LMFDB - Embedded newform 546.2.bv.a.317.12

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			317.12
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.664489 - 1.59952i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30125 - 0.616617i) q^{5} +(-0.227862 + 1.71700i) q^{6} +(2.49307 - 0.885767i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.11691 - 2.12572i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.664489 - 1.59952i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30125 - 0.616617i) q^{5} +(-0.227862 + 1.71700i) q^{6} +(2.49307 - 0.885767i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.11691 - 2.12572i) q^{9} +(-2.06324 + 1.19121i) q^{10} +(4.42909 + 1.18677i) q^{11} +(-0.224294 - 1.71747i) q^{12} +(-1.86076 - 3.08830i) q^{13} +(-2.17887 + 1.50084i) q^{14} +(0.542863 - 4.09062i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.95298 + 5.11472i) q^{17} +(2.59495 + 1.50539i) q^{18} +(0.323512 + 1.20736i) q^{19} +(1.68463 - 1.68463i) q^{20} +(0.239820 - 4.57630i) q^{21} -4.58533 q^{22} +(-3.26170 + 5.64943i) q^{23} +(0.661165 + 1.60089i) 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} +(0.534364 + 4.09174i) q^{30} +(-5.95364 - 1.59527i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(4.84134 - 6.29581i) 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} +(-6.17624 + 0.924172i) q^{39} +(-1.19121 + 2.06324i) q^{40} +(1.95111 + 1.95111i) q^{41} +(0.952784 + 4.48243i) q^{42} -9.07474i q^{43} +(4.42909 - 1.18677i) q^{44} +(-6.18229 - 3.58649i) 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} +(10.1433 - 1.32467i) q^{51} +(-3.15561 - 1.74417i) q^{52} +(3.46376 - 1.99980i) q^{53} +(4.13222 - 3.15036i) q^{54} +10.9242 q^{55} +(-1.13654 + 2.38920i) q^{56} +(2.14617 + 0.284816i) q^{57} +(0.681073 + 2.54180i) q^{58} +(-11.8887 - 3.18558i) q^{59} +(-1.57518 - 3.81401i) q^{60} +(-2.99008 + 5.17897i) q^{61} +6.16367 q^{62} +(-7.16051 - 3.42450i) q^{63} -1.00000i q^{64} +(-6.18636 - 5.95956i) q^{65} +(-3.04690 + 7.33431i) 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} +(2.99999 + 0.00623244i) q^{72} +(-2.85119 + 10.6408i) q^{73} +(1.56928 - 0.906026i) q^{74} +(-0.151612 - 1.16093i) q^{75} +(0.883851 + 0.883851i) q^{76} +(12.0932 - 0.964434i) q^{77} +(5.72659 - 2.49121i) q^{78} +(3.81078 - 6.60047i) q^{79} +(0.616617 - 2.30125i) q^{80} +(-0.0373946 + 8.99992i) q^{81} +(-2.38961 - 1.37964i) q^{82} +(-9.74816 - 9.74816i) q^{83} +(-2.08046 - 4.08310i) q^{84} +(9.94937 + 9.94937i) q^{85} +(2.34872 + 8.76553i) q^{86} +(-4.20907 - 1.74858i) 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} +(-6.50780 + 8.46291i) q^{93} +(-1.42344 - 2.46547i) q^{94} +(1.48896 + 2.57896i) q^{95} +(1.37303 + 1.05583i) q^{96} +(3.90221 - 3.90221i) q^{97} +(-4.10269 + 5.67168i) q^{98} +(-6.85323 - 11.9273i) 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
$3$	0.664489	−	1.59952i	0.383643	−	0.923482i
$3$	0.664489	−	1.59952i	0.383643	−	0.923482i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.30125	−	0.616617i	1.02915	−	0.275760i	0.295539	−	0.955331i	$-0.404501\pi$
$5$	2.30125	−	0.616617i	1.02915	−	0.275760i	0.733610	+	0.679571i	$0.237834\pi$
$6$	−0.227862	+	1.71700i	−0.0930241	+	0.700961i
$7$	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
$9$	−2.11691	−	2.12572i	−0.705636	−	0.708574i
$10$	−2.06324	+	1.19121i	−0.652454	+	0.376695i
$11$	4.42909	+	1.18677i	1.33542	+	0.357825i	0.854733	−	0.519067i	$-0.173721\pi$
$11$	4.42909	+	1.18677i	1.33542	+	0.357825i	0.480687	+	0.876892i	$0.340387\pi$
$12$	−0.224294	−	1.71747i	−0.0647481	−	0.495790i
$13$	−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
$15$	0.542863	−	4.09062i	0.140167	−	1.05619i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.95298	+	5.11472i	0.716204	+	1.24050i	0.962493	+	0.271305i	$0.0874553\pi$
$17$	2.95298	+	5.11472i	0.716204	+	1.24050i	−0.246289	+	0.969196i	$0.579211\pi$
$18$	2.59495	+	1.50539i	0.611637	+	0.354825i
$19$	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
$21$	0.239820	−	4.57630i	0.0523331	−	0.998630i
$22$	−4.58533			−0.977596
$23$	−3.26170	+	5.64943i	−0.680111	+	1.17799i	0.294836	+	0.955548i	$0.404735\pi$
$23$	−3.26170	+	5.64943i	−0.680111	+	1.17799i	−0.974947	+	0.222439i	$0.928598\pi$
$24$	0.661165	+	1.60089i	0.134960	+	0.326781i
$25$	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	$-0.921434\pi$
$29$		−	2.63146i		−	0.488650i	0.969693	−	0.244325i	$-0.0785664\pi$
$30$	0.534364	+	4.09174i	0.0975611	+	0.747046i
$31$	−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
$33$	4.84134	−	6.29581i	0.842769	−	1.09596i
$34$	−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
$39$	−6.17624	+	0.924172i	−0.988989	+	0.147986i
$40$	−1.19121	+	2.06324i	−0.188347	+	0.326227i
$41$	1.95111	+	1.95111i	0.304712	+	0.304712i	0.842854	−	0.538142i	$-0.180874\pi$
$41$	1.95111	+	1.95111i	0.304712	+	0.304712i	−0.538142	+	0.842854i	$0.680874\pi$
$42$	0.952784	+	4.48243i	0.147018	+	0.691654i
$43$		−	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
$45$	−6.18229	−	3.58649i	−0.921601	−	0.534642i
$46$	1.68838	−	6.30112i	0.248938	−	0.929049i
$47$	0.736826	+	2.74987i	0.107477	+	0.401110i	0.998614	−	0.0526238i	$-0.0167584\pi$
$47$	0.736826	+	2.74987i	0.107477	+	0.401110i	−0.891137	+	0.453734i	$0.850092\pi$
$48$	−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
$51$	10.1433	−	1.32467i	1.42035	−	0.185491i
$52$	−3.15561	−	1.74417i	−0.437605	−	0.241872i
$53$	3.46376	−	1.99980i	0.475784	−	0.274694i	−0.242874	−	0.970058i	$-0.578090\pi$
$53$	3.46376	−	1.99980i	0.475784	−	0.274694i	0.718658	+	0.695364i	$0.244757\pi$
$54$	4.13222	−	3.15036i	0.562324	−	0.428709i
$55$	10.9242			1.47302
$56$	−1.13654	+	2.38920i	−0.151876	+	0.319270i
$57$	2.14617	+	0.284816i	0.284267	+	0.0377249i
$58$	0.681073	+	2.54180i	0.0894292	+	0.333754i
$59$	−11.8887	−	3.18558i	−1.54778	−	0.414727i	−0.619010	−	0.785383i	$-0.712466\pi$
$59$	−11.8887	−	3.18558i	−1.54778	−	0.414727i	−0.928770	+	0.370656i	$0.879133\pi$
$60$	−1.57518	−	3.81401i	−0.203354	−	0.492387i
$61$	−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
$63$	−7.16051	−	3.42450i	−0.902139	−	0.431446i
$64$		−	1.00000i		−	0.125000i
$65$	−6.18636	−	5.95956i	−0.767323	−	0.739193i
$66$	−3.04690	+	7.33431i	−0.375048	+	0.902792i
$67$	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	0.000883786	−	1.00000i	$-0.499719\pi$
$71$	−8.41870	−	8.41870i	−0.999116	−	0.999116i	−1.00000		0.000883786i	$0.999719\pi$
$72$	2.99999	+	0.00623244i	0.353553	+	0.000734500i
$73$	−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
$75$	−0.151612	−	1.16093i	−0.0175067	−	0.134052i
$76$	0.883851	+	0.883851i	0.101385	+	0.101385i
$77$	12.0932	−	0.964434i	1.37815	−	0.109907i
$78$	5.72659	−	2.49121i	0.648409	−	0.282074i
$79$	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
$81$	−0.0373946	+	8.99992i	−0.00415495	+	0.999991i
$82$	−2.38961	−	1.37964i	−0.263888	−	0.152356i
$83$	−9.74816	−	9.74816i	−1.07000	−	1.07000i	−0.997358	−	0.0726418i	$-0.976857\pi$
$83$	−9.74816	−	9.74816i	−1.07000	−	1.07000i	−0.0726418	−	0.997358i	$-0.523143\pi$
$84$	−2.08046	−	4.08310i	−0.226997	−	0.445503i
$85$	9.94937	+	9.94937i	1.07916	+	1.07916i
$86$	2.34872	+	8.76553i	0.253269	+	0.945211i
$87$	−4.20907	−	1.74858i	−0.451260	−	0.187467i
$88$	−3.97101	+	2.29266i	−0.423311	+	0.244399i
$89$	2.47718	+	9.24498i	0.262581	+	0.979966i	0.963714	+	0.266936i	$0.0860111\pi$
$89$	2.47718	+	9.24498i	0.262581	+	0.979966i	−0.701133	+	0.713030i	$0.747322\pi$
$90$	6.89988	+	1.86419i	0.727311	+	0.196503i
$91$	−7.37452	−	6.05116i	−0.773059	−	0.634334i
$92$			6.52340i			0.680111i
$93$	−6.50780	+	8.46291i	−0.674827	+	0.877563i
$94$	−1.42344	−	2.46547i	−0.146816	−	0.254294i
$95$	1.48896	+	2.57896i	0.152764	+	0.264595i
$96$	1.37303	+	1.05583i	0.140135	+	0.107760i
$97$	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
$99$	−6.85323	−	11.9273i	−0.688776	−	1.19874i
$100$	0.337977	−	0.585393i	0.0337977	−	0.0585393i
$101$	1.78120	+	3.08513i	0.177236	+	0.306982i	0.940933	−	0.338593i	$-0.109951\pi$
$101$	1.78120	+	3.08513i	0.177236	+	0.306982i	−0.763697	+	0.645575i	$0.776618\pi$
$102$	−9.45483	+	3.90482i	−0.936168	+	0.386635i
$103$	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
$105$	−2.26994	−	10.6791i	−0.221523	−	1.04217i
$106$	−2.82815	+	2.82815i	−0.274694	+	0.274694i
$107$	4.79107	+	2.76613i	0.463170	+	0.267411i	0.713376	−	0.700781i	$-0.247165\pi$
$107$	4.79107	+	2.76613i	0.463170	+	0.267411i	−0.250206	+	0.968193i	$0.580498\pi$
$108$	−3.17605	+	4.11251i	−0.305615	+	0.395726i
$109$	−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
$111$	−0.412897	+	3.11129i	−0.0391904	+	0.295310i
$112$	0.479440	−	2.60195i	0.0453028	−	0.245861i
$113$			9.52648i			0.896176i	0.893989	+	0.448088i	$0.147895\pi$
$113$			9.52648i			0.896176i	−0.893989	+	0.448088i	$0.852105\pi$
$114$	−2.14675	+	0.280357i	−0.201062	+	0.0262579i
$115$	−4.02244	+	15.0119i	−0.375094	+	1.39987i
$116$	−1.31573	−	2.27891i	−0.122163	−	0.211592i
$117$	−2.62581	+	10.4931i	−0.242756	+	0.970087i
$118$	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
$123$	4.41732	−	1.82434i	0.398296	−	0.164495i
$124$	−5.95364	+	1.59527i	−0.534653	+	0.143260i
$125$	−7.28442	+	7.28442i	−0.651538	+	0.651538i
$126$	7.80284	+	1.45453i	0.695132	+	0.129580i
$127$			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
$129$	−14.5152	−	6.03007i	−1.27799	−	0.530918i
$130$	7.51801	+	4.15535i	0.659373	+	0.364448i
$131$	−10.0357	−	5.79409i	−0.876819	−	0.506232i	−0.00721095	−	0.999974i	$-0.502295\pi$
$131$	−10.0357	−	5.79409i	−0.876819	−	0.506232i	−0.869608	+	0.493742i	$0.835629\pi$
$132$	1.04482	−	7.87300i	0.0909400	−	0.685257i
$133$	1.87598	+	2.72349i	0.162668	+	0.236156i
$134$	−10.2815			−0.888185
$135$	−9.84471	+	7.50549i	−0.847298	+	0.645970i
$136$	−5.70473	−	1.52858i	−0.489176	−	0.131074i
$137$	10.5912	+	2.83789i	0.904864	+	0.242458i	0.681104	−	0.732187i	$-0.261500\pi$
$137$	10.5912	+	2.83789i	0.904864	+	0.242458i	0.223760	+	0.974644i	$0.428167\pi$
$138$	−8.95683	−	6.88761i	−0.762456	−	0.586313i
$139$	−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
$141$	4.88808	+	0.648694i	0.411650	+	0.0546299i
$142$	10.3108	+	5.95292i	0.865260	+	0.499558i
$143$	−4.57636	−	15.8866i	−0.382694	−	1.32851i
$144$	−2.89938	+	0.770435i	−0.241615	+	0.0642029i
$145$	−1.62261	−	6.05565i	−0.134750	−	0.502894i
$146$		−	11.0161i		−	0.911702i
$147$	−3.45564	−	11.6215i	−0.285017	−	0.958523i
$148$	−1.28131	+	1.28131i	−0.105323	+	0.105323i
$149$	6.71519	−	1.79933i	0.550130	−	0.147407i	0.0269619	−	0.999636i	$-0.491417\pi$
$149$	6.71519	−	1.79933i	0.550130	−	0.147407i	0.523168	+	0.852230i	$0.324750\pi$
$150$	0.446916	+	1.08213i	0.0364906	+	0.0883555i
$151$	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
$156$	−4.88669	+	3.88848i	−0.391249	+	0.311327i
$157$	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
$159$	−0.897089	−	6.86920i	−0.0711438	−	0.544763i
$160$			2.38243i			0.188347i
$161$	−3.12758	+	16.9735i	−0.246488	+	1.33770i
$162$	−2.29323	−	8.70294i	−0.180173	−	0.683767i
$163$	−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
$165$	7.25902	−	17.4735i	0.565114	−	1.36031i
$166$	11.9390	+	6.89299i	0.926647	+	0.535000i
$167$	−12.1133	+	12.1133i	−0.937356	+	0.937356i	−0.998150	−	0.0607939i	$-0.980637\pi$
$167$	−12.1133	+	12.1133i	−0.937356	+	0.937356i	0.0607939	+	0.998150i	$0.480637\pi$
$168$	3.06635	+	3.40551i	0.236574	+	0.262741i
$169$	−6.07517	+	11.4931i	−0.467321	+	0.884088i
$170$	−12.1854	−	7.03527i	−0.934581	−	0.539580i
$171$	1.88167	−	3.24357i	0.143895	−	0.248042i
$172$	−4.53737	−	7.85896i	−0.345971	−	0.599240i
$173$	2.78524	−	4.82417i	0.211758	−	0.366775i	−0.740507	−	0.672049i	$-0.765415\pi$
$173$	2.78524	−	4.82417i	0.211758	−	0.366775i	0.952265	+	0.305274i	$0.0987480\pi$
$174$	4.51821	+	0.599609i	0.342525	+	0.0454563i
$175$	1.16006	−	1.36112i	0.0876922	−	0.102891i
$176$	3.24232	−	3.24232i	0.244399	−	0.244399i
$177$	−12.9953	+	16.8994i	−0.976787	+	1.27024i
$178$	−4.78555	−	8.28882i	−0.358692	−	0.621273i
$179$	9.81003	+	16.9915i	0.733236	+	1.27000i	0.955493	+	0.295014i	$0.0953242\pi$
$179$	9.81003	+	16.9915i	0.733236	+	1.27000i	−0.222257	+	0.974988i	$0.571342\pi$
$180$	−7.14726	−	0.0148483i	−0.532725	−	0.00110673i
$181$		−	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
$186$	4.09569	−	9.85889i	0.300310	−	0.722889i
$187$	7.00903	+	26.1581i	0.512551	+	1.91287i
$188$	2.01305	+	2.01305i	0.146816	+	0.146816i
$189$	−10.2356	+	9.17781i	−0.744531	+	0.667587i
$190$	−2.10571	−	2.10571i	−0.152764	−	0.152764i
$191$	10.2093	+	5.89437i	0.738722	+	0.426501i	0.821604	−	0.570058i	$-0.193079\pi$
$191$	10.2093	+	5.89437i	0.738722	+	0.426501i	−0.0828824	+	0.996559i	$0.526413\pi$
$192$	−1.59952	−	0.664489i	−0.115435	−	0.0479554i
$193$	−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
$195$	−13.6432	+	5.93512i	−0.977009	+	0.425023i
$196$	2.49496	−	6.54027i	0.178211	−	0.467162i
$197$	7.28557	+	7.28557i	0.519075	+	0.519075i	0.917292	−	0.398216i	$-0.130371\pi$
$197$	7.28557	+	7.28557i	0.519075	+	0.519075i	−0.398216	+	0.917292i	$0.630371\pi$
$198$	9.70673	+	9.74714i	0.689827	+	0.692699i
$199$	−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
$201$	10.8555	−	14.1168i	0.765689	−	0.995723i
$202$	−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
$207$	18.9138	−	5.02585i	1.31460	−	0.349321i
$208$	−3.60492	+	0.0673138i	−0.249956	+	0.00466737i
$209$			5.73145i			0.396453i
$210$	4.95654	+	9.72768i	0.342033	+	0.671274i
$211$	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
$213$	−19.0600	+	7.87172i	−1.30597	+	0.539361i
$214$	−5.34374	−	1.43185i	−0.365291	−	0.0978794i
$215$	−5.59564	−	20.8832i	−0.381620	−	1.42422i
$216$	2.00343	−	4.79440i	0.136316	−	0.326218i
$217$	−16.2559	+	1.29641i	−1.10352	+	0.0880058i
$218$	17.5198			1.18659
$219$	15.1255	+	11.6312i	1.02209	+	0.785964i
$220$	9.46064	−	5.46210i	0.637836	−	0.368255i
$221$	10.3010	−	18.6369i	0.692920	−	1.25366i
$222$	−0.406432	−	3.11214i	−0.0272780	−	0.208873i
$223$	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	−0.939401	−	0.342819i	$-0.888618\pi$
$227$	0.686338	−	2.56145i	0.0455538	−	0.170009i	0.984955	+	0.172810i	$0.0552847\pi$
$228$	2.00104	−	0.826425i	0.132522	−	0.0547313i
$229$	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
$231$	6.49320	−	19.9842i	0.427221	−	1.31486i
$232$	1.86073	+	1.86073i	0.122163	+	0.122163i
$233$	1.67441	−	2.90016i	0.109694	−	0.189996i	−0.805952	−	0.591981i	$-0.798346\pi$
$233$	1.67441	−	2.90016i	0.109694	−	0.189996i	0.915646	+	0.401985i	$0.131680\pi$
$234$	−0.179473	−	10.8152i	−0.0117325	−	0.707009i
$235$	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	0.234509	−	0.972114i	$-0.424652\pi$
$239$	−11.4031	−	11.4031i	−0.737605	−	0.737605i	−0.972114	+	0.234509i	$0.924652\pi$
$240$	−3.27115	−	2.51544i	−0.211152	−	0.162371i
$241$	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
$243$	14.3707	+	6.04016i	0.921880	+	0.387477i
$244$			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
$249$	−22.0699	+	9.11480i	−1.39862	+	0.577627i
$250$	5.15086	−	8.92155i	0.325769	−	0.564249i
$251$	1.99521			0.125937			0.0629683	−	0.998016i	$-0.479943\pi$
$251$	1.99521			0.125937			0.0629683	+	0.998016i	$0.479943\pi$
$252$	−7.91343	+	0.614553i	−0.498499	+	0.0387132i
$253$	−21.1509	+	21.1509i	−1.32975	+	1.32975i
$254$	−2.55360	−	9.53017i	−0.160227	−	0.597976i
$255$	22.5254	−	9.30294i	1.41060	−	0.582573i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.34151	+	4.05562i	−0.146060	+	0.252983i	−0.929768	−	0.368147i	$-0.879992\pi$
$257$	−2.34151	+	4.05562i	−0.146060	+	0.252983i	0.783708	+	0.621129i	$0.213326\pi$
$258$	15.5813	+	2.06779i	0.970050	+	0.128735i
$259$	−3.94823	+	2.71960i	−0.245331	+	0.168988i
$260$	−8.33732	−	2.06795i	−0.517059	−	0.128249i
$261$	−5.59376	+	5.57057i	−0.346245	+	0.344809i
$262$	11.1933	+	2.99924i	0.691526	+	0.185294i
$263$	−7.97634	+	4.60514i	−0.491842	+	0.283965i	−0.725338	−	0.688392i	$-0.758317\pi$
$263$	−7.97634	+	4.60514i	−0.491842	+	0.283965i	0.233496	+	0.972358i	$0.424983\pi$
$264$	1.02846	+	7.87515i	0.0632975	+	0.484682i
$265$	6.73786	−	6.73786i	0.413903	−	0.413903i
$266$	−2.51695	−	2.14515i	−0.154324	−	0.131527i
$267$	16.4336	+	2.18089i	1.00572	+	0.133468i
$268$	9.93115	−	2.66104i	0.606641	−	0.162549i
$269$	11.1019	−	6.40967i	0.676893	−	0.390805i	−0.121790	−	0.992556i	$-0.538864\pi$
$269$	11.1019	−	6.40967i	0.676893	−	0.390805i	0.798683	+	0.601751i	$0.205530\pi$
$270$	7.56670	−	9.79774i	0.460495	−	0.596272i
$271$	−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
$273$	−14.5792	+	7.77474i	−0.882374	+	0.470549i
$274$	−10.9648			−0.662406
$275$	2.99386	−	0.802201i	0.180536	−	0.0483746i
$276$	10.4343	+	4.33472i	0.628070	+	0.260920i
$277$	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
$279$	9.21221	+	16.0328i	0.551521	+	0.959861i
$280$	−1.14223	+	6.19895i	−0.0682613	+	0.370458i
$281$	13.3466	−	13.3466i	0.796190	−	0.796190i	−0.186303	−	0.982492i	$-0.559651\pi$
$281$	13.3466	−	13.3466i	0.796190	−	0.796190i	0.982492	+	0.186303i	$0.0596506\pi$
$282$	−4.88942	+	0.638538i	−0.291160	+	0.0380244i
$283$	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
$285$	5.11448	−	0.667930i	0.302956	−	0.0395648i
$286$	8.53218	+	14.1609i	0.504519	+	0.837349i
$287$	6.59248	+	3.13603i	0.389142	+	0.185114i
$288$	2.60119	−	1.49460i	0.153276	−	0.0880701i
$289$	−8.94023	+	15.4849i	−0.525896	+	0.910879i
$290$	3.13463	+	5.42934i	0.184072	+	0.318822i
$291$	−3.64868	−	8.83464i	−0.213889	−	0.517895i
$292$	2.85119	+	10.6408i	0.166853	+	0.622704i
$293$	−11.8909	+	11.8909i	−0.694677	+	0.694677i	−0.963257	−	0.268581i	$-0.913445\pi$
$293$	−11.8909	+	11.8909i	−0.694677	+	0.694677i	0.268581	+	0.963257i	$0.413445\pi$
$294$	6.34575	+	10.3311i	0.370092	+	0.602521i
$295$	−29.3232			−1.70726
$296$	0.906026	−	1.56928i	0.0526617	−	0.0912127i
$297$	−23.6318	+	3.03630i	−1.37126	+	0.176184i
$298$	−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
$303$	6.11831	−	0.799026i	0.351488	−	0.0459029i
$304$	1.20736	+	0.323512i	0.0692470	+	0.0185547i
$305$	−3.68747	+	13.7618i	−0.211144	+	0.788000i
$306$	−0.0368086	+	17.7179i	−0.00210421	+	1.01286i
$307$	−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	0.705537	−	0.708673i	$-0.250706\pi$
$311$	−4.60208	−	7.97103i	−0.260960	−	0.451996i	−0.966497	+	0.256677i	$0.917372\pi$
$312$	3.71377	−	5.02075i	0.210251	−	0.284244i
$313$	−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
$315$	−18.5897	−	3.46532i	−1.04741	−	0.195249i
$316$		−	7.62157i		−	0.428747i
$317$	−15.8697	+	4.25228i	−0.891332	+	0.238832i	−0.675290	−	0.737552i	$-0.735982\pi$
$317$	−15.8697	+	4.25228i	−0.891332	+	0.238832i	−0.216042	+	0.976384i	$0.569315\pi$
$318$	2.64440	+	6.40295i	0.148291	+	0.359060i
$319$	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
$324$	4.46758	+	7.81286i	0.248199	+	0.434048i
$325$	−2.13305	−	1.17897i	−0.118320	−	0.0653977i
$326$	4.46043	−	2.57523i	0.247040	−	0.142629i
$327$	−18.4979	+	24.0552i	−1.02294	+	1.33026i
$328$	−2.75928			−0.152356
$329$	4.27271	+	6.20298i	0.235562	+	0.341981i
$330$	−2.48921	+	18.7568i	−0.137026	+	1.03253i
$331$	−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
$333$	4.70219	+	2.72785i	0.257678	+	0.149485i
$334$	8.56541	−	14.8357i	0.468678	−	0.811774i
$335$	24.4949			1.33830
$336$	−3.84328	−	2.49584i	−0.209668	−	0.136159i
$337$			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
$339$	15.2378	+	6.33024i	0.827602	+	0.343812i
$340$	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
$345$	21.3390	+	16.4092i	1.14885	+	0.883443i
$346$	−1.44174	+	5.38066i	−0.0775086	+	0.289266i
$347$	−16.7977	+	9.69816i	−0.901748	+	0.520624i	−0.877767	−	0.479088i	$-0.840967\pi$
$347$	−16.7977	+	9.69816i	−0.901748	+	0.520624i	−0.0239811	+	0.999712i	$0.507634\pi$
$348$	−4.51945	+	0.590222i	−0.242268	+	0.0316392i
$349$	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
$351$	15.0391	+	11.1726i	0.802726	+	0.596348i
$352$	−2.29266	+	3.97101i	−0.122199	+	0.211656i
$353$	4.17743	−	15.5904i	0.222342	−	0.829793i	−0.761109	−	0.648623i	$-0.775345\pi$
$353$	4.17743	−	15.5904i	0.222342	−	0.829793i	0.983452	−	0.181170i	$-0.0579883\pi$
$354$	8.17861	−	19.6870i	0.434688	−	1.04635i
$355$	−24.5646	−	14.1824i	−1.30375	−	0.752723i
$356$	6.76779	+	6.76779i	0.358692	+	0.358692i
$357$	24.1147	−	12.2871i	1.27628	−	0.650303i
$358$	−13.8735	−	13.8735i	−0.733236	−	0.733236i
$359$	−7.58226	−	28.2974i	−0.400176	−	1.49348i	−0.812782	−	0.582568i	$-0.802048\pi$
$359$	−7.58226	−	28.2974i	−0.400176	−	1.49348i	0.412606	−	0.910910i	$-0.364619\pi$
$360$	6.90757	−	1.83551i	0.364061	−	0.0967396i
$361$	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
$366$	−8.21095	−	6.31405i	−0.429193	−	0.330041i
$367$	−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
$369$	0.0171971	−	8.27782i	0.000895243	−	0.430926i
$370$	3.05264	−	3.05264i	0.158699	−	0.158699i
$371$	6.86406	−	8.05375i	0.356364	−	0.418130i
$372$	−1.40446	+	10.5830i	−0.0728180	+	0.548703i
$373$	−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
$375$	6.81113	+	16.4920i	0.351725	+	0.851641i
$376$	−2.46547	−	1.42344i	−0.127147	−	0.0734082i
$377$	−8.12674	+	4.89651i	−0.418548	+	0.252183i
$378$	7.51145	−	11.5143i	0.386347	−	0.592229i
$379$	−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
$381$	15.7814	+	6.55608i	0.808506	+	0.335878i
$382$	−11.3870	−	3.05115i	−0.582612	−	0.156110i
$383$	−19.5605	+	5.24121i	−0.999493	+	0.267813i	−0.721233	−	0.692693i	$-0.756424\pi$
$383$	−19.5605	+	5.24121i	−0.999493	+	0.267813i	−0.278260	+	0.960506i	$0.589758\pi$
$384$	1.71700	+	0.227862i	0.0876201	+	0.0116280i
$385$	27.2349	−	9.67631i	1.38802	−	0.493150i
$386$		−	14.3468i		−	0.730233i
$387$	−19.2904	+	19.2104i	−0.980585	+	0.976520i
$388$	1.42831	−	5.33052i	0.0725114	−	0.270616i
$389$	16.8379	+	29.1641i	0.853716	+	1.47868i	0.877831	+	0.478970i	$0.158990\pi$
$389$	16.8379	+	29.1641i	0.853716	+	1.47868i	−0.0241159	+	0.999709i	$0.507677\pi$
$390$	11.6422	−	9.26400i	0.589525	−	0.469101i
$391$	−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
$396$	−11.8987	−	6.90273i	−0.597933	−	0.346875i
$397$	−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
$399$	5.60283	−	1.19094i	0.280492	−	0.0596213i
$400$		−	0.675953i		−	0.0337977i
$401$	−1.00798	−	3.76183i	−0.0503361	−	0.187857i	0.936180	−	0.351521i	$-0.114335\pi$
$401$	−1.00798	−	3.76183i	−0.0503361	−	0.187857i	−0.986516	+	0.163664i	$0.947669\pi$
$402$	−6.83193	+	16.4454i	−0.340746	+	0.820222i
$403$	6.15160	+	21.3550i	0.306433	+	1.06377i
$404$	3.08513	+	1.78120i	0.153491	+	0.0886181i
$405$	5.46345	+	20.7341i	0.271481	+	1.03029i
$406$	3.94941	+	5.73362i	0.196006	+	0.284555i
$407$	−8.30885			−0.411855
$408$	−6.23571	+	8.10909i	−0.308714	+	0.401460i
$409$	−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
$411$	11.5770	−	15.0550i	0.571050	−	0.742608i
$412$	7.39592			0.364371
$413$	−32.4612	+	2.58877i	−1.59731	+	0.127385i
$414$	−16.9686	+	9.74986i	−0.833960	+	0.479180i
$415$	−28.4438	−	16.4220i	−1.39625	−	0.806126i
$416$	3.46467	−	0.998043i	0.169869	−	0.0489331i
$417$	−9.08237	+	21.8625i	−0.444766	+	1.07061i
$418$	−1.48341	−	5.53616i	−0.0725559	−	0.270782i
$419$			7.12445i			0.348052i	0.984741	+	0.174026i	$0.0556777\pi$
$419$			7.12445i			0.348052i	−0.984741	+	0.174026i	$0.944322\pi$
$420$	−7.30535	−	8.11337i	−0.356465	−	0.395892i
$421$	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
$423$	4.28567	−	7.38751i	0.208376	−	0.359193i
$424$	−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
$429$	−28.4519	−	3.23654i	−1.37367	−	0.156261i
$430$	10.8099	+	18.7234i	0.521302	+	0.902922i
$431$	−3.64052	+	13.5866i	−0.175358	+	0.654444i	0.821133	+	0.570737i	$0.193343\pi$
$431$	−3.64052	+	13.5866i	−0.175358	+	0.654444i	−0.996490	+	0.0837069i	$0.973324\pi$
$432$	−0.694285	+	5.14956i	−0.0334038	+	0.247758i
$433$			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
$435$	−10.7643	−	1.42853i	−0.516109	−	0.0684925i
$436$	−16.9228	+	4.53445i	−0.810455	+	0.217161i
$437$	−7.87610	−	2.11040i	−0.376765	−	0.100954i
$438$	−17.6205	−	7.32010i	−0.841940	−	0.349768i
$439$	−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
$441$	−20.8850	−	2.19498i	−0.994522	−	0.104523i
$442$	−5.12640	+	20.6680i	−0.243838	+	0.983076i
$443$	32.7373	+	18.9009i	1.55540	+	0.898009i	0.997687	+	0.0679735i	$0.0216533\pi$
$443$	32.7373	+	18.9009i	1.55540	+	0.898009i	0.557710	+	0.830036i	$0.311680\pi$
$444$	1.19806	+	2.90090i	0.0568576	+	0.137671i
$445$	11.4012	+	19.7475i	0.540470	+	0.936121i
$446$	−12.4067	+	21.4890i	−0.587473	+	1.01753i
$447$	1.58411	−	11.9367i	0.0749259	−	0.564586i
$448$	−0.885767	−	2.49307i	−0.0418486	−	0.117787i
$449$	13.4565	−	13.4565i	0.635052	−	0.635052i	−0.314279	−	0.949331i	$-0.601763\pi$
$449$	13.4565	−	13.4565i	0.635052	−	0.635052i	0.949331	+	0.314279i	$0.101763\pi$
$450$	2.02785	+	0.00421284i	0.0955940	+	0.000198595i
$451$	6.32611	+	10.9571i	0.297885	+	0.515951i
$452$	4.76324	+	8.25018i	0.224044	+	0.388056i
$453$	−2.13547	−	1.64213i	−0.100333	−	0.0771539i
$454$			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
$459$	−24.2883	−	18.7576i	−1.13368	−	0.875532i
$460$	4.02244	+	15.0119i	0.187547	+	0.699935i
$461$	−16.6508	−	16.6508i	−0.775507	−	0.775507i	0.203556	−	0.979063i	$-0.434750\pi$
$461$	−16.6508	−	16.6508i	−0.775507	−	0.775507i	−0.979063	+	0.203556i	$0.934750\pi$
$462$	−1.09966	+	20.9838i	−0.0511606	+	0.976256i
$463$	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
$465$	−9.75767	+	23.4881i	−0.452501	+	1.08923i
$466$	−0.866737	+	3.23471i	−0.0401508	+	0.149845i
$467$	−3.52969	+	6.11361i	−0.163335	+	0.282904i	−0.936063	−	0.351833i	$-0.885558\pi$
$467$	−3.52969	+	6.11361i	−0.163335	+	0.282904i	0.772728	+	0.634737i	$0.218892\pi$
$468$	2.97253	+	10.4002i	0.137405	+	0.480749i
$469$	27.1161	−	2.16251i	1.25211	−	0.0998553i
$470$	−4.79593	−	4.79593i	−0.221220	−	0.221220i
$471$	15.0441	−	1.96470i	0.693196	−	0.0905285i
$472$	10.6591	−	6.15406i	0.490627	−	0.283264i
$473$	10.7696	−	40.1928i	0.495188	−	1.84807i
$474$	10.4647	+	8.04710i	0.480658	+	0.369616i
$475$	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	−0.310769	−	0.950485i	$-0.600587\pi$
$479$	−23.0930	−	6.18775i	−1.05515	−	0.282725i	−0.744377	+	0.667760i	$0.767253\pi$
$480$	3.81073	+	1.58310i	0.173935	+	0.0722581i
$481$	4.70529	+	4.53279i	0.214543	+	0.206677i
$482$			0.170765i			0.00777813i
$483$	25.0712	+	16.2813i	1.14078	+	0.740827i
$484$	10.0253			0.455693
$485$	6.57378	−	11.3861i	0.298500	−	0.517017i
$486$	−15.4443	−	2.11494i	−0.700569	−	0.0959358i
$487$	−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
$489$	−1.17359	+	8.84332i	−0.0530717	+	0.399909i
$490$	−5.94405	+	15.5817i	−0.268525	+	0.703910i
$491$	14.7153			0.664093			0.332047	−	0.943263i	$-0.392261\pi$
$491$	14.7153			0.664093			0.332047	+	0.943263i	$0.392261\pi$
$492$	2.91334	−	3.78858i	0.131343	−	0.170802i
$493$	13.4592	−	7.77067i	0.606172	−	0.349973i
$494$	−2.18013	+	3.94437i	−0.0980885	+	0.177466i
$495$	−23.1256	−	23.2218i	−1.03942	−	1.04374i
$496$	−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
$501$	11.3263	+	27.4246i	0.506021	+	1.22524i
$502$	−1.92723	+	0.516399i	−0.0860164	+	0.0230480i
$503$		−	14.9068i		−	0.664661i	−0.943163	−	0.332330i	$-0.892165\pi$
$503$		−	14.9068i		−	0.664661i	0.943163	−	0.332330i	$-0.107835\pi$
$504$	7.48473	−	2.64176i	0.333396	−	0.117673i
$505$	6.00133	+	6.00133i	0.267056	+	0.267056i
$506$	14.9560	−	25.9045i	0.664874	−	1.15159i
$507$	14.3466	+	17.3544i	0.637155	+	0.770736i
$508$	4.93318	+	8.54451i	0.218874	+	0.379102i
$509$	11.7733	−	3.15465i	0.521842	−	0.139827i	0.0117237	−	0.999931i	$-0.496268\pi$
$509$	11.7733	−	3.15465i	0.521842	−	0.139827i	0.510119	+	0.860104i	$0.329601\pi$
$510$	−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
$513$	−3.93780	−	5.16509i	−0.173858	−	0.228044i
$514$	1.21206	−	4.52345i	0.0534615	−	0.199521i
$515$	17.0198	+	4.56045i	0.749984	+	0.200958i
$516$	−15.5856	+	2.03541i	−0.686116	+	0.0896040i
$517$			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	−0.802011	−	0.597310i	$-0.796236\pi$
$521$	−15.6521	+	9.03674i	−0.685730	+	0.395907i	0.116280	+	0.993216i	$0.462903\pi$
$522$	3.96139	−	6.82853i	0.173385	−	0.298876i
$523$	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
$525$	−1.40629	−	2.75998i	−0.0613756	−	0.120456i
$526$	6.51266	−	6.51266i	0.283965	−	0.283965i
$527$	−9.42164	−	35.1620i	−0.410413	−	1.53168i
$528$	−3.03166	−	7.34063i	−0.131936	−	0.319460i
$529$	−9.77735	−	16.9349i	−0.425102	−	0.736298i
$530$	−4.76439	+	8.25216i	−0.206952	+	0.358451i
$531$	18.3957	+	32.0157i	0.798306	+	1.38936i
$532$	2.98639	+	1.42062i	0.129476	+	0.0615916i
$533$	2.39506	−	9.65613i	0.103742	−	0.418253i
$534$	−16.4381	+	2.14674i	−0.711344	+	0.0928986i
$535$	12.7311	+	3.41128i	0.550412	+	0.147483i
$536$	−8.90402	+	5.14074i	−0.384595	+	0.222046i
$537$	33.6968	−	4.40066i	1.45412	−	0.189903i
$538$	−9.06464	+	9.06464i	−0.390805	+	0.390805i
$539$	29.2951	−	13.1162i	1.26183	−	0.564955i
$540$	−4.77303	+	11.4223i	−0.205398	+	0.491538i
$541$	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
$543$	−28.3684	−	11.7851i	−1.21741	−	0.505748i
$544$	−5.70473	+	1.52858i	−0.244588	+	0.0655372i
$545$	−41.7395			−1.78793
$546$	12.0702	−	11.2832i	0.516556	−	0.482876i
$547$	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
$549$	17.3388	−	4.60733i	0.740001	−	0.196636i
$550$	−2.68422	+	1.54973i	−0.114455	+	0.0660809i
$551$	3.17713	−	0.851309i	0.135350	−	0.0362670i
$552$	−11.2007	−	1.48643i	−0.476731	−	0.0632667i
$553$	3.65409	−	19.8309i	0.155388	−	0.843297i
$554$	−20.4230	+	20.4230i	−0.867691	+	0.867691i
$555$	0.968295	+	7.41444i	0.0411018	+	0.314725i
$556$	−11.8370	+	6.83410i	−0.502001	+	0.289831i
$557$	−26.3606	−	7.06329i	−1.11693	−	0.299281i	−0.347291	−	0.937757i	$-0.612899\pi$
$557$	−26.3606	−	7.06329i	−1.11693	−	0.299281i	−0.769642	+	0.638476i	$0.779565\pi$
$558$	−13.0479	−	13.1022i	−0.552362	−	0.554662i
$559$	−28.0255	+	16.8859i	−1.18535	+	0.714197i
$560$	−0.501097	−	6.28336i	−0.0211752	−	0.265520i
$561$	46.4977	+	6.17068i	1.96313	+	0.260526i
$562$	−9.43745	+	16.3461i	−0.398095	+	0.689520i
$563$	19.9093	+	34.4839i	0.839077	+	1.45332i	0.890667	+	0.454656i	$0.150238\pi$
$563$	19.9093	+	34.4839i	0.839077	+	1.45332i	−0.0515896	+	0.998668i	$0.516429\pi$
$564$	4.55755	−	1.88225i	0.191907	−	0.0792572i
$565$	5.87419	+	21.9228i	0.247129	+	0.922299i
$566$	−17.4810	+	17.4810i	−0.734780	+	0.734780i
$567$	7.87861	+	22.4706i	0.330870	+	0.943676i
$568$	11.9058			0.499558
$569$	4.97543	−	8.61769i	0.208581	−	0.361273i	−0.742687	−	0.669639i	$-0.766449\pi$
$569$	4.97543	−	8.61769i	0.208581	−	0.361273i	0.951268	+	0.308366i	$0.0997822\pi$
$570$	−4.76734	+	1.96890i	−0.199682	+	0.0824680i
$571$	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
$576$	−2.12572	+	2.11691i	−0.0885718	+	0.0882045i
$577$	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
$579$	19.6986	+	15.1478i	0.818647	+	0.629522i
$580$	−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
$585$	0.427582	+	25.7663i	0.0176783	+	1.06531i
$586$	8.40817	−	14.5634i	0.347338	−	0.601608i
$587$	−4.66629	−	4.66629i	−0.192598	−	0.192598i	0.604220	−	0.796818i	$-0.293485\pi$
$587$	−4.66629	−	4.66629i	−0.192598	−	0.192598i	−0.796818	+	0.604220i	$0.793485\pi$
$588$	−8.80341	−	8.33667i	−0.363046	−	0.343798i
$589$		−	7.70430i		−	0.317450i
$590$	28.3240	−	7.58940i	1.16608	−	0.312451i
$591$	16.4946	−	6.81221i	0.678496	−	0.280217i
$592$	−0.468993	+	1.75031i	−0.0192755	+	0.0719372i
$593$	−1.42643	−	5.32351i	−0.0585764	−	0.218610i	0.930433	−	0.366462i	$-0.119431\pi$
$593$	−1.42643	−	5.32351i	−0.0585764	−	0.218610i	−0.989010	+	0.147851i	$0.952764\pi$
$594$	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
$597$	1.09119	+	8.35544i	0.0446593	+	0.341966i
$598$	−22.6014	+	6.51063i	−0.924239	+	0.266239i
$599$	9.40210	−	5.42830i	0.384159	−	0.221794i	−0.295467	−	0.955353i	$-0.595475\pi$
$599$	9.40210	−	5.42830i	0.384159	−	0.221794i	0.679626	+	0.733558i	$0.262142\pi$
$600$	0.928105	+	0.713693i	0.0378897	+	0.0291364i
$601$	−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
$603$	−15.3667	−	26.7441i	−0.625780	−	1.08910i
$604$	−0.402539	−	1.50230i	−0.0163791	−	0.0611276i
$605$	23.0706	+	6.18174i	0.937952	+	0.251324i
$606$	−5.70303	+	2.35534i	−0.231670	+	0.0956790i
$607$	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
$609$	−12.0424	−	0.631079i	−0.487981	−	0.0255726i
$610$		−	14.2473i		−	0.576856i
$611$	7.12137	−	7.39238i	0.288100	−	0.299064i
$612$	−4.55017	−	17.1237i	−0.183930	−	0.692183i
$613$	−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	$0.0151574\pi$
$617$	25.9937	+	25.9937i	1.04647	+	1.04647i	0.0476003	+	0.998866i	$0.484843\pi$
$618$	−7.80885	+	10.1548i	−0.314118	+	0.408488i
$619$	−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
$621$	4.52909	−	33.5926i	0.181746	−	1.34803i
$622$	6.50832	+	6.50832i	0.260960	+	0.260960i
$623$	14.3647	+	20.8542i	0.575510	+	0.835506i
$624$	−2.28776	+	5.81086i	−0.0915838	+	0.232621i
$625$	−13.9614	+	24.1819i	−0.558457	+	0.967276i
$626$	0.173796	−	0.648615i	0.00694628	−	0.0259239i
$627$	9.16755	+	3.80849i	0.366117	+	0.152096i
$628$	7.58593	+	4.37974i	0.302711	+	0.174771i
$629$	−7.56740	−	7.56740i	−0.301732	−	0.301732i
$630$	18.8532	−	1.46413i	0.751128	−	0.0583322i
$631$	−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
$633$	8.40039	−	20.2209i	0.333885	−	0.803708i
$634$	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
$639$	−0.0742024	+	35.7174i	−0.00293540	+	1.41296i
$640$	1.19121	+	2.06324i	0.0470868	+	0.0815568i
$641$	9.26467	+	16.0469i	0.365932	+	0.633813i	0.988925	−	0.148414i	$-0.0474168\pi$
$641$	9.26467	+	16.0469i	0.365932	+	0.633813i	−0.622993	+	0.782227i	$0.714083\pi$
$642$	−5.84113	+	7.59596i	−0.230531	+	0.299789i
$643$	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
$645$	−37.1213	−	4.92635i	−1.46165	−	0.193975i
$646$	3.69109	−	6.39316i	0.145224	−	0.251536i
$647$	12.8937	+	22.3326i	0.506905	+	0.877984i	0.999968	+	0.00799108i	$0.00254367\pi$
$647$	12.8937	+	22.3326i	0.506905	+	0.877984i	−0.493064	+	0.869993i	$0.664123\pi$
$648$	−6.33746	−	6.39035i	−0.248959	−	0.251037i
$649$	−48.8757	−	28.2184i	−1.91854	−	1.10767i
$650$	2.36550	+	0.586729i	0.0927827	+	0.0230134i
$651$	−8.72825	+	26.8631i	−0.342087	+	1.05285i
$652$	−3.64192	+	3.64192i	−0.142629	+	0.142629i
$653$	9.02412	+	5.21008i	0.353141	+	0.203886i	0.666068	−	0.745891i	$-0.267976\pi$
$653$	9.02412	+	5.21008i	0.353141	+	0.203886i	−0.312927	+	0.949777i	$0.601309\pi$
$654$	11.6417	−	28.0232i	0.455226	−	1.09579i
$655$	−26.6673	−	7.14547i	−1.04198	−	0.279197i
$656$	2.66526	−	0.714154i	0.104061	−	0.0278830i
$657$	28.6550	−	16.4647i	1.11794	−	0.642350i
$658$	−5.73257	−	4.88576i	−0.223479	−	0.190467i
$659$		−	4.15768i		−	0.161960i	−0.996716	−	0.0809801i	$-0.974195\pi$
$659$		−	4.15768i		−	0.161960i	0.996716	−	0.0809801i	$-0.0258050\pi$
$660$	−2.45024	−	18.7620i	−0.0953753	−	0.730309i
$661$	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
$663$	−22.9652	−	28.8607i	−0.891895	−	1.12085i
$664$	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
$669$	−16.4057	−	39.7235i	−0.634281	−	1.53580i
$670$	−23.6602	+	6.33974i	−0.914074	+	0.244925i
$671$	−19.3896	+	19.3896i	−0.748527	+	0.748527i
$672$	4.35829	+	1.41608i	0.168125	+	0.0546265i
$673$		−	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
$675$	−2.14686	+	2.77986i	−0.0826327	+	0.106997i
$676$	0.485322	+	12.9909i	0.0186662	+	0.499651i
$677$	−5.93487	−	3.42650i	−0.228095	−	0.131691i	0.381598	−	0.924329i	$-0.375374\pi$
$677$	−5.93487	−	3.42650i	−0.228095	−	0.131691i	−0.609693	+	0.792638i	$0.708707\pi$
$678$	−16.3569	−	2.17072i	−0.628185	−	0.0833660i
$679$	6.27205	−	13.1850i	0.240699	−	0.505992i
$680$	−14.0705			−0.539580
$681$	−3.64101	−	2.79986i	−0.139524	−	0.107291i
$682$	27.2994	+	7.31486i	1.04535	+	0.280100i
$683$	−37.9107	−	10.1582i	−1.45061	−	0.388691i	−0.554377	−	0.832266i	$-0.687043\pi$
$683$	−37.9107	−	10.1582i	−1.45061	−	0.388691i	−0.896237	+	0.443575i	$0.853710\pi$
$684$	0.00779026	−	3.74985i	0.000297868	−	0.143379i
$685$	26.1228			0.998099
$686$	−5.20452	+	17.7739i	−0.198710	+	0.678612i
$687$	6.64732	−	50.0893i	0.253611	−	1.91103i
$688$	−7.85896	−	4.53737i	−0.299620	−	0.172986i
$689$	−12.6212	−	6.97598i	−0.480830	−	0.265764i
$690$	−24.8589	−	10.3272i	−0.946362	−	0.393148i
$691$	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
$693$	−27.6504	−	23.6653i	−1.05035	−	0.898969i
$694$	13.7153	−	13.7153i	0.520624	−	0.520624i
$695$	−31.4539	+	8.42805i	−1.19312	+	0.319694i
$696$	4.21269	−	1.73983i	0.159682	−	0.0659481i
$697$	−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	$-0.771984\pi$
$701$	−39.9380			−1.50844			−0.754219	+	0.656623i	$0.771984\pi$
$702$	−17.4183	−	6.89949i	−0.657411	−	0.260404i
$703$	−1.13249	−	1.96153i	−0.0427127	−	0.0739805i
$704$	1.18677	−	4.42909i	0.0447281	−	0.166928i
$705$	11.6487	−	1.52127i	0.438714	−	0.0572943i
$706$			16.1404i			0.607451i
$707$	7.17338	+	6.11373i	0.269783	+	0.229931i
$708$	−2.80455	+	21.1330i	−0.105401	+	0.794227i
$709$	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
$711$	−22.0979	+	5.87193i	−0.828734	+	0.220214i
$712$	−8.28882	−	4.78555i	−0.310637	−	0.179346i
$713$	28.4314	−	28.4314i	1.06476	−	1.06476i
$714$	−20.1128	+	18.1098i	−0.752704	+	0.677741i
$715$	−20.3273	−	33.7372i	−0.760198	−	1.26170i
$716$	16.9915	+	9.81003i	0.635001	+	0.366618i
$717$	−25.8167	+	10.6622i	−0.964142	+	0.398188i
$718$	14.6478	+	25.3707i	0.546651	+	0.946827i
$719$	7.00483	−	12.1327i	0.261236	−	0.452474i	−0.705334	−	0.708875i	$-0.749203\pi$
$719$	7.00483	−	12.1327i	0.261236	−	0.452474i	0.966571	+	0.256400i	$0.0825365\pi$
$720$	−6.19713	+	3.56077i	−0.230954	+	0.132702i
$721$	19.2438	+	3.54590i	0.716677	+	0.132056i
$722$	−12.3303	+	12.3303i	−0.458885	+	0.458885i
$723$	−0.234466	−	0.180299i	−0.00871988	−	0.00670540i
$724$	−8.86781	−	15.3595i	−0.329570	−	0.570831i
$725$	−0.889373	−	1.54044i	−0.0330305	−	0.0572105i
$726$	−10.5850	+	13.7650i	−0.392846	+	0.510867i
$727$		−	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
$732$	9.56537	+	3.97375i	0.353546	+	0.146874i
$733$	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
$735$	−15.1183	−	24.6131i	−0.557646	−	0.907866i
$736$	−4.61274	−	4.61274i	−0.170028	−	0.170028i
$737$	40.8279	+	23.5720i	1.50391	+	0.868285i
$738$	2.12585	+	8.00021i	0.0782535	+	0.294492i
$739$	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
$741$	−3.11390	−	7.15798i	−0.114392	−	0.262955i
$742$	−4.54571	+	9.55587i	−0.166878	+	0.350807i
$743$	−26.6794	−	26.6794i	−0.978774	−	0.978774i	0.0210054	−	0.999779i	$-0.493313\pi$
$743$	−26.6794	−	26.6794i	−0.978774	−	0.978774i	−0.999779	+	0.0210054i	$0.993313\pi$
$744$	−1.38247	−	10.5859i	−0.0506839	−	0.388098i
$745$	14.3438	−	8.28140i	0.525517	−	0.303407i
$746$	1.51096	−	5.63897i	0.0553201	−	0.206458i
$747$	−0.0859203	+	41.3579i	−0.00314366	+	1.51321i
$748$	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
$753$	1.32580	−	3.19138i	0.0483147	−	0.116300i
$754$	6.58252	−	6.83302i	0.239721	−	0.248844i
$755$		−	3.70537i		−	0.134852i
$756$	−4.27540	+	13.0660i	−0.155495	+	0.475207i
$757$	−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
$759$	19.7767	+	47.8858i	0.717849	+	1.73814i
$760$	−2.87645	−	0.770743i	−0.104340	−	0.0279578i
$761$	−1.61189	−	6.01567i	−0.0584311	−	0.218068i	0.930537	−	0.366199i	$-0.119341\pi$
$761$	−1.61189	−	6.01567i	−0.0584311	−	0.218068i	−0.988968	+	0.148131i	$0.952674\pi$
$762$	−16.9405	−	2.24816i	−0.613690	−	0.0814424i
$763$	−46.2062	+	3.68494i	−1.67278	+	0.133404i
$764$	11.7887			0.426501
$765$	0.0876938	−	42.2115i	0.00317057	−	1.52616i
$766$	17.5374	−	10.1252i	0.633653	−	0.365840i
$767$	12.2840	+	42.6435i	0.443551	+	1.53977i
$768$	−1.71747	+	0.224294i	−0.0619737	+	0.00809352i
$769$	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	−0.988176	−	0.153323i	$-0.951003\pi$
$773$	−1.54943	+	5.78255i	−0.0557291	+	0.207984i	0.932447	+	0.361307i	$0.117669\pi$
$774$	13.6611	−	23.5485i	0.491037	−	0.846435i
$775$	−4.02438	+	1.07833i	−0.144560	+	0.0387348i
$776$			5.51856i			0.198105i
$777$	1.72649	+	8.12240i	0.0619376	+	0.291389i
$778$	−23.8124	−	23.8124i	−0.853716	−	0.853716i
$779$	−1.72449	+	2.98690i	−0.0617861	+	0.107017i
$780$	−8.84778	+	11.9616i	−0.316801	+	0.428293i
$781$	−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
$786$	12.2352	−	15.9109i	0.436414	−	0.567524i
$787$	−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
$789$	2.06581	+	15.8184i	0.0735449	+	0.563149i
$790$			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
$795$	−6.30009	−	15.2546i	−0.223441	−	0.541023i
$796$	−2.43249	+	4.21320i	−0.0862173	+	0.149333i
$797$	−31.7658			−1.12520			−0.562600	−	0.826729i	$-0.690199\pi$
$797$	−31.7658			−1.12520			−0.562600	+	0.826729i	$0.690199\pi$
$798$	−5.10368	+	2.60048i	−0.180668	+	0.0920558i
$799$	−11.8890	+	11.8890i	−0.420602	+	0.420602i
$800$	0.174950	+	0.652921i	0.00618540	+	0.0230842i
$801$	14.4083	−	24.8366i	0.509092	−	0.877558i
$802$	1.94727	+	3.37277i	0.0687604	+	0.119097i
$803$	−25.2563	+	43.7452i	−0.891276	+	1.54374i
$804$	2.34276	−	17.6533i	0.0826226	−	0.622583i
$805$	3.26885	+	40.9888i	0.115212	+	1.44467i
$806$	−11.4691	−	19.0352i	−0.403981	−	0.670488i
$807$	−2.87530	−	22.0168i	−0.101215	−	0.775028i
$808$	−3.44102	−	0.922018i	−0.121055	−	0.0324365i
$809$	1.34055	−	0.773968i	0.0471313	−	0.0272113i	−0.476249	−	0.879310i	$-0.658004\pi$
$809$	1.34055	−	0.773968i	0.0471313	−	0.0272113i	0.523380	+	0.852099i	$0.324671\pi$
$810$	−10.6437	−	18.6136i	−0.373980	−	0.654014i
$811$	−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
$813$	−1.75077	+	13.1925i	−0.0614022	+	0.462682i
$814$	8.02574	−	2.15049i	0.281302	−	0.0753746i
$815$	−10.6266	+	6.13529i	−0.372235	+	0.214910i
$816$	3.92445	−	9.44670i	0.137383	−	0.330701i
$817$	10.9565	−	2.93579i	0.383319	−	0.102710i
$818$	25.5370			0.892882
$819$	2.74810	+	28.4859i	0.0960263	+	0.995379i
$820$	6.57378			0.229566
$821$	43.4028	−	11.6297i	1.51477	−	0.405881i	0.596752	−	0.802425i	$-0.296457\pi$
$821$	43.4028	−	11.6297i	1.51477	−	0.405881i	0.918015	+	0.396545i	$0.129791\pi$
$822$	−7.28597	+	17.5383i	−0.254127	+	0.611720i
$823$	−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
$825$	0.706250	−	5.32178i	0.0245885	−	0.185281i
$826$	30.6850	−	10.9021i	1.06767	−	0.379333i
$827$	24.9181	−	24.9181i	0.866489	−	0.866489i	−0.125593	−	0.992082i	$-0.540083\pi$
$827$	24.9181	−	24.9181i	0.866489	−	0.866489i	0.992082	+	0.125593i	$0.0400834\pi$
$828$	13.8669	−	13.8094i	0.481909	−	0.479911i
$829$	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
$831$	−6.47818	−	49.6047i	−0.224725	−	1.72077i
$832$	−3.08830	+	1.86076i	−0.107067	+	0.0645101i
$833$	38.6267	+	14.7351i	1.33833	+	0.510542i
$834$	3.11446	−	23.4683i	0.107845	−	0.812640i
$835$	−20.4064	+	35.3450i	−0.706194	+	1.22316i
$836$	2.86572	+	4.96358i	0.0991132	+	0.171669i
$837$	31.7662	−	4.08144i	1.09800	−	0.141075i
$838$	−1.84394	−	6.88169i	−0.0636979	−	0.237724i
$839$	34.7854	−	34.7854i	1.20092	−	1.20092i	0.227039	−	0.973886i	$-0.427096\pi$
$839$	34.7854	−	34.7854i	1.20092	−	1.20092i	0.973886	−	0.227039i	$-0.0729044\pi$
$840$	9.15633	+	5.94615i	0.315923	+	0.205162i
$841$	22.0754			0.761221
$842$	−15.8342	+	27.4257i	−0.545684	+	0.945152i
$843$	−12.4794	−	30.2167i	−0.429814	−	1.04072i
$844$	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
$849$	−5.54496	−	42.4589i	−0.190303	−	1.45719i
$850$	−3.85613	−	1.03325i	−0.132264	−	0.0354401i
$851$	3.05943	−	11.4179i	0.104876	−	0.391402i
$852$	−12.5706	+	16.3471i	−0.430661	+	0.560042i
$853$	−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	0.995671	−	0.0929492i	$-0.0296294\pi$
$857$	12.2174	+	21.1612i	0.417339	+	0.722853i	−0.578332	+	0.815802i	$0.696296\pi$
$858$	28.3201	−	4.23763i	0.966832	−	0.144670i
$859$	−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
$861$	9.39675	−	8.46092i	0.320241	−	0.288348i
$862$		−	14.0659i		−	0.479087i
$863$	4.93283	−	1.32175i	0.167915	−	0.0449928i	−0.173882	−	0.984767i	$-0.555631\pi$
$863$	4.93283	−	1.32175i	0.167915	−	0.0449928i	0.341797	+	0.939774i	$0.388964\pi$
$864$	−0.662177	−	5.15379i	−0.0225277	−	0.175335i
$865$	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
$870$	10.7673	−	1.40616i	0.365044	−	0.0476733i
$871$	−10.2614	−	35.6219i	−0.347693	−	1.20700i
$872$	15.1726	−	8.75988i	0.513808	−	0.296647i
$873$	−16.5557	−	0.0343941i	−0.560324	−	0.00116406i
$874$	8.15394			0.275811
$875$	−11.7083	+	24.6129i	−0.395812	+	0.832067i
$876$	18.9147	+	2.51016i	0.639068	+	0.0848103i
$877$	−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
$879$	11.1184	+	26.9212i	0.375013	+	0.908029i
$880$	5.46210	−	9.46064i	0.184128	−	0.318918i
$881$	−57.8655			−1.94954			−0.974769	−	0.223216i	$-0.928345\pi$
$881$	−57.8655			−1.94954			−0.974769	+	0.223216i	$0.928345\pi$
$882$	20.7414	−	3.28524i	0.698400	−	0.110620i
$883$			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
$885$	−19.4849	+	46.9029i	−0.654979	+	1.57662i
$886$	−36.5137	−	9.78383i	−1.22670	−	0.328694i
$887$	−5.53757	−	3.19712i	−0.185934	−	0.107349i	0.404144	−	0.914695i	$-0.367569\pi$
$887$	−5.53757	−	3.19712i	−0.185934	−	0.107349i	−0.590077	+	0.807347i	$0.700903\pi$
$888$	−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
$891$	−10.8465	+	39.8171i	−0.363370	+	1.33392i
$892$	6.42216	−	23.9678i	0.215030	−	0.802503i
$893$	−3.08172	+	1.77923i	−0.103126	+	0.0595397i
$894$	1.55931	+	11.9400i	0.0521511	+	0.399332i
$895$	33.0525	+	33.0525i	1.10482	+	1.10482i
$896$	1.50084	+	2.17887i	0.0501396	+	0.0727910i
$897$	14.9240	−	37.9066i	0.498297	−	1.26566i
$898$	−9.51518	+	16.4808i	−0.317526	+	0.549971i
$899$	−4.19790	+	15.6668i	−0.140008	+	0.522517i
$900$	−1.95985	+	0.520778i	−0.0653283	+	0.0173593i
$901$	20.4569	+	11.8108i	0.681517	+	0.393474i
$902$	−8.94647	−	8.94647i	−0.297885	−	0.297885i
$903$	−41.5287	−	2.17631i	−1.38199	−	0.0724230i
$904$	−6.73624	−	6.73624i	−0.224044	−	0.224044i
$905$	−10.9361	−	40.8140i	−0.363528	−	1.35670i
$906$	2.48772	+	1.03347i	0.0826488	+	0.0343349i
$907$	−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	$-0.944281\pi$
$911$		−	10.5129i		−	0.348308i	0.984718	−	0.174154i	$-0.0557190\pi$
$912$	1.31974	−	1.71623i	0.0437010	−	0.0568299i
$913$	−31.6066	−	54.7443i	−1.04603	−	1.81177i
$914$	−19.6250	−	33.9914i	−0.649136	−	1.12434i
$915$	19.5620	+	15.0428i	0.646699	+	0.497298i
$916$	20.6282	−	20.6282i	0.681573	−	0.681573i
$917$	−30.1518	−	5.55584i	−0.995702	−	0.183470i
$918$	28.3156	+	11.8322i	0.934553	+	0.390521i
$919$	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
$921$	−44.5090	+	18.3821i	−1.46662	+	0.605710i
$922$	20.3930	+	11.7739i	0.671609	+	0.387753i
$923$	−10.3343	+	41.6646i	−0.340158	+	1.37141i
$924$	−4.36883	−	20.5534i	−0.143724	−	0.676158i
$925$	−0.866108	+	0.866108i	−0.0284775	+	0.0284775i
$926$	−30.7712	−	17.7657i	−1.01120	−	0.583819i
$927$	−5.69808	−	21.4436i	−0.187149	−	0.704301i
$928$	2.54180	+	0.681073i	0.0834386	+	0.0223573i
$929$	1.97456	−	0.529082i	0.0647833	−	0.0173586i	−0.226282	−	0.974062i	$-0.572657\pi$
$929$	1.97456	−	0.529082i	0.0647833	−	0.0173586i	0.291065	+	0.956703i	$0.405990\pi$
$930$	3.34603	−	25.2132i	0.109721	−	0.826773i
$931$	7.08933	+	5.12817i	0.232344	+	0.168069i
$932$		−	3.34881i		−	0.109694i
$933$	−15.8078	+	2.06444i	−0.517525	+	0.0675866i
$934$	1.82710	−	6.81885i	0.0597847	−	0.223119i
$935$	32.2590	+	55.8743i	1.05498	+	1.82728i
$936$	−5.56301	−	9.27647i	−0.181833	−	0.303211i
$937$	−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	−0.999858	−	0.0168317i	$-0.994642\pi$
$941$	−3.85102	+	14.3722i	−0.125540	+	0.468521i	0.874319	+	0.485352i	$0.161309\pi$
$942$	−14.0230	+	5.79145i	−0.456894	+	0.188696i
$943$	−17.3865	+	4.65871i	−0.566184	+	0.151709i
$944$	−8.70315	+	8.70315i	−0.283264	+	0.283264i
$945$	−17.8955	+	27.4319i	−0.582140	+	0.892358i
$946$			41.6107i			1.35288i
$947$	1.23758	+	4.61870i	0.0402158	+	0.150087i	0.983114	−	0.182993i	$-0.0585786\pi$
$947$	1.23758	+	4.61870i	0.0402158	+	0.150087i	−0.942898	+	0.333080i	$0.891912\pi$
$948$	−12.1908	−	5.06445i	−0.395940	−	0.164486i
$949$	38.1673	−	10.9946i	1.23896	−	0.356899i
$950$	−0.731714	−	0.422455i	−0.0237399	−	0.0137063i
$951$	−3.74366	+	28.2095i	−0.121397	+	0.914755i
$952$	−15.5763	+	1.24220i	−0.504830	+	0.0402601i
$953$	28.4119			0.920353			0.460176	−	0.887828i	$-0.347786\pi$
$953$	28.4119			0.920353			0.460176	+	0.887828i	$0.347786\pi$
$954$	11.9988	+	0.0249273i	0.388476	+	0.000807052i
$955$	27.1288	+	7.26914i	0.877867	+	0.235224i
$956$	−15.5769	−	4.17382i	−0.503794	−	0.134991i
$957$	−16.5672	−	12.7398i	−0.535541	−	0.411820i
$958$	23.9076			0.772420
$959$	28.9183	−	2.30623i	0.933819	−	0.0744719i
$960$	−4.09062	−	0.542863i	−0.132024	−	0.0175208i
$961$	6.05418	+	3.49538i	0.195296	+	0.112754i
$962$	−5.71813	−	3.16052i	−0.184360	−	0.101899i
$963$	−4.26224	−	16.0401i	−0.137349	−	0.516886i
$964$	−0.0441972	−	0.164946i	−0.00142350	−	0.00531256i
$965$			34.1802i			1.10030i
$966$	−28.4309	−	9.23766i	−0.914748	−	0.297217i
$967$	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
$969$	4.88084	+	11.8181i	0.156795	+	0.379652i
$970$	−3.40284	+	12.6996i	−0.109259	+	0.407759i
$971$	30.0030	+	17.3223i	0.962843	+	0.555898i	0.897047	−	0.441935i	$-0.145708\pi$
$971$	30.0030	+	17.3223i	0.962843	+	0.555898i	0.0657963	+	0.997833i	$0.479041\pi$
$972$	15.4655	−	1.95441i	0.496055	−	0.0626876i
$973$	−34.0759	+	12.1069i	−1.09242	+	0.388128i
$974$	22.0362			0.706086
$975$	−3.30317	+	2.62843i	−0.105786	+	0.0841770i
$976$	2.99008	+	5.17897i	0.0957101	+	0.165775i
$977$	4.51000	−	16.8316i	0.144288	−	0.538489i	−0.855498	−	0.517806i	$-0.826749\pi$
$977$	4.51000	−	16.8316i	0.144288	−	0.538489i	0.999786	−	0.0206835i	$-0.00658424\pi$
$978$	−1.15522	−	8.84574i	−0.0369398	−	0.282856i
$979$			43.8867i			1.40262i
$980$	1.70866	−	16.5892i	0.0545813	−	0.529923i
$981$	26.1850	+	45.5722i	0.836024	+	1.45501i
$982$	−14.2139	+	3.80860i	−0.453584	+	0.121537i
$983$	−5.70148	−	1.52771i	−0.181849	−	0.0487263i	0.166745	−	0.986000i	$-0.446674\pi$
$983$	−5.70148	−	1.52771i	−0.181849	−	0.0487263i	−0.348594	+	0.937274i	$0.613341\pi$
$984$	−1.83351	+	4.41352i	−0.0584502	+	0.140698i
$985$	21.2583	+	12.2735i	0.677346	+	0.391066i
$986$	−10.9894	+	10.9894i	−0.349973	+	0.349973i
$987$	12.7609	−	2.71246i	0.406185	−	0.0863385i
$988$	1.08496	−	4.37423i	0.0345173	−	0.139163i
$989$	51.2671	+	29.5991i	1.63020	+	0.941196i
$990$	28.3478	+	16.4452i	0.900953	+	0.522664i
$991$	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
$993$	−36.1983	−	4.80385i	−1.14872	−	0.152446i
$994$	30.9784	+	5.70814i	0.982575	+	0.181051i
$995$	−8.19569	+	8.19569i	−0.259821	+	0.259821i
$996$	−14.5557	+	18.9286i	−0.461215	+	0.599776i
$997$	−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
$999$	7.48780	−	5.70861i	0.236903	−	0.180612i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.664489 - 1.59952i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30125 - 0.616617i) q^{5} +(-0.227862 + 1.71700i) q^{6} +(2.49307 - 0.885767i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.11691 - 2.12572i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.664489 - 1.59952i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30125 - 0.616617i) q^{5} +(-0.227862 + 1.71700i) q^{6} +(2.49307 - 0.885767i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.11691 - 2.12572i) q^{9} +(-2.06324 + 1.19121i) q^{10} +(4.42909 + 1.18677i) q^{11} +(-0.224294 - 1.71747i) q^{12} +(-1.86076 - 3.08830i) q^{13} +(-2.17887 + 1.50084i) q^{14} +(0.542863 - 4.09062i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.95298 + 5.11472i) q^{17} +(2.59495 + 1.50539i) q^{18} +(0.323512 + 1.20736i) q^{19} +(1.68463 - 1.68463i) q^{20} +(0.239820 - 4.57630i) q^{21} -4.58533 q^{22} +(-3.26170 + 5.64943i) q^{23} +(0.661165 + 1.60089i) 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} +(0.534364 + 4.09174i) q^{30} +(-5.95364 - 1.59527i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(4.84134 - 6.29581i) 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} +(-6.17624 + 0.924172i) q^{39} +(-1.19121 + 2.06324i) q^{40} +(1.95111 + 1.95111i) q^{41} +(0.952784 + 4.48243i) q^{42} -9.07474i q^{43} +(4.42909 - 1.18677i) q^{44} +(-6.18229 - 3.58649i) 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} +(10.1433 - 1.32467i) q^{51} +(-3.15561 - 1.74417i) q^{52} +(3.46376 - 1.99980i) q^{53} +(4.13222 - 3.15036i) q^{54} +10.9242 q^{55} +(-1.13654 + 2.38920i) q^{56} +(2.14617 + 0.284816i) q^{57} +(0.681073 + 2.54180i) q^{58} +(-11.8887 - 3.18558i) q^{59} +(-1.57518 - 3.81401i) q^{60} +(-2.99008 + 5.17897i) q^{61} +6.16367 q^{62} +(-7.16051 - 3.42450i) q^{63} -1.00000i q^{64} +(-6.18636 - 5.95956i) q^{65} +(-3.04690 + 7.33431i) 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} +(2.99999 + 0.00623244i) q^{72} +(-2.85119 + 10.6408i) q^{73} +(1.56928 - 0.906026i) q^{74} +(-0.151612 - 1.16093i) q^{75} +(0.883851 + 0.883851i) q^{76} +(12.0932 - 0.964434i) q^{77} +(5.72659 - 2.49121i) q^{78} +(3.81078 - 6.60047i) q^{79} +(0.616617 - 2.30125i) q^{80} +(-0.0373946 + 8.99992i) q^{81} +(-2.38961 - 1.37964i) q^{82} +(-9.74816 - 9.74816i) q^{83} +(-2.08046 - 4.08310i) q^{84} +(9.94937 + 9.94937i) q^{85} +(2.34872 + 8.76553i) q^{86} +(-4.20907 - 1.74858i) 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} +(-6.50780 + 8.46291i) q^{93} +(-1.42344 - 2.46547i) q^{94} +(1.48896 + 2.57896i) q^{95} +(1.37303 + 1.05583i) q^{96} +(3.90221 - 3.90221i) q^{97} +(-4.10269 + 5.67168i) q^{98} +(-6.85323 - 11.9273i) 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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