
$362$	−4.59032	−	17.1313i	−0.241262	−	0.900401i
$363$	−13.7870	−	10.5564i	−0.723627	−	0.554066i
$364$	−9.41210	−	1.55320i	−0.493328	−	0.0814097i
$365$		−	26.2451i		−	1.37373i
$366$	3.95387	−	9.57360i	0.206672	−	0.500420i
$367$	−5.01646	−	8.68876i	−0.261857	−	0.453550i	0.704878	−	0.709328i	$-0.251002\pi$
$367$	−5.01646	−	8.68876i	−0.261857	−	0.453550i	−0.966735	+	0.255778i	$0.917668\pi$
$368$	−3.26170	−	5.64943i	−0.170028	−	0.294497i
$369$	−4.15381	−	7.16021i	−0.216238	−	0.372746i
$370$	3.05264	−	3.05264i	0.158699	−	0.158699i
$371$	−6.86406	+	8.05375i	−0.356364	+	0.418130i
$372$	10.5830	−	1.40446i	0.548703	−	0.0728180i
$373$	−2.91895	+	5.05577i	−0.151137	+	0.261778i	−0.931646	−	0.363368i	$-0.881627\pi$
$373$	−2.91895	+	5.05577i	−0.151137	+	0.261778i	0.780508	+	0.625145i	$0.214960\pi$
$374$	13.5404	+	23.4527i	0.700158	+	1.21271i
$375$	−14.1446	+	10.8769i	−0.730424	+	0.561680i
$376$	−2.46547	−	1.42344i	−0.127147	−	0.0734082i
$377$	8.12674	−	4.89651i	0.418548	−	0.252183i
$378$	−13.4353	+	2.91420i	−0.691038	+	0.149890i
$379$	−3.71989	+	3.71989i	−0.191078	+	0.191078i	−0.796162	−	0.605084i	$-0.793140\pi$
$379$	−3.71989	+	3.71989i	−0.191078	+	0.191078i	0.605084	+	0.796162i	$0.293140\pi$
$380$	−2.57896	−	1.48896i	−0.132298	−	0.0763821i
$381$	2.21297	−	16.9451i	0.113374	−	0.868126i
$382$	−11.3870	−	3.05115i	−0.582612	−	0.156110i
$383$	19.5605	−	5.24121i	0.999493	−	0.267813i	0.278260	−	0.960506i	$-0.410242\pi$
$383$	19.5605	−	5.24121i	0.999493	−	0.267813i	0.721233	+	0.692693i	$0.243576\pi$
$384$	0.227862	+	1.71700i	0.0116280	+	0.0876201i
$385$	27.2349	−	9.67631i	1.38802	−	0.493150i
$386$			14.3468i			0.730233i
$387$	6.99150	−	26.3112i	0.355398	−	1.33747i
$388$	1.42831	−	5.33052i	0.0725114	−	0.270616i
$389$	−16.8379	−	29.1641i	−0.853716	−	1.47868i	−0.877831	−	0.478970i	$-0.841010\pi$
$389$	−16.8379	−	29.1641i	−0.853716	−	1.47868i	0.0241159	−	0.999709i	$-0.492323\pi$
$390$	−11.9799	−	8.82291i	−0.606627	−	0.446766i
$391$	−38.5270			−1.94839
$392$	0.717195	−	6.96316i	0.0362238	−	0.351693i
$393$	−15.9363	−	12.2021i	−0.803881	−	0.615514i
$394$	−8.92297	−	5.15168i	−0.449533	−	0.259538i
$395$	−4.69959	+	17.5391i	−0.236462	+	0.882488i
$396$	−13.7560	+	0.0285778i	−0.691263	+	0.00143609i
$397$	−18.2600	+	4.89277i	−0.916446	+	0.245561i	−0.686065	−	0.727540i	$-0.740664\pi$
$397$	−18.2600	+	4.89277i	−0.916446	+	0.245561i	−0.230380	+	0.973101i	$0.573997\pi$
$398$	−3.44006	+	3.44006i	−0.172435	+	0.172435i
$399$	−2.61107	−	5.09827i	−0.130717	−	0.255233i
$400$		−	0.675953i		−	0.0337977i
$401$	1.00798	+	3.76183i	0.0503361	+	0.187857i	0.986516	−	0.163664i	$-0.0523313\pi$
$401$	1.00798	+	3.76183i	0.0503361	+	0.187857i	−0.936180	+	0.351521i	$0.885665\pi$
$402$	−17.6581	−	2.30608i	−0.880706	−	0.115017i
$403$	6.15160	+	21.3550i	0.306433	+	1.06377i
$404$	−3.08513	−	1.78120i	−0.153491	−	0.0886181i
$405$	−20.7341	−	5.46345i	−1.03029	−	0.271481i
$406$	3.94941	+	5.73362i	0.196006	+	0.284555i
$407$	8.30885			0.411855
$408$	9.45483	+	3.90482i	0.468084	+	0.193317i
$409$	−24.6669	−	6.60947i	−1.21970	−	0.326817i	−0.409139	−	0.912472i	$-0.634171\pi$
$409$	−24.6669	−	6.60947i	−1.21970	−	0.326817i	−0.810561	+	0.585655i	$0.800837\pi$
$410$	6.34979	+	1.70142i	0.313594	+	0.0840271i
$411$	17.5534	+	7.24952i	0.865847	+	0.357592i
$412$	7.39592			0.364371
$413$	32.4612	−	2.58877i	1.59731	−	0.127385i
$414$	9.74986	−	16.9686i	0.479180	−	0.833960i
$415$	−28.4438	−	16.4220i	−1.39625	−	0.806126i
$416$	−3.46467	+	0.998043i	−0.169869	+	0.0489331i
$417$	23.4747	+	3.06570i	1.14956	+	0.150128i
$418$	−1.48341	−	5.53616i	−0.0725559	−	0.270782i
$419$		−	7.12445i		−	0.348052i	−0.984741	−	0.174026i	$-0.944322\pi$
$419$		−	7.12445i		−	0.348052i	0.984741	−	0.174026i	$-0.0556777\pi$
$420$	5.92712	−	9.16866i	0.289214	−	0.447385i
$421$	22.3930	−	22.3930i	1.09137	−	1.09137i	0.0959846	−	0.995383i	$-0.469400\pi$
$421$	22.3930	−	22.3930i	1.09137	−	1.09137i	0.995383	−	0.0959846i	$-0.0306000\pi$
$422$	12.2111	−	3.27196i	0.594428	−	0.159276i
$423$	−0.0177430	−	8.54061i	−0.000862693	−	0.415259i
$424$	−1.03518	+	3.86333i	−0.0502725	+	0.187620i
$425$	−3.45731	−	1.99608i	−0.167704	−	0.0968241i
$426$	−16.3732	−	12.5366i	−0.793283	−	0.607399i
$427$	−2.86713	+	15.5601i	−0.138750	+	0.753005i
$428$	−5.53225			−0.267411
$429$	−4.29646	−	28.3112i	−0.207435	−	1.36688i
$430$	10.8099	+	18.7234i	0.521302	+	0.902922i
$431$	3.64052	−	13.5866i	0.175358	−	0.654444i	−0.821133	−	0.570737i	$-0.806657\pi$
$431$	3.64052	−	13.5866i	0.175358	−	0.654444i	0.996490	−	0.0837069i	$-0.0266759\pi$
$432$	−4.11251	+	3.17605i	−0.197863	+	0.152808i
$433$			16.2153i			0.779258i	0.920972	+	0.389629i	$0.127397\pi$
$433$			16.2153i			0.779258i	−0.920972	+	0.389629i	$0.872603\pi$
$434$	−15.3665	+	5.45957i	−0.737614	+	0.262068i
$435$	1.42853	+	10.7643i	0.0684925	+	0.516109i
$436$	−16.9228	+	4.53445i	−0.810455	+	0.217161i
$437$	7.87610	+	2.11040i	0.376765	+	0.100954i
$438$	2.47086	−	18.9199i	0.118062	−	0.904026i
$439$	−26.9408	−	15.5543i	−1.28581	−	0.742364i	−0.307908	−	0.951416i	$-0.599629\pi$
$439$	−26.9408	−	15.5543i	−1.28581	−	0.742364i	−0.977904	+	0.209052i	$0.932962\pi$
$440$	7.72458	−	7.72458i	0.368255	−	0.368255i
$441$	19.1488	−	8.62122i	0.911845	−	0.410534i
$442$	−5.12640	+	20.6680i	−0.243838	+	0.983076i
$443$	−32.7373	−	18.9009i	−1.55540	−	0.898009i	−0.997687	−	0.0679735i	$-0.978347\pi$
$443$	−32.7373	−	18.9009i	−1.55540	−	0.898009i	−0.557710	−	0.830036i	$-0.688320\pi$
$444$	2.48801	−	1.91322i	0.118075	−	0.0907975i
$445$	11.4012	+	19.7475i	0.540470	+	0.936121i
$446$	12.4067	−	21.4890i	0.587473	−	1.01753i
$447$	11.9367	−	1.58411i	0.564586	−	0.0749259i
$448$	−0.885767	−	2.49307i	−0.0418486	−	0.117787i
$449$	−13.4565	+	13.4565i	−0.635052	+	0.635052i	−0.949331	−	0.314279i	$-0.898237\pi$
$449$	−13.4565	+	13.4565i	−0.635052	+	0.635052i	0.314279	+	0.949331i	$0.398237\pi$
$450$	1.75407	−	1.01758i	0.0826875	−	0.0479690i
$451$	6.32611	+	10.9571i	0.297885	+	0.515951i
$452$	−4.76324	−	8.25018i	−0.224044	−	0.388056i
$453$	−1.02830	+	2.48986i	−0.0483139	+	0.116984i
$454$			2.65180i			0.124455i
$455$	20.7018	+	9.37795i	0.970517	+	0.439645i
$456$	−1.71896	−	1.31617i	−0.0804979	−	0.0616355i
$457$	10.1586	+	37.9125i	0.475200	+	1.77347i	0.620630	+	0.784104i	$0.286877\pi$
$457$	10.1586	+	37.9125i	0.475200	+	1.77347i	−0.145429	+	0.989369i	$0.546456\pi$
$458$	25.2642	−	14.5863i	1.18052	−	0.681573i
$459$	4.10042	+	30.4131i	0.191391	+	1.41956i
$460$	4.02244	+	15.0119i	0.187547	+	0.699935i
$461$	16.6508	+	16.6508i	0.775507	+	0.775507i	0.979063	−	0.203556i	$-0.0652501\pi$
$461$	16.6508	+	16.6508i	0.775507	+	0.775507i	−0.203556	+	0.979063i	$0.565250\pi$
$462$	20.5443	−	4.41152i	0.955808	−	0.205242i
$463$	25.1246	+	25.1246i	1.16764	+	1.16764i	0.982762	+	0.184875i	$0.0591880\pi$
$463$	25.1246	+	25.1246i	1.16764	+	1.16764i	0.184875	+	0.982762i	$0.440812\pi$
$464$	2.27891	+	1.31573i	0.105796	+	0.0610813i
$465$	−25.2201	−	3.29364i	−1.16955	−	0.152739i
$466$	−0.866737	+	3.23471i	−0.0401508	+	0.149845i
$467$	3.52969	−	6.11361i	0.163335	−	0.282904i	−0.772728	−	0.634737i	$-0.781108\pi$
$467$	3.52969	−	6.11361i	0.163335	−	0.282904i	0.936063	+	0.351833i	$0.114442\pi$
$468$	−7.80556	−	7.48820i	−0.360812	−	0.346142i
$469$	27.1161	−	2.16251i	1.25211	−	0.0998553i
$470$	4.79593	+	4.79593i	0.221220	+	0.221220i
$471$	−5.82057	−	14.0109i	−0.268198	−	0.645589i
$472$	10.6591	−	6.15406i	0.490627	−	0.283264i
$473$	−10.7696	+	40.1928i	−0.495188	+	1.84807i
$474$	−5.03911	+	12.2013i	−0.231454	+	0.560425i
$475$	0.597442	+	0.597442i	0.0274125	+	0.0274125i
$476$	−15.3670	−	2.83156i	−0.704347	−	0.129784i
$477$	−11.5835	+	3.12960i	−0.530372	+	0.143294i
$478$	13.9659	+	8.06321i	0.638785	+	0.368803i
$479$	23.0930	+	6.18775i	1.05515	+	0.282725i	0.744377	−	0.667760i	$-0.232747\pi$
$479$	23.0930	+	6.18775i	1.05515	+	0.282725i	0.310769	+	0.950485i	$0.399413\pi$
$480$	0.534364	−	4.09174i	0.0243903	−	0.186761i
$481$	4.70529	+	4.53279i	0.214543	+	0.206677i
$482$		−	0.170765i		−	0.00777813i
$483$	−9.17857	+	28.4500i	−0.417640	+	1.29452i
$484$	10.0253			0.455693
$485$	−6.57378	+	11.3861i	−0.298500	+	0.517017i
$486$	−14.4326	−	5.89057i	−0.654678	−	0.267201i
$487$	−21.2854	−	5.70340i	−0.964532	−	0.258446i	−0.258014	−	0.966141i	$-0.583068\pi$
$487$	−21.2854	−	5.70340i	−0.964532	−	0.258446i	−0.706518	+	0.707696i	$0.749735\pi$
$488$	1.54778	+	5.77639i	0.0700647	+	0.261485i
$489$	8.84332	−	1.17359i	0.399909	−	0.0530717i
$490$	−5.94405	+	15.5817i	−0.268525	+	0.703910i
$491$	−14.7153			−0.664093			−0.332047	−	0.943263i	$-0.607739\pi$
$491$	−14.7153			−0.664093			−0.332047	+	0.943263i	$0.607739\pi$
$492$	4.41732	+	1.82434i	0.199148	+	0.0822475i
$493$	13.4592	−	7.77067i	0.606172	−	0.349973i
$494$	2.18013	−	3.94437i	0.0980885	−	0.177466i
$495$	31.6735	+	8.41640i	1.42362	+	0.378289i
$496$	−4.35837	+	4.35837i	−0.195697	+	0.195697i
$497$	28.4454	+	13.5314i	1.27595	+	0.606968i
$498$	−18.9588	−	14.5163i	−0.849564	−	0.650493i
$499$	−7.60278	−	28.3740i	−0.340347	−	1.27019i	−0.897955	−	0.440088i	$-0.854947\pi$
$499$	−7.60278	−	28.3740i	−0.340347	−	1.27019i	0.557607	−	0.830105i	$-0.311719\pi$
$500$	2.66628	−	9.95070i	0.119240	−	0.445009i
$501$	−23.5212	+	18.0873i	−1.05085	+	0.808080i
$502$	−1.92723	+	0.516399i	−0.0860164	+	0.0230480i
$503$			14.9068i			0.664661i	0.943163	+	0.332330i	$0.107835\pi$
$503$			14.9068i			0.664661i	−0.943163	+	0.332330i	$0.892165\pi$
$504$	5.13598	−	6.05158i	0.228775	−	0.269559i
$505$	6.00133	+	6.00133i	0.267056	+	0.267056i
$506$	−14.9560	+	25.9045i	−0.664874	+	1.15159i
$507$	13.0117	−	18.3765i	0.577872	−	0.816128i
$508$	4.93318	+	8.54451i	0.218874	+	0.379102i
$509$	−11.7733	+	3.15465i	−0.521842	+	0.139827i	−0.510119	−	0.860104i	$-0.670399\pi$
$509$	−11.7733	+	3.15465i	−0.521842	+	0.139827i	−0.0117237	+	0.999931i	$0.503732\pi$
$510$	−19.3501	−	14.8160i	−0.856838	−	0.656062i
$511$	2.31703	+	29.0537i	0.102499	+	1.28526i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.827690	−	6.44199i	0.0365434	−	0.284421i
$514$	1.21206	−	4.52345i	0.0534615	−	0.199521i
$515$	−17.0198	−	4.56045i	−0.749984	−	0.200958i
$516$	6.03007	+	14.5152i	0.265459	+	0.638996i
$517$			13.0539i			0.574108i
$518$	−3.10981	+	3.64881i	−0.136637	+	0.160319i
$519$	5.86558	−	7.66064i	0.257470	−	0.336265i
$520$	8.58846	−	0.160370i	0.376629	−	0.00703269i
$521$	15.6521	−	9.03674i	0.685730	−	0.395907i	−0.116280	−	0.993216i	$-0.537097\pi$
$521$	15.6521	−	9.03674i	0.685730	−	0.395907i	0.802011	+	0.597310i	$0.203764\pi$
$522$	0.0164004	+	7.89437i	0.000717828	+	0.345527i
$523$	20.6715	−	35.8040i	0.903900	−	1.56560i	0.0815139	−	0.996672i	$-0.474025\pi$
$523$	20.6715	−	35.8040i	0.903900	−	1.56560i	0.822387	−	0.568929i	$-0.192642\pi$
$524$	11.5882			0.506232
$525$	−2.29765	+	2.07749i	−0.100278	+	0.0906690i
$526$	6.51266	−	6.51266i	0.283965	−	0.283965i
$527$	9.42164	+	35.1620i	0.410413	+	1.53168i
$528$	6.29581	−	4.84134i	0.273990	−	0.210692i
$529$	−9.77735	−	16.9349i	−0.425102	−	0.736298i
$530$	4.76439	−	8.25216i	0.206952	−	0.358451i
$531$	32.0157	+	18.3957i	1.38936	+	0.798306i
$532$	2.98639	+	1.42062i	0.129476	+	0.0615916i
$533$	−2.39506	+	9.65613i	−0.103742	+	0.418253i
$534$	6.35989	+	15.3091i	0.275220	+	0.662492i
$535$	12.7311	+	3.41128i	0.550412	+	0.147483i
$536$	8.90402	−	5.14074i	0.384595	−	0.222046i
$537$	13.0373	+	31.3826i	0.562601	+	1.35426i
$538$	−9.06464	+	9.06464i	−0.390805	+	0.390805i
$539$	−29.2951	+	13.1162i	−1.26183	+	0.564955i
$540$	11.4223	−	4.77303i	0.491538	−	0.205398i
$541$	5.39985	−	1.44688i	0.232158	−	0.0622064i	−0.140865	−	0.990029i	$-0.544988\pi$
$541$	5.39985	−	1.44688i	0.232158	−	0.0622064i	0.373022	+	0.927822i	$0.378322\pi$
$542$	−6.65409	+	3.84174i	−0.285818	+	0.165017i
$543$	−3.97800	+	30.4603i	−0.170712	+	1.30718i
$544$	−5.70473	+	1.52858i	−0.244588	+	0.0655372i
$545$	41.7395			1.78793
$546$	14.0409	+	8.70945i	0.600893	+	0.372730i
$547$	17.8720			0.764151			0.382076	−	0.924131i	$-0.375209\pi$
$547$	17.8720			0.764151			0.382076	+	0.924131i	$0.375209\pi$
$548$	−10.5912	+	2.83789i	−0.452432	+	0.121229i
$549$	−12.6595	+	12.7122i	−0.540292	+	0.542542i
$550$	−2.68422	+	1.54973i	−0.114455	+	0.0660809i
$551$	−3.17713	+	0.851309i	−0.135350	+	0.0362670i
$552$	1.48643	+	11.2007i	0.0632667	+	0.476731i
$553$	3.65409	−	19.8309i	0.155388	−	0.843297i
$554$	20.4230	−	20.4230i	0.867691	−	0.867691i
$555$	−6.90524	+	2.86865i	−0.293111	+	0.121767i
$556$	−11.8370	+	6.83410i	−0.502001	+	0.289831i
$557$	26.3606	+	7.06329i	1.11693	+	0.299281i	0.769642	−	0.638476i	$-0.220435\pi$
$557$	26.3606	+	7.06329i	1.11693	+	0.299281i	0.347291	+	0.937757i	$0.387101\pi$
$558$	−17.8708	−	4.74871i	−0.756533	−	0.201029i
$559$	−28.0255	+	16.8859i	−1.18535	+	0.714197i
$560$	0.501097	+	6.28336i	0.0211752	+	0.265520i
$561$	−6.17068	−	46.4977i	−0.260526	−	1.96313i
$562$	−9.43745	+	16.3461i	−0.398095	+	0.689520i
$563$	−19.9093	−	34.4839i	−0.839077	−	1.45332i	−0.890667	−	0.454656i	$-0.849762\pi$
$563$	−19.9093	−	34.4839i	−0.839077	−	1.45332i	0.0515896	−	0.998668i	$-0.483571\pi$
$564$	3.00582	+	3.90885i	0.126568	+	0.164592i
$565$	5.87419	+	21.9228i	0.247129	+	0.922299i
$566$	17.4810	−	17.4810i	0.734780	−	0.734780i
$567$	23.4353	+	4.21762i	0.984189	+	0.177124i
$568$	11.9058			0.499558
$569$	−4.97543	+	8.61769i	−0.208581	+	0.361273i	−0.951268	−	0.308366i	$-0.900218\pi$
$569$	−4.97543	+	8.61769i	−0.208581	+	0.361273i	0.742687	+	0.669639i	$0.233551\pi$
$570$	3.14419	+	4.08878i	0.131695	+	0.171260i
$571$	7.41972	−	4.28378i	0.310506	−	0.179271i	−0.336647	−	0.941631i	$-0.609293\pi$
$571$	7.41972	−	4.28378i	0.310506	−	0.179271i	0.647153	+	0.762360i	$0.275960\pi$
$572$	11.9066	+	11.4701i	0.497838	+	0.479587i
$573$	16.2121	+	12.4133i	0.677272	+	0.518572i
$574$	−7.17951	−	1.32291i	−0.299667	−	0.0552172i
$575$		−	4.40951i		−	0.183889i
$576$	0.770435	−	2.89938i	0.0321015	−	0.120808i
$577$	15.8921	+	4.25827i	0.661595	+	0.177274i	0.573966	−	0.818879i	$-0.305404\pi$
$577$	15.8921	+	4.25827i	0.661595	+	0.177274i	0.0876294	+	0.996153i	$0.472071\pi$
$578$	−4.62781	+	17.2712i	−0.192491	+	0.718388i
$579$	9.48560	−	22.9677i	0.394208	−	0.954505i
$580$	−4.43304	−	4.43304i	−0.184072	−	0.184072i
$581$	32.9375	+	15.6683i	1.36648	+	0.650030i
$582$	−5.81093	+	7.58925i	−0.240871	+	0.314585i
$583$	17.7146	−	4.74662i	0.733665	−	0.196585i
$584$	5.50807	+	9.54026i	0.227926	+	0.394779i
$585$	13.3452	+	22.0452i	0.551755	+	0.911459i
$586$	8.40817	−	14.5634i	0.347338	−	0.601608i
$587$	4.66629	+	4.66629i	0.192598	+	0.192598i	0.796818	−	0.604220i	$-0.206515\pi$
$587$	4.66629	+	4.66629i	0.192598	+	0.192598i	−0.604220	+	0.796818i	$0.706515\pi$
$588$	−5.75195	+	10.6731i	−0.237206	+	0.440151i
$589$		−	7.70430i		−	0.317450i
$590$	−28.3240	+	7.58940i	−1.16608	+	0.312451i
$591$	10.8786	+	14.1468i	0.447486	+	0.581923i
$592$	−0.468993	+	1.75031i	−0.0192755	+	0.0719372i
$593$	1.42643	+	5.32351i	0.0585764	+	0.218610i	0.989010	−	0.147851i	$-0.0472358\pi$
$593$	1.42643	+	5.32351i	0.0585764	+	0.218610i	−0.930433	+	0.366462i	$0.880569\pi$
$594$	22.0407	+	9.04920i	0.904342	+	0.371293i
$595$	33.6173	+	15.9917i	1.37818	+	0.655595i
$596$	−4.91586	+	4.91586i	−0.201361	+	0.201361i
$597$	7.78162	−	3.23273i	0.318481	−	0.132307i
$598$	−22.6014	+	6.51063i	−0.924239	+	0.266239i
$599$	−9.40210	+	5.42830i	−0.384159	+	0.221794i	−0.679626	−	0.733558i	$-0.737858\pi$
$599$	−9.40210	+	5.42830i	−0.384159	+	0.221794i	0.295467	+	0.955353i	$0.404525\pi$
$600$	−0.446916	+	1.08213i	−0.0182453	+	0.0441777i
$601$	−26.6804			−1.08832			−0.544158	−	0.838983i	$-0.683151\pi$
$601$	−26.6804			−1.08832			−0.544158	+	0.838983i	$0.683151\pi$
$602$	−13.6197	−	19.7727i	−0.555099	−	0.805875i
$603$	26.7441	+	15.3667i	1.08910	+	0.625780i
$604$	−0.402539	−	1.50230i	−0.0163791	−	0.0611276i
$605$	−23.0706	−	6.18174i	−0.937952	−	0.251324i
$606$	3.76130	+	4.89130i	0.152792	+	0.198695i
$607$	12.6413	−	21.8954i	0.513096	−	0.888709i	−0.486788	−	0.873520i	$-0.661832\pi$
$607$	12.6413	−	21.8954i	0.513096	−	0.888709i	0.999885	−	0.0151889i	$-0.00483495\pi$
$608$	1.24995			0.0506923
$609$	−2.53171	−	11.7901i	−0.102590	−	0.477760i
$610$		−	14.2473i		−	0.576856i
$611$	−7.12137	+	7.39238i	−0.288100	+	0.299064i
$612$	−12.5545	−	12.5024i	−0.507484	−	0.505379i
$613$	−3.73761	−	1.00149i	−0.150961	−	0.0404498i	0.182547	−	0.983197i	$-0.441566\pi$
$613$	−3.73761	−	1.00149i	−0.150961	−	0.0404498i	−0.333508	+	0.942747i	$0.608232\pi$
$614$	−24.0777	−	13.9013i	−0.971698	−	0.561010i
$615$	−9.04041	−	6.92205i	−0.364545	−	0.279124i
$616$	−7.86926	+	9.23318i	−0.317061	+	0.372015i
$617$	−25.9937	−	25.9937i	−1.04647	−	1.04647i	−0.998866	−	0.0476003i	$-0.984843\pi$
$617$	−25.9937	−	25.9937i	−1.04647	−	1.04647i	−0.0476003	−	0.998866i	$-0.515157\pi$
$618$	−11.8401	−	4.88992i	−0.476278	−	0.196701i
$619$	−10.3156	+	38.4985i	−0.414620	+	1.54738i	0.370974	+	0.928643i	$0.379024\pi$
$619$	−10.3156	+	38.4985i	−0.414620	+	1.54738i	−0.785595	+	0.618741i	$0.787643\pi$
$620$	12.7171	−	7.34224i	0.510732	−	0.294871i
$621$	−26.8275	+	20.7186i	−1.07655	+	0.831410i
$622$	6.50832	+	6.50832i	0.260960	+	0.260960i
$623$	−14.3647	−	20.8542i	−0.575510	−	0.835506i
$624$	6.20643	+	0.692954i	0.248456	+	0.0277404i
$625$	−13.9614	+	24.1819i	−0.558457	+	0.967276i
$626$	−0.173796	+	0.648615i	−0.00694628	+	0.0259239i
$627$	−1.28553	+	9.84357i	−0.0513391	+	0.393114i
$628$	7.58593	+	4.37974i	0.302711	+	0.174771i
$629$	7.56740	+	7.56740i	0.301732	+	0.301732i
$630$	−15.5507	+	10.7593i	−0.619554	+	0.428659i
$631$	−10.6209	−	10.6209i	−0.422810	−	0.422810i	0.463360	−	0.886170i	$-0.346644\pi$
$631$	−10.6209	−	10.6209i	−0.422810	−	0.422810i	−0.886170	+	0.463360i	$0.846644\pi$
$632$	−1.97261	−	7.36187i	−0.0784661	−	0.292839i
$633$	−21.7120	−	2.83550i	−0.862974	−	0.112701i
$634$	14.2284	−	8.21477i	0.565082	−	0.326250i
$635$	−6.08376	−	22.7049i	−0.241427	−	0.901017i
$636$	4.21150	−	5.50035i	0.166997	−	0.218103i
$637$	−23.7451	−	8.55388i	−0.940816	−	0.338917i
$638$		−	12.0661i		−	0.477702i
$639$	17.9230	+	30.8951i	0.709022	+	1.22219i
$640$	1.19121	+	2.06324i	0.0470868	+	0.0815568i
$641$	−9.26467	−	16.0469i	−0.365932	−	0.633813i	0.622993	−	0.782227i	$-0.285917\pi$
$641$	−9.26467	−	16.0469i	−0.365932	−	0.633813i	−0.988925	+	0.148414i	$0.952583\pi$
$642$	8.85655	+	3.65773i	0.349540	+	0.144359i
$643$	3.00300	−	3.00300i	0.118427	−	0.118427i	−0.645410	−	0.763837i	$-0.723313\pi$
$643$	3.00300	−	3.00300i	0.118427	−	0.118427i	0.763837	+	0.645410i	$0.223313\pi$
$644$	−5.77821	−	16.2633i	−0.227693	−	0.640864i
$645$	−4.92635	−	37.1213i	−0.193975	−	1.46165i
$646$	3.69109	−	6.39316i	0.145224	−	0.251536i
$647$	−12.8937	−	22.3326i	−0.506905	−	0.877984i	−0.999968	−	0.00799108i	$-0.997456\pi$
$647$	−12.8937	−	22.3326i	−0.506905	−	0.877984i	0.493064	−	0.869993i	$-0.335877\pi$
$648$	8.68358	−	2.36547i	0.341123	−	0.0929245i
$649$	−48.8757	−	28.2184i	−1.91854	−	1.10767i
$650$	−2.36550	−	0.586729i	−0.0927827	−	0.0230134i
$651$	28.2098	+	1.41957i	1.10563	+	0.0556374i
$652$	−3.64192	+	3.64192i	−0.142629	+	0.142629i
$653$	−9.02412	−	5.21008i	−0.353141	−	0.203886i	0.312927	−	0.949777i	$-0.398691\pi$
$653$	−9.02412	−	5.21008i	−0.353141	−	0.203886i	−0.666068	+	0.745891i	$0.732024\pi$
$654$	30.0896	+	3.92958i	1.17660	+	0.153659i
$655$	−26.6673	−	7.14547i	−1.04198	−	0.279197i
$656$	−2.66526	+	0.714154i	−0.104061	+	0.0278830i
$657$	−16.4647	+	28.6550i	−0.642350	+	1.11794i
$658$	−5.73257	−	4.88576i	−0.223479	−	0.190467i
$659$			4.15768i			0.161960i	0.996716	+	0.0809801i	$0.0258050\pi$
$659$			4.15768i			0.161960i	−0.996716	+	0.0809801i	$0.974195\pi$
$660$	−17.4735	+	7.25902i	−0.680153	+	0.282557i
$661$	4.26508	−	15.9175i	0.165892	−	0.619119i	−0.832032	−	0.554727i	$-0.812823\pi$
$661$	4.26508	−	15.9175i	0.165892	−	0.619119i	0.997925	−	0.0643916i	$-0.0205107\pi$
$662$	−10.5412	−	18.2578i	−0.409694	−	0.709610i
$663$	21.8718	−	29.6979i	0.849429	−	1.15337i
$664$	13.7860			0.535000
$665$	−5.99644	−	5.11065i	−0.232532	−	0.198183i
$666$	−5.24799	+	1.41789i	−0.203355	+	0.0549420i
$667$	14.8663	+	8.58304i	0.575624	+	0.332337i
$668$	4.43378	−	16.5471i	0.171548	−	0.640226i
$669$	−34.0695	+	26.1987i	−1.31720	+	1.01290i
$670$	−23.6602	+	6.33974i	−0.914074	+	0.244925i
$671$	19.3896	−	19.3896i	0.748527	−	0.748527i
$672$	−0.230313	+	4.57678i	−0.00888451	+	0.176553i
$673$		−	38.1500i		−	1.47057i	−0.677756	−	0.735287i	$-0.737047\pi$
$673$		−	38.1500i		−	1.47057i	0.677756	−	0.735287i	$-0.262953\pi$
$674$	3.76857	+	14.0645i	0.145160	+	0.541744i
$675$	−3.48086	+	0.469304i	−0.133978	+	0.0180635i
$676$	0.485322	+	12.9909i	0.0186662	+	0.499651i
$677$	5.93487	+	3.42650i	0.228095	+	0.131691i	0.609693	−	0.792638i	$-0.291293\pi$
$677$	5.93487	+	3.42650i	0.228095	+	0.131691i	−0.381598	+	0.924329i	$0.624626\pi$
$678$	2.17072	+	16.3569i	0.0833660	+	0.628185i
$679$	6.27205	−	13.1850i	0.240699	−	0.505992i
$680$	14.0705			0.539580
$681$	1.75328	−	4.24526i	0.0671858	−	0.162679i
$682$	27.2994	+	7.31486i	1.04535	+	0.280100i
$683$	37.9107	+	10.1582i	1.45061	+	0.388691i	0.896237	−	0.443575i	$-0.146290\pi$
$683$	37.9107	+	10.1582i	1.45061	+	0.388691i	0.554377	+	0.832266i	$0.312957\pi$
$684$	1.88167	+	3.24357i	0.0719476	+	0.124021i
$685$	26.1228			0.998099
$686$	5.20452	−	17.7739i	0.198710	−	0.678612i
$687$	−50.0893	+	6.64732i	−1.91103	+	0.253611i
$688$	−7.85896	−	4.53737i	−0.299620	−	0.172986i
$689$	12.6212	+	6.97598i	0.480830	+	0.265764i
$690$	3.48587	−	26.6920i	0.132705	−	1.01615i
$691$	9.21173	+	34.3787i	0.350431	+	1.30783i	0.886138	+	0.463422i	$0.153379\pi$
$691$	9.21173	+	34.3787i	0.350431	+	1.30783i	−0.535707	+	0.844404i	$0.679955\pi$
$692$			5.57047i			0.211758i
$693$	−35.8060	−	6.52080i	−1.36016	−	0.247705i
$694$	13.7153	−	13.7153i	0.520624	−	0.520624i
$695$	31.4539	−	8.42805i	1.19312	−	0.319694i
$696$	−2.77838	−	3.61308i	−0.105314	−	0.136954i
$697$	−4.21777	+	15.7409i	−0.159760	+	0.596231i
$698$	13.0744	+	7.54849i	0.494872	+	0.285715i
$699$	3.52623	−	4.60537i	0.133374	−	0.174191i
$700$	0.324079	−	1.75880i	0.0122490	−	0.0664762i
$701$	39.9380			1.50844			0.754219	−	0.656623i	$-0.228016\pi$
$701$	39.9380			1.50844			0.754219	+	0.656623i	$0.228016\pi$
$702$	7.54495	+	17.1486i	0.284766	+	0.647231i
$703$	−1.13249	−	1.96153i	−0.0427127	−	0.0739805i
$704$	−1.18677	+	4.42909i	−0.0447281	+	0.166928i
$705$	−4.50688	−	10.8487i	−0.169739	−	0.408585i
$706$			16.1404i			0.607451i
$707$	−7.17338	−	6.11373i	−0.269783	−	0.229931i
$708$	−21.1330	+	2.80455i	−0.794227	+	0.105401i
$709$	7.29558	−	1.95485i	0.273991	−	0.0734157i	−0.119207	−	0.992869i	$-0.538035\pi$
$709$	7.29558	−	1.95485i	0.273991	−	0.0734157i	0.393198	+	0.919454i	$0.371369\pi$
$710$	−27.3983	−	7.34135i	−1.02824	−	0.275516i
$711$	16.1342	−	16.2013i	0.605079	−	0.607598i
$712$	−8.28882	−	4.78555i	−0.310637	−	0.179346i
$713$	−28.4314	+	28.4314i	−1.06476	+	1.06476i
$714$	22.7289	+	14.6932i	0.850606	+	0.549878i
$715$	−20.3273	−	33.7372i	−0.760198	−	1.26170i
$716$	−16.9915	−	9.81003i	−0.635001	−	0.366618i
$717$	−17.0268	−	22.1421i	−0.635877	−	0.826911i
$718$	14.6478	+	25.3707i	0.546651	+	0.946827i
$719$	−7.00483	+	12.1327i	−0.261236	+	0.452474i	−0.966571	−	0.256400i	$-0.917464\pi$
$719$	−7.00483	+	12.1327i	−0.261236	+	0.452474i	0.705334	+	0.708875i	$0.250797\pi$
$720$	−3.56077	+	6.19713i	−0.132702	+	0.230954i
$721$	19.2438	+	3.54590i	0.716677	+	0.132056i
$722$	12.3303	−	12.3303i	0.458885	−	0.458885i
$723$	−0.112904	+	0.273377i	−0.00419894	+	0.0101670i
$724$	−8.86781	−	15.3595i	−0.329570	−	0.570831i
$725$	0.889373	+	1.54044i	0.0330305	+	0.0572105i
$726$	−16.0494	−	6.62834i	−0.595648	−	0.246001i
$727$		−	12.8052i		−	0.474920i	−0.971397	−	0.237460i	$-0.923685\pi$
$727$		−	12.8052i		−	0.474920i	0.971397	−	0.237460i	$-0.0763148\pi$
$728$	−9.49339	+	0.935757i	−0.351848	+	0.0346815i
$729$	19.2105	+	18.9725i	0.711500	+	0.702686i
$730$	−6.79274	−	25.3509i	−0.251411	−	0.938277i
$731$	−46.4148	+	26.7976i	−1.71671	+	0.991144i
$732$	1.34131	−	10.2707i	0.0495764	−	0.379617i
$733$	1.69855	+	6.33907i	0.0627374	+	0.234139i	0.990174	−	0.139842i	$-0.0446593\pi$
$733$	1.69855	+	6.33907i	0.0627374	+	0.234139i	−0.927437	+	0.373981i	$0.877993\pi$
$734$	−7.09434	−	7.09434i	−0.261857	−	0.261857i
$735$	19.8179	−	21.0147i	0.730993	−	0.775138i
$736$	−4.61274	−	4.61274i	−0.170028	−	0.170028i
$737$	−40.8279	−	23.5720i	−1.50391	−	0.868285i
$738$	−5.86547	−	5.84115i	−0.215911	−	0.215016i
$739$	6.90336	−	25.7637i	0.253944	−	0.947733i	−0.714731	−	0.699400i	$-0.753451\pi$
$739$	6.90336	−	25.7637i	0.253944	−	0.947733i	0.968675	−	0.248333i	$-0.0798826\pi$
$740$	2.15854	−	3.73870i	0.0793495	−	0.137437i
$741$	−6.09803	+	4.87309i	−0.224017	+	0.179018i
$742$	−4.54571	+	9.55587i	−0.166878	+	0.350807i
$743$	26.6794	+	26.6794i	0.978774	+	0.978774i	0.999779	−	0.0210054i	$-0.00668672\pi$
$743$	26.6794	+	26.6794i	0.978774	+	0.978774i	−0.0210054	+	0.999779i	$0.506687\pi$
$744$	9.85889	−	4.09569i	0.361444	−	0.150155i
$745$	14.3438	−	8.28140i	0.525517	−	0.303407i
$746$	−1.51096	+	5.63897i	−0.0553201	+	0.206458i
$747$	20.7533	+	35.7740i	0.759325	+	1.30890i
$748$	19.1490	+	19.1490i	0.700158	+	0.700158i
$749$	−14.3946	−	2.65238i	−0.525968	−	0.0969159i
$750$	−10.8475	+	14.1672i	−0.396094	+	0.517312i
$751$	−30.1950	−	17.4331i	−1.10183	−	0.636143i	−0.165130	−	0.986272i	$-0.552804\pi$
$751$	−30.1950	−	17.4331i	−1.10183	−	0.636143i	−0.936702	+	0.350129i	$0.886138\pi$
$752$	−2.74987	−	0.736826i	−0.100277	−	0.0268693i
$753$	3.42671	+	0.447514i	0.124876	+	0.0163083i
$754$	6.58252	−	6.83302i	0.239721	−	0.248844i
$755$			3.70537i			0.134852i
$756$	−12.2233	+	6.29221i	−0.444556	+	0.228846i
$757$	−5.50127			−0.199947			−0.0999736	−	0.994990i	$-0.531876\pi$
$757$	−5.50127			−0.199947			−0.0999736	+	0.994990i	$0.531876\pi$
$758$	−2.63036	+	4.55592i	−0.0955391	+	0.165479i
$759$	41.0700	−	31.5820i	1.49075	−	1.14635i
$760$	−2.87645	−	0.770743i	−0.104340	−	0.0279578i
$761$	1.61189	+	6.01567i	0.0584311	+	0.218068i	0.988968	−	0.148131i	$-0.0473257\pi$
$761$	1.61189	+	6.01567i	0.0584311	+	0.218068i	−0.930537	+	0.366199i	$0.880659\pi$
$762$	−2.24816	−	16.9405i	−0.0814424	−	0.613690i
$763$	−46.2062	+	3.68494i	−1.67278	+	0.133404i
$764$	−11.7887			−0.426501
$765$	21.1817	+	36.5124i	0.765826	+	1.32011i
$766$	17.5374	−	10.1252i	0.633653	−	0.365840i
$767$	−12.2840	−	42.6435i	−0.443551	−	1.53977i
$768$	0.664489	+	1.59952i	0.0239777	+	0.0577176i
$769$	25.1323	−	25.1323i	0.906294	−	0.906294i	−0.0896769	−	0.995971i	$-0.528583\pi$
$769$	25.1323	−	25.1323i	0.906294	−	0.906294i	0.995971	+	0.0896769i	$0.0285834\pi$
$770$	23.8024	−	16.3955i	0.857780	−	0.590853i
$771$	−4.93112	+	6.44020i	−0.177590	+	0.231938i
$772$	3.71322	+	13.8579i	0.133642	+	0.498758i
$773$	1.54943	−	5.78255i	0.0557291	−	0.207984i	−0.932447	−	0.361307i	$-0.882331\pi$
$773$	1.54943	−	5.78255i	0.0557291	−	0.207984i	0.988176	+	0.153323i	$0.0489974\pi$
$774$	−0.0565578	−	27.2242i	−0.00203293	−	0.978552i
$775$	−4.02438	+	1.07833i	−0.144560	+	0.0387348i
$776$		−	5.51856i		−	0.198105i
$777$	7.39094	−	3.78526i	0.265148	−	0.135795i
$778$	−23.8124	−	23.8124i	−0.853716	−	0.853716i
$779$	1.72449	−	2.98690i	0.0617861	−	0.107017i
$780$	−13.8552	−	5.42165i	−0.496097	−	0.194126i
$781$	−27.2961	−	47.2782i	−0.976731	−	1.69175i
$782$	−37.2142	+	9.97151i	−1.33078	+	0.356581i
$783$	5.19322	−	12.6489i	0.185591	−	0.452035i
$784$	−1.10944	−	6.91152i	−0.0396229	−	0.246840i
$785$	−14.7565	−	14.7565i	−0.526681	−	0.526681i
$786$	−18.5514	−	7.66169i	−0.661708	−	0.273284i
$787$	−9.94477	+	37.1144i	−0.354493	+	1.32298i	0.526629	+	0.850095i	$0.323456\pi$
$787$	−9.94477	+	37.1144i	−0.354493	+	1.32298i	−0.881122	+	0.472890i	$0.843211\pi$
$788$	−9.95228	−	2.66670i	−0.354535	−	0.0949974i
$789$	−14.7320	+	6.12014i	−0.524474	+	0.217883i
$790$			18.1578i			0.646026i
$791$	−8.43825	−	23.7502i	−0.300029	−	0.844461i
$792$	−13.2798	+	3.58791i	−0.471879	+	0.127491i
$793$	21.5580	−	0.402547i	0.765548	−	0.0142949i
$794$	−16.3715	+	9.45210i	−0.581003	+	0.335442i
$795$	−13.0833	+	10.0608i	−0.464017	+	0.356819i
$796$	−2.43249	+	4.21320i	−0.0862173	+	0.149333i
$797$	31.7658			1.12520			0.562600	−	0.826729i	$-0.309801\pi$
$797$	31.7658			1.12520			0.562600	+	0.826729i	$0.309801\pi$
$798$	−3.84163	−	4.24876i	−0.135992	−	0.150404i
$799$	−11.8890	+	11.8890i	−0.420602	+	0.420602i
$800$	−0.174950	−	0.652921i	−0.00618540	−	0.0230842i
$801$	−0.0596513	−	28.7133i	−0.00210768	−	1.01453i
$802$	1.94727	+	3.37277i	0.0687604	+	0.119097i
$803$	25.2563	−	43.7452i	0.891276	−	1.54374i
$804$	−17.6533	+	2.34276i	−0.622583	+	0.0826226i
$805$	3.26885	+	40.9888i	0.115212	+	1.44467i
$806$	11.4691	+	19.0352i	0.403981	+	0.670488i
$807$	20.5048	−	8.51831i	0.721802	−	0.299859i
$808$	−3.44102	−	0.922018i	−0.121055	−	0.0324365i
$809$	−1.34055	+	0.773968i	−0.0471313	+	0.0272113i	−0.523380	−	0.852099i	$-0.675329\pi$
$809$	−1.34055	+	0.773968i	−0.0471313	+	0.0272113i	0.476249	+	0.879310i	$0.341996\pi$
$810$	−21.4416	+	0.0890898i	−0.753383	+	0.00313030i
$811$	−29.9875	+	29.9875i	−1.05300	+	1.05300i	−0.0544876	+	0.998514i	$0.517353\pi$
$811$	−29.9875	+	29.9875i	−1.05300	+	1.05300i	−0.998514	+	0.0544876i	$0.982647\pi$
$812$	5.29880	+	4.51607i	0.185952	+	0.158483i
$813$	13.1925	−	1.75077i	0.462682	−	0.0614022i
$814$	8.02574	−	2.15049i	0.281302	−	0.0753746i
$815$	10.6266	−	6.13529i	0.372235	−	0.214910i
$816$	10.1433	+	1.32467i	0.355087	+	0.0463729i
$817$	10.9565	−	2.93579i	0.383319	−	0.102710i
$818$	−25.5370			−0.892882
$819$	−16.7195	−	23.2262i	−0.584228	−	0.811590i
$820$	6.57378			0.229566
$821$	−43.4028	+	11.6297i	−1.51477	+	0.405881i	−0.918015	−	0.396545i	$-0.870209\pi$
$821$	−43.4028	+	11.6297i	−1.51477	+	0.405881i	−0.596752	+	0.802425i	$0.703543\pi$
$822$	18.8316	+	2.45933i	0.656829	+	0.0857791i
$823$	−1.76125	+	1.01686i	−0.0613932	+	0.0354454i	−0.530382	−	0.847759i	$-0.677952\pi$
$823$	−1.76125	+	1.01686i	−0.0613932	+	0.0354454i	0.468989	+	0.883204i	$0.344618\pi$
$824$	7.14391	−	1.91421i	0.248870	−	0.0666845i
$825$	5.32178	−	0.706250i	0.185281	−	0.0245885i
$826$	30.6850	−	10.9021i	1.06767	−	0.379333i
$827$	−24.9181	+	24.9181i	−0.866489	+	0.866489i	−0.992082	−	0.125593i	$-0.959917\pi$
$827$	−24.9181	+	24.9181i	−0.866489	+	0.866489i	0.125593	+	0.992082i	$0.459917\pi$
$828$	5.02585	−	18.9138i	0.174661	−	0.657301i
$829$	18.5382	−	10.7031i	0.643860	−	0.371733i	−0.142240	−	0.989832i	$-0.545430\pi$
$829$	18.5382	−	10.7031i	0.643860	−	0.371733i	0.786100	+	0.618099i	$0.212097\pi$
$830$	−31.7250	−	8.50068i	−1.10119	−	0.295063i
$831$	−46.1981	+	19.1921i	−1.60259	+	0.665767i
$832$	−3.08830	+	1.86076i	−0.107067	+	0.0645101i
$833$	−38.6267	−	14.7351i	−1.33833	−	0.510542i
$834$	23.4683	−	3.11446i	0.812640	−	0.107845i
$835$	−20.4064	+	35.3450i	−0.706194	+	1.22316i
$836$	−2.86572	−	4.96358i	−0.0991132	−	0.171669i
$837$	25.4696	+	19.4177i	0.880359	+	0.671175i
$838$	−1.84394	−	6.88169i	−0.0636979	−	0.237724i
$839$	−34.7854	+	34.7854i	−1.20092	+	1.20092i	−0.227039	+	0.973886i	$0.572904\pi$
$839$	−34.7854	+	34.7854i	−1.20092	+	1.20092i	−0.973886	+	0.227039i	$0.927096\pi$
$840$	3.35213	−	10.3903i	0.115659	−	0.358499i
$841$	22.0754			0.761221
$842$	15.8342	−	27.4257i	0.545684	−	0.945152i
$843$	25.9158	−	19.9287i	0.892589	−	0.686382i
$844$	10.9482	−	6.32094i	0.376852	−	0.217576i
$845$	6.89359	−	30.1946i	0.237147	−	1.03873i
$846$	−2.22761	−	8.24500i	−0.0765868	−	0.283469i
$847$	26.0852	+	4.80651i	0.896298	+	0.165154i
$848$			3.99961i			0.137347i
$849$	−39.5430	+	16.4274i	−1.35711	+	0.563786i
$850$	−3.85613	−	1.03325i	−0.132264	−	0.0354401i
$851$	−3.05943	+	11.4179i	−0.104876	+	0.391402i
$852$	−19.0600	−	7.87172i	−0.652984	−	0.269681i
$853$	−14.6626	−	14.6626i	−0.502039	−	0.502039i	0.410032	−	0.912071i	$-0.365517\pi$
$853$	−14.6626	−	14.6626i	−0.502039	−	0.502039i	−0.912071	+	0.410032i	$0.865517\pi$
$854$	1.25781	+	15.7719i	0.0430414	+	0.539705i
$855$	−2.33015	−	8.62453i	−0.0796895	−	0.294953i
$856$	−5.34374	+	1.43185i	−0.182645	+	0.0489397i
$857$	−12.2174	−	21.1612i	−0.417339	−	0.722853i	0.578332	−	0.815802i	$-0.303704\pi$
$857$	−12.2174	−	21.1612i	−0.417339	−	0.722853i	−0.995671	+	0.0929492i	$0.970371\pi$
$858$	−11.4775	−	26.2345i	−0.391837	−	0.895632i
$859$	−7.09489	+	12.2887i	−0.242075	+	0.419286i	−0.961305	−	0.275486i	$-0.911161\pi$
$859$	−7.09489	+	12.2887i	−0.242075	+	0.419286i	0.719230	+	0.694772i	$0.244495\pi$
$860$	15.2876	+	15.2876i	0.521302	+	0.521302i
$861$	10.6190	+	6.86467i	0.361893	+	0.233947i
$862$		−	14.0659i		−	0.479087i
$863$	−4.93283	+	1.32175i	−0.167915	+	0.0449928i	−0.341797	−	0.939774i	$-0.611036\pi$
$863$	−4.93283	+	1.32175i	−0.167915	+	0.0449928i	0.173882	+	0.984767i	$0.444369\pi$
$864$	−3.15036	+	4.13222i	−0.107177	+	0.140581i
$865$	3.43485	−	12.8190i	0.116788	−	0.435860i
$866$	4.19683	+	15.6628i	0.142614	+	0.532243i
$867$	18.8277	−	24.5896i	0.639423	−	0.835108i
$868$	−13.4298	+	9.25068i	−0.455838	+	0.313988i
$869$	−24.7115	+	24.7115i	−0.838282	+	0.838282i
$870$	4.16586	+	10.0278i	0.141236	+	0.339974i
$871$	−10.2614	−	35.6219i	−0.347693	−	1.20700i
$872$	−15.1726	+	8.75988i	−0.513808	+	0.296647i
$873$	14.3204	−	8.30761i	0.484673	−	0.281170i
$874$	8.15394			0.275811
$875$	11.7083	−	24.6129i	0.395812	−	0.832067i
$876$	−2.51016	−	18.9147i	−0.0848103	−	0.639068i
$877$	−6.54457	−	24.4247i	−0.220994	−	0.824762i	−0.983970	−	0.178335i	$-0.942929\pi$
$877$	−6.54457	−	24.4247i	−0.220994	−	0.824762i	0.762976	−	0.646427i	$-0.223738\pi$
$878$	−30.0485	−	8.05147i	−1.01409	−	0.271724i
$879$	−23.0894	+	17.7552i	−0.778786	+	0.598869i
$880$	5.46210	−	9.46064i	0.184128	−	0.318918i
$881$	57.8655			1.94954			0.974769	−	0.223216i	$-0.0716554\pi$
$881$	57.8655			1.94954			0.974769	+	0.223216i	$0.0716554\pi$
$882$	16.2649	−	13.2835i	0.547669	−	0.447279i
$883$			20.3204i			0.683835i	0.939730	+	0.341918i	$0.111076\pi$
$883$			20.3204i			0.683835i	−0.939730	+	0.341918i	$0.888924\pi$
$884$	0.397553	+	21.2906i	0.0133712	+	0.716079i
$885$	50.3616	+	6.57702i	1.69289	+	0.221084i
$886$	−36.5137	−	9.78383i	−1.22670	−	0.328694i
$887$	5.53757	+	3.19712i	0.185934	+	0.107349i	0.590077	−	0.807347i	$-0.299097\pi$
$887$	5.53757	+	3.19712i	0.185934	+	0.107349i	−0.404144	+	0.914695i	$0.632431\pi$
$888$	1.90805	−	2.49197i	0.0640300	−	0.0836252i
$889$	8.73929	+	24.5976i	0.293106	+	0.824975i
$890$	16.1238	+	16.1238i	0.540470	+	0.540470i
$891$	−29.3019	−	29.0594i	−0.981649	−	0.973525i
$892$	6.42216	−	23.9678i	0.215030	−	0.802503i
$893$	3.08172	−	1.77923i	0.103126	−	0.0595397i
$894$	11.1200	−	4.61958i	0.371907	−	0.154502i
$895$	33.0525	+	33.0525i	1.10482	+	1.10482i
$896$	−1.50084	−	2.17887i	−0.0501396	−	0.0727910i
$897$	40.4870	+	4.52041i	1.35182	+	0.150932i
$898$	−9.51518	+	16.4808i	−0.317526	+	0.549971i
$899$	4.19790	−	15.6668i	0.140008	−	0.522517i
$900$	1.43093	−	1.43689i	0.0476977	−	0.0478963i
$901$	20.4569	+	11.8108i	0.681517	+	0.393474i
$902$	8.94647	+	8.94647i	0.297885	+	0.297885i
$903$	8.73075	+	40.6589i	0.290541	+	1.35304i
$904$	−6.73624	−	6.73624i	−0.224044	−	0.224044i
$905$	10.9361	+	40.8140i	0.363528	+	1.35670i
$906$	−0.348843	+	2.67116i	−0.0115895	+	0.0887434i
$907$	−47.6189	+	27.4928i	−1.58116	+	0.912884i	−0.586471	+	0.809970i	$0.699483\pi$
$907$	−47.6189	+	27.4928i	−1.58116	+	0.912884i	−0.994690	+	0.102914i	$0.967184\pi$
$908$	0.686338	+	2.56145i	0.0227769	+	0.0850046i
$909$	−2.78749	−	10.3173i	−0.0924553	−	0.342203i
$910$	22.4236	+	3.70038i	0.743336	+	0.122666i
$911$			10.5129i			0.348308i	0.984718	+	0.174154i	$0.0557190\pi$
$911$			10.5129i			0.348308i	−0.984718	+	0.174154i	$0.944281\pi$
$912$	−2.00104	−	0.826425i	−0.0662612	−	0.0273657i
$913$	−31.6066	−	54.7443i	−1.04603	−	1.81177i
$914$	19.6250	+	33.9914i	0.649136	+	1.12434i
$915$	−9.41980	+	22.8084i	−0.311409	+	0.754022i
$916$	20.6282	−	20.6282i	0.681573	−	0.681573i
$917$	30.1518	+	5.55584i	0.995702	+	0.183470i
$918$	11.8322	+	28.3156i	0.390521	+	0.934553i
$919$	14.7316	−	25.5159i	0.485952	−	0.841693i	−0.513918	−	0.857839i	$-0.671806\pi$
$919$	14.7316	−	25.5159i	0.485952	−	0.841693i	0.999870	+	0.0161463i	$0.00513974\pi$
$920$	7.77075	+	13.4593i	0.256194	+	0.443741i
$921$	29.3548	+	38.1738i	0.967275	+	1.25787i
$922$	20.3930	+	11.7739i	0.671609	+	0.387753i
$923$	10.3343	−	41.6646i	0.340158	−	1.37141i
$924$	18.7025	−	9.57846i	0.615267	−	0.315108i
$925$	−0.866108	+	0.866108i	−0.0284775	+	0.0284775i
$926$	30.7712	+	17.7657i	1.01120	+	0.583819i
$927$	15.7217	+	15.6565i	0.516368	+	0.514227i
$928$	2.54180	+	0.681073i	0.0834386	+	0.0223573i
$929$	−1.97456	+	0.529082i	−0.0647833	+	0.0173586i	−0.291065	−	0.956703i	$-0.594010\pi$
$929$	−1.97456	+	0.529082i	−0.0647833	+	0.0173586i	0.226282	+	0.974062i	$0.427343\pi$
$930$	−25.2132	+	3.34603i	−0.826773	+	0.109721i
$931$	7.08933	+	5.12817i	0.232344	+	0.168069i
$932$			3.34881i			0.109694i
$933$	−6.11606	−	14.7222i	−0.200231	−	0.481983i
$934$	1.82710	−	6.81885i	0.0597847	−	0.223119i
$935$	−32.2590	−	55.8743i	−1.05498	−	1.82728i
$936$	−9.47768	−	5.21282i	−0.309788	−	0.170386i
$937$	−56.6302			−1.85003			−0.925014	−	0.379934i	$-0.875947\pi$
$937$	−56.6302			−1.85003			−0.925014	+	0.379934i	$0.875947\pi$
$938$	25.6325	−	9.10700i	0.836930	−	0.297354i
$939$	0.707070	−	0.923456i	0.0230744	−	0.0301358i
$940$	5.87379	+	3.39124i	0.191582	+	0.110610i
$941$	3.85102	−	14.3722i	0.125540	−	0.468521i	−0.874319	−	0.485352i	$-0.838691\pi$
$941$	3.85102	−	14.3722i	0.125540	−	0.468521i	0.999858	+	0.0168317i	$0.00535796\pi$
$942$	−9.24854	−	12.0270i	−0.301334	−	0.391862i
$943$	−17.3865	+	4.65871i	−0.566184	+	0.151709i
$944$	8.70315	−	8.70315i	0.283264	−	0.283264i
$945$	32.0086	−	6.94286i	1.04124	−	0.225851i
$946$			41.6107i			1.35288i
$947$	−1.23758	−	4.61870i	−0.0402158	−	0.150087i	0.942898	−	0.333080i	$-0.108088\pi$
$947$	−1.23758	−	4.61870i	−0.0402158	−	0.150087i	−0.983114	+	0.182993i	$0.941421\pi$
$948$	−1.70947	+	13.0898i	−0.0555211	+	0.425137i
$949$	38.1673	−	10.9946i	1.23896	−	0.356899i
$950$	0.731714	+	0.422455i	0.0237399	+	0.0137063i
$951$	−28.2095	+	3.74366i	−0.914755	+	0.121397i
$952$	−15.5763	+	1.24220i	−0.504830	+	0.0402601i
$953$	−28.4119			−0.920353			−0.460176	−	0.887828i	$-0.652214\pi$
$953$	−28.4119			−0.920353			−0.460176	+	0.887828i	$0.652214\pi$
$954$	−10.3788	+	6.02099i	−0.336026	+	0.194937i
$955$	27.1288	+	7.26914i	0.877867	+	0.235224i
$956$	15.5769	+	4.17382i	0.503794	+	0.134991i
$957$	−7.97770	+	19.3166i	−0.257882	+	0.624417i
$958$	23.9076			0.772420
$959$	−28.9183	+	2.30623i	−0.933819	+	0.0744719i
$960$	−0.542863	−	4.09062i	−0.0175208	−	0.132024i
$961$	6.05418	+	3.49538i	0.195296	+	0.112754i
$962$	5.71813	+	3.16052i	0.184360	+	0.101899i
$963$	−11.7600	−	11.7113i	−0.378962	−	0.377390i
$964$	−0.0441972	−	0.164946i	−0.00142350	−	0.00531256i
$965$		−	34.1802i		−	1.10030i
$966$	−1.50242	+	29.8562i	−0.0483396	+	0.960607i
$967$	31.4618	−	31.4618i	1.01174	−	1.01174i	0.0118120	−	0.999930i	$-0.496240\pi$
$967$	31.4618	−	31.4618i	1.01174	−	1.01174i	0.999930	−	0.0118120i	$-0.00375997\pi$
$968$	9.68365	−	2.59473i	0.311244	−	0.0833977i
$969$	−10.1360	+	7.79435i	−0.325615	+	0.250391i
$970$	−3.40284	+	12.6996i	−0.109259	+	0.407759i
$971$	−30.0030	−	17.3223i	−0.962843	−	0.555898i	−0.0657963	−	0.997833i	$-0.520959\pi$
$971$	−30.0030	−	17.3223i	−0.962843	−	0.555898i	−0.897047	+	0.441935i	$0.854292\pi$
$972$	−15.4655	−	1.95441i	−0.496055	−	0.0626876i
$973$	−34.0759	+	12.1069i	−1.09242	+	0.388128i
$974$	−22.0362			−0.706086
$975$	3.39900	+	2.50328i	0.108855	+	0.0801691i
$976$	2.99008	+	5.17897i	0.0957101	+	0.165775i
$977$	−4.51000	+	16.8316i	−0.144288	+	0.538489i	0.855498	+	0.517806i	$0.173251\pi$
$977$	−4.51000	+	16.8316i	−0.144288	+	0.538489i	−0.999786	+	0.0206835i	$0.993416\pi$
$978$	8.23825	−	3.42242i	0.263430	−	0.109437i
$979$			43.8867i			1.40262i
$980$	−1.70866	+	16.5892i	−0.0545813	+	0.529923i
$981$	−45.5722	−	26.1850i	−1.45501	−	0.836024i
$982$	−14.2139	+	3.80860i	−0.453584	+	0.121537i
$983$	5.70148	+	1.52771i	0.181849	+	0.0487263i	0.348594	−	0.937274i	$-0.386659\pi$
$983$	5.70148	+	1.52771i	0.181849	+	0.0487263i	−0.166745	+	0.986000i	$0.553326\pi$
$984$	4.73897	+	0.618890i	0.151073	+	0.0197295i
$985$	21.2583	+	12.2735i	0.677346	+	0.391066i
$986$	10.9894	−	10.9894i	0.349973	−	0.349973i
$987$	5.94694	+	11.6117i	0.189293	+	0.369606i
$988$	1.08496	−	4.37423i	0.0345173	−	0.139163i
$989$	−51.2671	−	29.5991i	−1.63020	−	0.941196i
$990$	32.7726	−	0.0680845i	1.04158	−	0.00216387i
$991$	4.49393	+	7.78372i	0.142755	+	0.247258i	0.928533	−	0.371250i	$-0.121071\pi$
$991$	4.49393	+	7.78372i	0.142755	+	0.247258i	−0.785778	+	0.618508i	$0.787737\pi$
$992$	−3.08183	+	5.33789i	−0.0978483	+	0.169478i
$993$	4.80385	+	36.1983i	0.152446	+	1.14872i
$994$	30.9784	+	5.70814i	0.982575	+	0.181051i
$995$	8.19569	−	8.19569i	0.259821	−	0.259821i
$996$	−22.0699	−	9.11480i	−0.699312	−	0.288814i
$997$	−2.31764	−	4.01427i	−0.0734005	−	0.127133i	0.826989	−	0.562218i	$-0.190052\pi$
$997$	−2.31764	−	4.01427i	−0.0734005	−	0.127133i	−0.900390	+	0.435085i	$0.856718\pi$
$998$	−14.6874	−	25.4394i	−0.464923	−	0.805270i
$999$	9.33893	+	1.19990i	0.295471	+	0.0379631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.20	yes	144
3.2	odd	2	inner	546.2.bv.a.317.12	✓	144
7.4	even	3	inner	546.2.bv.a.473.12	yes	144
13.8	odd	4	inner	546.2.bv.a.359.20	yes	144
21.11	odd	6	inner	546.2.bv.a.473.20	yes	144
39.8	even	4	inner	546.2.bv.a.359.12	yes	144
91.60	odd	12	inner	546.2.bv.a.515.12	yes	144
273.242	even	12	inner	546.2.bv.a.515.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.12	✓	144	3.2	odd	2	inner
546.2.bv.a.317.20	yes	144	1.1	even	1	trivial
546.2.bv.a.359.12	yes	144	39.8	even	4	inner
546.2.bv.a.359.20	yes	144	13.8	odd	4	inner
546.2.bv.a.473.12	yes	144	7.4	even	3	inner
546.2.bv.a.473.20	yes	144	21.11	odd	6	inner
546.2.bv.a.515.12	yes	144	91.60	odd	12	inner
546.2.bv.a.515.20	yes	144	273.242	even	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.71747 - 0.224294i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.30125 + 0.616617i) q^{5} +(-1.71700 + 0.227862i) q^{6} +(2.49307 - 0.885767i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.89938 + 0.770435i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.71747 - 0.224294i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.30125 + 0.616617i) q^{5} +(-1.71700 + 0.227862i) q^{6} +(2.49307 - 0.885767i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.89938 + 0.770435i) q^{9} +(-2.06324 + 1.19121i) q^{10} +(-4.42909 - 1.18677i) q^{11} +(-1.59952 + 0.664489i) q^{12} +(-1.86076 - 3.08830i) q^{13} +(2.17887 - 1.50084i) q^{14} +(4.09062 - 0.542863i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.95298 - 5.11472i) q^{17} +(2.99999 - 0.00623244i) q^{18} +(0.323512 + 1.20736i) q^{19} +(-1.68463 + 1.68463i) q^{20} +(-4.48044 + 0.962094i) q^{21} -4.58533 q^{22} +(3.26170 - 5.64943i) q^{23} +(-1.37303 + 1.05583i) q^{24} +(0.585393 - 0.337977i) q^{25} +(-2.59666 - 2.50147i) q^{26} +(-4.80679 - 1.97351i) q^{27} +(1.71618 - 2.01363i) q^{28} +2.63146i q^{29} +(3.81073 - 1.58310i) q^{30} +(-5.95364 - 1.59527i) q^{31} +(0.258819 - 0.965926i) q^{32} +(7.34063 + 3.03166i) q^{33} +(-4.17615 - 4.17615i) q^{34} +(-5.19100 + 3.57564i) q^{35} +(2.89616 - 0.782476i) q^{36} +(-1.75031 + 0.468993i) q^{37} +(0.624977 + 1.08249i) q^{38} +(2.50310 + 5.72141i) q^{39} +(-1.19121 + 2.06324i) q^{40} +(-1.95111 - 1.95111i) q^{41} +(-4.07877 + 2.08894i) q^{42} -9.07474i q^{43} +(-4.42909 + 1.18677i) q^{44} +(-7.14726 + 0.0148483i) q^{45} +(1.68838 - 6.30112i) q^{46} +(-0.736826 - 2.74987i) q^{47} +(-1.05298 + 1.37522i) q^{48} +(5.43083 - 4.41657i) q^{49} +(0.477971 - 0.477971i) q^{50} +(3.92445 + 9.44670i) q^{51} +(-3.15561 - 1.74417i) q^{52} +(-3.46376 + 1.99980i) q^{53} +(-5.15379 - 0.662177i) q^{54} +10.9242 q^{55} +(1.13654 - 2.38920i) q^{56} +(-0.284816 - 2.14617i) q^{57} +(0.681073 + 2.54180i) q^{58} +(11.8887 + 3.18558i) q^{59} +(3.27115 - 2.51544i) q^{60} +(-2.99008 + 5.17897i) q^{61} -6.16367 q^{62} +(7.91081 - 0.647427i) q^{63} -1.00000i q^{64} +(6.18636 + 5.95956i) q^{65} +(7.87515 + 1.02846i) q^{66} +(9.93115 + 2.66104i) q^{67} +(-5.11472 - 2.95298i) q^{68} +(-6.86899 + 8.97112i) q^{69} +(-4.08868 + 4.79733i) q^{70} +(8.41870 + 8.41870i) q^{71} +(2.59495 - 1.50539i) q^{72} +(-2.85119 + 10.6408i) q^{73} +(-1.56928 + 0.906026i) q^{74} +(-1.08120 + 0.449163i) q^{75} +(0.883851 + 0.883851i) q^{76} +(-12.0932 + 0.964434i) q^{77} +(3.89862 + 4.87860i) q^{78} +(3.81078 - 6.60047i) q^{79} +(-0.616617 + 2.30125i) q^{80} +(7.81286 + 4.46758i) q^{81} +(-2.38961 - 1.37964i) q^{82} +(9.74816 + 9.74816i) q^{83} +(-3.39913 + 3.07342i) q^{84} +(9.94937 + 9.94937i) q^{85} +(-2.34872 - 8.76553i) q^{86} +(0.590222 - 4.51945i) q^{87} +(-3.97101 + 2.29266i) q^{88} +(-2.47718 - 9.24498i) q^{89} +(-6.89988 + 1.86419i) q^{90} +(-7.37452 - 6.05116i) q^{91} -6.52340i q^{92} +(9.86737 + 4.07520i) q^{93} +(-1.42344 - 2.46547i) q^{94} +(-1.48896 - 2.57896i) q^{95} +(-0.661165 + 1.60089i) q^{96} +(3.90221 - 3.90221i) q^{97} +(4.10269 - 5.67168i) q^{98} +(-11.9273 - 6.85323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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