LMFDB - Embedded newform 49.2.g.a.23.1

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			23.1
Character	$\chi$	$=$	49.23
Dual form			49.2.g.a.32.1

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

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

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	0.644068	+	0.764969i	$0.277246\pi$
$2$	−0.151065	+	2.01582i	−0.106819	+	1.42540i	−0.750887	+	0.660431i	$0.770374\pi$
$3$	1.33832	−	0.412818i	0.772681	−	0.238341i	0.116750	−	0.993161i	$-0.462752\pi$
$3$	1.33832	−	0.412818i	0.772681	−	0.238341i	0.655931	+	0.754821i	$0.272276\pi$
$4$	−2.06305	−	0.310954i	−1.03152	−	0.155477i
$5$	−1.66779	−	1.54748i	−0.745857	−	0.692054i	0.212649	−	0.977129i	$-0.431791\pi$
$5$	−1.66779	−	1.54748i	−0.745857	−	0.692054i	−0.958505	+	0.285075i	$0.907982\pi$
$6$	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	0.777185	−	0.629272i	$-0.216647\pi$
$11$	1.57656	+	1.07488i	0.475350	+	0.324088i	−0.301835	+	0.953360i	$0.597599\pi$
$12$	−2.88939	+	0.435506i	−0.834095	+	0.125720i
$13$	4.29166	−	2.06676i	1.19029	−	0.573215i	0.269399	−	0.963029i	$-0.413175\pi$
$13$	4.29166	−	2.06676i	1.19029	−	0.573215i	0.920894	+	0.389814i	$0.127461\pi$
$14$	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	0.631602	+	0.775293i	$0.282398\pi$
$17$	−1.47907	+	3.76862i	−0.358728	+	0.914025i	−0.990330	+	0.138732i	$0.955697\pi$
$18$	−1.04962	−	1.81800i	−0.247398	−	0.428506i
$19$	0.218933	−	0.379203i	0.0502266	−	0.0869951i	−0.839819	−	0.542866i	$-0.817339\pi$
$19$	0.218933	−	0.379203i	0.0502266	−	0.0869951i	0.890046	+	0.455871i	$0.150672\pi$
$20$	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	0.913980	+	0.405760i	$0.132993\pi$
$23$	2.49370	+	6.35384i	0.519972	+	1.32487i	−0.394007	+	0.919107i	$0.628912\pi$
$24$	−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	−0.972057	−	0.234747i	$-0.924574\pi$
$29$	−5.30231	−	6.64889i	−0.984615	−	1.23467i	−0.0125582	−	0.999921i	$-0.503997\pi$
$30$	3.22063	−	5.57829i	0.588004	−	1.01845i
$31$	−0.409400	−	0.709102i	−0.0735305	−	0.127359i	0.826916	−	0.562326i	$-0.190093\pi$
$31$	−0.409400	−	0.709102i	−0.0735305	−	0.127359i	−0.900446	+	0.434967i	$0.856760\pi$
$32$	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	0.160896	−	0.986971i	$-0.448562\pi$
$37$	3.68347	−	0.555193i	0.605558	−	0.0912732i	0.444663	+	0.895698i	$0.353324\pi$
$38$	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	−0.336741	−	0.941597i	$-0.609325\pi$
$41$	2.40243	−	10.5257i	0.375196	−	1.64384i	0.711937	−	0.702243i	$-0.247818\pi$
$42$	4.28862	−	6.14135i	0.661748	−	0.947631i
$43$	1.79724	+	7.87423i	0.274077	+	1.20081i	0.905152	+	0.425088i	$0.139757\pi$
$43$	1.79724	+	7.87423i	0.274077	+	1.20081i	−0.631075	+	0.775722i	$0.717386\pi$
$44$	−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	−0.982545	−	0.186024i	$-0.940440\pi$
$47$	0.114840	−	1.53244i	0.0167512	−	0.223529i	0.999296	−	0.0375051i	$-0.0119410\pi$
$48$	−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	0.205001	−	0.978762i	$-0.434280\pi$
$53$	0.818284	+	0.123336i	0.112400	+	0.0169416i	−0.0926014	+	0.995703i	$0.529518\pi$
$54$	−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	−0.812336	−	0.583190i	$-0.801804\pi$
$59$	−2.23892	+	2.07741i	−0.291482	+	0.270456i	0.520854	+	0.853646i	$0.325614\pi$
$60$	5.49282	+	3.74494i	0.709120	+	0.483470i
$61$	0.0576570	−	0.00869039i	0.00738222	−	0.00111269i	−0.145350	−	0.989380i	$-0.546431\pi$
$61$	0.0576570	−	0.00869039i	0.00738222	−	0.00111269i	0.152732	+	0.988268i	$0.451193\pi$
$62$	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	0.952078	+	0.305857i	$0.0989429\pi$
$67$	6.06468	+	10.5043i	0.740918	+	1.28331i	−0.211159	+	0.977452i	$0.567724\pi$
$68$	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	−0.566606	−	0.823989i	$-0.691744\pi$
$71$	3.05705	−	3.83342i	0.362805	−	0.454944i	0.929411	+	0.369045i	$0.120315\pi$
$72$	0.0662246	+	0.168737i	0.00780464	+	0.0198859i
$73$	−0.809992	−	10.8086i	−0.0948024	−	1.26505i	−0.818328	−	0.574752i	$-0.805098\pi$
$73$	−0.809992	−	10.8086i	−0.0948024	−	1.26505i	0.723525	−	0.690298i	$-0.242521\pi$
$74$	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	−0.926884	−	0.375347i	$-0.877523\pi$
$79$	−1.22996	+	2.13036i	−0.138382	+	0.239684i	0.788502	+	0.615032i	$0.210857\pi$
$80$	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	0.191328	−	0.981526i	$-0.438721\pi$
$83$	−4.16137	−	2.00401i	−0.456769	−	0.219968i	−0.648097	+	0.761558i	$0.724435\pi$
$84$	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	−0.728160	−	0.685407i	$-0.759624\pi$
$89$	−3.36000	+	2.29081i	−0.356159	+	0.242825i	0.372001	+	0.928232i	$0.378672\pi$
$90$	−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	−0.460902	−	0.887451i	$-0.652474\pi$
$101$	−3.43504	+	1.05957i	−0.341799	+	0.105431i	0.119104	+	0.992882i	$0.461998\pi$
$102$	−11.3339	−	1.70831i	−1.12222	−	0.169148i
$103$	−10.0573	−	9.33178i	−0.990972	−	0.919487i	0.00578335	−	0.999983i	$-0.498159\pi$
$103$	−10.0573	−	9.33178i	−0.990972	−	0.919487i	−0.996755	+	0.0804960i	$0.974350\pi$
$104$	−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	−0.435529	−	0.900175i	$-0.643439\pi$
$107$	2.51675	−	1.71589i	0.243303	−	0.165881i	0.678832	+	0.734293i	$0.262486\pi$
$108$	8.65040	−	8.02640i	0.832385	−	0.772340i
$109$	2.73299	+	1.86332i	0.261773	+	0.178473i	0.687093	−	0.726569i	$-0.258886\pi$
$109$	2.73299	+	1.86332i	0.261773	+	0.178473i	−0.425321	+	0.905043i	$0.639839\pi$
$110$	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	0.549970	−	0.835185i	$-0.314639\pi$
$113$	2.55014	+	1.22808i	0.239897	+	0.115528i	−0.310073	+	0.950713i	$0.600353\pi$
$114$	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	0.916696	−	0.399585i	$-0.130846\pi$
$127$	3.64167	+	4.56651i	0.323146	+	0.405212i	−0.593550	+	0.804797i	$0.702274\pi$
$128$	−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	0.102797	−	0.994702i	$-0.467221\pi$
$131$	−4.26464	−	1.31547i	−0.372603	−	0.114933i	−0.475401	+	0.879769i	$0.657697\pi$
$132$	−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	−0.804721	−	0.593653i	$-0.797685\pi$
$137$	−3.19380	+	2.96341i	−0.272865	+	0.253181i	0.531856	+	0.846835i	$0.321495\pi$
$138$	−15.9667	+	10.8859i	−1.35918	+	0.926673i
$139$	−1.74312	+	7.63711i	−0.147849	+	0.647771i	0.845631	+	0.533768i	$0.179224\pi$
$139$	−1.74312	+	7.63711i	−0.147849	+	0.647771i	−0.993480	+	0.114003i	$0.963633\pi$
$140$	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	−0.938061	−	0.346471i	$-0.887380\pi$
$149$	0.502440	−	6.70459i	0.0411615	−	0.549262i	0.979222	−	0.202791i	$-0.0650011\pi$
$150$	−0.476700	+	0.147043i	−0.0389224	+	0.0120060i
$151$	−7.13195	−	1.07497i	−0.580390	−	0.0874796i	−0.147715	−	0.989030i	$-0.547192\pi$
$151$	−7.13195	−	1.07497i	−0.580390	−	0.0874796i	−0.432674	+	0.901550i	$0.642430\pi$
$152$	−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	−0.563334	+	0.826229i	$0.690482\pi$
$157$	−17.9097	+	16.6178i	−1.42935	+	1.32624i	−0.866017	+	0.500015i	$0.833328\pi$
$158$	−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	0.982097	−	0.188378i	$-0.0603230\pi$
$163$	21.5436	+	6.64532i	1.68743	+	0.520502i	0.705329	+	0.708880i	$0.250799\pi$
$164$	−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	0.460459	−	0.887681i	$-0.347685\pi$
$167$	−6.55741	−	8.22273i	−0.507427	−	0.636294i	−0.967887	+	0.251387i	$0.919113\pi$
$168$	−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	0.981031	−	0.193853i	$-0.0620985\pi$
$173$	1.71029	+	4.35774i	0.130031	+	0.331313i	−0.851000	+	0.525166i	$0.824003\pi$
$174$	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	−0.846643	−	0.532161i	$-0.821380\pi$
$179$	1.81890	−	4.63449i	0.135951	−	0.346398i	0.982595	+	0.185763i	$0.0594755\pi$
$180$	−4.71033	−	1.45294i	−0.351087	−	0.108296i
$181$	19.9703	+	9.61720i	1.48438	+	0.714841i	0.988170	−	0.153360i	$-0.0490095\pi$
$181$	19.9703	+	9.61720i	1.48438	+	0.714841i	0.496212	+	0.868201i	$0.334724\pi$
$182$	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	0.252895	−	0.967494i	$-0.418617\pi$
$191$	−9.57738	−	8.88651i	−0.692995	−	0.643005i	−0.945890	+	0.324488i	$0.894808\pi$
$192$	12.0144	+	1.81087i	0.867062	+	0.130689i
$193$	−10.2751	+	3.16945i	−0.739618	+	0.228142i	−0.641597	−	0.767042i	$-0.721728\pi$
$193$	−10.2751	+	3.16945i	−0.739618	+	0.228142i	−0.0980217	+	0.995184i	$0.531251\pi$
$194$	−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	0.203241	−	0.979129i	$-0.434853\pi$
$199$	13.0167	−	4.01512i	0.922729	−	0.284624i	0.719488	+	0.694505i	$0.244376\pi$
$200$	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	−0.139521	−	0.990219i	$-0.544556\pi$
$211$	−14.5359	−	7.00014i	−1.00069	−	0.481909i	−0.861174	+	0.508310i	$0.830270\pi$
$212$	−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	−0.912897	−	0.408190i	$-0.866160\pi$
$223$	−4.65621	+	5.83871i	−0.311803	+	0.390989i	0.601094	+	0.799178i	$0.294732\pi$
$224$	−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	0.980391	−	0.197062i	$-0.0631401\pi$
$227$	4.81428	+	8.33857i	0.319535	+	0.553450i	−0.660856	+	0.750512i	$0.729807\pi$
$228$	−0.467437	+	1.19101i	−0.0309568	+	0.0788766i
$229$	−13.3133	−	4.10660i	−0.879765	−	0.271372i	−0.178215	−	0.983992i	$-0.557032\pi$
$229$	−13.3133	−	4.10660i	−0.879765	−	0.271372i	−0.701550	+	0.712620i	$0.747508\pi$
$230$	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	0.0643811	−	0.997925i	$-0.479493\pi$
$233$	6.41172	−	0.966411i	0.420046	−	0.0633117i	0.355665	+	0.934614i	$0.384255\pi$
$234$	−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	0.935032	+	0.354563i	$0.115370\pi$
$239$	3.80981	+	16.6919i	0.246436	+	1.07971i	−0.688596	+	0.725145i	$0.741773\pi$
$240$	8.92244	+	8.27881i	0.575941	+	0.534395i
$241$	−1.56832	−	0.236387i	−0.101025	−	0.0152270i	0.0983354	−	0.995153i	$-0.468648\pi$
$241$	−1.56832	−	0.236387i	−0.101025	−	0.0152270i	−0.199360	+	0.979926i	$0.563886\pi$
$242$	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	0.945280	+	0.326261i	$0.105789\pi$
$251$	3.72581	+	16.3239i	0.235171	+	1.03035i	−0.710109	+	0.704092i	$0.751354\pi$
$252$	−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	0.845069	−	0.534658i	$-0.179559\pi$
$257$	29.0195	−	4.37399i	1.81019	−	0.272842i	0.965118	+	0.261816i	$0.0843214\pi$
$258$	−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	0.656391	−	0.754421i	$-0.272082\pi$
$263$	−5.27309	−	9.13326i	−0.325153	−	0.563181i	−0.981543	+	0.191240i	$0.938749\pi$
$264$	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	−0.968395	−	0.249423i	$-0.919759\pi$
$269$	−0.787107	−	10.5032i	−0.0479907	−	0.640392i	0.920404	−	0.390969i	$-0.127860\pi$
$270$	1.94394	+	25.9401i	0.118305	+	1.57866i
$271$	−9.07595	−	23.1251i	−0.551324	−	1.40475i	−0.886558	−	0.462617i	$-0.846911\pi$
$271$	−9.07595	−	23.1251i	−0.551324	−	1.40475i	0.335234	−	0.942135i	$-0.391185\pi$
$272$	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	−0.710112	−	0.704089i	$-0.751356\pi$
$277$	4.81556	−	12.2698i	0.289339	−	0.737223i	0.999451	−	0.0331346i	$-0.0105490\pi$
$278$	−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	0.202161	−	0.979352i	$-0.435204\pi$
$281$	18.3370	−	8.83064i	1.09389	−	0.526792i	0.891734	+	0.452561i	$0.149489\pi$
$282$	4.30215	−	0.648445i	0.256189	−	0.0386143i
$283$	19.0449	+	12.9846i	1.13210	+	0.771854i	0.976404	−	0.215950i	$-0.0692849\pi$
$283$	19.0449	+	12.9846i	1.13210	+	0.771854i	0.155698	+	0.987805i	$0.450237\pi$
$284$	−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	−0.0148260	−	0.999890i	$-0.504719\pi$
$307$	13.2755	−	6.39317i	0.757676	−	0.364877i	0.772502	+	0.635013i	$0.219005\pi$
$308$	−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	0.292238	+	0.956346i	$0.405600\pi$
$311$	−10.0956	+	25.7231i	−0.572468	+	1.45862i	−0.864706	+	0.502279i	$0.832495\pi$
$312$	−0.582249	−	1.00849i	−0.0329634	−	0.0570943i
$313$	12.5594	−	21.7536i	0.709901	−	1.22958i	−0.254993	−	0.966943i	$-0.582073\pi$
$313$	12.5594	−	21.7536i	0.709901	−	1.22958i	0.964894	−	0.262641i	$-0.0845936\pi$
$314$	−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	−0.958580	−	0.284824i	$-0.908065\pi$
$317$	−8.00526	−	20.3971i	−0.449620	−	1.14561i	0.508959	−	0.860791i	$-0.330030\pi$
$318$	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	−0.485067	−	0.874477i	$-0.661205\pi$
$331$	−12.5685	+	1.89440i	−0.690828	+	0.104126i	−0.205761	+	0.978602i	$0.565967\pi$
$332$	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	−0.998760	−	0.0497856i	$-0.984146\pi$
$337$	−2.21226	−	9.69255i	−0.120509	−	0.527987i	0.878250	−	0.478201i	$-0.158711\pi$
$338$	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	0.576066	−	0.817403i	$-0.304587\pi$
$347$	16.4970	+	2.48652i	0.885605	+	0.133483i	0.309539	+	0.950887i	$0.399825\pi$
$348$	18.2161	+	16.9021i	0.976485	+	0.906045i
$349$	0.185225	+	0.811522i	0.00991484	+	0.0434398i	0.979643	−	0.200746i	$-0.0643365\pi$
$349$	0.185225	+	0.811522i	0.00991484	+	0.0434398i	−0.969729	+	0.244186i	$0.921479\pi$
$350$	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	−0.0831665	+	0.996536i	$0.526503\pi$
$353$	−20.3502	+	18.8822i	−1.08313	+	1.00500i	−0.999964	+	0.00846270i	$0.997306\pi$
$354$	−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	0.861431	−	0.507875i	$-0.169569\pi$
$359$	24.3867	+	7.52231i	1.28708	+	0.397012i	0.425652	+	0.904887i	$0.360045\pi$
$360$	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	0.860314	+	0.509764i	$0.170267\pi$
$367$	1.63958	+	21.8787i	0.0855854	+	1.14206i	−0.774729	+	0.632293i	$0.782114\pi$
$368$	−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	0.166547	+	0.986034i	$0.446738\pi$
$373$	−14.8839	+	25.7796i	−0.770657	+	1.33482i	−0.937204	+	0.348783i	$0.886595\pi$
$374$	−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	−0.589935	−	0.807451i	$-0.700846\pi$
$379$	−6.35554	+	3.06067i	−0.326462	+	0.157216i	0.263473	+	0.964667i	$0.415132\pi$
$380$	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	−0.813066	−	0.582171i	$-0.802203\pi$
$383$	−11.1196	+	7.58121i	−0.568184	+	0.387382i	0.244882	+	0.969553i	$0.421251\pi$
$384$	−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	0.00860837	−	0.999963i	$-0.497260\pi$
$389$	11.4201	−	3.52262i	0.579020	−	0.178604i	0.570412	+	0.821359i	$0.306784\pi$
$390$	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	0.769426	−	0.638736i	$-0.220542\pi$
$397$	3.78525	+	3.51219i	0.189976	+	0.176272i	−0.579450	+	0.815008i	$0.696733\pi$
$398$	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	−0.154284	−	0.988027i	$-0.549307\pi$
$401$	14.1993	−	9.68089i	0.709077	−	0.483441i	0.863362	+	0.504586i	$0.168355\pi$
$402$	−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	−0.589243	−	0.807956i	$-0.700574\pi$
$409$	7.93281	−	20.2125i	0.392252	−	0.999442i	0.981495	−	0.191486i	$-0.0613308\pi$
$410$	−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	−0.914911	−	0.403656i	$-0.867739\pi$
$419$	−6.50497	+	8.15697i	−0.317788	+	0.398494i	0.597122	+	0.802150i	$0.296311\pi$
$420$	−2.42658	−	17.4207i	−0.118405	−	0.850044i
$421$	−6.92877	−	8.68841i	−0.337688	−	0.423447i	0.583774	−	0.811916i	$-0.301575\pi$
$421$	−6.92877	−	8.68841i	−0.337688	−	0.423447i	−0.921462	+	0.388469i	$0.873004\pi$
$422$	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	−0.165445	−	0.986219i	$-0.552906\pi$
$431$	16.7258	−	15.5193i	0.805653	−	0.747537i	0.971098	+	0.238682i	$0.0767154\pi$
$432$	17.8511	−	12.1707i	0.858863	−	0.585563i
$433$	−3.39696	+	14.8831i	−0.163247	+	0.715234i	0.825346	+	0.564627i	$0.190980\pi$
$433$	−3.39696	+	14.8831i	−0.163247	+	0.715234i	−0.988594	+	0.150607i	$0.951877\pi$
$434$	−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	0.960876	+	0.276980i	$0.0893336\pi$
$439$	−0.640084	+	8.54133i	−0.0305495	+	0.407655i	−0.991425	+	0.130675i	$0.958285\pi$
$440$	−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	0.966359	+	0.257195i	$0.0827984\pi$
$443$	−0.579640	+	7.73476i	−0.0275395	+	0.367490i	−0.993899	+	0.110294i	$0.964821\pi$
$444$	−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	−0.982802	−	0.184661i	$-0.940881\pi$
$449$	−0.364600	+	1.59742i	−0.0172065	+	0.0753867i	0.965596	+	0.260048i	$0.0837384\pi$
$450$	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	−0.139304	−	0.990250i	$-0.544487\pi$
$457$	−17.3635	−	5.35593i	−0.812231	−	0.250540i	−0.672926	+	0.739710i	$0.734963\pi$
$458$	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	0.990146	+	0.140039i	$0.0447227\pi$
$461$	19.4601	+	24.4021i	0.906345	+	1.13652i	−0.0838006	+	0.996483i	$0.526706\pi$
$462$	13.3625	−	5.07245i	0.621678	−	0.235992i
$463$	20.1031	−	25.2085i	0.934272	−	1.17154i	−0.0506807	−	0.998715i	$-0.516139\pi$
$463$	20.1031	−	25.2085i	0.934272	−	1.17154i	0.984953	−	0.172825i	$-0.0552895\pi$
$464$	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	−0.991907	−	0.126970i	$-0.959475\pi$
$467$	−7.58840	−	19.3349i	−0.351149	−	0.894713i	0.640757	−	0.767743i	$-0.278620\pi$
$468$	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	0.0257593	−	0.999668i	$-0.491800\pi$
$479$	−19.5967	−	13.3608i	−0.895395	−	0.610470i	−0.921154	+	0.389198i	$0.872752\pi$
$480$	−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	−0.761593	−	0.648056i	$-0.775582\pi$
$487$	−22.6372	+	6.98264i	−1.02579	+	0.316414i	−0.264195	+	0.964469i	$0.585106\pi$
$488$	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	−0.600385	−	0.799711i	$-0.704986\pi$
$499$	−1.68208	+	1.14682i	−0.0753004	+	0.0513389i	0.525085	+	0.851050i	$0.324034\pi$
$500$	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	−0.265920	−	0.963995i	$-0.585676\pi$
$503$	7.22087	−	3.47739i	0.321963	−	0.155049i	0.587883	+	0.808946i	$0.299961\pi$
$504$	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	−0.990276	−	0.139114i	$-0.955575\pi$
$509$	−8.45276	+	14.6406i	−0.374662	+	0.648934i	0.615614	+	0.788048i	$0.288908\pi$
$510$	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	0.951180	−	0.308637i	$-0.0998728\pi$
$521$	4.75459	+	8.23520i	0.208303	+	0.360791i	−0.742877	+	0.669427i	$0.766539\pi$
$522$	−6.52224	+	16.6184i	−0.285471	+	0.727367i
$523$	20.1529	+	6.21634i	0.881223	+	0.271821i	0.702163	−	0.712017i	$-0.252218\pi$
$523$	20.1529	+	6.21634i	0.881223	+	0.271821i	0.179061	+	0.983838i	$0.442694\pi$
$524$	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	0.843867	+	0.536553i	$0.180274\pi$
$541$	−1.64081	+	21.8950i	−0.0705438	+	0.941341i	−0.914410	+	0.404788i	$0.867345\pi$
$542$	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	−0.559423	−	0.828883i	$-0.688977\pi$
$547$	7.11554	−	31.1752i	0.304238	−	1.33296i	0.863661	−	0.504073i	$-0.168166\pi$
$548$	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	−0.998201	−	0.0599605i	$-0.980903\pi$
$557$	−13.0047	−	22.5248i	−0.551028	−	0.954408i	0.447173	−	0.894447i	$-0.352431\pi$
$558$	−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	0.994140	+	0.108098i	$0.0344761\pi$
$563$	0.645745	+	8.61687i	0.0272149	+	0.363158i	−0.966925	+	0.255060i	$0.917905\pi$
$564$	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	−0.757313	−	0.653053i	$-0.773488\pi$
$569$	4.45835	−	7.72209i	0.186904	−	0.323727i	0.944216	+	0.329326i	$0.106821\pi$
$570$	−1.41020	−	2.44254i	−0.0590669	−	0.102307i
$571$	9.98494	−	25.4412i	0.417857	−	1.06468i	−0.554707	−	0.832046i	$-0.687170\pi$
$571$	9.98494	−	25.4412i	0.417857	−	1.06468i	0.972564	−	0.232636i	$-0.0747350\pi$
$572$	−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	−0.975817	−	0.218591i	$-0.929854\pi$
$577$	−36.8913	−	25.1520i	−1.53580	−	1.04709i	−0.559986	−	0.828502i	$-0.689194\pi$
$578$	−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	0.115569	−	0.993299i	$-0.463131\pi$
$593$	−21.0962	−	19.5744i	−0.866317	−	0.803825i	−0.981886	+	0.189475i	$0.939321\pi$
$594$	−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	0.294126	−	0.955767i	$-0.404972\pi$
$599$	−11.9464	−	8.14491i	−0.488116	−	0.332792i	−0.782242	+	0.622975i	$0.785924\pi$
$600$	0.0425953	−	0.00642021i	0.00173895	−	0.000262104i
$601$	23.2856	−	11.2137i	0.949839	−	0.457418i	0.106209	−	0.994344i	$-0.466129\pi$
$601$	23.2856	−	11.2137i	0.949839	−	0.457418i	0.843630	+	0.536926i	$0.180414\pi$
$602$	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	0.470996	+	0.882136i	$0.343895\pi$
$607$	−13.0197	+	22.5508i	−0.528454	+	0.915309i	−0.999450	+	0.0331736i	$0.989439\pi$
$608$	−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	−0.932216	−	0.361903i	$-0.882127\pi$
$613$	−1.59326	−	21.2605i	−0.0643510	−	0.858704i	0.867865	−	0.496801i	$-0.165492\pi$
$614$	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	0.801733	+	0.597682i	$0.203911\pi$
$617$	29.9571	+	37.5650i	1.20603	+	1.51231i	0.404294	+	0.914629i	$0.367517\pi$
$618$	19.4214	−	33.6388i	0.781243	−	1.35315i
$619$	−18.6273	−	32.2635i	−0.748696	−	1.29678i	−0.948448	−	0.316934i	$-0.897347\pi$
$619$	−18.6273	−	32.2635i	−0.748696	−	1.29678i	0.199751	−	0.979847i	$-0.435987\pi$
$620$	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	0.976564	+	0.215226i	$0.0690489\pi$
$631$	4.77509	+	20.9210i	0.190093	+	0.832854i	−0.786471	+	0.617627i	$0.788094\pi$
$632$	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	−0.458983	−	0.888445i	$-0.651786\pi$
$641$	−29.3549	−	4.42454i	−1.15945	−	0.174759i	−0.700465	+	0.713686i	$0.747024\pi$
$642$	6.32169	+	5.86567i	0.249497	+	0.231500i
$643$	−4.65518	−	20.3957i	−0.183582	−	0.804326i	−0.979907	−	0.199457i	$-0.936082\pi$
$643$	−4.65518	−	20.3957i	−0.183582	−	0.804326i	0.796324	−	0.604870i	$-0.206775\pi$
$644$	−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	−0.365677	−	0.930742i	$-0.619162\pi$
$647$	13.6118	−	12.6299i	0.535135	−	0.496533i	0.900812	+	0.434209i	$0.142972\pi$
$648$	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	−0.0483560	−	0.998830i	$-0.515398\pi$
$653$	−16.6348	−	5.13116i	−0.650971	−	0.200798i	−0.602615	+	0.798032i	$0.705874\pi$
$654$	−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	−0.471981	−	0.881609i	$-0.656461\pi$
$659$	12.6442	−	15.8554i	0.492549	−	0.617637i	0.964531	+	0.263971i	$0.0850324\pi$
$660$	4.63439	+	11.8082i	0.180394	+	0.459635i
$661$	−0.580174	−	7.74188i	−0.0225661	−	0.301124i	−0.997055	−	0.0766887i	$-0.975565\pi$
$661$	−0.580174	−	7.74188i	−0.0225661	−	0.301124i	0.974489	−	0.224435i	$-0.0720538\pi$
$662$	−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	−0.971616	−	0.236562i	$-0.923979\pi$
$673$	−36.1235	+	17.3962i	−1.39246	+	0.670572i	−0.420841	+	0.907134i	$0.638265\pi$
$674$	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	0.0353108	−	0.999376i	$-0.488758\pi$
$677$	25.4599	−	17.3583i	0.978505	−	0.667133i	0.943194	+	0.332243i	$0.107806\pi$
$678$	−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	0.274268	−	0.961653i	$-0.411564\pi$
$683$	27.2475	−	8.40475i	1.04260	−	0.321599i	0.768329	+	0.640055i	$0.221088\pi$
$684$	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	0.851233	−	0.524788i	$-0.175855\pi$
$691$	10.2920	+	9.54955i	0.391525	+	0.363282i	−0.459708	+	0.888070i	$0.652046\pi$
$692$	−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	0.867005	−	0.498299i	$-0.166042\pi$
$701$	26.9527	+	12.9797i	1.01799	+	0.490238i	0.150983	+	0.988536i	$0.451756\pi$
$702$	−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	0.983192	−	0.182574i	$-0.0584428\pi$
$709$	3.68198	+	9.38153i	0.138280	+	0.352331i	−0.844912	+	0.534905i	$0.820348\pi$
$710$	−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	−0.222601	−	0.974910i	$-0.571455\pi$
$719$	−25.6265	−	7.90474i	−0.955709	−	0.294797i	−0.733108	+	0.680112i	$0.761931\pi$
$720$	−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	−0.839547	−	0.543287i	$-0.817180\pi$
$727$	4.11406	−	18.0249i	0.152582	−	0.668506i	0.992129	−	0.125219i	$-0.0399633\pi$
$728$	−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	0.195873	+	0.980629i	$0.437246\pi$
$733$	−3.89777	+	52.0121i	−0.143967	+	1.92111i	−0.339840	+	0.940483i	$0.610373\pi$
$734$	−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	−0.400089	−	0.916476i	$-0.631021\pi$
$739$	−28.6128	−	4.31269i	−1.05254	−	0.158645i	−0.652450	+	0.757832i	$0.726259\pi$
$740$	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	−0.893516	−	0.449031i	$-0.851769\pi$
$743$	2.89866	−	12.6998i	0.106341	−	0.465912i	0.999858	−	0.0168809i	$-0.00537360\pi$
$744$	−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	0.231974	−	0.972722i	$-0.425482\pi$
$751$	−3.40673	−	1.05084i	−0.124313	−	0.0383456i	−0.356288	+	0.934376i	$0.615958\pi$
$752$	−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	−0.725737	−	0.687973i	$-0.758501\pi$
$757$	2.92962	−	3.67362i	0.106479	−	0.133520i	0.832215	+	0.554453i	$0.187072\pi$
$758$	−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	0.965559	−	0.260185i	$-0.0837837\pi$
$761$	2.22850	+	5.67813i	0.0807831	+	0.205832i	−0.884776	+	0.466017i	$0.845688\pi$
$762$	−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	0.289045	−	0.957316i	$-0.406662\pi$
$769$	−7.74239	−	3.72854i	−0.279198	−	0.134455i	−0.568243	+	0.822861i	$0.692377\pi$
$770$	−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	0.999906	−	0.0137390i	$-0.00437340\pi$
$773$	37.6012	+	25.6361i	1.35242	+	0.922066i	0.352517	+	0.935805i	$0.385326\pi$
$774$	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	−0.951869	−	0.306504i	$-0.900841\pi$
$787$	−43.9229	+	13.5484i	−1.56568	+	0.482949i	−0.613812	+	0.789452i	$0.710365\pi$
$788$	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	−0.768507	−	0.639842i	$-0.779000\pi$
$797$	−21.1004	+	10.1614i	−0.747415	+	0.359936i	0.0210922	+	0.999778i	$0.493286\pi$
$798$	−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	−0.999915	−	0.0130520i	$-0.995845\pi$
$809$	−0.372987	−	4.97717i	−0.0131135	−	0.174988i	0.986801	−	0.161936i	$-0.0517738\pi$
$810$	8.07552	+	20.5761i	0.283745	+	0.722970i
$811$	−0.433526	+	0.543624i	−0.0152231	+	0.0190892i	−0.789385	−	0.613899i	$-0.789600\pi$
$811$	−0.433526	+	0.543624i	−0.0152231	+	0.0190892i	0.774162	+	0.632988i	$0.218172\pi$
$812$	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	−0.353273	−	0.935520i	$-0.614931\pi$
$821$	−11.8939	+	1.79272i	−0.415101	+	0.0625664i	−0.0618282	+	0.998087i	$0.519693\pi$
$822$	−10.1916	−	6.94853i	−0.355474	−	0.242358i
$823$	−31.0979	+	28.8547i	−1.08401	+	1.00581i	−0.0840500	+	0.996462i	$0.526786\pi$
$823$	−31.0979	+	28.8547i	−1.08401	+	1.00581i	−0.999956	+	0.00934933i	$0.997024\pi$
$824$	−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	0.989523	−	0.144375i	$-0.0461173\pi$
$827$	1.01662	+	4.45411i	0.0353514	+	0.154885i	−0.954172	+	0.299260i	$0.903260\pi$
$828$	10.8408	+	10.0588i	0.376744	+	0.349568i
$829$	1.30063	+	0.196038i	0.0451727	+	0.00680870i	0.171590	−	0.985168i	$-0.445110\pi$
$829$	1.30063	+	0.196038i	0.0451727	+	0.00680870i	−0.126417	+	0.991977i	$0.540348\pi$
$830$	−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	0.996725	−	0.0808707i	$-0.0257701\pi$
$839$	1.84273	+	8.07355i	0.0636183	+	0.278730i	−0.933106	+	0.359601i	$0.882913\pi$
$840$	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	0.846110	−	0.533008i	$-0.178938\pi$
$853$	4.03596	+	5.06093i	0.138189	+	0.173283i	−0.707922	+	0.706291i	$0.750367\pi$
$854$	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	−0.836223	−	0.548390i	$-0.815241\pi$
$857$	−2.66613	−	35.5770i	−0.0910732	−	1.21529i	0.745150	−	0.666897i	$-0.232378\pi$
$858$	1.92301	+	25.6607i	0.0656504	+	0.876043i
$859$	−10.2719	−	26.1724i	−0.350473	−	0.892991i	−0.992040	−	0.125924i	$-0.959811\pi$
$859$	−10.2719	−	26.1724i	−0.350473	−	0.892991i	0.641567	−	0.767067i	$-0.278285\pi$
$860$	−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	0.135658	+	0.990756i	$0.456685\pi$
$863$	−23.2133	+	40.2067i	−0.790191	+	1.36865i	−0.925849	+	0.377895i	$0.876648\pi$
$864$	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	0.967060	−	0.254550i	$-0.0819273\pi$
$877$	23.2616	+	21.5837i	0.785490	+	0.728828i	−0.181570	+	0.983378i	$0.558118\pi$
$878$	−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	0.277117	−	0.960836i	$-0.410621\pi$
$887$	−19.6661	−	18.2475i	−0.660323	−	0.612691i	−0.937440	+	0.348146i	$0.886811\pi$
$888$	−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	0.911616	+	0.411042i	$0.134835\pi$
$907$	2.15166	+	28.7119i	0.0714447	+	0.953363i	−0.840172	+	0.542321i	$0.817546\pi$
$908$	−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	−0.955336	−	0.295521i	$-0.904507\pi$
$911$	−31.1144	−	39.0162i	−1.03087	−	1.29266i	−0.0755295	−	0.997144i	$-0.524065\pi$
$912$	−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	−0.636341	−	0.771408i	$-0.719553\pi$
$919$	−30.8314	+	4.64709i	−1.01704	+	0.153293i	−0.380694	+	0.924701i	$0.624315\pi$
$920$	−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	−0.989888	−	0.141848i	$-0.954696\pi$
$929$	0.307388	−	4.10181i	0.0100851	−	0.134576i	0.999974	+	0.00727180i	$0.00231471\pi$
$930$	−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	−0.680338	−	0.732899i	$-0.738167\pi$
$937$	−11.7963	−	51.6829i	−0.385367	−	1.68841i	0.294970	−	0.955506i	$-0.404690\pi$
$938$	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	0.441670	−	0.897178i	$-0.354386\pi$
$941$	42.0056	−	38.9755i	1.36935	−	1.27057i	0.927675	−	0.373389i	$-0.121804\pi$
$942$	−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	0.795681	−	0.605716i	$-0.207113\pi$
$947$	34.2167	+	10.5544i	1.11189	+	0.342973i	0.316211	+	0.948689i	$0.397589\pi$
$948$	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	0.0386828	+	0.999252i	$0.487684\pi$
$953$	−29.1457	+	36.5476i	−0.944123	+	1.18389i	−0.982806	+	0.184641i	$0.940888\pi$
$954$	−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	−0.940369	−	0.340155i	$-0.889520\pi$
$967$	−39.2046	+	18.8800i	−1.26074	+	0.607139i	−0.320367	+	0.947294i	$0.603806\pi$
$968$	−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	−0.768824	−	0.639461i	$-0.779158\pi$
$971$	−14.1610	+	9.65483i	−0.454449	+	0.309838i	0.314375	+	0.949299i	$0.398205\pi$
$972$	−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	0.257360	−	0.966316i	$-0.417147\pi$
$977$	31.7054	−	9.77982i	1.01435	−	0.312884i	0.756986	+	0.653431i	$0.226671\pi$
$978$	−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	−0.838560	+	0.544809i	$0.816602\pi$
$983$	−57.6363	+	17.7784i	−1.83831	+	0.567044i	−0.999753	+	0.0222351i	$0.992922\pi$
$984$	−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	0.983921	−	0.178605i	$-0.0571583\pi$
$991$	37.0562	+	25.2645i	1.17713	+	0.802553i	0.193208	+	0.981158i	$0.438111\pi$
$992$	−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	−0.937392	−	0.348276i	$-0.886767\pi$
$997$	−0.421446	+	1.07383i	−0.0133473	+	0.0340084i	0.924045	+	0.382284i	$0.124862\pi$
$998$	−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.23.1	✓	48
3.2	odd	2		441.2.bb.d.415.4		48
4.3	odd	2		784.2.bg.c.513.1		48
7.2	even	3		343.2.e.d.148.7		48
7.3	odd	6		343.2.g.h.263.1		48
7.4	even	3		343.2.g.i.263.1		48
7.5	odd	6		343.2.e.c.148.7		48
7.6	odd	2		343.2.g.g.275.1		48
49.9	even	21		2401.2.a.h.1.5		24
49.12	odd	42		343.2.e.c.197.7		48
49.17	odd	42		343.2.g.g.116.1		48
49.20	odd	14		343.2.g.h.30.1		48
49.29	even	7		343.2.g.i.30.1		48
49.32	even	21	inner	49.2.g.a.32.1	yes	48
49.37	even	21		343.2.e.d.197.7		48
49.40	odd	42		2401.2.a.i.1.5		24
147.32	odd	42		441.2.bb.d.424.4		48
196.179	odd	42		784.2.bg.c.81.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.1	✓	48	1.1	even	1	trivial
49.2.g.a.32.1	yes	48	49.32	even	21	inner
343.2.e.c.148.7		48	7.5	odd	6
343.2.e.c.197.7		48	49.12	odd	42
343.2.e.d.148.7		48	7.2	even	3
343.2.e.d.197.7		48	49.37	even	21
343.2.g.g.116.1		48	49.17	odd	42
343.2.g.g.275.1		48	7.6	odd	2
343.2.g.h.30.1		48	49.20	odd	14
343.2.g.h.263.1		48	7.3	odd	6
343.2.g.i.30.1		48	49.29	even	7
343.2.g.i.263.1		48	7.4	even	3
441.2.bb.d.415.4		48	3.2	odd	2
441.2.bb.d.424.4		48	147.32	odd	42
784.2.bg.c.81.1		48	196.179	odd	42
784.2.bg.c.513.1		48	4.3	odd	2
2401.2.a.h.1.5		24	49.9	even	21
2401.2.a.i.1.5		24	49.40	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more