LMFDB - Embedded newform 462.2.y.d.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	462.235
Dual form			462.2.y.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.99535 - 1.77885i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.64091 + 0.160013i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.99535 - 1.77885i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.64091 + 0.160013i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(2.18673 - 3.78753i) q^{10} +(-1.81292 + 2.77729i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.79377 + 2.75634i) q^{13} +(-0.435186 + 2.60972i) q^{14} +(1.35147 + 4.15941i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.0781270 + 0.743329i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-3.87014 + 0.822624i) q^{19} +(3.53820 + 2.57065i) q^{20} +(-1.64820 - 2.06965i) q^{21} +(-2.57257 - 2.09329i) q^{22} +(2.65310 + 4.59530i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(9.45290 + 10.4985i) q^{25} +(-3.13780 + 3.48488i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.54993 - 0.705592i) q^{28} +(0.839781 + 2.58458i) q^{29} +(-4.27789 + 0.909293i) q^{30} +(-6.91022 + 3.07663i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.27701 - 0.511105i) q^{33} -0.747424 q^{34} +(-10.2667 - 5.33708i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-2.02801 + 2.25234i) q^{37} +(-0.413578 - 3.93493i) q^{38} +(-0.490172 - 4.66367i) q^{39} +(-2.92641 + 3.25011i) q^{40} +(1.28635 - 3.95899i) q^{41} +(2.23059 - 1.42283i) q^{42} +4.23100 q^{43} +(2.35073 - 2.33967i) q^{44} +(2.18673 - 3.78753i) q^{45} +(-4.84745 + 2.15823i) q^{46} +(11.4851 - 2.44124i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(6.94879 + 0.845159i) q^{49} +(-11.4291 + 8.30372i) q^{50} +(0.500124 - 0.555444i) q^{51} +(-3.13780 - 3.48488i) q^{52} +(-10.0318 + 4.46645i) q^{53} +(0.500000 + 0.866025i) q^{54} +(12.1836 - 7.87133i) q^{55} +(0.968267 - 2.46221i) q^{56} +(3.20096 + 2.32563i) q^{57} +(-2.65820 + 0.565019i) q^{58} +(7.20436 + 1.53133i) q^{59} +(-0.457151 - 4.34950i) q^{60} +(-7.12556 - 3.17250i) q^{61} +(-2.33746 - 7.19396i) q^{62} +(-0.435186 + 2.60972i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-10.2544 - 17.7611i) q^{65} +(0.165764 + 3.31248i) q^{66} +(-0.607017 + 1.05138i) q^{67} +(0.0781270 - 0.743329i) q^{68} +(1.63971 - 5.04649i) q^{69} +(6.38100 - 9.65260i) q^{70} +(-5.79643 + 4.21135i) q^{71} +(0.913545 + 0.406737i) q^{72} +(-2.29344 - 0.487485i) q^{73} +(-2.02801 - 2.25234i) q^{74} +(1.47669 - 14.0498i) q^{75} +3.95660 q^{76} +(-5.23216 + 7.04447i) q^{77} +4.68936 q^{78} +(-0.753990 + 7.17373i) q^{79} +(-2.92641 - 3.25011i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(3.80284 + 1.69313i) q^{82} +(-9.08761 + 6.60254i) q^{83} +(1.18188 + 2.36710i) q^{84} +(1.01012 - 3.10884i) q^{85} +(-0.442260 + 4.20783i) q^{86} +(1.35879 - 2.35350i) q^{87} +(2.08113 + 2.58242i) q^{88} +(1.31108 + 2.27086i) q^{89} +(3.53820 + 2.57065i) q^{90} +(9.57796 + 7.88629i) q^{91} +(-1.63971 - 5.04649i) q^{92} +(6.91022 + 3.07663i) q^{93} +(1.22734 + 11.6774i) q^{94} +(16.9259 + 3.59771i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-7.68168 - 5.58107i) q^{97} +(-1.56688 + 6.82238i) q^{98} +(-2.57257 - 2.09329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−3.99535	−	1.77885i	−1.78678	−	0.795524i	−0.978359	−	0.206914i	$-0.933658\pi$
$5$	−3.99535	−	1.77885i	−1.78678	−	0.795524i	−0.808417	−	0.588610i	$-0.799675\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	2.64091	+	0.160013i	0.998169	+	0.0604792i
$7$	2.64091	+	0.160013i	0.998169	+	0.0604792i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	2.18673	−	3.78753i	0.691505	−	1.19772i
$11$	−1.81292	+	2.77729i	−0.546616	+	0.837383i
$11$	−1.81292	+	2.77729i	−0.546616	+	0.837383i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.79377	+	2.75634i	1.05220	+	0.764471i	0.972630	−	0.232358i	$-0.0746442\pi$
$13$	3.79377	+	2.75634i	1.05220	+	0.764471i	0.0795733	+	0.996829i	$0.474644\pi$
$14$	−0.435186	+	2.60972i	−0.116308	+	0.697476i
$15$	1.35147	+	4.15941i	0.348949	+	1.07395i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.0781270	+	0.743329i	0.0189486	+	0.180284i	0.999903	−	0.0139563i	$-0.00444258\pi$
$17$	0.0781270	+	0.743329i	0.0189486	+	0.180284i	−0.980954	+	0.194240i	$0.937776\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	−3.87014	+	0.822624i	−0.887871	+	0.188723i	−0.629201	−	0.777243i	$-0.716618\pi$
$19$	−3.87014	+	0.822624i	−0.887871	+	0.188723i	−0.258670	+	0.965966i	$0.583284\pi$
$20$	3.53820	+	2.57065i	0.791166	+	0.574816i
$21$	−1.64820	−	2.06965i	−0.359667	−	0.451634i
$22$	−2.57257	−	2.09329i	−0.548474	−	0.446292i
$23$	2.65310	+	4.59530i	0.553209	+	0.958187i	0.998040	+	0.0625724i	$0.0199304\pi$
$23$	2.65310	+	4.59530i	0.553209	+	0.958187i	−0.444831	+	0.895615i	$0.646736\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	9.45290	+	10.4985i	1.89058	+	2.09970i
$26$	−3.13780	+	3.48488i	−0.615372	+	0.683440i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−2.54993	−	0.705592i	−0.481891	−	0.133344i
$29$	0.839781	+	2.58458i	0.155943	+	0.479945i	0.998255	−	0.0590459i	$-0.0188058\pi$
$29$	0.839781	+	2.58458i	0.155943	+	0.479945i	−0.842312	+	0.538991i	$0.818806\pi$
$30$	−4.27789	+	0.909293i	−0.781032	+	0.166013i
$31$	−6.91022	+	3.07663i	−1.24111	+	0.552578i	−0.919050	−	0.394140i	$-0.871042\pi$
$31$	−6.91022	+	3.07663i	−1.24111	+	0.552578i	−0.322061	+	0.946719i	$0.604376\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.27701	−	0.511105i	0.570454	−	0.0889719i
$34$	−0.747424			−0.128182
$35$	−10.2667	−	5.33708i	−1.73539	−	0.902131i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−2.02801	+	2.25234i	−0.333404	+	0.370282i	−0.886415	−	0.462892i	$-0.846812\pi$
$37$	−2.02801	+	2.25234i	−0.333404	+	0.370282i	0.553011	+	0.833174i	$0.313479\pi$
$38$	−0.413578	−	3.93493i	−0.0670911	−	0.638330i
$39$	−0.490172	−	4.66367i	−0.0784903	−	0.746785i
$40$	−2.92641	+	3.25011i	−0.462707	+	0.513888i
$41$	1.28635	−	3.95899i	0.200895	−	0.618290i	−0.798962	−	0.601381i	$-0.794617\pi$
$41$	1.28635	−	3.95899i	0.200895	−	0.618290i	0.999857	−	0.0169093i	$-0.00538264\pi$
$42$	2.23059	−	1.42283i	0.344188	−	0.219548i
$43$	4.23100			0.645222			0.322611	−	0.946532i	$-0.395439\pi$
$43$	4.23100			0.645222			0.322611	+	0.946532i	$0.395439\pi$
$44$	2.35073	−	2.33967i	0.354387	−	0.352718i
$45$	2.18673	−	3.78753i	0.325978	−	0.564611i
$46$	−4.84745	+	2.15823i	−0.714718	+	0.318213i
$47$	11.4851	−	2.44124i	1.67528	−	0.356091i	0.730275	−	0.683154i	$-0.239392\pi$
$47$	11.4851	−	2.44124i	1.67528	−	0.356091i	0.945003	+	0.327063i	$0.106059\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	6.94879	+	0.845159i	0.992685	+	0.120737i
$50$	−11.4291	+	8.30372i	−1.61632	+	1.17432i
$51$	0.500124	−	0.555444i	0.0700314	−	0.0777777i
$52$	−3.13780	−	3.48488i	−0.435134	−	0.483265i
$53$	−10.0318	+	4.46645i	−1.37798	+	0.613515i	−0.956074	−	0.293126i	$-0.905304\pi$
$53$	−10.0318	+	4.46645i	−1.37798	+	0.613515i	−0.421903	+	0.906641i	$0.638638\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	12.1836	−	7.87133i	1.64284	−	1.06137i
$56$	0.968267	−	2.46221i	0.129390	−	0.329026i
$57$	3.20096	+	2.32563i	0.423977	+	0.308038i
$58$	−2.65820	+	0.565019i	−0.349039	+	0.0741906i
$59$	7.20436	+	1.53133i	0.937928	+	0.199363i	0.651422	−	0.758716i	$-0.274173\pi$
$59$	7.20436	+	1.53133i	0.937928	+	0.199363i	0.286506	+	0.958078i	$0.407506\pi$
$60$	−0.457151	−	4.34950i	−0.0590179	−	0.561518i
$61$	−7.12556	−	3.17250i	−0.912335	−	0.406198i	−0.103768	−	0.994602i	$-0.533090\pi$
$61$	−7.12556	−	3.17250i	−0.912335	−	0.406198i	−0.808567	+	0.588404i	$0.799756\pi$
$62$	−2.33746	−	7.19396i	−0.296857	−	0.913633i
$63$	−0.435186	+	2.60972i	−0.0548283	+	0.328793i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−10.2544	−	17.7611i	−1.27190	−	2.20299i
$66$	0.165764	+	3.31248i	0.0204042	+	0.407738i
$67$	−0.607017	+	1.05138i	−0.0741589	+	0.128447i	−0.900720	−	0.434400i	$-0.856961\pi$
$67$	−0.607017	+	1.05138i	−0.0741589	+	0.128447i	0.826561	+	0.562847i	$0.190294\pi$
$68$	0.0781270	−	0.743329i	0.00947429	−	0.0901419i
$69$	1.63971	−	5.04649i	0.197397	−	0.607527i
$70$	6.38100	−	9.65260i	0.762676	−	1.15371i
$71$	−5.79643	+	4.21135i	−0.687909	+	0.499795i	−0.875972	−	0.482362i	$-0.839779\pi$
$71$	−5.79643	+	4.21135i	−0.687909	+	0.499795i	0.188063	+	0.982157i	$0.439779\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	−2.29344	−	0.487485i	−0.268427	−	0.0570558i	0.0717319	−	0.997424i	$-0.477147\pi$
$73$	−2.29344	−	0.487485i	−0.268427	−	0.0570558i	−0.340158	+	0.940368i	$0.610481\pi$
$74$	−2.02801	−	2.25234i	−0.235752	−	0.261829i
$75$	1.47669	−	14.0498i	0.170513	−	1.62233i
$76$	3.95660			0.453853
$77$	−5.23216	+	7.04447i	−0.596260	+	0.802792i
$78$	4.68936			0.530966
$79$	−0.753990	+	7.17373i	−0.0848305	+	0.807108i	0.866550	+	0.499090i	$0.166332\pi$
$79$	−0.753990	+	7.17373i	−0.0848305	+	0.807108i	−0.951381	+	0.308018i	$0.900334\pi$
$80$	−2.92641	−	3.25011i	−0.327183	−	0.363374i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	3.80284	+	1.69313i	0.419954	+	0.186975i
$83$	−9.08761	+	6.60254i	−0.997495	+	0.724723i	−0.961550	−	0.274631i	$-0.911444\pi$
$83$	−9.08761	+	6.60254i	−0.997495	+	0.724723i	−0.0359455	+	0.999354i	$0.511444\pi$
$84$	1.18188	+	2.36710i	0.128954	+	0.258272i
$85$	1.01012	−	3.10884i	0.109563	−	0.337201i
$86$	−0.442260	+	4.20783i	−0.0476902	+	0.453742i
$87$	1.35879	−	2.35350i	0.145678	−	0.252322i
$88$	2.08113	+	2.58242i	0.221850	+	0.275287i
$89$	1.31108	+	2.27086i	0.138974	+	0.240710i	0.927109	−	0.374793i	$-0.122286\pi$
$89$	1.31108	+	2.27086i	0.138974	+	0.240710i	−0.788134	+	0.615503i	$0.788953\pi$
$90$	3.53820	+	2.57065i	0.372959	+	0.270971i
$91$	9.57796	+	7.88629i	1.00404	+	0.826708i
$92$	−1.63971	−	5.04649i	−0.170951	−	0.526133i
$93$	6.91022	+	3.07663i	0.716556	+	0.319031i
$94$	1.22734	+	11.6774i	0.126591	+	1.20443i
$95$	16.9259	+	3.59771i	1.73656	+	0.369117i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	−7.68168	−	5.58107i	−0.779956	−	0.566672i	0.125009	−	0.992156i	$-0.460104\pi$
$97$	−7.68168	−	5.58107i	−0.779956	−	0.566672i	−0.904966	+	0.425484i	$0.860104\pi$
$98$	−1.56688	+	6.82238i	−0.158278	+	0.689165i
$99$	−2.57257	−	2.09329i	−0.258553	−	0.210384i
$100$	−7.06357	−	12.2345i	−0.706357	−	1.22345i
$101$	5.66095	−	2.52042i	0.563286	−	0.250791i	−0.105282	−	0.994442i	$-0.533574\pi$
$101$	5.66095	−	2.52042i	0.563286	−	0.250791i	0.668568	+	0.743651i	$0.266908\pi$
$102$	0.500124	+	0.555444i	0.0495196	+	0.0549971i
$103$	−4.79177	+	5.32179i	−0.472147	+	0.524372i	−0.931431	−	0.363917i	$-0.881439\pi$
$103$	−4.79177	+	5.32179i	−0.472147	+	0.524372i	0.459285	+	0.888289i	$0.348106\pi$
$104$	3.79377	−	2.75634i	0.372010	−	0.270281i
$105$	2.90356	+	11.2009i	0.283358	+	1.09309i
$106$	−3.39338	−	10.4437i	−0.329594	−	1.01439i
$107$	3.53093	−	0.750522i	0.341348	−	0.0725557i	−0.0340483	−	0.999420i	$-0.510840\pi$
$107$	3.53093	−	0.750522i	0.341348	−	0.0725557i	0.375396	+	0.926864i	$0.377507\pi$
$108$	−0.913545	+	0.406737i	−0.0879060	+	0.0391383i
$109$	3.07422	−	5.32471i	0.294457	−	0.510015i	−0.680401	−	0.732840i	$-0.738195\pi$
$109$	3.07422	−	5.32471i	0.294457	−	0.510015i	0.974858	+	0.222825i	$0.0715278\pi$
$110$	6.55468	+	12.9397i	0.624964	+	1.23375i
$111$	3.03082			0.287673
$112$	2.34751	+	1.22033i	0.221819	+	0.115311i
$113$	−3.15607	+	9.71337i	−0.296898	+	0.913757i	0.685680	+	0.727903i	$0.259505\pi$
$113$	−3.15607	+	9.71337i	−0.296898	+	0.913757i	−0.982577	+	0.185854i	$0.940495\pi$
$114$	−2.64748	+	2.94033i	−0.247960	+	0.275387i
$115$	−2.42573	−	23.0793i	−0.226201	−	2.15216i
$116$	−0.284065	−	2.70270i	−0.0263748	−	0.250940i
$117$	−3.13780	+	3.48488i	−0.290089	+	0.322177i
$118$	−2.27601	+	7.00482i	−0.209523	+	0.644846i
$119$	0.0873841	+	1.97557i	0.00801049	+	0.181100i
$120$	4.37346			0.399240
$121$	−4.42664	−	10.0700i	−0.402422	−	0.915454i
$122$	3.89995	−	6.75491i	0.353085	−	0.611561i
$123$	−3.80284	+	1.69313i	−0.342891	+	0.152665i
$124$	7.39888	−	1.57268i	0.664439	−	0.141231i
$125$	−12.3351	−	37.9635i	−1.10328	−	3.39556i
$126$	−2.54993	−	0.705592i	−0.227166	−	0.0628591i
$127$	13.4249	−	9.75378i	1.19127	−	0.865508i	0.197872	−	0.980228i	$-0.436597\pi$
$127$	13.4249	−	9.75378i	1.19127	−	0.865508i	0.993398	+	0.114720i	$0.0365970\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−2.83109	−	3.14425i	−0.249264	−	0.276836i
$130$	18.7357	−	8.34165i	1.64323	−	0.731611i
$131$	8.77427	+	15.1975i	0.766611	+	1.32781i	0.939390	+	0.342849i	$0.111392\pi$
$131$	8.77427	+	15.1975i	0.766611	+	1.32781i	−0.172779	+	0.984961i	$0.555275\pi$
$132$	−3.31166	−	0.181392i	−0.288243	−	0.0157882i
$133$	−10.3523	+	1.55320i	−0.897660	+	0.134680i
$134$	−0.982174	−	0.713591i	−0.0848469	−	0.0616449i
$135$	−4.27789	+	0.909293i	−0.368182	+	0.0782595i
$136$	0.731091	+	0.155398i	0.0626905	+	0.0133253i
$137$	0.624616	+	5.94283i	0.0533646	+	0.507730i	0.988257	+	0.152799i	$0.0488289\pi$
$137$	0.624616	+	5.94283i	0.0533646	+	0.507730i	−0.934893	+	0.354931i	$0.884504\pi$
$138$	4.84745	+	2.15823i	0.412643	+	0.183720i
$139$	5.00242	+	15.3959i	0.424300	+	1.30586i	0.903663	+	0.428244i	$0.140868\pi$
$139$	5.00242	+	15.3959i	0.424300	+	1.30586i	−0.479363	+	0.877616i	$0.659132\pi$
$140$	8.93273	+	7.35502i	0.754953	+	0.621613i
$141$	−9.49924	−	6.90160i	−0.799980	−	0.581220i
$142$	−3.58239	−	6.20488i	−0.300627	−	0.520702i
$143$	−14.5330	+	5.53937i	−1.21531	+	0.463226i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.24235	−	11.8202i	0.103171	−	0.981611i
$146$	0.724544	−	2.22992i	0.0599637	−	0.184549i
$147$	−4.02157	−	5.72948i	−0.331694	−	0.472560i
$148$	2.45199	−	1.78147i	0.201552	−	0.146436i
$149$	−14.0344	−	6.24852i	−1.14974	−	0.511898i	−0.258763	−	0.965941i	$-0.583315\pi$
$149$	−14.0344	−	6.24852i	−1.14974	−	0.511898i	−0.890980	+	0.454043i	$0.849981\pi$
$150$	13.8184	+	2.93720i	1.12827	+	0.239821i
$151$	2.26070	+	2.51076i	0.183973	+	0.204323i	0.828076	−	0.560616i	$-0.189436\pi$
$151$	2.26070	+	2.51076i	0.183973	+	0.204323i	−0.644103	+	0.764939i	$0.722769\pi$
$152$	−0.413578	+	3.93493i	−0.0335456	+	0.319165i
$153$	−0.747424			−0.0604256
$154$	−6.45897	−	5.93984i	−0.520478	−	0.478646i
$155$	33.0816			2.65718
$156$	−0.490172	+	4.66367i	−0.0392452	+	0.373393i
$157$	−9.70858	−	10.7825i	−0.774829	−	0.860535i	0.218501	−	0.975837i	$-0.429883\pi$
$157$	−9.70858	−	10.7825i	−0.774829	−	0.860535i	−0.993331	+	0.115301i	$0.963217\pi$
$158$	−7.05562	−	1.49972i	−0.561315	−	0.119311i
$159$	10.0318	+	4.46645i	0.795575	+	0.354213i
$160$	3.53820	−	2.57065i	0.279719	−	0.203228i
$161$	6.27128	+	12.5603i	0.494246	+	0.989891i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	1.74962	−	16.6465i	0.137041	−	1.30385i	−0.682522	−	0.730865i	$-0.739117\pi$
$163$	1.74962	−	16.6465i	0.137041	−	1.30385i	0.819563	−	0.572989i	$-0.194216\pi$
$164$	−2.08136	+	3.60503i	−0.162527	+	0.281505i
$165$	−14.0020	−	3.78725i	−1.09005	−	0.294837i
$166$	−5.61645	−	9.72798i	−0.435921	−	0.755038i
$167$	−6.63946	−	4.82385i	−0.513777	−	0.373281i	0.300478	−	0.953789i	$-0.402854\pi$
$167$	−6.63946	−	4.82385i	−0.513777	−	0.373281i	−0.814254	+	0.580508i	$0.802854\pi$
$168$	−2.47767	+	0.927975i	−0.191157	+	0.0715948i
$169$	2.77810	+	8.55011i	0.213700	+	0.657701i
$170$	2.98622	+	1.32955i	0.229033	+	0.101972i
$171$	−0.413578	−	3.93493i	−0.0316271	−	0.300911i
$172$	−4.13855	−	0.879675i	−0.315561	−	0.0670746i
$173$	−2.14652	+	0.456257i	−0.163197	+	0.0346886i	−0.288786	−	0.957394i	$-0.593251\pi$
$173$	−2.14652	+	0.456257i	−0.163197	+	0.0346886i	0.125588	+	0.992082i	$0.459918\pi$
$174$	2.19858	+	1.59736i	0.166674	+	0.121095i
$175$	23.2843	+	29.2382i	1.76013	+	2.21020i
$176$	−2.78581	+	1.79980i	−0.209988	+	0.135665i
$177$	−3.68265	−	6.37854i	−0.276805	−	0.479441i
$178$	−2.39546	+	1.06653i	−0.179547	+	0.0799396i
$179$	2.65179	+	2.94511i	0.198204	+	0.220128i	0.834051	−	0.551687i	$-0.186016\pi$
$179$	2.65179	+	2.94511i	0.198204	+	0.220128i	−0.635847	+	0.771815i	$0.719349\pi$
$180$	−2.92641	+	3.25011i	−0.218122	+	0.242249i
$181$	−8.63582	+	6.27429i	−0.641895	+	0.466364i	−0.860501	−	0.509449i	$-0.829849\pi$
$181$	−8.63582	+	6.27429i	−0.641895	+	0.466364i	0.218606	+	0.975813i	$0.429849\pi$
$182$	−8.84426	+	8.70115i	−0.655580	+	0.644972i
$183$	2.41030	+	7.41814i	0.178175	+	0.548365i
$184$	5.19025	−	1.10322i	0.382630	−	0.0813305i
$185$	12.1092	−	5.39136i	0.890286	−	0.396381i
$186$	−3.78209	+	6.55077i	−0.277316	+	0.480325i
$187$	−2.20608	−	1.13062i	−0.161324	−	0.0826788i
$188$	−11.7417			−0.856352
$189$	2.23059	−	1.42283i	0.162252	−	0.103496i
$190$	−5.34724	+	16.4571i	−0.387930	+	1.19392i
$191$	−0.586303	+	0.651156i	−0.0424234	+	0.0471160i	−0.763983	−	0.645236i	$-0.776759\pi$
$191$	−0.586303	+	0.651156i	−0.0424234	+	0.0471160i	0.721560	+	0.692352i	$0.243426\pi$
$192$	0.104528	+	0.994522i	0.00754369	+	0.0717734i
$193$	2.46277	+	23.4317i	0.177274	+	1.68665i	0.615777	+	0.787920i	$0.288842\pi$
$193$	2.46277	+	23.4317i	0.177274	+	1.68665i	−0.438503	+	0.898730i	$0.644491\pi$
$194$	6.35345	−	7.05622i	0.456151	−	0.506607i
$195$	−6.33755	+	19.5050i	−0.453841	+	1.39678i
$196$	−6.62123	−	2.27143i	−0.472945	−	0.162245i
$197$	−3.94787			−0.281274			−0.140637	−	0.990061i	$-0.544915\pi$
$197$	−3.94787			−0.281274			−0.140637	+	0.990061i	$0.544915\pi$
$198$	2.35073	−	2.33967i	0.167059	−	0.166273i
$199$	8.01302	−	13.8790i	0.568028	−	0.983853i	−0.428733	−	0.903431i	$-0.641040\pi$
$199$	8.01302	−	13.8790i	0.568028	−	0.983853i	0.996761	−	0.0804221i	$-0.0256268\pi$
$200$	12.9058	−	5.74603i	0.912577	−	0.406305i
$201$	1.18750	−	0.252412i	0.0837601	−	0.0178038i
$202$	1.91488	+	5.89340i	0.134731	+	0.414658i
$203$	1.80422	+	6.96002i	0.126631	+	0.488498i
$204$	−0.604678	+	0.439325i	−0.0423360	+	0.0307589i
$205$	−12.1819	+	13.5293i	−0.850819	+	0.944930i
$206$	−4.79177	−	5.32179i	−0.333858	−	0.370787i
$207$	−4.84745	+	2.15823i	−0.336921	+	0.150007i
$208$	2.34468	+	4.06111i	0.162574	+	0.281587i
$209$	4.73160	−	12.2398i	0.327291	−	0.846648i
$210$	−11.4430	+	1.71684i	−0.789643	+	0.118473i
$211$	−4.76541	−	3.46227i	−0.328064	−	0.238353i	0.411545	−	0.911390i	$-0.364989\pi$
$211$	−4.76541	−	3.46227i	−0.328064	−	0.238353i	−0.739609	+	0.673037i	$0.764989\pi$
$212$	10.7412	−	2.28312i	0.737711	−	0.156805i
$213$	7.00821	+	1.48964i	0.480195	+	0.102068i
$214$	0.377328	+	3.59004i	0.0257936	+	0.245410i
$215$	−16.9044	−	7.52630i	−1.15287	−	0.513290i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−18.7415	+	7.01936i	−1.27226	+	0.476505i
$218$	4.97420	+	3.61397i	0.336895	+	0.244769i
$219$	1.17234	+	2.03055i	0.0792192	+	0.137212i
$220$	−13.5539	+	5.16621i	−0.913805	+	0.348306i
$221$	−1.75247	+	3.03537i	−0.117884	+	0.204181i
$222$	−0.316807	+	3.01422i	−0.0212627	+	0.202301i
$223$	−4.78394	+	14.7234i	−0.320356	+	0.985955i	0.653137	+	0.757240i	$0.273452\pi$
$223$	−4.78394	+	14.7234i	−0.320356	+	0.985955i	−0.973493	+	0.228715i	$0.926548\pi$
$224$	−1.45903	+	2.20709i	−0.0974855	+	0.147467i
$225$	−11.4291	+	8.30372i	−0.761940	+	0.553582i
$226$	−9.33026	−	4.15410i	−0.620640	−	0.276327i
$227$	2.75168	+	0.584888i	0.182635	+	0.0388203i	0.298321	−	0.954465i	$-0.403573\pi$
$227$	2.75168	+	0.584888i	0.182635	+	0.0388203i	−0.115686	+	0.993286i	$0.536907\pi$
$228$	−2.64748	−	2.94033i	−0.175334	−	0.194728i
$229$	−1.40444	+	13.3623i	−0.0928078	+	0.883007i	0.844746	+	0.535167i	$0.179751\pi$
$229$	−1.40444	+	13.3623i	−0.0928078	+	0.883007i	−0.937554	+	0.347840i	$0.886915\pi$
$230$	23.2064			1.53019
$231$	8.73606	−	0.825417i	0.574790	−	0.0543084i
$232$	2.71759			0.178419
$233$	0.826902	−	7.86745i	0.0541722	−	0.515414i	−0.933466	−	0.358665i	$-0.883232\pi$
$233$	0.826902	−	7.86745i	0.0541722	−	0.515414i	0.987639	−	0.156749i	$-0.0501013\pi$
$234$	−3.13780	−	3.48488i	−0.205124	−	0.227813i
$235$	−50.2297	−	10.6767i	−3.27662	−	0.696468i
$236$	−6.72854	−	2.99574i	−0.437991	−	0.195006i
$237$	5.83564	−	4.23984i	0.379066	−	0.275407i
$238$	−1.97388	−	0.119597i	−0.127947	−	0.00775235i
$239$	7.12975	−	21.9431i	0.461185	−	1.41938i	−0.402532	−	0.915406i	$-0.631870\pi$
$239$	7.12975	−	21.9431i	0.461185	−	1.41938i	0.863717	−	0.503977i	$-0.168130\pi$
$240$	−0.457151	+	4.34950i	−0.0295090	+	0.280759i
$241$	−10.8083	+	18.7206i	−0.696226	+	1.20590i	0.273540	+	0.961861i	$0.411805\pi$
$241$	−10.8083	+	18.7206i	−0.696226	+	1.20590i	−0.969766	+	0.244038i	$0.921528\pi$
$242$	10.4775	−	3.34979i	0.673522	−	0.215332i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	6.31025	+	4.58466i	0.403972	+	0.293503i
$245$	−26.2595	−	15.7375i	−1.67766	−	1.00543i
$246$	−1.28635	−	3.95899i	−0.0820149	−	0.252416i
$247$	−16.9499	−	7.54657i	−1.07849	−	0.480177i
$248$	0.790671	+	7.52274i	0.0502077	+	0.477694i
$249$	10.9874	+	2.33545i	0.696301	+	0.148003i
$250$	39.0449	−	8.29925i	2.46942	−	0.524890i
$251$	25.1239	+	18.2536i	1.58581	+	1.15216i	0.909631	+	0.415417i	$0.136364\pi$
$251$	25.1239	+	18.2536i	1.58581	+	1.15216i	0.676176	+	0.736740i	$0.263636\pi$
$252$	0.968267	−	2.46221i	0.0609951	−	0.155104i
$253$	−17.5723	−	0.962504i	−1.10476	−	0.0605121i
$254$	8.29706	+	14.3709i	0.520604	+	0.901713i
$255$	−2.98622	+	1.32955i	−0.187004	+	0.0832597i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−5.75979	+	6.39690i	−0.359286	+	0.399028i	−0.895505	−	0.445051i	$-0.853185\pi$
$257$	−5.75979	+	6.39690i	−0.359286	+	0.399028i	0.536219	+	0.844079i	$0.319852\pi$
$258$	3.42295	−	2.48692i	0.213104	−	0.154829i
$259$	−5.71620	+	5.62371i	−0.355188	+	0.349440i
$260$	6.33755	+	19.5050i	0.393038	+	1.20965i
$261$	−2.65820	+	0.565019i	−0.164539	+	0.0349738i
$262$	−16.0314	+	7.13763i	−0.990422	+	0.440964i
$263$	−0.891882	+	1.54478i	−0.0549958	+	0.0952555i	−0.892213	−	0.451616i	$-0.850848\pi$
$263$	−0.891882	+	1.54478i	−0.0549958	+	0.0952555i	0.837217	+	0.546871i	$0.184181\pi$
$264$	0.526561	−	3.27456i	0.0324076	−	0.201535i
$265$	48.0258			2.95020
$266$	−0.462581	−	10.4580i	−0.0283627	−	0.641219i
$267$	0.810291	−	2.49382i	0.0495890	−	0.152619i
$268$	0.812347	−	0.902203i	0.0496220	−	0.0551108i
$269$	−0.911335	−	8.67077i	−0.0555650	−	0.528666i	−0.986533	−	0.163564i	$-0.947701\pi$
$269$	−0.911335	−	8.67077i	−0.0555650	−	0.528666i	0.930968	−	0.365102i	$-0.118966\pi$
$270$	−0.457151	−	4.34950i	−0.0278213	−	0.264702i
$271$	2.98112	−	3.31087i	0.181090	−	0.201121i	−0.645764	−	0.763537i	$-0.723461\pi$
$271$	2.98112	−	3.31087i	0.181090	−	0.201121i	0.826855	+	0.562416i	$0.190128\pi$
$272$	−0.230967	+	0.710842i	−0.0140044	+	0.0431011i
$273$	−0.548251	−	12.3948i	−0.0331817	−	0.750165i
$274$	−5.97556			−0.360997
$275$	−46.2947	+	7.22045i	−2.79168	+	0.435409i
$276$	−2.65310	+	4.59530i	−0.159698	+	0.276605i
$277$	12.2137	−	5.43789i	0.733850	−	0.326731i	−0.00556203	−	0.999985i	$-0.501770\pi$
$277$	12.2137	−	5.43789i	0.733850	−	0.326731i	0.739412	+	0.673254i	$0.235104\pi$
$278$	−15.8344	+	3.36571i	−0.949685	+	0.201862i
$279$	−2.33746	−	7.19396i	−0.139940	−	0.430691i
$280$	−8.24845	+	8.11499i	−0.492939	+	0.484963i
$281$	10.7300	−	7.79578i	0.640097	−	0.465057i	−0.219787	−	0.975548i	$-0.570536\pi$
$281$	10.7300	−	7.79578i	0.640097	−	0.465057i	0.859883	+	0.510490i	$0.170536\pi$
$282$	7.85674	−	8.72579i	0.467862	−	0.519613i
$283$	1.75435	+	1.94841i	0.104285	+	0.115821i	0.793028	−	0.609186i	$-0.208504\pi$
$283$	1.75435	+	1.94841i	0.104285	+	0.115821i	−0.688742	+	0.725006i	$0.741837\pi$
$284$	6.54535	−	2.91418i	0.388395	−	0.172925i
$285$	−8.65202	−	14.9857i	−0.512501	−	0.887678i
$286$	−3.98992	−	15.0324i	−0.235929	−	0.888882i
$287$	4.03063	−	10.2495i	0.237921	−	0.605009i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	16.0821	−	3.41835i	0.946004	−	0.201079i
$290$	11.6255	+	2.47109i	0.682676	+	0.145107i
$291$	0.992506	+	9.44306i	0.0581817	+	0.553562i
$292$	2.14197	+	0.953665i	0.125349	+	0.0558090i
$293$	−7.50706	−	23.1044i	−0.438567	−	1.34977i	−0.889387	−	0.457156i	$-0.848868\pi$
$293$	−7.50706	−	23.1044i	−0.438567	−	1.34977i	0.450820	−	0.892615i	$-0.351132\pi$
$294$	6.11846	−	3.40065i	0.356836	−	0.198330i
$295$	−26.0600	−	18.9337i	−1.51727	−	1.10236i
$296$	1.51541	+	2.62477i	0.0880814	+	0.152562i
$297$	0.165764	+	3.31248i	0.00961861	+	0.192210i
$298$	7.68128	−	13.3044i	0.444965	−	0.770701i
$299$	−2.60095	+	24.7464i	−0.150417	+	1.43112i
$300$	−4.36553	+	13.4357i	−0.252044	+	0.775711i
$301$	11.1737	+	0.677015i	0.644041	+	0.0390225i
$302$	−2.73331	+	1.98587i	−0.157285	+	0.114274i
$303$	−5.66095	−	2.52042i	−0.325213	−	0.144794i
$304$	−3.87014	−	0.822624i	−0.221968	−	0.0471807i
$305$	22.8257	+	25.3505i	1.30700	+	1.45157i
$306$	0.0781270	−	0.743329i	0.00446623	−	0.0424933i
$307$	4.41790			0.252143			0.126072	−	0.992021i	$-0.459763\pi$
$307$	4.41790			0.252143			0.126072	+	0.992021i	$0.459763\pi$
$308$	6.58245	−	5.80270i	0.375070	−	0.330640i
$309$	7.16118			0.407385
$310$	−3.45797	+	32.9004i	−0.196399	+	1.86862i
$311$	3.19457	+	3.54793i	0.181148	+	0.201185i	0.826879	−	0.562380i	$-0.190114\pi$
$311$	3.19457	+	3.54793i	0.181148	+	0.201185i	−0.645731	+	0.763565i	$0.723447\pi$
$312$	−4.58689	−	0.974973i	−0.259681	−	0.0551970i
$313$	−15.6428	−	6.96463i	−0.884184	−	0.393664i	−0.0861538	−	0.996282i	$-0.527458\pi$
$313$	−15.6428	−	6.96463i	−0.884184	−	0.393664i	−0.798030	+	0.602618i	$0.794124\pi$
$314$	11.7382	−	8.52832i	0.662427	−	0.481281i
$315$	6.38100	−	9.65260i	0.359529	−	0.543863i
$316$	2.22902	−	6.86021i	0.125392	−	0.385917i
$317$	0.273223	−	2.59954i	0.0153457	−	0.146005i	−0.984166	−	0.177249i	$-0.943280\pi$
$317$	0.273223	−	2.59954i	0.0153457	−	0.146005i	0.999512	+	0.0312441i	$0.00994691\pi$
$318$	−5.49060	+	9.50999i	−0.307897	+	0.533294i
$319$	−8.70058	−	2.35333i	−0.487139	−	0.131761i
$320$	2.18673	+	3.78753i	0.122242	+	0.211729i
$321$	−2.92040	−	2.12179i	−0.163001	−	0.118427i
$322$	−13.1470	+	4.92402i	−0.732655	+	0.274405i
$323$	−0.913843	−	2.81252i	−0.0508476	−	0.156493i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	6.92473	+	65.8844i	0.384115	+	3.65461i
$326$	16.3724	+	3.48006i	0.906784	+	0.192743i
$327$	−6.01409	+	1.27833i	−0.332580	+	0.0706920i
$328$	−3.36772	−	2.44679i	−0.185951	−	0.135101i
$329$	30.7218	−	4.60932i	1.69375	−	0.254120i
$330$	5.23010	−	13.5294i	0.287908	−	0.744769i
$331$	5.77209	+	9.99756i	0.317263	+	0.549516i	0.979916	−	0.199411i	$-0.0639029\pi$
$331$	5.77209	+	9.99756i	0.317263	+	0.549516i	−0.662653	+	0.748927i	$0.730570\pi$
$332$	10.2618	−	4.56884i	0.563188	−	0.250747i
$333$	−2.02801	−	2.25234i	−0.111135	−	0.123427i
$334$	5.49143	−	6.09886i	0.300478	−	0.333715i
$335$	4.29550	−	3.12086i	0.234688	−	0.170511i
$336$	−0.663904	−	2.56110i	−0.0362189	−	0.139719i
$337$	6.09372	+	18.7545i	0.331946	+	1.02162i	0.968207	+	0.250151i	$0.0804802\pi$
$337$	6.09372	+	18.7545i	0.331946	+	1.02162i	−0.636261	+	0.771474i	$0.719520\pi$
$338$	−8.79366	+	1.86915i	−0.478312	+	0.101668i
$339$	9.33026	−	4.15410i	0.506750	−	0.225620i
$340$	−1.63441	+	2.83089i	−0.0886385	+	0.153526i
$341$	3.98300	−	24.7693i	0.215692	−	1.34133i
$342$	3.95660			0.213949
$343$	18.2159	+	3.34388i	0.983565	+	0.180553i
$344$	1.30745	−	4.02392i	0.0704931	−	0.216955i
$345$	−15.5281	+	17.2457i	−0.836007	+	0.928480i
$346$	−0.229385	−	2.18246i	−0.0123318	−	0.117330i
$347$	0.569741	+	5.42072i	0.0305853	+	0.291000i	0.999114	+	0.0420961i	$0.0134036\pi$
$347$	0.569741	+	5.42072i	0.0305853	+	0.291000i	−0.968528	+	0.248904i	$0.919930\pi$
$348$	−1.81842	+	2.01956i	−0.0974777	+	0.108260i
$349$	−1.00581	+	3.09556i	−0.0538397	+	0.165702i	−0.974361	−	0.224991i	$-0.927765\pi$
$349$	−1.00581	+	3.09556i	−0.0538397	+	0.165702i	0.920521	+	0.390693i	$0.127765\pi$
$350$	−31.5119	+	20.1006i	−1.68438	+	1.07442i
$351$	4.68936			0.250300
$352$	−1.49874	−	2.95868i	−0.0798831	−	0.157698i
$353$	1.13892	−	1.97266i	0.0606184	−	0.104994i	−0.834124	−	0.551578i	$-0.814026\pi$
$353$	1.13892	−	1.97266i	0.0606184	−	0.104994i	0.894742	+	0.446583i	$0.147359\pi$
$354$	6.72854	−	2.99574i	0.357618	−	0.159222i
$355$	30.6501	−	6.51488i	1.62674	−	0.345774i
$356$	−0.810291	−	2.49382i	−0.0429454	−	0.132172i
$357$	1.40966	−	1.38685i	0.0746071	−	0.0733999i
$358$	−3.20616	+	2.32941i	−0.169451	+	0.123113i
$359$	11.6426	−	12.9304i	0.614473	−	0.682441i	−0.352940	−	0.935646i	$-0.614818\pi$
$359$	11.6426	−	12.9304i	0.614473	−	0.682441i	0.967413	+	0.253205i	$0.0814847\pi$
$360$	−2.92641	−	3.25011i	−0.154236	−	0.171296i
$361$	−3.05608	+	1.36066i	−0.160846	+	0.0716134i
$362$	−5.33723	−	9.24435i	−0.280519	−	0.485872i
$363$	−4.52147	+	10.0278i	−0.237316	+	0.526322i
$364$	−7.72901	−	9.70532i	−0.405110	−	0.508697i
$365$	8.29593	+	6.02735i	0.434229	+	0.315486i
$366$	−7.62945	+	1.62169i	−0.398798	+	0.0847671i
$367$	10.7236	+	2.27938i	0.559770	+	0.118983i	0.479103	−	0.877758i	$-0.340962\pi$
$367$	10.7236	+	2.27938i	0.559770	+	0.118983i	0.0806662	+	0.996741i	$0.474295\pi$
$368$	0.554649	+	5.27713i	0.0289131	+	0.275089i
$369$	3.80284	+	1.69313i	0.197968	+	0.0881410i
$370$	4.09607	+	12.6064i	0.212945	+	0.655376i
$371$	−27.2078	+	10.1903i	−1.41256	+	0.529053i
$372$	−6.11954	−	4.44611i	−0.317284	−	0.230520i
$373$	−6.74572	−	11.6839i	−0.349280	−	0.604971i	0.636841	−	0.770995i	$-0.280241\pi$
$373$	−6.74572	−	11.6839i	−0.349280	−	0.604971i	−0.986122	+	0.166024i	$0.946907\pi$
$374$	1.35502	−	2.07581i	0.0700664	−	0.107338i
$375$	−19.9586	+	34.5693i	−1.03066	+	1.78515i
$376$	1.22734	−	11.6774i	0.0632954	−	0.602215i
$377$	−3.93804	+	12.1200i	−0.202819	+	0.624214i
$378$	1.18188	+	2.36710i	0.0607893	+	0.121750i
$379$	14.6147	−	10.6182i	0.750707	−	0.545421i	−0.145339	−	0.989382i	$-0.546427\pi$
$379$	14.6147	−	10.6182i	0.750707	−	0.545421i	0.896046	+	0.443961i	$0.146427\pi$
$380$	−15.8080	−	7.03819i	−0.810935	−	0.361051i
$381$	−16.2315	−	3.45011i	−0.831565	−	0.176755i
$382$	−0.586303	−	0.651156i	−0.0299979	−	0.0333160i
$383$	0.561122	−	5.33872i	0.0286720	−	0.272796i	−0.970788	−	0.239939i	$-0.922873\pi$
$383$	0.561122	−	5.33872i	0.0286720	−	0.272796i	0.999460	−	0.0328573i	$-0.0104607\pi$
$384$	−1.00000			−0.0510310
$385$	33.4353	−	18.8379i	1.70402	−	0.960070i
$386$	−23.5608			−1.19921
$387$	−0.442260	+	4.20783i	−0.0224814	+	0.213896i
$388$	6.35345	+	7.05622i	0.322547	+	0.358225i
$389$	16.7042	+	3.55060i	0.846939	+	0.180022i	0.610887	−	0.791718i	$-0.290813\pi$
$389$	16.7042	+	3.55060i	0.846939	+	0.180022i	0.236052	+	0.971740i	$0.424146\pi$
$390$	−18.7357	−	8.34165i	−0.948717	−	0.422396i
$391$	−3.20854	+	2.33114i	−0.162263	+	0.117891i
$392$	2.95109	−	6.34753i	0.149052	−	0.320598i
$393$	5.42280	−	16.6896i	0.273544	−	0.841881i
$394$	0.412664	−	3.92624i	0.0207897	−	0.197801i
$395$	15.7734	−	27.3204i	0.793647	−	1.37464i
$396$	2.08113	+	2.58242i	0.104581	+	0.129771i
$397$	−4.48012	−	7.75980i	−0.224851	−	0.389453i	0.731424	−	0.681923i	$-0.238856\pi$
$397$	−4.48012	−	7.75980i	−0.224851	−	0.389453i	−0.956275	+	0.292470i	$0.905523\pi$
$398$	12.9653	+	9.41987i	0.649894	+	0.472176i
$399$	8.08131	+	6.65398i	0.404571	+	0.333115i
$400$	4.36553	+	13.4357i	0.218276	+	0.671785i
$401$	31.6784	+	14.1041i	1.58194	+	0.704326i	0.994480	−	0.104925i	$-0.0334602\pi$
$401$	31.6784	+	14.1041i	1.58194	+	0.704326i	0.587463	+	0.809251i	$0.300127\pi$
$402$	0.126901	+	1.20738i	0.00632925	+	0.0602188i
$403$	−34.6960	−	7.37487i	−1.72833	−	0.367368i
$404$	−6.06127	+	1.28836i	−0.301560	+	0.0640985i
$405$	3.53820	+	2.57065i	0.175815	+	0.127737i
$406$	−7.11048	+	1.06682i	−0.352887	+	0.0529452i
$407$	−2.57876	−	9.71569i	−0.127824	−	0.481589i
$408$	−0.373712	−	0.647288i	−0.0185015	−	0.0320455i
$409$	19.7938	−	8.81275i	0.978738	−	0.435762i	0.145912	−	0.989298i	$-0.453388\pi$
$409$	19.7938	−	8.81275i	0.978738	−	0.435762i	0.832826	+	0.553535i	$0.186722\pi$
$410$	−12.1819	−	13.5293i	−0.601620	−	0.668166i
$411$	3.99843	−	4.44071i	0.197228	−	0.219044i
$412$	5.79352	−	4.20924i	0.285426	−	0.207374i
$413$	18.7810	+	5.19690i	0.924153	+	0.255723i
$414$	−1.63971	−	5.04649i	−0.0805871	−	0.248022i
$415$	48.0531	−	10.2140i	2.35883	−	0.501386i
$416$	−4.28395	+	1.90734i	−0.210038	+	0.0935148i
$417$	8.09409	−	14.0194i	0.396369	−	0.686531i
$418$	11.6782	+	5.98509i	0.571200	+	0.292740i
$419$	−18.9825			−0.927357			−0.463678	−	0.886004i	$-0.653471\pi$
$419$	−18.9825			−0.927357			−0.463678	+	0.886004i	$0.653471\pi$
$420$	−0.511317	−	11.5598i	−0.0249497	−	0.564060i
$421$	9.42247	−	28.9994i	0.459223	−	1.41334i	−0.406882	−	0.913481i	$-0.633384\pi$
$421$	9.42247	−	28.9994i	0.459223	−	1.41334i	0.866105	−	0.499863i	$-0.166616\pi$
$422$	3.94143	−	4.37740i	0.191866	−	0.213088i
$423$	1.22734	+	11.6774i	0.0596754	+	0.567774i
$424$	1.14785	+	10.9210i	0.0557444	+	0.530373i
$425$	−7.06532	+	7.84683i	−0.342718	+	0.380627i
$426$	−2.21404	+	6.81411i	−0.107270	+	0.330145i
$427$	−18.3103	−	9.51847i	−0.886098	−	0.460631i
$428$	−3.60981			−0.174487
$429$	13.8410	+	7.09352i	0.668250	+	0.342479i
$430$	9.25206	−	16.0250i	0.446174	−	0.772796i
$431$	1.15021	−	0.512106i	0.0554036	−	0.0246673i	−0.378848	−	0.925459i	$-0.623680\pi$
$431$	1.15021	−	0.512106i	0.0554036	−	0.0246673i	0.434251	+	0.900792i	$0.357013\pi$
$432$	0.978148	−	0.207912i	0.0470611	−	0.0100032i
$433$	−4.45411	−	13.7083i	−0.214051	−	0.658781i	−0.999220	−	0.0394989i	$-0.987424\pi$
$433$	−4.45411	−	13.7083i	−0.214051	−	0.658781i	0.785169	−	0.619282i	$-0.212576\pi$
$434$	−5.02189	−	19.3726i	−0.241058	−	0.929915i
$435$	−9.61538	+	6.98598i	−0.461022	+	0.334952i
$436$	−4.11411	+	4.56919i	−0.197030	+	0.218824i
$437$	−14.0481	−	15.6020i	−0.672011	−	0.746343i
$438$	−2.14197	+	0.953665i	−0.102347	+	0.0455679i
$439$	−12.7838	−	22.1422i	−0.610137	−	1.05679i	−0.991217	−	0.132246i	$-0.957781\pi$
$439$	−12.7838	−	22.1422i	−0.610137	−	1.05679i	0.381080	−	0.924542i	$-0.375552\pi$
$440$	−3.72114	−	14.0197i	−0.177398	−	0.668362i
$441$	−1.56688	+	6.82238i	−0.0746131	+	0.324875i
$442$	−2.83556	−	2.06015i	−0.134874	−	0.0979914i
$443$	36.3613	−	7.72883i	1.72758	−	0.367208i	0.766234	−	0.642562i	$-0.222128\pi$
$443$	36.3613	−	7.72883i	1.72758	−	0.367208i	0.961343	+	0.275354i	$0.0887950\pi$
$444$	−2.96459	−	0.630143i	−0.140693	−	0.0299053i
$445$	−1.19872	−	11.4051i	−0.0568249	−	0.540652i
$446$	−14.1427	−	6.29675i	−0.669678	−	0.298160i
$447$	4.74729	+	14.6107i	0.224539	+	0.691061i
$448$	−2.04249	−	1.68174i	−0.0964984	−	0.0794547i
$449$	0.443321	+	0.322092i	0.0209216	+	0.0152004i	0.598197	−	0.801349i	$-0.295884\pi$
$449$	0.443321	+	0.322092i	0.0209216	+	0.0152004i	−0.577275	+	0.816550i	$0.695884\pi$
$450$	−7.06357	−	12.2345i	−0.332980	−	0.576738i
$451$	8.66319	+	10.7499i	0.407934	+	0.506193i
$452$	5.10662	−	8.84493i	0.240195	−	0.416030i
$453$	0.353156	−	3.36005i	0.0165927	−	0.157869i
$454$	−0.869312	+	2.67547i	−0.0407988	+	0.125566i
$455$	−24.2388	−	48.5462i	−1.13633	−	2.27588i
$456$	3.20096	−	2.32563i	0.149899	−	0.108908i
$457$	−26.1034	−	11.6220i	−1.22107	−	0.543653i	−0.307969	−	0.951397i	$-0.599649\pi$
$457$	−26.1034	−	11.6220i	−1.22107	−	0.543653i	−0.913097	+	0.407743i	$0.866316\pi$
$458$	−13.1423	−	2.79349i	−0.614100	−	0.130531i
$459$	0.500124	+	0.555444i	0.0233438	+	0.0259259i
$460$	−2.42573	+	23.0793i	−0.113100	+	1.07608i
$461$	−10.7442			−0.500406			−0.250203	−	0.968193i	$-0.580497\pi$
$461$	−10.7442			−0.500406			−0.250203	+	0.968193i	$0.580497\pi$
$462$	−0.0922715	+	8.77448i	−0.00429286	+	0.408226i
$463$	−6.03291			−0.280373			−0.140186	−	0.990125i	$-0.544770\pi$
$463$	−6.03291			−0.280373			−0.140186	+	0.990125i	$0.544770\pi$
$464$	−0.284065	+	2.70270i	−0.0131874	+	0.125470i
$465$	−22.1359	−	24.5844i	−1.02653	−	1.14008i
$466$	7.73792	+	1.64475i	0.358452	+	0.0761913i
$467$	10.5223	+	4.68485i	0.486916	+	0.216789i	0.635485	−	0.772113i	$-0.280800\pi$
$467$	10.5223	+	4.68485i	0.486916	+	0.216789i	−0.148569	+	0.988902i	$0.547467\pi$
$468$	3.79377	−	2.75634i	0.175367	−	0.127412i
$469$	−1.77131	+	2.67948i	−0.0817915	+	0.123727i
$470$	15.8686	−	48.8385i	0.731964	−	2.25275i
$471$	−1.51663	+	14.4298i	−0.0698826	+	0.664889i
$472$	3.68265	−	6.37854i	0.169508	−	0.293596i
$473$	−7.67048	+	11.7507i	−0.352689	+	0.540298i
$474$	3.60662	+	6.24686i	0.165658	+	0.286928i
$475$	−45.2204	−	32.8545i	−2.07485	−	1.50747i
$476$	0.325269	−	1.95056i	0.0149087	−	0.0894039i
$477$	−3.39338	−	10.4437i	−0.155372	−	0.478186i
$478$	21.0777	+	9.38438i	0.964070	+	0.429231i
$479$	1.23046	+	11.7071i	0.0562213	+	0.534910i	0.985995	+	0.166777i	$0.0533362\pi$
$479$	1.23046	+	11.7071i	0.0562213	+	0.534910i	−0.929773	+	0.368133i	$0.879997\pi$
$480$	−4.27789	−	0.909293i	−0.195258	−	0.0415034i
$481$	−13.9020	+	2.95497i	−0.633878	+	0.134735i
$482$	−17.4882	−	12.7060i	−0.796568	−	0.578740i
$483$	5.13782	−	13.0650i	0.233779	−	0.594476i
$484$	2.23623	+	10.7703i	0.101647	+	0.489559i
$485$	20.7632	+	35.9629i	0.942807	+	1.63299i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−4.14614	−	4.60476i	−0.187880	−	0.208662i	0.641845	−	0.766834i	$-0.278169\pi$
$487$	−4.14614	−	4.60476i	−0.187880	−	0.208662i	−0.829725	+	0.558173i	$0.811503\pi$
$488$	−5.21915	+	5.79645i	−0.236260	+	0.262393i
$489$	−13.5415	+	9.83846i	−0.612367	+	0.444910i
$490$	18.3962	−	24.4706i	0.831055	−	1.10547i
$491$	0.376674	+	1.15928i	0.0169991	+	0.0523177i	0.959196	−	0.282741i	$-0.0912438\pi$
$491$	0.376674	+	1.15928i	0.0169991	+	0.0523177i	−0.942197	+	0.335059i	$0.891244\pi$
$492$	4.07176	−	0.865480i	0.183569	−	0.0390188i
$493$	−1.85558	+	0.826160i	−0.0835713	+	0.0372084i
$494$	9.27697	−	16.0682i	0.417391	−	0.722942i
$495$	6.55468	+	12.9397i	0.294611	+	0.581594i
$496$	−7.56417			−0.339641
$497$	−15.9817	+	10.1943i	−0.716877	+	0.457276i
$498$	−3.47116	+	10.6831i	−0.155546	+	0.478722i
$499$	8.68222	−	9.64259i	0.388670	−	0.431661i	−0.516778	−	0.856119i	$-0.672869\pi$
$499$	8.68222	−	9.64259i	0.388670	−	0.431661i	0.905448	+	0.424458i	$0.139535\pi$
$500$	4.17248	+	39.6985i	0.186599	+	1.77537i
$501$	0.857846	+	8.16186i	0.0383257	+	0.364645i
$502$	−20.7798	+	23.0783i	−0.927446	+	1.03003i
$503$	−6.56276	+	20.1981i	−0.292619	+	0.900589i	0.691392	+	0.722480i	$0.256998\pi$
$503$	−6.56276	+	20.1981i	−0.292619	+	0.900589i	−0.984011	+	0.178109i	$0.943002\pi$
$504$	2.34751	+	1.22033i	0.104566	+	0.0543580i
$505$	−27.1009			−1.20598
$506$	2.79404	−	17.3755i	0.124210	−	0.772433i
$507$	4.49506	−	7.78567i	0.199633	−	0.345774i
$508$	−15.1595	+	6.74944i	−0.672593	+	0.299458i
$509$	9.73141	−	2.06847i	0.431337	−	0.0916835i	0.0128736	−	0.999917i	$-0.495902\pi$
$509$	9.73141	−	2.06847i	0.431337	−	0.0916835i	0.418464	+	0.908234i	$0.362569\pi$
$510$	−1.01012	−	3.10884i	−0.0447290	−	0.137662i
$511$	−5.97875	−	1.65438i	−0.264484	−	0.0731856i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−2.64748	+	2.94033i	−0.116889	+	0.129819i
$514$	−5.75979	−	6.39690i	−0.254054	−	0.282155i
$515$	28.6114	−	12.7386i	1.26077	−	0.561331i
$516$	2.11550	+	3.66416i	0.0931298	+	0.161306i
$517$	−14.0416	+	36.3232i	−0.617549	+	1.59749i
$518$	−4.99540	−	6.27273i	−0.219485	−	0.275608i
$519$	1.77537	+	1.28988i	0.0779301	+	0.0566195i
$520$	−20.0606	+	4.26401i	−0.879714	+	0.186989i
$521$	27.7751	+	5.90378i	1.21685	+	0.258649i	0.771220	−	0.636568i	$-0.219647\pi$
$521$	27.7751	+	5.90378i	1.21685	+	0.258649i	0.445629	+	0.895218i	$0.352980\pi$
$522$	−0.284065	−	2.70270i	−0.0124332	−	0.118294i
$523$	36.2044	+	16.1192i	1.58311	+	0.704846i	0.994613	−	0.103655i	$-0.0330537\pi$
$523$	36.2044	+	16.1192i	1.58311	+	0.704846i	0.588496	+	0.808500i	$0.299720\pi$
$524$	−5.42280	−	16.6896i	−0.236896	−	0.729091i
$525$	6.14794	−	36.8678i	0.268318	−	1.60904i
$526$	−1.44310	−	1.04847i	−0.0629219	−	0.0457155i
$527$	−2.82682	−	4.89620i	−0.123138	−	0.213282i
$528$	3.20158	+	0.865961i	0.139331	+	0.0376861i
$529$	−2.57787	+	4.46501i	−0.112081	+	0.194131i
$530$	−5.02006	+	47.7627i	−0.218058	+	2.07468i
$531$	−2.27601	+	7.00482i	−0.0987702	+	0.303984i
$532$	10.4490	+	0.633107i	0.453023	+	0.0274487i
$533$	15.7925	−	11.4739i	0.684047	−	0.496989i
$534$	2.39546	+	1.06653i	0.103662	+	0.0461532i
$535$	−15.4424	−	3.28238i	−0.667632	−	0.141910i
$536$	0.812347	+	0.902203i	0.0350881	+	0.0389692i
$537$	0.414250	−	3.94132i	0.0178762	−	0.170081i
$538$	8.71853			0.375883
$539$	−14.9449	+	17.7666i	−0.643721	+	0.765261i
$540$	4.37346			0.188204
$541$	0.558031	−	5.30931i	0.0239916	−	0.228265i	−0.975955	−	0.217970i	$-0.930056\pi$
$541$	0.558031	−	5.30931i	0.0239916	−	0.228265i	0.999947	−	0.0102946i	$-0.00327694\pi$
$542$	2.98112	+	3.31087i	0.128050	+	0.142214i
$543$	10.4412	+	2.21934i	0.448075	+	0.0952412i
$544$	−0.682805	−	0.304005i	−0.0292750	−	0.0130341i
$545$	−21.7544	+	15.8055i	−0.931858	+	0.677035i
$546$	12.3842	+	0.750358i	0.529994	+	0.0321124i
$547$	−2.80928	+	8.64608i	−0.120116	+	0.369680i	−0.992980	−	0.118285i	$-0.962260\pi$
$547$	−2.80928	+	8.64608i	−0.120116	+	0.369680i	0.872864	+	0.487964i	$0.162260\pi$
$548$	0.624616	−	5.94283i	0.0266823	−	0.253865i
$549$	3.89995	−	6.75491i	0.166446	−	0.288292i
$550$	−2.34177	−	46.7959i	−0.0998536	−	1.99538i
$551$	−5.37621	−	9.31187i	−0.229034	−	0.396699i
$552$	−4.29281	−	3.11891i	−0.182714	−	0.132749i
$553$	−3.13911	+	18.8245i	−0.133488	+	0.800500i
$554$	4.13142	+	12.7152i	0.175527	+	0.540217i
$555$	−12.1092	−	5.39136i	−0.514007	−	0.228851i
$556$	−1.69212	−	16.0995i	−0.0717621	−	0.682771i
$557$	31.1440	+	6.61986i	1.31961	+	0.280493i	0.813294	−	0.581853i	$-0.197672\pi$
$557$	31.1440	+	6.61986i	1.31961	+	0.280493i	0.506320	+	0.862346i	$0.331005\pi$
$558$	7.39888	−	1.57268i	0.313219	−	0.0665769i
$559$	16.0515	+	11.6621i	0.678905	+	0.493253i
$560$	−7.20833	−	9.05151i	−0.304608	−	0.382496i
$561$	0.635942	+	2.39596i	0.0268495	+	0.101158i
$562$	6.63149	+	11.4861i	0.279733	+	0.484511i
$563$	1.14440	−	0.509521i	0.0482309	−	0.0214738i	−0.382479	−	0.923964i	$-0.624930\pi$
$563$	1.14440	−	0.509521i	0.0482309	−	0.0214738i	0.430710	+	0.902490i	$0.358263\pi$
$564$	7.85674	+	8.72579i	0.330828	+	0.367422i
$565$	29.8882	−	33.1942i	1.25741	−	1.39649i
$566$	−2.12111	+	1.54108i	−0.0891570	+	0.0647763i
$567$	−2.54993	−	0.705592i	−0.107087	−	0.0296321i
$568$	2.21404	+	6.81411i	0.0928990	+	0.285914i
$569$	−44.0049	+	9.35353i	−1.84478	+	0.392120i	−0.991584	−	0.129467i	$-0.958673\pi$
$569$	−44.0049	+	9.35353i	−1.84478	+	0.392120i	−0.853198	+	0.521588i	$0.825340\pi$
$570$	15.8080	−	7.03819i	0.662125	−	0.294797i
$571$	−11.3774	+	19.7063i	−0.476131	+	0.824683i	−0.999626	−	0.0273458i	$-0.991294\pi$
$571$	−11.3774	+	19.7063i	−0.476131	+	0.824683i	0.523495	+	0.852029i	$0.324628\pi$
$572$	15.3671	−	2.39675i	0.642530	−	0.100213i
$573$	0.876217			0.0366045
$574$	9.77203	+	5.07992i	0.407877	+	0.212032i
$575$	−23.1644	+	71.2925i	−0.966020	+	2.97310i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−1.75953	−	16.7408i	−0.0732503	−	0.696930i	−0.968100	−	0.250563i	$-0.919384\pi$
$577$	−1.75953	−	16.7408i	−0.0732503	−	0.696930i	0.894850	−	0.446367i	$-0.147282\pi$
$578$	1.71859	+	16.3513i	0.0714839	+	0.680124i
$579$	15.7652	−	17.5091i	0.655180	−	0.727652i
$580$	−3.67275	+	11.3036i	−0.152503	+	0.469355i
$581$	−25.0560	+	15.9826i	−1.03950	+	0.663068i
$582$	−9.49508			−0.393584
$583$	5.78227	−	35.9586i	0.239477	−	1.48925i
$584$	−1.17234	+	2.03055i	−0.0485117	+	0.0840246i
$585$	18.7357	−	8.34165i	0.774624	−	0.344885i
$586$	23.7625	−	5.05087i	0.981619	−	0.208650i
$587$	2.17831	+	6.70415i	0.0899086	+	0.276710i	0.985893	−	0.167375i	$-0.0535289\pi$
$587$	2.17831	+	6.70415i	0.0899086	+	0.276710i	−0.895985	+	0.444085i	$0.853529\pi$
$588$	2.74247	+	6.44041i	0.113097	+	0.265598i
$589$	24.2126	−	17.5915i	0.997663	−	0.724845i
$590$	21.5539	−	23.9381i	0.887362	−	0.985515i
$591$	2.64164	+	2.93384i	0.108662	+	0.120682i
$592$	−2.76879	+	1.23275i	−0.113797	+	0.0506655i
$593$	−20.9799	−	36.3382i	−0.861540	−	1.49223i	−0.870442	−	0.492270i	$-0.836167\pi$
$593$	−20.9799	−	36.3382i	−0.861540	−	1.49223i	0.00890263	−	0.999960i	$-0.497166\pi$
$594$	−3.31166	−	0.181392i	−0.135879	−	0.00744262i
$595$	3.16510	−	8.04852i	0.129756	−	0.329957i
$596$	12.4286	+	9.02989i	0.509094	+	0.369879i
$597$	−15.6758	+	3.33200i	−0.641569	+	0.136370i
$598$	−24.3389	−	5.17340i	−0.995293	−	0.211556i
$599$	−3.02623	−	28.7927i	−0.123648	−	1.17644i	−0.863743	−	0.503933i	$-0.831886\pi$
$599$	−3.02623	−	28.7927i	−0.123648	−	1.17644i	0.740094	−	0.672503i	$-0.234781\pi$
$600$	−12.9058	−	5.74603i	−0.526876	−	0.234581i
$601$	−7.56888	−	23.2946i	−0.308741	−	0.950208i	−0.978255	−	0.207408i	$-0.933497\pi$
$601$	−7.56888	−	23.2946i	−0.308741	−	0.950208i	0.669513	−	0.742800i	$-0.266503\pi$
$602$	−1.84128	+	11.0417i	−0.0750448	+	0.450027i
$603$	−0.982174	−	0.713591i	−0.0399972	−	0.0290597i
$604$	−1.68928	−	2.92592i	−0.0687359	−	0.119054i
$605$	−0.226998	+	48.1075i	−0.00922877	+	1.95585i
$606$	3.09834	−	5.36649i	0.125862	−	0.217999i
$607$	−2.73047	+	25.9787i	−0.110827	+	1.05444i	0.787861	+	0.615854i	$0.211189\pi$
$607$	−2.73047	+	25.9787i	−0.110827	+	1.05444i	−0.898687	+	0.438590i	$0.855478\pi$
$608$	1.22266	−	3.76295i	0.0495853	−	0.152608i
$609$	3.96504	−	5.99796i	0.160672	−	0.243050i
$610$	−27.5976	+	20.0508i	−1.11739	+	0.811835i
$611$	50.3008	+	22.3954i	2.03495	+	0.906020i
$612$	0.731091	+	0.155398i	0.0295526	+	0.00628160i
$613$	−2.55579	−	2.83849i	−0.103227	−	0.114646i	0.689317	−	0.724460i	$-0.257911\pi$
$613$	−2.55579	−	2.83849i	−0.103227	−	0.114646i	−0.792544	+	0.609814i	$0.791244\pi$
$614$	−0.461797	+	4.39370i	−0.0186366	+	0.177315i
$615$	18.2055			0.734117
$616$	5.08286	+	7.15294i	0.204794	+	0.288200i
$617$	15.6204			0.628854			0.314427	−	0.949282i	$-0.398188\pi$
$617$	15.6204			0.628854			0.314427	+	0.949282i	$0.398188\pi$
$618$	−0.748547	+	7.12195i	−0.0301110	+	0.286487i
$619$	1.84061	+	2.04420i	0.0739804	+	0.0821635i	0.778999	−	0.627026i	$-0.215728\pi$
$619$	1.84061	+	2.04420i	0.0739804	+	0.0821635i	−0.705018	+	0.709189i	$0.749061\pi$
$620$	−32.3587	−	6.87805i	−1.29956	−	0.276229i
$621$	4.84745	+	2.15823i	0.194522	+	0.0866066i
$622$	−3.86242	+	2.80621i	−0.154869	+	0.112519i
$623$	3.09907	+	6.20691i	0.124162	+	0.248675i
$624$	1.44909	−	4.45985i	0.0580101	−	0.178537i
$625$	−10.8647	+	103.371i	−0.434589	+	4.13484i
$626$	8.56159	−	14.8291i	0.342190	−	0.592690i
$627$	−12.2620	+	4.67379i	−0.489698	+	0.186653i
$628$	7.25463	+	12.5654i	0.289491	+	0.501413i
$629$	−1.83267	−	1.33151i	−0.0730734	−	0.0530909i
$630$	8.93273	+	7.35502i	0.355888	+	0.293031i
$631$	8.16922	+	25.1423i	0.325211	+	1.00090i	0.971345	+	0.237674i	$0.0763848\pi$
$631$	8.16922	+	25.1423i	0.325211	+	1.00090i	−0.646134	+	0.763224i	$0.723615\pi$
$632$	6.58963	+	2.93389i	0.262121	+	0.116704i
$633$	0.615711	+	5.85810i	0.0244723	+	0.232839i
$634$	2.55674	+	0.543452i	0.101541	+	0.0215832i
$635$	−70.9878	+	15.0889i	−2.81707	+	0.598786i
$636$	−8.88397	−	6.45459i	−0.352272	−	0.255941i
$637$	24.0326	+	22.3596i	0.952206	+	0.885918i
$638$	3.24989	−	8.40693i	0.128665	−	0.332833i
$639$	−3.58239	−	6.20488i	−0.141717	−	0.245461i
$640$	−3.99535	+	1.77885i	−0.157930	+	0.0703151i
$641$	−27.5266	−	30.5713i	−1.08723	−	1.20750i	−0.976922	−	0.213598i	$-0.931482\pi$
$641$	−27.5266	−	30.5713i	−1.08723	−	1.20750i	−0.110312	−	0.993897i	$-0.535185\pi$
$642$	2.41544	−	2.68261i	0.0953297	−	0.105874i
$643$	−38.6082	+	28.0505i	−1.52256	+	1.10620i	−0.562360	+	0.826892i	$0.690107\pi$
$643$	−38.6082	+	28.0505i	−1.52256	+	1.10620i	−0.960200	+	0.279313i	$0.909893\pi$
$644$	−3.52281	−	13.5897i	−0.138818	−	0.535509i
$645$	5.71809	+	17.5985i	0.225150	+	0.692939i
$646$	2.89263	−	0.614848i	0.113809	−	0.0241909i
$647$	10.8243	−	4.81931i	0.425549	−	0.189466i	−0.182776	−	0.983155i	$-0.558508\pi$
$647$	10.8243	−	4.81931i	0.425549	−	0.189466i	0.608325	+	0.793688i	$0.291842\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−17.3139	+	17.2324i	−0.679629	+	0.676430i
$650$	−66.2473			−2.59843
$651$	17.7569	+	9.23081i	0.695950	+	0.361784i
$652$	−5.17238	+	15.9190i	−0.202566	+	0.623435i
$653$	8.62522	−	9.57927i	0.337531	−	0.374866i	−0.550354	−	0.834931i	$-0.685507\pi$
$653$	8.62522	−	9.57927i	0.337531	−	0.374866i	0.887885	+	0.460065i	$0.152174\pi$
$654$	−0.642688	−	6.11476i	−0.0251311	−	0.239106i
$655$	−8.02233	−	76.3274i	−0.313458	−	2.98236i
$656$	2.78541	−	3.09351i	0.108752	−	0.120781i
$657$	0.724544	−	2.22992i	0.0282672	−	0.0869974i
$658$	1.37277	+	31.0353i	0.0535160	+	1.20988i
$659$	15.2983			0.595937			0.297969	−	0.954576i	$-0.403691\pi$
$659$	15.2983			0.595937			0.297969	+	0.954576i	$0.403691\pi$
$660$	12.9086	+	6.61566i	0.502466	+	0.257514i
$661$	11.3875	−	19.7237i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$661$	11.3875	−	19.7237i	0.442921	−	0.767161i	0.997905	+	0.0646996i	$0.0206089\pi$
$662$	−10.5461	+	4.69544i	−0.409887	+	0.182494i
$663$	3.42835	−	0.728718i	0.133146	−	0.0283011i
$664$	3.47116	+	10.6831i	0.134707	+	0.414586i
$665$	44.1241	+	12.2096i	1.71106	+	0.473468i
$666$	2.45199	−	1.78147i	0.0950125	−	0.0690306i
$667$	−9.64891	+	10.7162i	−0.373607	+	0.414933i
$668$	5.49143	+	6.09886i	0.212470	+	0.235972i
$669$	14.1427	−	6.29675i	0.546790	−	0.243446i
$670$	2.65476	+	4.59818i	0.102562	+	0.177643i
$671$	21.7290	−	14.0382i	0.838840	−	0.541940i
$672$	2.61647	−	0.392559i	0.100932	−	0.0151433i
$673$	−8.72985	−	6.34261i	−0.336511	−	0.244490i	0.406677	−	0.913572i	$-0.366687\pi$
$673$	−8.72985	−	6.34261i	−0.336511	−	0.244490i	−0.743188	+	0.669082i	$0.766687\pi$
$674$	−19.2888	+	4.09995i	−0.742976	+	0.157924i
$675$	13.8184	+	2.93720i	0.531872	+	0.113053i
$676$	−0.939723	−	8.94087i	−0.0361432	−	0.343880i
$677$	38.7037	+	17.2320i	1.48750	+	0.662279i	0.979932	−	0.199331i	$-0.0638770\pi$
$677$	38.7037	+	17.2320i	1.48750	+	0.662279i	0.507571	+	0.861610i	$0.330544\pi$
$678$	3.15607	+	9.71337i	0.121208	+	0.373040i
$679$	−19.3936	−	15.9683i	−0.744257	−	0.612805i
$680$	−2.64454	−	1.92137i	−0.101413	−	0.0736811i
$681$	−1.40658	−	2.43626i	−0.0539001	−	0.0933578i
$682$	24.2173	+	6.55028i	0.927328	+	0.250823i
$683$	3.45014	−	5.97582i	0.132016	−	0.228658i	−0.792438	−	0.609953i	$-0.791188\pi$
$683$	3.45014	−	5.97582i	0.132016	−	0.228658i	0.924454	+	0.381295i	$0.124522\pi$
$684$	−0.413578	+	3.93493i	−0.0158135	+	0.150456i
$685$	8.07581	−	24.8548i	0.308561	−	0.949653i
$686$	−5.22964	+	17.7666i	−0.199669	+	0.678331i
$687$	10.8699	−	7.89744i	0.414712	−	0.301306i
$688$	3.86521	+	1.72090i	0.147360	+	0.0656089i
$689$	−50.3695	−	10.7064i	−1.91893	−	0.407880i
$690$	−15.5281	−	17.2457i	−0.591146	−	0.656534i
$691$	4.59158	−	43.6860i	0.174672	−	1.66189i	−0.459109	−	0.888380i	$-0.651831\pi$
$691$	4.59158	−	43.6860i	0.174672	−	1.66189i	0.633781	−	0.773513i	$-0.281502\pi$
$692$	2.19448			0.0834215
$693$	−6.45897	−	5.93984i	−0.245356	−	0.225636i
$694$	−5.45058			−0.206901
$695$	7.40044	−	70.4105i	0.280715	−	2.67082i
$696$	−1.81842	−	2.01956i	−0.0689271	−	0.0765513i
$697$	3.04333	+	0.646880i	0.115274	+	0.0245023i
$698$	−2.97347	−	1.32387i	−0.112547	−	0.0501093i
$699$	−6.39996	+	4.64984i	−0.242069	+	0.175873i
$700$	−16.6966	−	33.4404i	−0.631071	−	1.26393i
$701$	−12.5498	+	38.6244i	−0.474001	+	1.45882i	0.373300	+	0.927711i	$0.378226\pi$
$701$	−12.5498	+	38.6244i	−0.474001	+	1.45882i	−0.847301	+	0.531113i	$0.821774\pi$
$702$	−0.490172	+	4.66367i	−0.0185003	+	0.176019i
$703$	5.99588	−	10.3852i	0.226139	−	0.391684i
$704$	3.09913	−	1.18126i	0.116803	−	0.0445205i
$705$	25.6759	+	44.4720i	0.967012	+	1.67491i
$706$	1.84280	+	1.33888i	0.0693549	+	0.0503893i
$707$	15.3534	−	5.75037i	0.577422	−	0.216265i
$708$	2.27601	+	7.00482i	0.0855375	+	0.263257i
$709$	37.8081	+	16.8332i	1.41991	+	0.632186i	0.965925	−	0.258822i	$-0.0833344\pi$
$709$	37.8081	+	16.8332i	1.41991	+	0.632186i	0.453987	+	0.891008i	$0.350001\pi$
$710$	3.27538	+	31.1632i	0.122923	+	1.16953i
$711$	−7.05562	−	1.49972i	−0.264606	−	0.0562438i
$712$	2.56486	−	0.545177i	0.0961221	−	0.0204314i
$713$	−32.4715	−	23.5919i	−1.21607	−	0.883525i
$714$	1.23190	+	1.54690i	0.0461028	+	0.0578914i
$715$	67.9180	+	3.72013i	2.53999	+	0.139125i
$716$	−1.98152	−	3.43209i	−0.0740528	−	0.128263i
$717$	−21.0777	+	9.38438i	−0.787159	+	0.350466i
$718$	11.6426	+	12.9304i	0.434498	+	0.482559i
$719$	−24.0572	+	26.7182i	−0.897181	+	0.996420i	0.102818	+	0.994700i	$0.467214\pi$
$719$	−24.0572	+	26.7182i	−0.897181	+	0.996420i	−0.999999	+	0.00172006i	$0.999452\pi$
$720$	3.53820	−	2.57065i	0.131861	−	0.0958026i
$721$	−13.5062	+	13.2876i	−0.502996	+	0.494857i
$722$	−1.03375	−	3.18157i	−0.0384723	−	0.118406i
$723$	21.1443	−	4.49436i	0.786364	−	0.167147i
$724$	9.75160	−	4.34169i	0.362415	−	0.161358i
$725$	−19.1959	+	33.2482i	−0.712917	+	1.23481i
$726$	−9.50022	−	5.54489i	−0.352586	−	0.205790i
$727$	18.0316			0.668753			0.334377	−	0.942440i	$-0.391474\pi$
$727$	18.0316			0.668753			0.334377	+	0.942440i	$0.391474\pi$
$728$	10.4601	−	6.67218i	0.387676	−	0.247288i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−6.86149	+	7.62046i	−0.253955	+	0.282046i
$731$	0.330556	+	3.14503i	0.0122260	+	0.116323i
$732$	−0.815311	−	7.75717i	−0.0301348	−	0.286713i
$733$	−15.2244	+	16.9084i	−0.562326	+	0.624527i	−0.955519	−	0.294929i	$-0.904704\pi$
$733$	−15.2244	+	16.9084i	−0.562326	+	0.624527i	0.393193	+	0.919456i	$0.371371\pi$
$734$	−3.38782	+	10.4266i	−0.125047	+	0.384854i
$735$	5.87575	+	30.0451i	0.216730	+	1.10823i
$736$	−5.30620			−0.195589
$737$	−1.81952	−	3.59194i	−0.0670229	−	0.132311i
$738$	−2.08136	+	3.60503i	−0.0766161	+	0.132703i
$739$	34.3644	−	15.3000i	1.26411	−	0.562820i	0.338385	−	0.941008i	$-0.390119\pi$
$739$	34.3644	−	15.3000i	1.26411	−	0.562820i	0.925729	+	0.378188i	$0.123453\pi$
$740$	−12.9655	+	2.75590i	−0.476622	+	0.101309i
$741$	5.73348	+	17.6458i	0.210625	+	0.648236i
$742$	−7.29046	−	28.1239i	−0.267641	−	1.03246i
$743$	−27.6292	+	20.0738i	−1.01362	+	0.736436i	−0.964965	−	0.262379i	$-0.915493\pi$
$743$	−27.6292	+	20.0738i	−1.01362	+	0.736436i	−0.0486529	+	0.998816i	$0.515493\pi$
$744$	5.06142	−	5.62128i	0.185561	−	0.206086i
$745$	44.9572	+	49.9301i	1.64711	+	1.82930i
$746$	12.3250	−	5.48747i	0.451252	−	0.200910i
$747$	−5.61645	−	9.72798i	−0.205495	−	0.355928i
$748$	1.92280	+	1.56458i	0.0703045	+	0.0572066i
$749$	9.44495	−	1.41707i	0.345111	−	0.0517785i
$750$	−32.2937	−	23.4627i	−1.17920	−	0.856738i
$751$	−5.50667	+	1.17048i	−0.200941	+	0.0427114i	−0.307283	−	0.951618i	$-0.599420\pi$
$751$	−5.50667	+	1.17048i	−0.200941	+	0.0427114i	0.106341	+	0.994330i	$0.466086\pi$
$752$	11.4851	+	2.44124i	0.418819	+	0.0890228i
$753$	−3.24612	−	30.8847i	−0.118295	−	1.12550i
$754$	−11.6420	−	5.18336i	−0.423977	−	0.188767i
$755$	−4.56604	−	14.0528i	−0.166175	−	0.511434i
$756$	−2.47767	+	0.927975i	−0.0901121	+	0.0337501i
$757$	−23.2710	−	16.9074i	−0.845800	−	0.614510i	0.0781845	−	0.996939i	$-0.475088\pi$
$757$	−23.2710	−	16.9074i	−0.845800	−	0.614510i	−0.923985	+	0.382429i	$0.875088\pi$
$758$	9.03239	+	15.6446i	0.328071	+	0.568236i
$759$	11.0429	+	13.7028i	0.400832	+	0.497381i
$760$	8.65202	−	14.9857i	0.313842	−	0.543590i
$761$	−2.27549	+	21.6498i	−0.0824865	+	0.784806i	0.872591	+	0.488451i	$0.162438\pi$
$761$	−2.27549	+	21.6498i	−0.0824865	+	0.784806i	−0.955078	+	0.296355i	$0.904229\pi$
$762$	5.12787	−	15.7820i	0.185763	−	0.571720i
$763$	8.97076	−	13.5702i	0.324763	−	0.491273i
$764$	0.708874	−	0.515027i	0.0256462	−	0.0186330i
$765$	2.98622	+	1.32955i	0.107967	+	0.0480700i
$766$	5.25082	+	1.11610i	0.189720	+	0.0403262i
$767$	23.1108	+	25.6672i	0.834484	+	0.926788i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	16.6623			0.600859			0.300429	−	0.953804i	$-0.402870\pi$
$769$	16.6623			0.600859			0.300429	+	0.953804i	$0.402870\pi$
$770$	15.2398	+	35.2213i	0.549204	+	1.26929i
$771$	8.60788			0.310005
$772$	2.46277	−	23.4317i	0.0886370	−	0.843325i
$773$	−28.6460	−	31.8146i	−1.03032	−	1.14429i	−0.989413	−	0.145128i	$-0.953641\pi$
$773$	−28.6460	−	31.8146i	−1.03032	−	1.14429i	−0.0409107	−	0.999163i	$-0.513026\pi$
$774$	−4.13855	−	0.879675i	−0.148757	−	0.0316193i
$775$	−97.6216	−	43.4639i	−3.50667	−	1.56127i
$776$	−7.68168	+	5.58107i	−0.275756	+	0.200349i
$777$	8.00412	+	0.484970i	0.287146	+	0.0173982i
$778$	−5.27722	+	16.2416i	−0.189197	+	0.582290i
$779$	−1.72161	+	16.3800i	−0.0616831	+	0.586876i
$780$	10.2544	−	17.7611i	0.367165	−	0.635949i
$781$	−1.18766	−	23.7332i	−0.0424979	−	0.849240i
$782$	−1.98299	−	3.43464i	−0.0709115	−	0.122822i
$783$	2.19858	+	1.59736i	0.0785707	+	0.0570850i
$784$	6.00428	+	3.59842i	0.214439	+	0.128515i
$785$	19.6089	+	60.3499i	0.699870	+	2.15398i
$786$	16.0314	+	7.13763i	0.571821	+	0.254591i
$787$	−0.284273	−	2.70468i	−0.0101332	−	0.0964114i	0.988286	−	0.152611i	$-0.0487683\pi$
$787$	−0.284273	−	2.70468i	−0.0101332	−	0.0964114i	−0.998420	+	0.0561999i	$0.982102\pi$
$788$	3.86160	+	0.820807i	0.137564	+	0.0292401i
$789$	1.74478	−	0.370865i	0.0621160	−	0.0132032i
$790$	25.5219	+	18.5428i	0.908030	+	0.659722i
$791$	−9.88915	+	25.1471i	−0.351618	+	0.894128i
$792$	−2.78581	+	1.79980i	−0.0989894	+	0.0639530i
$793$	−18.2883	−	31.6762i	−0.649436	−	1.12486i
$794$	8.18559	−	3.64446i	0.290496	−	0.129337i
$795$	−32.1355	−	35.6901i	−1.13973	−	1.26580i
$796$	−10.7235	+	11.9097i	−0.380085	+	0.422127i
$797$	9.01375	−	6.54887i	0.319283	−	0.231973i	−0.416586	−	0.909096i	$-0.636774\pi$
$797$	9.01375	−	6.54887i	0.319283	−	0.231973i	0.735870	+	0.677123i	$0.236774\pi$
$798$	−7.46225	+	7.34151i	−0.264161	+	0.259886i
$799$	2.71194	+	8.34650i	0.0959416	+	0.295278i
$800$	−13.8184	+	2.93720i	−0.488555	+	0.103846i
$801$	−2.39546	+	1.06653i	−0.0846394	+	0.0376839i
$802$	−17.3382	+	30.0306i	−0.612231	+	1.06042i
$803$	5.51171	−	5.48576i	0.194504	−	0.193588i
$804$	−1.21403			−0.0428157
$805$	−2.71315	−	61.3385i	−0.0956260	−	2.16190i
$806$	10.9612	−	33.7351i	0.386091	−	1.18827i
$807$	−5.83384	+	6.47913i	−0.205361	+	0.228076i
$808$	−0.647730	−	6.16274i	−0.0227871	−	0.216804i
$809$	−5.40447	−	51.4201i	−0.190011	−	1.80784i	−0.509742	−	0.860327i	$-0.670259\pi$
$809$	−5.40447	−	51.4201i	−0.190011	−	1.80784i	0.319731	−	0.947508i	$-0.396407\pi$
$810$	−2.92641	+	3.25011i	−0.102824	+	0.114197i
$811$	−8.01657	+	24.6725i	−0.281500	+	0.866368i	0.705926	+	0.708286i	$0.250531\pi$
$811$	−8.01657	+	24.6725i	−0.281500	+	0.866368i	−0.987426	+	0.158082i	$0.949469\pi$
$812$	−0.317724	−	7.18304i	−0.0111499	−	0.252075i
$813$	−4.45522			−0.156251
$814$	9.93202	−	1.54907i	0.348117	−	0.0542947i
$815$	−36.6019	+	63.3963i	−1.28211	+	2.22068i
$816$	0.682805	−	0.304005i	0.0239030	−	0.0106423i
$817$	−16.3746	+	3.48053i	−0.572874	+	0.121768i
$818$	6.69546	+	20.6065i	0.234101	+	0.720490i
$819$	−8.84426	+	8.70115i	−0.309043	+	0.304043i
$820$	14.7286	−	10.7009i	0.514344	−	0.373693i
$821$	−23.4586	+	26.0534i	−0.818710	+	0.909270i	−0.997208	−	0.0746706i	$-0.976209\pi$
$821$	−23.4586	+	26.0534i	−0.818710	+	0.909270i	0.178498	+	0.983940i	$0.442876\pi$
$822$	3.99843	+	4.44071i	0.139461	+	0.154888i
$823$	0.245199	−	0.109170i	0.00854709	−	0.00380541i	−0.402459	−	0.915438i	$-0.631844\pi$
$823$	0.245199	−	0.109170i	0.00854709	−	0.00380541i	0.411006	+	0.911633i	$0.365178\pi$
$824$	3.58059	+	6.20176i	0.124736	+	0.216049i
$825$	36.3431	+	29.5723i	1.26530	+	1.02957i
$826$	−7.13158	+	18.1349i	−0.248140	+	0.630994i
$827$	−33.4757	−	24.3215i	−1.16407	−	0.845743i	−0.173779	−	0.984785i	$-0.555598\pi$
$827$	−33.4757	−	24.3215i	−1.16407	−	0.845743i	−0.990287	+	0.139042i	$0.955598\pi$
$828$	5.19025	−	1.10322i	0.180374	−	0.0383396i
$829$	−27.0260	−	5.74456i	−0.938653	−	0.199517i	−0.286911	−	0.957957i	$-0.592628\pi$
$829$	−27.0260	−	5.74456i	−0.938653	−	0.199517i	−0.651743	+	0.758440i	$0.725962\pi$
$830$	5.13513	+	48.8575i	0.178243	+	1.69587i
$831$	−12.2137	−	5.43789i	−0.423688	−	0.188638i
$832$	−1.44909	−	4.45985i	−0.0502382	−	0.154617i
$833$	−0.0853426	+	5.23127i	−0.00295695	+	0.181253i
$834$	13.0965	+	9.51517i	0.453495	+	0.329483i
$835$	17.9461	+	31.0835i	0.621050	+	1.07569i
$836$	−7.17301	+	10.9886i	−0.248084	+	0.380049i
$837$	−3.78209	+	6.55077i	−0.130728	+	0.226428i
$838$	1.98421	−	18.8785i	0.0685435	−	0.652148i
$839$	−4.36494	+	13.4339i	−0.150695	+	0.463790i	−0.997699	−	0.0677952i	$-0.978404\pi$
$839$	−4.36494	+	13.4339i	−0.150695	+	0.463790i	0.847005	+	0.531585i	$0.178404\pi$
$840$	11.5499	+	0.699810i	0.398509	+	0.0241457i
$841$	17.4867	−	12.7048i	0.602988	−	0.438097i
$842$	27.8556	+	12.4021i	0.959968	+	0.427405i
$843$	−12.9732	−	2.75753i	−0.446819	−	0.0949743i
$844$	3.94143	+	4.37740i	0.135669	+	0.150676i
$845$	4.10984	−	39.1025i	0.141383	−	1.34517i
$846$	−11.7417			−0.403688
$847$	−10.0790	−	27.3023i	−0.346319	−	0.938117i
$848$	−10.9812			−0.377096
$849$	0.274057	−	2.60747i	0.00940560	−	0.0894883i
$850$	−7.06532	−	7.84683i	−0.242339	−	0.269144i
$851$	−15.7307	−	3.34366i	−0.539242	−	0.114619i
$852$	−6.54535	−	2.91418i	−0.224240	−	0.0998381i
$853$	−36.5350	+	26.5442i	−1.25093	+	0.908856i	−0.998276	−	0.0586999i	$-0.981304\pi$
$853$	−36.5350	+	26.5442i	−1.25093	+	0.908856i	−0.252657	+	0.967556i	$0.581304\pi$
$854$	11.3803	−	17.2151i	0.389425	−	0.589087i
$855$	−5.34724	+	16.4571i	−0.182872	+	0.562822i
$856$	0.377328	−	3.59004i	0.0128968	−	0.122705i
$857$	−17.4781	+	30.2730i	−0.597041	+	1.03411i	0.396214	+	0.918158i	$0.370324\pi$
$857$	−17.4781	+	30.2730i	−0.597041	+	1.03411i	−0.993255	+	0.115947i	$0.963010\pi$
$858$	−8.50144	+	13.0237i	−0.290234	+	0.444622i
$859$	1.02976	+	1.78359i	0.0351349	+	0.0608554i	0.883058	−	0.469264i	$-0.155481\pi$
$859$	1.02976	+	1.78359i	0.0351349	+	0.0608554i	−0.847923	+	0.530119i	$0.822147\pi$
$860$	14.9701	+	10.8765i	0.510478	+	0.370884i
$861$	−10.3139	+	3.86291i	−0.351496	+	0.131648i
$862$	0.389071	+	1.19744i	0.0132518	+	0.0407849i
$863$	6.69109	+	2.97906i	0.227767	+	0.101408i	0.517447	−	0.855715i	$-0.326882\pi$
$863$	6.69109	+	2.97906i	0.227767	+	0.101408i	−0.289680	+	0.957123i	$0.593549\pi$
$864$	0.104528	+	0.994522i	0.00355613	+	0.0338343i
$865$	9.38773	+	1.99542i	0.319192	+	0.0678464i
$866$	14.0988	−	2.99680i	0.479098	−	0.101835i
$867$	−13.3013	−	9.66399i	−0.451737	−	0.328206i
$868$	19.7914	−	2.96939i	0.671764	−	0.100788i
$869$	−18.5566	−	15.0995i	−0.629489	−	0.512214i
$870$	−5.94263	−	10.2929i	−0.201474	−	0.348963i
$871$	−5.20085	+	2.31557i	−0.176224	+	0.0784601i
$872$	−4.11411	−	4.56919i	−0.139321	−	0.154732i
$873$	6.35345	−	7.05622i	0.215032	−	0.238817i
$874$	16.9849	−	12.3403i	0.574524	−	0.417416i
$875$	−26.5012	−	102.232i	−0.895903	−	3.45607i
$876$	−0.724544	−	2.22992i	−0.0244801	−	0.0753419i
$877$	17.9555	−	3.81656i	0.606314	−	0.128876i	0.105483	−	0.994421i	$-0.466361\pi$
$877$	17.9555	−	3.81656i	0.606314	−	0.128876i	0.500831	+	0.865545i	$0.333028\pi$
$878$	23.3571	−	10.3993i	0.788265	−	0.350958i
$879$	−12.1467	+	21.0387i	−0.409697	+	0.709616i
$880$	14.3319	−	2.23529i	0.483127	−	0.0753518i
$881$	−12.9880			−0.437578			−0.218789	−	0.975772i	$-0.570211\pi$
$881$	−12.9880			−0.437578			−0.218789	+	0.975772i	$0.570211\pi$
$882$	−6.62123	−	2.27143i	−0.222948	−	0.0764829i
$883$	4.07574	−	12.5438i	0.137160	−	0.422134i	−0.858760	−	0.512378i	$-0.828765\pi$
$883$	4.07574	−	12.5438i	0.137160	−	0.422134i	0.995920	+	0.0902440i	$0.0287647\pi$
$884$	2.34526	−	2.60468i	0.0788797	−	0.0876048i
$885$	3.36706	+	32.0354i	0.113182	+	1.07686i
$886$	3.88570	+	36.9700i	0.130543	+	1.24203i
$887$	18.8276	−	20.9102i	0.632170	−	0.702096i	−0.338918	−	0.940816i	$-0.610061\pi$
$887$	18.8276	−	20.9102i	0.632170	−	0.702096i	0.971088	+	0.238720i	$0.0767277\pi$
$888$	0.936575	−	2.88248i	0.0314294	−	0.0967297i
$889$	37.0147	−	23.6107i	1.24143	−	0.791877i
$890$	11.4679			0.384405
$891$	2.35073	−	2.33967i	0.0787526	−	0.0783818i
$892$	7.74057	−	13.4071i	0.259174	−	0.448902i
$893$	−42.4408	+	18.8959i	−1.42023	+	0.632326i
$894$	−15.0269	+	3.19406i	−0.502573	+	0.106825i
$895$	−5.35593	−	16.4839i	−0.179029	−	0.550995i
$896$	1.88603	−	1.85551i	0.0630077	−	0.0619882i
$897$	20.1305	−	14.6257i	0.672138	−	0.488337i
$898$	−0.366667	+	0.407225i	−0.0122358	+	0.0135893i
$899$	−13.7549	−	15.2763i	−0.458750	−	0.509494i
$900$	12.9058	−	5.74603i	0.430193	−	0.191534i
$901$	−4.10380	−	7.10799i	−0.136717	−	0.236802i
$902$	−11.5966	+	7.49206i	−0.386124	+	0.249458i
$903$	−6.97354	−	8.75668i	−0.232065	−	0.291404i
$904$	8.26269	+	6.00319i	0.274813	+	0.199663i
$905$	45.6641	−	9.70621i	1.51793	−	0.322645i
$906$	3.30473	+	0.702443i	0.109792	+	0.0233371i
$907$	4.92695	+	46.8768i	0.163597	+	1.55652i	0.700980	+	0.713181i	$0.252746\pi$
$907$	4.92695	+	46.8768i	0.163597	+	1.55652i	−0.537383	+	0.843338i	$0.680587\pi$
$908$	−2.56994	−	1.14421i	−0.0852866	−	0.0379720i
$909$	1.91488	+	5.89340i	0.0635126	+	0.195472i
$910$	50.8139	−	19.0316i	1.68447	−	0.630891i
$911$	−27.4462	−	19.9408i	−0.909332	−	0.660668i	0.0315138	−	0.999503i	$-0.489967\pi$
$911$	−27.4462	−	19.9408i	−0.909332	−	0.660668i	−0.940846	+	0.338835i	$0.889967\pi$
$912$	1.97830	+	3.42652i	0.0655081	+	0.113463i
$913$	−1.86201	−	37.2088i	−0.0616237	−	1.23143i
$914$	14.2869	−	24.7456i	0.472567	−	0.818511i
$915$	3.56573	−	33.9257i	0.117879	−	1.12155i
$916$	4.15193	−	12.7783i	0.137184	−	0.422208i
$917$	20.7402	+	41.5391i	0.684903	+	1.37174i
$918$	−0.604678	+	0.439325i	−0.0199574	+	0.0144999i
$919$	11.1285	+	4.95473i	0.367096	+	0.163442i	0.581990	−	0.813196i	$-0.302274\pi$
$919$	11.1285	+	4.95473i	0.367096	+	0.163442i	−0.214895	+	0.976637i	$0.568941\pi$
$920$	−22.6993	−	4.82489i	−0.748375	−	0.159072i
$921$	−2.95615	−	3.28314i	−0.0974086	−	0.108183i
$922$	1.12307	−	10.6853i	0.0369864	−	0.351902i
$923$	−33.5982			−1.10590
$924$	−8.71677	−	1.00895i	−0.286761	−	0.0331920i
$925$	−42.8168			−1.40781
$926$	0.630610	−	5.99986i	0.0207231	−	0.197168i
$927$	−4.79177	−	5.32179i	−0.157382	−	0.174791i
$928$	−2.65820	−	0.565019i	−0.0872598	−	0.0185476i
$929$	28.1797	+	12.5464i	0.924547	+	0.411635i	0.813092	−	0.582135i	$-0.197782\pi$
$929$	28.1797	+	12.5464i	0.924547	+	0.411635i	0.111455	+	0.993770i	$0.464449\pi$
$930$	26.7636	−	19.4449i	0.877612	−	0.637623i
$931$	−27.5881	+	2.44536i	−0.904162	+	0.0801434i
$932$	−2.44457	+	7.52361i	−0.0800745	+	0.246444i
$933$	0.499041	−	4.74806i	0.0163379	−	0.155444i
$934$	−5.75907	+	9.97500i	−0.188443	+	0.326392i
$935$	6.80286	+	8.44148i	0.222477	+	0.276066i
$936$	2.34468	+	4.06111i	0.0766383	+	0.132741i
$937$	21.8344	+	15.8636i	0.713299	+	0.518242i	0.884236	−	0.467040i	$-0.154680\pi$
$937$	21.8344	+	15.8636i	0.713299	+	0.518242i	−0.170937	+	0.985282i	$0.554680\pi$
$938$	−2.47965	−	2.04169i	−0.0809634	−	0.0666635i
$939$	5.29135	+	16.2851i	0.172677	+	0.531445i
$940$	46.9123	+	20.8867i	1.53011	+	0.681249i
$941$	−4.46517	−	42.4833i	−0.145560	−	1.38491i	−0.786627	−	0.617429i	$-0.788174\pi$
$941$	−4.46517	−	42.4833i	−0.145560	−	1.38491i	0.641066	−	0.767486i	$-0.278492\pi$
$942$	−14.1922	−	3.01664i	−0.462407	−	0.0982875i
$943$	21.6056	−	4.59241i	0.703575	−	0.149549i
$944$	5.95866	+	4.32922i	0.193938	+	0.140904i
$945$	−11.4430	+	1.71684i	−0.372241	+	0.0558489i
$946$	−10.8846	−	8.85674i	−0.353887	−	0.287957i
$947$	12.0428	+	20.8587i	0.391338	+	0.677817i	0.992626	−	0.121215i	$-0.0386791\pi$
$947$	12.0428	+	20.8587i	0.391338	+	0.677817i	−0.601289	+	0.799032i	$0.705346\pi$
$948$	−6.58963	+	2.93389i	−0.214021	+	0.0952884i
$949$	−7.35711	−	8.17090i	−0.238822	−	0.265239i
$950$	37.4014	−	41.5384i	1.21346	−	1.34768i
$951$	−2.11466	+	1.53639i	−0.0685725	+	0.0498208i
$952$	1.90588	+	0.527376i	0.0617698	+	0.0170924i
$953$	2.58644	+	7.96024i	0.0837830	+	0.257858i	0.984168	−	0.177236i	$-0.0567154\pi$
$953$	2.58644	+	7.96024i	0.0837830	+	0.257858i	−0.900385	+	0.435093i	$0.856715\pi$
$954$	10.7412	−	2.28312i	0.347760	−	0.0739187i
$955$	3.50079	−	1.55865i	0.113283	−	0.0504369i
$956$	−11.5362	+	19.9813i	−0.373107	+	0.646240i
$957$	4.07296	+	8.04047i	0.131660	+	0.259912i
$958$	−11.7716			−0.380322
$959$	0.698625	+	15.7944i	0.0225598	+	0.510028i
$960$	1.35147	−	4.15941i	0.0436186	−	0.134244i
$961$	17.5424	−	19.4828i	0.565884	−	0.628478i
$962$	−1.48562	−	14.1348i	−0.0478984	−	0.455723i
$963$	0.377328	+	3.59004i	0.0121592	+	0.115687i
$964$	14.4644	−	16.0643i	0.465866	−	0.517397i
$965$	31.8417	−	97.9988i	1.02502	−	3.15469i
$966$	12.4563	+	6.47533i	0.400776	+	0.208340i
$967$	−18.7947			−0.604398			−0.302199	−	0.953245i	$-0.597721\pi$
$967$	−18.7947			−0.604398			−0.302199	+	0.953245i	$0.597721\pi$
$968$	−10.9450	+	1.09818i	−0.351787	+	0.0352969i
$969$	−1.47863	+	2.56106i	−0.0475004	+	0.0822731i
$970$	−37.9362	+	16.8903i	−1.21806	+	0.542314i
$971$	−9.88548	+	2.10122i	−0.317240	+	0.0674315i	−0.363780	−	0.931485i	$-0.618514\pi$
$971$	−9.88548	+	2.10122i	−0.317240	+	0.0674315i	0.0465396	+	0.998916i	$0.485181\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	10.7474	+	41.4595i	0.344546	+	1.32913i
$974$	5.01292	−	3.64210i	0.160624	−	0.116701i
$975$	44.3281	−	49.2313i	1.41963	−	1.57666i
$976$	−5.21915	−	5.79645i	−0.167061	−	0.185540i
$977$	6.89906	−	3.07166i	0.220721	−	0.0982711i	−0.293398	−	0.955991i	$-0.594786\pi$
$977$	6.89906	−	3.07166i	0.220721	−	0.0982711i	0.514118	+	0.857719i	$0.328119\pi$
$978$	−8.36909	−	14.4957i	−0.267614	−	0.463521i
$979$	−8.68370	−	0.475639i	−0.277532	−	0.0152015i
$980$	22.4136	+	20.8533i	0.715977	+	0.666134i
$981$	4.97420	+	3.61397i	0.158814	+	0.115385i
$982$	−1.19231	+	0.253433i	−0.0380480	+	0.00808736i
$983$	−29.0902	−	6.18332i	−0.927835	−	0.197217i	−0.280878	−	0.959744i	$-0.590625\pi$
$983$	−29.0902	−	6.18332i	−0.927835	−	0.197217i	−0.646957	+	0.762526i	$0.723959\pi$
$984$	0.435124	+	4.13992i	0.0138712	+	0.131976i
$985$	15.7731	+	7.02264i	0.502573	+	0.223760i
$986$	−0.627672	−	1.93178i	−0.0199892	−	0.0615203i
$987$	−23.9823	−	19.7465i	−0.763364	−	0.628538i
$988$	15.0105	+	10.9057i	0.477546	+	0.346958i
$989$	11.2253	+	19.4427i	0.356943	+	0.618243i
$990$	−13.5539	+	5.16621i	−0.430772	+	0.164193i
$991$	−7.14071	+	12.3681i	−0.226832	+	0.392885i	−0.956868	−	0.290524i	$-0.906170\pi$
$991$	−7.14071	+	12.3681i	−0.226832	+	0.392885i	0.730035	+	0.683409i	$0.239504\pi$
$992$	0.790671	−	7.52274i	0.0251038	−	0.238847i
$993$	3.56735	−	10.9792i	0.113206	−	0.348414i
$994$	−8.46790	−	16.9597i	−0.268585	−	0.537930i
$995$	−56.7034	+	41.1974i	−1.79762	+	1.30605i
$996$	−10.2618	−	4.56884i	−0.325157	−	0.144769i
$997$	−39.3453	−	8.36311i	−1.24608	−	0.264862i	−0.462761	−	0.886483i	$-0.653141\pi$
$997$	−39.3453	−	8.36311i	−1.24608	−	0.264862i	−0.783318	+	0.621621i	$0.786475\pi$
$998$	8.68222	+	9.64259i	0.274831	+	0.305231i
$999$	−0.316807	+	3.01422i	−0.0100233	+	0.0953656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.235.1	yes	40
7.2	even	3	inner	462.2.y.d.37.5	yes	40
11.3	even	5	inner	462.2.y.d.25.5	✓	40
77.58	even	15	inner	462.2.y.d.289.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.5	✓	40	11.3	even	5	inner
462.2.y.d.37.5	yes	40	7.2	even	3	inner
462.2.y.d.235.1	yes	40	1.1	even	1	trivial
462.2.y.d.289.1	yes	40	77.58	even	15	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.99535 - 1.77885i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.64091 + 0.160013i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-3.99535 - 1.77885i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.64091 + 0.160013i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(2.18673 - 3.78753i) q^{10} +(-1.81292 + 2.77729i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.79377 + 2.75634i) q^{13} +(-0.435186 + 2.60972i) q^{14} +(1.35147 + 4.15941i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.0781270 + 0.743329i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-3.87014 + 0.822624i) q^{19} +(3.53820 + 2.57065i) q^{20} +(-1.64820 - 2.06965i) q^{21} +(-2.57257 - 2.09329i) q^{22} +(2.65310 + 4.59530i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(9.45290 + 10.4985i) q^{25} +(-3.13780 + 3.48488i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.54993 - 0.705592i) q^{28} +(0.839781 + 2.58458i) q^{29} +(-4.27789 + 0.909293i) q^{30} +(-6.91022 + 3.07663i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.27701 - 0.511105i) q^{33} -0.747424 q^{34} +(-10.2667 - 5.33708i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-2.02801 + 2.25234i) q^{37} +(-0.413578 - 3.93493i) q^{38} +(-0.490172 - 4.66367i) q^{39} +(-2.92641 + 3.25011i) q^{40} +(1.28635 - 3.95899i) q^{41} +(2.23059 - 1.42283i) q^{42} +4.23100 q^{43} +(2.35073 - 2.33967i) q^{44} +(2.18673 - 3.78753i) q^{45} +(-4.84745 + 2.15823i) q^{46} +(11.4851 - 2.44124i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(6.94879 + 0.845159i) q^{49} +(-11.4291 + 8.30372i) q^{50} +(0.500124 - 0.555444i) q^{51} +(-3.13780 - 3.48488i) q^{52} +(-10.0318 + 4.46645i) q^{53} +(0.500000 + 0.866025i) q^{54} +(12.1836 - 7.87133i) q^{55} +(0.968267 - 2.46221i) q^{56} +(3.20096 + 2.32563i) q^{57} +(-2.65820 + 0.565019i) q^{58} +(7.20436 + 1.53133i) q^{59} +(-0.457151 - 4.34950i) q^{60} +(-7.12556 - 3.17250i) q^{61} +(-2.33746 - 7.19396i) q^{62} +(-0.435186 + 2.60972i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-10.2544 - 17.7611i) q^{65} +(0.165764 + 3.31248i) q^{66} +(-0.607017 + 1.05138i) q^{67} +(0.0781270 - 0.743329i) q^{68} +(1.63971 - 5.04649i) q^{69} +(6.38100 - 9.65260i) q^{70} +(-5.79643 + 4.21135i) q^{71} +(0.913545 + 0.406737i) q^{72} +(-2.29344 - 0.487485i) q^{73} +(-2.02801 - 2.25234i) q^{74} +(1.47669 - 14.0498i) q^{75} +3.95660 q^{76} +(-5.23216 + 7.04447i) q^{77} +4.68936 q^{78} +(-0.753990 + 7.17373i) q^{79} +(-2.92641 - 3.25011i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(3.80284 + 1.69313i) q^{82} +(-9.08761 + 6.60254i) q^{83} +(1.18188 + 2.36710i) q^{84} +(1.01012 - 3.10884i) q^{85} +(-0.442260 + 4.20783i) q^{86} +(1.35879 - 2.35350i) q^{87} +(2.08113 + 2.58242i) q^{88} +(1.31108 + 2.27086i) q^{89} +(3.53820 + 2.57065i) q^{90} +(9.57796 + 7.88629i) q^{91} +(-1.63971 - 5.04649i) q^{92} +(6.91022 + 3.07663i) q^{93} +(1.22734 + 11.6774i) q^{94} +(16.9259 + 3.59771i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-7.68168 - 5.58107i) q^{97} +(-1.56688 + 6.82238i) q^{98} +(-2.57257 - 2.09329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

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