LMFDB - Embedded newform 336.2.bo.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38159 + 0.302030i) q^{2} +(-1.35899 + 1.07385i) q^{3} +(1.81756 - 0.834561i) q^{4} +(-3.09219 + 0.828549i) q^{5} +(1.55322 - 1.89407i) q^{6} +(-2.16452 + 1.52147i) q^{7} +(-2.25904 + 1.70197i) q^{8} +(0.693695 - 2.91870i) q^{9} +O(q^{10})$	\(q+(-1.38159 + 0.302030i) q^{2} +(-1.35899 + 1.07385i) q^{3} +(1.81756 - 0.834561i) q^{4} +(-3.09219 + 0.828549i) q^{5} +(1.55322 - 1.89407i) q^{6} +(-2.16452 + 1.52147i) q^{7} +(-2.25904 + 1.70197i) q^{8} +(0.693695 - 2.91870i) q^{9} +(4.02187 - 2.07865i) q^{10} +(3.12152 + 0.836408i) q^{11} +(-1.57384 + 3.08594i) q^{12} +(-3.07235 - 3.07235i) q^{13} +(2.53094 - 2.75579i) q^{14} +(3.31251 - 4.44653i) q^{15} +(2.60701 - 3.03372i) q^{16} +(1.36326 + 2.36124i) q^{17} +(-0.0768638 + 4.24194i) q^{18} +(-0.780112 + 0.209030i) q^{19} +(-4.92875 + 4.08655i) q^{20} +(1.30773 - 4.39202i) q^{21} +(-4.56526 - 0.212776i) q^{22} +(3.08514 - 5.34363i) q^{23} +(1.24235 - 4.73884i) q^{24} +(4.54500 - 2.62406i) q^{25} +(5.17266 + 3.31677i) q^{26} +(2.19152 + 4.71140i) q^{27} +(-2.66437 + 4.57177i) q^{28} +(-4.52350 - 4.52350i) q^{29} +(-3.23352 + 7.14374i) q^{30} +(6.79094 - 3.92075i) q^{31} +(-2.68554 + 4.97874i) q^{32} +(-5.14028 + 2.21537i) q^{33} +(-2.59663 - 2.85050i) q^{34} +(5.43248 - 6.49807i) q^{35} +(-1.17500 - 5.88382i) q^{36} +(2.78693 - 0.746757i) q^{37} +(1.01466 - 0.524411i) q^{38} +(7.47453 + 0.876045i) q^{39} +(5.57522 - 7.13455i) q^{40} -4.13241i q^{41} +(-0.480211 + 6.46292i) q^{42} +(-0.294513 - 0.294513i) q^{43} +(6.37157 - 1.08488i) q^{44} +(0.273248 + 9.59992i) q^{45} +(-2.64845 + 8.31448i) q^{46} +(2.24120 - 3.88187i) q^{47} +(-0.285139 + 6.92233i) q^{48} +(2.37027 - 6.58649i) q^{49} +(-5.48676 + 4.99809i) q^{50} +(-4.38827 - 1.74496i) q^{51} +(-8.14823 - 3.02010i) q^{52} +(-5.77126 - 1.54640i) q^{53} +(-4.45075 - 5.84729i) q^{54} -10.3453 q^{55} +(2.30024 - 7.12102i) q^{56} +(0.835696 - 1.12179i) q^{57} +(7.61583 + 4.88336i) q^{58} +(-1.56377 + 5.83606i) q^{59} +(2.30976 - 10.8463i) q^{60} +(-12.9350 + 3.46591i) q^{61} +(-8.19808 + 7.46793i) q^{62} +(2.93919 + 7.37300i) q^{63} +(2.20656 - 7.68967i) q^{64} +(12.0459 + 6.95469i) q^{65} +(6.43263 - 4.61325i) q^{66} +(2.48018 + 0.664561i) q^{67} +(4.44840 + 3.15395i) q^{68} +(1.54558 + 10.5749i) q^{69} +(-5.54282 + 10.6184i) q^{70} +0.885678 q^{71} +(3.40046 + 7.77412i) q^{72} +(-7.04045 - 12.1944i) q^{73} +(-3.62484 + 1.87345i) q^{74} +(-3.35876 + 8.44671i) q^{75} +(-1.24345 + 1.03098i) q^{76} +(-8.02915 + 2.93887i) q^{77} +(-10.5913 + 1.04720i) q^{78} +(-7.20211 + 12.4744i) q^{79} +(-5.54779 + 11.5409i) q^{80} +(-8.03757 - 4.04937i) q^{81} +(1.24811 + 5.70927i) q^{82} +(-5.44007 + 5.44007i) q^{83} +(-1.28855 - 9.07412i) q^{84} +(-6.17186 - 6.17186i) q^{85} +(0.495846 + 0.317943i) q^{86} +(11.0049 + 1.28982i) q^{87} +(-8.47520 + 3.42326i) q^{88} +(-2.90496 - 1.67718i) q^{89} +(-3.27698 - 13.1806i) q^{90} +(11.3246 + 1.97568i) q^{91} +(1.14784 - 12.2871i) q^{92} +(-5.01851 + 12.6207i) q^{93} +(-1.92396 + 6.04004i) q^{94} +(2.23906 - 1.29272i) q^{95} +(-1.69681 - 9.64991i) q^{96} +3.40029i q^{97} +(-1.28542 + 9.81569i) q^{98} +(4.60660 - 8.53055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38159	+	0.302030i	−0.976928	+	0.213568i
$2$	−1.38159	+	0.302030i	−0.976928	+	0.213568i
$3$	−1.35899	+	1.07385i	−0.784612	+	0.619987i
$3$	−1.35899	+	1.07385i	−0.784612	+	0.619987i
$4$	1.81756	−	0.834561i	0.908778	−	0.417281i
$5$	−3.09219	+	0.828549i	−1.38287	+	0.370538i	−0.872162	−	0.489217i	$-0.837283\pi$
$5$	−3.09219	+	0.828549i	−1.38287	+	0.370538i	−0.510706	+	0.859755i	$0.670616\pi$
$6$	1.55322	−	1.89407i	0.634100	−	0.773251i
$7$	−2.16452	+	1.52147i	−0.818111	+	0.575061i
$7$	−2.16452	+	1.52147i	−0.818111	+	0.575061i
$8$	−2.25904	+	1.70197i	−0.798693	+	0.601739i
$9$	0.693695	−	2.91870i	0.231232	−	0.972899i
$10$	4.02187	−	2.07865i	1.27183	−	0.657326i
$11$	3.12152	+	0.836408i	0.941173	+	0.252187i	0.696613	−	0.717447i	$-0.254690\pi$
$11$	3.12152	+	0.836408i	0.941173	+	0.252187i	0.244561	+	0.969634i	$0.421356\pi$
$12$	−1.57384	+	3.08594i	−0.454329	+	0.890834i
$13$	−3.07235	−	3.07235i	−0.852116	−	0.852116i	0.138277	−	0.990394i	$-0.455844\pi$
$13$	−3.07235	−	3.07235i	−0.852116	−	0.852116i	−0.990394	+	0.138277i	$0.955844\pi$
$14$	2.53094	−	2.75579i	0.676421	−	0.736515i
$15$	3.31251	−	4.44653i	0.855286	−	1.14809i
$16$	2.60701	−	3.03372i	0.651754	−	0.758431i
$17$	1.36326	+	2.36124i	0.330639	+	0.572684i	0.982637	−	0.185536i	$-0.0594023\pi$
$17$	1.36326	+	2.36124i	0.330639	+	0.572684i	−0.651998	+	0.758221i	$0.726069\pi$
$18$	−0.0768638	+	4.24194i	−0.0181170	+	0.999836i
$19$	−0.780112	+	0.209030i	−0.178970	+	0.0479549i	−0.347191	−	0.937794i	$-0.612864\pi$
$19$	−0.780112	+	0.209030i	−0.178970	+	0.0479549i	0.168221	+	0.985749i	$0.446198\pi$
$20$	−4.92875	+	4.08655i	−1.10210	+	0.913781i
$21$	1.30773	−	4.39202i	0.285369	−	0.958418i
$22$	−4.56526	−	0.212776i	−0.973318	−	0.0453640i
$23$	3.08514	−	5.34363i	0.643297	−	1.11422i	−0.341395	−	0.939920i	$-0.610899\pi$
$23$	3.08514	−	5.34363i	0.643297	−	1.11422i	0.984692	−	0.174303i	$-0.0557673\pi$
$24$	1.24235	−	4.73884i	0.253593	−	0.967311i
$25$	4.54500	−	2.62406i	0.909001	−	0.524812i
$26$	5.17266	+	3.31677i	1.01444	+	0.650472i
$27$	2.19152	+	4.71140i	0.421758	+	0.906709i
$28$	−2.66437	+	4.57177i	−0.503519	+	0.863984i
$29$	−4.52350	−	4.52350i	−0.839993	−	0.839993i	0.148865	−	0.988858i	$-0.452438\pi$
$29$	−4.52350	−	4.52350i	−0.839993	−	0.839993i	−0.988858	+	0.148865i	$0.952438\pi$
$30$	−3.23352	+	7.14374i	−0.590358	+	1.30426i
$31$	6.79094	−	3.92075i	1.21969	−	0.704188i	0.254838	−	0.966984i	$-0.417978\pi$
$31$	6.79094	−	3.92075i	1.21969	−	0.704188i	0.964852	+	0.262796i	$0.0846445\pi$
$32$	−2.68554	+	4.97874i	−0.474740	+	0.880126i
$33$	−5.14028	+	2.21537i	−0.894808	+	0.385647i
$34$	−2.59663	−	2.85050i	−0.445318	−	0.488857i
$35$	5.43248	−	6.49807i	0.918257	−	1.09837i
$36$	−1.17500	−	5.88382i	−0.195834	−	0.980637i
$37$	2.78693	−	0.746757i	0.458169	−	0.122766i	−0.0223502	−	0.999750i	$-0.507115\pi$
$37$	2.78693	−	0.746757i	0.458169	−	0.122766i	0.480519	+	0.876984i	$0.340448\pi$
$38$	1.01466	−	0.524411i	0.164599	−	0.0850707i
$39$	7.47453	+	0.876045i	1.19688	+	0.140279i
$40$	5.57522	−	7.13455i	0.881520	−	1.12807i
$41$		−	4.13241i		−	0.645373i	−0.946506	−	0.322687i	$-0.895414\pi$
$41$		−	4.13241i		−	0.645373i	0.946506	−	0.322687i	$-0.104586\pi$
$42$	−0.480211	+	6.46292i	−0.0740982	+	0.997251i
$43$	−0.294513	−	0.294513i	−0.0449128	−	0.0449128i	0.684294	−	0.729206i	$-0.260111\pi$
$43$	−0.294513	−	0.294513i	−0.0449128	−	0.0449128i	−0.729206	+	0.684294i	$0.760111\pi$
$44$	6.37157	−	1.08488i	0.960550	−	0.163552i
$45$	0.273248	+	9.59992i	0.0407334	+	1.43107i
$46$	−2.64845	+	8.31448i	−0.390493	+	1.22590i
$47$	2.24120	−	3.88187i	0.326912	−	0.566228i	−0.654985	−	0.755642i	$-0.727325\pi$
$47$	2.24120	−	3.88187i	0.326912	−	0.566228i	0.981897	+	0.189413i	$0.0606586\pi$
$48$	−0.285139	+	6.92233i	−0.0411563	+	0.999153i
$49$	2.37027	−	6.58649i	0.338611	−	0.940927i
$50$	−5.48676	+	4.99809i	−0.775946	+	0.706837i
$51$	−4.38827	−	1.74496i	−0.614480	−	0.244343i
$52$	−8.14823	−	3.02010i	−1.12996	−	0.418813i
$53$	−5.77126	−	1.54640i	−0.792744	−	0.212415i	−0.160348	−	0.987061i	$-0.551262\pi$
$53$	−5.77126	−	1.54640i	−0.792744	−	0.212415i	−0.632396	+	0.774646i	$0.717928\pi$
$54$	−4.45075	−	5.84729i	−0.605671	−	0.795715i
$55$	−10.3453			−1.39496
$56$	2.30024	−	7.12102i	0.307383	−	0.951586i
$57$	0.835696	−	1.12179i	0.110691	−	0.148585i
$58$	7.61583	+	4.88336i	1.00001	+	0.641217i
$59$	−1.56377	+	5.83606i	−0.203585	+	0.759791i	0.786291	+	0.617857i	$0.211999\pi$
$59$	−1.56377	+	5.83606i	−0.203585	+	0.759791i	−0.989876	+	0.141934i	$0.954668\pi$
$60$	2.30976	−	10.8463i	0.298189	−	1.40025i
$61$	−12.9350	+	3.46591i	−1.65615	+	0.443765i	−0.961326	−	0.275413i	$-0.911185\pi$
$61$	−12.9350	+	3.46591i	−1.65615	+	0.443765i	−0.694826	+	0.719178i	$0.744519\pi$
$62$	−8.19808	+	7.46793i	−1.04116	+	0.948428i
$63$	2.93919	+	7.37300i	0.370303	+	0.928911i
$64$	2.20656	−	7.68967i	0.275821	−	0.961209i
$65$	12.0459	+	6.95469i	1.49411	+	0.862623i
$66$	6.43263	−	4.61325i	0.791802	−	0.567851i
$67$	2.48018	+	0.664561i	0.303002	+	0.0811891i	0.407117	−	0.913376i	$-0.366534\pi$
$67$	2.48018	+	0.664561i	0.303002	+	0.0811891i	−0.104115	+	0.994565i	$0.533201\pi$
$68$	4.44840	+	3.15395i	0.539448	+	0.382473i
$69$	1.54558	+	10.5749i	0.186066	+	1.27307i
$70$	−5.54282	+	10.6184i	−0.662494	+	1.26914i
$71$	0.885678			0.105111			0.0525553	−	0.998618i	$-0.483263\pi$
$71$	0.885678			0.105111			0.0525553	+	0.998618i	$0.483263\pi$
$72$	3.40046	+	7.77412i	0.400748	+	0.916188i
$73$	−7.04045	−	12.1944i	−0.824022	−	1.42725i	−0.902664	−	0.430345i	$-0.858392\pi$
$73$	−7.04045	−	12.1944i	−0.824022	−	1.42725i	0.0786424	−	0.996903i	$-0.474941\pi$
$74$	−3.62484	+	1.87345i	−0.421379	+	0.217784i
$75$	−3.35876	+	8.44671i	−0.387836	+	0.975342i
$76$	−1.24345	+	1.03098i	−0.142633	+	0.118261i
$77$	−8.02915	+	2.93887i	−0.915007	+	0.334915i
$78$	−10.5913	+	1.04720i	−1.19923	+	0.118572i
$79$	−7.20211	+	12.4744i	−0.810301	+	1.40348i	0.102353	+	0.994748i	$0.467363\pi$
$79$	−7.20211	+	12.4744i	−0.810301	+	1.40348i	−0.912653	+	0.408734i	$0.865970\pi$
$80$	−5.54779	+	11.5409i	−0.620262	+	1.29031i
$81$	−8.03757	−	4.04937i	−0.893064	−	0.449930i
$82$	1.24811	+	5.70927i	0.137831	+	0.630483i
$83$	−5.44007	+	5.44007i	−0.597126	+	0.597126i	−0.939547	−	0.342421i	$-0.888753\pi$
$83$	−5.44007	+	5.44007i	−0.597126	+	0.597126i	0.342421	+	0.939547i	$0.388753\pi$
$84$	−1.28855	−	9.07412i	−0.140592	−	0.990068i
$85$	−6.17186	−	6.17186i	−0.669432	−	0.669432i
$86$	0.495846	+	0.317943i	0.0534685	+	0.0342846i
$87$	11.0049	+	1.28982i	1.17985	+	0.138283i
$88$	−8.47520	+	3.42326i	−0.903459	+	0.364921i
$89$	−2.90496	−	1.67718i	−0.307925	−	0.177780i	0.338073	−	0.941120i	$-0.390225\pi$
$89$	−2.90496	−	1.67718i	−0.307925	−	0.177780i	−0.645997	+	0.763340i	$0.723558\pi$
$90$	−3.27698	−	13.1806i	−0.345424	−	1.38935i
$91$	11.3246	+	1.97568i	1.18714	+	0.207107i
$92$	1.14784	−	12.2871i	0.119670	−	1.28102i
$93$	−5.01851	+	12.6207i	−0.520395	+	1.30871i
$94$	−1.92396	+	6.04004i	−0.198442	+	0.622982i
$95$	2.23906	−	1.29272i	0.229723	−	0.132631i
$96$	−1.69681	−	9.64991i	−0.173180	−	0.984890i
$97$			3.40029i			0.345247i	0.984988	+	0.172624i	$0.0552245\pi$
$97$			3.40029i			0.345247i	−0.984988	+	0.172624i	$0.944776\pi$
$98$	−1.28542	+	9.81569i	−0.129847	+	0.991534i
$99$	4.60660	−	8.53055i	0.462981	−	0.857353i
$100$	6.07086	−	8.56246i	0.607086	−	0.856246i
$101$	2.38352	−	8.89543i	0.237169	−	0.885128i	−0.739990	−	0.672618i	$-0.765170\pi$
$101$	2.38352	−	8.89543i	0.237169	−	0.885128i	0.977159	−	0.212510i	$-0.0681637\pi$
$102$	6.58980	+	1.08541i	0.652487	+	0.107472i
$103$	5.29432	−	9.17002i	0.521664	−	0.903549i	−0.478018	−	0.878350i	$-0.658645\pi$
$103$	5.29432	−	9.17002i	0.521664	−	0.903549i	0.999682	−	0.0251992i	$-0.00802200\pi$
$104$	12.1696	+	1.71151i	1.19333	+	0.167828i
$105$	−0.404729	+	14.6645i	−0.0394975	+	1.43111i
$106$	8.44055	+	0.393394i	0.819819	+	0.0382098i
$107$	−3.86844	−	14.4372i	−0.373976	−	1.39570i	−0.854835	−	0.518900i	$-0.826342\pi$
$107$	−3.86844	−	14.4372i	−0.373976	−	1.39570i	0.480859	−	0.876798i	$-0.340325\pi$
$108$	7.91515	+	6.73427i	0.761636	+	0.648005i
$109$	19.1852	+	5.14065i	1.83760	+	0.492385i	0.998656	−	0.0518264i	$-0.0165043\pi$
$109$	19.1852	+	5.14065i	1.83760	+	0.492385i	0.838948	+	0.544211i	$0.183171\pi$
$110$	14.2930	−	3.12460i	1.36278	−	0.297919i
$111$	−2.98550	+	4.00758i	−0.283372	+	0.380383i
$112$	−1.02722	+	10.5330i	−0.0970630	+	0.995278i
$113$		−	1.22170i		−	0.114928i	−0.998348	−	0.0574639i	$-0.981699\pi$
$113$		−	1.22170i		−	0.114928i	0.998348	−	0.0574639i	$-0.0183014\pi$
$114$	−0.815769	+	1.80226i	−0.0764038	+	0.168797i
$115$	−5.11239	+	19.0797i	−0.476733	+	1.77919i
$116$	−11.9968	−	4.44657i	−1.11388	−	0.412854i
$117$	−11.0985	+	6.83598i	−1.02606	+	0.631987i
$118$	0.397811	−	8.53533i	0.0366215	−	0.785740i
$119$	−6.54335	−	3.03678i	−0.599828	−	0.278381i
$120$	0.0847816	+	15.6827i	0.00773947	+	1.43163i
$121$	−0.481980	−	0.278271i	−0.0438164	−	0.0252974i
$122$	16.8239	−	8.69521i	1.52317	−	0.787227i
$123$	4.43758	+	5.61589i	0.400123	+	0.506368i
$124$	9.07081	−	12.7936i	0.814583	−	1.14890i
$125$	−0.561650	+	0.561650i	−0.0502355	+	0.0502355i
$126$	−6.28761	−	9.29871i	−0.560145	−	0.828395i
$127$	−11.5296			−1.02308			−0.511542	−	0.859258i	$-0.670926\pi$
$127$	−11.5296			−1.02308			−0.511542	+	0.859258i	$0.670926\pi$
$128$	−0.726042	+	11.2904i	−0.0641737	+	0.997939i
$129$	0.716502	+	0.0839769i	0.0630844	+	0.00739375i
$130$	−18.7429	−	5.97028i	−1.64386	−	0.523628i
$131$	−2.68990	−	10.0388i	−0.235018	−	0.877098i	−0.978141	−	0.207943i	$-0.933323\pi$
$131$	−2.68990	−	10.0388i	−0.235018	−	0.877098i	0.743123	−	0.669154i	$-0.233344\pi$
$132$	−7.49388	+	8.31644i	−0.652259	+	0.723853i
$133$	1.37053	−	1.63937i	0.118840	−	0.142151i
$134$	−3.62729	−	0.169059i	−0.313350	−	0.0146045i
$135$	−10.6802	−	12.7527i	−0.919206	−	1.09758i
$136$	−7.09843	−	3.01390i	−0.608686	−	0.258440i
$137$	4.46242	+	7.72914i	0.381250	+	0.660345i	0.991241	−	0.132063i	$-0.0421602\pi$
$137$	4.46242	+	7.72914i	0.381250	+	0.660345i	−0.609991	+	0.792408i	$0.708827\pi$
$138$	−5.32929	−	14.1433i	−0.453659	−	1.20396i
$139$	12.7852	−	12.7852i	1.08443	−	1.08443i	0.0883379	−	0.996091i	$-0.471844\pi$
$139$	12.7852	−	12.7852i	1.08443	−	1.08443i	0.996091	−	0.0883379i	$-0.0281555\pi$
$140$	4.45080	−	16.3443i	0.376161	−	1.38135i
$141$	1.12278	+	7.68211i	0.0945552	+	0.646951i
$142$	−1.22364	+	0.267502i	−0.102686	+	0.0224482i
$143$	−7.02066	−	12.1601i	−0.587097	−	1.01688i
$144$	−7.04604	−	9.71356i	−0.587170	−	0.809463i
$145$	17.7354	+	10.2396i	1.47285	+	0.850350i
$146$	13.4101	+	14.7212i	1.10982	+	1.21833i
$147$	3.85172	+	11.4963i	0.317685	+	0.948196i
$148$	4.44219	−	3.68314i	0.365146	−	0.302752i
$149$	−3.65614	−	13.6449i	−0.299523	−	1.11783i	−0.937559	−	0.347827i	$-0.886920\pi$
$149$	−3.65614	−	13.6449i	−0.299523	−	1.11783i	0.638036	−	0.770007i	$-0.279747\pi$
$150$	2.08925	−	12.6843i	0.170586	−	1.03567i
$151$	−3.47676	+	2.00731i	−0.282935	+	0.163352i	−0.634751	−	0.772717i	$-0.718897\pi$
$151$	−3.47676	+	2.00731i	−0.282935	+	0.163352i	0.351816	+	0.936069i	$0.385564\pi$
$152$	1.40654	−	1.79994i	0.114086	−	0.145994i
$153$	7.83742	−	2.34097i	0.633618	−	0.189256i
$154$	10.2053	−	6.48534i	0.822369	−	0.522604i
$155$	−17.7503	+	17.7503i	−1.42574	+	1.42574i
$156$	14.3165	−	4.64569i	1.14624	−	0.371953i
$157$	3.30659	−	12.3404i	0.263895	−	0.984869i	−0.699028	−	0.715094i	$-0.746384\pi$
$157$	3.30659	−	12.3404i	0.263895	−	0.984869i	0.962923	−	0.269775i	$-0.0869494\pi$
$158$	6.18268	−	19.4097i	0.491867	−	1.54416i
$159$	9.50368	−	4.09592i	0.753691	−	0.324828i
$160$	4.17905	−	17.6203i	0.330383	−	1.39301i
$161$	1.45230	+	16.2603i	0.114458	+	1.28149i
$162$	12.3276	+	3.16696i	0.968550	+	0.248820i
$163$	−3.12082	−	11.6471i	−0.244441	−	0.912268i	−0.973663	−	0.227991i	$-0.926784\pi$
$163$	−3.12082	−	11.6471i	−0.244441	−	0.912268i	0.729222	−	0.684277i	$-0.239882\pi$
$164$	−3.44875	−	7.51088i	−0.269302	−	0.586501i
$165$	14.0592	−	11.1093i	1.09451	−	0.864860i
$166$	5.87286	−	9.15899i	0.455822	−	0.710876i
$167$			12.0552i			0.932862i	0.884557	+	0.466431i	$0.154460\pi$
$167$			12.0552i			0.932862i	−0.884557	+	0.466431i	$0.845540\pi$
$168$	4.52090	+	12.1475i	0.348795	+	0.937199i
$169$			5.87867i			0.452205i
$170$	10.3910	+	6.66286i	0.796956	+	0.511018i
$171$	0.0689364	+	2.42191i	0.00527170	+	0.185208i
$172$	−0.781082	−	0.289504i	−0.0595570	−	0.0220745i
$173$	0.782328	+	2.91969i	0.0594793	+	0.221980i	0.989268	−	0.146115i	$-0.0466769\pi$
$173$	0.782328	+	2.91969i	0.0594793	+	0.221980i	−0.929788	+	0.368095i	$0.880010\pi$
$174$	−15.5938	+	1.54182i	−1.18216	+	0.116885i
$175$	−5.84532	+	12.5949i	−0.441865	+	0.952085i
$176$	10.6753	−	7.28929i	0.804679	−	0.549451i
$177$	−4.14191	−	9.61039i	−0.311325	−	0.722361i
$178$	4.52000	+	1.43978i	0.338789	+	0.107916i
$179$	−0.506593	+	1.89063i	−0.0378645	+	0.141312i	−0.982270	−	0.187470i	$-0.939971\pi$
$179$	−0.506593	+	1.89063i	−0.0378645	+	0.141312i	0.944406	+	0.328782i	$0.106638\pi$
$180$	8.50836	+	17.2203i	0.634176	+	1.28353i
$181$	0.910666	−	0.910666i	0.0676893	−	0.0676893i	−0.672452	−	0.740141i	$-0.734759\pi$
$181$	0.910666	−	0.910666i	0.0676893	−	0.0676893i	0.740141	+	0.672452i	$0.234759\pi$
$182$	−16.2427	+	0.690820i	−1.20399	+	0.0512070i
$183$	13.8566	−	18.6003i	1.02431	−	1.37498i
$184$	2.12524	+	17.3223i	0.156675	+	1.27702i
$185$	−7.99900	+	4.61822i	−0.588098	+	0.339538i
$186$	3.12166	−	18.9523i	0.228891	−	1.38965i
$187$	2.28049	+	8.51089i	0.166766	+	0.622378i
$188$	0.833843	−	8.92592i	0.0608142	−	0.650990i
$189$	−11.9118	−	6.86358i	−0.866457	−	0.499252i
$190$	−2.70301	+	2.46227i	−0.196097	+	0.178632i
$191$	−15.6679	−	9.04587i	−1.13369	−	0.654536i	−0.188830	−	0.982010i	$-0.560469\pi$
$191$	−15.6679	−	9.04587i	−1.13369	−	0.654536i	−0.944860	+	0.327474i	$0.893803\pi$
$192$	5.25886	+	12.8197i	0.379525	+	0.925181i
$193$	−0.442930	−	0.767177i	−0.0318828	−	0.0552226i	0.849644	−	0.527357i	$-0.176817\pi$
$193$	−0.442930	−	0.767177i	−0.0318828	−	0.0552226i	−0.881527	+	0.472134i	$0.843484\pi$
$194$	−1.02699	−	4.69779i	−0.0737337	−	0.337282i
$195$	−23.8385	+	3.48412i	−1.70711	+	0.249503i
$196$	−1.18872	−	13.9494i	−0.0849088	−	0.996389i
$197$	13.0264	−	13.0264i	0.928090	−	0.928090i	−0.0694925	−	0.997582i	$-0.522138\pi$
$197$	13.0264	−	13.0264i	0.928090	−	0.928090i	0.997582	+	0.0694925i	$0.0221380\pi$
$198$	−3.78793	+	13.1770i	−0.269196	+	0.936450i
$199$	5.32536	+	9.22380i	0.377505	+	0.653858i	0.990699	−	0.136075i	$-0.0434488\pi$
$199$	5.32536	+	9.22380i	0.377505	+	0.653858i	−0.613194	+	0.789933i	$0.710115\pi$
$200$	−5.80128	+	13.6633i	−0.410213	+	0.966145i
$201$	−4.08417	+	1.76021i	−0.288075	+	0.124155i
$202$	−0.606350	+	13.0097i	−0.0426627	+	0.915358i
$203$	16.6735	+	2.90884i	1.17025	+	0.204160i
$204$	−9.43219	+	0.490726i	−0.660386	+	0.0343577i
$205$	3.42390	+	12.7782i	0.239136	+	0.892466i
$206$	−4.54492	+	14.2682i	−0.316660	+	0.994113i
$207$	−13.4563	−	12.7114i	−0.935276	−	0.883507i
$208$	−17.3303	+	1.31100i	−1.20164	+	0.0909014i
$209$	−2.60997			−0.180535
$210$	−3.86995	−	20.3825i	−0.267052	−	1.40652i
$211$	−4.41753	+	4.41753i	−0.304116	+	0.304116i	−0.842622	−	0.538506i	$-0.818989\pi$
$211$	−4.41753	+	4.41753i	−0.304116	+	0.304116i	0.538506	+	0.842622i	$0.318989\pi$
$212$	−11.7802	+	2.00580i	−0.809064	+	0.137759i
$213$	−1.20363	+	0.951085i	−0.0824710	+	0.0651672i
$214$	9.70506	+	18.7779i	0.663424	+	1.28363i
$215$	1.15471	+	0.666670i	0.0787504	+	0.0454665i
$216$	−12.9694	−	6.91335i	−0.882457	−	0.470394i
$217$	−8.73382	+	18.8187i	−0.592890	+	1.27750i
$218$	−28.0586	−	1.30774i	−1.90037	−	0.0885714i
$219$	22.6628	+	9.01168i	1.53141	+	0.608953i
$220$	−18.8032	+	8.63381i	−1.26771	+	0.582091i
$221$	3.06613	−	11.4430i	0.206250	−	0.769737i
$222$	2.91432	−	6.43853i	0.195596	−	0.432126i
$223$		−	5.89677i		−	0.394877i	−0.980315	−	0.197438i	$-0.936738\pi$
$223$		−	5.89677i		−	0.394877i	0.980315	−	0.197438i	$-0.0632623\pi$
$224$	−1.76211	−	14.8625i	−0.117736	−	0.993045i
$225$	−4.50599	−	15.0858i	−0.300399	−	1.00572i
$226$	0.368990	+	1.68788i	0.0245449	+	0.112276i
$227$	13.4813	+	3.61231i	0.894788	+	0.239758i	0.676776	−	0.736189i	$-0.263376\pi$
$227$	13.4813	+	3.61231i	0.894788	+	0.239758i	0.218011	+	0.975946i	$0.430043\pi$
$228$	0.582718	−	2.73636i	0.0385914	−	0.181220i
$229$	5.26902	+	19.6643i	0.348187	+	1.29945i	0.888845	+	0.458209i	$0.151509\pi$
$229$	5.26902	+	19.6643i	0.348187	+	1.29945i	−0.540658	+	0.841243i	$0.681825\pi$
$230$	1.30055	−	27.9043i	0.0857559	−	1.83996i
$231$	7.75561	−	12.6160i	0.510282	−	0.830071i
$232$	17.9177	+	2.51991i	1.17635	+	0.165440i
$233$	13.9815	−	24.2166i	0.915955	−	1.58648i	0.110459	−	0.993881i	$-0.464768\pi$
$233$	13.9815	−	24.2166i	0.915955	−	1.58648i	0.805496	−	0.592601i	$-0.201899\pi$
$234$	13.2689	−	12.7966i	0.867414	−	0.836539i
$235$	−3.71388	+	13.8604i	−0.242267	+	0.904153i
$236$	2.02832	+	11.9124i	0.132032	+	0.775433i
$237$	−3.60807	−	24.6866i	−0.234369	−	1.60357i
$238$	9.95739	+	2.21928i	0.645442	+	0.143855i
$239$			19.6575i			1.27154i	0.771879	+	0.635770i	$0.219317\pi$
$239$			19.6575i			1.27154i	−0.771879	+	0.635770i	$0.780683\pi$
$240$	−4.85379	−	21.6414i	−0.313311	−	1.39695i
$241$	6.85775	−	3.95932i	0.441747	−	0.255042i	−0.262592	−	0.964907i	$-0.584577\pi$
$241$	6.85775	−	3.95932i	0.441747	−	0.255042i	0.704338	+	0.709865i	$0.251244\pi$
$242$	0.749943	+	0.238883i	0.0482082	+	0.0153560i
$243$	15.2714	−	3.12810i	0.979659	−	0.200668i
$244$	−20.6175	+	17.0945i	−1.31990	+	1.09436i
$245$	−1.87210	+	22.3305i	−0.119604	+	1.42665i
$246$	−7.82707	−	6.41854i	−0.499035	−	0.409231i
$247$	3.03899	+	1.75456i	0.193366	+	0.111640i
$248$	−8.66802	+	20.4152i	−0.550420	+	1.29636i
$249$	1.55117	−	13.2348i	0.0983016	−	0.838722i
$250$	0.606332	−	0.945603i	0.0383478	−	0.0598052i
$251$	1.64206	+	1.64206i	0.103646	+	0.103646i	0.757028	−	0.653382i	$-0.226651\pi$
$251$	1.64206	+	1.64206i	0.103646	+	0.103646i	−0.653382	+	0.757028i	$0.726651\pi$
$252$	11.4954	+	10.9479i	0.724139	+	0.689654i
$253$	14.0998	−	14.0998i	0.886446	−	0.886446i
$254$	15.9291	−	3.48228i	0.999480	−	0.218498i
$255$	15.0151	+	1.75983i	0.940284	+	0.110205i
$256$	−2.40695	−	15.8179i	−0.150434	−	0.988620i
$257$	−4.29474	+	7.43871i	−0.267898	+	0.464014i	−0.968319	−	0.249717i	$-0.919663\pi$
$257$	−4.29474	+	7.43871i	−0.267898	+	0.464014i	0.700420	+	0.713730i	$0.252996\pi$
$258$	−1.01527	+	0.100384i	−0.0632080	+	0.00624964i
$259$	−4.89620	+	5.85660i	−0.304235	+	0.363911i
$260$	27.6982	+	2.58751i	1.71777	+	0.160471i
$261$	−16.3406	+	10.0648i	−1.01146	+	0.622995i
$262$	6.74836	+	13.0571i	0.416915	+	0.806669i
$263$	7.68694	+	13.3142i	0.473997	+	0.820987i	0.999557	−	0.0297699i	$-0.00947747\pi$
$263$	7.68694	+	13.3142i	0.473997	+	0.820987i	−0.525560	+	0.850757i	$0.676144\pi$
$264$	7.84162	−	13.7533i	0.482618	−	0.846454i
$265$	19.1271			1.17497
$266$	−1.39837	+	2.67887i	−0.0857396	+	0.164252i
$267$	5.74883	−	0.840222i	0.351823	−	0.0514208i
$268$	5.06248	−	0.861983i	0.309240	−	0.0526540i
$269$	−22.1750	−	5.94177i	−1.35203	−	0.362276i	−0.491149	−	0.871076i	$-0.663423\pi$
$269$	−22.1750	−	5.94177i	−1.35203	−	0.362276i	−0.860885	+	0.508799i	$0.830089\pi$
$270$	18.6073	+	14.3933i	1.13241	+	0.875945i
$271$	−20.9133	−	12.0743i	−1.27039	−	0.733462i	−0.295331	−	0.955395i	$-0.595430\pi$
$271$	−20.9133	−	12.0743i	−1.27039	−	0.733462i	−0.975062	+	0.221933i	$0.928763\pi$
$272$	10.7174	+	2.02002i	0.649837	+	0.122482i
$273$	−17.5116	+	9.47603i	−1.05985	+	0.573516i
$274$	−8.49965	−	9.33068i	−0.513483	−	0.563687i
$275$	16.3821	−	4.38957i	0.987878	−	0.264701i
$276$	11.6346	+	17.9306i	0.700319	+	1.07929i
$277$	−1.44265	+	5.38405i	−0.0866805	+	0.323496i	−0.995627	−	0.0934164i	$-0.970221\pi$
$277$	−1.44265	+	5.38405i	−0.0866805	+	0.323496i	0.908947	+	0.416913i	$0.136888\pi$
$278$	−13.8023	+	21.5254i	−0.827810	+	1.29101i
$279$	−6.73264	−	22.5405i	−0.403073	−	1.34947i
$280$	−1.21267	+	23.9254i	−0.0724709	+	1.42982i
$281$	−8.08487			−0.482303			−0.241151	−	0.970488i	$-0.577525\pi$
$281$	−8.08487			−0.482303			−0.241151	+	0.970488i	$0.577525\pi$
$282$	−3.87145	−	10.2744i	−0.230541	−	0.611830i
$283$	−26.5652	−	7.11812i	−1.57914	−	0.423128i	−0.640477	−	0.767977i	$-0.721264\pi$
$283$	−26.5652	−	7.11812i	−1.57914	−	0.423128i	−0.938658	+	0.344849i	$0.887930\pi$
$284$	1.60977	−	0.739153i	0.0955222	−	0.0438606i
$285$	−1.65467	+	4.16121i	−0.0980140	+	0.246489i
$286$	13.3724	+	14.6798i	0.790725	+	0.868035i
$287$	6.28732	+	8.94467i	0.371129	+	0.527987i
$288$	12.6685	+	11.2920i	0.746498	+	0.665387i
$289$	4.78304	−	8.28447i	0.281355	−	0.487322i
$290$	−27.5957	−	8.79019i	−1.62047	−	0.516178i
$291$	−3.65140	−	4.62096i	−0.214049	−	0.270885i
$292$	−22.9734	−	16.2883i	−1.34442	−	0.953203i
$293$	−12.9861	−	12.9861i	−0.758657	−	0.758657i	0.217421	−	0.976078i	$-0.430236\pi$
$293$	−12.9861	−	12.9861i	−0.758657	−	0.758657i	−0.976078	+	0.217421i	$0.930236\pi$
$294$	−8.79370	−	14.7197i	−0.512859	−	0.858473i
$295$		−	19.3419i		−	1.12613i
$296$	−5.02485	+	6.43025i	−0.292063	+	0.373750i
$297$	2.90021	+	16.5397i	0.168287	+	0.959732i
$298$	9.17245	+	17.7473i	0.531346	+	1.02808i
$299$	−25.8961	+	6.93885i	−1.49761	+	0.401284i
$300$	0.944570	+	18.1555i	0.0545348	+	1.04821i
$301$	1.08557	+	0.189387i	0.0625712	+	0.0109161i
$302$	4.19717	−	3.82336i	0.241520	−	0.220009i
$303$	6.31317	+	14.6483i	0.362682	+	0.841524i
$304$	−1.39962	+	2.91159i	−0.0802739	+	0.166991i
$305$	37.1257	−	21.4345i	2.12581	−	1.22734i
$306$	−10.1210	+	5.60138i	−0.578580	+	0.320210i
$307$	10.1788	+	10.1788i	0.580933	+	0.580933i	0.935160	−	0.354227i	$-0.115256\pi$
$307$	10.1788	+	10.1788i	0.580933	+	0.580933i	−0.354227	+	0.935160i	$0.615256\pi$
$308$	−12.1408	+	12.0424i	−0.691784	+	0.686178i
$309$	2.65231	+	18.1472i	0.150885	+	1.03236i
$310$	19.1625	−	29.8847i	1.08835	−	1.69734i
$311$	4.06425	−	2.34649i	0.230462	−	0.133057i	−0.380323	−	0.924854i	$-0.624187\pi$
$311$	4.06425	−	2.34649i	0.230462	−	0.133057i	0.610785	+	0.791796i	$0.290854\pi$
$312$	−18.3763	+	10.7424i	−1.04035	+	0.608170i
$313$	10.3423	−	17.9133i	0.584579	−	1.01252i	−0.410349	−	0.911929i	$-0.634593\pi$
$313$	10.3423	−	17.9133i	0.584579	−	1.01252i	0.994928	−	0.100592i	$-0.0320736\pi$
$314$	−0.841172	+	18.0480i	−0.0474701	+	1.01851i
$315$	−15.1974	−	20.3635i	−0.856277	−	1.14735i
$316$	−2.67956	+	28.6836i	−0.150737	+	1.61358i
$317$	−14.0000	+	3.75128i	−0.786316	+	0.210693i	−0.629568	−	0.776946i	$-0.716768\pi$
$317$	−14.0000	+	3.75128i	−0.786316	+	0.210693i	−0.156749	+	0.987639i	$0.550101\pi$
$318$	−11.8930	+	8.52926i	−0.666929	+	0.478297i
$319$	−10.3367	−	17.9037i	−0.578744	−	1.00241i
$320$	−0.451840	+	25.6062i	−0.0252586	+	1.43143i
$321$	20.7606	+	15.4659i	1.15874	+	0.863221i
$322$	−6.91759	−	22.0264i	−0.385502	−	1.22748i
$323$	−1.55707	−	1.55707i	−0.0866375	−	0.0866375i
$324$	−17.9882	−	0.652104i	−0.999344	−	0.0362280i
$325$	−22.0259	−	5.90181i	−1.22178	−	0.327374i
$326$	7.82944	+	15.1488i	0.433633	+	0.839016i
$327$	−31.5927	+	13.6159i	−1.74708	+	0.752960i
$328$	7.03325	+	9.33529i	0.388346	+	0.515455i
$329$	1.05502	+	11.8123i	0.0581653	+	0.651232i
$330$	−16.0686	+	19.5948i	−0.884547	+	1.07866i
$331$	−25.8027	+	6.91380i	−1.41824	+	0.380017i	−0.884860	−	0.465857i	$-0.845746\pi$
$331$	−25.8027	+	6.91380i	−1.41824	+	0.380017i	−0.533383	+	0.845874i	$0.679079\pi$
$332$	−5.34756	+	14.4277i	−0.293485	+	0.791824i
$333$	−0.246274	−	8.65223i	−0.0134957	−	0.474139i
$334$	−3.64105	−	16.6553i	−0.199229	−	0.911340i
$335$	−8.21979			−0.449095
$336$	−9.91492	−	15.4173i	−0.540903	−	0.841085i
$337$	−15.2376			−0.830045			−0.415023	−	0.909811i	$-0.636226\pi$
$337$	−15.2376			−0.830045			−0.415023	+	0.909811i	$0.636226\pi$
$338$	−1.77554	−	8.12188i	−0.0965764	−	0.441772i
$339$	1.31192	+	1.66027i	0.0712537	+	0.0901737i
$340$	−16.3685	−	6.06690i	−0.887706	−	0.329024i
$341$	24.4774	−	6.55870i	1.32553	−	0.355174i
$342$	−0.826733	−	3.32526i	−0.0447046	−	0.179809i
$343$	4.89062	+	17.8629i	0.264069	+	0.964504i
$344$	1.16657	+	0.164064i	0.0628973	+	0.00884575i
$345$	−13.5410	−	31.4190i	−0.729025	−	1.69154i
$346$	−1.96269	−	3.79751i	−0.105515	−	0.204155i
$347$	6.97570	+	1.86913i	0.374475	+	0.100340i	0.441147	−	0.897435i	$-0.354572\pi$
$347$	6.97570	+	1.86913i	0.374475	+	0.100340i	−0.0666724	+	0.997775i	$0.521238\pi$
$348$	21.0785	−	6.83997i	1.12993	−	0.366661i
$349$	2.90538	+	2.90538i	0.155522	+	0.155522i	0.780579	−	0.625057i	$-0.214924\pi$
$349$	2.90538	+	2.90538i	0.155522	+	0.155522i	−0.625057	+	0.780579i	$0.714924\pi$
$350$	4.27177	−	19.1664i	0.228336	−	1.02449i
$351$	7.74195	−	21.2082i	0.413235	−	1.13201i
$352$	−12.5472	+	13.2950i	−0.668769	+	0.708628i
$353$	4.61030	+	7.98528i	0.245382	+	0.425014i	0.962239	−	0.272206i	$-0.0877534\pi$
$353$	4.61030	+	7.98528i	0.245382	+	0.425014i	−0.716857	+	0.697220i	$0.754420\pi$
$354$	8.62503	+	12.0266i	0.458415	+	0.639206i
$355$	−2.73868	+	0.733828i	−0.145354	+	0.0389475i
$356$	−6.67963	−	0.623998i	−0.354019	−	0.0330718i
$357$	12.1534	−	2.89962i	0.643225	−	0.153464i
$358$	0.128873	−	2.76507i	0.00681117	−	0.146139i
$359$	−18.4867	+	32.0198i	−0.975689	+	1.68994i	−0.298045	+	0.954552i	$0.596335\pi$
$359$	−18.4867	+	32.0198i	−0.975689	+	1.68994i	−0.677644	+	0.735390i	$0.736999\pi$
$360$	−16.9561	−	21.2216i	−0.893665	−	1.11848i
$361$	−15.8896	+	9.17387i	−0.836295	+	0.482835i
$362$	−0.983114	+	1.53321i	−0.0516713	+	0.0805838i
$363$	0.953827	−	0.139407i	0.0500629	−	0.00731696i
$364$	22.2320	−	5.86020i	1.16527	−	0.307158i
$365$	31.8741	+	31.8741i	1.66836	+	1.66836i
$366$	−13.5262	+	29.8831i	−0.707025	+	1.56201i
$367$	−4.05638	+	2.34195i	−0.211741	+	0.122249i	−0.602120	−	0.798405i	$-0.705677\pi$
$367$	−4.05638	+	2.34195i	−0.211741	+	0.122249i	0.390379	+	0.920654i	$0.372344\pi$
$368$	−8.16807	−	23.2904i	−0.425790	−	1.21410i
$369$	−12.0612	−	2.86663i	−0.627883	−	0.149231i
$370$	9.65645	−	8.79641i	0.502015	−	0.457303i
$371$	14.8448	−	5.43357i	0.770704	−	0.282097i
$372$	1.41133	+	27.1271i	0.0731743	+	1.40647i
$373$	12.0547	−	3.23006i	0.624171	−	0.167246i	0.0671475	−	0.997743i	$-0.478610\pi$
$373$	12.0547	−	3.23006i	0.624171	−	0.167246i	0.557023	+	0.830497i	$0.311944\pi$
$374$	−5.72123	−	11.0697i	−0.295838	−	0.572403i
$375$	0.160148	−	1.36640i	0.00827001	−	0.0705608i
$376$	1.54387	+	12.5838i	0.0796193	+	0.648958i
$377$			27.7955i			1.43154i
$378$	18.5302	+	5.88489i	0.953090	+	0.302686i
$379$	−11.7730	−	11.7730i	−0.604741	−	0.604741i	0.336826	−	0.941567i	$-0.390647\pi$
$379$	−11.7730	−	11.7730i	−0.604741	−	0.604741i	−0.941567	+	0.336826i	$0.890647\pi$
$380$	2.99076	−	4.21823i	0.153423	−	0.216391i
$381$	15.6685	−	12.3810i	0.802724	−	0.634299i
$382$	24.3787	+	7.76546i	1.24732	+	0.397315i
$383$	−1.34464	+	2.32898i	−0.0687077	+	0.119005i	−0.898333	−	0.439316i	$-0.855221\pi$
$383$	−1.34464	+	2.32898i	−0.0687077	+	0.119005i	0.829625	+	0.558321i	$0.188554\pi$
$384$	−11.1375	−	16.1232i	−0.568358	−	0.822781i
$385$	22.3926	−	15.7401i	1.14123	−	0.802189i
$386$	0.843656	+	0.926142i	0.0429410	+	0.0471394i
$387$	−1.06390	+	0.655291i	−0.0540808	+	0.0333103i
$388$	2.83775	+	6.18022i	0.144065	+	0.313753i
$389$	−4.74811	−	1.27225i	−0.240739	−	0.0645058i	0.136432	−	0.990649i	$-0.456436\pi$
$389$	−4.74811	−	1.27225i	−0.240739	−	0.0645058i	−0.377171	+	0.926144i	$0.623103\pi$
$390$	31.8826	−	12.0136i	1.61444	−	0.608330i
$391$	16.8234			0.850797
$392$	5.85548	+	18.9133i	0.295746	+	0.955267i
$393$	14.4357	+	10.7541i	0.728187	+	0.542473i
$394$	−14.0627	+	21.9314i	−0.708467	+	1.10489i
$395$	11.9346	−	44.5406i	0.600495	−	2.24108i
$396$	1.25349	−	19.3492i	0.0629901	−	0.972336i
$397$	−16.8517	+	4.51541i	−0.845765	+	0.226622i	−0.655579	−	0.755126i	$-0.727576\pi$
$397$	−16.8517	+	4.51541i	−0.845765	+	0.226622i	−0.190185	+	0.981748i	$0.560909\pi$
$398$	−10.1433	−	11.1350i	−0.508438	−	0.558149i
$399$	−0.102107	+	3.69962i	−0.00511174	+	0.185213i
$400$	3.88822	−	20.6292i	0.194411	−	1.03146i
$401$	8.64169	+	4.98928i	0.431546	+	0.249153i	0.700005	−	0.714138i	$-0.253181\pi$
$401$	8.64169	+	4.98928i	0.431546	+	0.249153i	−0.268459	+	0.963291i	$0.586514\pi$
$402$	5.11099	−	3.66542i	0.254913	−	0.182814i
$403$	−32.9101	−	8.81823i	−1.63937	−	0.439267i
$404$	−3.09160	−	18.1571i	−0.153813	−	0.903351i
$405$	28.2088	+	5.86189i	1.40171	+	0.291279i
$406$	−23.9145	+	1.01711i	−1.18686	+	0.0504784i
$407$	9.32406			0.462176
$408$	12.8832	−	3.52679i	0.637812	−	0.174602i
$409$	−12.3745	−	21.4332i	−0.611878	−	1.05980i	−0.990924	−	0.134426i	$-0.957081\pi$
$409$	−12.3745	−	21.4332i	−0.611878	−	1.05980i	0.379045	−	0.925378i	$-0.376252\pi$
$410$	−8.58981	−	16.6200i	−0.424220	−	0.820804i
$411$	−14.3643	−	5.71184i	−0.708539	−	0.281744i
$412$	1.96976	−	21.0855i	0.0970433	−	1.03881i
$413$	−5.49458	−	15.0115i	−0.270370	−	0.738667i
$414$	22.4302	+	13.4977i	1.10239	+	0.663378i
$415$	12.3144	−	21.3291i	0.604488	−	1.04700i
$416$	23.5474	−	7.04554i	1.15450	−	0.345436i
$417$	−3.64556	+	31.1044i	−0.178524	+	1.52319i
$418$	3.60590	−	0.788290i	0.176370	−	0.0385565i
$419$	15.2681	−	15.2681i	0.745898	−	0.745898i	−0.227808	−	0.973706i	$-0.573156\pi$
$419$	15.2681	−	15.2681i	0.745898	−	0.745898i	0.973706	+	0.227808i	$0.0731559\pi$
$420$	11.5028	+	26.9913i	0.561278	+	1.31704i
$421$	23.1878	+	23.1878i	1.13010	+	1.13010i	0.990159	+	0.139944i	$0.0446923\pi$
$421$	23.1878	+	23.1878i	1.13010	+	1.13010i	0.139944	+	0.990159i	$0.455308\pi$
$422$	4.76897	−	7.43743i	0.232150	−	0.362048i
$423$	−9.77528	−	9.23420i	−0.475290	−	0.448982i
$424$	15.6695	−	6.32914i	0.760977	−	0.307370i
$425$	12.3921	+	7.15456i	0.601103	+	0.347047i
$426$	1.37565	−	1.67754i	0.0666507	−	0.0812769i
$427$	22.7247	−	27.1822i	1.09972	−	1.31544i
$428$	−19.0798	−	23.0120i	−0.922259	−	1.11233i
$429$	22.5991	+	8.98635i	1.09110	+	0.433865i
$430$	−1.79668	−	0.572305i	−0.0866436	−	0.0275990i
$431$	−3.10766	+	1.79421i	−0.149691	+	0.0864240i	−0.572975	−	0.819573i	$-0.694211\pi$
$431$	−3.10766	+	1.79421i	−0.149691	+	0.0864240i	0.423284	+	0.905997i	$0.360877\pi$
$432$	20.0064	+	5.63422i	0.962558	+	0.271077i
$433$			11.1993i			0.538203i	0.963112	+	0.269102i	$0.0867267\pi$
$433$			11.1993i			0.538203i	−0.963112	+	0.269102i	$0.913273\pi$
$434$	6.38269	−	28.6376i	0.306379	−	1.37465i
$435$	−35.0980	+	5.12976i	−1.68282	+	0.245953i
$436$	39.1603	−	6.66778i	1.87544	−	0.319329i
$437$	−1.28978	+	4.81352i	−0.0616985	+	0.230262i
$438$	−34.0324	−	5.60553i	−1.62613	−	0.267843i
$439$	11.5183	−	19.9503i	0.549739	−	0.952176i	−0.448553	−	0.893756i	$-0.648061\pi$
$439$	11.5183	−	19.9503i	0.549739	−	0.952176i	0.998292	−	0.0584197i	$-0.0186062\pi$
$440$	23.3706	−	17.6075i	1.11415	−	0.839404i
$441$	−17.5797	−	11.4871i	−0.837129	−	0.547006i
$442$	−0.780001	+	16.7355i	−0.0371009	+	0.796026i
$443$	−5.37329	−	20.0534i	−0.255293	−	0.952765i	−0.967927	−	0.251230i	$-0.919165\pi$
$443$	−5.37329	−	20.0534i	−0.255293	−	0.952765i	0.712635	−	0.701535i	$-0.247502\pi$
$444$	−2.08175	+	9.77558i	−0.0987954	+	0.463929i
$445$	10.3723	+	2.77925i	0.491694	+	0.131749i
$446$	1.78100	+	8.14689i	0.0843330	+	0.385766i
$447$	19.6212	+	14.6171i	0.928052	+	0.691366i
$448$	6.92344	+	20.0017i	0.327102	+	0.944989i
$449$		−	17.1495i		−	0.809335i	−0.914464	−	0.404668i	$-0.867387\pi$
$449$		−	17.1495i		−	0.809335i	0.914464	−	0.404668i	$-0.132613\pi$
$450$	10.7818	+	19.4813i	0.508257	+	0.918360i
$451$	3.45638	−	12.8994i	0.162755	−	0.607408i
$452$	−1.01958	−	2.22051i	−0.0479571	−	0.104444i
$453$	2.56933	−	6.46143i	0.120718	−	0.303584i
$454$	−19.7166	−	0.918945i	−0.925348	−	0.0431282i
$455$	−36.6548	+	3.27386i	−1.71841	+	0.153481i
$456$	0.0213891	+	3.95651i	0.00100164	+	0.185281i
$457$	−5.58100	−	3.22219i	−0.261068	−	0.150728i	0.363753	−	0.931495i	$-0.381495\pi$
$457$	−5.58100	−	3.22219i	−0.261068	−	0.150728i	−0.624822	+	0.780767i	$0.714828\pi$
$458$	−13.2188	−	25.5765i	−0.617674	−	1.19511i
$459$	−8.13711	+	11.5976i	−0.379808	+	0.541328i
$460$	6.63113	+	38.9450i	0.309178	+	1.81582i
$461$	6.96625	−	6.96625i	0.324450	−	0.324450i	−0.526021	−	0.850472i	$-0.676317\pi$
$461$	6.96625	−	6.96625i	0.324450	−	0.324450i	0.850472	+	0.526021i	$0.176317\pi$
$462$	−6.90463	+	19.7725i	−0.321233	+	0.919899i
$463$	24.5781			1.14224			0.571120	−	0.820866i	$-0.306509\pi$
$463$	24.5781			1.14224			0.571120	+	0.820866i	$0.306509\pi$
$464$	−25.5159	+	1.93022i	−1.18454	+	0.0896080i
$465$	5.06130	−	43.1837i	0.234712	−	2.00260i
$466$	−12.0024	+	37.6801i	−0.556002	+	1.74550i
$467$	3.35603	+	12.5249i	0.155299	+	0.579582i	0.999080	+	0.0428945i	$0.0136579\pi$
$467$	3.35603	+	12.5249i	0.155299	+	0.579582i	−0.843781	+	0.536688i	$0.819675\pi$
$468$	−14.4671	+	21.6872i	−0.668744	+	1.00249i
$469$	−6.37950	+	2.33505i	−0.294578	+	0.107823i
$470$	0.944784	−	20.2710i	0.0435796	−	0.935033i
$471$	8.75808	+	20.3212i	0.403551	+	0.936351i
$472$	−6.40021	−	15.8454i	−0.294594	−	0.729345i
$473$	−0.672994	−	1.16566i	−0.0309443	−	0.0535971i
$474$	12.4410	+	33.0169i	0.571432	+	1.51651i
$475$	−2.99710	+	2.99710i	−0.137517	+	0.137517i
$476$	−14.4273	−	0.0586949i	−0.661273	−	0.00269028i
$477$	−8.51698	+	15.7718i	−0.389966	+	0.722142i
$478$	−5.93717	−	27.1585i	−0.271560	−	1.24220i
$479$	6.47377	+	11.2129i	0.295794	+	0.512330i	0.975169	−	0.221461i	$-0.0710825\pi$
$479$	6.47377	+	11.2129i	0.295794	+	0.512330i	−0.679375	+	0.733791i	$0.737749\pi$
$480$	13.2423	+	28.4335i	0.604425	+	1.29780i
$481$	−10.8567	−	6.26814i	−0.495024	−	0.285802i
$482$	−8.27873	+	7.54139i	−0.377086	+	0.343501i
$483$	−19.4348	−	20.5380i	−0.884314	−	0.934512i
$484$	−1.10826	−	0.103532i	−0.0503755	−	0.00470598i
$485$	−2.81731	−	10.5143i	−0.127927	−	0.477432i
$486$	−20.1539	+	8.93416i	−0.914201	+	0.405262i
$487$	−24.7476	+	14.2880i	−1.12142	+	0.647451i	−0.941763	−	0.336278i	$-0.890832\pi$
$487$	−24.7476	+	14.2880i	−1.12142	+	0.647451i	−0.179656	+	0.983729i	$0.557498\pi$
$488$	23.3218	−	29.8446i	1.05573	−	1.35100i
$489$	16.7483	+	12.4769i	0.757386	+	0.564226i
$490$	−4.15803	−	31.4170i	−0.187841	−	1.41927i
$491$	3.04583	−	3.04583i	0.137456	−	0.137456i	−0.635031	−	0.772487i	$-0.719013\pi$
$491$	3.04583	−	3.04583i	0.137456	−	0.137456i	0.772487	+	0.635031i	$0.219013\pi$
$492$	12.7524	+	6.50375i	0.574920	+	0.293212i
$493$	4.51434	−	16.8478i	0.203316	−	0.758785i
$494$	−4.72856	−	1.50621i	−0.212748	−	0.0677676i
$495$	−7.17650	+	30.1949i	−0.322560	+	1.35716i
$496$	5.80961	−	30.8233i	0.260859	−	1.38401i
$497$	−1.91707	+	1.34753i	−0.0859921	+	0.0604450i
$498$	1.85424	+	18.7535i	0.0830904	+	0.840365i
$499$	−2.58909	−	9.66262i	−0.115904	−	0.432558i	0.883449	−	0.468527i	$-0.155215\pi$
$499$	−2.58909	−	9.66262i	−0.115904	−	0.432558i	−0.999353	+	0.0359685i	$0.988548\pi$
$500$	−0.552099	+	1.48956i	−0.0246906	+	0.0666152i
$501$	−12.9455	−	16.3829i	−0.578363	−	0.731935i
$502$	−2.76459	−	1.77269i	−0.123390	−	0.0791190i
$503$		−	13.2588i		−	0.591182i	−0.955315	−	0.295591i	$-0.904483\pi$
$503$		−	13.2588i		−	0.591182i	0.955315	−	0.295591i	$-0.0955166\pi$
$504$	−19.1884	−	11.6535i	−0.854720	−	0.519089i
$505$			29.4812i			1.31190i
$506$	−15.2215	+	23.7386i	−0.676678	+	1.05531i
$507$	−6.31280	−	7.98903i	−0.280361	−	0.354805i
$508$	−20.9556	+	9.62213i	−0.929756	+	0.426913i
$509$	−1.58880	−	5.92948i	−0.0704223	−	0.262820i	0.921734	−	0.387823i	$-0.126773\pi$
$509$	−1.58880	−	5.92948i	−0.0704223	−	0.262820i	−0.992156	+	0.125003i	$0.960106\pi$
$510$	−21.2762	+	2.10367i	−0.942126	+	0.0931519i
$511$	33.7926	+	15.6832i	1.49490	+	0.693784i
$512$	8.10290	+	21.1268i	0.358101	+	0.933683i
$513$	−2.69445	−	3.21732i	−0.118963	−	0.142048i
$514$	3.68683	−	11.5743i	0.162619	−	0.510523i
$515$	−8.77320	+	32.7420i	−0.386593	+	1.44279i
$516$	1.37236	−	0.445332i	0.0604150	−	0.0196046i
$517$	10.2428	−	10.2428i	0.450476	−	0.450476i
$518$	4.99565	−	9.57019i	0.219496	−	0.420490i
$519$	−4.19848	−	3.12772i	−0.184293	−	0.137292i
$520$	−39.0489	+	4.79082i	−1.71241	+	0.210091i
$521$	−22.3422	+	12.8993i	−0.978830	+	0.565128i	−0.901917	−	0.431910i	$-0.857840\pi$
$521$	−22.3422	+	12.8993i	−0.978830	+	0.565128i	−0.0769136	+	0.997038i	$0.524507\pi$
$522$	19.5361	−	18.8407i	0.855073	−	0.824637i
$523$	3.84807	+	14.3612i	0.168264	+	0.627972i	0.997601	+	0.0692225i	$0.0220518\pi$
$523$	3.84807	+	14.3612i	0.168264	+	0.627972i	−0.829337	+	0.558749i	$0.811281\pi$
$524$	−13.2671	−	16.0013i	−0.579575	−	0.699018i
$525$	−5.58130	−	23.3933i	−0.243588	−	1.02097i
$526$	−14.6414	−	16.0730i	−0.638397	−	0.700815i
$527$	18.5157	+	10.6900i	0.806555	+	0.465665i
$528$	−6.67996	+	21.3697i	−0.290708	+	0.929997i
$529$	−7.53623	−	13.0531i	−0.327662	−	0.567528i
$530$	−26.4257	+	5.77696i	−1.14786	+	0.250935i
$531$	15.9489	+	8.61261i	0.692124	+	0.373756i
$532$	1.12287	−	4.12343i	0.0486826	−	0.178773i
$533$	−12.6962	+	12.6962i	−0.549933	+	0.549933i
$534$	−7.68873	+	2.89716i	−0.332724	+	0.125372i
$535$	23.9239	+	41.4374i	1.03432	+	1.79149i
$536$	−6.73390	+	2.71992i	−0.290860	+	0.117483i
$537$	−1.34180	−	3.11335i	−0.0579029	−	0.134351i
$538$	32.4313	+	1.51154i	1.39821	+	0.0651672i
$539$	12.9078	−	18.5773i	0.555980	−	0.800182i
$540$	−30.0548	−	14.2655i	−1.29335	−	0.613890i
$541$	0.578534	+	2.15912i	0.0248731	+	0.0928277i	0.977247	−	0.212106i	$-0.0680323\pi$
$541$	0.578534	+	2.15912i	0.0248731	+	0.0928277i	−0.952374	+	0.304934i	$0.901366\pi$
$542$	32.5403	+	10.3652i	1.39773	+	0.445225i
$543$	−0.259666	+	2.21550i	−0.0111433	+	0.0950763i
$544$	−15.4171	+	0.446140i	−0.661002	+	0.0191281i
$545$	−63.5834			−2.72361
$546$	21.3317	−	18.3810i	0.912914	−	0.786634i
$547$	23.6232	−	23.6232i	1.01006	−	1.01006i	0.0101074	−	0.999949i	$-0.496783\pi$
$547$	23.6232	−	23.6232i	1.01006	−	1.01006i	0.999949	−	0.0101074i	$-0.00321734\pi$
$548$	14.5611	+	10.3240i	0.622021	+	0.441018i
$549$	1.14303	+	40.1575i	0.0487832	+	1.71388i
$550$	−21.3075	+	11.0125i	−0.908554	+	0.469573i
$551$	4.47438	+	2.58329i	0.190615	+	0.110052i
$552$	−21.4897	−	21.2586i	−0.914664	−	0.904828i
$553$	−3.39033	−	37.9589i	−0.144172	−	1.61418i
$554$	0.367000	−	7.87425i	0.0155923	−	0.334545i
$555$	5.91126	−	14.8658i	0.250919	−	0.631019i
$556$	12.5678	−	33.9079i	0.532993	−	1.43802i
$557$	−8.09926	+	30.2269i	−0.343177	+	1.28075i	0.551551	+	0.834141i	$0.314036\pi$
$557$	−8.09926	+	30.2269i	−0.343177	+	1.28075i	−0.894728	+	0.446612i	$0.852630\pi$
$558$	16.1096	+	29.1082i	0.681976	+	1.23225i
$559$			1.80969i			0.0765418i
$560$	−5.55079	−	33.4212i	−0.234563	−	1.41230i
$561$	−12.2386	−	9.11730i	−0.516713	−	0.384933i
$562$	11.1699	−	2.44188i	0.471175	−	0.103004i
$563$	8.34601	+	2.23631i	0.351742	+	0.0942491i	0.430364	−	0.902655i	$-0.358385\pi$
$563$	8.34601	+	2.23631i	0.351742	+	0.0942491i	−0.0786216	+	0.996905i	$0.525052\pi$
$564$	8.45191	+	13.0256i	0.355890	+	0.548478i
$565$	1.01224	+	3.77772i	0.0425852	+	0.158930i
$566$	38.8519	+	1.81080i	1.63307	+	0.0761134i
$567$	23.5585	−	3.46397i	0.989362	−	0.145473i
$568$	−2.00079	+	1.50740i	−0.0839511	+	0.0632492i
$569$	−16.1599	+	27.9897i	−0.677457	+	1.17339i	0.298287	+	0.954476i	$0.403585\pi$
$569$	−16.1599	+	27.9897i	−0.677457	+	1.17339i	−0.975744	+	0.218914i	$0.929749\pi$
$570$	1.02925	−	6.24882i	0.0431106	−	0.261734i
$571$	1.46343	−	5.46161i	0.0612428	−	0.228561i	−0.928520	−	0.371282i	$-0.878918\pi$
$571$	1.46343	−	5.46161i	0.0612428	−	0.228561i	0.989763	+	0.142721i	$0.0455851\pi$
$572$	−22.9088	−	16.2425i	−0.957866	−	0.679135i
$573$	31.0064	−	4.53175i	1.29531	−	0.189316i
$574$	−11.3880	−	10.4589i	−0.475327	−	0.436544i
$575$		−	32.3824i		−	1.35044i
$576$	−20.9131	−	11.7746i	−0.871381	−	0.490607i
$577$	−21.5386	+	12.4353i	−0.896663	+	0.517688i	−0.876116	−	0.482101i	$-0.839874\pi$
$577$	−21.5386	+	12.4353i	−0.896663	+	0.517688i	−0.0205466	+	0.999789i	$0.506541\pi$
$578$	−4.10601	+	12.8903i	−0.170788	+	0.536167i
$579$	1.42577	+	0.566944i	0.0592529	+	0.0235614i
$580$	40.7807	+	3.80966i	1.69333	+	0.158187i
$581$	3.49824	−	20.0520i	0.145132	−	0.831898i
$582$	6.44039	+	5.28141i	0.266963	+	0.218921i
$583$	−16.7217	−	9.65426i	−0.692541	−	0.399839i
$584$	36.6593	+	15.5651i	1.51697	+	0.644087i
$585$	28.6548	−	30.3338i	1.18473	−	1.25415i
$586$	21.8636	+	14.0192i	0.903178	+	0.579129i
$587$	12.5678	+	12.5678i	0.518730	+	0.518730i	0.917187	−	0.398457i	$-0.130454\pi$
$587$	12.5678	+	12.5678i	0.518730	+	0.518730i	−0.398457	+	0.917187i	$0.630454\pi$
$588$	16.5951	+	17.6806i	0.684369	+	0.729136i
$589$	−4.47814	+	4.47814i	−0.184519	+	0.184519i
$590$	5.84183	+	26.7224i	0.240504	+	1.10015i
$591$	−3.71431	+	31.6910i	−0.152786	+	1.30359i
$592$	5.00012	−	10.4016i	0.205504	−	0.427503i
$593$	17.4043	−	30.1451i	0.714708	−	1.23791i	−0.248363	−	0.968667i	$-0.579893\pi$
$593$	17.4043	−	30.1451i	0.714708	−	1.23791i	0.963072	−	0.269244i	$-0.0867740\pi$
$594$	−9.00238	−	21.9751i	−0.369372	−	0.901648i
$595$	22.7494	+	3.96882i	0.932634	+	0.162706i
$596$	−18.0327	−	21.7491i	−0.738650	−	0.890878i
$597$	−17.1421	−	6.81639i	−0.701578	−	0.278976i
$598$	33.6820	−	17.4080i	1.37736	−	0.711867i
$599$	10.0044	+	17.3281i	0.408769	+	0.708008i	0.994752	−	0.102315i	$-0.0326250\pi$
$599$	10.0044	+	17.3281i	0.408769	+	0.708008i	−0.585983	+	0.810323i	$0.699292\pi$
$600$	−6.78850	−	24.7980i	−0.277140	−	1.01238i
$601$	1.71064			0.0697784			0.0348892	−	0.999391i	$-0.488892\pi$
$601$	1.71064			0.0697784			0.0348892	+	0.999391i	$0.488892\pi$
$602$	−1.55701	+	0.0662214i	−0.0634589	+	0.00269898i
$603$	3.66014	−	6.77788i	0.149052	−	0.276017i
$604$	−4.64398	+	6.54997i	−0.188961	+	0.266514i
$605$	1.72093	+	0.461123i	0.0699659	+	0.0187473i
$606$	−13.1464	−	18.3311i	−0.534037	−	0.744651i
$607$	7.19611	+	4.15467i	0.292081	+	0.168633i	0.638880	−	0.769306i	$-0.279398\pi$
$607$	7.19611	+	4.15467i	0.292081	+	0.168633i	−0.346799	+	0.937939i	$0.612731\pi$
$608$	1.05431	−	4.44534i	0.0427579	−	0.180282i
$609$	−25.7828	+	13.9518i	−1.04477	+	0.565356i
$610$	−44.8184	+	40.8267i	−1.81464	+	1.65302i
$611$	−18.8122	+	5.04071i	−0.761060	+	0.203925i
$612$	12.2913	−	10.7956i	0.496845	−	0.436388i
$613$	2.70551	−	10.0971i	0.109274	−	0.407818i	−0.889521	−	0.456895i	$-0.848961\pi$
$613$	2.70551	−	10.0971i	0.109274	−	0.407818i	0.998795	+	0.0490774i	$0.0156281\pi$
$614$	−17.1371	−	10.9885i	−0.691598	−	0.443461i
$615$	−18.3749	−	13.6886i	−0.740946	−	0.551979i
$616$	13.1363	−	20.3044i	0.529278	−	0.818089i
$617$	3.78979			0.152571			0.0762855	−	0.997086i	$-0.475694\pi$
$617$	3.78979			0.152571			0.0762855	+	0.997086i	$0.475694\pi$
$618$	−9.14542	−	24.2709i	−0.367883	−	0.976318i
$619$	20.9722	+	5.61949i	0.842945	+	0.225867i	0.654353	−	0.756189i	$-0.272941\pi$
$619$	20.9722	+	5.61949i	0.842945	+	0.225867i	0.188592	+	0.982056i	$0.439608\pi$
$620$	−17.4485	+	47.0760i	−0.700748	+	1.89062i
$621$	31.9371	+	2.82469i	1.28159	+	0.113351i
$622$	−4.90639	+	4.46941i	−0.196728	+	0.179207i
$623$	8.83960	−	0.789516i	0.354151	−	0.0316313i
$624$	22.1439	−	20.3918i	0.886464	−	0.816325i
$625$	−11.8489	+	20.5229i	−0.473957	+	0.820917i
$626$	−8.87834	+	27.8724i	−0.354850	+	1.11401i
$627$	3.54692	−	2.80271i	0.141650	−	0.111930i
$628$	−4.28888	−	25.1889i	−0.171145	−	1.00515i
$629$	5.56259	+	5.56259i	0.221795	+	0.221795i
$630$	27.1469	+	23.5438i	1.08156	+	0.938006i
$631$			14.1031i			0.561437i	0.959790	+	0.280718i	$0.0905727\pi$
$631$			14.1031i			0.561437i	−0.959790	+	0.280718i	$0.909427\pi$
$632$	−4.96126	−	40.4381i	−0.197348	−	1.60854i
$633$	1.25961	−	10.7471i	0.0500649	−	0.427160i
$634$	18.2091	−	9.41112i	0.723177	−	0.373763i
$635$	35.6516	−	9.55282i	1.41479	−	0.379092i
$636$	13.8552	−	15.3760i	0.549393	−	0.609697i
$637$	−27.5183	+	12.9537i	−1.09031	+	0.513243i
$638$	19.6885	+	21.6135i	0.779474	+	0.855685i
$639$	0.614390	−	2.58502i	0.0243049	−	0.102262i
$640$	−7.10958	−	35.5136i	−0.281031	−	1.40380i
$641$	−2.05928	+	1.18893i	−0.0813367	+	0.0469598i	−0.540117	−	0.841590i	$-0.681620\pi$
$641$	−2.05928	+	1.18893i	−0.0813367	+	0.0469598i	0.458780	+	0.888550i	$0.348287\pi$
$642$	−33.3536	−	15.0971i	−1.31636	−	0.595835i
$643$	7.07301	+	7.07301i	0.278932	+	0.278932i	0.832683	−	0.553751i	$-0.186804\pi$
$643$	7.07301	+	7.07301i	0.278932	+	0.278932i	−0.553751	+	0.832683i	$0.686804\pi$
$644$	16.2099	+	28.3420i	0.638759	+	1.11683i
$645$	−2.28514	+	0.333985i	−0.0899771	+	0.0131506i
$646$	2.62150	+	1.68094i	0.103142	+	0.0661357i
$647$	−0.937977	+	0.541541i	−0.0368757	+	0.0212902i	−0.518325	−	0.855184i	$-0.673444\pi$
$647$	−0.937977	+	0.541541i	−0.0368757	+	0.0212902i	0.481449	+	0.876474i	$0.340111\pi$
$648$	25.0492	−	4.53204i	0.984024	−	0.178035i
$649$	−9.76267	+	16.9094i	−0.383218	+	0.663753i
$650$	32.2131	+	1.50138i	1.26350	+	0.0588888i
$651$	−8.33934	−	34.9532i	−0.326844	−	1.36993i
$652$	−15.3924	−	18.5647i	−0.602815	−	0.727048i
$653$	−10.0058	+	2.68105i	−0.391558	+	0.104918i	−0.449226	−	0.893418i	$-0.648300\pi$
$653$	−10.0058	+	2.68105i	−0.391558	+	0.104918i	0.0576677	+	0.998336i	$0.481634\pi$
$654$	39.5355	−	28.3535i	1.54596	−	1.10871i
$655$	16.6353	+	28.8133i	0.649997	+	1.12583i
$656$	−12.5366	−	10.7732i	−0.489471	−	0.420624i
$657$	−40.4757	+	12.0897i	−1.57911	+	0.471665i
$658$	−5.02527	−	16.0010i	−0.195905	−	0.623784i
$659$	5.12487	+	5.12487i	0.199637	+	0.199637i	0.799844	−	0.600208i	$-0.204915\pi$
$659$	5.12487	+	5.12487i	0.199637	+	0.199637i	−0.600208	+	0.799844i	$0.704915\pi$
$660$	16.2819	−	31.9251i	0.633772	−	1.24268i
$661$	−33.7009	−	9.03013i	−1.31081	−	0.351231i	−0.465284	−	0.885161i	$-0.654048\pi$
$661$	−33.7009	−	9.03013i	−1.31081	−	0.351231i	−0.845529	+	0.533930i	$0.820714\pi$
$662$	33.5604	−	17.3452i	1.30436	−	0.674140i
$663$	8.12118	+	18.8434i	0.315401	+	0.731817i
$664$	3.03050	−	21.5482i	0.117606	−	0.836234i
$665$	−2.87965	+	6.20478i	−0.111668	+	0.240611i
$666$	2.95349	+	11.8794i	0.114445	+	0.460318i
$667$	−38.1275	+	10.2162i	−1.47630	+	0.395574i
$668$	10.0608	+	21.9111i	0.389265	+	0.847764i
$669$	6.33224	+	8.01364i	0.244819	+	0.309825i
$670$	11.3563	−	2.48263i	0.438734	−	0.0959123i
$671$	−43.2756			−1.67064
$672$	18.3548	+	18.3058i	0.708052	+	0.706160i
$673$	−43.5179			−1.67749			−0.838745	−	0.544524i	$-0.816710\pi$
$673$	−43.5179			−1.67749			−0.838745	+	0.544524i	$0.816710\pi$
$674$	21.0521	−	4.60222i	0.810895	−	0.177271i
$675$	22.3234	+	15.6626i	0.859229	+	0.602855i
$676$	4.90611	+	10.6848i	0.188696	+	0.410954i
$677$	−24.0812	+	6.45254i	−0.925516	+	0.247991i	−0.689942	−	0.723865i	$-0.742364\pi$
$677$	−24.0812	+	6.45254i	−0.925516	+	0.247991i	−0.235574	+	0.971856i	$0.575697\pi$
$678$	−2.31398	−	1.89757i	−0.0888680	−	0.0728757i
$679$	−5.17343	−	7.35999i	−0.198538	−	0.282451i
$680$	24.4469	+	3.43816i	0.937494	+	0.131847i
$681$	−22.2000	+	9.56783i	−0.850708	+	0.366640i
$682$	−31.8367	+	16.4543i	−1.21909	+	0.630069i
$683$	−20.7011	−	5.54684i	−0.792105	−	0.212244i	−0.159990	−	0.987119i	$-0.551146\pi$
$683$	−20.7011	−	5.54684i	−0.792105	−	0.212244i	−0.632115	+	0.774875i	$0.717813\pi$
$684$	2.14653	+	4.34443i	0.0820747	+	0.166113i
$685$	−20.2026	−	20.2026i	−0.771903	−	0.771903i
$686$	−12.1519	−	23.2019i	−0.463963	−	0.885854i
$687$	−28.2770	−	21.0654i	−1.07883	−	0.803693i
$688$	−1.66127	+	0.125671i	−0.0633353	+	0.00479117i
$689$	12.9802	+	22.4824i	0.494508	+	0.856512i
$690$	28.1976	+	39.3182i	1.07346	+	1.49682i
$691$	−3.06923	+	0.822397i	−0.116759	+	0.0312854i	−0.316725	−	0.948517i	$-0.602583\pi$
$691$	−3.06923	+	0.822397i	−0.116759	+	0.0312854i	0.199966	+	0.979803i	$0.435917\pi$
$692$	3.85858	+	4.65379i	0.146681	+	0.176911i
$693$	3.00788	+	25.4733i	0.114260	+	0.967652i
$694$	−10.2021	−	0.475493i	−0.387265	−	0.0180495i
$695$	−28.9411	+	50.1275i	−1.09780	+	1.90144i
$696$	−27.0559	+	15.8164i	−1.02555	+	0.599517i
$697$	9.75759	−	5.63355i	0.369595	−	0.213386i
$698$	−4.89155	−	3.13652i	−0.185148	−	0.118719i
$699$	7.00435	+	47.9240i	0.264929	+	1.81265i
$700$	−0.112978	+	27.7702i	−0.00427018	+	1.04961i
$701$	33.2184	+	33.2184i	1.25464	+	1.25464i	0.953617	+	0.301023i	$0.0973282\pi$
$701$	33.2184	+	33.2184i	1.25464	+	1.25464i	0.301023	+	0.953617i	$0.402672\pi$
$702$	−4.29065	+	31.6392i	−0.161940	+	1.19414i
$703$	−2.01803	+	1.16511i	−0.0761113	+	0.0439429i
$704$	13.3195	−	22.1579i	0.501999	−	0.835106i
$705$	−9.83686	−	22.8243i	−0.370478	−	0.859611i
$706$	−8.78132	−	9.63989i	−0.330490	−	0.362802i
$707$	8.37493	+	22.8808i	0.314972	+	0.860520i
$708$	−15.5486	−	14.0107i	−0.584353	−	0.526556i
$709$	36.1556	−	9.68785i	1.35785	−	0.363835i	0.494824	−	0.868993i	$-0.335233\pi$
$709$	36.1556	−	9.68785i	1.35785	−	0.363835i	0.863027	+	0.505158i	$0.168566\pi$
$710$	3.56208	−	1.84101i	0.133683	−	0.0690919i
$711$	31.4130	+	29.6742i	1.17808	+	1.11287i
$712$	9.41694	−	1.15534i	0.352915	−	0.0432983i
$713$		−	48.3844i		−	1.81201i
$714$	−15.9152	+	7.67676i	−0.595610	+	0.287296i
$715$	31.7845	+	31.7845i	1.18867	+	1.18867i
$716$	0.657086	+	3.85911i	0.0245565	+	0.144222i
$717$	−21.1092	−	26.7143i	−0.788338	−	0.997665i
$718$	15.8699	−	49.8217i	0.592261	−	1.85933i
$719$	9.79678	−	16.9685i	0.365358	−	0.632819i	−0.623475	−	0.781843i	$-0.714280\pi$
$719$	9.79678	−	16.9685i	0.365358	−	0.632819i	0.988834	+	0.149024i	$0.0476132\pi$
$720$	29.8359	+	24.1982i	1.11192	+	0.901812i
$721$	2.49225	+	27.9038i	0.0928163	+	1.03919i
$722$	19.1821	−	17.4736i	0.713882	−	0.650301i
$723$	−5.06788	+	12.7449i	−0.188476	+	0.473987i
$724$	0.895179	−	2.41519i	0.0332691	−	0.0897599i
$725$	−32.4292	−	8.68939i	−1.20439	−	0.322716i
$726$	−1.27569	+	0.480687i	−0.0473452	+	0.0178400i
$727$	−19.9612			−0.740321			−0.370161	−	0.928968i	$-0.620697\pi$
$727$	−19.9612			−0.740321			−0.370161	+	0.928968i	$0.620697\pi$
$728$	−28.9454	+	14.8111i	−1.07279	+	0.548936i
$729$	−17.3945	+	20.6502i	−0.644241	+	0.764823i
$730$	−53.6637	−	34.4098i	−1.98618	−	1.27356i
$731$	0.293917	−	1.09691i	0.0108709	−	0.0405708i
$732$	9.66199	−	45.3713i	0.357117	−	1.67697i
$733$	−0.710358	+	0.190340i	−0.0262377	+	0.00703036i	−0.271914	−	0.962322i	$-0.587657\pi$
$733$	−0.710358	+	0.190340i	−0.0262377	+	0.00703036i	0.245676	+	0.969352i	$0.420990\pi$
$734$	4.89689	−	4.46075i	0.180747	−	0.164649i
$735$	−21.4355	−	32.3573i	−0.790659	−	1.19352i
$736$	18.3193	+	29.7106i	0.675258	+	1.09515i
$737$	7.18607	+	4.14888i	0.264702	+	0.152826i
$738$	17.5294	+	0.317632i	0.645267	+	0.0116922i
$739$	26.1970	+	7.01946i	0.963671	+	0.258215i	0.706154	−	0.708059i	$-0.250429\pi$
$739$	26.1970	+	7.01946i	0.963671	+	0.258215i	0.257518	+	0.966274i	$0.417095\pi$
$740$	−10.6844	+	15.0695i	−0.392767	+	0.553967i
$741$	−6.01409	+	0.878990i	−0.220933	+	0.0322905i
$742$	−18.8683	+	11.9905i	−0.692675	+	0.440186i
$743$	−27.2589			−1.00003			−0.500015	−	0.866017i	$-0.666672\pi$
$743$	−27.2589			−1.00003			−0.500015	+	0.866017i	$0.666672\pi$
$744$	−10.1431	−	37.0521i	−0.371864	−	1.35840i
$745$	22.6109	+	39.1633i	0.828401	+	1.43483i
$746$	−15.6791	+	8.10349i	−0.574052	+	0.296690i
$747$	12.1042	+	19.6517i	0.442868	+	0.719017i
$748$	11.2478	+	13.5658i	0.411259	+	0.496015i
$749$	30.3391	+	25.3639i	1.10857	+	0.926777i
$750$	0.191437	+	1.93617i	0.00699030	+	0.0706990i
$751$	−0.698629	+	1.21006i	−0.0254933	+	0.0441557i	−0.878491	−	0.477760i	$-0.841449\pi$
$751$	−0.698629	+	1.21006i	−0.0254933	+	0.0441557i	0.852997	+	0.521915i	$0.174782\pi$
$752$	−5.93367	−	16.9192i	−0.216379	−	0.616981i
$753$	−3.99485	−	0.468213i	−0.145581	−	0.0170626i
$754$	−8.39510	−	38.4019i	−0.305731	−	1.39851i
$755$	9.08764	−	9.08764i	0.330733	−	0.330733i
$756$	−27.3785	−	2.53379i	−0.995745	−	0.0921532i
$757$	−22.1941	−	22.1941i	−0.806658	−	0.806658i	0.177468	−	0.984126i	$-0.443209\pi$
$757$	−22.1941	−	22.1941i	−0.806658	−	0.806658i	−0.984126	+	0.177468i	$0.943209\pi$
$758$	19.8213	+	12.7096i	0.719941	+	0.461635i
$759$	−4.02039	+	34.3025i	−0.145931	+	1.24510i
$760$	−2.85796	+	6.73114i	−0.103669	+	0.244164i
$761$	−0.550589	−	0.317882i	−0.0199588	−	0.0115232i	0.489987	−	0.871730i	$-0.337001\pi$
$761$	−0.550589	−	0.317882i	−0.0199588	−	0.0115232i	−0.509946	+	0.860206i	$0.670335\pi$
$762$	−17.9080	+	21.8378i	−0.648738	+	0.791100i
$763$	−49.3479	+	18.0626i	−1.78652	+	0.653909i
$764$	−36.0266	−	3.36554i	−1.30340	−	0.121761i
$765$	−22.2952	+	13.7324i	−0.806084	+	0.496496i
$766$	1.15431	−	3.62380i	0.0417068	−	0.130933i
$767$	22.7349	−	13.1260i	0.820909	−	0.473952i
$768$	20.2571	+	18.9117i	0.730964	+	0.682416i
$769$			4.70248i			0.169576i	0.996399	+	0.0847878i	$0.0270212\pi$
$769$			4.70248i			0.169576i	−0.996399	+	0.0847878i	$0.972979\pi$
$770$	−26.1834	+	28.5095i	−0.943583	+	1.02741i
$771$	−2.15155	−	14.7210i	−0.0774863	−	0.530164i
$772$	−1.44531	−	1.02473i	−0.0520177	−	0.0368810i
$773$	7.93184	−	29.6020i	0.285289	−	1.06471i	−0.663340	−	0.748318i	$-0.730862\pi$
$773$	7.93184	−	29.6020i	0.285289	−	1.06471i	0.948628	−	0.316393i	$-0.102472\pi$
$774$	1.27194	−	1.22667i	0.0457191	−	0.0440917i
$775$	20.5766	−	35.6397i	0.739133	−	1.28022i
$776$	−5.78721	−	7.68141i	−0.207749	−	0.275747i
$777$	0.364775	−	13.2168i	0.0130862	−	0.474151i
$778$	6.94418	+	0.323651i	0.248961	+	0.0116035i
$779$	0.863799	+	3.22374i	0.0309488	+	0.115502i
$780$	−40.4201	+	26.2273i	−1.44727	+	0.939086i
$781$	2.76466	+	0.740788i	0.0989273	+	0.0265075i
$782$	−23.2430	+	5.08119i	−0.831168	+	0.181703i
$783$	11.3987	−	31.2253i	0.407355	−	1.11590i
$784$	−13.8022	−	24.3618i	−0.492937	−	0.870065i
$785$			40.8984i			1.45973i
$786$	−23.1923	−	10.4977i	−0.827241	−	0.374440i
$787$	−2.27512	+	8.49085i	−0.0810992	+	0.302666i	−0.994547	−	0.104290i	$-0.966743\pi$
$787$	−2.27512	+	8.49085i	−0.0810992	+	0.302666i	0.913448	+	0.406956i	$0.133410\pi$
$788$	12.8048	−	34.5474i	0.456153	−	1.23070i
$789$	−24.7439	−	9.83917i	−0.880905	−	0.350284i
$790$	−3.03607	+	65.1412i	−0.108019	+	2.31762i
$791$	1.85878	+	2.64439i	0.0660904	+	0.0940236i
$792$	4.11226	+	27.1112i	0.146123	+	0.963355i
$793$	50.3892	+	29.0922i	1.78937	+	1.03310i
$794$	21.9183	−	11.3282i	0.777852	−	0.402022i
$795$	−25.9935	+	20.5396i	−0.921894	+	0.728465i
$796$	17.3770	+	12.3204i	0.615910	+	0.436686i
$797$	23.7446	−	23.7446i	0.841079	−	0.841079i	−0.147921	−	0.988999i	$-0.547258\pi$
$797$	23.7446	−	23.7446i	0.841079	−	0.841079i	0.988999	+	0.147921i	$0.0472580\pi$
$798$	−0.976329	−	5.14219i	−0.0345617	−	0.182031i
$799$	12.2213			0.432360
$800$	0.858748	+	29.6754i	0.0303613	+	1.04918i
$801$	−6.91032	+	7.31523i	−0.244164	+	0.258471i
$802$	−13.4462	−	4.28307i	−0.474800	−	0.151240i
$803$	−11.7774	−	43.9538i	−0.415615	−	1.55110i
$804$	−5.95420	+	6.60776i	−0.209989	+	0.233038i
$805$	−17.9633	−	49.0767i	−0.633122	−	1.72973i
$806$	48.1315	+	2.24329i	1.69536	+	0.0790166i
$807$	36.5161	−	15.7378i	1.28543	−	0.553997i
$808$	9.75531	+	24.1519i	0.343191	+	0.849660i
$809$	−15.3837	−	26.6453i	−0.540861	−	0.936799i	−0.998855	−	0.0478436i	$-0.984765\pi$
$809$	−15.3837	−	26.6453i	−0.540861	−	0.936799i	0.457994	−	0.888955i	$-0.348568\pi$
$810$	−40.7433	+	0.421218i	−1.43157	+	0.0148001i
$811$	24.1014	−	24.1014i	0.846316	−	0.846316i	−0.143355	−	0.989671i	$-0.545789\pi$
$811$	24.1014	−	24.1014i	0.846316	−	0.846316i	0.989671	+	0.143355i	$0.0457891\pi$
$812$	32.7327	−	8.62813i	1.14869	−	0.302788i
$813$	41.3869	−	6.04891i	1.45150	−	0.212145i
$814$	−12.8820	+	2.81615i	−0.451513	+	0.0987060i
$815$	19.3003	+	33.4291i	0.676061	+	1.17097i
$816$	−16.7340	+	8.76367i	−0.585807	+	0.306790i
$817$	0.291315	+	0.168191i	0.0101918	+	0.00588425i
$818$	23.5699	+	25.8743i	0.824101	+	0.904675i
$819$	13.6222	−	31.6827i	0.476000	−	1.10708i
$820$	16.8873	+	20.3676i	0.589730	+	0.711267i
$821$	5.56269	+	20.7602i	0.194139	+	0.724537i	0.992488	+	0.122342i	$0.0390404\pi$
$821$	5.56269	+	20.7602i	0.194139	+	0.724537i	−0.798349	+	0.602195i	$0.794293\pi$
$822$	21.5707	+	3.55293i	0.752364	+	0.123923i
$823$	−7.05576	+	4.07364i	−0.245948	+	0.141998i	−0.617908	−	0.786251i	$-0.712019\pi$
$823$	−7.05576	+	4.07364i	−0.245948	+	0.141998i	0.371959	+	0.928249i	$0.378686\pi$
$824$	3.64705	+	29.7263i	0.127051	+	1.03556i
$825$	−17.5493	+	23.5573i	−0.610989	+	0.820159i
$826$	12.1252	+	19.0801i	0.421888	+	0.663882i
$827$	−28.5061	+	28.5061i	−0.991254	+	0.991254i	−0.999962	−	0.00870782i	$-0.997228\pi$
$827$	−28.5061	+	28.5061i	−0.991254	+	0.991254i	0.00870782	+	0.999962i	$0.497228\pi$
$828$	−35.0660	−	11.8737i	−1.21863	−	0.412639i
$829$	7.25896	−	27.0908i	0.252114	−	0.940903i	−0.717559	−	0.696498i	$-0.754741\pi$
$829$	7.25896	−	27.0908i	0.252114	−	0.940903i	0.969673	−	0.244405i	$-0.0785928\pi$
$830$	−10.5713	+	33.1873i	−0.366935	+	1.15195i
$831$	−3.82111	−	8.86605i	−0.132553	−	0.307560i
$832$	−30.4047	+	16.8460i	−1.05409	+	0.584031i
$833$	18.7836	−	3.38232i	0.650812	−	0.117190i
$834$	−4.35782	−	44.0744i	−0.150899	−	1.52617i
$835$	−9.98836	−	37.2771i	−0.345661	−	1.29003i
$836$	−4.74376	+	2.17818i	−0.164066	+	0.0753339i
$837$	33.3547	+	23.4024i	1.15291	+	0.808906i
$838$	−16.4828	+	25.7057i	−0.569389	+	0.887988i
$839$		−	21.3679i		−	0.737701i	−0.929489	−	0.368850i	$-0.879751\pi$
$839$		−	21.3679i		−	0.737701i	0.929489	−	0.368850i	$-0.120249\pi$
$840$	−24.0443	−	33.8165i	−0.829606	−	1.16678i
$841$			11.9241i			0.411175i
$842$	−39.0393	−	25.0325i	−1.34538	−	0.862676i
$843$	10.9872	−	8.68193i	0.378420	−	0.299022i
$844$	−4.34241	+	11.7158i	−0.149472	+	0.403275i
$845$	−4.87076	−	18.1779i	−0.167559	−	0.625340i
$846$	16.2944	+	9.80540i	0.560213	+	0.337117i
$847$	1.46664	−	0.130994i	0.0503942	−	0.00450100i
$848$	−19.7371	+	13.4769i	−0.677776	+	0.462799i
$849$	43.7455	−	18.8536i	1.50134	−	0.647053i
$850$	−19.2816	−	6.14185i	−0.661352	−	0.210664i
$851$	4.60770	−	17.1962i	0.157950	−	0.589478i
$852$	−1.39392	+	2.73315i	−0.0477548	+	0.0936361i
$853$	−0.752939	+	0.752939i	−0.0257801	+	0.0257801i	−0.719879	−	0.694099i	$-0.755803\pi$
$853$	−0.752939	+	0.752939i	−0.0257801	+	0.0257801i	0.694099	+	0.719879i	$0.255803\pi$
$854$	−23.1863	+	44.4180i	−0.793417	+	1.51995i
$855$	−2.21984	−	7.43189i	−0.0759169	−	0.254165i
$856$	33.3108	+	26.0303i	1.13854	+	0.889698i
$857$	30.2686	−	17.4756i	1.03395	−	0.596954i	0.115839	−	0.993268i	$-0.463044\pi$
$857$	30.2686	−	17.4756i	1.03395	−	0.596954i	0.918115	+	0.396314i	$0.129711\pi$
$858$	−33.9368	−	5.58977i	−1.15858	−	0.190832i
$859$	−3.59657	−	13.4226i	−0.122713	−	0.457972i	0.877035	−	0.480427i	$-0.159518\pi$
$859$	−3.59657	−	13.4226i	−0.122713	−	0.457972i	−0.999748	+	0.0224550i	$0.992852\pi$
$860$	2.65512	+	0.248036i	0.0905389	+	0.00845797i
$861$	−18.1496	−	5.40405i	−0.618537	−	0.184170i
$862$	3.75159	−	3.41746i	0.127780	−	0.116399i
$863$	−17.1395	−	9.89550i	−0.583435	−	0.336847i	0.179062	−	0.983838i	$-0.442694\pi$
$863$	−17.1395	−	9.89550i	−0.583435	−	0.336847i	−0.762497	+	0.646991i	$0.776027\pi$
$864$	−29.3422	−	1.74162i	−0.998243	−	0.0592511i
$865$	−4.83821	−	8.38002i	−0.164504	−	0.284929i
$866$	−3.38252	−	15.4728i	−0.114943	−	0.525786i
$867$	2.39618	+	16.3947i	0.0813785	+	0.556795i
$868$	−0.168807	+	41.4930i	−0.00572969	+	1.40836i
$869$	−32.9152	+	32.9152i	−1.11657	+	1.11657i
$870$	46.9415	−	17.6879i	1.59147	−	0.599675i
$871$	−5.57821	−	9.66174i	−0.189010	−	0.327375i
$872$	−52.0894	+	21.0397i	−1.76397	+	0.712494i
$873$	9.92442	+	2.35877i	0.335891	+	0.0798321i
$874$	0.328110	−	7.03984i	0.0110985	−	0.238126i
$875$	0.361169	−	2.07023i	0.0122098	−	0.0699867i
$876$	48.7118	−	2.53432i	1.64582	−	0.0856266i
$877$	−2.83132	−	10.5666i	−0.0956070	−	0.356810i	0.901504	−	0.432771i	$-0.142464\pi$
$877$	−2.83132	−	10.5666i	−0.0956070	−	0.356810i	−0.997111	+	0.0759610i	$0.975798\pi$
$878$	−9.88793	+	31.0419i	−0.333702	+	1.04761i
$879$	31.5931	+	3.70284i	1.06561	+	0.124894i
$880$	−26.9704	+	31.3849i	−0.909173	+	1.05798i
$881$	−39.1624			−1.31942			−0.659708	−	0.751522i	$-0.729320\pi$
$881$	−39.1624			−1.31942			−0.659708	+	0.751522i	$0.729320\pi$
$882$	27.7573	+	10.5608i	0.934638	+	0.355602i
$883$	0.170282	−	0.170282i	0.00573046	−	0.00573046i	−0.704236	−	0.709966i	$-0.748710\pi$
$883$	0.170282	−	0.170282i	0.00573046	−	0.00573046i	0.709966	+	0.704236i	$0.248710\pi$
$884$	−3.97699	−	23.3571i	−0.133761	−	0.785584i
$885$	20.7703	+	26.2854i	0.698184	+	0.883573i
$886$	13.4804	+	26.0826i	0.452882	+	0.876261i
$887$	3.36796	+	1.94449i	0.113085	+	0.0652897i	0.555476	−	0.831533i	$-0.312536\pi$
$887$	3.36796	+	1.94449i	0.113085	+	0.0652897i	−0.442391	+	0.896822i	$0.645870\pi$
$888$	−0.0764122	−	14.1346i	−0.00256422	−	0.474325i
$889$	24.9560	−	17.5419i	0.836996	−	0.588335i
$890$	−15.1696	−	0.707020i	−0.508487	−	0.0236993i
$891$	−21.7025	−	19.3629i	−0.727061	−	0.648681i
$892$	−4.92122	−	10.7177i	−0.164775	−	0.358855i
$893$	−0.936956	+	3.49677i	−0.0313540	+	0.117015i
$894$	−31.5232	−	14.2686i	−1.05429	−	0.477213i
$895$		−	6.26592i		−	0.209447i
$896$	−15.6064	−	25.5429i	−0.521374	−	0.853328i
$897$	27.7412	−	37.2384i	0.926253	−	1.24335i
$898$	5.17967	+	23.6935i	0.172848	+	0.790663i
$899$	−48.4544	−	12.9833i	−1.61604	−	0.433017i
$900$	−20.7799	−	23.6587i	−0.692663	−	0.788624i
$901$	−4.21631	−	15.7355i	−0.140466	−	0.524225i
$902$	−0.879277	+	18.8655i	−0.0292767	+	0.628153i
$903$	−1.67865	+	0.908364i	−0.0558619	+	0.0302285i
$904$	2.07930	+	2.75987i	0.0691565	+	0.0917920i
$905$	−2.06142	+	3.57048i	−0.0685239	+	0.118687i
$906$	−1.59820	+	9.70303i	−0.0530966	+	0.322361i
$907$	8.50963	−	31.7584i	0.282558	−	1.05452i	−0.668048	−	0.744118i	$-0.732870\pi$
$907$	8.50963	−	31.7584i	0.282558	−	1.05452i	0.950606	−	0.310402i	$-0.100464\pi$
$908$	27.5178	−	4.68542i	0.913209	−	0.155491i
$909$	−24.3096	−	13.1275i	−0.806299	−	0.435411i
$910$	49.6530	−	15.5940i	1.64598	−	0.516936i
$911$			9.53186i			0.315805i	0.987455	+	0.157902i	$0.0504731\pi$
$911$			9.53186i			0.315805i	−0.987455	+	0.157902i	$0.949527\pi$
$912$	−1.22454	−	5.45980i	−0.0405485	−	0.180792i
$913$	−21.5314	+	12.4312i	−0.712586	+	0.411412i
$914$	8.68383	+	2.76610i	0.287236	+	0.0914945i
$915$	−27.4359	+	68.9966i	−0.907002	+	2.28096i
$916$	25.9878	+	31.3436i	0.858660	+	1.03562i
$917$	21.0961	+	17.6367i	0.696655	+	0.582414i
$918$	7.73930	−	18.4807i	0.255435	−	0.609953i
$919$	42.2445	+	24.3899i	1.39352	+	0.804548i	0.993703	−	0.112047i	$-0.0357408\pi$
$919$	42.2445	+	24.3899i	1.39352	+	0.804548i	0.399816	+	0.916596i	$0.369074\pi$
$920$	−20.9240	−	51.8030i	−0.689845	−	1.70790i
$921$	−24.7633	−	2.90236i	−0.815978	−	0.0956359i
$922$	−7.52045	+	11.7285i	−0.247673	+	0.386257i
$923$	−2.72111	−	2.72111i	−0.0895665	−	0.0895665i
$924$	3.56745	−	29.4028i	0.117360	−	0.967281i
$925$	10.7071	−	10.7071i	0.352047	−	0.352047i
$926$	−33.9567	+	7.42333i	−1.11589	+	0.243946i
$927$	−23.0919	−	21.8137i	−0.758437	−	0.716456i
$928$	34.6694	−	10.3733i	1.13808	−	0.340521i
$929$	9.34880	−	16.1926i	0.306724	−	0.531262i	−0.670920	−	0.741530i	$-0.734100\pi$
$929$	9.34880	−	16.1926i	0.306724	−	0.531262i	0.977644	+	0.210268i	$0.0674338\pi$
$930$	6.05017	+	61.1906i	0.198393	+	2.00652i
$931$	−0.472304	+	5.63366i	−0.0154791	+	0.184636i
$932$	5.20183	−	55.6834i	0.170392	−	1.82397i
$933$	−3.00348	+	7.55324i	−0.0983295	+	0.247282i
$934$	−8.41953	−	16.2906i	−0.275496	−	0.533043i
$935$	−14.1034	−	24.4278i	−0.461230	−	0.798874i
$936$	13.4374	−	34.3322i	0.439215	−	1.12218i
$937$	−50.9816			−1.66550			−0.832748	−	0.553653i	$-0.813234\pi$
$937$	−50.9816			−1.66550			−0.832748	+	0.553653i	$0.813234\pi$
$938$	8.10856	−	5.15288i	0.264754	−	0.168247i
$939$	5.18120	+	35.4500i	0.169082	+	1.15687i
$940$	4.81717	+	28.2915i	0.157119	+	0.922767i
$941$	−41.6909	−	11.1710i	−1.35908	−	0.364165i	−0.495604	−	0.868549i	$-0.665053\pi$
$941$	−41.6909	−	11.1710i	−1.35908	−	0.364165i	−0.863480	+	0.504383i	$0.831720\pi$
$942$	−18.2377	−	25.4303i	−0.594215	−	0.828563i
$943$	−22.0820	−	12.7491i	−0.719090	−	0.415167i
$944$	13.6282	+	19.9587i	0.443561	+	0.649602i
$945$	42.5204	+	11.3539i	1.38319	+	0.369344i
$946$	1.28186	+	1.40719i	0.0416770	+	0.0457518i
$947$	58.4304	−	15.6564i	1.89873	−	0.508764i	0.901646	−	0.432474i	$-0.142359\pi$
$947$	58.4304	−	15.6564i	1.89873	−	0.508764i	0.997086	−	0.0762895i	$-0.0243073\pi$
$948$	−27.1603	−	41.8581i	−0.882127	−	1.35949i
$949$	−15.8348	+	59.0962i	−0.514019	+	1.91834i
$950$	3.23554	−	5.04597i	0.104975	−	0.163713i
$951$	14.9975	−	20.1318i	0.486326	−	0.652818i
$952$	19.9502	−	4.27638i	0.646591	−	0.138598i
$953$	2.07708			0.0672833			0.0336416	−	0.999434i	$-0.489290\pi$
$953$	2.07708			0.0672833			0.0336416	+	0.999434i	$0.489290\pi$
$954$	7.00336	−	24.3625i	0.226742	−	0.788765i
$955$	55.9431	+	14.9899i	1.81027	+	0.485062i
$956$	16.4054	+	35.7286i	0.530589	+	1.15555i
$957$	33.2733	+	13.2308i	1.07557	+	0.427692i
$958$	−12.3307	−	13.5363i	−0.398387	−	0.437338i
$959$	−21.4186	−	9.94044i	−0.691644	−	0.320993i
$960$	−26.8831	−	35.2837i	−0.867649	−	1.13878i
$961$	15.2446	−	26.4045i	0.491762	−	0.851757i
$962$	16.8927	+	5.38090i	0.544641	+	0.173487i
$963$	−44.8214	+	1.27578i	−1.44435	+	0.0411114i
$964$	9.16004	−	12.9195i	0.295025	−	0.416109i
$965$	2.00527	+	2.00527i	0.0645518	+	0.0645518i
$966$	33.0539	+	22.5051i	1.06349	+	0.724091i
$967$		−	25.2751i		−	0.812794i	−0.913697	−	0.406397i	$-0.866785\pi$
$967$		−	25.2751i		−	0.812794i	0.913697	−	0.406397i	$-0.133215\pi$
$968$	1.56243	−	0.191691i	0.0502183	−	0.00616117i
$969$	3.78809	+	0.443979i	0.121691	+	0.0142627i
$970$	7.06800	+	13.6755i	0.226940	+	0.439095i
$971$	25.5797	−	6.85405i	0.820891	−	0.219957i	0.176155	−	0.984362i	$-0.443634\pi$
$971$	25.5797	−	6.85405i	0.820891	−	0.219957i	0.644736	+	0.764405i	$0.276967\pi$
$972$	25.1460	−	18.4304i	0.806558	−	0.591155i
$973$	−8.22154	+	47.1261i	−0.263571	+	1.51079i
$974$	29.8754	−	27.2146i	0.957271	−	0.872013i
$975$	36.2705	−	15.6320i	1.16159	−	0.500624i
$976$	−23.2070	+	48.2768i	−0.742839	+	1.54530i
$977$	42.9667	−	24.8068i	1.37462	−	0.793640i	0.383119	−	0.923699i	$-0.374850\pi$
$977$	42.9667	−	24.8068i	1.37462	−	0.793640i	0.991506	+	0.130059i	$0.0415167\pi$
$978$	−26.9077	−	12.1794i	−0.860412	−	0.389455i
$979$	−7.66507	−	7.66507i	−0.244977	−	0.244977i
$980$	15.2336	+	42.1494i	0.486618	+	1.34641i
$981$	28.3126	−	52.4296i	0.903953	−	1.67395i
$982$	−3.28814	+	5.12801i	−0.104929	+	0.163641i
$983$	32.0051	−	18.4781i	1.02080	−	0.589361i	0.106467	−	0.994316i	$-0.466046\pi$
$983$	32.0051	−	18.4781i	1.02080	−	0.589361i	0.914337	+	0.404955i	$0.132713\pi$
$984$	−19.5828	−	5.13389i	−0.624277	−	0.163662i
$985$	−29.4870	+	51.0729i	−0.939533	+	1.62732i
$986$	−1.14842	+	24.6401i	−0.0365730	+	0.784700i
$987$	−14.1184	−	14.9198i	−0.449393	−	0.474902i
$988$	6.98783	+	0.652790i	0.222312	+	0.0207680i
$989$	−2.48238	+	0.665152i	−0.0789351	+	0.0211506i
$990$	0.795181	−	43.8843i	0.0252725	−	1.39473i
$991$	7.96247	+	13.7914i	0.252936	+	0.438098i	0.964333	−	0.264692i	$-0.0852704\pi$
$991$	7.96247	+	13.7914i	0.252936	+	0.438098i	−0.711397	+	0.702791i	$0.751937\pi$
$992$	1.28310	+	44.3397i	0.0407386	+	1.40779i
$993$	27.6411	−	37.1039i	0.877164	−	1.17746i
$994$	2.24159	−	2.44074i	0.0710991	−	0.0774156i
$995$	−24.1094	−	24.1094i	−0.764319	−	0.764319i
$996$	−8.22592	−	25.3496i	−0.260648	−	0.803231i
$997$	17.4402	+	4.67309i	0.552337	+	0.147998i	0.524184	−	0.851605i	$-0.324371\pi$
$997$	17.4402	+	4.67309i	0.552337	+	0.147998i	0.0281537	+	0.999604i	$0.491037\pi$
$998$	6.49546	+	12.5678i	0.205610	+	0.397825i
$999$	9.62588	+	11.4938i	0.304549	+	0.363648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.5	✓	240
3.2	odd	2	inner	336.2.bo.a.5.56	yes	240
7.3	odd	6	inner	336.2.bo.a.101.36	yes	240
16.13	even	4	inner	336.2.bo.a.173.25	yes	240
21.17	even	6	inner	336.2.bo.a.101.25	yes	240
48.29	odd	4	inner	336.2.bo.a.173.36	yes	240
112.45	odd	12	inner	336.2.bo.a.269.56	yes	240
336.269	even	12	inner	336.2.bo.a.269.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.5	✓	240	1.1	even	1	trivial
336.2.bo.a.5.56	yes	240	3.2	odd	2	inner
336.2.bo.a.101.25	yes	240	21.17	even	6	inner
336.2.bo.a.101.36	yes	240	7.3	odd	6	inner
336.2.bo.a.173.25	yes	240	16.13	even	4	inner
336.2.bo.a.173.36	yes	240	48.29	odd	4	inner
336.2.bo.a.269.5	yes	240	336.269	even	12	inner
336.2.bo.a.269.56	yes	240	112.45	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38159 + 0.302030i) q^{2} +(-1.35899 + 1.07385i) q^{3} +(1.81756 - 0.834561i) q^{4} +(-3.09219 + 0.828549i) q^{5} +(1.55322 - 1.89407i) q^{6} +(-2.16452 + 1.52147i) q^{7} +(-2.25904 + 1.70197i) q^{8} +(0.693695 - 2.91870i) q^{9} +O(q^{10})\)	\(q+(-1.38159 + 0.302030i) q^{2} +(-1.35899 + 1.07385i) q^{3} +(1.81756 - 0.834561i) q^{4} +(-3.09219 + 0.828549i) q^{5} +(1.55322 - 1.89407i) q^{6} +(-2.16452 + 1.52147i) q^{7} +(-2.25904 + 1.70197i) q^{8} +(0.693695 - 2.91870i) q^{9} +(4.02187 - 2.07865i) q^{10} +(3.12152 + 0.836408i) q^{11} +(-1.57384 + 3.08594i) q^{12} +(-3.07235 - 3.07235i) q^{13} +(2.53094 - 2.75579i) q^{14} +(3.31251 - 4.44653i) q^{15} +(2.60701 - 3.03372i) q^{16} +(1.36326 + 2.36124i) q^{17} +(-0.0768638 + 4.24194i) q^{18} +(-0.780112 + 0.209030i) q^{19} +(-4.92875 + 4.08655i) q^{20} +(1.30773 - 4.39202i) q^{21} +(-4.56526 - 0.212776i) q^{22} +(3.08514 - 5.34363i) q^{23} +(1.24235 - 4.73884i) q^{24} +(4.54500 - 2.62406i) q^{25} +(5.17266 + 3.31677i) q^{26} +(2.19152 + 4.71140i) q^{27} +(-2.66437 + 4.57177i) q^{28} +(-4.52350 - 4.52350i) q^{29} +(-3.23352 + 7.14374i) q^{30} +(6.79094 - 3.92075i) q^{31} +(-2.68554 + 4.97874i) q^{32} +(-5.14028 + 2.21537i) q^{33} +(-2.59663 - 2.85050i) q^{34} +(5.43248 - 6.49807i) q^{35} +(-1.17500 - 5.88382i) q^{36} +(2.78693 - 0.746757i) q^{37} +(1.01466 - 0.524411i) q^{38} +(7.47453 + 0.876045i) q^{39} +(5.57522 - 7.13455i) q^{40} -4.13241i q^{41} +(-0.480211 + 6.46292i) q^{42} +(-0.294513 - 0.294513i) q^{43} +(6.37157 - 1.08488i) q^{44} +(0.273248 + 9.59992i) q^{45} +(-2.64845 + 8.31448i) q^{46} +(2.24120 - 3.88187i) q^{47} +(-0.285139 + 6.92233i) q^{48} +(2.37027 - 6.58649i) q^{49} +(-5.48676 + 4.99809i) q^{50} +(-4.38827 - 1.74496i) q^{51} +(-8.14823 - 3.02010i) q^{52} +(-5.77126 - 1.54640i) q^{53} +(-4.45075 - 5.84729i) q^{54} -10.3453 q^{55} +(2.30024 - 7.12102i) q^{56} +(0.835696 - 1.12179i) q^{57} +(7.61583 + 4.88336i) q^{58} +(-1.56377 + 5.83606i) q^{59} +(2.30976 - 10.8463i) q^{60} +(-12.9350 + 3.46591i) q^{61} +(-8.19808 + 7.46793i) q^{62} +(2.93919 + 7.37300i) q^{63} +(2.20656 - 7.68967i) q^{64} +(12.0459 + 6.95469i) q^{65} +(6.43263 - 4.61325i) q^{66} +(2.48018 + 0.664561i) q^{67} +(4.44840 + 3.15395i) q^{68} +(1.54558 + 10.5749i) q^{69} +(-5.54282 + 10.6184i) q^{70} +0.885678 q^{71} +(3.40046 + 7.77412i) q^{72} +(-7.04045 - 12.1944i) q^{73} +(-3.62484 + 1.87345i) q^{74} +(-3.35876 + 8.44671i) q^{75} +(-1.24345 + 1.03098i) q^{76} +(-8.02915 + 2.93887i) q^{77} +(-10.5913 + 1.04720i) q^{78} +(-7.20211 + 12.4744i) q^{79} +(-5.54779 + 11.5409i) q^{80} +(-8.03757 - 4.04937i) q^{81} +(1.24811 + 5.70927i) q^{82} +(-5.44007 + 5.44007i) q^{83} +(-1.28855 - 9.07412i) q^{84} +(-6.17186 - 6.17186i) q^{85} +(0.495846 + 0.317943i) q^{86} +(11.0049 + 1.28982i) q^{87} +(-8.47520 + 3.42326i) q^{88} +(-2.90496 - 1.67718i) q^{89} +(-3.27698 - 13.1806i) q^{90} +(11.3246 + 1.97568i) q^{91} +(1.14784 - 12.2871i) q^{92} +(-5.01851 + 12.6207i) q^{93} +(-1.92396 + 6.04004i) q^{94} +(2.23906 - 1.29272i) q^{95} +(-1.69681 - 9.64991i) q^{96} +3.40029i q^{97} +(-1.28542 + 9.81569i) q^{98} +(4.60660 - 8.53055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

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