LMFDB - Embedded newform 315.2.bs.a.178.1

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			178.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.178
Dual form			315.2.bs.a.292.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +1.73205i q^{4} +(2.23205 + 0.133975i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +1.73205i q^{4} +(2.23205 + 0.133975i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.866025 - 0.767949i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-2.59808 - 1.50000i) q^{12} +(0.366025 + 0.0980762i) q^{13} +(-0.598076 + 1.23205i) q^{14} +(-2.13397 + 3.23205i) q^{15} -2.46410 q^{16} +(-2.00000 + 0.535898i) q^{17} +(-1.50000 - 0.401924i) q^{18} +(0.366025 + 0.633975i) q^{19} +(-0.232051 + 3.86603i) q^{20} +(0.866025 - 4.50000i) q^{21} +(1.00000 + 0.267949i) q^{22} +(-6.09808 + 1.63397i) q^{23} +(-3.23205 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(0.169873 - 0.0980762i) q^{26} +5.19615 q^{27} +(-1.50000 - 4.33013i) q^{28} +(8.59808 + 4.96410i) q^{29} +(0.401924 + 1.96410i) q^{30} -5.46410i q^{31} +(-3.63397 + 3.63397i) q^{32} -3.46410 q^{33} +(-0.535898 + 0.928203i) q^{34} +(-5.69615 + 1.59808i) q^{35} +(4.50000 - 2.59808i) q^{36} +(8.83013 + 2.36603i) q^{37} +(0.366025 + 0.0980762i) q^{38} +(-0.464102 + 0.464102i) q^{39} +(2.86603 + 3.23205i) q^{40} +(2.59808 - 1.50000i) q^{41} +(-1.33013 - 1.96410i) q^{42} +(0.866025 - 0.232051i) 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} +(2.13397 - 3.69615i) q^{48} +(5.50000 - 4.33013i) q^{49} +(2.03590 - 1.59808i) q^{50} +(0.928203 - 3.46410i) q^{51} +(-0.169873 + 0.633975i) q^{52} +(-1.00000 + 0.267949i) q^{53} +(1.90192 - 1.90192i) q^{54} +(2.00000 + 4.00000i) q^{55} +(-4.59808 - 2.23205i) q^{56} -1.26795 q^{57} +(4.96410 - 1.33013i) q^{58} +9.12436 q^{59} +(-5.59808 - 3.69615i) q^{60} -10.9282i q^{61} +(-2.00000 - 2.00000i) q^{62} +(6.00000 + 5.19615i) q^{63} -2.26795i q^{64} +(0.803848 + 0.267949i) q^{65} +(-1.26795 + 1.26795i) q^{66} +(2.46410 - 2.46410i) q^{67} +(-0.928203 - 3.46410i) q^{68} +(2.83013 - 10.5622i) q^{69} +(-1.50000 + 2.66987i) q^{70} +1.26795 q^{71} +(1.50000 - 5.59808i) q^{72} +(-3.46410 - 12.9282i) q^{73} +(4.09808 - 2.36603i) q^{74} +(-5.19615 + 6.92820i) q^{75} +(-1.09808 + 0.633975i) q^{76} +(-4.00000 - 3.46410i) q^{77} +0.339746i q^{78} +11.4641i q^{79} +(-5.50000 - 0.330127i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(0.401924 - 1.50000i) q^{82} +(2.66987 + 9.96410i) q^{83} +(7.79423 + 1.50000i) q^{84} +(-4.53590 + 0.928203i) q^{85} +(0.232051 - 0.401924i) q^{86} +(-14.8923 + 8.59808i) q^{87} +(-1.00000 + 3.73205i) q^{88} +(-0.535898 - 0.928203i) q^{89} +(-3.29423 - 1.09808i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(-2.83013 - 10.5622i) q^{92} +(8.19615 + 4.73205i) q^{93} -2.66025 q^{94} +(0.732051 + 1.46410i) q^{95} +(-2.30385 - 8.59808i) q^{96} +(-9.09808 + 2.43782i) q^{97} +(0.428203 - 3.59808i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9} + 4 q^{11} - 2 q^{13} + 8 q^{14} - 12 q^{15} + 4 q^{16} - 8 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{22} - 14 q^{23} - 6 q^{24} + 6 q^{25} + 18 q^{26} - 6 q^{28} + 24 q^{29} + 12 q^{30} - 18 q^{32} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 2 q^{38} + 12 q^{39} + 8 q^{40} + 12 q^{42} - 12 q^{44} - 12 q^{45} - 10 q^{46} - 18 q^{47} + 12 q^{48} + 22 q^{49} + 22 q^{50} - 24 q^{51} - 18 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 8 q^{56} - 12 q^{57} + 6 q^{58} - 12 q^{59} - 12 q^{60} - 8 q^{62} + 24 q^{63} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 24 q^{68} - 6 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{72} + 6 q^{74} + 6 q^{76} - 16 q^{77} - 22 q^{80} - 18 q^{81} + 12 q^{82} + 28 q^{83} - 32 q^{85} - 6 q^{86} - 18 q^{87} - 4 q^{88} - 16 q^{89} + 18 q^{90} - 4 q^{91} + 6 q^{92} + 12 q^{93} + 24 q^{94} - 4 q^{95} - 30 q^{96} - 26 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9 + 4 * q^11 - 2 * q^13 + 8 * q^14 - 12 * q^15 + 4 * q^16 - 8 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^22 - 14 * q^23 - 6 * q^24 + 6 * q^25 + 18 * q^26 - 6 * q^28 + 24 * q^29 + 12 * q^30 - 18 * q^32 - 16 * q^34 - 2 * q^35 + 18 * q^36 + 18 * q^37 - 2 * q^38 + 12 * q^39 + 8 * q^40 + 12 * q^42 - 12 * q^44 - 12 * q^45 - 10 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 + 22 * q^50 - 24 * q^51 - 18 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 8 * q^56 - 12 * q^57 + 6 * q^58 - 12 * q^59 - 12 * q^60 - 8 * q^62 + 24 * q^63 + 24 * q^65 - 12 * q^66 - 4 * q^67 + 24 * q^68 - 6 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^72 + 6 * q^74 + 6 * q^76 - 16 * q^77 - 22 * q^80 - 18 * q^81 + 12 * q^82 + 28 * q^83 - 32 * q^85 - 6 * q^86 - 18 * q^87 - 4 * q^88 - 16 * q^89 + 18 * q^90 - 4 * q^91 + 6 * q^92 + 12 * q^93 + 24 * q^94 - 4 * q^95 - 30 * q^96 - 26 * q^97 - 26 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.565755	−	0.824574i	$-0.691415\pi$
$2$	0.366025	−	0.366025i	0.258819	−	0.258819i	0.824574	+	0.565755i	$0.191415\pi$
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$			1.73205i			0.866025i
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$6$	0.232051	+	0.866025i	0.0947343	+	0.353553i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	1.36603	+	1.36603i	0.482963	+	0.482963i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	0.866025	−	0.767949i	0.273861	−	0.242847i
$11$	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	$0.735842\pi$
$12$	−2.59808	−	1.50000i	−0.750000	−	0.433013i
$13$	0.366025	+	0.0980762i	0.101517	+	0.0272014i	0.309220	−	0.950991i	$-0.399932\pi$
$13$	0.366025	+	0.0980762i	0.101517	+	0.0272014i	−0.207703	+	0.978192i	$0.566599\pi$
$14$	−0.598076	+	1.23205i	−0.159843	+	0.329279i
$15$	−2.13397	+	3.23205i	−0.550990	+	0.834512i
$16$	−2.46410			−0.616025
$17$	−2.00000	+	0.535898i	−0.485071	+	0.129974i	−0.493063	−	0.869994i	$-0.664123\pi$
$17$	−2.00000	+	0.535898i	−0.485071	+	0.129974i	0.00799174	+	0.999968i	$0.497456\pi$
$18$	−1.50000	−	0.401924i	−0.353553	−	0.0947343i
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	0.904953	−	0.425512i	$-0.139906\pi$
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	−0.820981	+	0.570956i	$0.806573\pi$
$20$	−0.232051	+	3.86603i	−0.0518881	+	0.864470i
$21$	0.866025	−	4.50000i	0.188982	−	0.981981i
$22$	1.00000	+	0.267949i	0.213201	+	0.0571270i
$23$	−6.09808	+	1.63397i	−1.27154	+	0.340707i	−0.830619	−	0.556840i	$-0.812013\pi$
$23$	−6.09808	+	1.63397i	−1.27154	+	0.340707i	−0.440917	+	0.897548i	$0.645347\pi$
$24$	−3.23205	+	0.866025i	−0.659740	+	0.176777i
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$	0.169873	−	0.0980762i	0.0333148	−	0.0192343i
$27$	5.19615			1.00000
$28$	−1.50000	−	4.33013i	−0.283473	−	0.818317i
$29$	8.59808	+	4.96410i	1.59662	+	0.921811i	0.992132	+	0.125199i	$0.0399568\pi$
$29$	8.59808	+	4.96410i	1.59662	+	0.921811i	0.604491	+	0.796612i	$0.293377\pi$
$30$	0.401924	+	1.96410i	0.0733809	+	0.358594i
$31$		−	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
$33$	−3.46410			−0.603023
$34$	−0.535898	+	0.928203i	−0.0919058	+	0.159186i
$35$	−5.69615	+	1.59808i	−0.962825	+	0.270124i
$36$	4.50000	−	2.59808i	0.750000	−	0.433013i
$37$	8.83013	+	2.36603i	1.45166	+	0.388972i	0.896602	−	0.442837i	$-0.146028\pi$
$37$	8.83013	+	2.36603i	1.45166	+	0.388972i	0.555062	+	0.831809i	$0.312695\pi$
$38$	0.366025	+	0.0980762i	0.0593772	+	0.0159101i
$39$	−0.464102	+	0.464102i	−0.0743157	+	0.0743157i
$40$	2.86603	+	3.23205i	0.453158	+	0.511032i
$41$	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	$0.258066\pi$
$42$	−1.33013	−	1.96410i	−0.205243	−	0.303067i
$43$	0.866025	−	0.232051i	0.132068	−	0.0353874i	−0.192180	−	0.981360i	$-0.561556\pi$
$43$	0.866025	−	0.232051i	0.132068	−	0.0353874i	0.324247	+	0.945972i	$0.394889\pi$
$44$	−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	$-0.372294\pi$
$47$	−3.63397	−	3.63397i	−0.530070	−	0.530070i	−0.920593	+	0.390523i	$0.872294\pi$
$48$	2.13397	−	3.69615i	0.308013	−	0.533494i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	2.03590	−	1.59808i	0.287920	−	0.226002i
$51$	0.928203	−	3.46410i	0.129974	−	0.485071i
$52$	−0.169873	+	0.633975i	−0.0235571	+	0.0879165i
$53$	−1.00000	+	0.267949i	−0.137361	+	0.0368057i	−0.326844	−	0.945078i	$-0.605985\pi$
$53$	−1.00000	+	0.267949i	−0.137361	+	0.0368057i	0.189484	+	0.981884i	$0.439319\pi$
$54$	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
$57$	−1.26795			−0.167944
$58$	4.96410	−	1.33013i	0.651818	−	0.174654i
$59$	9.12436			1.18789			0.593945	−	0.804506i	$-0.297570\pi$
$59$	9.12436			1.18789			0.593945	+	0.804506i	$0.297570\pi$
$60$	−5.59808	−	3.69615i	−0.722709	−	0.477171i
$61$		−	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
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$		−	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	−0.540382	−	0.841420i	$-0.681720\pi$
$67$	2.46410	−	2.46410i	0.301038	−	0.301038i	0.841420	+	0.540382i	$0.181720\pi$
$68$	−0.928203	−	3.46410i	−0.112561	−	0.420084i
$69$	2.83013	−	10.5622i	0.340707	−	1.27154i
$70$	−1.50000	+	2.66987i	−0.179284	+	0.319111i
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	1.50000	−	5.59808i	0.176777	−	0.659740i
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	−0.803238	−	0.595658i	$-0.796891\pi$
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	0.397796	−	0.917474i	$-0.369775\pi$
$74$	4.09808	−	2.36603i	0.476392	−	0.275045i
$75$	−5.19615	+	6.92820i	−0.600000	+	0.800000i
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	−4.00000	−	3.46410i	−0.455842	−	0.394771i
$78$			0.339746i			0.0384687i
$79$			11.4641i			1.28981i	0.764262	+	0.644906i	$0.223104\pi$
$79$			11.4641i			1.28981i	−0.764262	+	0.644906i	$0.776896\pi$
$80$	−5.50000	−	0.330127i	−0.614919	−	0.0369093i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	0.401924	−	1.50000i	0.0443851	−	0.165647i
$83$	2.66987	+	9.96410i	0.293057	+	1.09370i	0.942748	+	0.333505i	$0.108231\pi$
$83$	2.66987	+	9.96410i	0.293057	+	1.09370i	−0.649692	+	0.760198i	$0.725102\pi$
$84$	7.79423	+	1.50000i	0.850420	+	0.163663i
$85$	−4.53590	+	0.928203i	−0.491987	+	0.100678i
$86$	0.232051	−	0.401924i	0.0250227	−	0.0433406i
$87$	−14.8923	+	8.59808i	−1.59662	+	0.921811i
$88$	−1.00000	+	3.73205i	−0.106600	+	0.397838i
$89$	−0.535898	−	0.928203i	−0.0568051	−	0.0983893i	0.836224	−	0.548387i	$-0.184758\pi$
$89$	−0.535898	−	0.928203i	−0.0568051	−	0.0983893i	−0.893030	+	0.449998i	$0.851425\pi$
$90$	−3.29423	−	1.09808i	−0.347242	−	0.115747i
$91$	−1.00000	+	0.0717968i	−0.104828	+	0.00752635i
$92$	−2.83013	−	10.5622i	−0.295061	−	1.10118i
$93$	8.19615	+	4.73205i	0.849901	+	0.490691i
$94$	−2.66025			−0.274384
$95$	0.732051	+	1.46410i	0.0751068	+	0.150214i
$96$	−2.30385	−	8.59808i	−0.235135	−	0.877537i
$97$	−9.09808	+	2.43782i	−0.923770	+	0.247523i	−0.689196	−	0.724575i	$-0.742036\pi$
$97$	−9.09808	+	2.43782i	−0.923770	+	0.247523i	−0.234574	+	0.972098i	$0.575369\pi$
$98$	0.428203	−	3.59808i	0.0432551	−	0.363461i
$99$	3.00000	−	5.19615i	0.301511	−	0.522233i
$100$	−1.03590	+	8.59808i	−0.103590	+	0.859808i
$101$	−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	$0.337577\pi$
$102$	−0.928203	−	1.60770i	−0.0919058	−	0.159186i
$103$	−1.69615	−	6.33013i	−0.167127	−	0.623726i	−0.997759	−	0.0669049i	$-0.978688\pi$
$103$	−1.69615	−	6.33013i	−0.167127	−	0.623726i	0.830632	−	0.556821i	$-0.187979\pi$
$104$	0.366025	+	0.633975i	0.0358917	+	0.0621663i
$105$	2.53590	−	9.92820i	0.247478	−	0.968893i
$106$	−0.267949	+	0.464102i	−0.0260255	+	0.0450775i
$107$	9.06218	+	2.42820i	0.876074	+	0.234743i	0.668712	−	0.743521i	$-0.266846\pi$
$107$	9.06218	+	2.42820i	0.876074	+	0.234743i	0.207361	+	0.978264i	$0.433512\pi$
$108$			9.00000i			0.866025i
$109$	8.42820	+	4.86603i	0.807275	+	0.466081i	0.846009	−	0.533169i	$-0.178999\pi$
$109$	8.42820	+	4.86603i	0.807275	+	0.466081i	−0.0387334	+	0.999250i	$0.512332\pi$
$110$	2.19615	+	0.732051i	0.209395	+	0.0697983i
$111$	−11.1962	+	11.1962i	−1.06269	+	1.06269i
$112$	6.16025	−	2.13397i	0.582089	−	0.201642i
$113$	−2.53590	+	9.46410i	−0.238557	+	0.890308i	0.737956	+	0.674849i	$0.235791\pi$
$113$	−2.53590	+	9.46410i	−0.238557	+	0.890308i	−0.976513	+	0.215459i	$0.930875\pi$
$114$	−0.464102	+	0.464102i	−0.0434671	+	0.0434671i
$115$	−13.8301	+	2.83013i	−1.28967	+	0.263911i
$116$	−8.59808	+	14.8923i	−0.798311	+	1.38272i
$117$	−0.294229	−	1.09808i	−0.0272014	−	0.101517i
$118$	3.33975	−	3.33975i	0.307449	−	0.307449i
$119$	4.53590	−	3.07180i	0.415805	−	0.281591i
$120$	−7.33013	+	1.50000i	−0.669146	+	0.136931i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−4.00000	−	4.00000i	−0.362143	−	0.362143i
$123$			5.19615i			0.468521i
$124$	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	0.00860872	−	0.999963i	$-0.497260\pi$
$127$	11.3660	−	11.3660i	1.00857	−	1.00857i	0.999963	−	0.00860872i	$-0.00274027\pi$
$128$	−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	$0.356779\pi$
$132$		−	6.00000i		−	0.522233i
$133$	−1.46410	−	1.26795i	−0.126954	−	0.109945i
$134$		−	1.80385i		−	0.155829i
$135$	11.5981	+	0.696152i	0.998203	+	0.0599153i
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	−1.36603	−	0.366025i	−0.116707	−	0.0312717i	0.199993	−	0.979797i	$-0.435908\pi$
$137$	−1.36603	−	0.366025i	−0.116707	−	0.0312717i	−0.316700	+	0.948526i	$0.602575\pi$
$138$	−2.83013	−	4.90192i	−0.240916	−	0.417279i
$139$	−9.29423	−	16.0981i	−0.788326	−	1.36542i	−0.926992	−	0.375082i	$-0.877615\pi$
$139$	−9.29423	−	16.0981i	−0.788326	−	1.36542i	0.138666	−	0.990339i	$-0.455719\pi$
$140$	−2.76795	−	9.86603i	−0.233934	−	0.833831i
$141$	8.59808	−	2.30385i	0.724089	−	0.194019i
$142$	0.464102	−	0.464102i	0.0389465	−	0.0389465i
$143$	0.196152	+	0.732051i	0.0164031	+	0.0612172i
$144$	3.69615	+	6.40192i	0.308013	+	0.533494i
$145$	18.5263	+	12.2321i	1.53852	+	1.01582i
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$	1.73205	+	12.0000i	0.142857	+	0.989743i
$148$	−4.09808	+	15.2942i	−0.336860	+	1.25718i
$149$	−7.39230	−	4.26795i	−0.605601	−	0.349644i	0.165641	−	0.986186i	$-0.447031\pi$
$149$	−7.39230	−	4.26795i	−0.605601	−	0.349644i	−0.771242	+	0.636542i	$0.780364\pi$
$150$	0.633975	+	4.43782i	0.0517638	+	0.362347i
$151$	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	$0.828933\pi$
$152$	−0.366025	+	1.36603i	−0.0296886	+	0.110799i
$153$	4.39230	+	4.39230i	0.355097	+	0.355097i
$154$	−2.73205	+	0.196152i	−0.220155	+	0.0158064i
$155$	0.732051	−	12.1962i	0.0587997	−	0.979619i
$156$	−0.803848	−	0.803848i	−0.0643593	−	0.0643593i
$157$	−3.19615	−	3.19615i	−0.255081	−	0.255081i	0.567969	−	0.823050i	$-0.307729\pi$
$157$	−3.19615	−	3.19615i	−0.255081	−	0.255081i	−0.823050	+	0.567969i	$0.807729\pi$
$158$	4.19615	+	4.19615i	0.333828	+	0.333828i
$159$	0.464102	−	1.73205i	0.0368057	−	0.137361i
$160$	−8.59808	+	7.62436i	−0.679738	+	0.602758i
$161$	13.8301	−	9.36603i	1.08997	−	0.738146i
$162$	1.20577	+	4.50000i	0.0947343	+	0.353553i
$163$	−6.29423	+	23.4904i	−0.493002	+	1.83991i	0.0479421	+	0.998850i	$0.484734\pi$
$163$	−6.29423	+	23.4904i	−0.493002	+	1.83991i	−0.540944	+	0.841059i	$0.681933\pi$
$164$	2.59808	+	4.50000i	0.202876	+	0.351391i
$165$	−7.73205	−	0.464102i	−0.601939	−	0.0361303i
$166$	4.62436	+	2.66987i	0.358920	+	0.207222i
$167$	1.63397	−	6.09808i	0.126441	−	0.471883i	−0.873446	−	0.486921i	$-0.838120\pi$
$167$	1.63397	−	6.09808i	0.126441	−	0.471883i	0.999887	+	0.0150374i	$0.00478673\pi$
$168$	7.33013	−	4.96410i	0.565532	−	0.382989i
$169$	−11.1340	−	6.42820i	−0.856460	−	0.494477i
$170$	−1.32051	+	2.00000i	−0.101278	+	0.153393i
$171$	1.09808	−	1.90192i	0.0839720	−	0.145444i
$172$	0.401924	+	1.50000i	0.0306464	+	0.114374i
$173$	−16.0000	+	16.0000i	−1.21646	+	1.21646i	−0.247593	+	0.968864i	$0.579640\pi$
$173$	−16.0000	+	16.0000i	−1.21646	+	1.21646i	−0.968864	+	0.247593i	$0.920360\pi$
$174$	−2.30385	+	8.59808i	−0.174654	+	0.651818i
$175$	−12.9282	+	2.80385i	−0.977280	+	0.211951i
$176$	−2.46410	−	4.26795i	−0.185739	−	0.321709i
$177$	−7.90192	+	13.6865i	−0.593945	+	1.02874i
$178$	−0.535898	−	0.143594i	−0.0401673	−	0.0107628i
$179$	−4.09808	−	2.36603i	−0.306305	−	0.176845i	0.338967	−	0.940798i	$-0.389922\pi$
$179$	−4.09808	−	2.36603i	−0.306305	−	0.176845i	−0.645272	+	0.763953i	$0.723256\pi$
$180$	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	$-0.0489838\pi$
$182$	−0.339746	+	0.392305i	−0.0251836	+	0.0290796i
$183$	16.3923	+	9.46410i	1.21175	+	0.699607i
$184$	−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	$0.760793\pi$
$192$	3.40192	+	1.96410i	0.245513	+	0.141747i
$193$	−10.1962	−	10.1962i	−0.733935	−	0.733935i	0.237462	−	0.971397i	$-0.423685\pi$
$193$	−10.1962	−	10.1962i	−0.733935	−	0.733935i	−0.971397	+	0.237462i	$0.923685\pi$
$194$	−2.43782	+	4.22243i	−0.175025	+	0.303153i
$195$	−1.09808	+	0.973721i	−0.0786349	+	0.0697296i
$196$	7.50000	+	9.52628i	0.535714	+	0.680449i
$197$	4.00000	−	4.00000i	0.284988	−	0.284988i	−0.550106	−	0.835095i	$-0.685413\pi$
$197$	4.00000	−	4.00000i	0.284988	−	0.284988i	0.835095	+	0.550106i	$0.185413\pi$
$198$	−0.803848	−	3.00000i	−0.0571270	−	0.213201i
$199$	−8.19615	+	14.1962i	−0.581010	+	1.00634i	0.414350	+	0.910118i	$0.364009\pi$
$199$	−8.19615	+	14.1962i	−0.581010	+	1.00634i	−0.995360	+	0.0962210i	$0.969324\pi$
$200$	5.96410	+	7.59808i	0.421726	+	0.537265i
$201$	1.56218	+	5.83013i	0.110188	+	0.411225i
$202$	−0.0358984	+	0.133975i	−0.00252580	+	0.00942642i
$203$	−25.7942	−	4.96410i	−1.81040	−	0.348412i
$204$	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
$208$	−0.901924	−	0.241670i	−0.0625372	−	0.0167568i
$209$	−0.732051	+	1.26795i	−0.0506370	+	0.0877059i
$210$	−2.70577	−	4.56218i	−0.186716	−	0.314820i
$211$	−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	$-0.544209\pi$
$212$	−0.464102	−	1.73205i	−0.0318746	−	0.118958i
$213$	−1.09808	+	1.90192i	−0.0752389	+	0.130318i
$214$	4.20577	−	2.42820i	0.287501	−	0.165989i
$215$	1.96410	−	0.401924i	0.133951	−	0.0274110i
$216$	7.09808	+	7.09808i	0.482963	+	0.482963i
$217$	4.73205	+	13.6603i	0.321233	+	0.927318i
$218$	4.86603	−	1.30385i	0.329569	−	0.0883077i
$219$	22.3923	+	6.00000i	1.51313	+	0.405442i
$220$	−6.92820	+	3.46410i	−0.467099	+	0.233550i
$221$	−0.784610			−0.0527786
$222$			8.19615i			0.550090i
$223$	1.33013	+	4.96410i	0.0890719	+	0.332421i	0.996054	−	0.0887481i	$-0.0282866\pi$
$223$	1.33013	+	4.96410i	0.0890719	+	0.332421i	−0.906982	+	0.421169i	$0.861620\pi$
$224$	5.93782	−	12.2321i	0.396737	−	0.817288i
$225$	−5.89230	−	13.7942i	−0.392820	−	0.919615i
$226$	2.53590	+	4.39230i	0.168685	+	0.292172i
$227$	6.43782	−	24.0263i	0.427293	−	1.59468i	−0.331570	−	0.943431i	$-0.607578\pi$
$227$	6.43782	−	24.0263i	0.427293	−	1.59468i	0.758864	−	0.651250i	$-0.225755\pi$
$228$		−	2.19615i		−	0.145444i
$229$	−11.3301	+	19.6244i	−0.748716	+	1.29681i	0.199723	+	0.979852i	$0.435996\pi$
$229$	−11.3301	+	19.6244i	−0.748716	+	1.29681i	−0.948438	+	0.316961i	$0.897337\pi$
$230$	−4.02628	+	6.09808i	−0.265485	+	0.402095i
$231$	8.66025	−	3.00000i	0.569803	−	0.197386i
$232$	4.96410	+	18.5263i	0.325909	+	1.21631i
$233$	5.53590	−	20.6603i	0.362669	−	1.35350i	−0.507885	−	0.861425i	$-0.669573\pi$
$233$	5.53590	−	20.6603i	0.362669	−	1.35350i	0.870554	−	0.492073i	$-0.163761\pi$
$234$	−0.509619	−	0.294229i	−0.0333148	−	0.0192343i
$235$	−7.62436	−	8.59808i	−0.497358	−	0.560877i
$236$			15.8038i			1.02874i
$237$	−17.1962	−	9.92820i	−1.11701	−	0.644906i
$238$	0.535898	−	2.78461i	0.0347371	−	0.180499i
$239$	−1.73205	+	1.00000i	−0.112037	+	0.0646846i	−0.554971	−	0.831869i	$-0.687271\pi$
$239$	−1.73205	+	1.00000i	−0.112037	+	0.0646846i	0.442934	+	0.896554i	$0.353937\pi$
$240$	5.25833	−	7.96410i	0.339424	−	0.514081i
$241$	−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	$0.500139\pi$
$242$	−0.937822	−	3.50000i	−0.0602855	−	0.224989i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	18.9282			1.21175
$245$	12.8564	−	8.92820i	0.821366	−	0.570402i
$246$	1.90192	+	1.90192i	0.121262	+	0.121262i
$247$	0.0717968	+	0.267949i	0.00456832	+	0.0170492i
$248$	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	$0.858121\pi$
$252$	−9.00000	+	10.3923i	−0.566947	+	0.654654i
$253$	−8.92820	−	8.92820i	−0.561311	−	0.561311i
$254$		−	8.32051i		−	0.522075i
$255$	2.53590	−	7.60770i	0.158804	−	0.476412i
$256$	−1.39230			−0.0870191
$257$	−13.9282	+	3.73205i	−0.868817	+	0.232799i	−0.665576	−	0.746330i	$-0.731814\pi$
$257$	−13.9282	+	3.73205i	−0.868817	+	0.232799i	−0.203241	+	0.979129i	$0.565148\pi$
$258$	0.401924	+	0.696152i	0.0250227	+	0.0433406i
$259$	−24.1244	+	1.73205i	−1.49901	+	0.107624i
$260$	−0.464102	+	1.39230i	−0.0287824	+	0.0863471i
$261$		−	29.7846i		−	1.84362i
$262$	9.46410	−	2.53590i	0.584694	−	0.156668i
$263$	3.33013	−	12.4282i	0.205344	−	0.766356i	−0.784000	−	0.620761i	$-0.786824\pi$
$263$	3.33013	−	12.4282i	0.205344	−	0.766356i	0.989344	−	0.145595i	$-0.0465096\pi$
$264$	−4.73205	−	4.73205i	−0.291238	−	0.291238i
$265$	−2.26795	+	0.464102i	−0.139319	+	0.0285095i
$266$	−1.00000	+	0.0717968i	−0.0613139	+	0.00440214i
$267$	1.85641			0.113610
$268$	4.26795	+	4.26795i	0.260706	+	0.260706i
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	−0.726450	−	0.687220i	$-0.758831\pi$
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	0.958374	+	0.285514i	$0.0921644\pi$
$270$	4.50000	−	3.99038i	0.273861	−	0.242847i
$271$	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	$0.319682\pi$
$272$	4.92820	−	1.32051i	0.298816	−	0.0800676i
$273$	0.758330	−	1.56218i	0.0458962	−	0.0945473i
$274$	−0.633975	+	0.366025i	−0.0382998	+	0.0221124i
$275$	3.92820	+	9.19615i	0.236880	+	0.554549i
$276$	18.2942	+	4.90192i	1.10118	+	0.295061i
$277$	−3.00000	−	0.803848i	−0.180253	−	0.0482985i	0.167564	−	0.985861i	$-0.446410\pi$
$277$	−3.00000	−	0.803848i	−0.180253	−	0.0482985i	−0.347816	+	0.937563i	$0.613077\pi$
$278$	−9.29423	−	2.49038i	−0.557431	−	0.149363i
$279$	−14.1962	+	8.19615i	−0.849901	+	0.490691i
$280$	−9.96410	−	5.59808i	−0.595469	−	0.334549i
$281$	−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	$0.888156\pi$
$282$	2.30385	−	3.99038i	0.137192	−	0.237624i
$283$	11.3660	−	11.3660i	0.675640	−	0.675640i	−0.283370	−	0.959011i	$-0.591453\pi$
$283$	11.3660	−	11.3660i	0.675640	−	0.675640i	0.959011	+	0.283370i	$0.0914526\pi$
$284$			2.19615i			0.130318i
$285$	−2.83013	−	0.169873i	−0.167642	−	0.0100624i
$286$	0.339746	+	0.196152i	0.0200896	+	0.0115987i
$287$	−5.19615	+	6.00000i	−0.306719	+	0.354169i
$288$	14.8923	+	3.99038i	0.877537	+	0.235135i
$289$	−11.0096	+	6.35641i	−0.647625	+	0.373906i
$290$	11.2583	−	2.30385i	0.661112	−	0.135287i
$291$	4.22243	−	15.7583i	0.247523	−	0.923770i
$292$	22.3923	−	6.00000i	1.31041	−	0.351123i
$293$	12.1962	+	3.26795i	0.712507	+	0.190916i	0.596826	−	0.802371i	$-0.296428\pi$
$293$	12.1962	+	3.26795i	0.712507	+	0.190916i	0.115681	+	0.993286i	$0.463095\pi$
$294$	5.02628	+	3.75833i	0.293139	+	0.219190i
$295$	20.3660	+	1.22243i	1.18576	+	0.0711727i
$296$	8.83013	+	15.2942i	0.513241	+	0.888959i
$297$	5.19615	+	9.00000i	0.301511	+	0.522233i
$298$	−4.26795	+	1.14359i	−0.247236	+	0.0662466i
$299$	−2.39230			−0.138351
$300$	−12.0000	−	9.00000i	−0.692820	−	0.519615i
$301$	−1.96410	+	1.33013i	−0.113209	+	0.0766672i
$302$	0.169873	+	0.0455173i	0.00977509	+	0.00261923i
$303$		−	0.464102i		−	0.0266619i
$304$	−0.901924	−	1.56218i	−0.0517289	−	0.0895970i
$305$	1.46410	−	24.3923i	0.0838342	−	1.39670i
$306$	3.21539			0.183812
$307$	−3.63397	−	3.63397i	−0.207402	−	0.207402i	0.595760	−	0.803162i	$-0.296851\pi$
$307$	−3.63397	−	3.63397i	−0.207402	−	0.207402i	−0.803162	+	0.595760i	$0.796851\pi$
$308$	6.00000	−	6.92820i	0.341882	−	0.394771i
$309$	10.9641	+	2.93782i	0.623726	+	0.167127i
$310$	−4.19615	−	4.73205i	−0.238325	−	0.268762i
$311$		−	17.1244i		−	0.971033i	−0.874227	−	0.485517i	$-0.838632\pi$
$311$		−	17.1244i		−	0.971033i	0.874227	−	0.485517i	$-0.161368\pi$
$312$	−1.26795			−0.0717835
$313$	22.3923	−	22.3923i	1.26569	−	1.26569i	0.317394	−	0.948294i	$-0.397192\pi$
$313$	22.3923	−	22.3923i	1.26569	−	1.26569i	0.948294	−	0.317394i	$-0.102808\pi$
$314$	−2.33975			−0.132040
$315$	12.6962	+	12.4019i	0.715347	+	0.698769i
$316$	−19.8564			−1.11701
$317$	1.53590	−	1.53590i	0.0862646	−	0.0862646i	−0.662658	−	0.748922i	$-0.730572\pi$
$317$	1.53590	−	1.53590i	0.0862646	−	0.0862646i	0.748922	+	0.662658i	$0.230572\pi$
$318$	−0.464102	−	0.803848i	−0.0260255	−	0.0450775i
$319$			19.8564i			1.11175i
$320$	0.303848	−	5.06218i	0.0169856	−	0.282984i
$321$	−11.4904	+	11.4904i	−0.641331	+	0.641331i
$322$	1.63397	−	8.49038i	0.0910578	−	0.473150i
$323$	−1.07180	−	1.07180i	−0.0596364	−	0.0596364i
$324$	−13.5000	−	7.79423i	−0.750000	−	0.433013i
$325$	1.75833	+	0.705771i	0.0975346	+	0.0391492i
$326$	6.29423	+	10.9019i	0.348605	+	0.603802i
$327$	−14.5981	+	8.42820i	−0.807275	+	0.466081i
$328$	5.59808	+	1.50000i	0.309102	+	0.0828236i
$329$	12.2321	+	5.93782i	0.674375	+	0.327363i
$330$	−3.00000	+	2.66025i	−0.165145	+	0.146442i
$331$	−6.00000			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$332$	−17.2583	+	4.62436i	−0.947174	+	0.253794i
$333$	−7.09808	−	26.4904i	−0.388972	−	1.45166i
$334$	−1.63397	−	2.83013i	−0.0894071	−	0.154858i
$335$	5.83013	−	5.16987i	0.318534	−	0.282460i
$336$	−2.13397	+	11.0885i	−0.116418	+	0.604925i
$337$	21.0263	+	5.63397i	1.14537	+	0.306902i	0.781110	−	0.624393i	$-0.214654\pi$
$337$	21.0263	+	5.63397i	1.14537	+	0.306902i	0.364264	+	0.931296i	$0.381320\pi$
$338$	−6.42820	+	1.72243i	−0.349648	+	0.0936879i
$339$	−12.0000	−	12.0000i	−0.651751	−	0.651751i
$340$	−1.60770	−	7.85641i	−0.0871895	−	0.426073i
$341$	9.46410	−	5.46410i	0.512510	−	0.295898i
$342$	−0.294229	−	1.09808i	−0.0159101	−	0.0593772i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	1.50000	+	0.866025i	0.0808746	+	0.0466930i
$345$	7.73205	−	23.1962i	0.416280	−	1.24884i
$346$			11.7128i			0.629685i
$347$	8.36603	−	8.36603i	0.449112	−	0.449112i	−0.445947	−	0.895059i	$-0.647133\pi$
$347$	8.36603	−	8.36603i	0.449112	−	0.449112i	0.895059	+	0.445947i	$0.147133\pi$
$348$	−14.8923	−	25.7942i	−0.798311	−	1.38272i
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	−3.70577	+	5.75833i	−0.198082	+	0.307796i
$351$	1.90192	+	0.509619i	0.101517	+	0.0272014i
$352$	−9.92820	−	2.66025i	−0.529175	−	0.141792i
$353$	7.56218	+	2.02628i	0.402494	+	0.107848i	0.454386	−	0.890805i	$-0.349859\pi$
$353$	7.56218	+	2.02628i	0.402494	+	0.107848i	−0.0518922	+	0.998653i	$0.516525\pi$
$354$	2.11731	+	7.90192i	0.112534	+	0.419983i
$355$	2.83013	+	0.169873i	0.150208	+	0.00901592i
$356$	1.60770	−	0.928203i	0.0852077	−	0.0491947i
$357$	0.679492	+	9.46410i	0.0359625	+	0.500893i
$358$	−2.36603	+	0.633975i	−0.125048	+	0.0335066i
$359$	2.53590	−	1.46410i	0.133840	−	0.0772723i	−0.431585	−	0.902072i	$-0.642046\pi$
$359$	2.53590	−	1.46410i	0.133840	−	0.0772723i	0.565425	+	0.824800i	$0.308712\pi$
$360$	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
$363$	6.06218	+	10.5000i	0.318182	+	0.551107i
$364$	−0.124356	−	1.73205i	−0.00651801	−	0.0907841i
$365$	−6.00000	−	29.3205i	−0.314054	−	1.53471i
$366$	9.46410	−	2.53590i	0.494697	−	0.132554i
$367$	3.33013	−	12.4282i	0.173831	−	0.648747i	−0.822917	−	0.568162i	$-0.807655\pi$
$367$	3.33013	−	12.4282i	0.173831	−	0.648747i	0.996748	−	0.0805847i	$-0.0256787\pi$
$368$	15.0263	−	4.02628i	0.783299	−	0.209884i
$369$	−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
$372$	−8.19615	+	14.1962i	−0.424951	+	0.736036i
$373$	17.0263	−	4.56218i	0.881587	−	0.236221i	0.210495	−	0.977595i	$-0.432492\pi$
$373$	17.0263	−	4.56218i	0.881587	−	0.236221i	0.671092	+	0.741374i	$0.265826\pi$
$374$	−2.14359			−0.110843
$375$	−12.5263	+	14.7679i	−0.646854	+	0.762614i
$376$		−	9.92820i		−	0.512008i
$377$	2.66025	+	2.66025i	0.137010	+	0.137010i
$378$	−3.10770	+	6.40192i	−0.159843	+	0.329279i
$379$		−	27.5167i		−	1.41344i	−0.707495	−	0.706718i	$-0.750175\pi$
$379$		−	27.5167i		−	1.41344i	0.707495	−	0.706718i	$-0.249825\pi$
$380$	−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
$383$	5.40192	+	20.1603i	0.276025	+	1.03014i	0.955151	+	0.296119i	$0.0956925\pi$
$383$	5.40192	+	20.1603i	0.276025	+	1.03014i	−0.679126	+	0.734022i	$0.737641\pi$
$384$	19.1603	−	5.13397i	0.977768	−	0.261992i
$385$	−8.46410	−	8.26795i	−0.431371	−	0.421374i
$386$	−7.46410			−0.379913
$387$	−1.90192	−	1.90192i	−0.0966802	−	0.0966802i
$388$	−4.22243	−	15.7583i	−0.214362	−	0.800008i
$389$	−25.1603	+	14.5263i	−1.27568	+	0.736512i	−0.976050	−	0.217545i	$-0.930195\pi$
$389$	−25.1603	+	14.5263i	−1.27568	+	0.736512i	−0.299625	+	0.954057i	$0.596862\pi$
$390$	−0.0455173	+	0.758330i	−0.00230486	+	0.0383995i
$391$	11.3205	−	6.53590i	0.572503	−	0.330535i
$392$	13.4282	+	1.59808i	0.678227	+	0.0807150i
$393$	−28.3923	+	16.3923i	−1.43220	+	0.826882i
$394$		−	2.92820i		−	0.147521i
$395$	−1.53590	+	25.5885i	−0.0772794	+	1.28750i
$396$	9.00000	+	5.19615i	0.452267	+	0.261116i
$397$	−5.32051	+	19.8564i	−0.267029	+	0.996564i	0.693968	+	0.720006i	$0.255861\pi$
$397$	−5.32051	+	19.8564i	−0.267029	+	0.996564i	−0.960997	+	0.276559i	$0.910806\pi$
$398$	2.19615	+	8.19615i	0.110083	+	0.410836i
$399$	3.16987	−	1.09808i	0.158692	−	0.0549726i
$400$	−12.2321	−	1.47372i	−0.611603	−	0.0736860i
$401$	−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	$0.258478\pi$
$402$	2.70577	+	1.56218i	0.134952	+	0.0779143i
$403$	0.535898	−	2.00000i	0.0266950	−	0.0996271i
$404$	−0.232051	−	0.401924i	−0.0115450	−	0.0199965i
$405$	−11.0885	+	16.7942i	−0.550990	+	0.834512i
$406$	−11.2583	+	7.62436i	−0.558742	+	0.378390i
$407$	4.73205	+	17.6603i	0.234559	+	0.875386i
$408$	6.00000	−	3.46410i	0.297044	−	0.171499i
$409$	12.3205			0.609210			0.304605	−	0.952479i	$-0.401476\pi$
$409$	12.3205			0.609210			0.304605	+	0.952479i	$0.401476\pi$
$410$	1.09808	−	3.29423i	0.0542301	−	0.162690i
$411$	1.73205	−	1.73205i	0.0854358	−	0.0854358i
$412$	10.9641	−	2.93782i	0.540163	−	0.144736i
$413$	−22.8109	+	7.90192i	−1.12245	+	0.388828i
$414$	9.80385			0.481833
$415$	4.62436	+	22.5981i	0.227001	+	1.10930i
$416$	−1.68653	+	0.973721i	−0.0826891	+	0.0477406i
$417$	32.1962			1.57665
$418$	0.196152	+	0.732051i	0.00959413	+	0.0358058i
$419$	−9.83013	−	17.0263i	−0.480233	−	0.831788i	0.519510	−	0.854465i	$-0.326115\pi$
$419$	−9.83013	−	17.0263i	−0.480233	−	0.831788i	−0.999743	+	0.0226764i	$0.992781\pi$
$420$	17.1962	+	4.39230i	0.839086	+	0.214323i
$421$	−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	$0.287414\pi$
$422$	−13.4641	−	3.60770i	−0.655422	−	0.175620i
$423$	−3.99038	+	14.8923i	−0.194019	+	0.724089i
$424$	−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
$427$	9.46410	+	27.3205i	0.458000	+	1.32213i
$428$	−4.20577	+	15.6962i	−0.203294	+	0.758702i
$429$	−1.26795	−	0.339746i	−0.0612172	−	0.0164031i
$430$	0.571797	−	0.866025i	0.0275745	−	0.0417635i
$431$	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	$0.0845866\pi$
$432$	−12.8038			−0.616025
$433$	24.1244	−	24.1244i	1.15934	−	1.15934i	0.174725	−	0.984617i	$-0.444096\pi$
$433$	24.1244	−	24.1244i	1.15934	−	1.15934i	0.984617	−	0.174725i	$-0.0559037\pi$
$434$	6.73205	+	3.26795i	0.323149	+	0.156867i
$435$	−34.3923	+	17.1962i	−1.64898	+	0.824492i
$436$	−8.42820	+	14.5981i	−0.403638	+	0.699121i
$437$	−3.26795	−	3.26795i	−0.156327	−	0.156327i
$438$	10.3923	−	6.00000i	0.496564	−	0.286691i
$439$	−8.14359			−0.388673			−0.194336	−	0.980935i	$-0.562255\pi$
$439$	−8.14359			−0.388673			−0.194336	+	0.980935i	$0.562255\pi$
$440$	−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	0.909095	−	0.416590i	$-0.136775\pi$
$443$	10.3660	+	10.3660i	0.492505	+	0.492505i	−0.416590	+	0.909095i	$0.636775\pi$
$444$	−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
$447$	12.8038	−	7.39230i	0.605601	−	0.349644i
$448$	1.96410	+	5.66987i	0.0927951	+	0.267876i
$449$			24.6603i			1.16379i	0.813264	+	0.581895i	$0.197688\pi$
$449$			24.6603i			1.16379i	−0.813264	+	0.581895i	$0.802312\pi$
$450$	−7.20577	−	2.89230i	−0.339683	−	0.136345i
$451$	5.19615	+	3.00000i	0.244677	+	0.141264i
$452$	−16.3923	−	4.39230i	−0.771029	−	0.206597i
$453$	−0.588457			−0.0276481
$454$	−6.43782	−	11.1506i	−0.302142	−	0.523325i
$455$	−2.24167	+	0.0262794i	−0.105091	+	0.00123200i
$456$	−1.73205	−	1.73205i	−0.0811107	−	0.0811107i
$457$	15.0526	−	15.0526i	0.704129	−	0.704129i	−0.261165	−	0.965294i	$-0.584107\pi$
$457$	15.0526	−	15.0526i	0.704129	−	0.704129i	0.965294	+	0.261165i	$0.0841067\pi$
$458$	3.03590	+	11.3301i	0.141858	+	0.529422i
$459$	−10.3923	+	2.78461i	−0.485071	+	0.129974i
$460$	−4.90192	−	23.9545i	−0.228553	−	1.11688i
$461$	−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	$0.892567\pi$
$462$	2.07180	−	4.26795i	0.0963887	−	0.198563i
$463$	−5.66987	+	21.1603i	−0.263501	+	0.983400i	0.699660	+	0.714476i	$0.253335\pi$
$463$	−5.66987	+	21.1603i	−0.263501	+	0.983400i	−0.963161	+	0.268924i	$0.913332\pi$
$464$	−21.1865	−	12.2321i	−0.983560	−	0.567859i
$465$	17.6603	+	11.6603i	0.818975	+	0.540731i
$466$	−5.53590	−	9.58846i	−0.256446	−	0.444177i
$467$	−2.50000	+	9.33013i	−0.115686	+	0.431747i	−0.999337	−	0.0363992i	$-0.988411\pi$
$467$	−2.50000	+	9.33013i	−0.115686	+	0.431747i	0.883651	+	0.468146i	$0.155078\pi$
$468$	1.90192	−	0.509619i	0.0879165	−	0.0235571i
$469$	−4.02628	+	8.29423i	−0.185916	+	0.382992i
$470$	−5.93782	−	0.356406i	−0.273891	−	0.0164398i
$471$	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
$475$	1.43782	+	3.36603i	0.0659718	+	0.154444i
$476$	5.32051	+	7.85641i	0.243865	+	0.360098i
$477$	2.19615	+	2.19615i	0.100555	+	0.100555i
$478$	−0.267949	+	1.00000i	−0.0122557	+	0.0457389i
$479$	10.3660	+	17.9545i	0.473636	+	0.820361i	0.999544	−	0.0301798i	$-0.00960798\pi$
$479$	10.3660	+	17.9545i	0.473636	+	0.820361i	−0.525909	+	0.850541i	$0.676275\pi$
$480$	−3.99038	−	19.5000i	−0.182135	−	0.890049i
$481$	3.00000	+	1.73205i	0.136788	+	0.0789747i
$482$	−2.08142	+	7.76795i	−0.0948059	+	0.353820i
$483$	2.07180	+	28.8564i	0.0942700	+	1.31301i
$484$	10.5000	+	6.06218i	0.477273	+	0.275554i
$485$	−20.6340	+	4.22243i	−0.936941	+	0.191731i
$486$	−7.79423	−	2.08846i	−0.353553	−	0.0947343i
$487$	−7.24167	−	27.0263i	−0.328151	−	1.22468i	−0.911106	−	0.412173i	$-0.864770\pi$
$487$	−7.24167	−	27.0263i	−0.328151	−	1.22468i	0.582954	−	0.812505i	$-0.301897\pi$
$488$	14.9282	−	14.9282i	0.675768	−	0.675768i
$489$	−29.7846	−	29.7846i	−1.34691	−	1.34691i
$490$	1.43782	−	7.97372i	0.0649542	−	0.360216i
$491$	−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	$0.940107\pi$
$492$	−9.00000			−0.405751
$493$	−19.8564	−	5.32051i	−0.894288	−	0.239624i
$494$	0.124356	+	0.0717968i	0.00559503	+	0.00323029i
$495$	7.39230	−	11.1962i	0.332259	−	0.503230i
$496$			13.4641i			0.604556i
$497$	−3.16987	+	1.09808i	−0.142188	+	0.0492554i
$498$	−8.00962	+	4.62436i	−0.358920	+	0.207222i
$499$	33.2487	+	19.1962i	1.48842	+	0.859338i	0.999913	−	0.0132238i	$-0.00420938\pi$
$499$	33.2487	+	19.1962i	1.48842	+	0.859338i	0.488504	+	0.872562i	$0.337543\pi$
$500$	−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	$-0.723536\pi$
$503$	2.63397	−	2.63397i	0.117443	−	0.117443i	0.763386	+	0.645943i	$0.223536\pi$
$504$	1.09808	+	15.2942i	0.0489122	+	0.681259i
$505$	−0.535898	+	0.267949i	−0.0238472	+	0.0119236i
$506$	−6.53590			−0.290556
$507$	19.2846	−	11.1340i	0.856460	−	0.494477i
$508$	19.6865	+	19.6865i	0.873449	+	0.873449i
$509$	−16.4545	+	28.5000i	−0.729332	+	1.26324i	0.227834	+	0.973700i	$0.426836\pi$
$509$	−16.4545	+	28.5000i	−0.729332	+	1.26324i	−0.957166	+	0.289540i	$0.906498\pi$
$510$	−1.85641	−	3.71281i	−0.0822031	−	0.164406i
$511$	19.8564	+	29.3205i	0.878396	+	1.29706i
$512$	15.6865	−	15.6865i	0.693253	−	0.693253i
$513$	1.90192	+	3.29423i	0.0839720	+	0.145444i
$514$	−3.73205	+	6.46410i	−0.164614	+	0.285119i
$515$	−2.93782	−	14.3564i	−0.129456	−	0.632619i
$516$	−2.59808	−	0.696152i	−0.114374	−	0.0306464i
$517$	2.66025	−	9.92820i	0.116998	−	0.436642i
$518$	−8.19615	+	9.46410i	−0.360118	+	0.415829i
$519$	−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
$523$	2.76795	+	0.741670i	0.121034	+	0.0324310i	0.318828	−	0.947813i	$-0.396711\pi$
$523$	2.76795	+	0.741670i	0.121034	+	0.0324310i	−0.197794	+	0.980244i	$0.563378\pi$
$524$	−16.3923	+	28.3923i	−0.716101	+	1.24032i
$525$	6.99038	−	21.8205i	0.305085	−	0.952325i
$526$	−3.33013	−	5.76795i	−0.145200	−	0.251495i
$527$	2.92820	+	10.9282i	0.127555	+	0.476040i
$528$	8.53590			0.371477
$529$	14.5981	−	8.42820i	0.634699	−	0.366444i
$530$	−0.660254	+	1.00000i	−0.0286796	+	0.0434372i
$531$	−13.6865	−	23.7058i	−0.593945	−	1.02874i
$532$	2.19615	−	2.53590i	0.0952153	−	0.109945i
$533$	1.09808	−	0.294229i	0.0475630	−	0.0127445i
$534$	0.679492	−	0.679492i	0.0294045	−	0.0294045i
$535$	19.9019	+	6.63397i	0.860435	+	0.286812i
$536$	6.73205			0.290780
$537$	7.09808	−	4.09808i	0.306305	−	0.176845i
$538$	−1.01924	−	3.80385i	−0.0439425	−	0.163996i
$539$	13.0000	+	5.19615i	0.559950	+	0.223814i
$540$	−1.20577	+	20.0885i	−0.0518881	+	0.864470i
$541$	−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	$0.880917\pi$
$542$	0.189111	−	0.705771i	0.00812301	−	0.0303155i
$543$	6.18653	+	3.57180i	0.265490	+	0.153280i
$544$	5.32051	−	9.21539i	0.228115	−	0.395107i
$545$	18.1603	+	11.9904i	0.777900	+	0.513611i
$546$	−0.294229	−	0.849365i	−0.0125918	−	0.0363495i
$547$	4.17949	+	15.5981i	0.178702	+	0.666926i	0.995891	+	0.0905561i	$0.0288644\pi$
$547$	4.17949	+	15.5981i	0.178702	+	0.666926i	−0.817189	+	0.576370i	$0.804469\pi$
$548$	0.633975	−	2.36603i	0.0270821	−	0.101072i
$549$	−28.3923	+	16.3923i	−1.21175	+	0.699607i
$550$	4.80385	+	1.92820i	0.204837	+	0.0822189i
$551$			7.26795i			0.309625i
$552$	18.2942	−	10.5622i	0.778654	−	0.449556i
$553$	−9.92820	−	28.6603i	−0.422190	−	1.21876i
$554$	−1.39230	+	0.803848i	−0.0591534	+	0.0341522i
$555$	−26.4904	+	23.4904i	−1.12445	+	0.997111i
$556$	27.8827	−	16.0981i	1.18249	−	0.682711i
$557$	6.67949	+	24.9282i	0.283019	+	1.05624i	0.950275	+	0.311413i	$0.100802\pi$
$557$	6.67949	+	24.9282i	0.283019	+	1.05624i	−0.667256	+	0.744829i	$0.732531\pi$
$558$	−2.19615	+	8.19615i	−0.0929705	+	0.346971i
$559$	0.339746			0.0143697
$560$	14.0359	−	3.93782i	0.593125	−	0.166403i
$561$	6.92820	−	1.85641i	0.292509	−	0.0783775i
$562$	3.44744	+	12.8660i	0.145422	+	0.542721i
$563$	−3.00000	+	3.00000i	−0.126435	+	0.126435i	−0.767493	−	0.641058i	$-0.778496\pi$
$563$	−3.00000	+	3.00000i	−0.126435	+	0.126435i	0.641058	+	0.767493i	$0.278496\pi$
$564$	3.99038	+	14.8923i	0.168025	+	0.627079i
$565$	−6.92820	+	20.7846i	−0.291472	+	0.874415i
$566$		−	8.32051i		−	0.349737i
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$	1.73205	+	1.73205i	0.0726752	+	0.0726752i
$569$		−	2.92820i		−	0.122757i	−0.998115	−	0.0613783i	$-0.980450\pi$
$569$		−	2.92820i		−	0.122757i	0.998115	−	0.0613783i	$-0.0195496\pi$
$570$	−1.09808	+	0.973721i	−0.0459934	+	0.0407847i
$571$	−4.19615			−0.175604			−0.0878018	−	0.996138i	$-0.527984\pi$
$571$	−4.19615			−0.175604			−0.0878018	+	0.996138i	$0.527984\pi$
$572$	−1.26795	+	0.339746i	−0.0530156	+	0.0142055i
$573$	17.4904	−	30.2942i	0.730671	−	1.26556i
$574$	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
$577$	19.1962	−	5.14359i	0.799146	−	0.214131i	0.163937	−	0.986471i	$-0.447581\pi$
$577$	19.1962	−	5.14359i	0.799146	−	0.214131i	0.635209	+	0.772340i	$0.280914\pi$
$578$	−1.70319	+	6.35641i	−0.0708435	+	0.264392i
$579$	24.1244	−	6.46410i	1.00257	−	0.268639i
$580$	−21.1865	+	32.0885i	−0.879723	+	1.33240i
$581$	−15.3038	−	22.5981i	−0.634911	−	0.937526i
$582$	−4.22243	−	7.31347i	−0.175025	−	0.303153i
$583$	−1.46410	−	1.46410i	−0.0606369	−	0.0606369i
$584$	12.9282	−	22.3923i	0.534973	−	0.926600i
$585$	−0.509619	−	2.49038i	−0.0210702	−	0.102965i
$586$	5.66025	−	3.26795i	0.233823	−	0.134998i
$587$	32.9904	−	8.83975i	1.36166	−	0.364855i	0.497234	−	0.867617i	$-0.334349\pi$
$587$	32.9904	−	8.83975i	1.36166	−	0.364855i	0.864425	+	0.502761i	$0.167683\pi$
$588$	−20.7846	+	3.00000i	−0.857143	+	0.123718i
$589$	3.46410	−	2.00000i	0.142736	−	0.0824086i
$590$	7.90192	−	7.00704i	0.325317	−	0.288475i
$591$	2.53590	+	9.46410i	0.104313	+	0.389301i
$592$	−21.7583	−	5.83013i	−0.894262	−	0.239617i
$593$	−14.7583	−	3.95448i	−0.606052	−	0.162391i	−0.0572729	−	0.998359i	$-0.518241\pi$
$593$	−14.7583	−	3.95448i	−0.606052	−	0.162391i	−0.548779	+	0.835967i	$0.684907\pi$
$594$	5.19615	+	1.39230i	0.213201	+	0.0571270i
$595$	10.5359	−	6.24871i	0.431930	−	0.256172i
$596$	7.39230	−	12.8038i	0.302801	−	0.524466i
$597$	−14.1962	−	24.5885i	−0.581010	−	1.00634i
$598$	−0.875644	+	0.875644i	−0.0358078	+	0.0358078i
$599$		−	45.8564i		−	1.87364i	−0.349809	−	0.936821i	$-0.613754\pi$
$599$		−	45.8564i		−	1.87364i	0.349809	−	0.936821i	$-0.386246\pi$
$600$	−16.5622	+	2.36603i	−0.676148	+	0.0965926i
$601$	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	$0.626677\pi$
$602$	−0.232051	+	1.20577i	−0.00945768	+	0.0491436i
$603$	−10.0981	−	2.70577i	−0.411225	−	0.110188i
$604$	−0.509619	+	0.294229i	−0.0207361	+	0.0119720i
$605$	8.62436	−	13.0622i	0.350630	−	0.531053i
$606$	−0.169873	−	0.169873i	−0.00690062	−	0.00690062i
$607$	−24.9904	+	6.69615i	−1.01433	+	0.271788i	−0.727437	−	0.686175i	$-0.759289\pi$
$607$	−24.9904	+	6.69615i	−1.01433	+	0.271788i	−0.286891	+	0.957963i	$0.592622\pi$
$608$	−3.63397	−	0.973721i	−0.147377	−	0.0394896i
$609$	29.7846	−	34.3923i	1.20693	−	1.39365i
$610$	−8.39230	−	9.46410i	−0.339794	−	0.383190i
$611$	−0.973721	−	1.68653i	−0.0393925	−	0.0682298i
$612$	−7.60770	+	7.60770i	−0.307523	+	0.307523i
$613$	0.901924	−	0.241670i	0.0364284	−	0.00976095i	−0.240559	−	0.970635i	$-0.577331\pi$
$613$	0.901924	−	0.241670i	0.0364284	−	0.00976095i	0.276987	+	0.960874i	$0.410664\pi$
$614$	−2.66025			−0.107359
$615$	−0.696152	+	11.5981i	−0.0280716	+	0.467680i
$616$	−0.732051	−	10.1962i	−0.0294952	−	0.410815i
$617$	31.3205	+	8.39230i	1.26092	+	0.337861i	0.826544	−	0.562872i	$-0.190304\pi$
$617$	31.3205	+	8.39230i	1.26092	+	0.337861i	0.434372	+	0.900734i	$0.356970\pi$
$618$	5.08846	−	2.93782i	0.204688	−	0.118177i
$619$	−0.392305	−	0.679492i	−0.0157681	−	0.0273111i	0.858034	−	0.513593i	$-0.171686\pi$
$619$	−0.392305	−	0.679492i	−0.0157681	−	0.0273111i	−0.873802	+	0.486282i	$0.838353\pi$
$620$	21.1244	+	1.26795i	0.848375	+	0.0509221i
$621$	−31.6865	+	8.49038i	−1.27154	+	0.340707i
$622$	−6.26795	−	6.26795i	−0.251322	−	0.251322i
$623$	2.14359	+	1.85641i	0.0858813	+	0.0743754i
$624$	1.14359	−	1.14359i	0.0457804	−	0.0457804i
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$		−	16.3923i		−	0.655168i
$627$	−1.26795	−	2.19615i	−0.0506370	−	0.0877059i
$628$	5.53590	−	5.53590i	0.220906	−	0.220906i
$629$	−18.9282			−0.754717
$630$	9.18653	−	0.107695i	0.366000	−	0.00429068i
$631$	−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
$633$	46.6410			1.85381
$634$		−	1.12436i		−	0.0446539i
$635$	26.8923	−	23.8468i	1.06719	−	0.946331i
$636$	3.00000	+	0.803848i	0.118958	+	0.0318746i
$637$	2.43782	−	1.04552i	0.0965900	−	0.0414249i
$638$	7.26795	+	7.26795i	0.287741	+	0.287741i
$639$	−1.90192	−	3.29423i	−0.0752389	−	0.130318i
$640$	−16.9904	−	19.1603i	−0.671604	−	0.757376i
$641$	−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	$0.946381\pi$
$642$			8.41154i			0.331977i
$643$	−24.8205	−	6.65064i	−0.978825	−	0.262275i	−0.266275	−	0.963897i	$-0.585793\pi$
$643$	−24.8205	−	6.65064i	−0.978825	−	0.262275i	−0.712550	+	0.701622i	$0.752460\pi$
$644$	16.2224	+	23.9545i	0.639253	+	0.943939i
$645$	−1.09808	+	3.29423i	−0.0432367	+	0.129710i
$646$	−0.784610			−0.0308701
$647$	−12.5981	+	3.37564i	−0.495281	+	0.132710i	−0.497809	−	0.867287i	$-0.665862\pi$
$647$	−12.5981	+	3.37564i	−0.495281	+	0.132710i	0.00252779	+	0.999997i	$0.499195\pi$
$648$	−16.7942	+	4.50000i	−0.659740	+	0.176777i
$649$	9.12436	+	15.8038i	0.358162	+	0.620355i
$650$	0.901924	−	0.385263i	0.0353764	−	0.0151113i
$651$	−24.5885	−	4.73205i	−0.963698	−	0.185464i
$652$	−40.6865	−	10.9019i	−1.59341	−	0.426952i
$653$	−20.1244	+	5.39230i	−0.787527	+	0.211017i	−0.630101	−	0.776514i	$-0.716986\pi$
$653$	−20.1244	+	5.39230i	−0.787527	+	0.211017i	−0.157426	+	0.987531i	$0.550320\pi$
$654$	−2.25833	+	8.42820i	−0.0883077	+	0.329569i
$655$	35.3205	+	23.3205i	1.38009	+	0.911208i
$656$	−6.40192	+	3.69615i	−0.249953	+	0.144311i
$657$	−28.3923	+	28.3923i	−1.10769	+	1.10769i
$658$	6.65064	−	2.30385i	0.259269	−	0.0898133i
$659$	19.3468	+	11.1699i	0.753644	+	0.435116i	0.827009	−	0.562189i	$-0.190041\pi$
$659$	19.3468	+	11.1699i	0.753644	+	0.435116i	−0.0733652	+	0.997305i	$0.523374\pi$
$660$	0.803848	−	13.3923i	0.0312897	−	0.521295i
$661$		−	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
$663$	0.679492	−	1.17691i	0.0263893	−	0.0457076i
$664$	−9.96410	+	17.2583i	−0.386682	+	0.669753i
$665$	−3.09808	−	3.02628i	−0.120138	−	0.117354i
$666$	−12.2942	−	7.09808i	−0.476392	−	0.275045i
$667$	−60.5429	−	16.2224i	−2.34423	−	0.628135i
$668$	10.5622	+	2.83013i	0.408663	+	0.109501i
$669$	−8.59808	−	2.30385i	−0.332421	−	0.0890719i
$670$	0.241670	−	4.02628i	0.00933652	−	0.155549i
$671$	18.9282	−	10.9282i	0.730715	−	0.421879i
$672$	13.2058	+	19.5000i	0.509424	+	0.752229i
$673$	5.36603	−	1.43782i	0.206845	−	0.0554240i	−0.153909	−	0.988085i	$-0.549186\pi$
$673$	5.36603	−	1.43782i	0.206845	−	0.0554240i	0.360754	+	0.932661i	$0.382519\pi$
$674$	9.75833	−	5.63397i	0.375877	−	0.217013i
$675$	25.7942	+	3.10770i	0.992820	+	0.119615i
$676$	11.1340	−	19.2846i	0.428230	−	0.741716i
$677$	10.5167	+	10.5167i	0.404188	+	0.404188i	0.879706	−	0.475518i	$-0.157739\pi$
$677$	10.5167	+	10.5167i	0.404188	+	0.404188i	−0.475518	+	0.879706i	$0.657739\pi$
$678$	−8.78461			−0.337371
$679$	20.6340	−	13.9737i	0.791859	−	0.536262i
$680$	−7.46410	−	4.92820i	−0.286235	−	0.188988i
$681$	30.4641	+	30.4641i	1.16739	+	1.16739i
$682$	1.46410	−	5.46410i	0.0560633	−	0.209231i
$683$	−42.9186	+	11.5000i	−1.64223	+	0.440035i	−0.957424	−	0.288686i	$-0.906782\pi$
$683$	−42.9186	+	11.5000i	−1.64223	+	0.440035i	−0.684810	+	0.728721i	$0.740115\pi$
$684$	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
$687$	−19.6244	−	33.9904i	−0.748716	−	1.29681i
$688$	−2.13397	+	0.571797i	−0.0813570	+	0.0217995i
$689$	−0.392305			−0.0149456
$690$	−5.66025	−	11.3205i	−0.215482	−	0.430964i
$691$			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
$693$	−3.00000	+	15.5885i	−0.113961	+	0.592157i
$694$		−	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
$698$	−1.33975	−	5.00000i	−0.0507101	−	0.189253i
$699$	26.1962	+	26.1962i	0.990829	+	0.990829i
$700$	−4.85641	−	22.3923i	−0.183555	−	0.846350i
$701$	11.0526			0.417449			0.208725	−	0.977974i	$-0.433069\pi$
$701$	11.0526			0.417449			0.208725	+	0.977974i	$0.433069\pi$
$702$	0.882686	−	0.509619i	0.0333148	−	0.0192343i
$703$	1.73205	+	6.46410i	0.0653255	+	0.243798i
$704$	3.92820	−	2.26795i	0.148050	−	0.0854766i
$705$	19.5000	−	3.99038i	0.734412	−	0.150286i
$706$	3.50962	−	2.02628i	0.132086	−	0.0762600i
$707$	0.464102	−	0.535898i	0.0174543	−	0.0201545i
$708$	−23.7058	−	13.6865i	−0.890917	−	0.514371i
$709$		−	40.6410i		−	1.52631i	−0.646218	−	0.763153i	$-0.723650\pi$
$709$		−	40.6410i		−	1.52631i	0.646218	−	0.763153i	$-0.276350\pi$
$710$	1.09808	−	0.973721i	0.0412101	−	0.0365431i
$711$	29.7846	−	17.1962i	1.11701	−	0.644906i
$712$	0.535898	−	2.00000i	0.0200836	−	0.0749532i
$713$	8.92820	+	33.3205i	0.334364	+	1.24786i
$714$	3.71281	+	3.21539i	0.138949	+	0.120333i
$715$	0.339746	+	1.66025i	0.0127058	+	0.0620900i
$716$	4.09808	−	7.09808i	0.153152	−	0.265268i
$717$		−	3.46410i		−	0.129369i
$718$	0.392305	−	1.46410i	0.0146407	−	0.0546398i
$719$	11.4641	+	19.8564i	0.427539	+	0.740519i	0.996654	−	0.0817390i	$-0.0260474\pi$
$719$	11.4641	+	19.8564i	0.427539	+	0.740519i	−0.569115	+	0.822258i	$0.692714\pi$
$720$	7.39230	+	14.7846i	0.275495	+	0.550990i
$721$	9.72243	+	14.3564i	0.362082	+	0.534661i
$722$	−2.47372	−	9.23205i	−0.0920623	−	0.343581i
$723$		−	26.9090i		−	1.00076i
$724$	7.14359			0.265490
$725$	39.7128	+	29.7846i	1.47490	+	1.10617i
$726$	6.06218	+	1.62436i	0.224989	+	0.0602855i
$727$	−25.2224	+	6.75833i	−0.935448	+	0.250653i	−0.694176	−	0.719805i	$-0.744231\pi$
$727$	−25.2224	+	6.75833i	−0.935448	+	0.250653i	−0.241272	+	0.970458i	$0.577565\pi$
$728$	−1.46410	−	1.26795i	−0.0542632	−	0.0469933i
$729$	27.0000			1.00000
$730$	−12.9282	−	8.53590i	−0.478494	−	0.315928i
$731$	−1.60770	+	0.928203i	−0.0594628	+	0.0343308i
$732$	−16.3923	+	28.3923i	−0.605877	+	1.04941i
$733$	−1.58142	−	5.90192i	−0.0584109	−	0.217993i	0.930551	−	0.366162i	$-0.119328\pi$
$733$	−1.58142	−	5.90192i	−0.0584109	−	0.217993i	−0.988962	+	0.148170i	$0.952662\pi$
$734$	−3.33013	−	5.76795i	−0.122917	−	0.212899i
$735$	2.25833	+	27.0167i	0.0832998	+	0.996525i
$736$	16.2224	−	28.0981i	0.597967	−	1.03571i
$737$	6.73205	+	1.80385i	0.247978	+	0.0664456i
$738$	−4.50000	+	1.20577i	−0.165647	+	0.0443851i
$739$	−0.679492	−	0.392305i	−0.0249955	−	0.0144312i	0.487450	−	0.873151i	$-0.337927\pi$
$739$	−0.679492	−	0.392305i	−0.0249955	−	0.0144312i	−0.512446	+	0.858720i	$0.671260\pi$
$740$	−11.1962	+	33.5885i	−0.411579	+	1.23474i
$741$	−0.464102	−	0.124356i	−0.0170492	−	0.00456832i
$742$	0.267949	−	1.39230i	0.00983672	−	0.0511131i
$743$	9.35641	−	34.9186i	0.343253	−	1.28104i	−0.551386	−	0.834250i	$-0.685901\pi$
$743$	9.35641	−	34.9186i	0.343253	−	1.28104i	0.894640	−	0.446789i	$-0.147432\pi$
$744$	4.73205	+	17.6603i	0.173485	+	0.647456i
$745$	−15.9282	−	10.5167i	−0.583564	−	0.385301i
$746$	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
$750$	0.820508	+	9.99038i	0.0299607	+	0.364797i
$751$	−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
$753$	−20.4904	−	11.8301i	−0.746711	−	0.431114i
$754$	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	−0.918505	−	0.395408i	$-0.870603\pi$
$757$	−14.3923	+	14.3923i	−0.523097	+	0.523097i	0.395408	+	0.918505i	$0.370603\pi$
$758$	−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	$0.719971\pi$
$762$	12.4808	+	7.20577i	0.452130	+	0.261038i
$763$	−25.2846	−	4.86603i	−0.915364	−	0.176162i
$764$		−	34.9808i		−	1.26556i
$765$	9.21539	+	10.3923i	0.333183	+	0.375735i
$766$	9.35641	+	5.40192i	0.338061	+	0.195179i
$767$	3.33975	+	0.894882i	0.120591	+	0.0323123i
$768$	1.20577	−	2.08846i	0.0435095	−	0.0753607i
$769$	−12.5981	−	21.8205i	−0.454298	−	0.786868i	0.544349	−	0.838859i	$-0.316777\pi$
$769$	−12.5981	−	21.8205i	−0.454298	−	0.786868i	−0.998648	+	0.0519910i	$0.983443\pi$
$770$	−6.12436	+	0.0717968i	−0.220706	+	0.00258738i
$771$	6.46410	−	24.1244i	0.232799	−	0.868817i
$772$	17.6603	−	17.6603i	0.635606	−	0.635606i
$773$	−4.58142	−	17.0981i	−0.164782	−	0.614975i	−0.998068	−	0.0621327i	$-0.980210\pi$
$773$	−4.58142	−	17.0981i	−0.164782	−	0.614975i	0.833286	−	0.552842i	$-0.186457\pi$
$774$	−1.39230			−0.0500454
$775$	3.26795	−	27.1244i	0.117388	−	0.974336i
$776$	−15.7583	−	9.09808i	−0.565691	−	0.326602i
$777$	18.2942	−	37.6865i	0.656302	−	1.35200i
$778$	−3.89230	+	14.5263i	−0.139546	+	0.520792i
$779$	1.90192	+	1.09808i	0.0681435	+	0.0393427i
$780$	−1.68653	−	1.90192i	−0.0603876	−	0.0680998i
$781$	1.26795	+	2.19615i	0.0453708	+	0.0785845i
$782$	1.75129	−	6.53590i	0.0626260	−	0.233723i
$783$	44.6769	+	25.7942i	1.59662	+	0.921811i
$784$	−13.5526	+	10.6699i	−0.484020	+	0.381067i
$785$	−6.70577	−	7.56218i	−0.239339	−	0.269906i
$786$	−4.39230	+	16.3923i	−0.156668	+	0.584694i
$787$	−29.1699	−	29.1699i	−1.03979	−	1.03979i	−0.999175	−	0.0406190i	$-0.987067\pi$
$787$	−29.1699	−	29.1699i	−1.03979	−	1.03979i	−0.0406190	−	0.999175i	$-0.512933\pi$
$788$	6.92820	+	6.92820i	0.246807	+	0.246807i
$789$	15.7583	+	15.7583i	0.561011	+	0.561011i
$790$	8.80385	+	9.92820i	0.313227	+	0.353230i
$791$	−1.85641	−	25.8564i	−0.0660062	−	0.919348i
$792$	11.1962	−	3.00000i	0.397838	−	0.106600i
$793$	1.07180	−	4.00000i	0.0380606	−	0.142044i
$794$	5.32051	+	9.21539i	0.188818	+	0.327042i
$795$	1.26795	−	3.80385i	0.0449695	−	0.134909i
$796$	−24.5885	−	14.1962i	−0.871515	−	0.503169i
$797$	−9.34679	+	34.8827i	−0.331080	+	1.23561i	0.576976	+	0.816761i	$0.304232\pi$
$797$	−9.34679	+	34.8827i	−0.331080	+	1.23561i	−0.908057	+	0.418847i	$0.862434\pi$
$798$	0.758330	−	1.56218i	0.0268446	−	0.0553005i
$799$	9.21539	+	5.32051i	0.326017	+	0.188226i
$800$	−20.2128	+	15.8660i	−0.714631	+	0.560949i
$801$	−1.60770	+	2.78461i	−0.0568051	+	0.0983893i
$802$	1.52628	+	5.69615i	0.0538948	+	0.201138i
$803$	18.9282	−	18.9282i	0.667962	−	0.667962i
$804$	−10.0981	+	2.70577i	−0.356132	+	0.0954252i
$805$	32.1244	−	19.0526i	1.13223	−	0.671514i
$806$	−0.535898	−	0.928203i	−0.0188762	−	0.0326946i
$807$	6.58846	+	11.4115i	0.231925	+	0.401705i
$808$	−0.500000	−	0.133975i	−0.0175899	−	0.00471321i
$809$	38.3827	+	22.1603i	1.34946	+	0.779113i	0.988173	−	0.153340i	$-0.0490031\pi$
$809$	38.3827	+	22.1603i	1.34946	+	0.779113i	0.361290	+	0.932454i	$0.382336\pi$
$810$	2.08846	+	10.2058i	0.0733809	+	0.358594i
$811$		−	6.58846i		−	0.231352i	−0.993287	−	0.115676i	$-0.963097\pi$
$811$		−	6.58846i		−	0.231352i	0.993287	−	0.115676i	$-0.0369034\pi$
$812$	8.59808	−	44.6769i	0.301733	−	1.56785i
$813$			2.44486i			0.0857451i
$814$	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	$0.241505\pi$
$822$		−	1.26795i		−	0.0442248i
$823$	7.43782	+	7.43782i	0.259266	+	0.259266i	0.824756	−	0.565489i	$-0.191313\pi$
$823$	7.43782	+	7.43782i	0.259266	+	0.259266i	−0.565489	+	0.824756i	$0.691313\pi$
$824$	6.33013	−	10.9641i	0.220520	−	0.381953i
$825$	−17.1962	−	2.07180i	−0.598693	−	0.0721307i
$826$	−5.45706	+	11.2417i	−0.189875	+	0.391148i
$827$	14.1699	−	14.1699i	0.492735	−	0.492735i	−0.416432	−	0.909167i	$-0.636720\pi$
$827$	14.1699	−	14.1699i	0.492735	−	0.492735i	0.909167	+	0.416432i	$0.136720\pi$
$828$	−23.1962	+	23.1962i	−0.806122	+	0.806122i
$829$	−22.1603	+	38.3827i	−0.769657	+	1.33309i	0.168091	+	0.985771i	$0.446240\pi$
$829$	−22.1603	+	38.3827i	−0.769657	+	1.33309i	−0.937749	+	0.347314i	$0.887094\pi$
$830$	9.96410	+	6.57884i	0.345859	+	0.228355i
$831$	3.80385	−	3.80385i	0.131954	−	0.131954i
$832$	0.222432	−	0.830127i	0.00771144	−	0.0287795i
$833$	−8.67949	+	11.6077i	−0.300727	+	0.402183i
$834$	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
$837$		−	28.3923i		−	0.981382i
$838$	−9.83013	−	2.63397i	−0.339576	−	0.0909891i
$839$	22.6147	−	39.1699i	0.780747	−	1.35229i	−0.150759	−	0.988570i	$-0.548172\pi$
$839$	22.6147	−	39.1699i	0.780747	−	1.35229i	0.931507	−	0.363724i	$-0.118495\pi$
$840$	17.0263	−	10.0981i	0.587462	−	0.348417i
$841$	34.7846	+	60.2487i	1.19947	+	2.07754i
$842$	2.03590	+	7.59808i	0.0701617	+	0.261847i
$843$	−22.2846	−	38.5981i	−0.767523	−	1.32939i
$844$	40.3923	−	23.3205i	1.39036	−	0.802725i
$845$	−23.9904	−	15.8397i	−0.825294	−	0.544904i
$846$	3.99038	+	6.91154i	0.137192	+	0.237624i
$847$	−3.50000	+	18.1865i	−0.120261	+	0.624897i
$848$	2.46410	−	0.660254i	0.0846176	−	0.0226732i
$849$	7.20577	+	26.8923i	0.247301	+	0.922942i
$850$	−3.21539	+	4.28719i	−0.110287	+	0.147049i
$851$	−57.7128			−1.97837
$852$	−3.29423	−	1.90192i	−0.112858	−	0.0651588i
$853$	6.46410	+	24.1244i	0.221327	+	0.826002i	0.983843	+	0.179033i	$0.0572970\pi$
$853$	6.46410	+	24.1244i	0.221327	+	0.826002i	−0.762516	+	0.646969i	$0.776036\pi$
$854$	13.4641	+	6.53590i	0.460732	+	0.223654i
$855$	2.70577	−	4.09808i	0.0925354	−	0.140151i
$856$	9.06218	+	15.6962i	0.309739	+	0.536483i
$857$	−3.26795	+	12.1962i	−0.111631	+	0.416613i	−0.999013	−	0.0444226i	$-0.985855\pi$
$857$	−3.26795	+	12.1962i	−0.111631	+	0.416613i	0.887382	+	0.461035i	$0.152522\pi$
$858$	−0.588457	+	0.339746i	−0.0200896	+	0.0115987i
$859$	−13.8301	+	23.9545i	−0.471878	+	0.817316i	−0.999482	−	0.0321738i	$-0.989757\pi$
$859$	−13.8301	+	23.9545i	−0.471878	+	0.817316i	0.527604	+	0.849490i	$0.323090\pi$
$860$	0.696152	+	3.40192i	0.0237386	+	0.116005i
$861$	−4.50000	−	12.9904i	−0.153360	−	0.442711i
$862$	−1.41858	−	5.29423i	−0.0483172	−	0.180322i
$863$	12.6147	−	47.0788i	0.429411	−	1.60258i	−0.324688	−	0.945821i	$-0.605259\pi$
$863$	12.6147	−	47.0788i	0.429411	−	1.60258i	0.754099	−	0.656761i	$-0.228074\pi$
$864$	−18.8827	+	18.8827i	−0.642402	+	0.642402i
$865$	−37.8564	+	33.5692i	−1.28716	+	1.14139i
$866$		−	17.6603i		−	0.600120i
$867$		−	22.0192i		−	0.747813i
$868$	−23.6603	+	8.19615i	−0.803081	+	0.278196i
$869$	−19.8564	+	11.4641i	−0.673582	+	0.388893i
$870$	−6.29423	+	18.8827i	−0.213394	+	0.640183i
$871$	1.14359	−	0.660254i	0.0387492	−	0.0223719i
$872$	4.86603	+	18.1603i	0.164784	+	0.614984i
$873$	19.9808	+	19.9808i	0.676246	+	0.676246i
$874$	−2.39230			−0.0809209
$875$	−29.2321	+	4.52628i	−0.988224	+	0.153016i
$876$	−10.3923	+	38.7846i	−0.351123	+	1.31041i
$877$	0.437822	+	1.63397i	0.0147842	+	0.0551754i	0.972924	−	0.231126i	$-0.0742409\pi$
$877$	0.437822	+	1.63397i	0.0147842	+	0.0551754i	−0.958140	+	0.286301i	$0.907574\pi$
$878$	−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	$0.771600\pi$
$882$	−9.99038	+	4.28461i	−0.336394	+	0.144270i
$883$	31.5622	+	31.5622i	1.06215	+	1.06215i	0.997936	+	0.0642158i	$0.0204546\pi$
$883$	31.5622	+	31.5622i	1.06215	+	1.06215i	0.0642158	+	0.997936i	$0.479545\pi$
$884$		−	1.35898i		−	0.0457076i
$885$	−19.4711	+	29.4904i	−0.654515	+	0.991308i
$886$	7.58846			0.254939
$887$	−26.6244	+	7.13397i	−0.893958	+	0.239535i	−0.676420	−	0.736516i	$-0.736469\pi$
$887$	−26.6244	+	7.13397i	−0.893958	+	0.239535i	−0.217539	+	0.976052i	$0.569803\pi$
$888$	−30.5885			−1.02648
$889$	−18.5718	+	38.2583i	−0.622878	+	1.28314i
$890$	−1.17691	−	0.392305i	−0.0394503	−	0.0131501i
$891$	−18.0000			−0.603023
$892$	−8.59808	+	2.30385i	−0.287885	+	0.0771385i
$893$	0.973721	−	3.63397i	0.0325843	−	0.121606i
$894$	1.98076	−	7.39230i	0.0662466	−	0.247236i
$895$	−8.83013	−	5.83013i	−0.295159	−	0.194880i
$896$	27.2583	+	13.2321i	0.910637	+	0.442052i
$897$	2.07180	−	3.58846i	0.0691753	−	0.119815i
$898$	9.02628	+	9.02628i	0.301211	+	0.301211i
$899$	27.1244	−	46.9808i	0.904648	−	1.56690i
$900$	23.8923	−	10.2058i	0.796410	−	0.340192i
$901$	1.85641	−	1.07180i	0.0618459	−	0.0357067i
$902$	3.00000	−	0.803848i	0.0998891	−	0.0267652i
$903$	−0.294229	−	4.09808i	−0.00979132	−	0.136375i
$904$	−16.3923	+	9.46410i	−0.545200	+	0.314771i
$905$	0.552559	−	9.20577i	0.0183677	−	0.306010i
$906$	−0.215390	+	0.215390i	−0.00715586	+	0.00715586i
$907$	−10.4282	−	2.79423i	−0.346263	−	0.0927808i	0.0814962	−	0.996674i	$-0.474030\pi$
$907$	−10.4282	−	2.79423i	−0.346263	−	0.0927808i	−0.427759	+	0.903893i	$0.640697\pi$
$908$	41.6147	+	11.1506i	1.38103	+	0.370047i
$909$	0.696152	+	0.401924i	0.0230899	+	0.0133310i
$910$	−0.810889	+	0.830127i	−0.0268807	+	0.0275184i
$911$	−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	$0.191645\pi$
$912$	3.12436			0.103458
$913$	−14.5885	+	14.5885i	−0.482807	+	0.482807i
$914$		−	11.0192i		−	0.364484i
$915$	35.3205	+	23.3205i	1.16766	+	0.770952i
$916$	−33.9904	−	19.6244i	−1.12307	−	0.648407i
$917$	−49.1769	−	9.46410i	−1.62396	−	0.312532i
$918$	−2.78461	+	4.82309i	−0.0919058	+	0.159186i
$919$	10.9019	−	6.29423i	0.359621	−	0.207627i	−0.309293	−	0.950967i	$-0.600092\pi$
$919$	10.9019	−	6.29423i	0.359621	−	0.207627i	0.668915	+	0.743339i	$0.266759\pi$
$920$	−22.7583	−	15.0263i	−0.750320	−	0.495402i
$921$	8.59808	−	2.30385i	0.283316	−	0.0759144i
$922$	−13.9904	+	3.74871i	−0.460749	+	0.123457i
$923$	0.464102	+	0.124356i	0.0152761	+	0.00409322i
$924$	5.19615	+	15.0000i	0.170941	+	0.493464i
$925$	42.4186	+	17.0263i	1.39471	+	0.559821i
$926$	5.66987	+	9.82051i	0.186324	+	0.322722i
$927$	−13.9019	+	13.9019i	−0.456599	+	0.456599i
$928$	−49.2846	+	13.2058i	−1.61785	+	0.433501i
$929$	−9.78461			−0.321023			−0.160511	−	0.987034i	$-0.551314\pi$
$929$	−9.78461			−0.321023			−0.160511	+	0.987034i	$0.551314\pi$
$930$	10.7321	−	2.19615i	0.351918	−	0.0720147i
$931$	4.75833	+	1.90192i	0.155948	+	0.0623330i
$932$	35.7846	+	9.58846i	1.17216	+	0.314080i
$933$	25.6865	+	14.8301i	0.840939	+	0.485517i
$934$	2.50000	+	4.33013i	0.0818025	+	0.141686i
$935$	−6.14359	−	6.92820i	−0.200917	−	0.226576i
$936$	1.09808	−	1.90192i	0.0358917	−	0.0621663i
$937$	12.4641	+	12.4641i	0.407184	+	0.407184i	0.880756	−	0.473571i	$-0.157035\pi$
$937$	12.4641	+	12.4641i	0.407184	+	0.407184i	−0.473571	+	0.880756i	$0.657035\pi$
$938$	1.56218	+	4.50962i	0.0510069	+	0.147244i
$939$	14.1962	+	52.9808i	0.463274	+	1.72896i
$940$	14.8923	−	13.2058i	0.485733	−	0.430725i
$941$		−	31.0526i		−	1.01228i	−0.862450	−	0.506142i	$-0.831071\pi$
$941$		−	31.0526i		−	1.01228i	0.862450	−	0.506142i	$-0.168929\pi$
$942$	2.02628	−	3.50962i	0.0660198	−	0.114350i
$943$	−13.3923	+	13.3923i	−0.436113	+	0.436113i
$944$	−22.4833			−0.731770
$945$	−29.5981	+	8.30385i	−0.962825	+	0.270124i
$946$	0.928203			0.0301785
$947$	5.00000	−	5.00000i	0.162478	−	0.162478i	−0.621185	−	0.783664i	$-0.713349\pi$
$947$	5.00000	−	5.00000i	0.162478	−	0.162478i	0.783664	+	0.621185i	$0.213349\pi$
$948$	17.1962	−	29.7846i	0.558505	−	0.967359i
$949$		−	5.07180i		−	0.164637i
$950$	1.75833	+	0.705771i	0.0570478	+	0.0228982i
$951$	0.973721	+	3.63397i	0.0315751	+	0.117840i
$952$	10.3923	+	2.00000i	0.336817	+	0.0648204i
$953$	−16.0526	−	16.0526i	−0.519993	−	0.519993i	0.397576	−	0.917569i	$-0.369852\pi$
$953$	−16.0526	−	16.0526i	−0.519993	−	0.519993i	−0.917569	+	0.397576i	$0.869852\pi$
$954$	1.60770			0.0520511
$955$	−45.0788	−	2.70577i	−1.45872	−	0.0875567i
$956$	−1.73205	−	3.00000i	−0.0560185	−	0.0970269i
$957$	−29.7846	−	17.1962i	−0.962800	−	0.555873i
$958$	10.3660	+	2.77757i	0.334911	+	0.0897392i
$959$	3.73205	−	0.267949i	0.120514	−	0.00865253i
$960$	7.33013	+	4.83975i	0.236579	+	0.156202i
$961$	1.14359			0.0368901
$962$	1.73205	−	0.464102i	0.0558436	−	0.0149632i
$963$	−7.28461	−	27.1865i	−0.234743	−	0.876074i
$964$	−13.4545	−	23.3038i	−0.433340	−	0.750566i
$965$	−21.3923	−	24.1244i	−0.688643	−	0.776590i
$966$	11.3205	+	9.80385i	0.364231	+	0.315434i
$967$	−22.6865	−	6.07884i	−0.729550	−	0.195482i	−0.125121	−	0.992141i	$-0.539932\pi$
$967$	−22.6865	−	6.07884i	−0.729550	−	0.195482i	−0.604429	+	0.796659i	$0.706599\pi$
$968$	13.0622	−	3.50000i	0.419834	−	0.112494i
$969$	2.53590	−	0.679492i	0.0814648	−	0.0218284i
$970$	−6.00704	+	9.09808i	−0.192874	+	0.292122i
$971$	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	$0.236156\pi$
$972$	23.3827	−	13.5000i	0.750000	−	0.433013i
$973$	37.1769	+	32.1962i	1.19184	+	1.03216i
$974$	−12.5429	−	7.24167i	−0.401902	−	0.232038i
$975$	−2.58142	+	2.02628i	−0.0826715	+	0.0648929i
$976$			26.9282i			0.861951i
$977$	−17.8038	+	17.8038i	−0.569596	+	0.569596i	−0.932015	−	0.362420i	$-0.881951\pi$
$977$	−17.8038	+	17.8038i	−0.569596	+	0.569596i	0.362420	+	0.932015i	$0.381951\pi$
$978$	−21.8038			−0.697210
$979$	1.07180	−	1.85641i	0.0342548	−	0.0593310i
$980$	15.4641	+	22.2679i	0.493983	+	0.711324i
$981$		−	29.1962i		−	0.932161i
$982$	−7.29423	−	1.95448i	−0.232768	−	0.0623700i
$983$	−54.6769	−	14.6506i	−1.74392	−	0.467283i	−0.760610	−	0.649209i	$-0.775100\pi$
$983$	−54.6769	−	14.6506i	−1.74392	−	0.467283i	−0.983312	+	0.181926i	$0.941767\pi$
$984$	−7.09808	+	7.09808i	−0.226278	+	0.226278i
$985$	9.46410	−	8.39230i	0.301551	−	0.267401i
$986$	−9.21539	+	5.32051i	−0.293478	+	0.169439i
$987$	−19.5000	+	13.2058i	−0.620692	+	0.420344i
$988$	−0.464102	+	0.124356i	−0.0147650	+	0.00395628i
$989$	−4.90192	+	2.83013i	−0.155872	+	0.0899928i
$990$	−1.39230	−	6.80385i	−0.0442504	−	0.216240i
$991$	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
$993$	5.19615	−	9.00000i	0.164895	−	0.285606i
$994$	−0.758330	+	1.56218i	−0.0240528	+	0.0495493i
$995$	−20.1962	+	30.5885i	−0.640261	+	0.969719i
$996$	8.00962	−	29.8923i	0.253794	−	0.947174i
$997$	9.07884	−	33.8827i	0.287530	−	1.07308i	−0.659441	−	0.751756i	$-0.729207\pi$
$997$	9.07884	−	33.8827i	0.287530	−	1.07308i	0.946971	−	0.321319i	$-0.104126\pi$
$998$	19.1962	−	5.14359i	0.607644	−	0.162818i
$999$	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.a.178.1	✓	4
3.2	odd	2		945.2.bv.b.73.1		4
5.2	odd	4		315.2.bs.d.52.1	yes	4
7.5	odd	6		315.2.cg.b.313.1	yes	4
9.4	even	3		315.2.cg.d.283.1	yes	4
9.5	odd	6		945.2.cj.b.388.1		4
15.2	even	4		945.2.bv.c.262.1		4
21.5	even	6		945.2.cj.c.208.1		4
35.12	even	12		315.2.cg.d.187.1	yes	4
45.22	odd	12		315.2.cg.b.157.1	yes	4
45.32	even	12		945.2.cj.c.577.1		4
63.5	even	6		945.2.bv.c.523.1		4
63.40	odd	6		315.2.bs.d.103.1	yes	4
105.47	odd	12		945.2.cj.b.397.1		4
315.257	odd	12		945.2.bv.b.712.1		4
315.292	even	12	inner	315.2.bs.a.292.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.a.178.1	✓	4	1.1	even	1	trivial
315.2.bs.a.292.1	yes	4	315.292	even	12	inner
315.2.bs.d.52.1	yes	4	5.2	odd	4
315.2.bs.d.103.1	yes	4	63.40	odd	6
315.2.cg.b.157.1	yes	4	45.22	odd	12
315.2.cg.b.313.1	yes	4	7.5	odd	6
315.2.cg.d.187.1	yes	4	35.12	even	12
315.2.cg.d.283.1	yes	4	9.4	even	3
945.2.bv.b.73.1		4	3.2	odd	2
945.2.bv.b.712.1		4	315.257	odd	12
945.2.bv.c.262.1		4	15.2	even	4
945.2.bv.c.523.1		4	63.5	even	6
945.2.cj.b.388.1		4	9.5	odd	6
945.2.cj.b.397.1		4	105.47	odd	12
945.2.cj.c.208.1		4	21.5	even	6
945.2.cj.c.577.1		4	45.32	even	12

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)

\(f(q)\)	\(=\)	\(q+(0.366025 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +1.73205i q^{4} +(2.23205 + 0.133975i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +1.73205i q^{4} +(2.23205 + 0.133975i) q^{5} +(0.232051 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.866025 - 0.767949i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-2.59808 - 1.50000i) q^{12} +(0.366025 + 0.0980762i) q^{13} +(-0.598076 + 1.23205i) q^{14} +(-2.13397 + 3.23205i) q^{15} -2.46410 q^{16} +(-2.00000 + 0.535898i) q^{17} +(-1.50000 - 0.401924i) q^{18} +(0.366025 + 0.633975i) q^{19} +(-0.232051 + 3.86603i) q^{20} +(0.866025 - 4.50000i) q^{21} +(1.00000 + 0.267949i) q^{22} +(-6.09808 + 1.63397i) q^{23} +(-3.23205 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(0.169873 - 0.0980762i) q^{26} +5.19615 q^{27} +(-1.50000 - 4.33013i) q^{28} +(8.59808 + 4.96410i) q^{29} +(0.401924 + 1.96410i) q^{30} -5.46410i q^{31} +(-3.63397 + 3.63397i) q^{32} -3.46410 q^{33} +(-0.535898 + 0.928203i) q^{34} +(-5.69615 + 1.59808i) q^{35} +(4.50000 - 2.59808i) q^{36} +(8.83013 + 2.36603i) q^{37} +(0.366025 + 0.0980762i) q^{38} +(-0.464102 + 0.464102i) q^{39} +(2.86603 + 3.23205i) q^{40} +(2.59808 - 1.50000i) q^{41} +(-1.33013 - 1.96410i) q^{42} +(0.866025 - 0.232051i) 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} +(2.13397 - 3.69615i) q^{48} +(5.50000 - 4.33013i) q^{49} +(2.03590 - 1.59808i) q^{50} +(0.928203 - 3.46410i) q^{51} +(-0.169873 + 0.633975i) q^{52} +(-1.00000 + 0.267949i) q^{53} +(1.90192 - 1.90192i) q^{54} +(2.00000 + 4.00000i) q^{55} +(-4.59808 - 2.23205i) q^{56} -1.26795 q^{57} +(4.96410 - 1.33013i) q^{58} +9.12436 q^{59} +(-5.59808 - 3.69615i) q^{60} -10.9282i q^{61} +(-2.00000 - 2.00000i) q^{62} +(6.00000 + 5.19615i) q^{63} -2.26795i q^{64} +(0.803848 + 0.267949i) q^{65} +(-1.26795 + 1.26795i) q^{66} +(2.46410 - 2.46410i) q^{67} +(-0.928203 - 3.46410i) q^{68} +(2.83013 - 10.5622i) q^{69} +(-1.50000 + 2.66987i) q^{70} +1.26795 q^{71} +(1.50000 - 5.59808i) q^{72} +(-3.46410 - 12.9282i) q^{73} +(4.09808 - 2.36603i) q^{74} +(-5.19615 + 6.92820i) q^{75} +(-1.09808 + 0.633975i) q^{76} +(-4.00000 - 3.46410i) q^{77} +0.339746i q^{78} +11.4641i q^{79} +(-5.50000 - 0.330127i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(0.401924 - 1.50000i) q^{82} +(2.66987 + 9.96410i) q^{83} +(7.79423 + 1.50000i) q^{84} +(-4.53590 + 0.928203i) q^{85} +(0.232051 - 0.401924i) q^{86} +(-14.8923 + 8.59808i) q^{87} +(-1.00000 + 3.73205i) q^{88} +(-0.535898 - 0.928203i) q^{89} +(-3.29423 - 1.09808i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(-2.83013 - 10.5622i) q^{92} +(8.19615 + 4.73205i) q^{93} -2.66025 q^{94} +(0.732051 + 1.46410i) q^{95} +(-2.30385 - 8.59808i) q^{96} +(-9.09808 + 2.43782i) q^{97} +(0.428203 - 3.59808i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9} + 4 q^{11} - 2 q^{13} + 8 q^{14} - 12 q^{15} + 4 q^{16} - 8 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{22} - 14 q^{23} - 6 q^{24} + 6 q^{25} + 18 q^{26} - 6 q^{28} + 24 q^{29} + 12 q^{30} - 18 q^{32} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 2 q^{38} + 12 q^{39} + 8 q^{40} + 12 q^{42} - 12 q^{44} - 12 q^{45} - 10 q^{46} - 18 q^{47} + 12 q^{48} + 22 q^{49} + 22 q^{50} - 24 q^{51} - 18 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 8 q^{56} - 12 q^{57} + 6 q^{58} - 12 q^{59} - 12 q^{60} - 8 q^{62} + 24 q^{63} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 24 q^{68} - 6 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{72} + 6 q^{74} + 6 q^{76} - 16 q^{77} - 22 q^{80} - 18 q^{81} + 12 q^{82} + 28 q^{83} - 32 q^{85} - 6 q^{86} - 18 q^{87} - 4 q^{88} - 16 q^{89} + 18 q^{90} - 4 q^{91} + 6 q^{92} + 12 q^{93} + 24 q^{94} - 4 q^{95} - 30 q^{96} - 26 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9 + 4 * q^11 - 2 * q^13 + 8 * q^14 - 12 * q^15 + 4 * q^16 - 8 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^22 - 14 * q^23 - 6 * q^24 + 6 * q^25 + 18 * q^26 - 6 * q^28 + 24 * q^29 + 12 * q^30 - 18 * q^32 - 16 * q^34 - 2 * q^35 + 18 * q^36 + 18 * q^37 - 2 * q^38 + 12 * q^39 + 8 * q^40 + 12 * q^42 - 12 * q^44 - 12 * q^45 - 10 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 + 22 * q^50 - 24 * q^51 - 18 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 8 * q^56 - 12 * q^57 + 6 * q^58 - 12 * q^59 - 12 * q^60 - 8 * q^62 + 24 * q^63 + 24 * q^65 - 12 * q^66 - 4 * q^67 + 24 * q^68 - 6 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^72 + 6 * q^74 + 6 * q^76 - 16 * q^77 - 22 * q^80 - 18 * q^81 + 12 * q^82 + 28 * q^83 - 32 * q^85 - 6 * q^86 - 18 * q^87 - 4 * q^88 - 16 * q^89 + 18 * q^90 - 4 * q^91 + 6 * q^92 + 12 * q^93 + 24 * q^94 - 4 * q^95 - 30 * q^96 - 26 * q^97 - 26 * q^98 + 12 * q^99

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