LMFDB - Embedded newform 160.2.u.a.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	160.43
Dual form			160.2.u.a.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04802 + 0.949552i) q^{2} +(-0.255424 + 0.616647i) q^{3} +(0.196703 - 1.99030i) q^{4} +(2.08980 - 0.795458i) q^{5} +(-0.317849 - 0.888798i) q^{6} -2.27809i q^{7} +(1.68375 + 2.27266i) q^{8} +(1.80631 + 1.80631i) q^{9} +O(q^{10})$	\(q+(-1.04802 + 0.949552i) q^{2} +(-0.255424 + 0.616647i) q^{3} +(0.196703 - 1.99030i) q^{4} +(2.08980 - 0.795458i) q^{5} +(-0.317849 - 0.888798i) q^{6} -2.27809i q^{7} +(1.68375 + 2.27266i) q^{8} +(1.80631 + 1.80631i) q^{9} +(-1.43482 + 2.81803i) q^{10} +(1.88993 - 4.56270i) q^{11} +(1.17707 + 0.629667i) q^{12} +(-1.89162 + 4.56679i) q^{13} +(2.16317 + 2.38749i) q^{14} +(-0.0432662 + 1.49185i) q^{15} +(-3.92262 - 0.782996i) q^{16} +(2.36314 + 2.36314i) q^{17} +(-3.60823 - 0.177869i) q^{18} +(1.19574 + 2.88676i) q^{19} +(-1.17213 - 4.31580i) q^{20} +(1.40478 + 0.581879i) q^{21} +(2.35183 + 6.57640i) q^{22} -0.960365i q^{23} +(-1.83150 + 0.457787i) q^{24} +(3.73449 - 3.32469i) q^{25} +(-2.35393 - 6.58229i) q^{26} +(-3.42517 + 1.41875i) q^{27} +(-4.53410 - 0.448107i) q^{28} +(-3.22326 - 7.78163i) q^{29} +(-1.37124 - 1.60457i) q^{30} +1.00099i q^{31} +(4.85449 - 2.90413i) q^{32} +(2.33084 + 2.33084i) q^{33} +(-4.72056 - 0.232701i) q^{34} +(-1.81213 - 4.76075i) q^{35} +(3.95041 - 3.23980i) q^{36} +(-1.18652 - 2.86451i) q^{37} +(-3.99429 - 1.88998i) q^{38} +(-2.33293 - 2.33293i) q^{39} +(5.32650 + 3.41005i) q^{40} +(-2.94778 + 2.94778i) q^{41} +(-2.02476 + 0.724089i) q^{42} +(-11.1240 + 4.60773i) q^{43} +(-8.70941 - 4.65904i) q^{44} +(5.21166 + 2.33797i) q^{45} +(0.911916 + 1.00648i) q^{46} +(4.79379 - 4.79379i) q^{47} +(1.48476 - 2.21887i) q^{48} +1.81029 q^{49} +(-0.756867 + 7.03044i) q^{50} +(-2.06083 + 0.853624i) q^{51} +(8.71720 + 4.66321i) q^{52} +(-1.53615 - 3.70859i) q^{53} +(2.24248 - 4.73926i) q^{54} +(0.320136 - 11.0385i) q^{55} +(5.17734 - 3.83573i) q^{56} -2.08553 q^{57} +(10.7671 + 5.09467i) q^{58} +(-5.13294 + 12.3920i) q^{59} +(2.96072 + 0.379563i) q^{60} +(-8.44314 + 3.49726i) q^{61} +(-0.950495 - 1.04906i) q^{62} +(4.11494 - 4.11494i) q^{63} +(-2.32999 + 7.65318i) q^{64} +(-0.320422 + 11.0484i) q^{65} +(-4.65603 - 0.229520i) q^{66} +(-4.91872 - 2.03740i) q^{67} +(5.16821 - 4.23854i) q^{68} +(0.592206 + 0.245300i) q^{69} +(6.41973 + 3.26866i) q^{70} +(-3.12109 + 3.12109i) q^{71} +(-1.06376 + 7.14649i) q^{72} +1.46777 q^{73} +(3.96351 + 1.87541i) q^{74} +(1.09628 + 3.15207i) q^{75} +(5.98074 - 1.81204i) q^{76} +(-10.3943 - 4.30544i) q^{77} +(4.66020 + 0.229725i) q^{78} +6.00281i q^{79} +(-8.82031 + 1.48398i) q^{80} +5.18901i q^{81} +(0.290270 - 5.88840i) q^{82} +(1.06251 + 0.440104i) q^{83} +(1.43444 - 2.68148i) q^{84} +(6.81827 + 3.05871i) q^{85} +(7.28297 - 15.3919i) q^{86} +5.62182 q^{87} +(13.5517 - 3.38726i) q^{88} +(10.3561 - 10.3561i) q^{89} +(-7.68196 + 2.49849i) q^{90} +(10.4036 + 4.30930i) q^{91} +(-1.91142 - 0.188906i) q^{92} +(-0.617260 - 0.255677i) q^{93} +(-0.472048 + 9.57595i) q^{94} +(4.79514 + 5.08158i) q^{95} +(0.550873 + 3.73529i) q^{96} +(-3.18989 + 3.18989i) q^{97} +(-1.89723 + 1.71897i) q^{98} +(11.6554 - 4.82784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.04802	+	0.949552i	−0.741064	+	0.671435i
$2$	−1.04802	+	0.949552i	−0.741064	+	0.671435i
$3$	−0.255424	+	0.616647i	−0.147469	+	0.356021i	−0.980302	−	0.197502i	$-0.936717\pi$
$3$	−0.255424	+	0.616647i	−0.147469	+	0.356021i	0.832834	+	0.553523i	$0.186717\pi$
$4$	0.196703	−	1.99030i	0.0983513	−	0.995152i
$5$	2.08980	−	0.795458i	0.934585	−	0.355740i
$5$	2.08980	−	0.795458i	0.934585	−	0.355740i
$6$	−0.317849	−	0.888798i	−0.129761	−	0.362850i
$7$		−	2.27809i		−	0.861038i	−0.902581	−	0.430519i	$-0.858331\pi$
$7$		−	2.27809i		−	0.861038i	0.902581	−	0.430519i	$-0.141669\pi$
$8$	1.68375	+	2.27266i	0.595295	+	0.803508i
$9$	1.80631	+	1.80631i	0.602103	+	0.602103i
$10$	−1.43482	+	2.81803i	−0.453731	+	0.891139i
$11$	1.88993	−	4.56270i	0.569836	−	1.37571i	−0.331857	−	0.943330i	$-0.607675\pi$
$11$	1.88993	−	4.56270i	0.569836	−	1.37571i	0.901693	−	0.432377i	$-0.142325\pi$
$12$	1.17707	+	0.629667i	0.339792	+	0.181769i
$13$	−1.89162	+	4.56679i	−0.524642	+	1.26660i	0.410349	+	0.911928i	$0.365407\pi$
$13$	−1.89162	+	4.56679i	−0.524642	+	1.26660i	−0.934991	+	0.354670i	$0.884593\pi$
$14$	2.16317	+	2.38749i	0.578131	+	0.638084i
$15$	−0.0432662	+	1.49185i	−0.0111713	+	0.385193i
$16$	−3.92262	−	0.782996i	−0.980654	−	0.195749i
$17$	2.36314	+	2.36314i	0.573147	+	0.573147i	0.933006	−	0.359860i	$-0.117175\pi$
$17$	2.36314	+	2.36314i	0.573147	+	0.573147i	−0.359860	+	0.933006i	$0.617175\pi$
$18$	−3.60823	−	0.177869i	−0.850469	−	0.0419240i
$19$	1.19574	+	2.88676i	0.274321	+	0.662269i	0.999659	−	0.0261242i	$-0.00831655\pi$
$19$	1.19574	+	2.88676i	0.274321	+	0.662269i	−0.725338	+	0.688393i	$0.758317\pi$
$20$	−1.17213	−	4.31580i	−0.262097	−	0.965041i
$21$	1.40478	+	0.581879i	0.306548	+	0.126976i
$22$	2.35183	+	6.57640i	0.501412	+	1.40209i
$23$		−	0.960365i		−	0.200250i	−0.994975	−	0.100125i	$-0.968076\pi$
$23$		−	0.960365i		−	0.200250i	0.994975	−	0.100125i	$-0.0319242\pi$
$24$	−1.83150	+	0.457787i	−0.373853	+	0.0934453i
$25$	3.73449	−	3.32469i	0.746899	−	0.664938i
$26$	−2.35393	−	6.58229i	−0.461645	−	1.29089i
$27$	−3.42517	+	1.41875i	−0.659174	+	0.273039i
$28$	−4.53410	−	0.448107i	−0.856864	−	0.0846842i
$29$	−3.22326	−	7.78163i	−0.598544	−	1.44501i	−0.875065	−	0.484005i	$-0.839182\pi$
$29$	−3.22326	−	7.78163i	−0.598544	−	1.44501i	0.276522	−	0.961008i	$-0.410818\pi$
$30$	−1.37124	−	1.60457i	−0.250353	−	0.292953i
$31$			1.00099i			0.179784i	0.995952	+	0.0898919i	$0.0286521\pi$
$31$			1.00099i			0.179784i	−0.995952	+	0.0898919i	$0.971348\pi$
$32$	4.85449	−	2.90413i	0.858160	−	0.513382i
$33$	2.33084	+	2.33084i	0.405748	+	0.405748i
$34$	−4.72056	−	0.232701i	−0.809569	−	0.0399078i
$35$	−1.81213	−	4.76075i	−0.306305	−	0.804713i
$36$	3.95041	−	3.23980i	0.658401	−	0.539966i
$37$	−1.18652	−	2.86451i	−0.195063	−	0.470923i	0.795839	−	0.605508i	$-0.207030\pi$
$37$	−1.18652	−	2.86451i	−0.195063	−	0.470923i	−0.990902	+	0.134585i	$0.957030\pi$
$38$	−3.99429	−	1.88998i	−0.647959	−	0.306595i
$39$	−2.33293	−	2.33293i	−0.373568	−	0.373568i
$40$	5.32650	+	3.41005i	0.842193	+	0.539176i
$41$	−2.94778	+	2.94778i	−0.460365	+	0.460365i	−0.898775	−	0.438410i	$-0.855542\pi$
$41$	−2.94778	+	2.94778i	−0.460365	+	0.460365i	0.438410	+	0.898775i	$0.355542\pi$
$42$	−2.02476	+	0.724089i	−0.312428	+	0.111729i
$43$	−11.1240	+	4.60773i	−1.69640	+	0.702672i	−0.999889	−	0.0148739i	$-0.995265\pi$
$43$	−11.1240	+	4.60773i	−1.69640	+	0.702672i	−0.696511	+	0.717546i	$0.745265\pi$
$44$	−8.70941	−	4.65904i	−1.31299	−	0.702376i
$45$	5.21166	+	2.33797i	0.776908	+	0.348524i
$46$	0.911916	+	1.00648i	0.134455	+	0.148398i
$47$	4.79379	−	4.79379i	0.699246	−	0.699246i	−0.265002	−	0.964248i	$-0.585373\pi$
$47$	4.79379	−	4.79379i	0.699246	−	0.699246i	0.964248	+	0.265002i	$0.0853725\pi$
$48$	1.48476	−	2.21887i	0.214307	−	0.320267i
$49$	1.81029			0.258613
$50$	−0.756867	+	7.03044i	−0.107037	+	0.994255i
$51$	−2.06083	+	0.853624i	−0.288574	+	0.119531i
$52$	8.71720	+	4.66321i	1.20886	+	0.646670i
$53$	−1.53615	−	3.70859i	−0.211006	−	0.509413i	0.782572	−	0.622560i	$-0.213907\pi$
$53$	−1.53615	−	3.70859i	−0.211006	−	0.509413i	−0.993578	+	0.113146i	$0.963907\pi$
$54$	2.24248	−	4.73926i	0.305163	−	0.644932i
$55$	0.320136	−	11.0385i	0.0431671	−	1.48843i
$56$	5.17734	−	3.83573i	0.691851	−	0.512571i
$57$	−2.08553			−0.276236
$58$	10.7671	+	5.09467i	1.41379	+	0.668964i
$59$	−5.13294	+	12.3920i	−0.668251	+	1.61330i	0.116283	+	0.993216i	$0.462902\pi$
$59$	−5.13294	+	12.3920i	−0.668251	+	1.61330i	−0.784534	+	0.620086i	$0.787098\pi$
$60$	2.96072	+	0.379563i	0.382227	+	0.0490014i
$61$	−8.44314	+	3.49726i	−1.08103	+	0.447778i	−0.850871	−	0.525374i	$-0.823925\pi$
$61$	−8.44314	+	3.49726i	−1.08103	+	0.447778i	−0.230161	+	0.973152i	$0.573925\pi$
$62$	−0.950495	−	1.04906i	−0.120713	−	0.133231i
$63$	4.11494	−	4.11494i	0.518433	−	0.518433i
$64$	−2.32999	+	7.65318i	−0.291249	+	0.956647i
$65$	−0.320422	+	11.0484i	−0.0397435	+	1.37038i
$66$	−4.65603	−	0.229520i	−0.573118	−	0.0282520i
$67$	−4.91872	−	2.03740i	−0.600917	−	0.248908i	0.0614226	−	0.998112i	$-0.480436\pi$
$67$	−4.91872	−	2.03740i	−0.600917	−	0.248908i	−0.662339	+	0.749204i	$0.730436\pi$
$68$	5.16821	−	4.23854i	0.626738	−	0.513998i
$69$	0.592206	+	0.245300i	0.0712932	+	0.0295306i
$70$	6.41973	+	3.26866i	0.767304	+	0.390680i
$71$	−3.12109	+	3.12109i	−0.370405	+	0.370405i	−0.867625	−	0.497220i	$-0.834354\pi$
$71$	−3.12109	+	3.12109i	−0.370405	+	0.370405i	0.497220	+	0.867625i	$0.334354\pi$
$72$	−1.06376	+	7.14649i	−0.125366	+	0.842222i
$73$	1.46777			0.171789			0.0858947	−	0.996304i	$-0.472625\pi$
$73$	1.46777			0.171789			0.0858947	+	0.996304i	$0.472625\pi$
$74$	3.96351	+	1.87541i	0.460748	+	0.218012i
$75$	1.09628	+	3.15207i	0.126588	+	0.363970i
$76$	5.98074	−	1.81204i	0.686038	−	0.207856i
$77$	−10.3943	−	4.30544i	−1.18454	−	0.490651i
$78$	4.66020	+	0.229725i	0.527664	+	0.0260113i
$79$			6.00281i			0.675369i	0.941259	+	0.337685i	$0.109644\pi$
$79$			6.00281i			0.675369i	−0.941259	+	0.337685i	$0.890356\pi$
$80$	−8.82031	+	1.48398i	−0.986140	+	0.165913i
$81$			5.18901i			0.576557i
$82$	0.290270	−	5.88840i	0.0320549	−	0.650265i
$83$	1.06251	+	0.440104i	0.116625	+	0.0483077i	0.440233	−	0.897884i	$-0.354896\pi$
$83$	1.06251	+	0.440104i	0.116625	+	0.0483077i	−0.323608	+	0.946191i	$0.604896\pi$
$84$	1.43444	−	2.68148i	0.156510	−	0.292574i
$85$	6.81827	+	3.05871i	0.739546	+	0.331763i
$86$	7.28297	−	15.3919i	0.785343	−	1.65975i
$87$	5.62182			0.602722
$88$	13.5517	−	3.38726i	1.44461	−	0.361083i
$89$	10.3561	−	10.3561i	1.09775	−	1.09775i	0.103074	−	0.994674i	$-0.467132\pi$
$89$	10.3561	−	10.3561i	1.09775	−	1.09775i	0.994674	−	0.103074i	$-0.0328679\pi$
$90$	−7.68196	+	2.49849i	−0.809750	+	0.263364i
$91$	10.4036	+	4.30930i	1.09059	+	0.451737i
$92$	−1.91142	−	0.188906i	−0.199279	−	0.0196948i
$93$	−0.617260	−	0.255677i	−0.0640069	−	0.0265125i
$94$	−0.472048	+	9.57595i	−0.0486881	+	0.987684i
$95$	4.79514	+	5.08158i	0.491971	+	0.521360i
$96$	0.550873	+	3.73529i	0.0562233	+	0.381231i
$97$	−3.18989	+	3.18989i	−0.323884	+	0.323884i	−0.850255	−	0.526371i	$-0.823552\pi$
$97$	−3.18989	+	3.18989i	−0.323884	+	0.323884i	0.526371	+	0.850255i	$0.323552\pi$
$98$	−1.89723	+	1.71897i	−0.191649	+	0.173642i
$99$	11.6554	−	4.82784i	1.17142	−	0.485217i
$100$	−5.88256	−	8.08675i	−0.588256	−	0.808675i
$101$	2.65231	−	6.40325i	0.263915	−	0.637147i	−0.735259	−	0.677786i	$-0.762939\pi$
$101$	2.65231	−	6.40325i	0.263915	−	0.637147i	0.999174	+	0.0406391i	$0.0129394\pi$
$102$	1.34924	−	2.85148i	0.133594	−	0.282339i
$103$	−12.6802			−1.24942			−0.624709	−	0.780857i	$-0.714782\pi$
$103$	−12.6802			−1.24942			−0.624709	+	0.780857i	$0.714782\pi$
$104$	−13.5638	+	3.39029i	−1.33004	+	0.332445i
$105$	3.39856	+	0.0985644i	0.331666	+	0.00961890i
$106$	5.13141	+	2.42803i	0.498407	+	0.235831i
$107$	−0.241029	−	0.581894i	−0.0233011	−	0.0562538i	0.911801	−	0.410633i	$-0.134692\pi$
$107$	−0.241029	−	0.581894i	−0.0233011	−	0.0562538i	−0.935102	+	0.354379i	$0.884692\pi$
$108$	2.15001	+	7.09620i	0.206885	+	0.682832i
$109$	−10.7032	+	4.43342i	−1.02518	+	0.424645i	−0.830972	−	0.556315i	$-0.812215\pi$
$109$	−10.7032	+	4.43342i	−1.02518	+	0.424645i	−0.194212	+	0.980960i	$0.562215\pi$
$110$	10.1461	+	11.8726i	0.967392	+	1.13200i
$111$	2.06946			0.196424
$112$	−1.78374	+	8.93608i	−0.168547	+	0.844380i
$113$	−4.74099	+	4.74099i	−0.445995	+	0.445995i	−0.894021	−	0.448026i	$-0.852127\pi$
$113$	−4.74099	+	4.74099i	−0.445995	+	0.445995i	0.448026	+	0.894021i	$0.352127\pi$
$114$	2.18569	−	1.98032i	0.204708	−	0.185474i
$115$	−0.763930	−	2.00697i	−0.0712368	−	0.187151i
$116$	−16.1218	+	4.88459i	−1.49687	+	0.453523i
$117$	−11.6659	+	4.83216i	−1.07851	+	0.446734i
$118$	−6.38742	−	17.8611i	−0.588009	−	1.64425i
$119$	5.38346	−	5.38346i	0.493501	−	0.493501i
$120$	−3.46331	+	2.41356i	−0.316156	+	0.220327i
$121$	−9.46823	−	9.46823i	−0.860748	−	0.860748i
$122$	5.52777	−	11.6824i	0.500460	−	1.05768i
$123$	−1.06481	−	2.57067i	−0.0960103	−	0.231789i
$124$	1.99228	+	0.196898i	0.178912	+	0.0176820i
$125$	5.15967	−	9.91856i	0.461495	−	0.887143i
$126$	−0.405201	+	8.21989i	−0.0360982	+	0.732286i
$127$	−4.34395	−	4.34395i	−0.385463	−	0.385463i	0.487603	−	0.873066i	$-0.337871\pi$
$127$	−4.34395	−	4.34395i	−0.385463	−	0.385463i	−0.873066	+	0.487603i	$0.837871\pi$
$128$	−4.82521	−	10.2331i	−0.426492	−	0.904491i
$129$		−	8.03653i		−	0.707577i
$130$	−10.1552	−	11.8832i	−0.890668	−	1.04222i
$131$	2.47746	+	5.98112i	0.216457	+	0.522573i	0.994390	−	0.105774i	$-0.0337320\pi$
$131$	2.47746	+	5.98112i	0.216457	+	0.522573i	−0.777933	+	0.628347i	$0.783732\pi$
$132$	5.09757	−	4.18060i	0.443687	−	0.363875i
$133$	6.57631	−	2.72400i	0.570238	−	0.236201i
$134$	7.08954	−	2.53534i	0.612443	−	0.219020i
$135$	−6.02935	+	5.68948i	−0.518924	+	0.489673i
$136$	−1.39169	+	9.34957i	−0.119337	+	0.801719i
$137$		−	0.682679i		−	0.0583252i	−0.999575	−	0.0291626i	$-0.990716\pi$
$137$		−	0.682679i		−	0.0583252i	0.999575	−	0.0291626i	$-0.00928405\pi$
$138$	−0.853570	+	0.305251i	−0.0726607	+	0.0259847i
$139$	−2.25525	−	0.934155i	−0.191288	−	0.0792340i	0.284983	−	0.958532i	$-0.408012\pi$
$139$	−2.25525	−	0.934155i	−0.191288	−	0.0792340i	−0.476271	+	0.879298i	$0.658012\pi$
$140$	−9.83178	+	2.67023i	−0.830937	+	0.225676i
$141$	1.73163	+	4.18053i	0.145830	+	0.352064i
$142$	0.307336	−	6.23461i	0.0257911	−	0.523197i
$143$	17.2618	+	17.2618i	1.44351	+	1.44351i
$144$	−5.67112	−	8.49978i	−0.472593	−	0.708315i
$145$	−12.9259	−	13.6981i	−1.07344	−	1.13756i
$146$	−1.53825	+	1.39372i	−0.127307	+	0.115345i
$147$	−0.462392	+	1.11631i	−0.0381374	+	0.0920719i
$148$	−5.93464	+	1.79808i	−0.487825	+	0.147801i
$149$	−0.223427	+	0.539401i	−0.0183039	+	0.0441895i	−0.932767	−	0.360479i	$-0.882613\pi$
$149$	−0.223427	+	0.539401i	−0.0183039	+	0.0441895i	0.914463	+	0.404669i	$0.132613\pi$
$150$	−4.14198	−	2.26246i	−0.338191	−	0.184729i
$151$	8.93114	+	8.93114i	0.726806	+	0.726806i	0.969982	−	0.243176i	$-0.0781893\pi$
$151$	8.93114	+	8.93114i	0.726806	+	0.726806i	−0.243176	+	0.969982i	$0.578189\pi$
$152$	−4.54732	+	7.57808i	−0.368836	+	0.614664i
$153$			8.53713i			0.690186i
$154$	14.9817	−	5.35769i	1.20726	−	0.431735i
$155$	0.796248	+	2.09187i	0.0639562	+	0.168023i
$156$	−5.10213	+	4.18435i	−0.408498	+	0.335016i
$157$	3.18422	−	7.68739i	0.254129	−	0.613521i	−0.744401	−	0.667733i	$-0.767265\pi$
$157$	3.18422	−	7.68739i	0.254129	−	0.613521i	0.998529	+	0.0542124i	$0.0172648\pi$
$158$	−5.69998	−	6.29109i	−0.453466	−	0.500492i
$159$	2.67926			0.212479
$160$	7.83477	−	9.93058i	0.619393	−	0.785081i
$161$	−2.18780			−0.172423
$162$	−4.92723	−	5.43820i	−0.387120	−	0.427265i
$163$	7.69915	−	18.5874i	0.603044	−	1.45588i	−0.267388	−	0.963589i	$-0.586160\pi$
$163$	7.69915	−	18.5874i	0.603044	−	1.45588i	0.870432	−	0.492289i	$-0.163840\pi$
$164$	5.28713	+	6.44680i	0.412856	+	0.503411i
$165$	6.72508	+	3.01690i	0.523547	+	0.234865i
$166$	−1.53143	+	0.547665i	−0.118862	+	0.0425071i
$167$		−	9.37503i		−	0.725462i	−0.931894	−	0.362731i	$-0.881844\pi$
$167$		−	9.37503i		−	0.725462i	0.931894	−	0.362731i	$-0.118156\pi$
$168$	1.04288	+	4.17233i	0.0804599	+	0.321902i
$169$	−8.08490	−	8.08490i	−0.621916	−	0.621916i
$170$	−10.0501	+	3.26871i	−0.770808	+	0.250699i
$171$	−3.05451	+	7.37425i	−0.233584	+	0.563923i
$172$	6.98265	+	23.0466i	0.532422	+	1.75728i
$173$	5.71570	−	13.7989i	0.434557	−	1.04911i	−0.543244	−	0.839575i	$-0.682804\pi$
$173$	5.71570	−	13.7989i	0.434557	−	1.04911i	0.977801	−	0.209538i	$-0.0671959\pi$
$174$	−5.89179	+	5.33821i	−0.446655	+	0.404688i
$175$	−7.57395	−	8.50752i	−0.572537	−	0.643108i
$176$	−10.9861	+	16.4179i	−0.828105	+	1.23755i
$177$	−6.33042	−	6.33042i	−0.475824	−	0.475824i
$178$	−1.01978	+	20.6871i	−0.0764355	+	1.55057i
$179$	5.14746	+	12.4271i	0.384740	+	0.928844i	0.991035	+	0.133604i	$0.0426550\pi$
$179$	5.14746	+	12.4271i	0.384740	+	0.928844i	−0.606295	+	0.795240i	$0.707345\pi$
$180$	5.67842	−	9.91289i	0.423244	−	0.738863i
$181$	5.27429	+	2.18468i	0.392035	+	0.162386i	0.569988	−	0.821653i	$-0.306948\pi$
$181$	5.27429	+	2.18468i	0.392035	+	0.162386i	−0.177954	+	0.984039i	$0.556948\pi$
$182$	−14.9951	+	5.36248i	−1.11151	+	0.397494i
$183$		−	6.09972i		−	0.450904i
$184$	2.18258	−	1.61701i	0.160902	−	0.119208i
$185$	−4.75819	−	5.04242i	−0.349829	−	0.370726i
$186$	0.889681	−	0.318164i	0.0652346	−	0.0233290i
$187$	15.2485	−	6.31614i	1.11508	−	0.461882i
$188$	−8.59815	−	10.4840i	−0.627084	−	0.764628i
$189$	3.23205	+	7.80286i	0.235097	+	0.567574i
$190$	−9.85065	−	0.772380i	−0.714641	−	0.0560343i
$191$			2.54394i			0.184073i	0.995756	+	0.0920364i	$0.0293376\pi$
$191$			2.54394i			0.184073i	−0.995756	+	0.0920364i	$0.970662\pi$
$192$	−4.12418	−	3.39158i	−0.297637	−	0.244767i
$193$	14.1226	+	14.1226i	1.01656	+	1.01656i	0.999860	+	0.0167029i	$0.00531695\pi$
$193$	14.1226	+	14.1226i	1.01656	+	1.01656i	0.0167029	+	0.999860i	$0.494683\pi$
$194$	0.314111	−	6.37204i	0.0225518	−	0.457486i
$195$	−6.73110	−	3.01960i	−0.482024	−	0.216238i
$196$	0.356090	−	3.60303i	0.0254350	−	0.257360i
$197$	8.53228	+	20.5988i	0.607900	+	1.46760i	0.865279	+	0.501290i	$0.167141\pi$
$197$	8.53228	+	20.5988i	0.607900	+	1.46760i	−0.257379	+	0.966310i	$0.582859\pi$
$198$	−7.63088	+	16.1271i	−0.542303	+	1.14611i
$199$	0.173744	+	0.173744i	0.0123164	+	0.0123164i	0.713238	−	0.700922i	$-0.247228\pi$
$199$	0.173744	+	0.173744i	0.0123164	+	0.0123164i	−0.700922	+	0.713238i	$0.747228\pi$
$200$	13.8438	+	2.88930i	0.978907	+	0.204305i
$201$	2.51271	−	2.51271i	0.177233	−	0.177233i
$202$	3.30053	+	9.22926i	0.232225	+	0.649369i
$203$	−17.7273	+	7.34288i	−1.24421	+	0.515369i
$204$	1.29360	+	4.26959i	0.0905701	+	0.298931i
$205$	−3.81542	+	8.50508i	−0.266480	+	0.594021i
$206$	13.2891	−	12.0405i	0.925899	−	0.838903i
$207$	1.73471	−	1.73471i	0.120571	−	0.120571i
$208$	10.9959	−	16.4326i	0.762428	−	1.13940i
$209$	15.4313			1.06741
$210$	−3.65536	+	3.12381i	−0.252244	+	0.215564i
$211$	19.8558	−	8.22454i	1.36693	−	0.566201i	0.425975	−	0.904735i	$-0.359931\pi$
$211$	19.8558	−	8.22454i	1.36693	−	0.566201i	0.940954	+	0.338534i	$0.109931\pi$
$212$	−7.68337	+	2.32791i	−0.527696	+	0.159881i
$213$	−1.12741	−	2.72181i	−0.0772490	−	0.186495i
$214$	0.805142	+	0.380969i	0.0550384	+	0.0260425i
$215$	−19.5817	+	18.4779i	−1.33546	+	1.26018i
$216$	−8.99147	−	5.39544i	−0.611792	−	0.367113i
$217$	2.28036			0.154801
$218$	7.00746	−	14.8096i	0.474605	−	1.00303i
$219$	−0.374903	+	0.905095i	−0.0253336	+	0.0611607i
$220$	−21.9070	−	2.80847i	−1.47697	−	0.189347i
$221$	−15.2622	+	6.32179i	−1.02664	+	0.425250i
$222$	−2.16884	+	1.96506i	−0.145563	+	0.131886i
$223$	7.39024	−	7.39024i	0.494887	−	0.494887i	−0.414955	−	0.909842i	$-0.636203\pi$
$223$	7.39024	−	7.39024i	0.494887	−	0.494887i	0.909842	+	0.414955i	$0.136203\pi$
$224$	−6.61588	−	11.0590i	−0.442042	−	0.738908i
$225$	12.7511	+	0.740229i	0.850070	+	0.0493486i
$226$	0.466849	−	9.47048i	0.0310543	−	0.629967i
$227$	22.6823	+	9.39530i	1.50548	+	0.623588i	0.974618	−	0.223873i	$-0.0718702\pi$
$227$	22.6823	+	9.39530i	1.50548	+	0.623588i	0.530857	+	0.847462i	$0.321870\pi$
$228$	−0.410230	+	4.15084i	−0.0271681	+	0.274896i
$229$	−7.52580	−	3.11729i	−0.497319	−	0.205996i	0.119903	−	0.992786i	$-0.461742\pi$
$229$	−7.52580	−	3.11729i	−0.497319	−	0.205996i	−0.617221	+	0.786790i	$0.711742\pi$
$230$	2.70633	+	1.37795i	0.178450	+	0.0908596i
$231$	5.30988	−	5.30988i	0.349364	−	0.349364i
$232$	12.2579	−	20.4277i	0.804768	−	1.34114i
$233$	−6.74680			−0.441998			−0.220999	−	0.975274i	$-0.570932\pi$
$233$	−6.74680			−0.441998			−0.220999	+	0.975274i	$0.570932\pi$
$234$	7.63771	−	16.1416i	0.499293	−	1.05521i
$235$	6.20478	−	13.8313i	0.404755	−	0.902255i
$236$	23.6542	+	12.6536i	1.53976	+	0.823682i
$237$	−3.70162	−	1.53326i	−0.240446	−	0.0995960i
$238$	−0.530114	+	10.7539i	−0.0343622	+	0.697070i
$239$			17.7334i			1.14708i	0.819179	+	0.573538i	$0.194430\pi$
$239$			17.7334i			1.14708i	−0.819179	+	0.573538i	$0.805570\pi$
$240$	1.33783	−	5.81806i	0.0863563	−	0.375554i
$241$			9.35989i			0.602923i	0.953478	+	0.301462i	$0.0974745\pi$
$241$			9.35989i			0.602923i	−0.953478	+	0.301462i	$0.902525\pi$
$242$	18.9135	+	0.932344i	1.21581	+	0.0599333i
$243$	−13.4753	−	5.58165i	−0.864441	−	0.358063i
$244$	5.29982	+	17.4923i	0.339286	+	1.11983i
$245$	3.78314	−	1.44001i	0.241696	−	0.0919991i
$246$	3.55692	+	1.68303i	0.226781	+	0.107306i
$247$	−15.4451			−0.982749
$248$	−2.27492	+	1.68542i	−0.144458	+	0.107024i
$249$	−0.542778	+	0.542778i	−0.0343972	+	0.0343972i
$250$	4.01073	+	15.2942i	0.253661	+	0.967293i
$251$	−15.7927	−	6.54153i	−0.996824	−	0.412898i	−0.176192	−	0.984356i	$-0.556378\pi$
$251$	−15.7927	−	6.54153i	−0.996824	−	0.412898i	−0.820632	+	0.571458i	$0.806378\pi$
$252$	−7.38055	−	8.99939i	−0.464931	−	0.566908i
$253$	−4.38186	−	1.81502i	−0.275485	−	0.114110i
$254$	8.67735	+	0.427752i	0.544466	+	0.0268395i
$255$	−3.62769	+	3.42320i	−0.227175	+	0.214369i
$256$	14.7738	+	6.14279i	0.923365	+	0.383924i
$257$	5.71494	−	5.71494i	0.356488	−	0.356488i	−0.506029	−	0.862517i	$-0.668887\pi$
$257$	5.71494	−	5.71494i	0.356488	−	0.356488i	0.862517	+	0.506029i	$0.168887\pi$
$258$	7.63110	+	8.42247i	0.475092	+	0.524360i
$259$	−6.52563	+	2.70300i	−0.405483	+	0.167956i
$260$	21.9266	+	2.81098i	1.35983	+	0.174330i
$261$	8.23382	−	19.8782i	0.509661	−	1.23043i
$262$	−8.27582	−	3.91587i	−0.511282	−	0.241923i
$263$	20.6036			1.27047			0.635237	−	0.772317i	$-0.280902\pi$
$263$	20.6036			1.27047			0.635237	+	0.772317i	$0.280902\pi$
$264$	−1.37267	+	9.22177i	−0.0844819	+	0.567561i
$265$	−6.16026	−	6.52825i	−0.378422	−	0.401027i
$266$	−4.30555	+	9.09936i	−0.263990	+	0.557917i
$267$	3.74088	+	9.03128i	0.228938	+	0.552705i
$268$	−5.02257	+	9.38897i	−0.306802	+	0.573523i
$269$	18.6076	−	7.70753i	1.13453	−	0.469936i	0.265209	−	0.964191i	$-0.414559\pi$
$269$	18.6076	−	7.70753i	1.13453	−	0.469936i	0.869317	+	0.494255i	$0.164559\pi$
$270$	0.916436	−	11.6879i	0.0557725	−	0.711302i
$271$	−27.7230			−1.68405			−0.842026	−	0.539437i	$-0.818637\pi$
$271$	−27.7230			−1.68405			−0.842026	+	0.539437i	$0.818637\pi$
$272$	−7.41938	−	11.1200i	−0.449866	−	0.674252i
$273$	−5.31463	+	5.31463i	−0.321656	+	0.321656i
$274$	0.648239	+	0.715463i	0.0391615	+	0.0432227i
$275$	−8.11163	−	23.3228i	−0.489150	−	1.40642i
$276$	0.604710	−	1.13042i	0.0363992	−	0.0680432i
$277$	−5.58777	+	2.31453i	−0.335737	+	0.139067i	−0.544182	−	0.838967i	$-0.683160\pi$
$277$	−5.58777	+	2.31453i	−0.335737	+	0.139067i	0.208445	+	0.978034i	$0.433160\pi$
$278$	3.25058	−	1.16246i	0.194957	−	0.0697198i
$279$	−1.80810	+	1.80810i	−0.108248	+	0.108248i
$280$	7.76841	−	12.1343i	0.464251	−	0.725160i
$281$	−13.6672	−	13.6672i	−0.815320	−	0.815320i	0.170106	−	0.985426i	$-0.445589\pi$
$281$	−13.6672	−	13.6672i	−0.815320	−	0.815320i	−0.985426	+	0.170106i	$0.945589\pi$
$282$	−5.78441	−	2.73701i	−0.344457	−	0.162987i
$283$	−4.69581	−	11.3367i	−0.279137	−	0.673896i	0.720676	−	0.693272i	$-0.243832\pi$
$283$	−4.69581	−	11.3367i	−0.279137	−	0.673896i	−0.999812	+	0.0193769i	$0.993832\pi$
$284$	5.59799	+	6.82584i	0.332180	+	0.405039i
$285$	−4.35834	+	1.65895i	−0.258166	+	0.0982680i
$286$	−34.4818	−	1.69979i	−2.03895	−	0.100510i
$287$	6.71531	+	6.71531i	0.396392	+	0.396392i
$288$	14.0144	+	3.52294i	0.825809	+	0.207591i
$289$		−	5.83109i		−	0.343005i
$290$	26.5537	+	2.08205i	1.55928	+	0.122262i
$291$	−1.15226	−	2.78181i	−0.0675469	−	0.163073i
$292$	0.288714	−	2.92130i	0.0168957	−	0.170956i
$293$	2.01210	−	0.833437i	0.117548	−	0.0486899i	−0.323134	−	0.946353i	$-0.604737\pi$
$293$	2.01210	−	0.833437i	0.117548	−	0.0486899i	0.440682	+	0.897663i	$0.354737\pi$
$294$	−0.575400	−	1.60899i	−0.0335580	−	0.0938380i
$295$	−0.869467	+	29.9798i	−0.0506224	+	1.74549i
$296$	4.51227	−	7.51968i	0.262271	−	0.437073i
$297$			18.3094i			1.06242i
$298$	−0.278033	−	0.777460i	−0.0161060	−	0.0450371i
$299$	4.38578	+	1.81665i	0.253636	+	0.105060i
$300$	6.48922	−	1.56192i	0.374655	−	0.0901773i
$301$	10.4968	+	25.3416i	0.605027	+	1.46067i
$302$	−17.8406	−	0.879456i	−1.02661	−	0.0506070i
$303$	3.27108	+	3.27108i	0.187919	+	0.187919i
$304$	−2.43009	−	12.2599i	−0.139375	−	0.703154i
$305$	−14.8625	+	14.0247i	−0.851025	+	0.803053i
$306$	−8.10645	−	8.94711i	−0.463415	−	0.511472i
$307$	−3.80970	+	9.19743i	−0.217431	+	0.524925i	−0.994530	−	0.104454i	$-0.966691\pi$
$307$	−3.80970	+	9.19743i	−0.217431	+	0.524925i	0.777099	+	0.629379i	$0.216691\pi$
$308$	−10.6137	+	19.8408i	−0.604773	+	1.13054i
$309$	3.23883	−	7.81922i	0.184250	−	0.444820i
$310$	−2.82083	−	1.43625i	−0.160212	−	0.0815735i
$311$	3.02827	+	3.02827i	0.171718	+	0.171718i	0.787734	−	0.616016i	$-0.211254\pi$
$311$	3.02827	+	3.02827i	0.171718	+	0.171718i	−0.616016	+	0.787734i	$0.711254\pi$
$312$	1.37390	−	9.23003i	0.0777816	−	0.522548i
$313$			13.6180i			0.769733i	0.922972	+	0.384867i	$0.125753\pi$
$313$			13.6180i			0.769733i	−0.922972	+	0.384867i	$0.874247\pi$
$314$	3.96244	+	11.0801i	0.223613	+	0.625289i
$315$	5.32612	−	11.8726i	0.300093	−	0.668947i
$316$	11.9474	+	1.18077i	0.672095	+	0.0664235i
$317$	−4.13899	+	9.99242i	−0.232469	+	0.561230i	−0.996467	−	0.0839890i	$-0.973234\pi$
$317$	−4.13899	+	9.99242i	−0.232469	+	0.561230i	0.763998	+	0.645219i	$0.223234\pi$
$318$	−2.80792	+	2.54409i	−0.157460	+	0.142666i
$319$	−41.5970			−2.32898
$320$	1.21858	+	17.8470i	0.0681209	+	0.997677i
$321$	0.420388			0.0234638
$322$	2.29286	−	2.07743i	0.127776	−	0.115771i
$323$	−3.99614	+	9.64753i	−0.222351	+	0.536803i
$324$	10.3277	+	1.02069i	0.573761	+	0.0567051i
$325$	8.11889	+	23.3437i	0.450355	+	1.29488i
$326$	9.58081	+	26.7908i	0.530632	+	1.48380i
$327$		−	7.73252i		−	0.427609i
$328$	−11.6626	−	1.73599i	−0.643960	−	0.0958540i
$329$	−10.9207	−	10.9207i	−0.602078	−	0.602078i
$330$	−9.91274	+	3.22403i	−0.545678	+	0.177477i
$331$	12.2766	−	29.6382i	0.674780	−	1.62906i	−0.0986041	−	0.995127i	$-0.531438\pi$
$331$	12.2766	−	29.6382i	0.674780	−	1.62906i	0.773385	−	0.633937i	$-0.218562\pi$
$332$	1.08494	−	2.02814i	0.0595438	−	0.111309i
$333$	3.03097	−	7.31742i	0.166096	−	0.400992i
$334$	8.90208	+	9.82525i	0.487100	+	0.537614i
$335$	−11.8998	−	0.345115i	−0.650154	−	0.0188556i
$336$	−5.05480	−	3.38242i	−0.275762	−	0.184526i
$337$	3.92703	+	3.92703i	0.213919	+	0.213919i	0.805930	−	0.592011i	$-0.201666\pi$
$337$	3.92703	+	3.92703i	0.213919	+	0.213919i	−0.592011	+	0.805930i	$0.701666\pi$
$338$	16.1502	+	0.796127i	0.878455	+	0.0433036i
$339$	−1.71256	−	4.13448i	−0.0930133	−	0.224554i
$340$	7.42893	−	12.9688i	0.402890	−	0.703331i
$341$	4.56723	+	1.89181i	0.247330	+	0.102447i
$342$	−3.80103	−	10.6288i	−0.205536	−	0.574739i
$343$		−	20.0707i		−	1.08371i
$344$	−29.2019	−	17.5229i	−1.57446	−	0.944774i
$345$	1.43272	+	0.0415513i	0.0771348	+	0.00223705i
$346$	7.11261	+	19.8889i	0.382376	+	1.06924i
$347$	−9.78416	+	4.05273i	−0.525241	+	0.217562i	−0.629517	−	0.776986i	$-0.716747\pi$
$347$	−9.78416	+	4.05273i	−0.525241	+	0.217562i	0.104276	+	0.994548i	$0.466747\pi$
$348$	1.10583	−	11.1891i	0.0592785	−	0.599800i
$349$	12.2025	+	29.4593i	0.653183	+	1.57692i	0.808133	+	0.589000i	$0.200478\pi$
$349$	12.2025	+	29.4593i	0.653183	+	1.57692i	−0.154950	+	0.987922i	$0.549522\pi$
$350$	16.0160	+	1.72421i	0.856091	+	0.0921631i
$351$		−	18.3258i		−	0.978157i
$352$	−4.07603	−	27.6382i	−0.217253	−	1.47312i
$353$	−23.2076	−	23.2076i	−1.23522	−	1.23522i	−0.961934	−	0.273281i	$-0.911891\pi$
$353$	−23.2076	−	23.2076i	−1.23522	−	1.23522i	−0.273281	−	0.961934i	$-0.588109\pi$
$354$	12.6455	+	0.623362i	0.672100	+	0.0331313i
$355$	−4.03974	+	9.00514i	−0.214407	+	0.477943i
$356$	−18.5748	−	22.6489i	−0.984461	−	1.20039i
$357$	1.94463	+	4.69476i	0.102921	+	0.248473i
$358$	−17.1948	−	8.13608i	−0.908774	−	0.430005i
$359$	−24.0361	−	24.0361i	−1.26858	−	1.26858i	−0.946823	−	0.321755i	$-0.895727\pi$
$359$	−24.0361	−	24.0361i	−1.26858	−	1.26858i	−0.321755	−	0.946823i	$-0.604273\pi$
$360$	3.46169	+	15.7809i	0.182447	+	0.831726i
$361$	6.53142	−	6.53142i	0.343759	−	0.343759i
$362$	−7.60204	+	2.71861i	−0.399554	+	0.142887i
$363$	8.25697	−	3.42015i	0.433378	−	0.179511i
$364$	10.6232	−	19.8586i	0.556808	−	1.04087i
$365$	3.06734	−	1.16755i	0.160552	−	0.0611123i
$366$	5.79200	+	6.39264i	0.302753	+	0.334149i
$367$	15.3156	−	15.3156i	0.799468	−	0.799468i	−0.183543	−	0.983012i	$-0.558757\pi$
$367$	15.3156	−	15.3156i	0.799468	−	0.799468i	0.983012	+	0.183543i	$0.0587568\pi$
$368$	−0.751962	+	3.76714i	−0.0391987	+	0.196376i
$369$	−10.6492			−0.554374
$370$	9.77473	+	0.766427i	0.508164	+	0.0398447i
$371$	−8.44850	+	3.49948i	−0.438624	+	0.181684i
$372$	−0.630292	+	1.17824i	−0.0326791	+	0.0610890i
$373$	−4.62057	−	11.1550i	−0.239244	−	0.577586i	0.757961	−	0.652300i	$-0.226196\pi$
$373$	−4.62057	−	11.1550i	−0.239244	−	0.577586i	−0.997205	+	0.0747137i	$0.976196\pi$
$374$	−9.98328	+	21.0987i	−0.516223	+	1.09099i
$375$	4.79835	+	5.71513i	0.247786	+	0.295128i
$376$	18.9662	+	2.82313i	0.978107	+	0.145592i
$377$	41.6342			2.14427
$378$	−10.7965	−	5.10857i	−0.555311	−	0.262757i
$379$	2.64869	−	6.39451i	0.136054	−	0.328464i	−0.841138	−	0.540821i	$-0.818114\pi$
$379$	2.64869	−	6.39451i	0.136054	−	0.328464i	0.977192	+	0.212357i	$0.0681138\pi$
$380$	11.0571	−	8.54423i	0.567218	−	0.438310i
$381$	3.78823	−	1.56914i	0.194077	−	0.0803892i
$382$	−2.41560	−	2.66610i	−0.123593	−	0.136410i
$383$	−9.00758	+	9.00758i	−0.460266	+	0.460266i	−0.898742	−	0.438477i	$-0.855518\pi$
$383$	−9.00758	+	9.00758i	−0.460266	+	0.460266i	0.438477	+	0.898742i	$0.355518\pi$
$384$	7.54272	−	0.361664i	0.384913	−	0.0184561i
$385$	−25.1467	−	0.729298i	−1.28159	−	0.0371685i
$386$	−28.2108	−	1.39066i	−1.43589	−	0.0707826i
$387$	−28.4164	−	11.7705i	−1.44449	−	0.598326i
$388$	5.72139	+	6.97631i	0.290459	+	0.354168i
$389$	−18.7703	−	7.77491i	−0.951691	−	0.394203i	−0.147825	−	0.989014i	$-0.547227\pi$
$389$	−18.7703	−	7.77491i	−0.951691	−	0.394203i	−0.803866	+	0.594810i	$0.797227\pi$
$390$	9.92161	−	3.22692i	0.502400	−	0.163401i
$391$	2.26948	−	2.26948i	0.114773	−	0.114773i
$392$	3.04808	+	4.11419i	0.153951	+	0.207798i
$393$	−4.32104			−0.217968
$394$	−28.5016	−	13.4861i	−1.43589	−	0.679421i
$395$	4.77499	+	12.5447i	0.240256	+	0.631190i
$396$	−7.31622	−	24.1475i	−0.367654	−	1.21346i
$397$	21.3075	+	8.82587i	1.06939	+	0.442958i	0.846777	−	0.531948i	$-0.178540\pi$
$397$	21.3075	+	8.82587i	1.06939	+	0.442958i	0.222618	+	0.974906i	$0.428540\pi$
$398$	−0.347066	−	0.0171087i	−0.0173969	−	0.000857581i
$399$			4.75104i			0.237849i
$400$	−17.2522	+	10.1174i	−0.862610	+	0.505870i
$401$		−	20.2626i		−	1.01187i	−0.862572	−	0.505934i	$-0.831148\pi$
$401$		−	20.2626i		−	1.01187i	0.862572	−	0.505934i	$-0.168852\pi$
$402$	−0.247429	+	5.01933i	−0.0123406	+	0.250341i
$403$	−4.57132	−	1.89350i	−0.227714	−	0.0943221i
$404$	−12.2227	−	6.53845i	−0.608102	−	0.325300i
$405$	4.12764	+	10.8440i	0.205104	+	0.538841i
$406$	11.6061	−	24.5285i	0.576003	−	1.21733i
$407$	−15.3124			−0.759006
$408$	−5.40992	−	3.24628i	−0.267831	−	0.160715i
$409$	−15.0309	+	15.0309i	−0.743230	+	0.743230i	−0.973198	−	0.229968i	$-0.926138\pi$
$409$	−15.0309	+	15.0309i	−0.743230	+	0.743230i	0.229968	+	0.973198i	$0.426138\pi$
$410$	−4.07737	−	12.5365i	−0.201367	−	0.619131i
$411$	0.420972	+	0.174372i	0.0207650	+	0.00860115i
$412$	−2.49423	+	25.2375i	−0.122882	+	1.24336i
$413$	28.2301	+	11.6933i	1.38911	+	0.575390i
$414$	−0.170819	+	3.46522i	−0.00839528	+	0.170306i
$415$	2.57051	+	0.0745492i	0.126181	+	0.00365948i
$416$	4.07967	+	27.6629i	0.200022	+	1.35629i
$417$	1.15209	−	1.15209i	0.0564180	−	0.0564180i
$418$	−16.1723	+	14.6528i	−0.791015	+	0.716693i
$419$	17.6728	−	7.32030i	0.863371	−	0.357620i	0.0933460	−	0.995634i	$-0.470244\pi$
$419$	17.6728	−	7.32030i	0.863371	−	0.357620i	0.770025	+	0.638014i	$0.220244\pi$
$420$	0.864679	−	6.74478i	0.0421920	−	0.329112i
$421$	−6.31724	+	15.2512i	−0.307883	+	0.743296i	0.691890	+	0.722003i	$0.256778\pi$
$421$	−6.31724	+	15.2512i	−0.307883	+	0.743296i	−0.999773	+	0.0212932i	$0.993222\pi$
$422$	−12.9997	+	27.4736i	−0.632815	+	1.33739i
$423$	17.3181			0.842036
$424$	5.84188	−	9.73546i	0.283707	−	0.472796i
$425$	16.6819	+	0.968422i	0.809190	+	0.0469754i
$426$	3.76605	+	1.78198i	0.182466	+	0.0863374i
$427$	7.96709	+	19.2342i	0.385554	+	0.930810i
$428$	−1.20556	+	0.365260i	−0.0582728	+	0.0176555i
$429$	−15.0535	+	6.23538i	−0.726792	+	0.301047i
$430$	2.97634	−	37.9591i	0.143532	−	1.83055i
$431$	−10.8055			−0.520483			−0.260241	−	0.965544i	$-0.583802\pi$
$431$	−10.8055			−0.520483			−0.260241	+	0.965544i	$0.583802\pi$
$432$	14.5465	−	2.88332i	0.699869	−	0.138724i
$433$	26.6655	−	26.6655i	1.28146	−	1.28146i	0.341626	−	0.939836i	$-0.389022\pi$
$433$	26.6655	−	26.6655i	1.28146	−	1.28146i	0.939836	−	0.341626i	$-0.110978\pi$
$434$	−2.38986	+	2.16532i	−0.114717	+	0.103938i
$435$	11.7484	−	4.47192i	0.563295	−	0.214412i
$436$	6.71850	+	22.1747i	0.321758	+	1.06198i
$437$	2.77234	−	1.14834i	0.132619	−	0.0549327i
$438$	−0.466528	−	1.30455i	−0.0222916	−	0.0623338i
$439$	−1.62927	+	1.62927i	−0.0777609	+	0.0777609i	−0.744918	−	0.667157i	$-0.767511\pi$
$439$	−1.62927	+	1.62927i	−0.0777609	+	0.0777609i	0.667157	+	0.744918i	$0.267511\pi$
$440$	25.6258	−	17.8585i	1.22166	−	0.851368i
$441$	3.26995	+	3.26995i	0.155712	+	0.155712i
$442$	9.99222	−	21.1176i	0.475281	−	1.00446i
$443$	7.24688	+	17.4955i	0.344309	+	0.831236i	0.997270	+	0.0738444i	$0.0235268\pi$
$443$	7.24688	+	17.4955i	0.344309	+	0.831236i	−0.652960	+	0.757392i	$0.726473\pi$
$444$	0.407068	−	4.11885i	0.0193186	−	0.195472i
$445$	13.4043	−	29.8801i	0.635426	−	1.41645i
$446$	−0.727723	+	14.7626i	−0.0344587	+	0.699027i
$447$	−0.275552	−	0.275552i	−0.0130331	−	0.0130331i
$448$	17.4347	+	5.30793i	0.823710	+	0.250776i
$449$		−	8.39784i		−	0.396319i	−0.980170	−	0.198159i	$-0.936504\pi$
$449$		−	8.39784i		−	0.396319i	0.980170	−	0.198159i	$-0.0634963\pi$
$450$	−14.0663	+	11.3320i	−0.663091	+	0.534196i
$451$	7.87872	+	19.0209i	0.370995	+	0.895660i
$452$	8.50344	+	10.3686i	0.399968	+	0.487697i
$453$	−7.78859	+	3.22614i	−0.365940	+	0.151577i
$454$	−32.6929	+	11.6915i	−1.53435	+	0.548709i
$455$	25.1692	+	0.729951i	1.17995	+	0.0342206i
$456$	−3.51151	−	4.73971i	−0.164442	−	0.221957i
$457$		−	4.51082i		−	0.211007i	−0.994419	−	0.105504i	$-0.966355\pi$
$457$		−	4.51082i		−	0.211007i	0.994419	−	0.105504i	$-0.0336455\pi$
$458$	10.8472	−	3.87915i	0.506858	−	0.181261i
$459$	−11.4469	−	4.74146i	−0.534295	−	0.221312i
$460$	−4.14474	+	1.12568i	−0.193249	+	0.0524849i
$461$	−12.2006	−	29.4549i	−0.568239	−	1.37185i	−0.903038	−	0.429560i	$-0.858669\pi$
$461$	−12.2006	−	29.4549i	−0.568239	−	1.37185i	0.334800	−	0.942289i	$-0.391331\pi$
$462$	−0.522868	+	10.6069i	−0.0243260	+	0.493477i
$463$	4.78295	+	4.78295i	0.222283	+	0.222283i	0.809459	−	0.587176i	$-0.199761\pi$
$463$	4.78295	+	4.78295i	0.222283	+	0.222283i	−0.587176	+	0.809459i	$0.699761\pi$
$464$	6.55061	+	33.0481i	0.304105	+	1.53422i
$465$	−1.49333	−	0.0433092i	−0.0692514	−	0.00200841i
$466$	7.07080	−	6.40644i	0.327549	−	0.296773i
$467$	3.35565	−	8.10126i	0.155281	−	0.374881i	−0.827025	−	0.562165i	$-0.809968\pi$
$467$	3.35565	−	8.10126i	0.155281	−	0.374881i	0.982306	+	0.187284i	$0.0599685\pi$
$468$	7.32277	+	24.1691i	0.338495	+	1.11722i
$469$	−4.64138	+	11.2053i	−0.214319	+	0.517412i
$470$	6.63079	+	20.3873i	0.305855	+	0.940395i
$471$	3.92708	+	3.92708i	0.180950	+	0.180950i
$472$	−36.8054	+	9.19958i	−1.69411	+	0.423445i
$473$			59.4640i			2.73416i
$474$	5.33529	−	1.90799i	0.245058	−	0.0876368i
$475$	14.0631	+	6.80514i	0.645257	+	0.312241i
$476$	−9.65578	−	11.7737i	−0.442572	−	0.539645i
$477$	3.92409	−	9.47360i	0.179672	−	0.433766i
$478$	−16.8387	−	18.5850i	−0.770186	−	0.850057i
$479$	35.5033			1.62219			0.811094	−	0.584916i	$-0.198873\pi$
$479$	35.5033			1.62219			0.811094	+	0.584916i	$0.198873\pi$
$480$	4.12248	+	7.36779i	0.188165	+	0.336292i
$481$	15.3261			0.698809
$482$	−8.88770	−	9.80937i	−0.404824	−	0.446805i
$483$	0.558816	−	1.34910i	0.0254270	−	0.0613862i
$484$	−20.7071	+	16.9822i	−0.941231	+	0.771919i
$485$	−4.12879	+	9.20364i	−0.187479	+	0.417916i
$486$	19.4225	−	6.94580i	0.881022	−	0.315068i
$487$			40.1030i			1.81724i	0.417623	+	0.908621i	$0.362863\pi$
$487$			40.1030i			1.81724i	−0.417623	+	0.908621i	$0.637137\pi$
$488$	−22.1642	−	13.2999i	−1.00333	−	0.602058i
$489$	9.49532	+	9.49532i	0.429393	+	0.429393i
$490$	−2.59745	+	5.10146i	−0.117341	+	0.230460i
$491$	12.7673	−	30.8229i	0.576179	−	1.39102i	−0.320039	−	0.947404i	$-0.603696\pi$
$491$	12.7673	−	30.8229i	0.576179	−	1.39102i	0.896218	−	0.443614i	$-0.146304\pi$
$492$	−5.32586	+	1.61363i	−0.240108	+	0.0727481i
$493$	10.7721	−	26.0061i	0.485151	−	1.17126i
$494$	16.1868	−	14.6659i	0.728280	−	0.659851i
$495$	20.5172	−	19.3606i	0.922177	−	0.870195i
$496$	0.783774	−	3.92651i	0.0351925	−	0.176306i
$497$	7.11013	+	7.11013i	0.318933	+	0.318933i
$498$	0.0534478	−	1.08424i	0.00239505	−	0.0485860i
$499$	12.9202	+	31.1921i	0.578387	+	1.39635i	0.894259	+	0.447549i	$0.147703\pi$
$499$	12.9202	+	31.1921i	0.578387	+	1.39635i	−0.315872	+	0.948802i	$0.602297\pi$
$500$	−18.7260	−	12.2203i	−0.837453	−	0.546510i
$501$	5.78109	+	2.39461i	0.258280	+	0.106983i
$502$	22.7626	−	8.14028i	1.01594	−	0.363318i
$503$			28.0753i			1.25182i	0.779897	+	0.625908i	$0.215272\pi$
$503$			28.0753i			1.25182i	−0.779897	+	0.625908i	$0.784728\pi$
$504$	16.2804	+	2.42335i	0.725186	+	0.107944i
$505$	0.449275	−	15.4913i	0.0199925	−	0.689354i
$506$	6.31575	−	2.25861i	0.280769	−	0.100408i
$507$	7.05061	−	2.92046i	0.313129	−	0.129702i
$508$	−9.50023	+	7.79130i	−0.421505	+	0.345683i
$509$	2.08239	+	5.02734i	0.0923004	+	0.222833i	0.963287	−	0.268474i	$-0.0865193\pi$
$509$	2.08239	+	5.02734i	0.0923004	+	0.222833i	−0.870987	+	0.491307i	$0.836519\pi$
$510$	0.551394	−	7.03228i	0.0244161	−	0.311394i
$511$		−	3.34371i		−	0.147917i
$512$	−21.3162	+	7.59074i	−0.942052	+	0.335467i
$513$	−8.19120	−	8.19120i	−0.361650	−	0.361650i
$514$	−0.562755	+	11.4160i	−0.0248220	+	0.503539i
$515$	−26.4991	+	10.0866i	−1.16769	+	0.444468i
$516$	−15.9951	−	1.58081i	−0.704147	−	0.0695912i
$517$	−12.8127	−	30.9326i	−0.563502	−	1.36041i
$518$	4.27236	−	9.02923i	0.187717	−	0.396722i
$519$	7.04914	+	7.04914i	0.309423	+	0.309423i
$520$	−25.6487	+	17.8744i	−1.12477	+	0.783846i
$521$	12.1069	−	12.1069i	0.530411	−	0.530411i	−0.390283	−	0.920695i	$-0.627623\pi$
$521$	12.1069	−	12.1069i	0.530411	−	0.530411i	0.920695	+	0.390283i	$0.127623\pi$
$522$	10.2462	+	28.6513i	0.448462	+	1.25403i
$523$	−6.94169	+	2.87534i	−0.303539	+	0.125730i	−0.529254	−	0.848463i	$-0.677528\pi$
$523$	−6.94169	+	2.87534i	−0.303539	+	0.125730i	0.225715	+	0.974193i	$0.427528\pi$
$524$	12.3916	−	3.75440i	0.541328	−	0.164012i
$525$	7.18071	−	2.49744i	0.313392	−	0.108997i
$526$	−21.5931	+	19.5642i	−0.941502	+	0.853040i
$527$	−2.36549	+	2.36549i	−0.103042	+	0.103042i
$528$	−7.31797	−	10.9680i	−0.318474	−	0.477323i
$529$	22.0777			0.959900
$530$	12.6550	+	0.992266i	0.549698	+	0.0431013i
$531$	−31.6554	+	13.1121i	−1.37373	+	0.569017i
$532$	−4.12800	−	13.6247i	−0.178972	−	0.590704i
$533$	−7.88578	−	19.0379i	−0.341571	−	0.824625i
$534$	−12.4962	−	5.91283i	−0.540763	−	0.255873i
$535$	−0.966573	−	1.02431i	−0.0417886	−	0.0442849i
$536$	−3.65156	−	14.6090i	−0.157723	−	0.631015i
$537$	−8.97791			−0.387425
$538$	−12.1825	+	25.7466i	−0.525225	+	1.11001i
$539$	3.42133	−	8.25983i	0.147367	−	0.355776i
$540$	10.1378	+	13.1194i	0.436262	+	0.564568i
$541$	1.26767	−	0.525087i	0.0545015	−	0.0225753i	−0.355266	−	0.934765i	$-0.615610\pi$
$541$	1.26767	−	0.525087i	0.0545015	−	0.0225753i	0.409768	+	0.912190i	$0.365610\pi$
$542$	29.0543	−	26.3244i	1.24799	−	1.13073i
$543$	−2.69435	+	2.69435i	−0.115626	+	0.115626i
$544$	18.3347	+	4.60897i	0.786095	+	0.197608i
$545$	−18.8410	+	17.7789i	−0.807058	+	0.761565i
$546$	0.523336	−	10.6164i	0.0223967	−	0.454339i
$547$	−7.02985	−	2.91186i	−0.300575	−	0.124502i	0.227299	−	0.973825i	$-0.427011\pi$
$547$	−7.02985	−	2.91186i	−0.300575	−	0.124502i	−0.527874	+	0.849323i	$0.677011\pi$
$548$	−1.35874	−	0.134285i	−0.0580424	−	0.00573636i
$549$	−21.5680	−	8.93377i	−0.920501	−	0.381284i
$550$	30.6474	+	16.7404i	1.30681	+	0.713814i
$551$	18.6095	−	18.6095i	0.792793	−	0.792793i
$552$	0.439642	+	1.75891i	0.0187124	+	0.0748641i
$553$	13.6750			0.581519
$554$	3.65834	−	7.73156i	0.155428	−	0.328482i
$555$	4.32475	−	1.64617i	0.183575	−	0.0698760i
$556$	−2.30287	+	4.30488i	−0.0976633	+	0.182568i
$557$	−32.1435	−	13.3143i	−1.36196	−	0.564144i	−0.422366	−	0.906425i	$-0.638800\pi$
$557$	−32.1435	−	13.3143i	−1.36196	−	0.564144i	−0.939597	+	0.342282i	$0.888800\pi$
$558$	0.178045	−	3.61182i	0.00753725	−	0.152900i
$559$		−	59.5172i		−	2.51731i
$560$	3.38063	+	20.0935i	0.142858	+	0.849104i
$561$			11.0162i			0.465106i
$562$	27.3013	+	1.34582i	1.15164	+	0.0567702i
$563$	17.3729	+	7.19609i	0.732180	+	0.303279i	0.717448	−	0.696613i	$-0.245310\pi$
$563$	17.3729	+	7.19609i	0.732180	+	0.303279i	0.0147326	+	0.999891i	$0.495310\pi$
$564$	8.66113	−	2.62415i	0.364699	−	0.110497i
$565$	−6.13644	+	13.6790i	−0.258162	+	0.575478i
$566$	15.6861	+	7.42218i	0.659335	+	0.311978i
$567$	11.8210			0.496437
$568$	−12.3483	−	1.83806i	−0.518124	−	0.0771231i
$569$	−18.8525	+	18.8525i	−0.790336	+	0.790336i	−0.981549	−	0.191213i	$-0.938758\pi$
$569$	−18.8525	+	18.8525i	−0.790336	+	0.790336i	0.191213	+	0.981549i	$0.438758\pi$
$570$	2.99237	−	5.87709i	0.125337	−	0.246164i
$571$	−5.46475	−	2.26357i	−0.228693	−	0.0947276i	0.265395	−	0.964140i	$-0.414498\pi$
$571$	−5.46475	−	2.26357i	−0.228693	−	0.0947276i	−0.494087	+	0.869412i	$0.664498\pi$
$572$	37.7518	−	30.9609i	1.57848	−	1.29454i
$573$	−1.56871	−	0.649782i	−0.0655339	−	0.0271450i
$574$	−13.4143	−	0.661261i	−0.559903	−	0.0276005i
$575$	−3.19291	−	3.58647i	−0.133154	−	0.149566i
$576$	−18.0327	+	9.61532i	−0.751361	+	0.400638i
$577$	4.65533	−	4.65533i	0.193804	−	0.193804i	−0.603534	−	0.797338i	$-0.706241\pi$
$577$	4.65533	−	4.65533i	0.193804	−	0.193804i	0.797338	+	0.603534i	$0.206241\pi$
$578$	5.53692	+	6.11112i	0.230306	+	0.254189i
$579$	−12.3159	+	5.10140i	−0.511830	+	0.212007i
$580$	−29.8058	+	23.0320i	−1.23762	+	0.956353i
$581$	1.00260	−	2.42049i	0.0415948	−	0.100419i
$582$	3.84907	+	1.82127i	0.159549	+	0.0754939i
$583$	−19.8244			−0.821042
$584$	2.47135	+	3.33574i	0.102265	+	0.138034i
$585$	−20.5355	+	19.3780i	−0.849039	+	0.801180i
$586$	−1.31733	+	2.78405i	−0.0544184	+	0.115008i
$587$	6.50511	+	15.7047i	0.268495	+	0.648203i	0.999413	−	0.0342617i	$-0.0109080\pi$
$587$	6.50511	+	15.7047i	0.268495	+	0.648203i	−0.730918	+	0.682465i	$0.760908\pi$
$588$	2.13085	+	1.13988i	0.0878747	+	0.0470079i
$589$	−2.88963	+	1.19692i	−0.119065	+	0.0493184i
$590$	−27.5562	−	32.2451i	−1.13447	−	1.32751i
$591$	−14.8815			−0.612144
$592$	2.41136	+	12.1654i	0.0991064	+	0.499996i
$593$	−1.81074	+	1.81074i	−0.0743583	+	0.0743583i	−0.743308	−	0.668950i	$-0.766744\pi$
$593$	−1.81074	+	1.81074i	−0.0743583	+	0.0743583i	0.668950	+	0.743308i	$0.266744\pi$
$594$	−17.3857	−	19.1886i	−0.713344	−	0.787320i
$595$	6.96802	−	15.5327i	0.285661	−	0.636777i
$596$	1.02962	+	0.550790i	0.0421750	+	0.0225612i
$597$	−0.151517	+	0.0627604i	−0.00620118	+	0.00256861i
$598$	−6.32140	+	2.26064i	−0.258501	+	0.0924443i
$599$	20.0996	−	20.0996i	0.821249	−	0.821249i	−0.165039	−	0.986287i	$-0.552775\pi$
$599$	20.0996	−	20.0996i	0.821249	−	0.821249i	0.986287	+	0.165039i	$0.0527749\pi$
$600$	−5.31772	+	7.79877i	−0.217095	+	0.318383i
$601$	−22.8571	−	22.8571i	−0.932362	−	0.932362i	0.0654910	−	0.997853i	$-0.479139\pi$
$601$	−22.8571	−	22.8571i	−0.932362	−	0.932362i	−0.997853	+	0.0654910i	$0.979139\pi$
$602$	−35.0641	−	16.5913i	−1.42911	−	0.676210i
$603$	−5.20454	−	12.5649i	−0.211945	−	0.511682i
$604$	19.5325	−	16.0189i	0.794765	−	0.651800i
$605$	−27.3182	−	12.2551i	−1.11064	−	0.498240i
$606$	−6.53423	−	0.322106i	−0.265435	−	0.0130847i
$607$	24.9096	+	24.9096i	1.01105	+	1.01105i	0.999938	+	0.0111117i	$0.00353704\pi$
$607$	24.9096	+	24.9096i	1.01105	+	1.01105i	0.0111117	+	0.999938i	$0.496463\pi$
$608$	14.1882	+	10.5412i	0.575408	+	0.427501i
$609$		−	12.8070i		−	0.518967i
$610$	2.25904	−	28.8109i	0.0914658	−	1.16652i
$611$	12.8242	+	30.9603i	0.518810	+	1.25252i
$612$	16.9915	+	1.67928i	0.686840	+	0.0678808i
$613$	−29.0593	+	12.0367i	−1.17369	+	0.486160i	−0.882412	−	0.470478i	$-0.844082\pi$
$613$	−29.0593	+	12.0367i	−1.17369	+	0.486160i	−0.291281	+	0.956637i	$0.594082\pi$
$614$	−4.74078	−	13.2566i	−0.191322	−	0.534993i
$615$	−4.27009	−	4.52517i	−0.172187	−	0.182472i
$616$	−7.71649	−	30.8719i	−0.310906	−	1.24387i
$617$		−	26.4187i		−	1.06358i	−0.846877	−	0.531788i	$-0.821520\pi$
$617$		−	26.4187i		−	1.06358i	0.846877	−	0.531788i	$-0.178480\pi$
$618$	4.03039	+	11.2702i	0.162126	+	0.453352i
$619$	8.97449	+	3.71736i	0.360715	+	0.149413i	0.555678	−	0.831397i	$-0.312459\pi$
$619$	8.97449	+	3.71736i	0.360715	+	0.149413i	−0.194963	+	0.980811i	$0.562459\pi$
$620$	4.32008	−	1.17330i	0.173499	−	0.0471208i
$621$	1.36252	+	3.28941i	0.0546760	+	0.132000i
$622$	−6.04920	−	0.298196i	−0.242551	−	0.0119566i
$623$	−23.5922	−	23.5922i	−0.945203	−	0.945203i
$624$	7.32452	+	10.9779i	0.293215	+	0.439466i
$625$	2.89287	−	24.8321i	0.115715	−	0.993282i
$626$	−12.9310	−	14.2719i	−0.516826	−	0.570422i
$627$	−3.94152	+	9.51567i	−0.157409	+	0.380019i
$628$	−14.6739	−	7.84970i	−0.585552	−	0.313237i
$629$	3.96534	−	9.57318i	0.158109	−	0.381708i
$630$	5.69179	+	17.5002i	0.226766	+	0.697225i
$631$	14.6697	+	14.6697i	0.583990	+	0.583990i	0.935997	−	0.352007i	$-0.114501\pi$
$631$	14.6697	+	14.6697i	0.583990	+	0.583990i	−0.352007	+	0.935997i	$0.614501\pi$
$632$	−13.6424	+	10.1072i	−0.542664	+	0.402044i
$633$			14.3448i			0.570153i
$634$	−5.15056	−	14.4025i	−0.204555	−	0.571995i
$635$	−12.5334	−	5.62253i	−0.497372	−	0.223123i
$636$	0.527017	−	5.33253i	0.0208976	−	0.211449i
$637$	−3.42440	+	8.26723i	−0.135680	+	0.327559i
$638$	43.5946	−	39.4985i	1.72593	−	1.56376i
$639$	−11.2753			−0.446044
$640$	−18.2237	−	17.5469i	−0.720357	−	0.693604i
$641$	−6.19032			−0.244503			−0.122251	−	0.992499i	$-0.539011\pi$
$641$	−6.19032			−0.244503			−0.122251	+	0.992499i	$0.539011\pi$
$642$	−0.440576	+	0.399180i	−0.0173881	+	0.0157544i
$643$	−5.41170	+	13.0650i	−0.213417	+	0.515234i	−0.993944	−	0.109888i	$-0.964951\pi$
$643$	−5.41170	+	13.0650i	−0.213417	+	0.515234i	0.780527	+	0.625122i	$0.214951\pi$
$644$	−0.430346	+	4.35439i	−0.0169580	+	0.171587i
$645$	−6.39273	−	16.7947i	−0.251713	−	0.661291i
$646$	−4.97279	−	13.9054i	−0.195652	−	0.547100i
$647$		−	20.7006i		−	0.813824i	−0.913467	−	0.406912i	$-0.866606\pi$
$647$		−	20.7006i		−	0.813824i	0.913467	−	0.406912i	$-0.133394\pi$
$648$	−11.7929	+	8.73698i	−0.463268	+	0.343221i
$649$	46.8401	+	46.8401i	1.83864	+	1.83864i
$650$	−30.6748	−	16.7554i	−1.20317	−	0.657201i
$651$	−0.582457	+	1.40618i	−0.0228283	+	0.0551123i
$652$	−35.4801	−	18.9798i	−1.38951	−	0.743308i
$653$	−8.48884	+	20.4939i	−0.332194	+	0.801987i	0.666224	+	0.745752i	$0.267910\pi$
$653$	−8.48884	+	20.4939i	−0.332194	+	0.801987i	−0.998418	+	0.0562350i	$0.982090\pi$
$654$	7.34243	+	8.10385i	0.287112	+	0.316886i
$655$	9.93512	+	10.5286i	0.388197	+	0.411386i
$656$	13.8711	−	9.25490i	0.541575	−	0.361343i
$657$	2.65124	+	2.65124i	0.103435	+	0.103435i
$658$	21.8149	+	1.07537i	0.850434	+	0.0419223i
$659$	−11.4376	−	27.6128i	−0.445546	−	1.07564i	−0.973973	−	0.226664i	$-0.927218\pi$
$659$	−11.4376	−	27.6128i	−0.445546	−	1.07564i	0.528427	−	0.848979i	$-0.322782\pi$
$660$	7.32739	−	12.7915i	0.285218	−	0.497909i
$661$	12.3436	+	5.11290i	0.480111	+	0.198869i	0.609595	−	0.792713i	$-0.291332\pi$
$661$	12.3436	+	5.11290i	0.480111	+	0.198869i	−0.129484	+	0.991582i	$0.541332\pi$
$662$	15.2769	+	42.7187i	0.593754	+	1.66031i
$663$		−	11.0261i		−	0.428218i
$664$	0.788783	+	3.15574i	0.0306107	+	0.122467i
$665$	11.5763	−	10.9238i	0.448910	−	0.423606i
$666$	3.77174	+	10.5469i	0.146152	+	0.408683i
$667$	−7.47320	+	3.09550i	−0.289364	+	0.119858i
$668$	−18.6592	−	1.84409i	−0.721945	−	0.0713501i
$669$	2.66953	+	6.44481i	0.103210	+	0.249171i
$670$	12.7989	−	10.9378i	0.494466	−	0.422563i
$671$			45.1331i			1.74234i
$672$	8.50933	−	1.25494i	0.328255	−	0.0484104i
$673$	−13.1679	−	13.1679i	−0.507585	−	0.507585i	0.406199	−	0.913785i	$-0.366854\pi$
$673$	−13.1679	−	13.1679i	−0.507585	−	0.507585i	−0.913785	+	0.406199i	$0.866854\pi$
$674$	−7.84453	−	0.386697i	−0.302160	−	0.0148950i
$675$	−8.07436	+	16.6859i	−0.310782	+	0.642242i
$676$	−17.6817	+	14.5011i	−0.680067	+	0.557734i
$677$	−1.45860	−	3.52137i	−0.0560585	−	0.135337i	0.893369	−	0.449324i	$-0.148335\pi$
$677$	−1.45860	−	3.52137i	−0.0560585	−	0.135337i	−0.949427	+	0.313987i	$0.898335\pi$
$678$	5.72070	+	2.70686i	0.219702	+	0.103957i
$679$	7.26686	+	7.26686i	0.278877	+	0.278877i
$680$	4.52884	+	20.6457i	0.173673	+	0.791727i
$681$	−11.5872	+	11.5872i	−0.444022	+	0.444022i
$682$	−6.58294	+	2.35417i	−0.252074	+	0.0901457i
$683$	−10.7129	+	4.43744i	−0.409918	+	0.169794i	−0.578107	−	0.815961i	$-0.696208\pi$
$683$	−10.7129	+	4.43744i	−0.409918	+	0.169794i	0.168188	+	0.985755i	$0.446208\pi$
$684$	14.0762	+	7.52994i	0.538215	+	0.287915i
$685$	−0.543042	−	1.42666i	−0.0207486	−	0.0545098i
$686$	19.0581	+	21.0345i	0.727643	+	0.803101i
$687$	3.84453	−	3.84453i	0.146678	−	0.146678i
$688$	47.2432	−	9.36427i	1.80113	−	0.357010i
$689$	19.8421			0.755925
$690$	−1.54097	+	1.31689i	−0.0586639	+	0.0501332i
$691$	−22.1048	+	9.15612i	−0.840908	+	0.348315i	−0.761211	−	0.648504i	$-0.775395\pi$
$691$	−22.1048	+	9.15612i	−0.840908	+	0.348315i	−0.0796962	+	0.996819i	$0.525395\pi$
$692$	−26.3397	−	14.0903i	−1.00129	−	0.535631i
$693$	−10.9983	−	26.5522i	−0.417790	−	1.00863i
$694$	6.40574	−	13.5379i	0.243159	−	0.513892i
$695$	−5.45610	−	0.158236i	−0.206961	−	0.00600225i
$696$	9.46572	+	12.7765i	0.358797	+	0.484292i
$697$	−13.9320			−0.527714
$698$	−40.7616	−	19.2872i	−1.54285	−	0.730031i
$699$	1.72329	−	4.16040i	0.0651809	−	0.157361i
$700$	−18.4224	+	13.4010i	−0.696300	+	0.506511i
$701$	−1.66675	+	0.690392i	−0.0629524	+	0.0260757i	−0.413937	−	0.910305i	$-0.635847\pi$
$701$	−1.66675	+	0.690392i	−0.0629524	+	0.0260757i	0.350985	+	0.936381i	$0.385847\pi$
$702$	17.4013	+	19.2058i	0.656768	+	0.724877i
$703$	6.85041	−	6.85041i	0.258368	−	0.258368i
$704$	30.5157	+	25.0950i	1.15010	+	0.945805i
$705$	6.94419	+	7.35900i	0.261533	+	0.277156i
$706$	46.3589	+	2.28527i	1.74474	+	0.0860072i
$707$	−14.5872	−	6.04222i	−0.548608	−	0.227241i
$708$	−13.8447	+	11.3543i	−0.520315	+	0.426719i
$709$	−7.35840	−	3.04795i	−0.276351	−	0.114468i	0.240204	−	0.970722i	$-0.422786\pi$
$709$	−7.35840	−	3.04795i	−0.276351	−	0.114468i	−0.516555	+	0.856254i	$0.672786\pi$
$710$	−4.31710	−	13.2735i	−0.162018	−	0.498147i
$711$	−10.8429	+	10.8429i	−0.406642	+	0.406642i
$712$	40.9731	+	6.09888i	1.53553	+	0.228565i
$713$	0.961319			0.0360017
$714$	−6.49594	−	3.07369i	−0.243104	−	0.115030i
$715$	49.8048	+	22.3426i	1.86259	+	0.835568i
$716$	25.7462	−	7.80058i	0.962180	−	0.291521i
$717$	−10.9352	−	4.52952i	−0.408384	−	0.169158i
$718$	48.0139	+	2.36686i	1.79186	+	0.0883303i
$719$		−	0.610708i		−	0.0227756i	−0.999935	−	0.0113878i	$-0.996375\pi$
$719$		−	0.610708i		−	0.0227756i	0.999935	−	0.0113878i	$-0.00362492\pi$
$720$	−18.6127	−	13.2517i	−0.693655	−	0.493861i
$721$			28.8867i			1.07580i
$722$	−0.643154	+	13.0470i	−0.0239357	+	0.485559i
$723$	−5.77175	−	2.39074i	−0.214654	−	0.0889125i
$724$	5.38564	−	10.0677i	0.200156	−	0.374163i
$725$	−37.9087	−	18.3441i	−1.40790	−	0.681283i
$726$	−5.40588	+	11.4248i	−0.200631	+	0.424015i
$727$	6.93007			0.257022			0.128511	−	0.991708i	$-0.458980\pi$
$727$	6.93007			0.257022			0.128511	+	0.991708i	$0.458980\pi$
$728$	7.72340	+	30.8996i	0.286248	+	1.14521i
$729$	−4.12373	+	4.12373i	−0.152731	+	0.152731i
$730$	−2.10599	+	4.13621i	−0.0779462	+	0.153088i
$731$	−37.1765	−	15.3990i	−1.37502	−	0.569552i
$732$	−12.1403	−	1.19983i	−0.448718	−	0.0443470i
$733$	14.5769	+	6.03796i	0.538411	+	0.223017i	0.635283	−	0.772280i	$-0.280884\pi$
$733$	14.5769	+	6.03796i	0.538411	+	0.223017i	−0.0968717	+	0.995297i	$0.530884\pi$
$734$	−1.50814	+	30.5941i	−0.0556665	+	1.12925i
$735$	−0.0783245	+	2.70068i	−0.00288904	+	0.0996160i
$736$	−2.78902	−	4.66208i	−0.102805	−	0.171846i
$737$	−18.5921	+	18.5921i	−0.684848	+	0.684848i
$738$	11.1606	−	10.1119i	0.410827	−	0.372226i
$739$	0.514314	−	0.213036i	0.0189194	−	0.00783665i	−0.373204	−	0.927749i	$-0.621741\pi$
$739$	0.514314	−	0.213036i	0.0189194	−	0.00783665i	0.392123	+	0.919913i	$0.371741\pi$
$740$	−10.9719	+	8.47838i	−0.403335	+	0.311671i
$741$	3.94505	−	9.52418i	0.144925	−	0.349880i
$742$	5.53128	−	11.6898i	0.203060	−	0.429147i
$743$	21.2995			0.781404			0.390702	−	0.920517i	$-0.372232\pi$
$743$	21.2995			0.781404			0.390702	+	0.920517i	$0.372232\pi$
$744$	−0.458241	−	1.83332i	−0.0167999	−	0.0672127i
$745$	−0.0378463	+	1.30497i	−0.00138658	+	0.0478102i
$746$	15.4348	+	7.30327i	0.565106	+	0.267392i
$747$	1.12425	+	2.71418i	0.0411341	+	0.0993065i
$748$	−9.57161	−	31.5916i	−0.349973	−	1.15510i
$749$	−1.32561	+	0.549085i	−0.0484367	+	0.0200631i
$750$	−10.4556	−	1.43331i	−0.381784	−	0.0523371i
$751$	−24.7566			−0.903383			−0.451691	−	0.892174i	$-0.649179\pi$
$751$	−24.7566			−0.903383			−0.451691	+	0.892174i	$0.649179\pi$
$752$	−22.5577	+	15.0507i	−0.822595	+	0.548842i
$753$	8.06764	−	8.06764i	0.294001	−	0.294001i
$754$	−43.6336	+	39.5339i	−1.58904	+	1.43974i
$755$	25.7686	+	11.5599i	0.937816	+	0.420708i
$756$	16.1658	−	4.89791i	0.587945	−	0.178135i
$757$	0.940956	−	0.389757i	0.0341996	−	0.0141659i	−0.365518	−	0.930804i	$-0.619108\pi$
$757$	0.940956	−	0.389757i	0.0341996	−	0.0141659i	0.399718	+	0.916638i	$0.369108\pi$
$758$	3.29603	+	9.21666i	0.119717	+	0.334764i
$759$	2.23846	−	2.23846i	0.0812510	−	0.0812510i
$760$	−3.47492	+	19.4538i	−0.126049	+	0.705665i
$761$	14.4717	+	14.4717i	0.524600	+	0.524600i	0.918957	−	0.394357i	$-0.129033\pi$
$761$	14.4717	+	14.4717i	0.524600	+	0.524600i	−0.394357	+	0.918957i	$0.629033\pi$
$762$	−2.48017	+	5.24161i	−0.0898472	+	0.189883i
$763$	10.0997	+	24.3829i	0.365635	+	0.882722i
$764$	5.06321	+	0.500399i	0.183180	+	0.0181038i
$765$	6.79093	+	17.8409i	0.245527	+	0.645038i
$766$	0.886983	−	17.9933i	0.0320480	−	0.650124i
$767$	−46.8821	−	46.8821i	−1.69281	−	1.69281i
$768$	−7.56152	+	7.54123i	−0.272853	+	0.272121i
$769$			3.33991i			0.120440i	0.998185	+	0.0602201i	$0.0191803\pi$
$769$			3.33991i			0.120440i	−0.998185	+	0.0602201i	$0.980820\pi$
$770$	27.0468	−	23.1138i	0.974699	−	0.832962i
$771$	2.06437	+	4.98383i	0.0743465	+	0.179488i
$772$	30.8861	−	25.3302i	1.11162	−	0.911654i
$773$	−31.4513	+	13.0276i	−1.13122	+	0.468568i	−0.868197	−	0.496220i	$-0.834721\pi$
$773$	−31.4513	+	13.0276i	−1.13122	+	0.468568i	−0.263027	+	0.964788i	$0.584721\pi$
$774$	40.9577	−	14.6471i	1.47219	−	0.526481i
$775$	3.32799	+	3.73820i	0.119545	+	0.134280i
$776$	−12.6205	−	1.87857i	−0.453050	−	0.0674368i
$777$		−	4.71442i		−	0.169129i
$778$	27.0544	−	9.67508i	0.969946	−	0.346868i
$779$	−12.0343	−	4.98477i	−0.431173	−	0.178598i
$780$	−7.33394	+	12.8030i	−0.262597	+	0.458420i
$781$	8.34195	+	20.1393i	0.298499	+	0.720639i
$782$	−0.223477	+	4.53346i	−0.00799154	+	0.162116i
$783$	22.0804	+	22.0804i	0.789089	+	0.789089i
$784$	−7.10109	−	1.41745i	−0.253610	−	0.0506233i
$785$	0.539375	−	18.5980i	0.0192511	−	0.663791i
$786$	4.52855	−	4.10305i	0.161528	−	0.146351i
$787$	4.83884	−	11.6820i	0.172486	−	0.416418i	−0.813869	−	0.581048i	$-0.802643\pi$
$787$	4.83884	−	11.6820i	0.172486	−	0.416418i	0.986355	+	0.164630i	$0.0526430\pi$
$788$	42.6761	−	12.9300i	1.52027	−	0.460612i
$789$	−5.26265	+	12.7052i	−0.187355	+	0.452316i
$790$	−16.9161	−	8.61298i	−0.601848	−	0.306436i
$791$	10.8004	+	10.8004i	0.384018	+	0.384018i
$792$	30.5969	+	18.3600i	1.08721	+	0.652395i
$793$		−	45.1735i		−	1.60416i
$794$	−30.7114	+	10.9829i	−1.08991	+	0.389769i
$795$	5.59910	−	2.13124i	0.198580	−	0.0755872i
$796$	0.379979	−	0.311627i	0.0134680	−	0.0110453i
$797$	16.1759	−	39.0522i	0.572981	−	1.38330i	−0.326024	−	0.945361i	$-0.605709\pi$
$797$	16.1759	−	39.0522i	0.572981	−	1.38330i	0.899005	−	0.437938i	$-0.144291\pi$
$798$	−4.51136	−	4.97919i	−0.159700	−	0.176262i
$799$	22.6568			0.801541
$800$	8.47371	−	26.9851i	0.299591	−	0.954068i
$801$	37.4127			1.32191
$802$	19.2404	+	21.2357i	0.679403	+	0.749858i
$803$	2.77398	−	6.69699i	0.0978918	−	0.236332i
$804$	−4.50680	−	5.49532i	−0.158943	−	0.193805i
$805$	−4.57205	+	1.74030i	−0.161144	+	0.0613376i
$806$	6.58883	−	2.35627i	0.232082	−	0.0829962i
$807$			13.4430i			0.473217i
$808$	19.0183	−	4.75365i	0.669060	−	0.167233i
$809$	−22.9365	−	22.9365i	−0.806405	−	0.806405i	0.177683	−	0.984088i	$-0.443140\pi$
$809$	−22.9365	−	22.9365i	−0.806405	−	0.806405i	−0.984088	+	0.177683i	$0.943140\pi$
$810$	−14.6228	−	7.44532i	−0.513792	−	0.261602i
$811$	5.90021	−	14.2444i	0.207184	−	0.500187i	−0.785793	−	0.618489i	$-0.787745\pi$
$811$	5.90021	−	14.2444i	0.207184	−	0.500187i	0.992978	+	0.118302i	$0.0377451\pi$
$812$	11.1276	+	36.7270i	0.390501	+	1.28887i
$813$	7.08111	−	17.0953i	0.248345	−	0.599559i
$814$	16.0477	−	14.5399i	0.562472	−	0.509623i
$815$	1.30416	−	44.9682i	0.0456827	−	1.57517i
$816$	8.75223	−	1.73482i	0.306389	−	0.0607307i
$817$	−26.6028	−	26.6028i	−0.930715	−	0.930715i
$818$	1.48010	−	30.0253i	0.0517506	−	1.04981i
$819$	11.0081	+	26.5760i	0.384655	+	0.928639i
$820$	16.1772	+	9.26681i	0.564932	+	0.323611i
$821$	51.1290	+	21.1783i	1.78441	+	0.739129i	0.991549	+	0.129732i	$0.0414118\pi$
$821$	51.1290	+	21.1783i	1.78441	+	0.739129i	0.792866	+	0.609396i	$0.208588\pi$
$822$	−0.606763	+	0.216989i	−0.0211633	+	0.00756834i
$823$		−	10.1918i		−	0.355265i	−0.984097	−	0.177632i	$-0.943156\pi$
$823$		−	10.1918i		−	0.355265i	0.984097	−	0.177632i	$-0.0568438\pi$
$824$	−21.3503	−	28.8178i	−0.743772	−	1.00392i
$825$	16.4539	+	0.955186i	0.572850	+	0.0332553i
$826$	−40.6892	+	14.5511i	−1.41576	+	0.506299i
$827$	−35.2436	+	14.5984i	−1.22554	+	0.507635i	−0.899167	−	0.437606i	$-0.855826\pi$
$827$	−35.2436	+	14.5984i	−1.22554	+	0.507635i	−0.326373	+	0.945241i	$0.605826\pi$
$828$	−3.11138	−	3.79383i	−0.108128	−	0.131845i
$829$	2.42791	+	5.86150i	0.0843249	+	0.203578i	0.960418	−	0.278565i	$-0.0898586\pi$
$829$	2.42791	+	5.86150i	0.0843249	+	0.203578i	−0.876093	+	0.482143i	$0.839859\pi$
$830$	−2.76474	+	2.36270i	−0.0959654	+	0.0820105i
$831$		−	4.03687i		−	0.140037i
$832$	−30.5430	−	25.1175i	−1.05889	−	0.870793i
$833$	4.27799	+	4.27799i	0.148223	+	0.148223i
$834$	−0.113447	+	2.30138i	−0.00392835	+	0.0796904i
$835$	−7.45745	−	19.5919i	−0.258076	−	0.678006i
$836$	3.03538	−	30.7130i	0.104981	−	1.06223i
$837$	−1.42016	−	3.42857i	−0.0490880	−	0.118509i
$838$	−11.5705	+	24.4530i	−0.399695	+	0.844716i
$839$	−8.52542	−	8.52542i	−0.294330	−	0.294330i	0.544458	−	0.838788i	$-0.316735\pi$
$839$	−8.52542	−	8.52542i	−0.294330	−	0.294330i	−0.838788	+	0.544458i	$0.816735\pi$
$840$	5.49832	+	7.88974i	0.189710	+	0.272222i
$841$	−29.6583	+	29.6583i	−1.02270	+	1.02270i
$842$	−7.86116	−	21.9821i	−0.270914	−	0.757554i
$843$	11.9188	−	4.93693i	0.410506	−	0.170037i
$844$	−12.4636	−	41.1368i	−0.429016	−	1.41599i
$845$	−23.3270	−	10.4646i	−0.802473	−	0.359993i
$846$	−18.1498	+	16.4445i	−0.624002	+	0.565372i
$847$	−21.5695	+	21.5695i	−0.741137	+	0.741137i
$848$	3.12190	+	15.7502i	0.107207	+	0.540862i
$849$	8.19015			0.281085
$850$	−18.4025	+	14.8254i	−0.631202	+	0.508506i
$851$	−2.75098	+	1.13949i	−0.0943023	+	0.0390613i
$852$	−5.63900	+	1.70850i	−0.193189	+	0.0585324i
$853$	9.45008	+	22.8145i	0.323564	+	0.781154i	0.999042	+	0.0437727i	$0.0139377\pi$
$853$	9.45008	+	22.8145i	0.323564	+	0.781154i	−0.675477	+	0.737381i	$0.736062\pi$
$854$	−26.6136	−	12.5928i	−0.910699	−	0.430916i
$855$	−0.517404	+	17.8404i	−0.0176948	+	0.610129i
$856$	0.916618	−	1.52754i	0.0313294	−	0.0522102i
$857$	28.5439			0.975041			0.487520	−	0.873112i	$-0.337902\pi$
$857$	28.5439			0.975041			0.487520	+	0.873112i	$0.337902\pi$
$858$	9.85564	−	20.8289i	0.336466	−	0.711089i
$859$	−6.35935	+	15.3528i	−0.216978	+	0.523832i	−0.994465	−	0.105067i	$-0.966494\pi$
$859$	−6.35935	+	15.3528i	−0.216978	+	0.523832i	0.777487	+	0.628899i	$0.216494\pi$
$860$	32.9249	+	42.6082i	1.12273	+	1.45293i
$861$	−5.85622	+	2.42573i	−0.199580	+	0.0826686i
$862$	11.3244	−	10.2604i	0.385711	−	0.349470i
$863$	−8.90971	+	8.90971i	−0.303290	+	0.303290i	−0.842300	−	0.539010i	$-0.818799\pi$
$863$	−8.90971	+	8.90971i	−0.303290	+	0.303290i	0.539010	+	0.842300i	$0.318799\pi$
$864$	−12.5072	+	16.8344i	−0.425504	+	0.572720i
$865$	0.968182	−	33.3835i	0.0329192	−	1.13507i
$866$	−2.62577	+	53.2663i	−0.0892273	+	1.81006i
$867$	3.59573	+	1.48940i	0.122117	+	0.0505826i
$868$	0.448552	−	4.53860i	0.0152248	−	0.154050i
$869$	27.3891	+	11.3449i	0.929110	+	0.384850i
$870$	−8.06632	+	15.8424i	−0.273474	+	0.537109i
$871$	18.6087	−	18.6087i	0.630533	−	0.630533i
$872$	−28.0972	−	16.8601i	−0.951491	−	0.570954i
$873$	−11.5238			−0.390023
$874$	−1.81507	+	3.83597i	−0.0613956	+	0.129754i
$875$	−22.5954	−	11.7542i	−0.763864	−	0.397365i
$876$	1.72767	+	0.924205i	0.0583726	+	0.0312260i
$877$	53.7656	+	22.2705i	1.81554	+	0.752020i	0.978924	+	0.204224i	$0.0654671\pi$
$877$	53.7656	+	22.2705i	1.81554	+	0.752020i	0.836612	+	0.547796i	$0.184533\pi$
$878$	0.160436	−	3.25459i	0.00541444	−	0.109837i
$879$			1.45363i			0.0490298i
$880$	−9.89885	+	43.0490i	−0.333690	+	1.45118i
$881$			51.0648i			1.72042i	0.509943	+	0.860208i	$0.329666\pi$
$881$			51.0648i			1.72042i	−0.509943	+	0.860208i	$0.670334\pi$
$882$	−6.53196	−	0.321994i	−0.219943	−	0.0108421i
$883$	44.8986	+	18.5976i	1.51096	+	0.625859i	0.975755	−	0.218865i	$-0.0702356\pi$
$883$	44.8986	+	18.5976i	1.51096	+	0.625859i	0.535202	+	0.844724i	$0.320236\pi$
$884$	9.58018	+	31.6198i	0.322216	+	1.06349i
$885$	−18.2649	−	8.19370i	−0.613967	−	0.275428i
$886$	−24.2078	−	11.4544i	−0.813276	−	0.384818i
$887$	−6.12880			−0.205785			−0.102893	−	0.994692i	$-0.532810\pi$
$887$	−6.12880			−0.205785			−0.102893	+	0.994692i	$0.532810\pi$
$888$	3.48445	+	4.70318i	0.116930	+	0.157829i
$889$	−9.89591	+	9.89591i	−0.331898	+	0.331898i
$890$	14.3246	+	44.0431i	0.480163	+	1.47633i
$891$	23.6759	+	9.80688i	0.793173	+	0.328543i
$892$	−13.2551	−	16.1625i	−0.443815	−	0.541161i
$893$	19.5706	+	8.10642i	0.654906	+	0.271271i
$894$	0.550435	+	0.0271338i	0.0184093	+	0.000907489i
$895$	20.6424	+	21.8755i	0.689998	+	0.731216i
$896$	−23.3121	+	10.9923i	−0.778801	+	0.367226i
$897$	−2.24046	+	2.24046i	−0.0748069	+	0.0748069i
$898$	7.97418	+	8.80113i	0.266102	+	0.293697i
$899$	7.78936	−	3.22646i	0.259790	−	0.107608i
$900$	3.98145	−	25.2329i	0.132715	−	0.841096i
$901$	5.13379	−	12.3941i	0.171031	−	0.412906i
$902$	−26.3184	−	12.4531i	−0.876308	−	0.414643i
$903$	−18.3080			−0.609251
$904$	−18.7573	−	2.79204i	−0.623858	−	0.0928618i
$905$	12.7600	+	0.370063i	0.424157	+	0.0123013i
$906$	5.09923	−	10.7767i	0.169411	−	0.358033i
$907$	−19.4530	−	46.9638i	−0.645928	−	1.55941i	−0.818560	−	0.574421i	$-0.805227\pi$
$907$	−19.4530	−	46.9638i	−0.645928	−	1.55941i	0.172632	−	0.984986i	$-0.444773\pi$
$908$	23.1612	−	43.2965i	0.768630	−	1.43685i
$909$	16.3571	−	6.77535i	0.542532	−	0.224724i
$910$	−27.0710	+	23.1344i	−0.897395	+	0.766899i
$911$	−16.0540			−0.531893			−0.265947	−	0.963988i	$-0.585684\pi$
$911$	−16.0540			−0.531893			−0.265947	+	0.963988i	$0.585684\pi$
$912$	8.18075	+	1.63296i	0.270892	+	0.0540728i
$913$	4.01613	−	4.01613i	0.132915	−	0.132915i
$914$	4.28326	+	4.72744i	0.141678	+	0.156370i
$915$	−4.85207	−	12.7472i	−0.160405	−	0.421408i
$916$	−7.68469	+	14.3654i	−0.253909	+	0.474647i
$917$	13.6255	−	5.64388i	0.449955	−	0.186377i
$918$	16.4989	−	5.90026i	0.544543	−	0.194738i
$919$	8.25493	−	8.25493i	0.272305	−	0.272305i	−0.557723	−	0.830027i	$-0.688325\pi$
$919$	8.25493	−	8.25493i	0.272305	−	0.272305i	0.830027	+	0.557723i	$0.188325\pi$
$920$	3.27489	−	5.11538i	0.107970	−	0.168649i
$921$	−4.69848	−	4.69848i	−0.154820	−	0.154820i
$922$	40.7554	+	19.2842i	1.34221	+	0.635093i
$923$	−8.34942	−	20.1573i	−0.274824	−	0.663485i
$924$	−9.52380	−	11.6127i	−0.313310	−	0.382031i
$925$	−13.9547	−	6.75269i	−0.458827	−	0.222027i
$926$	−9.55430	−	0.470981i	−0.313974	−	0.0154774i
$927$	−22.9044	−	22.9044i	−0.752278	−	0.752278i
$928$	−38.2461	−	28.4151i	−1.25549	−	0.932770i
$929$			34.6394i			1.13648i	0.822862	+	0.568241i	$0.192376\pi$
$929$			34.6394i			1.13648i	−0.822862	+	0.568241i	$0.807624\pi$
$930$	1.60617	−	1.37260i	0.0526682	−	0.0450094i
$931$	2.16463	+	5.22589i	0.0709430	+	0.171272i
$932$	−1.32711	+	13.4282i	−0.0434711	+	0.439855i
$933$	−2.64087	+	1.09388i	−0.0864582	+	0.0358122i
$934$	4.17576	+	11.6767i	0.136635	+	0.382072i
$935$	26.8421	−	25.3290i	0.877829	−	0.828347i
$936$	−30.6243	−	18.3765i	−1.00099	−	0.600653i
$937$			24.8203i			0.810845i	0.914129	+	0.405422i	$0.132876\pi$
$937$			24.8203i			0.810845i	−0.914129	+	0.405422i	$0.867124\pi$
$938$	−5.77573	−	16.1506i	−0.188584	−	0.527337i
$939$	−8.39749	−	3.47835i	−0.274042	−	0.113512i
$940$	−26.3080	−	15.0701i	−0.858072	−	0.491531i
$941$	−2.88504	−	6.96510i	−0.0940496	−	0.227056i	0.869853	−	0.493311i	$-0.164214\pi$
$941$	−2.88504	−	6.96510i	−0.0940496	−	0.227056i	−0.963903	+	0.266255i	$0.914214\pi$
$942$	−7.84464	−	0.386703i	−0.255592	−	0.0125995i
$943$	2.83094	+	2.83094i	0.0921881	+	0.0921881i
$944$	29.8374	−	44.5900i	0.971126	−	1.45128i
$945$	12.9612	+	13.7354i	0.421627	+	0.446813i
$946$	−56.4641	−	62.3196i	−1.83581	−	2.02619i
$947$	−1.00694	+	2.43096i	−0.0327211	+	0.0789956i	−0.939395	−	0.342836i	$-0.888613\pi$
$947$	−1.00694	+	2.43096i	−0.0327211	+	0.0789956i	0.906674	+	0.421831i	$0.138613\pi$
$948$	−3.77977	+	7.06575i	−0.122761	+	0.229485i
$949$	−2.77647	+	6.70299i	−0.0901279	+	0.217588i
$950$	−21.2002	+	6.22166i	−0.687826	+	0.201857i
$951$	−5.10460	−	5.10460i	−0.165528	−	0.165528i
$952$	21.2992	+	3.17040i	0.690311	+	0.102753i
$953$		−	30.6318i		−	0.992263i	−0.868248	−	0.496131i	$-0.834753\pi$
$953$		−	30.6318i		−	0.992263i	0.868248	−	0.496131i	$-0.165247\pi$
$954$	4.88314	+	13.6547i	0.158097	+	0.442086i
$955$	2.02360	+	5.31631i	0.0654820	+	0.172032i
$956$	35.2948	+	3.48820i	1.14151	+	0.112816i
$957$	10.6249	−	25.6507i	0.343453	−	0.829169i
$958$	−37.2083	+	33.7122i	−1.20214	+	1.08919i
$959$	−1.55520			−0.0502202
$960$	−11.3166	−	3.80711i	−0.365240	−	0.122874i
$961$	29.9980			0.967678
$962$	−16.0621	+	14.5529i	−0.517862	+	0.469204i
$963$	0.615709	−	1.48645i	0.0198409	−	0.0479002i
$964$	18.6290	+	1.84112i	0.600000	+	0.0592983i
$965$	40.7471	+	18.2793i	1.31170	+	0.588433i
$966$	0.695389	+	1.94451i	0.0223738	+	0.0625637i
$967$			3.34198i			0.107471i	0.998555	+	0.0537354i	$0.0171128\pi$
$967$			3.34198i			0.107471i	−0.998555	+	0.0537354i	$0.982887\pi$
$968$	5.57598	−	37.4602i	0.179219	−	1.20402i
$969$	−4.92842	−	4.92842i	−0.158324	−	0.158324i
$970$	−4.41226	−	13.5661i	−0.141669	−	0.435582i
$971$	−8.07048	+	19.4839i	−0.258994	+	0.625267i	−0.998872	−	0.0474738i	$-0.984883\pi$
$971$	−8.07048	+	19.4839i	−0.258994	+	0.625267i	0.739879	+	0.672740i	$0.234883\pi$
$972$	−13.7598	+	25.7220i	−0.441346	+	0.825034i
$973$	−2.12809	+	5.13767i	−0.0682235	+	0.164706i
$974$	−38.0799	−	42.0289i	−1.22016	−	1.34669i
$975$	−16.4686	−	0.956041i	−0.527417	−	0.0306178i
$976$	35.8575	−	7.10747i	1.14777	−	0.227505i
$977$	−4.66094	−	4.66094i	−0.149117	−	0.149117i	0.628607	−	0.777723i	$-0.283626\pi$
$977$	−4.66094	−	4.66094i	−0.149117	−	0.149117i	−0.777723	+	0.628607i	$0.783626\pi$
$978$	−18.9676	−	0.935012i	−0.606517	−	0.0298984i
$979$	−27.6796	−	66.8243i	−0.884642	−	2.13572i
$980$	−2.12191	−	7.81286i	−0.0677819	−	0.249573i
$981$	−27.3414	−	11.3252i	−0.872945	−	0.361586i
$982$	15.8876	+	44.4263i	0.506992	+	1.41770i
$983$		−	13.2113i		−	0.421375i	−0.977553	−	0.210688i	$-0.932430\pi$
$983$		−	13.2113i		−	0.421375i	0.977553	−	0.210688i	$-0.0675703\pi$
$984$	4.04940	−	6.74830i	0.129090	−	0.215128i
$985$	34.2162	+	36.2601i	1.09022	+	1.15534i
$986$	13.4048	+	37.4837i	0.426895	+	1.19372i
$987$	9.52362	−	3.94481i	0.303140	−	0.125565i
$988$	−3.03809	+	30.7405i	−0.0966547	+	0.977984i
$989$	4.42510	+	10.6831i	0.140710	+	0.339704i
$990$	−3.11852	+	39.7725i	−0.0991131	+	1.26405i
$991$		−	45.0100i		−	1.42979i	−0.699233	−	0.714894i	$-0.746475\pi$
$991$		−	45.0100i		−	1.42979i	0.699233	−	0.714894i	$-0.253525\pi$
$992$	2.90701	+	4.85931i	0.0922978	+	0.154283i
$993$	15.1406	+	15.1406i	0.480473	+	0.480473i
$994$	−14.2030	−	0.700140i	−0.450492	−	0.0222071i
$995$	0.501295	+	0.224883i	0.0158921	+	0.00712928i
$996$	0.973528	+	1.18706i	0.0308474	+	0.0376134i
$997$	4.78161	+	11.5438i	0.151435	+	0.365597i	0.981332	−	0.192319i	$-0.0616010\pi$
$997$	4.78161	+	11.5438i	0.151435	+	0.365597i	−0.829897	+	0.557916i	$0.811601\pi$
$998$	−43.1592	−	20.4216i	−1.36618	−	0.646436i
$999$	8.12807	+	8.12807i	0.257161	+	0.257161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.43.6	✓	88
4.3	odd	2		640.2.u.a.463.14		88
5.2	odd	4		160.2.ba.a.107.7	yes	88
5.3	odd	4		800.2.bb.b.107.16		88
5.4	even	2		800.2.v.b.43.17		88
20.7	even	4		640.2.ba.a.207.9		88
32.3	odd	8		160.2.ba.a.3.7	yes	88
32.29	even	8		640.2.ba.a.303.9		88
160.3	even	8		800.2.v.b.707.17		88
160.67	even	8	inner	160.2.u.a.67.6	yes	88
160.99	odd	8		800.2.bb.b.643.16		88
160.157	odd	8		640.2.u.a.47.14		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.6	✓	88	1.1	even	1	trivial
160.2.u.a.67.6	yes	88	160.67	even	8	inner
160.2.ba.a.3.7	yes	88	32.3	odd	8
160.2.ba.a.107.7	yes	88	5.2	odd	4
640.2.u.a.47.14		88	160.157	odd	8
640.2.u.a.463.14		88	4.3	odd	2
640.2.ba.a.207.9		88	20.7	even	4
640.2.ba.a.303.9		88	32.29	even	8
800.2.v.b.43.17		88	5.4	even	2
800.2.v.b.707.17		88	160.3	even	8
800.2.bb.b.107.16		88	5.3	odd	4
800.2.bb.b.643.16		88	160.99	odd	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04802 + 0.949552i) q^{2} +(-0.255424 + 0.616647i) q^{3} +(0.196703 - 1.99030i) q^{4} +(2.08980 - 0.795458i) q^{5} +(-0.317849 - 0.888798i) q^{6} -2.27809i q^{7} +(1.68375 + 2.27266i) q^{8} +(1.80631 + 1.80631i) q^{9} +O(q^{10})\)	\(q+(-1.04802 + 0.949552i) q^{2} +(-0.255424 + 0.616647i) q^{3} +(0.196703 - 1.99030i) q^{4} +(2.08980 - 0.795458i) q^{5} +(-0.317849 - 0.888798i) q^{6} -2.27809i q^{7} +(1.68375 + 2.27266i) q^{8} +(1.80631 + 1.80631i) q^{9} +(-1.43482 + 2.81803i) q^{10} +(1.88993 - 4.56270i) q^{11} +(1.17707 + 0.629667i) q^{12} +(-1.89162 + 4.56679i) q^{13} +(2.16317 + 2.38749i) q^{14} +(-0.0432662 + 1.49185i) q^{15} +(-3.92262 - 0.782996i) q^{16} +(2.36314 + 2.36314i) q^{17} +(-3.60823 - 0.177869i) q^{18} +(1.19574 + 2.88676i) q^{19} +(-1.17213 - 4.31580i) q^{20} +(1.40478 + 0.581879i) q^{21} +(2.35183 + 6.57640i) q^{22} -0.960365i q^{23} +(-1.83150 + 0.457787i) q^{24} +(3.73449 - 3.32469i) q^{25} +(-2.35393 - 6.58229i) q^{26} +(-3.42517 + 1.41875i) q^{27} +(-4.53410 - 0.448107i) q^{28} +(-3.22326 - 7.78163i) q^{29} +(-1.37124 - 1.60457i) q^{30} +1.00099i q^{31} +(4.85449 - 2.90413i) q^{32} +(2.33084 + 2.33084i) q^{33} +(-4.72056 - 0.232701i) q^{34} +(-1.81213 - 4.76075i) q^{35} +(3.95041 - 3.23980i) q^{36} +(-1.18652 - 2.86451i) q^{37} +(-3.99429 - 1.88998i) q^{38} +(-2.33293 - 2.33293i) q^{39} +(5.32650 + 3.41005i) q^{40} +(-2.94778 + 2.94778i) q^{41} +(-2.02476 + 0.724089i) q^{42} +(-11.1240 + 4.60773i) q^{43} +(-8.70941 - 4.65904i) q^{44} +(5.21166 + 2.33797i) q^{45} +(0.911916 + 1.00648i) q^{46} +(4.79379 - 4.79379i) q^{47} +(1.48476 - 2.21887i) q^{48} +1.81029 q^{49} +(-0.756867 + 7.03044i) q^{50} +(-2.06083 + 0.853624i) q^{51} +(8.71720 + 4.66321i) q^{52} +(-1.53615 - 3.70859i) q^{53} +(2.24248 - 4.73926i) q^{54} +(0.320136 - 11.0385i) q^{55} +(5.17734 - 3.83573i) q^{56} -2.08553 q^{57} +(10.7671 + 5.09467i) q^{58} +(-5.13294 + 12.3920i) q^{59} +(2.96072 + 0.379563i) q^{60} +(-8.44314 + 3.49726i) q^{61} +(-0.950495 - 1.04906i) q^{62} +(4.11494 - 4.11494i) q^{63} +(-2.32999 + 7.65318i) q^{64} +(-0.320422 + 11.0484i) q^{65} +(-4.65603 - 0.229520i) q^{66} +(-4.91872 - 2.03740i) q^{67} +(5.16821 - 4.23854i) q^{68} +(0.592206 + 0.245300i) q^{69} +(6.41973 + 3.26866i) q^{70} +(-3.12109 + 3.12109i) q^{71} +(-1.06376 + 7.14649i) q^{72} +1.46777 q^{73} +(3.96351 + 1.87541i) q^{74} +(1.09628 + 3.15207i) q^{75} +(5.98074 - 1.81204i) q^{76} +(-10.3943 - 4.30544i) q^{77} +(4.66020 + 0.229725i) q^{78} +6.00281i q^{79} +(-8.82031 + 1.48398i) q^{80} +5.18901i q^{81} +(0.290270 - 5.88840i) q^{82} +(1.06251 + 0.440104i) q^{83} +(1.43444 - 2.68148i) q^{84} +(6.81827 + 3.05871i) q^{85} +(7.28297 - 15.3919i) q^{86} +5.62182 q^{87} +(13.5517 - 3.38726i) q^{88} +(10.3561 - 10.3561i) q^{89} +(-7.68196 + 2.49849i) q^{90} +(10.4036 + 4.30930i) q^{91} +(-1.91142 - 0.188906i) q^{92} +(-0.617260 - 0.255677i) q^{93} +(-0.472048 + 9.57595i) q^{94} +(4.79514 + 5.08158i) q^{95} +(0.550873 + 3.73529i) q^{96} +(-3.18989 + 3.18989i) q^{97} +(-1.89723 + 1.71897i) q^{98} +(11.6554 - 4.82784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Introduction

L-functions

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