LMFDB - Embedded newform 49.2.g.a.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(2,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("49.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.g (of order $21$, degree $12$, 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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			32.1
Character	$\chi$	$=$	49.32
Dual form			49.2.g.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.151065 - 2.01582i) q^{2} +(1.33832 + 0.412818i) q^{3} +(-2.06305 + 0.310954i) q^{4} +(-1.66779 + 1.54748i) q^{5} +(0.629993 - 2.76018i) q^{6} +(-1.77774 + 1.95950i) q^{7} +(0.0388416 + 0.170176i) q^{8} +(-0.858025 - 0.584992i) q^{9} +O(q^{10})$	\(q+(-0.151065 - 2.01582i) q^{2} +(1.33832 + 0.412818i) q^{3} +(-2.06305 + 0.310954i) q^{4} +(-1.66779 + 1.54748i) q^{5} +(0.629993 - 2.76018i) q^{6} +(-1.77774 + 1.95950i) q^{7} +(0.0388416 + 0.170176i) q^{8} +(-0.858025 - 0.584992i) q^{9} +(3.37138 + 3.12819i) q^{10} +(1.57656 - 1.07488i) q^{11} +(-2.88939 - 0.435506i) q^{12} +(4.29166 + 2.06676i) q^{13} +(4.21856 + 3.28759i) q^{14} +(-2.87087 + 1.38254i) q^{15} +(-3.65014 + 1.12592i) q^{16} +(-1.47907 - 3.76862i) q^{17} +(-1.04962 + 1.81800i) q^{18} +(0.218933 + 0.379203i) q^{19} +(2.95953 - 3.71113i) q^{20} +(-3.18811 + 1.88857i) q^{21} +(-2.40493 - 3.01568i) q^{22} +(2.49370 - 6.35384i) q^{23} +(-0.0182692 + 0.243785i) q^{24} +(0.0131678 - 0.175712i) q^{25} +(3.51789 - 8.96343i) q^{26} +(-3.52650 - 4.42209i) q^{27} +(3.05824 - 4.59534i) q^{28} +(-5.30231 + 6.64889i) q^{29} +(3.22063 + 5.57829i) q^{30} +(-0.409400 + 0.709102i) q^{31} +(2.94860 + 7.51291i) q^{32} +(2.55367 - 0.787704i) q^{33} +(-7.37342 + 3.55085i) q^{34} +(-0.0674026 - 6.01904i) q^{35} +(1.95205 + 0.940059i) q^{36} +(3.68347 + 0.555193i) q^{37} +(0.731331 - 0.498613i) q^{38} +(4.89044 + 4.53766i) q^{39} +(-0.328124 - 0.223711i) q^{40} +(2.40243 + 10.5257i) q^{41} +(4.28862 + 6.14135i) q^{42} +(1.79724 - 7.87423i) q^{43} +(-2.91827 + 2.70776i) q^{44} +(2.33627 - 0.352135i) q^{45} +(-13.1849 - 4.06701i) q^{46} +(0.114840 + 1.53244i) q^{47} -5.34987 q^{48} +(-0.679297 - 6.96696i) q^{49} -0.356192 q^{50} +(-0.423725 - 5.65422i) q^{51} +(-9.49656 - 2.92930i) q^{52} +(0.818284 - 0.123336i) q^{53} +(-8.38140 + 7.77681i) q^{54} +(-0.966009 + 4.23236i) q^{55} +(-0.402511 - 0.226418i) q^{56} +(0.136461 + 0.597875i) q^{57} +(14.2040 + 9.68409i) q^{58} +(-2.23892 - 2.07741i) q^{59} +(5.49282 - 3.74494i) q^{60} +(0.0576570 + 0.00869039i) q^{61} +(1.49127 + 0.718157i) q^{62} +(2.67164 - 0.641340i) q^{63} +(7.81612 - 3.76404i) q^{64} +(-10.3558 + 3.19435i) q^{65} +(-1.97364 - 5.02875i) q^{66} +(6.06468 - 10.5043i) q^{67} +(4.22327 + 7.31491i) q^{68} +(5.96036 - 7.47405i) q^{69} +(-12.1231 + 1.04514i) q^{70} +(3.05705 + 3.83342i) q^{71} +(0.0662246 - 0.168737i) q^{72} +(-0.809992 + 10.8086i) q^{73} +(0.562728 - 7.50908i) q^{74} +(0.0901597 - 0.229723i) q^{75} +(-0.569583 - 0.714235i) q^{76} +(-0.696479 + 5.00012i) q^{77} +(8.40834 - 10.5437i) q^{78} +(-1.22996 - 2.13036i) q^{79} +(4.34532 - 7.52631i) q^{80} +(-1.75589 - 4.47393i) q^{81} +(20.8550 - 6.43292i) q^{82} +(-4.16137 + 2.00401i) q^{83} +(5.98995 - 4.88755i) q^{84} +(8.29864 + 3.99642i) q^{85} +(-16.1445 - 2.43340i) q^{86} +(-9.84099 + 6.70947i) q^{87} +(0.244155 + 0.226543i) q^{88} +(-3.36000 - 2.29081i) q^{89} +(-1.06277 - 4.65630i) q^{90} +(-11.6793 + 4.73537i) q^{91} +(-3.16886 + 13.8837i) q^{92} +(-0.840641 + 0.780000i) q^{93} +(3.07177 - 0.462994i) q^{94} +(-0.951941 - 0.293635i) q^{95} +(0.844715 + 11.2719i) q^{96} +4.05436 q^{97} +(-13.9415 + 2.42180i) q^{98} -1.98152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) $ 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{21}\right)$

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 $

$2$	−0.151065	−	2.01582i	−0.106819	−	1.42540i	−0.750887	−	0.660431i	$-0.770374\pi$
$2$	−0.151065	−	2.01582i	−0.106819	−	1.42540i	0.644068	−	0.764969i	$-0.277246\pi$
$3$	1.33832	+	0.412818i	0.772681	+	0.238341i	0.655931	−	0.754821i	$-0.272276\pi$
$3$	1.33832	+	0.412818i	0.772681	+	0.238341i	0.116750	+	0.993161i	$0.462752\pi$
$4$	−2.06305	+	0.310954i	−1.03152	+	0.155477i
$5$	−1.66779	+	1.54748i	−0.745857	+	0.692054i	−0.958505	−	0.285075i	$-0.907982\pi$
$5$	−1.66779	+	1.54748i	−0.745857	+	0.692054i	0.212649	+	0.977129i	$0.431791\pi$
$6$	0.629993	−	2.76018i	0.257194	−	1.12684i
$7$	−1.77774	+	1.95950i	−0.671922	+	0.740622i
$7$	−1.77774	+	1.95950i	−0.671922	+	0.740622i
$8$	0.0388416	+	0.170176i	0.0137326	+	0.0601663i
$9$	−0.858025	−	0.584992i	−0.286008	−	0.194997i
$10$	3.37138	+	3.12819i	1.06613	+	0.989219i
$11$	1.57656	−	1.07488i	0.475350	−	0.324088i	−0.301835	−	0.953360i	$-0.597599\pi$
$11$	1.57656	−	1.07488i	0.475350	−	0.324088i	0.777185	+	0.629272i	$0.216647\pi$
$12$	−2.88939	−	0.435506i	−0.834095	−	0.125720i
$13$	4.29166	+	2.06676i	1.19029	+	0.573215i	0.920894	−	0.389814i	$-0.127461\pi$
$13$	4.29166	+	2.06676i	1.19029	+	0.573215i	0.269399	+	0.963029i	$0.413175\pi$
$14$	4.21856	+	3.28759i	1.12746	+	0.878645i
$15$	−2.87087	+	1.38254i	−0.741254	+	0.356969i
$16$	−3.65014	+	1.12592i	−0.912535	+	0.281480i
$17$	−1.47907	−	3.76862i	−0.358728	−	0.914025i	−0.990330	−	0.138732i	$-0.955697\pi$
$17$	−1.47907	−	3.76862i	−0.358728	−	0.914025i	0.631602	−	0.775293i	$-0.282398\pi$
$18$	−1.04962	+	1.81800i	−0.247398	+	0.428506i
$19$	0.218933	+	0.379203i	0.0502266	+	0.0869951i	0.890046	−	0.455871i	$-0.150672\pi$
$19$	0.218933	+	0.379203i	0.0502266	+	0.0869951i	−0.839819	+	0.542866i	$0.817339\pi$
$20$	2.95953	−	3.71113i	0.661770	−	0.829833i
$21$	−3.18811	+	1.88857i	−0.695702	+	0.412119i
$22$	−2.40493	−	3.01568i	−0.512732	−	0.642945i
$23$	2.49370	−	6.35384i	0.519972	−	1.32487i	−0.394007	−	0.919107i	$-0.628912\pi$
$23$	2.49370	−	6.35384i	0.519972	−	1.32487i	0.913980	−	0.405760i	$-0.132993\pi$
$24$	−0.0182692	+	0.243785i	−0.00372918	+	0.0497624i
$25$	0.0131678	−	0.175712i	0.00263355	−	0.0351423i
$26$	3.51789	−	8.96343i	0.689914	−	1.75787i
$27$	−3.52650	−	4.42209i	−0.678675	−	0.851031i
$28$	3.05824	−	4.59534i	0.577953	−	0.868437i
$29$	−5.30231	+	6.64889i	−0.984615	+	1.23467i	−0.0125582	+	0.999921i	$0.503997\pi$
$29$	−5.30231	+	6.64889i	−0.984615	+	1.23467i	−0.972057	+	0.234747i	$0.924574\pi$
$30$	3.22063	+	5.57829i	0.588004	+	1.01845i
$31$	−0.409400	+	0.709102i	−0.0735305	+	0.127359i	−0.900446	−	0.434967i	$-0.856760\pi$
$31$	−0.409400	+	0.709102i	−0.0735305	+	0.127359i	0.826916	+	0.562326i	$0.190093\pi$
$32$	2.94860	+	7.51291i	0.521244	+	1.32811i
$33$	2.55367	−	0.787704i	0.444538	−	0.137122i
$34$	−7.37342	+	3.55085i	−1.26453	+	0.608966i
$35$	−0.0674026	−	6.01904i	−0.0113931	−	1.01740i
$36$	1.95205	+	0.940059i	0.325342	+	0.156676i
$37$	3.68347	+	0.555193i	0.605558	+	0.0912732i	0.444663	−	0.895698i	$-0.353324\pi$
$37$	3.68347	+	0.555193i	0.605558	+	0.0912732i	0.160896	+	0.986971i	$0.448562\pi$
$38$	0.731331	−	0.498613i	0.118638	−	0.0808857i
$39$	4.89044	+	4.53766i	0.783097	+	0.726608i
$40$	−0.328124	−	0.223711i	−0.0518809	−	0.0353718i
$41$	2.40243	+	10.5257i	0.375196	+	1.64384i	0.711937	+	0.702243i	$0.247818\pi$
$41$	2.40243	+	10.5257i	0.375196	+	1.64384i	−0.336741	+	0.941597i	$0.609325\pi$
$42$	4.28862	+	6.14135i	0.661748	+	0.947631i
$43$	1.79724	−	7.87423i	0.274077	−	1.20081i	−0.631075	−	0.775722i	$-0.717386\pi$
$43$	1.79724	−	7.87423i	0.274077	−	1.20081i	0.905152	−	0.425088i	$-0.139757\pi$
$44$	−2.91827	+	2.70776i	−0.439946	+	0.408211i
$45$	2.33627	−	0.352135i	0.348270	−	0.0524933i
$46$	−13.1849	−	4.06701i	−1.94401	−	0.599647i
$47$	0.114840	+	1.53244i	0.0167512	+	0.223529i	0.999296	+	0.0375051i	$0.0119410\pi$
$47$	0.114840	+	1.53244i	0.0167512	+	0.223529i	−0.982545	+	0.186024i	$0.940440\pi$
$48$	−5.34987			−0.772187
$49$	−0.679297	−	6.96696i	−0.0970424	−	0.995280i
$50$	−0.356192			−0.0503732
$51$	−0.423725	−	5.65422i	−0.0593334	−	0.791749i
$52$	−9.49656	−	2.92930i	−1.31694	−	0.406221i
$53$	0.818284	−	0.123336i	0.112400	−	0.0169416i	−0.0926014	−	0.995703i	$-0.529518\pi$
$53$	0.818284	−	0.123336i	0.112400	−	0.0169416i	0.205001	+	0.978762i	$0.434280\pi$
$54$	−8.38140	+	7.77681i	−1.14056	+	1.05829i
$55$	−0.966009	+	4.23236i	−0.130257	+	0.570691i
$56$	−0.402511	−	0.226418i	−0.0537877	−	0.0302564i
$57$	0.136461	+	0.597875i	0.0180747	+	0.0791905i
$58$	14.2040	+	9.68409i	1.86507	+	1.27158i
$59$	−2.23892	−	2.07741i	−0.291482	−	0.270456i	0.520854	−	0.853646i	$-0.325614\pi$
$59$	−2.23892	−	2.07741i	−0.291482	−	0.270456i	−0.812336	+	0.583190i	$0.801804\pi$
$60$	5.49282	−	3.74494i	0.709120	−	0.483470i
$61$	0.0576570	+	0.00869039i	0.00738222	+	0.00111269i	0.152732	−	0.988268i	$-0.451193\pi$
$61$	0.0576570	+	0.00869039i	0.00738222	+	0.00111269i	−0.145350	+	0.989380i	$0.546431\pi$
$62$	1.49127	+	0.718157i	0.189391	+	0.0912060i
$63$	2.67164	−	0.641340i	0.336595	−	0.0808013i
$64$	7.81612	−	3.76404i	0.977015	−	0.470506i
$65$	−10.3558	+	3.19435i	−1.28448	+	0.396211i
$66$	−1.97364	−	5.02875i	−0.242938	−	0.618997i
$67$	6.06468	−	10.5043i	0.740918	−	1.28331i	−0.211159	−	0.977452i	$-0.567724\pi$
$67$	6.06468	−	10.5043i	0.740918	−	1.28331i	0.952078	−	0.305857i	$-0.0989429\pi$
$68$	4.22327	+	7.31491i	0.512146	+	0.887064i
$69$	5.96036	−	7.47405i	0.717543	−	0.899770i
$70$	−12.1231	+	1.04514i	−1.44899	+	0.124918i
$71$	3.05705	+	3.83342i	0.362805	+	0.454944i	0.929411	−	0.369045i	$-0.120315\pi$
$71$	3.05705	+	3.83342i	0.362805	+	0.454944i	−0.566606	+	0.823989i	$0.691744\pi$
$72$	0.0662246	−	0.168737i	0.00780464	−	0.0198859i
$73$	−0.809992	+	10.8086i	−0.0948024	+	1.26505i	0.723525	+	0.690298i	$0.242521\pi$
$73$	−0.809992	+	10.8086i	−0.0948024	+	1.26505i	−0.818328	+	0.574752i	$0.805098\pi$
$74$	0.562728	−	7.50908i	0.0654157	−	0.872913i
$75$	0.0901597	−	0.229723i	0.0104107	−	0.0265261i
$76$	−0.569583	−	0.714235i	−0.0653357	−	0.0819283i
$77$	−0.696479	+	5.00012i	−0.0793712	+	0.569817i
$78$	8.40834	−	10.5437i	0.952057	−	1.19384i
$79$	−1.22996	−	2.13036i	−0.138382	−	0.239684i	0.788502	−	0.615032i	$-0.210857\pi$
$79$	−1.22996	−	2.13036i	−0.138382	−	0.239684i	−0.926884	+	0.375347i	$0.877523\pi$
$80$	4.34532	−	7.52631i	0.485821	−	0.841467i
$81$	−1.75589	−	4.47393i	−0.195099	−	0.497103i
$82$	20.8550	−	6.43292i	2.30305	−	0.710398i
$83$	−4.16137	+	2.00401i	−0.456769	+	0.219968i	−0.648097	−	0.761558i	$-0.724435\pi$
$83$	−4.16137	+	2.00401i	−0.456769	+	0.219968i	0.191328	+	0.981526i	$0.438721\pi$
$84$	5.98995	−	4.88755i	0.653558	−	0.533276i
$85$	8.29864	+	3.99642i	0.900114	+	0.433472i
$86$	−16.1445	−	2.43340i	−1.74091	−	0.262400i
$87$	−9.84099	+	6.70947i	−1.05507	+	0.719331i
$88$	0.244155	+	0.226543i	0.0260270	+	0.0241495i
$89$	−3.36000	−	2.29081i	−0.356159	−	0.242825i	0.372001	−	0.928232i	$-0.378672\pi$
$89$	−3.36000	−	2.29081i	−0.356159	−	0.242825i	−0.728160	+	0.685407i	$0.759624\pi$
$90$	−1.06277	−	4.65630i	−0.112026	−	0.490817i
$91$	−11.6793	+	4.73537i	−1.22432	+	0.496402i
$92$	−3.16886	+	13.8837i	−0.330377	+	1.44748i
$93$	−0.840641	+	0.780000i	−0.0871704	+	0.0808823i
$94$	3.07177	−	0.462994i	0.316828	−	0.0477542i
$95$	−0.951941	−	0.293635i	−0.0976671	−	0.0301263i
$96$	0.844715	+	11.2719i	0.0862134	+	1.15044i
$97$	4.05436			0.411658			0.205829	−	0.978588i	$-0.434011\pi$
$97$	4.05436			0.411658			0.205829	+	0.978588i	$0.434011\pi$
$98$	−13.9415	+	2.42180i	−1.40831	+	0.244639i
$99$	−1.98152			−0.199151
$100$	0.0274726	+	0.366596i	0.00274726	+	0.0366596i
$101$	−3.43504	−	1.05957i	−0.341799	−	0.105431i	0.119104	−	0.992882i	$-0.461998\pi$
$101$	−3.43504	−	1.05957i	−0.341799	−	0.105431i	−0.460902	+	0.887451i	$0.652474\pi$
$102$	−11.3339	+	1.70831i	−1.12222	+	0.169148i
$103$	−10.0573	+	9.33178i	−0.990972	+	0.919487i	−0.996755	−	0.0804960i	$-0.974350\pi$
$103$	−10.0573	+	9.33178i	−0.990972	+	0.919487i	0.00578335	+	0.999983i	$0.498159\pi$
$104$	−0.185017	+	0.810614i	−0.0181425	+	0.0794873i
$105$	2.39456	−	8.08325i	0.233686	−	0.788845i
$106$	−0.372238	−	1.63088i	−0.0361549	−	0.158405i
$107$	2.51675	+	1.71589i	0.243303	+	0.165881i	0.678832	−	0.734293i	$-0.262486\pi$
$107$	2.51675	+	1.71589i	0.243303	+	0.165881i	−0.435529	+	0.900175i	$0.643439\pi$
$108$	8.65040	+	8.02640i	0.832385	+	0.772340i
$109$	2.73299	−	1.86332i	0.261773	−	0.178473i	−0.425321	−	0.905043i	$-0.639839\pi$
$109$	2.73299	−	1.86332i	0.261773	−	0.178473i	0.687093	+	0.726569i	$0.258886\pi$
$110$	8.67761	+	1.30794i	0.827377	+	0.124707i
$111$	4.70048	+	2.26363i	0.446150	+	0.214854i
$112$	4.28275	−	9.15405i	0.404682	−	0.864976i
$113$	2.55014	−	1.22808i	0.239897	−	0.115528i	−0.310073	−	0.950713i	$-0.600353\pi$
$113$	2.55014	−	1.22808i	0.239897	−	0.115528i	0.549970	+	0.835185i	$0.314639\pi$
$114$	1.18459	−	0.365399i	0.110947	−	0.0342227i
$115$	5.67348	+	14.4558i	0.529055	+	1.34801i
$116$	8.87142	−	15.3657i	0.823690	−	1.42667i
$117$	−2.47332	−	4.28392i	−0.228658	−	0.396048i
$118$	−3.84946	+	4.82707i	−0.354372	+	0.444368i
$119$	10.0140	+	3.80137i	0.917984	+	0.348471i
$120$	−0.346784	−	0.434853i	−0.0316569	−	0.0396964i
$121$	−2.68858	+	6.85039i	−0.244416	+	0.622763i
$122$	0.00880832	−	0.117539i	0.000797468	−	0.0106415i
$123$	−1.12998	+	15.0786i	−0.101887	+	1.35959i
$124$	0.624114	−	1.59022i	0.0560471	−	0.142806i
$125$	−6.84264	−	8.58040i	−0.612025	−	0.767455i
$126$	−1.69642	−	5.28865i	−0.151129	−	0.471151i
$127$	3.64167	−	4.56651i	0.323146	−	0.405212i	−0.593550	−	0.804797i	$-0.702274\pi$
$127$	3.64167	−	4.56651i	0.323146	−	0.405212i	0.916696	+	0.399585i	$0.130846\pi$
$128$	−0.697559	−	1.20821i	−0.0616561	−	0.106792i
$129$	5.65592	−	9.79634i	0.497976	−	0.862519i
$130$	8.00364	+	20.3929i	0.701966	+	1.78858i
$131$	−4.26464	+	1.31547i	−0.372603	+	0.114933i	−0.475401	−	0.879769i	$-0.657697\pi$
$131$	−4.26464	+	1.31547i	−0.372603	+	0.114933i	0.102797	+	0.994702i	$0.467221\pi$
$132$	−5.02341	+	2.41915i	−0.437232	+	0.210560i
$133$	−1.13225	−	0.245124i	−0.0981788	−	0.0212549i
$134$	−22.0910	−	10.6385i	−1.90837	−	0.919023i
$135$	12.7245	+	1.91792i	1.09515	+	0.165068i
$136$	0.583880	−	0.398082i	0.0500673	−	0.0341353i
$137$	−3.19380	−	2.96341i	−0.272865	−	0.253181i	0.531856	−	0.846835i	$-0.321495\pi$
$137$	−3.19380	−	2.96341i	−0.272865	−	0.253181i	−0.804721	+	0.593653i	$0.797685\pi$
$138$	−15.9667	−	10.8859i	−1.35918	−	0.926673i
$139$	−1.74312	−	7.63711i	−0.147849	−	0.647771i	−0.993480	−	0.114003i	$-0.963633\pi$
$139$	−1.74312	−	7.63711i	−0.147849	−	0.647771i	0.845631	−	0.533768i	$-0.179224\pi$
$140$	2.01070	+	12.3966i	0.169935	+	1.04770i
$141$	−0.478924	+	2.09830i	−0.0403327	+	0.176709i
$142$	7.26567	−	6.74156i	0.609722	−	0.565739i
$143$	8.98757	−	1.35466i	0.751578	−	0.113282i
$144$	3.79057	+	1.16923i	0.315881	+	0.0974362i
$145$	−1.44590	−	19.2941i	−0.120075	−	1.60229i
$146$	21.9105			1.81333
$147$	1.96697	−	9.60447i	0.162233	−	0.792164i
$148$	−7.77181			−0.638838
$149$	0.502440	+	6.70459i	0.0411615	+	0.549262i	0.979222	+	0.202791i	$0.0650011\pi$
$149$	0.502440	+	6.70459i	0.0411615	+	0.549262i	−0.938061	+	0.346471i	$0.887380\pi$
$150$	−0.476700	−	0.147043i	−0.0389224	−	0.0120060i
$151$	−7.13195	+	1.07497i	−0.580390	+	0.0874796i	−0.432674	−	0.901550i	$-0.642430\pi$
$151$	−7.13195	+	1.07497i	−0.580390	+	0.0874796i	−0.147715	+	0.989030i	$0.547192\pi$
$152$	−0.0560275	+	0.0519860i	−0.00454443	+	0.00421662i
$153$	−0.935529	+	4.09882i	−0.0756330	+	0.331370i
$154$	10.1846	+	0.648634i	0.820695	+	0.0522684i
$155$	−0.414529	−	1.81617i	−0.0332958	−	0.145878i
$156$	−11.5002	−	7.84071i	−0.920753	−	0.627759i
$157$	−17.9097	−	16.6178i	−1.42935	−	1.32624i	−0.866017	−	0.500015i	$-0.833328\pi$
$157$	−17.9097	−	16.6178i	−1.42935	−	1.32624i	−0.563334	−	0.826229i	$-0.690482\pi$
$158$	−4.10862	+	2.80121i	−0.326864	+	0.222852i
$159$	1.14604	+	0.172738i	0.0908872	+	0.0136990i
$160$	−16.5437	−	7.96703i	−1.30790	−	0.629849i
$161$	8.01722	+	16.1819i	0.631846	+	1.27531i
$162$	−8.75338	+	4.21541i	−0.687731	+	0.331194i
$163$	21.5436	−	6.64532i	1.68743	−	0.520502i	0.705329	−	0.708880i	$-0.250799\pi$
$163$	21.5436	−	6.64532i	1.68743	−	0.520502i	0.982097	+	0.188378i	$0.0603230\pi$
$164$	−8.22933	−	20.9680i	−0.642603	−	1.63733i
$165$	−3.04003	+	5.26548i	−0.236666	+	0.409917i
$166$	4.66835	+	8.08583i	0.362335	+	0.627582i
$167$	−6.55741	+	8.22273i	−0.507427	+	0.636294i	−0.967887	−	0.251387i	$-0.919113\pi$
$167$	−6.55741	+	8.22273i	−0.507427	+	0.636294i	0.460459	+	0.887681i	$0.347685\pi$
$168$	−0.445220	−	0.469185i	−0.0343495	−	0.0361984i
$169$	6.04151	+	7.57582i	0.464732	+	0.582755i
$170$	6.80242	−	17.3323i	0.521722	−	1.32933i
$171$	0.0339806	−	0.453439i	0.00259856	−	0.0346754i
$172$	−1.25927	+	16.8038i	−0.0960183	+	1.28128i
$173$	1.71029	−	4.35774i	0.130031	−	0.331313i	−0.851000	−	0.525166i	$-0.824003\pi$
$173$	1.71029	−	4.35774i	0.130031	−	0.331313i	0.981031	+	0.193853i	$0.0620985\pi$
$174$	15.0117	+	18.8241i	1.13804	+	1.42705i
$175$	0.320899	+	0.338172i	0.0242576	+	0.0255634i
$176$	−4.54443	+	5.69854i	−0.342549	+	0.429543i
$177$	−2.13880	−	3.70451i	−0.160762	−	0.278448i
$178$	−4.11028	+	7.11921i	−0.308078	+	0.533607i
$179$	1.81890	+	4.63449i	0.135951	+	0.346398i	0.982595	−	0.185763i	$-0.0594755\pi$
$179$	1.81890	+	4.63449i	0.135951	+	0.346398i	−0.846643	+	0.532161i	$0.821380\pi$
$180$	−4.71033	+	1.45294i	−0.351087	+	0.108296i
$181$	19.9703	−	9.61720i	1.48438	−	0.714841i	0.496212	−	0.868201i	$-0.334724\pi$
$181$	19.9703	−	9.61720i	1.48438	−	0.714841i	0.988170	+	0.153360i	$0.0490095\pi$
$182$	11.3100	+	22.8279i	0.838351	+	1.69212i
$183$	0.0735762	+	0.0354324i	0.00543891	+	0.00261924i
$184$	1.17813	+	0.177575i	0.0868530	+	0.0130910i
$185$	−7.00239	+	4.77415i	−0.514826	+	0.351002i
$186$	1.69933	+	1.57675i	0.124601	+	0.115613i
$187$	−6.38266	−	4.35162i	−0.466746	−	0.318222i
$188$	−0.713438	−	3.12578i	−0.0520328	−	0.227971i
$189$	14.9343	+	0.951134i	1.08631	+	0.0691848i
$190$	−0.448110	+	1.96330i	−0.0325093	+	0.142433i
$191$	−9.57738	+	8.88651i	−0.692995	+	0.643005i	−0.945890	−	0.324488i	$-0.894808\pi$
$191$	−9.57738	+	8.88651i	−0.692995	+	0.643005i	0.252895	+	0.967494i	$0.418617\pi$
$192$	12.0144	−	1.81087i	0.867062	−	0.130689i
$193$	−10.2751	−	3.16945i	−0.739618	−	0.228142i	−0.0980217	−	0.995184i	$-0.531251\pi$
$193$	−10.2751	−	3.16945i	−0.739618	−	0.228142i	−0.641597	+	0.767042i	$0.721728\pi$
$194$	−0.612471	−	8.17285i	−0.0439728	−	0.586777i
$195$	−15.1781			−1.08693
$196$	3.56783	+	14.1619i	0.254845	+	1.01157i
$197$	−5.67753			−0.404507			−0.202254	−	0.979333i	$-0.564827\pi$
$197$	−5.67753			−0.404507			−0.202254	+	0.979333i	$0.564827\pi$
$198$	0.299338	+	3.99439i	0.0212730	+	0.283869i
$199$	13.0167	+	4.01512i	0.922729	+	0.284624i	0.719488	−	0.694505i	$-0.244376\pi$
$199$	13.0167	+	4.01512i	0.922729	+	0.284624i	0.203241	+	0.979129i	$0.434853\pi$
$200$	0.0304134	−	0.00458408i	0.00215055	−	0.000324143i
$201$	12.4529	−	11.5546i	0.878359	−	0.814998i
$202$	−1.61699	+	7.08448i	−0.113771	+	0.498462i
$203$	−3.60239	−	22.2099i	−0.252838	−	1.55883i
$204$	2.63237	+	11.5332i	0.184303	+	0.807483i
$205$	−20.2951	−	13.8369i	−1.41747	−	0.966414i
$206$	20.3305	+	18.8639i	1.41649	+	1.31431i
$207$	−5.85660	+	3.99296i	−0.407062	+	0.277530i
$208$	−17.9922	−	2.71188i	−1.24753	−	0.188035i
$209$	0.752757	+	0.362509i	0.0520693	+	0.0250753i
$210$	−16.6561	−	3.60591i	−1.14938	−	0.248832i
$211$	−14.5359	+	7.00014i	−1.00069	+	0.481909i	−0.861174	−	0.508310i	$-0.830270\pi$
$211$	−14.5359	+	7.00014i	−1.00069	+	0.481909i	−0.139521	+	0.990219i	$0.544556\pi$
$212$	−1.64981	+	0.508898i	−0.113309	+	0.0349512i
$213$	2.50882	+	6.39237i	0.171901	+	0.437998i
$214$	3.07873	−	5.33252i	0.210458	−	0.364523i
$215$	9.18780	+	15.9137i	0.626603	+	1.08531i
$216$	0.615559	−	0.771887i	0.0418835	−	0.0525202i
$217$	−0.661681	−	2.06282i	−0.0449178	−	0.140033i
$218$	−4.16897	−	5.22772i	−0.282358	−	0.354066i
$219$	−5.54601	+	14.1310i	−0.374765	+	0.954886i
$220$	0.676850	−	9.03194i	0.0456332	−	0.608933i
$221$	1.44113	−	19.2305i	0.0969408	−	1.29359i
$222$	3.85299	−	9.81727i	0.258596	−	0.658892i
$223$	−4.65621	−	5.83871i	−0.311803	−	0.390989i	0.601094	−	0.799178i	$-0.294732\pi$
$223$	−4.65621	−	5.83871i	−0.311803	−	0.390989i	−0.912897	+	0.408190i	$0.866160\pi$
$224$	−19.9634	−	7.57820i	−1.33386	−	0.506340i
$225$	−0.114088	+	0.143062i	−0.00760588	+	0.00953747i
$226$	−2.86083	−	4.95510i	−0.190299	−	0.329608i
$227$	4.81428	−	8.33857i	0.319535	−	0.553450i	−0.660856	−	0.750512i	$-0.729807\pi$
$227$	4.81428	−	8.33857i	0.319535	−	0.553450i	0.980391	+	0.197062i	$0.0631401\pi$
$228$	−0.467437	−	1.19101i	−0.0309568	−	0.0788766i
$229$	−13.3133	+	4.10660i	−0.879765	+	0.271372i	−0.701550	−	0.712620i	$-0.747508\pi$
$229$	−13.3133	+	4.10660i	−0.879765	+	0.271372i	−0.178215	+	0.983992i	$0.557032\pi$
$230$	28.2832	−	13.6205i	1.86494	−	0.898108i
$231$	−2.99626	+	6.40426i	−0.197139	+	0.421370i
$232$	−1.33743	−	0.644074i	−0.0878067	−	0.0422855i
$233$	6.41172	+	0.966411i	0.420046	+	0.0633117i	0.355665	−	0.934614i	$-0.384255\pi$
$233$	6.41172	+	0.966411i	0.420046	+	0.0633117i	0.0643811	+	0.997925i	$0.479493\pi$
$234$	−8.26197	+	5.63292i	−0.540102	+	0.368235i
$235$	−2.56294	−	2.37806i	−0.167188	−	0.155128i
$236$	5.26497	+	3.58959i	0.342720	+	0.233663i
$237$	−0.766639	−	3.35886i	−0.0497985	−	0.218182i
$238$	6.15011	−	20.7607i	0.398652	−	1.34572i
$239$	3.80981	−	16.6919i	0.246436	−	1.07971i	−0.688596	−	0.725145i	$-0.741773\pi$
$239$	3.80981	−	16.6919i	0.246436	−	1.07971i	0.935032	−	0.354563i	$-0.115370\pi$
$240$	8.92244	−	8.27881i	0.575941	−	0.534395i
$241$	−1.56832	+	0.236387i	−0.101025	+	0.0152270i	−0.199360	−	0.979926i	$-0.563886\pi$
$241$	−1.56832	+	0.236387i	−0.101025	+	0.0152270i	0.0983354	+	0.995153i	$0.468648\pi$
$242$	14.2153	+	4.38484i	0.913794	+	0.281868i
$243$	0.765008	+	10.2083i	0.0490753	+	0.654864i
$244$	−0.121651			−0.00778793
$245$	11.9142	+	10.5682i	0.761167	+	0.675178i
$246$	30.5664			1.94884
$247$	0.155866	+	2.07989i	0.00991753	+	0.132340i
$248$	−0.136574	−	0.0421275i	−0.00867246	−	0.00267510i
$249$	−6.39654	+	0.964124i	−0.405364	+	0.0610989i
$250$	−16.2629	+	15.0897i	−1.02855	+	0.954359i
$251$	3.72581	−	16.3239i	0.235171	−	1.03035i	−0.710109	−	0.704092i	$-0.751354\pi$
$251$	3.72581	−	16.3239i	0.235171	−	1.03035i	0.945280	−	0.326261i	$-0.105789\pi$
$252$	−5.31228	+	2.15387i	−0.334642	+	0.135681i
$253$	−2.89815	−	12.6976i	−0.182205	−	0.798293i
$254$	−9.75539	−	6.65111i	−0.612108	−	0.417328i
$255$	9.45648	+	8.77433i	0.592188	+	0.549470i
$256$	12.0055	−	8.18520i	0.750343	−	0.511575i
$257$	29.0195	+	4.37399i	1.81019	+	0.272842i	0.965118	−	0.261816i	$-0.0843214\pi$
$257$	29.0195	+	4.37399i	1.81019	+	0.272842i	0.845069	+	0.534658i	$0.179559\pi$
$258$	−20.6021	−	9.92143i	−1.28263	−	0.617681i
$259$	−7.63614	+	6.23077i	−0.474487	+	0.387162i
$260$	20.3713	−	9.81029i	1.26337	−	0.608408i
$261$	8.43906	−	2.60311i	0.522365	−	0.161128i
$262$	3.29598	+	8.39802i	0.203626	+	0.518831i
$263$	−5.27309	+	9.13326i	−0.325153	+	0.563181i	−0.981543	−	0.191240i	$-0.938749\pi$
$263$	−5.27309	+	9.13326i	−0.325153	+	0.563181i	0.656391	+	0.754421i	$0.272082\pi$
$264$	0.233237	+	0.403979i	0.0143548	+	0.0248632i
$265$	−1.17386	+	1.47198i	−0.0721098	+	0.0904228i
$266$	−0.323082	+	2.31945i	−0.0198094	+	0.142214i
$267$	−3.55108	−	4.45291i	−0.217322	−	0.272514i
$268$	−9.24535	+	23.5568i	−0.564750	+	1.43896i
$269$	−0.787107	+	10.5032i	−0.0479907	+	0.640392i	0.920404	+	0.390969i	$0.127860\pi$
$269$	−0.787107	+	10.5032i	−0.0479907	+	0.640392i	−0.968395	+	0.249423i	$0.919759\pi$
$270$	1.94394	−	25.9401i	0.118305	−	1.57866i
$271$	−9.07595	+	23.1251i	−0.551324	+	1.40475i	0.335234	+	0.942135i	$0.391185\pi$
$271$	−9.07595	+	23.1251i	−0.551324	+	1.40475i	−0.886558	+	0.462617i	$0.846911\pi$
$272$	9.64199	+	12.0907i	0.584632	+	0.733105i
$273$	−17.5855	+	1.51605i	−1.06432	+	0.0917554i
$274$	−5.49123	+	6.88579i	−0.331737	+	0.415986i
$275$	−0.168109	−	0.291173i	−0.0101374	−	0.0175584i
$276$	−9.97240	+	17.2727i	−0.600268	+	1.03970i
$277$	4.81556	+	12.2698i	0.289339	+	0.737223i	0.999451	+	0.0331346i	$0.0105490\pi$
$277$	4.81556	+	12.2698i	0.289339	+	0.737223i	−0.710112	+	0.704089i	$0.751356\pi$
$278$	−15.1317	+	4.66751i	−0.907539	+	0.279939i
$279$	0.766095	−	0.368932i	0.0458649	−	0.0220874i
$280$	1.02168	−	0.245260i	0.0610570	−	0.0146571i
$281$	18.3370	+	8.83064i	1.09389	+	0.526792i	0.891734	−	0.452561i	$-0.149489\pi$
$281$	18.3370	+	8.83064i	1.09389	+	0.526792i	0.202161	+	0.979352i	$0.435204\pi$
$282$	4.30215	+	0.648445i	0.256189	+	0.0386143i
$283$	19.0449	−	12.9846i	1.13210	−	0.771854i	0.155698	−	0.987805i	$-0.450237\pi$
$283$	19.0449	−	12.9846i	1.13210	−	0.771854i	0.976404	+	0.215950i	$0.0692849\pi$
$284$	−7.49886	−	6.95792i	−0.444975	−	0.412877i
$285$	−1.15279	−	0.785957i	−0.0682852	−	0.0465561i
$286$	−4.08845	−	17.9127i	−0.241755	−	1.05920i
$287$	−24.8960	−	14.0044i	−1.46957	−	0.826654i
$288$	1.86502	−	8.17117i	0.109897	−	0.481491i
$289$	0.447044	−	0.414796i	0.0262967	−	0.0243998i
$290$	−38.6751	+	5.82933i	−2.27108	+	0.342310i
$291$	5.42604	+	1.67371i	0.318080	+	0.0981147i
$292$	−1.68993	−	22.5505i	−0.0988955	−	1.31967i
$293$	−11.8715			−0.693539			−0.346769	−	0.937950i	$-0.612721\pi$
$293$	−11.8715			−0.693539			−0.346769	+	0.937950i	$0.612721\pi$
$294$	−19.6580	−	2.51416i	−1.14648	−	0.146629i
$295$	6.94878			0.404574
$296$	0.0485911	+	0.648403i	0.00282430	+	0.0376877i
$297$	−10.3129	−	3.18112i	−0.598418	−	0.184587i
$298$	13.4393	−	2.02566i	0.778521	−	0.117343i
$299$	23.8339	−	22.1147i	1.37835	−	1.27892i
$300$	−0.114570	+	0.501965i	−0.00661472	+	0.0289810i
$301$	12.2345	+	17.5200i	0.705188	+	1.00984i
$302$	3.24433	+	14.2143i	0.186690	+	0.817943i
$303$	−4.15978	−	2.83609i	−0.238973	−	0.162929i
$304$	−1.22609	−	1.13764i	−0.0703209	−	0.0652483i
$305$	−0.109608	+	0.0747293i	−0.00627612	+	0.00427899i
$306$	8.40380	+	1.26667i	0.480413	+	0.0724107i
$307$	13.2755	+	6.39317i	0.757676	+	0.364877i	0.772502	−	0.635013i	$-0.219005\pi$
$307$	13.2755	+	6.39317i	0.757676	+	0.364877i	−0.0148260	+	0.999890i	$0.504719\pi$
$308$	−0.117940	−	10.5321i	−0.00672027	−	0.600120i
$309$	−17.3122	+	8.33711i	−0.984857	+	0.474282i
$310$	−3.59845	+	1.10998i	−0.204378	+	0.0630423i
$311$	−10.0956	−	25.7231i	−0.572468	−	1.45862i	−0.864706	−	0.502279i	$-0.832495\pi$
$311$	−10.0956	−	25.7231i	−0.572468	−	1.45862i	0.292238	−	0.956346i	$-0.405600\pi$
$312$	−0.582249	+	1.00849i	−0.0329634	+	0.0570943i
$313$	12.5594	+	21.7536i	0.709901	+	1.22958i	0.964894	+	0.262641i	$0.0845936\pi$
$313$	12.5594	+	21.7536i	0.709901	+	1.22958i	−0.254993	+	0.966943i	$0.582073\pi$
$314$	−30.7929	+	38.6131i	−1.73775	+	2.17906i
$315$	−3.46326	+	5.20392i	−0.195132	+	0.293208i
$316$	3.19992	+	4.01257i	0.180009	+	0.225725i
$317$	−8.00526	+	20.3971i	−0.449620	+	1.14561i	0.508959	+	0.860791i	$0.330030\pi$
$317$	−8.00526	+	20.3971i	−0.449620	+	1.14561i	−0.958580	+	0.284824i	$0.908065\pi$
$318$	0.175082	−	2.33631i	0.00981814	−	0.131014i
$319$	−1.21265	+	16.1817i	−0.0678954	+	0.906002i
$320$	−7.21083	+	18.3729i	−0.403098	+	1.02708i
$321$	2.65987	+	3.33537i	0.148459	+	0.186162i
$322$	31.4086	−	18.6058i	1.75033	−	1.03686i
$323$	1.10525	−	1.38594i	0.0614979	−	0.0771160i
$324$	5.01367	+	8.68393i	0.278537	+	0.482440i
$325$	0.419665	−	0.726880i	0.0232788	−	0.0403201i
$326$	−16.6503	−	42.4242i	−0.922172	−	2.34966i
$327$	4.42683	−	1.36550i	0.244804	−	0.0755121i
$328$	−1.69791	+	0.817671i	−0.0937515	+	0.0451483i
$329$	−3.20697	−	2.49924i	−0.176806	−	0.137788i
$330$	11.0735	+	5.33272i	0.609576	+	0.293556i
$331$	−12.5685	−	1.89440i	−0.690828	−	0.104126i	−0.205761	−	0.978602i	$-0.565967\pi$
$331$	−12.5685	−	1.89440i	−0.690828	−	0.104126i	−0.485067	+	0.874477i	$0.661205\pi$
$332$	7.96193	−	5.42836i	0.436968	−	0.297920i
$333$	−2.83573	−	2.63117i	−0.155397	−	0.144187i
$334$	17.5661	+	11.9764i	0.961176	+	0.655318i
$335$	6.14065	+	26.9039i	0.335500	+	1.46992i
$336$	9.51066	−	10.4831i	0.518849	−	0.571899i
$337$	−2.21226	+	9.69255i	−0.120509	+	0.527987i	0.878250	+	0.478201i	$0.158711\pi$
$337$	−2.21226	+	9.69255i	−0.120509	+	0.527987i	−0.998760	+	0.0497856i	$0.984146\pi$
$338$	14.3588	−	13.3230i	0.781017	−	0.724678i
$339$	3.91988	−	0.590827i	0.212899	−	0.0320893i
$340$	−18.3632	−	5.66429i	−0.995884	−	0.307189i
$341$	0.116756	+	1.55800i	0.00632268	+	0.0843703i
$342$	−0.919185			−0.0497038
$343$	14.8594	+	11.0543i	0.802331	+	0.596879i
$344$	1.40981			0.0760121
$345$	1.62534	+	21.6886i	0.0875053	+	1.16768i
$346$	−9.04278	−	2.78933i	−0.486143	−	0.149955i
$347$	16.4970	−	2.48652i	0.885605	−	0.133483i	0.309539	−	0.950887i	$-0.399825\pi$
$347$	16.4970	−	2.48652i	0.885605	−	0.133483i	0.576066	+	0.817403i	$0.304587\pi$
$348$	18.2161	−	16.9021i	0.976485	−	0.906045i
$349$	0.185225	−	0.811522i	0.00991484	−	0.0434398i	−0.969729	−	0.244186i	$-0.921479\pi$
$349$	0.185225	−	0.811522i	0.00991484	−	0.0434398i	0.979643	+	0.200746i	$0.0643365\pi$
$350$	0.633216	−	0.697959i	0.0338468	−	0.0373075i
$351$	−5.99516	−	26.2665i	−0.319998	−	1.40200i
$352$	12.7241	+	8.67515i	0.678197	+	0.462387i
$353$	−20.3502	−	18.8822i	−1.08313	−	1.00500i	−0.999964	−	0.00846270i	$-0.997306\pi$
$353$	−20.3502	−	18.8822i	−1.08313	−	1.00500i	−0.0831665	−	0.996536i	$-0.526503\pi$
$354$	−7.14453	+	4.87106i	−0.379727	+	0.258894i
$355$	−11.0307	−	1.66260i	−0.585446	−	0.0882418i
$356$	7.64417	+	3.68124i	0.405140	+	0.195105i
$357$	11.8327	+	9.22143i	0.626255	+	0.488050i
$358$	9.06752	−	4.36669i	0.479233	−	0.230787i
$359$	24.3867	−	7.52231i	1.28708	−	0.397012i	0.425652	−	0.904887i	$-0.360045\pi$
$359$	24.3867	−	7.52231i	1.28708	−	0.397012i	0.861431	+	0.507875i	$0.169569\pi$
$360$	0.150669	+	0.383899i	0.00794097	+	0.0202333i
$361$	9.40414	−	16.2884i	0.494955	−	0.857286i
$362$	−22.4034	−	38.8038i	−1.17749	−	2.03948i
$363$	−6.42616	+	8.05814i	−0.337286	+	0.422943i
$364$	22.6224	−	13.4010i	1.18573	−	0.702403i
$365$	−15.3752	−	19.2799i	−0.804774	−	1.00915i
$366$	0.0603106	−	0.153669i	0.00315248	−	0.00803240i
$367$	1.63958	−	21.8787i	0.0855854	−	1.14206i	−0.774729	−	0.632293i	$-0.782114\pi$
$367$	1.63958	−	21.8787i	0.0855854	−	1.14206i	0.860314	−	0.509764i	$-0.170267\pi$
$368$	−1.94844	+	26.0001i	−0.101569	+	1.35535i
$369$	4.09612	−	10.4367i	0.213235	−	0.543315i
$370$	10.6816	+	13.3943i	0.555312	+	0.696339i
$371$	−1.21302	+	1.82269i	−0.0629767	+	0.0946293i
$372$	1.49174	−	1.87058i	0.0773429	−	0.0969849i
$373$	−14.8839	−	25.7796i	−0.770657	−	1.33482i	−0.937204	−	0.348783i	$-0.886595\pi$
$373$	−14.8839	−	25.7796i	−0.770657	−	1.33482i	0.166547	−	0.986034i	$-0.446738\pi$
$374$	−7.80789	+	13.5237i	−0.403737	+	0.699292i
$375$	−5.61552	−	14.3081i	−0.289984	−	0.738868i
$376$	−0.256323	+	0.0790653i	−0.0132189	+	0.00407748i
$377$	−36.4974	+	17.5762i	−1.87971	+	0.905220i
$378$	−0.338729	−	30.2485i	−0.0174224	−	1.55582i
$379$	−6.35554	−	3.06067i	−0.326462	−	0.157216i	0.263473	−	0.964667i	$-0.415132\pi$
$379$	−6.35554	−	3.06067i	−0.326462	−	0.157216i	−0.589935	+	0.807451i	$0.700846\pi$
$380$	2.05521	+	0.309773i	0.105430	+	0.0158910i
$381$	6.75887	−	4.60812i	0.346267	−	0.236081i
$382$	19.3604	+	17.9638i	0.990565	+	0.919110i
$383$	−11.1196	−	7.58121i	−0.568184	−	0.387382i	0.244882	−	0.969553i	$-0.421251\pi$
$383$	−11.1196	−	7.58121i	−0.568184	−	0.387382i	−0.813066	+	0.582171i	$0.802203\pi$
$384$	−0.434790	−	1.90494i	−0.0221878	−	0.0972110i
$385$	−6.57601	−	9.41692i	−0.335144	−	0.479931i
$386$	−4.83683	+	21.1916i	−0.246188	+	1.07862i
$387$	−6.14844	+	5.70492i	−0.312543	+	0.289997i
$388$	−8.36433	+	1.26072i	−0.424634	+	0.0640033i
$389$	11.4201	+	3.52262i	0.579020	+	0.178604i	0.570412	−	0.821359i	$-0.306784\pi$
$389$	11.4201	+	3.52262i	0.579020	+	0.178604i	0.00860837	+	0.999963i	$0.497260\pi$
$390$	2.29288	+	30.5964i	0.116105	+	1.54931i
$391$	−27.6336			−1.39749
$392$	1.15923	−	0.386208i	0.0585497	−	0.0195064i
$393$	−6.25051			−0.315297
$394$	0.857674	+	11.4449i	0.0432090	+	0.576584i
$395$	5.34801	+	1.64964i	0.269087	+	0.0830025i
$396$	4.08797	−	0.616163i	0.205428	−	0.0309633i
$397$	3.78525	−	3.51219i	0.189976	−	0.176272i	−0.579450	−	0.815008i	$-0.696733\pi$
$397$	3.78525	−	3.51219i	0.189976	−	0.176272i	0.769426	+	0.638736i	$0.220542\pi$
$398$	6.12739	−	26.8459i	0.307138	−	1.34566i
$399$	−1.41413	−	0.795470i	−0.0707950	−	0.0398233i
$400$	0.149773	+	0.656198i	0.00748865	+	0.0328099i
$401$	14.1993	+	9.68089i	0.709077	+	0.483441i	0.863362	−	0.504586i	$-0.168355\pi$
$401$	14.1993	+	9.68089i	0.709077	+	0.483441i	−0.154284	+	0.988027i	$0.549307\pi$
$402$	−25.1732	−	23.3573i	−1.25552	−	1.16495i
$403$	−3.22255	+	2.19710i	−0.160527	+	0.109445i
$404$	7.41611	+	1.11780i	0.368965	+	0.0556126i
$405$	9.85176	+	4.74436i	0.489538	+	0.235749i
$406$	−44.2269	+	10.6169i	−2.19494	+	0.526908i
$407$	6.40397	−	3.08399i	0.317433	−	0.152868i
$408$	0.945755	−	0.291727i	0.0468219	−	0.0144426i
$409$	7.93281	+	20.2125i	0.392252	+	0.999442i	0.981495	+	0.191486i	$0.0613308\pi$
$409$	7.93281	+	20.2125i	0.392252	+	0.999442i	−0.589243	+	0.807956i	$0.700574\pi$
$410$	−24.8269	+	43.0015i	−1.22611	+	2.12369i
$411$	−3.05098	−	5.28446i	−0.150494	−	0.260663i
$412$	17.8468	−	22.3792i	0.879251	−	1.10255i
$413$	8.05089	−	0.694069i	0.396159	−	0.0341529i
$414$	8.93382	+	11.2027i	0.439073	+	0.550581i
$415$	3.83911	−	9.78188i	0.188454	−	0.480174i
$416$	−2.87295	+	38.3369i	−0.140858	+	1.87962i
$417$	0.819878	−	10.9405i	0.0401496	−	0.535759i
$418$	0.617037	−	1.57219i	0.0301803	−	0.0768981i
$419$	−6.50497	−	8.15697i	−0.317788	−	0.398494i	0.597122	−	0.802150i	$-0.296311\pi$
$419$	−6.50497	−	8.15697i	−0.317788	−	0.398494i	−0.914911	+	0.403656i	$0.867739\pi$
$420$	−2.42658	+	17.4207i	−0.118405	+	0.850044i
$421$	−6.92877	+	8.68841i	−0.337688	+	0.423447i	−0.921462	−	0.388469i	$-0.873004\pi$
$421$	−6.92877	+	8.68841i	−0.337688	+	0.423447i	0.583774	+	0.811916i	$0.301575\pi$
$422$	16.3069	+	28.2443i	0.793806	+	1.37491i
$423$	0.797927	−	1.38205i	0.0387965	−	0.0671975i
$424$	0.0527724	+	0.134462i	0.00256285	+	0.00653004i
$425$	−0.681667	+	0.210266i	−0.0330657	+	0.0101994i
$426$	12.5069	−	6.02299i	0.605959	−	0.291815i
$427$	−0.119528	+	0.0975298i	−0.00578436	+	0.00471980i
$428$	−5.72573	−	2.75736i	−0.276763	−	0.133282i
$429$	12.5875	+	1.89726i	0.607730	+	0.0916006i
$430$	30.6913	−	20.9249i	1.48006	−	1.00909i
$431$	16.7258	+	15.5193i	0.805653	+	0.747537i	0.971098	−	0.238682i	$-0.0767154\pi$
$431$	16.7258	+	15.5193i	0.805653	+	0.747537i	−0.165445	+	0.986219i	$0.552906\pi$
$432$	17.8511	+	12.1707i	0.858863	+	0.585563i
$433$	−3.39696	−	14.8831i	−0.163247	−	0.715234i	−0.988594	−	0.150607i	$-0.951877\pi$
$433$	−3.39696	−	14.8831i	−0.163247	−	0.715234i	0.825346	−	0.564627i	$-0.190980\pi$
$434$	−4.05831	+	1.64545i	−0.194805	+	0.0789841i
$435$	6.02990	−	26.4187i	0.289111	−	1.26668i
$436$	−5.05887	+	4.69394i	−0.242276	+	0.224799i
$437$	2.95535	−	0.445447i	0.141373	−	0.0213086i
$438$	29.3234	+	9.04507i	1.40113	+	0.432190i
$439$	−0.640084	−	8.54133i	−0.0305495	−	0.407655i	−0.991425	−	0.130675i	$-0.958285\pi$
$439$	−0.640084	−	8.54133i	−0.0305495	−	0.407655i	0.960876	−	0.276980i	$-0.0893336\pi$
$440$	−0.757768			−0.0361252
$441$	−3.49276	+	6.37521i	−0.166322	+	0.303582i
$442$	−38.9830			−1.85423
$443$	−0.579640	−	7.73476i	−0.0275395	−	0.367490i	−0.993899	−	0.110294i	$-0.964821\pi$
$443$	−0.579640	−	7.73476i	−0.0275395	−	0.367490i	0.966359	−	0.257195i	$-0.0827984\pi$
$444$	−10.4012	−	3.20834i	−0.493619	−	0.152261i
$445$	9.14874	−	1.37895i	0.433692	−	0.0653685i
$446$	−11.0664	+	10.2681i	−0.524009	+	0.486209i
$447$	−2.09535	+	9.18033i	−0.0991067	+	0.434215i
$448$	−6.51936	+	22.0072i	−0.308011	+	1.03974i
$449$	−0.364600	−	1.59742i	−0.0172065	−	0.0753867i	0.965596	−	0.260048i	$-0.0837384\pi$
$449$	−0.364600	−	1.59742i	−0.0172065	−	0.0753867i	−0.982802	+	0.184661i	$0.940881\pi$
$450$	0.305622	+	0.208370i	0.0144072	+	0.00982263i
$451$	15.1014	+	14.0121i	0.711099	+	0.659804i
$452$	−4.87918	+	3.32657i	−0.229497	+	0.156468i
$453$	−9.98862	−	1.50554i	−0.469306	−	0.0707365i
$454$	−17.5363	−	8.44505i	−0.823020	−	0.396346i
$455$	12.1506	−	25.9710i	0.569630	−	1.21754i
$456$	−0.0964437	+	0.0464448i	−0.00451639	+	0.00217498i
$457$	−17.3635	+	5.35593i	−0.812231	+	0.250540i	−0.672926	−	0.739710i	$-0.734963\pi$
$457$	−17.3635	+	5.35593i	−0.812231	+	0.250540i	−0.139304	+	0.990250i	$0.544487\pi$
$458$	10.2893	+	26.2168i	0.480788	+	1.22503i
$459$	−11.4492	+	19.8306i	−0.534404	+	0.925615i
$460$	−16.1997	−	28.0588i	−0.755317	−	1.30825i
$461$	19.4601	−	24.4021i	0.906345	−	1.13652i	−0.0838006	−	0.996483i	$-0.526706\pi$
$461$	19.4601	−	24.4021i	0.906345	−	1.13652i	0.990146	−	0.140039i	$-0.0447227\pi$
$462$	13.3625	+	5.07245i	0.621678	+	0.235992i
$463$	20.1031	+	25.2085i	0.934272	+	1.17154i	0.984953	+	0.172825i	$0.0552895\pi$
$463$	20.1031	+	25.2085i	0.934272	+	1.17154i	−0.0506807	+	0.998715i	$0.516139\pi$
$464$	11.8681	−	30.2394i	0.550961	−	1.40383i
$465$	0.194974	−	2.60175i	0.00904171	−	0.120653i
$466$	0.979525	−	13.0709i	0.0453756	−	0.605496i
$467$	−7.58840	+	19.3349i	−0.351149	+	0.894713i	0.640757	+	0.767743i	$0.278620\pi$
$467$	−7.58840	+	19.3349i	−0.351149	+	0.894713i	−0.991907	+	0.126970i	$0.959475\pi$
$468$	6.43467	+	8.06883i	0.297443	+	0.372982i
$469$	9.80185	+	30.5577i	0.452607	+	1.41102i
$470$	−4.40658	+	5.52567i	−0.203260	+	0.254880i
$471$	−17.1089	−	29.6334i	−0.788335	−	1.36544i
$472$	0.266562	−	0.461700i	0.0122695	−	0.0212515i
$473$	−5.63039	−	14.3460i	−0.258886	−	0.659630i
$474$	−6.65505	+	2.05281i	−0.305677	+	0.0942887i
$475$	0.0695132	−	0.0334758i	0.00318948	−	0.00153597i
$476$	−21.8415	−	4.72850i	−1.00110	−	0.216730i
$477$	−0.774259	−	0.372864i	−0.0354509	−	0.0170722i
$478$	−34.2233	−	5.15834i	−1.56534	−	0.235937i
$479$	−19.5967	+	13.3608i	−0.895395	+	0.610470i	−0.921154	−	0.389198i	$-0.872752\pi$
$479$	−19.5967	+	13.3608i	−0.895395	+	0.610470i	0.0257593	+	0.999668i	$0.491800\pi$
$480$	−18.8519	−	17.4920i	−0.860468	−	0.798397i
$481$	14.6607	+	9.99553i	0.668473	+	0.455757i
$482$	0.713431	+	3.12575i	0.0324959	+	0.142374i
$483$	4.04947	+	24.9662i	0.184257	+	1.13600i
$484$	3.41651	−	14.9687i	0.155296	−	0.680395i
$485$	−6.76180	+	6.27404i	−0.307038	+	0.284889i
$486$	20.4626	−	3.08423i	0.928201	−	0.139904i
$487$	−22.6372	−	6.98264i	−1.02579	−	0.316414i	−0.264195	−	0.964469i	$-0.585106\pi$
$487$	−22.6372	−	6.98264i	−1.02579	−	0.316414i	−0.761593	+	0.648056i	$0.775582\pi$
$488$	0.000760592		0.0101494i	3.44304e−5		0.000459441i
$489$	31.5756			1.42790
$490$	19.5038	−	25.6133i	0.881091	−	1.15709i
$491$	2.93971			0.132667			0.0663337	−	0.997797i	$-0.478870\pi$
$491$	2.93971			0.132667			0.0663337	+	0.997797i	$0.478870\pi$
$492$	−2.35754	−	31.4592i	−0.106286	−	1.41829i
$493$	32.8997	+	10.1482i	1.48173	+	0.457052i
$494$	4.16914	−	0.628396i	0.187578	−	0.0282729i
$495$	3.30476	−	3.06637i	0.148538	−	0.137823i
$496$	0.695977	−	3.04928i	0.0312503	−	0.136916i
$497$	−12.9462	−	0.824520i	−0.580718	−	0.0369848i
$498$	2.90979	+	12.7486i	0.130391	+	0.571280i
$499$	−1.68208	−	1.14682i	−0.0753004	−	0.0513389i	0.525085	−	0.851050i	$-0.324034\pi$
$499$	−1.68208	−	1.14682i	−0.0753004	−	0.0513389i	−0.600385	+	0.799711i	$0.704986\pi$
$500$	16.7848	+	15.5740i	0.750639	+	0.696492i
$501$	−12.1704	+	8.29765i	−0.543734	+	0.370712i
$502$	−33.4688	−	5.04461i	−1.49379	−	0.225152i
$503$	7.22087	+	3.47739i	0.321963	+	0.155049i	0.587883	−	0.808946i	$-0.299961\pi$
$503$	7.22087	+	3.47739i	0.321963	+	0.155049i	−0.265920	+	0.963995i	$0.585676\pi$
$504$	0.212911	+	0.429738i	0.00948383	+	0.0191421i
$505$	7.36857	−	3.54851i	0.327897	−	0.157907i
$506$	−25.1583	+	7.76031i	−1.11842	+	0.344988i
$507$	4.95806	+	12.6329i	0.220195	+	0.561049i
$508$	−6.09296	+	10.5533i	−0.270331	+	0.468228i
$509$	−8.45276	−	14.6406i	−0.374662	−	0.648934i	0.615614	−	0.788048i	$-0.288908\pi$
$509$	−8.45276	−	14.6406i	−0.374662	−	0.648934i	−0.990276	+	0.139114i	$0.955575\pi$
$510$	16.2589	−	20.3880i	0.719957	−	0.902798i
$511$	−19.7395	−	20.8020i	−0.873224	−	0.920228i
$512$	−20.0532	−	25.1459i	−0.886233	−	1.11130i
$513$	0.904802	−	2.30540i	0.0399480	−	0.101786i
$514$	4.43334	−	59.1588i	0.195546	−	2.60938i
$515$	2.33263	−	31.1268i	0.102788	−	1.37161i
$516$	−8.62221	+	21.9690i	−0.379571	+	0.967132i
$517$	1.82824	+	2.29254i	0.0804057	+	0.100826i
$518$	13.7137	+	14.4518i	0.602544	+	0.634977i
$519$	4.08787	−	5.12603i	0.179438	−	0.225008i
$520$	−0.945840	−	1.63824i	−0.0414778	−	0.0718417i
$521$	4.75459	−	8.23520i	0.208303	−	0.360791i	−0.742877	−	0.669427i	$-0.766539\pi$
$521$	4.75459	−	8.23520i	0.208303	−	0.360791i	0.951180	+	0.308637i	$0.0998728\pi$
$522$	−6.52224	−	16.6184i	−0.285471	−	0.727367i
$523$	20.1529	−	6.21634i	0.881223	−	0.271821i	0.179061	−	0.983838i	$-0.442694\pi$
$523$	20.1529	−	6.21634i	0.881223	−	0.271821i	0.702163	+	0.712017i	$0.252218\pi$
$524$	8.38909	−	4.03997i	0.366479	−	0.176487i
$525$	0.289863	+	0.585056i	0.0126506	+	0.0255339i
$526$	19.2076	+	9.24989i	0.837490	+	0.403314i
$527$	3.27787	+	0.494060i	0.142786	+	0.0215216i
$528$	−8.43438	+	5.75046i	−0.367059	+	0.250257i
$529$	−17.2926	−	16.0452i	−0.751851	−	0.697616i
$530$	3.14457	+	2.14393i	0.136591	+	0.0931264i
$531$	0.705778	+	3.09222i	0.0306282	+	0.134191i
$532$	2.41211	+	0.153623i	0.104578	+	0.00666039i
$533$	−11.4437	+	50.1380i	−0.495681	+	2.17172i
$534$	−8.43982	+	7.83101i	−0.365227	+	0.338881i
$535$	−6.85270	+	1.03288i	−0.296268	+	0.0446552i
$536$	2.02315	+	0.624059i	0.0873867	+	0.0269552i
$537$	0.521079	+	6.95332i	0.0224862	+	0.300058i
$538$	21.2915			0.917941
$539$	−8.55959	−	10.2537i	−0.368688	−	0.441656i
$540$	−26.8477			−1.15534
$541$	−1.64081	−	21.8950i	−0.0705438	−	0.941341i	−0.914410	−	0.404788i	$-0.867345\pi$
$541$	−1.64081	−	21.8950i	−0.0705438	−	0.941341i	0.843867	−	0.536553i	$-0.180274\pi$
$542$	47.9872	+	14.8021i	2.06122	+	0.635804i
$543$	30.6969	−	4.62681i	1.31733	−	0.198556i
$544$	23.9521	−	22.2243i	1.02694	−	0.952859i
$545$	−1.67459	+	7.33685i	−0.0717315	+	0.314276i
$546$	5.71262	+	35.2201i	0.244478	+	1.50728i
$547$	7.11554	+	31.1752i	0.304238	+	1.33296i	0.863661	+	0.504073i	$0.168166\pi$
$547$	7.11554	+	31.1752i	0.304238	+	1.33296i	−0.559423	+	0.828883i	$0.688977\pi$
$548$	7.51044	+	5.12053i	0.320830	+	0.218738i
$549$	−0.0443874	−	0.0411855i	−0.00189441	−	0.00175775i
$550$	−0.561558	+	0.382864i	−0.0239449	+	0.0163254i
$551$	−3.68213	−	0.554991i	−0.156864	−	0.0236434i
$552$	1.50341	+	0.724006i	0.0639896	+	0.0308158i
$553$	6.36100	+	1.37710i	0.270497	+	0.0585605i
$554$	24.0063	−	11.5608i	1.01993	−	0.491173i
$555$	−11.3423	+	3.49864i	−0.481454	+	0.148509i
$556$	5.97093	+	15.2137i	0.253224	+	0.645204i
$557$	−13.0047	+	22.5248i	−0.551028	+	0.954408i	0.447173	+	0.894447i	$0.352431\pi$
$557$	−13.0047	+	22.5248i	−0.551028	+	0.954408i	−0.998201	+	0.0599605i	$0.980903\pi$
$558$	−0.859430	−	1.48858i	−0.0363826	−	0.0630165i
$559$	23.9873	−	30.0791i	1.01455	−	1.27221i
$560$	7.02299	+	21.8945i	0.296775	+	0.925210i
$561$	−6.74563	−	8.45876i	−0.284801	−	0.357129i
$562$	15.0309	−	38.2981i	0.634040	−	1.61551i
$563$	0.645745	−	8.61687i	0.0272149	−	0.363158i	−0.966925	−	0.255060i	$-0.917905\pi$
$563$	0.645745	−	8.61687i	0.0272149	−	0.363158i	0.994140	−	0.108098i	$-0.0344761\pi$
$564$	0.335566	−	4.47782i	0.0141299	−	0.188550i
$565$	−2.35265	+	5.99446i	−0.0989769	+	0.252189i
$566$	−29.0516	−	36.4296i	−1.22113	−	1.53125i
$567$	11.8882	+	4.51281i	0.499257	+	0.189520i
$568$	−0.533616	+	0.669133i	−0.0223900	+	0.0280762i
$569$	4.45835	+	7.72209i	0.186904	+	0.323727i	0.944216	−	0.329326i	$-0.106821\pi$
$569$	4.45835	+	7.72209i	0.186904	+	0.323727i	−0.757313	+	0.653053i	$0.773488\pi$
$570$	−1.41020	+	2.44254i	−0.0590669	+	0.102307i
$571$	9.98494	+	25.4412i	0.417857	+	1.06468i	0.972564	+	0.232636i	$0.0747350\pi$
$571$	9.98494	+	25.4412i	0.417857	+	1.06468i	−0.554707	+	0.832046i	$0.687170\pi$
$572$	−18.1205	+	5.58944i	−0.757658	+	0.233706i
$573$	−16.4861	+	7.93931i	−0.688719	+	0.331669i
$574$	−24.4694	+	52.3015i	−1.02133	+	2.18302i
$575$	−1.08361	−	0.521838i	−0.0451896	−	0.0217621i
$576$	−8.90836	−	1.34272i	−0.371182	−	0.0559467i
$577$	−36.8913	+	25.1520i	−1.53580	+	1.04709i	−0.559986	+	0.828502i	$0.689194\pi$
$577$	−36.8913	+	25.1520i	−1.53580	+	1.04709i	−0.975817	+	0.218591i	$0.929854\pi$
$578$	−0.903687	−	0.838499i	−0.0375884	−	0.0348770i
$579$	−12.4430	−	8.48350i	−0.517114	−	0.352562i
$580$	8.98255	+	39.3551i	0.372980	+	1.63413i
$581$	3.47096	−	11.7168i	0.144000	−	0.486095i
$582$	2.55422	−	11.1908i	0.105876	−	0.463872i
$583$	1.15750	−	1.07400i	0.0479388	−	0.0444807i
$584$	−1.87083	+	0.281982i	−0.0774153	+	0.0116685i
$585$	10.7542	+	3.31724i	0.444633	+	0.137151i
$586$	1.79336	+	23.9308i	0.0740831	+	0.988570i
$587$	−2.64680			−0.109245			−0.0546226	−	0.998507i	$-0.517396\pi$
$587$	−2.64680			−0.109245			−0.0546226	+	0.998507i	$0.517396\pi$
$588$	−1.07140	+	20.4261i	−0.0441837	+	0.842359i
$589$	−0.358525			−0.0147728
$590$	−1.04972	−	14.0075i	−0.0432161	−	0.576679i
$591$	−7.59837	−	2.34379i	−0.312555	−	0.0964105i
$592$	−14.0703	+	2.12075i	−0.578285	+	0.0871624i
$593$	−21.0962	+	19.5744i	−0.866317	+	0.803825i	−0.981886	−	0.189475i	$-0.939321\pi$
$593$	−21.0962	+	19.5744i	−0.866317	+	0.803825i	0.115569	+	0.993299i	$0.463131\pi$
$594$	−4.85464	+	21.2696i	−0.199188	+	0.872702i
$595$	−22.5838	+	9.15663i	−0.925845	+	0.375385i
$596$	−3.12138	−	13.6757i	−0.127857	−	0.560177i
$597$	15.7630	+	10.7471i	0.645138	+	0.439848i
$598$	−48.1797	−	44.7042i	−1.97021	−	1.82809i
$599$	−11.9464	+	8.14491i	−0.488116	+	0.332792i	−0.782242	−	0.622975i	$-0.785924\pi$
$599$	−11.9464	+	8.14491i	−0.488116	+	0.332792i	0.294126	+	0.955767i	$0.404972\pi$
$600$	0.0425953	+	0.00642021i	0.00173895	+	0.000262104i
$601$	23.2856	+	11.2137i	0.949839	+	0.457418i	0.843630	−	0.536926i	$-0.180414\pi$
$601$	23.2856	+	11.2137i	0.949839	+	0.457418i	0.106209	+	0.994344i	$0.466129\pi$
$602$	33.4690	−	27.3093i	1.36409	−	1.11304i
$603$	−11.3486	+	5.46520i	−0.462151	+	0.222560i
$604$	14.3793	−	4.43542i	0.585084	−	0.180475i
$605$	−6.11686	−	15.5855i	−0.248686	−	0.633641i
$606$	−5.08865	+	8.81380i	−0.206712	+	0.358036i
$607$	−13.0197	−	22.5508i	−0.528454	−	0.915309i	−0.999450	−	0.0331736i	$-0.989439\pi$
$607$	−13.0197	−	22.5508i	−0.528454	−	0.915309i	0.470996	−	0.882136i	$-0.343895\pi$
$608$	−2.20337	+	2.76294i	−0.0893585	+	0.112052i
$609$	4.34747	−	31.2111i	0.176169	−	1.26474i
$610$	0.167199	+	0.209661i	0.00676968	+	0.00848891i
$611$	−2.67431	+	6.81404i	−0.108191	+	0.275667i
$612$	0.655494	−	8.74696i	0.0264968	−	0.353575i
$613$	−1.59326	+	21.2605i	−0.0643510	+	0.858704i	0.867865	+	0.496801i	$0.165492\pi$
$613$	−1.59326	+	21.2605i	−0.0643510	+	0.858704i	−0.932216	+	0.361903i	$0.882127\pi$
$614$	10.8820	−	27.7269i	0.439162	−	1.11897i
$615$	−21.4492	−	26.8965i	−0.864916	−	1.08457i
$616$	−0.877954	+	0.0756886i	−0.0353738	+	0.00304958i
$617$	29.9571	−	37.5650i	1.20603	−	1.51231i	0.404294	−	0.914629i	$-0.367517\pi$
$617$	29.9571	−	37.5650i	1.20603	−	1.51231i	0.801733	−	0.597682i	$-0.203911\pi$
$618$	19.4214	+	33.6388i	0.781243	+	1.35315i
$619$	−18.6273	+	32.2635i	−0.748696	+	1.29678i	0.199751	+	0.979847i	$0.435987\pi$
$619$	−18.6273	+	32.2635i	−0.748696	+	1.29678i	−0.948448	+	0.316934i	$0.897347\pi$
$620$	1.41994	+	3.61794i	0.0570261	+	0.145300i
$621$	−36.8913	+	11.3795i	−1.48040	+	0.456642i
$622$	−50.3281	+	24.2367i	−2.01797	+	0.971804i
$623$	10.4620	−	2.51147i	0.419153	−	0.100620i
$624$	−22.9598	−	11.0569i	−0.919129	−	0.442629i
$625$	25.5613	+	3.85274i	1.02245	+	0.154110i
$626$	41.9540	−	28.6037i	1.67682	−	1.14324i
$627$	0.857783	+	0.795906i	0.0342565	+	0.0317854i
$628$	42.1160	+	28.7142i	1.68061	+	1.14582i
$629$	−3.35581	−	14.7028i	−0.133805	−	0.586238i
$630$	11.0133	+	6.19517i	0.438782	+	0.246822i
$631$	4.77509	−	20.9210i	0.190093	−	0.832854i	−0.786471	−	0.617627i	$-0.788094\pi$
$631$	4.77509	−	20.9210i	0.190093	−	0.832854i	0.976564	−	0.215226i	$-0.0690489\pi$
$632$	0.314763	−	0.292057i	0.0125206	−	0.0116174i
$633$	−22.3436	+	3.36775i	−0.888077	+	0.133856i
$634$	42.3262	+	13.0559i	1.68099	+	0.518516i
$635$	0.993053	+	13.2514i	0.0394081	+	0.525865i
$636$	−2.41806			−0.0958821
$637$	11.4837	−	31.3038i	0.455001	−	1.24030i
$638$	32.8026			1.29867
$639$	−0.380508	−	5.07752i	−0.0150527	−	0.200864i
$640$	3.03306	+	0.935574i	0.119892	+	0.0369818i
$641$	−29.3549	+	4.42454i	−1.15945	+	0.174759i	−0.700465	−	0.713686i	$-0.747024\pi$
$641$	−29.3549	+	4.42454i	−1.15945	+	0.174759i	−0.458983	+	0.888445i	$0.651786\pi$
$642$	6.32169	−	5.86567i	0.249497	−	0.231500i
$643$	−4.65518	+	20.3957i	−0.183582	+	0.804326i	0.796324	+	0.604870i	$0.206775\pi$
$643$	−4.65518	+	20.3957i	−0.183582	+	0.804326i	−0.979907	+	0.199457i	$0.936082\pi$
$644$	−21.5717	−	30.8910i	−0.850045	−	1.21727i
$645$	5.72677	+	25.0906i	0.225491	+	0.987942i
$646$	−2.96078	−	2.01862i	−0.116490	−	0.0794217i
$647$	13.6118	+	12.6299i	0.535135	+	0.496533i	0.900812	−	0.434209i	$-0.142972\pi$
$647$	13.6118	+	12.6299i	0.535135	+	0.496533i	−0.365677	+	0.930742i	$0.619162\pi$
$648$	0.693155	−	0.472585i	0.0272297	−	0.0185649i
$649$	−5.76275	−	0.868594i	−0.226208	−	0.0340953i
$650$	−1.52866	−	0.736162i	−0.0599588	−	0.0288747i
$651$	−0.0339740	−	3.03387i	−0.00133154	−	0.118907i
$652$	−42.3791	+	20.4087i	−1.65969	+	0.799266i
$653$	−16.6348	+	5.13116i	−0.650971	+	0.200798i	−0.602615	−	0.798032i	$-0.705874\pi$
$653$	−16.6348	+	5.13116i	−0.650971	+	0.200798i	−0.0483560	+	0.998830i	$0.515398\pi$
$654$	−3.42133	−	8.71741i	−0.133785	−	0.340878i
$655$	5.07685	−	8.79336i	0.198369	−	0.343585i
$656$	−20.6203	−	35.7154i	−0.805087	−	1.39445i
$657$	7.01793	−	8.80021i	0.273796	−	0.343329i
$658$	−4.55356	+	6.84221i	−0.177516	+	0.266737i
$659$	12.6442	+	15.8554i	0.492549	+	0.617637i	0.964531	−	0.263971i	$-0.0850324\pi$
$659$	12.6442	+	15.8554i	0.492549	+	0.617637i	−0.471981	+	0.881609i	$0.656461\pi$
$660$	4.63439	−	11.8082i	0.180394	−	0.459635i
$661$	−0.580174	+	7.74188i	−0.0225661	+	0.301124i	0.974489	+	0.224435i	$0.0720538\pi$
$661$	−0.580174	+	7.74188i	−0.0225661	+	0.301124i	−0.997055	+	0.0766887i	$0.975565\pi$
$662$	−1.92011	+	25.6220i	−0.0746271	+	0.995829i
$663$	9.86741	−	25.1417i	0.383218	−	0.976424i
$664$	−0.502668	−	0.630326i	−0.0195073	−	0.0244614i
$665$	2.26768	−	1.34333i	0.0879369	−	0.0520919i
$666$	−4.87558	+	6.11379i	−0.188925	+	0.236904i
$667$	29.0236	+	50.2704i	1.12380	+	1.94648i
$668$	10.9713	−	19.0029i	0.424494	−	0.735245i
$669$	−3.82120	−	9.73625i	−0.147736	−	0.376425i
$670$	53.3059	−	16.4427i	2.05939	−	0.635236i
$671$	0.100241	−	0.0482734i	0.00386975	−	0.00186357i
$672$	−23.5891	−	18.3833i	−0.909968	−	0.709152i
$673$	−36.1235	−	17.3962i	−1.39246	−	0.670572i	−0.420841	−	0.907134i	$-0.638265\pi$
$673$	−36.1235	−	17.3962i	−1.39246	−	0.670572i	−0.971616	+	0.236562i	$0.923979\pi$
$674$	19.8726	+	2.99532i	0.765465	+	0.115375i
$675$	−0.823449	+	0.561418i	−0.0316946	+	0.0216090i
$676$	−14.8197	−	13.7506i	−0.569987	−	0.528870i
$677$	25.4599	+	17.3583i	0.978505	+	0.667133i	0.943194	−	0.332243i	$-0.107806\pi$
$677$	25.4599	+	17.3583i	0.978505	+	0.667133i	0.0353108	+	0.999376i	$0.488758\pi$
$678$	−1.78316	−	7.81253i	−0.0684818	−	0.300038i
$679$	−7.20758	+	7.94452i	−0.276602	+	0.304883i
$680$	−0.357762	+	1.56746i	−0.0137195	+	0.0601093i
$681$	9.88537	−	9.17228i	0.378808	−	0.351483i
$682$	3.12300	−	0.470717i	0.119586	−	0.0180247i
$683$	27.2475	+	8.40475i	1.04260	+	0.321599i	0.768329	−	0.640055i	$-0.221088\pi$
$683$	27.2475	+	8.40475i	1.04260	+	0.321599i	0.274268	+	0.961653i	$0.411564\pi$
$684$	0.0708954	+	0.946033i	0.00271075	+	0.0361725i
$685$	9.91239			0.378733
$686$	20.0388	−	31.6238i	0.765087	−	1.20740i
$687$	−19.5127			−0.744457
$688$	2.30556	+	30.7656i	0.0878988	+	1.17293i
$689$	3.76670	+	1.16187i	0.143500	+	0.0442639i
$690$	43.4749	−	6.55278i	1.65506	−	0.249460i
$691$	10.2920	−	9.54955i	0.391525	−	0.363282i	−0.459708	−	0.888070i	$-0.652046\pi$
$691$	10.2920	−	9.54955i	0.391525	−	0.363282i	0.851233	+	0.524788i	$0.175855\pi$
$692$	−2.17334	+	9.52204i	−0.0826181	+	0.361973i
$693$	3.52263	−	3.88280i	0.133814	−	0.147495i
$694$	−7.50449	−	32.8793i	−0.284867	−	1.24808i
$695$	14.7254	+	10.0396i	0.558567	+	0.380824i
$696$	−1.52403	−	1.41410i	−0.0577683	−	0.0536011i
$697$	36.1141	−	24.6222i	1.36792	−	0.932630i
$698$	−1.66386	−	0.250787i	−0.0629781	−	0.00949242i
$699$	8.18200	+	3.94024i	0.309472	+	0.149034i
$700$	−0.767184	−	0.597879i	−0.0289968	−	0.0225977i
$701$	26.9527	−	12.9797i	1.01799	−	0.490238i	0.150983	−	0.988536i	$-0.451756\pi$
$701$	26.9527	−	12.9797i	1.01799	−	0.490238i	0.867005	+	0.498299i	$0.166042\pi$
$702$	−52.0429	+	16.0531i	−1.96423	+	0.605886i
$703$	0.595901	+	1.51833i	0.0224748	+	0.0572649i
$704$	8.27667	−	14.3356i	0.311939	−	0.540294i
$705$	−2.44834	−	4.24065i	−0.0922097	−	0.159712i
$706$	−34.9889	+	43.8747i	−1.31683	+	1.65125i
$707$	8.18282	−	4.84732i	0.307747	−	0.182302i
$708$	5.56438	+	6.97751i	0.209122	+	0.262231i
$709$	3.68198	−	9.38153i	0.138280	−	0.352331i	−0.844912	−	0.534905i	$-0.820348\pi$
$709$	3.68198	−	9.38153i	0.138280	−	0.352331i	0.983192	+	0.182574i	$0.0584428\pi$
$710$	−1.68517	+	22.4870i	−0.0632431	+	0.843921i
$711$	−0.190903	+	2.54742i	−0.00715942	+	0.0955358i
$712$	0.259333	−	0.660770i	0.00971892	−	0.0247634i
$713$	3.48460	+	4.36955i	0.130499	+	0.163641i
$714$	16.8012	−	25.2457i	0.628770	−	0.944796i
$715$	−12.8930	+	16.1674i	−0.482172	+	0.604625i
$716$	−5.19360	−	8.99557i	−0.194094	−	0.336180i
$717$	11.9895	−	20.7664i	0.447755	−	0.775534i
$718$	−18.8476	−	48.0229i	−0.703386	−	1.79220i
$719$	−25.6265	+	7.90474i	−0.955709	+	0.294797i	−0.733108	−	0.680112i	$-0.761931\pi$
$719$	−25.6265	+	7.90474i	−0.955709	+	0.294797i	−0.222601	+	0.974910i	$0.571455\pi$
$720$	−8.13122	+	3.91579i	−0.303033	+	0.145933i
$721$	−0.406458	−	36.2967i	−0.0151373	−	1.35176i
$722$	−34.2552	−	16.4964i	−1.27485	−	0.613934i
$723$	−2.19651	−	0.331070i	−0.0816890	−	0.0123126i
$724$	−38.2092	+	26.0506i	−1.42003	+	0.968163i
$725$	1.09847	+	1.01923i	0.0407961	+	0.0378532i
$726$	17.2145	+	11.7367i	0.638891	+	0.435589i
$727$	4.11406	+	18.0249i	0.152582	+	0.668506i	0.992129	+	0.125219i	$0.0399633\pi$
$727$	4.11406	+	18.0249i	0.152582	+	0.668506i	−0.839547	+	0.543287i	$0.817180\pi$
$728$	−1.25949	−	1.80360i	−0.0466797	−	0.0668459i
$729$	−6.39877	+	28.0348i	−0.236991	+	1.03833i
$730$	−36.5421	+	33.9061i	−1.35248	+	1.25492i
$731$	−32.3332	+	4.87345i	−1.19589	+	0.180251i
$732$	−0.162809	−	0.0502199i	−0.00601759	−	0.00185618i
$733$	−3.89777	−	52.0121i	−0.143967	−	1.92111i	−0.339840	−	0.940483i	$-0.610373\pi$
$733$	−3.89777	−	52.0121i	−0.143967	−	1.92111i	0.195873	−	0.980629i	$-0.437246\pi$
$734$	−44.3511			−1.63703
$735$	11.5822	+	19.0621i	0.427217	+	0.703115i
$736$	55.0888			2.03060
$737$	−1.72957	−	23.0795i	−0.0637095	−	0.850144i
$738$	−21.6573	−	6.68041i	−0.797218	−	0.245909i
$739$	−28.6128	+	4.31269i	−1.05254	+	0.158645i	−0.652450	−	0.757832i	$-0.726259\pi$
$739$	−28.6128	+	4.31269i	−1.05254	+	0.158645i	−0.400089	+	0.916476i	$0.631021\pi$
$740$	12.9617	−	12.0267i	0.476482	−	0.442111i
$741$	−0.650017	+	2.84791i	−0.0238790	+	0.104621i
$742$	3.85746	+	2.16988i	0.141612	+	0.0796587i
$743$	2.89866	+	12.6998i	0.106341	+	0.465912i	0.999858	+	0.0168809i	$0.00537360\pi$
$743$	2.89866	+	12.6998i	0.106341	+	0.465912i	−0.893516	+	0.449031i	$0.851769\pi$
$744$	−0.165389	−	0.112760i	−0.00606346	−	0.00413400i
$745$	−11.2132	−	10.4043i	−0.410819	−	0.381185i
$746$	−49.7186	+	33.8975i	−1.82033	+	1.24108i
$747$	4.74289	+	0.714875i	0.173533	+	0.0261559i
$748$	14.5209	+	6.99289i	0.530936	+	0.255685i
$749$	−7.83640	+	1.88117i	−0.286336	+	0.0687364i
$750$	−27.9943	+	13.4813i	−1.02221	+	0.492269i
$751$	−3.40673	+	1.05084i	−0.124313	+	0.0383456i	−0.356288	−	0.934376i	$-0.615958\pi$
$751$	−3.40673	+	1.05084i	−0.124313	+	0.0383456i	0.231974	+	0.972722i	$0.425482\pi$
$752$	−2.14458	−	5.46431i	−0.0782048	−	0.199263i
$753$	11.7251	−	20.3085i	0.427287	−	0.740084i
$754$	40.9439	+	70.9169i	1.49109	+	2.58264i
$755$	10.2311	−	12.8294i	0.372347	−	0.466908i
$756$	−31.1059	+	2.68164i	−1.13131	+	0.0975304i
$757$	2.92962	+	3.67362i	0.106479	+	0.133520i	0.832215	−	0.554453i	$-0.187072\pi$
$757$	2.92962	+	3.67362i	0.106479	+	0.133520i	−0.725737	+	0.687973i	$0.758501\pi$
$758$	−5.20965	+	13.2740i	−0.189223	+	0.482132i
$759$	1.36315	−	18.1899i	0.0494791	−	0.660253i
$760$	0.0129948	−	0.173403i	0.000471369	−	0.00628999i
$761$	2.22850	−	5.67813i	0.0807831	−	0.205832i	−0.884776	−	0.466017i	$-0.845688\pi$
$761$	2.22850	−	5.67813i	0.0807831	−	0.205832i	0.965559	+	0.260185i	$0.0837837\pi$
$762$	−10.3102	−	12.9285i	−0.373498	−	0.468352i
$763$	−1.20736	+	8.66778i	−0.0437092	+	0.313795i
$764$	16.9953	−	21.3114i	0.614868	−	0.771020i
$765$	−4.78258	−	8.28366i	−0.172914	−	0.299497i
$766$	−13.6026	+	23.5603i	−0.491481	+	0.851270i
$767$	−5.31517	−	13.5428i	−0.191920	−	0.489003i
$768$	19.4462	−	5.99836i	0.701705	−	0.216447i
$769$	−7.74239	+	3.72854i	−0.279198	+	0.134455i	−0.568243	−	0.822861i	$-0.692377\pi$
$769$	−7.74239	+	3.72854i	−0.279198	+	0.134455i	0.289045	+	0.957316i	$0.406662\pi$
$770$	−17.9894	+	14.6786i	−0.648294	+	0.528981i
$771$	37.0318	+	17.8336i	1.33367	+	0.642261i
$772$	22.1836	+	3.34364i	0.798404	+	0.120340i
$773$	37.6012	−	25.6361i	1.35242	−	0.922066i	0.352517	−	0.935805i	$-0.385326\pi$
$773$	37.6012	−	25.6361i	1.35242	−	0.922066i	0.999906	+	0.0137390i	$0.00437340\pi$
$774$	12.4289	+	11.5323i	0.446748	+	0.414521i
$775$	0.119207	+	0.0812737i	0.00428203	+	0.00291944i
$776$	0.157478	+	0.689955i	0.00565312	+	0.0247679i
$777$	−12.7918	+	5.18645i	−0.458904	+	0.186063i
$778$	5.37580	−	23.5529i	0.192732	−	0.844413i
$779$	−3.46541	+	3.21543i	−0.124161	+	0.115205i
$780$	31.3132	−	4.71971i	1.12119	−	0.168993i
$781$	8.94009	+	2.75765i	0.319901	+	0.0986765i
$782$	4.17446	+	55.7043i	0.149278	+	1.99198i
$783$	48.1006			1.71897
$784$	10.3238	+	24.6656i	0.368706	+	0.880913i
$785$	55.5853			1.98392
$786$	0.944232	+	12.5999i	0.0336797	+	0.449424i
$787$	−43.9229	−	13.5484i	−1.56568	−	0.482949i	−0.613812	−	0.789452i	$-0.710365\pi$
$787$	−43.9229	−	13.5484i	−1.56568	−	0.482949i	−0.951869	+	0.306504i	$0.900841\pi$
$788$	11.7130	−	1.76545i	0.417258	−	0.0628916i
$789$	−10.8275	+	10.0464i	−0.385468	+	0.357662i
$790$	2.51748	−	11.0298i	0.0895681	−	0.392423i
$791$	−2.12705	+	7.18021i	−0.0756291	+	0.255299i
$792$	−0.0769655	−	0.337208i	−0.00273485	−	0.0119822i
$793$	0.229483	+	0.156459i	0.00814919	+	0.00555603i
$794$	−7.65177	−	7.09980i	−0.271551	−	0.251963i
$795$	−2.17867	+	1.48539i	−0.0772693	+	0.0526813i
$796$	−28.1026	−	4.23578i	−0.996069	−	0.150133i
$797$	−21.1004	−	10.1614i	−0.747415	−	0.359936i	0.0210922	−	0.999778i	$-0.493286\pi$
$797$	−21.1004	−	10.1614i	−0.747415	−	0.359936i	−0.768507	+	0.639842i	$0.779000\pi$
$798$	−1.38990	+	2.97080i	−0.0492019	+	0.105165i
$799$	5.60531	−	2.69938i	0.198302	−	0.0954971i
$800$	1.35893	−	0.419175i	0.0480455	−	0.0148201i
$801$	1.54286	+	3.93114i	0.0545143	+	0.138900i
$802$	17.3699	−	30.0856i	0.613353	−	1.06236i
$803$	10.3409	+	17.9110i	0.364924	+	0.632066i
$804$	−22.0979	+	27.7099i	−0.779334	+	0.977254i
$805$	−38.4121	−	14.5814i	−1.35385	−	0.513927i
$806$	4.91576	+	6.16417i	0.173150	+	0.217124i
$807$	−5.38932	+	13.7318i	−0.189713	+	0.483381i
$808$	0.0468910	−	0.625716i	0.00164962	−	0.0220126i
$809$	−0.372987	+	4.97717i	−0.0131135	+	0.174988i	0.986801	+	0.161936i	$0.0517738\pi$
$809$	−0.372987	+	4.97717i	−0.0131135	+	0.174988i	−0.999915	+	0.0130520i	$0.995845\pi$
$810$	8.07552	−	20.5761i	0.283745	−	0.722970i
$811$	−0.433526	−	0.543624i	−0.0152231	−	0.0190892i	0.774162	−	0.632988i	$-0.218172\pi$
$811$	−0.433526	−	0.543624i	−0.0152231	−	0.0190892i	−0.789385	+	0.613899i	$0.789600\pi$
$812$	14.3382	+	44.6998i	0.503171	+	1.56866i
$813$	−21.6930	+	27.2022i	−0.760808	+	0.954023i
$814$	−7.18418	−	12.4434i	−0.251805	−	0.436140i
$815$	−25.6466	+	44.4213i	−0.898363	+	1.55601i
$816$	7.91285	+	20.1616i	0.277005	+	0.705798i
$817$	3.37940	−	1.04241i	0.118230	−	0.0364692i
$818$	39.5463	−	19.0445i	1.38270	−	0.665876i
$819$	12.7913	+	2.76920i	0.446963	+	0.0967638i
$820$	46.1723	+	22.2354i	1.61241	+	0.776494i
$821$	−11.8939	−	1.79272i	−0.415101	−	0.0625664i	−0.0618282	−	0.998087i	$-0.519693\pi$
$821$	−11.8939	−	1.79272i	−0.415101	−	0.0625664i	−0.353273	+	0.935520i	$0.614931\pi$
$822$	−10.1916	+	6.94853i	−0.355474	+	0.242358i
$823$	−31.0979	−	28.8547i	−1.08401	−	1.00581i	−0.999956	−	0.00934933i	$-0.997024\pi$
$823$	−31.0979	−	28.8547i	−1.08401	−	1.00581i	−0.0840500	−	0.996462i	$-0.526786\pi$
$824$	−1.97869	−	1.34904i	−0.0689308	−	0.0469962i
$825$	−0.104783	−	0.459083i	−0.00364806	−	0.0159832i
$826$	−2.61532	−	16.1243i	−0.0909988	−	0.561036i
$827$	1.01662	−	4.45411i	0.0353514	−	0.154885i	−0.954172	−	0.299260i	$-0.903260\pi$
$827$	1.01662	−	4.45411i	0.0353514	−	0.154885i	0.989523	+	0.144375i	$0.0461173\pi$
$828$	10.8408	−	10.0588i	0.376744	−	0.349568i
$829$	1.30063	−	0.196038i	0.0451727	−	0.00680870i	−0.126417	−	0.991977i	$-0.540348\pi$
$829$	1.30063	−	0.196038i	0.0451727	−	0.00680870i	0.171590	+	0.985168i	$0.445110\pi$
$830$	−20.2985	−	6.26125i	−0.704570	−	0.217331i
$831$	1.37956	+	18.4090i	0.0478565	+	0.638600i
$832$	41.3235			1.43263
$833$	−25.2511	+	12.8647i	−0.874899	+	0.445734i
$834$	−22.1779			−0.767960
$835$	−1.78815	−	23.8612i	−0.0618815	−	0.825751i
$836$	−1.66570	−	0.513799i	−0.0576093	−	0.0177701i
$837$	4.57946	−	0.690243i	0.158289	−	0.0238583i
$838$	−15.4603	+	14.3451i	−0.534067	+	0.495542i
$839$	1.84273	−	8.07355i	0.0636183	−	0.278730i	−0.933106	−	0.359601i	$-0.882913\pi$
$839$	1.84273	−	8.07355i	0.0636183	−	0.278730i	0.996725	+	0.0808707i	$0.0257701\pi$
$840$	1.46859	+	0.0935312i	0.0506710	+	0.00322713i
$841$	−9.64011	−	42.2361i	−0.332418	−	1.45642i
$842$	18.5610	+	12.6546i	0.639653	+	0.436108i
$843$	20.8954	+	19.3881i	0.719676	+	0.667762i
$844$	27.8116	−	18.9616i	0.957314	−	0.652686i
$845$	−21.7994	−	3.28573i	−0.749921	−	0.113032i
$846$	−2.90650	−	1.39970i	−0.0999276	−	0.0481226i
$847$	−8.64376	−	17.4465i	−0.297003	−	0.599468i
$848$	−2.84798	+	1.37152i	−0.0978002	+	0.0470981i
$849$	30.8485	−	9.51551i	1.05872	−	0.326572i
$850$	0.526835	+	1.34235i	0.0180703	+	0.0460423i
$851$	12.7131	−	22.0197i	0.435798	−	0.754825i
$852$	−7.16354	−	12.4076i	−0.245419	−	0.425078i
$853$	4.03596	−	5.06093i	0.138189	−	0.173283i	−0.707922	−	0.706291i	$-0.750367\pi$
$853$	4.03596	−	5.06093i	0.138189	−	0.173283i	0.846110	+	0.533008i	$0.178938\pi$
$854$	0.214659	+	0.226213i	0.00734548	+	0.00774086i
$855$	0.645016	+	0.808824i	0.0220591	+	0.0276612i
$856$	−0.194249	+	0.494938i	−0.00663929	+	0.0169166i
$857$	−2.66613	+	35.5770i	−0.0910732	+	1.21529i	0.745150	+	0.666897i	$0.232378\pi$
$857$	−2.66613	+	35.5770i	−0.0910732	+	1.21529i	−0.836223	+	0.548390i	$0.815241\pi$
$858$	1.92301	−	25.6607i	0.0656504	−	0.876043i
$859$	−10.2719	+	26.1724i	−0.350473	+	0.892991i	0.641567	+	0.767067i	$0.278285\pi$
$859$	−10.2719	+	26.1724i	−0.350473	+	0.892991i	−0.992040	+	0.125924i	$0.959811\pi$
$860$	−23.9033	−	29.9738i	−0.815096	−	1.02210i
$861$	−27.5377	−	29.0200i	−0.938482	−	0.988998i
$862$	28.7574	−	36.0606i	0.979480	−	1.22823i
$863$	−23.2133	−	40.2067i	−0.790191	−	1.36865i	−0.925849	−	0.377895i	$-0.876648\pi$
$863$	−23.2133	−	40.2067i	−0.790191	−	1.36865i	0.135658	−	0.990756i	$-0.456685\pi$
$864$	22.8245	−	39.5332i	0.776506	−	1.34495i
$865$	3.89112	+	9.91441i	0.132302	+	0.337100i
$866$	−29.4884	+	9.09596i	−1.00206	+	0.309093i
$867$	0.769525	−	0.370584i	0.0261344	−	0.0125857i
$868$	2.00652	+	4.04994i	0.0681058	+	0.137464i
$869$	−4.22899	−	2.03657i	−0.143459	−	0.0690861i
$870$	−54.1662	−	8.16425i	−1.83641	−	0.276794i
$871$	47.7374	−	32.5468i	1.61752	−	1.10281i
$872$	0.423246	+	0.392715i	0.0143329	+	0.0132990i
$873$	−3.47874	−	2.37177i	−0.117738	−	0.0802721i
$874$	−1.34439	−	5.89015i	−0.0454746	−	0.199237i
$875$	28.9777	+	1.84553i	0.979627	+	0.0623904i
$876$	7.04759	−	30.8775i	0.238116	−	1.04325i
$877$	23.2616	−	21.5837i	0.785490	−	0.728828i	−0.181570	−	0.983378i	$-0.558118\pi$
$877$	23.2616	−	21.5837i	0.785490	−	0.728828i	0.967060	+	0.254550i	$0.0819273\pi$
$878$	−17.1211	+	2.58059i	−0.577808	+	0.0870906i
$879$	−15.8879	−	4.90076i	−0.535885	−	0.165299i
$880$	−1.23923	−	16.5364i	−0.0417744	−	0.557441i
$881$	−39.5493			−1.33245			−0.666225	−	0.745750i	$-0.732091\pi$
$881$	−39.5493			−1.33245			−0.666225	+	0.745750i	$0.732091\pi$
$882$	13.3789	+	6.07771i	0.450491	+	0.204647i
$883$	−8.59085			−0.289105			−0.144553	−	0.989497i	$-0.546174\pi$
$883$	−8.59085			−0.289105			−0.144553	+	0.989497i	$0.546174\pi$
$884$	3.00670	+	40.1216i	0.101126	+	1.34944i
$885$	9.29972	+	2.86858i	0.312607	+	0.0964264i
$886$	−15.5043	+	2.33690i	−0.520878	+	0.0785097i
$887$	−19.6661	+	18.2475i	−0.660323	+	0.612691i	−0.937440	−	0.348146i	$-0.886811\pi$
$887$	−19.6661	+	18.2475i	−0.660323	+	0.612691i	0.277117	+	0.960836i	$0.410621\pi$
$888$	−0.202642	+	0.887832i	−0.00680022	+	0.0297937i
$889$	2.47415	+	15.2539i	0.0829804	+	0.511600i
$890$	−4.16177	−	18.2339i	−0.139503	−	0.611201i
$891$	−7.57720	−	5.16604i	−0.253846	−	0.173069i
$892$	11.4216	+	10.5977i	0.382422	+	0.354836i
$893$	−0.555961	+	0.379048i	−0.0186045	+	0.0126844i
$894$	18.8224	+	2.83702i	0.629516	+	0.0948843i
$895$	−10.2053	−	4.91462i	−0.341126	−	0.164278i
$896$	3.60756	+	0.781008i	0.120520	+	0.0260917i
$897$	41.0269	−	19.7575i	1.36985	−	0.659684i
$898$	−3.16502	+	0.976280i	−0.105618	+	0.0325789i
$899$	−2.54397	−	6.48194i	−0.0848463	−	0.216185i
$900$	0.190883	−	0.330620i	0.00636278	−	0.0110207i
$901$	−1.67511	−	2.90138i	−0.0558060	−	0.0966589i
$902$	25.9645	−	32.5585i	0.864525	−	1.08408i
$903$	9.14120	+	28.4981i	0.304200	+	0.948357i
$904$	0.308042	+	0.386272i	0.0102453	+	0.0128472i
$905$	−18.4238	+	46.9431i	−0.612428	+	1.56044i
$906$	−1.52597	+	20.3627i	−0.0506970	+	0.676505i
$907$	2.15166	−	28.7119i	0.0714447	−	0.953363i	−0.840172	−	0.542321i	$-0.817546\pi$
$907$	2.15166	−	28.7119i	0.0714447	−	0.953363i	0.911616	−	0.411042i	$-0.134835\pi$
$908$	−7.33916	+	18.6999i	−0.243559	+	0.620577i
$909$	2.32751	+	2.91860i	0.0771986	+	0.0968040i
$910$	−54.1884	−	20.5702i	−1.79633	−	0.681894i
$911$	−31.1144	+	39.0162i	−1.03087	+	1.29266i	−0.0755295	+	0.997144i	$0.524065\pi$
$911$	−31.1144	+	39.0162i	−1.03087	+	1.29266i	−0.955336	+	0.295521i	$0.904507\pi$
$912$	−1.17126	−	2.02868i	−0.0387843	−	0.0671764i
$913$	−4.40657	+	7.63240i	−0.145836	+	0.252596i
$914$	13.4196	+	34.1926i	0.443881	+	1.13099i
$915$	−0.177540	+	0.0547639i	−0.00586930	+	0.00181044i
$916$	26.1889	−	12.6119i	0.865306	−	0.416709i
$917$	5.00375	−	10.6951i	0.165238	−	0.353184i
$918$	41.7046	+	20.0839i	1.37646	+	0.662866i
$919$	−30.8314	−	4.64709i	−1.01704	−	0.153293i	−0.380694	−	0.924701i	$-0.624315\pi$
$919$	−30.8314	−	4.64709i	−1.01704	−	0.153293i	−0.636341	+	0.771408i	$0.719553\pi$
$920$	−2.23966	+	1.52698i	−0.0738395	+	0.0503430i
$921$	15.1278	+	14.0365i	0.498477	+	0.462519i
$922$	−52.1301	−	35.5417i	−1.71681	−	1.17050i
$923$	5.19709	+	22.7699i	0.171064	+	0.749481i
$924$	4.18998	−	14.1440i	0.137840	−	0.465303i
$925$	0.146057	−	0.639918i	0.00480233	−	0.0210404i
$926$	47.7790	−	44.3324i	1.57011	−	1.45685i
$927$	14.0884	−	2.12348i	0.462724	−	0.0697444i
$928$	−65.5869	−	20.2309i	−2.15300	−	0.664111i
$929$	0.307388	+	4.10181i	0.0100851	+	0.134576i	0.999974	−	0.00727180i	$-0.00231471\pi$
$929$	0.307388	+	4.10181i	0.0100851	+	0.134576i	−0.989888	+	0.141848i	$0.954696\pi$
$930$	−5.27411			−0.172945
$931$	2.49317	−	1.78289i	0.0817103	−	0.0584318i
$932$	−13.5282			−0.443130
$933$	−2.89218	−	38.5935i	−0.0946858	−	1.26349i
$934$	40.1221	+	12.3760i	1.31283	+	0.404956i
$935$	17.3790	−	2.61946i	0.568353	−	0.0856654i
$936$	0.632952	−	0.587294i	0.0206887	−	0.0191963i
$937$	−11.7963	+	51.6829i	−0.385367	+	1.68841i	0.294970	+	0.955506i	$0.404690\pi$
$937$	−11.7963	+	51.6829i	−0.385367	+	1.68841i	−0.680338	+	0.732899i	$0.738167\pi$
$938$	60.1181	−	24.3750i	1.96293	−	0.795871i
$939$	7.82831	+	34.2981i	0.255467	+	1.11928i
$940$	6.02694	+	4.10910i	0.196577	+	0.134024i
$941$	42.0056	+	38.9755i	1.36935	+	1.27057i	0.927675	+	0.373389i	$0.121804\pi$
$941$	42.0056	+	38.9755i	1.36935	+	1.27057i	0.441670	+	0.897178i	$0.354386\pi$
$942$	−57.1511	+	38.9650i	−1.86208	+	1.26955i
$943$	72.8697	+	10.9833i	2.37296	+	0.357667i
$944$	10.5114	+	5.06200i	0.342115	+	0.164754i
$945$	−26.3791	+	21.5242i	−0.858111	+	0.700183i
$946$	−28.0684	+	13.5170i	−0.912582	+	0.439477i
$947$	34.2167	−	10.5544i	1.11189	−	0.342973i	0.316211	−	0.948689i	$-0.397589\pi$
$947$	34.2167	−	10.5544i	1.11189	−	0.342973i	0.795681	+	0.605716i	$0.207113\pi$
$948$	2.62606	+	6.69110i	0.0852906	+	0.217317i
$949$	−25.8149	+	44.7128i	−0.837988	+	1.45144i
$950$	−0.0779821	−	0.135069i	−0.00253007	−	0.00438222i
$951$	−19.1339	+	23.9932i	−0.620460	+	0.778032i
$952$	−0.257942	+	1.85180i	−0.00835994	+	0.0600172i
$953$	−29.1457	−	36.5476i	−0.944123	−	1.18389i	−0.982806	−	0.184641i	$-0.940888\pi$
$953$	−29.1457	−	36.5476i	−0.944123	−	1.18389i	0.0386828	−	0.999252i	$-0.487684\pi$
$954$	−0.634662	+	1.61709i	−0.0205480	+	0.0523553i
$955$	2.22133	−	29.6416i	0.0718806	−	0.959180i
$956$	−2.66941	+	35.6208i	−0.0863349	+	1.15206i
$957$	−8.30302	+	21.1558i	−0.268399	+	0.683868i
$958$	29.8933	+	37.4850i	0.965808	+	1.21109i
$959$	11.4845	−	0.990085i	0.370855	−	0.0319715i
$960$	−17.2351	+	21.6121i	−0.556260	+	0.697528i
$961$	15.1648	+	26.2662i	0.489187	+	0.847296i
$962$	17.9345	−	31.0634i	0.578230	−	1.00152i
$963$	−1.15565	−	2.94455i	−0.0372403	−	0.0948868i
$964$	3.16202	−	0.975353i	0.101842	−	0.0314140i
$965$	22.0413	−	10.6146i	0.709536	−	0.341695i
$966$	49.7157	−	11.9345i	1.59958	−	0.383987i
$967$	−39.2046	−	18.8800i	−1.26074	−	0.607139i	−0.320367	−	0.947294i	$-0.603806\pi$
$967$	−39.2046	−	18.8800i	−1.26074	−	0.607139i	−0.940369	+	0.340155i	$0.889520\pi$
$968$	−1.27020	−	0.191452i	−0.0408258	−	0.00615350i
$969$	2.05133	−	1.39857i	0.0658982	−	0.0449286i
$970$	13.6688	+	12.6828i	0.438879	+	0.407220i
$971$	−14.1610	−	9.65483i	−0.454449	−	0.309838i	0.314375	−	0.949299i	$-0.398205\pi$
$971$	−14.1610	−	9.65483i	−0.454449	−	0.309838i	−0.768824	+	0.639461i	$0.779158\pi$
$972$	−4.75257	−	20.8224i	−0.152439	−	0.667877i
$973$	18.0637	+	10.1611i	0.579097	+	0.325751i
$974$	−10.6561	+	46.6873i	−0.341442	+	1.49596i
$975$	0.861716	−	0.799556i	0.0275970	−	0.0256063i
$976$	−0.220241	+	0.0331960i	−0.00704974	+	0.00106258i
$977$	31.7054	+	9.77982i	1.01435	+	0.312884i	0.756986	−	0.653431i	$-0.226671\pi$
$977$	31.7054	+	9.77982i	1.01435	+	0.312884i	0.257360	+	0.966316i	$0.417147\pi$
$978$	−4.76997	−	63.6508i	−0.152527	−	2.03533i
$979$	−7.75958			−0.247997
$980$	−27.8657	−	18.0979i	−0.890136	−	0.578118i
$981$	−3.43500			−0.109671
$982$	−0.444087	−	5.92593i	−0.0141714	−	0.189104i
$983$	−57.6363	−	17.7784i	−1.83831	−	0.567044i	−0.999753	−	0.0222351i	$-0.992922\pi$
$983$	−57.6363	−	17.7784i	−1.83831	−	0.567044i	−0.838560	−	0.544809i	$-0.816602\pi$
$984$	−2.60990	+	0.393380i	−0.0832007	+	0.0125405i
$985$	9.46890	−	8.78586i	0.301704	−	0.279941i
$986$	15.4870	−	67.8528i	0.493205	−	2.16087i
$987$	−3.26023	−	4.66868i	−0.103774	−	0.148606i
$988$	−0.968310	−	4.24244i	−0.0308060	−	0.134970i
$989$	−45.5498	−	31.0554i	−1.44840	−	0.987503i
$990$	−6.68047	−	6.19857i	−0.212319	−	0.197004i
$991$	37.0562	−	25.2645i	1.17713	−	0.802553i	0.193208	−	0.981158i	$-0.438111\pi$
$991$	37.0562	−	25.2645i	1.17713	−	0.802553i	0.983921	+	0.178605i	$0.0571583\pi$
$992$	−6.53458	−	0.984930i	−0.207473	−	0.0312715i
$993$	−16.0387	−	7.72383i	−0.508973	−	0.245108i
$994$	0.293638	+	26.2218i	0.00931362	+	0.831706i
$995$	−27.9224	+	13.4467i	−0.885199	+	0.426289i
$996$	12.8966	−	3.97806i	0.408643	−	0.126050i
$997$	−0.421446	−	1.07383i	−0.0133473	−	0.0340084i	0.924045	−	0.382284i	$-0.124862\pi$
$997$	−0.421446	−	1.07383i	−0.0133473	−	0.0340084i	−0.937392	+	0.348276i	$0.886767\pi$
$998$	−2.05769	+	3.56402i	−0.0651350	+	0.112817i
$999$	−10.5346	−	18.2465i	−0.333301	−	0.577294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.g.a.32.1	yes	48
3.2	odd	2		441.2.bb.d.424.4		48
4.3	odd	2		784.2.bg.c.81.1		48
7.2	even	3		343.2.g.i.30.1		48
7.3	odd	6		343.2.e.c.197.7		48
7.4	even	3		343.2.e.d.197.7		48
7.5	odd	6		343.2.g.h.30.1		48
7.6	odd	2		343.2.g.g.116.1		48
49.4	even	21		343.2.e.d.148.7		48
49.11	even	21		2401.2.a.h.1.5		24
49.22	even	7		343.2.g.i.263.1		48
49.23	even	21	inner	49.2.g.a.23.1	✓	48
49.26	odd	42		343.2.g.g.275.1		48
49.27	odd	14		343.2.g.h.263.1		48
49.38	odd	42		2401.2.a.i.1.5		24
49.45	odd	42		343.2.e.c.148.7		48
147.23	odd	42		441.2.bb.d.415.4		48
196.23	odd	42		784.2.bg.c.513.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.1	✓	48	49.23	even	21	inner
49.2.g.a.32.1	yes	48	1.1	even	1	trivial
343.2.e.c.148.7		48	49.45	odd	42
343.2.e.c.197.7		48	7.3	odd	6
343.2.e.d.148.7		48	49.4	even	21
343.2.e.d.197.7		48	7.4	even	3
343.2.g.g.116.1		48	7.6	odd	2
343.2.g.g.275.1		48	49.26	odd	42
343.2.g.h.30.1		48	7.5	odd	6
343.2.g.h.263.1		48	49.27	odd	14
343.2.g.i.30.1		48	7.2	even	3
343.2.g.i.263.1		48	49.22	even	7
441.2.bb.d.415.4		48	147.23	odd	42
441.2.bb.d.424.4		48	3.2	odd	2
784.2.bg.c.81.1		48	4.3	odd	2
784.2.bg.c.513.1		48	196.23	odd	42
2401.2.a.h.1.5		24	49.11	even	21
2401.2.a.i.1.5		24	49.38	odd	42

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.151065 - 2.01582i) q^{2} +(1.33832 + 0.412818i) q^{3} +(-2.06305 + 0.310954i) q^{4} +(-1.66779 + 1.54748i) q^{5} +(0.629993 - 2.76018i) q^{6} +(-1.77774 + 1.95950i) q^{7} +(0.0388416 + 0.170176i) q^{8} +(-0.858025 - 0.584992i) q^{9} +O(q^{10})\)	\(q+(-0.151065 - 2.01582i) q^{2} +(1.33832 + 0.412818i) q^{3} +(-2.06305 + 0.310954i) q^{4} +(-1.66779 + 1.54748i) q^{5} +(0.629993 - 2.76018i) q^{6} +(-1.77774 + 1.95950i) q^{7} +(0.0388416 + 0.170176i) q^{8} +(-0.858025 - 0.584992i) q^{9} +(3.37138 + 3.12819i) q^{10} +(1.57656 - 1.07488i) q^{11} +(-2.88939 - 0.435506i) q^{12} +(4.29166 + 2.06676i) q^{13} +(4.21856 + 3.28759i) q^{14} +(-2.87087 + 1.38254i) q^{15} +(-3.65014 + 1.12592i) q^{16} +(-1.47907 - 3.76862i) q^{17} +(-1.04962 + 1.81800i) q^{18} +(0.218933 + 0.379203i) q^{19} +(2.95953 - 3.71113i) q^{20} +(-3.18811 + 1.88857i) q^{21} +(-2.40493 - 3.01568i) q^{22} +(2.49370 - 6.35384i) q^{23} +(-0.0182692 + 0.243785i) q^{24} +(0.0131678 - 0.175712i) q^{25} +(3.51789 - 8.96343i) q^{26} +(-3.52650 - 4.42209i) q^{27} +(3.05824 - 4.59534i) q^{28} +(-5.30231 + 6.64889i) q^{29} +(3.22063 + 5.57829i) q^{30} +(-0.409400 + 0.709102i) q^{31} +(2.94860 + 7.51291i) q^{32} +(2.55367 - 0.787704i) q^{33} +(-7.37342 + 3.55085i) q^{34} +(-0.0674026 - 6.01904i) q^{35} +(1.95205 + 0.940059i) q^{36} +(3.68347 + 0.555193i) q^{37} +(0.731331 - 0.498613i) q^{38} +(4.89044 + 4.53766i) q^{39} +(-0.328124 - 0.223711i) q^{40} +(2.40243 + 10.5257i) q^{41} +(4.28862 + 6.14135i) q^{42} +(1.79724 - 7.87423i) q^{43} +(-2.91827 + 2.70776i) q^{44} +(2.33627 - 0.352135i) q^{45} +(-13.1849 - 4.06701i) q^{46} +(0.114840 + 1.53244i) q^{47} -5.34987 q^{48} +(-0.679297 - 6.96696i) q^{49} -0.356192 q^{50} +(-0.423725 - 5.65422i) q^{51} +(-9.49656 - 2.92930i) q^{52} +(0.818284 - 0.123336i) q^{53} +(-8.38140 + 7.77681i) q^{54} +(-0.966009 + 4.23236i) q^{55} +(-0.402511 - 0.226418i) q^{56} +(0.136461 + 0.597875i) q^{57} +(14.2040 + 9.68409i) q^{58} +(-2.23892 - 2.07741i) q^{59} +(5.49282 - 3.74494i) q^{60} +(0.0576570 + 0.00869039i) q^{61} +(1.49127 + 0.718157i) q^{62} +(2.67164 - 0.641340i) q^{63} +(7.81612 - 3.76404i) q^{64} +(-10.3558 + 3.19435i) q^{65} +(-1.97364 - 5.02875i) q^{66} +(6.06468 - 10.5043i) q^{67} +(4.22327 + 7.31491i) q^{68} +(5.96036 - 7.47405i) q^{69} +(-12.1231 + 1.04514i) q^{70} +(3.05705 + 3.83342i) q^{71} +(0.0662246 - 0.168737i) q^{72} +(-0.809992 + 10.8086i) q^{73} +(0.562728 - 7.50908i) q^{74} +(0.0901597 - 0.229723i) q^{75} +(-0.569583 - 0.714235i) q^{76} +(-0.696479 + 5.00012i) q^{77} +(8.40834 - 10.5437i) q^{78} +(-1.22996 - 2.13036i) q^{79} +(4.34532 - 7.52631i) q^{80} +(-1.75589 - 4.47393i) q^{81} +(20.8550 - 6.43292i) q^{82} +(-4.16137 + 2.00401i) q^{83} +(5.98995 - 4.88755i) q^{84} +(8.29864 + 3.99642i) q^{85} +(-16.1445 - 2.43340i) q^{86} +(-9.84099 + 6.70947i) q^{87} +(0.244155 + 0.226543i) q^{88} +(-3.36000 - 2.29081i) q^{89} +(-1.06277 - 4.65630i) q^{90} +(-11.6793 + 4.73537i) q^{91} +(-3.16886 + 13.8837i) q^{92} +(-0.840641 + 0.780000i) q^{93} +(3.07177 - 0.462994i) q^{94} +(-0.951941 - 0.293635i) q^{95} +(0.844715 + 11.2719i) q^{96} +4.05436 q^{97} +(-13.9415 + 2.42180i) q^{98} -1.98152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Introduction

L-functions

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