LMFDB - Embedded newform 112.2.w.b.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(37,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			109.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	112.109
Dual form			112.2.w.b.37.1

$q$-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} +(-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} + 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}+ \cdots + 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

Character values

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

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.111576	−	0.993756i	$-0.535590\pi$
$3$	0.500000	−	0.133975i	0.288675	−	0.0773503i	0.400251	+	0.916406i	$0.368923\pi$
$4$		−	2.00000i		−	1.00000i
$5$	−0.866025	−	0.232051i	−0.387298	−	0.103776i	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	−0.866025	−	0.232051i	−0.387298	−	0.103776i	−0.447214	+	0.894427i	$0.647584\pi$
$6$	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	−0.979676	−	0.200587i	$-0.935715\pi$
$11$	−0.767949	−	2.86603i	−0.231545	−	0.864139i	0.748130	−	0.663552i	$-0.230952\pi$
$12$	−0.267949	−	1.00000i	−0.0773503	−	0.288675i
$13$	3.73205	+	3.73205i	1.03508	+	1.03508i	0.999362	+	0.0357229i	$0.0113734\pi$
$13$	3.73205	+	3.73205i	1.03508	+	1.03508i	0.0357229	+	0.999362i	$0.488627\pi$
$14$	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	0.145774	+	0.989318i	$0.453433\pi$
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	−0.929661	+	0.368415i	$0.879901\pi$
$18$	−1.00000	+	3.73205i	−0.235702	+	0.879653i
$19$	0.767949	−	2.86603i	0.176180	−	0.657511i	−0.820168	−	0.572123i	$-0.806120\pi$
$19$	0.767949	−	2.86603i	0.176180	−	0.657511i	0.996348	−	0.0853887i	$-0.0272132\pi$
$20$	−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	−0.0394853	−	0.999220i	$-0.512572\pi$
$23$	3.86603	−	2.23205i	0.806122	−	0.465415i	0.845607	+	0.533805i	$0.179239\pi$
$24$	−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	0.681791	−	0.731547i	$-0.261202\pi$
$29$	−0.267949	−	0.267949i	−0.0497569	−	0.0497569i	−0.731547	+	0.681791i	$0.761202\pi$
$30$	−0.464102	+	0.464102i	−0.0847330	+	0.0847330i
$31$	−1.86603	+	3.23205i	−0.335148	+	0.580493i	−0.983513	−	0.180836i	$-0.942120\pi$
$31$	−1.86603	+	3.23205i	−0.335148	+	0.580493i	0.648365	+	0.761329i	$0.275453\pi$
$32$	−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	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−1.13397	−	0.303848i	−0.186424	−	0.0499522i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	−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	$-0.874261\pi$
$41$		−	4.92820i		−	0.769656i	0.922988	−	0.384828i	$-0.125739\pi$
$42$	1.90192	−	0.366025i	0.293473	−	0.0564789i
$43$	6.46410	−	6.46410i	0.985766	−	0.985766i	−0.0141339	−	0.999900i	$-0.504499\pi$
$43$	6.46410	−	6.46410i	0.985766	−	0.985766i	0.999900	+	0.0141339i	$0.00449910\pi$
$44$	−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	0.667366	−	0.744730i	$-0.267422\pi$
$47$	−2.13397	−	3.69615i	−0.311272	−	0.539139i	−0.978638	+	0.205591i	$0.934088\pi$
$48$	−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	−0.999714	−	0.0239302i	$-0.992382\pi$
$53$	−1.06218	−	3.96410i	−0.145901	−	0.544511i	0.853812	−	0.520581i	$-0.174285\pi$
$54$			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	−0.821370	−	0.570395i	$-0.806790\pi$
$59$	−3.03590	−	11.3301i	−0.395240	−	1.47506i	0.426130	−	0.904662i	$-0.359877\pi$
$60$			0.928203i			0.119831i
$61$	1.86603	−	6.96410i	0.238920	−	0.891662i	−0.737422	−	0.675432i	$-0.763957\pi$
$61$	1.86603	−	6.96410i	0.238920	−	0.891662i	0.976342	−	0.216230i	$-0.0693761\pi$
$62$	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	−0.548966	−	0.835845i	$-0.684978\pi$
$67$	−4.96410	+	1.33013i	−0.606462	+	0.162501i	−0.0574958	+	0.998346i	$0.518312\pi$
$68$	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	$0.0101239\pi$
$71$			0.535898i			0.0635994i	−0.999494	+	0.0317997i	$0.989876\pi$
$72$	7.46410	+	2.00000i	0.879653	+	0.235702i
$73$	6.23205	+	3.59808i	0.729406	+	0.421123i	0.818205	−	0.574927i	$-0.194969\pi$
$73$	6.23205	+	3.59808i	0.729406	+	0.421123i	−0.0887986	+	0.996050i	$0.528303\pi$
$74$	−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	0.770640	+	0.637270i	$0.219937\pi$
$79$	8.33013	+	14.4282i	0.937213	+	1.62330i	0.166572	+	0.986029i	$0.446730\pi$
$80$	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	0.786358	−	0.617771i	$-0.211964\pi$
$83$	1.53590	+	1.53590i	0.168587	+	0.168587i	−0.617771	+	0.786358i	$0.711964\pi$
$84$	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	−0.719165	−	0.694839i	$-0.755475\pi$
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	0.242166	+	0.970235i	$0.422142\pi$
$90$	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	0.474450	+	0.880283i	$0.342647\pi$
$101$	5.06218	+	18.8923i	0.503706	+	1.87985i	0.0292559	+	0.999572i	$0.490686\pi$
$102$	2.36603	+	4.09808i	0.234271	+	0.405770i
$103$	−5.59808	+	3.23205i	−0.551595	+	0.318463i	−0.749765	−	0.661704i	$-0.769833\pi$
$103$	−5.59808	+	3.23205i	−0.551595	+	0.318463i	0.198170	+	0.980168i	$0.436500\pi$
$104$		−	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	0.411638	−	0.911347i	$-0.364957\pi$
$107$	3.23205	+	0.866025i	0.312454	+	0.0837218i	−0.0991843	+	0.995069i	$0.531623\pi$
$108$	4.19615	+	4.19615i	0.403775	+	0.403775i
$109$	−2.13397	+	0.571797i	−0.204398	+	0.0547682i	−0.359565	−	0.933120i	$-0.617075\pi$
$109$	−2.13397	+	0.571797i	−0.204398	+	0.0547682i	0.155167	+	0.987888i	$0.450408\pi$
$110$	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	0.818166	+	0.574982i	$0.194991\pi$
$131$	−2.03590	+	7.59808i	−0.177877	+	0.663847i	−0.996044	+	0.0888654i	$0.971676\pi$
$132$	−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	0.980638	−	0.195831i	$-0.0627404\pi$
$137$	15.2321	+	8.79423i	1.30136	+	0.751342i	0.320724	+	0.947173i	$0.396074\pi$
$138$		−	3.26795i		−	0.278186i
$139$	−11.9282	+	11.9282i	−1.01174	+	1.01174i	−0.0118067	+	0.999930i	$0.503758\pi$
$139$	−11.9282	+	11.9282i	−1.01174	+	1.01174i	−0.999930	+	0.0118067i	$0.996242\pi$
$140$	−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	−0.0662134	−	0.997805i	$-0.521092\pi$
$149$	−7.59808	−	2.03590i	−0.622459	−	0.166787i	−0.556245	+	0.831018i	$0.687758\pi$
$150$	−2.66025	+	1.53590i	−0.217209	+	0.125406i
$151$	9.86603	+	5.69615i	0.802886	+	0.463546i	0.844479	−	0.535588i	$-0.179910\pi$
$151$	9.86603	+	5.69615i	0.802886	+	0.463546i	−0.0415935	+	0.999135i	$0.513243\pi$
$152$	−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	−0.898513	−	0.438948i	$-0.855351\pi$
$157$	−18.2583	+	4.89230i	−1.45717	+	0.390448i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	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	−0.715954	−	0.698147i	$-0.754008\pi$
$163$	3.23205	−	12.0622i	0.253154	−	0.944783i	0.969108	−	0.246636i	$-0.0793251\pi$
$164$	−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	$-0.679213\pi$
$167$		−	21.8564i		−	1.69130i	0.533738	−	0.845650i	$-0.320787\pi$
$168$	−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	−0.939456	−	0.342668i	$-0.888669\pi$
$173$	0.598076	−	2.23205i	0.0454709	−	0.169700i	0.984927	+	0.172969i	$0.0553359\pi$
$174$	−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	0.0922498	−	0.995736i	$-0.470594\pi$
$179$	8.96410	−	2.40192i	0.670008	−	0.179528i	0.577759	+	0.816208i	$0.303928\pi$
$180$	−1.26795	−	4.73205i	−0.0945074	−	0.352706i
$181$	13.3923	−	13.3923i	0.995442	−	0.995442i	−0.00454748	−	0.999990i	$-0.501448\pi$
$181$	13.3923	−	13.3923i	0.995442	−	0.995442i	0.999990	+	0.00454748i	$0.00144751\pi$
$182$	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	0.665761	−	0.746165i	$-0.268107\pi$
$191$	−4.33013	−	7.50000i	−0.313317	−	0.542681i	−0.979078	+	0.203484i	$0.934774\pi$
$192$	1.07180	+	4.00000i	0.0773503	+	0.288675i
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$	−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	−0.209100	+	0.977894i	$0.567053\pi$
$197$	−16.6603	+	16.6603i	−1.18699	+	1.18699i	−0.977894	+	0.209100i	$0.932947\pi$
$198$	11.4641			0.814718
$199$	−10.3301	−	5.96410i	−0.732283	−	0.422784i	0.0869736	−	0.996211i	$-0.472280\pi$
$199$	−10.3301	−	5.96410i	−0.732283	−	0.422784i	−0.819257	+	0.573427i	$0.805614\pi$
$200$	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	−0.994812	−	0.101731i	$-0.967562\pi$
$211$	−15.9282	−	15.9282i	−1.09654	−	1.09654i	−0.101731	−	0.994812i	$-0.532438\pi$
$212$	−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	0.131329	−	0.991339i	$-0.458076\pi$
$227$	11.1603	−	2.99038i	0.740732	−	0.198479i	0.609403	+	0.792860i	$0.291409\pi$
$228$	−3.07180			−0.203435
$229$	13.3301	+	3.57180i	0.880880	+	0.236031i	0.670787	−	0.741650i	$-0.265957\pi$
$229$	13.3301	+	3.57180i	0.880880	+	0.236031i	0.210093	+	0.977681i	$0.432623\pi$
$230$	−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	−0.477023	−	0.878891i	$-0.658284\pi$
$233$	0.696152	−	0.401924i	0.0456065	−	0.0263309i	0.522630	+	0.852560i	$0.324951\pi$
$234$	−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	−0.998295	−	0.0583704i	$-0.981410\pi$
$241$	−6.96410	+	12.0622i	−0.448597	+	0.776993i	0.549698	+	0.835364i	$0.314743\pi$
$242$	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	−0.117047	+	0.993126i	$0.537343\pi$
$251$	−17.5885	+	17.5885i	−1.11017	+	1.11017i	−0.993126	+	0.117047i	$0.962657\pi$
$252$	−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	0.992078	+	0.125620i	$0.0400920\pi$
$257$	9.69615	+	16.7942i	0.604829	+	1.04760i	−0.387249	+	0.921975i	$0.626575\pi$
$258$	−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	0.617958	−	0.786211i	$-0.287960\pi$
$263$	3.99038	+	2.30385i	0.246057	+	0.142061i	−0.371900	+	0.928273i	$0.621294\pi$
$264$	−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	0.0524390	−	0.998624i	$-0.483300\pi$
$269$	9.79423	−	2.62436i	0.597165	−	0.160010i	0.544726	+	0.838614i	$0.316634\pi$
$270$	0.973721	−	3.63397i	0.0592587	−	0.221157i
$271$	−6.06218	−	10.5000i	−0.368251	−	0.637830i	0.621041	−	0.783778i	$-0.286710\pi$
$271$	−6.06218	−	10.5000i	−0.368251	−	0.637830i	−0.989292	+	0.145948i	$0.953377\pi$
$272$	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	0.920195	−	0.391461i	$-0.128030\pi$
$277$	−1.20577	−	4.50000i	−0.0724478	−	0.270379i	−0.992642	+	0.121082i	$0.961364\pi$
$278$			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	$-0.991186\pi$
$281$		−	0.928203i		−	0.0553720i	0.999617	−	0.0276860i	$-0.00881385\pi$
$282$	−3.12436			−0.186053
$283$	−3.89230	−	14.5263i	−0.231374	−	0.863498i	−0.979750	−	0.200224i	$-0.935833\pi$
$283$	−3.89230	−	14.5263i	−0.231374	−	0.863498i	0.748377	−	0.663274i	$-0.230834\pi$
$284$	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	−0.899693	−	0.436523i	$-0.856210\pi$
$293$	−7.92820	+	7.92820i	−0.463171	+	0.463171i	0.436523	+	0.899693i	$0.356210\pi$
$294$	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	0.915645	−	0.401988i	$-0.131681\pi$
$307$	9.00000	+	9.00000i	0.513657	+	0.513657i	−0.401988	+	0.915645i	$0.631681\pi$
$308$	−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	0.650250	−	0.759720i	$-0.274664\pi$
$311$	5.59808	+	3.23205i	0.317438	+	0.183273i	−0.332812	+	0.942993i	$0.607998\pi$
$312$	−2.00000	−	7.46410i	−0.113228	−	0.422572i
$313$	−18.6962	+	10.7942i	−1.05677	+	0.610126i	−0.924537	−	0.381093i	$-0.875548\pi$
$313$	−18.6962	+	10.7942i	−1.05677	+	0.610126i	−0.132232	+	0.991219i	$0.542214\pi$
$314$	−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	0.773720	+	0.633528i	$0.218394\pi$
$317$	−3.79423	+	14.1603i	−0.213105	+	0.795319i	−0.986825	+	0.161791i	$0.948273\pi$
$318$	−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	−0.324609	−	0.945848i	$-0.605233\pi$
$331$	−19.6244	−	5.25833i	−1.07865	−	0.289024i	−0.754044	+	0.656824i	$0.771899\pi$
$332$	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	−0.900127	−	0.435628i	$-0.856526\pi$
$347$	−6.30385	−	23.5263i	−0.338408	−	1.26296i	0.561718	−	0.827329i	$-0.310140\pi$
$348$	−0.196152	+	0.339746i	−0.0105149	+	0.0182123i
$349$	6.12436	+	6.12436i	0.327829	+	0.327829i	0.851761	−	0.523931i	$-0.175535\pi$
$349$	6.12436	+	6.12436i	0.327829	+	0.327829i	−0.523931	+	0.851761i	$0.675535\pi$
$350$	−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	−0.213347	−	0.976976i	$-0.568437\pi$
$353$	13.8923	−	24.0622i	0.739413	−	1.28070i	0.952760	−	0.303724i	$-0.0982301\pi$
$354$	−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	−0.598539	−	0.801094i	$-0.704252\pi$
$359$	−3.86603	+	2.23205i	−0.204041	+	0.117803i	0.394498	+	0.918897i	$0.370919\pi$
$360$	−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	−0.934812	−	0.355142i	$-0.884433\pi$
$367$	−3.06218	+	5.30385i	−0.159844	+	0.276859i	0.774968	+	0.632000i	$0.217766\pi$
$368$	−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	0.281170	−	0.959658i	$-0.409278\pi$
$373$	0.866025	+	0.232051i	0.0448411	+	0.0120151i	−0.236329	+	0.971673i	$0.575944\pi$
$374$	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	−0.703906	−	0.710293i	$-0.748562\pi$
$379$	0.124356	−	0.124356i	0.00638772	−	0.00638772i	0.710293	+	0.703906i	$0.248562\pi$
$380$	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	0.984593	+	0.174862i	$0.0559480\pi$
$383$	12.5981	+	21.8205i	0.643732	+	1.11498i	−0.340861	+	0.940114i	$0.610719\pi$
$384$	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	0.934038	+	0.357174i	$0.116260\pi$
$389$	5.99038	+	22.3564i	0.303724	+	1.13351i	−0.630313	+	0.776341i	$0.717074\pi$
$390$	−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	−0.548488	−	0.836159i	$-0.684796\pi$
$397$	6.86603	−	25.6244i	0.344596	−	1.28605i	0.893084	−	0.449891i	$-0.148537\pi$
$398$	−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	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$	−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	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$	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	0.0693796	−	0.997590i	$-0.477898\pi$
$419$	−19.0000	−	19.0000i	−0.928211	−	0.928211i	−0.997590	+	0.0693796i	$0.977898\pi$
$420$	−1.85641	+	1.60770i	−0.0905834	+	0.0784475i
$421$	8.66025	−	8.66025i	0.422075	−	0.422075i	−0.463843	−	0.885918i	$-0.653530\pi$
$421$	8.66025	−	8.66025i	0.422075	−	0.422075i	0.885918	+	0.463843i	$0.153530\pi$
$422$	−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	0.214777	+	0.976663i	$0.431097\pi$
$431$	−15.3301	+	26.5526i	−0.738426	+	1.27899i	−0.953204	+	0.302329i	$0.902236\pi$
$432$	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	−0.336107	−	0.941824i	$-0.609110\pi$
$439$	6.52628	−	3.76795i	0.311482	−	0.179834i	0.647590	+	0.761989i	$0.275777\pi$
$440$	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	0.00243278	−	0.999997i	$-0.499226\pi$
$443$	−10.4282	−	2.79423i	−0.495459	−	0.132758i	−0.497892	+	0.867239i	$0.665892\pi$
$444$			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	−0.0681661	−	0.997674i	$-0.521715\pi$
$457$	16.2846	−	9.40192i	0.761762	−	0.439803i	0.829928	+	0.557871i	$0.188381\pi$
$458$	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	0.992372	−	0.123278i	$-0.0393405\pi$
$461$	18.6603	+	18.6603i	0.869095	+	0.869095i	−0.123278	+	0.992372i	$0.539341\pi$
$462$	−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	0.594777	+	0.803890i	$0.297240\pi$
$467$	−6.96410	+	25.9904i	−0.322260	+	1.20269i	−0.917038	+	0.398801i	$0.869426\pi$
$468$	−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	−0.987310	−	0.158803i	$-0.949236\pi$
$479$	−7.79423	+	13.5000i	−0.356127	+	0.616831i	0.631183	+	0.775634i	$0.282570\pi$
$480$	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	0.721873	−	0.692025i	$-0.243281\pi$
$487$	10.6699	+	6.16025i	0.483498	+	0.279148i	−0.238375	+	0.971173i	$0.576615\pi$
$488$	−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	−0.783428	−	0.621483i	$-0.786531\pi$
$491$	−3.58846	+	3.58846i	−0.161945	+	0.161945i	0.621483	+	0.783428i	$0.286531\pi$
$492$	−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	−0.637601	−	0.770367i	$-0.720073\pi$
$499$	6.69615	−	24.9904i	0.299761	−	1.11872i	0.937362	−	0.348356i	$-0.113260\pi$
$500$	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	$-0.748603\pi$
$503$		−	31.8564i		−	1.42041i	0.703996	−	0.710203i	$-0.251397\pi$
$504$	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	−0.887067	−	0.461640i	$-0.847261\pi$
$509$	2.52628	−	9.42820i	0.111975	−	0.417898i	0.999043	+	0.0437420i	$0.0139280\pi$
$510$	−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	0.177516	−	0.984118i	$-0.443194\pi$
$521$	−13.3756	−	7.72243i	−0.585998	−	0.338326i	−0.763513	+	0.645792i	$0.776527\pi$
$522$	1.26795	−	0.732051i	0.0554966	−	0.0320410i
$523$	−32.2846	−	8.65064i	−1.41171	−	0.378266i	−0.529173	−	0.848514i	$-0.677498\pi$
$523$	−32.2846	−	8.65064i	−1.41171	−	0.378266i	−0.882534	+	0.470248i	$0.844164\pi$
$524$	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	−0.892142	−	0.451756i	$-0.850798\pi$
$541$	2.47372	−	9.23205i	0.106354	−	0.396917i	0.998495	+	0.0548389i	$0.0174645\pi$
$542$	−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	0.0142423	−	0.999899i	$-0.495466\pi$
$547$	−23.0526	−	23.0526i	−0.985656	−	0.985656i	−0.999899	+	0.0142423i	$0.995466\pi$
$548$	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	−0.116310	−	0.993213i	$-0.537107\pi$
$557$	6.59808	−	1.76795i	0.279569	−	0.0749104i	0.395879	+	0.918303i	$0.370440\pi$
$558$	−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	−0.309624	−	0.950859i	$-0.600203\pi$
$563$	−2.42820	+	0.650635i	−0.102337	+	0.0274210i	0.207287	+	0.978280i	$0.433536\pi$
$564$	−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	−0.602853	−	0.797852i	$-0.705969\pi$
$569$	−5.08846	+	2.93782i	−0.213319	+	0.123160i	0.389534	+	0.921012i	$0.372636\pi$
$570$	0.973721	+	1.68653i	0.0407847	+	0.0706411i
$571$	−7.16025	−	26.7224i	−0.299647	−	1.11830i	−0.937456	−	0.348104i	$-0.886826\pi$
$571$	−7.16025	−	26.7224i	−0.299647	−	1.11830i	0.637809	−	0.770195i	$-0.279841\pi$
$572$	−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	−0.970330	−	0.241782i	$-0.922268\pi$
$577$	−6.62436	+	11.4737i	−0.275776	+	0.477657i	0.694555	+	0.719440i	$0.255601\pi$
$578$	−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	−0.0907957	−	0.995870i	$-0.528941\pi$
$587$	21.9282	−	21.9282i	0.905074	−	0.905074i	0.995870	+	0.0907957i	$0.0289410\pi$
$588$	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	0.958956	−	0.283554i	$-0.0915136\pi$
$593$	5.69615	+	9.86603i	0.233913	+	0.405149i	−0.725043	+	0.688703i	$0.758180\pi$
$594$	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	0.800274	−	0.599634i	$-0.204687\pi$
$599$	16.6699	+	9.62436i	0.681113	+	0.393241i	−0.119162	+	0.992875i	$0.538021\pi$
$600$	3.07180	+	5.32051i	0.125406	+	0.217209i
$601$			10.0000i			0.407909i	0.978980	+	0.203954i	$0.0653794\pi$
$601$			10.0000i			0.407909i	−0.978980	+	0.203954i	$0.934621\pi$
$602$	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	0.639477	−	0.768810i	$-0.279151\pi$
$607$	−8.52628	−	14.7679i	−0.346071	−	0.599413i	−0.985548	+	0.169398i	$0.945818\pi$
$608$	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	0.997718	−	0.0675126i	$-0.0215063\pi$
$613$	2.47372	+	9.23205i	0.0999126	+	0.372879i	−0.897806	+	0.440392i	$0.854840\pi$
$614$	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	$0.00343375\pi$
$617$			0.535898i			0.0215745i	−0.999942	+	0.0107872i	$0.996566\pi$
$618$			4.73205i			0.190351i
$619$	5.10770	+	19.0622i	0.205296	+	0.766174i	0.989359	+	0.145493i	$0.0464769\pi$
$619$	5.10770	+	19.0622i	0.205296	+	0.766174i	−0.784064	+	0.620680i	$0.786856\pi$
$620$	−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	$0.221854\pi$
$631$			32.2487i			1.28380i	−0.766788	+	0.641900i	$0.778146\pi$
$632$	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	−0.734757	−	0.678330i	$-0.762704\pi$
$641$	5.57180	−	9.65064i	0.220073	−	0.381177i	0.954830	+	0.297153i	$0.0960372\pi$
$642$	1.73205	−	1.73205i	0.0683586	−	0.0683586i
$643$	−5.39230	−	5.39230i	−0.212652	−	0.212652i	0.592741	−	0.805393i	$-0.298046\pi$
$643$	−5.39230	−	5.39230i	−0.212652	−	0.212652i	−0.805393	+	0.592741i	$0.798046\pi$
$644$	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	0.963513	−	0.267661i	$-0.0862507\pi$
$647$	30.8660	+	17.8205i	1.21347	+	0.700596i	0.249955	+	0.968257i	$0.419584\pi$
$648$	−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	0.555501	+	0.831516i	$0.312527\pi$
$653$	−8.72243	+	32.5526i	−0.341335	+	1.27388i	−0.896836	+	0.442364i	$0.854140\pi$
$654$	−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	0.971516	−	0.236975i	$-0.0761558\pi$
$659$	18.8564	+	18.8564i	0.734541	+	0.734541i	−0.236975	+	0.971516i	$0.576156\pi$
$660$	2.66025	−	0.712813i	0.103550	−	0.0277462i
$661$	−5.93782	−	22.1603i	−0.230955	−	0.861934i	−0.979931	−	0.199337i	$-0.936121\pi$
$661$	−5.93782	−	22.1603i	−0.230955	−	0.861934i	0.748976	−	0.662597i	$-0.230546\pi$
$662$	−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	−0.684611	−	0.728908i	$-0.740028\pi$
$677$	−42.7224	−	11.4474i	−1.64196	−	0.439961i	−0.957345	+	0.288947i	$0.906695\pi$
$678$	−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	0.649114	+	0.760691i	$0.275140\pi$
$683$	12.2128	+	45.5788i	0.467310	+	1.74403i	−0.181804	+	0.983335i	$0.558194\pi$
$684$	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	−0.744095	−	0.668074i	$-0.767119\pi$
$691$	6.16025	−	22.9904i	0.234347	−	0.874595i	0.978442	−	0.206521i	$-0.0662143\pi$
$692$	−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	0.407420	−	0.913241i	$-0.366428\pi$
$701$	−13.3923	−	13.3923i	−0.505820	−	0.505820i	−0.913241	+	0.407420i	$0.866428\pi$
$702$	−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	0.976507	−	0.215484i	$-0.0691329\pi$
$709$	45.6506	+	12.2321i	1.71445	+	0.459384i	0.737938	+	0.674868i	$0.235800\pi$
$710$	−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	0.862163	−	0.506631i	$-0.169109\pi$
$719$	−0.205771	−	0.356406i	−0.00767398	−	0.0132917i	−0.869837	+	0.493339i	$0.835776\pi$
$720$	−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	$-0.722122\pi$
$727$		−	41.3205i		−	1.53249i	0.642547	−	0.766246i	$-0.277878\pi$
$728$	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	0.588242	+	0.808685i	$0.299820\pi$
$733$	−8.81347	+	32.8923i	−0.325533	+	1.21490i	−0.913775	+	0.406220i	$0.866847\pi$
$734$	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	0.531639	−	0.846971i	$-0.321576\pi$
$739$	38.4808	−	10.3109i	1.41554	−	0.379292i	0.883899	+	0.467679i	$0.154910\pi$
$740$	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	$-0.934901\pi$
$743$		−	11.0718i		−	0.406185i	0.979160	−	0.203092i	$-0.0650992\pi$
$744$	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	0.722035	−	0.691856i	$-0.243207\pi$
$751$	−6.52628	−	11.3038i	−0.238147	−	0.412483i	−0.960183	+	0.279373i	$0.909873\pi$
$752$	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	−0.959597	−	0.281378i	$-0.909208\pi$
$757$	−18.6603	+	18.6603i	−0.678218	+	0.678218i	0.281378	+	0.959597i	$0.409208\pi$
$758$		−	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	−0.271304	−	0.962494i	$-0.587455\pi$
$761$	11.7679	−	6.79423i	0.426588	−	0.246291i	0.697892	+	0.716203i	$0.254122\pi$
$762$	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	0.892754	−	0.450545i	$-0.148770\pi$
$773$	−2.93782	−	10.9641i	−0.105666	−	0.394351i	−0.998420	+	0.0561936i	$0.982104\pi$
$774$	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	−0.485628	−	0.874165i	$-0.661409\pi$
$787$	−13.1603	+	3.52628i	−0.469112	+	0.125698i	0.0165161	+	0.999864i	$0.494743\pi$
$788$	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	0.430211	−	0.902729i	$-0.358439\pi$
$797$	−13.3397	−	13.3397i	−0.472518	−	0.472518i	−0.902729	+	0.430211i	$0.858439\pi$
$798$	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	−0.116330	−	0.993211i	$-0.537113\pi$
$809$	−29.4282	−	16.9904i	−1.03464	−	0.597350i	−0.918311	+	0.395861i	$0.870446\pi$
$810$			8.44486i			0.296722i
$811$	24.3205	−	24.3205i	0.854009	−	0.854009i	−0.136616	−	0.990624i	$-0.543623\pi$
$811$	24.3205	−	24.3205i	0.854009	−	0.854009i	0.990624	+	0.136616i	$0.0436225\pi$
$812$	−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	0.269240	−	0.963073i	$-0.413227\pi$
$821$	0.598076	+	0.160254i	0.0208730	+	0.00559290i	−0.248367	+	0.968666i	$0.579894\pi$
$822$	11.1506	−	6.43782i	0.388923	−	0.224545i
$823$	−14.9378	−	8.62436i	−0.520700	−	0.300626i	0.216521	−	0.976278i	$-0.430529\pi$
$823$	−14.9378	−	8.62436i	−0.520700	−	0.300626i	−0.737221	+	0.675652i	$0.763862\pi$
$824$	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	−0.769840	−	0.638237i	$-0.779664\pi$
$827$	−3.78461	+	3.78461i	−0.131604	+	0.131604i	0.638237	+	0.769840i	$0.279664\pi$
$828$	21.1244	+	12.1962i	0.734122	+	0.423846i
$829$	−3.06218	+	0.820508i	−0.106354	+	0.0284974i	−0.311603	−	0.950212i	$-0.600866\pi$
$829$	−3.06218	+	0.820508i	−0.106354	+	0.0284974i	0.205250	+	0.978710i	$0.434199\pi$
$830$	−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	$0.0989096\pi$
$839$			17.7128i			0.611514i	−0.952110	+	0.305757i	$0.901090\pi$
$840$	−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	−0.880556	−	0.473942i	$-0.842831\pi$
$853$	−11.8756	+	11.8756i	−0.406614	+	0.406614i	0.473942	+	0.880556i	$0.342831\pi$
$854$	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	0.689170	−	0.724600i	$-0.257975\pi$
$857$	11.8923	+	6.86603i	0.406233	+	0.234539i	−0.282937	+	0.959139i	$0.591309\pi$
$858$	−5.73205	−	9.92820i	−0.195689	−	0.338943i
$859$	13.6244	+	3.65064i	0.464857	+	0.124558i	0.483643	−	0.875265i	$-0.339313\pi$
$859$	13.6244	+	3.65064i	0.464857	+	0.124558i	−0.0187858	+	0.999824i	$0.505980\pi$
$860$	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	0.997834	+	0.0657797i	$0.0209535\pi$
$863$	16.3301	+	28.2846i	0.555884	+	0.962819i	−0.441950	+	0.897040i	$0.645713\pi$
$864$		−	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	−0.678431	−	0.734664i	$-0.737340\pi$
$877$	8.18653	−	30.5526i	0.276440	−	1.03169i	0.954871	−	0.297022i	$-0.0959936\pi$
$878$	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	0.617952	−	0.786216i	$-0.287963\pi$
$883$	−5.00000	−	5.00000i	−0.168263	−	0.168263i	−0.786216	+	0.617952i	$0.787963\pi$
$884$	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	−0.986139	−	0.165924i	$-0.946939\pi$
$887$	−39.7750	+	22.9641i	−1.33551	+	0.771059i	−0.349375	+	0.936983i	$0.613606\pi$
$888$	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	0.976889	+	0.213748i	$0.0685672\pi$
$907$	7.16025	+	26.7224i	0.237752	+	0.887304i	−0.739136	+	0.673556i	$0.764766\pi$
$908$	−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	−0.738313	−	0.674458i	$-0.764377\pi$
$919$	−15.8660	+	9.16025i	−0.523372	+	0.302169i	0.214941	+	0.976627i	$0.431044\pi$
$920$	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	−0.905110	−	0.425178i	$-0.860211\pi$
$929$	−25.0167	−	43.3301i	−0.820770	−	1.42162i	0.0843396	−	0.996437i	$-0.473122\pi$
$930$	−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	$-0.842496\pi$
$937$		−	29.0718i		−	0.949734i	0.880058	−	0.474867i	$-0.157504\pi$
$938$	−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	−0.621017	−	0.783797i	$-0.713280\pi$
$941$	−23.5263	+	6.30385i	−0.766935	+	0.205500i	−0.145918	+	0.989297i	$0.546614\pi$
$942$	−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	−0.985448	−	0.169979i	$-0.945630\pi$
$947$	−1.44744	+	5.40192i	−0.0470355	+	0.175539i	0.938412	+	0.345518i	$0.112297\pi$
$948$	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	$0.0863050\pi$
$953$			16.5359i			0.535650i	−0.963468	+	0.267825i	$0.913695\pi$
$954$	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	$-0.579807\pi$
$967$		−	60.2487i		−	1.93747i	0.248102	−	0.968734i	$-0.420193\pi$
$968$	−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	−0.713608	−	0.700545i	$-0.752940\pi$
$971$	−52.4090	−	14.0429i	−1.68188	−	0.450659i	−0.968275	+	0.249885i	$0.919607\pi$
$972$	−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	−0.695706	−	0.718327i	$-0.744908\pi$
$977$	8.57180	−	14.8468i	0.274236	−	0.474991i	0.969942	+	0.243336i	$0.0782417\pi$
$978$	−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	0.747705	−	0.664031i	$-0.231156\pi$
$983$	17.1340	+	9.89230i	0.546489	+	0.315516i	−0.201216	+	0.979547i	$0.564489\pi$
$984$	−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	−0.791461	−	0.611219i	$-0.790679\pi$
$991$	4.20577	−	7.28461i	0.133601	−	0.231403i	0.925062	+	0.379816i	$0.124013\pi$
$992$	−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	0.971998	−	0.234988i	$-0.0755051\pi$
$997$	0.401924	+	1.50000i	0.0127291	+	0.0475055i	−0.959269	+	0.282494i	$0.908838\pi$
$998$	−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.109.1	yes	4
4.3	odd	2		448.2.ba.a.81.1		4
7.2	even	3		112.2.w.a.93.1	yes	4
7.3	odd	6		784.2.m.d.589.2		4
7.4	even	3		784.2.m.e.589.2		4
7.5	odd	6		784.2.x.a.765.1		4
7.6	odd	2		784.2.x.h.557.1		4
8.3	odd	2		896.2.ba.c.417.1		4
8.5	even	2		896.2.ba.b.417.1		4
16.3	odd	4		896.2.ba.a.865.1		4
16.5	even	4		112.2.w.a.53.1	✓	4
16.11	odd	4		448.2.ba.b.305.1		4
16.13	even	4		896.2.ba.d.865.1		4
28.23	odd	6		448.2.ba.b.401.1		4
56.37	even	6		896.2.ba.d.289.1		4
56.51	odd	6		896.2.ba.a.289.1		4
112.5	odd	12		784.2.x.h.373.1		4
112.37	even	12	inner	112.2.w.b.37.1	yes	4
112.51	odd	12		896.2.ba.c.737.1		4
112.53	even	12		784.2.m.e.197.2		4
112.69	odd	4		784.2.x.a.165.1		4
112.93	even	12		896.2.ba.b.737.1		4
112.101	odd	12		784.2.m.d.197.2		4
112.107	odd	12		448.2.ba.a.177.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.53.1	✓	4	16.5	even	4
112.2.w.a.93.1	yes	4	7.2	even	3
112.2.w.b.37.1	yes	4	112.37	even	12	inner
112.2.w.b.109.1	yes	4	1.1	even	1	trivial
448.2.ba.a.81.1		4	4.3	odd	2
448.2.ba.a.177.1		4	112.107	odd	12
448.2.ba.b.305.1		4	16.11	odd	4
448.2.ba.b.401.1		4	28.23	odd	6
784.2.m.d.197.2		4	112.101	odd	12
784.2.m.d.589.2		4	7.3	odd	6
784.2.m.e.197.2		4	112.53	even	12
784.2.m.e.589.2		4	7.4	even	3
784.2.x.a.165.1		4	112.69	odd	4
784.2.x.a.765.1		4	7.5	odd	6
784.2.x.h.373.1		4	112.5	odd	12
784.2.x.h.557.1		4	7.6	odd	2
896.2.ba.a.289.1		4	56.51	odd	6
896.2.ba.a.865.1		4	16.3	odd	4
896.2.ba.b.417.1		4	8.5	even	2
896.2.ba.b.737.1		4	112.93	even	12
896.2.ba.c.417.1		4	8.3	odd	2
896.2.ba.c.737.1		4	112.51	odd	12
896.2.ba.d.289.1		4	56.37	even	6
896.2.ba.d.865.1		4	16.13	even	4

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 $\F_{q}$
Belyi maps

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9} + 6 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 8 q^{14} + 12 q^{15} - 16 q^{16} - 6 q^{17} - 4 q^{18} + 10 q^{19} + 12 q^{20} + 8 q^{21} - 18 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) \) 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

Introduction

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