LMFDB - Embedded newform 315.2.bs.b.52.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("315.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} -1.73205i q^{4} +(0.133975 - 2.23205i) q^{5} +(0.232051 - 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} -1.73205i q^{4} +(0.133975 - 2.23205i) q^{5} +(0.232051 - 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.866025 - 0.767949i) q^{10} +(-0.732051 - 1.26795i) q^{11} +(-2.59808 + 1.50000i) q^{12} +(0.267949 - 1.00000i) q^{13} +(-1.36603 + 0.0980762i) q^{14} +(-3.46410 + 1.73205i) q^{15} -2.46410 q^{16} +(0.732051 + 2.73205i) q^{17} +(-1.50000 + 0.401924i) q^{18} +(-3.36603 - 5.83013i) q^{19} +(-3.86603 - 0.232051i) q^{20} +(4.50000 + 0.866025i) q^{21} +(0.196152 - 0.732051i) q^{22} +(0.598076 + 2.23205i) q^{23} +(-3.23205 - 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(0.464102 - 0.267949i) q^{26} +5.19615 q^{27} +(3.46410 + 3.00000i) q^{28} +(6.00000 + 3.46410i) q^{29} +(-1.90192 - 0.633975i) q^{30} -10.1962i q^{31} +(-3.63397 - 3.63397i) q^{32} +(-1.26795 + 2.19615i) q^{33} +(-0.732051 + 1.26795i) q^{34} +(4.23205 + 4.13397i) q^{35} +(4.50000 + 2.59808i) q^{36} +(1.09808 - 4.09808i) q^{37} +(0.901924 - 3.36603i) q^{38} +(-1.73205 + 0.464102i) q^{39} +(-2.86603 - 3.23205i) q^{40} +(8.19615 - 4.73205i) q^{41} +(1.33013 + 1.96410i) q^{42} +(1.50000 + 5.59808i) q^{43} +(-2.19615 + 1.26795i) q^{44} +(5.59808 + 3.69615i) q^{45} +(-0.598076 + 1.03590i) q^{46} +(6.29423 - 6.29423i) q^{47} +(2.13397 + 3.69615i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-1.59808 - 2.03590i) q^{50} +(3.46410 - 3.46410i) q^{51} +(-1.73205 - 0.464102i) q^{52} +(0.901924 + 3.36603i) q^{53} +(1.90192 + 1.90192i) q^{54} +(-2.92820 + 1.46410i) q^{55} +(0.366025 + 5.09808i) q^{56} +(-5.83013 + 10.0981i) q^{57} +(0.928203 + 3.46410i) q^{58} -3.46410 q^{59} +(3.00000 + 6.00000i) q^{60} +9.39230i q^{61} +(3.73205 - 3.73205i) q^{62} +(-2.59808 - 7.50000i) q^{63} +2.26795i q^{64} +(-2.19615 - 0.732051i) q^{65} +(-1.26795 + 0.339746i) q^{66} +(6.09808 + 6.09808i) q^{67} +(4.73205 - 1.26795i) q^{68} +(2.83013 - 2.83013i) q^{69} +(0.0358984 + 3.06218i) q^{70} -6.00000 q^{71} +(1.50000 + 5.59808i) q^{72} +(-0.633975 + 0.169873i) q^{73} +(1.90192 - 1.09808i) q^{74} +(3.40192 + 7.96410i) q^{75} +(-10.0981 + 5.83013i) q^{76} +(3.80385 + 0.732051i) q^{77} +(-0.803848 - 0.464102i) q^{78} -11.4641i q^{79} +(-0.330127 + 5.50000i) 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} -12.0000i q^{87} +(-2.73205 - 0.732051i) q^{88} +(0.598076 + 1.03590i) q^{89} +(0.696152 + 3.40192i) q^{90} +(1.53590 + 2.26795i) q^{91} +(3.86603 - 1.03590i) q^{92} +(-15.2942 + 8.83013i) q^{93} +4.60770 q^{94} +(-13.4641 + 6.73205i) q^{95} +(-2.30385 + 8.59808i) q^{96} +(-0.830127 - 3.09808i) q^{97} +(2.16987 - 2.90192i) q^{98} +4.39230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 4 q^{11} + 8 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 12 q^{20} + 18 q^{21} - 20 q^{22} - 8 q^{23} - 6 q^{24} - 6 q^{25} - 12 q^{26} + 24 q^{29} - 18 q^{30} - 18 q^{32} - 12 q^{33} + 4 q^{34} + 10 q^{35} + 18 q^{36} - 6 q^{37} + 14 q^{38} - 8 q^{40} + 12 q^{41} - 12 q^{42} + 6 q^{43} + 12 q^{44} + 12 q^{45} + 8 q^{46} - 6 q^{47} + 12 q^{48} - 4 q^{49} + 4 q^{50} + 14 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{56} - 6 q^{57} - 24 q^{58} + 12 q^{60} + 8 q^{62} + 12 q^{65} - 12 q^{66} + 14 q^{67} + 12 q^{68} - 6 q^{69} + 14 q^{70} - 24 q^{71} + 6 q^{72} - 6 q^{73} + 18 q^{74} + 24 q^{75} - 30 q^{76} + 36 q^{77} - 24 q^{78} + 16 q^{80} - 18 q^{81} + 12 q^{82} + 2 q^{83} + 6 q^{84} + 4 q^{85} - 6 q^{86} - 4 q^{88} - 8 q^{89} - 18 q^{90} + 20 q^{91} + 12 q^{92} - 30 q^{93} + 60 q^{94} - 40 q^{95} - 30 q^{96} + 14 q^{97} + 26 q^{98} - 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 + 4 * q^11 + 8 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 - 6 * q^18 - 10 * q^19 - 12 * q^20 + 18 * q^21 - 20 * q^22 - 8 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 24 * q^29 - 18 * q^30 - 18 * q^32 - 12 * q^33 + 4 * q^34 + 10 * q^35 + 18 * q^36 - 6 * q^37 + 14 * q^38 - 8 * q^40 + 12 * q^41 - 12 * q^42 + 6 * q^43 + 12 * q^44 + 12 * q^45 + 8 * q^46 - 6 * q^47 + 12 * q^48 - 4 * q^49 + 4 * q^50 + 14 * q^53 + 18 * q^54 + 16 * q^55 - 2 * q^56 - 6 * q^57 - 24 * q^58 + 12 * q^60 + 8 * q^62 + 12 * q^65 - 12 * q^66 + 14 * q^67 + 12 * q^68 - 6 * q^69 + 14 * q^70 - 24 * q^71 + 6 * q^72 - 6 * q^73 + 18 * q^74 + 24 * q^75 - 30 * q^76 + 36 * q^77 - 24 * q^78 + 16 * q^80 - 18 * q^81 + 12 * q^82 + 2 * q^83 + 6 * q^84 + 4 * q^85 - 6 * q^86 - 4 * q^88 - 8 * q^89 - 18 * q^90 + 20 * q^91 + 12 * q^92 - 30 * q^93 + 60 * q^94 - 40 * q^95 - 30 * q^96 + 14 * q^97 + 26 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	0.824574	−	0.565755i	$-0.191415\pi$
$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	−0.565755	+	0.824574i	$0.691415\pi$
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$		−	1.73205i		−	0.866025i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$6$	0.232051	−	0.866025i	0.0947343	−	0.353553i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$	1.36603	−	1.36603i	0.482963	−	0.482963i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	0.866025	−	0.767949i	0.273861	−	0.242847i
$11$	−0.732051	−	1.26795i	−0.220722	−	0.382301i	0.734306	−	0.678819i	$-0.237508\pi$
$11$	−0.732051	−	1.26795i	−0.220722	−	0.382301i	−0.955027	+	0.296518i	$0.904175\pi$
$12$	−2.59808	+	1.50000i	−0.750000	+	0.433013i
$13$	0.267949	−	1.00000i	0.0743157	−	0.277350i	−0.918762	−	0.394813i	$-0.870809\pi$
$13$	0.267949	−	1.00000i	0.0743157	−	0.277350i	0.993077	+	0.117463i	$0.0374761\pi$
$14$	−1.36603	+	0.0980762i	−0.365086	+	0.0262120i
$15$	−3.46410	+	1.73205i	−0.894427	+	0.447214i
$16$	−2.46410			−0.616025
$17$	0.732051	+	2.73205i	0.177548	+	0.662620i	0.996104	+	0.0881917i	$0.0281088\pi$
$17$	0.732051	+	2.73205i	0.177548	+	0.662620i	−0.818555	+	0.574428i	$0.805225\pi$
$18$	−1.50000	+	0.401924i	−0.353553	+	0.0947343i
$19$	−3.36603	−	5.83013i	−0.772219	−	1.33752i	−0.936344	−	0.351083i	$-0.885813\pi$
$19$	−3.36603	−	5.83013i	−0.772219	−	1.33752i	0.164125	−	0.986440i	$-0.447520\pi$
$20$	−3.86603	−	0.232051i	−0.864470	−	0.0518881i
$21$	4.50000	+	0.866025i	0.981981	+	0.188982i
$22$	0.196152	−	0.732051i	0.0418198	−	0.156074i
$23$	0.598076	+	2.23205i	0.124708	+	0.465415i	0.999829	−	0.0184884i	$-0.00588537\pi$
$23$	0.598076	+	2.23205i	0.124708	+	0.465415i	−0.875122	+	0.483903i	$0.839219\pi$
$24$	−3.23205	−	0.866025i	−0.659740	−	0.176777i
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	0.464102	−	0.267949i	0.0910178	−	0.0525492i
$27$	5.19615			1.00000
$28$	3.46410	+	3.00000i	0.654654	+	0.566947i
$29$	6.00000	+	3.46410i	1.11417	+	0.643268i	0.939907	−	0.341431i	$-0.110912\pi$
$29$	6.00000	+	3.46410i	1.11417	+	0.643268i	0.174265	+	0.984699i	$0.444245\pi$
$30$	−1.90192	−	0.633975i	−0.347242	−	0.115747i
$31$		−	10.1962i		−	1.83128i	−0.401996	−	0.915642i	$-0.631683\pi$
$31$		−	10.1962i		−	1.83128i	0.401996	−	0.915642i	$-0.368317\pi$
$32$	−3.63397	−	3.63397i	−0.642402	−	0.642402i
$33$	−1.26795	+	2.19615i	−0.220722	+	0.382301i
$34$	−0.732051	+	1.26795i	−0.125546	+	0.217451i
$35$	4.23205	+	4.13397i	0.715347	+	0.698769i
$36$	4.50000	+	2.59808i	0.750000	+	0.433013i
$37$	1.09808	−	4.09808i	0.180523	−	0.673720i	−0.815022	−	0.579430i	$-0.803275\pi$
$37$	1.09808	−	4.09808i	0.180523	−	0.673720i	0.995545	−	0.0942898i	$-0.0300580\pi$
$38$	0.901924	−	3.36603i	0.146311	−	0.546041i
$39$	−1.73205	+	0.464102i	−0.277350	+	0.0743157i
$40$	−2.86603	−	3.23205i	−0.453158	−	0.511032i
$41$	8.19615	−	4.73205i	1.28002	−	0.739022i	0.303171	−	0.952936i	$-0.401955\pi$
$41$	8.19615	−	4.73205i	1.28002	−	0.739022i	0.976853	+	0.213914i	$0.0686212\pi$
$42$	1.33013	+	1.96410i	0.205243	+	0.303067i
$43$	1.50000	+	5.59808i	0.228748	+	0.853699i	0.980868	+	0.194673i	$0.0623645\pi$
$43$	1.50000	+	5.59808i	0.228748	+	0.853699i	−0.752120	+	0.659026i	$0.770969\pi$
$44$	−2.19615	+	1.26795i	−0.331082	+	0.191151i
$45$	5.59808	+	3.69615i	0.834512	+	0.550990i
$46$	−0.598076	+	1.03590i	−0.0881815	+	0.152735i
$47$	6.29423	−	6.29423i	0.918108	−	0.918108i	−0.0787841	−	0.996892i	$-0.525104\pi$
$47$	6.29423	−	6.29423i	0.918108	−	0.918108i	0.996892	+	0.0787841i	$0.0251038\pi$
$48$	2.13397	+	3.69615i	0.308013	+	0.533494i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	−1.59808	−	2.03590i	−0.226002	−	0.287920i
$51$	3.46410	−	3.46410i	0.485071	−	0.485071i
$52$	−1.73205	−	0.464102i	−0.240192	−	0.0643593i
$53$	0.901924	+	3.36603i	0.123889	+	0.462359i	0.999798	−	0.0201174i	$-0.00640401\pi$
$53$	0.901924	+	3.36603i	0.123889	+	0.462359i	−0.875909	+	0.482477i	$0.839737\pi$
$54$	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
$57$	−5.83013	+	10.0981i	−0.772219	+	1.33752i
$58$	0.928203	+	3.46410i	0.121879	+	0.454859i
$59$	−3.46410			−0.450988			−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410			−0.450988			−0.225494	+	0.974245i	$0.572400\pi$
$60$	3.00000	+	6.00000i	0.387298	+	0.774597i
$61$			9.39230i			1.20256i	0.799038	+	0.601281i	$0.205343\pi$
$61$			9.39230i			1.20256i	−0.799038	+	0.601281i	$0.794657\pi$
$62$	3.73205	−	3.73205i	0.473971	−	0.473971i
$63$	−2.59808	−	7.50000i	−0.327327	−	0.944911i
$64$			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	$0.573394\pi$
$68$	4.73205	−	1.26795i	0.573845	−	0.153761i
$69$	2.83013	−	2.83013i	0.340707	−	0.340707i
$70$	0.0358984	+	3.06218i	0.00429068	+	0.366000i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.50000	+	5.59808i	0.176777	+	0.659740i
$73$	−0.633975	+	0.169873i	−0.0742011	+	0.0198821i	−0.295729	−	0.955272i	$-0.595562\pi$
$73$	−0.633975	+	0.169873i	−0.0742011	+	0.0198821i	0.221528	+	0.975154i	$0.428896\pi$
$74$	1.90192	−	1.09808i	0.221094	−	0.127649i
$75$	3.40192	+	7.96410i	0.392820	+	0.919615i
$76$	−10.0981	+	5.83013i	−1.15833	+	0.668761i
$77$	3.80385	+	0.732051i	0.433489	+	0.0834249i
$78$	−0.803848	−	0.464102i	−0.0910178	−	0.0525492i
$79$		−	11.4641i		−	1.28981i	−0.764262	−	0.644906i	$-0.776896\pi$
$79$		−	11.4641i		−	1.28981i	0.764262	−	0.644906i	$-0.223104\pi$
$80$	−0.330127	+	5.50000i	−0.0369093	+	0.614919i
$81$	−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	$-0.558603\pi$
$83$	1.36603	−	0.366025i	0.149941	−	0.0401765i	0.333009	+	0.942924i	$0.391936\pi$
$84$	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
$87$		−	12.0000i		−	1.28654i
$88$	−2.73205	−	0.732051i	−0.291238	−	0.0780369i
$89$	0.598076	+	1.03590i	0.0633960	+	0.109805i	0.895981	−	0.444092i	$-0.146474\pi$
$89$	0.598076	+	1.03590i	0.0633960	+	0.109805i	−0.832585	+	0.553897i	$0.813140\pi$
$90$	0.696152	+	3.40192i	0.0733809	+	0.358594i
$91$	1.53590	+	2.26795i	0.161006	+	0.237746i
$92$	3.86603	−	1.03590i	0.403061	−	0.108000i
$93$	−15.2942	+	8.83013i	−1.58594	+	0.915642i
$94$	4.60770			0.475247
$95$	−13.4641	+	6.73205i	−1.38139	+	0.690694i
$96$	−2.30385	+	8.59808i	−0.235135	+	0.877537i
$97$	−0.830127	−	3.09808i	−0.0842866	−	0.314562i	0.910892	−	0.412646i	$-0.135395\pi$
$97$	−0.830127	−	3.09808i	−0.0842866	−	0.314562i	−0.995178	+	0.0980839i	$0.968729\pi$
$98$	2.16987	−	2.90192i	0.219190	−	0.293139i
$99$	4.39230			0.441443
$100$	−1.03590	+	8.59808i	−0.103590	+	0.859808i
$101$	11.7679	−	6.79423i	1.17095	−	0.676051i	0.217050	−	0.976160i	$-0.430357\pi$
$101$	11.7679	−	6.79423i	1.17095	−	0.676051i	0.953905	+	0.300109i	$0.0970232\pi$
$102$	2.53590			0.251091
$103$	−11.0622	+	2.96410i	−1.08999	+	0.292062i	−0.758682	−	0.651461i	$-0.774156\pi$
$103$	−11.0622	+	2.96410i	−1.08999	+	0.292062i	−0.331307	+	0.943523i	$0.607490\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$	2.53590	−	9.92820i	0.247478	−	0.968893i
$106$	−0.901924	+	1.56218i	−0.0876026	+	0.151732i
$107$	0.633975	−	2.36603i	0.0612886	−	0.228732i	−0.928487	−	0.371365i	$-0.878890\pi$
$107$	0.633975	−	2.36603i	0.0612886	−	0.228732i	0.989776	+	0.142632i	$0.0455566\pi$
$108$		−	9.00000i		−	0.866025i
$109$	−1.73205	−	1.00000i	−0.165900	−	0.0957826i	0.414751	−	0.909935i	$-0.363869\pi$
$109$	−1.73205	−	1.00000i	−0.165900	−	0.0957826i	−0.580651	+	0.814152i	$0.697202\pi$
$110$	−1.60770	−	0.535898i	−0.153288	−	0.0510959i
$111$	−7.09808	+	1.90192i	−0.673720	+	0.180523i
$112$	4.26795	−	4.92820i	0.403283	−	0.465671i
$113$	7.09808	+	1.90192i	0.667731	+	0.178918i	0.576732	−	0.816933i	$-0.304328\pi$
$113$	7.09808	+	1.90192i	0.667731	+	0.178918i	0.0909984	+	0.995851i	$0.470994\pi$
$114$	−5.83013	+	1.56218i	−0.546041	+	0.146311i
$115$	5.06218	−	1.03590i	0.472051	−	0.0965980i
$116$	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
$120$	−2.36603	+	7.09808i	−0.215988	+	0.647963i
$121$	4.42820	−	7.66987i	0.402564	−	0.697261i
$122$	−3.43782	+	3.43782i	−0.311246	+	0.311246i
$123$	−14.1962	−	8.19615i	−1.28002	−	0.739022i
$124$	−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	0.997289	−	0.0735897i	$-0.0234455\pi$
$131$	16.3923	+	9.46410i	1.43220	+	0.826882i	0.434914	+	0.900472i	$0.356779\pi$
$132$	3.80385	+	2.19615i	0.331082	+	0.191151i
$133$	17.4904	+	3.36603i	1.51661	+	0.291871i
$134$			4.46410i			0.385640i
$135$	0.696152	−	11.5981i	0.0599153	−	0.998203i
$136$	4.73205	+	2.73205i	0.405770	+	0.234271i
$137$	−2.00000	+	7.46410i	−0.170872	+	0.637701i	0.826347	+	0.563162i	$0.190415\pi$
$137$	−2.00000	+	7.46410i	−0.170872	+	0.637701i	−0.997218	+	0.0745393i	$0.976251\pi$
$138$	2.07180			0.176363
$139$	−3.46410	−	6.00000i	−0.293821	−	0.508913i	0.680889	−	0.732387i	$-0.261594\pi$
$139$	−3.46410	−	6.00000i	−0.293821	−	0.508913i	−0.974710	+	0.223474i	$0.928260\pi$
$140$	7.16025	−	7.33013i	0.605152	−	0.619509i
$141$	−14.8923	−	3.99038i	−1.25416	−	0.336051i
$142$	−2.19615	−	2.19615i	−0.184297	−	0.184297i
$143$	−1.46410	+	0.392305i	−0.122434	+	0.0328062i
$144$	3.69615	−	6.40192i	0.308013	−	0.533494i
$145$	8.53590	−	12.9282i	0.708868	−	1.07363i
$146$	−0.294229	−	0.169873i	−0.0243505	−	0.0140588i
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	−7.09808	−	1.90192i	−0.583458	−	0.156337i
$149$	17.8923	+	10.3301i	1.46579	+	0.846277i	0.999269	−	0.0382306i	$-0.0121722\pi$
$149$	17.8923	+	10.3301i	1.46579	+	0.846277i	0.466526	+	0.884508i	$0.345505\pi$
$150$	−1.66987	+	4.16025i	−0.136345	+	0.339683i
$151$	−0.633975	−	1.09808i	−0.0515921	−	0.0893602i	0.839076	−	0.544014i	$-0.183096\pi$
$151$	−0.633975	−	1.09808i	−0.0515921	−	0.0893602i	−0.890668	+	0.454654i	$0.849763\pi$
$152$	−12.5622	−	3.36603i	−1.01893	−	0.273021i
$153$	−8.19615	−	2.19615i	−0.662620	−	0.177548i
$154$	1.12436	+	1.66025i	0.0906032	+	0.133787i
$155$	−22.7583	−	1.36603i	−1.82799	−	0.109722i
$156$	0.803848	+	3.00000i	0.0643593	+	0.240192i
$157$	1.00000	−	1.00000i	0.0798087	−	0.0798087i	−0.666076	−	0.745884i	$-0.732027\pi$
$157$	1.00000	−	1.00000i	0.0798087	−	0.0798087i	0.745884	+	0.666076i	$0.232027\pi$
$158$	4.19615	−	4.19615i	0.333828	−	0.333828i
$159$	4.26795	−	4.26795i	0.338470	−	0.338470i
$160$	−8.59808	+	7.62436i	−0.679738	+	0.602758i
$161$	−5.50000	−	2.66987i	−0.433461	−	0.210415i
$162$	1.20577	−	4.50000i	0.0947343	−	0.353553i
$163$	0.633975	+	0.169873i	0.0496567	+	0.0133055i	0.283562	−	0.958954i	$-0.408484\pi$
$163$	0.633975	+	0.169873i	0.0496567	+	0.0133055i	−0.233905	+	0.972259i	$0.575151\pi$
$164$	−8.19615	−	14.1962i	−0.640012	−	1.10853i
$165$	4.73205	+	3.12436i	0.368390	+	0.243231i
$166$	0.633975	+	0.366025i	0.0492060	+	0.0284091i
$167$	−20.6244	−	5.52628i	−1.59596	−	0.427636i	−0.652141	−	0.758098i	$-0.726129\pi$
$167$	−20.6244	−	5.52628i	−1.59596	−	0.427636i	−0.943820	+	0.330461i	$0.892796\pi$
$168$	7.33013	−	4.96410i	0.565532	−	0.382989i
$169$	10.3301	+	5.96410i	0.794625	+	0.458777i
$170$	2.73205	+	1.80385i	0.209539	+	0.138349i
$171$	20.1962			1.54444
$172$	9.69615	−	2.59808i	0.739325	−	0.198101i
$173$	10.0000	+	10.0000i	0.760286	+	0.760286i	0.976374	−	0.216088i	$-0.0693298\pi$
$173$	10.0000	+	10.0000i	0.760286	+	0.760286i	−0.216088	+	0.976374i	$0.569330\pi$
$174$	4.39230	−	4.39230i	0.332980	−	0.332980i
$175$	9.79423	−	8.89230i	0.740374	−	0.672195i
$176$	1.80385	+	3.12436i	0.135970	+	0.235507i
$177$	3.00000	+	5.19615i	0.225494	+	0.390567i
$178$	−0.160254	+	0.598076i	−0.0120115	+	0.0448277i
$179$	−16.0981	−	9.29423i	−1.20323	−	0.694683i	−0.241955	−	0.970287i	$-0.577789\pi$
$179$	−16.0981	−	9.29423i	−1.20323	−	0.694683i	−0.961271	+	0.275604i	$0.911122\pi$
$180$	6.40192	−	9.69615i	0.477171	−	0.722709i
$181$			4.53590i			0.337151i	0.985689	+	0.168575i	$0.0539166\pi$
$181$			4.53590i			0.337151i	−0.985689	+	0.168575i	$0.946083\pi$
$182$	−0.267949	+	1.39230i	−0.0198617	+	0.103205i
$183$	14.0885	−	8.13397i	1.04145	−	0.601281i
$184$	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	$0.503913\pi$
$192$	3.40192	−	1.96410i	0.245513	−	0.141747i
$193$	−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
$195$	0.803848	+	3.92820i	0.0575647	+	0.281304i
$196$	−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	0.263334	+	0.964705i	$0.415178\pi$
$199$	−9.92820	+	17.1962i	−0.703792	+	1.21900i	−0.967126	+	0.254298i	$0.918156\pi$
$200$	−7.59808	+	5.96410i	−0.537265	+	0.421726i
$201$	3.86603	−	14.4282i	0.272688	−	1.01769i
$202$	6.79423	+	1.82051i	0.478040	+	0.128091i
$203$	−17.3205	+	6.00000i	−1.21566	+	0.421117i
$204$	−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
$207$	−6.69615	−	1.79423i	−0.465415	−	0.124708i
$208$	−0.660254	+	2.46410i	−0.0457804	+	0.170855i
$209$	−4.92820	+	8.53590i	−0.340891	+	0.590440i
$210$	4.56218	−	2.70577i	0.314820	−	0.186716i
$211$	2.46410	+	4.26795i	0.169636	+	0.293818i	0.938292	−	0.345845i	$-0.112408\pi$
$211$	2.46410	+	4.26795i	0.169636	+	0.293818i	−0.768656	+	0.639662i	$0.779074\pi$
$212$	5.83013	−	1.56218i	0.400415	−	0.107291i
$213$	5.19615	+	9.00000i	0.356034	+	0.616670i
$214$	1.09808	−	0.633975i	0.0750629	−	0.0433376i
$215$	12.6962	−	2.59808i	0.865870	−	0.177187i
$216$	7.09808	−	7.09808i	0.482963	−	0.482963i
$217$	20.3923	+	17.6603i	1.38432	+	1.19886i
$218$	−0.267949	−	1.00000i	−0.0181478	−	0.0677285i
$219$	0.803848	+	0.803848i	0.0543190	+	0.0543190i
$220$	2.53590	+	5.07180i	0.170970	+	0.341940i
$221$	2.92820			0.196972
$222$	−3.29423	−	1.90192i	−0.221094	−	0.127649i
$223$	−7.33013	+	1.96410i	−0.490862	+	0.131526i	−0.495756	−	0.868462i	$-0.665109\pi$
$223$	−7.33013	+	1.96410i	−0.490862	+	0.131526i	0.00489404	+	0.999988i	$0.498442\pi$
$224$	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
$227$	−9.09808	−	2.43782i	−0.603861	−	0.161804i	−0.0560804	−	0.998426i	$-0.517860\pi$
$227$	−9.09808	−	2.43782i	−0.603861	−	0.161804i	−0.547780	+	0.836622i	$0.684527\pi$
$228$	17.4904	+	10.0981i	1.15833	+	0.668761i
$229$	−6.33013	+	10.9641i	−0.418307	+	0.724528i	−0.995769	−	0.0918888i	$-0.970710\pi$
$229$	−6.33013	+	10.9641i	−0.418307	+	0.724528i	0.577463	+	0.816417i	$0.304043\pi$
$230$	2.23205	+	1.47372i	0.147177	+	0.0971743i
$231$	−2.19615	−	6.33975i	−0.144496	−	0.417125i
$232$	12.9282	−	3.46410i	0.848778	−	0.227429i
$233$	11.8301	+	3.16987i	0.775017	+	0.207665i	0.624587	−	0.780955i	$-0.285267\pi$
$233$	11.8301	+	3.16987i	0.775017	+	0.207665i	0.150430	+	0.988621i	$0.451934\pi$
$234$			1.60770i			0.105098i
$235$	−13.2058	−	14.8923i	−0.861450	−	0.971467i
$236$			6.00000i			0.390567i
$237$	−17.1962	+	9.92820i	−1.11701	+	0.644906i
$238$	−1.26795	−	3.66025i	−0.0821889	−	0.237259i
$239$	−19.0526	+	11.0000i	−1.23241	+	0.711531i	−0.967531	−	0.252752i	$-0.918664\pi$
$239$	−19.0526	+	11.0000i	−1.23241	+	0.711531i	−0.264876	+	0.964282i	$0.585331\pi$
$240$	8.53590	−	4.26795i	0.550990	−	0.275495i
$241$	−14.2583	+	8.23205i	−0.918460	+	0.530273i	−0.883143	−	0.469103i	$-0.844577\pi$
$241$	−14.2583	+	8.23205i	−0.918460	+	0.530273i	−0.0353164	+	0.999376i	$0.511244\pi$
$242$	4.42820	−	1.18653i	0.284656	−	0.0762733i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$	16.2679			1.04145
$245$	−15.5981	+	1.30385i	−0.996525	+	0.0832998i
$246$	−2.19615	−	8.19615i	−0.140022	−	0.522568i
$247$	−6.73205	+	1.80385i	−0.428350	+	0.114776i
$248$	−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	$0.242294\pi$
$251$			21.8564i			1.37956i	−0.724017	+	0.689782i	$0.757706\pi$
$252$	−12.9904	+	4.50000i	−0.818317	+	0.283473i
$253$	2.39230	−	2.39230i	0.150403	−	0.150403i
$254$			4.94744i			0.310430i
$255$	−7.26795	−	8.19615i	−0.455137	−	0.513263i
$256$	−1.39230			−0.0870191
$257$	−7.02628	−	26.2224i	−0.438287	−	1.63571i	−0.733075	−	0.680148i	$-0.761916\pi$
$257$	−7.02628	−	26.2224i	−0.438287	−	1.63571i	0.294788	−	0.955563i	$-0.404751\pi$
$258$	5.19615			0.323498
$259$	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
$262$	2.53590	+	9.46410i	0.156668	+	0.584694i
$263$	20.3564	+	5.45448i	1.25523	+	0.336338i	0.824355	−	0.566074i	$-0.191538\pi$
$263$	20.3564	+	5.45448i	1.25523	+	0.336338i	0.430875	+	0.902412i	$0.358205\pi$
$264$	1.26795	+	4.73205i	0.0780369	+	0.291238i
$265$	7.63397	−	1.56218i	0.468951	−	0.0959638i
$266$	5.16987	+	7.63397i	0.316985	+	0.468069i
$267$	1.03590	−	1.79423i	0.0633960	−	0.109805i
$268$	10.5622	−	10.5622i	0.645188	−	0.645188i
$269$	1.96410	−	3.40192i	0.119753	−	0.207419i	−0.799917	−	0.600111i	$-0.795123\pi$
$269$	1.96410	−	3.40192i	0.119753	−	0.207419i	0.919670	+	0.392692i	$0.128456\pi$
$270$	4.50000	−	3.99038i	0.273861	−	0.242847i
$271$	3.92820	−	2.26795i	0.238621	−	0.137768i	−0.375922	−	0.926651i	$-0.622674\pi$
$271$	3.92820	−	2.26795i	0.238621	−	0.137768i	0.614543	+	0.788883i	$0.289340\pi$
$272$	−1.80385	−	6.73205i	−0.109374	−	0.408191i
$273$	2.07180	−	4.26795i	0.125391	−	0.258308i
$274$	−3.46410	+	2.00000i	−0.209274	+	0.120824i
$275$	2.87564	+	6.73205i	0.173408	+	0.405958i
$276$	−4.90192	−	4.90192i	−0.295061	−	0.295061i
$277$	−1.39230	+	5.19615i	−0.0836555	+	0.312207i	−0.995056	−	0.0993135i	$-0.968335\pi$
$277$	−1.39230	+	5.19615i	−0.0836555	+	0.312207i	0.911401	+	0.411520i	$0.135002\pi$
$278$	0.928203	−	3.46410i	0.0556699	−	0.207763i
$279$	26.4904	+	15.2942i	1.58594	+	0.915642i
$280$	11.4282	−	0.133975i	0.682966	−	0.00800651i
$281$	5.13397	−	8.89230i	0.306267	−	0.530470i	−0.671275	−	0.741208i	$-0.734253\pi$
$281$	5.13397	−	8.89230i	0.306267	−	0.530470i	0.977543	+	0.210738i	$0.0675866\pi$
$282$	−3.99038	−	6.91154i	−0.237624	−	0.411576i
$283$	6.75833	+	6.75833i	0.401741	+	0.401741i	0.878846	−	0.477105i	$-0.158314\pi$
$283$	6.75833	+	6.75833i	0.401741	+	0.401741i	−0.477105	+	0.878846i	$0.658314\pi$
$284$			10.3923i			0.616670i
$285$	21.7583	+	14.3660i	1.28885	+	0.850970i
$286$	−0.679492	−	0.392305i	−0.0401792	−	0.0231975i
$287$	−4.73205	+	24.5885i	−0.279324	+	1.45141i
$288$	14.8923	−	3.99038i	0.877537	−	0.235135i
$289$	7.79423	−	4.50000i	0.458484	−	0.264706i
$290$	7.85641	−	1.60770i	0.461344	−	0.0944071i
$291$	−3.92820	+	3.92820i	−0.230275	+	0.230275i
$292$	0.294229	+	1.09808i	0.0172184	+	0.0642600i
$293$	4.70577	−	17.5622i	0.274914	−	1.02599i	−0.680985	−	0.732298i	$-0.738448\pi$
$293$	4.70577	−	17.5622i	0.274914	−	1.02599i	0.955899	−	0.293696i	$-0.0948853\pi$
$294$	−6.23205	−	0.741670i	−0.363461	−	0.0432551i
$295$	−0.464102	+	7.73205i	−0.0270210	+	0.450177i
$296$	−4.09808	−	7.09808i	−0.238196	−	0.412567i
$297$	−3.80385	−	6.58846i	−0.220722	−	0.382301i
$298$	2.76795	+	10.3301i	0.160343	+	0.598408i
$299$	2.39230			0.138351
$300$	13.7942	−	5.89230i	0.796410	−	0.340192i
$301$	−13.7942	−	6.69615i	−0.795086	−	0.385960i
$302$	0.169873	−	0.633975i	0.00977509	−	0.0364811i
$303$	−20.3827	−	11.7679i	−1.17095	−	0.676051i
$304$	8.29423	+	14.3660i	0.475707	+	0.823948i
$305$	20.9641	+	1.25833i	1.20040	+	0.0720518i
$306$	−2.19615	−	3.80385i	−0.125546	−	0.217451i
$307$	24.4641	−	24.4641i	1.39624	−	1.39624i	0.585744	−	0.810496i	$-0.300803\pi$
$307$	24.4641	−	24.4641i	1.39624	−	1.39624i	0.810496	−	0.585744i	$-0.199197\pi$
$308$	1.26795	−	6.58846i	0.0722481	−	0.375412i
$309$	14.0263	+	14.0263i	0.797927	+	0.797927i
$310$	−7.83013	−	8.83013i	−0.444721	−	0.501518i
$311$			16.0000i			0.907277i	0.891186	+	0.453638i	$0.149874\pi$
$311$			16.0000i			0.907277i	−0.891186	+	0.453638i	$0.850126\pi$
$312$	−1.73205	+	3.00000i	−0.0980581	+	0.169842i
$313$	5.19615	+	5.19615i	0.293704	+	0.293704i	0.838542	−	0.544838i	$-0.183409\pi$
$313$	5.19615	+	5.19615i	0.293704	+	0.293704i	−0.544838	+	0.838542i	$0.683409\pi$
$314$	0.732051			0.0413120
$315$	−17.0885	+	4.79423i	−0.962825	+	0.270124i
$316$	−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	$0.730572\pi$
$318$	3.12436			0.175205
$319$		−	10.1436i		−	0.567932i
$320$	5.06218	+	0.303848i	0.282984	+	0.0169856i
$321$	−4.09808	+	1.09808i	−0.228732	+	0.0612886i
$322$	−1.03590	−	2.99038i	−0.0577284	−	0.166647i
$323$	13.4641	−	13.4641i	0.749163	−	0.749163i
$324$	−13.5000	+	7.79423i	−0.750000	+	0.433013i
$325$	−1.92820	+	4.80385i	−0.106957	+	0.266470i
$326$	0.169873	+	0.294229i	0.00940839	+	0.0162958i
$327$			3.46410i			0.191565i
$328$	4.73205	−	17.6603i	0.261284	−	0.975124i
$329$	1.68653	+	23.4904i	0.0929816	+	1.29507i
$330$	0.588457	+	2.87564i	0.0323935	+	0.158299i
$331$	35.6603			1.96006			0.980032	−	0.198838i	$-0.0637167\pi$
$331$	35.6603			1.96006			0.980032	+	0.198838i	$0.0637167\pi$
$332$	−0.633975	−	2.36603i	−0.0347939	−	0.129853i
$333$	9.00000	+	9.00000i	0.493197	+	0.493197i
$334$	−5.52628	−	9.57180i	−0.302385	−	0.523745i
$335$	14.4282	−	12.7942i	0.788297	−	0.699023i
$336$	−11.0885	−	2.13397i	−0.604925	−	0.116418i
$337$	−2.46410	+	9.19615i	−0.134228	+	0.500946i	0.865772	+	0.500439i	$0.166828\pi$
$337$	−2.46410	+	9.19615i	−0.134228	+	0.500946i	−1.00000		0.000507178i	$0.999839\pi$
$338$	1.59808	+	5.96410i	0.0869239	+	0.324404i
$339$	−3.29423	−	12.2942i	−0.178918	−	0.667731i
$340$	−2.19615	−	10.7321i	−0.119103	−	0.582027i
$341$	−12.9282	+	7.46410i	−0.700101	+	0.404204i
$342$	7.39230	+	7.39230i	0.399730	+	0.399730i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	9.69615	+	5.59808i	0.522782	+	0.301828i
$345$	−5.93782	−	6.69615i	−0.319682	−	0.360509i
$346$			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	$0.825249\pi$
$348$	−20.7846			−1.11417
$349$	−4.93782	+	8.55256i	−0.264316	+	0.457808i	−0.967384	−	0.253314i	$-0.918479\pi$
$349$	−4.93782	+	8.55256i	−0.264316	+	0.457808i	0.703069	+	0.711122i	$0.251813\pi$
$350$	6.83975	+	0.330127i	0.365600	+	0.0176460i
$351$	1.39230	−	5.19615i	0.0743157	−	0.277350i
$352$	−1.94744	+	7.26795i	−0.103799	+	0.387383i
$353$	−7.26795	+	27.1244i	−0.386834	+	1.44368i	0.448422	+	0.893822i	$0.351986\pi$
$353$	−7.26795	+	27.1244i	−0.386834	+	1.44368i	−0.835256	+	0.549862i	$0.814680\pi$
$354$	−0.803848	+	3.00000i	−0.0427240	+	0.159448i
$355$	−0.803848	+	13.3923i	−0.0426638	+	0.710790i
$356$	1.79423	−	1.03590i	0.0950939	−	0.0549025i
$357$	0.928203	+	12.9282i	0.0491257	+	0.684233i
$358$	−2.49038	−	9.29423i	−0.131621	−	0.491215i
$359$	14.9545	−	8.63397i	0.789267	−	0.455684i	−0.0504372	−	0.998727i	$-0.516061\pi$
$359$	14.9545	−	8.63397i	0.789267	−	0.455684i	0.839705	+	0.543043i	$0.182728\pi$
$360$	12.6962	−	2.59808i	0.669146	−	0.136931i
$361$	−13.1603	+	22.7942i	−0.692645	+	1.19970i
$362$	−1.66025	+	1.66025i	−0.0872610	+	0.0872610i
$363$	−15.3397			−0.805128
$364$	3.92820	−	2.66025i	0.205894	−	0.139435i
$365$	0.294229	+	1.43782i	0.0154006	+	0.0752591i
$366$	8.13397	+	2.17949i	0.425170	+	0.113924i
$367$	−5.23205	−	1.40192i	−0.273111	−	0.0731798i	0.119664	−	0.992814i	$-0.461818\pi$
$367$	−5.23205	−	1.40192i	−0.273111	−	0.0731798i	−0.392775	+	0.919635i	$0.628485\pi$
$368$	−1.47372	−	5.50000i	−0.0768230	−	0.286707i
$369$			28.3923i			1.47804i
$370$	−2.19615	−	4.39230i	−0.114173	−	0.228345i
$371$	−8.29423	−	4.02628i	−0.430615	−	0.209034i
$372$	15.2942	+	26.4904i	0.792969	+	1.37346i
$373$	1.09808	+	4.09808i	0.0568562	+	0.212190i	0.988510	−	0.151158i	$-0.0483002\pi$
$373$	1.09808	+	4.09808i	0.0568562	+	0.212190i	−0.931653	+	0.363348i	$0.881634\pi$
$374$	2.14359			0.110843
$375$	18.2321	−	6.52628i	0.941499	−	0.337016i
$376$		−	17.1962i		−	0.886824i
$377$	5.07180	−	5.07180i	0.261211	−	0.261211i
$378$	−7.09808	+	0.509619i	−0.365086	+	0.0262120i
$379$		−	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
$383$	0.767949	−	0.205771i	0.0392404	−	0.0105144i	−0.239145	−	0.970984i	$-0.576867\pi$
$383$	0.767949	−	0.205771i	0.0392404	−	0.0105144i	0.278386	+	0.960469i	$0.410201\pi$
$384$	19.1603	+	5.13397i	0.977768	+	0.261992i
$385$	2.14359	−	8.39230i	0.109248	−	0.427711i
$386$	−5.51666			−0.280791
$387$	−16.7942	−	4.50000i	−0.853699	−	0.228748i
$388$	−5.36603	+	1.43782i	−0.272419	+	0.0729944i
$389$	7.96410	−	4.59808i	0.403796	−	0.233132i	−0.284325	−	0.958728i	$-0.591769\pi$
$389$	7.96410	−	4.59808i	0.403796	−	0.233132i	0.688121	+	0.725596i	$0.258436\pi$
$390$	−1.14359	+	1.73205i	−0.0579081	+	0.0877058i
$391$	−5.66025	+	3.26795i	−0.286251	+	0.165267i
$392$	−10.8301	−	8.09808i	−0.547004	−	0.409015i
$393$		−	32.7846i		−	1.65376i
$394$		−	7.71281i		−	0.388566i
$395$	−25.5885	−	1.53590i	−1.28750	−	0.0772794i
$396$		−	7.60770i		−	0.382301i
$397$	−32.7846	−	8.78461i	−1.64541	−	0.440887i	−0.687089	−	0.726573i	$-0.741112\pi$
$397$	−32.7846	−	8.78461i	−1.64541	−	0.440887i	−0.958323	+	0.285686i	$0.907779\pi$
$398$	−9.92820	+	2.66025i	−0.497656	+	0.133346i
$399$	−10.0981	−	29.1506i	−0.505536	−	1.45936i
$400$	12.2321	+	1.47372i	0.611603	+	0.0736860i
$401$	−1.30385	+	2.25833i	−0.0651110	+	0.112776i	−0.896743	−	0.442551i	$-0.854073\pi$
$401$	−1.30385	+	2.25833i	−0.0651110	+	0.112776i	0.831632	+	0.555327i	$0.187407\pi$
$402$	6.69615	−	3.86603i	0.333974	−	0.192820i
$403$	−10.1962	−	2.73205i	−0.507907	−	0.136093i
$404$	−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
$407$	−6.00000	+	1.60770i	−0.297409	+	0.0796905i
$408$		−	9.46410i		−	0.468543i
$409$	15.3923			0.761100			0.380550	−	0.924760i	$-0.375735\pi$
$409$	15.3923			0.761100			0.380550	+	0.924760i	$0.375735\pi$
$410$	3.46410	−	10.3923i	0.171080	−	0.513239i
$411$	12.9282	−	3.46410i	0.637701	−	0.170872i
$412$	5.13397	+	19.1603i	0.252933	+	0.943958i
$413$	6.00000	−	6.92820i	0.295241	−	0.340915i
$414$	−1.79423	−	3.10770i	−0.0881815	−	0.152735i
$415$	−0.633975	−	3.09808i	−0.0311206	−	0.152079i
$416$	−4.60770	+	2.66025i	−0.225911	+	0.130430i
$417$	−6.00000	+	10.3923i	−0.293821	+	0.508913i
$418$	−4.92820	+	1.32051i	−0.241046	+	0.0645882i
$419$	4.00000	+	6.92820i	0.195413	+	0.338465i	0.947036	−	0.321128i	$-0.104062\pi$
$419$	4.00000	+	6.92820i	0.195413	+	0.338465i	−0.751623	+	0.659593i	$0.770729\pi$
$420$	−17.1962	−	4.39230i	−0.839086	−	0.214323i
$421$	7.52628	−	13.0359i	0.366808	−	0.635331i	−0.622256	−	0.782814i	$-0.713784\pi$
$421$	7.52628	−	13.0359i	0.366808	−	0.635331i	0.989065	+	0.147483i	$0.0471171\pi$
$422$	−0.660254	+	2.46410i	−0.0321407	+	0.119951i
$423$	6.91154	+	25.7942i	0.336051	+	1.25416i
$424$	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
$427$	−18.7846	−	16.2679i	−0.909051	−	0.787261i
$428$	−4.09808	−	1.09808i	−0.198088	−	0.0530775i
$429$	1.85641	+	1.85641i	0.0896281	+	0.0896281i
$430$	5.59808	+	3.69615i	0.269963	+	0.178244i
$431$	6.90192	−	11.9545i	0.332454	−	0.575827i	−0.650538	−	0.759473i	$-0.725457\pi$
$431$	6.90192	−	11.9545i	0.332454	−	0.575827i	0.982992	+	0.183646i	$0.0587901\pi$
$432$	−12.8038			−0.616025
$433$	−20.1962	−	20.1962i	−0.970565	−	0.970565i	0.0290139	−	0.999579i	$-0.490763\pi$
$433$	−20.1962	−	20.1962i	−0.970565	−	0.970565i	−0.999579	+	0.0290139i	$0.990763\pi$
$434$	1.00000	+	13.9282i	0.0480015	+	0.668575i
$435$	−26.7846	−	1.60770i	−1.28422	−	0.0770831i
$436$	−1.73205	+	3.00000i	−0.0829502	+	0.143674i
$437$	11.0000	−	11.0000i	0.526201	−	0.526201i
$438$			0.588457i			0.0281176i
$439$	−21.8564			−1.04315			−0.521575	−	0.853206i	$-0.674655\pi$
$439$	−21.8564			−1.04315			−0.521575	+	0.853206i	$0.674655\pi$
$440$	−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
$447$		−	35.7846i		−	1.69255i
$448$	−4.53590	−	3.92820i	−0.214301	−	0.185590i
$449$			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
$452$	3.29423	−	12.2942i	0.154947	−	0.578272i
$453$	−1.09808	+	1.90192i	−0.0515921	+	0.0893602i
$454$	−2.43782	−	4.22243i	−0.114413	−	0.198169i
$455$	5.26795	−	3.12436i	0.246965	−	0.146472i
$456$	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	$-0.553642\pi$
$458$	−6.33013	+	1.69615i	−0.295787	+	0.0792560i
$459$	3.80385	+	14.1962i	0.177548	+	0.662620i
$460$	−1.79423	−	8.76795i	−0.0836563	−	0.408808i
$461$	7.96410	+	4.59808i	0.370925	+	0.214154i	0.673863	−	0.738857i	$-0.264634\pi$
$461$	7.96410	+	4.59808i	0.370925	+	0.214154i	−0.302937	+	0.953010i	$0.597967\pi$
$462$	1.51666	−	3.12436i	0.0705614	−	0.145358i
$463$	4.42820	+	1.18653i	0.205796	+	0.0551429i	0.360244	−	0.932858i	$-0.382693\pi$
$463$	4.42820	+	1.18653i	0.205796	+	0.0551429i	−0.154448	+	0.988001i	$0.549360\pi$
$464$	−14.7846	−	8.53590i	−0.686358	−	0.396269i
$465$	17.6603	+	35.3205i	0.818975	+	1.63795i
$466$	3.16987	+	5.49038i	0.146842	+	0.254337i
$467$	22.5263	+	6.03590i	1.04239	+	0.279308i	0.739104	−	0.673591i	$-0.235249\pi$
$467$	22.5263	+	6.03590i	1.04239	+	0.279308i	0.303288	+	0.952899i	$0.401916\pi$
$468$	3.80385	−	3.80385i	0.175833	−	0.175833i
$469$	−22.7583	+	1.63397i	−1.05088	+	0.0754499i
$470$	0.617314	−	10.2846i	0.0284746	−	0.474394i
$471$	−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
$475$	13.2224	+	30.9545i	0.606687	+	1.42029i
$476$	−5.66025	+	11.6603i	−0.259437	+	0.534447i
$477$	−10.0981	−	2.70577i	−0.462359	−	0.123889i
$478$	−11.0000	−	2.94744i	−0.503128	−	0.134813i
$479$	−4.36603	−	7.56218i	−0.199489	−	0.345525i	0.748874	−	0.662712i	$-0.230595\pi$
$479$	−4.36603	−	7.56218i	−0.199489	−	0.345525i	−0.948363	+	0.317188i	$0.897261\pi$
$480$	18.8827	+	6.29423i	0.861873	+	0.287291i
$481$	−3.80385	−	2.19615i	−0.173441	−	0.100136i
$482$	−8.23205	−	2.20577i	−0.374960	−	0.100470i
$483$	0.758330	+	10.5622i	0.0345052	+	0.480596i
$484$	−13.2846	−	7.66987i	−0.603846	−	0.348631i
$485$	−7.02628	+	1.43782i	−0.319047	+	0.0652881i
$486$	−7.79423	+	2.08846i	−0.353553	+	0.0947343i
$487$	−27.6865	+	7.41858i	−1.25460	+	0.336168i	−0.824110	−	0.566429i	$-0.808325\pi$
$487$	−27.6865	+	7.41858i	−1.25460	+	0.336168i	−0.430486	+	0.902597i	$0.641658\pi$
$488$	12.8301	+	12.8301i	0.580793	+	0.580793i
$489$	−0.294229	−	1.09808i	−0.0133055	−	0.0496567i
$490$	−6.18653	−	5.23205i	−0.279479	−	0.236360i
$491$	1.53590	+	2.66025i	0.0693141	+	0.120056i	0.898600	−	0.438770i	$-0.144586\pi$
$491$	1.53590	+	2.66025i	0.0693141	+	0.120056i	−0.829285	+	0.558825i	$0.811252\pi$
$492$	−14.1962	+	24.5885i	−0.640012	+	1.10853i
$493$	−5.07180	+	18.9282i	−0.228422	+	0.852483i
$494$	−3.12436	−	1.80385i	−0.140571	−	0.0811589i
$495$	0.588457	−	9.80385i	0.0264492	−	0.440650i
$496$			25.1244i			1.12812i
$497$	10.3923	−	12.0000i	0.466159	−	0.538274i
$498$		−	1.26795i		−	0.0568182i
$499$	18.1244	+	10.4641i	0.811358	+	0.468438i	0.847427	−	0.530912i	$-0.178150\pi$
$499$	18.1244	+	10.4641i	0.811358	+	0.468438i	−0.0360695	+	0.999349i	$0.511484\pi$
$500$	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	$-0.977920\pi$
$503$	−23.9282	−	23.9282i	−1.06691	−	1.06691i	−0.0693107	−	0.997595i	$-0.522080\pi$
$504$	−13.7942	−	6.69615i	−0.614444	−	0.298270i
$505$	−13.5885	−	27.1769i	−0.604678	−	1.20936i
$506$	1.75129			0.0778543
$507$		−	20.6603i		−	0.917554i
$508$	11.7058	−	11.7058i	0.519360	−	0.519360i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$	0.339746	−	5.66025i	0.0150442	−	0.250640i
$511$	0.758330	−	1.56218i	0.0335466	−	0.0691067i
$512$	15.6865	+	15.6865i	0.693253	+	0.693253i
$513$	−17.4904	−	30.2942i	−0.772219	−	1.33752i
$514$	7.02628	−	12.1699i	0.309916	−	0.536790i
$515$	5.13397	+	25.0885i	0.226230	+	1.10553i
$516$	−12.2942	−	12.2942i	−0.541223	−	0.541223i
$517$	−12.5885	−	3.37307i	−0.553640	−	0.148347i
$518$	−1.09808	+	5.70577i	−0.0482467	+	0.250697i
$519$	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	0.763513	−	0.645792i	$-0.223473\pi$
$521$	13.3756	+	7.72243i	0.585998	+	0.338326i	−0.177516	+	0.984118i	$0.556806\pi$
$522$	−10.3923	−	2.78461i	−0.454859	−	0.121879i
$523$	1.96410	−	7.33013i	0.0858842	−	0.320524i	−0.909596	−	0.415494i	$-0.863609\pi$
$523$	1.96410	−	7.33013i	0.0858842	−	0.320524i	0.995480	+	0.0949698i	$0.0302754\pi$
$524$	16.3923	−	28.3923i	0.716101	−	1.24032i
$525$	−21.8205	−	6.99038i	−0.952325	−	0.305085i
$526$	5.45448	+	9.44744i	0.237827	+	0.411928i
$527$	27.8564	−	7.46410i	1.21344	−	0.325141i
$528$	3.12436	−	5.41154i	0.135970	−	0.235507i
$529$	15.2942	−	8.83013i	0.664966	−	0.383919i
$530$	3.36603	+	2.22243i	0.146211	+	0.0965363i
$531$	5.19615	−	9.00000i	0.225494	−	0.390567i
$532$	5.83013	−	30.2942i	0.252768	−	1.31342i
$533$	−2.53590	−	9.46410i	−0.109842	−	0.409936i
$534$	1.03590	−	0.277568i	0.0448277	−	0.0120115i
$535$	−5.19615	−	1.73205i	−0.224649	−	0.0748831i
$536$	16.6603			0.719613
$537$			32.1962i			1.38937i
$538$	1.96410	−	0.526279i	0.0846784	−	0.0226895i
$539$	−8.05256	+	6.33975i	−0.346848	+	0.273072i
$540$	−20.0885	−	1.20577i	−0.864470	−	0.0518881i
$541$	−1.96410	−	3.40192i	−0.0844433	−	0.146260i	0.820711	−	0.571344i	$-0.193578\pi$
$541$	−1.96410	−	3.40192i	−0.0844433	−	0.146260i	−0.905154	+	0.425084i	$0.860245\pi$
$542$	2.26795	+	0.607695i	0.0974168	+	0.0261027i
$543$	6.80385	−	3.92820i	0.291981	−	0.168575i
$544$	7.26795	−	12.5885i	0.311611	−	0.539726i
$545$	−2.46410	+	3.73205i	−0.105551	+	0.159863i
$546$	2.32051	−	0.803848i	0.0993086	−	0.0344015i
$547$	39.6865	−	10.6340i	1.69687	−	0.454676i	0.724724	−	0.689039i	$-0.241967\pi$
$547$	39.6865	−	10.6340i	1.69687	−	0.454676i	0.972149	+	0.234363i	$0.0753004\pi$
$548$	12.9282	+	3.46410i	0.552265	+	0.147979i
$549$	−24.4019	−	14.0885i	−1.04145	−	0.601281i
$550$	−1.41154	+	3.51666i	−0.0601884	+	0.149951i
$551$		−	46.6410i		−	1.98697i
$552$		−	7.73205i		−	0.329098i
$553$	22.9282	+	19.8564i	0.975006	+	0.844380i
$554$	−2.41154	+	1.39230i	−0.102457	+	0.0591534i
$555$	3.29423	+	16.0981i	0.139832	+	0.683325i
$556$	−10.3923	+	6.00000i	−0.440732	+	0.254457i
$557$	−1.09808	+	0.294229i	−0.0465270	+	0.0124669i	−0.282007	−	0.959412i	$-0.591000\pi$
$557$	−1.09808	+	0.294229i	−0.0465270	+	0.0124669i	0.235480	+	0.971879i	$0.424334\pi$
$558$	4.09808	+	15.2942i	0.173485	+	0.647456i
$559$	6.00000			0.253773
$560$	−10.4282	−	10.1865i	−0.440672	−	0.430460i
$561$	−6.92820	−	1.85641i	−0.292509	−	0.0783775i
$562$	5.13397	−	1.37564i	0.216564	−	0.0580281i
$563$	−23.8301	−	23.8301i	−1.00432	−	1.00432i	−0.999991	−	0.00432948i	$-0.998622\pi$
$563$	−23.8301	−	23.8301i	−1.00432	−	1.00432i	−0.00432948	−	0.999991i	$-0.501378\pi$
$564$	−6.91154	+	25.7942i	−0.291028	+	1.08613i
$565$	5.19615	−	15.5885i	0.218604	−	0.655811i
$566$			4.94744i			0.207956i
$567$	23.3827	+	4.50000i	0.981981	+	0.188982i
$568$	−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	$0.841510\pi$
$570$	2.70577	+	13.2224i	0.113332	+	0.553827i
$571$	28.2487			1.18217			0.591086	−	0.806609i	$-0.298699\pi$
$571$	28.2487			1.18217			0.591086	+	0.806609i	$0.298699\pi$
$572$	0.679492	+	2.53590i	0.0284110	+	0.106031i
$573$	0.294229	+	0.509619i	0.0122916	+	0.0212896i
$574$	−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
$577$	−8.92820	−	33.3205i	−0.371686	−	1.38715i	−0.858127	−	0.513437i	$-0.828372\pi$
$577$	−8.92820	−	33.3205i	−0.371686	−	1.38715i	0.486441	−	0.873713i	$-0.338295\pi$
$578$	4.50000	+	1.20577i	0.187175	+	0.0501535i
$579$	17.8301	+	4.77757i	0.740995	+	0.198549i
$580$	−22.3923	−	14.7846i	−0.929790	−	0.613898i
$581$	−1.63397	+	3.36603i	−0.0677887	+	0.139646i
$582$	−2.87564			−0.119199
$583$	3.60770	−	3.60770i	0.149415	−	0.149415i
$584$	−0.633975	+	1.09808i	−0.0262341	+	0.0454387i
$585$	5.19615	−	4.60770i	0.214834	−	0.190505i
$586$	8.15064	−	4.70577i	0.336700	−	0.194394i
$587$	4.18653	+	15.6244i	0.172797	+	0.644886i	0.996916	+	0.0784705i	$0.0250036\pi$
$587$	4.18653	+	15.6244i	0.172797	+	0.644886i	−0.824120	+	0.566416i	$0.808330\pi$
$588$	12.9904	+	16.5000i	0.535714	+	0.680449i
$589$	−59.4449	+	34.3205i	−2.44938	+	1.41415i
$590$	−3.00000	+	2.66025i	−0.123508	+	0.109521i
$591$	−6.67949	+	24.9282i	−0.274758	+	1.02541i
$592$	−2.70577	+	10.0981i	−0.111207	+	0.415028i
$593$	0.732051	−	2.73205i	0.0300617	−	0.112192i	−0.949265	−	0.314478i	$-0.898170\pi$
$593$	0.732051	−	2.73205i	0.0300617	−	0.112192i	0.979326	+	0.202286i	$0.0648371\pi$
$594$	1.01924	−	3.80385i	0.0418198	−	0.156074i
$595$	−8.19615	+	14.5885i	−0.336009	+	0.598068i
$596$	17.8923	−	30.9904i	0.732897	−	1.26942i
$597$	34.3923			1.40758
$598$	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	$-0.141002\pi$
$600$	15.5263	+	6.23205i	0.633858	+	0.254422i
$601$	3.33975	+	1.92820i	0.136231	+	0.0786531i	0.566567	−	0.824016i	$-0.308271\pi$
$601$	3.33975	+	1.92820i	0.136231	+	0.0786531i	−0.430335	+	0.902669i	$0.641605\pi$
$602$	−2.59808	−	7.50000i	−0.105890	−	0.305677i
$603$	−24.9904	+	6.69615i	−1.01769	+	0.272688i
$604$	−1.90192	+	1.09808i	−0.0773882	+	0.0446801i
$605$	−16.5263	−	10.9115i	−0.671889	−	0.443617i
$606$	−3.15321	−	11.7679i	−0.128091	−	0.478040i
$607$	1.09808	+	4.09808i	0.0445695	+	0.166336i	0.984623	−	0.174690i	$-0.0558923\pi$
$607$	1.09808	+	4.09808i	0.0445695	+	0.166336i	−0.940054	+	0.341026i	$0.889226\pi$
$608$	−8.95448	+	33.4186i	−0.363152	+	1.35530i
$609$	24.0000	+	20.7846i	0.972529	+	0.842235i
$610$	7.21281	+	8.13397i	0.292038	+	0.329335i
$611$	−4.60770	−	7.98076i	−0.186407	−	0.322867i
$612$	−3.80385	+	14.1962i	−0.153761	+	0.573845i
$613$	1.58142	+	5.90192i	0.0638728	+	0.238376i	0.990481	−	0.137653i	$-0.0439558\pi$
$613$	1.58142	+	5.90192i	0.0638728	+	0.238376i	−0.926608	+	0.376029i	$0.877289\pi$
$614$	17.9090			0.722747
$615$	−20.1962	+	30.5885i	−0.814387	+	1.23345i
$616$	6.19615	−	4.19615i	0.249650	−	0.169068i
$617$	3.09808	−	11.5622i	0.124724	−	0.465476i	−0.875106	−	0.483932i	$-0.839208\pi$
$617$	3.09808	−	11.5622i	0.124724	−	0.465476i	0.999830	+	0.0184559i	$0.00587501\pi$
$618$			10.2679i			0.413037i
$619$	13.4904	+	23.3660i	0.542224	+	0.939160i	0.998776	+	0.0494630i	$0.0157510\pi$
$619$	13.4904	+	23.3660i	0.542224	+	0.939160i	−0.456552	+	0.889697i	$0.650916\pi$
$620$	−2.36603	+	39.4186i	−0.0950219	+	1.58309i
$621$	3.10770	+	11.5981i	0.124708	+	0.465415i
$622$	−5.85641	+	5.85641i	−0.234821	+	0.234821i
$623$	−3.10770	−	0.598076i	−0.124507	−	0.0239614i
$624$	4.26795	−	1.14359i	0.170855	−	0.0457804i
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$			3.80385i			0.152032i
$627$	17.0718			0.681782
$628$	−1.73205	−	1.73205i	−0.0691164	−	0.0691164i
$629$	12.0000			0.478471
$630$	−8.00962	−	4.50000i	−0.319111	−	0.179284i
$631$	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
$633$	4.26795	−	7.39230i	0.169636	−	0.293818i
$634$			1.12436i			0.0446539i
$635$	15.9904	−	14.1795i	0.634559	−	0.562696i
$636$	−7.39230	−	7.39230i	−0.293124	−	0.293124i
$637$	−7.19615	−	0.856406i	−0.285122	−	0.0339321i
$638$	3.71281	−	3.71281i	0.146992	−	0.146992i
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$	16.9904	+	19.1603i	0.671604	+	0.757376i
$641$	−13.7224	−	23.7679i	−0.542003	−	0.938778i	−0.998789	−	0.0492007i	$-0.984333\pi$
$641$	−13.7224	−	23.7679i	−0.542003	−	0.938778i	0.456785	−	0.889577i	$-0.349001\pi$
$642$	−1.90192	−	1.09808i	−0.0750629	−	0.0433376i
$643$	−9.69615	+	36.1865i	−0.382379	+	1.42706i	0.459878	+	0.887982i	$0.347893\pi$
$643$	−9.69615	+	36.1865i	−0.382379	+	1.42706i	−0.842257	+	0.539076i	$0.818774\pi$
$644$	−4.62436	+	9.52628i	−0.182225	+	0.375388i
$645$	−14.8923	−	16.7942i	−0.586384	−	0.661272i
$646$	9.85641			0.387795
$647$	10.1699	+	37.9545i	0.399819	+	1.49214i	0.813415	+	0.581684i	$0.197606\pi$
$647$	10.1699	+	37.9545i	0.399819	+	1.49214i	−0.413596	+	0.910461i	$0.635727\pi$
$648$	−16.7942	−	4.50000i	−0.659740	−	0.176777i
$649$	2.53590	+	4.39230i	0.0995427	+	0.172413i
$650$	−2.46410	+	1.05256i	−0.0966500	+	0.0412848i
$651$	8.83013	−	45.8827i	0.346080	−	1.79828i
$652$	0.294229	−	1.09808i	0.0115229	−	0.0430040i
$653$	5.22243	+	19.4904i	0.204370	+	0.762718i	0.989641	+	0.143566i	$0.0458568\pi$
$653$	5.22243	+	19.4904i	0.204370	+	0.762718i	−0.785271	+	0.619152i	$0.787477\pi$
$654$	−1.26795	+	1.26795i	−0.0495807	+	0.0495807i
$655$	23.3205	−	35.3205i	0.911208	−	1.38009i
$656$	−20.1962	+	11.6603i	−0.788527	+	0.455256i
$657$	0.509619	−	1.90192i	0.0198821	−	0.0742011i
$658$	−7.98076	+	9.21539i	−0.311122	+	0.359253i
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.869709	−	0.493564i	$-0.164306\pi$
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.00741531	+	0.999973i	$0.497640\pi$
$660$	5.41154	−	8.19615i	0.210644	−	0.319035i
$661$			11.0000i			0.427850i	0.976850	+	0.213925i	$0.0686249\pi$
$661$			11.0000i			0.427850i	−0.976850	+	0.213925i	$0.931375\pi$
$662$	13.0526	+	13.0526i	0.507302	+	0.507302i
$663$	−2.53590	−	4.39230i	−0.0984861	−	0.170583i
$664$	1.36603	−	2.36603i	0.0530121	−	0.0918196i
$665$	9.85641	−	38.5885i	0.382215	−	1.49640i
$666$			6.58846i			0.255298i
$667$	−4.14359	+	15.4641i	−0.160441	+	0.598772i
$668$	−9.57180	+	35.7224i	−0.370344	+	1.38214i
$669$	9.29423	+	9.29423i	0.359336	+	0.359336i
$670$	9.96410	+	0.598076i	0.384947	+	0.0231057i
$671$	11.9090	−	6.87564i	0.459741	−	0.265431i
$672$	−13.2058	−	19.5000i	−0.509424	−	0.752229i
$673$	−1.85641	−	6.92820i	−0.0715592	−	0.267063i	0.920872	−	0.389865i	$-0.127478\pi$
$673$	−1.85641	−	6.92820i	−0.0715592	−	0.267063i	−0.992431	+	0.122803i	$0.960812\pi$
$674$	−4.26795	+	2.46410i	−0.164395	+	0.0949136i
$675$	−25.7942	−	3.10770i	−0.992820	−	0.119615i
$676$	10.3301	−	17.8923i	0.397313	−	0.688166i
$677$	−29.9090	+	29.9090i	−1.14949	+	1.14949i	−0.162843	+	0.986652i	$0.552066\pi$
$677$	−29.9090	+	29.9090i	−1.14949	+	1.14949i	−0.986652	+	0.162843i	$0.947934\pi$
$678$	3.29423	−	5.70577i	0.126514	−	0.219129i
$679$	7.63397	+	3.70577i	0.292965	+	0.142214i
$680$	6.73205	−	10.1962i	0.258162	−	0.391005i
$681$	4.22243	+	15.7583i	0.161804	+	0.603861i
$682$	−7.46410	−	2.00000i	−0.285815	−	0.0765840i
$683$	8.03590	+	29.9904i	0.307485	+	1.14755i	0.930785	+	0.365567i	$0.119125\pi$
$683$	8.03590	+	29.9904i	0.307485	+	1.14755i	−0.623300	+	0.781983i	$0.714208\pi$
$684$		−	34.9808i		−	1.33752i
$685$	16.3923	+	5.46410i	0.626318	+	0.208773i
$686$	2.04552	+	9.36603i	0.0780982	+	0.357597i
$687$	21.9282			0.836613
$688$	−3.69615	−	13.7942i	−0.140914	−	0.525900i
$689$	3.60770			0.137442
$690$	0.277568	−	4.62436i	0.0105668	−	0.176046i
$691$		−	20.5885i		−	0.783222i	−0.920131	−	0.391611i	$-0.871918\pi$
$691$		−	20.5885i		−	0.783222i	0.920131	−	0.391611i	$-0.128082\pi$
$692$	17.3205	−	17.3205i	0.658427	−	0.658427i
$693$	−7.60770	+	8.78461i	−0.288992	+	0.333700i
$694$		−	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
$698$	−4.93782	+	1.32309i	−0.186899	+	0.0500795i
$699$	−5.49038	−	20.4904i	−0.207665	−	0.775017i
$700$	−15.4019	−	16.9641i	−0.582138	−	0.641183i
$701$	−40.5359			−1.53102			−0.765510	−	0.643424i	$-0.777513\pi$
$701$	−40.5359			−1.53102			−0.765510	+	0.643424i	$0.777513\pi$
$702$	2.41154	−	1.39230i	0.0910178	−	0.0525492i
$703$	−27.5885	+	7.39230i	−1.04052	+	0.278806i
$704$	2.87564	−	1.66025i	0.108380	−	0.0625732i
$705$	−10.9019	+	32.7058i	−0.410590	+	1.23177i
$706$	−12.5885	+	7.26795i	−0.473773	+	0.273533i
$707$	−6.79423	+	35.3038i	−0.255523	+	1.32774i
$708$	9.00000	−	5.19615i	0.338241	−	0.195283i
$709$		−	48.7128i		−	1.82945i	−0.404079	−	0.914724i	$-0.632408\pi$
$709$		−	48.7128i		−	1.82945i	0.404079	−	0.914724i	$-0.367592\pi$
$710$	−5.19615	+	4.60770i	−0.195008	+	0.172924i
$711$	29.7846	+	17.1962i	1.11701	+	0.644906i
$712$	2.23205	+	0.598076i	0.0836496	+	0.0224139i
$713$	22.7583	−	6.09808i	0.852306	−	0.228375i
$714$	−4.39230	+	5.07180i	−0.164378	+	0.189807i
$715$	0.679492	+	3.32051i	0.0254116	+	0.124180i
$716$	−16.0981	+	27.8827i	−0.601613	+	1.04202i
$717$	33.0000	+	19.0526i	1.23241	+	0.711531i
$718$	8.63397	+	2.31347i	0.322217	+	0.0863378i
$719$	−3.43782	−	5.95448i	−0.128209	−	0.222065i	0.794774	−	0.606906i	$-0.207590\pi$
$719$	−3.43782	−	5.95448i	−0.128209	−	0.222065i	−0.922983	+	0.384841i	$0.874256\pi$
$720$	−13.7942	−	9.10770i	−0.514081	−	0.339424i
$721$	13.2321	−	27.2583i	0.492787	−	1.01515i
$722$	−13.1603	+	3.52628i	−0.489774	+	0.131235i
$723$	24.6962	+	14.2583i	0.918460	+	0.530273i
$724$	7.85641			0.291981
$725$	−27.7128	−	20.7846i	−1.02923	−	0.771921i
$726$	−5.61474	−	5.61474i	−0.208382	−	0.208382i
$727$	6.86603	+	25.6244i	0.254647	+	0.950355i	0.968287	+	0.249842i	$0.0803787\pi$
$727$	6.86603	+	25.6244i	0.254647	+	0.950355i	−0.713640	+	0.700513i	$0.752955\pi$
$728$	5.19615	+	1.00000i	0.192582	+	0.0370625i
$729$	27.0000			1.00000
$730$	−0.418584	+	0.633975i	−0.0154925	+	0.0234645i
$731$	−14.1962	+	8.19615i	−0.525064	+	0.303146i
$732$	−14.0885	−	24.4019i	−0.520724	−	0.901921i
$733$	−2.26795	+	0.607695i	−0.0837686	+	0.0224457i	−0.300460	−	0.953794i	$-0.597140\pi$
$733$	−2.26795	+	0.607695i	−0.0837686	+	0.0224457i	0.216691	+	0.976240i	$0.430473\pi$
$734$	−1.40192	−	2.42820i	−0.0517460	−	0.0896266i
$735$	15.4641	+	22.2679i	0.570402	+	0.821366i
$736$	5.93782	−	10.2846i	0.218871	−	0.379096i
$737$	3.26795	−	12.1962i	0.120376	−	0.449251i
$738$	−10.3923	+	10.3923i	−0.382546	+	0.382546i
$739$	−3.12436	−	1.80385i	−0.114931	−	0.0663556i	0.441432	−	0.897295i	$-0.354471\pi$
$739$	−3.12436	−	1.80385i	−0.114931	−	0.0663556i	−0.556364	+	0.830939i	$0.687804\pi$
$740$	−5.19615	+	15.5885i	−0.191014	+	0.573043i
$741$	8.53590	+	8.53590i	0.313574	+	0.313574i
$742$	−1.56218	−	4.50962i	−0.0573494	−	0.165553i
$743$	−0.633975	−	0.169873i	−0.0232583	−	0.00623204i	0.247171	−	0.968972i	$-0.420499\pi$
$743$	−0.633975	−	0.169873i	−0.0232583	−	0.00623204i	−0.270429	+	0.962740i	$0.587166\pi$
$744$	−8.83013	+	32.9545i	−0.323728	+	1.20817i
$745$	25.4545	−	38.5526i	0.932580	−	1.41246i
$746$	−1.09808	+	1.90192i	−0.0402034	+	0.0696344i
$747$	−1.09808	+	4.09808i	−0.0401765	+	0.149941i
$748$	−5.07180	−	5.07180i	−0.185443	−	0.185443i
$749$	3.63397	+	5.36603i	0.132783	+	0.196070i
$750$	9.06218	+	4.28461i	0.330904	+	0.156452i
$751$	11.4378	−	19.8109i	0.417372	−	0.722910i	−0.578302	−	0.815823i	$-0.696285\pi$
$751$	11.4378	−	19.8109i	0.417372	−	0.722910i	0.995674	+	0.0929130i	$0.0296179\pi$
$752$	−15.5096	+	15.5096i	−0.565578	+	0.565578i
$753$	32.7846	−	18.9282i	1.19474	−	0.689782i
$754$	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	0.670747	−	0.741686i	$-0.265974\pi$
$761$	10.0359	+	5.79423i	0.363801	+	0.210041i	−0.306946	+	0.951727i	$0.599307\pi$
$762$	7.42116	−	4.28461i	0.268840	−	0.155215i
$763$	5.00000	−	1.73205i	0.181012	−	0.0627044i
$764$			0.588457i			0.0212896i
$765$	−6.00000	+	18.0000i	−0.216930	+	0.650791i
$766$	0.356406	+	0.205771i	0.0128775	+	0.00743482i
$767$	−0.928203	+	3.46410i	−0.0335155	+	0.125081i
$768$	1.20577	+	2.08846i	0.0435095	+	0.0753607i
$769$	−17.9904	−	31.1603i	−0.648750	−	1.12367i	−0.983422	−	0.181333i	$-0.941959\pi$
$769$	−17.9904	−	31.1603i	−0.648750	−	1.12367i	0.334672	−	0.942335i	$-0.391374\pi$
$770$	3.85641	−	2.28719i	0.138975	−	0.0824245i
$771$	−33.2487	+	33.2487i	−1.19742	+	1.19742i
$772$	13.0526	+	13.0526i	0.469772	+	0.469772i
$773$	44.8827	−	12.0263i	1.61432	−	0.432555i	0.664993	−	0.746850i	$-0.268435\pi$
$773$	44.8827	−	12.0263i	1.61432	−	0.432555i	0.949325	+	0.314295i	$0.101768\pi$
$774$	−4.50000	−	7.79423i	−0.161749	−	0.280158i
$775$	−6.09808	+	50.6147i	−0.219049	+	1.81814i
$776$	−5.36603	−	3.09808i	−0.192629	−	0.111214i
$777$	8.49038	−	17.4904i	0.304591	−	0.627464i
$778$	4.59808	+	1.23205i	0.164849	+	0.0441712i
$779$	−55.1769	−	31.8564i	−1.97692	−	1.14137i
$780$	6.80385	−	1.39230i	0.243617	−	0.0498525i
$781$	4.39230	+	7.60770i	0.157169	+	0.272225i
$782$	−3.26795	−	0.875644i	−0.116862	−	0.0313130i
$783$	31.1769	+	18.0000i	1.11417	+	0.643268i
$784$	2.46410	+	17.0718i	0.0880036	+	0.609707i
$785$	−2.09808	−	2.36603i	−0.0748836	−	0.0844471i
$786$	12.0000	−	12.0000i	0.428026	−	0.428026i
$787$	−4.29423	+	4.29423i	−0.153073	+	0.153073i	−0.779489	−	0.626416i	$-0.784521\pi$
$787$	−4.29423	+	4.29423i	−0.153073	+	0.153073i	0.626416	+	0.779489i	$0.284521\pi$
$788$	−18.2487	+	18.2487i	−0.650083	+	0.650083i
$789$	−9.44744	−	35.2583i	−0.336338	−	1.25523i
$790$	−8.80385	−	9.92820i	−0.313227	−	0.353230i
$791$	−16.0981	+	10.9019i	−0.572382	+	0.387628i
$792$	6.00000	−	6.00000i	0.213201	−	0.213201i
$793$	9.39230	+	2.51666i	0.333531	+	0.0893692i
$794$	−8.78461	−	15.2154i	−0.311754	−	0.539974i
$795$	−8.95448	−	10.0981i	−0.317583	−	0.358142i
$796$	29.7846	+	17.1962i	1.05569	+	0.609501i
$797$	47.0788	+	12.6147i	1.66762	+	0.446837i	0.964467	−	0.264204i	$-0.0851091\pi$
$797$	47.0788	+	12.6147i	1.66762	+	0.446837i	0.703151	+	0.711040i	$0.251776\pi$
$798$	6.97372	−	14.3660i	0.246867	−	0.508552i
$799$	21.8038	+	12.5885i	0.771365	+	0.445348i
$800$	15.8660	+	20.2128i	0.560949	+	0.714631i
$801$	−3.58846			−0.126792
$802$	−1.30385	+	0.349365i	−0.0460405	+	0.0123365i
$803$	0.679492	+	0.679492i	0.0239787	+	0.0239787i
$804$	−24.9904	−	6.69615i	−0.881343	−	0.236155i
$805$	−6.69615	+	11.9186i	−0.236008	+	0.420075i
$806$	−2.73205	−	4.73205i	−0.0962324	−	0.166679i
$807$	−6.80385			−0.239507
$808$	6.79423	−	25.3564i	0.239020	−	0.892035i
$809$	−41.5981	−	24.0167i	−1.46251	−	0.844381i	−0.463384	−	0.886158i	$-0.653365\pi$
$809$	−41.5981	−	24.0167i	−1.46251	−	0.844381i	−0.999127	+	0.0417770i	$0.986698\pi$
$810$	−9.88269	−	3.29423i	−0.347242	−	0.115747i
$811$		−	25.8564i		−	0.907941i	−0.891017	−	0.453971i	$-0.850007\pi$
$811$		−	25.8564i		−	0.907941i	0.891017	−	0.453971i	$-0.149993\pi$
$812$	10.3923	+	30.0000i	0.364698	+	1.05279i
$813$	−6.80385	−	3.92820i	−0.238621	−	0.137768i
$814$	−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	$0.540881\pi$
$822$	6.00000	+	3.46410i	0.209274	+	0.120824i
$823$	−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
$825$	7.60770	−	10.1436i	0.264866	−	0.353155i
$826$	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	$0.745244\pi$
$828$	−3.10770	+	11.5981i	−0.108000	+	0.403061i
$829$	−4.83975	+	8.38269i	−0.168091	+	0.291143i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−4.83975	+	8.38269i	−0.168091	+	0.291143i	0.769657	+	0.638457i	$0.220427\pi$
$830$	0.901924	−	1.36603i	0.0313062	−	0.0474154i
$831$	9.00000	−	2.41154i	0.312207	−	0.0836555i
$832$	2.26795	+	0.607695i	0.0786270	+	0.0210680i
$833$	18.1962	−	7.80385i	0.630459	−	0.270387i
$834$	−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
$837$		−	52.9808i		−	1.83128i
$838$	−1.07180	+	4.00000i	−0.0370246	+	0.138178i
$839$	−19.0263	+	32.9545i	−0.656860	+	1.13772i	0.324564	+	0.945864i	$0.394782\pi$
$839$	−19.0263	+	32.9545i	−0.656860	+	1.13772i	−0.981424	+	0.191851i	$0.938551\pi$
$840$	−10.0981	−	17.0263i	−0.348417	−	0.587462i
$841$	9.50000	+	16.4545i	0.327586	+	0.567396i
$842$	7.52628	−	2.01666i	0.259373	−	0.0694987i
$843$	−17.7846			−0.612534
$844$	7.39230	−	4.26795i	0.254454	−	0.146909i
$845$	14.6962	−	22.2583i	0.505563	−	0.765710i
$846$	−6.91154	+	11.9711i	−0.237624	+	0.411576i
$847$	7.66987	+	22.1410i	0.263540	+	0.760774i
$848$	−2.22243	−	8.29423i	−0.0763186	−	0.284825i
$849$	4.28461	−	15.9904i	0.147047	−	0.548788i
$850$	4.39230	−	5.85641i	0.150655	−	0.200873i
$851$	9.80385			0.336072
$852$	15.5885	−	9.00000i	0.534052	−	0.308335i
$853$	−16.8564	+	4.51666i	−0.577152	+	0.154648i	−0.535575	−	0.844488i	$-0.679905\pi$
$853$	−16.8564	+	4.51666i	−0.577152	+	0.154648i	−0.0415775	+	0.999135i	$0.513238\pi$
$854$	−0.921162	−	12.8301i	−0.0315215	−	0.439038i
$855$	2.70577	−	45.0788i	0.0925354	−	1.54166i
$856$	−2.36603	−	4.09808i	−0.0808691	−	0.140069i
$857$	23.2942	+	6.24167i	0.795716	+	0.213211i	0.633702	−	0.773577i	$-0.281534\pi$
$857$	23.2942	+	6.24167i	0.795716	+	0.213211i	0.162014	+	0.986789i	$0.448201\pi$
$858$			1.35898i			0.0463949i
$859$	4.49038	−	7.77757i	0.153210	−	0.265367i	−0.779196	−	0.626780i	$-0.784372\pi$
$859$	4.49038	−	7.77757i	0.153210	−	0.265367i	0.932406	+	0.361413i	$0.117706\pi$
$860$	−4.50000	−	21.9904i	−0.153449	−	0.749866i
$861$	40.9808	−	14.1962i	1.39662	−	0.483804i
$862$	6.90192	−	1.84936i	0.235080	−	0.0629896i
$863$	−39.4545	−	10.5718i	−1.34305	−	0.359868i	−0.485483	−	0.874246i	$-0.661356\pi$
$863$	−39.4545	−	10.5718i	−1.34305	−	0.359868i	−0.857563	+	0.514378i	$0.828023\pi$
$864$	−18.8827	−	18.8827i	−0.642402	−	0.642402i
$865$	23.6603	−	20.9808i	0.804473	−	0.713367i
$866$		−	14.7846i		−	0.502401i
$867$	−13.5000	−	7.79423i	−0.458484	−	0.264706i
$868$	30.5885	−	35.3205i	1.03824	−	1.19886i
$869$	−14.5359	+	8.39230i	−0.493097	+	0.284689i
$870$	−9.21539	−	10.3923i	−0.312431	−	0.352332i
$871$	7.73205	−	4.46410i	0.261991	−	0.151260i
$872$	−3.73205	+	1.00000i	−0.126383	+	0.0338643i
$873$	9.29423	+	2.49038i	0.314562	+	0.0842866i
$874$	8.05256			0.272382
$875$	−18.5359	−	23.0526i	−0.626628	−	0.779319i
$876$	1.39230	−	1.39230i	0.0470416	−	0.0470416i
$877$	−2.09808	+	0.562178i	−0.0708470	+	0.0189834i	−0.294068	−	0.955784i	$-0.595009\pi$
$877$	−2.09808	+	0.562178i	−0.0708470	+	0.0189834i	0.223221	+	0.974768i	$0.428343\pi$
$878$	−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	$-0.868780\pi$
$881$		−	23.7846i		−	0.801324i	0.916226	−	0.400662i	$-0.131220\pi$
$882$	4.28461	+	9.99038i	0.144270	+	0.336394i
$883$	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
$885$	12.0000	−	6.00000i	0.403376	−	0.201688i
$886$	12.1962			0.409738
$887$	2.20577	+	8.23205i	0.0740626	+	0.276405i	0.993019	−	0.117954i	$-0.0376334\pi$
$887$	2.20577	+	8.23205i	0.0740626	+	0.276405i	−0.918957	+	0.394359i	$0.870967\pi$
$888$	−7.09808	+	12.2942i	−0.238196	+	0.412567i
$889$	−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
$892$	3.40192	+	12.6962i	0.113905	+	0.425099i
$893$	−57.8827	−	15.5096i	−1.93697	−	0.519010i
$894$	13.0981	−	13.0981i	0.438065	−	0.438065i
$895$	−22.9019	+	34.6865i	−0.765527	+	1.15944i
$896$	−2.16987	−	30.2224i	−0.0724904	−	1.00966i
$897$	−2.07180	−	3.58846i	−0.0691753	−	0.119815i
$898$	−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
$902$	−1.85641	−	6.92820i	−0.0618116	−	0.230684i
$903$	1.90192	+	26.4904i	0.0632921	+	0.881545i
$904$	12.2942	−	7.09808i	0.408900	−	0.236079i
$905$	10.1244	+	0.607695i	0.336545	+	0.0202005i
$906$	−1.09808	+	0.294229i	−0.0364811	+	0.00977509i
$907$	−4.70577	+	17.5622i	−0.156253	+	0.583143i	0.842742	+	0.538317i	$0.180940\pi$
$907$	−4.70577	+	17.5622i	−0.156253	+	0.583143i	−0.998995	+	0.0448253i	$0.985727\pi$
$908$	−4.22243	+	15.7583i	−0.140126	+	0.522959i
$909$			40.7654i			1.35210i
$910$	3.07180	+	0.784610i	0.101829	+	0.0260096i
$911$	−19.5622	+	33.8827i	−0.648124	+	1.12258i	0.335447	+	0.942059i	$0.391113\pi$
$911$	−19.5622	+	33.8827i	−0.648124	+	1.12258i	−0.983571	+	0.180524i	$0.942221\pi$
$912$	14.3660	−	24.8827i	0.475707	−	0.823948i
$913$	−1.46410	−	1.46410i	−0.0484547	−	0.0484547i
$914$		−	18.0526i		−	0.597126i
$915$	−16.2679	−	32.5359i	−0.537802	−	1.07560i
$916$	18.9904	+	10.9641i	0.627460	+	0.362264i
$917$	−47.3205	+	16.3923i	−1.56266	+	0.541322i
$918$	−3.80385	+	6.58846i	−0.125546	+	0.217451i
$919$	−27.3731	+	15.8038i	−0.902954	+	0.521321i	−0.878157	−	0.478372i	$-0.841227\pi$
$919$	−27.3731	+	15.8038i	−0.902954	+	0.521321i	−0.0247967	+	0.999693i	$0.507894\pi$
$920$	5.50000	−	8.33013i	0.181330	−	0.274636i
$921$	−57.8827	−	15.5096i	−1.90730	−	0.511059i
$922$	1.23205	+	4.59808i	0.0405754	+	0.151430i
$923$	−1.60770	+	6.00000i	−0.0529179	+	0.197492i
$924$	−10.9808	+	3.80385i	−0.361241	+	0.125137i
$925$	−7.90192	+	19.6865i	−0.259814	+	0.647289i
$926$	1.18653	+	2.05514i	0.0389919	+	0.0675360i
$927$	8.89230	−	33.1865i	0.292062	−	1.08999i
$928$	−9.21539	−	34.3923i	−0.302510	−	1.12898i
$929$	1.67949			0.0551023			0.0275512	−	0.999620i	$-0.491229\pi$
$929$	1.67949			0.0551023			0.0275512	+	0.999620i	$0.491229\pi$
$930$	−6.46410	+	19.3923i	−0.211966	+	0.635899i
$931$	−37.0263	+	29.1506i	−1.21349	+	0.955373i
$932$	5.49038	−	20.4904i	0.179843	−	0.671185i
$933$	24.0000	−	13.8564i	0.785725	−	0.453638i
$934$	6.03590	+	10.4545i	0.197501	+	0.342081i
$935$	−6.14359	−	6.92820i	−0.200917	−	0.226576i
$936$	6.00000			0.196116
$937$	2.53590	−	2.53590i	0.0828442	−	0.0828442i	−0.664470	−	0.747315i	$-0.731343\pi$
$937$	2.53590	−	2.53590i	0.0828442	−	0.0828442i	0.747315	+	0.664470i	$0.231343\pi$
$938$	−8.92820	−	7.73205i	−0.291516	−	0.252460i
$939$	3.29423	−	12.2942i	0.107503	−	0.401207i
$940$	−25.7942	+	22.8731i	−0.841315	+	0.746037i
$941$		−	13.9808i		−	0.455760i	−0.973689	−	0.227880i	$-0.926821\pi$
$941$		−	13.9808i		−	0.455760i	0.973689	−	0.227880i	$-0.0731794\pi$
$942$	−0.633975	−	1.09808i	−0.0206560	−	0.0357773i
$943$	15.4641	+	15.4641i	0.503580	+	0.503580i
$944$	8.53590			0.277820
$945$	21.9904	+	21.4808i	0.715347	+	0.698769i
$946$	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	$0.833020\pi$
$948$	17.1962	+	29.7846i	0.558505	+	0.967359i
$949$			0.679492i			0.0220572i
$950$	−6.49038	+	16.1699i	−0.210576	+	0.524620i
$951$	0.973721	−	3.63397i	0.0315751	−	0.117840i
$952$	−13.6603	+	4.73205i	−0.442731	+	0.153367i
$953$	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
$955$	−0.0455173	+	0.758330i	−0.00147291	+	0.0245390i
$956$	19.0526	+	33.0000i	0.616204	+	1.06730i
$957$	−15.2154	+	8.78461i	−0.491844	+	0.283966i
$958$	1.16987	−	4.36603i	0.0377969	−	0.141060i
$959$	−11.4641	−	16.9282i	−0.370195	−	0.546640i
$960$	−3.92820	−	7.85641i	−0.126782	−	0.253564i
$961$	−72.9615			−2.35360
$962$	−0.588457	−	2.19615i	−0.0189726	−	0.0708068i
$963$	5.19615	+	5.19615i	0.167444	+	0.167444i
$964$	14.2583	+	24.6962i	0.459230	+	0.795410i
$965$	15.8109	+	17.8301i	0.508971	+	0.573972i
$966$	−3.58846	+	4.14359i	−0.115457	+	0.133318i
$967$	−10.3301	+	38.5526i	−0.332194	+	1.23977i	0.574684	+	0.818375i	$0.305125\pi$
$967$	−10.3301	+	38.5526i	−0.332194	+	1.23977i	−0.906879	+	0.421392i	$0.861542\pi$
$968$	−4.42820	−	16.5263i	−0.142328	−	0.531175i
$969$	−31.8564	−	8.53590i	−1.02338	−	0.274213i
$970$	−3.09808	−	2.04552i	−0.0994732	−	0.0656776i
$971$	−9.46410	+	5.46410i	−0.303717	+	0.175351i	−0.644112	−	0.764931i	$-0.722773\pi$
$971$	−9.46410	+	5.46410i	−0.303717	+	0.175351i	0.340394	+	0.940283i	$0.389439\pi$
$972$	23.3827	+	13.5000i	0.750000	+	0.433013i
$973$	18.0000	+	3.46410i	0.577054	+	0.111054i
$974$	−12.8494	−	7.41858i	−0.411720	−	0.237707i
$975$	8.87564	−	1.26795i	0.284248	−	0.0406069i
$976$		−	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	$0.520535\pi$
$978$	0.294229	−	0.509619i	0.00940839	−	0.0162958i
$979$	0.875644	−	1.51666i	0.0279857	−	0.0484727i
$980$	2.25833	+	27.0167i	0.0721397	+	0.863016i
$981$	5.19615	−	3.00000i	0.165900	−	0.0957826i
$982$	−0.411543	+	1.53590i	−0.0131329	+	0.0490125i
$983$	8.56218	−	31.9545i	0.273091	−	1.01919i	−0.684019	−	0.729464i	$-0.739769\pi$
$983$	8.56218	−	31.9545i	0.273091	−	1.01919i	0.957110	−	0.289725i	$-0.0935640\pi$
$984$	−30.5885	+	8.19615i	−0.975124	+	0.261284i
$985$	−24.9282	+	22.1051i	−0.794279	+	0.704328i
$986$	−8.78461	+	5.07180i	−0.279759	+	0.161519i
$987$	33.7750	−	22.8731i	1.07507	−	0.728058i
$988$	3.12436	+	11.6603i	0.0993990	+	0.370962i
$989$	−11.5981	+	6.69615i	−0.368797	+	0.212925i
$990$	3.80385	−	3.37307i	0.120894	−	0.107203i
$991$	5.26795	−	9.12436i	0.167342	−	0.289845i	−0.770143	−	0.637872i	$-0.779815\pi$
$991$	5.26795	−	9.12436i	0.167342	−	0.289845i	0.937484	+	0.348027i	$0.113148\pi$
$992$	−37.0526	+	37.0526i	−1.17642	+	1.17642i
$993$	−30.8827	−	53.4904i	−0.980032	−	1.69747i
$994$	8.19615	−	0.588457i	0.259966	−	0.0186647i
$995$	37.0526	+	24.4641i	1.17465	+	0.775564i
$996$	−3.00000	+	3.00000i	−0.0950586	+	0.0950586i
$997$	−27.2942	−	7.31347i	−0.864417	−	0.231620i	−0.200745	−	0.979644i	$-0.564336\pi$
$997$	−27.2942	−	7.31347i	−0.864417	−	0.231620i	−0.663672	+	0.748024i	$0.731003\pi$
$998$	2.80385	+	10.4641i	0.0887542	+	0.331235i
$999$	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.b.52.1	✓	4
3.2	odd	2		945.2.bv.a.262.1		4
5.3	odd	4		315.2.bs.c.178.1	yes	4
7.5	odd	6		315.2.cg.c.187.1	yes	4
9.4	even	3		315.2.cg.a.157.1	yes	4
9.5	odd	6		945.2.cj.d.577.1		4
15.8	even	4		945.2.bv.d.73.1		4
21.5	even	6		945.2.cj.a.397.1		4
35.33	even	12		315.2.cg.a.313.1	yes	4
45.13	odd	12		315.2.cg.c.283.1	yes	4
45.23	even	12		945.2.cj.a.388.1		4
63.5	even	6		945.2.bv.d.712.1		4
63.40	odd	6		315.2.bs.c.292.1	yes	4
105.68	odd	12		945.2.cj.d.208.1		4
315.68	odd	12		945.2.bv.a.523.1		4
315.103	even	12	inner	315.2.bs.b.103.1	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} -1.73205i q^{4} +(0.133975 - 2.23205i) q^{5} +(0.232051 - 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} -1.73205i q^{4} +(0.133975 - 2.23205i) q^{5} +(0.232051 - 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.866025 - 0.767949i) q^{10} +(-0.732051 - 1.26795i) q^{11} +(-2.59808 + 1.50000i) q^{12} +(0.267949 - 1.00000i) q^{13} +(-1.36603 + 0.0980762i) q^{14} +(-3.46410 + 1.73205i) q^{15} -2.46410 q^{16} +(0.732051 + 2.73205i) q^{17} +(-1.50000 + 0.401924i) q^{18} +(-3.36603 - 5.83013i) q^{19} +(-3.86603 - 0.232051i) q^{20} +(4.50000 + 0.866025i) q^{21} +(0.196152 - 0.732051i) q^{22} +(0.598076 + 2.23205i) q^{23} +(-3.23205 - 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(0.464102 - 0.267949i) q^{26} +5.19615 q^{27} +(3.46410 + 3.00000i) q^{28} +(6.00000 + 3.46410i) q^{29} +(-1.90192 - 0.633975i) q^{30} -10.1962i q^{31} +(-3.63397 - 3.63397i) q^{32} +(-1.26795 + 2.19615i) q^{33} +(-0.732051 + 1.26795i) q^{34} +(4.23205 + 4.13397i) q^{35} +(4.50000 + 2.59808i) q^{36} +(1.09808 - 4.09808i) q^{37} +(0.901924 - 3.36603i) q^{38} +(-1.73205 + 0.464102i) q^{39} +(-2.86603 - 3.23205i) q^{40} +(8.19615 - 4.73205i) q^{41} +(1.33013 + 1.96410i) q^{42} +(1.50000 + 5.59808i) q^{43} +(-2.19615 + 1.26795i) q^{44} +(5.59808 + 3.69615i) q^{45} +(-0.598076 + 1.03590i) q^{46} +(6.29423 - 6.29423i) q^{47} +(2.13397 + 3.69615i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-1.59808 - 2.03590i) q^{50} +(3.46410 - 3.46410i) q^{51} +(-1.73205 - 0.464102i) q^{52} +(0.901924 + 3.36603i) q^{53} +(1.90192 + 1.90192i) q^{54} +(-2.92820 + 1.46410i) q^{55} +(0.366025 + 5.09808i) q^{56} +(-5.83013 + 10.0981i) q^{57} +(0.928203 + 3.46410i) q^{58} -3.46410 q^{59} +(3.00000 + 6.00000i) q^{60} +9.39230i q^{61} +(3.73205 - 3.73205i) q^{62} +(-2.59808 - 7.50000i) q^{63} +2.26795i q^{64} +(-2.19615 - 0.732051i) q^{65} +(-1.26795 + 0.339746i) q^{66} +(6.09808 + 6.09808i) q^{67} +(4.73205 - 1.26795i) q^{68} +(2.83013 - 2.83013i) q^{69} +(0.0358984 + 3.06218i) q^{70} -6.00000 q^{71} +(1.50000 + 5.59808i) q^{72} +(-0.633975 + 0.169873i) q^{73} +(1.90192 - 1.09808i) q^{74} +(3.40192 + 7.96410i) q^{75} +(-10.0981 + 5.83013i) q^{76} +(3.80385 + 0.732051i) q^{77} +(-0.803848 - 0.464102i) q^{78} -11.4641i q^{79} +(-0.330127 + 5.50000i) 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} -12.0000i q^{87} +(-2.73205 - 0.732051i) q^{88} +(0.598076 + 1.03590i) q^{89} +(0.696152 + 3.40192i) q^{90} +(1.53590 + 2.26795i) q^{91} +(3.86603 - 1.03590i) q^{92} +(-15.2942 + 8.83013i) q^{93} +4.60770 q^{94} +(-13.4641 + 6.73205i) q^{95} +(-2.30385 + 8.59808i) q^{96} +(-0.830127 - 3.09808i) q^{97} +(2.16987 - 2.90192i) q^{98} +4.39230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 4 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 4 q^{11} + 8 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 12 q^{20} + 18 q^{21} - 20 q^{22} - 8 q^{23} - 6 q^{24} - 6 q^{25} - 12 q^{26} + 24 q^{29} - 18 q^{30} - 18 q^{32} - 12 q^{33} + 4 q^{34} + 10 q^{35} + 18 q^{36} - 6 q^{37} + 14 q^{38} - 8 q^{40} + 12 q^{41} - 12 q^{42} + 6 q^{43} + 12 q^{44} + 12 q^{45} + 8 q^{46} - 6 q^{47} + 12 q^{48} - 4 q^{49} + 4 q^{50} + 14 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{56} - 6 q^{57} - 24 q^{58} + 12 q^{60} + 8 q^{62} + 12 q^{65} - 12 q^{66} + 14 q^{67} + 12 q^{68} - 6 q^{69} + 14 q^{70} - 24 q^{71} + 6 q^{72} - 6 q^{73} + 18 q^{74} + 24 q^{75} - 30 q^{76} + 36 q^{77} - 24 q^{78} + 16 q^{80} - 18 q^{81} + 12 q^{82} + 2 q^{83} + 6 q^{84} + 4 q^{85} - 6 q^{86} - 4 q^{88} - 8 q^{89} - 18 q^{90} + 20 q^{91} + 12 q^{92} - 30 q^{93} + 60 q^{94} - 40 q^{95} - 30 q^{96} + 14 q^{97} + 26 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 + 4 * q^11 + 8 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 - 6 * q^18 - 10 * q^19 - 12 * q^20 + 18 * q^21 - 20 * q^22 - 8 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 24 * q^29 - 18 * q^30 - 18 * q^32 - 12 * q^33 + 4 * q^34 + 10 * q^35 + 18 * q^36 - 6 * q^37 + 14 * q^38 - 8 * q^40 + 12 * q^41 - 12 * q^42 + 6 * q^43 + 12 * q^44 + 12 * q^45 + 8 * q^46 - 6 * q^47 + 12 * q^48 - 4 * q^49 + 4 * q^50 + 14 * q^53 + 18 * q^54 + 16 * q^55 - 2 * q^56 - 6 * q^57 - 24 * q^58 + 12 * q^60 + 8 * q^62 + 12 * q^65 - 12 * q^66 + 14 * q^67 + 12 * q^68 - 6 * q^69 + 14 * q^70 - 24 * q^71 + 6 * q^72 - 6 * q^73 + 18 * q^74 + 24 * q^75 - 30 * q^76 + 36 * q^77 - 24 * q^78 + 16 * q^80 - 18 * q^81 + 12 * q^82 + 2 * q^83 + 6 * q^84 + 4 * q^85 - 6 * q^86 - 4 * q^88 - 8 * q^89 - 18 * q^90 + 20 * q^91 + 12 * q^92 - 30 * q^93 + 60 * q^94 - 40 * q^95 - 30 * q^96 + 14 * q^97 + 26 * q^98 - 24 * q^99

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