LMFDB - Embedded newform 966.2.be.a.493.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.8
Character	$\chi$	$=$	966.493
Dual form			966.2.be.a.145.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(4.16693 - 0.397894i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(0.0805154 + 2.64453i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(4.16693 - 0.397894i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(0.0805154 + 2.64453i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(0.986860 - 4.06789i) q^{10} +(-0.191641 + 0.0663276i) q^{11} +(-0.189251 + 0.981929i) q^{12} +(-1.51988 - 5.17624i) q^{13} +(2.52541 + 0.788853i) q^{14} +(-2.26306 - 3.52139i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-4.53091 - 1.81390i) q^{17} +(0.580057 + 0.814576i) q^{18} +(3.26152 - 1.30572i) q^{19} +(-3.52139 - 2.26306i) q^{20} +(2.31365 - 1.28336i) q^{21} +0.202795i q^{22} +(4.79547 + 0.0590619i) q^{23} +(0.866025 + 0.500000i) q^{24} +(12.2954 - 2.36973i) q^{25} +(-5.38866 - 0.256693i) q^{26} +(0.989821 + 0.142315i) q^{27} +(1.57145 - 2.12851i) q^{28} +(-0.707026 - 4.91747i) q^{29} +(-4.06789 + 0.986860i) q^{30} +(7.82864 - 0.372924i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.146769 + 0.139944i) q^{33} +(-3.19606 + 3.68845i) q^{34} +(1.38774 + 10.9875i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.879160 + 0.626047i) q^{37} +(-0.167164 - 3.50920i) q^{38} +(-3.90438 + 3.72281i) q^{39} +(-3.29033 + 2.58754i) q^{40} +(-2.62715 - 1.19978i) q^{41} +(-0.456051 - 2.60615i) q^{42} +(3.34614 - 5.20670i) q^{43} +(0.191641 + 0.0663276i) q^{44} +(-2.09294 + 3.62508i) q^{45} +(1.62426 - 4.51240i) q^{46} +(6.61082 - 3.81676i) q^{47} +(0.755750 - 0.654861i) q^{48} +(-6.98703 + 0.425850i) q^{49} +(1.78201 - 12.3942i) q^{50} +(0.463923 + 4.85842i) q^{51} +(-2.00503 + 5.00833i) q^{52} +(5.18032 + 5.43296i) q^{53} +(0.458227 - 0.888835i) q^{54} +(-0.772164 + 0.352635i) q^{55} +(-1.49747 - 2.18119i) q^{56} +(-2.65508 - 2.30064i) q^{57} +(-4.87826 - 0.940208i) q^{58} +(-9.75712 - 2.36705i) q^{59} +(-0.397894 + 4.16693i) q^{60} +(-5.15481 - 2.65749i) q^{61} +(2.20808 - 7.52004i) q^{62} +(-2.20087 - 1.46839i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-8.39283 - 20.9643i) q^{65} +(0.180251 - 0.0929259i) q^{66} +(2.09561 + 10.8731i) q^{67} +(2.44026 + 4.22665i) q^{68} +(-2.14491 - 4.28945i) q^{69} +(10.8371 + 2.28225i) q^{70} +(-0.0174983 - 0.0201942i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-6.57133 + 8.35613i) q^{73} +(0.879160 - 0.626047i) q^{74} +(-7.74036 - 9.84267i) q^{75} +(-3.37087 - 0.989776i) q^{76} +(-0.190835 - 0.501459i) q^{77} +(2.24107 + 4.90725i) q^{78} +(-11.2200 + 11.7672i) q^{79} +(1.36907 + 3.95566i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-1.99305 + 2.09025i) q^{82} +(2.10593 + 4.61134i) q^{83} +(-2.61197 - 0.421419i) q^{84} +(-19.6018 - 5.75559i) q^{85} +(-3.82592 - 4.86505i) q^{86} +(-4.04685 + 2.88175i) q^{87} +(0.125359 - 0.159407i) q^{88} +(-0.851693 + 17.8792i) q^{89} +(2.74117 + 3.16348i) q^{90} +(13.5663 - 4.43613i) q^{91} +(-3.73298 - 3.01079i) q^{92} +(-3.91876 - 6.78749i) q^{93} +(-1.44465 - 7.49557i) q^{94} +(13.0710 - 6.73857i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(0.146079 - 0.319868i) q^{97} +(-1.88281 + 6.74204i) q^{98} +(0.0571338 - 0.194580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	4.16693	−	0.397894i	1.86351	−	0.177943i	0.898292	−	0.439398i	$-0.144808\pi$
$5$	4.16693	−	0.397894i	1.86351	−	0.177943i	0.965216	+	0.261455i	$0.0842022\pi$
$6$	−0.989821	+	0.142315i	−0.404093	+	0.0580998i
$7$	0.0805154	+	2.64453i	0.0304320	+	0.999537i
$7$	0.0805154	+	2.64453i	0.0304320	+	0.999537i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	0.986860	−	4.06789i	0.312072	−	1.28638i
$11$	−0.191641	+	0.0663276i	−0.0577820	+	0.0199985i	−0.355806	−	0.934560i	$-0.615794\pi$
$11$	−0.191641	+	0.0663276i	−0.0577820	+	0.0199985i	0.298024	+	0.954558i	$0.403672\pi$
$12$	−0.189251	+	0.981929i	−0.0546321	+	0.283458i
$13$	−1.51988	−	5.17624i	−0.421539	−	1.43563i	−0.847455	−	0.530868i	$-0.821866\pi$
$13$	−1.51988	−	5.17624i	−0.421539	−	1.43563i	0.425915	−	0.904763i	$-0.359952\pi$
$14$	2.52541	+	0.788853i	0.674945	+	0.210830i
$15$	−2.26306	−	3.52139i	−0.584320	−	0.909219i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−4.53091	−	1.81390i	−1.09891	−	0.439936i	−0.249876	−	0.968278i	$-0.580390\pi$
$17$	−4.53091	−	1.81390i	−1.09891	−	0.439936i	−0.849032	+	0.528341i	$0.822814\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	3.26152	−	1.30572i	0.748244	−	0.299552i	0.0339747	−	0.999423i	$-0.489183\pi$
$19$	3.26152	−	1.30572i	0.748244	−	0.299552i	0.714269	+	0.699871i	$0.246759\pi$
$20$	−3.52139	−	2.26306i	−0.787407	−	0.506036i
$21$	2.31365	−	1.28336i	0.504881	−	0.280051i
$22$			0.202795i			0.0432360i
$23$	4.79547	+	0.0590619i	0.999924	+	0.0123153i
$23$	4.79547	+	0.0590619i	0.999924	+	0.0123153i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	12.2954	−	2.36973i	2.45907	−	0.473947i
$26$	−5.38866	−	0.256693i	−1.05680	−	0.0503417i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	1.57145	−	2.12851i	0.296976	−	0.402250i
$29$	−0.707026	−	4.91747i	−0.131291	−	0.913152i	−0.943874	−	0.330306i	$-0.892848\pi$
$29$	−0.707026	−	4.91747i	−0.131291	−	0.913152i	0.812583	−	0.582846i	$-0.198061\pi$
$30$	−4.06789	+	0.986860i	−0.742692	+	0.180175i
$31$	7.82864	−	0.372924i	1.40606	−	0.0669791i	0.669232	−	0.743054i	$-0.266623\pi$
$31$	7.82864	−	0.372924i	1.40606	−	0.0669791i	0.736833	+	0.676075i	$0.236320\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	0.146769	+	0.139944i	0.0255493	+	0.0243612i
$34$	−3.19606	+	3.68845i	−0.548119	+	0.632564i
$35$	1.38774	+	10.9875i	0.234571	+	1.85723i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	0.879160	+	0.626047i	0.144533	+	0.102922i	0.650036	−	0.759903i	$-0.274754\pi$
$37$	0.879160	+	0.626047i	0.144533	+	0.102922i	−0.505503	+	0.862825i	$0.668693\pi$
$38$	−0.167164	−	3.50920i	−0.0271175	−	0.569267i
$39$	−3.90438	+	3.72281i	−0.625200	+	0.596127i
$40$	−3.29033	+	2.58754i	−0.520247	+	0.409126i
$41$	−2.62715	−	1.19978i	−0.410292	−	0.187374i	0.199566	−	0.979884i	$-0.436047\pi$
$41$	−2.62715	−	1.19978i	−0.410292	−	0.187374i	−0.609859	+	0.792510i	$0.708774\pi$
$42$	−0.456051	−	2.60615i	−0.0703702	−	0.402138i
$43$	3.34614	−	5.20670i	0.510282	−	0.794014i	−0.486541	−	0.873658i	$-0.661742\pi$
$43$	3.34614	−	5.20670i	0.510282	−	0.794014i	0.996823	+	0.0796431i	$0.0253781\pi$
$44$	0.191641	+	0.0663276i	0.0288910	+	0.00999926i
$45$	−2.09294	+	3.62508i	−0.311997	+	0.540395i
$46$	1.62426	−	4.51240i	0.239484	−	0.665318i
$47$	6.61082	−	3.81676i	0.964287	−	0.556731i	0.0667970	−	0.997767i	$-0.478722\pi$
$47$	6.61082	−	3.81676i	0.964287	−	0.556731i	0.897490	+	0.441035i	$0.145389\pi$
$48$	0.755750	−	0.654861i	0.109083	−	0.0945210i
$49$	−6.98703	+	0.425850i	−0.998148	+	0.0608357i
$50$	1.78201	−	12.3942i	0.252015	−	1.75280i
$51$	0.463923	+	4.85842i	0.0649621	+	0.680314i
$52$	−2.00503	+	5.00833i	−0.278048	+	0.694530i
$53$	5.18032	+	5.43296i	0.711571	+	0.746274i	0.975914	−	0.218154i	$-0.0700036\pi$
$53$	5.18032	+	5.43296i	0.711571	+	0.746274i	−0.264343	+	0.964429i	$0.585155\pi$
$54$	0.458227	−	0.888835i	0.0623567	−	0.120955i
$55$	−0.772164	+	0.352635i	−0.104119	+	0.0475493i
$56$	−1.49747	−	2.18119i	−0.200108	−	0.291473i
$57$	−2.65508	−	2.30064i	−0.351674	−	0.304727i
$58$	−4.87826	−	0.940208i	−0.640547	−	0.123455i
$59$	−9.75712	−	2.36705i	−1.27027	−	0.308164i	−0.456694	−	0.889624i	$-0.650967\pi$
$59$	−9.75712	−	2.36705i	−1.27027	−	0.308164i	−0.813575	+	0.581460i	$0.802482\pi$
$60$	−0.397894	+	4.16693i	−0.0513679	+	0.537949i
$61$	−5.15481	−	2.65749i	−0.660005	−	0.340256i	0.0954712	−	0.995432i	$-0.469564\pi$
$61$	−5.15481	−	2.65749i	−0.660005	−	0.340256i	−0.755476	+	0.655176i	$0.772595\pi$
$62$	2.20808	−	7.52004i	0.280427	−	0.955046i
$63$	−2.20087	−	1.46839i	−0.277284	−	0.185000i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−8.39283	−	20.9643i	−1.04100	−	2.60030i
$66$	0.180251	−	0.0929259i	0.0221874	−	0.0114384i
$67$	2.09561	+	10.8731i	0.256019	+	1.32835i	0.851233	+	0.524788i	$0.175855\pi$
$67$	2.09561	+	10.8731i	0.256019	+	1.32835i	−0.595214	+	0.803567i	$0.702933\pi$
$68$	2.44026	+	4.22665i	0.295925	+	0.512557i
$69$	−2.14491	−	4.28945i	−0.258217	−	0.516389i
$70$	10.8371	+	2.28225i	1.29528	+	0.272781i
$71$	−0.0174983	−	0.0201942i	−0.00207667	−	0.00239660i	0.754710	−	0.656058i	$-0.227777\pi$
$71$	−0.0174983	−	0.0201942i	−0.00207667	−	0.00239660i	−0.756787	+	0.653662i	$0.773232\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	−6.57133	+	8.35613i	−0.769116	+	0.978011i	0.230871	+	0.972984i	$0.425842\pi$
$73$	−6.57133	+	8.35613i	−0.769116	+	0.978011i	−0.999987	+	0.00502642i	$0.998400\pi$
$74$	0.879160	−	0.626047i	0.102200	−	0.0727765i
$75$	−7.74036	−	9.84267i	−0.893780	−	1.13653i
$76$	−3.37087	−	0.989776i	−0.386665	−	0.113535i
$77$	−0.190835	−	0.501459i	−0.0217477	−	0.0571466i
$78$	2.24107	+	4.90725i	0.253751	+	0.555637i
$79$	−11.2200	+	11.7672i	−1.26235	+	1.32392i	−0.338596	+	0.940932i	$0.609952\pi$
$79$	−11.2200	+	11.7672i	−1.26235	+	1.32392i	−0.923755	+	0.382984i	$0.874897\pi$
$80$	1.36907	+	3.95566i	0.153067	+	0.442257i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−1.99305	+	2.09025i	−0.220096	+	0.230830i
$83$	2.10593	+	4.61134i	0.231156	+	0.506161i	0.989295	−	0.145933i	$-0.0466183\pi$
$83$	2.10593	+	4.61134i	0.231156	+	0.506161i	−0.758139	+	0.652093i	$0.773891\pi$
$84$	−2.61197	−	0.421419i	−0.284990	−	0.0459806i
$85$	−19.6018	−	5.75559i	−2.12611	−	0.624282i
$86$	−3.82592	−	4.86505i	−0.412560	−	0.524612i
$87$	−4.04685	+	2.88175i	−0.433867	+	0.308956i
$88$	0.125359	−	0.159407i	0.0133633	−	0.0169929i
$89$	−0.851693	+	17.8792i	−0.0902792	+	1.89519i	0.270764	+	0.962646i	$0.412724\pi$
$89$	−0.851693	+	17.8792i	−0.0902792	+	1.89519i	−0.361044	+	0.932549i	$0.617579\pi$
$90$	2.74117	+	3.16348i	0.288945	+	0.333460i
$91$	13.5663	−	4.43613i	1.42214	−	0.465033i
$92$	−3.73298	−	3.01079i	−0.389190	−	0.313896i
$93$	−3.91876	−	6.78749i	−0.406356	−	0.703830i
$94$	−1.44465	−	7.49557i	−0.149004	−	0.773109i
$95$	13.0710	−	6.73857i	1.34106	−	0.691362i
$96$	−0.371662	−	0.928368i	−0.0379326	−	0.0947512i
$97$	0.146079	−	0.319868i	0.0148321	−	0.0324777i	−0.902071	−	0.431588i	$-0.857954\pi$
$97$	0.146079	−	0.319868i	0.0148321	−	0.0324777i	0.916903	+	0.399110i	$0.130681\pi$
$98$	−1.88281	+	6.74204i	−0.190192	+	0.681048i
$99$	0.0571338	−	0.194580i	0.00574217	−	0.0195560i
$100$	−11.1297	−	5.73775i	−1.11297	−	0.573775i
$101$	0.860653	−	9.01316i	0.0856382	−	0.896843i	−0.845934	−	0.533287i	$-0.820956\pi$
$101$	0.860653	−	9.01316i	0.0856382	−	0.896843i	0.931572	−	0.363556i	$-0.118437\pi$
$102$	4.74294	+	1.15063i	0.469621	+	0.113929i
$103$	6.93576	+	1.33676i	0.683401	+	0.131715i	0.519123	−	0.854699i	$-0.326259\pi$
$103$	6.93576	+	1.33676i	0.683401	+	0.131715i	0.164278	+	0.986414i	$0.447471\pi$
$104$	4.07709	+	3.53282i	0.399792	+	0.346422i
$105$	9.13020	−	6.26825i	0.891016	−	0.611718i
$106$	6.82847	−	3.11846i	0.663239	−	0.302891i
$107$	−0.172244	+	0.334107i	−0.0166515	+	0.0322994i	−0.897014	−	0.442001i	$-0.854269\pi$
$107$	−0.172244	+	0.334107i	−0.0166515	+	0.0322994i	0.880363	+	0.474301i	$0.157299\pi$
$108$	−0.690079	−	0.723734i	−0.0664029	−	0.0696413i
$109$	4.73519	−	11.8279i	0.453549	−	1.13291i	−0.508750	−	0.860915i	$-0.669892\pi$
$109$	4.73519	−	11.8279i	0.453549	−	1.13291i	0.962298	−	0.271996i	$-0.0876837\pi$
$110$	0.0806907	+	0.845031i	0.00769356	+	0.0805706i
$111$	0.153598	−	1.06830i	0.0145789	−	0.101399i
$112$	−2.55100	+	0.701716i	−0.241047	+	0.0663060i
$113$	−2.34190	+	2.02927i	−0.220308	+	0.190898i	−0.758021	−	0.652230i	$-0.773834\pi$
$113$	−2.34190	+	2.02927i	−0.220308	+	0.190898i	0.537713	+	0.843128i	$0.319288\pi$
$114$	−3.04250	+	1.75659i	−0.284956	+	0.164520i
$115$	20.0059	−	1.66198i	1.86556	−	0.154980i
$116$	−2.48402	+	4.30245i	−0.230636	+	0.399472i
$117$	5.09806	+	1.76446i	0.471316	+	0.163124i
$118$	−5.42811	+	8.44630i	−0.499698	+	0.777545i
$119$	4.43211	−	12.1282i	0.406291	−	1.11179i
$120$	3.80762	+	1.73888i	0.347586	+	0.158737i
$121$	−8.61426	+	6.77433i	−0.783114	+	0.615848i
$122$	−4.19730	+	4.00212i	−0.380006	+	0.362335i
$123$	0.137424	+	2.88488i	0.0123911	+	0.260121i
$124$	−6.38425	−	4.54620i	−0.573323	−	0.408261i
$125$	30.2093	−	8.87027i	2.70201	−	0.793381i
$126$	−2.10746	+	1.59956i	−0.187748	+	0.142500i
$127$	−12.5039	+	14.4303i	−1.10955	+	1.28048i	−0.153217	+	0.988193i	$0.548963\pi$
$127$	−12.5039	+	14.4303i	−1.10955	+	1.28048i	−0.956329	+	0.292292i	$0.905582\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	−6.16119	−	0.588323i	−0.542463	−	0.0517989i
$130$	−22.5563	+	1.07449i	−1.97832	+	0.0942389i
$131$	−0.251655	+	0.0610509i	−0.0219872	+	0.00533404i	−0.246737	−	0.969082i	$-0.579359\pi$
$131$	−0.251655	+	0.0610509i	−0.0219872	+	0.00533404i	0.224750	+	0.974416i	$0.427843\pi$
$132$	−0.0288607	−	0.200730i	−0.00251200	−	0.0174713i
$133$	3.71560	+	8.52004i	0.322183	+	0.738781i
$134$	10.9605	+	1.57588i	0.946839	+	0.136135i
$135$	4.18114	+	0.199172i	0.359856	+	0.0171420i
$136$	4.79232	−	0.923644i	0.410938	−	0.0792018i
$137$	−6.75486	−	3.89992i	−0.577107	−	0.333193i	0.182876	−	0.983136i	$-0.441459\pi$
$137$	−6.75486	−	3.89992i	−0.577107	−	0.333193i	−0.759983	+	0.649943i	$0.774793\pi$
$138$	−4.75506	+	0.624005i	−0.404778	+	0.0531189i
$139$		−	0.870421i		−	0.0738282i	−0.999318	−	0.0369141i	$-0.988247\pi$
$139$		−	0.870421i		−	0.0738282i	0.999318	−	0.0369141i	$-0.0117528\pi$
$140$	5.70120	−	9.49462i	0.481839	−	0.802442i
$141$	−6.42172	−	4.12699i	−0.540806	−	0.347555i
$142$	−0.0248066	+	0.00993108i	−0.00208173	+	0.000833398i
$143$	0.634599	+	0.891170i	0.0530679	+	0.0745234i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	−4.90276	−	20.2095i	−0.407152	−	1.67830i
$146$	5.74728	+	8.94293i	0.475648	+	0.740123i
$147$	3.58016	+	6.01519i	0.295286	+	0.496124i
$148$	−0.304070	−	1.03557i	−0.0249944	−	0.0851231i
$149$	−1.69250	+	8.78150i	−0.138655	+	0.719409i	0.844345	+	0.535800i	$0.179990\pi$
$149$	−1.69250	+	8.78150i	−0.138655	+	0.719409i	−0.982999	+	0.183609i	$0.941222\pi$
$150$	−11.8330	+	4.09543i	−0.966157	+	0.334390i
$151$	−5.29839	+	21.8402i	−0.431177	+	1.77733i	0.177717	+	0.984082i	$0.443129\pi$
$151$	−5.29839	+	21.8402i	−0.431177	+	1.77733i	−0.608893	+	0.793252i	$0.708386\pi$
$152$	−2.03784	+	2.86175i	−0.165291	+	0.232118i
$153$	4.10575	−	2.63861i	0.331930	−	0.213319i
$154$	−0.536296	+	0.0163281i	−0.0432159	+	0.00131575i
$155$	32.4730	−	4.66891i	2.60829	−	0.375016i
$156$	5.37034	−	0.512805i	0.429971	−	0.0410573i
$157$	13.3253	+	10.4791i	1.06348	+	0.836326i	0.986996	−	0.160745i	$-0.0513897\pi$
$157$	13.3253	+	10.4791i	1.06348	+	0.836326i	0.0764791	+	0.997071i	$0.475632\pi$
$158$	7.45032	+	14.4516i	0.592716	+	1.14971i
$159$	2.45525	−	7.09398i	0.194714	−	0.562589i
$160$	4.18589			0.330923
$161$	0.229918	+	12.6865i	0.0181201	+	0.999836i
$162$	−1.00000			−0.0785674
$163$	−0.794715	+	2.29618i	−0.0622469	+	0.179851i	−0.971836	−	0.235659i	$-0.924275\pi$
$163$	−0.794715	+	2.29618i	−0.0622469	+	0.179851i	0.909589	+	0.415509i	$0.136397\pi$
$164$	1.32343	+	2.56709i	0.103342	+	0.200456i
$165$	0.667261	+	0.524740i	0.0519462	+	0.0408509i
$166$	5.04651	−	0.481883i	0.391685	−	0.0374014i
$167$	0.587025	−	0.0844015i	0.0454254	−	0.00653118i	−0.119565	−	0.992826i	$-0.538150\pi$
$167$	0.587025	−	0.0844015i	0.0454254	−	0.00653118i	0.164990	+	0.986295i	$0.447241\pi$
$168$	−1.25253	+	2.33048i	−0.0966351	+	0.179801i
$169$	−13.5471	+	8.70621i	−1.04209	+	0.669708i
$170$	−11.8501	+	16.6412i	−0.908865	+	1.27632i
$171$	−0.828263	+	3.41414i	−0.0633388	+	0.261086i
$172$	−5.84882	+	2.02429i	−0.445968	+	0.154351i
$173$	1.82777	−	9.48337i	0.138963	−	0.721008i	−0.843876	−	0.536539i	$-0.819731\pi$
$173$	1.82777	−	9.48337i	0.138963	−	0.721008i	0.982838	−	0.184469i	$-0.0590564\pi$
$174$	1.39966	+	4.76680i	0.106108	+	0.361370i
$175$	7.25679	+	32.3246i	0.548562	+	2.44351i
$176$	−0.109639	−	0.170602i	−0.00826435	−	0.0128596i
$177$	2.36705	+	9.75712i	0.177919	+	0.733390i
$178$	16.6173	+	6.65257i	1.24552	+	0.498631i
$179$	−2.95993	−	4.15665i	−0.221236	−	0.310682i	0.689009	−	0.724753i	$-0.258046\pi$
$179$	−2.95993	−	4.15665i	−0.221236	−	0.310682i	−0.910245	+	0.414071i	$0.864107\pi$
$180$	3.88604	−	1.55574i	0.289648	−	0.115958i
$181$	−3.99345	−	2.56644i	−0.296831	−	0.190762i	0.383745	−	0.923439i	$-0.374634\pi$
$181$	−3.99345	−	2.56644i	−0.296831	−	0.190762i	−0.680576	+	0.732677i	$0.738270\pi$
$182$	0.244962	−	14.2711i	0.0181578	−	1.05784i
$183$			5.79950i			0.428712i
$184$	−4.06614	+	2.54294i	−0.299759	+	0.187468i
$185$	3.91250	+	2.25888i	0.287653	+	0.166076i
$186$	−7.69588	+	1.48326i	−0.564289	+	0.108758i
$187$	0.988621	+	0.0470938i	0.0722951	+	0.00344384i
$188$	−7.55582	−	1.08636i	−0.551065	−	0.0792311i
$189$	−0.296659	+	2.62907i	−0.0215788	+	0.191236i
$190$	−2.09285	−	14.5561i	−0.151831	−	1.05601i
$191$	−2.10161	+	0.509845i	−0.152067	+	0.0368911i	−0.311070	−	0.950387i	$-0.600687\pi$
$191$	−2.10161	+	0.509845i	−0.152067	+	0.0368911i	0.159003	+	0.987278i	$0.449172\pi$
$192$	−0.998867	+	0.0475819i	−0.0720870	+	0.00343393i
$193$	−23.6082	−	2.25431i	−1.69935	−	0.162269i	−0.800150	−	0.599800i	$-0.795247\pi$
$193$	−23.6082	−	2.25431i	−1.69935	−	0.162269i	−0.899203	+	0.437532i	$0.855853\pi$
$194$	−0.254498	−	0.242663i	−0.0182719	−	0.0174222i
$195$	−14.7880	+	17.0662i	−1.05899	+	1.22214i
$196$	5.75542	+	3.98436i	0.411102	+	0.284597i
$197$	6.57468	−	1.93050i	0.468427	−	0.137542i	−0.0389967	−	0.999239i	$-0.512416\pi$
$197$	6.57468	−	1.93050i	0.468427	−	0.137542i	0.507423	+	0.861697i	$0.330598\pi$
$198$	−0.165192	−	0.117632i	−0.0117397	−	0.00835977i
$199$	0.258483	+	5.42622i	0.0183233	+	0.384654i	0.989338	+	0.145636i	$0.0465227\pi$
$199$	0.258483	+	5.42622i	0.0183233	+	0.384654i	−0.971015	+	0.239019i	$0.923174\pi$
$200$	−9.06233	+	8.64092i	−0.640804	+	0.611005i
$201$	8.70409	−	6.84497i	0.613939	−	0.482807i
$202$	−8.23596	−	3.76123i	−0.579480	−	0.264640i
$203$	12.9475	−	2.26568i	0.908733	−	0.159020i
$204$	2.63861	−	4.10575i	0.184739	−	0.287460i
$205$	−11.4246	−	3.95408i	−0.797925	−	0.276165i
$206$	3.53170	−	6.11709i	0.246065	−	0.426198i
$207$	−2.82975	+	3.87201i	−0.196682	+	0.269124i
$208$	4.67200	−	2.69738i	0.323945	−	0.187030i
$209$	−0.538436	+	0.466558i	−0.0372444	+	0.0322725i
$210$	−2.93730	−	10.6782i	−0.202693	−	0.736865i
$211$	−3.64017	+	25.3179i	−0.250600	+	1.74296i	0.344030	+	0.938959i	$0.388208\pi$
$211$	−3.64017	+	25.3179i	−0.250600	+	1.74296i	−0.594630	+	0.804000i	$0.702701\pi$
$212$	−0.713571	−	7.47285i	−0.0490083	−	0.513238i
$213$	−0.00993108	+	0.0248066i	−0.000680466	+	0.00169972i
$214$	0.259396	+	0.272047i	0.0177319	+	0.0185967i
$215$	11.8714	−	23.0274i	0.809625	−	1.57045i
$216$	−0.909632	+	0.415415i	−0.0618926	+	0.0282654i
$217$	1.61653	+	20.6730i	0.109737	+	1.40338i
$218$	−9.62868	−	8.34329i	−0.652136	−	0.565079i
$219$	10.4384	+	2.01183i	0.705360	+	0.135947i
$220$	0.824946	+	0.200130i	0.0556179	+	0.0134928i
$221$	−2.50275	+	26.2100i	−0.168353	+	1.76308i
$222$	−0.959307	−	0.494557i	−0.0643845	−	0.0331925i
$223$	2.03414	−	6.92766i	0.136216	−	0.463910i	−0.862925	−	0.505331i	$-0.831370\pi$
$223$	2.03414	−	6.92766i	0.136216	−	0.463910i	0.999142	+	0.0414210i	$0.0131885\pi$
$224$	−0.171227	+	2.64020i	−0.0114406	+	0.176406i
$225$	−5.20168	+	11.3901i	−0.346778	+	0.759339i
$226$	1.15170	+	2.87681i	0.0766100	+	0.191363i
$227$	−3.45895	+	1.78321i	−0.229579	+	0.118356i	−0.569178	−	0.822214i	$-0.692739\pi$
$227$	−3.45895	+	1.78321i	−0.229579	+	0.118356i	0.339600	+	0.940570i	$0.389708\pi$
$228$	0.664873	+	3.44969i	0.0440323	+	0.228461i
$229$	3.21963	+	5.57657i	0.212759	+	0.368510i	0.952577	−	0.304297i	$-0.0984216\pi$
$229$	3.21963	+	5.57657i	0.212759	+	0.368510i	−0.739818	+	0.672807i	$0.765088\pi$
$230$	4.97271	−	19.4492i	0.327891	−	1.28244i
$231$	−0.358269	+	0.399403i	−0.0235724	+	0.0262788i
$232$	3.25337	+	3.75459i	0.213595	+	0.246501i
$233$	0.111453	−	2.33969i	0.00730154	−	0.153278i	−0.992272	−	0.124081i	$-0.960402\pi$
$233$	0.111453	−	2.33969i	0.00730154	−	0.153278i	0.999574	−	0.0291974i	$-0.00929515\pi$
$234$	3.33482	−	4.24057i	0.218004	−	0.277215i
$235$	26.0282	−	18.5346i	1.69789	−	1.20906i
$236$	6.20640	+	7.89208i	0.404002	+	0.513731i
$237$	15.6004	+	4.58070i	1.01336	+	0.297548i
$238$	−10.0115	−	8.15508i	−0.648951	−	0.528615i
$239$	−11.7705	−	25.7739i	−0.761373	−	1.66717i	−0.744778	−	0.667313i	$-0.767444\pi$
$239$	−11.7705	−	25.7739i	−0.761373	−	1.66717i	−0.0165957	−	0.999862i	$-0.505283\pi$
$240$	2.88859	−	3.02947i	0.186458	−	0.195551i
$241$	7.71604	+	22.2940i	0.497034	+	1.43609i	0.862879	+	0.505410i	$0.168659\pi$
$241$	7.71604	+	22.2940i	0.497034	+	1.43609i	−0.365845	+	0.930676i	$0.619220\pi$
$242$	3.58430	+	10.3561i	0.230407	+	0.665718i
$243$	−0.690079	+	0.723734i	−0.0442686	+	0.0464276i
$244$	2.40920	+	5.27542i	0.154233	+	0.337724i
$245$	−28.9450	+	4.55459i	−1.84923	+	0.290982i
$246$	2.77116	+	0.813686i	0.176683	+	0.0518787i
$247$	−11.7158	−	14.8979i	−0.745460	−	0.947929i
$248$	−6.38425	+	4.54620i	−0.405400	+	0.288684i
$249$	3.13373	−	3.98487i	0.198592	−	0.252531i
$250$	1.49810	−	31.4490i	0.0947483	−	1.98901i
$251$	−7.23097	−	8.34498i	−0.456415	−	0.526730i	0.480168	−	0.877176i	$-0.340576\pi$
$251$	−7.23097	−	8.34498i	−0.456415	−	0.526730i	−0.936583	+	0.350446i	$0.886030\pi$
$252$	0.822303	+	2.51472i	0.0518002	+	0.158412i
$253$	−0.922926	+	0.306753i	−0.0580239	+	0.0192854i
$254$	9.54703	+	16.5359i	0.599034	+	1.03756i
$255$	3.86627	+	20.0601i	0.242115	+	1.25621i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−2.31112	−	5.77289i	−0.144164	−	0.360103i	0.838659	−	0.544657i	$-0.183340\pi$
$257$	−2.31112	−	5.77289i	−0.144164	−	0.360103i	−0.982822	+	0.184554i	$0.940916\pi$
$258$	−2.57109	+	5.62991i	−0.160069	+	0.350503i
$259$	−1.58481	+	2.37537i	−0.0984754	+	0.147598i
$260$	−6.36205	+	21.6671i	−0.394557	+	1.34374i
$261$	4.41577	+	2.27649i	0.273329	+	0.140911i
$262$	−0.0246152	+	0.257782i	−0.00152073	+	0.0159258i
$263$	16.7798	+	4.07074i	1.03469	+	0.251012i	0.716919	−	0.697156i	$-0.245552\pi$
$263$	16.7798	+	4.07074i	1.03469	+	0.251012i	0.317768	+	0.948169i	$0.397067\pi$
$264$	−0.199130	−	0.0383791i	−0.0122556	−	0.00236207i
$265$	23.7478	+	20.5776i	1.45881	+	1.26407i
$266$	9.26670	−	0.724613i	0.568178	−	0.0444289i
$267$	16.2820	−	7.43572i	0.996440	−	0.455059i
$268$	5.07402	−	9.84222i	0.309945	−	0.601209i
$269$	−19.8903	−	20.8604i	−1.21273	−	1.27188i	−0.951869	−	0.306504i	$-0.900841\pi$
$269$	−19.8903	−	20.8604i	−1.21273	−	1.27188i	−0.260865	−	0.965375i	$-0.584008\pi$
$270$	1.55574	−	3.88604i	0.0946791	−	0.236497i
$271$	−1.90452	−	19.9450i	−0.115691	−	1.21157i	−0.847775	−	0.530357i	$-0.822058\pi$
$271$	−1.90452	−	19.9450i	−0.115691	−	1.21157i	0.732084	−	0.681215i	$-0.238548\pi$
$272$	0.694570	−	4.83084i	0.0421145	−	0.292913i
$273$	−10.1594	−	10.0255i	−0.614877	−	0.606770i
$274$	−5.89473	+	5.10781i	−0.356113	+	0.308574i
$275$	−2.19912	+	1.26966i	−0.132612	+	0.0765634i
$276$	−0.965543	+	4.69763i	−0.0581188	+	0.282764i
$277$	12.1302	−	21.0102i	0.728835	−	1.26238i	−0.228540	−	0.973534i	$-0.573395\pi$
$277$	12.1302	−	21.0102i	0.728835	−	1.26238i	0.957376	−	0.288846i	$-0.0932714\pi$
$278$	−0.822549	−	0.284687i	−0.0493332	−	0.0170744i
$279$	−4.23728	+	6.59334i	−0.253679	+	0.394733i
$280$	−7.10775	−	8.49302i	−0.424769	−	0.507555i
$281$	20.3963	+	9.31466i	1.21674	+	0.555666i	0.917203	−	0.398419i	$-0.130441\pi$
$281$	20.3963	+	9.31466i	1.21674	+	0.555666i	0.299535	+	0.954085i	$0.403168\pi$
$282$	−6.00035	+	4.71873i	−0.357315	+	0.280996i
$283$	13.3991	−	12.7761i	0.796497	−	0.759458i	−0.177959	−	0.984038i	$-0.556949\pi$
$283$	13.3991	−	12.7761i	0.796497	−	0.759458i	0.974456	+	0.224580i	$0.0721009\pi$
$284$	0.00127142	+	0.0266904i	7.54450e−5	+	0.00158379i
$285$	−11.9790	−	8.53017i	−0.709572	−	0.505284i
$286$	1.04971	−	0.308224i	0.0620709	−	0.0182257i
$287$	2.96132	−	7.04418i	0.174801	−	0.415805i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	4.93546	+	4.70595i	0.290321	+	0.276821i
$290$	−20.7015	−	1.97675i	−1.21563	−	0.116079i
$291$	−0.351247	+	0.0167320i	−0.0205905	+	0.000980845i
$292$	10.3308	−	2.50623i	0.604566	−	0.146666i
$293$	0.0579166	+	0.402819i	0.00338352	+	0.0235329i	0.991443	−	0.130538i	$-0.0416706\pi$
$293$	0.0579166	+	0.402819i	0.00338352	+	0.0235329i	−0.988060	+	0.154071i	$0.950761\pi$
$294$	6.85531	−	1.41587i	0.399810	−	0.0825755i
$295$	−41.5991	−	5.98105i	−2.42199	−	0.348230i
$296$	−1.07806	−	0.0513545i	−0.0626612	−	0.00298492i
$297$	−0.199130	+	0.0383791i	−0.0115547	+	0.00222698i
$298$	7.74497	+	4.47156i	0.448654	+	0.259030i
$299$	−6.98282	−	24.9123i	−0.403827	−	1.44071i
$300$			12.5216i			0.722937i
$301$	14.0387	+	8.42974i	0.809176	+	0.485882i
$302$	18.9061	+	12.1502i	1.08792	+	0.699167i
$303$	−8.40559	+	3.36509i	−0.482889	+	0.193319i
$304$	2.03784	+	2.86175i	0.116878	+	0.164133i
$305$	−22.5371	−	9.02250i	−1.29047	−	0.516627i
$306$	−1.15063	−	4.74294i	−0.0657769	−	0.271136i
$307$	12.1303	+	18.8751i	0.692313	+	1.07726i	0.992365	+	0.123337i	$0.0393595\pi$
$307$	12.1303	+	18.8751i	0.692313	+	1.07726i	−0.300052	+	0.953923i	$0.597004\pi$
$308$	−0.159975	+	0.512140i	−0.00911542	+	0.0291819i
$309$	−1.98999	−	6.77729i	−0.113207	−	0.385546i
$310$	6.20875	−	32.2141i	0.352633	−	1.82964i
$311$	−2.59452	+	0.897972i	−0.147122	+	0.0509193i	−0.399636	−	0.916674i	$-0.630864\pi$
$311$	−2.59452	+	0.897972i	−0.147122	+	0.0509193i	0.252515	+	0.967593i	$0.418742\pi$
$312$	1.27186	−	5.24270i	0.0720051	−	0.296809i
$313$	6.50738	−	9.13834i	0.367819	−	0.516529i	−0.588640	−	0.808395i	$-0.700337\pi$
$313$	6.50738	−	9.13834i	0.367819	−	0.516529i	0.956459	+	0.291866i	$0.0942760\pi$
$314$	14.2611	−	9.16503i	0.804799	−	0.517213i
$315$	−9.75514	−	5.24297i	−0.549640	−	0.295408i
$316$	16.0935	−	2.31390i	0.905333	−	0.130167i
$317$	−4.89097	+	0.467031i	−0.274704	+	0.0262311i	−0.231499	−	0.972835i	$-0.574363\pi$
$317$	−4.89097	+	0.467031i	−0.274704	+	0.0262311i	−0.0432052	+	0.999066i	$0.513757\pi$
$318$	−5.90078	−	4.64042i	−0.330899	−	0.260222i
$319$	0.461660	+	0.895495i	0.0258480	+	0.0501381i
$320$	1.36907	−	3.95566i	0.0765333	−	0.221128i
$321$	0.375893			0.0209803
$322$	12.0639	+	3.93207i	0.672297	+	0.219126i
$323$	−17.1461			−0.954035
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	−30.9538	−	60.0420i	−1.71701	−	3.33053i
$326$	1.90996	+	1.50201i	0.105783	+	0.0831888i
$327$	−12.6829	+	1.21107i	−0.701365	+	0.0669722i
$328$	2.85875	−	0.411027i	0.157848	−	0.0226951i
$329$	10.6258	+	17.1752i	0.585819	+	0.946898i
$330$	0.714119	−	0.458936i	0.0393110	−	0.0252636i
$331$	−7.73764	+	10.8660i	−0.425299	+	0.597249i	−0.970513	−	0.241048i	$-0.922509\pi$
$331$	−7.73764	+	10.8660i	−0.425299	+	0.597249i	0.545214	+	0.838297i	$0.316448\pi$
$332$	1.19517	−	4.92656i	0.0655935	−	0.270380i
$333$	−1.01993	+	0.353000i	−0.0558916	+	0.0193443i
$334$	0.112238	−	0.582344i	0.00614137	−	0.0318645i
$335$	13.0586	+	44.4734i	0.713466	+	2.42984i
$336$	1.79265	+	1.94587i	0.0977968	+	0.106156i
$337$	13.5598	+	21.0995i	0.738651	+	1.14936i	0.983694	+	0.179852i	$0.0575618\pi$
$337$	13.5598	+	21.0995i	0.738651	+	1.14936i	−0.245042	+	0.969512i	$0.578802\pi$
$338$	3.79654	+	15.6496i	0.206505	+	0.851224i
$339$	2.87681	+	1.15170i	0.156247	+	0.0625518i
$340$	11.8501	+	16.6412i	0.642664	+	0.902496i
$341$	−1.47555	+	0.590722i	−0.0799057	+	0.0319894i
$342$	2.95547	+	1.89937i	0.159814	+	0.102706i
$343$	−1.68874	−	18.4431i	−0.0911831	−	0.995834i
$344$			6.18922i			0.333700i
$345$	−10.6445	−	17.0204i	−0.573078	−	0.916346i
$346$	−8.36399	−	4.82895i	−0.449651	−	0.259606i
$347$	−0.890395	+	0.171610i	−0.0477989	+	0.00921248i	−0.213095	−	0.977032i	$-0.568354\pi$
$347$	−0.890395	+	0.171610i	−0.0477989	+	0.00921248i	0.165296	+	0.986244i	$0.447142\pi$
$348$	4.96241	+	0.236389i	0.266013	+	0.0126718i
$349$	1.57243	+	0.226081i	0.0841702	+	0.0121018i	0.184271	−	0.982875i	$-0.441008\pi$
$349$	1.57243	+	0.226081i	0.0841702	+	0.0121018i	−0.100101	+	0.994977i	$0.531917\pi$
$350$	32.9202	+	3.71466i	1.75966	+	0.198557i
$351$	−0.767755	−	5.33986i	−0.0409797	−	0.285020i
$352$	−0.197078	+	0.0478106i	−0.0105043	+	0.00254832i
$353$	35.6036	−	1.69601i	1.89499	−	0.0902694i	0.932431	−	0.361349i	$-0.117684\pi$
$353$	35.6036	−	1.69601i	1.89499	−	0.0902694i	0.962557	+	0.271080i	$0.0873807\pi$
$354$	9.99468	+	0.954376i	0.531211	+	0.0507245i
$355$	−0.0809495	−	0.0771852i	−0.00429635	−	0.00409656i
$356$	11.7217	−	13.5275i	0.621248	−	0.716958i
$357$	−12.8109	+	1.61803i	−0.678022	+	0.0856354i
$358$	−4.89613	+	1.43763i	−0.258769	+	0.0759813i
$359$	−9.94412	−	7.08117i	−0.524830	−	0.373730i	0.286718	−	0.958015i	$-0.407436\pi$
$359$	−9.94412	−	7.08117i	−0.524830	−	0.373730i	−0.811549	+	0.584285i	$0.801375\pi$
$360$	−0.199172	−	4.18114i	−0.0104973	−	0.220366i
$361$	−4.81833	+	4.59427i	−0.253596	+	0.241804i
$362$	−3.73142	+	2.93442i	−0.196119	+	0.154230i
$363$	9.96854	+	4.55248i	0.523213	+	0.238943i
$364$	−13.4061	−	4.89911i	−0.702670	−	0.256783i
$365$	−24.0574	+	37.4341i	−1.25922	+	1.95939i
$366$	5.48054	+	1.89683i	0.286472	+	0.0991490i
$367$	−2.45082	+	4.24494i	−0.127932	+	0.221584i	−0.922875	−	0.385099i	$-0.874167\pi$
$367$	−2.45082	+	4.24494i	−0.127932	+	0.221584i	0.794943	+	0.606684i	$0.207500\pi$
$368$	1.07318	+	4.67422i	0.0559432	+	0.243660i
$369$	2.50121	−	1.44407i	0.130208	−	0.0751755i
$370$	3.41430	−	2.95851i	0.177501	−	0.153805i
$371$	−13.9505	+	14.1369i	−0.724274	+	0.733952i
$372$	−1.11539	+	7.75774i	−0.0578305	+	0.402220i
$373$	−2.04581	−	21.4247i	−0.105928	−	1.10933i	−0.879590	−	0.475732i	$-0.842183\pi$
$373$	−2.04581	−	21.4247i	−0.105928	−	1.10933i	0.773662	−	0.633599i	$-0.218423\pi$
$374$	0.367850	−	0.918845i	0.0190211	−	0.0475123i
$375$	−21.7269	−	22.7865i	−1.12197	−	1.17669i
$376$	−3.49788	+	6.78494i	−0.180389	+	0.349906i
$377$	−24.3794	+	11.1337i	−1.25560	+	0.573415i
$378$	2.38744	+	1.14023i	0.122797	+	0.0586469i
$379$	−6.20518	−	5.37682i	−0.318739	−	0.276189i	0.480765	−	0.876849i	$-0.340359\pi$
$379$	−6.20518	−	5.37682i	−0.318739	−	0.276189i	−0.799504	+	0.600661i	$0.794904\pi$
$380$	−14.4400	−	2.78308i	−0.740756	−	0.142769i
$381$	18.5558	+	4.50159i	0.950644	+	0.230624i
$382$	−0.205565	+	2.15278i	−0.0105176	+	0.110146i
$383$	1.48148	+	0.763758i	0.0757003	+	0.0390262i	0.495661	−	0.868516i	$-0.334926\pi$
$383$	1.48148	+	0.763758i	0.0757003	+	0.0390262i	−0.419961	+	0.907542i	$0.637956\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	−0.994725	−	2.01361i	−0.0506959	−	0.102623i
$386$	−9.85180	+	21.5724i	−0.501443	+	1.09801i
$387$	2.30030	+	5.74587i	0.116931	+	0.292079i
$388$	−0.312555	+	0.161133i	−0.0158676	+	0.00818030i
$389$	−4.69150	−	24.3418i	−0.237868	−	1.23418i	−0.882730	−	0.469880i	$-0.844297\pi$
$389$	−4.69150	−	24.3418i	−0.237868	−	1.23418i	0.644862	−	0.764299i	$-0.276915\pi$
$390$	11.2909	+	19.5565i	0.571739	+	0.990281i
$391$	−21.6207	−	8.96613i	−1.09341	−	0.453436i
$392$	5.64764	−	4.13572i	0.285249	−	0.208886i
$393$	0.169579	+	0.195705i	0.00855414	+	0.00987201i
$394$	0.326043	−	6.84448i	0.0164258	−	0.344820i
$395$	−42.0709	+	53.4976i	−2.11682	+	2.69175i
$396$	−0.165192	+	0.117632i	−0.00830119	+	0.00591125i
$397$	−0.541485	−	0.688554i	−0.0271763	−	0.0345575i	0.772275	−	0.635288i	$-0.219119\pi$
$397$	−0.541485	−	0.688554i	−0.0271763	−	0.0345575i	−0.799451	+	0.600731i	$0.794876\pi$
$398$	5.21232	+	1.53048i	0.261270	+	0.0767158i
$399$	5.87033	−	7.20667i	0.293884	−	0.360785i
$400$	5.20168	+	11.3901i	0.260084	+	0.569504i
$401$	4.41121	−	4.62634i	0.220285	−	0.231029i	−0.604313	−	0.796747i	$-0.706552\pi$
$401$	4.41121	−	4.62634i	0.220285	−	0.231029i	0.824599	+	0.565718i	$0.191401\pi$
$402$	−3.62168	−	10.4641i	−0.180633	−	0.521904i
$403$	−13.8289	−	39.9561i	−0.688869	−	1.99036i
$404$	−6.24809	+	6.55281i	−0.310854	+	0.326014i
$405$	−1.73888	−	3.80762i	−0.0864056	−	0.189202i
$406$	2.09363	−	12.9764i	0.103905	−	0.644007i
$407$	−0.210007	−	0.0616637i	−0.0104097	−	0.00305656i
$408$	−3.01693	−	3.83634i	−0.149361	−	0.189927i
$409$	28.4240	−	20.2407i	1.40548	−	1.00084i	0.409401	−	0.912355i	$-0.365738\pi$
$409$	28.4240	−	20.2407i	1.40548	−	1.00084i	0.996078	−	0.0884821i	$-0.0282016\pi$
$410$	−7.47321	+	9.50296i	−0.369075	+	0.469318i
$411$	−0.371131	+	7.79101i	−0.0183066	+	0.384302i
$412$	−4.62555	−	5.33817i	−0.227884	−	0.262993i
$413$	5.47413	−	25.9936i	0.269365	−	1.27906i
$414$	2.73353	+	3.94053i	0.134346	+	0.193667i
$415$	10.6101	+	18.3772i	0.520829	+	0.902102i
$416$	−1.02097	−	5.29728i	−0.0500570	−	0.259720i
$417$	−0.773661	+	0.398850i	−0.0378864	+	0.0195318i
$418$	0.264792	+	0.661419i	0.0129514	+	0.0323510i
$419$	0.519683	−	1.13795i	0.0253882	−	0.0555923i	−0.896513	−	0.443017i	$-0.853908\pi$
$419$	0.519683	−	1.13795i	0.0253882	−	0.0555923i	0.921901	+	0.387425i	$0.126635\pi$
$420$	−11.0516	−	0.716738i	−0.539263	−	0.0349732i
$421$	−6.95170	+	23.6753i	−0.338805	+	1.15386i	0.597263	+	0.802045i	$0.296255\pi$
$421$	−6.95170	+	23.6753i	−0.338805	+	1.15386i	−0.936068	+	0.351819i	$0.885563\pi$
$422$	22.7349	+	11.7206i	1.10672	+	0.570552i
$423$	−0.725612	+	7.59895i	−0.0352804	+	0.369474i
$424$	−7.29524	−	1.76981i	−0.354288	−	0.0859494i
$425$	−60.0077	−	11.5655i	−2.91080	−	0.561011i
$426$	0.0201942	+	0.0174983i	0.000978410	+	0.000847797i
$427$	6.61275	−	13.8460i	0.320013	−	0.670054i
$428$	0.341924	−	0.156152i	0.0165275	−	0.00754787i
$429$	0.501313	−	0.972412i	0.0242036	−	0.0469485i
$430$	−17.8781	−	18.7500i	−0.862160	−	0.904207i
$431$	−10.9469	+	27.3441i	−0.527295	+	1.31712i	0.390696	+	0.920520i	$0.372234\pi$
$431$	−10.9469	+	27.3441i	−0.527295	+	1.31712i	−0.917991	+	0.396600i	$0.870190\pi$
$432$	0.0950560	+	0.995472i	0.00457339	+	0.0478947i
$433$	−1.96149	+	13.6425i	−0.0942633	+	0.655616i	0.886832	+	0.462092i	$0.152901\pi$
$433$	−1.96149	+	13.6425i	−0.0942633	+	0.655616i	−0.981096	+	0.193524i	$0.938008\pi$
$434$	20.0647	+	5.23385i	0.963138	+	0.251233i
$435$	−15.7163	+	13.6183i	−0.753539	+	0.652945i
$436$	−11.0337	+	6.37028i	−0.528416	+	0.305081i
$437$	15.7176	−	6.06889i	0.751876	−	0.290314i
$438$	5.31524	−	9.20627i	0.253972	−	0.439893i
$439$	17.0342	+	5.89559i	0.812998	+	0.281381i	0.701761	−	0.712413i	$-0.252398\pi$
$439$	17.0342	+	5.89559i	0.812998	+	0.281381i	0.111237	+	0.993794i	$0.464519\pi$
$440$	0.458936	−	0.714119i	0.0218789	−	0.0340443i
$441$	3.70599	−	5.93849i	0.176476	−	0.282785i
$442$	23.9499	+	10.9376i	1.13918	+	0.520247i
$443$	−8.95801	+	7.04465i	−0.425608	+	0.334702i	−0.807879	−	0.589349i	$-0.799384\pi$
$443$	−8.95801	+	7.04465i	−0.425608	+	0.334702i	0.382271	+	0.924050i	$0.375142\pi$
$444$	−0.781116	+	0.744792i	−0.0370701	+	0.0353463i
$445$	3.56509	+	74.8404i	0.169001	+	3.54778i
$446$	−5.88134	−	4.18808i	−0.278490	−	0.198311i
$447$	8.58086	−	2.51957i	0.405861	−	0.119171i
$448$	2.43899	+	1.02534i	0.115232	+	0.0484426i
$449$	2.45898	−	2.83781i	0.116046	−	0.133925i	−0.694754	−	0.719248i	$-0.744487\pi$
$449$	2.45898	−	2.83781i	0.116046	−	0.133925i	0.810800	+	0.585323i	$0.199032\pi$
$450$	9.06233	+	8.64092i	0.427202	+	0.407337i
$451$	0.583049	+	0.0556744i	0.0274547	+	0.00262161i
$452$	3.09527	−	0.147446i	0.145589	−	0.00693528i
$453$	21.8402	−	5.29839i	1.02614	−	0.248940i
$454$	0.553826	+	3.85194i	0.0259923	+	0.180781i
$455$	54.7648	−	23.8830i	2.56742	−	1.11965i
$456$	3.47742	+	0.499977i	0.162845	+	0.0234136i
$457$	−40.2465	−	1.91718i	−1.88265	−	0.0896817i	−0.925409	−	0.378970i	$-0.876278\pi$
$457$	−40.2465	−	1.91718i	−1.88265	−	0.0896817i	−0.957242	+	0.289288i	$0.906581\pi$
$458$	6.32290	−	1.21864i	0.295450	−	0.0569433i
$459$	−4.22665	−	2.44026i	−0.197283	−	0.113901i
$460$	−16.7531	−	11.0604i	−0.781115	−	0.515694i
$461$		−	8.23274i		−	0.383437i	−0.981450	−	0.191718i	$-0.938594\pi$
$461$		−	8.23274i		−	0.383437i	0.981450	−	0.191718i	$-0.0614060\pi$
$462$	0.260258	+	0.469197i	0.0121083	+	0.0218290i
$463$	−24.0507	−	15.4565i	−1.11773	−	0.718323i	−0.154768	−	0.987951i	$-0.549463\pi$
$463$	−24.0507	−	15.4565i	−1.11773	−	0.718323i	−0.962965	+	0.269628i	$0.913099\pi$
$464$	4.61217	−	1.84643i	0.214115	−	0.0857186i
$465$	−19.0299	−	26.7237i	−0.882490	−	1.23928i
$466$	−2.17456	−	0.870561i	−0.100734	−	0.0403280i
$467$	5.28822	+	21.7984i	0.244710	+	1.00871i	0.953044	+	0.302831i	$0.0979317\pi$
$467$	5.28822	+	21.7984i	0.244710	+	1.00871i	−0.708335	+	0.705877i	$0.750553\pi$
$468$	−2.91663	−	4.53837i	−0.134821	−	0.209786i
$469$	−28.5853	+	6.41734i	−1.31995	+	0.296325i
$470$	−9.00220	−	30.6587i	−0.415241	−	1.41418i
$471$	3.20822	−	16.6458i	0.147827	−	0.766999i
$472$	9.48794	−	3.28381i	0.436718	−	0.151150i
$473$	−0.295910	+	1.21976i	−0.0136060	+	0.0560846i
$474$	9.43117	−	13.2442i	0.433188	−	0.608327i
$475$	37.0073	−	23.7832i	1.69801	−	1.09125i
$476$	−10.9810	+	6.79364i	−0.503314	+	0.311386i
$477$	−7.43044	+	1.06834i	−0.340216	+	0.0489157i
$478$	−28.2061	+	2.69336i	−1.29012	+	0.123191i
$479$	8.15238	+	6.41110i	0.372492	+	0.292931i	0.786803	−	0.617205i	$-0.211735\pi$
$479$	8.15238	+	6.41110i	0.372492	+	0.292931i	−0.414311	+	0.910135i	$0.635977\pi$
$480$	−1.91808	−	3.72056i	−0.0875481	−	0.169820i
$481$	1.90435	−	5.50226i	0.0868309	−	0.250882i
$482$	23.5916			1.07457
$483$	11.1709	−	6.01765i	0.508291	−	0.273812i
$484$	10.9589			0.498131
$485$	0.481427	−	1.39099i	0.0218605	−	0.0631617i
$486$	0.458227	+	0.888835i	0.0207856	+	0.0403184i
$487$	18.0967	+	14.2314i	0.820041	+	0.644887i	0.937420	−	0.348200i	$-0.113207\pi$
$487$	18.0967	+	14.2314i	0.820041	+	0.644887i	−0.117380	+	0.993087i	$0.537449\pi$
$488$	5.77324	−	0.551278i	0.261342	−	0.0249552i
$489$	2.40508	−	0.345799i	0.108762	−	0.0156376i
$490$	−5.16291	+	28.8428i	−0.233237	+	1.30298i
$491$	13.4988	−	8.67518i	0.609194	−	0.391505i	−0.199361	−	0.979926i	$-0.563886\pi$
$491$	13.4988	−	8.67518i	0.609194	−	0.391505i	0.808555	+	0.588421i	$0.200250\pi$
$492$	1.67529	−	2.35262i	0.0755279	−	0.106064i
$493$	−5.71635	+	23.5631i	−0.257452	+	1.06123i
$494$	−17.9104	+	6.19884i	−0.805826	+	0.278899i
$495$	0.160651	−	0.833535i	0.00722071	−	0.0374646i
$496$	2.20808	+	7.52004i	0.0991458	+	0.337660i
$497$	0.0519951	−	0.0479007i	0.00233230	−	0.00214864i
$498$	−2.74076	−	4.26470i	−0.122816	−	0.191106i
$499$	0.829132	+	3.41773i	0.0371170	+	0.152998i	0.987354	−	0.158528i	$-0.0506749\pi$
$499$	0.829132	+	3.41773i	0.0371170	+	0.152998i	−0.950237	+	0.311527i	$0.899160\pi$
$500$	−29.2294	−	11.7017i	−1.30718	−	0.523315i
$501$	−0.344009	−	0.483094i	−0.0153692	−	0.0215830i
$502$	−10.2510	+	4.10389i	−0.457526	+	0.183166i
$503$	−32.6498	−	20.9828i	−1.45578	−	0.935576i	−0.998940	−	0.0460291i	$-0.985343\pi$
$503$	−32.6498	−	20.9828i	−1.45578	−	0.935576i	−0.456844	−	0.889547i	$-0.651020\pi$
$504$	2.64536	+	0.0454074i	0.117834	+	0.00202261i
$505$		−	37.8997i		−	1.68651i
$506$	−0.0119774	+	0.972495i	−0.000532462	+	0.0432327i
$507$	13.9460	+	8.05175i	0.619365	+	0.357591i
$508$	18.7490	−	3.61357i	0.831852	−	0.160326i
$509$	11.1414	+	0.530731i	0.493834	+	0.0235242i	0.293022	−	0.956106i	$-0.405339\pi$
$509$	11.1414	+	0.530731i	0.493834	+	0.0235242i	0.200812	+	0.979630i	$0.435642\pi$
$510$	20.2213	+	2.90739i	0.895416	+	0.128741i
$511$	−22.6271	−	16.7053i	−1.00096	−	0.738997i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	3.41414	−	0.828263i	0.150738	−	0.0365687i
$514$	−6.21128	+	0.295880i	−0.273968	+	0.0130507i
$515$	29.4327	+	2.81048i	1.29696	+	0.123845i
$516$	4.47935	+	4.27105i	0.197192	+	0.188022i
$517$	−1.01375	+	1.16993i	−0.0445846	+	0.0514533i
$518$	1.72638	+	2.27456i	0.0758530	+	0.0999382i
$519$	−9.26669	+	2.72095i	−0.406763	+	0.119436i
$520$	18.3946	+	13.0988i	0.806659	+	0.574419i
$521$	−0.824047	−	17.2989i	−0.0361022	−	0.757878i	−0.942249	−	0.334914i	$-0.891293\pi$
$521$	−0.824047	−	17.2989i	−0.0361022	−	0.757878i	0.906147	−	0.422964i	$-0.139010\pi$
$522$	3.59554	−	3.42834i	0.157373	−	0.150054i
$523$	−13.7174	+	10.7875i	−0.599822	+	0.471705i	−0.871308	−	0.490737i	$-0.836727\pi$
$523$	−13.7174	+	10.7875i	−0.599822	+	0.471705i	0.271486	+	0.962442i	$0.412485\pi$
$524$	0.235554	+	0.107574i	0.0102902	+	0.00469938i
$525$	25.4060	−	21.2621i	1.10881	−	0.927953i
$526$	9.33499	−	14.5255i	0.407025	−	0.633343i
$527$	−36.1473	−	12.5107i	−1.57460	−	0.544975i
$528$	−0.101397	+	0.175625i	−0.00441275	+	0.00764311i
$529$	22.9930	+	0.566459i	0.999697	+	0.0246286i
$530$	27.2129	−	15.7114i	1.18205	−	0.682460i
$531$	7.58783	−	6.57489i	0.329284	−	0.285326i
$532$	2.34608	−	8.99404i	0.101716	−	0.389941i
$533$	−2.21739	+	15.4223i	−0.0960459	+	0.668014i
$534$	−1.70146	−	17.8185i	−0.0736292	−	0.771080i
$535$	−0.584791	+	1.46074i	−0.0252827	+	0.0631531i
$536$	−7.64136	−	8.01402i	−0.330056	−	0.346153i
$537$	−2.33825	+	4.53558i	−0.100903	+	0.195725i
$538$	−26.2186	+	11.9736i	−1.13036	+	0.516219i
$539$	1.31076	−	0.545044i	0.0564583	−	0.0234767i
$540$	−3.16348	−	2.74117i	−0.136135	−	0.117961i
$541$	15.0952	+	2.90937i	0.648995	+	0.125083i	0.503116	−	0.864219i	$-0.332187\pi$
$541$	15.0952	+	2.90937i	0.648995	+	0.125083i	0.145879	+	0.989302i	$0.453399\pi$
$542$	−19.4709	−	4.72360i	−0.836348	−	0.202896i
$543$	−0.451234	+	4.72553i	−0.0193643	+	0.202792i
$544$	−4.33798	−	2.23638i	−0.185989	−	0.0958841i
$545$	15.0249	−	51.1703i	0.643598	−	2.19189i
$546$	−12.7969	+	6.32167i	−0.547657	+	0.270542i
$547$	3.24790	−	7.11190i	0.138870	−	0.304083i	−0.827400	−	0.561613i	$-0.810181\pi$
$547$	3.24790	−	7.11190i	0.138870	−	0.304083i	0.966270	+	0.257529i	$0.0829085\pi$
$548$	2.89891	+	7.24112i	0.123835	+	0.309325i
$549$	5.15481	−	2.65749i	0.220002	−	0.113419i
$550$	0.480569	+	2.49343i	0.0204916	+	0.106320i
$551$	−8.72680	−	15.1153i	−0.371774	−	0.643932i
$552$	4.12347	+	2.44888i	0.175506	+	0.104231i
$553$	−32.0221	−	28.7242i	−1.36172	−	1.22148i
$554$	−15.8872	−	18.3348i	−0.674984	−	0.778973i
$555$	0.214964	−	4.51265i	0.00912471	−	0.191551i
$556$	−0.538059	+	0.684197i	−0.0228188	+	0.0290164i
$557$	34.5316	−	24.5899i	1.46315	−	1.04191i	0.476481	−	0.879185i	$-0.341912\pi$
$557$	34.5316	−	24.5899i	1.46315	−	1.04191i	0.986672	−	0.162721i	$-0.0520272\pi$
$558$	4.84483	+	6.16070i	0.205098	+	0.260803i
$559$	−32.0369	−	9.40688i	−1.35502	−	0.397868i
$560$	−10.3506	+	3.93903i	−0.437394	+	0.166454i
$561$	−0.411154	−	0.900301i	−0.0173589	−	0.0380107i
$562$	15.4733	−	16.2280i	0.652703	−	0.684535i
$563$	12.4310	+	35.9170i	0.523904	+	1.51372i	0.827805	+	0.561017i	$0.189590\pi$
$563$	12.4310	+	35.9170i	0.523904	+	1.51372i	−0.303901	+	0.952704i	$0.598289\pi$
$564$	2.49668	+	7.21368i	0.105129	+	0.303751i
$565$	−8.95112	+	9.38766i	−0.376576	+	0.394942i
$566$	−7.69096	−	16.8408i	−0.323275	−	0.707874i
$567$	2.47275	−	0.941027i	0.103846	−	0.0395194i
$568$	0.0256383	+	0.00752809i	0.00107576	+	0.000315872i
$569$	−26.7002	−	33.9520i	−1.11933	−	1.42334i	−0.893436	−	0.449191i	$-0.851712\pi$
$569$	−26.7002	−	33.9520i	−1.11933	−	1.42334i	−0.225893	−	0.974152i	$-0.572530\pi$
$570$	−11.9790	+	8.53017i	−0.501743	+	0.357290i
$571$	1.20249	−	1.52909i	0.0503227	−	0.0639905i	−0.760240	−	0.649642i	$-0.774919\pi$
$571$	1.20249	−	1.52909i	0.0503227	−	0.0639905i	0.810563	+	0.585651i	$0.199161\pi$
$572$	0.0520560	−	1.09279i	0.00217657	−	0.0456919i
$573$	1.41618	+	1.63436i	0.0591618	+	0.0682764i
$574$	−5.68820	−	5.10238i	−0.237421	−	0.212969i
$575$	59.1019	−	10.6378i	2.46472	−	0.443627i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	0.245862	+	1.27566i	0.0102354	+	0.0531062i	0.986687	−	0.162629i	$-0.0519973\pi$
$577$	0.245862	+	1.27566i	0.0102354	+	0.0531062i	−0.976452	+	0.215735i	$0.930785\pi$
$578$	6.06136	−	3.12485i	0.252119	−	0.129976i
$579$	8.81418	+	22.0168i	0.366305	+	0.914985i
$580$	−8.63882	+	18.9164i	−0.358708	+	0.785460i
$581$	−12.0253	+	5.94047i	−0.498892	+	0.246452i
$582$	−0.0990700	+	0.337401i	−0.00410658	+	0.0139857i
$583$	−1.35312	−	0.697580i	−0.0560404	−	0.0288908i
$584$	1.01049	−	10.5824i	0.0418145	−	0.437901i
$585$	21.9453	+	5.32388i	0.907327	+	0.220115i
$586$	0.399607	+	0.0770178i	0.0165076	+	0.00318158i
$587$	−27.1601	−	23.5344i	−1.12102	−	0.971368i	−0.121244	−	0.992623i	$-0.538688\pi$
$587$	−27.1601	−	23.5344i	−1.12102	−	0.971368i	−0.999774	+	0.0212548i	$0.993234\pi$
$588$	0.904151	−	6.94136i	0.0372865	−	0.286257i
$589$	25.0463	−	11.4383i	1.03202	−	0.471306i
$590$	−19.2578	+	37.3550i	−0.792832	+	1.53788i
$591$	−4.72859	−	4.95920i	−0.194508	−	0.203994i
$592$	−0.401130	+	1.00197i	−0.0164863	+	0.0411809i
$593$	1.68941	+	17.6923i	0.0693758	+	0.726537i	0.961511	+	0.274767i	$0.0886009\pi$
$593$	1.68941	+	17.6923i	0.0693758	+	0.726537i	−0.892135	+	0.451769i	$0.850793\pi$
$594$	−0.0288607	+	0.200730i	−0.00118417	+	0.00823607i
$595$	13.6426	−	52.3007i	0.559291	−	2.14412i
$596$	6.75876	−	5.85650i	0.276850	−	0.239891i
$597$	4.70457	−	2.71619i	0.192545	−	0.111166i
$598$	−25.8260	−	1.54923i	−1.05610	−	0.0633527i
$599$	−15.2865	+	26.4771i	−0.624591	+	1.08182i	0.364029	+	0.931388i	$0.381401\pi$
$599$	−15.2865	+	26.4771i	−0.624591	+	1.08182i	−0.988620	+	0.150436i	$0.951932\pi$
$600$	11.8330	+	4.09543i	0.483078	+	0.167195i
$601$	1.36697	−	2.12705i	0.0557601	−	0.0867643i	−0.812254	−	0.583304i	$-0.801760\pi$
$601$	1.36697	−	2.12705i	0.0557601	−	0.0867643i	0.868014	+	0.496539i	$0.165396\pi$
$602$	12.5577	−	10.5095i	0.511814	−	0.428334i
$603$	−10.0725	−	4.59996i	−0.410184	−	0.187325i
$604$	17.6656	−	13.8923i	0.718801	−	0.565272i
$605$	−33.1996	+	31.6557i	−1.34975	+	1.28699i
$606$	0.430814	+	9.04391i	0.0175006	+	0.367384i
$607$	34.8194	+	24.7948i	1.41328	+	1.00639i	0.995188	+	0.0979817i	$0.0312387\pi$
$607$	34.8194	+	24.7948i	1.41328	+	1.00639i	0.418087	+	0.908407i	$0.362701\pi$
$608$	3.37087	−	0.989776i	0.136707	−	0.0401407i
$609$	−7.94669	−	10.4700i	−0.322016	−	0.424264i
$610$	−15.8974	+	18.3466i	−0.643669	+	0.742833i
$611$	−29.8041	−	28.4182i	−1.20575	−	1.14968i
$612$	−4.85842	−	0.463923i	−0.196390	−	0.0187530i
$613$	−29.2812	+	1.39483i	−1.18266	+	0.0563368i	−0.629676	−	0.776858i	$-0.716812\pi$
$613$	−29.2812	+	1.39483i	−1.18266	+	0.0563368i	−0.552980	+	0.833195i	$0.686509\pi$
$614$	21.8044	−	5.28970i	0.879955	−	0.213475i
$615$	1.72051	+	11.9664i	0.0693776	+	0.482532i
$616$	0.431650	+	0.318681i	0.0173917	+	0.0128400i
$617$	−8.60356	−	1.23700i	−0.346366	−	0.0497999i	−0.0330635	−	0.999453i	$-0.510526\pi$
$617$	−8.60356	−	1.23700i	−0.346366	−	0.0497999i	−0.313303	+	0.949653i	$0.601435\pi$
$618$	−7.05540	−	0.336090i	−0.283810	−	0.0135195i
$619$	12.2958	−	2.36983i	0.494211	−	0.0952513i	0.0639447	−	0.997953i	$-0.479632\pi$
$619$	12.2958	−	2.36983i	0.494211	−	0.0952513i	0.430266	+	0.902702i	$0.358420\pi$
$620$	−28.4116	−	16.4035i	−1.14104	−	0.658779i
$621$	4.73825	+	0.740927i	0.190139	+	0.0297324i
$622$			2.74552i			0.110085i
$623$	−47.3507	−	0.812770i	−1.89706	−	0.0325629i
$624$	−4.53837	−	2.91663i	−0.181680	−	0.116759i
$625$	64.2274	−	25.7128i	2.56910	−	1.02851i
$626$	−6.50738	−	9.13834i	−0.260087	−	0.365241i
$627$	0.661419	+	0.264792i	0.0264145	+	0.0105748i
$628$	−3.99662	−	16.4743i	−0.159483	−	0.657397i
$629$	−2.84781	−	4.43128i	−0.113550	−	0.176687i
$630$	−8.14520	+	7.50381i	−0.324513	+	0.298959i
$631$	2.77241	+	9.44194i	0.110368	+	0.375878i	0.996091	−	0.0883362i	$-0.0281550\pi$
$631$	2.77241	+	9.44194i	0.110368	+	0.375878i	−0.885723	+	0.464214i	$0.846337\pi$
$632$	3.07704	−	15.9652i	0.122398	−	0.635062i
$633$	24.1715	−	8.36584i	0.960731	−	0.332512i
$634$	−1.15833	+	4.77472i	−0.0460033	+	0.189628i
$635$	−46.3614	+	65.1054i	−1.83979	+	2.58363i
$636$	−6.31516	+	4.05851i	−0.250412	+	0.160930i
$637$	12.8238	+	35.5193i	0.508096	+	1.40733i
$638$	0.997237	−	0.143381i	0.0394810	−	0.00567651i
$639$	0.0265997	−	0.00253996i	0.00105227	−	0.000100479i
$640$	−3.29033	−	2.58754i	−0.130062	−	0.102282i
$641$	−11.7583	−	22.8079i	−0.464425	−	0.900858i	−0.998464	−	0.0553986i	$-0.982357\pi$
$641$	−11.7583	−	22.8079i	−0.464425	−	0.900858i	0.534040	−	0.845459i	$-0.320673\pi$
$642$	0.122943	−	0.355219i	0.00485216	−	0.0140194i
$643$	14.2950			0.563740			0.281870	−	0.959453i	$-0.409045\pi$
$643$	14.2950			0.563740			0.281870	+	0.959453i	$0.409045\pi$
$644$	7.66154	−	10.1144i	0.301907	−	0.398563i
$645$	−25.9074			−1.02010
$646$	−5.60794	+	16.2031i	−0.220642	+	0.637502i
$647$	8.37330	+	16.2419i	0.329188	+	0.638536i	0.994110	−	0.108377i	$-0.0345653\pi$
$647$	8.37330	+	16.2419i	0.329188	+	0.638536i	−0.664921	+	0.746913i	$0.731535\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	2.02687	−	0.193542i	0.0795615	−	0.00759720i
$650$	−66.8637	+	9.61355i	−2.62261	+	0.377074i
$651$	17.6342	−	10.9098i	0.691137	−	0.427587i
$652$	2.04409	−	1.31366i	0.0800528	−	0.0514468i
$653$	−7.95824	+	11.1758i	−0.311430	+	0.437342i	−0.940391	−	0.340095i	$-0.889541\pi$
$653$	−7.95824	+	11.1758i	−0.311430	+	0.437342i	0.628961	+	0.777436i	$0.283480\pi$
$654$	−3.00370	+	12.3814i	−0.117454	+	0.484152i
$655$	−1.02434	+	0.354527i	−0.0400242	+	0.0138525i
$656$	0.546586	−	2.83596i	0.0213406	−	0.110726i
$657$	−2.99495	−	10.1999i	−0.116844	−	0.397935i
$658$	19.7059	−	4.42393i	0.768216	−	0.172463i
$659$	12.4218	+	19.3288i	0.483886	+	0.752941i	0.994258	−	0.107013i	$-0.0341285\pi$
$659$	12.4218	+	19.3288i	0.483886	+	0.752941i	−0.510372	+	0.859954i	$0.670492\pi$
$660$	−0.200130	−	0.824946i	−0.00779004	−	0.0321110i
$661$	0.401202	+	0.160617i	0.0156050	+	0.00624729i	0.379452	−	0.925212i	$-0.376113\pi$
$661$	0.401202	+	0.160617i	0.0156050	+	0.00624729i	−0.363847	+	0.931459i	$0.618537\pi$
$662$	7.73764	+	10.8660i	0.300732	+	0.422319i
$663$	24.4432	−	9.78559i	0.949296	−	0.380041i
$664$	−4.26470	−	2.74076i	−0.165503	−	0.106362i
$665$	18.8727	+	34.0240i	0.731853	+	1.31939i
$666$			1.07929i			0.0418215i
$667$	−3.10008	−	23.6233i	−0.120036	−	0.914700i
$668$	−0.513606	−	0.296531i	−0.0198720	−	0.0114731i
$669$	−7.08965	+	1.36642i	−0.274102	+	0.0528288i
$670$	46.2985	+	2.20547i	1.78867	+	0.0852047i
$671$	1.16414	+	0.167378i	0.0449410	+	0.00646154i
$672$	2.42517	−	1.05762i	0.0935529	−	0.0407985i
$673$	−1.25815	−	8.75061i	−0.0484980	−	0.337311i	−0.999596	−	0.0284219i	$-0.990952\pi$
$673$	−1.25815	−	8.75061i	−0.0484980	−	0.337311i	0.951098	−	0.308889i	$-0.0999573\pi$
$674$	24.3741	−	5.91308i	0.938853	−	0.227763i
$675$	12.5075	−	0.595803i	0.481412	−	0.0229325i
$676$	16.0306	+	1.53074i	0.616561	+	0.0588744i
$677$	20.6498	+	19.6895i	0.793634	+	0.756729i	0.973922	−	0.226885i	$-0.0728542\pi$
$677$	20.6498	+	19.6895i	0.793634	+	0.756729i	−0.180287	+	0.983614i	$0.557703\pi$
$678$	2.02927	−	2.34190i	0.0779337	−	0.0899403i
$679$	0.857661	+	0.360555i	0.0329140	+	0.0138368i
$680$	19.6018	−	5.75559i	0.751693	−	0.220717i
$681$	3.16997	+	2.25732i	0.121473	+	0.0865008i
$682$	0.0756270	+	1.58761i	0.00289591	+	0.0607926i
$683$	4.93973	−	4.71002i	0.189013	−	0.180224i	−0.589663	−	0.807649i	$-0.700740\pi$
$683$	4.93973	−	4.71002i	0.189013	−	0.180224i	0.778677	+	0.627425i	$0.215891\pi$
$684$	2.76154	−	2.17170i	0.105590	−	0.0830371i
$685$	−29.6988	−	13.5630i	−1.13473	−	0.518215i
$686$	−17.9811	−	4.43629i	−0.686521	−	0.169378i
$687$	3.48133	−	5.41706i	0.132821	−	0.206674i
$688$	5.84882	+	2.02429i	0.222984	+	0.0771755i
$689$	20.2488	−	35.0720i	0.771419	−	1.33614i
$690$	−19.5657	+	4.49220i	−0.744855	+	0.171015i
$691$	−30.7004	+	17.7249i	−1.16790	+	0.674287i	−0.953184	−	0.302390i	$-0.902215\pi$
$691$	−30.7004	+	17.7249i	−1.16790	+	0.674287i	−0.214715	+	0.976677i	$0.568882\pi$
$692$	−7.29896	+	6.32458i	−0.277465	+	0.240425i
$693$	0.519172	+	0.135425i	0.0197217	+	0.00514438i
$694$	−0.129048	+	0.897552i	−0.00489861	+	0.0340706i
$695$	−0.346335	−	3.62699i	−0.0131372	−	0.137579i
$696$	1.84643	−	4.61217i	0.0699889	−	0.174824i
$697$	9.72712	+	10.2015i	0.368441	+	0.386410i
$698$	0.727938	−	1.41200i	0.0275528	−	0.0534451i
$699$	−2.13067	+	0.973044i	−0.0805893	+	0.0368039i
$700$	14.2775	−	29.8947i	0.539639	−	1.12991i
$701$	−4.40710	−	3.81877i	−0.166454	−	0.144233i	0.567651	−	0.823269i	$-0.307852\pi$
$701$	−4.40710	−	3.81877i	−0.166454	−	0.144233i	−0.734105	+	0.679036i	$0.762398\pi$
$702$	−5.29728	−	1.02097i	−0.199933	−	0.0385339i
$703$	3.68484	+	0.893932i	0.138976	+	0.0337153i
$704$	−0.0192769	+	0.201876i	−0.000726524	+	0.00760850i
$705$	−28.4010	−	14.6417i	−1.06964	−	0.551439i
$706$	10.0421	−	34.2001i	0.377938	−	1.28714i
$707$	23.9048	+	1.55032i	0.899034	+	0.0583058i
$708$	4.17083	−	9.13283i	0.156749	−	0.343233i
$709$	−9.41685	−	23.5222i	−0.353657	−	0.883393i	−0.993389	−	0.114795i	$-0.963379\pi$
$709$	−9.41685	−	23.5222i	−0.353657	−	0.883393i	0.639732	−	0.768598i	$-0.279045\pi$
$710$	−0.0994160	+	0.0512525i	−0.00373102	+	0.00192347i
$711$	−3.07704	−	15.9652i	−0.115398	−	0.598742i
$712$	−8.94975	−	15.5014i	−0.335406	−	0.580940i
$713$	37.5640	−	1.32597i	1.40678	−	0.0496580i
$714$	−2.66098	+	12.6355i	−0.0995846	+	0.472871i
$715$	2.99892	+	3.46094i	0.112153	+	0.129432i
$716$	−0.242803	+	5.09705i	−0.00907396	+	0.190486i
$717$	−17.5152	+	22.2724i	−0.654116	+	0.831777i
$718$	−9.94412	+	7.08117i	−0.371111	+	0.264267i
$719$	−12.3637	−	15.7217i	−0.461087	−	0.586320i	0.498796	−	0.866719i	$-0.333776\pi$
$719$	−12.3637	−	15.7217i	−0.461087	−	0.586320i	−0.959883	+	0.280399i	$0.909533\pi$
$720$	−4.01633	−	1.17930i	−0.149680	−	0.0439499i
$721$	−2.97666	+	18.4494i	−0.110856	+	0.687093i
$722$	2.76567	+	6.05596i	0.102927	+	0.225380i
$723$	16.2800	−	17.0740i	0.605461	−	0.634990i
$724$	1.55260	+	4.48595i	0.0577020	+	0.166719i
$725$	−20.3462	−	58.7866i	−0.755640	−	2.18328i
$726$	7.56249	−	7.93131i	0.280670	−	0.294359i
$727$	−2.15718	−	4.72357i	−0.0800054	−	0.175187i	0.865402	−	0.501078i	$-0.167063\pi$
$727$	−2.15718	−	4.72357i	−0.0800054	−	0.175187i	−0.945407	+	0.325891i	$0.894336\pi$
$728$	−9.01437	+	11.0664i	−0.334095	+	0.410149i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	27.5068	+	34.9778i	1.01807	+	1.29459i
$731$	−24.6055	+	17.5215i	−0.910069	+	0.648057i
$732$	3.58502	−	4.55872i	0.132506	−	0.168495i
$733$	−0.449022	+	9.42613i	−0.0165850	+	0.348162i	0.975289	+	0.220935i	$0.0709108\pi$
$733$	−0.449022	+	9.42613i	−0.0165850	+	0.348162i	−0.991874	+	0.127227i	$0.959392\pi$
$734$	3.20989	+	3.70441i	0.118479	+	0.136732i
$735$	17.3117	+	23.6404i	0.638550	+	0.871988i
$736$	4.76814	+	0.514633i	0.175756	+	0.0189696i
$737$	−1.12279	−	1.94473i	−0.0413585	−	0.0716349i
$738$	−0.546586	−	2.83596i	−0.0201201	−	0.104393i
$739$	−13.1611	+	6.78503i	−0.484140	+	0.249591i	−0.682975	−	0.730442i	$-0.739314\pi$
$739$	−13.1611	+	6.78503i	−0.484140	+	0.249591i	0.198836	+	0.980033i	$0.436284\pi$
$740$	−1.67908	−	4.19415i	−0.0617244	−	0.154180i
$741$	−7.87326	+	17.2400i	−0.289232	+	0.633329i
$742$	8.79664	+	17.8070i	0.322935	+	0.653715i
$743$	10.4120	−	35.4601i	0.381980	−	1.30091i	−0.514374	−	0.857566i	$-0.671976\pi$
$743$	10.4120	−	35.4601i	0.381980	−	1.30091i	0.896354	−	0.443339i	$-0.146206\pi$
$744$	6.96626	+	3.59136i	0.255395	+	0.131666i
$745$	−3.55841	+	37.2654i	−0.130370	+	1.36530i
$746$	−20.9155	−	5.07405i	−0.765772	−	0.185774i
$747$	−4.97785	−	0.959402i	−0.182130	−	0.0351027i
$748$	−0.747997	−	0.648143i	−0.0273495	−	0.0236985i
$749$	−0.897423	−	0.428603i	−0.0327911	−	0.0156608i
$750$	−28.6395	+	13.0792i	−1.04577	+	0.477585i
$751$	−4.57855	+	8.88115i	−0.167074	+	0.324078i	−0.957477	−	0.288509i	$-0.906841\pi$
$751$	−4.57855	+	8.88115i	−0.167074	+	0.324078i	0.790404	+	0.612586i	$0.209871\pi$
$752$	5.26773	+	5.52463i	0.192094	+	0.201463i
$753$	−4.10389	+	10.2510i	−0.149554	+	0.373568i
$754$	2.54764	+	26.6801i	0.0927795	+	0.971630i
$755$	−13.3879	+	93.1150i	−0.487236	+	3.38880i
$756$	1.85837	−	1.88320i	0.0675883	−	0.0684915i
$757$	26.3447	−	22.8278i	0.957513	−	0.829690i	−0.0279451	−	0.999609i	$-0.508896\pi$
$757$	26.3447	−	22.8278i	0.957513	−	0.829690i	0.985458	+	0.169920i	$0.0543509\pi$
$758$	−7.11061	+	4.10532i	−0.258269	+	0.149112i
$759$	0.695562	+	0.679767i	0.0252473	+	0.0246740i
$760$	−7.35288	+	12.7356i	−0.266717	+	0.461967i
$761$	11.5826	+	4.00877i	0.419869	+	0.145318i	0.528830	−	0.848728i	$-0.322631\pi$
$761$	11.5826	+	4.00877i	0.419869	+	0.145318i	−0.108961	+	0.994046i	$0.534752\pi$
$762$	10.3230	−	16.0629i	0.373964	−	0.581899i
$763$	31.6605	+	11.5700i	1.14619	+	0.418862i
$764$	1.96714	+	0.898363i	0.0711687	+	0.0325016i
$765$	16.0585	−	12.6285i	0.580596	−	0.456586i
$766$	1.20630	−	1.15020i	0.0435853	−	0.0415585i
$767$	2.57724	+	54.1029i	0.0930586	+	1.95354i
$768$	0.814576	+	0.580057i	0.0293935	+	0.0209310i
$769$	−22.9956	+	6.75212i	−0.829242	+	0.243488i	−0.668691	−	0.743540i	$-0.733145\pi$
$769$	−22.9956	+	6.75212i	−0.829242	+	0.243488i	−0.160551	+	0.987028i	$0.551327\pi$
$770$	−2.22821	+	0.281427i	−0.0802991	+	0.0101419i
$771$	−4.07214	+	4.69950i	−0.146654	+	0.169248i
$772$	17.1638	+	16.3656i	0.617737	+	0.589011i
$773$	31.9881	+	3.05449i	1.15053	+	0.109862i	0.652842	−	0.757494i	$-0.273576\pi$
$773$	31.9881	+	3.05449i	1.15053	+	0.109862i	0.497688	+	0.867356i	$0.334182\pi$
$774$	6.18221	−	0.294495i	0.222215	−	0.0105854i
$775$	95.3721	−	23.1370i	3.42587	−	0.831107i
$776$	0.0500444	+	0.348066i	0.00179649	+	0.0124948i
$777$	2.83751	+	0.320180i	0.101795	+	0.0114864i
$778$	−24.5375	−	3.52796i	−0.879711	−	0.126483i
$779$	−10.1351	−	0.482794i	−0.363127	−	0.0172979i
$780$	22.1738	−	4.27365i	0.793949	−	0.153021i
$781$	0.00469283	+	0.00270941i	0.000167923	+	9.69502e-5i
$782$	−15.5444	+	17.4991i	−0.555868	+	0.625765i
$783$		−	4.96804i		−	0.177543i
$784$	−2.06110	−	6.68968i	−0.0736108	−	0.238917i
$785$	59.6952	+	38.3638i	2.13061	+	1.36926i
$786$	0.240405	−	0.0962437i	0.00857497	−	0.00343290i
$787$	6.81707	+	9.57324i	0.243002	+	0.341249i	0.918007	−	0.396565i	$-0.129798\pi$
$787$	6.81707	+	9.57324i	0.243002	+	0.341249i	−0.675004	+	0.737814i	$0.735858\pi$
$788$	−6.36141	−	2.54672i	−0.226616	−	0.0907232i
$789$	−4.07074	−	16.7798i	−0.144922	−	0.597377i
$790$	36.7952	+	57.2544i	1.30911	+	2.03702i
$791$	−5.55502	−	6.02984i	−0.197514	−	0.214396i
$792$	0.0571338	+	0.194580i	0.00203016	+	0.00691410i
$793$	−5.92110	+	30.7216i	−0.210264	+	1.09096i
$794$	−0.827786	+	0.286500i	−0.0293770	+	0.0101675i
$795$	7.40820	−	30.5370i	0.262742	−	1.08304i
$796$	3.15108	−	4.42508i	0.111687	−	0.156843i
$797$	−3.70187	+	2.37905i	−0.131127	+	0.0842702i	−0.604560	−	0.796560i	$-0.706651\pi$
$797$	−3.70187	+	2.37905i	−0.131127	+	0.0842702i	0.473433	+	0.880830i	$0.343015\pi$
$798$	−4.89031	−	7.90454i	−0.173115	−	0.279818i
$799$	−36.8763	+	5.30201i	−1.30459	+	0.187572i
$800$	12.4649	−	1.19026i	0.440702	−	0.0420819i
$801$	−14.0700	−	11.0647i	−0.497138	−	0.390953i
$802$	−2.92913	−	5.68173i	−0.103431	−	0.200629i
$803$	0.705095	−	2.03724i	0.0248823	−	0.0718926i
$804$	−11.0732			−0.390520
$805$	6.00593	+	52.7723i	0.211681	+	1.85998i
$806$	−42.2816			−1.48930
$807$	−9.42717	+	27.2380i	−0.331852	+	0.958823i
$808$	4.14886	+	8.04766i	0.145956	+	0.283116i
$809$	−27.8913	−	21.9340i	−0.980607	−	0.771158i	−0.00713716	−	0.999975i	$-0.502272\pi$
$809$	−27.8913	−	21.9340i	−0.980607	−	0.771158i	−0.973469	+	0.228817i	$0.926514\pi$
$810$	−4.16693	+	0.397894i	−0.146411	+	0.0139806i
$811$	−15.4232	+	2.21751i	−0.541580	+	0.0778675i	−0.407676	−	0.913127i	$-0.633661\pi$
$811$	−15.4232	+	2.21751i	−0.541580	+	0.0778675i	−0.133904	+	0.990994i	$0.542752\pi$
$812$	−11.5779	−	6.22264i	−0.406306	−	0.218372i
$813$	−16.8551	+	10.8321i	−0.591135	+	0.379899i
$814$	−0.126959	+	0.178289i	−0.00444991	+	0.00624902i
$815$	−2.39789	+	9.88423i	−0.0839943	+	0.346229i
$816$	−4.61209	+	1.59626i	−0.161455	+	0.0558803i
$817$	4.11504	−	21.3509i	0.143967	−	0.746972i
$818$	−9.83086	−	33.4808i	−0.343728	−	1.17063i
$819$	−4.25568	+	13.6240i	−0.148705	+	0.476062i
$820$	6.53606	+	10.1703i	0.228249	+	0.355162i
$821$	1.72928	+	7.12818i	0.0603522	+	0.248775i	0.993994	−	0.109432i	$-0.0349033\pi$
$821$	1.72928	+	7.12818i	0.0603522	+	0.248775i	−0.933642	+	0.358207i	$0.883388\pi$
$822$	7.24112	+	2.89891i	0.252563	+	0.101111i
$823$	31.0982	+	43.6714i	1.08402	+	1.52229i	0.832170	+	0.554521i	$0.187099\pi$
$823$	31.0982	+	43.6714i	1.08402	+	1.52229i	0.251847	+	0.967767i	$0.418962\pi$
$824$	−6.55744	+	2.62520i	−0.228439	+	0.0914533i
$825$	2.13621	+	1.37286i	0.0743734	+	0.0477969i
$826$	−22.7735	−	13.6747i	−0.792392	−	0.475804i
$827$		−	12.1981i		−	0.424169i	−0.977251	−	0.212084i	$-0.931975\pi$
$827$		−	12.1981i		−	0.424169i	0.977251	−	0.212084i	$-0.0680252\pi$
$828$	4.61786	−	1.29437i	0.160482	−	0.0449825i
$829$	−11.5146	−	6.64797i	−0.399920	−	0.230894i	0.286530	−	0.958071i	$-0.407498\pi$
$829$	−11.5146	−	6.64797i	−0.399920	−	0.230894i	−0.686449	+	0.727178i	$0.740832\pi$
$830$	20.8367	−	4.01595i	0.723253	−	0.139396i
$831$	−24.2330	−	1.15436i	−0.840633	−	0.0400443i
$832$	−5.33986	−	0.767755i	−0.185126	−	0.0266171i
$833$	32.4301	+	10.7443i	1.12364	+	0.372269i
$834$	0.123874	+	0.861562i	0.00428940	+	0.0298334i
$835$	2.41251	−	0.585269i	0.0834883	−	0.0202541i
$836$	0.711646	−	0.0338999i	0.0246128	−	0.00117245i
$837$	7.80203	+	0.745003i	0.269677	+	0.0257511i
$838$	−0.905389	−	0.863286i	−0.0312761	−	0.0298217i
$839$	−0.724848	+	0.836520i	−0.0250245	+	0.0288799i	−0.768124	−	0.640301i	$-0.778810\pi$
$839$	−0.724848	+	0.836520i	−0.0250245	+	0.0288799i	0.743099	+	0.669181i	$0.233355\pi$
$840$	−4.29194	+	10.2093i	−0.148086	+	0.352256i
$841$	4.14364	−	1.21668i	0.142884	−	0.0419545i
$842$	20.0995	+	14.3128i	0.692675	+	0.493252i
$843$	−1.06691	−	22.3971i	−0.0367462	−	0.771399i
$844$	18.5119	−	17.6510i	0.637205	−	0.607574i
$845$	−52.9858	+	41.6685i	−1.82277	+	1.43344i
$846$	6.94369	+	3.17108i	0.238729	+	0.109024i
$847$	−18.6085	−	22.2352i	−0.639394	−	0.764010i
$848$	−4.05851	+	6.31516i	−0.139370	+	0.216864i
$849$	−17.4957	−	6.05531i	−0.600450	−	0.207818i
$850$	−30.5560	+	52.9246i	−1.04806	+	1.81530i
$851$	4.17901	+	3.05411i	0.143255	+	0.104694i
$852$	0.0231408	−	0.0133603i	0.000792791	−	0.000457718i
$853$	24.1891	−	20.9600i	0.828218	−	0.717655i	−0.133691	−	0.991023i	$-0.542683\pi$
$853$	24.1891	−	20.9600i	0.828218	−	0.717655i	0.961910	+	0.273368i	$0.0881376\pi$
$854$	−10.9216	−	10.7776i	−0.373731	−	0.368803i
$855$	−2.09285	+	14.5561i	−0.0715738	+	0.497807i
$856$	−0.0357309	−	0.374191i	−0.00122126	−	0.0127896i
$857$	4.01901	−	10.0390i	0.137287	−	0.342925i	−0.843753	−	0.536731i	$-0.819659\pi$
$857$	4.01901	−	10.0390i	0.137287	−	0.342925i	0.981040	+	0.193806i	$0.0620832\pi$
$858$	−0.754967	−	0.791786i	−0.0257741	−	0.0270311i
$859$	−1.56150	+	3.02888i	−0.0532776	+	0.103344i	−0.913971	−	0.405780i	$-0.867000\pi$
$859$	−1.56150	+	3.02888i	−0.0532776	+	0.103344i	0.860693	+	0.509124i	$0.170030\pi$
$860$	−23.5662	+	10.7623i	−0.803599	+	0.366992i
$861$	−7.61807	+	0.595698i	−0.259623	+	0.0203013i
$862$	22.2598	+	19.2882i	0.758173	+	0.656960i
$863$	39.9813	+	7.70577i	1.36098	+	0.262308i	0.816926	−	0.576742i	$-0.195676\pi$
$863$	39.9813	+	7.70577i	1.36098	+	0.262308i	0.544055	+	0.839050i	$0.316888\pi$
$864$	0.971812	+	0.235759i	0.0330617	+	0.00802068i
$865$	3.84282	−	40.2438i	0.130660	−	1.36833i
$866$	12.2506	+	6.31563i	0.416293	+	0.214614i
$867$	1.92126	−	6.54320i	0.0652493	−	0.222219i
$868$	11.5085	−	17.2494i	0.390625	−	0.585481i
$869$	1.36973	−	2.99928i	0.0464647	−	0.101744i
$870$	7.72896	+	19.3060i	0.262036	+	0.654535i
$871$	53.0965	−	27.3731i	1.79910	−	0.927503i
$872$	2.41117	+	12.5103i	0.0816524	+	0.423653i
$873$	0.175823	+	0.304534i	0.00595070	+	0.0103069i
$874$	−0.594368	−	16.8381i	−0.0201048	−	0.569558i
$875$	25.8900	+	79.1752i	0.875241	+	2.67661i
$876$	−6.96149	−	8.03399i	−0.235207	−	0.271443i
$877$	−2.17608	+	45.6815i	−0.0734809	+	1.54255i	0.597978	+	0.801512i	$0.295971\pi$
$877$	−2.17608	+	45.6815i	−0.0734809	+	1.54255i	−0.671459	+	0.741041i	$0.734332\pi$
$878$	11.1427	−	14.1691i	0.376047	−	0.478183i
$879$	0.331501	−	0.236060i	0.0111812	−	0.00796212i
$880$	−0.524740	−	0.667261i	−0.0176890	−	0.0224934i
$881$	−29.6465	−	8.70501i	−0.998817	−	0.293279i	−0.258847	−	0.965918i	$-0.583342\pi$
$881$	−29.6465	−	8.70501i	−0.998817	−	0.293279i	−0.739971	+	0.672639i	$0.765161\pi$
$882$	−4.39976	−	5.44445i	−0.148148	−	0.183324i
$883$	−17.2184	−	37.7030i	−0.579445	−	1.26881i	−0.941614	−	0.336696i	$-0.890691\pi$
$883$	−17.2184	−	37.7030i	−0.579445	−	1.26881i	0.362168	−	0.932113i	$-0.382037\pi$
$884$	18.1693	−	19.0554i	0.611098	−	0.640901i
$885$	13.7456	+	39.7154i	0.462055	+	1.33502i
$886$	3.72733	+	10.7694i	0.125222	+	0.361805i
$887$	−3.83637	+	4.02347i	−0.128813	+	0.135095i	−0.784981	−	0.619519i	$-0.787328\pi$
$887$	−3.83637	+	4.02347i	−0.128813	+	0.135095i	0.656169	+	0.754614i	$0.272176\pi$
$888$	0.448352	+	0.981753i	0.0150457	+	0.0329455i
$889$	−39.1681	−	31.9052i	−1.31366	−	1.07006i
$890$	71.8903	+	21.1089i	2.40977	+	0.707572i
$891$	0.125359	+	0.159407i	0.00419969	+	0.00534035i
$892$	−5.88134	+	4.18808i	−0.196922	+	0.140227i
$893$	16.5777	−	21.0803i	0.554752	−	0.705425i
$894$	0.425531	−	8.93299i	0.0142319	−	0.298764i
$895$	−13.9877	−	16.1427i	−0.467559	−	0.539592i
$896$	1.76666	−	1.96950i	0.0590200	−	0.0657962i
$897$	−18.9432	+	17.6220i	−0.632495	+	0.588383i
$898$	−1.87748	−	3.25190i	−0.0626524	−	0.108517i
$899$	−7.36889	−	38.2334i	−0.245766	−	1.27516i
$900$	11.1297	−	5.73775i	0.370989	−	0.191258i
$901$	−13.6167	−	34.0129i	−0.453638	−	1.13313i
$902$	0.243309	−	0.532772i	0.00810130	−	0.0177394i
$903$	1.05976	−	16.3408i	0.0352667	−	0.543788i
$904$	0.873028	−	2.97326i	0.0290365	−	0.0988892i
$905$	−17.6616	−	9.10520i	−0.587092	−	0.302667i
$906$	2.13627	−	22.3720i	0.0709727	−	0.743259i
$907$	13.5502	+	3.28724i	0.449926	+	0.109151i	0.454318	−	0.890839i	$-0.349883\pi$
$907$	13.5502	+	3.28724i	0.449926	+	0.109151i	−0.00439193	+	0.999990i	$0.501398\pi$
$908$	3.82123	+	0.736481i	0.126812	+	0.0244410i
$909$	6.84268	+	5.92922i	0.226957	+	0.196660i
$910$	−4.65764	−	59.5642i	−0.154399	−	1.97453i
$911$	−36.8953	+	16.8495i	−1.22240	+	0.558249i	−0.918865	−	0.394572i	$-0.870893\pi$
$911$	−36.8953	+	16.8495i	−1.22240	+	0.558249i	−0.303531	+	0.952822i	$0.598166\pi$
$912$	1.60983	−	3.12264i	0.0533068	−	0.103401i
$913$	−0.709442	−	0.744042i	−0.0234791	−	0.0246242i
$914$	−14.9751	+	37.4059i	−0.495331	+	1.23728i
$915$	2.30759	+	24.1661i	0.0762865	+	0.798908i
$916$	0.916404	−	6.37373i	0.0302788	−	0.210594i
$917$	−0.181713	−	0.660593i	−0.00600068	−	0.0218147i
$918$	−3.68845	+	3.19606i	−0.121737	+	0.105486i
$919$	−15.8110	+	9.12848i	−0.521557	+	0.301121i	−0.737571	−	0.675269i	$-0.764027\pi$
$919$	−15.8110	+	9.12848i	−0.521557	+	0.301121i	0.216015	+	0.976390i	$0.430694\pi$
$920$	−15.9315	+	12.2141i	−0.525246	+	0.402688i
$921$	11.2184	−	19.4309i	0.369660	−	0.640270i
$922$	−7.77994	−	2.69266i	−0.256219	−	0.0886782i
$923$	−0.0779344	+	0.121268i	−0.00256524	+	0.00399159i
$924$	0.528513	−	0.0924847i	0.0173868	−	0.00304252i
$925$	12.2932	+	5.61409i	0.404196	+	0.184590i
$926$	−22.4726	+	17.6726i	−0.738495	+	0.580759i
$927$	−5.11203	+	4.87431i	−0.167901	+	0.160093i
$928$	−0.236389	−	4.96241i	−0.00775985	−	0.162899i
$929$	0.550576	+	0.392064i	0.0180638	+	0.0128632i	0.589053	−	0.808094i	$-0.299501\pi$
$929$	0.550576	+	0.392064i	0.0180638	+	0.0128632i	−0.570989	+	0.820957i	$0.693440\pi$
$930$	−31.4780	+	9.24278i	−1.03221	+	0.303083i
$931$	−22.2323	+	10.5120i	−0.728635	+	0.344517i
$932$	−1.53391	+	1.77022i	−0.0502448	+	0.0579856i
$933$	1.98703	+	1.89463i	0.0650523	+	0.0620273i
$934$	22.3291	+	2.13217i	0.730629	+	0.0697667i
$935$	4.13826	−	0.197129i	0.135335	−	0.00644682i
$936$	−5.24270	+	1.27186i	−0.171363	+	0.0415722i
$937$	−1.96729	−	13.6828i	−0.0642687	−	0.446998i	−0.996393	−	0.0848598i	$-0.972956\pi$
$937$	−1.96729	−	13.6828i	−0.0642687	−	0.446998i	0.932124	−	0.362139i	$-0.117953\pi$
$938$	−3.28496	+	29.1121i	−0.107258	+	0.950543i
$939$	−11.1043	−	1.59656i	−0.362376	−	0.0521018i
$940$	−31.9168	−	1.52039i	−1.04101	−	0.0495895i
$941$	2.47390	−	0.476805i	0.0806467	−	0.0155434i	−0.148768	−	0.988872i	$-0.547531\pi$
$941$	2.47390	−	0.476805i	0.0806467	−	0.0155434i	0.229415	+	0.973329i	$0.426319\pi$
$942$	−14.6810	−	8.47608i	−0.478333	−	0.276166i
$943$	−12.5276	−	5.90867i	−0.407954	−	0.192413i
$944$		−	10.0401i		−	0.326779i
$945$	−0.190070	+	11.0732i	−0.00618298	+	0.360211i
$946$	1.05589	+	0.678580i	0.0343300	+	0.0220625i
$947$	27.9399	−	11.1854i	0.907923	−	0.363478i	0.129764	−	0.991545i	$-0.458578\pi$
$947$	27.9399	−	11.1854i	0.907923	−	0.363478i	0.778159	+	0.628067i	$0.216154\pi$
$948$	−9.43117	−	13.2442i	−0.306310	−	0.430152i
$949$	53.2410	+	21.3145i	1.72827	+	0.691897i
$950$	−10.3712	−	42.7507i	−0.336486	−	1.38702i
$951$	2.65628	+	4.13326i	0.0861359	+	0.134030i
$952$	2.82846	+	12.5990i	0.0916708	+	0.408337i
$953$	−16.2712	−	55.4145i	−0.527075	−	1.79505i	−0.602763	−	0.797920i	$-0.705934\pi$
$953$	−16.2712	−	55.4145i	−0.527075	−	1.79505i	0.0756882	−	0.997132i	$-0.475885\pi$
$954$	−1.42068	+	7.37119i	−0.0459962	+	0.238651i
$955$	−8.55440	+	2.96070i	−0.276814	+	0.0958062i
$956$	−6.68009	+	27.5357i	−0.216050	+	0.890569i
$957$	0.584403	−	0.820679i	0.0188911	−	0.0265288i
$958$	8.72488	−	5.60714i	0.281888	−	0.181158i
$959$	9.76957	−	18.1774i	0.315476	−	0.586979i
$960$	−4.14328	+	0.595714i	−0.133724	+	0.0192266i
$961$	30.2889	−	2.89223i	0.977060	−	0.0932979i
$962$	−4.57679	−	3.59923i	−0.147562	−	0.116044i
$963$	−0.172244	−	0.334107i	−0.00555049	−	0.0107665i
$964$	7.71604	−	22.2940i	0.248517	−	0.718043i
$965$	−99.2706			−3.19563
$966$	−2.03305	−	12.5246i	−0.0654125	−	0.402974i
$967$	20.9394			0.673365			0.336683	−	0.941618i	$-0.390695\pi$
$967$	20.9394			0.673365			0.336683	+	0.941618i	$0.390695\pi$
$968$	3.58430	−	10.3561i	0.115204	−	0.332859i
$969$	7.85680	+	15.2401i	0.252397	+	0.489582i
$970$	−1.15703	−	0.909898i	−0.0371500	−	0.0292151i
$971$	−30.3617	+	2.89919i	−0.974353	+	0.0930395i	−0.570072	−	0.821595i	$-0.693085\pi$
$971$	−30.3617	+	2.89919i	−0.974353	+	0.0930395i	−0.404282	+	0.914635i	$0.632478\pi$
$972$	0.989821	−	0.142315i	0.0317485	−	0.00456475i
$973$	2.30185	−	0.0700823i	0.0737940	−	0.00224674i
$974$	19.3676	−	12.4468i	0.620577	−	0.398820i
$975$	−39.1836	+	55.0257i	−1.25488	+	1.76223i
$976$	1.36729	−	5.63603i	0.0437657	−	0.180405i
$977$	−6.17143	+	2.13595i	−0.197441	+	0.0683351i	−0.423999	−	0.905663i	$-0.639374\pi$
$977$	−6.17143	+	2.13595i	−0.197441	+	0.0683351i	0.226558	+	0.973998i	$0.427253\pi$
$978$	0.459846	−	2.38591i	0.0147042	−	0.0762928i
$979$	−1.02267	−	3.48289i	−0.0326846	−	0.111314i
$980$	25.5678	+	14.3125i	0.816734	+	0.457196i
$981$	6.88807	+	10.7180i	0.219919	+	0.342201i
$982$	−3.78301	−	15.5938i	−0.120721	−	0.497618i
$983$	41.8902	+	16.7703i	1.33609	+	0.534890i	0.926127	−	0.377212i	$-0.123117\pi$
$983$	41.8902	+	16.7703i	1.33609	+	0.534890i	0.409963	+	0.912102i	$0.365541\pi$
$984$	−1.67529	−	2.35262i	−0.0534063	−	0.0749987i
$985$	26.6281	−	10.6603i	0.848442	−	0.339665i
$986$	20.3975	+	13.1087i	0.649590	+	0.417466i
$987$	10.3969	−	17.3147i	0.330936	−	0.551133i
$988$			18.9528i			0.602968i
$989$	16.3538	−	24.7709i	0.520022	−	0.787670i
$990$	−0.735147	−	0.424437i	−0.0233645	−	0.0134895i
$991$	−7.55977	+	1.45703i	−0.240144	+	0.0462840i	−0.307903	−	0.951418i	$-0.599627\pi$
$991$	−7.55977	+	1.45703i	−0.240144	+	0.0462840i	0.0677590	+	0.997702i	$0.478415\pi$
$992$	7.82864	+	0.372924i	0.248559	+	0.0118403i
$993$	13.2037	+	1.89840i	0.419006	+	0.0602440i
$994$	−0.0282603	−	0.0648022i	−0.000896363	−	0.00205540i
$995$	3.23614	+	22.5078i	0.102592	+	0.713546i
$996$	−4.92656	+	1.19517i	−0.156104	+	0.0378704i
$997$	−36.9352	+	1.75944i	−1.16975	+	0.0557220i	−0.623447	−	0.781866i	$-0.714268\pi$
$997$	−36.9352	+	1.75944i	−1.16975	+	0.0557220i	−0.546302	+	0.837588i	$0.683965\pi$
$998$	3.50094	+	0.334299i	0.110820	+	0.0105820i
$999$	0.781116	+	0.744792i	0.0247134	+	0.0235642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.493.8	yes	320
7.5	odd	6	inner	966.2.be.a.355.8	yes	320
23.7	odd	22	inner	966.2.be.a.283.8	yes	320
161.145	even	66	inner	966.2.be.a.145.8	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.145.8	✓	320	161.145	even	66	inner
966.2.be.a.283.8	yes	320	23.7	odd	22	inner
966.2.be.a.355.8	yes	320	7.5	odd	6	inner
966.2.be.a.493.8	yes	320	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(4.16693 - 0.397894i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(0.0805154 + 2.64453i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(4.16693 - 0.397894i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(0.0805154 + 2.64453i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(0.986860 - 4.06789i) q^{10} +(-0.191641 + 0.0663276i) q^{11} +(-0.189251 + 0.981929i) q^{12} +(-1.51988 - 5.17624i) q^{13} +(2.52541 + 0.788853i) q^{14} +(-2.26306 - 3.52139i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-4.53091 - 1.81390i) q^{17} +(0.580057 + 0.814576i) q^{18} +(3.26152 - 1.30572i) q^{19} +(-3.52139 - 2.26306i) q^{20} +(2.31365 - 1.28336i) q^{21} +0.202795i q^{22} +(4.79547 + 0.0590619i) q^{23} +(0.866025 + 0.500000i) q^{24} +(12.2954 - 2.36973i) q^{25} +(-5.38866 - 0.256693i) q^{26} +(0.989821 + 0.142315i) q^{27} +(1.57145 - 2.12851i) q^{28} +(-0.707026 - 4.91747i) q^{29} +(-4.06789 + 0.986860i) q^{30} +(7.82864 - 0.372924i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.146769 + 0.139944i) q^{33} +(-3.19606 + 3.68845i) q^{34} +(1.38774 + 10.9875i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.879160 + 0.626047i) q^{37} +(-0.167164 - 3.50920i) q^{38} +(-3.90438 + 3.72281i) q^{39} +(-3.29033 + 2.58754i) q^{40} +(-2.62715 - 1.19978i) q^{41} +(-0.456051 - 2.60615i) q^{42} +(3.34614 - 5.20670i) q^{43} +(0.191641 + 0.0663276i) q^{44} +(-2.09294 + 3.62508i) q^{45} +(1.62426 - 4.51240i) q^{46} +(6.61082 - 3.81676i) q^{47} +(0.755750 - 0.654861i) q^{48} +(-6.98703 + 0.425850i) q^{49} +(1.78201 - 12.3942i) q^{50} +(0.463923 + 4.85842i) q^{51} +(-2.00503 + 5.00833i) q^{52} +(5.18032 + 5.43296i) q^{53} +(0.458227 - 0.888835i) q^{54} +(-0.772164 + 0.352635i) q^{55} +(-1.49747 - 2.18119i) q^{56} +(-2.65508 - 2.30064i) q^{57} +(-4.87826 - 0.940208i) q^{58} +(-9.75712 - 2.36705i) q^{59} +(-0.397894 + 4.16693i) q^{60} +(-5.15481 - 2.65749i) q^{61} +(2.20808 - 7.52004i) q^{62} +(-2.20087 - 1.46839i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-8.39283 - 20.9643i) q^{65} +(0.180251 - 0.0929259i) q^{66} +(2.09561 + 10.8731i) q^{67} +(2.44026 + 4.22665i) q^{68} +(-2.14491 - 4.28945i) q^{69} +(10.8371 + 2.28225i) q^{70} +(-0.0174983 - 0.0201942i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-6.57133 + 8.35613i) q^{73} +(0.879160 - 0.626047i) q^{74} +(-7.74036 - 9.84267i) q^{75} +(-3.37087 - 0.989776i) q^{76} +(-0.190835 - 0.501459i) q^{77} +(2.24107 + 4.90725i) q^{78} +(-11.2200 + 11.7672i) q^{79} +(1.36907 + 3.95566i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-1.99305 + 2.09025i) q^{82} +(2.10593 + 4.61134i) q^{83} +(-2.61197 - 0.421419i) q^{84} +(-19.6018 - 5.75559i) q^{85} +(-3.82592 - 4.86505i) q^{86} +(-4.04685 + 2.88175i) q^{87} +(0.125359 - 0.159407i) q^{88} +(-0.851693 + 17.8792i) q^{89} +(2.74117 + 3.16348i) q^{90} +(13.5663 - 4.43613i) q^{91} +(-3.73298 - 3.01079i) q^{92} +(-3.91876 - 6.78749i) q^{93} +(-1.44465 - 7.49557i) q^{94} +(13.0710 - 6.73857i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(0.146079 - 0.319868i) q^{97} +(-1.88281 + 6.74204i) q^{98} +(0.0571338 - 0.194580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

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