LMFDB - Embedded newform 315.2.bs.c.103.1

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			103.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.103
Dual form			315.2.bs.c.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 1.36603i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-0.133975 - 2.23205i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 1.36603i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-0.133975 - 2.23205i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +(3.23205 + 2.86603i) q^{10} +(2.73205 - 4.73205i) q^{11} +(1.50000 - 2.59808i) q^{12} +(1.00000 + 3.73205i) q^{13} +(-0.366025 + 5.09808i) q^{14} +(1.73205 - 3.46410i) q^{15} +4.46410 q^{16} +(-0.732051 + 2.73205i) q^{17} +(-5.59808 - 1.50000i) q^{18} +(1.63397 - 2.83013i) q^{19} +(-3.86603 + 0.232051i) q^{20} +(4.50000 - 0.866025i) q^{21} +(2.73205 + 10.1962i) q^{22} +(1.23205 - 4.59808i) q^{23} +(-0.232051 - 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(-6.46410 - 3.73205i) q^{26} +5.19615i q^{27} +(-3.00000 - 3.46410i) q^{28} +(-6.00000 + 3.46410i) q^{29} +(2.36603 + 7.09808i) q^{30} +0.196152i q^{31} +(-5.36603 + 5.36603i) q^{32} +(8.19615 - 4.73205i) q^{33} +(-2.73205 - 4.73205i) q^{34} +(-4.13397 - 4.23205i) q^{35} +(4.50000 - 2.59808i) q^{36} +(1.09808 + 4.09808i) q^{37} +(1.63397 + 6.09808i) q^{38} +(-1.73205 + 6.46410i) q^{39} +(-0.767949 + 0.866025i) q^{40} +(-2.19615 - 1.26795i) q^{41} +(-4.96410 + 7.33013i) q^{42} +(-0.401924 + 1.50000i) q^{43} +(-8.19615 - 4.73205i) q^{44} +(5.59808 - 3.69615i) q^{45} +(4.59808 + 7.96410i) q^{46} +(9.29423 + 9.29423i) q^{47} +(6.69615 + 3.86603i) q^{48} +(1.00000 - 6.92820i) q^{49} +(5.96410 - 7.59808i) q^{50} +(-3.46410 + 3.46410i) q^{51} +(6.46410 - 1.73205i) q^{52} +(-1.63397 + 6.09808i) q^{53} +(-7.09808 - 7.09808i) q^{54} +(-10.9282 - 5.46410i) q^{55} +(-1.36603 - 0.0980762i) q^{56} +(4.90192 - 2.83013i) q^{57} +(3.46410 - 12.9282i) q^{58} -3.46410 q^{59} +(-6.00000 - 3.00000i) q^{60} -11.3923i q^{61} +(-0.267949 - 0.267949i) q^{62} +(7.50000 + 2.59808i) q^{63} -5.73205i q^{64} +(8.19615 - 2.73205i) q^{65} +(-4.73205 + 17.6603i) q^{66} +(0.901924 - 0.901924i) q^{67} +(4.73205 + 1.26795i) q^{68} +(5.83013 - 5.83013i) q^{69} +(11.4282 + 0.133975i) q^{70} -6.00000 q^{71} +(0.401924 - 1.50000i) q^{72} +(-8.83013 - 2.36603i) q^{73} +(-7.09808 - 4.09808i) q^{74} +(-7.96410 - 3.40192i) q^{75} +(-4.90192 - 2.83013i) q^{76} +(-2.73205 - 14.1962i) q^{77} +(-6.46410 - 11.1962i) q^{78} +4.53590i q^{79} +(-0.598076 - 9.96410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.73205 - 1.26795i) q^{82} +(-1.36603 - 0.366025i) q^{83} +(-1.50000 - 7.79423i) q^{84} +(6.19615 + 1.26795i) q^{85} +(-1.50000 - 2.59808i) q^{86} -12.0000 q^{87} +(-2.73205 + 0.732051i) q^{88} +(4.59808 - 7.96410i) q^{89} +(-2.59808 + 12.6962i) q^{90} +(8.46410 + 5.73205i) q^{91} +(-7.96410 - 2.13397i) q^{92} +(-0.169873 + 0.294229i) q^{93} -25.3923 q^{94} +(-6.53590 - 3.26795i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(2.09808 - 7.83013i) q^{97} +(8.09808 + 10.8301i) q^{98} +16.3923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 2 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} + 6 q^{3} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 2 q^{8} + 6 q^{9} + 6 q^{10} + 4 q^{11} + 6 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{16} + 4 q^{17} - 12 q^{18} + 10 q^{19} - 12 q^{20} + 18 q^{21} + 4 q^{22} - 2 q^{23} + 6 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 24 q^{29} + 6 q^{30} - 18 q^{32} + 12 q^{33} - 4 q^{34} - 20 q^{35} + 18 q^{36} - 6 q^{37} + 10 q^{38} - 10 q^{40} + 12 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{44} + 12 q^{45} + 8 q^{46} + 6 q^{47} + 6 q^{48} + 4 q^{49} + 10 q^{50} + 12 q^{52} - 10 q^{53} - 18 q^{54} - 16 q^{55} - 2 q^{56} + 30 q^{57} - 24 q^{60} - 8 q^{62} + 30 q^{63} + 12 q^{65} - 12 q^{66} + 14 q^{67} + 12 q^{68} + 6 q^{69} + 18 q^{70} - 24 q^{71} + 12 q^{72} - 18 q^{73} - 18 q^{74} - 18 q^{75} - 30 q^{76} - 4 q^{77} - 12 q^{78} + 8 q^{80} - 18 q^{81} + 12 q^{82} - 2 q^{83} - 6 q^{84} + 4 q^{85} - 6 q^{86} - 48 q^{87} - 4 q^{88} + 8 q^{89} + 20 q^{91} - 18 q^{92} - 18 q^{93} - 60 q^{94} - 40 q^{95} - 30 q^{96} - 2 q^{97} + 22 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 2 * q^8 + 6 * q^9 + 6 * q^10 + 4 * q^11 + 6 * q^12 + 4 * q^13 + 2 * q^14 + 4 * q^16 + 4 * q^17 - 12 * q^18 + 10 * q^19 - 12 * q^20 + 18 * q^21 + 4 * q^22 - 2 * q^23 + 6 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 24 * q^29 + 6 * q^30 - 18 * q^32 + 12 * q^33 - 4 * q^34 - 20 * q^35 + 18 * q^36 - 6 * q^37 + 10 * q^38 - 10 * q^40 + 12 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^44 + 12 * q^45 + 8 * q^46 + 6 * q^47 + 6 * q^48 + 4 * q^49 + 10 * q^50 + 12 * q^52 - 10 * q^53 - 18 * q^54 - 16 * q^55 - 2 * q^56 + 30 * q^57 - 24 * q^60 - 8 * q^62 + 30 * q^63 + 12 * q^65 - 12 * q^66 + 14 * q^67 + 12 * q^68 + 6 * q^69 + 18 * q^70 - 24 * q^71 + 12 * q^72 - 18 * q^73 - 18 * q^74 - 18 * q^75 - 30 * q^76 - 4 * q^77 - 12 * q^78 + 8 * q^80 - 18 * q^81 + 12 * q^82 - 2 * q^83 - 6 * q^84 + 4 * q^85 - 6 * q^86 - 48 * q^87 - 4 * q^88 + 8 * q^89 + 20 * q^91 - 18 * q^92 - 18 * q^93 - 60 * q^94 - 40 * q^95 - 30 * q^96 - 2 * q^97 + 22 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.36603	+	1.36603i	−0.965926	+	0.965926i	−0.999438	−	0.0335125i	$-0.989331\pi$
$2$	−1.36603	+	1.36603i	−0.965926	+	0.965926i	0.0335125	+	0.999438i	$0.489331\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		−	1.73205i		−	0.866025i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$6$	−3.23205	+	0.866025i	−1.31948	+	0.353553i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	−0.366025	−	0.366025i	−0.129410	−	0.129410i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	3.23205	+	2.86603i	1.02206	+	0.906317i
$11$	2.73205	−	4.73205i	0.823744	−	1.42677i	−0.0791309	−	0.996864i	$-0.525215\pi$
$11$	2.73205	−	4.73205i	0.823744	−	1.42677i	0.902875	−	0.429903i	$-0.141452\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	1.00000	+	3.73205i	0.277350	+	1.03508i	0.954250	+	0.299010i	$0.0966563\pi$
$13$	1.00000	+	3.73205i	0.277350	+	1.03508i	−0.676900	+	0.736075i	$0.736677\pi$
$14$	−0.366025	+	5.09808i	−0.0978244	+	1.36252i
$15$	1.73205	−	3.46410i	0.447214	−	0.894427i
$16$	4.46410			1.11603
$17$	−0.732051	+	2.73205i	−0.177548	+	0.662620i	0.818555	+	0.574428i	$0.194775\pi$
$17$	−0.732051	+	2.73205i	−0.177548	+	0.662620i	−0.996104	+	0.0881917i	$0.971891\pi$
$18$	−5.59808	−	1.50000i	−1.31948	−	0.353553i
$19$	1.63397	−	2.83013i	0.374859	−	0.649276i	−0.615447	−	0.788179i	$-0.711024\pi$
$19$	1.63397	−	2.83013i	0.374859	−	0.649276i	0.990306	+	0.138903i	$0.0443576\pi$
$20$	−3.86603	+	0.232051i	−0.864470	+	0.0518881i
$21$	4.50000	−	0.866025i	0.981981	−	0.188982i
$22$	2.73205	+	10.1962i	0.582475	+	2.17383i
$23$	1.23205	−	4.59808i	0.256900	−	0.958765i	−0.710123	−	0.704078i	$-0.751361\pi$
$23$	1.23205	−	4.59808i	0.256900	−	0.958765i	0.967023	−	0.254688i	$-0.0819726\pi$
$24$	−0.232051	−	0.866025i	−0.0473672	−	0.176777i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−6.46410	−	3.73205i	−1.26771	−	0.731915i
$27$			5.19615i			1.00000i
$28$	−3.00000	−	3.46410i	−0.566947	−	0.654654i
$29$	−6.00000	+	3.46410i	−1.11417	+	0.643268i	−0.939907	−	0.341431i	$-0.889088\pi$
$29$	−6.00000	+	3.46410i	−1.11417	+	0.643268i	−0.174265	+	0.984699i	$0.555755\pi$
$30$	2.36603	+	7.09808i	0.431975	+	1.29593i
$31$			0.196152i			0.0352300i	0.999845	+	0.0176150i	$0.00560732\pi$
$31$			0.196152i			0.0352300i	−0.999845	+	0.0176150i	$0.994393\pi$
$32$	−5.36603	+	5.36603i	−0.948588	+	0.948588i
$33$	8.19615	−	4.73205i	1.42677	−	0.823744i
$34$	−2.73205	−	4.73205i	−0.468543	−	0.811540i
$35$	−4.13397	−	4.23205i	−0.698769	−	0.715347i
$36$	4.50000	−	2.59808i	0.750000	−	0.433013i
$37$	1.09808	+	4.09808i	0.180523	+	0.673720i	0.995545	+	0.0942898i	$0.0300580\pi$
$37$	1.09808	+	4.09808i	0.180523	+	0.673720i	−0.815022	+	0.579430i	$0.803275\pi$
$38$	1.63397	+	6.09808i	0.265066	+	0.989239i
$39$	−1.73205	+	6.46410i	−0.277350	+	1.03508i
$40$	−0.767949	+	0.866025i	−0.121423	+	0.136931i
$41$	−2.19615	−	1.26795i	−0.342981	−	0.198020i	0.318608	−	0.947886i	$-0.396785\pi$
$41$	−2.19615	−	1.26795i	−0.342981	−	0.198020i	−0.661590	+	0.749866i	$0.730118\pi$
$42$	−4.96410	+	7.33013i	−0.765978	+	1.13106i
$43$	−0.401924	+	1.50000i	−0.0612928	+	0.228748i	−0.989777	−	0.142624i	$-0.954446\pi$
$43$	−0.401924	+	1.50000i	−0.0612928	+	0.228748i	0.928484	+	0.371372i	$0.121113\pi$
$44$	−8.19615	−	4.73205i	−1.23562	−	0.713384i
$45$	5.59808	−	3.69615i	0.834512	−	0.550990i
$46$	4.59808	+	7.96410i	0.677949	+	1.17424i
$47$	9.29423	+	9.29423i	1.35570	+	1.35570i	0.879141	+	0.476561i	$0.158117\pi$
$47$	9.29423	+	9.29423i	1.35570	+	1.35570i	0.476561	+	0.879141i	$0.341883\pi$
$48$	6.69615	+	3.86603i	0.966506	+	0.558013i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	5.96410	−	7.59808i	0.843451	−	1.07453i
$51$	−3.46410	+	3.46410i	−0.485071	+	0.485071i
$52$	6.46410	−	1.73205i	0.896410	−	0.240192i
$53$	−1.63397	+	6.09808i	−0.224444	+	0.837635i	0.758183	+	0.652042i	$0.226087\pi$
$53$	−1.63397	+	6.09808i	−0.224444	+	0.837635i	−0.982627	+	0.185593i	$0.940579\pi$
$54$	−7.09808	−	7.09808i	−0.965926	−	0.965926i
$55$	−10.9282	−	5.46410i	−1.47356	−	0.736779i
$56$	−1.36603	−	0.0980762i	−0.182543	−	0.0131060i
$57$	4.90192	−	2.83013i	0.649276	−	0.374859i
$58$	3.46410	−	12.9282i	0.454859	−	1.69756i
$59$	−3.46410			−0.450988			−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410			−0.450988			−0.225494	+	0.974245i	$0.572400\pi$
$60$	−6.00000	−	3.00000i	−0.774597	−	0.387298i
$61$		−	11.3923i		−	1.45864i	−0.684175	−	0.729318i	$-0.739838\pi$
$61$		−	11.3923i		−	1.45864i	0.684175	−	0.729318i	$-0.260162\pi$
$62$	−0.267949	−	0.267949i	−0.0340296	−	0.0340296i
$63$	7.50000	+	2.59808i	0.944911	+	0.327327i
$64$		−	5.73205i		−	0.716506i
$65$	8.19615	−	2.73205i	1.01661	−	0.338869i
$66$	−4.73205	+	17.6603i	−0.582475	+	2.17383i
$67$	0.901924	−	0.901924i	0.110188	−	0.110188i	−0.649863	−	0.760051i	$-0.725174\pi$
$67$	0.901924	−	0.901924i	0.110188	−	0.110188i	0.760051	+	0.649863i	$0.225174\pi$
$68$	4.73205	+	1.26795i	0.573845	+	0.153761i
$69$	5.83013	−	5.83013i	0.701865	−	0.701865i
$70$	11.4282	+	0.133975i	1.36593	+	0.0160130i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	0.401924	−	1.50000i	0.0473672	−	0.176777i
$73$	−8.83013	−	2.36603i	−1.03349	−	0.276922i	−0.298076	−	0.954542i	$-0.596345\pi$
$73$	−8.83013	−	2.36603i	−1.03349	−	0.276922i	−0.735412	+	0.677620i	$0.763012\pi$
$74$	−7.09808	−	4.09808i	−0.825135	−	0.476392i
$75$	−7.96410	−	3.40192i	−0.919615	−	0.392820i
$76$	−4.90192	−	2.83013i	−0.562289	−	0.324638i
$77$	−2.73205	−	14.1962i	−0.311346	−	1.61780i
$78$	−6.46410	−	11.1962i	−0.731915	−	1.26771i
$79$			4.53590i			0.510328i	0.966898	+	0.255164i	$0.0821295\pi$
$79$			4.53590i			0.510328i	−0.966898	+	0.255164i	$0.917870\pi$
$80$	−0.598076	−	9.96410i	−0.0668670	−	1.11402i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	4.73205	−	1.26795i	0.522568	−	0.140022i
$83$	−1.36603	−	0.366025i	−0.149941	−	0.0401765i	0.183068	−	0.983100i	$-0.441397\pi$
$83$	−1.36603	−	0.366025i	−0.149941	−	0.0401765i	−0.333009	+	0.942924i	$0.608064\pi$
$84$	−1.50000	−	7.79423i	−0.163663	−	0.850420i
$85$	6.19615	+	1.26795i	0.672067	+	0.137528i
$86$	−1.50000	−	2.59808i	−0.161749	−	0.280158i
$87$	−12.0000			−1.28654
$88$	−2.73205	+	0.732051i	−0.291238	+	0.0780369i
$89$	4.59808	−	7.96410i	0.487395	−	0.844193i	−0.512500	−	0.858687i	$-0.671280\pi$
$89$	4.59808	−	7.96410i	0.487395	−	0.844193i	0.999895	+	0.0144942i	$0.00461382\pi$
$90$	−2.59808	+	12.6962i	−0.273861	+	1.33829i
$91$	8.46410	+	5.73205i	0.887279	+	0.600882i
$92$	−7.96410	−	2.13397i	−0.830315	−	0.222482i
$93$	−0.169873	+	0.294229i	−0.0176150	+	0.0305101i
$94$	−25.3923			−2.61902
$95$	−6.53590	−	3.26795i	−0.670569	−	0.335285i
$96$	−12.6962	+	3.40192i	−1.29580	+	0.347207i
$97$	2.09808	−	7.83013i	0.213027	−	0.795029i	−0.773824	−	0.633400i	$-0.781659\pi$
$97$	2.09808	−	7.83013i	0.213027	−	0.795029i	0.986852	−	0.161629i	$-0.0516747\pi$
$98$	8.09808	+	10.8301i	0.818029	+	1.09401i
$99$	16.3923			1.64749
$100$	1.03590	+	8.59808i	0.103590	+	0.859808i
$101$	15.2321	+	8.79423i	1.51565	+	0.875058i	0.999831	+	0.0183580i	$0.00584386\pi$
$101$	15.2321	+	8.79423i	1.51565	+	0.875058i	0.515814	+	0.856700i	$0.327489\pi$
$102$		−	9.46410i		−	0.937086i
$103$	3.96410	+	1.06218i	0.390595	+	0.104659i	0.448771	−	0.893647i	$-0.351862\pi$
$103$	3.96410	+	1.06218i	0.390595	+	0.104659i	−0.0581764	+	0.998306i	$0.518529\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	−2.53590	−	9.92820i	−0.247478	−	0.968893i
$106$	−6.09808	−	10.5622i	−0.592298	−	1.02589i
$107$	−0.633975	−	2.36603i	−0.0612886	−	0.228732i	0.928487	−	0.371365i	$-0.121110\pi$
$107$	−0.633975	−	2.36603i	−0.0612886	−	0.228732i	−0.989776	+	0.142632i	$0.954443\pi$
$108$	9.00000			0.866025
$109$	−1.73205	+	1.00000i	−0.165900	+	0.0957826i	−0.580651	−	0.814152i	$-0.697202\pi$
$109$	−1.73205	+	1.00000i	−0.165900	+	0.0957826i	0.414751	+	0.909935i	$0.363869\pi$
$110$	22.3923	−	7.46410i	2.13502	−	0.711674i
$111$	−1.90192	+	7.09808i	−0.180523	+	0.673720i
$112$	8.92820	−	7.73205i	0.843636	−	0.730610i
$113$	−7.09808	+	1.90192i	−0.667731	+	0.178918i	−0.576732	−	0.816933i	$-0.695672\pi$
$113$	−7.09808	+	1.90192i	−0.667731	+	0.178918i	−0.0909984	+	0.995851i	$0.529006\pi$
$114$	−2.83013	+	10.5622i	−0.265066	+	0.989239i
$115$	−10.4282	−	2.13397i	−0.972435	−	0.198994i
$116$	6.00000	+	10.3923i	0.557086	+	0.964901i
$117$	−8.19615	+	8.19615i	−0.757735	+	0.757735i
$118$	4.73205	−	4.73205i	0.435621	−	0.435621i
$119$	3.26795	+	6.73205i	0.299572	+	0.617126i
$120$	−1.90192	+	0.633975i	−0.173621	+	0.0578737i
$121$	−9.42820	−	16.3301i	−0.857109	−	1.48456i
$122$	15.5622	+	15.5622i	1.40893	+	1.40893i
$123$	−2.19615	−	3.80385i	−0.198020	−	0.342981i
$124$	0.339746			0.0305101
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−13.7942	+	6.69615i	−1.22889	+	0.596541i
$127$	−15.7583	+	15.7583i	−1.39833	+	1.39833i	−0.593468	+	0.804857i	$0.702242\pi$
$127$	−15.7583	+	15.7583i	−1.39833	+	1.39833i	−0.804857	+	0.593468i	$0.797758\pi$
$128$	−2.90192	−	2.90192i	−0.256496	−	0.256496i
$129$	−1.90192	+	1.90192i	−0.167455	+	0.167455i
$130$	−7.46410	+	14.9282i	−0.654645	+	1.30929i
$131$	−4.39230	+	2.53590i	−0.383757	+	0.221562i	−0.679452	−	0.733720i	$-0.737782\pi$
$131$	−4.39230	+	2.53590i	−0.383757	+	0.221562i	0.295694	+	0.955283i	$0.404449\pi$
$132$	−8.19615	−	14.1962i	−0.713384	−	1.23562i
$133$	−1.63397	−	8.49038i	−0.141684	−	0.736209i
$134$			2.46410i			0.212866i
$135$	11.5981	−	0.696152i	0.998203	−	0.0599153i
$136$	1.26795	−	0.732051i	0.108726	−	0.0627728i
$137$	0.535898	+	2.00000i	0.0457849	+	0.170872i	0.985032	−	0.172369i	$-0.0551421\pi$
$137$	0.535898	+	2.00000i	0.0457849	+	0.170872i	−0.939248	+	0.343240i	$0.888475\pi$
$138$			15.9282i			1.35590i
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	−0.974710	−	0.223474i	$-0.928260\pi$
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	0.680889	+	0.732387i	$0.261594\pi$
$140$	−7.33013	+	7.16025i	−0.619509	+	0.605152i
$141$	5.89230	+	21.9904i	0.496222	+	1.85192i
$142$	8.19615	−	8.19615i	0.687806	−	0.687806i
$143$	20.3923	+	5.46410i	1.70529	+	0.456931i
$144$	6.69615	+	11.5981i	0.558013	+	0.966506i
$145$	8.53590	+	12.9282i	0.708868	+	1.07363i
$146$	15.2942	−	8.83013i	1.26576	−	0.730787i
$147$	7.50000	−	9.52628i	0.618590	−	0.785714i
$148$	7.09808	−	1.90192i	0.583458	−	0.156337i
$149$	2.89230	−	1.66987i	0.236947	−	0.136801i	−0.376826	−	0.926284i	$-0.622984\pi$
$149$	2.89230	−	1.66987i	0.236947	−	0.136801i	0.613773	+	0.789483i	$0.289651\pi$
$150$	15.5263	−	6.23205i	1.26772	−	0.508845i
$151$	−2.36603	+	4.09808i	−0.192544	+	0.333497i	−0.946093	−	0.323896i	$-0.895007\pi$
$151$	−2.36603	+	4.09808i	−0.192544	+	0.333497i	0.753548	+	0.657392i	$0.228341\pi$
$152$	−1.63397	+	0.437822i	−0.132533	+	0.0355121i
$153$	−8.19615	+	2.19615i	−0.662620	+	0.177548i
$154$	23.1244	+	15.6603i	1.86341	+	1.26194i
$155$	0.437822	−	0.0262794i	0.0351667	−	0.00211082i
$156$	11.1962	+	3.00000i	0.896410	+	0.240192i
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	0.666076	−	0.745884i	$-0.267973\pi$
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	−0.745884	+	0.666076i	$0.767973\pi$
$158$	−6.19615	−	6.19615i	−0.492939	−	0.492939i
$159$	−7.73205	+	7.73205i	−0.613192	+	0.613192i
$160$	12.6962	+	11.2583i	1.00372	+	0.890049i
$161$	−5.50000	−	11.3301i	−0.433461	−	0.892939i
$162$	−4.50000	−	16.7942i	−0.353553	−	1.31948i
$163$	−8.83013	+	2.36603i	−0.691629	+	0.185321i	−0.587478	−	0.809240i	$-0.699879\pi$
$163$	−8.83013	+	2.36603i	−0.691629	+	0.185321i	−0.104151	+	0.994562i	$0.533212\pi$
$164$	−2.19615	+	3.80385i	−0.171491	+	0.297031i
$165$	−11.6603	−	17.6603i	−0.907750	−	1.37485i
$166$	2.36603	−	1.36603i	0.183639	−	0.106024i
$167$	13.5263	−	3.62436i	1.04669	−	0.280461i	0.305810	−	0.952093i	$-0.401073\pi$
$167$	13.5263	−	3.62436i	1.04669	−	0.280461i	0.740885	+	0.671632i	$0.234406\pi$
$168$	−1.96410	−	1.33013i	−0.151534	−	0.102622i
$169$	−1.66987	+	0.964102i	−0.128452	+	0.0741617i
$170$	−10.1962	+	6.73205i	−0.782009	+	0.516325i
$171$	9.80385			0.749719
$172$	2.59808	+	0.696152i	0.198101	+	0.0530811i
$173$	−10.0000	+	10.0000i	−0.760286	+	0.760286i	−0.976374	−	0.216088i	$-0.930670\pi$
$173$	−10.0000	+	10.0000i	−0.760286	+	0.760286i	0.216088	+	0.976374i	$0.430670\pi$
$174$	16.3923	−	16.3923i	1.24270	−	1.24270i
$175$	−8.89230	+	9.79423i	−0.672195	+	0.740374i
$176$	12.1962	−	21.1244i	0.919320	−	1.59231i
$177$	−5.19615	−	3.00000i	−0.390567	−	0.225494i
$178$	4.59808	+	17.1603i	0.344640	+	1.28622i
$179$	10.9019	−	6.29423i	0.814848	−	0.470453i	−0.0337886	−	0.999429i	$-0.510757\pi$
$179$	10.9019	−	6.29423i	0.814848	−	0.470453i	0.848637	+	0.528976i	$0.177424\pi$
$180$	−6.40192	−	9.69615i	−0.477171	−	0.722709i
$181$			11.4641i			0.852120i	0.904695	+	0.426060i	$0.140099\pi$
$181$			11.4641i			0.852120i	−0.904695	+	0.426060i	$0.859901\pi$
$182$	−19.3923	+	3.73205i	−1.43745	+	0.276638i
$183$	9.86603	−	17.0885i	0.729318	−	1.26322i
$184$	−2.13397	+	1.23205i	−0.157319	+	0.0908280i
$185$	9.00000	−	3.00000i	0.661693	−	0.220564i
$186$	−0.169873	−	0.633975i	−0.0124557	−	0.0464853i
$187$	10.9282	+	10.9282i	0.799149	+	0.799149i
$188$	16.0981	−	16.0981i	1.17407	−	1.17407i
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$	13.3923	−	4.46410i	0.971580	−	0.323860i
$191$	−17.6603			−1.27785			−0.638926	−	0.769269i	$-0.720621\pi$
$191$	−17.6603			−1.27785			−0.638926	+	0.769269i	$0.720621\pi$
$192$	4.96410	−	8.59808i	0.358253	−	0.620513i
$193$	−14.4641	−	14.4641i	−1.04115	−	1.04115i	−0.999116	−	0.0420326i	$-0.986617\pi$
$193$	−14.4641	−	14.4641i	−1.04115	−	1.04115i	−0.0420326	−	0.999116i	$-0.513383\pi$
$194$	7.83013	+	13.5622i	0.562170	+	0.973708i
$195$	14.6603	+	3.00000i	1.04984	+	0.214834i
$196$	−12.0000	−	1.73205i	−0.857143	−	0.123718i
$197$	−17.4641	+	17.4641i	−1.24427	+	1.24427i	−0.286051	+	0.958214i	$0.592343\pi$
$197$	−17.4641	+	17.4641i	−1.24427	+	1.24427i	−0.958214	+	0.286051i	$0.907657\pi$
$198$	−22.3923	+	22.3923i	−1.59135	+	1.59135i
$199$	−3.92820	−	6.80385i	−0.278463	−	0.482312i	0.692540	−	0.721379i	$-0.256492\pi$
$199$	−3.92820	−	6.80385i	−0.278463	−	0.482312i	−0.971003	+	0.239068i	$0.923158\pi$
$200$	2.03590	+	1.59808i	0.143960	+	0.113001i
$201$	2.13397	−	0.571797i	0.150519	−	0.0403314i
$202$	−32.8205	+	8.79423i	−2.30924	+	0.618760i
$203$	−6.00000	+	17.3205i	−0.421117	+	1.21566i
$204$	6.00000	+	6.00000i	0.420084	+	0.420084i
$205$	−2.53590	+	5.07180i	−0.177115	+	0.354230i
$206$	−6.86603	+	3.96410i	−0.478379	+	0.276192i
$207$	13.7942	−	3.69615i	0.958765	−	0.256900i
$208$	4.46410	+	16.6603i	0.309530	+	1.15518i
$209$	−8.92820	−	15.4641i	−0.617577	−	1.06967i
$210$	17.0263	+	10.0981i	1.17492	+	0.696833i
$211$	−4.46410	+	7.73205i	−0.307321	+	0.532296i	−0.977775	−	0.209655i	$-0.932766\pi$
$211$	−4.46410	+	7.73205i	−0.307321	+	0.532296i	0.670454	+	0.741951i	$0.266099\pi$
$212$	10.5622	+	2.83013i	0.725413	+	0.194374i
$213$	−9.00000	−	5.19615i	−0.616670	−	0.356034i
$214$	4.09808	+	2.36603i	0.280139	+	0.161738i
$215$	3.40192	+	0.696152i	0.232009	+	0.0474772i
$216$	1.90192	−	1.90192i	0.129410	−	0.129410i
$217$	0.339746	+	0.392305i	0.0230635	+	0.0266314i
$218$	1.00000	−	3.73205i	0.0677285	−	0.252766i
$219$	−11.1962	−	11.1962i	−0.756566	−	0.756566i
$220$	−9.46410	+	18.9282i	−0.638070	+	1.27614i
$221$	−10.9282			−0.735111
$222$	−7.09808	−	12.2942i	−0.476392	−	0.825135i
$223$	4.96410	+	1.33013i	0.332421	+	0.0890719i	0.421169	−	0.906982i	$-0.361620\pi$
$223$	4.96410	+	1.33013i	0.332421	+	0.0890719i	−0.0887481	+	0.996054i	$0.528287\pi$
$224$	−1.43782	+	20.0263i	−0.0960685	+	1.33806i
$225$	−9.00000	−	12.0000i	−0.600000	−	0.800000i
$226$	7.09808	−	12.2942i	0.472157	−	0.817800i
$227$	−14.5622	+	3.90192i	−0.966526	+	0.258980i	−0.707360	−	0.706853i	$-0.750114\pi$
$227$	−14.5622	+	3.90192i	−0.966526	+	0.258980i	−0.259165	+	0.965833i	$0.583447\pi$
$228$	−4.90192	−	8.49038i	−0.324638	−	0.562289i
$229$	−2.33013	−	4.03590i	−0.153979	−	0.266700i	0.778708	−	0.627387i	$-0.215876\pi$
$229$	−2.33013	−	4.03590i	−0.153979	−	0.266700i	−0.932687	+	0.360687i	$0.882542\pi$
$230$	17.1603	−	11.3301i	1.13151	−	0.747086i
$231$	8.19615	−	23.6603i	0.539267	−	1.55673i
$232$	3.46410	+	0.928203i	0.227429	+	0.0609395i
$233$	−11.8301	+	3.16987i	−0.775017	+	0.207665i	−0.624587	−	0.780955i	$-0.714733\pi$
$233$	−11.8301	+	3.16987i	−0.775017	+	0.207665i	−0.150430	+	0.988621i	$0.548066\pi$
$234$		−	22.3923i		−	1.46383i
$235$	19.5000	−	21.9904i	1.27204	−	1.43449i
$236$			6.00000i			0.390567i
$237$	−3.92820	+	6.80385i	−0.255164	+	0.441957i
$238$	−13.6603	−	4.73205i	−0.885463	−	0.306733i
$239$	−19.0526	−	11.0000i	−1.23241	−	0.711531i	−0.264876	−	0.964282i	$-0.585331\pi$
$239$	−19.0526	−	11.0000i	−1.23241	−	0.711531i	−0.967531	+	0.252752i	$0.918664\pi$
$240$	7.73205	−	15.4641i	0.499102	−	0.998203i
$241$	8.25833	+	4.76795i	0.531966	+	0.307131i	0.741817	−	0.670603i	$-0.233964\pi$
$241$	8.25833	+	4.76795i	0.531966	+	0.307131i	−0.209851	+	0.977733i	$0.567298\pi$
$242$	35.1865	+	9.42820i	2.26188	+	0.606068i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−19.7321			−1.26322
$245$	−15.5981	−	1.30385i	−0.996525	−	0.0832998i
$246$	8.19615	+	2.19615i	0.522568	+	0.140022i
$247$	12.1962	+	3.26795i	0.776023	+	0.207935i
$248$	0.0717968	−	0.0717968i	0.00455910	−	0.00455910i
$249$	−1.73205	−	1.73205i	−0.109764	−	0.109764i
$250$	−17.7583	−	12.2942i	−1.12314	−	0.777555i
$251$		−	5.85641i		−	0.369653i	−0.982771	−	0.184827i	$-0.940828\pi$
$251$		−	5.85641i		−	0.369653i	0.982771	−	0.184827i	$-0.0591723\pi$
$252$	4.50000	−	12.9904i	0.283473	−	0.818317i
$253$	−18.3923	−	18.3923i	−1.15631	−	1.15631i
$254$		−	43.0526i		−	2.70136i
$255$	8.19615	+	7.26795i	0.513263	+	0.455137i
$256$	19.3923			1.21202
$257$	3.22243	−	12.0263i	0.201010	−	0.750179i	−0.789619	−	0.613597i	$-0.789722\pi$
$257$	3.22243	−	12.0263i	0.201010	−	0.750179i	0.990629	−	0.136581i	$-0.0436115\pi$
$258$		−	5.19615i		−	0.323498i
$259$	9.29423	+	6.29423i	0.577515	+	0.391104i
$260$	−4.73205	−	14.1962i	−0.293469	−	0.880408i
$261$	−18.0000	−	10.3923i	−1.11417	−	0.643268i
$262$	2.53590	−	9.46410i	0.156668	−	0.584694i
$263$	27.4545	−	7.35641i	1.69292	−	0.453615i	0.721776	−	0.692127i	$-0.243326\pi$
$263$	27.4545	−	7.35641i	1.69292	−	0.453615i	0.971140	+	0.238511i	$0.0766593\pi$
$264$	−4.73205	−	1.26795i	−0.291238	−	0.0780369i
$265$	13.8301	+	2.83013i	0.849578	+	0.173853i
$266$	13.8301	+	9.36603i	0.847979	+	0.574268i
$267$	13.7942	−	7.96410i	0.844193	−	0.487395i
$268$	−1.56218	−	1.56218i	−0.0954252	−	0.0954252i
$269$	4.96410	+	8.59808i	0.302667	+	0.524234i	0.976739	−	0.214431i	$-0.0687898\pi$
$269$	4.96410	+	8.59808i	0.302667	+	0.524234i	−0.674072	+	0.738665i	$0.735456\pi$
$270$	−14.8923	+	16.7942i	−0.906317	+	1.02206i
$271$	−9.92820	−	5.73205i	−0.603095	−	0.348197i	0.167163	−	0.985929i	$-0.446539\pi$
$271$	−9.92820	−	5.73205i	−0.603095	−	0.348197i	−0.770258	+	0.637732i	$0.779873\pi$
$272$	−3.26795	+	12.1962i	−0.198149	+	0.739500i
$273$	7.73205	+	15.9282i	0.467965	+	0.964019i
$274$	−3.46410	−	2.00000i	−0.209274	−	0.120824i
$275$	−10.7321	+	25.1244i	−0.647167	+	1.51506i
$276$	−10.0981	−	10.0981i	−0.607833	−	0.607833i
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	−0.926562	−	0.376141i	$-0.877251\pi$
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	0.614356	−	0.789029i	$-0.289416\pi$
$278$	−3.46410	−	12.9282i	−0.207763	−	0.775382i
$279$	−0.509619	+	0.294229i	−0.0305101	+	0.0176150i
$280$	−0.0358984	+	3.06218i	−0.00214534	+	0.183000i
$281$	6.86603	+	11.8923i	0.409593	+	0.709435i	0.994844	−	0.101417i	$-0.0323375\pi$
$281$	6.86603	+	11.8923i	0.409593	+	0.709435i	−0.585251	+	0.810852i	$0.699004\pi$
$282$	−38.0885	−	21.9904i	−2.26813	−	1.30951i
$283$	15.7583	−	15.7583i	0.936736	−	0.936736i	−0.0613790	−	0.998115i	$-0.519550\pi$
$283$	15.7583	−	15.7583i	0.936736	−	0.936736i	0.998115	+	0.0613790i	$0.0195498\pi$
$284$			10.3923i			0.616670i
$285$	−6.97372	−	10.5622i	−0.413088	−	0.625649i
$286$	−35.3205	+	20.3923i	−2.08855	+	1.20582i
$287$	−6.58846	+	1.26795i	−0.388904	+	0.0748447i
$288$	−21.9904	−	5.89230i	−1.29580	−	0.347207i
$289$	7.79423	+	4.50000i	0.458484	+	0.264706i
$290$	−29.3205	−	6.00000i	−1.72176	−	0.352332i
$291$	9.92820	−	9.92820i	0.582002	−	0.582002i
$292$	−4.09808	+	15.2942i	−0.239822	+	0.895027i
$293$	5.43782	+	20.2942i	0.317681	+	1.18560i	0.921468	+	0.388455i	$0.126991\pi$
$293$	5.43782	+	20.2942i	0.317681	+	1.18560i	−0.603787	+	0.797146i	$0.706342\pi$
$294$	2.76795	+	23.2583i	0.161430	+	1.35645i
$295$	0.464102	+	7.73205i	0.0270210	+	0.450177i
$296$	1.09808	−	1.90192i	0.0638244	−	0.110547i
$297$	24.5885	+	14.1962i	1.42677	+	0.823744i
$298$	−1.66987	+	6.23205i	−0.0967331	+	0.361013i
$299$	18.3923			1.06365
$300$	−5.89230	+	13.7942i	−0.340192	+	0.796410i
$301$	1.79423	+	3.69615i	0.103418	+	0.213043i
$302$	−2.36603	−	8.83013i	−0.136149	−	0.508117i
$303$	15.2321	+	26.3827i	0.875058	+	1.51565i
$304$	7.29423	−	12.6340i	0.418353	−	0.724608i
$305$	−25.4282	+	1.52628i	−1.45601	+	0.0873945i
$306$	8.19615	−	14.1962i	0.468543	−	0.811540i
$307$	−17.5359	−	17.5359i	−1.00083	−	1.00083i	−1.00000		0.000826926i	$-0.999737\pi$
$307$	−17.5359	−	17.5359i	−1.00083	−	1.00083i	−0.000826926	−	1.00000i	$-0.500263\pi$
$308$	−24.5885	+	4.73205i	−1.40106	+	0.269634i
$309$	5.02628	+	5.02628i	0.285935	+	0.285935i
$310$	−0.562178	+	0.633975i	−0.0319296	+	0.0360073i
$311$			16.0000i			0.907277i	0.891186	+	0.453638i	$0.149874\pi$
$311$			16.0000i			0.907277i	−0.891186	+	0.453638i	$0.850126\pi$
$312$	3.00000	−	1.73205i	0.169842	−	0.0980581i
$313$	5.19615	−	5.19615i	0.293704	−	0.293704i	−0.544838	−	0.838542i	$-0.683409\pi$
$313$	5.19615	−	5.19615i	0.293704	−	0.293704i	0.838542	+	0.544838i	$0.183409\pi$
$314$	2.73205			0.154179
$315$	4.79423	−	17.0885i	0.270124	−	0.962825i
$316$	7.85641			0.441957
$317$	8.46410	−	8.46410i	0.475391	−	0.475391i	−0.428263	−	0.903654i	$-0.640874\pi$
$317$	8.46410	−	8.46410i	0.475391	−	0.475391i	0.903654	+	0.428263i	$0.140874\pi$
$318$		−	21.1244i		−	1.18460i
$319$			37.8564i			2.11955i
$320$	−12.7942	+	0.767949i	−0.715219	+	0.0429297i
$321$	1.09808	−	4.09808i	0.0612886	−	0.228732i
$322$	22.9904	+	7.96410i	1.28120	+	0.443822i
$323$	6.53590	+	6.53590i	0.363667	+	0.363667i
$324$	13.5000	+	7.79423i	0.750000	+	0.433013i
$325$	−7.19615	−	17.9282i	−0.399171	−	0.994478i
$326$	8.83013	−	15.2942i	0.489056	−	0.847069i
$327$	−3.46410			−0.191565
$328$	0.339746	+	1.26795i	0.0187593	+	0.0700108i
$329$	34.6865	+	2.49038i	1.91233	+	0.137299i
$330$	40.0526	+	8.19615i	2.20482	+	0.451183i
$331$	18.3397			1.00804			0.504022	−	0.863691i	$-0.331853\pi$
$331$	18.3397			1.00804			0.504022	+	0.863691i	$0.331853\pi$
$332$	−0.633975	+	2.36603i	−0.0347939	+	0.129853i
$333$	−9.00000	+	9.00000i	−0.493197	+	0.493197i
$334$	−13.5263	+	23.4282i	−0.740125	+	1.28193i
$335$	−2.13397	−	1.89230i	−0.116591	−	0.103388i
$336$	20.0885	−	3.86603i	1.09592	−	0.210909i
$337$	−1.19615	−	4.46410i	−0.0651586	−	0.243175i	0.925663	−	0.378348i	$-0.123508\pi$
$337$	−1.19615	−	4.46410i	−0.0651586	−	0.243175i	−0.990822	+	0.135173i	$0.956841\pi$
$338$	0.964102	−	3.59808i	0.0524402	−	0.195710i
$339$	−12.2942	−	3.29423i	−0.667731	−	0.178918i
$340$	2.19615	−	10.7321i	0.119103	−	0.582027i
$341$	0.928203	+	0.535898i	0.0502650	+	0.0290205i
$342$	−13.3923	+	13.3923i	−0.724173	+	0.724173i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	0.696152	−	0.401924i	0.0375340	−	0.0216703i
$345$	−13.7942	−	12.2321i	−0.742656	−	0.658551i
$346$		−	27.3205i		−	1.46876i
$347$	−14.8301	+	14.8301i	−0.796123	+	0.796123i	−0.982482	−	0.186359i	$-0.940331\pi$
$347$	−14.8301	+	14.8301i	−0.796123	+	0.796123i	0.186359	+	0.982482i	$0.440331\pi$
$348$			20.7846i			1.11417i
$349$	17.0622	+	29.5526i	0.913317	+	1.58191i	0.809346	+	0.587332i	$0.199822\pi$
$349$	17.0622	+	29.5526i	0.913317	+	1.58191i	0.103971	+	0.994580i	$0.466845\pi$
$350$	−1.23205	−	25.5263i	−0.0658559	−	1.36444i
$351$	−19.3923	+	5.19615i	−1.03508	+	0.277350i
$352$	10.7321	+	40.0526i	0.572020	+	2.13481i
$353$	−2.87564	−	10.7321i	−0.153055	−	0.571209i	−0.999264	−	0.0383582i	$-0.987787\pi$
$353$	−2.87564	−	10.7321i	−0.153055	−	0.571209i	0.846209	−	0.532851i	$-0.178879\pi$
$354$	11.1962	−	3.00000i	0.595069	−	0.159448i
$355$	0.803848	+	13.3923i	0.0426638	+	0.710790i
$356$	−13.7942	−	7.96410i	−0.731093	−	0.422097i
$357$	−0.928203	+	12.9282i	−0.0491257	+	0.684233i
$358$	−6.29423	+	23.4904i	−0.332660	+	1.24151i
$359$	17.9545	+	10.3660i	0.947601	+	0.547098i	0.892335	−	0.451374i	$-0.149066\pi$
$359$	17.9545	+	10.3660i	0.947601	+	0.547098i	0.0552664	+	0.998472i	$0.482399\pi$
$360$	−3.40192	−	0.696152i	−0.179297	−	0.0366905i
$361$	4.16025	+	7.20577i	0.218961	+	0.379251i
$362$	−15.6603	−	15.6603i	−0.823085	−	0.823085i
$363$		−	32.6603i		−	1.71422i
$364$	9.92820	−	14.6603i	0.520379	−	0.768406i
$365$	−4.09808	+	20.0263i	−0.214503	+	1.04822i
$366$	9.86603	+	36.8205i	0.515705	+	1.92464i
$367$	−6.59808	+	1.76795i	−0.344417	+	0.0922862i	−0.426881	−	0.904308i	$-0.640388\pi$
$367$	−6.59808	+	1.76795i	−0.344417	+	0.0922862i	0.0824642	+	0.996594i	$0.473721\pi$
$368$	5.50000	−	20.5263i	0.286707	−	1.07001i
$369$		−	7.60770i		−	0.396041i
$370$	−8.19615	+	16.3923i	−0.426098	+	0.852195i
$371$	7.29423	+	15.0263i	0.378697	+	0.780126i
$372$	0.509619	+	0.294229i	0.0264225	+	0.0152550i
$373$	1.09808	−	4.09808i	0.0568562	−	0.212190i	−0.931653	−	0.363348i	$-0.881634\pi$
$373$	1.09808	−	4.09808i	0.0568562	−	0.212190i	0.988510	+	0.151158i	$0.0483002\pi$
$374$	−29.8564			−1.54384
$375$	−6.52628	+	18.2321i	−0.337016	+	0.941499i
$376$		−	6.80385i		−	0.350882i
$377$	−18.9282	−	18.9282i	−0.974852	−	0.974852i
$378$	−26.4904	−	1.90192i	−1.36252	−	0.0978244i
$379$			12.5359i			0.643926i	0.946752	+	0.321963i	$0.104343\pi$
$379$			12.5359i			0.643926i	−0.946752	+	0.321963i	$0.895657\pi$
$380$	−5.66025	+	11.3205i	−0.290365	+	0.580730i
$381$	−37.2846	+	9.99038i	−1.91015	+	0.511823i
$382$	24.1244	−	24.1244i	1.23431	−	1.23431i
$383$	15.7942	+	4.23205i	0.807047	+	0.216248i	0.638676	−	0.769476i	$-0.279482\pi$
$383$	15.7942	+	4.23205i	0.807047	+	0.216248i	0.168372	+	0.985724i	$0.446149\pi$
$384$	−1.83975	−	6.86603i	−0.0938841	−	0.350380i
$385$	−31.3205	+	8.00000i	−1.59624	+	0.407718i
$386$	39.5167			2.01135
$387$	−4.50000	+	1.20577i	−0.228748	+	0.0612928i
$388$	−13.5622	−	3.63397i	−0.688515	−	0.184487i
$389$	−1.03590	−	0.598076i	−0.0525221	−	0.0303237i	0.473509	−	0.880789i	$-0.342987\pi$
$389$	−1.03590	−	0.598076i	−0.0525221	−	0.0303237i	−0.526031	+	0.850465i	$0.676320\pi$
$390$	−24.1244	+	15.9282i	−1.22158	+	0.806556i
$391$	11.6603	+	6.73205i	0.589684	+	0.340454i
$392$	−2.90192	+	2.16987i	−0.146569	+	0.109595i
$393$	−8.78461			−0.443125
$394$		−	47.7128i		−	2.40374i
$395$	10.1244	−	0.607695i	0.509412	−	0.0305765i
$396$		−	28.3923i		−	1.42677i
$397$	32.7846	−	8.78461i	1.64541	−	0.440887i	0.687089	−	0.726573i	$-0.258888\pi$
$397$	32.7846	−	8.78461i	1.64541	−	0.440887i	0.958323	+	0.285686i	$0.0922215\pi$
$398$	14.6603	+	3.92820i	0.734852	+	0.196903i
$399$	4.90192	−	14.1506i	0.245403	−	0.708418i
$400$	−22.1603	+	2.66987i	−1.10801	+	0.133494i
$401$	−11.6962	−	20.2583i	−0.584078	−	1.01165i	−0.994990	−	0.0999776i	$-0.968123\pi$
$401$	−11.6962	−	20.2583i	−0.584078	−	1.01165i	0.410912	−	0.911675i	$-0.365210\pi$
$402$	−2.13397	+	3.69615i	−0.106433	+	0.184347i
$403$	−0.732051	+	0.196152i	−0.0364660	+	0.00977105i
$404$	15.2321	−	26.3827i	0.757823	−	1.31259i
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$	−15.4641	−	31.8564i	−0.767470	−	1.58101i
$407$	22.3923	+	6.00000i	1.10995	+	0.297409i
$408$	2.53590			0.125546
$409$	5.39230			0.266632			0.133316	−	0.991074i	$-0.457437\pi$
$409$	5.39230			0.266632			0.133316	+	0.991074i	$0.457437\pi$
$410$	−3.46410	−	10.3923i	−0.171080	−	0.513239i
$411$	−0.928203	+	3.46410i	−0.0457849	+	0.170872i
$412$	1.83975	−	6.86603i	0.0906378	−	0.338265i
$413$	−6.92820	+	6.00000i	−0.340915	+	0.295241i
$414$	−13.7942	+	23.8923i	−0.677949	+	1.17424i
$415$	−0.633975	+	3.09808i	−0.0311206	+	0.152079i
$416$	−25.3923	−	14.6603i	−1.24496	−	0.718778i
$417$	−10.3923	+	6.00000i	−0.508913	+	0.293821i
$418$	33.3205	+	8.92820i	1.62976	+	0.436693i
$419$	−4.00000	+	6.92820i	−0.195413	+	0.338465i	−0.947036	−	0.321128i	$-0.895938\pi$
$419$	−4.00000	+	6.92820i	−0.195413	+	0.338465i	0.751623	+	0.659593i	$0.229271\pi$
$420$	−17.1962	+	4.39230i	−0.839086	+	0.214323i
$421$	−11.5263	−	19.9641i	−0.561756	−	0.972991i	−0.997343	−	0.0728441i	$-0.976792\pi$
$421$	−11.5263	−	19.9641i	−0.561756	−	0.972991i	0.435587	−	0.900147i	$-0.356541\pi$
$422$	−4.46410	−	16.6603i	−0.217309	−	0.811008i
$423$	−10.2058	+	38.0885i	−0.496222	+	1.85192i
$424$	2.83013	−	1.63397i	0.137443	−	0.0793528i
$425$	2.00000	−	14.0000i	0.0970143	−	0.679100i
$426$	19.3923	−	5.19615i	0.939560	−	0.251754i
$427$	−19.7321	−	22.7846i	−0.954901	−	1.10262i
$428$	−4.09808	+	1.09808i	−0.198088	+	0.0530775i
$429$	25.8564	+	25.8564i	1.24836	+	1.24836i
$430$	−5.59808	+	3.69615i	−0.269963	+	0.178244i
$431$	12.0981	+	20.9545i	0.582744	+	1.00934i	0.995153	+	0.0983430i	$0.0313542\pi$
$431$	12.0981	+	20.9545i	0.582744	+	1.00934i	−0.412409	+	0.910999i	$0.635312\pi$
$432$			23.1962i			1.11603i
$433$	9.80385	−	9.80385i	0.471143	−	0.471143i	−0.431141	−	0.902284i	$-0.641889\pi$
$433$	9.80385	−	9.80385i	0.471143	−	0.471143i	0.902284	+	0.431141i	$0.141889\pi$
$434$	−1.00000	−	0.0717968i	−0.0480015	−	0.00344636i
$435$	1.60770	+	26.7846i	0.0770831	+	1.28422i
$436$	1.73205	+	3.00000i	0.0829502	+	0.143674i
$437$	−11.0000	−	11.0000i	−0.526201	−	0.526201i
$438$	30.5885			1.46157
$439$	−5.85641			−0.279511			−0.139756	−	0.990186i	$-0.544632\pi$
$439$	−5.85641			−0.279511			−0.139756	+	0.990186i	$0.544632\pi$
$440$	2.00000	+	6.00000i	0.0953463	+	0.286039i
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$	14.9282	−	14.9282i	0.710062	−	0.710062i
$443$	−0.660254	−	0.660254i	−0.0313696	−	0.0313696i	0.691248	−	0.722618i	$-0.257061\pi$
$443$	−0.660254	−	0.660254i	−0.0313696	−	0.0313696i	−0.722618	+	0.691248i	$0.757061\pi$
$444$	12.2942	+	3.29423i	0.583458	+	0.156337i
$445$	−18.3923	−	9.19615i	−0.871879	−	0.435939i
$446$	−8.59808	+	4.96410i	−0.407131	+	0.235057i
$447$	5.78461			0.273603
$448$	−9.92820	−	11.4641i	−0.469064	−	0.541628i
$449$			1.58846i			0.0749639i	0.999297	+	0.0374820i	$0.0119337\pi$
$449$			1.58846i			0.0749639i	−0.999297	+	0.0374820i	$0.988066\pi$
$450$	28.6865	+	4.09808i	1.35230	+	0.193185i
$451$	−12.0000	+	6.92820i	−0.565058	+	0.326236i
$452$	3.29423	+	12.2942i	0.154947	+	0.578272i
$453$	−7.09808	+	4.09808i	−0.333497	+	0.192544i
$454$	14.5622	−	25.2224i	0.683437	−	1.18375i
$455$	11.6603	−	19.6603i	0.546641	−	0.921687i
$456$	−2.83013	−	0.758330i	−0.132533	−	0.0355121i
$457$	−7.33975	+	7.33975i	−0.343339	+	0.343339i	−0.857621	−	0.514282i	$-0.828058\pi$
$457$	−7.33975	+	7.33975i	−0.343339	+	0.343339i	0.514282	+	0.857621i	$0.328058\pi$
$458$	8.69615	+	2.33013i	0.406345	+	0.108880i
$459$	−14.1962	−	3.80385i	−0.662620	−	0.177548i
$460$	−3.69615	+	18.0622i	−0.172334	+	0.842153i
$461$	1.03590	−	0.598076i	0.0482466	−	0.0278552i	−0.475683	−	0.879617i	$-0.657799\pi$
$461$	1.03590	−	0.598076i	0.0482466	−	0.0278552i	0.523929	+	0.851762i	$0.324466\pi$
$462$	21.1244	+	43.5167i	0.982794	+	2.02458i
$463$	35.1865	−	9.42820i	1.63526	−	0.438166i	0.679824	−	0.733375i	$-0.262056\pi$
$463$	35.1865	−	9.42820i	1.63526	−	0.438166i	0.955433	+	0.295209i	$0.0953894\pi$
$464$	−26.7846	+	15.4641i	−1.24344	+	0.717903i
$465$	0.679492	+	0.339746i	0.0315107	+	0.0157553i
$466$	11.8301	−	20.4904i	0.548020	−	0.949199i
$467$	12.9641	−	3.47372i	0.599907	−	0.160745i	0.0539300	−	0.998545i	$-0.482825\pi$
$467$	12.9641	−	3.47372i	0.599907	−	0.160745i	0.545977	+	0.837800i	$0.316159\pi$
$468$	14.1962	+	14.1962i	0.656217	+	0.656217i
$469$	0.241670	−	3.36603i	0.0111593	−	0.155429i
$470$	3.40192	+	56.6769i	0.156919	+	2.61431i
$471$	−0.633975	−	2.36603i	−0.0292120	−	0.109021i
$472$	1.26795	+	1.26795i	0.0583621	+	0.0583621i
$473$	6.00000	+	6.00000i	0.275880	+	0.275880i
$474$	−3.92820	−	14.6603i	−0.180428	−	0.673368i
$475$	−6.41858	+	15.0263i	−0.294505	+	0.689453i
$476$	11.6603	−	5.66025i	0.534447	−	0.259437i
$477$	−18.2942	+	4.90192i	−0.837635	+	0.224444i
$478$	41.0526	−	11.0000i	1.87770	−	0.503128i
$479$	2.63397	−	4.56218i	0.120349	−	0.208451i	−0.799556	−	0.600591i	$-0.794932\pi$
$479$	2.63397	−	4.56218i	0.120349	−	0.208451i	0.919905	+	0.392140i	$0.128265\pi$
$480$	9.29423	+	27.8827i	0.424222	+	1.27266i
$481$	−14.1962	+	8.19615i	−0.647289	+	0.373712i
$482$	−17.7942	+	4.76795i	−0.810505	+	0.217174i
$483$	1.56218	−	21.7583i	0.0710816	−	0.990038i
$484$	−28.2846	+	16.3301i	−1.28566	+	0.742279i
$485$	−17.7583	−	3.63397i	−0.806364	−	0.165010i
$486$	7.79423	−	29.0885i	0.353553	−	1.31948i
$487$	−32.4186	−	8.68653i	−1.46903	−	0.393624i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−32.4186	−	8.68653i	−1.46903	−	0.393624i	−0.902597	+	0.430486i	$0.858342\pi$
$488$	−4.16987	+	4.16987i	−0.188761	+	0.188761i
$489$	−15.2942	−	4.09808i	−0.691629	−	0.185321i
$490$	23.0885	−	19.5263i	1.04303	−	0.882107i
$491$	8.46410	−	14.6603i	0.381980	−	0.661608i	−0.609366	−	0.792889i	$-0.708576\pi$
$491$	8.46410	−	14.6603i	0.381980	−	0.661608i	0.991345	+	0.131281i	$0.0419091\pi$
$492$	−6.58846	+	3.80385i	−0.297031	+	0.171491i
$493$	−5.07180	−	18.9282i	−0.228422	−	0.852483i
$494$	−21.1244	+	12.1962i	−0.950430	+	0.548731i
$495$	−2.19615	−	36.5885i	−0.0987097	−	1.64453i
$496$			0.875644i			0.0393176i
$497$	−12.0000	+	10.3923i	−0.538274	+	0.466159i
$498$	4.73205			0.212048
$499$	6.12436	−	3.53590i	0.274164	−	0.158289i	−0.356615	−	0.934252i	$-0.616069\pi$
$499$	6.12436	−	3.53590i	0.274164	−	0.158289i	0.630778	+	0.775963i	$0.282736\pi$
$500$	19.0526	−	3.46410i	0.852056	−	0.154919i
$501$	23.4282	+	6.27757i	1.04669	+	0.280461i
$502$	8.00000	+	8.00000i	0.357057	+	0.357057i
$503$	10.0718	−	10.0718i	0.449079	−	0.449079i	−0.445969	−	0.895048i	$-0.647141\pi$
$503$	10.0718	−	10.0718i	0.449079	−	0.449079i	0.895048	+	0.445969i	$0.147141\pi$
$504$	−1.79423	−	3.69615i	−0.0799213	−	0.164640i
$505$	17.5885	−	35.1769i	0.782676	−	1.56535i
$506$	50.2487			2.23383
$507$	−3.33975			−0.148323
$508$	27.2942	+	27.2942i	1.21099	+	1.21099i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$	−21.1244	+	1.26795i	−0.935402	+	0.0561457i
$511$	−21.7583	+	10.5622i	−0.962532	+	0.467243i
$512$	−20.6865	+	20.6865i	−0.914224	+	0.914224i
$513$	14.7058	+	8.49038i	0.649276	+	0.374859i
$514$	12.0263	+	20.8301i	0.530456	+	0.918778i
$515$	1.83975	−	8.99038i	0.0810689	−	0.396164i
$516$	3.29423	+	3.29423i	0.145020	+	0.145020i
$517$	69.3731	−	18.5885i	3.05102	−	0.817519i
$518$	−21.2942	+	4.09808i	−0.935615	+	0.180059i
$519$	−23.6603	+	6.33975i	−1.03857	+	0.278284i
$520$	−4.00000	−	2.00000i	−0.175412	−	0.0877058i
$521$	37.6244	−	21.7224i	1.64835	−	0.951677i	0.670626	−	0.741796i	$-0.266026\pi$
$521$	37.6244	−	21.7224i	1.64835	−	0.951677i	0.977727	−	0.209881i	$-0.0673078\pi$
$522$	38.7846	−	10.3923i	1.69756	−	0.454859i
$523$	−1.33013	−	4.96410i	−0.0581624	−	0.217065i	0.930728	−	0.365713i	$-0.119175\pi$
$523$	−1.33013	−	4.96410i	−0.0581624	−	0.217065i	−0.988890	+	0.148648i	$0.952508\pi$
$524$	4.39230	+	7.60770i	0.191879	+	0.332344i
$525$	−21.8205	+	6.99038i	−0.952325	+	0.305085i
$526$	−27.4545	+	47.5526i	−1.19707	+	2.07339i
$527$	−0.535898	−	0.143594i	−0.0233441	−	0.00625503i
$528$	36.5885	−	21.1244i	1.59231	−	0.919320i
$529$	0.294229	+	0.169873i	0.0127925	+	0.00738578i
$530$	−22.7583	+	15.0263i	−0.988559	+	0.652700i
$531$	−5.19615	−	9.00000i	−0.225494	−	0.390567i
$532$	−14.7058	+	2.83013i	−0.637576	+	0.122702i
$533$	2.53590	−	9.46410i	0.109842	−	0.409936i
$534$	−7.96410	+	29.7224i	−0.344640	+	1.28622i
$535$	−5.19615	+	1.73205i	−0.224649	+	0.0748831i
$536$	−0.660254			−0.0285186
$537$	21.8038			0.940905
$538$	−18.5263	−	4.96410i	−0.798725	−	0.214018i
$539$	−30.0526	−	23.6603i	−1.29446	−	1.01912i
$540$	−1.20577	−	20.0885i	−0.0518881	−	0.864470i
$541$	4.96410	−	8.59808i	0.213423	−	0.369660i	−0.739360	−	0.673310i	$-0.764872\pi$
$541$	4.96410	−	8.59808i	0.213423	−	0.369660i	0.952784	+	0.303650i	$0.0982053\pi$
$542$	21.3923	−	5.73205i	0.918878	−	0.246213i
$543$	−9.92820	+	17.1962i	−0.426060	+	0.737958i
$544$	−10.7321	−	18.5885i	−0.460133	−	0.796974i
$545$	2.46410	+	3.73205i	0.105551	+	0.159863i
$546$	−32.3205	−	11.1962i	−1.38319	−	0.479151i
$547$	−12.3660	−	3.31347i	−0.528733	−	0.141674i	−0.0154299	−	0.999881i	$-0.504912\pi$
$547$	−12.3660	−	3.31347i	−0.528733	−	0.141674i	−0.513303	+	0.858207i	$0.671578\pi$
$548$	3.46410	−	0.928203i	0.147979	−	0.0396509i
$549$	29.5981	−	17.0885i	1.26322	−	0.729318i
$550$	−19.6603	−	48.9808i	−0.838316	−	2.08855i
$551$			22.6410i			0.964540i
$552$	−4.26795			−0.181656
$553$	7.85641	+	9.07180i	0.334088	+	0.385772i
$554$	33.5885	+	19.3923i	1.42704	+	0.823900i
$555$	16.0981	+	3.29423i	0.683325	+	0.139832i
$556$	10.3923	+	6.00000i	0.440732	+	0.254457i
$557$	−15.2942	−	4.09808i	−0.648037	−	0.173641i	−0.0801960	−	0.996779i	$-0.525555\pi$
$557$	−15.2942	−	4.09808i	−0.648037	−	0.173641i	−0.567841	+	0.823138i	$0.692221\pi$
$558$	0.294229	−	1.09808i	0.0124557	−	0.0464853i
$559$	−6.00000			−0.253773
$560$	−18.4545	−	18.8923i	−0.779844	−	0.798346i
$561$	6.92820	+	25.8564i	0.292509	+	1.09166i
$562$	−25.6244	−	6.86603i	−1.08090	−	0.289626i
$563$	15.1699	−	15.1699i	0.639334	−	0.639334i	−0.311057	−	0.950391i	$-0.600683\pi$
$563$	15.1699	−	15.1699i	0.639334	−	0.639334i	0.950391	+	0.311057i	$0.100683\pi$
$564$	38.0885	−	10.2058i	1.60381	−	0.429740i
$565$	5.19615	+	15.5885i	0.218604	+	0.655811i
$566$			43.0526i			1.80963i
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$	2.19615	+	2.19615i	0.0921485	+	0.0921485i
$569$			18.7846i			0.787492i	0.919219	+	0.393746i	$0.128821\pi$
$569$			18.7846i			0.787492i	−0.919219	+	0.393746i	$0.871179\pi$
$570$	23.9545	+	4.90192i	1.00334	+	0.205319i
$571$	−20.2487			−0.847382			−0.423691	−	0.905807i	$-0.639266\pi$
$571$	−20.2487			−0.847382			−0.423691	+	0.905807i	$0.639266\pi$
$572$	9.46410	−	35.3205i	0.395714	−	1.47682i
$573$	−26.4904	−	15.2942i	−1.10665	−	0.638926i
$574$	7.26795	−	10.7321i	0.303358	−	0.447947i
$575$	−3.36603	+	23.5622i	−0.140373	+	0.982611i
$576$	14.8923	−	8.59808i	0.620513	−	0.358253i
$577$	1.32051	−	4.92820i	0.0549735	−	0.205164i	−0.932977	−	0.359937i	$-0.882798\pi$
$577$	1.32051	−	4.92820i	0.0549735	−	0.205164i	0.987950	+	0.154773i	$0.0494648\pi$
$578$	−16.7942	+	4.50000i	−0.698548	+	0.187175i
$579$	−9.16987	−	34.2224i	−0.381087	−	1.42224i
$580$	22.3923	−	14.7846i	0.929790	−	0.613898i
$581$	−3.36603	+	1.63397i	−0.139646	+	0.0677887i
$582$			27.1244i			1.12434i
$583$	24.3923	+	24.3923i	1.01023	+	1.01023i
$584$	2.36603	+	4.09808i	0.0979068	+	0.169580i
$585$	19.3923	+	17.1962i	0.801773	+	0.710973i
$586$	−35.1506	−	20.2942i	−1.45206	−	0.838347i
$587$	−8.62436	+	32.1865i	−0.355965	+	1.32848i	0.523300	+	0.852148i	$0.324701\pi$
$587$	−8.62436	+	32.1865i	−0.355965	+	1.32848i	−0.879265	+	0.476332i	$0.841966\pi$
$588$	−16.5000	−	12.9904i	−0.680449	−	0.535714i
$589$	0.555136	+	0.320508i	0.0228740	+	0.0132063i
$590$	−11.1962	−	9.92820i	−0.460938	−	0.408738i
$591$	−41.3205	+	11.0718i	−1.69970	+	0.455433i
$592$	4.90192	+	18.2942i	0.201468	+	0.751888i
$593$	−0.732051	−	2.73205i	−0.0300617	−	0.112192i	0.949265	−	0.314478i	$-0.101830\pi$
$593$	−0.732051	−	2.73205i	−0.0300617	−	0.112192i	−0.979326	+	0.202286i	$0.935163\pi$
$594$	−52.9808	+	14.1962i	−2.17383	+	0.582475i
$595$	14.5885	−	8.19615i	0.598068	−	0.336009i
$596$	−2.89230	−	5.00962i	−0.118473	−	0.205202i
$597$		−	13.6077i		−	0.556926i
$598$	−25.1244	+	25.1244i	−1.02741	+	1.02741i
$599$		−	30.9808i		−	1.26584i	−0.774217	−	0.632920i	$-0.781856\pi$
$599$		−	30.9808i		−	1.26584i	0.774217	−	0.632920i	$-0.218144\pi$
$600$	1.66987	+	4.16025i	0.0681723	+	0.169842i
$601$	20.6603	−	11.9282i	0.842749	−	0.486562i	−0.0154485	−	0.999881i	$-0.504918\pi$
$601$	20.6603	−	11.9282i	0.842749	−	0.486562i	0.858198	+	0.513319i	$0.171584\pi$
$602$	−7.50000	−	2.59808i	−0.305677	−	0.105890i
$603$	3.69615	+	0.990381i	0.150519	+	0.0403314i
$604$	7.09808	+	4.09808i	0.288817	+	0.166748i
$605$	−35.1865	+	23.2321i	−1.43054	+	0.944517i
$606$	−56.8468	−	15.2321i	−2.30924	−	0.618760i
$607$	−1.09808	+	4.09808i	−0.0445695	+	0.166336i	−0.984623	−	0.174690i	$-0.944108\pi$
$607$	−1.09808	+	4.09808i	−0.0445695	+	0.166336i	0.940054	+	0.341026i	$0.110774\pi$
$608$	6.41858	+	23.9545i	0.260308	+	0.971483i
$609$	−24.0000	+	20.7846i	−0.972529	+	0.842235i
$610$	32.6506	−	36.8205i	1.32199	−	1.49082i
$611$	−25.3923	+	43.9808i	−1.02726	+	1.77927i
$612$	3.80385	+	14.1962i	0.153761	+	0.573845i
$613$	−11.0981	+	41.4186i	−0.448247	+	1.67288i	0.258971	+	0.965885i	$0.416617\pi$
$613$	−11.0981	+	41.4186i	−0.448247	+	1.67288i	−0.707218	+	0.706996i	$0.750050\pi$
$614$	47.9090			1.93345
$615$	−8.19615	+	5.41154i	−0.330501	+	0.218214i
$616$	−4.19615	+	6.19615i	−0.169068	+	0.249650i
$617$	0.562178	+	2.09808i	0.0226324	+	0.0844654i	0.976318	−	0.216339i	$-0.0694116\pi$
$617$	0.562178	+	2.09808i	0.0226324	+	0.0844654i	−0.953686	+	0.300804i	$0.902745\pi$
$618$	−13.7321			−0.552384
$619$	12.4904	−	21.6340i	0.502031	−	0.869543i	−0.497966	−	0.867196i	$-0.665920\pi$
$619$	12.4904	−	21.6340i	0.502031	−	0.869543i	0.999997	−	0.00234656i	$-0.000746933\pi$
$620$	−0.0455173	−	0.758330i	−0.00182802	−	0.0304553i
$621$	23.8923	+	6.40192i	0.958765	+	0.256900i
$622$	−21.8564	−	21.8564i	−0.876362	−	0.876362i
$623$	−4.59808	−	23.8923i	−0.184218	−	0.957225i
$624$	−7.73205	+	28.8564i	−0.309530	+	1.15518i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$			14.1962i			0.567392i
$627$		−	30.9282i		−	1.23515i
$628$	−1.73205	+	1.73205i	−0.0691164	+	0.0691164i
$629$	−12.0000			−0.478471
$630$	16.7942	+	29.8923i	0.669098	+	1.19094i
$631$	37.3205			1.48571			0.742853	−	0.669455i	$-0.233472\pi$
$631$	37.3205			1.48571			0.742853	+	0.669455i	$0.233472\pi$
$632$	1.66025	−	1.66025i	0.0660414	−	0.0660414i
$633$	−13.3923	+	7.73205i	−0.532296	+	0.307321i
$634$			23.1244i			0.918385i
$635$	37.2846	+	33.0622i	1.47959	+	1.31203i
$636$	13.3923	+	13.3923i	0.531039	+	0.531039i
$637$	26.8564	−	3.19615i	1.06409	−	0.126636i
$638$	−51.7128	−	51.7128i	−2.04733	−	2.04733i
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$	−6.08846	+	6.86603i	−0.240667	+	0.271403i
$641$	15.7224	−	27.2321i	0.620999	−	1.07560i	−0.368301	−	0.929706i	$-0.620061\pi$
$641$	15.7224	−	27.2321i	0.620999	−	1.07560i	0.989300	−	0.145895i	$-0.0466061\pi$
$642$	4.09808	+	7.09808i	0.161738	+	0.280139i
$643$	0.186533	+	0.696152i	0.00735616	+	0.0274536i	0.969506	−	0.245066i	$-0.0788097\pi$
$643$	0.186533	+	0.696152i	0.00735616	+	0.0274536i	−0.962150	+	0.272520i	$0.912143\pi$
$644$	−19.6244	+	9.52628i	−0.773308	+	0.375388i
$645$	4.50000	+	3.99038i	0.177187	+	0.157121i
$646$	−17.8564			−0.702551
$647$	5.04552	−	18.8301i	0.198360	−	0.740289i	−0.793012	−	0.609206i	$-0.791488\pi$
$647$	5.04552	−	18.8301i	0.198360	−	0.740289i	0.991371	−	0.131082i	$-0.0418452\pi$
$648$	4.50000	−	1.20577i	0.176777	−	0.0473672i
$649$	−9.46410	+	16.3923i	−0.371498	+	0.643454i
$650$	34.3205	+	14.6603i	1.34616	+	0.575022i
$651$	0.169873	+	0.882686i	0.00665785	+	0.0345952i
$652$	4.09808	+	15.2942i	0.160493	+	0.598968i
$653$	6.49038	−	24.2224i	0.253988	−	0.947897i	−0.714662	−	0.699470i	$-0.753420\pi$
$653$	6.49038	−	24.2224i	0.253988	−	0.947897i	0.968651	−	0.248427i	$-0.0799137\pi$
$654$	4.73205	−	4.73205i	0.185038	−	0.185038i
$655$	6.24871	+	9.46410i	0.244157	+	0.369793i
$656$	−9.80385	−	5.66025i	−0.382776	−	0.220996i
$657$	−7.09808	−	26.4904i	−0.276922	−	1.03349i
$658$	−50.7846	+	43.9808i	−1.97979	+	1.71455i
$659$	22.5167	−	13.0000i	0.877125	−	0.506408i	0.00741531	−	0.999973i	$-0.497640\pi$
$659$	22.5167	−	13.0000i	0.877125	−	0.506408i	0.869709	+	0.493564i	$0.164306\pi$
$660$	−30.5885	+	20.1962i	−1.19065	+	0.786134i
$661$			11.0000i			0.427850i	0.976850	+	0.213925i	$0.0686249\pi$
$661$			11.0000i			0.427850i	−0.976850	+	0.213925i	$0.931375\pi$
$662$	−25.0526	+	25.0526i	−0.973695	+	0.973695i
$663$	−16.3923	−	9.46410i	−0.636624	−	0.367555i
$664$	0.366025	+	0.633975i	0.0142045	+	0.0246030i
$665$	−18.7321	+	4.78461i	−0.726398	+	0.185539i
$666$		−	24.5885i		−	0.952783i
$667$	8.53590	+	31.8564i	0.330511	+	1.23348i
$668$	−6.27757	−	23.4282i	−0.242886	−	0.906464i
$669$	6.29423	+	6.29423i	0.243349	+	0.243349i
$670$	5.50000	−	0.330127i	0.212484	−	0.0127539i
$671$	−53.9090	−	31.1244i	−2.08113	−	1.20154i
$672$	−19.5000	+	28.7942i	−0.752229	+	1.11076i
$673$	−6.92820	+	25.8564i	−0.267063	+	0.996691i	0.693913	+	0.720059i	$0.255885\pi$
$673$	−6.92820	+	25.8564i	−0.267063	+	0.996691i	−0.960976	+	0.276633i	$0.910782\pi$
$674$	7.73205	+	4.46410i	0.297827	+	0.171951i
$675$	−3.10770	−	25.7942i	−0.119615	−	0.992820i
$676$	1.66987	+	2.89230i	0.0642259	+	0.111242i
$677$	−35.9090	−	35.9090i	−1.38009	−	1.38009i	−0.844434	−	0.535660i	$-0.820063\pi$
$677$	−35.9090	−	35.9090i	−1.38009	−	1.38009i	−0.535660	−	0.844434i	$-0.679937\pi$
$678$	21.2942	−	12.2942i	0.817800	−	0.472157i
$679$	−9.36603	−	19.2942i	−0.359435	−	0.740445i
$680$	−1.80385	−	2.73205i	−0.0691744	−	0.104769i
$681$	−25.2224	−	6.75833i	−0.966526	−	0.258980i
$682$	−2.00000	+	0.535898i	−0.0765840	+	0.0205206i
$683$	−4.00962	+	14.9641i	−0.153424	+	0.572585i	0.845811	+	0.533482i	$0.179117\pi$
$683$	−4.00962	+	14.9641i	−0.153424	+	0.572585i	−0.999235	+	0.0391034i	$0.987550\pi$
$684$		−	16.9808i		−	0.649276i
$685$	4.39230	−	1.46410i	0.167821	−	0.0559404i
$686$	34.9545	+	7.63397i	1.33457	+	0.291467i
$687$		−	8.07180i		−	0.307958i
$688$	−1.79423	+	6.69615i	−0.0684043	+	0.255288i
$689$	−24.3923			−0.929273
$690$	35.5526	−	2.13397i	1.35346	−	0.0812390i
$691$			10.5885i			0.402804i	0.979509	+	0.201402i	$0.0645497\pi$
$691$			10.5885i			0.402804i	−0.979509	+	0.201402i	$0.935450\pi$
$692$	17.3205	+	17.3205i	0.658427	+	0.658427i
$693$	32.7846	−	28.3923i	1.24538	−	1.07853i
$694$		−	40.5167i		−	1.53799i
$695$	13.8564	+	6.92820i	0.525603	+	0.262802i
$696$	4.39230	+	4.39230i	0.166490	+	0.166490i
$697$	5.07180	−	5.07180i	0.192108	−	0.192108i
$698$	−63.6769	−	17.0622i	−2.41021	−	0.645813i
$699$	−20.4904	−	5.49038i	−0.775017	−	0.207665i
$700$	16.9641	+	15.4019i	0.641183	+	0.582138i
$701$	−47.4641			−1.79269			−0.896347	−	0.443353i	$-0.853789\pi$
$701$	−47.4641			−1.79269			−0.896347	+	0.443353i	$0.853789\pi$
$702$	19.3923	−	33.5885i	0.731915	−	1.26771i
$703$	13.3923	+	3.58846i	0.505100	+	0.135341i
$704$	−27.1244	−	15.6603i	−1.02229	−	0.590218i
$705$	48.2942	−	16.0981i	1.81887	−	0.606289i
$706$	18.5885	+	10.7321i	0.699586	+	0.403906i
$707$	45.6962	−	8.79423i	1.71858	−	0.330741i
$708$	−5.19615	+	9.00000i	−0.195283	+	0.338241i
$709$		−	6.71281i		−	0.252105i	−0.992024	−	0.126052i	$-0.959769\pi$
$709$		−	6.71281i		−	0.252105i	0.992024	−	0.126052i	$-0.0402308\pi$
$710$	−19.3923	−	17.1962i	−0.727780	−	0.645360i
$711$	−11.7846	+	6.80385i	−0.441957	+	0.255164i
$712$	−4.59808	+	1.23205i	−0.172320	+	0.0461731i
$713$	0.901924	+	0.241670i	0.0337773	+	0.00905060i
$714$	−16.3923	−	18.9282i	−0.613467	−	0.708370i
$715$	9.46410	−	46.2487i	0.353937	−	1.72960i
$716$	−10.9019	−	18.8827i	−0.407424	−	0.705679i
$717$	−19.0526	−	33.0000i	−0.711531	−	1.23241i
$718$	−38.6865	+	10.3660i	−1.44377	+	0.386857i
$719$	15.5622	−	26.9545i	0.580371	−	1.00523i	−0.415064	−	0.909792i	$-0.636241\pi$
$719$	15.5622	−	26.9545i	0.580371	−	1.00523i	0.995435	−	0.0954403i	$-0.0304259\pi$
$720$	24.9904	−	16.5000i	0.931337	−	0.614919i
$721$	9.76795	−	4.74167i	0.363777	−	0.176589i
$722$	−15.5263	−	4.16025i	−0.577828	−	0.154829i
$723$	8.25833	+	14.3038i	0.307131	+	0.531966i
$724$	19.8564			0.737958
$725$	27.7128	−	20.7846i	1.02923	−	0.771921i
$726$	44.6147	+	44.6147i	1.65581	+	1.65581i
$727$	1.37564	−	5.13397i	0.0510198	−	0.190409i	−0.935713	−	0.352763i	$-0.885242\pi$
$727$	1.37564	−	5.13397i	0.0510198	−	0.190409i	0.986732	+	0.162355i	$0.0519088\pi$
$728$	−1.00000	−	5.19615i	−0.0370625	−	0.192582i
$729$	−27.0000			−1.00000
$730$	−21.7583	−	32.9545i	−0.805312	−	1.21970i
$731$	−3.80385	−	2.19615i	−0.140690	−	0.0812276i
$732$	−29.5981	−	17.0885i	−1.09398	−	0.631608i
$733$	−21.3923	−	5.73205i	−0.790143	−	0.211718i	−0.158891	−	0.987296i	$-0.550792\pi$
$733$	−21.3923	−	5.73205i	−0.790143	−	0.211718i	−0.631252	+	0.775578i	$0.717459\pi$
$734$	6.59808	−	11.4282i	0.243539	−	0.421823i
$735$	−22.2679	−	15.4641i	−0.821366	−	0.570402i
$736$	18.0622	+	31.2846i	0.665781	+	1.15317i
$737$	−1.80385	−	6.73205i	−0.0664456	−	0.247978i
$738$	10.3923	+	10.3923i	0.382546	+	0.382546i
$739$	−21.1244	+	12.1962i	−0.777072	+	0.448643i	−0.835392	−	0.549655i	$-0.814759\pi$
$739$	−21.1244	+	12.1962i	−0.777072	+	0.448643i	0.0583196	+	0.998298i	$0.481426\pi$
$740$	−5.19615	−	15.5885i	−0.191014	−	0.573043i
$741$	15.4641	+	15.4641i	0.568088	+	0.568088i
$742$	−30.4904	−	10.5622i	−1.11934	−	0.387750i
$743$	8.83013	−	2.36603i	0.323946	−	0.0868011i	−0.0931813	−	0.995649i	$-0.529704\pi$
$743$	8.83013	−	2.36603i	0.323946	−	0.0868011i	0.417127	+	0.908848i	$0.363037\pi$
$744$	0.169873	−	0.0455173i	0.00622785	−	0.00166875i
$745$	−4.11474	−	6.23205i	−0.150752	−	0.228325i
$746$	4.09808	+	7.09808i	0.150041	+	0.259879i
$747$	−1.09808	−	4.09808i	−0.0401765	−	0.149941i
$748$	18.9282	−	18.9282i	0.692084	−	0.692084i
$749$	−5.36603	−	3.63397i	−0.196070	−	0.132783i
$750$	−15.9904	−	33.8205i	−0.583886	−	1.23495i
$751$	23.5622	+	40.8109i	0.859796	+	1.48921i	0.872123	+	0.489286i	$0.162743\pi$
$751$	23.5622	+	40.8109i	0.859796	+	1.48921i	−0.0123270	+	0.999924i	$0.503924\pi$
$752$	41.4904	+	41.4904i	1.51300	+	1.51300i
$753$	5.07180	−	8.78461i	0.184827	−	0.320129i
$754$	51.7128			1.88327
$755$	9.46410	+	4.73205i	0.344434	+	0.172217i
$756$	18.0000	−	15.5885i	0.654654	−	0.566947i
$757$	−8.26795	+	8.26795i	−0.300504	+	0.300504i	−0.841211	−	0.540707i	$-0.818157\pi$
$757$	−8.26795	+	8.26795i	−0.300504	+	0.300504i	0.540707	+	0.841211i	$0.318157\pi$
$758$	−17.1244	−	17.1244i	−0.621985	−	0.621985i
$759$	−11.6603	−	43.5167i	−0.423240	−	1.57955i
$760$	1.19615	+	3.58846i	0.0433890	+	0.130167i
$761$	16.9641	−	9.79423i	0.614948	−	0.355041i	−0.159951	−	0.987125i	$-0.551134\pi$
$761$	16.9641	−	9.79423i	0.614948	−	0.355041i	0.774900	+	0.632084i	$0.217800\pi$
$762$	37.2846	−	64.5788i	1.35068	−	2.33944i
$763$	−1.73205	+	5.00000i	−0.0627044	+	0.181012i
$764$			30.5885i			1.10665i
$765$	6.00000	+	18.0000i	0.216930	+	0.650791i
$766$	−27.3564	+	15.7942i	−0.988427	+	0.570669i
$767$	−3.46410	−	12.9282i	−0.125081	−	0.466810i
$768$	29.0885	+	16.7942i	1.04964	+	0.606010i
$769$	−7.99038	+	13.8397i	−0.288141	+	0.499074i	−0.973366	−	0.229257i	$-0.926370\pi$
$769$	−7.99038	+	13.8397i	−0.288141	+	0.499074i	0.685225	+	0.728331i	$0.259704\pi$
$770$	31.8564	−	53.7128i	1.14803	−	1.93568i
$771$	15.2487	−	15.2487i	0.549169	−	0.549169i
$772$	−25.0526	+	25.0526i	−0.901661	+	0.901661i
$773$	−7.02628	−	1.88269i	−0.252718	−	0.0677155i	0.130236	−	0.991483i	$-0.458426\pi$
$773$	−7.02628	−	1.88269i	−0.252718	−	0.0677155i	−0.382954	+	0.923768i	$0.625093\pi$
$774$	4.50000	−	7.79423i	0.161749	−	0.280158i
$775$	−0.117314	−	0.973721i	−0.00421405	−	0.0349771i
$776$	−3.63397	+	2.09808i	−0.130452	+	0.0753165i
$777$	8.49038	+	17.4904i	0.304591	+	0.627464i
$778$	2.23205	−	0.598076i	0.0800229	−	0.0214421i
$779$	−7.17691	+	4.14359i	−0.257140	+	0.148460i
$780$	5.19615	−	25.3923i	0.186052	−	0.909190i
$781$	−16.3923	+	28.3923i	−0.586563	+	1.01596i
$782$	−25.1244	+	6.73205i	−0.898445	+	0.240738i
$783$	−18.0000	−	31.1769i	−0.643268	−	1.11417i
$784$	4.46410	−	30.9282i	0.159432	−	1.10458i
$785$	−2.09808	+	2.36603i	−0.0748836	+	0.0844471i
$786$	12.0000	−	12.0000i	0.428026	−	0.428026i
$787$	−11.2942	−	11.2942i	−0.402596	−	0.402596i	0.476551	−	0.879147i	$-0.341887\pi$
$787$	−11.2942	−	11.2942i	−0.402596	−	0.402596i	−0.879147	+	0.476551i	$0.841887\pi$
$788$	30.2487	+	30.2487i	1.07757	+	1.07757i
$789$	47.5526	+	12.7417i	1.69292	+	0.453615i
$790$	−13.0000	+	14.6603i	−0.462519	+	0.521588i
$791$	−10.9019	+	16.0981i	−0.387628	+	0.572382i
$792$	−6.00000	−	6.00000i	−0.213201	−	0.213201i
$793$	42.5167	−	11.3923i	1.50981	−	0.404553i
$794$	−32.7846	+	56.7846i	−1.16348	+	2.01521i
$795$	18.2942	+	16.2224i	0.648829	+	0.575350i
$796$	−11.7846	+	6.80385i	−0.417694	+	0.241156i
$797$	−37.6147	+	10.0788i	−1.33238	+	0.357011i	−0.853603	−	0.520924i	$-0.825587\pi$
$797$	−37.6147	+	10.0788i	−1.33238	+	0.357011i	−0.478780	+	0.877935i	$0.658921\pi$
$798$	12.6340	+	26.0263i	0.447238	+	0.921320i
$799$	−32.1962	+	18.5885i	−1.13902	+	0.657612i
$800$	23.4282	−	29.8468i	0.828312	−	1.05524i
$801$	27.5885			0.974790
$802$	43.6506	+	11.6962i	1.54136	+	0.413005i
$803$	−35.3205	+	35.3205i	−1.24643	+	1.24643i
$804$	−0.990381	−	3.69615i	−0.0349280	−	0.130353i
$805$	−24.5526	+	13.7942i	−0.865364	+	0.486183i
$806$	0.732051	−	1.26795i	0.0257854	−	0.0446616i
$807$			17.1962i			0.605333i
$808$	−2.35641	−	8.79423i	−0.0828981	−	0.309380i
$809$	36.4019	−	21.0167i	1.27982	−	0.738906i	0.303008	−	0.952988i	$-0.402009\pi$
$809$	36.4019	−	21.0167i	1.27982	−	0.738906i	0.976816	+	0.214082i	$0.0686759\pi$
$810$	−36.8827	+	12.2942i	−1.29593	+	0.431975i
$811$			1.85641i			0.0651872i	0.999469	+	0.0325936i	$0.0103767\pi$
$811$			1.85641i			0.0651872i	−0.999469	+	0.0325936i	$0.989623\pi$
$812$	30.0000	+	10.3923i	1.05279	+	0.364698i
$813$	−9.92820	−	17.1962i	−0.348197	−	0.603095i
$814$	−38.7846	+	22.3923i	−1.35940	+	0.784850i
$815$	6.46410	+	19.3923i	0.226428	+	0.679283i
$816$	−15.4641	+	15.4641i	−0.541352	+	0.541352i
$817$	3.58846	+	3.58846i	0.125544	+	0.125544i
$818$	−7.36603	+	7.36603i	−0.257547	+	0.257547i
$819$	−2.19615	+	30.5885i	−0.0767398	+	1.06885i
$820$	8.78461	+	4.39230i	0.306772	+	0.153386i
$821$	−24.6603			−0.860649			−0.430324	−	0.902674i	$-0.641601\pi$
$821$	−24.6603			−0.860649			−0.430324	+	0.902674i	$0.641601\pi$
$822$	−3.46410	−	6.00000i	−0.120824	−	0.209274i
$823$	−14.0718	−	14.0718i	−0.490512	−	0.490512i	0.417956	−	0.908468i	$-0.362747\pi$
$823$	−14.0718	−	14.0718i	−0.490512	−	0.490512i	−0.908468	+	0.417956i	$0.862747\pi$
$824$	−1.06218	−	1.83975i	−0.0370027	−	0.0640906i
$825$	−37.8564	+	28.3923i	−1.31799	+	0.988493i
$826$	1.26795	−	17.6603i	0.0441176	−	0.614479i
$827$	21.3923	−	21.3923i	0.743883	−	0.743883i	−0.229440	−	0.973323i	$-0.573689\pi$
$827$	21.3923	−	21.3923i	0.743883	−	0.743883i	0.973323	+	0.229440i	$0.0736893\pi$
$828$	−6.40192	−	23.8923i	−0.222482	−	0.830315i
$829$	22.1603	+	38.3827i	0.769657	+	1.33309i	0.937749	+	0.347314i	$0.112906\pi$
$829$	22.1603	+	38.3827i	0.769657	+	1.33309i	−0.168091	+	0.985771i	$0.553760\pi$
$830$	−3.36603	−	5.09808i	−0.116836	−	0.176957i
$831$	9.00000	−	33.5885i	0.312207	−	1.16517i
$832$	21.3923	−	5.73205i	0.741645	−	0.198723i
$833$	18.1962	+	7.80385i	0.630459	+	0.270387i
$834$	6.00000	−	22.3923i	0.207763	−	0.775382i
$835$	−9.90192	−	29.7058i	−0.342670	−	1.02801i
$836$	−26.7846	+	15.4641i	−0.926365	+	0.534837i
$837$	−1.01924			−0.0352300
$838$	−4.00000	−	14.9282i	−0.138178	−	0.515686i
$839$	−0.0262794	−	0.0455173i	−0.000907267	−	0.00157143i	0.865571	−	0.500786i	$-0.166955\pi$
$839$	−0.0262794	−	0.0455173i	−0.000907267	−	0.00157143i	−0.866479	+	0.499214i	$0.833622\pi$
$840$	−2.70577	+	4.56218i	−0.0933580	+	0.157410i
$841$	9.50000	−	16.4545i	0.327586	−	0.567396i
$842$	43.0167	+	11.5263i	1.48245	+	0.397222i
$843$			23.7846i			0.819185i
$844$	13.3923	+	7.73205i	0.460982	+	0.266148i
$845$	2.37564	+	3.59808i	0.0817247	+	0.123778i
$846$	−38.0885	−	65.9711i	−1.30951	−	2.26813i
$847$	−47.1410	−	16.3301i	−1.61978	−	0.561110i
$848$	−7.29423	+	27.2224i	−0.250485	+	0.934822i
$849$	37.2846	−	9.99038i	1.27960	−	0.342869i
$850$	16.3923	+	21.8564i	0.562251	+	0.749669i
$851$	20.1962			0.692315
$852$	−9.00000	+	15.5885i	−0.308335	+	0.534052i
$853$	40.5167	+	10.8564i	1.38726	+	0.371716i	0.873754	−	0.486368i	$-0.161678\pi$
$853$	40.5167	+	10.8564i	1.38726	+	0.371716i	0.513510	+	0.858084i	$0.328345\pi$
$854$	58.0788	+	4.16987i	1.98742	+	0.142690i
$855$	−1.31347	−	21.8827i	−0.0449196	−	0.748372i
$856$	−0.633975	+	1.09808i	−0.0216688	+	0.0375315i
$857$	28.7583	−	7.70577i	0.982366	−	0.263224i	0.268325	−	0.963328i	$-0.413530\pi$
$857$	28.7583	−	7.70577i	0.982366	−	0.263224i	0.714041	+	0.700104i	$0.246863\pi$
$858$	−70.6410			−2.41164
$859$	21.4904	+	37.2224i	0.733242	+	1.27001i	0.955490	+	0.295023i	$0.0953272\pi$
$859$	21.4904	+	37.2224i	0.733242	+	1.27001i	−0.222248	+	0.974990i	$0.571339\pi$
$860$	1.20577	−	5.89230i	0.0411165	−	0.200926i
$861$	−10.9808	−	3.80385i	−0.374223	−	0.129635i
$862$	−45.1506	−	12.0981i	−1.53784	−	0.412062i
$863$	24.4282	−	6.54552i	0.831546	−	0.222812i	0.182158	−	0.983269i	$-0.441692\pi$
$863$	24.4282	−	6.54552i	0.831546	−	0.222812i	0.649388	+	0.760457i	$0.275025\pi$
$864$	−27.8827	−	27.8827i	−0.948588	−	0.948588i
$865$	23.6603	+	20.9808i	0.804473	+	0.713367i
$866$			26.7846i			0.910178i
$867$	7.79423	+	13.5000i	0.264706	+	0.458484i
$868$	0.679492	−	0.588457i	0.0230635	−	0.0199735i
$869$	21.4641	+	12.3923i	0.728120	+	0.420380i
$870$	−38.7846	−	34.3923i	−1.31492	−	1.16601i
$871$	4.26795	+	2.46410i	0.144614	+	0.0834929i
$872$	1.00000	+	0.267949i	0.0338643	+	0.00907390i
$873$	23.4904	−	6.29423i	0.795029	−	0.213027i
$874$	30.0526			1.01654
$875$	23.0526	+	18.5359i	0.779319	+	0.626628i
$876$	−19.3923	+	19.3923i	−0.655205	+	0.655205i
$877$	−11.5622	−	3.09808i	−0.390427	−	0.104615i	0.0582648	−	0.998301i	$-0.481443\pi$
$877$	−11.5622	−	3.09808i	−0.390427	−	0.104615i	−0.448692	+	0.893687i	$0.648110\pi$
$878$	8.00000	−	8.00000i	0.269987	−	0.269987i
$879$	−9.41858	+	35.1506i	−0.317681	+	1.18560i
$880$	−48.7846	−	24.3923i	−1.64453	−	0.822264i
$881$			17.7846i			0.599179i	0.954068	+	0.299589i	$0.0968497\pi$
$881$			17.7846i			0.599179i	−0.954068	+	0.299589i	$0.903150\pi$
$882$	−15.9904	+	37.2846i	−0.538424	+	1.25544i
$883$	−24.5429	−	24.5429i	−0.825936	−	0.825936i	0.161016	−	0.986952i	$-0.448523\pi$
$883$	−24.5429	−	24.5429i	−0.825936	−	0.825936i	−0.986952	+	0.161016i	$0.948523\pi$
$884$			18.9282i			0.636624i
$885$	−6.00000	+	12.0000i	−0.201688	+	0.403376i
$886$	1.80385			0.0606014
$887$	4.76795	−	17.7942i	0.160092	−	0.597472i	−0.838523	−	0.544866i	$-0.816581\pi$
$887$	4.76795	−	17.7942i	0.160092	−	0.597472i	0.998615	−	0.0526060i	$-0.0167527\pi$
$888$	3.29423	−	1.90192i	0.110547	−	0.0638244i
$889$	−4.22243	+	58.8109i	−0.141616	+	1.97245i
$890$	37.6865	−	12.5622i	1.26326	−	0.421085i
$891$	24.5885	+	42.5885i	0.823744	+	1.42677i
$892$	2.30385	−	8.59808i	0.0771385	−	0.287885i
$893$	41.4904	−	11.1173i	1.38842	−	0.372027i
$894$	−7.90192	+	7.90192i	−0.264280	+	0.264280i
$895$	−15.5096	−	23.4904i	−0.518429	−	0.785197i
$896$	−10.8301	−	0.777568i	−0.361809	−	0.0259767i
$897$	27.5885	+	15.9282i	0.921152	+	0.531827i
$898$	−2.16987	−	2.16987i	−0.0724096	−	0.0724096i
$899$	−0.679492	−	1.17691i	−0.0226623	−	0.0392523i
$900$	−20.7846	+	15.5885i	−0.692820	+	0.519615i
$901$	−15.4641	−	8.92820i	−0.515184	−	0.297442i
$902$	6.92820	−	25.8564i	0.230684	−	0.860924i
$903$	−0.509619	+	7.09808i	−0.0169591	+	0.236209i
$904$	3.29423	+	1.90192i	0.109564	+	0.0632570i
$905$	25.5885	−	1.53590i	0.850589	−	0.0510550i
$906$	4.09808	−	15.2942i	0.136149	−	0.508117i
$907$	5.43782	+	20.2942i	0.180560	+	0.673859i	0.995538	+	0.0943664i	$0.0300825\pi$
$907$	5.43782	+	20.2942i	0.180560	+	0.673859i	−0.814978	+	0.579492i	$0.803251\pi$
$908$	6.75833	+	25.2224i	0.224283	+	0.837036i
$909$			52.7654i			1.75012i
$910$	10.9282	+	42.7846i	0.362266	+	1.41830i
$911$	−7.43782	−	12.8827i	−0.246426	−	0.426822i	0.716106	−	0.697992i	$-0.245923\pi$
$911$	−7.43782	−	12.8827i	−0.246426	−	0.426822i	−0.962532	+	0.271170i	$0.912590\pi$
$912$	21.8827	−	12.6340i	0.724608	−	0.418353i
$913$	−5.46410	+	5.46410i	−0.180835	+	0.180835i
$914$		−	20.0526i		−	0.663280i
$915$	−39.4641	−	19.7321i	−1.30464	−	0.652321i
$916$	−6.99038	+	4.03590i	−0.230969	+	0.133350i
$917$	−4.39230	+	12.6795i	−0.145047	+	0.418714i
$918$	24.5885	−	14.1962i	0.811540	−	0.468543i
$919$	−45.3731	−	26.1962i	−1.49672	−	0.864131i	−0.496727	−	0.867907i	$-0.665465\pi$
$919$	−45.3731	−	26.1962i	−1.49672	−	0.864131i	−0.999993	+	0.00377579i	$0.998798\pi$
$920$	3.03590	+	4.59808i	0.100091	+	0.151594i
$921$	−11.1173	−	41.4904i	−0.366328	−	1.36715i
$922$	−0.598076	+	2.23205i	−0.0196966	+	0.0735087i
$923$	−6.00000	−	22.3923i	−0.197492	−	0.737052i
$924$	−40.9808	−	14.1962i	−1.34817	−	0.467019i
$925$	−7.90192	−	19.6865i	−0.259814	−	0.647289i
$926$	−35.1865	+	60.9449i	−1.15630	+	2.00277i
$927$	3.18653	+	11.8923i	0.104659	+	0.390595i
$928$	13.6077	−	50.7846i	0.446694	−	1.66709i
$929$	−36.3205			−1.19164			−0.595819	−	0.803119i	$-0.703172\pi$
$929$	−36.3205			−1.19164			−0.595819	+	0.803119i	$0.703172\pi$
$930$	−1.39230	+	0.464102i	−0.0456555	+	0.0152185i
$931$	−17.9737	−	14.1506i	−0.589065	−	0.463768i
$932$	5.49038	+	20.4904i	0.179843	+	0.671185i
$933$	−13.8564	+	24.0000i	−0.453638	+	0.785725i
$934$	−12.9641	+	22.4545i	−0.424198	+	0.734733i
$935$	22.9282	−	25.8564i	0.749832	−	0.845595i
$936$	6.00000			0.196116
$937$	−9.46410	−	9.46410i	−0.309179	−	0.309179i	0.535412	−	0.844591i	$-0.320156\pi$
$937$	−9.46410	−	9.46410i	−0.309179	−	0.309179i	−0.844591	+	0.535412i	$0.820156\pi$
$938$	4.26795	+	4.92820i	0.139353	+	0.160912i
$939$	12.2942	−	3.29423i	0.401207	−	0.107503i
$940$	−38.0885	−	33.7750i	−1.24231	−	1.10162i
$941$			37.9808i			1.23814i	0.785337	+	0.619069i	$0.212490\pi$
$941$			37.9808i			1.23814i	−0.785337	+	0.619069i	$0.787510\pi$
$942$	4.09808	+	2.36603i	0.133523	+	0.0770893i
$943$	−8.53590	+	8.53590i	−0.277967	+	0.277967i
$944$	−15.4641			−0.503314
$945$	21.9904	−	21.4808i	0.715347	−	0.698769i
$946$	−16.3923			−0.532960
$947$	18.2224	−	18.2224i	0.592149	−	0.592149i	−0.346062	−	0.938212i	$-0.612481\pi$
$947$	18.2224	−	18.2224i	0.592149	−	0.592149i	0.938212	+	0.346062i	$0.112481\pi$
$948$	11.7846	+	6.80385i	0.382746	+	0.220979i
$949$		−	35.3205i		−	1.14655i
$950$	−11.7583	−	29.2942i	−0.381491	−	0.950430i
$951$	20.0263	−	5.36603i	0.649397	−	0.174005i
$952$	1.26795	−	3.66025i	0.0410945	−	0.118630i
$953$	21.0000	+	21.0000i	0.680257	+	0.680257i	0.960058	−	0.279801i	$-0.0902686\pi$
$953$	21.0000	+	21.0000i	0.680257	+	0.680257i	−0.279801	+	0.960058i	$0.590269\pi$
$954$	18.2942	−	31.6865i	0.592298	−	1.02589i
$955$	2.36603	+	39.4186i	0.0765628	+	1.27556i
$956$	−19.0526	+	33.0000i	−0.616204	+	1.06730i
$957$	−32.7846	+	56.7846i	−1.05978	+	1.83559i
$958$	2.63397	+	9.83013i	0.0850999	+	0.317597i
$959$	4.53590	+	3.07180i	0.146472	+	0.0991935i
$960$	−19.8564	−	9.92820i	−0.640863	−	0.320431i
$961$	30.9615			0.998759
$962$	8.19615	−	30.5885i	0.264255	−	0.986211i
$963$	5.19615	−	5.19615i	0.167444	−	0.167444i
$964$	8.25833	−	14.3038i	0.265983	−	0.460696i
$965$	−30.3468	+	34.2224i	−0.976898	+	1.10166i
$966$	27.5885	+	31.8564i	0.887644	+	1.02496i
$967$	0.447441	+	1.66987i	0.0143887	+	0.0536995i	0.972747	−	0.231869i	$-0.0744842\pi$
$967$	0.447441	+	1.66987i	0.0143887	+	0.0536995i	−0.958358	+	0.285569i	$0.907817\pi$
$968$	−2.52628	+	9.42820i	−0.0811977	+	0.303034i
$969$	4.14359	+	15.4641i	0.133111	+	0.496779i
$970$	29.2224	−	19.2942i	0.938276	−	0.619500i
$971$	−2.53590	−	1.46410i	−0.0813809	−	0.0469853i	0.458757	−	0.888562i	$-0.348295\pi$
$971$	−2.53590	−	1.46410i	−0.0813809	−	0.0469853i	−0.540138	+	0.841576i	$0.681628\pi$
$972$	13.5000	+	23.3827i	0.433013	+	0.750000i
$973$	3.46410	+	18.0000i	0.111054	+	0.577054i
$974$	56.1506	−	32.4186i	1.79918	−	1.03876i
$975$	4.73205	−	33.1244i	0.151547	−	1.06083i
$976$		−	50.8564i		−	1.62787i
$977$	−33.1769	+	33.1769i	−1.06142	+	1.06142i	−0.0634377	+	0.997986i	$0.520206\pi$
$977$	−33.1769	+	33.1769i	−1.06142	+	1.06142i	−0.997986	+	0.0634377i	$0.979794\pi$
$978$	26.4904	−	15.2942i	0.847069	−	0.489056i
$979$	−25.1244	−	43.5167i	−0.802978	−	1.39080i
$980$	−2.25833	+	27.0167i	−0.0721397	+	0.863016i
$981$	−5.19615	−	3.00000i	−0.165900	−	0.0957826i
$982$	8.46410	+	31.5885i	0.270100	+	1.00803i
$983$	−0.954483	−	3.56218i	−0.0304433	−	0.113616i	0.949032	−	0.315179i	$-0.102065\pi$
$983$	−0.954483	−	3.56218i	−0.0304433	−	0.113616i	−0.979476	+	0.201563i	$0.935398\pi$
$984$	−0.588457	+	2.19615i	−0.0187593	+	0.0700108i
$985$	41.3205	+	36.6410i	1.31658	+	1.16748i
$986$	32.7846	+	18.9282i	1.04407	+	0.602797i
$987$	49.8731	+	33.7750i	1.58748	+	1.07507i
$988$	5.66025	−	21.1244i	0.180077	−	0.672055i
$989$	6.40192	+	3.69615i	0.203569	+	0.117531i
$990$	52.9808	+	46.9808i	1.68384	+	1.49315i
$991$	8.73205	+	15.1244i	0.277383	+	0.480441i	0.970734	−	0.240159i	$-0.0771997\pi$
$991$	8.73205	+	15.1244i	0.277383	+	0.480441i	−0.693351	+	0.720600i	$0.743866\pi$
$992$	−1.05256	−	1.05256i	−0.0334188	−	0.0334188i
$993$	27.5096	+	15.8827i	0.872991	+	0.504022i
$994$	2.19615	−	30.5885i	0.0696577	−	0.970207i
$995$	−14.6603	+	9.67949i	−0.464761	+	0.306861i
$996$	−3.00000	+	3.00000i	−0.0950586	+	0.0950586i
$997$	−43.6865	+	11.7058i	−1.38357	+	0.370725i	−0.872415	−	0.488765i	$-0.837447\pi$
$997$	−43.6865	+	11.7058i	−1.38357	+	0.370725i	−0.511151	+	0.859491i	$0.670781\pi$
$998$	−3.53590	+	13.1962i	−0.111927	+	0.417717i
$999$	−21.2942	+	5.70577i	−0.673720	+	0.180523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bs.c.103.1	yes	4
3.2	odd	2		945.2.bv.d.523.1		4
5.2	odd	4		315.2.bs.b.292.1	yes	4
7.3	odd	6		315.2.cg.a.283.1	yes	4
9.2	odd	6		945.2.cj.a.208.1		4
9.7	even	3		315.2.cg.c.313.1	yes	4
15.2	even	4		945.2.bv.a.712.1		4
21.17	even	6		945.2.cj.d.388.1		4
35.17	even	12		315.2.cg.c.157.1	yes	4
45.2	even	12		945.2.cj.d.397.1		4
45.7	odd	12		315.2.cg.a.187.1	yes	4
63.38	even	6		945.2.bv.a.73.1		4
63.52	odd	6		315.2.bs.b.178.1	✓	4
105.17	odd	12		945.2.cj.a.577.1		4
315.52	even	12	inner	315.2.bs.c.52.1	yes	4
315.227	odd	12		945.2.bv.d.262.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.b.178.1	✓	4	63.52	odd	6
315.2.bs.b.292.1	yes	4	5.2	odd	4
315.2.bs.c.52.1	yes	4	315.52	even	12	inner
315.2.bs.c.103.1	yes	4	1.1	even	1	trivial
315.2.cg.a.187.1	yes	4	45.7	odd	12
315.2.cg.a.283.1	yes	4	7.3	odd	6
315.2.cg.c.157.1	yes	4	35.17	even	12
315.2.cg.c.313.1	yes	4	9.7	even	3
945.2.bv.a.73.1		4	63.38	even	6
945.2.bv.a.712.1		4	15.2	even	4
945.2.bv.d.262.1		4	315.227	odd	12
945.2.bv.d.523.1		4	3.2	odd	2
945.2.cj.a.208.1		4	9.2	odd	6
945.2.cj.a.577.1		4	105.17	odd	12
945.2.cj.d.388.1		4	21.17	even	6
945.2.cj.d.397.1		4	45.2	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)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 1.36603i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-0.133975 - 2.23205i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 1.36603i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-0.133975 - 2.23205i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(1.50000 + 2.59808i) q^{9} +(3.23205 + 2.86603i) q^{10} +(2.73205 - 4.73205i) q^{11} +(1.50000 - 2.59808i) q^{12} +(1.00000 + 3.73205i) q^{13} +(-0.366025 + 5.09808i) q^{14} +(1.73205 - 3.46410i) q^{15} +4.46410 q^{16} +(-0.732051 + 2.73205i) q^{17} +(-5.59808 - 1.50000i) q^{18} +(1.63397 - 2.83013i) q^{19} +(-3.86603 + 0.232051i) q^{20} +(4.50000 - 0.866025i) q^{21} +(2.73205 + 10.1962i) q^{22} +(1.23205 - 4.59808i) q^{23} +(-0.232051 - 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(-6.46410 - 3.73205i) q^{26} +5.19615i q^{27} +(-3.00000 - 3.46410i) q^{28} +(-6.00000 + 3.46410i) q^{29} +(2.36603 + 7.09808i) q^{30} +0.196152i q^{31} +(-5.36603 + 5.36603i) q^{32} +(8.19615 - 4.73205i) q^{33} +(-2.73205 - 4.73205i) q^{34} +(-4.13397 - 4.23205i) q^{35} +(4.50000 - 2.59808i) q^{36} +(1.09808 + 4.09808i) q^{37} +(1.63397 + 6.09808i) q^{38} +(-1.73205 + 6.46410i) q^{39} +(-0.767949 + 0.866025i) q^{40} +(-2.19615 - 1.26795i) q^{41} +(-4.96410 + 7.33013i) q^{42} +(-0.401924 + 1.50000i) q^{43} +(-8.19615 - 4.73205i) q^{44} +(5.59808 - 3.69615i) q^{45} +(4.59808 + 7.96410i) q^{46} +(9.29423 + 9.29423i) q^{47} +(6.69615 + 3.86603i) q^{48} +(1.00000 - 6.92820i) q^{49} +(5.96410 - 7.59808i) q^{50} +(-3.46410 + 3.46410i) q^{51} +(6.46410 - 1.73205i) q^{52} +(-1.63397 + 6.09808i) q^{53} +(-7.09808 - 7.09808i) q^{54} +(-10.9282 - 5.46410i) q^{55} +(-1.36603 - 0.0980762i) q^{56} +(4.90192 - 2.83013i) q^{57} +(3.46410 - 12.9282i) q^{58} -3.46410 q^{59} +(-6.00000 - 3.00000i) q^{60} -11.3923i q^{61} +(-0.267949 - 0.267949i) q^{62} +(7.50000 + 2.59808i) q^{63} -5.73205i q^{64} +(8.19615 - 2.73205i) q^{65} +(-4.73205 + 17.6603i) q^{66} +(0.901924 - 0.901924i) q^{67} +(4.73205 + 1.26795i) q^{68} +(5.83013 - 5.83013i) q^{69} +(11.4282 + 0.133975i) q^{70} -6.00000 q^{71} +(0.401924 - 1.50000i) q^{72} +(-8.83013 - 2.36603i) q^{73} +(-7.09808 - 4.09808i) q^{74} +(-7.96410 - 3.40192i) q^{75} +(-4.90192 - 2.83013i) q^{76} +(-2.73205 - 14.1962i) q^{77} +(-6.46410 - 11.1962i) q^{78} +4.53590i q^{79} +(-0.598076 - 9.96410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.73205 - 1.26795i) q^{82} +(-1.36603 - 0.366025i) q^{83} +(-1.50000 - 7.79423i) q^{84} +(6.19615 + 1.26795i) q^{85} +(-1.50000 - 2.59808i) q^{86} -12.0000 q^{87} +(-2.73205 + 0.732051i) q^{88} +(4.59808 - 7.96410i) q^{89} +(-2.59808 + 12.6962i) q^{90} +(8.46410 + 5.73205i) q^{91} +(-7.96410 - 2.13397i) q^{92} +(-0.169873 + 0.294229i) q^{93} -25.3923 q^{94} +(-6.53590 - 3.26795i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(2.09808 - 7.83013i) q^{97} +(8.09808 + 10.8301i) q^{98} +16.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 2 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 2 q^{8} + 6 q^{9} + 6 q^{10} + 4 q^{11} + 6 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{16} + 4 q^{17} - 12 q^{18} + 10 q^{19} - 12 q^{20} + 18 q^{21} + 4 q^{22} - 2 q^{23} + 6 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 24 q^{29} + 6 q^{30} - 18 q^{32} + 12 q^{33} - 4 q^{34} - 20 q^{35} + 18 q^{36} - 6 q^{37} + 10 q^{38} - 10 q^{40} + 12 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{44} + 12 q^{45} + 8 q^{46} + 6 q^{47} + 6 q^{48} + 4 q^{49} + 10 q^{50} + 12 q^{52} - 10 q^{53} - 18 q^{54} - 16 q^{55} - 2 q^{56} + 30 q^{57} - 24 q^{60} - 8 q^{62} + 30 q^{63} + 12 q^{65} - 12 q^{66} + 14 q^{67} + 12 q^{68} + 6 q^{69} + 18 q^{70} - 24 q^{71} + 12 q^{72} - 18 q^{73} - 18 q^{74} - 18 q^{75} - 30 q^{76} - 4 q^{77} - 12 q^{78} + 8 q^{80} - 18 q^{81} + 12 q^{82} - 2 q^{83} - 6 q^{84} + 4 q^{85} - 6 q^{86} - 48 q^{87} - 4 q^{88} + 8 q^{89} + 20 q^{91} - 18 q^{92} - 18 q^{93} - 60 q^{94} - 40 q^{95} - 30 q^{96} - 2 q^{97} + 22 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 2 * q^8 + 6 * q^9 + 6 * q^10 + 4 * q^11 + 6 * q^12 + 4 * q^13 + 2 * q^14 + 4 * q^16 + 4 * q^17 - 12 * q^18 + 10 * q^19 - 12 * q^20 + 18 * q^21 + 4 * q^22 - 2 * q^23 + 6 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 24 * q^29 + 6 * q^30 - 18 * q^32 + 12 * q^33 - 4 * q^34 - 20 * q^35 + 18 * q^36 - 6 * q^37 + 10 * q^38 - 10 * q^40 + 12 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^44 + 12 * q^45 + 8 * q^46 + 6 * q^47 + 6 * q^48 + 4 * q^49 + 10 * q^50 + 12 * q^52 - 10 * q^53 - 18 * q^54 - 16 * q^55 - 2 * q^56 + 30 * q^57 - 24 * q^60 - 8 * q^62 + 30 * q^63 + 12 * q^65 - 12 * q^66 + 14 * q^67 + 12 * q^68 + 6 * q^69 + 18 * q^70 - 24 * q^71 + 12 * q^72 - 18 * q^73 - 18 * q^74 - 18 * q^75 - 30 * q^76 - 4 * q^77 - 12 * q^78 + 8 * q^80 - 18 * q^81 + 12 * q^82 - 2 * q^83 - 6 * q^84 + 4 * q^85 - 6 * q^86 - 48 * q^87 - 4 * q^88 + 8 * q^89 + 20 * q^91 - 18 * q^92 - 18 * q^93 - 60 * q^94 - 40 * q^95 - 30 * q^96 - 2 * q^97 + 22 * q^98 + 24 * q^99

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