LMFDB - Embedded newform 315.2.bs.c.292.1

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			292.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.292
Dual form			315.2.bs.c.178.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-1.86603 - 1.23205i) q^{5} +(0.232051 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-1.86603 - 1.23205i) q^{5} +(0.232051 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.232051 - 1.13397i) q^{10} +(-0.732051 + 1.26795i) q^{11} +(1.50000 - 2.59808i) q^{12} +(1.00000 - 0.267949i) q^{13} +(1.36603 + 0.0980762i) q^{14} +(-1.73205 - 3.46410i) q^{15} -2.46410 q^{16} +(2.73205 + 0.732051i) q^{17} +(-0.401924 + 1.50000i) q^{18} +(3.36603 - 5.83013i) q^{19} +(-2.13397 + 3.23205i) q^{20} +(4.50000 - 0.866025i) q^{21} +(-0.732051 + 0.196152i) q^{22} +(-2.23205 - 0.598076i) q^{23} +(3.23205 - 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(0.464102 + 0.267949i) q^{26} +5.19615i q^{27} +(-3.00000 - 3.46410i) q^{28} +(-6.00000 + 3.46410i) q^{29} +(0.633975 - 1.90192i) q^{30} +10.1962i q^{31} +(-3.63397 - 3.63397i) q^{32} +(-2.19615 + 1.26795i) q^{33} +(0.732051 + 1.26795i) q^{34} +(-5.86603 + 0.767949i) q^{35} +(4.50000 - 2.59808i) q^{36} +(-4.09808 + 1.09808i) q^{37} +(3.36603 - 0.901924i) q^{38} +(1.73205 + 0.464102i) q^{39} +(-4.23205 + 0.866025i) q^{40} +(8.19615 + 4.73205i) q^{41} +(1.96410 + 1.33013i) q^{42} +(-5.59808 - 1.50000i) q^{43} +(2.19615 + 1.26795i) q^{44} +(0.401924 - 6.69615i) q^{45} +(-0.598076 - 1.03590i) q^{46} +(-6.29423 + 6.29423i) q^{47} +(-3.69615 - 2.13397i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-0.964102 + 2.40192i) q^{50} +(3.46410 + 3.46410i) q^{51} +(-0.464102 - 1.73205i) q^{52} +(-3.36603 - 0.901924i) q^{53} +(-1.90192 + 1.90192i) q^{54} +(2.92820 - 1.46410i) q^{55} +(0.366025 - 5.09808i) q^{56} +(10.0981 - 5.83013i) q^{57} +(-3.46410 - 0.928203i) q^{58} +3.46410 q^{59} +(-6.00000 + 3.00000i) q^{60} -9.39230i q^{61} +(-3.73205 + 3.73205i) q^{62} +(7.50000 + 2.59808i) q^{63} +2.26795i q^{64} +(-2.19615 - 0.732051i) q^{65} +(-1.26795 - 0.339746i) q^{66} +(6.09808 + 6.09808i) q^{67} +(1.26795 - 4.73205i) q^{68} +(-2.83013 - 2.83013i) q^{69} +(-2.42820 - 1.86603i) q^{70} -6.00000 q^{71} +(5.59808 + 1.50000i) q^{72} +(-0.169873 + 0.633975i) q^{73} +(-1.90192 - 1.09808i) q^{74} +(-1.03590 + 8.59808i) q^{75} +(-10.0981 - 5.83013i) q^{76} +(0.732051 + 3.80385i) q^{77} +(0.464102 + 0.803848i) q^{78} -11.4641i q^{79} +(4.59808 + 3.03590i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.26795 + 4.73205i) q^{82} +(0.366025 - 1.36603i) q^{83} +(-1.50000 - 7.79423i) q^{84} +(-4.19615 - 4.73205i) q^{85} +(-1.50000 - 2.59808i) q^{86} -12.0000 q^{87} +(0.732051 + 2.73205i) q^{88} +(-0.598076 + 1.03590i) q^{89} +(2.59808 - 2.30385i) q^{90} +(1.53590 - 2.26795i) q^{91} +(-1.03590 + 3.86603i) q^{92} +(-8.83013 + 15.2942i) q^{93} -4.60770 q^{94} +(-13.4641 + 6.73205i) q^{95} +(-2.30385 - 8.59808i) q^{96} +(-3.09808 - 0.830127i) q^{97} +(2.90192 - 2.16987i) q^{98} -4.39230 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	0.824574	−	0.565755i	$-0.191415\pi$
$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	−0.565755	+	0.824574i	$0.691415\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		−	1.73205i		−	0.866025i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$	0.232051	+	0.866025i	0.0947343	+	0.353553i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	1.36603	−	1.36603i	0.482963	−	0.482963i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−0.232051	−	1.13397i	−0.0733809	−	0.358594i
$11$	−0.732051	+	1.26795i	−0.220722	+	0.382301i	−0.955027	−	0.296518i	$-0.904175\pi$
$11$	−0.732051	+	1.26795i	−0.220722	+	0.382301i	0.734306	+	0.678819i	$0.237508\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	1.00000	−	0.267949i	0.277350	−	0.0743157i	−0.117463	−	0.993077i	$-0.537476\pi$
$13$	1.00000	−	0.267949i	0.277350	−	0.0743157i	0.394813	+	0.918762i	$0.370809\pi$
$14$	1.36603	+	0.0980762i	0.365086	+	0.0262120i
$15$	−1.73205	−	3.46410i	−0.447214	−	0.894427i
$16$	−2.46410			−0.616025
$17$	2.73205	+	0.732051i	0.662620	+	0.177548i	0.574428	−	0.818555i	$-0.305225\pi$
$17$	2.73205	+	0.732051i	0.662620	+	0.177548i	0.0881917	+	0.996104i	$0.471891\pi$
$18$	−0.401924	+	1.50000i	−0.0947343	+	0.353553i
$19$	3.36603	−	5.83013i	0.772219	−	1.33752i	−0.164125	−	0.986440i	$-0.552480\pi$
$19$	3.36603	−	5.83013i	0.772219	−	1.33752i	0.936344	−	0.351083i	$-0.114187\pi$
$20$	−2.13397	+	3.23205i	−0.477171	+	0.722709i
$21$	4.50000	−	0.866025i	0.981981	−	0.188982i
$22$	−0.732051	+	0.196152i	−0.156074	+	0.0418198i
$23$	−2.23205	−	0.598076i	−0.465415	−	0.124708i	0.0184884	−	0.999829i	$-0.494115\pi$
$23$	−2.23205	−	0.598076i	−0.465415	−	0.124708i	−0.483903	+	0.875122i	$0.660781\pi$
$24$	3.23205	−	0.866025i	0.659740	−	0.176777i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	0.464102	+	0.267949i	0.0910178	+	0.0525492i
$27$			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	$0.555755\pi$
$30$	0.633975	−	1.90192i	0.115747	−	0.347242i
$31$			10.1962i			1.83128i	0.401996	+	0.915642i	$0.368317\pi$
$31$			10.1962i			1.83128i	−0.401996	+	0.915642i	$0.631683\pi$
$32$	−3.63397	−	3.63397i	−0.642402	−	0.642402i
$33$	−2.19615	+	1.26795i	−0.382301	+	0.220722i
$34$	0.732051	+	1.26795i	0.125546	+	0.217451i
$35$	−5.86603	+	0.767949i	−0.991539	+	0.129807i
$36$	4.50000	−	2.59808i	0.750000	−	0.433013i
$37$	−4.09808	+	1.09808i	−0.673720	+	0.180523i	−0.579430	−	0.815022i	$-0.696725\pi$
$37$	−4.09808	+	1.09808i	−0.673720	+	0.180523i	−0.0942898	+	0.995545i	$0.530058\pi$
$38$	3.36603	−	0.901924i	0.546041	−	0.146311i
$39$	1.73205	+	0.464102i	0.277350	+	0.0743157i
$40$	−4.23205	+	0.866025i	−0.669146	+	0.136931i
$41$	8.19615	+	4.73205i	1.28002	+	0.739022i	0.976853	−	0.213914i	$-0.0686212\pi$
$41$	8.19615	+	4.73205i	1.28002	+	0.739022i	0.303171	+	0.952936i	$0.401955\pi$
$42$	1.96410	+	1.33013i	0.303067	+	0.205243i
$43$	−5.59808	−	1.50000i	−0.853699	−	0.228748i	−0.194673	−	0.980868i	$-0.562365\pi$
$43$	−5.59808	−	1.50000i	−0.853699	−	0.228748i	−0.659026	+	0.752120i	$0.729031\pi$
$44$	2.19615	+	1.26795i	0.331082	+	0.191151i
$45$	0.401924	−	6.69615i	0.0599153	−	0.998203i
$46$	−0.598076	−	1.03590i	−0.0881815	−	0.152735i
$47$	−6.29423	+	6.29423i	−0.918108	+	0.918108i	−0.996892	−	0.0787841i	$-0.974896\pi$
$47$	−6.29423	+	6.29423i	−0.918108	+	0.918108i	0.0787841	+	0.996892i	$0.474896\pi$
$48$	−3.69615	−	2.13397i	−0.533494	−	0.308013i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−0.964102	+	2.40192i	−0.136345	+	0.339683i
$51$	3.46410	+	3.46410i	0.485071	+	0.485071i
$52$	−0.464102	−	1.73205i	−0.0643593	−	0.240192i
$53$	−3.36603	−	0.901924i	−0.462359	−	0.123889i	0.0201174	−	0.999798i	$-0.493596\pi$
$53$	−3.36603	−	0.901924i	−0.462359	−	0.123889i	−0.482477	+	0.875909i	$0.660263\pi$
$54$	−1.90192	+	1.90192i	−0.258819	+	0.258819i
$55$	2.92820	−	1.46410i	0.394839	−	0.197419i
$56$	0.366025	−	5.09808i	0.0489122	−	0.681259i
$57$	10.0981	−	5.83013i	1.33752	−	0.772219i
$58$	−3.46410	−	0.928203i	−0.454859	−	0.121879i
$59$	3.46410			0.450988			0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410			0.450988			0.225494	+	0.974245i	$0.427600\pi$
$60$	−6.00000	+	3.00000i	−0.774597	+	0.387298i
$61$		−	9.39230i		−	1.20256i	−0.799038	−	0.601281i	$-0.794657\pi$
$61$		−	9.39230i		−	1.20256i	0.799038	−	0.601281i	$-0.205343\pi$
$62$	−3.73205	+	3.73205i	−0.473971	+	0.473971i
$63$	7.50000	+	2.59808i	0.944911	+	0.327327i
$64$			2.26795i			0.283494i
$65$	−2.19615	−	0.732051i	−0.272399	−	0.0907997i
$66$	−1.26795	−	0.339746i	−0.156074	−	0.0418198i
$67$	6.09808	+	6.09808i	0.744999	+	0.744999i	0.973535	−	0.228537i	$-0.0733941\pi$
$67$	6.09808	+	6.09808i	0.744999	+	0.744999i	−0.228537	+	0.973535i	$0.573394\pi$
$68$	1.26795	−	4.73205i	0.153761	−	0.573845i
$69$	−2.83013	−	2.83013i	−0.340707	−	0.340707i
$70$	−2.42820	−	1.86603i	−0.290226	−	0.223033i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	5.59808	+	1.50000i	0.659740	+	0.176777i
$73$	−0.169873	+	0.633975i	−0.0198821	+	0.0742011i	−0.975154	−	0.221528i	$-0.928896\pi$
$73$	−0.169873	+	0.633975i	−0.0198821	+	0.0742011i	0.955272	+	0.295729i	$0.0955624\pi$
$74$	−1.90192	−	1.09808i	−0.221094	−	0.127649i
$75$	−1.03590	+	8.59808i	−0.119615	+	0.992820i
$76$	−10.0981	−	5.83013i	−1.15833	−	0.668761i
$77$	0.732051	+	3.80385i	0.0834249	+	0.433489i
$78$	0.464102	+	0.803848i	0.0525492	+	0.0910178i
$79$		−	11.4641i		−	1.28981i	−0.764262	−	0.644906i	$-0.776896\pi$
$79$		−	11.4641i		−	1.28981i	0.764262	−	0.644906i	$-0.223104\pi$
$80$	4.59808	+	3.03590i	0.514081	+	0.339424i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	1.26795	+	4.73205i	0.140022	+	0.522568i
$83$	0.366025	−	1.36603i	0.0401765	−	0.149941i	−0.942924	−	0.333009i	$-0.891936\pi$
$83$	0.366025	−	1.36603i	0.0401765	−	0.149941i	0.983100	+	0.183068i	$0.0586028\pi$
$84$	−1.50000	−	7.79423i	−0.163663	−	0.850420i
$85$	−4.19615	−	4.73205i	−0.455137	−	0.513263i
$86$	−1.50000	−	2.59808i	−0.161749	−	0.280158i
$87$	−12.0000			−1.28654
$88$	0.732051	+	2.73205i	0.0780369	+	0.291238i
$89$	−0.598076	+	1.03590i	−0.0633960	+	0.109805i	−0.895981	−	0.444092i	$-0.853526\pi$
$89$	−0.598076	+	1.03590i	−0.0633960	+	0.109805i	0.832585	+	0.553897i	$0.186860\pi$
$90$	2.59808	−	2.30385i	0.273861	−	0.242847i
$91$	1.53590	−	2.26795i	0.161006	−	0.237746i
$92$	−1.03590	+	3.86603i	−0.108000	+	0.403061i
$93$	−8.83013	+	15.2942i	−0.915642	+	1.58594i
$94$	−4.60770			−0.475247
$95$	−13.4641	+	6.73205i	−1.38139	+	0.690694i
$96$	−2.30385	−	8.59808i	−0.235135	−	0.877537i
$97$	−3.09808	−	0.830127i	−0.314562	−	0.0842866i	0.0980839	−	0.995178i	$-0.468729\pi$
$97$	−3.09808	−	0.830127i	−0.314562	−	0.0842866i	−0.412646	+	0.910892i	$0.635395\pi$
$98$	2.90192	−	2.16987i	0.293139	−	0.219190i
$99$	−4.39230			−0.441443
$100$	7.96410	−	3.40192i	0.796410	−	0.340192i
$101$	11.7679	+	6.79423i	1.17095	+	0.676051i	0.953905	−	0.300109i	$-0.0970232\pi$
$101$	11.7679	+	6.79423i	1.17095	+	0.676051i	0.217050	+	0.976160i	$0.430357\pi$
$102$			2.53590i			0.251091i
$103$	−2.96410	+	11.0622i	−0.292062	+	1.08999i	0.651461	+	0.758682i	$0.274156\pi$
$103$	−2.96410	+	11.0622i	−0.292062	+	1.08999i	−0.943523	+	0.331307i	$0.892510\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	−9.46410	−	3.92820i	−0.923602	−	0.383353i
$106$	−0.901924	−	1.56218i	−0.0876026	−	0.151732i
$107$	−2.36603	+	0.633975i	−0.228732	+	0.0612886i	−0.371365	−	0.928487i	$-0.621110\pi$
$107$	−2.36603	+	0.633975i	−0.228732	+	0.0612886i	0.142632	+	0.989776i	$0.454443\pi$
$108$	9.00000			0.866025
$109$	1.73205	−	1.00000i	0.165900	−	0.0957826i	−0.414751	−	0.909935i	$-0.636131\pi$
$109$	1.73205	−	1.00000i	0.165900	−	0.0957826i	0.580651	+	0.814152i	$0.302798\pi$
$110$	1.60770	+	0.535898i	0.153288	+	0.0510959i
$111$	−7.09808	−	1.90192i	−0.673720	−	0.180523i
$112$	−4.92820	+	4.26795i	−0.465671	+	0.403283i
$113$	−1.90192	−	7.09808i	−0.178918	−	0.667731i	−0.995851	−	0.0909984i	$-0.970994\pi$
$113$	−1.90192	−	7.09808i	−0.178918	−	0.667731i	0.816933	−	0.576732i	$-0.195672\pi$
$114$	5.83013	+	1.56218i	0.546041	+	0.146311i
$115$	3.42820	+	3.86603i	0.319682	+	0.360509i
$116$	6.00000	+	10.3923i	0.557086	+	0.964901i
$117$	2.19615	+	2.19615i	0.203034	+	0.203034i
$118$	1.26795	+	1.26795i	0.116724	+	0.116724i
$119$	6.73205	−	3.26795i	0.617126	−	0.299572i
$120$	−7.09808	−	2.36603i	−0.647963	−	0.215988i
$121$	4.42820	+	7.66987i	0.402564	+	0.697261i
$122$	3.43782	−	3.43782i	0.311246	−	0.311246i
$123$	8.19615	+	14.1962i	0.739022	+	1.28002i
$124$	17.6603			1.58594
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	1.79423	+	3.69615i	0.159843	+	0.329279i
$127$	6.75833	+	6.75833i	0.599705	+	0.599705i	0.940234	−	0.340529i	$-0.110606\pi$
$127$	6.75833	+	6.75833i	0.599705	+	0.599705i	−0.340529	+	0.940234i	$0.610606\pi$
$128$	−8.09808	+	8.09808i	−0.715776	+	0.715776i
$129$	−7.09808	−	7.09808i	−0.624951	−	0.624951i
$130$	−0.535898	−	1.07180i	−0.0470014	−	0.0940028i
$131$	16.3923	−	9.46410i	1.43220	−	0.826882i	0.434914	−	0.900472i	$-0.356779\pi$
$131$	16.3923	−	9.46410i	1.43220	−	0.826882i	0.997289	+	0.0735897i	$0.0234455\pi$
$132$	2.19615	+	3.80385i	0.191151	+	0.331082i
$133$	−3.36603	−	17.4904i	−0.291871	−	1.51661i
$134$			4.46410i			0.385640i
$135$	6.40192	−	9.69615i	0.550990	−	0.834512i
$136$	4.73205	−	2.73205i	0.405770	−	0.234271i
$137$	7.46410	−	2.00000i	0.637701	−	0.170872i	0.0745393	−	0.997218i	$-0.476251\pi$
$137$	7.46410	−	2.00000i	0.637701	−	0.170872i	0.563162	+	0.826347i	$0.309585\pi$
$138$		−	2.07180i		−	0.176363i
$139$	3.46410	−	6.00000i	0.293821	−	0.508913i	−0.680889	−	0.732387i	$-0.738406\pi$
$139$	3.46410	−	6.00000i	0.293821	−	0.508913i	0.974710	+	0.223474i	$0.0717396\pi$
$140$	1.33013	+	10.1603i	0.112416	+	0.858698i
$141$	−14.8923	+	3.99038i	−1.25416	+	0.336051i
$142$	−2.19615	−	2.19615i	−0.184297	−	0.184297i
$143$	−0.392305	+	1.46410i	−0.0328062	+	0.122434i
$144$	−3.69615	−	6.40192i	−0.308013	−	0.533494i
$145$	15.4641	+	0.928203i	1.28422	+	0.0770831i
$146$	−0.294229	+	0.169873i	−0.0243505	+	0.0140588i
$147$	7.50000	−	9.52628i	0.618590	−	0.785714i
$148$	1.90192	+	7.09808i	0.156337	+	0.583458i
$149$	−17.8923	+	10.3301i	−1.46579	+	0.846277i	−0.999269	−	0.0382306i	$-0.987828\pi$
$149$	−17.8923	+	10.3301i	−1.46579	+	0.846277i	−0.466526	+	0.884508i	$0.654495\pi$
$150$	−3.52628	+	2.76795i	−0.287920	+	0.226002i
$151$	−0.633975	+	1.09808i	−0.0515921	+	0.0893602i	−0.890668	−	0.454654i	$-0.849763\pi$
$151$	−0.633975	+	1.09808i	−0.0515921	+	0.0893602i	0.839076	+	0.544014i	$0.183096\pi$
$152$	−3.36603	−	12.5622i	−0.273021	−	1.01893i
$153$	2.19615	+	8.19615i	0.177548	+	0.662620i
$154$	−1.12436	+	1.66025i	−0.0906032	+	0.133787i
$155$	12.5622	−	19.0263i	1.00902	−	1.52823i
$156$	0.803848	−	3.00000i	0.0643593	−	0.240192i
$157$	−1.00000	+	1.00000i	−0.0798087	+	0.0798087i	−0.745884	−	0.666076i	$-0.767973\pi$
$157$	−1.00000	+	1.00000i	−0.0798087	+	0.0798087i	0.666076	+	0.745884i	$0.267973\pi$
$158$	4.19615	−	4.19615i	0.333828	−	0.333828i
$159$	−4.26795	−	4.26795i	−0.338470	−	0.338470i
$160$	2.30385	+	11.2583i	0.182135	+	0.890049i
$161$	−5.50000	+	2.66987i	−0.433461	+	0.210415i
$162$	−4.50000	+	1.20577i	−0.353553	+	0.0947343i
$163$	−0.169873	−	0.633975i	−0.0133055	−	0.0496567i	0.958954	−	0.283562i	$-0.0915161\pi$
$163$	−0.169873	−	0.633975i	−0.0133055	−	0.0496567i	−0.972259	+	0.233905i	$0.924849\pi$
$164$	8.19615	−	14.1962i	0.640012	−	1.10853i
$165$	5.66025	+	0.339746i	0.440650	+	0.0264492i
$166$	0.633975	−	0.366025i	0.0492060	−	0.0284091i
$167$	−5.52628	−	20.6244i	−0.427636	−	1.59596i	−0.758098	−	0.652141i	$-0.773871\pi$
$167$	−5.52628	−	20.6244i	−0.427636	−	1.59596i	0.330461	−	0.943820i	$-0.392796\pi$
$168$	4.96410	−	7.33013i	0.382989	−	0.565532i
$169$	−10.3301	+	5.96410i	−0.794625	+	0.458777i
$170$	0.196152	−	3.26795i	0.0150442	−	0.250640i
$171$	20.1962			1.54444
$172$	−2.59808	+	9.69615i	−0.198101	+	0.739325i
$173$	−10.0000	−	10.0000i	−0.760286	−	0.760286i	0.216088	−	0.976374i	$-0.430670\pi$
$173$	−10.0000	−	10.0000i	−0.760286	−	0.760286i	−0.976374	+	0.216088i	$0.930670\pi$
$174$	−4.39230	−	4.39230i	−0.332980	−	0.332980i
$175$	11.8923	+	5.79423i	0.898974	+	0.438003i
$176$	1.80385	−	3.12436i	0.135970	−	0.235507i
$177$	5.19615	+	3.00000i	0.390567	+	0.225494i
$178$	−0.598076	+	0.160254i	−0.0448277	+	0.0120115i
$179$	16.0981	−	9.29423i	1.20323	−	0.694683i	0.241955	−	0.970287i	$-0.422211\pi$
$179$	16.0981	−	9.29423i	1.20323	−	0.694683i	0.961271	+	0.275604i	$0.0888779\pi$
$180$	−11.5981	−	0.696152i	−0.864470	−	0.0518881i
$181$		−	4.53590i		−	0.337151i	−0.985689	−	0.168575i	$-0.946083\pi$
$181$		−	4.53590i		−	0.337151i	0.985689	−	0.168575i	$-0.0539166\pi$
$182$	1.39230	−	0.267949i	0.103205	−	0.0198617i
$183$	8.13397	−	14.0885i	0.601281	−	1.04145i
$184$	−3.86603	+	2.23205i	−0.285007	+	0.164549i
$185$	9.00000	+	3.00000i	0.661693	+	0.220564i
$186$	−8.83013	+	2.36603i	−0.647456	+	0.173485i
$187$	−2.92820	+	2.92820i	−0.214131	+	0.214131i
$188$	10.9019	+	10.9019i	0.795105	+	0.795105i
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$	−7.39230	−	2.46410i	−0.536294	−	0.178765i
$191$	−0.339746			−0.0245832			−0.0122916	−	0.999924i	$-0.503913\pi$
$191$	−0.339746			−0.0245832			−0.0122916	+	0.999924i	$0.503913\pi$
$192$	−1.96410	+	3.40192i	−0.141747	+	0.245513i
$193$	−7.53590	+	7.53590i	−0.542446	+	0.542446i	−0.924245	−	0.381799i	$-0.875305\pi$
$193$	−7.53590	+	7.53590i	−0.542446	+	0.542446i	0.381799	+	0.924245i	$0.375305\pi$
$194$	−0.830127	−	1.43782i	−0.0595996	−	0.103230i
$195$	−2.66025	−	3.00000i	−0.190505	−	0.214834i
$196$	−12.0000	−	1.73205i	−0.857143	−	0.123718i
$197$	−10.5359	−	10.5359i	−0.750652	−	0.750652i	0.223949	−	0.974601i	$-0.428105\pi$
$197$	−10.5359	−	10.5359i	−0.750652	−	0.750652i	−0.974601	+	0.223949i	$0.928105\pi$
$198$	−1.60770	−	1.60770i	−0.114254	−	0.114254i
$199$	9.92820	+	17.1962i	0.703792	+	1.21900i	0.967126	+	0.254298i	$0.0818445\pi$
$199$	9.92820	+	17.1962i	0.703792	+	1.21900i	−0.263334	+	0.964705i	$0.584822\pi$
$200$	8.96410	+	3.59808i	0.633858	+	0.254422i
$201$	3.86603	+	14.4282i	0.272688	+	1.01769i
$202$	1.82051	+	6.79423i	0.128091	+	0.478040i
$203$	−6.00000	+	17.3205i	−0.421117	+	1.21566i
$204$	6.00000	−	6.00000i	0.420084	−	0.420084i
$205$	−9.46410	−	18.9282i	−0.661002	−	1.32200i
$206$	−5.13397	+	2.96410i	−0.357701	+	0.206519i
$207$	−1.79423	−	6.69615i	−0.124708	−	0.465415i
$208$	−2.46410	+	0.660254i	−0.170855	+	0.0457804i
$209$	4.92820	+	8.53590i	0.340891	+	0.590440i
$210$	−2.02628	−	4.90192i	−0.139827	−	0.338265i
$211$	2.46410	−	4.26795i	0.169636	−	0.293818i	−0.768656	−	0.639662i	$-0.779074\pi$
$211$	2.46410	−	4.26795i	0.169636	−	0.293818i	0.938292	+	0.345845i	$0.112408\pi$
$212$	−1.56218	+	5.83013i	−0.107291	+	0.400415i
$213$	−9.00000	−	5.19615i	−0.616670	−	0.356034i
$214$	−1.09808	−	0.633975i	−0.0750629	−	0.0433376i
$215$	8.59808	+	9.69615i	0.586384	+	0.661272i
$216$	7.09808	+	7.09808i	0.482963	+	0.482963i
$217$	17.6603	+	20.3923i	1.19886	+	1.38432i
$218$	1.00000	+	0.267949i	0.0677285	+	0.0181478i
$219$	−0.803848	+	0.803848i	−0.0543190	+	0.0543190i
$220$	−2.53590	−	5.07180i	−0.170970	−	0.341940i
$221$	2.92820			0.196972
$222$	−1.90192	−	3.29423i	−0.127649	−	0.221094i
$223$	−1.96410	+	7.33013i	−0.131526	+	0.490862i	−0.999988	−	0.00489404i	$-0.998442\pi$
$223$	−1.96410	+	7.33013i	−0.131526	+	0.490862i	0.868462	+	0.495756i	$0.165109\pi$
$224$	−13.5622	−	0.973721i	−0.906161	−	0.0650594i
$225$	−9.00000	+	12.0000i	−0.600000	+	0.800000i
$226$	1.90192	−	3.29423i	0.126514	−	0.219129i
$227$	−2.43782	−	9.09808i	−0.161804	−	0.603861i	−0.998426	−	0.0560804i	$-0.982140\pi$
$227$	−2.43782	−	9.09808i	−0.161804	−	0.603861i	0.836622	−	0.547780i	$-0.184527\pi$
$228$	−10.0981	−	17.4904i	−0.668761	−	1.15833i
$229$	6.33013	+	10.9641i	0.418307	+	0.724528i	0.995769	−	0.0918888i	$-0.0292904\pi$
$229$	6.33013	+	10.9641i	0.418307	+	0.724528i	−0.577463	+	0.816417i	$0.695957\pi$
$230$	−0.160254	+	2.66987i	−0.0105668	+	0.176046i
$231$	−2.19615	+	6.33975i	−0.144496	+	0.417125i
$232$	−3.46410	+	12.9282i	−0.227429	+	0.848778i
$233$	−3.16987	−	11.8301i	−0.207665	−	0.775017i	−0.988621	−	0.150430i	$-0.951934\pi$
$233$	−3.16987	−	11.8301i	−0.207665	−	0.775017i	0.780955	−	0.624587i	$-0.214733\pi$
$234$			1.60770i			0.105098i
$235$	19.5000	−	3.99038i	1.27204	−	0.260304i
$236$		−	6.00000i		−	0.390567i
$237$	9.92820	−	17.1962i	0.644906	−	1.11701i
$238$	3.66025	+	1.26795i	0.237259	+	0.0821889i
$239$	19.0526	+	11.0000i	1.23241	+	0.711531i	0.967531	−	0.252752i	$-0.0813355\pi$
$239$	19.0526	+	11.0000i	1.23241	+	0.711531i	0.264876	+	0.964282i	$0.414669\pi$
$240$	4.26795	+	8.53590i	0.275495	+	0.550990i
$241$	−14.2583	−	8.23205i	−0.918460	−	0.530273i	−0.0353164	−	0.999376i	$-0.511244\pi$
$241$	−14.2583	−	8.23205i	−0.918460	−	0.530273i	−0.883143	+	0.469103i	$0.844577\pi$
$242$	−1.18653	+	4.42820i	−0.0762733	+	0.284656i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−16.2679			−1.04145
$245$	−10.4019	+	11.6962i	−0.664555	+	0.747240i
$246$	−2.19615	+	8.19615i	−0.140022	+	0.522568i
$247$	1.80385	−	6.73205i	0.114776	−	0.428350i
$248$	13.9282	+	13.9282i	0.884442	+	0.884442i
$249$	1.73205	−	1.73205i	0.109764	−	0.109764i
$250$	4.75833	−	3.29423i	0.300943	−	0.208345i
$251$		−	21.8564i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$251$		−	21.8564i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$252$	4.50000	−	12.9904i	0.283473	−	0.818317i
$253$	2.39230	−	2.39230i	0.150403	−	0.150403i
$254$			4.94744i			0.310430i
$255$	−2.19615	−	10.7321i	−0.137528	−	0.672067i
$256$	−1.39230			−0.0870191
$257$	−26.2224	−	7.02628i	−1.63571	−	0.438287i	−0.680148	−	0.733075i	$-0.738084\pi$
$257$	−26.2224	−	7.02628i	−1.63571	−	0.438287i	−0.955563	+	0.294788i	$0.904751\pi$
$258$		−	5.19615i		−	0.323498i
$259$	−6.29423	+	9.29423i	−0.391104	+	0.577515i
$260$	−1.26795	+	3.80385i	−0.0786349	+	0.235905i
$261$	−18.0000	−	10.3923i	−1.11417	−	0.643268i
$262$	9.46410	+	2.53590i	0.584694	+	0.156668i
$263$	−5.45448	−	20.3564i	−0.336338	−	1.25523i	−0.902412	−	0.430875i	$-0.858205\pi$
$263$	−5.45448	−	20.3564i	−0.336338	−	1.25523i	0.566074	−	0.824355i	$-0.308462\pi$
$264$	−1.26795	+	4.73205i	−0.0780369	+	0.291238i
$265$	5.16987	+	5.83013i	0.317583	+	0.358142i
$266$	5.16987	−	7.63397i	0.316985	−	0.468069i
$267$	−1.79423	+	1.03590i	−0.109805	+	0.0633960i
$268$	10.5622	−	10.5622i	0.645188	−	0.645188i
$269$	−1.96410	−	3.40192i	−0.119753	−	0.207419i	0.799917	−	0.600111i	$-0.204877\pi$
$269$	−1.96410	−	3.40192i	−0.119753	−	0.207419i	−0.919670	+	0.392692i	$0.871544\pi$
$270$	5.89230	−	1.20577i	0.358594	−	0.0733809i
$271$	3.92820	+	2.26795i	0.238621	+	0.137768i	0.614543	−	0.788883i	$-0.289340\pi$
$271$	3.92820	+	2.26795i	0.238621	+	0.137768i	−0.375922	+	0.926651i	$0.622674\pi$
$272$	−6.73205	−	1.80385i	−0.408191	−	0.109374i
$273$	4.26795	−	2.07180i	0.258308	−	0.125391i
$274$	3.46410	+	2.00000i	0.209274	+	0.120824i
$275$	−7.26795	−	0.875644i	−0.438274	−	0.0528033i
$276$	−4.90192	+	4.90192i	−0.295061	+	0.295061i
$277$	5.19615	−	1.39230i	0.312207	−	0.0836555i	−0.0993135	−	0.995056i	$-0.531665\pi$
$277$	5.19615	−	1.39230i	0.312207	−	0.0836555i	0.411520	+	0.911401i	$0.364998\pi$
$278$	3.46410	−	0.928203i	0.207763	−	0.0556699i
$279$	−26.4904	+	15.2942i	−1.58594	+	0.915642i
$280$	−6.96410	+	9.06218i	−0.416185	+	0.541569i
$281$	5.13397	+	8.89230i	0.306267	+	0.530470i	0.977543	−	0.210738i	$-0.0675866\pi$
$281$	5.13397	+	8.89230i	0.306267	+	0.530470i	−0.671275	+	0.741208i	$0.734253\pi$
$282$	−6.91154	−	3.99038i	−0.411576	−	0.237624i
$283$	−6.75833	−	6.75833i	−0.401741	−	0.401741i	0.477105	−	0.878846i	$-0.341686\pi$
$283$	−6.75833	−	6.75833i	−0.401741	−	0.401741i	−0.878846	+	0.477105i	$0.841686\pi$
$284$			10.3923i			0.616670i
$285$	−26.0263	−	1.56218i	−1.54166	−	0.0925354i
$286$	−0.679492	+	0.392305i	−0.0401792	+	0.0231975i
$287$	24.5885	−	4.73205i	1.45141	−	0.279324i
$288$	3.99038	−	14.8923i	0.235135	−	0.877537i
$289$	−7.79423	−	4.50000i	−0.458484	−	0.264706i
$290$	5.32051	+	6.00000i	0.312431	+	0.352332i
$291$	−3.92820	−	3.92820i	−0.230275	−	0.230275i
$292$	1.09808	+	0.294229i	0.0642600	+	0.0172184i
$293$	17.5622	−	4.70577i	1.02599	−	0.274914i	0.293696	−	0.955899i	$-0.405115\pi$
$293$	17.5622	−	4.70577i	1.02599	−	0.274914i	0.732298	+	0.680985i	$0.238448\pi$
$294$	6.23205	−	0.741670i	0.363461	−	0.0432551i
$295$	−6.46410	−	4.26795i	−0.376355	−	0.248490i
$296$	−4.09808	+	7.09808i	−0.238196	+	0.412567i
$297$	−6.58846	−	3.80385i	−0.382301	−	0.220722i
$298$	−10.3301	−	2.76795i	−0.598408	−	0.160343i
$299$	−2.39230			−0.138351
$300$	14.8923	+	1.79423i	0.859808	+	0.103590i
$301$	−13.7942	+	6.69615i	−0.795086	+	0.385960i
$302$	−0.633975	+	0.169873i	−0.0364811	+	0.00977509i
$303$	11.7679	+	20.3827i	0.676051	+	1.17095i
$304$	−8.29423	+	14.3660i	−0.475707	+	0.823948i
$305$	−11.5718	+	17.5263i	−0.662599	+	1.00355i
$306$	−2.19615	+	3.80385i	−0.125546	+	0.217451i
$307$	−24.4641	+	24.4641i	−1.39624	+	1.39624i	−0.585744	+	0.810496i	$0.699197\pi$
$307$	−24.4641	+	24.4641i	−1.39624	+	1.39624i	−0.810496	+	0.585744i	$0.800803\pi$
$308$	6.58846	−	1.26795i	0.375412	−	0.0722481i
$309$	−14.0263	+	14.0263i	−0.797927	+	0.797927i
$310$	11.5622	−	2.36603i	0.656688	−	0.134381i
$311$		−	16.0000i		−	0.907277i	−0.891186	−	0.453638i	$-0.850126\pi$
$311$		−	16.0000i		−	0.907277i	0.891186	−	0.453638i	$-0.149874\pi$
$312$	3.00000	−	1.73205i	0.169842	−	0.0980581i
$313$	−5.19615	−	5.19615i	−0.293704	−	0.293704i	0.544838	−	0.838542i	$-0.316591\pi$
$313$	−5.19615	−	5.19615i	−0.293704	−	0.293704i	−0.838542	+	0.544838i	$0.816591\pi$
$314$	−0.732051			−0.0413120
$315$	−10.7942	−	14.0885i	−0.608186	−	0.793795i
$316$	−19.8564			−1.11701
$317$	1.53590	+	1.53590i	0.0862646	+	0.0862646i	0.748922	−	0.662658i	$-0.230572\pi$
$317$	1.53590	+	1.53590i	0.0862646	+	0.0862646i	−0.662658	+	0.748922i	$0.730572\pi$
$318$		−	3.12436i		−	0.175205i
$319$		−	10.1436i		−	0.567932i
$320$	2.79423	−	4.23205i	0.156202	−	0.236579i
$321$	−4.09808	−	1.09808i	−0.228732	−	0.0612886i
$322$	−2.99038	−	1.03590i	−0.166647	−	0.0577284i
$323$	13.4641	−	13.4641i	0.749163	−	0.749163i
$324$	13.5000	+	7.79423i	0.750000	+	0.433013i
$325$	3.19615	+	4.07180i	0.177291	+	0.225863i
$326$	0.169873	−	0.294229i	0.00940839	−	0.0162958i
$327$	3.46410			0.191565
$328$	17.6603	−	4.73205i	0.975124	−	0.261284i
$329$	−1.68653	+	23.4904i	−0.0929816	+	1.29507i
$330$	1.94744	+	2.19615i	0.107203	+	0.120894i
$331$	35.6603			1.96006			0.980032	−	0.198838i	$-0.0637167\pi$
$331$	35.6603			1.96006			0.980032	+	0.198838i	$0.0637167\pi$
$332$	−2.36603	−	0.633975i	−0.129853	−	0.0347939i
$333$	−9.00000	−	9.00000i	−0.493197	−	0.493197i
$334$	5.52628	−	9.57180i	0.302385	−	0.523745i
$335$	−3.86603	−	18.8923i	−0.211224	−	1.03220i
$336$	−11.0885	+	2.13397i	−0.604925	+	0.116418i
$337$	9.19615	−	2.46410i	0.500946	−	0.134228i	0.000507178	−	1.00000i	$-0.499839\pi$
$337$	9.19615	−	2.46410i	0.500946	−	0.134228i	0.500439	+	0.865772i	$0.333172\pi$
$338$	−5.96410	−	1.59808i	−0.324404	−	0.0869239i
$339$	3.29423	−	12.2942i	0.178918	−	0.667731i
$340$	−8.19615	+	7.26795i	−0.444499	+	0.394160i
$341$	−12.9282	−	7.46410i	−0.700101	−	0.404204i
$342$	7.39230	+	7.39230i	0.399730	+	0.399730i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−9.69615	+	5.59808i	−0.522782	+	0.301828i
$345$	1.79423	+	8.76795i	0.0965980	+	0.472051i
$346$		−	7.32051i		−	0.393553i
$347$	−6.16987	−	6.16987i	−0.331216	−	0.331216i	0.521832	−	0.853048i	$-0.325249\pi$
$347$	−6.16987	−	6.16987i	−0.331216	−	0.331216i	−0.853048	+	0.521832i	$0.825249\pi$
$348$			20.7846i			1.11417i
$349$	4.93782	+	8.55256i	0.264316	+	0.457808i	0.967384	−	0.253314i	$-0.0815206\pi$
$349$	4.93782	+	8.55256i	0.264316	+	0.457808i	−0.703069	+	0.711122i	$0.748187\pi$
$350$	2.23205	+	6.47372i	0.119308	+	0.346035i
$351$	1.39230	+	5.19615i	0.0743157	+	0.277350i
$352$	7.26795	−	1.94744i	0.387383	−	0.103799i
$353$	−27.1244	+	7.26795i	−1.44368	+	0.386834i	−0.893822	−	0.448422i	$-0.851986\pi$
$353$	−27.1244	+	7.26795i	−1.44368	+	0.386834i	−0.549862	+	0.835256i	$0.685320\pi$
$354$	0.803848	+	3.00000i	0.0427240	+	0.159448i
$355$	11.1962	+	7.39230i	0.594230	+	0.392343i
$356$	1.79423	+	1.03590i	0.0950939	+	0.0549025i
$357$	12.9282	+	0.928203i	0.684233	+	0.0491257i
$358$	9.29423	+	2.49038i	0.491215	+	0.131621i
$359$	−14.9545	−	8.63397i	−0.789267	−	0.455684i	0.0504372	−	0.998727i	$-0.483939\pi$
$359$	−14.9545	−	8.63397i	−0.789267	−	0.455684i	−0.839705	+	0.543043i	$0.817272\pi$
$360$	−8.59808	−	9.69615i	−0.453158	−	0.511032i
$361$	−13.1603	−	22.7942i	−0.692645	−	1.19970i
$362$	1.66025	−	1.66025i	0.0872610	−	0.0872610i
$363$			15.3397i			0.805128i
$364$	−3.92820	−	2.66025i	−0.205894	−	0.139435i
$365$	1.09808	−	0.973721i	0.0574759	−	0.0509669i
$366$	8.13397	−	2.17949i	0.425170	−	0.113924i
$367$	−1.40192	−	5.23205i	−0.0731798	−	0.273111i	0.919635	−	0.392775i	$-0.128485\pi$
$367$	−1.40192	−	5.23205i	−0.0731798	−	0.273111i	−0.992814	+	0.119664i	$0.961818\pi$
$368$	5.50000	+	1.47372i	0.286707	+	0.0768230i
$369$			28.3923i			1.47804i
$370$	2.19615	+	4.39230i	0.114173	+	0.228345i
$371$	−8.29423	+	4.02628i	−0.430615	+	0.209034i
$372$	26.4904	+	15.2942i	1.37346	+	0.792969i
$373$	−4.09808	−	1.09808i	−0.212190	−	0.0568562i	0.151158	−	0.988510i	$-0.451700\pi$
$373$	−4.09808	−	1.09808i	−0.212190	−	0.0568562i	−0.363348	+	0.931653i	$0.618366\pi$
$374$	−2.14359			−0.110843
$375$	12.5263	−	14.7679i	0.646854	−	0.762614i
$376$			17.1962i			0.886824i
$377$	−5.07180	+	5.07180i	−0.261211	+	0.261211i
$378$	−0.509619	+	7.09808i	−0.0262120	+	0.365086i
$379$		−	19.4641i		−	0.999804i	−0.866082	−	0.499902i	$-0.833369\pi$
$379$		−	19.4641i		−	0.999804i	0.866082	−	0.499902i	$-0.166631\pi$
$380$	11.6603	+	23.3205i	0.598158	+	1.19632i
$381$	4.28461	+	15.9904i	0.219507	+	0.819212i
$382$	−0.124356	−	0.124356i	−0.00636259	−	0.00636259i
$383$	0.205771	−	0.767949i	0.0105144	−	0.0392404i	−0.960469	−	0.278386i	$-0.910201\pi$
$383$	0.205771	−	0.767949i	0.0105144	−	0.0392404i	0.970984	+	0.239145i	$0.0768673\pi$
$384$	−19.1603	+	5.13397i	−0.977768	+	0.261992i
$385$	3.32051	−	8.00000i	0.169229	−	0.407718i
$386$	−5.51666			−0.280791
$387$	−4.50000	−	16.7942i	−0.228748	−	0.853699i
$388$	−1.43782	+	5.36603i	−0.0729944	+	0.272419i
$389$	−7.96410	−	4.59808i	−0.403796	−	0.233132i	0.284325	−	0.958728i	$-0.408231\pi$
$389$	−7.96410	−	4.59808i	−0.403796	−	0.233132i	−0.688121	+	0.725596i	$0.741564\pi$
$390$	0.124356	−	2.07180i	0.00629699	−	0.104910i
$391$	−5.66025	−	3.26795i	−0.286251	−	0.165267i
$392$	−8.09808	−	10.8301i	−0.409015	−	0.547004i
$393$	32.7846			1.65376
$394$		−	7.71281i		−	0.388566i
$395$	−14.1244	+	21.3923i	−0.710673	+	1.07636i
$396$			7.60770i			0.382301i
$397$	−8.78461	−	32.7846i	−0.440887	−	1.64541i	−0.726573	−	0.687089i	$-0.758888\pi$
$397$	−8.78461	−	32.7846i	−0.440887	−	1.64541i	0.285686	−	0.958323i	$-0.407779\pi$
$398$	−2.66025	+	9.92820i	−0.133346	+	0.497656i
$399$	10.0981	−	29.1506i	0.505536	−	1.45936i
$400$	−4.83975	−	11.3301i	−0.241987	−	0.566506i
$401$	−1.30385	−	2.25833i	−0.0651110	−	0.112776i	0.831632	−	0.555327i	$-0.187407\pi$
$401$	−1.30385	−	2.25833i	−0.0651110	−	0.112776i	−0.896743	+	0.442551i	$0.854073\pi$
$402$	−3.86603	+	6.69615i	−0.192820	+	0.333974i
$403$	2.73205	+	10.1962i	0.136093	+	0.507907i
$404$	11.7679	−	20.3827i	0.585477	−	1.01408i
$405$	18.0000	−	9.00000i	0.894427	−	0.447214i
$406$	−8.53590	+	4.14359i	−0.423630	+	0.205643i
$407$	1.60770	−	6.00000i	0.0796905	−	0.297409i
$408$	9.46410			0.468543
$409$	−15.3923			−0.761100			−0.380550	−	0.924760i	$-0.624265\pi$
$409$	−15.3923			−0.761100			−0.380550	+	0.924760i	$0.624265\pi$
$410$	3.46410	−	10.3923i	0.171080	−	0.513239i
$411$	12.9282	+	3.46410i	0.637701	+	0.170872i
$412$	19.1603	+	5.13397i	0.943958	+	0.252933i
$413$	6.92820	−	6.00000i	0.340915	−	0.295241i
$414$	1.79423	−	3.10770i	0.0881815	−	0.152735i
$415$	−2.36603	+	2.09808i	−0.116144	+	0.102991i
$416$	−4.60770	−	2.66025i	−0.225911	−	0.130430i
$417$	10.3923	−	6.00000i	0.508913	−	0.293821i
$418$	−1.32051	+	4.92820i	−0.0645882	+	0.241046i
$419$	−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	$0.229271\pi$
$420$	−6.80385	+	16.3923i	−0.331994	+	0.799863i
$421$	7.52628	+	13.0359i	0.366808	+	0.635331i	0.989065	−	0.147483i	$-0.0471171\pi$
$421$	7.52628	+	13.0359i	0.366808	+	0.635331i	−0.622256	+	0.782814i	$0.713784\pi$
$422$	2.46410	−	0.660254i	0.119951	−	0.0321407i
$423$	−25.7942	−	6.91154i	−1.25416	−	0.336051i
$424$	−5.83013	+	3.36603i	−0.283136	+	0.163469i
$425$	2.00000	+	14.0000i	0.0970143	+	0.679100i
$426$	−1.39230	−	5.19615i	−0.0674574	−	0.251754i
$427$	−16.2679	−	18.7846i	−0.787261	−	0.909051i
$428$	1.09808	+	4.09808i	0.0530775	+	0.198088i
$429$	−1.85641	+	1.85641i	−0.0896281	+	0.0896281i
$430$	−0.401924	+	6.69615i	−0.0193825	+	0.322917i
$431$	6.90192	+	11.9545i	0.332454	+	0.575827i	0.982992	−	0.183646i	$-0.0587901\pi$
$431$	6.90192	+	11.9545i	0.332454	+	0.575827i	−0.650538	+	0.759473i	$0.725457\pi$
$432$		−	12.8038i		−	0.616025i
$433$	20.1962	+	20.1962i	0.970565	+	0.970565i	0.999579	−	0.0290139i	$-0.00923670\pi$
$433$	20.1962	+	20.1962i	0.970565	+	0.970565i	−0.0290139	+	0.999579i	$0.509237\pi$
$434$	−1.00000	+	13.9282i	−0.0480015	+	0.668575i
$435$	22.3923	+	14.7846i	1.07363	+	0.708868i
$436$	−1.73205	−	3.00000i	−0.0829502	−	0.143674i
$437$	−11.0000	+	11.0000i	−0.526201	+	0.526201i
$438$	−0.588457			−0.0281176
$439$	21.8564			1.04315			0.521575	−	0.853206i	$-0.325345\pi$
$439$	21.8564			1.04315			0.521575	+	0.853206i	$0.325345\pi$
$440$	2.00000	−	6.00000i	0.0953463	−	0.286039i
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$	1.07180	+	1.07180i	0.0509802	+	0.0509802i
$443$	16.6603	−	16.6603i	0.791553	−	0.791553i	−0.190194	−	0.981747i	$-0.560912\pi$
$443$	16.6603	−	16.6603i	0.791553	−	0.791553i	0.981747	+	0.190194i	$0.0609117\pi$
$444$	−3.29423	+	12.2942i	−0.156337	+	0.583458i
$445$	2.39230	−	1.19615i	0.113406	−	0.0567031i
$446$	−3.40192	+	1.96410i	−0.161086	+	0.0930029i
$447$	−35.7846			−1.69255
$448$	3.92820	+	4.53590i	0.185590	+	0.214301i
$449$			29.5885i			1.39637i	0.715920	+	0.698183i	$0.246008\pi$
$449$			29.5885i			1.39637i	−0.715920	+	0.698183i	$0.753992\pi$
$450$	−7.68653	+	1.09808i	−0.362347	+	0.0517638i
$451$	−12.0000	+	6.92820i	−0.565058	+	0.326236i
$452$	−12.2942	+	3.29423i	−0.578272	+	0.154947i
$453$	−1.90192	+	1.09808i	−0.0893602	+	0.0515921i
$454$	2.43782	−	4.22243i	0.114413	−	0.198169i
$455$	−5.66025	+	2.33975i	−0.265357	+	0.109689i
$456$	5.83013	−	21.7583i	0.273021	−	1.01893i
$457$	−24.6603	−	24.6603i	−1.15356	−	1.15356i	−0.985834	−	0.167724i	$-0.946358\pi$
$457$	−24.6603	−	24.6603i	−1.15356	−	1.15356i	−0.167724	−	0.985834i	$-0.553642\pi$
$458$	−1.69615	+	6.33013i	−0.0792560	+	0.295787i
$459$	−3.80385	+	14.1962i	−0.177548	+	0.662620i
$460$	6.69615	−	5.93782i	0.312210	−	0.276852i
$461$	7.96410	−	4.59808i	0.370925	−	0.214154i	−0.302937	−	0.953010i	$-0.597967\pi$
$461$	7.96410	−	4.59808i	0.370925	−	0.214154i	0.673863	+	0.738857i	$0.264634\pi$
$462$	−3.12436	+	1.51666i	−0.145358	+	0.0705614i
$463$	−1.18653	−	4.42820i	−0.0551429	−	0.205796i	0.932858	−	0.360244i	$-0.117307\pi$
$463$	−1.18653	−	4.42820i	−0.0551429	−	0.205796i	−0.988001	+	0.154448i	$0.950640\pi$
$464$	14.7846	−	8.53590i	0.686358	−	0.396269i
$465$	35.3205	−	17.6603i	1.63795	−	0.818975i
$466$	3.16987	−	5.49038i	0.146842	−	0.254337i
$467$	6.03590	+	22.5263i	0.279308	+	1.04239i	0.952899	+	0.303288i	$0.0980843\pi$
$467$	6.03590	+	22.5263i	0.279308	+	1.04239i	−0.673591	+	0.739104i	$0.735249\pi$
$468$	3.80385	−	3.80385i	0.175833	−	0.175833i
$469$	22.7583	+	1.63397i	1.05088	+	0.0754499i
$470$	8.59808	+	5.67691i	0.396600	+	0.261857i
$471$	−2.36603	+	0.633975i	−0.109021	+	0.0292120i
$472$	4.73205	−	4.73205i	0.217810	−	0.217810i
$473$	6.00000	−	6.00000i	0.275880	−	0.275880i
$474$	9.92820	−	2.66025i	0.456017	−	0.122190i
$475$	33.4186	+	4.02628i	1.53335	+	0.184738i
$476$	−5.66025	−	11.6603i	−0.259437	−	0.534447i
$477$	−2.70577	−	10.0981i	−0.123889	−	0.462359i
$478$	2.94744	+	11.0000i	0.134813	+	0.503128i
$479$	4.36603	−	7.56218i	0.199489	−	0.345525i	−0.748874	−	0.662712i	$-0.769405\pi$
$479$	4.36603	−	7.56218i	0.199489	−	0.345525i	0.948363	+	0.317188i	$0.102739\pi$
$480$	−6.29423	+	18.8827i	−0.287291	+	0.861873i
$481$	−3.80385	+	2.19615i	−0.173441	+	0.100136i
$482$	−2.20577	−	8.23205i	−0.100470	−	0.374960i
$483$	−10.5622	−	0.758330i	−0.480596	−	0.0345052i
$484$	13.2846	−	7.66987i	0.603846	−	0.348631i
$485$	4.75833	+	5.36603i	0.216065	+	0.243659i
$486$	−7.79423	−	2.08846i	−0.353553	−	0.0947343i
$487$	7.41858	−	27.6865i	0.336168	−	1.25460i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	7.41858	−	27.6865i	0.336168	−	1.25460i	0.902597	−	0.430486i	$-0.141658\pi$
$488$	−12.8301	−	12.8301i	−0.580793	−	0.580793i
$489$	0.294229	−	1.09808i	0.0133055	−	0.0496567i
$490$	−8.08846	+	0.473721i	−0.365399	+	0.0214005i
$491$	1.53590	−	2.66025i	0.0693141	−	0.120056i	−0.829285	−	0.558825i	$-0.811252\pi$
$491$	1.53590	−	2.66025i	0.0693141	−	0.120056i	0.898600	+	0.438770i	$0.144586\pi$
$492$	24.5885	−	14.1962i	1.10853	−	0.640012i
$493$	−18.9282	+	5.07180i	−0.852483	+	0.228422i
$494$	3.12436	−	1.80385i	0.140571	−	0.0811589i
$495$	8.19615	+	5.41154i	0.368390	+	0.243231i
$496$		−	25.1244i		−	1.12812i
$497$	−12.0000	+	10.3923i	−0.538274	+	0.466159i
$498$	1.26795			0.0568182
$499$	−18.1244	+	10.4641i	−0.811358	+	0.468438i	−0.847427	−	0.530912i	$-0.821850\pi$
$499$	−18.1244	+	10.4641i	−0.811358	+	0.468438i	0.0360695	+	0.999349i	$0.488516\pi$
$500$	−19.0526	−	3.46410i	−0.852056	−	0.154919i
$501$	9.57180	−	35.7224i	0.427636	−	1.59596i
$502$	8.00000	−	8.00000i	0.357057	−	0.357057i
$503$	23.9282	+	23.9282i	1.06691	+	1.06691i	0.997595	+	0.0693107i	$0.0220800\pi$
$503$	23.9282	+	23.9282i	1.06691	+	1.06691i	0.0693107	+	0.997595i	$0.477920\pi$
$504$	13.7942	−	6.69615i	0.614444	−	0.298270i
$505$	−13.5885	−	27.1769i	−0.604678	−	1.20936i
$506$	1.75129			0.0778543
$507$	−20.6603			−0.917554
$508$	11.7058	−	11.7058i	0.519360	−	0.519360i
$509$	−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	$0.963948\pi$
$510$	3.12436	−	4.73205i	0.138349	−	0.209539i
$511$	0.758330	+	1.56218i	0.0335466	+	0.0691067i
$512$	15.6865	+	15.6865i	0.693253	+	0.693253i
$513$	30.2942	+	17.4904i	1.33752	+	0.772219i
$514$	−7.02628	−	12.1699i	−0.309916	−	0.536790i
$515$	19.1603	−	16.9904i	0.844302	−	0.748686i
$516$	−12.2942	+	12.2942i	−0.541223	+	0.541223i
$517$	−3.37307	−	12.5885i	−0.148347	−	0.553640i
$518$	−5.70577	+	1.09808i	−0.250697	+	0.0482467i
$519$	−6.33975	−	23.6603i	−0.278284	−	1.03857i
$520$	−4.00000	+	2.00000i	−0.175412	+	0.0877058i
$521$	13.3756	−	7.72243i	0.585998	−	0.338326i	−0.177516	−	0.984118i	$-0.556806\pi$
$521$	13.3756	−	7.72243i	0.585998	−	0.338326i	0.763513	+	0.645792i	$0.223473\pi$
$522$	−2.78461	−	10.3923i	−0.121879	−	0.454859i
$523$	7.33013	−	1.96410i	0.320524	−	0.0858842i	−0.0949698	−	0.995480i	$-0.530275\pi$
$523$	7.33013	−	1.96410i	0.320524	−	0.0858842i	0.415494	+	0.909596i	$0.363609\pi$
$524$	−16.3923	−	28.3923i	−0.716101	−	1.24032i
$525$	12.8205	+	18.9904i	0.559533	+	0.828808i
$526$	5.45448	−	9.44744i	0.237827	−	0.411928i
$527$	−7.46410	+	27.8564i	−0.325141	+	1.21344i
$528$	5.41154	−	3.12436i	0.235507	−	0.135970i
$529$	−15.2942	−	8.83013i	−0.664966	−	0.383919i
$530$	−0.241670	+	4.02628i	−0.0104975	+	0.174890i
$531$	5.19615	+	9.00000i	0.225494	+	0.390567i
$532$	−30.2942	+	5.83013i	−1.31342	+	0.252768i
$533$	9.46410	+	2.53590i	0.409936	+	0.109842i
$534$	−1.03590	−	0.277568i	−0.0448277	−	0.0120115i
$535$	5.19615	+	1.73205i	0.224649	+	0.0748831i
$536$	16.6603			0.719613
$537$	32.1962			1.38937
$538$	0.526279	−	1.96410i	0.0226895	−	0.0846784i
$539$	8.05256	+	6.33975i	0.346848	+	0.273072i
$540$	−16.7942	−	11.0885i	−0.722709	−	0.477171i
$541$	−1.96410	+	3.40192i	−0.0844433	+	0.146260i	−0.905154	−	0.425084i	$-0.860245\pi$
$541$	−1.96410	+	3.40192i	−0.0844433	+	0.146260i	0.820711	+	0.571344i	$0.193578\pi$
$542$	0.607695	+	2.26795i	0.0261027	+	0.0974168i
$543$	3.92820	−	6.80385i	0.168575	−	0.291981i
$544$	−7.26795	−	12.5885i	−0.311611	−	0.539726i
$545$	−4.46410	−	0.267949i	−0.191221	−	0.0114777i
$546$	2.32051	+	0.803848i	0.0993086	+	0.0344015i
$547$	−10.6340	+	39.6865i	−0.454676	+	1.69687i	0.234363	+	0.972149i	$0.424700\pi$
$547$	−10.6340	+	39.6865i	−0.454676	+	1.69687i	−0.689039	+	0.724724i	$0.741967\pi$
$548$	−3.46410	−	12.9282i	−0.147979	−	0.552265i
$549$	24.4019	−	14.0885i	1.04145	−	0.601281i
$550$	−2.33975	−	2.98076i	−0.0997671	−	0.127100i
$551$			46.6410i			1.98697i
$552$	−7.73205			−0.329098
$553$	−19.8564	−	22.9282i	−0.844380	−	0.975006i
$554$	2.41154	+	1.39230i	0.102457	+	0.0591534i
$555$	10.9019	+	12.2942i	0.462761	+	0.521861i
$556$	−10.3923	−	6.00000i	−0.440732	−	0.254457i
$557$	0.294229	−	1.09808i	0.0124669	−	0.0465270i	−0.959412	−	0.282007i	$-0.909000\pi$
$557$	0.294229	−	1.09808i	0.0124669	−	0.0465270i	0.971879	+	0.235480i	$0.0756664\pi$
$558$	−15.2942	−	4.09808i	−0.647456	−	0.173485i
$559$	−6.00000			−0.253773
$560$	14.4545	−	1.89230i	0.610813	−	0.0799645i
$561$	−6.92820	+	1.85641i	−0.292509	+	0.0783775i
$562$	−1.37564	+	5.13397i	−0.0580281	+	0.216564i
$563$	23.8301	+	23.8301i	1.00432	+	1.00432i	0.999991	+	0.00432948i	$0.00137812\pi$
$563$	23.8301	+	23.8301i	1.00432	+	1.00432i	0.00432948	+	0.999991i	$0.498622\pi$
$564$	6.91154	+	25.7942i	0.291028	+	1.08613i
$565$	−5.19615	+	15.5885i	−0.218604	+	0.655811i
$566$		−	4.94744i		−	0.207956i
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$	−8.19615	+	8.19615i	−0.343903	+	0.343903i
$569$			22.7846i			0.955181i	0.878583	+	0.477590i	$0.158490\pi$
$569$			22.7846i			0.955181i	−0.878583	+	0.477590i	$0.841510\pi$
$570$	−8.95448	−	10.0981i	−0.375062	−	0.422962i
$571$	28.2487			1.18217			0.591086	−	0.806609i	$-0.298699\pi$
$571$	28.2487			1.18217			0.591086	+	0.806609i	$0.298699\pi$
$572$	2.53590	+	0.679492i	0.106031	+	0.0284110i
$573$	−0.509619	−	0.294229i	−0.0212896	−	0.0122916i
$574$	10.7321	+	7.26795i	0.447947	+	0.303358i
$575$	−1.63397	−	11.4378i	−0.0681415	−	0.476990i
$576$	−5.89230	+	3.40192i	−0.245513	+	0.141747i
$577$	−33.3205	−	8.92820i	−1.38715	−	0.371686i	−0.513437	−	0.858127i	$-0.671628\pi$
$577$	−33.3205	−	8.92820i	−1.38715	−	0.371686i	−0.873713	+	0.486441i	$0.838295\pi$
$578$	−1.20577	−	4.50000i	−0.0501535	−	0.187175i
$579$	−17.8301	+	4.77757i	−0.740995	+	0.198549i
$580$	1.60770	−	26.7846i	0.0667559	−	1.11217i
$581$	−1.63397	−	3.36603i	−0.0677887	−	0.139646i
$582$		−	2.87564i		−	0.119199i
$583$	3.60770	−	3.60770i	0.149415	−	0.149415i
$584$	0.633975	+	1.09808i	0.0262341	+	0.0454387i
$585$	−1.39230	−	6.80385i	−0.0575647	−	0.281304i
$586$	8.15064	+	4.70577i	0.336700	+	0.194394i
$587$	15.6244	+	4.18653i	0.644886	+	0.172797i	0.566416	−	0.824120i	$-0.308330\pi$
$587$	15.6244	+	4.18653i	0.644886	+	0.172797i	0.0784705	+	0.996916i	$0.474996\pi$
$588$	−16.5000	−	12.9904i	−0.680449	−	0.535714i
$589$	59.4449	+	34.3205i	2.44938	+	1.41415i
$590$	−0.803848	−	3.92820i	−0.0330939	−	0.161722i
$591$	−6.67949	−	24.9282i	−0.274758	−	1.02541i
$592$	10.0981	−	2.70577i	0.415028	−	0.111207i
$593$	2.73205	−	0.732051i	0.112192	−	0.0300617i	−0.202286	−	0.979326i	$-0.564837\pi$
$593$	2.73205	−	0.732051i	0.112192	−	0.0300617i	0.314478	+	0.949265i	$0.398170\pi$
$594$	−1.01924	−	3.80385i	−0.0418198	−	0.156074i
$595$	−16.5885	−	2.19615i	−0.680060	−	0.0900335i
$596$	17.8923	+	30.9904i	0.732897	+	1.26942i
$597$			34.3923i			1.40758i
$598$	−0.875644	−	0.875644i	−0.0358078	−	0.0358078i
$599$		−	20.9808i		−	0.857251i	−0.903482	−	0.428625i	$-0.858998\pi$
$599$		−	20.9808i		−	0.857251i	0.903482	−	0.428625i	$-0.141002\pi$
$600$	10.3301	+	13.1603i	0.421726	+	0.537265i
$601$	3.33975	−	1.92820i	0.136231	−	0.0786531i	−0.430335	−	0.902669i	$-0.641605\pi$
$601$	3.33975	−	1.92820i	0.136231	−	0.0786531i	0.566567	+	0.824016i	$0.308271\pi$
$602$	−7.50000	−	2.59808i	−0.305677	−	0.105890i
$603$	−6.69615	+	24.9904i	−0.272688	+	1.01769i
$604$	1.90192	+	1.09808i	0.0773882	+	0.0446801i
$605$	1.18653	−	19.7679i	0.0482394	−	0.803681i
$606$	−3.15321	+	11.7679i	−0.128091	+	0.478040i
$607$	4.09808	+	1.09808i	0.166336	+	0.0445695i	0.341026	−	0.940054i	$-0.389226\pi$
$607$	4.09808	+	1.09808i	0.166336	+	0.0445695i	−0.174690	+	0.984623i	$0.555892\pi$
$608$	−33.4186	+	8.95448i	−1.35530	+	0.363152i
$609$	−24.0000	+	20.7846i	−0.972529	+	0.842235i
$610$	−10.6506	+	2.17949i	−0.431232	+	0.0882450i
$611$	−4.60770	+	7.98076i	−0.186407	+	0.322867i
$612$	14.1962	−	3.80385i	0.573845	−	0.153761i
$613$	−5.90192	−	1.58142i	−0.238376	−	0.0638728i	0.137653	−	0.990481i	$-0.456044\pi$
$613$	−5.90192	−	1.58142i	−0.238376	−	0.0638728i	−0.376029	+	0.926608i	$0.622711\pi$
$614$	−17.9090			−0.722747
$615$	2.19615	−	36.5885i	0.0885574	−	1.47539i
$616$	6.19615	+	4.19615i	0.249650	+	0.169068i
$617$	−11.5622	+	3.09808i	−0.465476	+	0.124724i	−0.483932	−	0.875106i	$-0.660792\pi$
$617$	−11.5622	+	3.09808i	−0.465476	+	0.124724i	0.0184559	+	0.999830i	$0.494125\pi$
$618$	−10.2679			−0.413037
$619$	−13.4904	+	23.3660i	−0.542224	+	0.939160i	0.456552	+	0.889697i	$0.349084\pi$
$619$	−13.4904	+	23.3660i	−0.542224	+	0.939160i	−0.998776	+	0.0494630i	$0.984249\pi$
$620$	−32.9545	−	21.7583i	−1.32348	−	0.873836i
$621$	3.10770	−	11.5981i	0.124708	−	0.465415i
$622$	5.85641	−	5.85641i	0.234821	−	0.234821i
$623$	0.598076	+	3.10770i	0.0239614	+	0.124507i
$624$	−4.26795	−	1.14359i	−0.170855	−	0.0457804i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$		−	3.80385i		−	0.152032i
$627$			17.0718i			0.681782i
$628$	1.73205	+	1.73205i	0.0691164	+	0.0691164i
$629$	−12.0000			−0.478471
$630$	1.20577	−	9.10770i	0.0480391	−	0.362859i
$631$	2.67949			0.106669			0.0533344	−	0.998577i	$-0.483015\pi$
$631$	2.67949			0.106669			0.0533344	+	0.998577i	$0.483015\pi$
$632$	−15.6603	−	15.6603i	−0.622931	−	0.622931i
$633$	7.39230	−	4.26795i	0.293818	−	0.169636i
$634$			1.12436i			0.0446539i
$635$	−4.28461	−	20.9378i	−0.170030	−	0.830892i
$636$	−7.39230	+	7.39230i	−0.293124	+	0.293124i
$637$	−0.856406	−	7.19615i	−0.0339321	−	0.285122i
$638$	3.71281	−	3.71281i	0.146992	−	0.146992i
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$	25.0885	−	5.13397i	0.991708	−	0.202938i
$641$	−13.7224	+	23.7679i	−0.542003	+	0.938778i	0.456785	+	0.889577i	$0.349001\pi$
$641$	−13.7224	+	23.7679i	−0.542003	+	0.938778i	−0.998789	+	0.0492007i	$0.984333\pi$
$642$	−1.09808	−	1.90192i	−0.0433376	−	0.0750629i
$643$	−36.1865	+	9.69615i	−1.42706	+	0.382379i	−0.887982	−	0.459878i	$-0.847893\pi$
$643$	−36.1865	+	9.69615i	−1.42706	+	0.382379i	−0.539076	+	0.842257i	$0.681226\pi$
$644$	4.62436	+	9.52628i	0.182225	+	0.375388i
$645$	4.50000	+	21.9904i	0.177187	+	0.865870i
$646$	9.85641			0.387795
$647$	37.9545	+	10.1699i	1.49214	+	0.399819i	0.910461	−	0.413596i	$-0.135727\pi$
$647$	37.9545	+	10.1699i	1.49214	+	0.399819i	0.581684	+	0.813415i	$0.302394\pi$
$648$	4.50000	+	16.7942i	0.176777	+	0.659740i
$649$	−2.53590	+	4.39230i	−0.0995427	+	0.172413i
$650$	−0.320508	+	2.66025i	−0.0125714	+	0.104344i
$651$	8.83013	+	45.8827i	0.346080	+	1.79828i
$652$	−1.09808	+	0.294229i	−0.0430040	+	0.0115229i
$653$	−19.4904	−	5.22243i	−0.762718	−	0.204370i	−0.143566	−	0.989641i	$-0.545857\pi$
$653$	−19.4904	−	5.22243i	−0.762718	−	0.204370i	−0.619152	+	0.785271i	$0.712523\pi$
$654$	1.26795	+	1.26795i	0.0495807	+	0.0495807i
$655$	−42.2487	−	2.53590i	−1.65079	−	0.0990857i
$656$	−20.1962	−	11.6603i	−0.788527	−	0.455256i
$657$	−1.90192	+	0.509619i	−0.0742011	+	0.0198821i
$658$	−9.21539	+	7.98076i	−0.359253	+	0.311122i
$659$	−22.5167	+	13.0000i	−0.877125	+	0.506408i	−0.869709	−	0.493564i	$-0.835694\pi$
$659$	−22.5167	+	13.0000i	−0.877125	+	0.506408i	−0.00741531	+	0.999973i	$0.502360\pi$
$660$	0.588457	−	9.80385i	0.0229057	−	0.381614i
$661$		−	11.0000i		−	0.427850i	−0.976850	−	0.213925i	$-0.931375\pi$
$661$		−	11.0000i		−	0.427850i	0.976850	−	0.213925i	$-0.0686249\pi$
$662$	13.0526	+	13.0526i	0.507302	+	0.507302i
$663$	4.39230	+	2.53590i	0.170583	+	0.0984861i
$664$	−1.36603	−	2.36603i	−0.0530121	−	0.0918196i
$665$	−15.2679	+	36.7846i	−0.592066	+	1.42645i
$666$		−	6.58846i		−	0.255298i
$667$	15.4641	−	4.14359i	0.598772	−	0.160441i
$668$	−35.7224	+	9.57180i	−1.38214	+	0.370344i
$669$	−9.29423	+	9.29423i	−0.359336	+	0.359336i
$670$	5.50000	−	8.33013i	0.212484	−	0.321821i
$671$	11.9090	+	6.87564i	0.459741	+	0.265431i
$672$	−19.5000	−	13.2058i	−0.752229	−	0.509424i
$673$	6.92820	+	1.85641i	0.267063	+	0.0715592i	0.389865	−	0.920872i	$-0.372522\pi$
$673$	6.92820	+	1.85641i	0.267063	+	0.0715592i	−0.122803	+	0.992431i	$0.539188\pi$
$674$	4.26795	+	2.46410i	0.164395	+	0.0949136i
$675$	−23.8923	+	10.2058i	−0.919615	+	0.392820i
$676$	10.3301	+	17.8923i	0.397313	+	0.688166i
$677$	29.9090	−	29.9090i	1.14949	−	1.14949i	0.162843	−	0.986652i	$-0.447934\pi$
$677$	29.9090	−	29.9090i	1.14949	−	1.14949i	0.986652	−	0.162843i	$-0.0520664\pi$
$678$	5.70577	−	3.29423i	0.219129	−	0.126514i
$679$	−7.63397	+	3.70577i	−0.292965	+	0.142214i
$680$	−12.1962	−	0.732051i	−0.467701	−	0.0280729i
$681$	4.22243	−	15.7583i	0.161804	−	0.603861i
$682$	−2.00000	−	7.46410i	−0.0765840	−	0.285815i
$683$	−29.9904	−	8.03590i	−1.14755	−	0.307485i	−0.365567	−	0.930785i	$-0.619125\pi$
$683$	−29.9904	−	8.03590i	−1.14755	−	0.307485i	−0.781983	+	0.623300i	$0.785792\pi$
$684$		−	34.9808i		−	1.33752i
$685$	−16.3923	−	5.46410i	−0.626318	−	0.208773i
$686$	2.04552	−	9.36603i	0.0780982	−	0.357597i
$687$			21.9282i			0.836613i
$688$	13.7942	+	3.69615i	0.525900	+	0.140914i
$689$	−3.60770			−0.137442
$690$	−2.55256	+	3.86603i	−0.0971743	+	0.147177i
$691$			20.5885i			0.783222i	0.920131	+	0.391611i	$0.128082\pi$
$691$			20.5885i			0.783222i	−0.920131	+	0.391611i	$0.871918\pi$
$692$	−17.3205	+	17.3205i	−0.658427	+	0.658427i
$693$	−8.78461	+	7.60770i	−0.333700	+	0.288992i
$694$		−	4.51666i		−	0.171450i
$695$	−13.8564	+	6.92820i	−0.525603	+	0.262802i
$696$	−16.3923	+	16.3923i	−0.621349	+	0.621349i
$697$	18.9282	+	18.9282i	0.716957	+	0.716957i
$698$	−1.32309	+	4.93782i	−0.0500795	+	0.186899i
$699$	5.49038	−	20.4904i	0.207665	−	0.775017i
$700$	10.0359	−	20.5981i	0.379321	−	0.778534i
$701$	−40.5359			−1.53102			−0.765510	−	0.643424i	$-0.777513\pi$
$701$	−40.5359			−1.53102			−0.765510	+	0.643424i	$0.777513\pi$
$702$	−1.39230	+	2.41154i	−0.0525492	+	0.0910178i
$703$	−7.39230	+	27.5885i	−0.278806	+	1.04052i
$704$	−2.87564	−	1.66025i	−0.108380	−	0.0625732i
$705$	32.7058	+	10.9019i	1.23177	+	0.410590i
$706$	−12.5885	−	7.26795i	−0.473773	−	0.273533i
$707$	35.3038	−	6.79423i	1.32774	−	0.255523i
$708$	5.19615	−	9.00000i	0.195283	−	0.338241i
$709$		−	48.7128i		−	1.82945i	−0.404079	−	0.914724i	$-0.632408\pi$
$709$		−	48.7128i		−	1.82945i	0.404079	−	0.914724i	$-0.367592\pi$
$710$	1.39230	+	6.80385i	0.0522523	+	0.255344i
$711$	29.7846	−	17.1962i	1.11701	−	0.644906i
$712$	0.598076	+	2.23205i	0.0224139	+	0.0836496i
$713$	6.09808	−	22.7583i	0.228375	−	0.852306i
$714$	4.39230	+	5.07180i	0.164378	+	0.189807i
$715$	2.53590	−	2.24871i	0.0948372	−	0.0840970i
$716$	−16.0981	−	27.8827i	−0.601613	−	1.04202i
$717$	19.0526	+	33.0000i	0.711531	+	1.23241i
$718$	−2.31347	−	8.63397i	−0.0863378	−	0.322217i
$719$	3.43782	−	5.95448i	0.128209	−	0.222065i	−0.794774	−	0.606906i	$-0.792410\pi$
$719$	3.43782	−	5.95448i	0.128209	−	0.222065i	0.922983	+	0.384841i	$0.125744\pi$
$720$	−0.990381	+	16.5000i	−0.0369093	+	0.614919i
$721$	13.2321	+	27.2583i	0.492787	+	1.01515i
$722$	3.52628	−	13.1603i	0.131235	−	0.489774i
$723$	−14.2583	−	24.6962i	−0.530273	−	0.918460i
$724$	−7.85641			−0.291981
$725$	−27.7128	−	20.7846i	−1.02923	−	0.771921i
$726$	−5.61474	+	5.61474i	−0.208382	+	0.208382i
$727$	25.6244	+	6.86603i	0.950355	+	0.254647i	0.700513	−	0.713640i	$-0.252955\pi$
$727$	25.6244	+	6.86603i	0.950355	+	0.254647i	0.249842	+	0.968287i	$0.419621\pi$
$728$	−1.00000	−	5.19615i	−0.0370625	−	0.192582i
$729$	−27.0000			−1.00000
$730$	0.758330	+	0.0455173i	0.0280671	+	0.00168467i
$731$	−14.1962	−	8.19615i	−0.525064	−	0.303146i
$732$	−24.4019	−	14.0885i	−0.901921	−	0.520724i
$733$	−0.607695	+	2.26795i	−0.0224457	+	0.0837686i	−0.976240	−	0.216691i	$-0.930473\pi$
$733$	−0.607695	+	2.26795i	−0.0224457	+	0.0837686i	0.953794	+	0.300460i	$0.0971402\pi$
$734$	1.40192	−	2.42820i	0.0517460	−	0.0896266i
$735$	−25.7321	+	8.53590i	−0.949141	+	0.314851i
$736$	5.93782	+	10.2846i	0.218871	+	0.379096i
$737$	−12.1962	+	3.26795i	−0.449251	+	0.120376i
$738$	−10.3923	+	10.3923i	−0.382546	+	0.382546i
$739$	3.12436	−	1.80385i	0.114931	−	0.0663556i	−0.441432	−	0.897295i	$-0.645529\pi$
$739$	3.12436	−	1.80385i	0.114931	−	0.0663556i	0.556364	+	0.830939i	$0.312196\pi$
$740$	5.19615	−	15.5885i	0.191014	−	0.573043i
$741$	8.53590	−	8.53590i	0.313574	−	0.313574i
$742$	−4.50962	−	1.56218i	−0.165553	−	0.0573494i
$743$	0.169873	+	0.633975i	0.00623204	+	0.0232583i	0.968972	−	0.247171i	$-0.0795010\pi$
$743$	0.169873	+	0.633975i	0.00623204	+	0.0232583i	−0.962740	+	0.270429i	$0.912834\pi$
$744$	8.83013	+	32.9545i	0.323728	+	1.20817i
$745$	46.1147	+	2.76795i	1.68951	+	0.101410i
$746$	−1.09808	−	1.90192i	−0.0402034	−	0.0696344i
$747$	4.09808	−	1.09808i	0.149941	−	0.0401765i
$748$	5.07180	+	5.07180i	0.185443	+	0.185443i
$749$	−3.63397	+	5.36603i	−0.132783	+	0.196070i
$750$	9.99038	−	0.820508i	0.364797	−	0.0299607i
$751$	11.4378	+	19.8109i	0.417372	+	0.722910i	0.995674	−	0.0929130i	$-0.0296179\pi$
$751$	11.4378	+	19.8109i	0.417372	+	0.722910i	−0.578302	+	0.815823i	$0.696285\pi$
$752$	15.5096	−	15.5096i	0.565578	−	0.565578i
$753$	18.9282	−	32.7846i	0.689782	−	1.19474i
$754$	−3.71281			−0.135213
$755$	2.53590	−	1.26795i	0.0922908	−	0.0461454i
$756$	18.0000	−	15.5885i	0.654654	−	0.566947i
$757$	−11.7321	−	11.7321i	−0.426409	−	0.426409i	0.460994	−	0.887403i	$-0.347493\pi$
$757$	−11.7321	−	11.7321i	−0.426409	−	0.426409i	−0.887403	+	0.460994i	$0.847493\pi$
$758$	7.12436	−	7.12436i	0.258768	−	0.258768i
$759$	5.66025	−	1.51666i	0.205454	−	0.0550513i
$760$	−9.19615	+	27.5885i	−0.333580	+	1.00074i
$761$	10.0359	−	5.79423i	0.363801	−	0.210041i	−0.306946	−	0.951727i	$-0.599307\pi$
$761$	10.0359	−	5.79423i	0.363801	−	0.210041i	0.670747	+	0.741686i	$0.265974\pi$
$762$	−4.28461	+	7.42116i	−0.155215	+	0.268840i
$763$	1.73205	−	5.00000i	0.0627044	−	0.181012i
$764$			0.588457i			0.0212896i
$765$	6.00000	−	18.0000i	0.216930	−	0.650791i
$766$	0.356406	−	0.205771i	0.0128775	−	0.00743482i
$767$	3.46410	−	0.928203i	0.125081	−	0.0335155i
$768$	−2.08846	−	1.20577i	−0.0753607	−	0.0435095i
$769$	17.9904	−	31.1603i	0.648750	−	1.12367i	−0.334672	−	0.942335i	$-0.608626\pi$
$769$	17.9904	−	31.1603i	0.648750	−	1.12367i	0.983422	−	0.181333i	$-0.0580411\pi$
$770$	4.14359	−	1.71281i	0.149325	−	0.0617255i
$771$	−33.2487	−	33.2487i	−1.19742	−	1.19742i
$772$	13.0526	+	13.0526i	0.469772	+	0.469772i
$773$	12.0263	−	44.8827i	0.432555	−	1.61432i	−0.314295	−	0.949325i	$-0.601768\pi$
$773$	12.0263	−	44.8827i	0.432555	−	1.61432i	0.746850	−	0.664993i	$-0.231565\pi$
$774$	4.50000	−	7.79423i	0.161749	−	0.280158i
$775$	−46.8827	+	20.0263i	−1.68408	+	0.719365i
$776$	−5.36603	+	3.09808i	−0.192629	+	0.111214i
$777$	−17.4904	+	8.49038i	−0.627464	+	0.304591i
$778$	−1.23205	−	4.59808i	−0.0441712	−	0.164849i
$779$	55.1769	−	31.8564i	1.97692	−	1.14137i
$780$	−5.19615	+	4.60770i	−0.186052	+	0.164982i
$781$	4.39230	−	7.60770i	0.157169	−	0.272225i
$782$	−0.875644	−	3.26795i	−0.0313130	−	0.116862i
$783$	−18.0000	−	31.1769i	−0.643268	−	1.11417i
$784$	−2.46410	+	17.0718i	−0.0880036	+	0.609707i
$785$	3.09808	−	0.633975i	0.110575	−	0.0226275i
$786$	12.0000	+	12.0000i	0.428026	+	0.428026i
$787$	4.29423	−	4.29423i	0.153073	−	0.153073i	−0.626416	−	0.779489i	$-0.715479\pi$
$787$	4.29423	−	4.29423i	0.153073	−	0.153073i	0.779489	+	0.626416i	$0.215479\pi$
$788$	−18.2487	+	18.2487i	−0.650083	+	0.650083i
$789$	9.44744	−	35.2583i	0.336338	−	1.25523i
$790$	−13.0000	+	2.66025i	−0.462519	+	0.0946476i
$791$	−16.0981	−	10.9019i	−0.572382	−	0.387628i
$792$	−6.00000	+	6.00000i	−0.213201	+	0.213201i
$793$	−2.51666	−	9.39230i	−0.0893692	−	0.333531i
$794$	8.78461	−	15.2154i	0.311754	−	0.539974i
$795$	2.70577	+	13.2224i	0.0959638	+	0.468951i
$796$	29.7846	−	17.1962i	1.05569	−	0.609501i
$797$	12.6147	+	47.0788i	0.446837	+	1.66762i	0.711040	+	0.703151i	$0.248224\pi$
$797$	12.6147	+	47.0788i	0.446837	+	1.66762i	−0.264204	+	0.964467i	$0.585109\pi$
$798$	14.3660	−	6.97372i	0.508552	−	0.246867i
$799$	−21.8038	+	12.5885i	−0.771365	+	0.445348i
$800$	9.57180	−	23.8468i	0.338414	−	0.843111i
$801$	−3.58846			−0.126792
$802$	0.349365	−	1.30385i	0.0123365	−	0.0460405i
$803$	−0.679492	−	0.679492i	−0.0239787	−	0.0239787i
$804$	24.9904	−	6.69615i	0.881343	−	0.236155i
$805$	13.5526	+	1.79423i	0.477665	+	0.0632382i
$806$	−2.73205	+	4.73205i	−0.0962324	+	0.166679i
$807$		−	6.80385i		−	0.239507i
$808$	25.3564	−	6.79423i	0.892035	−	0.239020i
$809$	41.5981	−	24.0167i	1.46251	−	0.844381i	0.463384	−	0.886158i	$-0.346635\pi$
$809$	41.5981	−	24.0167i	1.46251	−	0.844381i	0.999127	+	0.0417770i	$0.0133019\pi$
$810$	9.88269	+	3.29423i	0.347242	+	0.115747i
$811$			25.8564i			0.907941i	0.891017	+	0.453971i	$0.149993\pi$
$811$			25.8564i			0.907941i	−0.891017	+	0.453971i	$0.850007\pi$
$812$	30.0000	+	10.3923i	1.05279	+	0.364698i
$813$	3.92820	+	6.80385i	0.137768	+	0.238621i
$814$	2.78461	−	1.60770i	0.0976005	−	0.0563497i
$815$	−0.464102	+	1.39230i	−0.0162568	+	0.0487703i
$816$	−8.53590	−	8.53590i	−0.298816	−	0.298816i
$817$	−27.5885	+	27.5885i	−0.965198	+	0.965198i
$818$	−5.63397	−	5.63397i	−0.196987	−	0.196987i
$819$	8.19615	+	0.588457i	0.286397	+	0.0205624i
$820$	−32.7846	+	16.3923i	−1.14489	+	0.572444i
$821$	−7.33975			−0.256159			−0.128079	−	0.991764i	$-0.540881\pi$
$821$	−7.33975			−0.256159			−0.128079	+	0.991764i	$0.540881\pi$
$822$	3.46410	+	6.00000i	0.120824	+	0.209274i
$823$	−27.9282	+	27.9282i	−0.973516	+	0.973516i	−0.999658	−	0.0261423i	$-0.991678\pi$
$823$	−27.9282	+	27.9282i	−0.973516	+	0.973516i	0.0261423	+	0.999658i	$0.491678\pi$
$824$	11.0622	+	19.1603i	0.385369	+	0.667479i
$825$	−10.1436	−	7.60770i	−0.353155	−	0.264866i
$826$	4.73205	+	0.339746i	0.164649	+	0.0118213i
$827$	0.607695	+	0.607695i	0.0211316	+	0.0211316i	0.717594	−	0.696462i	$-0.245244\pi$
$827$	0.607695	+	0.607695i	0.0211316	+	0.0211316i	−0.696462	+	0.717594i	$0.745244\pi$
$828$	−11.5981	+	3.10770i	−0.403061	+	0.108000i
$829$	4.83975	+	8.38269i	0.168091	+	0.291143i	0.937749	−	0.347314i	$-0.112906\pi$
$829$	4.83975	+	8.38269i	0.168091	+	0.291143i	−0.769657	+	0.638457i	$0.779573\pi$
$830$	−1.63397	−	0.0980762i	−0.0567161	−	0.00340427i
$831$	9.00000	+	2.41154i	0.312207	+	0.0836555i
$832$	0.607695	+	2.26795i	0.0210680	+	0.0786270i
$833$	7.80385	−	18.1962i	0.270387	−	0.630459i
$834$	6.00000	+	1.60770i	0.207763	+	0.0556699i
$835$	−15.0981	+	45.2942i	−0.522490	+	1.56747i
$836$	14.7846	−	8.53590i	0.511336	−	0.295220i
$837$	−52.9808			−1.83128
$838$	−4.00000	+	1.07180i	−0.138178	+	0.0370246i
$839$	19.0263	+	32.9545i	0.656860	+	1.13772i	0.981424	+	0.191851i	$0.0614491\pi$
$839$	19.0263	+	32.9545i	0.656860	+	1.13772i	−0.324564	+	0.945864i	$0.605218\pi$
$840$	−18.2942	+	7.56218i	−0.631211	+	0.260920i
$841$	9.50000	−	16.4545i	0.327586	−	0.567396i
$842$	−2.01666	+	7.52628i	−0.0694987	+	0.259373i
$843$			17.7846i			0.612534i
$844$	−7.39230	−	4.26795i	−0.254454	−	0.146909i
$845$	26.6244	+	1.59808i	0.915906	+	0.0549755i
$846$	−6.91154	−	11.9711i	−0.237624	−	0.411576i
$847$	22.1410	+	7.66987i	0.760774	+	0.263540i
$848$	8.29423	+	2.22243i	0.284825	+	0.0763186i
$849$	−4.28461	−	15.9904i	−0.147047	−	0.548788i
$850$	−4.39230	+	5.85641i	−0.150655	+	0.200873i
$851$	9.80385			0.336072
$852$	−9.00000	+	15.5885i	−0.308335	+	0.534052i
$853$	−4.51666	+	16.8564i	−0.154648	+	0.577152i	0.844488	+	0.535575i	$0.179905\pi$
$853$	−4.51666	+	16.8564i	−0.154648	+	0.577152i	−0.999135	+	0.0415775i	$0.986762\pi$
$854$	0.921162	−	12.8301i	0.0315215	−	0.439038i
$855$	−37.6865	−	24.8827i	−1.28885	−	0.850970i
$856$	−2.36603	+	4.09808i	−0.0808691	+	0.140069i
$857$	6.24167	+	23.2942i	0.213211	+	0.795716i	0.986789	+	0.162014i	$0.0517988\pi$
$857$	6.24167	+	23.2942i	0.213211	+	0.795716i	−0.773577	+	0.633702i	$0.781534\pi$
$858$	−1.35898			−0.0463949
$859$	−4.49038	−	7.77757i	−0.153210	−	0.265367i	0.779196	−	0.626780i	$-0.215628\pi$
$859$	−4.49038	−	7.77757i	−0.153210	−	0.265367i	−0.932406	+	0.361413i	$0.882294\pi$
$860$	16.7942	−	14.8923i	0.572678	−	0.507823i
$861$	40.9808	+	14.1962i	1.39662	+	0.483804i
$862$	−1.84936	+	6.90192i	−0.0629896	+	0.235080i
$863$	10.5718	+	39.4545i	0.359868	+	1.34305i	0.874246	+	0.485483i	$0.161356\pi$
$863$	10.5718	+	39.4545i	0.359868	+	1.34305i	−0.514378	+	0.857563i	$0.671977\pi$
$864$	18.8827	−	18.8827i	0.642402	−	0.642402i
$865$	6.33975	+	30.9808i	0.215558	+	1.05338i
$866$			14.7846i			0.502401i
$867$	−7.79423	−	13.5000i	−0.264706	−	0.458484i
$868$	35.3205	−	30.5885i	1.19886	−	1.03824i
$869$	14.5359	+	8.39230i	0.493097	+	0.284689i
$870$	2.78461	+	13.6077i	0.0944071	+	0.461344i
$871$	7.73205	+	4.46410i	0.261991	+	0.151260i
$872$	1.00000	−	3.73205i	0.0338643	−	0.126383i
$873$	−2.49038	−	9.29423i	−0.0842866	−	0.314562i
$874$	−8.05256			−0.272382
$875$	−15.0526	−	25.4641i	−0.508869	−	0.860844i
$876$	1.39230	+	1.39230i	0.0470416	+	0.0470416i
$877$	0.562178	−	2.09808i	0.0189834	−	0.0708470i	−0.955784	−	0.294068i	$-0.904991\pi$
$877$	0.562178	−	2.09808i	0.0189834	−	0.0708470i	0.974768	+	0.223221i	$0.0716573\pi$
$878$	8.00000	+	8.00000i	0.269987	+	0.269987i
$879$	30.4186	+	8.15064i	1.02599	+	0.274914i
$880$	−7.21539	+	3.60770i	−0.243231	+	0.121615i
$881$			23.7846i			0.801324i	0.916226	+	0.400662i	$0.131220\pi$
$881$			23.7846i			0.801324i	−0.916226	+	0.400662i	$0.868780\pi$
$882$	9.99038	+	4.28461i	0.336394	+	0.144270i
$883$	39.5429	−	39.5429i	1.33073	−	1.33073i	0.426005	−	0.904721i	$-0.359921\pi$
$883$	39.5429	−	39.5429i	1.33073	−	1.33073i	0.904721	−	0.426005i	$-0.140079\pi$
$884$		−	5.07180i		−	0.170583i
$885$	−6.00000	−	12.0000i	−0.201688	−	0.403376i
$886$	12.1962			0.409738
$887$	8.23205	+	2.20577i	0.276405	+	0.0740626i	0.394359	−	0.918957i	$-0.370967\pi$
$887$	8.23205	+	2.20577i	0.276405	+	0.0740626i	−0.117954	+	0.993019i	$0.537633\pi$
$888$	−12.2942	+	7.09808i	−0.412567	+	0.238196i
$889$	25.2224	+	1.81089i	0.845933	+	0.0607353i
$890$	1.31347	+	0.437822i	0.0440275	+	0.0146758i
$891$	−6.58846	−	11.4115i	−0.220722	−	0.382301i
$892$	12.6962	+	3.40192i	0.425099	+	0.113905i
$893$	15.5096	+	57.8827i	0.519010	+	1.93697i
$894$	−13.0981	−	13.0981i	−0.438065	−	0.438065i
$895$	−41.4904	−	2.49038i	−1.38687	−	0.0832443i
$896$	−2.16987	+	30.2224i	−0.0724904	+	1.00966i
$897$	−3.58846	−	2.07180i	−0.119815	−	0.0691753i
$898$	−10.8301	+	10.8301i	−0.361406	+	0.361406i
$899$	−35.3205	−	61.1769i	−1.17800	−	2.04036i
$900$	20.7846	+	15.5885i	0.692820	+	0.519615i
$901$	−8.53590	−	4.92820i	−0.284372	−	0.164182i
$902$	−6.92820	−	1.85641i	−0.230684	−	0.0618116i
$903$	−26.4904	−	1.90192i	−0.881545	−	0.0632921i
$904$	−12.2942	−	7.09808i	−0.408900	−	0.236079i
$905$	−5.58846	+	8.46410i	−0.185767	+	0.281356i
$906$	−1.09808	−	0.294229i	−0.0364811	−	0.00977509i
$907$	17.5622	−	4.70577i	0.583143	−	0.156253i	0.0448253	−	0.998995i	$-0.485727\pi$
$907$	17.5622	−	4.70577i	0.583143	−	0.156253i	0.538317	+	0.842742i	$0.319060\pi$
$908$	−15.7583	+	4.22243i	−0.522959	+	0.140126i
$909$			40.7654i			1.35210i
$910$	−2.92820	−	1.21539i	−0.0970690	−	0.0402898i
$911$	−19.5622	−	33.8827i	−0.648124	−	1.12258i	−0.983571	−	0.180524i	$-0.942221\pi$
$911$	−19.5622	−	33.8827i	−0.648124	−	1.12258i	0.335447	−	0.942059i	$-0.391113\pi$
$912$	−24.8827	+	14.3660i	−0.823948	+	0.475707i
$913$	1.46410	+	1.46410i	0.0484547	+	0.0484547i
$914$		−	18.0526i		−	0.597126i
$915$	−32.5359	+	16.2679i	−1.07560	+	0.537802i
$916$	18.9904	−	10.9641i	0.627460	−	0.362264i
$917$	16.3923	−	47.3205i	0.541322	−	1.56266i
$918$	−6.58846	+	3.80385i	−0.217451	+	0.125546i
$919$	27.3731	+	15.8038i	0.902954	+	0.521321i	0.878157	−	0.478372i	$-0.158773\pi$
$919$	27.3731	+	15.8038i	0.902954	+	0.521321i	0.0247967	+	0.999693i	$0.492106\pi$
$920$	9.96410	+	0.598076i	0.328507	+	0.0197180i
$921$	−57.8827	+	15.5096i	−1.90730	+	0.511059i
$922$	4.59808	+	1.23205i	0.151430	+	0.0405754i
$923$	−6.00000	+	1.60770i	−0.197492	+	0.0529179i
$924$	10.9808	+	3.80385i	0.361241	+	0.125137i
$925$	−13.0981	−	16.6865i	−0.430662	−	0.548650i
$926$	1.18653	−	2.05514i	0.0389919	−	0.0675360i
$927$	−33.1865	+	8.89230i	−1.08999	+	0.292062i
$928$	34.3923	+	9.21539i	1.12898	+	0.302510i
$929$	−1.67949			−0.0551023			−0.0275512	−	0.999620i	$-0.508771\pi$
$929$	−1.67949			−0.0551023			−0.0275512	+	0.999620i	$0.508771\pi$
$930$	19.3923	+	6.46410i	0.635899	+	0.211966i
$931$	−37.0263	−	29.1506i	−1.21349	−	0.955373i
$932$	−20.4904	+	5.49038i	−0.671185	+	0.179843i
$933$	13.8564	−	24.0000i	0.453638	−	0.785725i
$934$	−6.03590	+	10.4545i	−0.197501	+	0.342081i
$935$	9.07180	−	1.85641i	0.296679	−	0.0607110i
$936$	6.00000			0.196116
$937$	−2.53590	+	2.53590i	−0.0828442	+	0.0828442i	−0.747315	−	0.664470i	$-0.768657\pi$
$937$	−2.53590	+	2.53590i	−0.0828442	+	0.0828442i	0.664470	+	0.747315i	$0.268657\pi$
$938$	7.73205	+	8.92820i	0.252460	+	0.291516i
$939$	−3.29423	−	12.2942i	−0.107503	−	0.401207i
$940$	−6.91154	−	33.7750i	−0.225430	−	1.10162i
$941$			13.9808i			0.455760i	0.973689	+	0.227880i	$0.0731794\pi$
$941$			13.9808i			0.455760i	−0.973689	+	0.227880i	$0.926821\pi$
$942$	−1.09808	−	0.633975i	−0.0357773	−	0.0206560i
$943$	−15.4641	−	15.4641i	−0.503580	−	0.503580i
$944$	−8.53590			−0.277820
$945$	−3.99038	−	30.4808i	−0.129807	−	0.991539i
$946$	4.39230			0.142806
$947$	−11.2224	−	11.2224i	−0.364680	−	0.364680i	0.500853	−	0.865533i	$-0.333020\pi$
$947$	−11.2224	−	11.2224i	−0.364680	−	0.364680i	−0.865533	+	0.500853i	$0.833020\pi$
$948$	−29.7846	−	17.1962i	−0.967359	−	0.558505i
$949$			0.679492i			0.0220572i
$950$	10.7583	+	13.7058i	0.349046	+	0.444674i
$951$	0.973721	+	3.63397i	0.0315751	+	0.117840i
$952$	4.73205	−	13.6603i	0.153367	−	0.442731i
$953$	21.0000	−	21.0000i	0.680257	−	0.680257i	−0.279801	−	0.960058i	$-0.590269\pi$
$953$	21.0000	−	21.0000i	0.680257	−	0.680257i	0.960058	+	0.279801i	$0.0902686\pi$
$954$	2.70577	−	4.68653i	0.0876026	−	0.151732i
$955$	0.633975	+	0.418584i	0.0205149	+	0.0135451i
$956$	19.0526	−	33.0000i	0.616204	−	1.06730i
$957$	8.78461	−	15.2154i	0.283966	−	0.491844i
$958$	4.36603	−	1.16987i	0.141060	−	0.0377969i
$959$	11.4641	−	16.9282i	0.370195	−	0.546640i
$960$	7.85641	−	3.92820i	0.253564	−	0.126782i
$961$	−72.9615			−2.35360
$962$	−2.19615	−	0.588457i	−0.0708068	−	0.0189726i
$963$	−5.19615	−	5.19615i	−0.167444	−	0.167444i
$964$	−14.2583	+	24.6962i	−0.459230	+	0.795410i
$965$	23.3468	−	4.77757i	0.751560	−	0.153795i
$966$	−3.58846	−	4.14359i	−0.115457	−	0.133318i
$967$	38.5526	−	10.3301i	1.23977	−	0.332194i	0.421392	−	0.906879i	$-0.361542\pi$
$967$	38.5526	−	10.3301i	1.23977	−	0.332194i	0.818375	+	0.574684i	$0.194875\pi$
$968$	16.5263	+	4.42820i	0.531175	+	0.142328i
$969$	31.8564	−	8.53590i	1.02338	−	0.274213i
$970$	−0.222432	+	3.70577i	−0.00714186	+	0.118985i
$971$	−9.46410	−	5.46410i	−0.303717	−	0.175351i	0.340394	−	0.940283i	$-0.389439\pi$
$971$	−9.46410	−	5.46410i	−0.303717	−	0.175351i	−0.644112	+	0.764931i	$0.722773\pi$
$972$	13.5000	+	23.3827i	0.433013	+	0.750000i
$973$	−3.46410	−	18.0000i	−0.111054	−	0.577054i
$974$	12.8494	−	7.41858i	0.411720	−	0.237707i
$975$	1.26795	+	8.87564i	0.0406069	+	0.284248i
$976$			23.1436i			0.740808i
$977$	29.1769	+	29.1769i	0.933452	+	0.933452i	0.997920	−	0.0644676i	$-0.0205349\pi$
$977$	29.1769	+	29.1769i	0.933452	+	0.933452i	−0.0644676	+	0.997920i	$0.520535\pi$
$978$	0.509619	−	0.294229i	0.0162958	−	0.00940839i
$979$	−0.875644	−	1.51666i	−0.0279857	−	0.0484727i
$980$	20.2583	+	18.0167i	0.647129	+	0.575521i
$981$	5.19615	+	3.00000i	0.165900	+	0.0957826i
$982$	1.53590	−	0.411543i	0.0490125	−	0.0131329i
$983$	31.9545	−	8.56218i	1.01919	−	0.273091i	0.289725	−	0.957110i	$-0.406436\pi$
$983$	31.9545	−	8.56218i	1.01919	−	0.273091i	0.729464	+	0.684019i	$0.239769\pi$
$984$	30.5885	+	8.19615i	0.975124	+	0.261284i
$985$	6.67949	+	32.6410i	0.212826	+	1.04003i
$986$	−8.78461	−	5.07180i	−0.279759	−	0.161519i
$987$	−22.8731	+	33.7750i	−0.728058	+	1.07507i
$988$	−11.6603	−	3.12436i	−0.370962	−	0.0993990i
$989$	11.5981	+	6.69615i	0.368797	+	0.212925i
$990$	1.01924	+	4.98076i	0.0323935	+	0.158299i
$991$	5.26795	+	9.12436i	0.167342	+	0.289845i	0.937484	−	0.348027i	$-0.113148\pi$
$991$	5.26795	+	9.12436i	0.167342	+	0.289845i	−0.770143	+	0.637872i	$0.779815\pi$
$992$	37.0526	−	37.0526i	1.17642	−	1.17642i
$993$	53.4904	+	30.8827i	1.69747	+	0.980032i
$994$	−8.19615	−	0.588457i	−0.259966	−	0.0186647i
$995$	2.66025	−	44.3205i	0.0843357	−	1.40505i
$996$	−3.00000	−	3.00000i	−0.0950586	−	0.0950586i
$997$	−7.31347	−	27.2942i	−0.231620	−	0.864417i	−0.979644	−	0.200745i	$-0.935664\pi$
$997$	−7.31347	−	27.2942i	−0.231620	−	0.864417i	0.748024	−	0.663672i	$-0.231003\pi$
$998$	−10.4641	−	2.80385i	−0.331235	−	0.0887542i
$999$	−5.70577	−	21.2942i	−0.180523	−	0.673720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bs.c.292.1	yes	4
3.2	odd	2		945.2.bv.d.712.1		4
5.3	odd	4		315.2.bs.b.103.1	yes	4
7.3	odd	6		315.2.cg.a.157.1	yes	4
9.2	odd	6		945.2.cj.a.397.1		4
9.7	even	3		315.2.cg.c.187.1	yes	4
15.8	even	4		945.2.bv.a.523.1		4
21.17	even	6		945.2.cj.d.577.1		4
35.3	even	12		315.2.cg.c.283.1	yes	4
45.38	even	12		945.2.cj.d.208.1		4
45.43	odd	12		315.2.cg.a.313.1	yes	4
63.38	even	6		945.2.bv.a.262.1		4
63.52	odd	6		315.2.bs.b.52.1	✓	4
105.38	odd	12		945.2.cj.a.388.1		4
315.38	odd	12		945.2.bv.d.73.1		4
315.178	even	12	inner	315.2.bs.c.178.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.b.52.1	✓	4	63.52	odd	6
315.2.bs.b.103.1	yes	4	5.3	odd	4
315.2.bs.c.178.1	yes	4	315.178	even	12	inner
315.2.bs.c.292.1	yes	4	1.1	even	1	trivial
315.2.cg.a.157.1	yes	4	7.3	odd	6
315.2.cg.a.313.1	yes	4	45.43	odd	12
315.2.cg.c.187.1	yes	4	9.7	even	3
315.2.cg.c.283.1	yes	4	35.3	even	12
945.2.bv.a.262.1		4	63.38	even	6
945.2.bv.a.523.1		4	15.8	even	4
945.2.bv.d.73.1		4	315.38	odd	12
945.2.bv.d.712.1		4	3.2	odd	2
945.2.cj.a.388.1		4	105.38	odd	12
945.2.cj.a.397.1		4	9.2	odd	6
945.2.cj.d.208.1		4	45.38	even	12
945.2.cj.d.577.1		4	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-1.86603 - 1.23205i) q^{5} +(0.232051 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} +(-1.86603 - 1.23205i) q^{5} +(0.232051 + 0.866025i) q^{6} +(2.00000 - 1.73205i) q^{7} +(1.36603 - 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.232051 - 1.13397i) q^{10} +(-0.732051 + 1.26795i) q^{11} +(1.50000 - 2.59808i) q^{12} +(1.00000 - 0.267949i) q^{13} +(1.36603 + 0.0980762i) q^{14} +(-1.73205 - 3.46410i) q^{15} -2.46410 q^{16} +(2.73205 + 0.732051i) q^{17} +(-0.401924 + 1.50000i) q^{18} +(3.36603 - 5.83013i) q^{19} +(-2.13397 + 3.23205i) q^{20} +(4.50000 - 0.866025i) q^{21} +(-0.732051 + 0.196152i) q^{22} +(-2.23205 - 0.598076i) q^{23} +(3.23205 - 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(0.464102 + 0.267949i) q^{26} +5.19615i q^{27} +(-3.00000 - 3.46410i) q^{28} +(-6.00000 + 3.46410i) q^{29} +(0.633975 - 1.90192i) q^{30} +10.1962i q^{31} +(-3.63397 - 3.63397i) q^{32} +(-2.19615 + 1.26795i) q^{33} +(0.732051 + 1.26795i) q^{34} +(-5.86603 + 0.767949i) q^{35} +(4.50000 - 2.59808i) q^{36} +(-4.09808 + 1.09808i) q^{37} +(3.36603 - 0.901924i) q^{38} +(1.73205 + 0.464102i) q^{39} +(-4.23205 + 0.866025i) q^{40} +(8.19615 + 4.73205i) q^{41} +(1.96410 + 1.33013i) q^{42} +(-5.59808 - 1.50000i) q^{43} +(2.19615 + 1.26795i) q^{44} +(0.401924 - 6.69615i) q^{45} +(-0.598076 - 1.03590i) q^{46} +(-6.29423 + 6.29423i) q^{47} +(-3.69615 - 2.13397i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-0.964102 + 2.40192i) q^{50} +(3.46410 + 3.46410i) q^{51} +(-0.464102 - 1.73205i) q^{52} +(-3.36603 - 0.901924i) q^{53} +(-1.90192 + 1.90192i) q^{54} +(2.92820 - 1.46410i) q^{55} +(0.366025 - 5.09808i) q^{56} +(10.0981 - 5.83013i) q^{57} +(-3.46410 - 0.928203i) q^{58} +3.46410 q^{59} +(-6.00000 + 3.00000i) q^{60} -9.39230i q^{61} +(-3.73205 + 3.73205i) q^{62} +(7.50000 + 2.59808i) q^{63} +2.26795i q^{64} +(-2.19615 - 0.732051i) q^{65} +(-1.26795 - 0.339746i) q^{66} +(6.09808 + 6.09808i) q^{67} +(1.26795 - 4.73205i) q^{68} +(-2.83013 - 2.83013i) q^{69} +(-2.42820 - 1.86603i) q^{70} -6.00000 q^{71} +(5.59808 + 1.50000i) q^{72} +(-0.169873 + 0.633975i) q^{73} +(-1.90192 - 1.09808i) q^{74} +(-1.03590 + 8.59808i) q^{75} +(-10.0981 - 5.83013i) q^{76} +(0.732051 + 3.80385i) q^{77} +(0.464102 + 0.803848i) q^{78} -11.4641i q^{79} +(4.59808 + 3.03590i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.26795 + 4.73205i) q^{82} +(0.366025 - 1.36603i) q^{83} +(-1.50000 - 7.79423i) q^{84} +(-4.19615 - 4.73205i) q^{85} +(-1.50000 - 2.59808i) q^{86} -12.0000 q^{87} +(0.732051 + 2.73205i) q^{88} +(-0.598076 + 1.03590i) q^{89} +(2.59808 - 2.30385i) q^{90} +(1.53590 - 2.26795i) q^{91} +(-1.03590 + 3.86603i) q^{92} +(-8.83013 + 15.2942i) q^{93} -4.60770 q^{94} +(-13.4641 + 6.73205i) q^{95} +(-2.30385 - 8.59808i) q^{96} +(-3.09808 - 0.830127i) q^{97} +(2.90192 - 2.16987i) q^{98} -4.39230 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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