LMFDB - Embedded newform 111.2.k.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(7,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("111.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.k (of order $9$, 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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 33 x^{15} + 150 x^{14} - 231 x^{13} + 796 x^{12} - 801 x^{11} + \cdots + 361 $ x^18 - 3x^17 + 18x^16 - 33x^15 + 150x^14 - 231x^13 + 796x^12 - 801x^11 + 2382x^10 - 1621x^9 + 5184x^8 - 2001x^7 + 6622x^6 - 1269x^5 + 5964x^4 - 347x^3 + 1662x^2 - 57*x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.2
Root			$-0.272519 + 0.472016i$ of defining polynomial
Character	$\chi$	$=$	111.49
Dual form			111.2.k.a.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.417523 + 0.350343i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.295711 + 1.67706i) q^{4} +(-3.97962 + 1.44846i) q^{5} +0.545037 q^{6} +(-0.377882 + 0.137538i) q^{7} +(-1.00912 - 1.74784i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.417523 + 0.350343i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.295711 + 1.67706i) q^{4} +(-3.97962 + 1.44846i) q^{5} +0.545037 q^{6} +(-0.377882 + 0.137538i) q^{7} +(-1.00912 - 1.74784i) q^{8} +(0.173648 + 0.984808i) q^{9} +(1.15412 - 1.99900i) q^{10} +(1.65293 + 2.86295i) q^{11} +(1.30452 - 1.09463i) q^{12} +(-0.364518 + 2.06729i) q^{13} +(0.109589 - 0.189813i) q^{14} +(3.97962 + 1.44846i) q^{15} +(-2.16679 - 0.788648i) q^{16} +(-0.819059 - 4.64511i) q^{17} +(-0.417523 - 0.350343i) q^{18} +(2.26485 + 1.90043i) q^{19} +(-1.25234 - 7.10240i) q^{20} +(0.377882 + 0.137538i) q^{21} +(-1.69315 - 0.616257i) q^{22} +(-2.90400 + 5.02988i) q^{23} +(-0.350463 + 1.98758i) q^{24} +(9.90911 - 8.31473i) q^{25} +(-0.572065 - 0.990845i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.118915 - 0.674403i) q^{28} +(3.10093 + 5.37097i) q^{29} +(-2.16904 + 0.789467i) q^{30} -3.38224 q^{31} +(4.97403 - 1.81040i) q^{32} +(0.574055 - 3.25563i) q^{33} +(1.96936 + 1.65249i) q^{34} +(1.30461 - 1.09470i) q^{35} -1.70293 q^{36} +(5.01612 + 3.44072i) q^{37} -1.61143 q^{38} +(1.60806 - 1.34932i) q^{39} +(6.54760 + 5.49409i) q^{40} +(-0.156690 + 0.888630i) q^{41} +(-0.205960 + 0.0749632i) q^{42} -12.9281 q^{43} +(-5.29014 + 1.92545i) q^{44} +(-2.11751 - 3.66764i) q^{45} +(-0.549697 - 3.11749i) q^{46} +(0.622863 - 1.07883i) q^{47} +(1.15293 + 1.99693i) q^{48} +(-5.23843 + 4.39557i) q^{49} +(-1.22427 + 6.94318i) q^{50} +(-2.35839 + 4.08484i) q^{51} +(-3.35918 - 1.22264i) q^{52} +(4.37976 + 1.59410i) q^{53} +(0.0946447 + 0.536757i) q^{54} +(-10.7249 - 8.99926i) q^{55} +(0.621722 + 0.521687i) q^{56} +(-0.513399 - 2.91163i) q^{57} +(-3.17639 - 1.15611i) q^{58} +(0.643144 + 0.234085i) q^{59} +(-3.60598 + 6.24575i) q^{60} +(-0.687058 + 3.89650i) q^{61} +(1.41216 - 1.18494i) q^{62} +(-0.201067 - 0.348258i) q^{63} +(0.863344 - 1.49536i) q^{64} +(-1.54374 - 8.75500i) q^{65} +(0.900907 + 1.56042i) q^{66} +(6.03638 - 2.19706i) q^{67} +8.03235 q^{68} +(5.45774 - 1.98645i) q^{69} +(-0.161184 + 0.914121i) q^{70} +(7.55767 + 6.34164i) q^{71} +(1.54606 - 1.29730i) q^{72} -0.542560 q^{73} +(-3.29978 + 0.320787i) q^{74} -12.9354 q^{75} +(-3.85689 + 3.23631i) q^{76} +(-1.01838 - 0.854518i) q^{77} +(-0.198676 + 1.12675i) q^{78} +(-8.97787 + 3.26768i) q^{79} +9.76534 q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.245904 - 0.425919i) q^{82} +(1.60031 + 9.07583i) q^{83} +(-0.342403 + 0.593060i) q^{84} +(9.98782 + 17.2994i) q^{85} +(5.39780 - 4.52929i) q^{86} +(1.07694 - 6.10764i) q^{87} +(3.33600 - 5.77812i) q^{88} +(-2.83992 - 1.03365i) q^{89} +(2.16904 + 0.789467i) q^{90} +(-0.146585 - 0.831324i) q^{91} +(-7.57667 - 6.35758i) q^{92} +(2.59094 + 2.17406i) q^{93} +(0.117901 + 0.668652i) q^{94} +(-11.7659 - 4.28245i) q^{95} +(-4.97403 - 1.81040i) q^{96} +(9.20078 - 15.9362i) q^{97} +(0.647208 - 3.67050i) q^{98} +(-2.53243 + 2.12496i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{12} + 18 q^{13} - 9 q^{14} + 6 q^{15} - 9 q^{16} - 21 q^{17} - 3 q^{18} + 12 q^{19} - 6 q^{21} - 51 q^{22} + 6 q^{24} + 6 q^{25} + 15 q^{26} + 9 q^{27} - 39 q^{28} - 3 q^{29} + 15 q^{30} - 24 q^{31} + 21 q^{32} - 18 q^{34} - 12 q^{35} + 18 q^{36} + 27 q^{37} + 24 q^{38} + 18 q^{39} + 39 q^{40} + 9 q^{41} + 6 q^{42} - 72 q^{43} - 21 q^{44} + 21 q^{46} + 21 q^{47} - 3 q^{48} - 18 q^{49} + 24 q^{50} - 3 q^{51} - 30 q^{52} - 18 q^{53} + 3 q^{54} + 9 q^{55} + 54 q^{56} - 3 q^{57} - 66 q^{59} - 36 q^{60} + 33 q^{61} + 69 q^{62} + 18 q^{64} - 63 q^{65} + 42 q^{67} + 48 q^{68} - 12 q^{69} + 63 q^{70} + 15 q^{71} - 6 q^{72} - 24 q^{73} - 51 q^{74} - 6 q^{75} + 12 q^{76} + 39 q^{77} - 27 q^{78} - 6 q^{79} - 12 q^{80} + 15 q^{82} + 33 q^{83} - 6 q^{84} + 30 q^{85} - 60 q^{86} - 9 q^{87} - 3 q^{88} + 45 q^{89} - 15 q^{90} + 21 q^{91} - 24 q^{92} - 6 q^{93} + 18 q^{94} - 24 q^{95} - 21 q^{96} - 24 q^{97} - 36 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^12 + 18 * q^13 - 9 * q^14 + 6 * q^15 - 9 * q^16 - 21 * q^17 - 3 * q^18 + 12 * q^19 - 6 * q^21 - 51 * q^22 + 6 * q^24 + 6 * q^25 + 15 * q^26 + 9 * q^27 - 39 * q^28 - 3 * q^29 + 15 * q^30 - 24 * q^31 + 21 * q^32 - 18 * q^34 - 12 * q^35 + 18 * q^36 + 27 * q^37 + 24 * q^38 + 18 * q^39 + 39 * q^40 + 9 * q^41 + 6 * q^42 - 72 * q^43 - 21 * q^44 + 21 * q^46 + 21 * q^47 - 3 * q^48 - 18 * q^49 + 24 * q^50 - 3 * q^51 - 30 * q^52 - 18 * q^53 + 3 * q^54 + 9 * q^55 + 54 * q^56 - 3 * q^57 - 66 * q^59 - 36 * q^60 + 33 * q^61 + 69 * q^62 + 18 * q^64 - 63 * q^65 + 42 * q^67 + 48 * q^68 - 12 * q^69 + 63 * q^70 + 15 * q^71 - 6 * q^72 - 24 * q^73 - 51 * q^74 - 6 * q^75 + 12 * q^76 + 39 * q^77 - 27 * q^78 - 6 * q^79 - 12 * q^80 + 15 * q^82 + 33 * q^83 - 6 * q^84 + 30 * q^85 - 60 * q^86 - 9 * q^87 - 3 * q^88 + 45 * q^89 - 15 * q^90 + 21 * q^91 - 24 * q^92 - 6 * q^93 + 18 * q^94 - 24 * q^95 - 21 * q^96 - 24 * q^97 - 36 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.417523	+	0.350343i	−0.295233	+	0.247730i	−0.778357	−	0.627822i	$-0.783947\pi$
$2$	−0.417523	+	0.350343i	−0.295233	+	0.247730i	0.483124	+	0.875552i	$0.339502\pi$
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	−0.295711	+	1.67706i	−0.147856	+	0.838531i
$5$	−3.97962	+	1.44846i	−1.77974	+	0.647772i	−0.779982	+	0.625803i	$0.784772\pi$
$5$	−3.97962	+	1.44846i	−1.77974	+	0.647772i	−0.999759	+	0.0219699i	$0.993006\pi$
$6$	0.545037			0.222511
$7$	−0.377882	+	0.137538i	−0.142826	+	0.0519844i	−0.412444	−	0.910983i	$-0.635325\pi$
$7$	−0.377882	+	0.137538i	−0.142826	+	0.0519844i	0.269618	+	0.962967i	$0.413103\pi$
$8$	−1.00912	−	1.74784i	−0.356777	−	0.617957i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	1.15412	−	1.99900i	0.364966	−	0.632139i
$11$	1.65293	+	2.86295i	0.498376	+	0.863213i	0.999998	−	0.00187398i	$-0.000596506\pi$
$11$	1.65293	+	2.86295i	0.498376	+	0.863213i	−0.501622	+	0.865087i	$0.667263\pi$
$12$	1.30452	−	1.09463i	0.376583	−	0.315991i
$13$	−0.364518	+	2.06729i	−0.101099	+	0.573362i	0.891608	+	0.452809i	$0.149578\pi$
$13$	−0.364518	+	2.06729i	−0.101099	+	0.573362i	−0.992707	+	0.120553i	$0.961533\pi$
$14$	0.109589	−	0.189813i	0.0292889	−	0.0507298i
$15$	3.97962	+	1.44846i	1.02753	+	0.373992i
$16$	−2.16679	−	0.788648i	−0.541698	−	0.197162i
$17$	−0.819059	−	4.64511i	−0.198651	−	1.12661i	−0.907123	−	0.420866i	$-0.861726\pi$
$17$	−0.819059	−	4.64511i	−0.198651	−	1.12661i	0.708472	−	0.705739i	$-0.249385\pi$
$18$	−0.417523	−	0.350343i	−0.0984111	−	0.0825767i
$19$	2.26485	+	1.90043i	0.519592	+	0.435989i	0.864489	−	0.502651i	$-0.167642\pi$
$19$	2.26485	+	1.90043i	0.519592	+	0.435989i	−0.344898	+	0.938640i	$0.612086\pi$
$20$	−1.25234	−	7.10240i	−0.280033	−	1.58814i
$21$	0.377882	+	0.137538i	0.0824606	+	0.0300132i
$22$	−1.69315	−	0.616257i	−0.360981	−	0.131386i
$23$	−2.90400	+	5.02988i	−0.605526	+	1.04880i	0.386442	+	0.922314i	$0.373704\pi$
$23$	−2.90400	+	5.02988i	−0.605526	+	1.04880i	−0.991968	+	0.126488i	$0.959629\pi$
$24$	−0.350463	+	1.98758i	−0.0715380	+	0.405712i
$25$	9.90911	−	8.31473i	1.98182	−	1.66295i
$26$	−0.572065	−	0.990845i	−0.112191	−	0.194321i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.118915	−	0.674403i	−0.0224729	−	0.127450i
$29$	3.10093	+	5.37097i	0.575829	+	0.997364i	0.995951	+	0.0898970i	$0.0286538\pi$
$29$	3.10093	+	5.37097i	0.575829	+	0.997364i	−0.420122	+	0.907467i	$0.638013\pi$
$30$	−2.16904	+	0.789467i	−0.396011	+	0.144136i
$31$	−3.38224			−0.607468			−0.303734	−	0.952757i	$-0.598233\pi$
$31$	−3.38224			−0.607468			−0.303734	+	0.952757i	$0.598233\pi$
$32$	4.97403	−	1.81040i	0.879292	−	0.320036i
$33$	0.574055	−	3.25563i	0.0999302	−	0.566733i
$34$	1.96936	+	1.65249i	0.337742	+	0.283400i
$35$	1.30461	−	1.09470i	0.220519	−	0.185037i
$36$	−1.70293			−0.283822
$37$	5.01612	+	3.44072i	0.824645	+	0.565650i
$37$	5.01612	+	3.44072i	0.824645	+	0.565650i
$38$	−1.61143			−0.261408
$39$	1.60806	−	1.34932i	0.257496	−	0.216065i
$40$	6.54760	+	5.49409i	1.03527	+	0.868691i
$41$	−0.156690	+	0.888630i	−0.0244708	+	0.138781i	−0.994595	−	0.103826i	$-0.966891\pi$
$41$	−0.156690	+	0.888630i	−0.0244708	+	0.138781i	0.970125	+	0.242607i	$0.0780025\pi$
$42$	−0.205960	+	0.0749632i	−0.0317803	+	0.0115671i
$43$	−12.9281			−1.97152			−0.985762	−	0.168148i	$-0.946221\pi$
$43$	−12.9281			−1.97152			−0.985762	+	0.168148i	$0.946221\pi$
$44$	−5.29014	+	1.92545i	−0.797519	+	0.290273i
$45$	−2.11751	−	3.66764i	−0.315660	−	0.546739i
$46$	−0.549697	−	3.11749i	−0.0810484	−	0.459648i
$47$	0.622863	−	1.07883i	0.0908538	−	0.157363i	−0.817017	−	0.576614i	$-0.804374\pi$
$47$	0.622863	−	1.07883i	0.0908538	−	0.157363i	0.907871	+	0.419250i	$0.137707\pi$
$48$	1.15293	+	1.99693i	0.166411	+	0.288232i
$49$	−5.23843	+	4.39557i	−0.748348	+	0.627938i
$50$	−1.22427	+	6.94318i	−0.173138	+	0.981914i
$51$	−2.35839	+	4.08484i	−0.330240	+	0.571993i
$52$	−3.35918	−	1.22264i	−0.465834	−	0.169550i
$53$	4.37976	+	1.59410i	0.601607	+	0.218967i	0.624827	−	0.780763i	$-0.285170\pi$
$53$	4.37976	+	1.59410i	0.601607	+	0.218967i	−0.0232201	+	0.999730i	$0.507392\pi$
$54$	0.0946447	+	0.536757i	0.0128795	+	0.0730434i
$55$	−10.7249	−	8.99926i	−1.44615	−	1.21346i
$56$	0.621722	+	0.521687i	0.0830811	+	0.0697133i
$57$	−0.513399	−	2.91163i	−0.0680014	−	0.385655i
$58$	−3.17639	−	1.15611i	−0.417081	−	0.151805i
$59$	0.643144	+	0.234085i	0.0837303	+	0.0304753i	0.383546	−	0.923522i	$-0.374703\pi$
$59$	0.643144	+	0.234085i	0.0837303	+	0.0304753i	−0.299815	+	0.953997i	$0.596925\pi$
$60$	−3.60598	+	6.24575i	−0.465530	+	0.806322i
$61$	−0.687058	+	3.89650i	−0.0879687	+	0.498895i	0.908708	+	0.417433i	$0.137070\pi$
$61$	−0.687058	+	3.89650i	−0.0879687	+	0.498895i	−0.996676	+	0.0814623i	$0.974041\pi$
$62$	1.41216	−	1.18494i	0.179345	−	0.150488i
$63$	−0.201067	−	0.348258i	−0.0253320	−	0.0438763i
$64$	0.863344	−	1.49536i	0.107918	−	0.186919i
$65$	−1.54374	−	8.75500i	−0.191478	−	1.08592i
$66$	0.900907	+	1.56042i	0.110894	+	0.192074i
$67$	6.03638	−	2.19706i	0.737461	−	0.268414i	0.0541416	−	0.998533i	$-0.482758\pi$
$67$	6.03638	−	2.19706i	0.737461	−	0.268414i	0.683320	+	0.730119i	$0.260536\pi$
$68$	8.03235			0.974066
$69$	5.45774	−	1.98645i	0.657034	−	0.239141i
$70$	−0.161184	+	0.914121i	−0.0192652	+	0.109258i
$71$	7.55767	+	6.34164i	0.896930	+	0.752614i	0.969588	−	0.244743i	$-0.0787037\pi$
$71$	7.55767	+	6.34164i	0.896930	+	0.752614i	−0.0726579	+	0.997357i	$0.523148\pi$
$72$	1.54606	−	1.29730i	0.182205	−	0.152888i
$73$	−0.542560			−0.0635019			−0.0317509	−	0.999496i	$-0.510108\pi$
$73$	−0.542560			−0.0635019			−0.0317509	+	0.999496i	$0.510108\pi$
$74$	−3.29978	+	0.320787i	−0.383591	+	0.0372907i
$75$	−12.9354			−1.49365
$76$	−3.85689	+	3.23631i	−0.442415	+	0.371231i
$77$	−1.01838	−	0.854518i	−0.116055	−	0.0973814i
$78$	−0.198676	+	1.12675i	−0.0224956	+	0.127579i
$79$	−8.97787	+	3.26768i	−1.01009	+	0.367642i	−0.793467	−	0.608613i	$-0.791726\pi$
$79$	−8.97787	+	3.26768i	−1.01009	+	0.367642i	−0.216622	+	0.976256i	$0.569504\pi$
$80$	9.76534			1.09180
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−0.245904	−	0.425919i	−0.0271556	−	0.0470348i
$83$	1.60031	+	9.07583i	0.175657	+	0.996202i	0.937382	+	0.348302i	$0.113242\pi$
$83$	1.60031	+	9.07583i	0.175657	+	0.996202i	−0.761725	+	0.647900i	$0.775647\pi$
$84$	−0.342403	+	0.593060i	−0.0373593	+	0.0647082i
$85$	9.98782	+	17.2994i	1.08333	+	1.87638i
$86$	5.39780	−	4.52929i	0.582059	−	0.488406i
$87$	1.07694	−	6.10764i	0.115460	−	0.654808i
$88$	3.33600	−	5.77812i	0.355619	−	0.615950i
$89$	−2.83992	−	1.03365i	−0.301031	−	0.109566i	0.187089	−	0.982343i	$-0.440095\pi$
$89$	−2.83992	−	1.03365i	−0.301031	−	0.109566i	−0.488120	+	0.872777i	$0.662317\pi$
$90$	2.16904	+	0.789467i	0.228637	+	0.0832171i
$91$	−0.146585	−	0.831324i	−0.0153663	−	0.0871465i
$92$	−7.57667	−	6.35758i	−0.789923	−	0.662824i
$93$	2.59094	+	2.17406i	0.268668	+	0.225440i
$94$	0.117901	+	0.668652i	0.0121606	+	0.0689662i
$95$	−11.7659	−	4.28245i	−1.20716	−	0.439370i
$96$	−4.97403	−	1.81040i	−0.507660	−	0.184773i
$97$	9.20078	−	15.9362i	0.934197	−	1.61808i	0.158138	−	0.987417i	$-0.449451\pi$
$97$	9.20078	−	15.9362i	0.934197	−	1.61808i	0.776059	−	0.630660i	$-0.217216\pi$
$98$	0.647208	−	3.67050i	0.0653779	−	0.370776i
$99$	−2.53243	+	2.12496i	−0.254519	+	0.213567i
$100$	11.0141	+	19.0770i	1.10141	+	1.90770i
$101$	9.07920	−	15.7256i	0.903414	−	1.56476i	0.0803816	−	0.996764i	$-0.474386\pi$
$101$	9.07920	−	15.7256i	0.903414	−	1.56476i	0.823032	−	0.567995i	$-0.192281\pi$
$102$	−0.446418	−	2.53176i	−0.0442019	−	0.250682i
$103$	−0.239011	−	0.413979i	−0.0235505	−	0.0407906i	0.854010	−	0.520257i	$-0.174164\pi$
$103$	−0.239011	−	0.413979i	−0.0235505	−	0.0407906i	−0.877560	+	0.479466i	$0.840830\pi$
$104$	3.98114	−	1.44902i	0.390383	−	0.142088i
$105$	−1.70304			−0.166200
$106$	−2.38713	+	0.868846i	−0.231859	+	0.0843898i
$107$	−1.16828	+	6.62563i	−0.112942	+	0.640524i	0.874807	+	0.484471i	$0.160988\pi$
$107$	−1.16828	+	6.62563i	−0.112942	+	0.640524i	−0.987749	+	0.156053i	$0.950123\pi$
$108$	1.30452	+	1.09463i	0.125528	+	0.105330i
$109$	5.27437	−	4.42572i	0.505193	−	0.423907i	−0.354241	−	0.935154i	$-0.615261\pi$
$109$	5.27437	−	4.42572i	0.505193	−	0.423907i	0.859434	+	0.511247i	$0.170816\pi$
$110$	7.63072			0.727561
$111$	−1.63092	−	5.86004i	−0.154800	−	0.556211i
$112$	0.927261			0.0876179
$113$	13.0270	−	10.9310i	1.22548	−	1.02830i	0.226959	−	0.973904i	$-0.427122\pi$
$113$	13.0270	−	10.9310i	1.22548	−	1.02830i	0.998520	−	0.0543939i	$-0.0173227\pi$
$114$	1.23443	+	1.03581i	0.115615	+	0.0970122i
$115$	4.27123	−	24.2233i	0.398294	−	2.25884i
$116$	−9.92444	+	3.61220i	−0.921461	+	0.335384i
$117$	−2.09918			−0.194069
$118$	−0.350538	+	0.127585i	−0.0322696	+	0.0117452i
$119$	0.948386	+	1.64265i	0.0869384	+	0.150582i
$120$	−1.48422	−	8.41743i	−0.135490	−	0.768403i
$121$	0.0356654	−	0.0617743i	0.00324231	−	0.00561584i
$122$	−1.07825	−	1.86758i	−0.0976201	−	0.169083i
$123$	0.691232	−	0.580012i	0.0623263	−	0.0522980i
$124$	1.00017	−	5.67222i	0.0898176	−	0.509381i
$125$	−16.8033	+	29.1042i	−1.50294	+	2.60316i
$126$	0.205960	+	0.0749632i	0.0183483	+	0.00667825i
$127$	−11.7455	−	4.27502i	−1.04225	−	0.379347i	−0.236516	−	0.971628i	$-0.576005\pi$
$127$	−11.7455	−	4.27502i	−1.04225	−	0.379347i	−0.805732	+	0.592281i	$0.798228\pi$
$128$	2.00175	+	11.3525i	0.176931	+	1.00343i
$129$	9.90353	+	8.31005i	0.871957	+	0.731659i
$130$	3.71180	+	3.11457i	0.325547	+	0.273166i
$131$	−0.951414	−	5.39573i	−0.0831254	−	0.471427i	−0.997745	−	0.0671129i	$-0.978621\pi$
$131$	−0.951414	−	5.39573i	−0.0831254	−	0.471427i	0.914620	−	0.404315i	$-0.132490\pi$
$132$	5.29014	+	1.92545i	0.460448	+	0.167589i
$133$	−1.11723	−	0.406637i	−0.0968758	−	0.0352599i
$134$	−1.75060	+	3.03213i	−0.151229	+	0.261936i
$135$	−0.735404	+	4.17068i	−0.0632935	+	0.358955i
$136$	−7.29241	+	6.11906i	−0.625319	+	0.524705i
$137$	0.336547	+	0.582916i	0.0287531	+	0.0498019i	0.880044	−	0.474892i	$-0.157513\pi$
$137$	0.336547	+	0.582916i	0.0287531	+	0.0498019i	−0.851291	+	0.524694i	$0.824180\pi$
$138$	−1.58279	+	2.74147i	−0.134736	+	0.233370i
$139$	1.94180	+	11.0125i	0.164701	+	0.934067i	0.949372	+	0.314154i	$0.101721\pi$
$139$	1.94180	+	11.0125i	0.164701	+	0.934067i	−0.784671	+	0.619913i	$0.787168\pi$
$140$	1.45009	+	2.51162i	0.122555	+	0.212271i
$141$	−1.17060	+	0.426063i	−0.0985822	+	0.0358810i
$142$	−5.37725			−0.451249
$143$	−6.52106	+	2.37347i	−0.545319	+	0.198480i
$144$	0.400407	−	2.27082i	0.0333673	−	0.189235i
$145$	−20.1202	−	16.8828i	−1.67089	−	1.40204i
$146$	0.226531	−	0.190082i	0.0187479	−	0.0157313i
$147$	6.83829			0.564013
$148$	−7.25362	+	7.39489i	−0.596244	+	0.607856i
$149$	−13.6811			−1.12080			−0.560401	−	0.828221i	$-0.689353\pi$
$149$	−13.6811			−1.12080			−0.560401	+	0.828221i	$0.689353\pi$
$150$	5.40083	−	4.53184i	0.440976	−	0.370023i
$151$	14.0293	+	11.7720i	1.14169	+	0.957988i	0.999493	−	0.0318506i	$-0.0101401\pi$
$151$	14.0293	+	11.7720i	1.14169	+	0.957988i	0.142193	+	0.989839i	$0.454585\pi$
$152$	1.03616	−	5.87637i	0.0840438	−	0.476636i
$153$	4.43232	−	1.61323i	0.358331	−	0.130422i
$154$	0.724569			0.0583875
$155$	13.4600	−	4.89905i	1.08113	−	0.393501i
$156$	1.78738	+	3.09583i	0.143105	+	0.247865i
$157$	−0.754584	−	4.27946i	−0.0602223	−	0.341538i	0.939778	−	0.341786i	$-0.111032\pi$
$157$	−0.754584	−	4.27946i	−0.0602223	−	0.341538i	−1.00000		0.000248671i	$0.999921\pi$
$158$	2.60366	−	4.50967i	0.207136	−	0.358770i
$159$	−2.33042	−	4.03641i	−0.184815	−	0.320108i
$160$	−17.1725	+	14.4094i	−1.35760	+	1.13916i
$161$	0.405571	−	2.30011i	0.0319635	−	0.181274i
$162$	0.272519	−	0.472016i	0.0214111	−	0.0370851i
$163$	14.7478	+	5.36776i	1.15514	+	0.420436i	0.847358	−	0.531022i	$-0.178192\pi$
$163$	14.7478	+	5.36776i	1.15514	+	0.420436i	0.307779	+	0.951458i	$0.400414\pi$
$164$	−1.44395	−	0.525556i	−0.112754	−	0.0410391i
$165$	2.43114	+	13.7877i	0.189264	+	1.07337i
$166$	−3.84782	−	3.22871i	−0.298649	−	0.250596i
$167$	2.18480	+	1.83327i	0.169065	+	0.141862i	0.723395	−	0.690435i	$-0.242581\pi$
$167$	2.18480	+	1.83327i	0.169065	+	0.141862i	−0.554330	+	0.832297i	$0.687025\pi$
$168$	−0.140933	−	0.799271i	−0.0108732	−	0.0616651i
$169$	8.07521	+	2.93914i	0.621170	+	0.226087i
$170$	−10.2309	−	3.72373i	−0.784672	−	0.285597i
$171$	−1.47827	+	2.56045i	−0.113047	+	0.195802i
$172$	3.82300	−	21.6813i	0.291501	−	1.65318i
$173$	−11.2518	+	9.44139i	−0.855460	+	0.717816i	−0.960985	−	0.276601i	$-0.910792\pi$
$173$	−11.2518	+	9.44139i	−0.855460	+	0.717816i	0.105525	+	0.994417i	$0.466348\pi$
$174$	1.69012	+	2.92738i	0.128128	+	0.221924i
$175$	−2.60088	+	4.50486i	−0.196608	+	0.340535i
$176$	−1.32369	−	7.50701i	−0.0997767	−	0.565862i
$177$	−0.342210	−	0.592725i	−0.0257221	−	0.0445519i
$178$	1.54786	−	0.563376i	0.116017	−	0.0422268i
$179$	−12.0070			−0.897443			−0.448722	−	0.893672i	$-0.648121\pi$
$179$	−12.0070			−0.897443			−0.448722	+	0.893672i	$0.648121\pi$
$180$	6.77703	−	2.46664i	0.505130	−	0.183852i
$181$	−1.76396	+	10.0039i	−0.131114	+	0.743586i	0.846373	+	0.532591i	$0.178782\pi$
$181$	−1.76396	+	10.0039i	−0.131114	+	0.743586i	−0.977487	+	0.210995i	$0.932330\pi$
$182$	0.352451	+	0.295742i	0.0261254	+	0.0219218i
$183$	3.03094	−	2.54326i	0.224053	−	0.188003i
$184$	11.7219			0.864152
$185$	−24.9460	−	6.42707i	−1.83407	−	0.472528i
$186$	−1.84345			−0.135168
$187$	11.9449	−	10.0230i	0.873498	−	0.732951i
$188$	1.62508	+	1.36360i	0.118521	+	0.0994509i
$189$	−0.0698297	+	0.396024i	−0.00507937	+	0.0288065i
$190$	6.41288	−	2.33410i	0.465239	−	0.169333i
$191$	−1.81678			−0.131457			−0.0657287	−	0.997838i	$-0.520937\pi$
$191$	−1.81678			−0.131457			−0.0657287	+	0.997838i	$0.520937\pi$
$192$	−1.62256	+	0.590562i	−0.117098	+	0.0426201i
$193$	4.76081	+	8.24596i	0.342690	+	0.593557i	0.984931	−	0.172946i	$-0.0553285\pi$
$193$	4.76081	+	8.24596i	0.342690	+	0.593557i	−0.642241	+	0.766503i	$0.721995\pi$
$194$	1.74161	+	9.87716i	0.125040	+	0.709139i
$195$	−4.44503	+	7.69902i	−0.318315	+	0.551338i
$196$	−5.82258	−	10.0850i	−0.415898	−	0.720357i
$197$	0.508713	−	0.426861i	0.0362443	−	0.0304126i	−0.624486	−	0.781036i	$-0.714691\pi$
$197$	0.508713	−	0.426861i	0.0362443	−	0.0304126i	0.660730	+	0.750624i	$0.270247\pi$
$198$	0.312882	−	1.77444i	0.0222355	−	0.126104i
$199$	−9.19948	+	15.9340i	−0.652134	+	1.12953i	0.330470	+	0.943816i	$0.392793\pi$
$199$	−9.19948	+	15.9340i	−0.652134	+	1.12953i	−0.982604	+	0.185713i	$0.940541\pi$
$200$	−24.5323	−	8.92904i	−1.73470	−	0.631378i
$201$	−6.03638	−	2.19706i	−0.425773	−	0.154969i
$202$	1.71860	+	9.74665i	0.120920	+	0.685772i
$203$	−1.91050	−	1.60310i	−0.134091	−	0.112515i
$204$	−6.15314	−	5.16310i	−0.430806	−	0.361489i
$205$	−0.663584	−	3.76337i	−0.0463467	−	0.262845i
$206$	0.244827	+	0.0891099i	0.0170579	+	0.00620858i
$207$	−5.45774	−	1.98645i	−0.379339	−	0.138068i
$208$	2.42020	−	4.19190i	0.167810	−	0.290656i
$209$	−1.69722	+	9.62543i	−0.117399	+	0.665805i
$210$	0.711060	−	0.596650i	0.0490678	−	0.0411728i
$211$	7.10986	+	12.3146i	0.489463	+	0.847775i	0.999926	−	0.0121243i	$-0.00385939\pi$
$211$	7.10986	+	12.3146i	0.489463	+	0.847775i	−0.510463	+	0.859900i	$0.670526\pi$
$212$	−3.96856	+	6.87374i	−0.272562	+	0.472091i
$213$	−1.71318	−	9.71595i	−0.117385	−	0.665726i
$214$	−1.83346	−	3.17565i	−0.125333	−	0.217083i
$215$	51.4491	−	18.7259i	3.50880	−	1.27710i
$216$	−2.01824			−0.137324
$217$	1.27809	−	0.465185i	0.0867621	−	0.0315788i
$218$	−0.651648	+	3.69568i	−0.0441352	+	0.250303i
$219$	0.415625	+	0.348751i	0.0280854	+	0.0235664i
$220$	18.2638	−	15.3252i	1.23135	−	1.03322i
$221$	9.90134			0.666036
$222$	2.73397	+	1.87532i	0.183492	+	0.125863i
$223$	−4.50378			−0.301595			−0.150798	−	0.988565i	$-0.548184\pi$
$223$	−4.50378			−0.301595			−0.150798	+	0.988565i	$0.548184\pi$
$224$	−1.63060	+	1.36823i	−0.108949	+	0.0914189i
$225$	9.90911	+	8.31473i	0.660607	+	0.554315i
$226$	−1.60949	+	9.12785i	−0.107061	+	0.607176i
$227$	−14.4678	+	5.26585i	−0.960262	+	0.349507i	−0.774136	−	0.633019i	$-0.781815\pi$
$227$	−14.4678	+	5.26585i	−0.960262	+	0.349507i	−0.186126	+	0.982526i	$0.559593\pi$
$228$	5.03481			0.333438
$229$	10.8629	−	3.95378i	0.717842	−	0.261273i	0.0428328	−	0.999082i	$-0.486362\pi$
$229$	10.8629	−	3.95378i	0.717842	−	0.261273i	0.675009	+	0.737809i	$0.264140\pi$
$230$	6.70315	+	11.6102i	0.441992	+	0.765553i
$231$	0.230847	+	1.30920i	0.0151886	+	0.0861389i
$232$	6.25842	−	10.8399i	0.410885	−	0.711674i
$233$	−0.511415	−	0.885796i	−0.0335039	−	0.0580304i	0.848787	−	0.528735i	$-0.177333\pi$
$233$	−0.511415	−	0.885796i	−0.0335039	−	0.0580304i	−0.882291	+	0.470704i	$0.844000\pi$
$234$	0.876454	−	0.735432i	0.0572956	−	0.0480767i
$235$	−0.916111	+	5.19553i	−0.0597605	+	0.338919i
$236$	−0.582761	+	1.00937i	−0.0379345	+	0.0657045i
$237$	8.97787	+	3.26768i	0.583175	+	0.212258i
$238$	−0.971465	−	0.353584i	−0.0629707	−	0.0229195i
$239$	−3.64160	−	20.6525i	−0.235555	−	1.33590i	−0.841441	−	0.540349i	$-0.818292\pi$
$239$	−3.64160	−	20.6525i	−0.235555	−	1.33590i	0.605886	−	0.795552i	$-0.292819\pi$
$240$	−7.48069	−	6.27704i	−0.482876	−	0.405181i
$241$	−1.68098	−	1.41051i	−0.108282	−	0.0908590i	0.587039	−	0.809558i	$-0.300293\pi$
$241$	−1.68098	−	1.41051i	−0.108282	−	0.0908590i	−0.695321	+	0.718699i	$0.744738\pi$
$242$	0.00675109	+	0.0382873i	0.000433976	+	0.00246120i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	−6.33150	−	2.30448i	−0.405333	−	0.147529i
$245$	14.4802	−	25.0804i	0.925103	−	1.60233i
$246$	−0.0854016	+	0.484337i	−0.00544501	+	0.0308802i
$247$	−4.75432	+	3.98935i	−0.302510	+	0.253836i
$248$	3.41308	+	5.91163i	0.216731	+	0.375389i
$249$	4.60792	−	7.98115i	0.292015	−	0.505785i
$250$	−3.18070	−	18.0386i	−0.201165	−	1.14086i
$251$	−2.09450	−	3.62778i	−0.132204	−	0.228983i	0.792322	−	0.610103i	$-0.208872\pi$
$251$	−2.09450	−	3.62778i	−0.132204	−	0.228983i	−0.924526	+	0.381120i	$0.875539\pi$
$252$	0.643508	−	0.234218i	0.0405372	−	0.0147543i
$253$	−19.2004			−1.20712
$254$	6.40175	−	2.33005i	0.401682	−	0.146200i
$255$	3.46873	−	19.6722i	0.217221	−	1.23192i
$256$	−2.16760	−	1.81883i	−0.135475	−	0.113677i
$257$	−13.2178	+	11.0911i	−0.824504	+	0.691841i	−0.954022	−	0.299736i	$-0.903101\pi$
$257$	−13.2178	+	11.0911i	−0.824504	+	0.691841i	0.129518	+	0.991577i	$0.458657\pi$
$258$	−7.04632			−0.438685
$259$	−2.36873	−	0.610278i	−0.147186	−	0.0379208i
$260$	15.1392			0.938893
$261$	−4.75090	+	3.98648i	−0.294074	+	0.246757i
$262$	2.28760	+	1.91952i	0.141328	+	0.118588i
$263$	−1.81652	+	10.3020i	−0.112012	+	0.635250i	0.876175	+	0.481994i	$0.160087\pi$
$263$	−1.81652	+	10.3020i	−0.112012	+	0.635250i	−0.988186	+	0.153256i	$0.951024\pi$
$264$	−6.26963	+	2.28196i	−0.385869	+	0.140445i
$265$	−19.7388			−1.21254
$266$	0.608930	−	0.221632i	0.0373359	−	0.0135892i
$267$	1.51109	+	2.61729i	0.0924773	+	0.160175i
$268$	1.89959	+	10.7731i	0.116036	+	0.658071i
$269$	2.49974	−	4.32967i	0.152412	−	0.263985i	−0.779702	−	0.626151i	$-0.784629\pi$
$269$	2.49974	−	4.32967i	0.152412	−	0.263985i	0.932114	+	0.362166i	$0.117963\pi$
$270$	−1.15412	−	1.99900i	−0.0702377	−	0.121655i
$271$	13.4336	−	11.2722i	0.816036	−	0.684735i	−0.136004	−	0.990708i	$-0.543426\pi$
$271$	13.4336	−	11.2722i	0.816036	−	0.684735i	0.952040	+	0.305973i	$0.0989817\pi$
$272$	−1.88863	+	10.7110i	−0.114515	+	0.649447i
$273$	−0.422075	+	0.731054i	−0.0255451	+	0.0442454i
$274$	−0.344737	−	0.125474i	−0.0208263	−	0.00758016i
$275$	40.1837	+	14.6257i	2.42317	+	0.881961i
$276$	1.71749	+	9.74038i	0.103381	+	0.586302i
$277$	1.02836	+	0.862896i	0.0617881	+	0.0518464i	0.673159	−	0.739498i	$-0.264937\pi$
$277$	1.02836	+	0.862896i	0.0617881	+	0.0518464i	−0.611371	+	0.791344i	$0.709382\pi$
$278$	−4.66890	−	3.91767i	−0.280022	−	0.234966i
$279$	−0.587319	−	3.33085i	−0.0351619	−	0.199413i
$280$	−3.22986	−	1.17557i	−0.193021	−	0.0702540i
$281$	21.6227	+	7.87002i	1.28990	+	0.469486i	0.893695	−	0.448675i	$-0.148104\pi$
$281$	21.6227	+	7.87002i	1.28990	+	0.469486i	0.396207	+	0.918161i	$0.370326\pi$
$282$	0.339483	−	0.588002i	0.0202159	−	0.0350150i
$283$	0.360704	−	2.04565i	0.0214416	−	0.121601i	−0.972208	−	0.234118i	$-0.924780\pi$
$283$	0.360704	−	2.04565i	0.0214416	−	0.121601i	0.993650	+	0.112516i	$0.0358910\pi$
$284$	−12.8702	+	10.7994i	−0.763706	+	0.640826i
$285$	6.26053	+	10.8436i	0.370842	+	0.642317i
$286$	1.89116	−	3.27559i	0.111827	−	0.193690i
$287$	−0.0630101	−	0.357348i	−0.00371937	−	0.0210936i
$288$	2.64663	+	4.58409i	0.155954	+	0.270120i
$289$	−4.93145	+	1.79490i	−0.290085	+	0.105582i
$290$	14.3154			0.840631
$291$	−17.2918	+	6.29370i	−1.01366	+	0.368943i
$292$	0.160441	−	0.909908i	0.00938912	−	0.0532483i
$293$	−8.54215	−	7.16771i	−0.499038	−	0.418742i	0.358214	−	0.933639i	$-0.383386\pi$
$293$	−8.54215	−	7.16771i	−0.499038	−	0.418742i	−0.857252	+	0.514897i	$0.827830\pi$
$294$	−2.85514	+	2.39575i	−0.166515	+	0.139723i
$295$	−2.89853			−0.168759
$296$	0.951975	−	12.2395i	0.0553324	−	0.711406i
$297$	3.30585			0.191825
$298$	5.71219	−	4.79310i	0.330898	−	0.277657i
$299$	−9.33963	−	7.83688i	−0.540125	−	0.453219i
$300$	3.82515	−	21.6935i	0.220845	−	1.25248i
$301$	4.88531	−	1.77811i	0.281585	−	0.102488i
$302$	−9.98177			−0.574386
$303$	−17.0633	+	6.21054i	−0.980261	+	0.356786i
$304$	−3.40869	−	5.90402i	−0.195502	−	0.338619i
$305$	−2.90970	−	16.5018i	−0.166609	−	0.944888i
$306$	−1.28541	+	2.22639i	−0.0734819	+	0.127274i
$307$	4.91711	+	8.51669i	0.280634	+	0.486073i	0.971541	−	0.236871i	$-0.0761219\pi$
$307$	4.91711	+	8.51669i	0.280634	+	0.486073i	−0.690907	+	0.722944i	$0.742789\pi$
$308$	1.73423	−	1.45519i	0.0988167	−	0.0829170i
$309$	−0.0830077	+	0.470760i	−0.00472214	+	0.0267806i
$310$	−3.90352	+	6.76109i	−0.221705	+	0.384004i
$311$	19.4198	+	7.06825i	1.10120	+	0.400803i	0.827758	−	0.561085i	$-0.189616\pi$
$311$	19.4198	+	7.06825i	1.10120	+	0.400803i	0.273441	+	0.961889i	$0.411838\pi$
$312$	−3.98114	−	1.44902i	−0.225387	−	0.0820343i
$313$	4.36374	+	24.7480i	0.246653	+	1.39884i	0.816622	+	0.577173i	$0.195844\pi$
$313$	4.36374	+	24.7480i	0.246653	+	1.39884i	−0.569969	+	0.821666i	$0.693045\pi$
$314$	1.81433	+	1.52241i	0.102389	+	0.0859144i
$315$	1.30461	+	1.09470i	0.0735063	+	0.0616791i
$316$	−2.82524	−	16.0227i	−0.158932	−	0.901350i
$317$	−2.68181	−	0.976098i	−0.150625	−	0.0548231i	0.265607	−	0.964081i	$-0.414428\pi$
$317$	−2.68181	−	0.976098i	−0.150625	−	0.0548231i	−0.416233	+	0.909258i	$0.636650\pi$
$318$	2.38713	+	0.868846i	0.133864	+	0.0487225i
$319$	−10.2512	+	17.7556i	−0.573959	+	0.994125i
$320$	−1.26981	+	7.20147i	−0.0709847	+	0.402574i
$321$	5.15383	−	4.32457i	0.287659	−	0.241374i
$322$	0.636492	+	1.10244i	0.0354703	+	0.0614364i
$323$	6.97269	−	12.0770i	0.387971	−	0.671985i
$324$	−0.295711	−	1.67706i	−0.0164284	−	0.0931702i
$325$	13.5769	+	23.5158i	0.753109	+	1.30442i
$326$	−8.03811	+	2.92563i	−0.445189	+	0.162036i
$327$	−6.88520			−0.380752
$328$	1.71131	−	0.622865i	0.0944911	−	0.0343919i
$329$	−0.0869886	+	0.493337i	−0.00479584	+	0.0271986i
$330$	−5.84547	−	4.90493i	−0.321783	−	0.270008i
$331$	−14.1925	+	11.9090i	−0.780093	+	0.654576i	−0.943272	−	0.332021i	$-0.892270\pi$
$331$	−14.1925	+	11.9090i	−0.780093	+	0.654576i	0.163179	+	0.986596i	$0.447825\pi$
$332$	−15.6940			−0.861319
$333$	−2.51740	+	5.53739i	−0.137953	+	0.303447i
$334$	−1.55448			−0.0850572
$335$	−20.8401	+	17.4870i	−1.13862	+	0.955414i
$336$	−0.710323	−	0.596032i	−0.0387513	−	0.0325162i
$337$	0.892904	−	5.06391i	0.0486396	−	0.275849i	−0.950782	−	0.309861i	$-0.899717\pi$
$337$	0.892904	−	5.06391i	0.0486396	−	0.275849i	0.999421	+	0.0340123i	$0.0108285\pi$
$338$	−4.40129	+	1.60194i	−0.239399	+	0.0871340i
$339$	−17.0056			−0.923615
$340$	−31.9657	+	11.6346i	−1.73358	+	0.630973i
$341$	−5.59059	−	9.68319i	−0.302747	−	0.524374i
$342$	−0.279822	−	1.58695i	−0.0151310	−	0.0858124i
$343$	2.78242	−	4.81929i	0.150237	−	0.260217i
$344$	13.0460	+	22.5964i	0.703395	+	1.21832i
$345$	−18.8424	+	15.8107i	−1.01444	+	0.851217i
$346$	1.39016	−	7.88400i	0.0747355	−	0.423846i
$347$	0.670371	−	1.16112i	0.0359874	−	0.0623320i	−0.847471	−	0.530842i	$-0.821876\pi$
$347$	0.670371	−	1.16112i	0.0359874	−	0.0623320i	0.883458	+	0.468510i	$0.155209\pi$
$348$	9.92444	+	3.61220i	0.532006	+	0.193634i
$349$	−3.30725	−	1.20374i	−0.177033	−	0.0644348i	0.251983	−	0.967732i	$-0.418917\pi$
$349$	−3.30725	−	1.20374i	−0.177033	−	0.0644348i	−0.429016	+	0.903297i	$0.641140\pi$
$350$	−0.492320	−	2.79208i	−0.0263156	−	0.149243i
$351$	1.60806	+	1.34932i	0.0858320	+	0.0720216i
$352$	13.4048	+	11.2480i	0.714478	+	0.599518i
$353$	−0.596936	−	3.38539i	−0.0317717	−	0.180186i	0.964792	−	0.263013i	$-0.0847162\pi$
$353$	−0.596936	−	3.38539i	−0.0317717	−	0.180186i	−0.996564	+	0.0828270i	$0.973605\pi$
$354$	0.350538	+	0.127585i	0.0186309	+	0.00678108i
$355$	−39.2623	−	14.2903i	−2.08382	−	0.758450i
$356$	2.57329	−	4.45707i	0.136384	−	0.236224i
$357$	0.329371	−	1.86796i	0.0174322	−	0.0988627i
$358$	5.01319	−	4.20656i	0.264955	−	0.222324i
$359$	−1.01819	−	1.76356i	−0.0537381	−	0.0930770i	0.837905	−	0.545816i	$-0.183780\pi$
$359$	−1.01819	−	1.76356i	−0.0537381	−	0.0930770i	−0.891643	+	0.452739i	$0.850447\pi$
$360$	−4.27364	+	7.40216i	−0.225241	+	0.390128i
$361$	−1.78142	−	10.1030i	−0.0937592	−	0.531735i
$362$	−2.76832	−	4.79486i	−0.145499	−	0.252012i
$363$	−0.0670290	+	0.0243966i	−0.00351811	+	0.00128049i
$364$	1.43753			0.0753471
$365$	2.15918	−	0.785879i	0.113017	−	0.0411348i
$366$	−0.374472	+	2.12374i	−0.0195740	+	0.111009i
$367$	13.9885	+	11.7377i	0.730193	+	0.612704i	0.930184	−	0.367093i	$-0.119647\pi$
$367$	13.9885	+	11.7377i	0.730193	+	0.612704i	−0.199991	+	0.979798i	$0.564091\pi$
$368$	10.2592	−	8.60847i	0.534797	−	0.448748i
$369$	−0.902339			−0.0469739
$370$	12.6672	−	6.05622i	0.658537	−	0.314848i
$371$	−1.87428			−0.0973079
$372$	−4.41221	+	3.70228i	−0.228762	+	0.191954i
$373$	−26.4122	−	22.1624i	−1.36757	−	1.14753i	−0.973563	−	0.228420i	$-0.926644\pi$
$373$	−26.4122	−	22.1624i	−1.36757	−	1.14753i	−0.394007	−	0.919108i	$-0.628911\pi$
$374$	−1.47579	+	8.36963i	−0.0763114	+	0.432783i
$375$	31.5800	−	11.4942i	1.63078	−	0.593556i
$376$	−2.51417			−0.129658
$377$	−12.2337	+	4.45269i	−0.630066	+	0.229325i
$378$	−0.109589	−	0.189813i	−0.00563664	−	0.00976295i
$379$	−5.07999	−	28.8101i	−0.260942	−	1.47987i	−0.780348	−	0.625346i	$-0.784958\pi$
$379$	−5.07999	−	28.8101i	−0.260942	−	1.47987i	0.519406	−	0.854528i	$-0.326153\pi$
$380$	10.6613	−	18.4659i	0.546912	−	0.947279i
$381$	6.24967	+	10.8247i	0.320180	+	0.554568i
$382$	0.758546	−	0.636496i	0.0388106	−	0.0325660i
$383$	−4.68417	+	26.5653i	−0.239350	+	1.35742i	0.593906	+	0.804534i	$0.297585\pi$
$383$	−4.68417	+	26.5653i	−0.239350	+	1.35742i	−0.833256	+	0.552887i	$0.813526\pi$
$384$	5.76381	−	9.98320i	0.294133	−	0.509453i
$385$	5.29048	+	1.92558i	0.269628	+	0.0981366i
$386$	−4.87666	−	1.77496i	−0.248215	−	0.0903430i
$387$	−2.24495	−	12.7317i	−0.114117	−	0.647191i
$388$	24.0053	+	20.1428i	1.21868	+	1.02260i
$389$	17.0224	+	14.2835i	0.863068	+	0.724200i	0.962627	−	0.270832i	$-0.0872987\pi$
$389$	17.0224	+	14.2835i	0.863068	+	0.724200i	−0.0995588	+	0.995032i	$0.531743\pi$
$390$	−0.841398	−	4.77180i	−0.0426058	−	0.241630i
$391$	25.7429	+	9.36965i	1.30187	+	0.473844i
$392$	12.9690	+	4.72032i	0.655032	+	0.238412i
$393$	−2.73949	+	4.74493i	−0.138189	+	0.239350i
$394$	−0.0628515	+	0.356449i	−0.00316641	+	0.0179576i
$395$	30.9954	−	26.0082i	1.55955	−	1.30862i
$396$	−2.81483	−	4.87542i	−0.141450	−	0.244999i
$397$	−5.96051	+	10.3239i	−0.299150	+	0.518142i	−0.975942	−	0.218032i	$-0.930036\pi$
$397$	−5.96051	+	10.3239i	−0.299150	+	0.518142i	0.676792	+	0.736174i	$0.263370\pi$
$398$	−1.74137	−	9.87577i	−0.0872868	−	0.495028i
$399$	0.594464	+	1.02964i	0.0297604	+	0.0515465i
$400$	−28.0284	+	10.2015i	−1.40142	+	0.510075i
$401$	30.4880			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$401$	30.4880			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$402$	3.29005	−	1.19748i	0.164093	−	0.0597249i
$403$	1.23289	−	6.99205i	0.0614145	−	0.348299i
$404$	23.6880	+	19.8766i	1.17852	+	0.988899i
$405$	3.24422	−	2.72222i	0.161206	−	0.135268i
$406$	1.35931			0.0674614
$407$	−1.55933	+	20.0482i	−0.0772929	+	0.993751i
$408$	9.51957			0.471289
$409$	21.6718	−	18.1848i	1.07160	−	0.899182i	0.0764068	−	0.997077i	$-0.475655\pi$
$409$	21.6718	−	18.1848i	1.07160	−	0.899182i	0.995197	+	0.0978945i	$0.0312108\pi$
$410$	1.59553	+	1.33881i	0.0787978	+	0.0661192i
$411$	0.116882	−	0.662868i	0.00576534	−	0.0326969i
$412$	0.764948	−	0.278418i	0.0376863	−	0.0137167i
$413$	−0.275228			−0.0135431
$414$	2.97467	−	1.08269i	0.146197	−	0.0532114i
$415$	−19.5147	−	33.8004i	−0.957937	−	1.65919i
$416$	1.92949	+	10.9427i	0.0946009	+	0.536508i
$417$	5.59119	−	9.68422i	0.273802	−	0.474238i
$418$	−2.66358	−	4.61345i	−0.130280	−	0.225651i
$419$	4.35050	−	3.65050i	0.212536	−	0.178339i	−0.530305	−	0.847807i	$-0.677922\pi$
$419$	4.35050	−	3.65050i	0.212536	−	0.178339i	0.742841	+	0.669468i	$0.233478\pi$
$420$	0.503610	−	2.85611i	0.0245736	−	0.139364i
$421$	2.60574	−	4.51327i	0.126996	−	0.219963i	−0.795515	−	0.605933i	$-0.792800\pi$
$421$	2.60574	−	4.51327i	0.126996	−	0.219963i	0.922511	+	0.385970i	$0.126133\pi$
$422$	−7.28288	−	2.65075i	−0.354525	−	0.129037i
$423$	1.17060	+	0.426063i	0.0569165	+	0.0207159i
$424$	−1.63346	−	9.26378i	−0.0793276	−	0.449889i
$425$	−46.7390	−	39.2187i	−2.26717	−	1.90239i
$426$	4.11921	+	3.45643i	0.199576	+	0.167464i
$427$	−0.276289	−	1.56691i	−0.0133706	−	0.0758282i
$428$	−10.7661	−	3.91855i	−0.520400	−	0.189410i
$429$	6.52106	+	2.37347i	0.314840	+	0.114592i
$430$	−14.9207	+	25.8434i	−0.719538	+	1.24628i
$431$	3.94402	−	22.3676i	0.189977	−	1.07741i	−0.729416	−	0.684070i	$-0.760208\pi$
$431$	3.94402	−	22.3676i	0.189977	−	1.07741i	0.919393	−	0.393341i	$-0.128681\pi$
$432$	−1.76639	+	1.48217i	−0.0849853	+	0.0713111i
$433$	−10.5156	−	18.2136i	−0.505348	−	0.875288i	−0.999981	−	0.00618601i	$-0.998031\pi$
$433$	−10.5156	−	18.2136i	−0.505348	−	0.875288i	0.494633	−	0.869102i	$-0.335302\pi$
$434$	−0.370656	+	0.641994i	−0.0177920	+	0.0308167i
$435$	4.56088	+	25.8660i	0.218677	+	1.24018i
$436$	5.86252	+	10.1542i	0.280764	+	0.486297i
$437$	−16.1361	+	5.87305i	−0.771893	+	0.280946i
$438$	−0.295716			−0.0141298
$439$	30.6527	−	11.1567i	1.46297	−	0.532478i	0.516789	−	0.856113i	$-0.327127\pi$
$439$	30.6527	−	11.1567i	1.46297	−	0.532478i	0.946182	+	0.323635i	$0.104905\pi$
$440$	−4.90661	+	27.8268i	−0.233914	+	1.32659i
$441$	−5.23843	−	4.39557i	−0.249449	−	0.209313i
$442$	−4.13403	+	3.46887i	−0.196636	+	0.164997i
$443$	−14.8643			−0.706226			−0.353113	−	0.935581i	$-0.614877\pi$
$443$	−14.8643			−0.706226			−0.353113	+	0.935581i	$0.614877\pi$
$444$	10.3099	−	1.00228i	0.489288	−	0.0475660i
$445$	12.7990			0.606731
$446$	1.88043	−	1.57787i	0.0890409	−	0.0747142i
$447$	10.4804	+	8.79407i	0.495704	+	0.415945i
$448$	−0.120574	+	0.683810i	−0.00569659	+	0.0323070i
$449$	−19.2959	+	7.02312i	−0.910628	+	0.331441i	−0.754504	−	0.656296i	$-0.772122\pi$
$449$	−19.2959	+	7.02312i	−0.910628	+	0.331441i	−0.156124	+	0.987737i	$0.549900\pi$
$450$	−7.05029			−0.332354
$451$	−2.80310	+	1.02025i	−0.131993	+	0.0480415i
$452$	14.4797	+	25.0795i	0.681066	+	1.17964i
$453$	−3.18018	−	18.0357i	−0.149418	−	0.847390i
$454$	4.19578	−	7.26731i	0.196918	−	0.341072i
$455$	1.78750	+	3.09603i	0.0837991	+	0.145144i
$456$	−4.57100	+	3.83553i	−0.214057	+	0.179615i
$457$	−1.77443	+	10.0633i	−0.0830041	+	0.470740i	0.914765	+	0.403986i	$0.132375\pi$
$457$	−1.77443	+	10.0633i	−0.0830041	+	0.470740i	−0.997769	+	0.0667541i	$0.978736\pi$
$458$	−3.15034	+	5.45655i	−0.147206	+	0.254968i
$459$	−4.43232	−	1.61323i	−0.206883	−	0.0752992i
$460$	39.3610	+	14.3262i	1.83522	+	0.667964i
$461$	−2.71794	−	15.4142i	−0.126587	−	0.717911i	−0.980353	−	0.197253i	$-0.936798\pi$
$461$	−2.71794	−	15.4142i	−0.126587	−	0.717911i	0.853765	−	0.520658i	$-0.174313\pi$
$462$	−0.555052	−	0.465744i	−0.0258234	−	0.0216684i
$463$	−19.9781	−	16.7636i	−0.928462	−	0.779073i	0.0470783	−	0.998891i	$-0.485009\pi$
$463$	−19.9781	−	16.7636i	−0.928462	−	0.779073i	−0.975541	+	0.219819i	$0.929453\pi$
$464$	−2.48327	−	14.0833i	−0.115283	−	0.653802i
$465$	−13.4600	−	4.89905i	−0.624193	−	0.227188i
$466$	0.523860	+	0.190669i	0.0242673	+	0.00883259i
$467$	10.9733	−	19.0062i	0.507782	−	0.879504i	−0.492178	−	0.870495i	$-0.663799\pi$
$467$	10.9733	−	19.0062i	0.507782	−	0.879504i	0.999959	−	0.00900918i	$-0.00286775\pi$
$468$	0.620751	−	3.52045i	0.0286942	−	0.162733i
$469$	−1.97886	+	1.66046i	−0.0913752	+	0.0766729i
$470$	−1.43772	−	2.49020i	−0.0663171	−	0.114865i
$471$	−2.17274	+	3.76329i	−0.100114	+	0.173403i
$472$	−0.239864	−	1.36034i	−0.0110406	−	0.0626146i
$473$	−21.3693	−	37.0127i	−0.982560	−	1.70184i
$474$	−4.89327	+	1.78101i	−0.224756	+	0.0818043i
$475$	38.2442			1.75476
$476$	−3.03528	+	1.10475i	−0.139122	+	0.0506362i
$477$	−0.809347	+	4.59004i	−0.0370575	+	0.210163i
$478$	8.75592	+	7.34709i	0.400486	+	0.336048i
$479$	−2.09191	+	1.75532i	−0.0955819	+	0.0802027i	−0.689326	−	0.724451i	$-0.742093\pi$
$479$	−2.09191	+	1.75532i	−0.0955819	+	0.0802027i	0.593745	+	0.804654i	$0.297649\pi$
$480$	22.4170			1.02319
$481$	−8.94141	+	9.11555i	−0.407693	+	0.415633i
$482$	1.19601			0.0544768
$483$	−1.78917	+	1.50129i	−0.0814099	+	0.0683110i
$484$	0.0930527	+	0.0780805i	0.00422967	+	0.00354911i
$485$	−13.5326	+	76.7471i	−0.614483	+	3.48490i
$486$	−0.512168	+	0.186414i	−0.0232324	+	0.00845590i
$487$	1.92591			0.0872715			0.0436358	−	0.999048i	$-0.486106\pi$
$487$	1.92591			0.0872715			0.0436358	+	0.999048i	$0.486106\pi$
$488$	7.50379	−	2.73116i	0.339681	−	0.123634i
$489$	−7.84714	−	13.5917i	−0.354860	−	0.614636i
$490$	2.74094	+	15.5446i	0.123823	+	0.702236i
$491$	16.5867	−	28.7290i	0.748547	−	1.29652i	−0.199972	−	0.979802i	$-0.564085\pi$
$491$	16.5867	−	28.7290i	0.748547	−	1.29652i	0.948519	−	0.316720i	$-0.102581\pi$
$492$	0.768312	+	1.33076i	0.0346382	+	0.0599951i
$493$	22.4089	−	18.8033i	1.00925	−	0.846859i
$494$	0.587396	−	3.33129i	0.0264282	−	0.149882i
$495$	7.00018	−	12.1247i	0.314635	−	0.544964i
$496$	7.32861	+	2.66740i	0.329064	+	0.119770i
$497$	−3.72812	−	1.35692i	−0.167229	−	0.0608664i
$498$	0.872231	+	4.94667i	0.0390856	+	0.221665i
$499$	28.0784	+	23.5606i	1.25696	+	1.05472i	0.995999	+	0.0893666i	$0.0284843\pi$
$499$	28.0784	+	23.5606i	1.25696	+	1.05472i	0.260962	+	0.965349i	$0.415960\pi$
$500$	−43.8407	−	36.7867i	−1.96062	−	1.64515i
$501$	−0.495254	−	2.80873i	−0.0221263	−	0.125485i
$502$	2.14547	+	0.780886i	0.0957569	+	0.0348527i
$503$	−21.2321	−	7.72785i	−0.946692	−	0.344568i	−0.177887	−	0.984051i	$-0.556926\pi$
$503$	−21.2321	−	7.72785i	−0.946692	−	0.344568i	−0.768805	+	0.639483i	$0.779148\pi$
$504$	−0.405800	+	0.702867i	−0.0180758	+	0.0313082i
$505$	−13.3538	+	75.7329i	−0.594234	+	3.37007i
$506$	8.01661	−	6.72673i	0.356382	−	0.299040i
$507$	−4.29673	−	7.44215i	−0.190824	−	0.330518i
$508$	10.6428	−	18.4338i	0.472197	−	0.817869i
$509$	−0.489375	−	2.77539i	−0.0216912	−	0.123017i	0.972039	−	0.234818i	$-0.0754493\pi$
$509$	−0.489375	−	2.77539i	−0.0216912	−	0.123017i	−0.993731	+	0.111801i	$0.964338\pi$
$510$	5.44373	+	9.42882i	0.241053	+	0.417515i
$511$	0.205024	−	0.0746225i	0.00906971	−	0.00330111i
$512$	−21.5130			−0.950749
$513$	2.77825	−	1.01120i	0.122663	−	0.0446456i
$514$	1.63306	−	9.26153i	0.0720311	−	0.408509i
$515$	1.55081	+	1.30128i	0.0683367	+	0.0573413i
$516$	−16.8651	+	14.1515i	−0.742443	+	0.622984i
$517$	4.11818			0.181118
$518$	1.20281	−	0.575063i	0.0528482	−	0.0252668i
$519$	14.6882			0.644741
$520$	−13.7446	+	11.5331i	−0.602739	+	0.505758i
$521$	−7.20829	−	6.04848i	−0.315801	−	0.264989i	0.471084	−	0.882089i	$-0.343863\pi$
$521$	−7.20829	−	6.04848i	−0.315801	−	0.264989i	−0.786885	+	0.617100i	$0.788307\pi$
$522$	0.586974	−	3.32889i	0.0256911	−	0.145702i
$523$	−7.96210	+	2.89797i	−0.348158	+	0.126719i	−0.510179	−	0.860068i	$-0.670421\pi$
$523$	−7.96210	+	2.89797i	−0.348158	+	0.126719i	0.162021	+	0.986787i	$0.448199\pi$
$524$	9.33033			0.407597
$525$	4.88806	−	1.77911i	0.213332	−	0.0776467i
$526$	−2.85080	−	4.93774i	−0.124301	−	0.215296i
$527$	2.77025	+	15.7109i	0.120674	+	0.684377i
$528$	−3.81141	+	6.60155i	−0.165870	+	0.287296i
$529$	−5.36644	−	9.29495i	−0.233324	−	0.404128i
$530$	8.24140	−	6.91535i	0.357983	−	0.300384i
$531$	−0.118848	+	0.674022i	−0.00515758	+	0.0292501i
$532$	1.01233	−	1.75341i	0.0438902	−	0.0760200i
$533$	−1.77994	−	0.647844i	−0.0770976	−	0.0280612i
$534$	−1.54786	−	0.563376i	−0.0669826	−	0.0243797i
$535$	−4.94768	−	28.0597i	−0.213907	−	1.21313i
$536$	−9.93155	−	8.33356i	−0.428978	−	0.359955i
$537$	9.19788	+	7.71793i	0.396918	+	0.333053i
$538$	0.473174	+	2.68350i	0.0204000	+	0.115694i
$539$	−21.2431	−	7.73184i	−0.915003	−	0.333034i
$540$	−6.77703	−	2.46664i	−0.291637	−	0.106147i
$541$	−5.55117	+	9.61490i	−0.238663	+	0.413377i	−0.960331	−	0.278863i	$-0.910043\pi$
$541$	−5.55117	+	9.61490i	−0.238663	+	0.413377i	0.721668	+	0.692240i	$0.243376\pi$
$542$	−1.65973	+	9.41277i	−0.0712913	+	0.404313i
$543$	7.78168	−	6.52960i	0.333944	−	0.280212i
$544$	−12.4835	−	21.6221i	−0.535227	−	0.927040i
$545$	−14.5795	+	25.2524i	−0.624517	+	1.08169i
$546$	−0.0798943	−	0.453103i	−0.00341916	−	0.0193910i
$547$	7.39108	+	12.8017i	0.316020	+	0.547362i	0.979654	−	0.200695i	$-0.0643201\pi$
$547$	7.39108	+	12.8017i	0.316020	+	0.547362i	−0.663634	+	0.748057i	$0.730987\pi$
$548$	−1.07711	+	0.392035i	−0.0460118	+	0.0167469i
$549$	−3.95661			−0.168864
$550$	−21.9016	+	7.97154i	−0.933888	+	0.339908i
$551$	−3.18403	+	18.0576i	−0.135644	+	0.769278i
$552$	−8.97952	−	7.53471i	−0.382194	−	0.320699i
$553$	2.94314	−	2.46959i	0.125155	−	0.105018i
$554$	−0.731673			−0.0310858
$555$	14.9785	+	20.9584i	0.635802	+	0.889635i
$556$	−19.0428			−0.807597
$557$	−24.7115	+	20.7354i	−1.04706	+	0.878587i	−0.992781	−	0.119939i	$-0.961730\pi$
$557$	−24.7115	+	20.7354i	−1.04706	+	0.878587i	−0.0542782	+	0.998526i	$0.517286\pi$
$558$	1.41216	+	1.18494i	0.0597816	+	0.0501627i
$559$	4.71254	−	26.7262i	0.199319	−	1.13040i
$560$	−3.69015	+	1.34310i	−0.155937	+	0.0567565i
$561$	−15.5930			−0.658335
$562$	−11.7852	+	4.28945i	−0.497128	+	0.180940i
$563$	−3.35808	−	5.81637i	−0.141526	−	0.245131i	0.786545	−	0.617533i	$-0.211868\pi$
$563$	−3.35808	−	5.81637i	−0.141526	−	0.245131i	−0.928072	+	0.372402i	$0.878534\pi$
$564$	−0.368375	−	2.08916i	−0.0155114	−	0.0879695i
$565$	−36.0095	+	62.3702i	−1.51493	+	2.62393i
$566$	0.566078	+	0.980477i	0.0237941	+	0.0412125i
$567$	0.308052	−	0.258486i	0.0129370	−	0.0108554i
$568$	3.45761	−	19.6091i	0.145078	−	0.822779i
$569$	13.2266	−	22.9092i	0.554488	−	0.960402i	−0.443455	−	0.896297i	$-0.646247\pi$
$569$	13.2266	−	22.9092i	0.554488	−	0.960402i	0.997943	−	0.0641052i	$-0.0204193\pi$
$570$	−6.41288	−	2.33410i	−0.268606	−	0.0977646i
$571$	−37.7706	−	13.7474i	−1.58065	−	0.575309i	−0.605304	−	0.795994i	$-0.706949\pi$
$571$	−37.7706	−	13.7474i	−1.58065	−	0.575309i	−0.975345	+	0.220685i	$0.929171\pi$
$572$	−2.05211	−	11.6381i	−0.0858030	−	0.486613i
$573$	1.39173	+	1.16780i	0.0581404	+	0.0487856i
$574$	0.151503	+	0.127126i	0.00632360	+	0.00530613i
$575$	13.0460	+	73.9876i	0.544056	+	3.08550i
$576$	1.62256	+	0.590562i	0.0676065	+	0.0246068i
$577$	31.5262	+	11.4746i	1.31245	+	0.477694i	0.901032	−	0.433752i	$-0.142811\pi$
$577$	31.5262	+	11.4746i	1.31245	+	0.477694i	0.411421	+	0.911446i	$0.365033\pi$
$578$	1.43016	−	2.47711i	0.0594869	−	0.103034i
$579$	1.65341	−	9.37696i	0.0687134	−	0.389693i
$580$	34.2634	−	28.7504i	1.42271	−	1.19379i
$581$	−1.85300	−	3.20949i	−0.0768754	−	0.133152i
$582$	5.01477	−	8.68583i	0.207869	−	0.360039i
$583$	2.67558	+	15.1740i	0.110811	+	0.628443i
$584$	0.547508	+	0.948311i	0.0226560	+	0.0392414i
$585$	8.35393	−	3.04058i	0.345392	−	0.125713i
$586$	6.07770			0.251068
$587$	12.0834	−	4.39799i	0.498735	−	0.181525i	−0.0803901	−	0.996763i	$-0.525617\pi$
$587$	12.0834	−	4.39799i	0.498735	−	0.181525i	0.579125	+	0.815239i	$0.303394\pi$
$588$	−2.02216	+	11.4682i	−0.0833925	+	0.472942i
$589$	−7.66026	−	6.42772i	−0.315635	−	0.264849i
$590$	1.21020	−	1.01548i	0.0498233	−	0.0418067i
$591$	−0.664078			−0.0273165
$592$	−8.15539	−	11.4113i	−0.335184	−	0.469001i
$593$	34.9575			1.43553			0.717766	−	0.696285i	$-0.245165\pi$
$593$	34.9575			1.43553			0.717766	+	0.696285i	$0.245165\pi$
$594$	−1.38027	+	1.15818i	−0.0566331	+	0.0475208i
$595$	−6.15354	−	5.16343i	−0.252270	−	0.211680i
$596$	4.04567	−	22.9441i	0.165717	−	0.939828i
$597$	17.2894	−	6.29282i	0.707607	−	0.257548i
$598$	6.64511			0.271739
$599$	4.06994	−	1.48134i	0.166293	−	0.0605258i	−0.257532	−	0.966270i	$-0.582909\pi$
$599$	4.06994	−	1.48134i	0.166293	−	0.0605258i	0.423825	+	0.905744i	$0.360687\pi$
$600$	13.0534	+	22.6091i	0.532902	+	0.923013i
$601$	0.335024	+	1.90002i	0.0136659	+	0.0775033i	0.990878	−	0.134762i	$-0.0430270\pi$
$601$	0.335024	+	1.90002i	0.0136659	+	0.0775033i	−0.977212	+	0.212265i	$0.931916\pi$
$602$	−1.41678	+	2.45394i	−0.0577437	+	0.100015i
$603$	3.21189	+	5.56316i	0.130798	+	0.226549i
$604$	−23.8909	+	20.0469i	−0.972108	+	0.815696i
$605$	−0.0524570	+	0.297498i	−0.00213268	+	0.0120950i
$606$	4.94850	−	8.57106i	0.201019	−	0.348175i
$607$	7.57410	+	2.75675i	0.307423	+	0.111893i	0.491125	−	0.871089i	$-0.336586\pi$
$607$	7.57410	+	2.75675i	0.307423	+	0.111893i	−0.183702	+	0.982982i	$0.558808\pi$
$608$	14.7060	+	5.35253i	0.596406	+	0.217074i
$609$	0.433074	+	2.45609i	0.0175491	+	0.0995257i
$610$	6.99615	+	5.87046i	0.283266	+	0.237688i
$611$	2.00320	+	1.68089i	0.0810410	+	0.0680014i
$612$	1.39480	+	7.91032i	0.0563816	+	0.319756i
$613$	7.13767	+	2.59790i	0.288288	+	0.104928i	0.482116	−	0.876107i	$-0.339868\pi$
$613$	7.13767	+	2.59790i	0.288288	+	0.104928i	−0.193828	+	0.981035i	$0.562090\pi$
$614$	−5.03677	−	1.83323i	−0.203267	−	0.0739833i
$615$	−1.91071	+	3.30945i	−0.0770474	+	0.133450i
$616$	−0.465904	+	2.64227i	−0.0187718	+	0.106460i
$617$	−17.9740	+	15.0819i	−0.723604	+	0.607176i	−0.928380	−	0.371633i	$-0.878798\pi$
$617$	−17.9740	+	15.0819i	−0.723604	+	0.607176i	0.204776	+	0.978809i	$0.434354\pi$
$618$	−0.130270	−	0.225634i	−0.00524023	−	0.00907634i
$619$	−10.6445	+	18.4369i	−0.427840	+	0.741040i	−0.996681	−	0.0814071i	$-0.974059\pi$
$619$	−10.6445	+	18.4369i	−0.427840	+	0.741040i	0.568841	+	0.822447i	$0.307392\pi$
$620$	4.23573	+	24.0220i	0.170111	+	0.964747i
$621$	2.90400	+	5.02988i	0.116534	+	0.201842i
$622$	−10.5845	+	3.85246i	−0.424401	+	0.154469i
$623$	1.21532			0.0486908
$624$	−4.54848	+	1.65551i	−0.182085	+	0.0662735i
$625$	13.4834	−	76.4684i	0.539337	−	3.05873i
$626$	−10.4922	−	8.80404i	−0.419355	−	0.351880i
$627$	7.48726	−	6.28256i	0.299012	−	0.250901i
$628$	7.40006			0.295294
$629$	11.8740	−	26.1186i	0.473448	−	1.04142i
$630$	−0.928223			−0.0369813
$631$	21.2592	−	17.8386i	0.846315	−	0.710143i	−0.112660	−	0.993634i	$-0.535937\pi$
$631$	21.2592	−	17.8386i	0.846315	−	0.710143i	0.958975	+	0.283491i	$0.0914925\pi$
$632$	14.7711	+	12.3945i	0.587564	+	0.493025i
$633$	2.46923	−	14.0037i	0.0981431	−	0.556597i
$634$	1.46168	−	0.532010i	0.0580509	−	0.0211288i
$635$	52.9350			2.10066
$636$	7.45845	−	2.71465i	0.295747	−	0.107643i
$637$	−7.17739	−	12.4316i	−0.284378	−	0.492558i
$638$	−1.94045	−	11.0048i	−0.0768231	−	0.435686i
$639$	−4.93292	+	8.54406i	−0.195143	+	0.337998i
$640$	−24.4099	−	42.2791i	−0.964884	−	1.67123i
$641$	−9.34059	+	7.83769i	−0.368931	+	0.309570i	−0.808339	−	0.588718i	$-0.799633\pi$
$641$	−9.34059	+	7.83769i	−0.368931	+	0.309570i	0.439407	+	0.898288i	$0.355188\pi$
$642$	−0.636755	+	3.61122i	−0.0251307	+	0.142523i
$643$	−0.308900	+	0.535031i	−0.0121818	+	0.0210996i	−0.872052	−	0.489413i	$-0.837211\pi$
$643$	−0.308900	+	0.535031i	−0.0121818	+	0.0210996i	0.859870	+	0.510513i	$0.170544\pi$
$644$	3.73749	+	1.36034i	0.147278	+	0.0536048i
$645$	−51.4491	−	18.7259i	−2.02581	−	0.737333i
$646$	1.31986	+	7.48528i	0.0519290	+	0.294504i
$647$	25.0970	+	21.0589i	0.986664	+	0.827909i	0.985081	−	0.172090i	$-0.0550518\pi$
$647$	25.0970	+	21.0589i	0.986664	+	0.827909i	0.00158250	+	0.999999i	$0.499496\pi$
$648$	1.54606	+	1.29730i	0.0607350	+	0.0509627i
$649$	0.392895	+	2.22822i	0.0154225	+	0.0874652i
$650$	−13.9073	−	5.06183i	−0.545488	−	0.198541i
$651$	−1.27809	−	0.465185i	−0.0500921	−	0.0182320i
$652$	−13.3632	+	23.1457i	−0.523342	+	0.906455i
$653$	0.116258	−	0.659334i	0.00454954	−	0.0258017i	−0.982448	−	0.186534i	$-0.940275\pi$
$653$	0.116258	−	0.659334i	0.00454954	−	0.0258017i	0.986998	+	0.160732i	$0.0513856\pi$
$654$	2.87473	−	2.41218i	0.112411	−	0.0943238i
$655$	11.6018	+	20.0949i	0.453319	+	0.785172i
$656$	1.04033	−	1.80191i	0.0406181	−	0.0703526i
$657$	−0.0942146	−	0.534318i	−0.00367566	−	0.0208457i
$658$	−0.136518	−	0.236455i	−0.00532201	−	0.00921799i
$659$	10.4581	−	3.80643i	0.407389	−	0.148277i	−0.130194	−	0.991489i	$-0.541560\pi$
$659$	10.4581	−	3.80643i	0.407389	−	0.148277i	0.537582	+	0.843211i	$0.319338\pi$
$660$	−23.8417			−0.928037
$661$	−0.645313	+	0.234875i	−0.0250998	+	0.00913557i	−0.354540	−	0.935041i	$-0.615362\pi$
$661$	−0.645313	+	0.234875i	−0.0250998	+	0.00913557i	0.329440	+	0.944177i	$0.393140\pi$
$662$	1.75349	−	9.94453i	0.0681513	−	0.386505i
$663$	−7.58486	−	6.36446i	−0.294572	−	0.247175i
$664$	14.2482	−	11.9557i	0.552939	−	0.463971i
$665$	5.03513			0.195254
$666$	−0.888914	−	3.19394i	−0.0344447	−	0.123763i
$667$	−36.0204			−1.39472
$668$	−3.72057	+	3.12193i	−0.143953	+	0.120791i
$669$	3.45009	+	2.89497i	0.133388	+	0.111926i
$670$	2.57480	−	14.6024i	0.0994731	−	0.564140i
$671$	−12.2911	+	4.47361i	−0.474494	+	0.172702i
$672$	2.12859			0.0821123
$673$	4.35524	−	1.58518i	0.167882	−	0.0611042i	−0.256712	−	0.966488i	$-0.582639\pi$
$673$	4.35524	−	1.58518i	0.167882	−	0.0611042i	0.424594	+	0.905384i	$0.360417\pi$
$674$	1.40130	+	2.42712i	0.0539760	+	0.0934892i
$675$	−2.24621	−	12.7389i	−0.0864568	−	0.490321i
$676$	−7.31705	+	12.6735i	−0.281425	+	0.487442i
$677$	−3.27679	−	5.67557i	−0.125937	−	0.218130i	0.796162	−	0.605084i	$-0.206860\pi$
$677$	−3.27679	−	5.67557i	−0.125937	−	0.218130i	−0.922099	+	0.386954i	$0.873527\pi$
$678$	7.10021	−	5.95778i	0.272682	−	0.228807i
$679$	−1.28498	+	7.28746i	−0.0493128	+	0.279667i
$680$	20.1578	−	34.9143i	0.773016	−	1.33890i
$681$	14.4678	+	5.26585i	0.554408	+	0.201788i
$682$	5.72664	+	2.08433i	0.219284	+	0.0798130i
$683$	1.17041	+	6.63774i	0.0447846	+	0.253986i	0.998978	−	0.0452053i	$-0.0143942\pi$
$683$	1.17041	+	6.63774i	0.0447846	+	0.253986i	−0.954193	+	0.299191i	$0.903283\pi$
$684$	−3.85689	−	3.23631i	−0.147472	−	0.123744i
$685$	−2.18366	−	1.83231i	−0.0834334	−	0.0700089i
$686$	0.526683	+	2.98697i	0.0201088	+	0.114043i
$687$	−10.8629	−	3.95378i	−0.414446	−	0.150846i
$688$	28.0126	+	10.1958i	1.06797	+	0.388710i
$689$	−4.89197	+	8.47314i	−0.186369	+	0.322801i
$690$	2.32798	−	13.2026i	0.0886246	−	0.502615i
$691$	−36.2034	+	30.3783i	−1.37724	+	1.15564i	−0.407023	+	0.913418i	$0.633433\pi$
$691$	−36.2034	+	30.3783i	−1.37724	+	1.15564i	−0.970220	+	0.242227i	$0.922122\pi$
$692$	−12.5065	−	21.6619i	−0.475427	−	0.823463i
$693$	0.664697	−	1.15129i	0.0252498	−	0.0437339i
$694$	0.126894	+	0.719652i	0.00481684	+	0.0273176i
$695$	−23.6788	−	41.0129i	−0.898188	−	1.55571i
$696$	−11.7620	+	4.28101i	−0.445837	+	0.162271i
$697$	4.25613			0.161212
$698$	1.80258	−	0.656084i	0.0682285	−	0.0248331i
$699$	−0.177612	+	1.00729i	−0.00671792	+	0.0380992i
$700$	−6.78582	−	5.69398i	−0.256480	−	0.215212i
$701$	8.09918	−	6.79602i	0.305902	−	0.256682i	−0.476894	−	0.878961i	$-0.658237\pi$
$701$	8.09918	−	6.79602i	0.305902	−	0.256682i	0.782796	+	0.622279i	$0.213793\pi$
$702$	−1.14413			−0.0431824
$703$	4.82190	+	17.3255i	0.181862	+	0.653444i
$704$	5.70818			0.215135
$705$	4.04140	−	3.39114i	0.152208	−	0.127718i
$706$	1.43528	+	1.20435i	0.0540176	+	0.0453261i
$707$	−1.26800	+	7.19116i	−0.0476879	+	0.270451i
$708$	1.09523	−	0.398632i	0.0411614	−	0.0149815i
$709$	39.2402			1.47370			0.736849	−	0.676057i	$-0.236313\pi$
$709$	39.2402			1.47370			0.736849	+	0.676057i	$0.236313\pi$
$710$	21.3994	−	7.78875i	0.803105	−	0.292306i
$711$	−4.77703	−	8.27405i	−0.179152	−	0.310301i
$712$	1.05916	+	6.00682i	0.0396938	+	0.225115i
$713$	9.82202	−	17.0122i	0.367838	−	0.637113i
$714$	0.516906	+	0.895307i	0.0193447	+	0.0335060i
$715$	22.5135	−	18.8910i	0.841956	−	0.706485i
$716$	3.55060	−	20.1365i	0.132692	−	0.752535i
$717$	−10.4856	+	18.1615i	−0.391590	+	0.678254i
$718$	1.04297	+	0.379610i	0.0389232	+	0.0141669i
$719$	−13.0308	−	4.74284i	−0.485969	−	0.176878i	0.0874038	−	0.996173i	$-0.472143\pi$
$719$	−13.0308	−	4.74284i	−0.485969	−	0.176878i	−0.573372	+	0.819295i	$0.694365\pi$
$720$	1.69573	+	9.61699i	0.0631963	+	0.358404i
$721$	0.147256	+	0.123562i	0.00548409	+	0.00460170i
$722$	4.28329	+	3.59411i	0.159408	+	0.133759i
$723$	0.381048	+	2.16103i	0.0141713	+	0.0803695i
$724$	−16.2556	−	5.91655i	−0.604135	−	0.219887i
$725$	75.3856	+	27.4381i	2.79975	+	1.01903i
$726$	0.0194390	−	0.0336693i	0.000721448	−	0.00124958i
$727$	8.54314	−	48.4505i	0.316847	−	1.79693i	−0.244820	−	0.969568i	$-0.578729\pi$
$727$	8.54314	−	48.4505i	0.316847	−	1.79693i	0.561668	−	0.827363i	$-0.310160\pi$
$728$	−1.30510	+	1.09511i	−0.0483704	+	0.0405876i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−0.626181	+	1.08458i	−0.0231760	+	0.0401420i
$731$	10.5889	+	60.0527i	0.391645	+	2.22113i
$732$	3.36892	+	5.83514i	0.124519	+	0.215673i
$733$	15.5097	−	5.64508i	0.572865	−	0.208506i	−0.0393114	−	0.999227i	$-0.512516\pi$
$733$	15.5097	−	5.64508i	0.572865	−	0.208506i	0.612176	+	0.790721i	$0.290294\pi$
$734$	−9.95274			−0.367362
$735$	−27.2138	+	9.90501i	−1.00380	+	0.365352i
$736$	−5.33850	+	30.2762i	−0.196780	+	1.11599i
$737$	16.2678	+	13.6503i	0.599232	+	0.502815i
$738$	0.376747	−	0.316128i	0.0138683	−	0.0116368i
$739$	−12.7486			−0.468964			−0.234482	−	0.972121i	$-0.575339\pi$
$739$	−12.7486			−0.468964			−0.234482	+	0.972121i	$0.575339\pi$
$740$	18.1554	−	39.9355i	0.667407	−	1.46806i
$741$	6.20632			0.227995
$742$	0.782555	−	0.656642i	0.0287285	−	0.0241061i
$743$	−16.6755	−	13.9924i	−0.611764	−	0.513331i	0.283439	−	0.958990i	$-0.408525\pi$
$743$	−16.6755	−	13.9924i	−0.611764	−	0.513331i	−0.895203	+	0.445660i	$0.852969\pi$
$744$	1.18535	−	6.72245i	0.0434570	−	0.246457i
$745$	54.4457	−	19.8166i	1.99474	−	0.726025i
$746$	18.7921			0.688029
$747$	−8.66006	+	3.15200i	−0.316855	+	0.115326i
$748$	13.2769	+	22.9963i	0.485451	+	0.840826i
$749$	−0.469803	−	2.66439i	−0.0171662	−	0.0973546i
$750$	−9.15845	+	15.8629i	−0.334419	+	0.579231i
$751$	−20.9688	−	36.3190i	−0.765162	−	1.32530i	−0.940161	−	0.340731i	$-0.889326\pi$
$751$	−20.9688	−	36.3190i	−0.765162	−	1.32530i	0.174999	−	0.984569i	$-0.444008\pi$
$752$	−2.20043	+	1.84638i	−0.0802415	+	0.0673306i
$753$	−0.727412	+	4.12536i	−0.0265084	+	0.150336i
$754$	3.54787	−	6.14509i	0.129206	−	0.223791i
$755$	−72.8824	−	26.5270i	−2.65246	−	0.965418i
$756$	−0.643508	−	0.234218i	−0.0234042	−	0.00851842i
$757$	4.96621	+	28.1648i	0.180500	+	1.02367i	0.931602	+	0.363480i	$0.118412\pi$
$757$	4.96621	+	28.1648i	0.180500	+	1.02367i	−0.751102	+	0.660186i	$0.770477\pi$
$758$	12.2144	+	10.2491i	0.443648	+	0.372265i
$759$	14.7084	+	12.3418i	0.533880	+	0.447978i
$760$	4.38817	+	24.8866i	0.159176	+	0.902730i
$761$	36.8728	+	13.4206i	1.33664	+	0.486496i	0.908752	−	0.417336i	$-0.137036\pi$
$761$	36.8728	+	13.4206i	1.33664	+	0.486496i	0.427886	+	0.903833i	$0.359259\pi$
$762$	−6.40175	−	2.33005i	−0.231911	−	0.0844087i
$763$	−1.38438	+	2.39782i	−0.0501181	+	0.0868070i
$764$	0.537242	−	3.04685i	0.0194367	−	0.110231i
$765$	−15.3022	+	12.8401i	−0.553253	+	0.464235i
$766$	−7.35121	−	12.7327i	−0.265610	−	0.460050i
$767$	−0.718359	+	1.24423i	−0.0259384	+	0.0449267i
$768$	0.491355	+	2.78662i	0.0177303	+	0.100553i
$769$	−18.7842	−	32.5351i	−0.677374	−	1.17325i	−0.975769	−	0.218804i	$-0.929784\pi$
$769$	−18.7842	−	32.5351i	−0.677374	−	1.17325i	0.298394	−	0.954443i	$-0.403549\pi$
$770$	−2.88351	+	1.04951i	−0.103915	+	0.0378218i
$771$	17.2546			0.621410
$772$	−15.2368	+	5.54575i	−0.548385	+	0.199596i
$773$	−8.02223	+	45.4963i	−0.288540	+	1.63639i	0.403821	+	0.914838i	$0.367682\pi$
$773$	−8.02223	+	45.4963i	−0.288540	+	1.63639i	−0.692361	+	0.721552i	$0.743429\pi$
$774$	5.39780	+	4.52929i	0.194020	+	0.162802i
$775$	−33.5150	+	28.1224i	−1.20389	+	1.01019i
$776$	−37.1387			−1.33320
$777$	1.42227	+	1.99009i	0.0510238	+	0.0713941i
$778$	−12.1113			−0.434212
$779$	−2.04366	+	1.71484i	−0.0732218	+	0.0614404i
$780$	−11.5973	−	9.73128i	−0.415250	−	0.348436i
$781$	−5.66354	+	32.1195i	−0.202657	+	1.14933i
$782$	−14.0308	+	5.10681i	−0.501742	+	0.182619i
$783$	6.20186			0.221637
$784$	14.8172	−	5.39301i	0.529184	−	0.192607i
$785$	9.20159	+	15.9376i	0.328419	+	0.568838i
$786$	−0.518556	−	2.94088i	−0.0184963	−	0.104898i
$787$	−8.65056	+	14.9832i	−0.308359	+	0.534094i	−0.978004	−	0.208588i	$-0.933113\pi$
$787$	−8.65056	+	14.9832i	−0.308359	+	0.534094i	0.669645	+	0.742682i	$0.266446\pi$
$788$	0.565441	+	0.979372i	0.0201430	+	0.0348887i
$789$	8.01355	−	6.72417i	0.285290	−	0.239387i
$790$	−3.82948	+	21.7181i	−0.136247	+	0.772694i
$791$	−3.41925	+	5.92232i	−0.121575	+	0.210573i
$792$	6.26963	+	2.28196i	0.222782	+	0.0810858i
$793$	−7.80473	−	2.84069i	−0.277154	−	0.100876i
$794$	−1.12826	−	6.39869i	−0.0400405	−	0.227081i
$795$	15.1208	+	12.6878i	0.536279	+	0.449992i
$796$	−24.0019	−	20.1400i	−0.850724	−	0.713842i
$797$	5.51597	+	31.2826i	0.195386	+	1.10809i	0.911869	+	0.410482i	$0.134640\pi$
$797$	5.51597	+	31.2826i	0.195386	+	1.10809i	−0.716483	+	0.697604i	$0.754249\pi$
$798$	−0.608930	−	0.221632i	−0.0215559	−	0.00784570i
$799$	−5.52145	−	2.00964i	−0.195335	−	0.0710960i
$800$	34.2352	−	59.2971i	1.21040	−	2.09647i
$801$	0.524796	−	2.97627i	0.0185428	−	0.105161i
$802$	−12.7294	+	10.6813i	−0.449492	+	0.377169i
$803$	−0.896813	−	1.55332i	−0.0316478	−	0.0548156i
$804$	5.46964	−	9.47369i	0.192899	−	0.334111i
$805$	1.71760	+	9.74101i	0.0605376	+	0.343326i
$806$	1.93486	+	3.35127i	0.0681525	+	0.118044i
$807$	−4.69797	+	1.70992i	−0.165376	+	0.0601921i
$808$	−36.6480			−1.28927
$809$	34.4952	−	12.5552i	1.21278	−	0.441418i	0.345116	−	0.938560i	$-0.387840\pi$
$809$	34.4952	−	12.5552i	1.21278	−	0.441418i	0.867669	+	0.497142i	$0.165617\pi$
$810$	−0.400823	+	2.27318i	−0.0140835	+	0.0798713i
$811$	13.0889	+	10.9829i	0.459612	+	0.385661i	0.842988	−	0.537932i	$-0.180794\pi$
$811$	13.0889	+	10.9829i	0.459612	+	0.385661i	−0.383376	+	0.923592i	$0.625239\pi$
$812$	3.25345	−	2.72997i	0.114174	−	0.0958031i
$813$	−17.5364			−0.615028
$814$	−6.37269	−	8.91687i	−0.223363	−	0.312536i
$815$	−66.4657			−2.32819
$816$	8.33164	−	6.99108i	0.291666	−	0.244737i
$817$	−29.2803	−	24.5691i	−1.02439	−	0.859563i
$818$	−2.67755	+	15.1852i	−0.0936185	+	0.530937i
$819$	0.793241	−	0.288716i	0.0277181	−	0.0100886i
$820$	6.50764			0.227257
$821$	32.9700	−	12.0001i	1.15066	−	0.418807i	0.304909	−	0.952381i	$-0.401374\pi$
$821$	32.9700	−	12.0001i	1.15066	−	0.418807i	0.845753	+	0.533575i	$0.179152\pi$
$822$	0.183431	+	0.317711i	0.00639788	+	0.0110814i
$823$	−0.187651	−	1.06422i	−0.00654111	−	0.0370965i	0.981363	−	0.192166i	$-0.0615511\pi$
$823$	−0.187651	−	1.06422i	−0.00654111	−	0.0370965i	−0.987904	+	0.155069i	$0.950440\pi$
$824$	−0.482381	+	0.835509i	−0.0168045	+	0.0291063i
$825$	−21.3813	−	37.0335i	−0.744402	−	1.28934i
$826$	0.114914	−	0.0964243i	0.00399837	−	0.00335503i
$827$	5.74827	−	32.6000i	0.199887	−	1.13361i	−0.705399	−	0.708811i	$-0.749232\pi$
$827$	5.74827	−	32.6000i	0.199887	−	1.13361i	0.905285	−	0.424804i	$-0.139657\pi$
$828$	4.94532	−	8.56555i	0.171862	−	0.297673i
$829$	−44.9646	−	16.3658i	−1.56168	−	0.568407i	−0.590563	−	0.806992i	$-0.701094\pi$
$829$	−44.9646	−	16.3658i	−1.56168	−	0.568407i	−0.971122	+	0.238585i	$0.923316\pi$
$830$	19.9895	+	7.27560i	0.693847	+	0.252540i
$831$	−0.233110	−	1.32203i	−0.00808650	−	0.0458608i
$832$	2.77662	+	2.32986i	0.0962621	+	0.0807735i
$833$	24.7085	+	20.7329i	0.856099	+	0.718352i
$834$	1.05835	+	6.00222i	0.0366478	+	0.207840i
$835$	−11.3501	−	4.13110i	−0.392786	−	0.142963i
$836$	−15.6406	−	5.69270i	−0.540940	−	0.196886i
$837$	−1.69112	+	2.92910i	−0.0584536	+	0.101245i
$838$	−0.537504	+	3.04834i	−0.0185678	+	0.105303i
$839$	−21.2739	+	17.8509i	−0.734457	+	0.616282i	−0.931343	−	0.364144i	$-0.881362\pi$
$839$	−21.2739	+	17.8509i	−0.734457	+	0.616282i	0.196886	+	0.980426i	$0.436917\pi$
$840$	1.71857	+	2.97666i	0.0592964	+	0.102704i
$841$	−4.73156	+	8.19530i	−0.163157	+	0.282596i
$842$	0.493239	+	2.79730i	0.0169981	+	0.0964012i
$843$	−11.5052	−	19.9276i	−0.396260	−	0.686342i
$844$	−22.7549	+	8.28211i	−0.783256	+	0.285082i
$845$	−36.3935			−1.25197
$846$	−0.638020	+	0.232220i	−0.0219356	+	0.00798390i
$847$	−0.00498101	+	0.0282487i	−0.000171150	+	0.000970637i
$848$	−8.23286	−	6.90819i	−0.282717	−	0.237228i
$849$	−1.59124	+	1.33520i	−0.0546110	+	0.0458241i
$850$	33.2546			1.14062
$851$	−31.8732	+	15.2386i	−1.09260	+	0.522374i
$852$	16.8009			0.575588
$853$	3.67425	−	3.08306i	0.125804	−	0.105562i	−0.577715	−	0.816239i	$-0.696055\pi$
$853$	3.67425	−	3.08306i	0.125804	−	0.105562i	0.703519	+	0.710677i	$0.251611\pi$
$854$	0.664314	+	0.557425i	0.0227323	+	0.0190747i
$855$	2.17426	−	12.3308i	0.0743581	−	0.421706i
$856$	12.7595	−	4.64408i	0.436111	−	0.158731i
$857$	22.5057			0.768781			0.384391	−	0.923171i	$-0.374412\pi$
$857$	22.5057			0.768781			0.384391	+	0.923171i	$0.374412\pi$
$858$	−3.55422	+	1.29363i	−0.121339	+	0.0441638i
$859$	23.7776	+	41.1840i	0.811280	+	1.40518i	0.911968	+	0.410261i	$0.134562\pi$
$859$	23.7776	+	41.1840i	0.811280	+	1.40518i	−0.100688	+	0.994918i	$0.532104\pi$
$860$	16.1905	+	91.8208i	0.552091	+	3.13106i
$861$	−0.181430	+	0.314247i	−0.00618313	+	0.0107095i
$862$	6.18963	+	10.7208i	0.210820	+	0.365151i
$863$	21.6890	−	18.1992i	0.738302	−	0.619509i	−0.194079	−	0.980986i	$-0.562172\pi$
$863$	21.6890	−	18.1992i	0.738302	−	0.619509i	0.932381	+	0.361477i	$0.117727\pi$
$864$	0.919163	−	5.21284i	0.0312706	−	0.177344i
$865$	31.1024	−	53.8710i	1.05751	−	1.83167i
$866$	10.7715	+	3.92051i	0.366031	+	0.133224i
$867$	4.93145	+	1.79490i	0.167481	+	0.0609580i
$868$	0.402200	+	2.28099i	0.0136516	+	0.0774219i
$869$	−24.1950	−	20.3020i	−0.820758	−	0.688698i
$870$	−10.9663	−	9.20178i	−0.371791	−	0.311970i
$871$	2.34159	+	13.2798i	0.0793416	+	0.449969i
$872$	−13.0579	−	4.75270i	−0.442198	−	0.160947i
$873$	17.2918	+	6.29370i	0.585239	+	0.213010i
$874$	4.67959	−	8.10529i	0.158290	−	0.274166i
$875$	2.34675	−	13.3091i	0.0793345	−	0.449928i
$876$	−0.707783	+	0.593900i	−0.0239138	+	0.0200660i
$877$	−7.80707	−	13.5222i	−0.263626	−	0.456614i	0.703577	−	0.710619i	$-0.251585\pi$
$877$	−7.80707	−	13.5222i	−0.263626	−	0.456614i	−0.967203	+	0.254006i	$0.918252\pi$
$878$	−8.88952	+	15.3971i	−0.300007	+	0.519627i
$879$	1.93635	+	10.9816i	0.0653114	+	0.370399i
$880$	16.1414	+	27.9577i	0.544126	+	0.942455i
$881$	−13.9883	+	5.09131i	−0.471276	+	0.171531i	−0.566730	−	0.823903i	$-0.691792\pi$
$881$	−13.9883	+	5.09131i	−0.471276	+	0.171531i	0.0954541	+	0.995434i	$0.469570\pi$
$882$	3.72712			0.125499
$883$	−16.0755	+	5.85099i	−0.540982	+	0.196901i	−0.598035	−	0.801470i	$-0.704052\pi$
$883$	−16.0755	+	5.85099i	−0.540982	+	0.196901i	0.0570532	+	0.998371i	$0.481830\pi$
$884$	−2.92794	+	16.6052i	−0.0984772	+	0.558492i
$885$	2.22041	+	1.86314i	0.0746381	+	0.0626288i
$886$	6.20620	−	5.20762i	0.208501	−	0.174953i
$887$	−17.3645			−0.583041			−0.291521	−	0.956565i	$-0.594161\pi$
$887$	−17.3645			−0.583041			−0.291521	+	0.956565i	$0.594161\pi$
$888$	−8.59665	+	8.76408i	−0.288485	+	0.294103i
$889$	5.02640			0.168580
$890$	−5.34388	+	4.48405i	−0.179127	+	0.150306i
$891$	−2.53243	−	2.12496i	−0.0848396	−	0.0711889i
$892$	1.33182	−	7.55312i	0.0445926	−	0.252897i
$893$	3.46093	−	1.25968i	0.115816	−	0.0421535i
$894$	−7.45673			−0.249390
$895$	47.7832	−	17.3917i	1.59722	−	0.581339i
$896$	−2.31782	−	4.01458i	−0.0774329	−	0.134118i
$897$	2.11712	+	12.0068i	0.0706887	+	0.400895i
$898$	5.59596	−	9.69249i	0.186740	−	0.323443i
$899$	−10.4881	−	18.1659i	−0.349797	−	0.605867i
$900$	−16.8746	+	14.1594i	−0.562485	+	0.471981i
$901$	3.81751	−	21.6502i	0.127180	−	0.721271i
$902$	0.812923	−	1.40802i	0.0270674	−	0.0468821i
$903$	−4.88531	−	1.77811i	−0.162573	−	0.0591717i
$904$	−32.2514	−	11.7386i	−1.07267	−	0.390419i
$905$	−7.47042	−	42.3669i	−0.248325	−	1.40832i
$906$	7.64648	+	6.41616i	0.254037	+	0.213163i
$907$	25.5079	+	21.4037i	0.846975	+	0.710697i	0.959121	−	0.282995i	$-0.0913280\pi$
$907$	25.5079	+	21.4037i	0.846975	+	0.710697i	−0.112146	+	0.993692i	$0.535772\pi$
$908$	−4.55287	−	25.8206i	−0.151092	−	0.856887i
$909$	17.0633	+	6.21054i	0.565954	+	0.205990i
$910$	−1.83099	−	0.666427i	−0.0606969	−	0.0220919i
$911$	−0.242855	+	0.420637i	−0.00804614	+	0.0139363i	−0.870020	−	0.493016i	$-0.835895\pi$
$911$	−0.242855	+	0.420637i	−0.00804614	+	0.0139363i	0.861974	+	0.506952i	$0.169228\pi$
$912$	−1.18382	+	6.71380i	−0.0392003	+	0.222316i
$913$	−23.3385	+	19.5833i	−0.772391	+	0.648113i
$914$	−2.78473	−	4.82330i	−0.0921108	−	0.159541i
$915$	−8.37816	+	14.5114i	−0.276973	+	0.479732i
$916$	3.41845	+	19.3870i	0.112949	+	0.640564i
$917$	1.10164	+	1.90809i	0.0363793	+	0.0630108i
$918$	2.41578	−	0.879271i	0.0797325	−	0.0290203i
$919$	16.3837			0.540448			0.270224	−	0.962798i	$-0.412902\pi$
$919$	16.3837			0.540448			0.270224	+	0.962798i	$0.412902\pi$
$920$	−46.6488	+	16.9788i	−1.53797	+	0.559774i
$921$	1.70769	−	9.68482i	0.0562704	−	0.319126i
$922$	6.53507	+	5.48357i	0.215221	+	0.180592i
$923$	−15.8649	+	13.3122i	−0.522199	+	0.438177i
$924$	−2.26387			−0.0744759
$925$	78.3139	−	7.61327i	2.57495	−	0.250323i
$926$	14.2144			0.467113
$927$	0.366186	−	0.307267i	0.0120271	−	0.0100920i
$928$	25.1477	+	21.1014i	0.825515	+	0.692689i
$929$	0.682652	−	3.87151i	0.0223971	−	0.127020i	−0.971559	−	0.236797i	$-0.923902\pi$
$929$	0.682652	−	3.87151i	0.0223971	−	0.127020i	0.993956	+	0.109777i	$0.0350135\pi$
$930$	7.33621	−	2.67016i	0.240564	−	0.0875581i
$931$	−20.2177			−0.662610
$932$	1.63677	−	0.595734i	0.0536141	−	0.0195139i
$933$	−10.3331	−	17.8974i	−0.338290	−	0.585935i
$934$	2.07712	+	11.7799i	0.0679655	+	0.385452i
$935$	−33.0183	+	57.1893i	−1.07981	+	1.87029i
$936$	2.11832	+	3.66904i	0.0692394	+	0.119926i
$937$	−12.9989	+	10.9074i	−0.424657	+	0.356329i	−0.829931	−	0.557866i	$-0.811620\pi$
$937$	−12.9989	+	10.9074i	−0.424657	+	0.356329i	0.405275	+	0.914195i	$0.367176\pi$
$938$	0.244488	−	1.38656i	0.00798281	−	0.0452728i
$939$	12.5649	−	21.7630i	0.410039	−	0.710209i
$940$	−8.44232	−	3.07275i	−0.275358	−	0.100222i
$941$	−1.29812	−	0.472476i	−0.0423174	−	0.0154023i	0.320775	−	0.947156i	$-0.396057\pi$
$941$	−1.29812	−	0.472476i	−0.0423174	−	0.0154023i	−0.363092	+	0.931753i	$0.618279\pi$
$942$	−0.411276	−	2.33246i	−0.0134001	−	0.0759958i
$943$	−4.01468	−	3.36871i	−0.130736	−	0.109700i
$944$	−1.20895	−	1.01443i	−0.0393480	−	0.0330169i
$945$	−0.295731	−	1.67717i	−0.00962011	−	0.0545584i
$946$	21.8893	+	7.96705i	0.711683	+	0.259031i
$947$	−18.2175	−	6.63061i	−0.591988	−	0.215466i	0.0286157	−	0.999590i	$-0.490890\pi$
$947$	−18.2175	−	6.63061i	−0.591988	−	0.215466i	−0.620603	+	0.784125i	$0.713112\pi$
$948$	−8.13496	+	14.0902i	−0.264211	+	0.457627i
$949$	0.197773	−	1.12163i	0.00641999	−	0.0364096i
$950$	−15.9678	+	13.3986i	−0.518065	+	0.434708i
$951$	1.42696	+	2.47157i	0.0462723	+	0.0801460i
$952$	1.91407	−	3.31526i	0.0620353	−	0.107448i
$953$	−7.43342	−	42.1570i	−0.240792	−	1.36560i	−0.830065	−	0.557666i	$-0.811697\pi$
$953$	−7.43342	−	42.1570i	−0.240792	−	1.36560i	0.589273	−	0.807934i	$-0.299414\pi$
$954$	−1.27017	−	2.19999i	−0.0411232	−	0.0712275i
$955$	7.23008	−	2.63154i	0.233960	−	0.0851545i
$956$	35.7124			1.15502
$957$	19.2660	−	7.01225i	0.622782	−	0.226674i
$958$	0.258456	−	1.46577i	0.00835032	−	0.0473570i
$959$	−0.207348	−	0.173986i	−0.00669561	−	0.00561829i
$960$	5.60175	−	4.70042i	0.180796	−	0.151706i
$961$	−19.5605			−0.630983
$962$	0.539670	−	6.93851i	0.0173997	−	0.223707i
$963$	−6.72784			−0.216802
$964$	2.86260	−	2.40201i	0.0921982	−	0.0773634i
$965$	−30.8902	−	25.9199i	−0.994389	−	0.834392i
$966$	0.221051	−	1.25365i	0.00711221	−	0.0403354i
$967$	34.5838	−	12.5875i	1.11214	−	0.404786i	0.280362	−	0.959894i	$-0.409545\pi$
$967$	34.5838	−	12.5875i	1.11214	−	0.404786i	0.831778	+	0.555108i	$0.187323\pi$
$968$	−0.143963			−0.00462713
$969$	−13.1044	+	4.76960i	−0.420973	+	0.153222i
$970$	−21.2377	−	36.7847i	−0.681900	−	1.18109i
$971$	−7.11172	−	40.3325i	−0.228226	−	1.29433i	−0.856421	−	0.516278i	$-0.827317\pi$
$971$	−7.11172	−	40.3325i	−0.228226	−	1.29433i	0.628195	−	0.778056i	$-0.283794\pi$
$972$	−0.851467	+	1.47478i	−0.0273108	+	0.0473037i
$973$	−2.24840	−	3.89435i	−0.0720805	−	0.124847i
$974$	−0.804113	+	0.674731i	−0.0257655	+	0.0216198i
$975$	4.71520	−	26.7412i	0.151007	−	0.856404i
$976$	4.56168	−	7.90106i	0.146016	−	0.252907i
$977$	25.2608	+	9.19418i	0.808165	+	0.294148i	0.712865	−	0.701301i	$-0.247397\pi$
$977$	25.2608	+	9.19418i	0.808165	+	0.294148i	0.0952992	+	0.995449i	$0.469619\pi$
$978$	8.03811	+	2.92563i	0.257030	+	0.0935514i
$979$	−1.73490	−	9.83911i	−0.0554476	−	0.314459i
$980$	37.7794	+	31.7007i	1.20682	+	1.01264i
$981$	5.27437	+	4.42572i	0.168398	+	0.141302i
$982$	3.13969	+	17.8060i	0.100191	+	0.568214i
$983$	43.8566	+	15.9625i	1.39881	+	0.509124i	0.927824	−	0.373017i	$-0.121677\pi$
$983$	43.8566	+	15.9625i	1.39881	+	0.509124i	0.470984	+	0.882142i	$0.343899\pi$
$984$	−1.71131	−	0.622865i	−0.0545545	−	0.0198562i
$985$	−1.40619	+	2.43560i	−0.0448050	+	0.0776046i
$986$	−2.76862	+	15.7016i	−0.0881709	+	0.500042i
$987$	0.383748	−	0.322003i	0.0122148	−	0.0102495i
$988$	−5.28448	−	9.15298i	−0.168122	−	0.291195i
$989$	37.5433	−	65.0270i	1.19381	−	2.06774i
$990$	1.32506	+	7.51480i	0.0421132	+	0.238836i
$991$	0.0355519	+	0.0615778i	0.00112934	+	0.00195608i	0.866590	−	0.499022i	$-0.166307\pi$
$991$	0.0355519	+	0.0615778i	0.00112934	+	0.00195608i	−0.865460	+	0.500978i	$0.832974\pi$
$992$	−16.8233	+	6.12320i	−0.534142	+	0.194412i
$993$	18.5271			0.587938
$994$	2.03196	−	0.739574i	0.0644500	−	0.0234579i
$995$	13.5307	−	76.7363i	0.428951	−	2.43270i
$996$	12.0223	+	10.0879i	0.380941	+	0.319647i
$997$	0.588851	−	0.494105i	0.0186491	−	0.0156485i	−0.633415	−	0.773812i	$-0.718348\pi$
$997$	0.588851	−	0.494105i	0.0186491	−	0.0156485i	0.652065	+	0.758163i	$0.273903\pi$
$998$	−19.9776			−0.632381
$999$	5.48781	−	2.62373i	0.173627	−	0.0830112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.k.a.49.2	yes	18
3.2	odd	2		333.2.x.d.271.2		18
37.16	even	9		4107.2.a.n.1.4		9
37.21	even	18		4107.2.a.m.1.6		9
37.34	even	9	inner	111.2.k.a.34.2	✓	18
111.71	odd	18		333.2.x.d.145.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.k.a.34.2	✓	18	37.34	even	9	inner
111.2.k.a.49.2	yes	18	1.1	even	1	trivial
333.2.x.d.145.2		18	111.71	odd	18
333.2.x.d.271.2		18	3.2	odd	2
4107.2.a.m.1.6		9	37.21	even	18
4107.2.a.n.1.4		9	37.16	even	9

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:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.417523 + 0.350343i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.295711 + 1.67706i) q^{4} +(-3.97962 + 1.44846i) q^{5} +0.545037 q^{6} +(-0.377882 + 0.137538i) q^{7} +(-1.00912 - 1.74784i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.417523 + 0.350343i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.295711 + 1.67706i) q^{4} +(-3.97962 + 1.44846i) q^{5} +0.545037 q^{6} +(-0.377882 + 0.137538i) q^{7} +(-1.00912 - 1.74784i) q^{8} +(0.173648 + 0.984808i) q^{9} +(1.15412 - 1.99900i) q^{10} +(1.65293 + 2.86295i) q^{11} +(1.30452 - 1.09463i) q^{12} +(-0.364518 + 2.06729i) q^{13} +(0.109589 - 0.189813i) q^{14} +(3.97962 + 1.44846i) q^{15} +(-2.16679 - 0.788648i) q^{16} +(-0.819059 - 4.64511i) q^{17} +(-0.417523 - 0.350343i) q^{18} +(2.26485 + 1.90043i) q^{19} +(-1.25234 - 7.10240i) q^{20} +(0.377882 + 0.137538i) q^{21} +(-1.69315 - 0.616257i) q^{22} +(-2.90400 + 5.02988i) q^{23} +(-0.350463 + 1.98758i) q^{24} +(9.90911 - 8.31473i) q^{25} +(-0.572065 - 0.990845i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.118915 - 0.674403i) q^{28} +(3.10093 + 5.37097i) q^{29} +(-2.16904 + 0.789467i) q^{30} -3.38224 q^{31} +(4.97403 - 1.81040i) q^{32} +(0.574055 - 3.25563i) q^{33} +(1.96936 + 1.65249i) q^{34} +(1.30461 - 1.09470i) q^{35} -1.70293 q^{36} +(5.01612 + 3.44072i) q^{37} -1.61143 q^{38} +(1.60806 - 1.34932i) q^{39} +(6.54760 + 5.49409i) q^{40} +(-0.156690 + 0.888630i) q^{41} +(-0.205960 + 0.0749632i) q^{42} -12.9281 q^{43} +(-5.29014 + 1.92545i) q^{44} +(-2.11751 - 3.66764i) q^{45} +(-0.549697 - 3.11749i) q^{46} +(0.622863 - 1.07883i) q^{47} +(1.15293 + 1.99693i) q^{48} +(-5.23843 + 4.39557i) q^{49} +(-1.22427 + 6.94318i) q^{50} +(-2.35839 + 4.08484i) q^{51} +(-3.35918 - 1.22264i) q^{52} +(4.37976 + 1.59410i) q^{53} +(0.0946447 + 0.536757i) q^{54} +(-10.7249 - 8.99926i) q^{55} +(0.621722 + 0.521687i) q^{56} +(-0.513399 - 2.91163i) q^{57} +(-3.17639 - 1.15611i) q^{58} +(0.643144 + 0.234085i) q^{59} +(-3.60598 + 6.24575i) q^{60} +(-0.687058 + 3.89650i) q^{61} +(1.41216 - 1.18494i) q^{62} +(-0.201067 - 0.348258i) q^{63} +(0.863344 - 1.49536i) q^{64} +(-1.54374 - 8.75500i) q^{65} +(0.900907 + 1.56042i) q^{66} +(6.03638 - 2.19706i) q^{67} +8.03235 q^{68} +(5.45774 - 1.98645i) q^{69} +(-0.161184 + 0.914121i) q^{70} +(7.55767 + 6.34164i) q^{71} +(1.54606 - 1.29730i) q^{72} -0.542560 q^{73} +(-3.29978 + 0.320787i) q^{74} -12.9354 q^{75} +(-3.85689 + 3.23631i) q^{76} +(-1.01838 - 0.854518i) q^{77} +(-0.198676 + 1.12675i) q^{78} +(-8.97787 + 3.26768i) q^{79} +9.76534 q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.245904 - 0.425919i) q^{82} +(1.60031 + 9.07583i) q^{83} +(-0.342403 + 0.593060i) q^{84} +(9.98782 + 17.2994i) q^{85} +(5.39780 - 4.52929i) q^{86} +(1.07694 - 6.10764i) q^{87} +(3.33600 - 5.77812i) q^{88} +(-2.83992 - 1.03365i) q^{89} +(2.16904 + 0.789467i) q^{90} +(-0.146585 - 0.831324i) q^{91} +(-7.57667 - 6.35758i) q^{92} +(2.59094 + 2.17406i) q^{93} +(0.117901 + 0.668652i) q^{94} +(-11.7659 - 4.28245i) q^{95} +(-4.97403 - 1.81040i) q^{96} +(9.20078 - 15.9362i) q^{97} +(0.647208 - 3.67050i) q^{98} +(-2.53243 + 2.12496i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{12} + 18 q^{13} - 9 q^{14} + 6 q^{15} - 9 q^{16} - 21 q^{17} - 3 q^{18} + 12 q^{19} - 6 q^{21} - 51 q^{22} + 6 q^{24} + 6 q^{25} + 15 q^{26} + 9 q^{27} - 39 q^{28} - 3 q^{29} + 15 q^{30} - 24 q^{31} + 21 q^{32} - 18 q^{34} - 12 q^{35} + 18 q^{36} + 27 q^{37} + 24 q^{38} + 18 q^{39} + 39 q^{40} + 9 q^{41} + 6 q^{42} - 72 q^{43} - 21 q^{44} + 21 q^{46} + 21 q^{47} - 3 q^{48} - 18 q^{49} + 24 q^{50} - 3 q^{51} - 30 q^{52} - 18 q^{53} + 3 q^{54} + 9 q^{55} + 54 q^{56} - 3 q^{57} - 66 q^{59} - 36 q^{60} + 33 q^{61} + 69 q^{62} + 18 q^{64} - 63 q^{65} + 42 q^{67} + 48 q^{68} - 12 q^{69} + 63 q^{70} + 15 q^{71} - 6 q^{72} - 24 q^{73} - 51 q^{74} - 6 q^{75} + 12 q^{76} + 39 q^{77} - 27 q^{78} - 6 q^{79} - 12 q^{80} + 15 q^{82} + 33 q^{83} - 6 q^{84} + 30 q^{85} - 60 q^{86} - 9 q^{87} - 3 q^{88} + 45 q^{89} - 15 q^{90} + 21 q^{91} - 24 q^{92} - 6 q^{93} + 18 q^{94} - 24 q^{95} - 21 q^{96} - 24 q^{97} - 36 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^12 + 18 * q^13 - 9 * q^14 + 6 * q^15 - 9 * q^16 - 21 * q^17 - 3 * q^18 + 12 * q^19 - 6 * q^21 - 51 * q^22 + 6 * q^24 + 6 * q^25 + 15 * q^26 + 9 * q^27 - 39 * q^28 - 3 * q^29 + 15 * q^30 - 24 * q^31 + 21 * q^32 - 18 * q^34 - 12 * q^35 + 18 * q^36 + 27 * q^37 + 24 * q^38 + 18 * q^39 + 39 * q^40 + 9 * q^41 + 6 * q^42 - 72 * q^43 - 21 * q^44 + 21 * q^46 + 21 * q^47 - 3 * q^48 - 18 * q^49 + 24 * q^50 - 3 * q^51 - 30 * q^52 - 18 * q^53 + 3 * q^54 + 9 * q^55 + 54 * q^56 - 3 * q^57 - 66 * q^59 - 36 * q^60 + 33 * q^61 + 69 * q^62 + 18 * q^64 - 63 * q^65 + 42 * q^67 + 48 * q^68 - 12 * q^69 + 63 * q^70 + 15 * q^71 - 6 * q^72 - 24 * q^73 - 51 * q^74 - 6 * q^75 + 12 * q^76 + 39 * q^77 - 27 * q^78 - 6 * q^79 - 12 * q^80 + 15 * q^82 + 33 * q^83 - 6 * q^84 + 30 * q^85 - 60 * q^86 - 9 * q^87 - 3 * q^88 + 45 * q^89 - 15 * q^90 + 21 * q^91 - 24 * q^92 - 6 * q^93 + 18 * q^94 - 24 * q^95 - 21 * q^96 - 24 * q^97 - 36 * q^98 - 9 * q^99

Introduction

L-functions

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