LMFDB - Embedded newform 462.2.y.a.235.3

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.3
Character	$\chi$	$=$	462.235
Dual form			462.2.y.a.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.35782 + 1.04977i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.43391 - 2.22349i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.35782 + 1.04977i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.43391 - 2.22349i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(1.29048 - 2.23517i) q^{10} +(1.89143 - 2.72442i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.71598 - 2.69982i) q^{13} +(-2.36119 + 1.19364i) q^{14} +(-0.797558 - 2.45463i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.0531737 - 0.505914i) q^{17} +(0.978148 + 0.207912i) q^{18} +(7.29250 - 1.55007i) q^{19} +(-2.08803 - 1.51705i) q^{20} +(-0.692898 + 2.55341i) q^{21} +(-2.51179 - 2.16585i) q^{22} +(-2.63753 - 4.56834i) q^{23} +(0.913545 - 0.406737i) q^{24} +(1.11164 + 1.23460i) q^{25} +(-3.07345 + 3.41342i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.940289 + 2.47303i) q^{28} +(-1.41639 - 4.35919i) q^{29} +(-2.52455 + 0.536610i) q^{30} +(-2.85562 + 1.27140i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.29026 + 0.417385i) q^{33} -0.508700 q^{34} +(-1.04676 - 6.74785i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-6.29488 + 6.99117i) q^{37} +(-0.779303 - 7.41457i) q^{38} +(0.480120 + 4.56804i) q^{39} +(-1.72699 + 1.91802i) q^{40} +(0.269143 - 0.828337i) q^{41} +(2.46699 + 0.956006i) q^{42} +9.54037 q^{43} +(-2.41654 + 2.27164i) q^{44} +(-1.29048 + 2.23517i) q^{45} +(-4.81901 + 2.14556i) q^{46} +(-4.58611 + 0.974808i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-2.88779 + 6.37657i) q^{49} +(1.34403 - 0.976495i) q^{50} +(-0.340387 + 0.378038i) q^{51} +(3.07345 + 3.41342i) q^{52} +(-4.72176 + 2.10226i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(7.31967 - 4.43812i) q^{55} +(2.55777 - 0.676637i) q^{56} +(-6.03156 - 4.38218i) q^{57} +(-4.48336 + 0.952968i) q^{58} +(5.15889 + 1.09656i) q^{59} +(0.269783 + 2.56681i) q^{60} +(9.81572 + 4.37024i) q^{61} +(0.965945 + 2.97287i) q^{62} +(2.36119 - 1.19364i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-5.92742 - 10.2666i) q^{65} +(0.0711727 + 3.31586i) q^{66} +(2.02628 - 3.50961i) q^{67} +(-0.0531737 + 0.505914i) q^{68} +(-1.63009 + 5.01689i) q^{69} +(-6.82030 + 0.335682i) q^{70} +(9.68258 - 7.03481i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(8.56379 + 1.82029i) q^{73} +(6.29488 + 6.99117i) q^{74} +(0.173654 - 1.65221i) q^{75} -7.45541 q^{76} +(-8.76987 - 0.298996i) q^{77} +4.59320 q^{78} +(-0.859434 + 8.17697i) q^{79} +(1.72699 + 1.91802i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.795666 - 0.354253i) q^{82} +(4.44183 - 3.22718i) q^{83} +(1.20864 - 2.35355i) q^{84} +(0.405718 - 1.24867i) q^{85} +(0.997240 - 9.48810i) q^{86} +(-2.29176 + 3.96945i) q^{87} +(2.00659 + 2.64075i) q^{88} +(2.45001 + 4.24355i) q^{89} +(2.08803 + 1.51705i) q^{90} +(-0.674618 + 12.1337i) q^{91} +(1.63009 + 5.01689i) q^{92} +(2.85562 + 1.27140i) q^{93} +(0.490089 + 4.66288i) q^{94} +(18.8216 + 4.00065i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(12.1255 + 8.80966i) q^{97} +(6.03978 + 3.53850i) q^{98} +(2.51179 + 2.16585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * 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
$5$	2.35782	+	1.04977i	1.05445	+	0.469470i	0.859390	−	0.511321i	$-0.170844\pi$
$5$	2.35782	+	1.04977i	1.05445	+	0.469470i	0.195058	+	0.980792i	$0.437510\pi$
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−1.43391	−	2.22349i	−0.541968	−	0.840399i
$7$	−1.43391	−	2.22349i	−0.541968	−	0.840399i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	1.29048	−	2.23517i	0.408084	−	0.706823i
$11$	1.89143	−	2.72442i	0.570289	−	0.821444i
$11$	1.89143	−	2.72442i	0.570289	−	0.821444i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.71598	−	2.69982i	−1.03063	−	0.748795i	−0.0621932	−	0.998064i	$-0.519809\pi$
$13$	−3.71598	−	2.69982i	−1.03063	−	0.748795i	−0.968434	+	0.249270i	$0.919809\pi$
$14$	−2.36119	+	1.19364i	−0.631055	+	0.319014i
$15$	−0.797558	−	2.45463i	−0.205929	−	0.633783i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.0531737	−	0.505914i	−0.0128965	−	0.122702i	0.986179	−	0.165680i	$-0.0529820\pi$
$17$	−0.0531737	−	0.505914i	−0.0128965	−	0.122702i	−0.999076	+	0.0429783i	$0.986315\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	7.29250	−	1.55007i	1.67301	−	0.355610i	0.728745	−	0.684786i	$-0.240104\pi$
$19$	7.29250	−	1.55007i	1.67301	−	0.355610i	0.944269	+	0.329176i	$0.106771\pi$
$20$	−2.08803	−	1.51705i	−0.466899	−	0.339222i
$21$	−0.692898	+	2.55341i	−0.151203	+	0.557199i
$22$	−2.51179	−	2.16585i	−0.535515	−	0.461761i
$23$	−2.63753	−	4.56834i	−0.549964	−	0.952565i	−0.998276	−	0.0586883i	$-0.981308\pi$
$23$	−2.63753	−	4.56834i	−0.549964	−	0.952565i	0.448313	−	0.893877i	$-0.352025\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	1.11164	+	1.23460i	0.222327	+	0.246919i
$26$	−3.07345	+	3.41342i	−0.602754	+	0.669426i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.940289	+	2.47303i	0.177698	+	0.467358i
$29$	−1.41639	−	4.35919i	−0.263016	−	0.809481i	−0.992144	−	0.125103i	$-0.960074\pi$
$29$	−1.41639	−	4.35919i	−0.263016	−	0.809481i	0.729127	−	0.684378i	$-0.239926\pi$
$30$	−2.52455	+	0.536610i	−0.460918	+	0.0979711i
$31$	−2.85562	+	1.27140i	−0.512884	+	0.228351i	−0.646825	−	0.762639i	$-0.723904\pi$
$31$	−2.85562	+	1.27140i	−0.512884	+	0.228351i	0.133941	+	0.990989i	$0.457237\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.29026	+	0.417385i	−0.572760	+	0.0726573i
$34$	−0.508700			−0.0872414
$35$	−1.04676	−	6.74785i	−0.176935	−	1.14059i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−6.29488	+	6.99117i	−1.03487	+	1.14934i	−0.0462476	+	0.998930i	$0.514726\pi$
$37$	−6.29488	+	6.99117i	−1.03487	+	1.14934i	−0.988624	+	0.150411i	$0.951940\pi$
$38$	−0.779303	−	7.41457i	−0.126420	−	1.20280i
$39$	0.480120	+	4.56804i	0.0768808	+	0.731472i
$40$	−1.72699	+	1.91802i	−0.273062	+	0.303266i
$41$	0.269143	−	0.828337i	0.0420331	−	0.129365i	−0.927838	−	0.372984i	$-0.878335\pi$
$41$	0.269143	−	0.828337i	0.0420331	−	0.129365i	0.969871	+	0.243619i	$0.0783347\pi$
$42$	2.46699	+	0.956006i	0.380665	+	0.147515i
$43$	9.54037			1.45489			0.727446	−	0.686165i	$-0.240707\pi$
$43$	9.54037			1.45489			0.727446	+	0.686165i	$0.240707\pi$
$44$	−2.41654	+	2.27164i	−0.364307	+	0.342462i
$45$	−1.29048	+	2.23517i	−0.192373	+	0.333199i
$46$	−4.81901	+	2.14556i	−0.710525	+	0.316346i
$47$	−4.58611	+	0.974808i	−0.668953	+	0.142190i	−0.529855	−	0.848088i	$-0.677754\pi$
$47$	−4.58611	+	0.974808i	−0.668953	+	0.142190i	−0.139098	+	0.990279i	$0.544420\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−2.88779	+	6.37657i	−0.412541	+	0.910939i
$50$	1.34403	−	0.976495i	0.190075	−	0.138097i
$51$	−0.340387	+	0.378038i	−0.0476637	+	0.0529359i
$52$	3.07345	+	3.41342i	0.426211	+	0.473356i
$53$	−4.72176	+	2.10226i	−0.648583	+	0.288768i	−0.704539	−	0.709665i	$-0.748846\pi$
$53$	−4.72176	+	2.10226i	−0.648583	+	0.288768i	0.0559557	+	0.998433i	$0.482179\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	7.31967	−	4.43812i	0.986984	−	0.598436i
$56$	2.55777	−	0.676637i	0.341796	−	0.0904194i
$57$	−6.03156	−	4.38218i	−0.798899	−	0.580434i
$58$	−4.48336	+	0.952968i	−0.588694	+	0.125131i
$59$	5.15889	+	1.09656i	0.671630	+	0.142759i	0.531090	−	0.847316i	$-0.321783\pi$
$59$	5.15889	+	1.09656i	0.671630	+	0.142759i	0.140540	+	0.990075i	$0.455116\pi$
$60$	0.269783	+	2.56681i	0.0348288	+	0.331374i
$61$	9.81572	+	4.37024i	1.25677	+	0.559552i	0.923616	−	0.383319i	$-0.125219\pi$
$61$	9.81572	+	4.37024i	1.25677	+	0.559552i	0.333158	+	0.942871i	$0.391886\pi$
$62$	0.965945	+	2.97287i	0.122675	+	0.377555i
$63$	2.36119	−	1.19364i	0.297482	−	0.150384i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−5.92742	−	10.2666i	−0.735206	−	1.27341i
$66$	0.0711727	+	3.31586i	0.00876075	+	0.408154i
$67$	2.02628	−	3.50961i	0.247549	−	0.428767i	−0.715296	−	0.698821i	$-0.753708\pi$
$67$	2.02628	−	3.50961i	0.247549	−	0.428767i	0.962845	+	0.270054i	$0.0870416\pi$
$68$	−0.0531737	+	0.505914i	−0.00644825	+	0.0613510i
$69$	−1.63009	+	5.01689i	−0.196239	+	0.603962i
$70$	−6.82030	+	0.335682i	−0.815182	+	0.0401217i
$71$	9.68258	−	7.03481i	1.14911	−	0.834878i	0.160749	−	0.986995i	$-0.448609\pi$
$71$	9.68258	−	7.03481i	1.14911	−	0.834878i	0.988362	+	0.152117i	$0.0486091\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	8.56379	+	1.82029i	1.00232	+	0.213049i	0.679707	−	0.733484i	$-0.262107\pi$
$73$	8.56379	+	1.82029i	1.00232	+	0.213049i	0.322608	+	0.946532i	$0.395440\pi$
$74$	6.29488	+	6.99117i	0.731764	+	0.812707i
$75$	0.173654	−	1.65221i	0.0200519	−	0.190781i
$76$	−7.45541			−0.855195
$77$	−8.76987	−	0.298996i	−0.999419	−	0.0340737i
$78$	4.59320			0.520078
$79$	−0.859434	+	8.17697i	−0.0966939	+	0.919981i	0.833403	+	0.552666i	$0.186390\pi$
$79$	−0.859434	+	8.17697i	−0.0966939	+	0.919981i	−0.930097	+	0.367315i	$0.880277\pi$
$80$	1.72699	+	1.91802i	0.193084	+	0.214441i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−0.795666	−	0.354253i	−0.0878666	−	0.0391208i
$83$	4.44183	−	3.22718i	0.487554	−	0.354229i	−0.316689	−	0.948529i	$-0.602571\pi$
$83$	4.44183	−	3.22718i	0.487554	−	0.354229i	0.804243	+	0.594301i	$0.202571\pi$
$84$	1.20864	−	2.35355i	0.131873	−	0.256793i
$85$	0.405718	−	1.24867i	0.0440063	−	0.135437i
$86$	0.997240	−	9.48810i	0.107535	−	1.02313i
$87$	−2.29176	+	3.96945i	−0.245703	+	0.425570i
$88$	2.00659	+	2.64075i	0.213904	+	0.281505i
$89$	2.45001	+	4.24355i	0.259701	+	0.449815i	0.966162	−	0.257937i	$-0.0830427\pi$
$89$	2.45001	+	4.24355i	0.259701	+	0.449815i	−0.706461	+	0.707752i	$0.749709\pi$
$90$	2.08803	+	1.51705i	0.220098	+	0.159911i
$91$	−0.674618	+	12.1337i	−0.0707192	+	1.27196i
$92$	1.63009	+	5.01689i	0.169948	+	0.523047i
$93$	2.85562	+	1.27140i	0.296114	+	0.131838i
$94$	0.490089	+	4.66288i	0.0505488	+	0.480939i
$95$	18.8216	+	4.00065i	1.93105	+	0.410458i
$96$	−0.978148	+	0.207912i	−0.0998318	+	0.0212199i
$97$	12.1255	+	8.80966i	1.23115	+	0.894486i	0.996976	−	0.0777083i	$-0.0247603\pi$
$97$	12.1255	+	8.80966i	1.23115	+	0.894486i	0.234178	+	0.972194i	$0.424760\pi$
$98$	6.03978	+	3.53850i	0.610110	+	0.357443i
$99$	2.51179	+	2.16585i	0.252444	+	0.217676i
$100$	−0.830656	−	1.43874i	−0.0830656	−	0.143874i
$101$	14.8393	−	6.60689i	1.47657	−	0.657410i	0.498726	−	0.866760i	$-0.333801\pi$
$101$	14.8393	−	6.60689i	1.47657	−	0.657410i	0.977841	+	0.209350i	$0.0671348\pi$
$102$	0.340387	+	0.378038i	0.0337033	+	0.0374313i
$103$	4.91385	−	5.45739i	0.484176	−	0.537732i	−0.450714	−	0.892668i	$-0.648831\pi$
$103$	4.91385	−	5.45739i	0.484176	−	0.537732i	0.934891	+	0.354936i	$0.115497\pi$
$104$	3.71598	−	2.69982i	0.364382	−	0.264739i
$105$	−4.31421	+	5.29309i	−0.421024	+	0.516552i
$106$	1.59719	+	4.91564i	0.155133	+	0.477449i
$107$	−15.8160	+	3.36179i	−1.52899	+	0.324996i	−0.894192	−	0.447685i	$-0.852249\pi$
$107$	−15.8160	+	3.36179i	−1.52899	+	0.324996i	−0.634795	+	0.772681i	$0.718915\pi$
$108$	−0.913545	+	0.406737i	−0.0879060	+	0.0391383i
$109$	−0.799681	+	1.38509i	−0.0765955	+	0.132667i	−0.901779	−	0.432197i	$-0.857738\pi$
$109$	−0.799681	+	1.38509i	−0.0765955	+	0.132667i	0.825183	+	0.564865i	$0.191072\pi$
$110$	−3.64870	−	7.74348i	−0.347890	−	0.738312i
$111$	9.40754			0.892925
$112$	−0.405571	−	2.61448i	−0.0383228	−	0.247045i
$113$	−1.65303	+	5.08749i	−0.155504	+	0.478591i	−0.998212	−	0.0597800i	$-0.980960\pi$
$113$	−1.65303	+	5.08749i	−0.155504	+	0.478591i	0.842708	+	0.538371i	$0.180960\pi$
$114$	−4.98865	+	5.54045i	−0.467230	+	0.518911i
$115$	−1.42312	−	13.5401i	−0.132707	−	1.26262i
$116$	0.479109	+	4.55842i	0.0444841	+	0.423238i
$117$	3.07345	−	3.41342i	0.284141	−	0.315570i
$118$	1.62980	−	5.01601i	0.150035	−	0.461761i
$119$	−1.04865	+	0.843667i	−0.0961292	+	0.0773388i
$120$	2.58095			0.235608
$121$	−3.84495	−	10.3061i	−0.349541	−	0.936921i
$122$	5.37232	−	9.30514i	0.486387	−	0.842447i
$123$	−0.795666	+	0.354253i	−0.0717428	+	0.0319420i
$124$	3.05756	−	0.649904i	0.274577	−	0.0583631i
$125$	−2.66280	−	8.19525i	−0.238168	−	0.733005i
$126$	−0.940289	−	2.47303i	−0.0837676	−	0.220315i
$127$	−15.0027	+	10.9001i	−1.33128	+	0.967229i	−0.331560	+	0.943434i	$0.607575\pi$
$127$	−15.0027	+	10.9001i	−1.33128	+	0.967229i	−0.999717	+	0.0237948i	$0.992425\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	−6.38375	−	7.08987i	−0.562058	−	0.624229i
$130$	−10.8299	+	4.82180i	−0.949848	+	0.422900i
$131$	−0.739255	−	1.28043i	−0.0645890	−	0.111871i	0.831923	−	0.554892i	$-0.187240\pi$
$131$	−0.739255	−	1.28043i	−0.0645890	−	0.111871i	−0.896512	+	0.443020i	$0.853907\pi$
$132$	3.30514	+	0.275819i	0.287675	+	0.0240070i
$133$	−13.9034	−	13.9921i	−1.20557	−	1.21327i
$134$	−3.27858	−	2.38203i	−0.283226	−	0.205776i
$135$	2.52455	−	0.536610i	0.217279	−	0.0461840i
$136$	0.497584	+	0.105765i	0.0426675	+	0.00906925i
$137$	1.04744	+	9.96570i	0.0894886	+	0.851428i	0.943544	+	0.331246i	$0.107469\pi$
$137$	1.04744	+	9.96570i	0.0894886	+	0.851428i	−0.854056	+	0.520181i	$0.825864\pi$
$138$	4.81901	+	2.14556i	0.410222	+	0.182642i
$139$	2.61043	+	8.03409i	0.221414	+	0.681443i	0.998636	+	0.0522159i	$0.0166284\pi$
$139$	2.61043	+	8.03409i	0.221414	+	0.681443i	−0.777222	+	0.629227i	$0.783372\pi$
$140$	−0.379072	+	6.81803i	−0.0320375	+	0.576228i
$141$	3.79313	+	2.75587i	0.319439	+	0.232086i
$142$	−5.98417	−	10.3649i	−0.502180	−	0.869801i
$143$	−14.3840	+	5.01737i	−1.20285	+	0.419574i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.23656	−	11.7651i	0.102690	−	0.977034i
$146$	2.70548	−	8.32660i	0.223907	−	0.689114i
$147$	6.67102	−	2.12071i	0.550217	−	0.174914i
$148$	7.61086	−	5.52962i	0.625609	−	0.454532i
$149$	8.03624	+	3.57797i	0.658355	+	0.293118i	0.708592	−	0.705619i	$-0.249331\pi$
$149$	8.03624	+	3.57797i	0.658355	+	0.293118i	−0.0502368	+	0.998737i	$0.515998\pi$
$150$	−1.62501	−	0.345406i	−0.132681	−	0.0282023i
$151$	−11.7048	−	12.9995i	−0.952525	−	1.05789i	−0.998262	−	0.0589323i	$-0.981230\pi$
$151$	−11.7048	−	12.9995i	−0.952525	−	1.05789i	0.0457374	−	0.998953i	$-0.485436\pi$
$152$	−0.779303	+	7.41457i	−0.0632098	+	0.601401i
$153$	0.508700			0.0411260
$154$	−1.21406	+	8.69057i	−0.0978316	+	0.700306i
$155$	−8.06771			−0.648014
$156$	0.480120	−	4.56804i	0.0384404	−	0.365736i
$157$	4.67403	+	5.19104i	0.373028	+	0.414290i	0.900205	−	0.435466i	$-0.143416\pi$
$157$	4.67403	+	5.19104i	0.373028	+	0.414290i	−0.527177	+	0.849755i	$0.676750\pi$
$158$	8.04234	+	1.70945i	0.639814	+	0.135997i
$159$	4.72176	+	2.10226i	0.374460	+	0.166720i
$160$	2.08803	−	1.51705i	0.165074	−	0.119933i
$161$	−6.37566	+	12.4151i	−0.502472	+	0.978449i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	−2.03490	+	19.3608i	−0.159386	+	1.51646i	0.563862	+	0.825869i	$0.309315\pi$
$163$	−2.03490	+	19.3608i	−0.159386	+	1.51646i	−0.723248	+	0.690588i	$0.757352\pi$
$164$	−0.435483	+	0.754278i	−0.0340055	+	0.0588992i
$165$	−8.19598	−	2.46989i	−0.638056	−	0.192281i
$166$	−2.74520	−	4.75482i	−0.213069	−	0.369046i
$167$	12.8184	+	9.31311i	0.991918	+	0.720670i	0.960340	−	0.278831i	$-0.0899469\pi$
$167$	12.8184	+	9.31311i	0.991918	+	0.720670i	0.0315775	+	0.999501i	$0.489947\pi$
$168$	−2.21432	−	1.44803i	−0.170838	−	0.111718i
$169$	2.50227	+	7.70120i	0.192482	+	0.592400i
$170$	−1.19942	−	0.534017i	−0.0919915	−	0.0409573i
$171$	0.779303	+	7.41457i	0.0595948	+	0.567007i
$172$	−9.33189	−	1.98355i	−0.711550	−	0.151245i
$173$	−4.96181	+	1.05467i	−0.377239	+	0.0801847i	−0.392629	−	0.919697i	$-0.628434\pi$
$173$	−4.96181	+	1.05467i	−0.377239	+	0.0801847i	0.0153898	+	0.999882i	$0.495101\pi$
$174$	3.70815	+	2.69413i	0.281114	+	0.204241i
$175$	1.15112	−	4.24201i	0.0870165	−	0.320666i
$176$	2.83603	−	1.71957i	0.213774	−	0.129617i
$177$	−2.63707	−	4.56754i	−0.198214	−	0.343317i
$178$	4.47640	−	1.99302i	0.335520	−	0.149383i
$179$	−1.10576	−	1.22808i	−0.0826487	−	0.0917907i	0.700402	−	0.713749i	$-0.253004\pi$
$179$	−1.10576	−	1.22808i	−0.0826487	−	0.0917907i	−0.783051	+	0.621958i	$0.786337\pi$
$180$	1.72699	−	1.91802i	0.128723	−	0.142961i
$181$	5.26806	−	3.82747i	0.391572	−	0.284493i	−0.374528	−	0.927216i	$-0.622195\pi$
$181$	5.26806	−	3.82747i	0.391572	−	0.284493i	0.766099	+	0.642722i	$0.222195\pi$
$182$	11.9967	+	1.93924i	0.889258	+	0.143746i
$183$	−3.32028	−	10.2188i	−0.245442	−	0.755393i
$184$	5.15979	−	1.09675i	0.380385	−	0.0808533i
$185$	−22.1813	+	9.87574i	−1.63080	+	0.726079i
$186$	1.56293	−	2.70708i	0.114600	−	0.198493i
$187$	−1.47890	−	0.812035i	−0.108148	−	0.0593819i
$188$	4.68857			0.341949
$189$	−2.46699	−	0.956006i	−0.179447	−	0.0695392i
$190$	5.94613	−	18.3003i	0.431377	−	1.32764i
$191$	−7.43674	+	8.25934i	−0.538104	+	0.597625i	−0.949475	−	0.313843i	$-0.898383\pi$
$191$	−7.43674	+	8.25934i	−0.538104	+	0.597625i	0.411371	+	0.911468i	$0.365050\pi$
$192$	0.104528	+	0.994522i	0.00754369	+	0.0717734i
$193$	1.82134	+	17.3289i	0.131103	+	1.24736i	0.840211	+	0.542260i	$0.182431\pi$
$193$	1.82134	+	17.3289i	0.131103	+	1.24736i	−0.709108	+	0.705100i	$0.750902\pi$
$194$	10.0289	−	11.1382i	0.720030	−	0.799674i
$195$	−3.66335	+	11.2746i	−0.262338	+	0.807392i
$196$	4.15045	−	5.63682i	0.296461	−	0.402630i
$197$	−12.0569			−0.859016			−0.429508	−	0.903063i	$-0.641313\pi$
$197$	−12.0569			−0.859016			−0.429508	+	0.903063i	$0.641313\pi$
$198$	2.41654	−	2.27164i	0.171736	−	0.161438i
$199$	5.05611	−	8.75744i	0.358418	−	0.620798i	−0.629279	−	0.777180i	$-0.716650\pi$
$199$	5.05611	−	8.75744i	0.358418	−	0.620798i	0.987697	+	0.156381i	$0.0499829\pi$
$200$	−1.51768	+	0.675717i	−0.107317	+	0.0477804i
$201$	−3.96399	+	0.842573i	−0.279598	+	0.0594305i
$202$	−5.01956	−	15.4486i	−0.353175	−	1.08696i
$203$	−7.66163	+	9.40002i	−0.537741	+	0.659752i
$204$	0.411547	−	0.299007i	0.0288141	−	0.0209346i
$205$	1.50415	−	1.67053i	0.105055	−	0.116675i
$206$	−4.91385	−	5.45739i	−0.342364	−	0.380234i
$207$	4.81901	−	2.14556i	0.334945	−	0.149127i
$208$	−2.29660	−	3.97783i	−0.159241	−	0.275813i
$209$	9.57024	−	22.7997i	0.661987	−	1.57709i
$210$	4.81313	+	4.84386i	0.332138	+	0.334258i
$211$	1.03651	+	0.753066i	0.0713561	+	0.0518432i	0.622891	−	0.782308i	$-0.285958\pi$
$211$	1.03651	+	0.753066i	0.0713561	+	0.0518432i	−0.551535	+	0.834152i	$0.685958\pi$
$212$	5.05566	−	1.07461i	0.347224	−	0.0738048i
$213$	−11.7068	−	2.48836i	−0.802136	−	0.170499i
$214$	1.69015	+	16.0807i	0.115536	+	1.09926i
$215$	22.4944	+	10.0152i	1.53411	+	0.683029i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	6.92166	+	4.52635i	0.469873	+	0.307269i
$218$	1.29391	+	0.940081i	0.0876347	+	0.0636703i
$219$	−4.37755	−	7.58215i	−0.295808	−	0.512354i
$220$	−8.08245	+	2.81929i	−0.544919	+	0.190077i
$221$	−1.16828	+	2.02352i	−0.0785872	+	0.136117i
$222$	0.983356	−	9.35601i	0.0659985	−	0.627934i
$223$	3.33097	−	10.2517i	0.223058	−	0.686502i	−0.775425	−	0.631440i	$-0.782464\pi$
$223$	3.33097	−	10.2517i	0.223058	−	0.686502i	0.998483	−	0.0550623i	$-0.0175357\pi$
$224$	−2.64255	+	0.130061i	−0.176563	+	0.00869009i
$225$	−1.34403	+	0.976495i	−0.0896020	+	0.0650997i
$226$	4.88683	+	2.17576i	0.325067	+	0.144729i
$227$	0.210702	+	0.0447861i	0.0139848	+	0.00297256i	0.214899	−	0.976636i	$-0.431058\pi$
$227$	0.210702	+	0.0447861i	0.0139848	+	0.00297256i	−0.200914	+	0.979609i	$0.564391\pi$
$228$	4.98865	+	5.54045i	0.330381	+	0.366925i
$229$	−2.79448	+	26.5877i	−0.184665	+	1.75697i	0.373865	+	0.927483i	$0.378032\pi$
$229$	−2.79448	+	26.5877i	−0.184665	+	1.75697i	−0.558530	+	0.829484i	$0.688634\pi$
$230$	−13.6147			−0.897726
$231$	5.64599	+	6.71735i	0.371479	+	0.441969i
$232$	4.58352			0.300923
$233$	1.99814	−	19.0110i	0.130902	−	1.24545i	−0.709974	−	0.704227i	$-0.751294\pi$
$233$	1.99814	−	19.0110i	0.130902	−	1.24545i	0.840877	−	0.541226i	$-0.182040\pi$
$234$	−3.07345	−	3.41342i	−0.200918	−	0.223142i
$235$	−11.8365	−	2.51593i	−0.772130	−	0.164121i
$236$	−4.81817	−	2.14519i	−0.313636	−	0.139640i
$237$	6.65175	−	4.83278i	0.432077	−	0.313923i
$238$	0.729432	+	1.13109i	0.0472821	+	0.0733176i
$239$	5.96697	−	18.3645i	0.385971	−	1.18790i	−0.549802	−	0.835295i	$-0.685297\pi$
$239$	5.96697	−	18.3645i	0.385971	−	1.18790i	0.935773	−	0.352603i	$-0.114703\pi$
$240$	0.269783	−	2.56681i	0.0174144	−	0.165687i
$241$	3.38348	−	5.86035i	0.217949	−	0.377499i	−0.736232	−	0.676729i	$-0.763397\pi$
$241$	3.38348	−	5.86035i	0.217949	−	0.377499i	0.954181	+	0.299231i	$0.0967301\pi$
$242$	−10.6516	+	2.74661i	−0.684710	+	0.176558i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−8.69260	−	6.31554i	−0.556487	−	0.404311i
$245$	−13.5028	+	12.0033i	−0.862662	+	0.766862i
$246$	0.269143	+	0.828337i	0.0171599	+	0.0528128i
$247$	−31.2837	−	13.9284i	−1.99053	−	0.886242i
$248$	−0.326742	−	3.10874i	−0.0207481	−	0.197405i
$249$	−5.37042	−	1.14152i	−0.340337	−	0.0723408i
$250$	−8.42869	+	1.79157i	−0.533077	+	0.113309i
$251$	−21.4165	−	15.5600i	−1.35180	−	0.982140i	−0.998920	−	0.0464710i	$-0.985202\pi$
$251$	−21.4165	−	15.5600i	−1.35180	−	0.982140i	−0.352880	−	0.935669i	$-0.614798\pi$
$252$	−2.55777	+	0.676637i	−0.161124	+	0.0426241i
$253$	−17.4348	−	1.45496i	−1.09612	−	0.0914728i
$254$	9.27219	+	16.0599i	0.581789	+	1.00769i
$255$	−1.19942	+	0.534017i	−0.0751107	+	0.0334415i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−8.97914	+	9.97235i	−0.560103	+	0.622058i	−0.954978	−	0.296677i	$-0.904121\pi$
$257$	−8.97914	+	9.97235i	−0.560103	+	0.622058i	0.394874	+	0.918735i	$0.370788\pi$
$258$	−7.71832	+	5.60769i	−0.480522	+	0.349119i
$259$	24.5711	+	3.97185i	1.52677	+	0.246799i
$260$	3.66335	+	11.2746i	0.227191	+	0.699222i
$261$	4.48336	−	0.952968i	0.277513	−	0.0589873i
$262$	−1.35069	+	0.601364i	−0.0834457	+	0.0371524i
$263$	13.8015	−	23.9049i	0.851036	−	1.47404i	−0.0292379	−	0.999572i	$-0.509308\pi$
$263$	13.8015	−	23.9049i	0.851036	−	1.47404i	0.880274	−	0.474465i	$-0.157359\pi$
$264$	0.619789	−	3.25820i	0.0381454	−	0.200528i
$265$	−13.3399			−0.819465
$266$	−15.3688	+	12.3646i	−0.942319	+	0.758124i
$267$	1.51419	−	4.66020i	0.0926670	−	0.285200i
$268$	−2.71169	+	3.01163i	−0.165643	+	0.183965i
$269$	1.64701	+	15.6702i	0.100420	+	0.955430i	0.922484	+	0.386035i	$0.126156\pi$
$269$	1.64701	+	15.6702i	0.100420	+	0.955430i	−0.822064	+	0.569395i	$0.807178\pi$
$270$	−0.269783	−	2.56681i	−0.0164185	−	0.156211i
$271$	−9.39157	+	10.4304i	−0.570497	+	0.633601i	−0.957485	−	0.288484i	$-0.906849\pi$
$271$	−9.39157	+	10.4304i	−0.570497	+	0.633601i	0.386988	+	0.922085i	$0.373516\pi$
$272$	0.157197	−	0.483803i	0.00953147	−	0.0293349i
$273$	9.46853	−	7.61771i	0.573061	−	0.461045i
$274$	10.0206			0.605366
$275$	5.46615	−	0.693406i	0.329621	−	0.0418140i
$276$	2.63753	−	4.56834i	0.158761	−	0.274982i
$277$	8.12451	−	3.61726i	0.488154	−	0.217340i	−0.147874	−	0.989006i	$-0.547243\pi$
$277$	8.12451	−	3.61726i	0.488154	−	0.217340i	0.636028	+	0.771666i	$0.280576\pi$
$278$	8.26295	−	1.75634i	0.495579	−	0.105338i
$279$	−0.965945	−	2.97287i	−0.0578296	−	0.177981i
$280$	6.74105	+	1.08967i	0.402855	+	0.0651205i
$281$	−14.0048	+	10.1751i	−0.835457	+	0.606995i	−0.921098	−	0.389331i	$-0.872706\pi$
$281$	−14.0048	+	10.1751i	−0.835457	+	0.606995i	0.0856411	+	0.996326i	$0.472706\pi$
$282$	3.13726	−	3.48428i	0.186821	−	0.207486i
$283$	−20.0308	−	22.2465i	−1.19071	−	1.32242i	−0.934571	−	0.355778i	$-0.884216\pi$
$283$	−20.0308	−	22.2465i	−1.19071	−	1.32242i	−0.256139	−	0.966640i	$-0.582451\pi$
$284$	−10.9336	+	4.86796i	−0.648791	+	0.288860i
$285$	−9.62103	−	16.6641i	−0.569901	−	0.987097i
$286$	3.48635	+	14.8296i	0.206152	+	0.876895i
$287$	−2.22772	+	0.589327i	−0.131498	+	0.0347869i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	16.3754	−	3.48070i	0.963258	−	0.204747i
$290$	−11.5713	−	2.45957i	−0.679493	−	0.144431i
$291$	−1.56666	−	14.9058i	−0.0918393	−	0.873793i
$292$	−7.99819	−	3.56102i	−0.468059	−	0.208393i
$293$	−5.75889	−	17.7240i	−0.336438	−	1.03545i	−0.966009	−	0.258507i	$-0.916769\pi$
$293$	−5.75889	−	17.7240i	−0.336438	−	1.03545i	0.629571	−	0.776943i	$-0.283231\pi$
$294$	−1.41179	−	6.85616i	−0.0823370	−	0.399859i
$295$	11.0126	+	8.00111i	0.641178	+	0.465843i
$296$	−4.70377	−	8.14717i	−0.273401	−	0.473545i
$297$	−0.0711727	−	3.31586i	−0.00412986	−	0.192406i
$298$	4.39838	−	7.61822i	0.254791	−	0.441312i
$299$	−2.53267	+	24.0967i	−0.146468	+	1.39355i
$300$	−0.513374	+	1.58000i	−0.0296397	+	0.0912215i
$301$	−13.6801	−	21.2129i	−0.788505	−	1.22269i
$302$	−14.1518	+	10.2819i	−0.814344	+	0.591656i
$303$	−14.8393	−	6.60689i	−0.852496	−	0.379556i
$304$	7.29250	+	1.55007i	0.418253	+	0.0889025i
$305$	18.5559	+	20.6085i	1.06251	+	1.18004i
$306$	0.0531737	−	0.505914i	0.00303974	−	0.0289212i
$307$	20.6429			1.17815			0.589076	−	0.808078i	$-0.299492\pi$
$307$	20.6429			1.17815			0.589076	+	0.808078i	$0.299492\pi$
$308$	8.51606	+	2.11582i	0.485248	+	0.120560i
$309$	−7.34364			−0.417765
$310$	−0.843305	+	8.02351i	−0.0478965	+	0.455705i
$311$	8.51815	+	9.46037i	0.483020	+	0.536448i	0.934561	−	0.355802i	$-0.115792\pi$
$311$	8.51815	+	9.46037i	0.483020	+	0.536448i	−0.451541	+	0.892250i	$0.649126\pi$
$312$	−4.49283	−	0.954981i	−0.254356	−	0.0540651i
$313$	−6.17690	−	2.75013i	−0.349139	−	0.155447i	0.224672	−	0.974434i	$-0.427869\pi$
$313$	−6.17690	−	2.75013i	−0.349139	−	0.155447i	−0.573811	+	0.818988i	$0.694536\pi$
$314$	5.65117	−	4.10581i	0.318914	−	0.231704i
$315$	6.82030	−	0.335682i	0.384280	−	0.0189136i
$316$	2.54074	−	7.81960i	0.142928	−	0.439887i
$317$	2.14364	−	20.3953i	0.120399	−	1.14552i	−0.752833	−	0.658211i	$-0.771313\pi$
$317$	2.14364	−	20.3953i	0.120399	−	1.14552i	0.873232	−	0.487305i	$-0.162020\pi$
$318$	2.58430	−	4.47614i	0.144921	−	0.251010i
$319$	−14.5553	−	4.38629i	−0.814939	−	0.245585i
$320$	−1.29048	−	2.23517i	−0.0721398	−	0.124950i
$321$	13.0812	+	9.50407i	0.730123	+	0.530466i
$322$	11.6807	+	7.63846i	0.650939	+	0.425675i
$323$	−1.17197	−	3.60695i	−0.0652101	−	0.200696i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−0.797630	−	7.58895i	−0.0442446	−	0.420959i
$326$	19.0421	+	4.04751i	1.05464	+	0.224171i
$327$	1.56441	−	0.332526i	0.0865121	−	0.0183887i
$328$	0.704626	+	0.511941i	0.0389064	+	0.0282672i
$329$	8.74355	+	8.79937i	0.482048	+	0.485125i
$330$	−3.31307	+	7.89291i	−0.182379	+	0.434490i
$331$	−6.04337	−	10.4674i	−0.332174	−	0.575342i	0.650764	−	0.759280i	$-0.274449\pi$
$331$	−6.04337	−	10.4674i	−0.332174	−	0.575342i	−0.982938	+	0.183938i	$0.941115\pi$
$332$	−5.01573	+	2.23315i	−0.275274	+	0.122560i
$333$	−6.29488	−	6.99117i	−0.344957	−	0.383114i
$334$	10.6020	−	11.7747i	0.580115	−	0.644283i
$335$	8.46186	−	6.14790i	0.462321	−	0.335896i
$336$	−1.67156	+	2.05083i	−0.0911910	+	0.111882i
$337$	−3.94851	−	12.1523i	−0.215089	−	0.661977i	−0.999147	−	0.0412891i	$-0.986854\pi$
$337$	−3.94851	−	12.1523i	−0.215089	−	0.661977i	0.784058	−	0.620688i	$-0.213146\pi$
$338$	7.92057	−	1.68357i	0.430822	−	0.0915741i
$339$	4.88683	−	2.17576i	0.265416	−	0.118171i
$340$	−0.656466	+	1.13703i	−0.0356018	+	0.0616642i
$341$	−1.93738	+	10.1847i	−0.104915	+	0.551532i
$342$	7.45541			0.403143
$343$	18.3191	−	2.72249i	0.989136	−	0.147001i
$344$	−2.94814	+	9.07343i	−0.158953	+	0.489206i
$345$	−9.11001	+	10.1177i	−0.490466	+	0.544718i
$346$	0.530237	+	5.04487i	0.0285057	+	0.271214i
$347$	0.339811	+	3.23309i	0.0182420	+	0.173561i	0.999849	−	0.0173492i	$-0.00552270\pi$
$347$	0.339811	+	3.23309i	0.0182420	+	0.173561i	−0.981607	+	0.190910i	$0.938856\pi$
$348$	3.06698	−	3.40622i	0.164407	−	0.182593i
$349$	−8.06890	+	24.8335i	−0.431918	+	1.32931i	0.464294	+	0.885681i	$0.346308\pi$
$349$	−8.06890	+	24.8335i	−0.431918	+	1.32931i	−0.896212	+	0.443626i	$0.853692\pi$
$350$	−4.09845	−	1.58822i	−0.219071	−	0.0848942i
$351$	−4.59320			−0.245167
$352$	−1.41370	−	3.00024i	−0.0753506	−	0.159913i
$353$	4.55999	−	7.89813i	0.242704	−	0.420375i	−0.718780	−	0.695238i	$-0.755299\pi$
$353$	4.55999	−	7.89813i	0.242704	−	0.420375i	0.961483	+	0.274863i	$0.0886324\pi$
$354$	−4.81817	+	2.14519i	−0.256083	+	0.114015i
$355$	30.2147	−	6.42233i	1.60363	−	0.340862i
$356$	−1.51419	−	4.66020i	−0.0802520	−	0.246990i
$357$	1.32865	+	0.214772i	0.0703195	+	0.0113670i
$358$	−1.33693	+	0.971338i	−0.0706591	+	0.0513368i
$359$	9.83523	−	10.9231i	0.519084	−	0.576501i	−0.425422	−	0.904995i	$-0.639874\pi$
$359$	9.83523	−	10.9231i	0.519084	−	0.576501i	0.944506	+	0.328494i	$0.106541\pi$
$360$	−1.72699	−	1.91802i	−0.0910206	−	0.101089i
$361$	33.4204	−	14.8797i	1.75897	−	0.783144i
$362$	−3.25584	−	5.63928i	−0.171123	−	0.296394i
$363$	−5.08617	+	9.75350i	−0.266955	+	0.511926i
$364$	3.18262	−	11.7283i	0.166815	−	0.614731i
$365$	18.2810	+	13.2819i	0.956869	+	0.695206i
$366$	−10.5098	+	2.23394i	−0.549359	+	0.116770i
$367$	31.3559	+	6.66490i	1.63676	+	0.347905i	0.932259	−	0.361793i	$-0.117835\pi$
$367$	31.3559	+	6.66490i	1.63676	+	0.347905i	0.704506	+	0.709698i	$0.251168\pi$
$368$	−0.551395	−	5.24617i	−0.0287434	−	0.273476i
$369$	0.795666	+	0.354253i	0.0414207	+	0.0184417i
$370$	7.50306	+	23.0921i	0.390066	+	1.20050i
$371$	11.4449	+	7.48430i	0.594192	+	0.388566i
$372$	−2.52888	−	1.83734i	−0.131116	−	0.0952615i
$373$	8.00339	+	13.8623i	0.414400	+	0.717761i	0.995365	−	0.0961669i	$-0.0306583\pi$
$373$	8.00339	+	13.8623i	0.414400	+	0.717761i	−0.580966	+	0.813928i	$0.697325\pi$
$374$	−0.962173	+	1.38591i	−0.0497528	+	0.0716639i
$375$	−4.30850	+	7.46253i	−0.222490	+	0.385364i
$376$	0.490089	−	4.66288i	0.0252744	−	0.240470i
$377$	−6.50575	+	20.0226i	−0.335063	+	1.03122i
$378$	−1.20864	+	2.35355i	−0.0621657	+	0.121053i
$379$	−7.75602	+	5.63508i	−0.398400	+	0.289455i	−0.768889	−	0.639382i	$-0.779190\pi$
$379$	−7.75602	+	5.63508i	−0.398400	+	0.289455i	0.370489	+	0.928837i	$0.379190\pi$
$380$	−17.5785	−	7.82645i	−0.901758	−	0.401489i
$381$	18.1391	+	3.85559i	0.929297	+	0.197528i
$382$	7.43674	+	8.25934i	0.380497	+	0.422584i
$383$	−2.48563	+	23.6492i	−0.127010	+	1.20842i	0.726436	+	0.687234i	$0.241175\pi$
$383$	−2.48563	+	23.6492i	−0.127010	+	1.20842i	−0.853446	+	0.521182i	$0.825491\pi$
$384$	1.00000			0.0510310
$385$	−20.3639	−	9.91130i	−1.03784	−	0.505127i
$386$	17.4243			0.886875
$387$	−0.997240	+	9.48810i	−0.0506926	+	0.482307i
$388$	−10.0289	−	11.1382i	−0.509138	−	0.565455i
$389$	−27.0872	−	5.75755i	−1.37337	−	0.291919i	−0.538622	−	0.842547i	$-0.681055\pi$
$389$	−27.0872	−	5.75755i	−1.37337	−	0.291919i	−0.834751	+	0.550628i	$0.814388\pi$
$390$	10.8299	+	4.82180i	0.548395	+	0.244161i
$391$	−2.17094	+	1.57728i	−0.109789	+	0.0797665i
$392$	−5.17211	−	4.71692i	−0.261231	−	0.238240i
$393$	−0.456885	+	1.40615i	−0.0230468	+	0.0709307i
$394$	−1.26029	+	11.9908i	−0.0634923	+	0.604089i
$395$	−10.6103	+	18.3776i	−0.533863	+	0.924677i
$396$	−2.00659	−	2.64075i	−0.100835	−	0.132703i
$397$	6.15590	+	10.6623i	0.308956	+	0.535127i	0.978134	−	0.207975i	$-0.0666871\pi$
$397$	6.15590	+	10.6623i	0.308956	+	0.535127i	−0.669178	+	0.743102i	$0.733354\pi$
$398$	−8.18096	−	5.94381i	−0.410074	−	0.297936i
$399$	−1.09500	+	19.6948i	−0.0548185	+	0.985971i
$400$	0.513374	+	1.58000i	0.0256687	+	0.0790001i
$401$	3.25171	+	1.44776i	0.162383	+	0.0722975i	0.486319	−	0.873782i	$-0.338339\pi$
$401$	3.25171	+	1.44776i	0.162383	+	0.0722975i	−0.323936	+	0.946079i	$0.605006\pi$
$402$	0.423607	+	4.03035i	0.0211276	+	0.201016i
$403$	14.0440	+	2.98514i	0.699581	+	0.148700i
$404$	−15.8887	+	3.37724i	−0.790492	+	0.168024i
$405$	−2.08803	−	1.51705i	−0.103755	−	0.0753826i
$406$	8.54766	+	8.60223i	0.424213	+	0.426921i
$407$	7.14055	+	30.3732i	0.353944	+	1.50555i
$408$	−0.254350	−	0.440547i	−0.0125922	−	0.0218104i
$409$	−18.6429	+	8.30034i	−0.921831	+	0.410425i	−0.812088	−	0.583535i	$-0.801669\pi$
$409$	−18.6429	+	8.30034i	−0.921831	+	0.410425i	−0.109742	+	0.993960i	$0.535003\pi$
$410$	−1.50415	−	1.67053i	−0.0742848	−	0.0825016i
$411$	6.70509	−	7.44676i	0.330738	−	0.367321i
$412$	−5.94113	+	4.31648i	−0.292698	+	0.212658i
$413$	−4.95922	−	13.0431i	−0.244027	−	0.641808i
$414$	−1.63009	−	5.01689i	−0.0801143	−	0.246567i
$415$	13.8608	−	2.94620i	0.680400	−	0.144623i
$416$	−4.19610	+	1.86822i	−0.205731	+	0.0915972i
$417$	4.22377	−	7.31579i	0.206839	−	0.358256i
$418$	−21.6744	−	11.9010i	−1.06013	−	0.582098i
$419$	−25.0877			−1.22562			−0.612808	−	0.790232i	$-0.709960\pi$
$419$	−25.0877			−1.22562			−0.612808	+	0.790232i	$0.709960\pi$
$420$	5.32043	−	4.28045i	0.259610	−	0.208864i
$421$	0.137571	−	0.423401i	0.00670482	−	0.0206353i	−0.947648	−	0.319316i	$-0.896547\pi$
$421$	0.137571	−	0.423401i	0.00670482	−	0.0206353i	0.954353	+	0.298681i	$0.0965467\pi$
$422$	0.857285	−	0.952112i	0.0417320	−	0.0463481i
$423$	−0.490089	−	4.66288i	−0.0238289	−	0.226717i
$424$	−0.540266	−	5.14029i	−0.0262377	−	0.249635i
$425$	0.565489	−	0.628039i	0.0274303	−	0.0304644i
$426$	−3.69842	+	11.3826i	−0.179189	+	0.551487i
$427$	−4.35772	−	28.0917i	−0.210885	−	1.35945i
$428$	16.1693			0.781573
$429$	13.3534	+	7.33210i	0.644708	+	0.353997i
$430$	12.3116	−	21.3243i	0.593719	−	1.02835i
$431$	27.3936	−	12.1964i	1.31950	−	0.587481i	0.378414	−	0.925637i	$-0.376470\pi$
$431$	27.3936	−	12.1964i	1.31950	−	0.587481i	0.941090	+	0.338156i	$0.109803\pi$
$432$	0.978148	−	0.207912i	0.0470611	−	0.0100032i
$433$	−2.10253	−	6.47091i	−0.101041	−	0.310972i	0.887740	−	0.460345i	$-0.152274\pi$
$433$	−2.10253	−	6.47091i	−0.101041	−	0.310972i	−0.988781	+	0.149373i	$0.952274\pi$
$434$	5.22507	−	6.41061i	0.250811	−	0.307719i
$435$	−9.57055	+	6.95341i	−0.458873	+	0.333391i
$436$	1.07018	−	1.18856i	0.0512524	−	0.0569216i
$437$	−26.3154	−	29.2263i	−1.25884	−	1.39808i
$438$	−7.99819	+	3.56102i	−0.382168	+	0.170152i
$439$	−6.58209	−	11.4005i	−0.314146	−	0.544117i	0.665110	−	0.746746i	$-0.268385\pi$
$439$	−6.58209	−	11.4005i	−0.314146	−	0.544117i	−0.979256	+	0.202629i	$0.935051\pi$
$440$	1.95900	+	8.33287i	0.0933918	+	0.397254i
$441$	−6.03978	−	3.53850i	−0.287609	−	0.168500i
$442$	1.89032	+	1.37340i	0.0899134	+	0.0653259i
$443$	24.0649	−	5.11516i	1.14336	−	0.243029i	0.402975	−	0.915211i	$-0.367976\pi$
$443$	24.0649	−	5.11516i	1.14336	−	0.243029i	0.740386	+	0.672182i	$0.234643\pi$
$444$	−9.20197	−	1.95594i	−0.436706	−	0.0928247i
$445$	1.32194	+	12.5775i	0.0626661	+	0.596228i
$446$	−9.84732	−	4.38431i	−0.466284	−	0.207603i
$447$	−2.71835	−	8.36622i	−0.128574	−	0.395709i
$448$	−0.146873	+	2.64167i	−0.00693910	+	0.124807i
$449$	9.46220	+	6.87469i	0.446549	+	0.324437i	0.788232	−	0.615379i	$-0.210997\pi$
$449$	9.46220	+	6.87469i	0.446549	+	0.324437i	−0.341683	+	0.939815i	$0.610997\pi$
$450$	0.830656	+	1.43874i	0.0391575	+	0.0678228i
$451$	−1.74767	−	2.30000i	−0.0822947	−	0.108303i
$452$	2.67465	−	4.63264i	0.125805	−	0.217901i
$453$	−1.82847	+	17.3968i	−0.0859091	+	0.817371i
$454$	0.0665651	−	0.204866i	0.00312406	−	0.00961485i
$455$	−14.3282	+	27.9009i	−0.671718	+	1.30802i
$456$	6.03156	−	4.38218i	0.282454	−	0.205215i
$457$	34.0454	+	15.1580i	1.59258	+	0.709061i	0.995645	−	0.0932302i	$-0.0297193\pi$
$457$	34.0454	+	15.1580i	1.59258	+	0.709061i	0.596933	+	0.802291i	$0.296386\pi$
$458$	26.1500	+	5.55835i	1.22191	+	0.259725i
$459$	−0.340387	−	0.378038i	−0.0158879	−	0.0176453i
$460$	−1.42312	+	13.5401i	−0.0663535	+	0.631311i
$461$	−1.68668			−0.0785564			−0.0392782	−	0.999228i	$-0.512506\pi$
$461$	−1.68668			−0.0785564			−0.0392782	+	0.999228i	$0.512506\pi$
$462$	7.27072	−	4.91291i	0.338264	−	0.228569i
$463$	−28.2274			−1.31184			−0.655920	−	0.754831i	$-0.727719\pi$
$463$	−28.2274			−1.31184			−0.655920	+	0.754831i	$0.727719\pi$
$464$	0.479109	−	4.55842i	0.0222421	−	0.211619i
$465$	5.39835	+	5.99547i	0.250342	+	0.278033i
$466$	−18.6980	−	3.97439i	−0.866169	−	0.184110i
$467$	7.05396	+	3.14063i	0.326418	+	0.145331i	0.563402	−	0.826183i	$-0.309492\pi$
$467$	7.05396	+	3.14063i	0.326418	+	0.145331i	−0.236984	+	0.971514i	$0.576159\pi$
$468$	−3.71598	+	2.69982i	−0.171771	+	0.124799i
$469$	−10.7091	+	0.527080i	−0.494499	+	0.0243383i
$470$	−3.73940	+	11.5087i	−0.172486	+	0.530857i
$471$	0.730155	−	6.94696i	0.0336438	−	0.320099i
$472$	−2.63707	+	4.56754i	−0.121381	+	0.210238i
$473$	18.0450	−	25.9920i	0.829709	−	1.19511i
$474$	−4.11101	−	7.12047i	−0.188825	−	0.327054i
$475$	10.0203	+	7.28018i	0.459763	+	0.334037i
$476$	1.20114	−	0.607205i	0.0550541	−	0.0278312i
$477$	−1.59719	−	4.91564i	−0.0731302	−	0.225072i
$478$	−17.6401	−	7.85389i	−0.806841	−	0.359229i
$479$	1.82358	+	17.3502i	0.0833213	+	0.792749i	0.953780	+	0.300507i	$0.0971559\pi$
$479$	1.82358	+	17.3502i	0.0833213	+	0.792749i	−0.870458	+	0.492242i	$0.836177\pi$
$480$	−2.52455	−	0.536610i	−0.115230	−	0.0244928i
$481$	42.2665	−	8.98402i	1.92719	−	0.409636i
$482$	−5.47458	−	3.97752i	−0.249360	−	0.181171i
$483$	13.4924	−	3.56930i	0.613925	−	0.162409i
$484$	1.61817	+	10.8803i	0.0735530	+	0.494560i
$485$	19.3415	+	33.5005i	0.878253	+	1.52118i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−2.26434	−	2.51481i	−0.102607	−	0.113957i	0.689654	−	0.724139i	$-0.257763\pi$
$487$	−2.26434	−	2.51481i	−0.102607	−	0.113957i	−0.792261	+	0.610182i	$0.791096\pi$
$488$	−7.18957	+	7.98483i	−0.325457	+	0.361456i
$489$	15.7495	−	11.4427i	0.712218	−	0.517456i
$490$	10.5261	+	14.6835i	0.475521	+	0.663333i
$491$	−3.83059	−	11.7893i	−0.172872	−	0.532045i	0.826658	−	0.562705i	$-0.190239\pi$
$491$	−3.83059	−	11.7893i	−0.172872	−	0.532045i	−0.999530	+	0.0306595i	$0.990239\pi$
$492$	0.851933	−	0.181084i	0.0384081	−	0.00816389i
$493$	−2.13006	+	0.948364i	−0.0959331	+	0.0427122i
$494$	−17.1221	+	29.6564i	−0.770361	+	1.33430i
$495$	3.64870	+	7.74348i	0.163997	+	0.348043i
$496$	−3.12586			−0.140355
$497$	−29.5258	−	11.4418i	−1.32441	−	0.513235i
$498$	−1.69663	+	5.22168i	−0.0760277	+	0.233989i
$499$	−27.4331	+	30.4676i	−1.22807	+	1.36392i	−0.318745	+	0.947841i	$0.603261\pi$
$499$	−27.4331	+	30.4676i	−1.22807	+	1.36392i	−0.909330	+	0.416075i	$0.863405\pi$
$500$	0.900721	+	8.56979i	0.0402815	+	0.383252i
$501$	−1.65619	−	15.7576i	−0.0739932	−	0.703998i
$502$	−17.7134	+	19.6727i	−0.790588	+	0.878037i
$503$	10.1115	−	31.1201i	0.450851	−	1.38758i	−0.425087	−	0.905152i	$-0.639757\pi$
$503$	10.1115	−	31.1201i	0.450851	−	1.38758i	0.875938	−	0.482424i	$-0.160243\pi$
$504$	0.405571	+	2.61448i	0.0180656	+	0.116458i
$505$	41.9241			1.86560
$506$	−3.26943	+	17.1872i	−0.145344	+	0.764065i
$507$	4.04876	−	7.01266i	0.179812	−	0.311443i
$508$	16.9411	−	7.54268i	0.751642	−	0.334652i
$509$	−30.3225	+	6.44525i	−1.34402	+	0.285681i	−0.823087	−	0.567916i	$-0.807750\pi$
$509$	−30.3225	+	6.44525i	−1.34402	+	0.285681i	−0.520935	+	0.853596i	$0.674417\pi$
$510$	0.405718	+	1.24867i	0.0179655	+	0.0552921i
$511$	−8.23233	−	21.6516i	−0.364177	−	0.957811i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	4.98865	−	5.54045i	0.220254	−	0.244617i
$514$	8.97914	+	9.97235i	0.396053	+	0.439861i
$515$	17.3150	−	7.70911i	0.762988	−	0.339704i
$516$	4.77018	+	8.26220i	0.209996	+	0.363723i
$517$	−6.01854	+	14.3383i	−0.264695	+	0.630597i
$518$	6.51847	−	24.0213i	0.286405	−	1.05544i
$519$	4.10387	+	2.98163i	0.180140	+	0.130879i
$520$	11.5958	−	2.46476i	0.508509	−	0.108087i
$521$	41.3313	+	8.78525i	1.81076	+	0.384889i	0.984071	−	0.177773i	$-0.0568894\pi$
$521$	41.3313	+	8.78525i	1.81076	+	0.384889i	0.826687	+	0.562662i	$0.190223\pi$
$522$	−0.479109	−	4.55842i	−0.0209700	−	0.199516i
$523$	−24.7580	−	11.0230i	−1.08259	−	0.482001i	−0.213647	−	0.976911i	$-0.568534\pi$
$523$	−24.7580	−	11.0230i	−1.08259	−	0.482001i	−0.868944	+	0.494910i	$0.835201\pi$
$524$	0.456885	+	1.40615i	0.0199591	+	0.0614278i
$525$	−3.92268	+	1.98301i	−0.171200	+	0.0865456i
$526$	−22.3313	−	16.2246i	−0.973690	−	0.707427i
$527$	0.795064	+	1.37709i	0.0346335	+	0.0599871i
$528$	−3.17556	−	0.956968i	−0.138199	−	0.0416467i
$529$	−2.41317	+	4.17973i	−0.104920	+	0.181727i
$530$	−1.39440	+	13.2668i	−0.0605689	+	0.576275i
$531$	−1.62980	+	5.01601i	−0.0707273	+	0.217676i
$532$	10.6904	+	16.5770i	0.463488	+	0.718705i
$533$	−3.23649	+	2.35145i	−0.140188	+	0.101852i
$534$	−4.47640	−	1.99302i	−0.193713	−	0.0862464i
$535$	−40.8202	−	8.67661i	−1.76481	−	0.375122i
$536$	2.71169	+	3.01163i	0.117127	+	0.130083i
$537$	−0.172737	+	1.64349i	−0.00745417	+	0.0709217i
$538$	15.7565			0.679313
$539$	11.9104	+	19.9284i	0.513018	+	0.858378i
$540$	−2.58095			−0.111066
$541$	−0.296349	+	2.81958i	−0.0127411	+	0.121223i	−0.999044	−	0.0437226i	$-0.986078\pi$
$541$	−0.296349	+	2.81958i	−0.0127411	+	0.121223i	0.986303	+	0.164946i	$0.0527449\pi$
$542$	9.39157	+	10.4304i	0.403402	+	0.448024i
$543$	−6.36938	−	1.35385i	−0.273336	−	0.0580994i
$544$	−0.464721	−	0.206907i	−0.0199247	−	0.00887107i
$545$	−3.33952	+	2.42630i	−0.143049	+	0.103931i
$546$	−6.58625	−	10.2129i	−0.281866	−	0.437073i
$547$	−3.02609	+	9.31336i	−0.129386	+	0.398210i	−0.994675	−	0.103064i	$-0.967135\pi$
$547$	−3.02609	+	9.31336i	−0.129386	+	0.398210i	0.865288	+	0.501274i	$0.167135\pi$
$548$	1.04744	−	9.96570i	0.0447443	−	0.425714i
$549$	−5.37232	+	9.30514i	−0.229285	+	0.397134i
$550$	−0.118240	−	5.50868i	−0.00504178	−	0.234891i
$551$	−17.0860	−	29.5939i	−0.727890	−	1.26074i
$552$	−4.26762	−	3.10061i	−0.181642	−	0.131971i
$553$	19.4137	−	9.81412i	0.825556	−	0.417339i
$554$	−2.74821	−	8.45811i	−0.116760	−	0.359350i
$555$	22.1813	+	9.87574i	0.941542	+	0.419202i
$556$	−0.883009	−	8.40127i	−0.0374479	−	0.356293i
$557$	−8.16152	−	1.73478i	−0.345815	−	0.0735051i	0.0317303	−	0.999496i	$-0.489898\pi$
$557$	−8.16152	−	1.73478i	−0.345815	−	0.0735051i	−0.377545	+	0.925991i	$0.623232\pi$
$558$	−3.05756	+	0.649904i	−0.129437	+	0.0275126i
$559$	−35.4518	−	25.7572i	−1.49945	−	1.08942i
$560$	1.78834	−	6.59022i	0.0755710	−	0.278488i
$561$	0.386116	+	1.64239i	0.0163018	+	0.0693418i
$562$	8.65545	+	14.9917i	0.365108	+	0.632386i
$563$	11.3795	−	5.06646i	0.479587	−	0.213526i	−0.152681	−	0.988275i	$-0.548791\pi$
$563$	11.3795	−	5.06646i	0.479587	−	0.213526i	0.632268	+	0.774750i	$0.282124\pi$
$564$	−3.13726	−	3.48428i	−0.132103	−	0.146715i
$565$	−9.23822	+	10.2601i	−0.388655	+	0.431645i
$566$	−24.2184	+	17.5957i	−1.01798	+	0.739603i
$567$	0.940289	+	2.47303i	0.0394884	+	0.103857i
$568$	3.69842	+	11.3826i	0.155182	+	0.477602i
$569$	38.7629	−	8.23931i	1.62503	−	0.345410i	0.696753	−	0.717311i	$-0.254627\pi$
$569$	38.7629	−	8.23931i	1.62503	−	0.345410i	0.928272	+	0.371901i	$0.121294\pi$
$570$	−17.5785	+	7.82645i	−0.736282	+	0.327814i
$571$	−20.1798	+	34.9524i	−0.844496	+	1.46271i	0.0415614	+	0.999136i	$0.486767\pi$
$571$	−20.1798	+	34.9524i	−0.844496	+	1.46271i	−0.886058	+	0.463575i	$0.846567\pi$
$572$	15.1128	−	1.91713i	0.631899	−	0.0801593i
$573$	11.1140			0.464295
$574$	0.353238	+	2.27712i	0.0147439	+	0.0950452i
$575$	2.70808	−	8.33462i	0.112935	−	0.347578i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	0.846862	+	8.05736i	0.0352553	+	0.335432i	0.997906	+	0.0646847i	$0.0206042\pi$
$577$	0.846862	+	8.05736i	0.0352553	+	0.335432i	−0.962650	+	0.270747i	$0.912729\pi$
$578$	−1.74993	−	16.6495i	−0.0727877	−	0.692528i
$579$	11.6591	−	12.9488i	0.484538	−	0.538134i
$580$	−3.65563	+	11.2509i	−0.151792	+	0.467167i
$581$	−13.5448	−	5.24885i	−0.561932	−	0.217759i
$582$	−14.9879			−0.621268
$583$	−3.20344	+	16.8403i	−0.132673	+	0.697456i
$584$	−4.37755	+	7.58215i	−0.181144	+	0.313751i
$585$	10.8299	−	4.82180i	0.447763	−	0.199357i
$586$	−18.2289	+	3.87468i	−0.753030	+	0.160061i
$587$	1.23645	+	3.80539i	0.0510337	+	0.157065i	0.973325	−	0.229429i	$-0.0736859\pi$
$587$	1.23645	+	3.80539i	0.0510337	+	0.157065i	−0.922292	+	0.386494i	$0.873686\pi$
$588$	−6.96617	+	0.687388i	−0.287280	+	0.0283474i
$589$	−18.8538	+	13.6981i	−0.776859	+	0.564421i
$590$	9.10841	−	10.1159i	0.374987	−	0.416466i
$591$	8.06762	+	8.96000i	0.331858	+	0.368565i
$592$	−8.59422	+	3.82639i	−0.353220	+	0.157264i
$593$	−14.0678	−	24.3661i	−0.577695	−	1.00060i	−0.995743	−	0.0921723i	$-0.970619\pi$
$593$	−14.0678	−	24.3661i	−0.577695	−	1.00060i	0.418048	−	0.908425i	$-0.362714\pi$
$594$	−3.30514	−	0.275819i	−0.135611	−	0.0113170i
$595$	−3.35817	+	0.888378i	−0.137672	+	0.0364199i
$596$	−7.11673	−	5.17061i	−0.291513	−	0.211796i
$597$	−9.89124	+	2.10245i	−0.404822	+	0.0860475i
$598$	23.7000	+	5.03759i	0.969164	+	0.206002i
$599$	4.31597	+	41.0637i	0.176346	+	1.67782i	0.622313	+	0.782769i	$0.286193\pi$
$599$	4.31597	+	41.0637i	0.176346	+	1.67782i	−0.445967	+	0.895049i	$0.647140\pi$
$600$	1.51768	+	0.675717i	0.0619592	+	0.0275860i
$601$	7.31450	+	22.5117i	0.298365	+	0.918272i	0.982070	+	0.188514i	$0.0603671\pi$
$601$	7.31450	+	22.5117i	0.298365	+	0.918272i	−0.683706	+	0.729758i	$0.739633\pi$
$602$	−22.5266	+	11.3878i	−0.918117	+	0.464131i
$603$	3.27858	+	2.38203i	0.133514	+	0.0970037i
$604$	8.74629	+	15.1490i	0.355881	+	0.616405i
$605$	1.75335	−	28.3363i	0.0712838	−	1.15203i
$606$	−8.12182	+	14.0674i	−0.329927	+	0.571450i
$607$	3.12257	−	29.7093i	0.126741	−	1.20586i	−0.727545	−	0.686060i	$-0.759339\pi$
$607$	3.12257	−	29.7093i	0.126741	−	1.20586i	0.854286	−	0.519803i	$-0.173995\pi$
$608$	2.30385	−	7.09052i	0.0934334	−	0.287559i
$609$	12.1122	−	0.596140i	0.490811	−	0.0241568i
$610$	22.4352	−	16.3001i	0.908374	−	0.659972i
$611$	19.6737	+	8.75929i	0.795912	+	0.354363i
$612$	−0.497584	−	0.105765i	−0.0201136	−	0.00427529i
$613$	−8.11200	−	9.00929i	−0.327641	−	0.363882i	0.556708	−	0.830708i	$-0.312064\pi$
$613$	−8.11200	−	9.00929i	−0.327641	−	0.363882i	−0.884349	+	0.466826i	$0.845397\pi$
$614$	2.15777	−	20.5298i	0.0870805	−	0.828515i
$615$	−2.24792			−0.0906449
$616$	2.99440	−	8.24825i	0.120648	−	0.332331i
$617$	16.1100			0.648565			0.324282	−	0.945960i	$-0.394877\pi$
$617$	16.1100			0.648565			0.324282	+	0.945960i	$0.394877\pi$
$618$	−0.767619	+	7.30341i	−0.0308782	+	0.293786i
$619$	0.181041	+	0.201066i	0.00727663	+	0.00808152i	0.746772	−	0.665080i	$-0.231603\pi$
$619$	0.181041	+	0.201066i	0.00727663	+	0.00808152i	−0.739496	+	0.673161i	$0.764936\pi$
$620$	7.89141	+	1.67737i	0.316927	+	0.0673648i
$621$	−4.81901	−	2.14556i	−0.193380	−	0.0860985i
$622$	10.2989	−	7.48261i	0.412949	−	0.300025i
$623$	5.92237	−	11.5324i	0.237275	−	0.462038i
$624$	−1.41938	+	4.36840i	−0.0568206	+	0.174876i
$625$	3.19299	−	30.3793i	0.127720	−	1.21517i
$626$	−3.38073	+	5.85559i	−0.135121	+	0.234037i
$627$	−23.3472	+	8.14390i	−0.932398	+	0.325236i
$628$	−3.49261	−	6.04938i	−0.139370	−	0.241397i
$629$	3.87165	+	2.81292i	0.154373	+	0.112158i
$630$	0.379072	−	6.81803i	0.0151026	−	0.271637i
$631$	−7.60865	−	23.4170i	−0.302895	−	0.932216i	−0.980454	−	0.196748i	$-0.936962\pi$
$631$	−7.60865	−	23.4170i	−0.302895	−	0.932216i	0.677559	−	0.735469i	$-0.263038\pi$
$632$	−7.51118	−	3.34419i	−0.298779	−	0.133025i
$633$	−0.133921	−	1.27417i	−0.00532289	−	0.0506439i
$634$	−20.0595	−	4.26378i	−0.796666	−	0.169337i
$635$	−46.8163	+	9.95111i	−1.85785	+	0.394898i
$636$	−4.18149	−	3.03803i	−0.165807	−	0.120466i
$637$	27.9465	−	15.8987i	1.10728	−	0.629930i
$638$	−5.88370	+	14.0171i	−0.232938	+	0.554940i
$639$	5.98417	+	10.3649i	0.236730	+	0.410028i
$640$	−2.35782	+	1.04977i	−0.0932009	+	0.0414957i
$641$	−24.8203	−	27.5657i	−0.980343	−	1.08878i	−0.996040	−	0.0889045i	$-0.971663\pi$
$641$	−24.8203	−	27.5657i	−0.980343	−	1.08878i	0.0156970	−	0.999877i	$-0.495003\pi$
$642$	10.8194	−	12.0161i	0.427007	−	0.474239i
$643$	−1.97110	+	1.43209i	−0.0777325	+	0.0564760i	−0.625973	−	0.779845i	$-0.715298\pi$
$643$	−1.97110	+	1.43209i	−0.0777325	+	0.0564760i	0.548240	+	0.836321i	$0.315298\pi$
$644$	8.81758	−	10.8183i	0.347461	−	0.426299i
$645$	−7.60900	−	23.4181i	−0.299604	−	0.922086i
$646$	−3.70970	+	0.788520i	−0.145956	+	0.0310239i
$647$	11.8798	−	5.28922i	0.467042	−	0.207941i	−0.159703	−	0.987165i	$-0.551054\pi$
$647$	11.8798	−	5.28922i	0.467042	−	0.207941i	0.626745	+	0.779225i	$0.284387\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	12.7452	−	11.9809i	0.500292	−	0.470293i
$650$	−7.63075			−0.299303
$651$	−1.26776	−	8.17251i	−0.0496874	−	0.320306i
$652$	6.01578	−	18.5147i	0.235596	−	0.725090i
$653$	4.92185	−	5.46627i	0.192607	−	0.213912i	−0.639104	−	0.769120i	$-0.720695\pi$
$653$	4.92185	−	5.46627i	0.192607	−	0.213912i	0.831711	+	0.555208i	$0.187362\pi$
$654$	−0.167179	−	1.59060i	−0.00653721	−	0.0621974i
$655$	−0.398877	−	3.79506i	−0.0155854	−	0.148285i
$656$	0.582789	−	0.647253i	0.0227541	−	0.0252710i
$657$	−2.70548	+	8.32660i	−0.105551	+	0.324852i
$658$	9.66511	−	7.77587i	0.376785	−	0.303135i
$659$	−12.4588			−0.485325			−0.242663	−	0.970111i	$-0.578021\pi$
$659$	−12.4588			−0.485325			−0.242663	+	0.970111i	$0.578021\pi$
$660$	7.50336	+	4.11996i	0.292068	+	0.160369i
$661$	−7.54475	+	13.0679i	−0.293457	+	0.508282i	−0.974625	−	0.223845i	$-0.928139\pi$
$661$	−7.54475	+	13.0679i	−0.293457	+	0.508282i	0.681168	+	0.732127i	$0.261472\pi$
$662$	−11.0418	+	4.91612i	−0.429152	+	0.191071i
$663$	2.28550	−	0.485799i	0.0887617	−	0.0188669i
$664$	1.69663	+	5.22168i	0.0658419	+	0.202640i
$665$	−18.0931	−	47.5861i	−0.701621	−	1.84531i
$666$	−7.61086	+	5.52962i	−0.294915	+	0.214268i
$667$	−16.1785	+	17.9681i	−0.626434	+	0.695726i
$668$	−10.6020	−	11.7747i	−0.410203	−	0.455577i
$669$	−9.84732	+	4.38431i	−0.380720	+	0.169507i
$670$	−5.22972	−	9.05814i	−0.202042	−	0.349946i
$671$	30.4722	−	18.4761i	1.17637	−	0.713264i
$672$	1.86487	+	1.87677i	0.0719388	+	0.0723980i
$673$	10.1666	+	7.38648i	0.391894	+	0.284728i	0.766231	−	0.642565i	$-0.222130\pi$
$673$	10.1666	+	7.38648i	0.391894	+	0.284728i	−0.374337	+	0.927293i	$0.622130\pi$
$674$	−12.4984	+	2.65663i	−0.481422	+	0.102329i
$675$	1.62501	+	0.345406i	0.0625466	+	0.0132947i
$676$	−0.846421	−	8.05316i	−0.0325547	−	0.309737i
$677$	−22.3861	−	9.96694i	−0.860368	−	0.383061i	−0.0713654	−	0.997450i	$-0.522736\pi$
$677$	−22.3861	−	9.96694i	−0.860368	−	0.383061i	−0.789003	+	0.614390i	$0.789402\pi$
$678$	−1.65303	−	5.08749i	−0.0634841	−	0.195384i
$679$	2.20132	−	39.5931i	0.0844788	−	1.51944i
$680$	1.06218	+	0.771722i	0.0407329	+	0.0295942i
$681$	−0.107705	−	0.186550i	−0.00412725	−	0.00714861i
$682$	9.92639	+	2.99135i	0.380101	+	0.114545i
$683$	23.1899	−	40.1662i	0.887339	−	1.53692i	0.0443289	−	0.999017i	$-0.485885\pi$
$683$	23.1899	−	40.1662i	0.887339	−	1.53692i	0.843010	−	0.537898i	$-0.180782\pi$
$684$	0.779303	−	7.41457i	0.0297974	−	0.283503i
$685$	−7.99201	+	24.5969i	−0.305359	+	0.939798i
$686$	−0.792712	−	18.5033i	−0.0302659	−	0.706459i
$687$	21.6284	−	15.7140i	0.825176	−	0.599525i
$688$	8.71556	+	3.88042i	0.332278	+	0.147940i
$689$	23.2217	+	4.93592i	0.884675	+	0.188044i
$690$	9.11001	+	10.1177i	0.346812	+	0.385174i
$691$	−2.04413	+	19.4486i	−0.0777625	+	0.739861i	0.884279	+	0.466958i	$0.154650\pi$
$691$	−2.04413	+	19.4486i	−0.0777625	+	0.739861i	−0.962042	+	0.272902i	$0.912016\pi$
$692$	5.07266			0.192834
$693$	1.21406	−	8.69057i	0.0461183	−	0.330128i
$694$	3.25089			0.123402
$695$	−2.27900	+	21.6833i	−0.0864475	+	0.822493i
$696$	−3.06698	−	3.40622i	−0.116253	−	0.129113i
$697$	−0.433378	−	0.0921174i	−0.0164154	−	0.00348920i
$698$	23.8540	+	10.6205i	0.902889	+	0.401992i
$699$	−15.4650	+	11.2360i	−0.584939	+	0.424983i
$700$	−2.00793	+	3.90998i	−0.0758926	+	0.147783i
$701$	8.62894	−	26.5571i	0.325911	−	1.00305i	−0.645117	−	0.764083i	$-0.723192\pi$
$701$	8.62894	−	26.5571i	0.325911	−	1.00305i	0.971028	−	0.238966i	$-0.0768084\pi$
$702$	−0.480120	+	4.56804i	−0.0181210	+	0.172410i
$703$	−35.0686	+	60.7405i	−1.32264	+	2.29087i
$704$	−3.13158	+	1.09235i	−0.118026	+	0.0411694i
$705$	6.05048	+	10.4797i	0.227874	+	0.394690i
$706$	−7.37821	−	5.36059i	−0.277683	−	0.201748i
$707$	−35.9686	−	23.5213i	−1.35274	−	0.884610i
$708$	1.62980	+	5.01601i	0.0612516	+	0.188513i
$709$	−18.0231	−	8.02441i	−0.676873	−	0.301363i	0.0393595	−	0.999225i	$-0.487468\pi$
$709$	−18.0231	−	8.02441i	−0.676873	−	0.301363i	−0.716232	+	0.697862i	$0.754135\pi$
$710$	−3.22885	−	30.7205i	−0.121177	−	1.15292i
$711$	−8.04234	−	1.70945i	−0.301611	−	0.0641095i
$712$	−4.79295	+	1.01877i	−0.179623	+	0.0381801i
$713$	13.3400	+	9.69208i	0.499587	+	0.362971i
$714$	0.352477	−	1.29892i	0.0131911	−	0.0486108i
$715$	−39.1818	−	3.26979i	−1.46532	−	0.122283i
$716$	0.826270	+	1.43114i	0.0308791	+	0.0534842i
$717$	−17.6401	+	7.85389i	−0.658783	+	0.293309i
$718$	−9.83523	−	10.9231i	−0.367048	−	0.407648i
$719$	32.3788	−	35.9603i	1.20753	−	1.34109i	0.283403	−	0.959001i	$-0.408536\pi$
$719$	32.3788	−	35.9603i	1.20753	−	1.34109i	0.924124	−	0.382094i	$-0.124797\pi$
$720$	−2.08803	+	1.51705i	−0.0778164	+	0.0565369i
$721$	−19.1805	−	3.10047i	−0.714318	−	0.115468i
$722$	−11.3048	−	34.7927i	−0.420722	−	1.29485i
$723$	−6.61908	+	1.40693i	−0.246166	+	0.0523242i
$724$	−5.94871	+	2.64854i	−0.221082	+	0.0984321i
$725$	3.80733	−	6.59450i	0.141401	−	0.244913i
$726$	9.16842	+	6.07783i	0.340272	+	0.225569i
$727$	−31.9377			−1.18450			−0.592252	−	0.805753i	$-0.701761\pi$
$727$	−31.9377			−1.18450			−0.592252	+	0.805753i	$0.701761\pi$
$728$	−11.3314	−	4.39113i	−0.419970	−	0.162746i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	15.1200	−	16.7925i	0.559617	−	0.621518i
$731$	−0.507296	−	4.82660i	−0.0187630	−	0.178518i
$732$	1.12312	+	10.6858i	0.0415118	+	0.394958i
$733$	−2.18891	+	2.43103i	−0.0808493	+	0.0897923i	−0.782212	−	0.623012i	$-0.785909\pi$
$733$	−2.18891	+	2.43103i	−0.0808493	+	0.0897923i	0.701363	+	0.712805i	$0.252575\pi$
$734$	9.90598	−	30.4875i	0.365636	−	1.12531i
$735$	17.9553	+	2.00277i	0.662292	+	0.0738732i
$736$	−5.27507			−0.194442
$737$	−5.72910	−	12.1586i	−0.211034	−	0.447869i
$738$	0.435483	−	0.754278i	0.0160303	−	0.0277654i
$739$	−10.8594	+	4.83492i	−0.399470	+	0.177855i	−0.596631	−	0.802516i	$-0.703494\pi$
$739$	−10.8594	+	4.83492i	−0.399470	+	0.177855i	0.197161	+	0.980371i	$0.436828\pi$
$740$	23.7498	−	5.04818i	0.873061	−	0.185575i
$741$	10.5821	+	32.5682i	0.388741	+	1.19642i
$742$	8.63963	−	10.5999i	0.317171	−	0.389135i
$743$	−37.6046	+	27.3213i	−1.37958	+	1.00232i	−0.382660	+	0.923889i	$0.624992\pi$
$743$	−37.6046	+	27.3213i	−1.37958	+	1.00232i	−0.996919	+	0.0784338i	$0.975008\pi$
$744$	−2.09161	+	2.32297i	−0.0766822	+	0.0851642i
$745$	15.1920	+	16.8724i	0.556590	+	0.618156i
$746$	14.6229	−	6.51054i	0.535383	−	0.238368i
$747$	2.74520	+	4.75482i	0.100442	+	0.173970i
$748$	1.27775	+	1.10177i	0.0467191	+	0.0402847i
$749$	30.1536	+	30.3461i	1.10179	+	1.10882i
$750$	6.97129	+	5.06494i	0.254556	+	0.184945i
$751$	13.1446	−	2.79398i	0.479654	−	0.101954i	0.0382616	−	0.999268i	$-0.487818\pi$
$751$	13.1446	−	2.79398i	0.479654	−	0.101954i	0.441393	+	0.897314i	$0.354485\pi$
$752$	−4.58611	−	0.974808i	−0.167238	−	0.0355476i
$753$	2.76711	+	26.3273i	0.100839	+	0.959419i
$754$	19.2329	+	8.56305i	0.700422	+	0.311848i
$755$	−13.9513	−	42.9378i	−0.507741	−	1.56267i
$756$	2.21432	+	1.44803i	0.0805340	+	0.0526644i
$757$	6.06972	+	4.40991i	0.220608	+	0.160281i	0.692600	−	0.721322i	$-0.256465\pi$
$757$	6.06972	+	4.40991i	0.220608	+	0.160281i	−0.471992	+	0.881603i	$0.656465\pi$
$758$	4.79348	+	8.30256i	0.174107	+	0.301562i
$759$	10.5849	+	13.9302i	0.384208	+	0.505633i
$760$	−9.62103	+	16.6641i	−0.348992	+	0.604471i
$761$	0.528943	−	5.03256i	0.0191742	−	0.182430i	−0.980743	−	0.195303i	$-0.937431\pi$
$761$	0.528943	−	5.03256i	0.0191742	−	0.182430i	0.999917	+	0.0128728i	$0.00409765\pi$
$762$	5.73053	−	17.6368i	0.207595	−	0.638912i
$763$	4.22640	−	0.208015i	0.153006	−	0.00753065i
$764$	8.99144	−	6.53266i	0.325299	−	0.236344i
$765$	1.19942	+	0.534017i	0.0433652	+	0.0193074i
$766$	23.2598	+	4.94402i	0.840411	+	0.178635i
$767$	−16.2098	−	18.0028i	−0.585303	−	0.650045i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	−35.6313			−1.28490			−0.642449	−	0.766329i	$-0.722081\pi$
$769$	−35.6313			−1.28490			−0.642449	+	0.766329i	$0.722081\pi$
$770$	−11.9856	+	19.2163i	−0.431931	+	0.692507i
$771$	13.4191			0.483278
$772$	1.82134	−	17.3289i	0.0655514	−	0.623680i
$773$	25.7989	+	28.6526i	0.927922	+	1.03056i	0.999451	+	0.0331228i	$0.0105452\pi$
$773$	25.7989	+	28.6526i	0.927922	+	1.03056i	−0.0715298	+	0.997438i	$0.522788\pi$
$774$	9.33189	+	1.98355i	0.335428	+	0.0712974i
$775$	−4.74408	−	2.11220i	−0.170412	−	0.0758724i
$776$	−12.1255	+	8.80966i	−0.435279	+	0.316248i
$777$	−13.4896	−	20.9176i	−0.483937	−	0.750413i
$778$	−8.55739	+	26.3369i	−0.306797	+	0.944225i
$779$	0.678746	−	6.45784i	0.0243186	−	0.231376i
$780$	5.92742	−	10.2666i	0.212236	−	0.367603i
$781$	−0.851819	−	39.6853i	−0.0304805	−	1.42005i
$782$	1.34171	+	2.32392i	0.0479796	+	0.0831031i
$783$	−3.70815	−	2.69413i	−0.132518	−	0.0962803i
$784$	−5.23171	+	4.65072i	−0.186847	+	0.166097i
$785$	5.57112	+	17.1462i	0.198842	+	0.611973i
$786$	1.35069	+	0.601364i	0.0481774	+	0.0214500i
$787$	−3.65971	−	34.8198i	−0.130455	−	1.24119i	−0.842359	−	0.538916i	$-0.818834\pi$
$787$	−3.65971	−	34.8198i	−0.130455	−	1.24119i	0.711905	−	0.702276i	$-0.247833\pi$
$788$	11.7934	+	2.50676i	0.420122	+	0.0892998i
$789$	−26.9998	+	5.73898i	−0.961218	+	0.204313i
$790$	17.1678	+	12.4732i	0.610804	+	0.443775i
$791$	13.6823	−	3.61954i	0.486486	−	0.128696i
$792$	−2.83603	+	1.71957i	−0.100774	+	0.0611022i
$793$	−24.6762	−	42.7404i	−0.876277	−	1.51776i
$794$	11.2474	−	5.00766i	0.399155	−	0.177715i
$795$	8.92615	+	9.91349i	0.316578	+	0.351595i
$796$	−6.76639	+	7.51484i	−0.239828	+	0.266357i
$797$	−16.7370	+	12.1602i	−0.592856	+	0.430735i	−0.843336	−	0.537387i	$-0.819411\pi$
$797$	−16.7370	+	12.1602i	−0.592856	+	0.430735i	0.250480	+	0.968122i	$0.419411\pi$
$798$	19.4724	+	3.14766i	0.689316	+	0.111426i
$799$	0.737029	+	2.26834i	0.0260742	+	0.0802482i
$800$	1.62501	−	0.345406i	0.0574527	−	0.0122120i
$801$	−4.47640	+	1.99302i	−0.158166	+	0.0704199i
$802$	1.77972	−	3.08257i	0.0628442	−	0.108849i
$803$	21.1571	−	19.8884i	0.746617	−	0.701847i
$804$	4.05255			0.142922
$805$	−28.0656	+	22.5796i	−0.989183	+	0.795828i
$806$	4.43678	−	13.6550i	0.156279	−	0.480977i
$807$	10.5432	−	11.7094i	0.371138	−	0.412190i
$808$	1.69792	+	16.1547i	0.0597327	+	0.568319i
$809$	−1.94811	−	18.5350i	−0.0684918	−	0.651656i	−0.973879	−	0.227069i	$-0.927086\pi$
$809$	−1.94811	−	18.5350i	−0.0684918	−	0.651656i	0.905387	−	0.424587i	$-0.139581\pi$
$810$	−1.72699	+	1.91802i	−0.0606804	+	0.0673924i
$811$	0.654156	−	2.01328i	0.0229705	−	0.0706960i	−0.938914	−	0.344151i	$-0.888167\pi$
$811$	0.654156	−	2.01328i	0.0229705	−	0.0706960i	0.961885	+	0.273456i	$0.0881666\pi$
$812$	9.44858	−	7.60166i	0.331580	−	0.266766i
$813$	14.0355			0.492246
$814$	30.9532	−	3.92656i	1.08491	−	0.137626i
$815$	−25.1223	+	43.5131i	−0.879996	+	1.52420i
$816$	−0.464721	+	0.206907i	−0.0162685	+	0.00724320i
$817$	69.5731	−	14.7882i	2.43405	−	0.517374i
$818$	6.30616	+	19.4084i	0.220490	+	0.678598i
$819$	−11.9967	−	1.93924i	−0.419200	−	0.0677626i
$820$	−1.81860	+	1.32129i	−0.0635084	+	0.0461416i
$821$	−27.3926	+	30.4226i	−0.956010	+	1.06176i	0.0420267	+	0.999116i	$0.486619\pi$
$821$	−27.3926	+	30.4226i	−0.956010	+	1.06176i	−0.998036	+	0.0626397i	$0.980048\pi$
$822$	−6.70509	−	7.44676i	−0.233867	−	0.259735i
$823$	9.93863	−	4.42496i	0.346439	−	0.154245i	−0.226139	−	0.974095i	$-0.572610\pi$
$823$	9.93863	−	4.42496i	0.346439	−	0.154245i	0.572578	+	0.819851i	$0.305944\pi$
$824$	3.67182	+	6.35978i	0.127914	+	0.221553i
$825$	−4.17287	−	3.59816i	−0.145281	−	0.125272i
$826$	−13.4900	+	3.56868i	−0.469378	+	0.124170i
$827$	−8.93989	−	6.49521i	−0.310870	−	0.225861i	0.421399	−	0.906875i	$-0.361539\pi$
$827$	−8.93989	−	6.49521i	−0.310870	−	0.225861i	−0.732270	+	0.681015i	$0.761539\pi$
$828$	−5.15979	+	1.09675i	−0.179315	+	0.0381146i
$829$	15.0790	+	3.20515i	0.523717	+	0.111319i	0.462181	−	0.886785i	$-0.347067\pi$
$829$	15.0790	+	3.20515i	0.523717	+	0.111319i	0.0615355	+	0.998105i	$0.480400\pi$
$830$	−1.48122	−	14.0928i	−0.0514138	−	0.489169i
$831$	−8.12451	−	3.61726i	−0.281836	−	0.125481i
$832$	1.41938	+	4.36840i	0.0492081	+	0.151447i
$833$	3.37955	+	1.12191i	0.117094	+	0.0388717i
$834$	−6.83421	−	4.96534i	−0.236649	−	0.171936i
$835$	20.4468	+	35.4150i	0.707592	+	1.22559i
$836$	−14.1014	+	20.3117i	−0.487708	+	0.702495i
$837$	−1.56293	+	2.70708i	−0.0540228	+	0.0935703i
$838$	−2.62238	+	24.9503i	−0.0905887	+	0.861894i
$839$	−4.39758	+	13.5344i	−0.151821	+	0.467258i	−0.997825	−	0.0659191i	$-0.979002\pi$
$839$	−4.39758	+	13.5344i	−0.151821	+	0.467258i	0.846004	+	0.533177i	$0.179002\pi$
$840$	−3.70086	−	5.73871i	−0.127692	−	0.198004i
$841$	6.46510	−	4.69717i	0.222935	−	0.161971i
$842$	−0.406702	−	0.181075i	−0.0140159	−	0.00624026i
$843$	16.9326	+	3.59914i	0.583190	+	0.123961i
$844$	−0.857285	−	0.952112i	−0.0295090	−	0.0327730i
$845$	−2.18457	+	20.7848i	−0.0751516	+	0.715019i
$846$	−4.68857			−0.161196
$847$	−17.4022	+	23.3273i	−0.597947	+	0.801535i
$848$	−5.16861			−0.177491
$849$	−3.12912	+	29.7716i	−0.107391	+	1.02176i
$850$	−0.565489	−	0.628039i	−0.0193961	−	0.0215416i
$851$	48.5410	+	10.3177i	1.66396	+	0.353686i
$852$	10.9336	+	4.86796i	0.374580	+	0.166774i
$853$	4.48302	−	3.25711i	0.153496	−	0.111521i	−0.508387	−	0.861129i	$-0.669758\pi$
$853$	4.48302	−	3.25711i	0.153496	−	0.111521i	0.661882	+	0.749608i	$0.269758\pi$
$854$	−28.3933	+	1.39746i	−0.971598	+	0.0478202i
$855$	−5.94613	+	18.3003i	−0.203353	+	0.625857i
$856$	1.69015	−	16.0807i	0.0577682	−	0.549628i
$857$	18.5811	−	32.1834i	0.634718	−	1.09936i	−0.351857	−	0.936054i	$-0.614450\pi$
$857$	18.5811	−	32.1834i	0.634718	−	1.09936i	0.986575	−	0.163310i	$-0.0522170\pi$
$858$	8.68774	−	12.5138i	0.296595	−	0.427215i
$859$	9.85311	+	17.0661i	0.336184	+	0.582288i	0.983712	−	0.179754i	$-0.0575303\pi$
$859$	9.85311	+	17.0661i	0.336184	+	0.582288i	−0.647528	+	0.762042i	$0.724197\pi$
$860$	−19.9206	−	14.4732i	−0.679287	−	0.493531i
$861$	1.92859	+	1.26119i	0.0657263	+	0.0429811i
$862$	−9.26620	−	28.5184i	−0.315608	−	0.971341i
$863$	−26.1727	−	11.6528i	−0.890928	−	0.396667i	−0.0903606	−	0.995909i	$-0.528802\pi$
$863$	−26.1727	−	11.6528i	−0.890928	−	0.396667i	−0.800568	+	0.599242i	$0.795469\pi$
$864$	−0.104528	−	0.994522i	−0.00355613	−	0.0338343i
$865$	−12.8062	−	2.72204i	−0.435424	−	0.0925521i
$866$	−6.65524	+	1.41461i	−0.226154	+	0.0480706i
$867$	−13.5439	−	9.84024i	−0.459976	−	0.334192i
$868$	−5.82932	−	5.86653i	−0.197860	−	0.199123i
$869$	20.6520	+	17.8077i	0.700570	+	0.604084i
$870$	5.91493	+	10.2450i	0.200535	+	0.347337i
$871$	−17.0049	+	7.57107i	−0.576189	+	0.256536i
$872$	−1.07018	−	1.18856i	−0.0362409	−	0.0402496i
$873$	−10.0289	+	11.1382i	−0.339425	+	0.376970i
$874$	−31.8169	+	23.1163i	−1.07622	+	0.781921i
$875$	−14.4038	+	17.6720i	−0.486937	+	0.597421i
$876$	2.70548	+	8.32660i	0.0914096	+	0.281330i
$877$	37.5886	−	7.98971i	1.26928	−	0.269793i	0.476429	−	0.879213i	$-0.341931\pi$
$877$	37.5886	−	7.98971i	1.26928	−	0.269793i	0.792848	+	0.609420i	$0.208597\pi$
$878$	−12.0261	+	5.35435i	−0.405860	+	0.180701i
$879$	−9.31808	+	16.1394i	−0.314291	+	0.544368i
$880$	8.49199	−	1.07725i	0.286265	−	0.0363141i
$881$	6.20381			0.209012			0.104506	−	0.994524i	$-0.466674\pi$
$881$	6.20381			0.209012			0.104506	+	0.994524i	$0.466674\pi$
$882$	−4.15045	+	5.63682i	−0.139753	+	0.189802i
$883$	4.97604	−	15.3147i	0.167457	−	0.515380i	−0.831752	−	0.555148i	$-0.812662\pi$
$883$	4.97604	−	15.3147i	0.167457	−	0.515380i	0.999209	+	0.0397676i	$0.0126617\pi$
$884$	1.56347	−	1.73641i	0.0525851	−	0.0584016i
$885$	−1.42287	−	13.5377i	−0.0478294	−	0.455066i
$886$	−2.57167	−	24.4678i	−0.0863969	−	0.822012i
$887$	−20.8014	+	23.1023i	−0.698443	+	0.775700i	−0.983127	−	0.182922i	$-0.941445\pi$
$887$	−20.8014	+	23.1023i	−0.698443	+	0.775700i	0.284684	+	0.958621i	$0.408111\pi$
$888$	−2.90709	+	8.94711i	−0.0975556	+	0.300245i
$889$	45.7489	+	17.7285i	1.53437	+	0.594596i
$890$	12.6467			0.423919
$891$	−2.41654	+	2.27164i	−0.0809572	+	0.0761027i
$892$	−5.38962	+	9.33509i	−0.180458	+	0.312562i
$893$	−31.9332	+	14.2176i	−1.06860	+	0.475773i
$894$	−8.60453	+	1.82895i	−0.287779	+	0.0611692i
$895$	−1.31800	−	4.05637i	−0.0440557	−	0.135590i
$896$	2.61185	+	0.422198i	0.0872557	+	0.0141047i
$897$	19.6020	−	14.2417i	0.654493	−	0.475517i
$898$	7.82610	−	8.69177i	0.261160	−	0.290048i
$899$	9.58695	+	10.6474i	0.319743	+	0.355110i
$900$	1.51768	−	0.675717i	0.0505895	−	0.0225239i
$901$	1.31464	+	2.27702i	0.0437969	+	0.0758584i
$902$	−2.47009	+	1.49768i	−0.0822449	+	0.0498674i
$903$	−6.61050	+	24.3605i	−0.219984	+	0.810665i
$904$	−4.32768	−	3.14424i	−0.143936	−	0.104576i
$905$	16.4391	−	3.49423i	0.546453	−	0.116152i
$906$	17.1103	+	3.63691i	0.568452	+	0.120828i
$907$	−0.145738	−	1.38660i	−0.00483914	−	0.0460413i	0.991836	−	0.127521i	$-0.0407021\pi$
$907$	−0.145738	−	1.38660i	−0.00483914	−	0.0460413i	−0.996675	+	0.0814798i	$0.974035\pi$
$908$	−0.196786	−	0.0876148i	−0.00653058	−	0.00290760i
$909$	5.01956	+	15.4486i	0.166488	+	0.512399i
$910$	26.2504	+	17.1662i	0.870192	+	0.569053i
$911$	26.4978	+	19.2518i	0.877911	+	0.637840i	0.932698	−	0.360658i	$-0.117448\pi$
$911$	26.4978	+	19.2518i	0.877911	+	0.637840i	−0.0547868	+	0.998498i	$0.517448\pi$
$912$	−3.72771	−	6.45658i	−0.123437	−	0.213799i
$913$	−0.390767	−	18.2054i	−0.0129325	−	0.602511i
$914$	18.6337	−	32.2745i	0.616347	−	1.06754i
$915$	2.89872	−	27.5795i	0.0958288	−	0.911750i
$916$	8.26132	−	25.4257i	0.272962	−	0.840090i
$917$	−1.78699	+	3.47975i	−0.0590115	+	0.114911i
$918$	−0.411547	+	0.299007i	−0.0135831	+	0.00986869i
$919$	−17.5771	−	7.82584i	−0.579816	−	0.258151i	0.0958048	−	0.995400i	$-0.469458\pi$
$919$	−17.5771	−	7.82584i	−0.579816	−	0.258151i	−0.675621	+	0.737250i	$0.736124\pi$
$920$	13.3172	+	2.83065i	0.439054	+	0.0933239i
$921$	−13.8128	−	15.3407i	−0.455147	−	0.505492i
$922$	−0.176306	+	1.67744i	−0.00580632	+	0.0552435i
$923$	−54.9730			−1.80946
$924$	−4.12600	−	7.74443i	−0.135735	−	0.254773i
$925$	−15.6289			−0.513874
$926$	−2.95057	+	28.0728i	−0.0969617	+	0.922529i
$927$	4.91385	+	5.45739i	0.161392	+	0.179244i
$928$	−4.48336	−	0.952968i	−0.147174	−	0.0312827i
$929$	21.6891	+	9.65662i	0.711597	+	0.316823i	0.730419	−	0.683000i	$-0.239325\pi$
$929$	21.6891	+	9.65662i	0.711597	+	0.316823i	−0.0188220	+	0.999823i	$0.505992\pi$
$930$	6.52691	−	4.74208i	0.214026	−	0.155499i
$931$	−11.1751	+	50.9774i	−0.366248	+	1.67072i
$932$	−5.90709	+	18.1802i	−0.193493	+	0.595511i
$933$	1.33067	−	12.6604i	0.0435640	−	0.414484i
$934$	3.86076	−	6.68704i	0.126328	−	0.218806i
$935$	−2.63452	−	3.46713i	−0.0861580	−	0.113387i
$936$	2.29660	+	3.97783i	0.0750668	+	0.130019i
$937$	32.8897	+	23.8958i	1.07446	+	0.780641i	0.976709	−	0.214570i	$-0.0688351\pi$
$937$	32.8897	+	23.8958i	1.07446	+	0.780641i	0.0977512	+	0.995211i	$0.468835\pi$
$938$	−0.595210	+	10.7055i	−0.0194343	+	0.349547i
$939$	2.08941	+	6.43053i	0.0681852	+	0.209852i
$940$	11.0548	+	4.92191i	0.360567	+	0.160535i
$941$	−4.17777	−	39.7488i	−0.136191	−	1.29577i	−0.822626	−	0.568582i	$-0.807492\pi$
$941$	−4.17777	−	39.7488i	−0.136191	−	1.29577i	0.686435	−	0.727191i	$-0.259175\pi$
$942$	−6.83258	−	1.45231i	−0.222618	−	0.0473188i
$943$	−4.49400	+	0.955229i	−0.146345	+	0.0311066i
$944$	4.26687	+	3.10006i	0.138875	+	0.100898i
$945$	−4.81313	−	4.84386i	−0.156571	−	0.157571i
$946$	−23.9634	−	20.6630i	−0.779117	−	0.671813i
$947$	15.6774	+	27.1541i	0.509447	+	0.882388i	0.999940	+	0.0109430i	$0.00348335\pi$
$947$	15.6774	+	27.1541i	0.509447	+	0.882388i	−0.490493	+	0.871445i	$0.663183\pi$
$948$	−7.51118	+	3.34419i	−0.243952	+	0.108614i
$949$	−26.9084	−	29.8848i	−0.873484	−	0.970102i
$950$	8.28770	−	9.20443i	0.268889	−	0.298631i
$951$	−16.5911	+	12.0541i	−0.538002	+	0.390881i
$952$	−0.478326	−	1.25803i	−0.0155026	−	0.0407730i
$953$	−7.71526	−	23.7451i	−0.249922	−	0.769180i	−0.994788	−	0.101966i	$-0.967487\pi$
$953$	−7.71526	−	23.7451i	−0.249922	−	0.769180i	0.744866	−	0.667214i	$-0.232513\pi$
$954$	−5.05566	+	1.07461i	−0.163683	+	0.0347919i
$955$	−26.2049	+	11.6672i	−0.847969	+	0.377540i
$956$	−9.65477	+	16.7225i	−0.312257	+	0.540846i
$957$	6.47974	+	13.7517i	0.209460	+	0.444529i
$958$	17.4457			0.563646
$959$	20.6567	−	16.6189i	0.667039	−	0.536653i
$960$	−0.797558	+	2.45463i	−0.0257411	+	0.0792229i
$961$	−14.2050	+	15.7762i	−0.458224	+	0.508910i
$962$	−4.51675	−	42.9740i	−0.145626	−	1.38554i
$963$	−1.69015	−	16.0807i	−0.0544644	−	0.518194i
$964$	−4.52798	+	5.02883i	−0.145836	+	0.161968i
$965$	−13.8969	+	42.7703i	−0.447357	+	1.37682i
$966$	−2.13941	−	13.7916i	−0.0688345	−	0.443736i
$967$	4.99917			0.160762			0.0803812	−	0.996764i	$-0.474386\pi$
$967$	4.99917			0.160762			0.0803812	+	0.996764i	$0.474386\pi$
$968$	10.9899	−	0.471998i	0.353228	−	0.0151706i
$969$	−1.89629	+	3.28446i	−0.0609175	+	0.105512i
$970$	35.3387	−	15.7338i	1.13466	−	0.505182i
$971$	−57.3344	+	12.1868i	−1.83995	+	0.391093i	−0.990606	−	0.136749i	$-0.956335\pi$
$971$	−57.3344	+	12.1868i	−1.83995	+	0.391093i	−0.849343	+	0.527842i	$0.823001\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	14.1206	−	17.3245i	0.452685	−	0.555397i
$974$	−2.73772	+	1.98907i	−0.0877222	+	0.0637339i
$975$	−5.10597	+	5.67075i	−0.163522	+	0.181609i
$976$	7.18957	+	7.98483i	0.230133	+	0.255588i
$977$	17.6044	−	7.83797i	0.563214	−	0.250759i	−0.105323	−	0.994438i	$-0.533588\pi$
$977$	17.6044	−	7.83797i	0.563214	−	0.250759i	0.668537	+	0.743679i	$0.266921\pi$
$978$	−9.73373	−	16.8593i	−0.311250	−	0.539102i
$979$	16.1953	+	1.35152i	0.517602	+	0.0431948i
$980$	15.7034	−	8.93359i	0.501625	−	0.285373i
$981$	−1.29391	−	0.940081i	−0.0413114	−	0.0300145i
$982$	−12.1252	+	2.57728i	−0.386929	+	0.0822444i
$983$	−6.87855	−	1.46208i	−0.219392	−	0.0466332i	0.0969042	−	0.995294i	$-0.469106\pi$
$983$	−6.87855	−	1.46208i	−0.219392	−	0.0466332i	−0.316296	+	0.948661i	$0.602439\pi$
$984$	−0.0910407	−	0.866194i	−0.00290227	−	0.0276133i
$985$	−28.4279	−	12.6569i	−0.905788	−	0.403283i
$986$	0.720517	+	2.21752i	0.0229459	+	0.0706203i
$987$	0.688624	−	12.3857i	0.0219191	−	0.394240i
$988$	27.7042	+	20.1283i	0.881387	+	0.640365i
$989$	−25.1630	−	43.5837i	−0.800138	−	1.38588i
$990$	8.08245	−	2.81929i	0.256877	−	0.0896031i
$991$	−8.64239	+	14.9691i	−0.274534	+	0.475508i	−0.970018	−	0.243035i	$-0.921857\pi$
$991$	−8.64239	+	14.9691i	−0.274534	+	0.475508i	0.695483	+	0.718542i	$0.255190\pi$
$992$	−0.326742	+	3.10874i	−0.0103741	+	0.0987026i
$993$	−3.73501	+	11.4952i	−0.118527	+	0.364789i
$994$	−14.4654	+	28.1680i	−0.458815	+	0.893436i
$995$	21.1147	−	15.3407i	0.669380	−	0.486333i
$996$	5.01573	+	2.23315i	0.158929	+	0.0707600i
$997$	−5.95410	−	1.26558i	−0.188568	−	0.0400814i	0.112660	−	0.993634i	$-0.464063\pi$
$997$	−5.95410	−	1.26558i	−0.188568	−	0.0400814i	−0.301228	+	0.953552i	$0.597396\pi$
$998$	27.4331	+	30.4676i	0.868380	+	0.964434i
$999$	−0.983356	+	9.35601i	−0.0311120	+	0.296011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.a.235.3	yes	24
7.2	even	3	inner	462.2.y.a.37.1	yes	24
11.3	even	5	inner	462.2.y.a.25.1	✓	24
77.58	even	15	inner	462.2.y.a.289.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.a.25.1	✓	24	11.3	even	5	inner
462.2.y.a.37.1	yes	24	7.2	even	3	inner
462.2.y.a.235.3	yes	24	1.1	even	1	trivial
462.2.y.a.289.3	yes	24	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)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.35782 + 1.04977i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.43391 - 2.22349i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.35782 + 1.04977i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.43391 - 2.22349i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(1.29048 - 2.23517i) q^{10} +(1.89143 - 2.72442i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.71598 - 2.69982i) q^{13} +(-2.36119 + 1.19364i) q^{14} +(-0.797558 - 2.45463i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.0531737 - 0.505914i) q^{17} +(0.978148 + 0.207912i) q^{18} +(7.29250 - 1.55007i) q^{19} +(-2.08803 - 1.51705i) q^{20} +(-0.692898 + 2.55341i) q^{21} +(-2.51179 - 2.16585i) q^{22} +(-2.63753 - 4.56834i) q^{23} +(0.913545 - 0.406737i) q^{24} +(1.11164 + 1.23460i) q^{25} +(-3.07345 + 3.41342i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.940289 + 2.47303i) q^{28} +(-1.41639 - 4.35919i) q^{29} +(-2.52455 + 0.536610i) q^{30} +(-2.85562 + 1.27140i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.29026 + 0.417385i) q^{33} -0.508700 q^{34} +(-1.04676 - 6.74785i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-6.29488 + 6.99117i) q^{37} +(-0.779303 - 7.41457i) q^{38} +(0.480120 + 4.56804i) q^{39} +(-1.72699 + 1.91802i) q^{40} +(0.269143 - 0.828337i) q^{41} +(2.46699 + 0.956006i) q^{42} +9.54037 q^{43} +(-2.41654 + 2.27164i) q^{44} +(-1.29048 + 2.23517i) q^{45} +(-4.81901 + 2.14556i) q^{46} +(-4.58611 + 0.974808i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-2.88779 + 6.37657i) q^{49} +(1.34403 - 0.976495i) q^{50} +(-0.340387 + 0.378038i) q^{51} +(3.07345 + 3.41342i) q^{52} +(-4.72176 + 2.10226i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(7.31967 - 4.43812i) q^{55} +(2.55777 - 0.676637i) q^{56} +(-6.03156 - 4.38218i) q^{57} +(-4.48336 + 0.952968i) q^{58} +(5.15889 + 1.09656i) q^{59} +(0.269783 + 2.56681i) q^{60} +(9.81572 + 4.37024i) q^{61} +(0.965945 + 2.97287i) q^{62} +(2.36119 - 1.19364i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-5.92742 - 10.2666i) q^{65} +(0.0711727 + 3.31586i) q^{66} +(2.02628 - 3.50961i) q^{67} +(-0.0531737 + 0.505914i) q^{68} +(-1.63009 + 5.01689i) q^{69} +(-6.82030 + 0.335682i) q^{70} +(9.68258 - 7.03481i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(8.56379 + 1.82029i) q^{73} +(6.29488 + 6.99117i) q^{74} +(0.173654 - 1.65221i) q^{75} -7.45541 q^{76} +(-8.76987 - 0.298996i) q^{77} +4.59320 q^{78} +(-0.859434 + 8.17697i) q^{79} +(1.72699 + 1.91802i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.795666 - 0.354253i) q^{82} +(4.44183 - 3.22718i) q^{83} +(1.20864 - 2.35355i) q^{84} +(0.405718 - 1.24867i) q^{85} +(0.997240 - 9.48810i) q^{86} +(-2.29176 + 3.96945i) q^{87} +(2.00659 + 2.64075i) q^{88} +(2.45001 + 4.24355i) q^{89} +(2.08803 + 1.51705i) q^{90} +(-0.674618 + 12.1337i) q^{91} +(1.63009 + 5.01689i) q^{92} +(2.85562 + 1.27140i) q^{93} +(0.490089 + 4.66288i) q^{94} +(18.8216 + 4.00065i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(12.1255 + 8.80966i) q^{97} +(6.03978 + 3.53850i) q^{98} +(2.51179 + 2.16585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Introduction

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