LMFDB - Embedded newform 966.2.y.c.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, 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:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.4
Character	$\chi$	$=$	966.121
Dual form			966.2.y.c.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0167727 - 0.352103i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.88460 + 1.85696i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0167727 - 0.352103i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.88460 + 1.85696i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(0.277085 - 0.217902i) q^{10} +(3.07980 - 4.32497i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(-0.365162 - 2.53975i) q^{13} +(-2.60581 - 0.458008i) q^{14} +(-0.338223 + 0.0993113i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(3.67076 + 0.707481i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(1.72332 - 0.332143i) q^{19} +(0.338223 + 0.0993113i) q^{20} +(2.24892 + 1.39368i) q^{21} +5.30947 q^{22} +(4.54671 + 1.52560i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.85366 - 0.463469i) q^{25} +(1.85701 - 1.77065i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-1.13843 - 2.38830i) q^{28} +(2.48070 - 2.86288i) q^{29} +(-0.277085 - 0.217902i) q^{30} +(-0.649409 - 0.619210i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-4.92914 - 1.97333i) q^{33} +(1.55295 + 3.40049i) q^{34} +(0.685449 + 0.632426i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.873693 + 0.450420i) q^{37} +(1.27018 + 1.21112i) q^{38} +(-2.38207 + 0.953638i) q^{39} +(0.115292 + 0.333115i) q^{40} +(0.510708 - 0.328212i) q^{41} +(0.169244 + 2.64033i) q^{42} +(3.06442 + 0.899796i) q^{43} +(3.07980 + 4.32497i) q^{44} +(0.176251 + 0.305276i) q^{45} +(1.39463 + 4.58857i) q^{46} +(-3.57282 + 6.18831i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(0.103425 - 6.99924i) q^{49} +(3.19293 + 3.68484i) q^{50} +(-0.177876 - 3.73408i) q^{51} +(2.51950 + 0.485594i) q^{52} +(4.69926 - 1.88130i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-1.57449 - 1.01186i) q^{55} +(1.28509 - 2.31269i) q^{56} +(-0.729069 - 1.59644i) q^{57} +(3.77098 + 0.360085i) q^{58} +(0.237182 - 0.186522i) q^{59} +(0.0167727 - 0.352103i) q^{60} +(0.846799 - 3.49055i) q^{61} +(0.127700 - 0.888170i) q^{62} +(0.824191 - 2.51410i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.888130 + 0.171173i) q^{65} +(-1.25176 - 5.15980i) q^{66} +(11.8808 - 1.13448i) q^{67} +(-1.86916 + 3.23748i) q^{68} +(0.410667 - 4.77822i) q^{69} +(-0.117560 + 0.925194i) q^{70} +(-0.0210146 + 0.0460156i) q^{71} +(0.723734 - 0.690079i) q^{72} +(4.18250 - 12.0846i) q^{73} +(-0.873693 - 0.450420i) q^{74} +(-1.59470 - 4.60758i) q^{75} +(-0.249768 + 1.73717i) q^{76} +(2.22710 + 13.8699i) q^{77} +(-2.15855 - 1.38722i) q^{78} +(-12.3882 - 4.95948i) q^{79} +(-0.204471 + 0.287140i) q^{80} +(0.580057 - 0.814576i) q^{81} +(0.563594 + 0.225629i) q^{82} +(-10.2289 - 6.57369i) q^{83} +(-2.05258 + 1.66941i) q^{84} +(0.187537 - 1.30435i) q^{85} +(1.04459 + 3.01814i) q^{86} +(-3.36703 - 1.73582i) q^{87} +(-1.73656 + 5.01745i) q^{88} +(-9.97818 + 9.51418i) q^{89} +(-0.146435 + 0.320647i) q^{90} +(5.40440 + 4.10833i) q^{91} +(-2.92877 + 3.79767i) q^{92} +(-0.448652 + 0.777088i) q^{93} +(-7.11329 + 0.679237i) q^{94} +(-0.145853 - 0.601216i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(5.25167 - 3.37504i) q^{97} +(5.76140 - 3.97571i) q^{98} +(-0.755616 + 5.25543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	−0.0167727	−	0.352103i	−0.00750099	−	0.157465i	−0.999510	−	0.0312987i	$-0.990036\pi$
$5$	−0.0167727	−	0.352103i	−0.00750099	−	0.157465i	0.992009	−	0.126166i	$-0.0402673\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−1.88460	+	1.85696i	−0.712311	+	0.701864i
$7$	−1.88460	+	1.85696i	−0.712311	+	0.701864i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	0.277085	−	0.217902i	0.0876220	−	0.0689067i
$11$	3.07980	−	4.32497i	0.928593	−	1.30403i	−0.0239786	−	0.999712i	$-0.507633\pi$
$11$	3.07980	−	4.32497i	0.928593	−	1.30403i	0.952572	−	0.304314i	$-0.0984273\pi$
$12$	0.995472	+	0.0950560i	0.287368	+	0.0274403i
$13$	−0.365162	−	2.53975i	−0.101278	−	0.704401i	−0.975680	−	0.219200i	$-0.929655\pi$
$13$	−0.365162	−	2.53975i	−0.101278	−	0.704401i	0.874402	−	0.485201i	$-0.161254\pi$
$14$	−2.60581	−	0.458008i	−0.696431	−	0.122408i
$15$	−0.338223	+	0.0993113i	−0.0873288	+	0.0256421i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	3.67076	+	0.707481i	0.890290	+	0.171589i	0.613832	−	0.789437i	$-0.289627\pi$
$17$	3.67076	+	0.707481i	0.890290	+	0.171589i	0.276458	+	0.961026i	$0.410839\pi$
$18$	−0.888835	−	0.458227i	−0.209501	−	0.108005i
$19$	1.72332	−	0.332143i	0.395357	−	0.0761989i	0.0123021	−	0.999924i	$-0.496084\pi$
$19$	1.72332	−	0.332143i	0.395357	−	0.0761989i	0.383055	+	0.923725i	$0.374872\pi$
$20$	0.338223	+	0.0993113i	0.0756290	+	0.0222067i
$21$	2.24892	+	1.39368i	0.490755	+	0.304126i
$22$	5.30947			1.13198
$23$	4.54671	+	1.52560i	0.948054	+	0.318109i
$23$	4.54671	+	1.52560i	0.948054	+	0.318109i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.85366	−	0.463469i	0.970733	−	0.0926938i
$26$	1.85701	−	1.77065i	0.364189	−	0.347254i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−1.13843	−	2.38830i	−0.215144	−	0.451346i
$29$	2.48070	−	2.86288i	0.460655	−	0.531624i	−0.477134	−	0.878831i	$-0.658324\pi$
$29$	2.48070	−	2.86288i	0.460655	−	0.531624i	0.937789	+	0.347207i	$0.112870\pi$
$30$	−0.277085	−	0.217902i	−0.0505886	−	0.0397833i
$31$	−0.649409	−	0.619210i	−0.116637	−	0.111213i	0.629516	−	0.776987i	$-0.283253\pi$
$31$	−0.649409	−	0.619210i	−0.116637	−	0.111213i	−0.746154	+	0.665774i	$0.768102\pi$
$32$	0.0475819	−	0.998867i	0.00841137	−	0.176576i
$33$	−4.92914	−	1.97333i	−0.858054	−	0.343513i
$34$	1.55295	+	3.40049i	0.266329	+	0.583179i
$35$	0.685449	+	0.632426i	0.115862	+	0.106900i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.873693	+	0.450420i	−0.143634	+	0.0740486i	−0.528545	−	0.848905i	$-0.677262\pi$
$37$	−0.873693	+	0.450420i	−0.143634	+	0.0740486i	0.384911	+	0.922954i	$0.374232\pi$
$38$	1.27018	+	1.21112i	0.206051	+	0.196469i
$39$	−2.38207	+	0.953638i	−0.381437	+	0.152704i
$40$	0.115292	+	0.333115i	0.0182293	+	0.0526700i
$41$	0.510708	−	0.328212i	0.0797592	−	0.0512581i	−0.500153	−	0.865937i	$-0.666723\pi$
$41$	0.510708	−	0.328212i	0.0797592	−	0.0512581i	0.579913	+	0.814679i	$0.303087\pi$
$42$	0.169244	+	2.64033i	0.0261150	+	0.407412i
$43$	3.06442	+	0.899796i	0.467320	+	0.137218i	0.506911	−	0.861998i	$-0.330787\pi$
$43$	3.06442	+	0.899796i	0.467320	+	0.137218i	−0.0395909	+	0.999216i	$0.512605\pi$
$44$	3.07980	+	4.32497i	0.464297	+	0.652013i
$45$	0.176251	+	0.305276i	0.0262739	+	0.0455078i
$46$	1.39463	+	4.58857i	0.205628	+	0.676548i
$47$	−3.57282	+	6.18831i	−0.521150	+	0.902658i	0.478548	+	0.878062i	$0.341163\pi$
$47$	−3.57282	+	6.18831i	−0.521150	+	0.902658i	−0.999697	+	0.0245963i	$0.992170\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	0.103425	−	6.99924i	0.0147750	−	0.999891i
$50$	3.19293	+	3.68484i	0.451549	+	0.521115i
$51$	−0.177876	−	3.73408i	−0.0249076	−	0.522876i
$52$	2.51950	+	0.485594i	0.349392	+	0.0673398i
$53$	4.69926	−	1.88130i	0.645494	−	0.258417i	−0.0257330	−	0.999669i	$-0.508192\pi$
$53$	4.69926	−	1.88130i	0.645494	−	0.258417i	0.671227	+	0.741252i	$0.265768\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	−1.57449	−	1.01186i	−0.212304	−	0.136440i
$56$	1.28509	−	2.31269i	0.171728	−	0.309046i
$57$	−0.729069	−	1.59644i	−0.0965676	−	0.211454i
$58$	3.77098	+	0.360085i	0.495154	+	0.0472815i
$59$	0.237182	−	0.186522i	0.0308785	−	0.0242831i	−0.602600	−	0.798043i	$-0.705869\pi$
$59$	0.237182	−	0.186522i	0.0308785	−	0.0242831i	0.633479	+	0.773760i	$0.281626\pi$
$60$	0.0167727	−	0.352103i	0.00216535	−	0.0454563i
$61$	0.846799	−	3.49055i	0.108422	−	0.446920i	−0.891561	−	0.452901i	$-0.850389\pi$
$61$	0.846799	−	3.49055i	0.108422	−	0.446920i	0.999982	+	0.00598179i	$0.00190407\pi$
$62$	0.127700	−	0.888170i	0.0162179	−	0.112798i
$63$	0.824191	−	2.51410i	0.103838	−	0.316747i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.888130	+	0.171173i	−0.110159	+	0.0212314i
$66$	−1.25176	−	5.15980i	−0.154080	−	0.635128i
$67$	11.8808	−	1.13448i	1.45147	−	0.138599i	0.660673	−	0.750673i	$-0.270271\pi$
$67$	11.8808	−	1.13448i	1.45147	−	0.138599i	0.790800	+	0.612075i	$0.209665\pi$
$68$	−1.86916	+	3.23748i	−0.226669	+	0.392602i
$69$	0.410667	−	4.77822i	0.0494385	−	0.575230i
$70$	−0.117560	+	0.925194i	−0.0140510	+	0.110582i
$71$	−0.0210146	+	0.0460156i	−0.00249398	+	0.00546105i	−0.910875	−	0.412683i	$-0.864592\pi$
$71$	−0.0210146	+	0.0460156i	−0.00249398	+	0.00546105i	0.908381	+	0.418144i	$0.137319\pi$
$72$	0.723734	−	0.690079i	0.0852929	−	0.0813266i
$73$	4.18250	−	12.0846i	0.489525	−	1.41439i	−0.382056	−	0.924139i	$-0.624784\pi$
$73$	4.18250	−	12.0846i	0.489525	−	1.41439i	0.871581	−	0.490251i	$-0.163095\pi$
$74$	−0.873693	−	0.450420i	−0.101565	−	0.0523603i
$75$	−1.59470	−	4.60758i	−0.184140	−	0.532038i
$76$	−0.249768	+	1.73717i	−0.0286504	+	0.199268i
$77$	2.22710	+	13.8699i	0.253801	+	1.58062i
$78$	−2.15855	−	1.38722i	−0.244408	−	0.157071i
$79$	−12.3882	−	4.95948i	−1.39378	−	0.557986i	−0.451338	−	0.892353i	$-0.649053\pi$
$79$	−12.3882	−	4.95948i	−1.39378	−	0.557986i	−0.942443	+	0.334368i	$0.891477\pi$
$80$	−0.204471	+	0.287140i	−0.0228606	+	0.0321032i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	0.563594	+	0.225629i	0.0622385	+	0.0249165i
$83$	−10.2289	−	6.57369i	−1.12276	−	0.721557i	−0.158726	−	0.987323i	$-0.550739\pi$
$83$	−10.2289	−	6.57369i	−1.12276	−	0.721557i	−0.964038	+	0.265766i	$0.914375\pi$
$84$	−2.05258	+	1.66941i	−0.223955	+	0.182147i
$85$	0.187537	−	1.30435i	0.0203413	−	0.141477i
$86$	1.04459	+	3.01814i	0.112641	+	0.325454i
$87$	−3.36703	−	1.73582i	−0.360983	−	0.186100i
$88$	−1.73656	+	5.01745i	−0.185118	+	0.534862i
$89$	−9.97818	+	9.51418i	−1.05769	+	1.00850i	−0.0577370	+	0.998332i	$0.518388\pi$
$89$	−9.97818	+	9.51418i	−1.05769	+	1.00850i	−0.999948	+	0.0101691i	$0.996763\pi$
$90$	−0.146435	+	0.320647i	−0.0154356	+	0.0337992i
$91$	5.40440	+	4.10833i	0.566535	+	0.430670i
$92$	−2.92877	+	3.79767i	−0.305346	+	0.395934i
$93$	−0.448652	+	0.777088i	−0.0465230	+	0.0805803i
$94$	−7.11329	+	0.679237i	−0.733680	+	0.0700579i
$95$	−0.145853	−	0.601216i	−0.0149642	−	0.0616834i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	5.25167	−	3.37504i	0.533226	−	0.342684i	−0.246158	−	0.969230i	$-0.579168\pi$
$97$	5.25167	−	3.37504i	0.533226	−	0.342684i	0.779384	+	0.626546i	$0.215532\pi$
$98$	5.76140	−	3.97571i	0.581989	−	0.401607i
$99$	−0.755616	+	5.25543i	−0.0759423	+	0.528190i
$100$	−1.14950	+	4.73830i	−0.114950	+	0.473830i
$101$	0.0282481	−	0.593001i	0.00281079	−	0.0590058i	−0.997026	−	0.0770641i	$-0.975445\pi$
$101$	0.0282481	−	0.593001i	0.00281079	−	0.0590058i	0.999837	+	0.0180582i	$0.00574843\pi$
$102$	2.93851	−	2.31087i	0.290956	−	0.228811i
$103$	−7.44403	−	0.710818i	−0.733482	−	0.0700390i	−0.278371	−	0.960474i	$-0.589794\pi$
$103$	−7.44403	−	0.710818i	−0.733482	−	0.0700390i	−0.455111	+	0.890435i	$0.650400\pi$
$104$	1.06590	+	2.33400i	0.104520	+	0.228867i
$105$	0.452998	−	0.815228i	0.0442081	−	0.0795581i
$106$	4.25830	+	2.73665i	0.413603	+	0.265807i
$107$	−0.139316	+	0.574268i	−0.0134682	+	0.0555165i	−0.978149	−	0.207904i	$-0.933336\pi$
$107$	−0.139316	+	0.574268i	−0.0134682	+	0.0555165i	0.964681	+	0.263421i	$0.0848508\pi$
$108$	−0.928368	+	0.371662i	−0.0893322	+	0.0357632i
$109$	10.1683	+	1.95979i	0.973951	+	0.187714i	0.651313	−	0.758809i	$-0.274218\pi$
$109$	10.1683	+	1.95979i	0.973951	+	0.187714i	0.322638	+	0.946523i	$0.395430\pi$
$110$	−0.0890542	−	1.86948i	−0.00849099	−	0.178248i
$111$	0.643705	+	0.742875i	0.0610977	+	0.0705105i
$112$	2.62929	−	0.294685i	0.248444	−	0.0278451i
$113$	−6.16666	+	13.5031i	−0.580111	+	1.27027i	0.361125	+	0.932517i	$0.382393\pi$
$113$	−6.16666	+	13.5031i	−0.580111	+	1.27027i	−0.941236	+	0.337749i	$0.890335\pi$
$114$	0.877519	−	1.51991i	0.0821872	−	0.142352i
$115$	0.460907	−	1.62650i	0.0429798	−	0.151672i
$116$	1.89407	+	3.28062i	0.175860	+	0.304598i
$117$	1.48835	+	2.09010i	0.137598	+	0.193230i
$118$	0.289516	+	0.0850095i	0.0266521	+	0.00782576i
$119$	−8.23167	+	5.48312i	−0.754596	+	0.502637i
$120$	0.296543	−	0.190577i	0.0270706	−	0.0173972i
$121$	−5.62245	−	16.2450i	−0.511132	−	1.47682i
$122$	3.33451	−	1.33494i	0.301893	−	0.120860i
$123$	−0.439364	−	0.418933i	−0.0396162	−	0.0377739i
$124$	0.797555	−	0.411168i	0.0716226	−	0.0369240i
$125$	−0.495429	−	3.44578i	−0.0443125	−	0.308200i
$126$	2.52600	−	0.786956i	0.225034	−	0.0701076i
$127$	7.89004	+	17.2768i	0.700128	+	1.53307i	0.839816	+	0.542871i	$0.182663\pi$
$127$	7.89004	+	17.2768i	0.700128	+	1.53307i	−0.139688	+	0.990196i	$0.544610\pi$
$128$	0.928368	+	0.371662i	0.0820569	+	0.0328506i
$129$	0.151967	−	3.19018i	0.0133799	−	0.280879i
$130$	−0.654599	−	0.624159i	−0.0574121	−	0.0547424i
$131$	9.10926	+	7.16360i	0.795880	+	0.625887i	0.931032	−	0.364938i	$-0.118910\pi$
$131$	9.10926	+	7.16360i	0.795880	+	0.625887i	−0.135152	+	0.990825i	$0.543152\pi$
$132$	3.47696	−	4.01263i	0.302631	−	0.349255i
$133$	−2.63100	+	3.82609i	−0.228136	+	0.331764i
$134$	7.81567	+	9.01977i	0.675171	+	0.779189i
$135$	0.255118	−	0.243254i	0.0219570	−	0.0209360i
$136$	−3.72139	+	0.355349i	−0.319106	+	0.0304710i
$137$	3.13339	+	5.42720i	0.267704	+	0.463677i	0.968268	−	0.249912i	$-0.0804018\pi$
$137$	3.13339	+	5.42720i	0.267704	+	0.463677i	−0.700565	+	0.713589i	$0.747068\pi$
$138$	4.13043	−	2.43712i	0.351606	−	0.207461i
$139$	−20.1495			−1.70906			−0.854530	−	0.519401i	$-0.826155\pi$
$139$	−20.1495			−1.70906			−0.854530	+	0.519401i	$0.826155\pi$
$140$	−0.821832	+	0.440904i	−0.0694574	+	0.0372632i
$141$	6.85620	+	2.01316i	0.577396	+	0.169539i
$142$	−0.0496729	+	0.00957367i	−0.00416846	+	0.000803404i
$143$	−12.1090	−	6.24261i	−1.01260	−	0.522033i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−1.04964	−	0.825443i	−0.0871676	−	0.0685493i
$146$	12.2699	−	3.60276i	1.01546	−	0.298167i
$147$	−6.82632	+	1.54962i	−0.563026	+	0.127811i
$148$	−0.139890	−	0.972959i	−0.0114989	−	0.0799767i
$149$	−2.96231	−	0.282866i	−0.242682	−	0.0231733i	−0.0269936	−	0.999636i	$-0.508593\pi$
$149$	−2.96231	−	0.282866i	−0.242682	−	0.0231733i	−0.215688	+	0.976462i	$0.569199\pi$
$150$	2.82821	−	3.97166i	0.230922	−	0.324285i
$151$	−7.54979	+	5.93722i	−0.614393	+	0.483164i	−0.876195	−	0.481958i	$-0.839926\pi$
$151$	−7.54979	+	5.93722i	−0.614393	+	0.483164i	0.261801	+	0.965122i	$0.415684\pi$
$152$	−1.55994	+	0.804205i	−0.126528	+	0.0652297i
$153$	−3.58689	+	1.05320i	−0.289983	+	0.0851466i
$154$	−10.0062	+	9.85946i	−0.806324	+	0.794498i
$155$	−0.207133	+	0.239045i	−0.0166373	+	0.0192005i
$156$	−0.122089	−	2.56297i	−0.00977495	−	0.205201i
$157$	2.98638	−	8.62858i	0.238339	−	0.688636i	−0.760871	−	0.648903i	$-0.775228\pi$
$157$	2.98638	−	8.62858i	0.238339	−	0.688636i	0.999210	−	0.0397328i	$-0.0126507\pi$
$158$	−3.14598	−	12.9679i	−0.250281	−	1.03167i
$159$	−2.93616	−	4.12327i	−0.232853	−	0.326996i
$160$	−0.352502			−0.0278677
$161$	−11.4017	+	5.56790i	−0.898579	+	0.438812i
$162$	1.00000			0.0785674
$163$	0.617084	+	0.866573i	0.0483337	+	0.0678752i	0.838036	−	0.545616i	$-0.183704\pi$
$163$	0.617084	+	0.866573i	0.0483337	+	0.0678752i	−0.789702	+	0.613491i	$0.789765\pi$
$164$	0.143125	+	0.589967i	0.0111761	+	0.0460687i
$165$	−0.612140	+	1.76866i	−0.0476550	+	0.137690i
$166$	−0.578552	−	12.1453i	−0.0449044	−	0.942658i
$167$	−9.73093	+	11.2301i	−0.753002	+	0.869011i	−0.994856	−	0.101302i	$-0.967699\pi$
$167$	−9.73093	+	11.2301i	−0.753002	+	0.869011i	0.241853	+	0.970313i	$0.422245\pi$
$168$	−2.55047	−	0.703632i	−0.196773	−	0.0542864i
$169$	6.15640	−	1.80768i	0.473569	−	0.139052i
$170$	1.17127	−	0.603834i	0.0898327	−	0.0463120i
$171$	−1.37955	+	1.08489i	−0.105497	+	0.0829638i
$172$	−1.85258	+	2.60159i	−0.141258	+	0.198369i
$173$	−2.25951	−	0.215757i	−0.171788	−	0.0164037i	0.00880771	−	0.999961i	$-0.497196\pi$
$173$	−2.25951	−	0.215757i	−0.171788	−	0.0164037i	−0.180595	+	0.983557i	$0.557802\pi$
$174$	−0.539108	−	3.74958i	−0.0408697	−	0.284255i
$175$	−8.28657	+	9.88650i	−0.626406	+	0.747349i
$176$	−5.09440	+	1.49585i	−0.384005	+	0.112754i
$177$	−0.237182	−	0.186522i	−0.0178277	−	0.0140199i
$178$	−13.5379	−	2.60922i	−1.01471	−	0.195570i
$179$	3.63668	+	1.87484i	0.271818	+	0.140132i	0.588747	−	0.808317i	$-0.299621\pi$
$179$	3.63668	+	1.87484i	0.271818	+	0.140132i	−0.316929	+	0.948449i	$0.602652\pi$
$180$	−0.346132	+	0.0667114i	−0.0257991	+	0.00497238i
$181$	−6.56452	−	1.92752i	−0.487937	−	0.143271i	0.0285044	−	0.999594i	$-0.490926\pi$
$181$	−6.56452	−	1.92752i	−0.487937	−	0.143271i	−0.516442	+	0.856322i	$0.672744\pi$
$182$	−0.211688	+	6.78536i	−0.0156914	+	0.502964i
$183$	−3.59180			−0.265514
$184$	−4.79234	−	0.182845i	−0.353296	−	0.0134795i
$185$	0.173248	+	0.300075i	0.0127375	+	0.0220620i
$186$	−0.893241	+	0.0852941i	−0.0654956	+	0.00625407i
$187$	14.3650	−	13.6970i	1.05047	−	1.00162i
$188$	−4.67940	−	5.40032i	−0.341281	−	0.393859i
$189$	−2.63754	−	0.208237i	−0.191853	−	0.0151470i
$190$	0.405133	−	0.467548i	0.0293914	−	0.0339195i
$191$	−12.0267	−	9.45793i	−0.870224	−	0.684352i	0.0797044	−	0.996819i	$-0.474602\pi$
$191$	−12.0267	−	9.45793i	−0.870224	−	0.684352i	−0.949929	+	0.312467i	$0.898845\pi$
$192$	−0.723734	−	0.690079i	−0.0522310	−	0.0498022i
$193$	0.436341	−	9.15992i	0.0314085	−	0.659345i	−0.927191	−	0.374588i	$-0.877784\pi$
$193$	0.436341	−	9.15992i	0.0314085	−	0.659345i	0.958600	−	0.284757i	$-0.0919129\pi$
$194$	5.79549	+	2.32017i	0.416092	+	0.166578i
$195$	0.375732	+	0.822739i	0.0269068	+	0.0589176i
$196$	6.58046	+	2.38696i	0.470033	+	0.170497i
$197$	2.36014	+	16.4151i	0.168153	+	1.16953i	0.882698	+	0.469941i	$0.155725\pi$
$197$	2.36014	+	16.4151i	0.168153	+	1.16953i	−0.714545	+	0.699589i	$0.753366\pi$
$198$	−4.71925	+	2.43294i	−0.335382	+	0.172902i
$199$	−9.73604	−	9.28329i	−0.690169	−	0.658075i	0.261499	−	0.965204i	$-0.415783\pi$
$199$	−9.73604	−	9.28329i	−0.690169	−	0.658075i	−0.951668	+	0.307129i	$0.900632\pi$
$200$	−4.52648	+	1.81213i	−0.320071	+	0.128137i
$201$	−3.90351	−	11.2785i	−0.275332	−	0.795521i
$202$	0.499430	−	0.320964i	0.0351398	−	0.0225830i
$203$	0.641121	+	10.0019i	0.0449979	+	0.701999i
$204$	3.58689	+	1.05320i	0.251132	+	0.0737391i
$205$	−0.124130	−	0.174317i	−0.00866964	−	0.0121748i
$206$	−3.73894	−	6.47604i	−0.260505	−	0.451207i
$207$	−4.74034	+	0.727416i	−0.329477	+	0.0505589i
$208$	−1.28294	+	2.22211i	−0.0889556	+	0.154076i
$209$	3.87097	−	8.47625i	0.267761	−	0.586314i
$210$	0.926829	−	0.103877i	0.0639573	−	0.00716819i
$211$	−8.73840	−	10.0847i	−0.601577	−	0.694256i	0.370523	−	0.928823i	$-0.379178\pi$
$211$	−8.73840	−	10.0847i	−0.601577	−	0.694256i	−0.972100	+	0.234567i	$0.924633\pi$
$212$	0.240853	+	5.05612i	0.0165418	+	0.347256i
$213$	0.0496729	+	0.00957367i	0.00340353	+	0.000655977i
$214$	−0.548596	+	0.219625i	−0.0375012	+	0.0150132i
$215$	0.265422	−	1.09408i	0.0181016	−	0.0746159i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	2.37372	−	0.0389615i	0.161139	−	0.00264488i
$218$	4.30182	+	9.41968i	0.291356	+	0.637981i
$219$	−12.7300	−	1.21556i	−0.860212	−	0.0821402i
$220$	1.47118	−	1.15695i	0.0991867	−	0.0780012i
$221$	0.456407	−	9.58117i	0.0307013	−	0.644499i
$222$	−0.231743	+	0.955256i	−0.0155535	+	0.0641126i
$223$	−1.78740	+	12.4317i	−0.119693	+	0.832485i	0.838200	+	0.545362i	$0.183608\pi$
$223$	−1.78740	+	12.4317i	−0.119693	+	0.832485i	−0.957894	+	0.287123i	$0.907301\pi$
$224$	1.76518	+	1.97082i	0.117941	+	0.131681i
$225$	−4.10174	+	2.63603i	−0.273449	+	0.175735i
$226$	−14.5763	+	2.80936i	−0.969603	+	0.186876i
$227$	−2.34591	−	9.66996i	−0.155703	−	0.641818i	−0.995149	−	0.0983750i	$-0.968636\pi$
$227$	−2.34591	−	9.66996i	−0.155703	−	0.641818i	0.839446	−	0.543443i	$-0.182880\pi$
$228$	1.74709	−	0.166827i	0.115704	−	0.0110484i
$229$	1.34748	−	2.33391i	0.0890442	−	0.154229i	−0.818063	−	0.575128i	$-0.804952\pi$
$229$	1.34748	−	2.33391i	0.0890442	−	0.154229i	0.907107	+	0.420899i	$0.138285\pi$
$230$	1.59226	−	0.568017i	0.104990	−	0.0374539i
$231$	12.9538	−	5.43427i	0.852300	−	0.357548i
$232$	−1.57365	+	3.44581i	−0.103315	+	0.226228i
$233$	10.4530	−	9.96694i	0.684800	−	0.652956i	−0.265565	−	0.964093i	$-0.585558\pi$
$233$	10.4530	−	9.96694i	0.684800	−	0.652956i	0.950365	+	0.311137i	$0.100710\pi$
$234$	−0.839214	+	2.42475i	−0.0548612	+	0.158511i
$235$	2.23885	+	1.15421i	0.146046	+	0.0752921i
$236$	0.0986889	+	0.285143i	0.00642410	+	0.0185612i
$237$	−1.89906	+	13.2082i	−0.123357	+	0.857967i
$238$	−9.24125	−	3.52480i	−0.599022	−	0.228479i
$239$	18.2094	+	11.7025i	1.17787	+	0.756970i	0.974993	−	0.222235i	$-0.0713351\pi$
$239$	18.2094	+	11.7025i	1.17787	+	0.756970i	0.202875	+	0.979205i	$0.434971\pi$
$240$	0.327251	+	0.131012i	0.0211240	+	0.00845677i
$241$	1.41205	−	1.98295i	0.0909584	−	0.127733i	−0.766589	−	0.642138i	$-0.778048\pi$
$241$	1.41205	−	1.98295i	0.0909584	−	0.127733i	0.857548	+	0.514405i	$0.171987\pi$
$242$	9.97146	−	14.0029i	0.640989	−	0.900144i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	3.02162	+	1.94187i	0.193439	+	0.124316i
$245$	−2.46618	+	0.0809800i	−0.157559	+	0.00517362i
$246$	0.0863965	−	0.600901i	0.00550844	−	0.0383120i
$247$	−1.47285	−	4.25553i	−0.0937154	−	0.270773i
$248$	0.797555	+	0.411168i	0.0506448	+	0.0261092i
$249$	−3.97684	+	11.4903i	−0.252022	+	0.728171i
$250$	2.51948	−	2.40232i	0.159346	−	0.151936i
$251$	−8.72950	+	19.1149i	−0.551001	+	1.20652i	0.405311	+	0.914179i	$0.367163\pi$
$251$	−8.72950	+	19.1149i	−0.551001	+	1.20652i	−0.956313	+	0.292346i	$0.905564\pi$
$252$	2.10626	+	1.60114i	0.132682	+	0.100863i
$253$	20.6011	−	14.9658i	1.29518	−	0.940894i
$254$	−9.49658	+	16.4486i	−0.595868	+	1.03207i
$255$	−1.31180	+	0.125261i	−0.0821479	+	0.00784417i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	22.0583	−	4.25138i	1.37596	−	0.265194i	0.552945	−	0.833218i	$-0.313504\pi$
$257$	22.0583	−	4.25138i	1.37596	−	0.265194i	0.823012	+	0.568024i	$0.192292\pi$
$258$	2.68679	−	1.72670i	0.167272	−	0.107499i
$259$	0.810151	−	2.47127i	0.0503403	−	0.153557i
$260$	0.128720	−	0.895269i	0.00798289	−	0.0555222i
$261$	−0.893087	+	3.68135i	−0.0552807	+	0.227870i
$262$	−0.551408	+	11.5755i	−0.0340661	+	0.715136i
$263$	−15.2614	+	12.0017i	−0.941056	+	0.740055i	−0.965705	−	0.259642i	$-0.916396\pi$
$263$	−15.2614	+	12.0017i	−0.941056	+	0.740055i	0.0246491	+	0.999696i	$0.492153\pi$
$264$	5.28543	+	0.504697i	0.325296	+	0.0310620i
$265$	−0.741231	−	1.62307i	−0.0455334	−	0.0997043i
$266$	−4.64277	+	0.0762048i	−0.284667	+	0.00467242i
$267$	11.5984	+	7.45386i	0.709813	+	0.456169i
$268$	−2.81375	+	11.5984i	−0.171877	+	0.708487i
$269$	0.885575	−	0.354531i	0.0539945	−	0.0216161i	−0.344508	−	0.938783i	$-0.611954\pi$
$269$	0.885575	−	0.354531i	0.0539945	−	0.0216161i	0.398503	+	0.917167i	$0.369530\pi$
$270$	0.346132	+	0.0667114i	0.0210649	+	0.00405993i
$271$	0.876928	+	18.4090i	0.0532696	+	1.11827i	0.854346	+	0.519704i	$0.173958\pi$
$271$	0.876928	+	18.4090i	0.0532696	+	1.11827i	−0.801077	+	0.598562i	$0.795739\pi$
$272$	−2.44808	−	2.82523i	−0.148436	−	0.171305i
$273$	2.71839	−	6.22063i	0.164524	−	0.376490i
$274$	−2.60332	+	5.70047i	−0.157272	+	0.344378i
$275$	12.9438	−	22.4193i	0.780541	−	1.35194i
$276$	4.38110	+	1.95088i	0.263711	+	0.117429i
$277$	−9.11224	−	15.7829i	−0.547501	−	0.948300i	−0.998445	−	0.0557476i	$-0.982246\pi$
$277$	−9.11224	−	15.7829i	−0.547501	−	0.948300i	0.450944	−	0.892552i	$-0.351088\pi$
$278$	−11.6879	−	16.4133i	−0.700992	−	0.984406i
$279$	0.860957	+	0.252800i	0.0515441	+	0.0151347i
$280$	−0.835859	−	0.413695i	−0.0499521	−	0.0247230i
$281$	7.02566	−	4.51512i	0.419116	−	0.269349i	−0.314040	−	0.949410i	$-0.601683\pi$
$281$	7.02566	−	4.51512i	0.419116	−	0.269349i	0.733156	+	0.680060i	$0.238046\pi$
$282$	2.33711	+	6.75264i	0.139173	+	0.402114i
$283$	8.67746	−	3.47393i	0.515821	−	0.206504i	−0.0991216	−	0.995075i	$-0.531603\pi$
$283$	8.67746	−	3.47393i	0.515821	−	0.206504i	0.614943	+	0.788572i	$0.289179\pi$
$284$	−0.0366116	−	0.0349091i	−0.00217250	−	0.00207147i
$285$	−0.549882	+	0.283484i	−0.0325722	+	0.0167921i
$286$	−1.93881	−	13.4848i	−0.114645	−	0.797370i
$287$	−0.353004	+	1.56691i	−0.0208372	+	0.0924918i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	−2.80832	−	1.12428i	−0.165195	−	0.0661341i
$290$	0.0635373	−	1.33381i	0.00373104	−	0.0783242i
$291$	−4.51803	−	4.30793i	−0.264852	−	0.252536i
$292$	10.0519	+	7.90494i	0.588246	+	0.462602i
$293$	16.8224	−	19.4141i	0.982778	−	1.13419i	−0.00817362	−	0.999967i	$-0.502602\pi$
$293$	16.8224	−	19.4141i	0.982778	−	1.13419i	0.990952	−	0.134220i	$-0.0428528\pi$
$294$	−5.22194	−	4.66169i	−0.304550	−	0.271875i
$295$	−0.0696532	−	0.0803840i	−0.00405536	−	0.00468014i
$296$	0.711405	−	0.678323i	0.0413496	−	0.0394267i
$297$	5.28543	−	0.504697i	0.306692	−	0.0292855i
$298$	−1.48789	−	2.57710i	−0.0861912	−	0.149288i
$299$	2.21436	−	12.1046i	0.128060	−	0.700028i
$300$	4.87574			0.281501
$301$	−7.44609	+	3.99475i	−0.429185	+	0.230253i
$302$	−9.21563	−	2.70595i	−0.530300	−	0.155710i
$303$	−0.582945	+	0.112354i	−0.0334893	+	0.00645454i
$304$	−1.55994	−	0.804205i	−0.0894687	−	0.0461243i
$305$	−1.24324	−	0.239614i	−0.0711875	−	0.0137203i
$306$	−2.93851	−	2.31087i	−0.167984	−	0.132104i
$307$	26.3620	−	7.74058i	1.50456	−	0.441778i	0.577404	−	0.816458i	$-0.304066\pi$
$307$	26.3620	−	7.74058i	1.50456	−	0.441778i	0.927154	+	0.374680i	$0.122247\pi$
$308$	−13.8355	−	2.43178i	−0.788348	−	0.138564i
$309$	1.06421	+	7.40177i	0.0605410	+	0.421072i
$310$	−0.314869	−	0.0300663i	−0.0178834	−	0.00170765i
$311$	−15.7375	+	22.1002i	−0.892391	+	1.25319i	0.0742985	+	0.997236i	$0.476328\pi$
$311$	−15.7375	+	22.1002i	−0.892391	+	1.25319i	−0.966690	+	0.255952i	$0.917611\pi$
$312$	2.01691	−	1.58612i	0.114185	−	0.0897962i
$313$	−9.68618	+	4.99357i	−0.547495	+	0.282254i	−0.709700	−	0.704504i	$-0.751170\pi$
$313$	−9.68618	+	4.99357i	−0.547495	+	0.282254i	0.162205	+	0.986757i	$0.448139\pi$
$314$	8.76091	−	2.57243i	0.494407	−	0.145171i
$315$	−0.899046	−	0.248032i	−0.0506555	−	0.0139750i
$316$	8.73850	−	10.0848i	0.491579	−	0.567312i
$317$	1.48689	+	31.2137i	0.0835122	+	1.75314i	0.520675	+	0.853755i	$0.325680\pi$
$317$	1.48689	+	31.2137i	0.0835122	+	1.75314i	−0.437163	+	0.899382i	$0.644017\pi$
$318$	1.65557	−	4.78346i	0.0928398	−	0.268243i
$319$	−4.74182	−	19.5460i	−0.265491	−	1.09437i
$320$	−0.204471	−	0.287140i	−0.0114303	−	0.0160516i
$321$	0.590925			0.0329822
$322$	−11.1491	−	6.05784i	−0.621315	−	0.337590i
$323$	6.56089			0.365058
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−2.94947	−	12.1579i	−0.163607	−	0.674398i
$326$	−0.347946	+	1.00532i	−0.0192709	+	0.0556797i
$327$	−0.492734	−	10.3438i	−0.0272482	−	0.572011i
$328$	−0.397553	+	0.458800i	−0.0219512	+	0.0253330i
$329$	−4.75809	−	18.2971i	−0.262322	−	1.00875i
$330$	−1.79579	+	0.527290i	−0.0988548	+	0.0290264i
$331$	−16.2030	+	8.35321i	−0.890596	+	0.459134i	−0.841871	−	0.539678i	$-0.818546\pi$
$331$	−16.2030	+	8.35321i	−0.890596	+	0.459134i	−0.0487246	+	0.998812i	$0.515516\pi$
$332$	9.55768	−	7.51624i	0.524546	−	0.412507i
$333$	0.570175	−	0.800699i	0.0312454	−	0.0438780i
$334$	−14.7923	−	1.41249i	−0.809397	−	0.0772880i
$335$	−0.598727	−	4.16424i	−0.0327120	−	0.227517i
$336$	−0.906256	−	2.48570i	−0.0494403	−	0.135606i
$337$	−18.2582	+	5.36108i	−0.994586	+	0.292037i	−0.738232	−	0.674546i	$-0.764339\pi$
$337$	−18.2582	+	5.36108i	−0.994586	+	0.292037i	−0.256353	+	0.966583i	$0.582521\pi$
$338$	5.04355	+	3.96629i	0.274333	+	0.215738i
$339$	14.5763	+	2.80936i	0.791677	+	0.152583i
$340$	1.17127	+	0.603834i	0.0635213	+	0.0327475i
$341$	−4.67811	+	0.901632i	−0.253334	+	0.0488261i
$342$	−1.68395	−	0.494452i	−0.0910574	−	0.0267369i
$343$	12.8024	+	13.3828i	0.691263	+	0.722604i
$344$	−3.19379			−0.172198
$345$	−1.68931	−	0.0644533i	−0.0909494	−	0.00347005i
$346$	−1.13490	−	1.96570i	−0.0610124	−	0.105677i
$347$	9.46909	−	0.904188i	0.508327	−	0.0485394i	0.162258	−	0.986748i	$-0.448122\pi$
$347$	9.46909	−	0.904188i	0.508327	−	0.0485394i	0.346069	+	0.938209i	$0.387516\pi$
$348$	2.74160	−	2.61411i	0.146965	−	0.140131i
$349$	−11.7932	−	13.6100i	−0.631273	−	0.728528i	0.346533	−	0.938038i	$-0.387359\pi$
$349$	−11.7932	−	13.6100i	−0.631273	−	0.728528i	−0.977807	+	0.209510i	$0.932813\pi$
$350$	−12.8600	−	1.01531i	−0.687395	−	0.0542705i
$351$	1.68029	−	1.93916i	0.0896872	−	0.103505i
$352$	−4.17353	−	3.28210i	−0.222450	−	0.174936i
$353$	13.3650	+	12.7435i	0.711348	+	0.678269i	0.956671	−	0.291172i	$-0.0940453\pi$
$353$	13.3650	+	12.7435i	0.711348	+	0.678269i	−0.245322	+	0.969442i	$0.578894\pi$
$354$	0.0143573	−	0.301396i	0.000763081	−	0.0160190i
$355$	0.0165547	+	0.00662750i	0.000878632	+	0.000351751i
$356$	−5.72736	−	12.5412i	−0.303550	−	0.664681i
$357$	7.26925	+	6.70693i	0.384730	+	0.354969i
$358$	0.582282	+	4.04986i	0.0307746	+	0.214042i
$359$	−16.5759	+	8.54545i	−0.874840	+	0.451011i	−0.836317	−	0.548246i	$-0.815296\pi$
$359$	−16.5759	+	8.54545i	−0.874840	+	0.451011i	−0.0385231	+	0.999258i	$0.512265\pi$
$360$	−0.255118	−	0.243254i	−0.0134459	−	0.0128206i
$361$	−14.7795	+	5.91681i	−0.777867	+	0.311411i
$362$	−2.23769	−	6.46537i	−0.117610	−	0.339813i
$363$	−14.4615	+	9.29387i	−0.759035	+	0.487802i
$364$	−5.64998	+	3.76346i	−0.296139	+	0.197259i
$365$	−4.32515	−	1.26998i	−0.226389	−	0.0664738i
$366$	−2.08345	−	2.92580i	−0.108904	−	0.152934i
$367$	−14.1090	−	24.4374i	−0.736482	−	1.27562i	−0.954070	−	0.299584i	$-0.903152\pi$
$367$	−14.1090	−	24.4374i	−0.736482	−	1.27562i	0.217588	−	0.976041i	$-0.430181\pi$
$368$	−2.63089	−	4.00979i	−0.137145	−	0.209025i
$369$	−0.303540	+	0.525747i	−0.0158017	+	0.0273693i
$370$	−0.143940	+	0.315185i	−0.00748308	+	0.0163857i
$371$	−5.36273	+	12.2718i	−0.278419	+	0.637122i
$372$	−0.587609	−	0.678137i	−0.0304661	−	0.0351598i
$373$	0.655304	+	13.7565i	0.0339304	+	0.712286i	0.950184	+	0.311688i	$0.100895\pi$
$373$	0.655304	+	13.7565i	0.0339304	+	0.712286i	−0.916254	+	0.400598i	$0.868802\pi$
$374$	19.4898	+	3.75635i	1.00779	+	0.194236i
$375$	−3.23185	+	1.29384i	−0.166892	+	0.0668135i
$376$	1.68465	−	6.94422i	0.0868792	−	0.358121i
$377$	−8.17688	−	5.25496i	−0.421131	−	0.270644i
$378$	−1.36030	−	2.26927i	−0.0699663	−	0.116719i
$379$	11.1897	+	24.5021i	0.574778	+	1.25859i	0.944214	+	0.329332i	$0.106824\pi$
$379$	11.1897	+	24.5021i	0.574778	+	1.25859i	−0.369436	+	0.929256i	$0.620449\pi$
$380$	0.615853	+	0.0588069i	0.0315926	+	0.00301673i
$381$	14.9296	−	11.7408i	0.764868	−	0.601499i
$382$	0.728011	−	15.2828i	0.0372483	−	0.781938i
$383$	8.48025	−	34.9561i	0.433321	−	1.78617i	−0.166504	−	0.986041i	$-0.553248\pi$
$383$	8.48025	−	34.9561i	0.433321	−	1.78617i	0.599825	−	0.800131i	$-0.295237\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	4.84626	−	1.01680i	0.246989	−	0.0518211i
$386$	7.71455	−	4.95784i	0.392660	−	0.252347i
$387$	−3.13608	+	0.604429i	−0.159416	+	0.0307249i
$388$	1.47176	+	6.06670i	0.0747175	+	0.307990i
$389$	−5.04622	+	0.481856i	−0.255854	+	0.0244311i	−0.222195	−	0.975002i	$-0.571322\pi$
$389$	−5.04622	+	0.481856i	−0.255854	+	0.0244311i	−0.0336590	+	0.999433i	$0.510716\pi$
$390$	−0.452237	+	0.783298i	−0.0228999	+	0.0396638i
$391$	15.6105	+	8.81681i	0.789459	+	0.445885i
$392$	1.87268	+	6.74486i	0.0945845	+	0.340667i
$393$	4.81408	−	10.5414i	0.242838	−	0.531742i
$394$	−12.0024	+	11.4442i	−0.604670	+	0.576552i
$395$	−1.53846	+	4.44510i	−0.0774085	+	0.223657i
$396$	−4.71925	−	2.43294i	−0.237151	−	0.122260i
$397$	8.64818	+	24.9873i	0.434040	+	1.25408i	0.924021	+	0.382342i	$0.124883\pi$
$397$	8.64818	+	24.9873i	0.434040	+	1.25408i	−0.489981	+	0.871733i	$0.662996\pi$
$398$	1.91449	−	13.3156i	0.0959648	−	0.667450i
$399$	4.33852	+	1.65480i	0.217198	+	0.0828435i
$400$	−4.10174	−	2.63603i	−0.205087	−	0.131801i
$401$	18.2132	+	7.29145i	0.909521	+	0.364117i	0.778779	−	0.627299i	$-0.215840\pi$
$401$	18.2132	+	7.29145i	0.909521	+	0.364117i	0.130743	+	0.991416i	$0.458264\pi$
$402$	6.92290	−	9.72185i	0.345283	−	0.484882i
$403$	−1.33550	+	1.87545i	−0.0665262	+	0.0934229i
$404$	0.551148	+	0.220646i	0.0274206	+	0.0109776i
$405$	−0.296543	−	0.190577i	−0.0147354	−	0.00946984i
$406$	−7.77545	+	6.32394i	−0.385889	+	0.313852i
$407$	−0.742744	+	5.16590i	−0.0368164	+	0.256064i
$408$	1.22268	+	3.53271i	0.0605318	+	0.174895i
$409$	5.59293	+	2.88335i	0.276552	+	0.142573i	0.590924	−	0.806727i	$-0.298763\pi$
$409$	5.59293	+	2.88335i	0.276552	+	0.142573i	−0.314371	+	0.949300i	$0.601794\pi$
$410$	0.0699915	−	0.202227i	0.00345663	−	0.00998729i
$411$	4.53549	−	4.32458i	0.223719	−	0.213316i
$412$	3.10643	−	6.80213i	0.153043	−	0.335117i
$413$	−0.100630	+	0.791957i	−0.00495167	+	0.0389696i
$414$	−3.34221	−	3.43943i	−0.164260	−	0.169039i
$415$	−2.14305	+	3.71187i	−0.105198	+	0.182209i
$416$	−2.55425	+	0.243902i	−0.125233	+	0.0119583i
$417$	4.75043	+	19.5815i	0.232630	+	0.958912i
$418$	9.14993	−	1.76350i	0.447538	−	0.0862558i
$419$	−18.4266	+	11.8420i	−0.900196	+	0.578521i	−0.906848	−	0.421457i	$-0.861519\pi$
$419$	−18.4266	+	11.8420i	−0.900196	+	0.578521i	0.00665236	+	0.999978i	$0.497882\pi$
$420$	0.622229	+	0.694718i	0.0303617	+	0.0338988i
$421$	3.48881	−	24.2652i	0.170034	−	1.18261i	−0.708772	−	0.705437i	$-0.750751\pi$
$421$	3.48881	−	24.2652i	0.170034	−	1.18261i	0.878807	−	0.477178i	$-0.158340\pi$
$422$	3.14595	−	12.9678i	0.153142	−	0.631261i
$423$	0.340004	−	7.13755i	0.0165315	−	0.347040i
$424$	−3.97889	+	3.12903i	−0.193232	+	0.151959i
$425$	18.1445	+	1.73259i	0.880139	+	0.0840431i
$426$	0.0210146	+	0.0460156i	0.00101816	+	0.00222946i
$427$	4.88593	+	8.15076i	0.236447	+	0.394443i
$428$	−0.497118	−	0.319478i	−0.0240291	−	0.0154426i
$429$	−3.21184	+	13.2394i	−0.155069	+	0.639204i
$430$	1.04517	−	0.418424i	0.0504028	−	0.0201782i
$431$	33.1068	+	6.38082i	1.59470	+	0.307353i	0.907802	−	0.419399i	$-0.137759\pi$
$431$	33.1068	+	6.38082i	1.59470	+	0.307353i	0.686899	+	0.726753i	$0.258971\pi$
$432$	−0.0475819	−	0.998867i	−0.00228929	−	0.0480580i
$433$	−1.23646	−	1.42696i	−0.0594207	−	0.0685752i	0.725261	−	0.688474i	$-0.241719\pi$
$433$	−1.23646	−	1.42696i	−0.0594207	−	0.0685752i	−0.784682	+	0.619899i	$0.787174\pi$
$434$	1.40863	+	1.91098i	0.0676165	+	0.0917299i
$435$	−0.554714	+	1.21465i	−0.0265965	+	0.0582382i
$436$	−5.17774	+	8.96811i	−0.247969	+	0.429495i
$437$	8.34216	+	1.11894i	0.399060	+	0.0535262i
$438$	−6.39394	−	11.0746i	−0.305514	−	0.529166i
$439$	21.4027	+	30.0558i	1.02149	+	1.43449i	0.896876	+	0.442282i	$0.145831\pi$
$439$	21.4027	+	30.0558i	1.02149	+	1.43449i	0.124617	+	0.992205i	$0.460230\pi$
$440$	1.79579	+	0.527290i	0.0856107	+	0.0251376i
$441$	3.11531	+	6.26856i	0.148348	+	0.298503i
$442$	8.06933	−	5.18585i	0.383819	−	0.246666i
$443$	1.93477	+	5.59016i	0.0919238	+	0.265596i	0.981585	−	0.191024i	$-0.0611809\pi$
$443$	1.93477	+	5.59016i	0.0919238	+	0.265596i	−0.889662	+	0.456621i	$0.849060\pi$
$444$	−0.912552	+	0.365331i	−0.0433078	+	0.0173378i
$445$	3.51733	+	3.35377i	0.166737	+	0.158984i
$446$	−11.1633	+	5.75509i	−0.528599	+	0.272512i
$447$	0.423498	+	2.94549i	0.0200308	+	0.139317i
$448$	−0.581479	+	2.58106i	−0.0274723	+	0.121944i
$449$	11.7054	+	25.6314i	0.552414	+	1.20962i	0.955645	+	0.294520i	$0.0951599\pi$
$449$	11.7054	+	25.6314i	0.552414	+	1.20962i	−0.403231	+	0.915098i	$0.632113\pi$
$450$	−4.52648	−	1.81213i	−0.213380	−	0.0854246i
$451$	0.153370	−	3.21962i	0.00722189	−	0.151606i
$452$	−10.7435	−	10.2439i	−0.505333	−	0.481834i
$453$	7.54979	+	5.93722i	0.354720	+	0.278955i
$454$	6.51616	−	7.52005i	0.305819	−	0.352933i
$455$	1.35591	−	1.97181i	0.0635659	−	0.0924399i
$456$	1.14931	+	1.32637i	0.0538212	+	0.0621130i
$457$	18.0296	−	17.1912i	0.843391	−	0.804172i	−0.139139	−	0.990273i	$-0.544434\pi$
$457$	18.0296	−	17.1912i	0.843391	−	0.804172i	0.982531	+	0.186101i	$0.0595851\pi$
$458$	2.68276	−	0.256173i	0.125357	−	0.0119702i
$459$	1.86916	+	3.23748i	0.0872448	+	0.151112i
$460$	1.38629	+	0.967532i	0.0646362	+	0.0451114i
$461$	7.00768			0.326380			0.163190	−	0.986595i	$-0.447822\pi$
$461$	7.00768			0.326380			0.163190	+	0.986595i	$0.447822\pi$
$462$	11.9406	+	7.39971i	0.555526	+	0.344266i
$463$	−9.24659	−	2.71504i	−0.429725	−	0.126179i	0.0597151	−	0.998215i	$-0.480981\pi$
$463$	−9.24659	−	2.71504i	−0.429725	−	0.126179i	−0.489440	+	0.872037i	$0.662799\pi$
$464$	−3.71968	+	0.716909i	−0.172682	+	0.0332817i
$465$	0.281140	+	0.144938i	0.0130375	+	0.00672132i
$466$	14.1822	+	2.73339i	0.656977	+	0.126622i
$467$	−17.6132	−	13.8512i	−0.815043	−	0.640957i	0.121075	−	0.992643i	$-0.461366\pi$
$467$	−17.6132	−	13.8512i	−0.815043	−	0.640957i	−0.936118	+	0.351686i	$0.885608\pi$
$468$	−2.46194	+	0.722890i	−0.113803	+	0.0334156i
$469$	−20.2839	+	24.2002i	−0.936624	+	1.11746i
$470$	0.358470	+	2.49322i	0.0165350	+	0.115003i
$471$	−9.08942	−	0.867935i	−0.418818	−	0.0399923i
$472$	−0.175025	+	0.245789i	−0.00805619	+	0.0113133i
$473$	13.3294	−	10.4823i	0.612886	−	0.481979i
$474$	−11.8607	+	6.11460i	−0.544779	+	0.280853i
$475$	8.21049	−	2.41082i	0.376723	−	0.110616i
$476$	−2.48924	−	9.57229i	−0.114094	−	0.438745i
$477$	−3.31481	+	3.82550i	−0.151775	+	0.175157i
$478$	1.02994	+	21.6210i	0.0471082	+	0.988923i
$479$	−4.50009	+	13.0022i	−0.205614	+	0.594084i	−0.999910	−	0.0134484i	$-0.995719\pi$
$479$	−4.50009	+	13.0022i	−0.205614	+	0.594084i	0.794295	+	0.607532i	$0.207840\pi$
$480$	0.0831055	+	0.342565i	0.00379323	+	0.0156359i
$481$	1.46300	+	2.05449i	0.0667069	+	0.0936767i
$482$	2.43434			0.110881
$483$	8.09900	+	9.76761i	0.368517	+	0.444442i
$484$	17.1905			0.781385
$485$	−1.27645	−	1.79252i	−0.0579604	−	0.0813940i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	4.25531	−	12.2949i	0.192827	−	0.557136i	−0.806596	−	0.591103i	$-0.798693\pi$
$487$	4.25531	−	12.2949i	0.192827	−	0.557136i	0.999423	+	0.0339666i	$0.0108140\pi$
$488$	0.170905	+	3.58773i	0.00773650	+	0.162409i
$489$	0.696662	−	0.803991i	0.0315042	−	0.0363577i
$490$	−1.49649	−	1.96192i	−0.0676046	−	0.0886306i
$491$	18.7957	−	5.51893i	0.848240	−	0.249066i	0.171405	−	0.985201i	$-0.445169\pi$
$491$	18.7957	−	5.51893i	0.848240	−	0.249066i	0.676835	+	0.736135i	$0.263351\pi$
$492$	0.539594	−	0.278180i	0.0243268	−	0.0125413i
$493$	11.1315	−	8.75390i	0.501337	−	0.394256i
$494$	2.61211	−	3.66820i	0.117525	−	0.165040i
$495$	1.86312	+	0.177907i	0.0837412	+	0.00799631i
$496$	0.127700	+	0.888170i	0.00573388	+	0.0398800i
$497$	−0.0458449	−	0.125744i	−0.00205642	−	0.00564040i
$498$	−11.6665	+	3.42561i	−0.522791	+	0.153505i
$499$	−17.5180	−	13.7763i	−0.784214	−	0.616713i	0.143651	−	0.989628i	$-0.454116\pi$
$499$	−17.5180	−	13.7763i	−0.784214	−	0.616713i	−0.927865	+	0.372915i	$0.878358\pi$
$500$	3.41831	+	0.658825i	0.152871	+	0.0294635i
$501$	13.2077	+	6.80904i	0.590076	+	0.304205i
$502$	−20.6342	+	3.97691i	−0.920949	+	0.177498i
$503$	−37.2383	−	10.9342i	−1.66037	−	0.487530i	−0.688936	−	0.724823i	$-0.741922\pi$
$503$	−37.2383	−	10.9342i	−1.66037	−	0.487530i	−0.971438	+	0.237293i	$0.923740\pi$
$504$	−0.0825016	+	2.64446i	−0.00367491	+	0.117794i
$505$	−0.209271			−0.00931244
$506$	24.1406	+	8.10012i	1.07318	+	0.360094i
$507$	−3.20815	−	5.55668i	−0.142479	−	0.246781i
$508$	−18.9072	+	1.80541i	−0.838870	+	0.0801023i
$509$	18.0295	−	17.1911i	0.799145	−	0.761983i	−0.175801	−	0.984426i	$-0.556252\pi$
$509$	18.0295	−	17.1911i	0.799145	−	0.761983i	0.974946	+	0.222443i	$0.0714031\pi$
$510$	−0.862951	−	0.995899i	−0.0382121	−	0.0440991i
$511$	14.5581	+	30.5413i	0.644014	+	1.35107i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	1.37955	+	1.08489i	0.0609088	+	0.0478992i
$514$	16.2581	+	15.5021i	0.717115	+	0.683768i
$515$	−0.125425	+	2.63298i	−0.00552686	+	0.116023i
$516$	2.96502	+	1.18701i	0.130528	+	0.0522553i
$517$	15.7607	+	34.5111i	0.693154	+	1.51780i
$518$	2.48297	−	0.773549i	0.109096	−	0.0339878i
$519$	0.323025	+	2.24669i	0.0141792	+	0.0986187i
$520$	0.803929	−	0.414454i	0.0352546	−	0.0181750i
$521$	−9.02330	−	8.60370i	−0.395318	−	0.376935i	0.466185	−	0.884687i	$-0.345628\pi$
$521$	−9.02330	−	8.60370i	−0.395318	−	0.376935i	−0.861503	+	0.507752i	$0.830477\pi$
$522$	−3.51678	+	1.40791i	−0.153925	+	0.0616225i
$523$	11.0508	+	31.9291i	0.483216	+	1.39616i	0.878561	+	0.477630i	$0.158504\pi$
$523$	11.0508	+	31.9291i	0.483216	+	1.39616i	−0.395345	+	0.918533i	$0.629375\pi$
$524$	−9.74896	+	6.26527i	−0.425885	+	0.273700i
$525$	11.5614	+	5.72215i	0.504583	+	0.249735i
$526$	−18.6287	−	5.46989i	−0.812251	−	0.238498i
$527$	−1.94574	−	2.73242i	−0.0847580	−	0.119026i
$528$	2.65474	+	4.59814i	0.115533	+	0.200108i
$529$	18.3451	+	13.8729i	0.797613	+	0.603169i
$530$	0.892157	−	1.54526i	0.0387528	−	0.0671219i
$531$	−0.125347	+	0.274471i	−0.00543958	+	0.0119110i
$532$	−2.75515	−	3.73769i	−0.119451	−	0.162049i
$533$	−1.02007	−	1.17722i	−0.0441841	−	0.0509912i
$534$	0.656016	+	13.7715i	0.0283886	+	0.595950i
$535$	0.204538	+	0.0394214i	0.00884294	+	0.00170434i
$536$	−11.0799	+	4.43574i	−0.478581	+	0.191595i
$537$	0.964609	−	3.97617i	0.0416260	−	0.171585i
$538$	0.802477	+	0.515720i	0.0345972	+	0.0222343i
$539$	−29.9529	−	22.0035i	−1.29016	−	0.947759i
$540$	0.146435	+	0.320647i	0.00630154	+	0.0137985i
$541$	−27.3562	−	2.61220i	−1.17614	−	0.112307i	−0.511371	−	0.859360i	$-0.670862\pi$
$541$	−27.3562	−	2.61220i	−1.17614	−	0.112307i	−0.664765	+	0.747053i	$0.731468\pi$
$542$	−14.4868	+	11.3926i	−0.622263	+	0.489353i
$543$	−0.325539	+	6.83391i	−0.0139702	+	0.293271i
$544$	0.881341	−	3.63294i	0.0377872	−	0.155761i
$545$	0.519496	−	3.61317i	0.0222528	−	0.154771i
$546$	6.64400	−	1.39399i	0.284337	−	0.0596572i
$547$	−11.1403	+	7.15945i	−0.476326	+	0.306116i	−0.756686	−	0.653779i	$-0.773183\pi$
$547$	−11.1403	+	7.15945i	−0.476326	+	0.306116i	0.280360	+	0.959895i	$0.409546\pi$
$548$	−6.15354	+	1.18600i	−0.262866	+	0.0506633i
$549$	0.846799	+	3.49055i	0.0361405	+	0.148973i
$550$	25.7704	−	2.46077i	1.09885	−	0.104928i
$551$	3.32416	−	5.75762i	0.141614	−	0.245283i
$552$	0.952147	+	4.70036i	0.0405261	+	0.200061i
$553$	32.5563	−	13.6577i	1.38444	−	0.580784i
$554$	7.57072	−	16.5776i	0.321649	−	0.704313i
$555$	0.250771	−	0.239110i	0.0106447	−	0.0101497i
$556$	6.59027	−	19.0413i	0.279489	−	0.807532i
$557$	−2.56609	−	1.32291i	−0.108729	−	0.0560536i	0.403004	−	0.915198i	$-0.367966\pi$
$557$	−2.56609	−	1.32291i	−0.108729	−	0.0560536i	−0.511733	+	0.859145i	$0.670996\pi$
$558$	0.293479	+	0.847953i	0.0124240	+	0.0358967i
$559$	1.16625	−	8.11145i	0.0493272	−	0.343078i
$560$	−0.147860	−	0.920837i	−0.00624821	−	0.0389125i
$561$	−16.6976	−	10.7309i	−0.704973	−	0.453059i
$562$	7.75319	+	3.10391i	0.327049	+	0.130930i
$563$	−16.4367	+	23.0822i	−0.692726	+	0.972798i	0.307051	+	0.951693i	$0.400658\pi$
$563$	−16.4367	+	23.0822i	−0.692726	+	0.972798i	−0.999777	+	0.0211046i	$0.993282\pi$
$564$	−4.14488	+	5.82067i	−0.174531	+	0.245094i
$565$	4.85791	+	1.94482i	0.204374	+	0.0818190i
$566$	7.86320	+	5.05337i	0.330515	+	0.212409i
$567$	0.419458	+	2.61229i	0.0176156	+	0.109706i
$568$	0.00719929	−	0.0500722i	0.000302076	−	0.00210098i
$569$	−12.7197	−	36.7512i	−0.533237	−	1.54069i	−0.813973	−	0.580903i	$-0.802699\pi$
$569$	−12.7197	−	36.7512i	−0.533237	−	1.54069i	0.280735	−	0.959785i	$-0.409422\pi$
$570$	−0.549882	−	0.283484i	−0.0230320	−	0.0118738i
$571$	5.72387	−	16.5380i	0.239537	−	0.692096i	−0.759594	−	0.650398i	$-0.774602\pi$
$571$	5.72387	−	16.5380i	0.239537	−	0.692096i	0.999130	−	0.0416977i	$-0.0132766\pi$
$572$	9.85973	−	9.40124i	0.412256	−	0.393085i
$573$	−6.35592	+	13.9175i	−0.265522	+	0.581413i
$574$	−1.48113	+	0.621349i	−0.0618212	+	0.0259346i
$575$	22.7753	+	5.29748i	0.949794	+	0.220920i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−14.0301	+	1.33971i	−0.584080	+	0.0557729i	−0.382914	−	0.923784i	$-0.625079\pi$
$577$	−14.0301	+	1.33971i	−0.584080	+	0.0557729i	−0.201167	+	0.979557i	$0.564473\pi$
$578$	−0.713172	−	2.93973i	−0.0296640	−	0.122277i
$579$	−9.00459	+	1.73549i	−0.374218	+	0.0721246i
$580$	1.12335	−	0.721931i	0.0466445	−	0.0299766i
$581$	31.4844	−	6.60579i	1.30619	−	0.274054i
$582$	0.888424	−	6.17913i	0.0368264	−	0.256133i
$583$	6.33620	−	26.1182i	0.262419	−	1.08170i
$584$	−0.608471	+	12.7734i	−0.0251787	+	0.528567i
$585$	0.710965	−	0.559109i	0.0293948	−	0.0231163i
$586$	25.5723	+	2.44186i	1.05638	+	0.100872i
$587$	4.94949	+	10.8379i	0.204287	+	0.447327i	0.983849	−	0.178998i	$-0.0572855\pi$
$587$	4.94949	+	10.8379i	0.204287	+	0.447327i	−0.779562	+	0.626325i	$0.784558\pi$
$588$	0.768276	−	6.95771i	0.0316832	−	0.286931i
$589$	−1.32481	−	0.851403i	−0.0545878	−	0.0350814i
$590$	0.0250761	−	0.103365i	0.00103237	−	0.00425547i
$591$	15.3960	−	6.16363i	0.633307	−	0.253538i
$592$	0.965201	+	0.186027i	0.0396695	+	0.00764567i
$593$	2.13481	+	44.8151i	0.0876660	+	1.84034i	0.432454	+	0.901656i	$0.357648\pi$
$593$	2.13481	+	44.8151i	0.0876660	+	1.84034i	−0.344788	+	0.938680i	$0.612049\pi$
$594$	3.47696	+	4.01263i	0.142662	+	0.164640i
$595$	2.06869	+	2.80643i	0.0848080	+	0.115052i
$596$	1.23618	−	2.70687i	0.0506361	−	0.110878i
$597$	−6.72625	+	11.6502i	−0.275287	+	0.476811i
$598$	11.1446	−	5.21760i	0.455736	−	0.213363i
$599$	−13.1605	−	22.7946i	−0.537722	−	0.931362i	−0.999026	−	0.0441199i	$-0.985952\pi$
$599$	−13.1605	−	22.7946i	−0.537722	−	0.931362i	0.461304	−	0.887242i	$-0.347382\pi$
$600$	2.82821	+	3.97166i	0.115461	+	0.162142i
$601$	7.67582	+	2.25382i	0.313103	+	0.0919354i	0.434509	−	0.900668i	$-0.356922\pi$
$601$	7.67582	+	2.25382i	0.313103	+	0.0919354i	−0.121406	+	0.992603i	$0.538740\pi$
$602$	−7.57318	−	3.74822i	−0.308660	−	0.152766i
$603$	−10.0402	+	6.45247i	−0.408870	+	0.262765i
$604$	−3.14138	−	9.07644i	−0.127821	−	0.369315i
$605$	−5.62561	+	2.25215i	−0.228714	+	0.0915631i
$606$	−0.429662	−	0.409682i	−0.0174538	−	0.0166422i
$607$	20.1856	−	10.4064i	0.819310	−	0.422384i	0.00299850	−	0.999996i	$-0.499046\pi$
$607$	20.1856	−	10.4064i	0.819310	−	0.422384i	0.816312	+	0.577612i	$0.196015\pi$
$608$	−0.249768	−	1.73717i	−0.0101294	−	0.0704517i
$609$	9.56885	−	2.98110i	0.387749	−	0.120800i
$610$	−0.525964	−	1.15170i	−0.0212957	−	0.0466310i
$611$	17.0215	+	6.81436i	0.688614	+	0.275680i
$612$	0.177876	−	3.73408i	0.00719022	−	0.150941i
$613$	26.5662	+	25.3308i	1.07300	+	1.02310i	0.999667	+	0.0257935i	$0.00821123\pi$
$613$	26.5662	+	25.3308i	1.07300	+	1.02310i	0.0733303	+	0.997308i	$0.476637\pi$
$614$	21.5967	+	16.9839i	0.871574	+	0.685413i
$615$	−0.140138	+	0.161728i	−0.00565092	+	0.00652150i
$616$	−6.04448	−	12.6806i	−0.243539	−	0.510916i
$617$	−12.4796	−	14.4023i	−0.502411	−	0.579813i	0.446728	−	0.894670i	$-0.352589\pi$
$617$	−12.4796	−	14.4023i	−0.502411	−	0.579813i	−0.949139	+	0.314856i	$0.898044\pi$
$618$	−5.41200	+	5.16033i	−0.217703	+	0.207579i
$619$	26.9879	−	2.57703i	1.08474	−	0.103580i	0.462659	−	0.886536i	$-0.346895\pi$
$619$	26.9879	−	2.57703i	1.08474	−	0.103580i	0.622077	+	0.782956i	$0.286289\pi$
$620$	−0.158151	−	0.273925i	−0.00635148	−	0.0110011i
$621$	1.82449	+	4.43523i	0.0732143	+	0.177980i
$622$	−27.1309			−1.08785
$623$	1.13746	−	36.4595i	0.0455712	−	1.46072i
$624$	2.46194	+	0.722890i	0.0985563	+	0.0289387i
$625$	22.7332	−	4.38146i	0.909328	−	0.175259i
$626$	−9.68618	−	4.99357i	−0.387138	−	0.199583i
$627$	−9.14993	−	1.76350i	−0.365413	−	0.0704276i
$628$	7.17727	+	5.64427i	0.286404	+	0.225231i
$629$	−3.52578	+	1.03526i	−0.140582	+	0.0412786i
$630$	−0.319457	−	0.876214i	−0.0127275	−	0.0349092i
$631$	−3.34046	−	23.2334i	−0.132982	−	0.924907i	−0.941638	−	0.336626i	$-0.890714\pi$
$631$	−3.34046	−	23.2334i	−0.132982	−	0.924907i	0.808657	−	0.588281i	$-0.200195\pi$
$632$	13.2836	+	1.26843i	0.528395	+	0.0504556i
$633$	−7.74023	+	10.8696i	−0.307646	+	0.432029i
$634$	−24.5635	+	19.3169i	−0.975540	+	0.767173i
$635$	5.95087	−	3.06788i	0.236153	−	0.121745i
$636$	4.85682	−	1.42609i	0.192585	−	0.0565481i
$637$	−17.8141	+	2.29318i	−0.705821	+	0.0908590i
$638$	13.1712	−	15.2004i	0.521453	−	0.601789i
$639$	−0.00240703	−	0.0505298i	−9.52207e−5	−	0.00199893i
$640$	0.115292	−	0.333115i	0.00455732	−	0.0131675i
$641$	−4.54477	−	18.7338i	−0.179508	−	0.739941i	−0.988386	−	0.151965i	$-0.951440\pi$
$641$	−4.54477	−	18.7338i	−0.179508	−	0.739941i	0.808878	−	0.587976i	$-0.200075\pi$
$642$	0.342770	+	0.481353i	0.0135281	+	0.0189975i
$643$	−21.5310			−0.849098			−0.424549	−	0.905405i	$-0.639567\pi$
$643$	−21.5310			−0.849098			−0.424549	+	0.905405i	$0.639567\pi$
$644$	−1.53254	−	12.5957i	−0.0603906	−	0.496340i
$645$	−1.12582			−0.0443291
$646$	3.80569	+	5.34434i	0.149733	+	0.210270i
$647$	−0.761017	−	3.13696i	−0.0299187	−	0.123326i	0.954894	−	0.296947i	$-0.0959685\pi$
$647$	−0.761017	−	3.13696i	−0.0299187	−	0.123326i	−0.984813	+	0.173621i	$0.944453\pi$
$648$	−0.327068	+	0.945001i	−0.0128484	+	0.0371231i
$649$	−0.0762296	−	1.60026i	−0.00299227	−	0.0628155i
$650$	8.19265	−	9.45483i	0.321342	−	0.370849i
$651$	−0.597490	−	2.29763i	−0.0234175	−	0.0900511i
$652$	−1.02074	+	0.299716i	−0.0399753	+	0.0117378i
$653$	5.79090	−	2.98542i	0.226616	−	0.116828i	−0.341180	−	0.939998i	$-0.610827\pi$
$653$	5.79090	−	2.98542i	0.226616	−	0.116828i	0.567796	+	0.823169i	$0.307796\pi$
$654$	8.13996	−	6.40134i	0.318298	−	0.250312i
$655$	2.36954	−	3.32755i	0.0925854	−	0.130018i
$656$	−0.604331	−	0.0577066i	−0.0235952	−	0.00225306i
$657$	1.81990	+	12.6577i	0.0710012	+	0.493824i
$658$	12.1444	−	14.4892i	0.473437	−	0.564846i
$659$	−36.8158	+	10.8101i	−1.43414	+	0.421101i	−0.904264	−	0.426975i	$-0.859579\pi$
$659$	−36.8158	+	10.8101i	−1.43414	+	0.421101i	−0.529875	+	0.848076i	$0.677761\pi$
$660$	−1.47118	−	1.15695i	−0.0572654	−	0.0450340i
$661$	−23.0291	−	4.43850i	−0.895729	−	0.172638i	−0.279445	−	0.960162i	$-0.590150\pi$
$661$	−23.0291	−	4.43850i	−0.895729	−	0.172638i	−0.616284	+	0.787524i	$0.711363\pi$
$662$	−16.2030	−	8.35321i	−0.629747	−	0.324657i
$663$	−9.41870	+	1.81530i	−0.365792	+	0.0705006i
$664$	11.6665	+	3.42561i	0.452750	+	0.132939i
$665$	1.39131	+	0.862207i	0.0539525	+	0.0334350i
$666$	0.982964			0.0380891
$667$	15.6466	−	9.23213i	0.605840	−	0.357470i
$668$	−7.42977	−	12.8687i	−0.287467	−	0.497907i
$669$	12.5026	−	1.19386i	0.483379	−	0.0461571i
$670$	3.04479	−	2.90321i	0.117631	−	0.112161i
$671$	−12.4886	−	14.4126i	−0.482116	−	0.556391i
$672$	1.49911	−	2.18006i	0.0578294	−	0.0840977i
$673$	30.5670	−	35.2762i	1.17827	−	1.35980i	0.259142	−	0.965839i	$-0.416560\pi$
$673$	30.5670	−	35.2762i	1.17827	−	1.35980i	0.919129	−	0.393958i	$-0.128894\pi$
$674$	−14.9578	−	11.7629i	−0.576152	−	0.453091i
$675$	3.52874	+	3.36465i	0.135821	+	0.129505i
$676$	−0.305300	+	6.40903i	−0.0117423	+	0.246501i
$677$	−5.42493	−	2.17181i	−0.208497	−	0.0834696i	0.265063	−	0.964231i	$-0.414607\pi$
$677$	−5.42493	−	2.17181i	−0.208497	−	0.0834696i	−0.473560	+	0.880761i	$0.657031\pi$
$678$	6.16666	+	13.5031i	0.236829	+	0.518584i
$679$	−3.62998	+	16.1127i	−0.139306	+	0.618349i
$680$	0.187537	+	1.30435i	0.00719173	+	0.0500195i
$681$	−8.84431	+	4.55956i	−0.338915	+	0.174723i
$682$	−3.44802	−	3.28768i	−0.132031	−	0.125892i
$683$	−34.4044	+	13.7735i	−1.31645	+	0.527027i	−0.920320	−	0.391167i	$-0.872071\pi$
$683$	−34.4044	+	13.7735i	−1.31645	+	0.527027i	−0.396130	+	0.918194i	$0.629647\pi$
$684$	−0.574017	−	1.65851i	−0.0219481	−	0.0634148i
$685$	1.85837	−	1.19430i	0.0710048	−	0.0456320i
$686$	−3.47521	+	18.1913i	−0.132684	+	0.694547i
$687$	−2.58580	−	0.759260i	−0.0986545	−	0.0289676i
$688$	−1.85258	−	2.60159i	−0.0706290	−	0.0991846i
$689$	−6.49404	−	11.2480i	−0.247403	−	0.428515i
$690$	−0.927394	−	1.41346i	−0.0353053	−	0.0538094i
$691$	−9.30065	+	16.1092i	−0.353813	+	0.612823i	−0.986914	−	0.161247i	$-0.948449\pi$
$691$	−9.30065	+	16.1092i	−0.353813	+	0.612823i	0.633101	+	0.774069i	$0.281782\pi$
$692$	0.942905	−	2.06467i	0.0358439	−	0.0784872i
$693$	−8.33507	−	11.3075i	−0.316623	−	0.429537i
$694$	6.22914	+	7.18881i	0.236455	+	0.272884i
$695$	0.337962	+	7.09470i	0.0128196	+	0.269117i
$696$	3.71968	+	0.716909i	0.140994	+	0.0271744i
$697$	2.10689	−	0.843472i	0.0798042	−	0.0319488i
$698$	4.24570	−	17.5010i	0.160702	−	0.662423i
$699$	−12.1504	−	7.80857i	−0.459569	−	0.295347i
$700$	−6.63248	−	11.0644i	−0.250684	−	0.418194i
$701$	12.7698	+	27.9621i	0.482310	+	1.05611i	0.981822	+	0.189805i	$0.0607857\pi$
$701$	12.7698	+	27.9621i	0.482310	+	1.05611i	−0.499511	+	0.866307i	$0.666487\pi$
$702$	2.55425	+	0.243902i	0.0964041	+	0.00920547i
$703$	−1.35605	+	1.06641i	−0.0511445	+	0.0402204i
$704$	0.252635	−	5.30346i	0.00952153	−	0.199882i
$705$	0.593842	−	2.44785i	0.0223654	−	0.0921914i
$706$	−2.62809	+	18.2788i	−0.0989096	+	0.687932i
$707$	1.04794	+	1.17003i	0.0394119	+	0.0440033i
$708$	0.253838	−	0.163132i	0.00953983	−	0.00613088i
$709$	0.699257	−	0.134771i	0.0262612	−	0.00506142i	−0.176104	−	0.984372i	$-0.556349\pi$
$709$	0.699257	−	0.134771i	0.0262612	−	0.00506142i	0.202365	+	0.979310i	$0.435137\pi$
$710$	0.00420406	+	0.0173294i	0.000157776	+	0.000650360i
$711$	13.2836	−	1.26843i	0.498175	−	0.0475700i
$712$	6.89354	−	11.9400i	0.258346	−	0.447469i
$713$	−2.00801	−	3.80611i	−0.0752005	−	0.142540i
$714$	−1.24673	+	9.81176i	−0.0466577	+	0.367196i
$715$	−1.99494	+	4.36831i	−0.0746065	+	0.163366i
$716$	−2.96116	+	2.82346i	−0.110664	+	0.105518i
$717$	7.07957	−	20.4551i	0.264391	−	0.763909i
$718$	−16.5759	−	8.54545i	−0.618605	−	0.318913i
$719$	−10.2070	−	29.4911i	−0.380655	−	1.09983i	−0.958845	−	0.283929i	$-0.908362\pi$
$719$	−10.2070	−	29.4911i	−0.380655	−	1.09983i	0.578190	−	0.815902i	$-0.303759\pi$
$720$	0.0501663	−	0.348914i	0.00186959	−	0.0130033i
$721$	15.3490	−	12.4836i	0.571625	−	0.464915i
$722$	−13.3926	−	8.60691i	−0.498422	−	0.320316i
$723$	−2.25996	−	0.904752i	−0.0840489	−	0.0336481i
$724$	3.96855	−	5.57305i	0.147490	−	0.207121i
$725$	10.7136	−	15.0452i	0.397894	−	0.558765i
$726$	−15.9591	−	6.38906i	−0.592297	−	0.237120i
$727$	−25.1450	−	16.1597i	−0.932577	−	0.599331i	−0.0162963	−	0.999867i	$-0.505187\pi$
$727$	−25.1450	−	16.1597i	−0.932577	−	0.599331i	−0.916281	+	0.400536i	$0.868824\pi$
$728$	−6.34293	−	2.41932i	−0.235085	−	0.0896659i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−1.47434	−	4.25983i	−0.0545678	−	0.157663i
$731$	10.6122	+	5.47095i	0.392505	+	0.202350i
$732$	1.17476	−	3.39426i	0.0434205	−	0.125455i
$733$	−24.1054	+	22.9844i	−0.890351	+	0.848948i	−0.989263	−	0.146148i	$-0.953312\pi$
$733$	−24.1054	+	22.9844i	−0.890351	+	0.848948i	0.0989113	+	0.995096i	$0.468464\pi$
$734$	11.7222	−	25.6679i	0.432673	−	0.947421i
$735$	0.660122	+	2.37757i	0.0243490	+	0.0876982i
$736$	1.74021	−	4.46897i	0.0641450	−	0.164728i
$737$	31.6839	−	54.8781i	1.16709	−	2.02146i
$738$	−0.604331	+	0.0577066i	−0.0222457	+	0.00212421i
$739$	6.47323	+	26.6830i	0.238122	+	0.981550i	0.957844	+	0.287288i	$0.0927538\pi$
$739$	6.47323	+	26.6830i	0.238122	+	0.981550i	−0.719723	+	0.694262i	$0.755731\pi$
$740$	−0.340235	+	0.0655749i	−0.0125073	+	0.00241058i
$741$	−3.78834	+	2.43462i	−0.139168	+	0.0894379i
$742$	−13.1070	+	2.75001i	−0.481174	+	0.100956i
$743$	2.06125	−	14.3363i	0.0756199	−	0.525948i	−0.916439	−	0.400174i	$-0.868950\pi$
$743$	2.06125	−	14.3363i	0.0756199	−	0.525948i	0.992059	−	0.125774i	$-0.0401414\pi$
$744$	0.211547	−	0.872010i	0.00775570	−	0.0319694i
$745$	−0.0499120	+	1.04778i	−0.00182863	+	0.0383877i
$746$	−10.8256	+	8.51337i	−0.396354	+	0.311697i
$747$	12.1040	+	1.15579i	0.442863	+	0.0422883i
$748$	8.24535	+	18.0548i	0.301480	+	0.660149i
$749$	−0.803836	−	1.34097i	−0.0293715	−	0.0489979i
$750$	−2.92859	−	1.88209i	−0.106937	−	0.0687242i
$751$	−5.86253	+	24.1657i	−0.213927	+	0.881819i	0.759072	+	0.651007i	$0.225653\pi$
$751$	−5.86253	+	24.1657i	−0.213927	+	0.881819i	−0.972998	+	0.230812i	$0.925862\pi$
$752$	6.63379	−	2.65577i	0.241909	−	0.0968459i
$753$	20.6342	+	3.97691i	0.751952	+	0.144927i
$754$	−0.462490	−	9.70886i	−0.0168429	−	0.353576i
$755$	2.21714	+	2.55872i	0.0806901	+	0.0931213i
$756$	1.05944	−	2.42437i	0.0385315	−	0.0881736i
$757$	1.63212	−	3.57385i	0.0593206	−	0.129894i	−0.877650	−	0.479302i	$-0.840890\pi$
$757$	1.63212	−	3.57385i	0.0593206	−	0.129894i	0.936971	+	0.349408i	$0.113617\pi$
$758$	−13.4681	+	23.3275i	−0.489185	+	0.847293i
$759$	−19.4009	−	16.4920i	−0.704207	−	0.598623i
$760$	0.309327	+	0.535771i	0.0112205	+	0.0194344i
$761$	−10.1358	−	14.2337i	−0.367422	−	0.515971i	0.588932	−	0.808182i	$-0.299548\pi$
$761$	−10.1358	−	14.2337i	−0.367422	−	0.515971i	−0.956354	+	0.292211i	$0.905609\pi$
$762$	18.2238	+	5.35099i	0.660179	+	0.193846i
$763$	−22.8025	+	15.1888i	−0.825506	+	0.549870i
$764$	12.8713	−	8.27189i	0.465668	−	0.299267i
$765$	0.430998	+	1.24529i	0.0155828	+	0.0450235i
$766$	33.3934	−	13.3687i	1.20655	−	0.483031i
$767$	−0.560331	−	0.534274i	−0.0202324	−	0.0192915i
$768$	0.888835	−	0.458227i	0.0320731	−	0.0165348i
$769$	2.27653	+	15.8336i	0.0820938	+	0.570975i	0.988804	+	0.149221i	$0.0476765\pi$
$769$	2.27653	+	15.8336i	0.0820938	+	0.570975i	−0.906710	+	0.421754i	$0.861414\pi$
$770$	3.63937	+	3.35785i	0.131154	+	0.121008i
$771$	−9.33197	−	20.4342i	−0.336083	−	0.735919i
$772$	8.51342	+	3.40826i	0.306405	+	0.122666i
$773$	−0.720098	+	15.1167i	−0.0259001	+	0.543710i	0.948211	+	0.317641i	$0.102891\pi$
$773$	−0.720098	+	15.1167i	−0.0259001	+	0.543710i	−0.974111	+	0.226070i	$0.927412\pi$
$774$	−2.31146	−	2.20397i	−0.0830836	−	0.0792201i
$775$	−3.43900	−	2.70446i	−0.123533	−	0.0971470i
$776$	−4.08808	+	4.71789i	−0.146753	+	0.169363i
$777$	−2.59261	−	0.204689i	−0.0930094	−	0.00734319i
$778$	−3.31961	−	3.83103i	−0.119014	−	0.137349i
$779$	0.771102	−	0.735244i	0.0276276	−	0.0263428i
$780$	−0.900379	+	0.0859758i	−0.0322387	+	0.00307843i
$781$	0.134295	+	0.232606i	0.00480546	+	0.00832331i
$782$	1.87304	+	17.8302i	0.0669797	+	0.637607i
$783$	3.78814			0.135377
$784$	−4.40794	+	5.43784i	−0.157426	+	0.194208i
$785$	−3.08824	−	0.906788i	−0.110224	−	0.0323647i
$786$	11.3792	−	2.19316i	0.405882	−	0.0782274i
$787$	−18.0947	−	9.32848i	−0.645007	−	0.332524i	0.104496	−	0.994525i	$-0.466677\pi$
$787$	−18.0947	−	9.32848i	−0.645007	−	0.332524i	−0.749503	+	0.662001i	$0.769707\pi$
$788$	−16.2842	−	3.13853i	−0.580102	−	0.111806i
$789$	15.2614	+	12.0017i	0.543319	+	0.427271i
$790$	−4.51327	+	1.32522i	−0.160575	+	0.0471490i
$791$	−13.4530	−	36.8992i	−0.478334	−	1.31198i
$792$	−0.755616	−	5.25543i	−0.0268497	−	0.186743i
$793$	−9.17437	−	0.876046i	−0.325791	−	0.0311093i
$794$	−15.3376	+	21.5386i	−0.544311	+	0.764378i
$795$	−1.40257	+	1.10299i	−0.0497439	+	0.0391190i
$796$	11.9571	−	6.16429i	0.423807	−	0.218488i
$797$	−22.4070	+	6.57929i	−0.793697	+	0.233050i	−0.653354	−	0.757052i	$-0.726639\pi$
$797$	−22.4070	+	6.57929i	−0.793697	+	0.233050i	−0.140343	+	0.990103i	$0.544821\pi$
$798$	1.16863	+	4.49393i	0.0413691	+	0.159083i
$799$	−17.4931	+	20.1881i	−0.618861	+	0.714203i
$800$	−0.231997	−	4.87022i	−0.00820234	−	0.172188i
$801$	4.50931	−	13.0288i	0.159329	−	0.460350i
$802$	4.62523	+	19.0654i	0.163322	+	0.673224i
$803$	−39.3840	−	55.3071i	−1.38983	−	1.95175i
$804$	11.9349			0.420910
$805$	2.15171	+	3.92118i	0.0758378	+	0.138203i
$806$	−2.30237			−0.0810974
$807$	−0.553320	−	0.777029i	−0.0194778	−	0.0273527i
$808$	0.139964	+	0.576939i	0.00492391	+	0.0202966i
$809$	−9.79509	+	28.3011i	−0.344377	+	0.995012i	0.631250	+	0.775579i	$0.282542\pi$
$809$	−9.79509	+	28.3011i	−0.344377	+	0.995012i	−0.975628	+	0.219433i	$0.929579\pi$
$810$	−0.0167727	−	0.352103i	−0.000589333	−	0.0123716i
$811$	18.9698	−	21.8923i	0.666121	−	0.768744i	−0.317643	−	0.948210i	$-0.602892\pi$
$811$	18.9698	−	21.8923i	0.666121	−	0.768744i	0.983764	+	0.179466i	$0.0574370\pi$
$812$	−9.66153	−	2.66545i	−0.339053	−	0.0935391i
$813$	17.6833	−	5.19229i	0.620181	−	0.182102i
$814$	−4.63885	+	2.39149i	−0.162592	+	0.0838218i
$815$	0.294772	−	0.231812i	0.0103254	−	0.00812001i
$816$	−2.16844	+	3.04514i	−0.0759104	+	0.106601i
$817$	5.57985	+	0.532811i	0.195214	+	0.0186407i
$818$	0.895505	+	6.22837i	0.0313106	+	0.217770i
$819$	−6.68617	−	1.17519i	−0.233634	−	0.0410645i
$820$	0.205328	−	0.0602899i	0.00717038	−	0.00210541i
$821$	−11.2163	−	8.82058i	−0.391451	−	0.307840i	0.402964	−	0.915216i	$-0.367980\pi$
$821$	−11.2163	−	8.82058i	−0.391451	−	0.307840i	−0.794415	+	0.607376i	$0.792222\pi$
$822$	6.15354	+	1.18600i	0.214629	+	0.0413664i
$823$	−13.6580	−	7.04118i	−0.476087	−	0.245440i	0.203444	−	0.979087i	$-0.434786\pi$
$823$	−13.6580	−	7.04118i	−0.476087	−	0.245440i	−0.679531	+	0.733647i	$0.737817\pi$
$824$	7.34275	−	1.41520i	0.255797	−	0.0493008i
$825$	−24.8390	−	7.29338i	−0.864782	−	0.253923i
$826$	−0.703480	+	0.377409i	−0.0244772	+	0.0131317i
$827$	33.6298			1.16942			0.584711	−	0.811242i	$-0.301208\pi$
$827$	33.6298			1.16942			0.584711	+	0.811242i	$0.301208\pi$
$828$	0.863006	−	4.71754i	0.0299915	−	0.163946i
$829$	26.3652	+	45.6659i	0.915702	+	1.58604i	0.805871	+	0.592091i	$0.201698\pi$
$829$	26.3652	+	45.6659i	0.915702	+	1.58604i	0.109831	+	0.993950i	$0.464969\pi$
$830$	−4.26669	+	0.407420i	−0.148099	+	0.0141417i
$831$	−13.1897	+	12.5763i	−0.457545	+	0.436268i
$832$	−1.68029	−	1.93916i	−0.0582535	−	0.0672282i
$833$	5.33147	−	25.6193i	0.184725	−	0.887657i
$834$	−13.1951	+	15.2280i	−0.456910	+	0.527302i
$835$	4.11736	+	3.23793i	0.142487	+	0.112053i
$836$	6.74399	+	6.43038i	0.233246	+	0.222399i
$837$	0.0426954	−	0.896287i	0.00147577	−	0.0309802i
$838$	−20.3347	−	8.14078i	−0.702450	−	0.281218i
$839$	−9.64830	−	21.1268i	−0.333096	−	0.729379i	0.666778	−	0.745257i	$-0.267673\pi$
$839$	−9.64830	−	21.1268i	−0.333096	−	0.729379i	−0.999874	+	0.0158776i	$0.994946\pi$
$840$	−0.204972	+	0.909829i	−0.00707222	+	0.0313921i
$841$	2.08492	+	14.5009i	0.0718937	+	0.500031i
$842$	21.7896	−	11.2333i	0.750919	−	0.387125i
$843$	−6.04421	−	5.76314i	−0.208174	−	0.198493i
$844$	12.3881	−	4.95943i	0.426415	−	0.170711i
$845$	−0.739749	−	2.13736i	−0.0254481	−	0.0735276i
$846$	6.01130	−	3.86323i	0.206673	−	0.132821i
$847$	40.7624	+	20.1747i	1.40061	+	0.693210i
$848$	−4.85682	−	1.42609i	−0.166784	−	0.0489721i
$849$	−5.42179	−	7.61385i	−0.186076	−	0.261306i
$850$	9.11353	+	15.7851i	0.312591	+	0.541424i
$851$	−4.65959	+	0.715024i	−0.159729	+	0.0245107i
$852$	−0.0252935	+	0.0438097i	−0.000866542	+	0.00150090i
$853$	−12.1363	+	26.5748i	−0.415539	+	0.909904i	0.579916	+	0.814676i	$0.303085\pi$
$853$	−12.1363	+	26.5748i	−0.415539	+	0.909904i	−0.995456	+	0.0952276i	$0.969642\pi$
$854$	−3.80530	+	8.70787i	−0.130215	+	0.297977i
$855$	0.405133	+	0.467548i	0.0138552	+	0.0159898i
$856$	−0.0281173	−	0.590256i	−0.000961031	−	0.0201745i
$857$	6.29071	+	1.21244i	0.214887	+	0.0414160i	0.295558	−	0.955325i	$-0.404494\pi$
$857$	6.29071	+	1.21244i	0.214887	+	0.0414160i	−0.0806716	+	0.996741i	$0.525707\pi$
$858$	−12.6475	+	5.06331i	−0.431780	+	0.172859i
$859$	9.74685	−	40.1770i	0.332558	−	1.37082i	−0.522654	−	0.852545i	$-0.675058\pi$
$859$	9.74685	−	40.1770i	0.332558	−	1.37082i	0.855212	−	0.518278i	$-0.173427\pi$
$860$	0.947099	+	0.608663i	0.0322958	+	0.0207553i
$861$	1.60597	−	0.0263598i	0.0547312	−	0.000898339i
$862$	14.0062	+	30.6693i	0.477053	+	1.04460i
$863$	30.9748	+	2.95773i	1.05439	+	0.100682i	0.607828	−	0.794069i	$-0.292041\pi$
$863$	30.9748	+	2.95773i	1.05439	+	0.100682i	0.446566	+	0.894751i	$0.352647\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	−0.0380706	+	0.799200i	−0.00129444	+	0.0271736i
$866$	0.445144	−	1.83491i	0.0151266	−	0.0623528i
$867$	−0.430503	+	2.99421i	−0.0146206	+	0.101689i
$868$	−0.739550	+	2.25591i	−0.0251020	+	0.0765707i
$869$	−59.6027	+	38.3043i	−2.02188	+	1.29939i
$870$	−1.31119	+	0.252712i	−0.0444536	+	0.00856774i
$871$	−7.21972	−	29.7601i	−0.244631	−	1.00838i
$872$	−10.3086	+	0.984351i	−0.349093	+	0.0333343i
$873$	−3.12133	+	5.40631i	−0.105641	+	0.182976i
$874$	3.92747	+	7.44437i	0.132849	+	0.251810i
$875$	7.33236	+	5.57393i	0.247879	+	0.188433i
$876$	5.31227	−	11.6323i	0.179485	−	0.393018i
$877$	20.0949	−	19.1605i	0.678557	−	0.647002i	−0.270276	−	0.962783i	$-0.587115\pi$
$877$	20.0949	−	19.1605i	0.678557	−	0.647002i	0.948832	+	0.315781i	$0.102266\pi$
$878$	−12.0680	+	34.8682i	−0.407275	+	1.17674i
$879$	−22.8329	−	11.7712i	−0.770136	−	0.397033i
$880$	0.612140	+	1.76866i	0.0206352	+	0.0596216i
$881$	−4.65413	+	32.3702i	−0.156802	+	1.09058i	0.747677	+	0.664062i	$0.231169\pi$
$881$	−4.65413	+	32.3702i	−0.156802	+	1.09058i	−0.904479	+	0.426518i	$0.859740\pi$
$882$	−3.29916	+	6.17378i	−0.111089	+	0.207882i
$883$	15.1988	+	9.76765i	0.511479	+	0.328707i	0.770793	−	0.637086i	$-0.219860\pi$
$883$	15.1988	+	9.76765i	0.511479	+	0.328707i	−0.259314	+	0.965793i	$0.583497\pi$
$884$	8.90494	+	3.56500i	0.299505	+	0.119904i
$885$	−0.0616968	+	0.0866410i	−0.00207391	+	0.00291240i
$886$	−3.43133	+	4.81863i	−0.115278	+	0.161885i
$887$	37.5720	+	15.0415i	1.26154	+	0.505046i	0.903471	−	0.428648i	$-0.141010\pi$
$887$	37.5720	+	15.0415i	1.26154	+	0.505046i	0.358072	+	0.933694i	$0.383434\pi$
$888$	−0.826922	−	0.531431i	−0.0277497	−	0.0178336i
$889$	−46.9518	−	17.9083i	−1.57471	−	0.600627i
$890$	−0.691646	+	4.81051i	−0.0231840	+	0.161249i
$891$	−1.73656	−	5.01745i	−0.0581769	−	0.168091i
$892$	−11.1633	−	5.75509i	−0.373776	−	0.192695i
$893$	−4.10172	+	11.8511i	−0.137259	+	0.396583i
$894$	−2.15367	+	2.05352i	−0.0720297	+	0.0686801i
$895$	0.599138	−	1.31193i	0.0200270	−	0.0438530i
$896$	−2.43976	+	1.02350i	−0.0815067	+	0.0341929i
$897$	−12.2855	+	0.701828i	−0.410200	+	0.0234333i
$898$	−14.0889	+	24.4026i	−0.470151	+	0.814326i
$899$	−3.38372	+	0.323106i	−0.112853	+	0.0107762i
$900$	−1.14950	−	4.73830i	−0.0383167	−	0.157943i
$901$	18.5809	−	3.58117i	0.619018	−	0.119306i
$902$	2.71159	−	1.74263i	0.0902861	−	0.0580233i
$903$	5.63762	+	6.29440i	0.187608	+	0.209464i
$904$	2.11260	−	14.6935i	0.0702642	−	0.488698i
$905$	−0.568579	+	2.34372i	−0.0189002	+	0.0779078i
$906$	−0.457009	+	9.59381i	−0.0151831	+	0.318733i
$907$	−21.6652	+	17.0377i	−0.719382	+	0.565728i	−0.909335	−	0.416065i	$-0.863409\pi$
$907$	−21.6652	+	17.0377i	−0.719382	+	0.565728i	0.189953	+	0.981793i	$0.439166\pi$
$908$	9.90540	+	0.945851i	0.328722	+	0.0313892i
$909$	0.246621	+	0.540025i	0.00817990	+	0.0179115i
$910$	2.39269	−	0.0392728i	0.0793170	−	0.00130188i
$911$	34.9067	+	22.4332i	1.15651	+	0.743244i	0.970925	−	0.239385i	$-0.0769457\pi$
$911$	34.9067	+	22.4332i	1.15651	+	0.743244i	0.185585	+	0.982628i	$0.440582\pi$
$912$	−0.413766	+	1.70557i	−0.0137012	+	0.0564770i
$913$	−59.9338	+	23.9939i	−1.98352	+	0.794082i
$914$	24.4618	+	4.71462i	0.809124	+	0.155946i
$915$	0.0602443	+	1.26468i	0.00199161	+	0.0418091i
$916$	1.76483	+	2.03672i	0.0583116	+	0.0672951i
$917$	−30.4698	+	3.41499i	−1.00620	+	0.112773i
$918$	−1.55295	+	3.40049i	−0.0512551	+	0.112233i
$919$	−24.3418	+	42.1613i	−0.802963	+	1.39077i	0.114694	+	0.993401i	$0.463411\pi$
$919$	−24.3418	+	42.1613i	−0.802963	+	1.39077i	−0.917657	+	0.397372i	$0.869922\pi$
$920$	0.0160004	+	1.69046i	0.000527517	+	0.0557330i
$921$	−13.7375	−	23.7940i	−0.452665	−	0.784038i
$922$	4.06485	+	5.70828i	0.133869	+	0.187992i
$923$	0.124542	+	0.0365689i	0.00409936	+	0.00120368i
$924$	0.898598	+	14.0188i	0.0295617	+	0.461184i
$925$	−4.03186	+	2.59112i	−0.132567	+	0.0851954i
$926$	−3.15194	−	9.10693i	−0.103579	−	0.299272i
$927$	6.94223	−	2.77925i	0.228013	−	0.0912826i
$928$	−2.74160	−	2.61411i	−0.0899975	−	0.0858125i
$929$	−25.0615	+	12.9201i	−0.822242	+	0.423895i	−0.817384	−	0.576093i	$-0.804577\pi$
$929$	−25.0615	+	12.9201i	−0.822242	+	0.423895i	−0.00485776	+	0.999988i	$0.501546\pi$
$930$	0.0450144	+	0.313082i	0.00147608	+	0.0102664i
$931$	−2.14651	−	12.0963i	−0.0703492	−	0.396440i
$932$	5.99991	+	13.1380i	0.196534	+	0.430349i
$933$	25.1875	+	10.0836i	0.824601	+	0.330121i
$934$	1.06618	−	22.3818i	0.0348864	−	0.732355i
$935$	−5.06370	−	4.82822i	−0.165601	−	0.157900i
$936$	−2.01691	−	1.58612i	−0.0659248	−	0.0518438i
$937$	12.3149	−	14.2122i	0.402311	−	0.464292i	−0.518056	−	0.855347i	$-0.673344\pi$
$937$	12.3149	−	14.2122i	0.402311	−	0.464292i	0.920367	+	0.391055i	$0.127890\pi$
$938$	−31.4787	−	2.48528i	−1.02782	−	0.0811472i
$939$	7.13642	+	8.23587i	0.232888	+	0.268767i
$940$	−1.82298	+	1.73821i	−0.0594591	+	0.0566941i
$941$	−13.4855	+	1.28771i	−0.439616	+	0.0419782i	−0.312518	−	0.949912i	$-0.601172\pi$
$941$	−13.4855	+	1.28771i	−0.439616	+	0.0419782i	−0.127098	+	0.991890i	$0.540566\pi$
$942$	−4.56538	−	7.90748i	−0.148748	−	0.257639i
$943$	2.82276	−	0.713149i	0.0919217	−	0.0232233i
$944$	−0.301738			−0.00982074
$945$	−0.0290820	+	0.932179i	−0.000946036	+	0.0303238i
$946$	16.2705	+	4.77744i	0.528998	+	0.155328i
$947$	−17.8445	+	3.43925i	−0.579870	+	0.111761i	−0.470748	−	0.882268i	$-0.656016\pi$
$947$	−17.8445	+	3.43925i	−0.579870	+	0.111761i	−0.109122	+	0.994028i	$0.534804\pi$
$948$	−11.8607	−	6.11460i	−0.385217	−	0.198593i
$949$	−32.2191	−	6.20972i	−1.04588	−	0.201576i
$950$	6.72635	+	5.28966i	0.218232	+	0.171619i
$951$	29.9833	−	8.80389i	0.972275	−	0.285486i
$952$	6.35345	−	7.58015i	0.205917	−	0.245674i
$953$	−8.72514	−	60.6847i	−0.282635	−	1.96577i	−0.258299	−	0.966065i	$-0.583162\pi$
$953$	−8.72514	−	60.6847i	−0.282635	−	1.96577i	−0.0243361	−	0.999704i	$-0.507747\pi$
$954$	−5.03894	−	0.481160i	−0.163142	−	0.0155781i
$955$	−3.12844	+	4.39328i	−0.101234	+	0.142163i
$956$	−17.0146	+	13.3804i	−0.550290	+	0.432753i
$957$	−17.8771	+	9.21631i	−0.577886	+	0.297921i
$958$	−13.2015	+	3.87632i	−0.426523	+	0.125238i
$959$	−15.9833	−	4.40951i	−0.516126	−	0.142391i
$960$	−0.230840	+	0.266403i	−0.00745032	+	0.00859813i
$961$	−1.43673	−	30.1606i	−0.0463461	−	0.972924i
$962$	−0.824918	+	2.38344i	−0.0265964	+	0.0768453i
$963$	−0.139316	−	0.574268i	−0.00448939	−	0.0185055i
$964$	1.41205	+	1.98295i	0.0454792	+	0.0638666i
$965$	−3.23255			−0.104059
$966$	−3.25858	+	12.2630i	−0.104843	+	0.394556i
$967$	−33.1452			−1.06588			−0.532940	−	0.846153i	$-0.678913\pi$
$967$	−33.1452			−1.06588			−0.532940	+	0.846153i	$0.678913\pi$
$968$	9.97146	+	14.0029i	0.320495	+	0.450072i
$969$	−1.54679	−	6.37595i	−0.0496900	−	0.204825i
$970$	0.719730	−	2.07952i	0.0231091	−	0.0667695i
$971$	2.40199	+	50.4240i	0.0770835	+	1.61818i	0.624296	+	0.781188i	$0.285386\pi$
$971$	2.40199	+	50.4240i	0.0770835	+	1.61818i	−0.547212	+	0.836994i	$0.684311\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	37.9738	−	37.4168i	1.21738	−	1.19953i
$974$	12.4835	−	3.66548i	0.399996	−	0.117450i
$975$	−11.1198	+	5.73266i	−0.356119	+	0.183592i
$976$	−2.82335	+	2.22030i	−0.0903731	+	0.0710702i
$977$	−11.2280	+	15.7676i	−0.359216	+	0.504449i	−0.954151	−	0.299325i	$-0.903238\pi$
$977$	−11.2280	+	15.7676i	−0.359216	+	0.504449i	0.594935	+	0.803774i	$0.297178\pi$
$978$	1.05902	+	0.101124i	0.0338636	+	0.00323358i
$979$	10.4177	+	72.4570i	0.332953	+	2.31574i
$980$	0.730084	−	2.35703i	0.0233217	−	0.0752926i
$981$	−9.93601	+	2.91748i	−0.317233	+	0.0931479i
$982$	15.3982	+	12.1093i	0.491376	+	0.386422i
$983$	−10.1132	−	1.94915i	−0.322560	−	0.0621683i	0.0254013	−	0.999677i	$-0.491914\pi$
$983$	−10.1132	−	1.94915i	−0.322560	−	0.0621683i	−0.347961	+	0.937509i	$0.613126\pi$
$984$	0.539594	+	0.278180i	0.0172016	+	0.00886806i
$985$	5.74023	−	1.10634i	0.182899	−	0.0352509i
$986$	13.5876	+	3.98968i	0.432718	+	0.127057i
$987$	−16.6595	+	8.93766i	−0.530279	+	0.284489i
$988$	4.50320			0.143266
$989$	12.5603	+	8.76619i	0.399395	+	0.278748i
$990$	0.935799	+	1.62085i	0.0297417	+	0.0515141i
$991$	−17.6785	+	1.68809i	−0.561576	+	0.0536240i	−0.371984	−	0.928239i	$-0.621323\pi$
$991$	−17.6785	+	1.68809i	−0.561576	+	0.0536240i	−0.189592	+	0.981863i	$0.560716\pi$
$992$	−0.649409	+	0.619210i	−0.0206188	+	0.0196600i
$993$	11.9377	+	13.7769i	0.378833	+	0.437197i
$994$	0.0758356	−	0.110283i	0.00240536	−	0.00349796i
$995$	−3.10537	+	3.58379i	−0.0984469	+	0.113614i
$996$	−9.55768	−	7.51624i	−0.302847	−	0.238161i
$997$	2.77008	+	2.64127i	0.0877294	+	0.0836498i	0.732675	−	0.680579i	$-0.238272\pi$
$997$	2.77008	+	2.64127i	0.0877294	+	0.0836498i	−0.644946	+	0.764228i	$0.723120\pi$
$998$	1.06041	−	22.2608i	0.0335668	−	0.704654i
$999$	−0.912552	−	0.365331i	−0.0288719	−	0.0115586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.121.4	✓	160
7.4	even	3	inner	966.2.y.c.949.5	yes	160
23.4	even	11	inner	966.2.y.c.625.5	yes	160
161.4	even	33	inner	966.2.y.c.487.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.121.4	✓	160	1.1	even	1	trivial
966.2.y.c.487.4	yes	160	161.4	even	33	inner
966.2.y.c.625.5	yes	160	23.4	even	11	inner
966.2.y.c.949.5	yes	160	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0167727 - 0.352103i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.88460 + 1.85696i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0167727 - 0.352103i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.88460 + 1.85696i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(0.277085 - 0.217902i) q^{10} +(3.07980 - 4.32497i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(-0.365162 - 2.53975i) q^{13} +(-2.60581 - 0.458008i) q^{14} +(-0.338223 + 0.0993113i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(3.67076 + 0.707481i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(1.72332 - 0.332143i) q^{19} +(0.338223 + 0.0993113i) q^{20} +(2.24892 + 1.39368i) q^{21} +5.30947 q^{22} +(4.54671 + 1.52560i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.85366 - 0.463469i) q^{25} +(1.85701 - 1.77065i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-1.13843 - 2.38830i) q^{28} +(2.48070 - 2.86288i) q^{29} +(-0.277085 - 0.217902i) q^{30} +(-0.649409 - 0.619210i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-4.92914 - 1.97333i) q^{33} +(1.55295 + 3.40049i) q^{34} +(0.685449 + 0.632426i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.873693 + 0.450420i) q^{37} +(1.27018 + 1.21112i) q^{38} +(-2.38207 + 0.953638i) q^{39} +(0.115292 + 0.333115i) q^{40} +(0.510708 - 0.328212i) q^{41} +(0.169244 + 2.64033i) q^{42} +(3.06442 + 0.899796i) q^{43} +(3.07980 + 4.32497i) q^{44} +(0.176251 + 0.305276i) q^{45} +(1.39463 + 4.58857i) q^{46} +(-3.57282 + 6.18831i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(0.103425 - 6.99924i) q^{49} +(3.19293 + 3.68484i) q^{50} +(-0.177876 - 3.73408i) q^{51} +(2.51950 + 0.485594i) q^{52} +(4.69926 - 1.88130i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-1.57449 - 1.01186i) q^{55} +(1.28509 - 2.31269i) q^{56} +(-0.729069 - 1.59644i) q^{57} +(3.77098 + 0.360085i) q^{58} +(0.237182 - 0.186522i) q^{59} +(0.0167727 - 0.352103i) q^{60} +(0.846799 - 3.49055i) q^{61} +(0.127700 - 0.888170i) q^{62} +(0.824191 - 2.51410i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.888130 + 0.171173i) q^{65} +(-1.25176 - 5.15980i) q^{66} +(11.8808 - 1.13448i) q^{67} +(-1.86916 + 3.23748i) q^{68} +(0.410667 - 4.77822i) q^{69} +(-0.117560 + 0.925194i) q^{70} +(-0.0210146 + 0.0460156i) q^{71} +(0.723734 - 0.690079i) q^{72} +(4.18250 - 12.0846i) q^{73} +(-0.873693 - 0.450420i) q^{74} +(-1.59470 - 4.60758i) q^{75} +(-0.249768 + 1.73717i) q^{76} +(2.22710 + 13.8699i) q^{77} +(-2.15855 - 1.38722i) q^{78} +(-12.3882 - 4.95948i) q^{79} +(-0.204471 + 0.287140i) q^{80} +(0.580057 - 0.814576i) q^{81} +(0.563594 + 0.225629i) q^{82} +(-10.2289 - 6.57369i) q^{83} +(-2.05258 + 1.66941i) q^{84} +(0.187537 - 1.30435i) q^{85} +(1.04459 + 3.01814i) q^{86} +(-3.36703 - 1.73582i) q^{87} +(-1.73656 + 5.01745i) q^{88} +(-9.97818 + 9.51418i) q^{89} +(-0.146435 + 0.320647i) q^{90} +(5.40440 + 4.10833i) q^{91} +(-2.92877 + 3.79767i) q^{92} +(-0.448652 + 0.777088i) q^{93} +(-7.11329 + 0.679237i) q^{94} +(-0.145853 - 0.601216i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(5.25167 - 3.37504i) q^{97} +(5.76140 - 3.97571i) q^{98} +(-0.755616 + 5.25543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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