LMFDB - Embedded newform 112.2.w.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(37,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("112.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (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:	$0.894324502638$
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			37.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	112.37
Dual form			112.2.w.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.866025 + 0.232051i) q^{5} +(0.366025 + 0.633975i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.866025 + 0.232051i) q^{5} +(0.366025 + 0.633975i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +(-1.09808 - 0.633975i) q^{10} +(-0.767949 + 2.86603i) q^{11} +(-0.267949 + 1.00000i) q^{12} +(3.73205 - 3.73205i) q^{13} +(3.73205 - 0.267949i) q^{14} -0.464102 q^{15} -4.00000 q^{16} +(-3.23205 - 5.59808i) q^{17} +(-1.00000 - 3.73205i) q^{18} +(0.767949 + 2.86603i) q^{19} +(-0.464102 - 1.73205i) q^{20} +(1.13397 - 0.767949i) q^{21} +(-3.63397 + 2.09808i) q^{22} +(3.86603 + 2.23205i) q^{23} +(-1.26795 + 0.732051i) q^{24} +(-3.63397 + 2.09808i) q^{25} +7.46410 q^{26} +(-2.09808 - 2.09808i) q^{27} +(4.00000 + 3.46410i) q^{28} +(-0.267949 + 0.267949i) q^{29} +(-0.464102 - 0.464102i) q^{30} +(-1.86603 - 3.23205i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.767949 + 1.33013i) q^{33} +(2.36603 - 8.83013i) q^{34} +(-1.03590 + 2.13397i) q^{35} +(2.73205 - 4.73205i) q^{36} +(-1.13397 + 0.303848i) q^{37} +(-2.09808 + 3.63397i) q^{38} +(2.36603 - 1.36603i) q^{39} +(1.26795 - 2.19615i) q^{40} +4.92820i q^{41} +(1.90192 + 0.366025i) q^{42} +(6.46410 + 6.46410i) q^{43} +(-5.73205 - 1.53590i) q^{44} +(2.36603 + 0.633975i) q^{45} +(1.63397 + 6.09808i) q^{46} +(-2.13397 + 3.69615i) q^{47} +(-2.00000 - 0.535898i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-5.73205 - 1.53590i) q^{50} +(-0.866025 - 3.23205i) q^{51} +(7.46410 + 7.46410i) q^{52} +(-1.06218 + 3.96410i) q^{53} -4.19615i q^{54} -2.66025i q^{55} +(0.535898 + 7.46410i) q^{56} +1.53590i q^{57} -0.535898 q^{58} +(-3.03590 + 11.3301i) q^{59} -0.928203i q^{60} +(1.86603 + 6.96410i) q^{61} +(1.36603 - 5.09808i) q^{62} +(-6.83013 + 2.36603i) q^{63} -8.00000i q^{64} +(-2.36603 + 4.09808i) q^{65} +(-2.09808 + 0.562178i) q^{66} +(-4.96410 - 1.33013i) q^{67} +(11.1962 - 6.46410i) q^{68} +(1.63397 + 1.63397i) q^{69} +(-3.16987 + 1.09808i) q^{70} -0.535898i q^{71} +(7.46410 - 2.00000i) q^{72} +(6.23205 - 3.59808i) q^{73} +(-1.43782 - 0.830127i) q^{74} +(-2.09808 + 0.562178i) q^{75} +(-5.73205 + 1.53590i) q^{76} +(4.40192 + 6.50000i) q^{77} +(3.73205 + 1.00000i) q^{78} +(8.33013 - 14.4282i) q^{79} +(3.46410 - 0.928203i) q^{80} +(3.33013 + 5.76795i) q^{81} +(-4.92820 + 4.92820i) q^{82} +(1.53590 - 1.53590i) q^{83} +(1.53590 + 2.26795i) q^{84} +(4.09808 + 4.09808i) q^{85} +12.9282i q^{86} +(-0.169873 + 0.0980762i) q^{87} +(-4.19615 - 7.26795i) q^{88} +(-4.50000 - 2.59808i) q^{89} +(1.73205 + 3.00000i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(-4.46410 + 7.73205i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-5.83013 + 1.56218i) q^{94} +(-1.33013 - 2.30385i) q^{95} +(-1.46410 - 2.53590i) q^{96} -2.92820 q^{97} +(5.92820 - 7.92820i) q^{98} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 - 2 * q^6 - 8 * q^8 - 6 * q^9	$ 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9} + 6 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 8 q^{14} + 12 q^{15} - 16 q^{16} - 6 q^{17} - 4 q^{18} + 10 q^{19} + 12 q^{20} + 8 q^{21} - 18 q^{22} + 12 q^{23} - 12 q^{24} - 18 q^{25} + 16 q^{26} + 2 q^{27} + 16 q^{28} - 8 q^{29} + 12 q^{30} - 4 q^{31} - 16 q^{32} - 10 q^{33} + 6 q^{34} - 18 q^{35} + 4 q^{36} - 8 q^{37} + 2 q^{38} + 6 q^{39} + 12 q^{40} + 18 q^{42} + 12 q^{43} - 16 q^{44} + 6 q^{45} + 10 q^{46} - 12 q^{47} - 8 q^{48} - 4 q^{49} - 16 q^{50} + 16 q^{52} + 20 q^{53} + 16 q^{56} - 16 q^{58} - 26 q^{59} + 4 q^{61} + 2 q^{62} - 10 q^{63} - 6 q^{65} + 2 q^{66} - 6 q^{67} + 24 q^{68} + 10 q^{69} - 30 q^{70} + 16 q^{72} + 18 q^{73} - 30 q^{74} + 2 q^{75} - 16 q^{76} + 28 q^{77} + 8 q^{78} + 16 q^{79} - 4 q^{81} + 8 q^{82} + 20 q^{83} + 20 q^{84} + 6 q^{85} - 18 q^{87} + 4 q^{88} - 18 q^{89} - 4 q^{91} - 4 q^{92} - 2 q^{93} - 6 q^{94} + 12 q^{95} + 8 q^{96} + 16 q^{97} - 4 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 - 2 * q^6 - 8 * q^8 - 6 * q^9 + 6 * q^10 - 10 * q^11 - 8 * q^12 + 8 * q^13 + 8 * q^14 + 12 * q^15 - 16 * q^16 - 6 * q^17 - 4 * q^18 + 10 * q^19 + 12 * q^20 + 8 * q^21 - 18 * q^22 + 12 * q^23 - 12 * q^24 - 18 * q^25 + 16 * q^26 + 2 * q^27 + 16 * q^28 - 8 * q^29 + 12 * q^30 - 4 * q^31 - 16 * q^32 - 10 * q^33 + 6 * q^34 - 18 * q^35 + 4 * q^36 - 8 * q^37 + 2 * q^38 + 6 * q^39 + 12 * q^40 + 18 * q^42 + 12 * q^43 - 16 * q^44 + 6 * q^45 + 10 * q^46 - 12 * q^47 - 8 * q^48 - 4 * q^49 - 16 * q^50 + 16 * q^52 + 20 * q^53 + 16 * q^56 - 16 * q^58 - 26 * q^59 + 4 * q^61 + 2 * q^62 - 10 * q^63 - 6 * q^65 + 2 * q^66 - 6 * q^67 + 24 * q^68 + 10 * q^69 - 30 * q^70 + 16 * q^72 + 18 * q^73 - 30 * q^74 + 2 * q^75 - 16 * q^76 + 28 * q^77 + 8 * q^78 + 16 * q^79 - 4 * q^81 + 8 * q^82 + 20 * q^83 + 20 * q^84 + 6 * q^85 - 18 * q^87 + 4 * q^88 - 18 * q^89 - 4 * q^91 - 4 * q^92 - 2 * q^93 - 6 * q^94 + 12 * q^95 + 8 * q^96 + 16 * q^97 - 4 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	0.500000	+	0.133975i	0.288675	+	0.0773503i	0.400251	−	0.916406i	$-0.368923\pi$
$3$	0.500000	+	0.133975i	0.288675	+	0.0773503i	−0.111576	+	0.993756i	$0.535590\pi$
$4$			2.00000i			1.00000i
$5$	−0.866025	+	0.232051i	−0.387298	+	0.103776i	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−0.866025	+	0.232051i	−0.387298	+	0.103776i	0.0599153	+	0.998203i	$0.480917\pi$
$6$	0.366025	+	0.633975i	0.149429	+	0.258819i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−2.36603	−	1.36603i	−0.788675	−	0.455342i
$10$	−1.09808	−	0.633975i	−0.347242	−	0.200480i
$11$	−0.767949	+	2.86603i	−0.231545	+	0.864139i	0.748130	+	0.663552i	$0.230952\pi$
$11$	−0.767949	+	2.86603i	−0.231545	+	0.864139i	−0.979676	+	0.200587i	$0.935715\pi$
$12$	−0.267949	+	1.00000i	−0.0773503	+	0.288675i
$13$	3.73205	−	3.73205i	1.03508	−	1.03508i	0.0357229	−	0.999362i	$-0.488627\pi$
$13$	3.73205	−	3.73205i	1.03508	−	1.03508i	0.999362	−	0.0357229i	$-0.0113734\pi$
$14$	3.73205	−	0.267949i	0.997433	−	0.0716124i
$15$	−0.464102			−0.119831
$16$	−4.00000			−1.00000
$17$	−3.23205	−	5.59808i	−0.783887	−	1.35773i	−0.929661	−	0.368415i	$-0.879901\pi$
$17$	−3.23205	−	5.59808i	−0.783887	−	1.35773i	0.145774	−	0.989318i	$-0.453433\pi$
$18$	−1.00000	−	3.73205i	−0.235702	−	0.879653i
$19$	0.767949	+	2.86603i	0.176180	+	0.657511i	0.996348	+	0.0853887i	$0.0272132\pi$
$19$	0.767949	+	2.86603i	0.176180	+	0.657511i	−0.820168	+	0.572123i	$0.806120\pi$
$20$	−0.464102	−	1.73205i	−0.103776	−	0.387298i
$21$	1.13397	−	0.767949i	0.247454	−	0.167580i
$22$	−3.63397	+	2.09808i	−0.774766	+	0.447311i
$23$	3.86603	+	2.23205i	0.806122	+	0.465415i	0.845607	−	0.533805i	$-0.179239\pi$
$23$	3.86603	+	2.23205i	0.806122	+	0.465415i	−0.0394853	+	0.999220i	$0.512572\pi$
$24$	−1.26795	+	0.732051i	−0.258819	+	0.149429i
$25$	−3.63397	+	2.09808i	−0.726795	+	0.419615i
$26$	7.46410			1.46383
$27$	−2.09808	−	2.09808i	−0.403775	−	0.403775i
$28$	4.00000	+	3.46410i	0.755929	+	0.654654i
$29$	−0.267949	+	0.267949i	−0.0497569	+	0.0497569i	−0.731547	−	0.681791i	$-0.761202\pi$
$29$	−0.267949	+	0.267949i	−0.0497569	+	0.0497569i	0.681791	+	0.731547i	$0.261202\pi$
$30$	−0.464102	−	0.464102i	−0.0847330	−	0.0847330i
$31$	−1.86603	−	3.23205i	−0.335148	−	0.580493i	0.648365	−	0.761329i	$-0.275453\pi$
$31$	−1.86603	−	3.23205i	−0.335148	−	0.580493i	−0.983513	+	0.180836i	$0.942120\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	−0.767949	+	1.33013i	−0.133683	+	0.231545i
$34$	2.36603	−	8.83013i	0.405770	−	1.51435i
$35$	−1.03590	+	2.13397i	−0.175099	+	0.360708i
$36$	2.73205	−	4.73205i	0.455342	−	0.788675i
$37$	−1.13397	+	0.303848i	−0.186424	+	0.0499522i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	−1.13397	+	0.303848i	−0.186424	+	0.0499522i	0.164399	+	0.986394i	$0.447432\pi$
$38$	−2.09808	+	3.63397i	−0.340353	+	0.589509i
$39$	2.36603	−	1.36603i	0.378867	−	0.218739i
$40$	1.26795	−	2.19615i	0.200480	−	0.347242i
$41$			4.92820i			0.769656i	0.922988	+	0.384828i	$0.125739\pi$
$41$			4.92820i			0.769656i	−0.922988	+	0.384828i	$0.874261\pi$
$42$	1.90192	+	0.366025i	0.293473	+	0.0564789i
$43$	6.46410	+	6.46410i	0.985766	+	0.985766i	0.999900	−	0.0141339i	$-0.00449910\pi$
$43$	6.46410	+	6.46410i	0.985766	+	0.985766i	−0.0141339	+	0.999900i	$0.504499\pi$
$44$	−5.73205	−	1.53590i	−0.864139	−	0.231545i
$45$	2.36603	+	0.633975i	0.352706	+	0.0945074i
$46$	1.63397	+	6.09808i	0.240916	+	0.899112i
$47$	−2.13397	+	3.69615i	−0.311272	+	0.539139i	−0.978638	−	0.205591i	$-0.934088\pi$
$47$	−2.13397	+	3.69615i	−0.311272	+	0.539139i	0.667366	+	0.744730i	$0.267422\pi$
$48$	−2.00000	−	0.535898i	−0.288675	−	0.0773503i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	−5.73205	−	1.53590i	−0.810634	−	0.217209i
$51$	−0.866025	−	3.23205i	−0.121268	−	0.452578i
$52$	7.46410	+	7.46410i	1.03508	+	1.03508i
$53$	−1.06218	+	3.96410i	−0.145901	+	0.544511i	0.853812	+	0.520581i	$0.174285\pi$
$53$	−1.06218	+	3.96410i	−0.145901	+	0.544511i	−0.999714	+	0.0239302i	$0.992382\pi$
$54$		−	4.19615i		−	0.571024i
$55$		−	2.66025i		−	0.358709i
$56$	0.535898	+	7.46410i	0.0716124	+	0.997433i
$57$			1.53590i			0.203435i
$58$	−0.535898			−0.0703669
$59$	−3.03590	+	11.3301i	−0.395240	+	1.47506i	0.426130	+	0.904662i	$0.359877\pi$
$59$	−3.03590	+	11.3301i	−0.395240	+	1.47506i	−0.821370	+	0.570395i	$0.806790\pi$
$60$		−	0.928203i		−	0.119831i
$61$	1.86603	+	6.96410i	0.238920	+	0.891662i	0.976342	+	0.216230i	$0.0693761\pi$
$61$	1.86603	+	6.96410i	0.238920	+	0.891662i	−0.737422	+	0.675432i	$0.763957\pi$
$62$	1.36603	−	5.09808i	0.173485	−	0.647456i
$63$	−6.83013	+	2.36603i	−0.860515	+	0.298091i
$64$		−	8.00000i		−	1.00000i
$65$	−2.36603	+	4.09808i	−0.293469	+	0.508304i
$66$	−2.09808	+	0.562178i	−0.258255	+	0.0691993i
$67$	−4.96410	−	1.33013i	−0.606462	−	0.162501i	−0.0574958	−	0.998346i	$-0.518312\pi$
$67$	−4.96410	−	1.33013i	−0.606462	−	0.162501i	−0.548966	+	0.835845i	$0.684978\pi$
$68$	11.1962	−	6.46410i	1.35773	−	0.783887i
$69$	1.63397	+	1.63397i	0.196707	+	0.196707i
$70$	−3.16987	+	1.09808i	−0.378872	+	0.131245i
$71$		−	0.535898i		−	0.0635994i	−0.999494	−	0.0317997i	$-0.989876\pi$
$71$		−	0.535898i		−	0.0635994i	0.999494	−	0.0317997i	$-0.0101239\pi$
$72$	7.46410	−	2.00000i	0.879653	−	0.235702i
$73$	6.23205	−	3.59808i	0.729406	−	0.421123i	−0.0887986	−	0.996050i	$-0.528303\pi$
$73$	6.23205	−	3.59808i	0.729406	−	0.421123i	0.818205	+	0.574927i	$0.194969\pi$
$74$	−1.43782	−	0.830127i	−0.167143	−	0.0965003i
$75$	−2.09808	+	0.562178i	−0.242265	+	0.0649147i
$76$	−5.73205	+	1.53590i	−0.657511	+	0.176180i
$77$	4.40192	+	6.50000i	0.501646	+	0.740744i
$78$	3.73205	+	1.00000i	0.422572	+	0.113228i
$79$	8.33013	−	14.4282i	0.937213	−	1.62330i	0.166572	−	0.986029i	$-0.446730\pi$
$79$	8.33013	−	14.4282i	0.937213	−	1.62330i	0.770640	−	0.637270i	$-0.219937\pi$
$80$	3.46410	−	0.928203i	0.387298	−	0.103776i
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$	−4.92820	+	4.92820i	−0.544229	+	0.544229i
$83$	1.53590	−	1.53590i	0.168587	−	0.168587i	−0.617771	−	0.786358i	$-0.711964\pi$
$83$	1.53590	−	1.53590i	0.168587	−	0.168587i	0.786358	+	0.617771i	$0.211964\pi$
$84$	1.53590	+	2.26795i	0.167580	+	0.247454i
$85$	4.09808	+	4.09808i	0.444499	+	0.444499i
$86$			12.9282i			1.39408i
$87$	−0.169873	+	0.0980762i	−0.0182123	+	0.0105149i
$88$	−4.19615	−	7.26795i	−0.447311	−	0.774766i
$89$	−4.50000	−	2.59808i	−0.476999	−	0.275396i	0.242166	−	0.970235i	$-0.422142\pi$
$89$	−4.50000	−	2.59808i	−0.476999	−	0.275396i	−0.719165	+	0.694839i	$0.755475\pi$
$90$	1.73205	+	3.00000i	0.182574	+	0.316228i
$91$	−1.00000	−	13.9282i	−0.104828	−	1.46007i
$92$	−4.46410	+	7.73205i	−0.465415	+	0.806122i
$93$	−0.500000	−	1.86603i	−0.0518476	−	0.193498i
$94$	−5.83013	+	1.56218i	−0.601332	+	0.161126i
$95$	−1.33013	−	2.30385i	−0.136468	−	0.236370i
$96$	−1.46410	−	2.53590i	−0.149429	−	0.258819i
$97$	−2.92820			−0.297314			−0.148657	−	0.988889i	$-0.547495\pi$
$97$	−2.92820			−0.297314			−0.148657	+	0.988889i	$0.547495\pi$
$98$	5.92820	−	7.92820i	0.598839	−	0.800869i
$99$	5.73205	−	5.73205i	0.576093	−	0.576093i
$100$	−4.19615	−	7.26795i	−0.419615	−	0.726795i
$101$	5.06218	−	18.8923i	0.503706	−	1.87985i	0.0292559	−	0.999572i	$-0.490686\pi$
$101$	5.06218	−	18.8923i	0.503706	−	1.87985i	0.474450	−	0.880283i	$-0.342647\pi$
$102$	2.36603	−	4.09808i	0.234271	−	0.405770i
$103$	−5.59808	−	3.23205i	−0.551595	−	0.318463i	0.198170	−	0.980168i	$-0.436500\pi$
$103$	−5.59808	−	3.23205i	−0.551595	−	0.318463i	−0.749765	+	0.661704i	$0.769833\pi$
$104$			14.9282i			1.46383i
$105$	−0.803848	+	0.928203i	−0.0784475	+	0.0905834i
$106$	−5.02628	+	2.90192i	−0.488195	+	0.281860i
$107$	3.23205	−	0.866025i	0.312454	−	0.0837218i	−0.0991843	−	0.995069i	$-0.531623\pi$
$107$	3.23205	−	0.866025i	0.312454	−	0.0837218i	0.411638	+	0.911347i	$0.364957\pi$
$108$	4.19615	−	4.19615i	0.403775	−	0.403775i
$109$	−2.13397	−	0.571797i	−0.204398	−	0.0547682i	0.155167	−	0.987888i	$-0.450408\pi$
$109$	−2.13397	−	0.571797i	−0.204398	−	0.0547682i	−0.359565	+	0.933120i	$0.617075\pi$
$110$	2.66025	−	2.66025i	0.253645	−	0.253645i
$111$	−0.607695			−0.0576799
$112$	−6.92820	+	8.00000i	−0.654654	+	0.755929i
$113$	−1.46410			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$113$	−1.46410			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$114$	−1.53590	+	1.53590i	−0.143850	+	0.143850i
$115$	−3.86603	−	1.03590i	−0.360509	−	0.0965980i
$116$	−0.535898	−	0.535898i	−0.0497569	−	0.0497569i
$117$	−13.9282	+	3.73205i	−1.28766	+	0.345028i
$118$	−14.3660	+	8.29423i	−1.32250	+	0.763546i
$119$	−16.7942	−	3.23205i	−1.53952	−	0.296282i
$120$	0.928203	−	0.928203i	0.0847330	−	0.0847330i
$121$	1.90192	+	1.09808i	0.172902	+	0.0998251i
$122$	−5.09808	+	8.83013i	−0.461558	+	0.799442i
$123$	−0.660254	+	2.46410i	−0.0595331	+	0.222181i
$124$	6.46410	−	3.73205i	0.580493	−	0.335148i
$125$	5.83013	−	5.83013i	0.521462	−	0.521462i
$126$	−9.19615	−	4.46410i	−0.819258	−	0.397694i
$127$	9.46410			0.839803			0.419902	−	0.907570i	$-0.362065\pi$
$127$	9.46410			0.839803			0.419902	+	0.907570i	$0.362065\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	2.36603	+	4.09808i	0.208317	+	0.360815i
$130$	−6.46410	+	1.73205i	−0.566939	+	0.151911i
$131$	−2.03590	−	7.59808i	−0.177877	−	0.663847i	−0.996044	−	0.0888654i	$-0.971676\pi$
$131$	−2.03590	−	7.59808i	−0.177877	−	0.663847i	0.818166	−	0.574982i	$-0.194991\pi$
$132$	−2.66025	−	1.53590i	−0.231545	−	0.133683i
$133$	7.06218	+	3.42820i	0.612368	+	0.297263i
$134$	−3.63397	−	6.29423i	−0.313928	−	0.543739i
$135$	2.30385	+	1.33013i	0.198284	+	0.114479i
$136$	17.6603	+	4.73205i	1.51435	+	0.405770i
$137$	15.2321	−	8.79423i	1.30136	−	0.751342i	0.320724	−	0.947173i	$-0.396074\pi$
$137$	15.2321	−	8.79423i	1.30136	−	0.751342i	0.980638	+	0.195831i	$0.0627404\pi$
$138$			3.26795i			0.278186i
$139$	−11.9282	−	11.9282i	−1.01174	−	1.01174i	−0.999930	−	0.0118067i	$-0.996242\pi$
$139$	−11.9282	−	11.9282i	−1.01174	−	1.01174i	−0.0118067	−	0.999930i	$-0.503758\pi$
$140$	−4.26795	−	2.07180i	−0.360708	−	0.175099i
$141$	−1.56218	+	1.56218i	−0.131559	+	0.131559i
$142$	0.535898	−	0.535898i	0.0449716	−	0.0449716i
$143$	7.83013	+	13.5622i	0.654788	+	1.13413i
$144$	9.46410	+	5.46410i	0.788675	+	0.455342i
$145$	0.169873	−	0.294229i	0.0141072	−	0.0244344i
$146$	9.83013	+	2.63397i	0.813547	+	0.217989i
$147$	0.428203	−	3.59808i	0.0353176	−	0.296764i
$148$	−0.607695	−	2.26795i	−0.0499522	−	0.186424i
$149$	−7.59808	+	2.03590i	−0.622459	+	0.166787i	−0.556245	−	0.831018i	$-0.687758\pi$
$149$	−7.59808	+	2.03590i	−0.622459	+	0.166787i	−0.0662134	+	0.997805i	$0.521092\pi$
$150$	−2.66025	−	1.53590i	−0.217209	−	0.125406i
$151$	9.86603	−	5.69615i	0.802886	−	0.463546i	−0.0415935	−	0.999135i	$-0.513243\pi$
$151$	9.86603	−	5.69615i	0.802886	−	0.463546i	0.844479	+	0.535588i	$0.179910\pi$
$152$	−7.26795	−	4.19615i	−0.589509	−	0.340353i
$153$			17.6603i			1.42775i
$154$	−2.09808	+	10.9019i	−0.169068	+	0.878502i
$155$	2.36603	+	2.36603i	0.190044	+	0.190044i
$156$	2.73205	+	4.73205i	0.218739	+	0.378867i
$157$	−18.2583	−	4.89230i	−1.45717	−	0.390448i	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−18.2583	−	4.89230i	−1.45717	−	0.390448i	−0.898513	+	0.438948i	$0.855351\pi$
$158$	22.7583	−	6.09808i	1.81056	−	0.485137i
$159$	−1.06218	+	1.83975i	−0.0842362	+	0.145901i
$160$	4.39230	+	2.53590i	0.347242	+	0.200480i
$161$	11.1603	−	3.86603i	0.879551	−	0.304685i
$162$	−2.43782	+	9.09808i	−0.191533	+	0.714812i
$163$	3.23205	+	12.0622i	0.253154	+	0.944783i	0.969108	+	0.246636i	$0.0793251\pi$
$163$	3.23205	+	12.0622i	0.253154	+	0.944783i	−0.715954	+	0.698147i	$0.754008\pi$
$164$	−9.85641			−0.769656
$165$	0.356406	−	1.33013i	0.0277462	−	0.103550i
$166$	3.07180			0.238418
$167$			21.8564i			1.69130i	0.533738	+	0.845650i	$0.320787\pi$
$167$			21.8564i			1.69130i	−0.533738	+	0.845650i	$0.679213\pi$
$168$	−0.732051	+	3.80385i	−0.0564789	+	0.293473i
$169$		−	14.8564i		−	1.14280i
$170$			8.19615i			0.628616i
$171$	2.09808	−	7.83013i	0.160444	−	0.598785i
$172$	−12.9282	+	12.9282i	−0.985766	+	0.985766i
$173$	0.598076	+	2.23205i	0.0454709	+	0.169700i	0.984927	−	0.172969i	$-0.0553359\pi$
$173$	0.598076	+	2.23205i	0.0454709	+	0.169700i	−0.939456	+	0.342668i	$0.888669\pi$
$174$	−0.267949	−	0.0717968i	−0.0203132	−	0.00544290i
$175$	−2.09808	+	10.9019i	−0.158600	+	0.824108i
$176$	3.07180	−	11.4641i	0.231545	−	0.864139i
$177$	−3.03590	+	5.25833i	−0.228192	+	0.395240i
$178$	−1.90192	−	7.09808i	−0.142555	−	0.532023i
$179$	8.96410	+	2.40192i	0.670008	+	0.179528i	0.577759	−	0.816208i	$-0.303928\pi$
$179$	8.96410	+	2.40192i	0.670008	+	0.179528i	0.0922498	+	0.995736i	$0.470594\pi$
$180$	−1.26795	+	4.73205i	−0.0945074	+	0.352706i
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	0.999990	−	0.00454748i	$-0.00144751\pi$
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	−0.00454748	+	0.999990i	$0.501448\pi$
$182$	12.9282	−	14.9282i	0.958302	−	1.10655i
$183$			3.73205i			0.275881i
$184$	−12.1962	+	3.26795i	−0.899112	+	0.240916i
$185$	0.911543	−	0.526279i	0.0670180	−	0.0386928i
$186$	1.36603	−	2.36603i	0.100162	−	0.173485i
$187$	18.5263	−	4.96410i	1.35478	−	0.363011i
$188$	−7.39230	−	4.26795i	−0.539139	−	0.311272i
$189$	−7.83013	+	0.562178i	−0.569558	+	0.0408924i
$190$	0.973721	−	3.63397i	0.0706411	−	0.263636i
$191$	−4.33013	+	7.50000i	−0.313317	+	0.542681i	−0.979078	−	0.203484i	$-0.934774\pi$
$191$	−4.33013	+	7.50000i	−0.313317	+	0.542681i	0.665761	+	0.746165i	$0.268107\pi$
$192$	1.07180	−	4.00000i	0.0773503	−	0.288675i
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−2.92820	−	2.92820i	−0.210233	−	0.210233i
$195$	−1.73205	+	1.73205i	−0.124035	+	0.124035i
$196$	13.8564	−	2.00000i	0.989743	−	0.142857i
$197$	−16.6603	−	16.6603i	−1.18699	−	1.18699i	−0.977894	−	0.209100i	$-0.932947\pi$
$197$	−16.6603	−	16.6603i	−1.18699	−	1.18699i	−0.209100	−	0.977894i	$-0.567053\pi$
$198$	11.4641			0.814718
$199$	−10.3301	+	5.96410i	−0.732283	+	0.422784i	−0.819257	−	0.573427i	$-0.805614\pi$
$199$	−10.3301	+	5.96410i	−0.732283	+	0.422784i	0.0869736	+	0.996211i	$0.472280\pi$
$200$	3.07180	−	11.4641i	0.217209	−	0.810634i
$201$	−2.30385	−	1.33013i	−0.162501	−	0.0938199i
$202$	23.9545	−	13.8301i	1.68543	−	0.973084i
$203$	0.0717968	+	1.00000i	0.00503915	+	0.0701862i
$204$	6.46410	−	1.73205i	0.452578	−	0.121268i
$205$	−1.14359	−	4.26795i	−0.0798720	−	0.298087i
$206$	−2.36603	−	8.83013i	−0.164849	−	0.615224i
$207$	−6.09808	−	10.5622i	−0.423846	−	0.734122i
$208$	−14.9282	+	14.9282i	−1.03508	+	1.03508i
$209$	−8.80385			−0.608975
$210$	−1.73205	+	0.124356i	−0.119523	+	0.00858136i
$211$	−15.9282	+	15.9282i	−1.09654	+	1.09654i	−0.101731	+	0.994812i	$0.532438\pi$
$211$	−15.9282	+	15.9282i	−1.09654	+	1.09654i	−0.994812	+	0.101731i	$0.967562\pi$
$212$	−7.92820	−	2.12436i	−0.544511	−	0.145901i
$213$	0.0717968	−	0.267949i	0.00491943	−	0.0183596i
$214$	4.09808	+	2.36603i	0.280139	+	0.161738i
$215$	−7.09808	−	4.09808i	−0.484085	−	0.279486i
$216$	8.39230			0.571024
$217$	−9.69615	−	1.86603i	−0.658218	−	0.126674i
$218$	−1.56218	−	2.70577i	−0.105804	−	0.183258i
$219$	3.59808	−	0.964102i	0.243135	−	0.0651479i
$220$	5.32051			0.358709
$221$	−32.9545	−	8.83013i	−2.21676	−	0.593979i
$222$	−0.607695	−	0.607695i	−0.0407858	−	0.0407858i
$223$	9.85641			0.660034			0.330017	−	0.943975i	$-0.392946\pi$
$223$	9.85641			0.660034			0.330017	+	0.943975i	$0.392946\pi$
$224$	−14.9282	+	1.07180i	−0.997433	+	0.0716124i
$225$	11.4641			0.764273
$226$	−1.46410	−	1.46410i	−0.0973906	−	0.0973906i
$227$	11.1603	+	2.99038i	0.740732	+	0.198479i	0.609403	−	0.792860i	$-0.291409\pi$
$227$	11.1603	+	2.99038i	0.740732	+	0.198479i	0.131329	+	0.991339i	$0.458076\pi$
$228$	−3.07180			−0.203435
$229$	13.3301	−	3.57180i	0.880880	−	0.236031i	0.210093	−	0.977681i	$-0.432623\pi$
$229$	13.3301	−	3.57180i	0.880880	−	0.236031i	0.670787	+	0.741650i	$0.265957\pi$
$230$	−2.83013	−	4.90192i	−0.186613	−	0.323223i
$231$	1.33013	+	3.83975i	0.0875159	+	0.252637i
$232$		−	1.07180i		−	0.0703669i
$233$	0.696152	+	0.401924i	0.0456065	+	0.0263309i	0.522630	−	0.852560i	$-0.324951\pi$
$233$	0.696152	+	0.401924i	0.0456065	+	0.0263309i	−0.477023	+	0.878891i	$0.658284\pi$
$234$	−17.6603	−	10.1962i	−1.15449	−	0.666543i
$235$	0.990381	−	3.69615i	0.0646053	−	0.241110i
$236$	−22.6603	−	6.07180i	−1.47506	−	0.395240i
$237$	6.09808	−	6.09808i	0.396113	−	0.396113i
$238$	−13.5622	−	20.0263i	−0.879105	−	1.29811i
$239$	−8.53590			−0.552141			−0.276071	−	0.961137i	$-0.589032\pi$
$239$	−8.53590			−0.552141			−0.276071	+	0.961137i	$0.589032\pi$
$240$	1.85641			0.119831
$241$	−6.96410	−	12.0622i	−0.448597	−	0.776993i	0.549698	−	0.835364i	$-0.314743\pi$
$241$	−6.96410	−	12.0622i	−0.448597	−	0.776993i	−0.998295	+	0.0583704i	$0.981410\pi$
$242$	0.803848	+	3.00000i	0.0516733	+	0.192847i
$243$	3.19615	+	11.9282i	0.205033	+	0.765195i
$244$	−13.9282	+	3.73205i	−0.891662	+	0.238920i
$245$	2.47372	+	5.76795i	0.158040	+	0.368501i
$246$	−3.12436	+	1.80385i	−0.199202	+	0.115009i
$247$	13.5622	+	7.83013i	0.862941	+	0.498219i
$248$	10.1962	+	2.73205i	0.647456	+	0.173485i
$249$	0.973721	−	0.562178i	0.0617070	−	0.0356266i
$250$	11.6603			0.737459
$251$	−17.5885	−	17.5885i	−1.11017	−	1.11017i	−0.993126	−	0.117047i	$-0.962657\pi$
$251$	−17.5885	−	17.5885i	−1.11017	−	1.11017i	−0.117047	−	0.993126i	$-0.537343\pi$
$252$	−4.73205	−	13.6603i	−0.298091	−	0.860515i
$253$	−9.36603	+	9.36603i	−0.588837	+	0.588837i
$254$	9.46410	+	9.46410i	0.593831	+	0.593831i
$255$	1.50000	+	2.59808i	0.0939336	+	0.162698i
$256$	16.0000			1.00000
$257$	9.69615	−	16.7942i	0.604829	−	1.04760i	−0.387249	−	0.921975i	$-0.626575\pi$
$257$	9.69615	−	16.7942i	0.604829	−	1.04760i	0.992078	−	0.125620i	$-0.0400920\pi$
$258$	−1.73205	+	6.46410i	−0.107833	+	0.402437i
$259$	−1.35641	+	2.79423i	−0.0842830	+	0.173625i
$260$	−8.19615	−	4.73205i	−0.508304	−	0.293469i
$261$	1.00000	−	0.267949i	0.0618984	−	0.0165856i
$262$	5.56218	−	9.63397i	0.343632	−	0.595189i
$263$	3.99038	−	2.30385i	0.246057	−	0.142061i	−0.371900	−	0.928273i	$-0.621294\pi$
$263$	3.99038	−	2.30385i	0.246057	−	0.142061i	0.617958	+	0.786211i	$0.287960\pi$
$264$	−1.12436	−	4.19615i	−0.0691993	−	0.258255i
$265$		−	3.67949i		−	0.226029i
$266$	3.63397	+	10.4904i	0.222813	+	0.643207i
$267$	−1.90192	−	1.90192i	−0.116396	−	0.116396i
$268$	2.66025	−	9.92820i	0.162501	−	0.606462i
$269$	9.79423	+	2.62436i	0.597165	+	0.160010i	0.544726	−	0.838614i	$-0.316634\pi$
$269$	9.79423	+	2.62436i	0.597165	+	0.160010i	0.0524390	+	0.998624i	$0.483300\pi$
$270$	0.973721	+	3.63397i	0.0592587	+	0.221157i
$271$	−6.06218	+	10.5000i	−0.368251	+	0.637830i	−0.989292	−	0.145948i	$-0.953377\pi$
$271$	−6.06218	+	10.5000i	−0.368251	+	0.637830i	0.621041	+	0.783778i	$0.286710\pi$
$272$	12.9282	+	22.3923i	0.783887	+	1.35773i
$273$	1.36603	−	7.09808i	0.0826756	−	0.429595i
$274$	24.0263	+	6.43782i	1.45148	+	0.388923i
$275$	−3.22243	−	12.0263i	−0.194320	−	0.725212i
$276$	−3.26795	+	3.26795i	−0.196707	+	0.196707i
$277$	−1.20577	+	4.50000i	−0.0724478	+	0.270379i	−0.992642	−	0.121082i	$-0.961364\pi$
$277$	−1.20577	+	4.50000i	−0.0724478	+	0.270379i	0.920195	+	0.391461i	$0.128030\pi$
$278$		−	23.8564i		−	1.43081i
$279$			10.1962i			0.610428i
$280$	−2.19615	−	6.33975i	−0.131245	−	0.378872i
$281$			0.928203i			0.0553720i	0.999617	+	0.0276860i	$0.00881385\pi$
$281$			0.928203i			0.0553720i	−0.999617	+	0.0276860i	$0.991186\pi$
$282$	−3.12436			−0.186053
$283$	−3.89230	+	14.5263i	−0.231374	+	0.863498i	0.748377	+	0.663274i	$0.230834\pi$
$283$	−3.89230	+	14.5263i	−0.231374	+	0.863498i	−0.979750	+	0.200224i	$0.935833\pi$
$284$	1.07180			0.0635994
$285$	−0.356406	−	1.33013i	−0.0211117	−	0.0787899i
$286$	−5.73205	+	21.3923i	−0.338943	+	1.26495i
$287$	9.85641	+	8.53590i	0.581805	+	0.503858i
$288$	4.00000	+	14.9282i	0.235702	+	0.879653i
$289$	−12.3923	+	21.4641i	−0.728959	+	1.26259i
$290$	0.464102	−	0.124356i	0.0272530	−	0.00730242i
$291$	−1.46410	−	0.392305i	−0.0858272	−	0.0229973i
$292$	7.19615	+	12.4641i	0.421123	+	0.729406i
$293$	−7.92820	−	7.92820i	−0.463171	−	0.463171i	0.436523	−	0.899693i	$-0.356210\pi$
$293$	−7.92820	−	7.92820i	−0.463171	−	0.463171i	−0.899693	+	0.436523i	$0.856210\pi$
$294$	4.02628	−	3.16987i	0.234817	−	0.184871i
$295$		−	10.5167i		−	0.612304i
$296$	1.66025	−	2.87564i	0.0965003	−	0.167143i
$297$	7.62436	−	4.40192i	0.442410	−	0.255426i
$298$	−9.63397	−	5.56218i	−0.558081	−	0.322208i
$299$	22.7583	−	6.09808i	1.31615	−	0.352661i
$300$	−1.12436	−	4.19615i	−0.0649147	−	0.242265i
$301$	24.1244	−	1.73205i	1.39050	−	0.0998337i
$302$	15.5622	+	4.16987i	0.895503	+	0.239949i
$303$	5.06218	−	8.76795i	0.290815	−	0.503706i
$304$	−3.07180	−	11.4641i	−0.176180	−	0.657511i
$305$	−3.23205	−	5.59808i	−0.185067	−	0.320545i
$306$	−17.6603	+	17.6603i	−1.00957	+	1.00957i
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	−0.401988	−	0.915645i	$-0.631681\pi$
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	0.915645	+	0.401988i	$0.131681\pi$
$308$	−13.0000	+	8.80385i	−0.740744	+	0.501646i
$309$	−2.36603	−	2.36603i	−0.134598	−	0.134598i
$310$			4.73205i			0.268762i
$311$	5.59808	−	3.23205i	0.317438	−	0.183273i	−0.332812	−	0.942993i	$-0.607998\pi$
$311$	5.59808	−	3.23205i	0.317438	−	0.183273i	0.650250	+	0.759720i	$0.274664\pi$
$312$	−2.00000	+	7.46410i	−0.113228	+	0.422572i
$313$	−18.6962	−	10.7942i	−1.05677	−	0.610126i	−0.132232	−	0.991219i	$-0.542214\pi$
$313$	−18.6962	−	10.7942i	−1.05677	−	0.610126i	−0.924537	+	0.381093i	$0.875548\pi$
$314$	−13.3660	−	23.1506i	−0.754288	−	1.30647i
$315$	5.36603	−	3.63397i	0.302341	−	0.204751i
$316$	28.8564	+	16.6603i	1.62330	+	0.937213i
$317$	−3.79423	−	14.1603i	−0.213105	−	0.795319i	−0.986825	−	0.161791i	$-0.948273\pi$
$317$	−3.79423	−	14.1603i	−0.213105	−	0.795319i	0.773720	−	0.633528i	$-0.218394\pi$
$318$	−2.90192	+	0.777568i	−0.162732	+	0.0436039i
$319$	−0.562178	−	0.973721i	−0.0314759	−	0.0545179i
$320$	1.85641	+	6.92820i	0.103776	+	0.387298i
$321$	1.73205			0.0966736
$322$	15.0263	+	7.29423i	0.837382	+	0.406491i
$323$	13.5622	−	13.5622i	0.754620	−	0.754620i
$324$	−11.5359	+	6.66025i	−0.640883	+	0.370014i
$325$	−5.73205	+	21.3923i	−0.317957	+	1.18663i
$326$	−8.83013	+	15.2942i	−0.489056	+	0.847069i
$327$	−0.990381	−	0.571797i	−0.0547682	−	0.0316204i
$328$	−9.85641	−	9.85641i	−0.544229	−	0.544229i
$329$	3.69615	+	10.6699i	0.203775	+	0.588249i
$330$	1.68653	−	0.973721i	0.0928406	−	0.0536016i
$331$	−19.6244	+	5.25833i	−1.07865	+	0.289024i	−0.754044	−	0.656824i	$-0.771899\pi$
$331$	−19.6244	+	5.25833i	−1.07865	+	0.289024i	−0.324609	+	0.945848i	$0.605233\pi$
$332$	3.07180	+	3.07180i	0.168587	+	0.168587i
$333$	3.09808	+	0.830127i	0.169774	+	0.0454907i
$334$	−21.8564	+	21.8564i	−1.19593	+	1.19593i
$335$	4.60770			0.251745
$336$	−4.53590	+	3.07180i	−0.247454	+	0.167580i
$337$	−6.14359			−0.334663			−0.167331	−	0.985901i	$-0.553515\pi$
$337$	−6.14359			−0.334663			−0.167331	+	0.985901i	$0.553515\pi$
$338$	14.8564	−	14.8564i	0.808082	−	0.808082i
$339$	−0.732051	−	0.196152i	−0.0397595	−	0.0106535i
$340$	−8.19615	+	8.19615i	−0.444499	+	0.444499i
$341$	10.6962	−	2.86603i	0.579229	−	0.155204i
$342$	9.92820	−	5.73205i	0.536856	−	0.309954i
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	−25.8564			−1.39408
$345$	−1.79423	−	1.03590i	−0.0965980	−	0.0557709i
$346$	−1.63397	+	2.83013i	−0.0878430	+	0.152149i
$347$	−6.30385	+	23.5263i	−0.338408	+	1.26296i	0.561718	+	0.827329i	$0.310140\pi$
$347$	−6.30385	+	23.5263i	−0.338408	+	1.26296i	−0.900127	+	0.435628i	$0.856526\pi$
$348$	−0.196152	−	0.339746i	−0.0105149	−	0.0182123i
$349$	6.12436	−	6.12436i	0.327829	−	0.327829i	−0.523931	−	0.851761i	$-0.675535\pi$
$349$	6.12436	−	6.12436i	0.327829	−	0.327829i	0.851761	+	0.523931i	$0.175535\pi$
$350$	−13.0000	+	8.80385i	−0.694879	+	0.470585i
$351$	−15.6603			−0.835883
$352$	14.5359	−	8.39230i	0.774766	−	0.447311i
$353$	13.8923	+	24.0622i	0.739413	+	1.28070i	0.952760	+	0.303724i	$0.0982301\pi$
$353$	13.8923	+	24.0622i	0.739413	+	1.28070i	−0.213347	+	0.976976i	$0.568437\pi$
$354$	−8.29423	+	2.22243i	−0.440833	+	0.118121i
$355$	0.124356	+	0.464102i	0.00660011	+	0.0246320i
$356$	5.19615	−	9.00000i	0.275396	−	0.476999i
$357$	−7.96410	−	3.86603i	−0.421505	−	0.204612i
$358$	6.56218	+	11.3660i	0.346822	+	0.600713i
$359$	−3.86603	−	2.23205i	−0.204041	−	0.117803i	0.394498	−	0.918897i	$-0.370919\pi$
$359$	−3.86603	−	2.23205i	−0.204041	−	0.117803i	−0.598539	+	0.801094i	$0.704252\pi$
$360$	−6.00000	+	3.46410i	−0.316228	+	0.182574i
$361$	8.83013	−	5.09808i	0.464744	−	0.268320i
$362$			26.7846i			1.40777i
$363$	0.803848	+	0.803848i	0.0421911	+	0.0421911i
$364$	27.8564	−	2.00000i	1.46007	−	0.104828i
$365$	−4.56218	+	4.56218i	−0.238795	+	0.238795i
$366$	−3.73205	+	3.73205i	−0.195077	+	0.195077i
$367$	−3.06218	−	5.30385i	−0.159844	−	0.276859i	0.774968	−	0.632000i	$-0.217766\pi$
$367$	−3.06218	−	5.30385i	−0.159844	−	0.276859i	−0.934812	+	0.355142i	$0.884433\pi$
$368$	−15.4641	−	8.92820i	−0.806122	−	0.465415i
$369$	6.73205	−	11.6603i	0.350457	−	0.607009i
$370$	1.43782	+	0.385263i	0.0747488	+	0.0200289i
$371$	6.08846	+	8.99038i	0.316097	+	0.466757i
$372$	3.73205	−	1.00000i	0.193498	−	0.0518476i
$373$	0.866025	−	0.232051i	0.0448411	−	0.0120151i	−0.236329	−	0.971673i	$-0.575944\pi$
$373$	0.866025	−	0.232051i	0.0448411	−	0.0120151i	0.281170	+	0.959658i	$0.409278\pi$
$374$	23.4904	+	13.5622i	1.21466	+	0.701284i
$375$	3.69615	−	2.13397i	0.190868	−	0.110198i
$376$	−3.12436	−	11.6603i	−0.161126	−	0.601332i
$377$			2.00000i			0.103005i
$378$	−8.39230	−	7.26795i	−0.431654	−	0.373823i
$379$	0.124356	+	0.124356i	0.00638772	+	0.00638772i	0.710293	−	0.703906i	$-0.248562\pi$
$379$	0.124356	+	0.124356i	0.00638772	+	0.00638772i	−0.703906	+	0.710293i	$0.748562\pi$
$380$	4.60770	−	2.66025i	0.236370	−	0.136468i
$381$	4.73205	+	1.26795i	0.242430	+	0.0649590i
$382$	−11.8301	+	3.16987i	−0.605282	+	0.162185i
$383$	12.5981	−	21.8205i	0.643732	−	1.11498i	−0.340861	−	0.940114i	$-0.610719\pi$
$383$	12.5981	−	21.8205i	0.643732	−	1.11498i	0.984593	−	0.174862i	$-0.0559480\pi$
$384$	5.07180	−	2.92820i	0.258819	−	0.149429i
$385$	−5.32051	−	4.60770i	−0.271158	−	0.234830i
$386$	−8.41858	+	31.4186i	−0.428495	+	1.59916i
$387$	−6.46410	−	24.1244i	−0.328589	−	1.22631i
$388$		−	5.85641i		−	0.297314i
$389$	5.99038	−	22.3564i	0.303724	−	1.13351i	−0.630313	−	0.776341i	$-0.717074\pi$
$389$	5.99038	−	22.3564i	0.303724	−	1.13351i	0.934038	−	0.357174i	$-0.116260\pi$
$390$	−3.46410			−0.175412
$391$		−	28.8564i		−	1.45933i
$392$	15.8564	+	11.8564i	0.800869	+	0.598839i
$393$		−	4.07180i		−	0.205395i
$394$		−	33.3205i		−	1.67866i
$395$	−3.86603	+	14.4282i	−0.194521	+	0.725962i
$396$	11.4641	+	11.4641i	0.576093	+	0.576093i
$397$	6.86603	+	25.6244i	0.344596	+	1.28605i	0.893084	+	0.449891i	$0.148537\pi$
$397$	6.86603	+	25.6244i	0.344596	+	1.28605i	−0.548488	+	0.836159i	$0.684796\pi$
$398$	−16.2942	−	4.36603i	−0.816756	−	0.218849i
$399$	3.07180	+	2.66025i	0.153782	+	0.133179i
$400$	14.5359	−	8.39230i	0.726795	−	0.419615i
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	−0.973721	−	3.63397i	−0.0485648	−	0.181246i
$403$	−19.0263	−	5.09808i	−0.947766	−	0.253953i
$404$	37.7846	+	10.1244i	1.87985	+	0.503706i
$405$	−4.22243	−	4.22243i	−0.209814	−	0.209814i
$406$	−0.928203	+	1.07180i	−0.0460660	+	0.0531924i
$407$		−	3.48334i		−	0.172663i
$408$	8.19615	+	4.73205i	0.405770	+	0.234271i
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	−0.673830	−	0.738886i	$-0.735352\pi$
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	0.302979	+	0.952997i	$0.402019\pi$
$410$	3.12436	−	5.41154i	0.154301	−	0.267257i
$411$	8.79423	−	2.35641i	0.433787	−	0.116233i
$412$	6.46410	−	11.1962i	0.318463	−	0.551595i
$413$	17.4019	+	25.6962i	0.856293	+	1.26442i
$414$	4.46410	−	16.6603i	0.219399	−	0.818807i
$415$	−0.973721	+	1.68653i	−0.0477981	+	0.0827887i
$416$	−29.8564			−1.46383
$417$	−4.36603	−	7.56218i	−0.213805	−	0.370321i
$418$	−8.80385	−	8.80385i	−0.430610	−	0.430610i
$419$	−19.0000	+	19.0000i	−0.928211	+	0.928211i	−0.997590	−	0.0693796i	$-0.977898\pi$
$419$	−19.0000	+	19.0000i	−0.928211	+	0.928211i	0.0693796	+	0.997590i	$0.477898\pi$
$420$	−1.85641	−	1.60770i	−0.0905834	−	0.0784475i
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	0.885918	−	0.463843i	$-0.153530\pi$
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	−0.463843	+	0.885918i	$0.653530\pi$
$422$	−31.8564			−1.55075
$423$	10.0981	−	5.83013i	0.490985	−	0.283470i
$424$	−5.80385	−	10.0526i	−0.281860	−	0.488195i
$425$	23.4904	+	13.5622i	1.13945	+	0.657862i
$426$	0.339746	−	0.196152i	0.0164607	−	0.00950362i
$427$	17.1603	+	8.33013i	0.830443	+	0.403123i
$428$	1.73205	+	6.46410i	0.0837218	+	0.312454i
$429$	2.09808	+	7.83013i	0.101296	+	0.378042i
$430$	−3.00000	−	11.1962i	−0.144673	−	0.539926i
$431$	−15.3301	−	26.5526i	−0.738426	−	1.27899i	−0.953204	−	0.302329i	$-0.902236\pi$
$431$	−15.3301	−	26.5526i	−0.738426	−	1.27899i	0.214777	−	0.976663i	$-0.431097\pi$
$432$	8.39230	+	8.39230i	0.403775	+	0.403775i
$433$	−33.1769			−1.59438			−0.797190	−	0.603728i	$-0.793681\pi$
$433$	−33.1769			−1.59438			−0.797190	+	0.603728i	$0.793681\pi$
$434$	−7.83013	−	11.5622i	−0.375858	−	0.555002i
$435$	0.124356	−	0.124356i	0.00596240	−	0.00596240i
$436$	1.14359	−	4.26795i	0.0547682	−	0.204398i
$437$	−3.42820	+	12.7942i	−0.163993	+	0.612031i
$438$	4.56218	+	2.63397i	0.217989	+	0.125856i
$439$	6.52628	+	3.76795i	0.311482	+	0.179834i	0.647590	−	0.761989i	$-0.275777\pi$
$439$	6.52628	+	3.76795i	0.311482	+	0.179834i	−0.336107	+	0.941824i	$0.609110\pi$
$440$	5.32051	+	5.32051i	0.253645	+	0.253645i
$441$	−7.09808	+	17.7583i	−0.338004	+	0.845635i
$442$	−24.1244	−	41.7846i	−1.14748	−	1.98749i
$443$	−10.4282	+	2.79423i	−0.495459	+	0.132758i	−0.497892	−	0.867239i	$-0.665892\pi$
$443$	−10.4282	+	2.79423i	−0.495459	+	0.132758i	0.00243278	+	0.999997i	$0.499226\pi$
$444$		−	1.21539i		−	0.0576799i
$445$	4.50000	+	1.20577i	0.213320	+	0.0571590i
$446$	9.85641	+	9.85641i	0.466714	+	0.466714i
$447$	−4.07180			−0.192589
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	−23.3205			−1.10056			−0.550281	−	0.834979i	$-0.685480\pi$
$449$	−23.3205			−1.10056			−0.550281	+	0.834979i	$0.685480\pi$
$450$	11.4641	+	11.4641i	0.540423	+	0.540423i
$451$	−14.1244	−	3.78461i	−0.665090	−	0.178210i
$452$		−	2.92820i		−	0.137731i
$453$	5.69615	−	1.52628i	0.267629	−	0.0717109i
$454$	8.16987	+	14.1506i	0.383431	+	0.664122i
$455$	4.09808	+	11.8301i	0.192121	+	0.554605i
$456$	−3.07180	−	3.07180i	−0.143850	−	0.143850i
$457$	16.2846	+	9.40192i	0.761762	+	0.439803i	0.829928	−	0.557871i	$-0.188381\pi$
$457$	16.2846	+	9.40192i	0.761762	+	0.439803i	−0.0681661	+	0.997674i	$0.521715\pi$
$458$	16.9019	+	9.75833i	0.789775	+	0.455977i
$459$	−4.96410	+	18.5263i	−0.231704	+	0.864733i
$460$	2.07180	−	7.73205i	0.0965980	−	0.360509i
$461$	18.6603	−	18.6603i	0.869095	−	0.869095i	−0.123278	−	0.992372i	$-0.539341\pi$
$461$	18.6603	−	18.6603i	0.869095	−	0.869095i	0.992372	+	0.123278i	$0.0393405\pi$
$462$	−2.50962	+	5.16987i	−0.116758	+	0.240524i
$463$	2.14359			0.0996212			0.0498106	−	0.998759i	$-0.484138\pi$
$463$	2.14359			0.0996212			0.0498106	+	0.998759i	$0.484138\pi$
$464$	1.07180	−	1.07180i	0.0497569	−	0.0497569i
$465$	0.866025	+	1.50000i	0.0401610	+	0.0695608i
$466$	0.294229	+	1.09808i	0.0136299	+	0.0508674i
$467$	−6.96410	−	25.9904i	−0.322260	−	1.20269i	−0.917038	−	0.398801i	$-0.869426\pi$
$467$	−6.96410	−	25.9904i	−0.322260	−	1.20269i	0.594777	−	0.803890i	$-0.297240\pi$
$468$	−7.46410	−	27.8564i	−0.345028	−	1.28766i
$469$	−11.2583	+	7.62436i	−0.519861	+	0.352060i
$470$	4.68653	−	2.70577i	0.216174	−	0.124808i
$471$	−8.47372	−	4.89230i	−0.390448	−	0.225426i
$472$	−16.5885	−	28.7321i	−0.763546	−	1.32250i
$473$	−23.4904	+	13.5622i	−1.08009	+	0.623590i
$474$	12.1962			0.560188
$475$	−8.80385	−	8.80385i	−0.403948	−	0.403948i
$476$	6.46410	−	33.5885i	0.296282	−	1.53952i
$477$	7.92820	−	7.92820i	0.363007	−	0.363007i
$478$	−8.53590	−	8.53590i	−0.390423	−	0.390423i
$479$	−7.79423	−	13.5000i	−0.356127	−	0.616831i	0.631183	−	0.775634i	$-0.282570\pi$
$479$	−7.79423	−	13.5000i	−0.356127	−	0.616831i	−0.987310	+	0.158803i	$0.949236\pi$
$480$	1.85641	+	1.85641i	0.0847330	+	0.0847330i
$481$	−3.09808	+	5.36603i	−0.141260	+	0.244670i
$482$	5.09808	−	19.0263i	0.232211	−	0.866623i
$483$	6.09808	−	0.437822i	0.277472	−	0.0199216i
$484$	−2.19615	+	3.80385i	−0.0998251	+	0.172902i
$485$	2.53590	−	0.679492i	0.115149	−	0.0308541i
$486$	−8.73205	+	15.1244i	−0.396094	+	0.686055i
$487$	10.6699	−	6.16025i	0.483498	−	0.279148i	−0.238375	−	0.971173i	$-0.576615\pi$
$487$	10.6699	−	6.16025i	0.483498	−	0.279148i	0.721873	+	0.692025i	$0.243281\pi$
$488$	−17.6603	−	10.1962i	−0.799442	−	0.461558i
$489$			6.46410i			0.292317i
$490$	−3.29423	+	8.24167i	−0.148818	+	0.372321i
$491$	−3.58846	−	3.58846i	−0.161945	−	0.161945i	0.621483	−	0.783428i	$-0.286531\pi$
$491$	−3.58846	−	3.58846i	−0.161945	−	0.161945i	−0.783428	+	0.621483i	$0.786531\pi$
$492$	−4.92820	−	1.32051i	−0.222181	−	0.0595331i
$493$	2.36603	+	0.633975i	0.106560	+	0.0285528i
$494$	5.73205	+	21.3923i	0.257897	+	0.962485i
$495$	−3.63397	+	6.29423i	−0.163335	+	0.282905i
$496$	7.46410	+	12.9282i	0.335148	+	0.580493i
$497$	−1.07180	−	0.928203i	−0.0480767	−	0.0416356i
$498$	1.53590	+	0.411543i	0.0688253	+	0.0184417i
$499$	6.69615	+	24.9904i	0.299761	+	1.11872i	0.937362	+	0.348356i	$0.113260\pi$
$499$	6.69615	+	24.9904i	0.299761	+	1.11872i	−0.637601	+	0.770367i	$0.720073\pi$
$500$	11.6603	+	11.6603i	0.521462	+	0.521462i
$501$	−2.92820	+	10.9282i	−0.130822	+	0.488236i
$502$		−	35.1769i		−	1.57002i
$503$			31.8564i			1.42041i	0.703996	+	0.710203i	$0.251397\pi$
$503$			31.8564i			1.42041i	−0.703996	+	0.710203i	$0.748603\pi$
$504$	8.92820	−	18.3923i	0.397694	−	0.819258i
$505$			17.5359i			0.780337i
$506$	−18.7321			−0.832741
$507$	1.99038	−	7.42820i	0.0883959	−	0.329898i
$508$			18.9282i			0.839803i
$509$	2.52628	+	9.42820i	0.111975	+	0.417898i	0.999043	−	0.0437420i	$-0.0139280\pi$
$509$	2.52628	+	9.42820i	0.111975	+	0.417898i	−0.887067	+	0.461640i	$0.847261\pi$
$510$	−1.09808	+	4.09808i	−0.0486236	+	0.181466i
$511$	3.59808	−	18.6962i	0.159170	−	0.827069i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	4.40192	−	7.62436i	0.194350	−	0.336624i
$514$	26.4904	−	7.09808i	1.16844	−	0.313083i
$515$	5.59808	+	1.50000i	0.246681	+	0.0660979i
$516$	−8.19615	+	4.73205i	−0.360815	+	0.208317i
$517$	−8.95448	−	8.95448i	−0.393818	−	0.393818i
$518$	−4.15064	+	1.43782i	−0.182368	+	0.0631743i
$519$			1.19615i			0.0525053i
$520$	−3.46410	−	12.9282i	−0.151911	−	0.566939i
$521$	−13.3756	+	7.72243i	−0.585998	+	0.338326i	−0.763513	−	0.645792i	$-0.776527\pi$
$521$	−13.3756	+	7.72243i	−0.585998	+	0.338326i	0.177516	+	0.984118i	$0.443194\pi$
$522$	1.26795	+	0.732051i	0.0554966	+	0.0320410i
$523$	−32.2846	+	8.65064i	−1.41171	+	0.378266i	−0.882534	−	0.470248i	$-0.844164\pi$
$523$	−32.2846	+	8.65064i	−1.41171	+	0.378266i	−0.529173	+	0.848514i	$0.677498\pi$
$524$	15.1962	−	4.07180i	0.663847	−	0.177877i
$525$	−2.50962	+	5.16987i	−0.109529	+	0.225632i
$526$	6.29423	+	1.68653i	0.274441	+	0.0735364i
$527$	−12.0622	+	20.8923i	−0.525437	+	0.910083i
$528$	3.07180	−	5.32051i	0.133683	−	0.231545i
$529$	−1.53590	−	2.66025i	−0.0667782	−	0.115663i
$530$	3.67949	−	3.67949i	0.159827	−	0.159827i
$531$	22.6603	−	22.6603i	0.983371	−	0.983371i
$532$	−6.85641	+	14.1244i	−0.297263	+	0.612368i
$533$	18.3923	+	18.3923i	0.796659	+	0.796659i
$534$		−	3.80385i		−	0.164609i
$535$	−2.59808	+	1.50000i	−0.112325	+	0.0648507i
$536$	12.5885	−	7.26795i	0.543739	−	0.313928i
$537$	4.16025	+	2.40192i	0.179528	+	0.103651i
$538$	7.16987	+	12.4186i	0.309115	+	0.535403i
$539$	20.6244	+	2.45448i	0.888354	+	0.105722i
$540$	−2.66025	+	4.60770i	−0.114479	+	0.198284i
$541$	2.47372	+	9.23205i	0.106354	+	0.396917i	0.998495	−	0.0548389i	$-0.0174645\pi$
$541$	2.47372	+	9.23205i	0.106354	+	0.396917i	−0.892142	+	0.451756i	$0.850798\pi$
$542$	−16.5622	+	4.43782i	−0.711406	+	0.190621i
$543$	4.90192	+	8.49038i	0.210362	+	0.364357i
$544$	−9.46410	+	35.3205i	−0.405770	+	1.51435i
$545$	1.98076			0.0848465
$546$	8.46410	−	5.73205i	0.362230	−	0.245309i
$547$	−23.0526	+	23.0526i	−0.985656	+	0.985656i	−0.999899	−	0.0142423i	$-0.995466\pi$
$547$	−23.0526	+	23.0526i	−0.985656	+	0.985656i	0.0142423	+	0.999899i	$0.495466\pi$
$548$	17.5885	+	30.4641i	0.751342	+	1.30136i
$549$	5.09808	−	19.0263i	0.217581	−	0.812022i
$550$	8.80385	−	15.2487i	0.375397	−	0.650207i
$551$	−0.973721	−	0.562178i	−0.0414819	−	0.0239496i
$552$	−6.53590			−0.278186
$553$	−14.4282	−	41.6506i	−0.613550	−	1.77117i
$554$	−5.70577	+	3.29423i	−0.242415	+	0.139958i
$555$	0.526279	−	0.141016i	0.0223393	−	0.00598580i
$556$	23.8564	−	23.8564i	1.01174	−	1.01174i
$557$	6.59808	+	1.76795i	0.279569	+	0.0749104i	0.395879	−	0.918303i	$-0.370440\pi$
$557$	6.59808	+	1.76795i	0.279569	+	0.0749104i	−0.116310	+	0.993213i	$0.537107\pi$
$558$	−10.1962	+	10.1962i	−0.431638	+	0.431638i
$559$	48.2487			2.04070
$560$	4.14359	−	8.53590i	0.175099	−	0.360708i
$561$	9.92820			0.419169
$562$	−0.928203	+	0.928203i	−0.0391539	+	0.0391539i
$563$	−2.42820	−	0.650635i	−0.102337	−	0.0274210i	0.207287	−	0.978280i	$-0.433536\pi$
$563$	−2.42820	−	0.650635i	−0.102337	−	0.0274210i	−0.309624	+	0.950859i	$0.600203\pi$
$564$	−3.12436	−	3.12436i	−0.131559	−	0.131559i
$565$	1.26795	−	0.339746i	0.0533430	−	0.0142932i
$566$	−18.4186	+	10.6340i	−0.774191	+	0.446979i
$567$	17.3038	+	3.33013i	0.726693	+	0.139852i
$568$	1.07180	+	1.07180i	0.0449716	+	0.0449716i
$569$	−5.08846	−	2.93782i	−0.213319	−	0.123160i	0.389534	−	0.921012i	$-0.372636\pi$
$569$	−5.08846	−	2.93782i	−0.213319	−	0.123160i	−0.602853	+	0.797852i	$0.705969\pi$
$570$	0.973721	−	1.68653i	0.0407847	−	0.0706411i
$571$	−7.16025	+	26.7224i	−0.299647	+	1.11830i	0.637809	+	0.770195i	$0.279841\pi$
$571$	−7.16025	+	26.7224i	−0.299647	+	1.11830i	−0.937456	+	0.348104i	$0.886826\pi$
$572$	−27.1244	+	15.6603i	−1.13413	+	0.654788i
$573$	−3.16987	+	3.16987i	−0.132423	+	0.132423i
$574$	1.32051	+	18.3923i	0.0551169	+	0.767680i
$575$	−18.7321			−0.781181
$576$	−10.9282	+	18.9282i	−0.455342	+	0.788675i
$577$	−6.62436	−	11.4737i	−0.275776	−	0.477657i	0.694555	−	0.719440i	$-0.255601\pi$
$577$	−6.62436	−	11.4737i	−0.275776	−	0.477657i	−0.970330	+	0.241782i	$0.922268\pi$
$578$	−33.8564	+	9.07180i	−1.40824	+	0.377337i
$579$	3.08142	+	11.5000i	0.128059	+	0.477924i
$580$	0.588457	+	0.339746i	0.0244344	+	0.0141072i
$581$	−0.411543	−	5.73205i	−0.0170737	−	0.237806i
$582$	−1.07180	−	1.85641i	−0.0444274	−	0.0769505i
$583$	−10.5455	−	6.08846i	−0.436751	−	0.252158i
$584$	−5.26795	+	19.6603i	−0.217989	+	0.813547i
$585$	11.1962	−	6.46410i	0.462904	−	0.267258i
$586$		−	15.8564i		−	0.655022i
$587$	21.9282	+	21.9282i	0.905074	+	0.905074i	0.995870	−	0.0907957i	$-0.0289410\pi$
$587$	21.9282	+	21.9282i	0.905074	+	0.905074i	−0.0907957	+	0.995870i	$0.528941\pi$
$588$	7.19615	+	0.856406i	0.296764	+	0.0353176i
$589$	7.83013	−	7.83013i	0.322635	−	0.322635i
$590$	10.5167	−	10.5167i	0.432964	−	0.432964i
$591$	−6.09808	−	10.5622i	−0.250841	−	0.434470i
$592$	4.53590	−	1.21539i	0.186424	−	0.0499522i
$593$	5.69615	−	9.86603i	0.233913	−	0.405149i	−0.725043	−	0.688703i	$-0.758180\pi$
$593$	5.69615	−	9.86603i	0.233913	−	0.405149i	0.958956	+	0.283554i	$0.0915136\pi$
$594$	12.0263	+	3.22243i	0.493444	+	0.132218i
$595$	15.2942	−	1.09808i	0.627002	−	0.0450167i
$596$	−4.07180	−	15.1962i	−0.166787	−	0.622459i
$597$	−5.96410	+	1.59808i	−0.244094	+	0.0654049i
$598$	28.8564	+	16.6603i	1.18003	+	0.681288i
$599$	16.6699	−	9.62436i	0.681113	−	0.393241i	−0.119162	−	0.992875i	$-0.538021\pi$
$599$	16.6699	−	9.62436i	0.681113	−	0.393241i	0.800274	+	0.599634i	$0.204687\pi$
$600$	3.07180	−	5.32051i	0.125406	−	0.217209i
$601$		−	10.0000i		−	0.407909i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$		−	10.0000i		−	0.407909i	0.978980	−	0.203954i	$-0.0653794\pi$
$602$	25.8564	+	22.3923i	1.05383	+	0.912642i
$603$	9.92820	+	9.92820i	0.404308	+	0.404308i
$604$	11.3923	+	19.7321i	0.463546	+	0.802886i
$605$	−1.90192	−	0.509619i	−0.0773242	−	0.0207190i
$606$	13.8301	−	3.70577i	0.561811	−	0.150537i
$607$	−8.52628	+	14.7679i	−0.346071	+	0.599413i	−0.985548	−	0.169398i	$-0.945818\pi$
$607$	−8.52628	+	14.7679i	−0.346071	+	0.599413i	0.639477	+	0.768810i	$0.279151\pi$
$608$	8.39230	−	14.5359i	0.340353	−	0.589509i
$609$	−0.0980762	+	0.509619i	−0.00397425	+	0.0206508i
$610$	2.36603	−	8.83013i	0.0957976	−	0.357521i
$611$	5.83013	+	21.7583i	0.235862	+	0.880248i
$612$	−35.3205			−1.42775
$613$	2.47372	−	9.23205i	0.0999126	−	0.372879i	−0.897806	−	0.440392i	$-0.854840\pi$
$613$	2.47372	−	9.23205i	0.0999126	−	0.372879i	0.997718	+	0.0675126i	$0.0215063\pi$
$614$	18.0000			0.726421
$615$		−	2.28719i		−	0.0922283i
$616$	−21.8038	−	4.19615i	−0.878502	−	0.169068i
$617$		−	0.535898i		−	0.0215745i	−0.999942	−	0.0107872i	$-0.996566\pi$
$617$		−	0.535898i		−	0.0215745i	0.999942	−	0.0107872i	$-0.00343375\pi$
$618$		−	4.73205i		−	0.190351i
$619$	5.10770	−	19.0622i	0.205296	−	0.766174i	−0.784064	−	0.620680i	$-0.786856\pi$
$619$	5.10770	−	19.0622i	0.205296	−	0.766174i	0.989359	−	0.145493i	$-0.0464769\pi$
$620$	−4.73205	+	4.73205i	−0.190044	+	0.190044i
$621$	−3.42820	−	12.7942i	−0.137569	−	0.513415i
$622$	8.83013	+	2.36603i	0.354056	+	0.0948690i
$623$	−12.9904	+	4.50000i	−0.520449	+	0.180289i
$624$	−9.46410	+	5.46410i	−0.378867	+	0.218739i
$625$	6.79423	−	11.7679i	0.271769	−	0.470718i
$626$	−7.90192	−	29.4904i	−0.315824	−	1.17867i
$627$	−4.40192	−	1.17949i	−0.175796	−	0.0471044i
$628$	9.78461	−	36.5167i	0.390448	−	1.45717i
$629$	5.36603	+	5.36603i	0.213957	+	0.213957i
$630$	9.00000	+	1.73205i	0.358569	+	0.0690066i
$631$		−	32.2487i		−	1.28380i	−0.766788	−	0.641900i	$-0.778146\pi$
$631$		−	32.2487i		−	1.28380i	0.766788	−	0.641900i	$-0.221854\pi$
$632$	12.1962	+	45.5167i	0.485137	+	1.81056i
$633$	−10.0981	+	5.83013i	−0.401362	+	0.231727i
$634$	10.3660	−	17.9545i	0.411687	−	0.713064i
$635$	−8.19615	+	2.19615i	−0.325254	+	0.0871517i
$636$	−3.67949	−	2.12436i	−0.145901	−	0.0842362i
$637$	−29.5885	−	22.1244i	−1.17234	−	0.876599i
$638$	0.411543	−	1.53590i	0.0162931	−	0.0608068i
$639$	−0.732051	+	1.26795i	−0.0289595	+	0.0501593i
$640$	−5.07180	+	8.78461i	−0.200480	+	0.347242i
$641$	5.57180	+	9.65064i	0.220073	+	0.381177i	0.954830	−	0.297153i	$-0.0960372\pi$
$641$	5.57180	+	9.65064i	0.220073	+	0.381177i	−0.734757	+	0.678330i	$0.762704\pi$
$642$	1.73205	+	1.73205i	0.0683586	+	0.0683586i
$643$	−5.39230	+	5.39230i	−0.212652	+	0.212652i	−0.805393	−	0.592741i	$-0.798046\pi$
$643$	−5.39230	+	5.39230i	−0.212652	+	0.212652i	0.592741	+	0.805393i	$0.298046\pi$
$644$	7.73205	+	22.3205i	0.304685	+	0.879551i
$645$	−3.00000	−	3.00000i	−0.118125	−	0.118125i
$646$	27.1244			1.06719
$647$	30.8660	−	17.8205i	1.21347	−	0.700596i	0.249955	−	0.968257i	$-0.419584\pi$
$647$	30.8660	−	17.8205i	1.21347	−	0.700596i	0.963513	+	0.267661i	$0.0862507\pi$
$648$	−18.1962	−	4.87564i	−0.714812	−	0.191533i
$649$	−30.1410	−	17.4019i	−1.18314	−	0.683085i
$650$	−27.1244	+	15.6603i	−1.06390	+	0.614246i
$651$	−4.59808	−	2.23205i	−0.180213	−	0.0874810i
$652$	−24.1244	+	6.46410i	−0.944783	+	0.253154i
$653$	−8.72243	−	32.5526i	−0.341335	−	1.27388i	−0.896836	−	0.442364i	$-0.854140\pi$
$653$	−8.72243	−	32.5526i	−0.341335	−	1.27388i	0.555501	−	0.831516i	$-0.312527\pi$
$654$	−0.418584	−	1.56218i	−0.0163679	−	0.0610860i
$655$	3.52628	+	6.10770i	0.137783	+	0.238647i
$656$		−	19.7128i		−	0.769656i
$657$	−19.6603			−0.767020
$658$	−6.97372	+	14.3660i	−0.271864	+	0.560046i
$659$	18.8564	−	18.8564i	0.734541	−	0.734541i	−0.236975	−	0.971516i	$-0.576156\pi$
$659$	18.8564	−	18.8564i	0.734541	−	0.734541i	0.971516	+	0.236975i	$0.0761558\pi$
$660$	2.66025	+	0.712813i	0.103550	+	0.0277462i
$661$	−5.93782	+	22.1603i	−0.230955	+	0.861934i	0.748976	+	0.662597i	$0.230546\pi$
$661$	−5.93782	+	22.1603i	−0.230955	+	0.861934i	−0.979931	+	0.199337i	$0.936121\pi$
$662$	−24.8827	−	14.3660i	−0.967093	−	0.558351i
$663$	−15.2942	−	8.83013i	−0.593979	−	0.342934i
$664$			6.14359i			0.238418i
$665$	−6.91154	−	1.33013i	−0.268018	−	0.0515801i
$666$	2.26795	+	3.92820i	0.0878812	+	0.152215i
$667$	−1.63397	+	0.437822i	−0.0632677	+	0.0169525i
$668$	−43.7128			−1.69130
$669$	4.92820	+	1.32051i	0.190535	+	0.0510538i
$670$	4.60770	+	4.60770i	0.178011	+	0.178011i
$671$	−21.3923			−0.825841
$672$	−7.60770	−	1.46410i	−0.293473	−	0.0564789i
$673$	40.7846			1.57213			0.786066	−	0.618143i	$-0.212115\pi$
$673$	40.7846			1.57213			0.786066	+	0.618143i	$0.212115\pi$
$674$	−6.14359	−	6.14359i	−0.236642	−	0.236642i
$675$	12.0263	+	3.22243i	0.462892	+	0.124031i
$676$	29.7128			1.14280
$677$	−42.7224	+	11.4474i	−1.64196	+	0.439961i	−0.957345	−	0.288947i	$-0.906695\pi$
$677$	−42.7224	+	11.4474i	−1.64196	+	0.439961i	−0.684611	+	0.728908i	$0.740028\pi$
$678$	−0.535898	−	0.928203i	−0.0205811	−	0.0356474i
$679$	−5.07180	+	5.85641i	−0.194638	+	0.224748i
$680$	−16.3923			−0.628616
$681$	5.17949	+	2.99038i	0.198479	+	0.114592i
$682$	13.5622	+	7.83013i	0.519323	+	0.299831i
$683$	12.2128	−	45.5788i	0.467310	−	1.74403i	−0.181804	−	0.983335i	$-0.558194\pi$
$683$	12.2128	−	45.5788i	0.467310	−	1.74403i	0.649114	−	0.760691i	$-0.275140\pi$
$684$	15.6603	+	4.19615i	0.598785	+	0.160444i
$685$	−11.1506	+	11.1506i	−0.426044	+	0.426044i
$686$	−5.58846	−	25.5885i	−0.213368	−	0.976972i
$687$	7.14359			0.272545
$688$	−25.8564	−	25.8564i	−0.985766	−	0.985766i
$689$	10.8301	+	18.7583i	0.412595	+	0.714635i
$690$	−0.758330	−	2.83013i	−0.0288691	−	0.107741i
$691$	6.16025	+	22.9904i	0.234347	+	0.874595i	0.978442	+	0.206521i	$0.0662143\pi$
$691$	6.16025	+	22.9904i	0.234347	+	0.874595i	−0.744095	+	0.668074i	$0.767119\pi$
$692$	−4.46410	+	1.19615i	−0.169700	+	0.0454709i
$693$	−1.53590	−	21.3923i	−0.0583440	−	0.812626i
$694$	−29.8301	+	17.2224i	−1.13234	+	0.653755i
$695$	13.0981	+	7.56218i	0.496838	+	0.286850i
$696$	0.143594	−	0.535898i	0.00544290	−	0.0203132i
$697$	27.5885	−	15.9282i	1.04499	−	0.603324i
$698$	12.2487			0.463621
$699$	0.294229	+	0.294229i	0.0111287	+	0.0111287i
$700$	−21.8038	−	4.19615i	−0.824108	−	0.158600i
$701$	−13.3923	+	13.3923i	−0.505820	+	0.505820i	−0.913241	−	0.407420i	$-0.866428\pi$
$701$	−13.3923	+	13.3923i	−0.505820	+	0.505820i	0.407420	+	0.913241i	$0.366428\pi$
$702$	−15.6603	−	15.6603i	−0.591058	−	0.591058i
$703$	−1.74167	−	3.01666i	−0.0656883	−	0.113776i
$704$	22.9282	+	6.14359i	0.864139	+	0.231545i
$705$	0.990381	−	1.71539i	0.0372999	−	0.0646053i
$706$	−10.1699	+	37.9545i	−0.382748	+	1.42844i
$707$	−29.0167	−	42.8468i	−1.09128	−	1.61142i
$708$	−10.5167	−	6.07180i	−0.395240	−	0.228192i
$709$	45.6506	−	12.2321i	1.71445	−	0.459384i	0.737938	−	0.674868i	$-0.235800\pi$
$709$	45.6506	−	12.2321i	1.71445	−	0.459384i	0.976507	+	0.215484i	$0.0691329\pi$
$710$	−0.339746	+	0.588457i	−0.0127504	+	0.0220844i
$711$	−39.4186	+	22.7583i	−1.47831	+	0.853504i
$712$	14.1962	−	3.80385i	0.532023	−	0.142555i
$713$		−	16.6603i		−	0.623931i
$714$	−4.09808	−	11.8301i	−0.153367	−	0.442731i
$715$	−9.92820	−	9.92820i	−0.371294	−	0.371294i
$716$	−4.80385	+	17.9282i	−0.179528	+	0.670008i
$717$	−4.26795	−	1.14359i	−0.159389	−	0.0427083i
$718$	−1.63397	−	6.09808i	−0.0609794	−	0.227578i
$719$	−0.205771	+	0.356406i	−0.00767398	+	0.0132917i	−0.869837	−	0.493339i	$-0.835776\pi$
$719$	−0.205771	+	0.356406i	−0.00767398	+	0.0132917i	0.862163	+	0.506631i	$0.169109\pi$
$720$	−9.46410	−	2.53590i	−0.352706	−	0.0945074i
$721$	−16.1603	+	5.59808i	−0.601839	+	0.208483i
$722$	13.9282	+	3.73205i	0.518354	+	0.138893i
$723$	−1.86603	−	6.96410i	−0.0693982	−	0.258998i
$724$	−26.7846	+	26.7846i	−0.995442	+	0.995442i
$725$	0.411543	−	1.53590i	0.0152843	−	0.0570418i
$726$			1.60770i			0.0596672i
$727$			41.3205i			1.53249i	0.642547	+	0.766246i	$0.277878\pi$
$727$			41.3205i			1.53249i	−0.642547	+	0.766246i	$0.722122\pi$
$728$	29.8564	+	25.8564i	1.10655	+	0.958302i
$729$		−	13.5885i		−	0.503276i
$730$	−9.12436			−0.337708
$731$	15.2942	−	57.0788i	0.565677	−	2.11114i
$732$	−7.46410			−0.275881
$733$	−8.81347	−	32.8923i	−0.325533	−	1.21490i	−0.913775	−	0.406220i	$-0.866847\pi$
$733$	−8.81347	−	32.8923i	−0.325533	−	1.21490i	0.588242	−	0.808685i	$-0.299820\pi$
$734$	2.24167	−	8.36603i	0.0827415	−	0.308796i
$735$	0.464102	+	3.21539i	0.0171186	+	0.118601i
$736$	−6.53590	−	24.3923i	−0.240916	−	0.899112i
$737$	7.62436	−	13.2058i	0.280847	−	0.486441i
$738$	18.3923	−	4.92820i	0.677030	−	0.181410i
$739$	38.4808	+	10.3109i	1.41554	+	0.379292i	0.883899	−	0.467679i	$-0.154910\pi$
$739$	38.4808	+	10.3109i	1.41554	+	0.379292i	0.531639	+	0.846971i	$0.321576\pi$
$740$	1.05256	+	1.82309i	0.0386928	+	0.0670180i
$741$	5.73205	+	5.73205i	0.210572	+	0.210572i
$742$	−2.90192	+	15.0788i	−0.106533	+	0.553562i
$743$			11.0718i			0.406185i	0.979160	+	0.203092i	$0.0650992\pi$
$743$			11.0718i			0.406185i	−0.979160	+	0.203092i	$0.934901\pi$
$744$	4.73205	+	2.73205i	0.173485	+	0.100162i
$745$	6.10770	−	3.52628i	0.223769	−	0.129193i
$746$	1.09808	+	0.633975i	0.0402034	+	0.0232115i
$747$	−5.73205	+	1.53590i	−0.209725	+	0.0561956i
$748$	9.92820	+	37.0526i	0.363011	+	1.35478i
$749$	3.86603	−	7.96410i	0.141261	−	0.291002i
$750$	5.83013	+	1.56218i	0.212886	+	0.0570427i
$751$	−6.52628	+	11.3038i	−0.238147	+	0.412483i	−0.960183	−	0.279373i	$-0.909873\pi$
$751$	−6.52628	+	11.3038i	−0.238147	+	0.412483i	0.722035	+	0.691856i	$0.243207\pi$
$752$	8.53590	−	14.7846i	0.311272	−	0.539139i
$753$	−6.43782	−	11.1506i	−0.234607	−	0.406352i
$754$	−2.00000	+	2.00000i	−0.0728357	+	0.0728357i
$755$	−7.22243	+	7.22243i	−0.262851	+	0.262851i
$756$	−1.12436	−	15.6603i	−0.0408924	−	0.569558i
$757$	−18.6603	−	18.6603i	−0.678218	−	0.678218i	0.281378	−	0.959597i	$-0.409208\pi$
$757$	−18.6603	−	18.6603i	−0.678218	−	0.678218i	−0.959597	+	0.281378i	$0.909208\pi$
$758$			0.248711i			0.00903360i
$759$	−5.93782	+	3.42820i	−0.215529	+	0.124436i
$760$	7.26795	+	1.94744i	0.263636	+	0.0706411i
$761$	11.7679	+	6.79423i	0.426588	+	0.246291i	0.697892	−	0.716203i	$-0.254122\pi$
$761$	11.7679	+	6.79423i	0.426588	+	0.246291i	−0.271304	+	0.962494i	$0.587455\pi$
$762$	3.46410	+	6.00000i	0.125491	+	0.217357i
$763$	−4.83975	+	3.27757i	−0.175211	+	0.118656i
$764$	−15.0000	−	8.66025i	−0.542681	−	0.313317i
$765$	−4.09808	−	15.2942i	−0.148166	−	0.552964i
$766$	34.4186	−	9.22243i	1.24359	−	0.333220i
$767$	30.9545	+	53.6147i	1.11770	+	1.93592i
$768$	8.00000	+	2.14359i	0.288675	+	0.0773503i
$769$	9.85641			0.355431			0.177716	−	0.984082i	$-0.443129\pi$
$769$	9.85641			0.355431			0.177716	+	0.984082i	$0.443129\pi$
$770$	−0.712813	−	9.92820i	−0.0256880	−	0.357788i
$771$	7.09808	−	7.09808i	0.255631	−	0.255631i
$772$	−39.8372	+	23.0000i	−1.43377	+	0.827788i
$773$	−2.93782	+	10.9641i	−0.105666	+	0.394351i	−0.998420	−	0.0561936i	$-0.982104\pi$
$773$	−2.93782	+	10.9641i	−0.105666	+	0.394351i	0.892754	+	0.450545i	$0.148770\pi$
$774$	17.6603	−	30.5885i	0.634785	−	1.09948i
$775$	13.5622	+	7.83013i	0.487168	+	0.281266i
$776$	5.85641	−	5.85641i	0.210233	−	0.210233i
$777$	−1.05256	+	1.21539i	−0.0377603	+	0.0436019i
$778$	28.3468	−	16.3660i	1.01628	−	0.586750i
$779$	−14.1244	+	3.78461i	−0.506058	+	0.135598i
$780$	−3.46410	−	3.46410i	−0.124035	−	0.124035i
$781$	1.53590	+	0.411543i	0.0549588	+	0.0147262i
$782$	28.8564	−	28.8564i	1.03190	−	1.03190i
$783$	1.12436			0.0401812
$784$	4.00000	+	27.7128i	0.142857	+	0.989743i
$785$	16.9474			0.604880
$786$	4.07180	−	4.07180i	0.145236	−	0.145236i
$787$	−13.1603	−	3.52628i	−0.469112	−	0.125698i	0.0165161	−	0.999864i	$-0.494743\pi$
$787$	−13.1603	−	3.52628i	−0.469112	−	0.125698i	−0.485628	+	0.874165i	$0.661409\pi$
$788$	33.3205	−	33.3205i	1.18699	−	1.18699i
$789$	2.30385	−	0.617314i	0.0820191	−	0.0219770i
$790$	−18.2942	+	10.5622i	−0.650879	+	0.375785i
$791$	−2.53590	+	2.92820i	−0.0901662	+	0.104115i
$792$			22.9282i			0.814718i
$793$	32.9545	+	19.0263i	1.17025	+	0.675643i
$794$	−18.7583	+	32.4904i	−0.665708	+	1.15304i
$795$	0.492958	−	1.83975i	0.0174834	−	0.0652491i
$796$	−11.9282	−	20.6603i	−0.422784	−	0.732283i
$797$	−13.3397	+	13.3397i	−0.472518	+	0.472518i	−0.902729	−	0.430211i	$-0.858439\pi$
$797$	−13.3397	+	13.3397i	−0.472518	+	0.472518i	0.430211	+	0.902729i	$0.358439\pi$
$798$	0.411543	+	5.73205i	0.0145685	+	0.202912i
$799$	27.5885			0.976009
$800$	22.9282	+	6.14359i	0.810634	+	0.217209i
$801$	7.09808	+	12.2942i	0.250798	+	0.434395i
$802$	20.4904	−	5.49038i	0.723541	−	0.193872i
$803$	5.52628	+	20.6244i	0.195018	+	0.727818i
$804$	2.66025	−	4.60770i	0.0938199	−	0.162501i
$805$	−8.76795	+	5.93782i	−0.309030	+	0.209281i
$806$	−13.9282	−	24.1244i	−0.490600	−	0.849744i
$807$	4.54552	+	2.62436i	0.160010	+	0.0923817i
$808$	27.6603	+	47.9090i	0.973084	+	1.68543i
$809$	−29.4282	+	16.9904i	−1.03464	+	0.597350i	−0.918311	−	0.395861i	$-0.870446\pi$
$809$	−29.4282	+	16.9904i	−1.03464	+	0.597350i	−0.116330	+	0.993211i	$0.537113\pi$
$810$		−	8.44486i		−	0.296722i
$811$	24.3205	+	24.3205i	0.854009	+	0.854009i	0.990624	−	0.136616i	$-0.0436225\pi$
$811$	24.3205	+	24.3205i	0.854009	+	0.854009i	−0.136616	+	0.990624i	$0.543623\pi$
$812$	−2.00000	+	0.143594i	−0.0701862	+	0.00503915i
$813$	−4.43782	+	4.43782i	−0.155641	+	0.155641i
$814$	3.48334	−	3.48334i	0.122091	−	0.122091i
$815$	−5.59808	−	9.69615i	−0.196092	−	0.339641i
$816$	3.46410	+	12.9282i	0.121268	+	0.452578i
$817$	−13.5622	+	23.4904i	−0.474481	+	0.821824i
$818$	−11.8301	−	3.16987i	−0.413631	−	0.110832i
$819$	−16.6603	+	34.3205i	−0.582156	+	1.19926i
$820$	8.53590	−	2.28719i	0.298087	−	0.0798720i
$821$	0.598076	−	0.160254i	0.0208730	−	0.00559290i	−0.248367	−	0.968666i	$-0.579894\pi$
$821$	0.598076	−	0.160254i	0.0208730	−	0.00559290i	0.269240	+	0.963073i	$0.413227\pi$
$822$	11.1506	+	6.43782i	0.388923	+	0.224545i
$823$	−14.9378	+	8.62436i	−0.520700	+	0.300626i	−0.737221	−	0.675652i	$-0.763862\pi$
$823$	−14.9378	+	8.62436i	−0.520700	+	0.300626i	0.216521	+	0.976278i	$0.430529\pi$
$824$	17.6603	−	4.73205i	0.615224	−	0.164849i
$825$		−	6.44486i		−	0.224381i
$826$	−8.29423	+	43.0981i	−0.288593	+	1.49957i
$827$	−3.78461	−	3.78461i	−0.131604	−	0.131604i	0.638237	−	0.769840i	$-0.279664\pi$
$827$	−3.78461	−	3.78461i	−0.131604	−	0.131604i	−0.769840	+	0.638237i	$0.779664\pi$
$828$	21.1244	−	12.1962i	0.734122	−	0.423846i
$829$	−3.06218	−	0.820508i	−0.106354	−	0.0284974i	0.205250	−	0.978710i	$-0.434199\pi$
$829$	−3.06218	−	0.820508i	−0.106354	−	0.0284974i	−0.311603	+	0.950212i	$0.600866\pi$
$830$	−2.66025	+	0.712813i	−0.0923388	+	0.0247421i
$831$	−1.20577	+	2.08846i	−0.0418277	+	0.0724478i
$832$	−29.8564	−	29.8564i	−1.03508	−	1.03508i
$833$	−35.5526	+	27.9904i	−1.23182	+	0.969809i
$834$	3.19615	−	11.9282i	0.110674	−	0.413040i
$835$	−5.07180	−	18.9282i	−0.175517	−	0.655037i
$836$		−	17.6077i		−	0.608975i
$837$	−2.86603	+	10.6962i	−0.0990643	+	0.369713i
$838$	−38.0000			−1.31269
$839$		−	17.7128i		−	0.611514i	−0.952110	−	0.305757i	$-0.901090\pi$
$839$		−	17.7128i		−	0.611514i	0.952110	−	0.305757i	$-0.0989096\pi$
$840$	−0.248711	−	3.46410i	−0.00858136	−	0.119523i
$841$			28.8564i			0.995048i
$842$			17.3205i			0.596904i
$843$	−0.124356	+	0.464102i	−0.00428304	+	0.0159845i
$844$	−31.8564	−	31.8564i	−1.09654	−	1.09654i
$845$	3.44744	+	12.8660i	0.118596	+	0.442605i
$846$	15.9282	+	4.26795i	0.547623	+	0.146735i
$847$	5.49038	−	1.90192i	0.188652	−	0.0653509i
$848$	4.24871	−	15.8564i	0.145901	−	0.544511i
$849$	−3.89230	+	6.74167i	−0.133584	+	0.231374i
$850$	9.92820	+	37.0526i	0.340535	+	1.27089i
$851$	−5.06218	−	1.35641i	−0.173529	−	0.0464970i
$852$	0.535898	+	0.143594i	0.0183596	+	0.00491943i
$853$	−11.8756	−	11.8756i	−0.406614	−	0.406614i	0.473942	−	0.880556i	$-0.342831\pi$
$853$	−11.8756	−	11.8756i	−0.406614	−	0.406614i	−0.880556	+	0.473942i	$0.842831\pi$
$854$	8.83013	+	25.4904i	0.302161	+	0.872263i
$855$			7.26795i			0.248559i
$856$	−4.73205	+	8.19615i	−0.161738	+	0.280139i
$857$	11.8923	−	6.86603i	0.406233	−	0.234539i	−0.282937	−	0.959139i	$-0.591309\pi$
$857$	11.8923	−	6.86603i	0.406233	−	0.234539i	0.689170	+	0.724600i	$0.257975\pi$
$858$	−5.73205	+	9.92820i	−0.195689	+	0.338943i
$859$	13.6244	−	3.65064i	0.464857	−	0.124558i	−0.0187858	−	0.999824i	$-0.505980\pi$
$859$	13.6244	−	3.65064i	0.464857	−	0.124558i	0.483643	+	0.875265i	$0.339313\pi$
$860$	8.19615	−	14.1962i	0.279486	−	0.484085i
$861$	3.78461	+	5.58846i	0.128979	+	0.190454i
$862$	11.2224	−	41.8827i	0.382238	−	1.42653i
$863$	16.3301	−	28.2846i	0.555884	−	0.962819i	−0.441950	−	0.897040i	$-0.645713\pi$
$863$	16.3301	−	28.2846i	0.555884	−	0.962819i	0.997834	−	0.0657797i	$-0.0209535\pi$
$864$			16.7846i			0.571024i
$865$	−1.03590	−	1.79423i	−0.0352216	−	0.0610056i
$866$	−33.1769	−	33.1769i	−1.12740	−	1.12740i
$867$	−9.07180	+	9.07180i	−0.308094	+	0.308094i
$868$	3.73205	−	19.3923i	0.126674	−	0.658218i
$869$	34.9545	+	34.9545i	1.18575	+	1.18575i
$870$	0.248711			0.00843210
$871$	−23.4904	+	13.5622i	−0.795941	+	0.459537i
$872$	5.41154	−	3.12436i	0.183258	−	0.105804i
$873$	6.92820	+	4.00000i	0.234484	+	0.135379i
$874$	−16.2224	+	9.36603i	−0.548732	+	0.316811i
$875$	−1.56218	−	21.7583i	−0.0528112	−	0.735566i
$876$	1.92820	+	7.19615i	0.0651479	+	0.243135i
$877$	8.18653	+	30.5526i	0.276440	+	1.03169i	0.954871	+	0.297022i	$0.0959936\pi$
$877$	8.18653	+	30.5526i	0.276440	+	1.03169i	−0.678431	+	0.734664i	$0.737340\pi$
$878$	2.75833	+	10.2942i	0.0930891	+	0.347413i
$879$	−2.90192	−	5.02628i	−0.0978795	−	0.169532i
$880$			10.6410i			0.358709i
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$	−24.8564	+	10.6603i	−0.836959	+	0.358949i
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	−0.786216	−	0.617952i	$-0.787963\pi$
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	0.617952	+	0.786216i	$0.287963\pi$
$884$	17.6603	−	65.9090i	0.593979	−	2.21676i
$885$	1.40897	−	5.25833i	0.0473619	−	0.176757i
$886$	−13.2224	−	7.63397i	−0.444216	−	0.256468i
$887$	−39.7750	−	22.9641i	−1.33551	−	0.771059i	−0.349375	−	0.936983i	$-0.613606\pi$
$887$	−39.7750	−	22.9641i	−1.33551	−	0.771059i	−0.986139	+	0.165924i	$0.946939\pi$
$888$	1.21539	−	1.21539i	0.0407858	−	0.0407858i
$889$	16.3923	−	18.9282i	0.549780	−	0.634832i
$890$	3.29423	+	5.70577i	0.110423	+	0.191258i
$891$	−19.0885	+	5.11474i	−0.639487	+	0.171350i
$892$			19.7128i			0.660034i
$893$	−12.2321	−	3.27757i	−0.409330	−	0.109680i
$894$	−4.07180	−	4.07180i	−0.136181	−	0.136181i
$895$	−8.32051			−0.278124
$896$	−2.14359	−	29.8564i	−0.0716124	−	0.997433i
$897$	12.1962			0.407218
$898$	−23.3205	−	23.3205i	−0.778215	−	0.778215i
$899$	1.36603	+	0.366025i	0.0455595	+	0.0122076i
$900$			22.9282i			0.764273i
$901$	25.6244	−	6.86603i	0.853671	−	0.228740i
$902$	−10.3397	−	17.9090i	−0.344276	−	0.596303i
$903$	12.2942	+	2.36603i	0.409126	+	0.0787364i
$904$	2.92820	−	2.92820i	0.0973906	−	0.0973906i
$905$	−14.7058	−	8.49038i	−0.488836	−	0.282230i
$906$	7.22243	+	4.16987i	0.239949	+	0.138535i
$907$	7.16025	−	26.7224i	0.237752	−	0.887304i	−0.739136	−	0.673556i	$-0.764766\pi$
$907$	7.16025	−	26.7224i	0.237752	−	0.887304i	0.976889	−	0.213748i	$-0.0685672\pi$
$908$	−5.98076	+	22.3205i	−0.198479	+	0.740732i
$909$	−37.7846	+	37.7846i	−1.25324	+	1.25324i
$910$	−7.73205	+	15.9282i	−0.256315	+	0.528015i
$911$	7.32051			0.242539			0.121270	−	0.992620i	$-0.461303\pi$
$911$	7.32051			0.242539			0.121270	+	0.992620i	$0.461303\pi$
$912$		−	6.14359i		−	0.203435i
$913$	3.22243	+	5.58142i	0.106647	+	0.184718i
$914$	6.88269	+	25.6865i	0.227659	+	0.849635i
$915$	−0.866025	−	3.23205i	−0.0286299	−	0.106848i
$916$	7.14359	+	26.6603i	0.236031	+	0.880880i
$917$	−18.7224	−	9.08846i	−0.618269	−	0.300127i
$918$	−23.4904	+	13.5622i	−0.775298	+	0.447619i
$919$	−15.8660	−	9.16025i	−0.523372	−	0.302169i	0.214941	−	0.976627i	$-0.431044\pi$
$919$	−15.8660	−	9.16025i	−0.523372	−	0.302169i	−0.738313	+	0.674458i	$0.764377\pi$
$920$	9.80385	−	5.66025i	0.323223	−	0.186613i
$921$	5.70577	−	3.29423i	0.188012	−	0.108549i
$922$	37.3205			1.22909
$923$	−2.00000	−	2.00000i	−0.0658308	−	0.0658308i
$924$	−7.67949	+	2.66025i	−0.252637	+	0.0875159i
$925$	3.48334	−	3.48334i	0.114531	−	0.114531i
$926$	2.14359	+	2.14359i	0.0704429	+	0.0704429i
$927$	8.83013	+	15.2942i	0.290019	+	0.502328i
$928$	2.14359			0.0703669
$929$	−25.0167	+	43.3301i	−0.820770	+	1.42162i	0.0843396	+	0.996437i	$0.473122\pi$
$929$	−25.0167	+	43.3301i	−0.820770	+	1.42162i	−0.905110	+	0.425178i	$0.860211\pi$
$930$	−0.633975	+	2.36603i	−0.0207888	+	0.0775850i
$931$	19.0885	−	8.18653i	0.625599	−	0.268303i
$932$	−0.803848	+	1.39230i	−0.0263309	+	0.0456065i
$933$	3.23205	−	0.866025i	0.105813	−	0.0283524i
$934$	19.0263	−	32.9545i	0.622559	−	1.07830i
$935$	−14.8923	+	8.59808i	−0.487030	+	0.281187i
$936$	20.3923	−	35.3205i	0.666543	−	1.15449i
$937$			29.0718i			0.949734i	0.880058	+	0.474867i	$0.157504\pi$
$937$			29.0718i			0.949734i	−0.880058	+	0.474867i	$0.842496\pi$
$938$	−18.8827	−	3.63397i	−0.616542	−	0.118653i
$939$	−7.90192	−	7.90192i	−0.257870	−	0.257870i
$940$	7.39230	+	1.98076i	0.241110	+	0.0646053i
$941$	−23.5263	−	6.30385i	−0.766935	−	0.205500i	−0.145918	−	0.989297i	$-0.546614\pi$
$941$	−23.5263	−	6.30385i	−0.766935	−	0.205500i	−0.621017	+	0.783797i	$0.713280\pi$
$942$	−3.58142	−	13.3660i	−0.116689	−	0.435489i
$943$	−11.0000	+	19.0526i	−0.358209	+	0.620437i
$944$	12.1436	−	45.3205i	0.395240	−	1.47506i
$945$	6.65064	−	2.30385i	0.216345	−	0.0749442i
$946$	−37.0526	−	9.92820i	−1.20468	−	0.322794i
$947$	−1.44744	−	5.40192i	−0.0470355	−	0.175539i	0.938412	−	0.345518i	$-0.112297\pi$
$947$	−1.44744	−	5.40192i	−0.0470355	−	0.175539i	−0.985448	+	0.169979i	$0.945630\pi$
$948$	12.1962	+	12.1962i	0.396113	+	0.396113i
$949$	9.83013	−	36.6865i	0.319099	−	1.19090i
$950$		−	17.6077i		−	0.571269i
$951$		−	7.58846i		−	0.246073i
$952$	40.0526	−	27.1244i	1.29811	−	0.879105i
$953$		−	16.5359i		−	0.535650i	−0.963468	−	0.267825i	$-0.913695\pi$
$953$		−	16.5359i		−	0.535650i	0.963468	−	0.267825i	$-0.0863050\pi$
$954$	15.8564			0.513370
$955$	2.00962	−	7.50000i	0.0650297	−	0.242694i
$956$		−	17.0718i		−	0.552141i
$957$	−0.150635	−	0.562178i	−0.00486934	−	0.0181726i
$958$	5.70577	−	21.2942i	0.184345	−	0.687985i
$959$	8.79423	−	45.6962i	0.283980	−	1.47561i
$960$			3.71281i			0.119831i
$961$	8.53590	−	14.7846i	0.275352	−	0.476923i
$962$	−8.46410	+	2.26795i	−0.272894	+	0.0731216i
$963$	−8.83013	−	2.36603i	−0.284547	−	0.0762441i
$964$	24.1244	−	13.9282i	0.776993	−	0.448597i
$965$	−14.5814	−	14.5814i	−0.469392	−	0.469392i
$966$	6.53590	+	5.66025i	0.210289	+	0.182116i
$967$			60.2487i			1.93747i	0.248102	+	0.968734i	$0.420193\pi$
$967$			60.2487i			1.93747i	−0.248102	+	0.968734i	$0.579807\pi$
$968$	−6.00000	+	1.60770i	−0.192847	+	0.0516733i
$969$	8.59808	−	4.96410i	0.276210	−	0.159470i
$970$	3.21539	+	1.85641i	0.103240	+	0.0596056i
$971$	−52.4090	+	14.0429i	−1.68188	+	0.450659i	−0.968275	−	0.249885i	$-0.919607\pi$
$971$	−52.4090	+	14.0429i	−1.68188	+	0.450659i	−0.713608	+	0.700545i	$0.752940\pi$
$972$	−23.8564	+	6.39230i	−0.765195	+	0.205033i
$973$	−44.5167	+	3.19615i	−1.42714	+	0.102464i
$974$	16.8301	+	4.50962i	0.539272	+	0.144498i
$975$	−5.73205	+	9.92820i	−0.183573	+	0.317957i
$976$	−7.46410	−	27.8564i	−0.238920	−	0.891662i
$977$	8.57180	+	14.8468i	0.274236	+	0.474991i	0.969942	−	0.243336i	$-0.0782417\pi$
$977$	8.57180	+	14.8468i	0.274236	+	0.474991i	−0.695706	+	0.718327i	$0.744908\pi$
$978$	−6.46410	+	6.46410i	−0.206699	+	0.206699i
$979$	10.9019	−	10.9019i	0.348427	−	0.348427i
$980$	−11.5359	+	4.94744i	−0.368501	+	0.158040i
$981$	4.26795	+	4.26795i	0.136265	+	0.136265i
$982$		−	7.17691i		−	0.229025i
$983$	17.1340	−	9.89230i	0.546489	−	0.315516i	−0.201216	−	0.979547i	$-0.564489\pi$
$983$	17.1340	−	9.89230i	0.546489	−	0.315516i	0.747705	+	0.664031i	$0.231156\pi$
$984$	−3.60770	−	6.24871i	−0.115009	−	0.199202i
$985$	18.2942	+	10.5622i	0.582903	+	0.336539i
$986$	1.73205	+	3.00000i	0.0551597	+	0.0955395i
$987$	0.418584	+	5.83013i	0.0133237	+	0.185575i
$988$	−15.6603	+	27.1244i	−0.498219	+	0.862941i
$989$	10.5622	+	39.4186i	0.335858	+	1.25344i
$990$	−9.92820	+	2.66025i	−0.315539	+	0.0845484i
$991$	4.20577	+	7.28461i	0.133601	+	0.231403i	0.925062	−	0.379816i	$-0.124013\pi$
$991$	4.20577	+	7.28461i	0.133601	+	0.231403i	−0.791461	+	0.611219i	$0.790679\pi$
$992$	−5.46410	+	20.3923i	−0.173485	+	0.647456i
$993$	−10.5167			−0.333736
$994$	−0.143594	−	2.00000i	−0.00455451	−	0.0634361i
$995$	7.56218	−	7.56218i	0.239737	−	0.239737i
$996$	1.12436	+	1.94744i	0.0356266	+	0.0617070i
$997$	0.401924	−	1.50000i	0.0127291	−	0.0475055i	−0.959269	−	0.282494i	$-0.908838\pi$
$997$	0.401924	−	1.50000i	0.0127291	−	0.0475055i	0.971998	+	0.234988i	$0.0755051\pi$
$998$	−18.2942	+	31.6865i	−0.579094	+	1.00302i
$999$	3.01666	+	1.74167i	0.0954429	+	0.0551040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.b.37.1	yes	4
4.3	odd	2		448.2.ba.a.177.1		4
7.2	even	3		784.2.m.e.197.2		4
7.3	odd	6		784.2.x.a.165.1		4
7.4	even	3		112.2.w.a.53.1	✓	4
7.5	odd	6		784.2.m.d.197.2		4
7.6	odd	2		784.2.x.h.373.1		4
8.3	odd	2		896.2.ba.c.737.1		4
8.5	even	2		896.2.ba.b.737.1		4
16.3	odd	4		448.2.ba.b.401.1		4
16.5	even	4		896.2.ba.d.289.1		4
16.11	odd	4		896.2.ba.a.289.1		4
16.13	even	4		112.2.w.a.93.1	yes	4
28.11	odd	6		448.2.ba.b.305.1		4
56.11	odd	6		896.2.ba.a.865.1		4
56.53	even	6		896.2.ba.d.865.1		4
112.11	odd	12		896.2.ba.c.417.1		4
112.13	odd	4		784.2.x.a.765.1		4
112.45	odd	12		784.2.x.h.557.1		4
112.53	even	12		896.2.ba.b.417.1		4
112.61	odd	12		784.2.m.d.589.2		4
112.67	odd	12		448.2.ba.a.81.1		4
112.93	even	12		784.2.m.e.589.2		4
112.109	even	12	inner	112.2.w.b.109.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.53.1	✓	4	7.4	even	3
112.2.w.a.93.1	yes	4	16.13	even	4
112.2.w.b.37.1	yes	4	1.1	even	1	trivial
112.2.w.b.109.1	yes	4	112.109	even	12	inner
448.2.ba.a.81.1		4	112.67	odd	12
448.2.ba.a.177.1		4	4.3	odd	2
448.2.ba.b.305.1		4	28.11	odd	6
448.2.ba.b.401.1		4	16.3	odd	4
784.2.m.d.197.2		4	7.5	odd	6
784.2.m.d.589.2		4	112.61	odd	12
784.2.m.e.197.2		4	7.2	even	3
784.2.m.e.589.2		4	112.93	even	12
784.2.x.a.165.1		4	7.3	odd	6
784.2.x.a.765.1		4	112.13	odd	4
784.2.x.h.373.1		4	7.6	odd	2
784.2.x.h.557.1		4	112.45	odd	12
896.2.ba.a.289.1		4	16.11	odd	4
896.2.ba.a.865.1		4	56.11	odd	6
896.2.ba.b.417.1		4	112.53	even	12
896.2.ba.b.737.1		4	8.5	even	2
896.2.ba.c.417.1		4	112.11	odd	12
896.2.ba.c.737.1		4	8.3	odd	2
896.2.ba.d.289.1		4	16.5	even	4
896.2.ba.d.865.1		4	56.53	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.866025 + 0.232051i) q^{5} +(0.366025 + 0.633975i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.866025 + 0.232051i) q^{5} +(0.366025 + 0.633975i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +(-1.09808 - 0.633975i) q^{10} +(-0.767949 + 2.86603i) q^{11} +(-0.267949 + 1.00000i) q^{12} +(3.73205 - 3.73205i) q^{13} +(3.73205 - 0.267949i) q^{14} -0.464102 q^{15} -4.00000 q^{16} +(-3.23205 - 5.59808i) q^{17} +(-1.00000 - 3.73205i) q^{18} +(0.767949 + 2.86603i) q^{19} +(-0.464102 - 1.73205i) q^{20} +(1.13397 - 0.767949i) q^{21} +(-3.63397 + 2.09808i) q^{22} +(3.86603 + 2.23205i) q^{23} +(-1.26795 + 0.732051i) q^{24} +(-3.63397 + 2.09808i) q^{25} +7.46410 q^{26} +(-2.09808 - 2.09808i) q^{27} +(4.00000 + 3.46410i) q^{28} +(-0.267949 + 0.267949i) q^{29} +(-0.464102 - 0.464102i) q^{30} +(-1.86603 - 3.23205i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.767949 + 1.33013i) q^{33} +(2.36603 - 8.83013i) q^{34} +(-1.03590 + 2.13397i) q^{35} +(2.73205 - 4.73205i) q^{36} +(-1.13397 + 0.303848i) q^{37} +(-2.09808 + 3.63397i) q^{38} +(2.36603 - 1.36603i) q^{39} +(1.26795 - 2.19615i) q^{40} +4.92820i q^{41} +(1.90192 + 0.366025i) q^{42} +(6.46410 + 6.46410i) q^{43} +(-5.73205 - 1.53590i) q^{44} +(2.36603 + 0.633975i) q^{45} +(1.63397 + 6.09808i) q^{46} +(-2.13397 + 3.69615i) q^{47} +(-2.00000 - 0.535898i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-5.73205 - 1.53590i) q^{50} +(-0.866025 - 3.23205i) q^{51} +(7.46410 + 7.46410i) q^{52} +(-1.06218 + 3.96410i) q^{53} -4.19615i q^{54} -2.66025i q^{55} +(0.535898 + 7.46410i) q^{56} +1.53590i q^{57} -0.535898 q^{58} +(-3.03590 + 11.3301i) q^{59} -0.928203i q^{60} +(1.86603 + 6.96410i) q^{61} +(1.36603 - 5.09808i) q^{62} +(-6.83013 + 2.36603i) q^{63} -8.00000i q^{64} +(-2.36603 + 4.09808i) q^{65} +(-2.09808 + 0.562178i) q^{66} +(-4.96410 - 1.33013i) q^{67} +(11.1962 - 6.46410i) q^{68} +(1.63397 + 1.63397i) q^{69} +(-3.16987 + 1.09808i) q^{70} -0.535898i q^{71} +(7.46410 - 2.00000i) q^{72} +(6.23205 - 3.59808i) q^{73} +(-1.43782 - 0.830127i) q^{74} +(-2.09808 + 0.562178i) q^{75} +(-5.73205 + 1.53590i) q^{76} +(4.40192 + 6.50000i) q^{77} +(3.73205 + 1.00000i) q^{78} +(8.33013 - 14.4282i) q^{79} +(3.46410 - 0.928203i) q^{80} +(3.33013 + 5.76795i) q^{81} +(-4.92820 + 4.92820i) q^{82} +(1.53590 - 1.53590i) q^{83} +(1.53590 + 2.26795i) q^{84} +(4.09808 + 4.09808i) q^{85} +12.9282i q^{86} +(-0.169873 + 0.0980762i) q^{87} +(-4.19615 - 7.26795i) q^{88} +(-4.50000 - 2.59808i) q^{89} +(1.73205 + 3.00000i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(-4.46410 + 7.73205i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-5.83013 + 1.56218i) q^{94} +(-1.33013 - 2.30385i) q^{95} +(-1.46410 - 2.53590i) q^{96} -2.92820 q^{97} +(5.92820 - 7.92820i) q^{98} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 - 2 * q^6 - 8 * q^8 - 6 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9} + 6 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 8 q^{14} + 12 q^{15} - 16 q^{16} - 6 q^{17} - 4 q^{18} + 10 q^{19} + 12 q^{20} + 8 q^{21} - 18 q^{22} + 12 q^{23} - 12 q^{24} - 18 q^{25} + 16 q^{26} + 2 q^{27} + 16 q^{28} - 8 q^{29} + 12 q^{30} - 4 q^{31} - 16 q^{32} - 10 q^{33} + 6 q^{34} - 18 q^{35} + 4 q^{36} - 8 q^{37} + 2 q^{38} + 6 q^{39} + 12 q^{40} + 18 q^{42} + 12 q^{43} - 16 q^{44} + 6 q^{45} + 10 q^{46} - 12 q^{47} - 8 q^{48} - 4 q^{49} - 16 q^{50} + 16 q^{52} + 20 q^{53} + 16 q^{56} - 16 q^{58} - 26 q^{59} + 4 q^{61} + 2 q^{62} - 10 q^{63} - 6 q^{65} + 2 q^{66} - 6 q^{67} + 24 q^{68} + 10 q^{69} - 30 q^{70} + 16 q^{72} + 18 q^{73} - 30 q^{74} + 2 q^{75} - 16 q^{76} + 28 q^{77} + 8 q^{78} + 16 q^{79} - 4 q^{81} + 8 q^{82} + 20 q^{83} + 20 q^{84} + 6 q^{85} - 18 q^{87} + 4 q^{88} - 18 q^{89} - 4 q^{91} - 4 q^{92} - 2 q^{93} - 6 q^{94} + 12 q^{95} + 8 q^{96} + 16 q^{97} - 4 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 - 2 * q^6 - 8 * q^8 - 6 * q^9 + 6 * q^10 - 10 * q^11 - 8 * q^12 + 8 * q^13 + 8 * q^14 + 12 * q^15 - 16 * q^16 - 6 * q^17 - 4 * q^18 + 10 * q^19 + 12 * q^20 + 8 * q^21 - 18 * q^22 + 12 * q^23 - 12 * q^24 - 18 * q^25 + 16 * q^26 + 2 * q^27 + 16 * q^28 - 8 * q^29 + 12 * q^30 - 4 * q^31 - 16 * q^32 - 10 * q^33 + 6 * q^34 - 18 * q^35 + 4 * q^36 - 8 * q^37 + 2 * q^38 + 6 * q^39 + 12 * q^40 + 18 * q^42 + 12 * q^43 - 16 * q^44 + 6 * q^45 + 10 * q^46 - 12 * q^47 - 8 * q^48 - 4 * q^49 - 16 * q^50 + 16 * q^52 + 20 * q^53 + 16 * q^56 - 16 * q^58 - 26 * q^59 + 4 * q^61 + 2 * q^62 - 10 * q^63 - 6 * q^65 + 2 * q^66 - 6 * q^67 + 24 * q^68 + 10 * q^69 - 30 * q^70 + 16 * q^72 + 18 * q^73 - 30 * q^74 + 2 * q^75 - 16 * q^76 + 28 * q^77 + 8 * q^78 + 16 * q^79 - 4 * q^81 + 8 * q^82 + 20 * q^83 + 20 * q^84 + 6 * q^85 - 18 * q^87 + 4 * q^88 - 18 * q^89 - 4 * q^91 - 4 * q^92 - 2 * q^93 - 6 * q^94 + 12 * q^95 + 8 * q^96 + 16 * q^97 - 4 * q^98 + 16 * q^99

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