LMFDB - Embedded newform 112.2.w.a.53.1

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)

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);

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")

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,-2] 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			53.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	112.53
Dual form			112.2.w.a.93.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 + 0.366025i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.232051 - 0.866025i) 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} +1.26795i q^{10} +(2.86603 - 0.767949i) q^{11} +(-0.732051 - 0.732051i) q^{12} +(3.73205 - 3.73205i) q^{13} +(3.09808 + 2.09808i) q^{14} -0.464102 q^{15} +(2.00000 - 3.46410i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(-2.73205 + 2.73205i) q^{18} +(-2.86603 - 0.767949i) q^{19} +(-0.464102 - 1.73205i) q^{20} +(-0.767949 + 1.13397i) 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} +(-3.73205 + 6.46410i) q^{26} +(-2.09808 - 2.09808i) q^{27} +(-5.00000 - 1.73205i) q^{28} +(-0.267949 + 0.267949i) q^{29} +(0.633975 - 0.169873i) q^{30} +(-1.86603 + 3.23205i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-0.767949 - 1.33013i) q^{33} +(2.36603 - 8.83013i) q^{34} +(-2.13397 + 1.03590i) q^{35} +(2.73205 - 4.73205i) q^{36} +(0.303848 - 1.13397i) q^{37} +4.19615 q^{38} +(-2.36603 - 1.36603i) q^{39} +(1.26795 + 2.19615i) q^{40} +4.92820i q^{41} +(0.633975 - 1.83013i) q^{42} +(6.46410 + 6.46410i) q^{43} +(4.19615 - 4.19615i) q^{44} +(-0.633975 - 2.36603i) q^{45} +(4.46410 - 4.46410i) 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} +(3.23205 + 0.866025i) q^{51} +(2.73205 - 10.1962i) q^{52} +(3.96410 - 1.06218i) q^{53} +(3.63397 + 2.09808i) q^{54} -2.66025i q^{55} +(7.46410 + 0.535898i) q^{56} +1.53590i q^{57} +(0.267949 - 0.464102i) q^{58} +(11.3301 - 3.03590i) q^{59} +(-0.803848 + 0.464102i) q^{60} +(-6.96410 - 1.86603i) q^{61} +(1.36603 - 5.09808i) q^{62} +(-6.83013 - 2.36603i) q^{63} -8.00000i q^{64} +(-2.36603 - 4.09808i) q^{65} +(1.53590 + 1.53590i) q^{66} +(1.33013 + 4.96410i) q^{67} +12.9282i q^{68} +(1.63397 + 1.63397i) q^{69} +(2.53590 - 2.19615i) q^{70} -0.535898i q^{71} +(-2.00000 + 7.46410i) q^{72} +(-6.23205 - 3.59808i) q^{73} +1.66025i q^{74} +(0.562178 - 2.09808i) q^{75} +(-5.73205 + 1.53590i) q^{76} +(-6.50000 - 4.40192i) q^{77} +(3.73205 + 1.00000i) q^{78} +(8.33013 + 14.4282i) q^{79} +(-2.53590 - 2.53590i) q^{80} +(3.33013 - 5.76795i) q^{81} +(-1.80385 - 6.73205i) q^{82} +(1.53590 - 1.53590i) q^{83} +(-0.196152 + 2.73205i) q^{84} +(4.09808 + 4.09808i) q^{85} +(-11.1962 - 6.46410i) 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} +(-13.9282 - 1.00000i) q^{91} +(-4.46410 + 7.73205i) q^{92} +(1.86603 + 0.500000i) q^{93} +(4.26795 + 4.26795i) q^{94} +(-1.33013 + 2.30385i) q^{95} +2.92820 q^{96} -2.92820 q^{97} +(-1.16987 - 9.83013i) q^{98} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} - 6 q^{5} - 2 q^{6} - 8 q^{8} + 6 q^{9} + 8 q^{11} + 4 q^{12} + 8 q^{13} + 2 q^{14} + 12 q^{15} + 8 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} + 12 q^{20} - 10 q^{21} - 18 q^{22} - 12 q^{23}+ \cdots + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 - 6 * q^5 - 2 * q^6 - 8 * q^8 + 6 * q^9 + 8 * q^11 + 4 * q^12 + 8 * q^13 + 2 * q^14 + 12 * q^15 + 8 * q^16 - 6 * q^17 - 4 * q^18 - 8 * q^19 + 12 * q^20 - 10 * q^21 - 18 * q^22 - 12 * q^23 + 12 * q^24 + 18 * q^25 - 8 * q^26 + 2 * q^27 - 20 * q^28 - 8 * q^29 + 6 * q^30 - 4 * q^31 + 8 * q^32 - 10 * q^33 + 6 * q^34 - 12 * q^35 + 4 * q^36 + 22 * q^37 - 4 * q^38 - 6 * q^39 + 12 * q^40 + 6 * q^42 + 12 * q^43 - 4 * q^44 - 6 * q^45 + 4 * q^46 - 12 * q^47 - 8 * q^48 - 4 * q^49 - 16 * q^50 + 6 * q^51 + 4 * q^52 + 2 * q^53 + 18 * q^54 + 16 * q^56 + 8 * q^58 + 28 * q^59 - 24 * q^60 - 14 * q^61 + 2 * q^62 - 10 * q^63 - 6 * q^65 + 20 * q^66 - 12 * q^67 + 10 * q^69 + 24 * q^70 - 8 * q^72 - 18 * q^73 - 22 * q^75 - 16 * q^76 - 26 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 - 4 * q^81 - 28 * q^82 + 20 * q^83 + 20 * q^84 + 6 * q^85 - 24 * q^86 + 18 * q^87 + 4 * q^88 + 18 * q^89 - 28 * q^91 - 4 * q^92 + 4 * q^93 + 24 * q^94 + 12 * q^95 - 16 * q^96 + 16 * q^97 - 22 * q^98 + 16 * q^99

Character values

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

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

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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	−0.133975	−	0.500000i	−0.0773503	−	0.288675i	0.916406	−	0.400251i	$-0.131077\pi$
$3$	−0.133975	−	0.500000i	−0.0773503	−	0.288675i	−0.993756	+	0.111576i	$0.964410\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	0.232051	−	0.866025i	0.103776	−	0.387298i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	0.232051	−	0.866025i	0.103776	−	0.387298i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$	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
$10$			1.26795i			0.400961i
$11$	2.86603	−	0.767949i	0.864139	−	0.231545i	0.200587	−	0.979676i	$-0.435715\pi$
$11$	2.86603	−	0.767949i	0.864139	−	0.231545i	0.663552	+	0.748130i	$0.269048\pi$
$12$	−0.732051	−	0.732051i	−0.211325	−	0.211325i
$13$	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	$-0.0113734\pi$
$14$	3.09808	+	2.09808i	0.827996	+	0.560734i
$15$	−0.464102			−0.119831
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−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	$0.879901\pi$
$18$	−2.73205	+	2.73205i	−0.643951	+	0.643951i
$19$	−2.86603	−	0.767949i	−0.657511	−	0.176180i	−0.0853887	−	0.996348i	$-0.527213\pi$
$19$	−2.86603	−	0.767949i	−0.657511	−	0.176180i	−0.572123	+	0.820168i	$0.693880\pi$
$20$	−0.464102	−	1.73205i	−0.103776	−	0.387298i
$21$	−0.767949	+	1.13397i	−0.167580	+	0.247454i
$22$	−3.63397	+	2.09808i	−0.774766	+	0.447311i
$23$	−3.86603	+	2.23205i	−0.806122	+	0.465415i	−0.845607	−	0.533805i	$-0.820761\pi$
$23$	−3.86603	+	2.23205i	−0.806122	+	0.465415i	0.0394853	+	0.999220i	$0.487428\pi$
$24$	1.26795	+	0.732051i	0.258819	+	0.149429i
$25$	3.63397	+	2.09808i	0.726795	+	0.419615i
$26$	−3.73205	+	6.46410i	−0.731915	+	1.26771i
$27$	−2.09808	−	2.09808i	−0.403775	−	0.403775i
$28$	−5.00000	−	1.73205i	−0.944911	−	0.327327i
$29$	−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	$0.261202\pi$
$30$	0.633975	−	0.169873i	0.115747	−	0.0310144i
$31$	−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	$0.275453\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$	−0.767949	−	1.33013i	−0.133683	−	0.231545i
$34$	2.36603	−	8.83013i	0.405770	−	1.51435i
$35$	−2.13397	+	1.03590i	−0.360708	+	0.175099i
$36$	2.73205	−	4.73205i	0.455342	−	0.788675i
$37$	0.303848	−	1.13397i	0.0499522	−	0.186424i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	0.303848	−	1.13397i	0.0499522	−	0.186424i	0.986394	+	0.164399i	$0.0525685\pi$
$38$	4.19615			0.680706
$39$	−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	$0.874261\pi$
$42$	0.633975	−	1.83013i	0.0978244	−	0.282395i
$43$	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	$0.504499\pi$
$44$	4.19615	−	4.19615i	0.632594	−	0.632594i
$45$	−0.633975	−	2.36603i	−0.0945074	−	0.352706i
$46$	4.46410	−	4.46410i	0.658196	−	0.658196i
$47$	−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
$51$	3.23205	+	0.866025i	0.452578	+	0.121268i
$52$	2.73205	−	10.1962i	0.378867	−	1.41395i
$53$	3.96410	−	1.06218i	0.544511	−	0.145901i	0.0239302	−	0.999714i	$-0.492382\pi$
$53$	3.96410	−	1.06218i	0.544511	−	0.145901i	0.520581	+	0.853812i	$0.325715\pi$
$54$	3.63397	+	2.09808i	0.494521	+	0.285512i
$55$		−	2.66025i		−	0.358709i
$56$	7.46410	+	0.535898i	0.997433	+	0.0716124i
$57$			1.53590i			0.203435i
$58$	0.267949	−	0.464102i	0.0351835	−	0.0609395i
$59$	11.3301	−	3.03590i	1.47506	−	0.395240i	0.570395	−	0.821370i	$-0.306790\pi$
$59$	11.3301	−	3.03590i	1.47506	−	0.395240i	0.904662	+	0.426130i	$0.140123\pi$
$60$	−0.803848	+	0.464102i	−0.103776	+	0.0599153i
$61$	−6.96410	−	1.86603i	−0.891662	−	0.238920i	−0.216230	−	0.976342i	$-0.569376\pi$
$61$	−6.96410	−	1.86603i	−0.891662	−	0.238920i	−0.675432	+	0.737422i	$0.736043\pi$
$62$	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
$66$	1.53590	+	1.53590i	0.189056	+	0.189056i
$67$	1.33013	+	4.96410i	0.162501	+	0.606462i	0.998346	+	0.0574958i	$0.0183116\pi$
$67$	1.33013	+	4.96410i	0.162501	+	0.606462i	−0.835845	+	0.548966i	$0.815022\pi$
$68$			12.9282i			1.56777i
$69$	1.63397	+	1.63397i	0.196707	+	0.196707i
$70$	2.53590	−	2.19615i	0.303098	−	0.262490i
$71$		−	0.535898i		−	0.0635994i	−0.999494	−	0.0317997i	$-0.989876\pi$
$71$		−	0.535898i		−	0.0635994i	0.999494	−	0.0317997i	$-0.0101239\pi$
$72$	−2.00000	+	7.46410i	−0.235702	+	0.879653i
$73$	−6.23205	−	3.59808i	−0.729406	−	0.421123i	0.0887986	−	0.996050i	$-0.471697\pi$
$73$	−6.23205	−	3.59808i	−0.729406	−	0.421123i	−0.818205	+	0.574927i	$0.805031\pi$
$74$			1.66025i			0.193001i
$75$	0.562178	−	2.09808i	0.0649147	−	0.242265i
$76$	−5.73205	+	1.53590i	−0.657511	+	0.176180i
$77$	−6.50000	−	4.40192i	−0.740744	−	0.501646i
$78$	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	$0.446730\pi$
$80$	−2.53590	−	2.53590i	−0.283522	−	0.283522i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$	−1.80385	−	6.73205i	−0.199202	−	0.743431i
$83$	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	$0.211964\pi$
$84$	−0.196152	+	2.73205i	−0.0214020	+	0.298091i
$85$	4.09808	+	4.09808i	0.444499	+	0.444499i
$86$	−11.1962	−	6.46410i	−1.20731	−	0.697042i
$87$	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	$-0.577858\pi$
$89$	4.50000	−	2.59808i	0.476999	−	0.275396i	0.719165	+	0.694839i	$0.244525\pi$
$90$	1.73205	+	3.00000i	0.182574	+	0.316228i
$91$	−13.9282	−	1.00000i	−1.46007	−	0.104828i
$92$	−4.46410	+	7.73205i	−0.465415	+	0.806122i
$93$	1.86603	+	0.500000i	0.193498	+	0.0518476i
$94$	4.26795	+	4.26795i	0.440205	+	0.440205i
$95$	−1.33013	+	2.30385i	−0.136468	+	0.236370i
$96$	2.92820			0.298858
$97$	−2.92820			−0.297314			−0.148657	−	0.988889i	$-0.547495\pi$
$97$	−2.92820			−0.297314			−0.148657	+	0.988889i	$0.547495\pi$
$98$	−1.16987	−	9.83013i	−0.118175	−	0.992993i
$99$	5.73205	−	5.73205i	0.576093	−	0.576093i
$100$	8.39230			0.839230
$101$	−18.8923	+	5.06218i	−1.87985	+	0.503706i	−0.880283	+	0.474450i	$0.842647\pi$
$101$	−18.8923	+	5.06218i	−1.87985	+	0.503706i	−0.999572	+	0.0292559i	$0.990686\pi$
$102$	−4.73205			−0.468543
$103$	5.59808	−	3.23205i	0.551595	−	0.318463i	−0.198170	−	0.980168i	$-0.563500\pi$
$103$	5.59808	−	3.23205i	0.551595	−	0.318463i	0.749765	+	0.661704i	$0.230167\pi$
$104$			14.9282i			1.46383i
$105$	0.803848	+	0.928203i	0.0784475	+	0.0905834i
$106$	−5.02628	+	2.90192i	−0.488195	+	0.281860i
$107$	−0.866025	+	3.23205i	−0.0837218	+	0.312454i	−0.995069	−	0.0991843i	$-0.968377\pi$
$107$	−0.866025	+	3.23205i	−0.0837218	+	0.312454i	0.911347	+	0.411638i	$0.135043\pi$
$108$	−5.73205	−	1.53590i	−0.551567	−	0.147792i
$109$	0.571797	+	2.13397i	0.0547682	+	0.204398i	0.987888	−	0.155167i	$-0.0495917\pi$
$109$	0.571797	+	2.13397i	0.0547682	+	0.204398i	−0.933120	+	0.359565i	$0.882925\pi$
$110$	0.973721	+	3.63397i	0.0928406	+	0.346486i
$111$	−0.607695			−0.0576799
$112$	−10.3923	+	2.00000i	−0.981981	+	0.188982i
$113$	−1.46410			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$113$	−1.46410			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$114$	−0.562178	−	2.09808i	−0.0526528	−	0.196503i
$115$	1.03590	+	3.86603i	0.0965980	+	0.360509i
$116$	−0.196152	+	0.732051i	−0.0182123	+	0.0679692i
$117$	3.73205	−	13.9282i	0.345028	−	1.28766i
$118$	−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
$122$	10.1962			0.923116
$123$	2.46410	−	0.660254i	0.222181	−	0.0595331i
$124$			7.46410i			0.670296i
$125$	5.83013	−	5.83013i	0.521462	−	0.521462i
$126$	10.1962	+	0.732051i	0.908345	+	0.0652163i
$127$	9.46410			0.839803			0.419902	−	0.907570i	$-0.362065\pi$
$127$	9.46410			0.839803			0.419902	+	0.907570i	$0.362065\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	2.36603	−	4.09808i	0.208317	−	0.360815i
$130$	4.73205	+	4.73205i	0.415028	+	0.415028i
$131$	7.59808	+	2.03590i	0.663847	+	0.177877i	0.574982	−	0.818166i	$-0.305009\pi$
$131$	7.59808	+	2.03590i	0.663847	+	0.177877i	0.0888654	+	0.996044i	$0.471676\pi$
$132$	−2.66025	−	1.53590i	−0.231545	−	0.133683i
$133$	3.42820	+	7.06218i	0.297263	+	0.612368i
$134$	−3.63397	−	6.29423i	−0.313928	−	0.543739i
$135$	−2.30385	+	1.33013i	−0.198284	+	0.114479i
$136$	−4.73205	−	17.6603i	−0.405770	−	1.51435i
$137$	−15.2321	−	8.79423i	−1.30136	−	0.751342i	−0.320724	−	0.947173i	$-0.603926\pi$
$137$	−15.2321	−	8.79423i	−1.30136	−	0.751342i	−0.980638	+	0.195831i	$0.937260\pi$
$138$	−2.83013	−	1.63397i	−0.240916	−	0.139093i
$139$	−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	$-0.503758\pi$
$140$	−2.66025	+	3.92820i	−0.224833	+	0.331994i
$141$	−1.56218	+	1.56218i	−0.131559	+	0.131559i
$142$	0.196152	+	0.732051i	0.0164607	+	0.0614323i
$143$	7.83013	−	13.5622i	0.654788	−	1.13413i
$144$		−	10.9282i		−	0.910684i
$145$	0.169873	+	0.294229i	0.0141072	+	0.0244344i
$146$	9.83013	+	2.63397i	0.813547	+	0.217989i
$147$	3.59808	−	0.428203i	0.296764	−	0.0353176i
$148$	−0.607695	−	2.26795i	−0.0499522	−	0.186424i
$149$	2.03590	−	7.59808i	0.166787	−	0.622459i	−0.831018	−	0.556245i	$-0.812242\pi$
$149$	2.03590	−	7.59808i	0.166787	−	0.622459i	0.997805	−	0.0662134i	$-0.0210918\pi$
$150$			3.07180i			0.250811i
$151$	−9.86603	−	5.69615i	−0.802886	−	0.463546i	0.0415935	−	0.999135i	$-0.486757\pi$
$151$	−9.86603	−	5.69615i	−0.802886	−	0.463546i	−0.844479	+	0.535588i	$0.820090\pi$
$152$	7.26795	−	4.19615i	0.589509	−	0.340353i
$153$			17.6603i			1.42775i
$154$	10.4904	+	3.63397i	0.845339	+	0.292834i
$155$	2.36603	+	2.36603i	0.190044	+	0.190044i
$156$	−5.46410			−0.437478
$157$	4.89230	+	18.2583i	0.390448	+	1.45717i	0.829396	+	0.558661i	$0.188685\pi$
$157$	4.89230	+	18.2583i	0.390448	+	1.45717i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−16.6603	−	16.6603i	−1.32542	−	1.32542i
$159$	−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
$163$	−12.0622	−	3.23205i	−0.944783	−	0.253154i	−0.246636	−	0.969108i	$-0.579325\pi$
$163$	−12.0622	−	3.23205i	−0.944783	−	0.253154i	−0.698147	+	0.715954i	$0.745992\pi$
$164$	4.92820	+	8.53590i	0.384828	+	0.666542i
$165$	−1.33013	+	0.356406i	−0.103550	+	0.0277462i
$166$	−1.53590	+	2.66025i	−0.119209	+	0.206476i
$167$			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
$170$	−7.09808	−	4.09808i	−0.544398	−	0.314308i
$171$	−7.83013	+	2.09808i	−0.598785	+	0.160444i
$172$	17.6603	+	4.73205i	1.34658	+	0.360815i
$173$	−2.23205	−	0.598076i	−0.169700	−	0.0454709i	0.172969	−	0.984927i	$-0.444664\pi$
$173$	−2.23205	−	0.598076i	−0.169700	−	0.0454709i	−0.342668	+	0.939456i	$0.611331\pi$
$174$	−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
$178$	−5.19615	+	5.19615i	−0.389468	+	0.389468i
$179$	−2.40192	−	8.96410i	−0.179528	−	0.670008i	−0.995736	−	0.0922498i	$-0.970594\pi$
$179$	−2.40192	−	8.96410i	−0.179528	−	0.670008i	0.816208	−	0.577759i	$-0.196072\pi$
$180$	−3.46410	−	3.46410i	−0.258199	−	0.258199i
$181$	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	$0.501448\pi$
$182$	19.3923	−	3.73205i	1.43745	−	0.276638i
$183$			3.73205i			0.275881i
$184$	3.26795	−	12.1962i	0.240916	−	0.899112i
$185$	−0.911543	−	0.526279i	−0.0670180	−	0.0386928i
$186$	−2.73205			−0.200324
$187$	−4.96410	+	18.5263i	−0.363011	+	1.35478i
$188$	−7.39230	−	4.26795i	−0.539139	−	0.311272i
$189$	−0.562178	+	7.83013i	−0.0408924	+	0.569558i
$190$	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	$0.934774\pi$
$192$	−4.00000	+	1.07180i	−0.288675	+	0.0773503i
$193$	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	$-0.143734\pi$
$194$	4.00000	−	1.07180i	0.287183	−	0.0769505i
$195$	−1.73205	+	1.73205i	−0.124035	+	0.124035i
$196$	5.19615	+	13.0000i	0.371154	+	0.928571i
$197$	−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	$-0.567053\pi$
$198$	−5.73205	+	9.92820i	−0.407359	+	0.705567i
$199$	10.3301	+	5.96410i	0.732283	+	0.422784i	0.819257	−	0.573427i	$-0.194386\pi$
$199$	10.3301	+	5.96410i	0.732283	+	0.422784i	−0.0869736	+	0.996211i	$0.527720\pi$
$200$	−11.4641	+	3.07180i	−0.810634	+	0.217209i
$201$	2.30385	−	1.33013i	0.162501	−	0.0938199i
$202$	23.9545	−	13.8301i	1.68543	−	0.973084i
$203$	1.00000	+	0.0717968i	0.0701862	+	0.00503915i
$204$	6.46410	−	1.73205i	0.452578	−	0.121268i
$205$	4.26795	+	1.14359i	0.298087	+	0.0798720i
$206$	−6.46410	+	6.46410i	−0.450375	+	0.450375i
$207$	−6.09808	+	10.5622i	−0.423846	+	0.734122i
$208$	−5.46410	−	20.3923i	−0.378867	−	1.41395i
$209$	−8.80385			−0.608975
$210$	−1.43782	−	0.973721i	−0.0992192	−	0.0671931i
$211$	−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	$0.967562\pi$
$212$	5.80385	−	5.80385i	0.398610	−	0.398610i
$213$	−0.267949	+	0.0717968i	−0.0183596	+	0.00491943i
$214$		−	4.73205i		−	0.323476i
$215$	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
$219$	−0.964102	+	3.59808i	−0.0651479	+	0.243135i
$220$	−2.66025	−	4.60770i	−0.179354	−	0.310651i
$221$	8.83013	+	32.9545i	0.593979	+	2.21676i
$222$	0.830127	−	0.222432i	0.0557145	−	0.0149286i
$223$	9.85641			0.660034			0.330017	−	0.943975i	$-0.392946\pi$
$223$	9.85641			0.660034			0.330017	+	0.943975i	$0.392946\pi$
$224$	13.4641	−	6.53590i	0.899608	−	0.436698i
$225$	11.4641			0.764273
$226$	2.00000	−	0.535898i	0.133038	−	0.0356474i
$227$	−2.99038	−	11.1603i	−0.198479	−	0.740732i	−0.991339	−	0.131329i	$-0.958076\pi$
$227$	−2.99038	−	11.1603i	−0.198479	−	0.740732i	0.792860	−	0.609403i	$-0.208591\pi$
$228$	1.53590	+	2.66025i	0.101717	+	0.176180i
$229$	−3.57180	+	13.3301i	−0.236031	+	0.880880i	0.741650	+	0.670787i	$0.234043\pi$
$229$	−3.57180	+	13.3301i	−0.236031	+	0.880880i	−0.977681	+	0.210093i	$0.932623\pi$
$230$	−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	$-0.675049\pi$
$233$	−0.696152	+	0.401924i	−0.0456065	+	0.0263309i	0.477023	+	0.878891i	$0.341716\pi$
$234$			20.3923i			1.33309i
$235$	−3.69615	+	0.990381i	−0.241110	+	0.0646053i
$236$	16.5885	−	16.5885i	1.07982	−	1.07982i
$237$	6.09808	−	6.09808i	0.396113	−	0.396113i
$238$	−21.7583	+	10.5622i	−1.41038	+	0.684644i
$239$	−8.53590			−0.552141			−0.276071	−	0.961137i	$-0.589032\pi$
$239$	−8.53590			−0.552141			−0.276071	+	0.961137i	$0.589032\pi$
$240$	−0.928203	+	1.60770i	−0.0599153	+	0.103776i
$241$	−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	$0.314743\pi$
$242$	2.19615	−	2.19615i	0.141174	−	0.141174i
$243$	−11.9282	−	3.19615i	−0.765195	−	0.205033i
$244$	−13.9282	+	3.73205i	−0.891662	+	0.238920i
$245$	5.76795	+	2.47372i	0.368501	+	0.158040i
$246$	−3.12436	+	1.80385i	−0.199202	+	0.115009i
$247$	−13.5622	+	7.83013i	−0.862941	+	0.498219i
$248$	−2.73205	−	10.1962i	−0.173485	−	0.647456i
$249$	−0.973721	−	0.562178i	−0.0617070	−	0.0356266i
$250$	−5.83013	+	10.0981i	−0.368730	+	0.638658i
$251$	−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	$-0.537343\pi$
$252$	−14.1962	+	2.73205i	−0.894274	+	0.172103i
$253$	−9.36603	+	9.36603i	−0.588837	+	0.588837i
$254$	−12.9282	+	3.46410i	−0.811188	+	0.217357i
$255$	1.50000	−	2.59808i	0.0939336	−	0.162698i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	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
$259$	−2.79423	+	1.35641i	−0.173625	+	0.0842830i
$260$	−8.19615	−	4.73205i	−0.508304	−	0.293469i
$261$	−0.267949	+	1.00000i	−0.0165856	+	0.0618984i
$262$	−11.1244			−0.687265
$263$	−3.99038	−	2.30385i	−0.246057	−	0.142061i	0.371900	−	0.928273i	$-0.378706\pi$
$263$	−3.99038	−	2.30385i	−0.246057	−	0.142061i	−0.617958	+	0.786211i	$0.712040\pi$
$264$	4.19615	+	1.12436i	0.258255	+	0.0691993i
$265$		−	3.67949i		−	0.226029i
$266$	−7.26795	−	8.39230i	−0.445627	−	0.514565i
$267$	−1.90192	−	1.90192i	−0.116396	−	0.116396i
$268$	7.26795	+	7.26795i	0.443961	+	0.443961i
$269$	−2.62436	−	9.79423i	−0.160010	−	0.597165i	−0.998624	−	0.0524390i	$-0.983300\pi$
$269$	−2.62436	−	9.79423i	−0.160010	−	0.597165i	0.838614	−	0.544726i	$-0.183366\pi$
$270$	2.66025	−	2.66025i	0.161898	−	0.161898i
$271$	−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
$275$	12.0263	+	3.22243i	0.725212	+	0.194320i
$276$	4.46410	+	1.19615i	0.268707	+	0.0719999i
$277$	4.50000	−	1.20577i	0.270379	−	0.0724478i	−0.121082	−	0.992642i	$-0.538636\pi$
$277$	4.50000	−	1.20577i	0.270379	−	0.0724478i	0.391461	+	0.920195i	$0.371970\pi$
$278$	20.6603	+	11.9282i	1.23912	+	0.715406i
$279$			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	$0.991186\pi$
$282$	1.56218	−	2.70577i	0.0930263	−	0.161126i
$283$	14.5263	−	3.89230i	0.863498	−	0.231374i	0.200224	−	0.979750i	$-0.435833\pi$
$283$	14.5263	−	3.89230i	0.863498	−	0.231374i	0.663274	+	0.748377i	$0.269166\pi$
$284$	−0.535898	−	0.928203i	−0.0317997	−	0.0550787i
$285$	1.33013	+	0.356406i	0.0787899	+	0.0211117i
$286$	−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
$290$	−0.339746	−	0.339746i	−0.0199506	−	0.0199506i
$291$	0.392305	+	1.46410i	0.0229973	+	0.0858272i
$292$	−14.3923			−0.842246
$293$	−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	$0.856210\pi$
$294$	−4.75833	+	1.90192i	−0.277511	+	0.110922i
$295$		−	10.5167i		−	0.612304i
$296$	1.66025	+	2.87564i	0.0965003	+	0.167143i
$297$	−7.62436	−	4.40192i	−0.442410	−	0.255426i
$298$			11.1244i			0.644417i
$299$	−6.09808	+	22.7583i	−0.352661	+	1.31615i
$300$	−1.12436	−	4.19615i	−0.0649147	−	0.242265i
$301$	1.73205	−	24.1244i	0.0998337	−	1.39050i
$302$	15.5622	+	4.16987i	0.895503	+	0.239949i
$303$	5.06218	+	8.76795i	0.290815	+	0.503706i
$304$	−8.39230	+	8.39230i	−0.481332	+	0.481332i
$305$	−3.23205	+	5.59808i	−0.185067	+	0.320545i
$306$	−6.46410	−	24.1244i	−0.369528	−	1.37910i
$307$	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	$0.131681\pi$
$308$	−15.6603	−	1.12436i	−0.892326	−	0.0640661i
$309$	−2.36603	−	2.36603i	−0.134598	−	0.134598i
$310$	−4.09808	−	2.36603i	−0.232755	−	0.134381i
$311$	−5.59808	−	3.23205i	−0.317438	−	0.183273i	0.332812	−	0.942993i	$-0.392002\pi$
$311$	−5.59808	−	3.23205i	−0.317438	−	0.183273i	−0.650250	+	0.759720i	$0.725336\pi$
$312$	7.46410	−	2.00000i	0.422572	−	0.113228i
$313$	18.6962	−	10.7942i	1.05677	−	0.610126i	0.132232	−	0.991219i	$-0.457786\pi$
$313$	18.6962	−	10.7942i	1.05677	−	0.610126i	0.924537	+	0.381093i	$0.124452\pi$
$314$	−13.3660	−	23.1506i	−0.754288	−	1.30647i
$315$	−3.63397	+	5.36603i	−0.204751	+	0.302341i
$316$	28.8564	+	16.6603i	1.62330	+	0.937213i
$317$	14.1603	+	3.79423i	0.795319	+	0.213105i	0.633528	−	0.773720i	$-0.281606\pi$
$317$	14.1603	+	3.79423i	0.795319	+	0.213105i	0.161791	+	0.986825i	$0.448273\pi$
$318$	2.12436	+	2.12436i	0.119128	+	0.119128i
$319$	−0.562178	+	0.973721i	−0.0314759	+	0.0545179i
$320$	−6.92820	−	1.85641i	−0.387298	−	0.103776i
$321$	1.73205			0.0966736
$322$	−16.6603	−	1.19615i	−0.928440	−	0.0666590i
$323$	13.5622	−	13.5622i	0.754620	−	0.754620i
$324$		−	13.3205i		−	0.740028i
$325$	21.3923	−	5.73205i	1.18663	−	0.317957i
$326$	17.6603			0.978111
$327$	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
$331$	5.25833	−	19.6244i	0.289024	−	1.07865i	−0.656824	−	0.754044i	$-0.728101\pi$
$331$	5.25833	−	19.6244i	0.289024	−	1.07865i	0.945848	−	0.324609i	$-0.105233\pi$
$332$	1.12436	−	4.19615i	0.0617070	−	0.230294i
$333$	−0.830127	−	3.09808i	−0.0454907	−	0.169774i
$334$	−8.00000	−	29.8564i	−0.437741	−	1.63367i
$335$	4.60770			0.251745
$336$	2.39230	+	4.92820i	0.130511	+	0.268856i
$337$	−6.14359			−0.334663			−0.167331	−	0.985901i	$-0.553515\pi$
$337$	−6.14359			−0.334663			−0.167331	+	0.985901i	$0.553515\pi$
$338$	5.43782	+	20.2942i	0.295779	+	1.10386i
$339$	0.196152	+	0.732051i	0.0106535	+	0.0397595i
$340$	11.1962	+	3.00000i	0.607197	+	0.162698i
$341$	−2.86603	+	10.6962i	−0.155204	+	0.579229i
$342$	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
$346$	3.26795			0.175686
$347$	23.5263	−	6.30385i	1.26296	−	0.338408i	0.435628	−	0.900127i	$-0.356526\pi$
$347$	23.5263	−	6.30385i	1.26296	−	0.338408i	0.827329	+	0.561718i	$0.189860\pi$
$348$	0.392305			0.0210297
$349$	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	$0.175535\pi$
$350$	6.85641	+	14.1244i	0.366490	+	0.754979i
$351$	−15.6603			−0.835883
$352$			16.7846i			0.894623i
$353$	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	$-0.0982301\pi$
$354$	6.07180	+	6.07180i	0.322712	+	0.322712i
$355$	−0.464102	−	0.124356i	−0.0246320	−	0.00660011i
$356$	5.19615	−	9.00000i	0.275396	−	0.476999i
$357$	−3.86603	−	7.96410i	−0.204612	−	0.421505i
$358$	6.56218	+	11.3660i	0.346822	+	0.600713i
$359$	3.86603	−	2.23205i	0.204041	−	0.117803i	−0.394498	−	0.918897i	$-0.629081\pi$
$359$	3.86603	−	2.23205i	0.204041	−	0.117803i	0.598539	+	0.801094i	$0.295748\pi$
$360$	6.00000	+	3.46410i	0.316228	+	0.182574i
$361$	−8.83013	−	5.09808i	−0.464744	−	0.268320i
$362$	−23.1962	−	13.3923i	−1.21916	−	0.703884i
$363$	0.803848	+	0.803848i	0.0421911	+	0.0421911i
$364$	−25.1244	+	12.1962i	−1.31687	+	0.639252i
$365$	−4.56218	+	4.56218i	−0.238795	+	0.238795i
$366$	−1.36603	−	5.09808i	−0.0714033	−	0.266481i
$367$	−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	$0.217766\pi$
$368$			17.8564i			0.930830i
$369$	6.73205	+	11.6603i	0.350457	+	0.607009i
$370$	1.43782	+	0.385263i	0.0747488	+	0.0200289i
$371$	−8.99038	−	6.08846i	−0.466757	−	0.316097i
$372$	3.73205	−	1.00000i	0.193498	−	0.0518476i
$373$	−0.232051	+	0.866025i	−0.0120151	+	0.0448411i	−0.971673	−	0.236329i	$-0.924056\pi$
$373$	−0.232051	+	0.866025i	−0.0120151	+	0.0448411i	0.959658	+	0.281170i	$0.0907224\pi$
$374$		−	27.1244i		−	1.40257i
$375$	−3.69615	−	2.13397i	−0.190868	−	0.110198i
$376$	11.6603	+	3.12436i	0.601332	+	0.161126i
$377$			2.00000i			0.103005i
$378$	−2.09808	−	10.9019i	−0.107913	−	0.560734i
$379$	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	$0.748562\pi$
$380$			5.32051i			0.272936i
$381$	−1.26795	−	4.73205i	−0.0649590	−	0.242430i
$382$	8.66025	+	8.66025i	0.443097	+	0.443097i
$383$	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
$387$	24.1244	+	6.46410i	1.22631	+	0.328589i
$388$	−5.07180	+	2.92820i	−0.257481	+	0.148657i
$389$	−22.3564	+	5.99038i	−1.13351	+	0.303724i	−0.776341	−	0.630313i	$-0.782926\pi$
$389$	−22.3564	+	5.99038i	−1.13351	+	0.303724i	−0.357174	+	0.934038i	$0.616260\pi$
$390$	1.73205	−	3.00000i	0.0877058	−	0.151911i
$391$		−	28.8564i		−	1.45933i
$392$	−11.8564	−	15.8564i	−0.598839	−	0.800869i
$393$		−	4.07180i		−	0.205395i
$394$	28.8564	+	16.6603i	1.45376	+	0.839331i
$395$	14.4282	−	3.86603i	0.725962	−	0.194521i
$396$	4.19615	−	15.6603i	0.210865	−	0.786957i
$397$	−25.6244	−	6.86603i	−1.28605	−	0.344596i	−0.449891	−	0.893084i	$-0.648537\pi$
$397$	−25.6244	−	6.86603i	−1.28605	−	0.344596i	−0.836159	+	0.548488i	$0.815204\pi$
$398$	−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	$0.711137\pi$
$402$	−2.66025	+	2.66025i	−0.132681	+	0.132681i
$403$	5.09808	+	19.0263i	0.253953	+	0.947766i
$404$	−27.6603	+	27.6603i	−1.37615	+	1.37615i
$405$	−4.22243	−	4.22243i	−0.209814	−	0.209814i
$406$	−1.39230	+	0.267949i	−0.0690989	+	0.0132981i
$407$		−	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	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$	−6.24871			−0.308602
$411$	−2.35641	+	8.79423i	−0.116233	+	0.433787i
$412$	6.46410	−	11.1962i	0.318463	−	0.551595i
$413$	−25.6962	−	17.4019i	−1.26442	−	0.856293i
$414$	4.46410	−	16.6603i	0.219399	−	0.818807i
$415$	−0.973721	−	1.68653i	−0.0477981	−	0.0827887i
$416$	14.9282	+	25.8564i	0.731915	+	1.26771i
$417$	−4.36603	+	7.56218i	−0.213805	+	0.370321i
$418$	12.0263	−	3.22243i	0.588225	−	0.157614i
$419$	−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	$0.477898\pi$
$420$	2.32051	+	0.803848i	0.113229	+	0.0392237i
$421$	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	$0.653530\pi$
$422$	15.9282	−	27.5885i	0.775373	−	1.34299i
$423$	−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
$427$	8.33013	+	17.1603i	0.403123	+	0.830443i
$428$	1.73205	+	6.46410i	0.0837218	+	0.312454i
$429$	−7.83013	−	2.09808i	−0.378042	−	0.101296i
$430$	−8.19615	+	8.19615i	−0.395254	+	0.395254i
$431$	−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	$0.902236\pi$
$432$	−11.4641	+	3.07180i	−0.551567	+	0.147792i
$433$	−33.1769			−1.59438			−0.797190	−	0.603728i	$-0.793681\pi$
$433$	−33.1769			−1.59438			−0.797190	+	0.603728i	$0.793681\pi$
$434$	−12.5622	+	6.09808i	−0.603004	+	0.292717i
$435$	0.124356	−	0.124356i	0.00596240	−	0.00596240i
$436$	3.12436	+	3.12436i	0.149629	+	0.149629i
$437$	12.7942	−	3.42820i	0.612031	−	0.163993i
$438$		−	5.26795i		−	0.251712i
$439$	−6.52628	+	3.76795i	−0.311482	+	0.179834i	−0.647590	−	0.761989i	$-0.724223\pi$
$439$	−6.52628	+	3.76795i	−0.311482	+	0.179834i	0.336107	+	0.941824i	$0.390890\pi$
$440$	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
$443$	2.79423	−	10.4282i	0.132758	−	0.495459i	−0.867239	−	0.497892i	$-0.834108\pi$
$443$	2.79423	−	10.4282i	0.132758	−	0.495459i	0.999997	+	0.00243278i	$0.000774379\pi$
$444$	−1.05256	+	0.607695i	−0.0499522	+	0.0288399i
$445$	−1.20577	−	4.50000i	−0.0571590	−	0.213320i
$446$	−13.4641	+	3.60770i	−0.637544	+	0.170829i
$447$	−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	$0.685480\pi$
$450$	−15.6603	+	4.19615i	−0.738231	+	0.197809i
$451$	3.78461	+	14.1244i	0.178210	+	0.665090i
$452$	−2.53590	+	1.46410i	−0.119279	+	0.0688655i
$453$	−1.52628	+	5.69615i	−0.0717109	+	0.267629i
$454$	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	$-0.811619\pi$
$457$	−16.2846	+	9.40192i	−0.761762	+	0.439803i	0.0681661	+	0.997674i	$0.478285\pi$
$458$		−	19.5167i		−	0.911954i
$459$	18.5263	−	4.96410i	0.864733	−	0.231704i
$460$	5.66025	+	5.66025i	0.263911	+	0.263911i
$461$	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	$0.0393405\pi$
$462$	0.411543	−	5.73205i	0.0191467	−	0.266679i
$463$	2.14359			0.0996212			0.0498106	−	0.998759i	$-0.484138\pi$
$463$	2.14359			0.0996212			0.0498106	+	0.998759i	$0.484138\pi$
$464$	0.392305	+	1.46410i	0.0182123	+	0.0679692i
$465$	0.866025	−	1.50000i	0.0401610	−	0.0695608i
$466$	0.803848	−	0.803848i	0.0372375	−	0.0372375i
$467$	25.9904	+	6.96410i	1.20269	+	0.322260i	0.803890	−	0.594777i	$-0.202760\pi$
$467$	25.9904	+	6.96410i	1.20269	+	0.322260i	0.398801	+	0.917038i	$0.369426\pi$
$468$	−7.46410	−	27.8564i	−0.345028	−	1.28766i
$469$	7.62436	−	11.2583i	0.352060	−	0.519861i
$470$	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
$474$	−6.09808	+	10.5622i	−0.280094	+	0.485137i
$475$	−8.80385	−	8.80385i	−0.403948	−	0.403948i
$476$	25.8564	−	22.3923i	1.18513	−	1.02635i
$477$	7.92820	−	7.92820i	0.363007	−	0.363007i
$478$	11.6603	−	3.12436i	0.533328	−	0.142905i
$479$	−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	$0.282570\pi$
$480$	0.679492	−	2.53590i	0.0310144	−	0.115747i
$481$	−3.09808	−	5.36603i	−0.141260	−	0.244670i
$482$	5.09808	−	19.0263i	0.232211	−	0.866623i
$483$	0.437822	−	6.09808i	0.0199216	−	0.277472i
$484$	−2.19615	+	3.80385i	−0.0998251	+	0.172902i
$485$	−0.679492	+	2.53590i	−0.0308541	+	0.115149i
$486$	17.4641			0.792188
$487$	−10.6699	−	6.16025i	−0.483498	−	0.279148i	0.238375	−	0.971173i	$-0.423385\pi$
$487$	−10.6699	−	6.16025i	−0.483498	−	0.279148i	−0.721873	+	0.692025i	$0.756719\pi$
$488$	17.6603	−	10.1962i	0.799442	−	0.461558i
$489$			6.46410i			0.292317i
$490$	−8.78461	−	1.26795i	−0.396848	−	0.0572801i
$491$	−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	$0.786531\pi$
$492$	3.60770	−	3.60770i	0.162647	−	0.162647i
$493$	−0.633975	−	2.36603i	−0.0285528	−	0.106560i
$494$	15.6603	−	15.6603i	0.704588	−	0.704588i
$495$	−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
$499$	−24.9904	−	6.69615i	−1.11872	−	0.299761i	−0.348356	−	0.937362i	$-0.613260\pi$
$499$	−24.9904	−	6.69615i	−1.11872	−	0.299761i	−0.770367	+	0.637601i	$0.779927\pi$
$500$	4.26795	−	15.9282i	0.190868	−	0.712331i
$501$	10.9282	−	2.92820i	0.488236	−	0.130822i
$502$	30.4641	+	17.5885i	1.35968	+	0.785011i
$503$			31.8564i			1.42041i	0.703996	+	0.710203i	$0.251397\pi$
$503$			31.8564i			1.42041i	−0.703996	+	0.710203i	$0.748603\pi$
$504$	18.3923	−	8.92820i	0.819258	−	0.397694i
$505$			17.5359i			0.780337i
$506$	9.36603	−	16.2224i	0.416371	−	0.721175i
$507$	−7.42820	+	1.99038i	−0.329898	+	0.0883959i
$508$	16.3923	−	9.46410i	0.727291	−	0.419902i
$509$	−9.42820	−	2.52628i	−0.417898	−	0.111975i	0.0437420	−	0.999043i	$-0.486072\pi$
$509$	−9.42820	−	2.52628i	−0.417898	−	0.111975i	−0.461640	+	0.887067i	$0.652739\pi$
$510$	−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
$514$	−19.3923	−	19.3923i	−0.855358	−	0.855358i
$515$	−1.50000	−	5.59808i	−0.0660979	−	0.246681i
$516$		−	9.46410i		−	0.416634i
$517$	−8.95448	−	8.95448i	−0.393818	−	0.393818i
$518$	3.32051	−	2.87564i	0.145895	−	0.126349i
$519$			1.19615i			0.0525053i
$520$	12.9282	+	3.46410i	0.566939	+	0.151911i
$521$	13.3756	+	7.72243i	0.585998	+	0.338326i	0.763513	−	0.645792i	$-0.223473\pi$
$521$	13.3756	+	7.72243i	0.585998	+	0.338326i	−0.177516	+	0.984118i	$0.556806\pi$
$522$		−	1.46410i		−	0.0640820i
$523$	8.65064	−	32.2846i	0.378266	−	1.41171i	−0.470248	−	0.882534i	$-0.655836\pi$
$523$	8.65064	−	32.2846i	0.378266	−	1.41171i	0.848514	−	0.529173i	$-0.177498\pi$
$524$	15.1962	−	4.07180i	0.663847	−	0.177877i
$525$	−5.16987	+	2.50962i	−0.225632	+	0.109529i
$526$	6.29423	+	1.68653i	0.274441	+	0.0735364i
$527$	−12.0622	−	20.8923i	−0.525437	−	0.910083i
$528$	−6.14359			−0.267366
$529$	−1.53590	+	2.66025i	−0.0667782	+	0.115663i
$530$	1.34679	+	5.02628i	0.0585007	+	0.218328i
$531$	22.6603	−	22.6603i	0.983371	−	0.983371i
$532$	13.0000	+	8.80385i	0.563621	+	0.381695i
$533$	18.3923	+	18.3923i	0.796659	+	0.796659i
$534$	3.29423	+	1.90192i	0.142555	+	0.0823043i
$535$	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
$539$	2.45448	+	20.6244i	0.105722	+	0.888354i
$540$	−2.66025	+	4.60770i	−0.114479	+	0.198284i
$541$	−9.23205	−	2.47372i	−0.396917	−	0.106354i	0.0548389	−	0.998495i	$-0.482535\pi$
$541$	−9.23205	−	2.47372i	−0.396917	−	0.106354i	−0.451756	+	0.892142i	$0.649202\pi$
$542$	12.1244	+	12.1244i	0.520786	+	0.520786i
$543$	4.90192	−	8.49038i	0.210362	−	0.364357i
$544$	−25.8564	−	25.8564i	−1.10858	−	1.10858i
$545$	1.98076			0.0848465
$546$	−4.46410	−	9.19615i	−0.191046	−	0.393559i
$547$	−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	$0.495466\pi$
$548$	−35.1769			−1.50268
$549$	−19.0263	+	5.09808i	−0.812022	+	0.217581i
$550$	−17.6077			−0.750795
$551$	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
$555$	−0.141016	+	0.526279i	−0.00598580	+	0.0223393i
$556$	−32.5885	−	8.73205i	−1.38206	−	0.370321i
$557$	−1.76795	−	6.59808i	−0.0749104	−	0.279569i	0.918303	−	0.395879i	$-0.129560\pi$
$557$	−1.76795	−	6.59808i	−0.0749104	−	0.279569i	−0.993213	+	0.116310i	$0.962893\pi$
$558$	−3.73205	−	13.9282i	−0.157990	−	0.589628i
$559$	48.2487			2.04070
$560$	−0.679492	+	9.46410i	−0.0287138	+	0.399931i
$561$	9.92820			0.419169
$562$	−0.339746	−	1.26795i	−0.0143313	−	0.0534852i
$563$	0.650635	+	2.42820i	0.0274210	+	0.102337i	0.978280	−	0.207287i	$-0.0664635\pi$
$563$	0.650635	+	2.42820i	0.0274210	+	0.102337i	−0.950859	+	0.309624i	$0.899797\pi$
$564$	−1.14359	+	4.26795i	−0.0481540	+	0.179713i
$565$	−0.339746	+	1.26795i	−0.0142932	+	0.0533430i
$566$	−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	$-0.627364\pi$
$569$	5.08846	−	2.93782i	0.213319	−	0.123160i	0.602853	+	0.797852i	$0.294031\pi$
$570$	−1.94744			−0.0815693
$571$	26.7224	−	7.16025i	1.11830	−	0.299647i	0.348104	−	0.937456i	$-0.386826\pi$
$571$	26.7224	−	7.16025i	1.11830	−	0.299647i	0.770195	+	0.637809i	$0.220159\pi$
$572$		−	31.3205i		−	1.30958i
$573$	−3.16987	+	3.16987i	−0.132423	+	0.132423i
$574$	−10.3397	+	15.2679i	−0.431573	+	0.637272i
$575$	−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	$0.255601\pi$
$578$	24.7846	+	24.7846i	1.03090	+	1.03090i
$579$	−11.5000	−	3.08142i	−0.477924	−	0.128059i
$580$	0.588457	+	0.339746i	0.0244344	+	0.0141072i
$581$	−5.73205	−	0.411543i	−0.237806	−	0.0170737i
$582$	−1.07180	−	1.85641i	−0.0444274	−	0.0769505i
$583$	10.5455	−	6.08846i	0.436751	−	0.252158i
$584$	19.6603	−	5.26795i	0.813547	−	0.217989i
$585$	−11.1962	−	6.46410i	−0.462904	−	0.267258i
$586$	13.7321	+	7.92820i	0.567266	+	0.327511i
$587$	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	$0.528941\pi$
$588$	5.80385	−	4.33975i	0.239347	−	0.178968i
$589$	7.83013	−	7.83013i	0.322635	−	0.322635i
$590$	3.84936	+	14.3660i	0.158476	+	0.591440i
$591$	−6.09808	+	10.5622i	−0.250841	+	0.434470i
$592$	−3.32051	−	3.32051i	−0.136472	−	0.136472i
$593$	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
$595$	1.09808	−	15.2942i	0.0450167	−	0.627002i
$596$	−4.07180	−	15.1962i	−0.166787	−	0.622459i
$597$	1.59808	−	5.96410i	0.0654049	−	0.244094i
$598$		−	33.3205i		−	1.36258i
$599$	−16.6699	−	9.62436i	−0.681113	−	0.393241i	0.119162	−	0.992875i	$-0.461979\pi$
$599$	−16.6699	−	9.62436i	−0.681113	−	0.393241i	−0.800274	+	0.599634i	$0.795313\pi$
$600$	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	$-0.0653794\pi$
$602$	6.46410	+	33.5885i	0.263457	+	1.36896i
$603$	9.92820	+	9.92820i	0.404308	+	0.404308i
$604$	−22.7846			−0.927093
$605$	0.509619	+	1.90192i	0.0207190	+	0.0773242i
$606$	−10.1244	−	10.1244i	−0.411274	−	0.411274i
$607$	−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
$611$	−21.7583	−	5.83013i	−0.880248	−	0.235862i
$612$	17.6603	+	30.5885i	0.713873	+	1.23647i
$613$	−9.23205	+	2.47372i	−0.372879	+	0.0999126i	−0.440392	−	0.897806i	$-0.645160\pi$
$613$	−9.23205	+	2.47372i	−0.372879	+	0.0999126i	0.0675126	+	0.997718i	$0.478494\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$		−	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	$-0.00343375\pi$
$618$	4.09808	+	2.36603i	0.164849	+	0.0951755i
$619$	−19.0622	+	5.10770i	−0.766174	+	0.205296i	−0.620680	−	0.784064i	$-0.713144\pi$
$619$	−19.0622	+	5.10770i	−0.766174	+	0.205296i	−0.145493	+	0.989359i	$0.546477\pi$
$620$	6.46410	+	1.73205i	0.259605	+	0.0695608i
$621$	12.7942	+	3.42820i	0.513415	+	0.137569i
$622$	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
$626$	−21.5885	+	21.5885i	−0.862848	+	0.862848i
$627$	1.17949	+	4.40192i	0.0471044	+	0.175796i
$628$	26.7321	+	26.7321i	1.06672	+	1.06672i
$629$	5.36603	+	5.36603i	0.213957	+	0.213957i
$630$	3.00000	−	8.66025i	0.119523	−	0.345033i
$631$		−	32.2487i		−	1.28380i	−0.766788	−	0.641900i	$-0.778146\pi$
$631$		−	32.2487i		−	1.28380i	0.766788	−	0.641900i	$-0.221854\pi$
$632$	−45.5167	−	12.1962i	−1.81056	−	0.485137i
$633$	10.0981	+	5.83013i	0.401362	+	0.231727i
$634$	−20.7321			−0.823375
$635$	2.19615	−	8.19615i	0.0871517	−	0.325254i
$636$	−3.67949	−	2.12436i	−0.145901	−	0.0842362i
$637$	22.1244	+	29.5885i	0.876599	+	1.17234i
$638$	0.411543	−	1.53590i	0.0162931	−	0.0608068i
$639$	−0.732051	−	1.26795i	−0.0289595	−	0.0501593i
$640$	10.1436			0.400961
$641$	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	$0.0960372\pi$
$642$	−2.36603	+	0.633975i	−0.0933796	+	0.0250210i
$643$	−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	$0.298046\pi$
$644$	23.1962	−	4.46410i	0.914056	−	0.175910i
$645$	−3.00000	−	3.00000i	−0.118125	−	0.118125i
$646$	−13.5622	+	23.4904i	−0.533597	+	0.924217i
$647$	−30.8660	−	17.8205i	−1.21347	−	0.700596i	−0.249955	−	0.968257i	$-0.580416\pi$
$647$	−30.8660	−	17.8205i	−1.21347	−	0.700596i	−0.963513	+	0.267661i	$0.913749\pi$
$648$	4.87564	+	18.1962i	0.191533	+	0.714812i
$649$	30.1410	−	17.4019i	1.18314	−	0.683085i
$650$	−27.1244	+	15.6603i	−1.06390	+	0.614246i
$651$	−2.23205	−	4.59808i	−0.0874810	−	0.180213i
$652$	−24.1244	+	6.46410i	−0.944783	+	0.253154i
$653$	32.5526	+	8.72243i	1.27388	+	0.341335i	0.831516	−	0.555501i	$-0.187473\pi$
$653$	32.5526	+	8.72243i	1.27388	+	0.341335i	0.442364	+	0.896836i	$0.354140\pi$
$654$	−1.14359	+	1.14359i	−0.0447180	+	0.0447180i
$655$	3.52628	−	6.10770i	0.137783	−	0.238647i
$656$	17.0718	+	9.85641i	0.666542	+	0.384828i
$657$	−19.6603			−0.767020
$658$	1.14359	−	15.9282i	0.0445819	−	0.620946i
$659$	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	$0.0761558\pi$
$660$	−1.94744	+	1.94744i	−0.0758040	+	0.0758040i
$661$	22.1603	−	5.93782i	0.861934	−	0.230955i	0.199337	−	0.979931i	$-0.436121\pi$
$661$	22.1603	−	5.93782i	0.861934	−	0.230955i	0.662597	+	0.748976i	$0.269454\pi$
$662$			28.7321i			1.11670i
$663$	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
$667$	0.437822	−	1.63397i	0.0169525	−	0.0632677i
$668$	21.8564	+	37.8564i	0.845650	+	1.46471i
$669$	−1.32051	−	4.92820i	−0.0510538	−	0.190535i
$670$	−6.29423	+	1.68653i	−0.243167	+	0.0651565i
$671$	−21.3923			−0.825841
$672$	−5.07180	−	5.85641i	−0.195649	−	0.225916i
$673$	40.7846			1.57213			0.786066	−	0.618143i	$-0.212115\pi$
$673$	40.7846			1.57213			0.786066	+	0.618143i	$0.212115\pi$
$674$	8.39230	−	2.24871i	0.323260	−	0.0866171i
$675$	−3.22243	−	12.0263i	−0.124031	−	0.462892i
$676$	−14.8564	−	25.7321i	−0.571400	−	0.989694i
$677$	11.4474	−	42.7224i	0.439961	−	1.64196i	−0.288947	−	0.957345i	$-0.593305\pi$
$677$	11.4474	−	42.7224i	0.439961	−	1.64196i	0.728908	−	0.684611i	$-0.240028\pi$
$678$	−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
$682$		−	15.6603i		−	0.599662i
$683$	−45.5788	+	12.2128i	−1.74403	+	0.467310i	−0.983335	−	0.181804i	$-0.941806\pi$
$683$	−45.5788	+	12.2128i	−1.74403	+	0.467310i	−0.760691	+	0.649114i	$0.775140\pi$
$684$	−11.4641	+	11.4641i	−0.438341	+	0.438341i
$685$	−11.1506	+	11.1506i	−0.426044	+	0.426044i
$686$	−17.6340	+	19.3660i	−0.673268	+	0.739398i
$687$	7.14359			0.272545
$688$	35.3205	−	9.46410i	1.34658	−	0.360815i
$689$	10.8301	−	18.7583i	0.412595	−	0.714635i
$690$	−2.07180	+	2.07180i	−0.0788720	+	0.0788720i
$691$	−22.9904	−	6.16025i	−0.874595	−	0.234347i	−0.206521	−	0.978442i	$-0.566214\pi$
$691$	−22.9904	−	6.16025i	−0.874595	−	0.234347i	−0.668074	+	0.744095i	$0.732881\pi$
$692$	−4.46410	+	1.19615i	−0.169700	+	0.0454709i
$693$	−21.3923	−	1.53590i	−0.812626	−	0.0583440i
$694$	−29.8301	+	17.2224i	−1.13234	+	0.653755i
$695$	−13.0981	+	7.56218i	−0.496838	+	0.286850i
$696$	−0.535898	+	0.143594i	−0.0203132	+	0.00544290i
$697$	−27.5885	−	15.9282i	−1.04499	−	0.603324i
$698$	−6.12436	+	10.6077i	−0.231810	+	0.401507i
$699$	0.294229	+	0.294229i	0.0111287	+	0.0111287i
$700$	−14.5359	−	16.7846i	−0.549405	−	0.634399i
$701$	−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	$0.366428\pi$
$702$	21.3923	−	5.73205i	0.807401	−	0.216342i
$703$	−1.74167	+	3.01666i	−0.0656883	+	0.113776i
$704$	−6.14359	−	22.9282i	−0.231545	−	0.864139i
$705$	0.990381	+	1.71539i	0.0372999	+	0.0646053i
$706$	−10.1699	+	37.9545i	−0.382748	+	1.42844i
$707$	42.8468	+	29.0167i	1.61142	+	1.09128i
$708$	−10.5167	−	6.07180i	−0.395240	−	0.228192i
$709$	−12.2321	+	45.6506i	−0.459384	+	1.71445i	0.215484	+	0.976507i	$0.430867\pi$
$709$	−12.2321	+	45.6506i	−0.459384	+	1.71445i	−0.674868	+	0.737938i	$0.735800\pi$
$710$	0.679492			0.0255009
$711$	39.4186	+	22.7583i	1.47831	+	0.853504i
$712$	−3.80385	+	14.1962i	−0.142555	+	0.532023i
$713$		−	16.6603i		−	0.623931i
$714$	8.19615	+	9.46410i	0.306733	+	0.354185i
$715$	−9.92820	−	9.92820i	−0.371294	−	0.371294i
$716$	−13.1244	−	13.1244i	−0.490480	−	0.490480i
$717$	1.14359	+	4.26795i	0.0427083	+	0.159389i
$718$	−4.46410	+	4.46410i	−0.166599	+	0.166599i
$719$	−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
$723$	6.96410	+	1.86603i	0.258998	+	0.0693982i
$724$	36.5885	+	9.80385i	1.35980	+	0.364357i
$725$	−1.53590	+	0.411543i	−0.0570418	+	0.0152843i
$726$	−1.39230	−	0.803848i	−0.0516733	−	0.0298336i
$727$			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
$730$	4.56218	−	7.90192i	0.168854	−	0.292463i
$731$	−57.0788	+	15.2942i	−2.11114	+	0.565677i
$732$	3.73205	+	6.46410i	0.137941	+	0.238920i
$733$	32.8923	+	8.81347i	1.21490	+	0.325533i	0.808685	−	0.588242i	$-0.200180\pi$
$733$	32.8923	+	8.81347i	1.21490	+	0.325533i	0.406220	+	0.913775i	$0.366847\pi$
$734$	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
$738$	−13.4641	−	13.4641i	−0.495620	−	0.495620i
$739$	−10.3109	−	38.4808i	−0.379292	−	1.41554i	−0.846971	−	0.531639i	$-0.821576\pi$
$739$	−10.3109	−	38.4808i	−0.379292	−	1.41554i	0.467679	−	0.883899i	$-0.345090\pi$
$740$	−2.10512			−0.0773857
$741$	5.73205	+	5.73205i	0.210572	+	0.210572i
$742$	14.5096	+	5.02628i	0.532665	+	0.184521i
$743$			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
$746$		−	1.26795i		−	0.0464229i
$747$	1.53590	−	5.73205i	0.0561956	−	0.209725i
$748$	9.92820	+	37.0526i	0.363011	+	1.35478i
$749$	7.96410	−	3.86603i	0.291002	−	0.141261i
$750$	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	$0.909873\pi$
$752$	−17.0718			−0.622544
$753$	−6.43782	+	11.1506i	−0.234607	+	0.406352i
$754$	−0.732051	−	2.73205i	−0.0266597	−	0.0994954i
$755$	−7.22243	+	7.22243i	−0.262851	+	0.262851i
$756$	6.85641	+	14.1244i	0.249365	+	0.513698i
$757$	−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	$0.909208\pi$
$758$	−0.215390	−	0.124356i	−0.00782333	−	0.00451680i
$759$	5.93782	+	3.42820i	0.215529	+	0.124436i
$760$	−1.94744	−	7.26795i	−0.0706411	−	0.263636i
$761$	−11.7679	+	6.79423i	−0.426588	+	0.246291i	−0.697892	−	0.716203i	$-0.745878\pi$
$761$	−11.7679	+	6.79423i	−0.426588	+	0.246291i	0.271304	+	0.962494i	$0.412545\pi$
$762$	3.46410	+	6.00000i	0.125491	+	0.217357i
$763$	3.27757	−	4.83975i	0.118656	−	0.175211i
$764$	−15.0000	−	8.66025i	−0.542681	−	0.313317i
$765$	15.2942	+	4.09808i	0.552964	+	0.148166i
$766$	−25.1962	−	25.1962i	−0.910374	−	0.910374i
$767$	30.9545	−	53.6147i	1.11770	−	1.93592i
$768$	−5.85641	+	5.85641i	−0.211325	+	0.211325i
$769$	9.85641			0.355431			0.177716	−	0.984082i	$-0.443129\pi$
$769$	9.85641			0.355431			0.177716	+	0.984082i	$0.443129\pi$
$770$	5.58142	−	8.24167i	0.201140	−	0.297009i
$771$	7.09808	−	7.09808i	0.255631	−	0.255631i
$772$		−	46.0000i		−	1.65558i
$773$	10.9641	−	2.93782i	0.394351	−	0.105666i	−0.0561936	−	0.998420i	$-0.517896\pi$
$773$	10.9641	−	2.93782i	0.394351	−	0.105666i	0.450545	+	0.892754i	$0.351230\pi$
$774$	−35.3205			−1.26957
$775$	−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
$779$	3.78461	−	14.1244i	0.135598	−	0.506058i
$780$	−1.26795	+	4.73205i	−0.0453999	+	0.169435i
$781$	−0.411543	−	1.53590i	−0.0147262	−	0.0549588i
$782$	10.5622	+	39.4186i	0.377703	+	1.40961i
$783$	1.12436			0.0401812
$784$	22.0000	+	17.3205i	0.785714	+	0.618590i
$785$	16.9474			0.604880
$786$	1.49038	+	5.56218i	0.0531601	+	0.198396i
$787$	3.52628	+	13.1603i	0.125698	+	0.469112i	0.999864	−	0.0165161i	$-0.00525747\pi$
$787$	3.52628	+	13.1603i	0.125698	+	0.469112i	−0.874165	+	0.485628i	$0.838591\pi$
$788$	−45.5167	−	12.1962i	−1.62146	−	0.434470i
$789$	−0.617314	+	2.30385i	−0.0219770	+	0.0820191i
$790$	−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
$794$	37.5167			1.33142
$795$	−1.83975	+	0.492958i	−0.0652491	+	0.0174834i
$796$	23.8564			0.845568
$797$	−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	$0.358439\pi$
$798$	−3.22243	+	4.75833i	−0.114073	+	0.168443i
$799$	27.5885			0.976009
$800$	−16.7846	+	16.7846i	−0.593426	+	0.593426i
$801$	7.09808	−	12.2942i	0.250798	−	0.434395i
$802$	−15.0000	−	15.0000i	−0.529668	−	0.529668i
$803$	−20.6244	−	5.52628i	−0.727818	−	0.195018i
$804$	2.66025	−	4.60770i	0.0938199	−	0.162501i
$805$	5.93782	−	8.76795i	0.209281	−	0.309030i
$806$	−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	$-0.129554\pi$
$809$	29.4282	+	16.9904i	1.03464	+	0.597350i	0.116330	+	0.993211i	$0.462887\pi$
$810$	7.31347	+	4.22243i	0.256969	+	0.148361i
$811$	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	$0.543623\pi$
$812$	1.80385	−	0.875644i	0.0633026	−	0.0307291i
$813$	−4.43782	+	4.43782i	−0.155641	+	0.155641i
$814$	1.27499	+	4.75833i	0.0446884	+	0.166779i
$815$	−5.59808	+	9.69615i	−0.196092	+	0.339641i
$816$	9.46410	−	9.46410i	0.331310	−	0.331310i
$817$	−13.5622	−	23.4904i	−0.474481	−	0.821824i
$818$	−11.8301	−	3.16987i	−0.413631	−	0.110832i
$819$	−34.3205	+	16.6603i	−1.19926	+	0.582156i
$820$	8.53590	−	2.28719i	0.298087	−	0.0798720i
$821$	−0.160254	+	0.598076i	−0.00559290	+	0.0208730i	−0.968666	−	0.248367i	$-0.920106\pi$
$821$	−0.160254	+	0.598076i	−0.00559290	+	0.0208730i	0.963073	+	0.269240i	$0.0867726\pi$
$822$		−	12.8756i		−	0.449090i
$823$	14.9378	+	8.62436i	0.520700	+	0.300626i	0.737221	−	0.675652i	$-0.236138\pi$
$823$	14.9378	+	8.62436i	0.520700	+	0.300626i	−0.216521	+	0.976278i	$0.569471\pi$
$824$	−4.73205	+	17.6603i	−0.164849	+	0.615224i
$825$		−	6.44486i		−	0.224381i
$826$	41.4711	+	14.3660i	1.44297	+	0.499858i
$827$	−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	$0.779664\pi$
$828$			24.3923i			0.847691i
$829$	0.820508	+	3.06218i	0.0284974	+	0.106354i	0.978710	−	0.205250i	$-0.0658006\pi$
$829$	0.820508	+	3.06218i	0.0284974	+	0.106354i	−0.950212	+	0.311603i	$0.899134\pi$
$830$	1.94744	+	1.94744i	0.0675967	+	0.0675967i
$831$	−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
$835$	18.9282	+	5.07180i	0.655037	+	0.175517i
$836$	−15.2487	+	8.80385i	−0.527388	+	0.304487i
$837$	10.6962	−	2.86603i	0.369713	−	0.0990643i
$838$	19.0000	−	32.9090i	0.656344	−	1.13682i
$839$		−	17.7128i		−	0.611514i	−0.952110	−	0.305757i	$-0.901090\pi$
$839$		−	17.7128i		−	0.611514i	0.952110	−	0.305757i	$-0.0989096\pi$
$840$	−3.46410	−	0.248711i	−0.119523	−	0.00858136i
$841$			28.8564i			0.995048i
$842$	−15.0000	−	8.66025i	−0.516934	−	0.298452i
$843$	0.464102	−	0.124356i	0.0159845	−	0.00428304i
$844$	−11.6603	+	43.5167i	−0.401362	+	1.49791i
$845$	−12.8660	−	3.44744i	−0.442605	−	0.118596i
$846$	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
$850$	27.1244	−	27.1244i	0.930358	−	0.930358i
$851$	1.35641	+	5.06218i	0.0464970	+	0.173529i
$852$	−0.392305	+	0.392305i	−0.0134401	+	0.0134401i
$853$	−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	$0.842831\pi$
$854$	−17.6603	−	20.3923i	−0.604321	−	0.697810i
$855$			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	$-0.408691\pi$
$857$	−11.8923	−	6.86603i	−0.406233	−	0.234539i	−0.689170	+	0.724600i	$0.742025\pi$
$858$	11.4641			0.391378
$859$	−3.65064	+	13.6244i	−0.124558	+	0.464857i	−0.999824	−	0.0187858i	$-0.994020\pi$
$859$	−3.65064	+	13.6244i	−0.124558	+	0.464857i	0.875265	+	0.483643i	$0.160687\pi$
$860$	8.19615	−	14.1962i	0.279486	−	0.484085i
$861$	−5.58846	−	3.78461i	−0.190454	−	0.128979i
$862$	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	$0.645713\pi$
$864$	14.5359	−	8.39230i	0.494521	−	0.285512i
$865$	−1.03590	+	1.79423i	−0.0352216	+	0.0610056i
$866$	45.3205	−	12.1436i	1.54005	−	0.412656i
$867$	−9.07180	+	9.07180i	−0.308094	+	0.308094i
$868$	14.9282	−	12.9282i	0.506696	−	0.438812i
$869$	34.9545	+	34.9545i	1.18575	+	1.18575i
$870$	−0.124356	+	0.215390i	−0.00421605	+	0.00730242i
$871$	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
$875$	−21.7583	−	1.56218i	−0.735566	−	0.0528112i
$876$	1.92820	+	7.19615i	0.0651479	+	0.243135i
$877$	−30.5526	−	8.18653i	−1.03169	−	0.276440i	−0.297022	−	0.954871i	$-0.595994\pi$
$877$	−30.5526	−	8.18653i	−1.03169	−	0.276440i	−0.734664	+	0.678431i	$0.762660\pi$
$878$	7.53590	−	7.53590i	0.254324	−	0.254324i
$879$	−2.90192	+	5.02628i	−0.0978795	+	0.169532i
$880$	−9.21539	−	5.32051i	−0.310651	−	0.179354i
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$	−16.1962	−	21.6603i	−0.545353	−	0.729339i
$883$	−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	$0.287963\pi$
$884$	48.2487	+	48.2487i	1.62278	+	1.62278i
$885$	−5.25833	+	1.40897i	−0.176757	+	0.0473619i
$886$			15.2679i			0.512937i
$887$	39.7750	−	22.9641i	1.33551	−	0.771059i	0.349375	−	0.936983i	$-0.386394\pi$
$887$	39.7750	−	22.9641i	1.33551	−	0.771059i	0.986139	+	0.165924i	$0.0530606\pi$
$888$	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
$891$	5.11474	−	19.0885i	0.171350	−	0.639487i
$892$	17.0718	−	9.85641i	0.571606	−	0.330017i
$893$	3.27757	+	12.2321i	0.109680	+	0.409330i
$894$	5.56218	−	1.49038i	0.186027	−	0.0498458i
$895$	−8.32051			−0.278124
$896$	16.7846	−	24.7846i	0.560734	−	0.827996i
$897$	12.1962			0.407218
$898$	31.8564	−	8.53590i	1.06306	−	0.284847i
$899$	−0.366025	−	1.36603i	−0.0122076	−	0.0455595i
$900$	19.8564	−	11.4641i	0.661880	−	0.382137i
$901$	−6.86603	+	25.6244i	−0.228740	+	0.853671i
$902$	−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
$906$		−	8.33975i		−	0.277070i
$907$	−26.7224	+	7.16025i	−0.887304	+	0.237752i	−0.673556	−	0.739136i	$-0.735234\pi$
$907$	−26.7224	+	7.16025i	−0.887304	+	0.237752i	−0.213748	+	0.976889i	$0.568567\pi$
$908$	−16.3397	−	16.3397i	−0.542254	−	0.542254i
$909$	−37.7846	+	37.7846i	−1.25324	+	1.25324i
$910$	1.26795	−	17.6603i	0.0420321	−	0.585432i
$911$	7.32051			0.242539			0.121270	−	0.992620i	$-0.461303\pi$
$911$	7.32051			0.242539			0.121270	+	0.992620i	$0.461303\pi$
$912$	5.32051	+	3.07180i	0.176180	+	0.101717i
$913$	3.22243	−	5.58142i	0.106647	−	0.184718i
$914$	18.8038	−	18.8038i	0.621976	−	0.621976i
$915$	3.23205	+	0.866025i	0.106848	+	0.0286299i
$916$	7.14359	+	26.6603i	0.236031	+	0.880880i
$917$	−9.08846	−	18.7224i	−0.300127	−	0.618269i
$918$	−23.4904	+	13.5622i	−0.775298	+	0.447619i
$919$	15.8660	−	9.16025i	0.523372	−	0.302169i	−0.214941	−	0.976627i	$-0.568956\pi$
$919$	15.8660	−	9.16025i	0.523372	−	0.302169i	0.738313	+	0.674458i	$0.235623\pi$
$920$	−9.80385	−	5.66025i	−0.323223	−	0.186613i
$921$	−5.70577	−	3.29423i	−0.188012	−	0.108549i
$922$	−18.6603	+	32.3205i	−0.614543	+	1.06442i
$923$	−2.00000	−	2.00000i	−0.0658308	−	0.0658308i
$924$	1.53590	+	7.98076i	0.0505273	+	0.262548i
$925$	3.48334	−	3.48334i	0.114531	−	0.114531i
$926$	−2.92820	+	0.784610i	−0.0962267	+	0.0257839i
$927$	8.83013	−	15.2942i	0.290019	−	0.502328i
$928$	−1.07180	−	1.85641i	−0.0351835	−	0.0609395i
$929$	−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
$931$	8.18653	−	19.0885i	0.268303	−	0.625599i
$932$	−0.803848	+	1.39230i	−0.0263309	+	0.0456065i
$933$	−0.866025	+	3.23205i	−0.0283524	+	0.105813i
$934$	−38.0526			−1.24512
$935$	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	$0.842496\pi$
$938$	−6.29423	+	18.1699i	−0.205514	+	0.593267i
$939$	−7.90192	−	7.90192i	−0.257870	−	0.257870i
$940$	−5.41154	+	5.41154i	−0.176505	+	0.176505i
$941$	6.30385	+	23.5263i	0.205500	+	0.766935i	0.989297	+	0.145918i	$0.0466135\pi$
$941$	6.30385	+	23.5263i	0.205500	+	0.766935i	−0.783797	+	0.621017i	$0.786720\pi$
$942$	−9.78461	+	9.78461i	−0.318800	+	0.318800i
$943$	−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
$947$	5.40192	+	1.44744i	0.175539	+	0.0470355i	0.345518	−	0.938412i	$-0.387703\pi$
$947$	5.40192	+	1.44744i	0.175539	+	0.0470355i	−0.169979	+	0.985448i	$0.554370\pi$
$948$	4.46410	−	16.6603i	0.144987	−	0.541100i
$949$	−36.6865	+	9.83013i	−1.19090	+	0.319099i
$950$	15.2487	+	8.80385i	0.494734	+	0.285635i
$951$		−	7.58846i		−	0.246073i
$952$	−27.1244	+	40.0526i	−0.879105	+	1.29811i
$953$		−	16.5359i		−	0.535650i	−0.963468	−	0.267825i	$-0.913695\pi$
$953$		−	16.5359i		−	0.535650i	0.963468	−	0.267825i	$-0.0863050\pi$
$954$	−7.92820	+	13.7321i	−0.256685	+	0.444592i
$955$	−7.50000	+	2.00962i	−0.242694	+	0.0650297i
$956$	−14.7846	+	8.53590i	−0.478168	+	0.276071i
$957$	0.562178	+	0.150635i	0.0181726	+	0.00486934i
$958$	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
$962$	6.19615	+	6.19615i	0.199772	+	0.199772i
$963$	2.36603	+	8.83013i	0.0762441	+	0.284547i
$964$			27.8564i			0.897194i
$965$	−14.5814	−	14.5814i	−0.469392	−	0.469392i
$966$	1.63397	+	8.49038i	0.0525723	+	0.273174i
$967$			60.2487i			1.93747i	0.248102	+	0.968734i	$0.420193\pi$
$967$			60.2487i			1.93747i	−0.248102	+	0.968734i	$0.579807\pi$
$968$	1.60770	−	6.00000i	0.0516733	−	0.192847i
$969$	−8.59808	−	4.96410i	−0.276210	−	0.159470i
$970$		−	3.71281i		−	0.119211i
$971$	14.0429	−	52.4090i	0.450659	−	1.68188i	−0.249885	−	0.968275i	$-0.580393\pi$
$971$	14.0429	−	52.4090i	0.450659	−	1.68188i	0.700545	−	0.713608i	$-0.252940\pi$
$972$	−23.8564	+	6.39230i	−0.765195	+	0.205033i
$973$	−3.19615	+	44.5167i	−0.102464	+	1.42714i
$974$	16.8301	+	4.50962i	0.539272	+	0.144498i
$975$	−5.73205	−	9.92820i	−0.183573	−	0.317957i
$976$	−20.3923	+	20.3923i	−0.652742	+	0.652742i
$977$	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	$0.0782417\pi$
$978$	−2.36603	−	8.83013i	−0.0756571	−	0.282356i
$979$	10.9019	−	10.9019i	0.348427	−	0.348427i
$980$	12.4641	−	1.48334i	0.398151	−	0.0473835i
$981$	4.26795	+	4.26795i	0.136265	+	0.136265i
$982$	6.21539	+	3.58846i	0.198341	+	0.114512i
$983$	−17.1340	−	9.89230i	−0.546489	−	0.315516i	0.201216	−	0.979547i	$-0.435511\pi$
$983$	−17.1340	−	9.89230i	−0.546489	−	0.315516i	−0.747705	+	0.664031i	$0.768844\pi$
$984$	−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
$987$	5.83013	+	0.418584i	0.185575	+	0.0133237i
$988$	−15.6603	+	27.1244i	−0.498219	+	0.862941i
$989$	−39.4186	−	10.5622i	−1.25344	−	0.335858i
$990$	7.26795	+	7.26795i	0.230991	+	0.230991i
$991$	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	$0.124013\pi$
$992$	−14.9282	−	14.9282i	−0.473971	−	0.473971i
$993$	−10.5167			−0.333736
$994$	1.12436	−	1.66025i	0.0356624	−	0.0526601i
$995$	7.56218	−	7.56218i	0.239737	−	0.239737i
$996$	−2.24871			−0.0712531
$997$	−1.50000	+	0.401924i	−0.0475055	+	0.0127291i	−0.282494	−	0.959269i	$-0.591162\pi$
$997$	−1.50000	+	0.401924i	−0.0475055	+	0.0127291i	0.234988	+	0.971998i	$0.424495\pi$
$998$	36.5885			1.15819
$999$	−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.a.53.1	✓	4
4.3	odd	2		448.2.ba.b.305.1		4
7.2	even	3		112.2.w.b.37.1	yes	4
7.3	odd	6		784.2.m.d.197.2		4
7.4	even	3		784.2.m.e.197.2		4
7.5	odd	6		784.2.x.h.373.1		4
7.6	odd	2		784.2.x.a.165.1		4
8.3	odd	2		896.2.ba.a.865.1		4
8.5	even	2		896.2.ba.d.865.1		4
16.3	odd	4		448.2.ba.a.81.1		4
16.5	even	4		896.2.ba.b.417.1		4
16.11	odd	4		896.2.ba.c.417.1		4
16.13	even	4		112.2.w.b.109.1	yes	4
28.23	odd	6		448.2.ba.a.177.1		4
56.37	even	6		896.2.ba.b.737.1		4
56.51	odd	6		896.2.ba.c.737.1		4
112.13	odd	4		784.2.x.h.557.1		4
112.37	even	12		896.2.ba.d.289.1		4
112.45	odd	12		784.2.m.d.589.2		4
112.51	odd	12		448.2.ba.b.401.1		4
112.61	odd	12		784.2.x.a.765.1		4
112.93	even	12	inner	112.2.w.a.93.1	yes	4
112.107	odd	12		896.2.ba.a.289.1		4
112.109	even	12		784.2.m.e.589.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.53.1	✓	4	1.1	even	1	trivial
112.2.w.a.93.1	yes	4	112.93	even	12	inner
112.2.w.b.37.1	yes	4	7.2	even	3
112.2.w.b.109.1	yes	4	16.13	even	4
448.2.ba.a.81.1		4	16.3	odd	4
448.2.ba.a.177.1		4	28.23	odd	6
448.2.ba.b.305.1		4	4.3	odd	2
448.2.ba.b.401.1		4	112.51	odd	12
784.2.m.d.197.2		4	7.3	odd	6
784.2.m.d.589.2		4	112.45	odd	12
784.2.m.e.197.2		4	7.4	even	3
784.2.m.e.589.2		4	112.109	even	12
784.2.x.a.165.1		4	7.6	odd	2
784.2.x.a.765.1		4	112.61	odd	12
784.2.x.h.373.1		4	7.5	odd	6
784.2.x.h.557.1		4	112.13	odd	4
896.2.ba.a.289.1		4	112.107	odd	12
896.2.ba.a.865.1		4	8.3	odd	2
896.2.ba.b.417.1		4	16.5	even	4
896.2.ba.b.737.1		4	56.37	even	6
896.2.ba.c.417.1		4	16.11	odd	4
896.2.ba.c.737.1		4	56.51	odd	6
896.2.ba.d.289.1		4	112.37	even	12
896.2.ba.d.865.1		4	8.5	even	2

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+(-1.36603 + 0.366025i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.232051 - 0.866025i) 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} +1.26795i q^{10} +(2.86603 - 0.767949i) q^{11} +(-0.732051 - 0.732051i) q^{12} +(3.73205 - 3.73205i) q^{13} +(3.09808 + 2.09808i) q^{14} -0.464102 q^{15} +(2.00000 - 3.46410i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(-2.73205 + 2.73205i) q^{18} +(-2.86603 - 0.767949i) q^{19} +(-0.464102 - 1.73205i) q^{20} +(-0.767949 + 1.13397i) 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} +(-3.73205 + 6.46410i) q^{26} +(-2.09808 - 2.09808i) q^{27} +(-5.00000 - 1.73205i) q^{28} +(-0.267949 + 0.267949i) q^{29} +(0.633975 - 0.169873i) q^{30} +(-1.86603 + 3.23205i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-0.767949 - 1.33013i) q^{33} +(2.36603 - 8.83013i) q^{34} +(-2.13397 + 1.03590i) q^{35} +(2.73205 - 4.73205i) q^{36} +(0.303848 - 1.13397i) q^{37} +4.19615 q^{38} +(-2.36603 - 1.36603i) q^{39} +(1.26795 + 2.19615i) q^{40} +4.92820i q^{41} +(0.633975 - 1.83013i) q^{42} +(6.46410 + 6.46410i) q^{43} +(4.19615 - 4.19615i) q^{44} +(-0.633975 - 2.36603i) q^{45} +(4.46410 - 4.46410i) 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} +(3.23205 + 0.866025i) q^{51} +(2.73205 - 10.1962i) q^{52} +(3.96410 - 1.06218i) q^{53} +(3.63397 + 2.09808i) q^{54} -2.66025i q^{55} +(7.46410 + 0.535898i) q^{56} +1.53590i q^{57} +(0.267949 - 0.464102i) q^{58} +(11.3301 - 3.03590i) q^{59} +(-0.803848 + 0.464102i) q^{60} +(-6.96410 - 1.86603i) q^{61} +(1.36603 - 5.09808i) q^{62} +(-6.83013 - 2.36603i) q^{63} -8.00000i q^{64} +(-2.36603 - 4.09808i) q^{65} +(1.53590 + 1.53590i) q^{66} +(1.33013 + 4.96410i) q^{67} +12.9282i q^{68} +(1.63397 + 1.63397i) q^{69} +(2.53590 - 2.19615i) q^{70} -0.535898i q^{71} +(-2.00000 + 7.46410i) q^{72} +(-6.23205 - 3.59808i) q^{73} +1.66025i q^{74} +(0.562178 - 2.09808i) q^{75} +(-5.73205 + 1.53590i) q^{76} +(-6.50000 - 4.40192i) q^{77} +(3.73205 + 1.00000i) q^{78} +(8.33013 + 14.4282i) q^{79} +(-2.53590 - 2.53590i) q^{80} +(3.33013 - 5.76795i) q^{81} +(-1.80385 - 6.73205i) q^{82} +(1.53590 - 1.53590i) q^{83} +(-0.196152 + 2.73205i) q^{84} +(4.09808 + 4.09808i) q^{85} +(-11.1962 - 6.46410i) 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} +(-13.9282 - 1.00000i) q^{91} +(-4.46410 + 7.73205i) q^{92} +(1.86603 + 0.500000i) q^{93} +(4.26795 + 4.26795i) q^{94} +(-1.33013 + 2.30385i) q^{95} +2.92820 q^{96} -2.92820 q^{97} +(-1.16987 - 9.83013i) q^{98} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} - 6 q^{5} - 2 q^{6} - 8 q^{8} + 6 q^{9} + 8 q^{11} + 4 q^{12} + 8 q^{13} + 2 q^{14} + 12 q^{15} + 8 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} + 12 q^{20} - 10 q^{21} - 18 q^{22} - 12 q^{23}+ \cdots + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 - 6 * q^5 - 2 * q^6 - 8 * q^8 + 6 * q^9 + 8 * q^11 + 4 * q^12 + 8 * q^13 + 2 * q^14 + 12 * q^15 + 8 * q^16 - 6 * q^17 - 4 * q^18 - 8 * q^19 + 12 * q^20 - 10 * q^21 - 18 * q^22 - 12 * q^23 + 12 * q^24 + 18 * q^25 - 8 * q^26 + 2 * q^27 - 20 * q^28 - 8 * q^29 + 6 * q^30 - 4 * q^31 + 8 * q^32 - 10 * q^33 + 6 * q^34 - 12 * q^35 + 4 * q^36 + 22 * q^37 - 4 * q^38 - 6 * q^39 + 12 * q^40 + 6 * q^42 + 12 * q^43 - 4 * q^44 - 6 * q^45 + 4 * q^46 - 12 * q^47 - 8 * q^48 - 4 * q^49 - 16 * q^50 + 6 * q^51 + 4 * q^52 + 2 * q^53 + 18 * q^54 + 16 * q^56 + 8 * q^58 + 28 * q^59 - 24 * q^60 - 14 * q^61 + 2 * q^62 - 10 * q^63 - 6 * q^65 + 20 * q^66 - 12 * q^67 + 10 * q^69 + 24 * q^70 - 8 * q^72 - 18 * q^73 - 22 * q^75 - 16 * q^76 - 26 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 - 4 * q^81 - 28 * q^82 + 20 * q^83 + 20 * q^84 + 6 * q^85 - 24 * q^86 + 18 * q^87 + 4 * q^88 + 18 * q^89 - 28 * q^91 - 4 * q^92 + 4 * q^93 + 24 * q^94 + 12 * q^95 - 16 * q^96 + 16 * q^97 - 22 * q^98 + 16 * q^99

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