LMFDB - Embedded newform 117.2.z.b.86.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(5,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("117.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			86.4
Character	$\chi$	$=$	117.86
Dual form			117.2.z.b.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.999012 - 0.267684i) q^{2} +(-1.73168 - 0.0358377i) q^{3} +(-0.805681 - 0.465160i) q^{4} +(0.483213 + 1.80337i) q^{5} +(1.72038 + 0.499346i) q^{6} +(3.99567 + 1.07064i) q^{7} +(2.14302 + 2.14302i) q^{8} +(2.99743 + 0.124119i) q^{9} +O(q^{10})$	\(q+(-0.999012 - 0.267684i) q^{2} +(-1.73168 - 0.0358377i) q^{3} +(-0.805681 - 0.465160i) q^{4} +(0.483213 + 1.80337i) q^{5} +(1.72038 + 0.499346i) q^{6} +(3.99567 + 1.07064i) q^{7} +(2.14302 + 2.14302i) q^{8} +(2.99743 + 0.124119i) q^{9} -1.93094i q^{10} +(-0.995710 + 3.71604i) q^{11} +(1.37851 + 0.834382i) q^{12} +(-2.74203 - 2.34121i) q^{13} +(-3.70513 - 2.13916i) q^{14} +(-0.772141 - 3.14018i) q^{15} +(-0.636932 - 1.10320i) q^{16} -0.582460 q^{17} +(-2.96125 - 0.926362i) q^{18} +(4.41048 + 4.41048i) q^{19} +(0.449542 - 1.67772i) q^{20} +(-6.88085 - 1.99720i) q^{21} +(1.98945 - 3.44583i) q^{22} +(-2.65310 + 4.59531i) q^{23} +(-3.63423 - 3.78783i) q^{24} +(1.31146 - 0.757174i) q^{25} +(2.11262 + 3.07289i) q^{26} +(-5.18614 - 0.322355i) q^{27} +(-2.72122 - 2.72122i) q^{28} +(5.19577 - 2.99978i) q^{29} +(-0.0692004 + 3.34377i) q^{30} +(2.14445 - 0.574604i) q^{31} +(-1.22781 - 4.58224i) q^{32} +(1.85742 - 6.39931i) q^{33} +(0.581885 + 0.155916i) q^{34} +7.72303i q^{35} +(-2.35724 - 1.49429i) q^{36} +(-4.32606 + 4.32606i) q^{37} +(-3.22551 - 5.58674i) q^{38} +(4.66442 + 4.15249i) q^{39} +(-2.82914 + 4.90021i) q^{40} +(-1.64290 - 6.13140i) q^{41} +(6.33944 + 3.83712i) q^{42} +(-5.20669 + 3.00608i) q^{43} +(2.53078 - 2.53078i) q^{44} +(1.22456 + 5.46547i) q^{45} +(3.88057 - 3.88057i) q^{46} +(1.64988 - 6.15742i) q^{47} +(1.06343 + 1.93321i) q^{48} +(8.75694 + 5.05582i) q^{49} +(-1.51285 + 0.405367i) q^{50} +(1.00863 + 0.0208740i) q^{51} +(1.12017 + 3.16175i) q^{52} -1.69062i q^{53} +(5.09473 + 1.71029i) q^{54} -7.18255 q^{55} +(6.26842 + 10.8572i) q^{56} +(-7.47948 - 7.79561i) q^{57} +(-5.99363 + 1.60599i) q^{58} +(6.45229 - 1.72888i) q^{59} +(-0.838589 + 2.88916i) q^{60} +(-1.12715 - 1.95228i) q^{61} -2.29614 q^{62} +(11.8439 + 3.70510i) q^{63} +7.45411i q^{64} +(2.89709 - 6.07621i) q^{65} +(-3.56858 + 5.89578i) q^{66} +(-2.21763 + 0.594213i) q^{67} +(0.469277 + 0.270937i) q^{68} +(4.75901 - 7.86252i) q^{69} +(2.06734 - 7.71540i) q^{70} +(-1.87415 + 1.87415i) q^{71} +(6.15758 + 6.68956i) q^{72} +(5.42937 - 5.42937i) q^{73} +(5.47981 - 3.16377i) q^{74} +(-2.29817 + 1.26418i) q^{75} +(-1.50186 - 5.60502i) q^{76} +(-7.95706 + 13.7820i) q^{77} +(-3.54825 - 5.39698i) q^{78} +(-1.10654 - 1.91658i) q^{79} +(1.68171 - 1.68171i) q^{80} +(8.96919 + 0.744075i) q^{81} +6.56512i q^{82} +(-11.0196 - 2.95269i) q^{83} +(4.61476 + 4.80980i) q^{84} +(-0.281452 - 1.05039i) q^{85} +(6.00623 - 1.60936i) q^{86} +(-9.10492 + 5.00845i) q^{87} +(-10.0974 + 5.82973i) q^{88} +(-0.110864 - 0.110864i) q^{89} +(0.239666 - 5.78786i) q^{90} +(-8.44967 - 12.2904i) q^{91} +(4.27511 - 2.46823i) q^{92} +(-3.73409 + 0.918178i) q^{93} +(-3.29649 + 5.70969i) q^{94} +(-5.82255 + 10.0850i) q^{95} +(1.96195 + 7.97898i) q^{96} +(2.91212 - 10.8682i) q^{97} +(-7.39493 - 7.39493i) q^{98} +(-3.44580 + 11.0150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9}+O(q^{10}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33} - 12 q^{34} - 16 q^{37} + 16 q^{39} + 36 q^{40} + 36 q^{41} + 20 q^{42} - 56 q^{45} - 12 q^{46} - 18 q^{47} - 8 q^{48} + 120 q^{50} - 8 q^{52} + 52 q^{54} - 64 q^{55} - 8 q^{57} - 40 q^{58} - 24 q^{59} + 8 q^{60} + 2 q^{61} + 64 q^{63} - 42 q^{65} - 4 q^{66} - 36 q^{68} + 20 q^{70} + 18 q^{72} + 48 q^{73} + 216 q^{74} - 26 q^{76} + 22 q^{78} - 22 q^{79} + 10 q^{81} + 30 q^{83} + 94 q^{84} - 18 q^{85} - 120 q^{86} + 68 q^{87} - 72 q^{92} - 62 q^{93} + 32 q^{94} + 16 q^{96} - 4 q^{97} - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.999012	−	0.267684i	−0.706408	−	0.189281i	−0.112309	−	0.993673i	$-0.535825\pi$
$2$	−0.999012	−	0.267684i	−0.706408	−	0.189281i	−0.594099	+	0.804392i	$0.702491\pi$
$3$	−1.73168	−	0.0358377i	−0.999786	−	0.0206909i
$3$	−1.73168	−	0.0358377i	−0.999786	−	0.0206909i
$4$	−0.805681	−	0.465160i	−0.402840	−	0.232580i
$5$	0.483213	+	1.80337i	0.216099	+	0.806493i	0.985777	+	0.168060i	$0.0537504\pi$
$5$	0.483213	+	1.80337i	0.216099	+	0.806493i	−0.769677	+	0.638433i	$0.779583\pi$
$6$	1.72038	+	0.499346i	0.702340	+	0.203857i
$7$	3.99567	+	1.07064i	1.51022	+	0.404663i	0.916509	−	0.400014i	$-0.130995\pi$
$7$	3.99567	+	1.07064i	1.51022	+	0.404663i	0.593713	+	0.804677i	$0.297662\pi$
$8$	2.14302	+	2.14302i	0.757673	+	0.757673i
$9$	2.99743	+	0.124119i	0.999144	+	0.0413729i
$10$		−	1.93094i		−	0.610617i
$11$	−0.995710	+	3.71604i	−0.300218	+	1.12043i	0.636767	+	0.771057i	$0.280271\pi$
$11$	−0.995710	+	3.71604i	−0.300218	+	1.12043i	−0.936984	+	0.349371i	$0.886395\pi$
$12$	1.37851	+	0.834382i	0.397942	+	0.240865i
$13$	−2.74203	−	2.34121i	−0.760503	−	0.649334i
$13$	−2.74203	−	2.34121i	−0.760503	−	0.649334i
$14$	−3.70513	−	2.13916i	−0.990238	−	0.571714i
$15$	−0.772141	−	3.14018i	−0.199366	−	0.810792i
$16$	−0.636932	−	1.10320i	−0.159233	−	0.275800i
$17$	−0.582460			−0.141267			−0.0706337	−	0.997502i	$-0.522502\pi$
$17$	−0.582460			−0.141267			−0.0706337	+	0.997502i	$0.522502\pi$
$18$	−2.96125	−	0.926362i	−0.697972	−	0.218346i
$19$	4.41048	+	4.41048i	1.01183	+	1.01183i	0.999929	+	0.0119052i	$0.00378963\pi$
$19$	4.41048	+	4.41048i	1.01183	+	1.01183i	0.0119052	+	0.999929i	$0.496210\pi$
$20$	0.449542	−	1.67772i	0.100521	−	0.375149i
$21$	−6.88085	−	1.99720i	−1.50153	−	0.435824i
$22$	1.98945	−	3.44583i	0.424153	−	0.734654i
$23$	−2.65310	+	4.59531i	−0.553210	+	0.958187i	0.444831	+	0.895615i	$0.353264\pi$
$23$	−2.65310	+	4.59531i	−0.553210	+	0.958187i	−0.998040	+	0.0625727i	$0.980069\pi$
$24$	−3.63423	−	3.78783i	−0.741834	−	0.773188i
$25$	1.31146	−	0.757174i	0.262293	−	0.151435i
$26$	2.11262	+	3.07289i	0.414318	+	0.602644i
$27$	−5.18614	−	0.322355i	−0.998074	−	0.0620372i
$28$	−2.72122	−	2.72122i	−0.514262	−	0.514262i
$29$	5.19577	−	2.99978i	0.964830	−	0.557045i	0.0671740	−	0.997741i	$-0.478602\pi$
$29$	5.19577	−	2.99978i	0.964830	−	0.557045i	0.897656	+	0.440696i	$0.145268\pi$
$30$	−0.0692004	+	3.34377i	−0.0126342	+	0.610486i
$31$	2.14445	−	0.574604i	0.385155	−	0.103202i	−0.0610457	−	0.998135i	$-0.519444\pi$
$31$	2.14445	−	0.574604i	0.385155	−	0.103202i	0.446200	+	0.894933i	$0.352777\pi$
$32$	−1.22781	−	4.58224i	−0.217048	−	0.810034i
$33$	1.85742	−	6.39931i	0.323336	−	1.11398i
$34$	0.581885	+	0.155916i	0.0997924	+	0.0267393i
$35$			7.72303i			1.30543i
$36$	−2.35724	−	1.49429i	−0.392873	−	0.249048i
$37$	−4.32606	+	4.32606i	−0.711200	+	0.711200i	−0.966786	−	0.255586i	$-0.917732\pi$
$37$	−4.32606	+	4.32606i	−0.711200	+	0.711200i	0.255586	+	0.966786i	$0.417732\pi$
$38$	−3.22551	−	5.58674i	−0.523246	−	0.906289i
$39$	4.66442	+	4.15249i	0.746905	+	0.664931i
$40$	−2.82914	+	4.90021i	−0.447326	+	0.774791i
$41$	−1.64290	−	6.13140i	−0.256578	−	0.957564i	−0.967206	−	0.253995i	$-0.918255\pi$
$41$	−1.64290	−	6.13140i	−0.256578	−	0.957564i	0.710627	−	0.703569i	$-0.248411\pi$
$42$	6.33944	+	3.83712i	0.978196	+	0.592080i
$43$	−5.20669	+	3.00608i	−0.794013	+	0.458424i	−0.841373	−	0.540454i	$-0.818252\pi$
$43$	−5.20669	+	3.00608i	−0.794013	+	0.458424i	0.0473604	+	0.998878i	$0.484919\pi$
$44$	2.53078	−	2.53078i	0.381529	−	0.381529i
$45$	1.22456	+	5.46547i	0.182547	+	0.814744i
$46$	3.88057	−	3.88057i	0.572159	−	0.572159i
$47$	1.64988	−	6.15742i	0.240659	−	0.898152i	−0.734856	−	0.678223i	$-0.762751\pi$
$47$	1.64988	−	6.15742i	0.240659	−	0.898152i	0.975516	−	0.219930i	$-0.0705828\pi$
$48$	1.06343	+	1.93321i	0.153492	+	0.279035i
$49$	8.75694	+	5.05582i	1.25099	+	0.722261i
$50$	−1.51285	+	0.405367i	−0.213949	+	0.0573276i
$51$	1.00863	+	0.0208740i	0.141237	+	0.00292295i
$52$	1.12017	+	3.16175i	0.155339	+	0.438456i
$53$		−	1.69062i		−	0.232225i	−0.993236	−	0.116112i	$-0.962957\pi$
$53$		−	1.69062i		−	0.232225i	0.993236	−	0.116112i	$-0.0370433\pi$
$54$	5.09473	+	1.71029i	0.693305	+	0.232740i
$55$	−7.18255			−0.968495
$56$	6.26842	+	10.8572i	0.837653	+	1.45086i
$57$	−7.47948	−	7.79561i	−0.990682	−	1.03255i
$58$	−5.99363	+	1.60599i	−0.787002	+	0.210877i
$59$	6.45229	−	1.72888i	0.840016	−	0.225082i	0.186938	−	0.982372i	$-0.440144\pi$
$59$	6.45229	−	1.72888i	0.840016	−	0.225082i	0.653079	+	0.757290i	$0.273477\pi$
$60$	−0.838589	+	2.88916i	−0.108261	+	0.372988i
$61$	−1.12715	−	1.95228i	−0.144316	−	0.249963i	0.784801	−	0.619747i	$-0.212765\pi$
$61$	−1.12715	−	1.95228i	−0.144316	−	0.249963i	−0.929118	+	0.369784i	$0.879432\pi$
$62$	−2.29614			−0.291611
$63$	11.8439	+	3.70510i	1.49219	+	0.466798i
$64$			7.45411i			0.931764i
$65$	2.89709	−	6.07621i	0.359340	−	0.753661i
$66$	−3.56858	+	5.89578i	−0.439262	+	0.725720i
$67$	−2.21763	+	0.594213i	−0.270927	+	0.0725947i	−0.391725	−	0.920082i	$-0.628121\pi$
$67$	−2.21763	+	0.594213i	−0.270927	+	0.0725947i	0.120798	+	0.992677i	$0.461455\pi$
$68$	0.469277	+	0.270937i	0.0569082	+	0.0328560i
$69$	4.75901	−	7.86252i	0.572917	−	0.946536i
$70$	2.06734	−	7.71540i	0.247094	−	0.922167i
$71$	−1.87415	+	1.87415i	−0.222420	+	0.222420i	−0.809517	−	0.587097i	$-0.800271\pi$
$71$	−1.87415	+	1.87415i	−0.222420	+	0.222420i	0.587097	+	0.809517i	$0.300271\pi$
$72$	6.15758	+	6.68956i	0.725677	+	0.788372i
$73$	5.42937	−	5.42937i	0.635460	−	0.635460i	−0.313972	−	0.949432i	$-0.601660\pi$
$73$	5.42937	−	5.42937i	0.635460	−	0.635460i	0.949432	+	0.313972i	$0.101660\pi$
$74$	5.47981	−	3.16377i	0.637015	−	0.367781i
$75$	−2.29817	+	1.26418i	−0.265370	+	0.145975i
$76$	−1.50186	−	5.60502i	−0.172275	−	0.642940i
$77$	−7.95706	+	13.7820i	−0.906791	+	1.57061i
$78$	−3.54825	−	5.39698i	−0.401761	−	0.611088i
$79$	−1.10654	−	1.91658i	−0.124495	−	0.215632i	0.797040	−	0.603926i	$-0.206398\pi$
$79$	−1.10654	−	1.91658i	−0.124495	−	0.215632i	−0.921535	+	0.388294i	$0.873064\pi$
$80$	1.68171	−	1.68171i	0.188020	−	0.188020i
$81$	8.96919	+	0.744075i	0.996577	+	0.0826750i
$82$			6.56512i			0.724996i
$83$	−11.0196	−	2.95269i	−1.20956	−	0.324100i	−0.402969	−	0.915213i	$-0.632022\pi$
$83$	−11.0196	−	2.95269i	−1.20956	−	0.324100i	−0.806588	+	0.591113i	$0.798689\pi$
$84$	4.61476	+	4.80980i	0.503511	+	0.524792i
$85$	−0.281452	−	1.05039i	−0.0305278	−	0.113931i
$86$	6.00623	−	1.60936i	0.647668	−	0.173542i
$87$	−9.10492	+	5.00845i	−0.976150	+	0.536963i
$88$	−10.0974	+	5.82973i	−1.07639	+	0.621451i
$89$	−0.110864	−	0.110864i	−0.0117515	−	0.0117515i	0.701207	−	0.712958i	$-0.252645\pi$
$89$	−0.110864	−	0.110864i	−0.0117515	−	0.0117515i	−0.712958	+	0.701207i	$0.752645\pi$
$90$	0.239666	−	5.78786i	0.0252630	−	0.610094i
$91$	−8.44967	−	12.2904i	−0.885767	−	1.28839i
$92$	4.27511	−	2.46823i	0.445711	−	0.257331i
$93$	−3.73409	+	0.918178i	−0.387207	+	0.0952106i
$94$	−3.29649	+	5.70969i	−0.340007	+	0.588910i
$95$	−5.82255	+	10.0850i	−0.597381	+	1.03469i
$96$	1.96195	+	7.97898i	0.200241	+	0.814352i
$97$	2.91212	−	10.8682i	0.295681	−	1.10350i	−0.644994	−	0.764187i	$-0.723140\pi$
$97$	2.91212	−	10.8682i	0.295681	−	1.10350i	0.940675	−	0.339308i	$-0.110193\pi$
$98$	−7.39493	−	7.39493i	−0.747000	−	0.747000i
$99$	−3.44580	+	11.0150i	−0.346316	+	1.10705i
$100$	−1.40883			−0.140883
$101$	−3.68805	−	6.38789i	−0.366975	−	0.635619i	0.622116	−	0.782925i	$-0.286273\pi$
$101$	−3.68805	−	6.38789i	−0.366975	−	0.635619i	−0.989091	+	0.147306i	$0.952940\pi$
$102$	−1.00205	−	0.290849i	−0.0992178	−	0.0287984i
$103$	10.0414	+	5.79738i	0.989404	+	0.571233i	0.905096	−	0.425207i	$-0.139799\pi$
$103$	10.0414	+	5.79738i	0.989404	+	0.571233i	0.0843082	+	0.996440i	$0.473132\pi$
$104$	−0.858975	−	10.8935i	−0.0842294	−	1.06820i
$105$	0.276776	−	13.3738i	0.0270105	−	1.30515i
$106$	−0.452553	+	1.68895i	−0.0439559	+	0.164045i
$107$		−	13.0948i		−	1.26592i	−0.774184	−	0.632960i	$-0.781840\pi$
$107$		−	13.0948i		−	1.26592i	0.774184	−	0.632960i	$-0.218160\pi$
$108$	4.02843	+	2.67210i	0.387636	+	0.257123i
$109$	4.03976	+	4.03976i	0.386939	+	0.386939i	0.873594	−	0.486655i	$-0.161783\pi$
$109$	4.03976	+	4.03976i	0.386939	+	0.386939i	−0.486655	+	0.873594i	$0.661783\pi$
$110$	7.17545	+	1.92266i	0.684152	+	0.183318i
$111$	7.64639	−	7.33632i	0.725763	−	0.696333i
$112$	−1.36385	−	5.08994i	−0.128871	−	0.480954i
$113$	−11.5455	−	6.66581i	−1.08611	−	0.627066i	−0.153572	−	0.988137i	$-0.549078\pi$
$113$	−11.5455	−	6.66581i	−1.08611	−	0.627066i	−0.932538	+	0.361071i	$0.882411\pi$
$114$	5.38533	+	9.79005i	0.504383	+	0.916922i
$115$	−9.56907	−	2.56402i	−0.892320	−	0.239096i
$116$	−5.58151			−0.518230
$117$	−7.92847	−	7.35795i	−0.732987	−	0.680243i
$118$	−6.90871			−0.635998
$119$	−2.32732	−	0.623603i	−0.213345	−	0.0571656i
$120$	5.07477	−	8.38421i	0.463261	−	0.765370i
$121$	−3.29123	−	1.90019i	−0.299203	−	0.172745i
$122$	0.603439	+	2.25207i	0.0546328	+	0.203892i
$123$	2.62525	+	10.6765i	0.236711	+	0.962668i
$124$	−1.99503	−	0.534565i	−0.179159	−	0.0480054i
$125$	8.59999	+	8.59999i	0.769207	+	0.769207i
$126$	−10.8404	−	6.87185i	−0.965736	−	0.612193i
$127$		−	3.14850i		−	0.279384i	−0.990195	−	0.139692i	$-0.955389\pi$
$127$		−	3.14850i		−	0.279384i	0.990195	−	0.139692i	$-0.0446112\pi$
$128$	−0.460268	+	1.71774i	−0.0406823	+	0.151829i
$129$	9.12405	−	5.01898i	0.803328	−	0.441897i
$130$	−4.52074	+	5.29470i	−0.396495	+	0.464376i
$131$	11.0320	+	6.36931i	0.963868	+	0.556489i	0.897361	−	0.441297i	$-0.145481\pi$
$131$	11.0320	+	6.36931i	0.963868	+	0.556489i	0.0665064	+	0.997786i	$0.478815\pi$
$132$	−4.47319	+	4.29180i	−0.389342	+	0.373553i
$133$	12.9008	+	22.3449i	1.11864	+	1.93755i
$134$	2.37451			0.205126
$135$	−1.92468	−	9.50832i	−0.165650	−	0.818346i
$136$	−1.24823	−	1.24823i	−0.107035	−	0.107035i
$137$	−2.67645	+	9.98866i	−0.228665	+	0.853389i	0.752238	+	0.658891i	$0.228974\pi$
$137$	−2.67645	+	9.98866i	−0.228665	+	0.853389i	−0.980903	+	0.194498i	$0.937692\pi$
$138$	−6.85898	+	6.58084i	−0.583875	+	0.560198i
$139$	8.51145	−	14.7423i	0.721932	−	1.25042i	−0.238292	−	0.971193i	$-0.576588\pi$
$139$	8.51145	−	14.7423i	0.721932	−	1.25042i	0.960224	−	0.279229i	$-0.0900790\pi$
$140$	3.59245	−	6.22230i	0.303617	−	0.525880i
$141$	−3.07773	+	10.6036i	−0.259191	+	0.892981i
$142$	2.37398	−	1.37062i	0.199220	−	0.115020i
$143$	11.4303	−	7.85834i	0.955849	−	0.657147i
$144$	−1.77223	−	3.38582i	−0.147686	−	0.282151i
$145$	7.92039	+	7.92039i	0.657752	+	0.657752i
$146$	−6.87737	+	3.97065i	−0.569175	+	0.328613i
$147$	−14.9830	−	9.06890i	−1.23578	−	0.747990i
$148$	5.49774	−	1.47311i	0.451911	−	0.121089i
$149$	−0.649181	−	2.42278i	−0.0531830	−	0.198482i	0.934223	−	0.356690i	$-0.116095\pi$
$149$	−0.649181	−	2.42278i	−0.0531830	−	0.198482i	−0.987406	+	0.158209i	$0.949428\pi$
$150$	2.63430	−	0.647749i	0.215090	−	0.0528885i
$151$	−6.58685	−	1.76494i	−0.536030	−	0.143629i	−0.0193588	−	0.999813i	$-0.506162\pi$
$151$	−6.58685	−	1.76494i	−0.536030	−	0.143629i	−0.516672	+	0.856184i	$0.672829\pi$
$152$			18.9035i			1.53328i
$153$	−1.74588	−	0.0722942i	−0.141146	−	0.00584464i
$154$	11.6384	−	11.6384i	0.937851	−	0.937851i
$155$	2.07245	+	3.58959i	0.166463	+	0.288323i
$156$	−1.82646	−	5.51529i	−0.146234	−	0.441576i
$157$	−2.09675	+	3.63167i	−0.167339	+	0.289839i	−0.937483	−	0.348030i	$-0.886851\pi$
$157$	−2.09675	+	3.63167i	−0.167339	+	0.289839i	0.770145	+	0.637869i	$0.220184\pi$
$158$	0.592405	+	2.21088i	0.0471292	+	0.175889i
$159$	−0.0605879	+	2.92762i	−0.00480494	+	0.232175i
$160$	7.67021	−	4.42840i	0.606383	−	0.350096i
$161$	−15.5208	+	15.5208i	−1.22321	+	1.22321i
$162$	−8.76115	−	3.14425i	−0.688341	−	0.247036i
$163$	−5.06027	+	5.06027i	−0.396351	+	0.396351i	−0.876944	−	0.480593i	$-0.840421\pi$
$163$	−5.06027	+	5.06027i	−0.396351	+	0.396351i	0.480593	+	0.876944i	$0.340421\pi$
$164$	−1.52843	+	5.70417i	−0.119350	+	0.445420i
$165$	12.4379	+	0.257406i	0.968287	+	0.0200390i
$166$	10.2183	+	5.89955i	0.793095	+	0.457894i
$167$	14.4728	−	3.87797i	1.11994	−	0.300086i	0.349079	−	0.937093i	$-0.386494\pi$
$167$	14.4728	−	3.87797i	1.11994	−	0.300086i	0.770858	+	0.637007i	$0.219828\pi$
$168$	−10.4658	−	19.0259i	−0.807454	−	1.46788i
$169$	2.03748	+	12.8393i	0.156729	+	0.987642i
$170$			1.12470i			0.0862603i
$171$	12.6727	+	13.7675i	0.969105	+	1.05283i
$172$	5.59324			0.426481
$173$	−4.14686	−	7.18257i	−0.315280	−	0.546081i	0.664217	−	0.747540i	$-0.268765\pi$
$173$	−4.14686	−	7.18257i	−0.315280	−	0.546081i	−0.979497	+	0.201459i	$0.935432\pi$
$174$	10.4366	−	2.56626i	0.791197	−	0.194548i
$175$	6.05083	−	1.62132i	0.457400	−	0.122560i
$176$	4.73373	−	1.26840i	0.356818	−	0.0956092i
$177$	−11.2353	+	2.76264i	−0.844493	+	0.207653i
$178$	0.0810777	+	0.140431i	0.00607703	+	0.0105257i
$179$	11.3122			0.845516			0.422758	−	0.906243i	$-0.361062\pi$
$179$	11.3122			0.845516			0.422758	+	0.906243i	$0.361062\pi$
$180$	1.55571	−	4.97304i	0.115956	−	0.370669i
$181$		−	5.84729i		−	0.434625i	−0.976102	−	0.217313i	$-0.930271\pi$
$181$		−	5.84729i		−	0.434625i	0.976102	−	0.217313i	$-0.0697291\pi$
$182$	5.15137	+	14.5401i	0.381845	+	1.07779i
$183$	1.88189	+	3.42111i	0.139113	+	0.252896i
$184$	−15.5335	+	4.16219i	−1.14515	+	0.306841i
$185$	−9.89192	−	5.71110i	−0.727268	−	0.419889i
$186$	3.97619	+	0.0822884i	0.291548	+	0.00603368i
$187$	0.579961	−	2.16445i	0.0424110	−	0.158280i
$188$	−4.19346	+	4.19346i	−0.305840	+	0.305840i
$189$	−20.3770	−	6.84050i	−1.48221	−	0.497573i
$190$	8.51638	−	8.51638i	0.617843	−	0.617843i
$191$	−9.02346	+	5.20970i	−0.652915	+	0.376961i	−0.789572	−	0.613658i	$-0.789697\pi$
$191$	−9.02346	+	5.20970i	−0.652915	+	0.376961i	0.136657	+	0.990618i	$0.456364\pi$
$192$	0.267138	−	12.9081i	0.0192790	−	0.931564i
$193$	−1.11825	−	4.17338i	−0.0804937	−	0.300407i	0.913929	−	0.405874i	$-0.133033\pi$
$193$	−1.11825	−	4.17338i	−0.0804937	−	0.300407i	−0.994423	+	0.105467i	$0.966366\pi$
$194$	−5.81848	+	10.0779i	−0.417743	+	0.723551i
$195$	−5.23459	+	10.4182i	−0.374857	+	0.746065i
$196$	−4.70354	−	8.14676i	−0.335967	−	0.581912i
$197$	13.2865	−	13.2865i	0.946621	−	0.946621i	−0.0520252	−	0.998646i	$-0.516568\pi$
$197$	13.2865	−	13.2865i	0.946621	−	0.946621i	0.998646	+	0.0520252i	$0.0165676\pi$
$198$	6.39094	−	10.0817i	0.454184	−	0.716476i
$199$		−	1.03922i		−	0.0736684i	−0.999321	−	0.0368342i	$-0.988273\pi$
$199$		−	1.03922i		−	0.0736684i	0.999321	−	0.0368342i	$-0.0117273\pi$
$200$	4.43314	+	1.18786i	0.313470	+	0.0839941i
$201$	3.86153	−	0.949513i	0.272371	−	0.0669735i
$202$	1.97447	+	7.36881i	0.138923	+	0.518468i
$203$	23.9723	−	6.42335i	1.68252	−	0.450831i
$204$	−0.802928	−	0.485994i	−0.0562162	−	0.0340264i
$205$	10.2633	−	5.92554i	0.716823	−	0.413858i
$206$	−8.47957	−	8.47957i	−0.590799	−	0.590799i
$207$	−8.52285	+	13.4448i	−0.592379	+	0.934479i
$208$	−0.836330	+	4.51620i	−0.0579891	+	0.313142i
$209$	−20.7811	+	11.9980i	−1.43746	+	0.829917i
$210$	−3.85647	+	13.2865i	−0.266121	+	0.916857i
$211$	−12.1856	+	21.1061i	−0.838893	+	1.45300i	0.0519286	+	0.998651i	$0.483463\pi$
$211$	−12.1856	+	21.1061i	−0.838893	+	1.45300i	−0.890821	+	0.454354i	$0.849870\pi$
$212$	−0.786410	+	1.36210i	−0.0540109	+	0.0935495i
$213$	3.31259	−	3.17826i	0.226975	−	0.217771i
$214$	−3.50527	+	13.0818i	−0.239615	+	0.894257i
$215$	−7.93703	−	7.93703i	−0.541301	−	0.541301i
$216$	−10.4232	−	11.8048i	−0.709210	−	0.803218i
$217$	9.18371			0.623431
$218$	−2.95439	−	5.11715i	−0.200096	−	0.346577i
$219$	−9.59651	+	9.20736i	−0.648472	+	0.622176i
$220$	5.78684	+	3.34103i	0.390149	+	0.225253i
$221$	1.59712	+	1.36366i	0.107434	+	0.0917298i
$222$	−9.60266	+	5.28225i	−0.644488	+	0.354521i
$223$	4.53123	−	16.9108i	0.303433	−	1.13243i	−0.630852	−	0.775903i	$-0.717294\pi$
$223$	4.53123	−	16.9108i	0.303433	−	1.13243i	0.934285	−	0.356526i	$-0.116039\pi$
$224$		−	19.6237i		−	1.31116i
$225$	4.02500	−	2.10680i	0.268333	−	0.140453i
$226$	9.74977	+	9.74977i	0.648545	+	0.648545i
$227$	4.81770	+	1.29090i	0.319762	+	0.0856800i	0.415130	−	0.909762i	$-0.363736\pi$
$227$	4.81770	+	1.29090i	0.319762	+	0.0856800i	−0.0953678	+	0.995442i	$0.530403\pi$
$228$	2.39987	+	9.75993i	0.158935	+	0.646367i
$229$	−4.13081	−	15.4164i	−0.272972	−	1.01875i	−0.957188	−	0.289466i	$-0.906522\pi$
$229$	−4.13081	−	15.4164i	−0.272972	−	1.01875i	0.684216	−	0.729279i	$-0.260144\pi$
$230$	8.87326	+	5.12298i	0.585086	+	0.337799i
$231$	14.2730	−	23.5809i	0.939094	−	1.55151i
$232$	17.5633	+	4.70606i	1.15308	+	0.308968i
$233$	5.29023			0.346575			0.173287	−	0.984871i	$-0.444561\pi$
$233$	5.29023			0.346575			0.173287	+	0.984871i	$0.444561\pi$
$234$	5.95102	+	9.47301i	0.389031	+	0.619270i
$235$	11.9014			0.776360
$236$	−6.00269	−	1.60842i	−0.390742	−	0.104699i
$237$	1.84748	+	3.35855i	0.120007	+	0.218161i
$238$	2.15809	+	1.24597i	0.139888	+	0.0807645i
$239$	2.10350	+	7.85038i	0.136064	+	0.507799i	0.999991	+	0.00418163i	$0.00133106\pi$
$239$	2.10350	+	7.85038i	0.136064	+	0.507799i	−0.863927	+	0.503617i	$0.832002\pi$
$240$	−2.97245	+	2.85191i	−0.191871	+	0.184090i
$241$	−5.92226	−	1.58687i	−0.381486	−	0.102219i	0.0629793	−	0.998015i	$-0.479940\pi$
$241$	−5.92226	−	1.58687i	−0.381486	−	0.102219i	−0.444466	+	0.895796i	$0.646606\pi$
$242$	2.77933	+	2.77933i	0.178662	+	0.178662i
$243$	−15.5051	−	1.60993i	−0.994653	−	0.103277i
$244$			2.09721i			0.134260i
$245$	−4.88608	+	18.2351i	−0.312160	+	1.16500i
$246$	0.235279	−	11.3687i	0.0150008	−	0.724841i
$247$	−1.76783	−	22.4196i	−0.112484	−	1.42652i
$248$	5.82700	+	3.36422i	0.370015	+	0.213628i
$249$	18.9766	+	5.50803i	1.20259	+	0.349057i
$250$	−6.28941	−	10.8936i	−0.397777	−	0.688970i
$251$	−13.2914			−0.838945			−0.419472	−	0.907768i	$-0.637785\pi$
$251$	−13.2914			−0.838945			−0.419472	+	0.907768i	$0.637785\pi$
$252$	−7.81891	−	8.49442i	−0.492545	−	0.535098i
$253$	−14.4346	−	14.4346i	−0.907497	−	0.907497i
$254$	−0.842804	+	3.14539i	−0.0528822	+	0.197359i
$255$	0.449741	+	1.82903i	0.0281639	+	0.114538i
$256$	8.37374	−	14.5037i	0.523359	−	0.906484i
$257$	−10.9925	+	19.0396i	−0.685694	+	1.18766i	0.287525	+	0.957773i	$0.407168\pi$
$257$	−10.9925	+	19.0396i	−0.685694	+	1.18766i	−0.973218	+	0.229883i	$0.926166\pi$
$258$	−10.4585	+	2.57165i	−0.651120	+	0.160104i
$259$	−21.9172	+	12.6539i	−1.36187	+	0.786274i
$260$	−5.16054	+	3.54788i	−0.320043	+	0.220030i
$261$	15.9463	−	8.34674i	0.987051	−	0.516650i
$262$	−9.31610	−	9.31610i	−0.575551	−	0.575551i
$263$	−2.98325	+	1.72238i	−0.183955	+	0.106206i	−0.589149	−	0.808024i	$-0.700537\pi$
$263$	−2.98325	+	1.72238i	−0.183955	+	0.106206i	0.405195	+	0.914230i	$0.367204\pi$
$264$	17.6944	−	9.73336i	1.08901	−	0.599047i
$265$	3.04882	−	0.816930i	0.187288	−	0.0501836i
$266$	−6.90669	−	25.7761i	−0.423477	−	1.58044i
$267$	0.188007	+	0.195954i	0.0115059	+	0.0119922i
$268$	2.06311	+	0.552809i	0.126025	+	0.0337682i
$269$		−	11.4792i		−	0.699897i	−0.936769	−	0.349949i	$-0.886199\pi$
$269$		−	11.4792i		−	0.699897i	0.936769	−	0.349949i	$-0.113801\pi$
$270$	−0.622448	+	10.0141i	−0.0378810	+	0.609441i
$271$	−12.6571	+	12.6571i	−0.768862	+	0.768862i	−0.977906	−	0.209044i	$-0.932965\pi$
$271$	−12.6571	+	12.6571i	−0.768862	+	0.768862i	0.209044	+	0.977906i	$0.432965\pi$
$272$	0.370988	+	0.642569i	0.0224944	+	0.0389615i
$273$	14.1917	+	21.5859i	0.858919	+	1.30644i
$274$	5.34762	−	9.26235i	0.323061	−	0.559559i
$275$	1.50785	+	5.62737i	0.0909268	+	0.339343i
$276$	−7.49157	+	4.12098i	−0.450940	+	0.248054i
$277$	8.64049	−	4.98859i	0.519157	−	0.299735i	−0.217433	−	0.976075i	$-0.569768\pi$
$277$	8.64049	−	4.98859i	0.519157	−	0.299735i	0.736590	+	0.676340i	$0.236435\pi$
$278$	−12.4493	+	12.4493i	−0.746660	+	0.746660i
$279$	6.49916	−	1.45617i	0.389095	−	0.0871785i
$280$	−16.5506	+	16.5506i	−0.989090	+	0.989090i
$281$	2.28589	−	8.53106i	0.136365	−	0.508920i	−0.863624	−	0.504137i	$-0.831811\pi$
$281$	2.28589	−	8.53106i	0.136365	−	0.508920i	0.999989	−	0.00478344i	$-0.00152262\pi$
$282$	5.91309	−	9.76922i	0.352120	−	0.581749i
$283$	−21.0010	−	12.1249i	−1.24838	−	0.720751i	−0.277592	−	0.960699i	$-0.589536\pi$
$283$	−21.0010	−	12.1249i	−1.24838	−	0.720751i	−0.970786	+	0.239947i	$0.922870\pi$
$284$	2.38174	−	0.638186i	0.141330	−	0.0378694i
$285$	10.4442	−	17.2552i	0.618662	−	1.02211i
$286$	−13.5226	+	4.79086i	−0.799605	+	0.283289i
$287$		−	26.2580i		−	1.54996i
$288$	−3.11153	−	13.8874i	−0.183349	−	0.818320i
$289$	−16.6607			−0.980044
$290$	−5.79240	−	10.0327i	−0.340141	−	0.589142i
$291$	−5.43235	+	18.7158i	−0.318450	+	1.09714i
$292$	−6.89987	+	1.84881i	−0.403784	+	0.108194i
$293$	−24.3812	+	6.53292i	−1.42436	+	0.381657i	−0.887030	−	0.461712i	$-0.847235\pi$
$293$	−24.3812	+	6.53292i	−1.42436	+	0.381657i	−0.537334	+	0.843369i	$0.680569\pi$
$294$	12.5406	+	13.0707i	0.731384	+	0.762297i
$295$	6.23565	+	10.8005i	0.363054	+	0.628828i
$296$	−18.5417			−1.07771
$297$	6.36178	−	18.9509i	0.369148	−	1.09965i
$298$			2.59416i			0.150276i
$299$	18.0335	−	6.38901i	1.04290	−	0.369486i
$300$	2.43964	+	0.0504891i	0.140853	+	0.00291499i
$301$	−24.0227	+	6.43685i	−1.38464	+	0.371014i
$302$	6.10790	+	3.52640i	0.351470	+	0.202921i
$303$	6.15760	+	11.1940i	0.353745	+	0.643076i
$304$	2.05646	−	7.67482i	0.117946	−	0.440181i
$305$	2.97603	−	2.97603i	0.170407	−	0.170407i
$306$	1.72481	+	0.539569i	0.0986007	+	0.0308451i
$307$	−3.40491	+	3.40491i	−0.194329	+	0.194329i	−0.797564	−	0.603235i	$-0.793878\pi$
$307$	−3.40491	+	3.40491i	−0.194329	+	0.194329i	0.603235	+	0.797564i	$0.293878\pi$
$308$	12.8217	−	7.40261i	0.730584	−	0.421803i
$309$	−17.1807	−	10.3991i	−0.977373	−	0.591582i
$310$	−1.10953	−	4.14081i	−0.0630168	−	0.235182i
$311$	12.5475	−	21.7329i	0.711502	−	1.23236i	−0.252791	−	0.967521i	$-0.581348\pi$
$311$	12.5475	−	21.7329i	0.711502	−	1.23236i	0.964293	−	0.264837i	$-0.0853182\pi$
$312$	1.09707	+	18.8949i	0.0621094	+	1.06971i
$313$	7.79376	+	13.4992i	0.440529	+	0.763019i	0.997729	−	0.0673596i	$-0.0214575\pi$
$313$	7.79376	+	13.4992i	0.440529	+	0.763019i	−0.557199	+	0.830379i	$0.688124\pi$
$314$	3.06682	−	3.06682i	0.173071	−	0.173071i
$315$	−0.958573	+	23.1493i	−0.0540095	+	1.30431i
$316$			2.05886i			0.115820i
$317$	31.6351	+	8.47660i	1.77680	+	0.476093i	0.989995	−	0.141104i	$-0.0450652\pi$
$317$	31.6351	+	8.47660i	1.77680	+	0.476093i	0.786809	+	0.617197i	$0.211732\pi$
$318$	0.844205	−	2.90851i	0.0473407	−	0.163101i
$319$	5.97382	+	22.2946i	0.334470	+	1.24826i
$320$	−13.4425	+	3.60192i	−0.751461	+	0.201353i
$321$	−0.469287	+	22.6760i	−0.0261930	+	1.26565i
$322$	19.6602	−	11.3508i	1.09562	−	0.632556i
$323$	−2.56893	−	2.56893i	−0.142939	−	0.142939i
$324$	−6.88019	−	4.77160i	−0.382233	−	0.265089i
$325$	−5.36878	−	0.994215i	−0.297806	−	0.0551491i
$326$	6.40982	−	3.70071i	0.355007	−	0.204963i
$327$	−6.85080	−	7.14035i	−0.378850	−	0.394862i
$328$	9.61895	−	16.6605i	0.531118	−	0.919923i
$329$	13.1847	−	22.8366i	0.726897	−	1.25902i
$330$	−12.3567	−	3.58658i	−0.680213	−	0.197435i
$331$	1.49412	−	5.57612i	0.0821241	−	0.306491i	−0.912630	−	0.408787i	$-0.865952\pi$
$331$	1.49412	−	5.57612i	0.0821241	−	0.306491i	0.994754	+	0.102295i	$0.0326187\pi$
$332$	7.50480	+	7.50480i	0.411880	+	0.411880i
$333$	−13.5040	+	12.4301i	−0.740016	+	0.681167i
$334$	−15.4965			−0.847933
$335$	−2.14318	−	3.71209i	−0.117094	−	0.202813i
$336$	2.17933	+	8.86303i	0.118892	+	0.483518i
$337$	28.5632	+	16.4910i	1.55594	+	0.898321i	0.997639	+	0.0686811i	$0.0218791\pi$
$337$	28.5632	+	16.4910i	1.55594	+	0.898321i	0.558299	+	0.829640i	$0.311454\pi$
$338$	1.40142	−	13.3721i	0.0762273	−	0.727344i
$339$	19.7542	+	11.9568i	1.07290	+	0.649405i
$340$	−0.261841	+	0.977203i	−0.0142003	+	0.0529962i
$341$			8.54100i			0.462521i
$342$	−8.97482	−	17.1462i	−0.485303	−	0.927162i
$343$	9.10168	+	9.10168i	0.491444	+	0.491444i
$344$	−17.6002	−	4.71595i	−0.948938	−	0.254267i
$345$	16.4787	+	4.78300i	0.887182	+	0.257508i
$346$	2.22010	+	8.28553i	0.119353	+	0.445433i
$347$	21.4908	+	12.4077i	1.15369	+	0.666082i	0.949783	−	0.312909i	$-0.101303\pi$
$347$	21.4908	+	12.4077i	1.15369	+	0.666082i	0.203905	+	0.978991i	$0.434637\pi$
$348$	9.66539	+	0.200028i	0.518119	+	0.0107226i
$349$	19.6619	+	5.26839i	1.05248	+	0.282011i	0.743275	−	0.668986i	$-0.233271\pi$
$349$	19.6619	+	5.26839i	1.05248	+	0.282011i	0.309203	+	0.950996i	$0.399938\pi$
$350$	−6.47886			−0.346309
$351$	13.4659	+	13.0258i	0.718755	+	0.695263i
$352$	18.2503			0.972746
$353$	−0.522838	−	0.140094i	−0.0278279	−	0.00745645i	0.244878	−	0.969554i	$-0.421252\pi$
$353$	−0.522838	−	0.140094i	−0.0278279	−	0.00745645i	−0.272706	+	0.962097i	$0.587919\pi$
$354$	11.9637	+	0.247592i	0.635862	+	0.0131594i
$355$	−4.28540	−	2.47418i	−0.227445	−	0.131316i
$356$	0.0377514	+	0.140890i	0.00200082	+	0.00746716i
$357$	4.00782	+	1.16329i	0.212117	+	0.0615677i
$358$	−11.3010	−	3.02811i	−0.597279	−	0.160040i
$359$	19.0909	+	19.0909i	1.00758	+	1.00758i	0.999971	+	0.00760632i	$0.00242119\pi$
$359$	19.0909	+	19.0909i	1.00758	+	1.00758i	0.00760632	+	0.999971i	$0.497579\pi$
$360$	−9.08835	+	14.3369i	−0.478998	+	0.755621i
$361$			19.9047i			1.04762i
$362$	−1.56523	+	5.84151i	−0.0822665	+	0.307023i
$363$	5.63126	+	3.40847i	0.295564	+	0.178898i
$364$	1.09073	+	13.8326i	0.0571697	+	0.725026i
$365$	12.4147	+	7.16765i	0.649817	+	0.375172i
$366$	−0.964255	−	3.92148i	−0.0504024	−	0.204979i
$367$	−12.2840	−	21.2764i	−0.641217	−	1.11062i	−0.985161	−	0.171631i	$-0.945096\pi$
$367$	−12.2840	−	21.2764i	−0.641217	−	1.11062i	0.343944	−	0.938990i	$-0.388237\pi$
$368$	6.75938			0.352357
$369$	−4.16347	−	18.5824i	−0.216742	−	0.967359i
$370$	8.35337	+	8.35337i	0.434271	+	0.434271i
$371$	1.81004	−	6.75517i	0.0939727	−	0.350711i
$372$	3.43559	+	0.997193i	0.178127	+	0.0517021i
$373$	−17.9289	+	31.0537i	−0.928322	+	1.60790i	−0.142193	+	0.989839i	$0.545415\pi$
$373$	−17.9289	+	31.0537i	−0.928322	+	1.60790i	−0.786129	+	0.618062i	$0.787918\pi$
$374$	−1.15878	+	2.00706i	−0.0599189	+	0.103783i
$375$	−14.5842	−	15.2006i	−0.753126	−	0.784957i
$376$	16.7312	−	9.65978i	0.862847	−	0.498165i
$377$	−21.2701	−	3.93889i	−1.09546	−	0.202863i
$378$	18.5258	+	12.2883i	0.952863	+	0.632044i
$379$	4.51433	+	4.51433i	0.231886	+	0.231886i	0.813479	−	0.581594i	$-0.197571\pi$
$379$	4.51433	+	4.51433i	0.231886	+	0.231886i	−0.581594	+	0.813479i	$0.697571\pi$
$380$	9.38224	−	5.41684i	0.481299	−	0.277878i
$381$	−0.112835	+	5.45219i	−0.00578070	+	0.279324i
$382$	10.4091	−	2.78911i	0.532576	−	0.142703i
$383$	−0.108533	−	0.405052i	−0.00554580	−	0.0206972i	0.963097	−	0.269153i	$-0.0867437\pi$
$383$	−0.108533	−	0.405052i	−0.00554580	−	0.0206972i	−0.968643	+	0.248456i	$0.920077\pi$
$384$	0.858597	−	2.95809i	0.0438151	−	0.150954i
$385$	−28.6991	−	7.68990i	−1.46264	−	0.391914i
$386$			4.46860i			0.227446i
$387$	−15.9798	+	8.36428i	−0.812299	+	0.425180i
$388$	−7.40168	+	7.40168i	−0.375763	+	0.375763i
$389$	−13.7379	−	23.7947i	−0.696539	−	1.20644i	−0.969659	−	0.244460i	$-0.921389\pi$
$389$	−13.7379	−	23.7947i	−0.696539	−	1.20644i	0.273121	−	0.961980i	$-0.411944\pi$
$390$	8.01822	−	9.00672i	0.406018	−	0.456073i
$391$	1.54533	−	2.67658i	0.0781505	−	0.135361i
$392$	7.93159	+	29.6011i	0.400606	+	1.49508i
$393$	−18.8756	−	11.4250i	−0.952147	−	0.576313i
$394$	−16.8299	+	9.71675i	−0.847878	+	0.489523i
$395$	2.92161	−	2.92161i	0.147002	−	0.147002i
$396$	7.89995	−	7.27171i	0.396987	−	0.365417i
$397$	14.8082	−	14.8082i	0.743200	−	0.743200i	−0.229992	−	0.973192i	$-0.573870\pi$
$397$	14.8082	−	14.8082i	0.743200	−	0.743200i	0.973192	+	0.229992i	$0.0738701\pi$
$398$	−0.278183	+	1.03819i	−0.0139441	+	0.0520399i
$399$	−21.5393	−	39.1565i	−1.07831	−	1.96028i
$400$	−1.67063	−	0.964536i	−0.0835313	−	0.0482268i
$401$	14.3586	−	3.84739i	0.717036	−	0.192129i	0.118187	−	0.992991i	$-0.462292\pi$
$401$	14.3586	−	3.84739i	0.717036	−	0.192129i	0.598849	+	0.800862i	$0.295625\pi$
$402$	−4.11188	−	0.0850967i	−0.205082	−	0.00424424i
$403$	−7.22542	−	3.44502i	−0.359924	−	0.171609i
$404$			6.86214i			0.341404i
$405$	2.99218	+	16.5343i	0.148683	+	0.821598i
$406$	−25.6680			−1.27388
$407$	−11.7683	−	20.3833i	−0.583334	−	1.01036i
$408$	2.11679	+	2.20626i	0.104797	+	0.109226i
$409$	−24.9027	+	6.67267i	−1.23136	+	0.329942i	−0.815110	−	0.579307i	$-0.803323\pi$
$409$	−24.9027	+	6.67267i	−1.23136	+	0.329942i	−0.416252	+	0.909249i	$0.636657\pi$
$410$	−11.8394	+	3.17235i	−0.584705	+	0.156671i
$411$	4.99273	−	17.2012i	0.246273	−	0.848475i
$412$	−5.39342	−	9.34168i	−0.265715	−	0.460231i
$413$	27.6322			1.35969
$414$	12.1134	−	11.1501i	0.595341	−	0.547997i
$415$		−	21.2992i		−	1.04554i
$416$	−7.36130	+	15.4392i	−0.360917	+	0.756970i
$417$	−15.2674	+	25.2239i	−0.747650	+	1.23522i
$418$	23.9722	−	6.42334i	1.17252	−	0.314176i
$419$	−30.4159	−	17.5606i	−1.48592	−	0.857894i	−0.486044	−	0.873934i	$-0.661561\pi$
$419$	−30.4159	−	17.5606i	−1.48592	−	0.857894i	−0.999871	+	0.0160405i	$0.994894\pi$
$420$	−6.44396	+	10.6463i	−0.314433	+	0.519486i
$421$	3.30996	−	12.3529i	0.161318	−	0.602045i	−0.837164	−	0.546952i	$-0.815788\pi$
$421$	3.30996	−	12.3529i	0.161318	−	0.602045i	0.998481	−	0.0550929i	$-0.0175455\pi$
$422$	17.8234	−	17.8234i	0.867627	−	0.867627i
$423$	5.70964	−	18.2517i	0.277612	−	0.887427i
$424$	3.62304	−	3.62304i	0.175951	−	0.175951i
$425$	−0.763875	+	0.441024i	−0.0370534	+	0.0213928i
$426$	−4.16009	+	2.28839i	−0.201557	+	0.110873i
$427$	−2.41353	−	9.00741i	−0.116799	−	0.435899i
$428$	−6.09117	+	10.5502i	−0.294428	+	0.509964i
$429$	−20.0752	+	13.1985i	−0.969241	+	0.637229i
$430$	5.80457	+	10.0538i	0.279921	+	0.484838i
$431$	23.5930	−	23.5930i	1.13643	−	1.13643i	0.147349	−	0.989084i	$-0.452926\pi$
$431$	23.5930	−	23.5930i	1.13643	−	1.13643i	0.989084	−	0.147349i	$-0.0470742\pi$
$432$	2.94760	+	5.92666i	0.141816	+	0.285147i
$433$		−	10.2411i		−	0.492156i	−0.969250	−	0.246078i	$-0.920858\pi$
$433$		−	10.2411i		−	0.492156i	0.969250	−	0.246078i	$-0.0791419\pi$
$434$	−9.17463	−	2.45834i	−0.440397	−	0.118004i
$435$	−13.4317	−	13.9994i	−0.644002	−	0.671221i
$436$	−1.37562	−	5.13390i	−0.0658804	−	0.245869i
$437$	−31.9690	+	8.56606i	−1.52928	+	0.409770i
$438$	12.0517	−	6.62943i	0.575852	−	0.316766i
$439$	−15.7968	+	9.12026i	−0.753938	+	0.435286i	−0.827115	−	0.562033i	$-0.810020\pi$
$439$	−15.7968	+	9.12026i	−0.753938	+	0.435286i	0.0731771	+	0.997319i	$0.476686\pi$
$440$	−15.3924	−	15.3924i	−0.733802	−	0.733802i
$441$	25.6208	+	16.2414i	1.22004	+	0.773399i
$442$	−1.23052	−	1.78984i	−0.0585297	−	0.0851340i
$443$	−8.26190	+	4.77001i	−0.392535	+	0.226630i	−0.683258	−	0.730177i	$-0.739437\pi$
$443$	−8.26190	+	4.77001i	−0.392535	+	0.226630i	0.290723	+	0.956807i	$0.406104\pi$
$444$	−9.57312	+	2.35394i	−0.454320	+	0.111713i
$445$	0.146358	−	0.253500i	0.00693803	−	0.0120170i
$446$	−9.05350	+	15.6811i	−0.428696	+	0.742523i
$447$	1.03735	+	4.21874i	0.0490648	+	0.199539i
$448$	−7.98064	+	29.7842i	−0.377050	+	1.40717i
$449$	3.01171	+	3.01171i	0.142132	+	0.142132i	0.774592	−	0.632461i	$-0.217955\pi$
$449$	3.01171	+	3.01171i	0.142132	+	0.142132i	−0.632461	+	0.774592i	$0.717955\pi$
$450$	−4.58498	+	1.02729i	−0.216138	+	0.0484268i
$451$	24.4204			1.14991
$452$	6.20133	+	10.7410i	0.291686	+	0.505215i
$453$	11.3431	+	3.29237i	0.532944	+	0.154689i
$454$	−4.46739	−	2.57925i	−0.209665	−	0.121050i
$455$	18.0812	−	21.1768i	0.847661	−	0.992784i
$456$	0.677459	−	32.7349i	0.0317249	−	1.53295i
$457$	−7.05949	+	26.3464i	−0.330229	+	1.23243i	0.578721	+	0.815526i	$0.303552\pi$
$457$	−7.05949	+	26.3464i	−0.330229	+	1.23243i	−0.908950	+	0.416906i	$0.863115\pi$
$458$			16.5069i			0.771318i
$459$	3.02072	+	0.187759i	0.140995	+	0.00876384i
$460$	6.51693	+	6.51693i	0.303854	+	0.303854i
$461$	26.7760	+	7.17460i	1.24708	+	0.334154i	0.821208	−	0.570629i	$-0.193301\pi$
$461$	26.7760	+	7.17460i	1.24708	+	0.334154i	0.425873	+	0.904783i	$0.359967\pi$
$462$	−20.5711	+	19.7369i	−0.957055	+	0.918245i
$463$	−6.20741	−	23.1664i	−0.288483	−	1.07663i	−0.946257	−	0.323416i	$-0.895169\pi$
$463$	−6.20741	−	23.1664i	−0.288483	−	1.07663i	0.657774	−	0.753215i	$-0.271498\pi$
$464$	−6.61870	−	3.82131i	−0.307266	−	0.177400i
$465$	−3.46018	−	6.29029i	−0.160462	−	0.291705i
$466$	−5.28501	−	1.41611i	−0.244823	−	0.0656002i
$467$	−36.2129			−1.67573			−0.837866	−	0.545875i	$-0.816197\pi$
$467$	−36.2129			−1.67573			−0.837866	+	0.545875i	$0.816197\pi$
$468$	2.96519	+	9.61617i	0.137066	+	0.444507i
$469$	−9.49713			−0.438536
$470$	−11.8896	−	3.18581i	−0.548427	−	0.146951i
$471$	3.76105	−	6.21376i	0.173300	−	0.286315i
$472$	17.5324	+	10.1224i	0.806996	+	0.465919i
$473$	−5.98638	−	22.3415i	−0.275254	−	1.02726i
$474$	−0.946622	−	3.84977i	−0.0434798	−	0.176826i
$475$	9.12369	+	2.44469i	0.418624	+	0.112170i
$476$	1.58500	+	1.58500i	0.0726484	+	0.0726484i
$477$	0.209838	−	5.06752i	0.00960782	−	0.232026i
$478$		−	8.40569i		−	0.384468i
$479$	3.00409	−	11.2114i	0.137260	−	0.512263i	−0.862718	−	0.505685i	$-0.831240\pi$
$479$	3.00409	−	11.2114i	0.137260	−	0.512263i	0.999978	−	0.00657751i	$-0.00209370\pi$
$480$	−13.4410	+	7.39368i	−0.613497	+	0.337474i
$481$	21.9904	−	1.73399i	1.00268	−	0.0790631i
$482$	5.49163	+	3.17059i	0.250137	+	0.144417i
$483$	27.4333	−	26.3209i	1.24826	−	1.19764i
$484$	1.76779	+	3.06190i	0.0803539	+	0.139177i
$485$	21.0066			0.953858
$486$	15.0588	+	5.75882i	0.683082	+	0.261225i
$487$	−19.9178	−	19.9178i	−0.902563	−	0.902563i	0.0930945	−	0.995657i	$-0.470324\pi$
$487$	−19.9178	−	19.9178i	−0.902563	−	0.902563i	−0.995657	+	0.0930945i	$0.970324\pi$
$488$	1.76827	−	6.59927i	0.0800458	−	0.298735i
$489$	8.94411	−	8.58141i	0.404467	−	0.388065i
$490$	9.76250	−	16.9091i	0.441025	−	0.763877i
$491$	−18.2158	+	31.5507i	−0.822069	+	1.42386i	0.0820707	+	0.996627i	$0.473847\pi$
$491$	−18.2158	+	31.5507i	−0.822069	+	1.42386i	−0.904139	+	0.427238i	$0.859487\pi$
$492$	2.85117	−	9.82301i	0.128541	−	0.442856i
$493$	−3.02633	+	1.74725i	−0.136299	+	0.0786923i
$494$	−4.23529	+	22.8706i	−0.190555	+	1.02900i
$495$	−21.5292	−	0.891489i	−0.967665	−	0.0400694i
$496$	−1.99977	−	1.99977i	−0.0897924	−	0.0897924i
$497$	−9.49501	+	5.48195i	−0.425909	+	0.245899i
$498$	−17.4834	−	10.5823i	−0.783451	−	0.474206i
$499$	−27.3198	+	7.32032i	−1.22300	+	0.327702i	−0.811851	−	0.583865i	$-0.801540\pi$
$499$	−27.3198	+	7.32032i	−1.22300	+	0.327702i	−0.411151	+	0.911567i	$0.634873\pi$
$500$	−2.92848	−	10.9292i	−0.130965	−	0.488770i
$501$	−25.2012	+	6.19673i	−1.12591	+	0.276849i
$502$	13.2783	+	3.55790i	0.592637	+	0.158797i
$503$			25.6015i			1.14151i	0.821119	+	0.570757i	$0.193350\pi$
$503$			25.6015i			1.14151i	−0.821119	+	0.570757i	$0.806650\pi$
$504$	17.4416	+	33.3218i	0.776909	+	1.48427i
$505$	9.73764	−	9.73764i	0.433319	−	0.433319i
$506$	10.5564	+	18.2843i	0.469291	+	0.812835i
$507$	−3.06814	−	22.3066i	−0.136261	−	0.990673i
$508$	−1.46456	+	2.53668i	−0.0649791	+	0.112547i
$509$	−0.678425	−	2.53192i	−0.0300707	−	0.112225i	0.949259	−	0.314495i	$-0.101835\pi$
$509$	−0.678425	−	2.53192i	−0.0300707	−	0.112225i	−0.979330	+	0.202269i	$0.935168\pi$
$510$	0.0403065	−	1.94761i	0.00178480	−	0.0862418i
$511$	27.5069	−	15.8811i	1.21683	−	0.702538i
$512$	−9.73294	+	9.73294i	−0.430139	+	0.430139i
$513$	−21.4517	−	24.2951i	−0.947114	−	1.07266i
$514$	16.0782	−	16.0782i	0.709181	−	0.709181i
$515$	−5.60274	+	20.9097i	−0.246886	+	0.921391i
$516$	−9.68571	−	0.200449i	−0.426389	−	0.00882426i
$517$	21.2384	+	12.2620i	0.934065	+	0.539283i
$518$	25.2828	−	6.77449i	1.11086	−	0.297654i
$519$	6.92363	+	12.5865i	0.303914	+	0.552487i
$520$	19.2300	−	6.81293i	0.843291	−	0.298767i
$521$			17.0961i			0.748995i	0.927228	+	0.374497i	$0.122185\pi$
$521$			17.0961i			0.748995i	−0.927228	+	0.374497i	$0.877815\pi$
$522$	−18.1648	+	4.06992i	−0.795053	+	0.178135i
$523$	27.8541			1.21797			0.608987	−	0.793180i	$-0.291576\pi$
$523$	27.8541			1.21797			0.608987	+	0.793180i	$0.291576\pi$
$524$	−5.92550	−	10.2633i	−0.258857	−	0.448353i
$525$	−10.5362	+	2.59075i	−0.459838	+	0.113070i
$526$	3.44135	−	0.922108i	0.150050	−	0.0402058i
$527$	−1.24906	+	0.334684i	−0.0544098	+	0.0145791i
$528$	−8.24276	+	2.02681i	−0.358720	+	0.0882058i
$529$	−2.57789	−	4.46504i	−0.112082	−	0.194132i
$530$	−3.26449			−0.141800
$531$	19.5549	−	4.38136i	0.848609	−	0.190135i
$532$		−	24.0038i		−	1.04070i
$533$	−9.84999	+	20.6589i	−0.426651	+	0.894835i
$534$	−0.135368	−	0.246087i	−0.00585794	−	0.0106492i
$535$	23.6148	−	6.32757i	1.02096	−	0.273565i
$536$	−6.02586	−	3.47903i	−0.260277	−	0.150271i
$537$	−19.5892	−	0.405404i	−0.845334	−	0.0174945i
$538$	−3.07279	+	11.4678i	−0.132478	+	0.494413i
$539$	−27.5070	+	27.5070i	−1.18481	+	1.18481i
$540$	−2.87221	+	8.55596i	−0.123600	+	0.368190i
$541$	−1.32533	+	1.32533i	−0.0569802	+	0.0569802i	−0.735023	−	0.678043i	$-0.762829\pi$
$541$	−1.32533	+	1.32533i	−0.0569802	+	0.0569802i	0.678043	+	0.735023i	$0.262829\pi$
$542$	16.0327	−	9.25646i	0.688662	−	0.397599i
$543$	−0.209553	+	10.1256i	−0.00899278	+	0.434532i
$544$	0.715150	+	2.66898i	0.0306618	+	0.114431i
$545$	−5.33314	+	9.23727i	−0.228447	+	0.395681i
$546$	−8.39944	−	25.3635i	−0.359463	−	1.08546i
$547$	−13.9248	−	24.1185i	−0.595383	−	1.03123i	−0.993493	−	0.113895i	$-0.963667\pi$
$547$	−13.9248	−	24.1185i	−0.595383	−	1.03123i	0.398110	−	0.917338i	$-0.369666\pi$
$548$	6.80269	−	6.80269i	0.290597	−	0.290597i
$549$	−3.13623	−	5.99171i	−0.133851	−	0.255720i
$550$		−	6.02544i		−	0.256926i
$551$	36.1463	+	9.68538i	1.53989	+	0.412611i
$552$	27.0482	−	6.65090i	1.15125	−	0.283081i
$553$	−2.36940	−	8.84270i	−0.100757	−	0.376030i
$554$	−9.96732	+	2.67074i	−0.423471	+	0.113469i
$555$	16.9250	+	10.2443i	0.718425	+	0.434846i
$556$	−13.7150	+	7.91838i	−0.581647	+	0.335814i
$557$	19.8794	+	19.8794i	0.842316	+	0.842316i	0.989160	−	0.146844i	$-0.0469115\pi$
$557$	19.8794	+	19.8794i	0.842316	+	0.842316i	−0.146844	+	0.989160i	$0.546911\pi$
$558$	−6.88253	−	0.284994i	−0.291361	−	0.0120648i
$559$	21.3148	+	3.94717i	0.901520	+	0.166948i
$560$	8.52004	−	4.91905i	0.360037	−	0.207868i
$561$	−1.08188	+	3.72734i	−0.0456768	+	0.157368i
$562$	−4.56726	+	7.91073i	−0.192658	+	0.333694i
$563$	−11.1038	+	19.2324i	−0.467971	+	0.810550i	−0.999330	−	0.0365971i	$-0.988348\pi$
$563$	−11.1038	+	19.2324i	−0.467971	+	0.810550i	0.531359	+	0.847147i	$0.321682\pi$
$564$	7.41202	−	7.11145i	0.312102	−	0.299446i
$565$	6.44200	−	24.0419i	0.271017	−	1.01145i
$566$	17.7346	+	17.7346i	0.745440	+	0.745440i
$567$	35.0413	+	12.5758i	1.47160	+	0.528135i
$568$	−8.03269			−0.337044
$569$	−18.3923	−	31.8565i	−0.771047	−	1.33549i	−0.936990	−	0.349357i	$-0.886400\pi$
$569$	−18.3923	−	31.8565i	−0.771047	−	1.33549i	0.165943	−	0.986135i	$-0.446933\pi$
$570$	−15.0529	+	14.4424i	−0.630495	+	0.604927i
$571$	−9.94938	−	5.74427i	−0.416368	−	0.240390i	0.277154	−	0.960826i	$-0.410609\pi$
$571$	−9.94938	−	5.74427i	−0.416368	−	0.240390i	−0.693522	+	0.720435i	$0.743942\pi$
$572$	−12.8646	+	1.01440i	−0.537894	+	0.0424140i
$573$	15.8125	−	8.69815i	0.660575	−	0.363370i
$574$	−7.02886	+	26.2321i	−0.293379	+	1.09491i
$575$			8.03543i			0.335101i
$576$	−0.925195	+	22.3432i	−0.0385498	+	0.930966i
$577$	−0.440859	−	0.440859i	−0.0183532	−	0.0183532i	0.697871	−	0.716224i	$-0.254131\pi$
$577$	−0.440859	−	0.440859i	−0.0183532	−	0.0183532i	−0.716224	+	0.697871i	$0.754131\pi$
$578$	16.6443	+	4.45982i	0.692311	+	0.185504i
$579$	1.78690	+	7.26704i	0.0742608	+	0.302008i
$580$	−2.69706	−	10.0656i	−0.111989	−	0.417949i
$581$	−40.8694	−	23.5960i	−1.69555	−	0.978926i
$582$	10.4369	−	17.2432i	0.432624	−	0.714753i
$583$	6.28242	+	1.68337i	0.260191	+	0.0697180i
$584$	23.2705			0.962942
$585$	9.43800	−	17.8534i	0.390213	−	0.738149i
$586$	26.1059			1.07842
$587$	−13.5752	−	3.63747i	−0.560309	−	0.150134i	−0.0324605	−	0.999473i	$-0.510334\pi$
$587$	−13.5752	−	3.63747i	−0.560309	−	0.150134i	−0.527848	+	0.849339i	$0.677001\pi$
$588$	7.85306	+	14.2761i	0.323855	+	0.588738i
$589$	11.9923	+	6.92378i	0.494136	+	0.285289i
$590$	−3.33837	−	12.4590i	−0.137439	−	0.512928i
$591$	−23.4840	+	22.5317i	−0.966004	+	0.926831i
$592$	7.52791	+	2.01710i	0.309395	+	0.0829022i
$593$	−8.84434	−	8.84434i	−0.363194	−	0.363194i	0.501794	−	0.864987i	$-0.332674\pi$
$593$	−8.84434	−	8.84434i	−0.363194	−	0.363194i	−0.864987	+	0.501794i	$0.832674\pi$
$594$	−11.4284	+	17.2293i	−0.468911	+	0.706925i
$595$		−	4.49836i		−	0.184415i
$596$	−0.603946	+	2.25396i	−0.0247386	+	0.0923257i
$597$	−0.0372432	+	1.79960i	−0.00152426	+	0.0736526i
$598$	−19.7259	+	1.55542i	−0.806651	+	0.0636060i
$599$	−12.8510	−	7.41956i	−0.525080	−	0.303155i	0.213931	−	0.976849i	$-0.431373\pi$
$599$	−12.8510	−	7.41956i	−0.525080	−	0.303155i	−0.739010	+	0.673694i	$0.764707\pi$
$600$	−7.63421	−	2.21586i	−0.311665	−	0.0904621i
$601$	22.5672	+	39.0875i	0.920535	+	1.59441i	0.798588	+	0.601878i	$0.205580\pi$
$601$	22.5672	+	39.0875i	0.920535	+	1.59441i	0.121947	+	0.992537i	$0.461086\pi$
$602$	25.7220			1.04835
$603$	−6.72096	+	1.50586i	−0.273699	+	0.0613235i
$604$	4.48592	+	4.48592i	0.182529	+	0.182529i
$605$	1.83639	−	6.85351i	0.0746600	−	0.278635i
$606$	−3.15506	−	12.8312i	−0.128166	−	0.521231i
$607$	−16.1981	+	28.0560i	−0.657462	+	1.13876i	0.323809	+	0.946123i	$0.395037\pi$
$607$	−16.1981	+	28.0560i	−0.657462	+	1.13876i	−0.981271	+	0.192635i	$0.938297\pi$
$608$	14.7947	−	25.6251i	0.600004	−	1.03924i
$609$	−41.7425	+	10.2641i	−1.69149	+	0.415921i
$610$	−3.76973	+	2.17645i	−0.152632	+	0.0881220i
$611$	−18.9398	+	13.0211i	−0.766223	+	0.526779i
$612$	1.37300	+	0.870362i	0.0555001	+	0.0351823i
$613$	6.23484	+	6.23484i	0.251823	+	0.251823i	0.821718	−	0.569895i	$-0.193016\pi$
$613$	6.23484	+	6.23484i	0.251823	+	0.251823i	−0.569895	+	0.821718i	$0.693016\pi$
$614$	4.31299	−	2.49011i	0.174058	−	0.100492i
$615$	−17.9852	+	9.89333i	−0.725232	+	0.398937i
$616$	−46.5874	+	12.4830i	−1.87706	+	0.502956i
$617$	10.4431	+	38.9743i	0.420425	+	1.56905i	0.773715	+	0.633533i	$0.218396\pi$
$617$	10.4431	+	38.9743i	0.420425	+	1.56905i	−0.353290	+	0.935514i	$0.614937\pi$
$618$	14.3800	+	14.9878i	0.578449	+	0.602897i
$619$	15.4143	+	4.13024i	0.619552	+	0.166008i	0.554924	−	0.831901i	$-0.312747\pi$
$619$	15.4143	+	4.13024i	0.619552	+	0.166008i	0.0646279	+	0.997909i	$0.479414\pi$
$620$		−	3.85609i		−	0.154864i
$621$	15.2407	−	22.9767i	0.611588	−	0.922022i
$622$	−18.3526	+	18.3526i	−0.735874	+	0.735874i
$623$	−0.324280	−	0.561670i	−0.0129920	−	0.0225028i
$624$	1.61011	−	7.79064i	0.0644558	−	0.311875i
$625$	−7.56751	+	13.1073i	−0.302700	+	0.524292i
$626$	−4.17254	−	15.5721i	−0.166768	−	0.622387i
$627$	36.4162	−	20.0319i	1.45432	−	0.799997i
$628$	3.37862	−	1.95065i	0.134822	−	0.0778393i
$629$	2.51976	−	2.51976i	0.100469	−	0.100469i
$630$	7.15432	−	22.8698i	0.285035	−	0.911155i
$631$	−0.416393	+	0.416393i	−0.0165763	+	0.0165763i	−0.715346	−	0.698770i	$-0.753731\pi$
$631$	−0.416393	+	0.416393i	−0.0165763	+	0.0165763i	0.698770	+	0.715346i	$0.253731\pi$
$632$	1.73594	−	6.47860i	0.0690518	−	0.257705i
$633$	21.8580	−	36.1123i	0.868777	−	1.43534i
$634$	−29.3348	−	16.9364i	−1.16503	−	0.672632i
$635$	5.67792	−	1.52139i	0.225321	−	0.0603747i
$636$	1.41062	−	2.33054i	0.0559349	−	0.0924120i
$637$	−12.1751	−	34.3651i	−0.482394	−	1.36159i
$638$		−	23.8717i		−	0.945088i
$639$	−5.85025	+	5.38501i	−0.231432	+	0.213028i
$640$	−3.32014			−0.131240
$641$	−1.11318	−	1.92808i	−0.0439678	−	0.0761545i	0.843204	−	0.537594i	$-0.180667\pi$
$641$	−1.11318	−	1.92808i	−0.0439678	−	0.0761545i	−0.887172	+	0.461439i	$0.847333\pi$
$642$	6.53883	−	22.5280i	0.258067	−	0.889107i
$643$	40.8604	−	10.9485i	1.61138	−	0.431767i	0.662923	−	0.748687i	$-0.269316\pi$
$643$	40.8604	−	10.9485i	1.61138	−	0.431767i	0.948452	+	0.316921i	$0.102649\pi$
$644$	19.7245	−	5.28516i	0.777254	−	0.208265i
$645$	13.4600	+	14.0288i	0.529985	+	0.552385i
$646$	1.87873	+	3.25406i	0.0739177	+	0.128029i
$647$	39.4845			1.55230			0.776148	−	0.630551i	$-0.217171\pi$
$647$	39.4845			1.55230			0.776148	+	0.630551i	$0.217171\pi$
$648$	17.6266	+	20.8158i	0.692439	+	0.817720i
$649$			25.6984i			1.00875i
$650$	5.09734	+	2.43037i	0.199934	+	0.0953270i
$651$	−15.9032	−	0.329123i	−0.623297	−	0.0128993i
$652$	6.43079	−	1.72313i	0.251849	−	0.0674828i
$653$	24.0076	+	13.8608i	0.939489	+	0.542414i	0.889800	−	0.456350i	$-0.150844\pi$
$653$	24.0076	+	13.8608i	0.939489	+	0.542414i	0.0496892	+	0.998765i	$0.484177\pi$
$654$	4.93267	+	8.96715i	0.192883	+	0.350643i
$655$	−6.15546	+	22.9725i	−0.240514	+	0.897610i
$656$	−5.71773	+	5.71773i	−0.223240	+	0.223240i
$657$	16.9481	−	15.6003i	0.661207	−	0.608625i
$658$	−19.2847	+	19.2847i	−0.751796	+	0.751796i
$659$	15.0701	−	8.70074i	0.587048	−	0.338933i	−0.176881	−	0.984232i	$-0.556601\pi$
$659$	15.0701	−	8.70074i	0.587048	−	0.338933i	0.763930	+	0.645300i	$0.223267\pi$
$660$	−9.90122	−	5.99299i	−0.385405	−	0.233277i
$661$	−2.93383	−	10.9492i	−0.114113	−	0.425875i	0.885106	−	0.465389i	$-0.154086\pi$
$661$	−2.93383	−	10.9492i	−0.114113	−	0.425875i	−0.999219	+	0.0395143i	$0.987419\pi$
$662$	−2.98528	+	5.17066i	−0.116026	+	0.200963i
$663$	−2.71684	−	2.41866i	−0.105513	−	0.0939330i
$664$	−17.2876	−	29.9429i	−0.670888	−	1.16201i
$665$	−34.0623	+	34.0623i	−1.32088	+	1.32088i
$666$	16.8180	−	8.80303i	0.651685	−	0.341111i
$667$			31.8349i			1.23265i
$668$	−13.4643	−	3.60775i	−0.520950	−	0.139588i
$669$	−8.45268	+	29.1217i	−0.326800	+	1.12591i
$670$	1.14739	+	4.28212i	0.0443276	+	0.165433i
$671$	8.37704	−	2.24462i	0.323392	−	0.0866526i
$672$	−0.703267	+	33.9819i	−0.0271291	+	1.31088i
$673$	−0.0645645	+	0.0372764i	−0.00248878	+	0.00143690i	−0.501244	−	0.865306i	$-0.667124\pi$
$673$	−0.0645645	+	0.0372764i	−0.00248878	+	0.00143690i	0.498755	+	0.866743i	$0.333791\pi$
$674$	−24.1206	−	24.1206i	−0.929091	−	0.929091i
$675$	−7.04552	+	3.50405i	−0.271182	+	0.134871i
$676$	4.33079	−	11.2922i	0.166569	−	0.434314i
$677$	−11.3297	+	6.54119i	−0.435435	+	0.251398i	−0.701659	−	0.712513i	$-0.747557\pi$
$677$	−11.3297	+	6.54119i	−0.435435	+	0.251398i	0.266224	+	0.963911i	$0.414224\pi$
$678$	−16.5341	−	17.2329i	−0.634987	−	0.661825i
$679$	23.2717	−	40.3078i	0.893087	−	1.54687i
$680$	1.64786	−	2.85418i	0.0631926	−	0.109453i
$681$	−8.29646	−	2.40808i	−0.317921	−	0.0922779i
$682$	2.28629	−	8.53256i	0.0875467	−	0.326729i
$683$	−18.4883	−	18.4883i	−0.707435	−	0.707435i	0.258560	−	0.965995i	$-0.416752\pi$
$683$	−18.4883	−	18.4883i	−0.707435	−	0.707435i	−0.965995	+	0.258560i	$0.916752\pi$
$684$	−3.80604	−	16.9871i	−0.145528	−	0.649517i
$685$	−19.3066			−0.737667
$686$	−6.65631	−	11.5291i	−0.254139	−	0.440182i
$687$	6.60076	+	26.8443i	0.251835	+	1.02418i
$688$	6.63262	+	3.82934i	0.252866	+	0.145992i
$689$	−3.95810	+	4.63574i	−0.150792	+	0.176608i
$690$	−15.1821	−	9.18936i	−0.577971	−	0.349833i
$691$	6.49655	−	24.2455i	0.247140	−	0.922341i	−0.725155	−	0.688586i	$-0.758232\pi$
$691$	6.49655	−	24.2455i	0.247140	−	0.922341i	0.972295	−	0.233755i	$-0.0751014\pi$
$692$			7.71582i			0.293311i
$693$	−25.5613	+	40.3231i	−0.970995	+	1.53175i
$694$	−18.1482	−	18.1482i	−0.688898	−	0.688898i
$695$	30.6987	+	8.22568i	1.16447	+	0.312018i
$696$	−30.2453	−	8.77882i	−1.14644	−	0.332760i
$697$	0.956926	+	3.57130i	0.0362462	+	0.135273i
$698$	−18.2322	−	10.5264i	−0.690100	−	0.398429i
$699$	−9.16099	−	0.189590i	−0.346500	−	0.00717094i
$700$	−5.62921	−	1.50834i	−0.212764	−	0.0570100i
$701$	29.8002			1.12554			0.562770	−	0.826614i	$-0.309736\pi$
$701$	29.8002			1.12554			0.562770	+	0.826614i	$0.309736\pi$
$702$	−9.96578	−	16.6175i	−0.376134	−	0.627187i
$703$	−38.1601			−1.43923
$704$	−27.6998	−	7.42213i	−1.04397	−	0.279732i
$705$	−20.6094	−	0.426518i	−0.776194	−	0.0160636i
$706$	0.484821	+	0.279911i	0.0182465	+	0.0105346i
$707$	−7.89712	−	29.4725i	−0.297002	−	1.10843i
$708$	10.3371	+	3.00039i	0.388492	+	0.112761i
$709$	−17.2147	−	4.61268i	−0.646513	−	0.173233i	−0.0793614	−	0.996846i	$-0.525288\pi$
$709$	−17.2147	−	4.61268i	−0.646513	−	0.173233i	−0.567152	+	0.823613i	$0.691955\pi$
$710$	3.61887	+	3.61887i	0.135814	+	0.135814i
$711$	−3.07888	−	5.88215i	−0.115467	−	0.220598i
$712$		−	0.475167i		−	0.0178076i
$713$	−3.04896	+	11.3789i	−0.114185	+	0.426143i
$714$	−3.69247	−	2.23497i	−0.138187	−	0.0836417i
$715$	19.6948	+	16.8158i	0.736543	+	0.628877i
$716$	−9.11404	−	5.26200i	−0.340608	−	0.196650i
$717$	−3.36125	−	13.6697i	−0.125528	−	0.510505i
$718$	−13.9617	−	24.1823i	−0.521045	−	0.902477i
$719$	−21.4168			−0.798713			−0.399356	−	0.916796i	$-0.630766\pi$
$719$	−21.4168			−0.798713			−0.399356	+	0.916796i	$0.630766\pi$
$720$	5.24953	−	4.83207i	0.195638	−	0.180081i
$721$	33.9151	+	33.9151i	1.26306	+	1.26306i
$722$	5.32819	−	19.8851i	0.198295	−	0.740045i
$723$	10.1986	+	2.96018i	0.379290	+	0.110090i
$724$	−2.71992	+	4.71105i	−0.101085	+	0.175085i
$725$	4.54271	−	7.86820i	0.168712	−	0.292218i
$726$	−4.71330	−	4.91251i	−0.174927	−	0.182320i
$727$	−24.4305	+	14.1050i	−0.906079	+	0.523125i	−0.879167	−	0.476513i	$-0.841901\pi$
$727$	−24.4305	+	14.1050i	−0.906079	+	0.523125i	−0.0269114	+	0.999638i	$0.508567\pi$
$728$	8.23081	−	44.4465i	0.305054	−	1.64730i
$729$	26.7922	+	3.34356i	0.992303	+	0.123835i
$730$	−10.4838	−	10.4838i	−0.388023	−	0.388023i
$731$	3.03269	−	1.75093i	0.112168	−	0.0647603i
$732$	0.0751593	−	3.63170i	0.00277797	−	0.134232i
$733$	41.0517	−	10.9998i	1.51628	−	0.406286i	0.597764	−	0.801672i	$-0.296056\pi$
$733$	41.0517	−	10.9998i	1.51628	−	0.406286i	0.918515	+	0.395386i	$0.129389\pi$
$734$	6.57645	+	24.5436i	0.242741	+	0.905922i
$735$	9.11462	−	31.4022i	0.336198	−	1.15829i
$736$	24.3143	+	6.51500i	0.896237	+	0.240146i
$737$		−	8.83248i		−	0.325349i
$738$	−0.814855	+	19.6785i	−0.0299952	+	0.724376i
$739$	−30.0670	+	30.0670i	−1.10603	+	1.10603i	−0.112367	+	0.993667i	$0.535843\pi$
$739$	−30.0670	+	30.0670i	−1.10603	+	1.10603i	−0.993667	+	0.112367i	$0.964157\pi$
$740$	5.31315	+	9.20265i	0.195315	+	0.338296i
$741$	2.25784	+	38.8868i	0.0829440	+	1.42854i
$742$	−3.61651	+	6.26397i	−0.132766	+	0.229958i
$743$	9.53650	+	35.5907i	0.349860	+	1.30570i	0.886831	+	0.462095i	$0.152902\pi$
$743$	9.53650	+	35.5907i	0.349860	+	1.30570i	−0.536970	+	0.843601i	$0.680431\pi$
$744$	−9.96993	−	6.03458i	−0.365515	−	0.221238i
$745$	4.05548	−	2.34143i	0.148581	−	0.0857834i
$746$	26.2238	−	26.2238i	0.960120	−	0.960120i
$747$	−32.6640	−	10.2182i	−1.19511	−	0.373865i
$748$	−1.47408	+	1.47408i	−0.0538976	+	0.0538976i
$749$	14.0198	−	52.3224i	0.512271	−	1.91182i
$750$	10.5008	+	19.0896i	0.383437	+	0.697053i
$751$	−4.86388	−	2.80816i	−0.177486	−	0.102471i	0.408625	−	0.912702i	$-0.366008\pi$
$751$	−4.86388	−	2.80816i	−0.177486	−	0.102471i	−0.586111	+	0.810231i	$0.699342\pi$
$752$	−7.84372	+	2.10172i	−0.286031	+	0.0766418i
$753$	23.0164	+	0.476332i	0.838765	+	0.0173585i
$754$	20.1947	+	9.62867i	0.735447	+	0.350655i
$755$		−	12.7314i		−	0.463343i
$756$	13.2354	+	14.9898i	0.481368	+	0.545175i
$757$	−1.31552			−0.0478135			−0.0239067	−	0.999714i	$-0.507610\pi$
$757$	−1.31552			−0.0478135			−0.0239067	+	0.999714i	$0.507610\pi$
$758$	−3.30146	−	5.71829i	−0.119914	−	0.207698i
$759$	24.4788	+	25.5134i	0.888525	+	0.926079i
$760$	−34.0902	+	9.13443i	−1.23658	+	0.331341i
$761$	19.6846	−	5.27446i	0.713565	−	0.191199i	0.116266	−	0.993218i	$-0.462907\pi$
$761$	19.6846	−	5.27446i	0.713565	−	0.191199i	0.597299	+	0.802019i	$0.296241\pi$
$762$	1.57219	−	5.41660i	0.0569544	−	0.196223i
$763$	11.8164	+	20.4667i	0.427784	+	0.740944i
$764$	9.69338			0.350694
$765$	−0.713260	−	3.18342i	−0.0257880	−	0.115097i
$766$			0.433704i			0.0156704i
$767$	−21.7401	−	10.3655i	−0.784988	−	0.374276i
$768$	−15.0204	+	24.8157i	−0.542002	+	0.895461i
$769$	−11.8005	+	3.16193i	−0.425536	+	0.114022i	−0.465230	−	0.885190i	$-0.654028\pi$
$769$	−11.8005	+	3.16193i	−0.425536	+	0.114022i	0.0396941	+	0.999212i	$0.487362\pi$
$770$	26.6123	+	15.3646i	0.959040	+	0.553702i
$771$	19.7178	−	32.5765i	0.710120	−	1.17321i
$772$	−1.04033	+	3.88258i	−0.0374425	+	0.139737i
$773$	−13.6325	+	13.6325i	−0.490328	+	0.490328i	−0.908409	−	0.418082i	$-0.862703\pi$
$773$	−13.6325	+	13.6325i	−0.490328	+	0.490328i	0.418082	+	0.908409i	$0.362703\pi$
$774$	18.2030	−	4.07847i	0.654294	−	0.146598i
$775$	2.37729	−	2.37729i	0.0853949	−	0.0853949i
$776$	29.5315	−	17.0500i	1.06012	−	0.612060i
$777$	38.4070	−	21.1270i	1.37784	−	0.757927i
$778$	7.35484	+	27.4486i	0.263684	+	0.984081i
$779$	19.7964	−	34.2884i	0.709281	−	1.22851i
$780$	9.06355	−	5.95885i	0.324527	−	0.213361i
$781$	−5.09830	−	8.83051i	−0.182431	−	0.315981i
$782$	−2.26028	+	2.26028i	−0.0808274	+	0.0808274i
$783$	−27.9130	+	13.8824i	−0.997529	+	0.496117i
$784$		−	12.8809i		−	0.460031i
$785$	−7.56244	−	2.02635i	−0.269915	−	0.0723236i
$786$	15.7986	+	16.4664i	0.563519	+	0.587336i
$787$	2.29650	+	8.57064i	0.0818612	+	0.305510i	0.994701	−	0.102807i	$-0.0327824\pi$
$787$	2.29650	+	8.57064i	0.0818612	+	0.305510i	−0.912840	+	0.408317i	$0.866116\pi$
$788$	−16.8850	+	4.52431i	−0.601502	+	0.161172i
$789$	5.22775	−	2.87569i	0.186113	−	0.102377i
$790$	−3.70079	+	2.13665i	−0.131668	+	0.0760188i
$791$	−38.9954	−	38.9954i	−1.38652	−	1.38652i
$792$	−30.9898	+	16.2209i	−1.10117	+	0.576386i
$793$	−1.48001	+	7.99209i	−0.0525567	+	0.283807i
$794$	−18.7574	+	10.8296i	−0.665677	+	0.384329i
$795$	−5.30886	+	1.30540i	−0.188286	+	0.0462977i
$796$	−0.483404	+	0.837280i	−0.0171338	+	0.0296766i
$797$	−15.0420	+	26.0535i	−0.532815	+	0.922862i	0.466451	+	0.884547i	$0.345532\pi$
$797$	−15.0420	+	26.0535i	−0.532815	+	0.922862i	−0.999266	+	0.0383151i	$0.987801\pi$
$798$	11.0364	+	44.8835i	0.390685	+	1.58886i
$799$	−0.960988	+	3.58645i	−0.0339973	+	0.126880i
$800$	−5.07978	−	5.07978i	−0.179597	−	0.179597i
$801$	−0.318546	−	0.346067i	−0.0112553	−	0.0122277i
$802$	−15.3743			−0.542887
$803$	14.7697	+	25.5818i	0.521211	+	0.902764i
$804$	−3.55284	−	1.03122i	−0.125299	−	0.0363685i
$805$	−35.4897	−	20.4900i	−1.25085	−	0.722177i
$806$	6.29610	+	5.37575i	0.221771	+	0.189353i
$807$	−0.411386	+	19.8782i	−0.0144815	+	0.699747i
$808$	5.78582	−	21.5930i	0.203544	−	0.759638i
$809$		−	6.00821i		−	0.211237i	−0.994407	−	0.105619i	$-0.966318\pi$
$809$		−	6.00821i		−	0.211237i	0.994407	−	0.105619i	$-0.0336823\pi$
$810$	1.43676	−	17.3190i	0.0504828	−	0.608527i
$811$	−23.4539	−	23.4539i	−0.823577	−	0.823577i	0.163042	−	0.986619i	$-0.447869\pi$
$811$	−23.4539	−	23.4539i	−0.823577	−	0.823577i	−0.986619	+	0.163042i	$0.947869\pi$
$812$	−22.3019	−	5.97577i	−0.782642	−	0.209708i
$813$	22.3716	−	21.4644i	0.784606	−	0.752789i
$814$	6.30039	+	23.5134i	0.220829	+	0.824143i
$815$	−11.5707	−	6.68037i	−0.405305	−	0.234003i
$816$	−0.619404	−	1.12602i	−0.0216835	−	0.0394186i
$817$	−36.2223	−	9.70574i	−1.26726	−	0.339561i
$818$	26.6643			0.932296
$819$	−23.8018	−	37.8885i	−0.831704	−	1.32393i
$820$	−11.0253			−0.385020
$821$	24.9494	+	6.68517i	0.870740	+	0.233314i	0.666408	−	0.745588i	$-0.267831\pi$
$821$	24.9494	+	6.68517i	0.870740	+	0.233314i	0.204332	+	0.978902i	$0.434498\pi$
$822$	−9.59231	+	15.8478i	−0.334570	+	0.552755i
$823$	−30.3848	−	17.5427i	−1.05915	−	0.611500i	−0.133952	−	0.990988i	$-0.542767\pi$
$823$	−30.3848	−	17.5427i	−1.05915	−	0.611500i	−0.925197	+	0.379488i	$0.876100\pi$
$824$	9.09494	+	33.9428i	0.316837	+	1.18245i
$825$	−2.40944	−	9.79885i	−0.0838860	−	0.341152i
$826$	−27.6049	−	7.39672i	−0.960498	−	0.257365i
$827$	−24.5496	−	24.5496i	−0.853673	−	0.853673i	0.136910	−	0.990583i	$-0.456283\pi$
$827$	−24.5496	−	24.5496i	−0.853673	−	0.853673i	−0.990583	+	0.136910i	$0.956283\pi$
$828$	13.1207	−	6.86774i	0.455975	−	0.238670i
$829$		−	17.7371i		−	0.616036i	−0.951380	−	0.308018i	$-0.900334\pi$
$829$		−	17.7371i		−	0.616036i	0.951380	−	0.308018i	$-0.0996658\pi$
$830$	−5.70147	+	21.2782i	−0.197901	+	0.738577i
$831$	−15.1413	+	8.32898i	−0.525247	+	0.288929i
$832$	17.4516	−	20.4394i	0.605026	−	0.708609i
$833$	−5.10057	−	2.94482i	−0.176724	−	0.102032i
$834$	22.0044	−	21.1121i	0.761950	−	0.731052i
$835$	13.9869	+	24.2259i	0.484035	+	0.838373i
$836$	22.3239			0.772088
$837$	−11.3067	+	2.28870i	−0.390815	+	0.0791092i
$838$	25.6852	+	25.6852i	0.887279	+	0.887279i
$839$	−9.27344	+	34.6089i	−0.320155	+	1.19483i	0.598939	+	0.800795i	$0.295589\pi$
$839$	−9.27344	+	34.6089i	−0.320155	+	1.19483i	−0.919094	+	0.394039i	$0.871078\pi$
$840$	29.2536	−	28.0673i	1.00934	−	0.968413i
$841$	3.49735	−	6.05759i	0.120598	−	0.208882i
$842$	−6.61338	+	11.4547i	−0.227912	+	0.394755i
$843$	−4.26416	+	14.6911i	−0.146866	+	0.505990i
$844$	19.6354	−	11.3365i	0.675880	−	0.390219i
$845$	−22.1696	+	9.87848i	−0.762657	+	0.339830i
$846$	−10.5897	+	16.7053i	−0.364081	+	0.574338i
$847$	−11.1163	−	11.1163i	−0.381959	−	0.381959i
$848$	−1.86509	+	1.07681i	−0.0640475	+	0.0369779i
$849$	35.9324	+	21.7491i	1.23320	+	0.746427i
$850$	0.881176	−	0.236110i	0.0302241	−	0.00809852i
$851$	−8.40210	−	31.3571i	−0.288020	−	1.07491i
$852$	−4.14729	+	1.01978i	−0.142084	+	0.0349370i
$853$	9.38509	+	2.51473i	0.321339	+	0.0861026i	0.415883	−	0.909418i	$-0.363473\pi$
$853$	9.38509	+	2.51473i	0.321339	+	0.0861026i	−0.0945437	+	0.995521i	$0.530139\pi$
$854$			9.64458i			0.330031i
$855$	−18.7044	+	29.5063i	−0.639678	+	1.00909i
$856$	28.0624	−	28.0624i	0.959154	−	0.959154i
$857$	−13.1258	−	22.7345i	−0.448367	−	0.776595i	0.549913	−	0.835222i	$-0.314661\pi$
$857$	−13.1258	−	22.7345i	−0.448367	−	0.776595i	−0.998280	+	0.0586274i	$0.981328\pi$
$858$	23.5884	−	7.81162i	0.805296	−	0.266684i
$859$	−7.14845	+	12.3815i	−0.243902	+	0.422450i	−0.961822	−	0.273675i	$-0.911761\pi$
$859$	−7.14845	+	12.3815i	−0.243902	+	0.422450i	0.717920	+	0.696125i	$0.245094\pi$
$860$	2.70273	+	10.0867i	0.0921622	+	0.343954i
$861$	−0.941026	+	45.4705i	−0.0320701	+	1.54963i
$862$	−29.8851	+	17.2542i	−1.01789	+	0.587680i
$863$	−5.14669	+	5.14669i	−0.175195	+	0.175195i	−0.789258	−	0.614062i	$-0.789534\pi$
$863$	−5.14669	+	5.14669i	−0.175195	+	0.175195i	0.614062	+	0.789258i	$0.289534\pi$
$864$	4.89048	+	24.1600i	0.166378	+	0.821939i
$865$	10.9490	−	10.9490i	0.372279	−	0.372279i
$866$	−2.74138	+	10.2310i	−0.0931560	+	0.347663i
$867$	28.8511	+	0.597082i	0.979834	+	0.0202780i
$868$	−7.39914	−	4.27189i	−0.251143	−	0.144998i
$869$	8.22386	−	2.20358i	0.278975	−	0.0747512i
$870$	9.67103	+	17.5811i	0.327879	+	0.596054i
$871$	7.47200	+	3.56259i	0.253179	+	0.120714i
$872$			17.3146i			0.586347i
$873$	10.0778	−	32.2151i	0.341082	−	1.09032i
$874$	34.2304			1.15786
$875$	25.1553	+	43.5702i	0.850403	+	1.47294i
$876$	12.0146	−	2.95428i	0.405936	−	0.0998159i
$877$	19.3771	−	5.19207i	0.654318	−	0.175324i	0.0836374	−	0.996496i	$-0.473346\pi$
$877$	19.3771	−	5.19207i	0.654318	−	0.175324i	0.570680	+	0.821172i	$0.306680\pi$
$878$	18.2225	−	4.88270i	0.614980	−	0.164783i
$879$	42.4545	−	10.4392i	1.43196	−	0.352104i
$880$	4.57479	+	7.92378i	0.154216	+	0.267110i
$881$	−26.1641			−0.881491			−0.440746	−	0.897632i	$-0.645286\pi$
$881$	−26.1641			−0.881491			−0.440746	+	0.897632i	$0.645286\pi$
$882$	−21.2479	−	23.0836i	−0.715455	−	0.777266i
$883$			18.8889i			0.635661i	0.948148	+	0.317830i	$0.102954\pi$
$883$			18.8889i			0.635661i	−0.948148	+	0.317830i	$0.897046\pi$
$884$	−0.652452	−	1.84159i	−0.0219443	−	0.0619395i
$885$	−10.4111	−	18.9264i	−0.349965	−	0.636205i
$886$	9.53059	−	2.55372i	0.320187	−	0.0857937i
$887$	24.3843	+	14.0783i	0.818745	+	0.472702i	0.849983	−	0.526810i	$-0.176612\pi$
$887$	24.3843	+	14.0783i	0.818745	+	0.472702i	−0.0312387	+	0.999512i	$0.509945\pi$
$888$	32.1083	+	0.664492i	1.07748	+	0.0222989i
$889$	3.37090	−	12.5804i	0.113056	−	0.421932i
$890$	−0.214071	+	0.214071i	−0.00717569	+	0.00717569i
$891$	−11.6957	+	32.5890i	−0.391821	+	1.09177i
$892$	−11.5169	+	11.5169i	−0.385616	+	0.385616i
$893$	34.4340	−	19.8805i	1.15229	−	0.665274i
$894$	0.0929686	−	4.49225i	0.00310933	−	0.150243i
$895$	5.46621	+	20.4002i	0.182715	+	0.681903i
$896$	−3.67816	+	6.37076i	−0.122879	+	0.212832i
$897$	−31.4571	+	10.4175i	−1.05032	+	0.347829i
$898$	−2.20255	−	3.81493i	−0.0735000	−	0.127306i
$899$	9.41839	−	9.41839i	0.314121	−	0.314121i
$900$	−4.22286	−	0.174862i	−0.140762	−	0.00582873i
$901$			0.984720i			0.0328058i
$902$	−24.3962	−	6.53696i	−0.812306	−	0.217657i
$903$	41.8302	−	10.2856i	1.39202	−	0.342285i
$904$	−10.4573	−	39.0273i	−0.347806	−	1.29803i
$905$	10.5448	−	2.82548i	0.350523	−	0.0939222i
$906$	−10.4505	−	6.32548i	−0.347196	−	0.210150i
$907$	47.3000	−	27.3087i	1.57057	−	0.906770i	0.574473	−	0.818524i	$-0.305207\pi$
$907$	47.3000	−	27.3087i	1.57057	−	0.906770i	0.996099	−	0.0882463i	$-0.0281263\pi$
$908$	−3.28106	−	3.28106i	−0.108886	−	0.108886i
$909$	−10.2618	−	19.6050i	−0.340363	−	0.650257i
$910$	−23.7321	+	16.3158i	−0.786711	+	0.540864i
$911$	−40.4995	+	23.3824i	−1.34181	+	0.774694i	−0.987073	−	0.160272i	$-0.948763\pi$
$911$	−40.4995	+	23.3824i	−1.34181	+	0.774694i	−0.354736	+	0.934966i	$0.615429\pi$
$912$	−3.83618	+	13.2166i	−0.127029	+	0.437646i
$913$	21.9446	−	38.0092i	0.726261	−	1.25792i
$914$	14.1050	−	24.4306i	0.466553	−	0.808093i
$915$	−5.26019	+	5.04688i	−0.173896	+	0.166845i
$916$	−3.84298	+	14.3422i	−0.126976	+	0.473880i
$917$	37.2609	+	37.2609i	1.23046	+	1.23046i
$918$	−2.96748	−	0.996174i	−0.0979414	−	0.0328786i
$919$	12.6186			0.416249			0.208125	−	0.978102i	$-0.433264\pi$
$919$	12.6186			0.416249			0.208125	+	0.978102i	$0.433264\pi$
$920$	−15.0120	−	26.0015i	−0.494930	−	0.857244i
$921$	6.01824	−	5.77419i	0.198308	−	0.190266i
$922$	−24.8290	−	14.3350i	−0.817699	−	0.472099i
$923$	9.52674	−	0.751203i	0.313577	−	0.0247261i
$924$	−22.4684	+	12.3595i	−0.739155	+	0.406596i
$925$	−2.39789	+	8.94905i	−0.0788422	+	0.294243i
$926$			24.8051i			0.815146i
$927$	29.3787	+	18.6236i	0.964924	+	0.611678i
$928$	−20.1251	−	20.1251i	−0.660640	−	0.660640i
$929$	−0.458170	−	0.122766i	−0.0150321	−	0.00402783i	0.251295	−	0.967911i	$-0.419144\pi$
$929$	−0.458170	−	0.122766i	−0.0150321	−	0.00402783i	−0.266327	+	0.963883i	$0.585810\pi$
$930$	1.77295	+	7.21031i	0.0581372	+	0.236436i
$931$	16.3237	+	60.9210i	0.534989	+	1.99660i
$932$	−4.26224	−	2.46081i	−0.139614	−	0.0806064i
$933$	−22.5071	+	37.1847i	−0.736849	+	1.21737i
$934$	36.1771	+	9.69363i	1.18375	+	0.317185i
$935$	4.18355			0.136817
$936$	−1.22263	−	32.7592i	−0.0399629	−	1.07077i
$937$	17.5439			0.573135			0.286567	−	0.958060i	$-0.407486\pi$
$937$	17.5439			0.573135			0.286567	+	0.958060i	$0.407486\pi$
$938$	9.48774	+	2.54223i	0.309786	+	0.0830068i
$939$	−13.0125	−	23.6556i	−0.424647	−	0.771971i
$940$	−9.58871	−	5.53605i	−0.312749	−	0.180566i
$941$	−6.06819	−	22.6468i	−0.197817	−	0.738264i	−0.991520	−	0.129958i	$-0.958516\pi$
$941$	−6.06819	−	22.6468i	−0.197817	−	0.738264i	0.793702	−	0.608306i	$-0.208151\pi$
$942$	−5.42066	+	5.20084i	−0.176615	+	0.169453i
$943$	32.5344	+	8.71758i	1.05947	+	0.283883i
$944$	−6.01697	−	6.01697i	−0.195836	−	0.195836i
$945$	2.48956	−	40.0528i	0.0809853	−	1.30292i
$946$			23.9218i			0.777766i
$947$	−8.39653	+	31.3363i	−0.272851	+	1.01829i	0.684418	+	0.729090i	$0.260057\pi$
$947$	−8.39653	+	31.3363i	−0.272851	+	1.01829i	−0.957268	+	0.289202i	$0.906610\pi$
$948$	0.0737849	−	3.56529i	0.00239642	−	0.115795i
$949$	−27.5988	+	2.17622i	−0.895895	+	0.0706431i
$950$	−8.46027	−	4.88454i	−0.274487	−	0.158475i
$951$	−54.4781	−	15.8125i	−1.76657	−	0.512755i
$952$	−3.65110	−	6.32390i	−0.118333	−	0.204959i
$953$	−34.3236			−1.11185			−0.555925	−	0.831232i	$-0.687636\pi$
$953$	−34.3236			−1.11185			−0.555925	+	0.831232i	$0.687636\pi$
$954$	−1.56613	+	5.00635i	−0.0507053	+	0.162086i
$955$	−13.7553	−	13.7553i	−0.445111	−	0.445111i
$956$	1.95693	−	7.30336i	0.0632917	−	0.236208i
$957$	−9.54576	−	38.8212i	−0.308570	−	1.25491i
$958$	−6.00225	+	10.3962i	−0.193924	+	0.335886i
$959$	−21.3885	+	37.0459i	−0.690669	+	1.19627i
$960$	23.4073	−	5.75562i	0.755467	−	0.185762i
$961$	−22.5783	+	13.0356i	−0.728332	+	0.420503i
$962$	−22.4329	−	4.15422i	−0.723264	−	0.133937i
$963$	1.62531	−	39.2507i	0.0523748	−	1.26484i
$964$	4.03331	+	4.03331i	0.129904	+	0.129904i
$965$	6.98582	−	4.03326i	0.224881	−	0.129835i
$966$	−34.4519	+	18.9514i	−1.10847	+	0.609751i
$967$	−2.55438	+	0.684445i	−0.0821434	+	0.0220103i	−0.299657	−	0.954047i	$-0.596872\pi$
$967$	−2.55438	+	0.684445i	−0.0821434	+	0.0220103i	0.217513	+	0.976057i	$0.430205\pi$
$968$	−2.98103	−	11.1253i	−0.0958138	−	0.357582i
$969$	4.35650	+	4.54063i	0.139951	+	0.145866i
$970$	−20.9858	−	5.62313i	−0.673813	−	0.180548i
$971$			29.5656i			0.948806i	0.880308	+	0.474403i	$0.157336\pi$
$971$			29.5656i			0.948806i	−0.880308	+	0.474403i	$0.842664\pi$
$972$	11.7433	+	8.50945i	0.376666	+	0.272941i
$973$	49.7926	−	49.7926i	1.59628	−	1.59628i
$974$	14.5665	+	25.2298i	0.466739	+	0.808416i
$975$	9.26137	+	1.91407i	0.296601	+	0.0612992i
$976$	−1.43583	+	2.48693i	−0.0459598	+	0.0796048i
$977$	−1.14736	−	4.28200i	−0.0367072	−	0.136993i	0.945141	−	0.326664i	$-0.105925\pi$
$977$	−1.14736	−	4.28200i	−0.0367072	−	0.136993i	−0.981848	+	0.189671i	$0.939258\pi$
$978$	−11.2324	+	6.17874i	−0.359172	+	0.197574i
$979$	0.522362	−	0.301586i	0.0166948	−	0.00963872i
$980$	12.4189	−	12.4189i	0.396706	−	0.396706i
$981$	11.6075	+	12.6103i	0.370599	+	0.402617i
$982$	26.6435	−	26.6435i	0.850227	−	0.850227i
$983$	−11.7947	+	44.0183i	−0.376191	+	1.40396i	0.475406	+	0.879767i	$0.342301\pi$
$983$	−11.7947	+	44.0183i	−0.376191	+	1.40396i	−0.851597	+	0.524198i	$0.824365\pi$
$984$	−17.2540	+	28.5060i	−0.550038	+	0.908737i
$985$	30.3806	+	17.5403i	0.968007	+	0.558879i
$986$	3.49105	−	0.935425i	0.111178	−	0.0297900i
$987$	−23.6501	+	39.0732i	−0.752792	+	1.24371i
$988$	−9.00438	+	18.8853i	−0.286467	+	0.600822i
$989$		−	31.9018i		−	1.01442i
$990$	21.2693	+	6.65364i	0.675982	+	0.211467i
$991$	18.3655			0.583399			0.291700	−	0.956510i	$-0.405779\pi$
$991$	18.3655			0.583399			0.291700	+	0.956510i	$0.405779\pi$
$992$	−5.26595	−	9.12089i	−0.167194	−	0.289589i
$993$	−2.78717	+	9.60251i	−0.0884481	+	0.304727i
$994$	10.9531	−	2.93486i	0.347410	−	0.0930882i
$995$	1.87410	−	0.502164i	0.0594130	−	0.0159197i
$996$	−12.7270	−	13.2649i	−0.403269	−	0.420314i
$997$	−7.61410	−	13.1880i	−0.241141	−	0.417668i	0.719899	−	0.694079i	$-0.244188\pi$
$997$	−7.61410	−	13.1880i	−0.241141	−	0.417668i	−0.961040	+	0.276411i	$0.910855\pi$
$998$	29.2523			0.925966
$999$	23.8301	−	21.0411i	0.753951	−	0.665710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.86.4	yes	44
3.2	odd	2		351.2.bc.b.125.8		44
9.2	odd	6	inner	117.2.z.b.47.4	yes	44
9.7	even	3		351.2.bc.b.8.8		44
13.5	odd	4	inner	117.2.z.b.5.4	✓	44
39.5	even	4		351.2.bc.b.44.8		44
117.70	odd	12		351.2.bc.b.278.8		44
117.83	even	12	inner	117.2.z.b.83.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.4	✓	44	13.5	odd	4	inner
117.2.z.b.47.4	yes	44	9.2	odd	6	inner
117.2.z.b.83.4	yes	44	117.83	even	12	inner
117.2.z.b.86.4	yes	44	1.1	even	1	trivial
351.2.bc.b.8.8		44	9.7	even	3
351.2.bc.b.44.8		44	39.5	even	4
351.2.bc.b.125.8		44	3.2	odd	2
351.2.bc.b.278.8		44	117.70	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.999012 - 0.267684i) q^{2} +(-1.73168 - 0.0358377i) q^{3} +(-0.805681 - 0.465160i) q^{4} +(0.483213 + 1.80337i) q^{5} +(1.72038 + 0.499346i) q^{6} +(3.99567 + 1.07064i) q^{7} +(2.14302 + 2.14302i) q^{8} +(2.99743 + 0.124119i) q^{9} +O(q^{10})\)	\(q+(-0.999012 - 0.267684i) q^{2} +(-1.73168 - 0.0358377i) q^{3} +(-0.805681 - 0.465160i) q^{4} +(0.483213 + 1.80337i) q^{5} +(1.72038 + 0.499346i) q^{6} +(3.99567 + 1.07064i) q^{7} +(2.14302 + 2.14302i) q^{8} +(2.99743 + 0.124119i) q^{9} -1.93094i q^{10} +(-0.995710 + 3.71604i) q^{11} +(1.37851 + 0.834382i) q^{12} +(-2.74203 - 2.34121i) q^{13} +(-3.70513 - 2.13916i) q^{14} +(-0.772141 - 3.14018i) q^{15} +(-0.636932 - 1.10320i) q^{16} -0.582460 q^{17} +(-2.96125 - 0.926362i) q^{18} +(4.41048 + 4.41048i) q^{19} +(0.449542 - 1.67772i) q^{20} +(-6.88085 - 1.99720i) q^{21} +(1.98945 - 3.44583i) q^{22} +(-2.65310 + 4.59531i) q^{23} +(-3.63423 - 3.78783i) q^{24} +(1.31146 - 0.757174i) q^{25} +(2.11262 + 3.07289i) q^{26} +(-5.18614 - 0.322355i) q^{27} +(-2.72122 - 2.72122i) q^{28} +(5.19577 - 2.99978i) q^{29} +(-0.0692004 + 3.34377i) q^{30} +(2.14445 - 0.574604i) q^{31} +(-1.22781 - 4.58224i) q^{32} +(1.85742 - 6.39931i) q^{33} +(0.581885 + 0.155916i) q^{34} +7.72303i q^{35} +(-2.35724 - 1.49429i) q^{36} +(-4.32606 + 4.32606i) q^{37} +(-3.22551 - 5.58674i) q^{38} +(4.66442 + 4.15249i) q^{39} +(-2.82914 + 4.90021i) q^{40} +(-1.64290 - 6.13140i) q^{41} +(6.33944 + 3.83712i) q^{42} +(-5.20669 + 3.00608i) q^{43} +(2.53078 - 2.53078i) q^{44} +(1.22456 + 5.46547i) q^{45} +(3.88057 - 3.88057i) q^{46} +(1.64988 - 6.15742i) q^{47} +(1.06343 + 1.93321i) q^{48} +(8.75694 + 5.05582i) q^{49} +(-1.51285 + 0.405367i) q^{50} +(1.00863 + 0.0208740i) q^{51} +(1.12017 + 3.16175i) q^{52} -1.69062i q^{53} +(5.09473 + 1.71029i) q^{54} -7.18255 q^{55} +(6.26842 + 10.8572i) q^{56} +(-7.47948 - 7.79561i) q^{57} +(-5.99363 + 1.60599i) q^{58} +(6.45229 - 1.72888i) q^{59} +(-0.838589 + 2.88916i) q^{60} +(-1.12715 - 1.95228i) q^{61} -2.29614 q^{62} +(11.8439 + 3.70510i) q^{63} +7.45411i q^{64} +(2.89709 - 6.07621i) q^{65} +(-3.56858 + 5.89578i) q^{66} +(-2.21763 + 0.594213i) q^{67} +(0.469277 + 0.270937i) q^{68} +(4.75901 - 7.86252i) q^{69} +(2.06734 - 7.71540i) q^{70} +(-1.87415 + 1.87415i) q^{71} +(6.15758 + 6.68956i) q^{72} +(5.42937 - 5.42937i) q^{73} +(5.47981 - 3.16377i) q^{74} +(-2.29817 + 1.26418i) q^{75} +(-1.50186 - 5.60502i) q^{76} +(-7.95706 + 13.7820i) q^{77} +(-3.54825 - 5.39698i) q^{78} +(-1.10654 - 1.91658i) q^{79} +(1.68171 - 1.68171i) q^{80} +(8.96919 + 0.744075i) q^{81} +6.56512i q^{82} +(-11.0196 - 2.95269i) q^{83} +(4.61476 + 4.80980i) q^{84} +(-0.281452 - 1.05039i) q^{85} +(6.00623 - 1.60936i) q^{86} +(-9.10492 + 5.00845i) q^{87} +(-10.0974 + 5.82973i) q^{88} +(-0.110864 - 0.110864i) q^{89} +(0.239666 - 5.78786i) q^{90} +(-8.44967 - 12.2904i) q^{91} +(4.27511 - 2.46823i) q^{92} +(-3.73409 + 0.918178i) q^{93} +(-3.29649 + 5.70969i) q^{94} +(-5.82255 + 10.0850i) q^{95} +(1.96195 + 7.97898i) q^{96} +(2.91212 - 10.8682i) q^{97} +(-7.39493 - 7.39493i) q^{98} +(-3.44580 + 11.0150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9}+O(q^{10}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33} - 12 q^{34} - 16 q^{37} + 16 q^{39} + 36 q^{40} + 36 q^{41} + 20 q^{42} - 56 q^{45} - 12 q^{46} - 18 q^{47} - 8 q^{48} + 120 q^{50} - 8 q^{52} + 52 q^{54} - 64 q^{55} - 8 q^{57} - 40 q^{58} - 24 q^{59} + 8 q^{60} + 2 q^{61} + 64 q^{63} - 42 q^{65} - 4 q^{66} - 36 q^{68} + 20 q^{70} + 18 q^{72} + 48 q^{73} + 216 q^{74} - 26 q^{76} + 22 q^{78} - 22 q^{79} + 10 q^{81} + 30 q^{83} + 94 q^{84} - 18 q^{85} - 120 q^{86} + 68 q^{87} - 72 q^{92} - 62 q^{93} + 32 q^{94} + 16 q^{96} - 4 q^{97} - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

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