LMFDB - Embedded newform 966.2.y.d.193.4

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			193.4
Character	$\chi$	$=$	966.193
Dual form			966.2.y.d.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.222621 - 0.175071i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.0819249 + 2.64448i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})$	\(q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.222621 - 0.175071i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.0819249 + 2.64448i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +(0.281932 + 0.0269212i) q^{10} +(0.559293 - 0.533285i) q^{11} +(0.235759 + 0.971812i) q^{12} +(-0.0379206 - 0.0830345i) q^{13} +(-1.88419 + 1.85737i) q^{14} +(0.185466 - 0.214039i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(-2.62045 + 1.35093i) q^{17} +(0.928368 + 0.371662i) q^{18} +(6.90929 + 3.56198i) q^{19} +(0.185466 + 0.214039i) q^{20} +(0.420027 + 2.61220i) q^{21} +0.772788 q^{22} +(3.41657 + 3.36557i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.15988 + 4.78111i) q^{25} +(0.0298560 - 0.0862631i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-2.64539 + 0.0439974i) q^{28} +(-1.47402 - 0.947298i) q^{29} +(0.281932 - 0.0269212i) q^{30} +(-0.795481 - 2.29839i) q^{31} +(-0.786053 - 0.618159i) q^{32} +(0.448261 - 0.629495i) q^{33} +(-2.82876 - 0.830598i) q^{34} +(0.444735 + 0.603061i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.80806 - 0.723838i) q^{37} +(2.54243 + 7.34588i) q^{38} +(-0.0529497 - 0.0743575i) q^{39} +(-0.0134759 + 0.282893i) q^{40} +(-0.0592609 - 0.412169i) q^{41} +(-1.49863 + 2.18039i) q^{42} +(-2.78289 - 3.21162i) q^{43} +(0.559293 + 0.533285i) q^{44} +(0.141607 - 0.245271i) q^{45} +(0.150185 + 4.79348i) q^{46} +(-3.32370 - 5.75682i) q^{47} +(-0.959493 + 0.281733i) q^{48} +(-6.98658 - 0.433298i) q^{49} +(-4.13879 + 2.65984i) q^{50} +(-2.31743 + 1.82244i) q^{51} +(0.0811361 - 0.0418286i) q^{52} +(0.579196 + 0.813367i) q^{53} +(0.981929 + 0.189251i) q^{54} +(0.0311477 - 0.216637i) q^{55} +(-1.94492 - 1.79368i) q^{56} +(7.45854 + 2.19002i) q^{57} +(-0.413091 - 1.70279i) q^{58} +(2.97411 + 0.283993i) q^{59} +(0.222621 + 0.175071i) q^{60} +(10.1952 + 1.96497i) q^{61} +(1.01035 - 2.21237i) q^{62} +(0.906798 + 2.48550i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.0229789 - 0.0118464i) q^{65} +(0.758823 - 0.146251i) q^{66} +(2.78899 - 11.4964i) q^{67} +(-1.47409 - 2.55320i) q^{68} +(3.99177 + 2.65815i) q^{69} +(-0.0942899 + 0.743358i) q^{70} +(0.539661 - 0.158459i) q^{71} +(-0.327068 + 0.945001i) q^{72} +(0.660375 + 13.8630i) q^{73} +(1.80806 + 0.723838i) q^{74} +(-0.234093 + 4.91422i) q^{75} +(-3.22919 + 7.07095i) q^{76} +(1.36444 + 1.52273i) q^{77} +(0.0129910 - 0.0903545i) q^{78} +(-7.06381 + 9.91973i) q^{79} +(-0.204972 + 0.195440i) q^{80} +(0.723734 - 0.690079i) q^{81} +(0.241540 - 0.339195i) q^{82} +(1.85626 - 12.9106i) q^{83} +(-2.58925 + 0.543845i) q^{84} +(-0.346857 + 0.759512i) q^{85} +(0.202203 - 4.24477i) q^{86} +(-1.62666 - 0.651218i) q^{87} +(0.0367707 + 0.771913i) q^{88} +(5.89126 - 17.0217i) q^{89} +(0.271742 - 0.0797906i) q^{90} +(0.222690 - 0.0934778i) q^{91} +(-3.19919 + 3.57284i) q^{92} +(-1.21608 - 2.10631i) q^{93} +(1.56718 - 6.46002i) q^{94} +(2.16176 - 0.416644i) q^{95} +(-0.888835 - 0.458227i) q^{96} +(-1.50876 - 10.4936i) q^{97} +(-4.75741 - 5.13488i) q^{98} +(0.321028 - 0.702953i) 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} + 6 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 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	0.723734	+	0.690079i	0.511757	+	0.487960i
$2$	0.723734	+	0.690079i	0.511757	+	0.487960i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$4$	0.0475819	+	0.998867i	0.0237910	+	0.499434i
$5$	0.222621	−	0.175071i	0.0995593	−	0.0782943i	−0.567139	−	0.823622i	$-0.691950\pi$
$5$	0.222621	−	0.175071i	0.0995593	−	0.0782943i	0.666698	+	0.745328i	$0.267707\pi$
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−0.0819249	+	2.64448i	−0.0309647	+	0.999520i
$7$	−0.0819249	+	2.64448i	−0.0309647	+	0.999520i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.928368	−	0.371662i	0.309456	−	0.123887i
$10$	0.281932	+	0.0269212i	0.0891546	+	0.00851323i
$11$	0.559293	−	0.533285i	0.168633	−	0.160791i	−0.601063	−	0.799201i	$-0.705256\pi$
$11$	0.559293	−	0.533285i	0.168633	−	0.160791i	0.769696	+	0.638410i	$0.220408\pi$
$12$	0.235759	+	0.971812i	0.0680577	+	0.280538i
$13$	−0.0379206	−	0.0830345i	−0.0105173	−	0.0230296i	0.904300	−	0.426897i	$-0.140393\pi$
$13$	−0.0379206	−	0.0830345i	−0.0105173	−	0.0230296i	−0.914818	+	0.403867i	$0.867666\pi$
$14$	−1.88419	+	1.85737i	−0.503572	+	0.496402i
$15$	0.185466	−	0.214039i	0.0478871	−	0.0552646i
$16$	−0.995472	+	0.0950560i	−0.248868	+	0.0237640i
$17$	−2.62045	+	1.35093i	−0.635552	+	0.327650i	−0.745716	−	0.666264i	$-0.767892\pi$
$17$	−2.62045	+	1.35093i	−0.635552	+	0.327650i	0.110165	+	0.993913i	$0.464862\pi$
$18$	0.928368	+	0.371662i	0.218818	+	0.0876017i
$19$	6.90929	+	3.56198i	1.58510	+	0.817175i	0.999981	+	0.00622728i	$0.00198222\pi$
$19$	6.90929	+	3.56198i	1.58510	+	0.817175i	0.585118	+	0.810948i	$0.301048\pi$
$20$	0.185466	+	0.214039i	0.0414714	+	0.0478606i
$21$	0.420027	+	2.61220i	0.0916575	+	0.570028i
$22$	0.772788			0.164759
$23$	3.41657	+	3.36557i	0.712405	+	0.701769i
$23$	3.41657	+	3.36557i	0.712405	+	0.701769i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.15988	+	4.78111i	−0.231977	+	0.956222i
$26$	0.0298560	−	0.0862631i	0.00585523	−	0.0169176i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−2.64539	+	0.0439974i	−0.499931	+	0.00831473i
$29$	−1.47402	−	0.947298i	−0.273720	−	0.175909i	0.396579	−	0.918001i	$-0.370197\pi$
$29$	−1.47402	−	0.947298i	−0.273720	−	0.175909i	−0.670298	+	0.742092i	$0.733834\pi$
$30$	0.281932	−	0.0269212i	0.0514734	−	0.00491512i
$31$	−0.795481	−	2.29839i	−0.142873	−	0.412803i	0.850749	−	0.525573i	$-0.176149\pi$
$31$	−0.795481	−	2.29839i	−0.142873	−	0.412803i	−0.993621	+	0.112770i	$0.964028\pi$
$32$	−0.786053	−	0.618159i	−0.138956	−	0.109276i
$33$	0.448261	−	0.629495i	0.0780323	−	0.109581i
$34$	−2.82876	−	0.830598i	−0.485128	−	0.142446i
$35$	0.444735	+	0.603061i	0.0751739	+	0.101936i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	1.80806	−	0.723838i	0.297243	−	0.118998i	−0.218247	−	0.975893i	$-0.570034\pi$
$37$	1.80806	−	0.723838i	0.297243	−	0.118998i	0.515491	+	0.856895i	$0.327610\pi$
$38$	2.54243	+	7.34588i	0.412437	+	1.19166i
$39$	−0.0529497	−	0.0743575i	−0.00847874	−	0.0119067i
$40$	−0.0134759	+	0.282893i	−0.00213072	+	0.0447294i
$41$	−0.0592609	−	0.412169i	−0.00925500	−	0.0643700i	0.984671	−	0.174425i	$-0.0558065\pi$
$41$	−0.0592609	−	0.412169i	−0.00925500	−	0.0643700i	−0.993926	+	0.110055i	$0.964897\pi$
$42$	−1.49863	+	2.18039i	−0.231244	+	0.336441i
$43$	−2.78289	−	3.21162i	−0.424386	−	0.489768i	0.502782	−	0.864413i	$-0.332310\pi$
$43$	−2.78289	−	3.21162i	−0.424386	−	0.489768i	−0.927168	+	0.374646i	$0.877764\pi$
$44$	0.559293	+	0.533285i	0.0843166	+	0.0803957i
$45$	0.141607	−	0.245271i	0.0211095	−	0.0365628i
$46$	0.150185	+	4.79348i	0.0221435	+	0.706760i
$47$	−3.32370	−	5.75682i	−0.484811	−	0.839718i	0.515036	−	0.857168i	$-0.327778\pi$
$47$	−3.32370	−	5.75682i	−0.484811	−	0.839718i	−0.999848	+	0.0174503i	$0.994445\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	−6.98658	−	0.433298i	−0.998082	−	0.0618997i
$50$	−4.13879	+	2.65984i	−0.585313	+	0.376158i
$51$	−2.31743	+	1.82244i	−0.324504	+	0.255193i
$52$	0.0811361	−	0.0418286i	0.0112516	−	0.00580058i
$53$	0.579196	+	0.813367i	0.0795587	+	0.111725i	0.852438	−	0.522829i	$-0.175123\pi$
$53$	0.579196	+	0.813367i	0.0795587	+	0.111725i	−0.772879	+	0.634554i	$0.781184\pi$
$54$	0.981929	+	0.189251i	0.133624	+	0.0257538i
$55$	0.0311477	−	0.216637i	0.00419995	−	0.0292113i
$56$	−1.94492	−	1.79368i	−0.259900	−	0.239691i
$57$	7.45854	+	2.19002i	0.987907	+	0.290076i
$58$	−0.413091	−	1.70279i	−0.0542415	−	0.223587i
$59$	2.97411	+	0.283993i	0.387196	+	0.0369727i	0.286839	−	0.957979i	$-0.407395\pi$
$59$	2.97411	+	0.283993i	0.387196	+	0.0369727i	0.100357	+	0.994951i	$0.468002\pi$
$60$	0.222621	+	0.175071i	0.0287403	+	0.0226016i
$61$	10.1952	+	1.96497i	1.30537	+	0.251589i	0.794075	−	0.607819i	$-0.207955\pi$
$61$	10.1952	+	1.96497i	1.30537	+	0.251589i	0.511291	+	0.859408i	$0.329168\pi$
$62$	1.01035	−	2.21237i	0.128315	−	0.280971i
$63$	0.906798	+	2.48550i	0.114246	+	0.313144i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−0.0229789	−	0.0118464i	−0.00285018	−	0.00146937i
$66$	0.758823	−	0.146251i	0.0934047	−	0.0180023i
$67$	2.78899	−	11.4964i	0.340730	−	1.40451i	−0.501393	−	0.865220i	$-0.667179\pi$
$67$	2.78899	−	11.4964i	0.340730	−	1.40451i	0.842122	−	0.539287i	$-0.181306\pi$
$68$	−1.47409	−	2.55320i	−0.178760	−	0.309621i
$69$	3.99177	+	2.65815i	0.480552	+	0.320004i
$70$	−0.0942899	+	0.743358i	−0.0112698	+	0.0888483i
$71$	0.539661	−	0.158459i	0.0640460	−	0.0188056i	−0.249553	−	0.968361i	$-0.580284\pi$
$71$	0.539661	−	0.158459i	0.0640460	−	0.0188056i	0.313599	+	0.949556i	$0.398465\pi$
$72$	−0.327068	+	0.945001i	−0.0385453	+	0.111369i
$73$	0.660375	+	13.8630i	0.0772911	+	1.62254i	0.621379	+	0.783510i	$0.286573\pi$
$73$	0.660375	+	13.8630i	0.0772911	+	1.62254i	−0.544088	+	0.839028i	$0.683124\pi$
$74$	1.80806	+	0.723838i	0.210183	+	0.0841445i
$75$	−0.234093	+	4.91422i	−0.0270307	+	0.567445i
$76$	−3.22919	+	7.07095i	−0.370414	+	0.811093i
$77$	1.36444	+	1.52273i	0.155493	+	0.173531i
$78$	0.0129910	−	0.0903545i	0.00147094	−	0.0102306i
$79$	−7.06381	+	9.91973i	−0.794740	+	1.11606i	0.196042	+	0.980595i	$0.437191\pi$
$79$	−7.06381	+	9.91973i	−0.794740	+	1.11606i	−0.990783	+	0.135461i	$0.956748\pi$
$80$	−0.204972	+	0.195440i	−0.0229165	+	0.0218509i
$81$	0.723734	−	0.690079i	0.0804149	−	0.0766754i
$82$	0.241540	−	0.339195i	0.0266736	−	0.0374579i
$83$	1.85626	−	12.9106i	0.203751	−	1.41712i	−0.589275	−	0.807932i	$-0.700587\pi$
$83$	1.85626	−	12.9106i	0.203751	−	1.41712i	0.793026	−	0.609187i	$-0.208504\pi$
$84$	−2.58925	+	0.543845i	−0.282511	+	0.0593383i
$85$	−0.346857	+	0.759512i	−0.0376220	+	0.0823806i
$86$	0.202203	−	4.24477i	0.0218042	−	0.457725i
$87$	−1.62666	−	0.651218i	−0.174397	−	0.0698179i
$88$	0.0367707	+	0.771913i	0.00391978	+	0.0822862i
$89$	5.89126	−	17.0217i	0.624473	−	1.80430i	0.0308889	−	0.999523i	$-0.490166\pi$
$89$	5.89126	−	17.0217i	0.624473	−	1.80430i	0.593584	−	0.804772i	$-0.297713\pi$
$90$	0.271742	−	0.0797906i	0.0286441	−	0.00841067i
$91$	0.222690	−	0.0934778i	0.0233443	−	0.00979913i
$92$	−3.19919	+	3.57284i	−0.333538	+	0.372495i
$93$	−1.21608	−	2.10631i	−0.126102	−	0.218414i
$94$	1.56718	−	6.46002i	0.161643	−	0.666300i
$95$	2.16176	−	0.416644i	0.221791	−	0.0427468i
$96$	−0.888835	−	0.458227i	−0.0907164	−	0.0467675i
$97$	−1.50876	−	10.4936i	−0.153191	−	1.06547i	−0.910827	−	0.412789i	$-0.864555\pi$
$97$	−1.50876	−	10.4936i	−0.153191	−	1.06547i	0.757636	−	0.652678i	$-0.226354\pi$
$98$	−4.75741	−	5.13488i	−0.480571	−	0.518701i
$99$	0.321028	−	0.702953i	0.0322645	−	0.0706494i
$100$	−4.83088	−	0.931076i	−0.483088	−	0.0931076i
$101$	4.00870	+	3.15247i	0.398880	+	0.313683i	0.797371	−	0.603489i	$-0.206223\pi$
$101$	4.00870	+	3.15247i	0.398880	+	0.313683i	−0.398491	+	0.917172i	$0.630466\pi$
$102$	−2.93483	−	0.280242i	−0.290591	−	0.0277481i
$103$	−1.65261	−	6.81217i	−0.162837	−	0.671223i	−0.993440	−	0.114357i	$-0.963519\pi$
$103$	−1.65261	−	6.81217i	−0.162837	−	0.671223i	0.830603	−	0.556865i	$-0.187996\pi$
$104$	0.0875860	+	0.0257176i	0.00858851	+	0.00252182i
$105$	0.550828	+	0.507996i	0.0537553	+	0.0495753i
$106$	−0.142104	+	0.988352i	−0.0138023	+	0.0959972i
$107$	−17.2318	−	3.32115i	−1.66586	−	0.321068i	−0.732704	−	0.680548i	$-0.761742\pi$
$107$	−17.2318	−	3.32115i	−1.66586	−	0.321068i	−0.933153	+	0.359480i	$0.882954\pi$
$108$	0.580057	+	0.814576i	0.0558160	+	0.0783826i
$109$	−6.55496	+	3.37932i	−0.627851	+	0.323680i	−0.742621	−	0.669712i	$-0.766417\pi$
$109$	−6.55496	+	3.37932i	−0.627851	+	0.323680i	0.114770	+	0.993392i	$0.463387\pi$
$110$	0.172039	−	0.135293i	0.0164033	−	0.0128997i
$111$	1.63840	−	1.05293i	0.155510	−	0.0999402i
$112$	−0.169820	−	2.64030i	−0.0160465	−	0.249484i
$113$	2.25427	−	0.661914i	0.212064	−	0.0622676i	−0.173975	−	0.984750i	$-0.555661\pi$
$113$	2.25427	−	0.661914i	0.212064	−	0.0622676i	0.386039	+	0.922482i	$0.373843\pi$
$114$	3.88671	+	6.73197i	0.364023	+	0.630507i
$115$	1.34982	+	0.151102i	0.125871	+	0.0140904i
$116$	0.876088	−	1.51743i	0.0813428	−	0.140890i
$117$	−0.0660651	−	0.0629929i	−0.00610772	−	0.00582370i
$118$	1.95649	+	2.25791i	0.180109	+	0.207857i
$119$	−3.35784	−	7.04040i	−0.307813	−	0.645392i
$120$	0.0403056	+	0.280331i	0.00367938	+	0.0255906i
$121$	−0.494985	+	10.3910i	−0.0449986	+	0.944638i
$122$	6.02265	+	8.45763i	0.545265	+	0.765718i
$123$	−0.136193	−	0.393505i	−0.0122802	−	0.0354812i
$124$	2.25794	−	0.903942i	0.202769	−	0.0811764i
$125$	1.16708	+	2.55554i	0.104387	+	0.228575i
$126$	−1.05891	+	2.42460i	−0.0943353	+	0.216001i
$127$	−5.89425	−	1.73071i	−0.523030	−	0.153575i	0.00955121	−	0.999954i	$-0.496960\pi$
$127$	−5.89425	−	1.73071i	−0.523030	−	0.153575i	−0.532581	+	0.846379i	$0.678778\pi$
$128$	0.580057	−	0.814576i	0.0512703	−	0.0719990i
$129$	−3.34040	−	2.62692i	−0.294106	−	0.231287i
$130$	−0.00845563	−	0.0244309i	−0.000741608	−	0.00214273i
$131$	12.3838	−	1.18251i	1.08198	−	0.103316i	0.461195	−	0.887299i	$-0.347421\pi$
$131$	12.3838	−	1.18251i	1.08198	−	0.103316i	0.620783	+	0.783982i	$0.286815\pi$
$132$	0.650111	+	0.417801i	0.0565849	+	0.0363649i
$133$	−9.98565	+	17.9797i	−0.865866	+	1.55904i
$134$	9.95190	−	6.39570i	0.859713	−	0.552504i
$135$	0.0926303	−	0.267638i	0.00797234	−	0.0230346i
$136$	0.695060	−	2.86507i	0.0596009	−	0.245678i
$137$	9.48623	−	16.4306i	0.810464	−	1.40376i	−0.102076	−	0.994777i	$-0.532549\pi$
$137$	9.48623	−	16.4306i	0.810464	−	1.40376i	0.912540	−	0.408988i	$-0.134118\pi$
$138$	1.05464	+	4.67843i	0.0897771	+	0.398255i
$139$	1.58902			0.134779			0.0673893	−	0.997727i	$-0.478533\pi$
$139$	1.58902			0.134779			0.0673893	+	0.997727i	$0.478533\pi$
$140$	−0.581216	+	0.472926i	−0.0491218	+	0.0399695i
$141$	−4.35312	−	5.02377i	−0.366599	−	0.423078i
$142$	0.499920	+	0.257727i	0.0419524	+	0.0216280i
$143$	−0.0654898	−	0.0262182i	−0.00547653	−	0.00219247i
$144$	−0.888835	+	0.458227i	−0.0740696	+	0.0381855i
$145$	−0.493994	+	0.0471707i	−0.0410240	+	0.00391731i
$146$	−9.08861	+	10.4888i	−0.752179	+	0.868061i
$147$	−6.94232	+	0.896751i	−0.572593	+	0.0739627i
$148$	0.809049	+	1.77157i	0.0665034	+	0.145622i
$149$	−3.02371	−	12.4639i	−0.247712	−	1.02108i	−0.950757	−	0.309938i	$-0.899692\pi$
$149$	−3.02371	−	12.4639i	−0.247712	−	1.02108i	0.703045	−	0.711146i	$-0.251823\pi$
$150$	−3.56062	+	3.39504i	−0.290723	+	0.277204i
$151$	−9.29462	−	0.887528i	−0.756385	−	0.0722260i	−0.290264	−	0.956947i	$-0.593743\pi$
$151$	−9.29462	−	0.887528i	−0.756385	−	0.0722260i	−0.466122	+	0.884721i	$0.654349\pi$
$152$	−7.21659	+	2.88909i	−0.585343	+	0.234336i
$153$	−1.93065	+	2.22809i	−0.156084	+	0.180130i
$154$	−0.0633106	+	2.04363i	−0.00510171	+	0.164680i
$155$	−0.579473	−	0.372405i	−0.0465444	−	0.0299123i
$156$	0.0717538	−	0.0564278i	0.00574490	−	0.00451784i
$157$	−0.705954	−	14.8198i	−0.0563413	−	1.18275i	−0.833163	−	0.553028i	$-0.813472\pi$
$157$	−0.705954	−	14.8198i	−0.0563413	−	1.18275i	0.776821	−	0.629721i	$-0.216831\pi$
$158$	−11.9577	+	2.30466i	−0.951304	+	0.183349i
$159$	0.722660	+	0.689055i	0.0573106	+	0.0546456i
$160$	−0.283214			−0.0223900
$161$	−9.18008	+	8.75934i	−0.723492	+	0.690333i
$162$	1.00000			0.0785674
$163$	2.80203	+	2.67173i	0.219472	+	0.209266i	0.791836	−	0.610733i	$-0.209125\pi$
$163$	2.80203	+	2.67173i	0.219472	+	0.209266i	−0.572365	+	0.819999i	$0.693974\pi$
$164$	0.408882	−	0.0788056i	0.0319283	−	0.00615368i
$165$	−0.0104140	−	0.218617i	−0.000810728	−	0.0170193i
$166$	10.2528	−	8.06285i	0.795768	−	0.625799i
$167$	1.16014	+	0.745575i	0.0897741	+	0.0576943i	0.584758	−	0.811208i	$-0.301190\pi$
$167$	1.16014	+	0.745575i	0.0897741	+	0.0576943i	−0.494984	+	0.868902i	$0.664826\pi$
$168$	−2.24923	−	1.39319i	−0.173532	−	0.107487i
$169$	8.50773	−	9.81845i	0.654441	−	0.755265i
$170$	−0.775155	+	0.310325i	−0.0594517	+	0.0238009i
$171$	7.73822	+	0.738910i	0.591756	+	0.0565059i
$172$	3.07557	−	2.93255i	0.234510	−	0.223605i
$173$	−2.43014	−	10.0172i	−0.184760	−	0.761593i	−0.986479	−	0.163890i	$-0.947596\pi$
$173$	−2.43014	−	10.0172i	−0.184760	−	0.761593i	0.801718	−	0.597702i	$-0.203920\pi$
$174$	−0.727881	−	1.59384i	−0.0551805	−	0.120828i
$175$	−12.5485	−	3.45899i	−0.948580	−	0.261475i
$176$	−0.506069	+	0.584034i	−0.0381464	+	0.0440233i
$177$	2.97411	−	0.283993i	0.223548	−	0.0213462i
$178$	16.0100	−	8.25374i	1.20000	−	0.618644i
$179$	8.06045	+	3.22692i	0.602466	+	0.241191i	0.652786	−	0.757542i	$-0.273600\pi$
$179$	8.06045	+	3.22692i	0.602466	+	0.241191i	−0.0503200	+	0.998733i	$0.516024\pi$
$180$	0.251731	+	0.129776i	0.0187629	+	0.00967295i
$181$	2.39422	+	2.76307i	0.177961	+	0.205378i	0.837721	−	0.546099i	$-0.183888\pi$
$181$	2.39422	+	2.76307i	0.177961	+	0.205378i	−0.659760	+	0.751476i	$0.729342\pi$
$182$	0.225675	+	0.0860206i	0.0167282	+	0.00637627i
$183$	10.3829			0.767524
$184$	−4.78090	+	0.378097i	−0.352453	+	0.0278737i
$185$	0.275789	−	0.477681i	0.0202764	−	0.0351198i
$186$	0.573403	−	2.36360i	0.0420439	−	0.173307i
$187$	−0.745165	+	2.15301i	−0.0544919	+	0.157444i
$188$	5.59215	−	3.59386i	0.407849	−	0.262109i
$189$	1.36080	+	2.26897i	0.0989833	+	0.165043i
$190$	1.85205	+	1.19024i	0.134362	+	0.0863493i
$191$	−22.1080	+	2.11106i	−1.59968	+	0.152751i	−0.856429	−	0.516264i	$-0.827322\pi$
$191$	−22.1080	+	2.11106i	−1.59968	+	0.152751i	−0.743249	+	0.669015i	$0.766716\pi$
$192$	−0.327068	−	0.945001i	−0.0236041	−	0.0681996i
$193$	14.1025	+	11.0903i	1.01512	+	0.798299i	0.979577	−	0.201069i	$-0.0644415\pi$
$193$	14.1025	+	11.0903i	1.01512	+	0.798299i	0.0355430	+	0.999368i	$0.488684\pi$
$194$	6.14950	−	8.63576i	0.441508	−	0.620011i
$195$	−0.0248056	−	0.00728358i	−0.00177637	−	0.000521588i
$196$	0.100373	−	6.99928i	0.00716947	−	0.499949i
$197$	−7.16360	−	15.6861i	−0.510386	−	1.11759i	−0.972953	−	0.231004i	$-0.925799\pi$
$197$	−7.16360	−	15.6861i	−0.510386	−	1.11759i	0.462567	−	0.886584i	$-0.346928\pi$
$198$	0.717432	−	0.287216i	0.0509857	−	0.0204116i
$199$	0.784536	+	2.26677i	0.0556142	+	0.160687i	0.969386	−	0.245540i	$-0.0789654\pi$
$199$	0.784536	+	2.26677i	0.0556142	+	0.160687i	−0.913772	+	0.406227i	$0.866844\pi$
$200$	−2.85376	−	4.00754i	−0.201791	−	0.283376i
$201$	0.562887	−	11.8164i	0.0397030	−	0.833468i
$202$	0.725774	+	5.04787i	0.0510653	+	0.355167i
$203$	2.62587	−	3.82043i	0.184300	−	0.268141i
$204$	−1.93065	−	2.22809i	−0.135172	−	0.155997i
$205$	−0.0853517	−	0.0813827i	−0.00596122	−	0.00568401i
$206$	3.50488	−	6.07063i	0.244197	−	0.422961i
$207$	4.42269	+	1.85467i	0.307398	+	0.128909i
$208$	0.0456418	+	0.0790540i	0.00316469	+	0.00548141i
$209$	5.76387	−	1.69242i	0.398695	−	0.117067i
$210$	0.0480954	+	0.747769i	0.00331890	+	0.0516010i
$211$	−1.26773	+	0.814724i	−0.0872745	+	0.0560879i	−0.583550	−	0.812077i	$-0.698337\pi$
$211$	−1.26773	+	0.814724i	−0.0872745	+	0.0560879i	0.496276	+	0.868165i	$0.334700\pi$
$212$	−0.784886	+	0.617241i	−0.0539062	+	0.0423923i
$213$	0.499920	−	0.257727i	0.0342540	−	0.0176592i
$214$	−10.1794	−	14.2949i	−0.695846	−	0.977179i
$215$	−1.18179	−	0.227772i	−0.0805976	−	0.0155339i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	6.14323	−	1.91534i	0.417029	−	0.130022i
$218$	−7.07604	−	2.07771i	−0.479250	−	0.140720i
$219$	3.27203	+	13.4875i	0.221103	+	0.911399i
$220$	0.217874	+	0.0208044i	0.0146890	+	0.00140263i
$221$	0.211543	+	0.166359i	0.0142299	+	0.0111905i
$222$	1.91237	+	0.368580i	0.128350	+	0.0247375i
$223$	0.0296424	−	0.0649079i	0.00198500	−	0.00434655i	−0.908637	−	0.417587i	$-0.862876\pi$
$223$	0.0296424	−	0.0649079i	0.00198500	−	0.00434655i	0.910622	+	0.413241i	$0.135603\pi$
$224$	1.69911	−	2.02806i	0.113526	−	0.135506i
$225$	0.700159	+	4.86971i	0.0466773	+	0.324648i
$226$	2.08826	+	1.07658i	0.138909	+	0.0716127i
$227$	10.5415	−	2.03171i	0.699666	−	0.134850i	0.173000	−	0.984922i	$-0.444654\pi$
$227$	10.5415	−	2.03171i	0.699666	−	0.134850i	0.526666	+	0.850072i	$0.323442\pi$
$228$	−1.83265	+	7.55429i	−0.121370	+	0.500295i
$229$	9.69105	+	16.7854i	0.640403	+	1.10921i	0.985343	+	0.170585i	$0.0545659\pi$
$229$	9.69105	+	16.7854i	0.640403	+	1.10921i	−0.344940	+	0.938625i	$0.612101\pi$
$230$	0.872635	+	1.04084i	0.0575399	+	0.0686308i
$231$	1.62796	+	1.23699i	0.107112	+	0.0813880i
$232$	1.68120	−	0.493645i	0.110376	−	0.0324094i
$233$	4.31900	−	12.4789i	0.282947	−	0.817522i	−0.710548	−	0.703648i	$-0.751553\pi$
$233$	4.31900	−	12.4789i	0.282947	−	0.817522i	0.993495	−	0.113873i	$-0.0363257\pi$
$234$	−0.00434345	−	0.0911802i	−0.000283940	−	0.00596064i
$235$	−1.74778	−	0.699706i	−0.114013	−	0.0456438i
$236$	−0.142158	+	2.98425i	−0.00925367	+	0.194258i
$237$	−5.05883	+	11.0773i	−0.328606	+	0.719548i
$238$	2.42825	−	7.41255i	0.157400	−	0.480484i
$239$	1.67825	−	11.6725i	0.108557	−	0.755029i	−0.860724	−	0.509072i	$-0.829989\pi$
$239$	1.67825	−	11.6725i	0.108557	−	0.755029i	0.969281	−	0.245957i	$-0.0791022\pi$
$240$	−0.164280	+	0.230699i	−0.0106042	+	0.0148916i
$241$	−12.0400	+	11.4801i	−0.775564	+	0.739499i	−0.970444	−	0.241328i	$-0.922417\pi$
$241$	−12.0400	+	11.4801i	−0.775564	+	0.739499i	0.194879	+	0.980827i	$0.437568\pi$
$242$	−7.52886	+	7.17875i	−0.483973	+	0.461468i
$243$	0.580057	−	0.814576i	0.0372107	−	0.0522551i
$244$	−1.47764	+	10.2772i	−0.0945960	+	0.657929i
$245$	−1.63122	+	1.12669i	−0.104215	+	0.0719814i
$246$	0.172982	−	0.378777i	0.0110289	−	0.0241500i
$247$	0.0337634	−	0.708782i	0.00214832	−	0.0450987i
$248$	2.25794	+	0.903942i	0.143379	+	0.0574004i
$249$	−0.620627	−	13.0286i	−0.0393306	−	0.825651i
$250$	−0.918873	+	2.65491i	−0.0581146	+	0.167911i
$251$	11.1594	−	3.27669i	0.704374	−	0.206823i	0.0901196	−	0.995931i	$-0.471275\pi$
$251$	11.1594	−	3.27669i	0.704374	−	0.206823i	0.614254	+	0.789108i	$0.289457\pi$
$252$	−2.43954	+	1.02404i	−0.153677	+	0.0645082i
$253$	3.70567	+	0.0603304i	0.232974	+	0.00379294i
$254$	−3.07154	−	5.32007i	−0.192726	−	0.333811i
$255$	−0.196851	+	0.811429i	−0.0123273	+	0.0508137i
$256$	0.981929	−	0.189251i	0.0613705	−	0.0118282i
$257$	−13.7514	−	7.08935i	−0.857790	−	0.442221i	−0.0275452	−	0.999621i	$-0.508769\pi$
$257$	−13.7514	−	7.08935i	−0.857790	−	0.442221i	−0.830245	+	0.557399i	$0.811799\pi$
$258$	−0.604779	−	4.20633i	−0.0376519	−	0.261875i
$259$	1.76605	+	4.84068i	0.109737	+	0.300785i
$260$	0.0107396	−	0.0235165i	0.000666045	−	0.00145843i
$261$	−1.72051	−	0.331602i	−0.106497	−	0.0205256i
$262$	9.77861	+	7.68999i	0.604125	+	0.475089i
$263$	−25.2952	−	2.41540i	−1.55977	−	0.148940i	−0.720808	−	0.693135i	$-0.756229\pi$
$263$	−25.2952	−	2.41540i	−1.55977	−	0.148940i	−0.838959	+	0.544195i	$0.816835\pi$
$264$	0.182192	+	0.751005i	0.0112131	+	0.0462211i
$265$	0.271339	+	0.0796722i	0.0166682	+	0.00489422i
$266$	−19.6343	+	6.12161i	−1.20386	+	0.375340i
$267$	2.56342	−	17.8290i	0.156879	−	1.09112i
$268$	11.6161	+	2.23881i	0.709564	+	0.136757i
$269$	12.4759	+	17.5199i	0.760668	+	1.06821i	0.995368	+	0.0961403i	$0.0306497\pi$
$269$	12.4759	+	17.5199i	0.760668	+	1.06821i	−0.234700	+	0.972068i	$0.575411\pi$
$270$	0.251731	−	0.129776i	0.0153198	−	0.00789793i
$271$	−0.199897	+	0.157201i	−0.0121429	+	0.00954927i	−0.624212	−	0.781255i	$-0.714580\pi$
$271$	−0.199897	+	0.157201i	−0.0121429	+	0.00954927i	0.612069	+	0.790804i	$0.290337\pi$
$272$	2.48017	−	1.59391i	0.150382	−	0.0966447i
$273$	0.200975	−	0.133933i	0.0121636	−	0.00810598i
$274$	18.2039	−	5.34516i	1.09974	−	0.322913i
$275$	1.90098	+	3.29259i	0.114633	+	0.198551i
$276$	−2.46521	+	4.11373i	−0.148388	+	0.247617i
$277$	3.74954	−	6.49439i	0.225288	−	0.390210i	−0.731118	−	0.682251i	$-0.761001\pi$
$277$	3.74954	−	6.49439i	0.225288	−	0.390210i	0.956406	+	0.292041i	$0.0943344\pi$
$278$	1.15002	+	1.09655i	0.0689739	+	0.0657665i
$279$	−1.59272	−	1.83810i	−0.0953539	−	0.110044i
$280$	−0.747002	−	0.0588127i	−0.0446419	−	0.00351473i
$281$	−0.558186	−	3.88227i	−0.0332986	−	0.231597i	0.966375	−	0.257136i	$-0.0827788\pi$
$281$	−0.558186	−	3.88227i	−0.0332986	−	0.231597i	−0.999674	+	0.0255393i	$0.991870\pi$
$282$	0.316296	−	6.63987i	0.0188352	−	0.395399i
$283$	−2.38866	−	3.35441i	−0.141991	−	0.199399i	0.737456	−	0.675395i	$-0.236027\pi$
$283$	−2.38866	−	3.35441i	−0.141991	−	0.199399i	−0.879447	+	0.475996i	$0.842088\pi$
$284$	0.183958	+	0.531510i	0.0109159	+	0.0315393i
$285$	2.04384	−	0.818230i	0.121067	−	0.0484678i
$286$	−0.0293046	−	0.0641681i	−0.00173282	−	0.00379434i
$287$	1.09483	−	0.122948i	0.0646257	−	0.00725737i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	−4.81925	+	6.76769i	−0.283485	+	0.398100i
$290$	−0.390072	−	0.306756i	−0.0229058	−	0.0180133i
$291$	−3.46742	−	10.0185i	−0.203264	−	0.587293i
$292$	−13.8159	+	1.31925i	−0.808512	+	0.0772035i
$293$	16.4099	+	10.5460i	0.958674	+	0.616102i	0.923631	−	0.383284i	$-0.125207\pi$
$293$	16.4099	+	10.5460i	0.958674	+	0.616102i	0.0350430	+	0.999386i	$0.488843\pi$
$294$	−5.64322	−	4.14174i	−0.329119	−	0.241551i
$295$	0.711819	−	0.457458i	0.0414437	−	0.0266343i
$296$	−0.636987	+	1.84045i	−0.0370241	+	0.106974i
$297$	0.182192	−	0.751005i	0.0105718	−	0.0435777i
$298$	6.41272	−	11.1072i	0.371479	−	0.643421i
$299$	0.149900	−	0.411318i	0.00866892	−	0.0237871i
$300$	−4.91979			−0.284044
$301$	8.72107	−	7.09618i	0.502674	−	0.409017i
$302$	−6.11437	−	7.05635i	−0.351842	−	0.406048i
$303$	4.53287	+	2.33685i	0.260406	+	0.134249i
$304$	−7.21659	−	2.88909i	−0.413900	−	0.165700i
$305$	2.61369	−	1.34745i	0.149659	−	0.0771547i
$306$	−2.93483	+	0.280242i	−0.167773	+	0.0160204i
$307$	−17.1688	+	19.8139i	−0.979877	+	1.13084i	0.0115178	+	0.999934i	$0.496334\pi$
$307$	−17.1688	+	19.8139i	−0.979877	+	1.13084i	−0.991395	+	0.130905i	$0.958212\pi$
$308$	−1.45608	+	1.43535i	−0.0829680	+	0.0817868i
$309$	−2.91196	−	6.37630i	−0.165656	−	0.362735i
$310$	−0.162396	−	0.669405i	−0.00922346	−	0.0380196i
$311$	−10.6347	+	10.1402i	−0.603038	+	0.574996i	−0.928858	−	0.370436i	$-0.879208\pi$
$311$	−10.6347	+	10.1402i	−0.603038	+	0.574996i	0.325820	+	0.945432i	$0.394360\pi$
$312$	0.0908703	+	0.00867706i	0.00514452	+	0.000491242i
$313$	28.0068	−	11.2122i	1.58304	−	0.633754i	0.597299	−	0.802019i	$-0.296241\pi$
$313$	28.0068	−	11.2122i	1.58304	−	0.633754i	0.985742	+	0.168265i	$0.0538165\pi$
$314$	9.71591	−	11.2128i	0.548301	−	0.632773i
$315$	0.637013	+	0.394571i	0.0358916	+	0.0222316i
$316$	−10.2446	−	6.58380i	−0.576304	−	0.370368i
$317$	−12.0837	+	9.50270i	−0.678686	+	0.533725i	−0.896932	−	0.442169i	$-0.854209\pi$
$317$	−12.0837	+	9.50270i	−0.678686	+	0.533725i	0.218246	+	0.975894i	$0.429967\pi$
$318$	0.0475113	+	0.997385i	0.00266430	+	0.0559306i
$319$	−1.32959	+	0.256258i	−0.0744429	+	0.0143477i
$320$	−0.204972	−	0.195440i	−0.0114583	−	0.0109254i
$321$	−17.5489			−0.979483
$322$	−12.6886	+	0.00445496i	−0.707107	+	0.000248265i
$323$	−22.9174			−1.27516
$324$	0.723734	+	0.690079i	0.0402074	+	0.0383377i
$325$	0.440981	−	0.0849920i	0.0244612	−	0.00471451i
$326$	0.184219	+	3.86724i	0.0102030	+	0.214187i
$327$	−5.79696	+	4.55878i	−0.320573	+	0.252101i
$328$	0.350304	+	0.225127i	0.0193423	+	0.0124305i
$329$	15.4961	−	8.31784i	0.854327	−	0.458577i
$330$	0.143326	−	0.165407i	0.00788983	−	0.00910534i
$331$	−3.76623	+	1.50777i	−0.207011	+	0.0828747i	−0.472851	−	0.881143i	$-0.656775\pi$
$331$	−3.76623	+	1.50777i	−0.207011	+	0.0828747i	0.265840	+	0.964017i	$0.414351\pi$
$332$	12.9843	+	1.23985i	0.712605	+	0.0680455i
$333$	1.40952	−	1.34398i	0.0772413	−	0.0736494i
$334$	0.325125	+	1.34018i	0.0177901	+	0.0733316i
$335$	−1.39180	−	3.04761i	−0.0760420	−	0.166509i
$336$	−0.666430	−	2.56044i	−0.0363568	−	0.139684i
$337$	1.73956	−	2.00756i	0.0947600	−	0.109359i	−0.706389	−	0.707824i	$-0.749677\pi$
$337$	1.73956	−	2.00756i	0.0947600	−	0.109359i	0.801149	+	0.598465i	$0.204222\pi$
$338$	12.9328	−	1.23494i	0.703454	−	0.0671717i
$339$	2.08826	−	1.07658i	0.113419	−	0.0584715i
$340$	−0.775155	−	0.310325i	−0.0420387	−	0.0168298i
$341$	−1.67060	−	0.861257i	−0.0904683	−	0.0466397i
$342$	5.09050	+	5.87475i	0.275263	+	0.317670i
$343$	1.71822	−	18.4404i	0.0927754	−	0.995687i
$344$	4.24958			0.229122
$345$	1.35402	−	0.107082i	0.0728979	−	0.00576513i
$346$	5.15387	−	8.92677i	0.277074	−	0.479906i
$347$	3.81633	−	15.7311i	0.204871	−	0.844491i	−0.772851	−	0.634588i	$-0.781170\pi$
$347$	3.81633	−	15.7311i	0.204871	−	0.844491i	0.977722	−	0.209903i	$-0.0673149\pi$
$348$	0.573081	−	1.65581i	0.0307204	−	0.0887606i
$349$	14.1930	−	9.12131i	0.759736	−	0.488252i	−0.102517	−	0.994731i	$-0.532690\pi$
$349$	14.1930	−	9.12131i	0.759736	−	0.488252i	0.862252	+	0.506479i	$0.169053\pi$
$350$	−6.69483	−	11.1629i	−0.357854	−	0.596680i
$351$	−0.0767927	−	0.0493517i	−0.00409889	−	0.00263420i
$352$	−0.769289	+	0.0734582i	−0.0410032	+	0.00391534i
$353$	6.95979	+	20.1090i	0.370432	+	1.07029i	0.964090	+	0.265576i	$0.0855621\pi$
$353$	6.95979	+	20.1090i	0.370432	+	1.07029i	−0.593658	+	0.804718i	$0.702317\pi$
$354$	2.34844	+	1.84684i	0.124818	+	0.0981582i
$355$	0.0923985	−	0.129756i	0.00490400	−	0.00688671i
$356$	17.2827	+	5.07467i	0.915983	+	0.268957i
$357$	−4.62956	−	6.27769i	−0.245023	−	0.332251i
$358$	3.60680	+	7.89778i	0.190625	+	0.417411i
$359$	−22.7593	+	9.11144i	−1.20119	+	0.480883i	−0.884004	−	0.467480i	$-0.845162\pi$
$359$	−22.7593	+	9.11144i	−1.20119	+	0.480883i	−0.317185	+	0.948364i	$0.602738\pi$
$360$	0.0926303	+	0.267638i	0.00488204	+	0.0141057i
$361$	24.0294	+	33.7446i	1.26471	+	1.77603i
$362$	−0.173963	+	3.65193i	−0.00914328	+	0.191941i
$363$	1.48047	+	10.2969i	0.0777047	+	0.540448i
$364$	0.103968	+	0.217990i	0.00544940	+	0.0114258i
$365$	2.57402	+	2.97058i	0.134731	+	0.155487i
$366$	7.51443	+	7.16500i	0.392786	+	0.374520i
$367$	10.3881	−	17.9928i	0.542256	−	0.939214i	−0.456519	−	0.889714i	$-0.650904\pi$
$367$	10.3881	−	17.9928i	0.542256	−	0.939214i	0.998774	−	0.0495002i	$-0.0157629\pi$
$368$	−3.72102	−	3.02556i	−0.193972	−	0.157718i
$369$	−0.208204	−	0.360619i	−0.0108386	−	0.0187731i
$370$	0.529236	−	0.155398i	0.0275137	−	0.00807874i
$371$	−2.19838	+	1.46504i	−0.114134	+	0.0760610i
$372$	2.04606	−	1.31492i	0.106083	−	0.0681756i
$373$	−10.0657	+	7.91575i	−0.521182	+	0.409862i	−0.843792	−	0.536670i	$-0.819682\pi$
$373$	−10.0657	+	7.91575i	−0.521182	+	0.409862i	0.322610	+	0.946532i	$0.395440\pi$
$374$	−2.02505	+	1.04399i	−0.104713	+	0.0539832i
$375$	1.62963	+	2.28849i	0.0841535	+	0.118177i
$376$	6.52727	+	1.25803i	0.336618	+	0.0648779i
$377$	−0.0227626	+	0.158317i	−0.00117233	+	0.00815374i
$378$	−0.580916	+	2.58119i	−0.0298791	+	0.132762i
$379$	−31.9909	−	9.39337i	−1.64326	−	0.482505i	−0.676130	−	0.736782i	$-0.736344\pi$
$379$	−31.9909	−	9.39337i	−1.64326	−	0.482505i	−0.967131	+	0.254277i	$0.918163\pi$
$380$	0.519033	+	2.13948i	0.0266258	+	0.109753i
$381$	−6.11527	−	0.583937i	−0.313295	−	0.0299160i
$382$	−17.4571	−	13.7284i	−0.893183	−	0.702407i
$383$	22.5123	+	4.33889i	1.15032	+	0.221707i	0.728549	−	0.684994i	$-0.240195\pi$
$383$	22.5123	+	4.33889i	1.15032	+	0.221707i	0.421775	+	0.906700i	$0.361407\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	0.570341	+	0.100117i	0.0290672	+	0.00510246i
$386$	2.55326	+	17.7583i	0.129957	+	0.903873i
$387$	−3.77718	−	1.94727i	−0.192005	−	0.0989854i
$388$	10.4100	−	2.00635i	0.528485	−	0.101857i
$389$	−3.13180	+	12.9095i	−0.158789	+	0.654535i	0.835654	+	0.549256i	$0.185089\pi$
$389$	−3.13180	+	12.9095i	−0.158789	+	0.654535i	−0.994443	+	0.105279i	$0.966426\pi$
$390$	−0.0129264	−	0.0223892i	−0.000654554	−	0.00113372i
$391$	−13.4996	−	4.20372i	−0.682704	−	0.212591i
$392$	4.90270	−	4.99635i	0.247624	−	0.252354i
$393$	11.9362	−	3.50479i	0.602103	−	0.176793i
$394$	5.64011	−	16.2960i	0.284145	−	0.820982i
$395$	0.164106	+	3.44501i	0.00825708	+	0.173337i
$396$	0.717432	+	0.287216i	0.0360523	+	0.0144332i
$397$	−0.477382	+	10.0215i	−0.0239591	+	0.502964i	0.954712	+	0.297531i	$0.0961632\pi$
$397$	−0.477382	+	10.0215i	−0.0239591	+	0.502964i	−0.978671	+	0.205433i	$0.934140\pi$
$398$	−0.996453	+	2.18193i	−0.0499477	+	0.109370i
$399$	−6.40252	+	19.5446i	−0.320527	+	0.978451i
$400$	0.700159	−	4.86971i	0.0350080	−	0.243486i
$401$	−1.04012	+	1.46064i	−0.0519411	+	0.0729410i	−0.839730	−	0.543005i	$-0.817287\pi$
$401$	−1.04012	+	1.46064i	−0.0519411	+	0.0729410i	0.787789	+	0.615946i	$0.211226\pi$
$402$	8.56166	−	8.16353i	0.427017	−	0.407160i
$403$	−0.160681	+	0.153209i	−0.00800408	+	0.00763187i
$404$	−2.95816	+	4.15416i	−0.147174	+	0.206677i
$405$	0.0403056	−	0.280331i	0.00200280	−	0.0139298i
$406$	4.53683	−	0.952912i	0.225159	−	0.0472922i
$407$	0.625224	−	1.36905i	0.0309912	−	0.0678612i
$408$	0.140280	−	2.94484i	0.00694490	−	0.145791i
$409$	15.0248	+	6.01503i	0.742930	+	0.297424i	0.712079	−	0.702100i	$-0.247754\pi$
$409$	15.0248	+	6.01503i	0.742930	+	0.297424i	0.0308512	+	0.999524i	$0.490178\pi$
$410$	−0.00561145	−	0.117799i	−0.000277130	−	0.00581767i
$411$	6.20529	−	17.9290i	0.306084	−	0.884372i
$412$	6.72582	−	1.97488i	0.331357	−	0.0972953i
$413$	−0.994668	+	7.84172i	−0.0489444	+	0.385866i
$414$	1.92098	+	4.39429i	0.0944112	+	0.215968i
$415$	−1.84703	−	3.19915i	−0.0906670	−	0.157040i
$416$	−0.0215209	+	0.0887105i	−0.00105515	+	0.00434939i
$417$	1.56030	−	0.300723i	0.0764082	−	0.0147265i
$418$	5.33942	+	2.75266i	0.261159	+	0.134637i
$419$	−3.43151	−	23.8667i	−0.167640	−	1.16596i	−0.883744	−	0.467970i	$-0.844985\pi$
$419$	−3.43151	−	23.8667i	−0.167640	−	1.16596i	0.716104	−	0.697994i	$-0.245924\pi$
$420$	−0.481211	+	0.574375i	−0.0234807	+	0.0280267i
$421$	−11.9894	+	26.2531i	−0.584328	+	1.27950i	0.354482	+	0.935063i	$0.384657\pi$
$421$	−11.9894	+	26.2531i	−0.584328	+	1.27950i	−0.938810	+	0.344437i	$0.888070\pi$
$422$	−1.47973	−	0.285194i	−0.0720320	−	0.0138830i
$423$	−5.22521	−	4.10915i	−0.254058	−	0.199794i
$424$	−0.993994	−	0.0949149i	−0.0482726	−	0.00460948i
$425$	−3.41955	−	14.0956i	−0.165872	−	0.683735i
$426$	0.539661	+	0.158459i	0.0261467	+	0.00767736i
$427$	−6.03157	+	26.8001i	−0.291888	+	1.29695i
$428$	2.49747	−	17.3703i	0.120720	−	0.839623i
$429$	−0.0692681	−	0.0133503i	−0.00334430	−	0.000644560i
$430$	−0.698123	−	0.980377i	−0.0336665	−	0.0472780i
$431$	17.3546	−	8.94693i	0.835942	−	0.430958i	0.0135700	−	0.999908i	$-0.495680\pi$
$431$	17.3546	−	8.94693i	0.835942	−	0.430958i	0.822372	+	0.568950i	$0.192650\pi$
$432$	−0.786053	+	0.618159i	−0.0378190	+	0.0297412i
$433$	−0.368053	+	0.236533i	−0.0176875	+	0.0113671i	−0.549455	−	0.835524i	$-0.685164\pi$
$433$	−0.368053	+	0.236533i	−0.0176875	+	0.0113671i	0.531767	+	0.846891i	$0.321528\pi$
$434$	5.76780	+	2.85311i	0.276863	+	0.136954i
$435$	−0.476140	+	0.139807i	−0.0228292	+	0.00670325i
$436$	−3.68738	−	6.38674i	−0.176594	−	0.305869i
$437$	11.6180	+	35.4234i	0.555764	+	1.69453i
$438$	−6.93935	+	12.0193i	−0.331575	+	0.574305i
$439$	4.58034	+	4.36735i	0.218608	+	0.208442i	0.791467	−	0.611211i	$-0.209318\pi$
$439$	4.58034	+	4.36735i	0.218608	+	0.208442i	−0.572860	+	0.819653i	$0.694166\pi$
$440$	0.143326	+	0.165407i	0.00683279	+	0.00788546i
$441$	−6.64715	+	2.19439i	−0.316531	+	0.104495i
$442$	0.0382998	+	0.266381i	0.00182174	+	0.0126705i
$443$	−0.786479	+	16.5102i	−0.0373667	+	0.784424i	0.899960	+	0.435972i	$0.143596\pi$
$443$	−0.786479	+	16.5102i	−0.0373667	+	0.784424i	−0.937327	+	0.348452i	$0.886708\pi$
$444$	1.12970	+	1.58644i	0.0536132	+	0.0752892i
$445$	−1.66849	−	4.82078i	−0.0790939	−	0.228527i
$446$	0.0662448	−	0.0265204i	0.00313678	−	0.00125578i
$447$	−5.32788	−	11.6664i	−0.252000	−	0.551803i
$448$	2.62922	−	0.295258i	0.124219	−	0.0139496i
$449$	−5.13812	−	1.50869i	−0.242483	−	0.0711994i	0.158233	−	0.987402i	$-0.449420\pi$
$449$	−5.13812	−	1.50869i	−0.242483	−	0.0711994i	−0.400716	+	0.916202i	$0.631239\pi$
$450$	−2.85376	+	4.00754i	−0.134527	+	0.188917i
$451$	−0.252948	−	0.198920i	−0.0119108	−	0.00936679i
$452$	0.768426	+	2.22022i	0.0361437	+	0.104430i
$453$	−9.29462	+	0.887528i	−0.436699	+	0.0416997i
$454$	9.03131	+	5.80407i	0.423860	+	0.272398i
$455$	0.0332103	−	0.0597968i	0.00155692	−	0.00280332i
$456$	−6.53941	+	4.20262i	−0.306236	+	0.196806i
$457$	2.80647	−	8.10875i	0.131281	−	0.379311i	−0.860133	−	0.510069i	$-0.829620\pi$
$457$	2.80647	−	8.10875i	0.131281	−	0.379311i	0.991414	+	0.130758i	$0.0417410\pi$
$458$	−4.56950	+	18.8358i	−0.213519	+	0.880137i
$459$	−1.47409	+	2.55320i	−0.0688046	+	0.119173i
$460$	−0.0867045	+	1.35548i	−0.00404262	+	0.0631994i
$461$	−35.6889			−1.66220			−0.831099	−	0.556124i	$-0.812288\pi$
$461$	−35.6889			−1.66220			−0.831099	+	0.556124i	$0.812288\pi$
$462$	0.324592	+	2.01868i	0.0151014	+	0.0939173i
$463$	−13.8512	−	15.9851i	−0.643720	−	0.742893i	0.336308	−	0.941752i	$-0.390822\pi$
$463$	−13.8512	−	15.9851i	−0.643720	−	0.742893i	−0.980028	+	0.198860i	$0.936276\pi$
$464$	1.55740	+	0.802894i	0.0723003	+	0.0372734i
$465$	−0.639480	−	0.256009i	−0.0296552	−	0.0118721i
$466$	11.7372	−	6.05097i	0.543718	−	0.280306i
$467$	−11.4537	+	1.09369i	−0.530013	+	0.0506101i	−0.356632	−	0.934245i	$-0.616075\pi$
$467$	−11.4537	+	1.09369i	−0.530013	+	0.0506101i	−0.173381	+	0.984855i	$0.555469\pi$
$468$	0.0597781	−	0.0689876i	0.00276324	−	0.00318895i
$469$	30.1735	+	8.31728i	1.39328	+	0.384056i
$470$	−0.782076	−	1.71251i	−0.0360745	−	0.0789921i
$471$	−3.49786	−	14.4184i	−0.161173	−	0.664364i
$472$	−2.16226	+	2.06171i	−0.0995259	+	0.0948977i
$473$	−3.26916	−	0.312167i	−0.150316	−	0.0143534i
$474$	−11.3055	+	4.52602i	−0.519277	+	0.207887i
$475$	−25.0442	+	28.9026i	−1.14911	+	1.32614i
$476$	6.87265	−	3.68903i	0.315007	−	0.169087i
$477$	0.840005	+	0.539838i	0.0384612	+	0.0247175i
$478$	9.26953	−	7.28964i	0.423978	−	0.333420i
$479$	0.623861	+	13.0964i	0.0285049	+	0.598392i	0.967257	+	0.253799i	$0.0816801\pi$
$479$	0.623861	+	13.0964i	0.0285049	+	0.598392i	−0.938752	+	0.344593i	$0.888017\pi$
$480$	−0.278096	+	0.0535986i	−0.0126933	+	0.00244643i
$481$	−0.128666	−	0.122683i	−0.00586668	−	0.00559386i
$482$	−16.6359			−0.757746
$483$	−7.35647	+	10.3384i	−0.334731	+	0.470413i
$484$	−10.4028			−0.472854
$485$	−2.17302	−	2.07197i	−0.0986716	−	0.0940831i
$486$	0.981929	−	0.189251i	0.0445412	−	0.00858461i
$487$	2.01813	+	42.3657i	0.0914500	+	1.91977i	0.322049	+	0.946723i	$0.395628\pi$
$487$	2.01813	+	42.3657i	0.0914500	+	1.91977i	−0.230599	+	0.973049i	$0.574069\pi$
$488$	−8.16149	+	6.41826i	−0.369453	+	0.290541i
$489$	3.25702	+	2.09316i	0.147288	+	0.0946559i
$490$	−1.95807	−	0.310248i	−0.0884567	−	0.0140156i
$491$	6.92330	−	7.98991i	0.312444	−	0.360580i	−0.577708	−	0.816244i	$-0.696053\pi$
$491$	6.92330	−	7.98991i	0.312444	−	0.360580i	0.890152	+	0.455664i	$0.150598\pi$
$492$	0.386579	−	0.154763i	0.0174283	−	0.00697725i
$493$	5.14234	+	0.491034i	0.231599	+	0.0221151i
$494$	0.513551	−	0.489670i	0.0231058	−	0.0220313i
$495$	−0.0515993	−	0.212695i	−0.00231921	−	0.00955993i
$496$	1.01035	+	2.21237i	0.0453663	+	0.0993383i
$497$	0.374830	+	1.44011i	0.0168134	+	0.0645976i
$498$	8.54157	−	9.85749i	0.382757	−	0.441725i
$499$	8.41289	−	0.803333i	0.376613	−	0.0359621i	0.0949664	−	0.995480i	$-0.469726\pi$
$499$	8.41289	−	0.803333i	0.376613	−	0.0359621i	0.281646	+	0.959518i	$0.409120\pi$
$500$	−2.49712	+	1.28735i	−0.111674	+	0.0575722i
$501$	1.28027	+	0.512544i	0.0571984	+	0.0228988i
$502$	10.3376	+	5.32940i	0.461390	+	0.237863i
$503$	12.1962	+	14.0752i	0.543803	+	0.627582i	0.959428	−	0.281954i	$-0.0909826\pi$
$503$	12.1962	+	14.0752i	0.543803	+	0.627582i	−0.415625	+	0.909536i	$0.636437\pi$
$504$	−2.47224	−	0.942345i	−0.110122	−	0.0419754i
$505$	1.44433			0.0642718
$506$	2.64029	+	2.60087i	0.117375	+	0.115623i
$507$	6.49583	−	11.2511i	0.288490	−	0.499680i
$508$	1.44829	−	5.96992i	0.0642574	−	0.264872i
$509$	−13.4339	+	38.8147i	−0.595447	+	1.72043i	0.0934990	+	0.995619i	$0.470195\pi$
$509$	−13.4339	+	38.8147i	−0.595447	+	1.72043i	−0.688946	+	0.724812i	$0.741926\pi$
$510$	−0.702418	+	0.451417i	−0.0311036	+	0.0199891i
$511$	−36.7145	+	0.610627i	−1.62415	+	0.0270125i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	7.73822	−	0.738910i	0.341651	−	0.0326237i
$514$	−5.06016	−	14.6204i	−0.223194	−	0.644877i
$515$	−1.56052	−	1.22721i	−0.0687648	−	0.0540773i
$516$	2.46500	−	3.46161i	0.108516	−	0.152389i
$517$	−4.92895	−	1.44727i	−0.216775	−	0.0636508i
$518$	−2.06230	+	4.72208i	−0.0906124	+	0.207476i
$519$	−4.28199	−	9.37626i	−0.187959	−	0.411572i
$520$	0.0240009	−	0.00960852i	0.00105251	−	0.000421361i
$521$	5.07766	+	14.6709i	0.222456	+	0.642746i	0.999905	+	0.0137989i	$0.00439247\pi$
$521$	5.07766	+	14.6709i	0.222456	+	0.642746i	−0.777448	+	0.628947i	$0.783486\pi$
$522$	−1.01636	−	1.42728i	−0.0444850	−	0.0624704i
$523$	−0.0864857	+	1.81556i	−0.00378176	+	0.0793888i	−0.999969	−	0.00784991i	$-0.997501\pi$
$523$	−0.0864857	+	1.81556i	−0.00378176	+	0.0793888i	0.996187	+	0.0872388i	$0.0278043\pi$
$524$	1.77042	+	12.3135i	0.0773410	+	0.537919i
$525$	−12.9764	−	1.02165i	−0.566336	−	0.0445885i
$526$	−16.6402	−	19.2038i	−0.725545	−	0.837324i
$527$	5.18949	+	4.94817i	0.226058	+	0.215546i
$528$	−0.386394	+	0.669254i	−0.0168156	+	0.0291256i
$529$	0.345944	+	22.9974i	0.0150411	+	0.999887i
$530$	0.141397	+	0.244907i	0.00614189	+	0.0106381i
$531$	2.86662	−	0.841715i	0.124401	−	0.0365273i
$532$	−18.4344	−	9.11883i	−0.799234	−	0.395351i
$533$	−0.0319770	+	0.0205504i	−0.00138508	+	0.000890136i
$534$	14.1587	−	11.1345i	0.612705	−	0.481837i
$535$	−4.41759	+	2.27743i	−0.190989	+	0.0984618i
$536$	6.86198	+	9.63631i	0.296393	+	0.416225i
$537$	8.52549	+	1.64315i	0.367902	+	0.0709073i
$538$	−3.06091	+	21.2891i	−0.131965	+	0.917838i
$539$	−4.13862	+	3.48350i	−0.178263	+	0.150045i
$540$	0.271742	+	0.0797906i	0.0116939	+	0.00343364i
$541$	5.72368	+	23.5933i	0.246080	+	1.01436i	0.952008	+	0.306072i	$0.0990150\pi$
$541$	5.72368	+	23.5933i	0.246080	+	1.01436i	−0.705928	+	0.708283i	$0.749470\pi$
$542$	−0.253153	−	0.0241732i	−0.0108739	−	0.00103833i
$543$	2.87386	+	2.26003i	0.123329	+	0.0969872i
$544$	2.89490	+	0.557947i	0.124118	+	0.0239218i
$545$	−0.867652	+	1.89989i	−0.0371661	+	0.0813825i
$546$	0.237877	+	0.0417568i	0.0101802	+	0.00178703i
$547$	−0.159348	−	1.10829i	−0.00681322	−	0.0473870i	0.986131	−	0.165968i	$-0.0530747\pi$
$547$	−0.159348	−	1.10829i	−0.00681322	−	0.0473870i	−0.992944	+	0.118581i	$0.962166\pi$
$548$	16.8634	+	8.69369i	0.720369	+	0.371376i
$549$	10.1952	−	1.96497i	0.435122	−	0.0838629i
$550$	−0.896345	+	3.69478i	−0.0382203	+	0.157546i
$551$	−6.81020	−	11.7956i	−0.290124	−	0.502510i
$552$	−4.62295	+	1.27606i	−0.196766	+	0.0543126i
$553$	−25.6538	−	19.4928i	−1.09091	−	0.828917i
$554$	7.19531	−	2.11273i	0.305700	−	0.0897615i
$555$	0.180404	−	0.521242i	0.00765771	−	0.0221255i
$556$	0.0756084	+	1.58722i	0.00320651	+	0.0673129i
$557$	−6.81769	−	2.72939i	−0.288875	−	0.115648i	0.222699	−	0.974887i	$-0.428513\pi$
$557$	−6.81769	−	2.72939i	−0.288875	−	0.115648i	−0.511574	+	0.859239i	$0.670937\pi$
$558$	0.115727	−	2.42940i	0.00489910	−	0.102845i
$559$	−0.161147	+	0.352862i	−0.00681578	+	0.0149245i
$560$	−0.500046	−	0.558055i	−0.0211308	−	0.0235821i
$561$	−0.324239	+	2.25513i	−0.0136894	+	0.0952116i
$562$	2.27509	−	3.19492i	0.0959690	−	0.134770i
$563$	1.24406	−	1.18621i	0.0524308	−	0.0499926i	−0.663411	−	0.748255i	$-0.730892\pi$
$563$	1.24406	−	1.18621i	0.0524308	−	0.0499926i	0.715842	+	0.698263i	$0.246043\pi$
$564$	4.81095	−	4.58723i	0.202578	−	0.193157i
$565$	0.385967	−	0.542014i	0.0162377	−	0.0228027i
$566$	0.586049	−	4.07606i	0.0246335	−	0.171330i
$567$	1.76561	+	1.97044i	0.0741487	+	0.0827506i
$568$	−0.233648	+	0.511617i	−0.00980364	+	0.0214670i
$569$	−2.01976	+	42.4000i	−0.0846728	+	1.77750i	0.413579	+	0.910468i	$0.364278\pi$
$569$	−2.01976	+	42.4000i	−0.0846728	+	1.77750i	−0.498252	+	0.867032i	$0.666025\pi$
$570$	2.04384	+	0.818230i	0.0856070	+	0.0342719i
$571$	0.144554	+	3.03457i	0.00604940	+	0.126993i	0.999872	+	0.0160106i	$0.00509656\pi$
$571$	0.144554	+	3.03457i	0.00604940	+	0.126993i	−0.993822	+	0.110982i	$0.964600\pi$
$572$	0.0230723	−	0.0666631i	0.000964703	−	0.00278733i
$573$	−21.3090	+	6.25687i	−0.890194	+	0.261385i
$574$	0.877208	+	0.666537i	0.0366140	+	0.0278207i
$575$	−20.0540	+	12.4313i	−0.836308	+	0.518423i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	2.19000	−	9.02730i	0.0911708	−	0.375811i	−0.907887	−	0.419215i	$-0.862305\pi$
$577$	2.19000	−	9.02730i	0.0911708	−	0.375811i	0.999058	+	0.0434042i	$0.0138203\pi$
$578$	−8.15810	+	1.57234i	−0.339332	+	0.0654009i
$579$	15.9465	+	8.22100i	0.662714	+	0.341653i
$580$	−0.0706225	−	0.491190i	−0.00293244	−	0.0203956i
$581$	33.9897	+	5.96654i	1.41013	+	0.247534i
$582$	4.40404	−	9.64350i	0.182553	−	0.399736i
$583$	0.757697	+	0.146034i	0.0313806	+	0.00604811i
$584$	−10.9094	−	8.57924i	−0.451434	−	0.355012i
$585$	−0.0257357	−	0.00245747i	−0.00106404	−	0.000101604i
$586$	4.59881	+	18.9566i	0.189975	+	0.783089i
$587$	26.8290	+	7.87771i	1.10735	+	0.325148i	0.783770	−	0.621052i	$-0.213294\pi$
$587$	26.8290	+	7.87771i	1.10735	+	0.325148i	0.323583	+	0.946200i	$0.395113\pi$
$588$	−1.22606	−	6.89179i	−0.0505620	−	0.284213i
$589$	2.69063	−	18.7137i	0.110865	−	0.771086i
$590$	0.830850	+	0.160133i	0.0342056	+	0.00659258i
$591$	−10.0028	−	14.0469i	−0.411459	−	0.577813i
$592$	−1.73107	+	0.892427i	−0.0711464	+	0.0366785i
$593$	−4.51037	+	3.54699i	−0.185219	+	0.145657i	−0.706463	−	0.707750i	$-0.749710\pi$
$593$	−4.51037	+	3.54699i	−0.185219	+	0.145657i	0.521245	+	0.853407i	$0.325468\pi$
$594$	0.650111	−	0.417801i	0.0266744	−	0.0171426i
$595$	−1.98010	−	0.979481i	−0.0811761	−	0.0401548i
$596$	12.3059	−	3.61335i	0.504070	−	0.148008i
$597$	1.19935	+	2.07733i	0.0490860	+	0.0850194i
$598$	0.392329	−	0.194242i	0.0160435	−	0.00794315i
$599$	−6.39632	+	11.0788i	−0.261347	+	0.452666i	−0.966600	−	0.256290i	$-0.917500\pi$
$599$	−6.39632	+	11.0788i	−0.261347	+	0.452666i	0.705253	+	0.708955i	$0.250833\pi$
$600$	−3.56062	−	3.39504i	−0.145362	−	0.138602i
$601$	−22.6452	−	26.1339i	−0.923716	−	1.06603i	−0.997633	−	0.0687612i	$-0.978095\pi$
$601$	−22.6452	−	26.1339i	−0.923716	−	1.06603i	0.0739167	−	0.997264i	$-0.476450\pi$
$602$	11.2087	+	0.882476i	0.456831	+	0.0359670i
$603$	−1.68356	−	11.7094i	−0.0685600	−	0.476845i
$604$	0.444267	−	9.32632i	0.0180770	−	0.379483i
$605$	1.70897	+	2.39992i	0.0694797	+	0.0975706i
$606$	1.66797	+	4.81930i	0.0677568	+	0.195771i
$607$	−11.1902	+	4.47989i	−0.454197	+	0.181833i	−0.587470	−	0.809246i	$-0.699876\pi$
$607$	−11.1902	+	4.47989i	−0.454197	+	0.181833i	0.133272	+	0.991079i	$0.457452\pi$
$608$	−3.22919	−	7.07095i	−0.130961	−	0.286765i
$609$	1.85540	−	4.24834i	0.0751846	−	0.172151i
$610$	2.82146	+	0.828456i	0.114238	+	0.0335432i
$611$	−0.351978	+	0.494284i	−0.0142395	+	0.0199966i
$612$	−2.31743	−	1.82244i	−0.0936764	−	0.0736679i
$613$	13.8755	+	40.0906i	0.560426	+	1.61924i	0.767592	+	0.640939i	$0.221455\pi$
$613$	13.8755	+	40.0906i	0.560426	+	1.61924i	−0.207166	+	0.978306i	$0.566424\pi$
$614$	−26.0988	+	2.49214i	−1.05326	+	0.100574i
$615$	−0.0992111	−	0.0637591i	−0.00400058	−	0.00257101i
$616$	−2.04432	+	0.0340007i	−0.0823681	+	0.00136993i
$617$	−1.06395	+	0.683761i	−0.0428331	+	0.0275272i	−0.561882	−	0.827217i	$-0.689923\pi$
$617$	−1.06395	+	0.683761i	−0.0428331	+	0.0275272i	0.519049	+	0.854744i	$0.326286\pi$
$618$	2.29267	−	6.62423i	0.0922247	−	0.266466i
$619$	8.20961	−	33.8405i	0.329972	−	1.36016i	−0.529209	−	0.848492i	$-0.677511\pi$
$619$	8.20961	−	33.8405i	0.329972	−	1.36016i	0.859181	−	0.511672i	$-0.170974\pi$
$620$	0.344411	−	0.596537i	0.0138319	−	0.0239575i
$621$	4.69377	+	0.984155i	0.188354	+	0.0394928i
$622$	−14.6942			−0.589184
$623$	44.5309	+	16.9738i	1.78409	+	0.680043i
$624$	0.0597781	+	0.0689876i	0.00239304	+	0.00276171i
$625$	−21.1572	−	10.9073i	−0.846288	−	0.436292i
$626$	28.0068	+	11.2122i	1.11938	+	0.448132i
$627$	5.33942	−	2.75266i	0.213236	−	0.109931i
$628$	14.7694	−	1.41031i	0.589364	−	0.0562775i
$629$	−3.76007	+	4.33935i	−0.149924	+	0.173021i
$630$	0.188742	+	0.725154i	0.00751968	+	0.0288908i
$631$	−15.5515	−	34.0530i	−0.619094	−	1.35563i	−0.916176	−	0.400775i	$-0.868741\pi$
$631$	−15.5515	−	34.0530i	−0.619094	−	1.35563i	0.297082	−	0.954852i	$-0.403987\pi$
$632$	−2.87102	−	11.8345i	−0.114203	−	0.470751i
$633$	−1.09064	+	1.03992i	−0.0433490	+	0.0413331i
$634$	−15.3030	−	1.46126i	−0.607758	−	0.0580339i
$635$	−1.61518	+	0.646622i	−0.0640966	+	0.0256604i
$636$	−0.653889	+	0.754628i	−0.0259284	+	0.0299229i
$637$	0.228956	+	0.596558i	0.00907158	+	0.0236365i
$638$	−1.13911	−	0.732061i	−0.0450978	−	0.0289826i
$639$	0.442111	−	0.347680i	0.0174896	−	0.0137540i
$640$	−0.0134759	−	0.282893i	−0.000532680	−	0.0111823i
$641$	33.3923	−	6.43585i	1.31892	−	0.254201i	0.519239	−	0.854629i	$-0.326215\pi$
$641$	33.3923	−	6.43585i	1.31892	−	0.254201i	0.799679	+	0.600428i	$0.205003\pi$
$642$	−12.7007	−	12.1101i	−0.501258	−	0.477948i
$643$	13.3995			0.528424			0.264212	−	0.964465i	$-0.414888\pi$
$643$	13.3995			0.528424			0.264212	+	0.964465i	$0.414888\pi$
$644$	−9.18623	−	8.75290i	−0.361988	−	0.344912i
$645$	−1.20354			−0.0473894
$646$	−16.5861	−	15.8148i	−0.652572	−	0.622226i
$647$	−18.7134	+	3.60670i	−0.735698	+	0.141794i	−0.543319	−	0.839527i	$-0.682832\pi$
$647$	−18.7134	+	3.60670i	−0.735698	+	0.141794i	−0.192379	+	0.981321i	$0.561620\pi$
$648$	0.0475819	+	0.998867i	0.00186919	+	0.0392392i
$649$	1.81485	−	1.42721i	0.0712390	−	0.0560230i
$650$	0.377804	+	0.242800i	0.0148187	+	0.00952339i
$651$	5.66973	−	3.04334i	0.222214	−	0.119278i
$652$	−2.53538	+	2.92598i	−0.0992930	+	0.114590i
$653$	−23.2469	+	9.30663i	−0.909720	+	0.364197i	−0.778855	−	0.627204i	$-0.784199\pi$
$653$	−23.2469	+	9.30663i	−0.909720	+	0.364197i	−0.130864	+	0.991400i	$0.541775\pi$
$654$	−7.34138	−	0.701016i	−0.287071	−	0.0274119i
$655$	2.54988	−	2.43130i	0.0996319	−	0.0949988i
$656$	0.0981717	+	0.404669i	0.00383296	+	0.0157997i
$657$	5.76542	+	12.6245i	0.224930	+	0.492529i
$658$	16.9550	+	4.67363i	0.660975	+	0.182197i
$659$	13.5880	−	15.6814i	0.529313	−	0.610859i	−0.426625	−	0.904429i	$-0.640298\pi$
$659$	13.5880	−	15.6814i	0.529313	−	0.610859i	0.955938	+	0.293569i	$0.0948431\pi$
$660$	0.217874	−	0.0208044i	0.00848071	−	0.000809810i
$661$	−5.41191	+	2.79003i	−0.210499	+	0.108520i	−0.560252	−	0.828322i	$-0.689296\pi$
$661$	−5.41191	+	2.79003i	−0.210499	+	0.108520i	0.349753	+	0.936842i	$0.386265\pi$
$662$	−3.76623	−	1.50777i	−0.146379	−	0.0586013i
$663$	0.239204	+	0.123318i	0.00928991	+	0.00478928i
$664$	8.54157	+	9.85749i	0.331477	+	0.382545i
$665$	0.924707	+	5.75086i	0.0358586	+	0.223009i
$666$	1.94757			0.0754667
$667$	−1.84792	−	8.19744i	−0.0715517	−	0.317406i
$668$	−0.689529	+	1.19430i	−0.0266787	+	0.0462088i
$669$	0.0168229	−	0.0693448i	0.000650410	−	0.00268102i
$670$	1.09580	−	3.16611i	0.0423345	−	0.122318i
$671$	6.75002	−	4.33797i	0.260581	−	0.167466i
$672$	1.28459	−	2.31297i	0.0495541	−	0.0892247i
$673$	5.24795	+	3.37265i	0.202294	+	0.130006i	0.637866	−	0.770148i	$-0.279818\pi$
$673$	5.24795	+	3.37265i	0.202294	+	0.130006i	−0.435572	+	0.900154i	$0.643454\pi$
$674$	2.64436	−	0.252505i	0.101857	−	0.00972615i
$675$	1.60911	+	4.64921i	0.0619345	+	0.178948i
$676$	10.2121	+	8.03092i	0.392775	+	0.308881i
$677$	−13.6938	+	19.2302i	−0.526295	+	0.739078i	−0.989078	−	0.147394i	$-0.952912\pi$
$677$	−13.6938	+	19.2302i	−0.526295	+	0.739078i	0.462783	+	0.886472i	$0.346851\pi$
$678$	2.25427	+	0.661914i	0.0865747	+	0.0254206i
$679$	27.8738	−	3.13019i	1.06970	−	0.120126i
$680$	−0.346857	−	0.759512i	−0.0133014	−	0.0291259i
$681$	9.96653	−	3.99000i	0.381918	−	0.152897i
$682$	−0.614738	−	1.77617i	−0.0235395	−	0.0680131i
$683$	1.95745	+	2.74886i	0.0748999	+	0.105182i	0.850326	−	0.526256i	$-0.176404\pi$
$683$	1.95745	+	2.74886i	0.0748999	+	0.105182i	−0.775427	+	0.631438i	$0.782465\pi$
$684$	−0.369874	+	7.76461i	−0.0141425	+	0.296887i
$685$	−0.764696	−	5.31858i	−0.0292175	−	0.203212i
$686$	13.9689	−	12.1602i	0.533333	−	0.464279i
$687$	12.6926	+	14.6480i	0.484252	+	0.558857i
$688$	3.07557	+	2.93255i	0.117255	+	0.111802i
$689$	0.0455741	−	0.0789366i	0.00173623	−	0.00300725i
$690$	1.05385	+	0.856881i	0.0401192	+	0.0326209i
$691$	−14.2125	−	24.6168i	−0.540670	−	0.936468i	−0.998866	−	0.0476167i	$-0.984837\pi$
$691$	−14.2125	−	24.6168i	−0.540670	−	0.936468i	0.458196	−	0.888851i	$-0.348496\pi$
$692$	9.89021	−	2.90403i	0.375969	−	0.110395i
$693$	1.83265	+	0.906542i	0.0696165	+	0.0344367i
$694$	13.6177	−	8.75158i	0.516922	−	0.332205i
$695$	0.353749	−	0.278191i	0.0134185	−	0.0105524i
$696$	1.55740	−	0.802894i	0.0590330	−	0.0304336i
$697$	0.712103	+	1.00001i	0.0269728	+	0.0378780i
$698$	16.5664	+	3.19291i	0.627048	+	0.120854i
$699$	1.87930	−	13.0708i	0.0710815	−	0.494383i
$700$	2.85798	−	12.6989i	0.108022	−	0.479974i
$701$	44.8129	+	13.1583i	1.69256	+	0.496980i	0.979042	−	0.203657i	$-0.0652826\pi$
$701$	44.8129	+	13.1583i	1.69256	+	0.496980i	0.713518	+	0.700637i	$0.247101\pi$
$702$	−0.0215209	−	0.0887105i	−0.000812255	−	0.00334816i
$703$	15.0707	+	1.43908i	0.568402	+	0.0542758i
$704$	−0.607453	−	0.477706i	−0.0228942	−	0.0180042i
$705$	−1.84862	−	0.356291i	−0.0696229	−	0.0134187i
$706$	−8.83976	+	19.3564i	−0.332689	+	0.728486i
$707$	−8.66508	+	10.3427i	−0.325884	+	0.388976i
$708$	0.425185	+	2.95723i	0.0159794	+	0.111139i
$709$	11.7893	+	6.07782i	0.442757	+	0.228257i	0.665165	−	0.746697i	$-0.268361\pi$
$709$	11.7893	+	6.07782i	0.442757	+	0.228257i	−0.222408	+	0.974954i	$0.571392\pi$
$710$	0.156414	−	0.0301462i	0.00587010	−	0.00113137i
$711$	−2.87102	+	11.8345i	−0.107672	+	0.443829i
$712$	9.00618	+	15.5992i	0.337521	+	0.584603i
$713$	5.01757	−	10.5299i	0.187909	−	0.394347i
$714$	0.981531	−	7.73815i	0.0367329	−	0.289593i
$715$	−0.0191695	+	0.00562866i	−0.000716898	+	0.000210500i
$716$	−2.83973	+	8.20487i	−0.106126	+	0.306630i
$717$	−0.561110	−	11.7791i	−0.0209550	−	0.439900i
$718$	−22.7593	−	9.11144i	−0.849369	−	0.340036i
$719$	−0.451780	+	9.48402i	−0.0168485	+	0.353694i	0.974663	+	0.223677i	$0.0718062\pi$
$719$	−0.451780	+	9.48402i	−0.0168485	+	0.353694i	−0.991512	+	0.130017i	$0.958497\pi$
$720$	−0.117651	+	0.257621i	−0.00438461	+	0.00960095i
$721$	18.1500	−	3.81222i	0.675943	−	0.141975i
$722$	−5.89553	+	41.0043i	−0.219409	+	1.52602i
$723$	−9.64979	+	13.5512i	−0.358880	+	0.503976i
$724$	−2.64602	+	2.52298i	−0.0983386	+	0.0937657i
$725$	6.23883	−	5.94872i	0.231704	−	0.220930i
$726$	−6.03421	+	8.47387i	−0.223951	+	0.314495i
$727$	5.86686	−	40.8049i	0.217590	−	1.51337i	−0.529308	−	0.848430i	$-0.677548\pi$
$727$	5.86686	−	40.8049i	0.217590	−	1.51337i	0.746897	−	0.664939i	$-0.231543\pi$
$728$	−0.0751852	+	0.229513i	−0.00278655	+	0.00850631i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−0.187028	+	3.92619i	−0.00692220	+	0.145315i
$731$	11.6311	+	4.65639i	0.430191	+	0.172223i
$732$	0.494037	+	10.3711i	0.0182601	+	0.383327i
$733$	−7.56956	+	21.8708i	−0.279588	+	0.807816i	0.714539	+	0.699596i	$0.246636\pi$
$733$	−7.56956	+	21.8708i	−0.279588	+	0.807816i	−0.994127	+	0.108221i	$0.965485\pi$
$734$	19.9347	−	5.85334i	0.735802	−	0.216051i
$735$	−1.38851	+	1.41504i	−0.0512161	+	0.0521944i
$736$	−0.605154	−	4.75750i	−0.0223063	−	0.175364i
$737$	−4.57098	−	7.91718i	−0.168374	−	0.291633i
$738$	0.0981717	−	0.404669i	0.00361375	−	0.0148961i
$739$	26.7211	−	5.15006i	0.982950	−	0.189448i	0.327635	−	0.944804i	$-0.393748\pi$
$739$	26.7211	−	5.15006i	0.982950	−	0.189448i	0.655314	+	0.755356i	$0.272536\pi$
$740$	0.490263	+	0.252748i	0.0180224	+	0.00929120i
$741$	−0.100985	−	0.702363i	−0.00370976	−	0.0258019i
$742$	−2.60204	−	0.456761i	−0.0955238	−	0.0167682i
$743$	−4.48064	+	9.81123i	−0.164379	+	0.359939i	−0.973840	−	0.227234i	$-0.927032\pi$
$743$	−4.48064	+	9.81123i	−0.164379	+	0.359939i	0.809462	+	0.587173i	$0.199759\pi$
$744$	2.38821	+	0.460289i	0.0875559	+	0.0168750i
$745$	−2.85522	−	2.24537i	−0.104607	−	0.0822639i
$746$	−12.7474	−	1.21723i	−0.466715	−	0.0445659i
$747$	−3.07508	−	12.6757i	−0.112511	−	0.463778i
$748$	−2.18603	−	0.641876i	−0.0799292	−	0.0234693i
$749$	10.1944	−	45.2970i	0.372496	−	1.65512i
$750$	−0.399823	+	2.78083i	−0.0145995	+	0.101541i
$751$	−20.2800	−	3.90865i	−0.740028	−	0.142629i	−0.194713	−	0.980860i	$-0.562378\pi$
$751$	−20.2800	−	3.90865i	−0.740028	−	0.142629i	−0.545314	+	0.838232i	$0.683590\pi$
$752$	3.85587	+	5.41481i	0.140609	+	0.197458i
$753$	10.3376	−	5.32940i	0.376723	−	0.194214i
$754$	−0.125725	+	0.0988715i	−0.00457865	+	0.00360069i
$755$	−2.22456	+	1.42964i	−0.0809600	+	0.0520299i
$756$	−2.20165	+	1.46722i	−0.0800733	+	0.0533621i
$757$	20.8838	−	6.13205i	0.759036	−	0.222873i	0.120761	−	0.992682i	$-0.461466\pi$
$757$	20.8838	−	6.13205i	0.759036	−	0.222873i	0.638275	+	0.769808i	$0.279648\pi$
$758$	−16.6707	−	28.8745i	−0.605508	−	1.04877i
$759$	3.65012	−	0.642063i	0.132491	−	0.0233054i
$760$	−1.10077	+	1.90659i	−0.0399291	+	0.0691593i
$761$	18.8165	+	17.9415i	0.682099	+	0.650380i	0.949704	−	0.313149i	$-0.101384\pi$
$761$	18.8165	+	17.9415i	0.682099	+	0.650380i	−0.267605	+	0.963529i	$0.586232\pi$
$762$	−4.02287	−	4.64263i	−0.145733	−	0.168185i
$763$	−8.39953	−	17.6113i	−0.304083	−	0.637573i
$764$	−3.16061	−	21.9825i	−0.114347	−	0.795299i
$765$	−0.0397293	+	0.834020i	−0.00143641	+	0.0301541i
$766$	13.2987	+	18.6755i	0.480503	+	0.674772i
$767$	−0.0891988	−	0.257723i	−0.00322078	−	0.00930584i
$768$	0.928368	−	0.371662i	0.0334996	−	0.0134112i
$769$	−17.4237	−	38.1525i	−0.628313	−	1.37581i	−0.909315	−	0.416107i	$-0.863394\pi$
$769$	−17.4237	−	38.1525i	−0.628313	−	1.37581i	0.281002	−	0.959707i	$-0.409333\pi$
$770$	0.343686	+	0.466038i	0.0123856	+	0.0167949i
$771$	−14.8446	−	4.35876i	−0.534614	−	0.156977i
$772$	−10.4067	+	14.6142i	−0.374547	+	0.525977i
$773$	−18.1845	−	14.3004i	−0.654050	−	0.514351i	0.235097	−	0.971972i	$-0.424459\pi$
$773$	−18.1845	−	14.3004i	−0.654050	−	0.514351i	−0.889147	+	0.457621i	$0.848702\pi$
$774$	−1.38990	−	4.01586i	−0.0499590	−	0.144347i
$775$	11.9115	−	1.13741i	0.427875	−	0.0408571i
$776$	8.91858	+	5.73163i	0.320158	+	0.205753i
$777$	2.65024	+	4.41898i	0.0950769	+	0.158530i
$778$	−11.1751	+	7.18182i	−0.400648	+	0.257481i
$779$	1.05869	−	3.05888i	0.0379314	−	0.109596i
$780$	0.00609503	−	0.0251241i	0.000218237	−	0.000899586i
$781$	0.217325	−	0.376418i	0.00777651	−	0.0134693i
$782$	−6.86922	−	12.3582i	−0.245643	−	0.441927i
$783$	−1.75218			−0.0626177
$784$	6.99613	−	0.232780i	0.249862	−	0.00831358i
$785$	−2.75168	−	3.17561i	−0.0982118	−	0.113342i
$786$	11.0572	+	5.70040i	0.394399	+	0.203327i
$787$	−49.2458	−	19.7150i	−1.75542	−	0.702766i	−0.998803	−	0.0489111i	$-0.984425\pi$
$787$	−49.2458	−	19.7150i	−1.75542	−	0.702766i	−0.756620	−	0.653854i	$-0.773151\pi$
$788$	15.3275	−	7.90186i	0.546019	−	0.281492i
$789$	−25.2952	+	2.41540i	−0.900532	+	0.0859904i
$790$	−2.25856	+	2.60652i	−0.0803560	+	0.0927358i
$791$	1.56574	+	6.01561i	0.0556712	+	0.213890i
$792$	0.321028	+	0.702953i	0.0114072	+	0.0249783i
$793$	−0.223449	−	0.921069i	−0.00793491	−	0.0327081i
$794$	−7.26111	+	6.92346i	−0.257687	+	0.245704i
$795$	0.281513	+	0.0268812i	0.00998424	+	0.000953380i
$796$	−2.22687	+	0.891504i	−0.0789293	+	0.0315985i
$797$	15.5663	−	17.9645i	0.551386	−	0.636334i	−0.409819	−	0.912167i	$-0.634408\pi$
$797$	15.5663	−	17.9645i	0.551386	−	0.636334i	0.961206	+	0.275833i	$0.0889536\pi$
$798$	−18.1210	+	9.72681i	−0.641477	+	0.344325i
$799$	16.4867	+	10.5953i	0.583256	+	0.374836i
$800$	3.86722	−	3.04121i	0.136727	−	0.107523i
$801$	−0.857062	−	17.9919i	−0.0302828	−	0.635714i
$802$	−1.76073	+	0.339353i	−0.0621735	+	0.0119830i
$803$	7.76226	+	7.40130i	0.273924	+	0.261186i
$804$	11.8298			0.417206
$805$	−0.510171	+	3.55719i	−0.0179812	+	0.125374i
$806$	−0.222016			−0.00782019
$807$	15.5661	+	14.8422i	0.547952	+	0.522471i
$808$	−5.00762	+	0.965140i	−0.176167	+	0.0339535i
$809$	0.682663	+	14.3309i	0.0240011	+	0.503846i	0.978577	+	0.205879i	$0.0660054\pi$
$809$	0.682663	+	14.3309i	0.0240011	+	0.503846i	−0.954576	+	0.297967i	$0.903692\pi$
$810$	0.222621	−	0.175071i	0.00782212	−	0.00615138i
$811$	6.14183	+	3.94711i	0.215669	+	0.138602i	0.644015	−	0.765013i	$-0.277267\pi$
$811$	6.14183	+	3.94711i	0.215669	+	0.138602i	−0.428346	+	0.903615i	$0.640904\pi$
$812$	3.94104	+	2.44112i	0.138303	+	0.0856664i
$813$	−0.166534	+	0.192191i	−0.00584061	+	0.00674042i
$814$	1.39725	−	0.559374i	0.0489735	−	0.0196060i
$815$	1.09153	+	0.104229i	0.0382348	+	0.00365098i
$816$	2.13370	−	2.03448i	0.0746944	−	0.0712209i
$817$	−7.78801	−	32.1026i	−0.272468	−	1.12313i
$818$	6.72313	+	14.7216i	0.235069	+	0.514729i
$819$	0.171996	−	0.169547i	0.00601003	−	0.00592446i
$820$	0.0772293	−	0.0891274i	0.00269696	−	0.00311246i
$821$	−42.4355	+	4.05210i	−1.48101	+	0.141419i	−0.804033	−	0.594585i	$-0.797316\pi$
$821$	−42.4355	+	4.05210i	−1.48101	+	0.141419i	−0.676977	+	0.736004i	$0.736710\pi$
$822$	16.8634	−	8.69369i	0.588179	−	0.303227i
$823$	−9.06993	−	3.63105i	−0.316158	−	0.126570i	0.208156	−	0.978096i	$-0.433254\pi$
$823$	−9.06993	−	3.63105i	−0.316158	−	0.126570i	−0.524314	+	0.851525i	$0.675678\pi$
$824$	6.23052	+	3.21206i	0.217051	+	0.111897i
$825$	2.48975	+	2.87333i	0.0866820	+	0.100036i
$826$	−6.13128	+	4.98892i	−0.213334	+	0.173587i
$827$	18.2887			0.635959			0.317980	−	0.948098i	$-0.396996\pi$
$827$	18.2887			0.635959			0.317980	+	0.948098i	$0.396996\pi$
$828$	−1.64213	+	4.50593i	−0.0570680	+	0.156592i
$829$	−10.0951	+	17.4851i	−0.350616	+	0.607284i	−0.986357	−	0.164618i	$-0.947361\pi$
$829$	−10.0951	+	17.4851i	−0.350616	+	0.607284i	0.635742	+	0.771902i	$0.280694\pi$
$830$	0.870907	−	3.58993i	0.0302296	−	0.124608i
$831$	2.45271	−	7.08664i	0.0850835	−	0.245833i
$832$	−0.0767927	+	0.0493517i	−0.00266231	+	0.00171096i
$833$	18.8933	−	8.30297i	0.654614	−	0.287681i
$834$	1.33676	+	0.859087i	0.0462884	+	0.0297477i
$835$	0.388800	−	0.0371259i	0.0134550	−	0.00128479i
$836$	1.96476	+	5.67681i	0.0679528	+	0.196337i
$837$	−1.91181	−	1.50346i	−0.0660817	−	0.0519672i
$838$	13.9864	−	19.6411i	0.483152	−	0.678492i
$839$	−16.1257	−	4.73493i	−0.556721	−	0.163468i	−0.00874453	−	0.999962i	$-0.502784\pi$
$839$	−16.1257	−	4.73493i	−0.556721	−	0.163468i	−0.547977	+	0.836494i	$0.684602\pi$
$840$	−0.744633	+	0.0836212i	−0.0256923	+	0.00288521i
$841$	−10.7717	−	23.5866i	−0.371437	−	0.813333i
$842$	−26.7939	+	10.7267i	−0.923378	+	0.369665i
$843$	−1.28282	−	3.70647i	−0.0441828	−	0.127658i
$844$	−0.874122	−	1.22753i	−0.0300885	−	0.0422534i
$845$	0.175074	−	3.67526i	0.00602273	−	0.126433i
$846$	−0.946024	−	6.57974i	−0.0325250	−	0.226216i
$847$	−27.4383	−	2.16026i	−0.942791	−	0.0742275i
$848$	−0.653889	−	0.754628i	−0.0224546	−	0.0259140i
$849$	−2.98032	−	2.84173i	−0.102284	−	0.0975279i
$850$	7.25221	−	12.5612i	0.248749	−	0.430846i
$851$	8.61349	+	3.61210i	0.295267	+	0.123821i
$852$	0.281222	+	0.487091i	0.00963451	+	0.0166875i
$853$	37.7247	−	11.0770i	1.29167	−	0.379268i	0.437479	−	0.899229i	$-0.355871\pi$
$853$	37.7247	−	11.0770i	1.29167	−	0.379268i	0.854191	+	0.519960i	$0.174053\pi$
$854$	−22.8595	+	15.2339i	−0.782235	+	0.521294i
$855$	1.85205	−	1.19024i	0.0633389	−	0.0407054i
$856$	13.7944	−	10.8480i	0.471481	−	0.370777i
$857$	−21.3758	+	11.0200i	−0.730183	+	0.376435i	−0.782878	−	0.622175i	$-0.786249\pi$
$857$	−21.3758	+	11.0200i	−0.730183	+	0.376435i	0.0526951	+	0.998611i	$0.483219\pi$
$858$	−0.0409189	−	0.0574626i	−0.00139695	−	0.00196174i
$859$	−43.8484	−	8.45109i	−1.49609	−	0.288347i	−0.625447	−	0.780266i	$-0.715084\pi$
$859$	−43.8484	−	8.45109i	−1.49609	−	0.288347i	−0.870641	+	0.491919i	$0.836296\pi$
$860$	0.171282	−	1.19129i	0.00584067	−	0.0406227i
$861$	1.05178	−	0.327923i	0.0358444	−	0.0111756i
$862$	18.7342	+	5.50086i	0.638090	+	0.187360i
$863$	3.03980	+	12.5302i	0.103476	+	0.426534i	0.999860	−	0.0167448i	$-0.00533028\pi$
$863$	3.03980	+	12.5302i	0.103476	+	0.426534i	−0.896384	+	0.443279i	$0.853815\pi$
$864$	−0.995472	−	0.0950560i	−0.0338666	−	0.00323387i
$865$	−2.29472	−	1.80459i	−0.0780230	−	0.0613579i
$866$	−0.429599	−	0.0827984i	−0.0145984	−	0.00281360i
$867$	−3.45137	+	7.55744i	−0.117215	+	0.256664i
$868$	2.20548	+	6.04513i	0.0748588	+	0.205185i
$869$	1.33930	+	9.31506i	0.0454327	+	0.315992i
$870$	−0.441077	−	0.227391i	−0.0149539	−	0.00770927i
$871$	−1.06036	+	0.204367i	−0.0359288	+	0.00692471i
$872$	1.73867	−	7.16689i	0.0588787	−	0.242701i
$873$	−5.30077	−	9.18120i	−0.179404	−	0.310737i
$874$	−16.0366	+	33.6545i	−0.542447	+	1.13838i
$875$	−6.85370	+	2.87695i	−0.231697	+	0.0972587i
$876$	−13.3165	+	3.91008i	−0.449923	+	0.132109i
$877$	10.6418	−	30.7475i	0.359348	−	1.03827i	−0.609963	−	0.792430i	$-0.708816\pi$
$877$	10.6418	−	30.7475i	0.359348	−	1.03827i	0.969311	−	0.245838i	$-0.0790632\pi$
$878$	0.301135	+	6.32159i	0.0101628	+	0.213343i
$879$	18.1091	+	7.24981i	0.610806	+	0.244530i
$880$	−0.0104140	+	0.218617i	−0.000351056	+	0.00736957i
$881$	1.04737	−	2.29343i	0.0352869	−	0.0772676i	−0.891168	−	0.453674i	$-0.850113\pi$
$881$	1.04737	−	2.29343i	0.0352869	−	0.0772676i	0.926455	+	0.376406i	$0.122840\pi$
$882$	−6.32507	−	2.99891i	−0.212976	−	0.100978i
$883$	0.980594	−	6.82018i	0.0329996	−	0.229517i	−0.966647	−	0.256114i	$-0.917558\pi$
$883$	0.980594	−	6.82018i	0.0329996	−	0.229517i	0.999646	+	0.0265965i	$0.00846692\pi$
$884$	−0.156105	+	0.219219i	−0.00525039	+	0.00737314i
$885$	0.612381	−	0.583904i	0.0205850	−	0.0196277i
$886$	−11.9626	+	11.4063i	−0.401890	+	0.383201i
$887$	−5.19878	+	7.30067i	−0.174558	+	0.245132i	−0.892581	−	0.450887i	$-0.851108\pi$
$887$	−5.19878	+	7.30067i	−0.174558	+	0.245132i	0.718023	+	0.696019i	$0.245047\pi$
$888$	−0.277168	+	1.92774i	−0.00930114	+	0.0646909i
$889$	5.05971	−	15.4454i	0.169697	−	0.518024i
$890$	2.11918	−	4.64035i	0.0710350	−	0.155545i
$891$	0.0367707	−	0.771913i	0.00123187	−	0.0258601i
$892$	0.0662448	+	0.0265204i	0.00221804	+	0.000887970i
$893$	−2.45870	−	51.6145i	−0.0822773	−	1.72721i
$894$	4.19479	−	12.1201i	0.140295	−	0.405355i
$895$	2.35937	−	0.692773i	0.0788650	−	0.0231569i
$896$	2.10661	+	1.60068i	0.0703769	+	0.0534751i
$897$	0.0693483	−	0.432253i	0.00231547	−	0.0144325i
$898$	−2.67752	−	4.63760i	−0.0893500	−	0.154759i
$899$	−1.00470	+	4.14144i	−0.0335087	+	0.138125i
$900$	−4.83088	+	0.931076i	−0.161029	+	0.0310359i
$901$	−2.61656	−	1.34893i	−0.0871701	−	0.0449393i
$902$	−0.0457962	−	0.318519i	−0.00152485	−	0.0106055i
$903$	7.22050	−	8.61842i	0.240283	−	0.286803i
$904$	−0.975992	+	2.13713i	−0.0324610	+	0.0710797i
$905$	1.01674	+	0.195960i	0.0337975	+	0.00651394i
$906$	−7.33930	−	5.77169i	−0.243832	−	0.191751i
$907$	1.67138	+	0.159598i	0.0554974	+	0.00529936i	0.122768	−	0.992435i	$-0.460823\pi$
$907$	1.67138	+	0.159598i	0.0554974	+	0.00529936i	−0.0672704	+	0.997735i	$0.521429\pi$
$908$	2.53100	+	10.4329i	0.0839942	+	0.346229i
$909$	4.89320	+	1.43677i	0.162297	+	0.0476548i
$910$	0.0652999	−	0.0203593i	0.00216467	−	0.000674903i
$911$	2.71679	−	18.8957i	0.0900113	−	0.626042i	−0.894017	−	0.448032i	$-0.852125\pi$
$911$	2.71679	−	18.8957i	0.0900113	−	0.626042i	0.984029	−	0.178010i	$-0.0569659\pi$
$912$	−7.63294	−	1.47113i	−0.252752	−	0.0487139i
$913$	−5.84682	−	8.21071i	−0.193502	−	0.271735i
$914$	7.62682	−	3.93190i	0.252273	−	0.130056i
$915$	2.31145	−	1.81774i	0.0764141	−	0.0600927i
$916$	−16.3053	+	10.4788i	−0.538741	+	0.346228i
$917$	2.11259	+	32.8457i	0.0697637	+	1.08466i
$918$	−2.82876	+	0.830598i	−0.0933629	+	0.0274138i
$919$	19.7076	+	34.1346i	0.650094	+	1.12600i	0.983100	+	0.183071i	$0.0586038\pi$
$919$	19.7076	+	34.1346i	0.650094	+	1.12600i	−0.333006	+	0.942925i	$0.608063\pi$
$920$	−0.998137	+	0.921172i	−0.0329076	+	0.0303701i
$921$	−13.1088	+	22.7051i	−0.431949	+	0.748157i
$922$	−25.8293	−	24.6282i	−0.850642	−	0.811085i
$923$	−0.0336218	−	0.0388017i	−0.00110668	−	0.00127717i
$924$	−1.15813	+	1.68498i	−0.0380996	+	0.0554317i
$925$	1.36361	+	9.48410i	0.0448351	+	0.311835i
$926$	1.00642	−	21.1274i	0.0330731	−	0.694290i
$927$	−4.06606	−	5.70998i	−0.133547	−	0.187540i
$928$	0.573081	+	1.65581i	0.0188123	+	0.0543546i
$929$	27.6284	−	11.0607i	0.906459	−	0.362891i	0.128868	−	0.991662i	$-0.458866\pi$
$929$	27.6284	−	11.0607i	0.906459	−	0.362891i	0.777591	+	0.628771i	$0.216442\pi$
$930$	−0.286147	−	0.626574i	−0.00938312	−	0.0205462i
$931$	−46.7289	−	27.8799i	−1.53148	−	0.913725i
$932$	12.6703	+	3.72033i	0.415029	+	0.121864i
$933$	−8.52347	+	11.9695i	−0.279046	+	0.391865i
$934$	−9.04415	−	7.11240i	−0.295934	−	0.232725i
$935$	0.211041	+	0.609764i	0.00690179	+	0.0199414i
$936$	0.0908703	−	0.00867706i	0.00297019	−	0.000283619i
$937$	18.3492	+	11.7923i	0.599441	+	0.385237i	0.804884	−	0.593432i	$-0.202227\pi$
$937$	18.3492	+	11.7923i	0.599441	+	0.385237i	−0.205443	+	0.978669i	$0.565864\pi$
$938$	16.0980	+	26.8416i	0.525618	+	0.876409i
$939$	25.3788	−	16.3100i	0.828206	−	0.532255i
$940$	0.615750	−	1.77909i	0.0200836	−	0.0580276i
$941$	6.97222	−	28.7399i	0.227288	−	0.936894i	−0.737811	−	0.675007i	$-0.764140\pi$
$941$	6.97222	−	28.7399i	0.227288	−	0.936894i	0.965099	−	0.261886i	$-0.0843445\pi$
$942$	7.41831	−	12.8489i	0.241701	−	0.418639i
$943$	1.18471	−	1.60765i	0.0385795	−	0.0523523i
$944$	−2.98764			−0.0972393
$945$	0.700174	+	0.266885i	0.0227767	+	0.00868178i
$946$	−2.15058	−	2.48190i	−0.0699215	−	0.0806937i
$947$	−48.5195	−	25.0135i	−1.57667	−	0.812831i	−0.576681	−	0.816969i	$-0.695652\pi$
$947$	−48.5195	−	25.0135i	−1.57667	−	0.812831i	−0.999991	+	0.00413829i	$0.998683\pi$
$948$	−11.3055	−	4.52602i	−0.367184	−	0.146998i
$949$	1.12606	−	0.580526i	0.0365536	−	0.0188447i
$950$	−38.0704	+	3.63528i	−1.23517	+	0.117944i
$951$	−10.0669	+	11.6178i	−0.326441	+	0.376734i
$952$	7.51970	+	2.07279i	0.243715	+	0.0671796i
$953$	5.82580	+	12.7567i	0.188716	+	0.413230i	0.980214	−	0.197942i	$-0.0634256\pi$
$953$	5.82580	+	12.7567i	0.188716	+	0.413230i	−0.791498	+	0.611172i	$0.790698\pi$
$954$	0.235409	+	0.970369i	0.00762165	+	0.0314169i
$955$	−4.55212	+	4.34044i	−0.147303	+	0.140453i
$956$	11.7391	+	1.12095i	0.379670	+	0.0362541i
$957$	−1.25707	+	0.503254i	−0.0406352	+	0.0162679i
$958$	−8.58607	+	9.90886i	−0.277403	+	0.320141i
$959$	42.6734	+	26.4323i	1.37800	+	0.853542i
$960$	−0.238255	−	0.153117i	−0.00768964	−	0.00494183i
$961$	19.7178	−	15.5063i	0.636059	−	0.500202i
$962$	−0.00845917	−	0.177580i	−0.000272734	−	0.00572540i
$963$	−17.2318	+	3.32115i	−0.555286	+	0.107023i
$964$	−12.0400	−	11.4801i	−0.387782	−	0.369750i
$965$	5.08112			0.163567
$966$	−12.4584	+	2.40570i	−0.400844	+	0.0774022i
$967$	−33.9492			−1.09173			−0.545867	−	0.837872i	$-0.683799\pi$
$967$	−33.9492			−1.09173			−0.545867	+	0.837872i	$0.683799\pi$
$968$	−7.52886	−	7.17875i	−0.241987	−	0.230734i
$969$	−22.5033	+	4.33715i	−0.722909	+	0.139329i
$970$	−0.142865	−	2.99910i	−0.00458712	−	0.0962955i
$971$	19.7136	−	15.5030i	0.632641	−	0.497514i	−0.249578	−	0.968355i	$-0.580292\pi$
$971$	19.7136	−	15.5030i	0.632641	−	0.497514i	0.882218	+	0.470841i	$0.156049\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	−0.130180	+	4.20212i	−0.00417338	+	0.134714i
$974$	−27.7751	+	32.0541i	−0.889971	+	1.02708i
$975$	0.416927	−	0.166912i	0.0133523	−	0.00534547i
$976$	−10.3359	−	0.986954i	−0.330843	−	0.0315916i
$977$	13.7389	−	13.1000i	0.439547	−	0.419107i	−0.437719	−	0.899112i	$-0.644214\pi$
$977$	13.7389	−	13.1000i	0.439547	−	0.419107i	0.877266	+	0.480005i	$0.159365\pi$
$978$	0.912771	+	3.76249i	0.0291872	+	0.120311i
$979$	−5.78247	−	12.6618i	−0.184808	−	0.404674i
$980$	−1.20303	−	1.57576i	−0.0384293	−	0.0503358i
$981$	−4.82945	+	5.57348i	−0.154192	+	0.177947i
$982$	10.5243	−	1.00495i	0.335844	−	0.0320692i
$983$	51.8128	−	26.7114i	1.65257	−	0.851960i	0.657430	−	0.753516i	$-0.271644\pi$
$983$	51.8128	−	26.7114i	1.65257	−	0.851960i	0.995143	−	0.0984445i	$-0.0313867\pi$
$984$	0.386579	+	0.154763i	0.0123237	+	0.00493366i
$985$	−4.34096	−	2.23792i	−0.138314	−	0.0713060i
$986$	3.38283	+	3.90400i	0.107731	+	0.124329i
$987$	13.6419	−	11.1002i	0.434226	−	0.353323i
$988$	0.709586			0.0225749
$989$	1.30099	−	20.3387i	0.0413690	−	0.646734i
$990$	0.109432	−	0.189542i	0.00347799	−	0.00602405i
$991$	6.39575	−	26.3636i	0.203168	−	0.837468i	−0.775388	−	0.631485i	$-0.782446\pi$
$991$	6.39575	−	26.3636i	0.203168	−	0.837468i	0.978556	−	0.205983i	$-0.0660392\pi$
$992$	−0.795481	+	2.29839i	−0.0252565	+	0.0729740i
$993$	−3.41283	+	2.19329i	−0.108303	+	0.0696019i
$994$	−0.722510	+	1.30092i	−0.0229166	+	0.0412626i
$995$	0.571500	+	0.367281i	0.0181178	+	0.0116436i
$996$	12.9843	−	1.23985i	0.411422	−	0.0392861i
$997$	−11.5244	−	33.2977i	−0.364983	−	1.05455i	−0.966716	−	0.255852i	$-0.917644\pi$
$997$	−11.5244	−	33.2977i	−0.364983	−	1.05455i	0.601733	−	0.798697i	$-0.294477\pi$
$998$	6.64306	+	5.22416i	0.210282	+	0.165368i
$999$	1.12970	−	1.58644i	0.0357421	−	0.0501928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.193.4	✓	160
7.2	even	3	inner	966.2.y.d.331.5	yes	160
23.18	even	11	inner	966.2.y.d.823.5	yes	160
161.156	even	33	inner	966.2.y.d.961.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.193.4	✓	160	1.1	even	1	trivial
966.2.y.d.331.5	yes	160	7.2	even	3	inner
966.2.y.d.823.5	yes	160	23.18	even	11	inner
966.2.y.d.961.4	yes	160	161.156	even	33	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)

\(f(q)\)	\(=\)	\(q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.222621 - 0.175071i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.0819249 + 2.64448i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})\)	\(q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(0.222621 - 0.175071i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-0.0819249 + 2.64448i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +(0.281932 + 0.0269212i) q^{10} +(0.559293 - 0.533285i) q^{11} +(0.235759 + 0.971812i) q^{12} +(-0.0379206 - 0.0830345i) q^{13} +(-1.88419 + 1.85737i) q^{14} +(0.185466 - 0.214039i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(-2.62045 + 1.35093i) q^{17} +(0.928368 + 0.371662i) q^{18} +(6.90929 + 3.56198i) q^{19} +(0.185466 + 0.214039i) q^{20} +(0.420027 + 2.61220i) q^{21} +0.772788 q^{22} +(3.41657 + 3.36557i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.15988 + 4.78111i) q^{25} +(0.0298560 - 0.0862631i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-2.64539 + 0.0439974i) q^{28} +(-1.47402 - 0.947298i) q^{29} +(0.281932 - 0.0269212i) q^{30} +(-0.795481 - 2.29839i) q^{31} +(-0.786053 - 0.618159i) q^{32} +(0.448261 - 0.629495i) q^{33} +(-2.82876 - 0.830598i) q^{34} +(0.444735 + 0.603061i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.80806 - 0.723838i) q^{37} +(2.54243 + 7.34588i) q^{38} +(-0.0529497 - 0.0743575i) q^{39} +(-0.0134759 + 0.282893i) q^{40} +(-0.0592609 - 0.412169i) q^{41} +(-1.49863 + 2.18039i) q^{42} +(-2.78289 - 3.21162i) q^{43} +(0.559293 + 0.533285i) q^{44} +(0.141607 - 0.245271i) q^{45} +(0.150185 + 4.79348i) q^{46} +(-3.32370 - 5.75682i) q^{47} +(-0.959493 + 0.281733i) q^{48} +(-6.98658 - 0.433298i) q^{49} +(-4.13879 + 2.65984i) q^{50} +(-2.31743 + 1.82244i) q^{51} +(0.0811361 - 0.0418286i) q^{52} +(0.579196 + 0.813367i) q^{53} +(0.981929 + 0.189251i) q^{54} +(0.0311477 - 0.216637i) q^{55} +(-1.94492 - 1.79368i) q^{56} +(7.45854 + 2.19002i) q^{57} +(-0.413091 - 1.70279i) q^{58} +(2.97411 + 0.283993i) q^{59} +(0.222621 + 0.175071i) q^{60} +(10.1952 + 1.96497i) q^{61} +(1.01035 - 2.21237i) q^{62} +(0.906798 + 2.48550i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.0229789 - 0.0118464i) q^{65} +(0.758823 - 0.146251i) q^{66} +(2.78899 - 11.4964i) q^{67} +(-1.47409 - 2.55320i) q^{68} +(3.99177 + 2.65815i) q^{69} +(-0.0942899 + 0.743358i) q^{70} +(0.539661 - 0.158459i) q^{71} +(-0.327068 + 0.945001i) q^{72} +(0.660375 + 13.8630i) q^{73} +(1.80806 + 0.723838i) q^{74} +(-0.234093 + 4.91422i) q^{75} +(-3.22919 + 7.07095i) q^{76} +(1.36444 + 1.52273i) q^{77} +(0.0129910 - 0.0903545i) q^{78} +(-7.06381 + 9.91973i) q^{79} +(-0.204972 + 0.195440i) q^{80} +(0.723734 - 0.690079i) q^{81} +(0.241540 - 0.339195i) q^{82} +(1.85626 - 12.9106i) q^{83} +(-2.58925 + 0.543845i) q^{84} +(-0.346857 + 0.759512i) q^{85} +(0.202203 - 4.24477i) q^{86} +(-1.62666 - 0.651218i) q^{87} +(0.0367707 + 0.771913i) q^{88} +(5.89126 - 17.0217i) q^{89} +(0.271742 - 0.0797906i) q^{90} +(0.222690 - 0.0934778i) q^{91} +(-3.19919 + 3.57284i) q^{92} +(-1.21608 - 2.10631i) q^{93} +(1.56718 - 6.46002i) q^{94} +(2.16176 - 0.416644i) q^{95} +(-0.888835 - 0.458227i) q^{96} +(-1.50876 - 10.4936i) q^{97} +(-4.75741 - 5.13488i) q^{98} +(0.321028 - 0.702953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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