LMFDB - Embedded newform 418.2.q.b.21.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.5
Character	$\chi$	$=$	418.21
Dual form			418.2.q.b.219.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.138226 + 0.164732i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(3.86845 - 1.40800i) q^{5} +(0.138226 + 0.164732i) q^{6} +(1.22696 - 0.708384i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.512915 + 2.90888i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.138226 + 0.164732i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(3.86845 - 1.40800i) q^{5} +(0.138226 + 0.164732i) q^{6} +(1.22696 - 0.708384i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.512915 + 2.90888i) q^{9} +(-0.714861 - 4.05418i) q^{10} +(3.24512 - 0.684983i) q^{11} +(0.186232 - 0.107521i) q^{12} +(-3.86833 + 3.24592i) q^{13} +(-0.484563 - 1.33133i) q^{14} +(-0.302780 + 0.831880i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.553826 + 0.0976545i) q^{17} +2.95376 q^{18} +(-3.36996 - 2.76466i) q^{19} -4.11672 q^{20} +(-0.0529045 + 0.300036i) q^{21} +(-0.111067 - 3.31476i) q^{22} +(1.60507 + 0.584196i) q^{23} +(-0.0735487 - 0.202073i) q^{24} +(9.15224 - 7.67964i) q^{25} +(2.52488 + 4.37321i) q^{26} +(-1.10878 - 0.640154i) q^{27} +(-1.39524 + 0.246019i) q^{28} +(-0.797876 - 4.52498i) q^{29} +(0.766665 + 0.442634i) q^{30} +(-5.62850 + 3.24961i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.335723 + 0.629257i) q^{33} +(0.192342 - 0.528455i) q^{34} +(3.74902 - 4.46791i) q^{35} +(0.512915 - 2.90888i) q^{36} -3.77123i q^{37} +(-3.30785 + 2.83869i) q^{38} -1.08591i q^{39} +(-0.714861 + 4.05418i) q^{40} +(2.96644 + 2.48914i) q^{41} +(0.286291 + 0.104201i) q^{42} +(-3.37974 - 9.28576i) q^{43} +(-3.28369 - 0.466223i) q^{44} +(6.07990 + 10.5307i) q^{45} +(0.854038 - 1.47924i) q^{46} +(-0.746107 - 4.23138i) q^{47} +(-0.211775 + 0.0373417i) q^{48} +(-2.49638 + 4.32387i) q^{49} +(-5.97370 - 10.3467i) q^{50} +(-0.0926402 + 0.0777344i) q^{51} +(4.74521 - 1.72712i) q^{52} +(-3.79320 + 10.4217i) q^{53} +(-0.822966 + 0.980773i) q^{54} +(11.5891 - 7.21896i) q^{55} +1.41677i q^{56} +(0.921245 - 0.172992i) q^{57} -4.59479 q^{58} +(3.13539 + 0.552854i) q^{59} +(0.569039 - 0.678155i) q^{60} +(-3.86156 + 10.6095i) q^{61} +(2.22287 + 6.10728i) q^{62} +(2.68993 + 3.20573i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-10.3942 + 18.0033i) q^{65} +(0.561399 + 0.439892i) q^{66} +(-10.6542 + 1.87862i) q^{67} +(-0.487027 - 0.281185i) q^{68} +(-0.318098 + 0.183654i) q^{69} +(-3.74902 - 4.46791i) q^{70} +(-5.30270 - 14.5691i) q^{71} +(-2.77562 - 1.01024i) q^{72} +(-1.20315 + 1.43386i) q^{73} +(-3.71394 - 0.654867i) q^{74} +2.56919i q^{75} +(2.22116 + 3.75053i) q^{76} +(3.49639 - 3.13923i) q^{77} +(-1.06941 - 0.188566i) q^{78} +(9.24677 + 7.75896i) q^{79} +(3.86845 + 1.40800i) q^{80} +(-8.06815 + 2.93657i) q^{81} +(2.96644 - 2.48914i) q^{82} +(-8.53602 + 4.92827i) q^{83} +(0.152332 - 0.263847i) q^{84} +(2.27995 - 0.402017i) q^{85} +(-9.73157 + 1.71594i) q^{86} +(0.855696 + 0.494036i) q^{87} +(-1.02935 + 3.15285i) q^{88} +(-0.856385 - 1.02060i) q^{89} +(11.4265 - 4.15889i) q^{90} +(-2.44692 + 6.72287i) q^{91} +(-1.30846 - 1.09793i) q^{92} +(0.242692 - 1.37637i) q^{93} -4.29666 q^{94} +(-16.9292 - 5.95003i) q^{95} +0.215042i q^{96} +(4.78896 + 0.844423i) q^{97} +(3.82468 + 3.20929i) q^{98} +(3.65700 + 9.08833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.138226	+	0.164732i	−0.0798050	+	0.0951079i	−0.804470	−	0.593994i	$-0.797550\pi$
$3$	−0.138226	+	0.164732i	−0.0798050	+	0.0951079i	0.724664	+	0.689102i	$0.241995\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	3.86845	−	1.40800i	1.73002	−	0.629678i	0.731392	−	0.681957i	$-0.238871\pi$
$5$	3.86845	−	1.40800i	1.73002	−	0.629678i	0.998632	+	0.0522795i	$0.0166487\pi$
$6$	0.138226	+	0.164732i	0.0564307	+	0.0672515i
$7$	1.22696	−	0.708384i	0.463746	−	0.267744i	−0.249872	−	0.968279i	$-0.580389\pi$
$7$	1.22696	−	0.708384i	0.463746	−	0.267744i	0.713618	+	0.700535i	$0.247055\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.512915	+	2.90888i	0.170972	+	0.969628i
$10$	−0.714861	−	4.05418i	−0.226059	−	1.28204i
$11$	3.24512	−	0.684983i	0.978440	−	0.206530i
$11$	3.24512	−	0.684983i	0.978440	−	0.206530i
$12$	0.186232	−	0.107521i	0.0537605	−	0.0310386i
$13$	−3.86833	+	3.24592i	−1.07288	+	0.900256i	−0.995311	−	0.0967311i	$-0.969161\pi$
$13$	−3.86833	+	3.24592i	−1.07288	+	0.900256i	−0.0775724	+	0.996987i	$0.524717\pi$
$14$	−0.484563	−	1.33133i	−0.129505	−	0.355812i
$15$	−0.302780	+	0.831880i	−0.0781774	+	0.214791i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.553826	+	0.0976545i	0.134323	+	0.0236847i	0.240405	−	0.970673i	$-0.422720\pi$
$17$	0.553826	+	0.0976545i	0.134323	+	0.0236847i	−0.106083	+	0.994357i	$0.533831\pi$
$18$	2.95376			0.696207
$19$	−3.36996	−	2.76466i	−0.773123	−	0.634256i
$19$	−3.36996	−	2.76466i	−0.773123	−	0.634256i
$20$	−4.11672			−0.920527
$21$	−0.0529045	+	0.300036i	−0.0115447	+	0.0654732i
$22$	−0.111067	−	3.31476i	−0.0236796	−	0.706710i
$23$	1.60507	+	0.584196i	0.334680	+	0.121813i	0.503893	−	0.863766i	$-0.331901\pi$
$23$	1.60507	+	0.584196i	0.334680	+	0.121813i	−0.169214	+	0.985579i	$0.554123\pi$
$24$	−0.0735487	−	0.202073i	−0.0150131	−	0.0412481i
$25$	9.15224	−	7.67964i	1.83045	−	1.53593i
$26$	2.52488	+	4.37321i	0.495169	+	0.857658i
$27$	−1.10878	−	0.640154i	−0.213385	−	0.123198i
$28$	−1.39524	+	0.246019i	−0.263676	+	0.0464932i
$29$	−0.797876	−	4.52498i	−0.148162	−	0.840268i	−0.964774	−	0.263081i	$-0.915261\pi$
$29$	−0.797876	−	4.52498i	−0.148162	−	0.840268i	0.816612	−	0.577187i	$-0.195850\pi$
$30$	0.766665	+	0.442634i	0.139973	+	0.0808136i
$31$	−5.62850	+	3.24961i	−1.01091	+	0.583648i	−0.911457	−	0.411395i	$-0.865042\pi$
$31$	−5.62850	+	3.24961i	−1.01091	+	0.583648i	−0.0994505	+	0.995043i	$0.531708\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−0.335723	+	0.629257i	−0.0584418	+	0.109540i
$34$	0.192342	−	0.528455i	0.0329864	−	0.0906293i
$35$	3.74902	−	4.46791i	0.633700	−	0.755214i
$36$	0.512915	−	2.90888i	0.0854858	−	0.484814i
$37$		−	3.77123i		−	0.619986i	−0.950739	−	0.309993i	$-0.899673\pi$
$37$		−	3.77123i		−	0.619986i	0.950739	−	0.309993i	$-0.100327\pi$
$38$	−3.30785	+	2.83869i	−0.536603	+	0.460496i
$39$		−	1.08591i		−	0.173885i
$40$	−0.714861	+	4.05418i	−0.113029	+	0.641022i
$41$	2.96644	+	2.48914i	0.463281	+	0.388739i	0.844336	−	0.535814i	$-0.179995\pi$
$41$	2.96644	+	2.48914i	0.463281	+	0.388739i	−0.381056	+	0.924552i	$0.624439\pi$
$42$	0.286291	+	0.104201i	0.0441757	+	0.0160786i
$43$	−3.37974	−	9.28576i	−0.515406	−	1.41607i	−0.875531	−	0.483161i	$-0.839488\pi$
$43$	−3.37974	−	9.28576i	−0.515406	−	1.41607i	0.360126	−	0.932904i	$-0.382734\pi$
$44$	−3.28369	−	0.466223i	−0.495035	−	0.0702858i
$45$	6.07990	+	10.5307i	0.906338	+	1.56982i
$46$	0.854038	−	1.47924i	0.125921	−	0.218102i
$47$	−0.746107	−	4.23138i	−0.108831	−	0.617211i	−0.989621	−	0.143704i	$-0.954099\pi$
$47$	−0.746107	−	4.23138i	−0.108831	−	0.617211i	0.880790	−	0.473507i	$-0.157012\pi$
$48$	−0.211775	+	0.0373417i	−0.0305671	+	0.00538980i
$49$	−2.49638	+	4.32387i	−0.356626	+	0.617695i
$50$	−5.97370	−	10.3467i	−0.844809	−	1.46325i
$51$	−0.0926402	+	0.0777344i	−0.0129722	+	0.0108850i
$52$	4.74521	−	1.72712i	0.658043	−	0.239508i
$53$	−3.79320	+	10.4217i	−0.521036	+	1.43153i	0.348333	+	0.937371i	$0.386748\pi$
$53$	−3.79320	+	10.4217i	−0.521036	+	1.43153i	−0.869369	+	0.494164i	$0.835474\pi$
$54$	−0.822966	+	0.980773i	−0.111992	+	0.133466i
$55$	11.5891	−	7.21896i	1.56268	−	0.973404i
$56$			1.41677i			0.189324i
$57$	0.921245	−	0.172992i	0.122022	−	0.0229133i
$58$	−4.59479			−0.603325
$59$	3.13539	+	0.552854i	0.408193	+	0.0719755i	0.373975	−	0.927439i	$-0.377995\pi$
$59$	3.13539	+	0.552854i	0.408193	+	0.0719755i	0.0342186	+	0.999414i	$0.489106\pi$
$60$	0.569039	−	0.678155i	0.0734627	−	0.0875494i
$61$	−3.86156	+	10.6095i	−0.494422	+	1.35841i	0.402174	+	0.915563i	$0.368255\pi$
$61$	−3.86156	+	10.6095i	−0.494422	+	1.35841i	−0.896596	+	0.442850i	$0.853967\pi$
$62$	2.22287	+	6.10728i	0.282304	+	0.775625i
$63$	2.68993	+	3.20573i	0.338899	+	0.403884i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−10.3942	+	18.0033i	−1.28924	+	2.23303i
$66$	0.561399	+	0.439892i	0.0691035	+	0.0541469i
$67$	−10.6542	+	1.87862i	−1.30162	+	0.229510i	−0.781134	−	0.624363i	$-0.785359\pi$
$67$	−10.6542	+	1.87862i	−1.30162	+	0.229510i	−0.520481	+	0.853873i	$0.674247\pi$
$68$	−0.487027	−	0.281185i	−0.0590607	−	0.0340987i
$69$	−0.318098	+	0.183654i	−0.0382945	+	0.0221094i
$70$	−3.74902	−	4.46791i	−0.448093	−	0.534017i
$71$	−5.30270	−	14.5691i	−0.629315	−	1.72903i	−0.682947	−	0.730468i	$-0.739302\pi$
$71$	−5.30270	−	14.5691i	−0.629315	−	1.72903i	0.0536317	−	0.998561i	$-0.482920\pi$
$72$	−2.77562	−	1.01024i	−0.327110	−	0.119058i
$73$	−1.20315	+	1.43386i	−0.140818	+	0.167821i	−0.831844	−	0.555009i	$-0.812715\pi$
$73$	−1.20315	+	1.43386i	−0.140818	+	0.167821i	0.691026	+	0.722830i	$0.257159\pi$
$74$	−3.71394	−	0.654867i	−0.431736	−	0.0761268i
$75$			2.56919i			0.296665i
$76$	2.22116	+	3.75053i	0.254785	+	0.430215i
$77$	3.49639	−	3.13923i	0.398451	−	0.357749i
$78$	−1.06941	−	0.188566i	−0.121087	−	0.0213509i
$79$	9.24677	+	7.75896i	1.04034	+	0.872951i	0.992045	−	0.125882i	$-0.0401760\pi$
$79$	9.24677	+	7.75896i	1.04034	+	0.872951i	0.0482975	+	0.998833i	$0.484620\pi$
$80$	3.86845	+	1.40800i	0.432506	+	0.157419i
$81$	−8.06815	+	2.93657i	−0.896462	+	0.326285i
$82$	2.96644	−	2.48914i	0.327589	−	0.274880i
$83$	−8.53602	+	4.92827i	−0.936949	+	0.540948i	−0.889003	−	0.457902i	$-0.848601\pi$
$83$	−8.53602	+	4.92827i	−0.936949	+	0.540948i	−0.0479467	+	0.998850i	$0.515268\pi$
$84$	0.152332	−	0.263847i	0.0166208	−	0.0287881i
$85$	2.27995	−	0.402017i	0.247295	−	0.0436048i
$86$	−9.73157	+	1.71594i	−1.04938	+	0.185034i
$87$	0.855696	+	0.494036i	0.0917402	+	0.0529662i
$88$	−1.02935	+	3.15285i	−0.109729	+	0.336095i
$89$	−0.856385	−	1.02060i	−0.0907767	−	0.108183i	0.718744	−	0.695275i	$-0.244717\pi$
$89$	−0.856385	−	1.02060i	−0.0907767	−	0.108183i	−0.809521	+	0.587091i	$0.800273\pi$
$90$	11.4265	−	4.15889i	1.20446	−	0.438386i
$91$	−2.44692	+	6.72287i	−0.256507	+	0.704748i
$92$	−1.30846	−	1.09793i	−0.136417	−	0.114467i
$93$	0.242692	−	1.37637i	0.0251660	−	0.142723i
$94$	−4.29666			−0.443167
$95$	−16.9292	−	5.95003i	−1.73690	−	0.610461i
$96$			0.215042i			0.0219476i
$97$	4.78896	+	0.844423i	0.486245	+	0.0857382i	0.411396	−	0.911457i	$-0.365041\pi$
$97$	4.78896	+	0.844423i	0.486245	+	0.0857382i	0.0748493	+	0.997195i	$0.476152\pi$
$98$	3.82468	+	3.20929i	0.386351	+	0.324187i
$99$	3.65700	+	9.08833i	0.367543	+	0.913412i
$100$	−11.2269	+	4.08625i	−1.12269	+	0.408625i
$101$	9.32662	+	11.1150i	0.928034	+	1.10599i	0.994132	+	0.108175i	$0.0345005\pi$
$101$	9.32662	+	11.1150i	0.928034	+	1.10599i	−0.0660981	+	0.997813i	$0.521055\pi$
$102$	0.0604666	+	0.104731i	0.00598709	+	0.0103699i
$103$	1.45111	+	0.837800i	0.142982	+	0.0825509i	0.569785	−	0.821794i	$-0.307027\pi$
$103$	1.45111	+	0.837800i	0.142982	+	0.0825509i	−0.426802	+	0.904345i	$0.640360\pi$
$104$	−0.876880	−	4.97303i	−0.0859852	−	0.487646i
$105$	0.217793	+	1.23516i	0.0212544	+	0.120540i
$106$	9.60472	+	5.54529i	0.932893	+	0.538606i
$107$	2.30077	+	3.98504i	0.222423	+	0.385249i	0.955543	−	0.294851i	$-0.0952699\pi$
$107$	2.30077	+	3.98504i	0.222423	+	0.385249i	−0.733120	+	0.680099i	$0.761937\pi$
$108$	0.822966	+	0.980773i	0.0791900	+	0.0943749i
$109$	14.0575	−	5.11650i	1.34646	−	0.490072i	0.434619	−	0.900614i	$-0.356883\pi$
$109$	14.0575	−	5.11650i	1.34646	−	0.490072i	0.911841	+	0.410543i	$0.134661\pi$
$110$	−5.09685	−	12.6666i	−0.485966	−	1.20772i
$111$	0.621241	+	0.521283i	0.0589656	+	0.0494780i
$112$	1.39524	+	0.246019i	0.131838	+	0.0232466i
$113$			9.17964i			0.863548i	0.901982	+	0.431774i	$0.142112\pi$
$113$			9.17964i			0.863548i	−0.901982	+	0.431774i	$0.857888\pi$
$114$	−0.0103909	−	0.937289i	−0.000973199	−	0.0877852i
$115$	7.03167			0.655707
$116$	−0.797876	+	4.52498i	−0.0740810	+	0.420134i
$117$	−11.4261	−	9.58765i	−1.05635	−	0.886379i
$118$	1.08891	−	2.99176i	0.100242	−	0.275414i
$119$	0.748698	−	0.272504i	0.0686330	−	0.0249804i
$120$	−0.569039	−	0.678155i	−0.0519460	−	0.0619068i
$121$	10.0616	−	4.44570i	0.914691	−	0.404155i
$122$	9.77781	+	5.64522i	0.885241	+	0.511094i
$123$	−0.820081	+	0.144602i	−0.0739442	+	0.0130384i
$124$	6.40049	−	1.12858i	0.574781	−	0.101349i
$125$	14.3003	−	24.7688i	1.27905	−	2.21539i
$126$	3.62413	−	2.09239i	0.322863	−	0.186405i
$127$	13.7784	−	11.5614i	1.22263	−	1.02591i	0.223949	−	0.974601i	$-0.428105\pi$
$127$	13.7784	−	11.5614i	1.22263	−	1.02591i	0.998683	−	0.0513093i	$-0.0163394\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	1.99683	+	0.726786i	0.175811	+	0.0639900i
$130$	15.9249	+	13.3625i	1.39670	+	1.17197i
$131$	−6.04277	−	1.06550i	−0.527959	−	0.0930934i	−0.0966861	−	0.995315i	$-0.530824\pi$
$131$	−6.04277	−	1.06550i	−0.527959	−	0.0930934i	−0.431273	+	0.902222i	$0.641935\pi$
$132$	0.530695	−	0.476484i	0.0461910	−	0.0414726i
$133$	−6.09324	−	1.00489i	−0.528351	−	0.0871348i
$134$			10.8185i			0.934580i
$135$	−5.19060	−	0.915243i	−0.446736	−	0.0787715i
$136$	−0.361485	+	0.430800i	−0.0309970	+	0.0369408i
$137$	−8.38055	−	3.05027i	−0.715998	−	0.260602i	−0.0417723	−	0.999127i	$-0.513300\pi$
$137$	−8.38055	−	3.05027i	−0.715998	−	0.260602i	−0.674226	+	0.738525i	$0.735523\pi$
$138$	0.125627	+	0.345157i	0.0106941	+	0.0293817i
$139$	−2.81145	−	3.35056i	−0.238464	−	0.284191i	0.633518	−	0.773728i	$-0.281610\pi$
$139$	−2.81145	−	3.35056i	−0.238464	−	0.284191i	−0.871982	+	0.489537i	$0.837166\pi$
$140$	−5.05104	+	2.91622i	−0.426891	+	0.246465i
$141$	0.800175	+	0.461981i	0.0673869	+	0.0389059i
$142$	−15.2685	+	2.69225i	−1.28131	+	0.225929i
$143$	−10.3298	+	13.1831i	−0.863822	+	1.10243i
$144$	−1.47688	+	2.55803i	−0.123073	+	0.213169i
$145$	−9.45773	−	16.3813i	−0.785422	−	1.36039i
$146$	1.20315	+	1.43386i	0.0995735	+	0.118667i
$147$	−0.367212	−	1.00891i	−0.0302871	−	0.0832132i
$148$	−1.28984	+	3.54380i	−0.106024	+	0.291298i
$149$	−7.51926	+	8.96111i	−0.616002	+	0.734122i	−0.980377	−	0.197130i	$-0.936838\pi$
$149$	−7.51926	+	8.96111i	−0.616002	+	0.734122i	0.364376	+	0.931252i	$0.381282\pi$
$150$	2.53016	+	0.446136i	0.206587	+	0.0364268i
$151$	7.15712			0.582438			0.291219	−	0.956656i	$-0.405939\pi$
$151$	7.15712			0.582438			0.291219	+	0.956656i	$0.405939\pi$
$152$	4.07925	−	1.53615i	0.330871	−	0.124598i
$153$			1.66110i			0.134292i
$154$	−2.48440	−	3.98839i	−0.200199	−	0.321394i
$155$	−17.1981	+	20.4959i	−1.38139	+	1.64627i
$156$	−0.371403	+	1.02042i	−0.0297360	+	0.0816990i
$157$	−12.1368	+	4.41744i	−0.968622	+	0.352550i	−0.777407	−	0.628998i	$-0.783465\pi$
$157$	−12.1368	+	4.41744i	−0.968622	+	0.352550i	−0.191216	+	0.981548i	$0.561243\pi$
$158$	9.24677	−	7.75896i	0.735633	−	0.617270i
$159$	−1.19247	−	2.06542i	−0.0945690	−	0.163798i
$160$	2.05836	−	3.56519i	0.162728	−	0.281853i
$161$	2.38318	−	0.420219i	0.187821	−	0.0331179i
$162$	1.49093	+	8.45551i	0.117139	+	0.664328i
$163$	−1.90524	+	3.29997i	−0.149230	+	0.258473i	−0.930943	−	0.365165i	$-0.881013\pi$
$163$	−1.90524	+	3.29997i	−0.149230	+	0.258473i	0.781713	+	0.623638i	$0.214346\pi$
$164$	−1.93621	−	3.35361i	−0.151192	−	0.261873i
$165$	−0.412732	+	2.90695i	−0.0321312	+	0.226306i
$166$	3.37114	+	9.26212i	0.261651	+	0.718880i
$167$	−5.60065	−	2.03847i	−0.433391	−	0.157742i	0.116106	−	0.993237i	$-0.462959\pi$
$167$	−5.60065	−	2.03847i	−0.433391	−	0.157742i	−0.549498	+	0.835495i	$0.685181\pi$
$168$	−0.233387	−	0.195835i	−0.0180062	−	0.0151090i
$169$	2.17060	−	12.3101i	0.166969	−	0.946930i
$170$		−	2.31512i		−	0.177562i
$171$	6.31356	−	11.2209i	0.482810	−	0.858081i
$172$			9.88170i			0.753473i
$173$	2.91293	−	16.5201i	0.221466	−	1.25600i	−0.647861	−	0.761759i	$-0.724336\pi$
$173$	2.91293	−	16.5201i	0.221466	−	1.25600i	0.869327	−	0.494238i	$-0.164553\pi$
$174$	0.635121	−	0.756907i	0.0481484	−	0.0573810i
$175$	5.78927	−	15.9059i	0.437627	−	1.20237i
$176$	2.92620	+	1.56120i	0.220571	+	0.117680i
$177$	−0.524467	+	0.440080i	−0.0394213	+	0.0330784i
$178$	−1.15380	+	0.666150i	−0.0864813	+	0.0499300i
$179$	−4.25445	−	2.45631i	−0.317992	−	0.183593i	0.332505	−	0.943101i	$-0.392106\pi$
$179$	−4.25445	−	2.45631i	−0.317992	−	0.183593i	−0.650497	+	0.759509i	$0.725439\pi$
$180$	−2.11153	−	11.9751i	−0.157384	−	0.892568i
$181$	−6.57709	+	1.15972i	−0.488871	+	0.0862012i	−0.412650	−	0.910890i	$-0.635397\pi$
$181$	−6.57709	+	1.15972i	−0.488871	+	0.0862012i	−0.0762214	+	0.997091i	$0.524286\pi$
$182$	6.19583	+	3.57716i	0.459265	+	0.265157i
$183$	−1.21396	−	2.10264i	−0.0897385	−	0.155432i
$184$	−1.30846	+	1.09793i	−0.0964611	+	0.0809405i
$185$	−5.30990	−	14.5888i	−0.390391	−	1.07259i
$186$	−1.31332	−	0.478010i	−0.0962974	−	0.0350494i
$187$	1.86412	−	0.0624609i	0.136318	−	0.00456759i
$188$	−0.746107	+	4.23138i	−0.0544155	+	0.308605i
$189$	−1.81390			−0.131942
$190$	−8.79936	+	15.6388i	−0.638373	+	1.13456i
$191$	11.5824			0.838073			0.419037	−	0.907969i	$-0.362368\pi$
$191$	11.5824			0.838073			0.419037	+	0.907969i	$0.362368\pi$
$192$	0.211775	+	0.0373417i	0.0152836	+	0.00269490i
$193$	6.15058	+	5.16095i	0.442728	+	0.371493i	0.836729	−	0.547617i	$-0.184465\pi$
$193$	6.15058	+	5.16095i	0.442728	+	0.371493i	−0.394001	+	0.919110i	$0.628909\pi$
$194$	1.66319	−	4.56957i	0.119410	−	0.328076i
$195$	−1.52896	−	4.20079i	−0.109491	−	0.300825i
$196$	3.82468	−	3.20929i	0.273192	−	0.229235i
$197$	−6.99678	+	4.03959i	−0.498500	+	0.287809i	−0.728094	−	0.685477i	$-0.759594\pi$
$197$	−6.99678	+	4.03959i	−0.498500	+	0.287809i	0.229594	+	0.973287i	$0.426260\pi$
$198$	9.58529	−	2.02327i	0.681197	−	0.143788i
$199$	0.307366	+	1.74316i	0.0217886	+	0.123569i	0.993762	−	0.111521i	$-0.0355724\pi$
$199$	0.307366	+	1.74316i	0.0217886	+	0.123569i	−0.971973	+	0.235091i	$0.924461\pi$
$200$	2.07464	+	11.7659i	0.146699	+	0.831974i
$201$	1.16322	−	2.01476i	0.0820473	−	0.142110i
$202$	12.5657	−	7.25483i	0.884121	−	0.510448i
$203$	−4.18438	−	4.98675i	−0.293686	−	0.350002i
$204$	0.113640	−	0.0413616i	0.00795640	−	0.00289589i
$205$	14.9803	+	5.45237i	1.04627	+	0.380810i
$206$	1.07706	−	1.28358i	0.0750420	−	0.0894315i
$207$	−0.876097	+	4.96859i	−0.0608930	+	0.345341i
$208$	−5.04975			−0.350137
$209$	−12.8297	−	6.66328i	−0.887448	−	0.460909i
$210$	1.25422			0.0865494
$211$	0.419488	−	2.37903i	0.0288787	−	0.163779i	−0.966958	−	0.254936i	$-0.917945\pi$
$211$	0.419488	−	2.37903i	0.0288787	−	0.163779i	0.995837	+	0.0911571i	$0.0290565\pi$
$212$	7.12888	−	8.49587i	0.489614	−	0.583499i
$213$	3.13296	+	1.14030i	0.214667	+	0.0781324i
$214$	4.32403	−	1.57382i	0.295584	−	0.107584i
$215$	−26.1487	−	31.1628i	−1.78333	−	2.12529i
$216$	1.10878	−	0.640154i	0.0754429	−	0.0435570i
$217$	−4.60395	+	7.97427i	−0.312536	+	0.541329i
$218$	−2.59771	−	14.7324i	−0.175939	−	0.997802i
$219$	−0.0698950	−	0.396394i	−0.00472307	−	0.0267859i
$220$	−13.3593	+	2.81988i	−0.900681	+	0.190116i
$221$	−2.45936	+	1.41991i	−0.165435	+	0.0955138i
$222$	0.621241	−	0.521283i	0.0416950	−	0.0349862i
$223$	4.85993	+	13.3526i	0.325445	+	0.894153i	0.989248	+	0.146246i	$0.0467190\pi$
$223$	4.85993	+	13.3526i	0.325445	+	0.894153i	−0.663803	+	0.747907i	$0.731059\pi$
$224$	0.484563	−	1.33133i	0.0323762	−	0.0889530i
$225$	27.0335	+	22.6838i	1.80223	+	1.51225i
$226$	9.04018	+	1.59403i	0.601344	+	0.106033i
$227$	−9.99644			−0.663487			−0.331744	−	0.943370i	$-0.607637\pi$
$227$	−9.99644			−0.663487			−0.331744	+	0.943370i	$0.607637\pi$
$228$	−0.924854	−	0.152525i	−0.0612499	−	0.0101012i
$229$	15.6394			1.03348			0.516739	−	0.856143i	$-0.327146\pi$
$229$	15.6394			1.03348			0.516739	+	0.856143i	$0.327146\pi$
$230$	1.22104	−	6.92485i	0.0805128	−	0.456611i
$231$	0.0338382	+	1.00989i	0.00222639	+	0.0664460i
$232$	4.31769	+	1.57151i	0.283470	+	0.103175i
$233$	−9.88892	−	27.1696i	−0.647845	−	1.77994i	−0.625546	−	0.780188i	$-0.715124\pi$
$233$	−9.88892	−	27.1696i	−0.647845	−	1.77994i	−0.0222992	−	0.999751i	$-0.507099\pi$
$234$	−11.4261	+	9.58765i	−0.746949	+	0.626764i
$235$	−8.84408	−	15.3184i	−0.576924	−	0.999262i
$236$	−2.75722	−	1.59188i	−0.179480	−	0.103623i
$237$	−2.55629	+	0.450744i	−0.166049	+	0.0292789i
$238$	−0.138354	−	0.784643i	−0.00896814	−	0.0508609i
$239$	−6.49700	−	3.75105i	−0.420256	−	0.242635i	0.274931	−	0.961464i	$-0.411345\pi$
$239$	−6.49700	−	3.75105i	−0.420256	−	0.242635i	−0.695187	+	0.718829i	$0.744678\pi$
$240$	−0.766665	+	0.442634i	−0.0494880	+	0.0285719i
$241$	7.48302	−	6.27900i	0.482024	−	0.404466i	−0.369134	−	0.929376i	$-0.620346\pi$
$241$	7.48302	−	6.27900i	0.482024	−	0.404466i	0.851157	+	0.524910i	$0.175901\pi$
$242$	−2.63098	−	10.6807i	−0.169126	−	0.686583i
$243$	1.94516	−	5.34428i	0.124782	−	0.342836i
$244$	7.25736	−	8.64898i	0.464605	−	0.553694i
$245$	−3.56914	+	20.2416i	−0.228024	+	1.29319i
$246$			0.832732i			0.0530931i
$247$	22.0100	−	0.244006i	1.40046	−	0.0155257i
$248$		−	6.49923i		−	0.412701i
$249$	0.368060	−	2.08737i	0.0233248	−	0.132282i
$250$	−21.9093	−	18.3840i	−1.38566	−	1.16271i
$251$	−9.36670	−	3.40920i	−0.591221	−	0.215187i	0.0290455	−	0.999578i	$-0.490753\pi$
$251$	−9.36670	−	3.40920i	−0.591221	−	0.215187i	−0.620266	+	0.784391i	$0.712975\pi$
$252$	−1.43128	−	3.93241i	−0.0901622	−	0.247719i
$253$	5.60880	+	0.796344i	0.352622	+	0.0500657i
$254$	−8.99319	−	15.5767i	−0.564283	−	0.977366i
$255$	−0.248924	+	0.431149i	−0.0155882	+	0.0269996i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	21.7459	−	3.83438i	1.35647	−	0.239182i	0.552331	−	0.833625i	$-0.313738\pi$
$257$	21.7459	−	3.83438i	1.35647	−	0.239182i	0.804138	+	0.594442i	$0.202627\pi$
$258$	1.06249	−	1.84029i	0.0661478	−	0.114571i
$259$	−2.67148	−	4.62713i	−0.165998	−	0.287516i
$260$	15.9249	−	13.3625i	0.987618	−	0.828710i
$261$	12.7534	−	4.64186i	0.789416	−	0.287324i
$262$	−2.09863	+	5.76594i	−0.129654	+	0.356221i
$263$	−6.27962	+	7.48376i	−0.387218	+	0.461469i	−0.924079	−	0.382202i	$-0.875166\pi$
$263$	−6.27962	+	7.48376i	−0.387218	+	0.461469i	0.536861	+	0.843671i	$0.319610\pi$
$264$	−0.377091	−	0.605373i	−0.0232084	−	0.0372581i
$265$			45.6568i			2.80468i
$266$	−2.04770	+	5.82617i	−0.125553	+	0.357226i
$267$	0.286500			0.0175335
$268$	10.6542	+	1.87862i	0.650808	+	0.114755i
$269$	18.7291	−	22.3204i	1.14193	−	1.36090i	0.219098	−	0.975703i	$-0.429689\pi$
$269$	18.7291	−	22.3204i	1.14193	−	1.36090i	0.922834	−	0.385198i	$-0.125867\pi$
$270$	−1.80268	+	4.95281i	−0.109707	+	0.301419i
$271$	6.01741	+	16.5327i	0.365532	+	1.00429i	0.977041	+	0.213053i	$0.0683406\pi$
$271$	6.01741	+	16.5327i	0.365532	+	1.00429i	−0.611509	+	0.791238i	$0.709437\pi$
$272$	0.361485	+	0.430800i	0.0219182	+	0.0261211i
$273$	−0.769240	−	1.33236i	−0.0465565	−	0.0806383i
$274$	−4.45920	+	7.72355i	−0.269390	+	0.466597i
$275$	24.4397	−	31.1905i	1.47377	−	1.88086i
$276$	0.361728	−	0.0637824i	0.0217735	−	0.00383925i
$277$	−26.6335	−	15.3769i	−1.60025	−	0.923906i	−0.991436	−	0.130595i	$-0.958311\pi$
$277$	−26.6335	−	15.3769i	−1.60025	−	0.923906i	−0.608817	−	0.793311i	$-0.708356\pi$
$278$	−3.78786	+	2.18692i	−0.227181	+	0.131163i
$279$	−12.3397	−	14.7059i	−0.738757	−	0.880417i
$280$	1.99481	+	5.48070i	0.119213	+	0.327534i
$281$	19.3141	+	7.02977i	1.15218	+	0.419361i	0.846299	−	0.532708i	$-0.178825\pi$
$281$	19.3141	+	7.02977i	1.15218	+	0.419361i	0.305885	+	0.952068i	$0.401048\pi$
$282$	0.593912	−	0.707797i	0.0353669	−	0.0421487i
$283$	19.3882	+	3.41866i	1.15251	+	0.203218i	0.717071	−	0.697000i	$-0.245482\pi$
$283$	19.3882	+	3.41866i	1.15251	+	0.203218i	0.435438	+	0.900219i	$0.356594\pi$
$284$			15.5041i			0.919997i
$285$	3.32022	−	1.96632i	0.196673	−	0.116475i
$286$	11.1891	+	12.4621i	0.661625	+	0.736900i
$287$	5.40296	+	0.952688i	0.318927	+	0.0562354i
$288$	2.26271	+	1.89864i	0.133331	+	0.111878i
$289$	−15.6776	−	5.70618i	−0.922211	−	0.335657i
$290$	−17.7747	+	6.46947i	−1.04377	+	0.379900i
$291$	−0.801064	+	0.672172i	−0.0469592	+	0.0394034i
$292$	1.62100	−	0.935885i	0.0948619	−	0.0547686i
$293$	0.611755	−	1.05959i	0.0357391	−	0.0619019i	−0.847603	−	0.530632i	$-0.821955\pi$
$293$	0.611755	−	1.05959i	0.0357391	−	0.0619019i	0.883342	+	0.468730i	$0.155288\pi$
$294$	−1.05734	+	0.186438i	−0.0616656	+	0.0108733i
$295$	12.9075	−	2.27595i	0.751506	−	0.132511i
$296$	3.26598	+	1.88561i	0.189831	+	0.109599i
$297$	−4.03662	−	1.31788i	−0.234228	−	0.0764712i
$298$	7.51926	+	8.96111i	0.435579	+	0.519103i
$299$	−8.10519	+	2.95005i	−0.468735	+	0.170606i
$300$	0.878716	−	2.41425i	0.0507327	−	0.139387i
$301$	−10.7247	−	8.99907i	−0.618160	−	0.518698i
$302$	1.24282	−	7.04839i	0.0715163	−	0.405589i
$303$	−3.12019			−0.179250
$304$	−0.804455	−	4.28402i	−0.0461386	−	0.245706i
$305$			46.4796i			2.66141i
$306$	1.63587	+	0.288448i	0.0935164	+	0.0164895i
$307$	6.32793	+	5.30977i	0.361154	+	0.303044i	0.805251	−	0.592935i	$-0.202031\pi$
$307$	6.32793	+	5.30977i	0.361154	+	0.303044i	−0.444096	+	0.895979i	$0.646475\pi$
$308$	−4.35921	+	1.75408i	−0.248389	+	0.0999479i
$309$	−0.338594	+	0.123238i	−0.0192620	+	0.00701078i
$310$	17.1981	+	20.4959i	0.976787	+	1.16409i
$311$	16.6387	+	28.8191i	0.943496	+	1.63418i	0.758735	+	0.651399i	$0.225818\pi$
$311$	16.6387	+	28.8191i	0.943496	+	1.63418i	0.184761	+	0.982784i	$0.440849\pi$
$312$	0.940425	+	0.542955i	0.0532411	+	0.0307387i
$313$	−2.45934	−	13.9476i	−0.139010	−	0.788365i	−0.971983	−	0.235051i	$-0.924474\pi$
$313$	−2.45934	−	13.9476i	−0.139010	−	0.788365i	0.832973	−	0.553314i	$-0.186637\pi$
$314$	2.24279	+	12.7195i	0.126568	+	0.717803i
$315$	14.9195	+	8.61380i	0.840621	+	0.485333i
$316$	−6.03540	−	10.4536i	−0.339518	−	0.588062i
$317$	−5.07285	−	6.04559i	−0.284920	−	0.339554i	0.604534	−	0.796579i	$-0.293359\pi$
$317$	−5.07285	−	6.04559i	−0.284920	−	0.339554i	−0.889454	+	0.457025i	$0.848915\pi$
$318$	−2.24111	+	0.815697i	−0.125675	+	0.0457420i
$319$	−5.68874	−	14.1376i	−0.318508	−	0.791552i
$320$	−3.15359	−	2.64618i	−0.176291	−	0.147926i
$321$	−0.974490	−	0.171829i	−0.0543907	−	0.00959055i
$322$		−	2.41995i		−	0.134858i
$323$	−1.59639	−	1.86023i	−0.0888257	−	0.103506i
$324$	8.58595			0.476997
$325$	−10.4764	+	59.4148i	−0.581128	+	3.29574i
$326$	2.91899	+	2.44932i	0.161668	+	0.135656i
$327$	−1.10026	+	3.02295i	−0.0608446	+	0.167169i
$328$	−3.63888	+	1.32444i	−0.200924	+	0.0731302i
$329$	−3.91289	−	4.66320i	−0.215724	−	0.257090i
$330$	2.79112	+	0.911248i	0.153646	+	0.0501626i
$331$	−2.55890	−	1.47738i	−0.140650	−	0.0812044i	0.428024	−	0.903768i	$-0.359210\pi$
$331$	−2.55890	−	1.47738i	−0.140650	−	0.0812044i	−0.568674	+	0.822563i	$0.692543\pi$
$332$	9.70680	−	1.71157i	0.532730	−	0.0939346i
$333$	10.9701	−	1.93432i	0.601156	−	0.106000i
$334$	−2.98004	+	5.16159i	−0.163061	+	0.282430i
$335$	−38.5701	+	22.2685i	−2.10731	+	1.21666i
$336$	−0.233387	+	0.195835i	−0.0127323	+	0.0106837i
$337$	−18.0279	+	6.56161i	−0.982041	+	0.357434i	−0.782633	−	0.622483i	$-0.786124\pi$
$337$	−18.0279	+	6.56161i	−0.982041	+	0.357434i	−0.199407	+	0.979917i	$0.563902\pi$
$338$	−11.7462	−	4.27525i	−0.638906	−	0.232543i
$339$	−1.51218	−	1.26887i	−0.0821303	−	0.0689155i
$340$	−2.27995	−	0.402017i	−0.123648	−	0.0218024i
$341$	−16.0392	+	14.4008i	−0.868572	+	0.779847i
$342$	−9.95406	−	8.16613i	−0.538254	−	0.441574i
$343$			16.9910i			0.917426i
$344$	9.73157	+	1.71594i	0.524691	+	0.0925172i
$345$	−0.971963	+	1.15834i	−0.0523287	+	0.0623629i
$346$	−15.7633	−	5.73735i	−0.847438	−	0.308442i
$347$	−9.75198	−	26.7933i	−0.523514	−	1.43834i	−0.866583	−	0.499032i	$-0.833689\pi$
$347$	−9.75198	−	26.7933i	−0.523514	−	1.43834i	0.343070	−	0.939310i	$-0.388533\pi$
$348$	−0.635121	−	0.756907i	−0.0340460	−	0.0405745i
$349$	28.2998	−	16.3389i	1.51485	−	0.874600i	0.515003	−	0.857188i	$-0.327791\pi$
$349$	28.2998	−	16.3389i	1.51485	−	0.874600i	0.999848	−	0.0174113i	$-0.00554248\pi$
$350$	−14.6589	−	8.46334i	−0.783553	−	0.452385i
$351$	6.36702	−	1.12268i	0.339846	−	0.0599241i
$352$	2.04561	−	2.61065i	0.109031	−	0.139148i
$353$	−7.57584	+	13.1217i	−0.403221	+	0.698400i	−0.994113	−	0.108352i	$-0.965443\pi$
$353$	−7.57584	+	13.1217i	−0.403221	+	0.698400i	0.590891	+	0.806751i	$0.298776\pi$
$354$	0.342321	+	0.592918i	0.0181942	+	0.0315132i
$355$	−41.0265	−	48.8935i	−2.17746	−	2.59500i
$356$	0.455673	+	1.25195i	0.0241506	+	0.0663533i
$357$	−0.0585998	+	0.161002i	−0.00310143	+	0.00852110i
$358$	−3.15777	+	3.76328i	−0.166893	+	0.198895i
$359$	−4.19946	−	0.740479i	−0.221639	−	0.0390810i	0.0617256	−	0.998093i	$-0.480340\pi$
$359$	−4.19946	−	0.740479i	−0.221639	−	0.0390810i	−0.283365	+	0.959012i	$0.591451\pi$
$360$	−12.1598			−0.640877
$361$	3.71333	+	18.6336i	0.195438	+	0.980716i
$362$			6.67855i			0.351017i
$363$	−0.658430	+	2.27198i	−0.0345586	+	0.119248i
$364$	4.59871	−	5.48053i	0.241038	−	0.287258i
$365$	−2.63546	+	7.24086i	−0.137946	+	0.379004i
$366$	−2.28150	+	0.830398i	−0.119256	+	0.0434056i
$367$	11.9983	−	10.0678i	0.626308	−	0.525535i	−0.273471	−	0.961880i	$-0.588172\pi$
$367$	11.9983	−	10.0678i	0.626308	−	0.525535i	0.899779	+	0.436345i	$0.143727\pi$
$368$	0.854038	+	1.47924i	0.0445198	+	0.0771106i
$369$	−5.71909	+	9.90575i	−0.297724	+	0.515673i
$370$	−15.2892	+	2.69591i	−0.794850	+	0.140153i
$371$	2.72849	+	15.4741i	0.141656	+	0.803373i
$372$	−0.698804	+	1.21036i	−0.0362313	+	0.0627544i
$373$	−8.99249	−	15.5754i	−0.465613	−	0.806466i	0.533616	−	0.845727i	$-0.320833\pi$
$373$	−8.99249	−	15.5754i	−0.465613	−	0.806466i	−0.999229	+	0.0392612i	$0.987500\pi$
$374$	0.262190	−	1.84665i	0.0135575	−	0.0954880i
$375$	2.10353	+	5.77940i	0.108626	+	0.298447i
$376$	4.03754	+	1.46954i	0.208220	+	0.0757860i
$377$	17.7742	+	14.9143i	0.915417	+	0.768126i
$378$	−0.314980	+	1.78634i	−0.0162008	+	0.0918795i
$379$		−	1.14207i		−	0.0586644i	−0.999570	−	0.0293322i	$-0.990662\pi$
$379$		−	1.14207i		−	0.0586644i	0.999570	−	0.0293322i	$-0.00933807\pi$
$380$	13.8732	+	11.3813i	0.711681	+	0.583850i
$381$			3.86783i			0.198155i
$382$	2.01126	−	11.4064i	0.102905	−	0.583604i
$383$	−21.0198	+	25.0504i	−1.07406	+	1.28002i	−0.116062	+	0.993242i	$0.537027\pi$
$383$	−21.0198	+	25.0504i	−1.07406	+	1.28002i	−0.957999	+	0.286773i	$0.907417\pi$
$384$	0.0735487	−	0.202073i	0.00375327	−	0.0103120i
$385$	9.10557	−	17.0669i	0.464063	−	0.869810i
$386$	6.15058	−	5.16095i	0.313056	−	0.262685i
$387$	25.2777	−	14.5941i	1.28494	−	0.741858i
$388$	−4.21134	−	2.43142i	−0.213798	−	0.123437i
$389$	4.12109	+	23.3719i	0.208948	+	1.18500i	0.891106	+	0.453796i	$0.149931\pi$
$389$	4.12109	+	23.3719i	0.208948	+	1.18500i	−0.682158	+	0.731205i	$0.738958\pi$
$390$	−4.40247	+	0.776274i	−0.222928	+	0.0393082i
$391$	0.831879	+	0.480285i	0.0420699	+	0.0242891i
$392$	−2.49638	−	4.32387i	−0.126086	−	0.218388i
$393$	1.01079	−	0.848155i	0.0509877	−	0.0427838i
$394$	2.76324	+	7.59195i	0.139210	+	0.382477i
$395$	46.6953	+	16.9957i	2.34950	+	0.855147i
$396$	−0.328066	−	9.79101i	−0.0164859	−	0.492017i
$397$	5.57166	−	31.5985i	0.279634	−	1.58588i	−0.444213	−	0.895921i	$-0.646517\pi$
$397$	5.57166	−	31.5985i	0.279634	−	1.58588i	0.723847	−	0.689960i	$-0.242372\pi$
$398$	1.77005			0.0887247
$399$	1.00778	−	0.864848i	0.0504523	−	0.0432966i
$400$	11.9474			0.597370
$401$	−11.0847	−	1.95453i	−0.553544	−	0.0976047i	−0.110123	−	0.993918i	$-0.535124\pi$
$401$	−11.0847	−	1.95453i	−0.553544	−	0.0976047i	−0.443421	+	0.896313i	$0.646235\pi$
$402$	−1.78216	−	1.49541i	−0.0888859	−	0.0745842i
$403$	11.2249	−	30.8402i	0.559153	−	1.53626i
$404$	−4.96259	−	13.6346i	−0.246898	−	0.678347i
$405$	−27.0766	+	22.7200i	−1.34545	+	1.12896i
$406$	−5.63760	+	3.25487i	−0.279790	+	0.161537i
$407$	−2.58323	−	12.2381i	−0.128046	−	0.606620i
$408$	−0.0209998	−	0.119096i	−0.00103965	−	0.00589613i
$409$	−0.151377	−	0.858502i	−0.00748511	−	0.0424502i	0.980836	−	0.194833i	$-0.0624165\pi$
$409$	−0.151377	−	0.858502i	−0.00748511	−	0.0424502i	−0.988322	+	0.152383i	$0.951305\pi$
$410$	7.97083	−	13.8059i	0.393651	−	0.681824i
$411$	1.66089	−	0.958915i	0.0819256	−	0.0472998i
$412$	−1.07706	−	1.28358i	−0.0530627	−	0.0632377i
$413$	4.23862	−	1.54273i	0.208569	−	0.0759129i
$414$	4.74098	+	1.72557i	0.233006	+	0.0848073i
$415$	−26.0822	+	31.0835i	−1.28032	+	1.52583i
$416$	−0.876880	+	4.97303i	−0.0429926	+	0.243823i
$417$	0.940560			0.0460594
$418$	−8.78990	+	11.4777i	−0.429928	+	0.561393i
$419$	23.0391			1.12553			0.562767	−	0.826615i	$-0.309737\pi$
$419$	23.0391			1.12553			0.562767	+	0.826615i	$0.309737\pi$
$420$	0.217793	−	1.23516i	0.0106272	−	0.0602699i
$421$	11.1071	−	13.2369i	0.541326	−	0.645127i	−0.424158	−	0.905588i	$-0.639430\pi$
$421$	11.1071	−	13.2369i	0.541326	−	0.645127i	0.965484	+	0.260461i	$0.0838745\pi$
$422$	−2.27005	−	0.826229i	−0.110504	−	0.0402202i
$423$	11.9259	−	4.34068i	0.579858	−	0.211051i
$424$	−7.12888	−	8.49587i	−0.346209	−	0.412596i
$425$	5.81870	−	3.35943i	0.282249	−	0.162956i
$426$	1.66701	−	2.88735i	0.0807671	−	0.139893i
$427$	2.77766	+	15.7529i	0.134421	+	0.762337i
$428$	−0.799048	−	4.53162i	−0.0386234	−	0.219044i
$429$	−0.743829	−	3.52390i	−0.0359124	−	0.170136i
$430$	−35.2301	+	20.3401i	−1.69895	+	0.980887i
$431$	−18.9086	+	15.8662i	−0.910795	+	0.764248i	−0.972270	−	0.233861i	$-0.924864\pi$
$431$	−18.9086	+	15.8662i	−0.910795	+	0.764248i	0.0614753	+	0.998109i	$0.480419\pi$
$432$	−0.437891	−	1.20310i	−0.0210680	−	0.0578840i
$433$	1.21059	−	3.32608i	0.0581774	−	0.159841i	−0.907199	−	0.420701i	$-0.861784\pi$
$433$	1.21059	−	3.32608i	0.0581774	−	0.159841i	0.965377	+	0.260860i	$0.0840062\pi$
$434$	7.05366	+	5.91872i	0.338586	+	0.284108i
$435$	4.00582	+	0.706335i	0.192065	+	0.0338662i
$436$	−14.9596			−0.716437
$437$	−3.79391	−	6.40618i	−0.181488	−	0.306449i
$438$	−0.402509			−0.0192326
$439$	−4.38289	+	24.8566i	−0.209184	+	1.18634i	0.681534	+	0.731786i	$0.261313\pi$
$439$	−4.38289	+	24.8566i	−0.209184	+	1.18634i	−0.890718	+	0.454555i	$0.849798\pi$
$440$	0.457233	+	13.6460i	0.0217977	+	0.650546i
$441$	−13.8580	−	5.04392i	−0.659907	−	0.240187i
$442$	0.971279	+	2.66857i	0.0461990	+	0.126931i
$443$	26.4344	−	22.1811i	1.25594	−	1.05386i	0.259833	−	0.965653i	$-0.416332\pi$
$443$	26.4344	−	22.1811i	1.25594	−	1.05386i	0.996103	−	0.0882019i	$-0.0281121\pi$
$444$	−0.405486	−	0.702323i	−0.0192435	−	0.0333308i
$445$	−4.74989	−	2.74235i	−0.225167	−	0.130000i
$446$	13.9936	−	2.46745i	0.662617	−	0.116837i
$447$	−0.436819	−	2.47732i	−0.0206608	−	0.117173i
$448$	−1.22696	−	0.708384i	−0.0579683	−	0.0334680i
$449$	−2.24348	+	1.29527i	−0.105876	+	0.0611276i	−0.552003	−	0.833842i	$-0.686136\pi$
$449$	−2.24348	+	1.29527i	−0.105876	+	0.0611276i	0.446127	+	0.894970i	$0.352803\pi$
$450$	27.0335	−	22.6838i	1.27437	−	1.06932i
$451$	11.3315	+	6.04560i	0.533579	+	0.284676i
$452$	3.13962	−	8.62604i	0.147675	−	0.405735i
$453$	−0.989303	+	1.17901i	−0.0464815	+	0.0553945i
$454$	−1.73586	+	9.84458i	−0.0814681	+	0.462029i
$455$			29.4524i			1.38075i
$456$	−0.310807	+	0.884317i	−0.0145549	+	0.0414120i
$457$		−	19.4616i		−	0.910376i	−0.890395	−	0.455188i	$-0.849572\pi$
$457$		−	19.4616i		−	0.910376i	0.890395	−	0.455188i	$-0.150428\pi$
$458$	2.71575	−	15.4018i	0.126899	−	0.719677i
$459$	−0.551557	−	0.462812i	−0.0257445	−	0.0216022i
$460$	−6.60761	−	2.40497i	−0.308082	−	0.112132i
$461$	9.03892	+	24.8342i	0.420984	+	1.15665i	0.951144	+	0.308747i	$0.0999097\pi$
$461$	9.03892	+	24.8342i	0.420984	+	1.15665i	−0.530160	+	0.847898i	$0.677868\pi$
$462$	1.00042	+	0.142042i	0.0465440	+	0.00660837i
$463$	−0.710075	−	1.22989i	−0.0330000	−	0.0571576i	0.849054	−	0.528306i	$-0.177173\pi$
$463$	−0.710075	−	1.22989i	−0.0330000	−	0.0571576i	−0.882054	+	0.471149i	$0.843839\pi$
$464$	2.29739	−	3.97920i	0.106654	−	0.184730i
$465$	−0.999095	−	5.66615i	−0.0463319	−	0.262761i
$466$	−28.4740	+	5.02074i	−1.31903	+	0.232581i
$467$	3.88554	−	6.72995i	0.179801	−	0.311425i	−0.762011	−	0.647564i	$-0.775788\pi$
$467$	3.88554	−	6.72995i	0.179801	−	0.311425i	0.941812	+	0.336139i	$0.109121\pi$
$468$	7.45787	+	12.9174i	0.344740	+	0.597107i
$469$	−11.7414	+	9.85223i	−0.542169	+	0.454934i
$470$	−16.6214	+	6.04971i	−0.766689	+	0.279052i
$471$	0.949934	−	2.60992i	0.0437707	−	0.120259i
$472$	−2.04648	+	2.43890i	−0.0941970	+	0.112260i
$473$	−17.3282	−	27.8183i	−0.796754	−	1.27909i
$474$			2.59573i			0.119226i
$475$	−52.0743	+	0.577303i	−2.38933	+	0.0264885i
$476$	−0.796748			−0.0365189
$477$	−32.2612	−	5.68852i	−1.47714	−	0.260459i
$478$	−4.82225	+	5.74694i	−0.220565	+	0.262859i
$479$	2.54951	−	7.00472i	0.116490	−	0.320054i	−0.867721	−	0.497051i	$-0.834416\pi$
$479$	2.54951	−	7.00472i	0.116490	−	0.320054i	0.984211	+	0.176997i	$0.0566383\pi$
$480$	0.302780	+	0.831880i	0.0138199	+	0.0379700i
$481$	12.2411	+	14.5884i	0.558146	+	0.665173i
$482$	−4.88419	−	8.45967i	−0.222469	−	0.385327i
$483$	−0.260195	+	0.450671i	−0.0118393	+	0.0205063i
$484$	−10.9753	+	0.736323i	−0.498879	+	0.0334692i
$485$	19.7148	−	3.47625i	0.895204	−	0.157849i
$486$	−4.92532	−	2.84363i	−0.223417	−	0.128990i
$487$	1.14184	−	0.659243i	0.0517418	−	0.0298732i	−0.473906	−	0.880575i	$-0.657156\pi$
$487$	1.14184	−	0.659243i	0.0517418	−	0.0298732i	0.525648	+	0.850702i	$0.323823\pi$
$488$	−7.25736	−	8.64898i	−0.328525	−	0.391521i
$489$	−0.280255	−	0.769995i	−0.0126736	−	0.0348204i
$490$	19.3143	+	7.02983i	0.872531	+	0.317575i
$491$	−14.5297	+	17.3158i	−0.655714	+	0.781449i	−0.986764	−	0.162164i	$-0.948153\pi$
$491$	−14.5297	+	17.3158i	−0.655714	+	0.781449i	0.331050	+	0.943613i	$0.392597\pi$
$492$	0.820081	+	0.144602i	0.0369721	+	0.00651918i
$493$		−	2.58397i		−	0.116376i
$494$	3.58170	−	21.7180i	0.161148	−	0.977139i
$495$	26.9433	+	30.0087i	1.21101	+	1.34879i
$496$	−6.40049	−	1.12858i	−0.287390	−	0.0506747i
$497$	−16.8267	−	14.1193i	−0.754779	−	0.633335i
$498$	−1.99175	−	0.724936i	−0.0892522	−	0.0324852i
$499$	−32.8270	+	11.9480i	−1.46954	+	0.534868i	−0.947975	−	0.318346i	$-0.896873\pi$
$499$	−32.8270	+	11.9480i	−1.46954	+	0.534868i	−0.521562	+	0.853213i	$0.674650\pi$
$500$	−21.9093	+	18.3840i	−0.979812	+	0.822160i
$501$	1.10996	−	0.640835i	0.0495893	−	0.0286304i
$502$	−4.98392	+	8.63240i	−0.222443	+	0.385283i
$503$	2.91678	−	0.514307i	0.130053	−	0.0229318i	−0.108243	−	0.994124i	$-0.534522\pi$
$503$	2.91678	−	0.514307i	0.130053	−	0.0229318i	0.238296	+	0.971193i	$0.423411\pi$
$504$	−4.12121	+	0.726681i	−0.183573	+	0.0323689i
$505$	51.7296	+	29.8661i	2.30194	+	1.32902i
$506$	1.75820	−	5.38530i	0.0781617	−	0.239406i
$507$	1.72783	+	2.05915i	0.0767356	+	0.0914499i
$508$	−16.9017	+	6.15170i	−0.749890	+	0.272938i
$509$	0.426741	−	1.17246i	0.0189150	−	0.0519684i	−0.929876	−	0.367874i	$-0.880086\pi$
$509$	0.426741	−	1.17246i	0.0189150	−	0.0519684i	0.948791	+	0.315905i	$0.102308\pi$
$510$	0.381374	+	0.320011i	0.0168875	+	0.0141703i
$511$	−0.460491	+	2.61158i	−0.0203709	+	0.115529i
$512$	1.00000			0.0441942
$513$	1.96674	+	5.22269i	0.0868337	+	0.230588i
$514$		−	22.0813i		−	0.973966i
$515$	6.79318	+	1.19782i	0.299343	+	0.0527823i
$516$	−1.62783	−	1.36591i	−0.0716612	−	0.0601309i
$517$	−5.31963	−	13.2203i	−0.233957	−	0.581427i
$518$	−5.02074	+	1.82740i	−0.220598	+	0.0802913i
$519$	2.31873	+	2.76336i	0.101781	+	0.121298i
$520$	−10.3942	−	18.0033i	−0.455816	−	0.789497i
$521$	−2.60421	−	1.50354i	−0.114093	−	0.0658714i	0.441868	−	0.897080i	$-0.354316\pi$
$521$	−2.60421	−	1.50354i	−0.114093	−	0.0658714i	−0.555960	+	0.831209i	$0.687649\pi$
$522$	−2.35673	−	13.3657i	−0.103151	−	0.585001i
$523$	−6.16485	−	34.9626i	−0.269570	−	1.52881i	−0.755698	−	0.654920i	$-0.772702\pi$
$523$	−6.16485	−	34.9626i	−0.269570	−	1.52881i	0.486128	−	0.873888i	$-0.338409\pi$
$524$	5.31392	+	3.06799i	0.232140	+	0.134026i
$525$	1.81997	+	3.15229i	0.0794302	+	0.137577i
$526$	6.27962	+	7.48376i	0.273805	+	0.326308i
$527$	−3.43455	+	1.25007i	−0.149611	+	0.0544541i
$528$	−0.661657	+	0.266240i	−0.0287949	+	0.0115866i
$529$	−15.3841	−	12.9088i	−0.668873	−	0.561251i
$530$	44.9632	+	7.92822i	1.95308	+	0.344380i
$531$			9.40406i			0.408101i
$532$	5.38208	+	3.02830i	0.233343	+	0.131293i
$533$	−19.5547			−0.847010
$534$	0.0497503	−	0.282148i	0.00215290	−	0.0122097i
$535$	14.5114	+	12.1765i	0.627381	+	0.526435i
$536$	3.70016	−	10.1661i	0.159823	−	0.439109i
$537$	0.992708	−	0.361316i	0.0428385	−	0.0155919i
$538$	−18.7291	−	22.3204i	−0.807468	−	0.962302i
$539$	−5.13929	+	15.7414i	−0.221365	+	0.678032i
$540$	4.56454	+	2.63534i	0.196426	+	0.113407i
$541$	21.3878	−	3.77125i	0.919534	−	0.162139i	0.306205	−	0.951966i	$-0.400941\pi$
$541$	21.3878	−	3.77125i	0.919534	−	0.162139i	0.613330	+	0.789827i	$0.289830\pi$
$542$	17.3265	−	3.05512i	0.744235	−	0.131229i
$543$	0.718085	−	1.24376i	0.0308160	−	0.0533748i
$544$	0.487027	−	0.281185i	0.0208811	−	0.0120557i
$545$	47.1766	−	39.5859i	2.02082	−	1.69567i
$546$	−1.44570	+	0.526191i	−0.0618702	+	0.0225189i
$547$	−24.2026	−	8.80903i	−1.03483	−	0.376647i	−0.231911	−	0.972737i	$-0.574498\pi$
$547$	−24.2026	−	8.80903i	−1.03483	−	0.376647i	−0.802918	+	0.596090i	$0.796720\pi$
$548$	6.83188	+	5.73263i	0.291844	+	0.244886i
$549$	−32.8426	−	5.79103i	−1.40169	−	0.247155i
$550$	−26.4727	−	29.4846i	−1.12880	−	1.25723i
$551$	−9.82122	+	17.4549i	−0.418398	+	0.743603i
$552$		−	0.367308i		−	0.0156337i
$553$	16.8417	+	2.96965i	0.716182	+	0.126282i
$554$	−19.7681	+	23.5587i	−0.839867	+	1.00091i
$555$	3.13721	+	1.14185i	0.133167	+	0.0484689i
$556$	1.49594	+	4.11007i	0.0634421	+	0.174306i
$557$	15.8238	+	18.8580i	0.670475	+	0.799041i	0.988849	−	0.148924i	$-0.0475811\pi$
$557$	15.8238	+	18.8580i	0.670475	+	0.799041i	−0.318374	+	0.947965i	$0.603137\pi$
$558$	−16.6252	+	9.59857i	−0.703801	+	0.406340i
$559$	43.2148	+	24.9501i	1.82779	+	1.05528i
$560$	5.74383	−	1.01279i	0.242721	−	0.0427983i
$561$	−0.247382	+	0.315714i	−0.0104445	+	0.0133295i
$562$	10.2768	−	17.8000i	0.433502	−	0.750848i
$563$	4.83017	+	8.36609i	0.203567	+	0.352589i	0.949675	−	0.313236i	$-0.101413\pi$
$563$	4.83017	+	8.36609i	0.203567	+	0.352589i	−0.746108	+	0.665825i	$0.768080\pi$
$564$	−0.593912	−	0.707797i	−0.0250082	−	0.0298036i
$565$	12.9249	+	35.5110i	0.543757	+	1.49396i
$566$	6.73345	−	18.5000i	0.283028	−	0.777613i
$567$	−7.81906	+	9.31839i	−0.328370	+	0.391336i
$568$	15.2685	+	2.69225i	0.640653	+	0.112964i
$569$	22.3511			0.937007			0.468503	−	0.883462i	$-0.344793\pi$
$569$	22.3511			0.937007			0.468503	+	0.883462i	$0.344793\pi$
$570$	−1.35990	−	3.61123i	−0.0569600	−	0.151258i
$571$		−	21.8681i		−	0.915150i	−0.889171	−	0.457575i	$-0.848718\pi$
$571$		−	21.8681i		−	0.915150i	0.889171	−	0.457575i	$-0.151282\pi$
$572$	14.2157	−	8.85509i	0.594390	−	0.370250i
$573$	−1.60099	+	1.90799i	−0.0668824	+	0.0797074i
$574$	1.87643	−	5.15545i	0.0783207	−	0.215184i
$575$	19.1764	−	6.97963i	0.799710	−	0.291071i
$576$	2.26271	−	1.89864i	0.0942795	−	0.0791099i
$577$	4.16257	+	7.20978i	0.173290	+	0.300147i	0.939568	−	0.342362i	$-0.111227\pi$
$577$	4.16257	+	7.20978i	0.173290	+	0.300147i	−0.766278	+	0.642509i	$0.777894\pi$
$578$	−8.34187	+	14.4485i	−0.346976	+	0.600980i
$579$	−1.70034	+	0.299816i	−0.0706639	+	0.0124599i
$580$	3.28464	+	18.6281i	0.136387	+	0.773489i
$581$	−6.98221	+	12.0935i	−0.289671	+	0.501725i
$582$	0.522857	+	0.905616i	0.0216731	+	0.0375390i
$583$	−5.17068	+	36.4180i	−0.214148	+	1.50828i
$584$	−0.640183	−	1.75889i	−0.0264910	−	0.0727834i
$585$	−57.7008	−	21.0014i	−2.38564	−	0.868300i
$586$	−0.937263	−	0.786457i	−0.0387180	−	0.0324882i
$587$	3.56767	−	20.2333i	0.147253	−	0.835116i	−0.818277	−	0.574824i	$-0.805070\pi$
$587$	3.56767	−	20.2333i	0.147253	−	0.835116i	0.965530	−	0.260291i	$-0.0838186\pi$
$588$			1.07366i			0.0442768i
$589$	27.9519	+	4.60979i	1.15174	+	0.189943i
$590$		−	13.1067i		−	0.539593i
$591$	0.301690	−	1.71097i	0.0124099	−	0.0703799i
$592$	2.42410	−	2.88893i	0.0996299	−	0.118734i
$593$	−9.24313	+	25.3953i	−0.379570	+	1.04286i	0.591965	+	0.805964i	$0.298352\pi$
$593$	−9.24313	+	25.3953i	−0.379570	+	1.04286i	−0.971535	+	0.236896i	$0.923870\pi$
$594$	−1.99881	+	3.74644i	−0.0820122	+	0.153718i
$595$	2.51262	−	2.10834i	0.103007	−	0.0864333i
$596$	10.1307	−	5.84895i	0.414968	−	0.239582i
$597$	−0.329640	−	0.190318i	−0.0134913	−	0.00778919i
$598$	1.49778	+	8.49432i	0.0612487	+	0.347359i
$599$	38.8069	−	6.84270i	1.58561	−	0.279585i	0.689789	−	0.724010i	$-0.257703\pi$
$599$	38.8069	−	6.84270i	1.58561	−	0.279585i	0.895816	+	0.444425i	$0.146592\pi$
$600$	−2.22499	−	1.28460i	−0.0908347	−	0.0524434i
$601$	−17.9238	−	31.0449i	−0.731125	−	1.26635i	−0.956403	−	0.292051i	$-0.905662\pi$
$601$	−17.9238	−	31.0449i	−0.731125	−	1.26635i	0.225278	−	0.974295i	$-0.427671\pi$
$602$	−10.7247	+	8.99907i	−0.437105	+	0.366775i
$603$	−10.9294	−	30.0282i	−0.445078	−	1.22284i
$604$	−6.72550	−	2.44788i	−0.273657	−	0.0996028i
$605$	32.6633	−	31.3647i	1.32795	−	1.27516i
$606$	−0.541815	+	3.07278i	−0.0220097	+	0.124823i
$607$	−27.5820			−1.11952			−0.559760	−	0.828655i	$-0.689106\pi$
$607$	−27.5820			−1.11952			−0.559760	+	0.828655i	$0.689106\pi$
$608$	−4.35863	+	0.0483204i	−0.176766	+	0.00195965i
$609$	1.39987			0.0567256
$610$	45.7735	+	8.07110i	1.85331	+	0.326789i
$611$	16.6209	+	13.9466i	0.672410	+	0.564219i
$612$	0.568131	−	1.56093i	0.0229653	−	0.0630968i
$613$	−2.00096	−	5.49760i	−0.0808182	−	0.222046i	0.892702	−	0.450648i	$-0.148807\pi$
$613$	−2.00096	−	5.49760i	−0.0808182	−	0.222046i	−0.973520	+	0.228602i	$0.926585\pi$
$614$	6.32793	−	5.30977i	0.255375	−	0.214285i
$615$	−2.96885	+	1.71406i	−0.119715	+	0.0691177i
$616$	0.970461	+	4.59758i	0.0391010	+	0.185242i
$617$	−1.79000	−	10.1516i	−0.0720626	−	0.408687i	−0.999406	−	0.0344747i	$-0.989024\pi$
$617$	−1.79000	−	10.1516i	−0.0720626	−	0.408687i	0.927343	−	0.374212i	$-0.122087\pi$
$618$	0.0625697	+	0.354850i	0.00251692	+	0.0142742i
$619$	−1.20969	+	2.09525i	−0.0486217	+	0.0842152i	−0.889312	−	0.457301i	$-0.848816\pi$
$619$	−1.20969	+	2.09525i	−0.0486217	+	0.0842152i	0.840690	+	0.541516i	$0.182150\pi$
$620$	23.1710	−	13.3778i	0.930568	−	0.537264i
$621$	−1.40569	−	1.67523i	−0.0564084	−	0.0672249i
$622$	31.2706	−	11.3816i	1.25384	−	0.456359i
$623$	−1.77372	−	0.645583i	−0.0710628	−	0.0258647i
$624$	0.698009	−	0.831855i	0.0279427	−	0.0333008i
$625$	10.0722	−	57.1221i	0.402887	−	2.28488i
$626$	−14.1628			−0.566058
$627$	2.87105	−	1.19242i	0.114659	−	0.0476205i
$628$	12.9157			0.515393
$629$	0.368278	−	2.08861i	0.0146842	−	0.0832782i
$630$	11.0737	−	13.1971i	0.441186	−	0.525785i
$631$	42.5301	+	15.4797i	1.69310	+	0.616236i	0.995010	−	0.0997774i	$-0.0318131\pi$
$631$	42.5301	+	15.4797i	1.69310	+	0.616236i	0.698086	+	0.716014i	$0.254035\pi$
$632$	−11.3428	+	4.12846i	−0.451194	+	0.164221i
$633$	0.333918	+	0.397948i	0.0132720	+	0.0158170i
$634$	−6.83464	+	3.94598i	−0.271438	+	0.156715i
$635$	37.0225	−	64.1248i	1.46919	−	2.54471i
$636$	0.414140	+	2.34871i	0.0164217	+	0.0931323i
$637$	−4.37806	−	24.8292i	−0.173465	−	0.983769i
$638$	−14.9106	+	3.14735i	−0.590318	+	0.124605i
$639$	39.6598	−	22.8976i	1.56892	−	0.905816i
$640$	−3.15359	+	2.64618i	−0.124657	+	0.104599i
$641$	−12.2708	−	33.7137i	−0.484667	−	1.33161i	−0.905451	−	0.424451i	$-0.860467\pi$
$641$	−12.2708	−	33.7137i	−0.484667	−	1.33161i	0.420784	−	0.907161i	$-0.361755\pi$
$642$	−0.338437	+	0.929847i	−0.0133570	+	0.0366982i
$643$	−9.12364	−	7.65564i	−0.359801	−	0.301909i	0.444910	−	0.895575i	$-0.353236\pi$
$643$	−9.12364	−	7.65564i	−0.359801	−	0.301909i	−0.804711	+	0.593666i	$0.797680\pi$
$644$	−2.38318	−	0.420219i	−0.0939105	−	0.0165590i
$645$	8.74796			0.344450
$646$	−2.10918	+	1.24912i	−0.0829847	+	0.0491458i
$647$	−8.91401			−0.350446			−0.175223	−	0.984529i	$-0.556065\pi$
$647$	−8.91401			−0.350446			−0.175223	+	0.984529i	$0.556065\pi$
$648$	1.49093	−	8.45551i	0.0585694	−	0.332164i
$649$	10.5534	−	0.353611i	0.414258	−	0.0138805i
$650$	56.6930	+	20.6346i	2.22368	+	0.809354i
$651$	−0.677229	−	1.86067i	−0.0265427	−	0.0729254i
$652$	2.91899	−	2.44932i	0.114316	−	0.0959229i
$653$	1.83480	+	3.17797i	0.0718013	+	0.124364i	0.899691	−	0.436528i	$-0.143792\pi$
$653$	1.83480	+	3.17797i	0.0718013	+	0.124364i	−0.827889	+	0.560891i	$0.810459\pi$
$654$	2.78596	+	1.60848i	0.108940	+	0.0628964i
$655$	−24.8764	+	4.38638i	−0.972001	+	0.171390i
$656$	0.672438	+	3.81359i	0.0262543	+	0.148895i
$657$	−4.78804	−	2.76438i	−0.186799	−	0.107849i
$658$	−5.27182	+	3.04368i	−0.205517	+	0.118655i
$659$	14.6409	−	12.2852i	0.570328	−	0.478562i	−0.311427	−	0.950270i	$-0.600807\pi$
$659$	14.6409	−	12.2852i	0.570328	−	0.478562i	0.881755	+	0.471708i	$0.156363\pi$
$660$	1.38208	−	2.59048i	0.0537973	−	0.100834i
$661$	−0.923366	+	2.53693i	−0.0359148	+	0.0986751i	−0.956354	−	0.292211i	$-0.905609\pi$
$661$	−0.923366	+	2.53693i	−0.0359148	+	0.0986751i	0.920439	+	0.390886i	$0.127831\pi$
$662$	−1.89929	+	2.26348i	−0.0738179	+	0.0879728i
$663$	0.106044	−	0.601405i	0.00411841	−	0.0233566i
$664$		−	9.85654i		−	0.382508i
$665$	−24.9863	+	4.69193i	−0.968927	+	0.181945i
$666$		−	11.1393i		−	0.431639i
$667$	1.36283	−	7.72901i	0.0527691	−	0.299269i
$668$	4.56569	+	3.83107i	0.176652	+	0.148229i
$669$	−2.87136	−	1.04509i	−0.111013	−	0.0404055i
$670$	15.2325	+	41.8510i	0.588484	+	1.61685i
$671$	−5.26386	+	37.0743i	−0.203209	+	1.43124i
$672$	0.152332	+	0.263847i	0.00587635	+	0.0101781i
$673$	22.5373	−	39.0358i	0.868749	−	1.50472i	0.00547405	−	0.999985i	$-0.498258\pi$
$673$	22.5373	−	39.0358i	0.868749	−	1.50472i	0.863275	−	0.504733i	$-0.168409\pi$
$674$	3.33142	+	18.8934i	0.128321	+	0.727746i
$675$	−15.0640	+	2.65618i	−0.579812	+	0.102237i
$676$	−6.25000	+	10.8253i	−0.240384	+	0.416358i
$677$	−6.50017	−	11.2586i	−0.249822	−	0.432704i	0.713654	−	0.700498i	$-0.247039\pi$
$677$	−6.50017	−	11.2586i	−0.249822	−	0.432704i	−0.963476	+	0.267794i	$0.913705\pi$
$678$	−1.51218	+	1.26887i	−0.0580749	+	0.0487306i
$679$	6.47402	−	2.35635i	0.248450	−	0.0904285i
$680$	−0.791818	+	2.17550i	−0.0303648	+	0.0834267i
$681$	1.38177	−	1.64673i	0.0529496	−	0.0631029i
$682$	11.3968	+	18.2962i	0.436408	+	0.700598i
$683$		−	38.4112i		−	1.46976i	−0.678196	−	0.734881i	$-0.737238\pi$
$683$		−	38.4112i		−	1.46976i	0.678196	−	0.734881i	$-0.262762\pi$
$684$	−9.77057	+	8.38480i	−0.373587	+	0.320601i
$685$	−36.7145			−1.40279
$686$	16.7328	+	2.95045i	0.638863	+	0.112649i
$687$	−2.16177	+	2.57630i	−0.0824768	+	0.0982920i
$688$	3.37974	−	9.28576i	0.128851	−	0.354016i
$689$	−19.1547	−	52.6272i	−0.729737	−	2.00493i
$690$	0.971963	+	1.15834i	0.0370020	+	0.0440973i
$691$	−3.36321	−	5.82526i	−0.127943	−	0.221603i	0.794937	−	0.606692i	$-0.207504\pi$
$691$	−3.36321	−	5.82526i	−0.127943	−	0.221603i	−0.922879	+	0.385089i	$0.874171\pi$
$692$	−8.38745	+	14.5275i	−0.318843	+	0.552252i
$693$	10.9250	+	8.56043i	0.415007	+	0.325184i
$694$	−28.0797	+	4.95121i	−1.06589	+	0.187945i
$695$	−15.5936	−	9.00295i	−0.591497	−	0.341501i
$696$	−0.855696	+	0.494036i	−0.0324351	+	0.0187264i
$697$	1.39982	+	1.66824i	0.0530219	+	0.0631890i
$698$	−11.1764	−	30.7070i	−0.423035	−	1.16228i
$699$	5.84260	+	2.12653i	0.220988	+	0.0804329i
$700$	−10.8803	+	12.9666i	−0.411235	+	0.490091i
$701$	−11.5379	−	2.03444i	−0.435780	−	0.0768398i	−0.0485456	−	0.998821i	$-0.515459\pi$
$701$	−11.5379	−	2.03444i	−0.435780	−	0.0768398i	−0.387235	+	0.921981i	$0.626570\pi$
$702$		−	6.46524i		−	0.244015i
$703$	−10.4262	+	12.7089i	−0.393230	+	0.479326i
$704$	−2.21577	−	2.46786i	−0.0835100	−	0.0930111i
$705$	3.74591	+	0.660505i	0.141079	+	0.0248761i
$706$	11.6069	+	9.73931i	0.436830	+	0.366544i
$707$	19.3171	+	7.03084i	0.726493	+	0.264422i
$708$	0.643353	−	0.234162i	0.0241787	−	0.00880033i
$709$	10.3469	−	8.68208i	0.388586	−	0.326062i	−0.427476	−	0.904027i	$-0.640597\pi$
$709$	10.3469	−	8.68208i	0.388586	−	0.326062i	0.816062	+	0.577964i	$0.196153\pi$
$710$	−55.2749	+	31.9130i	−2.07443	+	1.19767i
$711$	−17.8271	+	30.8774i	−0.668569	+	1.15799i
$712$	1.31206	−	0.231351i	0.0491715	−	0.00867026i
$713$	−10.9325	+	1.92770i	−0.409426	+	0.0721929i
$714$	0.148380	+	0.0856671i	0.00555298	+	0.00320601i
$715$	−21.3985	+	65.5427i	−0.800259	+	2.45116i
$716$	3.15777	+	3.76328i	0.118011	+	0.140640i
$717$	1.51597	−	0.551769i	0.0566151	−	0.0206062i
$718$	−1.45846	+	4.00708i	−0.0544292	+	0.149543i
$719$	19.4048	+	16.2826i	0.723677	+	0.607237i	0.928400	−	0.371583i	$-0.121185\pi$
$719$	19.4048	+	16.2826i	0.723677	+	0.607237i	−0.204723	+	0.978820i	$0.565629\pi$
$720$	−2.11153	+	11.9751i	−0.0786919	+	0.446284i
$721$	2.37394			0.0884100
$722$	18.9953	−	0.421222i	0.706933	−	0.0156762i
$723$			2.10061i			0.0781227i
$724$	6.57709	+	1.15972i	0.244436	+	0.0431006i
$725$	−42.0526	−	35.2863i	−1.56179	−	1.31050i
$726$	2.12313	+	1.04295i	0.0787966	+	0.0387076i
$727$	−13.8932	+	5.05671i	−0.515271	+	0.187543i	−0.586550	−	0.809913i	$-0.699514\pi$
$727$	−13.8932	+	5.05671i	−0.515271	+	0.187543i	0.0712791	+	0.997456i	$0.477292\pi$
$728$	−4.59871	−	5.48053i	−0.170440	−	0.203122i
$729$	−12.2674	−	21.2478i	−0.454349	−	0.786956i
$730$	6.67321	+	3.85278i	0.246987	+	0.142598i
$731$	−0.964993	−	5.47275i	−0.0356916	−	0.202417i
$732$	0.421604	+	2.39103i	0.0155829	+	0.0883752i
$733$	2.42263	+	1.39871i	0.0894819	+	0.0516624i	0.544073	−	0.839038i	$-0.316881\pi$
$733$	2.42263	+	1.39871i	0.0894819	+	0.0516624i	−0.454591	+	0.890700i	$0.650215\pi$
$734$	−7.83136	−	13.5643i	−0.289061	−	0.500668i
$735$	−2.84108	−	3.38587i	−0.104795	−	0.124890i
$736$	1.60507	−	0.584196i	0.0591635	−	0.0215338i
$737$	−33.2873	+	13.3943i	−1.22615	+	0.493384i
$738$	8.76215	+	7.35232i	0.322539	+	0.270643i
$739$	33.0045	+	5.81958i	1.21409	+	0.214077i	0.743780	−	0.668425i	$-0.233031\pi$
$739$	33.0045	+	5.81958i	1.21409	+	0.214077i	0.470309	+	0.882502i	$0.344142\pi$
$740$			15.5251i			0.570714i
$741$	−3.00217	+	3.65948i	−0.110287	+	0.134434i
$742$	15.7128			0.576834
$743$	−8.03916	+	45.5923i	−0.294928	+	1.67262i	0.372566	+	0.928006i	$0.378478\pi$
$743$	−8.03916	+	45.5923i	−0.294928	+	1.67262i	−0.667494	+	0.744615i	$0.732633\pi$
$744$	1.07063	+	0.898365i	0.0392512	+	0.0329356i
$745$	−16.4707	+	45.2527i	−0.603438	+	1.65793i
$746$	−16.9003	+	6.15122i	−0.618766	+	0.225212i
$747$	−18.7140	−	22.3025i	−0.684710	−	0.816005i
$748$	−1.77307	−	0.578874i	−0.0648297	−	0.0211657i
$749$	5.64588	+	3.25965i	0.206296	+	0.119105i
$750$	6.05687	−	1.06799i	0.221166	−	0.0389975i
$751$	1.36213	−	0.240181i	0.0497050	−	0.00876432i	−0.148740	−	0.988876i	$-0.547522\pi$
$751$	1.36213	−	0.240181i	0.0497050	−	0.00876432i	0.198445	+	0.980112i	$0.436411\pi$
$752$	2.14833	−	3.72102i	0.0783415	−	0.135692i
$753$	1.85633	−	1.07175i	0.0676484	−	0.0390568i
$754$	17.7742	−	14.9143i	0.647297	−	0.543147i
$755$	27.6870	−	10.0772i	1.00763	−	0.366748i
$756$	1.70451	+	0.620390i	0.0619923	+	0.0225634i
$757$	2.83489	+	2.37875i	0.103036	+	0.0864573i	0.692850	−	0.721082i	$-0.256355\pi$
$757$	2.83489	+	2.37875i	0.103036	+	0.0864573i	−0.589814	+	0.807539i	$0.700799\pi$
$758$	−1.12472	−	0.198319i	−0.0408518	−	0.00720327i
$759$	−0.906467	+	0.813871i	−0.0329027	+	0.0295417i
$760$	13.6175	−	11.6861i	0.493958	−	0.423899i
$761$			26.9964i			0.978618i	0.872110	+	0.489309i	$0.162751\pi$
$761$			26.9964i			0.978618i	−0.872110	+	0.489309i	$0.837249\pi$
$762$	3.80907	+	0.671641i	0.137988	+	0.0243310i
$763$	13.6235	−	16.2358i	0.493202	−	0.587775i
$764$	−10.8839	−	3.96141i	−0.393766	−	0.143319i
$765$	2.33884	+	6.42590i	0.0845609	+	0.232329i
$766$	21.0198	+	25.0504i	0.759475	+	0.905107i
$767$	−13.9233	+	8.03860i	−0.502740	+	0.290257i
$768$	−0.186232	−	0.107521i	−0.00672006	−	0.00387983i
$769$	34.6420	−	6.10832i	1.24922	−	0.220272i	0.490359	−	0.871521i	$-0.336866\pi$
$769$	34.6420	−	6.10832i	1.24922	−	0.220272i	0.758864	+	0.651249i	$0.225755\pi$
$770$	−15.2265	−	11.9309i	−0.548723	−	0.429959i
$771$	−2.37421	+	4.11225i	−0.0855050	+	0.148099i
$772$	−4.01450	−	6.95332i	−0.144485	−	0.250256i
$773$	15.1614	+	18.0687i	0.545318	+	0.649885i	0.966371	−	0.257151i	$-0.0827838\pi$
$773$	15.1614	+	18.0687i	0.545318	+	0.649885i	−0.421053	+	0.907036i	$0.638339\pi$
$774$	−9.98293	−	27.4279i	−0.358829	−	0.985875i
$775$	−26.5575	+	72.9661i	−0.953973	+	2.62102i
$776$	−3.12577	+	3.72515i	−0.112209	+	0.133725i
$777$	1.13150	+	0.199515i	0.0405925	+	0.00715755i
$778$	23.7324			0.850848
$779$	−3.11518	−	16.5895i	−0.111613	−	0.594381i
$780$			4.47039i			0.160065i
$781$	−27.1875	−	43.6461i	−0.972844	−	1.56178i
$782$	0.617443	−	0.735840i	0.0220797	−	0.0263136i
$783$	−2.01202	+	5.52797i	−0.0719036	+	0.197554i
$784$	−4.69167	+	1.70763i	−0.167560	+	0.0609867i
$785$	−40.7309	+	34.1773i	−1.45375	+	1.21984i
$786$	−0.659748	−	1.14272i	−0.0235324	−	0.0407593i
$787$	−16.5011	+	28.5808i	−0.588201	+	1.01879i	0.406267	+	0.913754i	$0.366830\pi$
$787$	−16.5011	+	28.5808i	−0.588201	+	1.01879i	−0.994468	+	0.105040i	$0.966503\pi$
$788$	7.95645	−	1.40294i	0.283437	−	0.0499775i
$789$	−0.364804	−	2.06891i	−0.0129874	−	0.0736550i
$790$	24.8461	−	43.0346i	0.883983	−	1.53110i
$791$	6.50271	+	11.2630i	0.231210	+	0.400467i
$792$	−9.69923	−	1.37711i	−0.344647	−	0.0489334i
$793$	−19.4999	−	53.5756i	−0.692462	−	1.90252i
$794$	−30.1509	−	10.9740i	−1.07002	−	0.389454i
$795$	−7.52113	−	6.31097i	−0.266747	−	0.223827i
$796$	0.307366	−	1.74316i	0.0108943	−	0.0617847i
$797$		−	22.6440i		−	0.802090i	−0.916058	−	0.401045i	$-0.868647\pi$
$797$		−	22.6440i		−	0.802090i	0.916058	−	0.401045i	$-0.131353\pi$
$798$	−0.676709	−	1.14265i	−0.0239553	−	0.0404494i
$799$		−	2.41631i		−	0.0854830i
$800$	2.07464	−	11.7659i	0.0733497	−	0.415987i
$801$	2.52955	−	3.01461i	0.0893774	−	0.106516i
$802$	−3.84968	+	10.5769i	−0.135937	+	0.373484i
$803$	−2.92220	+	5.47718i	−0.103122	+	0.193286i
$804$	−1.78216	+	1.49541i	−0.0628518	+	0.0527390i
$805$	8.62756	−	4.98112i	0.304081	−	0.175562i
$806$	−28.4225	−	16.4097i	−1.00114	−	0.578009i
$807$	1.08803	+	6.17055i	0.0383006	+	0.217214i
$808$	−14.2892	+	2.51957i	−0.502693	+	0.0886383i
$809$	28.7639	+	16.6068i	1.01128	+	0.583865i	0.911567	−	0.411151i	$-0.134873\pi$
$809$	28.7639	+	16.6068i	1.01128	+	0.583865i	0.0997164	+	0.995016i	$0.468206\pi$
$810$	17.6730	+	30.6105i	0.620965	+	1.07554i
$811$	−11.8978	+	9.98342i	−0.417787	+	0.350565i	−0.827321	−	0.561730i	$-0.810136\pi$
$811$	−11.8978	+	9.98342i	−0.417787	+	0.350565i	0.409533	+	0.912295i	$0.365692\pi$
$812$	2.22646	+	6.11716i	0.0781336	+	0.214670i
$813$	−3.55523	−	1.29400i	−0.124687	−	0.0453825i
$814$	−12.5007	+	0.418860i	−0.438151	+	0.0146810i
$815$	−2.72396	+	15.4483i	−0.0954161	+	0.541132i
$816$	−0.120933			−0.00423351
$817$	−14.2823	+	40.6365i	−0.499676	+	1.42169i
$818$	−0.871746			−0.0304799
$819$	−20.8111	−	3.66956i	−0.727198	−	0.128225i
$820$	−12.2120	−	10.2471i	−0.426462	−	0.357844i
$821$	2.91764	−	8.01615i	0.101826	−	0.279766i	−0.878310	−	0.478092i	$-0.841328\pi$
$821$	2.91764	−	8.01615i	0.101826	−	0.279766i	0.980136	+	0.198327i	$0.0635507\pi$
$822$	−0.655936	−	1.80217i	−0.0228784	−	0.0628579i
$823$	28.8787	−	24.2321i	1.00665	−	0.844677i	0.0187559	−	0.999824i	$-0.494029\pi$
$823$	28.8787	−	24.2321i	1.00665	−	0.844677i	0.987891	+	0.155147i	$0.0495850\pi$
$824$	−1.45111	+	0.837800i	−0.0505519	+	0.0291861i
$825$	1.75985	+	8.33734i	0.0612702	+	0.290269i
$826$	−0.783266	−	4.44212i	−0.0272533	−	0.154561i
$827$	0.244142	+	1.38460i	0.00848963	+	0.0481471i	0.988758	−	0.149523i	$-0.0477737\pi$
$827$	0.244142	+	1.38460i	0.00848963	+	0.0481471i	−0.980269	+	0.197670i	$0.936663\pi$
$828$	2.52262	−	4.36931i	0.0876671	−	0.151844i
$829$	−4.00137	+	2.31019i	−0.138973	+	0.0802363i	−0.567875	−	0.823115i	$-0.692234\pi$
$829$	−4.00137	+	2.31019i	−0.138973	+	0.0802363i	0.428901	+	0.903351i	$0.358901\pi$
$830$	26.0822	+	31.0835i	0.905325	+	1.07892i
$831$	6.21451	−	2.26190i	0.215579	−	0.0784643i
$832$	4.74521	+	1.72712i	0.164511	+	0.0598770i
$833$	−1.80481	+	2.15089i	−0.0625329	+	0.0745238i
$834$	0.163327	−	0.926271i	0.00565554	−	0.0320741i
$835$	−24.5360			−0.849104
$836$	9.77698	+	10.6494i	0.338144	+	0.368319i
$837$	8.32101			0.287616
$838$	4.00070	−	22.6891i	0.138202	−	0.783782i
$839$	−11.7679	+	14.0244i	−0.406272	+	0.484176i	−0.929922	−	0.367758i	$-0.880126\pi$
$839$	−11.7679	+	14.0244i	−0.406272	+	0.484176i	0.523650	+	0.851933i	$0.324570\pi$
$840$	−1.17858	−	0.428968i	−0.0406649	−	0.0148008i
$841$	7.41223	−	2.69783i	0.255594	−	0.0930286i
$842$	−11.1071	−	13.2369i	−0.382775	−	0.456174i
$843$	−3.82775	+	2.20995i	−0.131835	+	0.0761148i
$844$	−1.20787	+	2.09209i	−0.0415765	+	0.0720126i
$845$	−8.93576	−	50.6772i	−0.307400	−	1.74335i
$846$	−2.20382	−	12.4985i	−0.0757689	−	0.429707i
$847$	9.19588	−	12.5822i	0.315974	−	0.432328i
$848$	−9.60472	+	5.54529i	−0.329827	+	0.190426i
$849$	−3.24312	+	2.72130i	−0.111304	+	0.0933948i
$850$	−2.29799	−	6.31366i	−0.0788202	−	0.216557i
$851$	2.20314	−	6.05307i	0.0755226	−	0.207497i
$852$	−2.55401	−	2.14307i	−0.0874990	−	0.0734204i
$853$	−10.4035	−	1.83441i	−0.356208	−	0.0628092i	−0.00731943	−	0.999973i	$-0.502330\pi$
$853$	−10.4035	−	1.83441i	−0.356208	−	0.0628092i	−0.348889	+	0.937164i	$0.613441\pi$
$854$	15.9959			0.547370
$855$	8.62472	−	52.2969i	0.294959	−	1.78852i
$856$	−4.60153			−0.157277
$857$	−0.926611	+	5.25507i	−0.0316524	+	0.179510i	−0.996535	−	0.0831705i	$-0.973495\pi$
$857$	−0.926611	+	5.25507i	−0.0316524	+	0.179510i	0.964883	+	0.262680i	$0.0846065\pi$
$858$	−3.59953	+	0.120609i	−0.122886	+	0.00411752i
$859$	−29.7838	−	10.8404i	−1.01621	−	0.369871i	−0.220396	−	0.975410i	$-0.570735\pi$
$859$	−29.7838	−	10.8404i	−1.01621	−	0.369871i	−0.795815	+	0.605540i	$0.792957\pi$
$860$	13.9135	+	38.2269i	0.474445	+	1.30353i
$861$	−0.903770	+	0.758353i	−0.0308004	+	0.0258446i
$862$	12.3417	+	21.3765i	0.420360	+	0.728085i
$863$	48.2126	+	27.8356i	1.64118	+	0.947534i	0.980416	+	0.196938i	$0.0630998\pi$
$863$	48.2126	+	27.8356i	1.64118	+	0.947534i	0.660761	+	0.750596i	$0.270234\pi$
$864$	−1.26086	+	0.222323i	−0.0428952	+	0.00756359i
$865$	−11.9917	−	68.0085i	−0.407731	−	2.31236i
$866$	−3.06533	−	1.76977i	−0.104164	−	0.0601392i
$867$	3.10704	−	1.79385i	0.105521	−	0.0609224i
$868$	7.05366	−	5.91872i	0.239417	−	0.200894i
$869$	35.3216	+	18.8449i	1.19820	+	0.639269i
$870$	1.39121	−	3.82231i	0.0471664	−	0.129589i
$871$	35.1161	−	41.8497i	1.18986	−	1.41802i
$872$	−2.59771	+	14.7324i	−0.0879697	+	0.498901i
$873$			14.3636i			0.486136i
$874$	−6.96766	+	2.62385i	−0.235685	+	0.0887532i
$875$		−	40.5203i		−	1.36983i
$876$	−0.0698950	+	0.396394i	−0.00236153	+	0.0133929i
$877$	2.43576	+	2.04385i	0.0822499	+	0.0690159i	0.682986	−	0.730432i	$-0.260681\pi$
$877$	2.43576	+	2.04385i	0.0822499	+	0.0690159i	−0.600736	+	0.799448i	$0.705126\pi$
$878$	23.7179	+	8.63261i	0.800441	+	0.291337i
$879$	0.0899875	+	0.247239i	0.00303520	+	0.00833916i
$880$	13.5180	+	1.91931i	0.455693	+	0.0646999i
$881$	24.8010	+	42.9565i	0.835565	+	1.44724i	0.893569	+	0.448925i	$0.148193\pi$
$881$	24.8010	+	42.9565i	0.835565	+	1.44724i	−0.0580042	+	0.998316i	$0.518474\pi$
$882$	−7.37371	+	12.7716i	−0.248286	+	0.430044i
$883$	6.02495	+	34.1692i	0.202756	+	1.14988i	0.900932	+	0.433959i	$0.142884\pi$
$883$	6.02495	+	34.1692i	0.202756	+	1.14988i	−0.698177	+	0.715925i	$0.746005\pi$
$884$	2.79669	−	0.493131i	0.0940627	−	0.0165858i
$885$	−1.40924	+	2.44088i	−0.0473711	+	0.0820492i
$886$	−17.2538	−	29.8845i	−0.579654	−	1.00399i
$887$	−29.2905	+	24.5777i	−0.983479	+	0.825237i	−0.984611	−	0.174763i	$-0.944084\pi$
$887$	−29.2905	+	24.5777i	−0.983479	+	0.825237i	0.00113174	+	0.999999i	$0.499640\pi$
$888$	−0.762065	+	0.277369i	−0.0255732	+	0.00930790i
$889$	8.71553	−	23.9457i	0.292310	−	0.803114i
$890$	−3.52550	+	4.20153i	−0.118175	+	0.140836i
$891$	−24.1706	+	15.0561i	−0.809746	+	0.504397i
$892$		−	14.2095i		−	0.475769i
$893$	−9.18398	+	16.3224i	−0.307330	+	0.546207i
$894$	−2.51554			−0.0841322
$895$	−19.9166	−	3.51184i	−0.665739	−	0.117388i
$896$	−0.910681	+	1.08531i	−0.0304237	+	0.0362576i
$897$	0.634384	−	1.74296i	0.0211815	−	0.0581956i
$898$	0.886018	+	2.43431i	0.0295668	+	0.0812341i
$899$	19.1953	+	22.8761i	0.640199	+	0.762959i
$900$	−17.6449	−	30.5618i	−0.588162	−	1.01873i
$901$	−3.11850	+	5.40141i	−0.103892	+	0.179947i
$902$	7.92144	−	10.1095i	0.263755	−	0.336610i
$903$	2.96487	−	0.522786i	0.0986646	−	0.0173972i
$904$	−7.94980	−	4.58982i	−0.264406	−	0.152655i
$905$	−23.8103	+	13.7469i	−0.791481	+	0.456962i
$906$	0.989303	+	1.17901i	0.0328674	+	0.0391698i
$907$	−2.30414	−	6.33056i	−0.0765076	−	0.210203i	0.895543	−	0.444976i	$-0.146788\pi$
$907$	−2.30414	−	6.33056i	−0.0765076	−	0.210203i	−0.972050	+	0.234773i	$0.924565\pi$
$908$	9.39358	+	3.41899i	0.311737	+	0.113463i
$909$	−27.5486	+	32.8311i	−0.913729	+	1.08894i
$910$	29.0049	+	5.11435i	0.961504	+	0.169539i
$911$		−	39.0709i		−	1.29448i	−0.762287	−	0.647239i	$-0.775924\pi$
$911$		−	39.0709i		−	1.29448i	0.762287	−	0.647239i	$-0.224076\pi$
$912$	0.816912	+	0.459646i	0.0270506	+	0.0152204i
$913$	−24.3246	+	21.8398i	−0.805027	+	0.722794i
$914$	−19.1659	−	3.37947i	−0.633953	−	0.111783i
$915$	−7.65667	−	6.42471i	−0.253122	−	0.212394i
$916$	−14.6962	−	5.34898i	−0.485576	−	0.176735i
$917$	−8.16900	+	2.97327i	−0.269764	+	0.0981861i
$918$	−0.551557	+	0.462812i	−0.0182041	+	0.0152751i
$919$	−47.4846	+	27.4153i	−1.56637	+	0.904346i	−0.569787	+	0.821793i	$0.692974\pi$
$919$	−47.4846	+	27.4153i	−1.56637	+	0.904346i	−0.996587	+	0.0825536i	$0.973692\pi$
$920$	−3.51584	+	6.08961i	−0.115914	+	0.200768i
$921$	−1.74937	+	0.308462i	−0.0576438	+	0.0101642i
$922$	26.0265	−	4.58918i	0.857138	−	0.151137i
$923$	67.8026	+	39.1458i	2.23175	+	1.28850i
$924$	0.313606	−	0.960561i	0.0103169	−	0.0316001i
$925$	−28.9617	−	34.5152i	−0.952254	−	1.13485i
$926$	−1.33450	+	0.485720i	−0.0438545	+	0.0159617i
$927$	−1.69277	+	4.65084i	−0.0555977	+	0.152753i
$928$	−3.51981	−	2.95347i	−0.115543	−	0.0969525i
$929$	−3.75315	+	21.2852i	−0.123137	+	0.698345i	0.859260	+	0.511539i	$0.170925\pi$
$929$	−3.75315	+	21.2852i	−0.123137	+	0.698345i	−0.982397	+	0.186805i	$0.940187\pi$
$930$	−5.75356			−0.188667
$931$	20.3667	−	7.66962i	0.667493	−	0.251362i
$932$			28.9133i			0.947086i
$933$	−7.04734	−	1.24264i	−0.230719	−	0.0406821i
$934$	−5.95299	−	4.99515i	−0.194788	−	0.163446i
$935$	7.12333	−	2.86632i	0.232958	−	0.0937386i
$936$	14.0162	−	5.10148i	0.458134	−	0.166747i
$937$	30.5799	+	36.4436i	0.999000	+	1.19056i	0.981646	+	0.190713i	$0.0610799\pi$
$937$	30.5799	+	36.4436i	0.999000	+	1.19056i	0.0173543	+	0.999849i	$0.494476\pi$
$938$	7.66368	+	13.2739i	0.250228	+	0.433408i
$939$	2.63756	+	1.52279i	0.0860734	+	0.0496945i
$940$	3.07152	+	17.4194i	0.100182	+	0.568159i
$941$	−0.668325	−	3.79026i	−0.0217868	−	0.123559i	0.971975	−	0.235086i	$-0.0755371\pi$
$941$	−0.668325	−	3.79026i	−0.0217868	−	0.123559i	−0.993761	+	0.111527i	$0.964426\pi$
$942$	−2.40532	−	1.38871i	−0.0783695	−	0.0452467i
$943$	3.30719	+	5.72822i	0.107697	+	0.186537i
$944$	2.04648	+	2.43890i	0.0666073	+	0.0793795i
$945$	−7.01698	+	2.55397i	−0.228262	+	0.0830807i
$946$	−30.4047	+	12.2344i	−0.988543	+	0.397774i
$947$	−19.9491	−	16.7392i	−0.648257	−	0.543952i	0.258284	−	0.966069i	$-0.416843\pi$
$947$	−19.9491	−	16.7392i	−0.648257	−	0.543952i	−0.906542	+	0.422117i	$0.861287\pi$
$948$	2.55629	+	0.450744i	0.0830246	+	0.0146395i
$949$		−	9.45198i		−	0.306824i
$950$	−8.47407	+	51.3834i	−0.274935	+	1.66710i
$951$	1.69710			0.0550323
$952$	−0.138354	+	0.784643i	−0.00448407	+	0.0254304i
$953$	−15.1684	−	12.7278i	−0.491352	−	0.412294i	0.363158	−	0.931727i	$-0.381698\pi$
$953$	−15.1684	−	12.7278i	−0.491352	−	0.412294i	−0.854511	+	0.519434i	$0.826143\pi$
$954$	−11.2042	+	30.7833i	−0.362749	+	0.996645i
$955$	44.8060	−	16.3080i	1.44989	−	0.527716i
$956$	4.82225	+	5.74694i	0.155963	+	0.185869i
$957$	3.11524	+	1.01707i	0.100701	+	0.0328772i
$958$	−6.45559	−	3.72714i	−0.208571	−	0.120418i
$959$	−12.4433	+	2.19409i	−0.401816	+	0.0708510i
$960$	0.871819	−	0.153725i	0.0281378	−	0.00496146i
$961$	5.61998	−	9.73409i	0.181290	−	0.314003i
$962$	16.4924	−	9.52189i	0.531736	−	0.306998i
$963$	−10.4119	+	8.73665i	−0.335520	+	0.281534i
$964$	−9.17928	+	3.34099i	−0.295645	+	0.107606i
$965$	31.0598	+	11.3049i	0.999851	+	0.363916i
$966$	0.398642	+	0.334500i	0.0128261	+	0.0107624i
$967$	18.3206	+	3.23041i	0.589150	+	0.103883i	0.460273	−	0.887777i	$-0.347752\pi$
$967$	18.3206	+	3.23041i	0.589150	+	0.103883i	0.128877	+	0.991661i	$0.458863\pi$
$968$	−1.18071	+	10.9364i	−0.0379494	+	0.351511i
$969$	0.527103	−	0.00584354i	0.0169330	−	0.000187722i
$970$		−	20.0190i		−	0.642770i
$971$	−57.4212	−	10.1249i	−1.84273	−	0.324924i	−0.860049	−	0.510212i	$-0.829567\pi$
$971$	−57.4212	−	10.1249i	−1.84273	−	0.324924i	−0.982684	+	0.185288i	$0.940678\pi$
$972$	−3.65570	+	4.35670i	−0.117257	+	0.139741i
$973$	−5.82301	−	2.11940i	−0.186677	−	0.0679449i
$974$	−0.450949	−	1.23897i	−0.0144493	−	0.0396992i
$975$	−8.33939	−	9.93850i	−0.267074	−	0.318287i
$976$	−9.77781	+	5.64522i	−0.312980	+	0.180699i
$977$	19.6699	+	11.3564i	0.629297	+	0.363325i	0.780480	−	0.625181i	$-0.214975\pi$
$977$	19.6699	+	11.3564i	0.629297	+	0.363325i	−0.151183	+	0.988506i	$0.548308\pi$
$978$	−0.806963	+	0.142289i	−0.0258038	+	0.00454991i
$979$	−3.47817	−	2.72536i	−0.111163	−	0.0871029i
$980$	10.2769	−	17.8002i	0.328284	−	0.568605i
$981$	22.0936	+	38.2672i	0.705393	+	1.22178i
$982$	14.5297	+	17.3158i	0.463660	+	0.552568i
$983$	−8.90836	−	24.4755i	−0.284132	−	0.780648i	−0.996858	−	0.0792049i	$-0.974762\pi$
$983$	−8.90836	−	24.4755i	−0.284132	−	0.780648i	0.712726	−	0.701443i	$-0.247460\pi$
$984$	0.284811	−	0.782512i	0.00907945	−	0.0249456i
$985$	−21.3790	+	25.4785i	−0.681190	+	0.811811i
$986$	−2.54471	−	0.448702i	−0.0810402	−	0.0142896i
$987$	1.30904			0.0416672
$988$	−20.7661	−	7.29857i	−0.660657	−	0.232199i
$989$		−	16.8787i		−	0.536711i
$990$	34.2315	−	21.3230i	1.08795	−	0.677691i
$991$	14.4809	−	17.2577i	0.460001	−	0.548208i	−0.485325	−	0.874334i	$-0.661299\pi$
$991$	14.4809	−	17.2577i	0.460001	−	0.548208i	0.945326	+	0.326126i	$0.105743\pi$
$992$	−2.22287	+	6.10728i	−0.0705761	+	0.193906i
$993$	0.597080	−	0.217319i	0.0189478	−	0.00689642i
$994$	−16.8267	+	14.1193i	−0.533710	+	0.447835i
$995$	3.64341	+	6.31056i	0.115504	+	0.200058i
$996$	−1.05979	+	1.83560i	−0.0335806	+	0.0581633i
$997$	−39.5045	+	6.96571i	−1.25112	+	0.220606i	−0.759676	−	0.650302i	$-0.774642\pi$
$997$	−39.5045	+	6.96571i	−1.25112	+	0.220606i	−0.491445	+	0.870908i	$0.663531\pi$
$998$	6.06618	+	34.4030i	0.192021	+	1.08901i
$999$	−2.41417	+	4.18146i	−0.0763809	+	0.132296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.b.21.5	yes	60
11.10	odd	2		418.2.q.a.21.5	✓	60
19.10	odd	18		418.2.q.a.219.5	yes	60
209.10	even	18	inner	418.2.q.b.219.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.21.5	✓	60	11.10	odd	2
418.2.q.a.219.5	yes	60	19.10	odd	18
418.2.q.b.21.5	yes	60	1.1	even	1	trivial
418.2.q.b.219.5	yes	60	209.10	even	18	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.138226 + 0.164732i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(3.86845 - 1.40800i) q^{5} +(0.138226 + 0.164732i) q^{6} +(1.22696 - 0.708384i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.512915 + 2.90888i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.138226 + 0.164732i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(3.86845 - 1.40800i) q^{5} +(0.138226 + 0.164732i) q^{6} +(1.22696 - 0.708384i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.512915 + 2.90888i) q^{9} +(-0.714861 - 4.05418i) q^{10} +(3.24512 - 0.684983i) q^{11} +(0.186232 - 0.107521i) q^{12} +(-3.86833 + 3.24592i) q^{13} +(-0.484563 - 1.33133i) q^{14} +(-0.302780 + 0.831880i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.553826 + 0.0976545i) q^{17} +2.95376 q^{18} +(-3.36996 - 2.76466i) q^{19} -4.11672 q^{20} +(-0.0529045 + 0.300036i) q^{21} +(-0.111067 - 3.31476i) q^{22} +(1.60507 + 0.584196i) q^{23} +(-0.0735487 - 0.202073i) q^{24} +(9.15224 - 7.67964i) q^{25} +(2.52488 + 4.37321i) q^{26} +(-1.10878 - 0.640154i) q^{27} +(-1.39524 + 0.246019i) q^{28} +(-0.797876 - 4.52498i) q^{29} +(0.766665 + 0.442634i) q^{30} +(-5.62850 + 3.24961i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.335723 + 0.629257i) q^{33} +(0.192342 - 0.528455i) q^{34} +(3.74902 - 4.46791i) q^{35} +(0.512915 - 2.90888i) q^{36} -3.77123i q^{37} +(-3.30785 + 2.83869i) q^{38} -1.08591i q^{39} +(-0.714861 + 4.05418i) q^{40} +(2.96644 + 2.48914i) q^{41} +(0.286291 + 0.104201i) q^{42} +(-3.37974 - 9.28576i) q^{43} +(-3.28369 - 0.466223i) q^{44} +(6.07990 + 10.5307i) q^{45} +(0.854038 - 1.47924i) q^{46} +(-0.746107 - 4.23138i) q^{47} +(-0.211775 + 0.0373417i) q^{48} +(-2.49638 + 4.32387i) q^{49} +(-5.97370 - 10.3467i) q^{50} +(-0.0926402 + 0.0777344i) q^{51} +(4.74521 - 1.72712i) q^{52} +(-3.79320 + 10.4217i) q^{53} +(-0.822966 + 0.980773i) q^{54} +(11.5891 - 7.21896i) q^{55} +1.41677i q^{56} +(0.921245 - 0.172992i) q^{57} -4.59479 q^{58} +(3.13539 + 0.552854i) q^{59} +(0.569039 - 0.678155i) q^{60} +(-3.86156 + 10.6095i) q^{61} +(2.22287 + 6.10728i) q^{62} +(2.68993 + 3.20573i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-10.3942 + 18.0033i) q^{65} +(0.561399 + 0.439892i) q^{66} +(-10.6542 + 1.87862i) q^{67} +(-0.487027 - 0.281185i) q^{68} +(-0.318098 + 0.183654i) q^{69} +(-3.74902 - 4.46791i) q^{70} +(-5.30270 - 14.5691i) q^{71} +(-2.77562 - 1.01024i) q^{72} +(-1.20315 + 1.43386i) q^{73} +(-3.71394 - 0.654867i) q^{74} +2.56919i q^{75} +(2.22116 + 3.75053i) q^{76} +(3.49639 - 3.13923i) q^{77} +(-1.06941 - 0.188566i) q^{78} +(9.24677 + 7.75896i) q^{79} +(3.86845 + 1.40800i) q^{80} +(-8.06815 + 2.93657i) q^{81} +(2.96644 - 2.48914i) q^{82} +(-8.53602 + 4.92827i) q^{83} +(0.152332 - 0.263847i) q^{84} +(2.27995 - 0.402017i) q^{85} +(-9.73157 + 1.71594i) q^{86} +(0.855696 + 0.494036i) q^{87} +(-1.02935 + 3.15285i) q^{88} +(-0.856385 - 1.02060i) q^{89} +(11.4265 - 4.15889i) q^{90} +(-2.44692 + 6.72287i) q^{91} +(-1.30846 - 1.09793i) q^{92} +(0.242692 - 1.37637i) q^{93} -4.29666 q^{94} +(-16.9292 - 5.95003i) q^{95} +0.215042i q^{96} +(4.78896 + 0.844423i) q^{97} +(3.82468 + 3.20929i) q^{98} +(3.65700 + 9.08833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Introduction

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