LMFDB - Embedded newform 154.2.f.e.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(15,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("154.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.f (of order $5$, 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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.2
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	154.113
Dual form			154.2.f.e.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.220859 + 0.679734i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.451659 + 0.328150i) q^{5} +(0.578217 + 0.420099i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.01379 - 1.46310i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.220859 + 0.679734i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.451659 + 0.328150i) q^{5} +(0.578217 + 0.420099i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.01379 - 1.46310i) q^{9} +0.558282 q^{10} +(1.91711 + 2.70642i) q^{11} +0.714715 q^{12} +(-3.67164 + 2.66760i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.123302 + 0.379483i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.44084 - 3.95300i) q^{17} +(0.769200 - 2.36735i) q^{18} +(0.872566 + 2.68548i) q^{19} +(0.451659 - 0.328150i) q^{20} +0.714715 q^{21} +(3.14177 + 1.06269i) q^{22} -5.77447 q^{23} +(0.578217 - 0.420099i) q^{24} +(-1.44877 - 4.45886i) q^{25} +(-1.40244 + 4.31627i) q^{26} +(3.17394 + 2.30600i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-1.93031 + 5.94087i) q^{29} +(0.123302 + 0.379483i) q^{30} +(-1.43557 + 1.04301i) q^{31} -1.00000 q^{32} +(-1.41623 + 1.90086i) q^{33} -6.72525 q^{34} +(0.451659 - 0.328150i) q^{35} +(-0.769200 - 2.36735i) q^{36} +(3.16023 - 9.72619i) q^{37} +(2.28441 + 1.65972i) q^{38} +(-2.62418 - 1.90658i) q^{39} +(0.172519 - 0.530958i) q^{40} +(1.38723 + 4.26947i) q^{41} +(0.578217 - 0.420099i) q^{42} -0.188604 q^{43} +(3.16637 - 0.986951i) q^{44} +1.38967 q^{45} +(-4.67164 + 3.39415i) q^{46} +(3.65117 + 11.2371i) q^{47} +(0.220859 - 0.679734i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.79293 - 2.75573i) q^{50} +(1.48533 - 4.57138i) q^{51} +(1.40244 + 4.31627i) q^{52} +(1.27914 - 0.929350i) q^{53} +3.92320 q^{54} +(-0.0222293 + 1.85148i) q^{55} -1.00000 q^{56} +(-1.63270 + 1.18623i) q^{57} +(1.93031 + 5.94087i) q^{58} +(2.85883 - 8.79857i) q^{59} +(0.322808 + 0.234534i) q^{60} +(-2.25215 - 1.63629i) q^{61} +(-0.548341 + 1.68762i) q^{62} +(-0.769200 - 2.36735i) q^{63} +(-0.809017 + 0.587785i) q^{64} -2.53371 q^{65} +(-0.0284581 + 2.37027i) q^{66} +3.36968 q^{67} +(-5.44084 + 3.95300i) q^{68} +(-1.27534 - 3.92510i) q^{69} +(0.172519 - 0.530958i) q^{70} +(9.75128 + 7.08472i) q^{71} +(-2.01379 - 1.46310i) q^{72} +(4.68920 - 14.4319i) q^{73} +(-3.16023 - 9.72619i) q^{74} +(2.71087 - 1.96956i) q^{75} +2.82368 q^{76} +(3.16637 - 0.986951i) q^{77} -3.24366 q^{78} +(1.68869 - 1.22690i) q^{79} +(-0.172519 - 0.530958i) q^{80} +(1.44112 - 4.43532i) q^{81} +(3.63182 + 2.63868i) q^{82} +(2.75074 + 1.99853i) q^{83} +(0.220859 - 0.679734i) q^{84} +(-1.16023 - 3.57082i) q^{85} +(-0.152584 + 0.110859i) q^{86} -4.46454 q^{87} +(1.98154 - 2.65961i) q^{88} -8.40304 q^{89} +(1.12426 - 0.816825i) q^{90} +(1.40244 + 4.31627i) q^{91} +(-1.78441 + 5.49184i) q^{92} +(-1.02603 - 0.745452i) q^{93} +(9.55888 + 6.94493i) q^{94} +(-0.487138 + 1.49926i) q^{95} +(-0.220859 - 0.679734i) q^{96} +(6.78826 - 4.93196i) q^{97} -1.00000 q^{98} +(7.82043 + 2.64522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} + 10 q^{10} - 5 q^{11} - 6 q^{12} + 3 q^{13} + 2 q^{14} + 30 q^{15} - 2 q^{16} - 7 q^{17} + 2 q^{18} - 14 q^{19} + 5 q^{20} - 6 q^{21} - 20 q^{23} - 4 q^{24} - 25 q^{25} + 17 q^{26} + 32 q^{27} - 2 q^{28} - 23 q^{29} - 30 q^{30} + 3 q^{31} - 8 q^{32} + 40 q^{33} + 2 q^{34} + 5 q^{35} - 2 q^{36} + 6 q^{37} - q^{38} - 21 q^{39} - 2 q^{41} - 4 q^{42} - 16 q^{43} + 15 q^{44} - 40 q^{45} - 5 q^{46} + 34 q^{47} - q^{48} - 2 q^{49} - 10 q^{50} + 4 q^{51} - 17 q^{52} + 13 q^{53} + 48 q^{54} - 25 q^{55} - 8 q^{56} - 12 q^{57} + 23 q^{58} - 3 q^{59} - 25 q^{60} - 16 q^{61} - 3 q^{62} - 2 q^{63} - 2 q^{64} + 10 q^{65} + 15 q^{66} + 18 q^{67} - 7 q^{68} - 15 q^{69} + 45 q^{71} + 7 q^{72} + q^{73} - 6 q^{74} + 40 q^{75} + 26 q^{76} + 15 q^{77} - 4 q^{78} - 21 q^{79} + 57 q^{81} - 3 q^{82} + 12 q^{83} - q^{84} + 10 q^{85} - 14 q^{86} - 4 q^{87} + 10 q^{88} + 12 q^{89} - 40 q^{90} - 17 q^{91} + 5 q^{92} - 31 q^{93} + 31 q^{94} - 30 q^{95} + q^{96} + 5 q^{97} - 8 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 + 10 * q^10 - 5 * q^11 - 6 * q^12 + 3 * q^13 + 2 * q^14 + 30 * q^15 - 2 * q^16 - 7 * q^17 + 2 * q^18 - 14 * q^19 + 5 * q^20 - 6 * q^21 - 20 * q^23 - 4 * q^24 - 25 * q^25 + 17 * q^26 + 32 * q^27 - 2 * q^28 - 23 * q^29 - 30 * q^30 + 3 * q^31 - 8 * q^32 + 40 * q^33 + 2 * q^34 + 5 * q^35 - 2 * q^36 + 6 * q^37 - q^38 - 21 * q^39 - 2 * q^41 - 4 * q^42 - 16 * q^43 + 15 * q^44 - 40 * q^45 - 5 * q^46 + 34 * q^47 - q^48 - 2 * q^49 - 10 * q^50 + 4 * q^51 - 17 * q^52 + 13 * q^53 + 48 * q^54 - 25 * q^55 - 8 * q^56 - 12 * q^57 + 23 * q^58 - 3 * q^59 - 25 * q^60 - 16 * q^61 - 3 * q^62 - 2 * q^63 - 2 * q^64 + 10 * q^65 + 15 * q^66 + 18 * q^67 - 7 * q^68 - 15 * q^69 + 45 * q^71 + 7 * q^72 + q^73 - 6 * q^74 + 40 * q^75 + 26 * q^76 + 15 * q^77 - 4 * q^78 - 21 * q^79 + 57 * q^81 - 3 * q^82 + 12 * q^83 - q^84 + 10 * q^85 - 14 * q^86 - 4 * q^87 + 10 * q^88 + 12 * q^89 - 40 * q^90 - 17 * q^91 + 5 * q^92 - 31 * q^93 + 31 * q^94 - 30 * q^95 + q^96 + 5 * q^97 - 8 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.220859	+	0.679734i	0.127513	+	0.392445i	0.994351	−	0.106146i	$-0.0338511\pi$
$3$	0.220859	+	0.679734i	0.127513	+	0.392445i	−0.866838	+	0.498591i	$0.833851\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.451659	+	0.328150i	0.201988	+	0.146753i	0.684181	−	0.729312i	$-0.260160\pi$
$5$	0.451659	+	0.328150i	0.201988	+	0.146753i	−0.482193	+	0.876065i	$0.660160\pi$
$6$	0.578217	+	0.420099i	0.236056	+	0.171505i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.01379	−	1.46310i	0.671264	−	0.487702i
$10$	0.558282			0.176544
$11$	1.91711	+	2.70642i	0.578030	+	0.816015i
$11$	1.91711	+	2.70642i	0.578030	+	0.816015i
$12$	0.714715			0.206320
$13$	−3.67164	+	2.66760i	−1.01833	+	0.739860i	−0.965940	−	0.258766i	$-0.916684\pi$
$13$	−3.67164	+	2.66760i	−1.01833	+	0.739860i	−0.0523904	+	0.998627i	$0.516684\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−0.123302	+	0.379483i	−0.0318363	+	0.0979822i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.44084	−	3.95300i	−1.31960	−	0.958744i	−0.999937	−	0.0112120i	$-0.996431\pi$
$17$	−5.44084	−	3.95300i	−1.31960	−	0.958744i	−0.319661	−	0.947532i	$-0.603569\pi$
$18$	0.769200	−	2.36735i	0.181302	−	0.557990i
$19$	0.872566	+	2.68548i	0.200180	+	0.616092i	0.999877	+	0.0156876i	$0.00499373\pi$
$19$	0.872566	+	2.68548i	0.200180	+	0.616092i	−0.799696	+	0.600404i	$0.795006\pi$
$20$	0.451659	−	0.328150i	0.100994	−	0.0733765i
$21$	0.714715			0.155964
$22$	3.14177	+	1.06269i	0.669827	+	0.226566i
$23$	−5.77447			−1.20406			−0.602030	−	0.798474i	$-0.705641\pi$
$23$	−5.77447			−1.20406			−0.602030	+	0.798474i	$0.705641\pi$
$24$	0.578217	−	0.420099i	0.118028	−	0.0857523i
$25$	−1.44877	−	4.45886i	−0.289754	−	0.891772i
$26$	−1.40244	+	4.31627i	−0.275042	+	0.846491i
$27$	3.17394	+	2.30600i	0.610824	+	0.443790i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−1.93031	+	5.94087i	−0.358449	+	1.10319i	0.595534	+	0.803330i	$0.296941\pi$
$29$	−1.93031	+	5.94087i	−0.358449	+	1.10319i	−0.953983	+	0.299862i	$0.903059\pi$
$30$	0.123302	+	0.379483i	0.0225117	+	0.0692839i
$31$	−1.43557	+	1.04301i	−0.257837	+	0.187329i	−0.709193	−	0.705015i	$-0.750940\pi$
$31$	−1.43557	+	1.04301i	−0.257837	+	0.187329i	0.451356	+	0.892344i	$0.350940\pi$
$32$	−1.00000			−0.176777
$33$	−1.41623	+	1.90086i	−0.246535	+	0.330898i
$34$	−6.72525			−1.15337
$35$	0.451659	−	0.328150i	0.0763444	−	0.0554674i
$36$	−0.769200	−	2.36735i	−0.128200	−	0.394559i
$37$	3.16023	−	9.72619i	0.519539	−	1.59898i	−0.255330	−	0.966854i	$-0.582184\pi$
$37$	3.16023	−	9.72619i	0.519539	−	1.59898i	0.774869	−	0.632122i	$-0.217816\pi$
$38$	2.28441	+	1.65972i	0.370580	+	0.269242i
$39$	−2.62418	−	1.90658i	−0.420205	−	0.305297i
$40$	0.172519	−	0.530958i	0.0272776	−	0.0839518i
$41$	1.38723	+	4.26947i	0.216649	+	0.666779i	0.999032	+	0.0439808i	$0.0140041\pi$
$41$	1.38723	+	4.26947i	0.216649	+	0.666779i	−0.782383	+	0.622798i	$0.785996\pi$
$42$	0.578217	−	0.420099i	0.0892208	−	0.0648227i
$43$	−0.188604			−0.0287618			−0.0143809	−	0.999897i	$-0.504578\pi$
$43$	−0.188604			−0.0287618			−0.0143809	+	0.999897i	$0.504578\pi$
$44$	3.16637	−	0.986951i	0.477349	−	0.148788i
$45$	1.38967			0.207159
$46$	−4.67164	+	3.39415i	−0.688796	+	0.500440i
$47$	3.65117	+	11.2371i	0.532577	+	1.63910i	0.748827	+	0.662766i	$0.230618\pi$
$47$	3.65117	+	11.2371i	0.532577	+	1.63910i	−0.216249	+	0.976338i	$0.569382\pi$
$48$	0.220859	−	0.679734i	0.0318783	−	0.0981112i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−3.79293	−	2.75573i	−0.536402	−	0.389719i
$51$	1.48533	−	4.57138i	0.207988	−	0.640122i
$52$	1.40244	+	4.31627i	0.194484	+	0.598560i
$53$	1.27914	−	0.929350i	0.175704	−	0.127656i	−0.496458	−	0.868061i	$-0.665366\pi$
$53$	1.27914	−	0.929350i	0.175704	−	0.127656i	0.672161	+	0.740405i	$0.265366\pi$
$54$	3.92320			0.533880
$55$	−0.0222293	+	1.85148i	−0.00299740	+	0.249653i
$56$	−1.00000			−0.133631
$57$	−1.63270	+	1.18623i	−0.216257	+	0.157120i
$58$	1.93031	+	5.94087i	0.253462	+	0.780075i
$59$	2.85883	−	8.79857i	0.372188	−	1.14548i	−0.573169	−	0.819437i	$-0.694286\pi$
$59$	2.85883	−	8.79857i	0.372188	−	1.14548i	0.945356	−	0.326039i	$-0.105714\pi$
$60$	0.322808	+	0.234534i	0.0416743	+	0.0302782i
$61$	−2.25215	−	1.63629i	−0.288359	−	0.209505i	0.434196	−	0.900818i	$-0.357032\pi$
$61$	−2.25215	−	1.63629i	−0.288359	−	0.209505i	−0.722555	+	0.691313i	$0.757032\pi$
$62$	−0.548341	+	1.68762i	−0.0696393	+	0.214328i
$63$	−0.769200	−	2.36735i	−0.0969100	−	0.298258i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−2.53371			−0.314268
$66$	−0.0284581	+	2.37027i	−0.00350294	+	0.291760i
$67$	3.36968			0.411672			0.205836	−	0.978587i	$-0.434009\pi$
$67$	3.36968			0.411672			0.205836	+	0.978587i	$0.434009\pi$
$68$	−5.44084	+	3.95300i	−0.659799	+	0.479372i
$69$	−1.27534	−	3.92510i	−0.153533	−	0.472527i
$70$	0.172519	−	0.530958i	0.0206199	−	0.0634616i
$71$	9.75128	+	7.08472i	1.15726	+	0.840801i	0.989430	−	0.145014i	$-0.0463227\pi$
$71$	9.75128	+	7.08472i	1.15726	+	0.840801i	0.167834	+	0.985815i	$0.446323\pi$
$72$	−2.01379	−	1.46310i	−0.237328	−	0.172429i
$73$	4.68920	−	14.4319i	0.548829	−	1.68912i	−0.162878	−	0.986646i	$-0.552078\pi$
$73$	4.68920	−	14.4319i	0.548829	−	1.68912i	0.711707	−	0.702476i	$-0.247922\pi$
$74$	−3.16023	−	9.72619i	−0.367369	−	1.13065i
$75$	2.71087	−	1.96956i	0.313024	−	0.227425i
$76$	2.82368			0.323899
$77$	3.16637	−	0.986951i	0.360842	−	0.112474i
$78$	−3.24366			−0.367272
$79$	1.68869	−	1.22690i	0.189992	−	0.138037i	−0.488723	−	0.872439i	$-0.662537\pi$
$79$	1.68869	−	1.22690i	0.189992	−	0.138037i	0.678715	+	0.734402i	$0.262537\pi$
$80$	−0.172519	−	0.530958i	−0.0192882	−	0.0593629i
$81$	1.44112	−	4.43532i	0.160125	−	0.492814i
$82$	3.63182	+	2.63868i	0.401068	+	0.291393i
$83$	2.75074	+	1.99853i	0.301932	+	0.219367i	0.728427	−	0.685123i	$-0.240252\pi$
$83$	2.75074	+	1.99853i	0.301932	+	0.219367i	−0.426495	+	0.904490i	$0.640252\pi$
$84$	0.220859	−	0.679734i	0.0240977	−	0.0741651i
$85$	−1.16023	−	3.57082i	−0.125845	−	0.387310i
$86$	−0.152584	+	0.110859i	−0.0164535	+	0.0119542i
$87$	−4.46454			−0.478649
$88$	1.98154	−	2.65961i	0.211232	−	0.283515i
$89$	−8.40304			−0.890720			−0.445360	−	0.895352i	$-0.646924\pi$
$89$	−8.40304			−0.890720			−0.445360	+	0.895352i	$0.646924\pi$
$90$	1.12426	−	0.816825i	0.118508	−	0.0861009i
$91$	1.40244	+	4.31627i	0.147016	+	0.452468i
$92$	−1.78441	+	5.49184i	−0.186037	+	0.572564i
$93$	−1.02603	−	0.745452i	−0.106394	−	0.0772998i
$94$	9.55888	+	6.94493i	0.985923	+	0.716315i
$95$	−0.487138	+	1.49926i	−0.0499793	+	0.153820i
$96$	−0.220859	−	0.679734i	−0.0225413	−	0.0693751i
$97$	6.78826	−	4.93196i	0.689243	−	0.500764i	−0.187168	−	0.982328i	$-0.559931\pi$
$97$	6.78826	−	4.93196i	0.689243	−	0.500764i	0.876411	+	0.481563i	$0.159931\pi$
$98$	−1.00000			−0.101015
$99$	7.82043	+	2.64522i	0.785983	+	0.265855i
$100$	−4.68832			−0.468832
$101$	−6.90771	+	5.01875i	−0.687343	+	0.499384i	−0.875786	−	0.482700i	$-0.839656\pi$
$101$	−6.90771	+	5.01875i	−0.687343	+	0.499384i	0.188443	+	0.982084i	$0.439656\pi$
$102$	−1.48533	−	4.57138i	−0.147070	−	0.452634i
$103$	2.74368	−	8.44419i	0.270343	−	0.832030i	−0.720071	−	0.693900i	$-0.755891\pi$
$103$	2.74368	−	8.44419i	0.270343	−	0.832030i	0.990414	−	0.138130i	$-0.0441092\pi$
$104$	3.67164	+	2.66760i	0.360034	+	0.261580i
$105$	0.322808	+	0.234534i	0.0315028	+	0.0228881i
$106$	0.488588	−	1.50372i	0.0474559	−	0.146054i
$107$	0.619504	+	1.90664i	0.0598898	+	0.184322i	0.976525	−	0.215402i	$-0.0691061\pi$
$107$	0.619504	+	1.90664i	0.0598898	+	0.184322i	−0.916636	+	0.399724i	$0.869106\pi$
$108$	3.17394	−	2.30600i	0.305412	−	0.221895i
$109$	1.78676			0.171140			0.0855701	−	0.996332i	$-0.472729\pi$
$109$	1.78676			0.171140			0.0855701	+	0.996332i	$0.472729\pi$
$110$	1.07029	+	1.51094i	0.102048	+	0.144063i
$111$	7.30919			0.693758
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	3.59722	+	11.0711i	0.338398	+	1.04148i	0.965024	+	0.262162i	$0.0844356\pi$
$113$	3.59722	+	11.0711i	0.338398	+	1.04148i	−0.626626	+	0.779320i	$0.715564\pi$
$114$	−0.623636	+	1.91936i	−0.0584089	+	0.179764i
$115$	−2.60809	−	1.89489i	−0.243206	−	0.176699i
$116$	5.05361	+	3.67166i	0.469216	+	0.340905i
$117$	−3.49094	+	10.7440i	−0.322737	+	0.993283i
$118$	−2.85883	−	8.79857i	−0.263176	−	0.809974i
$119$	−5.44084	+	3.95300i	−0.498761	+	0.362371i
$120$	0.399012			0.0364247
$121$	−3.64938	+	10.3770i	−0.331762	+	0.943363i
$122$	−2.78381			−0.252035
$123$	−2.59572	+	1.88590i	−0.234048	+	0.170046i
$124$	0.548341	+	1.68762i	0.0492424	+	0.151553i
$125$	1.67142	−	5.14409i	0.149496	−	0.460101i
$126$	−2.01379	−	1.46310i	−0.179403	−	0.130344i
$127$	−8.83802	−	6.42119i	−0.784247	−	0.569789i	0.122003	−	0.992530i	$-0.461068\pi$
$127$	−8.83802	−	6.42119i	−0.784247	−	0.569789i	−0.906251	+	0.422741i	$0.861068\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.0416549	−	0.128201i	−0.00366751	−	0.0112874i
$130$	−2.04981	+	1.48927i	−0.179780	+	0.130618i
$131$	−0.831279			−0.0726292			−0.0363146	−	0.999340i	$-0.511562\pi$
$131$	−0.831279			−0.0726292			−0.0363146	+	0.999340i	$0.511562\pi$
$132$	1.37019	+	1.93432i	0.119259	+	0.168361i
$133$	2.82368			0.244844
$134$	2.72613	−	1.98065i	0.235501	−	0.171102i
$135$	0.676825	+	2.08305i	0.0582518	+	0.179281i
$136$	−2.07822	+	6.39609i	−0.178206	+	0.548460i
$137$	3.31896	+	2.41136i	0.283558	+	0.206017i	0.720468	−	0.693488i	$-0.243927\pi$
$137$	3.31896	+	2.41136i	0.283558	+	0.206017i	−0.436910	+	0.899505i	$0.643927\pi$
$138$	−3.33889	−	2.42585i	−0.284225	−	0.206502i
$139$	2.13939	−	6.58436i	0.181460	−	0.558478i	−0.818409	−	0.574636i	$-0.805144\pi$
$139$	2.13939	−	6.58436i	0.181460	−	0.558478i	0.999869	+	0.0161584i	$0.00514359\pi$
$140$	−0.172519	−	0.530958i	−0.0145805	−	0.0448741i
$141$	−6.83187	+	4.96365i	−0.575347	+	0.418014i
$142$	12.0532			1.01149
$143$	−14.2586	−	4.82290i	−1.19236	−	0.403311i
$144$	−2.48918			−0.207432
$145$	−2.82134	+	2.04982i	−0.234299	+	0.170228i
$146$	−4.68920	−	14.4319i	−0.388081	−	1.19439i
$147$	0.220859	−	0.679734i	0.0182162	−	0.0560636i
$148$	−8.27359	−	6.01112i	−0.680085	−	0.494111i
$149$	−11.1968	−	8.13495i	−0.917277	−	0.666441i	0.0255678	−	0.999673i	$-0.491861\pi$
$149$	−11.1968	−	8.13495i	−0.917277	−	0.666441i	−0.942845	+	0.333232i	$0.891861\pi$
$150$	1.03546	−	3.18681i	0.0845448	−	0.260202i
$151$	2.65496	+	8.17114i	0.216058	+	0.664958i	0.999077	+	0.0429598i	$0.0136787\pi$
$151$	2.65496	+	8.17114i	0.216058	+	0.664958i	−0.783019	+	0.621998i	$0.786321\pi$
$152$	2.28441	−	1.65972i	0.185290	−	0.134621i
$153$	−16.7404			−1.35338
$154$	1.98154	−	2.65961i	0.159677	−	0.214317i
$155$	−0.990653			−0.0795711
$156$	−2.62418	+	1.90658i	−0.210102	+	0.152648i
$157$	4.29998	+	13.2340i	0.343176	+	1.05619i	0.962553	+	0.271094i	$0.0873853\pi$
$157$	4.29998	+	13.2340i	0.343176	+	1.05619i	−0.619377	+	0.785094i	$0.712615\pi$
$158$	0.645022	−	1.98517i	0.0513152	−	0.157932i
$159$	0.914221	+	0.664221i	0.0725025	+	0.0526761i
$160$	−0.451659	−	0.328150i	−0.0357068	−	0.0259425i
$161$	−1.78441	+	5.49184i	−0.140631	+	0.432818i
$162$	−1.44112	−	4.43532i	−0.113225	−	0.348472i
$163$	−12.7941	+	9.29543i	−1.00211	+	0.728075i	−0.962539	−	0.271142i	$-0.912599\pi$
$163$	−12.7941	+	9.29543i	−1.00211	+	0.728075i	−0.0395694	+	0.999217i	$0.512599\pi$
$164$	4.48918			0.350546
$165$	−1.26342	+	0.393806i	−0.0983573	+	0.0306577i
$166$	3.40010			0.263899
$167$	−13.2476	+	9.62492i	−1.02513	+	0.744799i	−0.967328	−	0.253530i	$-0.918408\pi$
$167$	−13.2476	+	9.62492i	−1.02513	+	0.744799i	−0.0577997	+	0.998328i	$0.518408\pi$
$168$	−0.220859	−	0.679734i	−0.0170396	−	0.0524427i
$169$	2.34762	−	7.22524i	0.180586	−	0.555788i
$170$	−3.03752	−	2.20689i	−0.232967	−	0.169261i
$171$	5.68631	+	4.13135i	0.434843	+	0.315932i
$172$	−0.0582818	+	0.179373i	−0.00444394	+	0.0136771i
$173$	−5.94084	−	18.2840i	−0.451674	−	1.39011i	−0.874996	−	0.484130i	$-0.839136\pi$
$173$	−5.94084	−	18.2840i	−0.451674	−	1.39011i	0.423322	−	0.905979i	$-0.360864\pi$
$174$	−3.61189	+	2.62419i	−0.273817	+	0.198939i
$175$	−4.68832			−0.354404
$176$	0.0398173	−	3.31639i	0.00300135	−	0.249982i
$177$	6.61209			0.496995
$178$	−6.79820	+	4.93918i	−0.509547	+	0.370207i
$179$	0.690107	+	2.12393i	0.0515810	+	0.158750i	0.973529	−	0.228564i	$-0.0734030\pi$
$179$	0.690107	+	2.12393i	0.0515810	+	0.158750i	−0.921948	+	0.387314i	$0.873403\pi$
$180$	0.429430	−	1.32165i	0.0320078	−	0.0985100i
$181$	15.8922	+	11.5464i	1.18126	+	0.858235i	0.992313	−	0.123752i	$-0.0394928\pi$
$181$	15.8922	+	11.5464i	1.18126	+	0.858235i	0.188946	+	0.981987i	$0.439493\pi$
$182$	3.67164	+	2.66760i	0.272160	+	0.197736i
$183$	0.614831	−	1.89225i	0.0454496	−	0.139879i
$184$	1.78441	+	5.49184i	0.131548	+	0.404864i
$185$	4.61900	−	3.35590i	0.339595	−	0.246730i
$186$	−1.26824			−0.0929918
$187$	0.267782	−	22.3035i	0.0195821	−	1.63100i
$188$	11.8154			0.861728
$189$	3.17394	−	2.30600i	0.230870	−	0.167737i
$190$	0.487138	+	1.49926i	0.0353407	+	0.108767i
$191$	−4.30848	+	13.2601i	−0.311750	+	0.959469i	0.665321	+	0.746557i	$0.268295\pi$
$191$	−4.30848	+	13.2601i	−0.311750	+	0.959469i	−0.977071	+	0.212912i	$0.931705\pi$
$192$	−0.578217	−	0.420099i	−0.0417292	−	0.0303180i
$193$	9.57496	+	6.95662i	0.689221	+	0.500748i	0.876404	−	0.481577i	$-0.159936\pi$
$193$	9.57496	+	6.95662i	0.689221	+	0.500748i	−0.187183	+	0.982325i	$0.559936\pi$
$194$	2.59288	−	7.98008i	0.186158	−	0.572936i
$195$	−0.559592	−	1.72225i	−0.0400732	−	0.123333i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	7.03042			0.500897			0.250448	−	0.968130i	$-0.419422\pi$
$197$	7.03042			0.500897			0.250448	+	0.968130i	$0.419422\pi$
$198$	7.88168	−	2.45670i	0.560127	−	0.174590i
$199$	−9.84073			−0.697591			−0.348795	−	0.937199i	$-0.613409\pi$
$199$	−9.84073			−0.697591			−0.348795	+	0.937199i	$0.613409\pi$
$200$	−3.79293	+	2.75573i	−0.268201	+	0.194859i
$201$	0.744224	+	2.29049i	0.0524935	+	0.161558i
$202$	−2.63851	+	8.12050i	−0.185645	+	0.571356i
$203$	5.05361	+	3.67166i	0.354694	+	0.257700i
$204$	−3.88865	−	2.82527i	−0.272260	−	0.197809i
$205$	−0.774467	+	2.38357i	−0.0540911	+	0.166475i
$206$	−2.74368	−	8.44419i	−0.191161	−	0.588334i
$207$	−11.6286	+	8.44865i	−0.808241	+	0.587222i
$208$	4.53840			0.314681
$209$	−5.59523	+	7.50989i	−0.387030	+	0.519470i
$210$	0.399012			0.0275345
$211$	13.0182	−	9.45826i	0.896209	−	0.651134i	−0.0412808	−	0.999148i	$-0.513144\pi$
$211$	13.0182	−	9.45826i	0.896209	−	0.651134i	0.937489	+	0.348014i	$0.113144\pi$
$212$	−0.488588	−	1.50372i	−0.0335564	−	0.103276i
$213$	−2.66207	+	8.19300i	−0.182402	+	0.561375i
$214$	1.62188	+	1.17837i	0.110870	+	0.0805515i
$215$	−0.0851847	−	0.0618903i	−0.00580955	−	0.00422088i
$216$	1.21234	−	3.73119i	0.0824890	−	0.253875i
$217$	0.548341	+	1.68762i	0.0372238	+	0.114563i
$218$	1.44552	−	1.05023i	0.0979027	−	0.0711304i
$219$	10.8455			0.732870
$220$	1.75399	+	0.593279i	0.118254	+	0.0399989i
$221$	30.5219			2.05312
$222$	5.91326	−	4.29623i	0.396872	−	0.288344i
$223$	−6.91530	−	21.2831i	−0.463083	−	1.42522i	−0.861377	−	0.507965i	$-0.830398\pi$
$223$	−6.91530	−	21.2831i	−0.463083	−	1.42522i	0.398294	−	0.917258i	$-0.369602\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	−9.44130	−	6.85951i	−0.629420	−	0.457300i
$226$	9.41765	+	6.84232i	0.626453	+	0.455145i
$227$	3.58583	−	11.0361i	0.238000	−	0.732489i	−0.758709	−	0.651429i	$-0.774170\pi$
$227$	3.58583	−	11.0361i	0.238000	−	0.732489i	0.996709	−	0.0810593i	$-0.0258303\pi$
$228$	0.623636	+	1.91936i	0.0413013	+	0.127112i
$229$	−0.209447	+	0.152172i	−0.0138407	+	0.0100558i	−0.594684	−	0.803959i	$-0.702723\pi$
$229$	−0.209447	+	0.152172i	−0.0138407	+	0.0100558i	0.580843	+	0.814015i	$0.302723\pi$
$230$	−3.22378			−0.212570
$231$	1.37019	+	1.93432i	0.0901517	+	0.127269i
$232$	6.24660			0.410110
$233$	22.7970	−	16.5630i	1.49348	−	1.08508i	0.520596	−	0.853803i	$-0.325710\pi$
$233$	22.7970	−	16.5630i	1.49348	−	1.08508i	0.972888	−	0.231276i	$-0.0742901\pi$
$234$	3.49094	+	10.7440i	0.228210	+	0.702357i
$235$	−2.03838	+	6.27349i	−0.132969	+	0.409237i
$236$	−7.48451	−	5.43781i	−0.487200	−	0.353972i
$237$	1.20693	+	0.876887i	0.0783986	+	0.0569599i
$238$	−2.07822	+	6.39609i	−0.134711	+	0.414597i
$239$	1.49298	+	4.59492i	0.0965728	+	0.297221i	0.987660	−	0.156611i	$-0.0500568\pi$
$239$	1.49298	+	4.59492i	0.0965728	+	0.297221i	−0.891088	+	0.453831i	$0.850057\pi$
$240$	0.322808	−	0.234534i	0.0208372	−	0.0151391i
$241$	18.6789			1.20321			0.601606	−	0.798793i	$-0.294528\pi$
$241$	18.6789			1.20321			0.601606	+	0.798793i	$0.294528\pi$
$242$	3.14703	+	10.5402i	0.202299	+	0.677551i
$243$	15.1027			0.968841
$244$	−2.25215	+	1.63629i	−0.144179	+	0.104752i
$245$	−0.172519	−	0.530958i	−0.0110218	−	0.0339216i
$246$	−0.991477	+	3.05145i	−0.0632143	+	0.194553i
$247$	−10.3676	−	7.53247i	−0.659672	−	0.479280i
$248$	1.43557	+	1.04301i	0.0911591	+	0.0662309i
$249$	−0.750942	+	2.31116i	−0.0475890	+	0.146464i
$250$	−1.67142	−	5.14409i	−0.105710	−	0.325341i
$251$	20.1283	−	14.6241i	1.27049	−	0.923062i	0.271264	−	0.962505i	$-0.412558\pi$
$251$	20.1283	−	14.6241i	1.27049	−	0.923062i	0.999222	+	0.0394426i	$0.0125582\pi$
$252$	−2.48918			−0.156804
$253$	−11.0703	−	15.6281i	−0.695983	−	0.982531i
$254$	−10.9244			−0.685457
$255$	2.17096	−	1.57730i	0.135951	−	0.0987742i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	0.00467362	−	0.0143839i	0.000291532	−	0.000897244i	−0.950911	−	0.309466i	$-0.899850\pi$
$257$	0.00467362	−	0.0143839i	0.000291532	−	0.000897244i	0.951202	+	0.308568i	$0.0998499\pi$
$258$	−0.109054	−	0.0792323i	−0.00678940	−	0.00493279i
$259$	−8.27359	−	6.01112i	−0.514096	−	0.373513i
$260$	−0.782958	+	2.40970i	−0.0485570	+	0.149443i
$261$	4.80489	+	14.7879i	0.297415	+	0.915349i
$262$	−0.672519	+	0.488613i	−0.0415483	+	0.0301866i
$263$	−29.4195			−1.81409			−0.907043	−	0.421039i	$-0.861666\pi$
$263$	−29.4195			−1.81409			−0.907043	+	0.421039i	$0.861666\pi$
$264$	2.24547	+	0.759519i	0.138199	+	0.0467452i
$265$	0.882702			0.0542240
$266$	2.28441	−	1.65972i	0.140066	−	0.101764i
$267$	−1.85589	−	5.71183i	−0.113578	−	0.349559i
$268$	1.04129	−	3.20475i	0.0636068	−	0.195762i
$269$	−9.58929	−	6.96703i	−0.584670	−	0.424787i	0.255735	−	0.966747i	$-0.417683\pi$
$269$	−9.58929	−	6.96703i	−0.584670	−	0.424787i	−0.840405	+	0.541960i	$0.817683\pi$
$270$	1.77195	+	1.28740i	0.107838	+	0.0783485i
$271$	5.29727	−	16.3033i	0.321786	−	0.990356i	−0.651084	−	0.759006i	$-0.725686\pi$
$271$	5.29727	−	16.3033i	0.321786	−	0.990356i	0.972870	−	0.231351i	$-0.0743145\pi$
$272$	2.07822	+	6.39609i	0.126010	+	0.387820i
$273$	−2.62418	+	1.90658i	−0.158822	+	0.115391i
$274$	4.10246			0.247839
$275$	9.29008	−	12.4691i	0.560213	−	0.751915i
$276$	−4.12710			−0.248422
$277$	−7.96132	+	5.78424i	−0.478349	+	0.347541i	−0.800686	−	0.599084i	$-0.795532\pi$
$277$	−7.96132	+	5.78424i	−0.478349	+	0.347541i	0.322337	+	0.946625i	$0.395532\pi$
$278$	−2.13939	−	6.58436i	−0.128312	−	0.394903i
$279$	−1.36492	+	4.20079i	−0.0817156	+	0.251495i
$280$	−0.451659	−	0.328150i	−0.0269918	−	0.0196107i
$281$	−1.75688	−	1.27645i	−0.104807	−	0.0761465i	0.534148	−	0.845391i	$-0.320633\pi$
$281$	−1.75688	−	1.27645i	−0.104807	−	0.0761465i	−0.638954	+	0.769245i	$0.720633\pi$
$282$	−2.60954	+	8.03135i	−0.155396	+	0.478260i
$283$	8.40244	+	25.8601i	0.499473	+	1.53722i	0.809867	+	0.586613i	$0.199539\pi$
$283$	8.40244	+	25.8601i	0.499473	+	1.53722i	−0.310394	+	0.950608i	$0.600461\pi$
$284$	9.75128	−	7.08472i	0.578632	−	0.420401i
$285$	−1.12669			−0.0667391
$286$	−14.3703	+	4.47918i	−0.849732	+	0.264859i
$287$	4.48918			0.264988
$288$	−2.01379	+	1.46310i	−0.118664	+	0.0862143i
$289$	8.72324	+	26.8474i	0.513132	+	1.57926i
$290$	−1.07765	+	3.31668i	−0.0632821	+	0.194762i
$291$	4.85167	+	3.52494i	0.284410	+	0.206636i
$292$	−12.2765	−	8.91938i	−0.718427	−	0.521967i
$293$	−6.04710	+	18.6111i	−0.353275	+	1.08727i	0.603728	+	0.797191i	$0.293681\pi$
$293$	−6.04710	+	18.6111i	−0.353275	+	1.08727i	−0.957003	+	0.290079i	$0.906319\pi$
$294$	−0.220859	−	0.679734i	−0.0128808	−	0.0396429i
$295$	4.17846	−	3.03583i	0.243280	−	0.176753i
$296$	−10.2267			−0.594416
$297$	−0.156211	+	13.0108i	−0.00906431	+	0.754966i
$298$	−13.8400			−0.801729
$299$	21.2018	−	15.4040i	1.22613	−	0.890836i
$300$	−1.03546	−	3.18681i	−0.0597822	−	0.183991i
$301$	−0.0582818	+	0.179373i	−0.00335931	+	0.0103389i
$302$	6.95078	+	5.05004i	0.399973	+	0.290597i
$303$	−4.93704	−	3.58697i	−0.283626	−	0.206066i
$304$	0.872566	−	2.68548i	0.0500451	−	0.154023i
$305$	−0.480260	−	1.47809i	−0.0274996	−	0.0846350i
$306$	−13.5432	+	9.83975i	−0.774216	+	0.562501i
$307$	−29.9321			−1.70831			−0.854157	−	0.520015i	$-0.825926\pi$
$307$	−29.9321			−1.70831			−0.854157	+	0.520015i	$0.825926\pi$
$308$	0.0398173	−	3.31639i	0.00226880	−	0.188969i
$309$	6.34577			0.360998
$310$	−0.801455	+	0.582291i	−0.0455196	+	0.0330719i
$311$	−6.00059	−	18.4679i	−0.340262	−	1.04722i	−0.964071	−	0.265643i	$-0.914416\pi$
$311$	−6.00059	−	18.4679i	−0.340262	−	1.04722i	0.623809	−	0.781577i	$-0.285584\pi$
$312$	−1.00235	+	3.08491i	−0.0567467	+	0.174648i
$313$	−22.8339	−	16.5898i	−1.29065	−	0.937712i	−0.290832	−	0.956774i	$-0.593932\pi$
$313$	−22.8339	−	16.5898i	−1.29065	−	0.937712i	−0.999818	+	0.0190617i	$0.993932\pi$
$314$	11.2575	+	8.17906i	0.635298	+	0.461571i
$315$	0.429430	−	1.32165i	0.0241956	−	0.0744665i
$316$	−0.645022	−	1.98517i	−0.0362853	−	0.111675i
$317$	1.36647	−	0.992802i	0.0767489	−	0.0557613i	−0.548749	−	0.835987i	$-0.684896\pi$
$317$	1.36647	−	0.992802i	0.0767489	−	0.0557613i	0.625498	+	0.780226i	$0.284896\pi$
$318$	1.13004			0.0633695
$319$	−19.7791	+	6.16509i	−1.10742	+	0.345179i
$320$	−0.558282			−0.0312089
$321$	−1.15918	+	0.842197i	−0.0646994	+	0.0470068i
$322$	1.78441	+	5.49184i	0.0994412	+	0.306049i
$323$	5.86823	−	18.0605i	0.326517	−	1.00492i
$324$	−3.77291	−	2.74118i	−0.209606	−	0.152288i
$325$	17.2138	+	12.5066i	0.954852	+	0.693741i
$326$	−4.88690	+	15.0403i	−0.270660	+	0.833007i
$327$	0.394621	+	1.21452i	0.0218226	+	0.0671631i
$328$	3.63182	−	2.63868i	0.200534	−	0.145696i
$329$	11.8154			0.651405
$330$	−0.790657	+	1.06122i	−0.0435243	+	0.0584181i
$331$	−24.7036			−1.35783			−0.678917	−	0.734215i	$-0.737550\pi$
$331$	−24.7036			−1.35783			−0.678917	+	0.734215i	$0.737550\pi$
$332$	2.75074	−	1.99853i	0.150966	−	0.109683i
$333$	−7.86639	−	24.2103i	−0.431076	−	1.32671i
$334$	−5.06012	+	15.5734i	−0.276877	+	0.852141i
$335$	1.52195	+	1.10576i	0.0831528	+	0.0604141i
$336$	−0.578217	−	0.420099i	−0.0315443	−	0.0229183i
$337$	−7.42295	+	22.8455i	−0.404354	+	1.24447i	0.517080	+	0.855937i	$0.327019\pi$
$337$	−7.42295	+	22.8455i	−0.404354	+	1.24447i	−0.921434	+	0.388536i	$0.872981\pi$
$338$	−2.34762	−	7.22524i	−0.127694	−	0.393001i
$339$	−6.73094	+	4.89031i	−0.365574	+	0.265605i
$340$	−3.75458			−0.203621
$341$	−5.57496	−	1.88571i	−0.301901	−	0.102117i
$342$	7.02866			0.380067
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.0582818	+	0.179373i	0.00314234	+	0.00967114i
$345$	0.712001	−	2.19131i	0.0383329	−	0.117976i
$346$	−15.5533	−	11.3002i	−0.836152	−	0.607500i
$347$	2.79064	+	2.02752i	0.149809	+	0.108843i	0.660165	−	0.751121i	$-0.270486\pi$
$347$	2.79064	+	2.02752i	0.149809	+	0.108843i	−0.510356	+	0.859963i	$0.670486\pi$
$348$	−1.37962	+	4.24603i	−0.0739554	+	0.227611i
$349$	1.57351	+	4.84277i	0.0842281	+	0.259227i	0.984297	−	0.176520i	$-0.0564841\pi$
$349$	1.57351	+	4.84277i	0.0842281	+	0.259227i	−0.900069	+	0.435748i	$0.856484\pi$
$350$	−3.79293	+	2.75573i	−0.202741	+	0.147300i
$351$	−17.8051			−0.950364
$352$	−1.91711	−	2.70642i	−0.102182	−	0.144252i
$353$	1.00284			0.0533756			0.0266878	−	0.999644i	$-0.491504\pi$
$353$	1.00284			0.0533756			0.0266878	+	0.999644i	$0.491504\pi$
$354$	5.34929	−	3.88649i	0.284312	−	0.206564i
$355$	2.07941	+	6.39976i	0.110364	+	0.339664i
$356$	−2.59668	+	7.99176i	−0.137624	+	0.423563i
$357$	−3.88865	−	2.82527i	−0.205809	−	0.149529i
$358$	1.80672	+	1.31266i	0.0954883	+	0.0693763i
$359$	−1.53401	+	4.72119i	−0.0809618	+	0.249175i	−0.983342	−	0.181767i	$-0.941818\pi$
$359$	−1.53401	+	4.72119i	−0.0809618	+	0.249175i	0.902380	+	0.430942i	$0.141818\pi$
$360$	−0.429430	−	1.32165i	−0.0226330	−	0.0696571i
$361$	8.92087	−	6.48139i	0.469520	−	0.341126i
$362$	19.6439			1.03246
$363$	−7.85960	−	0.188756i	−0.412522	−	0.00990711i
$364$	4.53840			0.237877
$365$	6.85373	−	4.97953i	0.358741	−	0.260641i
$366$	−0.614831	−	1.89225i	−0.0321377	−	0.0989097i
$367$	−8.40714	+	25.8745i	−0.438849	+	1.35064i	0.450242	+	0.892907i	$0.351338\pi$
$367$	−8.40714	+	25.8745i	−0.438849	+	1.35064i	−0.889091	+	0.457731i	$0.848662\pi$
$368$	4.67164	+	3.39415i	0.243526	+	0.176932i
$369$	9.04027	+	6.56814i	0.470618	+	0.341924i
$370$	1.76430	−	5.42995i	0.0917215	−	0.282290i
$371$	−0.488588	−	1.50372i	−0.0253662	−	0.0780693i
$372$	−1.02603	+	0.745452i	−0.0531970	+	0.0386499i
$373$	27.7238			1.43549			0.717743	−	0.696308i	$-0.245175\pi$
$373$	27.7238			1.43549			0.717743	+	0.696308i	$0.245175\pi$
$374$	−12.8930	−	18.2013i	−0.666683	−	0.941168i
$375$	3.86576			0.199627
$376$	9.55888	−	6.94493i	0.492961	−	0.358157i
$377$	−8.76050	−	26.9621i	−0.451189	−	1.38862i
$378$	1.21234	−	3.73119i	0.0623558	−	0.191912i
$379$	−6.42003	−	4.66443i	−0.329775	−	0.239595i	0.410560	−	0.911833i	$-0.365333\pi$
$379$	−6.42003	−	4.66443i	−0.329775	−	0.239595i	−0.740335	+	0.672238i	$0.765333\pi$
$380$	1.27534	+	0.926591i	0.0654238	+	0.0475331i
$381$	2.41275	−	7.42568i	0.123609	−	0.380429i
$382$	4.30848	+	13.2601i	0.220441	+	0.678447i
$383$	2.56346	−	1.86247i	0.130987	−	0.0951676i	−0.520363	−	0.853945i	$-0.674203\pi$
$383$	2.56346	−	1.86247i	0.130987	−	0.0951676i	0.651349	+	0.758778i	$0.274203\pi$
$384$	−0.714715			−0.0364727
$385$	1.75399	+	0.593279i	0.0893916	+	0.0302363i
$386$	11.8353			0.602401
$387$	−0.379809	+	0.275947i	−0.0193068	+	0.0140272i
$388$	−2.59288	−	7.98008i	−0.131634	−	0.405127i
$389$	−7.18414	+	22.1105i	−0.364250	+	1.12105i	0.586199	+	0.810167i	$0.300624\pi$
$389$	−7.18414	+	22.1105i	−0.364250	+	1.12105i	−0.950449	+	0.310880i	$0.899376\pi$
$390$	−1.46503	−	1.06441i	−0.0741847	−	0.0538984i
$391$	31.4180	+	22.8265i	1.58887	+	1.15439i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	−0.183595	−	0.565049i	−0.00926117	−	0.0285029i
$394$	5.68773	−	4.13238i	0.286544	−	0.208186i
$395$	1.16532			0.0586336
$396$	4.93240	−	6.62025i	0.247863	−	0.332680i
$397$	−24.6203			−1.23566			−0.617829	−	0.786313i	$-0.711988\pi$
$397$	−24.6203			−1.23566			−0.617829	+	0.786313i	$0.711988\pi$
$398$	−7.96132	+	5.78424i	−0.399065	+	0.289938i
$399$	0.623636	+	1.91936i	0.0312209	+	0.0960880i
$400$	−1.44877	+	4.45886i	−0.0724386	+	0.222943i
$401$	−15.0438	−	10.9300i	−0.751254	−	0.545818i	0.144962	−	0.989437i	$-0.453694\pi$
$401$	−15.0438	−	10.9300i	−0.751254	−	0.545818i	−0.896215	+	0.443620i	$0.853694\pi$
$402$	1.94840	+	1.41560i	0.0971776	+	0.0706036i
$403$	2.48859	−	7.65909i	0.123965	−	0.381526i
$404$	2.63851	+	8.12050i	0.131271	+	0.404010i
$405$	2.10635	−	1.53035i	0.104665	−	0.0760438i
$406$	6.24660			0.310014
$407$	32.3816	−	10.0933i	1.60510	−	0.500305i
$408$	−4.80664			−0.237964
$409$	−7.09173	+	5.15244i	−0.350663	+	0.254772i	−0.749147	−	0.662404i	$-0.769536\pi$
$409$	−7.09173	+	5.15244i	−0.350663	+	0.254772i	0.398484	+	0.917175i	$0.369536\pi$
$410$	0.774467	+	2.38357i	0.0382482	+	0.117716i
$411$	−0.906065	+	2.78858i	−0.0446929	+	0.137551i
$412$	−7.18305	−	5.21879i	−0.353884	−	0.257112i
$413$	−7.48451	−	5.43781i	−0.368289	−	0.267577i
$414$	−4.44172	+	13.6702i	−0.218299	+	0.671854i
$415$	0.586580	+	1.80531i	0.0287941	+	0.0886190i
$416$	3.67164	−	2.66760i	0.180017	−	0.130790i
$417$	4.94812			0.242310
$418$	−0.112432	+	9.36443i	−0.00549921	+	0.458029i
$419$	8.74219			0.427084			0.213542	−	0.976934i	$-0.431500\pi$
$419$	8.74219			0.427084			0.213542	+	0.976934i	$0.431500\pi$
$420$	0.322808	−	0.234534i	0.0157514	−	0.0114441i
$421$	1.43937	+	4.42993i	0.0701507	+	0.215902i	0.979985	−	0.199069i	$-0.0637918\pi$
$421$	1.43937	+	4.42993i	0.0701507	+	0.215902i	−0.909835	+	0.414971i	$0.863792\pi$
$422$	4.97250	−	15.3038i	0.242058	−	0.744977i
$423$	23.7938	+	17.2872i	1.15689	+	0.840532i
$424$	−1.27914	−	0.929350i	−0.0621206	−	0.0451332i
$425$	−9.74335	+	29.9869i	−0.472622	+	1.45458i
$426$	2.66207	+	8.19300i	0.128978	+	0.396952i
$427$	−2.25215	+	1.63629i	−0.108989	+	0.0791854i
$428$	2.00476			0.0969037
$429$	0.129154	−	10.7572i	0.00623561	−	0.519364i
$430$	−0.105294			−0.00507773
$431$	20.6008	−	14.9673i	0.992305	−	0.720952i	0.0318804	−	0.999492i	$-0.489850\pi$
$431$	20.6008	−	14.9673i	0.992305	−	0.720952i	0.960425	+	0.278540i	$0.0898504\pi$
$432$	−1.21234	−	3.73119i	−0.0583285	−	0.179517i
$433$	6.20532	−	19.0980i	0.298208	−	0.917791i	−0.683916	−	0.729560i	$-0.739725\pi$
$433$	6.20532	−	19.0980i	0.298208	−	0.917791i	0.982125	−	0.188231i	$-0.0602753\pi$
$434$	1.43557	+	1.04301i	0.0689098	+	0.0500659i
$435$	−2.01645	−	1.46504i	−0.0966815	−	0.0702432i
$436$	0.552138	−	1.69931i	0.0264426	−	0.0813820i
$437$	−5.03861	−	15.5072i	−0.241029	−	0.741812i
$438$	8.77418	−	6.37482i	0.419247	−	0.304601i
$439$	5.87482			0.280390			0.140195	−	0.990124i	$-0.455227\pi$
$439$	5.87482			0.280390			0.140195	+	0.990124i	$0.455227\pi$
$440$	1.76773	−	0.550997i	0.0842732	−	0.0262677i
$441$	−2.48918			−0.118532
$442$	24.6927	−	17.9403i	1.17451	−	0.853333i
$443$	3.95058	+	12.1586i	0.187698	+	0.577674i	0.999984	−	0.00558450i	$-0.00177761\pi$
$443$	3.95058	+	12.1586i	0.187698	+	0.577674i	−0.812287	+	0.583258i	$0.801778\pi$
$444$	2.25866	−	6.95145i	0.107191	−	0.329901i
$445$	−3.79531	−	2.75745i	−0.179915	−	0.130716i
$446$	−18.1045	−	13.1537i	−0.857273	−	0.622845i
$447$	3.05669	−	9.40752i	0.144576	−	0.444961i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	−26.5207	+	19.2684i	−1.25159	+	0.909333i	−0.998313	−	0.0580611i	$-0.981508\pi$
$449$	−26.5207	+	19.2684i	−1.25159	+	0.909333i	−0.253276	+	0.967394i	$0.581508\pi$
$450$	−11.6701			−0.550133
$451$	−8.89547	+	11.9395i	−0.418872	+	0.562208i
$452$	11.6409			0.547540
$453$	−4.96783	+	3.60934i	−0.233409	+	0.169582i
$454$	−3.58583	−	11.0361i	−0.168291	−	0.517948i
$455$	−0.782958	+	2.40970i	−0.0367056	+	0.112968i
$456$	1.63270	+	1.18623i	0.0764582	+	0.0555502i
$457$	1.27919	+	0.929388i	0.0598381	+	0.0434750i	0.617302	−	0.786726i	$-0.288226\pi$
$457$	1.27919	+	0.929388i	0.0598381	+	0.0434750i	−0.557464	+	0.830201i	$0.688226\pi$
$458$	−0.0800018	+	0.246220i	−0.00373824	+	0.0115051i
$459$	−8.15326	−	25.0932i	−0.380562	−	1.17125i
$460$	−2.60809	+	1.89489i	−0.121603	+	0.0883497i
$461$	13.5215			0.629757			0.314879	−	0.949132i	$-0.398036\pi$
$461$	13.5215			0.629757			0.314879	+	0.949132i	$0.398036\pi$
$462$	2.24547	+	0.759519i	0.104469	+	0.0353360i
$463$	−31.6964			−1.47306			−0.736528	−	0.676407i	$-0.763536\pi$
$463$	−31.6964			−1.47306			−0.736528	+	0.676407i	$0.763536\pi$
$464$	5.05361	−	3.67166i	0.234608	−	0.170453i
$465$	−0.218795	−	0.673381i	−0.0101464	−	0.0312273i
$466$	8.70769	−	26.7995i	0.403376	−	1.24146i
$467$	13.2803	+	9.64872i	0.614540	+	0.446490i	0.851010	−	0.525149i	$-0.175990\pi$
$467$	13.2803	+	9.64872i	0.614540	+	0.446490i	−0.236470	+	0.971639i	$0.575990\pi$
$468$	9.13939	+	6.64015i	0.422468	+	0.306941i
$469$	1.04129	−	3.20475i	0.0480822	−	0.147982i
$470$	2.03838	+	6.27349i	0.0940234	+	0.289374i
$471$	−8.04591	+	5.84570i	−0.370736	+	0.269355i
$472$	−9.25136			−0.425828
$473$	−0.361574	−	0.510441i	−0.0166252	−	0.0234701i
$474$	1.49185			0.0685229
$475$	10.7100	−	7.78130i	0.491410	−	0.357031i
$476$	2.07822	+	6.39609i	0.0952549	+	0.293164i
$477$	1.21619	−	3.74303i	0.0556853	−	0.171382i
$478$	3.90867	+	2.83982i	0.178778	+	0.129890i
$479$	−9.13939	−	6.64015i	−0.417589	−	0.303396i	0.359078	−	0.933308i	$-0.383091\pi$
$479$	−9.13939	−	6.64015i	−0.417589	−	0.303396i	−0.776667	+	0.629911i	$0.783091\pi$
$480$	0.123302	−	0.379483i	0.00562792	−	0.0173210i
$481$	14.3424	+	44.1413i	0.653957	+	2.01267i
$482$	15.1115	−	10.9792i	0.688311	−	0.500087i
$483$	−4.12710			−0.187789
$484$	8.74139	+	6.67743i	0.397336	+	0.303520i
$485$	4.68440			0.212708
$486$	12.2184	−	8.87716i	0.554236	−	0.402676i
$487$	−11.3257	−	34.8571i	−0.513219	−	1.57952i	−0.786500	−	0.617590i	$-0.788109\pi$
$487$	−11.3257	−	34.8571i	−0.513219	−	1.57952i	0.273281	−	0.961934i	$-0.411891\pi$
$488$	−0.860246	+	2.64756i	−0.0389415	+	0.119850i
$489$	−9.14411	−	6.64359i	−0.413511	−	0.300433i
$490$	−0.451659	−	0.328150i	−0.0204039	−	0.0148243i
$491$	−13.3120	+	40.9701i	−0.600762	+	1.84895i	−0.0771088	+	0.997023i	$0.524569\pi$
$491$	−13.3120	+	40.9701i	−0.600762	+	1.84895i	−0.523653	+	0.851932i	$0.675431\pi$
$492$	0.991477	+	3.05145i	0.0446992	+	0.137570i
$493$	33.9868	−	24.6928i	1.53069	−	1.11211i
$494$	−12.8150			−0.576574
$495$	2.66414	+	3.76101i	0.119744	+	0.169045i
$496$	1.77447			0.0796759
$497$	9.75128	−	7.08472i	0.437405	−	0.317793i
$498$	0.750942	+	2.31116i	0.0336505	+	0.103566i
$499$	−6.65029	+	20.4675i	−0.297708	+	0.916250i	0.684591	+	0.728928i	$0.259981\pi$
$499$	−6.65029	+	20.4675i	−0.297708	+	0.916250i	−0.982298	+	0.187323i	$0.940019\pi$
$500$	−4.37582	−	3.17922i	−0.195693	−	0.142179i
$501$	−9.46823	−	6.87907i	−0.423009	−	0.307334i
$502$	7.68832	−	23.6622i	0.343147	−	1.05610i
$503$	−0.386584	−	1.18978i	−0.0172369	−	0.0530498i	0.942068	−	0.335422i	$-0.108879\pi$
$503$	−0.386584	−	1.18978i	−0.0172369	−	0.0530498i	−0.959305	+	0.282372i	$0.908879\pi$
$504$	−2.01379	+	1.46310i	−0.0897014	+	0.0651719i
$505$	−4.76683			−0.212121
$506$	−18.1420	−	6.13646i	−0.806511	−	0.272799i
$507$	5.42974			0.241143
$508$	−8.83802	+	6.42119i	−0.392124	+	0.284894i
$509$	5.83597	+	17.9613i	0.258675	+	0.796120i	0.993083	+	0.117412i	$0.0374597\pi$
$509$	5.83597	+	17.9613i	0.258675	+	0.796120i	−0.734408	+	0.678708i	$0.762540\pi$
$510$	0.829234	−	2.55212i	0.0367191	−	0.113010i
$511$	−12.2765	−	8.91938i	−0.543079	−	0.394570i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−3.42325	+	10.5357i	−0.151140	+	0.465162i
$514$	−0.00467362	−	0.0143839i	−0.000206144	−	0.000634447i
$515$	4.01017	−	2.91356i	0.176709	−	0.128387i
$516$	−0.134798			−0.00593415
$517$	−23.4127	+	31.4244i	−1.02969	+	1.38204i
$518$	−10.2267			−0.449336
$519$	11.1162	−	8.07639i	0.487947	−	0.354514i
$520$	0.782958	+	2.40970i	0.0343350	+	0.105672i
$521$	3.81847	−	11.7520i	0.167290	−	0.514866i	−0.831908	−	0.554914i	$-0.812751\pi$
$521$	3.81847	−	11.7520i	0.167290	−	0.514866i	0.999198	+	0.0400480i	$0.0127511\pi$
$522$	12.5794	+	9.13943i	0.550583	+	0.400022i
$523$	34.4876	+	25.0567i	1.50804	+	1.09565i	0.967039	+	0.254628i	$0.0819530\pi$
$523$	34.4876	+	25.0567i	1.50804	+	1.09565i	0.540997	+	0.841024i	$0.318047\pi$
$524$	−0.256879	+	0.790593i	−0.0112218	+	0.0345372i
$525$	−1.03546	−	3.18681i	−0.0451911	−	0.139084i
$526$	−23.8009	+	17.2924i	−1.03777	+	0.753983i
$527$	11.9337			0.519842
$528$	2.26306	−	0.705389i	0.0984869	−	0.0306981i
$529$	10.3445			0.449760
$530$	0.714121	−	0.518839i	0.0310194	−	0.0225369i
$531$	−7.11614	−	21.9012i	−0.308814	−	0.950433i
$532$	0.872566	−	2.68548i	0.0378306	−	0.116430i
$533$	−16.4827	−	11.9754i	−0.713944	−	0.518710i
$534$	−4.85878	−	3.53011i	−0.210260	−	0.152763i
$535$	−0.345858	+	1.06444i	−0.0149527	+	0.0460198i
$536$	−1.04129	−	3.20475i	−0.0449768	−	0.138424i
$537$	−1.29129	+	0.938178i	−0.0557234	+	0.0404854i
$538$	−11.8530			−0.511020
$539$	0.0398173	−	3.31639i	0.00171505	−	0.142847i
$540$	2.19025			0.0942534
$541$	22.5180	−	16.3602i	0.968122	−	0.703382i	0.0130995	−	0.999914i	$-0.495830\pi$
$541$	22.5180	−	16.3602i	0.968122	−	0.703382i	0.955023	+	0.296532i	$0.0958302\pi$
$542$	−5.29727	−	16.3033i	−0.227537	−	0.700288i
$543$	−4.33853	+	13.3526i	−0.186184	+	0.573015i
$544$	5.44084	+	3.95300i	0.233274	+	0.169484i
$545$	0.807005	+	0.586323i	0.0345683	+	0.0251153i
$546$	−1.00235	+	3.08491i	−0.0428965	+	0.132022i
$547$	−1.99389	−	6.13656i	−0.0852525	−	0.262380i	0.899339	−	0.437253i	$-0.144049\pi$
$547$	−1.99389	−	6.13656i	−0.0852525	−	0.262380i	−0.984591	+	0.174873i	$0.944049\pi$
$548$	3.31896	−	2.41136i	0.141779	−	0.103008i
$549$	−6.92942			−0.295741
$550$	0.186677	−	15.5483i	0.00795991	−	0.662981i
$551$	−17.6384			−0.751423
$552$	−3.33889	+	2.42585i	−0.142113	+	0.103251i
$553$	−0.645022	−	1.98517i	−0.0274291	−	0.0844181i
$554$	−3.04095	+	9.35909i	−0.129198	+	0.397630i
$555$	3.30127	+	2.39851i	0.140131	+	0.101811i
$556$	−5.60099	−	4.06936i	−0.237535	−	0.172579i
$557$	2.23775	−	6.88707i	0.0948163	−	0.291815i	−0.892389	−	0.451266i	$-0.850973\pi$
$557$	2.23775	−	6.88707i	0.0948163	−	0.291815i	0.987206	+	0.159451i	$0.0509725\pi$
$558$	1.36492	+	4.20079i	0.0577817	+	0.177834i
$559$	0.692486	−	0.503120i	0.0292890	−	0.0212797i
$560$	−0.558282			−0.0235917
$561$	15.2196	−	4.74392i	0.642573	−	0.200288i
$562$	−2.17162			−0.0916044
$563$	−0.360476	+	0.261901i	−0.0151923	+	0.0110378i	−0.595355	−	0.803462i	$-0.702989\pi$
$563$	−0.360476	+	0.261901i	−0.0151923	+	0.0110378i	0.580163	+	0.814500i	$0.302989\pi$
$564$	2.60954	+	8.03135i	0.109882	+	0.338181i
$565$	−2.00826	+	6.18080i	−0.0844883	+	0.260028i
$566$	21.9979	+	15.9824i	0.924640	+	0.671790i
$567$	−3.77291	−	2.74118i	−0.158447	−	0.115119i
$568$	3.72466	−	11.4633i	0.156283	−	0.480990i
$569$	−6.10141	−	18.7782i	−0.255784	−	0.787223i	−0.993674	−	0.112302i	$-0.964178\pi$
$569$	−6.10141	−	18.7782i	−0.255784	−	0.787223i	0.737890	−	0.674921i	$-0.235822\pi$
$570$	−0.911507	+	0.662249i	−0.0381788	+	0.0277386i
$571$	6.23141			0.260777			0.130388	−	0.991463i	$-0.458378\pi$
$571$	6.23141			0.260777			0.130388	+	0.991463i	$0.458378\pi$
$572$	−8.99300	+	12.0704i	−0.376016	+	0.504687i
$573$	−9.96493			−0.416291
$574$	3.63182	−	2.63868i	0.151589	−	0.110136i
$575$	8.36588	+	25.7475i	0.348881	+	1.07375i
$576$	−0.769200	+	2.36735i	−0.0320500	+	0.0986397i
$577$	−3.40176	−	2.47153i	−0.141617	−	0.102891i	0.514721	−	0.857358i	$-0.327896\pi$
$577$	−3.40176	−	2.47153i	−0.141617	−	0.102891i	−0.656338	+	0.754467i	$0.727896\pi$
$578$	22.8377	+	16.5926i	0.949925	+	0.690161i
$579$	−2.61393	+	8.04486i	−0.108631	+	0.334333i
$580$	1.07765	+	3.31668i	0.0447472	+	0.137718i
$581$	2.75074	−	1.99853i	0.114120	−	0.0829128i
$582$	5.99699			0.248583
$583$	4.96746	+	1.68022i	0.205731	+	0.0695877i
$584$	−15.1746			−0.627928
$585$	−5.10235	+	3.70708i	−0.210956	+	0.153269i
$586$	6.04710	+	18.6111i	0.249803	+	0.768815i
$587$	−10.9277	+	33.6319i	−0.451033	+	1.38814i	0.424697	+	0.905336i	$0.360381\pi$
$587$	−10.9277	+	33.6319i	−0.451033	+	1.38814i	−0.875730	+	0.482801i	$0.839619\pi$
$588$	−0.578217	−	0.420099i	−0.0238453	−	0.0173246i
$589$	−4.05361	−	2.94512i	−0.167026	−	0.121352i
$590$	1.59603	−	4.91208i	0.0657076	−	0.202227i
$591$	1.55273	+	4.77882i	0.0638709	+	0.196574i
$592$	−8.27359	+	6.01112i	−0.340042	+	0.247055i
$593$	−22.1812			−0.910872			−0.455436	−	0.890269i	$-0.650517\pi$
$593$	−22.1812			−0.910872			−0.455436	+	0.890269i	$0.650517\pi$
$594$	7.52121	+	10.6178i	0.308599	+	0.435654i
$595$	−3.75458			−0.153923
$596$	−11.1968	+	8.13495i	−0.458638	+	0.333220i
$597$	−2.17341	−	6.68908i	−0.0889520	−	0.273766i
$598$	8.09836	−	24.9242i	0.331167	−	1.01923i
$599$	9.97681	+	7.24858i	0.407641	+	0.296169i	0.772646	−	0.634837i	$-0.218933\pi$
$599$	9.97681	+	7.24858i	0.407641	+	0.296169i	−0.365005	+	0.931006i	$0.618933\pi$
$600$	−2.71087	−	1.96956i	−0.110671	−	0.0804069i
$601$	14.9291	−	45.9469i	0.608969	−	1.87421i	0.142193	−	0.989839i	$-0.454585\pi$
$601$	14.9291	−	45.9469i	0.608969	−	1.87421i	0.466776	−	0.884375i	$-0.345415\pi$
$602$	0.0582818	+	0.179373i	0.00237539	+	0.00731069i
$603$	6.78583	−	4.93019i	0.276340	−	0.200773i
$604$	8.59164			0.349589
$605$	−5.05349	+	3.48932i	−0.205453	+	0.141861i
$606$	−6.10252			−0.247898
$607$	−8.47604	+	6.15820i	−0.344032	+	0.249954i	−0.746361	−	0.665541i	$-0.768201\pi$
$607$	−8.47604	+	6.15820i	−0.344032	+	0.249954i	0.402329	+	0.915495i	$0.368201\pi$
$608$	−0.872566	−	2.68548i	−0.0353872	−	0.108911i
$609$	−1.37962	+	4.24603i	−0.0559050	+	0.172058i
$610$	−1.25734	−	0.913508i	−0.0509081	−	0.0369869i
$611$	−43.3820	−	31.5189i	−1.75505	−	1.27512i
$612$	−5.17306	+	15.9210i	−0.209109	+	0.643570i
$613$	−1.19709	−	3.68428i	−0.0483502	−	0.148807i	0.923967	−	0.382473i	$-0.124928\pi$
$613$	−1.19709	−	3.68428i	−0.0483502	−	0.148807i	−0.972317	+	0.233667i	$0.924928\pi$
$614$	−24.2156	+	17.5936i	−0.977261	+	0.710022i
$615$	−1.79124			−0.0722297
$616$	−1.91711	−	2.70642i	−0.0772426	−	0.109045i
$617$	13.1950			0.531211			0.265606	−	0.964082i	$-0.414428\pi$
$617$	13.1950			0.531211			0.265606	+	0.964082i	$0.414428\pi$
$618$	5.13384	−	3.72995i	0.206513	−	0.150041i
$619$	0.838351	+	2.58018i	0.0336962	+	0.103706i	0.966490	−	0.256704i	$-0.0826366\pi$
$619$	0.838351	+	2.58018i	0.0336962	+	0.103706i	−0.932794	+	0.360410i	$0.882637\pi$
$620$	−0.306129	+	0.942167i	−0.0122944	+	0.0378383i
$621$	−18.3278	−	13.3159i	−0.735469	−	0.534350i
$622$	−15.7098	−	11.4138i	−0.629904	−	0.457652i
$623$	−2.59668	+	7.99176i	−0.104034	+	0.320183i
$624$	1.00235	+	3.08491i	0.0401260	+	0.123495i
$625$	−16.5217	+	12.0037i	−0.660869	+	0.480149i
$626$	−28.2243			−1.12807
$627$	−6.34049	−	2.14464i	−0.253215	−	0.0856488i
$628$	13.9150			0.555271
$629$	−55.6420	+	40.4263i	−2.21859	+	1.61190i
$630$	−0.429430	−	1.32165i	−0.0171089	−	0.0526558i
$631$	−6.71151	+	20.6559i	−0.267181	+	0.822299i	0.724002	+	0.689798i	$0.242301\pi$
$631$	−6.71151	+	20.6559i	−0.267181	+	0.822299i	−0.991183	+	0.132501i	$0.957699\pi$
$632$	−1.68869	−	1.22690i	−0.0671724	−	0.0488036i
$633$	9.30429	+	6.75996i	0.369812	+	0.268684i
$634$	0.521947	−	1.60639i	0.0207292	−	0.0637978i
$635$	−1.88466	−	5.80039i	−0.0747904	−	0.230181i
$636$	0.914221	−	0.664221i	0.0362512	−	0.0263381i
$637$	4.53840			0.179818
$638$	−12.3779	+	16.6135i	−0.490044	+	0.657735i
$639$	30.0027			1.18689
$640$	−0.451659	+	0.328150i	−0.0178534	+	0.0129713i
$641$	−11.4078	−	35.1095i	−0.450580	−	1.38674i	−0.876247	−	0.481863i	$-0.839960\pi$
$641$	−11.4078	−	35.1095i	−0.450580	−	1.38674i	0.425667	−	0.904880i	$-0.360040\pi$
$642$	−0.442769	+	1.36270i	−0.0174747	+	0.0537816i
$643$	32.0697	+	23.3000i	1.26470	+	0.918861i	0.998979	−	0.0451872i	$-0.0143884\pi$
$643$	32.0697	+	23.3000i	1.26470	+	0.918861i	0.265726	+	0.964049i	$0.414388\pi$
$644$	4.67164	+	3.39415i	0.184088	+	0.133748i
$645$	0.0232552	−	0.0715720i	0.000915671	−	0.00281815i
$646$	−5.86823	−	18.0605i	−0.230882	−	0.710583i
$647$	−8.22058	+	5.97260i	−0.323184	+	0.234807i	−0.737533	−	0.675311i	$-0.764009\pi$
$647$	−8.22058	+	5.97260i	−0.323184	+	0.234807i	0.414349	+	0.910118i	$0.364009\pi$
$648$	−4.66358			−0.183203
$649$	29.2933	−	9.13064i	1.14986	−	0.358409i
$650$	21.2775			0.834571
$651$	−1.02603	+	0.745452i	−0.0402131	+	0.0292166i
$652$	4.88690	+	15.0403i	0.191386	+	0.589025i
$653$	−1.94784	+	5.99484i	−0.0762250	+	0.234596i	−0.981908	−	0.189360i	$-0.939359\pi$
$653$	−1.94784	+	5.99484i	−0.0762250	+	0.234596i	0.905683	+	0.423956i	$0.139359\pi$
$654$	1.03313	+	0.750614i	0.0403986	+	0.0293513i
$655$	−0.375455	−	0.272784i	−0.0146702	−	0.0106586i
$656$	1.38723	−	4.26947i	0.0541624	−	0.166695i
$657$	−11.6723	−	35.9235i	−0.455379	−	1.40151i
$658$	9.55888	−	6.94493i	0.372644	−	0.270742i
$659$	28.8155			1.12249			0.561246	−	0.827649i	$-0.310322\pi$
$659$	28.8155			1.12249			0.561246	+	0.827649i	$0.310322\pi$
$660$	−0.0158876	+	1.32328i	−0.000618425	+	0.0515086i
$661$	18.1283			0.705109			0.352554	−	0.935791i	$-0.385313\pi$
$661$	18.1283			0.705109			0.352554	+	0.935791i	$0.385313\pi$
$662$	−19.9856	+	14.5204i	−0.776764	+	0.564352i
$663$	6.74103	+	20.7468i	0.261800	+	0.805738i
$664$	1.05069	−	3.23368i	0.0407746	−	0.125491i
$665$	1.27534	+	0.926591i	0.0494557	+	0.0359317i
$666$	−20.5945	−	14.9628i	−0.798020	−	0.579795i
$667$	11.1465	−	34.3054i	0.431594	−	1.32831i
$668$	5.06012	+	15.5734i	0.195782	+	0.602555i
$669$	12.9396	−	9.40114i	0.500272	−	0.363469i
$670$	1.88123			0.0726782
$671$	0.110844	−	9.23220i	0.00427909	−	0.356405i
$672$	−0.714715			−0.0275707
$673$	−22.7227	+	16.5090i	−0.875897	+	0.636376i	−0.932163	−	0.362040i	$-0.882081\pi$
$673$	−22.7227	+	16.5090i	−0.875897	+	0.636376i	0.0562660	+	0.998416i	$0.482081\pi$
$674$	7.42295	+	22.8455i	0.285921	+	0.879976i
$675$	5.68382	−	17.4930i	0.218770	−	0.673306i
$676$	−6.14616	−	4.46544i	−0.236391	−	0.171748i
$677$	3.72525	+	2.70655i	0.143173	+	0.104021i	0.657066	−	0.753833i	$-0.271797\pi$
$677$	3.72525	+	2.70655i	0.143173	+	0.104021i	−0.513893	+	0.857854i	$0.671797\pi$
$678$	−2.57099	+	7.91269i	−0.0987383	+	0.303885i
$679$	−2.59288	−	7.98008i	−0.0995058	−	0.306247i
$680$	−3.03752	+	2.20689i	−0.116484	+	0.0846304i
$681$	8.29355			0.317809
$682$	−5.61863	+	1.75131i	−0.215148	+	0.0670612i
$683$	−43.3341			−1.65813			−0.829067	−	0.559150i	$-0.811128\pi$
$683$	−43.3341			−1.65813			−0.829067	+	0.559150i	$0.811128\pi$
$684$	5.68631	−	4.13135i	0.217421	−	0.157966i
$685$	0.707750	+	2.17823i	0.0270417	+	0.0832259i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	−0.149695	−	0.108760i	−0.00571123	−	0.00414945i
$688$	0.152584	+	0.110859i	0.00581720	+	0.00422644i
$689$	−2.21741	+	6.82448i	−0.0844766	+	0.259992i
$690$	−0.712001	−	2.19131i	−0.0271054	−	0.0834219i
$691$	−18.0642	+	13.1244i	−0.687196	+	0.499277i	−0.875737	−	0.482788i	$-0.839624\pi$
$691$	−18.0642	+	13.1244i	−0.687196	+	0.499277i	0.188541	+	0.982065i	$0.439624\pi$
$692$	−19.2250			−0.730824
$693$	4.93240	−	6.62025i	0.187367	−	0.251483i
$694$	3.44942			0.130938
$695$	3.12693	−	2.27185i	0.118611	−	0.0861761i
$696$	1.37962	+	4.24603i	0.0522943	+	0.160945i
$697$	9.32949	−	28.7132i	0.353380	−	1.08759i
$698$	4.11950	+	2.99300i	0.155926	+	0.113287i
$699$	16.2934	+	11.8378i	0.616273	+	0.447748i
$700$	−1.44877	+	4.45886i	−0.0547584	+	0.168529i
$701$	−11.3779	−	35.0177i	−0.429739	−	1.32260i	−0.898383	−	0.439213i	$-0.855257\pi$
$701$	−11.3779	−	35.0177i	−0.429739	−	1.32260i	0.468644	−	0.883387i	$-0.344743\pi$
$702$	−14.4046	+	10.4655i	−0.543666	+	0.394997i
$703$	28.8770			1.08912
$704$	−3.14177	−	1.06269i	−0.118410	−	0.0400516i
$705$	−4.71450			−0.177558
$706$	0.811311	−	0.589452i	0.0305341	−	0.0221843i
$707$	2.63851	+	8.12050i	0.0992314	+	0.305403i
$708$	2.04325	−	6.28847i	0.0767899	−	0.236335i
$709$	−16.7642	−	12.1799i	−0.629591	−	0.457425i	0.226667	−	0.973972i	$-0.427217\pi$
$709$	−16.7642	−	12.1799i	−0.629591	−	0.457425i	−0.856259	+	0.516547i	$0.827217\pi$
$710$	5.44396	+	3.95527i	0.204308	+	0.148439i
$711$	1.60558	−	4.94146i	0.0602138	−	0.185319i
$712$	2.59668	+	7.99176i	0.0973147	+	0.299504i
$713$	8.28968	−	6.02280i	0.310451	−	0.225556i
$714$	−4.80664			−0.179884
$715$	−4.85739	−	6.85726i	−0.181656	−	0.256447i
$716$	2.23323			0.0834598
$717$	−2.79359	+	2.02966i	−0.104328	+	0.0757990i
$718$	1.53401	+	4.72119i	0.0572487	+	0.176193i
$719$	14.7970	−	45.5404i	0.551835	−	1.69837i	−0.152325	−	0.988330i	$-0.548676\pi$
$719$	14.7970	−	45.5404i	0.551835	−	1.69837i	0.704160	−	0.710042i	$-0.251324\pi$
$720$	−1.12426	−	0.816825i	−0.0418988	−	0.0304413i
$721$	−7.18305	−	5.21879i	−0.267511	−	0.194358i
$722$	3.40747	−	10.4871i	0.126813	−	0.390290i
$723$	4.12540	+	12.6967i	0.153425	+	0.472194i
$724$	15.8922	−	11.5464i	0.590630	−	0.429118i
$725$	29.2861			1.08766
$726$	−6.46950	+	4.46705i	−0.240106	+	0.165788i
$727$	8.09538			0.300241			0.150121	−	0.988668i	$-0.452034\pi$
$727$	8.09538			0.300241			0.150121	+	0.988668i	$0.452034\pi$
$728$	3.67164	−	2.66760i	0.136080	−	0.0988680i
$729$	−0.987797	−	3.04013i	−0.0365851	−	0.112597i
$730$	2.61789	−	8.05705i	0.0968926	−	0.298205i
$731$	1.02616	+	0.745552i	0.0379540	+	0.0275752i
$732$	−1.60965	−	1.16948i	−0.0594943	−	0.0432251i
$733$	−2.04475	+	6.29309i	−0.0755246	+	0.232441i	−0.981691	−	0.190481i	$-0.938995\pi$
$733$	−2.04475	+	6.29309i	−0.0755246	+	0.232441i	0.906166	+	0.422921i	$0.138995\pi$
$734$	8.40714	+	25.8745i	0.310313	+	0.955045i
$735$	0.322808	−	0.234534i	0.0119069	−	0.00865090i
$736$	5.77447			0.212850
$737$	6.46004	+	9.11975i	0.237959	+	0.335930i
$738$	11.1744			0.411335
$739$	−6.81191	+	4.94914i	−0.250580	+	0.182057i	−0.705984	−	0.708228i	$-0.749495\pi$
$739$	−6.81191	+	4.94914i	−0.250580	+	0.182057i	0.455404	+	0.890285i	$0.349495\pi$
$740$	−1.76430	−	5.42995i	−0.0648569	−	0.199609i
$741$	2.83031	−	8.71080i	0.103974	−	0.319999i
$742$	−1.27914	−	0.929350i	−0.0469587	−	0.0341175i
$743$	18.5732	+	13.4942i	0.681385	+	0.495055i	0.873817	−	0.486255i	$-0.161637\pi$
$743$	18.5732	+	13.4942i	0.681385	+	0.495055i	−0.192432	+	0.981310i	$0.561637\pi$
$744$	−0.391907	+	1.20617i	−0.0143680	+	0.0442202i
$745$	−2.38766	−	7.34845i	−0.0874770	−	0.269226i
$746$	22.4291	−	16.2957i	0.821186	−	0.596627i
$747$	8.46346			0.309662
$748$	−21.1292	−	7.14684i	−0.772559	−	0.261314i
$749$	2.00476			0.0732523
$750$	3.12747	−	2.27224i	0.114199	−	0.0829704i
$751$	6.41238	+	19.7353i	0.233991	+	0.720151i	0.997254	+	0.0740623i	$0.0235964\pi$
$751$	6.41238	+	19.7353i	0.233991	+	0.720151i	−0.763262	+	0.646089i	$0.776404\pi$
$752$	3.65117	−	11.2371i	0.133144	−	0.409776i
$753$	14.3860	+	10.4520i	0.524255	+	0.380893i
$754$	−22.9353	−	16.6635i	−0.835254	−	0.606848i
$755$	−1.48222	+	4.56180i	−0.0539434	+	0.166021i
$756$	−1.21234	−	3.73119i	−0.0440922	−	0.135702i
$757$	16.8579	−	12.2480i	0.612711	−	0.445160i	−0.237657	−	0.971349i	$-0.576379\pi$
$757$	16.8579	−	12.2480i	0.612711	−	0.445160i	0.850368	+	0.526189i	$0.176379\pi$
$758$	−7.93559			−0.288234
$759$	8.17799	−	10.9765i	0.296842	−	0.398421i
$760$	1.57641			0.0571825
$761$	−8.33326	+	6.05447i	−0.302080	+	0.219474i	−0.728491	−	0.685056i	$-0.759778\pi$
$761$	−8.33326	+	6.05447i	−0.302080	+	0.219474i	0.426410	+	0.904530i	$0.359778\pi$
$762$	−2.41275	−	7.42568i	−0.0874047	−	0.269004i
$763$	0.552138	−	1.69931i	0.0199887	−	0.0615190i
$764$	11.2797	+	8.19521i	0.408086	+	0.296492i
$765$	−7.56095	−	5.49335i	−0.273367	−	0.198613i
$766$	0.979156	−	3.01353i	0.0353784	−	0.108883i
$767$	12.9745	+	39.9314i	0.468482	+	1.44184i
$768$	−0.578217	+	0.420099i	−0.0208646	+	0.0151590i
$769$	14.0069			0.505100			0.252550	−	0.967584i	$-0.418731\pi$
$769$	14.0069			0.505100			0.252550	+	0.967584i	$0.418731\pi$
$770$	1.76773	−	0.550997i	0.0637045	−	0.0198565i
$771$	0.0108095			0.000389293
$772$	9.57496	−	6.95662i	0.344610	−	0.250374i
$773$	3.88519	+	11.9574i	0.139741	+	0.430077i	0.996297	−	0.0859758i	$-0.0274008\pi$
$773$	3.88519	+	11.9574i	0.139741	+	0.430077i	−0.856557	+	0.516053i	$0.827401\pi$
$774$	−0.145074	+	0.446492i	−0.00521458	+	0.0160488i
$775$	6.73043	+	4.88995i	0.241764	+	0.175652i
$776$	−6.78826	−	4.93196i	−0.243684	−	0.177047i
$777$	2.25866	−	6.95145i	0.0810291	−	0.249382i
$778$	7.18414	+	22.1105i	0.257564	+	0.792700i
$779$	−10.2551	+	7.45079i	−0.367428	+	0.266952i
$780$	−1.81088			−0.0648398
$781$	−0.479928	+	39.9732i	−0.0171732	+	1.43035i
$782$	38.8347			1.38873
$783$	−19.8263	+	14.4047i	−0.708535	+	0.514781i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−2.40060	+	7.38830i	−0.0856812	+	0.263700i
$786$	−0.480659	−	0.349219i	−0.0171445	−	0.0124562i
$787$	−18.8065	−	13.6637i	−0.670380	−	0.487060i	0.199772	−	0.979842i	$-0.435980\pi$
$787$	−18.8065	−	13.6637i	−0.670380	−	0.487060i	−0.870152	+	0.492783i	$0.835980\pi$
$788$	2.17252	−	6.68632i	0.0773928	−	0.238190i
$789$	−6.49757	−	19.9975i	−0.231320	−	0.711928i
$790$	0.942764	−	0.684958i	0.0335420	−	0.0243697i
$791$	11.6409			0.413901
$792$	0.0991126	−	8.25509i	0.00352181	−	0.293332i
$793$	12.6341			0.448649
$794$	−19.9182	+	14.4715i	−0.706872	+	0.513573i
$795$	0.194953	+	0.600003i	0.00691426	+	0.0212799i
$796$	−3.04095	+	9.35909i	−0.107784	+	0.331724i
$797$	10.9994	+	7.99156i	0.389620	+	0.283075i	0.765300	−	0.643674i	$-0.222591\pi$
$797$	10.9994	+	7.99156i	0.389620	+	0.283075i	−0.375680	+	0.926750i	$0.622591\pi$
$798$	1.63270	+	1.18623i	0.0577970	+	0.0419920i
$799$	24.5550	−	75.5725i	0.868694	−	2.67356i
$800$	1.44877	+	4.45886i	0.0512218	+	0.157644i
$801$	−16.9220	+	12.2945i	−0.597908	+	0.434406i
$802$	−18.5952			−0.656620
$803$	48.0483	−	14.9766i	1.69559	−	0.528511i
$804$	2.40836			0.0849363
$805$	−2.60809	+	1.89489i	−0.0919232	+	0.0667861i
$806$	−2.48859	−	7.65909i	−0.0876568	−	0.269780i
$807$	2.61785	−	8.05690i	0.0921526	−	0.283616i
$808$	6.90771	+	5.01875i	0.243012	+	0.176559i
$809$	−11.9024	−	8.64763i	−0.418468	−	0.304035i	0.358553	−	0.933509i	$-0.383270\pi$
$809$	−11.9024	−	8.64763i	−0.418468	−	0.304035i	−0.777021	+	0.629475i	$0.783270\pi$
$810$	0.804553	−	2.47616i	0.0282691	−	0.0870034i
$811$	0.555728	+	1.71036i	0.0195143	+	0.0600587i	0.960339	−	0.278834i	$-0.0899478\pi$
$811$	0.555728	+	1.71036i	0.0195143	+	0.0600587i	−0.940825	+	0.338892i	$0.889948\pi$
$812$	5.05361	−	3.67166i	0.177347	−	0.128850i
$813$	12.2519			0.429692
$814$	20.2646	−	27.1991i	0.710274	−	0.953327i
$815$	−8.82886			−0.309261
$816$	−3.88865	+	2.82527i	−0.136130	+	0.0989043i
$817$	−0.164569	−	0.506492i	−0.00575755	−	0.0177199i
$818$	−2.70880	+	8.33682i	−0.0947109	+	0.291490i
$819$	9.13939	+	6.64015i	0.319356	+	0.232026i
$820$	2.02758	+	1.47312i	0.0708062	+	0.0514437i
$821$	−2.30160	+	7.08359i	−0.0803263	+	0.247219i	−0.983153	−	0.182786i	$-0.941488\pi$
$821$	−2.30160	+	7.08359i	−0.0803263	+	0.247219i	0.902826	+	0.430005i	$0.141488\pi$
$822$	0.906065	+	2.78858i	0.0316027	+	0.0972630i
$823$	18.4185	−	13.3818i	0.642030	−	0.466462i	−0.218517	−	0.975833i	$-0.570122\pi$
$823$	18.4185	−	13.3818i	0.642030	−	0.466462i	0.860547	+	0.509371i	$0.170122\pi$
$824$	−8.87874			−0.309306
$825$	10.5275	+	3.56087i	0.366520	+	0.123974i
$826$	−9.25136			−0.321896
$827$	−10.8072	+	7.85190i	−0.375804	+	0.273037i	−0.759613	−	0.650375i	$-0.774612\pi$
$827$	−10.8072	+	7.85190i	−0.375804	+	0.273037i	0.383810	+	0.923412i	$0.374612\pi$
$828$	4.44172	+	13.6702i	0.154360	+	0.475072i
$829$	−4.10956	+	12.6479i	−0.142731	+	0.439281i	−0.996712	−	0.0810229i	$-0.974181\pi$
$829$	−4.10956	+	12.6479i	−0.142731	+	0.439281i	0.853981	+	0.520304i	$0.174181\pi$
$830$	1.53569	+	1.11574i	0.0533044	+	0.0387279i
$831$	−5.69007	−	4.13408i	−0.197386	−	0.143410i
$832$	1.40244	−	4.31627i	0.0486209	−	0.149640i
$833$	2.07822	+	6.39609i	0.0720059	+	0.221611i
$834$	4.00311	−	2.90843i	0.138616	−	0.100711i
$835$	−9.14180			−0.316365
$836$	5.41331	+	7.64207i	0.187223	+	0.264306i
$837$	−6.96159			−0.240628
$838$	7.07258	−	5.13853i	0.244318	−	0.177508i
$839$	−8.27914	−	25.4806i	−0.285828	−	0.879687i	−0.986149	−	0.165860i	$-0.946960\pi$
$839$	−8.27914	−	25.4806i	−0.285828	−	0.879687i	0.700322	−	0.713827i	$-0.253040\pi$
$840$	0.123302	−	0.379483i	0.00425431	−	0.0130934i
$841$	−8.10639	−	5.88964i	−0.279531	−	0.203091i
$842$	3.76832	+	2.73785i	0.129865	+	0.0943524i
$843$	0.479623	−	1.47613i	0.0165191	−	0.0508405i
$844$	−4.97250	−	15.3038i	−0.171161	−	0.526778i
$845$	3.43129	−	2.49298i	0.118040	−	0.0857610i
$846$	29.4107			1.01116
$847$	8.74139	+	6.67743i	0.300358	+	0.229439i
$848$	−1.58111			−0.0542954
$849$	−15.7222	+	11.4229i	−0.539585	+	0.392032i
$850$	9.74335	+	29.9869i	0.334194	+	1.02854i
$851$	−18.2486	+	56.1636i	−0.625556	+	1.92526i
$852$	6.96938	+	5.06355i	0.238767	+	0.173475i
$853$	42.0513	+	30.5521i	1.43981	+	1.04608i	0.988082	+	0.153926i	$0.0491917\pi$
$853$	42.0513	+	30.5521i	1.43981	+	1.04608i	0.451726	+	0.892157i	$0.350808\pi$
$854$	−0.860246	+	2.64756i	−0.0294370	+	0.0905978i
$855$	1.21258	+	3.73192i	0.0414692	+	0.127629i
$856$	1.62188	−	1.17837i	0.0554348	−	0.0402758i
$857$	−24.2963			−0.829945			−0.414972	−	0.909834i	$-0.636209\pi$
$857$	−24.2963			−0.829945			−0.414972	+	0.909834i	$0.636209\pi$
$858$	−6.21846	−	8.77870i	−0.212295	−	0.299700i
$859$	−52.9269			−1.80584			−0.902921	−	0.429807i	$-0.858582\pi$
$859$	−52.9269			−1.80584			−0.902921	+	0.429807i	$0.858582\pi$
$860$	−0.0851847	+	0.0618903i	−0.00290477	+	0.00211044i
$861$	0.991477	+	3.05145i	0.0337894	+	0.103993i
$862$	7.86880	−	24.2177i	0.268012	−	0.824857i
$863$	23.3221	+	16.9445i	0.793893	+	0.576797i	0.909116	−	0.416543i	$-0.136758\pi$
$863$	23.3221	+	16.9445i	0.793893	+	0.576797i	−0.115223	+	0.993340i	$0.536758\pi$
$864$	−3.17394	−	2.30600i	−0.107980	−	0.0784517i
$865$	3.31666	−	10.2076i	0.112770	−	0.347070i
$866$	−6.20532	−	19.0980i	−0.210865	−	0.648976i
$867$	−16.3225	+	11.8590i	−0.554340	+	0.402752i
$868$	1.77447			0.0602293
$869$	6.55791	+	2.21818i	0.222462	+	0.0752468i
$870$	−2.49247			−0.0845027
$871$	−12.3723	+	8.98897i	−0.419218	+	0.304580i
$872$	−0.552138	−	1.69931i	−0.0186977	−	0.0575457i
$873$	6.45416	−	19.8639i	0.218440	−	0.672290i
$874$	−13.1912	−	9.58400i	−0.446200	−	0.324184i
$875$	−4.37582	−	3.17922i	−0.147930	−	0.107477i
$876$	3.35144	−	10.3147i	0.113235	−	0.348501i
$877$	−13.8225	−	42.5414i	−0.466754	−	1.43652i	−0.856764	−	0.515709i	$-0.827529\pi$
$877$	−13.8225	−	42.5414i	−0.466754	−	1.43652i	0.390010	−	0.920811i	$-0.372471\pi$
$878$	4.75283	−	3.45313i	0.160400	−	0.116538i
$879$	−13.9861			−0.471740
$880$	1.10626	−	1.48481i	0.0372919	−	0.0500530i
$881$	12.2826			0.413810			0.206905	−	0.978361i	$-0.433661\pi$
$881$	12.2826			0.413810			0.206905	+	0.978361i	$0.433661\pi$
$882$	−2.01379	+	1.46310i	−0.0678079	+	0.0492653i
$883$	15.9180	+	48.9907i	0.535685	+	1.64867i	0.742165	+	0.670217i	$0.233799\pi$
$883$	15.9180	+	48.9907i	0.535685	+	1.64867i	−0.206480	+	0.978451i	$0.566201\pi$
$884$	9.43178	−	29.0280i	0.317225	−	0.976318i
$885$	2.98641	+	2.16976i	0.100387	+	0.0729355i
$886$	10.3427	+	7.51444i	0.347471	+	0.252453i
$887$	−3.47023	+	10.6803i	−0.116519	+	0.358609i	−0.992261	−	0.124171i	$-0.960373\pi$
$887$	−3.47023	+	10.6803i	−0.116519	+	0.358609i	0.875742	+	0.482780i	$0.160373\pi$
$888$	−2.25866	−	6.95145i	−0.0757958	−	0.233276i
$889$	−8.83802	+	6.42119i	−0.296418	+	0.215360i
$890$	−4.69126			−0.157251
$891$	14.7666	−	4.60272i	0.494701	−	0.154197i
$892$	−22.3784			−0.749284
$893$	−26.9912	+	19.6103i	−0.903228	+	0.656233i
$894$	−3.05669	−	9.40752i	−0.102231	−	0.314635i
$895$	−0.385274	+	1.18575i	−0.0128783	+	0.0396353i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	15.1532	+	11.0095i	0.505952	+	0.367595i
$898$	−10.1300	+	31.1770i	−0.338043	+	1.04039i
$899$	−3.42527	−	10.5419i	−0.114239	−	0.351592i
$900$	−9.44130	+	6.85951i	−0.314710	+	0.228650i
$901$	−10.6333			−0.354248
$902$	−0.178747	+	14.8879i	−0.00595163	+	0.495712i
$903$	−0.134798			−0.00448580
$904$	9.41765	−	6.84232i	0.313226	−	0.227572i
$905$	3.38893	+	10.4301i	0.112652	+	0.346707i
$906$	−1.89754	+	5.84003i	−0.0630416	+	0.194022i
$907$	−11.0319	−	8.01514i	−0.366308	−	0.266138i	0.389370	−	0.921081i	$-0.372693\pi$
$907$	−11.0319	−	8.01514i	−0.366308	−	0.266138i	−0.755678	+	0.654943i	$0.772693\pi$
$908$	−9.38783	−	6.82066i	−0.311546	−	0.226351i
$909$	−6.56773	+	20.2134i	−0.217838	+	0.670436i
$910$	0.782958	+	2.40970i	0.0259548	+	0.0798807i
$911$	−2.03121	+	1.47576i	−0.0672970	+	0.0488941i	−0.620925	−	0.783870i	$-0.713243\pi$
$911$	−2.03121	+	1.47576i	−0.0672970	+	0.0488941i	0.553628	+	0.832764i	$0.313243\pi$
$912$	2.01813			0.0668270
$913$	−0.135383	+	11.2760i	−0.00448052	+	0.373182i
$914$	1.58117			0.0523004
$915$	0.898637	−	0.652898i	0.0297080	−	0.0215841i
$916$	0.0800018	+	0.246220i	0.00264333	+	0.00813535i
$917$	−0.256879	+	0.790593i	−0.00848290	+	0.0261077i
$918$	−21.3455	−	15.5084i	−0.704507	−	0.511854i
$919$	−20.3875	−	14.8124i	−0.672523	−	0.488617i	0.198346	−	0.980132i	$-0.436443\pi$
$919$	−20.3875	−	14.8124i	−0.672523	−	0.488617i	−0.870869	+	0.491516i	$0.836443\pi$
$920$	−0.996203	+	3.06600i	−0.0328438	+	0.101083i
$921$	−6.61077	−	20.3459i	−0.217832	−	0.670419i
$922$	10.9391	−	7.94771i	0.360260	−	0.261744i
$923$	−54.7024			−1.80055
$924$	2.26306	−	0.705389i	0.0744491	−	0.0232056i
$925$	−47.9462			−1.57646
$926$	−25.6429	+	18.6307i	−0.842678	+	0.612241i
$927$	−6.82953	−	21.0191i	−0.224311	−	0.690358i
$928$	1.93031	−	5.94087i	0.0633654	−	0.195019i
$929$	−25.7393	−	18.7007i	−0.844479	−	0.613550i	0.0791392	−	0.996864i	$-0.474783\pi$
$929$	−25.7393	−	18.7007i	−0.844479	−	0.613550i	−0.923618	+	0.383314i	$0.874783\pi$
$930$	−0.572812	−	0.416172i	−0.0187832	−	0.0136468i
$931$	0.872566	−	2.68548i	0.0285972	−	0.0880132i
$932$	−8.70769	−	26.7995i	−0.285230	−	0.877848i
$933$	11.2280	−	8.15762i	0.367588	−	0.267069i
$934$	16.4154			0.537128
$935$	7.43984	−	9.98573i	0.243309	−	0.326568i
$936$	11.2969			0.369251
$937$	−43.7465	+	31.7837i	−1.42914	+	1.03833i	−0.438960	+	0.898507i	$0.644653\pi$
$937$	−43.7465	+	31.7837i	−1.42914	+	1.03833i	−0.990177	+	0.139822i	$0.955347\pi$
$938$	−1.04129	−	3.20475i	−0.0339993	−	0.104639i
$939$	6.23359	−	19.1850i	0.203426	−	0.626080i
$940$	5.33655	+	3.87723i	0.174059	+	0.126461i
$941$	−35.8037	−	26.0129i	−1.16717	−	0.847997i	−0.176501	−	0.984300i	$-0.556478\pi$
$941$	−35.8037	−	26.0129i	−1.16717	−	0.847997i	−0.990667	+	0.136303i	$0.956478\pi$
$942$	−3.07326	+	9.45853i	−0.100132	+	0.308176i
$943$	−8.01054	−	24.6539i	−0.260859	−	0.802841i
$944$	−7.48451	+	5.43781i	−0.243600	+	0.176986i
$945$	2.19025			0.0712489
$946$	−0.592549	−	0.200427i	−0.0192654	−	0.00651645i
$947$	9.32918			0.303158			0.151579	−	0.988445i	$-0.451564\pi$
$947$	9.32918			0.303158			0.151579	+	0.988445i	$0.451564\pi$
$948$	1.20693	−	0.876887i	0.0391993	−	0.0284800i
$949$	21.2815	+	65.4976i	0.690825	+	2.12614i
$950$	4.09087	−	12.5904i	0.132725	−	0.408487i
$951$	0.976640	+	0.709571i	0.0316697	+	0.0230094i
$952$	5.44084	+	3.95300i	0.176339	+	0.128118i
$953$	4.79596	−	14.7604i	0.155356	−	0.478138i	−0.842840	−	0.538164i	$-0.819118\pi$
$953$	4.79596	−	14.7604i	0.155356	−	0.478138i	0.998197	+	0.0600257i	$0.0191183\pi$
$954$	−1.21619	−	3.74303i	−0.0393755	−	0.121185i
$955$	−6.29727	+	4.57523i	−0.203775	+	0.148051i
$956$	4.83138			0.156258
$957$	−8.55902	−	12.0829i	−0.276674	−	0.390585i
$958$	−11.2969			−0.364986
$959$	3.31896	−	2.41136i	0.107175	−	0.0778670i
$960$	−0.123302	−	0.379483i	−0.00397954	−	0.0122478i
$961$	−8.60651	+	26.4881i	−0.277629	+	0.854456i
$962$	37.5489	+	27.2808i	1.21062	+	0.879570i
$963$	4.03716	+	2.93317i	0.130096	+	0.0945201i
$964$	5.77209	−	17.7647i	0.185906	−	0.572161i
$965$	2.04181	+	6.28404i	0.0657282	+	0.202291i
$966$	−3.33889	+	2.42585i	−0.107427	+	0.0780504i
$967$	−14.3635			−0.461897			−0.230949	−	0.972966i	$-0.574183\pi$
$967$	−14.3635			−0.461897			−0.230949	+	0.972966i	$0.574183\pi$
$968$	10.9968	+	0.264099i	0.353451	+	0.00848847i
$969$	13.5724			0.436009
$970$	3.78976	−	2.75342i	0.121682	−	0.0884071i
$971$	−8.75838	−	26.9555i	−0.281070	−	0.865044i	−0.987549	−	0.157310i	$-0.949718\pi$
$971$	−8.75838	−	26.9555i	−0.281070	−	0.865044i	0.706479	−	0.707734i	$-0.250282\pi$
$972$	4.66700	−	14.3636i	0.149694	−	0.460711i
$973$	−5.60099	−	4.06936i	−0.179559	−	0.130458i
$974$	−29.6512	−	21.5429i	−0.950086	−	0.690278i
$975$	−4.69932	+	14.4630i	−0.150499	+	0.463188i
$976$	0.860246	+	2.64756i	0.0275358	+	0.0847465i
$977$	−39.7816	+	28.9030i	−1.27273	+	0.924690i	−0.999308	−	0.0372054i	$-0.988154\pi$
$977$	−39.7816	+	28.9030i	−1.27273	+	0.924690i	−0.273419	+	0.961895i	$0.588154\pi$
$978$	−11.3027			−0.361422
$979$	−16.1095	−	22.7421i	−0.514863	−	0.726841i
$980$	−0.558282			−0.0178337
$981$	3.59815	−	2.61421i	0.114880	−	0.0834653i
$982$	13.3120	+	40.9701i	0.424803	+	1.30741i
$983$	−8.24195	+	25.3661i	−0.262877	+	0.809053i	0.729297	+	0.684197i	$0.239847\pi$
$983$	−8.24195	+	25.3661i	−0.262877	+	0.809053i	−0.992175	+	0.124857i	$0.960153\pi$
$984$	2.59572	+	1.88590i	0.0827485	+	0.0601203i
$985$	3.17535	+	2.30703i	0.101175	+	0.0735081i
$986$	12.9818	−	39.9539i	0.413425	−	1.27239i
$987$	2.60954	+	8.03135i	0.0830627	+	0.255641i
$988$	−10.3676	+	7.53247i	−0.329836	+	0.239640i
$989$	1.08909			0.0346309
$990$	4.36600	+	1.47678i	0.138761	+	0.0469352i
$991$	36.6057			1.16282			0.581409	−	0.813611i	$-0.302502\pi$
$991$	36.6057			1.16282			0.581409	+	0.813611i	$0.302502\pi$
$992$	1.43557	−	1.04301i	0.0455795	−	0.0331155i
$993$	−5.45602	−	16.7919i	−0.173142	−	0.532875i
$994$	3.72466	−	11.4633i	0.118139	−	0.363594i
$995$	−4.44466	−	3.22923i	−0.140905	−	0.102374i
$996$	1.96599	+	1.42838i	0.0622948	+	0.0452598i
$997$	−2.44954	+	7.53891i	−0.0775777	+	0.238760i	−0.982323	−	0.187193i	$-0.940061\pi$
$997$	−2.44954	+	7.53891i	−0.0775777	+	0.238760i	0.904745	+	0.425953i	$0.140061\pi$
$998$	6.65029	+	20.4675i	0.210511	+	0.647887i
$999$	32.4590	−	23.5828i	1.02696	−	0.746127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.f.e.113.2	yes	8
11.2	odd	10		1694.2.a.z.1.3		4
11.4	even	5	inner	154.2.f.e.15.2	✓	8
11.9	even	5		1694.2.a.x.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.f.e.15.2	✓	8	11.4	even	5	inner
154.2.f.e.113.2	yes	8	1.1	even	1	trivial
1694.2.a.x.1.3		4	11.9	even	5
1694.2.a.z.1.3		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.220859 + 0.679734i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.451659 + 0.328150i) q^{5} +(0.578217 + 0.420099i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.01379 - 1.46310i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.220859 + 0.679734i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.451659 + 0.328150i) q^{5} +(0.578217 + 0.420099i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.01379 - 1.46310i) q^{9} +0.558282 q^{10} +(1.91711 + 2.70642i) q^{11} +0.714715 q^{12} +(-3.67164 + 2.66760i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.123302 + 0.379483i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.44084 - 3.95300i) q^{17} +(0.769200 - 2.36735i) q^{18} +(0.872566 + 2.68548i) q^{19} +(0.451659 - 0.328150i) q^{20} +0.714715 q^{21} +(3.14177 + 1.06269i) q^{22} -5.77447 q^{23} +(0.578217 - 0.420099i) q^{24} +(-1.44877 - 4.45886i) q^{25} +(-1.40244 + 4.31627i) q^{26} +(3.17394 + 2.30600i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-1.93031 + 5.94087i) q^{29} +(0.123302 + 0.379483i) q^{30} +(-1.43557 + 1.04301i) q^{31} -1.00000 q^{32} +(-1.41623 + 1.90086i) q^{33} -6.72525 q^{34} +(0.451659 - 0.328150i) q^{35} +(-0.769200 - 2.36735i) q^{36} +(3.16023 - 9.72619i) q^{37} +(2.28441 + 1.65972i) q^{38} +(-2.62418 - 1.90658i) q^{39} +(0.172519 - 0.530958i) q^{40} +(1.38723 + 4.26947i) q^{41} +(0.578217 - 0.420099i) q^{42} -0.188604 q^{43} +(3.16637 - 0.986951i) q^{44} +1.38967 q^{45} +(-4.67164 + 3.39415i) q^{46} +(3.65117 + 11.2371i) q^{47} +(0.220859 - 0.679734i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.79293 - 2.75573i) q^{50} +(1.48533 - 4.57138i) q^{51} +(1.40244 + 4.31627i) q^{52} +(1.27914 - 0.929350i) q^{53} +3.92320 q^{54} +(-0.0222293 + 1.85148i) q^{55} -1.00000 q^{56} +(-1.63270 + 1.18623i) q^{57} +(1.93031 + 5.94087i) q^{58} +(2.85883 - 8.79857i) q^{59} +(0.322808 + 0.234534i) q^{60} +(-2.25215 - 1.63629i) q^{61} +(-0.548341 + 1.68762i) q^{62} +(-0.769200 - 2.36735i) q^{63} +(-0.809017 + 0.587785i) q^{64} -2.53371 q^{65} +(-0.0284581 + 2.37027i) q^{66} +3.36968 q^{67} +(-5.44084 + 3.95300i) q^{68} +(-1.27534 - 3.92510i) q^{69} +(0.172519 - 0.530958i) q^{70} +(9.75128 + 7.08472i) q^{71} +(-2.01379 - 1.46310i) q^{72} +(4.68920 - 14.4319i) q^{73} +(-3.16023 - 9.72619i) q^{74} +(2.71087 - 1.96956i) q^{75} +2.82368 q^{76} +(3.16637 - 0.986951i) q^{77} -3.24366 q^{78} +(1.68869 - 1.22690i) q^{79} +(-0.172519 - 0.530958i) q^{80} +(1.44112 - 4.43532i) q^{81} +(3.63182 + 2.63868i) q^{82} +(2.75074 + 1.99853i) q^{83} +(0.220859 - 0.679734i) q^{84} +(-1.16023 - 3.57082i) q^{85} +(-0.152584 + 0.110859i) q^{86} -4.46454 q^{87} +(1.98154 - 2.65961i) q^{88} -8.40304 q^{89} +(1.12426 - 0.816825i) q^{90} +(1.40244 + 4.31627i) q^{91} +(-1.78441 + 5.49184i) q^{92} +(-1.02603 - 0.745452i) q^{93} +(9.55888 + 6.94493i) q^{94} +(-0.487138 + 1.49926i) q^{95} +(-0.220859 - 0.679734i) q^{96} +(6.78826 - 4.93196i) q^{97} -1.00000 q^{98} +(7.82043 + 2.64522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 5 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} + 10 q^{10} - 5 q^{11} - 6 q^{12} + 3 q^{13} + 2 q^{14} + 30 q^{15} - 2 q^{16} - 7 q^{17} + 2 q^{18} - 14 q^{19} + 5 q^{20} - 6 q^{21} - 20 q^{23} - 4 q^{24} - 25 q^{25} + 17 q^{26} + 32 q^{27} - 2 q^{28} - 23 q^{29} - 30 q^{30} + 3 q^{31} - 8 q^{32} + 40 q^{33} + 2 q^{34} + 5 q^{35} - 2 q^{36} + 6 q^{37} - q^{38} - 21 q^{39} - 2 q^{41} - 4 q^{42} - 16 q^{43} + 15 q^{44} - 40 q^{45} - 5 q^{46} + 34 q^{47} - q^{48} - 2 q^{49} - 10 q^{50} + 4 q^{51} - 17 q^{52} + 13 q^{53} + 48 q^{54} - 25 q^{55} - 8 q^{56} - 12 q^{57} + 23 q^{58} - 3 q^{59} - 25 q^{60} - 16 q^{61} - 3 q^{62} - 2 q^{63} - 2 q^{64} + 10 q^{65} + 15 q^{66} + 18 q^{67} - 7 q^{68} - 15 q^{69} + 45 q^{71} + 7 q^{72} + q^{73} - 6 q^{74} + 40 q^{75} + 26 q^{76} + 15 q^{77} - 4 q^{78} - 21 q^{79} + 57 q^{81} - 3 q^{82} + 12 q^{83} - q^{84} + 10 q^{85} - 14 q^{86} - 4 q^{87} + 10 q^{88} + 12 q^{89} - 40 q^{90} - 17 q^{91} + 5 q^{92} - 31 q^{93} + 31 q^{94} - 30 q^{95} + q^{96} + 5 q^{97} - 8 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 5 * q^5 - 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 + 10 * q^10 - 5 * q^11 - 6 * q^12 + 3 * q^13 + 2 * q^14 + 30 * q^15 - 2 * q^16 - 7 * q^17 + 2 * q^18 - 14 * q^19 + 5 * q^20 - 6 * q^21 - 20 * q^23 - 4 * q^24 - 25 * q^25 + 17 * q^26 + 32 * q^27 - 2 * q^28 - 23 * q^29 - 30 * q^30 + 3 * q^31 - 8 * q^32 + 40 * q^33 + 2 * q^34 + 5 * q^35 - 2 * q^36 + 6 * q^37 - q^38 - 21 * q^39 - 2 * q^41 - 4 * q^42 - 16 * q^43 + 15 * q^44 - 40 * q^45 - 5 * q^46 + 34 * q^47 - q^48 - 2 * q^49 - 10 * q^50 + 4 * q^51 - 17 * q^52 + 13 * q^53 + 48 * q^54 - 25 * q^55 - 8 * q^56 - 12 * q^57 + 23 * q^58 - 3 * q^59 - 25 * q^60 - 16 * q^61 - 3 * q^62 - 2 * q^63 - 2 * q^64 + 10 * q^65 + 15 * q^66 + 18 * q^67 - 7 * q^68 - 15 * q^69 + 45 * q^71 + 7 * q^72 + q^73 - 6 * q^74 + 40 * q^75 + 26 * q^76 + 15 * q^77 - 4 * q^78 - 21 * q^79 + 57 * q^81 - 3 * q^82 + 12 * q^83 - q^84 + 10 * q^85 - 14 * q^86 - 4 * q^87 + 10 * q^88 + 12 * q^89 - 40 * q^90 - 17 * q^91 + 5 * q^92 - 31 * q^93 + 31 * q^94 - 30 * q^95 + q^96 + 5 * q^97 - 8 * q^98 + 45 * q^99

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