LMFDB - Embedded newform 315.2.bs.d.52.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(52,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3, 2]))

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

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

chi := DirichletCharacter("315.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bs (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			52.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.52
Dual form			315.2.bs.d.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(1.23205 + 1.86603i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(1.23205 + 1.86603i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.232051 + 1.13397i) q^{10} +(1.00000 + 1.73205i) q^{11} +(1.50000 - 2.59808i) q^{12} +(0.0980762 - 0.366025i) q^{13} +(0.598076 - 1.23205i) q^{14} +(0.232051 + 3.86603i) q^{15} -2.46410 q^{16} +(-0.535898 - 2.00000i) q^{17} +(-0.401924 + 1.50000i) q^{18} +(-0.366025 - 0.633975i) q^{19} +(3.23205 - 2.13397i) q^{20} +(0.866025 - 4.50000i) q^{21} +(-0.267949 + 1.00000i) q^{22} +(1.63397 + 6.09808i) q^{23} +(3.23205 - 0.866025i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(0.169873 - 0.0980762i) q^{26} +5.19615i q^{27} +(-4.33013 + 1.50000i) q^{28} +(-8.59808 - 4.96410i) q^{29} +(-1.33013 + 1.50000i) q^{30} -5.46410i q^{31} +(-3.63397 - 3.63397i) q^{32} +3.46410i q^{33} +(0.535898 - 0.928203i) q^{34} +(3.59808 - 4.69615i) q^{35} +(4.50000 - 2.59808i) q^{36} +(-2.36603 + 8.83013i) q^{37} +(0.0980762 - 0.366025i) q^{38} +(0.464102 - 0.464102i) q^{39} +(4.23205 + 0.866025i) q^{40} +(2.59808 - 1.50000i) q^{41} +(1.96410 - 1.33013i) q^{42} +(-0.232051 - 0.866025i) q^{43} +(3.00000 - 1.73205i) q^{44} +(-3.00000 + 6.00000i) q^{45} +(-1.63397 + 2.83013i) q^{46} +(3.63397 - 3.63397i) q^{47} +(-3.69615 - 2.13397i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(-2.40192 + 0.964102i) q^{50} +(0.928203 - 3.46410i) q^{51} +(-0.633975 - 0.169873i) q^{52} +(0.267949 + 1.00000i) q^{53} +(-1.90192 + 1.90192i) q^{54} +(-2.00000 + 4.00000i) q^{55} +(-4.59808 - 2.23205i) q^{56} -1.26795i q^{57} +(-1.33013 - 4.96410i) q^{58} -9.12436 q^{59} +(6.69615 - 0.401924i) q^{60} -10.9282i q^{61} +(2.00000 - 2.00000i) q^{62} +(5.19615 - 6.00000i) q^{63} +2.26795i q^{64} +(0.803848 - 0.267949i) q^{65} +(-1.26795 + 1.26795i) q^{66} +(2.46410 + 2.46410i) q^{67} +(-3.46410 + 0.928203i) q^{68} +(-2.83013 + 10.5622i) q^{69} +(3.03590 - 0.401924i) q^{70} +1.26795 q^{71} +(5.59808 + 1.50000i) q^{72} +(-12.9282 + 3.46410i) q^{73} +(-4.09808 + 2.36603i) q^{74} +(-6.92820 + 5.19615i) q^{75} +(-1.09808 + 0.633975i) q^{76} +(3.46410 - 4.00000i) q^{77} +0.339746 q^{78} -11.4641i q^{79} +(-3.03590 - 4.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.50000 + 0.401924i) q^{82} +(9.96410 - 2.66987i) q^{83} +(-7.79423 - 1.50000i) q^{84} +(3.07180 - 3.46410i) q^{85} +(0.232051 - 0.401924i) q^{86} +(-8.59808 - 14.8923i) q^{87} +(3.73205 + 1.00000i) q^{88} +(0.535898 + 0.928203i) q^{89} +(-3.29423 + 1.09808i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(10.5622 - 2.83013i) q^{92} +(4.73205 - 8.19615i) q^{93} +2.66025 q^{94} +(0.732051 - 1.46410i) q^{95} +(-2.30385 - 8.59808i) q^{96} +(-2.43782 - 9.09808i) q^{97} +(-3.59808 - 0.428203i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 2 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 2 q^{8} + 6 q^{9} + 6 q^{10} + 4 q^{11} + 6 q^{12} - 10 q^{13} - 8 q^{14} - 6 q^{15} + 4 q^{16} - 16 q^{17} - 12 q^{18} + 2 q^{19} + 6 q^{20} - 8 q^{22} + 10 q^{23} + 6 q^{24} + 6 q^{25} + 18 q^{26} - 24 q^{29} + 12 q^{30} - 18 q^{32} + 16 q^{34} + 4 q^{35} + 18 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} + 10 q^{40} - 6 q^{42} + 6 q^{43} + 12 q^{44} - 12 q^{45} - 10 q^{46} + 18 q^{47} + 6 q^{48} - 22 q^{49} - 20 q^{50} - 24 q^{51} - 6 q^{52} + 8 q^{53} - 18 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{58} + 12 q^{59} + 6 q^{60} + 8 q^{62} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 6 q^{69} + 26 q^{70} + 12 q^{71} + 12 q^{72} - 24 q^{73} - 6 q^{74} + 6 q^{76} + 36 q^{78} - 26 q^{80} - 18 q^{81} + 6 q^{82} + 26 q^{83} + 40 q^{85} - 6 q^{86} - 24 q^{87} + 8 q^{88} + 16 q^{89} + 18 q^{90} - 4 q^{91} + 18 q^{92} + 12 q^{93} - 24 q^{94} - 4 q^{95} - 30 q^{96} - 34 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 2 * q^8 + 6 * q^9 + 6 * q^10 + 4 * q^11 + 6 * q^12 - 10 * q^13 - 8 * q^14 - 6 * q^15 + 4 * q^16 - 16 * q^17 - 12 * q^18 + 2 * q^19 + 6 * q^20 - 8 * q^22 + 10 * q^23 + 6 * q^24 + 6 * q^25 + 18 * q^26 - 24 * q^29 + 12 * q^30 - 18 * q^32 + 16 * q^34 + 4 * q^35 + 18 * q^36 - 6 * q^37 - 10 * q^38 - 12 * q^39 + 10 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 12 * q^45 - 10 * q^46 + 18 * q^47 + 6 * q^48 - 22 * q^49 - 20 * q^50 - 24 * q^51 - 6 * q^52 + 8 * q^53 - 18 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^58 + 12 * q^59 + 6 * q^60 + 8 * q^62 + 24 * q^65 - 12 * q^66 - 4 * q^67 + 6 * q^69 + 26 * q^70 + 12 * q^71 + 12 * q^72 - 24 * q^73 - 6 * q^74 + 6 * q^76 + 36 * q^78 - 26 * q^80 - 18 * q^81 + 6 * q^82 + 26 * q^83 + 40 * q^85 - 6 * q^86 - 24 * q^87 + 8 * q^88 + 16 * q^89 + 18 * q^90 - 4 * q^91 + 18 * q^92 + 12 * q^93 - 24 * q^94 - 4 * q^95 - 30 * q^96 - 34 * q^97 - 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	0.824574	−	0.565755i	$-0.191415\pi$
$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	−0.565755	+	0.824574i	$0.691415\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		−	1.73205i		−	0.866025i
$5$	1.23205	+	1.86603i	0.550990	+	0.834512i
$5$	1.23205	+	1.86603i	0.550990	+	0.834512i
$6$	0.232051	+	0.866025i	0.0947343	+	0.353553i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	1.36603	−	1.36603i	0.482963	−	0.482963i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−0.232051	+	1.13397i	−0.0733809	+	0.358594i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	0.0980762	−	0.366025i	0.0272014	−	0.101517i	−0.950991	−	0.309220i	$-0.899932\pi$
$13$	0.0980762	−	0.366025i	0.0272014	−	0.101517i	0.978192	+	0.207703i	$0.0665987\pi$
$14$	0.598076	−	1.23205i	0.159843	−	0.329279i
$15$	0.232051	+	3.86603i	0.0599153	+	0.998203i
$16$	−2.46410			−0.616025
$17$	−0.535898	−	2.00000i	−0.129974	−	0.485071i	0.869994	−	0.493063i	$-0.164123\pi$
$17$	−0.535898	−	2.00000i	−0.129974	−	0.485071i	−0.999968	+	0.00799174i	$0.997456\pi$
$18$	−0.401924	+	1.50000i	−0.0947343	+	0.353553i
$19$	−0.366025	−	0.633975i	−0.0839720	−	0.145444i	0.820981	−	0.570956i	$-0.193427\pi$
$19$	−0.366025	−	0.633975i	−0.0839720	−	0.145444i	−0.904953	+	0.425512i	$0.860094\pi$
$20$	3.23205	−	2.13397i	0.722709	−	0.477171i
$21$	0.866025	−	4.50000i	0.188982	−	0.981981i
$22$	−0.267949	+	1.00000i	−0.0571270	+	0.213201i
$23$	1.63397	+	6.09808i	0.340707	+	1.27154i	0.897548	+	0.440917i	$0.145347\pi$
$23$	1.63397	+	6.09808i	0.340707	+	1.27154i	−0.556840	+	0.830619i	$0.687987\pi$
$24$	3.23205	−	0.866025i	0.659740	−	0.176777i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	0.169873	−	0.0980762i	0.0333148	−	0.0192343i
$27$			5.19615i			1.00000i
$28$	−4.33013	+	1.50000i	−0.818317	+	0.283473i
$29$	−8.59808	−	4.96410i	−1.59662	−	0.921811i	−0.992132	−	0.125199i	$-0.960043\pi$
$29$	−8.59808	−	4.96410i	−1.59662	−	0.921811i	−0.604491	−	0.796612i	$-0.706623\pi$
$30$	−1.33013	+	1.50000i	−0.242847	+	0.273861i
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	−3.63397	−	3.63397i	−0.642402	−	0.642402i
$33$			3.46410i			0.603023i
$34$	0.535898	−	0.928203i	0.0919058	−	0.159186i
$35$	3.59808	−	4.69615i	0.608186	−	0.793795i
$36$	4.50000	−	2.59808i	0.750000	−	0.433013i
$37$	−2.36603	+	8.83013i	−0.388972	+	1.45166i	0.442837	+	0.896602i	$0.353972\pi$
$37$	−2.36603	+	8.83013i	−0.388972	+	1.45166i	−0.831809	+	0.555062i	$0.812695\pi$
$38$	0.0980762	−	0.366025i	0.0159101	−	0.0593772i
$39$	0.464102	−	0.464102i	0.0743157	−	0.0743157i
$40$	4.23205	+	0.866025i	0.669146	+	0.136931i
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	1.96410	−	1.33013i	0.303067	−	0.205243i
$43$	−0.232051	−	0.866025i	−0.0353874	−	0.132068i	0.945972	−	0.324247i	$-0.105111\pi$
$43$	−0.232051	−	0.866025i	−0.0353874	−	0.132068i	−0.981360	+	0.192180i	$0.938444\pi$
$44$	3.00000	−	1.73205i	0.452267	−	0.261116i
$45$	−3.00000	+	6.00000i	−0.447214	+	0.894427i
$46$	−1.63397	+	2.83013i	−0.240916	+	0.417279i
$47$	3.63397	−	3.63397i	0.530070	−	0.530070i	−0.390523	−	0.920593i	$-0.627706\pi$
$47$	3.63397	−	3.63397i	0.530070	−	0.530070i	0.920593	+	0.390523i	$0.127706\pi$
$48$	−3.69615	−	2.13397i	−0.533494	−	0.308013i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	−2.40192	+	0.964102i	−0.339683	+	0.136345i
$51$	0.928203	−	3.46410i	0.129974	−	0.485071i
$52$	−0.633975	−	0.169873i	−0.0879165	−	0.0235571i
$53$	0.267949	+	1.00000i	0.0368057	+	0.137361i	0.981884	−	0.189484i	$-0.0606814\pi$
$53$	0.267949	+	1.00000i	0.0368057	+	0.137361i	−0.945078	+	0.326844i	$0.894015\pi$
$54$	−1.90192	+	1.90192i	−0.258819	+	0.258819i
$55$	−2.00000	+	4.00000i	−0.269680	+	0.539360i
$56$	−4.59808	−	2.23205i	−0.614444	−	0.298270i
$57$		−	1.26795i		−	0.167944i
$58$	−1.33013	−	4.96410i	−0.174654	−	0.651818i
$59$	−9.12436			−1.18789			−0.593945	−	0.804506i	$-0.702430\pi$
$59$	−9.12436			−1.18789			−0.593945	+	0.804506i	$0.702430\pi$
$60$	6.69615	−	0.401924i	0.864470	−	0.0518881i
$61$		−	10.9282i		−	1.39921i	−0.714528	−	0.699607i	$-0.753359\pi$
$61$		−	10.9282i		−	1.39921i	0.714528	−	0.699607i	$-0.246641\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$	5.19615	−	6.00000i	0.654654	−	0.755929i
$64$			2.26795i			0.283494i
$65$	0.803848	−	0.267949i	0.0997050	−	0.0332350i
$66$	−1.26795	+	1.26795i	−0.156074	+	0.156074i
$67$	2.46410	+	2.46410i	0.301038	+	0.301038i	0.841420	−	0.540382i	$-0.181720\pi$
$67$	2.46410	+	2.46410i	0.301038	+	0.301038i	−0.540382	+	0.841420i	$0.681720\pi$
$68$	−3.46410	+	0.928203i	−0.420084	+	0.112561i
$69$	−2.83013	+	10.5622i	−0.340707	+	1.27154i
$70$	3.03590	−	0.401924i	0.362859	−	0.0480391i
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	5.59808	+	1.50000i	0.659740	+	0.176777i
$73$	−12.9282	+	3.46410i	−1.51313	+	0.405442i	−0.917474	−	0.397796i	$-0.869775\pi$
$73$	−12.9282	+	3.46410i	−1.51313	+	0.405442i	−0.595658	+	0.803238i	$0.703109\pi$
$74$	−4.09808	+	2.36603i	−0.476392	+	0.275045i
$75$	−6.92820	+	5.19615i	−0.800000	+	0.600000i
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	3.46410	−	4.00000i	0.394771	−	0.455842i
$78$	0.339746			0.0384687
$79$		−	11.4641i		−	1.28981i	−0.764262	−	0.644906i	$-0.776896\pi$
$79$		−	11.4641i		−	1.28981i	0.764262	−	0.644906i	$-0.223104\pi$
$80$	−3.03590	−	4.59808i	−0.339424	−	0.514081i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	1.50000	+	0.401924i	0.165647	+	0.0443851i
$83$	9.96410	−	2.66987i	1.09370	−	0.293057i	0.333505	−	0.942748i	$-0.391769\pi$
$83$	9.96410	−	2.66987i	1.09370	−	0.293057i	0.760198	+	0.649692i	$0.225102\pi$
$84$	−7.79423	−	1.50000i	−0.850420	−	0.163663i
$85$	3.07180	−	3.46410i	0.333183	−	0.375735i
$86$	0.232051	−	0.401924i	0.0250227	−	0.0433406i
$87$	−8.59808	−	14.8923i	−0.921811	−	1.59662i
$88$	3.73205	+	1.00000i	0.397838	+	0.106600i
$89$	0.535898	+	0.928203i	0.0568051	+	0.0983893i	0.893030	−	0.449998i	$-0.148575\pi$
$89$	0.535898	+	0.928203i	0.0568051	+	0.0983893i	−0.836224	+	0.548387i	$0.815242\pi$
$90$	−3.29423	+	1.09808i	−0.347242	+	0.115747i
$91$	−1.00000	+	0.0717968i	−0.104828	+	0.00752635i
$92$	10.5622	−	2.83013i	1.10118	−	0.295061i
$93$	4.73205	−	8.19615i	0.490691	−	0.849901i
$94$	2.66025			0.274384
$95$	0.732051	−	1.46410i	0.0751068	−	0.150214i
$96$	−2.30385	−	8.59808i	−0.235135	−	0.877537i
$97$	−2.43782	−	9.09808i	−0.247523	−	0.923770i	−0.972098	−	0.234574i	$-0.924631\pi$
$97$	−2.43782	−	9.09808i	−0.247523	−	0.923770i	0.724575	−	0.689196i	$-0.242036\pi$
$98$	−3.59808	−	0.428203i	−0.363461	−	0.0432551i
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$	7.96410	+	3.40192i	0.796410	+	0.340192i
$101$	−0.232051	+	0.133975i	−0.0230899	+	0.0133310i	−0.511501	−	0.859283i	$-0.670910\pi$
$101$	−0.232051	+	0.133975i	−0.0230899	+	0.0133310i	0.488411	+	0.872614i	$0.337577\pi$
$102$	1.60770	−	0.928203i	0.159186	−	0.0919058i
$103$	−6.33013	+	1.69615i	−0.623726	+	0.167127i	−0.556821	−	0.830632i	$-0.687979\pi$
$103$	−6.33013	+	1.69615i	−0.623726	+	0.167127i	−0.0669049	+	0.997759i	$0.521312\pi$
$104$	−0.366025	−	0.633975i	−0.0358917	−	0.0621663i
$105$	9.46410	−	3.92820i	0.923602	−	0.383353i
$106$	−0.267949	+	0.464102i	−0.0260255	+	0.0450775i
$107$	−2.42820	+	9.06218i	−0.234743	+	0.876074i	0.743521	+	0.668712i	$0.233154\pi$
$107$	−2.42820	+	9.06218i	−0.234743	+	0.876074i	−0.978264	+	0.207361i	$0.933512\pi$
$108$	9.00000			0.866025
$109$	−8.42820	−	4.86603i	−0.807275	−	0.466081i	0.0387334	−	0.999250i	$-0.487668\pi$
$109$	−8.42820	−	4.86603i	−0.807275	−	0.466081i	−0.846009	+	0.533169i	$0.821001\pi$
$110$	−2.19615	+	0.732051i	−0.209395	+	0.0697983i
$111$	−11.1962	+	11.1962i	−1.06269	+	1.06269i
$112$	2.13397	+	6.16025i	0.201642	+	0.582089i
$113$	9.46410	+	2.53590i	0.890308	+	0.238557i	0.674849	−	0.737956i	$-0.264209\pi$
$113$	9.46410	+	2.53590i	0.890308	+	0.238557i	0.215459	+	0.976513i	$0.430875\pi$
$114$	0.464102	−	0.464102i	0.0434671	−	0.0434671i
$115$	−9.36603	+	10.5622i	−0.873386	+	0.984928i
$116$	−8.59808	+	14.8923i	−0.798311	+	1.38272i
$117$	1.09808	−	0.294229i	0.101517	−	0.0272014i
$118$	−3.33975	−	3.33975i	−0.307449	−	0.307449i
$119$	−4.53590	+	3.07180i	−0.415805	+	0.281591i
$120$	5.59808	+	4.96410i	0.511032	+	0.453158i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	4.00000	−	4.00000i	0.362143	−	0.362143i
$123$	5.19615			0.468521
$124$	−9.46410			−0.849901
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	4.09808	−	0.294229i	0.365086	−	0.0262120i
$127$	11.3660	+	11.3660i	1.00857	+	1.00857i	0.999963	+	0.00860872i	$0.00274027\pi$
$127$	11.3660	+	11.3660i	1.00857	+	1.00857i	0.00860872	+	0.999963i	$0.497260\pi$
$128$	−8.09808	+	8.09808i	−0.715776	+	0.715776i
$129$	0.401924	−	1.50000i	0.0353874	−	0.132068i
$130$	0.392305	+	0.196152i	0.0344074	+	0.0172037i
$131$	16.3923	+	9.46410i	1.43220	+	0.826882i	0.997289	−	0.0735897i	$-0.0234455\pi$
$131$	16.3923	+	9.46410i	1.43220	+	0.826882i	0.434914	+	0.900472i	$0.356779\pi$
$132$	6.00000			0.522233
$133$	−1.26795	+	1.46410i	−0.109945	+	0.126954i
$134$			1.80385i			0.155829i
$135$	−9.69615	+	6.40192i	−0.834512	+	0.550990i
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	0.366025	−	1.36603i	0.0312717	−	0.116707i	−0.948526	−	0.316700i	$-0.897425\pi$
$137$	0.366025	−	1.36603i	0.0312717	−	0.116707i	0.979797	+	0.199993i	$0.0640918\pi$
$138$	−4.90192	+	2.83013i	−0.417279	+	0.240916i
$139$	9.29423	+	16.0981i	0.788326	+	1.36542i	0.926992	+	0.375082i	$0.122385\pi$
$139$	9.29423	+	16.0981i	0.788326	+	1.36542i	−0.138666	+	0.990339i	$0.544281\pi$
$140$	−8.13397	−	6.23205i	−0.687446	−	0.526704i
$141$	8.59808	−	2.30385i	0.724089	−	0.194019i
$142$	0.464102	+	0.464102i	0.0389465	+	0.0389465i
$143$	0.732051	−	0.196152i	0.0612172	−	0.0164031i
$144$	−3.69615	−	6.40192i	−0.308013	−	0.533494i
$145$	−1.33013	−	22.1603i	−0.110461	−	1.84031i
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$	15.2942	+	4.09808i	1.25718	+	0.336860i
$149$	7.39230	+	4.26795i	0.605601	+	0.349644i	0.771242	−	0.636542i	$-0.219636\pi$
$149$	7.39230	+	4.26795i	0.605601	+	0.349644i	−0.165641	+	0.986186i	$0.552969\pi$
$150$	−4.43782	−	0.633975i	−0.362347	−	0.0517638i
$151$	0.169873	+	0.294229i	0.0138241	+	0.0239440i	0.872855	−	0.487980i	$-0.162266\pi$
$151$	0.169873	+	0.294229i	0.0138241	+	0.0239440i	−0.859031	+	0.511924i	$0.828933\pi$
$152$	−1.36603	−	0.366025i	−0.110799	−	0.0296886i
$153$	4.39230	−	4.39230i	0.355097	−	0.355097i
$154$	2.73205	−	0.196152i	0.220155	−	0.0158064i
$155$	10.1962	−	6.73205i	0.818975	−	0.540731i
$156$	−0.803848	−	0.803848i	−0.0643593	−	0.0643593i
$157$	3.19615	−	3.19615i	0.255081	−	0.255081i	−0.567969	−	0.823050i	$-0.692271\pi$
$157$	3.19615	−	3.19615i	0.255081	−	0.255081i	0.823050	+	0.567969i	$0.192271\pi$
$158$	4.19615	−	4.19615i	0.333828	−	0.333828i
$159$	−0.464102	+	1.73205i	−0.0368057	+	0.137361i
$160$	2.30385	−	11.2583i	0.182135	−	0.890049i
$161$	13.8301	−	9.36603i	1.08997	−	0.738146i
$162$	−4.50000	+	1.20577i	−0.353553	+	0.0947343i
$163$	23.4904	+	6.29423i	1.83991	+	0.493002i	0.998850	−	0.0479421i	$-0.0152663\pi$
$163$	23.4904	+	6.29423i	1.83991	+	0.493002i	0.841059	+	0.540944i	$0.181933\pi$
$164$	−2.59808	−	4.50000i	−0.202876	−	0.351391i
$165$	−6.46410	+	4.26795i	−0.503230	+	0.332259i
$166$	4.62436	+	2.66987i	0.358920	+	0.207222i
$167$	6.09808	+	1.63397i	0.471883	+	0.126441i	0.486921	−	0.873446i	$-0.338120\pi$
$167$	6.09808	+	1.63397i	0.471883	+	0.126441i	−0.0150374	+	0.999887i	$0.504787\pi$
$168$	−4.96410	−	7.33013i	−0.382989	−	0.565532i
$169$	11.1340	+	6.42820i	0.856460	+	0.494477i
$170$	2.39230	−	0.143594i	0.183481	−	0.0110131i
$171$	1.09808	−	1.90192i	0.0839720	−	0.145444i
$172$	−1.50000	+	0.401924i	−0.114374	+	0.0306464i
$173$	16.0000	+	16.0000i	1.21646	+	1.21646i	0.968864	+	0.247593i	$0.0796397\pi$
$173$	16.0000	+	16.0000i	1.21646	+	1.21646i	0.247593	+	0.968864i	$0.420360\pi$
$174$	2.30385	−	8.59808i	0.174654	−	0.651818i
$175$	13.1962	+	0.928203i	0.997535	+	0.0701656i
$176$	−2.46410	−	4.26795i	−0.185739	−	0.321709i
$177$	−13.6865	−	7.90192i	−1.02874	−	0.593945i
$178$	−0.143594	+	0.535898i	−0.0107628	+	0.0401673i
$179$	4.09808	+	2.36603i	0.306305	+	0.176845i	0.645272	−	0.763953i	$-0.276744\pi$
$179$	4.09808	+	2.36603i	0.306305	+	0.176845i	−0.338967	+	0.940798i	$0.610078\pi$
$180$	10.3923	+	5.19615i	0.774597	+	0.387298i
$181$		−	4.12436i		−	0.306561i	−0.988183	−	0.153280i	$-0.951016\pi$
$181$		−	4.12436i		−	0.306561i	0.988183	−	0.153280i	$-0.0489838\pi$
$182$	−0.392305	−	0.339746i	−0.0290796	−	0.0251836i
$183$	9.46410	−	16.3923i	0.699607	−	1.21175i
$184$	10.5622	+	6.09808i	0.778654	+	0.449556i
$185$	−19.3923	+	6.46410i	−1.42575	+	0.475250i
$186$	4.73205	−	1.26795i	0.346971	−	0.0929705i
$187$	2.92820	−	2.92820i	0.214131	−	0.214131i
$188$	−6.29423	−	6.29423i	−0.459054	−	0.459054i
$189$	12.9904	−	4.50000i	0.944911	−	0.327327i
$190$	0.803848	−	0.267949i	0.0583172	−	0.0194391i
$191$	−20.1962			−1.46134			−0.730671	−	0.682730i	$-0.760793\pi$
$191$	−20.1962			−1.46134			−0.730671	+	0.682730i	$0.760793\pi$
$192$	−1.96410	+	3.40192i	−0.141747	+	0.245513i
$193$	−10.1962	+	10.1962i	−0.733935	+	0.733935i	−0.971397	−	0.237462i	$-0.923685\pi$
$193$	−10.1962	+	10.1962i	−0.733935	+	0.733935i	0.237462	+	0.971397i	$0.423685\pi$
$194$	2.43782	−	4.22243i	0.175025	−	0.303153i
$195$	1.43782	+	0.294229i	0.102965	+	0.0210702i
$196$	7.50000	+	9.52628i	0.535714	+	0.680449i
$197$	4.00000	+	4.00000i	0.284988	+	0.284988i	0.835095	−	0.550106i	$-0.185413\pi$
$197$	4.00000	+	4.00000i	0.284988	+	0.284988i	−0.550106	+	0.835095i	$0.685413\pi$
$198$	−3.00000	+	0.803848i	−0.213201	+	0.0571270i
$199$	8.19615	−	14.1962i	0.581010	−	1.00634i	−0.414350	−	0.910118i	$-0.635991\pi$
$199$	8.19615	−	14.1962i	0.581010	−	1.00634i	0.995360	−	0.0962210i	$-0.0306756\pi$
$200$	3.59808	+	8.96410i	0.254422	+	0.633858i
$201$	1.56218	+	5.83013i	0.110188	+	0.411225i
$202$	−0.133975	−	0.0358984i	−0.00942642	−	0.00252580i
$203$	−4.96410	+	25.7942i	−0.348412	+	1.81040i
$204$	−6.00000	−	1.60770i	−0.420084	−	0.112561i
$205$	6.00000	+	3.00000i	0.419058	+	0.209529i
$206$	−2.93782	−	1.69615i	−0.204688	−	0.118177i
$207$	−13.3923	+	13.3923i	−0.930830	+	0.930830i
$208$	−0.241670	+	0.901924i	−0.0167568	+	0.0625372i
$209$	0.732051	−	1.26795i	0.0506370	−	0.0877059i
$210$	4.90192	+	2.02628i	0.338265	+	0.139827i
$211$	−13.4641	−	23.3205i	−0.926907	−	1.60545i	−0.788465	−	0.615079i	$-0.789124\pi$
$211$	−13.4641	−	23.3205i	−0.926907	−	1.60545i	−0.138442	−	0.990371i	$-0.544209\pi$
$212$	1.73205	−	0.464102i	0.118958	−	0.0318746i
$213$	1.90192	+	1.09808i	0.130318	+	0.0752389i
$214$	−4.20577	+	2.42820i	−0.287501	+	0.165989i
$215$	1.33013	−	1.50000i	0.0907139	−	0.102299i
$216$	7.09808	+	7.09808i	0.482963	+	0.482963i
$217$	−13.6603	+	4.73205i	−0.927318	+	0.321233i
$218$	−1.30385	−	4.86603i	−0.0883077	−	0.329569i
$219$	−22.3923	−	6.00000i	−1.51313	−	0.405442i
$220$	6.92820	+	3.46410i	0.467099	+	0.233550i
$221$	−0.784610			−0.0527786
$222$	−8.19615			−0.550090
$223$	4.96410	−	1.33013i	0.332421	−	0.0890719i	−0.0887481	−	0.996054i	$-0.528287\pi$
$223$	4.96410	−	1.33013i	0.332421	−	0.0890719i	0.421169	+	0.906982i	$0.361620\pi$
$224$	−5.93782	+	12.2321i	−0.396737	+	0.817288i
$225$	−14.8923	+	1.79423i	−0.992820	+	0.119615i
$226$	2.53590	+	4.39230i	0.168685	+	0.292172i
$227$	24.0263	+	6.43782i	1.59468	+	0.427293i	0.943431	−	0.331570i	$-0.107578\pi$
$227$	24.0263	+	6.43782i	1.59468	+	0.427293i	0.651250	+	0.758864i	$0.274245\pi$
$228$	−2.19615			−0.145444
$229$	11.3301	−	19.6244i	0.748716	−	1.29681i	−0.199723	−	0.979852i	$-0.564004\pi$
$229$	11.3301	−	19.6244i	0.748716	−	1.29681i	0.948438	−	0.316961i	$-0.102663\pi$
$230$	−7.29423	+	0.437822i	−0.480967	+	0.0288691i
$231$	8.66025	−	3.00000i	0.569803	−	0.197386i
$232$	−18.5263	+	4.96410i	−1.21631	+	0.325909i
$233$	−20.6603	−	5.53590i	−1.35350	−	0.362669i	−0.492073	−	0.870554i	$-0.663761\pi$
$233$	−20.6603	−	5.53590i	−1.35350	−	0.362669i	−0.861425	+	0.507885i	$0.830427\pi$
$234$	0.509619	+	0.294229i	0.0333148	+	0.0192343i
$235$	11.2583	+	2.30385i	0.734412	+	0.150286i
$236$			15.8038i			1.02874i
$237$	9.92820	−	17.1962i	0.644906	−	1.11701i
$238$	−2.78461	−	0.535898i	−0.180499	−	0.0347371i
$239$	1.73205	−	1.00000i	0.112037	−	0.0646846i	−0.442934	−	0.896554i	$-0.646063\pi$
$239$	1.73205	−	1.00000i	0.112037	−	0.0646846i	0.554971	+	0.831869i	$0.312729\pi$
$240$	−0.571797	−	9.52628i	−0.0369093	−	0.614919i
$241$	−13.4545	+	7.76795i	−0.866679	+	0.500378i	−0.866243	−	0.499622i	$-0.833472\pi$
$241$	−13.4545	+	7.76795i	−0.866679	+	0.500378i	−0.000436064		1.00000i	$0.500139\pi$
$242$	3.50000	−	0.937822i	0.224989	−	0.0602855i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−18.9282			−1.21175
$245$	−14.8564	−	4.92820i	−0.949141	−	0.314851i
$246$	1.90192	+	1.90192i	0.121262	+	0.121262i
$247$	−0.267949	+	0.0717968i	−0.0170492	+	0.00456832i
$248$	−7.46410	−	7.46410i	−0.473971	−	0.473971i
$249$	17.2583	+	4.62436i	1.09370	+	0.293057i
$250$	−4.75833	−	3.29423i	−0.300943	−	0.208345i
$251$			13.6603i			0.862228i	0.902298	+	0.431114i	$0.141879\pi$
$251$			13.6603i			0.862228i	−0.902298	+	0.431114i	$0.858121\pi$
$252$	−10.3923	−	9.00000i	−0.654654	−	0.566947i
$253$	−8.92820	+	8.92820i	−0.561311	+	0.561311i
$254$			8.32051i			0.522075i
$255$	7.60770	−	2.53590i	0.476412	−	0.158804i
$256$	−1.39230			−0.0870191
$257$	−3.73205	−	13.9282i	−0.232799	−	0.868817i	−0.979129	−	0.203241i	$-0.934852\pi$
$257$	−3.73205	−	13.9282i	−0.232799	−	0.868817i	0.746330	−	0.665576i	$-0.231814\pi$
$258$	0.696152	−	0.401924i	0.0433406	−	0.0250227i
$259$	24.1244	−	1.73205i	1.49901	−	0.107624i
$260$	−0.464102	−	1.39230i	−0.0287824	−	0.0863471i
$261$		−	29.7846i		−	1.84362i
$262$	2.53590	+	9.46410i	0.156668	+	0.584694i
$263$	−12.4282	−	3.33013i	−0.766356	−	0.205344i	−0.145595	−	0.989344i	$-0.546510\pi$
$263$	−12.4282	−	3.33013i	−0.766356	−	0.205344i	−0.620761	+	0.784000i	$0.713176\pi$
$264$	4.73205	+	4.73205i	0.291238	+	0.291238i
$265$	−1.53590	+	1.73205i	−0.0943495	+	0.106399i
$266$	−1.00000	+	0.0717968i	−0.0613139	+	0.00440214i
$267$			1.85641i			0.113610i
$268$	4.26795	−	4.26795i	0.260706	−	0.260706i
$269$	−3.80385	+	6.58846i	−0.231925	+	0.401705i	−0.958374	−	0.285514i	$-0.907836\pi$
$269$	−3.80385	+	6.58846i	−0.231925	+	0.401705i	0.726450	+	0.687220i	$0.241169\pi$
$270$	−5.89230	−	1.20577i	−0.358594	−	0.0733809i
$271$	1.22243	−	0.705771i	0.0742574	−	0.0428726i	−0.462412	−	0.886665i	$-0.653016\pi$
$271$	1.22243	−	0.705771i	0.0742574	−	0.0428726i	0.536669	+	0.843793i	$0.319682\pi$
$272$	1.32051	+	4.92820i	0.0800676	+	0.298816i
$273$	−1.56218	−	0.758330i	−0.0945473	−	0.0458962i
$274$	0.633975	−	0.366025i	0.0382998	−	0.0221124i
$275$	−9.92820	+	1.19615i	−0.598693	+	0.0721307i
$276$	18.2942	+	4.90192i	1.10118	+	0.295061i
$277$	0.803848	−	3.00000i	0.0482985	−	0.180253i	−0.937563	−	0.347816i	$-0.886923\pi$
$277$	0.803848	−	3.00000i	0.0482985	−	0.180253i	0.985861	+	0.167564i	$0.0535900\pi$
$278$	−2.49038	+	9.29423i	−0.149363	+	0.557431i
$279$	14.1962	−	8.19615i	0.849901	−	0.490691i
$280$	−1.50000	−	11.3301i	−0.0896421	−	0.677105i
$281$	−12.8660	+	22.2846i	−0.767523	+	1.32939i	0.171380	+	0.985205i	$0.445178\pi$
$281$	−12.8660	+	22.2846i	−0.767523	+	1.32939i	−0.938902	+	0.344183i	$0.888156\pi$
$282$	3.99038	+	2.30385i	0.237624	+	0.137192i
$283$	−11.3660	−	11.3660i	−0.675640	−	0.675640i	0.283370	−	0.959011i	$-0.408547\pi$
$283$	−11.3660	−	11.3660i	−0.675640	−	0.675640i	−0.959011	+	0.283370i	$0.908547\pi$
$284$		−	2.19615i		−	0.130318i
$285$	2.36603	−	1.56218i	0.140151	−	0.0925354i
$286$	0.339746	+	0.196152i	0.0200896	+	0.0115987i
$287$	−6.00000	−	5.19615i	−0.354169	−	0.306719i
$288$	3.99038	−	14.8923i	0.235135	−	0.877537i
$289$	11.0096	−	6.35641i	0.647625	−	0.373906i
$290$	7.62436	−	8.59808i	0.447718	−	0.504896i
$291$	4.22243	−	15.7583i	0.247523	−	0.923770i
$292$	6.00000	+	22.3923i	0.351123	+	1.31041i
$293$	3.26795	−	12.1962i	0.190916	−	0.712507i	−0.802371	−	0.596826i	$-0.796428\pi$
$293$	3.26795	−	12.1962i	0.190916	−	0.712507i	0.993286	−	0.115681i	$-0.0369050\pi$
$294$	−5.02628	−	3.75833i	−0.293139	−	0.219190i
$295$	−11.2417	−	17.0263i	−0.654515	−	0.991308i
$296$	8.83013	+	15.2942i	0.513241	+	0.888959i
$297$	−9.00000	+	5.19615i	−0.522233	+	0.301511i
$298$	1.14359	+	4.26795i	0.0662466	+	0.247236i
$299$	2.39230			0.138351
$300$	9.00000	+	12.0000i	0.519615	+	0.692820i
$301$	−1.96410	+	1.33013i	−0.113209	+	0.0766672i
$302$	−0.0455173	+	0.169873i	−0.00261923	+	0.00977509i
$303$	−0.464102			−0.0266619
$304$	0.901924	+	1.56218i	0.0517289	+	0.0895970i
$305$	20.3923	−	13.4641i	1.16766	−	0.770952i
$306$	3.21539			0.183812
$307$	3.63397	−	3.63397i	0.207402	−	0.207402i	−0.595760	−	0.803162i	$-0.703149\pi$
$307$	3.63397	−	3.63397i	0.207402	−	0.207402i	0.803162	+	0.595760i	$0.203149\pi$
$308$	−6.92820	−	6.00000i	−0.394771	−	0.341882i
$309$	−10.9641	−	2.93782i	−0.623726	−	0.167127i
$310$	6.19615	+	1.26795i	0.351918	+	0.0720147i
$311$		−	17.1244i		−	0.971033i	−0.874227	−	0.485517i	$-0.838632\pi$
$311$		−	17.1244i		−	0.971033i	0.874227	−	0.485517i	$-0.161368\pi$
$312$		−	1.26795i		−	0.0717835i
$313$	−22.3923	−	22.3923i	−1.26569	−	1.26569i	−0.948294	−	0.317394i	$-0.897192\pi$
$313$	−22.3923	−	22.3923i	−1.26569	−	1.26569i	−0.317394	−	0.948294i	$-0.602808\pi$
$314$	2.33975			0.132040
$315$	17.5981	+	2.30385i	0.991539	+	0.129807i
$316$	−19.8564			−1.11701
$317$	1.53590	+	1.53590i	0.0862646	+	0.0862646i	0.748922	−	0.662658i	$-0.230572\pi$
$317$	1.53590	+	1.53590i	0.0862646	+	0.0862646i	−0.662658	+	0.748922i	$0.730572\pi$
$318$	−0.803848	+	0.464102i	−0.0450775	+	0.0260255i
$319$		−	19.8564i		−	1.11175i
$320$	−4.23205	+	2.79423i	−0.236579	+	0.156202i
$321$	−11.4904	+	11.4904i	−0.641331	+	0.641331i
$322$	8.49038	+	1.63397i	0.473150	+	0.0910578i
$323$	−1.07180	+	1.07180i	−0.0596364	+	0.0596364i
$324$	13.5000	+	7.79423i	0.750000	+	0.433013i
$325$	1.49038	+	1.16987i	0.0826715	+	0.0648929i
$326$	6.29423	+	10.9019i	0.348605	+	0.603802i
$327$	−8.42820	−	14.5981i	−0.466081	−	0.807275i
$328$	1.50000	−	5.59808i	0.0828236	−	0.309102i
$329$	−12.2321	−	5.93782i	−0.674375	−	0.327363i
$330$	−3.92820	−	0.803848i	−0.216240	−	0.0442504i
$331$	−6.00000			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$332$	−4.62436	−	17.2583i	−0.253794	−	0.947174i
$333$	−26.4904	+	7.09808i	−1.45166	+	0.388972i
$334$	1.63397	+	2.83013i	0.0894071	+	0.154858i
$335$	−1.56218	+	7.63397i	−0.0853509	+	0.417089i
$336$	−2.13397	+	11.0885i	−0.116418	+	0.604925i
$337$	−5.63397	+	21.0263i	−0.306902	+	1.14537i	0.624393	+	0.781110i	$0.285346\pi$
$337$	−5.63397	+	21.0263i	−0.306902	+	1.14537i	−0.931296	+	0.364264i	$0.881320\pi$
$338$	1.72243	+	6.42820i	0.0936879	+	0.349648i
$339$	12.0000	+	12.0000i	0.651751	+	0.651751i
$340$	−6.00000	−	5.32051i	−0.325396	−	0.288545i
$341$	9.46410	−	5.46410i	0.512510	−	0.295898i
$342$	1.09808	−	0.294229i	0.0593772	−	0.0159101i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−1.50000	−	0.866025i	−0.0808746	−	0.0466930i
$345$	−23.1962	+	7.73205i	−1.24884	+	0.416280i
$346$			11.7128i			0.629685i
$347$	8.36603	+	8.36603i	0.449112	+	0.449112i	0.895059	−	0.445947i	$-0.147133\pi$
$347$	8.36603	+	8.36603i	0.449112	+	0.449112i	−0.445947	+	0.895059i	$0.647133\pi$
$348$	−25.7942	+	14.8923i	−1.38272	+	0.798311i
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	4.49038	+	5.16987i	0.240021	+	0.276341i
$351$	1.90192	+	0.509619i	0.101517	+	0.0272014i
$352$	2.66025	−	9.92820i	0.141792	−	0.529175i
$353$	2.02628	−	7.56218i	0.107848	−	0.402494i	−0.890805	−	0.454386i	$-0.849859\pi$
$353$	2.02628	−	7.56218i	0.107848	−	0.402494i	0.998653	+	0.0518922i	$0.0165252\pi$
$354$	−2.11731	−	7.90192i	−0.112534	−	0.419983i
$355$	1.56218	+	2.36603i	0.0829118	+	0.125576i
$356$	1.60770	−	0.928203i	0.0852077	−	0.0491947i
$357$	−9.46410	+	0.679492i	−0.500893	+	0.0359625i
$358$	0.633975	+	2.36603i	0.0335066	+	0.125048i
$359$	−2.53590	+	1.46410i	−0.133840	+	0.0772723i	−0.565425	−	0.824800i	$-0.691288\pi$
$359$	−2.53590	+	1.46410i	−0.133840	+	0.0772723i	0.431585	+	0.902072i	$0.357954\pi$
$360$	4.09808	+	12.2942i	0.215988	+	0.647963i
$361$	9.23205	−	15.9904i	0.485897	−	0.841599i
$362$	1.50962	−	1.50962i	0.0793438	−	0.0793438i
$363$	10.5000	−	6.06218i	0.551107	−	0.318182i
$364$	0.124356	+	1.73205i	0.00651801	+	0.0907841i
$365$	−22.3923	−	19.8564i	−1.17207	−	1.03933i
$366$	9.46410	−	2.53590i	0.494697	−	0.132554i
$367$	12.4282	+	3.33013i	0.648747	+	0.173831i	0.568162	−	0.822917i	$-0.307655\pi$
$367$	12.4282	+	3.33013i	0.648747	+	0.173831i	0.0805847	+	0.996748i	$0.474321\pi$
$368$	−4.02628	−	15.0263i	−0.209884	−	0.783299i
$369$	7.79423	+	4.50000i	0.405751	+	0.234261i
$370$	−9.46410	−	4.73205i	−0.492015	−	0.246008i
$371$	2.26795	−	1.53590i	0.117746	−	0.0797399i
$372$	−14.1962	−	8.19615i	−0.736036	−	0.424951i
$373$	−4.56218	−	17.0263i	−0.236221	−	0.881587i	−0.977595	−	0.210495i	$-0.932492\pi$
$373$	−4.56218	−	17.0263i	−0.236221	−	0.881587i	0.741374	−	0.671092i	$-0.234174\pi$
$374$	2.14359			0.110843
$375$	−18.2321	−	6.52628i	−0.941499	−	0.337016i
$376$		−	9.92820i		−	0.512008i
$377$	−2.66025	+	2.66025i	−0.137010	+	0.137010i
$378$	6.40192	+	3.10770i	0.329279	+	0.159843i
$379$			27.5167i			1.41344i	0.707495	+	0.706718i	$0.249825\pi$
$379$			27.5167i			1.41344i	−0.707495	+	0.706718i	$0.750175\pi$
$380$	−2.53590	−	1.26795i	−0.130089	−	0.0650444i
$381$	7.20577	+	26.8923i	0.369163	+	1.37773i
$382$	−7.39230	−	7.39230i	−0.378223	−	0.378223i
$383$	20.1603	−	5.40192i	1.03014	−	0.276025i	0.296119	−	0.955151i	$-0.404308\pi$
$383$	20.1603	−	5.40192i	1.03014	−	0.276025i	0.734022	+	0.679126i	$0.237641\pi$
$384$	−19.1603	+	5.13397i	−0.977768	+	0.261992i
$385$	11.7321	+	1.53590i	0.597921	+	0.0782766i
$386$	−7.46410			−0.379913
$387$	1.90192	−	1.90192i	0.0966802	−	0.0966802i
$388$	−15.7583	+	4.22243i	−0.800008	+	0.214362i
$389$	25.1603	−	14.5263i	1.27568	−	0.736512i	0.299625	−	0.954057i	$-0.403138\pi$
$389$	25.1603	−	14.5263i	1.27568	−	0.736512i	0.976050	+	0.217545i	$0.0698050\pi$
$390$	0.418584	+	0.633975i	0.0211958	+	0.0321026i
$391$	11.3205	−	6.53590i	0.572503	−	0.330535i
$392$	−1.59808	+	13.4282i	−0.0807150	+	0.678227i
$393$	16.3923	+	28.3923i	0.826882	+	1.43220i
$394$			2.92820i			0.147521i
$395$	21.3923	−	14.1244i	1.07636	−	0.710673i
$396$	9.00000	+	5.19615i	0.452267	+	0.261116i
$397$	−19.8564	−	5.32051i	−0.996564	−	0.267029i	−0.276559	−	0.960997i	$-0.589194\pi$
$397$	−19.8564	−	5.32051i	−0.996564	−	0.267029i	−0.720006	+	0.693968i	$0.755861\pi$
$398$	8.19615	−	2.19615i	0.410836	−	0.110083i
$399$	−3.16987	+	1.09808i	−0.158692	+	0.0549726i
$400$	4.83975	−	11.3301i	0.241987	−	0.566506i
$401$	−5.69615	+	9.86603i	−0.284452	+	0.492686i	−0.972476	−	0.233002i	$-0.925145\pi$
$401$	−5.69615	+	9.86603i	−0.284452	+	0.492686i	0.688024	+	0.725688i	$0.258478\pi$
$402$	−1.56218	+	2.70577i	−0.0779143	+	0.134952i
$403$	−2.00000	−	0.535898i	−0.0996271	−	0.0266950i
$404$	0.232051	+	0.401924i	0.0115450	+	0.0199965i
$405$	−20.0885	+	1.20577i	−0.998203	+	0.0599153i
$406$	−11.2583	+	7.62436i	−0.558742	+	0.378390i
$407$	−17.6603	+	4.73205i	−0.875386	+	0.234559i
$408$	−3.46410	−	6.00000i	−0.171499	−	0.297044i
$409$	−12.3205			−0.609210			−0.304605	−	0.952479i	$-0.598524\pi$
$409$	−12.3205			−0.609210			−0.304605	+	0.952479i	$0.598524\pi$
$410$	1.09808	+	3.29423i	0.0542301	+	0.162690i
$411$	1.73205	−	1.73205i	0.0854358	−	0.0854358i
$412$	2.93782	+	10.9641i	0.144736	+	0.540163i
$413$	7.90192	+	22.8109i	0.388828	+	1.12245i
$414$	−9.80385			−0.481833
$415$	17.2583	+	15.3038i	0.847178	+	0.751236i
$416$	−1.68653	+	0.973721i	−0.0826891	+	0.0477406i
$417$			32.1962i			1.57665i
$418$	0.732051	−	0.196152i	0.0358058	−	0.00959413i
$419$	9.83013	+	17.0263i	0.480233	+	0.831788i	0.999743	−	0.0226764i	$-0.00721873\pi$
$419$	9.83013	+	17.0263i	0.480233	+	0.831788i	−0.519510	+	0.854465i	$0.673885\pi$
$420$	−6.80385	−	16.3923i	−0.331994	−	0.799863i
$421$	−7.59808	+	13.1603i	−0.370308	+	0.641392i	−0.989613	−	0.143759i	$-0.954081\pi$
$421$	−7.59808	+	13.1603i	−0.370308	+	0.641392i	0.619305	+	0.785150i	$0.287414\pi$
$422$	3.60770	−	13.4641i	0.175620	−	0.655422i
$423$	14.8923	+	3.99038i	0.724089	+	0.194019i
$424$	1.73205	+	1.00000i	0.0841158	+	0.0485643i
$425$	10.2487	+	1.46410i	0.497136	+	0.0710194i
$426$	0.294229	+	1.09808i	0.0142554	+	0.0532020i
$427$	−27.3205	+	9.46410i	−1.32213	+	0.458000i
$428$	15.6962	+	4.20577i	0.758702	+	0.203294i
$429$	1.26795	+	0.339746i	0.0612172	+	0.0164031i
$430$	1.03590	−	0.0621778i	0.0499555	−	0.00299848i
$431$	5.29423	−	9.16987i	0.255014	−	0.441697i	−0.709885	−	0.704317i	$-0.751253\pi$
$431$	5.29423	−	9.16987i	0.255014	−	0.441697i	0.964899	+	0.262620i	$0.0845866\pi$
$432$		−	12.8038i		−	0.616025i
$433$	−24.1244	−	24.1244i	−1.15934	−	1.15934i	−0.984617	−	0.174725i	$-0.944096\pi$
$433$	−24.1244	−	24.1244i	−1.15934	−	1.15934i	−0.174725	−	0.984617i	$-0.555904\pi$
$434$	−6.73205	−	3.26795i	−0.323149	−	0.156867i
$435$	17.1962	−	34.3923i	0.824492	−	1.64898i
$436$	−8.42820	+	14.5981i	−0.403638	+	0.699121i
$437$	3.26795	−	3.26795i	0.156327	−	0.156327i
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$	8.14359			0.388673			0.194336	−	0.980935i	$-0.437745\pi$
$439$	8.14359			0.388673			0.194336	+	0.980935i	$0.437745\pi$
$440$	2.73205	+	8.19615i	0.130245	+	0.390736i
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$	−0.287187	−	0.287187i	−0.0136601	−	0.0136601i
$443$	10.3660	−	10.3660i	0.492505	−	0.492505i	−0.416590	−	0.909095i	$-0.636775\pi$
$443$	10.3660	−	10.3660i	0.492505	−	0.492505i	0.909095	+	0.416590i	$0.136775\pi$
$444$	19.3923	+	19.3923i	0.920318	+	0.920318i
$445$	−1.07180	+	2.14359i	−0.0508080	+	0.101616i
$446$	2.30385	+	1.33013i	0.109090	+	0.0629833i
$447$	7.39230	+	12.8038i	0.349644	+	0.605601i
$448$	5.66987	−	1.96410i	0.267876	−	0.0927951i
$449$		−	24.6603i		−	1.16379i	−0.813264	−	0.581895i	$-0.802312\pi$
$449$		−	24.6603i		−	1.16379i	0.813264	−	0.581895i	$-0.197688\pi$
$450$	−6.10770	−	4.79423i	−0.287920	−	0.226002i
$451$	5.19615	+	3.00000i	0.244677	+	0.141264i
$452$	4.39230	−	16.3923i	0.206597	−	0.771029i
$453$			0.588457i			0.0276481i
$454$	6.43782	+	11.1506i	0.302142	+	0.523325i
$455$	−1.36603	−	1.77757i	−0.0640403	−	0.0833337i
$456$	−1.73205	−	1.73205i	−0.0811107	−	0.0811107i
$457$	15.0526	+	15.0526i	0.704129	+	0.704129i	0.965294	−	0.261165i	$-0.0841067\pi$
$457$	15.0526	+	15.0526i	0.704129	+	0.704129i	−0.261165	+	0.965294i	$0.584107\pi$
$458$	11.3301	−	3.03590i	0.529422	−	0.141858i
$459$	10.3923	−	2.78461i	0.485071	−	0.129974i
$460$	18.2942	+	16.2224i	0.852973	+	0.756375i
$461$	−24.2321	−	13.9904i	−1.12860	−	0.651597i	−0.185017	−	0.982735i	$-0.559234\pi$
$461$	−24.2321	−	13.9904i	−1.12860	−	0.651597i	−0.943582	+	0.331138i	$0.892567\pi$
$462$	4.26795	+	2.07180i	0.198563	+	0.0963887i
$463$	21.1603	+	5.66987i	0.983400	+	0.263501i	0.714476	−	0.699660i	$-0.246665\pi$
$463$	21.1603	+	5.66987i	0.983400	+	0.263501i	0.268924	+	0.963161i	$0.413332\pi$
$464$	21.1865	+	12.2321i	0.983560	+	0.567859i
$465$	21.1244	−	1.26795i	0.979619	−	0.0587997i
$466$	−5.53590	−	9.58846i	−0.256446	−	0.444177i
$467$	−9.33013	−	2.50000i	−0.431747	−	0.115686i	0.0363992	−	0.999337i	$-0.488411\pi$
$467$	−9.33013	−	2.50000i	−0.431747	−	0.115686i	−0.468146	+	0.883651i	$0.655078\pi$
$468$	−0.509619	−	1.90192i	−0.0235571	−	0.0879165i
$469$	4.02628	−	8.29423i	0.185916	−	0.382992i
$470$	3.27757	+	4.96410i	0.151183	+	0.228977i
$471$	7.56218	−	2.02628i	0.348447	−	0.0933660i
$472$	−12.4641	+	12.4641i	−0.573707	+	0.573707i
$473$	1.26795	−	1.26795i	0.0583004	−	0.0583004i
$474$	9.92820	−	2.66025i	0.456017	−	0.122190i
$475$	3.63397	−	0.437822i	0.166738	−	0.0200887i
$476$	5.32051	+	7.85641i	0.243865	+	0.360098i
$477$	−2.19615	+	2.19615i	−0.100555	+	0.100555i
$478$	1.00000	+	0.267949i	0.0457389	+	0.0122557i
$479$	−10.3660	−	17.9545i	−0.473636	−	0.820361i	0.525909	−	0.850541i	$-0.323725\pi$
$479$	−10.3660	−	17.9545i	−0.473636	−	0.820361i	−0.999544	+	0.0301798i	$0.990392\pi$
$480$	13.2058	−	14.8923i	0.602758	−	0.679738i
$481$	3.00000	+	1.73205i	0.136788	+	0.0789747i
$482$	−7.76795	−	2.08142i	−0.353820	−	0.0948059i
$483$	28.8564	−	2.07180i	1.31301	−	0.0942700i
$484$	−10.5000	−	6.06218i	−0.477273	−	0.275554i
$485$	13.9737	−	15.7583i	0.634514	−	0.715549i
$486$	−7.79423	−	2.08846i	−0.353553	−	0.0947343i
$487$	27.0263	−	7.24167i	1.22468	−	0.328151i	0.412173	−	0.911106i	$-0.364770\pi$
$487$	27.0263	−	7.24167i	1.22468	−	0.328151i	0.812505	+	0.582954i	$0.198103\pi$
$488$	−14.9282	−	14.9282i	−0.675768	−	0.675768i
$489$	29.7846	+	29.7846i	1.34691	+	1.34691i
$490$	−3.63397	−	7.24167i	−0.164166	−	0.327145i
$491$	−7.29423	−	12.6340i	−0.329184	−	0.570163i	0.653166	−	0.757215i	$-0.273440\pi$
$491$	−7.29423	−	12.6340i	−0.329184	−	0.570163i	−0.982350	+	0.187051i	$0.940107\pi$
$492$		−	9.00000i		−	0.405751i
$493$	−5.32051	+	19.8564i	−0.239624	+	0.894288i
$494$	−0.124356	−	0.0717968i	−0.00559503	−	0.00323029i
$495$	−13.3923	+	0.803848i	−0.601939	+	0.0361303i
$496$			13.4641i			0.604556i
$497$	−1.09808	−	3.16987i	−0.0492554	−	0.142188i
$498$	4.62436	+	8.00962i	0.207222	+	0.358920i
$499$	−33.2487	−	19.1962i	−1.48842	−	0.859338i	−0.488504	−	0.872562i	$-0.662457\pi$
$499$	−33.2487	−	19.1962i	−1.48842	−	0.859338i	−0.999913	+	0.0132238i	$0.995791\pi$
$500$	3.46410	+	19.0526i	0.154919	+	0.852056i
$501$	7.73205	+	7.73205i	0.345443	+	0.345443i
$502$	−5.00000	+	5.00000i	−0.223161	+	0.223161i
$503$	−2.63397	−	2.63397i	−0.117443	−	0.117443i	0.645943	−	0.763386i	$-0.276464\pi$
$503$	−2.63397	−	2.63397i	−0.117443	−	0.117443i	−0.763386	+	0.645943i	$0.776464\pi$
$504$	−1.09808	−	15.2942i	−0.0489122	−	0.681259i
$505$	−0.535898	−	0.267949i	−0.0238472	−	0.0119236i
$506$	−6.53590			−0.290556
$507$	11.1340	+	19.2846i	0.494477	+	0.856460i
$508$	19.6865	−	19.6865i	0.873449	−	0.873449i
$509$	16.4545	−	28.5000i	0.729332	−	1.26324i	−0.227834	−	0.973700i	$-0.573164\pi$
$509$	16.4545	−	28.5000i	0.729332	−	1.26324i	0.957166	−	0.289540i	$-0.0935024\pi$
$510$	3.71281	+	1.85641i	0.164406	+	0.0822031i
$511$	19.8564	+	29.3205i	0.878396	+	1.29706i
$512$	15.6865	+	15.6865i	0.693253	+	0.693253i
$513$	3.29423	−	1.90192i	0.145444	−	0.0839720i
$514$	3.73205	−	6.46410i	0.164614	−	0.285119i
$515$	−10.9641	−	9.72243i	−0.483136	−	0.428422i
$516$	−2.59808	−	0.696152i	−0.114374	−	0.0306464i
$517$	9.92820	+	2.66025i	0.436642	+	0.116998i
$518$	9.46410	+	8.19615i	0.415829	+	0.360118i
$519$	10.1436	+	37.8564i	0.445254	+	1.66171i
$520$	0.732051	−	1.46410i	0.0321026	−	0.0642051i
$521$	21.3564	+	12.3301i	0.935641	+	0.540193i	0.888591	−	0.458700i	$-0.151685\pi$
$521$	21.3564	+	12.3301i	0.935641	+	0.540193i	0.0470499	+	0.998893i	$0.485018\pi$
$522$	10.9019	−	10.9019i	0.477164	−	0.477164i
$523$	0.741670	−	2.76795i	0.0324310	−	0.121034i	−0.947813	−	0.318828i	$-0.896711\pi$
$523$	0.741670	−	2.76795i	0.0324310	−	0.121034i	0.980244	+	0.197794i	$0.0633776\pi$
$524$	16.3923	−	28.3923i	0.716101	−	1.24032i
$525$	18.9904	+	12.8205i	0.828808	+	0.559533i
$526$	−3.33013	−	5.76795i	−0.145200	−	0.251495i
$527$	−10.9282	+	2.92820i	−0.476040	+	0.127555i
$528$		−	8.53590i		−	0.371477i
$529$	−14.5981	+	8.42820i	−0.634699	+	0.366444i
$530$	−1.19615	+	0.0717968i	−0.0519575	+	0.00311865i
$531$	−13.6865	−	23.7058i	−0.593945	−	1.02874i
$532$	2.53590	+	2.19615i	0.109945	+	0.0952153i
$533$	−0.294229	−	1.09808i	−0.0127445	−	0.0475630i
$534$	−0.679492	+	0.679492i	−0.0294045	+	0.0294045i
$535$	−19.9019	+	6.63397i	−0.860435	+	0.286812i
$536$	6.73205			0.290780
$537$	4.09808	+	7.09808i	0.176845	+	0.306305i
$538$	−3.80385	+	1.01924i	−0.163996	+	0.0439425i
$539$	−13.0000	−	5.19615i	−0.559950	−	0.223814i
$540$	11.0885	+	16.7942i	0.477171	+	0.722709i
$541$	−3.46410	−	6.00000i	−0.148933	−	0.257960i	0.781900	−	0.623404i	$-0.214251\pi$
$541$	−3.46410	−	6.00000i	−0.148933	−	0.257960i	−0.930834	+	0.365444i	$0.880917\pi$
$542$	0.705771	+	0.189111i	0.0303155	+	0.00812301i
$543$	3.57180	−	6.18653i	0.153280	−	0.265490i
$544$	−5.32051	+	9.21539i	−0.228115	+	0.395107i
$545$	−1.30385	−	21.7224i	−0.0558507	−	0.930487i
$546$	−0.294229	−	0.849365i	−0.0125918	−	0.0363495i
$547$	−15.5981	+	4.17949i	−0.666926	+	0.178702i	−0.576370	−	0.817189i	$-0.695531\pi$
$547$	−15.5981	+	4.17949i	−0.666926	+	0.178702i	−0.0905561	+	0.995891i	$0.528864\pi$
$548$	−2.36603	−	0.633975i	−0.101072	−	0.0270821i
$549$	28.3923	−	16.3923i	1.21175	−	0.699607i
$550$	−4.07180	−	3.19615i	−0.173622	−	0.136284i
$551$			7.26795i			0.309625i
$552$	10.5622	+	18.2942i	0.449556	+	0.778654i
$553$	−28.6603	+	9.92820i	−1.21876	+	0.422190i
$554$	1.39230	−	0.803848i	0.0591534	−	0.0341522i
$555$	−34.6865	−	7.09808i	−1.47236	−	0.301297i
$556$	27.8827	−	16.0981i	1.18249	−	0.682711i
$557$	−24.9282	+	6.67949i	−1.05624	+	0.283019i	−0.744829	−	0.667256i	$-0.767469\pi$
$557$	−24.9282	+	6.67949i	−1.05624	+	0.283019i	−0.311413	+	0.950275i	$0.600802\pi$
$558$	8.19615	+	2.19615i	0.346971	+	0.0929705i
$559$	−0.339746			−0.0143697
$560$	−8.86603	+	11.5718i	−0.374658	+	0.488998i
$561$	6.92820	−	1.85641i	0.292509	−	0.0783775i
$562$	−12.8660	+	3.44744i	−0.542721	+	0.145422i
$563$	3.00000	+	3.00000i	0.126435	+	0.126435i	0.767493	−	0.641058i	$-0.221504\pi$
$563$	3.00000	+	3.00000i	0.126435	+	0.126435i	−0.641058	+	0.767493i	$0.721504\pi$
$564$	−3.99038	−	14.8923i	−0.168025	−	0.627079i
$565$	6.92820	+	20.7846i	0.291472	+	0.874415i
$566$		−	8.32051i		−	0.349737i
$567$	23.3827	+	4.50000i	0.981981	+	0.188982i
$568$	1.73205	−	1.73205i	0.0726752	−	0.0726752i
$569$			2.92820i			0.122757i	0.998115	+	0.0613783i	$0.0195496\pi$
$569$			2.92820i			0.122757i	−0.998115	+	0.0613783i	$0.980450\pi$
$570$	1.43782	+	0.294229i	0.0602237	+	0.0123239i
$571$	−4.19615			−0.175604			−0.0878018	−	0.996138i	$-0.527984\pi$
$571$	−4.19615			−0.175604			−0.0878018	+	0.996138i	$0.527984\pi$
$572$	−0.339746	−	1.26795i	−0.0142055	−	0.0530156i
$573$	−30.2942	−	17.4904i	−1.26556	−	0.730671i
$574$	−0.294229	−	4.09808i	−0.0122809	−	0.171050i
$575$	−31.2487	−	4.46410i	−1.30316	−	0.186166i
$576$	−5.89230	+	3.40192i	−0.245513	+	0.141747i
$577$	5.14359	+	19.1962i	0.214131	+	0.799146i	0.986471	+	0.163937i	$0.0524194\pi$
$577$	5.14359	+	19.1962i	0.214131	+	0.799146i	−0.772340	+	0.635209i	$0.780914\pi$
$578$	6.35641	+	1.70319i	0.264392	+	0.0708435i
$579$	−24.1244	+	6.46410i	−1.00257	+	0.268639i
$580$	−38.3827	+	2.30385i	−1.59375	+	0.0956621i
$581$	−15.3038	−	22.5981i	−0.634911	−	0.937526i
$582$	7.31347	−	4.22243i	0.303153	−	0.175025i
$583$	−1.46410	+	1.46410i	−0.0606369	+	0.0606369i
$584$	−12.9282	+	22.3923i	−0.534973	+	0.926600i
$585$	1.90192	+	1.68653i	0.0786349	+	0.0697296i
$586$	5.66025	−	3.26795i	0.233823	−	0.134998i
$587$	8.83975	+	32.9904i	0.364855	+	1.36166i	0.867617	+	0.497234i	$0.165651\pi$
$587$	8.83975	+	32.9904i	0.364855	+	1.36166i	−0.502761	+	0.864425i	$0.667683\pi$
$588$	3.00000	+	20.7846i	0.123718	+	0.857143i
$589$	−3.46410	+	2.00000i	−0.142736	+	0.0824086i
$590$	2.11731	−	10.3468i	0.0871684	−	0.425971i
$591$	2.53590	+	9.46410i	0.104313	+	0.389301i
$592$	5.83013	−	21.7583i	0.239617	−	0.894262i
$593$	−3.95448	+	14.7583i	−0.162391	+	0.606052i	0.835967	+	0.548779i	$0.184907\pi$
$593$	−3.95448	+	14.7583i	−0.162391	+	0.606052i	−0.998359	+	0.0572729i	$0.981759\pi$
$594$	−5.19615	−	1.39230i	−0.213201	−	0.0571270i
$595$	−11.3205	−	4.67949i	−0.464096	−	0.191840i
$596$	7.39230	−	12.8038i	0.302801	−	0.524466i
$597$	24.5885	−	14.1962i	1.00634	−	0.581010i
$598$	0.875644	+	0.875644i	0.0358078	+	0.0358078i
$599$			45.8564i			1.87364i	0.349809	+	0.936821i	$0.386246\pi$
$599$			45.8564i			1.87364i	−0.349809	+	0.936821i	$0.613754\pi$
$600$	−2.36603	+	16.5622i	−0.0965926	+	0.676148i
$601$	5.32051	+	3.07180i	0.217028	+	0.125301i	0.604573	−	0.796549i	$-0.293344\pi$
$601$	5.32051	+	3.07180i	0.217028	+	0.125301i	−0.387545	+	0.921851i	$0.626677\pi$
$602$	−1.20577	−	0.232051i	−0.0491436	−	0.00945768i
$603$	−2.70577	+	10.0981i	−0.110188	+	0.411225i
$604$	0.509619	−	0.294229i	0.0207361	−	0.0119720i
$605$	15.6244	−	0.937822i	0.635220	−	0.0381279i
$606$	−0.169873	−	0.169873i	−0.00690062	−	0.00690062i
$607$	−6.69615	−	24.9904i	−0.271788	−	1.01433i	−0.957963	−	0.286891i	$-0.907378\pi$
$607$	−6.69615	−	24.9904i	−0.271788	−	1.01433i	0.686175	−	0.727437i	$-0.259289\pi$
$608$	−0.973721	+	3.63397i	−0.0394896	+	0.147377i
$609$	−29.7846	+	34.3923i	−1.20693	+	1.39365i
$610$	12.3923	+	2.53590i	0.501750	+	0.102676i
$611$	−0.973721	−	1.68653i	−0.0393925	−	0.0682298i
$612$	−7.60770	−	7.60770i	−0.307523	−	0.307523i
$613$	−0.241670	−	0.901924i	−0.00976095	−	0.0364284i	0.960874	−	0.276987i	$-0.0893360\pi$
$613$	−0.241670	−	0.901924i	−0.00976095	−	0.0364284i	−0.970635	+	0.240559i	$0.922669\pi$
$614$	2.66025			0.107359
$615$	6.40192	+	9.69615i	0.258150	+	0.390987i
$616$	−0.732051	−	10.1962i	−0.0294952	−	0.410815i
$617$	−8.39230	+	31.3205i	−0.337861	+	1.26092i	0.562872	+	0.826544i	$0.309696\pi$
$617$	−8.39230	+	31.3205i	−0.337861	+	1.26092i	−0.900734	+	0.434372i	$0.856970\pi$
$618$	−2.93782	−	5.08846i	−0.118177	−	0.204688i
$619$	0.392305	+	0.679492i	0.0157681	+	0.0273111i	0.873802	−	0.486282i	$-0.161647\pi$
$619$	0.392305	+	0.679492i	0.0157681	+	0.0273111i	−0.858034	+	0.513593i	$0.828314\pi$
$620$	−11.6603	−	17.6603i	−0.468287	−	0.709253i
$621$	−31.6865	+	8.49038i	−1.27154	+	0.340707i
$622$	6.26795	−	6.26795i	0.251322	−	0.251322i
$623$	1.85641	−	2.14359i	0.0743754	−	0.0858813i
$624$	−1.14359	+	1.14359i	−0.0457804	+	0.0457804i
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		−	16.3923i		−	0.655168i
$627$	2.19615	−	1.26795i	0.0877059	−	0.0506370i
$628$	−5.53590	−	5.53590i	−0.220906	−	0.220906i
$629$	18.9282			0.754717
$630$	5.59808	+	7.28461i	0.223033	+	0.290226i
$631$	−11.8564			−0.471996			−0.235998	−	0.971754i	$-0.575836\pi$
$631$	−11.8564			−0.471996			−0.235998	+	0.971754i	$0.575836\pi$
$632$	−15.6603	−	15.6603i	−0.622931	−	0.622931i
$633$		−	46.6410i		−	1.85381i
$634$			1.12436i			0.0446539i
$635$	−7.20577	+	35.2128i	−0.285952	+	1.39738i
$636$	3.00000	+	0.803848i	0.118958	+	0.0318746i
$637$	1.04552	+	2.43782i	0.0414249	+	0.0965900i
$638$	7.26795	−	7.26795i	0.287741	−	0.287741i
$639$	1.90192	+	3.29423i	0.0752389	+	0.130318i
$640$	−25.0885	−	5.13397i	−0.991708	−	0.202938i
$641$	−8.80385	−	15.2487i	−0.347731	−	0.602288i	0.638115	−	0.769941i	$-0.279714\pi$
$641$	−8.80385	−	15.2487i	−0.347731	−	0.602288i	−0.985846	+	0.167653i	$0.946381\pi$
$642$	−8.41154			−0.331977
$643$	−6.65064	+	24.8205i	−0.262275	+	0.978825i	0.701622	+	0.712550i	$0.252460\pi$
$643$	−6.65064	+	24.8205i	−0.262275	+	0.978825i	−0.963897	+	0.266275i	$0.914207\pi$
$644$	−16.2224	−	23.9545i	−0.639253	−	0.943939i
$645$	3.29423	−	1.09808i	0.129710	−	0.0432367i
$646$	−0.784610			−0.0308701
$647$	−3.37564	−	12.5981i	−0.132710	−	0.495281i	0.867287	−	0.497809i	$-0.165862\pi$
$647$	−3.37564	−	12.5981i	−0.132710	−	0.495281i	−0.999997	+	0.00252779i	$0.999195\pi$
$648$	4.50000	+	16.7942i	0.176777	+	0.659740i
$649$	−9.12436	−	15.8038i	−0.358162	−	0.620355i
$650$	0.117314	+	0.973721i	0.00460144	+	0.0381925i
$651$	−24.5885	−	4.73205i	−0.963698	−	0.185464i
$652$	10.9019	−	40.6865i	0.426952	−	1.59341i
$653$	5.39230	+	20.1244i	0.211017	+	0.787527i	0.987531	+	0.157426i	$0.0503197\pi$
$653$	5.39230	+	20.1244i	0.211017	+	0.787527i	−0.776514	+	0.630101i	$0.783014\pi$
$654$	2.25833	−	8.42820i	0.0883077	−	0.329569i
$655$	2.53590	+	42.2487i	0.0990857	+	1.65079i
$656$	−6.40192	+	3.69615i	−0.249953	+	0.144311i
$657$	−28.3923	−	28.3923i	−1.10769	−	1.10769i
$658$	−2.30385	−	6.65064i	−0.0898133	−	0.259269i
$659$	−19.3468	−	11.1699i	−0.753644	−	0.435116i	0.0733652	−	0.997305i	$-0.476626\pi$
$659$	−19.3468	−	11.1699i	−0.753644	−	0.435116i	−0.827009	+	0.562189i	$0.809959\pi$
$660$	7.39230	+	11.1962i	0.287745	+	0.435810i
$661$		−	2.60770i		−	0.101428i	−0.998713	−	0.0507138i	$-0.983850\pi$
$661$		−	2.60770i		−	0.101428i	0.998713	−	0.0507138i	$-0.0161496\pi$
$662$	−2.19615	−	2.19615i	−0.0853559	−	0.0853559i
$663$	−1.17691	−	0.679492i	−0.0457076	−	0.0263893i
$664$	9.96410	−	17.2583i	0.386682	−	0.669753i
$665$	−4.29423	−	0.562178i	−0.166523	−	0.0218003i
$666$	−12.2942	−	7.09808i	−0.476392	−	0.275045i
$667$	16.2224	−	60.5429i	0.628135	−	2.34423i
$668$	2.83013	−	10.5622i	0.109501	−	0.408663i
$669$	8.59808	+	2.30385i	0.332421	+	0.0890719i
$670$	−3.36603	+	2.22243i	−0.130041	+	0.0858600i
$671$	18.9282	−	10.9282i	0.730715	−	0.421879i
$672$	−19.5000	+	13.2058i	−0.752229	+	0.509424i
$673$	−1.43782	−	5.36603i	−0.0554240	−	0.206845i	0.932661	−	0.360754i	$-0.117481\pi$
$673$	−1.43782	−	5.36603i	−0.0554240	−	0.206845i	−0.988085	+	0.153909i	$0.950814\pi$
$674$	−9.75833	+	5.63397i	−0.375877	+	0.217013i
$675$	−23.8923	−	10.2058i	−0.919615	−	0.392820i
$676$	11.1340	−	19.2846i	0.428230	−	0.741716i
$677$	−10.5167	+	10.5167i	−0.404188	+	0.404188i	−0.879706	−	0.475518i	$-0.842261\pi$
$677$	−10.5167	+	10.5167i	−0.404188	+	0.404188i	0.475518	+	0.879706i	$0.342261\pi$
$678$			8.78461i			0.337371i
$679$	−20.6340	+	13.9737i	−0.791859	+	0.536262i
$680$	−0.535898	−	8.92820i	−0.0205508	−	0.342381i
$681$	30.4641	+	30.4641i	1.16739	+	1.16739i
$682$	5.46410	+	1.46410i	0.209231	+	0.0560633i
$683$	11.5000	+	42.9186i	0.440035	+	1.64223i	0.728721	+	0.684810i	$0.240115\pi$
$683$	11.5000	+	42.9186i	0.440035	+	1.64223i	−0.288686	+	0.957424i	$0.593218\pi$
$684$	−3.29423	−	1.90192i	−0.125958	−	0.0727219i
$685$	3.00000	−	1.00000i	0.114624	−	0.0382080i
$686$	2.04552	+	9.36603i	0.0780982	+	0.357597i
$687$	33.9904	−	19.6244i	1.29681	−	0.748716i
$688$	0.571797	+	2.13397i	0.0217995	+	0.0813570i
$689$	0.392305			0.0149456
$690$	−11.3205	−	5.66025i	−0.430964	−	0.215482i
$691$			19.4641i			0.740449i	0.928942	+	0.370225i	$0.120719\pi$
$691$			19.4641i			0.740449i	−0.928942	+	0.370225i	$0.879281\pi$
$692$	27.7128	−	27.7128i	1.05348	−	1.05348i
$693$	15.5885	+	3.00000i	0.592157	+	0.113961i
$694$			6.12436i			0.232477i
$695$	−18.5885	+	37.1769i	−0.705100	+	1.41020i
$696$	−32.0885	−	8.59808i	−1.21631	−	0.325909i
$697$	−4.39230	−	4.39230i	−0.166370	−	0.166370i
$698$	−5.00000	+	1.33975i	−0.189253	+	0.0507101i
$699$	−26.1962	−	26.1962i	−0.990829	−	0.990829i
$700$	1.60770	−	22.8564i	0.0607652	−	0.863891i
$701$	11.0526			0.417449			0.208725	−	0.977974i	$-0.433069\pi$
$701$	11.0526			0.417449			0.208725	+	0.977974i	$0.433069\pi$
$702$	0.509619	+	0.882686i	0.0192343	+	0.0333148i
$703$	6.46410	−	1.73205i	0.243798	−	0.0653255i
$704$	−3.92820	+	2.26795i	−0.148050	+	0.0854766i
$705$	14.8923	+	13.2058i	0.560877	+	0.497358i
$706$	3.50962	−	2.02628i	0.132086	−	0.0762600i
$707$	0.535898	+	0.464102i	0.0201545	+	0.0174543i
$708$	−13.6865	+	23.7058i	−0.514371	+	0.890917i
$709$			40.6410i			1.52631i	0.646218	+	0.763153i	$0.276350\pi$
$709$			40.6410i			1.52631i	−0.646218	+	0.763153i	$0.723650\pi$
$710$	−0.294229	+	1.43782i	−0.0110422	+	0.0539605i
$711$	29.7846	−	17.1962i	1.11701	−	0.644906i
$712$	2.00000	+	0.535898i	0.0749532	+	0.0200836i
$713$	33.3205	−	8.92820i	1.24786	−	0.334364i
$714$	−3.71281	−	3.21539i	−0.138949	−	0.120333i
$715$	1.26795	+	1.12436i	0.0474186	+	0.0420485i
$716$	4.09808	−	7.09808i	0.153152	−	0.265268i
$717$	3.46410			0.129369
$718$	−1.46410	−	0.392305i	−0.0546398	−	0.0146407i
$719$	−11.4641	−	19.8564i	−0.427539	−	0.740519i	0.569115	−	0.822258i	$-0.307286\pi$
$719$	−11.4641	−	19.8564i	−0.427539	−	0.740519i	−0.996654	+	0.0817390i	$0.973953\pi$
$720$	7.39230	−	14.7846i	0.275495	−	0.550990i
$721$	9.72243	+	14.3564i	0.362082	+	0.534661i
$722$	9.23205	−	2.47372i	0.343581	−	0.0920623i
$723$	−26.9090			−1.00076
$724$	−7.14359			−0.265490
$725$	39.7128	−	29.7846i	1.47490	−	1.10617i
$726$	6.06218	+	1.62436i	0.224989	+	0.0602855i
$727$	−6.75833	−	25.2224i	−0.250653	−	0.935448i	−0.970458	−	0.241272i	$-0.922435\pi$
$727$	−6.75833	−	25.2224i	−0.250653	−	0.935448i	0.719805	−	0.694176i	$-0.244231\pi$
$728$	−1.26795	+	1.46410i	−0.0469933	+	0.0542632i
$729$	−27.0000			−1.00000
$730$	−0.928203	−	15.4641i	−0.0343543	−	0.572352i
$731$	−1.60770	+	0.928203i	−0.0594628	+	0.0343308i
$732$	−28.3923	−	16.3923i	−1.04941	−	0.605877i
$733$	−5.90192	+	1.58142i	−0.217993	+	0.0584109i	−0.366162	−	0.930551i	$-0.619328\pi$
$733$	−5.90192	+	1.58142i	−0.217993	+	0.0584109i	0.148170	+	0.988962i	$0.452662\pi$
$734$	3.33013	+	5.76795i	0.122917	+	0.212899i
$735$	−18.0167	−	20.2583i	−0.664555	−	0.747240i
$736$	16.2224	−	28.0981i	0.597967	−	1.03571i
$737$	−1.80385	+	6.73205i	−0.0664456	+	0.247978i
$738$	1.20577	+	4.50000i	0.0443851	+	0.165647i
$739$	0.679492	+	0.392305i	0.0249955	+	0.0144312i	0.512446	−	0.858720i	$-0.328740\pi$
$739$	0.679492	+	0.392305i	0.0249955	+	0.0144312i	−0.487450	+	0.873151i	$0.662073\pi$
$740$	11.1962	+	33.5885i	0.411579	+	1.23474i
$741$	−0.464102	−	0.124356i	−0.0170492	−	0.00456832i
$742$	1.39230	+	0.267949i	0.0511131	+	0.00983672i
$743$	−34.9186	−	9.35641i	−1.28104	−	0.343253i	−0.446789	−	0.894640i	$-0.647432\pi$
$743$	−34.9186	−	9.35641i	−1.28104	−	0.343253i	−0.834250	+	0.551386i	$0.814099\pi$
$744$	−4.73205	−	17.6603i	−0.173485	−	0.647456i
$745$	1.14359	+	19.0526i	0.0418980	+	0.698032i
$746$	4.56218	−	7.90192i	0.167033	−	0.289310i
$747$	21.8827	+	21.8827i	0.800646	+	0.800646i
$748$	−5.07180	−	5.07180i	−0.185443	−	0.185443i
$749$	24.7583	−	1.77757i	0.904650	−	0.0649509i
$750$	−4.28461	−	9.06218i	−0.156452	−	0.330904i
$751$	−12.4378	+	21.5429i	−0.453863	+	0.786113i	−0.998622	−	0.0524793i	$-0.983288\pi$
$751$	−12.4378	+	21.5429i	−0.453863	+	0.786113i	0.544759	+	0.838592i	$0.316621\pi$
$752$	−8.95448	+	8.95448i	−0.326536	+	0.326536i
$753$	−11.8301	+	20.4904i	−0.431114	+	0.746711i
$754$	−1.94744			−0.0709216
$755$	−0.339746	+	0.679492i	−0.0123646	+	0.0247292i
$756$	−7.79423	−	22.5000i	−0.283473	−	0.818317i
$757$	−14.3923	−	14.3923i	−0.523097	−	0.523097i	0.395408	−	0.918505i	$-0.370603\pi$
$757$	−14.3923	−	14.3923i	−0.523097	−	0.523097i	−0.918505	+	0.395408i	$0.870603\pi$
$758$	−10.0718	+	10.0718i	−0.365824	+	0.365824i
$759$	−21.1244	+	5.66025i	−0.766766	+	0.205454i
$760$	−1.00000	−	3.00000i	−0.0362738	−	0.108821i
$761$	−7.96410	−	4.59808i	−0.288698	−	0.166680i	0.348656	−	0.937251i	$-0.386638\pi$
$761$	−7.96410	−	4.59808i	−0.288698	−	0.166680i	−0.637355	+	0.770571i	$0.719971\pi$
$762$	−7.20577	+	12.4808i	−0.261038	+	0.452130i
$763$	−4.86603	+	25.2846i	−0.176162	+	0.915364i
$764$			34.9808i			1.26556i
$765$	13.6077	+	2.78461i	0.491987	+	0.100678i
$766$	9.35641	+	5.40192i	0.338061	+	0.195179i
$767$	−0.894882	+	3.33975i	−0.0323123	+	0.120591i
$768$	−2.08846	−	1.20577i	−0.0753607	−	0.0435095i
$769$	12.5981	+	21.8205i	0.454298	+	0.786868i	0.998648	−	0.0519910i	$-0.0165567\pi$
$769$	12.5981	+	21.8205i	0.454298	+	0.786868i	−0.544349	+	0.838859i	$0.683223\pi$
$770$	3.73205	+	4.85641i	0.134494	+	0.175013i
$771$	6.46410	−	24.1244i	0.232799	−	0.868817i
$772$	17.6603	+	17.6603i	0.635606	+	0.635606i
$773$	−17.0981	+	4.58142i	−0.614975	+	0.164782i	−0.552842	−	0.833286i	$-0.686457\pi$
$773$	−17.0981	+	4.58142i	−0.614975	+	0.164782i	−0.0621327	+	0.998068i	$0.519790\pi$
$774$	1.39230			0.0500454
$775$	25.1244	+	10.7321i	0.902493	+	0.385507i
$776$	−15.7583	−	9.09808i	−0.565691	−	0.326602i
$777$	37.6865	+	18.2942i	1.35200	+	0.656302i
$778$	14.5263	+	3.89230i	0.520792	+	0.139546i
$779$	−1.90192	−	1.09808i	−0.0681435	−	0.0393427i
$780$	0.509619	−	2.49038i	0.0182473	−	0.0891699i
$781$	1.26795	+	2.19615i	0.0453708	+	0.0785845i
$782$	6.53590	+	1.75129i	0.233723	+	0.0626260i
$783$	25.7942	−	44.6769i	0.921811	−	1.59662i
$784$	13.5526	−	10.6699i	0.484020	−	0.381067i
$785$	9.90192	+	2.02628i	0.353415	+	0.0723210i
$786$	−4.39230	+	16.3923i	−0.156668	+	0.584694i
$787$	29.1699	−	29.1699i	1.03979	−	1.03979i	0.0406190	−	0.999175i	$-0.487067\pi$
$787$	29.1699	−	29.1699i	1.03979	−	1.03979i	0.999175	−	0.0406190i	$-0.0129330\pi$
$788$	6.92820	−	6.92820i	0.246807	−	0.246807i
$789$	−15.7583	−	15.7583i	−0.561011	−	0.561011i
$790$	13.0000	+	2.66025i	0.462519	+	0.0946476i
$791$	−1.85641	−	25.8564i	−0.0660062	−	0.919348i
$792$	3.00000	+	11.1962i	0.106600	+	0.397838i
$793$	−4.00000	−	1.07180i	−0.142044	−	0.0380606i
$794$	−5.32051	−	9.21539i	−0.188818	−	0.327042i
$795$	−3.80385	+	1.26795i	−0.134909	+	0.0449695i
$796$	−24.5885	−	14.1962i	−0.871515	−	0.503169i
$797$	−34.8827	−	9.34679i	−1.23561	−	0.331080i	−0.418847	−	0.908057i	$-0.637566\pi$
$797$	−34.8827	−	9.34679i	−1.23561	−	0.331080i	−0.816761	+	0.576976i	$0.804232\pi$
$798$	−1.56218	−	0.758330i	−0.0553005	−	0.0268446i
$799$	−9.21539	−	5.32051i	−0.326017	−	0.188226i
$800$	23.8468	−	9.57180i	0.843111	−	0.338414i
$801$	−1.60770	+	2.78461i	−0.0568051	+	0.0983893i
$802$	−5.69615	+	1.52628i	−0.201138	+	0.0538948i
$803$	−18.9282	−	18.9282i	−0.667962	−	0.667962i
$804$	10.0981	−	2.70577i	0.356132	−	0.0954252i
$805$	34.5167	+	14.2679i	1.21655	+	0.502879i
$806$	−0.535898	−	0.928203i	−0.0188762	−	0.0326946i
$807$	−11.4115	+	6.58846i	−0.401705	+	0.231925i
$808$	−0.133975	+	0.500000i	−0.00471321	+	0.0175899i
$809$	−38.3827	−	22.1603i	−1.34946	−	0.779113i	−0.361290	−	0.932454i	$-0.617664\pi$
$809$	−38.3827	−	22.1603i	−1.34946	−	0.779113i	−0.988173	+	0.153340i	$0.950997\pi$
$810$	−7.79423	−	6.91154i	−0.273861	−	0.242847i
$811$		−	6.58846i		−	0.231352i	−0.993287	−	0.115676i	$-0.963097\pi$
$811$		−	6.58846i		−	0.231352i	0.993287	−	0.115676i	$-0.0369034\pi$
$812$	44.6769	+	8.59808i	1.56785	+	0.301733i
$813$	2.44486			0.0857451
$814$	−8.19615	−	4.73205i	−0.287275	−	0.165858i
$815$	17.1962	+	51.5885i	0.602355	+	1.80706i
$816$	−2.28719	+	8.53590i	−0.0800676	+	0.298816i
$817$	−0.464102	+	0.464102i	−0.0162369	+	0.0162369i
$818$	−4.50962	−	4.50962i	−0.157675	−	0.157675i
$819$	−1.68653	−	2.49038i	−0.0589322	−	0.0870210i
$820$	5.19615	−	10.3923i	0.181458	−	0.362915i
$821$	41.5885			1.45145			0.725724	−	0.687986i	$-0.241505\pi$
$821$	41.5885			1.45145			0.725724	+	0.687986i	$0.241505\pi$
$822$	1.26795			0.0442248
$823$	7.43782	−	7.43782i	0.259266	−	0.259266i	−0.565489	−	0.824756i	$-0.691313\pi$
$823$	7.43782	−	7.43782i	0.259266	−	0.259266i	0.824756	+	0.565489i	$0.191313\pi$
$824$	−6.33013	+	10.9641i	−0.220520	+	0.381953i
$825$	−15.9282	−	6.80385i	−0.554549	−	0.236880i
$826$	−5.45706	+	11.2417i	−0.189875	+	0.391148i
$827$	14.1699	+	14.1699i	0.492735	+	0.492735i	0.909167	−	0.416432i	$-0.136720\pi$
$827$	14.1699	+	14.1699i	0.492735	+	0.492735i	−0.416432	+	0.909167i	$0.636720\pi$
$828$	23.1962	+	23.1962i	0.806122	+	0.806122i
$829$	22.1603	−	38.3827i	0.769657	−	1.33309i	−0.168091	−	0.985771i	$-0.553760\pi$
$829$	22.1603	−	38.3827i	0.769657	−	1.33309i	0.937749	−	0.347314i	$-0.112906\pi$
$830$	0.715390	+	11.9186i	0.0248316	+	0.413700i
$831$	3.80385	−	3.80385i	0.131954	−	0.131954i
$832$	0.830127	+	0.222432i	0.0287795	+	0.00771144i
$833$	11.6077	+	8.67949i	0.402183	+	0.300727i
$834$	−11.7846	+	11.7846i	−0.408068	+	0.408068i
$835$	4.46410	+	13.3923i	0.154487	+	0.463460i
$836$	−2.19615	−	1.26795i	−0.0759555	−	0.0438529i
$837$	28.3923			0.981382
$838$	−2.63397	+	9.83013i	−0.0909891	+	0.339576i
$839$	−22.6147	+	39.1699i	−0.780747	+	1.35229i	0.150759	+	0.988570i	$0.451828\pi$
$839$	−22.6147	+	39.1699i	−0.780747	+	1.35229i	−0.931507	+	0.363724i	$0.881505\pi$
$840$	7.56218	−	18.2942i	0.260920	−	0.631211i
$841$	34.7846	+	60.2487i	1.19947	+	2.07754i
$842$	−7.59808	+	2.03590i	−0.261847	+	0.0701617i
$843$	−38.5981	+	22.2846i	−1.32939	+	0.767523i
$844$	−40.3923	+	23.3205i	−1.39036	+	0.802725i
$845$	1.72243	+	28.6962i	0.0592535	+	0.987178i
$846$	3.99038	+	6.91154i	0.137192	+	0.237624i
$847$	−18.1865	−	3.50000i	−0.624897	−	0.120261i
$848$	−0.660254	−	2.46410i	−0.0226732	−	0.0846176i
$849$	−7.20577	−	26.8923i	−0.247301	−	0.922942i
$850$	3.21539	+	4.28719i	0.110287	+	0.147049i
$851$	−57.7128			−1.97837
$852$	1.90192	−	3.29423i	0.0651588	−	0.112858i
$853$	24.1244	−	6.46410i	0.826002	−	0.221327i	0.179033	−	0.983843i	$-0.442703\pi$
$853$	24.1244	−	6.46410i	0.826002	−	0.221327i	0.646969	+	0.762516i	$0.276036\pi$
$854$	−13.4641	−	6.53590i	−0.460732	−	0.223654i
$855$	4.90192	−	0.294229i	0.167642	−	0.0100624i
$856$	9.06218	+	15.6962i	0.309739	+	0.536483i
$857$	−12.1962	−	3.26795i	−0.416613	−	0.111631i	0.0444226	−	0.999013i	$-0.485855\pi$
$857$	−12.1962	−	3.26795i	−0.416613	−	0.111631i	−0.461035	+	0.887382i	$0.652522\pi$
$858$	0.339746	+	0.588457i	0.0115987	+	0.0200896i
$859$	13.8301	−	23.9545i	0.471878	−	0.817316i	−0.527604	−	0.849490i	$-0.676910\pi$
$859$	13.8301	−	23.9545i	0.471878	−	0.817316i	0.999482	+	0.0321738i	$0.0102430\pi$
$860$	−2.59808	−	2.30385i	−0.0885937	−	0.0785606i
$861$	−4.50000	−	12.9904i	−0.153360	−	0.442711i
$862$	5.29423	−	1.41858i	0.180322	−	0.0483172i
$863$	−47.0788	−	12.6147i	−1.60258	−	0.429411i	−0.656761	−	0.754099i	$-0.728074\pi$
$863$	−47.0788	−	12.6147i	−1.60258	−	0.429411i	−0.945821	+	0.324688i	$0.894741\pi$
$864$	18.8827	−	18.8827i	0.642402	−	0.642402i
$865$	−10.1436	+	49.5692i	−0.344893	+	1.68540i
$866$		−	17.6603i		−	0.600120i
$867$	22.0192			0.747813
$868$	8.19615	+	23.6603i	0.278196	+	0.803081i
$869$	19.8564	−	11.4641i	0.673582	−	0.388893i
$870$	18.8827	−	6.29423i	0.640183	−	0.213394i
$871$	1.14359	−	0.660254i	0.0387492	−	0.0223719i
$872$	−18.1603	+	4.86603i	−0.614984	+	0.164784i
$873$	19.9808	−	19.9808i	0.676246	−	0.676246i
$874$	2.39230			0.0809209
$875$	14.5263	+	25.7679i	0.491078	+	0.871116i
$876$	−10.3923	+	38.7846i	−0.351123	+	1.31041i
$877$	−1.63397	+	0.437822i	−0.0551754	+	0.0147842i	−0.286301	−	0.958140i	$-0.592426\pi$
$877$	−1.63397	+	0.437822i	−0.0551754	+	0.0147842i	0.231126	+	0.972924i	$0.425759\pi$
$878$	2.98076	+	2.98076i	0.100596	+	0.100596i
$879$	15.4641	−	15.4641i	0.521591	−	0.521591i
$880$	4.92820	−	9.85641i	0.166130	−	0.332259i
$881$			39.0333i			1.31507i	0.753426	+	0.657533i	$0.228400\pi$
$881$			39.0333i			1.31507i	−0.753426	+	0.657533i	$0.771600\pi$
$882$	−4.28461	−	9.99038i	−0.144270	−	0.336394i
$883$	31.5622	−	31.5622i	1.06215	−	1.06215i	0.0642158	−	0.997936i	$-0.479545\pi$
$883$	31.5622	−	31.5622i	1.06215	−	1.06215i	0.997936	−	0.0642158i	$-0.0204546\pi$
$884$			1.35898i			0.0457076i
$885$	−2.11731	−	35.2750i	−0.0711727	−	1.18576i
$886$	7.58846			0.254939
$887$	−7.13397	−	26.6244i	−0.239535	−	0.893958i	−0.976052	−	0.217539i	$-0.930197\pi$
$887$	−7.13397	−	26.6244i	−0.239535	−	0.893958i	0.736516	−	0.676420i	$-0.236469\pi$
$888$			30.5885i			1.02648i
$889$	18.5718	−	38.2583i	0.622878	−	1.28314i
$890$	−1.17691	+	0.392305i	−0.0394503	+	0.0131501i
$891$	−18.0000			−0.603023
$892$	−2.30385	−	8.59808i	−0.0771385	−	0.287885i
$893$	−3.63397	−	0.973721i	−0.121606	−	0.0325843i
$894$	−1.98076	+	7.39230i	−0.0662466	+	0.247236i
$895$	0.633975	+	10.5622i	0.0211914	+	0.353055i
$896$	27.2583	+	13.2321i	0.910637	+	0.442052i
$897$	3.58846	+	2.07180i	0.119815	+	0.0691753i
$898$	9.02628	−	9.02628i	0.301211	−	0.301211i
$899$	−27.1244	+	46.9808i	−0.904648	+	1.56690i
$900$	3.10770	+	25.7942i	0.103590	+	0.859808i
$901$	1.85641	−	1.07180i	0.0618459	−	0.0357067i
$902$	0.803848	+	3.00000i	0.0267652	+	0.0998891i
$903$	−4.09808	+	0.294229i	−0.136375	+	0.00979132i
$904$	16.3923	−	9.46410i	0.545200	−	0.314771i
$905$	7.69615	−	5.08142i	0.255829	−	0.168912i
$906$	−0.215390	+	0.215390i	−0.00715586	+	0.00715586i
$907$	2.79423	−	10.4282i	0.0927808	−	0.346263i	−0.903893	−	0.427759i	$-0.859303\pi$
$907$	2.79423	−	10.4282i	0.0927808	−	0.346263i	0.996674	+	0.0814962i	$0.0259699\pi$
$908$	11.1506	−	41.6147i	0.370047	−	1.38103i
$909$	−0.696152	−	0.401924i	−0.0230899	−	0.0133310i
$910$	0.150635	−	1.15064i	0.00499350	−	0.0381432i
$911$	−2.36603	+	4.09808i	−0.0783899	+	0.135775i	−0.902555	−	0.430574i	$-0.858311\pi$
$911$	−2.36603	+	4.09808i	−0.0783899	+	0.135775i	0.824165	+	0.566349i	$0.191645\pi$
$912$			3.12436i			0.103458i
$913$	14.5885	+	14.5885i	0.482807	+	0.482807i
$914$			11.0192i			0.364484i
$915$	42.2487	−	2.53590i	1.39670	−	0.0838342i
$916$	−33.9904	−	19.6244i	−1.12307	−	0.648407i
$917$	9.46410	−	49.1769i	0.312532	−	1.62396i
$918$	4.82309	+	2.78461i	0.159186	+	0.0919058i
$919$	−10.9019	+	6.29423i	−0.359621	+	0.207627i	−0.668915	−	0.743339i	$-0.733241\pi$
$919$	−10.9019	+	6.29423i	−0.359621	+	0.207627i	0.309293	+	0.950967i	$0.399908\pi$
$920$	1.63397	+	27.2224i	0.0538705	+	0.897497i
$921$	8.59808	−	2.30385i	0.283316	−	0.0759144i
$922$	−3.74871	−	13.9904i	−0.123457	−	0.460749i
$923$	0.124356	−	0.464102i	0.00409322	−	0.0152761i
$924$	−5.19615	−	15.0000i	−0.170941	−	0.493464i
$925$	−35.9545	−	28.2224i	−1.18218	−	0.927948i
$926$	5.66987	+	9.82051i	0.186324	+	0.322722i
$927$	−13.9019	−	13.9019i	−0.456599	−	0.456599i
$928$	13.2058	+	49.2846i	0.433501	+	1.61785i
$929$	9.78461			0.321023			0.160511	−	0.987034i	$-0.448686\pi$
$929$	9.78461			0.321023			0.160511	+	0.987034i	$0.448686\pi$
$930$	8.19615	+	7.26795i	0.268762	+	0.238325i
$931$	4.75833	+	1.90192i	0.155948	+	0.0623330i
$932$	−9.58846	+	35.7846i	−0.314080	+	1.17216i
$933$	14.8301	−	25.6865i	0.485517	−	0.840939i
$934$	−2.50000	−	4.33013i	−0.0818025	−	0.141686i
$935$	9.07180	+	1.85641i	0.296679	+	0.0607110i
$936$	1.09808	−	1.90192i	0.0358917	−	0.0621663i
$937$	−12.4641	+	12.4641i	−0.407184	+	0.407184i	−0.880756	−	0.473571i	$-0.842965\pi$
$937$	−12.4641	+	12.4641i	−0.407184	+	0.407184i	0.473571	+	0.880756i	$0.342965\pi$
$938$	4.50962	−	1.56218i	0.147244	−	0.0510069i
$939$	−14.1962	−	52.9808i	−0.463274	−	1.72896i
$940$	3.99038	−	19.5000i	0.130152	−	0.636020i
$941$		−	31.0526i		−	1.01228i	−0.862450	−	0.506142i	$-0.831071\pi$
$941$		−	31.0526i		−	1.01228i	0.862450	−	0.506142i	$-0.168929\pi$
$942$	3.50962	+	2.02628i	0.114350	+	0.0660198i
$943$	13.3923	+	13.3923i	0.436113	+	0.436113i
$944$	22.4833			0.731770
$945$	24.4019	+	18.6962i	0.793795	+	0.608186i
$946$	0.928203			0.0301785
$947$	5.00000	+	5.00000i	0.162478	+	0.162478i	0.783664	−	0.621185i	$-0.213349\pi$
$947$	5.00000	+	5.00000i	0.162478	+	0.162478i	−0.621185	+	0.783664i	$0.713349\pi$
$948$	−29.7846	−	17.1962i	−0.967359	−	0.558505i
$949$			5.07180i			0.164637i
$950$	1.49038	+	1.16987i	0.0483543	+	0.0379557i
$951$	0.973721	+	3.63397i	0.0315751	+	0.117840i
$952$	−2.00000	+	10.3923i	−0.0648204	+	0.336817i
$953$	−16.0526	+	16.0526i	−0.519993	+	0.519993i	−0.917569	−	0.397576i	$-0.869852\pi$
$953$	−16.0526	+	16.0526i	−0.519993	+	0.519993i	0.397576	+	0.917569i	$0.369852\pi$
$954$	−1.60770			−0.0520511
$955$	−24.8827	−	37.6865i	−0.805185	−	1.21951i
$956$	−1.73205	−	3.00000i	−0.0560185	−	0.0970269i
$957$	17.1962	−	29.7846i	0.555873	−	0.962800i
$958$	2.77757	−	10.3660i	0.0897392	−	0.334911i
$959$	−3.73205	+	0.267949i	−0.120514	+	0.00865253i
$960$	−8.76795	+	0.526279i	−0.282984	+	0.0169856i
$961$	1.14359			0.0368901
$962$	0.464102	+	1.73205i	0.0149632	+	0.0558436i
$963$	−27.1865	+	7.28461i	−0.876074	+	0.234743i
$964$	13.4545	+	23.3038i	0.433340	+	0.750566i
$965$	−31.5885	−	6.46410i	−1.01687	−	0.208087i
$966$	11.3205	+	9.80385i	0.364231	+	0.315434i
$967$	6.07884	−	22.6865i	0.195482	−	0.729550i	−0.796659	−	0.604429i	$-0.793401\pi$
$967$	6.07884	−	22.6865i	0.195482	−	0.729550i	0.992141	−	0.125121i	$-0.0399319\pi$
$968$	−3.50000	−	13.0622i	−0.112494	−	0.419834i
$969$	−2.53590	+	0.679492i	−0.0814648	+	0.0218284i
$970$	10.8827	−	0.653212i	0.349422	−	0.0209734i
$971$	16.2224	−	9.36603i	0.520603	−	0.300570i	−0.216579	−	0.976265i	$-0.569490\pi$
$971$	16.2224	−	9.36603i	0.520603	−	0.300570i	0.737181	+	0.675695i	$0.236156\pi$
$972$	13.5000	+	23.3827i	0.433013	+	0.750000i
$973$	32.1962	−	37.1769i	1.03216	−	1.19184i
$974$	12.5429	+	7.24167i	0.401902	+	0.232038i
$975$	1.22243	+	3.04552i	0.0391492	+	0.0975346i
$976$			26.9282i			0.861951i
$977$	−17.8038	−	17.8038i	−0.569596	−	0.569596i	0.362420	−	0.932015i	$-0.381951\pi$
$977$	−17.8038	−	17.8038i	−0.569596	−	0.569596i	−0.932015	+	0.362420i	$0.881951\pi$
$978$			21.8038i			0.697210i
$979$	−1.07180	+	1.85641i	−0.0342548	+	0.0593310i
$980$	−8.53590	+	25.7321i	−0.272669	+	0.821980i
$981$		−	29.1962i		−	0.932161i
$982$	1.95448	−	7.29423i	0.0623700	−	0.232768i
$983$	−14.6506	+	54.6769i	−0.467283	+	1.74392i	0.181926	+	0.983312i	$0.441767\pi$
$983$	−14.6506	+	54.6769i	−0.467283	+	1.74392i	−0.649209	+	0.760610i	$0.724900\pi$
$984$	7.09808	−	7.09808i	0.226278	−	0.226278i
$985$	−2.53590	+	12.3923i	−0.0808004	+	0.394852i
$986$	−9.21539	+	5.32051i	−0.293478	+	0.169439i
$987$	−13.2058	−	19.5000i	−0.420344	−	0.620692i
$988$	0.124356	+	0.464102i	0.00395628	+	0.0147650i
$989$	4.90192	−	2.83013i	0.155872	−	0.0899928i
$990$	−5.19615	−	4.60770i	−0.165145	−	0.146442i
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	−19.8564	+	19.8564i	−0.630442	+	0.630442i
$993$	−9.00000	−	5.19615i	−0.285606	−	0.164895i
$994$	0.758330	−	1.56218i	0.0240528	−	0.0495493i
$995$	36.5885	−	2.19615i	1.15993	−	0.0696227i
$996$	8.00962	−	29.8923i	0.253794	−	0.947174i
$997$	33.8827	+	9.07884i	1.07308	+	0.287530i	0.751756	−	0.659441i	$-0.229207\pi$
$997$	33.8827	+	9.07884i	1.07308	+	0.287530i	0.321319	+	0.946971i	$0.395874\pi$
$998$	−5.14359	−	19.1962i	−0.162818	−	0.607644i
$999$	−45.8827	−	12.2942i	−1.45166	−	0.388972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bs.d.52.1	yes	4
3.2	odd	2		945.2.bv.c.262.1		4
5.3	odd	4		315.2.bs.a.178.1	✓	4
7.5	odd	6		315.2.cg.d.187.1	yes	4
9.4	even	3		315.2.cg.b.157.1	yes	4
9.5	odd	6		945.2.cj.c.577.1		4
15.8	even	4		945.2.bv.b.73.1		4
21.5	even	6		945.2.cj.b.397.1		4
35.33	even	12		315.2.cg.b.313.1	yes	4
45.13	odd	12		315.2.cg.d.283.1	yes	4
45.23	even	12		945.2.cj.b.388.1		4
63.5	even	6		945.2.bv.b.712.1		4
63.40	odd	6		315.2.bs.a.292.1	yes	4
105.68	odd	12		945.2.cj.c.208.1		4
315.68	odd	12		945.2.bv.c.523.1		4
315.103	even	12	inner	315.2.bs.d.103.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.a.178.1	✓	4	5.3	odd	4
315.2.bs.a.292.1	yes	4	63.40	odd	6
315.2.bs.d.52.1	yes	4	1.1	even	1	trivial
315.2.bs.d.103.1	yes	4	315.103	even	12	inner
315.2.cg.b.157.1	yes	4	9.4	even	3
315.2.cg.b.313.1	yes	4	35.33	even	12
315.2.cg.d.187.1	yes	4	7.5	odd	6
315.2.cg.d.283.1	yes	4	45.13	odd	12
945.2.bv.b.73.1		4	15.8	even	4
945.2.bv.b.712.1		4	63.5	even	6
945.2.bv.c.262.1		4	3.2	odd	2
945.2.bv.c.523.1		4	315.68	odd	12
945.2.cj.b.388.1		4	45.23	even	12
945.2.cj.b.397.1		4	21.5	even	6
945.2.cj.c.208.1		4	105.68	odd	12
945.2.cj.c.577.1		4	9.5	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(1.23205 + 1.86603i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(1.23205 + 1.86603i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.232051 + 1.13397i) q^{10} +(1.00000 + 1.73205i) q^{11} +(1.50000 - 2.59808i) q^{12} +(0.0980762 - 0.366025i) q^{13} +(0.598076 - 1.23205i) q^{14} +(0.232051 + 3.86603i) q^{15} -2.46410 q^{16} +(-0.535898 - 2.00000i) q^{17} +(-0.401924 + 1.50000i) q^{18} +(-0.366025 - 0.633975i) q^{19} +(3.23205 - 2.13397i) q^{20} +(0.866025 - 4.50000i) q^{21} +(-0.267949 + 1.00000i) q^{22} +(1.63397 + 6.09808i) q^{23} +(3.23205 - 0.866025i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(0.169873 - 0.0980762i) q^{26} +5.19615i q^{27} +(-4.33013 + 1.50000i) q^{28} +(-8.59808 - 4.96410i) q^{29} +(-1.33013 + 1.50000i) q^{30} -5.46410i q^{31} +(-3.63397 - 3.63397i) q^{32} +3.46410i q^{33} +(0.535898 - 0.928203i) q^{34} +(3.59808 - 4.69615i) q^{35} +(4.50000 - 2.59808i) q^{36} +(-2.36603 + 8.83013i) q^{37} +(0.0980762 - 0.366025i) q^{38} +(0.464102 - 0.464102i) q^{39} +(4.23205 + 0.866025i) q^{40} +(2.59808 - 1.50000i) q^{41} +(1.96410 - 1.33013i) q^{42} +(-0.232051 - 0.866025i) q^{43} +(3.00000 - 1.73205i) q^{44} +(-3.00000 + 6.00000i) q^{45} +(-1.63397 + 2.83013i) q^{46} +(3.63397 - 3.63397i) q^{47} +(-3.69615 - 2.13397i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(-2.40192 + 0.964102i) q^{50} +(0.928203 - 3.46410i) q^{51} +(-0.633975 - 0.169873i) q^{52} +(0.267949 + 1.00000i) q^{53} +(-1.90192 + 1.90192i) q^{54} +(-2.00000 + 4.00000i) q^{55} +(-4.59808 - 2.23205i) q^{56} -1.26795i q^{57} +(-1.33013 - 4.96410i) q^{58} -9.12436 q^{59} +(6.69615 - 0.401924i) q^{60} -10.9282i q^{61} +(2.00000 - 2.00000i) q^{62} +(5.19615 - 6.00000i) q^{63} +2.26795i q^{64} +(0.803848 - 0.267949i) q^{65} +(-1.26795 + 1.26795i) q^{66} +(2.46410 + 2.46410i) q^{67} +(-3.46410 + 0.928203i) q^{68} +(-2.83013 + 10.5622i) q^{69} +(3.03590 - 0.401924i) q^{70} +1.26795 q^{71} +(5.59808 + 1.50000i) q^{72} +(-12.9282 + 3.46410i) q^{73} +(-4.09808 + 2.36603i) q^{74} +(-6.92820 + 5.19615i) q^{75} +(-1.09808 + 0.633975i) q^{76} +(3.46410 - 4.00000i) q^{77} +0.339746 q^{78} -11.4641i q^{79} +(-3.03590 - 4.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.50000 + 0.401924i) q^{82} +(9.96410 - 2.66987i) q^{83} +(-7.79423 - 1.50000i) q^{84} +(3.07180 - 3.46410i) q^{85} +(0.232051 - 0.401924i) q^{86} +(-8.59808 - 14.8923i) q^{87} +(3.73205 + 1.00000i) q^{88} +(0.535898 + 0.928203i) q^{89} +(-3.29423 + 1.09808i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(10.5622 - 2.83013i) q^{92} +(4.73205 - 8.19615i) q^{93} +2.66025 q^{94} +(0.732051 - 1.46410i) q^{95} +(-2.30385 - 8.59808i) q^{96} +(-2.43782 - 9.09808i) q^{97} +(-3.59808 - 0.428203i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 2 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 2 q^{8} + 6 q^{9} + 6 q^{10} + 4 q^{11} + 6 q^{12} - 10 q^{13} - 8 q^{14} - 6 q^{15} + 4 q^{16} - 16 q^{17} - 12 q^{18} + 2 q^{19} + 6 q^{20} - 8 q^{22} + 10 q^{23} + 6 q^{24} + 6 q^{25} + 18 q^{26} - 24 q^{29} + 12 q^{30} - 18 q^{32} + 16 q^{34} + 4 q^{35} + 18 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} + 10 q^{40} - 6 q^{42} + 6 q^{43} + 12 q^{44} - 12 q^{45} - 10 q^{46} + 18 q^{47} + 6 q^{48} - 22 q^{49} - 20 q^{50} - 24 q^{51} - 6 q^{52} + 8 q^{53} - 18 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{58} + 12 q^{59} + 6 q^{60} + 8 q^{62} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 6 q^{69} + 26 q^{70} + 12 q^{71} + 12 q^{72} - 24 q^{73} - 6 q^{74} + 6 q^{76} + 36 q^{78} - 26 q^{80} - 18 q^{81} + 6 q^{82} + 26 q^{83} + 40 q^{85} - 6 q^{86} - 24 q^{87} + 8 q^{88} + 16 q^{89} + 18 q^{90} - 4 q^{91} + 18 q^{92} + 12 q^{93} - 24 q^{94} - 4 q^{95} - 30 q^{96} - 34 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 2 * q^8 + 6 * q^9 + 6 * q^10 + 4 * q^11 + 6 * q^12 - 10 * q^13 - 8 * q^14 - 6 * q^15 + 4 * q^16 - 16 * q^17 - 12 * q^18 + 2 * q^19 + 6 * q^20 - 8 * q^22 + 10 * q^23 + 6 * q^24 + 6 * q^25 + 18 * q^26 - 24 * q^29 + 12 * q^30 - 18 * q^32 + 16 * q^34 + 4 * q^35 + 18 * q^36 - 6 * q^37 - 10 * q^38 - 12 * q^39 + 10 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 12 * q^45 - 10 * q^46 + 18 * q^47 + 6 * q^48 - 22 * q^49 - 20 * q^50 - 24 * q^51 - 6 * q^52 + 8 * q^53 - 18 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^58 + 12 * q^59 + 6 * q^60 + 8 * q^62 + 24 * q^65 - 12 * q^66 - 4 * q^67 + 6 * q^69 + 26 * q^70 + 12 * q^71 + 12 * q^72 - 24 * q^73 - 6 * q^74 + 6 * q^76 + 36 * q^78 - 26 * q^80 - 18 * q^81 + 6 * q^82 + 26 * q^83 + 40 * q^85 - 6 * q^86 - 24 * q^87 + 8 * q^88 + 16 * q^89 + 18 * q^90 - 4 * q^91 + 18 * q^92 + 12 * q^93 - 24 * q^94 - 4 * q^95 - 30 * q^96 - 34 * q^97 - 4 * q^98 - 12 * q^99

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