LMFDB - Embedded newform 462.2.y.d.163.5

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			163.5
Character	$\chi$	$=$	462.163
Dual form			462.2.y.d.445.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.65870 + 0.777681i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.31914 - 1.27341i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.65870 + 0.777681i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.31914 - 1.27341i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(1.87022 + 3.23932i) q^{10} +(-3.31637 + 0.0414312i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.49767 - 4.60936i) q^{13} +(2.49814 + 0.871382i) q^{14} +(-3.02608 - 2.19857i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(1.21236 - 1.34647i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(0.679317 + 6.46327i) q^{19} +(-1.15586 + 3.55737i) q^{20} +(-2.63659 + 0.220037i) q^{21} +(-2.24987 - 2.43682i) q^{22} +(-0.282077 + 0.488571i) q^{23} +(0.978148 - 0.207912i) q^{24} +(8.21358 + 3.65692i) q^{25} +(4.42756 - 1.97128i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.02402 + 2.43955i) q^{28} +(-0.00462018 - 0.00335675i) q^{29} +(-0.390982 - 3.71995i) q^{30} +(-5.81785 + 1.23662i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.04650 + 1.31104i) q^{33} +1.81185 q^{34} +(9.47536 - 2.85547i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(5.65276 - 2.51677i) q^{37} +(-4.34859 + 4.82960i) q^{38} +(-3.24299 + 3.60170i) q^{39} +(-3.41706 + 1.52137i) q^{40} +(-5.08799 + 3.69664i) q^{41} +(-1.92774 - 1.81213i) q^{42} +1.95863 q^{43} +(0.305450 - 3.30253i) q^{44} +(1.87022 + 3.23932i) q^{45} +(-0.551826 + 0.117294i) q^{46} +(1.12878 + 10.7396i) q^{47} +(0.809017 + 0.587785i) q^{48} +(3.75685 - 5.90644i) q^{49} +(2.77834 + 8.55084i) q^{50} +(-1.65521 + 0.736945i) q^{51} +(4.42756 + 1.97128i) q^{52} +(-3.84143 + 0.816522i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-12.1658 - 2.42749i) q^{55} +(-1.12773 + 2.39337i) q^{56} +(2.00826 - 6.18079i) q^{57} +(-0.000596946 - 0.00567957i) q^{58} +(-0.289297 + 2.75247i) q^{59} +(2.50284 - 2.77969i) q^{60} +(-11.7041 - 2.48778i) q^{61} +(-4.81189 - 3.49604i) q^{62} +(2.49814 + 0.871382i) q^{63} +(0.309017 - 0.951057i) q^{64} +(9.06414 - 15.6996i) q^{65} +(1.06422 + 3.14125i) q^{66} +(-7.68529 - 13.3113i) q^{67} +(1.21236 + 1.34647i) q^{68} +(0.456410 - 0.331601i) q^{69} +(8.46228 + 5.13088i) q^{70} +(0.0939727 + 0.289218i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(1.29763 - 12.3462i) q^{73} +(5.65276 + 2.51677i) q^{74} +(-6.01608 - 6.68153i) q^{75} -6.49887 q^{76} +(-7.63837 + 4.31918i) q^{77} -4.84657 q^{78} +(-11.4079 - 12.6697i) q^{79} +(-3.41706 - 1.52137i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-6.15167 - 1.30758i) q^{82} +(0.625117 + 1.92391i) q^{83} +(0.0567662 - 2.64514i) q^{84} +(5.48280 - 3.98348i) q^{85} +(1.31058 + 1.45554i) q^{86} +(0.00285543 + 0.00494574i) q^{87} +(2.65864 - 1.98283i) q^{88} +(-2.80876 + 4.86492i) q^{89} +(-1.15586 + 3.55737i) q^{90} +(-2.39629 - 12.5969i) q^{91} +(-0.456410 - 0.331601i) q^{92} +(5.81785 + 1.23662i) q^{93} +(-7.22579 + 8.02505i) q^{94} +(-2.54094 + 24.1755i) q^{95} +(0.104528 + 0.994522i) q^{96} +(-3.80824 + 11.7206i) q^{97} +(6.90317 - 1.16030i) q^{98} +(-2.24987 - 2.43682i) 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	3.65870	+	0.777681i	1.63622	+	0.347790i	0.932075	−	0.362266i	$-0.117997\pi$
$5$	3.65870	+	0.777681i	1.63622	+	0.347790i	0.704146	+	0.710055i	$0.251330\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	2.31914	−	1.27341i	0.876554	−	0.481304i
$7$	2.31914	−	1.27341i	0.876554	−	0.481304i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	1.87022	+	3.23932i	0.591415	+	1.02436i
$11$	−3.31637	+	0.0414312i	−0.999922	+	0.0124920i
$11$	−3.31637	+	0.0414312i	−0.999922	+	0.0124920i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.49767	−	4.60936i	0.415379	−	1.27841i	−0.496532	−	0.868018i	$-0.665393\pi$
$13$	1.49767	−	4.60936i	0.415379	−	1.27841i	0.911911	−	0.410387i	$-0.134607\pi$
$14$	2.49814	+	0.871382i	0.667655	+	0.232887i
$15$	−3.02608	−	2.19857i	−0.781330	−	0.567670i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	1.21236	−	1.34647i	0.294041	−	0.326566i	−0.577964	−	0.816062i	$-0.696153\pi$
$17$	1.21236	−	1.34647i	0.294041	−	0.326566i	0.872005	+	0.489496i	$0.162819\pi$
$18$	−0.104528	+	0.994522i	−0.0246376	+	0.234411i
$19$	0.679317	+	6.46327i	0.155846	+	1.48278i	0.740809	+	0.671715i	$0.234442\pi$
$19$	0.679317	+	6.46327i	0.155846	+	1.48278i	−0.584963	+	0.811060i	$0.698891\pi$
$20$	−1.15586	+	3.55737i	−0.258458	+	0.795452i
$21$	−2.63659	+	0.220037i	−0.575350	+	0.0480161i
$22$	−2.24987	−	2.43682i	−0.479674	−	0.519531i
$23$	−0.282077	+	0.488571i	−0.0588171	+	0.101874i	−0.893935	−	0.448197i	$-0.852066\pi$
$23$	−0.282077	+	0.488571i	−0.0588171	+	0.101874i	0.835118	+	0.550071i	$0.185400\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	8.21358	+	3.65692i	1.64272	+	0.731384i
$26$	4.42756	−	1.97128i	0.868315	−	0.386599i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.02402	+	2.43955i	0.193521	+	0.461031i
$29$	−0.00462018	−	0.00335675i	−0.000857945	−	0.000623334i	0.587356	−	0.809329i	$-0.300169\pi$
$29$	−0.00462018	−	0.00335675i	−0.000857945	−	0.000623334i	−0.588214	+	0.808705i	$0.700169\pi$
$30$	−0.390982	−	3.71995i	−0.0713833	−	0.679167i
$31$	−5.81785	+	1.23662i	−1.04492	+	0.222104i	−0.698227	−	0.715876i	$-0.746027\pi$
$31$	−5.81785	+	1.23662i	−1.04492	+	0.222104i	−0.346689	+	0.937980i	$0.612694\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.04650	+	1.31104i	0.530328	+	0.228222i
$34$	1.81185			0.310729
$35$	9.47536	−	2.85547i	1.60163	−	0.482663i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	5.65276	−	2.51677i	0.929308	−	0.413755i	0.114459	−	0.993428i	$-0.463487\pi$
$37$	5.65276	−	2.51677i	0.929308	−	0.413755i	0.814849	+	0.579673i	$0.196820\pi$
$38$	−4.34859	+	4.82960i	−0.705435	+	0.783465i
$39$	−3.24299	+	3.60170i	−0.519293	+	0.576734i
$40$	−3.41706	+	1.52137i	−0.540285	+	0.240550i
$41$	−5.08799	+	3.69664i	−0.794610	+	0.577318i	−0.909328	−	0.416080i	$-0.863404\pi$
$41$	−5.08799	+	3.69664i	−0.794610	+	0.577318i	0.114718	+	0.993398i	$0.463404\pi$
$42$	−1.92774	−	1.81213i	−0.297457	−	0.279618i
$43$	1.95863			0.298688			0.149344	−	0.988785i	$-0.452284\pi$
$43$	1.95863			0.298688			0.149344	+	0.988785i	$0.452284\pi$
$44$	0.305450	−	3.30253i	0.0460484	−	0.497875i
$45$	1.87022	+	3.23932i	0.278796	+	0.482889i
$46$	−0.551826	+	0.117294i	−0.0813622	+	0.0172941i
$47$	1.12878	+	10.7396i	0.164649	+	1.56653i	0.695160	+	0.718856i	$0.255334\pi$
$47$	1.12878	+	10.7396i	0.164649	+	1.56653i	−0.530510	+	0.847679i	$0.678000\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	3.75685	−	5.90644i	0.536693	−	0.843777i
$50$	2.77834	+	8.55084i	0.392916	+	1.20927i
$51$	−1.65521	+	0.736945i	−0.231775	+	0.103193i
$52$	4.42756	+	1.97128i	0.613992	+	0.273367i
$53$	−3.84143	+	0.816522i	−0.527661	+	0.112158i	−0.464037	−	0.885816i	$-0.653599\pi$
$53$	−3.84143	+	0.816522i	−0.527661	+	0.112158i	−0.0636248	+	0.997974i	$0.520266\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−12.1658	−	2.42749i	−1.64044	−	0.327323i
$56$	−1.12773	+	2.39337i	−0.150700	+	0.319827i
$57$	2.00826	−	6.18079i	0.266001	−	0.818666i
$58$	−0.000596946	−	0.00567957i	−7.83829e−5	−	0.000745764i
$59$	−0.289297	+	2.75247i	−0.0376632	+	0.358342i	0.959418	+	0.281989i	$0.0909941\pi$
$59$	−0.289297	+	2.75247i	−0.0376632	+	0.358342i	−0.997081	+	0.0763526i	$0.975673\pi$
$60$	2.50284	−	2.77969i	0.323116	−	0.358856i
$61$	−11.7041	−	2.48778i	−1.49856	−	0.318528i	−0.615629	−	0.788036i	$-0.711098\pi$
$61$	−11.7041	−	2.48778i	−1.49856	−	0.318528i	−0.882928	+	0.469508i	$0.844431\pi$
$62$	−4.81189	−	3.49604i	−0.611110	−	0.443998i
$63$	2.49814	+	0.871382i	0.314736	+	0.109784i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	9.06414	−	15.6996i	1.12427	−	1.94729i
$66$	1.06422	+	3.14125i	0.130996	+	0.386661i
$67$	−7.68529	−	13.3113i	−0.938907	−	1.62624i	−0.767513	−	0.641033i	$-0.778506\pi$
$67$	−7.68529	−	13.3113i	−0.938907	−	1.62624i	−0.171394	−	0.985203i	$-0.554827\pi$
$68$	1.21236	+	1.34647i	0.147021	+	0.163283i
$69$	0.456410	−	0.331601i	0.0549453	−	0.0399201i
$70$	8.46228	+	5.13088i	1.01144	+	0.613257i
$71$	0.0939727	+	0.289218i	0.0111525	+	0.0343239i	0.956478	−	0.291805i	$-0.0942557\pi$
$71$	0.0939727	+	0.289218i	0.0111525	+	0.0343239i	−0.945325	+	0.326129i	$0.894256\pi$
$72$	−0.978148	−	0.207912i	−0.115276	−	0.0245026i
$73$	1.29763	−	12.3462i	0.151876	−	1.44501i	−0.607481	−	0.794334i	$-0.707820\pi$
$73$	1.29763	−	12.3462i	0.151876	−	1.44501i	0.759357	−	0.650674i	$-0.225513\pi$
$74$	5.65276	+	2.51677i	0.657120	+	0.292569i
$75$	−6.01608	−	6.68153i	−0.694677	−	0.771517i
$76$	−6.49887			−0.745471
$77$	−7.63837	+	4.31918i	−0.870473	+	0.492216i
$78$	−4.84657			−0.548765
$79$	−11.4079	−	12.6697i	−1.28349	−	1.42546i	−0.852178	−	0.523252i	$-0.824718\pi$
$79$	−11.4079	−	12.6697i	−1.28349	−	1.42546i	−0.431309	−	0.902204i	$-0.641948\pi$
$80$	−3.41706	−	1.52137i	−0.382039	−	0.170095i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−6.15167	−	1.30758i	−0.679338	−	0.144398i
$83$	0.625117	+	1.92391i	0.0686156	+	0.211177i	0.979485	−	0.201518i	$-0.0645875\pi$
$83$	0.625117	+	1.92391i	0.0686156	+	0.211177i	−0.910869	+	0.412695i	$0.864587\pi$
$84$	0.0567662	−	2.64514i	0.00619370	−	0.288609i
$85$	5.48280	−	3.98348i	0.594693	−	0.432070i
$86$	1.31058	+	1.45554i	0.141323	+	0.156955i
$87$	0.00285543	+	0.00494574i	0.000306134	+	0.000530239i
$88$	2.65864	−	1.98283i	0.283412	−	0.211370i
$89$	−2.80876	+	4.86492i	−0.297728	+	0.515680i	−0.975616	−	0.219485i	$-0.929562\pi$
$89$	−2.80876	+	4.86492i	−0.297728	+	0.515680i	0.677888	+	0.735165i	$0.262896\pi$
$90$	−1.15586	+	3.55737i	−0.121838	+	0.374980i
$91$	−2.39629	−	12.5969i	−0.251199	−	1.32052i
$92$	−0.456410	−	0.331601i	−0.0475840	−	0.0345718i
$93$	5.81785	+	1.23662i	0.603283	+	0.128232i
$94$	−7.22579	+	8.02505i	−0.745283	+	0.827721i
$95$	−2.54094	+	24.1755i	−0.260695	+	2.48035i
$96$	0.104528	+	0.994522i	0.0106684	+	0.101503i
$97$	−3.80824	+	11.7206i	−0.386668	+	1.19004i	0.548595	+	0.836088i	$0.315163\pi$
$97$	−3.80824	+	11.7206i	−0.386668	+	1.19004i	−0.935263	+	0.353953i	$0.884837\pi$
$98$	6.90317	−	1.16030i	0.697325	−	0.117208i
$99$	−2.24987	−	2.43682i	−0.226121	−	0.244909i
$100$	−4.49544	+	7.78633i	−0.449544	+	0.778633i
$101$	3.08350	−	0.655418i	0.306820	−	0.0652165i	−0.0519289	−	0.998651i	$-0.516537\pi$
$101$	3.08350	−	0.655418i	0.306820	−	0.0652165i	0.358748	+	0.933434i	$0.383204\pi$
$102$	−1.65521	−	0.736945i	−0.163890	−	0.0729684i
$103$	1.28865	−	0.573744i	0.126974	−	0.0565327i	−0.342266	−	0.939603i	$-0.611194\pi$
$103$	1.28865	−	0.573744i	0.126974	−	0.0565327i	0.469240	+	0.883070i	$0.344528\pi$
$104$	1.49767	+	4.60936i	0.146859	+	0.451985i
$105$	−9.81760	−	1.24537i	−0.958100	−	0.121536i
$106$	−3.17721	−	2.30838i	−0.308598	−	0.224210i
$107$	−1.90084	−	18.0853i	−0.183761	−	1.74837i	−0.566088	−	0.824345i	$-0.691544\pi$
$107$	−1.90084	−	18.0853i	−0.183761	−	1.74837i	0.382326	−	0.924027i	$-0.375123\pi$
$108$	0.978148	−	0.207912i	0.0941223	−	0.0200063i
$109$	0.556312	+	0.963560i	0.0532850	+	0.0922923i	0.891438	−	0.453143i	$-0.149697\pi$
$109$	0.556312	+	0.963560i	0.0532850	+	0.0922923i	−0.838153	+	0.545436i	$0.816364\pi$
$110$	−6.33654	−	10.6653i	−0.604165	−	1.01689i
$111$	−6.18772			−0.587312
$112$	−2.53322	+	0.763406i	−0.239367	+	0.0721351i
$113$	−12.8185	+	9.31321i	−1.20587	+	0.876113i	−0.994849	−	0.101369i	$-0.967678\pi$
$113$	−12.8185	+	9.31321i	−1.20587	+	0.876113i	−0.211017	+	0.977482i	$0.567678\pi$
$114$	5.93701	−	2.64333i	0.556052	−	0.247570i
$115$	−1.41199	+	1.56817i	−0.131669	+	0.146233i
$116$	0.00382130	−	0.00424399i	0.000354799	−	0.000394044i
$117$	4.42756	−	1.97128i	0.409328	−	0.182244i
$118$	−2.23906	+	1.62678i	−0.206123	+	0.149757i
$119$	1.09704	−	4.66648i	0.100566	−	0.427776i
$120$	3.74044			0.341454
$121$	10.9966	−	0.274802i	0.999688	−	0.0249820i
$122$	−5.98279	−	10.3625i	−0.541656	−	0.938176i
$123$	6.15167	−	1.30758i	0.554677	−	0.117900i
$124$	−0.621717	−	5.91524i	−0.0558318	−	0.531204i
$125$	12.0767	+	8.77426i	1.08018	+	0.784793i
$126$	1.02402	+	2.43955i	0.0912268	+	0.217332i
$127$	0.589560	+	1.81448i	0.0523150	+	0.161009i	0.973801	−	0.227403i	$-0.0730236\pi$
$127$	0.589560	+	1.81448i	0.0523150	+	0.161009i	−0.921486	+	0.388412i	$0.873024\pi$
$128$	0.913545	−	0.406737i	0.0807468	−	0.0359508i
$129$	−1.78929	−	0.796645i	−0.157539	−	0.0701407i
$130$	17.7321	−	3.76908i	1.55521	−	0.330570i
$131$	5.86307	−	10.1551i	0.512258	−	0.887258i	−0.487641	−	0.873044i	$-0.662142\pi$
$131$	5.86307	−	10.1551i	0.512258	−	0.887258i	0.999899	−	0.0142131i	$-0.00452434\pi$
$132$	−1.62230	+	2.89277i	−0.141203	+	0.251784i
$133$	9.80582	+	14.1242i	0.850273	+	1.22472i
$134$	4.74977	−	14.6183i	0.410318	−	1.26283i
$135$	−0.390982	−	3.71995i	−0.0336504	−	0.320162i
$136$	−0.189390	+	1.80192i	−0.0162400	+	0.154514i
$137$	−0.817667	+	0.908111i	−0.0698580	+	0.0775852i	−0.777061	−	0.629426i	$-0.783290\pi$
$137$	−0.817667	+	0.908111i	−0.0698580	+	0.0775852i	0.707203	+	0.707011i	$0.249957\pi$
$138$	0.551826	+	0.117294i	0.0469745	+	0.00998474i
$139$	13.5031	+	9.81059i	1.14532	+	0.832124i	0.987852	−	0.155401i	$-0.0496668\pi$
$139$	13.5031	+	9.81059i	1.14532	+	0.832124i	0.157468	+	0.987524i	$0.449667\pi$
$140$	1.84939	+	9.72193i	0.156302	+	0.821653i
$141$	3.33700	−	10.2702i	0.281026	−	0.864911i
$142$	−0.152051	+	0.263360i	−0.0127598	+	0.0221007i
$143$	−4.77585	+	15.3484i	−0.399377	+	1.28349i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.0142934	−	0.0158744i	−0.00118700	−	0.00131830i
$146$	10.0433	−	7.29686i	0.831187	−	0.603892i
$147$	−5.83442	+	3.86775i	−0.481215	+	0.319007i
$148$	1.91211	+	5.88487i	0.157174	+	0.483733i
$149$	9.74784	+	2.07197i	0.798575	+	0.169742i	0.589088	−	0.808069i	$-0.299487\pi$
$149$	9.74784	+	2.07197i	0.798575	+	0.169742i	0.209487	+	0.977811i	$0.432821\pi$
$150$	0.939803	−	8.94163i	0.0767346	−	0.730081i
$151$	8.60070	+	3.82928i	0.699915	+	0.311622i	0.725667	−	0.688046i	$-0.241531\pi$
$151$	8.60070	+	3.82928i	0.699915	+	0.311622i	−0.0257518	+	0.999668i	$0.508198\pi$
$152$	−4.34859	−	4.82960i	−0.352717	−	0.391732i
$153$	1.81185			0.146479
$154$	−8.32084	−	2.78632i	−0.670513	−	0.224528i
$155$	−22.2475			−1.78696
$156$	−3.24299	−	3.60170i	−0.259647	−	0.288367i
$157$	−14.4591	−	6.43761i	−1.15396	−	0.513777i	−0.261636	−	0.965167i	$-0.584262\pi$
$157$	−14.4591	−	6.43761i	−1.15396	−	0.513777i	−0.892327	+	0.451389i	$0.850929\pi$
$158$	1.78209	−	16.9554i	0.141775	−	1.34890i
$159$	3.84143	+	0.816522i	0.304645	+	0.0647544i
$160$	−1.15586	−	3.55737i	−0.0913787	−	0.281235i
$161$	−0.0320248	+	1.49227i	−0.00252391	+	0.117607i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−1.94053	−	2.15518i	−0.151994	−	0.168807i	0.662339	−	0.749204i	$-0.269564\pi$
$163$	−1.94053	−	2.15518i	−0.151994	−	0.168807i	−0.814333	+	0.580398i	$0.802897\pi$
$164$	−3.14455	−	5.44652i	−0.245548	−	0.425302i
$165$	10.1267	+	7.16590i	0.788361	+	0.557865i
$166$	−1.01146	+	1.75190i	−0.0785046	+	0.135974i
$167$	1.34291	−	4.13306i	0.103918	−	0.319826i	−0.885557	−	0.464530i	$-0.846223\pi$
$167$	1.34291	−	4.13306i	0.103918	−	0.319826i	0.989475	+	0.144704i	$0.0462231\pi$
$168$	2.00371	−	1.72776i	0.154589	−	0.133300i
$169$	−8.48594	−	6.16539i	−0.652764	−	0.474261i
$170$	6.62901	+	1.40904i	0.508422	+	0.108068i
$171$	−4.34859	+	4.82960i	−0.332545	+	0.369329i
$172$	−0.204732	+	1.94790i	−0.0156107	+	0.148526i
$173$	2.39645	+	22.8007i	0.182198	+	1.73350i	0.578763	+	0.815496i	$0.303536\pi$
$173$	2.39645	+	22.8007i	0.182198	+	1.73350i	−0.396565	+	0.918007i	$0.629798\pi$
$174$	−0.00176475	+	0.00543134i	−0.000133785	+	0.000411749i
$175$	23.7052	−	1.97833i	1.79195	−	0.149548i
$176$	3.25251	+	0.648985i	0.245167	+	0.0489191i
$177$	1.38382	−	2.39684i	0.104014	−	0.180158i
$178$	−5.49477	+	1.16795i	−0.411850	+	0.0875415i
$179$	3.55913	+	1.58463i	0.266022	+	0.118441i	0.535413	−	0.844590i	$-0.320156\pi$
$179$	3.55913	+	1.58463i	0.266022	+	0.118441i	−0.269391	+	0.963031i	$0.586822\pi$
$180$	−3.41706	+	1.52137i	−0.254693	+	0.113396i
$181$	3.91110	+	12.0371i	0.290710	+	0.894713i	0.984629	+	0.174660i	$0.0558825\pi$
$181$	3.91110	+	12.0371i	0.290710	+	0.894713i	−0.693919	+	0.720053i	$0.744117\pi$
$182$	7.75790	−	10.2098i	0.575054	−	0.756798i
$183$	9.68036	+	7.03319i	0.715593	+	0.519909i
$184$	−0.0589701	−	0.561063i	−0.00434733	−	0.0413621i
$185$	22.6390	−	4.81207i	1.66445	−	0.353790i
$186$	2.97391	+	5.15096i	0.218058	+	0.377687i
$187$	−3.96485	+	4.51560i	−0.289939	+	0.330214i
$188$	−10.7988			−0.787581
$189$	−1.92774	−	1.81213i	−0.140222	−	0.131813i
$190$	−19.6661	+	14.2882i	−1.42673	+	1.03658i
$191$	−7.78222	+	3.46487i	−0.563102	+	0.250709i	−0.668489	−	0.743722i	$-0.733059\pi$
$191$	−7.78222	+	3.46487i	−0.563102	+	0.250709i	0.105387	+	0.994431i	$0.466392\pi$
$192$	−0.669131	+	0.743145i	−0.0482903	+	0.0536319i
$193$	11.2898	−	12.5386i	0.812659	−	0.902549i	−0.184107	−	0.982906i	$-0.558939\pi$
$193$	11.2898	−	12.5386i	0.812659	−	0.902549i	0.996766	+	0.0803569i	$0.0256060\pi$
$194$	−11.2583	+	5.01251i	−0.808297	+	0.359877i
$195$	−14.6661	+	10.6555i	−1.05026	+	0.763059i
$196$	5.48139	+	4.35366i	0.391528	+	0.310976i
$197$	−3.77453			−0.268924			−0.134462	−	0.990919i	$-0.542931\pi$
$197$	−3.77453			−0.268924			−0.134462	+	0.990919i	$0.542931\pi$
$198$	0.305450	−	3.30253i	0.0217074	−	0.234701i
$199$	−10.2754	−	17.7976i	−0.728406	−	1.26164i	−0.957557	−	0.288246i	$-0.906928\pi$
$199$	−10.2754	−	17.7976i	−0.728406	−	1.26164i	0.229150	−	0.973391i	$-0.426405\pi$
$200$	−8.79441	+	1.86931i	−0.621859	+	0.132180i
$201$	1.60666	+	15.2864i	0.113325	+	1.07822i
$202$	2.55033	+	1.85293i	0.179441	+	0.130371i
$203$	−0.0149894	−	0.00190142i	−0.00105205	−	0.000133453i
$204$	−0.559892	−	1.72317i	−0.0392003	−	0.120646i
$205$	−21.4902	+	9.56807i	−1.50094	+	0.668263i
$206$	1.28865	+	0.573744i	0.0897845	+	0.0399746i
$207$	−0.551826	+	0.117294i	−0.0383545	+	0.00815251i
$208$	−2.42328	+	4.19725i	−0.168024	+	0.291027i
$209$	−2.52064	−	21.4064i	−0.174357	−	1.48071i
$210$	−5.64376	−	8.12921i	−0.389457	−	0.560969i
$211$	0.407808	−	1.25510i	0.0280746	−	0.0864049i	−0.936037	−	0.351900i	$-0.885536\pi$
$211$	0.407808	−	1.25510i	0.0280746	−	0.0864049i	0.964112	+	0.265496i	$0.0855356\pi$
$212$	−0.410510	−	3.90574i	−0.0281939	−	0.268247i
$213$	0.0317873	−	0.302436i	0.00217803	−	0.0207226i
$214$	12.1681	−	13.5140i	0.831793	−	0.923800i
$215$	7.16603	+	1.52319i	0.488719	+	0.103880i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−11.9177	+	10.2764i	−0.809026	+	0.697608i
$218$	−0.343820	+	1.05817i	−0.0232864	+	0.0716682i
$219$	−6.20708	+	10.7510i	−0.419436	+	0.726484i
$220$	3.68587	−	11.8454i	0.248501	−	0.798618i
$221$	−4.39062	−	7.60478i	−0.295345	−	0.511553i
$222$	−4.14039	−	4.59837i	−0.277885	−	0.308622i
$223$	−19.2281	+	13.9701i	−1.28761	+	0.935504i	−0.999754	−	0.0221690i	$-0.992943\pi$
$223$	−19.2281	+	13.9701i	−1.28761	+	0.935504i	−0.287857	+	0.957673i	$0.592943\pi$
$224$	−2.26238	−	1.37173i	−0.151161	−	0.0916527i
$225$	2.77834	+	8.55084i	0.185222	+	0.570056i
$226$	−15.4983	−	3.29427i	−1.03093	−	0.219132i
$227$	0.622465	−	5.92236i	0.0413144	−	0.393081i	−0.954251	−	0.299007i	$-0.903344\pi$
$227$	0.622465	−	5.92236i	0.0413144	−	0.393081i	0.995565	−	0.0940734i	$-0.0299888\pi$
$228$	5.93701	+	2.64333i	0.393188	+	0.175059i
$229$	−9.34497	−	10.3786i	−0.617533	−	0.685840i	0.350529	−	0.936552i	$-0.386002\pi$
$229$	−9.34497	−	10.3786i	−0.617533	−	0.685840i	−0.968062	+	0.250712i	$0.919335\pi$
$230$	−2.11018			−0.139141
$231$	8.73477	−	0.838962i	0.574705	−	0.0551996i
$232$	0.00571085			0.000374936
$233$	8.07478	+	8.96795i	0.528997	+	0.587510i	0.947120	−	0.320880i	$-0.103979\pi$
$233$	8.07478	+	8.96795i	0.528997	+	0.587510i	−0.418123	+	0.908390i	$0.637312\pi$
$234$	4.42756	+	1.97128i	0.289438	+	0.128866i
$235$	−4.22213	+	40.1709i	−0.275421	+	2.62046i
$236$	−2.70716	−	0.575424i	−0.176221	−	0.0374569i
$237$	5.26837	+	16.2144i	0.342218	+	1.05324i
$238$	4.20194	−	2.30723i	0.272371	−	0.149555i
$239$	8.82906	−	6.41469i	0.571104	−	0.414932i	−0.264402	−	0.964413i	$-0.585175\pi$
$239$	8.82906	−	6.41469i	0.571104	−	0.414932i	0.835506	+	0.549481i	$0.185175\pi$
$240$	2.50284	+	2.77969i	0.161558	+	0.179428i
$241$	−2.03058	−	3.51706i	−0.130801	−	0.226554i	0.793185	−	0.608981i	$-0.208422\pi$
$241$	−2.03058	−	3.51706i	−0.130801	−	0.226554i	−0.923986	+	0.382427i	$0.875088\pi$
$242$	7.56236	+	7.98816i	0.486127	+	0.513499i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.69757	−	11.3799i	0.236713	−	0.728526i
$245$	18.3385	−	18.6883i	1.17161	−	1.19395i
$246$	5.08799	+	3.69664i	0.324398	+	0.235689i
$247$	30.8089	+	6.54863i	1.96032	+	0.416680i
$248$	3.97987	−	4.42009i	0.252722	−	0.280676i
$249$	0.211453	−	2.01184i	0.0134003	−	0.127495i
$250$	1.56037	+	14.8459i	0.0986862	+	0.938936i
$251$	3.50620	−	10.7910i	0.221309	−	0.681120i	−0.777336	−	0.629086i	$-0.783430\pi$
$251$	3.50620	−	10.7910i	0.221309	−	0.681120i	0.998645	−	0.0520342i	$-0.0165705\pi$
$252$	−1.12773	+	2.39337i	−0.0710406	+	0.150768i
$253$	0.915228	−	1.63197i	0.0575399	−	0.102601i
$254$	−0.953928	+	1.65225i	−0.0598548	+	0.103672i
$255$	−6.62901	+	1.40904i	−0.415125	+	0.0882375i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−5.62558	+	2.50467i	−0.350914	+	0.156237i	−0.574621	−	0.818419i	$-0.694851\pi$
$257$	−5.62558	+	2.50467i	−0.350914	+	0.156237i	0.223707	+	0.974656i	$0.428184\pi$
$258$	−0.605249	−	1.86276i	−0.0376811	−	0.115971i
$259$	9.90468	−	13.0350i	0.615447	−	0.809958i
$260$	14.6661	+	10.6555i	0.909552	+	0.660828i
$261$	−0.000596946	−	0.00567957i	−3.69501e−5	−	0.000351556i
$262$	11.4699	−	2.43800i	0.708612	−	0.150620i
$263$	5.43584	+	9.41515i	0.335188	+	0.580563i	0.983521	−	0.180794i	$-0.0578668\pi$
$263$	5.43584	+	9.41515i	0.335188	+	0.580563i	−0.648333	+	0.761357i	$0.724533\pi$
$264$	−3.23528	+	0.730037i	−0.199118	+	0.0449307i
$265$	−14.6897			−0.902378
$266$	−3.93495	+	16.7381i	−0.241267	+	1.02628i
$267$	4.54467	−	3.30190i	0.278129	−	0.202073i
$268$	14.0417	−	6.25178i	0.857735	−	0.381888i
$269$	−11.1445	+	12.3772i	−0.679490	+	0.754650i	−0.979972	−	0.199137i	$-0.936186\pi$
$269$	−11.1445	+	12.3772i	−0.679490	+	0.754650i	0.300481	+	0.953788i	$0.402853\pi$
$270$	2.50284	−	2.77969i	0.152318	−	0.169166i
$271$	21.6806	−	9.65284i	1.31700	−	0.586368i	0.376584	−	0.926382i	$-0.377098\pi$
$271$	21.6806	−	9.65284i	1.31700	−	0.586368i	0.940420	+	0.340014i	$0.110432\pi$
$272$	−1.46582	+	1.06498i	−0.0888782	+	0.0645738i
$273$	−2.93451	+	12.4825i	−0.177604	+	0.755476i
$274$	−1.22198			−0.0738228
$275$	−27.3908	−	11.7874i	−1.65172	−	0.710807i
$276$	0.282077	+	0.488571i	0.0169790	+	0.0294085i
$277$	−7.63561	+	1.62300i	−0.458779	+	0.0975165i	−0.431503	−	0.902111i	$-0.642017\pi$
$277$	−7.63561	+	1.62300i	−0.458779	+	0.0975165i	−0.0272760	+	0.999628i	$0.508683\pi$
$278$	1.74466	+	16.5993i	0.104638	+	0.995562i
$279$	−4.81189	−	3.49604i	−0.288080	−	0.209303i
$280$	−5.98732	+	7.87960i	−0.357811	+	0.470896i
$281$	3.47963	+	10.7092i	0.207577	+	0.638857i	0.999598	+	0.0283626i	$0.00902932\pi$
$281$	3.47963	+	10.7092i	0.207577	+	0.638857i	−0.792020	+	0.610495i	$0.790971\pi$
$282$	9.86517	−	4.39226i	0.587462	−	0.261555i
$283$	8.21264	+	3.65650i	0.488191	+	0.217357i	0.636044	−	0.771653i	$-0.280570\pi$
$283$	8.21264	+	3.65650i	0.488191	+	0.217357i	−0.147853	+	0.989009i	$0.547236\pi$
$284$	−0.297457	+	0.0632263i	−0.0176508	+	0.00375179i
$285$	12.1543	−	21.0519i	0.719959	−	1.24701i
$286$	−14.6017	+	6.72091i	−0.863418	+	0.397416i
$287$	−7.09244	+	15.0521i	−0.418653	+	0.888499i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	1.43384	+	13.6421i	0.0843434	+	0.802474i
$290$	0.00223284	−	0.0212441i	0.000131117	−	0.00124749i
$291$	8.24618	−	9.15831i	0.483399	−	0.536869i
$292$	12.1429	+	2.58105i	0.710608	+	0.151044i
$293$	1.13744	+	0.826395i	0.0664497	+	0.0482785i	0.620514	−	0.784195i	$-0.286924\pi$
$293$	1.13744	+	0.826395i	0.0664497	+	0.0482785i	−0.554065	+	0.832474i	$0.686924\pi$
$294$	−6.77829	−	1.74779i	−0.395318	−	0.101933i
$295$	−3.19900	+	9.84550i	−0.186253	+	0.573227i
$296$	−3.09386	+	5.35872i	−0.179827	+	0.311469i
$297$	1.06422	+	3.14125i	0.0617521	+	0.182274i
$298$	4.98281	+	8.63048i	0.288646	+	0.499950i
$299$	1.82954	+	2.03191i	0.105805	+	0.117509i
$300$	7.27378	−	5.28471i	0.419952	−	0.305113i
$301$	4.54234	−	2.49413i	0.261816	−	0.143760i
$302$	2.90928	+	8.95385i	0.167410	+	0.515236i
$303$	−3.08350	−	0.655418i	−0.177142	−	0.0376528i
$304$	0.679317	−	6.46327i	0.0389615	−	0.370694i
$305$	−40.8871	−	18.2041i	−2.34119	−	1.04236i
$306$	1.21236	+	1.34647i	0.0693062	+	0.0769723i
$307$	26.2166			1.49626			0.748130	−	0.663552i	$-0.230952\pi$
$307$	26.2166			1.49626			0.748130	+	0.663552i	$0.230952\pi$
$308$	−3.49709	−	8.04800i	−0.199265	−	0.458578i
$309$	−1.41060			−0.0802464
$310$	−14.8865	−	16.5331i	−0.845494	−	0.939016i
$311$	−4.31676	−	1.92194i	−0.244781	−	0.108983i	0.280680	−	0.959802i	$-0.409440\pi$
$311$	−4.31676	−	1.92194i	−0.244781	−	0.108983i	−0.525460	+	0.850818i	$0.676107\pi$
$312$	0.506604	−	4.82002i	0.0286808	−	0.272880i
$313$	29.7602	+	6.32573i	1.68215	+	0.357552i	0.947218	−	0.320591i	$-0.103882\pi$
$313$	29.7602	+	6.32573i	1.68215	+	0.357552i	0.734930	+	0.678143i	$0.237215\pi$
$314$	−4.89096	−	15.0528i	−0.276013	−	0.849480i
$315$	8.46228	+	5.13088i	0.476796	+	0.289092i
$316$	13.7928	−	10.0210i	0.775904	−	0.563728i
$317$	−21.0612	−	23.3908i	−1.18291	−	1.31376i	−0.938982	−	0.343965i	$-0.888230\pi$
$317$	−21.0612	−	23.3908i	−1.18291	−	1.31376i	−0.243931	−	0.969793i	$-0.578437\pi$
$318$	1.96363	+	3.40110i	0.110115	+	0.190724i
$319$	0.0154613	+	0.0109408i	0.000865665	+	0.000612567i
$320$	1.87022	−	3.23932i	0.104548	−	0.181083i
$321$	−5.61945	+	17.2949i	−0.313647	+	0.965307i
$322$	−1.13040	+	0.974722i	−0.0629947	+	0.0543191i
$323$	9.52615	+	6.92115i	0.530049	+	0.385103i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	29.1573	−	32.3825i	1.61736	−	1.79626i
$326$	0.303141	−	2.88419i	0.0167894	−	0.159741i
$327$	−0.116301	−	1.10653i	−0.00643145	−	0.0611912i
$328$	1.94344	−	5.98129i	0.107308	−	0.330261i
$329$	16.2937	+	23.4693i	0.898303	+	1.29391i
$330$	1.45076	+	12.3205i	0.0798618	+	0.678222i
$331$	−7.44512	+	12.8953i	−0.409221	+	0.708791i	−0.994803	−	0.101822i	$-0.967533\pi$
$331$	−7.44512	+	12.8953i	−0.409221	+	0.708791i	0.585582	+	0.810613i	$0.300866\pi$
$332$	−1.97872	+	0.420589i	−0.108596	+	0.0230828i
$333$	5.65276	+	2.51677i	0.309769	+	0.137918i
$334$	3.97005	−	1.76758i	0.217231	−	0.0967176i
$335$	−17.7662	−	54.6788i	−0.970672	−	2.98742i
$336$	2.62472	+	0.332948i	0.143190	+	0.0181638i
$337$	−6.19523	−	4.50110i	−0.337476	−	0.245191i	0.406120	−	0.913820i	$-0.366881\pi$
$337$	−6.19523	−	4.50110i	−0.337476	−	0.245191i	−0.743596	+	0.668629i	$0.766881\pi$
$338$	−1.09642	−	10.4317i	−0.0596373	−	0.567411i
$339$	15.4983	−	3.29427i	0.841754	−	0.178920i
$340$	3.38855	+	5.86915i	0.183770	+	0.318299i
$341$	19.2429	−	4.34213i	1.04206	−	0.235139i
$342$	−6.49887			−0.351419
$343$	1.19136	−	18.4819i	0.0643273	−	0.997929i
$344$	−1.58456	+	1.15125i	−0.0854339	+	0.0620713i
$345$	1.92775	−	0.858288i	0.103786	−	0.0462087i
$346$	−15.3407	+	17.0375i	−0.824719	+	0.915943i
$347$	−4.07794	+	4.52902i	−0.218915	+	0.243130i	−0.842592	−	0.538552i	$-0.818972\pi$
$347$	−4.07794	+	4.52902i	−0.218915	+	0.243130i	0.623677	+	0.781682i	$0.285638\pi$
$348$	−0.00521712	+	0.00232281i	−0.000279667	+	0.000124516i
$349$	17.9845	−	13.0665i	0.962686	−	0.699432i	0.00891273	−	0.999960i	$-0.497163\pi$
$349$	17.9845	−	13.0665i	0.962686	−	0.699432i	0.953773	+	0.300528i	$0.0971630\pi$
$350$	17.3321	+	16.2927i	0.926439	+	0.870879i
$351$	−4.84657			−0.258691
$352$	1.69406	+	2.85134i	0.0902939	+	0.151977i
$353$	15.1837	+	26.2990i	0.808148	+	1.39975i	0.914145	+	0.405387i	$0.132863\pi$
$353$	15.1837	+	26.2990i	0.808148	+	1.39975i	−0.105997	+	0.994366i	$0.533804\pi$
$354$	2.70716	−	0.575424i	0.143884	−	0.0305834i
$355$	0.118898	+	1.13124i	0.00631048	+	0.0600402i
$356$	−4.54467	−	3.30190i	−0.240867	−	0.175000i
$357$	−2.90023	+	3.81684i	−0.153496	+	0.202008i
$358$	1.20392	+	3.70528i	0.0636290	+	0.195830i
$359$	−16.4425	+	7.32065i	−0.867800	+	0.386369i	−0.791830	−	0.610741i	$-0.790872\pi$
$359$	−16.4425	+	7.32065i	−0.867800	+	0.386369i	−0.0759690	+	0.997110i	$0.524205\pi$
$360$	−3.41706	−	1.52137i	−0.180095	−	0.0801834i
$361$	−22.7275	+	4.83089i	−1.19619	+	0.254257i
$362$	−6.32829	+	10.9609i	−0.332608	+	0.576093i
$363$	−10.1576	−	4.22166i	−0.533138	−	0.221580i
$364$	12.7784	−	1.06643i	0.669769	−	0.0558959i
$365$	14.3490	−	44.1617i	0.751062	−	2.31153i
$366$	1.25074	+	11.9000i	0.0653774	+	0.622025i
$367$	−2.71428	+	25.8246i	−0.141684	+	1.34804i	0.660440	+	0.750878i	$0.270370\pi$
$367$	−2.71428	+	25.8246i	−0.141684	+	1.34804i	−0.802125	+	0.597157i	$0.796297\pi$
$368$	0.377492	−	0.419248i	0.0196782	−	0.0218548i
$369$	−6.15167	−	1.30758i	−0.320243	−	0.0680698i
$370$	18.7245	+	13.6042i	0.973441	+	0.707246i
$371$	−7.86907	+	6.78535i	−0.408542	+	0.352278i
$372$	−1.83798	+	5.65671i	−0.0952947	+	0.293287i
$373$	3.68577	−	6.38395i	0.190842	−	0.330548i	−0.754687	−	0.656085i	$-0.772211\pi$
$373$	3.68577	−	6.38395i	0.190842	−	0.330548i	0.945530	+	0.325536i	$0.105545\pi$
$374$	−6.00875	+	0.0750671i	−0.310705	+	0.00388163i
$375$	−7.46383	−	12.9277i	−0.385431	−	0.667585i
$376$	−7.22579	−	8.02505i	−0.372642	−	0.413860i
$377$	−0.0223920	+	0.0162687i	−0.00115325	+	0.000837882i
$378$	0.0567662	−	2.64514i	0.00291974	−	0.136051i
$379$	−0.737390	−	2.26945i	−0.0378772	−	0.116574i	0.930330	−	0.366723i	$-0.119520\pi$
$379$	−0.737390	−	2.26945i	−0.0378772	−	0.116574i	−0.968207	+	0.250149i	$0.919520\pi$
$380$	−23.7774	−	5.05405i	−1.21976	−	0.259267i
$381$	0.199425	−	1.89741i	0.0102169	−	0.0972070i
$382$	−7.78222	−	3.46487i	−0.398173	−	0.177278i
$383$	7.62445	+	8.46781i	0.389591	+	0.432685i	0.905753	−	0.423806i	$-0.139306\pi$
$383$	7.62445	+	8.46781i	0.389591	+	0.432685i	−0.516162	+	0.856491i	$0.672640\pi$
$384$	−1.00000			−0.0510310
$385$	−31.3055	+	9.86237i	−1.59547	+	0.502633i
$386$	16.8724			0.858781
$387$	1.31058	+	1.45554i	0.0666204	+	0.0739894i
$388$	−11.2583	−	5.01251i	−0.571552	−	0.254471i
$389$	1.64904	−	15.6896i	0.0836096	−	0.795492i	−0.869717	−	0.493551i	$-0.835699\pi$
$389$	1.64904	−	15.6896i	0.0836096	−	0.795492i	0.953326	−	0.301941i	$-0.0976347\pi$
$390$	−17.7321	−	3.76908i	−0.897902	−	0.190855i
$391$	0.315865	+	0.972133i	0.0159740	+	0.0491629i
$392$	0.432362	+	6.98663i	0.0218376	+	0.352878i
$393$	−9.48664	+	6.89245i	−0.478538	+	0.347678i
$394$	−2.52566	−	2.80502i	−0.127241	−	0.141315i
$395$	−31.8850	−	55.2265i	−1.60431	−	2.77875i
$396$	2.65864	−	1.98283i	0.133602	−	0.0996409i
$397$	−1.63670	+	2.83484i	−0.0821435	+	0.142277i	−0.904170	−	0.427172i	$-0.859510\pi$
$397$	−1.63670	+	2.83484i	−0.0821435	+	0.142277i	0.822027	+	0.569449i	$0.192843\pi$
$398$	6.35057	−	19.5450i	0.318325	−	0.979704i
$399$	−3.21324	−	16.8915i	−0.160863	−	0.845632i
$400$	−7.27378	−	5.28471i	−0.363689	−	0.264235i
$401$	24.0094	+	5.10336i	1.19897	+	0.254849i	0.763773	−	0.645485i	$-0.223345\pi$
$401$	24.0094	+	5.10336i	1.19897	+	0.254849i	0.435199	+	0.900334i	$0.356678\pi$
$402$	−10.2849	+	11.4226i	−0.512965	+	0.569706i
$403$	−3.01319	+	28.6686i	−0.150098	+	1.42808i
$404$	0.329514	+	3.13512i	0.0163939	+	0.155978i
$405$	−1.15586	+	3.55737i	−0.0574351	+	0.176767i
$406$	−0.00861682	−	0.0124116i	−0.000427646	−	0.000615976i
$407$	−18.6423	+	8.58073i	−0.924067	+	0.425331i
$408$	0.905924	−	1.56911i	0.0448499	−	0.0776824i
$409$	6.12301	−	1.30148i	0.302763	−	0.0643543i	−0.0540251	−	0.998540i	$-0.517205\pi$
$409$	6.12301	−	1.30148i	0.302763	−	0.0643543i	0.356788	+	0.934185i	$0.383872\pi$
$410$	−21.4902	−	9.56807i	−1.06133	−	0.472533i
$411$	1.11634	−	0.497026i	0.0550649	−	0.0245165i
$412$	0.435900	+	1.34156i	0.0214753	+	0.0660941i
$413$	2.83411	+	6.75177i	0.139457	+	0.332233i
$414$	−0.456410	−	0.331601i	−0.0224313	−	0.0162973i
$415$	0.790927	+	7.52517i	0.0388251	+	0.369396i
$416$	−4.74066	+	1.00766i	−0.232430	+	0.0494045i
$417$	−8.34539	−	14.4546i	−0.408675	−	0.707847i
$418$	14.2214	−	16.1969i	0.695593	−	0.792216i
$419$	−2.24186			−0.109522			−0.0547611	−	0.998499i	$-0.517440\pi$
$419$	−2.24186			−0.109522			−0.0547611	+	0.998499i	$0.517440\pi$
$420$	2.26477	−	9.63364i	0.110509	−	0.470073i
$421$	1.27174	−	0.923975i	0.0619809	−	0.0450318i	−0.556363	−	0.830939i	$-0.687804\pi$
$421$	1.27174	−	0.923975i	0.0619809	−	0.0450318i	0.618344	+	0.785907i	$0.287804\pi$
$422$	1.20560	−	0.536768i	0.0586877	−	0.0261294i
$423$	−7.22579	+	8.02505i	−0.351330	+	0.390191i
$424$	2.62785	−	2.91852i	0.127619	−	0.141736i
$425$	14.8818	−	6.62579i	0.721872	−	0.321398i
$426$	0.246024	−	0.178747i	0.0119199	−	0.00866030i
$427$	−30.3115	+	9.13460i	−1.46687	+	0.442054i
$428$	18.1849			0.879001
$429$	10.6057	−	12.0789i	0.512048	−	0.583176i
$430$	3.66306	+	6.34461i	0.176649	+	0.305964i
$431$	−12.8765	+	2.73699i	−0.620240	+	0.131836i	−0.507306	−	0.861766i	$-0.669358\pi$
$431$	−12.8765	+	2.73699i	−0.620240	+	0.131836i	−0.112935	+	0.993602i	$0.536025\pi$
$432$	0.104528	+	0.994522i	0.00502913	+	0.0478490i
$433$	11.2116	+	8.14568i	0.538794	+	0.391457i	0.823637	−	0.567118i	$-0.191942\pi$
$433$	11.2116	+	8.14568i	0.538794	+	0.391457i	−0.284843	+	0.958574i	$0.591942\pi$
$434$	−15.6114	−	1.98031i	−0.749369	−	0.0950581i
$435$	0.00660094	+	0.0203156i	0.000316491	+	0.000974059i
$436$	−1.01643	+	0.452545i	−0.0486783	+	0.0216730i
$437$	−3.34939	−	1.49124i	−0.160223	−	0.0713358i
$438$	−12.1429	+	2.58105i	−0.580209	+	0.123327i
$439$	−7.97309	+	13.8098i	−0.380535	+	0.659106i	−0.991139	−	0.132830i	$-0.957593\pi$
$439$	−7.97309	+	13.8098i	−0.380535	+	0.659106i	0.610604	+	0.791936i	$0.290927\pi$
$440$	11.2692	−	5.18700i	0.537238	−	0.247281i
$441$	6.90317	−	1.16030i	0.328722	−	0.0552522i
$442$	2.71355	−	8.35146i	0.129071	−	0.397238i
$443$	−3.45512	−	32.8733i	−0.164158	−	1.56186i	−0.697890	−	0.716205i	$-0.745878\pi$
$443$	−3.45512	−	32.8733i	−0.164158	−	1.56186i	0.533732	−	0.845653i	$-0.320789\pi$
$444$	0.646792	−	6.15382i	0.0306954	−	0.292047i
$445$	−14.0598	+	15.6150i	−0.666497	+	0.740220i
$446$	−23.2479	−	4.94150i	−1.10082	−	0.233987i
$447$	−8.06235	−	5.85764i	−0.381336	−	0.277057i
$448$	−0.494430	−	2.59914i	−0.0233596	−	0.122798i
$449$	−4.01132	+	12.3456i	−0.189306	+	0.582624i	−0.999996	−	0.00285170i	$-0.999092\pi$
$449$	−4.01132	+	12.3456i	−0.189306	+	0.582624i	0.810690	+	0.585476i	$0.199092\pi$
$450$	−4.49544	+	7.78633i	−0.211917	+	0.367051i
$451$	16.7205	−	12.4702i	0.787336	−	0.587199i
$452$	−7.92229	−	13.7218i	−0.372633	−	0.645420i
$453$	−6.29962	−	6.99644i	−0.295982	−	0.328721i
$454$	4.81768	−	3.50025i	0.226105	−	0.164275i
$455$	1.02907	−	47.9519i	0.0482437	−	2.24802i
$456$	2.00826	+	6.18079i	0.0940454	+	0.289442i
$457$	−0.489580	−	0.104063i	−0.0229016	−	0.00486788i	0.196447	−	0.980515i	$-0.437060\pi$
$457$	−0.489580	−	0.104063i	−0.0229016	−	0.00486788i	−0.219348	+	0.975647i	$0.570393\pi$
$458$	1.45983	−	13.8893i	0.0682133	−	0.649006i
$459$	−1.65521	−	0.736945i	−0.0772584	−	0.0343977i
$460$	−1.41199	−	1.56817i	−0.0658343	−	0.0731164i
$461$	17.6826			0.823563			0.411781	−	0.911283i	$-0.364907\pi$
$461$	17.6826			0.823563			0.411781	+	0.911283i	$0.364907\pi$
$462$	6.46817	+	5.92982i	0.300926	+	0.275880i
$463$	25.6897			1.19390			0.596952	−	0.802277i	$-0.296378\pi$
$463$	25.6897			1.19390			0.596952	+	0.802277i	$0.296378\pi$
$464$	0.00382130	+	0.00424399i	0.000177400	+	0.000197022i
$465$	20.3241	+	9.04886i	0.942506	+	0.419631i
$466$	−1.26140	+	12.0015i	−0.0584334	+	0.555957i
$467$	34.2713	+	7.28458i	1.58589	+	0.337090i	0.914679	−	0.404180i	$-0.132443\pi$
$467$	34.2713	+	7.28458i	1.58589	+	0.337090i	0.671206	+	0.741271i	$0.265776\pi$
$468$	1.49767	+	4.60936i	0.0692299	+	0.213068i
$469$	−34.7740	−	21.0843i	−1.60572	−	0.973583i
$470$	−32.6779	+	23.7419i	−1.50732	+	1.09513i
$471$	10.5906	+	11.7621i	0.487991	+	0.541969i
$472$	−1.38382	−	2.39684i	−0.0636954	−	0.110324i
$473$	−6.49552	+	0.0811483i	−0.298664	+	0.00373120i
$474$	−8.52441	+	14.7647i	−0.391539	+	0.678165i
$475$	−18.0560	+	55.5708i	−0.828468	+	2.54976i
$476$	4.52625	+	1.57881i	0.207460	+	0.0723647i
$477$	−3.17721	−	2.30838i	−0.145475	−	0.105694i
$478$	10.6748	+	2.26901i	0.488256	+	0.103782i
$479$	−25.0202	+	27.7877i	−1.14320	+	1.26965i	−0.185258	+	0.982690i	$0.559312\pi$
$479$	−25.0202	+	27.7877i	−1.14320	+	1.26965i	−0.957942	+	0.286962i	$0.907355\pi$
$480$	−0.390982	+	3.71995i	−0.0178458	+	0.169792i
$481$	−3.13472	−	29.8249i	−0.142931	−	1.35990i
$482$	1.25497	−	3.86239i	0.0571621	−	0.175927i
$483$	0.636216	−	1.35023i	0.0289488	−	0.0614375i
$484$	−0.876158	+	10.9651i	−0.0398253	+	0.498411i
$485$	−23.0481	+	39.9204i	−1.04656	+	1.81269i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	25.4466	+	11.3295i	1.15309	+	0.513390i	0.892050	−	0.451937i	$-0.149267\pi$
$487$	25.4466	+	11.3295i	1.15309	+	0.513390i	0.261044	+	0.965327i	$0.415933\pi$
$488$	10.9311	−	4.86684i	0.494828	−	0.220312i
$489$	0.896174	+	2.75814i	0.0405264	+	0.124727i
$490$	26.1590	+	1.12329i	1.18174	+	0.0507450i
$491$	−16.9348	−	12.3039i	−0.764259	−	0.555266i	0.135955	−	0.990715i	$-0.456590\pi$
$491$	−16.9348	−	12.3039i	−0.764259	−	0.555266i	−0.900214	+	0.435449i	$0.856590\pi$
$492$	0.657390	+	6.25465i	0.0296374	+	0.281981i
$493$	−0.0101211	+	0.00215130i	−0.000455831	+	9.68898e-5i
$494$	15.7486	+	27.2774i	0.708563	+	1.22727i
$495$	−6.33654	−	10.6653i	−0.284806	−	0.479368i
$496$	5.94782			0.267065
$497$	0.586229	+	0.551073i	0.0262960	+	0.0247190i
$498$	1.63658	−	1.18904i	0.0733369	−	0.0532823i
$499$	−2.83459	+	1.26204i	−0.126894	+	0.0564968i	−0.469201	−	0.883091i	$-0.655458\pi$
$499$	−2.83459	+	1.26204i	−0.126894	+	0.0564968i	0.342308	+	0.939588i	$0.388792\pi$
$500$	−9.98855	+	11.0934i	−0.446702	+	0.496112i
$501$	−2.90788	+	3.22953i	−0.129914	+	0.144285i
$502$	10.3654	−	4.61495i	0.462628	−	0.205975i
$503$	−18.8459	+	13.6923i	−0.840296	+	0.610511i	−0.922453	−	0.386109i	$-0.873819\pi$
$503$	−18.8459	+	13.6923i	−0.840296	+	0.610511i	0.0821573	+	0.996619i	$0.473819\pi$
$504$	−2.53322	+	0.763406i	−0.112839	+	0.0340048i
$505$	11.7913			0.524706
$506$	1.82520	−	0.411853i	0.0811399	−	0.0183091i
$507$	5.24460	+	9.08391i	0.232921	+	0.403431i
$508$	−1.86617	+	0.396666i	−0.0827977	+	0.0175992i
$509$	−2.93231	−	27.8990i	−0.129972	−	1.23660i	−0.843945	−	0.536429i	$-0.819773\pi$
$509$	−2.93231	−	27.8990i	−0.129972	−	1.23660i	0.713973	−	0.700173i	$-0.246894\pi$
$510$	−5.48280	−	3.98348i	−0.242782	−	0.176392i
$511$	−12.7123	−	30.2849i	−0.562360	−	1.33973i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	5.93701	−	2.64333i	0.262125	−	0.116706i
$514$	−5.62558	−	2.50467i	−0.248134	−	0.110476i
$515$	5.16098	−	1.09700i	0.227420	−	0.0483396i
$516$	0.979313	−	1.69622i	0.0431119	−	0.0746719i
$517$	−4.18840	−	35.5697i	−0.184206	−	1.56436i
$518$	16.3144	−	1.36153i	0.716816	−	0.0598222i
$519$	7.08460	−	21.8042i	0.310980	−	0.957097i
$520$	1.89492	+	18.0290i	0.0830978	+	0.790623i
$521$	−0.905032	+	8.61081i	−0.0396502	+	0.377246i	0.956646	+	0.291254i	$0.0940726\pi$
$521$	−0.905032	+	8.61081i	−0.0396502	+	0.377246i	−0.996296	+	0.0859919i	$0.972594\pi$
$522$	0.00382130	−	0.00424399i	0.000167254	−	0.000185754i
$523$	−23.2602	−	4.94411i	−1.01710	−	0.216191i	−0.330947	−	0.943649i	$-0.607368\pi$
$523$	−23.2602	−	4.94411i	−1.01710	−	0.216191i	−0.686152	+	0.727458i	$0.740701\pi$
$524$	9.48664	+	6.89245i	0.414426	+	0.301098i
$525$	−22.4605	−	7.83449i	−0.980255	−	0.341925i
$526$	−3.35953	+	10.3396i	−0.146483	+	0.450827i
$527$	−5.38827	+	9.33277i	−0.234717	+	0.406542i
$528$	−2.70735	−	1.91579i	−0.117822	−	0.0833742i
$529$	11.3409	+	19.6430i	0.493081	+	0.854042i
$530$	−9.82930	−	10.9165i	−0.426957	−	0.474184i
$531$	−2.23906	+	1.62678i	−0.0971671	+	0.0705960i
$532$	−15.0718	+	8.27573i	−0.653446	+	0.358798i
$533$	9.41900	+	28.9887i	0.407982	+	1.25564i
$534$	5.49477	+	1.16795i	0.237782	+	0.0505421i
$535$	7.10998	−	67.6470i	0.307391	−	2.92463i
$536$	14.0417	+	6.25178i	0.606510	+	0.270036i
$537$	−2.60690	−	2.89526i	−0.112496	−	0.124940i
$538$	−16.6551			−0.718054
$539$	−12.2144	+	19.7436i	−0.526111	+	0.850416i
$540$	3.74044			0.160963
$541$	19.7284	+	21.9106i	0.848191	+	0.942011i	0.998915	−	0.0465647i	$-0.0148274\pi$
$541$	19.7284	+	21.9106i	0.848191	+	0.942011i	−0.150725	+	0.988576i	$0.548161\pi$
$542$	21.6806	+	9.65284i	0.931263	+	0.414625i
$543$	1.32297	−	12.5873i	0.0567742	−	0.540171i
$544$	−1.77226	−	0.376704i	−0.0759848	−	0.0161511i
$545$	1.28604	+	3.95801i	0.0550877	+	0.169543i
$546$	−11.2399	+	6.17167i	−0.481022	+	0.264123i
$547$	16.4845	−	11.9767i	0.704827	−	0.512086i	−0.176674	−	0.984269i	$-0.556534\pi$
$547$	16.4845	−	11.9767i	0.704827	−	0.512086i	0.881501	+	0.472183i	$0.156534\pi$
$548$	−0.817667	−	0.908111i	−0.0349290	−	0.0387926i
$549$	−5.98279	−	10.3625i	−0.255339	−	0.442261i
$550$	−9.56825	−	28.2426i	−0.407992	−	1.20427i
$551$	0.0185570	−	0.0321417i	0.000790556	−	0.00136928i
$552$	−0.174333	+	0.536542i	−0.00742011	+	0.0228367i
$553$	−42.5903	−	14.8560i	−1.81112	−	0.631742i
$554$	−6.31534	−	4.58836i	−0.268313	−	0.194941i
$555$	−22.6390	−	4.81207i	−0.960972	−	0.204261i
$556$	−11.1683	+	12.4037i	−0.473642	+	0.526033i
$557$	4.49355	−	42.7532i	0.190398	−	1.81151i	−0.315507	−	0.948923i	$-0.602174\pi$
$557$	4.49355	−	42.7532i	0.190398	−	1.81151i	0.505904	−	0.862590i	$-0.331159\pi$
$558$	−0.621717	−	5.91524i	−0.0263194	−	0.250412i
$559$	2.93338	−	9.02801i	0.124069	−	0.381844i
$560$	−9.86199	+	0.823037i	−0.416745	+	0.0347797i
$561$	5.45874	−	2.51256i	0.230468	−	0.106080i
$562$	−5.63016	+	9.75172i	−0.237494	+	0.411352i
$563$	29.6501	−	6.30231i	1.24960	−	0.265611i	0.464832	−	0.885399i	$-0.346115\pi$
$563$	29.6501	−	6.30231i	1.24960	−	0.265611i	0.784769	+	0.619788i	$0.212781\pi$
$564$	9.86517	+	4.39226i	0.415399	+	0.184947i
$565$	−54.1419	+	24.1055i	−2.27777	+	1.01413i
$566$	2.77802	+	8.54986i	0.116769	+	0.359377i
$567$	1.02402	+	2.43955i	0.0430047	+	0.102451i
$568$	−0.246024	−	0.178747i	−0.0103229	−	0.00750004i
$569$	−2.99234	−	28.4702i	−0.125445	−	1.19353i	−0.858300	−	0.513148i	$-0.828479\pi$
$569$	−2.99234	−	28.4702i	−0.125445	−	1.19353i	0.732855	−	0.680385i	$-0.238187\pi$
$570$	23.7774	−	5.05405i	0.995926	−	0.211691i
$571$	−22.0747	−	38.2345i	−0.923797	−	1.60006i	−0.793485	−	0.608590i	$-0.791735\pi$
$571$	−22.0747	−	38.2345i	−0.923797	−	1.60006i	−0.130312	−	0.991473i	$-0.541598\pi$
$572$	−14.7651	−	6.35403i	−0.617359	−	0.265675i
$573$	8.51870			0.355874
$574$	−15.9317	+	4.80114i	−0.664976	+	0.200396i
$575$	−4.10353	+	2.98139i	−0.171129	+	0.124332i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−21.1297	+	23.4669i	−0.879641	+	0.976940i	−0.999875	−	0.0158056i	$-0.994969\pi$
$577$	−21.1297	+	23.4669i	−0.879641	+	0.976940i	0.120234	+	0.992746i	$0.461635\pi$
$578$	−9.17860	+	10.1939i	−0.381780	+	0.424009i
$579$	−15.4137	+	6.86261i	−0.640571	+	0.285200i
$580$	0.0172815	−	0.0125557i	0.000717575	−	0.000521348i
$581$	3.89967	+	3.66580i	0.161786	+	0.152083i
$582$	12.3237			0.510834
$583$	12.7058	−	2.86704i	0.526219	−	0.118741i
$584$	6.20708	+	10.7510i	0.256851	+	0.444879i
$585$	17.7321	−	3.76908i	0.733134	−	0.155832i
$586$	0.146962	+	1.39825i	0.00607093	+	0.0577610i
$587$	22.3569	+	16.2433i	0.922769	+	0.670431i	0.944212	−	0.329339i	$-0.106826\pi$
$587$	22.3569	+	16.2433i	0.922769	+	0.670431i	−0.0214426	+	0.999770i	$0.506826\pi$
$588$	−3.23670	−	6.20675i	−0.133479	−	0.255962i
$589$	−11.9448	−	36.7622i	−0.492176	−	1.51476i
$590$	−9.45718	+	4.21061i	−0.389346	+	0.173348i
$591$	3.44821	+	1.53524i	0.141840	+	0.0631514i
$592$	−6.05250	+	1.28650i	−0.248756	+	0.0528748i
$593$	−21.5850	+	37.3864i	−0.886391	+	1.53527i	−0.0422796	+	0.999106i	$0.513462\pi$
$593$	−21.5850	+	37.3864i	−0.886391	+	1.53527i	−0.844111	+	0.536168i	$0.819871\pi$
$594$	−1.62230	+	2.89277i	−0.0665639	+	0.118692i
$595$	7.64278	−	16.2201i	0.313323	−	0.664960i
$596$	−3.07955	+	9.47787i	−0.126143	+	0.388228i
$597$	2.14815	+	20.4383i	0.0879180	+	0.836484i
$598$	−0.285803	+	2.71923i	−0.0116873	+	0.111198i
$599$	2.14566	−	2.38300i	0.0876694	−	0.0973667i	−0.697714	−	0.716377i	$-0.745799\pi$
$599$	2.14566	−	2.38300i	0.0876694	−	0.0973667i	0.785383	+	0.619010i	$0.212466\pi$
$600$	8.79441	+	1.86931i	0.359030	+	0.0763143i
$601$	−13.4722	−	9.78813i	−0.549543	−	0.399266i	0.278074	−	0.960560i	$-0.410304\pi$
$601$	−13.4722	−	9.78813i	−0.549543	−	0.399266i	−0.827617	+	0.561293i	$0.810304\pi$
$602$	4.89292	+	1.70671i	0.199421	+	0.0695604i
$603$	4.74977	−	14.6183i	0.193426	−	0.595303i
$604$	−4.70732	+	8.15332i	−0.191538	+	0.331754i
$605$	40.4469	+	7.54640i	1.64440	+	0.306805i
$606$	−1.57619	−	2.73005i	−0.0640285	−	0.110901i
$607$	9.36213	+	10.3977i	0.379997	+	0.422029i	0.902555	−	0.430574i	$-0.141689\pi$
$607$	9.36213	+	10.3977i	0.379997	+	0.422029i	−0.522558	+	0.852604i	$0.675022\pi$
$608$	5.25769	−	3.81994i	0.213228	−	0.154919i
$609$	0.0129201	+	0.00783376i	0.000523549	+	0.000317440i
$610$	−13.8305	−	42.5660i	−0.559982	−	1.72345i
$611$	51.1933	+	10.8815i	2.07106	+	0.440217i
$612$	−0.189390	+	1.80192i	−0.00765563	+	0.0728384i
$613$	−6.05544	−	2.69606i	−0.244577	−	0.108893i	0.280787	−	0.959770i	$-0.409404\pi$
$613$	−6.05544	−	2.69606i	−0.244577	−	0.108893i	−0.525365	+	0.850877i	$0.676071\pi$
$614$	17.5423	+	19.4827i	0.707951	+	0.786259i
$615$	23.5240			0.948579
$616$	3.64082	−	7.98401i	0.146693	−	0.321685i
$617$	19.2129			0.773481			0.386741	−	0.922189i	$-0.373601\pi$
$617$	19.2129			0.773481			0.386741	+	0.922189i	$0.373601\pi$
$618$	−0.943878	−	1.04828i	−0.0379683	−	0.0421681i
$619$	33.9397	+	15.1109i	1.36415	+	0.607359i	0.952655	−	0.304053i	$-0.0983401\pi$
$619$	33.9397	+	15.1109i	1.36415	+	0.607359i	0.411495	+	0.911412i	$0.365007\pi$
$620$	2.32549	−	22.1256i	0.0933940	−	0.888585i
$621$	0.551826	+	0.117294i	0.0221440	+	0.00470685i
$622$	−1.46019	−	4.49401i	−0.0585483	−	0.180193i
$623$	−0.318885	+	14.8591i	−0.0127759	+	0.595319i
$624$	3.92095	−	2.84874i	0.156964	−	0.114041i
$625$	7.28120	+	8.08659i	0.291248	+	0.323464i
$626$	15.2125	+	26.3489i	0.608016	+	1.05311i
$627$	−6.40405	+	20.5810i	−0.255753	+	0.821925i
$628$	7.91373	−	13.7070i	0.315792	−	0.546968i
$629$	3.46445	−	10.6625i	0.138137	−	0.425141i
$630$	1.84939	+	9.72193i	0.0736813	+	0.387331i
$631$	15.1219	+	10.9867i	0.601992	+	0.437373i	0.846585	−	0.532253i	$-0.178655\pi$
$631$	15.1219	+	10.9867i	0.601992	+	0.437373i	−0.244594	+	0.969626i	$0.578655\pi$
$632$	16.6763	+	3.54465i	0.663346	+	0.140998i
$633$	−0.883047	+	0.980724i	−0.0350980	+	0.0389803i
$634$	3.29008	−	31.3030i	0.130666	−	1.24320i
$635$	0.745938	+	7.09713i	0.0296017	+	0.281641i
$636$	−1.21359	+	3.73504i	−0.0481219	+	0.148104i
$637$	−21.5984	−	26.1626i	−0.855759	−	1.03660i
$638$	0.00221500	+	0.0188108i	8.76929e−5	+	0.000744726i
$639$	−0.152051	+	0.263360i	−0.00601504	+	0.0104184i
$640$	3.65870	−	0.777681i	0.144623	−	0.0307405i
$641$	−6.15354	−	2.73973i	−0.243050	−	0.108213i	0.281597	−	0.959533i	$-0.409136\pi$
$641$	−6.15354	−	2.73973i	−0.243050	−	0.108213i	−0.524647	+	0.851320i	$0.675803\pi$
$642$	−16.6128	+	7.39647i	−0.655653	+	0.291916i
$643$	10.7989	+	33.2356i	0.425867	+	1.31069i	0.902161	+	0.431399i	$0.141980\pi$
$643$	10.7989	+	33.2356i	0.425867	+	1.31069i	−0.476294	+	0.879286i	$0.658020\pi$
$644$	−1.48074	−	0.187834i	−0.0583495	−	0.00740169i
$645$	−5.92696	−	4.30619i	−0.233374	−	0.169556i
$646$	1.23082	+	11.7105i	0.0484259	+	0.460742i
$647$	−37.4323	+	7.95648i	−1.47162	+	0.312801i	−0.872797	−	0.488083i	$-0.837696\pi$
$647$	−37.4323	+	7.95648i	−1.47162	+	0.312801i	−0.598818	+	0.800885i	$0.704363\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	0.845375	−	9.14020i	0.0331839	−	0.358784i
$650$	43.5749			1.70915
$651$	15.0671	−	4.54060i	0.590528	−	0.177960i
$652$	2.34621	−	1.70462i	0.0918848	−	0.0667582i
$653$	2.09163	−	0.931252i	0.0818516	−	0.0364427i	−0.365402	−	0.930850i	$-0.619069\pi$
$653$	2.09163	−	0.931252i	0.0818516	−	0.0364427i	0.447254	+	0.894407i	$0.352402\pi$
$654$	0.744491	−	0.826841i	0.0291119	−	0.0323320i
$655$	29.3487	−	32.5950i	1.14675	−	1.27359i
$656$	5.74538	−	2.55801i	0.224319	−	0.0998734i
$657$	10.0433	−	7.29686i	0.391825	−	0.284678i
$658$	−6.53846	+	27.8126i	−0.254896	+	1.08425i
$659$	0.451032			0.0175697			0.00878486	−	0.999961i	$-0.497204\pi$
$659$	0.451032			0.0175697			0.00878486	+	0.999961i	$0.497204\pi$
$660$	−8.18518	+	9.32216i	−0.318608	+	0.362865i
$661$	7.24066	+	12.5412i	0.281629	+	0.487796i	0.971786	−	0.235864i	$-0.0757920\pi$
$661$	7.24066	+	12.5412i	0.281629	+	0.487796i	−0.690157	+	0.723659i	$0.742459\pi$
$662$	−14.5648	+	3.09585i	−0.566079	+	0.120324i
$663$	0.917890	+	8.73314i	0.0356479	+	0.339167i
$664$	−1.63658	−	1.18904i	−0.0635116	−	0.0461439i
$665$	24.8925	+	59.3020i	0.965288	+	2.29963i
$666$	1.91211	+	5.88487i	0.0740927	+	0.228034i
$667$	0.00294326	−	0.00131042i	0.000113963	−	5.07398e-5i
$668$	3.97005	+	1.76758i	0.153606	+	0.0683897i
$669$	23.2479	−	4.94150i	0.898816	−	0.191049i
$670$	28.7464	−	49.7901i	1.11057	−	1.92356i
$671$	38.9182	+	7.76549i	1.50242	+	0.299783i
$672$	1.50885	+	2.17333i	0.0582052	+	0.0838381i
$673$	−6.50730	+	20.0274i	−0.250838	+	0.772000i	0.743783	+	0.668421i	$0.233029\pi$
$673$	−6.50730	+	20.0274i	−0.250838	+	0.772000i	−0.994621	+	0.103579i	$0.966971\pi$
$674$	−0.800451	−	7.61578i	−0.0308322	−	0.293349i
$675$	0.939803	−	8.94163i	0.0361730	−	0.344164i
$676$	7.01864	−	7.79499i	0.269948	−	0.299807i
$677$	−21.0718	−	4.47895i	−0.809856	−	0.172140i	−0.215668	−	0.976467i	$-0.569193\pi$
$677$	−21.0718	−	4.47895i	−0.809856	−	0.172140i	−0.594188	+	0.804327i	$0.702526\pi$
$678$	12.8185	+	9.31321i	0.492293	+	0.357672i
$679$	6.09322	+	32.0311i	0.233836	+	1.22924i
$680$	−2.09424	+	6.44541i	−0.0803105	+	0.247170i
$681$	−2.97749	+	5.15716i	−0.114098	+	0.197623i
$682$	16.1028	+	11.3948i	0.616609	+	0.436329i
$683$	−8.68963	−	15.0509i	−0.332499	−	0.575906i	0.650502	−	0.759505i	$-0.274559\pi$
$683$	−8.68963	−	15.0509i	−0.332499	−	0.575906i	−0.983001	+	0.183599i	$0.941225\pi$
$684$	−4.34859	−	4.82960i	−0.166273	−	0.184664i
$685$	−3.69782	+	2.68662i	−0.141286	+	0.102651i
$686$	14.5319	−	11.4815i	0.554831	−	0.438364i
$687$	4.31568	+	13.2823i	0.164653	+	0.506751i
$688$	−1.91583	−	0.407221i	−0.0730402	−	0.0155252i
$689$	−1.98956	+	18.9294i	−0.0757963	+	0.721154i
$690$	1.92775	+	0.858288i	0.0733881	+	0.0326745i
$691$	−3.21636	−	3.57213i	−0.122356	−	0.135890i	0.678854	−	0.734273i	$-0.262477\pi$
$691$	−3.21636	−	3.57213i	−0.122356	−	0.135890i	−0.801210	+	0.598383i	$0.795810\pi$
$692$	−22.9263			−0.871525
$693$	−8.32084	−	2.78632i	−0.316083	−	0.105844i
$694$	−6.09439			−0.231340
$695$	41.7744	+	46.3951i	1.58459	+	1.75987i
$696$	−0.00521712	−	0.00232281i	−0.000197754	−	8.80460e-5i
$697$	−1.19109	+	11.3325i	−0.0451158	+	0.429248i
$698$	21.7442	+	4.62188i	0.823031	+	0.174941i
$699$	−3.72908	−	11.4769i	−0.141047	−	0.434098i
$700$	−0.510378	+	23.7822i	−0.0192905	+	0.898881i
$701$	34.4836	−	25.0538i	1.30243	−	0.946269i	0.302451	−	0.953165i	$-0.402195\pi$
$701$	34.4836	−	25.0538i	1.30243	−	0.946269i	0.999976	+	0.00689599i	$0.00219508\pi$
$702$	−3.24299	−	3.60170i	−0.122399	−	0.135937i
$703$	20.1066	+	34.8256i	0.758334	+	1.31347i
$704$	−0.985410	+	3.16685i	−0.0371390	+	0.119355i
$705$	20.1961	−	34.9806i	0.760628	−	1.31745i
$706$	−9.38405	+	28.8812i	−0.353174	+	1.08696i
$707$	6.31646	−	5.44657i	0.237555	−	0.204839i
$708$	2.23906	+	1.62678i	0.0841492	+	0.0611380i
$709$	−18.7402	−	3.98334i	−0.703802	−	0.149598i	−0.157910	−	0.987454i	$-0.550476\pi$
$709$	−18.7402	−	3.98334i	−0.703802	−	0.149598i	−0.545891	+	0.837856i	$0.683809\pi$
$710$	−0.761119	+	0.845308i	−0.0285643	+	0.0317239i
$711$	1.78209	−	16.9554i	0.0668334	−	0.635878i
$712$	−0.587191	−	5.58675i	−0.0220059	−	0.209372i
$713$	1.03690	−	3.19126i	0.0388323	−	0.119513i
$714$	−4.77709	+	0.398675i	−0.178778	+	0.0149200i
$715$	−29.4096	+	52.4410i	−1.09986	+	1.96118i
$716$	−1.94798	+	3.37400i	−0.0727994	+	0.126092i
$717$	−10.6748	+	2.26901i	−0.398659	+	0.0847376i
$718$	−16.4425	−	7.32065i	−0.613627	−	0.273204i
$719$	34.5307	−	15.3741i	1.28778	−	0.573356i	0.355358	−	0.934730i	$-0.384359\pi$
$719$	34.5307	−	15.3741i	1.28778	−	0.573356i	0.932421	+	0.361374i	$0.117692\pi$
$720$	−1.15586	−	3.55737i	−0.0430763	−	0.132575i
$721$	2.25795	−	2.97157i	0.0840906	−	0.110667i
$722$	−18.7977	−	13.6574i	−0.699580	−	0.508274i
$723$	0.424506	+	4.03891i	0.0157876	+	0.150209i
$724$	−12.3800	+	2.63145i	−0.460099	+	0.0977971i
$725$	−0.0256728	−	0.0444666i	−0.000953464	−	0.00165145i
$726$	−3.65948	−	10.3734i	−0.135816	−	0.384994i
$727$	31.1602			1.15567			0.577834	−	0.816154i	$-0.303898\pi$
$727$	31.1602			1.15567			0.577834	+	0.816154i	$0.303898\pi$
$728$	9.34292	+	8.78261i	0.346272	+	0.325505i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	42.4199	−	18.8866i	1.57003	−	0.699024i
$731$	2.37457	−	2.63722i	0.0878265	−	0.0975412i
$732$	−8.00654	+	8.89216i	−0.295930	+	0.328664i
$733$	−6.63883	+	2.95580i	−0.245211	+	0.109175i	−0.525662	−	0.850693i	$-0.676182\pi$
$733$	−6.63883	+	2.95580i	−0.245211	+	0.109175i	0.280452	+	0.959868i	$0.409516\pi$
$734$	−21.0077	+	15.2630i	−0.775407	+	0.563366i
$735$	−24.3543	+	9.61364i	−0.898321	+	0.354604i
$736$	0.564154			0.0207950
$737$	26.0387	+	43.8268i	0.959149	+	1.61438i
$738$	−3.14455	−	5.44652i	−0.115752	−	0.200489i
$739$	12.1259	−	2.57744i	0.446059	−	0.0948127i	0.0205943	−	0.999788i	$-0.493444\pi$
$739$	12.1259	−	2.57744i	0.446059	−	0.0948127i	0.425464	+	0.904975i	$0.360111\pi$
$740$	2.41929	+	23.0180i	0.0889348	+	0.846158i
$741$	−25.4818	−	18.5136i	−0.936096	−	0.680113i
$742$	−10.3079	−	1.30757i	−0.378416	−	0.0480024i
$743$	1.12636	+	3.46658i	0.0413221	+	0.127176i	0.969589	−	0.244737i	$-0.0787017\pi$
$743$	1.12636	+	3.46658i	0.0413221	+	0.127176i	−0.928267	+	0.371914i	$0.878702\pi$
$744$	−5.43360	+	2.41920i	−0.199206	+	0.0886920i
$745$	34.0531	+	15.1614i	1.24761	+	0.555472i
$746$	7.21046	−	1.53263i	0.263994	−	0.0561136i
$747$	−1.01146	+	1.75190i	−0.0370074	+	0.0640988i
$748$	−4.07643	−	4.41514i	−0.149049	−	0.161434i
$749$	−27.4383	−	39.5219i	−1.00257	−	1.44410i
$750$	4.61290	−	14.1970i	0.168439	−	0.518403i
$751$	−3.45515	−	32.8735i	−0.126080	−	1.19957i	−0.856344	−	0.516406i	$-0.827269\pi$
$751$	−3.45515	−	32.8735i	−0.126080	−	1.19957i	0.730264	−	0.683166i	$-0.239397\pi$
$752$	1.12878	−	10.7396i	0.0411623	−	0.391634i
$753$	−7.59215	+	8.43194i	−0.276673	+	0.307277i
$754$	−0.0270732	−	0.00575458i	−0.000985947	−	0.000209570i
$755$	28.4894	+	20.6988i	1.03684	+	0.753306i
$756$	2.00371	−	1.72776i	0.0728741	−	0.0628380i
$757$	3.43094	−	10.5594i	0.124700	−	0.383786i	−0.869147	−	0.494555i	$-0.835331\pi$
$757$	3.43094	−	10.5594i	0.124700	−	0.383786i	0.993846	+	0.110768i	$0.0353312\pi$
$758$	1.19312	−	2.06655i	0.0433361	−	0.0750604i
$759$	−1.49988	+	1.11862i	−0.0544423	+	0.0406034i
$760$	−12.1543	−	21.0519i	−0.440883	−	0.763632i
$761$	16.1288	+	17.9128i	0.584668	+	0.649340i	0.960805	−	0.277224i	$-0.0894144\pi$
$761$	16.1288	+	17.9128i	0.584668	+	0.649340i	−0.376137	+	0.926564i	$0.622748\pi$
$762$	1.54349	−	1.12141i	0.0559147	−	0.0406244i
$763$	2.51717	+	1.52622i	0.0911278	+	0.0552529i
$764$	−2.63242	−	8.10177i	−0.0952377	−	0.293112i
$765$	6.62901	+	1.40904i	0.239672	+	0.0509440i
$766$	−1.19106	+	11.3321i	−0.0430346	+	0.409447i
$767$	12.2539	+	5.45577i	0.442461	+	0.196996i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	−16.6200			−0.599334			−0.299667	−	0.954044i	$-0.596876\pi$
$769$	−16.6200			−0.599334			−0.299667	+	0.954044i	$0.596876\pi$
$770$	−28.2766	−	16.6653i	−1.01902	−	0.600575i
$771$	6.15796			0.221774
$772$	11.2898	+	12.5386i	0.406330	+	0.451275i
$773$	−9.04374	−	4.02653i	−0.325281	−	0.144824i	0.237599	−	0.971363i	$-0.423640\pi$
$773$	−9.04374	−	4.02653i	−0.325281	−	0.144824i	−0.562879	+	0.826539i	$0.690306\pi$
$774$	−0.204732	+	1.94790i	−0.00735895	+	0.0700157i
$775$	−52.3076	−	11.1183i	−1.87894	−	0.399382i
$776$	−3.80824	−	11.7206i	−0.136708	−	0.420743i
$777$	−14.3502	+	7.87950i	−0.514811	+	0.282676i
$778$	12.7630	−	9.27289i	0.457577	−	0.332449i
$779$	−27.3487	−	30.3738i	−0.979870	−	1.08826i
$780$	−9.06414	−	15.6996i	−0.324548	−	0.562134i
$781$	−0.323630	−	0.955260i	−0.0115804	−	0.0341819i
$782$	−0.511080	+	0.885217i	−0.0182762	+	0.0316553i
$783$	−0.00176475	+	0.00543134i	−6.30670e−5	+	0.000194100i
$784$	−4.90278	+	4.99628i	−0.175099	+	0.178439i
$785$	−47.8952	−	34.7979i	−1.70945	−	1.24199i
$786$	−11.4699	−	2.43800i	−0.409117	−	0.0869606i
$787$	0.383273	−	0.425667i	0.0136622	−	0.0151734i	−0.736275	−	0.676682i	$-0.763417\pi$
$787$	0.383273	−	0.425667i	0.0136622	−	0.0151734i	0.749937	+	0.661509i	$0.230084\pi$
$788$	0.394546	−	3.75386i	0.0140551	−	0.133726i
$789$	−1.13640	−	10.8121i	−0.0404569	−	0.384922i
$790$	19.7060	−	60.6489i	0.701109	−	2.15779i
$791$	−17.8685	+	37.9219i	−0.635330	+	1.34835i
$792$	3.25251	+	0.648985i	0.115573	+	0.0230607i
$793$	−28.9960	+	50.2225i	−1.02968	+	1.78345i
$794$	−3.20186	+	0.680577i	−0.113630	+	0.0241528i
$795$	13.4197	+	5.97482i	0.475946	+	0.211905i
$796$	18.7742	−	8.35879i	0.665432	−	0.296270i
$797$	−13.0061	−	40.0286i	−0.460699	−	1.41789i	−0.864312	−	0.502956i	$-0.832246\pi$
$797$	−13.0061	−	40.0286i	−0.460699	−	1.41789i	0.403613	−	0.914930i	$-0.367754\pi$
$798$	10.4027	−	13.6905i	0.368253	−	0.484639i
$799$	15.8290	+	11.5005i	0.559990	+	0.406857i
$800$	−0.939803	−	8.94163i	−0.0332271	−	0.316134i
$801$	−5.49477	+	1.16795i	−0.194148	+	0.0412674i
$802$	12.2729	+	21.2573i	0.433371	+	0.750621i
$803$	−3.79191	+	40.9981i	−0.133814	+	1.44679i
$804$	−15.3706			−0.542078
$805$	−1.27768	+	5.43485i	−0.0450322	+	0.191553i
$806$	−23.3211	+	16.9438i	−0.821452	+	0.596820i
$807$	15.2152	−	6.77426i	0.535602	−	0.238465i
$808$	−2.10936	+	2.34268i	−0.0742070	+	0.0824152i
$809$	−37.3118	+	41.4390i	−1.31181	+	1.45692i	−0.508894	+	0.860829i	$0.669946\pi$
$809$	−37.3118	+	41.4390i	−1.31181	+	1.45692i	−0.802919	+	0.596088i	$0.796721\pi$
$810$	−3.41706	+	1.52137i	−0.120063	+	0.0534556i
$811$	−13.0010	+	9.44575i	−0.456526	+	0.331685i	−0.792167	−	0.610305i	$-0.791047\pi$
$811$	−13.0010	+	9.44575i	−0.456526	+	0.331685i	0.335641	+	0.941990i	$0.391047\pi$
$812$	0.00345782	−	0.0147085i	0.000121346	−	0.000516167i
$813$	−23.7324			−0.832332
$814$	−18.8509	−	8.11233i	−0.660724	−	0.284337i
$815$	−5.42379	−	9.39427i	−0.189987	−	0.329067i
$816$	1.77226	−	0.376704i	0.0620413	−	0.0131873i
$817$	1.33053	+	12.6591i	0.0465493	+	0.442887i
$818$	5.06428	+	3.67942i	0.177068	+	0.128648i
$819$	7.75790	−	10.2098i	0.271083	−	0.356758i
$820$	−7.26931	−	22.3726i	−0.253855	−	0.781287i
$821$	−13.1516	+	5.85548i	−0.458995	+	0.204358i	−0.623190	−	0.782070i	$-0.714164\pi$
$821$	−13.1516	+	5.85548i	−0.458995	+	0.204358i	0.164196	+	0.986428i	$0.447497\pi$
$822$	1.11634	+	0.497026i	0.0389368	+	0.0173358i
$823$	37.1783	−	7.90249i	1.29595	−	0.275463i	0.492229	−	0.870466i	$-0.336182\pi$
$823$	37.1783	−	7.90249i	1.29595	−	0.275463i	0.803724	+	0.595002i	$0.202849\pi$
$824$	−0.705301	+	1.22162i	−0.0245703	+	0.0425571i
$825$	20.2283	+	21.9091i	0.704260	+	0.762778i
$826$	−3.12116	+	6.62397i	−0.108599	+	0.230477i
$827$	7.78525	−	23.9605i	0.270720	−	0.833190i	−0.719600	−	0.694388i	$-0.755675\pi$
$827$	7.78525	−	23.9605i	0.270720	−	0.833190i	0.990320	−	0.138801i	$-0.0443250\pi$
$828$	−0.0589701	−	0.561063i	−0.00204935	−	0.0194983i
$829$	−1.66045	+	15.7981i	−0.0576697	+	0.548690i	0.927099	+	0.374818i	$0.122295\pi$
$829$	−1.66045	+	15.7981i	−0.0576697	+	0.548690i	−0.984768	+	0.173872i	$0.944372\pi$
$830$	−5.06306	+	5.62309i	−0.175741	+	0.195180i
$831$	7.63561	+	1.62300i	0.264876	+	0.0563012i
$832$	−3.92095	−	2.84874i	−0.135935	−	0.0987623i
$833$	−3.39815	−	12.2192i	−0.117739	−	0.423371i
$834$	5.15773	−	15.8739i	0.178598	−	0.549667i
$835$	8.12752	−	14.0773i	0.281264	−	0.487164i
$836$	21.5526	−	0.269256i	0.745413	−	0.00931241i
$837$	2.97391	+	5.15096i	0.102793	+	0.178043i
$838$	−1.50010	−	1.66603i	−0.0518200	−	0.0575520i
$839$	16.7717	−	12.1853i	0.579022	−	0.420684i	−0.259350	−	0.965784i	$-0.583508\pi$
$839$	16.7717	−	12.1853i	0.579022	−	0.420684i	0.838371	+	0.545100i	$0.183508\pi$
$840$	8.67461	−	4.76311i	0.299303	−	0.164343i
$841$	−8.96148	−	27.5806i	−0.309017	−	0.951055i
$842$	1.53761	+	0.326829i	0.0529895	+	0.0112633i
$843$	1.17702	−	11.1986i	0.0405389	−	0.385701i
$844$	1.20560	+	0.536768i	0.0414985	+	0.0184763i
$845$	−26.2528	−	29.1567i	−0.903124	−	1.00302i
$846$	−10.7988			−0.371269
$847$	25.1527	−	14.6404i	0.864256	−	0.503052i
$848$	3.92725			0.134862
$849$	−6.01539	−	6.68076i	−0.206448	−	0.229283i
$850$	14.8818	+	6.62579i	0.510440	+	0.227263i
$851$	−0.364890	+	3.47170i	−0.0125083	+	0.119008i
$852$	0.297457	+	0.0632263i	0.0101907	+	0.00216610i
$853$	−4.45109	−	13.6990i	−0.152402	−	0.469046i	0.845486	−	0.533997i	$-0.179311\pi$
$853$	−4.45109	−	13.6990i	−0.152402	−	0.469046i	−0.997888	+	0.0649514i	$0.979311\pi$
$854$	−27.0707	−	16.4136i	−0.926339	−	0.561661i
$855$	−19.6661	+	14.2882i	−0.672566	+	0.488648i
$856$	12.1681	+	13.5140i	0.415897	+	0.461900i
$857$	−19.0656	−	33.0226i	−0.651270	−	1.12803i	−0.982815	−	0.184593i	$-0.940903\pi$
$857$	−19.0656	−	33.0226i	−0.651270	−	1.12803i	0.331546	−	0.943439i	$-0.392430\pi$
$858$	16.0730	−	0.200799i	0.548723	−	0.00685517i
$859$	13.6972	−	23.7242i	0.467342	−	0.809460i	−0.531962	−	0.846768i	$-0.678545\pi$
$859$	13.6972	−	23.7242i	0.467342	−	0.809460i	0.999304	+	0.0373082i	$0.0118783\pi$
$860$	−2.26390	+	6.96756i	−0.0771982	+	0.237592i
$861$	12.6015	−	10.8661i	0.429459	−	0.370314i
$862$	−10.6501	−	7.73772i	−0.362742	−	0.263548i
$863$	−49.3022	−	10.4795i	−1.67827	−	0.356727i	−0.732298	−	0.680984i	$-0.761552\pi$
$863$	−49.3022	−	10.4795i	−1.67827	−	0.356727i	−0.945969	+	0.324257i	$0.894886\pi$
$864$	−0.669131	+	0.743145i	−0.0227643	+	0.0252823i
$865$	−8.96376	+	85.2845i	−0.304777	+	2.89976i
$866$	1.44858	+	13.7823i	0.0492249	+	0.468343i
$867$	4.23885	−	13.0458i	0.143959	−	0.443060i
$868$	−8.97437	−	12.9266i	−0.304610	−	0.438757i
$869$	38.3576	+	41.5448i	1.30119	+	1.40931i
$870$	−0.0106805	+	0.0184992i	−0.000362104	+	0.000627183i
$871$	−72.8666	+	15.4883i	−2.46899	+	0.524800i
$872$	−1.01643	−	0.452545i	−0.0344207	−	0.0153251i
$873$	−11.2583	+	5.01251i	−0.381035	+	0.169648i
$874$	−1.13297	−	3.48692i	−0.0383232	−	0.117947i
$875$	39.1809	+	4.97013i	1.32456	+	0.168021i
$876$	−10.0433	−	7.29686i	−0.339331	−	0.246538i
$877$	0.611793	+	5.82083i	0.0206588	+	0.196555i	0.999984	−	0.00573918i	$-0.00182685\pi$
$877$	0.611793	+	5.82083i	0.0206588	+	0.196555i	−0.979325	+	0.202295i	$0.935160\pi$
$878$	−15.5977	+	3.31540i	−0.526398	+	0.111889i
$879$	−0.702974	−	1.21759i	−0.0237107	−	0.0410682i
$880$	11.3953	+	4.90386i	0.384134	+	0.165309i
$881$	−13.2234			−0.445507			−0.222753	−	0.974875i	$-0.571504\pi$
$881$	−13.2234			−0.445507			−0.222753	+	0.974875i	$0.571504\pi$
$882$	5.48139	+	4.35366i	0.184568	+	0.146595i
$883$	−32.7135	+	23.7677i	−1.10090	+	0.799848i	−0.981206	−	0.192963i	$-0.938190\pi$
$883$	−32.7135	+	23.7677i	−1.10090	+	0.799848i	−0.119691	+	0.992811i	$0.538190\pi$
$884$	8.02206	−	3.57165i	0.269811	−	0.120128i
$885$	6.92695	−	7.69316i	0.232847	−	0.258603i
$886$	22.1177	−	24.5642i	0.743059	−	0.825250i
$887$	52.5085	−	23.3783i	1.76306	−	0.784966i	0.774800	−	0.632207i	$-0.217851\pi$
$887$	52.5085	−	23.3783i	1.76306	−	0.784966i	0.988263	−	0.152759i	$-0.0488159\pi$
$888$	5.00597	−	3.63705i	0.167989	−	0.122051i
$889$	3.67785	+	3.45729i	0.123351	+	0.115954i
$890$	−21.0120			−0.704324
$891$	0.305450	−	3.30253i	0.0102330	−	0.110639i
$892$	−11.8836	−	20.5831i	−0.397894	−	0.689172i
$893$	−68.6462	+	14.5912i	−2.29716	+	0.488276i
$894$	−1.04169	−	9.91102i	−0.0348393	−	0.331474i
$895$	11.7895	+	8.56555i	0.394079	+	0.286315i
$896$	1.60070	−	2.10660i	0.0534756	−	0.0703765i
$897$	−0.844917	−	2.60039i	−0.0282109	−	0.0868244i
$898$	−11.8587	+	5.27981i	−0.395728	+	0.176190i
$899$	0.0310305	+	0.0138157i	0.00103493	+	0.000460778i
$900$	−8.79441	+	1.86931i	−0.293147	+	0.0623103i
$901$	−3.55779	+	6.16228i	−0.118527	+	0.205295i
$902$	20.4554	+	4.08153i	0.681089	+	0.135900i
$903$	−5.16409	+	0.430971i	−0.171850	+	0.0143418i
$904$	4.89624	−	15.0691i	0.162847	−	0.501191i
$905$	4.94850	+	47.0818i	0.164494	+	1.56505i
$906$	0.984098	−	9.36307i	0.0326945	−	0.311067i
$907$	17.5252	−	19.4637i	0.581916	−	0.646283i	−0.378254	−	0.925702i	$-0.623475\pi$
$907$	17.5252	−	19.4637i	0.581916	−	0.646283i	0.960169	+	0.279419i	$0.0901419\pi$
$908$	5.82485	+	1.23811i	0.193304	+	0.0410881i
$909$	2.55033	+	1.85293i	0.0845892	+	0.0614577i
$910$	36.3238	−	31.3213i	1.20412	−	1.03829i
$911$	−4.99225	+	15.3646i	−0.165401	+	0.509051i	−0.999066	−	0.0432197i	$-0.986238\pi$
$911$	−4.99225	+	15.3646i	−0.165401	+	0.509051i	0.833665	+	0.552271i	$0.186238\pi$
$912$	−3.24943	+	5.62819i	−0.107600	+	0.186368i
$913$	−2.15283	−	6.35450i	−0.0712482	−	0.210303i
$914$	−0.250259	−	0.433461i	−0.00827782	−	0.0143376i
$915$	29.9480	+	33.2606i	0.990049	+	1.09956i
$916$	11.2986	−	8.20891i	0.373316	−	0.271230i
$917$	0.665647	−	31.0173i	0.0219816	−	1.02428i
$918$	−0.559892	−	1.72317i	−0.0184792	−	0.0568731i
$919$	6.19986	+	1.31782i	0.204515	+	0.0434709i	0.309030	−	0.951052i	$-0.399996\pi$
$919$	6.19986	+	1.31782i	0.204515	+	0.0434709i	−0.104515	+	0.994523i	$0.533329\pi$
$920$	0.220574	−	2.09862i	0.00727211	−	0.0691895i
$921$	−23.9501	−	10.6633i	−0.789181	−	0.351366i
$922$	11.8320	+	13.1408i	0.389666	+	0.432768i
$923$	1.47385			0.0485124
$924$	−0.0786659	+	8.77461i	−0.00258792	+	0.288664i
$925$	55.6330			1.82920
$926$	17.1898	+	19.0912i	0.564892	+	0.627376i
$927$	1.28865	+	0.573744i	0.0423248	+	0.0188442i
$928$	−0.000596946		0.00567957i	−1.95957e−5		0.000186441i
$929$	−8.57546	−	1.82277i	−0.281352	−	0.0598031i	0.0650744	−	0.997880i	$-0.479272\pi$
$929$	−8.57546	−	1.82277i	−0.281352	−	0.0598031i	−0.346426	+	0.938077i	$0.612605\pi$
$930$	6.87484	+	21.1586i	0.225435	+	0.693818i
$931$	40.7270	+	20.2692i	1.33477	+	0.664296i
$932$	−9.76287	+	7.09314i	−0.319793	+	0.232344i
$933$	3.16183	+	3.51157i	0.103514	+	0.114964i
$934$	17.5185	+	30.3429i	0.573221	+	0.992849i
$935$	−18.0179	+	13.4379i	−0.589249	+	0.439465i
$936$	−2.42328	+	4.19725i	−0.0792075	+	0.137191i
$937$	3.21814	−	9.90440i	0.105132	−	0.323563i	−0.884629	−	0.466295i	$-0.845589\pi$
$937$	3.21814	−	9.90440i	0.105132	−	0.323563i	0.989761	+	0.142732i	$0.0455887\pi$
$938$	−7.59968	−	39.9503i	−0.248138	−	1.30442i
$939$	−24.6144	−	17.8834i	−0.803261	−	0.583603i
$940$	−39.5095	−	8.39800i	−1.28866	−	0.273913i
$941$	−5.49906	+	6.10733i	−0.179264	+	0.199093i	−0.826080	−	0.563554i	$-0.809434\pi$
$941$	−5.49906	+	6.10733i	−0.179264	+	0.199093i	0.646815	+	0.762647i	$0.276101\pi$
$942$	−1.65442	+	15.7408i	−0.0539039	+	0.512862i
$943$	−0.370869	−	3.52858i	−0.0120772	−	0.114906i
$944$	0.855246	−	2.63218i	0.0278359	−	0.0856701i
$945$	−5.64376	−	8.12921i	−0.183592	−	0.264443i
$946$	−4.40666	−	4.77281i	−0.143273	−	0.155178i
$947$	16.9579	−	29.3719i	0.551057	−	0.954459i	−0.447141	−	0.894463i	$-0.647558\pi$
$947$	16.9579	−	29.3719i	0.551057	−	0.954459i	0.998199	−	0.0599959i	$-0.0191088\pi$
$948$	−16.6763	+	3.54465i	−0.541620	+	0.115125i
$949$	−54.9644	−	24.4717i	−1.78422	−	0.794386i
$950$	−53.3790	+	23.7659i	−1.73184	+	0.771066i
$951$	9.72644	+	29.9349i	0.315401	+	0.970706i
$952$	1.85537	+	4.42009i	0.0601327	+	0.143256i
$953$	34.6968	+	25.2087i	1.12394	+	0.816590i	0.984802	−	0.173684i	$-0.0555670\pi$
$953$	34.6968	+	25.2087i	1.12394	+	0.816590i	0.139138	+	0.990273i	$0.455567\pi$
$954$	−0.410510	−	3.90574i	−0.0132907	−	0.126453i
$955$	−31.1674	+	6.62483i	−1.00855	+	0.214375i
$956$	5.45666	+	9.45121i	0.176481	+	0.305674i
$957$	−0.00967454	−	0.0162836i	−0.000312734	−	0.000526374i
$958$	−37.3920			−1.20808
$959$	−0.739889	+	3.14727i	−0.0238923	+	0.101631i
$960$	−3.02608	+	2.19857i	−0.0976663	+	0.0709587i
$961$	3.99819	−	1.78011i	0.128974	−	0.0574229i
$962$	20.0667	−	22.2863i	0.646975	−	0.718539i
$963$	12.1681	−	13.5140i	0.392111	−	0.435484i
$964$	3.71005	−	1.65182i	0.119493	−	0.0532016i
$965$	51.0571	−	37.0952i	1.64359	−	1.19414i
$966$	1.42913	−	0.430678i	0.0459814	−	0.0138568i
$967$	26.1020			0.839384			0.419692	−	0.907667i	$-0.362138\pi$
$967$	26.1020			0.839384			0.419692	+	0.907667i	$0.362138\pi$
$968$	−8.73488	+	6.68594i	−0.280750	+	0.214894i
$969$	−5.88748	−	10.1974i	−0.189133	−	0.327588i
$970$	−45.0888	+	9.58392i	−1.44771	+	0.307721i
$971$	−1.72256	−	16.3890i	−0.0552795	−	0.525950i	−0.986763	−	0.162167i	$-0.948152\pi$
$971$	−1.72256	−	16.3890i	−0.0552795	−	0.525950i	0.931484	−	0.363783i	$-0.118515\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	43.8086	+	5.55716i	1.40444	+	0.178154i
$974$	8.60758	+	26.4914i	0.275805	+	0.848840i
$975$	−39.8077	+	17.7235i	−1.27487	+	0.567607i
$976$	10.9311	+	4.86684i	0.349896	+	0.155784i
$977$	42.6102	−	9.05709i	1.36322	−	0.289762i	0.532491	−	0.846436i	$-0.321256\pi$
$977$	42.6102	−	9.05709i	1.36322	−	0.289762i	0.830731	+	0.556674i	$0.187923\pi$
$978$	−1.45004	+	2.51154i	−0.0463672	+	0.0803103i
$979$	9.11332	−	16.2502i	0.291263	−	0.519359i
$980$	16.6690	+	20.1915i	0.532472	+	0.644995i
$981$	−0.343820	+	1.05817i	−0.0109773	+	0.0337847i
$982$	−2.18805	−	20.8179i	−0.0698236	−	0.664327i
$983$	−2.85532	+	27.1666i	−0.0910707	+	0.866480i	0.849661	+	0.527329i	$0.176806\pi$
$983$	−2.85532	+	27.1666i	−0.0910707	+	0.866480i	−0.940732	+	0.339151i	$0.889860\pi$
$984$	−4.20823	+	4.67371i	−0.134153	+	0.148992i
$985$	−13.8099	−	2.93538i	−0.440020	−	0.0935291i
$986$	−0.00837106	−	0.00608193i	−0.000266589	−	0.000193688i
$987$	−5.33924	−	28.0675i	−0.169950	−	0.893400i
$988$	−9.73317	+	29.9556i	−0.309653	+	0.953015i
$989$	−0.552483	+	0.956929i	−0.0175679	+	0.0304286i
$990$	3.68587	−	11.8454i	0.117145	−	0.376472i
$991$	−22.6366	−	39.2077i	−0.719075	−	1.24548i	−0.961367	−	0.275272i	$-0.911232\pi$
$991$	−22.6366	−	39.2077i	−0.719075	−	1.24548i	0.242291	−	0.970204i	$-0.422101\pi$
$992$	3.97987	+	4.42009i	0.126361	+	0.140338i
$993$	12.0465	−	8.75226i	0.382283	−	0.277745i
$994$	−0.0172627	+	0.804393i	−0.000547540	+	0.0255138i
$995$	−23.7539	−	73.1070i	−0.753050	−	2.31765i
$996$	1.97872	+	0.420589i	0.0626980	+	0.0133269i
$997$	−2.32053	+	22.0784i	−0.0734921	+	0.699230i	0.894298	+	0.447472i	$0.147676\pi$
$997$	−2.32053	+	22.0784i	−0.0734921	+	0.699230i	−0.967790	+	0.251759i	$0.918991\pi$
$998$	−2.83459	−	1.26204i	−0.0897275	−	0.0399493i
$999$	−4.14039	−	4.59837i	−0.130996	−	0.145486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.163.5	✓	40
7.4	even	3	inner	462.2.y.d.361.1	yes	40
11.5	even	5	inner	462.2.y.d.247.1	yes	40
77.60	even	15	inner	462.2.y.d.445.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.163.5	✓	40	1.1	even	1	trivial
462.2.y.d.247.1	yes	40	11.5	even	5	inner
462.2.y.d.361.1	yes	40	7.4	even	3	inner
462.2.y.d.445.5	yes	40	77.60	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)

\(f(q)\)	\(=\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.65870 + 0.777681i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.31914 - 1.27341i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.65870 + 0.777681i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.31914 - 1.27341i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(1.87022 + 3.23932i) q^{10} +(-3.31637 + 0.0414312i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.49767 - 4.60936i) q^{13} +(2.49814 + 0.871382i) q^{14} +(-3.02608 - 2.19857i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(1.21236 - 1.34647i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(0.679317 + 6.46327i) q^{19} +(-1.15586 + 3.55737i) q^{20} +(-2.63659 + 0.220037i) q^{21} +(-2.24987 - 2.43682i) q^{22} +(-0.282077 + 0.488571i) q^{23} +(0.978148 - 0.207912i) q^{24} +(8.21358 + 3.65692i) q^{25} +(4.42756 - 1.97128i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.02402 + 2.43955i) q^{28} +(-0.00462018 - 0.00335675i) q^{29} +(-0.390982 - 3.71995i) q^{30} +(-5.81785 + 1.23662i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.04650 + 1.31104i) q^{33} +1.81185 q^{34} +(9.47536 - 2.85547i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(5.65276 - 2.51677i) q^{37} +(-4.34859 + 4.82960i) q^{38} +(-3.24299 + 3.60170i) q^{39} +(-3.41706 + 1.52137i) q^{40} +(-5.08799 + 3.69664i) q^{41} +(-1.92774 - 1.81213i) q^{42} +1.95863 q^{43} +(0.305450 - 3.30253i) q^{44} +(1.87022 + 3.23932i) q^{45} +(-0.551826 + 0.117294i) q^{46} +(1.12878 + 10.7396i) q^{47} +(0.809017 + 0.587785i) q^{48} +(3.75685 - 5.90644i) q^{49} +(2.77834 + 8.55084i) q^{50} +(-1.65521 + 0.736945i) q^{51} +(4.42756 + 1.97128i) q^{52} +(-3.84143 + 0.816522i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-12.1658 - 2.42749i) q^{55} +(-1.12773 + 2.39337i) q^{56} +(2.00826 - 6.18079i) q^{57} +(-0.000596946 - 0.00567957i) q^{58} +(-0.289297 + 2.75247i) q^{59} +(2.50284 - 2.77969i) q^{60} +(-11.7041 - 2.48778i) q^{61} +(-4.81189 - 3.49604i) q^{62} +(2.49814 + 0.871382i) q^{63} +(0.309017 - 0.951057i) q^{64} +(9.06414 - 15.6996i) q^{65} +(1.06422 + 3.14125i) q^{66} +(-7.68529 - 13.3113i) q^{67} +(1.21236 + 1.34647i) q^{68} +(0.456410 - 0.331601i) q^{69} +(8.46228 + 5.13088i) q^{70} +(0.0939727 + 0.289218i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(1.29763 - 12.3462i) q^{73} +(5.65276 + 2.51677i) q^{74} +(-6.01608 - 6.68153i) q^{75} -6.49887 q^{76} +(-7.63837 + 4.31918i) q^{77} -4.84657 q^{78} +(-11.4079 - 12.6697i) q^{79} +(-3.41706 - 1.52137i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-6.15167 - 1.30758i) q^{82} +(0.625117 + 1.92391i) q^{83} +(0.0567662 - 2.64514i) q^{84} +(5.48280 - 3.98348i) q^{85} +(1.31058 + 1.45554i) q^{86} +(0.00285543 + 0.00494574i) q^{87} +(2.65864 - 1.98283i) q^{88} +(-2.80876 + 4.86492i) q^{89} +(-1.15586 + 3.55737i) q^{90} +(-2.39629 - 12.5969i) q^{91} +(-0.456410 - 0.331601i) q^{92} +(5.81785 + 1.23662i) q^{93} +(-7.22579 + 8.02505i) q^{94} +(-2.54094 + 24.1755i) q^{95} +(0.104528 + 0.994522i) q^{96} +(-3.80824 + 11.7206i) q^{97} +(6.90317 - 1.16030i) q^{98} +(-2.24987 - 2.43682i) 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

Introduction

L-functions

Modular forms

Varieties

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Database

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